Properties

Label 450.2.q.b.331.1
Level $450$
Weight $2$
Character 450.331
Analytic conductor $3.593$
Analytic rank $0$
Dimension $112$
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] = [450,2,Mod(31,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.q (of order \(15\), degree \(8\), 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: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 331.1
Character \(\chi\) \(=\) 450.331
Dual form 450.2.q.b.121.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.978148 - 0.207912i) q^{2} +(-1.72536 - 0.152123i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.62343 + 1.53769i) q^{5} +(1.65603 + 0.507521i) q^{6} +(-1.38192 + 2.39355i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.95372 + 0.524934i) q^{9} +O(q^{10})\) \(q+(-0.978148 - 0.207912i) q^{2} +(-1.72536 - 0.152123i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.62343 + 1.53769i) q^{5} +(1.65603 + 0.507521i) q^{6} +(-1.38192 + 2.39355i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.95372 + 0.524934i) q^{9} +(-1.26825 - 1.84161i) q^{10} +(-2.02450 - 0.430321i) q^{11} +(-1.51432 - 0.840738i) q^{12} +(0.737149 - 0.156686i) q^{13} +(1.84937 - 2.05393i) q^{14} +(-2.56708 - 2.90002i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-3.69560 - 2.68501i) q^{17} +(-2.78003 - 1.12758i) q^{18} +(-0.0538055 - 0.0390920i) q^{19} +(0.857644 + 2.06505i) q^{20} +(2.74842 - 3.91951i) q^{21} +(1.89079 + 0.841835i) q^{22} +(-3.69647 + 4.10534i) q^{23} +(1.30643 + 1.13721i) q^{24} +(0.271050 + 4.99265i) q^{25} -0.753618 q^{26} +(-5.01636 - 1.35503i) q^{27} +(-2.23599 + 1.62454i) q^{28} +(-0.355748 - 3.38471i) q^{29} +(1.90803 + 3.37037i) q^{30} +(-0.723621 + 6.88479i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.42753 + 1.05043i) q^{33} +(3.05660 + 3.39470i) q^{34} +(-5.92397 + 1.76081i) q^{35} +(2.48484 + 1.68094i) q^{36} +(-0.533760 + 1.64274i) q^{37} +(0.0445021 + 0.0494245i) q^{38} +(-1.29568 + 0.158202i) q^{39} +(-0.409554 - 2.19824i) q^{40} +(-5.68847 + 1.20912i) q^{41} +(-3.50327 + 3.26243i) q^{42} +(-5.69373 + 9.86184i) q^{43} +(-1.67445 - 1.21656i) q^{44} +(3.98797 + 5.39408i) q^{45} +(4.46924 - 3.24709i) q^{46} +(-0.660693 - 6.28608i) q^{47} +(-1.04144 - 1.38398i) q^{48} +(-0.319388 - 0.553196i) q^{49} +(0.772903 - 4.93990i) q^{50} +(5.96778 + 5.19479i) q^{51} +(0.737149 + 0.156686i) q^{52} +(-6.08008 + 4.41743i) q^{53} +(4.62502 + 2.36838i) q^{54} +(-2.62494 - 3.81164i) q^{55} +(2.52489 - 1.12415i) q^{56} +(0.0868870 + 0.0756327i) q^{57} +(-0.355748 + 3.38471i) q^{58} +(-6.35161 + 1.35008i) q^{59} +(-1.16560 - 3.69342i) q^{60} +(7.30186 + 1.55206i) q^{61} +(2.13924 - 6.58389i) q^{62} +(-5.33825 + 6.34445i) q^{63} +(0.309017 + 0.951057i) q^{64} +(1.43764 + 0.879135i) q^{65} +(-3.13423 - 1.74010i) q^{66} +(0.310385 - 2.95312i) q^{67} +(-2.28401 - 3.95602i) q^{68} +(7.00225 - 6.52087i) q^{69} +(6.16061 - 0.490667i) q^{70} +(-4.06787 + 2.95548i) q^{71} +(-2.08106 - 2.16083i) q^{72} +(-0.246066 - 0.757312i) q^{73} +(0.863642 - 1.49587i) q^{74} +(0.291840 - 8.65534i) q^{75} +(-0.0332536 - 0.0575970i) q^{76} +(3.82769 - 4.25108i) q^{77} +(1.30026 + 0.114643i) q^{78} +(-1.45268 - 13.8214i) q^{79} +(-0.0564360 + 2.23536i) q^{80} +(8.44889 + 3.10101i) q^{81} +5.81555 q^{82} +(14.3350 - 6.38237i) q^{83} +(4.10501 - 2.46277i) q^{84} +(-1.87085 - 10.0416i) q^{85} +(7.61970 - 8.46254i) q^{86} +(0.0988984 + 5.89396i) q^{87} +(1.38492 + 1.53811i) q^{88} +(-0.320840 - 0.987443i) q^{89} +(-2.77933 - 6.10535i) q^{90} +(-0.643643 + 1.98093i) q^{91} +(-5.04668 + 2.24693i) q^{92} +(2.29584 - 11.7686i) q^{93} +(-0.660693 + 6.28608i) q^{94} +(-0.0272383 - 0.146199i) q^{95} +(0.730936 + 1.57027i) q^{96} +(0.910985 + 8.66745i) q^{97} +(0.197393 + 0.607512i) q^{98} +(-5.75391 - 2.33378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q + 14 q^{2} + 2 q^{3} + 14 q^{4} + 9 q^{5} - 7 q^{6} - 8 q^{7} - 28 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q + 14 q^{2} + 2 q^{3} + 14 q^{4} + 9 q^{5} - 7 q^{6} - 8 q^{7} - 28 q^{8} + 8 q^{9} - 8 q^{10} - 3 q^{11} - 3 q^{14} + 32 q^{15} + 14 q^{16} + 10 q^{17} - 6 q^{18} - 32 q^{19} - 6 q^{20} - 7 q^{21} + 2 q^{22} - 5 q^{23} + 2 q^{24} + 21 q^{25} + 20 q^{26} - 16 q^{27} - 14 q^{28} + 18 q^{29} + 3 q^{30} - 27 q^{31} - 56 q^{32} - 25 q^{33} - 15 q^{34} - 12 q^{35} - 7 q^{36} + 16 q^{37} - 9 q^{38} + 12 q^{39} - q^{40} + 16 q^{41} - 13 q^{42} - 44 q^{43} - 4 q^{44} + 69 q^{45} - 10 q^{46} + 27 q^{47} + 3 q^{48} - 64 q^{49} + 11 q^{50} + 138 q^{51} - 14 q^{53} - 30 q^{54} - 8 q^{55} + 7 q^{56} - 50 q^{57} + 18 q^{58} + 14 q^{59} - 20 q^{60} - 5 q^{61} - 66 q^{62} - 12 q^{63} - 28 q^{64} - 102 q^{65} + 18 q^{66} + 11 q^{67} + 40 q^{68} - 78 q^{69} + 6 q^{70} + 38 q^{71} - 17 q^{72} - 44 q^{73} + 12 q^{74} + 10 q^{75} - 14 q^{76} - 3 q^{77} - 55 q^{78} + 16 q^{79} + 12 q^{80} + 72 q^{81} + 28 q^{82} - 56 q^{83} - 30 q^{84} + 35 q^{85} + 21 q^{86} - 44 q^{87} - 3 q^{88} - 64 q^{89} + 38 q^{90} - 40 q^{91} + 5 q^{92} - 22 q^{93} + 27 q^{94} + 24 q^{95} + 5 q^{96} + 34 q^{97} + 38 q^{98} + 68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.978148 0.207912i −0.691655 0.147016i
\(3\) −1.72536 0.152123i −0.996136 0.0878284i
\(4\) 0.913545 + 0.406737i 0.456773 + 0.203368i
\(5\) 1.62343 + 1.53769i 0.726020 + 0.687674i
\(6\) 1.65603 + 0.507521i 0.676070 + 0.207195i
\(7\) −1.38192 + 2.39355i −0.522315 + 0.904677i 0.477347 + 0.878715i \(0.341598\pi\)
−0.999663 + 0.0259623i \(0.991735\pi\)
\(8\) −0.809017 0.587785i −0.286031 0.207813i
\(9\) 2.95372 + 0.524934i 0.984572 + 0.174978i
\(10\) −1.26825 1.84161i −0.401056 0.582369i
\(11\) −2.02450 0.430321i −0.610410 0.129747i −0.107673 0.994186i \(-0.534340\pi\)
−0.502737 + 0.864440i \(0.667673\pi\)
\(12\) −1.51432 0.840738i −0.437146 0.242700i
\(13\) 0.737149 0.156686i 0.204448 0.0434569i −0.104549 0.994520i \(-0.533340\pi\)
0.308997 + 0.951063i \(0.400007\pi\)
\(14\) 1.84937 2.05393i 0.494264 0.548936i
\(15\) −2.56708 2.90002i −0.662817 0.748781i
\(16\) 0.669131 + 0.743145i 0.167283 + 0.185786i
\(17\) −3.69560 2.68501i −0.896315 0.651211i 0.0412018 0.999151i \(-0.486881\pi\)
−0.937517 + 0.347940i \(0.886881\pi\)
\(18\) −2.78003 1.12758i −0.655260 0.265772i
\(19\) −0.0538055 0.0390920i −0.0123438 0.00896832i 0.581596 0.813478i \(-0.302428\pi\)
−0.593940 + 0.804509i \(0.702428\pi\)
\(20\) 0.857644 + 2.06505i 0.191775 + 0.461760i
\(21\) 2.74842 3.91951i 0.599753 0.855307i
\(22\) 1.89079 + 0.841835i 0.403118 + 0.179480i
\(23\) −3.69647 + 4.10534i −0.770767 + 0.856023i −0.992895 0.118994i \(-0.962033\pi\)
0.222128 + 0.975017i \(0.428700\pi\)
\(24\) 1.30643 + 1.13721i 0.266673 + 0.232132i
\(25\) 0.271050 + 4.99265i 0.0542099 + 0.998530i
\(26\) −0.753618 −0.147797
\(27\) −5.01636 1.35503i −0.965400 0.260775i
\(28\) −2.23599 + 1.62454i −0.422562 + 0.307009i
\(29\) −0.355748 3.38471i −0.0660607 0.628525i −0.976594 0.215090i \(-0.930996\pi\)
0.910534 0.413435i \(-0.135671\pi\)
\(30\) 1.90803 + 3.37037i 0.348358 + 0.615343i
\(31\) −0.723621 + 6.88479i −0.129966 + 1.23654i 0.713999 + 0.700147i \(0.246882\pi\)
−0.843965 + 0.536398i \(0.819785\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 3.42753 + 1.05043i 0.596656 + 0.182857i
\(34\) 3.05660 + 3.39470i 0.524202 + 0.582186i
\(35\) −5.92397 + 1.76081i −1.00133 + 0.297631i
\(36\) 2.48484 + 1.68094i 0.414141 + 0.280156i
\(37\) −0.533760 + 1.64274i −0.0877496 + 0.270065i −0.985296 0.170854i \(-0.945347\pi\)
0.897547 + 0.440919i \(0.145347\pi\)
\(38\) 0.0445021 + 0.0494245i 0.00721919 + 0.00801772i
\(39\) −1.29568 + 0.158202i −0.207475 + 0.0253325i
\(40\) −0.409554 2.19824i −0.0647561 0.347572i
\(41\) −5.68847 + 1.20912i −0.888389 + 0.188833i −0.629432 0.777056i \(-0.716712\pi\)
−0.258957 + 0.965889i \(0.583379\pi\)
\(42\) −3.50327 + 3.26243i −0.540566 + 0.503404i
\(43\) −5.69373 + 9.86184i −0.868286 + 1.50392i −0.00453946 + 0.999990i \(0.501445\pi\)
−0.863747 + 0.503926i \(0.831888\pi\)
\(44\) −1.67445 1.21656i −0.252432 0.183403i
\(45\) 3.98797 + 5.39408i 0.594491 + 0.804102i
\(46\) 4.46924 3.24709i 0.658953 0.478758i
\(47\) −0.660693 6.28608i −0.0963720 0.916919i −0.930733 0.365700i \(-0.880830\pi\)
0.834361 0.551219i \(-0.185837\pi\)
\(48\) −1.04144 1.38398i −0.150319 0.199760i
\(49\) −0.319388 0.553196i −0.0456269 0.0790280i
\(50\) 0.772903 4.93990i 0.109305 0.698607i
\(51\) 5.96778 + 5.19479i 0.835657 + 0.727416i
\(52\) 0.737149 + 0.156686i 0.102224 + 0.0217284i
\(53\) −6.08008 + 4.41743i −0.835163 + 0.606781i −0.921015 0.389527i \(-0.872639\pi\)
0.0858526 + 0.996308i \(0.472639\pi\)
\(54\) 4.62502 + 2.36838i 0.629385 + 0.322295i
\(55\) −2.62494 3.81164i −0.353946 0.513961i
\(56\) 2.52489 1.12415i 0.337402 0.150221i
\(57\) 0.0868870 + 0.0756327i 0.0115085 + 0.0100178i
\(58\) −0.355748 + 3.38471i −0.0467119 + 0.444434i
\(59\) −6.35161 + 1.35008i −0.826910 + 0.175765i −0.601880 0.798587i \(-0.705581\pi\)
−0.225030 + 0.974352i \(0.572248\pi\)
\(60\) −1.16560 3.69342i −0.150478 0.476819i
\(61\) 7.30186 + 1.55206i 0.934907 + 0.198721i 0.650087 0.759860i \(-0.274733\pi\)
0.284821 + 0.958581i \(0.408066\pi\)
\(62\) 2.13924 6.58389i 0.271683 0.836155i
\(63\) −5.33825 + 6.34445i −0.672556 + 0.799326i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 1.43764 + 0.879135i 0.178318 + 0.109043i
\(66\) −3.13423 1.74010i −0.385797 0.214191i
\(67\) 0.310385 2.95312i 0.0379196 0.360781i −0.959065 0.283185i \(-0.908609\pi\)
0.996985 0.0775958i \(-0.0247244\pi\)
\(68\) −2.28401 3.95602i −0.276977 0.479738i
\(69\) 7.00225 6.52087i 0.842971 0.785020i
\(70\) 6.16061 0.490667i 0.736334 0.0586460i
\(71\) −4.06787 + 2.95548i −0.482767 + 0.350751i −0.802396 0.596792i \(-0.796442\pi\)
0.319629 + 0.947543i \(0.396442\pi\)
\(72\) −2.08106 2.16083i −0.245255 0.254656i
\(73\) −0.246066 0.757312i −0.0287998 0.0886367i 0.935623 0.353000i \(-0.114838\pi\)
−0.964423 + 0.264363i \(0.914838\pi\)
\(74\) 0.863642 1.49587i 0.100396 0.173892i
\(75\) 0.291840 8.65534i 0.0336988 0.999432i
\(76\) −0.0332536 0.0575970i −0.00381445 0.00660683i
\(77\) 3.82769 4.25108i 0.436205 0.484455i
\(78\) 1.30026 + 0.114643i 0.147225 + 0.0129807i
\(79\) −1.45268 13.8214i −0.163440 1.55502i −0.701840 0.712335i \(-0.747638\pi\)
0.538400 0.842689i \(-0.319029\pi\)
\(80\) −0.0564360 + 2.23536i −0.00630974 + 0.249920i
\(81\) 8.44889 + 3.10101i 0.938765 + 0.344557i
\(82\) 5.81555 0.642220
\(83\) 14.3350 6.38237i 1.57347 0.700556i 0.580001 0.814616i \(-0.303052\pi\)
0.993474 + 0.114060i \(0.0363855\pi\)
\(84\) 4.10501 2.46277i 0.447893 0.268710i
\(85\) −1.87085 10.0416i −0.202922 1.08916i
\(86\) 7.61970 8.46254i 0.821654 0.912539i
\(87\) 0.0988984 + 5.89396i 0.0106030 + 0.631898i
\(88\) 1.38492 + 1.53811i 0.147633 + 0.163963i
\(89\) −0.320840 0.987443i −0.0340089 0.104669i 0.932611 0.360883i \(-0.117525\pi\)
−0.966620 + 0.256214i \(0.917525\pi\)
\(90\) −2.77933 6.10535i −0.292967 0.643561i
\(91\) −0.643643 + 1.98093i −0.0674722 + 0.207658i
\(92\) −5.04668 + 2.24693i −0.526153 + 0.234259i
\(93\) 2.29584 11.7686i 0.238068 1.22035i
\(94\) −0.660693 + 6.28608i −0.0681453 + 0.648359i
\(95\) −0.0272383 0.146199i −0.00279459 0.0149997i
\(96\) 0.730936 + 1.57027i 0.0746009 + 0.160265i
\(97\) 0.910985 + 8.66745i 0.0924966 + 0.880046i 0.938130 + 0.346282i \(0.112556\pi\)
−0.845634 + 0.533764i \(0.820777\pi\)
\(98\) 0.197393 + 0.607512i 0.0199397 + 0.0613680i
\(99\) −5.75391 2.33378i −0.578290 0.234553i
\(100\) −1.78308 + 4.67126i −0.178308 + 0.467126i
\(101\) −4.16666 + 7.21686i −0.414598 + 0.718104i −0.995386 0.0959502i \(-0.969411\pi\)
0.580788 + 0.814055i \(0.302744\pi\)
\(102\) −4.75731 6.32204i −0.471044 0.625976i
\(103\) 10.0164 + 4.45958i 0.986944 + 0.439416i 0.835763 0.549090i \(-0.185026\pi\)
0.151181 + 0.988506i \(0.451692\pi\)
\(104\) −0.688464 0.306524i −0.0675094 0.0300571i
\(105\) 10.4888 2.13685i 1.02360 0.208535i
\(106\) 6.86565 3.05678i 0.666851 0.296901i
\(107\) 18.0127 1.74136 0.870679 0.491852i \(-0.163680\pi\)
0.870679 + 0.491852i \(0.163680\pi\)
\(108\) −4.03154 3.27822i −0.387935 0.315447i
\(109\) 4.27404 13.1541i 0.409378 1.25994i −0.507805 0.861472i \(-0.669543\pi\)
0.917183 0.398465i \(-0.130457\pi\)
\(110\) 1.77509 + 4.27410i 0.169248 + 0.407520i
\(111\) 1.17083 2.75312i 0.111130 0.261315i
\(112\) −2.70344 + 0.574633i −0.255451 + 0.0542977i
\(113\) −9.53418 + 2.02655i −0.896900 + 0.190642i −0.633224 0.773969i \(-0.718269\pi\)
−0.263677 + 0.964611i \(0.584935\pi\)
\(114\) −0.0692633 0.0920448i −0.00648711 0.00862079i
\(115\) −12.3137 + 0.980734i −1.14826 + 0.0914539i
\(116\) 1.05169 3.23678i 0.0976474 0.300528i
\(117\) 2.25958 0.0758512i 0.208898 0.00701245i
\(118\) 6.49351 0.597776
\(119\) 11.5337 5.13514i 1.05729 0.470738i
\(120\) 0.372223 + 3.85506i 0.0339792 + 0.351917i
\(121\) −6.13557 2.73173i −0.557779 0.248339i
\(122\) −6.81960 3.03628i −0.617418 0.274892i
\(123\) 9.99857 1.22082i 0.901541 0.110077i
\(124\) −3.46136 + 5.99525i −0.310839 + 0.538389i
\(125\) −7.23709 + 8.52200i −0.647305 + 0.762231i
\(126\) 6.54068 5.09593i 0.582690 0.453981i
\(127\) −4.94644 15.2236i −0.438925 1.35087i −0.889010 0.457887i \(-0.848606\pi\)
0.450085 0.892986i \(-0.351394\pi\)
\(128\) −0.104528 0.994522i −0.00923910 0.0879041i
\(129\) 11.3239 16.1490i 0.997017 1.42184i
\(130\) −1.22345 1.15883i −0.107303 0.101636i
\(131\) −1.77515 + 16.8895i −0.155096 + 1.47564i 0.589308 + 0.807909i \(0.299401\pi\)
−0.744404 + 0.667730i \(0.767266\pi\)
\(132\) 2.70395 + 2.35372i 0.235349 + 0.204865i
\(133\) 0.167923 0.0747643i 0.0145608 0.00648289i
\(134\) −0.917590 + 2.82405i −0.0792677 + 0.243961i
\(135\) −6.06011 9.91338i −0.521571 0.853208i
\(136\) 1.41159 + 4.34444i 0.121043 + 0.372533i
\(137\) 0.845829 + 0.939388i 0.0722640 + 0.0802573i 0.778193 0.628026i \(-0.216137\pi\)
−0.705929 + 0.708283i \(0.749470\pi\)
\(138\) −8.20499 + 4.92252i −0.698456 + 0.419033i
\(139\) −11.2166 + 12.4573i −0.951383 + 1.05662i 0.0469493 + 0.998897i \(0.485050\pi\)
−0.998333 + 0.0577211i \(0.981617\pi\)
\(140\) −6.12800 0.800918i −0.517911 0.0676899i
\(141\) 0.183674 + 10.9462i 0.0154681 + 0.921840i
\(142\) 4.59345 2.04514i 0.385474 0.171624i
\(143\) −1.55978 −0.130436
\(144\) 1.58632 + 2.54629i 0.132193 + 0.212191i
\(145\) 4.62709 6.04187i 0.384259 0.501750i
\(146\) 0.0832345 + 0.791923i 0.00688853 + 0.0655400i
\(147\) 0.466905 + 1.00305i 0.0385096 + 0.0827300i
\(148\) −1.15578 + 1.28362i −0.0950044 + 0.105513i
\(149\) 8.97672 + 15.5481i 0.735402 + 1.27375i 0.954547 + 0.298061i \(0.0963399\pi\)
−0.219145 + 0.975692i \(0.570327\pi\)
\(150\) −2.08501 + 8.40552i −0.170240 + 0.686308i
\(151\) −3.44283 + 5.96316i −0.280174 + 0.485275i −0.971427 0.237337i \(-0.923725\pi\)
0.691254 + 0.722612i \(0.257059\pi\)
\(152\) 0.0205519 + 0.0632522i 0.00166698 + 0.00513043i
\(153\) −9.50631 9.87071i −0.768539 0.798000i
\(154\) −4.62789 + 3.36236i −0.372926 + 0.270947i
\(155\) −11.7614 + 10.0643i −0.944697 + 0.808382i
\(156\) −1.24801 0.382477i −0.0999208 0.0306226i
\(157\) −3.05002 5.28278i −0.243418 0.421612i 0.718268 0.695767i \(-0.244935\pi\)
−0.961686 + 0.274155i \(0.911602\pi\)
\(158\) −1.45268 + 13.8214i −0.115569 + 1.09957i
\(159\) 11.1623 6.69673i 0.885228 0.531085i
\(160\) 0.519959 2.17477i 0.0411064 0.171931i
\(161\) −4.71813 14.5209i −0.371841 1.14441i
\(162\) −7.61952 4.78987i −0.598646 0.376328i
\(163\) −1.30677 + 4.02182i −0.102354 + 0.315014i −0.989100 0.147243i \(-0.952960\pi\)
0.886746 + 0.462257i \(0.152960\pi\)
\(164\) −5.68847 1.20912i −0.444195 0.0944165i
\(165\) 3.94912 + 6.97576i 0.307438 + 0.543062i
\(166\) −15.3488 + 3.26248i −1.19129 + 0.253217i
\(167\) 1.63221 15.5294i 0.126304 1.20170i −0.729344 0.684147i \(-0.760175\pi\)
0.855649 0.517557i \(-0.173159\pi\)
\(168\) −4.52734 + 1.55547i −0.349292 + 0.120007i
\(169\) −11.3573 + 5.05657i −0.873635 + 0.388967i
\(170\) −0.257801 + 10.2111i −0.0197724 + 0.783159i
\(171\) −0.138406 0.143711i −0.0105841 0.0109899i
\(172\) −9.21265 + 6.69339i −0.702458 + 0.510366i
\(173\) 23.3676 + 4.96694i 1.77661 + 0.377630i 0.975345 0.220683i \(-0.0708288\pi\)
0.801262 + 0.598313i \(0.204162\pi\)
\(174\) 1.12868 5.78572i 0.0855654 0.438614i
\(175\) −12.3247 6.25065i −0.931661 0.472505i
\(176\) −1.03486 1.79244i −0.0780059 0.135110i
\(177\) 11.1642 1.36314i 0.839151 0.102460i
\(178\) 0.108528 + 1.03257i 0.00813449 + 0.0773945i
\(179\) 14.6530 10.6460i 1.09521 0.795720i 0.114942 0.993372i \(-0.463332\pi\)
0.980272 + 0.197652i \(0.0633317\pi\)
\(180\) 1.44922 + 6.54979i 0.108019 + 0.488193i
\(181\) 13.2505 + 9.62705i 0.984902 + 0.715573i 0.958799 0.284086i \(-0.0916902\pi\)
0.0261031 + 0.999659i \(0.491690\pi\)
\(182\) 1.04144 1.80382i 0.0771964 0.133708i
\(183\) −12.3622 3.78864i −0.913841 0.280064i
\(184\) 5.40357 1.14856i 0.398356 0.0846732i
\(185\) −3.39254 + 1.84613i −0.249425 + 0.135730i
\(186\) −4.69251 + 11.0341i −0.344072 + 0.809062i
\(187\) 6.32633 + 7.02610i 0.462627 + 0.513799i
\(188\) 1.95320 6.01135i 0.142452 0.438422i
\(189\) 10.1755 10.1344i 0.740160 0.737168i
\(190\) −0.00375341 + 0.148667i −0.000272301 + 0.0107855i
\(191\) 5.43383 + 6.03488i 0.393178 + 0.436668i 0.906937 0.421266i \(-0.138414\pi\)
−0.513759 + 0.857935i \(0.671747\pi\)
\(192\) −0.388487 1.68792i −0.0280366 0.121815i
\(193\) 6.55141 + 11.3474i 0.471581 + 0.816802i 0.999471 0.0325106i \(-0.0103503\pi\)
−0.527891 + 0.849312i \(0.677017\pi\)
\(194\) 0.910985 8.66745i 0.0654049 0.622286i
\(195\) −2.34671 1.73552i −0.168052 0.124283i
\(196\) −0.0667703 0.635277i −0.00476931 0.0453769i
\(197\) 9.23625 6.71053i 0.658056 0.478106i −0.207950 0.978139i \(-0.566679\pi\)
0.866006 + 0.500034i \(0.166679\pi\)
\(198\) 5.14296 + 3.47908i 0.365494 + 0.247248i
\(199\) 1.07373 0.0761150 0.0380575 0.999276i \(-0.487883\pi\)
0.0380575 + 0.999276i \(0.487883\pi\)
\(200\) 2.71532 4.19846i 0.192002 0.296876i
\(201\) −0.984763 + 5.04797i −0.0694598 + 0.356056i
\(202\) 5.57607 6.19286i 0.392331 0.435728i
\(203\) 8.59309 + 3.82589i 0.603117 + 0.268525i
\(204\) 3.33893 + 7.17299i 0.233772 + 0.502210i
\(205\) −11.0941 6.78415i −0.774844 0.473825i
\(206\) −8.87030 6.44465i −0.618023 0.449020i
\(207\) −13.0734 + 10.1856i −0.908661 + 0.707950i
\(208\) 0.609689 + 0.442965i 0.0422744 + 0.0307141i
\(209\) 0.0921072 + 0.102295i 0.00637119 + 0.00707592i
\(210\) −10.7039 0.0905954i −0.738639 0.00625168i
\(211\) 13.2955 14.7661i 0.915298 1.01654i −0.0844999 0.996423i \(-0.526929\pi\)
0.999798 0.0201176i \(-0.00640407\pi\)
\(212\) −7.35116 + 1.56254i −0.504880 + 0.107315i
\(213\) 7.46812 4.48044i 0.511707 0.306995i
\(214\) −17.6191 3.74506i −1.20442 0.256007i
\(215\) −24.4078 + 7.25483i −1.66460 + 0.494775i
\(216\) 3.26186 + 4.04478i 0.221941 + 0.275213i
\(217\) −15.4791 11.2462i −1.05079 0.763444i
\(218\) −6.91554 + 11.9781i −0.468379 + 0.811257i
\(219\) 0.309346 + 1.34407i 0.0209037 + 0.0908236i
\(220\) −0.847665 4.54976i −0.0571496 0.306745i
\(221\) −3.14491 1.40021i −0.211550 0.0941880i
\(222\) −1.71765 + 2.44953i −0.115281 + 0.164402i
\(223\) 17.4183 + 3.70238i 1.16642 + 0.247929i 0.750121 0.661300i \(-0.229995\pi\)
0.416295 + 0.909230i \(0.363328\pi\)
\(224\) 2.76383 0.184666
\(225\) −1.82021 + 14.8892i −0.121347 + 0.992610i
\(226\) 9.74718 0.648373
\(227\) −2.61855 0.556590i −0.173799 0.0369422i 0.120190 0.992751i \(-0.461650\pi\)
−0.293989 + 0.955809i \(0.594983\pi\)
\(228\) 0.0486126 + 0.104434i 0.00321945 + 0.00691631i
\(229\) −24.4433 10.8829i −1.61526 0.719159i −0.617531 0.786547i \(-0.711867\pi\)
−0.997727 + 0.0673878i \(0.978534\pi\)
\(230\) 12.2485 + 1.60086i 0.807642 + 0.105557i
\(231\) −7.25081 + 6.75235i −0.477069 + 0.444272i
\(232\) −1.70168 + 2.94739i −0.111721 + 0.193506i
\(233\) 2.90506 + 2.11065i 0.190317 + 0.138273i 0.678863 0.734264i \(-0.262473\pi\)
−0.488547 + 0.872538i \(0.662473\pi\)
\(234\) −2.22597 0.395599i −0.145516 0.0258611i
\(235\) 8.59342 11.2209i 0.560573 0.731974i
\(236\) −6.35161 1.35008i −0.413455 0.0878825i
\(237\) 0.403848 + 24.0678i 0.0262328 + 1.56337i
\(238\) −12.3493 + 2.62493i −0.800489 + 0.170149i
\(239\) −5.88859 + 6.53994i −0.380901 + 0.423034i −0.902858 0.429938i \(-0.858535\pi\)
0.521957 + 0.852972i \(0.325202\pi\)
\(240\) 0.437422 3.84820i 0.0282355 0.248400i
\(241\) 11.8741 + 13.1875i 0.764875 + 0.849480i 0.992241 0.124329i \(-0.0396779\pi\)
−0.227366 + 0.973809i \(0.573011\pi\)
\(242\) 5.43354 + 3.94770i 0.349281 + 0.253768i
\(243\) −14.1056 6.63563i −0.904876 0.425676i
\(244\) 6.03930 + 4.38781i 0.386627 + 0.280901i
\(245\) 0.332138 1.38919i 0.0212195 0.0887523i
\(246\) −10.0339 0.884680i −0.639738 0.0564051i
\(247\) −0.0457879 0.0203861i −0.00291341 0.00129713i
\(248\) 4.63220 5.14458i 0.294145 0.326681i
\(249\) −25.7040 + 8.83118i −1.62892 + 0.559653i
\(250\) 8.85077 6.83110i 0.559772 0.432037i
\(251\) −13.6691 −0.862785 −0.431392 0.902164i \(-0.641978\pi\)
−0.431392 + 0.902164i \(0.641978\pi\)
\(252\) −7.45725 + 3.62469i −0.469763 + 0.228334i
\(253\) 9.25012 6.72060i 0.581550 0.422521i
\(254\) 1.67319 + 15.9193i 0.104985 + 0.998867i
\(255\) 1.70032 + 17.6099i 0.106478 + 1.10278i
\(256\) −0.104528 + 0.994522i −0.00653303 + 0.0621576i
\(257\) 6.52925 + 11.3090i 0.407284 + 0.705436i 0.994584 0.103933i \(-0.0331427\pi\)
−0.587301 + 0.809369i \(0.699809\pi\)
\(258\) −14.4341 + 13.4418i −0.898625 + 0.836848i
\(259\) −3.19438 3.54772i −0.198489 0.220444i
\(260\) 0.955777 + 1.38787i 0.0592748 + 0.0860722i
\(261\) 0.725972 10.1842i 0.0449366 0.630388i
\(262\) 5.24788 16.1513i 0.324215 0.997831i
\(263\) −11.3654 12.6225i −0.700819 0.778338i 0.282687 0.959212i \(-0.408774\pi\)
−0.983506 + 0.180874i \(0.942107\pi\)
\(264\) −2.15550 2.86447i −0.132662 0.176296i
\(265\) −16.6632 2.17785i −1.02361 0.133784i
\(266\) −0.179798 + 0.0382173i −0.0110241 + 0.00234325i
\(267\) 0.403350 + 1.75250i 0.0246846 + 0.107251i
\(268\) 1.48469 2.57156i 0.0906920 0.157083i
\(269\) 22.4192 + 16.2885i 1.36692 + 0.993127i 0.997970 + 0.0636780i \(0.0202831\pi\)
0.368951 + 0.929449i \(0.379717\pi\)
\(270\) 3.86657 + 10.9567i 0.235312 + 0.666804i
\(271\) 3.02279 2.19619i 0.183622 0.133409i −0.492177 0.870495i \(-0.663799\pi\)
0.675799 + 0.737086i \(0.263799\pi\)
\(272\) −0.477488 4.54299i −0.0289519 0.275459i
\(273\) 1.41186 3.31990i 0.0854497 0.200930i
\(274\) −0.632036 1.09472i −0.0381827 0.0661343i
\(275\) 1.59970 10.2243i 0.0964656 0.616546i
\(276\) 9.04915 3.10904i 0.544695 0.187142i
\(277\) 22.2786 + 4.73545i 1.33859 + 0.284526i 0.820914 0.571052i \(-0.193464\pi\)
0.517675 + 0.855578i \(0.326798\pi\)
\(278\) 13.5616 9.85305i 0.813369 0.590947i
\(279\) −5.75143 + 19.9559i −0.344329 + 1.19473i
\(280\) 5.82757 + 2.05750i 0.348264 + 0.122959i
\(281\) −18.3615 + 8.17509i −1.09536 + 0.487685i −0.873218 0.487330i \(-0.837971\pi\)
−0.222140 + 0.975015i \(0.571304\pi\)
\(282\) 2.09619 10.7452i 0.124826 0.639869i
\(283\) −2.49307 + 23.7200i −0.148198 + 1.41001i 0.627358 + 0.778731i \(0.284136\pi\)
−0.775556 + 0.631278i \(0.782531\pi\)
\(284\) −4.91828 + 1.04541i −0.291846 + 0.0620339i
\(285\) 0.0247556 + 0.256389i 0.00146639 + 0.0151872i
\(286\) 1.52570 + 0.324297i 0.0902165 + 0.0191761i
\(287\) 4.96690 15.2865i 0.293187 0.902335i
\(288\) −1.02225 2.82046i −0.0602368 0.166197i
\(289\) 1.19489 + 3.67751i 0.0702879 + 0.216324i
\(290\) −5.78215 + 4.94781i −0.339540 + 0.290546i
\(291\) −0.253255 15.0930i −0.0148461 0.884769i
\(292\) 0.0832345 0.791923i 0.00487093 0.0463438i
\(293\) 5.30129 + 9.18210i 0.309704 + 0.536424i 0.978298 0.207205i \(-0.0664366\pi\)
−0.668593 + 0.743628i \(0.733103\pi\)
\(294\) −0.248156 1.07820i −0.0144728 0.0628821i
\(295\) −12.3874 7.57503i −0.721222 0.441035i
\(296\) 1.39740 1.01527i 0.0812223 0.0590115i
\(297\) 9.57253 + 4.90190i 0.555455 + 0.284437i
\(298\) −5.54792 17.0747i −0.321382 0.989113i
\(299\) −2.08160 + 3.60544i −0.120382 + 0.208508i
\(300\) 3.78705 7.78834i 0.218646 0.449660i
\(301\) −15.7365 27.2565i −0.907039 1.57104i
\(302\) 4.60741 5.11704i 0.265126 0.294453i
\(303\) 8.28682 11.8178i 0.476066 0.678916i
\(304\) −0.00695190 0.0661430i −0.000398719 0.00379356i
\(305\) 9.46748 + 13.7476i 0.542106 + 0.787186i
\(306\) 7.24634 + 11.6315i 0.414245 + 0.664928i
\(307\) 29.9210 1.70768 0.853842 0.520532i \(-0.174266\pi\)
0.853842 + 0.520532i \(0.174266\pi\)
\(308\) 5.22583 2.32669i 0.297769 0.132576i
\(309\) −16.6034 9.21810i −0.944537 0.524399i
\(310\) 13.5969 7.39902i 0.772249 0.420236i
\(311\) 9.11001 10.1177i 0.516581 0.573721i −0.427257 0.904130i \(-0.640520\pi\)
0.943838 + 0.330409i \(0.107187\pi\)
\(312\) 1.14122 + 0.633595i 0.0646087 + 0.0358702i
\(313\) −1.65917 1.84270i −0.0937820 0.104156i 0.694427 0.719563i \(-0.255658\pi\)
−0.788209 + 0.615408i \(0.788991\pi\)
\(314\) 1.88501 + 5.80147i 0.106377 + 0.327396i
\(315\) −18.4220 + 2.09124i −1.03796 + 0.117828i
\(316\) 4.29456 13.2173i 0.241588 0.743531i
\(317\) −31.9813 + 14.2390i −1.79625 + 0.799742i −0.823710 + 0.567012i \(0.808099\pi\)
−0.972541 + 0.232731i \(0.925234\pi\)
\(318\) −12.3107 + 4.22962i −0.690350 + 0.237185i
\(319\) −0.736301 + 7.00544i −0.0412249 + 0.392229i
\(320\) −0.960758 + 2.01914i −0.0537080 + 0.112874i
\(321\) −31.0784 2.74016i −1.73463 0.152941i
\(322\) 1.59596 + 15.1846i 0.0889395 + 0.846203i
\(323\) 0.0938813 + 0.288937i 0.00522370 + 0.0160769i
\(324\) 6.45715 + 6.26939i 0.358730 + 0.348299i
\(325\) 0.982082 + 3.63786i 0.0544761 + 0.201792i
\(326\) 2.11440 3.66225i 0.117106 0.202833i
\(327\) −9.37529 + 22.0454i −0.518455 + 1.21911i
\(328\) 5.31277 + 2.36540i 0.293349 + 0.130607i
\(329\) 15.9591 + 7.10543i 0.879852 + 0.391735i
\(330\) −2.41248 7.64439i −0.132802 0.420810i
\(331\) 15.0391 6.69584i 0.826623 0.368036i 0.0505832 0.998720i \(-0.483892\pi\)
0.776040 + 0.630683i \(0.217225\pi\)
\(332\) 15.6917 0.861191
\(333\) −2.43891 + 4.57201i −0.133651 + 0.250545i
\(334\) −4.82529 + 14.8507i −0.264028 + 0.812596i
\(335\) 5.04485 4.31690i 0.275630 0.235858i
\(336\) 4.75181 0.580192i 0.259233 0.0316521i
\(337\) −1.08211 + 0.230010i −0.0589464 + 0.0125294i −0.237290 0.971439i \(-0.576259\pi\)
0.178344 + 0.983968i \(0.442926\pi\)
\(338\) 12.1604 2.58477i 0.661438 0.140593i
\(339\) 16.7582 2.04616i 0.910178 0.111132i
\(340\) 2.37518 9.93440i 0.128812 0.538768i
\(341\) 4.42764 13.6269i 0.239770 0.737937i
\(342\) 0.105502 + 0.169347i 0.00570489 + 0.00915722i
\(343\) −17.5814 −0.949304
\(344\) 10.4030 4.63170i 0.560890 0.249725i
\(345\) 21.3947 + 0.181080i 1.15185 + 0.00974902i
\(346\) −21.8243 9.71681i −1.17328 0.522379i
\(347\) 16.6518 + 7.41385i 0.893915 + 0.397996i 0.801689 0.597742i \(-0.203935\pi\)
0.0922258 + 0.995738i \(0.470602\pi\)
\(348\) −2.30694 + 5.42462i −0.123665 + 0.290790i
\(349\) 7.71031 13.3547i 0.412724 0.714858i −0.582463 0.812857i \(-0.697911\pi\)
0.995187 + 0.0979991i \(0.0312442\pi\)
\(350\) 10.7558 + 8.67651i 0.574922 + 0.463779i
\(351\) −3.91012 0.212864i −0.208707 0.0113619i
\(352\) 0.639581 + 1.96843i 0.0340898 + 0.104918i
\(353\) −2.25479 21.4529i −0.120010 1.14182i −0.874336 0.485321i \(-0.838703\pi\)
0.754326 0.656500i \(-0.227964\pi\)
\(354\) −11.2036 0.987814i −0.595466 0.0525017i
\(355\) −11.1485 1.45709i −0.591700 0.0773341i
\(356\) 0.108528 1.03257i 0.00575195 0.0547262i
\(357\) −20.6810 + 7.10541i −1.09455 + 0.376058i
\(358\) −16.5462 + 7.36684i −0.874494 + 0.389350i
\(359\) −6.14818 + 18.9222i −0.324489 + 0.998674i 0.647182 + 0.762335i \(0.275947\pi\)
−0.971671 + 0.236338i \(0.924053\pi\)
\(360\) −0.0557746 6.70797i −0.00293958 0.353541i
\(361\) −5.86996 18.0659i −0.308945 0.950835i
\(362\) −10.9594 12.1716i −0.576012 0.639726i
\(363\) 10.1705 + 5.64658i 0.533813 + 0.296369i
\(364\) −1.39371 + 1.54788i −0.0730505 + 0.0811308i
\(365\) 0.765037 1.60781i 0.0400439 0.0841569i
\(366\) 11.3044 + 6.27609i 0.590889 + 0.328057i
\(367\) 12.7768 5.68860i 0.666943 0.296942i −0.0451983 0.998978i \(-0.514392\pi\)
0.712142 + 0.702036i \(0.247725\pi\)
\(368\) −5.52428 −0.287973
\(369\) −17.4368 + 0.585332i −0.907725 + 0.0304712i
\(370\) 3.70224 1.10043i 0.192470 0.0572088i
\(371\) −2.17119 20.6575i −0.112723 1.07248i
\(372\) 6.88409 9.81739i 0.356924 0.509008i
\(373\) 17.0867 18.9767i 0.884716 0.982576i −0.115227 0.993339i \(-0.536759\pi\)
0.999942 + 0.0107631i \(0.00342607\pi\)
\(374\) −4.72728 8.18788i −0.244442 0.423385i
\(375\) 13.7830 13.6026i 0.711749 0.702434i
\(376\) −3.16035 + 5.47389i −0.162983 + 0.282294i
\(377\) −0.792576 2.43930i −0.0408197 0.125630i
\(378\) −12.0602 + 7.79731i −0.620311 + 0.401050i
\(379\) −20.5734 + 14.9474i −1.05678 + 0.767798i −0.973491 0.228727i \(-0.926544\pi\)
−0.0832927 + 0.996525i \(0.526544\pi\)
\(380\) 0.0345811 0.144638i 0.00177397 0.00741979i
\(381\) 6.21851 + 27.0186i 0.318584 + 1.38420i
\(382\) −4.06037 7.03276i −0.207746 0.359827i
\(383\) −1.58112 + 15.0434i −0.0807916 + 0.768681i 0.876859 + 0.480748i \(0.159635\pi\)
−0.957651 + 0.287933i \(0.907032\pi\)
\(384\) 0.0290591 + 1.73181i 0.00148292 + 0.0883759i
\(385\) 12.7508 1.01555i 0.649841 0.0517571i
\(386\) −4.04899 12.4615i −0.206088 0.634275i
\(387\) −21.9945 + 26.1402i −1.11804 + 1.32878i
\(388\) −2.69314 + 8.28864i −0.136724 + 0.420792i
\(389\) 7.51323 + 1.59699i 0.380936 + 0.0809704i 0.394400 0.918939i \(-0.370953\pi\)
−0.0134640 + 0.999909i \(0.504286\pi\)
\(390\) 1.93460 + 2.18550i 0.0979621 + 0.110667i
\(391\) 24.6836 5.24665i 1.24830 0.265335i
\(392\) −0.0667703 + 0.635277i −0.00337241 + 0.0320863i
\(393\) 5.63205 28.8703i 0.284099 1.45631i
\(394\) −10.4296 + 4.64357i −0.525437 + 0.233939i
\(395\) 18.8946 24.6718i 0.950689 1.24137i
\(396\) −4.30723 4.47234i −0.216446 0.224743i
\(397\) −18.0107 + 13.0855i −0.903931 + 0.656744i −0.939473 0.342624i \(-0.888684\pi\)
0.0355417 + 0.999368i \(0.488684\pi\)
\(398\) −1.05027 0.223242i −0.0526453 0.0111901i
\(399\) −0.301101 + 0.103450i −0.0150739 + 0.00517898i
\(400\) −3.52889 + 3.54216i −0.176445 + 0.177108i
\(401\) 7.27370 + 12.5984i 0.363231 + 0.629135i 0.988491 0.151282i \(-0.0483402\pi\)
−0.625259 + 0.780417i \(0.715007\pi\)
\(402\) 2.01278 4.73291i 0.100388 0.236056i
\(403\) 0.545333 + 5.18850i 0.0271650 + 0.258458i
\(404\) −6.74179 + 4.89820i −0.335417 + 0.243694i
\(405\) 8.94780 + 18.0260i 0.444620 + 0.895719i
\(406\) −7.60986 5.52889i −0.377671 0.274394i
\(407\) 1.78750 3.09605i 0.0886033 0.153465i
\(408\) −1.77461 7.71045i −0.0878565 0.381724i
\(409\) 14.4643 3.07447i 0.715211 0.152023i 0.164087 0.986446i \(-0.447532\pi\)
0.551125 + 0.834423i \(0.314199\pi\)
\(410\) 9.44114 + 8.94248i 0.466265 + 0.441638i
\(411\) −1.31645 1.74945i −0.0649359 0.0862940i
\(412\) 7.33655 + 8.14806i 0.361446 + 0.401426i
\(413\) 5.54592 17.0686i 0.272897 0.839891i
\(414\) 14.9054 7.24494i 0.732559 0.356069i
\(415\) 33.0860 + 11.6814i 1.62413 + 0.573419i
\(416\) −0.504269 0.560047i −0.0247238 0.0274586i
\(417\) 21.2478 19.7871i 1.04051 0.968977i
\(418\) −0.0688260 0.119210i −0.00336639 0.00583076i
\(419\) 2.89966 27.5884i 0.141658 1.34778i −0.660570 0.750764i \(-0.729686\pi\)
0.802228 0.597018i \(-0.203648\pi\)
\(420\) 10.4512 + 2.31408i 0.509964 + 0.112916i
\(421\) −2.26361 21.5368i −0.110322 1.04964i −0.899932 0.436031i \(-0.856384\pi\)
0.789610 0.613609i \(-0.210283\pi\)
\(422\) −16.0750 + 11.6792i −0.782518 + 0.568532i
\(423\) 1.34827 18.9141i 0.0655553 0.919636i
\(424\) 7.51539 0.364979
\(425\) 12.4036 19.1786i 0.601664 0.930299i
\(426\) −8.23646 + 2.82982i −0.399058 + 0.137105i
\(427\) −13.8055 + 15.3325i −0.668094 + 0.741994i
\(428\) 16.4555 + 7.32644i 0.795405 + 0.354137i
\(429\) 2.69119 + 0.237279i 0.129932 + 0.0114560i
\(430\) 25.3828 2.02163i 1.22407 0.0974918i
\(431\) −16.5013 11.9889i −0.794840 0.577485i 0.114556 0.993417i \(-0.463455\pi\)
−0.909396 + 0.415932i \(0.863455\pi\)
\(432\) −2.34962 4.63457i −0.113046 0.222981i
\(433\) −24.9139 18.1010i −1.19729 0.869879i −0.203270 0.979123i \(-0.565157\pi\)
−0.994015 + 0.109244i \(0.965157\pi\)
\(434\) 12.8026 + 14.2188i 0.614546 + 0.682522i
\(435\) −8.90249 + 9.72050i −0.426842 + 0.466062i
\(436\) 9.25479 10.2785i 0.443224 0.492250i
\(437\) 0.359376 0.0763878i 0.0171913 0.00365413i
\(438\) −0.0231393 1.37901i −0.00110564 0.0658918i
\(439\) 2.04413 + 0.434493i 0.0975610 + 0.0207372i 0.256433 0.966562i \(-0.417453\pi\)
−0.158872 + 0.987299i \(0.550786\pi\)
\(440\) −0.116807 + 4.62658i −0.00556857 + 0.220564i
\(441\) −0.652990 1.80164i −0.0310948 0.0857925i
\(442\) 2.78507 + 2.02347i 0.132472 + 0.0962468i
\(443\) 12.2352 21.1920i 0.581313 1.00686i −0.414012 0.910272i \(-0.635873\pi\)
0.995324 0.0965913i \(-0.0307940\pi\)
\(444\) 2.18940 2.03889i 0.103904 0.0967612i
\(445\) 0.997515 2.09639i 0.0472868 0.0993786i
\(446\) −16.2679 7.24294i −0.770308 0.342963i
\(447\) −13.1228 28.1917i −0.620688 1.33342i
\(448\) −2.70344 0.574633i −0.127725 0.0271489i
\(449\) −13.1523 −0.620697 −0.310349 0.950623i \(-0.600446\pi\)
−0.310349 + 0.950623i \(0.600446\pi\)
\(450\) 4.87606 14.1853i 0.229860 0.668704i
\(451\) 12.0366 0.566782
\(452\) −9.53418 2.02655i −0.448450 0.0953210i
\(453\) 6.84725 9.76484i 0.321712 0.458792i
\(454\) 2.44561 + 1.08885i 0.114778 + 0.0511025i
\(455\) −4.09096 + 2.22618i −0.191787 + 0.104365i
\(456\) −0.0258372 0.112259i −0.00120994 0.00525701i
\(457\) −1.19032 + 2.06169i −0.0556807 + 0.0964418i −0.892522 0.451003i \(-0.851066\pi\)
0.836842 + 0.547445i \(0.184400\pi\)
\(458\) 21.6465 + 15.7271i 1.01147 + 0.734878i
\(459\) 14.9002 + 18.4766i 0.695482 + 0.862416i
\(460\) −11.6480 4.11248i −0.543091 0.191745i
\(461\) 18.4208 + 3.91547i 0.857943 + 0.182361i 0.615823 0.787885i \(-0.288824\pi\)
0.242120 + 0.970246i \(0.422157\pi\)
\(462\) 8.49626 5.09726i 0.395282 0.237146i
\(463\) −32.2995 + 6.86547i −1.50109 + 0.319066i −0.883871 0.467730i \(-0.845072\pi\)
−0.617214 + 0.786795i \(0.711739\pi\)
\(464\) 2.27729 2.52919i 0.105721 0.117415i
\(465\) 21.8236 15.5753i 1.01205 0.722287i
\(466\) −2.40275 2.66852i −0.111305 0.123617i
\(467\) 21.8609 + 15.8829i 1.01160 + 0.734972i 0.964545 0.263920i \(-0.0850155\pi\)
0.0470578 + 0.998892i \(0.485016\pi\)
\(468\) 2.09508 + 0.849761i 0.0968451 + 0.0392802i
\(469\) 6.63951 + 4.82389i 0.306584 + 0.222746i
\(470\) −10.7386 + 9.18907i −0.495335 + 0.423860i
\(471\) 4.45873 + 9.57867i 0.205448 + 0.441362i
\(472\) 5.93212 + 2.64115i 0.273048 + 0.121569i
\(473\) 15.7707 17.5152i 0.725138 0.805348i
\(474\) 4.60895 23.6258i 0.211696 1.08517i
\(475\) 0.180589 0.279228i 0.00828597 0.0128119i
\(476\) 12.6252 0.578677
\(477\) −20.2777 + 9.85621i −0.928451 + 0.451285i
\(478\) 7.11964 5.17272i 0.325645 0.236595i
\(479\) 1.69851 + 16.1603i 0.0776071 + 0.738382i 0.962260 + 0.272132i \(0.0877287\pi\)
−0.884653 + 0.466250i \(0.845605\pi\)
\(480\) −1.22795 + 3.67316i −0.0560480 + 0.167656i
\(481\) −0.136066 + 1.29458i −0.00620407 + 0.0590278i
\(482\) −8.87275 15.3681i −0.404143 0.699996i
\(483\) 5.93150 + 25.7715i 0.269893 + 1.17264i
\(484\) −4.49403 4.99113i −0.204274 0.226869i
\(485\) −11.8489 + 15.4718i −0.538030 + 0.702538i
\(486\) 12.4178 + 9.42335i 0.563281 + 0.427452i
\(487\) −2.77191 + 8.53106i −0.125607 + 0.386579i −0.994011 0.109278i \(-0.965146\pi\)
0.868404 + 0.495857i \(0.165146\pi\)
\(488\) −4.99505 5.54757i −0.226115 0.251126i
\(489\) 2.86646 6.74029i 0.129626 0.304807i
\(490\) −0.613709 + 1.28978i −0.0277246 + 0.0582664i
\(491\) −28.0822 + 5.96906i −1.26733 + 0.269380i −0.792051 0.610454i \(-0.790987\pi\)
−0.475281 + 0.879834i \(0.657654\pi\)
\(492\) 9.63070 + 2.95151i 0.434186 + 0.133064i
\(493\) −7.77329 + 13.4637i −0.350091 + 0.606376i
\(494\) 0.0405488 + 0.0294604i 0.00182438 + 0.00132549i
\(495\) −5.75246 12.6364i −0.258554 0.567965i
\(496\) −5.60059 + 4.06907i −0.251474 + 0.182707i
\(497\) −1.45263 13.8209i −0.0651594 0.619951i
\(498\) 26.9784 3.29404i 1.20893 0.147609i
\(499\) 2.74633 + 4.75678i 0.122942 + 0.212943i 0.920927 0.389736i \(-0.127434\pi\)
−0.797984 + 0.602678i \(0.794100\pi\)
\(500\) −10.0776 + 4.84165i −0.450685 + 0.216525i
\(501\) −5.17853 + 26.5455i −0.231360 + 1.18597i
\(502\) 13.3704 + 2.84196i 0.596749 + 0.126843i
\(503\) −15.0901 + 10.9636i −0.672835 + 0.488843i −0.870973 0.491331i \(-0.836511\pi\)
0.198138 + 0.980174i \(0.436511\pi\)
\(504\) 8.04791 1.99503i 0.358482 0.0888657i
\(505\) −17.8615 + 5.30906i −0.794828 + 0.236250i
\(506\) −10.4453 + 4.65053i −0.464349 + 0.206741i
\(507\) 20.3645 6.99670i 0.904421 0.310734i
\(508\) 1.67319 15.9193i 0.0742357 0.706305i
\(509\) −33.1861 + 7.05392i −1.47095 + 0.312659i −0.872544 0.488536i \(-0.837531\pi\)
−0.598403 + 0.801195i \(0.704198\pi\)
\(510\) 1.99815 17.5786i 0.0884795 0.778396i
\(511\) 2.15271 + 0.457572i 0.0952301 + 0.0202418i
\(512\) 0.309017 0.951057i 0.0136568 0.0420312i
\(513\) 0.216937 + 0.269008i 0.00957802 + 0.0118770i
\(514\) −4.03530 12.4194i −0.177990 0.547795i
\(515\) 9.40347 + 22.6419i 0.414366 + 0.997720i
\(516\) 16.9133 10.1470i 0.744568 0.446698i
\(517\) −1.36746 + 13.0105i −0.0601407 + 0.572200i
\(518\) 2.38696 + 4.13434i 0.104877 + 0.181652i
\(519\) −39.5619 12.1245i −1.73658 0.532207i
\(520\) −0.646336 1.55626i −0.0283437 0.0682466i
\(521\) −23.3645 + 16.9753i −1.02362 + 0.743701i −0.967021 0.254696i \(-0.918025\pi\)
−0.0565960 + 0.998397i \(0.518025\pi\)
\(522\) −2.82753 + 9.81074i −0.123758 + 0.429404i
\(523\) 5.06625 + 15.5923i 0.221532 + 0.681804i 0.998625 + 0.0524191i \(0.0166932\pi\)
−0.777094 + 0.629385i \(0.783307\pi\)
\(524\) −8.49124 + 14.7073i −0.370942 + 0.642490i
\(525\) 20.3137 + 12.6595i 0.886562 + 0.552505i
\(526\) 8.49264 + 14.7097i 0.370297 + 0.641373i
\(527\) 21.1600 23.5005i 0.921742 1.02370i
\(528\) 1.51284 + 3.25002i 0.0658379 + 0.141439i
\(529\) −0.785815 7.47653i −0.0341659 0.325067i
\(530\) 15.8463 + 5.59473i 0.688318 + 0.243020i
\(531\) −19.4696 + 0.653569i −0.844907 + 0.0283625i
\(532\) 0.183815 0.00796939
\(533\) −4.00380 + 1.78261i −0.173424 + 0.0772132i
\(534\) −0.0301709 1.79806i −0.00130562 0.0778098i
\(535\) 29.2424 + 27.6979i 1.26426 + 1.19749i
\(536\) −1.98691 + 2.20668i −0.0858213 + 0.0953142i
\(537\) −26.9011 + 16.1391i −1.16087 + 0.696454i
\(538\) −18.5427 20.5938i −0.799433 0.887860i
\(539\) 0.408549 + 1.25739i 0.0175975 + 0.0541594i
\(540\) −1.50405 11.5212i −0.0647240 0.495793i
\(541\) −2.45867 + 7.56701i −0.105707 + 0.325331i −0.989896 0.141798i \(-0.954712\pi\)
0.884189 + 0.467129i \(0.154712\pi\)
\(542\) −3.41335 + 1.51972i −0.146616 + 0.0652777i
\(543\) −21.3974 18.6258i −0.918248 0.799310i
\(544\) −0.477488 + 4.54299i −0.0204721 + 0.194779i
\(545\) 27.1655 14.7827i 1.16364 0.633221i
\(546\) −2.07125 + 2.95381i −0.0886415 + 0.126411i
\(547\) −3.38757 32.2306i −0.144842 1.37808i −0.789566 0.613666i \(-0.789694\pi\)
0.644724 0.764416i \(-0.276972\pi\)
\(548\) 0.390620 + 1.20220i 0.0166864 + 0.0513556i
\(549\) 20.7529 + 8.41733i 0.885712 + 0.359243i
\(550\) −3.69049 + 9.66824i −0.157363 + 0.412255i
\(551\) −0.113174 + 0.196023i −0.00482137 + 0.00835086i
\(552\) −9.49781 + 1.15967i −0.404253 + 0.0493590i
\(553\) 35.0896 + 15.6229i 1.49216 + 0.664353i
\(554\) −20.8072 9.26394i −0.884012 0.393587i
\(555\) 6.13419 2.66914i 0.260382 0.113299i
\(556\) −15.3138 + 6.81813i −0.649449 + 0.289153i
\(557\) −39.2468 −1.66294 −0.831470 0.555569i \(-0.812500\pi\)
−0.831470 + 0.555569i \(0.812500\pi\)
\(558\) 9.77481 18.3240i 0.413801 0.775717i
\(559\) −2.65192 + 8.16177i −0.112164 + 0.345206i
\(560\) −5.27245 3.22416i −0.222802 0.136246i
\(561\) −9.84635 13.0849i −0.415713 0.552446i
\(562\) 19.6600 4.17886i 0.829307 0.176275i
\(563\) −23.1371 + 4.91795i −0.975114 + 0.207267i −0.667800 0.744341i \(-0.732764\pi\)
−0.307314 + 0.951608i \(0.599430\pi\)
\(564\) −4.28444 + 10.0746i −0.180408 + 0.424217i
\(565\) −18.5943 11.3706i −0.782267 0.478365i
\(566\) 7.37026 22.6833i 0.309795 0.953452i
\(567\) −19.0981 + 15.9375i −0.802044 + 0.669312i
\(568\) 5.02816 0.210977
\(569\) 4.10453 1.82745i 0.172071 0.0766109i −0.318893 0.947791i \(-0.603311\pi\)
0.490964 + 0.871180i \(0.336645\pi\)
\(570\) 0.0290917 0.255933i 0.00121852 0.0107199i
\(571\) −1.90197 0.846811i −0.0795949 0.0354379i 0.366553 0.930397i \(-0.380538\pi\)
−0.446148 + 0.894959i \(0.647204\pi\)
\(572\) −1.42493 0.634421i −0.0595795 0.0265265i
\(573\) −8.45725 11.2389i −0.353307 0.469513i
\(574\) −8.03661 + 13.9198i −0.335441 + 0.581002i
\(575\) −21.4985 17.3424i −0.896548 0.723228i
\(576\) 0.413507 + 2.97137i 0.0172295 + 0.123807i
\(577\) 5.77193 + 17.7642i 0.240289 + 0.739532i 0.996376 + 0.0850612i \(0.0271086\pi\)
−0.756087 + 0.654471i \(0.772891\pi\)
\(578\) −0.404186 3.84558i −0.0168119 0.159955i
\(579\) −9.57732 20.5749i −0.398020 0.855064i
\(580\) 6.68451 3.63752i 0.277559 0.151040i
\(581\) −4.53331 + 43.1315i −0.188073 + 1.78940i
\(582\) −2.89030 + 14.8159i −0.119807 + 0.614137i
\(583\) 14.2100 6.32671i 0.588519 0.262026i
\(584\) −0.246066 + 0.757312i −0.0101823 + 0.0313378i
\(585\) 3.78491 + 3.35138i 0.156487 + 0.138563i
\(586\) −3.27637 10.0836i −0.135346 0.416552i
\(587\) 5.23045 + 5.80901i 0.215884 + 0.239763i 0.841354 0.540485i \(-0.181759\pi\)
−0.625470 + 0.780248i \(0.715093\pi\)
\(588\) 0.0185622 + 1.10624i 0.000765494 + 0.0456204i
\(589\) 0.308075 0.342152i 0.0126940 0.0140981i
\(590\) 10.5418 + 9.98498i 0.433998 + 0.411075i
\(591\) −16.9567 + 10.1730i −0.697504 + 0.418462i
\(592\) −1.57795 + 0.702549i −0.0648534 + 0.0288746i
\(593\) −28.0328 −1.15117 −0.575585 0.817742i \(-0.695226\pi\)
−0.575585 + 0.817742i \(0.695226\pi\)
\(594\) −8.34419 6.78502i −0.342366 0.278393i
\(595\) 26.6204 + 9.39869i 1.09133 + 0.385309i
\(596\) 1.87665 + 17.8551i 0.0768704 + 0.731373i
\(597\) −1.85258 0.163340i −0.0758209 0.00668506i
\(598\) 2.78572 3.09386i 0.113917 0.126517i
\(599\) −18.1642 31.4612i −0.742167 1.28547i −0.951507 0.307628i \(-0.900465\pi\)
0.209339 0.977843i \(-0.432869\pi\)
\(600\) −5.32358 + 6.83077i −0.217334 + 0.278865i
\(601\) −7.22866 + 12.5204i −0.294863 + 0.510718i −0.974953 0.222411i \(-0.928607\pi\)
0.680090 + 0.733129i \(0.261941\pi\)
\(602\) 9.72571 + 29.9327i 0.396390 + 1.21996i
\(603\) 2.46698 8.55974i 0.100463 0.348580i
\(604\) −5.57062 + 4.04729i −0.226665 + 0.164682i
\(605\) −5.76013 13.8694i −0.234183 0.563870i
\(606\) −10.5628 + 9.83664i −0.429084 + 0.399586i
\(607\) 11.7111 + 20.2843i 0.475341 + 0.823314i 0.999601 0.0282440i \(-0.00899154\pi\)
−0.524261 + 0.851558i \(0.675658\pi\)
\(608\) −0.00695190 + 0.0661430i −0.000281937 + 0.00268245i
\(609\) −14.2441 7.90824i −0.577202 0.320458i
\(610\) −6.40230 15.4156i −0.259222 0.624159i
\(611\) −1.47197 4.53026i −0.0595495 0.183275i
\(612\) −4.66966 12.8839i −0.188760 0.520801i
\(613\) −3.60885 + 11.1069i −0.145760 + 0.448603i −0.997108 0.0759984i \(-0.975786\pi\)
0.851348 + 0.524601i \(0.175786\pi\)
\(614\) −29.2672 6.22093i −1.18113 0.251056i
\(615\) 18.1092 + 13.3927i 0.730234 + 0.540048i
\(616\) −5.59538 + 1.18934i −0.225444 + 0.0479197i
\(617\) −0.524675 + 4.99195i −0.0211226 + 0.200968i −0.999994 0.00350946i \(-0.998883\pi\)
0.978871 + 0.204478i \(0.0655496\pi\)
\(618\) 14.3241 + 12.4687i 0.576198 + 0.501565i
\(619\) 0.232630 0.103574i 0.00935020 0.00416298i −0.402056 0.915615i \(-0.631704\pi\)
0.411406 + 0.911452i \(0.365038\pi\)
\(620\) −14.8381 + 4.41039i −0.595911 + 0.177125i
\(621\) 24.1057 15.5851i 0.967328 0.625408i
\(622\) −11.0145 + 8.00252i −0.441642 + 0.320872i
\(623\) 2.80687 + 0.596618i 0.112455 + 0.0239030i
\(624\) −0.984547 0.857022i −0.0394134 0.0343083i
\(625\) −24.8531 + 2.70651i −0.994123 + 0.108260i
\(626\) 1.23980 + 2.14739i 0.0495523 + 0.0858271i
\(627\) −0.143356 0.190508i −0.00572510 0.00760815i
\(628\) −0.637627 6.06661i −0.0254441 0.242084i
\(629\) 6.38335 4.63778i 0.254521 0.184920i
\(630\) 18.4543 + 1.78462i 0.735236 + 0.0711010i
\(631\) −15.5311 11.2840i −0.618282 0.449208i 0.234039 0.972227i \(-0.424806\pi\)
−0.852321 + 0.523019i \(0.824806\pi\)
\(632\) −6.94874 + 12.0356i −0.276406 + 0.478750i
\(633\) −25.1857 + 23.4543i −1.00104 + 0.932224i
\(634\) 34.2429 7.27856i 1.35996 0.289069i
\(635\) 15.3789 32.3204i 0.610291 1.28260i
\(636\) 12.9211 1.57765i 0.512354 0.0625580i
\(637\) −0.322115 0.357745i −0.0127627 0.0141744i
\(638\) 2.17672 6.69927i 0.0861773 0.265226i
\(639\) −13.5668 + 6.59428i −0.536693 + 0.260866i
\(640\) 1.35957 1.77527i 0.0537416 0.0701736i
\(641\) 5.79918 + 6.44064i 0.229054 + 0.254390i 0.846706 0.532062i \(-0.178583\pi\)
−0.617652 + 0.786452i \(0.711916\pi\)
\(642\) 29.8296 + 9.14185i 1.17728 + 0.360800i
\(643\) 15.6629 + 27.1289i 0.617683 + 1.06986i 0.989907 + 0.141715i \(0.0452617\pi\)
−0.372225 + 0.928143i \(0.621405\pi\)
\(644\) 1.59596 15.1846i 0.0628897 0.598356i
\(645\) 43.2158 8.80419i 1.70162 0.346665i
\(646\) −0.0317564 0.302142i −0.00124944 0.0118876i
\(647\) 12.2140 8.87401i 0.480183 0.348873i −0.321213 0.947007i \(-0.604091\pi\)
0.801397 + 0.598133i \(0.204091\pi\)
\(648\) −5.01257 7.47490i −0.196912 0.293642i
\(649\) 13.4398 0.527559
\(650\) −0.204268 3.76255i −0.00801204 0.147579i
\(651\) 24.9962 + 21.7585i 0.979678 + 0.852783i
\(652\) −2.82962 + 3.14261i −0.110816 + 0.123074i
\(653\) 15.3366 + 6.82831i 0.600169 + 0.267212i 0.684251 0.729246i \(-0.260129\pi\)
−0.0840822 + 0.996459i \(0.526796\pi\)
\(654\) 13.7539 19.6144i 0.537821 0.766985i
\(655\) −28.8525 + 24.6892i −1.12736 + 0.964688i
\(656\) −4.70488 3.41829i −0.183695 0.133462i
\(657\) −0.329269 2.36605i −0.0128460 0.0923086i
\(658\) −14.1330 10.2682i −0.550962 0.400298i
\(659\) 28.3496 + 31.4855i 1.10434 + 1.22650i 0.971921 + 0.235306i \(0.0756092\pi\)
0.132423 + 0.991193i \(0.457724\pi\)
\(660\) 0.770401 + 7.97892i 0.0299878 + 0.310579i
\(661\) 13.6355 15.1438i 0.530359 0.589024i −0.417116 0.908853i \(-0.636959\pi\)
0.947475 + 0.319830i \(0.103626\pi\)
\(662\) −16.1026 + 3.42271i −0.625845 + 0.133028i
\(663\) 5.21310 + 2.89427i 0.202460 + 0.112404i
\(664\) −15.3488 3.26248i −0.595647 0.126609i
\(665\) 0.387576 + 0.136839i 0.0150295 + 0.00530638i
\(666\) 3.33619 3.96503i 0.129275 0.153642i
\(667\) 15.2104 + 11.0510i 0.588950 + 0.427897i
\(668\) 7.80749 13.5230i 0.302081 0.523219i
\(669\) −29.4896 9.03765i −1.14013 0.349416i
\(670\) −5.83215 + 3.17369i −0.225315 + 0.122610i
\(671\) −14.1147 6.28428i −0.544893 0.242602i
\(672\) −4.76860 0.420443i −0.183953 0.0162190i
\(673\) −34.3204 7.29504i −1.32296 0.281203i −0.508316 0.861170i \(-0.669732\pi\)
−0.814640 + 0.579967i \(0.803065\pi\)
\(674\) 1.10629 0.0426126
\(675\) 5.40549 25.4122i 0.208058 0.978117i
\(676\) −12.4321 −0.478156
\(677\) −3.87181 0.822978i −0.148806 0.0316296i 0.132906 0.991129i \(-0.457569\pi\)
−0.281712 + 0.959499i \(0.590902\pi\)
\(678\) −16.8174 1.48277i −0.645867 0.0569455i
\(679\) −22.0049 9.79720i −0.844470 0.375982i
\(680\) −4.38876 + 9.22348i −0.168301 + 0.353704i
\(681\) 4.43327 + 1.35866i 0.169883 + 0.0520639i
\(682\) −7.16407 + 12.4085i −0.274326 + 0.475147i
\(683\) 24.7679 + 17.9949i 0.947716 + 0.688556i 0.950266 0.311440i \(-0.100811\pi\)
−0.00254923 + 0.999997i \(0.500811\pi\)
\(684\) −0.0679872 0.187581i −0.00259956 0.00717235i
\(685\) −0.0713392 + 2.82565i −0.00272573 + 0.107963i
\(686\) 17.1972 + 3.65537i 0.656591 + 0.139563i
\(687\) 40.5179 + 22.4952i 1.54585 + 0.858245i
\(688\) −11.1386 + 2.36759i −0.424656 + 0.0902634i
\(689\) −3.78977 + 4.20897i −0.144379 + 0.160349i
\(690\) −20.8895 4.62533i −0.795250 0.176083i
\(691\) 12.4225 + 13.7966i 0.472574 + 0.524847i 0.931556 0.363599i \(-0.118452\pi\)
−0.458981 + 0.888446i \(0.651786\pi\)
\(692\) 19.3272 + 14.0420i 0.734708 + 0.533797i
\(693\) 13.5374 10.5472i 0.514245 0.400655i
\(694\) −14.7465 10.7139i −0.559769 0.406696i
\(695\) −37.3649 + 2.97596i −1.41733 + 0.112885i
\(696\) 3.38437 4.82644i 0.128284 0.182946i
\(697\) 24.2688 + 10.8052i 0.919247 + 0.409275i
\(698\) −10.3184 + 11.4598i −0.390558 + 0.433758i
\(699\) −4.69119 4.08355i −0.177437 0.154454i
\(700\) −8.71682 10.7232i −0.329465 0.405298i
\(701\) −24.9923 −0.943945 −0.471973 0.881613i \(-0.656458\pi\)
−0.471973 + 0.881613i \(0.656458\pi\)
\(702\) 3.78042 + 1.02117i 0.142683 + 0.0385417i
\(703\) 0.0929374 0.0675230i 0.00350520 0.00254668i
\(704\) −0.216346 2.05839i −0.00815383 0.0775785i
\(705\) −16.5337 + 18.0529i −0.622695 + 0.679911i
\(706\) −2.25479 + 21.4529i −0.0848600 + 0.807389i
\(707\) −11.5159 19.9462i −0.433102 0.750154i
\(708\) 10.7534 + 3.29559i 0.404139 + 0.123856i
\(709\) −8.43683 9.37005i −0.316852 0.351899i 0.563589 0.826055i \(-0.309420\pi\)
−0.880441 + 0.474156i \(0.842753\pi\)
\(710\) 10.6019 + 3.74315i 0.397883 + 0.140478i
\(711\) 2.96448 41.5869i 0.111177 1.55963i
\(712\) −0.320840 + 0.987443i −0.0120240 + 0.0370060i
\(713\) −25.5896 28.4201i −0.958338 1.06434i
\(714\) 21.7063 2.65033i 0.812339 0.0991860i
\(715\) −2.53220 2.39846i −0.0946989 0.0896972i
\(716\) 17.7163 3.76571i 0.662088 0.140731i
\(717\) 11.1548 10.3879i 0.416584 0.387945i
\(718\) 9.94797 17.2304i 0.371255 0.643033i
\(719\) 19.7551 + 14.3529i 0.736739 + 0.535272i 0.891688 0.452650i \(-0.149521\pi\)
−0.154949 + 0.987922i \(0.549521\pi\)
\(720\) −1.34011 + 6.57298i −0.0499430 + 0.244961i
\(721\) −24.5160 + 17.8119i −0.913025 + 0.663352i
\(722\) 1.98558 + 18.8915i 0.0738956 + 0.703069i
\(723\) −18.4809 24.5594i −0.687311 0.913375i
\(724\) 8.18926 + 14.1842i 0.304351 + 0.527152i
\(725\) 16.8022 2.69355i 0.624020 0.100036i
\(726\) −8.77426 7.63775i −0.325643 0.283464i
\(727\) −16.5821 3.52463i −0.614995 0.130721i −0.110127 0.993918i \(-0.535126\pi\)
−0.504868 + 0.863196i \(0.668459\pi\)
\(728\) 1.68508 1.22428i 0.0624532 0.0453749i
\(729\) 23.3278 + 13.5946i 0.863993 + 0.503505i
\(730\) −1.08260 + 1.41362i −0.0400689 + 0.0523204i
\(731\) 47.5209 21.1577i 1.75762 0.782545i
\(732\) −9.75246 8.48926i −0.360461 0.313772i
\(733\) 3.05862 29.1008i 0.112973 1.07486i −0.780318 0.625383i \(-0.784943\pi\)
0.893291 0.449480i \(-0.148391\pi\)
\(734\) −13.6803 + 2.90784i −0.504950 + 0.107330i
\(735\) −0.784385 + 2.34633i −0.0289325 + 0.0865457i
\(736\) 5.40357 + 1.14856i 0.199178 + 0.0423366i
\(737\) −1.89916 + 5.84502i −0.0699566 + 0.215304i
\(738\) 17.1775 + 3.05278i 0.632312 + 0.112374i
\(739\) −6.87844 21.1697i −0.253028 0.778739i −0.994212 0.107437i \(-0.965736\pi\)
0.741184 0.671302i \(-0.234264\pi\)
\(740\) −3.85013 + 0.306647i −0.141534 + 0.0112726i
\(741\) 0.0758993 + 0.0421387i 0.00278823 + 0.00154800i
\(742\) −2.17119 + 20.6575i −0.0797069 + 0.758360i
\(743\) −13.7385 23.7958i −0.504017 0.872984i −0.999989 0.00464517i \(-0.998521\pi\)
0.495972 0.868339i \(-0.334812\pi\)
\(744\) −8.77481 + 8.17157i −0.321700 + 0.299584i
\(745\) −9.33506 + 39.0447i −0.342010 + 1.43049i
\(746\) −20.6588 + 15.0095i −0.756372 + 0.549536i
\(747\) 45.6920 11.3268i 1.67178 0.414425i
\(748\) 2.92162 + 8.99181i 0.106825 + 0.328773i
\(749\) −24.8921 + 43.1144i −0.909538 + 1.57537i
\(750\) −16.3099 + 10.4397i −0.595554 + 0.381203i
\(751\) −2.34086 4.05449i −0.0854191 0.147950i 0.820151 0.572148i \(-0.193890\pi\)
−0.905570 + 0.424197i \(0.860556\pi\)
\(752\) 4.22938 4.69720i 0.154229 0.171289i
\(753\) 23.5840 + 2.07938i 0.859450 + 0.0757770i
\(754\) 0.268098 + 2.55078i 0.00976354 + 0.0928939i
\(755\) −14.7587 + 4.38678i −0.537122 + 0.159651i
\(756\) 13.4178 5.11946i 0.488002 0.186193i
\(757\) −31.5537 −1.14684 −0.573420 0.819262i \(-0.694384\pi\)
−0.573420 + 0.819262i \(0.694384\pi\)
\(758\) 23.2315 10.3433i 0.843808 0.375687i
\(759\) −16.9821 + 10.1883i −0.616412 + 0.369811i
\(760\) −0.0638974 + 0.134288i −0.00231780 + 0.00487113i
\(761\) −1.81116 + 2.01149i −0.0656544 + 0.0729166i −0.775077 0.631867i \(-0.782289\pi\)
0.709423 + 0.704783i \(0.248956\pi\)
\(762\) −0.465149 27.7210i −0.0168506 1.00423i
\(763\) 25.5787 + 28.4080i 0.926012 + 1.02844i
\(764\) 2.50944 + 7.72327i 0.0907885 + 0.279418i
\(765\) −0.254779 30.6421i −0.00921156 1.10787i
\(766\) 4.67427 14.3859i 0.168888 0.519784i
\(767\) −4.47055 + 1.99042i −0.161422 + 0.0718698i
\(768\) 0.331639 1.70000i 0.0119670 0.0613436i
\(769\) 2.09828 19.9638i 0.0756659 0.719913i −0.889262 0.457398i \(-0.848781\pi\)
0.964928 0.262515i \(-0.0845519\pi\)
\(770\) −12.6833 1.65768i −0.457075 0.0597388i
\(771\) −9.54494 20.5053i −0.343752 0.738481i
\(772\) 1.36962 + 13.0310i 0.0492936 + 0.468997i
\(773\) −4.80576 14.7906i −0.172851 0.531981i 0.826678 0.562676i \(-0.190228\pi\)
−0.999529 + 0.0306945i \(0.990228\pi\)
\(774\) 26.9487 20.9961i 0.968652 0.754689i
\(775\) −34.5695 1.74666i −1.24177 0.0627420i
\(776\) 4.35759 7.54758i 0.156429 0.270942i
\(777\) 4.97175 + 6.60702i 0.178361 + 0.237025i
\(778\) −7.01701 3.12418i −0.251572 0.112007i
\(779\) 0.353338 + 0.157316i 0.0126596 + 0.00563644i
\(780\) −1.43793 2.53997i −0.0514861 0.0909456i
\(781\) 9.50720 4.23288i 0.340194 0.151464i
\(782\) −25.2350 −0.902402
\(783\) −2.80182 + 17.4610i −0.100129 + 0.624005i
\(784\) 0.197393 0.607512i 0.00704974 0.0216969i
\(785\) 3.17177 13.2662i 0.113205 0.473491i
\(786\) −11.5115 + 27.0685i −0.410600 + 0.965500i
\(787\) 25.1375 5.34315i 0.896057 0.190463i 0.263209 0.964739i \(-0.415219\pi\)
0.632848 + 0.774276i \(0.281886\pi\)
\(788\) 11.1672 2.37365i 0.397814 0.0845579i
\(789\) 17.6891 + 23.5073i 0.629750 + 0.836882i
\(790\) −23.6112 + 20.2042i −0.840050 + 0.718834i
\(791\) 8.32479 25.6211i 0.295995 0.910980i
\(792\) 3.28325 + 5.27013i 0.116665 + 0.187266i
\(793\) 5.62575 0.199776
\(794\) 20.3378 9.05495i 0.721760 0.321348i
\(795\) 28.4187 + 6.29242i 1.00791 + 0.223169i
\(796\) 0.980906 + 0.436727i 0.0347673 + 0.0154794i
\(797\) −14.2286 6.33497i −0.504002 0.224396i 0.138954 0.990299i \(-0.455626\pi\)
−0.642957 + 0.765903i \(0.722292\pi\)
\(798\) 0.316030 0.0385870i 0.0111873 0.00136597i
\(799\) −14.4365 + 25.0048i −0.510728 + 0.884607i
\(800\) 4.18824 2.73106i 0.148076 0.0965575i
\(801\) −0.429327 3.08505i −0.0151695 0.109005i
\(802\) −4.49539 13.8354i −0.158738 0.488545i
\(803\) 0.172273 + 1.63907i 0.00607937 + 0.0578414i
\(804\) −2.95282 + 4.21101i −0.104138 + 0.148511i
\(805\) 14.6690 30.8287i 0.517016 1.08657i
\(806\) 0.545333 5.18850i 0.0192085 0.182757i
\(807\) −36.2032 31.5139i −1.27441 1.10934i
\(808\) 7.61286 3.38946i 0.267819 0.119241i
\(809\) 6.56420 20.2025i 0.230785 0.710283i −0.766868 0.641805i \(-0.778186\pi\)
0.997653 0.0684777i \(-0.0218142\pi\)
\(810\) −5.00445 19.4924i −0.175838 0.684895i
\(811\) 3.74381 + 11.5223i 0.131463 + 0.404601i 0.995023 0.0996444i \(-0.0317705\pi\)
−0.863560 + 0.504246i \(0.831771\pi\)
\(812\) 6.29405 + 6.99025i 0.220878 + 0.245310i
\(813\) −5.54949 + 3.32937i −0.194629 + 0.116766i
\(814\) −2.39215 + 2.65675i −0.0838447 + 0.0931190i
\(815\) −8.30575 + 4.51975i −0.290938 + 0.158320i
\(816\) 0.132742 + 7.91092i 0.00464691 + 0.276938i
\(817\) 0.691873 0.308042i 0.0242056 0.0107770i
\(818\) −14.7874 −0.517029
\(819\) −2.94100 + 5.51324i −0.102767 + 0.192648i
\(820\) −7.37558 10.7100i −0.257566 0.374009i
\(821\) 1.79247 + 17.0542i 0.0625575 + 0.595195i 0.980231 + 0.197859i \(0.0633987\pi\)
−0.917673 + 0.397336i \(0.869935\pi\)
\(822\) 0.923956 + 1.98493i 0.0322267 + 0.0692323i
\(823\) −13.6414 + 15.1503i −0.475508 + 0.528105i −0.932405 0.361414i \(-0.882294\pi\)
0.456897 + 0.889519i \(0.348961\pi\)
\(824\) −5.48215 9.49536i −0.190980 0.330787i
\(825\) −4.31540 + 17.3971i −0.150243 + 0.605691i
\(826\) −8.97349 + 15.5425i −0.312228 + 0.540794i
\(827\) 7.90828 + 24.3392i 0.274998 + 0.846357i 0.989220 + 0.146437i \(0.0467807\pi\)
−0.714222 + 0.699919i \(0.753219\pi\)
\(828\) −16.0860 + 3.98762i −0.559026 + 0.138579i
\(829\) −2.53900 + 1.84469i −0.0881831 + 0.0640688i −0.631003 0.775780i \(-0.717357\pi\)
0.542820 + 0.839849i \(0.317357\pi\)
\(830\) −29.9343 18.3051i −1.03903 0.635381i
\(831\) −37.7181 11.5594i −1.30843 0.400992i
\(832\) 0.376809 + 0.652652i 0.0130635 + 0.0226266i
\(833\) −0.305008 + 2.90195i −0.0105679 + 0.100547i
\(834\) −24.8974 + 14.9370i −0.862127 + 0.517226i
\(835\) 26.5292 22.7011i 0.918080 0.785605i
\(836\) 0.0425368 + 0.130915i 0.00147117 + 0.00452779i
\(837\) 12.9590 33.5561i 0.447929 1.15987i
\(838\) −8.57225 + 26.3827i −0.296123 + 0.911374i
\(839\) −4.10140 0.871778i −0.141596 0.0300971i 0.136568 0.990631i \(-0.456393\pi\)
−0.278164 + 0.960534i \(0.589726\pi\)
\(840\) −9.74165 4.43643i −0.336119 0.153071i
\(841\) 17.0366 3.62123i 0.587468 0.124870i
\(842\) −2.26361 + 21.5368i −0.0780092 + 0.742208i
\(843\) 32.9239 11.3117i 1.13396 0.389597i
\(844\) 18.1519 8.08176i 0.624815 0.278186i
\(845\) −26.2131 9.25488i −0.901759 0.318378i
\(846\) −5.25128 + 18.2205i −0.180543 + 0.626433i
\(847\) 15.0174 10.9108i 0.516004 0.374899i
\(848\) −7.35116 1.56254i −0.252440 0.0536577i
\(849\) 7.90981 40.5463i 0.271464 1.39154i
\(850\) −16.1200 + 16.1807i −0.552913 + 0.554992i
\(851\) −4.77100 8.26362i −0.163548 0.283273i
\(852\) 8.64483 1.05553i 0.296167 0.0361617i
\(853\) 0.422046 + 4.01550i 0.0144506 + 0.137488i 0.999368 0.0355345i \(-0.0113134\pi\)
−0.984918 + 0.173022i \(0.944647\pi\)
\(854\) 16.6916 12.1272i 0.571176 0.414983i
\(855\) −0.00370942 0.446129i −0.000126859 0.0152573i
\(856\) −14.5726 10.5876i −0.498082 0.361878i
\(857\) 12.8987 22.3413i 0.440612 0.763163i −0.557123 0.830430i \(-0.688095\pi\)
0.997735 + 0.0672672i \(0.0214280\pi\)
\(858\) −2.58304 0.791623i −0.0881837 0.0270256i
\(859\) 43.4966 9.24548i 1.48408 0.315452i 0.606581 0.795022i \(-0.292541\pi\)
0.877504 + 0.479570i \(0.159207\pi\)
\(860\) −25.2484 3.29992i −0.860964 0.112526i
\(861\) −10.8951 + 25.6192i −0.371304 + 0.873098i
\(862\) 13.6481 + 15.1577i 0.464855 + 0.516274i
\(863\) 9.43350 29.0333i 0.321120 0.988306i −0.652042 0.758183i \(-0.726087\pi\)
0.973162 0.230122i \(-0.0739127\pi\)
\(864\) 1.33469 + 5.02181i 0.0454072 + 0.170846i
\(865\) 30.2981 + 43.9955i 1.03017 + 1.49589i
\(866\) 20.6061 + 22.8853i 0.700222 + 0.777676i
\(867\) −1.50219 6.52679i −0.0510169 0.221661i
\(868\) −9.56661 16.5699i −0.324712 0.562418i
\(869\) −3.00666 + 28.6065i −0.101994 + 0.970408i
\(870\) 10.7290 7.65715i 0.363746 0.259602i
\(871\) −0.233912 2.22552i −0.00792580 0.0754089i
\(872\) −11.1896 + 8.12970i −0.378927 + 0.275306i
\(873\) −1.85904 + 26.0794i −0.0629191 + 0.882654i
\(874\) −0.367405 −0.0124277
\(875\) −10.3968 29.0990i −0.351475 0.983727i
\(876\) −0.264079 + 1.35369i −0.00892241 + 0.0457369i
\(877\) −33.2444 + 36.9217i −1.12258 + 1.24676i −0.156738 + 0.987640i \(0.550098\pi\)
−0.965846 + 0.259116i \(0.916569\pi\)
\(878\) −1.90913 0.849997i −0.0644299 0.0286860i
\(879\) −7.74980 16.6488i −0.261394 0.561552i
\(880\) 1.07617 4.50119i 0.0362779 0.151735i
\(881\) 30.5661 + 22.2076i 1.02980 + 0.748192i 0.968268 0.249913i \(-0.0804020\pi\)
0.0615302 + 0.998105i \(0.480402\pi\)
\(882\) 0.264138 + 1.89804i 0.00889400 + 0.0639102i
\(883\) 2.60162 + 1.89019i 0.0875515 + 0.0636099i 0.630700 0.776027i \(-0.282768\pi\)
−0.543148 + 0.839637i \(0.682768\pi\)
\(884\) −2.30351 2.55830i −0.0774753 0.0860451i
\(885\) 20.2203 + 14.9540i 0.679700 + 0.502675i
\(886\) −16.3739 + 18.1851i −0.550092 + 0.610939i
\(887\) 0.288538 0.0613307i 0.00968816 0.00205928i −0.203065 0.979165i \(-0.565090\pi\)
0.212753 + 0.977106i \(0.431757\pi\)
\(888\) −2.56546 + 1.53913i −0.0860913 + 0.0516498i
\(889\) 43.2739 + 9.19816i 1.45136 + 0.308496i
\(890\) −1.41158 + 1.84319i −0.0473163 + 0.0617838i
\(891\) −15.7703 9.91373i −0.528327 0.332123i
\(892\) 14.4065 + 10.4670i 0.482366 + 0.350459i
\(893\) −0.210186 + 0.364054i −0.00703362 + 0.0121826i
\(894\) 6.97468 + 30.3040i 0.233268 + 1.01352i
\(895\) 40.1583 + 5.24861i 1.34234 + 0.175442i
\(896\) 2.52489 + 1.12415i 0.0843506 + 0.0375553i
\(897\) 4.13997 5.90401i 0.138230 0.197129i
\(898\) 12.8649 + 2.73453i 0.429308 + 0.0912523i
\(899\) 23.5605 0.785785
\(900\) −7.71881 + 12.8616i −0.257294 + 0.428719i
\(901\) 34.3304 1.14371
\(902\) −11.7736 2.50255i −0.392017 0.0833259i
\(903\) 23.0048 + 49.4211i 0.765552 + 1.64463i
\(904\) 8.90449 + 3.96454i 0.296159 + 0.131859i
\(905\) 6.70788 + 36.0039i 0.222978 + 1.19681i
\(906\) −8.72784 + 8.12783i −0.289963 + 0.270029i
\(907\) −7.84758 + 13.5924i −0.260575 + 0.451329i −0.966395 0.257063i \(-0.917245\pi\)
0.705820 + 0.708391i \(0.250579\pi\)
\(908\) −2.16578 1.57353i −0.0718739 0.0522195i
\(909\) −16.0955 + 19.1293i −0.533854 + 0.634480i
\(910\) 4.46441 1.32698i 0.147994 0.0439888i
\(911\) 12.7587 + 2.71195i 0.422715 + 0.0898509i 0.414357 0.910114i \(-0.364006\pi\)
0.00835761 + 0.999965i \(0.497340\pi\)
\(912\) 0.00193264 + 0.115178i 6.39961e−5 + 0.00381392i
\(913\) −31.7678 + 6.75245i −1.05136 + 0.223473i
\(914\) 1.59296 1.76916i 0.0526903 0.0585185i
\(915\) −14.2435 25.1598i −0.470874 0.831756i
\(916\) −17.9036 19.8840i −0.591551 0.656984i
\(917\) −37.9726 27.5887i −1.25397 0.911060i
\(918\) −10.7331 21.1708i −0.354245 0.698741i
\(919\) −0.432552 0.314268i −0.0142686 0.0103667i 0.580628 0.814169i \(-0.302807\pi\)
−0.594897 + 0.803802i \(0.702807\pi\)
\(920\) 10.5384 + 6.44437i 0.347442 + 0.212465i
\(921\) −51.6245 4.55169i −1.70108 0.149983i
\(922\) −17.2042 7.65981i −0.566590 0.252262i
\(923\) −2.53554 + 2.81601i −0.0834584 + 0.0926900i
\(924\) −9.37037 + 3.21940i −0.308263 + 0.105911i
\(925\) −8.34632 2.21961i −0.274425 0.0729803i
\(926\) 33.0211 1.08514
\(927\) 27.2446 + 18.4303i 0.894830 + 0.605330i
\(928\) −2.75337 + 2.00044i −0.0903839 + 0.0656677i
\(929\) 0.773100 + 7.35555i 0.0253646 + 0.241328i 0.999857 + 0.0169077i \(0.00538214\pi\)
−0.974492 + 0.224420i \(0.927951\pi\)
\(930\) −24.5850 + 10.6976i −0.806174 + 0.350786i
\(931\) −0.00444071 + 0.0422505i −0.000145538 + 0.00138471i
\(932\) 1.79543 + 3.10977i 0.0588111 + 0.101864i
\(933\) −17.2572 + 16.0708i −0.564974 + 0.526134i
\(934\) −18.0810 20.0809i −0.591627 0.657068i
\(935\) −0.533577 + 21.1343i −0.0174498 + 0.691165i
\(936\) −1.87262 1.26678i −0.0612086 0.0414061i
\(937\) 4.20251 12.9340i 0.137290 0.422535i −0.858649 0.512564i \(-0.828696\pi\)
0.995939 + 0.0900285i \(0.0286958\pi\)
\(938\) −5.49148 6.09890i −0.179303 0.199136i
\(939\) 2.58235 + 3.43171i 0.0842718 + 0.111990i
\(940\) 12.4144 6.75559i 0.404915 0.220343i
\(941\) −19.6400 + 4.17461i −0.640245 + 0.136088i −0.516584 0.856236i \(-0.672797\pi\)
−0.123661 + 0.992325i \(0.539463\pi\)
\(942\) −2.36978 10.2964i −0.0772117 0.335474i
\(943\) 16.0634 27.8226i 0.523095 0.906028i
\(944\) −5.25336 3.81679i −0.170982 0.124226i
\(945\) 32.1027 0.805708i 1.04430 0.0262097i
\(946\) −19.0677 + 13.8535i −0.619944 + 0.450416i
\(947\) 4.04148 + 38.4521i 0.131331 + 1.24953i 0.839451 + 0.543435i \(0.182877\pi\)
−0.708120 + 0.706092i \(0.750457\pi\)
\(948\) −9.42031 + 22.1513i −0.305957 + 0.719439i
\(949\) −0.300047 0.519697i −0.00973995 0.0168701i
\(950\) −0.234697 + 0.235580i −0.00761458 + 0.00764321i
\(951\) 57.3453 19.7023i 1.85955 0.638890i
\(952\) −12.3493 2.62493i −0.400244 0.0850746i
\(953\) −39.5104 + 28.7060i −1.27987 + 0.929879i −0.999549 0.0300274i \(-0.990441\pi\)
−0.280320 + 0.959907i \(0.590441\pi\)
\(954\) 21.8838 5.42486i 0.708514 0.175636i
\(955\) −0.458302 + 18.1527i −0.0148303 + 0.587408i
\(956\) −8.03953 + 3.57943i −0.260017 + 0.115767i
\(957\) 2.33607 11.9749i 0.0755145 0.387093i
\(958\) 1.69851 16.1603i 0.0548765 0.522115i
\(959\) −3.41734 + 0.726378i −0.110352 + 0.0234560i
\(960\) 1.96481 3.33759i 0.0634140 0.107720i
\(961\) −16.5541 3.51869i −0.534004 0.113506i
\(962\) 0.402251 1.23800i 0.0129691 0.0399148i
\(963\) 53.2045 + 9.45550i 1.71449 + 0.304699i
\(964\) 5.48366 + 16.8770i 0.176617 + 0.543571i
\(965\) −6.81293 + 28.4957i −0.219316 + 0.917308i
\(966\) −0.443680 26.4416i −0.0142752 0.850744i
\(967\) 3.53597 33.6425i 0.113709 1.08187i −0.777689 0.628649i \(-0.783608\pi\)
0.891398 0.453221i \(-0.149725\pi\)
\(968\) 3.35811 + 5.81642i 0.107934 + 0.186947i
\(969\) −0.118025 0.512801i −0.00379150 0.0164735i
\(970\) 14.8067 12.6702i 0.475415 0.406815i
\(971\) 49.9298 36.2761i 1.60232 1.16416i 0.719455 0.694539i \(-0.244392\pi\)
0.882870 0.469618i \(-0.155608\pi\)
\(972\) −10.1872 11.7992i −0.326754 0.378460i
\(973\) −14.3168 44.0626i −0.458976 1.41258i
\(974\) 4.48504 7.76832i 0.143710 0.248913i
\(975\) −1.14104 6.42600i −0.0365425 0.205797i
\(976\) 3.73249 + 6.46487i 0.119474 + 0.206935i
\(977\) 18.6875 20.7546i 0.597867 0.663999i −0.365928 0.930643i \(-0.619248\pi\)
0.963795 + 0.266644i \(0.0859149\pi\)
\(978\) −4.20521 + 5.99703i −0.134468 + 0.191764i
\(979\) 0.224623 + 2.13714i 0.00717897 + 0.0683034i
\(980\) 0.868459 1.13400i 0.0277419 0.0362243i
\(981\) 19.5293 36.6100i 0.623524 1.16887i
\(982\) 28.7096 0.916160
\(983\) 6.15520 2.74047i 0.196321 0.0874075i −0.306222 0.951960i \(-0.599065\pi\)
0.502542 + 0.864553i \(0.332398\pi\)
\(984\) −8.80659 4.88935i −0.280744 0.155867i
\(985\) 25.3131 + 3.30837i 0.806542 + 0.105414i
\(986\) 10.4027 11.5534i 0.331289 0.367934i
\(987\) −26.4542 14.6872i −0.842046 0.467497i
\(988\) −0.0335375 0.0372472i −0.00106697 0.00118499i
\(989\) −19.4395 59.8287i −0.618141 1.90244i
\(990\) 2.99950 + 13.5563i 0.0953302 + 0.430847i
\(991\) −12.6586 + 38.9590i −0.402112 + 1.23757i 0.521170 + 0.853453i \(0.325496\pi\)
−0.923283 + 0.384121i \(0.874504\pi\)
\(992\) 6.32421 2.81572i 0.200794 0.0893992i
\(993\) −26.9664 + 9.26492i −0.855753 + 0.294013i
\(994\) −1.45263 + 13.8209i −0.0460747 + 0.438371i
\(995\) 1.74313 + 1.65107i 0.0552610 + 0.0523423i
\(996\) −27.0737 2.38706i −0.857863 0.0756370i
\(997\) −5.72449 54.4649i −0.181297 1.72492i −0.585861 0.810412i \(-0.699243\pi\)
0.404564 0.914510i \(-0.367423\pi\)
\(998\) −1.69732 5.22382i −0.0537278 0.165357i
\(999\) 4.90350 7.51734i 0.155140 0.237838i
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 450.2.q.b.331.1 yes 112
9.4 even 3 inner 450.2.q.b.31.6 112
25.21 even 5 inner 450.2.q.b.421.6 yes 112
225.121 even 15 inner 450.2.q.b.121.1 yes 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.q.b.31.6 112 9.4 even 3 inner
450.2.q.b.121.1 yes 112 225.121 even 15 inner
450.2.q.b.331.1 yes 112 1.1 even 1 trivial
450.2.q.b.421.6 yes 112 25.21 even 5 inner