Properties

Label 882.2.y.a.457.2
Level $882$
Weight $2$
Character 882.457
Analytic conductor $7.043$
Analytic rank $0$
Dimension $336$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(193,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 22]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.y (of order \(21\), degree \(12\), 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(28\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 457.2
Character \(\chi\) \(=\) 882.457
Dual form 882.2.y.a.193.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.988831 + 0.149042i) q^{2} +(-1.67319 + 0.447706i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.697157 - 0.335733i) q^{5} +(-1.72123 + 0.193329i) q^{6} +(-1.34035 - 2.28111i) q^{7} +(0.900969 + 0.433884i) q^{8} +(2.59912 - 1.49819i) q^{9} +O(q^{10})\) \(q+(0.988831 + 0.149042i) q^{2} +(-1.67319 + 0.447706i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.697157 - 0.335733i) q^{5} +(-1.72123 + 0.193329i) q^{6} +(-1.34035 - 2.28111i) q^{7} +(0.900969 + 0.433884i) q^{8} +(2.59912 - 1.49819i) q^{9} +(-0.639332 - 0.435889i) q^{10} +(-3.78623 + 4.74778i) q^{11} +(-1.73082 - 0.0653658i) q^{12} +(2.78280 + 0.419439i) q^{13} +(-0.985400 - 2.45540i) q^{14} +(1.31678 + 0.249624i) q^{15} +(0.826239 + 0.563320i) q^{16} +(7.16814 - 2.21108i) q^{17} +(2.79338 - 1.09408i) q^{18} +(2.86472 - 4.96184i) q^{19} +(-0.567225 - 0.526308i) q^{20} +(3.26393 + 3.21664i) q^{21} +(-4.45156 + 4.13045i) q^{22} +(-1.34365 - 5.88692i) q^{23} +(-1.70174 - 0.322601i) q^{24} +(-2.74414 - 3.44104i) q^{25} +(2.68920 + 0.829508i) q^{26} +(-3.67807 + 3.67040i) q^{27} +(-0.608436 - 2.57484i) q^{28} +(6.05560 + 5.61877i) q^{29} +(1.26487 + 0.443092i) q^{30} +(4.15743 - 7.20088i) q^{31} +(0.733052 + 0.680173i) q^{32} +(4.20947 - 9.63905i) q^{33} +(7.41762 - 1.11803i) q^{34} +(0.168592 + 2.04029i) q^{35} +(2.92525 - 0.665527i) q^{36} +(4.42514 + 4.10593i) q^{37} +(3.57225 - 4.47946i) q^{38} +(-4.84393 + 0.544073i) q^{39} +(-0.482447 - 0.604970i) q^{40} +(-0.274313 - 3.66045i) q^{41} +(2.74806 + 3.66718i) q^{42} +(0.358592 - 4.78508i) q^{43} +(-5.01745 + 3.42084i) q^{44} +(-2.31499 + 0.171864i) q^{45} +(-0.451243 - 6.02142i) q^{46} +(3.87549 + 0.584136i) q^{47} +(-1.63465 - 0.572629i) q^{48} +(-3.40691 + 6.11498i) q^{49} +(-2.20063 - 3.81160i) q^{50} +(-11.0037 + 6.90876i) q^{51} +(2.53553 + 1.22105i) q^{52} +(3.11020 - 2.88585i) q^{53} +(-4.18403 + 3.08121i) q^{54} +(4.23358 - 2.03879i) q^{55} +(-0.217880 - 2.63676i) q^{56} +(-2.57177 + 9.58465i) q^{57} +(5.15052 + 6.45855i) q^{58} +(0.248466 - 3.31554i) q^{59} +(1.18471 + 0.626662i) q^{60} +(-1.65059 + 0.509138i) q^{61} +(5.18423 - 6.50082i) q^{62} +(-6.90127 - 3.92077i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-1.79923 - 1.22669i) q^{65} +(5.59908 - 8.90400i) q^{66} +(-3.20774 + 5.55596i) q^{67} +7.50140 q^{68} +(4.88378 + 9.24836i) q^{69} +(-0.137380 + 2.04263i) q^{70} +(1.86822 + 8.18520i) q^{71} +(2.99177 - 0.222108i) q^{72} +(-0.515859 + 1.31439i) q^{73} +(3.76376 + 4.71960i) q^{74} +(6.13203 + 4.52894i) q^{75} +(4.19998 - 3.89701i) q^{76} +(15.9051 + 2.27310i) q^{77} +(-4.87091 - 0.183954i) q^{78} +(1.05625 + 1.82947i) q^{79} +(-0.386893 - 0.670118i) q^{80} +(4.51084 - 7.78796i) q^{81} +(0.274313 - 3.66045i) q^{82} +(15.1171 - 2.27853i) q^{83} +(2.17080 + 4.03579i) q^{84} +(-5.73965 - 0.865112i) q^{85} +(1.06777 - 4.67819i) q^{86} +(-12.6477 - 6.69014i) q^{87} +(-5.47126 + 2.63482i) q^{88} +(-8.53753 + 1.28682i) q^{89} +(-2.31474 - 0.175086i) q^{90} +(-2.77314 - 6.91006i) q^{91} +(0.451243 - 6.02142i) q^{92} +(-3.73229 + 13.9097i) q^{93} +(3.74514 + 1.15522i) q^{94} +(-3.66301 + 2.49740i) q^{95} +(-1.53105 - 0.809866i) q^{96} +(2.51891 - 4.36287i) q^{97} +(-4.28025 + 5.53891i) q^{98} +(-2.72778 + 18.0126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q - 28 q^{2} - 13 q^{3} + 28 q^{4} - 4 q^{5} - 5 q^{6} - q^{7} + 56 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 336 q - 28 q^{2} - 13 q^{3} + 28 q^{4} - 4 q^{5} - 5 q^{6} - q^{7} + 56 q^{8} + 29 q^{9} - 2 q^{10} + q^{12} - 23 q^{13} + q^{14} + q^{15} + 28 q^{16} + 7 q^{17} - q^{18} + 38 q^{19} + 2 q^{20} + 13 q^{21} + 21 q^{23} - q^{24} - 48 q^{25} + 9 q^{26} - 28 q^{27} + 2 q^{28} + 11 q^{29} - 7 q^{30} + 44 q^{31} - 28 q^{32} - 25 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} - 22 q^{38} - 51 q^{39} + 4 q^{40} + 3 q^{41} + 13 q^{42} + q^{43} - 75 q^{45} - 42 q^{46} - 33 q^{47} - 2 q^{48} - 41 q^{49} + 172 q^{50} + 4 q^{51} + 11 q^{52} - 78 q^{53} + 11 q^{54} + 23 q^{55} + q^{56} - 30 q^{57} - 13 q^{58} + 14 q^{59} - 8 q^{60} + 92 q^{61} - 24 q^{62} - 22 q^{63} - 56 q^{64} + 7 q^{65} + 29 q^{66} + 29 q^{67} + 42 q^{68} + 19 q^{69} - 34 q^{70} + 7 q^{71} - q^{72} - 8 q^{73} - 8 q^{74} - 5 q^{75} - 4 q^{76} + 2 q^{77} + 4 q^{78} - 9 q^{79} - 12 q^{80} + 45 q^{81} - 3 q^{82} - 109 q^{83} + 28 q^{84} + 93 q^{85} + 2 q^{86} - 15 q^{87} + 47 q^{89} - 3 q^{90} + 45 q^{91} + 42 q^{92} + 155 q^{93} - 9 q^{94} - 13 q^{95} - q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.988831 + 0.149042i 0.699209 + 0.105389i
\(3\) −1.67319 + 0.447706i −0.966016 + 0.258483i
\(4\) 0.955573 + 0.294755i 0.477786 + 0.147378i
\(5\) −0.697157 0.335733i −0.311778 0.150144i 0.271451 0.962452i \(-0.412497\pi\)
−0.583229 + 0.812308i \(0.698211\pi\)
\(6\) −1.72123 + 0.193329i −0.702688 + 0.0789263i
\(7\) −1.34035 2.28111i −0.506606 0.862178i
\(8\) 0.900969 + 0.433884i 0.318541 + 0.153401i
\(9\) 2.59912 1.49819i 0.866373 0.499397i
\(10\) −0.639332 0.435889i −0.202174 0.137840i
\(11\) −3.78623 + 4.74778i −1.14159 + 1.43151i −0.256225 + 0.966617i \(0.582479\pi\)
−0.885367 + 0.464893i \(0.846093\pi\)
\(12\) −1.73082 0.0653658i −0.499644 0.0188695i
\(13\) 2.78280 + 0.419439i 0.771809 + 0.116331i 0.523128 0.852254i \(-0.324765\pi\)
0.248681 + 0.968586i \(0.420003\pi\)
\(14\) −0.985400 2.45540i −0.263359 0.656233i
\(15\) 1.31678 + 0.249624i 0.339992 + 0.0644525i
\(16\) 0.826239 + 0.563320i 0.206560 + 0.140830i
\(17\) 7.16814 2.21108i 1.73853 0.536265i 0.746849 0.664994i \(-0.231566\pi\)
0.991680 + 0.128729i \(0.0410898\pi\)
\(18\) 2.79338 1.09408i 0.658407 0.257877i
\(19\) 2.86472 4.96184i 0.657212 1.13832i −0.324122 0.946015i \(-0.605069\pi\)
0.981334 0.192309i \(-0.0615977\pi\)
\(20\) −0.567225 0.526308i −0.126835 0.117686i
\(21\) 3.26393 + 3.21664i 0.712247 + 0.701929i
\(22\) −4.45156 + 4.13045i −0.949076 + 0.880614i
\(23\) −1.34365 5.88692i −0.280170 1.22751i −0.897575 0.440861i \(-0.854673\pi\)
0.617405 0.786646i \(-0.288184\pi\)
\(24\) −1.70174 0.322601i −0.347367 0.0658506i
\(25\) −2.74414 3.44104i −0.548828 0.688208i
\(26\) 2.68920 + 0.829508i 0.527396 + 0.162680i
\(27\) −3.67807 + 3.67040i −0.707845 + 0.706368i
\(28\) −0.608436 2.57484i −0.114984 0.486599i
\(29\) 6.05560 + 5.61877i 1.12450 + 1.04338i 0.998682 + 0.0513258i \(0.0163447\pi\)
0.125814 + 0.992054i \(0.459846\pi\)
\(30\) 1.26487 + 0.443092i 0.230933 + 0.0808972i
\(31\) 4.15743 7.20088i 0.746697 1.29332i −0.202701 0.979241i \(-0.564972\pi\)
0.949398 0.314076i \(-0.101695\pi\)
\(32\) 0.733052 + 0.680173i 0.129586 + 0.120239i
\(33\) 4.20947 9.63905i 0.732775 1.67794i
\(34\) 7.41762 1.11803i 1.27211 0.191740i
\(35\) 0.168592 + 2.04029i 0.0284973 + 0.344872i
\(36\) 2.92525 0.665527i 0.487541 0.110921i
\(37\) 4.42514 + 4.10593i 0.727488 + 0.675010i 0.954274 0.298934i \(-0.0966312\pi\)
−0.226786 + 0.973945i \(0.572822\pi\)
\(38\) 3.57225 4.47946i 0.579495 0.726664i
\(39\) −4.84393 + 0.544073i −0.775649 + 0.0871213i
\(40\) −0.482447 0.604970i −0.0762816 0.0956541i
\(41\) −0.274313 3.66045i −0.0428405 0.571666i −0.976781 0.214239i \(-0.931273\pi\)
0.933941 0.357428i \(-0.116346\pi\)
\(42\) 2.74806 + 3.66718i 0.424034 + 0.565858i
\(43\) 0.358592 4.78508i 0.0546847 0.729717i −0.900717 0.434407i \(-0.856958\pi\)
0.955401 0.295310i \(-0.0954230\pi\)
\(44\) −5.01745 + 3.42084i −0.756410 + 0.515711i
\(45\) −2.31499 + 0.171864i −0.345098 + 0.0256200i
\(46\) −0.451243 6.02142i −0.0665322 0.887811i
\(47\) 3.87549 + 0.584136i 0.565298 + 0.0852049i 0.425473 0.904971i \(-0.360108\pi\)
0.139825 + 0.990176i \(0.455346\pi\)
\(48\) −1.63465 0.572629i −0.235942 0.0826519i
\(49\) −3.40691 + 6.11498i −0.486702 + 0.873568i
\(50\) −2.20063 3.81160i −0.311216 0.539042i
\(51\) −11.0037 + 6.90876i −1.54083 + 0.967420i
\(52\) 2.53553 + 1.22105i 0.351615 + 0.169329i
\(53\) 3.11020 2.88585i 0.427219 0.396402i −0.437045 0.899440i \(-0.643975\pi\)
0.864264 + 0.503038i \(0.167784\pi\)
\(54\) −4.18403 + 3.08121i −0.569375 + 0.419300i
\(55\) 4.23358 2.03879i 0.570856 0.274910i
\(56\) −0.217880 2.63676i −0.0291154 0.352353i
\(57\) −2.57177 + 9.58465i −0.340640 + 1.26952i
\(58\) 5.15052 + 6.45855i 0.676297 + 0.848050i
\(59\) 0.248466 3.31554i 0.0323475 0.431647i −0.957395 0.288782i \(-0.906750\pi\)
0.989742 0.142865i \(-0.0456314\pi\)
\(60\) 1.18471 + 0.626662i 0.152945 + 0.0809018i
\(61\) −1.65059 + 0.509138i −0.211336 + 0.0651885i −0.398615 0.917118i \(-0.630509\pi\)
0.187280 + 0.982307i \(0.440033\pi\)
\(62\) 5.18423 6.50082i 0.658398 0.825605i
\(63\) −6.90127 3.92077i −0.869479 0.493970i
\(64\) 0.623490 + 0.781831i 0.0779362 + 0.0977289i
\(65\) −1.79923 1.22669i −0.223166 0.152152i
\(66\) 5.59908 8.90400i 0.689199 1.09601i
\(67\) −3.20774 + 5.55596i −0.391887 + 0.678769i −0.992698 0.120622i \(-0.961511\pi\)
0.600811 + 0.799391i \(0.294844\pi\)
\(68\) 7.50140 0.909679
\(69\) 4.88378 + 9.24836i 0.587939 + 1.11337i
\(70\) −0.137380 + 2.04263i −0.0164201 + 0.244141i
\(71\) 1.86822 + 8.18520i 0.221717 + 0.971404i 0.956185 + 0.292762i \(0.0945743\pi\)
−0.734469 + 0.678643i \(0.762569\pi\)
\(72\) 2.99177 0.222108i 0.352583 0.0261757i
\(73\) −0.515859 + 1.31439i −0.0603767 + 0.153837i −0.957879 0.287173i \(-0.907285\pi\)
0.897502 + 0.441010i \(0.145380\pi\)
\(74\) 3.76376 + 4.71960i 0.437528 + 0.548642i
\(75\) 6.13203 + 4.52894i 0.708066 + 0.522957i
\(76\) 4.19998 3.89701i 0.481770 0.447018i
\(77\) 15.9051 + 2.27310i 1.81255 + 0.259044i
\(78\) −4.87091 0.183954i −0.551522 0.0208287i
\(79\) 1.05625 + 1.82947i 0.118837 + 0.205832i 0.919307 0.393541i \(-0.128750\pi\)
−0.800470 + 0.599373i \(0.795417\pi\)
\(80\) −0.386893 0.670118i −0.0432559 0.0749215i
\(81\) 4.51084 7.78796i 0.501205 0.865329i
\(82\) 0.274313 3.66045i 0.0302928 0.404229i
\(83\) 15.1171 2.27853i 1.65932 0.250102i 0.748566 0.663060i \(-0.230743\pi\)
0.910750 + 0.412958i \(0.135504\pi\)
\(84\) 2.17080 + 4.03579i 0.236854 + 0.440341i
\(85\) −5.73965 0.865112i −0.622552 0.0938346i
\(86\) 1.06777 4.67819i 0.115140 0.504462i
\(87\) −12.6477 6.69014i −1.35598 0.717258i
\(88\) −5.47126 + 2.63482i −0.583239 + 0.280873i
\(89\) −8.53753 + 1.28682i −0.904976 + 0.136403i −0.585010 0.811026i \(-0.698909\pi\)
−0.319966 + 0.947429i \(0.603671\pi\)
\(90\) −2.31474 0.175086i −0.243995 0.0184557i
\(91\) −2.77314 6.91006i −0.290704 0.724371i
\(92\) 0.451243 6.02142i 0.0470454 0.627777i
\(93\) −3.73229 + 13.9097i −0.387021 + 1.44237i
\(94\) 3.74514 + 1.15522i 0.386282 + 0.119152i
\(95\) −3.66301 + 2.49740i −0.375817 + 0.256228i
\(96\) −1.53105 0.809866i −0.156262 0.0826566i
\(97\) 2.51891 4.36287i 0.255756 0.442983i −0.709344 0.704862i \(-0.751009\pi\)
0.965101 + 0.261879i \(0.0843422\pi\)
\(98\) −4.28025 + 5.53891i −0.432370 + 0.559514i
\(99\) −2.72778 + 18.0126i −0.274152 + 1.81033i
\(100\) −1.60796 4.09701i −0.160796 0.409701i
\(101\) −10.4847 5.04915i −1.04326 0.502409i −0.167864 0.985810i \(-0.553687\pi\)
−0.875399 + 0.483401i \(0.839401\pi\)
\(102\) −11.9105 + 5.19158i −1.17932 + 0.514043i
\(103\) −9.49712 4.57357i −0.935779 0.450647i −0.0971006 0.995275i \(-0.530957\pi\)
−0.838678 + 0.544627i \(0.816671\pi\)
\(104\) 2.32522 + 1.58531i 0.228007 + 0.155453i
\(105\) −1.19554 3.33831i −0.116672 0.325786i
\(106\) 3.50558 2.39006i 0.340492 0.232143i
\(107\) −6.08485 + 0.917144i −0.588245 + 0.0886636i −0.436419 0.899744i \(-0.643753\pi\)
−0.151826 + 0.988407i \(0.548515\pi\)
\(108\) −4.59653 + 2.42320i −0.442301 + 0.233173i
\(109\) −11.6420 1.75475i −1.11510 0.168074i −0.434459 0.900692i \(-0.643060\pi\)
−0.680641 + 0.732617i \(0.738299\pi\)
\(110\) 4.49016 1.38503i 0.428120 0.132058i
\(111\) −9.24234 4.88883i −0.877244 0.464027i
\(112\) 0.177543 2.63979i 0.0167762 0.249436i
\(113\) −4.70809 + 11.9960i −0.442900 + 1.12849i 0.518923 + 0.854821i \(0.326333\pi\)
−0.961823 + 0.273671i \(0.911762\pi\)
\(114\) −3.97157 + 9.09429i −0.371971 + 0.851758i
\(115\) −1.03970 + 4.55521i −0.0969523 + 0.424776i
\(116\) 4.13040 + 7.15406i 0.383498 + 0.664238i
\(117\) 7.86122 3.07899i 0.726770 0.284653i
\(118\) 0.739847 3.24148i 0.0681084 0.298402i
\(119\) −14.6515 13.3877i −1.34310 1.22725i
\(120\) 1.07807 + 0.796234i 0.0984142 + 0.0726859i
\(121\) −5.75817 25.2282i −0.523470 2.29347i
\(122\) −1.70803 + 0.257445i −0.154638 + 0.0233079i
\(123\) 2.09778 + 6.00181i 0.189151 + 0.541165i
\(124\) 6.09523 5.65554i 0.547367 0.507883i
\(125\) 1.61874 + 7.09217i 0.144785 + 0.634343i
\(126\) −6.23983 4.90556i −0.555888 0.437022i
\(127\) 2.17984 9.55050i 0.193429 0.847470i −0.781313 0.624139i \(-0.785450\pi\)
0.974743 0.223331i \(-0.0716930\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 1.54231 + 8.16688i 0.135793 + 0.719053i
\(130\) −1.59630 1.48115i −0.140005 0.129905i
\(131\) 3.92388 1.88964i 0.342831 0.165099i −0.254543 0.967061i \(-0.581925\pi\)
0.597374 + 0.801963i \(0.296211\pi\)
\(132\) 6.86362 7.97005i 0.597401 0.693704i
\(133\) −15.1582 + 0.115878i −1.31439 + 0.0100479i
\(134\) −3.99998 + 5.01582i −0.345546 + 0.433301i
\(135\) 3.79646 1.32399i 0.326748 0.113951i
\(136\) 7.41762 + 1.11803i 0.636055 + 0.0958699i
\(137\) 13.4899 6.49641i 1.15252 0.555026i 0.242733 0.970093i \(-0.421956\pi\)
0.909791 + 0.415067i \(0.136242\pi\)
\(138\) 3.45084 + 9.87295i 0.293755 + 0.840442i
\(139\) 0.728685 + 9.72363i 0.0618063 + 0.824747i 0.938848 + 0.344333i \(0.111895\pi\)
−0.877041 + 0.480415i \(0.840486\pi\)
\(140\) −0.440284 + 1.99934i −0.0372108 + 0.168975i
\(141\) −6.74594 + 0.757708i −0.568111 + 0.0638105i
\(142\) 0.627411 + 8.37222i 0.0526512 + 0.702581i
\(143\) −12.5277 + 11.6240i −1.04762 + 0.972049i
\(144\) 2.99145 + 0.226272i 0.249288 + 0.0188560i
\(145\) −2.33529 5.95023i −0.193935 0.494139i
\(146\) −0.705996 + 1.22282i −0.0584287 + 0.101201i
\(147\) 2.96269 11.7568i 0.244359 0.969685i
\(148\) 3.01830 + 5.22784i 0.248103 + 0.429726i
\(149\) 5.04421 6.32524i 0.413238 0.518184i −0.531034 0.847351i \(-0.678196\pi\)
0.944272 + 0.329167i \(0.106768\pi\)
\(150\) 5.38854 + 5.39229i 0.439972 + 0.440279i
\(151\) 1.49170 + 6.53556i 0.121393 + 0.531857i 0.998655 + 0.0518453i \(0.0165103\pi\)
−0.877262 + 0.480011i \(0.840633\pi\)
\(152\) 4.73389 3.22751i 0.383969 0.261786i
\(153\) 15.3182 16.4861i 1.23841 1.33282i
\(154\) 15.3887 + 4.61824i 1.24005 + 0.372149i
\(155\) −5.31595 + 3.62436i −0.426988 + 0.291115i
\(156\) −4.78909 0.907872i −0.383434 0.0726879i
\(157\) 0.0853826 1.13935i 0.00681428 0.0909302i −0.992760 0.120117i \(-0.961673\pi\)
0.999574 + 0.0291873i \(0.00929192\pi\)
\(158\) 0.771780 + 1.96646i 0.0613995 + 0.156443i
\(159\) −3.91195 + 6.22102i −0.310238 + 0.493359i
\(160\) −0.282696 0.720297i −0.0223490 0.0569444i
\(161\) −11.6277 + 10.9556i −0.916393 + 0.863419i
\(162\) 5.62120 7.02867i 0.441643 0.552224i
\(163\) 0.576733 7.69596i 0.0451732 0.602794i −0.927979 0.372632i \(-0.878455\pi\)
0.973152 0.230162i \(-0.0739257\pi\)
\(164\) 0.816811 3.57868i 0.0637822 0.279448i
\(165\) −6.17081 + 5.30667i −0.480397 + 0.413124i
\(166\) 15.2878 1.18657
\(167\) −10.7162 + 3.30552i −0.829246 + 0.255789i −0.680186 0.733040i \(-0.738101\pi\)
−0.149060 + 0.988828i \(0.547625\pi\)
\(168\) 1.54505 + 4.31426i 0.119203 + 0.332852i
\(169\) −4.85442 1.49739i −0.373417 0.115184i
\(170\) −5.54660 1.71090i −0.425405 0.131220i
\(171\) 0.0119627 17.1883i 0.000914809 1.31442i
\(172\) 1.75309 4.46679i 0.133672 0.340590i
\(173\) −8.25118 + 7.65598i −0.627326 + 0.582073i −0.928425 0.371519i \(-0.878837\pi\)
0.301099 + 0.953593i \(0.402646\pi\)
\(174\) −11.5093 8.50046i −0.872520 0.644418i
\(175\) −4.17127 + 10.8719i −0.315319 + 0.821837i
\(176\) −5.80285 + 1.78994i −0.437406 + 0.134922i
\(177\) 1.06866 + 5.65877i 0.0803252 + 0.425339i
\(178\) −8.63396 −0.647143
\(179\) 1.26771 0.391036i 0.0947530 0.0292274i −0.247016 0.969011i \(-0.579450\pi\)
0.341769 + 0.939784i \(0.388974\pi\)
\(180\) −2.26280 0.518125i −0.168659 0.0386188i
\(181\) −0.918100 1.15126i −0.0682418 0.0855725i 0.746539 0.665342i \(-0.231714\pi\)
−0.814781 + 0.579769i \(0.803143\pi\)
\(182\) −1.71228 7.24619i −0.126922 0.537123i
\(183\) 2.53380 1.59086i 0.187304 0.117600i
\(184\) 1.34365 5.88692i 0.0990552 0.433989i
\(185\) −1.70652 4.34814i −0.125466 0.319682i
\(186\) −5.76374 + 13.1981i −0.422618 + 0.967732i
\(187\) −16.6425 + 42.4044i −1.21702 + 3.10092i
\(188\) 3.53113 + 1.70050i 0.257534 + 0.124022i
\(189\) 13.3025 + 3.47045i 0.967613 + 0.252438i
\(190\) −3.99432 + 1.92356i −0.289778 + 0.139550i
\(191\) 1.79661 + 23.9741i 0.129998 + 1.73471i 0.557048 + 0.830480i \(0.311934\pi\)
−0.427050 + 0.904228i \(0.640447\pi\)
\(192\) −1.39325 1.02901i −0.100549 0.0742625i
\(193\) 3.27712 2.23430i 0.235892 0.160829i −0.439605 0.898191i \(-0.644881\pi\)
0.675497 + 0.737363i \(0.263929\pi\)
\(194\) 3.14103 3.93872i 0.225512 0.282784i
\(195\) 3.55964 + 1.24696i 0.254911 + 0.0892968i
\(196\) −5.05797 + 4.83910i −0.361284 + 0.345650i
\(197\) 2.75770 0.196478 0.0982392 0.995163i \(-0.468679\pi\)
0.0982392 + 0.995163i \(0.468679\pi\)
\(198\) −5.38194 + 17.4048i −0.382478 + 1.23691i
\(199\) 1.08108 + 14.4260i 0.0766359 + 1.02263i 0.894455 + 0.447159i \(0.147564\pi\)
−0.817819 + 0.575476i \(0.804817\pi\)
\(200\) −0.979372 4.29091i −0.0692520 0.303413i
\(201\) 2.87971 10.7323i 0.203119 0.756997i
\(202\) −9.61502 6.55541i −0.676511 0.461237i
\(203\) 4.70039 21.3446i 0.329903 1.49810i
\(204\) −12.5513 + 3.35842i −0.878764 + 0.235136i
\(205\) −1.03769 + 2.64400i −0.0724758 + 0.184665i
\(206\) −8.70939 5.93796i −0.606812 0.413717i
\(207\) −12.3120 13.2878i −0.855746 0.923563i
\(208\) 2.06298 + 1.91416i 0.143042 + 0.132723i
\(209\) 12.7113 + 32.3878i 0.879256 + 2.24031i
\(210\) −0.684634 3.47921i −0.0472442 0.240088i
\(211\) 10.2110 26.0172i 0.702953 1.79110i 0.0974684 0.995239i \(-0.468926\pi\)
0.605485 0.795857i \(-0.292979\pi\)
\(212\) 3.82264 1.84089i 0.262540 0.126433i
\(213\) −6.79044 12.8590i −0.465273 0.881082i
\(214\) −6.15358 −0.420650
\(215\) −1.85650 + 3.21556i −0.126612 + 0.219299i
\(216\) −4.90635 + 1.71106i −0.333835 + 0.116423i
\(217\) −21.9984 + 0.168168i −1.49335 + 0.0114160i
\(218\) −11.2504 3.47030i −0.761975 0.235038i
\(219\) 0.274671 2.43017i 0.0185605 0.164216i
\(220\) 4.64644 0.700338i 0.313263 0.0472168i
\(221\) 20.8749 3.14638i 1.40420 0.211648i
\(222\) −8.41046 6.21173i −0.564473 0.416904i
\(223\) 11.6094 + 3.58101i 0.777420 + 0.239802i 0.657976 0.753039i \(-0.271413\pi\)
0.119444 + 0.992841i \(0.461889\pi\)
\(224\) 0.569000 2.58384i 0.0380179 0.172640i
\(225\) −12.2877 4.83243i −0.819179 0.322162i
\(226\) −6.44342 + 11.1603i −0.428610 + 0.742375i
\(227\) −0.709064 −0.0470622 −0.0235311 0.999723i \(-0.507491\pi\)
−0.0235311 + 0.999723i \(0.507491\pi\)
\(228\) −5.28264 + 8.40078i −0.349851 + 0.556356i
\(229\) 1.66611 0.802355i 0.110099 0.0530211i −0.378023 0.925796i \(-0.623396\pi\)
0.488123 + 0.872775i \(0.337682\pi\)
\(230\) −1.70700 + 4.34937i −0.112556 + 0.286789i
\(231\) −27.6299 + 3.31747i −1.81791 + 0.218274i
\(232\) 3.01801 + 7.68976i 0.198142 + 0.504858i
\(233\) 15.3311 + 14.2252i 1.00437 + 0.931924i 0.997682 0.0680539i \(-0.0216790\pi\)
0.00669328 + 0.999978i \(0.497869\pi\)
\(234\) 8.23232 1.87295i 0.538163 0.122438i
\(235\) −2.50571 1.70836i −0.163454 0.111441i
\(236\) 1.21470 3.09501i 0.0790703 0.201468i
\(237\) −2.58636 2.58816i −0.168002 0.168119i
\(238\) −12.4926 15.4218i −0.809772 0.999650i
\(239\) 8.60396 + 5.86608i 0.556544 + 0.379445i 0.808682 0.588246i \(-0.200181\pi\)
−0.252138 + 0.967691i \(0.581134\pi\)
\(240\) 0.947360 + 0.948020i 0.0611518 + 0.0611944i
\(241\) −4.73438 20.7427i −0.304968 1.33615i −0.862525 0.506015i \(-0.831118\pi\)
0.557557 0.830139i \(-0.311739\pi\)
\(242\) −1.93379 25.8046i −0.124309 1.65878i
\(243\) −4.06078 + 15.0503i −0.260499 + 0.965474i
\(244\) −1.72733 −0.110581
\(245\) 4.42815 3.11929i 0.282904 0.199284i
\(246\) 1.17983 + 6.24744i 0.0752230 + 0.398322i
\(247\) 10.0531 12.6062i 0.639665 0.802114i
\(248\) 6.87006 4.68393i 0.436249 0.297430i
\(249\) −24.2736 + 10.5804i −1.53828 + 0.670507i
\(250\) 0.543628 + 7.25421i 0.0343821 + 0.458797i
\(251\) 0.0375420 0.0180793i 0.00236963 0.00114115i −0.432699 0.901539i \(-0.642439\pi\)
0.435068 + 0.900398i \(0.356724\pi\)
\(252\) −5.43900 5.78077i −0.342625 0.364154i
\(253\) 33.0372 + 15.9099i 2.07703 + 1.00024i
\(254\) 3.57892 9.11894i 0.224561 0.572173i
\(255\) 9.99082 1.12217i 0.625650 0.0702733i
\(256\) 0.365341 + 0.930874i 0.0228338 + 0.0581796i
\(257\) −1.64510 + 7.20767i −0.102619 + 0.449602i 0.897347 + 0.441326i \(0.145492\pi\)
−0.999966 + 0.00827642i \(0.997366\pi\)
\(258\) 0.307877 + 8.30553i 0.0191676 + 0.517080i
\(259\) 3.43482 15.5976i 0.213429 0.969188i
\(260\) −1.35772 1.70252i −0.0842020 0.105586i
\(261\) 24.1572 + 5.53142i 1.49529 + 0.342386i
\(262\) 4.16169 1.28371i 0.257110 0.0793080i
\(263\) −25.4258 −1.56782 −0.783910 0.620875i \(-0.786777\pi\)
−0.783910 + 0.620875i \(0.786777\pi\)
\(264\) 7.97483 6.85807i 0.490817 0.422085i
\(265\) −3.13717 + 0.967690i −0.192715 + 0.0594447i
\(266\) −15.0062 2.14463i −0.920089 0.131496i
\(267\) 13.7088 5.97540i 0.838963 0.365688i
\(268\) −4.70287 + 4.36363i −0.287274 + 0.266551i
\(269\) 2.55058 6.49877i 0.155512 0.396237i −0.831791 0.555089i \(-0.812684\pi\)
0.987302 + 0.158852i \(0.0507793\pi\)
\(270\) 3.95139 0.743371i 0.240474 0.0452401i
\(271\) −18.1817 5.60832i −1.10446 0.340681i −0.311679 0.950187i \(-0.600891\pi\)
−0.792781 + 0.609507i \(0.791368\pi\)
\(272\) 7.16814 + 2.21108i 0.434632 + 0.134066i
\(273\) 7.73366 + 10.3203i 0.468062 + 0.624611i
\(274\) 14.3075 4.41328i 0.864348 0.266616i
\(275\) 26.7273 1.61171
\(276\) 1.94081 + 10.2770i 0.116823 + 0.618603i
\(277\) −0.744399 + 3.26143i −0.0447266 + 0.195960i −0.992355 0.123414i \(-0.960616\pi\)
0.947629 + 0.319374i \(0.103473\pi\)
\(278\) −0.728685 + 9.72363i −0.0437036 + 0.583185i
\(279\) 0.0173609 24.9446i 0.00103937 1.49339i
\(280\) −0.733352 + 1.91139i −0.0438262 + 0.114227i
\(281\) 11.3583 + 28.9404i 0.677578 + 1.72644i 0.687181 + 0.726487i \(0.258848\pi\)
−0.00960251 + 0.999954i \(0.503057\pi\)
\(282\) −6.78352 0.256186i −0.403953 0.0152556i
\(283\) −3.66262 9.33220i −0.217720 0.554742i 0.779729 0.626117i \(-0.215357\pi\)
−0.997450 + 0.0713747i \(0.977261\pi\)
\(284\) −0.627411 + 8.37222i −0.0372300 + 0.496800i
\(285\) 5.01081 5.81857i 0.296815 0.344662i
\(286\) −14.1203 + 9.62703i −0.834949 + 0.569258i
\(287\) −7.98221 + 5.53203i −0.471175 + 0.326545i
\(288\) 2.92432 + 0.669598i 0.172317 + 0.0394565i
\(289\) 32.4473 22.1222i 1.90866 1.30130i
\(290\) −1.42237 6.23183i −0.0835246 0.365945i
\(291\) −2.26132 + 8.42764i −0.132561 + 0.494037i
\(292\) −0.880363 + 1.10394i −0.0515194 + 0.0646032i
\(293\) 5.92772 + 10.2671i 0.346301 + 0.599811i 0.985589 0.169156i \(-0.0541042\pi\)
−0.639288 + 0.768967i \(0.720771\pi\)
\(294\) 4.68186 11.1839i 0.273052 0.652260i
\(295\) −1.28636 + 2.22804i −0.0748946 + 0.129721i
\(296\) 2.20542 + 5.61931i 0.128187 + 0.326616i
\(297\) −3.50023 31.3596i −0.203104 1.81967i
\(298\) 5.93060 5.50279i 0.343550 0.318768i
\(299\) −1.26990 16.9457i −0.0734403 0.979993i
\(300\) 4.52467 + 6.13518i 0.261232 + 0.354215i
\(301\) −11.3959 + 5.59570i −0.656850 + 0.322531i
\(302\) 0.500963 + 6.68489i 0.0288272 + 0.384672i
\(303\) 19.8034 + 3.75413i 1.13767 + 0.215669i
\(304\) 5.16205 2.48591i 0.296064 0.142577i
\(305\) 1.32165 + 0.199207i 0.0756776 + 0.0114066i
\(306\) 17.6043 14.0189i 1.00637 0.801407i
\(307\) −1.00726 + 1.26307i −0.0574876 + 0.0720872i −0.809744 0.586783i \(-0.800394\pi\)
0.752256 + 0.658870i \(0.228965\pi\)
\(308\) 14.5285 + 6.86022i 0.827836 + 0.390897i
\(309\) 17.9381 + 3.40053i 1.02046 + 0.193450i
\(310\) −5.79676 + 2.79157i −0.329234 + 0.158551i
\(311\) −1.51509 1.40580i −0.0859130 0.0797156i 0.636047 0.771650i \(-0.280568\pi\)
−0.721960 + 0.691934i \(0.756759\pi\)
\(312\) −4.60029 1.61151i −0.260440 0.0912337i
\(313\) 8.58094 + 14.8626i 0.485023 + 0.840085i 0.999852 0.0172082i \(-0.00547782\pi\)
−0.514829 + 0.857293i \(0.672144\pi\)
\(314\) 0.254241 1.11390i 0.0143476 0.0628611i
\(315\) 3.49494 + 5.05038i 0.196917 + 0.284556i
\(316\) 0.470074 + 2.05953i 0.0264437 + 0.115857i
\(317\) −6.18259 + 5.73661i −0.347249 + 0.322200i −0.834444 0.551093i \(-0.814211\pi\)
0.487194 + 0.873294i \(0.338020\pi\)
\(318\) −4.79545 + 5.56849i −0.268915 + 0.312266i
\(319\) −49.6046 + 7.47669i −2.77732 + 0.418614i
\(320\) −0.172183 0.754385i −0.00962535 0.0421714i
\(321\) 9.77049 4.25878i 0.545336 0.237702i
\(322\) −13.1307 + 9.10017i −0.731745 + 0.507132i
\(323\) 9.56369 41.9013i 0.532138 2.33145i
\(324\) 6.60598 6.11237i 0.366999 0.339576i
\(325\) −6.19307 10.7267i −0.343530 0.595011i
\(326\) 1.71732 7.52405i 0.0951133 0.416719i
\(327\) 20.2648 2.27616i 1.12065 0.125872i
\(328\) 1.34106 3.41697i 0.0740478 0.188671i
\(329\) −3.86204 9.62335i −0.212921 0.530553i
\(330\) −6.89280 + 4.32769i −0.379436 + 0.238232i
\(331\) −12.2135 + 3.76736i −0.671313 + 0.207073i −0.611629 0.791145i \(-0.709486\pi\)
−0.0596842 + 0.998217i \(0.519009\pi\)
\(332\) 15.1171 + 2.27853i 0.829658 + 0.125051i
\(333\) 17.6529 + 4.04209i 0.967374 + 0.221505i
\(334\) −11.0892 + 1.67143i −0.606773 + 0.0914564i
\(335\) 4.10161 2.79643i 0.224095 0.152785i
\(336\) 0.884785 + 4.49635i 0.0482690 + 0.245296i
\(337\) 7.49218 + 5.10808i 0.408125 + 0.278255i 0.749932 0.661515i \(-0.230086\pi\)
−0.341806 + 0.939770i \(0.611039\pi\)
\(338\) −4.57703 2.20418i −0.248957 0.119892i
\(339\) 2.50684 22.1795i 0.136153 1.20462i
\(340\) −5.22965 2.51847i −0.283618 0.136583i
\(341\) 18.4472 + 47.0028i 0.998974 + 2.54534i
\(342\) 2.57362 16.9946i 0.139165 0.918960i
\(343\) 18.5154 0.424693i 0.999737 0.0229313i
\(344\) 2.39925 4.15562i 0.129359 0.224056i
\(345\) −0.299784 8.08720i −0.0161398 0.435400i
\(346\) −9.30009 + 6.34069i −0.499976 + 0.340878i
\(347\) 5.34101 + 1.64748i 0.286720 + 0.0884416i 0.434779 0.900537i \(-0.356826\pi\)
−0.148059 + 0.988979i \(0.547303\pi\)
\(348\) −10.1139 10.1209i −0.542159 0.542537i
\(349\) 2.52288 33.6655i 0.135047 1.80207i −0.359732 0.933056i \(-0.617132\pi\)
0.494779 0.869019i \(-0.335249\pi\)
\(350\) −5.74505 + 10.1288i −0.307086 + 0.541405i
\(351\) −11.7748 + 8.67124i −0.628493 + 0.462837i
\(352\) −6.00482 + 0.905081i −0.320058 + 0.0482410i
\(353\) 21.0139 10.1198i 1.11846 0.538620i 0.219041 0.975716i \(-0.429707\pi\)
0.899415 + 0.437096i \(0.143993\pi\)
\(354\) 0.213326 + 5.75484i 0.0113381 + 0.305866i
\(355\) 1.44560 6.33359i 0.0767245 0.336152i
\(356\) −8.53753 1.28682i −0.452488 0.0682016i
\(357\) 30.5085 + 15.8405i 1.61468 + 0.838370i
\(358\) 1.31183 0.197727i 0.0693324 0.0104502i
\(359\) 1.49879 19.9999i 0.0791030 1.05556i −0.806537 0.591184i \(-0.798661\pi\)
0.885640 0.464373i \(-0.153720\pi\)
\(360\) −2.16030 0.849591i −0.113858 0.0447774i
\(361\) −6.91325 11.9741i −0.363855 0.630215i
\(362\) −0.736259 1.27524i −0.0386969 0.0670250i
\(363\) 20.9293 + 39.6336i 1.09850 + 2.08022i
\(364\) −0.613164 7.42046i −0.0321385 0.388938i
\(365\) 0.800918 0.743143i 0.0419219 0.0388979i
\(366\) 2.74260 1.19545i 0.143358 0.0624872i
\(367\) 18.0903 + 22.6845i 0.944304 + 1.18412i 0.982765 + 0.184859i \(0.0591829\pi\)
−0.0384615 + 0.999260i \(0.512246\pi\)
\(368\) 2.20604 5.62090i 0.114998 0.293010i
\(369\) −6.19703 9.10298i −0.322604 0.473882i
\(370\) −1.03940 4.55392i −0.0540359 0.236747i
\(371\) −10.7517 3.22666i −0.558200 0.167520i
\(372\) −7.66644 + 12.1917i −0.397487 + 0.632108i
\(373\) −15.2684 −0.790568 −0.395284 0.918559i \(-0.629354\pi\)
−0.395284 + 0.918559i \(0.629354\pi\)
\(374\) −22.7767 + 39.4504i −1.17775 + 2.03993i
\(375\) −5.88366 11.1418i −0.303831 0.575361i
\(376\) 3.23825 + 2.20780i 0.167000 + 0.113859i
\(377\) 14.4948 + 18.1758i 0.746518 + 0.936104i
\(378\) 12.6367 + 5.41432i 0.649960 + 0.278482i
\(379\) −22.7495 + 28.5270i −1.16856 + 1.46533i −0.311406 + 0.950277i \(0.600800\pi\)
−0.857157 + 0.515055i \(0.827771\pi\)
\(380\) −4.23640 + 1.30676i −0.217323 + 0.0670351i
\(381\) 0.628529 + 16.9557i 0.0322005 + 0.868667i
\(382\) −1.79661 + 23.9741i −0.0919228 + 1.22662i
\(383\) 10.9444 + 13.7238i 0.559232 + 0.701255i 0.978416 0.206647i \(-0.0662551\pi\)
−0.419184 + 0.907901i \(0.637684\pi\)
\(384\) −1.22432 1.22517i −0.0624782 0.0625217i
\(385\) −10.3252 6.92457i −0.526220 0.352909i
\(386\) 3.57353 1.72092i 0.181888 0.0875925i
\(387\) −6.23694 12.9742i −0.317041 0.659517i
\(388\) 3.69298 3.42658i 0.187483 0.173958i
\(389\) −13.0164 6.26837i −0.659958 0.317819i 0.0737573 0.997276i \(-0.476501\pi\)
−0.733715 + 0.679457i \(0.762215\pi\)
\(390\) 3.33403 + 1.76357i 0.168825 + 0.0893019i
\(391\) −22.6479 39.2273i −1.14535 1.98381i
\(392\) −5.72271 + 4.03120i −0.289041 + 0.203606i
\(393\) −5.71939 + 4.91847i −0.288505 + 0.248104i
\(394\) 2.72690 + 0.411015i 0.137379 + 0.0207066i
\(395\) −0.122155 1.63004i −0.00614628 0.0820165i
\(396\) −7.91589 + 16.4083i −0.397788 + 0.824547i
\(397\) −2.52710 + 1.72294i −0.126831 + 0.0864721i −0.625074 0.780565i \(-0.714931\pi\)
0.498243 + 0.867038i \(0.333979\pi\)
\(398\) −1.08108 + 14.4260i −0.0541897 + 0.723112i
\(399\) 25.3107 6.98031i 1.26712 0.349453i
\(400\) −0.328906 4.38895i −0.0164453 0.219447i
\(401\) −15.5387 19.4849i −0.775963 0.973027i 0.224035 0.974581i \(-0.428077\pi\)
−0.999999 + 0.00155371i \(0.999505\pi\)
\(402\) 4.44711 10.1832i 0.221802 0.507893i
\(403\) 14.5896 18.2948i 0.726760 0.911329i
\(404\) −8.53060 7.91524i −0.424413 0.393798i
\(405\) −5.75944 + 3.91499i −0.286189 + 0.194537i
\(406\) 7.82914 20.4056i 0.388554 1.01272i
\(407\) −36.2486 + 5.46360i −1.79678 + 0.270821i
\(408\) −12.9116 + 1.45024i −0.639220 + 0.0717976i
\(409\) −6.16127 5.71682i −0.304655 0.282679i 0.512998 0.858390i \(-0.328535\pi\)
−0.817653 + 0.575711i \(0.804725\pi\)
\(410\) −1.42017 + 2.45981i −0.0701373 + 0.121481i
\(411\) −19.6627 + 16.9092i −0.969891 + 0.834071i
\(412\) −7.72710 7.16970i −0.380687 0.353226i
\(413\) −7.89615 + 3.87722i −0.388544 + 0.190786i
\(414\) −10.1941 14.9744i −0.501012 0.735949i
\(415\) −11.3040 3.48681i −0.554890 0.171161i
\(416\) 1.75464 + 2.20025i 0.0860284 + 0.107876i
\(417\) −5.57255 15.9432i −0.272889 0.780743i
\(418\) 7.74214 + 33.9205i 0.378680 + 1.65911i
\(419\) 1.28592 1.19316i 0.0628214 0.0582897i −0.648137 0.761523i \(-0.724452\pi\)
0.710959 + 0.703234i \(0.248261\pi\)
\(420\) −0.158437 3.54239i −0.00773095 0.172851i
\(421\) 8.58326 + 7.96410i 0.418323 + 0.388147i 0.861059 0.508505i \(-0.169802\pi\)
−0.442736 + 0.896652i \(0.645992\pi\)
\(422\) 13.9746 24.2047i 0.680273 1.17827i
\(423\) 10.9480 4.28798i 0.532310 0.208489i
\(424\) 4.05432 1.25059i 0.196895 0.0607341i
\(425\) −27.2788 18.5983i −1.32321 0.902152i
\(426\) −4.79807 13.7274i −0.232467 0.665095i
\(427\) 3.37377 + 3.08274i 0.163268 + 0.149184i
\(428\) −6.08485 0.917144i −0.294122 0.0443318i
\(429\) 15.7571 25.0579i 0.760759 1.20981i
\(430\) −2.31502 + 2.90294i −0.111640 + 0.139992i
\(431\) −1.54911 1.05617i −0.0746181 0.0508737i 0.525436 0.850833i \(-0.323902\pi\)
−0.600054 + 0.799959i \(0.704854\pi\)
\(432\) −5.10657 + 0.960694i −0.245690 + 0.0462214i
\(433\) 30.9027 + 14.8819i 1.48509 + 0.715181i 0.988276 0.152678i \(-0.0487897\pi\)
0.496812 + 0.867858i \(0.334504\pi\)
\(434\) −21.7778 3.11240i −1.04537 0.149400i
\(435\) 6.57133 + 8.91033i 0.315071 + 0.427218i
\(436\) −10.6075 5.10832i −0.508009 0.244644i
\(437\) −33.0591 10.1974i −1.58143 0.487807i
\(438\) 0.633801 2.36209i 0.0302842 0.112865i
\(439\) −0.402312 0.0606387i −0.0192013 0.00289413i 0.139435 0.990231i \(-0.455471\pi\)
−0.158636 + 0.987337i \(0.550710\pi\)
\(440\) 4.69892 0.224012
\(441\) 0.306439 + 20.9978i 0.0145924 + 0.999894i
\(442\) 21.1107 1.00413
\(443\) 10.8576 + 1.63652i 0.515861 + 0.0777536i 0.401813 0.915722i \(-0.368380\pi\)
0.114048 + 0.993475i \(0.463618\pi\)
\(444\) −7.39072 7.39586i −0.350748 0.350992i
\(445\) 6.38402 + 1.96921i 0.302632 + 0.0933495i
\(446\) 10.9460 + 5.27130i 0.518307 + 0.249603i
\(447\) −5.60807 + 12.8416i −0.265253 + 0.607389i
\(448\) 0.947746 2.47018i 0.0447768 0.116705i
\(449\) −11.2869 5.43549i −0.532663 0.256517i 0.148162 0.988963i \(-0.452664\pi\)
−0.680825 + 0.732446i \(0.738379\pi\)
\(450\) −11.4302 6.60984i −0.538825 0.311591i
\(451\) 18.4176 + 12.5569i 0.867253 + 0.591283i
\(452\) −8.03482 + 10.0753i −0.377926 + 0.473904i
\(453\) −5.42190 10.2674i −0.254743 0.482404i
\(454\) −0.701144 0.105680i −0.0329063 0.00495983i
\(455\) −0.386619 + 5.74843i −0.0181250 + 0.269490i
\(456\) −6.47571 + 7.51962i −0.303253 + 0.352138i
\(457\) 12.6522 + 8.62615i 0.591847 + 0.403514i 0.821874 0.569670i \(-0.192929\pi\)
−0.230027 + 0.973184i \(0.573881\pi\)
\(458\) 1.76708 0.545073i 0.0825703 0.0254696i
\(459\) −18.2494 + 34.4424i −0.851807 + 1.60763i
\(460\) −2.33618 + 4.04638i −0.108925 + 0.188663i
\(461\) −26.5962 24.6776i −1.23871 1.14935i −0.983197 0.182546i \(-0.941566\pi\)
−0.255510 0.966806i \(-0.582243\pi\)
\(462\) −27.8157 0.837603i −1.29411 0.0389688i
\(463\) 10.3588 9.61156i 0.481414 0.446687i −0.401751 0.915749i \(-0.631598\pi\)
0.883165 + 0.469062i \(0.155408\pi\)
\(464\) 1.83820 + 8.05369i 0.0853363 + 0.373883i
\(465\) 7.27195 8.44421i 0.337229 0.391591i
\(466\) 13.0397 + 16.3513i 0.604054 + 0.757459i
\(467\) 10.6920 + 3.29803i 0.494765 + 0.152615i 0.532089 0.846688i \(-0.321407\pi\)
−0.0373240 + 0.999303i \(0.511883\pi\)
\(468\) 8.41952 0.625063i 0.389192 0.0288936i
\(469\) 16.9732 0.129753i 0.783752 0.00599145i
\(470\) −2.22310 2.06274i −0.102544 0.0951470i
\(471\) 0.367233 + 1.94458i 0.0169212 + 0.0896014i
\(472\) 1.66242 2.87940i 0.0765191 0.132535i
\(473\) 21.3608 + 19.8199i 0.982170 + 0.911321i
\(474\) −2.17173 2.94473i −0.0997508 0.135256i
\(475\) −24.9351 + 3.75836i −1.14410 + 0.172445i
\(476\) −10.0545 17.1115i −0.460848 0.784305i
\(477\) 3.76024 12.1603i 0.172170 0.556784i
\(478\) 7.63357 + 7.08291i 0.349151 + 0.323965i
\(479\) 1.17453 1.47282i 0.0536657 0.0672947i −0.754274 0.656559i \(-0.772011\pi\)
0.807940 + 0.589265i \(0.200583\pi\)
\(480\) 0.795484 + 1.07863i 0.0363087 + 0.0492324i
\(481\) 10.5921 + 13.2820i 0.482957 + 0.605609i
\(482\) −1.58997 21.2166i −0.0724210 0.966391i
\(483\) 14.5505 23.5365i 0.662072 1.07095i
\(484\) 1.93379 25.8046i 0.0878996 1.17294i
\(485\) −3.22083 + 2.19593i −0.146251 + 0.0997119i
\(486\) −6.25855 + 14.2769i −0.283894 + 0.647614i
\(487\) 2.33384 + 31.1429i 0.105756 + 1.41122i 0.757527 + 0.652803i \(0.226407\pi\)
−0.651771 + 0.758416i \(0.725974\pi\)
\(488\) −1.70803 0.257445i −0.0773191 0.0116540i
\(489\) 2.48054 + 13.1350i 0.112174 + 0.593985i
\(490\) 4.84360 2.42446i 0.218811 0.109526i
\(491\) 14.0834 + 24.3931i 0.635574 + 1.10085i 0.986393 + 0.164403i \(0.0525698\pi\)
−0.350819 + 0.936443i \(0.614097\pi\)
\(492\) 0.235517 + 6.35350i 0.0106179 + 0.286438i
\(493\) 55.8309 + 26.8867i 2.51450 + 1.21092i
\(494\) 11.8197 10.9671i 0.531793 0.493432i
\(495\) 7.94910 11.6418i 0.357285 0.523259i
\(496\) 7.49143 3.60768i 0.336375 0.161990i
\(497\) 16.1673 15.2327i 0.725201 0.683278i
\(498\) −25.5794 + 6.84445i −1.14624 + 0.306707i
\(499\) 14.1509 + 17.7447i 0.633481 + 0.794360i 0.990171 0.139863i \(-0.0446661\pi\)
−0.356690 + 0.934223i \(0.616095\pi\)
\(500\) −0.543628 + 7.25421i −0.0243118 + 0.324418i
\(501\) 16.4504 10.3285i 0.734948 0.461442i
\(502\) 0.0398173 0.0122820i 0.00177713 0.000548173i
\(503\) 0.230146 0.288594i 0.0102617 0.0128678i −0.776674 0.629903i \(-0.783095\pi\)
0.786936 + 0.617035i \(0.211666\pi\)
\(504\) −4.51667 6.52684i −0.201189 0.290729i
\(505\) 5.61429 + 7.04009i 0.249833 + 0.313280i
\(506\) 30.2969 + 20.6561i 1.34686 + 0.918276i
\(507\) 8.79275 + 0.332066i 0.390500 + 0.0147476i
\(508\) 4.89805 8.48368i 0.217316 0.376402i
\(509\) −34.3370 −1.52196 −0.760980 0.648776i \(-0.775281\pi\)
−0.760980 + 0.648776i \(0.775281\pi\)
\(510\) 10.0465 + 0.379414i 0.444866 + 0.0168007i
\(511\) 3.68969 0.585012i 0.163222 0.0258794i
\(512\) 0.222521 + 0.974928i 0.00983413 + 0.0430861i
\(513\) 7.67529 + 28.7647i 0.338872 + 1.26999i
\(514\) −2.70098 + 6.88198i −0.119135 + 0.303551i
\(515\) 5.08548 + 6.37699i 0.224093 + 0.281004i
\(516\) −0.933437 + 8.25865i −0.0410923 + 0.363567i
\(517\) −17.4468 + 16.1883i −0.767311 + 0.711961i
\(518\) 5.72116 14.9115i 0.251373 0.655172i
\(519\) 10.3782 16.5040i 0.455551 0.724445i
\(520\) −1.08880 1.88587i −0.0477472 0.0827007i
\(521\) −12.7911 22.1548i −0.560388 0.970620i −0.997462 0.0711947i \(-0.977319\pi\)
0.437075 0.899425i \(-0.356015\pi\)
\(522\) 23.0630 + 9.07008i 1.00944 + 0.396987i
\(523\) −2.37689 + 31.7174i −0.103934 + 1.38691i 0.664649 + 0.747156i \(0.268581\pi\)
−0.768583 + 0.639750i \(0.779038\pi\)
\(524\) 4.30654 0.649106i 0.188132 0.0283563i
\(525\) 2.11193 20.0582i 0.0921720 0.875412i
\(526\) −25.1418 3.78951i −1.09623 0.165231i
\(527\) 13.8793 60.8093i 0.604593 2.64889i
\(528\) 8.90790 5.59288i 0.387667 0.243399i
\(529\) −12.1281 + 5.84059i −0.527309 + 0.253939i
\(530\) −3.24636 + 0.489310i −0.141013 + 0.0212543i
\(531\) −4.32153 8.98974i −0.187538 0.390122i
\(532\) −14.5190 4.35724i −0.629476 0.188910i
\(533\) 0.771979 10.3013i 0.0334381 0.446201i
\(534\) 14.4462 3.86547i 0.625150 0.167275i
\(535\) 4.55001 + 1.40349i 0.196714 + 0.0606783i
\(536\) −5.30071 + 3.61396i −0.228956 + 0.156099i
\(537\) −1.94605 + 1.22184i −0.0839781 + 0.0527262i
\(538\) 3.49068 6.04604i 0.150494 0.260663i
\(539\) −16.1332 39.3280i −0.694908 1.69398i
\(540\) 4.01805 0.146144i 0.172909 0.00628905i
\(541\) 3.20916 + 8.17681i 0.137973 + 0.351548i 0.983114 0.182994i \(-0.0585790\pi\)
−0.845141 + 0.534543i \(0.820484\pi\)
\(542\) −17.1428 8.25552i −0.736345 0.354605i
\(543\) 2.05158 + 1.51524i 0.0880417 + 0.0650251i
\(544\) 6.75853 + 3.25474i 0.289770 + 0.139546i
\(545\) 7.52716 + 5.13193i 0.322428 + 0.219828i
\(546\) 6.10912 + 11.3576i 0.261446 + 0.486062i
\(547\) −20.7936 + 14.1768i −0.889071 + 0.606158i −0.919375 0.393382i \(-0.871305\pi\)
0.0303041 + 0.999541i \(0.490352\pi\)
\(548\) 14.8055 2.23157i 0.632458 0.0953278i
\(549\) −3.52728 + 3.79621i −0.150541 + 0.162018i
\(550\) 26.4287 + 3.98349i 1.12693 + 0.169857i
\(551\) 45.2270 13.9507i 1.92674 0.594320i
\(552\) 0.387425 + 10.4515i 0.0164899 + 0.444845i
\(553\) 2.75748 4.86155i 0.117260 0.206734i
\(554\) −1.22218 + 3.11405i −0.0519253 + 0.132303i
\(555\) 4.80201 + 6.51124i 0.203834 + 0.276387i
\(556\) −2.16978 + 9.50642i −0.0920191 + 0.403162i
\(557\) 7.14102 + 12.3686i 0.302575 + 0.524075i 0.976718 0.214526i \(-0.0688205\pi\)
−0.674144 + 0.738600i \(0.735487\pi\)
\(558\) 3.73496 24.6634i 0.158114 1.04408i
\(559\) 3.00494 13.1655i 0.127095 0.556841i
\(560\) −1.01004 + 1.78074i −0.0426819 + 0.0752499i
\(561\) 8.86136 78.4015i 0.374127 3.31011i
\(562\) 6.91807 + 30.3100i 0.291821 + 1.27855i
\(563\) −22.9292 + 3.45603i −0.966352 + 0.145654i −0.613214 0.789917i \(-0.710124\pi\)
−0.353138 + 0.935571i \(0.614886\pi\)
\(564\) −6.66958 1.26436i −0.280840 0.0532390i
\(565\) 7.30974 6.78245i 0.307523 0.285340i
\(566\) −2.23082 9.77386i −0.0937683 0.410826i
\(567\) −23.8113 + 0.148881i −0.999980 + 0.00625243i
\(568\) −1.86822 + 8.18520i −0.0783887 + 0.343443i
\(569\) −21.2444 36.7964i −0.890612 1.54259i −0.839143 0.543911i \(-0.816943\pi\)
−0.0514689 0.998675i \(-0.516390\pi\)
\(570\) 5.82206 5.00676i 0.243859 0.209710i
\(571\) 1.07800 + 1.00024i 0.0451131 + 0.0418588i 0.702407 0.711775i \(-0.252109\pi\)
−0.657294 + 0.753634i \(0.728299\pi\)
\(572\) −15.3974 + 7.41499i −0.643797 + 0.310036i
\(573\) −13.7394 39.3089i −0.573973 1.64215i
\(574\) −8.71756 + 4.28056i −0.363864 + 0.178667i
\(575\) −16.5700 + 20.7781i −0.691015 + 0.866505i
\(576\) 2.79186 + 1.09797i 0.116327 + 0.0457486i
\(577\) −7.40135 1.11557i −0.308122 0.0464420i −0.00683896 0.999977i \(-0.502177\pi\)
−0.301283 + 0.953535i \(0.597415\pi\)
\(578\) 35.3820 17.0391i 1.47170 0.708732i
\(579\) −4.48293 + 5.20560i −0.186304 + 0.216337i
\(580\) −0.477681 6.37421i −0.0198346 0.264675i
\(581\) −25.4598 31.4297i −1.05625 1.30392i
\(582\) −3.49214 + 7.99648i −0.144754 + 0.331465i
\(583\) 1.92543 + 25.6931i 0.0797431 + 1.06410i
\(584\) −1.03506 + 0.960399i −0.0428313 + 0.0397416i
\(585\) −6.51422 0.492733i −0.269330 0.0203720i
\(586\) 4.33128 + 11.0359i 0.178923 + 0.455890i
\(587\) −8.60346 + 14.9016i −0.355103 + 0.615056i −0.987136 0.159886i \(-0.948887\pi\)
0.632033 + 0.774942i \(0.282221\pi\)
\(588\) 6.29645 10.3612i 0.259661 0.427289i
\(589\) −23.8198 41.2570i −0.981476 1.69997i
\(590\) −1.60406 + 2.01143i −0.0660381 + 0.0828092i
\(591\) −4.61416 + 1.23464i −0.189801 + 0.0507863i
\(592\) 1.34327 + 5.88524i 0.0552080 + 0.241882i
\(593\) −13.2602 + 9.04064i −0.544531 + 0.371255i −0.804122 0.594464i \(-0.797364\pi\)
0.259592 + 0.965718i \(0.416412\pi\)
\(594\) 1.21277 31.5311i 0.0497607 1.29374i
\(595\) 5.71973 + 14.2523i 0.234486 + 0.584288i
\(596\) 6.68451 4.55742i 0.273808 0.186679i
\(597\) −8.26747 23.6535i −0.338365 0.968072i
\(598\) 1.26990 16.9457i 0.0519302 0.692960i
\(599\) 15.3394 + 39.0841i 0.626750 + 1.59693i 0.791890 + 0.610663i \(0.209097\pi\)
−0.165140 + 0.986270i \(0.552808\pi\)
\(600\) 3.55974 + 6.74103i 0.145326 + 0.275201i
\(601\) −15.9442 40.6251i −0.650377 1.65713i −0.749456 0.662054i \(-0.769685\pi\)
0.0990788 0.995080i \(-0.468410\pi\)
\(602\) −12.1026 + 3.83473i −0.493266 + 0.156292i
\(603\) −0.0133951 + 19.2464i −0.000545489 + 0.783774i
\(604\) −0.500963 + 6.68489i −0.0203839 + 0.272004i
\(605\) −4.45559 + 19.5212i −0.181146 + 0.793650i
\(606\) 19.0226 + 6.66374i 0.772742 + 0.270696i
\(607\) −11.2708 −0.457468 −0.228734 0.973489i \(-0.573459\pi\)
−0.228734 + 0.973489i \(0.573459\pi\)
\(608\) 5.47490 1.68878i 0.222036 0.0684892i
\(609\) 1.69145 + 37.8179i 0.0685410 + 1.53246i
\(610\) 1.27720 + 0.393964i 0.0517123 + 0.0159511i
\(611\) 10.5397 + 3.25106i 0.426390 + 0.131524i
\(612\) 19.4970 11.2385i 0.788121 0.454291i
\(613\) 5.98852 15.2585i 0.241874 0.616285i −0.757456 0.652886i \(-0.773558\pi\)
0.999330 + 0.0366012i \(0.0116531\pi\)
\(614\) −1.18426 + 1.09884i −0.0477930 + 0.0443455i
\(615\) 0.552524 4.88850i 0.0222799 0.197123i
\(616\) 13.3437 + 8.94895i 0.537634 + 0.360564i
\(617\) −4.36093 + 1.34517i −0.175565 + 0.0541545i −0.381291 0.924455i \(-0.624520\pi\)
0.205727 + 0.978610i \(0.434044\pi\)
\(618\) 17.2309 + 6.03609i 0.693129 + 0.242807i
\(619\) 19.1884 0.771246 0.385623 0.922656i \(-0.373987\pi\)
0.385623 + 0.922656i \(0.373987\pi\)
\(620\) −6.14808 + 1.89643i −0.246913 + 0.0761625i
\(621\) 26.5494 + 16.7208i 1.06539 + 0.670981i
\(622\) −1.28865 1.61591i −0.0516700 0.0647922i
\(623\) 14.3787 + 17.7502i 0.576070 + 0.711148i
\(624\) −4.30873 2.27915i −0.172487 0.0912389i
\(625\) −3.64430 + 15.9667i −0.145772 + 0.638669i
\(626\) 6.26994 + 15.9755i 0.250597 + 0.638511i
\(627\) −35.7685 48.4999i −1.42846 1.93690i
\(628\) 0.417419 1.06357i 0.0166568 0.0424409i
\(629\) 40.7985 + 19.6475i 1.62674 + 0.783398i
\(630\) 2.70318 + 5.51486i 0.107697 + 0.219717i
\(631\) 9.04767 4.35713i 0.360182 0.173455i −0.245037 0.969514i \(-0.578800\pi\)
0.605219 + 0.796059i \(0.293086\pi\)
\(632\) 0.157867 + 2.10658i 0.00627960 + 0.0837954i
\(633\) −5.43687 + 48.1031i −0.216096 + 1.91193i
\(634\) −6.96854 + 4.75107i −0.276756 + 0.188689i
\(635\) −4.72611 + 5.92635i −0.187550 + 0.235180i
\(636\) −5.57183 + 4.79157i −0.220937 + 0.189998i
\(637\) −12.0456 + 15.5877i −0.477264 + 0.617609i
\(638\) −50.1649 −1.98605
\(639\) 17.1187 + 18.4754i 0.677206 + 0.730874i
\(640\) −0.0578251 0.771622i −0.00228574 0.0305010i
\(641\) 5.20114 + 22.7877i 0.205433 + 0.900059i 0.967562 + 0.252634i \(0.0812970\pi\)
−0.762129 + 0.647425i \(0.775846\pi\)
\(642\) 10.2961 2.75499i 0.406355 0.108731i
\(643\) 36.8611 + 25.1315i 1.45366 + 0.991089i 0.994720 + 0.102622i \(0.0327234\pi\)
0.458941 + 0.888467i \(0.348229\pi\)
\(644\) −14.3403 + 7.04150i −0.565089 + 0.277474i
\(645\) 1.66666 6.21140i 0.0656245 0.244574i
\(646\) 15.7019 40.0079i 0.617784 1.57409i
\(647\) −34.7696 23.7055i −1.36694 0.931961i −0.999999 0.00171530i \(-0.999454\pi\)
−0.366937 0.930246i \(-0.619594\pi\)
\(648\) 7.44320 5.05952i 0.292396 0.198757i
\(649\) 14.8007 + 13.7331i 0.580980 + 0.539070i
\(650\) −4.52517 11.5299i −0.177492 0.452241i
\(651\) 36.7322 10.1302i 1.43965 0.397033i
\(652\) 2.81954 7.18406i 0.110422 0.281349i
\(653\) 12.1216 5.83743i 0.474353 0.228436i −0.181404 0.983409i \(-0.558064\pi\)
0.655757 + 0.754972i \(0.272350\pi\)
\(654\) 20.3777 + 0.769583i 0.796833 + 0.0300931i
\(655\) −3.36998 −0.131676
\(656\) 1.83536 3.17893i 0.0716587 0.124116i
\(657\) 0.628425 + 4.18910i 0.0245172 + 0.163433i
\(658\) −2.38462 10.0915i −0.0929621 0.393407i
\(659\) −23.5051 7.25037i −0.915630 0.282434i −0.199090 0.979981i \(-0.563799\pi\)
−0.716539 + 0.697547i \(0.754275\pi\)
\(660\) −7.46083 + 3.25203i −0.290412 + 0.126585i
\(661\) 2.33872 0.352505i 0.0909657 0.0137109i −0.103402 0.994640i \(-0.532973\pi\)
0.194367 + 0.980929i \(0.437735\pi\)
\(662\) −12.6386 + 1.90496i −0.491212 + 0.0740382i
\(663\) −33.5189 + 14.6103i −1.30177 + 0.567416i
\(664\) 14.6086 + 4.50617i 0.566925 + 0.174873i
\(665\) 10.6066 + 5.00833i 0.411305 + 0.194215i
\(666\) 16.8533 + 6.62798i 0.653053 + 0.256829i
\(667\) 24.9406 43.1984i 0.965705 1.67265i
\(668\) −11.2144 −0.433900
\(669\) −21.0279 0.794136i −0.812985 0.0307031i
\(670\) 4.47259 2.15389i 0.172791 0.0832118i
\(671\) 3.83222 9.76434i 0.147941 0.376948i
\(672\) 0.204756 + 4.57800i 0.00789864 + 0.176600i
\(673\) 3.18567 + 8.11696i 0.122799 + 0.312886i 0.979033 0.203702i \(-0.0652973\pi\)
−0.856234 + 0.516588i \(0.827202\pi\)
\(674\) 6.64718 + 6.16768i 0.256040 + 0.237570i
\(675\) 22.7231 + 2.58431i 0.874613 + 0.0994700i
\(676\) −4.19739 2.86173i −0.161438 0.110067i
\(677\) −11.8419 + 30.1726i −0.455121 + 1.15963i 0.500685 + 0.865629i \(0.333081\pi\)
−0.955806 + 0.293999i \(0.905014\pi\)
\(678\) 5.78452 21.5581i 0.222153 0.827934i
\(679\) −13.3284 + 0.101890i −0.511498 + 0.00391018i
\(680\) −4.79588 3.26978i −0.183914 0.125390i
\(681\) 1.18640 0.317452i 0.0454628 0.0121648i
\(682\) 11.2358 + 49.2272i 0.430241 + 1.88501i
\(683\) −1.07213 14.3066i −0.0410240 0.547427i −0.979416 0.201854i \(-0.935303\pi\)
0.938392 0.345573i \(-0.112316\pi\)
\(684\) 5.07778 16.4212i 0.194154 0.627879i
\(685\) −11.5857 −0.442665
\(686\) 18.3719 + 2.33963i 0.701442 + 0.0893273i
\(687\) −2.42849 + 2.08842i −0.0926527 + 0.0796780i
\(688\) 2.99181 3.75161i 0.114062 0.143029i
\(689\) 9.86550 6.72618i 0.375846 0.256247i
\(690\) 0.908900 8.04156i 0.0346012 0.306137i
\(691\) 1.08091 + 14.4238i 0.0411198 + 0.548706i 0.979281 + 0.202507i \(0.0649088\pi\)
−0.938161 + 0.346199i \(0.887472\pi\)
\(692\) −10.1412 + 4.88377i −0.385512 + 0.185653i
\(693\) 44.7448 17.9208i 1.69971 0.680755i
\(694\) 5.03581 + 2.42512i 0.191157 + 0.0920563i
\(695\) 2.75654 7.02354i 0.104561 0.266418i
\(696\) −8.49245 11.5152i −0.321905 0.436484i
\(697\) −10.0599 25.6321i −0.381044 0.970884i
\(698\) 7.51229 32.9135i 0.284344 1.24579i
\(699\) −32.0206 16.9376i −1.21113 0.640639i
\(700\) −7.19050 + 9.15937i −0.271775 + 0.346192i
\(701\) 31.6821 + 39.7281i 1.19662 + 1.50051i 0.818261 + 0.574847i \(0.194938\pi\)
0.378354 + 0.925661i \(0.376490\pi\)
\(702\) −12.9357 + 6.81944i −0.488226 + 0.257383i
\(703\) 33.0497 10.1945i 1.24649 0.384493i
\(704\) −6.07264 −0.228871
\(705\) 4.95737 + 1.73659i 0.186705 + 0.0654039i
\(706\) 22.2874 6.87477i 0.838799 0.258735i
\(707\) 2.53549 + 30.6843i 0.0953569 + 1.15400i
\(708\) −0.646772 + 5.72236i −0.0243072 + 0.215059i
\(709\) −20.8664 + 19.3612i −0.783656 + 0.727126i −0.966682 0.255982i \(-0.917601\pi\)
0.183026 + 0.983108i \(0.441411\pi\)
\(710\) 2.37343 6.04739i 0.0890731 0.226955i
\(711\) 5.48621 + 3.17256i 0.205749 + 0.118980i
\(712\) −8.25038 2.54490i −0.309196 0.0953743i
\(713\) −47.9771 14.7990i −1.79676 0.554226i
\(714\) 27.8069 + 20.2107i 1.04065 + 0.756365i
\(715\) 12.6363 3.89780i 0.472573 0.145769i
\(716\) 1.32665 0.0495792
\(717\) −17.0223 5.96302i −0.635710 0.222693i
\(718\) 4.46288 19.5532i 0.166553 0.729718i
\(719\) 1.01966 13.6064i 0.0380269 0.507434i −0.945374 0.325988i \(-0.894303\pi\)
0.983401 0.181446i \(-0.0580778\pi\)
\(720\) −2.00955 1.16208i −0.0748913 0.0433081i
\(721\) 2.29667 + 27.7942i 0.0855326 + 1.03511i
\(722\) −5.05139 12.8707i −0.187993 0.478999i
\(723\) 17.2081 + 32.5868i 0.639977 + 1.21192i
\(724\) −0.537971 1.37073i −0.0199935 0.0509427i
\(725\) 2.71703 36.2562i 0.100908 1.34652i
\(726\) 14.7885 + 42.3103i 0.548852 + 1.57028i
\(727\) 36.4874 24.8767i 1.35324 0.922625i 0.353326 0.935500i \(-0.385051\pi\)
0.999917 + 0.0128749i \(0.00409831\pi\)
\(728\) 0.499647 7.42897i 0.0185181 0.275336i
\(729\) 0.0563741 26.9999i 0.00208793 0.999998i
\(730\) 0.902732 0.615472i 0.0334116 0.0227796i
\(731\) −8.00974 35.0929i −0.296251 1.29796i
\(732\) 2.89014 0.773334i 0.106823 0.0285832i
\(733\) −1.32579 + 1.66249i −0.0489693 + 0.0614056i −0.805713 0.592306i \(-0.798218\pi\)
0.756744 + 0.653712i \(0.226789\pi\)
\(734\) 14.5073 + 25.1273i 0.535473 + 0.927466i
\(735\) −6.01261 + 7.20166i −0.221778 + 0.265637i
\(736\) 3.01915 5.22933i 0.111288 0.192756i
\(737\) −14.2333 36.2658i −0.524289 1.33587i
\(738\) −4.77108 9.92492i −0.175626 0.365341i
\(739\) 17.3603 16.1080i 0.638607 0.592541i −0.292953 0.956127i \(-0.594638\pi\)
0.931561 + 0.363586i \(0.118448\pi\)
\(740\) −0.349066 4.65797i −0.0128319 0.171230i
\(741\) −11.1769 + 25.5934i −0.410594 + 0.940198i
\(742\) −10.1507 4.79308i −0.372644 0.175959i
\(743\) 2.86829 + 38.2746i 0.105227 + 1.40416i 0.760780 + 0.649010i \(0.224817\pi\)
−0.655553 + 0.755149i \(0.727564\pi\)
\(744\) −9.39789 + 10.9129i −0.344543 + 0.400085i
\(745\) −5.64020 + 2.71618i −0.206641 + 0.0995130i
\(746\) −15.0979 2.27564i −0.552772 0.0833170i
\(747\) 35.8774 28.5705i 1.31269 1.04534i
\(748\) −28.4020 + 35.6150i −1.03848 + 1.30221i
\(749\) 10.2480 + 12.6509i 0.374452 + 0.462254i
\(750\) −4.15734 11.8943i −0.151805 0.434318i
\(751\) −17.7270 + 8.53686i −0.646867 + 0.311515i −0.728396 0.685156i \(-0.759734\pi\)
0.0815293 + 0.996671i \(0.474020\pi\)
\(752\) 2.87302 + 2.66578i 0.104768 + 0.0972108i
\(753\) −0.0547207 + 0.0470578i −0.00199413 + 0.00171488i
\(754\) 11.6239 + 20.1332i 0.423317 + 0.733207i
\(755\) 1.15426 5.05712i 0.0420077 0.184048i
\(756\) 11.6886 + 7.23724i 0.425109 + 0.263216i
\(757\) −8.11818 35.5681i −0.295060 1.29274i −0.877385 0.479787i \(-0.840714\pi\)
0.582325 0.812956i \(-0.302143\pi\)
\(758\) −26.7471 + 24.8177i −0.971499 + 0.901420i
\(759\) −62.4004 11.8293i −2.26499 0.429376i
\(760\) −4.38384 + 0.660758i −0.159019 + 0.0239682i
\(761\) −8.39434 36.7780i −0.304295 1.33320i −0.863574 0.504223i \(-0.831779\pi\)
0.559279 0.828979i \(-0.311078\pi\)
\(762\) −1.90561 + 16.8600i −0.0690329 + 0.610774i
\(763\) 11.6016 + 28.9086i 0.420006 + 1.04656i
\(764\) −5.34971 + 23.4386i −0.193546 + 0.847979i
\(765\) −16.2141 + 6.35056i −0.586223 + 0.229605i
\(766\) 8.77671 + 15.2017i 0.317116 + 0.549260i
\(767\) 2.08210 9.12227i 0.0751802 0.329386i
\(768\) −1.02804 1.39396i −0.0370963 0.0503003i
\(769\) −0.786756 + 2.00462i −0.0283712 + 0.0722885i −0.944357 0.328921i \(-0.893315\pi\)
0.915986 + 0.401210i \(0.131410\pi\)
\(770\) −9.17781 8.38612i −0.330745 0.302215i
\(771\) −0.474345 12.7963i −0.0170831 0.460848i
\(772\) 3.79010 1.16909i 0.136409 0.0420765i
\(773\) 7.91907 + 1.19361i 0.284829 + 0.0429311i 0.289903 0.957056i \(-0.406377\pi\)
−0.00507391 + 0.999987i \(0.501615\pi\)
\(774\) −4.23357 13.7589i −0.152172 0.494553i
\(775\) −36.1871 + 5.45433i −1.29988 + 0.195925i
\(776\) 4.16244 2.83790i 0.149423 0.101875i
\(777\) 1.23603 + 27.6355i 0.0443423 + 0.991419i
\(778\) −11.9368 8.13835i −0.427954 0.291774i
\(779\) −18.9484 9.12507i −0.678897 0.326940i
\(780\) 3.03395 + 2.24079i 0.108633 + 0.0802330i
\(781\) −45.9351 22.1212i −1.64369 0.791557i
\(782\) −16.5484 42.1647i −0.591770 1.50781i
\(783\) −42.8960 + 1.56021i −1.53298 + 0.0557575i
\(784\) −6.25961 + 3.13325i −0.223558 + 0.111902i
\(785\) −0.442043 + 0.765641i −0.0157772 + 0.0273269i
\(786\) −6.38857 + 4.01111i −0.227873 + 0.143071i
\(787\) 21.7159 14.8056i 0.774088 0.527764i −0.110646 0.993860i \(-0.535292\pi\)
0.884734 + 0.466096i \(0.154340\pi\)
\(788\) 2.63519 + 0.812848i 0.0938747 + 0.0289565i
\(789\) 42.5421 11.3833i 1.51454 0.405254i
\(790\) 0.122155 1.63004i 0.00434608 0.0579944i
\(791\) 33.6747 5.33923i 1.19734 0.189841i
\(792\) −10.2730 + 15.0452i −0.365035 + 0.534608i
\(793\) −4.80680 + 0.724508i −0.170694 + 0.0257280i
\(794\) −2.75566 + 1.32706i −0.0977948 + 0.0470955i
\(795\) 4.81584 3.02366i 0.170800 0.107238i
\(796\) −3.21910 + 14.1038i −0.114098 + 0.499895i
\(797\) −22.2263 3.35008i −0.787298 0.118666i −0.256926 0.966431i \(-0.582710\pi\)
−0.530372 + 0.847765i \(0.677948\pi\)
\(798\) 26.0684 3.12998i 0.922810 0.110800i
\(799\) 29.0716 4.38184i 1.02848 0.155018i
\(800\) 0.328906 4.38895i 0.0116286 0.155173i
\(801\) −20.2621 + 16.1355i −0.715927 + 0.570118i
\(802\) −12.4610 21.5831i −0.440014 0.762127i
\(803\) −4.28726 7.42576i −0.151294 0.262049i
\(804\) 5.91517 9.40668i 0.208612 0.331748i
\(805\) 11.7845 3.73393i 0.415349 0.131604i
\(806\) 17.1534 15.9160i 0.604201 0.560617i
\(807\) −1.35806 + 12.0156i −0.0478061 + 0.422968i
\(808\) −7.25561 9.09825i −0.255252 0.320075i
\(809\) −3.16916 + 8.07489i −0.111422 + 0.283898i −0.975698 0.219119i \(-0.929682\pi\)
0.864276 + 0.503017i \(0.167777\pi\)
\(810\) −6.27861 + 3.01286i −0.220608 + 0.105861i
\(811\) −0.413291 1.81075i −0.0145126 0.0635839i 0.967153 0.254195i \(-0.0818103\pi\)
−0.981666 + 0.190611i \(0.938953\pi\)
\(812\) 10.7830 19.0109i 0.378409 0.667150i
\(813\) 32.9323 + 1.24372i 1.15499 + 0.0436190i
\(814\) −36.6581 −1.28487
\(815\) −2.98586 + 5.17166i −0.104590 + 0.181156i
\(816\) −12.9836 0.490335i −0.454515 0.0171652i
\(817\) −22.7155 15.4872i −0.794716 0.541828i
\(818\) −5.24040 6.57126i −0.183226 0.229759i
\(819\) −17.5603 13.8054i −0.613607 0.482398i
\(820\) −1.77093 + 2.22067i −0.0618434 + 0.0775492i
\(821\) −41.9662 + 12.9449i −1.46463 + 0.451778i −0.921668 0.387979i \(-0.873173\pi\)
−0.542961 + 0.839758i \(0.682697\pi\)
\(822\) −21.9633 + 13.7898i −0.766058 + 0.480975i
\(823\) −1.82033 + 24.2907i −0.0634529 + 0.846720i 0.871148 + 0.491021i \(0.163376\pi\)
−0.934601 + 0.355699i \(0.884243\pi\)
\(824\) −6.57221 8.24129i −0.228954 0.287099i
\(825\) −44.7197 + 11.9659i −1.55694 + 0.416601i
\(826\) −8.38582 + 2.65705i −0.291780 + 0.0924508i
\(827\) −41.1807 + 19.8316i −1.43199 + 0.689612i −0.979367 0.202088i \(-0.935227\pi\)
−0.452627 + 0.891700i \(0.649513\pi\)
\(828\) −7.84841 16.3265i −0.272751 0.567383i
\(829\) −32.3304 + 29.9982i −1.12288 + 1.04188i −0.124112 + 0.992268i \(0.539608\pi\)
−0.998769 + 0.0496128i \(0.984201\pi\)
\(830\) −10.6580 5.13263i −0.369945 0.178156i
\(831\) −0.214638 5.79025i −0.00744572 0.200862i
\(832\) 1.40711 + 2.43719i 0.0487829 + 0.0844945i
\(833\) −10.9005 + 51.3659i −0.377680 + 1.77972i
\(834\) −3.13409 16.5957i −0.108525 0.574662i
\(835\) 8.58065 + 1.29333i 0.296946 + 0.0447574i
\(836\) 2.60007 + 34.6956i 0.0899254 + 1.19997i
\(837\) 11.1388 + 41.7448i 0.385012 + 1.44291i
\(838\) 1.44939 0.988178i 0.0500684 0.0341360i
\(839\) −4.09055 + 54.5846i −0.141221 + 1.88447i 0.255902 + 0.966703i \(0.417628\pi\)
−0.397123 + 0.917765i \(0.629991\pi\)
\(840\) 0.371298 3.52644i 0.0128110 0.121674i
\(841\) 2.93247 + 39.1311i 0.101120 + 1.34935i
\(842\) 7.30040 + 9.15442i 0.251589 + 0.315482i
\(843\) −31.9613 43.3376i −1.10081 1.49263i
\(844\) 17.4260 21.8516i 0.599829 0.752162i
\(845\) 2.88157 + 2.67371i 0.0991290 + 0.0919783i
\(846\) 11.4648 2.60837i 0.394168 0.0896778i
\(847\) −49.8303 + 46.9497i −1.71219 + 1.61321i
\(848\) 4.19543 0.632359i 0.144072 0.0217153i
\(849\) 10.3063 + 13.9748i 0.353712 + 0.479613i
\(850\) −24.2021 22.4563i −0.830127 0.770245i
\(851\) 18.2254 31.5673i 0.624759 1.08211i
\(852\) −2.69851 14.2892i −0.0924495 0.489540i
\(853\) 27.5288 + 25.5430i 0.942567 + 0.874574i 0.992258 0.124190i \(-0.0396333\pi\)
−0.0496914 + 0.998765i \(0.515824\pi\)
\(854\) 2.87663 + 3.55114i 0.0984361 + 0.121518i
\(855\) −5.77902 + 11.9789i −0.197638 + 0.409671i
\(856\) −5.88020 1.81380i −0.200981 0.0619944i
\(857\) 6.09049 + 7.63723i 0.208047 + 0.260883i 0.874897 0.484309i \(-0.160929\pi\)
−0.666850 + 0.745192i \(0.732358\pi\)
\(858\) 19.3158 22.4296i 0.659430 0.765732i
\(859\) 6.43279 + 28.1839i 0.219484 + 0.961622i 0.957861 + 0.287233i \(0.0927355\pi\)
−0.738377 + 0.674388i \(0.764407\pi\)
\(860\) −2.72183 + 2.52548i −0.0928135 + 0.0861183i
\(861\) 10.8790 12.8298i 0.370756 0.437239i
\(862\) −1.37440 1.27525i −0.0468121 0.0434353i
\(863\) 6.99354 12.1132i 0.238063 0.412337i −0.722095 0.691793i \(-0.756821\pi\)
0.960158 + 0.279456i \(0.0901542\pi\)
\(864\) −5.19272 + 0.188869i −0.176660 + 0.00642547i
\(865\) 8.32273 2.56722i 0.282981 0.0872882i
\(866\) 28.3395 + 19.3215i 0.963015 + 0.656572i
\(867\) −44.3862 + 51.5414i −1.50743 + 1.75044i
\(868\) −21.0707 6.32345i −0.715185 0.214632i
\(869\) −12.6851 1.91197i −0.430313 0.0648593i
\(870\) 5.16992 + 9.79021i 0.175277 + 0.331919i
\(871\) −11.2569 + 14.1157i −0.381424 + 0.478291i
\(872\) −9.72771 6.63224i −0.329422 0.224596i
\(873\) 0.0105186 15.1134i 0.000356001 0.511512i
\(874\) −31.1700 15.0107i −1.05434 0.507745i
\(875\) 14.0083 13.1985i 0.473568 0.446192i
\(876\) 0.978773 2.24124i 0.0330697 0.0757246i
\(877\) −35.3825 17.0393i −1.19478 0.575377i −0.272598 0.962128i \(-0.587883\pi\)
−0.922184 + 0.386752i \(0.873597\pi\)
\(878\) −0.388780 0.119923i −0.0131207 0.00404720i
\(879\) −14.5148 14.5249i −0.489573 0.489914i
\(880\) 4.64644 + 0.700338i 0.156631 + 0.0236084i
\(881\) −28.1910 −0.949777 −0.474889 0.880046i \(-0.657512\pi\)
−0.474889 + 0.880046i \(0.657512\pi\)
\(882\) −2.82654 + 20.8089i −0.0951745 + 0.700672i
\(883\) 4.64998 0.156484 0.0782421 0.996934i \(-0.475069\pi\)
0.0782421 + 0.996934i \(0.475069\pi\)
\(884\) 20.8749 + 3.14638i 0.702098 + 0.105824i
\(885\) 1.15481 4.30383i 0.0388186 0.144672i
\(886\) 10.4924 + 3.23649i 0.352501 + 0.108732i
\(887\) −53.2033 25.6213i −1.78639 0.860280i −0.950068 0.312042i \(-0.898987\pi\)
−0.836322 0.548239i \(-0.815299\pi\)
\(888\) −6.20587 8.41478i −0.208255 0.282382i
\(889\) −24.7075 + 7.82858i −0.828662 + 0.262562i
\(890\) 6.01922 + 2.89870i 0.201765 + 0.0971648i
\(891\) 19.8964 + 50.9035i 0.666556 + 1.70533i
\(892\) 10.0381 + 6.84384i 0.336099 + 0.229149i
\(893\) 14.0006 17.5562i 0.468511 0.587495i
\(894\) −7.45938 + 11.8624i −0.249479 + 0.396737i
\(895\) −1.01508 0.152998i −0.0339302 0.00511416i
\(896\) 1.30532 2.30133i 0.0436077 0.0768822i
\(897\) 9.71145 + 27.7848i 0.324256 + 0.927706i
\(898\) −10.3507 7.05701i −0.345409 0.235496i
\(899\) 65.6358 20.2460i 2.18908 0.675241i
\(900\) −10.3174 8.23960i −0.343913 0.274653i
\(901\) 15.9135 27.5630i 0.530157 0.918258i
\(902\) 16.3404 + 15.1617i 0.544076 + 0.504829i
\(903\) 16.5623 14.4647i 0.551158 0.481354i
\(904\) −9.44673 + 8.76528i −0.314193 + 0.291529i
\(905\) 0.253543 + 1.11085i 0.00842806 + 0.0369257i
\(906\) −3.83107 10.9608i −0.127279 0.364148i
\(907\) 2.30469 + 2.88999i 0.0765261 + 0.0959607i 0.818621 0.574334i \(-0.194739\pi\)
−0.742095 + 0.670295i \(0.766168\pi\)
\(908\) −0.677562 0.209000i −0.0224857 0.00693591i
\(909\) −34.8155 + 2.58469i −1.15476 + 0.0857289i
\(910\) −1.23906 + 5.62660i −0.0410744 + 0.186520i
\(911\) −23.1915 21.5186i −0.768368 0.712942i 0.195094 0.980785i \(-0.437499\pi\)
−0.963463 + 0.267843i \(0.913689\pi\)
\(912\) −7.52412 + 6.47048i −0.249149 + 0.214259i
\(913\) −46.4188 + 80.3997i −1.53624 + 2.66084i
\(914\) 11.2253 + 10.4155i 0.371299 + 0.344515i
\(915\) −2.30056 + 0.258400i −0.0760541 + 0.00854244i
\(916\) 1.82858 0.275615i 0.0604181 0.00910657i
\(917\) −9.56987 6.41802i −0.316025 0.211942i
\(918\) −23.1789 + 31.3378i −0.765018 + 1.03430i
\(919\) 17.0570 + 15.8266i 0.562658 + 0.522070i 0.909418 0.415884i \(-0.136528\pi\)
−0.346760 + 0.937954i \(0.612718\pi\)
\(920\) −2.91317 + 3.65300i −0.0960443 + 0.120436i
\(921\) 1.11986 2.56431i 0.0369006 0.0844969i
\(922\) −22.6211 28.3660i −0.744987 0.934184i
\(923\) 1.76568 + 23.5613i 0.0581180 + 0.775531i
\(924\) −27.3802 4.97397i −0.900743 0.163632i
\(925\) 1.98547 26.4943i 0.0652820 0.871127i
\(926\) 11.6756 7.96030i 0.383685 0.261592i
\(927\) −31.5362 + 2.34124i −1.03579 + 0.0768965i
\(928\) 0.617330 + 8.23770i 0.0202649 + 0.270416i
\(929\) −25.2054 3.79911i −0.826964 0.124645i −0.278095 0.960553i \(-0.589703\pi\)
−0.548869 + 0.835909i \(0.684941\pi\)
\(930\) 8.44927 7.26607i 0.277063 0.238264i
\(931\) 20.5817 + 34.4223i 0.674538 + 1.12814i
\(932\) 10.4570 + 18.1121i 0.342532 + 0.593283i
\(933\) 3.16442 + 1.67385i 0.103598 + 0.0547995i
\(934\) 10.0810 + 4.85475i 0.329860 + 0.158852i
\(935\) 25.8390 23.9751i 0.845025 0.784069i
\(936\) 8.41864 + 0.636782i 0.275172 + 0.0208139i
\(937\) −6.56384 + 3.16098i −0.214431 + 0.103265i −0.538016 0.842934i \(-0.680826\pi\)
0.323585 + 0.946199i \(0.395112\pi\)
\(938\) 16.8030 + 2.40143i 0.548638 + 0.0784094i
\(939\) −21.0116 21.0262i −0.685688 0.686165i
\(940\) −1.89084 2.37104i −0.0616723 0.0773346i
\(941\) 1.19389 15.9314i 0.0389198 0.519348i −0.943341 0.331826i \(-0.892335\pi\)
0.982260 0.187522i \(-0.0600457\pi\)
\(942\) 0.0733071 + 1.97759i 0.00238847 + 0.0644334i
\(943\) −21.1802 + 6.53322i −0.689722 + 0.212751i
\(944\) 2.07300 2.59946i 0.0674705 0.0846054i
\(945\) −8.10877 6.88553i −0.263778 0.223986i
\(946\) 18.1682 + 22.7822i 0.590699 + 0.740713i
\(947\) 9.20070 + 6.27293i 0.298983 + 0.203843i 0.703514 0.710681i \(-0.251613\pi\)
−0.404532 + 0.914524i \(0.632565\pi\)
\(948\) −1.70858 3.23552i −0.0554922 0.105085i
\(949\) −1.98684 + 3.44130i −0.0644954 + 0.111709i
\(950\) −25.2167 −0.818139
\(951\) 7.77633 12.3664i 0.252165 0.401008i
\(952\) −7.39188 18.4189i −0.239572 0.596961i
\(953\) 4.89738 + 21.4568i 0.158642 + 0.695055i 0.990205 + 0.139624i \(0.0445894\pi\)
−0.831563 + 0.555431i \(0.812553\pi\)
\(954\) 5.53065 11.4641i 0.179061 0.371164i
\(955\) 6.79639 17.3169i 0.219926 0.560362i
\(956\) 6.49265 + 8.14153i 0.209987 + 0.263316i
\(957\) 79.6505 34.7182i 2.57473 1.12228i
\(958\) 1.38093 1.28131i 0.0446157 0.0413973i
\(959\) −32.9003 22.0645i −1.06241 0.712501i
\(960\) 0.625838 + 1.18514i 0.0201988 + 0.0382503i
\(961\) −19.0685 33.0276i −0.615112 1.06540i
\(962\) 8.49418 + 14.7123i 0.273863 + 0.474345i
\(963\) −14.4412 + 11.5000i −0.465361 + 0.370584i
\(964\) 1.58997 21.2166i 0.0512094 0.683342i
\(965\) −3.03480 + 0.457422i −0.0976936 + 0.0147249i
\(966\) 17.8959 21.1050i 0.575792 0.679042i
\(967\) 25.3026 + 3.81375i 0.813676 + 0.122642i 0.542681 0.839939i \(-0.317409\pi\)
0.270995 + 0.962581i \(0.412647\pi\)
\(968\) 5.75817 25.2282i 0.185075 0.810865i
\(969\) 2.75757 + 74.3904i 0.0885859 + 2.38977i
\(970\) −3.51215 + 1.69136i −0.112768 + 0.0543063i
\(971\) −32.0362 + 4.82867i −1.02809 + 0.154959i −0.641365 0.767236i \(-0.721632\pi\)
−0.386724 + 0.922195i \(0.626393\pi\)
\(972\) −8.31651 + 13.1847i −0.266752 + 0.422899i
\(973\) 21.2040 14.6953i 0.679768 0.471110i
\(974\) −2.33384 + 31.1429i −0.0747810 + 0.997882i
\(975\) 15.1646 + 15.1751i 0.485655 + 0.485993i
\(976\) −1.65059 0.509138i −0.0528340 0.0162971i
\(977\) 35.6609 24.3132i 1.14089 0.777848i 0.162933 0.986637i \(-0.447905\pi\)
0.977961 + 0.208789i \(0.0669522\pi\)
\(978\) 0.495166 + 13.3580i 0.0158337 + 0.427142i
\(979\) 26.2155 45.4065i 0.837850 1.45120i
\(980\) 5.15085 1.67548i 0.164538 0.0535214i
\(981\) −32.8879 + 12.8811i −1.05003 + 0.411263i
\(982\) 10.2905 + 26.2197i 0.328382 + 0.836704i
\(983\) 18.8091 + 9.05801i 0.599919 + 0.288906i 0.709091 0.705117i \(-0.249106\pi\)
−0.109172 + 0.994023i \(0.534820\pi\)
\(984\) −0.714053 + 6.31764i −0.0227632 + 0.201399i
\(985\) −1.92255 0.925852i −0.0612576 0.0295001i
\(986\) 51.2000 + 34.9076i 1.63054 + 1.11168i
\(987\) 10.7704 + 14.3726i 0.342824 + 0.457486i
\(988\) 13.3222 9.08295i 0.423837 0.288967i
\(989\) −28.6512 + 4.31847i −0.911054 + 0.137319i
\(990\) 9.59543 10.3270i 0.304963 0.328213i
\(991\) −47.8008 7.20482i −1.51844 0.228869i −0.663731 0.747971i \(-0.731028\pi\)
−0.854712 + 0.519102i \(0.826266\pi\)
\(992\) 7.94546 2.45085i 0.252268 0.0778145i
\(993\) 18.7488 11.7715i 0.594975 0.373559i
\(994\) 18.2570 12.6529i 0.579077 0.401326i
\(995\) 4.08961 10.4202i 0.129649 0.330341i
\(996\) −26.3139 + 2.95559i −0.833786 + 0.0936513i
\(997\) −2.26106 + 9.90633i −0.0716084 + 0.313737i −0.998029 0.0627532i \(-0.980012\pi\)
0.926421 + 0.376490i \(0.122869\pi\)
\(998\) 11.3481 + 19.6555i 0.359219 + 0.622186i
\(999\) −31.3463 + 1.14013i −0.991754 + 0.0360721i
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 882.2.y.a.457.2 yes 336
9.4 even 3 882.2.bb.b.751.27 yes 336
49.46 even 21 882.2.bb.b.781.27 yes 336
441.193 even 21 inner 882.2.y.a.193.2 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
882.2.y.a.193.2 336 441.193 even 21 inner
882.2.y.a.457.2 yes 336 1.1 even 1 trivial
882.2.bb.b.751.27 yes 336 9.4 even 3
882.2.bb.b.781.27 yes 336 49.46 even 21