Properties

Label 882.2.f.n.295.3
Level $882$
Weight $2$
Character 882.295
Analytic conductor $7.043$
Analytic rank $0$
Dimension $6$
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(295,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.f (of order \(3\), degree \(2\), 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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.3
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 882.295
Dual form 882.2.f.n.589.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.349814 + 1.69636i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.794182 - 1.37556i) q^{5} +(1.64400 + 0.545231i) q^{6} -1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.349814 + 1.69636i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.794182 - 1.37556i) q^{5} +(1.64400 + 0.545231i) q^{6} -1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} -1.58836 q^{10} +(0.794182 - 1.37556i) q^{11} +(1.29418 - 1.15113i) q^{12} +(2.40545 + 4.16635i) q^{13} +(2.05563 - 1.82841i) q^{15} +(-0.500000 + 0.866025i) q^{16} +5.39926 q^{17} +(-0.349814 + 2.97954i) q^{18} +7.09888 q^{19} +(-0.794182 + 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} +(-0.150186 - 0.260130i) q^{23} +(-0.349814 - 1.69636i) q^{24} +(1.23855 - 2.14523i) q^{25} +4.81089 q^{26} +(-2.97710 - 4.25874i) q^{27} +(4.13781 - 7.16689i) q^{29} +(-0.555632 - 2.69443i) q^{30} +(1.35600 + 2.34867i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.61126 + 0.866025i) q^{33} +(2.69963 - 4.67589i) q^{34} +(2.40545 + 1.79272i) q^{36} -1.00000 q^{37} +(3.54944 - 6.14781i) q^{38} +(-6.22617 + 5.53795i) q^{39} +(0.794182 + 1.37556i) q^{40} +(2.93818 + 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} -1.58836 q^{44} +(3.82072 + 2.84748i) q^{45} -0.300372 q^{46} +(-1.33310 + 2.30900i) q^{47} +(-1.64400 - 0.545231i) q^{48} +(-1.23855 - 2.14523i) q^{50} +(1.88874 + 9.15907i) q^{51} +(2.40545 - 4.16635i) q^{52} -4.88874 q^{53} +(-5.17673 + 0.448873i) q^{54} -2.52290 q^{55} +(2.48329 + 12.0422i) q^{57} +(-4.13781 - 7.16689i) q^{58} +(-3.23855 - 5.60933i) q^{59} +(-2.61126 - 0.866025i) q^{60} +(2.23855 - 3.87728i) q^{61} +2.71201 q^{62} +1.00000 q^{64} +(3.82072 - 6.61769i) q^{65} +(2.05563 - 1.82841i) q^{66} +(5.02654 + 8.70623i) q^{67} +(-2.69963 - 4.67589i) q^{68} +(0.388736 - 0.345766i) q^{69} +12.7207 q^{71} +(2.75526 - 1.18682i) q^{72} -16.0531 q^{73} +(-0.500000 + 0.866025i) q^{74} +(4.07234 + 1.35059i) q^{75} +(-3.54944 - 6.14781i) q^{76} +(1.68292 + 8.16100i) q^{78} +(-4.19344 + 7.26325i) q^{79} +1.58836 q^{80} +(6.18292 - 6.53999i) q^{81} +5.87636 q^{82} +(1.18292 - 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +(0.833104 + 1.44298i) q^{86} +(13.6051 + 4.51212i) q^{87} +(-0.794182 + 1.37556i) q^{88} -3.21015 q^{89} +(4.37636 - 1.88510i) q^{90} +(-0.150186 + 0.260130i) q^{92} +(-3.50983 + 3.12186i) q^{93} +(1.33310 + 2.30900i) q^{94} +(-5.63781 - 9.76497i) q^{95} +(-1.29418 + 1.15113i) q^{96} +(0.712008 - 1.23323i) q^{97} +(-0.555632 + 4.73259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - 4 q^{9} + 2 q^{10} - q^{11} + 2 q^{12} + 8 q^{13} + 12 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + q^{20} + q^{22} - 7 q^{23} + 4 q^{24} + 2 q^{25} + 16 q^{26} - 7 q^{27} - 5 q^{29} - 3 q^{30} + 20 q^{31} + 3 q^{32} + 15 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} + 3 q^{38} + 4 q^{39} - q^{40} - 6 q^{43} + 2 q^{44} - 12 q^{45} - 14 q^{46} - 9 q^{47} + 2 q^{48} - 2 q^{50} + 12 q^{51} + 8 q^{52} - 30 q^{53} - 8 q^{54} - 26 q^{55} + 22 q^{57} + 5 q^{58} - 14 q^{59} - 15 q^{60} + 8 q^{61} + 40 q^{62} + 6 q^{64} - 12 q^{65} + 12 q^{66} + q^{67} - 4 q^{68} + 3 q^{69} + 14 q^{71} + 4 q^{72} - 38 q^{73} - 3 q^{74} + 17 q^{75} - 3 q^{76} + 5 q^{78} + 5 q^{79} - 2 q^{80} + 32 q^{81} + 2 q^{83} - 2 q^{85} + 6 q^{86} + 63 q^{87} + q^{88} + 18 q^{89} - 9 q^{90} - 7 q^{92} + q^{93} + 9 q^{94} - 4 q^{95} - 2 q^{96} + 28 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(199\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.349814 + 1.69636i 0.201965 + 0.979393i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.794182 1.37556i −0.355169 0.615171i 0.631978 0.774986i \(-0.282243\pi\)
−0.987147 + 0.159816i \(0.948910\pi\)
\(6\) 1.64400 + 0.545231i 0.671159 + 0.222590i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.75526 + 1.18682i −0.918420 + 0.395607i
\(10\) −1.58836 −0.502285
\(11\) 0.794182 1.37556i 0.239455 0.414748i −0.721103 0.692828i \(-0.756365\pi\)
0.960558 + 0.278080i \(0.0896979\pi\)
\(12\) 1.29418 1.15113i 0.373598 0.332302i
\(13\) 2.40545 + 4.16635i 0.667151 + 1.15554i 0.978697 + 0.205308i \(0.0658196\pi\)
−0.311547 + 0.950231i \(0.600847\pi\)
\(14\) 0 0
\(15\) 2.05563 1.82841i 0.530762 0.472093i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 5.39926 1.30951 0.654756 0.755840i \(-0.272771\pi\)
0.654756 + 0.755840i \(0.272771\pi\)
\(18\) −0.349814 + 2.97954i −0.0824520 + 0.702283i
\(19\) 7.09888 1.62860 0.814298 0.580447i \(-0.197122\pi\)
0.814298 + 0.580447i \(0.197122\pi\)
\(20\) −0.794182 + 1.37556i −0.177584 + 0.307585i
\(21\) 0 0
\(22\) −0.794182 1.37556i −0.169320 0.293271i
\(23\) −0.150186 0.260130i −0.0313159 0.0542408i 0.849943 0.526875i \(-0.176636\pi\)
−0.881259 + 0.472634i \(0.843303\pi\)
\(24\) −0.349814 1.69636i −0.0714055 0.346268i
\(25\) 1.23855 2.14523i 0.247710 0.429046i
\(26\) 4.81089 0.943494
\(27\) −2.97710 4.25874i −0.572943 0.819595i
\(28\) 0 0
\(29\) 4.13781 7.16689i 0.768371 1.33086i −0.170074 0.985431i \(-0.554401\pi\)
0.938446 0.345427i \(-0.112266\pi\)
\(30\) −0.555632 2.69443i −0.101444 0.491934i
\(31\) 1.35600 + 2.34867i 0.243545 + 0.421833i 0.961722 0.274028i \(-0.0883561\pi\)
−0.718176 + 0.695861i \(0.755023\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 2.61126 + 0.866025i 0.454563 + 0.150756i
\(34\) 2.69963 4.67589i 0.462982 0.801909i
\(35\) 0 0
\(36\) 2.40545 + 1.79272i 0.400908 + 0.298786i
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 3.54944 6.14781i 0.575796 0.997307i
\(39\) −6.22617 + 5.53795i −0.996985 + 0.886781i
\(40\) 0.794182 + 1.37556i 0.125571 + 0.217496i
\(41\) 2.93818 + 5.08907i 0.458866 + 0.794780i 0.998901 0.0468628i \(-0.0149223\pi\)
−0.540035 + 0.841643i \(0.681589\pi\)
\(42\) 0 0
\(43\) −0.833104 + 1.44298i −0.127047 + 0.220052i −0.922531 0.385922i \(-0.873883\pi\)
0.795484 + 0.605974i \(0.207217\pi\)
\(44\) −1.58836 −0.239455
\(45\) 3.82072 + 2.84748i 0.569560 + 0.424478i
\(46\) −0.300372 −0.0442874
\(47\) −1.33310 + 2.30900i −0.194453 + 0.336803i −0.946721 0.322055i \(-0.895627\pi\)
0.752268 + 0.658857i \(0.228960\pi\)
\(48\) −1.64400 0.545231i −0.237290 0.0786973i
\(49\) 0 0
\(50\) −1.23855 2.14523i −0.175157 0.303382i
\(51\) 1.88874 + 9.15907i 0.264476 + 1.28253i
\(52\) 2.40545 4.16635i 0.333575 0.577769i
\(53\) −4.88874 −0.671520 −0.335760 0.941948i \(-0.608993\pi\)
−0.335760 + 0.941948i \(0.608993\pi\)
\(54\) −5.17673 + 0.448873i −0.704463 + 0.0610839i
\(55\) −2.52290 −0.340188
\(56\) 0 0
\(57\) 2.48329 + 12.0422i 0.328920 + 1.59503i
\(58\) −4.13781 7.16689i −0.543321 0.941059i
\(59\) −3.23855 5.60933i −0.421623 0.730273i 0.574475 0.818522i \(-0.305206\pi\)
−0.996098 + 0.0882491i \(0.971873\pi\)
\(60\) −2.61126 0.866025i −0.337113 0.111803i
\(61\) 2.23855 3.87728i 0.286617 0.496435i −0.686383 0.727240i \(-0.740803\pi\)
0.973000 + 0.230805i \(0.0741360\pi\)
\(62\) 2.71201 0.344425
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.82072 6.61769i 0.473902 0.820823i
\(66\) 2.05563 1.82841i 0.253031 0.225062i
\(67\) 5.02654 + 8.70623i 0.614090 + 1.06363i 0.990543 + 0.137199i \(0.0438101\pi\)
−0.376454 + 0.926435i \(0.622857\pi\)
\(68\) −2.69963 4.67589i −0.327378 0.567035i
\(69\) 0.388736 0.345766i 0.0467983 0.0416253i
\(70\) 0 0
\(71\) 12.7207 1.50967 0.754833 0.655917i \(-0.227718\pi\)
0.754833 + 0.655917i \(0.227718\pi\)
\(72\) 2.75526 1.18682i 0.324711 0.139868i
\(73\) −16.0531 −1.87887 −0.939436 0.342725i \(-0.888650\pi\)
−0.939436 + 0.342725i \(0.888650\pi\)
\(74\) −0.500000 + 0.866025i −0.0581238 + 0.100673i
\(75\) 4.07234 + 1.35059i 0.470234 + 0.155953i
\(76\) −3.54944 6.14781i −0.407149 0.705203i
\(77\) 0 0
\(78\) 1.68292 + 8.16100i 0.190553 + 0.924051i
\(79\) −4.19344 + 7.26325i −0.471799 + 0.817179i −0.999479 0.0322635i \(-0.989728\pi\)
0.527681 + 0.849443i \(0.323062\pi\)
\(80\) 1.58836 0.177584
\(81\) 6.18292 6.53999i 0.686991 0.726666i
\(82\) 5.87636 0.648935
\(83\) 1.18292 2.04887i 0.129842 0.224893i −0.793773 0.608214i \(-0.791886\pi\)
0.923615 + 0.383321i \(0.125220\pi\)
\(84\) 0 0
\(85\) −4.28799 7.42702i −0.465098 0.805573i
\(86\) 0.833104 + 1.44298i 0.0898359 + 0.155600i
\(87\) 13.6051 + 4.51212i 1.45862 + 0.483750i
\(88\) −0.794182 + 1.37556i −0.0846601 + 0.146636i
\(89\) −3.21015 −0.340275 −0.170138 0.985420i \(-0.554421\pi\)
−0.170138 + 0.985420i \(0.554421\pi\)
\(90\) 4.37636 1.88510i 0.461308 0.198707i
\(91\) 0 0
\(92\) −0.150186 + 0.260130i −0.0156580 + 0.0271204i
\(93\) −3.50983 + 3.12186i −0.363953 + 0.323722i
\(94\) 1.33310 + 2.30900i 0.137499 + 0.238156i
\(95\) −5.63781 9.76497i −0.578427 1.00186i
\(96\) −1.29418 + 1.15113i −0.132087 + 0.117486i
\(97\) 0.712008 1.23323i 0.0722934 0.125216i −0.827613 0.561300i \(-0.810302\pi\)
0.899906 + 0.436084i \(0.143635\pi\)
\(98\) 0 0
\(99\) −0.555632 + 4.73259i −0.0558431 + 0.475643i
\(100\) −2.47710 −0.247710
\(101\) −6.01671 + 10.4212i −0.598685 + 1.03695i 0.394330 + 0.918969i \(0.370977\pi\)
−0.993015 + 0.117984i \(0.962357\pi\)
\(102\) 8.87636 + 2.94384i 0.878890 + 0.291484i
\(103\) 3.04944 + 5.28179i 0.300470 + 0.520430i 0.976243 0.216680i \(-0.0695230\pi\)
−0.675772 + 0.737111i \(0.736190\pi\)
\(104\) −2.40545 4.16635i −0.235873 0.408545i
\(105\) 0 0
\(106\) −2.44437 + 4.23377i −0.237418 + 0.411220i
\(107\) 3.08650 0.298384 0.149192 0.988808i \(-0.452333\pi\)
0.149192 + 0.988808i \(0.452333\pi\)
\(108\) −2.19963 + 4.70761i −0.211659 + 0.452990i
\(109\) −2.28799 −0.219150 −0.109575 0.993979i \(-0.534949\pi\)
−0.109575 + 0.993979i \(0.534949\pi\)
\(110\) −1.26145 + 2.18490i −0.120275 + 0.208322i
\(111\) −0.349814 1.69636i −0.0332029 0.161011i
\(112\) 0 0
\(113\) −9.73236 16.8569i −0.915543 1.58577i −0.806104 0.591774i \(-0.798428\pi\)
−0.109440 0.993993i \(-0.534906\pi\)
\(114\) 11.6705 + 3.87053i 1.09305 + 0.362509i
\(115\) −0.238550 + 0.413181i −0.0222449 + 0.0385293i
\(116\) −8.27561 −0.768371
\(117\) −11.5723 8.62456i −1.06986 0.797341i
\(118\) −6.47710 −0.596265
\(119\) 0 0
\(120\) −2.05563 + 1.82841i −0.187653 + 0.166910i
\(121\) 4.23855 + 7.34138i 0.385323 + 0.667399i
\(122\) −2.23855 3.87728i −0.202669 0.351033i
\(123\) −7.60507 + 6.76443i −0.685726 + 0.609928i
\(124\) 1.35600 2.34867i 0.121773 0.210917i
\(125\) −11.8764 −1.06225
\(126\) 0 0
\(127\) −13.4400 −1.19260 −0.596302 0.802760i \(-0.703364\pi\)
−0.596302 + 0.802760i \(0.703364\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −2.73924 0.908468i −0.241177 0.0799862i
\(130\) −3.82072 6.61769i −0.335100 0.580410i
\(131\) 1.58836 + 2.75113i 0.138776 + 0.240367i 0.927034 0.374978i \(-0.122350\pi\)
−0.788258 + 0.615345i \(0.789017\pi\)
\(132\) −0.555632 2.69443i −0.0483616 0.234520i
\(133\) 0 0
\(134\) 10.0531 0.868454
\(135\) −3.49381 + 7.47741i −0.300699 + 0.643553i
\(136\) −5.39926 −0.462982
\(137\) 10.6316 18.4145i 0.908320 1.57326i 0.0919231 0.995766i \(-0.470699\pi\)
0.816397 0.577491i \(-0.195968\pi\)
\(138\) −0.105074 0.509538i −0.00894452 0.0433748i
\(139\) 6.52654 + 11.3043i 0.553574 + 0.958818i 0.998013 + 0.0630092i \(0.0200698\pi\)
−0.444439 + 0.895809i \(0.646597\pi\)
\(140\) 0 0
\(141\) −4.38323 1.45370i −0.369135 0.122424i
\(142\) 6.36033 11.0164i 0.533747 0.924478i
\(143\) 7.64145 0.639010
\(144\) 0.349814 2.97954i 0.0291512 0.248295i
\(145\) −13.1447 −1.09161
\(146\) −8.02654 + 13.9024i −0.664281 + 1.15057i
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) −2.60439 4.51093i −0.213360 0.369550i 0.739404 0.673262i \(-0.235107\pi\)
−0.952764 + 0.303712i \(0.901774\pi\)
\(150\) 3.20582 2.85146i 0.261754 0.232820i
\(151\) 0.261450 0.452845i 0.0212765 0.0368520i −0.855191 0.518313i \(-0.826560\pi\)
0.876468 + 0.481461i \(0.159894\pi\)
\(152\) −7.09888 −0.575796
\(153\) −14.8764 + 6.40794i −1.20268 + 0.518052i
\(154\) 0 0
\(155\) 2.15383 3.73054i 0.173000 0.299644i
\(156\) 7.90909 + 2.62305i 0.633234 + 0.210012i
\(157\) −4.43199 7.67643i −0.353711 0.612646i 0.633185 0.774000i \(-0.281747\pi\)
−0.986897 + 0.161354i \(0.948414\pi\)
\(158\) 4.19344 + 7.26325i 0.333612 + 0.577833i
\(159\) −1.71015 8.29305i −0.135624 0.657681i
\(160\) 0.794182 1.37556i 0.0627856 0.108748i
\(161\) 0 0
\(162\) −2.57234 8.62456i −0.202102 0.677610i
\(163\) −21.9629 −1.72026 −0.860132 0.510071i \(-0.829619\pi\)
−0.860132 + 0.510071i \(0.829619\pi\)
\(164\) 2.93818 5.08907i 0.229433 0.397390i
\(165\) −0.882546 4.27974i −0.0687061 0.333177i
\(166\) −1.18292 2.04887i −0.0918122 0.159023i
\(167\) 1.65019 + 2.85821i 0.127695 + 0.221175i 0.922783 0.385319i \(-0.125909\pi\)
−0.795088 + 0.606494i \(0.792575\pi\)
\(168\) 0 0
\(169\) −5.07234 + 8.78555i −0.390180 + 0.675812i
\(170\) −8.57598 −0.657748
\(171\) −19.5593 + 8.42510i −1.49574 + 0.644283i
\(172\) 1.66621 0.127047
\(173\) −9.55377 + 16.5476i −0.726360 + 1.25809i 0.232052 + 0.972703i \(0.425456\pi\)
−0.958412 + 0.285389i \(0.907877\pi\)
\(174\) 10.7101 9.52628i 0.811934 0.722185i
\(175\) 0 0
\(176\) 0.794182 + 1.37556i 0.0598637 + 0.103687i
\(177\) 8.38255 7.45596i 0.630071 0.560425i
\(178\) −1.60507 + 2.78007i −0.120305 + 0.208375i
\(179\) 16.0741 1.20144 0.600718 0.799461i \(-0.294881\pi\)
0.600718 + 0.799461i \(0.294881\pi\)
\(180\) 0.555632 4.73259i 0.0414144 0.352746i
\(181\) 8.05308 0.598581 0.299291 0.954162i \(-0.403250\pi\)
0.299291 + 0.954162i \(0.403250\pi\)
\(182\) 0 0
\(183\) 7.36033 + 2.44105i 0.544092 + 0.180448i
\(184\) 0.150186 + 0.260130i 0.0110719 + 0.0191770i
\(185\) 0.794182 + 1.37556i 0.0583894 + 0.101133i
\(186\) 0.948699 + 4.60054i 0.0695620 + 0.337328i
\(187\) 4.28799 7.42702i 0.313569 0.543118i
\(188\) 2.66621 0.194453
\(189\) 0 0
\(190\) −11.2756 −0.818019
\(191\) 11.9814 20.7524i 0.866946 1.50159i 0.00184390 0.999998i \(-0.499413\pi\)
0.865102 0.501596i \(-0.167254\pi\)
\(192\) 0.349814 + 1.69636i 0.0252457 + 0.122424i
\(193\) −4.88255 8.45682i −0.351453 0.608735i 0.635051 0.772470i \(-0.280979\pi\)
−0.986504 + 0.163735i \(0.947646\pi\)
\(194\) −0.712008 1.23323i −0.0511192 0.0885410i
\(195\) 12.5625 + 4.16635i 0.899620 + 0.298359i
\(196\) 0 0
\(197\) −18.2436 −1.29980 −0.649900 0.760020i \(-0.725189\pi\)
−0.649900 + 0.760020i \(0.725189\pi\)
\(198\) 3.82072 + 2.84748i 0.271527 + 0.202362i
\(199\) −18.0989 −1.28300 −0.641498 0.767125i \(-0.721687\pi\)
−0.641498 + 0.767125i \(0.721687\pi\)
\(200\) −1.23855 + 2.14523i −0.0875787 + 0.151691i
\(201\) −13.0105 + 11.5724i −0.917691 + 0.816252i
\(202\) 6.01671 + 10.4212i 0.423334 + 0.733236i
\(203\) 0 0
\(204\) 6.98762 6.21523i 0.489231 0.435153i
\(205\) 4.66690 8.08330i 0.325950 0.564562i
\(206\) 6.09888 0.424929
\(207\) 0.722528 + 0.538481i 0.0502192 + 0.0374270i
\(208\) −4.81089 −0.333575
\(209\) 5.63781 9.76497i 0.389975 0.675457i
\(210\) 0 0
\(211\) 0.166208 + 0.287880i 0.0114422 + 0.0198185i 0.871690 0.490058i \(-0.163024\pi\)
−0.860248 + 0.509877i \(0.829691\pi\)
\(212\) 2.44437 + 4.23377i 0.167880 + 0.290776i
\(213\) 4.44987 + 21.5788i 0.304900 + 1.47856i
\(214\) 1.54325 2.67299i 0.105495 0.182722i
\(215\) 2.64654 0.180493
\(216\) 2.97710 + 4.25874i 0.202566 + 0.289771i
\(217\) 0 0
\(218\) −1.14400 + 1.98146i −0.0774812 + 0.134201i
\(219\) −5.61559 27.2318i −0.379467 1.84015i
\(220\) 1.26145 + 2.18490i 0.0850469 + 0.147306i
\(221\) 12.9876 + 22.4952i 0.873642 + 1.51319i
\(222\) −1.64400 0.545231i −0.110338 0.0365935i
\(223\) 3.16621 5.48403i 0.212025 0.367238i −0.740323 0.672251i \(-0.765328\pi\)
0.952348 + 0.305013i \(0.0986609\pi\)
\(224\) 0 0
\(225\) −0.866524 + 7.38061i −0.0577683 + 0.492040i
\(226\) −19.4647 −1.29477
\(227\) 11.6545 20.1862i 0.773537 1.33981i −0.162075 0.986778i \(-0.551819\pi\)
0.935613 0.353028i \(-0.114848\pi\)
\(228\) 9.18725 8.17172i 0.608440 0.541185i
\(229\) 2.47710 + 4.29046i 0.163691 + 0.283522i 0.936190 0.351495i \(-0.114327\pi\)
−0.772498 + 0.635017i \(0.780993\pi\)
\(230\) 0.238550 + 0.413181i 0.0157295 + 0.0272443i
\(231\) 0 0
\(232\) −4.13781 + 7.16689i −0.271660 + 0.470529i
\(233\) 14.2756 0.935226 0.467613 0.883933i \(-0.345114\pi\)
0.467613 + 0.883933i \(0.345114\pi\)
\(234\) −13.2553 + 5.70966i −0.866523 + 0.373252i
\(235\) 4.23491 0.276255
\(236\) −3.23855 + 5.60933i −0.210812 + 0.365136i
\(237\) −13.7880 4.57279i −0.895626 0.297034i
\(238\) 0 0
\(239\) 2.48762 + 4.30868i 0.160911 + 0.278706i 0.935196 0.354132i \(-0.115224\pi\)
−0.774285 + 0.632837i \(0.781890\pi\)
\(240\) 0.555632 + 2.69443i 0.0358659 + 0.173925i
\(241\) 6.50000 11.2583i 0.418702 0.725213i −0.577107 0.816668i \(-0.695819\pi\)
0.995809 + 0.0914555i \(0.0291519\pi\)
\(242\) 8.47710 0.544929
\(243\) 13.2570 + 8.20066i 0.850440 + 0.526073i
\(244\) −4.47710 −0.286617
\(245\) 0 0
\(246\) 2.05563 + 9.96840i 0.131062 + 0.635562i
\(247\) 17.0760 + 29.5765i 1.08652 + 1.88191i
\(248\) −1.35600 2.34867i −0.0861063 0.149141i
\(249\) 3.88942 + 1.28993i 0.246482 + 0.0817458i
\(250\) −5.93818 + 10.2852i −0.375563 + 0.650495i
\(251\) 2.43268 0.153549 0.0767746 0.997048i \(-0.475538\pi\)
0.0767746 + 0.997048i \(0.475538\pi\)
\(252\) 0 0
\(253\) −0.477100 −0.0299950
\(254\) −6.71998 + 11.6393i −0.421649 + 0.730318i
\(255\) 11.0989 9.87205i 0.695039 0.618211i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.493810 + 0.855304i 0.0308030 + 0.0533524i 0.881016 0.473087i \(-0.156860\pi\)
−0.850213 + 0.526439i \(0.823527\pi\)
\(258\) −2.15638 + 1.91802i −0.134250 + 0.119410i
\(259\) 0 0
\(260\) −7.64145 −0.473902
\(261\) −2.89493 + 24.6575i −0.179191 + 1.52626i
\(262\) 3.17673 0.196259
\(263\) −8.59269 + 14.8830i −0.529848 + 0.917724i 0.469545 + 0.882908i \(0.344418\pi\)
−0.999394 + 0.0348158i \(0.988916\pi\)
\(264\) −2.61126 0.866025i −0.160712 0.0533002i
\(265\) 3.88255 + 6.72477i 0.238503 + 0.413099i
\(266\) 0 0
\(267\) −1.12296 5.44556i −0.0687237 0.333263i
\(268\) 5.02654 8.70623i 0.307045 0.531817i
\(269\) −22.9047 −1.39652 −0.698262 0.715843i \(-0.746043\pi\)
−0.698262 + 0.715843i \(0.746043\pi\)
\(270\) 4.72872 + 6.76443i 0.287781 + 0.411670i
\(271\) −14.0073 −0.850882 −0.425441 0.904986i \(-0.639881\pi\)
−0.425441 + 0.904986i \(0.639881\pi\)
\(272\) −2.69963 + 4.67589i −0.163689 + 0.283518i
\(273\) 0 0
\(274\) −10.6316 18.4145i −0.642279 1.11246i
\(275\) −1.96727 3.40741i −0.118631 0.205474i
\(276\) −0.493810 0.163772i −0.0297239 0.00985792i
\(277\) −14.1476 + 24.5044i −0.850049 + 1.47233i 0.0311139 + 0.999516i \(0.490095\pi\)
−0.881163 + 0.472813i \(0.843239\pi\)
\(278\) 13.0531 0.782872
\(279\) −6.52359 4.86186i −0.390557 0.291072i
\(280\) 0 0
\(281\) −8.79782 + 15.2383i −0.524834 + 0.909039i 0.474748 + 0.880122i \(0.342539\pi\)
−0.999582 + 0.0289175i \(0.990794\pi\)
\(282\) −3.45056 + 3.06914i −0.205478 + 0.182765i
\(283\) 9.26145 + 16.0413i 0.550536 + 0.953556i 0.998236 + 0.0593725i \(0.0189100\pi\)
−0.447700 + 0.894184i \(0.647757\pi\)
\(284\) −6.36033 11.0164i −0.377416 0.653704i
\(285\) 14.5927 12.9797i 0.864397 0.768849i
\(286\) 3.82072 6.61769i 0.225924 0.391312i
\(287\) 0 0
\(288\) −2.40545 1.79272i −0.141742 0.105637i
\(289\) 12.1520 0.714822
\(290\) −6.57234 + 11.3836i −0.385941 + 0.668470i
\(291\) 2.34108 + 0.776418i 0.137236 + 0.0455144i
\(292\) 8.02654 + 13.9024i 0.469718 + 0.813575i
\(293\) −7.04256 12.1981i −0.411431 0.712619i 0.583616 0.812030i \(-0.301638\pi\)
−0.995046 + 0.0994108i \(0.968304\pi\)
\(294\) 0 0
\(295\) −5.14400 + 8.90966i −0.299495 + 0.518741i
\(296\) 1.00000 0.0581238
\(297\) −8.22253 + 0.712974i −0.477119 + 0.0413710i
\(298\) −5.20877 −0.301736
\(299\) 0.722528 1.25146i 0.0417849 0.0723736i
\(300\) −0.866524 4.20205i −0.0500288 0.242605i
\(301\) 0 0
\(302\) −0.261450 0.452845i −0.0150448 0.0260583i
\(303\) −19.7829 6.56099i −1.13650 0.376919i
\(304\) −3.54944 + 6.14781i −0.203574 + 0.352601i
\(305\) −7.11126 −0.407190
\(306\) −1.88874 + 16.0873i −0.107972 + 0.919648i
\(307\) −5.85532 −0.334180 −0.167090 0.985942i \(-0.553437\pi\)
−0.167090 + 0.985942i \(0.553437\pi\)
\(308\) 0 0
\(309\) −7.89307 + 7.02059i −0.449021 + 0.399387i
\(310\) −2.15383 3.73054i −0.122329 0.211880i
\(311\) −0.405446 0.702253i −0.0229907 0.0398211i 0.854301 0.519778i \(-0.173985\pi\)
−0.877292 + 0.479957i \(0.840652\pi\)
\(312\) 6.22617 5.53795i 0.352487 0.313525i
\(313\) −5.28799 + 9.15907i −0.298895 + 0.517701i −0.975883 0.218292i \(-0.929951\pi\)
0.676988 + 0.735994i \(0.263285\pi\)
\(314\) −8.86398 −0.500223
\(315\) 0 0
\(316\) 8.38688 0.471799
\(317\) −6.09820 + 10.5624i −0.342509 + 0.593243i −0.984898 0.173136i \(-0.944610\pi\)
0.642389 + 0.766379i \(0.277943\pi\)
\(318\) −8.03706 2.66549i −0.450696 0.149473i
\(319\) −6.57234 11.3836i −0.367981 0.637361i
\(320\) −0.794182 1.37556i −0.0443961 0.0768963i
\(321\) 1.07970 + 5.23582i 0.0602631 + 0.292235i
\(322\) 0 0
\(323\) 38.3287 2.13267
\(324\) −8.75526 2.08457i −0.486403 0.115809i
\(325\) 11.9171 0.661040
\(326\) −10.9814 + 19.0204i −0.608205 + 1.05344i
\(327\) −0.800372 3.88125i −0.0442607 0.214634i
\(328\) −2.93818 5.08907i −0.162234 0.280997i
\(329\) 0 0
\(330\) −4.14764 1.37556i −0.228320 0.0757223i
\(331\) 7.83310 13.5673i 0.430546 0.745728i −0.566374 0.824148i \(-0.691654\pi\)
0.996920 + 0.0784202i \(0.0249876\pi\)
\(332\) −2.36584 −0.129842
\(333\) 2.75526 1.18682i 0.150987 0.0650373i
\(334\) 3.30037 0.180588
\(335\) 7.98398 13.8287i 0.436211 0.755540i
\(336\) 0 0
\(337\) −4.21201 7.29541i −0.229443 0.397406i 0.728200 0.685364i \(-0.240357\pi\)
−0.957643 + 0.287958i \(0.907024\pi\)
\(338\) 5.07234 + 8.78555i 0.275899 + 0.477871i
\(339\) 25.1909 22.4064i 1.36818 1.21695i
\(340\) −4.28799 + 7.42702i −0.232549 + 0.402787i
\(341\) 4.30766 0.233273
\(342\) −2.48329 + 21.1514i −0.134281 + 1.14374i
\(343\) 0 0
\(344\) 0.833104 1.44298i 0.0449179 0.0778002i
\(345\) −0.784350 0.260130i −0.0422280 0.0140049i
\(346\) 9.55377 + 16.5476i 0.513614 + 0.889606i
\(347\) −0.283662 0.491316i −0.0152277 0.0263752i 0.858311 0.513130i \(-0.171514\pi\)
−0.873539 + 0.486754i \(0.838181\pi\)
\(348\) −2.89493 14.0384i −0.155184 0.752537i
\(349\) −0.00364189 + 0.00630794i −0.000194946 + 0.000337656i −0.866123 0.499831i \(-0.833395\pi\)
0.865928 + 0.500169i \(0.166729\pi\)
\(350\) 0 0
\(351\) 10.5822 22.6478i 0.564835 1.20885i
\(352\) 1.58836 0.0846601
\(353\) −3.32691 + 5.76238i −0.177074 + 0.306701i −0.940877 0.338748i \(-0.889996\pi\)
0.763803 + 0.645449i \(0.223330\pi\)
\(354\) −2.26578 10.9875i −0.120425 0.583978i
\(355\) −10.1025 17.4981i −0.536186 0.928702i
\(356\) 1.60507 + 2.78007i 0.0850688 + 0.147343i
\(357\) 0 0
\(358\) 8.03706 13.9206i 0.424772 0.735727i
\(359\) 0.797135 0.0420712 0.0210356 0.999779i \(-0.493304\pi\)
0.0210356 + 0.999779i \(0.493304\pi\)
\(360\) −3.82072 2.84748i −0.201370 0.150076i
\(361\) 31.3942 1.65232
\(362\) 4.02654 6.97418i 0.211630 0.366555i
\(363\) −10.9709 + 9.75822i −0.575823 + 0.512174i
\(364\) 0 0
\(365\) 12.7491 + 22.0820i 0.667317 + 1.15583i
\(366\) 5.79418 5.15371i 0.302867 0.269389i
\(367\) 7.71634 13.3651i 0.402790 0.697652i −0.591272 0.806472i \(-0.701374\pi\)
0.994061 + 0.108820i \(0.0347073\pi\)
\(368\) 0.300372 0.0156580
\(369\) −14.1353 10.5346i −0.735852 0.548411i
\(370\) 1.58836 0.0825751
\(371\) 0 0
\(372\) 4.45853 + 1.47867i 0.231164 + 0.0766655i
\(373\) −5.12110 8.87000i −0.265160 0.459271i 0.702445 0.711738i \(-0.252092\pi\)
−0.967606 + 0.252467i \(0.918758\pi\)
\(374\) −4.28799 7.42702i −0.221727 0.384042i
\(375\) −4.15452 20.1466i −0.214538 1.04036i
\(376\) 1.33310 2.30900i 0.0687496 0.119078i
\(377\) 39.8131 2.05048
\(378\) 0 0
\(379\) 25.0087 1.28461 0.642304 0.766450i \(-0.277979\pi\)
0.642304 + 0.766450i \(0.277979\pi\)
\(380\) −5.63781 + 9.76497i −0.289213 + 0.500932i
\(381\) −4.70149 22.7990i −0.240864 1.16803i
\(382\) −11.9814 20.7524i −0.613023 1.06179i
\(383\) 3.13348 + 5.42734i 0.160113 + 0.277324i 0.934909 0.354887i \(-0.115481\pi\)
−0.774796 + 0.632211i \(0.782147\pi\)
\(384\) 1.64400 + 0.545231i 0.0838948 + 0.0278237i
\(385\) 0 0
\(386\) −9.76509 −0.497030
\(387\) 0.582863 4.96452i 0.0296286 0.252361i
\(388\) −1.42402 −0.0722934
\(389\) 10.8171 18.7357i 0.548448 0.949940i −0.449933 0.893062i \(-0.648552\pi\)
0.998381 0.0568774i \(-0.0181144\pi\)
\(390\) 9.88942 8.79628i 0.500770 0.445417i
\(391\) −0.810892 1.40451i −0.0410086 0.0710290i
\(392\) 0 0
\(393\) −4.11126 + 3.65682i −0.207386 + 0.184462i
\(394\) −9.12178 + 15.7994i −0.459549 + 0.795962i
\(395\) 13.3214 0.670273
\(396\) 4.37636 1.88510i 0.219920 0.0947299i
\(397\) −4.10617 −0.206083 −0.103041 0.994677i \(-0.532857\pi\)
−0.103041 + 0.994677i \(0.532857\pi\)
\(398\) −9.04944 + 15.6741i −0.453608 + 0.785671i
\(399\) 0 0
\(400\) 1.23855 + 2.14523i 0.0619275 + 0.107262i
\(401\) −8.37085 14.4987i −0.418021 0.724033i 0.577720 0.816235i \(-0.303943\pi\)
−0.995740 + 0.0922024i \(0.970609\pi\)
\(402\) 3.51671 + 17.0536i 0.175398 + 0.850558i
\(403\) −6.52359 + 11.2992i −0.324963 + 0.562853i
\(404\) 12.0334 0.598685
\(405\) −13.9065 3.31105i −0.691022 0.164527i
\(406\) 0 0
\(407\) −0.794182 + 1.37556i −0.0393661 + 0.0681842i
\(408\) −1.88874 9.15907i −0.0935064 0.453442i
\(409\) 4.38255 + 7.59079i 0.216703 + 0.375341i 0.953798 0.300449i \(-0.0971364\pi\)
−0.737095 + 0.675789i \(0.763803\pi\)
\(410\) −4.66690 8.08330i −0.230482 0.399206i
\(411\) 34.9567 + 11.5934i 1.72429 + 0.571859i
\(412\) 3.04944 5.28179i 0.150235 0.260215i
\(413\) 0 0
\(414\) 0.827603 0.356487i 0.0406744 0.0175204i
\(415\) −3.75781 −0.184464
\(416\) −2.40545 + 4.16635i −0.117937 + 0.204272i
\(417\) −16.8931 + 15.0258i −0.827257 + 0.735814i
\(418\) −5.63781 9.76497i −0.275754 0.477620i
\(419\) −0.210149 0.363988i −0.0102664 0.0177820i 0.860847 0.508865i \(-0.169935\pi\)
−0.871113 + 0.491083i \(0.836601\pi\)
\(420\) 0 0
\(421\) 3.28799 5.69497i 0.160247 0.277556i −0.774710 0.632316i \(-0.782104\pi\)
0.934957 + 0.354761i \(0.115438\pi\)
\(422\) 0.332415 0.0161817
\(423\) 0.932677 7.94406i 0.0453483 0.386253i
\(424\) 4.88874 0.237418
\(425\) 6.68725 11.5827i 0.324379 0.561841i
\(426\) 20.9127 + 6.93570i 1.01323 + 0.336036i
\(427\) 0 0
\(428\) −1.54325 2.67299i −0.0745959 0.129204i
\(429\) 2.67309 + 12.9626i 0.129058 + 0.625842i
\(430\) 1.32327 2.29197i 0.0638138 0.110529i
\(431\) −22.0879 −1.06394 −0.531968 0.846765i \(-0.678547\pi\)
−0.531968 + 0.846765i \(0.678547\pi\)
\(432\) 5.17673 0.448873i 0.249065 0.0215964i
\(433\) −9.43268 −0.453306 −0.226653 0.973976i \(-0.572778\pi\)
−0.226653 + 0.973976i \(0.572778\pi\)
\(434\) 0 0
\(435\) −4.59820 22.2981i −0.220467 1.06911i
\(436\) 1.14400 + 1.98146i 0.0547875 + 0.0948947i
\(437\) −1.06615 1.84663i −0.0510010 0.0883363i
\(438\) −26.3912 8.75264i −1.26102 0.418217i
\(439\) 15.6032 27.0256i 0.744701 1.28986i −0.205634 0.978629i \(-0.565926\pi\)
0.950334 0.311231i \(-0.100741\pi\)
\(440\) 2.52290 0.120275
\(441\) 0 0
\(442\) 25.9752 1.23552
\(443\) −6.52723 + 11.3055i −0.310118 + 0.537140i −0.978388 0.206779i \(-0.933702\pi\)
0.668270 + 0.743919i \(0.267035\pi\)
\(444\) −1.29418 + 1.15113i −0.0614192 + 0.0546301i
\(445\) 2.54944 + 4.41576i 0.120855 + 0.209327i
\(446\) −3.16621 5.48403i −0.149924 0.259676i
\(447\) 6.74110 5.99596i 0.318843 0.283599i
\(448\) 0 0
\(449\) −9.91706 −0.468015 −0.234008 0.972235i \(-0.575184\pi\)
−0.234008 + 0.972235i \(0.575184\pi\)
\(450\) 5.95853 + 4.44074i 0.280888 + 0.209338i
\(451\) 9.33379 0.439511
\(452\) −9.73236 + 16.8569i −0.457772 + 0.792884i
\(453\) 0.859646 + 0.285101i 0.0403897 + 0.0133952i
\(454\) −11.6545 20.1862i −0.546974 0.947386i
\(455\) 0 0
\(456\) −2.48329 12.0422i −0.116291 0.563930i
\(457\) 12.2615 21.2375i 0.573566 0.993446i −0.422629 0.906303i \(-0.638893\pi\)
0.996196 0.0871436i \(-0.0277739\pi\)
\(458\) 4.95420 0.231495
\(459\) −16.0741 22.9940i −0.750276 1.07327i
\(460\) 0.477100 0.0222449
\(461\) 1.75526 3.04020i 0.0817506 0.141596i −0.822251 0.569125i \(-0.807282\pi\)
0.904002 + 0.427528i \(0.140616\pi\)
\(462\) 0 0
\(463\) 8.69413 + 15.0587i 0.404050 + 0.699836i 0.994210 0.107451i \(-0.0342687\pi\)
−0.590160 + 0.807286i \(0.700935\pi\)
\(464\) 4.13781 + 7.16689i 0.192093 + 0.332715i
\(465\) 7.08177 + 2.34867i 0.328409 + 0.108917i
\(466\) 7.13781 12.3630i 0.330652 0.572707i
\(467\) −13.3979 −0.619980 −0.309990 0.950740i \(-0.600326\pi\)
−0.309990 + 0.950740i \(0.600326\pi\)
\(468\) −1.68292 + 14.3342i −0.0777929 + 0.662600i
\(469\) 0 0
\(470\) 2.11745 3.66754i 0.0976709 0.169171i
\(471\) 11.4716 10.2036i 0.528583 0.470155i
\(472\) 3.23855 + 5.60933i 0.149066 + 0.258190i
\(473\) 1.32327 + 2.29197i 0.0608441 + 0.105385i
\(474\) −10.8541 + 9.65436i −0.498547 + 0.443439i
\(475\) 8.79232 15.2287i 0.403419 0.698743i
\(476\) 0 0
\(477\) 13.4697 5.80205i 0.616737 0.265658i
\(478\) 4.97524 0.227562
\(479\) −10.4029 + 18.0183i −0.475321 + 0.823279i −0.999600 0.0282667i \(-0.991001\pi\)
0.524280 + 0.851546i \(0.324335\pi\)
\(480\) 2.61126 + 0.866025i 0.119187 + 0.0395285i
\(481\) −2.40545 4.16635i −0.109679 0.189969i
\(482\) −6.50000 11.2583i −0.296067 0.512803i
\(483\) 0 0
\(484\) 4.23855 7.34138i 0.192661 0.333699i
\(485\) −2.26186 −0.102706
\(486\) 13.7305 7.38061i 0.622828 0.334791i
\(487\) −32.4944 −1.47246 −0.736231 0.676730i \(-0.763397\pi\)
−0.736231 + 0.676730i \(0.763397\pi\)
\(488\) −2.23855 + 3.87728i −0.101334 + 0.175516i
\(489\) −7.68292 37.2569i −0.347434 1.68481i
\(490\) 0 0
\(491\) −9.66071 16.7328i −0.435982 0.755142i 0.561394 0.827549i \(-0.310265\pi\)
−0.997375 + 0.0724067i \(0.976932\pi\)
\(492\) 9.66071 + 3.20397i 0.435538 + 0.144446i
\(493\) 22.3411 38.6959i 1.00619 1.74277i
\(494\) 34.1520 1.53657
\(495\) 6.95125 2.99423i 0.312435 0.134581i
\(496\) −2.71201 −0.121773
\(497\) 0 0
\(498\) 3.06182 2.72338i 0.137204 0.122037i
\(499\) 5.57530 + 9.65670i 0.249585 + 0.432293i 0.963411 0.268030i \(-0.0863726\pi\)
−0.713826 + 0.700323i \(0.753039\pi\)
\(500\) 5.93818 + 10.2852i 0.265563 + 0.459969i
\(501\) −4.27128 + 3.79915i −0.190827 + 0.169733i
\(502\) 1.21634 2.10676i 0.0542878 0.0940293i
\(503\) −40.7651 −1.81763 −0.908813 0.417204i \(-0.863010\pi\)
−0.908813 + 0.417204i \(0.863010\pi\)
\(504\) 0 0
\(505\) 19.1135 0.850537
\(506\) −0.238550 + 0.413181i −0.0106048 + 0.0183681i
\(507\) −16.6778 5.53120i −0.740688 0.245649i
\(508\) 6.71998 + 11.6393i 0.298151 + 0.516413i
\(509\) −0.722528 1.25146i −0.0320255 0.0554698i 0.849568 0.527478i \(-0.176862\pi\)
−0.881594 + 0.472009i \(0.843529\pi\)
\(510\) −3.00000 14.5479i −0.132842 0.644194i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −21.1341 30.2323i −0.933093 1.33479i
\(514\) 0.987620 0.0435621
\(515\) 4.84362 8.38940i 0.213436 0.369681i
\(516\) 0.582863 + 2.82648i 0.0256591 + 0.124429i
\(517\) 2.11745 + 3.66754i 0.0931255 + 0.161298i
\(518\) 0 0
\(519\) −31.4127 10.4180i −1.37887 0.457301i
\(520\) −3.82072 + 6.61769i −0.167550 + 0.290205i
\(521\) −19.2843 −0.844859 −0.422430 0.906396i \(-0.638823\pi\)
−0.422430 + 0.906396i \(0.638823\pi\)
\(522\) 19.9065 + 14.8358i 0.871286 + 0.649346i
\(523\) 36.6908 1.60438 0.802189 0.597071i \(-0.203669\pi\)
0.802189 + 0.597071i \(0.203669\pi\)
\(524\) 1.58836 2.75113i 0.0693880 0.120184i
\(525\) 0 0
\(526\) 8.59269 + 14.8830i 0.374659 + 0.648929i
\(527\) 7.32141 + 12.6811i 0.318926 + 0.552396i
\(528\) −2.05563 + 1.82841i −0.0894599 + 0.0795713i
\(529\) 11.4549 19.8404i 0.498039 0.862628i
\(530\) 7.76509 0.337294
\(531\) 15.5803 + 11.6116i 0.676128 + 0.503900i
\(532\) 0 0
\(533\) −14.1353 + 24.4830i −0.612266 + 1.06048i
\(534\) −5.27747 1.75027i −0.228379 0.0757417i
\(535\) −2.45125 4.24568i −0.105977 0.183557i
\(536\) −5.02654 8.70623i −0.217114 0.376052i
\(537\) 5.62296 + 27.2675i 0.242648 + 1.17668i
\(538\) −11.4523 + 19.8360i −0.493745 + 0.855192i
\(539\) 0 0
\(540\) 8.22253 0.712974i 0.353841 0.0306815i
\(541\) 3.25085 0.139765 0.0698825 0.997555i \(-0.477738\pi\)
0.0698825 + 0.997555i \(0.477738\pi\)
\(542\) −7.00364 + 12.1307i −0.300832 + 0.521057i
\(543\) 2.81708 + 13.6609i 0.120893 + 0.586246i
\(544\) 2.69963 + 4.67589i 0.115746 + 0.200477i
\(545\) 1.81708 + 3.14728i 0.0778352 + 0.134815i
\(546\) 0 0
\(547\) −2.95853 + 5.12432i −0.126498 + 0.219100i −0.922317 0.386433i \(-0.873707\pi\)
0.795820 + 0.605534i \(0.207040\pi\)
\(548\) −21.2632 −0.908320
\(549\) −1.56615 + 13.3397i −0.0668418 + 0.569324i
\(550\) −3.93454 −0.167769
\(551\) 29.3738 50.8769i 1.25137 2.16743i
\(552\) −0.388736 + 0.345766i −0.0165457 + 0.0147168i
\(553\) 0 0
\(554\) 14.1476 + 24.5044i 0.601076 + 1.04109i
\(555\) −2.05563 + 1.82841i −0.0872567 + 0.0776116i
\(556\) 6.52654 11.3043i 0.276787 0.479409i
\(557\) −25.6080 −1.08505 −0.542523 0.840041i \(-0.682531\pi\)
−0.542523 + 0.840041i \(0.682531\pi\)
\(558\) −7.47229 + 3.21866i −0.316327 + 0.136257i
\(559\) −8.01594 −0.339038
\(560\) 0 0
\(561\) 14.0989 + 4.67589i 0.595255 + 0.197416i
\(562\) 8.79782 + 15.2383i 0.371114 + 0.642788i
\(563\) 23.3189 + 40.3895i 0.982773 + 1.70221i 0.651443 + 0.758698i \(0.274164\pi\)
0.331330 + 0.943515i \(0.392503\pi\)
\(564\) 0.932677 + 4.52284i 0.0392728 + 0.190446i
\(565\) −15.4585 + 26.7750i −0.650345 + 1.12643i
\(566\) 18.5229 0.778576
\(567\) 0 0
\(568\) −12.7207 −0.533747
\(569\) −15.5989 + 27.0181i −0.653939 + 1.13266i 0.328219 + 0.944602i \(0.393551\pi\)
−0.982159 + 0.188054i \(0.939782\pi\)
\(570\) −3.94437 19.1275i −0.165211 0.801162i
\(571\) 7.83812 + 13.5760i 0.328015 + 0.568139i 0.982118 0.188267i \(-0.0602869\pi\)
−0.654103 + 0.756406i \(0.726954\pi\)
\(572\) −3.82072 6.61769i −0.159752 0.276699i
\(573\) 39.3948 + 13.0653i 1.64574 + 0.545811i
\(574\) 0 0
\(575\) −0.744051 −0.0310291
\(576\) −2.75526 + 1.18682i −0.114803 + 0.0494508i
\(577\) −13.9913 −0.582467 −0.291234 0.956652i \(-0.594066\pi\)
−0.291234 + 0.956652i \(0.594066\pi\)
\(578\) 6.07598 10.5239i 0.252728 0.437737i
\(579\) 12.6378 11.2409i 0.525209 0.467154i
\(580\) 6.57234 + 11.3836i 0.272902 + 0.472680i
\(581\) 0 0
\(582\) 1.84294 1.63922i 0.0763921 0.0679480i
\(583\) −3.88255 + 6.72477i −0.160799 + 0.278511i
\(584\) 16.0531 0.664281
\(585\) −2.67309 + 22.7680i −0.110519 + 0.941339i
\(586\) −14.0851 −0.581851
\(587\) 1.44801 2.50803i 0.0597658 0.103517i −0.834594 0.550865i \(-0.814298\pi\)
0.894360 + 0.447348i \(0.147631\pi\)
\(588\) 0 0
\(589\) 9.62612 + 16.6729i 0.396637 + 0.686996i
\(590\) 5.14400 + 8.90966i 0.211775 + 0.366805i
\(591\) −6.38186 30.9476i −0.262515 1.27302i
\(592\) 0.500000 0.866025i 0.0205499 0.0355934i
\(593\) 4.08788 0.167869 0.0839346 0.996471i \(-0.473251\pi\)
0.0839346 + 0.996471i \(0.473251\pi\)
\(594\) −3.49381 + 7.47741i −0.143353 + 0.306802i
\(595\) 0 0
\(596\) −2.60439 + 4.51093i −0.106680 + 0.184775i
\(597\) −6.33124 30.7022i −0.259121 1.25656i
\(598\) −0.722528 1.25146i −0.0295464 0.0511758i
\(599\) 9.88255 + 17.1171i 0.403790 + 0.699385i 0.994180 0.107734i \(-0.0343593\pi\)
−0.590390 + 0.807118i \(0.701026\pi\)
\(600\) −4.07234 1.35059i −0.166253 0.0551377i
\(601\) −13.4320 + 23.2649i −0.547902 + 0.948994i 0.450516 + 0.892768i \(0.351240\pi\)
−0.998418 + 0.0562261i \(0.982093\pi\)
\(602\) 0 0
\(603\) −24.1822 18.0223i −0.984773 0.733926i
\(604\) −0.522900 −0.0212765
\(605\) 6.73236 11.6608i 0.273709 0.474079i
\(606\) −15.5734 + 13.8520i −0.632628 + 0.562699i
\(607\) 7.62110 + 13.2001i 0.309331 + 0.535777i 0.978216 0.207589i \(-0.0665617\pi\)
−0.668885 + 0.743366i \(0.733228\pi\)
\(608\) 3.54944 + 6.14781i 0.143949 + 0.249327i
\(609\) 0 0
\(610\) −3.55563 + 6.15854i −0.143963 + 0.249352i
\(611\) −12.8268 −0.518918
\(612\) 12.9876 + 9.67933i 0.524993 + 0.391264i
\(613\) 2.72067 0.109887 0.0549434 0.998489i \(-0.482502\pi\)
0.0549434 + 0.998489i \(0.482502\pi\)
\(614\) −2.92766 + 5.07085i −0.118151 + 0.204643i
\(615\) 15.3447 + 5.08907i 0.618759 + 0.205211i
\(616\) 0 0
\(617\) −9.21812 15.9663i −0.371108 0.642777i 0.618629 0.785684i \(-0.287689\pi\)
−0.989736 + 0.142906i \(0.954355\pi\)
\(618\) 2.13348 + 10.3459i 0.0858210 + 0.416173i
\(619\) −0.0537728 + 0.0931373i −0.00216131 + 0.00374350i −0.867104 0.498127i \(-0.834021\pi\)
0.864943 + 0.501871i \(0.167355\pi\)
\(620\) −4.30766 −0.173000
\(621\) −0.660706 + 1.41403i −0.0265132 + 0.0567433i
\(622\) −0.810892 −0.0325138
\(623\) 0 0
\(624\) −1.68292 8.16100i −0.0673706 0.326701i
\(625\) 3.23924 + 5.61053i 0.129570 + 0.224421i
\(626\) 5.28799 + 9.15907i 0.211351 + 0.366070i
\(627\) 18.5371 + 6.14781i 0.740299 + 0.245520i
\(628\) −4.43199 + 7.67643i −0.176856 + 0.306323i
\(629\) −5.39926 −0.215282
\(630\) 0 0
\(631\) 35.7266 1.42225 0.711126 0.703064i \(-0.248185\pi\)
0.711126 + 0.703064i \(0.248185\pi\)
\(632\) 4.19344 7.26325i 0.166806 0.288916i
\(633\) −0.430206 + 0.382652i −0.0170991 + 0.0152090i
\(634\) 6.09820 + 10.5624i 0.242190 + 0.419486i
\(635\) 10.6738 + 18.4875i 0.423576 + 0.733655i
\(636\) −6.32691 + 5.62755i −0.250878 + 0.223147i
\(637\) 0 0
\(638\) −13.1447 −0.520403
\(639\) −35.0488 + 15.0971i −1.38651 + 0.597234i
\(640\) −1.58836 −0.0627856
\(641\) −8.65638 + 14.9933i −0.341906 + 0.592199i −0.984787 0.173767i \(-0.944406\pi\)
0.642880 + 0.765967i \(0.277739\pi\)
\(642\) 5.07420 + 1.68286i 0.200263 + 0.0664171i
\(643\) 14.4821 + 25.0838i 0.571119 + 0.989207i 0.996451 + 0.0841700i \(0.0268239\pi\)
−0.425332 + 0.905037i \(0.639843\pi\)
\(644\) 0 0
\(645\) 0.925798 + 4.48949i 0.0364533 + 0.176773i
\(646\) 19.1643 33.1936i 0.754011 1.30599i
\(647\) −2.55632 −0.100499 −0.0502497 0.998737i \(-0.516002\pi\)
−0.0502497 + 0.998737i \(0.516002\pi\)
\(648\) −6.18292 + 6.53999i −0.242888 + 0.256915i
\(649\) −10.2880 −0.403839
\(650\) 5.95853 10.3205i 0.233713 0.404802i
\(651\) 0 0
\(652\) 10.9814 + 19.0204i 0.430066 + 0.744896i
\(653\) −14.9883 25.9605i −0.586538 1.01591i −0.994682 0.102996i \(-0.967157\pi\)
0.408144 0.912918i \(-0.366176\pi\)
\(654\) −3.76145 1.24748i −0.147084 0.0487805i
\(655\) 2.52290 4.36979i 0.0985779 0.170742i
\(656\) −5.87636 −0.229433
\(657\) 44.2304 19.0521i 1.72559 0.743294i
\(658\) 0 0
\(659\) −7.63162 + 13.2183i −0.297286 + 0.514914i −0.975514 0.219937i \(-0.929415\pi\)
0.678228 + 0.734851i \(0.262748\pi\)
\(660\) −3.26509 + 2.90418i −0.127094 + 0.113045i
\(661\) 13.6261 + 23.6011i 0.529994 + 0.917977i 0.999388 + 0.0349881i \(0.0111393\pi\)
−0.469393 + 0.882989i \(0.655527\pi\)
\(662\) −7.83310 13.5673i −0.304442 0.527309i
\(663\) −33.6167 + 29.9008i −1.30556 + 1.16125i
\(664\) −1.18292 + 2.04887i −0.0459061 + 0.0795117i
\(665\) 0 0
\(666\) 0.349814 2.97954i 0.0135550 0.115455i
\(667\) −2.48576 −0.0962491
\(668\) 1.65019 2.85821i 0.0638476 0.110587i
\(669\) 10.4105 + 3.45263i 0.402492 + 0.133486i
\(670\) −7.98398 13.8287i −0.308448 0.534248i
\(671\) −3.55563 6.15854i −0.137264 0.237748i
\(672\) 0 0
\(673\) 23.2280 40.2320i 0.895372 1.55083i 0.0620280 0.998074i \(-0.480243\pi\)
0.833344 0.552755i \(-0.186423\pi\)
\(674\) −8.42402 −0.324481
\(675\) −12.8233 + 1.11190i −0.493568 + 0.0427972i
\(676\) 10.1447 0.390180
\(677\) −2.54944 + 4.41576i −0.0979830 + 0.169712i −0.910850 0.412738i \(-0.864572\pi\)
0.812867 + 0.582450i \(0.197906\pi\)
\(678\) −6.80903 33.0191i −0.261499 1.26809i
\(679\) 0 0
\(680\) 4.28799 + 7.42702i 0.164437 + 0.284813i
\(681\) 38.3200 + 12.7088i 1.46842 + 0.487003i
\(682\) 2.15383 3.73054i 0.0824743 0.142850i
\(683\) 15.5439 0.594772 0.297386 0.954757i \(-0.403885\pi\)
0.297386 + 0.954757i \(0.403885\pi\)
\(684\) 17.0760 + 12.7263i 0.652917 + 0.486601i
\(685\) −33.7738 −1.29043
\(686\) 0 0
\(687\) −6.41164 + 5.70291i −0.244619 + 0.217580i
\(688\) −0.833104 1.44298i −0.0317618 0.0550130i
\(689\) −11.7596 20.3682i −0.448005 0.775967i
\(690\) −0.617454 + 0.549202i −0.0235061 + 0.0209078i
\(691\) −11.6483 + 20.1755i −0.443123 + 0.767512i −0.997919 0.0644744i \(-0.979463\pi\)
0.554796 + 0.831986i \(0.312796\pi\)
\(692\) 19.1075 0.726360
\(693\) 0 0
\(694\) −0.567323 −0.0215353
\(695\) 10.3665 17.9553i 0.393225 0.681085i
\(696\) −13.6051 4.51212i −0.515699 0.171032i
\(697\) 15.8640 + 27.4772i 0.600891 + 1.04077i
\(698\) 0.00364189 + 0.00630794i 0.000137848 + 0.000238759i
\(699\) 4.99381 + 24.2165i 0.188883 + 0.915954i
\(700\) 0 0
\(701\) −45.6464 −1.72404 −0.862020 0.506874i \(-0.830801\pi\)
−0.862020 + 0.506874i \(0.830801\pi\)
\(702\) −14.3225 20.4883i −0.540568 0.773283i
\(703\) −7.09888 −0.267739
\(704\) 0.794182 1.37556i 0.0299319 0.0518435i
\(705\) 1.48143 + 7.18392i 0.0557939 + 0.270562i
\(706\) 3.32691 + 5.76238i 0.125210 + 0.216870i
\(707\) 0 0
\(708\) −10.6483 3.53152i −0.400189 0.132723i
\(709\) −9.00069 + 15.5897i −0.338028 + 0.585482i −0.984062 0.177827i \(-0.943093\pi\)
0.646034 + 0.763309i \(0.276427\pi\)
\(710\) −20.2051 −0.758282
\(711\) 2.93385 24.9890i 0.110028 0.937160i
\(712\) 3.21015 0.120305
\(713\) 0.407305 0.705474i 0.0152537 0.0264202i
\(714\) 0 0
\(715\) −6.06870 10.5113i −0.226957 0.393100i
\(716\) −8.03706 13.9206i −0.300359 0.520237i
\(717\) −6.43887 + 5.72713i −0.240464 + 0.213884i
\(718\) 0.398568 0.690339i 0.0148744 0.0257632i
\(719\) −36.8777 −1.37531 −0.687654 0.726039i \(-0.741359\pi\)
−0.687654 + 0.726039i \(0.741359\pi\)
\(720\) −4.37636 + 1.88510i −0.163097 + 0.0702536i
\(721\) 0 0
\(722\) 15.6971 27.1881i 0.584185 1.01184i
\(723\) 21.3719 + 7.08800i 0.794831 + 0.263606i
\(724\) −4.02654 6.97418i −0.149645 0.259193i
\(725\) −10.2498 17.7531i −0.380666 0.659334i
\(726\) 2.96541 + 14.3802i 0.110057 + 0.533699i
\(727\) 15.2429 26.4014i 0.565327 0.979175i −0.431692 0.902021i \(-0.642083\pi\)
0.997019 0.0771543i \(-0.0245834\pi\)
\(728\) 0 0
\(729\) −9.27375 + 25.3574i −0.343472 + 0.939163i
\(730\) 25.4981 0.943729
\(731\) −4.49814 + 7.79101i −0.166370 + 0.288161i
\(732\) −1.56615 7.59476i −0.0578867 0.280711i
\(733\) −3.07530 5.32657i −0.113589 0.196741i 0.803626 0.595135i \(-0.202901\pi\)
−0.917215 + 0.398393i \(0.869568\pi\)
\(734\) −7.71634 13.3651i −0.284815 0.493314i
\(735\) 0 0
\(736\) 0.150186 0.260130i 0.00553593 0.00958851i
\(737\) 15.9680 0.588187
\(738\) −16.1909 + 6.97418i −0.595995 + 0.256723i
\(739\) 40.7824 1.50021 0.750103 0.661321i \(-0.230004\pi\)
0.750103 + 0.661321i \(0.230004\pi\)
\(740\) 0.794182 1.37556i 0.0291947 0.0505667i
\(741\) −44.1989 + 39.3132i −1.62369 + 1.44421i
\(742\) 0 0
\(743\) 7.25271 + 12.5621i 0.266076 + 0.460858i 0.967845 0.251547i \(-0.0809394\pi\)
−0.701769 + 0.712405i \(0.747606\pi\)
\(744\) 3.50983 3.12186i 0.128677 0.114453i
\(745\) −4.13671 + 7.16500i −0.151557 + 0.262505i
\(746\) −10.2422 −0.374993
\(747\) −0.827603 + 7.04909i −0.0302804 + 0.257913i
\(748\) −8.57598 −0.313569
\(749\) 0 0
\(750\) −19.5247 6.47536i −0.712941 0.236447i
\(751\) −2.09455 3.62787i −0.0764314 0.132383i 0.825276 0.564729i \(-0.191019\pi\)
−0.901708 + 0.432346i \(0.857686\pi\)
\(752\) −1.33310 2.30900i −0.0486133 0.0842007i
\(753\) 0.850985 + 4.12669i 0.0310116 + 0.150385i
\(754\) 19.9065 34.4791i 0.724953 1.25566i
\(755\) −0.830556 −0.0302270
\(756\) 0 0
\(757\) 2.38688 0.0867525 0.0433763 0.999059i \(-0.486189\pi\)
0.0433763 + 0.999059i \(0.486189\pi\)
\(758\) 12.5043 21.6581i 0.454178 0.786659i
\(759\) −0.166896 0.809332i −0.00605795 0.0293769i
\(760\) 5.63781 + 9.76497i 0.204505 + 0.354213i
\(761\) −1.81708 3.14728i −0.0658692 0.114089i 0.831210 0.555959i \(-0.187649\pi\)
−0.897079 + 0.441870i \(0.854315\pi\)
\(762\) −22.0952 7.32788i −0.800426 0.265461i
\(763\) 0 0
\(764\) −23.9629 −0.866946
\(765\) 20.6291 + 15.3743i 0.745846 + 0.555859i
\(766\) 6.26695 0.226434
\(767\) 15.5803 26.9859i 0.562573 0.974404i
\(768\) 1.29418 1.15113i 0.0466998 0.0415377i
\(769\) −19.9672 34.5842i −0.720035 1.24714i −0.960985 0.276600i \(-0.910792\pi\)
0.240950 0.970538i \(-0.422541\pi\)
\(770\) 0 0
\(771\) −1.27816 + 1.13688i −0.0460318 + 0.0409436i
\(772\) −4.88255 + 8.45682i −0.175727 + 0.304368i
\(773\) −36.1396 −1.29985 −0.649925