Properties

Label 882.2.h.p.79.1
Level $882$
Weight $2$
Character 882.79
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(67,882)]
 
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([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.04280545828\)
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 79.1
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 882.79
Dual form 882.2.h.p.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.29418 + 1.15113i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.58836 q^{5} +(-1.64400 - 0.545231i) q^{6} -1.00000 q^{8} +(0.349814 - 2.97954i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.29418 + 1.15113i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.58836 q^{5} +(-1.64400 - 0.545231i) q^{6} -1.00000 q^{8} +(0.349814 - 2.97954i) q^{9} +(-0.794182 - 1.37556i) q^{10} -1.58836 q^{11} +(-0.349814 - 1.69636i) q^{12} +(-2.40545 - 4.16635i) q^{13} +(2.05563 - 1.82841i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.69963 + 4.67589i) q^{17} +(2.75526 - 1.18682i) q^{18} +(3.54944 - 6.14781i) q^{19} +(0.794182 - 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} +0.300372 q^{23} +(1.29418 - 1.15113i) q^{24} -2.47710 q^{25} +(2.40545 - 4.16635i) q^{26} +(2.97710 + 4.25874i) q^{27} +(4.13781 - 7.16689i) q^{29} +(2.61126 + 0.866025i) q^{30} +(-1.35600 + 2.34867i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.05563 - 1.82841i) q^{33} +(-2.69963 + 4.67589i) q^{34} +(2.40545 + 1.79272i) q^{36} +(0.500000 - 0.866025i) q^{37} +7.09888 q^{38} +(7.90909 + 2.62305i) q^{39} +1.58836 q^{40} +(-2.93818 - 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} +(0.794182 - 1.37556i) q^{44} +(-0.555632 + 4.73259i) q^{45} +(0.150186 + 0.260130i) q^{46} +(1.33310 + 2.30900i) q^{47} +(1.64400 + 0.545231i) q^{48} +(-1.23855 - 2.14523i) q^{50} +(-8.87636 - 2.94384i) q^{51} +4.81089 q^{52} +(2.44437 + 4.23377i) q^{53} +(-2.19963 + 4.70761i) q^{54} +2.52290 q^{55} +(2.48329 + 12.0422i) q^{57} +8.27561 q^{58} +(3.23855 - 5.60933i) q^{59} +(0.555632 + 2.69443i) q^{60} +(-2.23855 - 3.87728i) q^{61} -2.71201 q^{62} +1.00000 q^{64} +(3.82072 + 6.61769i) q^{65} +(2.61126 + 0.866025i) q^{66} +(5.02654 - 8.70623i) q^{67} -5.39926 q^{68} +(-0.388736 + 0.345766i) q^{69} +12.7207 q^{71} +(-0.349814 + 2.97954i) q^{72} +(-8.02654 - 13.9024i) q^{73} +1.00000 q^{74} +(3.20582 - 2.85146i) q^{75} +(3.54944 + 6.14781i) q^{76} +(1.68292 + 8.16100i) q^{78} +(-4.19344 - 7.26325i) q^{79} +(0.794182 + 1.37556i) q^{80} +(-8.75526 - 2.08457i) q^{81} +(2.93818 - 5.08907i) q^{82} +(-1.18292 + 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} -1.66621 q^{86} +(2.89493 + 14.0384i) q^{87} +1.58836 q^{88} +(-1.60507 + 2.78007i) q^{89} +(-4.37636 + 1.88510i) q^{90} +(-0.150186 + 0.260130i) q^{92} +(-0.948699 - 4.60054i) q^{93} +(-1.33310 + 2.30900i) q^{94} +(-5.63781 + 9.76497i) q^{95} +(0.349814 + 1.69636i) q^{96} +(-0.712008 + 1.23323i) q^{97} +(-0.555632 + 4.73259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23} + 2 q^{24} - 4 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} + 15 q^{30} - 20 q^{31} + 3 q^{32} + 12 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} + 6 q^{38} + q^{39} - 2 q^{40} - 6 q^{43} - q^{44} - 3 q^{45} + 7 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} - 18 q^{51} + 16 q^{52} + 15 q^{53} - q^{54} + 26 q^{55} + 22 q^{57} - 10 q^{58} + 14 q^{59} + 3 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} + 15 q^{66} + q^{67} - 8 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} - 19 q^{73} + 6 q^{74} + 25 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} - q^{80} - 40 q^{81} - 2 q^{83} - 2 q^{85} - 12 q^{86} + 36 q^{87} - 2 q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} + 37 q^{93} - 9 q^{94} - 4 q^{95} - 4 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −1.29418 + 1.15113i −0.747196 + 0.664603i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.58836 −0.710338 −0.355169 0.934802i \(-0.615577\pi\)
−0.355169 + 0.934802i \(0.615577\pi\)
\(6\) −1.64400 0.545231i −0.671159 0.222590i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0.349814 2.97954i 0.116605 0.993178i
\(10\) −0.794182 1.37556i −0.251142 0.434991i
\(11\) −1.58836 −0.478910 −0.239455 0.970907i \(-0.576969\pi\)
−0.239455 + 0.970907i \(0.576969\pi\)
\(12\) −0.349814 1.69636i −0.100983 0.489696i
\(13\) −2.40545 4.16635i −0.667151 1.15554i −0.978697 0.205308i \(-0.934180\pi\)
0.311547 0.950231i \(-0.399153\pi\)
\(14\) 0 0
\(15\) 2.05563 1.82841i 0.530762 0.472093i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.69963 + 4.67589i 0.654756 + 1.13407i 0.981955 + 0.189115i \(0.0605620\pi\)
−0.327199 + 0.944955i \(0.606105\pi\)
\(18\) 2.75526 1.18682i 0.649421 0.279736i
\(19\) 3.54944 6.14781i 0.814298 1.41041i −0.0955331 0.995426i \(-0.530456\pi\)
0.909831 0.414979i \(-0.136211\pi\)
\(20\) 0.794182 1.37556i 0.177584 0.307585i
\(21\) 0 0
\(22\) −0.794182 1.37556i −0.169320 0.293271i
\(23\) 0.300372 0.0626319 0.0313159 0.999510i \(-0.490030\pi\)
0.0313159 + 0.999510i \(0.490030\pi\)
\(24\) 1.29418 1.15113i 0.264174 0.234973i
\(25\) −2.47710 −0.495420
\(26\) 2.40545 4.16635i 0.471747 0.817089i
\(27\) 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 \(-0.112266\pi\)
\(30\) 2.61126 + 0.866025i 0.476749 + 0.158114i
\(31\) −1.35600 + 2.34867i −0.243545 + 0.421833i −0.961722 0.274028i \(-0.911644\pi\)
0.718176 + 0.695861i \(0.244977\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 2.05563 1.82841i 0.357840 0.318285i
\(34\) −2.69963 + 4.67589i −0.462982 + 0.801909i
\(35\) 0 0
\(36\) 2.40545 + 1.79272i 0.400908 + 0.298786i
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 7.09888 1.15159
\(39\) 7.90909 + 2.62305i 1.26647 + 0.420024i
\(40\) 1.58836 0.251142
\(41\) −2.93818 5.08907i −0.458866 0.794780i 0.540035 0.841643i \(-0.318411\pi\)
−0.998901 + 0.0468628i \(0.985078\pi\)
\(42\) 0 0
\(43\) −0.833104 + 1.44298i −0.127047 + 0.220052i −0.922531 0.385922i \(-0.873883\pi\)
0.795484 + 0.605974i \(0.207217\pi\)
\(44\) 0.794182 1.37556i 0.119727 0.207374i
\(45\) −0.555632 + 4.73259i −0.0828287 + 0.705492i
\(46\) 0.150186 + 0.260130i 0.0221437 + 0.0383540i
\(47\) 1.33310 + 2.30900i 0.194453 + 0.336803i 0.946721 0.322055i \(-0.104373\pi\)
−0.752268 + 0.658857i \(0.771040\pi\)
\(48\) 1.64400 + 0.545231i 0.237290 + 0.0786973i
\(49\) 0 0
\(50\) −1.23855 2.14523i −0.175157 0.303382i
\(51\) −8.87636 2.94384i −1.24294 0.412220i
\(52\) 4.81089 0.667151
\(53\) 2.44437 + 4.23377i 0.335760 + 0.581553i 0.983630 0.180197i \(-0.0576736\pi\)
−0.647871 + 0.761750i \(0.724340\pi\)
\(54\) −2.19963 + 4.70761i −0.299331 + 0.640625i
\(55\) 2.52290 0.340188
\(56\) 0 0
\(57\) 2.48329 + 12.0422i 0.328920 + 1.59503i
\(58\) 8.27561 1.08664
\(59\) 3.23855 5.60933i 0.421623 0.730273i −0.574475 0.818522i \(-0.694794\pi\)
0.996098 + 0.0882491i \(0.0281271\pi\)
\(60\) 0.555632 + 2.69443i 0.0717318 + 0.347850i
\(61\) −2.23855 3.87728i −0.286617 0.496435i 0.686383 0.727240i \(-0.259197\pi\)
−0.973000 + 0.230805i \(0.925864\pi\)
\(62\) −2.71201 −0.344425
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.82072 + 6.61769i 0.473902 + 0.820823i
\(66\) 2.61126 + 0.866025i 0.321424 + 0.106600i
\(67\) 5.02654 8.70623i 0.614090 1.06363i −0.376454 0.926435i \(-0.622857\pi\)
0.990543 0.137199i \(-0.0438101\pi\)
\(68\) −5.39926 −0.654756
\(69\) −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 \(0.227718\pi\)
\(72\) −0.349814 + 2.97954i −0.0412260 + 0.351142i
\(73\) −8.02654 13.9024i −0.939436 1.62715i −0.766527 0.642213i \(-0.778017\pi\)
−0.172909 0.984938i \(-0.555317\pi\)
\(74\) 1.00000 0.116248
\(75\) 3.20582 2.85146i 0.370176 0.329258i
\(76\) 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 0.527681 0.849443i \(-0.323062\pi\)
−0.999479 + 0.0322635i \(0.989728\pi\)
\(80\) 0.794182 + 1.37556i 0.0887922 + 0.153793i
\(81\) −8.75526 2.08457i −0.972807 0.231619i
\(82\) 2.93818 5.08907i 0.324467 0.561994i
\(83\) −1.18292 + 2.04887i −0.129842 + 0.224893i −0.923615 0.383321i \(-0.874780\pi\)
0.793773 + 0.608214i \(0.208114\pi\)
\(84\) 0 0
\(85\) −4.28799 7.42702i −0.465098 0.805573i
\(86\) −1.66621 −0.179672
\(87\) 2.89493 + 14.0384i 0.310369 + 1.50507i
\(88\) 1.58836 0.169320
\(89\) −1.60507 + 2.78007i −0.170138 + 0.294687i −0.938468 0.345367i \(-0.887755\pi\)
0.768330 + 0.640054i \(0.221088\pi\)
\(90\) −4.37636 + 1.88510i −0.461308 + 0.198707i
\(91\) 0 0
\(92\) −0.150186 + 0.260130i −0.0156580 + 0.0271204i
\(93\) −0.948699 4.60054i −0.0983755 0.477053i
\(94\) −1.33310 + 2.30900i −0.137499 + 0.238156i
\(95\) −5.63781 + 9.76497i −0.578427 + 1.00186i
\(96\) 0.349814 + 1.69636i 0.0357027 + 0.173134i
\(97\) −0.712008 + 1.23323i −0.0722934 + 0.125216i −0.899906 0.436084i \(-0.856365\pi\)
0.827613 + 0.561300i \(0.189698\pi\)
\(98\) 0 0
\(99\) −0.555632 + 4.73259i −0.0558431 + 0.475643i
\(100\) 1.23855 2.14523i 0.123855 0.214523i
\(101\) −12.0334 −1.19737 −0.598685 0.800985i \(-0.704310\pi\)
−0.598685 + 0.800985i \(0.704310\pi\)
\(102\) −1.88874 9.15907i −0.187013 0.906883i
\(103\) 6.09888 0.600941 0.300470 0.953791i \(-0.402856\pi\)
0.300470 + 0.953791i \(0.402856\pi\)
\(104\) 2.40545 + 4.16635i 0.235873 + 0.408545i
\(105\) 0 0
\(106\) −2.44437 + 4.23377i −0.237418 + 0.411220i
\(107\) −1.54325 + 2.67299i −0.149192 + 0.258408i −0.930929 0.365200i \(-0.881001\pi\)
0.781737 + 0.623608i \(0.214334\pi\)
\(108\) −5.17673 + 0.448873i −0.498131 + 0.0431929i
\(109\) 1.14400 + 1.98146i 0.109575 + 0.189789i 0.915598 0.402095i \(-0.131718\pi\)
−0.806023 + 0.591884i \(0.798384\pi\)
\(110\) 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 \(-0.534906\pi\)
\(114\) −9.18725 + 8.17172i −0.860465 + 0.765351i
\(115\) −0.477100 −0.0444898
\(116\) 4.13781 + 7.16689i 0.384186 + 0.665429i
\(117\) −13.2553 + 5.70966i −1.22545 + 0.527858i
\(118\) 6.47710 0.596265
\(119\) 0 0
\(120\) −2.05563 + 1.82841i −0.187653 + 0.166910i
\(121\) −8.47710 −0.770645
\(122\) 2.23855 3.87728i 0.202669 0.351033i
\(123\) 9.66071 + 3.20397i 0.871077 + 0.288892i
\(124\) −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
\(129\) −0.582863 2.82648i −0.0513182 0.248858i
\(130\) −3.82072 + 6.61769i −0.335100 + 0.580410i
\(131\) 3.17673 0.277552 0.138776 0.990324i \(-0.455683\pi\)
0.138776 + 0.990324i \(0.455683\pi\)
\(132\) 0.555632 + 2.69443i 0.0483616 + 0.234520i
\(133\) 0 0
\(134\) 10.0531 0.868454
\(135\) −4.72872 6.76443i −0.406983 0.582190i
\(136\) −2.69963 4.67589i −0.231491 0.400955i
\(137\) −21.2632 −1.81664 −0.908320 0.418275i \(-0.862635\pi\)
−0.908320 + 0.418275i \(0.862635\pi\)
\(138\) −0.493810 0.163772i −0.0420359 0.0139412i
\(139\) −6.52654 11.3043i −0.553574 0.958818i −0.998013 0.0630092i \(-0.979930\pi\)
0.444439 0.895809i \(-0.353403\pi\)
\(140\) 0 0
\(141\) −4.38323 1.45370i −0.369135 0.122424i
\(142\) 6.36033 + 11.0164i 0.533747 + 0.924478i
\(143\) 3.82072 + 6.61769i 0.319505 + 0.553399i
\(144\) −2.75526 + 1.18682i −0.229605 + 0.0989016i
\(145\) −6.57234 + 11.3836i −0.545803 + 0.945359i
\(146\) 8.02654 13.9024i 0.664281 1.15057i
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 5.20877 0.426719 0.213360 0.976974i \(-0.431559\pi\)
0.213360 + 0.976974i \(0.431559\pi\)
\(150\) 4.07234 + 1.35059i 0.332505 + 0.110275i
\(151\) −0.522900 −0.0425530 −0.0212765 0.999774i \(-0.506773\pi\)
−0.0212765 + 0.999774i \(0.506773\pi\)
\(152\) −3.54944 + 6.14781i −0.287898 + 0.498654i
\(153\) 14.8764 6.40794i 1.20268 0.518052i
\(154\) 0 0
\(155\) 2.15383 3.73054i 0.173000 0.299644i
\(156\) −6.22617 + 5.53795i −0.498493 + 0.443391i
\(157\) 4.43199 7.67643i 0.353711 0.612646i −0.633185 0.774000i \(-0.718253\pi\)
0.986897 + 0.161354i \(0.0515862\pi\)
\(158\) 4.19344 7.26325i 0.333612 0.577833i
\(159\) −8.03706 2.66549i −0.637381 0.211387i
\(160\) −0.794182 + 1.37556i −0.0627856 + 0.108748i
\(161\) 0 0
\(162\) −2.57234 8.62456i −0.202102 0.677610i
\(163\) 10.9814 19.0204i 0.860132 1.48979i −0.0116689 0.999932i \(-0.503714\pi\)
0.871801 0.489860i \(-0.162952\pi\)
\(164\) 5.87636 0.458866
\(165\) −3.26509 + 2.90418i −0.254187 + 0.226090i
\(166\) −2.36584 −0.183624
\(167\) −1.65019 2.85821i −0.127695 0.221175i 0.795088 0.606494i \(-0.207425\pi\)
−0.922783 + 0.385319i \(0.874091\pi\)
\(168\) 0 0
\(169\) −5.07234 + 8.78555i −0.390180 + 0.675812i
\(170\) 4.28799 7.42702i 0.328874 0.569626i
\(171\) −17.0760 12.7263i −1.30583 0.973203i
\(172\) −0.833104 1.44298i −0.0635236 0.110026i
\(173\) 9.55377 + 16.5476i 0.726360 + 1.25809i 0.958412 + 0.285389i \(0.0921227\pi\)
−0.232052 + 0.972703i \(0.574544\pi\)
\(174\) −10.7101 + 9.52628i −0.811934 + 0.722185i
\(175\) 0 0
\(176\) 0.794182 + 1.37556i 0.0598637 + 0.103687i
\(177\) 2.26578 + 10.9875i 0.170307 + 0.825870i
\(178\) −3.21015 −0.240611
\(179\) −8.03706 13.9206i −0.600718 1.04047i −0.992712 0.120507i \(-0.961548\pi\)
0.391994 0.919968i \(-0.371785\pi\)
\(180\) −3.82072 2.84748i −0.284780 0.212239i
\(181\) −8.05308 −0.598581 −0.299291 0.954162i \(-0.596750\pi\)
−0.299291 + 0.954162i \(0.596750\pi\)
\(182\) 0 0
\(183\) 7.36033 + 2.44105i 0.544092 + 0.180448i
\(184\) −0.300372 −0.0221437
\(185\) −0.794182 + 1.37556i −0.0583894 + 0.101133i
\(186\) 3.50983 3.12186i 0.257353 0.228906i
\(187\) −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 0.865102 + 0.501596i \(0.167254\pi\)
0.00184390 + 0.999998i \(0.499413\pi\)
\(192\) −1.29418 + 1.15113i −0.0933995 + 0.0830754i
\(193\) −4.88255 + 8.45682i −0.351453 + 0.608735i −0.986504 0.163735i \(-0.947646\pi\)
0.635051 + 0.772470i \(0.280979\pi\)
\(194\) −1.42402 −0.102238
\(195\) −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 \(0.725189\pi\)
\(198\) −4.37636 + 1.88510i −0.311014 + 0.133968i
\(199\) −9.04944 15.6741i −0.641498 1.11111i −0.985098 0.171991i \(-0.944980\pi\)
0.343601 0.939116i \(-0.388353\pi\)
\(200\) 2.47710 0.175157
\(201\) 3.51671 + 17.0536i 0.248050 + 1.20287i
\(202\) −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
\(206\) 3.04944 + 5.28179i 0.212465 + 0.368000i
\(207\) 0.105074 0.894969i 0.00730317 0.0622046i
\(208\) −2.40545 + 4.16635i −0.166788 + 0.288885i
\(209\) −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 \(0.829691\pi\)
\(212\) −4.88874 −0.335760
\(213\) −16.4629 + 14.6431i −1.12802 + 1.00333i
\(214\) −3.08650 −0.210989
\(215\) 1.32327 2.29197i 0.0902464 0.156311i
\(216\) −2.97710 4.25874i −0.202566 0.289771i
\(217\) 0 0
\(218\) −1.14400 + 1.98146i −0.0774812 + 0.134201i
\(219\) 26.3912 + 8.75264i 1.78335 + 0.591449i
\(220\) −1.26145 + 2.18490i −0.0850469 + 0.147306i
\(221\) 12.9876 22.4952i 0.873642 1.51319i
\(222\) −1.29418 + 1.15113i −0.0868598 + 0.0772586i
\(223\) −3.16621 + 5.48403i −0.212025 + 0.367238i −0.952348 0.305013i \(-0.901339\pi\)
0.740323 + 0.672251i \(0.234672\pi\)
\(224\) 0 0
\(225\) −0.866524 + 7.38061i −0.0577683 + 0.492040i
\(226\) 9.73236 16.8569i 0.647387 1.12131i
\(227\) 23.3090 1.54707 0.773537 0.633751i \(-0.218485\pi\)
0.773537 + 0.633751i \(0.218485\pi\)
\(228\) −11.6705 3.87053i −0.772900 0.256332i
\(229\) 4.95420 0.327383 0.163691 0.986512i \(-0.447660\pi\)
0.163691 + 0.986512i \(0.447660\pi\)
\(230\) −0.238550 0.413181i −0.0157295 0.0272443i
\(231\) 0 0
\(232\) −4.13781 + 7.16689i −0.271660 + 0.470529i
\(233\) −7.13781 + 12.3630i −0.467613 + 0.809930i −0.999315 0.0370017i \(-0.988219\pi\)
0.531702 + 0.846932i \(0.321553\pi\)
\(234\) −11.5723 8.62456i −0.756508 0.563805i
\(235\) −2.11745 3.66754i −0.138127 0.239244i
\(236\) 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 \(0.781890\pi\)
\(240\) −2.61126 0.866025i −0.168556 0.0559017i
\(241\) 13.0000 0.837404 0.418702 0.908124i \(-0.362485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(242\) −4.23855 7.34138i −0.272464 0.471922i
\(243\) 13.7305 7.38061i 0.880812 0.473466i
\(244\) 4.47710 0.286617
\(245\) 0 0
\(246\) 2.05563 + 9.96840i 0.131062 + 0.635562i
\(247\) −34.1520 −2.17304
\(248\) 1.35600 2.34867i 0.0861063 0.149141i
\(249\) −0.827603 4.01330i −0.0524472 0.254333i
\(250\) 5.93818 + 10.2852i 0.375563 + 0.650495i
\(251\) −2.43268 −0.153549 −0.0767746 0.997048i \(-0.524462\pi\)
−0.0767746 + 0.997048i \(0.524462\pi\)
\(252\) 0 0
\(253\) −0.477100 −0.0299950
\(254\) −6.71998 11.6393i −0.421649 0.730318i
\(255\) 14.0989 + 4.67589i 0.882906 + 0.292816i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.987620 0.0616061 0.0308030 0.999525i \(-0.490194\pi\)
0.0308030 + 0.999525i \(0.490194\pi\)
\(258\) 2.15638 1.91802i 0.134250 0.119410i
\(259\) 0 0
\(260\) −7.64145 −0.473902
\(261\) −19.9065 14.8358i −1.23218 0.918314i
\(262\) 1.58836 + 2.75113i 0.0981295 + 0.169965i
\(263\) 17.1854 1.05970 0.529848 0.848092i \(-0.322249\pi\)
0.529848 + 0.848092i \(0.322249\pi\)
\(264\) −2.05563 + 1.82841i −0.126515 + 0.112531i
\(265\) −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
\(269\) −11.4523 19.8360i −0.698262 1.20942i −0.969069 0.246791i \(-0.920624\pi\)
0.270807 0.962634i \(-0.412709\pi\)
\(270\) 3.49381 7.47741i 0.212627 0.455060i
\(271\) −7.00364 + 12.1307i −0.425441 + 0.736885i −0.996462 0.0840504i \(-0.973214\pi\)
0.571021 + 0.820936i \(0.306548\pi\)
\(272\) 2.69963 4.67589i 0.163689 0.283518i
\(273\) 0 0
\(274\) −10.6316 18.4145i −0.642279 1.11246i
\(275\) 3.93454 0.237261
\(276\) −0.105074 0.509538i −0.00632473 0.0306706i
\(277\) 28.2953 1.70010 0.850049 0.526703i \(-0.176572\pi\)
0.850049 + 0.526703i \(0.176572\pi\)
\(278\) 6.52654 11.3043i 0.391436 0.677987i
\(279\) 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 \(0.990794\pi\)
\(282\) −0.932677 4.52284i −0.0555401 0.269331i
\(283\) −9.26145 + 16.0413i −0.550536 + 0.953556i 0.447700 + 0.894184i \(0.352243\pi\)
−0.998236 + 0.0593725i \(0.981090\pi\)
\(284\) −6.36033 + 11.0164i −0.377416 + 0.653704i
\(285\) −3.94437 19.1275i −0.233644 1.13301i
\(286\) −3.82072 + 6.61769i −0.225924 + 0.391312i
\(287\) 0 0
\(288\) −2.40545 1.79272i −0.141742 0.105637i
\(289\) −6.07598 + 10.5239i −0.357411 + 0.619054i
\(290\) −13.1447 −0.771882
\(291\) −0.498141 2.41564i −0.0292015 0.141607i
\(292\) 16.0531 0.939436
\(293\) 7.04256 + 12.1981i 0.411431 + 0.712619i 0.995046 0.0994108i \(-0.0316958\pi\)
−0.583616 + 0.812030i \(0.698362\pi\)
\(294\) 0 0
\(295\) −5.14400 + 8.90966i −0.299495 + 0.518741i
\(296\) −0.500000 + 0.866025i −0.0290619 + 0.0503367i
\(297\) −4.72872 6.76443i −0.274388 0.392512i
\(298\) 2.60439 + 4.51093i 0.150868 + 0.261311i
\(299\) −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
\(303\) 15.5734 13.8520i 0.894671 0.795776i
\(304\) −7.09888 −0.407149
\(305\) 3.55563 + 6.15854i 0.203595 + 0.352637i
\(306\) 12.9876 + 9.67933i 0.742453 + 0.553330i
\(307\) 5.85532 0.334180 0.167090 0.985942i \(-0.446563\pi\)
0.167090 + 0.985942i \(0.446563\pi\)
\(308\) 0 0
\(309\) −7.89307 + 7.02059i −0.449021 + 0.399387i
\(310\) 4.30766 0.244658
\(311\) 0.405446 0.702253i 0.0229907 0.0398211i −0.854301 0.519778i \(-0.826015\pi\)
0.877292 + 0.479957i \(0.159348\pi\)
\(312\) −7.90909 2.62305i −0.447764 0.148501i
\(313\) 5.28799 + 9.15907i 0.298895 + 0.517701i 0.975883 0.218292i \(-0.0700486\pi\)
−0.676988 + 0.735994i \(0.736715\pi\)
\(314\) 8.86398 0.500223
\(315\) 0 0
\(316\) 8.38688 0.471799
\(317\) −6.09820 10.5624i −0.342509 0.593243i 0.642389 0.766379i \(-0.277943\pi\)
−0.984898 + 0.173136i \(0.944610\pi\)
\(318\) −1.71015 8.29305i −0.0959004 0.465051i
\(319\) −6.57234 + 11.3836i −0.367981 + 0.637361i
\(320\) −1.58836 −0.0887922
\(321\) −1.07970 5.23582i −0.0602631 0.292235i
\(322\) 0 0
\(323\) 38.3287 2.13267
\(324\) 6.18292 6.53999i 0.343495 0.363333i
\(325\) 5.95853 + 10.3205i 0.330520 + 0.572477i
\(326\) 21.9629 1.21641
\(327\) −3.76145 1.24748i −0.208009 0.0689860i
\(328\) 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 0.996920 0.0784202i \(-0.0249876\pi\)
−0.566374 + 0.824148i \(0.691654\pi\)
\(332\) −1.18292 2.04887i −0.0649211 0.112447i
\(333\) −2.40545 1.79272i −0.131818 0.0982402i
\(334\) 1.65019 2.85821i 0.0902942 0.156394i
\(335\) −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 \(0.907024\pi\)
\(338\) −10.1447 −0.551798
\(339\) 31.9999 + 10.6128i 1.73800 + 0.576407i
\(340\) 8.57598 0.465098
\(341\) 2.15383 3.73054i 0.116636 0.202020i
\(342\) 2.48329 21.1514i 0.134281 1.14374i
\(343\) 0 0
\(344\) 0.833104 1.44298i 0.0449179 0.0778002i
\(345\) 0.617454 0.549202i 0.0332426 0.0295681i
\(346\) −9.55377 + 16.5476i −0.513614 + 0.889606i
\(347\) −0.283662 + 0.491316i −0.0152277 + 0.0263752i −0.873539 0.486754i \(-0.838181\pi\)
0.858311 + 0.513130i \(0.171514\pi\)
\(348\) −13.6051 4.51212i −0.729309 0.241875i
\(349\) 0.00364189 0.00630794i 0.000194946 0.000337656i −0.865928 0.500169i \(-0.833271\pi\)
0.866123 + 0.499831i \(0.166605\pi\)
\(350\) 0 0
\(351\) 10.5822 22.6478i 0.564835 1.20885i
\(352\) −0.794182 + 1.37556i −0.0423300 + 0.0733178i
\(353\) −6.65383 −0.354148 −0.177074 0.984198i \(-0.556663\pi\)
−0.177074 + 0.984198i \(0.556663\pi\)
\(354\) −8.38255 + 7.45596i −0.445527 + 0.396280i
\(355\) −20.2051 −1.07237
\(356\) −1.60507 2.78007i −0.0850688 0.147343i
\(357\) 0 0
\(358\) 8.03706 13.9206i 0.424772 0.735727i
\(359\) −0.398568 + 0.690339i −0.0210356 + 0.0364347i −0.876352 0.481672i \(-0.840030\pi\)
0.855316 + 0.518107i \(0.173363\pi\)
\(360\) 0.555632 4.73259i 0.0292844 0.249429i
\(361\) −15.6971 27.1881i −0.826162 1.43095i
\(362\) −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
\(366\) 1.56615 + 7.59476i 0.0818641 + 0.396985i
\(367\) 15.4327 0.805579 0.402790 0.915293i \(-0.368041\pi\)
0.402790 + 0.915293i \(0.368041\pi\)
\(368\) −0.150186 0.260130i −0.00782898 0.0135602i
\(369\) −16.1909 + 6.97418i −0.842864 + 0.363061i
\(370\) −1.58836 −0.0825751
\(371\) 0 0
\(372\) 4.45853 + 1.47867i 0.231164 + 0.0766655i
\(373\) 10.2422 0.530321 0.265160 0.964204i \(-0.414575\pi\)
0.265160 + 0.964204i \(0.414575\pi\)
\(374\) 4.28799 7.42702i 0.221727 0.384042i
\(375\) −15.3702 + 13.6712i −0.793712 + 0.705977i
\(376\) −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
\(381\) 17.3938 15.4711i 0.891109 0.792608i
\(382\) −11.9814 + 20.7524i −0.613023 + 1.06179i
\(383\) 6.26695 0.320226 0.160113 0.987099i \(-0.448814\pi\)
0.160113 + 0.987099i \(0.448814\pi\)
\(384\) −1.64400 0.545231i −0.0838948 0.0278237i
\(385\) 0 0
\(386\) −9.76509 −0.497030
\(387\) 4.00797 + 2.98704i 0.203737 + 0.151840i
\(388\) −0.712008 1.23323i −0.0361467 0.0626080i
\(389\) −21.6342 −1.09690 −0.548448 0.836185i \(-0.684781\pi\)
−0.548448 + 0.836185i \(0.684781\pi\)
\(390\) −2.67309 12.9626i −0.135357 0.656388i
\(391\) 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
\(395\) 6.66071 + 11.5367i 0.335137 + 0.580473i
\(396\) −3.82072 2.84748i −0.191999 0.143091i
\(397\) −2.05308 + 3.55605i −0.103041 + 0.178473i −0.912936 0.408102i \(-0.866191\pi\)
0.809895 + 0.586575i \(0.199524\pi\)
\(398\) 9.04944 15.6741i 0.453608 0.785671i
\(399\) 0 0
\(400\) 1.23855 + 2.14523i 0.0619275 + 0.107262i
\(401\) 16.7417 0.836041 0.418021 0.908438i \(-0.362724\pi\)
0.418021 + 0.908438i \(0.362724\pi\)
\(402\) −13.0105 + 11.5724i −0.648906 + 0.577178i
\(403\) 13.0472 0.649926
\(404\) 6.01671 10.4212i 0.299343 0.518476i
\(405\) 13.9065 + 3.31105i 0.691022 + 0.164527i
\(406\) 0 0
\(407\) −0.794182 + 1.37556i −0.0393661 + 0.0681842i
\(408\) 8.87636 + 2.94384i 0.439445 + 0.145742i
\(409\) −4.38255 + 7.59079i −0.216703 + 0.375341i −0.953798 0.300449i \(-0.902864\pi\)
0.737095 + 0.675789i \(0.236197\pi\)
\(410\) −4.66690 + 8.08330i −0.230482 + 0.399206i
\(411\) 27.5185 24.4767i 1.35739 1.20735i
\(412\) −3.04944 + 5.28179i −0.150235 + 0.260215i
\(413\) 0 0
\(414\) 0.827603 0.356487i 0.0406744 0.0175204i
\(415\) 1.87890 3.25436i 0.0922318 0.159750i
\(416\) −4.81089 −0.235873
\(417\) 21.4592 + 7.11695i 1.05086 + 0.348518i
\(418\) −11.2756 −0.551508
\(419\) 0.210149 + 0.363988i 0.0102664 + 0.0177820i 0.871113 0.491083i \(-0.163399\pi\)
−0.860847 + 0.508865i \(0.830065\pi\)
\(420\) 0 0
\(421\) 3.28799 5.69497i 0.160247 0.277556i −0.774710 0.632316i \(-0.782104\pi\)
0.934957 + 0.354761i \(0.115438\pi\)
\(422\) −0.166208 + 0.287880i −0.00809086 + 0.0140138i
\(423\) 7.34610 3.16431i 0.357179 0.153854i
\(424\) −2.44437 4.23377i −0.118709 0.205610i
\(425\) −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
\(429\) −12.5625 4.16635i −0.606524 0.201154i
\(430\) 2.64654 0.127628
\(431\) 11.0439 + 19.1287i 0.531968 + 0.921395i 0.999304 + 0.0373155i \(0.0118806\pi\)
−0.467336 + 0.884080i \(0.654786\pi\)
\(432\) 2.19963 4.70761i 0.105830 0.226495i
\(433\) 9.43268 0.453306 0.226653 0.973976i \(-0.427222\pi\)
0.226653 + 0.973976i \(0.427222\pi\)
\(434\) 0 0
\(435\) −4.59820 22.2981i −0.220467 1.06911i
\(436\) −2.28799 −0.109575
\(437\) 1.06615 1.84663i 0.0510010 0.0883363i
\(438\) 5.61559 + 27.2318i 0.268323 + 1.30118i
\(439\) −15.6032 27.0256i −0.744701 1.28986i −0.950334 0.311231i \(-0.899259\pi\)
0.205634 0.978629i \(-0.434074\pi\)
\(440\) −2.52290 −0.120275
\(441\) 0 0
\(442\) 25.9752 1.23552
\(443\) −6.52723 11.3055i −0.310118 0.537140i 0.668270 0.743919i \(-0.267035\pi\)
−0.978388 + 0.206779i \(0.933702\pi\)
\(444\) −1.64400 0.545231i −0.0780206 0.0258755i
\(445\) 2.54944 4.41576i 0.120855 0.209327i
\(446\) −6.33242 −0.299849
\(447\) −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 \(0.575184\pi\)
\(450\) −6.82505 + 2.93987i −0.321736 + 0.138587i
\(451\) 4.66690 + 8.08330i 0.219756 + 0.380628i
\(452\) 19.4647 0.915543
\(453\) 0.676728 0.601924i 0.0317955 0.0282809i
\(454\) 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 0.996196 + 0.0871436i \(0.0277739\pi\)
−0.422629 + 0.906303i \(0.638893\pi\)
\(458\) 2.47710 + 4.29046i 0.115747 + 0.200480i
\(459\) −11.8764 + 25.4176i −0.554341 + 1.18639i
\(460\) 0.238550 0.413181i 0.0111224 0.0192646i
\(461\) −1.75526 + 3.04020i −0.0817506 + 0.141596i −0.904002 0.427528i \(-0.859384\pi\)
0.822251 + 0.569125i \(0.192718\pi\)
\(462\) 0 0
\(463\) 8.69413 + 15.0587i 0.404050 + 0.699836i 0.994210 0.107451i \(-0.0342687\pi\)
−0.590160 + 0.807286i \(0.700935\pi\)
\(464\) −8.27561 −0.384186
\(465\) 1.50688 + 7.30733i 0.0698798 + 0.338869i
\(466\) −14.2756 −0.661305
\(467\) −6.69894 + 11.6029i −0.309990 + 0.536918i −0.978360 0.206911i \(-0.933659\pi\)
0.668370 + 0.743829i \(0.266992\pi\)
\(468\) 1.68292 14.3342i 0.0777929 0.662600i
\(469\) 0 0
\(470\) 2.11745 3.66754i 0.0976709 0.169171i
\(471\) 3.10074 + 15.0365i 0.142875 + 0.692844i
\(472\) −3.23855 + 5.60933i −0.149066 + 0.258190i
\(473\) 1.32327 2.29197i 0.0608441 0.105385i
\(474\) 2.93385 + 14.2271i 0.134756 + 0.653474i
\(475\) −8.79232 + 15.2287i −0.403419 + 0.698743i
\(476\) 0 0
\(477\) 13.4697 5.80205i 0.616737 0.265658i
\(478\) −2.48762 + 4.30868i −0.113781 + 0.197075i
\(479\) −20.8058 −0.950641 −0.475321 0.879813i \(-0.657668\pi\)
−0.475321 + 0.879813i \(0.657668\pi\)
\(480\) −0.555632 2.69443i −0.0253610 0.122984i
\(481\) −4.81089 −0.219358
\(482\) 6.50000 + 11.2583i 0.296067 + 0.512803i
\(483\) 0 0
\(484\) 4.23855 7.34138i 0.192661 0.333699i
\(485\) 1.13093 1.95882i 0.0513528 0.0889456i
\(486\) 13.2570 + 8.20066i 0.601352 + 0.371989i
\(487\) 16.2472 + 28.1410i 0.736231 + 1.27519i 0.954181 + 0.299230i \(0.0967298\pi\)
−0.217950 + 0.975960i \(0.569937\pi\)
\(488\) 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 \(0.976932\pi\)
\(492\) −7.60507 + 6.76443i −0.342863 + 0.304964i
\(493\) 44.6822 2.01238
\(494\) −17.0760 29.5765i −0.768285 1.33071i
\(495\) 0.882546 7.51707i 0.0396675 0.337867i
\(496\) 2.71201 0.121773
\(497\) 0 0
\(498\) 3.06182 2.72338i 0.137204 0.122037i
\(499\) −11.1506 −0.499169 −0.249585 0.968353i \(-0.580294\pi\)
−0.249585 + 0.968353i \(0.580294\pi\)
\(500\) −5.93818 + 10.2852i −0.265563 + 0.459969i
\(501\) 5.42580 + 1.79947i 0.242407 + 0.0803942i
\(502\) −1.21634 2.10676i −0.0542878 0.0940293i
\(503\) 40.7651 1.81763 0.908813 0.417204i \(-0.136990\pi\)
0.908813 + 0.417204i \(0.136990\pi\)
\(504\) 0 0
\(505\) 19.1135 0.850537
\(506\) −0.238550 0.413181i −0.0106048 0.0183681i
\(507\) −3.54875 17.2090i −0.157606 0.764279i
\(508\) 6.71998 11.6393i 0.298151 0.516413i
\(509\) −1.44506 −0.0640510 −0.0320255 0.999487i \(-0.510196\pi\)
−0.0320255 + 0.999487i \(0.510196\pi\)
\(510\) 3.00000 + 14.5479i 0.132842 + 0.644194i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 36.7490 3.18650i 1.62251 0.140687i
\(514\) 0.493810 + 0.855304i 0.0217810 + 0.0377259i
\(515\) −9.68725 −0.426871
\(516\) 2.73924 + 0.908468i 0.120588 + 0.0399931i
\(517\) −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
\(521\) −9.64214 16.7007i −0.422430 0.731670i 0.573747 0.819033i \(-0.305489\pi\)
−0.996177 + 0.0873630i \(0.972156\pi\)
\(522\) 2.89493 24.6575i 0.126707 1.07923i
\(523\) 18.3454 31.7752i 0.802189 1.38943i −0.115984 0.993251i \(-0.537002\pi\)
0.918173 0.396180i \(-0.129665\pi\)
\(524\) −1.58836 + 2.75113i −0.0693880 + 0.120184i
\(525\) 0 0
\(526\) 8.59269 + 14.8830i 0.374659 + 0.648929i
\(527\) −14.6428 −0.637851
\(528\) −2.61126 0.866025i −0.113641 0.0376889i
\(529\) −22.9098 −0.996077
\(530\) 3.88255 6.72477i 0.168647 0.292105i
\(531\) −15.5803 11.6116i −0.676128 0.503900i
\(532\) 0 0
\(533\) −14.1353 + 24.4830i −0.612266 + 1.06048i
\(534\) 4.15452 3.69529i 0.179784 0.159911i
\(535\) 2.45125 4.24568i 0.105977 0.183557i
\(536\) −5.02654 + 8.70623i −0.217114 + 0.376052i
\(537\) 26.4258 + 8.76411i 1.14036 + 0.378199i
\(538\) 11.4523 19.8360i 0.493745 0.855192i
\(539\) 0 0
\(540\) 8.22253 0.712974i 0.353841 0.0306815i
\(541\) −1.62543 + 2.81532i −0.0698825 + 0.121040i −0.898849 0.438258i \(-0.855596\pi\)
0.828967 + 0.559298i \(0.188929\pi\)
\(542\) −14.0073 −0.601664
\(543\) 10.4222 9.27012i 0.447258 0.397819i
\(544\) 5.39926 0.231491
\(545\) −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 \(0.207040\pi\)
\(548\) 10.6316 18.4145i 0.454160 0.786628i
\(549\) −12.3356 + 5.31351i −0.526470 + 0.226775i
\(550\) 1.96727 + 3.40741i 0.0838846 + 0.145292i
\(551\) −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
\(555\) −0.555632 2.69443i −0.0235853 0.114372i
\(556\) 13.0531 0.553574
\(557\) 12.8040 + 22.1772i 0.542523 + 0.939678i 0.998758 + 0.0498188i \(0.0158644\pi\)
−0.456235 + 0.889859i \(0.650802\pi\)
\(558\) −0.948699 + 8.08052i −0.0401616 + 0.342076i
\(559\) 8.01594 0.339038
\(560\) 0 0
\(561\) 14.0989 + 4.67589i 0.595255 + 0.197416i
\(562\) −17.5956 −0.742228
\(563\) −23.3189 + 40.3895i −0.982773 + 1.70221i −0.331330 + 0.943515i \(0.607497\pi\)
−0.651443 + 0.758698i \(0.725836\pi\)
\(564\) 3.45056 3.06914i 0.145295 0.129234i
\(565\) 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 −0.982159 0.188054i \(-0.939782\pi\)
0.328219 0.944602i \(-0.393551\pi\)
\(570\) 14.5927 12.9797i 0.611221 0.543658i
\(571\) 7.83812 13.5760i 0.328015 0.568139i −0.654103 0.756406i \(-0.726954\pi\)
0.982118 + 0.188267i \(0.0602869\pi\)
\(572\) −7.64145 −0.319505
\(573\) −39.3948 13.0653i −1.64574 0.545811i
\(574\) 0 0
\(575\) −0.744051 −0.0310291
\(576\) 0.349814 2.97954i 0.0145756 0.124147i
\(577\) −6.99567 12.1169i −0.291234 0.504431i 0.682868 0.730542i \(-0.260732\pi\)
−0.974102 + 0.226110i \(0.927399\pi\)
\(578\) −12.1520 −0.505455
\(579\) −3.41597 16.5651i −0.141963 0.688422i
\(580\) −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
\(584\) 8.02654 + 13.9024i 0.332141 + 0.575285i
\(585\) 21.0542 9.06902i 0.870483 0.374958i
\(586\) −7.04256 + 12.1981i −0.290926 + 0.503898i
\(587\) −1.44801 + 2.50803i −0.0597658 + 0.103517i −0.894360 0.447348i \(-0.852369\pi\)
0.834594 + 0.550865i \(0.185702\pi\)
\(588\) 0 0
\(589\) 9.62612 + 16.6729i 0.396637 + 0.686996i
\(590\) −10.2880 −0.423550
\(591\) 23.6105 21.0007i 0.971206 0.863852i
\(592\) −1.00000 −0.0410997
\(593\) 2.04394 3.54021i 0.0839346 0.145379i −0.821002 0.570925i \(-0.806585\pi\)
0.904937 + 0.425546i \(0.139918\pi\)
\(594\) 3.49381 7.47741i 0.143353 0.306802i
\(595\) 0 0
\(596\) −2.60439 + 4.51093i −0.106680 + 0.184775i
\(597\) 29.7545 + 9.86807i 1.21777 + 0.403873i
\(598\) 0.722528 1.25146i 0.0295464 0.0511758i
\(599\) 9.88255 17.1171i 0.403790 0.699385i −0.590390 0.807118i \(-0.701026\pi\)
0.994180 + 0.107734i \(0.0343593\pi\)
\(600\) −3.20582 + 2.85146i −0.130877 + 0.116410i
\(601\) 13.4320 23.2649i 0.547902 0.948994i −0.450516 0.892768i \(-0.648760\pi\)
0.998418 0.0562261i \(-0.0179068\pi\)
\(602\) 0 0
\(603\) −24.1822 18.0223i −0.984773 0.733926i
\(604\) 0.261450 0.452845i 0.0106383 0.0184260i
\(605\) 13.4647 0.547419
\(606\) 19.7829 + 6.56099i 0.803625 + 0.266522i
\(607\) 15.2422 0.618661 0.309331 0.950955i \(-0.399895\pi\)
0.309331 + 0.950955i \(0.399895\pi\)
\(608\) −3.54944 6.14781i −0.143949 0.249327i
\(609\) 0 0
\(610\) −3.55563 + 6.15854i −0.143963 + 0.249352i
\(611\) 6.41342 11.1084i 0.259459 0.449396i
\(612\) −1.88874 + 16.0873i −0.0763476 + 0.650290i
\(613\) −1.36033 2.35617i −0.0549434 0.0951648i 0.837246 0.546827i \(-0.184165\pi\)
−0.892189 + 0.451662i \(0.850831\pi\)
\(614\) 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 \(0.954355\pi\)
\(618\) −10.0265 3.32530i −0.403327 0.133763i
\(619\) −0.107546 −0.00432262 −0.00216131 0.999998i \(-0.500688\pi\)
−0.00216131 + 0.999998i \(0.500688\pi\)
\(620\) 2.15383 + 3.73054i 0.0864998 + 0.149822i
\(621\) 0.894237 + 1.27921i 0.0358845 + 0.0513328i
\(622\) 0.810892 0.0325138
\(623\) 0 0
\(624\) −1.68292 8.16100i −0.0673706 0.326701i
\(625\) −6.47848 −0.259139
\(626\) −5.28799 + 9.15907i −0.211351 + 0.366070i
\(627\) −3.94437 19.1275i −0.157523 0.763878i
\(628\) 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
\(633\) −0.546489 0.181243i −0.0217210 0.00720376i
\(634\) 6.09820 10.5624i 0.242190 0.419486i
\(635\) 21.3475 0.847152
\(636\) 6.32691 5.62755i 0.250878 0.223147i
\(637\) 0 0
\(638\) −13.1447 −0.520403
\(639\) 4.44987 37.9017i 0.176034 1.49937i
\(640\) −0.794182 1.37556i −0.0313928 0.0543739i
\(641\) 17.3128 0.683813 0.341906 0.939734i \(-0.388927\pi\)
0.341906 + 0.939734i \(0.388927\pi\)
\(642\) 3.99450 3.55296i 0.157650 0.140224i
\(643\) −14.4821 25.0838i −0.571119 0.989207i −0.996451 0.0841700i \(-0.973176\pi\)
0.425332 0.905037i \(-0.360157\pi\)
\(644\) 0 0
\(645\) 0.925798 + 4.48949i 0.0364533 + 0.176773i
\(646\) 19.1643 + 33.1936i 0.754011 + 1.30599i
\(647\) −1.27816 2.21384i −0.0502497 0.0870350i 0.839807 0.542886i \(-0.182668\pi\)
−0.890056 + 0.455851i \(0.849335\pi\)
\(648\) 8.75526 + 2.08457i 0.343939 + 0.0818895i
\(649\) −5.14400 + 8.90966i −0.201920 + 0.349735i
\(650\) −5.95853 + 10.3205i −0.233713 + 0.404802i
\(651\) 0 0
\(652\) 10.9814 + 19.0204i 0.430066 + 0.744896i
\(653\) 29.9766 1.17308 0.586538 0.809922i \(-0.300491\pi\)
0.586538 + 0.809922i \(0.300491\pi\)
\(654\) −0.800372 3.88125i −0.0312970 0.151769i
\(655\) −5.04580 −0.197156
\(656\) −2.93818 + 5.08907i −0.114717 + 0.198695i
\(657\) −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 \(0.262748\pi\)
\(660\) −0.882546 4.27974i −0.0343531 0.166589i
\(661\) −13.6261 + 23.6011i −0.529994 + 0.917977i 0.469393 + 0.882989i \(0.344473\pi\)
−0.999388 + 0.0349881i \(0.988861\pi\)
\(662\) −7.83310 + 13.5673i −0.304442 + 0.527309i
\(663\) 9.08650 + 44.0633i 0.352891 + 1.71128i
\(664\) 1.18292 2.04887i 0.0459061 0.0795117i
\(665\) 0 0
\(666\) 0.349814 2.97954i 0.0135550 0.115455i
\(667\) 1.24288 2.15273i 0.0481245 0.0833541i
\(668\) 3.30037 0.127695
\(669\) −2.21517 10.7420i −0.0856433 0.415311i
\(670\) −15.9680 −0.616896
\(671\) 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 \(-0.186423\pi\)
\(674\) 4.21201 7.29541i 0.162240 0.281009i
\(675\) −7.37457 10.5493i −0.283847 0.406044i
\(676\) −5.07234 8.78555i −0.195090 0.337906i
\(677\) 2.54944 + 4.41576i 0.0979830 + 0.169712i 0.910850 0.412738i \(-0.135428\pi\)
−0.812867 + 0.582450i \(0.802094\pi\)
\(678\) 6.80903 + 33.0191i 0.261499 + 1.26809i
\(679\) 0 0
\(680\) 4.28799 + 7.42702i 0.164437 + 0.284813i
\(681\) −30.1661 + 26.8317i −1.15597 + 1.02819i
\(682\) 4.30766 0.164949
\(683\) −7.77197 13.4614i −0.297386 0.515088i 0.678151 0.734923i \(-0.262782\pi\)
−0.975537 + 0.219835i \(0.929448\pi\)
\(684\) 19.5593 8.42510i 0.747868 0.322142i
\(685\) 33.7738 1.29043
\(686\) 0 0
\(687\) −6.41164 + 5.70291i −0.244619 + 0.217580i
\(688\) 1.66621 0.0635236
\(689\) 11.7596 20.3682i 0.448005 0.775967i
\(690\) 0.784350 + 0.260130i 0.0298597 + 0.00990297i
\(691\) 11.6483 + 20.1755i 0.443123 + 0.767512i 0.997919 0.0644744i \(-0.0205371\pi\)
−0.554796 + 0.831986i \(0.687204\pi\)
\(692\) −19.1075 −0.726360
\(693\) 0 0
\(694\) −0.567323 −0.0215353
\(695\) 10.3665 + 17.9553i 0.393225 + 0.681085i
\(696\) −2.89493 14.0384i −0.109732 0.532124i
\(697\) 15.8640 27.4772i 0.600891 1.04077i
\(698\) 0.00728378 0.000275695
\(699\) −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 \(0.830801\pi\)
\(702\) 24.9047 2.15948i 0.939967 0.0815044i
\(703\) −3.54944 6.14781i −0.133870 0.231869i
\(704\) −1.58836 −0.0598637
\(705\) 6.96217 + 2.30900i 0.262211 + 0.0869621i
\(706\) −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 0.646034 0.763309i \(-0.276427\pi\)
−0.984062 + 0.177827i \(0.943093\pi\)
\(710\) −10.1025 17.4981i −0.379141 0.656692i
\(711\) −23.1080 + 9.95371i −0.866619 + 0.373293i
\(712\) 1.60507 2.78007i 0.0601527 0.104188i
\(713\) −0.407305 + 0.705474i −0.0152537 + 0.0264202i
\(714\) 0 0
\(715\) −6.06870 10.5113i −0.226957 0.393100i
\(716\) 16.0741 0.600718
\(717\) −8.17928 2.71266i −0.305461 0.101306i
\(718\) −0.797135 −0.0297488
\(719\) −18.4389 + 31.9371i −0.687654 + 1.19105i 0.284941 + 0.958545i \(0.408026\pi\)
−0.972595 + 0.232506i \(0.925307\pi\)
\(720\) 4.37636 1.88510i 0.163097 0.0702536i
\(721\) 0 0
\(722\) 15.6971 27.1881i 0.584185 1.01184i
\(723\) −16.8244 + 14.9646i −0.625705 + 0.556541i
\(724\) 4.02654 6.97418i 0.149645 0.259193i
\(725\) −10.2498 + 17.7531i −0.380666 + 0.659334i
\(726\) 13.9363 + 4.62198i 0.517225 + 0.171538i
\(727\) −15.2429 + 26.4014i −0.565327 + 0.979175i 0.431692 + 0.902021i \(0.357917\pi\)
−0.997019 + 0.0771543i \(0.975417\pi\)
\(728\) 0 0
\(729\) −9.27375 + 25.3574i −0.343472 + 0.939163i
\(730\) −12.7491 + 22.0820i −0.471864 + 0.817293i
\(731\) −8.99628 −0.332739
\(732\) −5.79418 + 5.15371i −0.214159 + 0.190487i
\(733\) −6.15059 −0.227177 −0.113589 0.993528i \(-0.536235\pi\)
−0.113589 + 0.993528i \(0.536235\pi\)
\(734\) 7.71634 + 13.3651i 0.284815 + 0.493314i
\(735\) 0 0
\(736\) 0.150186 0.260130i 0.00553593 0.00958851i
\(737\) −7.98398 + 13.8287i −0.294094 + 0.509385i
\(738\) −14.1353 10.5346i −0.520326 0.387785i
\(739\) −20.3912 35.3186i −0.750103 1.29922i −0.947772 0.318947i \(-0.896671\pi\)
0.197670 0.980269i \(-0.436663\pi\)
\(740\) −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 \(0.747606\pi\)
\(744\) 0.948699 + 4.60054i 0.0347810 + 0.168664i
\(745\) −8.27342 −0.303115
\(746\) 5.12110 + 8.87000i 0.187497 + 0.324754i
\(747\) 5.69089 + 4.24127i 0.208219 + 0.155180i
\(748\) 8.57598 0.313569
\(749\) 0 0
\(750\) −19.5247 6.47536i −0.712941 0.236447i
\(751\) 4.18911 0.152863 0.0764314 0.997075i \(-0.475647\pi\)
0.0764314 + 0.997075i \(0.475647\pi\)
\(752\) 1.33310 2.30900i 0.0486133 0.0842007i
\(753\) 3.14833 2.80032i 0.114731 0.102049i
\(754\) −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
\(759\) 0.617454 0.549202i 0.0224122 0.0199348i
\(760\) 5.63781 9.76497i 0.204505 0.354213i
\(761\) −3.63416 −0.131738 −0.0658692 0.997828i \(-0.520982\pi\)
−0.0658692 + 0.997828i \(0.520982\pi\)
\(762\) 22.0952 + 7.32788i 0.800426 + 0.265461i
\(763\) 0 0
\(764\) −23.9629 −0.866946
\(765\) −23.6291 + 10.1781i −0.854311 + 0.367992i
\(766\) 3.13348 + 5.42734i 0.113217 + 0.196098i
\(767\) −31.1606 −1.12515
\(768\) −0.349814 1.69636i −0.0126228 0.0612120i
\(769\) 19.9672 + 34.5842i 0.720035 + 1.24714i 0.960985 + 0.276600i \(0.0892078\pi\)
−0.240950 + 0.970538i \(0.577459\pi\)
\(770\) 0 0
\(771\) −1.27816 + 1.13688i −0.0460318 + 0.0409436i
\(772\) −4.88255 8.45682i −0.175727 0.304368i
\(773\) −18.0698 31.2978i −0.649925 1.12570i −0.983140 0.182853i \(-0.941467\pi\)
0.333215 &minu