Properties

Label 882.2.h.p.67.1
Level $882$
Weight $2$
Character 882.67
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 67.1
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 882.67
Dual form 882.2.h.p.79.1

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

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

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 0.311547 + 0.950231i \(0.399153\pi\)
−0.978697 + 0.205308i \(0.934180\pi\)
\(14\) 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 −0.327199 0.944955i \(-0.606105\pi\)
0.981955 0.189115i \(-0.0605620\pi\)
\(18\) 2.75526 + 1.18682i 0.649421 + 0.279736i
\(19\) 3.54944 + 6.14781i 0.814298 + 1.41041i 0.909831 + 0.414979i \(0.136211\pi\)
−0.0955331 + 0.995426i \(0.530456\pi\)
\(20\) 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 0.938446 + 0.345427i \(0.112266\pi\)
−0.170074 + 0.985431i \(0.554401\pi\)
\(30\) 2.61126 0.866025i 0.476749 0.158114i
\(31\) −1.35600 2.34867i −0.243545 0.421833i 0.718176 0.695861i \(-0.244977\pi\)
−0.961722 + 0.274028i \(0.911644\pi\)
\(32\) 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 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 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 −0.998901 0.0468628i \(-0.985078\pi\)
0.540035 + 0.841643i \(0.318411\pi\)
\(42\) 0 0
\(43\) −0.833104 1.44298i −0.127047 0.220052i 0.795484 0.605974i \(-0.207217\pi\)
−0.922531 + 0.385922i \(0.873883\pi\)
\(44\) 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 −0.752268 0.658857i \(-0.771040\pi\)
0.946721 + 0.322055i \(0.104373\pi\)
\(48\) 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 −0.647871 0.761750i \(-0.724340\pi\)
0.983630 + 0.180197i \(0.0576736\pi\)
\(54\) −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 0.996098 0.0882491i \(-0.0281271\pi\)
−0.574475 + 0.818522i \(0.694794\pi\)
\(60\) 0.555632 2.69443i 0.0717318 0.347850i
\(61\) −2.23855 + 3.87728i −0.286617 + 0.496435i −0.973000 0.230805i \(-0.925864\pi\)
0.686383 + 0.727240i \(0.259197\pi\)
\(62\) −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 0.990543 + 0.137199i \(0.0438101\pi\)
−0.376454 + 0.926435i \(0.622857\pi\)
\(68\) −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 −0.172909 + 0.984938i \(0.555317\pi\)
−0.766527 + 0.642213i \(0.778017\pi\)
\(74\) 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 −0.999479 0.0322635i \(-0.989728\pi\)
0.527681 + 0.849443i \(0.323062\pi\)
\(80\) 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 0.793773 0.608214i \(-0.208114\pi\)
−0.923615 + 0.383321i \(0.874780\pi\)
\(84\) 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 0.768330 0.640054i \(-0.221088\pi\)
−0.938468 + 0.345367i \(0.887755\pi\)
\(90\) −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 0.827613 0.561300i \(-0.189698\pi\)
−0.899906 + 0.436084i \(0.856365\pi\)
\(98\) 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 0.781737 0.623608i \(-0.214334\pi\)
−0.930929 + 0.365200i \(0.881001\pi\)
\(108\) −5.17673 0.448873i −0.498131 0.0431929i
\(109\) 1.14400 1.98146i 0.109575 0.189789i −0.806023 0.591884i \(-0.798384\pi\)
0.915598 + 0.402095i \(0.131718\pi\)
\(110\) 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 −0.109440 + 0.993993i \(0.534906\pi\)
−0.806104 + 0.591774i \(0.798428\pi\)
\(114\) −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 0.444439 + 0.895809i \(0.353403\pi\)
−0.998013 + 0.0630092i \(0.979930\pi\)
\(140\) 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 0.986897 0.161354i \(-0.0515862\pi\)
−0.633185 + 0.774000i \(0.718253\pi\)
\(158\) 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 0.871801 + 0.489860i \(0.162952\pi\)
−0.0116689 + 0.999932i \(0.503714\pi\)
\(164\) 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 −0.922783 0.385319i \(-0.874091\pi\)
0.795088 + 0.606494i \(0.207425\pi\)
\(168\) 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 −0.232052 0.972703i \(-0.574544\pi\)
0.958412 0.285389i \(-0.0921227\pi\)
\(174\) −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 0.391994 + 0.919968i \(0.371785\pi\)
−0.992712 + 0.120507i \(0.961548\pi\)
\(180\) −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 0.00184390 0.999998i \(-0.499413\pi\)
0.865102 0.501596i \(-0.167254\pi\)
\(192\) −1.29418 1.15113i −0.0933995 0.0830754i
\(193\) −4.88255 8.45682i −0.351453 0.608735i 0.635051 0.772470i \(-0.280979\pi\)
−0.986504 + 0.163735i \(0.947646\pi\)
\(194\) −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 0.343601 + 0.939116i \(0.388353\pi\)
−0.985098 + 0.171991i \(0.944980\pi\)
\(200\) 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 −0.860248 0.509877i \(-0.829691\pi\)
0.871690 + 0.490058i \(0.163024\pi\)
\(212\) −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 0.740323 0.672251i \(-0.234672\pi\)
−0.952348 + 0.305013i \(0.901339\pi\)
\(224\) 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 0.531702 0.846932i \(-0.321553\pi\)
−0.999315 + 0.0370017i \(0.988219\pi\)
\(234\) −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 −0.774285 0.632837i \(-0.781890\pi\)
0.935196 + 0.354132i \(0.115224\pi\)
\(240\) −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 0.270807 + 0.962634i \(0.412709\pi\)
−0.969069 + 0.246791i \(0.920624\pi\)
\(270\) 3.49381 + 7.47741i 0.212627 + 0.455060i
\(271\) −7.00364 12.1307i −0.425441 0.736885i 0.571021 0.820936i \(-0.306548\pi\)
−0.996462 + 0.0840504i \(0.973214\pi\)
\(272\) 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 −0.999582 0.0289175i \(-0.990794\pi\)
0.474748 0.880122i \(-0.342539\pi\)
\(282\) −0.932677 + 4.52284i −0.0555401 + 0.269331i
\(283\) −9.26145 16.0413i −0.550536 0.953556i −0.998236 0.0593725i \(-0.981090\pi\)
0.447700 0.894184i \(-0.352243\pi\)
\(284\) −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 −0.583616 0.812030i \(-0.698362\pi\)
0.995046 + 0.0994108i \(0.0316958\pi\)
\(294\) 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 0.877292 0.479957i \(-0.159348\pi\)
−0.854301 + 0.519778i \(0.826015\pi\)
\(312\) −7.90909 + 2.62305i −0.447764 + 0.148501i
\(313\) 5.28799 9.15907i 0.298895 0.517701i −0.676988 0.735994i \(-0.736715\pi\)
0.975883 + 0.218292i \(0.0700486\pi\)
\(314\) 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 \(0.277943\pi\)
\(318\) −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 −0.566374 0.824148i \(-0.691654\pi\)
0.996920 + 0.0784202i \(0.0249876\pi\)
\(332\) −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 −0.957643 0.287958i \(-0.907024\pi\)
0.728200 + 0.685364i \(0.240357\pi\)
\(338\) −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 0.858311 0.513130i \(-0.171514\pi\)
−0.873539 + 0.486754i \(0.838181\pi\)
\(348\) −13.6051 + 4.51212i −0.729309 + 0.241875i
\(349\) 0.00364189 + 0.00630794i 0.000194946 + 0.000337656i 0.866123 0.499831i \(-0.166605\pi\)
−0.865928 + 0.500169i \(0.833271\pi\)
\(350\) 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 0.855316 0.518107i \(-0.173363\pi\)
−0.876352 + 0.481672i \(0.840030\pi\)
\(360\) 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 0.809895 0.586575i \(-0.199524\pi\)
−0.912936 + 0.408102i \(0.866191\pi\)
\(398\) 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 0.737095 0.675789i \(-0.236197\pi\)
−0.953798 + 0.300449i \(0.902864\pi\)
\(410\) −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 −0.860847 0.508865i \(-0.830065\pi\)
0.871113 + 0.491083i \(0.163399\pi\)
\(420\) 0 0
\(421\) 3.28799 + 5.69497i 0.160247 + 0.277556i 0.934957 0.354761i \(-0.115438\pi\)
−0.774710 + 0.632316i \(0.782104\pi\)
\(422\) −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 −0.467336 0.884080i \(-0.654786\pi\)
0.999304 0.0373155i \(-0.0118806\pi\)
\(432\) 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 0.205634 + 0.978629i \(0.434074\pi\)
−0.950334 + 0.311231i \(0.899259\pi\)
\(440\) −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 \(0.267035\pi\)
\(444\) −1.64400 + 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 −0.422629 0.906303i \(-0.638893\pi\)
0.996196 0.0871436i \(-0.0277739\pi\)
\(458\) 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 0.822251 0.569125i \(-0.192718\pi\)
−0.904002 + 0.427528i \(0.859384\pi\)
\(462\) 0 0
\(463\) 8.69413 15.0587i 0.404050 0.699836i −0.590160 0.807286i \(-0.700935\pi\)
0.994210 + 0.107451i \(0.0342687\pi\)
\(464\) −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 0.668370 0.743829i \(-0.266992\pi\)
−0.978360 + 0.206911i \(0.933659\pi\)
\(468\) 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 −0.217950 0.975960i \(-0.569937\pi\)
0.954181 0.299230i \(-0.0967298\pi\)
\(488\) 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 −0.997375 0.0724067i \(-0.976932\pi\)
0.561394 + 0.827549i \(0.310265\pi\)
\(492\) −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 −0.996177 0.0873630i \(-0.972156\pi\)
0.573747 + 0.819033i \(0.305489\pi\)
\(522\) 2.89493 + 24.6575i 0.126707 + 1.07923i
\(523\) 18.3454 + 31.7752i 0.802189 + 1.38943i 0.918173 + 0.396180i \(0.129665\pi\)
−0.115984 + 0.993251i \(0.537002\pi\)
\(524\) −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 0.828967 0.559298i \(-0.188929\pi\)
−0.898849 + 0.438258i \(0.855596\pi\)
\(542\) −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 0.795820 0.605534i \(-0.207040\pi\)
−0.922317 + 0.386433i \(0.873707\pi\)
\(548\) 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 −0.456235 0.889859i \(-0.650802\pi\)
0.998758 0.0498188i \(-0.0158644\pi\)
\(558\) −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 −0.651443 0.758698i \(-0.725836\pi\)
−0.331330 0.943515i \(-0.607497\pi\)
\(564\) 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 0.328219 + 0.944602i \(0.393551\pi\)
−0.982159 + 0.188054i \(0.939782\pi\)
\(570\) 14.5927 + 12.9797i 0.611221 + 0.543658i
\(571\) 7.83812 + 13.5760i 0.328015 + 0.568139i 0.982118 0.188267i \(-0.0602869\pi\)
−0.654103 + 0.756406i \(0.726954\pi\)
\(572\) −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 −0.974102 0.226110i \(-0.927399\pi\)
0.682868 + 0.730542i \(0.260732\pi\)
\(578\) −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 0.834594 0.550865i \(-0.185702\pi\)
−0.894360 + 0.447348i \(0.852369\pi\)
\(588\) 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 0.904937 0.425546i \(-0.139918\pi\)
−0.821002 + 0.570925i \(0.806585\pi\)
\(594\) 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 0.994180 0.107734i \(-0.0343593\pi\)
−0.590390 + 0.807118i \(0.701026\pi\)
\(600\) −3.20582 2.85146i −0.130877 0.116410i
\(601\) 13.4320 + 23.2649i 0.547902 + 0.948994i 0.998418 + 0.0562261i \(0.0179068\pi\)
−0.450516 + 0.892768i \(0.648760\pi\)
\(602\) 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 −0.892189 0.451662i \(-0.850831\pi\)
0.837246 + 0.546827i \(0.184165\pi\)
\(614\) 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 −0.989736 0.142906i \(-0.954355\pi\)
0.618629 + 0.785684i \(0.287689\pi\)
\(618\) −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 0.425332 + 0.905037i \(0.360157\pi\)
−0.996451 + 0.0841700i \(0.973176\pi\)
\(644\) 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 −0.890056 0.455851i \(-0.849335\pi\)
0.839807 + 0.542886i \(0.182668\pi\)
\(648\) 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 0.678228 0.734851i \(-0.262748\pi\)
−0.975514 + 0.219937i \(0.929415\pi\)
\(660\) −0.882546 + 4.27974i −0.0343531 + 0.166589i
\(661\) −13.6261 23.6011i −0.529994 0.917977i −0.999388 0.0349881i \(-0.988861\pi\)
0.469393 0.882989i \(-0.344473\pi\)
\(662\) −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 0.833344 + 0.552755i \(0.186423\pi\)
0.0620280 + 0.998074i \(0.480243\pi\)
\(674\) 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 −0.812867 0.582450i \(-0.802094\pi\)
0.910850 + 0.412738i \(0.135428\pi\)
\(678\) 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 −0.975537 0.219835i \(-0.929448\pi\)
0.678151 + 0.734923i \(0.262782\pi\)
\(684\) 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 −0.554796 0.831986i \(-0.687204\pi\)
0.997919 + 0.0644744i \(0.0205371\pi\)
\(692\) −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 −0.984062 0.177827i \(-0.943093\pi\)
0.646034 + 0.763309i \(0.276427\pi\)
\(710\) −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 −0.972595 0.232506i \(-0.925307\pi\)
0.284941 0.958545i \(-0.408026\pi\)
\(720\) 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 −0.997019 0.0771543i \(-0.975417\pi\)
0.431692 0.902021i \(-0.357917\pi\)
\(728\) 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 0.197670 + 0.980269i \(0.436663\pi\)
−0.947772 + 0.318947i \(0.896671\pi\)
\(740\) −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 −0.701769 0.712405i \(-0.747606\pi\)
0.967845 + 0.251547i \(0.0809394\pi\)
\(744\) 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 −0.240950 0.970538i \(-0.577459\pi\)
0.960985 0.276600i \(-0.0892078\pi\)
\(770\) 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 0.333215 + 0.942851i \(0.391867\pi\)
−0.983140 + 0.182853i \(0.941467\pi\)