Properties

Label 175.2.t.a.109.6
Level $175$
Weight $2$
Character 175.109
Analytic conductor $1.397$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,2,Mod(4,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([3, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.t (of order \(30\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(18\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 109.6
Character \(\chi\) \(=\) 175.109
Dual form 175.2.t.a.114.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.34851 - 0.141734i) q^{2} +(-0.0597933 + 0.281305i) q^{3} +(-0.157907 - 0.0335641i) q^{4} +(-1.89013 - 1.19475i) q^{5} +(0.120502 - 0.370868i) q^{6} +(0.848315 + 2.50606i) q^{7} +(2.78733 + 0.905658i) q^{8} +(2.66508 + 1.18657i) q^{9} +O(q^{10})\) \(q+(-1.34851 - 0.141734i) q^{2} +(-0.0597933 + 0.281305i) q^{3} +(-0.157907 - 0.0335641i) q^{4} +(-1.89013 - 1.19475i) q^{5} +(0.120502 - 0.370868i) q^{6} +(0.848315 + 2.50606i) q^{7} +(2.78733 + 0.905658i) q^{8} +(2.66508 + 1.18657i) q^{9} +(2.37952 + 1.87902i) q^{10} +(-0.130473 + 0.0580902i) q^{11} +(0.0188835 - 0.0424131i) q^{12} +(2.82682 + 3.89078i) q^{13} +(-0.788766 - 3.49969i) q^{14} +(0.449105 - 0.460265i) q^{15} +(-3.33542 - 1.48502i) q^{16} +(-3.77325 + 3.39745i) q^{17} +(-3.42571 - 1.97783i) q^{18} +(0.807335 - 0.171604i) q^{19} +(0.258363 + 0.252099i) q^{20} +(-0.755693 + 0.0887897i) q^{21} +(0.184177 - 0.0598427i) q^{22} +(7.09767 + 0.745995i) q^{23} +(-0.421430 + 0.729938i) q^{24} +(2.14517 + 4.51644i) q^{25} +(-3.26053 - 5.64741i) q^{26} +(-1.00027 + 1.37675i) q^{27} +(-0.0498408 - 0.424197i) q^{28} +(-1.86695 - 5.74589i) q^{29} +(-0.670858 + 0.557019i) q^{30} +(0.249623 + 0.277235i) q^{31} +(-0.788877 - 0.455459i) q^{32} +(-0.00853969 - 0.0401761i) q^{33} +(5.56980 - 4.04670i) q^{34} +(1.39068 - 5.75030i) q^{35} +(-0.381008 - 0.276818i) q^{36} +(-3.68380 + 8.27395i) q^{37} +(-1.11302 + 0.116983i) q^{38} +(-1.26352 + 0.562556i) q^{39} +(-4.18638 - 5.04195i) q^{40} +(2.77346 - 2.01504i) q^{41} +(1.03164 - 0.0126263i) q^{42} -1.35463i q^{43} +(0.0225523 - 0.00479363i) q^{44} +(-3.61969 - 5.42686i) q^{45} +(-9.46554 - 2.01196i) q^{46} +(-5.18913 - 4.67231i) q^{47} +(0.617181 - 0.849477i) q^{48} +(-5.56072 + 4.25187i) q^{49} +(-2.25265 - 6.39451i) q^{50} +(-0.730107 - 1.26458i) q^{51} +(-0.315783 - 0.709260i) q^{52} +(0.470762 - 2.21476i) q^{53} +(1.54400 - 1.71479i) q^{54} +(0.316013 + 0.0460837i) q^{55} +(0.0948953 + 7.75351i) q^{56} +0.237368i q^{57} +(1.70321 + 8.01299i) q^{58} +(0.344714 + 3.27973i) q^{59} +(-0.0863652 + 0.0576052i) q^{60} +(0.179533 - 1.70814i) q^{61} +(-0.297326 - 0.409234i) q^{62} +(-0.712794 + 7.68545i) q^{63} +(6.90681 + 5.01809i) q^{64} +(-0.694556 - 10.7314i) q^{65} +(0.00582153 + 0.0553882i) q^{66} +(8.34782 - 7.51641i) q^{67} +(0.709855 - 0.409835i) q^{68} +(-0.634245 + 1.95201i) q^{69} +(-2.69036 + 7.55723i) q^{70} +(1.44811 + 4.45682i) q^{71} +(6.35382 + 5.72101i) q^{72} +(4.12157 + 9.25719i) q^{73} +(6.14034 - 10.6354i) q^{74} +(-1.39877 + 0.333394i) q^{75} -0.133243 q^{76} +(-0.256260 - 0.277694i) q^{77} +(1.78360 - 0.579528i) q^{78} +(7.64875 - 8.49480i) q^{79} +(4.53014 + 6.79186i) q^{80} +(5.52867 + 6.14021i) q^{81} +(-4.02564 + 2.32420i) q^{82} +(-14.8328 - 4.81947i) q^{83} +(0.122309 + 0.0113437i) q^{84} +(11.1910 - 1.91355i) q^{85} +(-0.191997 + 1.82673i) q^{86} +(1.72798 - 0.181618i) q^{87} +(-0.416280 + 0.0437528i) q^{88} +(-1.42961 + 13.6018i) q^{89} +(4.11202 + 7.83120i) q^{90} +(-7.35251 + 10.3848i) q^{91} +(-1.09573 - 0.356024i) q^{92} +(-0.0929134 + 0.0536436i) q^{93} +(6.33536 + 7.03613i) q^{94} +(-1.73099 - 0.640205i) q^{95} +(0.175293 - 0.194682i) q^{96} +(4.17760 - 1.35738i) q^{97} +(8.10132 - 4.94554i) q^{98} -0.416648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22} + 25 q^{23} + 50 q^{24} - 11 q^{25} - 60 q^{26} + 40 q^{27} - 24 q^{29} + 53 q^{30} + 15 q^{31} + 20 q^{33} - 20 q^{34} - 14 q^{35} + 16 q^{36} - 5 q^{37} - 20 q^{38} + 13 q^{39} + 7 q^{40} - 62 q^{41} + 40 q^{42} - 15 q^{44} - 41 q^{45} - 27 q^{46} - 5 q^{47} - 38 q^{49} + 54 q^{50} - 8 q^{51} - 130 q^{52} + 25 q^{53} - 29 q^{54} - 20 q^{55} + 32 q^{56} - 65 q^{58} - 39 q^{59} + 79 q^{60} + 7 q^{61} - 20 q^{62} - 45 q^{63} + 34 q^{64} - 13 q^{65} + 11 q^{66} + 25 q^{67} + 74 q^{69} + 85 q^{70} - 46 q^{71} + 60 q^{72} + 35 q^{73} + 6 q^{74} - 107 q^{75} + 180 q^{76} - 5 q^{77} + 10 q^{78} + 9 q^{79} + 88 q^{80} - 59 q^{81} + 90 q^{83} - 51 q^{84} - 6 q^{85} + 11 q^{86} - 5 q^{87} + 140 q^{88} - 42 q^{89} + 4 q^{90} + 22 q^{91} + 10 q^{92} + 5 q^{94} + 13 q^{95} + 53 q^{96} + 120 q^{97} - 180 q^{98} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34851 0.141734i −0.953540 0.100221i −0.385036 0.922902i \(-0.625811\pi\)
−0.568504 + 0.822680i \(0.692478\pi\)
\(3\) −0.0597933 + 0.281305i −0.0345217 + 0.162412i −0.992032 0.125988i \(-0.959790\pi\)
0.957510 + 0.288400i \(0.0931232\pi\)
\(4\) −0.157907 0.0335641i −0.0789534 0.0167821i
\(5\) −1.89013 1.19475i −0.845291 0.534306i
\(6\) 0.120502 0.370868i 0.0491949 0.151406i
\(7\) 0.848315 + 2.50606i 0.320633 + 0.947204i
\(8\) 2.78733 + 0.905658i 0.985469 + 0.320198i
\(9\) 2.66508 + 1.18657i 0.888360 + 0.395523i
\(10\) 2.37952 + 1.87902i 0.752470 + 0.594198i
\(11\) −0.130473 + 0.0580902i −0.0393390 + 0.0175149i −0.426312 0.904576i \(-0.640187\pi\)
0.386973 + 0.922091i \(0.373521\pi\)
\(12\) 0.0188835 0.0424131i 0.00545121 0.0122436i
\(13\) 2.82682 + 3.89078i 0.784018 + 1.07911i 0.994827 + 0.101581i \(0.0323900\pi\)
−0.210810 + 0.977527i \(0.567610\pi\)
\(14\) −0.788766 3.49969i −0.210807 0.935331i
\(15\) 0.449105 0.460265i 0.115958 0.118840i
\(16\) −3.33542 1.48502i −0.833855 0.371256i
\(17\) −3.77325 + 3.39745i −0.915149 + 0.824004i −0.984822 0.173566i \(-0.944471\pi\)
0.0696735 + 0.997570i \(0.477804\pi\)
\(18\) −3.42571 1.97783i −0.807447 0.466180i
\(19\) 0.807335 0.171604i 0.185215 0.0393687i −0.114370 0.993438i \(-0.536485\pi\)
0.299585 + 0.954069i \(0.403152\pi\)
\(20\) 0.258363 + 0.252099i 0.0577718 + 0.0563710i
\(21\) −0.755693 + 0.0887897i −0.164906 + 0.0193755i
\(22\) 0.184177 0.0598427i 0.0392667 0.0127585i
\(23\) 7.09767 + 0.745995i 1.47997 + 0.155551i 0.809820 0.586679i \(-0.199565\pi\)
0.670146 + 0.742229i \(0.266231\pi\)
\(24\) −0.421430 + 0.729938i −0.0860240 + 0.148998i
\(25\) 2.14517 + 4.51644i 0.429034 + 0.903289i
\(26\) −3.26053 5.64741i −0.639443 1.10755i
\(27\) −1.00027 + 1.37675i −0.192501 + 0.264955i
\(28\) −0.0498408 0.424197i −0.00941903 0.0801658i
\(29\) −1.86695 5.74589i −0.346684 1.06698i −0.960676 0.277672i \(-0.910437\pi\)
0.613992 0.789312i \(-0.289563\pi\)
\(30\) −0.670858 + 0.557019i −0.122481 + 0.101697i
\(31\) 0.249623 + 0.277235i 0.0448336 + 0.0497928i 0.765144 0.643859i \(-0.222668\pi\)
−0.720311 + 0.693651i \(0.756001\pi\)
\(32\) −0.788877 0.455459i −0.139455 0.0805145i
\(33\) −0.00853969 0.0401761i −0.00148657 0.00699376i
\(34\) 5.56980 4.04670i 0.955213 0.694003i
\(35\) 1.39068 5.75030i 0.235069 0.971979i
\(36\) −0.381008 0.276818i −0.0635013 0.0461364i
\(37\) −3.68380 + 8.27395i −0.605613 + 1.36023i 0.307119 + 0.951671i \(0.400635\pi\)
−0.912732 + 0.408559i \(0.866032\pi\)
\(38\) −1.11302 + 0.116983i −0.180556 + 0.0189772i
\(39\) −1.26352 + 0.562556i −0.202325 + 0.0900811i
\(40\) −4.18638 5.04195i −0.661924 0.797203i
\(41\) 2.77346 2.01504i 0.433142 0.314696i −0.349762 0.936839i \(-0.613738\pi\)
0.782904 + 0.622142i \(0.213738\pi\)
\(42\) 1.03164 0.0126263i 0.159186 0.00194828i
\(43\) 1.35463i 0.206579i −0.994651 0.103290i \(-0.967063\pi\)
0.994651 0.103290i \(-0.0329369\pi\)
\(44\) 0.0225523 0.00479363i 0.00339988 0.000722667i
\(45\) −3.61969 5.42686i −0.539592 0.808988i
\(46\) −9.46554 2.01196i −1.39562 0.296648i
\(47\) −5.18913 4.67231i −0.756912 0.681527i 0.197405 0.980322i \(-0.436749\pi\)
−0.954317 + 0.298795i \(0.903415\pi\)
\(48\) 0.617181 0.849477i 0.0890824 0.122611i
\(49\) −5.56072 + 4.25187i −0.794389 + 0.607409i
\(50\) −2.25265 6.39451i −0.318572 0.904320i
\(51\) −0.730107 1.26458i −0.102235 0.177077i
\(52\) −0.315783 0.709260i −0.0437912 0.0983566i
\(53\) 0.470762 2.21476i 0.0646642 0.304221i −0.933916 0.357493i \(-0.883632\pi\)
0.998580 + 0.0532718i \(0.0169650\pi\)
\(54\) 1.54400 1.71479i 0.210112 0.233353i
\(55\) 0.316013 + 0.0460837i 0.0426112 + 0.00621393i
\(56\) 0.0948953 + 7.75351i 0.0126809 + 1.03611i
\(57\) 0.237368i 0.0314402i
\(58\) 1.70321 + 8.01299i 0.223643 + 1.05216i
\(59\) 0.344714 + 3.27973i 0.0448779 + 0.426985i 0.993776 + 0.111401i \(0.0355338\pi\)
−0.948898 + 0.315584i \(0.897800\pi\)
\(60\) −0.0863652 + 0.0576052i −0.0111497 + 0.00743680i
\(61\) 0.179533 1.70814i 0.0229868 0.218705i −0.976998 0.213247i \(-0.931596\pi\)
0.999985 0.00545771i \(-0.00173725\pi\)
\(62\) −0.297326 0.409234i −0.0377604 0.0519727i
\(63\) −0.712794 + 7.68545i −0.0898036 + 0.968275i
\(64\) 6.90681 + 5.01809i 0.863351 + 0.627261i
\(65\) −0.694556 10.7314i −0.0861490 1.33107i
\(66\) 0.00582153 + 0.0553882i 0.000716581 + 0.00681781i
\(67\) 8.34782 7.51641i 1.01985 0.918276i 0.0231719 0.999731i \(-0.492623\pi\)
0.996677 + 0.0814554i \(0.0259568\pi\)
\(68\) 0.709855 0.409835i 0.0860825 0.0496998i
\(69\) −0.634245 + 1.95201i −0.0763542 + 0.234994i
\(70\) −2.69036 + 7.55723i −0.321560 + 0.903262i
\(71\) 1.44811 + 4.45682i 0.171859 + 0.528928i 0.999476 0.0323654i \(-0.0103040\pi\)
−0.827617 + 0.561293i \(0.810304\pi\)
\(72\) 6.35382 + 5.72101i 0.748805 + 0.674227i
\(73\) 4.12157 + 9.25719i 0.482393 + 1.08347i 0.976783 + 0.214232i \(0.0687249\pi\)
−0.494390 + 0.869240i \(0.664608\pi\)
\(74\) 6.14034 10.6354i 0.713800 1.23634i
\(75\) −1.39877 + 0.333394i −0.161516 + 0.0384971i
\(76\) −0.133243 −0.0152841
\(77\) −0.256260 0.277694i −0.0292035 0.0316462i
\(78\) 1.78360 0.579528i 0.201953 0.0656186i
\(79\) 7.64875 8.49480i 0.860552 0.955740i −0.138850 0.990313i \(-0.544341\pi\)
0.999402 + 0.0345738i \(0.0110074\pi\)
\(80\) 4.53014 + 6.79186i 0.506485 + 0.759353i
\(81\) 5.52867 + 6.14021i 0.614297 + 0.682246i
\(82\) −4.02564 + 2.32420i −0.444558 + 0.256665i
\(83\) −14.8328 4.81947i −1.62811 0.529005i −0.654275 0.756257i \(-0.727026\pi\)
−0.973836 + 0.227252i \(0.927026\pi\)
\(84\) 0.122309 + 0.0113437i 0.0133450 + 0.00123770i
\(85\) 11.1910 1.91355i 1.21384 0.207553i
\(86\) −0.191997 + 1.82673i −0.0207036 + 0.196982i
\(87\) 1.72798 0.181618i 0.185259 0.0194715i
\(88\) −0.416280 + 0.0437528i −0.0443756 + 0.00466406i
\(89\) −1.42961 + 13.6018i −0.151538 + 1.44179i 0.609346 + 0.792905i \(0.291432\pi\)
−0.760884 + 0.648888i \(0.775235\pi\)
\(90\) 4.11202 + 7.83120i 0.433445 + 0.825481i
\(91\) −7.35251 + 10.3848i −0.770753 + 1.08862i
\(92\) −1.09573 0.356024i −0.114238 0.0371181i
\(93\) −0.0929134 + 0.0536436i −0.00963467 + 0.00556258i
\(94\) 6.33536 + 7.03613i 0.653443 + 0.725722i
\(95\) −1.73099 0.640205i −0.177596 0.0656837i
\(96\) 0.175293 0.194682i 0.0178907 0.0198697i
\(97\) 4.17760 1.35738i 0.424171 0.137821i −0.0891501 0.996018i \(-0.528415\pi\)
0.513321 + 0.858197i \(0.328415\pi\)
\(98\) 8.10132 4.94554i 0.818357 0.499575i
\(99\) −0.416648 −0.0418747
\(100\) −0.187146 0.785177i −0.0187146 0.0785177i
\(101\) 3.76146 6.51503i 0.374279 0.648270i −0.615940 0.787793i \(-0.711224\pi\)
0.990219 + 0.139523i \(0.0445570\pi\)
\(102\) 0.805321 + 1.80878i 0.0797387 + 0.179096i
\(103\) −13.7205 12.3540i −1.35192 1.21727i −0.953983 0.299862i \(-0.903059\pi\)
−0.397937 0.917413i \(-0.630274\pi\)
\(104\) 4.35555 + 13.4050i 0.427097 + 1.31447i
\(105\) 1.53444 + 0.735037i 0.149746 + 0.0717323i
\(106\) −0.948734 + 2.91990i −0.0921492 + 0.283606i
\(107\) −2.68869 + 1.55232i −0.259926 + 0.150068i −0.624301 0.781184i \(-0.714616\pi\)
0.364375 + 0.931252i \(0.381283\pi\)
\(108\) 0.204158 0.183825i 0.0196451 0.0176885i
\(109\) −0.389344 3.70436i −0.0372924 0.354814i −0.997217 0.0745548i \(-0.976246\pi\)
0.959925 0.280259i \(-0.0904202\pi\)
\(110\) −0.419615 0.106934i −0.0400087 0.0101958i
\(111\) −2.10724 1.53100i −0.200011 0.145316i
\(112\) 0.892081 9.61854i 0.0842937 0.908867i
\(113\) 4.37471 + 6.02127i 0.411538 + 0.566434i 0.963593 0.267374i \(-0.0861560\pi\)
−0.552055 + 0.833808i \(0.686156\pi\)
\(114\) 0.0336432 0.320094i 0.00315097 0.0299795i
\(115\) −12.5242 9.88993i −1.16789 0.922241i
\(116\) 0.101949 + 0.969977i 0.00946570 + 0.0900601i
\(117\) 2.91701 + 13.7234i 0.269678 + 1.26873i
\(118\) 4.47161i 0.411645i
\(119\) −11.7151 6.57391i −1.07393 0.602629i
\(120\) 1.66865 0.876175i 0.152326 0.0799835i
\(121\) −7.34679 + 8.15943i −0.667890 + 0.741767i
\(122\) −0.484203 + 2.27799i −0.0438377 + 0.206240i
\(123\) 0.401007 + 0.900676i 0.0361576 + 0.0812112i
\(124\) −0.0301120 0.0521556i −0.00270414 0.00468371i
\(125\) 1.34136 11.0996i 0.119974 0.992777i
\(126\) 2.05050 10.2629i 0.182673 0.914289i
\(127\) 8.53310 11.7448i 0.757190 1.04218i −0.240253 0.970710i \(-0.577230\pi\)
0.997443 0.0714722i \(-0.0227697\pi\)
\(128\) −7.24878 6.52683i −0.640707 0.576895i
\(129\) 0.381065 + 0.0809979i 0.0335509 + 0.00713147i
\(130\) −0.584389 + 14.5698i −0.0512543 + 1.27786i
\(131\) 14.7815 3.14191i 1.29147 0.274510i 0.489565 0.871967i \(-0.337155\pi\)
0.801901 + 0.597457i \(0.203822\pi\)
\(132\) 0.00663070i 0.000577128i
\(133\) 1.11493 + 1.87766i 0.0966763 + 0.162814i
\(134\) −12.3224 + 8.95278i −1.06450 + 0.773403i
\(135\) 3.53549 1.40717i 0.304287 0.121110i
\(136\) −13.5942 + 6.05254i −1.16570 + 0.519001i
\(137\) 15.9508 1.67649i 1.36277 0.143233i 0.605243 0.796041i \(-0.293076\pi\)
0.757523 + 0.652808i \(0.226409\pi\)
\(138\) 1.13195 2.54240i 0.0963581 0.216424i
\(139\) −2.65128 1.92627i −0.224879 0.163384i 0.469641 0.882857i \(-0.344383\pi\)
−0.694520 + 0.719473i \(0.744383\pi\)
\(140\) −0.412602 + 0.861335i −0.0348713 + 0.0727961i
\(141\) 1.62462 1.18036i 0.136818 0.0994040i
\(142\) −1.32111 6.21531i −0.110865 0.521578i
\(143\) −0.594838 0.343430i −0.0497429 0.0287191i
\(144\) −7.12707 7.91541i −0.593922 0.659618i
\(145\) −3.33609 + 13.0910i −0.277047 + 1.08715i
\(146\) −4.24591 13.0676i −0.351394 1.08148i
\(147\) −0.863579 1.81849i −0.0712268 0.149987i
\(148\) 0.859405 1.18287i 0.0706427 0.0972313i
\(149\) −5.39761 9.34893i −0.442189 0.765894i 0.555663 0.831408i \(-0.312465\pi\)
−0.997852 + 0.0655140i \(0.979131\pi\)
\(150\) 1.93350 0.251333i 0.157870 0.0205212i
\(151\) 8.70042 15.0696i 0.708030 1.22634i −0.257557 0.966263i \(-0.582917\pi\)
0.965587 0.260081i \(-0.0837492\pi\)
\(152\) 2.40572 + 0.252851i 0.195130 + 0.0205090i
\(153\) −14.0873 + 4.57725i −1.13889 + 0.370049i
\(154\) 0.306210 + 0.410794i 0.0246751 + 0.0331027i
\(155\) −0.140595 0.822245i −0.0112929 0.0660443i
\(156\) 0.218400 0.0464224i 0.0174860 0.00371677i
\(157\) −7.20222 4.15820i −0.574800 0.331861i 0.184264 0.982877i \(-0.441010\pi\)
−0.759064 + 0.651016i \(0.774343\pi\)
\(158\) −11.5184 + 10.3712i −0.916356 + 0.825090i
\(159\) 0.594876 + 0.264856i 0.0471768 + 0.0210044i
\(160\) 0.946922 + 1.80338i 0.0748608 + 0.142570i
\(161\) 4.15155 + 18.4201i 0.327188 + 1.45170i
\(162\) −6.58519 9.06373i −0.517381 0.712114i
\(163\) 5.57419 12.5198i 0.436604 0.980630i −0.552513 0.833504i \(-0.686331\pi\)
0.989118 0.147126i \(-0.0470022\pi\)
\(164\) −0.505581 + 0.225099i −0.0394793 + 0.0175773i
\(165\) −0.0318591 + 0.0861407i −0.00248023 + 0.00670604i
\(166\) 19.3191 + 8.60141i 1.49945 + 0.667599i
\(167\) −16.4112 5.33231i −1.26993 0.412626i −0.404910 0.914357i \(-0.632697\pi\)
−0.865024 + 0.501730i \(0.832697\pi\)
\(168\) −2.18678 0.436913i −0.168714 0.0337086i
\(169\) −3.13005 + 9.63330i −0.240773 + 0.741023i
\(170\) −15.3624 + 0.994284i −1.17824 + 0.0762581i
\(171\) 2.35523 + 0.500620i 0.180109 + 0.0382834i
\(172\) −0.0454670 + 0.213905i −0.00346683 + 0.0163101i
\(173\) 5.73912 + 0.603206i 0.436337 + 0.0458609i 0.320151 0.947367i \(-0.396266\pi\)
0.116186 + 0.993227i \(0.462933\pi\)
\(174\) −2.35594 −0.178603
\(175\) −9.49872 + 9.20730i −0.718036 + 0.696006i
\(176\) 0.521446 0.0393055
\(177\) −0.943219 0.0991363i −0.0708967 0.00745154i
\(178\) 3.85569 18.1396i 0.288996 1.35962i
\(179\) −12.8846 2.73871i −0.963043 0.204701i −0.300548 0.953767i \(-0.597169\pi\)
−0.662496 + 0.749066i \(0.730503\pi\)
\(180\) 0.389426 + 0.978429i 0.0290261 + 0.0729278i
\(181\) 5.86832 18.0608i 0.436189 1.34245i −0.455674 0.890147i \(-0.650602\pi\)
0.891863 0.452305i \(-0.149398\pi\)
\(182\) 11.3868 12.9619i 0.844047 0.960799i
\(183\) 0.469774 + 0.152639i 0.0347267 + 0.0112834i
\(184\) 19.1079 + 8.50739i 1.40865 + 0.627173i
\(185\) 16.8481 11.2376i 1.23870 0.826207i
\(186\) 0.132898 0.0591699i 0.00974453 0.00433854i
\(187\) 0.294948 0.662464i 0.0215687 0.0484442i
\(188\) 0.662576 + 0.911958i 0.0483234 + 0.0665114i
\(189\) −4.29876 1.33881i −0.312689 0.0973845i
\(190\) 2.24352 + 1.10866i 0.162762 + 0.0804308i
\(191\) 13.4652 + 5.99510i 0.974309 + 0.433790i 0.831235 0.555922i \(-0.187635\pi\)
0.143074 + 0.989712i \(0.454301\pi\)
\(192\) −1.82460 + 1.64287i −0.131679 + 0.118564i
\(193\) −3.43318 1.98215i −0.247125 0.142678i 0.371322 0.928504i \(-0.378905\pi\)
−0.618447 + 0.785826i \(0.712238\pi\)
\(194\) −5.82591 + 1.23834i −0.418276 + 0.0889074i
\(195\) 3.06033 + 0.446283i 0.219155 + 0.0319590i
\(196\) 1.02079 0.484757i 0.0729133 0.0346255i
\(197\) −18.9759 + 6.16564i −1.35198 + 0.439283i −0.893356 0.449350i \(-0.851656\pi\)
−0.458619 + 0.888633i \(0.651656\pi\)
\(198\) 0.561854 + 0.0590532i 0.0399292 + 0.00419673i
\(199\) −2.37463 + 4.11297i −0.168333 + 0.291561i −0.937834 0.347085i \(-0.887172\pi\)
0.769501 + 0.638646i \(0.220505\pi\)
\(200\) 1.88894 + 14.5316i 0.133568 + 1.02754i
\(201\) 1.61526 + 2.79772i 0.113932 + 0.197336i
\(202\) −5.99576 + 8.25245i −0.421860 + 0.580641i
\(203\) 12.8158 9.55303i 0.899493 0.670491i
\(204\) 0.0728442 + 0.224191i 0.00510011 + 0.0156965i
\(205\) −7.64966 + 0.495100i −0.534275 + 0.0345793i
\(206\) 16.7512 + 18.6041i 1.16711 + 1.29621i
\(207\) 18.0307 + 10.4100i 1.25322 + 0.723546i
\(208\) −3.65072 17.1753i −0.253132 1.19089i
\(209\) −0.0953666 + 0.0692879i −0.00659665 + 0.00479274i
\(210\) −1.96502 1.20869i −0.135600 0.0834073i
\(211\) −1.61068 1.17023i −0.110884 0.0805619i 0.530961 0.847396i \(-0.321831\pi\)
−0.641845 + 0.766834i \(0.721831\pi\)
\(212\) −0.148673 + 0.333925i −0.0102109 + 0.0229341i
\(213\) −1.34032 + 0.140873i −0.0918369 + 0.00965245i
\(214\) 3.84574 1.71224i 0.262890 0.117046i
\(215\) −1.61844 + 2.56043i −0.110377 + 0.174620i
\(216\) −4.03493 + 2.93155i −0.274542 + 0.199467i
\(217\) −0.483009 + 0.860754i −0.0327888 + 0.0584318i
\(218\) 5.05055i 0.342066i
\(219\) −2.85054 + 0.605901i −0.192622 + 0.0409430i
\(220\) −0.0483538 0.0178836i −0.00326001 0.00120571i
\(221\) −23.8850 5.07692i −1.60668 0.341511i
\(222\) 2.62464 + 2.36324i 0.176154 + 0.158610i
\(223\) −9.57365 + 13.1770i −0.641099 + 0.882397i −0.998674 0.0514874i \(-0.983604\pi\)
0.357575 + 0.933885i \(0.383604\pi\)
\(224\) 0.472192 2.36335i 0.0315497 0.157908i
\(225\) 0.357969 + 14.5821i 0.0238646 + 0.972138i
\(226\) −5.04592 8.73979i −0.335649 0.581362i
\(227\) −0.448022 1.00627i −0.0297363 0.0667888i 0.898067 0.439859i \(-0.144972\pi\)
−0.927803 + 0.373070i \(0.878305\pi\)
\(228\) 0.00796706 0.0374821i 0.000527632 0.00248231i
\(229\) 4.12813 4.58476i 0.272795 0.302969i −0.591144 0.806566i \(-0.701324\pi\)
0.863939 + 0.503597i \(0.167990\pi\)
\(230\) 15.4873 + 15.1118i 1.02120 + 0.996440i
\(231\) 0.0934395 0.0554830i 0.00614787 0.00365051i
\(232\) 17.7065i 1.16249i
\(233\) 2.15421 + 10.1348i 0.141127 + 0.663950i 0.990653 + 0.136404i \(0.0435544\pi\)
−0.849526 + 0.527546i \(0.823112\pi\)
\(234\) −1.98853 18.9196i −0.129995 1.23682i
\(235\) 4.22590 + 15.0310i 0.275667 + 0.980512i
\(236\) 0.0556487 0.529462i 0.00362242 0.0344651i
\(237\) 1.93229 + 2.65957i 0.125516 + 0.172757i
\(238\) 14.8662 + 10.5254i 0.963635 + 0.682261i
\(239\) −5.80855 4.22016i −0.375724 0.272979i 0.383857 0.923393i \(-0.374596\pi\)
−0.759580 + 0.650413i \(0.774596\pi\)
\(240\) −2.18146 + 0.868246i −0.140813 + 0.0560450i
\(241\) −2.10935 20.0691i −0.135875 1.29277i −0.823757 0.566943i \(-0.808126\pi\)
0.687882 0.725822i \(-0.258541\pi\)
\(242\) 11.0637 9.96178i 0.711200 0.640368i
\(243\) −6.47914 + 3.74073i −0.415637 + 0.239968i
\(244\) −0.0856816 + 0.263701i −0.00548520 + 0.0168817i
\(245\) 15.5904 1.39292i 0.996032 0.0889907i
\(246\) −0.413105 1.27141i −0.0263386 0.0810619i
\(247\) 2.94986 + 2.65607i 0.187695 + 0.169002i
\(248\) 0.444702 + 0.998817i 0.0282386 + 0.0634249i
\(249\) 2.24264 3.88437i 0.142122 0.246162i
\(250\) −3.38202 + 14.7778i −0.213898 + 0.934629i
\(251\) 26.6764 1.68380 0.841901 0.539632i \(-0.181437\pi\)
0.841901 + 0.539632i \(0.181437\pi\)
\(252\) 0.370510 1.18966i 0.0233399 0.0749415i
\(253\) −0.969387 + 0.314973i −0.0609448 + 0.0198022i
\(254\) −13.1716 + 14.6285i −0.826460 + 0.917876i
\(255\) −0.130858 + 3.26251i −0.00819464 + 0.204307i
\(256\) −2.57515 2.86000i −0.160947 0.178750i
\(257\) 1.53581 0.886703i 0.0958015 0.0553110i −0.451334 0.892355i \(-0.649052\pi\)
0.547135 + 0.837044i \(0.315718\pi\)
\(258\) −0.502390 0.163236i −0.0312774 0.0101626i
\(259\) −23.8601 2.21293i −1.48259 0.137505i
\(260\) −0.250515 + 1.71787i −0.0155363 + 0.106538i
\(261\) 1.84232 17.5285i 0.114037 1.08499i
\(262\) −20.3783 + 2.14185i −1.25898 + 0.132324i
\(263\) −0.0677999 + 0.00712606i −0.00418072 + 0.000439412i −0.106619 0.994300i \(-0.534002\pi\)
0.102438 + 0.994739i \(0.467336\pi\)
\(264\) 0.0125829 0.119718i 0.000774422 0.00736813i
\(265\) −3.53588 + 3.62374i −0.217207 + 0.222605i
\(266\) −1.23736 2.69006i −0.0758674 0.164938i
\(267\) −3.74079 1.21546i −0.228933 0.0743847i
\(268\) −1.57046 + 0.906705i −0.0959311 + 0.0553858i
\(269\) 3.65949 + 4.06427i 0.223123 + 0.247803i 0.844305 0.535863i \(-0.180014\pi\)
−0.621182 + 0.783666i \(0.713347\pi\)
\(270\) −4.96709 + 1.39648i −0.302287 + 0.0849869i
\(271\) 2.12393 2.35887i 0.129020 0.143291i −0.675173 0.737659i \(-0.735931\pi\)
0.804193 + 0.594368i \(0.202598\pi\)
\(272\) 17.6307 5.72856i 1.06902 0.347345i
\(273\) −2.48167 2.68924i −0.150197 0.162760i
\(274\) −21.7474 −1.31381
\(275\) −0.542247 0.464659i −0.0326987 0.0280200i
\(276\) 0.165669 0.286947i 0.00997210 0.0172722i
\(277\) 3.99112 + 8.96419i 0.239803 + 0.538606i 0.992851 0.119359i \(-0.0380840\pi\)
−0.753048 + 0.657965i \(0.771417\pi\)
\(278\) 3.30226 + 2.97337i 0.198057 + 0.178331i
\(279\) 0.336307 + 1.03505i 0.0201342 + 0.0619667i
\(280\) 9.08410 14.7685i 0.542879 0.882586i
\(281\) −6.68442 + 20.5725i −0.398759 + 1.22725i 0.527236 + 0.849719i \(0.323228\pi\)
−0.925995 + 0.377536i \(0.876772\pi\)
\(282\) −2.35811 + 1.36146i −0.140424 + 0.0810737i
\(283\) 15.8761 14.2949i 0.943738 0.849746i −0.0450630 0.998984i \(-0.514349\pi\)
0.988801 + 0.149238i \(0.0476822\pi\)
\(284\) −0.0790770 0.752367i −0.00469235 0.0446448i
\(285\) 0.283595 0.448657i 0.0167987 0.0265761i
\(286\) 0.753469 + 0.547428i 0.0445536 + 0.0323701i
\(287\) 7.40259 + 5.24109i 0.436961 + 0.309372i
\(288\) −1.56199 2.14989i −0.0920410 0.126684i
\(289\) 0.917775 8.73204i 0.0539868 0.513650i
\(290\) 6.35419 17.1805i 0.373131 1.00887i
\(291\) 0.132047 + 1.25634i 0.00774073 + 0.0736481i
\(292\) −0.340114 1.60011i −0.0199037 0.0936393i
\(293\) 3.83275i 0.223911i −0.993713 0.111956i \(-0.964289\pi\)
0.993713 0.111956i \(-0.0357115\pi\)
\(294\) 0.906801 + 2.57466i 0.0528857 + 0.150157i
\(295\) 3.26689 6.61096i 0.190206 0.384905i
\(296\) −17.7613 + 19.7260i −1.03236 + 1.14655i
\(297\) 0.0505318 0.237734i 0.00293215 0.0137947i
\(298\) 5.95366 + 13.3721i 0.344886 + 0.774627i
\(299\) 17.1613 + 29.7242i 0.992464 + 1.71900i
\(300\) 0.232065 0.00569686i 0.0133983 0.000328908i
\(301\) 3.39479 1.14915i 0.195673 0.0662362i
\(302\) −13.8685 + 19.0883i −0.798041 + 1.09841i
\(303\) 1.60780 + 1.44767i 0.0923659 + 0.0831667i
\(304\) −2.94764 0.626539i −0.169059 0.0359345i
\(305\) −2.38013 + 3.01411i −0.136286 + 0.172587i
\(306\) 19.6457 4.17581i 1.12307 0.238715i
\(307\) 19.4072i 1.10763i 0.832641 + 0.553814i \(0.186828\pi\)
−0.832641 + 0.553814i \(0.813172\pi\)
\(308\) 0.0311446 + 0.0524509i 0.00177463 + 0.00298867i
\(309\) 4.29564 3.12096i 0.244370 0.177545i
\(310\) 0.0730536 + 1.12873i 0.00414917 + 0.0641077i
\(311\) 2.48883 1.10810i 0.141128 0.0628344i −0.334957 0.942233i \(-0.608722\pi\)
0.476086 + 0.879399i \(0.342055\pi\)
\(312\) −4.03133 + 0.423710i −0.228229 + 0.0239879i
\(313\) 10.3886 23.3332i 0.587200 1.31887i −0.338626 0.940921i \(-0.609962\pi\)
0.925826 0.377951i \(-0.123371\pi\)
\(314\) 9.12290 + 6.62817i 0.514835 + 0.374049i
\(315\) 10.5294 13.6749i 0.593266 0.770492i
\(316\) −1.49291 + 1.08466i −0.0839827 + 0.0610170i
\(317\) 2.15677 + 10.1468i 0.121137 + 0.569903i 0.996290 + 0.0860574i \(0.0274269\pi\)
−0.875154 + 0.483845i \(0.839240\pi\)
\(318\) −0.764657 0.441475i −0.0428798 0.0247567i
\(319\) 0.577366 + 0.641230i 0.0323263 + 0.0359020i
\(320\) −7.05942 17.7367i −0.394633 0.991512i
\(321\) −0.275909 0.849162i −0.0153998 0.0473956i
\(322\) −2.98765 25.4280i −0.166495 1.41705i
\(323\) −2.46326 + 3.39039i −0.137060 + 0.188646i
\(324\) −0.666924 1.15515i −0.0370513 0.0641748i
\(325\) −11.5085 + 21.1135i −0.638376 + 1.17117i
\(326\) −9.29134 + 16.0931i −0.514600 + 0.891313i
\(327\) 1.06534 + 0.111971i 0.0589133 + 0.00619204i
\(328\) 9.55548 3.10476i 0.527613 0.171432i
\(329\) 7.30710 16.9679i 0.402854 0.935470i
\(330\) 0.0551713 0.111646i 0.00303708 0.00614591i
\(331\) 12.8193 2.72482i 0.704611 0.149770i 0.158348 0.987383i \(-0.449383\pi\)
0.546263 + 0.837614i \(0.316050\pi\)
\(332\) 2.18044 + 1.25888i 0.119667 + 0.0690898i
\(333\) −19.6352 + 17.6797i −1.07600 + 0.968839i
\(334\) 21.3748 + 9.51669i 1.16958 + 0.520730i
\(335\) −24.7587 + 4.23346i −1.35271 + 0.231299i
\(336\) 2.65241 + 0.826072i 0.144701 + 0.0450659i
\(337\) −6.06126 8.34261i −0.330178 0.454451i 0.611363 0.791351i \(-0.290622\pi\)
−0.941541 + 0.336899i \(0.890622\pi\)
\(338\) 5.58627 12.5470i 0.303853 0.682465i
\(339\) −1.95539 + 0.870598i −0.106202 + 0.0472844i
\(340\) −1.83136 0.0734552i −0.0993197 0.00398367i
\(341\) −0.0486736 0.0216709i −0.00263582 0.00117354i
\(342\) −3.10510 1.00891i −0.167904 0.0545554i
\(343\) −15.3727 10.3286i −0.830048 0.557693i
\(344\) 1.22683 3.77580i 0.0661464 0.203578i
\(345\) 3.53096 2.93178i 0.190100 0.157842i
\(346\) −7.65376 1.62686i −0.411469 0.0874603i
\(347\) −1.02728 + 4.83296i −0.0551471 + 0.259447i −0.997081 0.0763517i \(-0.975673\pi\)
0.941934 + 0.335799i \(0.109006\pi\)
\(348\) −0.278956 0.0293194i −0.0149536 0.00157169i
\(349\) 16.4954 0.882977 0.441488 0.897267i \(-0.354451\pi\)
0.441488 + 0.897267i \(0.354451\pi\)
\(350\) 14.1141 11.0698i 0.754430 0.591707i
\(351\) −8.18419 −0.436840
\(352\) 0.129385 + 0.0135989i 0.00689622 + 0.000724822i
\(353\) −6.58363 + 30.9736i −0.350411 + 1.64856i 0.351423 + 0.936217i \(0.385698\pi\)
−0.701835 + 0.712340i \(0.747636\pi\)
\(354\) 1.25789 + 0.267372i 0.0668560 + 0.0142107i
\(355\) 2.58766 10.1541i 0.137338 0.538923i
\(356\) 0.682279 2.09984i 0.0361607 0.111291i
\(357\) 2.54976 2.90246i 0.134948 0.153614i
\(358\) 16.9869 + 5.51937i 0.897785 + 0.291708i
\(359\) −24.7508 11.0198i −1.30630 0.581602i −0.368773 0.929519i \(-0.620222\pi\)
−0.937525 + 0.347918i \(0.886889\pi\)
\(360\) −5.17439 18.4046i −0.272714 0.970009i
\(361\) −16.7350 + 7.45091i −0.880791 + 0.392153i
\(362\) −10.4733 + 23.5235i −0.550466 + 1.23637i
\(363\) −1.85600 2.55457i −0.0974150 0.134080i
\(364\) 1.50957 1.39305i 0.0791228 0.0730156i
\(365\) 3.26969 22.4215i 0.171144 1.17360i
\(366\) −0.611860 0.272418i −0.0319824 0.0142395i
\(367\) 15.5681 14.0175i 0.812646 0.731710i −0.153932 0.988081i \(-0.549194\pi\)
0.966578 + 0.256371i \(0.0825270\pi\)
\(368\) −22.5659 13.0284i −1.17633 0.679153i
\(369\) 9.78248 2.07933i 0.509256 0.108246i
\(370\) −24.3126 + 12.7661i −1.26395 + 0.663678i
\(371\) 5.94969 0.699056i 0.308893 0.0362932i
\(372\) 0.0164721 0.00535213i 0.000854041 0.000277495i
\(373\) 1.39088 + 0.146187i 0.0720168 + 0.00756927i 0.140468 0.990085i \(-0.455139\pi\)
−0.0684515 + 0.997654i \(0.521806\pi\)
\(374\) −0.491634 + 0.851535i −0.0254218 + 0.0440318i
\(375\) 3.04217 + 1.04101i 0.157097 + 0.0537576i
\(376\) −10.2323 17.7228i −0.527690 0.913986i
\(377\) 17.0784 23.5065i 0.879585 1.21064i
\(378\) 5.60716 + 2.41468i 0.288401 + 0.124198i
\(379\) 4.54620 + 13.9918i 0.233522 + 0.718708i 0.997314 + 0.0732451i \(0.0233355\pi\)
−0.763792 + 0.645463i \(0.776664\pi\)
\(380\) 0.251847 + 0.159192i 0.0129195 + 0.00816637i
\(381\) 2.79365 + 3.10267i 0.143123 + 0.158954i
\(382\) −17.3083 9.99293i −0.885568 0.511283i
\(383\) 5.04328 + 23.7268i 0.257700 + 1.21238i 0.896512 + 0.443019i \(0.146093\pi\)
−0.638812 + 0.769363i \(0.720574\pi\)
\(384\) 2.26946 1.64886i 0.115813 0.0841430i
\(385\) 0.152590 + 0.831043i 0.00777670 + 0.0423539i
\(386\) 4.34873 + 3.15954i 0.221345 + 0.160816i
\(387\) 1.60736 3.61020i 0.0817069 0.183517i
\(388\) −0.705230 + 0.0741227i −0.0358026 + 0.00376301i
\(389\) 23.3117 10.3790i 1.18195 0.526238i 0.280809 0.959764i \(-0.409397\pi\)
0.901141 + 0.433526i \(0.142731\pi\)
\(390\) −4.06363 1.03557i −0.205770 0.0524381i
\(391\) −29.3158 + 21.2992i −1.48256 + 1.07715i
\(392\) −19.3503 + 6.81523i −0.977337 + 0.344221i
\(393\) 4.34598i 0.219226i
\(394\) 26.4630 5.62489i 1.33319 0.283378i
\(395\) −24.6062 + 6.91795i −1.23807 + 0.348080i
\(396\) 0.0657915 + 0.0139844i 0.00330615 + 0.000702744i
\(397\) −3.74278 3.37001i −0.187844 0.169136i 0.569843 0.821754i \(-0.307004\pi\)
−0.757687 + 0.652618i \(0.773671\pi\)
\(398\) 3.78515 5.20982i 0.189733 0.261145i
\(399\) −0.594861 + 0.201363i −0.0297803 + 0.0100808i
\(400\) −0.448008 18.2499i −0.0224004 0.912493i
\(401\) −14.8506 25.7220i −0.741605 1.28450i −0.951764 0.306830i \(-0.900732\pi\)
0.210159 0.977667i \(-0.432602\pi\)
\(402\) −1.78167 4.00169i −0.0888614 0.199586i
\(403\) −0.373020 + 1.75492i −0.0185814 + 0.0874188i
\(404\) −0.812630 + 0.902517i −0.0404299 + 0.0449019i
\(405\) −3.11391 18.2111i −0.154731 0.904919i
\(406\) −18.6362 + 11.0659i −0.924900 + 0.549192i
\(407\) 1.29352i 0.0641173i
\(408\) −0.889768 4.18603i −0.0440501 0.207239i
\(409\) 2.23540 + 21.2684i 0.110533 + 1.05165i 0.899411 + 0.437103i \(0.143996\pi\)
−0.788878 + 0.614550i \(0.789338\pi\)
\(410\) 10.3858 + 0.416570i 0.512918 + 0.0205729i
\(411\) −0.482143 + 4.58728i −0.0237823 + 0.226274i
\(412\) 1.75191 + 2.41129i 0.0863103 + 0.118796i
\(413\) −7.92680 + 3.64612i −0.390052 + 0.179414i
\(414\) −22.8391 16.5936i −1.12248 0.815529i
\(415\) 22.2778 + 26.8308i 1.09358 + 1.31707i
\(416\) −0.457923 4.35684i −0.0224515 0.213612i
\(417\) 0.700399 0.630642i 0.0342987 0.0308827i
\(418\) 0.138423 0.0799187i 0.00677050 0.00390895i
\(419\) 7.11650 21.9023i 0.347664 1.07000i −0.612479 0.790487i \(-0.709827\pi\)
0.960142 0.279512i \(-0.0901726\pi\)
\(420\) −0.217627 0.167569i −0.0106191 0.00817655i
\(421\) 5.15258 + 15.8580i 0.251121 + 0.772872i 0.994569 + 0.104078i \(0.0331892\pi\)
−0.743448 + 0.668794i \(0.766811\pi\)
\(422\) 2.00616 + 1.80635i 0.0976583 + 0.0879319i
\(423\) −8.28542 18.6093i −0.402851 0.904817i
\(424\) 3.31798 5.74692i 0.161136 0.279095i
\(425\) −23.4387 9.75358i −1.13694 0.473118i
\(426\) 1.82739 0.0885376
\(427\) 4.43301 0.999120i 0.214528 0.0483508i
\(428\) 0.476665 0.154878i 0.0230405 0.00748630i
\(429\) 0.132176 0.146796i 0.00638152 0.00708740i
\(430\) 2.54538 3.22337i 0.122749 0.155445i
\(431\) −4.71885 5.24082i −0.227299 0.252441i 0.618698 0.785629i \(-0.287661\pi\)
−0.845997 + 0.533188i \(0.820994\pi\)
\(432\) 5.38081 3.10661i 0.258884 0.149467i
\(433\) −0.997867 0.324227i −0.0479544 0.0155813i 0.284942 0.958545i \(-0.408026\pi\)
−0.332896 + 0.942964i \(0.608026\pi\)
\(434\) 0.773340 1.09228i 0.0371215 0.0524309i
\(435\) −3.48309 1.72121i −0.167001 0.0825259i
\(436\) −0.0628536 + 0.598012i −0.00301014 + 0.0286396i
\(437\) 5.85821 0.615723i 0.280236 0.0294540i
\(438\) 3.92986 0.413045i 0.187776 0.0197360i
\(439\) 0.830281 7.89959i 0.0396271 0.377027i −0.956678 0.291147i \(-0.905963\pi\)
0.996305 0.0858800i \(-0.0273702\pi\)
\(440\) 0.839096 + 0.414650i 0.0400023 + 0.0197677i
\(441\) −19.8649 + 4.73337i −0.945948 + 0.225399i
\(442\) 31.4896 + 10.2316i 1.49781 + 0.486668i
\(443\) −17.8294 + 10.2938i −0.847099 + 0.489073i −0.859671 0.510848i \(-0.829331\pi\)
0.0125723 + 0.999921i \(0.495998\pi\)
\(444\) 0.281361 + 0.312483i 0.0133528 + 0.0148298i
\(445\) 18.9529 24.0012i 0.898453 1.13777i
\(446\) 14.7778 16.4124i 0.699748 0.777149i
\(447\) 2.95264 0.959372i 0.139655 0.0453768i
\(448\) −6.71651 + 21.5658i −0.317325 + 1.01889i
\(449\) 14.6499 0.691371 0.345685 0.938350i \(-0.387646\pi\)
0.345685 + 0.938350i \(0.387646\pi\)
\(450\) 1.58405 19.7148i 0.0746728 0.929364i
\(451\) −0.244807 + 0.424019i −0.0115275 + 0.0199663i
\(452\) −0.488698 1.09763i −0.0229864 0.0516283i
\(453\) 3.71892 + 3.34853i 0.174730 + 0.157328i
\(454\) 0.461539 + 1.42047i 0.0216611 + 0.0666660i
\(455\) 26.3044 10.8442i 1.23317 0.508384i
\(456\) −0.214975 + 0.661624i −0.0100671 + 0.0309834i
\(457\) −29.9385 + 17.2850i −1.40046 + 0.808557i −0.994440 0.105306i \(-0.966418\pi\)
−0.406023 + 0.913863i \(0.633085\pi\)
\(458\) −6.21664 + 5.59749i −0.290485 + 0.261554i
\(459\) −0.903179 8.59318i −0.0421568 0.401095i
\(460\) 1.64571 + 1.98205i 0.0767318 + 0.0924136i
\(461\) −12.8239 9.31709i −0.597267 0.433940i 0.247641 0.968852i \(-0.420345\pi\)
−0.844908 + 0.534912i \(0.820345\pi\)
\(462\) −0.133868 + 0.0615758i −0.00622810 + 0.00286476i
\(463\) −7.65984 10.5429i −0.355983 0.489969i 0.593041 0.805172i \(-0.297927\pi\)
−0.949024 + 0.315204i \(0.897927\pi\)
\(464\) −2.30571 + 21.9374i −0.107040 + 1.01842i
\(465\) 0.239709 + 0.00961460i 0.0111162 + 0.000445866i
\(466\) −1.46853 13.9721i −0.0680283 0.647246i
\(467\) 6.35092 + 29.8787i 0.293885 + 1.38262i 0.838941 + 0.544222i \(0.183175\pi\)
−0.545056 + 0.838400i \(0.683492\pi\)
\(468\) 2.26493i 0.104696i
\(469\) 25.9182 + 14.5439i 1.19679 + 0.671575i
\(470\) −3.56826 20.8683i −0.164592 0.962585i
\(471\) 1.60037 1.77739i 0.0737411 0.0818978i
\(472\) −2.00949 + 9.45389i −0.0924941 + 0.435150i
\(473\) 0.0786908 + 0.176742i 0.00361821 + 0.00812663i
\(474\) −2.22876 3.86032i −0.102370 0.177310i
\(475\) 2.50691 + 3.27816i 0.115025 + 0.150412i
\(476\) 1.62925 + 1.43127i 0.0746767 + 0.0656023i
\(477\) 3.88259 5.34392i 0.177772 0.244681i
\(478\) 7.23474 + 6.51419i 0.330909 + 0.297952i
\(479\) −6.64926 1.41334i −0.303812 0.0645773i 0.0534830 0.998569i \(-0.482968\pi\)
−0.357295 + 0.933991i \(0.616301\pi\)
\(480\) −0.563921 + 0.158544i −0.0257393 + 0.00723652i
\(481\) −42.6056 + 9.05609i −1.94265 + 0.412922i
\(482\) 27.3623i 1.24632i
\(483\) −5.42990 + 0.0664566i −0.247069 + 0.00302388i
\(484\) 1.43397 1.04184i 0.0651805 0.0473564i
\(485\) −9.51792 2.42553i −0.432186 0.110138i
\(486\) 9.26737 4.12610i 0.420376 0.187164i
\(487\) 27.3581 2.87545i 1.23971 0.130299i 0.538114 0.842872i \(-0.319137\pi\)
0.701598 + 0.712573i \(0.252470\pi\)
\(488\) 2.04740 4.59855i 0.0926817 0.208166i
\(489\) 3.18860 + 2.31665i 0.144193 + 0.104763i
\(490\) −21.2212 0.331316i −0.958676 0.0149673i
\(491\) 3.14168 2.28256i 0.141782 0.103011i −0.514633 0.857410i \(-0.672072\pi\)
0.656415 + 0.754400i \(0.272072\pi\)
\(492\) −0.0330913 0.155682i −0.00149187 0.00701870i
\(493\) 26.5659 + 15.3378i 1.19647 + 0.690780i
\(494\) −3.60146 3.99983i −0.162037 0.179961i
\(495\) 0.787518 + 0.497788i 0.0353963 + 0.0223739i
\(496\) −0.420898 1.29539i −0.0188989 0.0581647i
\(497\) −9.94064 + 7.40985i −0.445898 + 0.332377i
\(498\) −3.57477 + 4.92025i −0.160189 + 0.220482i
\(499\) 9.17007 + 15.8830i 0.410509 + 0.711022i 0.994945 0.100417i \(-0.0320177\pi\)
−0.584437 + 0.811439i \(0.698684\pi\)
\(500\) −0.584357 + 1.70768i −0.0261332 + 0.0763697i
\(501\) 2.48129 4.29771i 0.110856 0.192008i
\(502\) −35.9734 3.78096i −1.60557 0.168752i
\(503\) 32.5781 10.5853i 1.45259 0.471974i 0.526790 0.849995i \(-0.323395\pi\)
0.925797 + 0.378021i \(0.123395\pi\)
\(504\) −8.94717 + 20.7763i −0.398539 + 0.925450i
\(505\) −14.8934 + 7.82026i −0.662749 + 0.347997i
\(506\) 1.35187 0.287349i 0.0600979 0.0127742i
\(507\) −2.52274 1.45651i −0.112039 0.0646857i
\(508\) −1.74164 + 1.56818i −0.0772727 + 0.0695766i
\(509\) −13.0256 5.79939i −0.577352 0.257054i 0.0972200 0.995263i \(-0.469005\pi\)
−0.674572 + 0.738209i \(0.735672\pi\)
\(510\) 0.638872 4.38098i 0.0282897 0.193993i
\(511\) −19.7027 + 18.1819i −0.871598 + 0.804321i
\(512\) 14.5340 + 20.0043i 0.642318 + 0.884075i
\(513\) −0.571294 + 1.28315i −0.0252232 + 0.0566523i
\(514\) −2.19674 + 0.978050i −0.0968939 + 0.0431399i
\(515\) 11.1736 + 39.7431i 0.492369 + 1.75129i
\(516\) −0.0574541 0.0255802i −0.00252928 0.00112611i
\(517\) 0.948455 + 0.308172i 0.0417130 + 0.0135534i
\(518\) 31.8619 + 6.36594i 1.39993 + 0.279703i
\(519\) −0.512846 + 1.57838i −0.0225114 + 0.0692831i
\(520\) 7.78301 30.5409i 0.341308 1.33931i
\(521\) 38.7121 + 8.22852i 1.69601 + 0.360498i 0.951627 0.307256i \(-0.0994108\pi\)
0.744382 + 0.667754i \(0.232744\pi\)
\(522\) −4.96877 + 23.3762i −0.217477 + 1.02315i
\(523\) −3.42093 0.359554i −0.149587 0.0157222i 0.0294391 0.999567i \(-0.490628\pi\)
−0.179026 + 0.983844i \(0.557295\pi\)
\(524\) −2.43956 −0.106572
\(525\) −2.02210 3.22258i −0.0882518 0.140645i
\(526\) 0.0924388 0.00403053
\(527\) −1.88378 0.197994i −0.0820589 0.00862474i
\(528\) −0.0311790 + 0.146686i −0.00135689 + 0.00638368i
\(529\) 27.3230 + 5.80768i 1.18796 + 0.252508i
\(530\) 5.28177 4.38550i 0.229425 0.190494i
\(531\) −2.97294 + 9.14978i −0.129015 + 0.397067i
\(532\) −0.113032 0.333916i −0.00490057 0.0144771i
\(533\) 15.6801 + 5.09479i 0.679182 + 0.220680i
\(534\) 4.87222 + 2.16925i 0.210842 + 0.0938727i
\(535\) 6.93660 + 0.278224i 0.299895 + 0.0120287i
\(536\) 30.0754 13.3904i 1.29906 0.578379i
\(537\) 1.54083 3.46076i 0.0664918 0.149343i
\(538\) −4.35880 5.99938i −0.187921 0.258652i
\(539\) 0.478531 0.877776i 0.0206118 0.0378085i
\(540\) −0.605508 + 0.103535i −0.0260569 + 0.00445546i
\(541\) 37.5468 + 16.7169i 1.61426 + 0.718717i 0.997648 0.0685469i \(-0.0218363\pi\)
0.616616 + 0.787264i \(0.288503\pi\)
\(542\) −3.19847 + 2.87992i −0.137386 + 0.123703i
\(543\) 4.72973 + 2.73071i 0.202972 + 0.117186i
\(544\) 4.52403 0.961613i 0.193966 0.0412288i
\(545\) −3.68986 + 7.46689i −0.158056 + 0.319846i
\(546\) 2.96539 + 3.97821i 0.126907 + 0.170251i
\(547\) 8.10774 2.63436i 0.346662 0.112637i −0.130511 0.991447i \(-0.541662\pi\)
0.477172 + 0.878810i \(0.341662\pi\)
\(548\) −2.57500 0.270644i −0.109999 0.0115613i
\(549\) 2.50529 4.33930i 0.106923 0.185197i
\(550\) 0.665367 + 0.703452i 0.0283713 + 0.0299953i
\(551\) −2.49327 4.31848i −0.106217 0.183973i
\(552\) −3.53570 + 4.86647i −0.150489 + 0.207131i
\(553\) 27.7771 + 11.9620i 1.18120 + 0.508676i
\(554\) −4.11153 12.6540i −0.174682 0.537616i
\(555\) 2.15380 + 5.41140i 0.0914238 + 0.229701i
\(556\) 0.354002 + 0.393159i 0.0150130 + 0.0166737i
\(557\) −30.0382 17.3425i −1.27276 0.734827i −0.297252 0.954799i \(-0.596070\pi\)
−0.975506 + 0.219972i \(0.929403\pi\)
\(558\) −0.306812 1.44344i −0.0129884 0.0611056i
\(559\) 5.27057 3.82929i 0.222921 0.161962i
\(560\) −13.1779 + 17.1145i −0.556866 + 0.723218i
\(561\) 0.168719 + 0.122581i 0.00712331 + 0.00517539i
\(562\) 11.9298 26.7948i 0.503230 1.13027i
\(563\) −0.649382 + 0.0682528i −0.0273682 + 0.00287651i −0.118203 0.992989i \(-0.537713\pi\)
0.0908345 + 0.995866i \(0.471047\pi\)
\(564\) −0.296156 + 0.131857i −0.0124704 + 0.00555220i
\(565\) −1.07488 16.6076i −0.0452204 0.698689i
\(566\) −23.4352 + 17.0267i −0.985055 + 0.715684i
\(567\) −10.6977 + 19.0640i −0.449262 + 0.800615i
\(568\) 13.7341i 0.576271i
\(569\) −3.24739 + 0.690255i −0.136138 + 0.0289370i −0.275477 0.961308i \(-0.588836\pi\)
0.139339 + 0.990245i \(0.455502\pi\)
\(570\) −0.446020 + 0.564823i −0.0186817 + 0.0236578i
\(571\) −27.3242 5.80794i −1.14348 0.243055i −0.403045 0.915180i \(-0.632048\pi\)
−0.740437 + 0.672126i \(0.765381\pi\)
\(572\) 0.0824021 + 0.0741952i 0.00344540 + 0.00310226i
\(573\) −2.49158 + 3.42937i −0.104087 + 0.143264i
\(574\) −9.23962 8.11686i −0.385654 0.338791i
\(575\) 11.8564 + 33.6565i 0.494448 + 1.40357i
\(576\) 12.4529 + 21.5690i 0.518870 + 0.898709i
\(577\) 4.83939 + 10.8694i 0.201466 + 0.452501i 0.985818 0.167815i \(-0.0536712\pi\)
−0.784352 + 0.620316i \(0.787004\pi\)
\(578\) −2.47526 + 11.6452i −0.102957 + 0.484375i
\(579\) 0.762869 0.847252i 0.0317038 0.0352106i
\(580\) 0.966179 1.95518i 0.0401184 0.0811846i
\(581\) −0.504987 41.2604i −0.0209504 1.71177i
\(582\) 1.71291i 0.0710022i
\(583\) 0.0672343 + 0.316313i 0.00278456 + 0.0131003i
\(584\) 3.10431 + 29.5356i 0.128457 + 1.22219i
\(585\) 10.8825 29.4242i 0.449936 1.21654i
\(586\) −0.543230 + 5.16849i −0.0224406 + 0.213508i
\(587\) −2.61107 3.59382i −0.107770 0.148333i 0.751725 0.659477i \(-0.229222\pi\)
−0.859495 + 0.511144i \(0.829222\pi\)
\(588\) 0.0753287 + 0.316138i 0.00310651 + 0.0130373i
\(589\) 0.249104 + 0.180985i 0.0102642 + 0.00745735i
\(590\) −5.34243 + 8.45192i −0.219945 + 0.347960i
\(591\) −0.599796 5.70668i −0.0246723 0.234741i
\(592\) 24.5740 22.1266i 1.00999 0.909396i
\(593\) −1.72608 + 0.996551i −0.0708815 + 0.0409234i −0.535022 0.844838i \(-0.679697\pi\)
0.464140 + 0.885762i \(0.346363\pi\)
\(594\) −0.101838 + 0.313424i −0.00417845 + 0.0128599i
\(595\) 14.2890 + 26.4221i 0.585791 + 1.08320i
\(596\) 0.538530 + 1.65742i 0.0220590 + 0.0678907i
\(597\) −1.01502 0.913924i −0.0415418 0.0374044i
\(598\) −18.9292 42.5158i −0.774074 1.73860i
\(599\) −4.67970 + 8.10548i −0.191207 + 0.331181i −0.945651 0.325184i \(-0.894574\pi\)
0.754443 + 0.656365i \(0.227907\pi\)
\(600\) −4.20076 0.337524i −0.171495 0.0137794i
\(601\) 5.74535 0.234358 0.117179 0.993111i \(-0.462615\pi\)
0.117179 + 0.993111i \(0.462615\pi\)
\(602\) −4.74079 + 1.06849i −0.193220 + 0.0435483i
\(603\) 31.1664 10.1266i 1.26919 0.412386i
\(604\) −1.87965 + 2.08756i −0.0764819 + 0.0849418i
\(605\) 23.6348 6.64484i 0.960892 0.270151i
\(606\) −1.96295 2.18008i −0.0797395 0.0885597i
\(607\) 9.08358 5.24441i 0.368691 0.212864i −0.304195 0.952610i \(-0.598388\pi\)
0.672886 + 0.739746i \(0.265054\pi\)
\(608\) −0.715047 0.232333i −0.0289990 0.00942234i
\(609\) 1.92102 + 4.17636i 0.0778436 + 0.169235i
\(610\) 3.63683 3.72720i 0.147251 0.150910i
\(611\) 3.51022 33.3975i 0.142008 1.35112i
\(612\) 2.37812 0.249950i 0.0961297 0.0101036i
\(613\) −13.0378 + 1.37033i −0.526592 + 0.0553470i −0.364095 0.931362i \(-0.618621\pi\)
−0.162497 + 0.986709i \(0.551955\pi\)
\(614\) 2.75066 26.1708i 0.111008 1.05617i
\(615\) 0.318124 2.18149i 0.0128280 0.0879663i
\(616\) −0.462784 1.00611i −0.0186461 0.0405373i
\(617\) −41.5637 13.5049i −1.67329 0.543685i −0.689700 0.724095i \(-0.742257\pi\)
−0.983591 + 0.180410i \(0.942257\pi\)
\(618\) −6.23505 + 3.59981i −0.250811 + 0.144806i
\(619\) −24.8400 27.5877i −0.998405 1.10884i −0.994058 0.108851i \(-0.965283\pi\)
−0.00434711 0.999991i \(-0.501384\pi\)
\(620\) −0.00539702 + 0.134557i −0.000216749 + 0.00540394i
\(621\) −8.12660 + 9.02550i −0.326109 + 0.362181i
\(622\) −3.51326 + 1.14153i −0.140869 + 0.0457711i
\(623\) −35.2999 + 7.95595i −1.41426 + 0.318748i
\(624\) 5.04978 0.202153
\(625\) −15.7965 + 19.3771i −0.631860 + 0.775082i
\(626\) −17.3163 + 29.9926i −0.692097 + 1.19875i
\(627\) −0.0137888 0.0309701i −0.000550671 0.00123683i
\(628\) 0.997712 + 0.898344i 0.0398131 + 0.0358478i
\(629\) −14.2105 43.7353i −0.566608 1.74384i
\(630\) −16.1372 + 16.9483i −0.642922 + 0.675237i
\(631\) −0.484202 + 1.49022i −0.0192758 + 0.0593247i −0.960232 0.279204i \(-0.909929\pi\)
0.940956 + 0.338529i \(0.109929\pi\)
\(632\) 29.0130 16.7506i 1.15407 0.666304i
\(633\) 0.425500 0.383122i 0.0169121 0.0152277i
\(634\) −1.47028 13.9888i −0.0583923 0.555565i
\(635\) −30.1607 + 12.0043i −1.19689 + 0.476376i
\(636\) −0.0850453 0.0617890i −0.00337227 0.00245009i
\(637\) −32.2622 9.61630i −1.27828 0.381012i
\(638\) −0.687699 0.946537i −0.0272263 0.0374737i
\(639\) −1.42900 + 13.5961i −0.0565305 + 0.537852i
\(640\) 5.90322 + 20.9970i 0.233345 + 0.829978i
\(641\) −3.49220 33.2260i −0.137933 1.31235i −0.816301 0.577627i \(-0.803979\pi\)
0.678368 0.734723i \(-0.262688\pi\)
\(642\) 0.251711 + 1.18421i 0.00993425 + 0.0467370i
\(643\) 1.80161i 0.0710485i 0.999369 + 0.0355242i \(0.0113101\pi\)
−0.999369 + 0.0355242i \(0.988690\pi\)
\(644\) −0.0373045 3.04799i −0.00147000 0.120108i
\(645\) −0.623490 0.608372i −0.0245499 0.0239546i
\(646\) 3.80227 4.22284i 0.149598 0.166146i
\(647\) 0.0895664 0.421377i 0.00352122 0.0165660i −0.976352 0.216187i \(-0.930638\pi\)
0.979873 + 0.199621i \(0.0639712\pi\)
\(648\) 9.84929 + 22.1219i 0.386917 + 0.869029i
\(649\) −0.235496 0.407891i −0.00924403 0.0160111i
\(650\) 18.5118 26.8406i 0.726093 1.05278i
\(651\) −0.213254 0.187340i −0.00835809 0.00734245i
\(652\) −1.30042 + 1.78987i −0.0509284 + 0.0700969i
\(653\) −27.9831 25.1961i −1.09506 0.985999i −0.0951078 0.995467i \(-0.530320\pi\)
−0.999955 + 0.00946787i \(0.996986\pi\)
\(654\) −1.42075 0.301989i −0.0555556 0.0118087i
\(655\) −31.6927 11.7215i −1.23834 0.457998i
\(656\) −12.2430 + 2.60234i −0.478010 + 0.101604i
\(657\) 29.5617i 1.15331i
\(658\) −12.2586 + 21.8457i −0.477891 + 0.851634i
\(659\) 11.2546 8.17693i 0.438416 0.318528i −0.346589 0.938017i \(-0.612660\pi\)
0.785005 + 0.619489i \(0.212660\pi\)
\(660\) 0.00792200 0.0125329i 0.000308363 0.000487841i
\(661\) −38.4504 + 17.1192i −1.49555 + 0.665860i −0.981423 0.191857i \(-0.938549\pi\)
−0.514123 + 0.857717i \(0.671882\pi\)
\(662\) −17.6731 + 1.85752i −0.686885 + 0.0721945i
\(663\) 2.85633 6.41542i 0.110931 0.249154i
\(664\) −36.9791 26.8669i −1.43507 1.04264i
\(665\) 0.135971 4.88107i 0.00527273 0.189280i
\(666\) 28.9841 21.0582i 1.12311 0.815988i
\(667\) −8.96460 42.1751i −0.347111 1.63303i
\(668\) 2.41246 + 1.39283i 0.0933408 + 0.0538903i
\(669\) −3.13432 3.48102i −0.121180 0.134584i
\(670\) 33.9873 2.19972i 1.31304 0.0849826i
\(671\) 0.0758020 + 0.233295i 0.00292630 + 0.00900624i
\(672\) 0.636589 + 0.274143i 0.0245570 + 0.0105753i
\(673\) 26.2517 36.1323i 1.01193 1.39280i 0.0942163 0.995552i \(-0.469965\pi\)
0.917712 0.397247i \(-0.130035\pi\)
\(674\) 6.99124 + 12.1092i 0.269292 + 0.466428i
\(675\) −8.36374 1.56429i −0.321921 0.0602095i
\(676\) 0.817589 1.41611i 0.0314457 0.0544656i
\(677\) −6.40589 0.673286i −0.246198 0.0258765i −0.0193745 0.999812i \(-0.506167\pi\)
−0.226824 + 0.973936i \(0.572834\pi\)
\(678\) 2.76026 0.896863i 0.106007 0.0344438i
\(679\) 6.94561 + 9.31784i 0.266548 + 0.357586i
\(680\) 32.9261 + 4.80156i 1.26266 + 0.184131i
\(681\) 0.309859 0.0658626i 0.0118738 0.00252386i
\(682\) 0.0625653 + 0.0361221i 0.00239575 + 0.00138319i
\(683\) 27.8772 25.1007i 1.06669 0.960453i 0.0673864 0.997727i \(-0.478534\pi\)
0.999305 + 0.0372736i \(0.0118673\pi\)
\(684\) −0.355104 0.158102i −0.0135777 0.00604520i
\(685\) −32.1520 15.8883i −1.22846 0.607061i
\(686\) 19.2663 + 16.1071i 0.735591 + 0.614970i
\(687\) 1.04288 + 1.43540i 0.0397884 + 0.0547641i
\(688\) −2.01166 + 4.51826i −0.0766938 + 0.172257i
\(689\) 9.94791 4.42909i 0.378985 0.168735i
\(690\) −5.17706 + 3.45308i −0.197087 + 0.131456i
\(691\) 16.4183 + 7.30988i 0.624580 + 0.278081i 0.694524 0.719470i \(-0.255615\pi\)
−0.0699433 + 0.997551i \(0.522282\pi\)
\(692\) −0.885999 0.287879i −0.0336806 0.0109435i
\(693\) −0.353449 1.04415i −0.0134264 0.0396639i
\(694\) 2.07029 6.37169i 0.0785870 0.241866i
\(695\) 2.70986 + 6.80851i 0.102791 + 0.258261i
\(696\) 4.98093 + 1.05873i 0.188802 + 0.0401310i
\(697\) −3.61898 + 17.0260i −0.137079 + 0.644904i
\(698\) −22.2442 2.33795i −0.841954 0.0884929i
\(699\) −2.97977 −0.112705
\(700\) 1.80895 1.13508i 0.0683718 0.0429019i
\(701\) −14.1055 −0.532756 −0.266378 0.963869i \(-0.585827\pi\)
−0.266378 + 0.963869i \(0.585827\pi\)
\(702\) 11.0365 + 1.15998i 0.416544 + 0.0437805i
\(703\) −1.55422 + 7.31201i −0.0586183 + 0.275778i
\(704\) −1.19265 0.253506i −0.0449498 0.00955437i
\(705\) −4.48097 + 0.290017i −0.168763 + 0.0109227i
\(706\) 13.2681 40.8350i 0.499351 1.53685i
\(707\) 19.5180 + 3.89965i 0.734050 + 0.146661i
\(708\) 0.145613 + 0.0473126i 0.00547248 + 0.00177812i
\(709\) −41.2318 18.3576i −1.54849 0.689433i −0.558364 0.829596i \(-0.688571\pi\)
−0.990128 + 0.140163i \(0.955237\pi\)
\(710\) −4.92866 + 13.3261i −0.184969 + 0.500121i
\(711\) 30.4642 13.5635i 1.14250 0.508672i
\(712\) −16.3034 + 36.6180i −0.610996 + 1.37232i
\(713\) 1.56493 + 2.15394i 0.0586070 + 0.0806656i
\(714\) −3.84976 + 3.55260i −0.144074 + 0.132953i
\(715\) 0.714009 + 1.35981i 0.0267024 + 0.0508539i
\(716\) 1.94265 + 0.864923i 0.0726002 + 0.0323237i
\(717\) 1.53447 1.38164i 0.0573057 0.0515982i
\(718\) 31.8148 + 18.3683i 1.18732 + 0.685499i
\(719\) 0.0315305 0.00670202i 0.00117589 0.000249943i −0.207324 0.978272i \(-0.566475\pi\)
0.208500 + 0.978022i \(0.433142\pi\)
\(720\) 4.01417 + 23.4762i 0.149599 + 0.874905i
\(721\) 19.3206 44.8645i 0.719536 1.67084i
\(722\) 23.6234 7.67570i 0.879171 0.285660i
\(723\) 5.77168 + 0.606627i 0.214651 + 0.0225607i
\(724\) −1.53284 + 2.65496i −0.0569677 + 0.0986709i
\(725\) 21.9460 20.7579i 0.815056 0.770928i
\(726\) 2.14077 + 3.70792i 0.0794514 + 0.137614i
\(727\) 20.9280 28.8050i 0.776178 1.06832i −0.219516 0.975609i \(-0.570448\pi\)
0.995693 0.0927080i \(-0.0295523\pi\)
\(728\) −29.8989 + 22.2870i −1.10813 + 0.826009i
\(729\) 6.99485 + 21.5279i 0.259069 + 0.797331i
\(730\) −7.58710 + 29.7722i −0.280811 + 1.10192i
\(731\) 4.60230 + 5.11137i 0.170222 + 0.189051i
\(732\) −0.0690573 0.0398702i −0.00255243 0.00147365i
\(733\) −6.03495 28.3922i −0.222906 1.04869i −0.937186 0.348830i \(-0.886579\pi\)
0.714280 0.699860i \(-0.246754\pi\)
\(734\) −22.9804 + 16.6963i −0.848224 + 0.616270i
\(735\) −0.540363 + 4.46894i −0.0199316 + 0.164839i
\(736\) −5.25942 3.82119i −0.193865 0.140851i
\(737\) −0.652533 + 1.46561i −0.0240364 + 0.0539866i
\(738\) −13.4865 + 1.41749i −0.496444 + 0.0521784i
\(739\) −33.6345 + 14.9750i −1.23727 + 0.550866i −0.917917 0.396772i \(-0.870130\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(740\) −3.03761 + 1.20901i −0.111665 + 0.0444439i
\(741\) −0.923548 + 0.670997i −0.0339274 + 0.0246497i
\(742\) −8.12230 + 0.0994090i −0.298179 + 0.00364942i
\(743\) 15.3528i 0.563240i −0.959526 0.281620i \(-0.909128\pi\)
0.959526 0.281620i \(-0.0908718\pi\)
\(744\) −0.307563 + 0.0653745i −0.0112758 + 0.00239674i
\(745\) −0.967419 + 24.1194i −0.0354435 + 0.883668i
\(746\) −1.85489 0.394269i −0.0679123 0.0144352i
\(747\) −33.8119 30.4444i −1.23711 1.11390i
\(748\) −0.0688093 + 0.0947079i −0.00251592 + 0.00346286i
\(749\) −6.17107 5.42118i −0.225486 0.198086i
\(750\) −3.95485 1.83499i −0.144411 0.0670044i
\(751\) 22.6383 + 39.2107i 0.826083 + 1.43082i 0.901089 + 0.433634i \(0.142769\pi\)
−0.0750064 + 0.997183i \(0.523898\pi\)
\(752\) 10.3694 + 23.2901i 0.378134 + 0.849303i
\(753\) −1.59507 + 7.50423i −0.0581277 + 0.273469i
\(754\) −26.3621 + 29.2781i −0.960051 + 1.06624i
\(755\) −34.4492 + 18.0886i −1.25373 + 0.658313i
\(756\) 0.633867 + 0.355692i 0.0230535 + 0.0129364i
\(757\) 28.8407i 1.04823i −0.851647 0.524116i \(-0.824396\pi\)
0.851647 0.524116i \(-0.175604\pi\)
\(758\) −4.14748 19.5124i −0.150643 0.708721i
\(759\) −0.0306407 0.291527i −0.00111219 0.0105818i
\(760\) −4.24503 3.35215i −0.153983 0.121595i
\(761\) 2.19935 20.9254i 0.0797264 0.758546i −0.879499 0.475902i \(-0.842122\pi\)
0.959225 0.282644i \(-0.0912115\pi\)
\(762\) −3.32751 4.57993i −0.120543 0.165913i
\(763\) 8.95308 4.11819i 0.324123 0.149088i
\(764\) −1.92503 1.39861i −0.0696451 0.0506001i
\(765\) 32.0955 + 8.17918i 1.16042 + 0.295719i
\(766\) −3.43802 32.7106i −0.124221 1.18188i
\(767\) −11.7863 + 10.6124i −0.425578 + 0.383192i
\(768\) 0.958509 0.553396i 0.0345872 0.0199689i
\(769\) −13.9262 + 42.8606i −0.502193 + 1.54559i 0.303245 + 0.952913i \(0.401930\pi\)
−0.805438 + 0.592680i \(0.798070\pi\)
\(770\) −0.0879818 1.14230i −0.00317064 0.0411655i
\(771\) 0.157603 + 0.485052i 0.00567593 + 0.0174687i
\(772\) 0.475593 + 0.428226i 0.0171170 + 0.0154122i
\(773\) 0.420904 + 0.945366i 0.0151389 + 0.0340024i 0.920957 0.389665i \(-0.127409\pi\)
−0.905818 + 0.423667i \(0.860743\pi\)
\(774\) −2.67923 + 4.64057i −0.0963031 + 0.166802i
\(775\) −0.716631 + 1.72212i −0.0257421 + 0.0618605i
\(776\) 12.8737 0.462137
\(777\) 2.04918 6.57966i 0.0735140 0.236044i
\(778\) −32.9071 + 10.6922i −1.17978 + 0.383333i
\(779\) 1.89332 2.10275i 0.0678354 0.0753388i
\(780\) −0.468268 0.173188i −0.0167667 0.00620114i
\(781\) −0.447837 0.497373i −0.0160249 0.0177974i
\(782\) 42.5514 24.5671i 1.52164 0.878517i
\(783\) 9.77808 + 3.17709i 0.349440 + 0.113540i
\(784\) 24.8615 5.92394i 0.887909 0.211569i
\(785\) 8.64512 + 16.4643i 0.308558 + 0.587638i
\(786\) 0.615974 5.86060i 0.0219711 0.209041i
\(787\) −3.78423 + 0.397738i −0.134893 + 0.0141778i −0.171734 0.985143i \(-0.554937\pi\)
0.0368413 + 0.999321i \(0.488270\pi\)
\(788\) 3.20336 0.336687i 0.114115 0.0119940i
\(789\) 0.00204938 0.0194986i 7.29600e−5 0.000694168i
\(790\) 34.1622 5.84138i 1.21544 0.207827i
\(791\) −11.3786 + 16.0712i −0.404575 + 0.571428i
\(792\) −1.16133 0.377340i −0.0412662 0.0134082i
\(793\) 7.15350 4.13007i 0.254028 0.146663i
\(794\) 4.56952 + 5.07497i 0.162166 + 0.180104i
\(795\) −0.807957 1.21134i −0.0286553 0.0429617i
\(796\) 0.513018 0.569764i 0.0181834 0.0201948i
\(797\) 41.6324 13.5272i 1.47469 0.479157i 0.542172 0.840268i \(-0.317602\pi\)
0.932523 + 0.361111i \(0.117602\pi\)
\(798\) 0.830715 0.187228i 0.0294070 0.00662781i
\(799\) 35.4539 1.25427
\(800\) 0.364778 4.53995i 0.0128968 0.160512i
\(801\) −19.9496 + 34.5536i −0.704883 + 1.22089i
\(802\) 16.3805 + 36.7912i 0.578416 + 1.29914i
\(803\) −1.07550 0.968388i −0.0379537 0.0341737i
\(804\) −0.161158 0.495994i −0.00568361 0.0174923i
\(805\) 14.1603 39.7763i 0.499085 1.40193i
\(806\) 0.751752 2.31366i 0.0264793 0.0814951i
\(807\) −1.36211 + 0.786417i −0.0479487 + 0.0276832i
\(808\) 16.3848 14.7529i 0.576415 0.519006i
\(809\) 1.28858 + 12.2601i 0.0453042 + 0.431041i 0.993541 + 0.113476i \(0.0361985\pi\)
−0.948237 + 0.317565i \(0.897135\pi\)
\(810\) 1.61800 + 24.9992i 0.0568506 + 0.878384i
\(811\) 42.0610 + 30.5591i 1.47696 + 1.07308i 0.978520 + 0.206154i \(0.0660947\pi\)
0.498443 + 0.866922i \(0.333905\pi\)
\(812\) −2.34434 + 1.07834i −0.0822702 + 0.0378422i
\(813\) 0.536565 + 0.738518i 0.0188181 + 0.0259010i
\(814\) −0.183336 + 1.74432i −0.00642591 + 0.0611384i
\(815\) −25.4940 + 17.0044i −0.893014 + 0.595637i
\(816\) 0.557277 + 5.30214i 0.0195086 + 0.185612i
\(817\) −0.232461 1.09364i −0.00813277 0.0382617i
\(818\) 28.9974i 1.01387i
\(819\) −31.9173 + 18.9520i −1.11528 + 0.662237i
\(820\) 1.22455 + 0.178574i 0.0427631 + 0.00623609i
\(821\) −4.00582 + 4.44892i −0.139804 + 0.155268i −0.808981 0.587835i \(-0.799980\pi\)
0.669177 + 0.743103i \(0.266647\pi\)
\(822\) 1.30035 6.11766i 0.0453548 0.213378i
\(823\) −7.80767 17.5363i −0.272158 0.611277i 0.724822 0.688936i \(-0.241922\pi\)
−0.996980 + 0.0776590i \(0.975255\pi\)
\(824\) −27.0550 46.8607i −0.942506 1.63247i
\(825\) 0.163134 0.124753i 0.00567959 0.00434336i
\(826\) 11.2061 3.79333i 0.389912 0.131987i
\(827\) −3.88032 + 5.34080i −0.134932 + 0.185718i −0.871136 0.491042i \(-0.836616\pi\)
0.736204 + 0.676760i \(0.236616\pi\)
\(828\) −2.49776 2.24899i −0.0868032 0.0781579i
\(829\) 5.32594 + 1.13206i 0.184978 + 0.0393182i 0.299469 0.954106i \(-0.403190\pi\)
−0.114491 + 0.993424i \(0.536524\pi\)
\(830\) −26.2390 39.3391i −0.910770 1.36548i
\(831\) −2.76032 + 0.586724i −0.0957544 + 0.0203532i
\(832\) 41.0581i 1.42343i
\(833\) 6.53651 34.9357i 0.226477 1.21045i
\(834\) −1.03388 + 0.751157i −0.0358003 + 0.0260104i
\(835\) 24.6484 + 29.6859i 0.852995 + 1.02732i
\(836\) 0.0173846 0.00774013i 0.000601260 0.000267698i
\(837\) −0.631372 + 0.0663598i −0.0218234 + 0.00229373i
\(838\) −12.7010 + 28.5268i −0.438748 + 0.985444i
\(839\) 32.8580 + 23.8727i 1.13438 + 0.824178i 0.986327 0.164801i \(-0.0526981\pi\)
0.148057 + 0.988979i \(0.452698\pi\)
\(840\) 3.61129 + 3.43846i 0.124601 + 0.118638i
\(841\) −6.06822 + 4.40882i −0.209249 + 0.152028i
\(842\) −4.70068 22.1150i −0.161996 0.762132i
\(843\) −5.38748 3.11046i −0.185555 0.107130i
\(844\) 0.215060 + 0.238848i 0.00740267 + 0.00822150i
\(845\) 17.4255 14.4686i 0.599456 0.497734i
\(846\) 8.53538 + 26.2692i 0.293452 + 0.903154i
\(847\) −26.6805 11.4898i −0.916752 0.394793i
\(848\) −4.85916 + 6.68807i −0.166864 + 0.229669i
\(849\) 3.07196 + 5.32078i 0.105429 + 0.182609i
\(850\) 30.2248 + 16.4748i 1.03670 + 0.565083i
\(851\) −32.3187 + 55.9777i −1.10787 + 1.91889i
\(852\) 0.216373 + 0.0227417i 0.00741282 + 0.000779119i
\(853\) −2.62128 + 0.851704i −0.0897508 + 0.0291618i −0.353548 0.935416i \(-0.615025\pi\)
0.263797 + 0.964578i \(0.415025\pi\)
\(854\) −6.11956 + 0.719014i −0.209407 + 0.0246042i
\(855\) −3.85358 3.76014i −0.131790 0.128594i
\(856\) −8.90013 + 1.89178i −0.304200 + 0.0646598i
\(857\) 2.51108 + 1.44978i 0.0857770 + 0.0495234i 0.542275 0.840201i \(-0.317563\pi\)
−0.456498 + 0.889724i \(0.650896\pi\)
\(858\) −0.199047 + 0.179223i −0.00679534 + 0.00611856i
\(859\) 1.67772 + 0.746969i 0.0572431 + 0.0254863i 0.435159 0.900354i \(-0.356692\pi\)
−0.377915 + 0.925840i \(0.623359\pi\)
\(860\) 0.341501 0.349987i 0.0116451 0.0119345i
\(861\) −1.91697 + 1.76901i −0.0653302 + 0.0602876i
\(862\) 5.62061 + 7.73611i 0.191439 + 0.263493i
\(863\) −2.01755 + 4.53148i −0.0686780 + 0.154253i −0.944623 0.328158i \(-0.893572\pi\)
0.875945 + 0.482411i \(0.160239\pi\)
\(864\) 1.41614 0.630505i 0.0481780 0.0214502i
\(865\) −10.1270 7.99692i −0.344328 0.271903i
\(866\) 1.29968 + 0.578654i 0.0441649 + 0.0196635i
\(867\) 2.40149 + 0.780293i 0.0815590 + 0.0265001i
\(868\) 0.105161 0.119707i 0.00356939 0.00406312i
\(869\) −0.504489 + 1.55266i −0.0171136 + 0.0526703i
\(870\) 4.45303 + 2.81475i 0.150972 + 0.0954288i
\(871\) 52.8425 + 11.2320i 1.79050 + 0.380582i
\(872\) 2.26965 10.6779i 0.0768602 0.361599i
\(873\) 12.7443 + 1.33948i 0.431328 + 0.0453344i
\(874\) −7.98712 −0.270168
\(875\) 28.9542 6.05442i 0.978830 0.204677i
\(876\) 0.470456 0.0158952
\(877\) 20.2217 + 2.12539i 0.682838 + 0.0717692i 0.439595 0.898196i \(-0.355122\pi\)
0.243243 + 0.969965i \(0.421789\pi\)
\(878\) −2.23928 + 10.5350i −0.0755721 + 0.355539i
\(879\) 1.07817 + 0.229173i 0.0363658 + 0.00772980i
\(880\) −0.985600 0.622995i −0.0332246 0.0210012i
\(881\) −1.46453 + 4.50737i −0.0493413 + 0.151857i −0.972691 0.232102i \(-0.925440\pi\)
0.923350 + 0.383959i \(0.125440\pi\)
\(882\) 27.4589 3.56746i 0.924589 0.120123i
\(883\) −31.7053 10.3017i −1.06697 0.346678i −0.277661 0.960679i \(-0.589559\pi\)
−0.789306 + 0.614001i \(0.789559\pi\)
\(884\) 3.60121 + 1.60336i 0.121122 + 0.0539268i
\(885\) 1.66436 + 1.31429i 0.0559469 + 0.0441792i
\(886\) 25.5020 11.3542i 0.856758 0.381453i
\(887\) 20.6082 46.2868i 0.691956 1.55416i −0.134349 0.990934i \(-0.542894\pi\)
0.826304 0.563224i \(-0.190439\pi\)
\(888\) −4.48701 6.17584i −0.150574 0.207248i
\(889\) 36.6720 + 11.4212i 1.22994 + 0.383055i
\(890\) −28.9599 + 29.6796i −0.970739 + 0.994861i
\(891\) −1.07803 0.479968i −0.0361153 0.0160795i
\(892\) 1.95402 1.75941i 0.0654254 0.0589093i
\(893\) −4.99115 2.88164i −0.167023 0.0964305i
\(894\) −4.11764 + 0.875232i −0.137715 + 0.0292721i
\(895\) 21.0816 + 20.5704i 0.704679 + 0.687592i
\(896\) 10.2074 23.7027i 0.341005 0.791852i
\(897\) −9.38772 + 3.05026i −0.313447 + 0.101845i
\(898\) −19.7555 2.07639i −0.659250 0.0692899i
\(899\) 1.12692 1.95189i 0.0375850 0.0650992i
\(900\) 0.432908 2.31462i 0.0144303 0.0771540i
\(901\) 5.74825 + 9.95626i 0.191502 + 0.331691i
\(902\) 0.390223 0.537095i 0.0129930 0.0178833i
\(903\) 0.120277 + 1.02369i 0.00400258 + 0.0340661i
\(904\) 6.74054 + 20.7452i 0.224187 + 0.689977i
\(905\) −32.6700 + 27.1261i −1.08599 + 0.901704i
\(906\) −4.54040 5.04263i −0.150845 0.167530i
\(907\) −43.9780 25.3907i −1.46027 0.843085i −0.461242 0.887274i \(-0.652596\pi\)
−0.999023 + 0.0441895i \(0.985929\pi\)
\(908\) 0.0369710 + 0.173935i 0.00122693 + 0.00577224i
\(909\) 17.7551 12.8998i 0.588900 0.427861i
\(910\) −37.0087 + 10.8953i −1.22683 + 0.361175i
\(911\) −4.32719 3.14388i −0.143366 0.104162i 0.513790 0.857916i \(-0.328241\pi\)
−0.657156 + 0.753754i \(0.728241\pi\)
\(912\) 0.352498 0.791723i 0.0116724 0.0262166i
\(913\) 2.21524 0.232831i 0.0733137 0.00770558i
\(914\) 42.8222 19.0657i 1.41643 0.630636i
\(915\) −0.705568 0.849767i −0.0233254 0.0280924i
\(916\) −0.805743 + 0.585407i −0.0266225 + 0.0193424i
\(917\) 20.4132 + 34.3781i 0.674103 + 1.13526i
\(918\) 11.7160i 0.386685i
\(919\) −36.0168 + 7.65560i −1.18808 + 0.252535i −0.759220 0.650834i \(-0.774419\pi\)
−0.428864 + 0.903369i \(0.641086\pi\)
\(920\) −25.9522 38.9091i −0.855620 1.28280i
\(921\) −5.45935 1.16042i −0.179892 0.0382372i
\(922\) 15.9726 + 14.3818i 0.526028 + 0.473638i
\(923\) −13.2470 + 18.2329i −0.436030 + 0.600143i
\(924\) −0.0166170 + 0.00562492i −0.000546658 + 0.000185046i
\(925\) −45.2712 + 1.11134i −1.48851 + 0.0365408i
\(926\) 8.83508 + 15.3028i 0.290339 + 0.502882i
\(927\) −21.9073 49.2047i −0.719531 1.61609i
\(928\) −1.14422 + 5.38312i −0.0375608 + 0.176710i
\(929\) 7.25628 8.05891i 0.238071 0.264404i −0.612256 0.790660i \(-0.709738\pi\)
0.850327 + 0.526255i \(0.176404\pi\)
\(930\) −0.321887 0.0469402i −0.0105551 0.00153923i
\(931\) −3.75973 + 4.38692i −0.123220 + 0.143776i
\(932\) 1.67265i 0.0547895i
\(933\) 0.162899 + 0.766377i 0.00533306 + 0.0250901i
\(934\) −4.32944 41.1919i −0.141664 1.34784i
\(935\) −1.34897 + 0.899754i −0.0441159 + 0.0294251i
\(936\) −4.29808 + 40.8935i −0.140487 + 1.33665i
\(937\) −22.6610 31.1902i −0.740302 1.01894i −0.998601 0.0528734i \(-0.983162\pi\)
0.258299 0.966065i \(-0.416838\pi\)
\(938\) −32.8896 23.2861i −1.07388 0.760317i
\(939\) 5.94259 + 4.31755i 0.193929 + 0.140898i
\(940\) −0.162797 2.51533i −0.00530984 0.0820410i
\(941\) −3.12194 29.7033i −0.101772 0.968300i −0.919605 0.392844i \(-0.871491\pi\)
0.817833 0.575456i \(-0.195175\pi\)
\(942\) −2.41003 + 2.17000i −0.0785230 + 0.0707024i
\(943\) 21.1883 12.2331i 0.689987 0.398364i
\(944\) 3.72072 11.4512i 0.121099 0.372705i
\(945\) 6.52566 + 7.66645i 0.212280 + 0.249390i
\(946\) −0.0810649 0.249492i −0.00263565 0.00811168i
\(947\) 11.1243 + 10.0164i 0.361492 + 0.325489i 0.829784 0.558085i \(-0.188464\pi\)
−0.468292 + 0.883574i \(0.655130\pi\)
\(948\) −0.215855 0.484819i −0.00701066 0.0157462i
\(949\) −24.3668 + 42.2045i −0.790979 + 1.37002i
\(950\) −2.91596 4.77594i −0.0946064 0.154952i
\(951\) −2.98332 −0.0967407
\(952\) −26.7002 28.9335i −0.865360 0.937742i
\(953\) −42.1237 + 13.6868i −1.36452 + 0.443360i −0.897550 0.440913i \(-0.854655\pi\)
−0.466971 + 0.884273i \(0.654655\pi\)
\(954\) −5.99312 + 6.65604i −0.194034 + 0.215497i
\(955\) −18.2884 27.4190i −0.591798 0.887258i
\(956\) 0.775563 + 0.861350i 0.0250835 + 0.0278580i
\(957\) −0.214904 + 0.124075i −0.00694686 + 0.00401077i
\(958\) 8.76626 + 2.84833i 0.283225 + 0.0920254i
\(959\) 17.7327 + 38.5515i 0.572618 + 1.24489i
\(960\) 5.41154 0.925315i 0.174657 0.0298644i
\(961\) 3.22584 30.6918i 0.104059 0.990057i
\(962\) 58.7375 6.17356i 1.89377 0.199044i
\(963\) −9.00751 + 0.946728i −0.290263 + 0.0305079i
\(964\) −0.340522 + 3.23985i −0.0109675 + 0.104348i
\(965\) 4.12098 + 7.84828i 0.132659 + 0.252645i
\(966\) 7.33168 + 0.679984i 0.235893 + 0.0218781i
\(967\) 43.0905 + 14.0009i 1.38570 + 0.450240i 0.904538 0.426394i \(-0.140216\pi\)
0.481159 + 0.876634i \(0.340216\pi\)
\(968\) −27.8676 + 16.0893i −0.895697 + 0.517131i
\(969\) −0.806448 0.895652i −0.0259069 0.0287725i
\(970\) 12.4912 + 4.61987i 0.401069 + 0.148335i
\(971\) 15.7647 17.5085i 0.505914 0.561875i −0.435039 0.900412i \(-0.643265\pi\)
0.940953 + 0.338537i \(0.109932\pi\)
\(972\) 1.14865 0.373220i 0.0368431 0.0119710i
\(973\) 2.57823 8.27837i 0.0826544 0.265392i
\(974\) −37.3001 −1.19517
\(975\) −5.25122 4.49985i −0.168174 0.144110i
\(976\) −3.13544 + 5.43075i −0.100363 + 0.173834i
\(977\) −0.993512 2.23146i −0.0317853 0.0713909i 0.896955 0.442121i \(-0.145774\pi\)
−0.928740 + 0.370731i \(0.879107\pi\)
\(978\) −3.97151 3.57596i −0.126995 0.114347i
\(979\) −0.603608 1.85772i −0.0192914 0.0593728i
\(980\) −2.50858 0.303325i −0.0801336 0.00968936i
\(981\) 3.35785 10.3344i 0.107208 0.329952i
\(982\) −4.56010 + 2.63278i −0.145519 + 0.0840153i
\(983\) 7.86290 7.07979i 0.250788 0.225810i −0.534143 0.845394i \(-0.679365\pi\)
0.784930 + 0.619584i \(0.212699\pi\)
\(984\) 0.302033 + 2.87365i 0.00962847 + 0.0916087i
\(985\) 43.2332 + 11.0175i 1.37752 + 0.351047i
\(986\) −33.6504 24.4485i −1.07165 0.778598i
\(987\) 4.33624 + 3.07009i 0.138024 + 0.0977222i
\(988\) −0.376654 0.518420i −0.0119830 0.0164931i
\(989\) 1.01055 9.61472i 0.0321336 0.305730i
\(990\) −0.991422 0.782890i −0.0315095 0.0248819i
\(991\) 5.04243 + 47.9755i 0.160178 + 1.52399i 0.719178 + 0.694826i \(0.244519\pi\)
−0.559000 + 0.829168i \(0.688815\pi\)
\(992\) −0.0706532 0.332397i −0.00224324 0.0105536i
\(993\) 3.76906i 0.119607i
\(994\) 14.4553 8.58332i 0.458493 0.272246i
\(995\) 9.40230 4.93697i 0.298073 0.156513i
\(996\) −0.484504 + 0.538096i −0.0153521 + 0.0170502i
\(997\) −2.75348 + 12.9541i −0.0872035 + 0.410260i 0.912795 + 0.408418i \(0.133920\pi\)
−0.999998 + 0.00184172i \(0.999414\pi\)
\(998\) −10.1148 22.7181i −0.320177 0.719130i
\(999\) −7.70637 13.3478i −0.243819 0.422306i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 175.2.t.a.109.6 yes 144
5.2 odd 4 875.2.q.b.326.25 288
5.3 odd 4 875.2.q.b.326.12 288
5.4 even 2 875.2.u.a.424.13 144
7.2 even 3 inner 175.2.t.a.9.13 144
25.2 odd 20 875.2.q.b.676.12 288
25.11 even 5 875.2.u.a.74.6 144
25.14 even 10 inner 175.2.t.a.39.13 yes 144
25.23 odd 20 875.2.q.b.676.25 288
35.2 odd 12 875.2.q.b.576.12 288
35.9 even 6 875.2.u.a.674.6 144
35.23 odd 12 875.2.q.b.576.25 288
175.2 odd 60 875.2.q.b.51.25 288
175.23 odd 60 875.2.q.b.51.12 288
175.86 even 15 875.2.u.a.324.13 144
175.114 even 30 inner 175.2.t.a.114.6 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.t.a.9.13 144 7.2 even 3 inner
175.2.t.a.39.13 yes 144 25.14 even 10 inner
175.2.t.a.109.6 yes 144 1.1 even 1 trivial
175.2.t.a.114.6 yes 144 175.114 even 30 inner
875.2.q.b.51.12 288 175.23 odd 60
875.2.q.b.51.25 288 175.2 odd 60
875.2.q.b.326.12 288 5.3 odd 4
875.2.q.b.326.25 288 5.2 odd 4
875.2.q.b.576.12 288 35.2 odd 12
875.2.q.b.576.25 288 35.23 odd 12
875.2.q.b.676.12 288 25.2 odd 20
875.2.q.b.676.25 288 25.23 odd 20
875.2.u.a.74.6 144 25.11 even 5
875.2.u.a.324.13 144 175.86 even 15
875.2.u.a.424.13 144 5.4 even 2
875.2.u.a.674.6 144 35.9 even 6