Properties

Label 45.2.j.a.4.2
Level $45$
Weight $2$
Character 45.4
Analytic conductor $0.359$
Analytic rank $0$
Dimension $8$
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] = [45,2,Mod(4,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45.j (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.359326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.2
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 45.4
Dual form 45.2.j.a.34.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.448288 + 0.258819i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-0.358719 - 2.20711i) q^{5} +(-0.633975 - 0.633975i) q^{6} +(2.89778 - 1.67303i) q^{7} -1.93185i q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.448288 + 0.258819i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-0.358719 - 2.20711i) q^{5} +(-0.633975 - 0.633975i) q^{6} +(2.89778 - 1.67303i) q^{7} -1.93185i q^{8} +(-2.59808 + 1.50000i) q^{9} +(0.732051 + 0.896575i) q^{10} +(-0.633975 - 1.09808i) q^{11} +(-2.89778 - 0.776457i) q^{12} +(-2.12132 - 1.22474i) q^{13} +(-0.866025 + 1.50000i) q^{14} +(3.53175 - 1.58957i) q^{15} +(-1.23205 - 2.13397i) q^{16} +5.27792i q^{17} +(0.776457 - 1.34486i) q^{18} +0.732051 q^{19} +(3.62132 + 1.37333i) q^{20} +(4.09808 + 4.09808i) q^{21} +(0.568406 + 0.328169i) q^{22} +(0.448288 + 0.258819i) q^{23} +(3.23205 - 0.866025i) q^{24} +(-4.74264 + 1.58346i) q^{25} +1.26795 q^{26} +(-3.67423 - 3.67423i) q^{27} +5.79555i q^{28} +(-0.232051 - 0.401924i) q^{29} +(-1.17183 + 1.62667i) q^{30} +(-0.366025 + 0.633975i) q^{31} +(4.45069 + 2.56961i) q^{32} +(1.55291 - 1.55291i) q^{33} +(-1.36603 - 2.36603i) q^{34} +(-4.73205 - 5.79555i) q^{35} -5.19615i q^{36} -4.24264i q^{37} +(-0.328169 + 0.189469i) q^{38} +(1.09808 - 4.09808i) q^{39} +(-4.26380 + 0.692993i) q^{40} +(-3.86603 + 6.69615i) q^{41} +(-2.89778 - 0.776457i) q^{42} +(0.568406 - 0.328169i) q^{43} +2.19615 q^{44} +(4.24264 + 5.19615i) q^{45} -0.267949 q^{46} +(-2.56961 + 1.48356i) q^{47} +(3.01790 - 3.01790i) q^{48} +(2.09808 - 3.63397i) q^{49} +(1.71624 - 1.93733i) q^{50} +(-8.83013 + 2.36603i) q^{51} +(3.67423 - 2.12132i) q^{52} +1.03528i q^{53} +(2.59808 + 0.696152i) q^{54} +(-2.19615 + 1.79315i) q^{55} +(-3.23205 - 5.59808i) q^{56} +(0.328169 + 1.22474i) q^{57} +(0.208051 + 0.120118i) q^{58} +(4.73205 - 8.19615i) q^{59} +(-0.674235 + 6.67423i) q^{60} +(3.33013 + 5.76795i) q^{61} -0.378937i q^{62} +(-5.01910 + 8.69333i) q^{63} +2.26795 q^{64} +(-1.94218 + 5.12132i) q^{65} +(-0.294229 + 1.09808i) q^{66} +(6.57201 + 3.79435i) q^{67} +(-7.91688 - 4.57081i) q^{68} +(-0.232051 + 0.866025i) q^{69} +(3.62132 + 1.37333i) q^{70} +14.1962 q^{71} +(2.89778 + 5.01910i) q^{72} -8.48528i q^{73} +(1.09808 + 1.90192i) q^{74} +(-4.77526 - 7.22474i) q^{75} +(-0.633975 + 1.09808i) q^{76} +(-3.67423 - 2.12132i) q^{77} +(0.568406 + 2.12132i) q^{78} +(3.73205 + 6.46410i) q^{79} +(-4.26795 + 3.48477i) q^{80} +(4.50000 - 7.79423i) q^{81} -4.00240i q^{82} +(6.90018 - 3.98382i) q^{83} +(-9.69615 + 2.59808i) q^{84} +(11.6489 - 1.89329i) q^{85} +(-0.169873 + 0.294229i) q^{86} +(0.568406 - 0.568406i) q^{87} +(-2.12132 + 1.22474i) q^{88} -13.3923 q^{89} +(-3.24679 - 1.23130i) q^{90} -8.19615 q^{91} +(-0.776457 + 0.448288i) q^{92} +(-1.22474 - 0.328169i) q^{93} +(0.767949 - 1.33013i) q^{94} +(-0.262601 - 1.61571i) q^{95} +(-2.30385 + 8.59808i) q^{96} +(-13.1440 + 7.58871i) q^{97} +2.17209i q^{98} +(3.29423 + 1.90192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{6} - 8 q^{10} - 12 q^{11} + 12 q^{15} + 4 q^{16} - 8 q^{19} + 12 q^{20} + 12 q^{21} + 12 q^{24} - 4 q^{25} + 24 q^{26} + 12 q^{29} - 12 q^{30} + 4 q^{31} - 4 q^{34} - 24 q^{35} - 12 q^{39} - 4 q^{40} - 24 q^{41} - 24 q^{44} - 16 q^{46} - 4 q^{49} + 24 q^{50} - 36 q^{51} + 24 q^{55} - 12 q^{56} + 24 q^{59} + 24 q^{60} - 8 q^{61} + 32 q^{64} + 60 q^{66} + 12 q^{69} + 12 q^{70} + 72 q^{71} - 12 q^{74} - 48 q^{75} - 12 q^{76} + 16 q^{79} - 48 q^{80} + 36 q^{81} - 36 q^{84} + 16 q^{85} - 36 q^{86} - 24 q^{89} - 36 q^{90} - 24 q^{91} + 20 q^{94} + 12 q^{95} - 60 q^{96} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.448288 + 0.258819i −0.316987 + 0.183013i −0.650049 0.759892i \(-0.725252\pi\)
0.333062 + 0.942905i \(0.391918\pi\)
\(3\) 0.448288 + 1.67303i 0.258819 + 0.965926i
\(4\) −0.866025 + 1.50000i −0.433013 + 0.750000i
\(5\) −0.358719 2.20711i −0.160424 0.987048i
\(6\) −0.633975 0.633975i −0.258819 0.258819i
\(7\) 2.89778 1.67303i 1.09526 0.632347i 0.160286 0.987071i \(-0.448758\pi\)
0.934971 + 0.354724i \(0.115425\pi\)
\(8\) 1.93185i 0.683013i
\(9\) −2.59808 + 1.50000i −0.866025 + 0.500000i
\(10\) 0.732051 + 0.896575i 0.231495 + 0.283522i
\(11\) −0.633975 1.09808i −0.191151 0.331082i 0.754481 0.656322i \(-0.227889\pi\)
−0.945632 + 0.325239i \(0.894555\pi\)
\(12\) −2.89778 0.776457i −0.836516 0.224144i
\(13\) −2.12132 1.22474i −0.588348 0.339683i 0.176096 0.984373i \(-0.443653\pi\)
−0.764444 + 0.644690i \(0.776986\pi\)
\(14\) −0.866025 + 1.50000i −0.231455 + 0.400892i
\(15\) 3.53175 1.58957i 0.911894 0.410425i
\(16\) −1.23205 2.13397i −0.308013 0.533494i
\(17\) 5.27792i 1.28008i 0.768340 + 0.640041i \(0.221083\pi\)
−0.768340 + 0.640041i \(0.778917\pi\)
\(18\) 0.776457 1.34486i 0.183013 0.316987i
\(19\) 0.732051 0.167944 0.0839720 0.996468i \(-0.473239\pi\)
0.0839720 + 0.996468i \(0.473239\pi\)
\(20\) 3.62132 + 1.37333i 0.809752 + 0.307086i
\(21\) 4.09808 + 4.09808i 0.894274 + 0.894274i
\(22\) 0.568406 + 0.328169i 0.121185 + 0.0699660i
\(23\) 0.448288 + 0.258819i 0.0934745 + 0.0539675i 0.546009 0.837780i \(-0.316147\pi\)
−0.452534 + 0.891747i \(0.649480\pi\)
\(24\) 3.23205 0.866025i 0.659740 0.176777i
\(25\) −4.74264 + 1.58346i −0.948528 + 0.316693i
\(26\) 1.26795 0.248665
\(27\) −3.67423 3.67423i −0.707107 0.707107i
\(28\) 5.79555i 1.09526i
\(29\) −0.232051 0.401924i −0.0430908 0.0746354i 0.843676 0.536853i \(-0.180387\pi\)
−0.886766 + 0.462218i \(0.847054\pi\)
\(30\) −1.17183 + 1.62667i −0.213946 + 0.296988i
\(31\) −0.366025 + 0.633975i −0.0657401 + 0.113865i −0.897022 0.441986i \(-0.854274\pi\)
0.831282 + 0.555851i \(0.187607\pi\)
\(32\) 4.45069 + 2.56961i 0.786779 + 0.454247i
\(33\) 1.55291 1.55291i 0.270328 0.270328i
\(34\) −1.36603 2.36603i −0.234271 0.405770i
\(35\) −4.73205 5.79555i −0.799863 0.979628i
\(36\) 5.19615i 0.866025i
\(37\) 4.24264i 0.697486i −0.937218 0.348743i \(-0.886609\pi\)
0.937218 0.348743i \(-0.113391\pi\)
\(38\) −0.328169 + 0.189469i −0.0532361 + 0.0307359i
\(39\) 1.09808 4.09808i 0.175833 0.656217i
\(40\) −4.26380 + 0.692993i −0.674166 + 0.109572i
\(41\) −3.86603 + 6.69615i −0.603772 + 1.04576i 0.388473 + 0.921460i \(0.373003\pi\)
−0.992244 + 0.124303i \(0.960331\pi\)
\(42\) −2.89778 0.776457i −0.447137 0.119810i
\(43\) 0.568406 0.328169i 0.0866811 0.0500454i −0.456033 0.889963i \(-0.650730\pi\)
0.542714 + 0.839918i \(0.317397\pi\)
\(44\) 2.19615 0.331082
\(45\) 4.24264 + 5.19615i 0.632456 + 0.774597i
\(46\) −0.267949 −0.0395070
\(47\) −2.56961 + 1.48356i −0.374816 + 0.216400i −0.675560 0.737305i \(-0.736098\pi\)
0.300744 + 0.953705i \(0.402765\pi\)
\(48\) 3.01790 3.01790i 0.435596 0.435596i
\(49\) 2.09808 3.63397i 0.299725 0.519139i
\(50\) 1.71624 1.93733i 0.242713 0.273980i
\(51\) −8.83013 + 2.36603i −1.23647 + 0.331310i
\(52\) 3.67423 2.12132i 0.509525 0.294174i
\(53\) 1.03528i 0.142206i 0.997469 + 0.0711031i \(0.0226519\pi\)
−0.997469 + 0.0711031i \(0.977348\pi\)
\(54\) 2.59808 + 0.696152i 0.353553 + 0.0947343i
\(55\) −2.19615 + 1.79315i −0.296129 + 0.241788i
\(56\) −3.23205 5.59808i −0.431901 0.748074i
\(57\) 0.328169 + 1.22474i 0.0434671 + 0.162221i
\(58\) 0.208051 + 0.120118i 0.0273184 + 0.0157723i
\(59\) 4.73205 8.19615i 0.616061 1.06705i −0.374137 0.927373i \(-0.622061\pi\)
0.990197 0.139675i \(-0.0446057\pi\)
\(60\) −0.674235 + 6.67423i −0.0870433 + 0.861640i
\(61\) 3.33013 + 5.76795i 0.426379 + 0.738510i 0.996548 0.0830172i \(-0.0264556\pi\)
−0.570169 + 0.821527i \(0.693122\pi\)
\(62\) 0.378937i 0.0481251i
\(63\) −5.01910 + 8.69333i −0.632347 + 1.09526i
\(64\) 2.26795 0.283494
\(65\) −1.94218 + 5.12132i −0.240898 + 0.635222i
\(66\) −0.294229 + 1.09808i −0.0362170 + 0.135164i
\(67\) 6.57201 + 3.79435i 0.802899 + 0.463554i 0.844484 0.535581i \(-0.179907\pi\)
−0.0415848 + 0.999135i \(0.513241\pi\)
\(68\) −7.91688 4.57081i −0.960062 0.554292i
\(69\) −0.232051 + 0.866025i −0.0279356 + 0.104257i
\(70\) 3.62132 + 1.37333i 0.432831 + 0.164144i
\(71\) 14.1962 1.68477 0.842387 0.538874i \(-0.181150\pi\)
0.842387 + 0.538874i \(0.181150\pi\)
\(72\) 2.89778 + 5.01910i 0.341506 + 0.591506i
\(73\) 8.48528i 0.993127i −0.868000 0.496564i \(-0.834595\pi\)
0.868000 0.496564i \(-0.165405\pi\)
\(74\) 1.09808 + 1.90192i 0.127649 + 0.221094i
\(75\) −4.77526 7.22474i −0.551399 0.834242i
\(76\) −0.633975 + 1.09808i −0.0727219 + 0.125958i
\(77\) −3.67423 2.12132i −0.418718 0.241747i
\(78\) 0.568406 + 2.12132i 0.0643593 + 0.240192i
\(79\) 3.73205 + 6.46410i 0.419889 + 0.727268i 0.995928 0.0901537i \(-0.0287358\pi\)
−0.576039 + 0.817422i \(0.695403\pi\)
\(80\) −4.26795 + 3.48477i −0.477171 + 0.389609i
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) 4.00240i 0.441992i
\(83\) 6.90018 3.98382i 0.757393 0.437281i −0.0709657 0.997479i \(-0.522608\pi\)
0.828359 + 0.560198i \(0.189275\pi\)
\(84\) −9.69615 + 2.59808i −1.05794 + 0.283473i
\(85\) 11.6489 1.89329i 1.26350 0.205356i
\(86\) −0.169873 + 0.294229i −0.0183179 + 0.0317275i
\(87\) 0.568406 0.568406i 0.0609395 0.0609395i
\(88\) −2.12132 + 1.22474i −0.226134 + 0.130558i
\(89\) −13.3923 −1.41958 −0.709791 0.704413i \(-0.751211\pi\)
−0.709791 + 0.704413i \(0.751211\pi\)
\(90\) −3.24679 1.23130i −0.342241 0.129790i
\(91\) −8.19615 −0.859190
\(92\) −0.776457 + 0.448288i −0.0809513 + 0.0467372i
\(93\) −1.22474 0.328169i −0.127000 0.0340296i
\(94\) 0.767949 1.33013i 0.0792079 0.137192i
\(95\) −0.262601 1.61571i −0.0269423 0.165769i
\(96\) −2.30385 + 8.59808i −0.235135 + 0.877537i
\(97\) −13.1440 + 7.58871i −1.33457 + 0.770516i −0.985997 0.166764i \(-0.946668\pi\)
−0.348577 + 0.937280i \(0.613335\pi\)
\(98\) 2.17209i 0.219414i
\(99\) 3.29423 + 1.90192i 0.331082 + 0.191151i
\(100\) 1.73205 8.48528i 0.173205 0.848528i
\(101\) −4.73205 8.19615i −0.470857 0.815548i 0.528588 0.848879i \(-0.322722\pi\)
−0.999444 + 0.0333310i \(0.989388\pi\)
\(102\) 3.34607 3.34607i 0.331310 0.331310i
\(103\) 0.568406 + 0.328169i 0.0560067 + 0.0323355i 0.527742 0.849405i \(-0.323039\pi\)
−0.471735 + 0.881740i \(0.656372\pi\)
\(104\) −2.36603 + 4.09808i −0.232008 + 0.401849i
\(105\) 7.57483 10.5150i 0.739228 1.02615i
\(106\) −0.267949 0.464102i −0.0260255 0.0450775i
\(107\) 10.3156i 0.997246i −0.866819 0.498623i \(-0.833839\pi\)
0.866819 0.498623i \(-0.166161\pi\)
\(108\) 8.69333 2.32937i 0.836516 0.224144i
\(109\) −12.6603 −1.21263 −0.606316 0.795224i \(-0.707353\pi\)
−0.606316 + 0.795224i \(0.707353\pi\)
\(110\) 0.520407 1.37225i 0.0496188 0.130839i
\(111\) 7.09808 1.90192i 0.673720 0.180523i
\(112\) −7.14042 4.12252i −0.674706 0.389542i
\(113\) 14.9372 + 8.62398i 1.40517 + 0.811276i 0.994917 0.100695i \(-0.0321067\pi\)
0.410254 + 0.911971i \(0.365440\pi\)
\(114\) −0.464102 0.464102i −0.0434671 0.0434671i
\(115\) 0.410432 1.08226i 0.0382730 0.100921i
\(116\) 0.803848 0.0746354
\(117\) 7.34847 0.679366
\(118\) 4.89898i 0.450988i
\(119\) 8.83013 + 15.2942i 0.809456 + 1.40202i
\(120\) −3.07081 6.82282i −0.280325 0.622836i
\(121\) 4.69615 8.13397i 0.426923 0.739452i
\(122\) −2.98571 1.72380i −0.270314 0.156066i
\(123\) −12.9360 3.46618i −1.16640 0.312535i
\(124\) −0.633975 1.09808i −0.0569326 0.0986102i
\(125\) 5.19615 + 9.89949i 0.464758 + 0.885438i
\(126\) 5.19615i 0.462910i
\(127\) 17.3867i 1.54282i 0.636340 + 0.771409i \(0.280447\pi\)
−0.636340 + 0.771409i \(0.719553\pi\)
\(128\) −9.91808 + 5.72620i −0.876642 + 0.506130i
\(129\) 0.803848 + 0.803848i 0.0707748 + 0.0707748i
\(130\) −0.454838 2.79850i −0.0398919 0.245445i
\(131\) −6.46410 + 11.1962i −0.564771 + 0.978212i 0.432300 + 0.901730i \(0.357702\pi\)
−0.997071 + 0.0764824i \(0.975631\pi\)
\(132\) 0.984508 + 3.67423i 0.0856904 + 0.319801i
\(133\) 2.12132 1.22474i 0.183942 0.106199i
\(134\) −3.92820 −0.339345
\(135\) −6.79141 + 9.42745i −0.584511 + 0.811386i
\(136\) 10.1962 0.874313
\(137\) 13.6245 7.86611i 1.16402 0.672047i 0.211755 0.977323i \(-0.432082\pi\)
0.952264 + 0.305276i \(0.0987487\pi\)
\(138\) −0.120118 0.448288i −0.0102252 0.0381608i
\(139\) −4.00000 + 6.92820i −0.339276 + 0.587643i −0.984297 0.176522i \(-0.943515\pi\)
0.645021 + 0.764165i \(0.276849\pi\)
\(140\) 12.7914 2.07898i 1.08107 0.175706i
\(141\) −3.63397 3.63397i −0.306036 0.306036i
\(142\) −6.36396 + 3.67423i −0.534052 + 0.308335i
\(143\) 3.10583i 0.259722i
\(144\) 6.40192 + 3.69615i 0.533494 + 0.308013i
\(145\) −0.803848 + 0.656339i −0.0667559 + 0.0545060i
\(146\) 2.19615 + 3.80385i 0.181755 + 0.314809i
\(147\) 7.02030 + 1.88108i 0.579025 + 0.155149i
\(148\) 6.36396 + 3.67423i 0.523114 + 0.302020i
\(149\) 2.13397 3.69615i 0.174822 0.302801i −0.765278 0.643700i \(-0.777398\pi\)
0.940100 + 0.340900i \(0.110732\pi\)
\(150\) 4.01059 + 2.00284i 0.327463 + 0.163531i
\(151\) −4.29423 7.43782i −0.349459 0.605281i 0.636694 0.771116i \(-0.280301\pi\)
−0.986154 + 0.165835i \(0.946968\pi\)
\(152\) 1.41421i 0.114708i
\(153\) −7.91688 13.7124i −0.640041 1.10858i
\(154\) 2.19615 0.176971
\(155\) 1.53055 + 0.580438i 0.122937 + 0.0466219i
\(156\) 5.19615 + 5.19615i 0.416025 + 0.416025i
\(157\) −11.1750 6.45189i −0.891863 0.514917i −0.0173114 0.999850i \(-0.505511\pi\)
−0.874551 + 0.484933i \(0.838844\pi\)
\(158\) −3.34607 1.93185i −0.266199 0.153690i
\(159\) −1.73205 + 0.464102i −0.137361 + 0.0368057i
\(160\) 4.07485 10.7449i 0.322145 0.849461i
\(161\) 1.73205 0.136505
\(162\) 4.65874i 0.366025i
\(163\) 10.4543i 0.818844i −0.912345 0.409422i \(-0.865730\pi\)
0.912345 0.409422i \(-0.134270\pi\)
\(164\) −6.69615 11.5981i −0.522882 0.905658i
\(165\) −3.98451 2.87039i −0.310194 0.223459i
\(166\) −2.06218 + 3.57180i −0.160056 + 0.277225i
\(167\) −8.60540 4.96833i −0.665906 0.384461i 0.128618 0.991694i \(-0.458946\pi\)
−0.794524 + 0.607233i \(0.792279\pi\)
\(168\) 7.91688 7.91688i 0.610800 0.610800i
\(169\) −3.50000 6.06218i −0.269231 0.466321i
\(170\) −4.73205 + 3.86370i −0.362932 + 0.296333i
\(171\) −1.90192 + 1.09808i −0.145444 + 0.0839720i
\(172\) 1.13681i 0.0866811i
\(173\) −9.14162 + 5.27792i −0.695025 + 0.401273i −0.805492 0.592607i \(-0.798099\pi\)
0.110467 + 0.993880i \(0.464765\pi\)
\(174\) −0.107695 + 0.401924i −0.00816435 + 0.0304698i
\(175\) −11.0939 + 12.5231i −0.838622 + 0.946659i
\(176\) −1.56218 + 2.70577i −0.117754 + 0.203955i
\(177\) 15.8338 + 4.24264i 1.19014 + 0.318896i
\(178\) 6.00361 3.46618i 0.449989 0.259801i
\(179\) 6.58846 0.492444 0.246222 0.969213i \(-0.420811\pi\)
0.246222 + 0.969213i \(0.420811\pi\)
\(180\) −11.4685 + 1.86396i −0.854809 + 0.138931i
\(181\) 1.53590 0.114162 0.0570812 0.998370i \(-0.481821\pi\)
0.0570812 + 0.998370i \(0.481821\pi\)
\(182\) 3.67423 2.12132i 0.272352 0.157243i
\(183\) −8.15711 + 8.15711i −0.602991 + 0.602991i
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −9.36396 + 1.52192i −0.688452 + 0.111894i
\(186\) 0.633975 0.169873i 0.0464853 0.0124557i
\(187\) 5.79555 3.34607i 0.423813 0.244689i
\(188\) 5.13922i 0.374816i
\(189\) −16.7942 4.50000i −1.22160 0.327327i
\(190\) 0.535898 + 0.656339i 0.0388782 + 0.0476158i
\(191\) −8.83013 15.2942i −0.638926 1.10665i −0.985669 0.168691i \(-0.946046\pi\)
0.346743 0.937960i \(-0.387287\pi\)
\(192\) 1.01669 + 3.79435i 0.0733736 + 0.273834i
\(193\) 3.25813 + 1.88108i 0.234526 + 0.135403i 0.612658 0.790348i \(-0.290100\pi\)
−0.378133 + 0.925751i \(0.623434\pi\)
\(194\) 3.92820 6.80385i 0.282029 0.488488i
\(195\) −9.43879 0.953512i −0.675926 0.0682824i
\(196\) 3.63397 + 6.29423i 0.259570 + 0.449588i
\(197\) 15.9353i 1.13534i −0.823255 0.567671i \(-0.807845\pi\)
0.823255 0.567671i \(-0.192155\pi\)
\(198\) −1.96902 −0.139932
\(199\) 26.5885 1.88481 0.942403 0.334480i \(-0.108561\pi\)
0.942403 + 0.334480i \(0.108561\pi\)
\(200\) 3.05902 + 9.16208i 0.216305 + 0.647857i
\(201\) −3.40192 + 12.6962i −0.239953 + 0.895518i
\(202\) 4.24264 + 2.44949i 0.298511 + 0.172345i
\(203\) −1.34486 0.776457i −0.0943909 0.0544966i
\(204\) 4.09808 15.2942i 0.286923 1.07081i
\(205\) 16.1659 + 6.13069i 1.12908 + 0.428186i
\(206\) −0.339746 −0.0236712
\(207\) −1.55291 −0.107935
\(208\) 6.03579i 0.418507i
\(209\) −0.464102 0.803848i −0.0321026 0.0556033i
\(210\) −0.674235 + 6.67423i −0.0465266 + 0.460566i
\(211\) −5.56218 + 9.63397i −0.382916 + 0.663230i −0.991478 0.130276i \(-0.958414\pi\)
0.608562 + 0.793507i \(0.291747\pi\)
\(212\) −1.55291 0.896575i −0.106655 0.0615771i
\(213\) 6.36396 + 23.7506i 0.436051 + 1.62737i
\(214\) 2.66987 + 4.62436i 0.182509 + 0.316114i
\(215\) −0.928203 1.13681i −0.0633029 0.0775299i
\(216\) −7.09808 + 7.09808i −0.482963 + 0.482963i
\(217\) 2.44949i 0.166282i
\(218\) 5.67544 3.27671i 0.384389 0.221927i
\(219\) 14.1962 3.80385i 0.959287 0.257040i
\(220\) −0.787803 4.84714i −0.0531136 0.326794i
\(221\) 6.46410 11.1962i 0.434823 0.753135i
\(222\) −2.68973 + 2.68973i −0.180523 + 0.180523i
\(223\) 3.88229 2.24144i 0.259977 0.150098i −0.364347 0.931263i \(-0.618708\pi\)
0.624324 + 0.781165i \(0.285374\pi\)
\(224\) 17.1962 1.14897
\(225\) 9.94655 11.2279i 0.663103 0.748528i
\(226\) −8.92820 −0.593895
\(227\) −22.8541 + 13.1948i −1.51688 + 0.875769i −0.517073 + 0.855941i \(0.672979\pi\)
−0.999803 + 0.0198279i \(0.993688\pi\)
\(228\) −2.12132 0.568406i −0.140488 0.0376436i
\(229\) 3.03590 5.25833i 0.200618 0.347480i −0.748110 0.663575i \(-0.769038\pi\)
0.948728 + 0.316095i \(0.102372\pi\)
\(230\) 0.0961186 + 0.591392i 0.00633787 + 0.0389953i
\(231\) 1.90192 7.09808i 0.125137 0.467019i
\(232\) −0.776457 + 0.448288i −0.0509769 + 0.0294315i
\(233\) 7.07107i 0.463241i 0.972806 + 0.231621i \(0.0744028\pi\)
−0.972806 + 0.231621i \(0.925597\pi\)
\(234\) −3.29423 + 1.90192i −0.215350 + 0.124333i
\(235\) 4.19615 + 5.13922i 0.273727 + 0.335245i
\(236\) 8.19615 + 14.1962i 0.533524 + 0.924091i
\(237\) −9.14162 + 9.14162i −0.593812 + 0.593812i
\(238\) −7.91688 4.57081i −0.513175 0.296282i
\(239\) −0.464102 + 0.803848i −0.0300202 + 0.0519966i −0.880645 0.473776i \(-0.842891\pi\)
0.850625 + 0.525773i \(0.176224\pi\)
\(240\) −7.74340 5.57824i −0.499834 0.360074i
\(241\) −4.86603 8.42820i −0.313448 0.542908i 0.665658 0.746257i \(-0.268151\pi\)
−0.979106 + 0.203348i \(0.934818\pi\)
\(242\) 4.86181i 0.312529i
\(243\) 15.0573 + 4.03459i 0.965926 + 0.258819i
\(244\) −11.5359 −0.738510
\(245\) −8.77319 3.32710i −0.560499 0.212561i
\(246\) 6.69615 1.79423i 0.426931 0.114396i
\(247\) −1.55291 0.896575i −0.0988096 0.0570477i
\(248\) 1.22474 + 0.707107i 0.0777714 + 0.0449013i
\(249\) 9.75833 + 9.75833i 0.618409 + 0.618409i
\(250\) −4.89155 3.09296i −0.309369 0.195616i
\(251\) −12.5885 −0.794576 −0.397288 0.917694i \(-0.630049\pi\)
−0.397288 + 0.917694i \(0.630049\pi\)
\(252\) −8.69333 15.0573i −0.547628 0.948520i
\(253\) 0.656339i 0.0412637i
\(254\) −4.50000 7.79423i −0.282355 0.489053i
\(255\) 8.38961 + 18.6403i 0.525378 + 1.16730i
\(256\) 0.696152 1.20577i 0.0435095 0.0753607i
\(257\) 14.5211 + 8.38375i 0.905800 + 0.522964i 0.879077 0.476679i \(-0.158160\pi\)
0.0267223 + 0.999643i \(0.491493\pi\)
\(258\) −0.568406 0.152304i −0.0353874 0.00948203i
\(259\) −7.09808 12.2942i −0.441053 0.763926i
\(260\) −6.00000 7.34847i −0.372104 0.455733i
\(261\) 1.20577 + 0.696152i 0.0746354 + 0.0430908i
\(262\) 6.69213i 0.413441i
\(263\) 18.8516 10.8840i 1.16244 0.671136i 0.210554 0.977582i \(-0.432473\pi\)
0.951888 + 0.306446i \(0.0991398\pi\)
\(264\) −3.00000 3.00000i −0.184637 0.184637i
\(265\) 2.28497 0.371374i 0.140364 0.0228133i
\(266\) −0.633975 + 1.09808i −0.0388715 + 0.0673274i
\(267\) −6.00361 22.4058i −0.367415 1.37121i
\(268\) −11.3831 + 6.57201i −0.695331 + 0.401450i
\(269\) −6.80385 −0.414838 −0.207419 0.978252i \(-0.566506\pi\)
−0.207419 + 0.978252i \(0.566506\pi\)
\(270\) 0.604502 5.98396i 0.0367888 0.364172i
\(271\) 21.5167 1.30704 0.653522 0.756908i \(-0.273291\pi\)
0.653522 + 0.756908i \(0.273291\pi\)
\(272\) 11.2629 6.50266i 0.682916 0.394282i
\(273\) −3.67423 13.7124i −0.222375 0.829914i
\(274\) −4.07180 + 7.05256i −0.245986 + 0.426061i
\(275\) 4.74548 + 4.20390i 0.286163 + 0.253505i
\(276\) −1.09808 1.09808i −0.0660964 0.0660964i
\(277\) 10.6066 6.12372i 0.637289 0.367939i −0.146281 0.989243i \(-0.546730\pi\)
0.783569 + 0.621304i \(0.213397\pi\)
\(278\) 4.14110i 0.248367i
\(279\) 2.19615i 0.131480i
\(280\) −11.1962 + 9.14162i −0.669098 + 0.546316i
\(281\) 9.86603 + 17.0885i 0.588558 + 1.01941i 0.994422 + 0.105478i \(0.0336374\pi\)
−0.405864 + 0.913934i \(0.633029\pi\)
\(282\) 2.56961 + 0.688524i 0.153018 + 0.0410010i
\(283\) −14.4889 8.36516i −0.861275 0.497257i 0.00316407 0.999995i \(-0.498993\pi\)
−0.864439 + 0.502738i \(0.832326\pi\)
\(284\) −12.2942 + 21.2942i −0.729528 + 1.26358i
\(285\) 2.58542 1.16364i 0.153147 0.0689284i
\(286\) −0.803848 1.39230i −0.0475325 0.0823287i
\(287\) 25.8719i 1.52717i
\(288\) −15.4176 −0.908494
\(289\) −10.8564 −0.638612
\(290\) 0.190482 0.502280i 0.0111855 0.0294949i
\(291\) −18.5885 18.5885i −1.08967 1.08967i
\(292\) 12.7279 + 7.34847i 0.744845 + 0.430037i
\(293\) −11.9193 6.88160i −0.696332 0.402027i 0.109648 0.993970i \(-0.465028\pi\)
−0.805980 + 0.591943i \(0.798361\pi\)
\(294\) −3.63397 + 0.973721i −0.211938 + 0.0567885i
\(295\) −19.7873 7.50402i −1.15206 0.436901i
\(296\) −8.19615 −0.476392
\(297\) −1.70522 + 6.36396i −0.0989468 + 0.369274i
\(298\) 2.20925i 0.127979i
\(299\) −0.633975 1.09808i −0.0366637 0.0635034i
\(300\) 14.9726 0.906070i 0.864444 0.0523120i
\(301\) 1.09808 1.90192i 0.0632921 0.109625i
\(302\) 3.85010 + 2.22286i 0.221548 + 0.127911i
\(303\) 11.5911 11.5911i 0.665892 0.665892i
\(304\) −0.901924 1.56218i −0.0517289 0.0895970i
\(305\) 11.5359 9.41902i 0.660544 0.539332i
\(306\) 7.09808 + 4.09808i 0.405770 + 0.234271i
\(307\) 3.82654i 0.218392i −0.994020 0.109196i \(-0.965172\pi\)
0.994020 0.109196i \(-0.0348276\pi\)
\(308\) 6.36396 3.67423i 0.362620 0.209359i
\(309\) −0.294229 + 1.09808i −0.0167381 + 0.0624674i
\(310\) −0.836355 + 0.135932i −0.0475018 + 0.00772043i
\(311\) 5.02628 8.70577i 0.285014 0.493659i −0.687598 0.726091i \(-0.741335\pi\)
0.972613 + 0.232432i \(0.0746684\pi\)
\(312\) −7.91688 2.12132i −0.448205 0.120096i
\(313\) −12.1595 + 7.02030i −0.687296 + 0.396811i −0.802598 0.596520i \(-0.796550\pi\)
0.115302 + 0.993330i \(0.463216\pi\)
\(314\) 6.67949 0.376946
\(315\) 20.9876 + 7.95922i 1.18252 + 0.448451i
\(316\) −12.9282 −0.727268
\(317\) −3.49837 + 2.01978i −0.196488 + 0.113442i −0.595016 0.803714i \(-0.702854\pi\)
0.398528 + 0.917156i \(0.369521\pi\)
\(318\) 0.656339 0.656339i 0.0368057 0.0368057i
\(319\) −0.294229 + 0.509619i −0.0164736 + 0.0285332i
\(320\) −0.813558 5.00561i −0.0454792 0.279822i
\(321\) 17.2583 4.62436i 0.963266 0.258106i
\(322\) −0.776457 + 0.448288i −0.0432703 + 0.0249821i
\(323\) 3.86370i 0.214982i
\(324\) 7.79423 + 13.5000i 0.433013 + 0.750000i
\(325\) 12.0000 + 2.44949i 0.665640 + 0.135873i
\(326\) 2.70577 + 4.68653i 0.149859 + 0.259563i
\(327\) −5.67544 21.1810i −0.313852 1.17131i
\(328\) 12.9360 + 7.46859i 0.714270 + 0.412384i
\(329\) −4.96410 + 8.59808i −0.273680 + 0.474027i
\(330\) 2.52912 + 0.255493i 0.139223 + 0.0140644i
\(331\) 4.19615 + 7.26795i 0.230641 + 0.399483i 0.957997 0.286778i \(-0.0925842\pi\)
−0.727356 + 0.686261i \(0.759251\pi\)
\(332\) 13.8004i 0.757393i
\(333\) 6.36396 + 11.0227i 0.348743 + 0.604040i
\(334\) 5.14359 0.281445
\(335\) 6.01703 15.8662i 0.328746 0.866865i
\(336\) 3.69615 13.7942i 0.201642 0.752537i
\(337\) −5.79555 3.34607i −0.315704 0.182272i 0.333772 0.942654i \(-0.391678\pi\)
−0.649476 + 0.760382i \(0.725012\pi\)
\(338\) 3.13801 + 1.81173i 0.170685 + 0.0985453i
\(339\) −7.73205 + 28.8564i −0.419947 + 1.56726i
\(340\) −7.24833 + 19.1130i −0.393096 + 1.03655i
\(341\) 0.928203 0.0502650
\(342\) 0.568406 0.984508i 0.0307359 0.0532361i
\(343\) 9.38186i 0.506573i
\(344\) −0.633975 1.09808i −0.0341816 0.0592043i
\(345\) 1.99465 + 0.201501i 0.107388 + 0.0108484i
\(346\) 2.73205 4.73205i 0.146876 0.254397i
\(347\) 8.57321 + 4.94975i 0.460234 + 0.265716i 0.712143 0.702035i \(-0.247725\pi\)
−0.251909 + 0.967751i \(0.581058\pi\)
\(348\) 0.360355 + 1.34486i 0.0193171 + 0.0720922i
\(349\) 14.2321 + 24.6506i 0.761824 + 1.31952i 0.941909 + 0.335867i \(0.109029\pi\)
−0.180085 + 0.983651i \(0.557637\pi\)
\(350\) 1.73205 8.48528i 0.0925820 0.453557i
\(351\) 3.29423 + 12.2942i 0.175833 + 0.656217i
\(352\) 6.51626i 0.347318i
\(353\) −17.6269 + 10.1769i −0.938185 + 0.541662i −0.889391 0.457147i \(-0.848871\pi\)
−0.0487943 + 0.998809i \(0.515538\pi\)
\(354\) −8.19615 + 2.19615i −0.435621 + 0.116724i
\(355\) −5.09244 31.3324i −0.270278 1.66295i
\(356\) 11.5981 20.0885i 0.614697 1.06469i
\(357\) −21.6293 + 21.6293i −1.14474 + 1.14474i
\(358\) −2.95352 + 1.70522i −0.156099 + 0.0901236i
\(359\) −20.1962 −1.06591 −0.532956 0.846143i \(-0.678919\pi\)
−0.532956 + 0.846143i \(0.678919\pi\)
\(360\) 10.0382 8.19615i 0.529059 0.431975i
\(361\) −18.4641 −0.971795
\(362\) −0.688524 + 0.397520i −0.0361880 + 0.0208932i
\(363\) 15.7136 + 4.21046i 0.824752 + 0.220992i
\(364\) 7.09808 12.2942i 0.372040 0.644393i
\(365\) −18.7279 + 3.04384i −0.980264 + 0.159322i
\(366\) 1.54552 5.76795i 0.0807855 0.301496i
\(367\) 29.9623 17.2987i 1.56402 0.902986i 0.567175 0.823597i \(-0.308036\pi\)
0.996844 0.0793890i \(-0.0252969\pi\)
\(368\) 1.27551i 0.0664907i
\(369\) 23.1962i 1.20754i
\(370\) 3.80385 3.10583i 0.197753 0.161464i
\(371\) 1.73205 + 3.00000i 0.0899236 + 0.155752i
\(372\) 1.55291 1.55291i 0.0805149 0.0805149i
\(373\) 23.5983 + 13.6245i 1.22187 + 0.705450i 0.965317 0.261079i \(-0.0840784\pi\)
0.256557 + 0.966529i \(0.417412\pi\)
\(374\) −1.73205 + 3.00000i −0.0895622 + 0.155126i
\(375\) −14.2328 + 13.1312i −0.734979 + 0.678090i
\(376\) 2.86603 + 4.96410i 0.147804 + 0.256004i
\(377\) 1.13681i 0.0585488i
\(378\) 8.69333 2.32937i 0.447137 0.119810i
\(379\) −19.4641 −0.999804 −0.499902 0.866082i \(-0.666631\pi\)
−0.499902 + 0.866082i \(0.666631\pi\)
\(380\) 2.65099 + 1.00535i 0.135993 + 0.0515733i
\(381\) −29.0885 + 7.79423i −1.49025 + 0.399310i
\(382\) 7.91688 + 4.57081i 0.405063 + 0.233863i
\(383\) −9.22955 5.32868i −0.471608 0.272283i 0.245305 0.969446i \(-0.421112\pi\)
−0.716913 + 0.697163i \(0.754445\pi\)
\(384\) −14.0263 14.0263i −0.715776 0.715776i
\(385\) −3.36396 + 8.87039i −0.171443 + 0.452077i
\(386\) −1.94744 −0.0991221
\(387\) −0.984508 + 1.70522i −0.0500454 + 0.0866811i
\(388\) 26.2880i 1.33457i
\(389\) 0.0621778 + 0.107695i 0.00315254 + 0.00546036i 0.867597 0.497267i \(-0.165663\pi\)
−0.864445 + 0.502728i \(0.832330\pi\)
\(390\) 4.47808 2.01549i 0.226757 0.102058i
\(391\) −1.36603 + 2.36603i −0.0690829 + 0.119655i
\(392\) −7.02030 4.05317i −0.354579 0.204716i
\(393\) −21.6293 5.79555i −1.09105 0.292347i
\(394\) 4.12436 + 7.14359i 0.207782 + 0.359889i
\(395\) 12.9282 10.5558i 0.650488 0.531122i
\(396\) −5.70577 + 3.29423i −0.286726 + 0.165541i
\(397\) 29.3939i 1.47524i −0.675218 0.737618i \(-0.735950\pi\)
0.675218 0.737618i \(-0.264050\pi\)
\(398\) −11.9193 + 6.88160i −0.597459 + 0.344943i
\(399\) 3.00000 + 3.00000i 0.150188 + 0.150188i
\(400\) 9.22225 + 8.16977i 0.461112 + 0.408488i
\(401\) 8.53590 14.7846i 0.426262 0.738308i −0.570275 0.821454i \(-0.693163\pi\)
0.996537 + 0.0831457i \(0.0264967\pi\)
\(402\) −1.76097 6.57201i −0.0878290 0.327782i
\(403\) 1.55291 0.896575i 0.0773562 0.0446616i
\(404\) 16.3923 0.815548
\(405\) −18.8169 7.13604i −0.935021 0.354593i
\(406\) 0.803848 0.0398943
\(407\) −4.65874 + 2.68973i −0.230925 + 0.133325i
\(408\) 4.57081 + 17.0585i 0.226289 + 0.844521i
\(409\) −8.26795 + 14.3205i −0.408824 + 0.708104i −0.994758 0.102255i \(-0.967394\pi\)
0.585934 + 0.810358i \(0.300728\pi\)
\(410\) −8.83373 + 1.43574i −0.436267 + 0.0709062i
\(411\) 19.2679 + 19.2679i 0.950418 + 0.950418i
\(412\) −0.984508 + 0.568406i −0.0485032 + 0.0280034i
\(413\) 31.6675i 1.55826i
\(414\) 0.696152 0.401924i 0.0342140 0.0197535i
\(415\) −11.2679 13.8004i −0.553122 0.677433i
\(416\) −6.29423 10.9019i −0.308600 0.534511i
\(417\) −13.3843 3.58630i −0.655430 0.175622i
\(418\) 0.416102 + 0.240237i 0.0203522 + 0.0117504i
\(419\) 11.0263 19.0981i 0.538669 0.933002i −0.460307 0.887760i \(-0.652261\pi\)
0.998976 0.0452423i \(-0.0144060\pi\)
\(420\) 9.21243 + 20.4685i 0.449521 + 0.998759i
\(421\) 9.73205 + 16.8564i 0.474311 + 0.821531i 0.999567 0.0294132i \(-0.00936385\pi\)
−0.525256 + 0.850944i \(0.676031\pi\)
\(422\) 5.75839i 0.280314i
\(423\) 4.45069 7.70882i 0.216400 0.374816i
\(424\) 2.00000 0.0971286
\(425\) −8.35739 25.0313i −0.405393 1.21419i
\(426\) −9.00000 9.00000i −0.436051 0.436051i
\(427\) 19.2999 + 11.1428i 0.933989 + 0.539239i
\(428\) 15.4734 + 8.93357i 0.747935 + 0.431820i
\(429\) −5.19615 + 1.39230i −0.250873 + 0.0672211i
\(430\) 0.710331 + 0.269382i 0.0342552 + 0.0129908i
\(431\) −6.00000 −0.289010 −0.144505 0.989504i \(-0.546159\pi\)
−0.144505 + 0.989504i \(0.546159\pi\)
\(432\) −3.31388 + 12.3676i −0.159439 + 0.595035i
\(433\) 13.5601i 0.651658i 0.945429 + 0.325829i \(0.105643\pi\)
−0.945429 + 0.325829i \(0.894357\pi\)
\(434\) −0.633975 1.09808i −0.0304318 0.0527093i
\(435\) −1.45843 1.05063i −0.0699264 0.0503741i
\(436\) 10.9641 18.9904i 0.525085 0.909474i
\(437\) 0.328169 + 0.189469i 0.0156985 + 0.00906352i
\(438\) −5.37945 + 5.37945i −0.257040 + 0.257040i
\(439\) −12.6603 21.9282i −0.604241 1.04658i −0.992171 0.124887i \(-0.960143\pi\)
0.387930 0.921689i \(-0.373190\pi\)
\(440\) 3.46410 + 4.24264i 0.165145 + 0.202260i
\(441\) 12.5885i 0.599450i
\(442\) 6.69213i 0.318312i
\(443\) −1.43280 + 0.827225i −0.0680742 + 0.0393027i −0.533651 0.845705i \(-0.679180\pi\)
0.465577 + 0.885008i \(0.345847\pi\)
\(444\) −3.29423 + 12.2942i −0.156337 + 0.583458i
\(445\) 4.80408 + 29.5582i 0.227735 + 1.40120i
\(446\) −1.16025 + 2.00962i −0.0549396 + 0.0951582i
\(447\) 7.14042 + 1.91327i 0.337730 + 0.0904945i
\(448\) 6.57201 3.79435i 0.310498 0.179266i
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) −1.55291 + 7.60770i −0.0732051 + 0.358630i
\(451\) 9.80385 0.461645
\(452\) −25.8719 + 14.9372i −1.21691 + 0.702586i
\(453\) 10.5187 10.5187i 0.494210 0.494210i
\(454\) 6.83013 11.8301i 0.320554 0.555215i
\(455\) 2.94012 + 18.0898i 0.137835 + 0.848062i
\(456\) 2.36603 0.633975i 0.110799 0.0296886i
\(457\) −21.4770 + 12.3998i −1.00465 + 0.580036i −0.909621 0.415438i \(-0.863628\pi\)
−0.0950304 + 0.995474i \(0.530295\pi\)
\(458\) 3.14299i 0.146862i
\(459\) 19.3923 19.3923i 0.905155 0.905155i
\(460\) 1.26795 + 1.55291i 0.0591184 + 0.0724050i
\(461\) 18.3564 + 31.7942i 0.854943 + 1.48080i 0.876698 + 0.481042i \(0.159741\pi\)
−0.0217547 + 0.999763i \(0.506925\pi\)
\(462\) 0.984508 + 3.67423i 0.0458035 + 0.170941i
\(463\) −29.5462 17.0585i −1.37313 0.792776i −0.381807 0.924242i \(-0.624698\pi\)
−0.991321 + 0.131467i \(0.958031\pi\)
\(464\) −0.571797 + 0.990381i −0.0265450 + 0.0459773i
\(465\) −0.284965 + 2.82086i −0.0132149 + 0.130814i
\(466\) −1.83013 3.16987i −0.0847790 0.146842i
\(467\) 25.3543i 1.17326i 0.809856 + 0.586629i \(0.199545\pi\)
−0.809856 + 0.586629i \(0.800455\pi\)
\(468\) −6.36396 + 11.0227i −0.294174 + 0.509525i
\(469\) 25.3923 1.17251
\(470\) −3.21121 1.21780i −0.148122 0.0561731i
\(471\) 5.78461 21.5885i 0.266541 0.994744i
\(472\) −15.8338 9.14162i −0.728807 0.420777i
\(473\) −0.720710 0.416102i −0.0331383 0.0191324i
\(474\) 1.73205 6.46410i 0.0795557 0.296906i
\(475\) −3.47185 + 1.15918i −0.159300 + 0.0531867i
\(476\) −30.5885 −1.40202
\(477\) −1.55291 2.68973i −0.0711031 0.123154i
\(478\) 0.480473i 0.0219763i
\(479\) 2.07180 + 3.58846i 0.0946628 + 0.163961i 0.909468 0.415774i \(-0.136489\pi\)
−0.814805 + 0.579735i \(0.803156\pi\)
\(480\) 19.8033 + 2.00054i 0.903893 + 0.0913118i
\(481\) −5.19615 + 9.00000i −0.236924 + 0.410365i
\(482\) 4.36276 + 2.51884i 0.198718 + 0.114730i
\(483\) 0.776457 + 2.89778i 0.0353300 + 0.131853i
\(484\) 8.13397 + 14.0885i 0.369726 + 0.640384i
\(485\) 21.4641 + 26.2880i 0.974635 + 1.19368i
\(486\) −7.79423 + 2.08846i −0.353553 + 0.0947343i
\(487\) 15.8338i 0.717496i 0.933435 + 0.358748i \(0.116796\pi\)
−0.933435 + 0.358748i \(0.883204\pi\)
\(488\) 11.1428 6.43331i 0.504412 0.291222i
\(489\) 17.4904 4.68653i 0.790942 0.211932i
\(490\) 4.79403 0.779170i 0.216572 0.0351993i
\(491\) −16.8564 + 29.1962i −0.760719 + 1.31760i 0.181761 + 0.983343i \(0.441820\pi\)
−0.942480 + 0.334261i \(0.891513\pi\)
\(492\) 16.4022 16.4022i 0.739466 0.739466i
\(493\) 2.12132 1.22474i 0.0955395 0.0551597i
\(494\) 0.928203 0.0417618
\(495\) 3.01604 7.95297i 0.135561 0.357459i
\(496\) 1.80385 0.0809951
\(497\) 41.1373 23.7506i 1.84526 1.06536i
\(498\) −6.90018 1.84890i −0.309205 0.0828511i
\(499\) 11.9282 20.6603i 0.533980 0.924880i −0.465232 0.885189i \(-0.654029\pi\)
0.999212 0.0396914i \(-0.0126375\pi\)
\(500\) −19.3492 0.778985i −0.865324 0.0348373i
\(501\) 4.45448 16.6244i 0.199012 0.742721i
\(502\) 5.64325 3.25813i 0.251871 0.145418i
\(503\) 2.48665i 0.110874i −0.998462 0.0554372i \(-0.982345\pi\)
0.998462 0.0554372i \(-0.0176553\pi\)
\(504\) 16.7942 + 9.69615i 0.748074 + 0.431901i
\(505\) −16.3923 + 13.3843i −0.729448 + 0.595592i
\(506\) 0.169873 + 0.294229i 0.00755178 + 0.0130801i
\(507\) 8.57321 8.57321i 0.380750 0.380750i
\(508\) −26.0800 15.0573i −1.15711 0.668059i
\(509\) 8.42820 14.5981i 0.373574 0.647048i −0.616539 0.787324i \(-0.711466\pi\)
0.990112 + 0.140276i \(0.0447990\pi\)
\(510\) −8.58542 6.18482i −0.380169 0.273869i
\(511\) −14.1962 24.5885i −0.628001 1.08773i
\(512\) 22.1841i 0.980408i
\(513\) −2.68973 2.68973i −0.118754 0.118754i
\(514\) −8.67949 −0.382836
\(515\) 0.520407 1.37225i 0.0229319 0.0604687i
\(516\) −1.90192 + 0.509619i −0.0837275 + 0.0224347i
\(517\) 3.25813 + 1.88108i 0.143293 + 0.0827300i
\(518\) 6.36396 + 3.67423i 0.279616 + 0.161437i
\(519\) −12.9282 12.9282i −0.567485 0.567485i
\(520\) 9.89363 + 3.75201i 0.433864 + 0.164537i
\(521\) −19.3923 −0.849592 −0.424796 0.905289i \(-0.639654\pi\)
−0.424796 + 0.905289i \(0.639654\pi\)
\(522\) −0.720710 −0.0315446
\(523\) 35.1894i 1.53873i 0.638812 + 0.769363i \(0.279426\pi\)
−0.638812 + 0.769363i \(0.720574\pi\)
\(524\) −11.1962 19.3923i −0.489106 0.847157i
\(525\) −25.9249 12.9465i −1.13145 0.565034i
\(526\) −5.63397 + 9.75833i −0.245653 + 0.425483i
\(527\) −3.34607 1.93185i −0.145757 0.0841528i
\(528\) −5.22715 1.40061i −0.227482 0.0609537i
\(529\) −11.3660 19.6865i −0.494175 0.855936i
\(530\) −0.928203 + 0.757875i −0.0403186 + 0.0329200i
\(531\) 28.3923i 1.23212i
\(532\) 4.24264i 0.183942i
\(533\) 16.4022 9.46979i 0.710456 0.410182i
\(534\) 8.49038 + 8.49038i 0.367415 + 0.367415i
\(535\) −22.7676 + 3.70041i −0.984330 + 0.159982i
\(536\) 7.33013 12.6962i 0.316613 0.548390i
\(537\) 2.95352 + 11.0227i 0.127454 + 0.475665i
\(538\) 3.05008 1.76097i 0.131498 0.0759206i
\(539\) −5.32051 −0.229171
\(540\) −8.25964 18.3515i −0.355438 0.789724i
\(541\) 0.607695 0.0261269 0.0130634 0.999915i \(-0.495842\pi\)
0.0130634 + 0.999915i \(0.495842\pi\)
\(542\) −9.64566 + 5.56892i −0.414316 + 0.239206i
\(543\) 0.688524 + 2.56961i 0.0295474 + 0.110272i
\(544\) −13.5622 + 23.4904i −0.581474 + 1.00714i
\(545\) 4.54148 + 27.9425i 0.194536 + 1.19693i
\(546\) 5.19615 + 5.19615i 0.222375 + 0.222375i
\(547\) −22.5581 + 13.0239i −0.964513 + 0.556862i −0.897559 0.440894i \(-0.854661\pi\)
−0.0669541 + 0.997756i \(0.521328\pi\)
\(548\) 27.2490i 1.16402i
\(549\) −17.3038 9.99038i −0.738510 0.426379i
\(550\) −3.21539 0.656339i −0.137105 0.0279864i
\(551\) −0.169873 0.294229i −0.00723683 0.0125346i
\(552\) 1.67303 + 0.448288i 0.0712090 + 0.0190804i
\(553\) 21.6293 + 12.4877i 0.919772 + 0.531030i
\(554\) −3.16987 + 5.49038i −0.134675 + 0.233264i
\(555\) −6.74397 14.9840i −0.286265 0.636033i
\(556\) −6.92820 12.0000i −0.293821 0.508913i
\(557\) 31.1127i 1.31829i −0.752017 0.659144i \(-0.770919\pi\)
0.752017 0.659144i \(-0.229081\pi\)
\(558\) 0.568406 + 0.984508i 0.0240625 + 0.0416776i
\(559\) −1.60770 −0.0679983
\(560\) −6.53744 + 17.2385i −0.276257 + 0.728459i
\(561\) 8.19615 + 8.19615i 0.346042 + 0.346042i
\(562\) −8.84564 5.10703i −0.373131 0.215427i
\(563\) 7.94906 + 4.58939i 0.335013 + 0.193420i 0.658065 0.752962i \(-0.271375\pi\)
−0.323052 + 0.946381i \(0.604709\pi\)
\(564\) 8.59808 2.30385i 0.362044 0.0970095i
\(565\) 13.6758 36.0615i 0.575345 1.51712i
\(566\) 8.66025 0.364018
\(567\) 30.1146i 1.26469i
\(568\) 27.4249i 1.15072i
\(569\) 14.6603 + 25.3923i 0.614590 + 1.06450i 0.990456 + 0.137827i \(0.0440118\pi\)
−0.375867 + 0.926674i \(0.622655\pi\)
\(570\) −0.857840 + 1.19080i −0.0359309 + 0.0498773i
\(571\) 0.732051 1.26795i 0.0306354 0.0530620i −0.850301 0.526296i \(-0.823580\pi\)
0.880937 + 0.473234i \(0.156914\pi\)
\(572\) −4.65874 2.68973i −0.194792 0.112463i
\(573\) 21.6293 21.6293i 0.903577 0.903577i
\(574\) −6.69615 11.5981i −0.279492 0.484094i
\(575\) −2.53590 0.517638i −0.105754 0.0215870i
\(576\) −5.89230 + 3.40192i −0.245513 + 0.141747i
\(577\) 13.8647i 0.577196i 0.957450 + 0.288598i \(0.0931892\pi\)
−0.957450 + 0.288598i \(0.906811\pi\)
\(578\) 4.86679 2.80984i 0.202432 0.116874i
\(579\) −1.68653 + 6.29423i −0.0700899 + 0.261579i
\(580\) −0.288356 1.77418i −0.0119733 0.0736687i
\(581\) 13.3301 23.0885i 0.553027 0.957871i
\(582\) 13.1440 + 3.52193i 0.544837 + 0.145989i
\(583\) 1.13681 0.656339i 0.0470819 0.0271828i
\(584\) −16.3923 −0.678318
\(585\) −2.63604 16.2189i −0.108987 0.670567i
\(586\) 7.12436 0.294304
\(587\) 4.21046 2.43091i 0.173784 0.100334i −0.410585 0.911822i \(-0.634675\pi\)
0.584369 + 0.811488i \(0.301342\pi\)
\(588\) −8.90138 + 8.90138i −0.367087 + 0.367087i
\(589\) −0.267949 + 0.464102i −0.0110407 + 0.0191230i
\(590\) 10.8126 1.75736i 0.445146 0.0723493i
\(591\) 26.6603 7.14359i 1.09666 0.293848i
\(592\) −9.05369 + 5.22715i −0.372104 + 0.214834i
\(593\) 19.1427i 0.786094i 0.919518 + 0.393047i \(0.128579\pi\)
−0.919518 + 0.393047i \(0.871421\pi\)
\(594\) −0.882686 3.29423i −0.0362170 0.135164i
\(595\) 30.5885 24.9754i 1.25400 1.02389i
\(596\) 3.69615 + 6.40192i 0.151400 + 0.262233i
\(597\) 11.9193 + 44.4834i 0.487824 + 1.82058i
\(598\) 0.568406 + 0.328169i 0.0232439 + 0.0134198i
\(599\) −10.8564 + 18.8038i −0.443581 + 0.768304i −0.997952 0.0639650i \(-0.979625\pi\)
0.554371 + 0.832269i \(0.312959\pi\)
\(600\) −13.9571 + 9.22508i −0.569798 + 0.376612i
\(601\) 1.53590 + 2.66025i 0.0626506 + 0.108514i 0.895649 0.444761i \(-0.146711\pi\)
−0.832999 + 0.553275i \(0.813378\pi\)
\(602\) 1.13681i 0.0463330i
\(603\) −22.7661 −0.927108
\(604\) 14.8756 0.605281
\(605\) −19.6372 7.44709i −0.798364 0.302767i
\(606\) −2.19615 + 8.19615i −0.0892126 + 0.332946i
\(607\) −18.1631 10.4865i −0.737218 0.425633i 0.0838387 0.996479i \(-0.473282\pi\)
−0.821057 + 0.570846i \(0.806615\pi\)
\(608\) 3.25813 + 1.88108i 0.132135 + 0.0762880i
\(609\) 0.696152 2.59808i 0.0282095 0.105279i
\(610\) −2.73358 + 7.20814i −0.110679 + 0.291849i
\(611\) 7.26795 0.294030
\(612\) 27.4249 1.10858
\(613\) 9.62209i 0.388633i 0.980939 + 0.194316i \(0.0622488\pi\)
−0.980939 + 0.194316i \(0.937751\pi\)
\(614\) 0.990381 + 1.71539i 0.0399685 + 0.0692275i
\(615\) −3.00985 + 29.7945i −0.121369 + 1.20143i
\(616\) −4.09808 + 7.09808i −0.165116 + 0.285990i
\(617\) −15.5935 9.00292i −0.627771 0.362444i 0.152117 0.988362i \(-0.451391\pi\)
−0.779888 + 0.625919i \(0.784724\pi\)
\(618\) −0.152304 0.568406i −0.00612656 0.0228646i
\(619\) 15.0981 + 26.1506i 0.606843 + 1.05108i 0.991757 + 0.128130i \(0.0408976\pi\)
−0.384914 + 0.922952i \(0.625769\pi\)
\(620\) −2.19615 + 1.79315i −0.0881996 + 0.0720147i
\(621\) −0.696152 2.59808i −0.0279356 0.104257i
\(622\) 5.20359i 0.208645i
\(623\) −38.8079 + 22.4058i −1.55481 + 0.897668i
\(624\) −10.0981 + 2.70577i −0.404247 + 0.108318i
\(625\) 19.9853 15.0196i 0.799411 0.600784i
\(626\) 3.63397 6.29423i 0.145243 0.251568i
\(627\) 1.13681 1.13681i 0.0453999 0.0453999i
\(628\) 19.3557 11.1750i 0.772376 0.445931i
\(629\) 22.3923 0.892840
\(630\) −11.4685 + 1.86396i −0.456915 + 0.0742620i
\(631\) 1.32051 0.0525686 0.0262843 0.999655i \(-0.491632\pi\)
0.0262843 + 0.999655i \(0.491632\pi\)
\(632\) 12.4877 7.20977i 0.496733 0.286789i
\(633\) −18.6114 4.98691i −0.739737 0.198212i
\(634\) 1.04552 1.81089i 0.0415228 0.0719196i
\(635\) 38.3742 6.23694i 1.52283 0.247505i
\(636\) 0.803848 3.00000i 0.0318746 0.118958i
\(637\) −8.90138 + 5.13922i −0.352686 + 0.203623i
\(638\) 0.304608i 0.0120595i
\(639\) −36.8827 + 21.2942i −1.45906 + 0.842387i
\(640\) 16.1962 + 19.8362i 0.640209 + 0.784093i
\(641\) −6.52628 11.3038i −0.257773 0.446475i 0.707872 0.706340i \(-0.249655\pi\)
−0.965645 + 0.259865i \(0.916322\pi\)
\(642\) −6.53983 + 6.53983i −0.258106 + 0.258106i
\(643\) 11.2308 + 6.48408i 0.442898 + 0.255707i 0.704826 0.709380i \(-0.251025\pi\)
−0.261928 + 0.965087i \(0.584358\pi\)
\(644\) −1.50000 + 2.59808i −0.0591083 + 0.102379i
\(645\) 1.48582 2.06253i 0.0585042 0.0812122i
\(646\) −1.00000 1.73205i −0.0393445 0.0681466i
\(647\) 19.4572i 0.764942i −0.923967 0.382471i \(-0.875073\pi\)
0.923967 0.382471i \(-0.124927\pi\)
\(648\) −15.0573 8.69333i −0.591506 0.341506i
\(649\) −12.0000 −0.471041
\(650\) −6.01343 + 2.00775i −0.235866 + 0.0787505i
\(651\) −4.09808 + 1.09808i −0.160616 + 0.0430370i
\(652\) 15.6814 + 9.05369i 0.614133 + 0.354570i
\(653\) −42.0339 24.2683i −1.64491 0.949691i −0.979051 0.203615i \(-0.934731\pi\)
−0.665861 0.746076i \(-0.731936\pi\)
\(654\) 8.02628 + 8.02628i 0.313852 + 0.313852i
\(655\) 27.0299 + 10.2507i 1.05615 + 0.400527i
\(656\) 19.0526 0.743877
\(657\) 12.7279 + 22.0454i 0.496564 + 0.860073i
\(658\) 5.13922i 0.200348i
\(659\) −6.12436 10.6077i −0.238571 0.413217i 0.721733 0.692171i \(-0.243346\pi\)
−0.960304 + 0.278954i \(0.910012\pi\)
\(660\) 7.75627 3.49093i 0.301912 0.135884i
\(661\) −5.39230 + 9.33975i −0.209736 + 0.363274i −0.951631 0.307242i \(-0.900594\pi\)
0.741895 + 0.670516i \(0.233927\pi\)
\(662\) −3.76217 2.17209i −0.146221 0.0844206i
\(663\) 21.6293 + 5.79555i 0.840013 + 0.225081i
\(664\) −7.69615 13.3301i −0.298669 0.517309i
\(665\) −3.46410 4.24264i −0.134332 0.164523i
\(666\) −5.70577 3.29423i −0.221094 0.127649i
\(667\) 0.240237i 0.00930200i
\(668\) 14.9050 8.60540i 0.576691 0.332953i
\(669\) 5.49038 + 5.49038i 0.212270 + 0.212270i
\(670\) 1.40912 + 8.66996i 0.0544392 + 0.334950i
\(671\) 4.22243 7.31347i 0.163005 0.282333i
\(672\) 7.70882 + 28.7697i 0.297374 + 1.10982i
\(673\) 35.3417 20.4046i 1.36232 0.786538i 0.372391 0.928076i \(-0.378538\pi\)
0.989933 + 0.141538i \(0.0452047\pi\)
\(674\) 3.46410 0.133432
\(675\) 23.2436 + 11.6076i 0.894646 + 0.446775i
\(676\) 12.1244 0.466321
\(677\) −3.19376 + 1.84392i −0.122746 + 0.0708676i −0.560116 0.828414i \(-0.689243\pi\)
0.437370 + 0.899282i \(0.355910\pi\)
\(678\) −4.00240 14.9372i −0.153711 0.573659i
\(679\) −25.3923 + 43.9808i −0.974467 + 1.68783i
\(680\) −3.65756 22.5040i −0.140261 0.862989i
\(681\) −32.3205 32.3205i −1.23852 1.23852i
\(682\) −0.416102 + 0.240237i −0.0159334 + 0.00919914i
\(683\) 0.101536i 0.00388517i −0.999998 0.00194258i \(-0.999382\pi\)
0.999998 0.00194258i \(-0.000618344\pi\)
\(684\) 3.80385i 0.145444i
\(685\) −22.2487 27.2490i −0.850080 1.04113i
\(686\) −2.42820 4.20577i −0.0927092 0.160577i
\(687\) 10.1583 + 2.72191i 0.387564 + 0.103847i
\(688\) −1.40061 0.808643i −0.0533978 0.0308292i
\(689\) 1.26795 2.19615i 0.0483050 0.0836667i
\(690\) −0.946330 + 0.425924i −0.0360262 + 0.0162146i
\(691\) 14.1244 + 24.4641i 0.537316 + 0.930658i 0.999047 + 0.0436386i \(0.0138950\pi\)
−0.461732 + 0.887020i \(0.652772\pi\)
\(692\) 18.2832i 0.695025i
\(693\) 12.7279 0.483494
\(694\) −5.12436 −0.194518
\(695\) 16.7262 + 6.34315i 0.634459 + 0.240609i
\(696\) −1.09808 1.09808i −0.0416225 0.0416225i
\(697\) −35.3417 20.4046i −1.33866 0.772878i
\(698\) −12.7601 7.36705i −0.482977 0.278847i
\(699\) −11.8301 + 3.16987i −0.447456 + 0.119896i
\(700\) −9.17705 27.4862i −0.346860 1.03888i
\(701\) −12.8038 −0.483595 −0.241797 0.970327i \(-0.577737\pi\)
−0.241797 + 0.970327i \(0.577737\pi\)
\(702\) −4.65874 4.65874i −0.175833 0.175833i
\(703\) 3.10583i 0.117139i
\(704\) −1.43782 2.49038i −0.0541900 0.0938598i
\(705\) −6.71699 + 9.32415i −0.252977 + 0.351168i
\(706\) 5.26795 9.12436i 0.198262 0.343400i
\(707\) −27.4249 15.8338i −1.03142 0.595489i
\(708\) −20.0764 + 20.0764i −0.754517 + 0.754517i
\(709\) 4.89230 + 8.47372i 0.183734 + 0.318237i 0.943149 0.332369i \(-0.107848\pi\)
−0.759415 + 0.650607i \(0.774515\pi\)
\(710\) 10.3923 + 12.7279i 0.390016 + 0.477670i
\(711\) −19.3923 11.1962i −0.727268 0.419889i
\(712\) 25.8719i 0.969592i
\(713\) −0.328169 + 0.189469i −0.0122900 + 0.00709566i
\(714\) 4.09808 15.2942i 0.153367 0.572372i
\(715\) 6.85490 1.11412i 0.256359 0.0416658i
\(716\) −5.70577 + 9.88269i −0.213235 + 0.369333i
\(717\) −1.55291 0.416102i −0.0579946 0.0155396i
\(718\) 9.05369 5.22715i 0.337881 0.195075i
\(719\) −40.3923 −1.50638 −0.753189 0.657804i \(-0.771486\pi\)
−0.753189 + 0.657804i \(0.771486\pi\)
\(720\) 5.86131 15.4556i 0.218438 0.575997i
\(721\) 2.19615 0.0817890
\(722\) 8.27723 4.77886i 0.308047 0.177851i
\(723\) 11.9193 11.9193i 0.443283 0.443283i
\(724\) −1.33013 + 2.30385i −0.0494338 + 0.0856218i
\(725\) 1.73697 + 1.53874i 0.0645093 + 0.0571472i
\(726\) −8.13397 + 2.17949i −0.301880 + 0.0808885i
\(727\) 1.19256 0.688524i 0.0442296 0.0255360i −0.477722 0.878511i \(-0.658537\pi\)
0.521952 + 0.852975i \(0.325204\pi\)
\(728\) 15.8338i 0.586838i
\(729\) 27.0000i 1.00000i
\(730\) 7.60770 6.21166i 0.281573 0.229904i
\(731\) 1.73205 + 3.00000i 0.0640622 + 0.110959i
\(732\) −5.17140 19.2999i −0.191141 0.713346i
\(733\) −6.51626 3.76217i −0.240684 0.138959i 0.374807 0.927103i \(-0.377709\pi\)
−0.615491 + 0.788144i \(0.711042\pi\)
\(734\) −8.95448 + 15.5096i −0.330516 + 0.572470i
\(735\) 1.63343 16.1693i 0.0602501 0.596415i
\(736\) 1.33013 + 2.30385i 0.0490291 + 0.0849209i
\(737\) 9.62209i 0.354434i
\(738\) 6.00361 + 10.3986i 0.220996 + 0.382776i
\(739\) 18.1436 0.667423 0.333711 0.942675i \(-0.391699\pi\)
0.333711 + 0.942675i \(0.391699\pi\)
\(740\) 5.82655 15.3640i 0.214188 0.564790i
\(741\) 0.803848 3.00000i 0.0295301 0.110208i
\(742\) −1.55291 0.896575i −0.0570093 0.0329143i
\(743\) 28.2893 + 16.3328i 1.03783 + 0.599193i 0.919218 0.393748i \(-0.128822\pi\)
0.118613 + 0.992941i \(0.462155\pi\)
\(744\) −0.633975 + 2.36603i −0.0232426 + 0.0867427i
\(745\) −8.92330 3.38403i −0.326924 0.123981i
\(746\) −14.1051 −0.516425
\(747\) −11.9515 + 20.7005i −0.437281 + 0.757393i
\(748\) 11.5911i 0.423813i
\(749\) −17.2583 29.8923i −0.630606 1.09224i
\(750\) 2.98180 9.57026i 0.108880 0.349456i
\(751\) 12.2224 21.1699i 0.446003 0.772500i −0.552119 0.833766i \(-0.686180\pi\)
0.998121 + 0.0612659i \(0.0195138\pi\)
\(752\) 6.33178 + 3.65565i 0.230896 + 0.133308i
\(753\) −5.64325 21.0609i −0.205651 0.767502i
\(754\) −0.294229 0.509619i −0.0107152 0.0185592i
\(755\) −14.8756 + 12.1459i −0.541380 + 0.442035i
\(756\) 21.2942 21.2942i 0.774464 0.774464i
\(757\) 7.34847i 0.267085i −0.991043 0.133542i \(-0.957365\pi\)
0.991043 0.133542i \(-0.0426352\pi\)
\(758\) 8.72552 5.03768i 0.316925 0.182977i
\(759\) 1.09808 0.294229i 0.0398576 0.0106798i
\(760\) −3.12132 + 0.507306i −0.113222 + 0.0184019i
\(761\) −7.96410 + 13.7942i −0.288698 + 0.500040i −0.973499 0.228690i \(-0.926556\pi\)
0.684801 + 0.728730i \(0.259889\pi\)
\(762\) 11.0227 11.0227i 0.399310 0.399310i
\(763\) −36.6866 + 21.1810i −1.32814 + 0.766804i
\(764\) 30.5885 1.10665
\(765\) −27.4249 + 22.3923i −0.991548 + 0.809595i
\(766\) 5.51666 0.199325
\(767\) −20.0764 + 11.5911i −0.724916 + 0.418531i
\(768\) 2.32937 + 0.624153i 0.0840540 + 0.0225222i
\(769\) 20.8205 36.0622i 0.750807 1.30044i −0.196625 0.980479i \(-0.562998\pi\)
0.947432 0.319957i \(-0.103668\pi\)
\(770\) −0.787803 4.84714i −0.0283904 0.174679i
\(771\) −7.51666 + 28.0526i −0.270706 + 1.01029i
\(772\) −5.64325 + 3.25813i −0.203105 + 0.117263i
\(773\) 2.07055i 0.0744726i −0.999306 0.0372363i \(-0.988145\pi\)
0.999306 0.0372363i \(-0.0118554\pi\)
\(774\) 1.01924i 0.0366357i
\(775\) 0.732051 3.58630i 0.0262960 0.128824i
\(776\) 14.6603 + 25.3923i 0.526272 + 0.911531i
\(777\) 17.3867 17.3867i 0.623743 0.623743i
\(778\) −0.0557471 0.0321856i −0.00199863 0.00115391i
\(779\) −2.83013 + 4.90192i −0.101400 + 0.175630i
\(780\) 9.60450 13.3324i 0.343896 0.477377i
\(781\) −9.00000 15.5885i −0.322045 0.557799i
\(782\) 1.41421i 0.0505722i
\(783\) −0.624153 + 2.32937i −0.0223054 + 0.0832449i
\(784\) −10.3397 −0.369277
\(785\) −10.2313 + 26.9789i −0.365172 + 0.962917i
\(786\) 11.1962 3.00000i 0.399354 0.107006i
\(787\) 22.6138 + 13.0561i 0.806095 + 0.465399i 0.845598 0.533820i \(-0.179244\pi\)
−0.0395027 + 0.999219i \(0.512577\pi\)
\(788\) 23.9029 + 13.8004i 0.851507 + 0.491618i
\(789\) 26.6603 + 26.6603i 0.949130 + 0.949130i
\(790\) −3.06350 + 8.07812i −0.108995 + 0.287406i
\(791\) 57.7128 2.05203
\(792\) 3.67423 6.36396i 0.130558 0.226134i
\(793\) 16.3142i 0.579335i
\(794\) 7.60770 + 13.1769i 0.269987 + 0.467631i
\(795\) 1.64564 + 3.65634i 0.0583649 + 0.129677i
\(796\) −23.0263 + 39.8827i −0.816145 + 1.41360i
\(797\) 45.6202 + 26.3388i 1.61595 + 0.932969i 0.987953 + 0.154752i \(0.0494579\pi\)
0.627996 + 0.778217i \(0.283875\pi\)
\(798\) −2.12132 0.568406i −0.0750939 0.0201214i
\(799\) −7.83013 13.5622i −0.277010 0.479795i
\(800\) −25.1769 5.13922i −0.890138 0.181699i
\(801\) 34.7942 20.0885i 1.22939 0.709791i
\(802\) 8.83701i 0.312046i
\(803\) −9.31749 + 5.37945i −0.328807 + 0.189837i
\(804\) −16.0981 16.0981i −0.567735 0.567735i
\(805\) −0.621320 3.82282i −0.0218987 0.134737i
\(806\) −0.464102 + 0.803848i −0.0163473 + 0.0283143i
\(807\) −3.05008 11.3831i −0.107368 0.400703i
\(808\) −15.8338 + 9.14162i −0.557029 + 0.321601i
\(809\) 25.1769 0.885173 0.442587 0.896726i \(-0.354061\pi\)
0.442587 + 0.896726i \(0.354061\pi\)
\(810\) 10.2823 1.67118i 0.361285 0.0587193i
\(811\) −39.5692 −1.38946 −0.694732 0.719269i \(-0.744477\pi\)
−0.694732 + 0.719269i \(0.744477\pi\)
\(812\) 2.32937 1.34486i 0.0817449 0.0471954i
\(813\) 9.64566 + 35.9981i 0.338288 + 1.26251i
\(814\) 1.39230 2.41154i 0.0488003 0.0845245i
\(815\) −23.0738 + 3.75016i −0.808238 + 0.131362i
\(816\) 15.9282 + 15.9282i 0.557599 + 0.557599i
\(817\) 0.416102 0.240237i 0.0145576 0.00840482i
\(818\) 8.55961i 0.299280i
\(819\) 21.2942 12.2942i 0.744081 0.429595i
\(820\) −23.1962 + 18.9396i −0.810045 + 0.661399i
\(821\) −14.7224 25.5000i −0.513816 0.889956i −0.999872 0.0160280i \(-0.994898\pi\)
0.486055 0.873928i \(-0.338435\pi\)
\(822\) −13.6245 3.65067i −0.475209 0.127332i
\(823\) 16.6102 + 9.58991i 0.578995 + 0.334283i 0.760734 0.649064i \(-0.224839\pi\)
−0.181739 + 0.983347i \(0.558172\pi\)
\(824\) 0.633975 1.09808i 0.0220856 0.0382533i
\(825\) −4.90593 + 9.82390i −0.170803 + 0.342024i
\(826\) 8.19615 + 14.1962i 0.285181 + 0.493947i
\(827\) 23.8014i 0.827656i 0.910355 + 0.413828i \(0.135808\pi\)
−0.910355 + 0.413828i \(0.864192\pi\)
\(828\) 1.34486 2.32937i 0.0467372 0.0809513i
\(829\) −0.411543 −0.0142935 −0.00714673 0.999974i \(-0.502275\pi\)
−0.00714673 + 0.999974i \(0.502275\pi\)
\(830\) 8.62308 + 3.27017i 0.299311 + 0.113509i
\(831\) 15.0000 + 15.0000i 0.520344 + 0.520344i
\(832\) −4.81105 2.77766i −0.166793 0.0962980i
\(833\) 19.1798 + 11.0735i 0.664541 + 0.383673i
\(834\) 6.92820 1.85641i 0.239904 0.0642821i
\(835\) −7.87871 + 20.7753i −0.272654 + 0.718958i
\(836\) 1.60770 0.0556033
\(837\) 3.67423 0.984508i 0.127000 0.0340296i
\(838\) 11.4152i 0.394333i
\(839\) 2.36603 + 4.09808i 0.0816843 + 0.141481i 0.903974 0.427588i \(-0.140637\pi\)
−0.822289 + 0.569070i \(0.807303\pi\)
\(840\) −20.3133 14.6335i −0.700876 0.504902i
\(841\) 14.3923 24.9282i 0.496286 0.859593i
\(842\) −8.72552 5.03768i −0.300701 0.173610i
\(843\) −24.1667 + 24.1667i −0.832346 + 0.832346i
\(844\) −9.63397 16.6865i −0.331615 0.574374i
\(845\) −12.1244 + 9.89949i −0.417091 + 0.340553i
\(846\) 4.60770i 0.158416i
\(847\) 31.4273i 1.07985i
\(848\) 2.20925 1.27551i 0.0758661 0.0438013i
\(849\) 7.50000 27.9904i 0.257399 0.960627i
\(850\) 10.2251 + 9.05816i 0.350718 + 0.310692i
\(851\) 1.09808 1.90192i 0.0376416 0.0651971i
\(852\) −41.1373 11.0227i −1.40934 0.377632i
\(853\) −37.6154 + 21.7172i −1.28793 + 0.743584i −0.978284 0.207269i \(-0.933542\pi\)
−0.309641 + 0.950853i \(0.600209\pi\)
\(854\) −11.5359 −0.394750
\(855\) 3.10583 + 3.80385i 0.106217 + 0.130089i
\(856\) −19.9282 −0.681132
\(857\) 11.9193 6.88160i 0.407155 0.235071i −0.282412 0.959293i \(-0.591134\pi\)
0.689567 + 0.724222i \(0.257801\pi\)
\(858\) 1.96902 1.96902i 0.0672211 0.0672211i
\(859\) 18.2224 31.5622i 0.621741 1.07689i −0.367420 0.930055i \(-0.619759\pi\)
0.989161 0.146832i \(-0.0469078\pi\)
\(860\) 2.50907 0.407797i 0.0855584 0.0139058i
\(861\) −43.2846 + 11.5981i −1.47514 + 0.395261i
\(862\) 2.68973 1.55291i 0.0916124 0.0528925i
\(863\) 44.9131i 1.52886i −0.644708 0.764429i \(-0.723021\pi\)
0.644708 0.764429i \(-0.276979\pi\)
\(864\) −6.91154 25.7942i −0.235135 0.877537i
\(865\) 14.9282 + 18.2832i 0.507574 + 0.621649i
\(866\) −3.50962 6.07884i −0.119262 0.206567i
\(867\) −4.86679 18.1631i −0.165285 0.616852i
\(868\) −3.67423 2.12132i −0.124712 0.0720023i
\(869\) 4.73205 8.19615i 0.160524 0.278035i
\(870\) 0.925721 + 0.0935168i 0.0313849 + 0.00317052i
\(871\) −9.29423 16.0981i −0.314923 0.545463i
\(872\) 24.4577i 0.828243i
\(873\) 22.7661 39.4321i 0.770516 1.33457i
\(874\) −0.196152 −0.00663495
\(875\) 31.6195 + 19.9932i 1.06893 + 0.675894i
\(876\) −6.58846 + 24.5885i −0.222603 + 0.830767i
\(877\) 25.3035 + 14.6090i 0.854440 + 0.493311i 0.862146 0.506659i \(-0.169120\pi\)
−0.00770656 + 0.999970i \(0.502453\pi\)
\(878\) 11.3509 + 6.55343i 0.383073 + 0.221168i
\(879\) 6.16987 23.0263i 0.208105 0.776657i
\(880\) 6.53231 + 2.47728i 0.220204 + 0.0835091i
\(881\) −39.5885 −1.33377 −0.666885 0.745161i \(-0.732373\pi\)
−0.666885 + 0.745161i \(0.732373\pi\)
\(882\) −3.25813 5.64325i −0.109707 0.190018i
\(883\) 54.4336i 1.83184i −0.401364 0.915919i \(-0.631464\pi\)
0.401364 0.915919i \(-0.368536\pi\)
\(884\) 11.1962 + 19.3923i 0.376567 + 0.652234i
\(885\) 3.68409 36.4687i 0.123839 1.22588i
\(886\) 0.428203 0.741670i 0.0143858 0.0249169i
\(887\) 7.43640 + 4.29341i 0.249690 + 0.144159i 0.619622 0.784900i \(-0.287286\pi\)
−0.369932 + 0.929059i \(0.620619\pi\)
\(888\) −3.67423 13.7124i −0.123299 0.460159i
\(889\) 29.0885 + 50.3827i 0.975596 + 1.68978i
\(890\) −9.80385 12.0072i −0.328626 0.402483i
\(891\) −11.4115 −0.382301
\(892\) 7.76457i 0.259977i
\(893\) −1.88108 + 1.08604i −0.0629481 + 0.0363431i
\(894\) −3.69615 + 0.990381i −0.123618 + 0.0331233i
\(895\) −2.36341 14.5414i −0.0790000 0.486066i
\(896\) −19.1603 + 33.1865i −0.640099 + 1.10868i
\(897\) 1.55291 1.55291i 0.0518503 0.0518503i
\(898\) −5.37945 + 3.10583i −0.179515 + 0.103643i
\(899\) 0.339746 0.0113312
\(900\) 8.22792 + 24.6435i 0.274264 + 0.821449i
\(901\) −5.46410 −0.182036
\(902\) −4.39494 + 2.53742i −0.146336 + 0.0844869i
\(903\) 3.67423 + 0.984508i 0.122271 + 0.0327624i
\(904\) 16.6603 28.8564i 0.554112 0.959750i
\(905\) −0.550957 3.38989i −0.0183144 0.112684i
\(906\) −1.99296 + 7.43782i −0.0662116 + 0.247105i
\(907\) 9.98245 5.76337i 0.331462 0.191370i −0.325028 0.945704i \(-0.605374\pi\)
0.656490 + 0.754335i \(0.272040\pi\)
\(908\) 45.7081i 1.51688i
\(909\) 24.5885 + 14.1962i 0.815548 + 0.470857i
\(910\) −6.00000 7.34847i −0.198898 0.243599i
\(911\) −24.9282 43.1769i −0.825908 1.43051i −0.901223 0.433355i \(-0.857330\pi\)
0.0753150 0.997160i \(-0.476004\pi\)
\(912\) 2.20925 2.20925i 0.0731557 0.0731557i
\(913\) −8.74908 5.05128i −0.289552 0.167173i
\(914\) 6.41858 11.1173i 0.212308 0.367728i
\(915\) 20.9297 + 15.0775i 0.691916 + 0.498447i
\(916\) 5.25833 + 9.10770i 0.173740 + 0.300927i
\(917\) 43.2586i 1.42853i
\(918\) −3.67423 + 13.7124i −0.121268 + 0.452578i
\(919\) −47.1769 −1.55622 −0.778111 0.628126i \(-0.783822\pi\)
−0.778111 + 0.628126i \(0.783822\pi\)
\(920\) −2.09077 0.792893i −0.0689307 0.0261409i
\(921\) 6.40192 1.71539i 0.210951 0.0565240i
\(922\) −16.4579 9.50198i −0.542012 0.312931i
\(923\) −30.1146 17.3867i −0.991234 0.572289i
\(924\) 9.00000 + 9.00000i 0.296078 + 0.296078i
\(925\) 6.71807 + 20.1213i 0.220889 + 0.661585i
\(926\) 17.6603 0.580352
\(927\) −1.96902 −0.0646710
\(928\) 2.38512i 0.0782954i
\(929\) −1.73205 3.00000i −0.0568267 0.0984268i 0.836213 0.548405i \(-0.184765\pi\)
−0.893039 + 0.449979i \(0.851432\pi\)
\(930\) −0.602347 1.33831i −0.0197517 0.0438850i
\(931\) 1.53590 2.66025i 0.0503370 0.0871863i
\(932\) −10.6066 6.12372i −0.347431 0.200589i
\(933\) 16.8183 + 4.50644i 0.550605 + 0.147534i
\(934\) −6.56218 11.3660i −0.214721 0.371908i
\(935\) −9.46410 11.5911i −0.309509 0.379070i
\(936\) 14.1962i 0.464016i
\(937\) 28.5617i 0.933069i −0.884503 0.466535i \(-0.845502\pi\)
0.884503 0.466535i \(-0.154498\pi\)
\(938\) −11.3831 + 6.57201i −0.371670 + 0.214584i
\(939\) −17.1962 17.1962i −0.561175 0.561175i
\(940\) −11.3428 + 1.84354i −0.369961 + 0.0601295i
\(941\) −13.1603 + 22.7942i −0.429012 + 0.743071i −0.996786 0.0801141i \(-0.974472\pi\)
0.567774 + 0.823185i \(0.307805\pi\)
\(942\) 2.99433 + 11.1750i 0.0975607 + 0.364101i
\(943\) −3.46618 + 2.00120i −0.112874 + 0.0651681i
\(944\) −23.3205 −0.759018
\(945\) −3.90756 + 38.6809i −0.127113 + 1.25829i
\(946\) 0.430781 0.0140059
\(947\) −4.12252 + 2.38014i −0.133964 + 0.0773441i −0.565484 0.824759i \(-0.691311\pi\)
0.431520 + 0.902103i \(0.357977\pi\)
\(948\) −5.79555 21.6293i −0.188231 0.702487i
\(949\) −10.3923 + 18.0000i −0.337348 + 0.584305i
\(950\) 1.25637 1.41823i 0.0407621 0.0460133i
\(951\) −4.94744 4.94744i −0.160432 0.160432i
\(952\) 29.5462 17.0585i 0.957597 0.552869i
\(953\) 51.1619i 1.65730i 0.559770 + 0.828648i \(0.310889\pi\)
−0.559770 + 0.828648i \(0.689111\pi\)
\(954\) 1.39230 + 0.803848i 0.0450775 + 0.0260255i
\(955\) −30.5885 + 24.9754i −0.989819 + 0.808184i
\(956\) −0.803848 1.39230i −0.0259983 0.0450304i
\(957\) −0.984508 0.263798i −0.0318246 0.00852738i
\(958\) −1.85752 1.07244i −0.0600138 0.0346490i
\(959\) 26.3205 45.5885i 0.849934 1.47213i
\(960\) 8.00983 3.60506i 0.258516 0.116353i
\(961\) 15.2321 + 26.3827i 0.491356 + 0.851054i
\(962\) 5.37945i 0.173441i
\(963\) 15.4734 + 26.8007i 0.498623 + 0.863641i
\(964\) 16.8564 0.542908
\(965\) 2.98300 7.86583i 0.0960261 0.253210i
\(966\) −1.09808 1.09808i −0.0353300 0.0353300i
\(967\) 48.4300 + 27.9611i 1.55740 + 0.899168i 0.997504 + 0.0706076i \(0.0224938\pi\)
0.559900 + 0.828560i \(0.310840\pi\)
\(968\) −15.7136 9.07227i −0.505055 0.291594i
\(969\) −6.46410 + 1.73205i −0.207657 + 0.0556415i
\(970\) −16.4259 6.22929i −0.527405 0.200010i
\(971\) 38.1962 1.22577 0.612886 0.790171i \(-0.290008\pi\)
0.612886 + 0.790171i \(0.290008\pi\)
\(972\) −19.0919 + 19.0919i −0.612372 + 0.612372i
\(973\) 26.7685i 0.858159i
\(974\) −4.09808 7.09808i −0.131311 0.227437i
\(975\) 1.28138 + 21.1745i 0.0410369 + 0.678126i
\(976\) 8.20577 14.2128i 0.262660 0.454941i
\(977\) −13.4722 7.77817i −0.431014 0.248846i 0.268765 0.963206i \(-0.413385\pi\)
−0.699778 + 0.714360i \(0.746718\pi\)
\(978\) −6.62776 + 6.62776i −0.211932 + 0.211932i
\(979\) 8.49038 + 14.7058i 0.271354 + 0.469998i
\(980\) 12.5885 10.2784i 0.402124 0.328332i
\(981\) 32.8923 18.9904i 1.05017 0.606316i
\(982\) 17.4510i 0.556885i
\(983\) 28.9456 16.7117i 0.923221 0.533022i 0.0385597 0.999256i \(-0.487723\pi\)
0.884661 + 0.466234i \(0.154390\pi\)
\(984\) −6.69615 + 24.9904i −0.213466 + 0.796664i
\(985\) −35.1709 + 5.71630i −1.12064 + 0.182136i
\(986\) −0.633975 + 1.09808i −0.0201899 + 0.0349699i
\(987\) −16.6102 4.45069i −0.528709 0.141667i
\(988\) 2.68973 1.55291i 0.0855716 0.0494048i
\(989\) 0.339746 0.0108033
\(990\) 0.706325 + 4.34583i 0.0224485 + 0.138120i
\(991\) 38.9282 1.23660 0.618298 0.785944i \(-0.287823\pi\)
0.618298 + 0.785944i \(0.287823\pi\)
\(992\) −3.25813 + 1.88108i −0.103446 + 0.0597245i
\(993\) −10.2784 + 10.2784i −0.326176 + 0.326176i
\(994\) −12.2942 + 21.2942i −0.389949 + 0.675412i
\(995\) −9.53780 58.6836i −0.302368 1.86039i
\(996\) −23.0885 + 6.18653i −0.731586 + 0.196028i
\(997\) 8.90138 5.13922i 0.281910 0.162761i −0.352378 0.935858i \(-0.614627\pi\)
0.634288 + 0.773097i \(0.281294\pi\)
\(998\) 12.3490i 0.390900i
\(999\) −15.5885 + 15.5885i −0.493197 + 0.493197i
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 45.2.j.a.4.2 8
3.2 odd 2 135.2.j.a.64.3 8
4.3 odd 2 720.2.by.d.49.2 8
5.2 odd 4 225.2.e.d.76.2 8
5.3 odd 4 225.2.e.d.76.3 8
5.4 even 2 inner 45.2.j.a.4.3 yes 8
9.2 odd 6 135.2.j.a.19.2 8
9.4 even 3 405.2.b.d.244.2 4
9.5 odd 6 405.2.b.c.244.3 4
9.7 even 3 inner 45.2.j.a.34.3 yes 8
12.11 even 2 2160.2.by.c.1009.3 8
15.2 even 4 675.2.e.d.226.3 8
15.8 even 4 675.2.e.d.226.2 8
15.14 odd 2 135.2.j.a.64.2 8
20.19 odd 2 720.2.by.d.49.3 8
36.7 odd 6 720.2.by.d.529.3 8
36.11 even 6 2160.2.by.c.289.1 8
45.2 even 12 675.2.e.d.451.3 8
45.4 even 6 405.2.b.d.244.3 4
45.7 odd 12 225.2.e.d.151.2 8
45.13 odd 12 2025.2.a.t.1.2 4
45.14 odd 6 405.2.b.c.244.2 4
45.22 odd 12 2025.2.a.t.1.3 4
45.23 even 12 2025.2.a.r.1.3 4
45.29 odd 6 135.2.j.a.19.3 8
45.32 even 12 2025.2.a.r.1.2 4
45.34 even 6 inner 45.2.j.a.34.2 yes 8
45.38 even 12 675.2.e.d.451.2 8
45.43 odd 12 225.2.e.d.151.3 8
60.59 even 2 2160.2.by.c.1009.1 8
180.79 odd 6 720.2.by.d.529.2 8
180.119 even 6 2160.2.by.c.289.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.2.j.a.4.2 8 1.1 even 1 trivial
45.2.j.a.4.3 yes 8 5.4 even 2 inner
45.2.j.a.34.2 yes 8 45.34 even 6 inner
45.2.j.a.34.3 yes 8 9.7 even 3 inner
135.2.j.a.19.2 8 9.2 odd 6
135.2.j.a.19.3 8 45.29 odd 6
135.2.j.a.64.2 8 15.14 odd 2
135.2.j.a.64.3 8 3.2 odd 2
225.2.e.d.76.2 8 5.2 odd 4
225.2.e.d.76.3 8 5.3 odd 4
225.2.e.d.151.2 8 45.7 odd 12
225.2.e.d.151.3 8 45.43 odd 12
405.2.b.c.244.2 4 45.14 odd 6
405.2.b.c.244.3 4 9.5 odd 6
405.2.b.d.244.2 4 9.4 even 3
405.2.b.d.244.3 4 45.4 even 6
675.2.e.d.226.2 8 15.8 even 4
675.2.e.d.226.3 8 15.2 even 4
675.2.e.d.451.2 8 45.38 even 12
675.2.e.d.451.3 8 45.2 even 12
720.2.by.d.49.2 8 4.3 odd 2
720.2.by.d.49.3 8 20.19 odd 2
720.2.by.d.529.2 8 180.79 odd 6
720.2.by.d.529.3 8 36.7 odd 6
2025.2.a.r.1.2 4 45.32 even 12
2025.2.a.r.1.3 4 45.23 even 12
2025.2.a.t.1.2 4 45.13 odd 12
2025.2.a.t.1.3 4 45.22 odd 12
2160.2.by.c.289.1 8 36.11 even 6
2160.2.by.c.289.3 8 180.119 even 6
2160.2.by.c.1009.1 8 60.59 even 2
2160.2.by.c.1009.3 8 12.11 even 2