Properties

Label 45.2.j.a.4.1
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 4.1
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 45.4
Dual form 45.2.j.a.34.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.67303 + 0.965926i) q^{2} +(1.67303 - 0.448288i) q^{3} +(0.866025 - 1.50000i) q^{4} +(0.358719 + 2.20711i) q^{5} +(-2.36603 + 2.36603i) q^{6} +(-0.776457 + 0.448288i) q^{7} -0.517638i q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(-1.67303 + 0.965926i) q^{2} +(1.67303 - 0.448288i) q^{3} +(0.866025 - 1.50000i) q^{4} +(0.358719 + 2.20711i) q^{5} +(-2.36603 + 2.36603i) q^{6} +(-0.776457 + 0.448288i) q^{7} -0.517638i q^{8} +(2.59808 - 1.50000i) q^{9} +(-2.73205 - 3.34607i) q^{10} +(-2.36603 - 4.09808i) q^{11} +(0.776457 - 2.89778i) q^{12} +(-2.12132 - 1.22474i) q^{13} +(0.866025 - 1.50000i) q^{14} +(1.58957 + 3.53175i) q^{15} +(2.23205 + 3.86603i) q^{16} -0.378937i q^{17} +(-2.89778 + 5.01910i) q^{18} -2.73205 q^{19} +(3.62132 + 1.37333i) q^{20} +(-1.09808 + 1.09808i) q^{21} +(7.91688 + 4.57081i) q^{22} +(1.67303 + 0.965926i) q^{23} +(-0.232051 - 0.866025i) q^{24} +(-4.74264 + 1.58346i) q^{25} +4.73205 q^{26} +(3.67423 - 3.67423i) q^{27} +1.55291i q^{28} +(3.23205 + 5.59808i) q^{29} +(-6.07081 - 4.37333i) q^{30} +(1.36603 - 2.36603i) q^{31} +(-6.57201 - 3.79435i) q^{32} +(-5.79555 - 5.79555i) q^{33} +(0.366025 + 0.633975i) q^{34} +(-1.26795 - 1.55291i) q^{35} -5.19615i q^{36} +4.24264i q^{37} +(4.57081 - 2.63896i) q^{38} +(-4.09808 - 1.09808i) q^{39} +(1.14248 - 0.185687i) q^{40} +(-2.13397 + 3.69615i) q^{41} +(0.776457 - 2.89778i) q^{42} +(7.91688 - 4.57081i) q^{43} -8.19615 q^{44} +(4.24264 + 5.19615i) q^{45} -3.73205 q^{46} +(-3.79435 + 2.19067i) q^{47} +(5.46739 + 5.46739i) q^{48} +(-3.09808 + 5.36603i) q^{49} +(6.40508 - 7.23023i) q^{50} +(-0.169873 - 0.633975i) q^{51} +(-3.67423 + 2.12132i) q^{52} +3.86370i q^{53} +(-2.59808 + 9.69615i) q^{54} +(8.19615 - 6.69213i) q^{55} +(0.232051 + 0.401924i) q^{56} +(-4.57081 + 1.22474i) q^{57} +(-10.8147 - 6.24384i) q^{58} +(1.26795 - 2.19615i) q^{59} +(6.67423 + 0.674235i) q^{60} +(-5.33013 - 9.23205i) q^{61} +5.27792i q^{62} +(-1.34486 + 2.32937i) q^{63} +5.73205 q^{64} +(1.94218 - 5.12132i) q^{65} +(15.2942 + 4.09808i) q^{66} +(-4.45069 - 2.56961i) q^{67} +(-0.568406 - 0.328169i) q^{68} +(3.23205 + 0.866025i) q^{69} +(3.62132 + 1.37333i) q^{70} +3.80385 q^{71} +(-0.776457 - 1.34486i) q^{72} +8.48528i q^{73} +(-4.09808 - 7.09808i) q^{74} +(-7.22474 + 4.77526i) q^{75} +(-2.36603 + 4.09808i) q^{76} +(3.67423 + 2.12132i) q^{77} +(7.91688 - 2.12132i) q^{78} +(0.267949 + 0.464102i) q^{79} +(-7.73205 + 6.31319i) q^{80} +(4.50000 - 7.79423i) q^{81} -8.24504i q^{82} +(-9.02150 + 5.20857i) q^{83} +(0.696152 + 2.59808i) q^{84} +(0.836355 - 0.135932i) q^{85} +(-8.83013 + 15.2942i) q^{86} +(7.91688 + 7.91688i) q^{87} +(-2.12132 + 1.22474i) q^{88} +7.39230 q^{89} +(-12.1172 - 4.59526i) q^{90} +2.19615 q^{91} +(2.89778 - 1.67303i) q^{92} +(1.22474 - 4.57081i) q^{93} +(4.23205 - 7.33013i) q^{94} +(-0.980040 - 6.02993i) q^{95} +(-12.6962 - 3.40192i) q^{96} +(8.90138 - 5.13922i) q^{97} -11.9700i q^{98} +(-12.2942 - 7.09808i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.67303 + 0.965926i −1.18301 + 0.683013i −0.956710 0.291044i \(-0.905997\pi\)
−0.226303 + 0.974057i \(0.572664\pi\)
\(3\) 1.67303 0.448288i 0.965926 0.258819i
\(4\) 0.866025 1.50000i 0.433013 0.750000i
\(5\) 0.358719 + 2.20711i 0.160424 + 0.987048i
\(6\) −2.36603 + 2.36603i −0.965926 + 0.965926i
\(7\) −0.776457 + 0.448288i −0.293473 + 0.169437i −0.639507 0.768785i \(-0.720862\pi\)
0.346034 + 0.938222i \(0.387528\pi\)
\(8\) 0.517638i 0.183013i
\(9\) 2.59808 1.50000i 0.866025 0.500000i
\(10\) −2.73205 3.34607i −0.863950 1.05812i
\(11\) −2.36603 4.09808i −0.713384 1.23562i −0.963580 0.267421i \(-0.913828\pi\)
0.250196 0.968195i \(-0.419505\pi\)
\(12\) 0.776457 2.89778i 0.224144 0.836516i
\(13\) −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
\(15\) 1.58957 + 3.53175i 0.410425 + 0.911894i
\(16\) 2.23205 + 3.86603i 0.558013 + 0.966506i
\(17\) 0.378937i 0.0919058i −0.998944 0.0459529i \(-0.985368\pi\)
0.998944 0.0459529i \(-0.0146324\pi\)
\(18\) −2.89778 + 5.01910i −0.683013 + 1.18301i
\(19\) −2.73205 −0.626775 −0.313388 0.949625i \(-0.601464\pi\)
−0.313388 + 0.949625i \(0.601464\pi\)
\(20\) 3.62132 + 1.37333i 0.809752 + 0.307086i
\(21\) −1.09808 + 1.09808i −0.239620 + 0.239620i
\(22\) 7.91688 + 4.57081i 1.68788 + 0.974500i
\(23\) 1.67303 + 0.965926i 0.348851 + 0.201409i 0.664179 0.747573i \(-0.268781\pi\)
−0.315328 + 0.948983i \(0.602114\pi\)
\(24\) −0.232051 0.866025i −0.0473672 0.176777i
\(25\) −4.74264 + 1.58346i −0.948528 + 0.316693i
\(26\) 4.73205 0.928032
\(27\) 3.67423 3.67423i 0.707107 0.707107i
\(28\) 1.55291i 0.293473i
\(29\) 3.23205 + 5.59808i 0.600177 + 1.03954i 0.992794 + 0.119835i \(0.0382364\pi\)
−0.392617 + 0.919702i \(0.628430\pi\)
\(30\) −6.07081 4.37333i −1.10837 0.798457i
\(31\) 1.36603 2.36603i 0.245345 0.424951i −0.716883 0.697193i \(-0.754432\pi\)
0.962229 + 0.272243i \(0.0877653\pi\)
\(32\) −6.57201 3.79435i −1.16178 0.670753i
\(33\) −5.79555 5.79555i −1.00888 1.00888i
\(34\) 0.366025 + 0.633975i 0.0627728 + 0.108726i
\(35\) −1.26795 1.55291i −0.214323 0.262490i
\(36\) 5.19615i 0.866025i
\(37\) 4.24264i 0.697486i 0.937218 + 0.348743i \(0.113391\pi\)
−0.937218 + 0.348743i \(0.886609\pi\)
\(38\) 4.57081 2.63896i 0.741483 0.428096i
\(39\) −4.09808 1.09808i −0.656217 0.175833i
\(40\) 1.14248 0.185687i 0.180642 0.0293597i
\(41\) −2.13397 + 3.69615i −0.333271 + 0.577242i −0.983151 0.182795i \(-0.941486\pi\)
0.649880 + 0.760037i \(0.274819\pi\)
\(42\) 0.776457 2.89778i 0.119810 0.447137i
\(43\) 7.91688 4.57081i 1.20731 0.697042i 0.245141 0.969487i \(-0.421166\pi\)
0.962171 + 0.272445i \(0.0878324\pi\)
\(44\) −8.19615 −1.23562
\(45\) 4.24264 + 5.19615i 0.632456 + 0.774597i
\(46\) −3.73205 −0.550261
\(47\) −3.79435 + 2.19067i −0.553463 + 0.319542i −0.750518 0.660850i \(-0.770196\pi\)
0.197054 + 0.980393i \(0.436862\pi\)
\(48\) 5.46739 + 5.46739i 0.789149 + 0.789149i
\(49\) −3.09808 + 5.36603i −0.442582 + 0.766575i
\(50\) 6.40508 7.23023i 0.905816 1.02251i
\(51\) −0.169873 0.633975i −0.0237870 0.0887742i
\(52\) −3.67423 + 2.12132i −0.509525 + 0.294174i
\(53\) 3.86370i 0.530720i 0.964149 + 0.265360i \(0.0854909\pi\)
−0.964149 + 0.265360i \(0.914509\pi\)
\(54\) −2.59808 + 9.69615i −0.353553 + 1.31948i
\(55\) 8.19615 6.69213i 1.10517 0.902367i
\(56\) 0.232051 + 0.401924i 0.0310091 + 0.0537093i
\(57\) −4.57081 + 1.22474i −0.605419 + 0.162221i
\(58\) −10.8147 6.24384i −1.42003 0.819857i
\(59\) 1.26795 2.19615i 0.165073 0.285915i −0.771608 0.636098i \(-0.780547\pi\)
0.936681 + 0.350183i \(0.113881\pi\)
\(60\) 6.67423 + 0.674235i 0.861640 + 0.0870433i
\(61\) −5.33013 9.23205i −0.682453 1.18204i −0.974230 0.225557i \(-0.927580\pi\)
0.291777 0.956486i \(-0.405753\pi\)
\(62\) 5.27792i 0.670296i
\(63\) −1.34486 + 2.32937i −0.169437 + 0.293473i
\(64\) 5.73205 0.716506
\(65\) 1.94218 5.12132i 0.240898 0.635222i
\(66\) 15.2942 + 4.09808i 1.88259 + 0.504438i
\(67\) −4.45069 2.56961i −0.543739 0.313928i 0.202854 0.979209i \(-0.434978\pi\)
−0.746593 + 0.665281i \(0.768312\pi\)
\(68\) −0.568406 0.328169i −0.0689294 0.0397964i
\(69\) 3.23205 + 0.866025i 0.389093 + 0.104257i
\(70\) 3.62132 + 1.37333i 0.432831 + 0.164144i
\(71\) 3.80385 0.451434 0.225717 0.974193i \(-0.427528\pi\)
0.225717 + 0.974193i \(0.427528\pi\)
\(72\) −0.776457 1.34486i −0.0915064 0.158494i
\(73\) 8.48528i 0.993127i 0.868000 + 0.496564i \(0.165405\pi\)
−0.868000 + 0.496564i \(0.834595\pi\)
\(74\) −4.09808 7.09808i −0.476392 0.825135i
\(75\) −7.22474 + 4.77526i −0.834242 + 0.551399i
\(76\) −2.36603 + 4.09808i −0.271402 + 0.470082i
\(77\) 3.67423 + 2.12132i 0.418718 + 0.241747i
\(78\) 7.91688 2.12132i 0.896410 0.240192i
\(79\) 0.267949 + 0.464102i 0.0301466 + 0.0522155i 0.880705 0.473665i \(-0.157069\pi\)
−0.850558 + 0.525880i \(0.823736\pi\)
\(80\) −7.73205 + 6.31319i −0.864470 + 0.705836i
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) 8.24504i 0.910513i
\(83\) −9.02150 + 5.20857i −0.990238 + 0.571714i −0.905346 0.424676i \(-0.860388\pi\)
−0.0848929 + 0.996390i \(0.527055\pi\)
\(84\) 0.696152 + 2.59808i 0.0759565 + 0.283473i
\(85\) 0.836355 0.135932i 0.0907155 0.0147439i
\(86\) −8.83013 + 15.2942i −0.952177 + 1.64922i
\(87\) 7.91688 + 7.91688i 0.848778 + 0.848778i
\(88\) −2.12132 + 1.22474i −0.226134 + 0.130558i
\(89\) 7.39230 0.783583 0.391791 0.920054i \(-0.371856\pi\)
0.391791 + 0.920054i \(0.371856\pi\)
\(90\) −12.1172 4.59526i −1.27726 0.484383i
\(91\) 2.19615 0.230219
\(92\) 2.89778 1.67303i 0.302114 0.174426i
\(93\) 1.22474 4.57081i 0.127000 0.473971i
\(94\) 4.23205 7.33013i 0.436503 0.756045i
\(95\) −0.980040 6.02993i −0.100550 0.618658i
\(96\) −12.6962 3.40192i −1.29580 0.347207i
\(97\) 8.90138 5.13922i 0.903799 0.521808i 0.0253679 0.999678i \(-0.491924\pi\)
0.878431 + 0.477870i \(0.158591\pi\)
\(98\) 11.9700i 1.20916i
\(99\) −12.2942 7.09808i −1.23562 0.713384i
\(100\) −1.73205 + 8.48528i −0.173205 + 0.848528i
\(101\) −1.26795 2.19615i −0.126166 0.218525i 0.796022 0.605267i \(-0.206934\pi\)
−0.922188 + 0.386742i \(0.873600\pi\)
\(102\) 0.896575 + 0.896575i 0.0887742 + 0.0887742i
\(103\) 7.91688 + 4.57081i 0.780073 + 0.450375i 0.836456 0.548034i \(-0.184624\pi\)
−0.0563832 + 0.998409i \(0.517957\pi\)
\(104\) −0.633975 + 1.09808i −0.0621663 + 0.107675i
\(105\) −2.81747 2.02967i −0.274957 0.198076i
\(106\) −3.73205 6.46410i −0.362489 0.627849i
\(107\) 11.7298i 1.13396i −0.823730 0.566982i \(-0.808111\pi\)
0.823730 0.566982i \(-0.191889\pi\)
\(108\) −2.32937 8.69333i −0.224144 0.836516i
\(109\) 4.66025 0.446371 0.223186 0.974776i \(-0.428354\pi\)
0.223186 + 0.974776i \(0.428354\pi\)
\(110\) −7.24833 + 19.1130i −0.691101 + 1.82236i
\(111\) 1.90192 + 7.09808i 0.180523 + 0.673720i
\(112\) −3.46618 2.00120i −0.327524 0.189096i
\(113\) −2.20925 1.27551i −0.207829 0.119990i 0.392473 0.919764i \(-0.371620\pi\)
−0.600302 + 0.799773i \(0.704953\pi\)
\(114\) 6.46410 6.46410i 0.605419 0.605419i
\(115\) −1.53175 + 4.03906i −0.142837 + 0.376644i
\(116\) 11.1962 1.03954
\(117\) −7.34847 −0.679366
\(118\) 4.89898i 0.450988i
\(119\) 0.169873 + 0.294229i 0.0155722 + 0.0269719i
\(120\) 1.82817 0.822821i 0.166888 0.0751129i
\(121\) −5.69615 + 9.86603i −0.517832 + 0.896911i
\(122\) 17.8350 + 10.2970i 1.61470 + 0.932248i
\(123\) −1.91327 + 7.14042i −0.172514 + 0.643830i
\(124\) −2.36603 4.09808i −0.212475 0.368018i
\(125\) −5.19615 9.89949i −0.464758 0.885438i
\(126\) 5.19615i 0.462910i
\(127\) 4.65874i 0.413397i 0.978405 + 0.206698i \(0.0662719\pi\)
−0.978405 + 0.206698i \(0.933728\pi\)
\(128\) 3.55412 2.05197i 0.314142 0.181370i
\(129\) 11.1962 11.1962i 0.985766 0.985766i
\(130\) 1.69748 + 10.4441i 0.148879 + 0.916012i
\(131\) 0.464102 0.803848i 0.0405487 0.0702325i −0.845039 0.534705i \(-0.820423\pi\)
0.885588 + 0.464473i \(0.153756\pi\)
\(132\) −13.7124 + 3.67423i −1.19351 + 0.319801i
\(133\) 2.12132 1.22474i 0.183942 0.106199i
\(134\) 9.92820 0.857666
\(135\) 9.42745 + 6.79141i 0.811386 + 0.584511i
\(136\) −0.196152 −0.0168199
\(137\) 16.0740 9.28032i 1.37329 0.792871i 0.381952 0.924182i \(-0.375252\pi\)
0.991341 + 0.131311i \(0.0419186\pi\)
\(138\) −6.24384 + 1.67303i −0.531511 + 0.142418i
\(139\) −4.00000 + 6.92820i −0.339276 + 0.587643i −0.984297 0.176522i \(-0.943515\pi\)
0.645021 + 0.764165i \(0.276849\pi\)
\(140\) −3.42745 + 0.557061i −0.289672 + 0.0470802i
\(141\) −5.36603 + 5.36603i −0.451901 + 0.451901i
\(142\) −6.36396 + 3.67423i −0.534052 + 0.308335i
\(143\) 11.5911i 0.969297i
\(144\) 11.5981 + 6.69615i 0.966506 + 0.558013i
\(145\) −11.1962 + 9.14162i −0.929790 + 0.759170i
\(146\) −8.19615 14.1962i −0.678318 1.17488i
\(147\) −2.77766 + 10.3664i −0.229097 + 0.855003i
\(148\) 6.36396 + 3.67423i 0.523114 + 0.302020i
\(149\) 3.86603 6.69615i 0.316717 0.548570i −0.663084 0.748545i \(-0.730753\pi\)
0.979801 + 0.199975i \(0.0640861\pi\)
\(150\) 7.47469 14.9677i 0.610306 1.22211i
\(151\) 11.2942 + 19.5622i 0.919111 + 1.59195i 0.800768 + 0.598975i \(0.204425\pi\)
0.118343 + 0.992973i \(0.462242\pi\)
\(152\) 1.41421i 0.114708i
\(153\) −0.568406 0.984508i −0.0459529 0.0795928i
\(154\) −8.19615 −0.660465
\(155\) 5.71209 + 2.16622i 0.458806 + 0.173995i
\(156\) −5.19615 + 5.19615i −0.416025 + 0.416025i
\(157\) −18.5235 10.6945i −1.47833 0.853517i −0.478635 0.878014i \(-0.658868\pi\)
−0.999700 + 0.0244975i \(0.992201\pi\)
\(158\) −0.896575 0.517638i −0.0713277 0.0411811i
\(159\) 1.73205 + 6.46410i 0.137361 + 0.512637i
\(160\) 6.01703 15.8662i 0.475688 1.25434i
\(161\) −1.73205 −0.136505
\(162\) 17.3867i 1.36603i
\(163\) 18.9396i 1.48346i −0.670697 0.741731i \(-0.734005\pi\)
0.670697 0.741731i \(-0.265995\pi\)
\(164\) 3.69615 + 6.40192i 0.288621 + 0.499906i
\(165\) 10.7124 14.8704i 0.833962 1.15766i
\(166\) 10.0622 17.4282i 0.780976 1.35269i
\(167\) −14.7291 8.50386i −1.13977 0.658049i −0.193399 0.981120i \(-0.561951\pi\)
−0.946375 + 0.323071i \(0.895285\pi\)
\(168\) 0.568406 + 0.568406i 0.0438535 + 0.0438535i
\(169\) −3.50000 6.06218i −0.269231 0.466321i
\(170\) −1.26795 + 1.03528i −0.0972473 + 0.0794021i
\(171\) −7.09808 + 4.09808i −0.542803 + 0.313388i
\(172\) 15.8338i 1.20731i
\(173\) 0.656339 0.378937i 0.0499005 0.0288101i −0.474842 0.880071i \(-0.657495\pi\)
0.524743 + 0.851261i \(0.324162\pi\)
\(174\) −20.8923 5.59808i −1.58384 0.424389i
\(175\) 2.97261 3.35556i 0.224708 0.253656i
\(176\) 10.5622 18.2942i 0.796154 1.37898i
\(177\) 1.13681 4.24264i 0.0854480 0.318896i
\(178\) −12.3676 + 7.14042i −0.926988 + 0.535197i
\(179\) −24.5885 −1.83783 −0.918914 0.394458i \(-0.870932\pi\)
−0.918914 + 0.394458i \(0.870932\pi\)
\(180\) 11.4685 1.86396i 0.854809 0.138931i
\(181\) 8.46410 0.629132 0.314566 0.949236i \(-0.398141\pi\)
0.314566 + 0.949236i \(0.398141\pi\)
\(182\) −3.67423 + 2.12132i −0.272352 + 0.157243i
\(183\) −13.0561 13.0561i −0.965134 0.965134i
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −9.36396 + 1.52192i −0.688452 + 0.111894i
\(186\) 2.36603 + 8.83013i 0.173485 + 0.647456i
\(187\) −1.55291 + 0.896575i −0.113560 + 0.0655641i
\(188\) 7.58871i 0.553463i
\(189\) −1.20577 + 4.50000i −0.0877070 + 0.327327i
\(190\) 7.46410 + 9.14162i 0.541503 + 0.663203i
\(191\) −0.169873 0.294229i −0.0122916 0.0212896i 0.859814 0.510607i \(-0.170579\pi\)
−0.872106 + 0.489317i \(0.837246\pi\)
\(192\) 9.58991 2.56961i 0.692092 0.185445i
\(193\) 17.9551 + 10.3664i 1.29243 + 0.746187i 0.979085 0.203451i \(-0.0652157\pi\)
0.313349 + 0.949638i \(0.398549\pi\)
\(194\) −9.92820 + 17.1962i −0.712803 + 1.23461i
\(195\) 0.953512 9.43879i 0.0682824 0.675926i
\(196\) 5.36603 + 9.29423i 0.383288 + 0.663873i
\(197\) 20.8343i 1.48438i 0.670190 + 0.742190i \(0.266213\pi\)
−0.670190 + 0.742190i \(0.733787\pi\)
\(198\) 27.4249 1.94900
\(199\) −4.58846 −0.325267 −0.162634 0.986687i \(-0.551999\pi\)
−0.162634 + 0.986687i \(0.551999\pi\)
\(200\) 0.819661 + 2.45497i 0.0579588 + 0.173593i
\(201\) −8.59808 2.30385i −0.606462 0.162501i
\(202\) 4.24264 + 2.44949i 0.298511 + 0.172345i
\(203\) −5.01910 2.89778i −0.352272 0.203384i
\(204\) −1.09808 0.294229i −0.0768807 0.0206001i
\(205\) −8.92330 3.38403i −0.623230 0.236351i
\(206\) −17.6603 −1.23045
\(207\) 5.79555 0.402819
\(208\) 10.9348i 0.758190i
\(209\) 6.46410 + 11.1962i 0.447131 + 0.774454i
\(210\) 6.67423 + 0.674235i 0.460566 + 0.0465266i
\(211\) 6.56218 11.3660i 0.451759 0.782469i −0.546736 0.837305i \(-0.684130\pi\)
0.998495 + 0.0548353i \(0.0174634\pi\)
\(212\) 5.79555 + 3.34607i 0.398040 + 0.229809i
\(213\) 6.36396 1.70522i 0.436051 0.116840i
\(214\) 11.3301 + 19.6244i 0.774512 + 1.34149i
\(215\) 12.9282 + 15.8338i 0.881696 + 1.07985i
\(216\) −1.90192 1.90192i −0.129410 0.129410i
\(217\) 2.44949i 0.166282i
\(218\) −7.79676 + 4.50146i −0.528063 + 0.304877i
\(219\) 3.80385 + 14.1962i 0.257040 + 0.959287i
\(220\) −2.94012 18.0898i −0.198223 1.21961i
\(221\) −0.464102 + 0.803848i −0.0312189 + 0.0540726i
\(222\) −10.0382 10.0382i −0.673720 0.673720i
\(223\) −14.4889 + 8.36516i −0.970248 + 0.560173i −0.899312 0.437308i \(-0.855932\pi\)
−0.0709359 + 0.997481i \(0.522599\pi\)
\(224\) 6.80385 0.454601
\(225\) −9.94655 + 11.2279i −0.663103 + 0.748528i
\(226\) 4.92820 0.327819
\(227\) 1.64085 0.947343i 0.108907 0.0628774i −0.444557 0.895750i \(-0.646639\pi\)
0.553464 + 0.832873i \(0.313306\pi\)
\(228\) −2.12132 + 7.91688i −0.140488 + 0.524308i
\(229\) 9.96410 17.2583i 0.658446 1.14046i −0.322571 0.946545i \(-0.604547\pi\)
0.981018 0.193917i \(-0.0621194\pi\)
\(230\) −1.33876 8.23703i −0.0882752 0.543134i
\(231\) 7.09808 + 1.90192i 0.467019 + 0.125137i
\(232\) 2.89778 1.67303i 0.190248 0.109840i
\(233\) 7.07107i 0.463241i −0.972806 0.231621i \(-0.925597\pi\)
0.972806 0.231621i \(-0.0744028\pi\)
\(234\) 12.2942 7.09808i 0.803699 0.464016i
\(235\) −6.19615 7.58871i −0.404192 0.495033i
\(236\) −2.19615 3.80385i −0.142957 0.247609i
\(237\) 0.656339 + 0.656339i 0.0426338 + 0.0426338i
\(238\) −0.568406 0.328169i −0.0368443 0.0212721i
\(239\) 6.46410 11.1962i 0.418128 0.724219i −0.577623 0.816304i \(-0.696020\pi\)
0.995751 + 0.0920846i \(0.0293530\pi\)
\(240\) −10.1058 + 14.0284i −0.652330 + 0.905527i
\(241\) −3.13397 5.42820i −0.201877 0.349661i 0.747256 0.664536i \(-0.231371\pi\)
−0.949133 + 0.314875i \(0.898037\pi\)
\(242\) 22.0082i 1.41474i
\(243\) 4.03459 15.0573i 0.258819 0.965926i
\(244\) −18.4641 −1.18204
\(245\) −12.9547 4.91289i −0.827647 0.313873i
\(246\) −3.69615 13.7942i −0.235658 0.879488i
\(247\) 5.79555 + 3.34607i 0.368762 + 0.212905i
\(248\) −1.22474 0.707107i −0.0777714 0.0449013i
\(249\) −12.7583 + 12.7583i −0.808526 + 0.808526i
\(250\) 18.2555 + 11.5431i 1.15458 + 0.730048i
\(251\) 18.5885 1.17329 0.586647 0.809843i \(-0.300448\pi\)
0.586647 + 0.809843i \(0.300448\pi\)
\(252\) 2.32937 + 4.03459i 0.146737 + 0.254155i
\(253\) 9.14162i 0.574729i
\(254\) −4.50000 7.79423i −0.282355 0.489053i
\(255\) 1.33831 0.602347i 0.0838084 0.0377204i
\(256\) −9.69615 + 16.7942i −0.606010 + 1.04964i
\(257\) 19.4201 + 11.2122i 1.21139 + 0.699396i 0.963062 0.269280i \(-0.0867857\pi\)
0.248328 + 0.968676i \(0.420119\pi\)
\(258\) −7.91688 + 29.5462i −0.492883 + 1.83946i
\(259\) −1.90192 3.29423i −0.118180 0.204693i
\(260\) −6.00000 7.34847i −0.372104 0.455733i
\(261\) 16.7942 + 9.69615i 1.03954 + 0.600177i
\(262\) 1.79315i 0.110781i
\(263\) 6.60420 3.81294i 0.407232 0.235116i −0.282368 0.959306i \(-0.591120\pi\)
0.689600 + 0.724191i \(0.257786\pi\)
\(264\) −3.00000 + 3.00000i −0.184637 + 0.184637i
\(265\) −8.52761 + 1.38599i −0.523847 + 0.0851404i
\(266\) −2.36603 + 4.09808i −0.145070 + 0.251269i
\(267\) 12.3676 3.31388i 0.756883 0.202806i
\(268\) −7.70882 + 4.45069i −0.470891 + 0.271869i
\(269\) −17.1962 −1.04847 −0.524234 0.851574i \(-0.675648\pi\)
−0.524234 + 0.851574i \(0.675648\pi\)
\(270\) −22.3324 2.25603i −1.35911 0.137298i
\(271\) −23.5167 −1.42854 −0.714268 0.699873i \(-0.753240\pi\)
−0.714268 + 0.699873i \(0.753240\pi\)
\(272\) 1.46498 0.845807i 0.0888276 0.0512846i
\(273\) 3.67423 0.984508i 0.222375 0.0595851i
\(274\) −17.9282 + 31.0526i −1.08308 + 1.87595i
\(275\) 17.7104 + 15.6892i 1.06798 + 0.946094i
\(276\) 4.09808 4.09808i 0.246675 0.246675i
\(277\) 10.6066 6.12372i 0.637289 0.367939i −0.146281 0.989243i \(-0.546730\pi\)
0.783569 + 0.621304i \(0.213397\pi\)
\(278\) 15.4548i 0.926918i
\(279\) 8.19615i 0.490691i
\(280\) −0.803848 + 0.656339i −0.0480391 + 0.0392237i
\(281\) 8.13397 + 14.0885i 0.485232 + 0.840447i 0.999856 0.0169692i \(-0.00540173\pi\)
−0.514624 + 0.857416i \(0.672068\pi\)
\(282\) 3.79435 14.1607i 0.225950 0.843258i
\(283\) 3.88229 + 2.24144i 0.230778 + 0.133240i 0.610931 0.791684i \(-0.290795\pi\)
−0.380153 + 0.924924i \(0.624129\pi\)
\(284\) 3.29423 5.70577i 0.195477 0.338575i
\(285\) −4.34278 9.64893i −0.257244 0.571553i
\(286\) −11.1962 19.3923i −0.662042 1.14669i
\(287\) 3.82654i 0.225873i
\(288\) −22.7661 −1.34151
\(289\) 16.8564 0.991553
\(290\) 9.90140 26.1089i 0.581430 1.53317i
\(291\) 12.5885 12.5885i 0.737948 0.737948i
\(292\) 12.7279 + 7.34847i 0.744845 + 0.430037i
\(293\) 7.67664 + 4.43211i 0.448474 + 0.258927i 0.707186 0.707028i \(-0.249965\pi\)
−0.258711 + 0.965955i \(0.583298\pi\)
\(294\) −5.36603 20.0263i −0.312953 1.16796i
\(295\) 5.30198 + 2.01070i 0.308693 + 0.117067i
\(296\) 2.19615 0.127649
\(297\) −23.7506 6.36396i −1.37815 0.369274i
\(298\) 14.9372i 0.865287i
\(299\) −2.36603 4.09808i −0.136831 0.236998i
\(300\) 0.906070 + 14.9726i 0.0523120 + 0.864444i
\(301\) −4.09808 + 7.09808i −0.236209 + 0.409126i
\(302\) −37.7912 21.8188i −2.17464 1.25553i
\(303\) −3.10583 3.10583i −0.178425 0.178425i
\(304\) −6.09808 10.5622i −0.349749 0.605782i
\(305\) 18.4641 15.0759i 1.05725 0.863242i
\(306\) 1.90192 + 1.09808i 0.108726 + 0.0627728i
\(307\) 25.8719i 1.47659i 0.674478 + 0.738295i \(0.264369\pi\)
−0.674478 + 0.738295i \(0.735631\pi\)
\(308\) 6.36396 3.67423i 0.362620 0.209359i
\(309\) 15.2942 + 4.09808i 0.870058 + 0.233131i
\(310\) −11.6489 + 1.89329i −0.661615 + 0.107532i
\(311\) −14.0263 + 24.2942i −0.795357 + 1.37760i 0.127255 + 0.991870i \(0.459383\pi\)
−0.922612 + 0.385729i \(0.873950\pi\)
\(312\) −0.568406 + 2.12132i −0.0321797 + 0.120096i
\(313\) −4.81105 + 2.77766i −0.271936 + 0.157003i −0.629767 0.776784i \(-0.716850\pi\)
0.357831 + 0.933786i \(0.383516\pi\)
\(314\) 41.3205 2.33185
\(315\) −5.62360 2.13267i −0.316854 0.120162i
\(316\) 0.928203 0.0522155
\(317\) −30.4428 + 17.5761i −1.70984 + 0.987174i −0.775094 + 0.631846i \(0.782297\pi\)
−0.934742 + 0.355328i \(0.884369\pi\)
\(318\) −9.14162 9.14162i −0.512637 0.512637i
\(319\) 15.2942 26.4904i 0.856312 1.48318i
\(320\) 2.05620 + 12.6512i 0.114945 + 0.707226i
\(321\) −5.25833 19.6244i −0.293491 1.09532i
\(322\) 2.89778 1.67303i 0.161487 0.0932345i
\(323\) 1.03528i 0.0576043i
\(324\) −7.79423 13.5000i −0.433013 0.750000i
\(325\) 12.0000 + 2.44949i 0.665640 + 0.135873i
\(326\) 18.2942 + 31.6865i 1.01322 + 1.75495i
\(327\) 7.79676 2.08913i 0.431162 0.115529i
\(328\) 1.91327 + 1.10463i 0.105643 + 0.0609928i
\(329\) 1.96410 3.40192i 0.108284 0.187554i
\(330\) −3.55855 + 35.2261i −0.195892 + 1.93913i
\(331\) −6.19615 10.7321i −0.340571 0.589887i 0.643968 0.765053i \(-0.277287\pi\)
−0.984539 + 0.175166i \(0.943954\pi\)
\(332\) 18.0430i 0.990238i
\(333\) 6.36396 + 11.0227i 0.348743 + 0.604040i
\(334\) 32.8564 1.79782
\(335\) 4.07485 10.7449i 0.222633 0.587058i
\(336\) −6.69615 1.79423i −0.365305 0.0978832i
\(337\) 1.55291 + 0.896575i 0.0845926 + 0.0488396i 0.541700 0.840572i \(-0.317781\pi\)
−0.457107 + 0.889412i \(0.651114\pi\)
\(338\) 11.7112 + 6.76148i 0.637007 + 0.367776i
\(339\) −4.26795 1.14359i −0.231803 0.0621115i
\(340\) 0.520407 1.37225i 0.0282230 0.0744209i
\(341\) −12.9282 −0.700101
\(342\) 7.91688 13.7124i 0.428096 0.741483i
\(343\) 11.8313i 0.638833i
\(344\) −2.36603 4.09808i −0.127568 0.220953i
\(345\) −0.752011 + 7.44414i −0.0404869 + 0.400779i
\(346\) −0.732051 + 1.26795i −0.0393553 + 0.0681654i
\(347\) −8.57321 4.94975i −0.460234 0.265716i 0.251909 0.967751i \(-0.418942\pi\)
−0.712143 + 0.702035i \(0.752275\pi\)
\(348\) 18.7315 5.01910i 1.00412 0.269052i
\(349\) 10.7679 + 18.6506i 0.576395 + 0.998346i 0.995889 + 0.0905872i \(0.0288744\pi\)
−0.419493 + 0.907758i \(0.637792\pi\)
\(350\) −1.73205 + 8.48528i −0.0925820 + 0.453557i
\(351\) −12.2942 + 3.29423i −0.656217 + 0.175833i
\(352\) 35.9101i 1.91402i
\(353\) −7.82894 + 4.52004i −0.416693 + 0.240578i −0.693661 0.720301i \(-0.744004\pi\)
0.276969 + 0.960879i \(0.410670\pi\)
\(354\) 2.19615 + 8.19615i 0.116724 + 0.435621i
\(355\) 1.36451 + 8.39550i 0.0724209 + 0.445587i
\(356\) 6.40192 11.0885i 0.339301 0.587687i
\(357\) 0.416102 + 0.416102i 0.0220225 + 0.0220225i
\(358\) 41.1373 23.7506i 2.17417 1.25526i
\(359\) −9.80385 −0.517427 −0.258714 0.965954i \(-0.583299\pi\)
−0.258714 + 0.965954i \(0.583299\pi\)
\(360\) 2.68973 2.19615i 0.141761 0.115747i
\(361\) −11.5359 −0.607153
\(362\) −14.1607 + 8.17569i −0.744271 + 0.429705i
\(363\) −5.10703 + 19.0597i −0.268050 + 1.00037i
\(364\) 1.90192 3.29423i 0.0996879 0.172664i
\(365\) −18.7279 + 3.04384i −0.980264 + 0.159322i
\(366\) 34.4545 + 9.23205i 1.80096 + 0.482567i
\(367\) −21.4770 + 12.3998i −1.12109 + 0.647262i −0.941679 0.336512i \(-0.890753\pi\)
−0.179411 + 0.983774i \(0.557419\pi\)
\(368\) 8.62398i 0.449556i
\(369\) 12.8038i 0.666542i
\(370\) 14.1962 11.5911i 0.738023 0.602593i
\(371\) −1.73205 3.00000i −0.0899236 0.155752i
\(372\) −5.79555 5.79555i −0.300486 0.300486i
\(373\) −27.8410 16.0740i −1.44155 0.832280i −0.443597 0.896226i \(-0.646298\pi\)
−0.997953 + 0.0639468i \(0.979631\pi\)
\(374\) 1.73205 3.00000i 0.0895622 0.155126i
\(375\) −13.1312 14.2328i −0.678090 0.734979i
\(376\) 1.13397 + 1.96410i 0.0584803 + 0.101291i
\(377\) 15.8338i 0.815480i
\(378\) −2.32937 8.69333i −0.119810 0.447137i
\(379\) −12.5359 −0.643926 −0.321963 0.946752i \(-0.604343\pi\)
−0.321963 + 0.946752i \(0.604343\pi\)
\(380\) −9.89363 3.75201i −0.507533 0.192474i
\(381\) 2.08846 + 7.79423i 0.106995 + 0.399310i
\(382\) 0.568406 + 0.328169i 0.0290822 + 0.0167906i
\(383\) 17.7148 + 10.2277i 0.905186 + 0.522609i 0.878879 0.477045i \(-0.158292\pi\)
0.0263067 + 0.999654i \(0.491625\pi\)
\(384\) 5.02628 5.02628i 0.256496 0.256496i
\(385\) −3.36396 + 8.87039i −0.171443 + 0.452077i
\(386\) −40.0526 −2.03862
\(387\) 13.7124 23.7506i 0.697042 1.20731i
\(388\) 17.8028i 0.903799i
\(389\) −12.0622 20.8923i −0.611577 1.05928i −0.990975 0.134048i \(-0.957202\pi\)
0.379398 0.925234i \(-0.376131\pi\)
\(390\) 7.52192 + 16.7124i 0.380887 + 0.846267i
\(391\) 0.366025 0.633975i 0.0185107 0.0320615i
\(392\) 2.77766 + 1.60368i 0.140293 + 0.0809982i
\(393\) 0.416102 1.55291i 0.0209896 0.0783342i
\(394\) −20.1244 34.8564i −1.01385 1.75604i
\(395\) −0.928203 + 0.757875i −0.0467030 + 0.0381328i
\(396\) −21.2942 + 12.2942i −1.07008 + 0.617808i
\(397\) 29.3939i 1.47524i −0.675218 0.737618i \(-0.735950\pi\)
0.675218 0.737618i \(-0.264050\pi\)
\(398\) 7.67664 4.43211i 0.384795 0.222162i
\(399\) 3.00000 3.00000i 0.150188 0.150188i
\(400\) −16.7075 14.8008i −0.835376 0.740040i
\(401\) 15.4641 26.7846i 0.772240 1.33756i −0.164092 0.986445i \(-0.552469\pi\)
0.936333 0.351115i \(-0.114197\pi\)
\(402\) 16.6102 4.45069i 0.828442 0.221980i
\(403\) −5.79555 + 3.34607i −0.288697 + 0.166679i
\(404\) −4.39230 −0.218525
\(405\) 18.8169 + 7.13604i 0.935021 + 0.354593i
\(406\) 11.1962 0.555656
\(407\) 17.3867 10.0382i 0.861825 0.497575i
\(408\) −0.328169 + 0.0879327i −0.0162468 + 0.00435332i
\(409\) −11.7321 + 20.3205i −0.580113 + 1.00478i 0.415353 + 0.909660i \(0.363658\pi\)
−0.995465 + 0.0951241i \(0.969675\pi\)
\(410\) 18.1977 2.95766i 0.898720 0.146068i
\(411\) 22.7321 22.7321i 1.12129 1.12129i
\(412\) 13.7124 7.91688i 0.675563 0.390036i
\(413\) 2.27362i 0.111878i
\(414\) −9.69615 + 5.59808i −0.476540 + 0.275130i
\(415\) −14.7321 18.0430i −0.723168 0.885696i
\(416\) 9.29423 + 16.0981i 0.455687 + 0.789273i
\(417\) −3.58630 + 13.3843i −0.175622 + 0.655430i
\(418\) −21.6293 12.4877i −1.05792 0.610793i
\(419\) −8.02628 + 13.9019i −0.392109 + 0.679153i −0.992728 0.120383i \(-0.961588\pi\)
0.600618 + 0.799536i \(0.294921\pi\)
\(420\) −5.48451 + 2.46846i −0.267617 + 0.120449i
\(421\) 6.26795 + 10.8564i 0.305481 + 0.529109i 0.977368 0.211545i \(-0.0678494\pi\)
−0.671887 + 0.740653i \(0.734516\pi\)
\(422\) 25.3543i 1.23423i
\(423\) −6.57201 + 11.3831i −0.319542 + 0.553463i
\(424\) 2.00000 0.0971286
\(425\) 0.600034 + 1.79716i 0.0291059 + 0.0871753i
\(426\) −9.00000 + 9.00000i −0.436051 + 0.436051i
\(427\) 8.27723 + 4.77886i 0.400563 + 0.231265i
\(428\) −17.5947 10.1583i −0.850473 0.491021i
\(429\) 5.19615 + 19.3923i 0.250873 + 0.936269i
\(430\) −36.9235 14.0027i −1.78061 0.675270i
\(431\) −6.00000 −0.289010 −0.144505 0.989504i \(-0.546159\pi\)
−0.144505 + 0.989504i \(0.546159\pi\)
\(432\) 22.4058 + 6.00361i 1.07800 + 0.288849i
\(433\) 30.5307i 1.46721i 0.679575 + 0.733606i \(0.262164\pi\)
−0.679575 + 0.733606i \(0.737836\pi\)
\(434\) −2.36603 4.09808i −0.113573 0.196714i
\(435\) −14.6335 + 20.3133i −0.701620 + 0.973949i
\(436\) 4.03590 6.99038i 0.193284 0.334779i
\(437\) −4.57081 2.63896i −0.218651 0.126239i
\(438\) −20.0764 20.0764i −0.959287 0.959287i
\(439\) 4.66025 + 8.07180i 0.222422 + 0.385246i 0.955543 0.294852i \(-0.0952705\pi\)
−0.733121 + 0.680098i \(0.761937\pi\)
\(440\) −3.46410 4.24264i −0.165145 0.202260i
\(441\) 18.5885i 0.885165i
\(442\) 1.79315i 0.0852915i
\(443\) 12.0394 6.95095i 0.572009 0.330250i −0.185942 0.982561i \(-0.559534\pi\)
0.757951 + 0.652311i \(0.226200\pi\)
\(444\) 12.2942 + 3.29423i 0.583458 + 0.156337i
\(445\) 2.65176 + 16.3156i 0.125706 + 0.773434i
\(446\) 16.1603 27.9904i 0.765210 1.32538i
\(447\) 3.46618 12.9360i 0.163945 0.611851i
\(448\) −4.45069 + 2.56961i −0.210275 + 0.121403i
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 5.79555 28.3923i 0.273205 1.33843i
\(451\) 20.1962 0.951000
\(452\) −3.82654 + 2.20925i −0.179985 + 0.103915i
\(453\) 27.6651 + 27.6651i 1.29982 + 1.29982i
\(454\) −1.83013 + 3.16987i −0.0858921 + 0.148770i
\(455\) 0.787803 + 4.84714i 0.0369328 + 0.227238i
\(456\) 0.633975 + 2.36603i 0.0296886 + 0.110799i
\(457\) 29.9623 17.2987i 1.40158 0.809201i 0.407022 0.913418i \(-0.366567\pi\)
0.994554 + 0.104218i \(0.0332339\pi\)
\(458\) 38.4983i 1.79891i
\(459\) −1.39230 1.39230i −0.0649872 0.0649872i
\(460\) 4.73205 + 5.79555i 0.220633 + 0.270219i
\(461\) −9.35641 16.2058i −0.435771 0.754778i 0.561587 0.827418i \(-0.310191\pi\)
−0.997358 + 0.0726397i \(0.976858\pi\)
\(462\) −13.7124 + 3.67423i −0.637960 + 0.170941i
\(463\) −0.152304 0.0879327i −0.00707816 0.00408658i 0.496457 0.868061i \(-0.334634\pi\)
−0.503535 + 0.863975i \(0.667967\pi\)
\(464\) −14.4282 + 24.9904i −0.669813 + 1.16015i
\(465\) 10.5276 + 1.06350i 0.488206 + 0.0493188i
\(466\) 6.83013 + 11.8301i 0.316400 + 0.548020i
\(467\) 5.75839i 0.266467i −0.991085 0.133233i \(-0.957464\pi\)
0.991085 0.133233i \(-0.0425359\pi\)
\(468\) −6.36396 + 11.0227i −0.294174 + 0.509525i
\(469\) 4.60770 0.212764
\(470\) 17.6965 + 6.71113i 0.816278 + 0.309561i
\(471\) −35.7846 9.58846i −1.64887 0.441813i
\(472\) −1.13681 0.656339i −0.0523260 0.0302104i
\(473\) −37.4631 21.6293i −1.72255 0.994517i
\(474\) −1.73205 0.464102i −0.0795557 0.0213169i
\(475\) 12.9571 4.32611i 0.594514 0.198495i
\(476\) 0.588457 0.0269719
\(477\) 5.79555 + 10.0382i 0.265360 + 0.459617i
\(478\) 24.9754i 1.14235i
\(479\) 15.9282 + 27.5885i 0.727778 + 1.26055i 0.957820 + 0.287368i \(0.0927803\pi\)
−0.230042 + 0.973181i \(0.573886\pi\)
\(480\) 2.95405 29.2421i 0.134833 1.33471i
\(481\) 5.19615 9.00000i 0.236924 0.410365i
\(482\) 10.4865 + 6.05437i 0.477646 + 0.275769i
\(483\) −2.89778 + 0.776457i −0.131853 + 0.0353300i
\(484\) 9.86603 + 17.0885i 0.448456 + 0.776748i
\(485\) 14.5359 + 17.8028i 0.660041 + 0.808382i
\(486\) 7.79423 + 29.0885i 0.353553 + 1.31948i
\(487\) 1.13681i 0.0515139i −0.999668 0.0257569i \(-0.991800\pi\)
0.999668 0.0257569i \(-0.00819959\pi\)
\(488\) −4.77886 + 2.75908i −0.216329 + 0.124898i
\(489\) −8.49038 31.6865i −0.383948 1.43291i
\(490\) 26.4192 4.29389i 1.19350 0.193978i
\(491\) 10.8564 18.8038i 0.489943 0.848606i −0.509990 0.860180i \(-0.670351\pi\)
0.999933 + 0.0115744i \(0.00368433\pi\)
\(492\) 9.05369 + 9.05369i 0.408172 + 0.408172i
\(493\) 2.12132 1.22474i 0.0955395 0.0551597i
\(494\) −12.9282 −0.581667
\(495\) 11.2560 29.6809i 0.505921 1.33406i
\(496\) 12.1962 0.547623
\(497\) −2.95352 + 1.70522i −0.132484 + 0.0764895i
\(498\) 9.02150 33.6687i 0.404263 1.50873i
\(499\) −1.92820 + 3.33975i −0.0863182 + 0.149508i −0.905952 0.423380i \(-0.860844\pi\)
0.819634 + 0.572888i \(0.194177\pi\)
\(500\) −19.3492 0.778985i −0.865324 0.0348373i
\(501\) −28.4545 7.62436i −1.27125 0.340631i
\(502\) −31.0991 + 17.9551i −1.38802 + 0.801374i
\(503\) 29.3567i 1.30895i −0.756083 0.654476i \(-0.772889\pi\)
0.756083 0.654476i \(-0.227111\pi\)
\(504\) 1.20577 + 0.696152i 0.0537093 + 0.0310091i
\(505\) 4.39230 3.58630i 0.195455 0.159588i
\(506\) 8.83013 + 15.2942i 0.392547 + 0.679911i
\(507\) −8.57321 8.57321i −0.380750 0.380750i
\(508\) 6.98811 + 4.03459i 0.310047 + 0.179006i
\(509\) −5.42820 + 9.40192i −0.240601 + 0.416733i −0.960886 0.276946i \(-0.910678\pi\)
0.720285 + 0.693679i \(0.244011\pi\)
\(510\) −1.65722 + 2.30046i −0.0733829 + 0.101866i
\(511\) −3.80385 6.58846i −0.168272 0.291456i
\(512\) 29.2552i 1.29291i
\(513\) −10.0382 + 10.0382i −0.443197 + 0.443197i
\(514\) −43.3205 −1.91079
\(515\) −7.24833 + 19.1130i −0.319400 + 0.842221i
\(516\) −7.09808 26.4904i −0.312475 1.16617i
\(517\) 17.9551 + 10.3664i 0.789663 + 0.455912i
\(518\) 6.36396 + 3.67423i 0.279616 + 0.161437i
\(519\) 0.928203 0.928203i 0.0407436 0.0407436i
\(520\) −2.65099 1.00535i −0.116254 0.0440874i
\(521\) 1.39230 0.0609980 0.0304990 0.999535i \(-0.490290\pi\)
0.0304990 + 0.999535i \(0.490290\pi\)
\(522\) −37.4631 −1.63971
\(523\) 30.9468i 1.35321i 0.736347 + 0.676604i \(0.236549\pi\)
−0.736347 + 0.676604i \(0.763451\pi\)
\(524\) −0.803848 1.39230i −0.0351162 0.0608231i
\(525\) 3.46902 6.94655i 0.151400 0.303172i
\(526\) −7.36603 + 12.7583i −0.321174 + 0.556290i
\(527\) −0.896575 0.517638i −0.0390554 0.0225487i
\(528\) 9.46979 35.3417i 0.412120 1.53805i
\(529\) −9.63397 16.6865i −0.418868 0.725501i
\(530\) 12.9282 10.5558i 0.561565 0.458516i
\(531\) 7.60770i 0.330146i
\(532\) 4.24264i 0.183942i
\(533\) 9.05369 5.22715i 0.392159 0.226413i
\(534\) −17.4904 + 17.4904i −0.756883 + 0.756883i
\(535\) 25.8889 4.20771i 1.11928 0.181915i
\(536\) −1.33013 + 2.30385i −0.0574527 + 0.0995111i
\(537\) −41.1373 + 11.0227i −1.77521 + 0.475665i
\(538\) 28.7697 16.6102i 1.24035 0.716117i
\(539\) 29.3205 1.26292
\(540\) 18.3515 8.25964i 0.789724 0.355438i
\(541\) 21.3923 0.919727 0.459864 0.887990i \(-0.347898\pi\)
0.459864 + 0.887990i \(0.347898\pi\)
\(542\) 39.3441 22.7153i 1.68998 0.975708i
\(543\) 14.1607 3.79435i 0.607695 0.162831i
\(544\) −1.43782 + 2.49038i −0.0616461 + 0.106774i
\(545\) 1.67172 + 10.2857i 0.0716088 + 0.440590i
\(546\) −5.19615 + 5.19615i −0.222375 + 0.222375i
\(547\) −26.2323 + 15.1452i −1.12161 + 0.647563i −0.941812 0.336140i \(-0.890878\pi\)
−0.179800 + 0.983703i \(0.557545\pi\)
\(548\) 32.1480i 1.37329i
\(549\) −27.6962 15.9904i −1.18204 0.682453i
\(550\) −44.7846 9.14162i −1.90962 0.389800i
\(551\) −8.83013 15.2942i −0.376176 0.651556i
\(552\) 0.448288 1.67303i 0.0190804 0.0712090i
\(553\) −0.416102 0.240237i −0.0176945 0.0102159i
\(554\) −11.8301 + 20.4904i −0.502614 + 0.870553i
\(555\) −14.9840 + 6.74397i −0.636033 + 0.286265i
\(556\) 6.92820 + 12.0000i 0.293821 + 0.508913i
\(557\) 31.1127i 1.31829i 0.752017 + 0.659144i \(0.229081\pi\)
−0.752017 + 0.659144i \(0.770919\pi\)
\(558\) 7.91688 + 13.7124i 0.335148 + 0.580493i
\(559\) −22.3923 −0.947094
\(560\) 3.17348 8.36811i 0.134104 0.353617i
\(561\) −2.19615 + 2.19615i −0.0927216 + 0.0927216i
\(562\) −27.2168 15.7136i −1.14807 0.662840i
\(563\) 23.8707 + 13.7818i 1.00603 + 0.580833i 0.910027 0.414548i \(-0.136060\pi\)
0.0960045 + 0.995381i \(0.469394\pi\)
\(564\) 3.40192 + 12.6962i 0.143247 + 0.534604i
\(565\) 2.02269 5.33361i 0.0850952 0.224387i
\(566\) −8.66025 −0.364018
\(567\) 8.06918i 0.338874i
\(568\) 1.96902i 0.0826181i
\(569\) −2.66025 4.60770i −0.111524 0.193165i 0.804861 0.593463i \(-0.202240\pi\)
−0.916385 + 0.400299i \(0.868906\pi\)
\(570\) 16.5858 + 11.9482i 0.694701 + 0.500453i
\(571\) −2.73205 + 4.73205i −0.114333 + 0.198030i −0.917513 0.397706i \(-0.869806\pi\)
0.803180 + 0.595736i \(0.203140\pi\)
\(572\) 17.3867 + 10.0382i 0.726973 + 0.419718i
\(573\) −0.416102 0.416102i −0.0173829 0.0173829i
\(574\) 3.69615 + 6.40192i 0.154274 + 0.267211i
\(575\) −9.46410 1.93185i −0.394680 0.0805638i
\(576\) 14.8923 8.59808i 0.620513 0.358253i
\(577\) 28.5617i 1.18904i −0.804082 0.594519i \(-0.797343\pi\)
0.804082 0.594519i \(-0.202657\pi\)
\(578\) −28.2013 + 16.2820i −1.17302 + 0.677244i
\(579\) 34.6865 + 9.29423i 1.44152 + 0.386255i
\(580\) 4.01628 + 24.7111i 0.166767 + 1.02607i
\(581\) 4.66987 8.08846i 0.193739 0.335566i
\(582\) −8.90138 + 33.2204i −0.368974 + 1.37703i
\(583\) 15.8338 9.14162i 0.655767 0.378607i
\(584\) 4.39230 0.181755
\(585\) −2.63604 16.2189i −0.108987 0.670567i
\(586\) −17.1244 −0.707401
\(587\) −19.0597 + 11.0041i −0.786678 + 0.454189i −0.838792 0.544452i \(-0.816737\pi\)
0.0521138 + 0.998641i \(0.483404\pi\)
\(588\) 13.1440 + 13.1440i 0.542050 + 0.542050i
\(589\) −3.73205 + 6.46410i −0.153776 + 0.266349i
\(590\) −10.8126 + 1.75736i −0.445146 + 0.0723493i
\(591\) 9.33975 + 34.8564i 0.384186 + 1.43380i
\(592\) −16.4022 + 9.46979i −0.674124 + 0.389206i
\(593\) 28.9406i 1.18845i −0.804299 0.594224i \(-0.797459\pi\)
0.804299 0.594224i \(-0.202541\pi\)
\(594\) 45.8827 12.2942i 1.88259 0.504438i
\(595\) −0.588457 + 0.480473i −0.0241244 + 0.0196975i
\(596\) −6.69615 11.5981i −0.274285 0.475076i
\(597\) −7.67664 + 2.05695i −0.314184 + 0.0841853i
\(598\) 7.91688 + 4.57081i 0.323745 + 0.186914i
\(599\) 16.8564 29.1962i 0.688734 1.19292i −0.283514 0.958968i \(-0.591500\pi\)
0.972248 0.233954i \(-0.0751666\pi\)
\(600\) 2.47185 + 3.73980i 0.100913 + 0.152677i
\(601\) 8.46410 + 14.6603i 0.345258 + 0.598004i 0.985401 0.170252i \(-0.0544581\pi\)
−0.640143 + 0.768256i \(0.721125\pi\)
\(602\) 15.8338i 0.645335i
\(603\) −15.4176 −0.627855
\(604\) 39.1244 1.59195
\(605\) −23.8187 9.03288i −0.968368 0.367239i
\(606\) 8.19615 + 2.19615i 0.332946 + 0.0892126i
\(607\) 7.55652 + 4.36276i 0.306710 + 0.177079i 0.645453 0.763800i \(-0.276669\pi\)
−0.338743 + 0.940879i \(0.610002\pi\)
\(608\) 17.9551 + 10.3664i 0.728174 + 0.420412i
\(609\) −9.69615 2.59808i −0.392908 0.105279i
\(610\) −16.3289 + 43.0574i −0.661136 + 1.74334i
\(611\) 10.7321 0.434172
\(612\) −1.96902 −0.0795928
\(613\) 24.3190i 0.982236i −0.871093 0.491118i \(-0.836588\pi\)
0.871093 0.491118i \(-0.163412\pi\)
\(614\) −24.9904 43.2846i −1.00853 1.74682i
\(615\) −16.4460 1.66138i −0.663166 0.0669934i
\(616\) 1.09808 1.90192i 0.0442428 0.0766307i
\(617\) 11.3509 + 6.55343i 0.456969 + 0.263831i 0.710769 0.703426i \(-0.248347\pi\)
−0.253800 + 0.967257i \(0.581680\pi\)
\(618\) −29.5462 + 7.91688i −1.18852 + 0.318463i
\(619\) 9.90192 + 17.1506i 0.397992 + 0.689342i 0.993478 0.114023i \(-0.0363739\pi\)
−0.595486 + 0.803366i \(0.703041\pi\)
\(620\) 8.19615 6.69213i 0.329165 0.268762i
\(621\) 9.69615 2.59808i 0.389093 0.104257i
\(622\) 54.1934i 2.17296i
\(623\) −5.73981 + 3.31388i −0.229961 + 0.132768i
\(624\) −4.90192 18.2942i −0.196234 0.732355i
\(625\) 19.9853 15.0196i 0.799411 0.600784i
\(626\) 5.36603 9.29423i 0.214470 0.371472i
\(627\) 15.8338 + 15.8338i 0.632339 + 0.632339i
\(628\) −32.0836 + 18.5235i −1.28028 + 0.739167i
\(629\) 1.60770 0.0641030
\(630\) 11.4685 1.86396i 0.456915 0.0742620i
\(631\) −33.3205 −1.32647 −0.663234 0.748412i \(-0.730817\pi\)
−0.663234 + 0.748412i \(0.730817\pi\)
\(632\) 0.240237 0.138701i 0.00955610 0.00551722i
\(633\) 5.88349 21.9575i 0.233848 0.872731i
\(634\) 33.9545 58.8109i 1.34850 2.33568i
\(635\) −10.2823 + 1.67118i −0.408042 + 0.0663188i
\(636\) 11.1962 + 3.00000i 0.443956 + 0.118958i
\(637\) 13.1440 7.58871i 0.520785 0.300675i
\(638\) 59.0924i 2.33949i
\(639\) 9.88269 5.70577i 0.390953 0.225717i
\(640\) 5.80385 + 7.10823i 0.229417 + 0.280978i
\(641\) 12.5263 + 21.6962i 0.494758 + 0.856946i 0.999982 0.00604207i \(-0.00192326\pi\)
−0.505223 + 0.862989i \(0.668590\pi\)
\(642\) 27.7530 + 27.7530i 1.09532 + 1.09532i
\(643\) −21.8374 12.6078i −0.861181 0.497203i 0.00322641 0.999995i \(-0.498973\pi\)
−0.864408 + 0.502792i \(0.832306\pi\)
\(644\) −1.50000 + 2.59808i −0.0591083 + 0.102379i
\(645\) 28.7274 + 20.6948i 1.13114 + 0.814858i
\(646\) −1.00000 1.73205i −0.0393445 0.0681466i
\(647\) 12.3861i 0.486950i −0.969907 0.243475i \(-0.921713\pi\)
0.969907 0.243475i \(-0.0782873\pi\)
\(648\) −4.03459 2.32937i −0.158494 0.0915064i
\(649\) −12.0000 −0.471041
\(650\) −22.4424 + 7.49303i −0.880264 + 0.293901i
\(651\) 1.09808 + 4.09808i 0.0430370 + 0.160616i
\(652\) −28.4094 16.4022i −1.11260 0.642358i
\(653\) −0.392541 0.226633i −0.0153613 0.00886885i 0.492300 0.870426i \(-0.336156\pi\)
−0.507661 + 0.861557i \(0.669490\pi\)
\(654\) −11.0263 + 11.0263i −0.431162 + 0.431162i
\(655\) 1.94066 + 0.735966i 0.0758279 + 0.0287566i
\(656\) −19.0526 −0.743877
\(657\) 12.7279 + 22.0454i 0.496564 + 0.860073i
\(658\) 7.58871i 0.295839i
\(659\) 18.1244 + 31.3923i 0.706025 + 1.22287i 0.966320 + 0.257342i \(0.0828466\pi\)
−0.260296 + 0.965529i \(0.583820\pi\)
\(660\) −13.0283 28.9468i −0.507128 1.12675i
\(661\) 15.3923 26.6603i 0.598691 1.03696i −0.394323 0.918972i \(-0.629021\pi\)
0.993015 0.117992i \(-0.0376457\pi\)
\(662\) 20.7327 + 11.9700i 0.805800 + 0.465229i
\(663\) −0.416102 + 1.55291i −0.0161601 + 0.0603102i
\(664\) 2.69615 + 4.66987i 0.104631 + 0.181226i
\(665\) 3.46410 + 4.24264i 0.134332 + 0.164523i
\(666\) −21.2942 12.2942i −0.825135 0.476392i
\(667\) 12.4877i 0.483525i
\(668\) −25.5116 + 14.7291i −0.987073 + 0.569887i
\(669\) −20.4904 + 20.4904i −0.792204 + 0.792204i
\(670\) 3.56144 + 21.9126i 0.137590 + 0.846558i
\(671\) −25.2224 + 43.6865i −0.973701 + 1.68650i
\(672\) 11.3831 3.05008i 0.439111 0.117659i
\(673\) −1.40061 + 0.808643i −0.0539896 + 0.0311709i −0.526752 0.850019i \(-0.676590\pi\)
0.472762 + 0.881190i \(0.343257\pi\)
\(674\) −3.46410 −0.133432
\(675\) −11.6076 + 23.2436i −0.446775 + 0.894646i
\(676\) −12.1244 −0.466321
\(677\) 28.6496 16.5409i 1.10109 0.635717i 0.164586 0.986363i \(-0.447371\pi\)
0.936508 + 0.350646i \(0.114038\pi\)
\(678\) 8.24504 2.20925i 0.316649 0.0848459i
\(679\) −4.60770 + 7.98076i −0.176827 + 0.306274i
\(680\) −0.0703637 0.432929i −0.00269832 0.0166021i
\(681\) 2.32051 2.32051i 0.0889221 0.0889221i
\(682\) 21.6293 12.4877i 0.828229 0.478178i
\(683\) 19.6975i 0.753702i 0.926274 + 0.376851i \(0.122993\pi\)
−0.926274 + 0.376851i \(0.877007\pi\)
\(684\) 14.1962i 0.542803i
\(685\) 26.2487 + 32.1480i 1.00291 + 1.22831i
\(686\) 11.4282 + 19.7942i 0.436331 + 0.755747i
\(687\) 8.93357 33.3405i 0.340837 1.27202i
\(688\) 35.3417 + 20.4046i 1.34739 + 0.777917i
\(689\) 4.73205 8.19615i 0.180277 0.312249i
\(690\) −5.93235 13.1807i −0.225841 0.501780i
\(691\) −10.1244 17.5359i −0.385149 0.667097i 0.606641 0.794976i \(-0.292516\pi\)
−0.991790 + 0.127879i \(0.959183\pi\)
\(692\) 1.31268i 0.0499005i
\(693\) 12.7279 0.483494
\(694\) 19.1244 0.725951
\(695\) −16.7262 6.34315i −0.634459 0.240609i
\(696\) 4.09808 4.09808i 0.155337 0.155337i
\(697\) 1.40061 + 0.808643i 0.0530519 + 0.0306295i
\(698\) −36.0303 20.8021i −1.36377 0.787370i
\(699\) −3.16987 11.8301i −0.119896 0.447456i
\(700\) −2.45898 7.36491i −0.0929409 0.278368i
\(701\) −23.1962 −0.876107 −0.438053 0.898949i \(-0.644332\pi\)
−0.438053 + 0.898949i \(0.644332\pi\)
\(702\) 17.3867 17.3867i 0.656217 0.656217i
\(703\) 11.5911i 0.437167i
\(704\) −13.5622 23.4904i −0.511144 0.885327i
\(705\) −13.7683 9.91849i −0.518544 0.373552i
\(706\) 8.73205 15.1244i 0.328635 0.569213i
\(707\) 1.96902 + 1.13681i 0.0740525 + 0.0427542i
\(708\) −5.37945 5.37945i −0.202172 0.202172i
\(709\) −15.8923 27.5263i −0.596848 1.03377i −0.993283 0.115708i \(-0.963086\pi\)
0.396435 0.918063i \(-0.370247\pi\)
\(710\) −10.3923 12.7279i −0.390016 0.477670i
\(711\) 1.39230 + 0.803848i 0.0522155 + 0.0301466i
\(712\) 3.82654i 0.143406i
\(713\) 4.57081 2.63896i 0.171178 0.0988298i
\(714\) −1.09808 0.294229i −0.0410945 0.0110112i
\(715\) −25.5828 + 4.15796i −0.956743 + 0.155499i
\(716\) −21.2942 + 36.8827i −0.795803 + 1.37837i
\(717\) 5.79555 21.6293i 0.216439 0.807761i
\(718\) 16.4022 9.46979i 0.612123 0.353409i
\(719\) −19.6077 −0.731244 −0.365622 0.930763i \(-0.619144\pi\)
−0.365622 + 0.930763i \(0.619144\pi\)
\(720\) −10.6187 + 28.0002i −0.395734 + 1.04351i
\(721\) −8.19615 −0.305241
\(722\) 19.2999 11.1428i 0.718269 0.414693i
\(723\) −7.67664 7.67664i −0.285497 0.285497i
\(724\) 7.33013 12.6962i 0.272422 0.471849i
\(725\) −24.1928 21.4318i −0.898498 0.795958i
\(726\) −9.86603 36.8205i −0.366163 1.36654i
\(727\) −24.5271 + 14.1607i −0.909659 + 0.525192i −0.880321 0.474378i \(-0.842673\pi\)
−0.0293377 + 0.999570i \(0.509340\pi\)
\(728\) 1.13681i 0.0421331i
\(729\) 27.0000i 1.00000i
\(730\) 28.3923 23.1822i 1.05085 0.858012i
\(731\) −1.73205 3.00000i −0.0640622 0.110959i
\(732\) −30.8910 + 8.27723i −1.14177 + 0.305935i
\(733\) −35.9101 20.7327i −1.32637 0.765781i −0.341635 0.939833i \(-0.610981\pi\)
−0.984736 + 0.174052i \(0.944314\pi\)
\(734\) 23.9545 41.4904i 0.884176 1.53144i
\(735\) −23.8761 2.41197i −0.880682 0.0889670i
\(736\) −7.33013 12.6962i −0.270192 0.467986i
\(737\) 24.3190i 0.895803i
\(738\) −12.3676 21.4213i −0.455256 0.788527i
\(739\) 45.8564 1.68686 0.843428 0.537243i \(-0.180534\pi\)
0.843428 + 0.537243i \(0.180534\pi\)
\(740\) −5.82655 + 15.3640i −0.214188 + 0.564790i
\(741\) 11.1962 + 3.00000i 0.411301 + 0.110208i
\(742\) 5.79555 + 3.34607i 0.212762 + 0.122838i
\(743\) −21.9253 12.6586i −0.804361 0.464398i 0.0406329 0.999174i \(-0.487063\pi\)
−0.844994 + 0.534776i \(0.820396\pi\)
\(744\) −2.36603 0.633975i −0.0867427 0.0232426i
\(745\) 16.1659 + 6.13069i 0.592274 + 0.224611i
\(746\) 62.1051 2.27383
\(747\) −15.6257 + 27.0645i −0.571714 + 0.990238i
\(748\) 3.10583i 0.113560i
\(749\) 5.25833 + 9.10770i 0.192135 + 0.332788i
\(750\) 35.7167 + 11.1282i 1.30419 + 0.406345i
\(751\) −17.2224 + 29.8301i −0.628455 + 1.08852i 0.359406 + 0.933181i \(0.382979\pi\)
−0.987862 + 0.155336i \(0.950354\pi\)
\(752\) −16.9384 9.77938i −0.617679 0.356617i
\(753\) 31.0991 8.33298i 1.13331 0.303671i
\(754\) 15.2942 + 26.4904i 0.556983 + 0.964723i
\(755\) −39.1244 + 31.9449i −1.42388 + 1.16259i
\(756\) 5.70577 + 5.70577i 0.207517 + 0.207517i
\(757\) 7.34847i 0.267085i −0.991043 0.133542i \(-0.957365\pi\)
0.991043 0.133542i \(-0.0426352\pi\)
\(758\) 20.9730 12.1087i 0.761772 0.439810i
\(759\) −4.09808 15.2942i −0.148751 0.555145i
\(760\) −3.12132 + 0.507306i −0.113222 + 0.0184019i
\(761\) −1.03590 + 1.79423i −0.0375513 + 0.0650407i −0.884190 0.467127i \(-0.845289\pi\)
0.846639 + 0.532168i \(0.178622\pi\)
\(762\) −11.0227 11.0227i −0.399310 0.399310i
\(763\) −3.61849 + 2.08913i −0.130998 + 0.0756318i
\(764\) −0.588457 −0.0212896
\(765\) 1.96902 1.60770i 0.0711899 0.0581263i
\(766\) −39.5167 −1.42779
\(767\) −5.37945 + 3.10583i −0.194241 + 0.112145i
\(768\) −8.69333 + 32.4440i −0.313694 + 1.17072i
\(769\) −13.8205 + 23.9378i −0.498380 + 0.863220i −0.999998 0.00186930i \(-0.999405\pi\)
0.501618 + 0.865089i \(0.332738\pi\)
\(770\) −2.94012 18.0898i −0.105955 0.651911i
\(771\) 37.5167 + 10.0526i 1.35113 + 0.362034i
\(772\) 31.0991 17.9551i 1.11928 0.646217i
\(773\) 7.72741i 0.277935i −0.990297 0.138968i \(-0.955622\pi\)
0.990297 0.138968i \(-0.0443784\pi\)
\(774\) 52.9808i 1.90435i
\(775\) −2.73205 + 13.3843i −0.0981382 + 0.480777i
\(776\) −2.66025 4.60770i −0.0954976 0.165407i
\(777\) −4.65874 4.65874i −0.167131 0.167131i
\(778\) 40.3608 + 23.3023i 1.44701 + 0.835429i
\(779\) 5.83013 10.0981i 0.208886 0.361801i
\(780\) −13.3324 9.60450i −0.477377 0.343896i
\(781\) −9.00000 15.5885i −0.322045 0.557799i
\(782\) 1.41421i 0.0505722i
\(783\) 32.4440 + 8.69333i 1.15945 + 0.310674i
\(784\) −27.6603 −0.987866
\(785\) 16.9592 44.7196i 0.605302 1.59611i
\(786\) 0.803848 + 3.00000i 0.0286723 + 0.107006i
\(787\) −14.1285 8.15711i −0.503628 0.290770i 0.226583 0.973992i \(-0.427245\pi\)
−0.730210 + 0.683222i \(0.760578\pi\)
\(788\) 31.2514 + 18.0430i 1.11328 + 0.642755i
\(789\) 9.33975 9.33975i 0.332504 0.332504i
\(790\) 0.820863 2.16452i 0.0292050 0.0770103i
\(791\) 2.28719 0.0813230
\(792\) −3.67423 + 6.36396i −0.130558 + 0.226134i
\(793\) 26.1122i 0.927271i
\(794\) 28.3923 + 49.1769i 1.00761 + 1.74522i
\(795\) −13.6456 + 6.14162i −0.483961 + 0.217821i
\(796\) −3.97372 + 6.88269i −0.140845 + 0.243950i
\(797\) 13.7768 + 7.95404i 0.487999 + 0.281747i 0.723744 0.690068i \(-0.242420\pi\)
−0.235745 + 0.971815i \(0.575753\pi\)
\(798\) −2.12132 + 7.91688i −0.0750939 + 0.280254i
\(799\) 0.830127 + 1.43782i 0.0293678 + 0.0508665i
\(800\) 37.1769 + 7.58871i 1.31440 + 0.268301i
\(801\) 19.2058 11.0885i 0.678603 0.391791i
\(802\) 59.7487i 2.10980i
\(803\) 34.7733 20.0764i 1.22712 0.708480i
\(804\) −10.9019 + 10.9019i −0.384481 + 0.384481i
\(805\) −0.621320 3.82282i −0.0218987 0.134737i
\(806\) 6.46410 11.1962i 0.227688 0.394368i
\(807\) −28.7697 + 7.70882i −1.01274 + 0.271363i
\(808\) −1.13681 + 0.656339i −0.0399929 + 0.0230899i
\(809\) −37.1769 −1.30707 −0.653535 0.756896i \(-0.726715\pi\)
−0.653535 + 0.756896i \(0.726715\pi\)
\(810\) −38.3742 + 6.23694i −1.34833 + 0.219144i
\(811\) 43.5692 1.52992 0.764961 0.644076i \(-0.222758\pi\)
0.764961 + 0.644076i \(0.222758\pi\)
\(812\) −8.69333 + 5.01910i −0.305076 + 0.176136i
\(813\) −39.3441 + 10.5422i −1.37986 + 0.369732i
\(814\) −19.3923 + 33.5885i −0.679700 + 1.17727i
\(815\) 41.8017 6.79400i 1.46425 0.237983i
\(816\) 2.07180 2.07180i 0.0725274 0.0725274i
\(817\) −21.6293 + 12.4877i −0.756714 + 0.436889i
\(818\) 45.3292i 1.58490i
\(819\) 5.70577 3.29423i 0.199376 0.115110i
\(820\) −12.8038 + 10.4543i −0.447130 + 0.365080i
\(821\) 14.7224 + 25.5000i 0.513816 + 0.889956i 0.999872 + 0.0160280i \(0.00510208\pi\)
−0.486055 + 0.873928i \(0.661565\pi\)
\(822\) −16.0740 + 59.9889i −0.560645 + 2.09235i
\(823\) −1.76097 1.01669i −0.0613834 0.0354397i 0.468994 0.883201i \(-0.344617\pi\)
−0.530378 + 0.847762i \(0.677950\pi\)
\(824\) 2.36603 4.09808i 0.0824244 0.142763i
\(825\) 36.6633 + 18.3092i 1.27645 + 0.637444i
\(826\) −2.19615 3.80385i −0.0764139 0.132353i
\(827\) 11.5539i 0.401770i −0.979615 0.200885i \(-0.935618\pi\)
0.979615 0.200885i \(-0.0643818\pi\)
\(828\) 5.01910 8.69333i 0.174426 0.302114i
\(829\) −31.5885 −1.09711 −0.548556 0.836114i \(-0.684822\pi\)
−0.548556 + 0.836114i \(0.684822\pi\)
\(830\) 42.0754 + 15.9565i 1.46046 + 0.553857i
\(831\) 15.0000 15.0000i 0.520344 0.520344i
\(832\) −12.1595 7.02030i −0.421555 0.243385i
\(833\) 2.03339 + 1.17398i 0.0704527 + 0.0406759i
\(834\) −6.92820 25.8564i −0.239904 0.895334i
\(835\) 13.4853 35.5593i 0.466678 1.23058i
\(836\) 22.3923 0.774454
\(837\) −3.67423 13.7124i −0.127000 0.473971i
\(838\) 31.0112i 1.07126i
\(839\) 0.633975 + 1.09808i 0.0218872 + 0.0379098i 0.876762 0.480925i \(-0.159699\pi\)
−0.854874 + 0.518835i \(0.826366\pi\)
\(840\) −1.05063 + 1.45843i −0.0362503 + 0.0503207i
\(841\) −6.39230 + 11.0718i −0.220424 + 0.381786i
\(842\) −20.9730 12.1087i −0.722776 0.417295i
\(843\) 19.9241 + 19.9241i 0.686222 + 0.686222i
\(844\) −11.3660 19.6865i −0.391235 0.677638i
\(845\) 12.1244 9.89949i 0.417091 0.340553i
\(846\) 25.3923i 0.873005i
\(847\) 10.2141i 0.350959i
\(848\) −14.9372 + 8.62398i −0.512945 + 0.296149i
\(849\) 7.50000 + 2.00962i 0.257399 + 0.0689699i
\(850\) −2.73980 2.42713i −0.0939745 0.0832497i
\(851\) −4.09808 + 7.09808i −0.140480 + 0.243319i
\(852\) 2.95352 11.0227i 0.101186 0.377632i
\(853\) −30.2669 + 17.4746i −1.03632 + 0.598319i −0.918788 0.394750i \(-0.870831\pi\)
−0.117530 + 0.993069i \(0.537498\pi\)
\(854\) −18.4641 −0.631829
\(855\) −11.5911 14.1962i −0.396408 0.485498i
\(856\) −6.07180 −0.207530
\(857\) −7.67664 + 4.43211i −0.262229 + 0.151398i −0.625351 0.780344i \(-0.715044\pi\)
0.363122 + 0.931742i \(0.381711\pi\)
\(858\) −27.4249 27.4249i −0.936269 0.936269i
\(859\) −11.2224 + 19.4378i −0.382904 + 0.663210i −0.991476 0.130289i \(-0.958409\pi\)
0.608572 + 0.793499i \(0.291743\pi\)
\(860\) 34.9468 5.67987i 1.19168 0.193682i
\(861\) −1.71539 6.40192i −0.0584603 0.218177i
\(862\) 10.0382 5.79555i 0.341902 0.197397i
\(863\) 13.0697i 0.444898i 0.974944 + 0.222449i \(0.0714050\pi\)
−0.974944 + 0.222449i \(0.928595\pi\)
\(864\) −38.0885 + 10.2058i −1.29580 + 0.347207i
\(865\) 1.07180 + 1.31268i 0.0364422 + 0.0446324i
\(866\) −29.4904 51.0788i −1.00212 1.73573i
\(867\) 28.2013 7.55652i 0.957767 0.256633i
\(868\) 3.67423 + 2.12132i 0.124712 + 0.0720023i
\(869\) 1.26795 2.19615i 0.0430122 0.0744994i
\(870\) 4.86108 48.1197i 0.164806 1.63141i
\(871\) 6.29423 + 10.9019i 0.213272 + 0.369398i
\(872\) 2.41233i 0.0816916i
\(873\) 15.4176 26.7042i 0.521808 0.903799i
\(874\) 10.1962 0.344890
\(875\) 8.47241 + 5.35716i 0.286420 + 0.181105i
\(876\) 24.5885 + 6.58846i 0.830767 + 0.222603i
\(877\) −4.09034 2.36156i −0.138121 0.0797441i 0.429347 0.903139i \(-0.358744\pi\)
−0.567468 + 0.823395i \(0.692077\pi\)
\(878\) −15.5935 9.00292i −0.526256 0.303834i
\(879\) 14.8301 + 3.97372i 0.500208 + 0.134030i
\(880\) 44.1662 + 16.7494i 1.48884 + 0.564621i
\(881\) −8.41154 −0.283392 −0.141696 0.989910i \(-0.545256\pi\)
−0.141696 + 0.989910i \(0.545256\pi\)
\(882\) −17.9551 31.0991i −0.604579 1.04716i
\(883\) 17.6913i 0.595359i 0.954666 + 0.297679i \(0.0962126\pi\)
−0.954666 + 0.297679i \(0.903787\pi\)
\(884\) 0.803848 + 1.39230i 0.0270363 + 0.0468283i
\(885\) 9.77176 + 0.987148i 0.328474 + 0.0331826i
\(886\) −13.4282 + 23.2583i −0.451129 + 0.781379i
\(887\) −24.4070 14.0914i −0.819506 0.473142i 0.0307403 0.999527i \(-0.490214\pi\)
−0.850246 + 0.526386i \(0.823547\pi\)
\(888\) 3.67423 0.984508i 0.123299 0.0330379i
\(889\) −2.08846 3.61731i −0.0700446 0.121321i
\(890\) −20.1962 24.7351i −0.676977 0.829124i
\(891\) −42.5885 −1.42677
\(892\) 28.9778i 0.970248i
\(893\) 10.3664 5.98502i 0.346897 0.200281i
\(894\) 6.69615 + 24.9904i 0.223953 + 0.835803i
\(895\) −8.82036 54.2694i −0.294832 1.81402i
\(896\) −1.83975 + 3.18653i −0.0614616 + 0.106455i
\(897\) −5.79555 5.79555i −0.193508 0.193508i
\(898\) −20.0764 + 11.5911i −0.669958 + 0.386800i
\(899\) 17.6603 0.589002
\(900\) 8.22792 + 24.6435i 0.274264 + 0.821449i
\(901\) 1.46410 0.0487763
\(902\) −33.7888 + 19.5080i −1.12504 + 0.649545i
\(903\) −3.67423 + 13.7124i −0.122271 + 0.456321i
\(904\) −0.660254 + 1.14359i −0.0219597 + 0.0380354i
\(905\) 3.03624 + 18.6812i 0.100928 + 0.620983i
\(906\) −73.0070 19.5622i −2.42550 0.649910i
\(907\) 43.0506 24.8553i 1.42947 0.825305i 0.432392 0.901686i \(-0.357670\pi\)
0.997079 + 0.0763808i \(0.0243365\pi\)
\(908\) 3.28169i 0.108907i
\(909\) −6.58846 3.80385i −0.218525 0.126166i
\(910\) −6.00000 7.34847i −0.198898 0.243599i
\(911\) −11.0718 19.1769i −0.366825 0.635360i 0.622242 0.782825i \(-0.286222\pi\)
−0.989067 + 0.147465i \(0.952889\pi\)
\(912\) −14.9372 14.9372i −0.494619 0.494619i
\(913\) 42.6902 + 24.6472i 1.41284 + 0.815703i
\(914\) −33.4186 + 57.8827i −1.10539 + 1.91459i
\(915\) 24.1327 33.4997i 0.797803 1.10746i
\(916\) −17.2583 29.8923i −0.570231 0.987670i
\(917\) 0.832204i 0.0274818i
\(918\) 3.67423 + 0.984508i 0.121268 + 0.0324936i
\(919\) 15.1769 0.500640 0.250320 0.968163i \(-0.419464\pi\)
0.250320 + 0.968163i \(0.419464\pi\)
\(920\) 2.09077 + 0.792893i 0.0689307 + 0.0261409i
\(921\) 11.5981 + 43.2846i 0.382170 + 1.42628i
\(922\) 31.3071 + 18.0752i 1.03105 + 0.595275i
\(923\) −8.06918 4.65874i −0.265600 0.153344i
\(924\) 9.00000 9.00000i 0.296078 0.296078i
\(925\) −6.71807 20.1213i −0.220889 0.661585i
\(926\) 0.339746 0.0111647
\(927\) 27.4249 0.900751
\(928\) 49.0542i 1.61028i
\(929\) 1.73205 + 3.00000i 0.0568267 + 0.0984268i 0.893039 0.449979i \(-0.148568\pi\)
−0.836213 + 0.548405i \(0.815235\pi\)
\(930\) −18.6403 + 8.38961i −0.611239 + 0.275106i
\(931\) 8.46410 14.6603i 0.277400 0.480470i
\(932\) −10.6066 6.12372i −0.347431 0.200589i
\(933\) −12.5756 + 46.9328i −0.411707 + 1.53651i
\(934\) 5.56218 + 9.63397i 0.182000 + 0.315233i
\(935\) −2.53590 3.10583i −0.0829327 0.101571i
\(936\) 3.80385i 0.124333i
\(937\) 13.8647i 0.452941i 0.974018 + 0.226471i \(0.0727187\pi\)
−0.974018 + 0.226471i \(0.927281\pi\)
\(938\) −7.70882 + 4.45069i −0.251702 + 0.145320i
\(939\) −6.80385 + 6.80385i −0.222035 + 0.222035i
\(940\) −16.7491 + 2.72222i −0.546295 + 0.0887889i
\(941\) 4.16025 7.20577i 0.135620 0.234901i −0.790214 0.612831i \(-0.790031\pi\)
0.925834 + 0.377930i \(0.123364\pi\)
\(942\) 69.1306 18.5235i 2.25240 0.603527i
\(943\) −7.14042 + 4.12252i −0.232524 + 0.134248i
\(944\) 11.3205 0.368451
\(945\) −10.3645 1.04703i −0.337158 0.0340598i
\(946\) 83.5692 2.71707
\(947\) 2.00120 1.15539i 0.0650303 0.0375453i −0.467132 0.884187i \(-0.654713\pi\)
0.532163 + 0.846642i \(0.321379\pi\)
\(948\) 1.55291 0.416102i 0.0504363 0.0135144i
\(949\) 10.3923 18.0000i 0.337348 0.584305i
\(950\) −17.4990 + 19.7533i −0.567743 + 0.640883i
\(951\) −43.0526 + 43.0526i −1.39607 + 1.39607i
\(952\) 0.152304 0.0879327i 0.00493620 0.00284992i
\(953\) 37.0197i 1.19919i 0.800305 + 0.599594i \(0.204671\pi\)
−0.800305 + 0.599594i \(0.795329\pi\)
\(954\) −19.3923 11.1962i −0.627849 0.362489i
\(955\) 0.588457 0.480473i 0.0190420 0.0155478i
\(956\) −11.1962 19.3923i −0.362109 0.627192i
\(957\) 13.7124 51.1755i 0.443260 1.65427i
\(958\) −53.2968 30.7709i −1.72194 0.994163i
\(959\) −8.32051 + 14.4115i −0.268683 + 0.465373i
\(960\) 9.11149 + 20.2442i 0.294072 + 0.653378i
\(961\) 11.7679 + 20.3827i 0.379611 + 0.657506i
\(962\) 20.0764i 0.647289i
\(963\) −17.5947 30.4749i −0.566982 0.982041i
\(964\) −10.8564 −0.349661
\(965\) −16.4388 + 43.3474i −0.529185 + 1.39540i
\(966\) 4.09808 4.09808i 0.131853 0.131853i
\(967\) 30.0588 + 17.3545i 0.966627 + 0.558082i 0.898206 0.439574i \(-0.144871\pi\)
0.0684208 + 0.997657i \(0.478204\pi\)
\(968\) 5.10703 + 2.94855i 0.164146 + 0.0947698i
\(969\) 0.464102 + 1.73205i 0.0149091 + 0.0556415i
\(970\) −41.5152 15.7440i −1.33297 0.505510i
\(971\) 27.8038 0.892268 0.446134 0.894966i \(-0.352800\pi\)
0.446134 + 0.894966i \(0.352800\pi\)
\(972\) −19.0919 19.0919i −0.612372 0.612372i
\(973\) 7.17260i 0.229943i
\(974\) 1.09808 + 1.90192i 0.0351846 + 0.0609416i
\(975\) 21.1745 1.28138i 0.678126 0.0410369i
\(976\) 23.7942 41.2128i 0.761635 1.31919i
\(977\) 13.4722 + 7.77817i 0.431014 + 0.248846i 0.699778 0.714360i \(-0.253282\pi\)
−0.268765 + 0.963206i \(0.586615\pi\)
\(978\) 44.8115 + 44.8115i 1.43291 + 1.43291i
\(979\) −17.4904 30.2942i −0.558995 0.968208i
\(980\) −18.5885 + 15.1774i −0.593786 + 0.484825i
\(981\) 12.1077 6.99038i 0.386569 0.223186i
\(982\) 41.9459i 1.33855i
\(983\) −31.0669 + 17.9365i −0.990881 + 0.572085i −0.905537 0.424266i \(-0.860532\pi\)
−0.0853431 + 0.996352i \(0.527199\pi\)
\(984\) 3.69615 + 0.990381i 0.117829 + 0.0315722i
\(985\) −45.9834 + 7.47366i −1.46515 + 0.238131i
\(986\) −2.36603 + 4.09808i −0.0753496 + 0.130509i
\(987\) 1.76097 6.57201i 0.0560521 0.209189i
\(988\) 10.0382 5.79555i 0.319358 0.184381i
\(989\) 17.6603 0.561563
\(990\) 9.83783 + 60.5296i 0.312667 + 1.92376i
\(991\) 25.0718 0.796432 0.398216 0.917292i \(-0.369629\pi\)
0.398216 + 0.917292i \(0.369629\pi\)
\(992\) −17.9551 + 10.3664i −0.570074 + 0.329132i
\(993\) −15.1774 15.1774i −0.481641 0.481641i
\(994\) 3.29423 5.70577i 0.104487 0.180976i
\(995\) −1.64597 10.1272i −0.0521807 0.321054i
\(996\) 8.08846 + 30.1865i 0.256293 + 0.956497i
\(997\) −13.1440 + 7.58871i −0.416275 + 0.240337i −0.693483 0.720473i \(-0.743925\pi\)
0.277207 + 0.960810i \(0.410591\pi\)
\(998\) 7.45001i 0.235826i
\(999\) 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.4.1 8
3.2 odd 2 135.2.j.a.64.4 8
4.3 odd 2 720.2.by.d.49.1 8
5.2 odd 4 225.2.e.d.76.1 8
5.3 odd 4 225.2.e.d.76.4 8
5.4 even 2 inner 45.2.j.a.4.4 yes 8
9.2 odd 6 135.2.j.a.19.1 8
9.4 even 3 405.2.b.d.244.1 4
9.5 odd 6 405.2.b.c.244.4 4
9.7 even 3 inner 45.2.j.a.34.4 yes 8
12.11 even 2 2160.2.by.c.1009.2 8
15.2 even 4 675.2.e.d.226.4 8
15.8 even 4 675.2.e.d.226.1 8
15.14 odd 2 135.2.j.a.64.1 8
20.19 odd 2 720.2.by.d.49.4 8
36.7 odd 6 720.2.by.d.529.4 8
36.11 even 6 2160.2.by.c.289.4 8
45.2 even 12 675.2.e.d.451.4 8
45.4 even 6 405.2.b.d.244.4 4
45.7 odd 12 225.2.e.d.151.1 8
45.13 odd 12 2025.2.a.t.1.1 4
45.14 odd 6 405.2.b.c.244.1 4
45.22 odd 12 2025.2.a.t.1.4 4
45.23 even 12 2025.2.a.r.1.4 4
45.29 odd 6 135.2.j.a.19.4 8
45.32 even 12 2025.2.a.r.1.1 4
45.34 even 6 inner 45.2.j.a.34.1 yes 8
45.38 even 12 675.2.e.d.451.1 8
45.43 odd 12 225.2.e.d.151.4 8
60.59 even 2 2160.2.by.c.1009.4 8
180.79 odd 6 720.2.by.d.529.1 8
180.119 even 6 2160.2.by.c.289.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.2.j.a.4.1 8 1.1 even 1 trivial
45.2.j.a.4.4 yes 8 5.4 even 2 inner
45.2.j.a.34.1 yes 8 45.34 even 6 inner
45.2.j.a.34.4 yes 8 9.7 even 3 inner
135.2.j.a.19.1 8 9.2 odd 6
135.2.j.a.19.4 8 45.29 odd 6
135.2.j.a.64.1 8 15.14 odd 2
135.2.j.a.64.4 8 3.2 odd 2
225.2.e.d.76.1 8 5.2 odd 4
225.2.e.d.76.4 8 5.3 odd 4
225.2.e.d.151.1 8 45.7 odd 12
225.2.e.d.151.4 8 45.43 odd 12
405.2.b.c.244.1 4 45.14 odd 6
405.2.b.c.244.4 4 9.5 odd 6
405.2.b.d.244.1 4 9.4 even 3
405.2.b.d.244.4 4 45.4 even 6
675.2.e.d.226.1 8 15.8 even 4
675.2.e.d.226.4 8 15.2 even 4
675.2.e.d.451.1 8 45.38 even 12
675.2.e.d.451.4 8 45.2 even 12
720.2.by.d.49.1 8 4.3 odd 2
720.2.by.d.49.4 8 20.19 odd 2
720.2.by.d.529.1 8 180.79 odd 6
720.2.by.d.529.4 8 36.7 odd 6
2025.2.a.r.1.1 4 45.32 even 12
2025.2.a.r.1.4 4 45.23 even 12
2025.2.a.t.1.1 4 45.13 odd 12
2025.2.a.t.1.4 4 45.22 odd 12
2160.2.by.c.289.2 8 180.119 even 6
2160.2.by.c.289.4 8 36.11 even 6
2160.2.by.c.1009.2 8 12.11 even 2
2160.2.by.c.1009.4 8 60.59 even 2