Properties

Label 80.2.j.b.67.2
Level $80$
Weight $2$
Character 80.67
Analytic conductor $0.639$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [80,2,Mod(43,80)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(80, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("80.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.j (of order \(4\), 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: \(0.638803216170\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 67.2
Root \(1.41323 - 0.0526497i\) of defining polynomial
Character \(\chi\) \(=\) 80.67
Dual form 80.2.j.b.43.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31641 - 0.516777i) q^{2} -1.28110i q^{3} +(1.46588 + 1.36058i) q^{4} +(-0.841703 - 2.07160i) q^{5} +(-0.662041 + 1.68645i) q^{6} +(-1.13975 - 1.13975i) q^{7} +(-1.22659 - 2.54862i) q^{8} +1.35879 q^{9} +O(q^{10})\) \(q+(-1.31641 - 0.516777i) q^{2} -1.28110i q^{3} +(1.46588 + 1.36058i) q^{4} +(-0.841703 - 2.07160i) q^{5} +(-0.662041 + 1.68645i) q^{6} +(-1.13975 - 1.13975i) q^{7} +(-1.22659 - 2.54862i) q^{8} +1.35879 q^{9} +(0.0374711 + 3.16206i) q^{10} +(-2.32204 - 2.32204i) q^{11} +(1.74304 - 1.87794i) q^{12} +1.36502 q^{13} +(0.911384 + 2.08938i) q^{14} +(-2.65392 + 1.07830i) q^{15} +(0.297625 + 3.98891i) q^{16} +(5.25380 + 5.25380i) q^{17} +(-1.78873 - 0.702192i) q^{18} +(3.69752 + 3.69752i) q^{19} +(1.58475 - 4.18193i) q^{20} +(-1.46013 + 1.46013i) q^{21} +(1.85678 + 4.25673i) q^{22} +(-0.911118 + 0.911118i) q^{23} +(-3.26503 + 1.57138i) q^{24} +(-3.58307 + 3.48735i) q^{25} +(-1.79693 - 0.705412i) q^{26} -5.58403i q^{27} +(-0.120015 - 3.22146i) q^{28} +(2.37343 - 2.37343i) q^{29} +(4.05090 - 0.0480041i) q^{30} -0.242577i q^{31} +(1.66958 - 5.40486i) q^{32} +(-2.97475 + 2.97475i) q^{33} +(-4.20112 - 9.63121i) q^{34} +(-1.40178 + 3.32044i) q^{35} +(1.99183 + 1.84875i) q^{36} -3.34494 q^{37} +(-2.95666 - 6.77825i) q^{38} -1.74872i q^{39} +(-4.24731 + 4.68619i) q^{40} -2.66956i q^{41} +(2.67669 - 1.16757i) q^{42} +9.04874 q^{43} +(-0.244509 - 6.56316i) q^{44} +(-1.14370 - 2.81488i) q^{45} +(1.67025 - 0.728562i) q^{46} +(-7.87820 + 7.87820i) q^{47} +(5.11018 - 0.381287i) q^{48} -4.40194i q^{49} +(6.51898 - 2.73914i) q^{50} +(6.73063 - 6.73063i) q^{51} +(2.00096 + 1.85723i) q^{52} +5.80113i q^{53} +(-2.88570 + 7.35089i) q^{54} +(-2.85587 + 6.76480i) q^{55} +(-1.50679 + 4.30279i) q^{56} +(4.73688 - 4.73688i) q^{57} +(-4.35095 + 1.89788i) q^{58} +(-5.91474 + 5.91474i) q^{59} +(-5.35746 - 2.03022i) q^{60} +(-6.67404 - 6.67404i) q^{61} +(-0.125358 + 0.319332i) q^{62} +(-1.54868 - 1.54868i) q^{63} +(-4.99096 + 6.25222i) q^{64} +(-1.14894 - 2.82778i) q^{65} +(5.45328 - 2.37872i) q^{66} -4.54673 q^{67} +(0.553222 + 14.8497i) q^{68} +(1.16723 + 1.16723i) q^{69} +(3.56124 - 3.64666i) q^{70} +15.4389 q^{71} +(-1.66668 - 3.46305i) q^{72} +(1.49307 + 1.49307i) q^{73} +(4.40332 + 1.72859i) q^{74} +(4.46763 + 4.59026i) q^{75} +(0.389347 + 10.4509i) q^{76} +5.29308i q^{77} +(-0.903701 + 2.30204i) q^{78} +10.3024 q^{79} +(8.01293 - 3.97404i) q^{80} -3.07731 q^{81} +(-1.37957 + 3.51424i) q^{82} -3.26589i q^{83} +(-4.12701 + 0.153751i) q^{84} +(6.46165 - 15.3059i) q^{85} +(-11.9119 - 4.67618i) q^{86} +(-3.04060 - 3.04060i) q^{87} +(-3.06981 + 8.76618i) q^{88} -9.77206 q^{89} +(0.0509154 + 4.29657i) q^{90} +(-1.55578 - 1.55578i) q^{91} +(-2.57524 + 0.0959403i) q^{92} -0.310765 q^{93} +(14.4422 - 6.29969i) q^{94} +(4.54758 - 10.7720i) q^{95} +(-6.92415 - 2.13889i) q^{96} +(-1.63587 - 1.63587i) q^{97} +(-2.27482 + 5.79477i) q^{98} +(-3.15516 - 3.15516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31641 0.516777i −0.930844 0.365417i
\(3\) 1.28110i 0.739642i −0.929103 0.369821i \(-0.879419\pi\)
0.929103 0.369821i \(-0.120581\pi\)
\(4\) 1.46588 + 1.36058i 0.732941 + 0.680292i
\(5\) −0.841703 2.07160i −0.376421 0.926449i
\(6\) −0.662041 + 1.68645i −0.270277 + 0.688491i
\(7\) −1.13975 1.13975i −0.430785 0.430785i 0.458111 0.888895i \(-0.348526\pi\)
−0.888895 + 0.458111i \(0.848526\pi\)
\(8\) −1.22659 2.54862i −0.433664 0.901074i
\(9\) 1.35879 0.452930
\(10\) 0.0374711 + 3.16206i 0.0118494 + 0.999930i
\(11\) −2.32204 2.32204i −0.700120 0.700120i 0.264316 0.964436i \(-0.414854\pi\)
−0.964436 + 0.264316i \(0.914854\pi\)
\(12\) 1.74304 1.87794i 0.503172 0.542114i
\(13\) 1.36502 0.378589 0.189294 0.981920i \(-0.439380\pi\)
0.189294 + 0.981920i \(0.439380\pi\)
\(14\) 0.911384 + 2.08938i 0.243578 + 0.558409i
\(15\) −2.65392 + 1.07830i −0.685240 + 0.278416i
\(16\) 0.297625 + 3.98891i 0.0744064 + 0.997228i
\(17\) 5.25380 + 5.25380i 1.27423 + 1.27423i 0.943845 + 0.330389i \(0.107180\pi\)
0.330389 + 0.943845i \(0.392820\pi\)
\(18\) −1.78873 0.702192i −0.421608 0.165508i
\(19\) 3.69752 + 3.69752i 0.848269 + 0.848269i 0.989917 0.141648i \(-0.0452403\pi\)
−0.141648 + 0.989917i \(0.545240\pi\)
\(20\) 1.58475 4.18193i 0.354361 0.935109i
\(21\) −1.46013 + 1.46013i −0.318626 + 0.318626i
\(22\) 1.85678 + 4.25673i 0.395867 + 0.907538i
\(23\) −0.911118 + 0.911118i −0.189981 + 0.189981i −0.795688 0.605707i \(-0.792890\pi\)
0.605707 + 0.795688i \(0.292890\pi\)
\(24\) −3.26503 + 1.57138i −0.666472 + 0.320756i
\(25\) −3.58307 + 3.48735i −0.716615 + 0.697469i
\(26\) −1.79693 0.705412i −0.352407 0.138343i
\(27\) 5.58403i 1.07465i
\(28\) −0.120015 3.22146i −0.0226807 0.608799i
\(29\) 2.37343 2.37343i 0.440736 0.440736i −0.451524 0.892259i \(-0.649119\pi\)
0.892259 + 0.451524i \(0.149119\pi\)
\(30\) 4.05090 0.0480041i 0.739590 0.00876431i
\(31\) 0.242577i 0.0435681i −0.999763 0.0217841i \(-0.993065\pi\)
0.999763 0.0217841i \(-0.00693463\pi\)
\(32\) 1.66958 5.40486i 0.295143 0.955453i
\(33\) −2.97475 + 2.97475i −0.517838 + 0.517838i
\(34\) −4.20112 9.63121i −0.720487 1.65174i
\(35\) −1.40178 + 3.32044i −0.236944 + 0.561256i
\(36\) 1.99183 + 1.84875i 0.331971 + 0.308125i
\(37\) −3.34494 −0.549905 −0.274953 0.961458i \(-0.588662\pi\)
−0.274953 + 0.961458i \(0.588662\pi\)
\(38\) −2.95666 6.77825i −0.479634 1.09958i
\(39\) 1.74872i 0.280020i
\(40\) −4.24731 + 4.68619i −0.671559 + 0.740951i
\(41\) 2.66956i 0.416915i −0.978031 0.208457i \(-0.933156\pi\)
0.978031 0.208457i \(-0.0668442\pi\)
\(42\) 2.67669 1.16757i 0.413023 0.180160i
\(43\) 9.04874 1.37992 0.689960 0.723847i \(-0.257628\pi\)
0.689960 + 0.723847i \(0.257628\pi\)
\(44\) −0.244509 6.56316i −0.0368611 0.989433i
\(45\) −1.14370 2.81488i −0.170492 0.419617i
\(46\) 1.67025 0.728562i 0.246265 0.107421i
\(47\) −7.87820 + 7.87820i −1.14915 + 1.14915i −0.162435 + 0.986719i \(0.551935\pi\)
−0.986719 + 0.162435i \(0.948065\pi\)
\(48\) 5.11018 0.381287i 0.737591 0.0550340i
\(49\) 4.40194i 0.628849i
\(50\) 6.51898 2.73914i 0.921923 0.387372i
\(51\) 6.73063 6.73063i 0.942476 0.942476i
\(52\) 2.00096 + 1.85723i 0.277483 + 0.257551i
\(53\) 5.80113i 0.796846i 0.917202 + 0.398423i \(0.130442\pi\)
−0.917202 + 0.398423i \(0.869558\pi\)
\(54\) −2.88570 + 7.35089i −0.392694 + 1.00033i
\(55\) −2.85587 + 6.76480i −0.385086 + 0.912165i
\(56\) −1.50679 + 4.30279i −0.201353 + 0.574985i
\(57\) 4.73688 4.73688i 0.627415 0.627415i
\(58\) −4.35095 + 1.89788i −0.571308 + 0.249204i
\(59\) −5.91474 + 5.91474i −0.770033 + 0.770033i −0.978112 0.208079i \(-0.933279\pi\)
0.208079 + 0.978112i \(0.433279\pi\)
\(60\) −5.35746 2.03022i −0.691645 0.262100i
\(61\) −6.67404 6.67404i −0.854523 0.854523i 0.136163 0.990686i \(-0.456523\pi\)
−0.990686 + 0.136163i \(0.956523\pi\)
\(62\) −0.125358 + 0.319332i −0.0159205 + 0.0405551i
\(63\) −1.54868 1.54868i −0.195116 0.195116i
\(64\) −4.99096 + 6.25222i −0.623870 + 0.781528i
\(65\) −1.14894 2.82778i −0.142509 0.350743i
\(66\) 5.45328 2.37872i 0.671253 0.292800i
\(67\) −4.54673 −0.555471 −0.277736 0.960658i \(-0.589584\pi\)
−0.277736 + 0.960658i \(0.589584\pi\)
\(68\) 0.553222 + 14.8497i 0.0670881 + 1.80079i
\(69\) 1.16723 + 1.16723i 0.140518 + 0.140518i
\(70\) 3.56124 3.64666i 0.425650 0.435859i
\(71\) 15.4389 1.83226 0.916128 0.400885i \(-0.131297\pi\)
0.916128 + 0.400885i \(0.131297\pi\)
\(72\) −1.66668 3.46305i −0.196420 0.408124i
\(73\) 1.49307 + 1.49307i 0.174750 + 0.174750i 0.789063 0.614313i \(-0.210567\pi\)
−0.614313 + 0.789063i \(0.710567\pi\)
\(74\) 4.40332 + 1.72859i 0.511876 + 0.200944i
\(75\) 4.46763 + 4.59026i 0.515877 + 0.530038i
\(76\) 0.389347 + 10.4509i 0.0446611 + 1.19880i
\(77\) 5.29308i 0.603202i
\(78\) −0.903701 + 2.30204i −0.102324 + 0.260655i
\(79\) 10.3024 1.15911 0.579556 0.814932i \(-0.303226\pi\)
0.579556 + 0.814932i \(0.303226\pi\)
\(80\) 8.01293 3.97404i 0.895873 0.444311i
\(81\) −3.07731 −0.341924
\(82\) −1.37957 + 3.51424i −0.152348 + 0.388083i
\(83\) 3.26589i 0.358478i −0.983806 0.179239i \(-0.942636\pi\)
0.983806 0.179239i \(-0.0573636\pi\)
\(84\) −4.12701 + 0.153751i −0.450293 + 0.0167756i
\(85\) 6.46165 15.3059i 0.700864 1.66016i
\(86\) −11.9119 4.67618i −1.28449 0.504246i
\(87\) −3.04060 3.04060i −0.325986 0.325986i
\(88\) −3.06981 + 8.76618i −0.327243 + 0.934477i
\(89\) −9.77206 −1.03584 −0.517918 0.855430i \(-0.673293\pi\)
−0.517918 + 0.855430i \(0.673293\pi\)
\(90\) 0.0509154 + 4.29657i 0.00536695 + 0.452899i
\(91\) −1.55578 1.55578i −0.163090 0.163090i
\(92\) −2.57524 + 0.0959403i −0.268488 + 0.0100025i
\(93\) −0.310765 −0.0322248
\(94\) 14.4422 6.29969i 1.48960 0.649763i
\(95\) 4.54758 10.7720i 0.466571 1.10518i
\(96\) −6.92415 2.13889i −0.706693 0.218300i
\(97\) −1.63587 1.63587i −0.166097 0.166097i 0.619164 0.785262i \(-0.287472\pi\)
−0.785262 + 0.619164i \(0.787472\pi\)
\(98\) −2.27482 + 5.79477i −0.229792 + 0.585360i
\(99\) −3.15516 3.15516i −0.317106 0.317106i
\(100\) −9.99719 + 0.236971i −0.999719 + 0.0236971i
\(101\) −6.63953 + 6.63953i −0.660658 + 0.660658i −0.955535 0.294877i \(-0.904721\pi\)
0.294877 + 0.955535i \(0.404721\pi\)
\(102\) −12.3385 + 5.38205i −1.22170 + 0.532902i
\(103\) 1.62219 1.62219i 0.159839 0.159839i −0.622656 0.782496i \(-0.713946\pi\)
0.782496 + 0.622656i \(0.213946\pi\)
\(104\) −1.67432 3.47893i −0.164180 0.341137i
\(105\) 4.25380 + 1.79581i 0.415129 + 0.175253i
\(106\) 2.99789 7.63667i 0.291181 0.741739i
\(107\) 3.65206i 0.353058i 0.984295 + 0.176529i \(0.0564869\pi\)
−0.984295 + 0.176529i \(0.943513\pi\)
\(108\) 7.59754 8.18554i 0.731074 0.787654i
\(109\) −5.20757 + 5.20757i −0.498795 + 0.498795i −0.911063 0.412268i \(-0.864737\pi\)
0.412268 + 0.911063i \(0.364737\pi\)
\(110\) 7.25540 7.42941i 0.691775 0.708367i
\(111\) 4.28519i 0.406733i
\(112\) 4.20714 4.88558i 0.397537 0.461644i
\(113\) −4.27905 + 4.27905i −0.402539 + 0.402539i −0.879127 0.476588i \(-0.841873\pi\)
0.476588 + 0.879127i \(0.341873\pi\)
\(114\) −8.68359 + 3.78777i −0.813293 + 0.354757i
\(115\) 2.65437 + 1.12058i 0.247521 + 0.104495i
\(116\) 6.70843 0.249921i 0.622862 0.0232046i
\(117\) 1.85478 0.171474
\(118\) 10.8428 4.72963i 0.998164 0.435398i
\(119\) 11.9760i 1.09784i
\(120\) 6.00346 + 5.44122i 0.548038 + 0.496713i
\(121\) 0.216302i 0.0196639i
\(122\) 5.33680 + 12.2348i 0.483171 + 1.10768i
\(123\) −3.41996 −0.308367
\(124\) 0.330046 0.355590i 0.0296390 0.0319329i
\(125\) 10.2403 + 4.48739i 0.915918 + 0.401365i
\(126\) 1.23838 + 2.83903i 0.110324 + 0.252921i
\(127\) 7.29257 7.29257i 0.647111 0.647111i −0.305183 0.952294i \(-0.598718\pi\)
0.952294 + 0.305183i \(0.0987175\pi\)
\(128\) 9.80117 5.65129i 0.866309 0.499508i
\(129\) 11.5923i 1.02065i
\(130\) 0.0511488 + 4.31627i 0.00448605 + 0.378562i
\(131\) −11.9793 + 11.9793i −1.04664 + 1.04664i −0.0477778 + 0.998858i \(0.515214\pi\)
−0.998858 + 0.0477778i \(0.984786\pi\)
\(132\) −8.40804 + 0.313240i −0.731826 + 0.0272640i
\(133\) 8.42848i 0.730842i
\(134\) 5.98537 + 2.34965i 0.517057 + 0.202978i
\(135\) −11.5679 + 4.70010i −0.995606 + 0.404520i
\(136\) 6.94571 19.8342i 0.595590 1.70077i
\(137\) 4.92762 4.92762i 0.420995 0.420995i −0.464551 0.885546i \(-0.653784\pi\)
0.885546 + 0.464551i \(0.153784\pi\)
\(138\) −0.933359 2.13975i −0.0794528 0.182148i
\(139\) −10.3015 + 10.3015i −0.873761 + 0.873761i −0.992880 0.119119i \(-0.961993\pi\)
0.119119 + 0.992880i \(0.461993\pi\)
\(140\) −6.57257 + 2.96014i −0.555484 + 0.250177i
\(141\) 10.0927 + 10.0927i 0.849962 + 0.849962i
\(142\) −20.3239 7.97845i −1.70555 0.669537i
\(143\) −3.16963 3.16963i −0.265058 0.265058i
\(144\) 0.404411 + 5.42010i 0.0337009 + 0.451675i
\(145\) −6.91454 2.91909i −0.574221 0.242417i
\(146\) −1.19391 2.73707i −0.0988086 0.226522i
\(147\) −5.63931 −0.465123
\(148\) −4.90329 4.55107i −0.403048 0.374096i
\(149\) 15.2040 + 15.2040i 1.24556 + 1.24556i 0.957662 + 0.287896i \(0.0929557\pi\)
0.287896 + 0.957662i \(0.407044\pi\)
\(150\) −3.50910 8.35145i −0.286517 0.681893i
\(151\) −10.7055 −0.871204 −0.435602 0.900139i \(-0.643464\pi\)
−0.435602 + 0.900139i \(0.643464\pi\)
\(152\) 4.88825 13.9589i 0.396489 1.13222i
\(153\) 7.13882 + 7.13882i 0.577139 + 0.577139i
\(154\) 2.73534 6.96787i 0.220420 0.561487i
\(155\) −0.502523 + 0.204178i −0.0403636 + 0.0164000i
\(156\) 2.37929 2.56343i 0.190495 0.205238i
\(157\) 2.34588i 0.187222i 0.995609 + 0.0936108i \(0.0298409\pi\)
−0.995609 + 0.0936108i \(0.970159\pi\)
\(158\) −13.5622 5.32405i −1.07895 0.423559i
\(159\) 7.43180 0.589380
\(160\) −12.6020 + 1.09058i −0.996276 + 0.0862177i
\(161\) 2.07689 0.163682
\(162\) 4.05101 + 1.59028i 0.318278 + 0.124945i
\(163\) 2.73625i 0.214319i 0.994242 + 0.107160i \(0.0341756\pi\)
−0.994242 + 0.107160i \(0.965824\pi\)
\(164\) 3.63215 3.91326i 0.283624 0.305574i
\(165\) 8.66636 + 3.65865i 0.674675 + 0.284825i
\(166\) −1.68774 + 4.29926i −0.130994 + 0.333687i
\(167\) 10.1328 + 10.1328i 0.784097 + 0.784097i 0.980519 0.196423i \(-0.0629325\pi\)
−0.196423 + 0.980519i \(0.562932\pi\)
\(168\) 5.51230 + 1.93034i 0.425283 + 0.148929i
\(169\) −11.1367 −0.856670
\(170\) −16.4159 + 16.8097i −1.25905 + 1.28924i
\(171\) 5.02415 + 5.02415i 0.384207 + 0.384207i
\(172\) 13.2644 + 12.3116i 1.01140 + 0.938748i
\(173\) −8.79590 −0.668740 −0.334370 0.942442i \(-0.608523\pi\)
−0.334370 + 0.942442i \(0.608523\pi\)
\(174\) 2.43137 + 5.57399i 0.184322 + 0.422563i
\(175\) 8.05851 + 0.109105i 0.609166 + 0.00824753i
\(176\) 8.57130 9.95349i 0.646086 0.750273i
\(177\) 7.57735 + 7.57735i 0.569549 + 0.569549i
\(178\) 12.8641 + 5.04998i 0.964202 + 0.378512i
\(179\) −6.62071 6.62071i −0.494855 0.494855i 0.414977 0.909832i \(-0.363790\pi\)
−0.909832 + 0.414977i \(0.863790\pi\)
\(180\) 2.15335 5.68237i 0.160501 0.423539i
\(181\) −5.84339 + 5.84339i −0.434336 + 0.434336i −0.890100 0.455765i \(-0.849366\pi\)
0.455765 + 0.890100i \(0.349366\pi\)
\(182\) 1.24406 + 2.85204i 0.0922157 + 0.211408i
\(183\) −8.55009 + 8.55009i −0.632041 + 0.632041i
\(184\) 3.43966 + 1.20453i 0.253575 + 0.0887992i
\(185\) 2.81545 + 6.92939i 0.206996 + 0.509459i
\(186\) 0.409095 + 0.160596i 0.0299963 + 0.0117755i
\(187\) 24.3990i 1.78423i
\(188\) −22.2675 + 0.829571i −1.62402 + 0.0605027i
\(189\) −6.36440 + 6.36440i −0.462942 + 0.462942i
\(190\) −11.5532 + 11.8303i −0.838158 + 0.858260i
\(191\) 1.83906i 0.133070i −0.997784 0.0665349i \(-0.978806\pi\)
0.997784 0.0665349i \(-0.0211944\pi\)
\(192\) 8.00970 + 6.39391i 0.578050 + 0.461440i
\(193\) 6.18343 6.18343i 0.445093 0.445093i −0.448626 0.893719i \(-0.648087\pi\)
0.893719 + 0.448626i \(0.148087\pi\)
\(194\) 1.30810 + 2.99886i 0.0939160 + 0.215305i
\(195\) −3.62266 + 1.47191i −0.259424 + 0.105405i
\(196\) 5.98921 6.45273i 0.427801 0.460910i
\(197\) 5.55669 0.395898 0.197949 0.980212i \(-0.436572\pi\)
0.197949 + 0.980212i \(0.436572\pi\)
\(198\) 2.52298 + 5.78401i 0.179300 + 0.411052i
\(199\) 6.96413i 0.493674i 0.969057 + 0.246837i \(0.0793912\pi\)
−0.969057 + 0.246837i \(0.920609\pi\)
\(200\) 13.2829 + 4.85437i 0.939242 + 0.343256i
\(201\) 5.82480i 0.410850i
\(202\) 12.1715 5.30920i 0.856385 0.373554i
\(203\) −5.41024 −0.379724
\(204\) 19.0239 0.708731i 1.33194 0.0496211i
\(205\) −5.53026 + 2.24697i −0.386250 + 0.156935i
\(206\) −2.97379 + 1.29716i −0.207194 + 0.0903776i
\(207\) −1.23802 + 1.23802i −0.0860483 + 0.0860483i
\(208\) 0.406265 + 5.44495i 0.0281694 + 0.377539i
\(209\) 17.1715i 1.18778i
\(210\) −4.67172 4.56230i −0.322379 0.314828i
\(211\) 5.43389 5.43389i 0.374084 0.374084i −0.494878 0.868962i \(-0.664787\pi\)
0.868962 + 0.494878i \(0.164787\pi\)
\(212\) −7.89291 + 8.50377i −0.542088 + 0.584041i
\(213\) 19.7787i 1.35521i
\(214\) 1.88730 4.80761i 0.129013 0.328642i
\(215\) −7.61635 18.7454i −0.519431 1.27843i
\(216\) −14.2316 + 6.84931i −0.968338 + 0.466036i
\(217\) −0.276477 + 0.276477i −0.0187685 + 0.0187685i
\(218\) 9.54647 4.16416i 0.646568 0.282032i
\(219\) 1.91276 1.91276i 0.129253 0.129253i
\(220\) −13.3904 + 6.03075i −0.902784 + 0.406593i
\(221\) 7.17155 + 7.17155i 0.482411 + 0.482411i
\(222\) 2.21449 5.64108i 0.148627 0.378605i
\(223\) −8.61776 8.61776i −0.577088 0.577088i 0.357012 0.934100i \(-0.383796\pi\)
−0.934100 + 0.357012i \(0.883796\pi\)
\(224\) −8.06309 + 4.25728i −0.538738 + 0.284452i
\(225\) −4.86865 + 4.73858i −0.324577 + 0.315905i
\(226\) 7.84431 3.42168i 0.521796 0.227607i
\(227\) 6.01977 0.399546 0.199773 0.979842i \(-0.435980\pi\)
0.199773 + 0.979842i \(0.435980\pi\)
\(228\) 13.3886 0.498791i 0.886683 0.0330332i
\(229\) 0.568504 + 0.568504i 0.0375678 + 0.0375678i 0.725641 0.688073i \(-0.241543\pi\)
−0.688073 + 0.725641i \(0.741543\pi\)
\(230\) −2.91515 2.84687i −0.192219 0.187717i
\(231\) 6.78094 0.446153
\(232\) −8.96022 3.13776i −0.588267 0.206004i
\(233\) −12.6979 12.6979i −0.831869 0.831869i 0.155904 0.987772i \(-0.450171\pi\)
−0.987772 + 0.155904i \(0.950171\pi\)
\(234\) −2.44165 0.958508i −0.159616 0.0626596i
\(235\) 22.9516 + 9.68940i 1.49720 + 0.632067i
\(236\) −16.7178 + 0.622819i −1.08824 + 0.0405421i
\(237\) 13.1984i 0.857327i
\(238\) −6.18894 + 15.7654i −0.401169 + 1.02192i
\(239\) −1.78306 −0.115336 −0.0576682 0.998336i \(-0.518367\pi\)
−0.0576682 + 0.998336i \(0.518367\pi\)
\(240\) −5.09113 10.2653i −0.328631 0.662625i
\(241\) 10.4440 0.672754 0.336377 0.941727i \(-0.390798\pi\)
0.336377 + 0.941727i \(0.390798\pi\)
\(242\) −0.111780 + 0.284743i −0.00718550 + 0.0183040i
\(243\) 12.8098i 0.821747i
\(244\) −0.702773 18.8639i −0.0449904 1.20764i
\(245\) −9.11908 + 3.70513i −0.582596 + 0.236712i
\(246\) 4.50208 + 1.76736i 0.287042 + 0.112683i
\(247\) 5.04719 + 5.04719i 0.321145 + 0.321145i
\(248\) −0.618238 + 0.297542i −0.0392581 + 0.0188939i
\(249\) −4.18392 −0.265145
\(250\) −11.1614 11.1992i −0.705912 0.708300i
\(251\) −12.6497 12.6497i −0.798445 0.798445i 0.184406 0.982850i \(-0.440964\pi\)
−0.982850 + 0.184406i \(0.940964\pi\)
\(252\) −0.163075 4.37730i −0.0102728 0.275744i
\(253\) 4.23130 0.266019
\(254\) −13.3687 + 5.83140i −0.838825 + 0.365894i
\(255\) −19.6084 8.27800i −1.22792 0.518388i
\(256\) −15.8228 + 2.37440i −0.988927 + 0.148400i
\(257\) −4.13062 4.13062i −0.257661 0.257661i 0.566441 0.824102i \(-0.308320\pi\)
−0.824102 + 0.566441i \(0.808320\pi\)
\(258\) −5.99064 + 15.2603i −0.372961 + 0.950063i
\(259\) 3.81240 + 3.81240i 0.236891 + 0.236891i
\(260\) 2.16322 5.70843i 0.134157 0.354022i
\(261\) 3.22500 3.22500i 0.199623 0.199623i
\(262\) 21.9603 9.57907i 1.35671 0.591797i
\(263\) 17.1303 17.1303i 1.05630 1.05630i 0.0579798 0.998318i \(-0.481534\pi\)
0.998318 0.0579798i \(-0.0184659\pi\)
\(264\) 11.2303 + 3.93273i 0.691178 + 0.242043i
\(265\) 12.0176 4.88282i 0.738237 0.299949i
\(266\) −4.35565 + 11.0954i −0.267062 + 0.680300i
\(267\) 12.5190i 0.766147i
\(268\) −6.66497 6.18620i −0.407128 0.377883i
\(269\) 19.8075 19.8075i 1.20768 1.20768i 0.235910 0.971775i \(-0.424193\pi\)
0.971775 0.235910i \(-0.0758070\pi\)
\(270\) 17.6570 0.209240i 1.07457 0.0127339i
\(271\) 27.9542i 1.69810i 0.528316 + 0.849048i \(0.322824\pi\)
−0.528316 + 0.849048i \(0.677176\pi\)
\(272\) −19.3933 + 22.5206i −1.17589 + 1.36551i
\(273\) −1.99311 + 1.99311i −0.120628 + 0.120628i
\(274\) −9.03326 + 3.94030i −0.545719 + 0.238042i
\(275\) 16.4178 + 0.222281i 0.990029 + 0.0134041i
\(276\) 0.122909 + 3.29914i 0.00739824 + 0.198585i
\(277\) −26.0257 −1.56373 −0.781866 0.623447i \(-0.785732\pi\)
−0.781866 + 0.623447i \(0.785732\pi\)
\(278\) 18.8846 8.23743i 1.13262 0.494048i
\(279\) 0.329612i 0.0197333i
\(280\) 10.1819 0.500206i 0.608488 0.0298930i
\(281\) 24.1001i 1.43769i −0.695170 0.718846i \(-0.744671\pi\)
0.695170 0.718846i \(-0.255329\pi\)
\(282\) −8.07051 18.5019i −0.480592 1.10177i
\(283\) 4.73708 0.281590 0.140795 0.990039i \(-0.455034\pi\)
0.140795 + 0.990039i \(0.455034\pi\)
\(284\) 22.6316 + 21.0059i 1.34294 + 1.24647i
\(285\) −13.8000 5.82588i −0.817439 0.345096i
\(286\) 2.53455 + 5.81053i 0.149871 + 0.343584i
\(287\) −3.04262 + 3.04262i −0.179600 + 0.179600i
\(288\) 2.26861 7.34408i 0.133679 0.432754i
\(289\) 38.2049i 2.24734i
\(290\) 7.59387 + 7.41600i 0.445927 + 0.435482i
\(291\) −2.09571 + 2.09571i −0.122852 + 0.122852i
\(292\) 0.157219 + 4.22010i 0.00920056 + 0.246963i
\(293\) 3.11001i 0.181689i 0.995865 + 0.0908445i \(0.0289566\pi\)
−0.995865 + 0.0908445i \(0.971043\pi\)
\(294\) 7.42366 + 2.91427i 0.432957 + 0.169964i
\(295\) 17.2314 + 7.27454i 1.00325 + 0.423540i
\(296\) 4.10287 + 8.52500i 0.238474 + 0.495505i
\(297\) −12.9663 + 12.9663i −0.752382 + 0.752382i
\(298\) −12.1576 27.8718i −0.704273 1.61457i
\(299\) −1.24370 + 1.24370i −0.0719248 + 0.0719248i
\(300\) 0.303583 + 12.8074i 0.0175274 + 0.739434i
\(301\) −10.3133 10.3133i −0.594449 0.594449i
\(302\) 14.0929 + 5.53238i 0.810955 + 0.318352i
\(303\) 8.50588 + 8.50588i 0.488650 + 0.488650i
\(304\) −13.6486 + 15.8495i −0.782801 + 0.909034i
\(305\) −8.20840 + 19.4435i −0.470012 + 1.11333i
\(306\) −5.70845 13.0868i −0.326330 0.748123i
\(307\) 14.5670 0.831382 0.415691 0.909506i \(-0.363540\pi\)
0.415691 + 0.909506i \(0.363540\pi\)
\(308\) −7.20167 + 7.75903i −0.410353 + 0.442112i
\(309\) −2.07819 2.07819i −0.118224 0.118224i
\(310\) 0.767042 0.00908963i 0.0435651 0.000516256i
\(311\) −14.4572 −0.819791 −0.409896 0.912132i \(-0.634435\pi\)
−0.409896 + 0.912132i \(0.634435\pi\)
\(312\) −4.45684 + 2.14496i −0.252319 + 0.121435i
\(313\) 10.1273 + 10.1273i 0.572429 + 0.572429i 0.932807 0.360377i \(-0.117352\pi\)
−0.360377 + 0.932807i \(0.617352\pi\)
\(314\) 1.21230 3.08815i 0.0684139 0.174274i
\(315\) −1.90472 + 4.51178i −0.107319 + 0.254210i
\(316\) 15.1021 + 14.0173i 0.849561 + 0.788534i
\(317\) 13.8750i 0.779295i −0.920964 0.389648i \(-0.872597\pi\)
0.920964 0.389648i \(-0.127403\pi\)
\(318\) −9.78332 3.84058i −0.548621 0.215369i
\(319\) −11.0224 −0.617136
\(320\) 17.1530 + 5.07678i 0.958883 + 0.283801i
\(321\) 4.67864 0.261136
\(322\) −2.73405 1.07329i −0.152362 0.0598121i
\(323\) 38.8520i 2.16179i
\(324\) −4.51098 4.18694i −0.250610 0.232608i
\(325\) −4.89097 + 4.76030i −0.271302 + 0.264054i
\(326\) 1.41403 3.60203i 0.0783158 0.199498i
\(327\) 6.67140 + 6.67140i 0.368930 + 0.368930i
\(328\) −6.80369 + 3.27445i −0.375671 + 0.180801i
\(329\) 17.9584 0.990076
\(330\) −9.51780 9.29486i −0.523938 0.511665i
\(331\) 1.69458 + 1.69458i 0.0931425 + 0.0931425i 0.752143 0.659000i \(-0.229020\pi\)
−0.659000 + 0.752143i \(0.729020\pi\)
\(332\) 4.44352 4.78741i 0.243870 0.262743i
\(333\) −4.54508 −0.249069
\(334\) −8.10251 18.5753i −0.443350 1.01639i
\(335\) 3.82699 + 9.41902i 0.209091 + 0.514616i
\(336\) −6.25890 5.38975i −0.341451 0.294035i
\(337\) −9.53338 9.53338i −0.519316 0.519316i 0.398048 0.917364i \(-0.369688\pi\)
−0.917364 + 0.398048i \(0.869688\pi\)
\(338\) 14.6605 + 5.75520i 0.797427 + 0.313042i
\(339\) 5.48188 + 5.48188i 0.297735 + 0.297735i
\(340\) 30.2970 13.6451i 1.64309 0.740008i
\(341\) −0.563273 + 0.563273i −0.0305029 + 0.0305029i
\(342\) −4.01749 9.21023i −0.217241 0.498032i
\(343\) −12.9954 + 12.9954i −0.701683 + 0.701683i
\(344\) −11.0991 23.0618i −0.598422 1.24341i
\(345\) 1.43558 3.40050i 0.0772888 0.183077i
\(346\) 11.5790 + 4.54552i 0.622492 + 0.244369i
\(347\) 6.67273i 0.358211i −0.983830 0.179105i \(-0.942680\pi\)
0.983830 0.179105i \(-0.0573203\pi\)
\(348\) −0.320173 8.59415i −0.0171631 0.460695i
\(349\) −2.02618 + 2.02618i −0.108459 + 0.108459i −0.759254 0.650795i \(-0.774436\pi\)
0.650795 + 0.759254i \(0.274436\pi\)
\(350\) −10.5519 4.30808i −0.564025 0.230276i
\(351\) 7.62233i 0.406850i
\(352\) −16.4271 + 8.67345i −0.875567 + 0.462296i
\(353\) −5.36542 + 5.36542i −0.285572 + 0.285572i −0.835327 0.549754i \(-0.814721\pi\)
0.549754 + 0.835327i \(0.314721\pi\)
\(354\) −6.05912 13.8907i −0.322039 0.738284i
\(355\) −12.9949 31.9832i −0.689700 1.69749i
\(356\) −14.3247 13.2957i −0.759207 0.704671i
\(357\) −15.3425 −0.812009
\(358\) 5.29416 + 12.1370i 0.279805 + 0.641462i
\(359\) 7.76117i 0.409619i −0.978802 0.204809i \(-0.934343\pi\)
0.978802 0.204809i \(-0.0656574\pi\)
\(360\) −5.77121 + 6.36755i −0.304170 + 0.335599i
\(361\) 8.34326i 0.439119i
\(362\) 10.7120 4.67258i 0.563012 0.245585i
\(363\) −0.277104 −0.0145442
\(364\) −0.163823 4.39737i −0.00858666 0.230485i
\(365\) 1.83632 4.34976i 0.0961175 0.227677i
\(366\) 15.6739 6.83695i 0.819290 0.357373i
\(367\) −18.0536 + 18.0536i −0.942389 + 0.942389i −0.998429 0.0560392i \(-0.982153\pi\)
0.0560392 + 0.998429i \(0.482153\pi\)
\(368\) −3.90554 3.36320i −0.203590 0.175319i
\(369\) 3.62737i 0.188833i
\(370\) −0.125339 10.5769i −0.00651605 0.549866i
\(371\) 6.61183 6.61183i 0.343269 0.343269i
\(372\) −0.455545 0.422821i −0.0236189 0.0219223i
\(373\) 4.36197i 0.225854i 0.993603 + 0.112927i \(0.0360226\pi\)
−0.993603 + 0.112927i \(0.963977\pi\)
\(374\) −12.6089 + 32.1192i −0.651988 + 1.66084i
\(375\) 5.74879 13.1188i 0.296866 0.677451i
\(376\) 29.7419 + 10.4153i 1.53382 + 0.537126i
\(377\) 3.23979 3.23979i 0.166858 0.166858i
\(378\) 11.6671 5.08920i 0.600093 0.261760i
\(379\) 5.93072 5.93072i 0.304641 0.304641i −0.538186 0.842826i \(-0.680890\pi\)
0.842826 + 0.538186i \(0.180890\pi\)
\(380\) 21.3224 9.60313i 1.09382 0.492630i
\(381\) −9.34249 9.34249i −0.478630 0.478630i
\(382\) −0.950385 + 2.42096i −0.0486259 + 0.123867i
\(383\) 19.3340 + 19.3340i 0.987922 + 0.987922i 0.999928 0.0120057i \(-0.00382161\pi\)
−0.0120057 + 0.999928i \(0.503822\pi\)
\(384\) −7.23984 12.5562i −0.369457 0.640758i
\(385\) 10.9652 4.45520i 0.558836 0.227058i
\(386\) −11.3354 + 4.94449i −0.576957 + 0.251668i
\(387\) 12.2954 0.625008
\(388\) −0.172256 4.62373i −0.00874498 0.234734i
\(389\) −6.28607 6.28607i −0.318716 0.318716i 0.529558 0.848274i \(-0.322358\pi\)
−0.848274 + 0.529558i \(0.822358\pi\)
\(390\) 5.52956 0.0655266i 0.280000 0.00331807i
\(391\) −9.57367 −0.484161
\(392\) −11.2189 + 5.39937i −0.566640 + 0.272709i
\(393\) 15.3466 + 15.3466i 0.774135 + 0.774135i
\(394\) −7.31489 2.87157i −0.368519 0.144668i
\(395\) −8.67157 21.3425i −0.436314 1.07386i
\(396\) −0.332237 8.91796i −0.0166955 0.448144i
\(397\) 6.58413i 0.330448i 0.986256 + 0.165224i \(0.0528347\pi\)
−0.986256 + 0.165224i \(0.947165\pi\)
\(398\) 3.59890 9.16767i 0.180397 0.459534i
\(399\) −10.7977 −0.540561
\(400\) −14.9771 13.2546i −0.748857 0.662732i
\(401\) 19.7951 0.988522 0.494261 0.869313i \(-0.335439\pi\)
0.494261 + 0.869313i \(0.335439\pi\)
\(402\) 3.01012 7.66784i 0.150131 0.382437i
\(403\) 0.331123i 0.0164944i
\(404\) −18.7664 + 0.699139i −0.933664 + 0.0347835i
\(405\) 2.59018 + 6.37497i 0.128707 + 0.316775i
\(406\) 7.12211 + 2.79589i 0.353464 + 0.138758i
\(407\) 7.76707 + 7.76707i 0.385000 + 0.385000i
\(408\) −25.4095 8.89813i −1.25796 0.440523i
\(409\) −5.76937 −0.285277 −0.142638 0.989775i \(-0.545559\pi\)
−0.142638 + 0.989775i \(0.545559\pi\)
\(410\) 8.44128 0.100031i 0.416885 0.00494019i
\(411\) −6.31276 6.31276i −0.311385 0.311385i
\(412\) 4.58507 0.170816i 0.225890 0.00841550i
\(413\) 13.4826 0.663437
\(414\) 2.26952 0.989964i 0.111541 0.0486541i
\(415\) −6.76563 + 2.74891i −0.332112 + 0.134939i
\(416\) 2.27901 7.37775i 0.111738 0.361724i
\(417\) 13.1972 + 13.1972i 0.646270 + 0.646270i
\(418\) −8.87385 + 22.6048i −0.434034 + 1.10564i
\(419\) −8.68932 8.68932i −0.424501 0.424501i 0.462249 0.886750i \(-0.347043\pi\)
−0.886750 + 0.462249i \(0.847043\pi\)
\(420\) 3.79222 + 8.42010i 0.185041 + 0.410859i
\(421\) 20.1193 20.1193i 0.980555 0.980555i −0.0192594 0.999815i \(-0.506131\pi\)
0.999815 + 0.0192594i \(0.00613083\pi\)
\(422\) −9.96134 + 4.34513i −0.484911 + 0.211517i
\(423\) −10.7048 + 10.7048i −0.520487 + 0.520487i
\(424\) 14.7849 7.11559i 0.718017 0.345564i
\(425\) −37.1466 0.502930i −1.80187 0.0243957i
\(426\) −10.2212 + 26.0369i −0.495217 + 1.26149i
\(427\) 15.2135i 0.736231i
\(428\) −4.96893 + 5.35349i −0.240182 + 0.258770i
\(429\) −4.06060 + 4.06060i −0.196048 + 0.196048i
\(430\) 0.339066 + 28.6126i 0.0163512 + 1.37982i
\(431\) 33.6247i 1.61965i −0.586675 0.809823i \(-0.699563\pi\)
0.586675 0.809823i \(-0.300437\pi\)
\(432\) 22.2742 1.66195i 1.07167 0.0799606i
\(433\) 7.46558 7.46558i 0.358773 0.358773i −0.504588 0.863361i \(-0.668355\pi\)
0.863361 + 0.504588i \(0.168355\pi\)
\(434\) 0.506835 0.221081i 0.0243289 0.0106122i
\(435\) −3.73963 + 8.85819i −0.179302 + 0.424718i
\(436\) −14.7190 + 0.548355i −0.704914 + 0.0262614i
\(437\) −6.73775 −0.322310
\(438\) −3.50646 + 1.52951i −0.167545 + 0.0730829i
\(439\) 7.91929i 0.377967i −0.981980 0.188984i \(-0.939481\pi\)
0.981980 0.188984i \(-0.0605193\pi\)
\(440\) 20.7439 1.01908i 0.988927 0.0485827i
\(441\) 5.98132i 0.284825i
\(442\) −5.73463 13.1468i −0.272768 0.625330i
\(443\) 10.6463 0.505823 0.252911 0.967489i \(-0.418612\pi\)
0.252911 + 0.967489i \(0.418612\pi\)
\(444\) −5.83036 + 6.28159i −0.276697 + 0.298111i
\(445\) 8.22517 + 20.2438i 0.389910 + 0.959649i
\(446\) 6.89106 + 15.7980i 0.326301 + 0.748056i
\(447\) 19.4778 19.4778i 0.921266 0.921266i
\(448\) 12.8144 1.43752i 0.605424 0.0679164i
\(449\) 6.08115i 0.286987i −0.989651 0.143494i \(-0.954166\pi\)
0.989651 0.143494i \(-0.0458336\pi\)
\(450\) 8.85794 3.72191i 0.417567 0.175453i
\(451\) −6.19880 + 6.19880i −0.291890 + 0.291890i
\(452\) −12.0946 + 0.450582i −0.568882 + 0.0211936i
\(453\) 13.7148i 0.644379i
\(454\) −7.92450 3.11088i −0.371915 0.146001i
\(455\) −1.91346 + 4.53247i −0.0897042 + 0.212485i
\(456\) −17.8827 6.26232i −0.837435 0.293260i
\(457\) −0.313815 + 0.313815i −0.0146796 + 0.0146796i −0.714409 0.699729i \(-0.753304\pi\)
0.699729 + 0.714409i \(0.253304\pi\)
\(458\) −0.454596 1.04218i −0.0212419 0.0486977i
\(459\) 29.3374 29.3374i 1.36935 1.36935i
\(460\) 2.36634 + 5.25413i 0.110331 + 0.244975i
\(461\) 9.90949 + 9.90949i 0.461531 + 0.461531i 0.899157 0.437626i \(-0.144181\pi\)
−0.437626 + 0.899157i \(0.644181\pi\)
\(462\) −8.92652 3.50424i −0.415299 0.163032i
\(463\) −17.3430 17.3430i −0.805999 0.805999i 0.178027 0.984026i \(-0.443029\pi\)
−0.984026 + 0.178027i \(0.943029\pi\)
\(464\) 10.1738 + 8.76103i 0.472307 + 0.406720i
\(465\) 0.261571 + 0.643781i 0.0121301 + 0.0298546i
\(466\) 10.1537 + 23.2777i 0.470361 + 1.07832i
\(467\) 1.52267 0.0704606 0.0352303 0.999379i \(-0.488784\pi\)
0.0352303 + 0.999379i \(0.488784\pi\)
\(468\) 2.71889 + 2.52358i 0.125681 + 0.116653i
\(469\) 5.18213 + 5.18213i 0.239289 + 0.239289i
\(470\) −25.2065 24.6161i −1.16269 1.13546i
\(471\) 3.00530 0.138477
\(472\) 22.3294 + 7.81950i 1.02779 + 0.359921i
\(473\) −21.0115 21.0115i −0.966110 0.966110i
\(474\) −6.82062 + 17.3745i −0.313282 + 0.798038i
\(475\) −26.1430 0.353952i −1.19952 0.0162404i
\(476\) 16.2944 17.5555i 0.746852 0.804653i
\(477\) 7.88252i 0.360916i
\(478\) 2.34724 + 0.921443i 0.107360 + 0.0421458i
\(479\) −0.507657 −0.0231955 −0.0115977 0.999933i \(-0.503692\pi\)
−0.0115977 + 0.999933i \(0.503692\pi\)
\(480\) 1.39713 + 16.1444i 0.0637702 + 0.736887i
\(481\) −4.56592 −0.208188
\(482\) −13.7486 5.39720i −0.626229 0.245836i
\(483\) 2.66070i 0.121066i
\(484\) 0.294297 0.317074i 0.0133772 0.0144125i
\(485\) −2.01195 + 4.76578i −0.0913581 + 0.216403i
\(486\) −6.61979 + 16.8629i −0.300280 + 0.764918i
\(487\) −25.9809 25.9809i −1.17730 1.17730i −0.980428 0.196876i \(-0.936920\pi\)
−0.196876 0.980428i \(-0.563080\pi\)
\(488\) −8.82332 + 25.1959i −0.399413 + 1.14057i
\(489\) 3.50539 0.158519
\(490\) 13.9192 0.164946i 0.628805 0.00745148i
\(491\) −3.28208 3.28208i −0.148118 0.148118i 0.629159 0.777277i \(-0.283400\pi\)
−0.777277 + 0.629159i \(0.783400\pi\)
\(492\) −5.01326 4.65314i −0.226015 0.209780i
\(493\) 24.9391 1.12320
\(494\) −4.03591 9.25246i −0.181584 0.416288i
\(495\) −3.88053 + 9.19195i −0.174417 + 0.413147i
\(496\) 0.967619 0.0721971i 0.0434474 0.00324175i
\(497\) −17.5964 17.5964i −0.789308 0.789308i
\(498\) 5.50777 + 2.16215i 0.246809 + 0.0968885i
\(499\) 6.73907 + 6.73907i 0.301682 + 0.301682i 0.841672 0.539990i \(-0.181572\pi\)
−0.539990 + 0.841672i \(0.681572\pi\)
\(500\) 8.90557 + 20.5107i 0.398269 + 0.917269i
\(501\) 12.9810 12.9810i 0.579950 0.579950i
\(502\) 10.1152 + 23.1894i 0.451463 + 1.03499i
\(503\) −6.12090 + 6.12090i −0.272918 + 0.272918i −0.830274 0.557356i \(-0.811816\pi\)
0.557356 + 0.830274i \(0.311816\pi\)
\(504\) −2.04741 + 5.84660i −0.0911990 + 0.260428i
\(505\) 19.3430 + 8.16596i 0.860752 + 0.363380i
\(506\) −5.57013 2.18664i −0.247623 0.0972079i
\(507\) 14.2672i 0.633629i
\(508\) 20.6122 0.767904i 0.914519 0.0340702i
\(509\) −13.8727 + 13.8727i −0.614894 + 0.614894i −0.944217 0.329323i \(-0.893180\pi\)
0.329323 + 0.944217i \(0.393180\pi\)
\(510\) 21.5348 + 21.0304i 0.953578 + 0.931242i
\(511\) 3.40344i 0.150559i
\(512\) 22.0564 + 5.05119i 0.974765 + 0.223233i
\(513\) 20.6471 20.6471i 0.911590 0.911590i
\(514\) 3.30299 + 7.57221i 0.145689 + 0.333996i
\(515\) −4.72594 1.99514i −0.208250 0.0879162i
\(516\) 15.7723 16.9930i 0.694337 0.748074i
\(517\) 36.5869 1.60909
\(518\) −3.04853 6.98884i −0.133945 0.307072i
\(519\) 11.2684i 0.494628i
\(520\) −5.79767 + 6.39674i −0.254245 + 0.280516i
\(521\) 5.87686i 0.257470i 0.991679 + 0.128735i \(0.0410917\pi\)
−0.991679 + 0.128735i \(0.958908\pi\)
\(522\) −5.91204 + 2.57883i −0.258763 + 0.112872i
\(523\) −26.0176 −1.13767 −0.568834 0.822452i \(-0.692605\pi\)
−0.568834 + 0.822452i \(0.692605\pi\)
\(524\) −33.8591 + 1.26141i −1.47914 + 0.0551051i
\(525\) 0.139774 10.3237i 0.00610022 0.450564i
\(526\) −31.4030 + 13.6980i −1.36924 + 0.597260i
\(527\) 1.27445 1.27445i 0.0555160 0.0555160i
\(528\) −12.7514 10.9807i −0.554933 0.477872i
\(529\) 21.3397i 0.927814i
\(530\) −18.3435 + 0.217374i −0.796790 + 0.00944214i
\(531\) −8.03690 + 8.03690i −0.348772 + 0.348772i
\(532\) 11.4677 12.3552i 0.497186 0.535665i
\(533\) 3.64400i 0.157839i
\(534\) 6.46951 16.4801i 0.279963 0.713164i
\(535\) 7.56561 3.07394i 0.327090 0.132898i
\(536\) 5.57696 + 11.5879i 0.240888 + 0.500521i
\(537\) −8.48177 + 8.48177i −0.366016 + 0.366016i
\(538\) −36.3109 + 15.8388i −1.56547 + 0.682858i
\(539\) −10.2215 + 10.2215i −0.440270 + 0.440270i
\(540\) −23.3521 8.84930i −1.00491 0.380813i
\(541\) −6.57691 6.57691i −0.282764 0.282764i 0.551447 0.834210i \(-0.314076\pi\)
−0.834210 + 0.551447i \(0.814076\pi\)
\(542\) 14.4461 36.7992i 0.620513 1.58066i
\(543\) 7.48594 + 7.48594i 0.321253 + 0.321253i
\(544\) 37.1677 19.6244i 1.59355 0.841390i
\(545\) 15.1712 + 6.40479i 0.649865 + 0.274351i
\(546\) 3.65374 1.59376i 0.156366 0.0682066i
\(547\) −10.6170 −0.453951 −0.226976 0.973900i \(-0.572884\pi\)
−0.226976 + 0.973900i \(0.572884\pi\)
\(548\) 13.9277 0.518876i 0.594964 0.0221653i
\(549\) −9.06863 9.06863i −0.387040 0.387040i
\(550\) −21.4977 8.77694i −0.916664 0.374250i
\(551\) 17.5516 0.747724
\(552\) 1.54312 4.40654i 0.0656796 0.187555i
\(553\) −11.7422 11.7422i −0.499328 0.499328i
\(554\) 34.2605 + 13.4495i 1.45559 + 0.571414i
\(555\) 8.87722 3.60686i 0.376817 0.153103i
\(556\) −29.1168 + 1.08474i −1.23483 + 0.0460033i
\(557\) 20.9610i 0.888146i 0.895991 + 0.444073i \(0.146467\pi\)
−0.895991 + 0.444073i \(0.853533\pi\)
\(558\) −0.170336 + 0.433905i −0.00721089 + 0.0183687i
\(559\) 12.3517 0.522422
\(560\) −13.6621 4.60332i −0.577331 0.194526i
\(561\) −31.2575 −1.31969
\(562\) −12.4544 + 31.7257i −0.525356 + 1.33827i
\(563\) 16.5598i 0.697911i −0.937139 0.348955i \(-0.886536\pi\)
0.937139 0.348955i \(-0.113464\pi\)
\(564\) 1.06276 + 28.5268i 0.0447503 + 1.20119i
\(565\) 12.4662 + 5.26280i 0.524456 + 0.221408i
\(566\) −6.23594 2.44801i −0.262116 0.102898i
\(567\) 3.50736 + 3.50736i 0.147295 + 0.147295i
\(568\) −18.9371 39.3479i −0.794584 1.65100i
\(569\) 39.6751 1.66327 0.831634 0.555325i \(-0.187406\pi\)
0.831634 + 0.555325i \(0.187406\pi\)
\(570\) 15.1558 + 14.8008i 0.634805 + 0.619936i
\(571\) 24.0292 + 24.0292i 1.00559 + 1.00559i 0.999984 + 0.00560819i \(0.00178515\pi\)
0.00560819 + 0.999984i \(0.498215\pi\)
\(572\) −0.333760 8.95885i −0.0139552 0.374588i
\(573\) −2.35602 −0.0984240
\(574\) 5.57771 2.43299i 0.232809 0.101551i
\(575\) 0.0872185 6.44199i 0.00363726 0.268649i
\(576\) −6.78168 + 8.49547i −0.282570 + 0.353978i
\(577\) −28.7705 28.7705i −1.19773 1.19773i −0.974844 0.222888i \(-0.928451\pi\)
−0.222888 0.974844i \(-0.571549\pi\)
\(578\) 19.7434 50.2933i 0.821217 2.09193i
\(579\) −7.92157 7.92157i −0.329209 0.329209i
\(580\) −6.16424 13.6868i −0.255956 0.568315i
\(581\) −3.72230 + 3.72230i −0.154427 + 0.154427i
\(582\) 3.84182 1.67580i 0.159249 0.0694641i
\(583\) 13.4704 13.4704i 0.557888 0.557888i
\(584\) 1.97389 5.63664i 0.0816800 0.233246i
\(585\) −1.56117 3.84237i −0.0645466 0.158862i
\(586\) 1.60718 4.09406i 0.0663922 0.169124i
\(587\) 33.4854i 1.38209i 0.722811 + 0.691046i \(0.242850\pi\)
−0.722811 + 0.691046i \(0.757150\pi\)
\(588\) −8.26657 7.67276i −0.340908 0.316419i
\(589\) 0.896933 0.896933i 0.0369575 0.0369575i
\(590\) −18.9244 18.4811i −0.779104 0.760855i
\(591\) 7.11866i 0.292822i
\(592\) −0.995540 13.3427i −0.0409164 0.548381i
\(593\) 11.5298 11.5298i 0.473472 0.473472i −0.429564 0.903036i \(-0.641333\pi\)
0.903036 + 0.429564i \(0.141333\pi\)
\(594\) 23.7697 10.3683i 0.975284 0.425418i
\(595\) −24.8096 + 10.0803i −1.01709 + 0.413250i
\(596\) 1.60097 + 42.9735i 0.0655783 + 1.76026i
\(597\) 8.92172 0.365142
\(598\) 2.27993 0.994503i 0.0932333 0.0406683i
\(599\) 20.0148i 0.817781i 0.912583 + 0.408891i \(0.134084\pi\)
−0.912583 + 0.408891i \(0.865916\pi\)
\(600\) 6.21891 17.0167i 0.253886 0.694702i
\(601\) 27.5924i 1.12552i 0.826621 + 0.562759i \(0.190260\pi\)
−0.826621 + 0.562759i \(0.809740\pi\)
\(602\) 8.24688 + 18.9062i 0.336118 + 0.770560i
\(603\) −6.17806 −0.251590
\(604\) −15.6931 14.5658i −0.638542 0.592673i
\(605\) −0.448093 + 0.182062i −0.0182176 + 0.00740188i
\(606\) −6.80160 15.5929i −0.276296 0.633418i
\(607\) 30.4850 30.4850i 1.23735 1.23735i 0.276265 0.961081i \(-0.410903\pi\)
0.961081 0.276265i \(-0.0890968\pi\)
\(608\) 26.1579 13.8113i 1.06084 0.560120i
\(609\) 6.93104i 0.280860i
\(610\) 20.8536 21.3538i 0.844338 0.864589i
\(611\) −10.7539 + 10.7539i −0.435057 + 0.435057i
\(612\) 0.751714 + 20.1776i 0.0303862 + 0.815632i
\(613\) 20.2657i 0.818523i 0.912417 + 0.409261i \(0.134214\pi\)
−0.912417 + 0.409261i \(0.865786\pi\)
\(614\) −19.1762 7.52788i −0.773887 0.303801i
\(615\) 2.87859 + 7.08480i 0.116076 + 0.285687i
\(616\) 13.4901 6.49242i 0.543530 0.261587i
\(617\) −1.61302 + 1.61302i −0.0649378 + 0.0649378i −0.738830 0.673892i \(-0.764621\pi\)
0.673892 + 0.738830i \(0.264621\pi\)
\(618\) 1.66179 + 3.80971i 0.0668470 + 0.153249i
\(619\) 2.46756 2.46756i 0.0991797 0.0991797i −0.655776 0.754956i \(-0.727658\pi\)
0.754956 + 0.655776i \(0.227658\pi\)
\(620\) −1.01444 0.384424i −0.0407409 0.0154388i
\(621\) 5.08771 + 5.08771i 0.204163 + 0.204163i
\(622\) 19.0316 + 7.47114i 0.763098 + 0.299565i
\(623\) 11.1377 + 11.1377i 0.446222 + 0.446222i
\(624\) 6.97551 0.520465i 0.279244 0.0208353i
\(625\) 0.676829 24.9908i 0.0270732 0.999633i
\(626\) −8.09815 18.5653i −0.323667 0.742017i
\(627\) −21.9984 −0.878531
\(628\) −3.19177 + 3.43879i −0.127365 + 0.137222i
\(629\) −17.5737 17.5737i −0.700708 0.700708i
\(630\) 4.83899 4.95505i 0.192790 0.197414i
\(631\) −29.9602 −1.19270 −0.596348 0.802726i \(-0.703382\pi\)
−0.596348 + 0.802726i \(0.703382\pi\)
\(632\) −12.6368 26.2570i −0.502666 1.04445i
\(633\) −6.96133 6.96133i −0.276688 0.276688i
\(634\) −7.17026 + 18.2652i −0.284767 + 0.725402i
\(635\) −21.2455 8.96913i −0.843101 0.355929i
\(636\) 10.8942 + 10.1116i 0.431981 + 0.400950i
\(637\) 6.00875i 0.238075i
\(638\) 14.5100 + 5.69612i 0.574457 + 0.225512i
\(639\) 20.9782 0.829885
\(640\) −19.9569 15.5474i −0.788865 0.614566i
\(641\) −37.3386 −1.47478 −0.737392 0.675465i \(-0.763943\pi\)
−0.737392 + 0.675465i \(0.763943\pi\)
\(642\) −6.15901 2.41781i −0.243077 0.0954234i
\(643\) 24.5635i 0.968691i −0.874877 0.484345i \(-0.839058\pi\)
0.874877 0.484345i \(-0.160942\pi\)
\(644\) 3.04448 + 2.82579i 0.119969 + 0.111352i
\(645\) −24.0147 + 9.75728i −0.945577 + 0.384193i
\(646\) 20.0778 51.1453i 0.789952 2.01229i
\(647\) −23.1347 23.1347i −0.909519 0.909519i 0.0867142 0.996233i \(-0.472363\pi\)
−0.996233 + 0.0867142i \(0.972363\pi\)
\(648\) 3.77459 + 7.84291i 0.148280 + 0.308099i
\(649\) 27.4685 1.07823
\(650\) 8.89855 3.73898i 0.349030 0.146655i
\(651\) 0.354194 + 0.354194i 0.0138820 + 0.0138820i
\(652\) −3.72289 + 4.01101i −0.145800 + 0.157083i
\(653\) −50.8060 −1.98819 −0.994097 0.108496i \(-0.965397\pi\)
−0.994097 + 0.108496i \(0.965397\pi\)
\(654\) −5.33469 12.2299i −0.208603 0.478229i
\(655\) 34.8993 + 14.7333i 1.36363 + 0.575679i
\(656\) 10.6486 0.794528i 0.415759 0.0310211i
\(657\) 2.02877 + 2.02877i 0.0791497 + 0.0791497i
\(658\) −23.6406 9.28047i −0.921607 0.361790i
\(659\) 9.97780 + 9.97780i 0.388680 + 0.388680i 0.874216 0.485537i \(-0.161376\pi\)
−0.485537 + 0.874216i \(0.661376\pi\)
\(660\) 7.72597 + 17.1545i 0.300733 + 0.667736i
\(661\) −5.09643 + 5.09643i −0.198228 + 0.198228i −0.799240 0.601012i \(-0.794764\pi\)
0.601012 + 0.799240i \(0.294764\pi\)
\(662\) −1.35505 3.10648i −0.0526653 0.120737i
\(663\) 9.18745 9.18745i 0.356811 0.356811i
\(664\) −8.32353 + 4.00590i −0.323015 + 0.155459i
\(665\) −17.4605 + 7.09428i −0.677088 + 0.275104i
\(666\) 5.98320 + 2.34879i 0.231844 + 0.0910139i
\(667\) 4.32496i 0.167463i
\(668\) 1.06697 + 28.6399i 0.0412825 + 1.10811i
\(669\) −11.0402 + 11.0402i −0.426838 + 0.426838i
\(670\) −0.170371 14.3770i −0.00658200 0.555432i
\(671\) 30.9947i 1.19654i
\(672\) 5.45399 + 10.3296i 0.210392 + 0.398473i
\(673\) −31.6322 + 31.6322i −1.21933 + 1.21933i −0.251464 + 0.967867i \(0.580912\pi\)
−0.967867 + 0.251464i \(0.919088\pi\)
\(674\) 7.62323 + 17.4765i 0.293636 + 0.673169i
\(675\) 19.4735 + 20.0080i 0.749534 + 0.770108i
\(676\) −16.3251 15.1524i −0.627889 0.582786i
\(677\) 25.6600 0.986196 0.493098 0.869974i \(-0.335864\pi\)
0.493098 + 0.869974i \(0.335864\pi\)
\(678\) −4.38350 10.0493i −0.168347 0.385942i
\(679\) 3.72896i 0.143104i
\(680\) −46.9348 + 2.30575i −1.79987 + 0.0884216i
\(681\) 7.71190i 0.295521i
\(682\) 1.03259 0.450413i 0.0395397 0.0172472i
\(683\) 12.3536 0.472698 0.236349 0.971668i \(-0.424049\pi\)
0.236349 + 0.971668i \(0.424049\pi\)
\(684\) 0.529041 + 14.2006i 0.0202284 + 0.542974i
\(685\) −14.3557 6.06048i −0.548501 0.231559i
\(686\) 23.8230 10.3915i 0.909564 0.396751i
\(687\) 0.728309 0.728309i 0.0277867 0.0277867i
\(688\) 2.69314 + 36.0946i 0.102675 + 1.37610i
\(689\) 7.91866i 0.301677i
\(690\) −3.64711 + 3.73458i −0.138843 + 0.142173i
\(691\) 22.5426 22.5426i 0.857561 0.857561i −0.133489 0.991050i \(-0.542618\pi\)
0.991050 + 0.133489i \(0.0426180\pi\)
\(692\) −12.8938 11.9676i −0.490147 0.454938i
\(693\) 7.19219i 0.273209i
\(694\) −3.44831 + 8.78406i −0.130896 + 0.333438i
\(695\) 30.0114 + 12.6698i 1.13840 + 0.480593i
\(696\) −4.01978 + 11.4789i −0.152369 + 0.435107i
\(697\) 14.0253 14.0253i 0.531247 0.531247i
\(698\) 3.71438 1.62021i 0.140591 0.0613258i
\(699\) −16.2673 + 16.2673i −0.615285 + 0.615285i
\(700\) 11.6644 + 11.1242i 0.440872 + 0.420455i
\(701\) 26.9530 + 26.9530i 1.01800 + 1.01800i 0.999835 + 0.0181663i \(0.00578284\pi\)
0.0181663 + 0.999835i \(0.494217\pi\)
\(702\) −3.93904 + 10.0341i −0.148670 + 0.378714i
\(703\) −12.3680 12.3680i −0.466467 0.466467i
\(704\) 26.1071 2.92869i 0.983947 0.110379i
\(705\) 12.4131 29.4032i 0.467503 1.10739i
\(706\) 9.83583 4.29038i 0.370176 0.161471i
\(707\) 15.1348 0.569203
\(708\) 0.797891 + 21.4171i 0.0299866 + 0.804905i
\(709\) −7.78615 7.78615i −0.292415 0.292415i 0.545619 0.838034i \(-0.316295\pi\)
−0.838034 + 0.545619i \(0.816295\pi\)
\(710\) 0.578511 + 48.8186i 0.0217111 + 1.83213i
\(711\) 13.9988 0.524997
\(712\) 11.9863 + 24.9053i 0.449205 + 0.933365i
\(713\) 0.221016 + 0.221016i 0.00827713 + 0.00827713i
\(714\) 20.1970 + 7.92863i 0.755854 + 0.296721i
\(715\) −3.89833 + 9.23410i −0.145789 + 0.345336i
\(716\) −0.697158 18.7132i −0.0260540 0.699346i
\(717\) 2.28427i 0.0853076i
\(718\) −4.01079 + 10.2169i −0.149681 + 0.381291i
\(719\) −20.6777 −0.771150 −0.385575 0.922677i \(-0.625997\pi\)
−0.385575 + 0.922677i \(0.625997\pi\)
\(720\) 10.8879 5.39989i 0.405768 0.201242i
\(721\) −3.69779 −0.137713
\(722\) 4.31161 10.9832i 0.160461 0.408751i
\(723\) 13.3797i 0.497597i
\(724\) −16.5161 + 0.615306i −0.613817 + 0.0228677i
\(725\) −0.227201 + 16.7812i −0.00843805 + 0.623237i
\(726\) 0.364783 + 0.143201i 0.0135384 + 0.00531469i
\(727\) 20.4994 + 20.4994i 0.760280 + 0.760280i 0.976373 0.216093i \(-0.0693315\pi\)
−0.216093 + 0.976373i \(0.569331\pi\)
\(728\) −2.05680 + 5.87341i −0.0762301 + 0.217683i
\(729\) −25.6425 −0.949722
\(730\) −4.66521 + 4.77711i −0.172667 + 0.176809i
\(731\) 47.5403 + 47.5403i 1.75834 + 1.75834i
\(732\) −24.1665 + 0.900320i −0.893221 + 0.0332768i
\(733\) 10.7306 0.396344 0.198172 0.980167i \(-0.436500\pi\)
0.198172 + 0.980167i \(0.436500\pi\)
\(734\) 33.0956 14.4363i 1.22158 0.532853i
\(735\) 4.74663 + 11.6824i 0.175082 + 0.430912i
\(736\) 3.40328 + 6.44565i 0.125447 + 0.237590i
\(737\) 10.5577 + 10.5577i 0.388897 + 0.388897i
\(738\) −1.87454 + 4.77511i −0.0690028 + 0.175774i
\(739\) −2.93837 2.93837i −0.108090 0.108090i 0.650994 0.759083i \(-0.274352\pi\)
−0.759083 + 0.650994i \(0.774352\pi\)
\(740\) −5.30090 + 13.9883i −0.194865 + 0.514221i
\(741\) 6.46594 6.46594i 0.237532 0.237532i
\(742\) −12.1207 + 5.28705i −0.444966 + 0.194094i
\(743\) −0.223404 + 0.223404i −0.00819590 + 0.00819590i −0.711193 0.702997i \(-0.751845\pi\)
0.702997 + 0.711193i \(0.251845\pi\)
\(744\) 0.381180 + 0.792022i 0.0139747 + 0.0290369i
\(745\) 18.6994 44.2938i 0.685091 1.62280i
\(746\) 2.25416 5.74215i 0.0825308 0.210235i
\(747\) 4.43766i 0.162366i
\(748\) 33.1969 35.7661i 1.21380 1.30774i
\(749\) 4.16243 4.16243i 0.152092 0.152092i
\(750\) −14.3473 + 14.2989i −0.523888 + 0.522122i
\(751\) 39.9939i 1.45940i −0.683769 0.729699i \(-0.739660\pi\)
0.683769 0.729699i \(-0.260340\pi\)
\(752\) −33.7702 29.0807i −1.23147 1.06046i
\(753\) −16.2055 + 16.2055i −0.590563 + 0.590563i
\(754\) −5.93915 + 2.59065i −0.216291 + 0.0943459i
\(755\) 9.01088 + 22.1776i 0.327939 + 0.807126i
\(756\) −17.9888 + 0.670168i −0.654245 + 0.0243738i
\(757\) 32.9120 1.19621 0.598103 0.801419i \(-0.295921\pi\)
0.598103 + 0.801419i \(0.295921\pi\)
\(758\) −10.8721 + 4.74241i −0.394894 + 0.172252i
\(759\) 5.42070i 0.196759i
\(760\) −33.0318 + 1.62274i −1.19819 + 0.0588631i
\(761\) 33.9591i 1.23102i 0.788130 + 0.615509i \(0.211049\pi\)
−0.788130 + 0.615509i \(0.788951\pi\)
\(762\) 7.47058 + 17.1266i 0.270631 + 0.620430i
\(763\) 11.8707 0.429747
\(764\) 2.50220 2.69585i 0.0905263 0.0975324i
\(765\) 8.78003 20.7976i 0.317443 0.751937i
\(766\) −15.4602 35.4429i −0.558598 1.28060i
\(767\) −8.07375 + 8.07375i −0.291526 + 0.291526i
\(768\) 3.04184 + 20.2706i 0.109763 + 0.731452i
\(769\) 40.2535i 1.45158i −0.687917 0.725789i \(-0.741475\pi\)
0.687917 0.725789i \(-0.258525\pi\)
\(770\) −16.7370 + 0.198337i −0.603160 + 0.00714758i
\(771\) −5.29172 + 5.29172i −0.190577 + 0.190577i
\(772\) 17.4773 0.651112i 0.629020 0.0234340i
\(773\) 9.47175i 0.340675i −0.985386 0.170338i \(-0.945514\pi\)
0.985386 0.170338i \(-0.0544858\pi\)
\(774\) −16.1858 6.35396i −0.581785 0.228388i
\(775\) 0.845950 + 0.869172i 0.0303874 + 0.0312216i
\(776\) −2.16268 + 6.17575i −0.0776355 + 0.221696i
\(777\) 4.88405 4.88405i 0.175214 0.175214i
\(778\) 5.02656 + 11.5236i 0.180211 + 0.413139i
\(779\) 9.87073 9.87073i 0.353656 0.353656i
\(780\) −7.31305 2.77129i −0.261849 0.0992282i
\(781\) −35.8496 35.8496i −1.28280 1.28280i
\(782\) 12.6029 + 4.94745i 0.450679 + 0.176921i
\(783\) −13.2533 13.2533i −0.473636 0.473636i
\(784\) 17.5590 1.31013i 0.627106 0.0467904i
\(785\) 4.85973 1.97453i 0.173451 0.0704741i
\(786\) −12.2717 28.1333i −0.437717 1.00348i
\(787\) −48.1367 −1.71589 −0.857945 0.513742i \(-0.828259\pi\)
−0.857945 + 0.513742i \(0.828259\pi\)
\(788\) 8.14546 + 7.56034i 0.290170 + 0.269326i
\(789\) −21.9455 21.9455i −0.781282 0.781282i
\(790\) 0.386043 + 32.5768i 0.0137348 + 1.15903i
\(791\) 9.75409 0.346815
\(792\) −4.17124 + 11.9114i −0.148218 + 0.423253i
\(793\) −9.11021 9.11021i −0.323513 0.323513i
\(794\) 3.40253 8.66743i 0.120751 0.307596i
\(795\) −6.25537 15.3957i −0.221855 0.546031i
\(796\) −9.47528 + 10.2086i −0.335842 + 0.361834i
\(797\) 33.8962i 1.20066i −0.799751 0.600332i \(-0.795035\pi\)
0.799751 0.600332i \(-0.204965\pi\)
\(798\) 14.2142 + 5.58001i 0.503178 + 0.197530i
\(799\) −82.7810 −2.92858
\(800\) 12.8664 + 25.1884i 0.454895 + 0.890545i
\(801\) −13.2782 −0.469162
\(802\) −26.0586 10.2297i −0.920160 0.361222i
\(803\) 6.93391i 0.244692i
\(804\) −7.92513 + 8.53847i −0.279498 + 0.301129i
\(805\) −1.74813 4.30250i −0.0616133 0.151643i
\(806\) −0.171117 + 0.435894i −0.00602733 + 0.0153537i
\(807\) −25.3753 25.3753i −0.893254 0.893254i
\(808\) 25.0656 + 8.77770i 0.881806 + 0.308798i
\(809\) −27.5625 −0.969047 −0.484523 0.874778i \(-0.661007\pi\)
−0.484523 + 0.874778i \(0.661007\pi\)
\(810\) −0.115310 9.73063i −0.00405159 0.341900i
\(811\) −24.1817 24.1817i −0.849133 0.849133i 0.140892 0.990025i \(-0.455003\pi\)
−0.990025 + 0.140892i \(0.955003\pi\)
\(812\) −7.93078 7.36108i −0.278316 0.258323i
\(813\) 35.8120 1.25598
\(814\) −6.21083 14.2385i −0.217689 0.499060i
\(815\) 5.66841 2.30310i 0.198556 0.0806742i
\(816\) 28.8511 + 24.8447i 1.00999 + 0.869738i
\(817\) 33.4579 + 33.4579i 1.17054 + 1.17054i
\(818\) 7.59486 + 2.98148i 0.265548 + 0.104245i
\(819\) −2.11398 2.11398i −0.0738686 0.0738686i
\(820\) −11.1639 4.23058i −0.389860 0.147738i
\(821\) 0.0575735 0.0575735i 0.00200933 0.00200933i −0.706101 0.708111i \(-0.749548\pi\)
0.708111 + 0.706101i \(0.249548\pi\)
\(822\) 5.04790 + 11.5725i 0.176066 + 0.403636i
\(823\) 28.5594 28.5594i 0.995518 0.995518i −0.00447159 0.999990i \(-0.501423\pi\)
0.999990 + 0.00447159i \(0.00142335\pi\)
\(824\) −6.12412 2.14460i −0.213344 0.0747106i
\(825\) 0.284764 21.0327i 0.00991420 0.732266i
\(826\) −17.7487 6.96752i −0.617557 0.242431i
\(827\) 23.0863i 0.802788i −0.915905 0.401394i \(-0.868526\pi\)
0.915905 0.401394i \(-0.131474\pi\)
\(828\) −3.49922 + 0.130363i −0.121606 + 0.00453042i
\(829\) 33.3543 33.3543i 1.15844 1.15844i 0.173631 0.984811i \(-0.444450\pi\)
0.984811 0.173631i \(-0.0555499\pi\)
\(830\) 10.3269 0.122376i 0.358453 0.00424775i
\(831\) 33.3414i 1.15660i
\(832\) −6.81277 + 8.53442i −0.236190 + 0.295878i
\(833\) 23.1269 23.1269i 0.801301 0.801301i
\(834\) −10.5529 24.1930i −0.365419 0.837734i
\(835\) 12.4623 29.5198i 0.431275 1.02158i
\(836\) 23.3633 25.1715i 0.808037 0.870573i
\(837\) −1.35456 −0.0468204
\(838\) 6.94829 + 15.9292i 0.240025 + 0.550264i
\(839\) 49.4524i 1.70729i 0.520859 + 0.853643i \(0.325612\pi\)
−0.520859 + 0.853643i \(0.674388\pi\)
\(840\) −0.640812 13.0441i −0.0221101 0.450063i
\(841\) 17.7336i 0.611504i
\(842\) −36.8825 + 16.0881i −1.27106 + 0.554433i
\(843\) −30.8746 −1.06338
\(844\) 15.3587 0.572185i 0.528668 0.0196954i
\(845\) 9.37380 + 23.0708i 0.322469 + 0.793661i
\(846\) 19.6240 8.55996i 0.674687 0.294298i
\(847\) −0.246530 + 0.246530i −0.00847089 + 0.00847089i
\(848\) −23.1402 + 1.72656i −0.794637 + 0.0592904i
\(849\) 6.06865i 0.208276i
\(850\) 48.6403 + 19.8586i 1.66835 + 0.681143i
\(851\) 3.04764 3.04764i 0.104472 0.104472i
\(852\) 26.9105 28.9932i 0.921940 0.993292i
\(853\) 31.3639i 1.07388i 0.843621 + 0.536939i \(0.180419\pi\)
−0.843621 + 0.536939i \(0.819581\pi\)
\(854\) 7.86197 20.0272i 0.269031 0.685316i
\(855\) 6.17921 14.6369i 0.211324 0.500571i
\(856\) 9.30771 4.47957i 0.318131 0.153108i
\(857\) −16.1594 + 16.1594i −0.551996 + 0.551996i −0.927016 0.375021i \(-0.877636\pi\)
0.375021 + 0.927016i \(0.377636\pi\)
\(858\) 7.44385 3.24700i 0.254129 0.110851i
\(859\) 30.7369 30.7369i 1.04873 1.04873i 0.0499792 0.998750i \(-0.484085\pi\)
0.998750 0.0499792i \(-0.0159155\pi\)
\(860\) 14.3400 37.8412i 0.488990 1.29038i
\(861\) 3.89790 + 3.89790i 0.132840 + 0.132840i
\(862\) −17.3765 + 44.2640i −0.591845 + 1.50764i
\(863\) 18.9353 + 18.9353i 0.644565 + 0.644565i 0.951674 0.307109i \(-0.0993618\pi\)
−0.307109 + 0.951674i \(0.599362\pi\)
\(864\) −30.1809 9.32299i −1.02678 0.317175i
\(865\) 7.40353 + 18.2216i 0.251728 + 0.619553i
\(866\) −13.6858 + 5.96974i −0.465063 + 0.202860i
\(867\) 48.9441 1.66223
\(868\) −0.781453 + 0.0291129i −0.0265242 + 0.000988156i
\(869\) −23.9226 23.9226i −0.811517 0.811517i
\(870\) 9.50061 9.72848i 0.322101 0.329826i
\(871\) −6.20638 −0.210295
\(872\) 19.6597 + 6.88460i 0.665761 + 0.233142i
\(873\) −2.22280 2.22280i −0.0752305 0.0752305i
\(874\) 8.86966 + 3.48191i 0.300021 + 0.117778i
\(875\) −6.55684 16.7859i −0.221662 0.567465i
\(876\) 5.40636 0.201413i 0.182664 0.00680511i
\(877\) 49.7461i 1.67981i 0.542737 + 0.839903i \(0.317388\pi\)
−0.542737 + 0.839903i \(0.682612\pi\)
\(878\) −4.09251 + 10.4250i −0.138115 + 0.351828i
\(879\) 3.98423 0.134385
\(880\) −27.8342 9.37844i −0.938289 0.316147i
\(881\) 27.7694 0.935574 0.467787 0.883841i \(-0.345051\pi\)
0.467787 + 0.883841i \(0.345051\pi\)
\(882\) −3.09101 + 7.87389i −0.104080 + 0.265128i
\(883\) 42.4602i 1.42890i 0.699686 + 0.714450i \(0.253323\pi\)
−0.699686 + 0.714450i \(0.746677\pi\)
\(884\) 0.755161 + 20.2702i 0.0253988 + 0.681759i
\(885\) 9.31938 22.0751i 0.313268 0.742048i
\(886\) −14.0150 5.50178i −0.470842 0.184836i
\(887\) −16.1076 16.1076i −0.540842 0.540842i 0.382934 0.923776i \(-0.374914\pi\)
−0.923776 + 0.382934i \(0.874914\pi\)
\(888\) 10.9213 5.25617i 0.366496 0.176385i
\(889\) −16.6234 −0.557531
\(890\) −0.366170 30.8998i −0.0122740 1.03576i
\(891\) 7.14563 + 7.14563i 0.239388 + 0.239388i
\(892\) −0.907445 24.3578i −0.0303835 0.815560i
\(893\) −58.2596 −1.94958
\(894\) −35.7064 + 15.5751i −1.19420 + 0.520909i
\(895\) −8.14281 + 19.2882i −0.272184 + 0.644732i
\(896\) −17.6119 4.72983i −0.588373 0.158012i
\(897\) 1.59329 + 1.59329i 0.0531986 + 0.0531986i
\(898\) −3.14260 + 8.00530i −0.104870 + 0.267140i
\(899\) −0.575741 0.575741i −0.0192020 0.0192020i
\(900\) −13.5841 + 0.321995i −0.452803 + 0.0107332i
\(901\) −30.4780 + 30.4780i −1.01537 + 1.01537i
\(902\) 11.3636 4.95678i 0.378366 0.165043i
\(903\) −13.2123 + 13.2123i −0.439679 + 0.439679i
\(904\) 16.1543 + 5.65706i 0.537285 + 0.188151i
\(905\) 17.0236 + 7.18678i 0.565883 + 0.238897i
\(906\) 7.08751 18.0544i 0.235467 0.599816i
\(907\) 9.20991i 0.305810i −0.988241 0.152905i \(-0.951137\pi\)
0.988241 0.152905i \(-0.0488628\pi\)
\(908\) 8.82427 + 8.19040i 0.292844 + 0.271808i
\(909\) −9.02174 + 9.02174i −0.299232 + 0.299232i
\(910\) 4.86117 4.97777i 0.161146 0.165011i
\(911\) 45.8065i 1.51764i −0.651302 0.758819i \(-0.725777\pi\)
0.651302 0.758819i \(-0.274223\pi\)
\(912\) 20.3048 + 17.4852i 0.672359 + 0.578992i
\(913\) −7.58351 + 7.58351i −0.250978 + 0.250978i
\(914\) 0.575282 0.250938i 0.0190286 0.00830028i
\(915\) 24.9090 + 10.5158i 0.823467 + 0.347640i
\(916\) 0.0598632 + 1.60686i 0.00197794 + 0.0530921i
\(917\) 27.3068 0.901749
\(918\) −53.7810 + 23.4592i −1.77504 + 0.774270i
\(919\) 5.52468i 0.182242i 0.995840 + 0.0911211i \(0.0290450\pi\)
−0.995840 + 0.0911211i \(0.970955\pi\)
\(920\) −0.399866 8.13947i −0.0131832 0.268350i
\(921\) 18.6617i 0.614924i
\(922\) −7.92398 18.1660i −0.260962 0.598264i
\(923\) 21.0744 0.693672
\(924\) 9.94007 + 9.22604i 0.327004 + 0.303514i
\(925\) 11.9852 11.6650i 0.394070 0.383542i
\(926\) 13.8681 + 31.7930i 0.455734 + 1.04478i
\(927\) 2.20422 2.20422i 0.0723961 0.0723961i
\(928\) −8.86544 16.7907i −0.291022 0.551182i
\(929\) 43.4288i 1.42485i 0.701746 + 0.712427i \(0.252404\pi\)
−0.701746 + 0.712427i \(0.747596\pi\)
\(930\) −0.0116447 0.982655i −0.000381845 0.0322225i
\(931\) 16.2763 16.2763i 0.533433 0.533433i
\(932\) −1.33708 35.8903i −0.0437977 1.17562i
\(933\) 18.5210i 0.606352i
\(934\) −2.00446 0.786879i −0.0655878 0.0257475i
\(935\) −50.5451 + 20.5367i −1.65300 + 0.671623i
\(936\) −2.27505 4.72713i −0.0743623 0.154511i
\(937\) −20.7275 + 20.7275i −0.677138 + 0.677138i −0.959352 0.282213i \(-0.908931\pi\)
0.282213 + 0.959352i \(0.408931\pi\)
\(938\) −4.14381 9.49983i −0.135300 0.310180i
\(939\) 12.9741 12.9741i 0.423392 0.423392i
\(940\) 20.4611 + 45.4311i 0.667369 + 1.48180i
\(941\) 12.3393 + 12.3393i 0.402251 + 0.402251i 0.879026 0.476775i \(-0.158194\pi\)
−0.476775 + 0.879026i \(0.658194\pi\)
\(942\) −3.95621 1.55307i −0.128900 0.0506017i
\(943\) 2.43228 + 2.43228i 0.0792060 + 0.0792060i
\(944\) −25.3538 21.8330i −0.825194 0.710604i
\(945\) 18.5414 + 7.82757i 0.603153 + 0.254631i
\(946\) 16.8015 + 38.5181i 0.546265 + 1.25233i
\(947\) −48.3611 −1.57152 −0.785762 0.618529i \(-0.787729\pi\)
−0.785762 + 0.618529i \(0.787729\pi\)
\(948\) 17.9575 19.3473i 0.583233 0.628371i
\(949\) 2.03807 + 2.03807i 0.0661585 + 0.0661585i
\(950\) 34.2320 + 13.9760i 1.11063 + 0.453443i
\(951\) −17.7752 −0.576399
\(952\) −30.5224 + 14.6897i −0.989237 + 0.476095i
\(953\) 34.0371 + 34.0371i 1.10257 + 1.10257i 0.994100 + 0.108471i \(0.0345953\pi\)
0.108471 + 0.994100i \(0.465405\pi\)
\(954\) 4.07350 10.3766i 0.131885 0.335956i
\(955\) −3.80980 + 1.54794i −0.123282 + 0.0500903i
\(956\) −2.61375 2.42600i −0.0845348 0.0784624i
\(957\) 14.1208i 0.456459i
\(958\) 0.668286 + 0.262346i 0.0215913 + 0.00847600i
\(959\) −11.2325 −0.362716
\(960\) 6.50385 21.9747i 0.209911 0.709230i
\(961\) 30.9412 0.998102
\(962\) 6.01063 + 2.35956i 0.193791 + 0.0760753i
\(963\) 4.96238i 0.159911i
\(964\) 15.3096 + 14.2099i 0.493090 + 0.457669i
\(965\) −18.0142 7.60500i −0.579898 0.244814i
\(966\) −1.37499 + 3.50258i −0.0442395 + 0.112694i
\(967\) −18.9307 18.9307i −0.608770 0.608770i 0.333855 0.942625i \(-0.391651\pi\)
−0.942625 + 0.333855i \(0.891651\pi\)
\(968\) −0.551273 + 0.265314i −0.0177186 + 0.00852751i
\(969\) 49.7732 1.59895
\(970\) 5.11141 5.23400i 0.164117 0.168054i
\(971\) −21.2698 21.2698i −0.682580 0.682580i 0.278001 0.960581i \(-0.410328\pi\)
−0.960581 + 0.278001i \(0.910328\pi\)
\(972\) 17.4288 18.7776i 0.559028 0.602292i
\(973\) 23.4822 0.752805
\(974\) 20.7752 + 47.6278i 0.665681 + 1.52609i
\(975\) 6.09841 + 6.26581i 0.195305 + 0.200666i
\(976\) 24.6358 28.6085i 0.788573 0.915736i
\(977\) 2.13884 + 2.13884i 0.0684275 + 0.0684275i 0.740492 0.672065i \(-0.234592\pi\)
−0.672065 + 0.740492i \(0.734592\pi\)
\(978\) −4.61454 1.81151i −0.147557 0.0579256i
\(979\) 22.6911 + 22.6911i 0.725210 + 0.725210i
\(980\) −18.4086 6.97598i −0.588042 0.222840i
\(981\) −7.07601 + 7.07601i −0.225919 + 0.225919i
\(982\) 2.62447 + 6.01667i 0.0837501 + 0.192000i
\(983\) −6.18193 + 6.18193i −0.197173 + 0.197173i −0.798787 0.601614i \(-0.794525\pi\)
0.601614 + 0.798787i \(0.294525\pi\)
\(984\) 4.19488 + 8.71619i 0.133728 + 0.277862i
\(985\) −4.67708 11.5113i −0.149024 0.366779i
\(986\) −32.8301 12.8880i −1.04552 0.410436i
\(987\) 23.0064i 0.732302i
\(988\) 0.531466 + 14.2657i 0.0169082 + 0.453853i
\(989\) −8.24447 + 8.24447i −0.262159 + 0.262159i
\(990\) 9.85857 10.0950i 0.313326 0.320841i
\(991\) 43.4847i 1.38134i 0.723172 + 0.690668i \(0.242683\pi\)
−0.723172 + 0.690668i \(0.757317\pi\)
\(992\) −1.31110 0.405002i −0.0416273 0.0128588i
\(993\) 2.17092 2.17092i 0.0688921 0.0688921i
\(994\) 14.0707 + 32.2576i 0.446297 + 1.02315i
\(995\) 14.4269 5.86173i 0.457364 0.185829i
\(996\) −6.13314 5.69257i −0.194336 0.180376i
\(997\) −33.4043 −1.05793 −0.528963 0.848645i \(-0.677419\pi\)
−0.528963 + 0.848645i \(0.677419\pi\)
\(998\) −5.38879 12.3540i −0.170579 0.391059i
\(999\) 18.6783i 0.590954i
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 80.2.j.b.67.2 yes 18
3.2 odd 2 720.2.bd.g.307.8 18
4.3 odd 2 320.2.j.b.47.7 18
5.2 odd 4 400.2.s.d.243.6 18
5.3 odd 4 80.2.s.b.3.4 yes 18
5.4 even 2 400.2.j.d.307.8 18
8.3 odd 2 640.2.j.c.607.3 18
8.5 even 2 640.2.j.d.607.7 18
15.8 even 4 720.2.z.g.163.6 18
16.3 odd 4 640.2.s.d.287.3 18
16.5 even 4 320.2.s.b.207.3 18
16.11 odd 4 80.2.s.b.27.4 yes 18
16.13 even 4 640.2.s.c.287.7 18
20.3 even 4 320.2.s.b.303.3 18
20.7 even 4 1600.2.s.d.943.7 18
20.19 odd 2 1600.2.j.d.1007.3 18
40.3 even 4 640.2.s.c.223.7 18
40.13 odd 4 640.2.s.d.223.3 18
48.11 even 4 720.2.z.g.667.6 18
80.3 even 4 640.2.j.d.543.3 18
80.13 odd 4 640.2.j.c.543.7 18
80.27 even 4 400.2.j.d.43.8 18
80.37 odd 4 1600.2.j.d.143.7 18
80.43 even 4 inner 80.2.j.b.43.2 18
80.53 odd 4 320.2.j.b.143.3 18
80.59 odd 4 400.2.s.d.107.6 18
80.69 even 4 1600.2.s.d.207.7 18
240.203 odd 4 720.2.bd.g.523.8 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.2.j.b.43.2 18 80.43 even 4 inner
80.2.j.b.67.2 yes 18 1.1 even 1 trivial
80.2.s.b.3.4 yes 18 5.3 odd 4
80.2.s.b.27.4 yes 18 16.11 odd 4
320.2.j.b.47.7 18 4.3 odd 2
320.2.j.b.143.3 18 80.53 odd 4
320.2.s.b.207.3 18 16.5 even 4
320.2.s.b.303.3 18 20.3 even 4
400.2.j.d.43.8 18 80.27 even 4
400.2.j.d.307.8 18 5.4 even 2
400.2.s.d.107.6 18 80.59 odd 4
400.2.s.d.243.6 18 5.2 odd 4
640.2.j.c.543.7 18 80.13 odd 4
640.2.j.c.607.3 18 8.3 odd 2
640.2.j.d.543.3 18 80.3 even 4
640.2.j.d.607.7 18 8.5 even 2
640.2.s.c.223.7 18 40.3 even 4
640.2.s.c.287.7 18 16.13 even 4
640.2.s.d.223.3 18 40.13 odd 4
640.2.s.d.287.3 18 16.3 odd 4
720.2.z.g.163.6 18 15.8 even 4
720.2.z.g.667.6 18 48.11 even 4
720.2.bd.g.307.8 18 3.2 odd 2
720.2.bd.g.523.8 18 240.203 odd 4
1600.2.j.d.143.7 18 80.37 odd 4
1600.2.j.d.1007.3 18 20.19 odd 2
1600.2.s.d.207.7 18 80.69 even 4
1600.2.s.d.943.7 18 20.7 even 4