Properties

Label 370.2.q.b.273.1
Level $370$
Weight $2$
Character 370.273
Analytic conductor $2.954$
Analytic rank $0$
Dimension $4$
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] = [370,2,Mod(97,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.q (of order \(12\), degree \(4\), 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: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 273.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 370.273
Dual form 370.2.q.b.267.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(2.36603 + 0.633975i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(-1.36603 - 0.366025i) q^{7} +1.00000 q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(2.36603 + 0.633975i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(-1.36603 - 0.366025i) q^{7} +1.00000 q^{8} +(2.59808 + 1.50000i) q^{9} +(-1.00000 + 2.00000i) q^{10} -0.464102i q^{11} +(-0.633975 - 2.36603i) q^{12} +(1.86603 + 3.23205i) q^{13} +(1.00000 - 1.00000i) q^{14} +(5.36603 + 1.09808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.633975 - 0.366025i) q^{17} +(-2.59808 + 1.50000i) q^{18} +(0.133975 - 0.500000i) q^{19} +(-1.23205 - 1.86603i) q^{20} +(-3.00000 - 1.73205i) q^{21} +(0.401924 + 0.232051i) q^{22} -0.267949 q^{23} +(2.36603 + 0.633975i) q^{24} +(4.96410 - 0.598076i) q^{25} -3.73205 q^{26} +(0.366025 + 1.36603i) q^{28} +(1.46410 - 1.46410i) q^{29} +(-3.63397 + 4.09808i) q^{30} +(-6.19615 - 6.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.294229 - 1.09808i) q^{33} +(0.633975 - 0.366025i) q^{34} +(-3.09808 - 0.633975i) q^{35} -3.00000i q^{36} +(0.500000 + 6.06218i) q^{37} +(0.366025 + 0.366025i) q^{38} +(2.36603 + 8.83013i) q^{39} +(2.23205 - 0.133975i) q^{40} +(-8.19615 + 4.73205i) q^{41} +(3.00000 - 1.73205i) q^{42} +4.00000 q^{43} +(-0.401924 + 0.232051i) q^{44} +(6.00000 + 3.00000i) q^{45} +(0.133975 - 0.232051i) q^{46} +(2.09808 - 2.09808i) q^{47} +(-1.73205 + 1.73205i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(-1.96410 + 4.59808i) q^{50} +(-1.26795 - 1.26795i) q^{51} +(1.86603 - 3.23205i) q^{52} +(-8.56218 + 2.29423i) q^{53} +(-0.0621778 - 1.03590i) q^{55} +(-1.36603 - 0.366025i) q^{56} +(0.633975 - 1.09808i) q^{57} +(0.535898 + 2.00000i) q^{58} +(-4.59808 + 1.23205i) q^{59} +(-1.73205 - 5.19615i) q^{60} +(-0.562178 + 2.09808i) q^{61} +(8.46410 - 2.26795i) q^{62} +(-3.00000 - 3.00000i) q^{63} +1.00000 q^{64} +(4.59808 + 6.96410i) q^{65} +(0.803848 + 0.803848i) q^{66} +(2.83013 - 10.5622i) q^{67} +0.732051i q^{68} +(-0.633975 - 0.169873i) q^{69} +(2.09808 - 2.36603i) q^{70} +(3.00000 + 5.19615i) q^{71} +(2.59808 + 1.50000i) q^{72} +(5.92820 - 5.92820i) q^{73} +(-5.50000 - 2.59808i) q^{74} +(12.1244 + 1.73205i) q^{75} +(-0.500000 + 0.133975i) q^{76} +(-0.169873 + 0.633975i) q^{77} +(-8.83013 - 2.36603i) q^{78} +(-0.928203 + 3.46410i) q^{79} +(-1.00000 + 2.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} -9.46410i q^{82} +(-5.46410 + 1.46410i) q^{83} +3.46410i q^{84} +(-1.46410 - 0.732051i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(4.39230 - 2.53590i) q^{87} -0.464102i q^{88} +(-3.79423 - 14.1603i) q^{89} +(-5.59808 + 3.69615i) q^{90} +(-1.36603 - 5.09808i) q^{91} +(0.133975 + 0.232051i) q^{92} +(-10.7321 - 18.5885i) q^{93} +(0.767949 + 2.86603i) q^{94} +(0.232051 - 1.13397i) q^{95} +(-0.633975 - 2.36603i) q^{96} -9.46410i q^{97} +(4.33013 - 2.50000i) q^{98} +(0.696152 - 1.20577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8} - 4 q^{10} - 6 q^{12} + 4 q^{13} + 4 q^{14} + 18 q^{15} - 2 q^{16} - 6 q^{17} + 4 q^{19} + 2 q^{20} - 12 q^{21} + 12 q^{22} - 8 q^{23} + 6 q^{24} + 6 q^{25} - 8 q^{26} - 2 q^{28} - 8 q^{29} - 18 q^{30} - 4 q^{31} - 2 q^{32} - 30 q^{33} + 6 q^{34} - 2 q^{35} + 2 q^{37} - 2 q^{38} + 6 q^{39} + 2 q^{40} - 12 q^{41} + 12 q^{42} + 16 q^{43} - 12 q^{44} + 24 q^{45} + 4 q^{46} - 2 q^{47} + 6 q^{50} - 12 q^{51} + 4 q^{52} - 10 q^{53} + 24 q^{55} - 2 q^{56} + 6 q^{57} + 16 q^{58} - 8 q^{59} + 22 q^{61} + 20 q^{62} - 12 q^{63} + 4 q^{64} + 8 q^{65} + 24 q^{66} - 6 q^{67} - 6 q^{69} - 2 q^{70} + 12 q^{71} - 4 q^{73} - 22 q^{74} - 2 q^{76} - 18 q^{77} - 18 q^{78} + 24 q^{79} - 4 q^{80} - 18 q^{81} - 8 q^{83} + 8 q^{85} - 8 q^{86} - 24 q^{87} + 16 q^{89} - 12 q^{90} - 2 q^{91} + 4 q^{92} - 36 q^{93} + 10 q^{94} - 6 q^{95} - 6 q^{96} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 2.36603 + 0.633975i 1.36603 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.23205 0.133975i 0.998203 0.0599153i
\(6\) −1.73205 + 1.73205i −0.707107 + 0.707107i
\(7\) −1.36603 0.366025i −0.516309 0.138345i −0.00875026 0.999962i \(-0.502785\pi\)
−0.507559 + 0.861617i \(0.669452\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.59808 + 1.50000i 0.866025 + 0.500000i
\(10\) −1.00000 + 2.00000i −0.316228 + 0.632456i
\(11\) 0.464102i 0.139932i −0.997549 0.0699660i \(-0.977711\pi\)
0.997549 0.0699660i \(-0.0222891\pi\)
\(12\) −0.633975 2.36603i −0.183013 0.683013i
\(13\) 1.86603 + 3.23205i 0.517542 + 0.896410i 0.999792 + 0.0203760i \(0.00648633\pi\)
−0.482250 + 0.876034i \(0.660180\pi\)
\(14\) 1.00000 1.00000i 0.267261 0.267261i
\(15\) 5.36603 + 1.09808i 1.38550 + 0.283522i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.633975 0.366025i −0.153761 0.0887742i 0.421145 0.906993i \(-0.361628\pi\)
−0.574907 + 0.818219i \(0.694962\pi\)
\(18\) −2.59808 + 1.50000i −0.612372 + 0.353553i
\(19\) 0.133975 0.500000i 0.0307359 0.114708i −0.948854 0.315716i \(-0.897755\pi\)
0.979590 + 0.201008i \(0.0644219\pi\)
\(20\) −1.23205 1.86603i −0.275495 0.417256i
\(21\) −3.00000 1.73205i −0.654654 0.377964i
\(22\) 0.401924 + 0.232051i 0.0856904 + 0.0494734i
\(23\) −0.267949 −0.0558713 −0.0279356 0.999610i \(-0.508893\pi\)
−0.0279356 + 0.999610i \(0.508893\pi\)
\(24\) 2.36603 + 0.633975i 0.482963 + 0.129410i
\(25\) 4.96410 0.598076i 0.992820 0.119615i
\(26\) −3.73205 −0.731915
\(27\) 0 0
\(28\) 0.366025 + 1.36603i 0.0691723 + 0.258155i
\(29\) 1.46410 1.46410i 0.271877 0.271877i −0.557979 0.829855i \(-0.688423\pi\)
0.829855 + 0.557979i \(0.188423\pi\)
\(30\) −3.63397 + 4.09808i −0.663470 + 0.748203i
\(31\) −6.19615 6.19615i −1.11286 1.11286i −0.992762 0.120100i \(-0.961678\pi\)
−0.120100 0.992762i \(-0.538322\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.294229 1.09808i 0.0512186 0.191151i
\(34\) 0.633975 0.366025i 0.108726 0.0627728i
\(35\) −3.09808 0.633975i −0.523670 0.107161i
\(36\) 3.00000i 0.500000i
\(37\) 0.500000 + 6.06218i 0.0821995 + 0.996616i
\(38\) 0.366025 + 0.366025i 0.0593772 + 0.0593772i
\(39\) 2.36603 + 8.83013i 0.378867 + 1.41395i
\(40\) 2.23205 0.133975i 0.352918 0.0211832i
\(41\) −8.19615 + 4.73205i −1.28002 + 0.739022i −0.976853 0.213914i \(-0.931379\pi\)
−0.303171 + 0.952936i \(0.598045\pi\)
\(42\) 3.00000 1.73205i 0.462910 0.267261i
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −0.401924 + 0.232051i −0.0605923 + 0.0349830i
\(45\) 6.00000 + 3.00000i 0.894427 + 0.447214i
\(46\) 0.133975 0.232051i 0.0197535 0.0342140i
\(47\) 2.09808 2.09808i 0.306036 0.306036i −0.537334 0.843370i \(-0.680568\pi\)
0.843370 + 0.537334i \(0.180568\pi\)
\(48\) −1.73205 + 1.73205i −0.250000 + 0.250000i
\(49\) −4.33013 2.50000i −0.618590 0.357143i
\(50\) −1.96410 + 4.59808i −0.277766 + 0.650266i
\(51\) −1.26795 1.26795i −0.177548 0.177548i
\(52\) 1.86603 3.23205i 0.258771 0.448205i
\(53\) −8.56218 + 2.29423i −1.17611 + 0.315137i −0.793381 0.608726i \(-0.791681\pi\)
−0.382725 + 0.923862i \(0.625014\pi\)
\(54\) 0 0
\(55\) −0.0621778 1.03590i −0.00838406 0.139681i
\(56\) −1.36603 0.366025i −0.182543 0.0489122i
\(57\) 0.633975 1.09808i 0.0839720 0.145444i
\(58\) 0.535898 + 2.00000i 0.0703669 + 0.262613i
\(59\) −4.59808 + 1.23205i −0.598619 + 0.160399i −0.545389 0.838183i \(-0.683618\pi\)
−0.0532294 + 0.998582i \(0.516951\pi\)
\(60\) −1.73205 5.19615i −0.223607 0.670820i
\(61\) −0.562178 + 2.09808i −0.0719795 + 0.268631i −0.992531 0.121989i \(-0.961073\pi\)
0.920552 + 0.390620i \(0.127739\pi\)
\(62\) 8.46410 2.26795i 1.07494 0.288030i
\(63\) −3.00000 3.00000i −0.377964 0.377964i
\(64\) 1.00000 0.125000
\(65\) 4.59808 + 6.96410i 0.570321 + 0.863790i
\(66\) 0.803848 + 0.803848i 0.0989468 + 0.0989468i
\(67\) 2.83013 10.5622i 0.345755 1.29038i −0.545973 0.837803i \(-0.683840\pi\)
0.891728 0.452572i \(-0.149494\pi\)
\(68\) 0.732051i 0.0887742i
\(69\) −0.633975 0.169873i −0.0763216 0.0204503i
\(70\) 2.09808 2.36603i 0.250768 0.282794i
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) 2.59808 + 1.50000i 0.306186 + 0.176777i
\(73\) 5.92820 5.92820i 0.693844 0.693844i −0.269232 0.963075i \(-0.586770\pi\)
0.963075 + 0.269232i \(0.0867697\pi\)
\(74\) −5.50000 2.59808i −0.639362 0.302020i
\(75\) 12.1244 + 1.73205i 1.40000 + 0.200000i
\(76\) −0.500000 + 0.133975i −0.0573539 + 0.0153679i
\(77\) −0.169873 + 0.633975i −0.0193588 + 0.0722481i
\(78\) −8.83013 2.36603i −0.999815 0.267900i
\(79\) −0.928203 + 3.46410i −0.104431 + 0.389742i −0.998280 0.0586263i \(-0.981328\pi\)
0.893849 + 0.448368i \(0.147995\pi\)
\(80\) −1.00000 + 2.00000i −0.111803 + 0.223607i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 9.46410i 1.04514i
\(83\) −5.46410 + 1.46410i −0.599763 + 0.160706i −0.545911 0.837843i \(-0.683816\pi\)
−0.0538517 + 0.998549i \(0.517150\pi\)
\(84\) 3.46410i 0.377964i
\(85\) −1.46410 0.732051i −0.158804 0.0794021i
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 4.39230 2.53590i 0.470905 0.271877i
\(88\) 0.464102i 0.0494734i
\(89\) −3.79423 14.1603i −0.402187 1.50098i −0.809185 0.587555i \(-0.800091\pi\)
0.406997 0.913429i \(-0.366576\pi\)
\(90\) −5.59808 + 3.69615i −0.590089 + 0.389609i
\(91\) −1.36603 5.09808i −0.143198 0.534424i
\(92\) 0.133975 + 0.232051i 0.0139678 + 0.0241930i
\(93\) −10.7321 18.5885i −1.11286 1.92753i
\(94\) 0.767949 + 2.86603i 0.0792079 + 0.295608i
\(95\) 0.232051 1.13397i 0.0238079 0.116343i
\(96\) −0.633975 2.36603i −0.0647048 0.241481i
\(97\) 9.46410i 0.960934i −0.877013 0.480467i \(-0.840467\pi\)
0.877013 0.480467i \(-0.159533\pi\)
\(98\) 4.33013 2.50000i 0.437409 0.252538i
\(99\) 0.696152 1.20577i 0.0699660 0.121185i
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 12.3923i 1.23308i 0.787323 + 0.616540i \(0.211466\pi\)
−0.787323 + 0.616540i \(0.788534\pi\)
\(102\) 1.73205 0.464102i 0.171499 0.0459529i
\(103\) 17.3923i 1.71371i −0.515554 0.856857i \(-0.672414\pi\)
0.515554 0.856857i \(-0.327586\pi\)
\(104\) 1.86603 + 3.23205i 0.182979 + 0.316929i
\(105\) −6.92820 3.46410i −0.676123 0.338062i
\(106\) 2.29423 8.56218i 0.222835 0.831632i
\(107\) 10.1962 + 2.73205i 0.985699 + 0.264117i 0.715443 0.698671i \(-0.246225\pi\)
0.270256 + 0.962788i \(0.412892\pi\)
\(108\) 0 0
\(109\) −5.83013 + 1.56218i −0.558425 + 0.149629i −0.526983 0.849876i \(-0.676677\pi\)
−0.0314423 + 0.999506i \(0.510010\pi\)
\(110\) 0.928203 + 0.464102i 0.0885007 + 0.0442504i
\(111\) −2.66025 + 14.6603i −0.252500 + 1.39149i
\(112\) 1.00000 1.00000i 0.0944911 0.0944911i
\(113\) 5.36603 + 3.09808i 0.504793 + 0.291442i 0.730691 0.682709i \(-0.239198\pi\)
−0.225898 + 0.974151i \(0.572531\pi\)
\(114\) 0.633975 + 1.09808i 0.0593772 + 0.102844i
\(115\) −0.598076 + 0.0358984i −0.0557709 + 0.00334754i
\(116\) −2.00000 0.535898i −0.185695 0.0497569i
\(117\) 11.1962i 1.03508i
\(118\) 1.23205 4.59808i 0.113419 0.423287i
\(119\) 0.732051 + 0.732051i 0.0671070 + 0.0671070i
\(120\) 5.36603 + 1.09808i 0.489849 + 0.100240i
\(121\) 10.7846 0.980419
\(122\) −1.53590 1.53590i −0.139054 0.139054i
\(123\) −22.3923 + 6.00000i −2.01905 + 0.541002i
\(124\) −2.26795 + 8.46410i −0.203668 + 0.760099i
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 4.09808 1.09808i 0.365086 0.0978244i
\(127\) −4.13397 15.4282i −0.366831 1.36903i −0.864922 0.501907i \(-0.832632\pi\)
0.498091 0.867125i \(-0.334035\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 9.46410 + 2.53590i 0.833268 + 0.223273i
\(130\) −8.33013 + 0.500000i −0.730600 + 0.0438529i
\(131\) −5.36603 + 1.43782i −0.468832 + 0.125623i −0.485498 0.874238i \(-0.661362\pi\)
0.0166658 + 0.999861i \(0.494695\pi\)
\(132\) −1.09808 + 0.294229i −0.0955753 + 0.0256093i
\(133\) −0.366025 + 0.633975i −0.0317384 + 0.0549726i
\(134\) 7.73205 + 7.73205i 0.667947 + 0.667947i
\(135\) 0 0
\(136\) −0.633975 0.366025i −0.0543629 0.0313864i
\(137\) −6.19615 + 6.19615i −0.529373 + 0.529373i −0.920385 0.391012i \(-0.872125\pi\)
0.391012 + 0.920385i \(0.372125\pi\)
\(138\) 0.464102 0.464102i 0.0395070 0.0395070i
\(139\) −4.13397 + 7.16025i −0.350639 + 0.607325i −0.986362 0.164593i \(-0.947369\pi\)
0.635722 + 0.771918i \(0.280702\pi\)
\(140\) 1.00000 + 3.00000i 0.0845154 + 0.253546i
\(141\) 6.29423 3.63397i 0.530070 0.306036i
\(142\) −6.00000 −0.503509
\(143\) 1.50000 0.866025i 0.125436 0.0724207i
\(144\) −2.59808 + 1.50000i −0.216506 + 0.125000i
\(145\) 3.07180 3.46410i 0.255099 0.287678i
\(146\) 2.16987 + 8.09808i 0.179580 + 0.670202i
\(147\) −8.66025 8.66025i −0.714286 0.714286i
\(148\) 5.00000 3.46410i 0.410997 0.284747i
\(149\) 14.5359i 1.19083i 0.803419 + 0.595414i \(0.203012\pi\)
−0.803419 + 0.595414i \(0.796988\pi\)
\(150\) −7.56218 + 9.63397i −0.617449 + 0.786611i
\(151\) −5.83013 + 3.36603i −0.474449 + 0.273923i −0.718100 0.695940i \(-0.754988\pi\)
0.243651 + 0.969863i \(0.421655\pi\)
\(152\) 0.133975 0.500000i 0.0108668 0.0405554i
\(153\) −1.09808 1.90192i −0.0887742 0.153761i
\(154\) −0.464102 0.464102i −0.0373984 0.0373984i
\(155\) −14.6603 13.0000i −1.17754 1.04419i
\(156\) 6.46410 6.46410i 0.517542 0.517542i
\(157\) 5.23205 + 19.5263i 0.417563 + 1.55837i 0.779646 + 0.626221i \(0.215399\pi\)
−0.362083 + 0.932146i \(0.617934\pi\)
\(158\) −2.53590 2.53590i −0.201745 0.201745i
\(159\) −21.7128 −1.72194
\(160\) −1.23205 1.86603i −0.0974022 0.147522i
\(161\) 0.366025 + 0.0980762i 0.0288468 + 0.00772949i
\(162\) 9.00000 0.707107
\(163\) 4.09808 + 2.36603i 0.320986 + 0.185321i 0.651832 0.758363i \(-0.274001\pi\)
−0.330846 + 0.943685i \(0.607334\pi\)
\(164\) 8.19615 + 4.73205i 0.640012 + 0.369511i
\(165\) 0.509619 2.49038i 0.0396738 0.193876i
\(166\) 1.46410 5.46410i 0.113636 0.424097i
\(167\) 13.8564 8.00000i 1.07224 0.619059i 0.143448 0.989658i \(-0.454181\pi\)
0.928793 + 0.370599i \(0.120848\pi\)
\(168\) −3.00000 1.73205i −0.231455 0.133631i
\(169\) −0.464102 + 0.803848i −0.0357001 + 0.0618344i
\(170\) 1.36603 0.901924i 0.104769 0.0691744i
\(171\) 1.09808 1.09808i 0.0839720 0.0839720i
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) 5.83975 + 21.7942i 0.443988 + 1.65698i 0.718596 + 0.695428i \(0.244785\pi\)
−0.274608 + 0.961556i \(0.588548\pi\)
\(174\) 5.07180i 0.384492i
\(175\) −7.00000 1.00000i −0.529150 0.0755929i
\(176\) 0.401924 + 0.232051i 0.0302961 + 0.0174915i
\(177\) −11.6603 −0.876438
\(178\) 14.1603 + 3.79423i 1.06136 + 0.284389i
\(179\) 12.5622 12.5622i 0.938941 0.938941i −0.0592990 0.998240i \(-0.518887\pi\)
0.998240 + 0.0592990i \(0.0188865\pi\)
\(180\) −0.401924 6.69615i −0.0299576 0.499102i
\(181\) 6.02628 + 10.4378i 0.447930 + 0.775837i 0.998251 0.0591158i \(-0.0188281\pi\)
−0.550321 + 0.834953i \(0.685495\pi\)
\(182\) 5.09808 + 1.36603i 0.377895 + 0.101257i
\(183\) −2.66025 + 4.60770i −0.196652 + 0.340611i
\(184\) −0.267949 −0.0197535
\(185\) 1.92820 + 13.4641i 0.141764 + 0.989900i
\(186\) 21.4641 1.57382
\(187\) −0.169873 + 0.294229i −0.0124223 + 0.0215161i
\(188\) −2.86603 0.767949i −0.209026 0.0560085i
\(189\) 0 0
\(190\) 0.866025 + 0.767949i 0.0628281 + 0.0557129i
\(191\) −16.1962 + 16.1962i −1.17191 + 1.17191i −0.190159 + 0.981753i \(0.560900\pi\)
−0.981753 + 0.190159i \(0.939100\pi\)
\(192\) 2.36603 + 0.633975i 0.170753 + 0.0457532i
\(193\) 22.1962 1.59771 0.798857 0.601521i \(-0.205438\pi\)
0.798857 + 0.601521i \(0.205438\pi\)
\(194\) 8.19615 + 4.73205i 0.588449 + 0.339741i
\(195\) 6.46410 + 19.3923i 0.462904 + 1.38871i
\(196\) 5.00000i 0.357143i
\(197\) 4.56218 + 17.0263i 0.325042 + 1.21307i 0.914270 + 0.405106i \(0.132765\pi\)
−0.589228 + 0.807967i \(0.700568\pi\)
\(198\) 0.696152 + 1.20577i 0.0494734 + 0.0856904i
\(199\) 10.9282 10.9282i 0.774680 0.774680i −0.204241 0.978921i \(-0.565473\pi\)
0.978921 + 0.204241i \(0.0654726\pi\)
\(200\) 4.96410 0.598076i 0.351015 0.0422904i
\(201\) 13.3923 23.1962i 0.944620 1.63613i
\(202\) −10.7321 6.19615i −0.755104 0.435960i
\(203\) −2.53590 + 1.46410i −0.177985 + 0.102760i
\(204\) −0.464102 + 1.73205i −0.0324936 + 0.121268i
\(205\) −17.6603 + 11.6603i −1.23345 + 0.814387i
\(206\) 15.0622 + 8.69615i 1.04943 + 0.605890i
\(207\) −0.696152 0.401924i −0.0483859 0.0279356i
\(208\) −3.73205 −0.258771
\(209\) −0.232051 0.0621778i −0.0160513 0.00430093i
\(210\) 6.46410 4.26795i 0.446065 0.294516i
\(211\) −0.856406 −0.0589575 −0.0294787 0.999565i \(-0.509385\pi\)
−0.0294787 + 0.999565i \(0.509385\pi\)
\(212\) 6.26795 + 6.26795i 0.430485 + 0.430485i
\(213\) 3.80385 + 14.1962i 0.260635 + 0.972704i
\(214\) −7.46410 + 7.46410i −0.510235 + 0.510235i
\(215\) 8.92820 0.535898i 0.608898 0.0365480i
\(216\) 0 0
\(217\) 6.19615 + 10.7321i 0.420622 + 0.728539i
\(218\) 1.56218 5.83013i 0.105804 0.394866i
\(219\) 17.7846 10.2679i 1.20177 0.693844i
\(220\) −0.866025 + 0.571797i −0.0583874 + 0.0385505i
\(221\) 2.73205i 0.183778i
\(222\) −11.3660 9.63397i −0.762838 0.646590i
\(223\) 11.3660 + 11.3660i 0.761125 + 0.761125i 0.976526 0.215400i \(-0.0691057\pi\)
−0.215400 + 0.976526i \(0.569106\pi\)
\(224\) 0.366025 + 1.36603i 0.0244561 + 0.0912714i
\(225\) 13.7942 + 5.89230i 0.919615 + 0.392820i
\(226\) −5.36603 + 3.09808i −0.356943 + 0.206081i
\(227\) −25.0981 + 14.4904i −1.66582 + 0.961760i −0.695963 + 0.718078i \(0.745022\pi\)
−0.969855 + 0.243682i \(0.921645\pi\)
\(228\) −1.26795 −0.0839720
\(229\) 10.8564 6.26795i 0.717412 0.414198i −0.0963877 0.995344i \(-0.530729\pi\)
0.813799 + 0.581146i \(0.197396\pi\)
\(230\) 0.267949 0.535898i 0.0176680 0.0353361i
\(231\) −0.803848 + 1.39230i −0.0528893 + 0.0916069i
\(232\) 1.46410 1.46410i 0.0961230 0.0961230i
\(233\) −3.19615 + 3.19615i −0.209387 + 0.209387i −0.804007 0.594620i \(-0.797303\pi\)
0.594620 + 0.804007i \(0.297303\pi\)
\(234\) −9.69615 5.59808i −0.633857 0.365958i
\(235\) 4.40192 4.96410i 0.287150 0.323822i
\(236\) 3.36603 + 3.36603i 0.219110 + 0.219110i
\(237\) −4.39230 + 7.60770i −0.285311 + 0.494173i
\(238\) −1.00000 + 0.267949i −0.0648204 + 0.0173686i
\(239\) −24.4904 + 6.56218i −1.58415 + 0.424472i −0.940208 0.340601i \(-0.889369\pi\)
−0.643943 + 0.765073i \(0.722703\pi\)
\(240\) −3.63397 + 4.09808i −0.234572 + 0.264530i
\(241\) −8.96410 2.40192i −0.577429 0.154722i −0.0417272 0.999129i \(-0.513286\pi\)
−0.535701 + 0.844408i \(0.679953\pi\)
\(242\) −5.39230 + 9.33975i −0.346630 + 0.600382i
\(243\) −5.70577 21.2942i −0.366025 1.36603i
\(244\) 2.09808 0.562178i 0.134316 0.0359897i
\(245\) −10.0000 5.00000i −0.638877 0.319438i
\(246\) 6.00000 22.3923i 0.382546 1.42768i
\(247\) 1.86603 0.500000i 0.118732 0.0318142i
\(248\) −6.19615 6.19615i −0.393456 0.393456i
\(249\) −13.8564 −0.878114
\(250\) −3.76795 + 10.5263i −0.238306 + 0.665740i
\(251\) −12.0981 12.0981i −0.763624 0.763624i 0.213352 0.976975i \(-0.431562\pi\)
−0.976975 + 0.213352i \(0.931562\pi\)
\(252\) −1.09808 + 4.09808i −0.0691723 + 0.258155i
\(253\) 0.124356i 0.00781817i
\(254\) 15.4282 + 4.13397i 0.968052 + 0.259389i
\(255\) −3.00000 2.66025i −0.187867 0.166592i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 13.0981 + 7.56218i 0.817036 + 0.471716i 0.849393 0.527761i \(-0.176968\pi\)
−0.0323576 + 0.999476i \(0.510302\pi\)
\(258\) −6.92820 + 6.92820i −0.431331 + 0.431331i
\(259\) 1.53590 8.46410i 0.0954361 0.525934i
\(260\) 3.73205 7.46410i 0.231452 0.462904i
\(261\) 6.00000 1.60770i 0.371391 0.0995138i
\(262\) 1.43782 5.36603i 0.0888290 0.331514i
\(263\) 2.50000 + 0.669873i 0.154157 + 0.0413061i 0.335072 0.942193i \(-0.391239\pi\)
−0.180915 + 0.983499i \(0.557906\pi\)
\(264\) 0.294229 1.09808i 0.0181085 0.0675819i
\(265\) −18.8038 + 6.26795i −1.15511 + 0.385037i
\(266\) −0.366025 0.633975i −0.0224425 0.0388715i
\(267\) 35.9090i 2.19759i
\(268\) −10.5622 + 2.83013i −0.645188 + 0.172878i
\(269\) 9.26795i 0.565077i −0.959256 0.282538i \(-0.908824\pi\)
0.959256 0.282538i \(-0.0911765\pi\)
\(270\) 0 0
\(271\) −14.8564 + 25.7321i −0.902462 + 1.56311i −0.0781747 + 0.996940i \(0.524909\pi\)
−0.824288 + 0.566171i \(0.808424\pi\)
\(272\) 0.633975 0.366025i 0.0384404 0.0221936i
\(273\) 12.9282i 0.782450i
\(274\) −2.26795 8.46410i −0.137012 0.511335i
\(275\) −0.277568 2.30385i −0.0167380 0.138927i
\(276\) 0.169873 + 0.633975i 0.0102252 + 0.0381608i
\(277\) 7.26795 + 12.5885i 0.436689 + 0.756367i 0.997432 0.0716228i \(-0.0228178\pi\)
−0.560743 + 0.827990i \(0.689484\pi\)
\(278\) −4.13397 7.16025i −0.247939 0.429443i
\(279\) −6.80385 25.3923i −0.407336 1.52020i
\(280\) −3.09808 0.633975i −0.185145 0.0378872i
\(281\) −6.50000 24.2583i −0.387757 1.44713i −0.833774 0.552106i \(-0.813824\pi\)
0.446016 0.895025i \(-0.352842\pi\)
\(282\) 7.26795i 0.432800i
\(283\) 12.2942 7.09808i 0.730816 0.421937i −0.0879046 0.996129i \(-0.528017\pi\)
0.818721 + 0.574192i \(0.194684\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) 1.26795 2.53590i 0.0751068 0.150214i
\(286\) 1.73205i 0.102418i
\(287\) 12.9282 3.46410i 0.763128 0.204479i
\(288\) 3.00000i 0.176777i
\(289\) −8.23205 14.2583i −0.484238 0.838725i
\(290\) 1.46410 + 4.39230i 0.0859750 + 0.257925i
\(291\) 6.00000 22.3923i 0.351726 1.31266i
\(292\) −8.09808 2.16987i −0.473904 0.126982i
\(293\) 3.06218 11.4282i 0.178894 0.667643i −0.816961 0.576693i \(-0.804343\pi\)
0.995855 0.0909500i \(-0.0289903\pi\)
\(294\) 11.8301 3.16987i 0.689947 0.184871i
\(295\) −10.0981 + 3.36603i −0.587933 + 0.195978i
\(296\) 0.500000 + 6.06218i 0.0290619 + 0.352357i
\(297\) 0 0
\(298\) −12.5885 7.26795i −0.729230 0.421021i
\(299\) −0.500000 0.866025i −0.0289157 0.0500835i
\(300\) −4.56218 11.3660i −0.263397 0.656218i
\(301\) −5.46410 1.46410i −0.314946 0.0843894i
\(302\) 6.73205i 0.387386i
\(303\) −7.85641 + 29.3205i −0.451339 + 1.68442i
\(304\) 0.366025 + 0.366025i 0.0209930 + 0.0209930i
\(305\) −0.973721 + 4.75833i −0.0557551 + 0.272461i
\(306\) 2.19615 0.125546
\(307\) 1.73205 + 1.73205i 0.0988534 + 0.0988534i 0.754804 0.655951i \(-0.227732\pi\)
−0.655951 + 0.754804i \(0.727732\pi\)
\(308\) 0.633975 0.169873i 0.0361241 0.00967941i
\(309\) 11.0263 41.1506i 0.627263 2.34098i
\(310\) 18.5885 6.19615i 1.05575 0.351918i
\(311\) −0.366025 + 0.0980762i −0.0207554 + 0.00556139i −0.269182 0.963089i \(-0.586753\pi\)
0.248426 + 0.968651i \(0.420087\pi\)
\(312\) 2.36603 + 8.83013i 0.133950 + 0.499908i
\(313\) 0.0717968 0.124356i 0.00405819 0.00702900i −0.863989 0.503510i \(-0.832042\pi\)
0.868047 + 0.496481i \(0.165375\pi\)
\(314\) −19.5263 5.23205i −1.10193 0.295262i
\(315\) −7.09808 6.29423i −0.399931 0.354640i
\(316\) 3.46410 0.928203i 0.194871 0.0522155i
\(317\) −22.5263 + 6.03590i −1.26520 + 0.339010i −0.828191 0.560446i \(-0.810630\pi\)
−0.437011 + 0.899456i \(0.643963\pi\)
\(318\) 10.8564 18.8038i 0.608797 1.05447i
\(319\) −0.679492 0.679492i −0.0380442 0.0380442i
\(320\) 2.23205 0.133975i 0.124775 0.00748941i
\(321\) 22.3923 + 12.9282i 1.24982 + 0.721582i
\(322\) −0.267949 + 0.267949i −0.0149322 + 0.0149322i
\(323\) −0.267949 + 0.267949i −0.0149091 + 0.0149091i
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 11.1962 + 14.9282i 0.621051 + 0.828068i
\(326\) −4.09808 + 2.36603i −0.226971 + 0.131042i
\(327\) −14.7846 −0.817591
\(328\) −8.19615 + 4.73205i −0.452557 + 0.261284i
\(329\) −3.63397 + 2.09808i −0.200348 + 0.115671i
\(330\) 1.90192 + 1.68653i 0.104697 + 0.0928406i
\(331\) 1.33013 + 4.96410i 0.0731104 + 0.272852i 0.992798 0.119799i \(-0.0382249\pi\)
−0.919688 + 0.392650i \(0.871558\pi\)
\(332\) 4.00000 + 4.00000i 0.219529 + 0.219529i
\(333\) −7.79423 + 16.5000i −0.427121 + 0.904194i
\(334\) 16.0000i 0.875481i
\(335\) 4.90192 23.9545i 0.267821 1.30877i
\(336\) 3.00000 1.73205i 0.163663 0.0944911i
\(337\) 0.679492 2.53590i 0.0370143 0.138139i −0.944946 0.327226i \(-0.893886\pi\)
0.981960 + 0.189087i \(0.0605528\pi\)
\(338\) −0.464102 0.803848i −0.0252438 0.0437235i
\(339\) 10.7321 + 10.7321i 0.582885 + 0.582885i
\(340\) 0.0980762 + 1.63397i 0.00531893 + 0.0886147i
\(341\) −2.87564 + 2.87564i −0.155725 + 0.155725i
\(342\) 0.401924 + 1.50000i 0.0217335 + 0.0811107i
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) 4.00000 0.215666
\(345\) −1.43782 0.294229i −0.0774097 0.0158407i
\(346\) −21.7942 5.83975i −1.17166 0.313947i
\(347\) −9.12436 −0.489821 −0.244911 0.969546i \(-0.578759\pi\)
−0.244911 + 0.969546i \(0.578759\pi\)
\(348\) −4.39230 2.53590i −0.235452 0.135938i
\(349\) 15.9282 + 9.19615i 0.852617 + 0.492259i 0.861533 0.507701i \(-0.169505\pi\)
−0.00891587 + 0.999960i \(0.502838\pi\)
\(350\) 4.36603 5.56218i 0.233374 0.297311i
\(351\) 0 0
\(352\) −0.401924 + 0.232051i −0.0214226 + 0.0123683i
\(353\) 11.4904 + 6.63397i 0.611571 + 0.353091i 0.773580 0.633698i \(-0.218464\pi\)
−0.162009 + 0.986789i \(0.551797\pi\)
\(354\) 5.83013 10.0981i 0.309868 0.536707i
\(355\) 7.39230 + 11.1962i 0.392343 + 0.594230i
\(356\) −10.3660 + 10.3660i −0.549398 + 0.549398i
\(357\) 1.26795 + 2.19615i 0.0671070 + 0.116233i
\(358\) 4.59808 + 17.1603i 0.243016 + 0.906948i
\(359\) 3.12436i 0.164897i −0.996595 0.0824486i \(-0.973726\pi\)
0.996595 0.0824486i \(-0.0262740\pi\)
\(360\) 6.00000 + 3.00000i 0.316228 + 0.158114i
\(361\) 16.2224 + 9.36603i 0.853812 + 0.492949i
\(362\) −12.0526 −0.633468
\(363\) 25.5167 + 6.83717i 1.33928 + 0.358858i
\(364\) −3.73205 + 3.73205i −0.195613 + 0.195613i
\(365\) 12.4378 14.0263i 0.651025 0.734169i
\(366\) −2.66025 4.60770i −0.139054 0.240848i
\(367\) −14.2583 3.82051i −0.744279 0.199429i −0.133300 0.991076i \(-0.542557\pi\)
−0.610979 + 0.791647i \(0.709224\pi\)
\(368\) 0.133975 0.232051i 0.00698391 0.0120965i
\(369\) −28.3923 −1.47804
\(370\) −12.6244 5.06218i −0.656309 0.263170i
\(371\) 12.5359 0.650831
\(372\) −10.7321 + 18.5885i −0.556431 + 0.963767i
\(373\) −1.76795 0.473721i −0.0915409 0.0245283i 0.212758 0.977105i \(-0.431755\pi\)
−0.304299 + 0.952577i \(0.598422\pi\)
\(374\) −0.169873 0.294229i −0.00878392 0.0152142i
\(375\) 27.2942 + 2.24167i 1.40947 + 0.115759i
\(376\) 2.09808 2.09808i 0.108200 0.108200i
\(377\) 7.46410 + 2.00000i 0.384421 + 0.103005i
\(378\) 0 0
\(379\) 8.87564 + 5.12436i 0.455911 + 0.263220i 0.710323 0.703875i \(-0.248549\pi\)
−0.254412 + 0.967096i \(0.581882\pi\)
\(380\) −1.09808 + 0.366025i −0.0563301 + 0.0187767i
\(381\) 39.1244i 2.00440i
\(382\) −5.92820 22.1244i −0.303313 1.13198i
\(383\) 10.3301 + 17.8923i 0.527845 + 0.914254i 0.999473 + 0.0324566i \(0.0103331\pi\)
−0.471628 + 0.881797i \(0.656334\pi\)
\(384\) −1.73205 + 1.73205i −0.0883883 + 0.0883883i
\(385\) −0.294229 + 1.43782i −0.0149953 + 0.0732782i
\(386\) −11.0981 + 19.2224i −0.564877 + 0.978396i
\(387\) 10.3923 + 6.00000i 0.528271 + 0.304997i
\(388\) −8.19615 + 4.73205i −0.416097 + 0.240233i
\(389\) 4.00000 14.9282i 0.202808 0.756890i −0.787298 0.616572i \(-0.788521\pi\)
0.990107 0.140318i \(-0.0448124\pi\)
\(390\) −20.0263 4.09808i −1.01407 0.207514i
\(391\) 0.169873 + 0.0980762i 0.00859085 + 0.00495993i
\(392\) −4.33013 2.50000i −0.218704 0.126269i
\(393\) −13.6077 −0.686417
\(394\) −17.0263 4.56218i −0.857772 0.229839i
\(395\) −1.60770 + 7.85641i −0.0808919 + 0.395299i
\(396\) −1.39230 −0.0699660
\(397\) −11.9019 11.9019i −0.597340 0.597340i 0.342264 0.939604i \(-0.388806\pi\)
−0.939604 + 0.342264i \(0.888806\pi\)
\(398\) 4.00000 + 14.9282i 0.200502 + 0.748283i
\(399\) −1.26795 + 1.26795i −0.0634769 + 0.0634769i
\(400\) −1.96410 + 4.59808i −0.0982051 + 0.229904i
\(401\) 14.5622 + 14.5622i 0.727200 + 0.727200i 0.970061 0.242861i \(-0.0780858\pi\)
−0.242861 + 0.970061i \(0.578086\pi\)
\(402\) 13.3923 + 23.1962i 0.667947 + 1.15692i
\(403\) 8.46410 31.5885i 0.421627 1.57353i
\(404\) 10.7321 6.19615i 0.533939 0.308270i
\(405\) −11.0885 16.7942i −0.550990 0.834512i
\(406\) 2.92820i 0.145324i
\(407\) 2.81347 0.232051i 0.139458 0.0115023i
\(408\) −1.26795 1.26795i −0.0627728 0.0627728i
\(409\) −2.43782 9.09808i −0.120543 0.449871i 0.879099 0.476639i \(-0.158145\pi\)
−0.999642 + 0.0267681i \(0.991478\pi\)
\(410\) −1.26795 21.1244i −0.0626195 1.04326i
\(411\) −18.5885 + 10.7321i −0.916901 + 0.529373i
\(412\) −15.0622 + 8.69615i −0.742060 + 0.428429i
\(413\) 6.73205 0.331263
\(414\) 0.696152 0.401924i 0.0342140 0.0197535i
\(415\) −12.0000 + 4.00000i −0.589057 + 0.196352i
\(416\) 1.86603 3.23205i 0.0914894 0.158464i
\(417\) −14.3205 + 14.3205i −0.701278 + 0.701278i
\(418\) 0.169873 0.169873i 0.00830876 0.00830876i
\(419\) 23.0885 + 13.3301i 1.12794 + 0.651219i 0.943417 0.331608i \(-0.107591\pi\)
0.184528 + 0.982827i \(0.440924\pi\)
\(420\) 0.464102 + 7.73205i 0.0226458 + 0.377285i
\(421\) 19.3205 + 19.3205i 0.941624 + 0.941624i 0.998388 0.0567637i \(-0.0180782\pi\)
−0.0567637 + 0.998388i \(0.518078\pi\)
\(422\) 0.428203 0.741670i 0.0208446 0.0361039i
\(423\) 8.59808 2.30385i 0.418053 0.112017i
\(424\) −8.56218 + 2.29423i −0.415816 + 0.111418i
\(425\) −3.36603 1.43782i −0.163276 0.0697446i
\(426\) −14.1962 3.80385i −0.687806 0.184297i
\(427\) 1.53590 2.66025i 0.0743273 0.128739i
\(428\) −2.73205 10.1962i −0.132059 0.492850i
\(429\) 4.09808 1.09808i 0.197857 0.0530156i
\(430\) −4.00000 + 8.00000i −0.192897 + 0.385794i
\(431\) 7.24167 27.0263i 0.348819 1.30181i −0.539268 0.842134i \(-0.681299\pi\)
0.888087 0.459676i \(-0.152034\pi\)
\(432\) 0 0
\(433\) 28.5167 + 28.5167i 1.37042 + 1.37042i 0.859811 + 0.510612i \(0.170581\pi\)
0.510612 + 0.859811i \(0.329419\pi\)
\(434\) −12.3923 −0.594850
\(435\) 9.46410 6.24871i 0.453769 0.299603i
\(436\) 4.26795 + 4.26795i 0.204398 + 0.204398i
\(437\) −0.0358984 + 0.133975i −0.00171725 + 0.00640887i
\(438\) 20.5359i 0.981243i
\(439\) 6.36603 + 1.70577i 0.303834 + 0.0814120i 0.407515 0.913199i \(-0.366395\pi\)
−0.103681 + 0.994611i \(0.533062\pi\)
\(440\) −0.0621778 1.03590i −0.00296421 0.0493845i
\(441\) −7.50000 12.9904i −0.357143 0.618590i
\(442\) 2.36603 + 1.36603i 0.112540 + 0.0649752i
\(443\) −9.85641 + 9.85641i −0.468292 + 0.468292i −0.901361 0.433069i \(-0.857431\pi\)
0.433069 + 0.901361i \(0.357431\pi\)
\(444\) 14.0263 5.02628i 0.665658 0.238537i
\(445\) −10.3660 31.0981i −0.491397 1.47419i
\(446\) −15.5263 + 4.16025i −0.735191 + 0.196994i
\(447\) −9.21539 + 34.3923i −0.435873 + 1.62670i
\(448\) −1.36603 0.366025i −0.0645386 0.0172931i
\(449\) 3.22243 12.0263i 0.152076 0.567555i −0.847262 0.531175i \(-0.821751\pi\)
0.999338 0.0363801i \(-0.0115827\pi\)
\(450\) −12.0000 + 9.00000i −0.565685 + 0.424264i
\(451\) 2.19615 + 3.80385i 0.103413 + 0.179116i
\(452\) 6.19615i 0.291442i
\(453\) −15.9282 + 4.26795i −0.748372 + 0.200526i
\(454\) 28.9808i 1.36013i
\(455\) −3.73205 11.1962i −0.174961 0.524884i
\(456\) 0.633975 1.09808i 0.0296886 0.0514221i
\(457\) −1.26795 + 0.732051i −0.0593122 + 0.0342439i −0.529363 0.848396i \(-0.677569\pi\)
0.470051 + 0.882639i \(0.344236\pi\)
\(458\) 12.5359i 0.585764i
\(459\) 0 0
\(460\) 0.330127 + 0.500000i 0.0153923 + 0.0233126i
\(461\) −5.90192 22.0263i −0.274880 1.02587i −0.955922 0.293622i \(-0.905139\pi\)
0.681042 0.732245i \(-0.261527\pi\)
\(462\) −0.803848 1.39230i −0.0373984 0.0647759i
\(463\) −18.3923 31.8564i −0.854763 1.48049i −0.876865 0.480737i \(-0.840369\pi\)
0.0221019 0.999756i \(-0.492964\pi\)
\(464\) 0.535898 + 2.00000i 0.0248785 + 0.0928477i
\(465\) −26.4449 40.0526i −1.22635 1.85739i
\(466\) −1.16987 4.36603i −0.0541933 0.202252i
\(467\) 10.3397i 0.478466i 0.970962 + 0.239233i \(0.0768960\pi\)
−0.970962 + 0.239233i \(0.923104\pi\)
\(468\) 9.69615 5.59808i 0.448205 0.258771i
\(469\) −7.73205 + 13.3923i −0.357033 + 0.618399i
\(470\) 2.09808 + 6.29423i 0.0967770 + 0.290331i
\(471\) 49.5167i 2.28161i
\(472\) −4.59808 + 1.23205i −0.211644 + 0.0567097i
\(473\) 1.85641i 0.0853577i
\(474\) −4.39230 7.60770i −0.201745 0.349433i
\(475\) 0.366025 2.56218i 0.0167944 0.117561i
\(476\) 0.267949 1.00000i 0.0122814 0.0458349i
\(477\) −25.6865 6.88269i −1.17611 0.315137i
\(478\) 6.56218 24.4904i 0.300147 1.12016i
\(479\) −8.92820 + 2.39230i −0.407940 + 0.109307i −0.456953 0.889491i \(-0.651059\pi\)
0.0490128 + 0.998798i \(0.484393\pi\)
\(480\) −1.73205 5.19615i −0.0790569 0.237171i
\(481\) −18.6603 + 12.9282i −0.850834 + 0.589475i
\(482\) 6.56218 6.56218i 0.298899 0.298899i
\(483\) 0.803848 + 0.464102i 0.0365763 + 0.0211174i
\(484\) −5.39230 9.33975i −0.245105 0.424534i
\(485\) −1.26795 21.1244i −0.0575746 0.959208i
\(486\) 21.2942 + 5.70577i 0.965926 + 0.258819i
\(487\) 10.7846i 0.488697i 0.969687 + 0.244349i \(0.0785741\pi\)
−0.969687 + 0.244349i \(0.921426\pi\)
\(488\) −0.562178 + 2.09808i −0.0254486 + 0.0949754i
\(489\) 8.19615 + 8.19615i 0.370643 + 0.370643i
\(490\) 9.33013 6.16025i 0.421492 0.278292i
\(491\) 2.60770 0.117684 0.0588418 0.998267i \(-0.481259\pi\)
0.0588418 + 0.998267i \(0.481259\pi\)
\(492\) 16.3923 + 16.3923i 0.739022 + 0.739022i
\(493\) −1.46410 + 0.392305i −0.0659398 + 0.0176685i
\(494\) −0.500000 + 1.86603i −0.0224961 + 0.0839565i
\(495\) 1.39230 2.78461i 0.0625794 0.125159i
\(496\) 8.46410 2.26795i 0.380049 0.101834i
\(497\) −2.19615 8.19615i −0.0985109 0.367648i
\(498\) 6.92820 12.0000i 0.310460 0.537733i
\(499\) 21.2224 + 5.68653i 0.950047 + 0.254564i 0.700382 0.713768i \(-0.253013\pi\)
0.249665 + 0.968332i \(0.419680\pi\)
\(500\) −7.23205 8.52628i −0.323427 0.381307i
\(501\) 37.8564 10.1436i 1.69130 0.453182i
\(502\) 16.5263 4.42820i 0.737604 0.197640i
\(503\) 10.6603 18.4641i 0.475317 0.823274i −0.524283 0.851544i \(-0.675667\pi\)
0.999600 + 0.0282704i \(0.00899996\pi\)
\(504\) −3.00000 3.00000i −0.133631 0.133631i
\(505\) 1.66025 + 27.6603i 0.0738803 + 1.23087i
\(506\) −0.107695 0.0621778i −0.00478763 0.00276414i
\(507\) −1.60770 + 1.60770i −0.0714002 + 0.0714002i
\(508\) −11.2942 + 11.2942i −0.501100 + 0.501100i
\(509\) −16.7321 + 28.9808i −0.741635 + 1.28455i 0.210115 + 0.977677i \(0.432616\pi\)
−0.951750 + 0.306873i \(0.900717\pi\)
\(510\) 3.80385 1.26795i 0.168437 0.0561457i
\(511\) −10.2679 + 5.92820i −0.454227 + 0.262248i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −13.0981 + 7.56218i −0.577731 + 0.333553i
\(515\) −2.33013 38.8205i −0.102678 1.71064i
\(516\) −2.53590 9.46410i −0.111637 0.416634i
\(517\) −0.973721 0.973721i −0.0428242 0.0428242i
\(518\) 6.56218 + 5.56218i 0.288326 + 0.244388i
\(519\) 55.2679i 2.42599i
\(520\) 4.59808 + 6.96410i 0.201639 + 0.305396i
\(521\) 18.8660 10.8923i 0.826536 0.477201i −0.0261294 0.999659i \(-0.508318\pi\)
0.852665 + 0.522458i \(0.174985\pi\)
\(522\) −1.60770 + 6.00000i −0.0703669 + 0.262613i
\(523\) 11.9545 + 20.7058i 0.522733 + 0.905400i 0.999650 + 0.0264519i \(0.00842087\pi\)
−0.476917 + 0.878948i \(0.658246\pi\)
\(524\) 3.92820 + 3.92820i 0.171604 + 0.171604i
\(525\) −15.9282 6.80385i −0.695164 0.296944i
\(526\) −1.83013 + 1.83013i −0.0797973 + 0.0797973i
\(527\) 1.66025 + 6.19615i 0.0723218 + 0.269909i
\(528\) 0.803848 + 0.803848i 0.0349830 + 0.0349830i
\(529\) −22.9282 −0.996878
\(530\) 3.97372 19.4186i 0.172607 0.843489i
\(531\) −13.7942 3.69615i −0.598619 0.160399i
\(532\) 0.732051 0.0317384
\(533\) −30.5885 17.6603i −1.32493 0.764951i
\(534\) 31.0981 + 17.9545i 1.34575 + 0.776966i
\(535\) 23.1244 + 4.73205i 0.999753 + 0.204584i
\(536\) 2.83013 10.5622i 0.122243 0.456217i
\(537\) 37.6865 21.7583i 1.62629 0.938941i
\(538\) 8.02628 + 4.63397i 0.346037 + 0.199785i
\(539\) −1.16025 + 2.00962i −0.0499757 + 0.0865604i
\(540\) 0 0
\(541\) 1.07180 1.07180i 0.0460801 0.0460801i −0.683691 0.729771i \(-0.739626\pi\)
0.729771 + 0.683691i \(0.239626\pi\)
\(542\) −14.8564 25.7321i −0.638137 1.10529i
\(543\) 7.64102 + 28.5167i 0.327907 + 1.22377i
\(544\) 0.732051i 0.0313864i
\(545\) −12.8038 + 4.26795i −0.548457 + 0.182819i
\(546\) 11.1962 + 6.46410i 0.479151 + 0.276638i
\(547\) −0.535898 −0.0229134 −0.0114567 0.999934i \(-0.503647\pi\)
−0.0114567 + 0.999934i \(0.503647\pi\)
\(548\) 8.46410 + 2.26795i 0.361569 + 0.0968820i
\(549\) −4.60770 + 4.60770i −0.196652 + 0.196652i
\(550\) 2.13397 + 0.911543i 0.0909930 + 0.0388683i
\(551\) −0.535898 0.928203i −0.0228300 0.0395428i
\(552\) −0.633975 0.169873i −0.0269838 0.00723027i
\(553\) 2.53590 4.39230i 0.107837 0.186780i
\(554\) −14.5359 −0.617571
\(555\) −3.97372 + 33.0788i −0.168675 + 1.40412i
\(556\) 8.26795 0.350639
\(557\) 3.40192 5.89230i 0.144144 0.249665i −0.784909 0.619611i \(-0.787290\pi\)
0.929053 + 0.369946i \(0.120624\pi\)
\(558\) 25.3923 + 6.80385i 1.07494 + 0.288030i
\(559\) 7.46410 + 12.9282i 0.315698 + 0.546805i
\(560\) 2.09808 2.36603i 0.0886599 0.0999828i
\(561\) −0.588457 + 0.588457i −0.0248447 + 0.0248447i
\(562\) 24.2583 + 6.50000i 1.02328 + 0.274186i
\(563\) 33.1244 1.39603 0.698013 0.716086i \(-0.254068\pi\)
0.698013 + 0.716086i \(0.254068\pi\)
\(564\) −6.29423 3.63397i −0.265035 0.153018i
\(565\) 12.3923 + 6.19615i 0.521348 + 0.260674i
\(566\) 14.1962i 0.596709i
\(567\) 3.29423 + 12.2942i 0.138345 + 0.516309i
\(568\) 3.00000 + 5.19615i 0.125877 + 0.218026i
\(569\) −25.3468 + 25.3468i −1.06259 + 1.06259i −0.0646870 + 0.997906i \(0.520605\pi\)
−0.997906 + 0.0646870i \(0.979395\pi\)
\(570\) 1.56218 + 2.36603i 0.0654324 + 0.0991019i
\(571\) 20.7224 35.8923i 0.867207 1.50205i 0.00236761 0.999997i \(-0.499246\pi\)
0.864839 0.502049i \(-0.167420\pi\)
\(572\) −1.50000 0.866025i −0.0627182 0.0362103i
\(573\) −48.5885 + 28.0526i −2.02981 + 1.17191i
\(574\) −3.46410 + 12.9282i −0.144589 + 0.539613i
\(575\) −1.33013 + 0.160254i −0.0554701 + 0.00668306i
\(576\) 2.59808 + 1.50000i 0.108253 + 0.0625000i
\(577\) −37.1769 21.4641i −1.54770 0.893562i −0.998317 0.0579883i \(-0.981531\pi\)
−0.549378 0.835574i \(-0.685135\pi\)
\(578\) 16.4641 0.684816
\(579\) 52.5167 + 14.0718i 2.18252 + 0.584804i
\(580\) −4.53590 0.928203i −0.188343 0.0385415i
\(581\) 8.00000 0.331896
\(582\) 16.3923 + 16.3923i 0.679483 + 0.679483i
\(583\) 1.06476 + 3.97372i 0.0440977 + 0.164575i
\(584\) 5.92820 5.92820i 0.245311 0.245311i
\(585\) 1.50000 + 24.9904i 0.0620174 + 1.03323i
\(586\) 8.36603 + 8.36603i 0.345597 + 0.345597i
\(587\) 10.1699 + 17.6147i 0.419756 + 0.727038i 0.995915 0.0902996i \(-0.0287825\pi\)
−0.576159 + 0.817338i \(0.695449\pi\)
\(588\) −3.16987 + 11.8301i −0.130723 + 0.487866i
\(589\) −3.92820 + 2.26795i −0.161859 + 0.0934492i
\(590\) 2.13397 10.4282i 0.0878543 0.429322i
\(591\) 43.1769i 1.77606i
\(592\) −5.50000 2.59808i −0.226049 0.106780i
\(593\) −30.7846 30.7846i −1.26417 1.26417i −0.949052 0.315121i \(-0.897955\pi\)
−0.315121 0.949052i \(-0.602045\pi\)
\(594\) 0 0
\(595\) 1.73205 + 1.53590i 0.0710072 + 0.0629657i
\(596\) 12.5885 7.26795i 0.515643 0.297707i
\(597\) 32.7846 18.9282i 1.34178 0.774680i
\(598\) 1.00000 0.0408930
\(599\) −6.58846 + 3.80385i −0.269197 + 0.155421i −0.628523 0.777791i \(-0.716340\pi\)
0.359326 + 0.933212i \(0.383007\pi\)
\(600\) 12.1244 + 1.73205i 0.494975 + 0.0707107i
\(601\) −0.303848 + 0.526279i −0.0123942 + 0.0214674i −0.872156 0.489228i \(-0.837279\pi\)
0.859762 + 0.510695i \(0.170612\pi\)
\(602\) 4.00000 4.00000i 0.163028 0.163028i
\(603\) 23.1962 23.1962i 0.944620 0.944620i
\(604\) 5.83013 + 3.36603i 0.237225 + 0.136962i
\(605\) 24.0718 1.44486i 0.978658 0.0587421i
\(606\) −21.4641 21.4641i −0.871920 0.871920i
\(607\) 1.73205 3.00000i 0.0703018 0.121766i −0.828732 0.559646i \(-0.810937\pi\)
0.899034 + 0.437880i \(0.144270\pi\)
\(608\) −0.500000 + 0.133975i −0.0202777 + 0.00543339i
\(609\) −6.92820 + 1.85641i −0.280745 + 0.0752254i
\(610\) −3.63397 3.22243i −0.147135 0.130472i
\(611\) 10.6962 + 2.86603i 0.432720 + 0.115947i
\(612\) −1.09808 + 1.90192i −0.0443871 + 0.0768807i
\(613\) −4.86603 18.1603i −0.196537 0.733486i −0.991864 0.127305i \(-0.959367\pi\)
0.795327 0.606181i \(-0.207299\pi\)
\(614\) −2.36603 + 0.633975i −0.0954850 + 0.0255851i
\(615\) −49.1769 + 16.3923i −1.98300 + 0.661002i
\(616\) −0.169873 + 0.633975i −0.00684438 + 0.0255436i
\(617\) −2.53590 + 0.679492i −0.102091 + 0.0273553i −0.309503 0.950898i \(-0.600163\pi\)
0.207412 + 0.978254i \(0.433496\pi\)
\(618\) 30.1244 + 30.1244i 1.21178 + 1.21178i
\(619\) −41.3205 −1.66081 −0.830406 0.557159i \(-0.811891\pi\)
−0.830406 + 0.557159i \(0.811891\pi\)
\(620\) −3.92820 + 19.1962i −0.157760 + 0.770936i
\(621\) 0 0
\(622\) 0.0980762 0.366025i 0.00393250 0.0146763i
\(623\) 20.7321i 0.830612i
\(624\) −8.83013 2.36603i −0.353488 0.0947168i
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) 0.0717968 + 0.124356i 0.00286958 + 0.00497025i
\(627\) −0.509619 0.294229i −0.0203522 0.0117504i
\(628\) 14.2942 14.2942i 0.570402 0.570402i
\(629\) 1.90192 4.02628i 0.0758347 0.160538i
\(630\) 9.00000 3.00000i 0.358569 0.119523i
\(631\) 15.8301 4.24167i 0.630187 0.168858i 0.0704327 0.997517i \(-0.477562\pi\)
0.559755 + 0.828658i \(0.310895\pi\)
\(632\) −0.928203 + 3.46410i −0.0369219 + 0.137795i
\(633\) −2.02628 0.542940i −0.0805374 0.0215799i
\(634\) 6.03590 22.5263i 0.239716 0.894633i
\(635\) −11.2942 33.8827i −0.448198 1.34459i
\(636\) 10.8564 + 18.8038i 0.430485 + 0.745621i
\(637\) 18.6603i 0.739346i
\(638\) 0.928203 0.248711i 0.0367479 0.00984657i
\(639\) 18.0000i 0.712069i
\(640\) −1.00000 + 2.00000i −0.0395285 + 0.0790569i
\(641\) 16.1603 27.9904i 0.638292 1.10555i −0.347516 0.937674i \(-0.612975\pi\)
0.985808 0.167879i \(-0.0536919\pi\)
\(642\) −22.3923 + 12.9282i −0.883754 + 0.510235i
\(643\) 46.2487i 1.82387i −0.410333 0.911936i \(-0.634588\pi\)
0.410333 0.911936i \(-0.365412\pi\)
\(644\) −0.0980762 0.366025i −0.00386474 0.0144234i
\(645\) 21.4641 + 4.39230i 0.845148 + 0.172947i
\(646\) −0.0980762 0.366025i −0.00385876 0.0144011i
\(647\) 9.08846 + 15.7417i 0.357304 + 0.618869i 0.987509 0.157560i \(-0.0503626\pi\)
−0.630205 + 0.776428i \(0.717029\pi\)
\(648\) −4.50000 7.79423i −0.176777 0.306186i
\(649\) 0.571797 + 2.13397i 0.0224450 + 0.0837658i
\(650\) −18.5263 + 2.23205i −0.726660 + 0.0875482i
\(651\) 7.85641 + 29.3205i 0.307917 + 1.14916i
\(652\) 4.73205i 0.185321i
\(653\) 1.45448 0.839746i 0.0569183 0.0328618i −0.471271 0.881989i \(-0.656205\pi\)
0.528189 + 0.849127i \(0.322871\pi\)
\(654\) 7.39230 12.8038i 0.289062 0.500670i
\(655\) −11.7846 + 3.92820i −0.460463 + 0.153488i
\(656\) 9.46410i 0.369511i
\(657\) 24.2942 6.50962i 0.947808 0.253964i
\(658\) 4.19615i 0.163583i
\(659\) −5.79423 10.0359i −0.225711 0.390943i 0.730821 0.682569i \(-0.239137\pi\)
−0.956533 + 0.291626i \(0.905804\pi\)
\(660\) −2.41154 + 0.803848i −0.0938692 + 0.0312897i
\(661\) 9.29423 34.6865i 0.361504 1.34915i −0.510596 0.859821i \(-0.670575\pi\)
0.872099 0.489329i \(-0.162758\pi\)
\(662\) −4.96410 1.33013i −0.192935 0.0516969i
\(663\) 1.73205 6.46410i 0.0672673 0.251045i
\(664\) −5.46410 + 1.46410i −0.212048 + 0.0568182i
\(665\) −0.732051 + 1.46410i −0.0283877 + 0.0567754i
\(666\) −10.3923 15.0000i −0.402694 0.581238i
\(667\) −0.392305 + 0.392305i −0.0151901 + 0.0151901i
\(668\) −13.8564 8.00000i −0.536120 0.309529i
\(669\) 19.6865 + 34.0981i 0.761125 + 1.31831i
\(670\) 18.2942 + 16.2224i 0.706768 + 0.626727i
\(671\) 0.973721 + 0.260908i 0.0375901 + 0.0100722i
\(672\) 3.46410i 0.133631i
\(673\) −8.07180 + 30.1244i −0.311145 + 1.16121i 0.616381 + 0.787448i \(0.288598\pi\)
−0.927525 + 0.373760i \(0.878068\pi\)
\(674\) 1.85641 + 1.85641i 0.0715061 + 0.0715061i
\(675\) 0 0
\(676\) 0.928203 0.0357001
\(677\) 14.4378 + 14.4378i 0.554891 + 0.554891i 0.927848 0.372958i \(-0.121656\pi\)
−0.372958 + 0.927848i \(0.621656\pi\)
\(678\) −14.6603 + 3.92820i −0.563024 + 0.150862i
\(679\) −3.46410 + 12.9282i −0.132940 + 0.496139i
\(680\) −1.46410 0.732051i −0.0561457 0.0280729i
\(681\) −68.5692 + 18.3731i −2.62758 + 0.704057i
\(682\) −1.05256 3.92820i −0.0403046 0.150419i
\(683\) −0.803848 + 1.39230i −0.0307584 + 0.0532751i −0.880995 0.473126i \(-0.843126\pi\)
0.850236 + 0.526401i \(0.176459\pi\)
\(684\) −1.50000 0.401924i −0.0573539 0.0153679i
\(685\) −13.0000 + 14.6603i −0.496704 + 0.560140i
\(686\) −16.3923 + 4.39230i −0.625861 + 0.167699i
\(687\) 29.6603 7.94744i 1.13161 0.303214i
\(688\) −2.00000 + 3.46410i −0.0762493 + 0.132068i
\(689\) −23.3923 23.3923i −0.891176 0.891176i
\(690\) 0.973721 1.09808i 0.0370689 0.0418030i
\(691\) −41.6603 24.0526i −1.58483 0.915002i −0.994140 0.108105i \(-0.965522\pi\)
−0.590691 0.806898i \(-0.701145\pi\)
\(692\) 15.9545 15.9545i 0.606498 0.606498i
\(693\) −1.39230 + 1.39230i −0.0528893 + 0.0528893i
\(694\) 4.56218 7.90192i 0.173178 0.299953i
\(695\) −8.26795 + 16.5359i −0.313621 + 0.627242i
\(696\) 4.39230 2.53590i 0.166490 0.0961230i
\(697\) 6.92820 0.262424
\(698\) −15.9282 + 9.19615i −0.602891 + 0.348080i
\(699\) −9.58846 + 5.53590i −0.362669 + 0.209387i
\(700\) 2.63397 + 6.56218i 0.0995549 + 0.248027i
\(701\) −3.68653 13.7583i −0.139238 0.519645i −0.999944 0.0105426i \(-0.996644\pi\)
0.860706 0.509102i \(-0.170023\pi\)
\(702\) 0 0
\(703\) 3.09808 + 0.562178i 0.116846 + 0.0212029i
\(704\) 0.464102i 0.0174915i
\(705\) 13.5622 8.95448i 0.510781 0.337245i
\(706\) −11.4904 + 6.63397i −0.432446 + 0.249673i
\(707\) 4.53590 16.9282i 0.170590 0.636651i
\(708\) 5.83013 + 10.0981i 0.219110 + 0.379509i
\(709\) −20.1962 20.1962i −0.758482 0.758482i 0.217564 0.976046i \(-0.430189\pi\)
−0.976046 + 0.217564i \(0.930189\pi\)
\(710\) −13.3923 + 0.803848i −0.502604 + 0.0301679i
\(711\) −7.60770 + 7.60770i −0.285311 + 0.285311i
\(712\) −3.79423 14.1603i −0.142195 0.530678i
\(713\) 1.66025 + 1.66025i 0.0621770 + 0.0621770i
\(714\) −2.53590 −0.0949036
\(715\) 3.23205 2.13397i 0.120872 0.0798061i
\(716\) −17.1603 4.59808i −0.641309 0.171838i
\(717\) −62.1051 −2.31936
\(718\) 2.70577 + 1.56218i 0.100978 + 0.0583000i
\(719\) 10.2679 + 5.92820i 0.382930 + 0.221085i 0.679092 0.734053i \(-0.262374\pi\)
−0.296162 + 0.955138i \(0.595707\pi\)
\(720\) −5.59808 + 3.69615i −0.208628 + 0.137747i
\(721\) −6.36603 + 23.7583i −0.237083 + 0.884806i
\(722\) −16.2224 + 9.36603i −0.603736 + 0.348567i
\(723\) −19.6865 11.3660i −0.732150 0.422707i
\(724\) 6.02628 10.4378i 0.223965 0.387919i
\(725\) 6.39230 8.14359i 0.237404 0.302445i
\(726\) −18.6795 + 18.6795i −0.693261 + 0.693261i
\(727\) 8.79423 + 15.2321i 0.326160 + 0.564925i 0.981746 0.190195i \(-0.0609119\pi\)
−0.655587 + 0.755120i \(0.727579\pi\)
\(728\) −1.36603 5.09808i −0.0506283 0.188947i
\(729\) 27.0000i 1.00000i
\(730\) 5.92820 + 17.7846i 0.219413 + 0.658238i
\(731\) −2.53590 1.46410i −0.0937936 0.0541518i
\(732\) 5.32051 0.196652
\(733\) −12.6962 3.40192i −0.468943 0.125653i 0.0166064 0.999862i \(-0.494714\pi\)
−0.485549 + 0.874209i \(0.661380\pi\)
\(734\) 10.4378 10.4378i 0.385267 0.385267i
\(735\) −20.4904 18.1699i −0.755799 0.670206i
\(736\) 0.133975 + 0.232051i 0.00493837 + 0.00855351i
\(737\) −4.90192 1.31347i −0.180565 0.0483822i
\(738\) 14.1962 24.5885i 0.522568 0.905114i
\(739\) 47.7321 1.75585 0.877926 0.478796i \(-0.158927\pi\)
0.877926 + 0.478796i \(0.158927\pi\)
\(740\) 10.6962 8.40192i 0.393198 0.308861i
\(741\) 4.73205 0.173836
\(742\) −6.26795 + 10.8564i −0.230104 + 0.398551i
\(743\) −21.4282 5.74167i −0.786125 0.210641i −0.156641 0.987656i \(-0.550067\pi\)
−0.629483 + 0.777014i \(0.716733\pi\)
\(744\) −10.7321 18.5885i −0.393456 0.681486i
\(745\) 1.94744 + 32.4449i 0.0713487 + 1.18869i
\(746\) 1.29423 1.29423i 0.0473851 0.0473851i
\(747\) −16.3923 4.39230i −0.599763 0.160706i
\(748\) 0.339746 0.0124223
\(749\) −12.9282 7.46410i −0.472386 0.272732i
\(750\) −15.5885 + 22.5167i −0.569210 + 0.822192i
\(751\) 45.1769i 1.64853i 0.566205 + 0.824265i \(0.308411\pi\)
−0.566205 + 0.824265i \(0.691589\pi\)
\(752\) 0.767949 + 2.86603i 0.0280042 + 0.104513i
\(753\) −20.9545 36.2942i −0.763624 1.32264i
\(754\) −5.46410 + 5.46410i −0.198991 + 0.198991i
\(755\) −12.5622 + 8.29423i −0.457184 + 0.301858i
\(756\) 0 0
\(757\) 35.0429 + 20.2321i 1.27366 + 0.735346i 0.975674 0.219225i \(-0.0703528\pi\)
0.297983 + 0.954571i \(0.403686\pi\)
\(758\) −8.87564 + 5.12436i −0.322378 + 0.186125i
\(759\) −0.0788383 + 0.294229i −0.00286165 + 0.0106798i
\(760\) 0.232051 1.13397i 0.00841737 0.0411336i
\(761\) 7.50000 + 4.33013i 0.271875 + 0.156967i 0.629739 0.776807i \(-0.283162\pi\)
−0.357865 + 0.933774i \(0.616495\pi\)
\(762\) 33.8827 + 19.5622i 1.22744 + 0.708663i
\(763\) 8.53590 0.309020
\(764\) 22.1244 + 5.92820i 0.800431 + 0.214475i
\(765\) −2.70577 4.09808i −0.0978274 0.148166i
\(766\) −20.6603 −0.746485
\(767\) −12.5622 12.5622i −0.453594 0.453594i
\(768\) −0.633975 2.36603i −0.0228766 0.0853766i
\(769\) 3.58846 3.58846i 0.129403 0.129403i −0.639439 0.768842i \(-0.720833\pi\)
0.768842 + 0.639439i \(0.220833\pi\)
\(770\) −1.09808 0.973721i −0.0395719 0.0350905i
\(771\) 26.1962 + 26.1962i 0.943431 + 0.943431i
\(772\) −11.0981 19.2224i −0.399429 0.691830i
\(773\) 8.55256 31.9186i 0.307614 1.14803i −0.623057 0.782176i \(-0.714110\pi\)
0.930672 0.365856i \(-0.119224\pi\)
\(774\) −10.3923 + 6.00000i −0.373544 + 0.215666i
\(775\) −34.4641 27.0526i −1.23799 0.971757i
\(776\) 9.46410i 0.339741i
\(777\) 9.00000 19.0526i 0.322873 0.683507i
\(778\) 10.9282 + 10.9282i 0.391795 + 0.391795i
\(779\) 1.26795 + 4.73205i 0.0454290 + 0.169543i
\(780\) 13.5622 15.2942i 0.485604 0.547621i
\(781\) 2.41154 1.39230i 0.0862918 0.0498206i
\(782\) −0.169873 + 0.0980762i −0.00607465 + 0.00350720i
\(783\) 0 0
\(784\) 4.33013 2.50000i 0.154647 0.0892857i
\(785\) 14.2942 + 42.8827i 0.510183 + 1.53055i
\(786\) 6.80385 11.7846i 0.242685 0.420343i
\(787\) 21.9282 21.9282i 0.781656 0.781656i −0.198454 0.980110i \(-0.563592\pi\)
0.980110 + 0.198454i \(0.0635921\pi\)
\(788\) 12.4641 12.4641i 0.444015 0.444015i
\(789\) 5.49038 + 3.16987i 0.195463 + 0.112850i
\(790\) −6.00000 5.32051i −0.213470 0.189295i
\(791\) −6.19615 6.19615i −0.220310 0.220310i
\(792\) 0.696152 1.20577i 0.0247367 0.0428452i
\(793\) −7.83013 + 2.09808i −0.278056 + 0.0745049i
\(794\) 16.2583 4.35641i 0.576987 0.154603i
\(795\) −48.4641 + 2.90897i −1.71884 + 0.103170i
\(796\) −14.9282 4.00000i −0.529116 0.141776i
\(797\) −4.30385 + 7.45448i −0.152450 + 0.264051i −0.932128 0.362130i \(-0.882050\pi\)
0.779678 + 0.626181i \(0.215383\pi\)
\(798\) −0.464102 1.73205i −0.0164290 0.0613139i
\(799\) −2.09808 + 0.562178i −0.0742246 + 0.0198884i
\(800\) −3.00000 4.00000i −0.106066 0.141421i
\(801\) 11.3827 42.4808i 0.402187 1.50098i
\(802\) −19.8923 + 5.33013i −0.702422 + 0.188213i
\(803\) −2.75129 2.75129i −0.0970909 0.0970909i
\(804\) −26.7846 −0.944620
\(805\) 0.830127 + 0.169873i 0.0292581 + 0.00598724i
\(806\) 23.1244 + 23.1244i 0.814521 + 0.814521i
\(807\) 5.87564 21.9282i 0.206832 0.771909i
\(808\) 12.3923i 0.435960i
\(809\) 30.2583 + 8.10770i 1.06383 + 0.285051i 0.747954 0.663750i \(-0.231036\pi\)
0.315872 + 0.948802i \(0.397703\pi\)
\(810\) 20.0885 1.20577i 0.705836 0.0423665i
\(811\) −14.9378 25.8731i −0.524538 0.908526i −0.999592 0.0285696i \(-0.990905\pi\)
0.475054 0.879957i \(-0.342429\pi\)
\(812\) 2.53590 + 1.46410i 0.0889926 + 0.0513799i
\(813\) −51.4641 + 51.4641i −1.80492 + 1.80492i
\(814\) −1.20577 + 2.55256i −0.0422623 + 0.0894671i
\(815\) 9.46410 + 4.73205i 0.331513 + 0.165757i
\(816\) 1.73205 0.464102i 0.0606339 0.0162468i
\(817\) 0.535898 2.00000i 0.0187487 0.0699711i
\(818\) 9.09808 + 2.43782i 0.318107 + 0.0852365i
\(819\) 4.09808 15.2942i 0.143198 0.534424i
\(820\) 18.9282 + 9.46410i 0.661002 + 0.330501i
\(821\) −14.6603 25.3923i −0.511646 0.886198i −0.999909 0.0135007i \(-0.995702\pi\)
0.488262 0.872697i \(-0.337631\pi\)
\(822\) 21.4641i 0.748647i
\(823\) −8.90192 + 2.38526i −0.310302 + 0.0831451i −0.410609 0.911811i \(-0.634684\pi\)
0.100308 + 0.994956i \(0.468017\pi\)
\(824\) 17.3923i 0.605890i
\(825\) 0.803848 5.62693i 0.0279864 0.195905i
\(826\) −3.36603 + 5.83013i −0.117119 + 0.202856i
\(827\) −20.8301 + 12.0263i −0.724334 + 0.418195i −0.816346 0.577563i \(-0.804004\pi\)
0.0920115 + 0.995758i \(0.470670\pi\)
\(828\) 0.803848i 0.0279356i
\(829\) −10.8301 40.4186i −0.376146 1.40380i −0.851663 0.524089i \(-0.824406\pi\)
0.475518 0.879706i \(-0.342261\pi\)
\(830\) 2.53590 12.3923i 0.0880223 0.430143i
\(831\) 9.21539 + 34.3923i 0.319678 + 1.19306i
\(832\) 1.86603 + 3.23205i 0.0646928 + 0.112051i
\(833\) 1.83013 + 3.16987i 0.0634101 + 0.109830i
\(834\) −5.24167 19.5622i −0.181504 0.677383i
\(835\) 29.8564 19.7128i 1.03322 0.682190i
\(836\) 0.0621778 + 0.232051i 0.00215047 + 0.00802564i
\(837\) 0 0
\(838\) −23.0885 + 13.3301i −0.797578 + 0.460482i
\(839\) 11.8301 20.4904i 0.408421 0.707407i −0.586292 0.810100i \(-0.699413\pi\)
0.994713 + 0.102694i \(0.0327461\pi\)
\(840\) −6.92820 3.46410i −0.239046 0.119523i
\(841\) 24.7128i 0.852166i
\(842\) −26.3923 + 7.07180i −0.909539 + 0.243710i
\(843\) 61.5167i 2.11875i
\(844\) 0.428203 + 0.741670i 0.0147394 + 0.0255293i
\(845\) −0.928203 + 1.85641i −0.0319312 + 0.0638623i
\(846\) −2.30385 + 8.59808i −0.0792079 + 0.295608i
\(847\) −14.7321 3.94744i −0.506199 0.135636i
\(848\) 2.29423 8.56218i 0.0787841 0.294026i
\(849\) 33.5885 9.00000i 1.15275 0.308879i
\(850\) 2.92820 2.19615i 0.100437 0.0753274i
\(851\) −0.133975 1.62436i −0.00459259 0.0556822i
\(852\) 10.3923 10.3923i 0.356034 0.356034i
\(853\) −7.45448 4.30385i −0.255237 0.147361i 0.366923 0.930251i \(-0.380411\pi\)
−0.622160 + 0.782890i \(0.713745\pi\)
\(854\) 1.53590 + 2.66025i 0.0525574 + 0.0910320i
\(855\) 2.30385 2.59808i 0.0787899 0.0888523i
\(856\) 10.1962 + 2.73205i 0.348497 + 0.0933796i
\(857\) 23.0718i 0.788118i −0.919085 0.394059i \(-0.871071\pi\)
0.919085 0.394059i \(-0.128929\pi\)
\(858\) −1.09808 + 4.09808i −0.0374877 + 0.139906i
\(859\) −1.31347 1.31347i −0.0448149 0.0448149i 0.684344 0.729159i \(-0.260089\pi\)
−0.729159 + 0.684344i \(0.760089\pi\)
\(860\) −4.92820 7.46410i −0.168050 0.254524i
\(861\) 32.7846 1.11730
\(862\) 19.7846 + 19.7846i 0.673866 + 0.673866i
\(863\) −48.7487 + 13.0622i −1.65943 + 0.444642i −0.962230 0.272239i \(-0.912236\pi\)
−0.697196 + 0.716881i \(0.745569\pi\)
\(864\) 0 0
\(865\) 15.9545 + 47.8634i 0.542469 + 1.62741i
\(866\) −38.9545 + 10.4378i −1.32373 + 0.354692i
\(867\) −10.4378 38.9545i −0.354487 1.32296i
\(868\) 6.19615 10.7321i 0.210311 0.364270i
\(869\) 1.60770 + 0.430781i 0.0545373 + 0.0146132i
\(870\) 0.679492 + 11.3205i 0.0230369 + 0.383801i
\(871\) 39.4186 10.5622i 1.33565 0.357886i
\(872\) −5.83013 + 1.56218i −0.197433 + 0.0529020i
\(873\) 14.1962 24.5885i 0.480467 0.832193i
\(874\) −0.0980762 0.0980762i −0.00331748 0.00331748i
\(875\) −15.7583 1.29423i −0.532729 0.0437529i
\(876\) −17.7846 10.2679i −0.600886 0.346922i
\(877\) 12.2224 12.2224i 0.412722 0.412722i −0.469964 0.882686i \(-0.655733\pi\)
0.882686 + 0.469964i \(0.155733\pi\)
\(878\) −4.66025 + 4.66025i −0.157276 + 0.157276i
\(879\) 14.4904 25.0981i 0.488748 0.846537i
\(880\) 0.928203 + 0.464102i 0.0312897 + 0.0156449i
\(881\) −31.5788 + 18.2321i −1.06392 + 0.614253i −0.926513 0.376262i \(-0.877209\pi\)
−0.137405 + 0.990515i \(0.543876\pi\)
\(882\) 15.0000 0.505076
\(883\) −10.9808 + 6.33975i −0.369532 + 0.213349i −0.673254 0.739411i \(-0.735104\pi\)
0.303722 + 0.952761i \(0.401771\pi\)
\(884\) −2.36603 + 1.36603i −0.0795780 + 0.0459444i
\(885\) −26.0263 + 1.56218i −0.874864 + 0.0525120i
\(886\) −3.60770 13.4641i −0.121203 0.452335i
\(887\) 33.1962 + 33.1962i 1.11462 + 1.11462i 0.992518 + 0.122100i \(0.0389628\pi\)
0.122100 + 0.992518i \(0.461037\pi\)
\(888\) −2.66025 + 14.6603i −0.0892723 + 0.491966i
\(889\) 22.5885i 0.757593i
\(890\) 32.1147 + 6.57180i 1.07649 + 0.220287i
\(891\) −3.61731 + 2.08846i −0.121185 + 0.0699660i
\(892\) 4.16025 15.5263i 0.139296 0.519858i
\(893\) −0.767949 1.33013i −0.0256984 0.0445110i
\(894\) −25.1769 25.1769i −0.842042 0.842042i
\(895\) 26.3564 29.7224i 0.880998 0.993511i
\(896\) 1.00000 1.00000i 0.0334077 0.0334077i
\(897\) −0.633975 2.36603i −0.0211678 0.0789993i
\(898\) 8.80385 + 8.80385i 0.293788 + 0.293788i
\(899\) −18.1436 −0.605123
\(900\) −1.79423 14.8923i −0.0598076 0.496410i
\(901\) 6.26795 + 1.67949i 0.208816 + 0.0559520i
\(902\) −4.39230 −0.146248
\(903\) −12.0000 6.92820i −0.399335 0.230556i
\(904\) 5.36603 + 3.09808i 0.178471 + 0.103040i
\(905\) 14.8494 + 22.4904i 0.493610 + 0.747606i
\(906\) 4.26795 15.9282i 0.141793 0.529179i
\(907\) −5.61474 + 3.24167i −0.186434 + 0.107638i −0.590312 0.807175i \(-0.700995\pi\)
0.403878 + 0.914813i \(0.367662\pi\)
\(908\) 25.0981 + 14.4904i 0.832909 + 0.480880i
\(909\) −18.5885 + 32.1962i −0.616540 + 1.06788i
\(910\) 11.5622 + 2.36603i 0.383282 + 0.0784330i
\(911\) 15.5359 15.5359i 0.514727 0.514727i −0.401244 0.915971i \(-0.631422\pi\)
0.915971 + 0.401244i \(0.131422\pi\)
\(912\) 0.633975 + 1.09808i 0.0209930 + 0.0363609i
\(913\) 0.679492 + 2.53590i 0.0224879 + 0.0839260i
\(914\) 1.46410i 0.0484282i
\(915\) −5.32051 + 10.6410i −0.175891 + 0.351781i
\(916\) −10.8564 6.26795i −0.358706 0.207099i
\(917\) 7.85641 0.259441
\(918\) 0 0
\(919\) −7.33975 + 7.33975i −0.242116 + 0.242116i −0.817725 0.575609i \(-0.804765\pi\)
0.575609 + 0.817725i \(0.304765\pi\)
\(920\) −0.598076 + 0.0358984i −0.0197180 + 0.00118353i
\(921\) 3.00000 + 5.19615i 0.0988534 + 0.171219i
\(922\) 22.0263 + 5.90192i 0.725397 + 0.194370i
\(923\) −11.1962 + 19.3923i −0.368526 + 0.638305i
\(924\) 1.60770 0.0528893
\(925\) 6.10770 + 29.7942i 0.200820 + 0.979628i
\(926\) 36.7846 1.20882
\(927\) 26.0885 45.1865i 0.856857 1.48412i
\(928\) −2.00000 0.535898i −0.0656532 0.0175917i
\(929\) −5.45448 9.44744i −0.178956 0.309960i 0.762567 0.646909i \(-0.223939\pi\)
−0.941523 + 0.336948i \(0.890605\pi\)
\(930\) 47.9090 2.87564i 1.57100 0.0942961i
\(931\) −1.83013 + 1.83013i −0.0599800 + 0.0599800i
\(932\) 4.36603 + 1.16987i 0.143014 + 0.0383205i
\(933\) −0.928203 −0.0303880
\(934\) −8.95448 5.16987i −0.293000 0.169163i
\(935\) −0.339746 + 0.679492i −0.0111109 + 0.0222218i
\(936\) 11.1962i 0.365958i
\(937\) −7.97372 29.7583i −0.260490 0.972162i −0.964953 0.262422i \(-0.915479\pi\)
0.704463 0.709741i \(-0.251188\pi\)
\(938\) −7.73205 13.3923i −0.252460 0.437274i
\(939\) 0.248711 0.248711i 0.00811639 0.00811639i
\(940\) −6.50000 1.33013i −0.212007 0.0433840i
\(941\) 24.6603 42.7128i 0.803901 1.39240i −0.113129 0.993580i \(-0.536087\pi\)
0.917030 0.398818i \(-0.130579\pi\)
\(942\) −42.8827 24.7583i −1.39719 0.806670i
\(943\) 2.19615 1.26795i 0.0715166 0.0412901i
\(944\) 1.23205 4.59808i 0.0400998 0.149655i
\(945\) 0 0
\(946\) 1.60770 + 0.928203i 0.0522707 + 0.0301785i
\(947\) −14.0263 8.09808i −0.455793 0.263152i 0.254481 0.967078i \(-0.418095\pi\)
−0.710274 + 0.703926i \(0.751429\pi\)
\(948\) 8.78461 0.285311
\(949\) 30.2224 + 8.09808i 0.981062 + 0.262875i
\(950\) 2.03590 + 1.59808i 0.0660533 + 0.0518484i
\(951\) −57.1244 −1.85238
\(952\) 0.732051 + 0.732051i 0.0237259 + 0.0237259i
\(953\) 1.60770 + 6.00000i 0.0520784 + 0.194359i 0.987064 0.160326i \(-0.0512546\pi\)
−0.934986 + 0.354685i \(0.884588\pi\)
\(954\) 18.8038 18.8038i 0.608797 0.608797i
\(955\) −33.9808 + 38.3205i −1.09959 + 1.24002i
\(956\) 17.9282 + 17.9282i 0.579840 + 0.579840i
\(957\) −1.17691 2.03848i −0.0380442 0.0658946i
\(958\) 2.39230 8.92820i 0.0772919 0.288457i
\(959\) 10.7321 6.19615i 0.346556 0.200084i
\(960\) 5.36603 + 1.09808i 0.173188 + 0.0354403i
\(961\) 45.7846i 1.47692i
\(962\) −1.86603 22.6244i −0.0601631 0.729439i
\(963\) 22.3923 + 22.3923i 0.721582 + 0.721582i
\(964\) 2.40192 + 8.96410i 0.0773608 + 0.288714i
\(965\) 49.5429 2.97372i 1.59484 0.0957275i
\(966\) −0.803848 + 0.464102i −0.0258634 + 0.0149322i
\(967\) −35.0885 + 20.2583i −1.12837 + 0.651464i −0.943524 0.331304i \(-0.892512\pi\)
−0.184845 + 0.982768i \(0.559178\pi\)
\(968\) 10.7846 0.346630
\(969\) −0.803848 + 0.464102i −0.0258233 + 0.0149091i
\(970\) 18.9282 + 9.46410i 0.607748 + 0.303874i
\(971\) 17.9641 31.1147i 0.576495 0.998519i −0.419382 0.907810i \(-0.637753\pi\)
0.995877 0.0907095i \(-0.0289135\pi\)
\(972\) −15.5885 + 15.5885i −0.500000 + 0.500000i
\(973\) 8.26795 8.26795i 0.265058 0.265058i
\(974\) −9.33975 5.39230i −0.299265 0.172781i
\(975\) 17.0263 + 42.4186i 0.545277 + 1.35848i
\(976\) −1.53590 1.53590i −0.0491629 0.0491629i
\(977\) −25.0981 + 43.4711i −0.802959 + 1.39077i 0.114702 + 0.993400i \(0.463409\pi\)
−0.917661 + 0.397365i \(0.869925\pi\)
\(978\) −11.1962 + 3.00000i −0.358013 + 0.0959294i
\(979\) −6.57180 + 1.76091i −0.210036 + 0.0562789i
\(980\) 0.669873 + 11.1603i 0.0213983 + 0.356501i
\(981\) −17.4904 4.68653i −0.558425 0.149629i
\(982\) −1.30385 + 2.25833i −0.0416074 + 0.0720662i
\(983\) 13.9641 + 52.1147i 0.445386 + 1.66220i 0.714916 + 0.699210i \(0.246465\pi\)
−0.269531 + 0.962992i \(0.586869\pi\)
\(984\) −22.3923 + 6.00000i −0.713841 + 0.191273i
\(985\) 12.4641 + 37.3923i 0.397139 + 1.19142i
\(986\) 0.392305 1.46410i 0.0124935 0.0466265i
\(987\) −9.92820 + 2.66025i −0.316018 + 0.0846768i
\(988\) −1.36603 1.36603i −0.0434591 0.0434591i
\(989\) −1.07180 −0.0340812
\(990\) 1.71539 + 2.59808i 0.0545187 + 0.0825723i
\(991\) −18.5359 18.5359i −0.588812 0.588812i 0.348497 0.937310i \(-0.386692\pi\)
−0.937310 + 0.348497i \(0.886692\pi\)
\(992\) −2.26795 + 8.46410i −0.0720075 + 0.268735i
\(993\) 12.5885i 0.399483i
\(994\) 8.19615 + 2.19615i 0.259966 + 0.0696577i
\(995\) 22.9282 25.8564i 0.726873 0.819703i
\(996\) 6.92820 + 12.0000i 0.219529 + 0.380235i
\(997\) −34.1147 19.6962i −1.08042 0.623783i −0.149414 0.988775i \(-0.547739\pi\)
−0.931011 + 0.364991i \(0.881072\pi\)
\(998\) −15.5359 + 15.5359i −0.491780 + 0.491780i
\(999\) 0 0
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 370.2.q.b.273.1 yes 4
5.2 odd 4 370.2.r.b.347.1 yes 4
37.8 odd 12 370.2.r.b.193.1 yes 4
185.82 even 12 inner 370.2.q.b.267.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.q.b.267.1 4 185.82 even 12 inner
370.2.q.b.273.1 yes 4 1.1 even 1 trivial
370.2.r.b.193.1 yes 4 37.8 odd 12
370.2.r.b.347.1 yes 4 5.2 odd 4