Properties

Label 360.2.br.c.173.1
Level $360$
Weight $2$
Character 360.173
Analytic conductor $2.875$
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] = [360,2,Mod(77,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.77");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.br (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: \(2.87461447277\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 173.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 360.173
Dual form 360.2.br.c.77.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36603 - 0.366025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.23205 - 0.133975i) q^{5} +(2.36603 - 0.633975i) q^{6} +(1.13397 + 4.23205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.36603 - 0.366025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.23205 - 0.133975i) q^{5} +(2.36603 - 0.633975i) q^{6} +(1.13397 + 4.23205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +(-3.09808 - 0.633975i) q^{10} +(1.00000 - 1.73205i) q^{11} -3.46410 q^{12} +(-1.73205 - 0.464102i) q^{13} -6.19615i q^{14} +(-3.23205 + 2.13397i) q^{15} +(2.00000 + 3.46410i) q^{16} +(3.00000 + 3.00000i) q^{17} +(-3.00000 + 3.00000i) q^{18} -4.73205 q^{19} +(4.00000 + 2.00000i) q^{20} +(-5.36603 - 5.36603i) q^{21} +(-2.00000 + 2.00000i) q^{22} +(0.866025 + 0.232051i) q^{23} +(4.73205 + 1.26795i) q^{24} +(4.96410 - 0.598076i) q^{25} +(2.19615 + 1.26795i) q^{26} +5.19615i q^{27} +(-2.26795 + 8.46410i) q^{28} +(2.76795 + 1.59808i) q^{29} +(5.19615 - 1.73205i) q^{30} +(4.09808 + 7.09808i) q^{31} +(-1.46410 - 5.46410i) q^{32} +3.46410i q^{33} +(-3.00000 - 5.19615i) q^{34} +(3.09808 + 9.29423i) q^{35} +(5.19615 - 3.00000i) q^{36} +(-0.464102 - 0.464102i) q^{37} +(6.46410 + 1.73205i) q^{38} +(3.00000 - 0.803848i) q^{39} +(-4.73205 - 4.19615i) q^{40} +(-5.59808 + 3.23205i) q^{41} +(5.36603 + 9.29423i) q^{42} +(2.36603 + 8.83013i) q^{43} +(3.46410 - 2.00000i) q^{44} +(3.00000 - 6.00000i) q^{45} +(-1.09808 - 0.633975i) q^{46} +(-1.50000 + 0.401924i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-10.5622 + 6.09808i) q^{49} +(-7.00000 - 1.00000i) q^{50} +(-7.09808 - 1.90192i) q^{51} +(-2.53590 - 2.53590i) q^{52} +(-5.19615 - 5.19615i) q^{53} +(1.90192 - 7.09808i) q^{54} +(2.00000 - 4.00000i) q^{55} +(6.19615 - 10.7321i) q^{56} +(7.09808 - 4.09808i) q^{57} +(-3.19615 - 3.19615i) q^{58} +(1.56218 - 0.901924i) q^{59} +(-7.73205 + 0.464102i) q^{60} +(12.6962 + 7.33013i) q^{61} +(-3.00000 - 11.1962i) q^{62} +(12.6962 + 3.40192i) q^{63} +8.00000i q^{64} +(-3.92820 - 0.803848i) q^{65} +(1.26795 - 4.73205i) q^{66} +(1.96410 - 7.33013i) q^{67} +(2.19615 + 8.19615i) q^{68} +(-1.50000 + 0.401924i) q^{69} +(-0.830127 - 13.8301i) q^{70} -12.0000i q^{71} +(-8.19615 + 2.19615i) q^{72} +(-10.1962 - 10.1962i) q^{73} +(0.464102 + 0.803848i) q^{74} +(-6.92820 + 5.19615i) q^{75} +(-8.19615 - 4.73205i) q^{76} +(8.46410 + 2.26795i) q^{77} -4.39230 q^{78} +(1.90192 + 1.09808i) q^{79} +(4.92820 + 7.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(8.83013 - 2.36603i) q^{82} +(-11.3301 + 3.03590i) q^{83} +(-3.92820 - 14.6603i) q^{84} +(7.09808 + 6.29423i) q^{85} -12.9282i q^{86} -5.53590 q^{87} +(-5.46410 + 1.46410i) q^{88} +2.66025 q^{89} +(-6.29423 + 7.09808i) q^{90} -7.85641i q^{91} +(1.26795 + 1.26795i) q^{92} +(-12.2942 - 7.09808i) q^{93} +2.19615 q^{94} +(-10.5622 + 0.633975i) q^{95} +(6.92820 + 6.92820i) q^{96} +(1.83013 + 6.83013i) q^{97} +(16.6603 - 4.46410i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 6 q^{3} + 2 q^{5} + 6 q^{6} + 8 q^{7} - 8 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 6 q^{3} + 2 q^{5} + 6 q^{6} + 8 q^{7} - 8 q^{8} + 6 q^{9} - 2 q^{10} + 4 q^{11} - 6 q^{15} + 8 q^{16} + 12 q^{17} - 12 q^{18} - 12 q^{19} + 16 q^{20} - 18 q^{21} - 8 q^{22} + 12 q^{24} + 6 q^{25} - 12 q^{26} - 16 q^{28} + 18 q^{29} + 6 q^{31} + 8 q^{32} - 12 q^{34} + 2 q^{35} + 12 q^{37} + 12 q^{38} + 12 q^{39} - 12 q^{40} - 12 q^{41} + 18 q^{42} + 6 q^{43} + 12 q^{45} + 6 q^{46} - 6 q^{47} - 24 q^{48} - 18 q^{49} - 28 q^{50} - 18 q^{51} - 24 q^{52} + 18 q^{54} + 8 q^{55} + 4 q^{56} + 18 q^{57} + 8 q^{58} - 18 q^{59} - 24 q^{60} + 30 q^{61} - 12 q^{62} + 30 q^{63} + 12 q^{65} + 12 q^{66} - 6 q^{67} - 12 q^{68} - 6 q^{69} + 14 q^{70} - 12 q^{72} - 20 q^{73} - 12 q^{74} - 12 q^{76} + 20 q^{77} + 24 q^{78} + 18 q^{79} - 8 q^{80} - 18 q^{81} + 18 q^{82} - 28 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{87} - 8 q^{88} - 24 q^{89} + 6 q^{90} + 12 q^{92} - 18 q^{93} - 12 q^{94} - 18 q^{95} - 10 q^{97} + 32 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 0.366025i −0.965926 0.258819i
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) 2.23205 0.133975i 0.998203 0.0599153i
\(6\) 2.36603 0.633975i 0.965926 0.258819i
\(7\) 1.13397 + 4.23205i 0.428602 + 1.59956i 0.755929 + 0.654654i \(0.227186\pi\)
−0.327327 + 0.944911i \(0.606148\pi\)
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −3.09808 0.633975i −0.979698 0.200480i
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) −3.46410 −1.00000
\(13\) −1.73205 0.464102i −0.480384 0.128719i 0.0104972 0.999945i \(-0.496659\pi\)
−0.490882 + 0.871226i \(0.663325\pi\)
\(14\) 6.19615i 1.65599i
\(15\) −3.23205 + 2.13397i −0.834512 + 0.550990i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 3.00000 + 3.00000i 0.727607 + 0.727607i 0.970143 0.242536i \(-0.0779791\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −3.00000 + 3.00000i −0.707107 + 0.707107i
\(19\) −4.73205 −1.08561 −0.542803 0.839860i \(-0.682637\pi\)
−0.542803 + 0.839860i \(0.682637\pi\)
\(20\) 4.00000 + 2.00000i 0.894427 + 0.447214i
\(21\) −5.36603 5.36603i −1.17096 1.17096i
\(22\) −2.00000 + 2.00000i −0.426401 + 0.426401i
\(23\) 0.866025 + 0.232051i 0.180579 + 0.0483859i 0.347975 0.937504i \(-0.386869\pi\)
−0.167396 + 0.985890i \(0.553536\pi\)
\(24\) 4.73205 + 1.26795i 0.965926 + 0.258819i
\(25\) 4.96410 0.598076i 0.992820 0.119615i
\(26\) 2.19615 + 1.26795i 0.430701 + 0.248665i
\(27\) 5.19615i 1.00000i
\(28\) −2.26795 + 8.46410i −0.428602 + 1.59956i
\(29\) 2.76795 + 1.59808i 0.513995 + 0.296755i 0.734474 0.678636i \(-0.237429\pi\)
−0.220479 + 0.975392i \(0.570762\pi\)
\(30\) 5.19615 1.73205i 0.948683 0.316228i
\(31\) 4.09808 + 7.09808i 0.736036 + 1.27485i 0.954267 + 0.298955i \(0.0966380\pi\)
−0.218231 + 0.975897i \(0.570029\pi\)
\(32\) −1.46410 5.46410i −0.258819 0.965926i
\(33\) 3.46410i 0.603023i
\(34\) −3.00000 5.19615i −0.514496 0.891133i
\(35\) 3.09808 + 9.29423i 0.523670 + 1.57101i
\(36\) 5.19615 3.00000i 0.866025 0.500000i
\(37\) −0.464102 0.464102i −0.0762978 0.0762978i 0.667928 0.744226i \(-0.267181\pi\)
−0.744226 + 0.667928i \(0.767181\pi\)
\(38\) 6.46410 + 1.73205i 1.04862 + 0.280976i
\(39\) 3.00000 0.803848i 0.480384 0.128719i
\(40\) −4.73205 4.19615i −0.748203 0.663470i
\(41\) −5.59808 + 3.23205i −0.874273 + 0.504762i −0.868766 0.495223i \(-0.835086\pi\)
−0.00550690 + 0.999985i \(0.501753\pi\)
\(42\) 5.36603 + 9.29423i 0.827996 + 1.43413i
\(43\) 2.36603 + 8.83013i 0.360815 + 1.34658i 0.873006 + 0.487710i \(0.162168\pi\)
−0.512190 + 0.858872i \(0.671166\pi\)
\(44\) 3.46410 2.00000i 0.522233 0.301511i
\(45\) 3.00000 6.00000i 0.447214 0.894427i
\(46\) −1.09808 0.633975i −0.161903 0.0934745i
\(47\) −1.50000 + 0.401924i −0.218797 + 0.0586266i −0.366552 0.930397i \(-0.619462\pi\)
0.147755 + 0.989024i \(0.452795\pi\)
\(48\) −6.00000 3.46410i −0.866025 0.500000i
\(49\) −10.5622 + 6.09808i −1.50888 + 0.871154i
\(50\) −7.00000 1.00000i −0.989949 0.141421i
\(51\) −7.09808 1.90192i −0.993929 0.266323i
\(52\) −2.53590 2.53590i −0.351666 0.351666i
\(53\) −5.19615 5.19615i −0.713746 0.713746i 0.253570 0.967317i \(-0.418395\pi\)
−0.967317 + 0.253570i \(0.918395\pi\)
\(54\) 1.90192 7.09808i 0.258819 0.965926i
\(55\) 2.00000 4.00000i 0.269680 0.539360i
\(56\) 6.19615 10.7321i 0.827996 1.43413i
\(57\) 7.09808 4.09808i 0.940163 0.542803i
\(58\) −3.19615 3.19615i −0.419675 0.419675i
\(59\) 1.56218 0.901924i 0.203378 0.117420i −0.394852 0.918745i \(-0.629204\pi\)
0.598230 + 0.801324i \(0.295871\pi\)
\(60\) −7.73205 + 0.464102i −0.998203 + 0.0599153i
\(61\) 12.6962 + 7.33013i 1.62558 + 0.938527i 0.985391 + 0.170305i \(0.0544754\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) −3.00000 11.1962i −0.381000 1.42191i
\(63\) 12.6962 + 3.40192i 1.59956 + 0.428602i
\(64\) 8.00000i 1.00000i
\(65\) −3.92820 0.803848i −0.487234 0.0997050i
\(66\) 1.26795 4.73205i 0.156074 0.582475i
\(67\) 1.96410 7.33013i 0.239953 0.895518i −0.735900 0.677090i \(-0.763241\pi\)
0.975853 0.218427i \(-0.0700927\pi\)
\(68\) 2.19615 + 8.19615i 0.266323 + 0.993929i
\(69\) −1.50000 + 0.401924i −0.180579 + 0.0483859i
\(70\) −0.830127 13.8301i −0.0992192 1.65302i
\(71\) 12.0000i 1.42414i −0.702109 0.712069i \(-0.747758\pi\)
0.702109 0.712069i \(-0.252242\pi\)
\(72\) −8.19615 + 2.19615i −0.965926 + 0.258819i
\(73\) −10.1962 10.1962i −1.19337 1.19337i −0.976115 0.217254i \(-0.930290\pi\)
−0.217254 0.976115i \(-0.569710\pi\)
\(74\) 0.464102 + 0.803848i 0.0539507 + 0.0934454i
\(75\) −6.92820 + 5.19615i −0.800000 + 0.600000i
\(76\) −8.19615 4.73205i −0.940163 0.542803i
\(77\) 8.46410 + 2.26795i 0.964574 + 0.258457i
\(78\) −4.39230 −0.497331
\(79\) 1.90192 + 1.09808i 0.213983 + 0.123543i 0.603161 0.797619i \(-0.293908\pi\)
−0.389178 + 0.921163i \(0.627241\pi\)
\(80\) 4.92820 + 7.46410i 0.550990 + 0.834512i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 8.83013 2.36603i 0.975124 0.261284i
\(83\) −11.3301 + 3.03590i −1.24364 + 0.333233i −0.819878 0.572539i \(-0.805959\pi\)
−0.423765 + 0.905772i \(0.639292\pi\)
\(84\) −3.92820 14.6603i −0.428602 1.59956i
\(85\) 7.09808 + 6.29423i 0.769894 + 0.682705i
\(86\) 12.9282i 1.39408i
\(87\) −5.53590 −0.593511
\(88\) −5.46410 + 1.46410i −0.582475 + 0.156074i
\(89\) 2.66025 0.281986 0.140993 0.990011i \(-0.454970\pi\)
0.140993 + 0.990011i \(0.454970\pi\)
\(90\) −6.29423 + 7.09808i −0.663470 + 0.748203i
\(91\) 7.85641i 0.823575i
\(92\) 1.26795 + 1.26795i 0.132193 + 0.132193i
\(93\) −12.2942 7.09808i −1.27485 0.736036i
\(94\) 2.19615 0.226516
\(95\) −10.5622 + 0.633975i −1.08366 + 0.0650444i
\(96\) 6.92820 + 6.92820i 0.707107 + 0.707107i
\(97\) 1.83013 + 6.83013i 0.185821 + 0.693494i 0.994453 + 0.105180i \(0.0335417\pi\)
−0.808632 + 0.588315i \(0.799792\pi\)
\(98\) 16.6603 4.46410i 1.68294 0.450942i
\(99\) −3.00000 5.19615i −0.301511 0.522233i
\(100\) 9.19615 + 3.92820i 0.919615 + 0.392820i
\(101\) −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 9.00000 + 5.19615i 0.891133 + 0.514496i
\(103\) 4.16987 15.5622i 0.410870 1.53339i −0.382097 0.924122i \(-0.624798\pi\)
0.792967 0.609265i \(-0.208535\pi\)
\(104\) 2.53590 + 4.39230i 0.248665 + 0.430701i
\(105\) −12.6962 11.2583i −1.23902 1.09870i
\(106\) 5.19615 + 9.00000i 0.504695 + 0.874157i
\(107\) −6.09808 + 6.09808i −0.589523 + 0.589523i −0.937502 0.347979i \(-0.886868\pi\)
0.347979 + 0.937502i \(0.386868\pi\)
\(108\) −5.19615 + 9.00000i −0.500000 + 0.866025i
\(109\) 8.66025 0.829502 0.414751 0.909935i \(-0.363869\pi\)
0.414751 + 0.909935i \(0.363869\pi\)
\(110\) −4.19615 + 4.73205i −0.400087 + 0.451183i
\(111\) 1.09808 + 0.294229i 0.104225 + 0.0279269i
\(112\) −12.3923 + 12.3923i −1.17096 + 1.17096i
\(113\) 1.73205 + 0.464102i 0.162938 + 0.0436590i 0.339366 0.940655i \(-0.389788\pi\)
−0.176428 + 0.984314i \(0.556454\pi\)
\(114\) −11.1962 + 3.00000i −1.04862 + 0.280976i
\(115\) 1.96410 + 0.401924i 0.183153 + 0.0374796i
\(116\) 3.19615 + 5.53590i 0.296755 + 0.513995i
\(117\) −3.80385 + 3.80385i −0.351666 + 0.351666i
\(118\) −2.46410 + 0.660254i −0.226839 + 0.0607813i
\(119\) −9.29423 + 16.0981i −0.852001 + 1.47571i
\(120\) 10.7321 + 2.19615i 0.979698 + 0.200480i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −14.6603 14.6603i −1.32728 1.32728i
\(123\) 5.59808 9.69615i 0.504762 0.874273i
\(124\) 16.3923i 1.47207i
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) −16.0981 9.29423i −1.43413 0.827996i
\(127\) 5.90192 5.90192i 0.523711 0.523711i −0.394979 0.918690i \(-0.629248\pi\)
0.918690 + 0.394979i \(0.129248\pi\)
\(128\) 2.92820 10.9282i 0.258819 0.965926i
\(129\) −11.1962 11.1962i −0.985766 0.985766i
\(130\) 5.07180 + 2.53590i 0.444826 + 0.222413i
\(131\) 3.90192 + 6.75833i 0.340913 + 0.590478i 0.984602 0.174808i \(-0.0559306\pi\)
−0.643690 + 0.765287i \(0.722597\pi\)
\(132\) −3.46410 + 6.00000i −0.301511 + 0.522233i
\(133\) −5.36603 20.0263i −0.465293 1.73650i
\(134\) −5.36603 + 9.29423i −0.463554 + 0.802899i
\(135\) 0.696152 + 11.5981i 0.0599153 + 0.998203i
\(136\) 12.0000i 1.02899i
\(137\) 12.9282 3.46410i 1.10453 0.295958i 0.339923 0.940453i \(-0.389599\pi\)
0.764608 + 0.644495i \(0.222932\pi\)
\(138\) 2.19615 0.186949
\(139\) −3.46410 6.00000i −0.293821 0.508913i 0.680889 0.732387i \(-0.261594\pi\)
−0.974710 + 0.223474i \(0.928260\pi\)
\(140\) −3.92820 + 19.1962i −0.331994 + 1.62237i
\(141\) 1.90192 1.90192i 0.160171 0.160171i
\(142\) −4.39230 + 16.3923i −0.368594 + 1.37561i
\(143\) −2.53590 + 2.53590i −0.212062 + 0.212062i
\(144\) 12.0000 1.00000
\(145\) 6.39230 + 3.19615i 0.530852 + 0.265426i
\(146\) 10.1962 + 17.6603i 0.843840 + 1.46157i
\(147\) 10.5622 18.2942i 0.871154 1.50888i
\(148\) −0.339746 1.26795i −0.0279269 0.104225i
\(149\) −6.06218 + 3.50000i −0.496633 + 0.286731i −0.727322 0.686296i \(-0.759235\pi\)
0.230689 + 0.973028i \(0.425902\pi\)
\(150\) 11.3660 4.56218i 0.928032 0.372500i
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 9.46410 + 9.46410i 0.767640 + 0.767640i
\(153\) 12.2942 3.29423i 0.993929 0.266323i
\(154\) −10.7321 6.19615i −0.864813 0.499300i
\(155\) 10.0981 + 15.2942i 0.811097 + 1.22846i
\(156\) 6.00000 + 1.60770i 0.480384 + 0.128719i
\(157\) 3.29423 12.2942i 0.262908 0.981186i −0.700610 0.713544i \(-0.747089\pi\)
0.963518 0.267642i \(-0.0862445\pi\)
\(158\) −2.19615 2.19615i −0.174717 0.174717i
\(159\) 12.2942 + 3.29423i 0.974996 + 0.261249i
\(160\) −4.00000 12.0000i −0.316228 0.948683i
\(161\) 3.92820i 0.309586i
\(162\) 3.29423 + 12.2942i 0.258819 + 0.965926i
\(163\) 6.46410 6.46410i 0.506308 0.506308i −0.407083 0.913391i \(-0.633454\pi\)
0.913391 + 0.407083i \(0.133454\pi\)
\(164\) −12.9282 −1.00952
\(165\) 0.464102 + 7.73205i 0.0361303 + 0.601939i
\(166\) 16.5885 1.28751
\(167\) 4.79423 17.8923i 0.370989 1.38455i −0.488130 0.872771i \(-0.662321\pi\)
0.859118 0.511777i \(-0.171013\pi\)
\(168\) 21.4641i 1.65599i
\(169\) −8.47372 4.89230i −0.651825 0.376331i
\(170\) −7.39230 11.1962i −0.566964 0.858706i
\(171\) −7.09808 + 12.2942i −0.542803 + 0.940163i
\(172\) −4.73205 + 17.6603i −0.360815 + 1.34658i
\(173\) 2.73205 0.732051i 0.207714 0.0556568i −0.153462 0.988155i \(-0.549042\pi\)
0.361176 + 0.932498i \(0.382375\pi\)
\(174\) 7.56218 + 2.02628i 0.573287 + 0.153612i
\(175\) 8.16025 + 20.3301i 0.616857 + 1.53681i
\(176\) 8.00000 0.603023
\(177\) −1.56218 + 2.70577i −0.117420 + 0.203378i
\(178\) −3.63397 0.973721i −0.272378 0.0729834i
\(179\) 6.39230i 0.477783i −0.971046 0.238892i \(-0.923216\pi\)
0.971046 0.238892i \(-0.0767841\pi\)
\(180\) 11.1962 7.39230i 0.834512 0.550990i
\(181\) 3.00000i 0.222988i −0.993765 0.111494i \(-0.964436\pi\)
0.993765 0.111494i \(-0.0355636\pi\)
\(182\) −2.87564 + 10.7321i −0.213157 + 0.795513i
\(183\) −25.3923 −1.87705
\(184\) −1.26795 2.19615i −0.0934745 0.161903i
\(185\) −1.09808 0.973721i −0.0807322 0.0715894i
\(186\) 14.1962 + 14.1962i 1.04091 + 1.04091i
\(187\) 8.19615 2.19615i 0.599362 0.160599i
\(188\) −3.00000 0.803848i −0.218797 0.0586266i
\(189\) −21.9904 + 5.89230i −1.59956 + 0.428602i
\(190\) 14.6603 + 3.00000i 1.06357 + 0.217643i
\(191\) −16.0981 9.29423i −1.16482 0.672507i −0.212362 0.977191i \(-0.568116\pi\)
−0.952453 + 0.304684i \(0.901449\pi\)
\(192\) −6.92820 12.0000i −0.500000 0.866025i
\(193\) −3.66025 + 13.6603i −0.263471 + 0.983287i 0.699709 + 0.714428i \(0.253313\pi\)
−0.963180 + 0.268858i \(0.913354\pi\)
\(194\) 10.0000i 0.717958i
\(195\) 6.58846 2.19615i 0.471809 0.157270i
\(196\) −24.3923 −1.74231
\(197\) 12.0000 12.0000i 0.854965 0.854965i −0.135775 0.990740i \(-0.543352\pi\)
0.990740 + 0.135775i \(0.0433525\pi\)
\(198\) 2.19615 + 8.19615i 0.156074 + 0.582475i
\(199\) 4.19615i 0.297457i −0.988878 0.148729i \(-0.952482\pi\)
0.988878 0.148729i \(-0.0475181\pi\)
\(200\) −11.1244 8.73205i −0.786611 0.617449i
\(201\) 3.40192 + 12.6962i 0.239953 + 0.895518i
\(202\) 2.00000 2.00000i 0.140720 0.140720i
\(203\) −3.62436 + 13.5263i −0.254380 + 0.949359i
\(204\) −10.3923 10.3923i −0.727607 0.727607i
\(205\) −12.0622 + 7.96410i −0.842459 + 0.556237i
\(206\) −11.3923 + 19.7321i −0.793739 + 1.37480i
\(207\) 1.90192 1.90192i 0.132193 0.132193i
\(208\) −1.85641 6.92820i −0.128719 0.480384i
\(209\) −4.73205 + 8.19615i −0.327323 + 0.566940i
\(210\) 13.2224 + 20.0263i 0.912434 + 1.38194i
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) −3.80385 14.1962i −0.261249 0.974996i
\(213\) 10.3923 + 18.0000i 0.712069 + 1.23334i
\(214\) 10.5622 6.09808i 0.722016 0.416856i
\(215\) 6.46410 + 19.3923i 0.440848 + 1.32254i
\(216\) 10.3923 10.3923i 0.707107 0.707107i
\(217\) −25.3923 + 25.3923i −1.72374 + 1.72374i
\(218\) −11.8301 3.16987i −0.801237 0.214691i
\(219\) 24.1244 + 6.46410i 1.63017 + 0.436804i
\(220\) 7.46410 4.92820i 0.503230 0.332259i
\(221\) −3.80385 6.58846i −0.255874 0.443188i
\(222\) −1.39230 0.803848i −0.0934454 0.0539507i
\(223\) −16.5263 + 4.42820i −1.10668 + 0.296534i −0.765483 0.643457i \(-0.777500\pi\)
−0.341199 + 0.939991i \(0.610833\pi\)
\(224\) 21.4641 12.3923i 1.43413 0.827996i
\(225\) 5.89230 13.7942i 0.392820 0.919615i
\(226\) −2.19615 1.26795i −0.146086 0.0843427i
\(227\) −2.70577 10.0981i −0.179588 0.670233i −0.995724 0.0923731i \(-0.970555\pi\)
0.816136 0.577860i \(-0.196112\pi\)
\(228\) 16.3923 1.08561
\(229\) 5.76795 + 9.99038i 0.381157 + 0.660183i 0.991228 0.132164i \(-0.0421925\pi\)
−0.610071 + 0.792347i \(0.708859\pi\)
\(230\) −2.53590 1.26795i −0.167212 0.0836061i
\(231\) −14.6603 + 3.92820i −0.964574 + 0.258457i
\(232\) −2.33975 8.73205i −0.153612 0.573287i
\(233\) 18.1244 18.1244i 1.18737 1.18737i 0.209573 0.977793i \(-0.432793\pi\)
0.977793 0.209573i \(-0.0672074\pi\)
\(234\) 6.58846 3.80385i 0.430701 0.248665i
\(235\) −3.29423 + 1.09808i −0.214892 + 0.0716306i
\(236\) 3.60770 0.234841
\(237\) −3.80385 −0.247086
\(238\) 18.5885 18.5885i 1.20491 1.20491i
\(239\) −9.46410 16.3923i −0.612182 1.06033i −0.990872 0.134807i \(-0.956959\pi\)
0.378690 0.925524i \(-0.376375\pi\)
\(240\) −13.8564 6.92820i −0.894427 0.447214i
\(241\) 9.40192 16.2846i 0.605631 1.04898i −0.386320 0.922365i \(-0.626254\pi\)
0.991951 0.126619i \(-0.0404126\pi\)
\(242\) −2.56218 9.56218i −0.164703 0.614680i
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) 14.6603 + 25.3923i 0.938527 + 1.62558i
\(245\) −22.7583 + 15.0263i −1.45398 + 0.959994i
\(246\) −11.1962 + 11.1962i −0.713841 + 0.713841i
\(247\) 8.19615 + 2.19615i 0.521509 + 0.139738i
\(248\) 6.00000 22.3923i 0.381000 1.42191i
\(249\) 14.3660 14.3660i 0.910410 0.910410i
\(250\) −15.7583 1.29423i −0.996644 0.0818542i
\(251\) −26.5885 −1.67825 −0.839124 0.543940i \(-0.816932\pi\)
−0.839124 + 0.543940i \(0.816932\pi\)
\(252\) 18.5885 + 18.5885i 1.17096 + 1.17096i
\(253\) 1.26795 1.26795i 0.0797153 0.0797153i
\(254\) −10.2224 + 5.90192i −0.641412 + 0.370320i
\(255\) −16.0981 3.29423i −1.00810 0.206293i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −4.22243 + 15.7583i −0.263388 + 0.982978i 0.699842 + 0.714298i \(0.253254\pi\)
−0.963230 + 0.268680i \(0.913413\pi\)
\(258\) 11.1962 + 19.3923i 0.697042 + 1.20731i
\(259\) 1.43782 2.49038i 0.0893419 0.154745i
\(260\) −6.00000 5.32051i −0.372104 0.329964i
\(261\) 8.30385 4.79423i 0.513995 0.296755i
\(262\) −2.85641 10.6603i −0.176469 0.658593i
\(263\) 3.63397 + 13.5622i 0.224080 + 0.836280i 0.982771 + 0.184828i \(0.0591729\pi\)
−0.758690 + 0.651451i \(0.774160\pi\)
\(264\) 6.92820 6.92820i 0.426401 0.426401i
\(265\) −12.2942 10.9019i −0.755228 0.669700i
\(266\) 29.3205i 1.79776i
\(267\) −3.99038 + 2.30385i −0.244207 + 0.140993i
\(268\) 10.7321 10.7321i 0.655564 0.655564i
\(269\) 1.00000i 0.0609711i 0.999535 + 0.0304855i \(0.00970535\pi\)
−0.999535 + 0.0304855i \(0.990295\pi\)
\(270\) 3.29423 16.0981i 0.200480 0.979698i
\(271\) 4.58846 0.278729 0.139364 0.990241i \(-0.455494\pi\)
0.139364 + 0.990241i \(0.455494\pi\)
\(272\) −4.39230 + 16.3923i −0.266323 + 0.993929i
\(273\) 6.80385 + 11.7846i 0.411788 + 0.713237i
\(274\) −18.9282 −1.14349
\(275\) 3.92820 9.19615i 0.236880 0.554549i
\(276\) −3.00000 0.803848i −0.180579 0.0483859i
\(277\) 8.83013 2.36603i 0.530551 0.142161i 0.0164083 0.999865i \(-0.494777\pi\)
0.514143 + 0.857705i \(0.328110\pi\)
\(278\) 2.53590 + 9.46410i 0.152093 + 0.567619i
\(279\) 24.5885 1.47207
\(280\) 12.3923 24.7846i 0.740582 1.48116i
\(281\) −1.79423 1.03590i −0.107035 0.0617965i 0.445527 0.895268i \(-0.353016\pi\)
−0.552562 + 0.833472i \(0.686350\pi\)
\(282\) −3.29423 + 1.90192i −0.196168 + 0.113258i
\(283\) −4.50000 1.20577i −0.267497 0.0716757i 0.122577 0.992459i \(-0.460884\pi\)
−0.390074 + 0.920783i \(0.627551\pi\)
\(284\) 12.0000 20.7846i 0.712069 1.23334i
\(285\) 15.2942 10.0981i 0.905952 0.598158i
\(286\) 4.39230 2.53590i 0.259722 0.149951i
\(287\) −20.0263 20.0263i −1.18211 1.18211i
\(288\) −16.3923 4.39230i −0.965926 0.258819i
\(289\) 1.00000i 0.0588235i
\(290\) −7.56218 6.70577i −0.444066 0.393776i
\(291\) −8.66025 8.66025i −0.507673 0.507673i
\(292\) −7.46410 27.8564i −0.436804 1.63017i
\(293\) −0.294229 + 1.09808i −0.0171890 + 0.0641503i −0.973988 0.226601i \(-0.927239\pi\)
0.956799 + 0.290751i \(0.0939053\pi\)
\(294\) −21.1244 + 21.1244i −1.23200 + 1.23200i
\(295\) 3.36603 2.22243i 0.195978 0.129395i
\(296\) 1.85641i 0.107901i
\(297\) 9.00000 + 5.19615i 0.522233 + 0.301511i
\(298\) 9.56218 2.56218i 0.553922 0.148423i
\(299\) −1.39230 0.803848i −0.0805191 0.0464877i
\(300\) −17.1962 + 2.07180i −0.992820 + 0.119615i
\(301\) −34.6865 + 20.0263i −1.99930 + 1.15430i
\(302\) −16.0000 + 16.0000i −0.920697 + 0.920697i
\(303\) 3.46410i 0.199007i
\(304\) −9.46410 16.3923i −0.542803 0.940163i
\(305\) 29.3205 + 14.6603i 1.67889 + 0.839444i
\(306\) −18.0000 −1.02899
\(307\) −14.3660 14.3660i −0.819912 0.819912i 0.166183 0.986095i \(-0.446856\pi\)
−0.986095 + 0.166183i \(0.946856\pi\)
\(308\) 12.3923 + 12.3923i 0.706117 + 0.706117i
\(309\) 7.22243 + 26.9545i 0.410870 + 1.53339i
\(310\) −8.19615 24.5885i −0.465510 1.39653i
\(311\) 12.2942 7.09808i 0.697142 0.402495i −0.109140 0.994026i \(-0.534810\pi\)
0.806282 + 0.591531i \(0.201476\pi\)
\(312\) −7.60770 4.39230i −0.430701 0.248665i
\(313\) 14.4641 3.87564i 0.817559 0.219064i 0.174280 0.984696i \(-0.444240\pi\)
0.643279 + 0.765632i \(0.277573\pi\)
\(314\) −9.00000 + 15.5885i −0.507899 + 0.879708i
\(315\) 28.7942 + 5.89230i 1.62237 + 0.331994i
\(316\) 2.19615 + 3.80385i 0.123543 + 0.213983i
\(317\) 3.66025 + 13.6603i 0.205580 + 0.767236i 0.989272 + 0.146086i \(0.0466677\pi\)
−0.783692 + 0.621150i \(0.786666\pi\)
\(318\) −15.5885 9.00000i −0.874157 0.504695i
\(319\) 5.53590 3.19615i 0.309951 0.178950i
\(320\) 1.07180 + 17.8564i 0.0599153 + 0.998203i
\(321\) 3.86603 14.4282i 0.215780 0.805304i
\(322\) 1.43782 5.36603i 0.0801267 0.299037i
\(323\) −14.1962 14.1962i −0.789895 0.789895i
\(324\) 18.0000i 1.00000i
\(325\) −8.87564 1.26795i −0.492332 0.0703332i
\(326\) −11.1962 + 6.46410i −0.620098 + 0.358013i
\(327\) −12.9904 + 7.50000i −0.718370 + 0.414751i
\(328\) 17.6603 + 4.73205i 0.975124 + 0.261284i
\(329\) −3.40192 5.89230i −0.187554 0.324853i
\(330\) 2.19615 10.7321i 0.120894 0.590780i
\(331\) 0.509619 + 0.294229i 0.0280112 + 0.0161723i 0.513940 0.857826i \(-0.328185\pi\)
−0.485929 + 0.873998i \(0.661519\pi\)
\(332\) −22.6603 6.07180i −1.24364 0.333233i
\(333\) −1.90192 + 0.509619i −0.104225 + 0.0279269i
\(334\) −13.0981 + 22.6865i −0.716695 + 1.24135i
\(335\) 3.40192 16.6244i 0.185867 0.908286i
\(336\) 7.85641 29.3205i 0.428602 1.59956i
\(337\) −0.267949 0.0717968i −0.0145961 0.00391102i 0.251514 0.967854i \(-0.419072\pi\)
−0.266110 + 0.963943i \(0.585738\pi\)
\(338\) 9.78461 + 9.78461i 0.532213 + 0.532213i
\(339\) −3.00000 + 0.803848i −0.162938 + 0.0436590i
\(340\) 6.00000 + 18.0000i 0.325396 + 0.976187i
\(341\) 16.3923 0.887693
\(342\) 14.1962 14.1962i 0.767640 0.767640i
\(343\) −16.0981 16.0981i −0.869214 0.869214i
\(344\) 12.9282 22.3923i 0.697042 1.20731i
\(345\) −3.29423 + 1.09808i −0.177355 + 0.0591184i
\(346\) −4.00000 −0.215041
\(347\) −7.09808 1.90192i −0.381045 0.102101i 0.0632121 0.998000i \(-0.479866\pi\)
−0.444257 + 0.895899i \(0.646532\pi\)
\(348\) −9.58846 5.53590i −0.513995 0.296755i
\(349\) −18.2321 + 31.5788i −0.975939 + 1.69038i −0.299139 + 0.954209i \(0.596700\pi\)
−0.676800 + 0.736167i \(0.736634\pi\)
\(350\) −3.70577 30.7583i −0.198082 1.64410i
\(351\) 2.41154 9.00000i 0.128719 0.480384i
\(352\) −10.9282 2.92820i −0.582475 0.156074i
\(353\) 3.46410 + 12.9282i 0.184376 + 0.688099i 0.994763 + 0.102205i \(0.0325898\pi\)
−0.810388 + 0.585894i \(0.800744\pi\)
\(354\) 3.12436 3.12436i 0.166058 0.166058i
\(355\) −1.60770 26.7846i −0.0853276 1.42158i
\(356\) 4.60770 + 2.66025i 0.244207 + 0.140993i
\(357\) 32.1962i 1.70400i
\(358\) −2.33975 + 8.73205i −0.123659 + 0.461503i
\(359\) −2.19615 −0.115908 −0.0579542 0.998319i \(-0.518458\pi\)
−0.0579542 + 0.998319i \(0.518458\pi\)
\(360\) −18.0000 + 6.00000i −0.948683 + 0.316228i
\(361\) 3.39230 0.178542
\(362\) −1.09808 + 4.09808i −0.0577136 + 0.215390i
\(363\) −10.5000 6.06218i −0.551107 0.318182i
\(364\) 7.85641 13.6077i 0.411788 0.713237i
\(365\) −24.1244 21.3923i −1.26273 1.11972i
\(366\) 34.6865 + 9.29423i 1.81309 + 0.485817i
\(367\) 2.56218 + 9.56218i 0.133745 + 0.499142i 1.00000 0.000459976i \(-0.000146415\pi\)
−0.866255 + 0.499602i \(0.833480\pi\)
\(368\) 0.928203 + 3.46410i 0.0483859 + 0.180579i
\(369\) 19.3923i 1.00952i
\(370\) 1.14359 + 1.73205i 0.0594526 + 0.0900450i
\(371\) 16.0981 27.8827i 0.835770 1.44760i
\(372\) −14.1962 24.5885i −0.736036 1.27485i
\(373\) −3.63397 0.973721i −0.188160 0.0504173i 0.163508 0.986542i \(-0.447719\pi\)
−0.351669 + 0.936125i \(0.614386\pi\)
\(374\) −12.0000 −0.620505
\(375\) −14.7679 + 12.5263i −0.762614 + 0.646854i
\(376\) 3.80385 + 2.19615i 0.196168 + 0.113258i
\(377\) −4.05256 4.05256i −0.208717 0.208717i
\(378\) 32.1962 1.65599
\(379\) 33.1244 1.70148 0.850742 0.525584i \(-0.176153\pi\)
0.850742 + 0.525584i \(0.176153\pi\)
\(380\) −18.9282 9.46410i −0.970996 0.485498i
\(381\) −3.74167 + 13.9641i −0.191692 + 0.715403i
\(382\) 18.5885 + 18.5885i 0.951068 + 0.951068i
\(383\) 27.7583 + 7.43782i 1.41838 + 0.380055i 0.884910 0.465761i \(-0.154220\pi\)
0.533474 + 0.845816i \(0.320886\pi\)
\(384\) 5.07180 + 18.9282i 0.258819 + 0.965926i
\(385\) 19.1962 + 3.92820i 0.978327 + 0.200200i
\(386\) 10.0000 17.3205i 0.508987 0.881591i
\(387\) 26.4904 + 7.09808i 1.34658 + 0.360815i
\(388\) −3.66025 + 13.6603i −0.185821 + 0.693494i
\(389\) −15.0622 8.69615i −0.763683 0.440912i 0.0669337 0.997757i \(-0.478678\pi\)
−0.830616 + 0.556845i \(0.812012\pi\)
\(390\) −9.80385 + 0.588457i −0.496437 + 0.0297977i
\(391\) 1.90192 + 3.29423i 0.0961844 + 0.166596i
\(392\) 33.3205 + 8.92820i 1.68294 + 0.450942i
\(393\) −11.7058 6.75833i −0.590478 0.340913i
\(394\) −20.7846 + 12.0000i −1.04711 + 0.604551i
\(395\) 4.39230 + 2.19615i 0.221001 + 0.110500i
\(396\) 12.0000i 0.603023i
\(397\) 0.803848 + 0.803848i 0.0403440 + 0.0403440i 0.726991 0.686647i \(-0.240918\pi\)
−0.686647 + 0.726991i \(0.740918\pi\)
\(398\) −1.53590 + 5.73205i −0.0769876 + 0.287322i
\(399\) 25.3923 + 25.3923i 1.27121 + 1.27121i
\(400\) 12.0000 + 16.0000i 0.600000 + 0.800000i
\(401\) −31.3923 + 18.1244i −1.56766 + 0.905087i −0.571215 + 0.820800i \(0.693528\pi\)
−0.996442 + 0.0842869i \(0.973139\pi\)
\(402\) 18.5885i 0.927108i
\(403\) −3.80385 14.1962i −0.189483 0.707161i
\(404\) −3.46410 + 2.00000i −0.172345 + 0.0995037i
\(405\) −11.0885 16.7942i −0.550990 0.834512i
\(406\) 9.90192 17.1506i 0.491424 0.851172i
\(407\) −1.26795 + 0.339746i −0.0628499 + 0.0168406i
\(408\) 10.3923 + 18.0000i 0.514496 + 0.891133i
\(409\) 5.19615 3.00000i 0.256933 0.148340i −0.366002 0.930614i \(-0.619274\pi\)
0.622935 + 0.782274i \(0.285940\pi\)
\(410\) 19.3923 6.46410i 0.957718 0.319239i
\(411\) −16.3923 + 16.3923i −0.808573 + 0.808573i
\(412\) 22.7846 22.7846i 1.12252 1.12252i
\(413\) 5.58846 + 5.58846i 0.274990 + 0.274990i
\(414\) −3.29423 + 1.90192i −0.161903 + 0.0934745i
\(415\) −24.8827 + 8.29423i −1.22144 + 0.407148i
\(416\) 10.1436i 0.497331i
\(417\) 10.3923 + 6.00000i 0.508913 + 0.293821i
\(418\) 9.46410 9.46410i 0.462904 0.462904i
\(419\) 10.7321 6.19615i 0.524295 0.302702i −0.214395 0.976747i \(-0.568778\pi\)
0.738690 + 0.674045i \(0.235445\pi\)
\(420\) −10.7321 32.1962i −0.523670 1.57101i
\(421\) 4.60770 + 2.66025i 0.224565 + 0.129653i 0.608062 0.793889i \(-0.291947\pi\)
−0.383497 + 0.923542i \(0.625280\pi\)
\(422\) 0 0
\(423\) −1.20577 + 4.50000i −0.0586266 + 0.218797i
\(424\) 20.7846i 1.00939i
\(425\) 16.6865 + 13.0981i 0.809416 + 0.635350i
\(426\) −7.60770 28.3923i −0.368594 1.37561i
\(427\) −16.6244 + 62.0429i −0.804509 + 3.00247i
\(428\) −16.6603 + 4.46410i −0.805304 + 0.215780i
\(429\) 1.60770 6.00000i 0.0776203 0.289683i
\(430\) −1.73205 28.8564i −0.0835269 1.39158i
\(431\) 22.0526i 1.06223i 0.847298 + 0.531117i \(0.178228\pi\)
−0.847298 + 0.531117i \(0.821772\pi\)
\(432\) −18.0000 + 10.3923i −0.866025 + 0.500000i
\(433\) −15.3923 15.3923i −0.739707 0.739707i 0.232814 0.972521i \(-0.425207\pi\)
−0.972521 + 0.232814i \(0.925207\pi\)
\(434\) 43.9808 25.3923i 2.11114 1.21887i
\(435\) −12.3564 + 0.741670i −0.592444 + 0.0355603i
\(436\) 15.0000 + 8.66025i 0.718370 + 0.414751i
\(437\) −4.09808 1.09808i −0.196038 0.0525281i
\(438\) −30.5885 17.6603i −1.46157 0.843840i
\(439\) 16.2679 + 9.39230i 0.776427 + 0.448270i 0.835162 0.550003i \(-0.185374\pi\)
−0.0587356 + 0.998274i \(0.518707\pi\)
\(440\) −12.0000 + 4.00000i −0.572078 + 0.190693i
\(441\) 36.5885i 1.74231i
\(442\) 2.78461 + 10.3923i 0.132450 + 0.494312i
\(443\) 37.2846 9.99038i 1.77145 0.474657i 0.782464 0.622696i \(-0.213963\pi\)
0.988982 + 0.148039i \(0.0472961\pi\)
\(444\) 1.60770 + 1.60770i 0.0762978 + 0.0762978i
\(445\) 5.93782 0.356406i 0.281480 0.0168953i
\(446\) 24.1962 1.14572
\(447\) 6.06218 10.5000i 0.286731 0.496633i
\(448\) −33.8564 + 9.07180i −1.59956 + 0.428602i
\(449\) −32.7846 −1.54720 −0.773601 0.633673i \(-0.781546\pi\)
−0.773601 + 0.633673i \(0.781546\pi\)
\(450\) −13.0981 + 16.6865i −0.617449 + 0.786611i
\(451\) 12.9282i 0.608765i
\(452\) 2.53590 + 2.53590i 0.119279 + 0.119279i
\(453\) 27.7128i 1.30206i
\(454\) 14.7846i 0.693876i
\(455\) −1.05256 17.5359i −0.0493447 0.822096i
\(456\) −22.3923 6.00000i −1.04862 0.280976i
\(457\) −2.63397 9.83013i −0.123212 0.459834i 0.876558 0.481297i \(-0.159834\pi\)
−0.999770 + 0.0214632i \(0.993168\pi\)
\(458\) −4.22243 15.7583i −0.197301 0.736338i
\(459\) −15.5885 + 15.5885i −0.727607 + 0.727607i
\(460\) 3.00000 + 2.66025i 0.139876 + 0.124035i
\(461\) 6.79423 11.7679i 0.316439 0.548088i −0.663304 0.748350i \(-0.730846\pi\)
0.979742 + 0.200262i \(0.0641795\pi\)
\(462\) 21.4641 0.998600
\(463\) −1.75833 + 6.56218i −0.0817165 + 0.304970i −0.994672 0.103089i \(-0.967127\pi\)
0.912956 + 0.408059i \(0.133794\pi\)
\(464\) 12.7846i 0.593511i
\(465\) −28.3923 14.1962i −1.31666 0.658331i
\(466\) −31.3923 + 18.1244i −1.45422 + 0.839595i
\(467\) −8.60770 + 8.60770i −0.398317 + 0.398317i −0.877639 0.479322i \(-0.840882\pi\)
0.479322 + 0.877639i \(0.340882\pi\)
\(468\) −10.3923 + 2.78461i −0.480384 + 0.128719i
\(469\) 33.2487 1.53528
\(470\) 4.90192 0.294229i 0.226109 0.0135718i
\(471\) 5.70577 + 21.2942i 0.262908 + 0.981186i
\(472\) −4.92820 1.32051i −0.226839 0.0607813i
\(473\) 17.6603 + 4.73205i 0.812019 + 0.217580i
\(474\) 5.19615 + 1.39230i 0.238667 + 0.0639507i
\(475\) −23.4904 + 2.83013i −1.07781 + 0.129855i
\(476\) −32.1962 + 18.5885i −1.47571 + 0.852001i
\(477\) −21.2942 + 5.70577i −0.974996 + 0.261249i
\(478\) 6.92820 + 25.8564i 0.316889 + 1.18264i
\(479\) 10.5622 18.2942i 0.482598 0.835885i −0.517202 0.855863i \(-0.673026\pi\)
0.999800 + 0.0199786i \(0.00635981\pi\)
\(480\) 16.3923 + 14.5359i 0.748203 + 0.663470i
\(481\) 0.588457 + 1.01924i 0.0268313 + 0.0464732i
\(482\) −18.8038 + 18.8038i −0.856492 + 0.856492i
\(483\) −3.40192 5.89230i −0.154793 0.268109i
\(484\) 14.0000i 0.636364i
\(485\) 5.00000 + 15.0000i 0.227038 + 0.681115i
\(486\) −15.5885 15.5885i −0.707107 0.707107i
\(487\) 3.39230 3.39230i 0.153720 0.153720i −0.626057 0.779777i \(-0.715332\pi\)
0.779777 + 0.626057i \(0.215332\pi\)
\(488\) −10.7321 40.0526i −0.485817 1.81309i
\(489\) −4.09808 + 15.2942i −0.185321 + 0.691629i
\(490\) 36.5885 12.1962i 1.65290 0.550966i
\(491\) 12.3923 + 21.4641i 0.559257 + 0.968661i 0.997559 + 0.0698335i \(0.0222468\pi\)
−0.438302 + 0.898828i \(0.644420\pi\)
\(492\) 19.3923 11.1962i 0.874273 0.504762i
\(493\) 3.50962 + 13.0981i 0.158065 + 0.589908i
\(494\) −10.3923 6.00000i −0.467572 0.269953i
\(495\) −7.39230 11.1962i −0.332259 0.503230i
\(496\) −16.3923 + 28.3923i −0.736036 + 1.27485i
\(497\) 50.7846 13.6077i 2.27800 0.610389i
\(498\) −24.8827 + 14.3660i −1.11502 + 0.643757i
\(499\) −13.3923 23.1962i −0.599522 1.03840i −0.992892 0.119022i \(-0.962024\pi\)
0.393370 0.919380i \(-0.371309\pi\)
\(500\) 21.0526 + 7.53590i 0.941499 + 0.337016i
\(501\) 8.30385 + 30.9904i 0.370989 + 1.38455i
\(502\) 36.3205 + 9.73205i 1.62106 + 0.434363i
\(503\) −3.97372 + 3.97372i −0.177179 + 0.177179i −0.790125 0.612946i \(-0.789984\pi\)
0.612946 + 0.790125i \(0.289984\pi\)
\(504\) −18.5885 32.1962i −0.827996 1.43413i
\(505\) −2.00000 + 4.00000i −0.0889988 + 0.177998i
\(506\) −2.19615 + 1.26795i −0.0976309 + 0.0563672i
\(507\) 16.9474 0.752662
\(508\) 16.1244 4.32051i 0.715403 0.191692i
\(509\) −6.57180 + 3.79423i −0.291290 + 0.168176i −0.638523 0.769602i \(-0.720454\pi\)
0.347234 + 0.937779i \(0.387121\pi\)
\(510\) 20.7846 + 10.3923i 0.920358 + 0.460179i
\(511\) 31.5885 54.7128i 1.39739 2.42035i
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 24.5885i 1.08561i
\(514\) 11.5359 19.9808i 0.508827 0.881314i
\(515\) 7.22243 35.2942i 0.318258 1.55525i
\(516\) −8.19615 30.5885i −0.360815 1.34658i
\(517\) −0.803848 + 3.00000i −0.0353532 + 0.131940i
\(518\) −2.87564 + 2.87564i −0.126349 + 0.126349i
\(519\) −3.46410 + 3.46410i −0.152057 + 0.152057i
\(520\) 6.24871 + 9.46410i 0.274024 + 0.415028i
\(521\) 14.6603i 0.642277i −0.947032 0.321139i \(-0.895934\pi\)
0.947032 0.321139i \(-0.104066\pi\)
\(522\) −13.0981 + 3.50962i −0.573287 + 0.153612i
\(523\) 1.56218 1.56218i 0.0683093 0.0683093i −0.672127 0.740436i \(-0.734619\pi\)
0.740436 + 0.672127i \(0.234619\pi\)
\(524\) 15.6077i 0.681825i
\(525\) −29.8468 23.4282i −1.30262 1.02249i
\(526\) 19.8564i 0.865780i
\(527\) −9.00000 + 33.5885i −0.392046 + 1.46314i
\(528\) −12.0000 + 6.92820i −0.522233 + 0.301511i
\(529\) −19.2224 11.0981i −0.835758 0.482525i
\(530\) 12.8038 + 19.3923i 0.556164 + 0.842348i
\(531\) 5.41154i 0.234841i
\(532\) 10.7321 40.0526i 0.465293 1.73650i
\(533\) 11.1962 3.00000i 0.484959 0.129944i
\(534\) 6.29423 1.68653i 0.272378 0.0729834i
\(535\) −12.7942 + 14.4282i −0.553143 + 0.623786i
\(536\) −18.5885 + 10.7321i −0.802899 + 0.463554i
\(537\) 5.53590 + 9.58846i 0.238892 + 0.413772i
\(538\) 0.366025 1.36603i 0.0157805 0.0588935i
\(539\) 24.3923i 1.05065i
\(540\) −10.3923 + 20.7846i −0.447214 + 0.894427i
\(541\) 12.4641i 0.535874i 0.963436 + 0.267937i \(0.0863418\pi\)
−0.963436 + 0.267937i \(0.913658\pi\)
\(542\) −6.26795 1.67949i −0.269231 0.0721404i
\(543\) 2.59808 + 4.50000i 0.111494 + 0.193113i
\(544\) 12.0000 20.7846i 0.514496 0.891133i
\(545\) 19.3301 1.16025i 0.828012 0.0496998i
\(546\) −4.98076 18.5885i −0.213157 0.795513i
\(547\) −26.5526 + 7.11474i −1.13531 + 0.304204i −0.777062 0.629424i \(-0.783291\pi\)
−0.358243 + 0.933628i \(0.616624\pi\)
\(548\) 25.8564 + 6.92820i 1.10453 + 0.295958i
\(549\) 38.0885 21.9904i 1.62558 0.938527i
\(550\) −8.73205 + 11.1244i −0.372336 + 0.474344i
\(551\) −13.0981 7.56218i −0.557997 0.322160i
\(552\) 3.80385 + 2.19615i 0.161903 + 0.0934745i
\(553\) −2.49038 + 9.29423i −0.105902 + 0.395231i
\(554\) −12.9282 −0.549267
\(555\) 2.49038 + 0.509619i 0.105711 + 0.0216321i
\(556\) 13.8564i 0.587643i
\(557\) 0.803848 0.803848i 0.0340601 0.0340601i −0.689872 0.723932i \(-0.742333\pi\)
0.723932 + 0.689872i \(0.242333\pi\)
\(558\) −33.5885 9.00000i −1.42191 0.381000i
\(559\) 16.3923i 0.693321i
\(560\) −26.0000 + 29.3205i −1.09870 + 1.23902i
\(561\) −10.3923 + 10.3923i −0.438763 + 0.438763i
\(562\) 2.07180 + 2.07180i 0.0873935 + 0.0873935i
\(563\) −8.59808 + 32.0885i −0.362366 + 1.35237i 0.508591 + 0.861008i \(0.330166\pi\)
−0.870957 + 0.491359i \(0.836500\pi\)
\(564\) 5.19615 1.39230i 0.218797 0.0586266i
\(565\) 3.92820 + 0.803848i 0.165261 + 0.0338181i
\(566\) 5.70577 + 3.29423i 0.239831 + 0.138467i
\(567\) 27.8827 27.8827i 1.17096 1.17096i
\(568\) −24.0000 + 24.0000i −1.00702 + 1.00702i
\(569\) −1.26795 + 2.19615i −0.0531552 + 0.0920675i −0.891379 0.453259i \(-0.850261\pi\)
0.838223 + 0.545327i \(0.183594\pi\)
\(570\) −24.5885 + 8.19615i −1.02990 + 0.343299i
\(571\) 3.00000 1.73205i 0.125546 0.0724841i −0.435912 0.899989i \(-0.643574\pi\)
0.561458 + 0.827505i \(0.310241\pi\)
\(572\) −6.92820 + 1.85641i −0.289683 + 0.0776203i
\(573\) 32.1962 1.34501
\(574\) 20.0263 + 34.6865i 0.835881 + 1.44779i
\(575\) 4.43782 + 0.633975i 0.185070 + 0.0264386i
\(576\) 20.7846 + 12.0000i 0.866025 + 0.500000i
\(577\) 5.39230 5.39230i 0.224485 0.224485i −0.585899 0.810384i \(-0.699259\pi\)
0.810384 + 0.585899i \(0.199259\pi\)
\(578\) 0.366025 1.36603i 0.0152246 0.0568192i
\(579\) −6.33975 23.6603i −0.263471 0.983287i
\(580\) 7.87564 + 11.9282i 0.327018 + 0.495292i
\(581\) −25.6962 44.5070i −1.06606 1.84646i
\(582\) 8.66025 + 15.0000i 0.358979 + 0.621770i
\(583\) −14.1962 + 3.80385i −0.587945 + 0.157539i
\(584\) 40.7846i 1.68768i
\(585\) −7.98076 + 9.00000i −0.329964 + 0.372104i
\(586\) 0.803848 1.39230i 0.0332066 0.0575156i
\(587\) −8.74871 32.6506i −0.361098 1.34764i −0.872634 0.488374i \(-0.837590\pi\)
0.511536 0.859262i \(-0.329077\pi\)
\(588\) 36.5885 21.1244i 1.50888 0.871154i
\(589\) −19.3923 33.5885i −0.799046 1.38399i
\(590\) −5.41154 + 1.80385i −0.222790 + 0.0742632i
\(591\) −7.60770 + 28.3923i −0.312939 + 1.16790i
\(592\) 0.679492 2.53590i 0.0279269 0.104225i
\(593\) −14.6603 + 14.6603i −0.602024 + 0.602024i −0.940849 0.338825i \(-0.889971\pi\)
0.338825 + 0.940849i \(0.389971\pi\)
\(594\) −10.3923 10.3923i −0.426401 0.426401i
\(595\) −18.5885 + 37.1769i −0.762052 + 1.52410i
\(596\) −14.0000 −0.573462
\(597\) 3.63397 + 6.29423i 0.148729 + 0.257606i
\(598\) 1.60770 + 1.60770i 0.0657435 + 0.0657435i
\(599\) 15.2942 + 26.4904i 0.624905 + 1.08237i 0.988559 + 0.150834i \(0.0481957\pi\)
−0.363654 + 0.931534i \(0.618471\pi\)
\(600\) 24.2487 + 3.46410i 0.989949 + 0.141421i
\(601\) −21.1962 + 36.7128i −0.864609 + 1.49755i 0.00282571 + 0.999996i \(0.499101\pi\)
−0.867435 + 0.497551i \(0.834233\pi\)
\(602\) 54.7128 14.6603i 2.22993 0.597507i
\(603\) −16.0981 16.0981i −0.655564 0.655564i
\(604\) 27.7128 16.0000i 1.12762 0.651031i
\(605\) 8.62436 + 13.0622i 0.350630 + 0.531053i
\(606\) −1.26795 + 4.73205i −0.0515069 + 0.192226i
\(607\) −28.2583 7.57180i −1.14697 0.307330i −0.365220 0.930921i \(-0.619006\pi\)
−0.781750 + 0.623592i \(0.785673\pi\)
\(608\) 6.92820 + 25.8564i 0.280976 + 1.04862i
\(609\) −6.27757 23.4282i −0.254380 0.949359i
\(610\) −34.6865 30.7583i −1.40442 1.24537i
\(611\) 2.78461 0.112653
\(612\) 24.5885 + 6.58846i 0.993929 + 0.266323i
\(613\) −23.7846 + 23.7846i −0.960651 + 0.960651i −0.999255 0.0386033i \(-0.987709\pi\)
0.0386033 + 0.999255i \(0.487709\pi\)
\(614\) 14.3660 + 24.8827i 0.579766 + 1.00418i
\(615\) 11.1962 22.3923i 0.451472 0.902945i
\(616\) −12.3923 21.4641i −0.499300 0.864813i
\(617\) 7.51666 28.0526i 0.302609 1.12935i −0.632374 0.774663i \(-0.717920\pi\)
0.934984 0.354691i \(-0.115414\pi\)
\(618\) 39.4641i 1.58748i
\(619\) 1.90192 3.29423i 0.0764448 0.132406i −0.825269 0.564740i \(-0.808976\pi\)
0.901714 + 0.432334i \(0.142310\pi\)
\(620\) 2.19615 + 36.5885i 0.0881996 + 1.46943i
\(621\) −1.20577 + 4.50000i −0.0483859 + 0.180579i
\(622\) −19.3923 + 5.19615i −0.777561 + 0.208347i
\(623\) 3.01666 + 11.2583i 0.120860 + 0.451055i
\(624\) 8.78461 + 8.78461i 0.351666 + 0.351666i
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) −21.1769 −0.846400
\(627\) 16.3923i 0.654646i
\(628\) 18.0000 18.0000i 0.718278 0.718278i
\(629\) 2.78461i 0.111030i
\(630\) −37.1769 18.5885i −1.48116 0.740582i
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) −1.60770 6.00000i −0.0639507 0.238667i
\(633\) 0 0
\(634\) 20.0000i 0.794301i
\(635\) 12.3827 13.9641i 0.491392 0.554148i
\(636\) 18.0000 + 18.0000i 0.713746 + 0.713746i
\(637\) 21.1244 5.66025i 0.836977 0.224267i
\(638\) −8.73205 + 2.33975i −0.345705 + 0.0926314i
\(639\) −31.1769 18.0000i −1.23334 0.712069i
\(640\) 5.07180 24.7846i 0.200480 0.979698i
\(641\) −36.1865 20.8923i −1.42928 0.825196i −0.432218 0.901769i \(-0.642269\pi\)
−0.997064 + 0.0765727i \(0.975602\pi\)
\(642\) −10.5622 + 18.2942i −0.416856 + 0.722016i
\(643\) 25.7942 + 6.91154i 1.01723 + 0.272565i 0.728645 0.684891i \(-0.240150\pi\)
0.288580 + 0.957456i \(0.406817\pi\)
\(644\) −3.92820 + 6.80385i −0.154793 + 0.268109i
\(645\) −26.4904 23.4904i −1.04306 0.924933i
\(646\) 14.1962 + 24.5885i 0.558540 + 0.967420i
\(647\) 19.6865 + 19.6865i 0.773957 + 0.773957i 0.978796 0.204838i \(-0.0656669\pi\)
−0.204838 + 0.978796i \(0.565667\pi\)
\(648\) −6.58846 + 24.5885i −0.258819 + 0.965926i
\(649\) 3.60770i 0.141614i
\(650\) 11.6603 + 4.98076i 0.457353 + 0.195362i
\(651\) 16.0981 60.0788i 0.630933 2.35468i
\(652\) 17.6603 4.73205i 0.691629 0.185321i
\(653\) 7.83013 29.2224i 0.306417 1.14356i −0.625303 0.780382i \(-0.715024\pi\)
0.931719 0.363180i \(-0.118309\pi\)
\(654\) 20.4904 5.49038i 0.801237 0.214691i
\(655\) 9.61474 + 14.5622i 0.375679 + 0.568991i
\(656\) −22.3923 12.9282i −0.874273 0.504762i
\(657\) −41.7846 + 11.1962i −1.63017 + 0.436804i
\(658\) 2.49038 + 9.29423i 0.0970852 + 0.362327i
\(659\) −10.7321 6.19615i −0.418061 0.241368i 0.276186 0.961104i \(-0.410929\pi\)
−0.694248 + 0.719736i \(0.744263\pi\)
\(660\) −6.92820 + 13.8564i −0.269680 + 0.539360i
\(661\) −6.00000 + 3.46410i −0.233373 + 0.134738i −0.612127 0.790759i \(-0.709686\pi\)
0.378754 + 0.925497i \(0.376353\pi\)
\(662\) −0.588457 0.588457i −0.0228710 0.0228710i
\(663\) 11.4115 + 6.58846i 0.443188 + 0.255874i
\(664\) 28.7321 + 16.5885i 1.11502 + 0.643757i
\(665\) −14.6603 43.9808i −0.568500 1.70550i
\(666\) 2.78461 0.107901
\(667\) 2.02628 + 2.02628i 0.0784579 + 0.0784579i
\(668\) 26.1962 26.1962i 1.01356 1.01356i
\(669\) 20.9545 20.9545i 0.810147 0.810147i
\(670\) −10.7321 + 21.4641i −0.414615 + 0.829231i
\(671\) 25.3923 14.6603i 0.980259 0.565953i
\(672\) −21.4641 + 37.1769i −0.827996 + 1.43413i
\(673\) 4.66025 1.24871i 0.179640 0.0481343i −0.167878 0.985808i \(-0.553691\pi\)
0.347517 + 0.937674i \(0.387025\pi\)
\(674\) 0.339746 + 0.196152i 0.0130865 + 0.00755551i
\(675\) 3.10770 + 25.7942i 0.119615 + 0.992820i
\(676\) −9.78461 16.9474i −0.376331 0.651825i
\(677\) 10.5359 + 39.3205i 0.404927 + 1.51121i 0.804189 + 0.594373i \(0.202600\pi\)
−0.399262 + 0.916837i \(0.630734\pi\)
\(678\) 4.39230 0.168685
\(679\) −26.8301 + 15.4904i −1.02965 + 0.594466i
\(680\) −1.60770 26.7846i −0.0616523 1.02714i
\(681\) 12.8038 + 12.8038i 0.490645 + 0.490645i
\(682\) −22.3923 6.00000i −0.857446 0.229752i
\(683\) −7.00000 7.00000i −0.267848 0.267848i 0.560385 0.828232i \(-0.310653\pi\)
−0.828232 + 0.560385i \(0.810653\pi\)
\(684\) −24.5885 + 14.1962i −0.940163 + 0.542803i
\(685\) 28.3923 9.46410i 1.08481 0.361605i
\(686\) 16.0981 + 27.8827i 0.614627 + 1.06457i
\(687\) −17.3038 9.99038i −0.660183 0.381157i
\(688\) −25.8564 + 25.8564i −0.985766 + 0.985766i
\(689\) 6.58846 + 11.4115i 0.251000 + 0.434745i
\(690\) 4.90192 0.294229i 0.186613 0.0112011i
\(691\) 40.4711 + 23.3660i 1.53959 + 0.888885i 0.998862 + 0.0476910i \(0.0151863\pi\)
0.540733 + 0.841194i \(0.318147\pi\)
\(692\) 5.46410 + 1.46410i 0.207714 + 0.0556568i
\(693\) 18.5885 18.5885i 0.706117 0.706117i
\(694\) 9.00000 + 5.19615i 0.341635 + 0.197243i
\(695\) −8.53590 12.9282i −0.323785 0.490395i
\(696\) 11.0718 + 11.0718i 0.419675 + 0.419675i
\(697\) −26.4904 7.09808i −1.00339 0.268859i
\(698\) 36.4641 36.4641i 1.38019 1.38019i
\(699\) −11.4904 + 42.8827i −0.434606 + 1.62197i
\(700\) −6.19615 + 43.3731i −0.234193 + 1.63935i
\(701\) 50.1769 1.89516 0.947578 0.319525i \(-0.103523\pi\)
0.947578 + 0.319525i \(0.103523\pi\)
\(702\) −6.58846 + 11.4115i −0.248665 + 0.430701i
\(703\) 2.19615 + 2.19615i 0.0828295 + 0.0828295i
\(704\) 13.8564 + 8.00000i 0.522233 + 0.301511i
\(705\) 3.99038 4.50000i 0.150286 0.169480i
\(706\) 18.9282i 0.712372i
\(707\) −8.46410 2.26795i −0.318325 0.0852950i
\(708\) −5.41154 + 3.12436i −0.203378 + 0.117420i
\(709\) 9.57180 16.5788i 0.359476 0.622631i −0.628397 0.777893i \(-0.716289\pi\)
0.987873 + 0.155261i \(0.0496220\pi\)
\(710\) −7.60770 + 37.1769i −0.285512 + 1.39522i
\(711\) 5.70577 3.29423i 0.213983 0.123543i
\(712\) −5.32051 5.32051i −0.199394 0.199394i
\(713\) 1.90192 + 7.09808i 0.0712276 + 0.265825i
\(714\) −11.7846 + 43.9808i −0.441028 + 1.64594i
\(715\) −5.32051 + 6.00000i −0.198976 + 0.224387i
\(716\) 6.39230 11.0718i 0.238892 0.413772i
\(717\) 28.3923 + 16.3923i 1.06033 + 0.612182i
\(718\) 3.00000 + 0.803848i 0.111959 + 0.0299993i
\(719\) −1.51666 −0.0565619 −0.0282809 0.999600i \(-0.509003\pi\)
−0.0282809 + 0.999600i \(0.509003\pi\)
\(720\) 26.7846 1.60770i 0.998203 0.0599153i
\(721\) 70.5885 2.62885
\(722\) −4.63397 1.24167i −0.172459 0.0462102i
\(723\) 32.5692i 1.21126i
\(724\) 3.00000 5.19615i 0.111494 0.193113i
\(725\) 14.6962 + 6.27757i 0.545801 + 0.233143i
\(726\) 12.1244 + 12.1244i 0.449977 + 0.449977i
\(727\) −0.767949 2.86603i −0.0284817 0.106295i 0.950222 0.311574i \(-0.100856\pi\)
−0.978703 + 0.205279i \(0.934190\pi\)
\(728\) −15.7128 + 15.7128i −0.582356 + 0.582356i
\(729\) −27.0000 −1.00000
\(730\) 25.1244 + 38.0526i 0.929894 + 1.40839i
\(731\) −19.3923 + 33.5885i −0.717250 + 1.24231i
\(732\) −43.9808 25.3923i −1.62558 0.938527i
\(733\) 10.5622 + 2.83013i 0.390123 + 0.104533i 0.448548 0.893759i \(-0.351941\pi\)
−0.0584252 + 0.998292i \(0.518608\pi\)
\(734\) 14.0000i 0.516749i
\(735\) 21.1244 42.2487i 0.779184 1.55837i
\(736\) 5.07180i 0.186949i
\(737\) −10.7321 10.7321i −0.395320 0.395320i
\(738\) 7.09808 26.4904i 0.261284 0.975124i
\(739\) −22.7321 −0.836212 −0.418106 0.908398i \(-0.637306\pi\)
−0.418106 + 0.908398i \(0.637306\pi\)
\(740\) −0.928203 2.78461i −0.0341214 0.102364i
\(741\) −14.1962 + 3.80385i −0.521509 + 0.139738i
\(742\) −32.1962 + 32.1962i −1.18196 + 1.18196i
\(743\) −25.4545 6.82051i −0.933834 0.250220i −0.240345 0.970687i \(-0.577261\pi\)
−0.693489 + 0.720467i \(0.743927\pi\)
\(744\) 10.3923 + 38.7846i 0.381000 + 1.42191i
\(745\) −13.0622 + 8.62436i −0.478561 + 0.315972i
\(746\) 4.60770 + 2.66025i 0.168700 + 0.0973988i
\(747\) −9.10770 + 33.9904i −0.333233 + 1.24364i
\(748\) 16.3923 + 4.39230i 0.599362 + 0.160599i
\(749\) −32.7224 18.8923i −1.19565 0.690310i
\(750\) 24.7583 11.7058i 0.904046 0.427434i
\(751\) −6.80385 11.7846i −0.248276 0.430027i 0.714772 0.699358i \(-0.246531\pi\)
−0.963048 + 0.269331i \(0.913197\pi\)
\(752\) −4.39230 4.39230i −0.160171 0.160171i
\(753\) 39.8827 23.0263i 1.45341 0.839124i
\(754\) 4.05256 + 7.01924i 0.147585 + 0.255626i
\(755\) 16.0000 32.0000i 0.582300 1.16460i
\(756\) −43.9808 11.7846i −1.59956 0.428602i
\(757\) −34.0526 34.0526i −1.23766 1.23766i −0.960954 0.276707i \(-0.910757\pi\)
−0.276707 0.960954i \(-0.589243\pi\)
\(758\) −45.2487 12.1244i −1.64351 0.440376i
\(759\) −0.803848 + 3.00000i −0.0291778 + 0.108893i
\(760\) 22.3923 + 19.8564i 0.812254 + 0.720268i
\(761\) 21.4808 12.4019i 0.778677 0.449569i −0.0572842 0.998358i \(-0.518244\pi\)
0.835961 + 0.548789i \(0.184911\pi\)
\(762\) 10.2224 17.7058i 0.370320 0.641412i
\(763\) 9.82051 + 36.6506i 0.355526 + 1.32684i
\(764\) −18.5885 32.1962i −0.672507 1.16482i
\(765\) 27.0000 9.00000i 0.976187 0.325396i
\(766\) −35.1962 20.3205i −1.27169 0.734210i
\(767\) −3.12436 + 0.837169i −0.112814 + 0.0302284i
\(768\) 27.7128i 1.00000i
\(769\) 29.9378 17.2846i 1.07959 0.623299i 0.148801 0.988867i \(-0.452459\pi\)
0.930785 + 0.365568i \(0.119125\pi\)
\(770\) −24.7846 12.3923i −0.893175 0.446588i
\(771\) −7.31347 27.2942i −0.263388 0.982978i
\(772\) −20.0000 + 20.0000i −0.719816 + 0.719816i
\(773\) −16.1962 16.1962i −0.582535 0.582535i 0.353064 0.935599i \(-0.385140\pi\)
−0.935599 + 0.353064i \(0.885140\pi\)
\(774\) −33.5885 19.3923i −1.20731 0.697042i
\(775\) 24.5885 + 32.7846i 0.883243 + 1.17766i
\(776\) 10.0000 17.3205i 0.358979 0.621770i
\(777\) 4.98076i 0.178684i
\(778\) 17.3923 + 17.3923i 0.623544 + 0.623544i
\(779\) 26.4904 15.2942i 0.949116 0.547973i
\(780\) 13.6077 + 2.78461i 0.487234 + 0.0997050i
\(781\) −20.7846 12.0000i −0.743732 0.429394i
\(782\) −1.39230 5.19615i −0.0497887 0.185814i
\(783\) −8.30385 + 14.3827i −0.296755 + 0.513995i
\(784\) −42.2487 24.3923i −1.50888 0.871154i
\(785\) 5.70577 27.8827i 0.203648 0.995176i
\(786\) 13.5167 + 13.5167i 0.482123 + 0.482123i
\(787\) −10.4378 + 38.9545i −0.372068 + 1.38858i 0.485513 + 0.874229i \(0.338633\pi\)
−0.857582 + 0.514348i \(0.828034\pi\)
\(788\) 32.7846 8.78461i 1.16790 0.312939i
\(789\) −17.1962 17.1962i −0.612199 0.612199i
\(790\) −5.19615 4.60770i −0.184871 0.163934i
\(791\) 7.85641i 0.279342i
\(792\) −4.39230 + 16.3923i −0.156074 + 0.582475i
\(793\) −18.5885 18.5885i −0.660095 0.660095i
\(794\) −0.803848 1.39230i −0.0285275 0.0494111i
\(795\) 27.8827 + 5.70577i 0.988897 + 0.202363i
\(796\) 4.19615 7.26795i 0.148729 0.257606i
\(797\) 22.1244 + 5.92820i 0.783685 + 0.209988i 0.628409 0.777883i \(-0.283707\pi\)
0.155276 + 0.987871i \(0.450373\pi\)
\(798\) −25.3923 43.9808i −0.898878 1.55690i
\(799\) −5.70577 3.29423i −0.201856 0.116541i
\(800\) −10.5359 26.2487i −0.372500 0.928032i
\(801\) 3.99038 6.91154i 0.140993 0.244207i
\(802\) 49.5167 13.2679i 1.74849 0.468508i
\(803\) −27.8564 + 7.46410i −0.983031 + 0.263402i
\(804\) −6.80385 + 25.3923i −0.239953 + 0.895518i
\(805\) 0.526279 + 8.76795i 0.0185489 + 0.309030i
\(806\) 20.7846i 0.732107i
\(807\) −0.866025 1.50000i −0.0304855 0.0528025i
\(808\) 5.46410 1.46410i 0.192226 0.0515069i
\(809\) −45.7128 −1.60718 −0.803588 0.595185i \(-0.797079\pi\)
−0.803588 + 0.595185i \(0.797079\pi\)
\(810\) 9.00000 + 27.0000i 0.316228 + 0.948683i
\(811\) 16.7321i 0.587542i 0.955876 + 0.293771i \(0.0949103\pi\)
−0.955876 + 0.293771i \(0.905090\pi\)
\(812\) −19.8038 + 19.8038i −0.694979 + 0.694979i
\(813\) −6.88269 + 3.97372i −0.241386 + 0.139364i
\(814\) 1.85641 0.0650670
\(815\) 13.5622 15.2942i 0.475062 0.535733i
\(816\) −7.60770 28.3923i −0.266323 0.993929i
\(817\) −11.1962 41.7846i −0.391704 1.46186i
\(818\) −8.19615 + 2.19615i −0.286572 + 0.0767867i
\(819\) −20.4115 11.7846i −0.713237 0.411788i
\(820\) −28.8564 + 1.73205i −1.00771 + 0.0604858i
\(821\) 14.2846 24.7417i 0.498536 0.863490i −0.501462 0.865180i \(-0.667204\pi\)
0.999999 + 0.00168929i \(0.000537719\pi\)
\(822\) 28.3923 16.3923i 0.990295 0.571747i
\(823\) 2.96410 11.0622i 0.103322 0.385603i −0.894827 0.446412i \(-0.852701\pi\)
0.998149 + 0.0608092i \(0.0193681\pi\)
\(824\) −39.4641 + 22.7846i −1.37480 + 0.793739i
\(825\) 2.07180 + 17.1962i 0.0721307 + 0.598693i
\(826\) −5.58846 9.67949i −0.194447 0.336793i
\(827\) −9.29423 + 9.29423i −0.323192 + 0.323192i −0.849990 0.526798i \(-0.823392\pi\)
0.526798 + 0.849990i \(0.323392\pi\)
\(828\) 5.19615 1.39230i 0.180579 0.0483859i
\(829\) −25.0526 −0.870111 −0.435056 0.900404i \(-0.643271\pi\)
−0.435056 + 0.900404i \(0.643271\pi\)
\(830\) 37.0263 2.22243i 1.28520 0.0771417i
\(831\) −11.1962 + 11.1962i −0.388390 + 0.388390i
\(832\) 3.71281 13.8564i 0.128719 0.480384i
\(833\) −49.9808 13.3923i −1.73173 0.464016i
\(834\) −12.0000 12.0000i −0.415526 0.415526i
\(835\) 8.30385 40.5788i 0.287366 1.40429i
\(836\) −16.3923 + 9.46410i −0.566940 + 0.327323i
\(837\) −36.8827 + 21.2942i −1.27485 + 0.736036i
\(838\) −16.9282 + 4.53590i −0.584775 + 0.156690i
\(839\) 14.0263 24.2942i 0.484241 0.838730i −0.515595 0.856832i \(-0.672429\pi\)
0.999836 + 0.0181024i \(0.00576248\pi\)
\(840\) 2.87564 + 47.9090i 0.0992192 + 1.65302i
\(841\) −9.39230 16.2679i −0.323873 0.560964i
\(842\) −5.32051 5.32051i −0.183357 0.183357i
\(843\) 3.58846 0.123593
\(844\) 0 0
\(845\) −19.5692 9.78461i −0.673202 0.336601i
\(846\) 3.29423 5.70577i 0.113258 0.196168i
\(847\) −21.6865 + 21.6865i −0.745158 + 0.745158i
\(848\) 7.60770 28.3923i 0.261249 0.974996i
\(849\) 7.79423 2.08846i 0.267497 0.0716757i
\(850\) −18.0000 24.0000i −0.617395 0.823193i
\(851\) −0.294229 0.509619i −0.0100860 0.0174695i
\(852\) 41.5692i 1.42414i
\(853\) −12.0000 44.7846i −0.410872 1.53340i −0.792962 0.609271i \(-0.791462\pi\)
0.382090 0.924125i \(-0.375204\pi\)
\(854\) 45.4186 78.6673i 1.55419 2.69194i
\(855\) −14.1962 + 28.3923i −0.485498 + 0.970996i
\(856\) 24.3923 0.833712
\(857\) −27.9282 + 7.48334i −0.954009 + 0.255626i −0.702063 0.712115i \(-0.747737\pi\)
−0.251947 + 0.967741i \(0.581071\pi\)
\(858\) −4.39230 + 7.60770i −0.149951 + 0.259722i
\(859\) −8.66025 15.0000i −0.295484 0.511793i 0.679613 0.733571i \(-0.262148\pi\)
−0.975097 + 0.221777i \(0.928814\pi\)
\(860\) −8.19615 + 40.0526i −0.279486 + 1.36578i
\(861\) 47.3827 + 12.6962i 1.61480 + 0.432684i
\(862\) 8.07180 30.1244i 0.274926 1.02604i
\(863\) −12.4186 + 12.4186i −0.422734 + 0.422734i −0.886144 0.463410i \(-0.846626\pi\)
0.463410 + 0.886144i \(0.346626\pi\)
\(864\) 28.3923 7.60770i 0.965926 0.258819i
\(865\) 6.00000 2.00000i 0.204006 0.0680020i
\(866\) 15.3923 + 26.6603i 0.523052 + 0.905952i
\(867\) −0.866025 1.50000i −0.0294118 0.0509427i
\(868\) −69.3731 + 18.5885i −2.35468 + 0.630933i
\(869\) 3.80385 2.19615i 0.129037 0.0744994i
\(870\) 17.1506 + 3.50962i 0.581461 + 0.118987i
\(871\) −6.80385 + 11.7846i −0.230540 + 0.399306i
\(872\) −17.3205 17.3205i −0.586546 0.586546i
\(873\) 20.4904 + 5.49038i 0.693494 + 0.185821i
\(874\) 5.19615 + 3.00000i 0.175762 + 0.101477i
\(875\) 20.9378 + 44.2846i 0.707828 + 1.49709i
\(876\) 35.3205 + 35.3205i 1.19337 + 1.19337i
\(877\) 6.46410 24.1244i 0.218277 0.814622i −0.766710 0.641994i \(-0.778108\pi\)
0.984987 0.172628i \(-0.0552258\pi\)
\(878\) −18.7846 18.7846i −0.633950 0.633950i
\(879\) −0.509619 1.90192i −0.0171890 0.0641503i
\(880\) 17.8564 1.07180i 0.601939 0.0361303i
\(881\) 2.07180i 0.0698006i −0.999391 0.0349003i \(-0.988889\pi\)
0.999391 0.0349003i \(-0.0111114\pi\)
\(882\) 13.3923 49.9808i 0.450942 1.68294i
\(883\) 27.4186 27.4186i 0.922709 0.922709i −0.0745113 0.997220i \(-0.523740\pi\)
0.997220 + 0.0745113i \(0.0237397\pi\)
\(884\) 15.2154i 0.511749i
\(885\) −3.12436 + 6.24871i −0.105024 + 0.210048i
\(886\) −54.5885 −1.83394
\(887\) −0.418584 + 1.56218i −0.0140547 + 0.0524528i −0.972597 0.232497i \(-0.925310\pi\)
0.958542 + 0.284950i \(0.0919770\pi\)
\(888\) −1.60770 2.78461i −0.0539507 0.0934454i
\(889\) 31.6699 + 18.2846i 1.06217 + 0.613246i
\(890\) −8.24167 1.68653i −0.276261 0.0565327i
\(891\) −18.0000 −0.603023
\(892\) −33.0526 8.85641i −1.10668 0.296534i
\(893\) 7.09808 1.90192i 0.237528 0.0636455i
\(894\) −12.1244 + 12.1244i −0.405499 + 0.405499i
\(895\) −0.856406 14.2679i −0.0286265 0.476925i
\(896\) 49.5692 1.65599
\(897\) 2.78461 0.0929754
\(898\) 44.7846 + 12.0000i 1.49448 + 0.400445i
\(899\) 26.1962i 0.873691i
\(900\) 24.0000 18.0000i 0.800000 0.600000i
\(901\) 31.1769i 1.03865i
\(902\) 4.73205 17.6603i 0.157560 0.588022i
\(903\) 34.6865 60.0788i 1.15430 1.99930i
\(904\) −2.53590 4.39230i −0.0843427 0.146086i
\(905\) −0.401924 6.69615i −0.0133604 0.222588i
\(906\) 10.1436 37.8564i 0.336998 1.25769i
\(907\) −3.52628 + 0.944864i −0.117088 + 0.0313737i −0.316887 0.948463i \(-0.602638\pi\)
0.199799 + 0.979837i \(0.435971\pi\)
\(908\) 5.41154 20.1962i 0.179588 0.670233i
\(909\) 3.00000 + 5.19615i 0.0995037 + 0.172345i
\(910\) −4.98076 + 24.3397i −0.165111 + 0.806855i
\(911\) 23.4904 + 13.5622i 0.778271 + 0.449335i 0.835817 0.549008i \(-0.184994\pi\)
−0.0575461 + 0.998343i \(0.518328\pi\)
\(912\) 28.3923 + 16.3923i 0.940163 + 0.542803i
\(913\) −6.07180 + 22.6603i −0.200947 + 0.749945i
\(914\) 14.3923i 0.476055i
\(915\) −56.6769 + 3.40192i −1.87368 + 0.112464i
\(916\) 23.0718i 0.762314i
\(917\) −24.1769 + 24.1769i −0.798392 + 0.798392i
\(918\) 27.0000 15.5885i 0.891133 0.514496i
\(919\) 20.1962i 0.666210i 0.942890 + 0.333105i \(0.108096\pi\)
−0.942890 + 0.333105i \(0.891904\pi\)
\(920\) −3.12436 4.73205i −0.103007 0.156011i
\(921\) 33.9904 + 9.10770i 1.12002 + 0.300109i
\(922\) −13.5885 + 13.5885i −0.447512 + 0.447512i
\(923\) −5.56922 + 20.7846i −0.183313 + 0.684134i
\(924\) −29.3205 7.85641i −0.964574 0.258457i
\(925\) −2.58142 2.02628i −0.0848764 0.0666237i
\(926\) 4.80385 8.32051i 0.157864 0.273429i
\(927\) −34.1769 34.1769i −1.12252 1.12252i
\(928\) 4.67949 17.4641i 0.153612 0.573287i
\(929\) 2.19615 3.80385i 0.0720534 0.124800i −0.827748 0.561100i \(-0.810378\pi\)
0.899801 + 0.436300i \(0.143711\pi\)
\(930\) 33.5885 + 29.7846i 1.10141 + 0.976676i
\(931\) 49.9808 28.8564i 1.63805 0.945731i
\(932\) 49.5167 13.2679i 1.62197 0.434606i
\(933\) −12.2942 + 21.2942i −0.402495 + 0.697142i
\(934\) 14.9090 8.60770i 0.487836 0.281652i
\(935\) 18.0000 6.00000i 0.588663 0.196221i
\(936\) 15.2154 0.497331
\(937\) −4.58846 + 4.58846i −0.149898 + 0.149898i −0.778073 0.628174i \(-0.783802\pi\)
0.628174 + 0.778073i \(0.283802\pi\)
\(938\) −45.4186 12.1699i −1.48297 0.397360i
\(939\) −18.3397 + 18.3397i −0.598495 + 0.598495i
\(940\) −6.80385 1.39230i −0.221917 0.0454120i
\(941\) 4.40192 + 7.62436i 0.143499 + 0.248547i 0.928812 0.370552i \(-0.120831\pi\)
−0.785313 + 0.619099i \(0.787498\pi\)
\(942\) 31.1769i 1.01580i
\(943\) −5.59808 + 1.50000i −0.182298 + 0.0488467i
\(944\) 6.24871 + 3.60770i 0.203378 + 0.117420i
\(945\) −48.2942 + 16.0981i −1.57101 + 0.523670i
\(946\) −22.3923 12.9282i −0.728037 0.420332i
\(947\) −6.18653 23.0885i −0.201035 0.750274i −0.990622 0.136634i \(-0.956371\pi\)
0.789586 0.613640i \(-0.210295\pi\)
\(948\) −6.58846 3.80385i −0.213983 0.123543i
\(949\) 12.9282 + 22.3923i 0.419667 + 0.726885i
\(950\) 33.1244 + 4.73205i 1.07470 + 0.153528i
\(951\) −17.3205 17.3205i −0.561656 0.561656i
\(952\) 50.7846 13.6077i 1.64594 0.441028i
\(953\) −24.9282 + 24.9282i −0.807504 + 0.807504i −0.984255 0.176752i \(-0.943441\pi\)
0.176752 + 0.984255i \(0.443441\pi\)
\(954\) 31.1769 1.00939
\(955\) −37.1769 18.5885i −1.20302 0.601508i
\(956\) 37.8564i 1.22436i
\(957\) −5.53590 + 9.58846i −0.178950 + 0.309951i
\(958\) −21.1244 + 21.1244i −0.682497 + 0.682497i
\(959\) 29.3205 + 50.7846i 0.946809 + 1.63992i
\(960\) −17.0718 25.8564i −0.550990 0.834512i
\(961\) −18.0885 + 31.3301i −0.583499 + 1.01065i
\(962\) −0.430781 1.60770i −0.0138889 0.0518342i
\(963\) 6.69615 + 24.9904i 0.215780 + 0.805304i
\(964\) 32.5692 18.8038i 1.04898 0.605631i
\(965\) −6.33975 + 30.9808i −0.204084 + 0.997306i
\(966\) 2.49038 + 9.29423i 0.0801267 + 0.299037i
\(967\) 15.9641 + 4.27757i 0.513371 + 0.137557i 0.506199 0.862417i \(-0.331050\pi\)
0.00717234 + 0.999974i \(0.497717\pi\)
\(968\) 5.12436 19.1244i 0.164703 0.614680i
\(969\) 33.5885 + 9.00000i 1.07902 + 0.289122i
\(970\) −1.33975 22.3205i −0.0430167 0.716668i
\(971\) 29.8038 0.956451 0.478225 0.878237i \(-0.341280\pi\)
0.478225 + 0.878237i \(0.341280\pi\)
\(972\) 15.5885 + 27.0000i 0.500000 + 0.866025i
\(973\) 21.4641 21.4641i 0.688108 0.688108i
\(974\) −5.87564 + 3.39230i −0.188268 + 0.108696i
\(975\) 14.4115 5.78461i 0.461539 0.185256i
\(976\) 58.6410i 1.87705i
\(977\) −10.7321 + 40.0526i −0.343349 + 1.28139i 0.551181 + 0.834386i \(0.314177\pi\)
−0.894529 + 0.447009i \(0.852489\pi\)
\(978\) 11.1962 19.3923i 0.358013 0.620098i
\(979\) 2.66025 4.60770i 0.0850221 0.147263i
\(980\) −54.4449 + 3.26795i −1.73918 + 0.104391i
\(981\) 12.9904 22.5000i 0.414751 0.718370i
\(982\) −9.07180 33.8564i −0.289493 1.08040i
\(983\) 3.57180 + 13.3301i 0.113923 + 0.425165i 0.999204 0.0398907i \(-0.0127010\pi\)
−0.885281 + 0.465056i \(0.846034\pi\)
\(984\) −30.5885 + 8.19615i −0.975124 + 0.261284i
\(985\) 25.1769 28.3923i 0.802203 0.904654i
\(986\) 19.1769i 0.610717i
\(987\) 10.2058 + 5.89230i 0.324853 + 0.187554i
\(988\) 12.0000 + 12.0000i 0.381771 + 0.381771i
\(989\) 8.19615i 0.260622i
\(990\) 6.00000 + 18.0000i 0.190693 + 0.572078i
\(991\) 10.1962 0.323891 0.161946 0.986800i \(-0.448223\pi\)
0.161946 + 0.986800i \(0.448223\pi\)
\(992\) 32.7846 32.7846i 1.04091 1.04091i
\(993\) −1.01924 −0.0323445
\(994\) −74.3538 −2.35836
\(995\) −0.562178 9.36603i −0.0178222 0.296923i
\(996\) 39.2487 10.5167i 1.24364 0.333233i
\(997\) −6.63397 + 1.77757i −0.210100 + 0.0562961i −0.362334 0.932048i \(-0.618020\pi\)
0.152234 + 0.988345i \(0.451353\pi\)
\(998\) 9.80385 + 36.5885i 0.310335 + 1.15819i
\(999\) 2.41154 2.41154i 0.0762978 0.0762978i
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 360.2.br.c.173.1 yes 4
5.2 odd 4 360.2.br.d.317.1 yes 4
8.5 even 2 360.2.br.b.173.1 yes 4
9.5 odd 6 360.2.br.a.293.1 4
40.37 odd 4 360.2.br.a.317.1 yes 4
45.32 even 12 360.2.br.b.77.1 yes 4
72.5 odd 6 360.2.br.d.293.1 yes 4
360.77 even 12 inner 360.2.br.c.77.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.br.a.293.1 4 9.5 odd 6
360.2.br.a.317.1 yes 4 40.37 odd 4
360.2.br.b.77.1 yes 4 45.32 even 12
360.2.br.b.173.1 yes 4 8.5 even 2
360.2.br.c.77.1 yes 4 360.77 even 12 inner
360.2.br.c.173.1 yes 4 1.1 even 1 trivial
360.2.br.d.293.1 yes 4 72.5 odd 6
360.2.br.d.317.1 yes 4 5.2 odd 4