Properties

Label 360.2.bf.a.301.2
Level $360$
Weight $2$
Character 360.301
Analytic conductor $2.875$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(61,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
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: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 301.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 360.301
Dual form 360.2.bf.a.61.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(2.00000 + 3.46410i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(2.00000 + 3.46410i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.00000i) q^{10} +(4.33013 - 2.50000i) q^{11} -3.46410i q^{12} +(5.19615 + 3.00000i) q^{13} +(5.46410 - 1.46410i) q^{14} -1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} -3.00000 q^{17} +(3.00000 + 3.00000i) q^{18} -7.00000i q^{19} +(1.00000 + 1.73205i) q^{20} +(-3.46410 + 6.00000i) q^{21} +(-1.83013 - 6.83013i) q^{22} +(-1.00000 + 1.73205i) q^{23} +(-4.73205 - 1.26795i) q^{24} +(0.500000 + 0.866025i) q^{25} +(6.00000 - 6.00000i) q^{26} -5.19615 q^{27} -8.00000i q^{28} +(-2.36603 - 0.633975i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(5.46410 - 1.46410i) q^{32} +(7.50000 + 4.33013i) q^{33} +(-1.09808 + 4.09808i) q^{34} -4.00000i q^{35} +(5.19615 - 3.00000i) q^{36} +2.00000i q^{37} +(-9.56218 - 2.56218i) q^{38} +10.3923i q^{39} +(2.73205 - 0.732051i) q^{40} +(2.50000 - 4.33013i) q^{41} +(6.92820 + 6.92820i) q^{42} +(-4.33013 + 2.50000i) q^{43} -10.0000 q^{44} +(2.59808 - 1.50000i) q^{45} +(2.00000 + 2.00000i) q^{46} +(-1.00000 - 1.73205i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(1.36603 - 0.366025i) q^{50} +(-2.59808 - 4.50000i) q^{51} +(-6.00000 - 10.3923i) q^{52} -8.00000i q^{53} +(-1.90192 + 7.09808i) q^{54} -5.00000 q^{55} +(-10.9282 - 2.92820i) q^{56} +(10.5000 - 6.06218i) q^{57} +(-6.06218 - 3.50000i) q^{59} +(-1.73205 + 3.00000i) q^{60} +(-3.46410 + 2.00000i) q^{61} +(4.00000 + 4.00000i) q^{62} -12.0000 q^{63} -8.00000i q^{64} +(-3.00000 - 5.19615i) q^{65} +(8.66025 - 8.66025i) q^{66} +(-2.59808 - 1.50000i) q^{67} +(5.19615 + 3.00000i) q^{68} -3.46410 q^{69} +(-5.46410 - 1.46410i) q^{70} +2.00000 q^{71} +(-2.19615 - 8.19615i) q^{72} +1.00000 q^{73} +(2.73205 + 0.732051i) q^{74} +(-0.866025 + 1.50000i) q^{75} +(-7.00000 + 12.1244i) q^{76} +(17.3205 + 10.0000i) q^{77} +(14.1962 + 3.80385i) q^{78} +(-5.00000 - 8.66025i) q^{79} -4.00000i q^{80} +(-4.50000 - 7.79423i) q^{81} +(-5.00000 - 5.00000i) q^{82} +(10.3923 - 6.00000i) q^{83} +(12.0000 - 6.92820i) q^{84} +(2.59808 + 1.50000i) q^{85} +(1.83013 + 6.83013i) q^{86} +(-3.66025 + 13.6603i) q^{88} +2.00000 q^{89} +(-1.09808 - 4.09808i) q^{90} +24.0000i q^{91} +(3.46410 - 2.00000i) q^{92} -6.92820 q^{93} +(-2.73205 + 0.732051i) q^{94} +(-3.50000 + 6.06218i) q^{95} +(6.92820 + 6.92820i) q^{96} +(3.50000 + 6.06218i) q^{97} +(9.00000 + 9.00000i) q^{98} +15.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 6 q^{6} + 8 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 6 q^{6} + 8 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{17} + 12 q^{18} + 4 q^{20} + 10 q^{22} - 4 q^{23} - 12 q^{24} + 2 q^{25} + 24 q^{26} - 6 q^{30} - 8 q^{31} + 8 q^{32} + 30 q^{33} + 6 q^{34} - 14 q^{38} + 4 q^{40} + 10 q^{41} - 40 q^{44} + 8 q^{46} - 4 q^{47} - 18 q^{49} + 2 q^{50} - 24 q^{52} - 18 q^{54} - 20 q^{55} - 16 q^{56} + 42 q^{57} + 16 q^{62} - 48 q^{63} - 12 q^{65} - 8 q^{70} + 8 q^{71} + 12 q^{72} + 4 q^{73} + 4 q^{74} - 28 q^{76} + 36 q^{78} - 20 q^{79} - 18 q^{81} - 20 q^{82} + 48 q^{84} - 10 q^{86} + 20 q^{88} + 8 q^{89} + 6 q^{90} - 4 q^{94} - 14 q^{95} + 14 q^{97} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 1.36603i 0.258819 0.965926i
\(3\) 0.866025 + 1.50000i 0.500000 + 0.866025i
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) −0.866025 0.500000i −0.387298 0.223607i
\(6\) 2.36603 0.633975i 0.965926 0.258819i
\(7\) 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i \(0.106148\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(10\) −1.00000 + 1.00000i −0.316228 + 0.316228i
\(11\) 4.33013 2.50000i 1.30558 0.753778i 0.324227 0.945979i \(-0.394896\pi\)
0.981356 + 0.192201i \(0.0615626\pi\)
\(12\) 3.46410i 1.00000i
\(13\) 5.19615 + 3.00000i 1.44115 + 0.832050i 0.997927 0.0643593i \(-0.0205004\pi\)
0.443227 + 0.896410i \(0.353834\pi\)
\(14\) 5.46410 1.46410i 1.46034 0.391298i
\(15\) 1.73205i 0.447214i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 3.00000 + 3.00000i 0.707107 + 0.707107i
\(19\) 7.00000i 1.60591i −0.596040 0.802955i \(-0.703260\pi\)
0.596040 0.802955i \(-0.296740\pi\)
\(20\) 1.00000 + 1.73205i 0.223607 + 0.387298i
\(21\) −3.46410 + 6.00000i −0.755929 + 1.30931i
\(22\) −1.83013 6.83013i −0.390184 1.45619i
\(23\) −1.00000 + 1.73205i −0.208514 + 0.361158i −0.951247 0.308431i \(-0.900196\pi\)
0.742732 + 0.669588i \(0.233529\pi\)
\(24\) −4.73205 1.26795i −0.965926 0.258819i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 6.00000 6.00000i 1.17670 1.17670i
\(27\) −5.19615 −1.00000
\(28\) 8.00000i 1.51186i
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) −2.36603 0.633975i −0.431975 0.115747i
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 5.46410 1.46410i 0.965926 0.258819i
\(33\) 7.50000 + 4.33013i 1.30558 + 0.753778i
\(34\) −1.09808 + 4.09808i −0.188319 + 0.702814i
\(35\) 4.00000i 0.676123i
\(36\) 5.19615 3.00000i 0.866025 0.500000i
\(37\) 2.00000i 0.328798i 0.986394 + 0.164399i \(0.0525685\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) −9.56218 2.56218i −1.55119 0.415640i
\(39\) 10.3923i 1.66410i
\(40\) 2.73205 0.732051i 0.431975 0.115747i
\(41\) 2.50000 4.33013i 0.390434 0.676252i −0.602072 0.798441i \(-0.705658\pi\)
0.992507 + 0.122189i \(0.0389915\pi\)
\(42\) 6.92820 + 6.92820i 1.06904 + 1.06904i
\(43\) −4.33013 + 2.50000i −0.660338 + 0.381246i −0.792406 0.609994i \(-0.791172\pi\)
0.132068 + 0.991241i \(0.457838\pi\)
\(44\) −10.0000 −1.50756
\(45\) 2.59808 1.50000i 0.387298 0.223607i
\(46\) 2.00000 + 2.00000i 0.294884 + 0.294884i
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) −3.46410 + 6.00000i −0.500000 + 0.866025i
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) 1.36603 0.366025i 0.193185 0.0517638i
\(51\) −2.59808 4.50000i −0.363803 0.630126i
\(52\) −6.00000 10.3923i −0.832050 1.44115i
\(53\) 8.00000i 1.09888i −0.835532 0.549442i \(-0.814840\pi\)
0.835532 0.549442i \(-0.185160\pi\)
\(54\) −1.90192 + 7.09808i −0.258819 + 0.965926i
\(55\) −5.00000 −0.674200
\(56\) −10.9282 2.92820i −1.46034 0.391298i
\(57\) 10.5000 6.06218i 1.39076 0.802955i
\(58\) 0 0
\(59\) −6.06218 3.50000i −0.789228 0.455661i 0.0504625 0.998726i \(-0.483930\pi\)
−0.839691 + 0.543065i \(0.817264\pi\)
\(60\) −1.73205 + 3.00000i −0.223607 + 0.387298i
\(61\) −3.46410 + 2.00000i −0.443533 + 0.256074i −0.705095 0.709113i \(-0.749096\pi\)
0.261562 + 0.965187i \(0.415762\pi\)
\(62\) 4.00000 + 4.00000i 0.508001 + 0.508001i
\(63\) −12.0000 −1.51186
\(64\) 8.00000i 1.00000i
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 8.66025 8.66025i 1.06600 1.06600i
\(67\) −2.59808 1.50000i −0.317406 0.183254i 0.332830 0.942987i \(-0.391996\pi\)
−0.650236 + 0.759733i \(0.725330\pi\)
\(68\) 5.19615 + 3.00000i 0.630126 + 0.363803i
\(69\) −3.46410 −0.417029
\(70\) −5.46410 1.46410i −0.653085 0.174994i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −2.19615 8.19615i −0.258819 0.965926i
\(73\) 1.00000 0.117041 0.0585206 0.998286i \(-0.481362\pi\)
0.0585206 + 0.998286i \(0.481362\pi\)
\(74\) 2.73205 + 0.732051i 0.317594 + 0.0850992i
\(75\) −0.866025 + 1.50000i −0.100000 + 0.173205i
\(76\) −7.00000 + 12.1244i −0.802955 + 1.39076i
\(77\) 17.3205 + 10.0000i 1.97386 + 1.13961i
\(78\) 14.1962 + 3.80385i 1.60740 + 0.430701i
\(79\) −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i \(-0.976489\pi\)
0.434730 0.900561i \(-0.356844\pi\)
\(80\) 4.00000i 0.447214i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −5.00000 5.00000i −0.552158 0.552158i
\(83\) 10.3923 6.00000i 1.14070 0.658586i 0.194099 0.980982i \(-0.437822\pi\)
0.946605 + 0.322396i \(0.104488\pi\)
\(84\) 12.0000 6.92820i 1.30931 0.755929i
\(85\) 2.59808 + 1.50000i 0.281801 + 0.162698i
\(86\) 1.83013 + 6.83013i 0.197348 + 0.736512i
\(87\) 0 0
\(88\) −3.66025 + 13.6603i −0.390184 + 1.45619i
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) −1.09808 4.09808i −0.115747 0.431975i
\(91\) 24.0000i 2.51588i
\(92\) 3.46410 2.00000i 0.361158 0.208514i
\(93\) −6.92820 −0.718421
\(94\) −2.73205 + 0.732051i −0.281790 + 0.0755053i
\(95\) −3.50000 + 6.06218i −0.359092 + 0.621966i
\(96\) 6.92820 + 6.92820i 0.707107 + 0.707107i
\(97\) 3.50000 + 6.06218i 0.355371 + 0.615521i 0.987181 0.159602i \(-0.0510211\pi\)
−0.631810 + 0.775123i \(0.717688\pi\)
\(98\) 9.00000 + 9.00000i 0.909137 + 0.909137i
\(99\) 15.0000i 1.50756i
\(100\) 2.00000i 0.200000i
\(101\) −12.1244 + 7.00000i −1.20642 + 0.696526i −0.961975 0.273138i \(-0.911939\pi\)
−0.244443 + 0.969664i \(0.578605\pi\)
\(102\) −7.09808 + 1.90192i −0.702814 + 0.188319i
\(103\) 7.00000 12.1244i 0.689730 1.19465i −0.282194 0.959357i \(-0.591062\pi\)
0.971925 0.235291i \(-0.0756043\pi\)
\(104\) −16.3923 + 4.39230i −1.60740 + 0.430701i
\(105\) 6.00000 3.46410i 0.585540 0.338062i
\(106\) −10.9282 2.92820i −1.06144 0.284412i
\(107\) 13.0000i 1.25676i −0.777908 0.628379i \(-0.783719\pi\)
0.777908 0.628379i \(-0.216281\pi\)
\(108\) 9.00000 + 5.19615i 0.866025 + 0.500000i
\(109\) 4.00000i 0.383131i −0.981480 0.191565i \(-0.938644\pi\)
0.981480 0.191565i \(-0.0613564\pi\)
\(110\) −1.83013 + 6.83013i −0.174496 + 0.651227i
\(111\) −3.00000 + 1.73205i −0.284747 + 0.164399i
\(112\) −8.00000 + 13.8564i −0.755929 + 1.30931i
\(113\) −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i \(-0.924403\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(114\) −4.43782 16.5622i −0.415640 1.55119i
\(115\) 1.73205 1.00000i 0.161515 0.0932505i
\(116\) 0 0
\(117\) −15.5885 + 9.00000i −1.44115 + 0.832050i
\(118\) −7.00000 + 7.00000i −0.644402 + 0.644402i
\(119\) −6.00000 10.3923i −0.550019 0.952661i
\(120\) 3.46410 + 3.46410i 0.316228 + 0.316228i
\(121\) 7.00000 12.1244i 0.636364 1.10221i
\(122\) 1.46410 + 5.46410i 0.132554 + 0.494697i
\(123\) 8.66025 0.780869
\(124\) 6.92820 4.00000i 0.622171 0.359211i
\(125\) 1.00000i 0.0894427i
\(126\) −4.39230 + 16.3923i −0.391298 + 1.46034i
\(127\) −18.0000 −1.59724 −0.798621 0.601834i \(-0.794437\pi\)
−0.798621 + 0.601834i \(0.794437\pi\)
\(128\) −10.9282 2.92820i −0.965926 0.258819i
\(129\) −7.50000 4.33013i −0.660338 0.381246i
\(130\) −8.19615 + 2.19615i −0.718850 + 0.192615i
\(131\) −10.3923 6.00000i −0.907980 0.524222i −0.0281993 0.999602i \(-0.508977\pi\)
−0.879781 + 0.475380i \(0.842311\pi\)
\(132\) −8.66025 15.0000i −0.753778 1.30558i
\(133\) 24.2487 14.0000i 2.10263 1.21395i
\(134\) −3.00000 + 3.00000i −0.259161 + 0.259161i
\(135\) 4.50000 + 2.59808i 0.387298 + 0.223607i
\(136\) 6.00000 6.00000i 0.514496 0.514496i
\(137\) 8.50000 + 14.7224i 0.726204 + 1.25782i 0.958477 + 0.285171i \(0.0920506\pi\)
−0.232273 + 0.972651i \(0.574616\pi\)
\(138\) −1.26795 + 4.73205i −0.107935 + 0.402819i
\(139\) 9.52628 + 5.50000i 0.808008 + 0.466504i 0.846264 0.532764i \(-0.178847\pi\)
−0.0382553 + 0.999268i \(0.512180\pi\)
\(140\) −4.00000 + 6.92820i −0.338062 + 0.585540i
\(141\) 1.73205 3.00000i 0.145865 0.252646i
\(142\) 0.732051 2.73205i 0.0614323 0.229269i
\(143\) 30.0000 2.50873
\(144\) −12.0000 −1.00000
\(145\) 0 0
\(146\) 0.366025 1.36603i 0.0302925 0.113053i
\(147\) −15.5885 −1.28571
\(148\) 2.00000 3.46410i 0.164399 0.284747i
\(149\) 5.19615 + 3.00000i 0.425685 + 0.245770i 0.697507 0.716578i \(-0.254293\pi\)
−0.271821 + 0.962348i \(0.587626\pi\)
\(150\) 1.73205 + 1.73205i 0.141421 + 0.141421i
\(151\) −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i \(-0.300055\pi\)
−0.994540 + 0.104357i \(0.966722\pi\)
\(152\) 14.0000 + 14.0000i 1.13555 + 1.13555i
\(153\) 4.50000 7.79423i 0.363803 0.630126i
\(154\) 20.0000 20.0000i 1.61165 1.61165i
\(155\) 3.46410 2.00000i 0.278243 0.160644i
\(156\) 10.3923 18.0000i 0.832050 1.44115i
\(157\) 17.3205 + 10.0000i 1.38233 + 0.798087i 0.992435 0.122774i \(-0.0391789\pi\)
0.389892 + 0.920860i \(0.372512\pi\)
\(158\) −13.6603 + 3.66025i −1.08675 + 0.291194i
\(159\) 12.0000 6.92820i 0.951662 0.549442i
\(160\) −5.46410 1.46410i −0.431975 0.115747i
\(161\) −8.00000 −0.630488
\(162\) −12.2942 + 3.29423i −0.965926 + 0.258819i
\(163\) 20.0000i 1.56652i −0.621694 0.783260i \(-0.713555\pi\)
0.621694 0.783260i \(-0.286445\pi\)
\(164\) −8.66025 + 5.00000i −0.676252 + 0.390434i
\(165\) −4.33013 7.50000i −0.337100 0.583874i
\(166\) −4.39230 16.3923i −0.340909 1.27229i
\(167\) −3.00000 + 5.19615i −0.232147 + 0.402090i −0.958440 0.285295i \(-0.907908\pi\)
0.726293 + 0.687386i \(0.241242\pi\)
\(168\) −5.07180 18.9282i −0.391298 1.46034i
\(169\) 11.5000 + 19.9186i 0.884615 + 1.53220i
\(170\) 3.00000 3.00000i 0.230089 0.230089i
\(171\) 18.1865 + 10.5000i 1.39076 + 0.802955i
\(172\) 10.0000 0.762493
\(173\) −6.92820 + 4.00000i −0.526742 + 0.304114i −0.739689 0.672949i \(-0.765027\pi\)
0.212947 + 0.977064i \(0.431694\pi\)
\(174\) 0 0
\(175\) −2.00000 + 3.46410i −0.151186 + 0.261861i
\(176\) 17.3205 + 10.0000i 1.30558 + 0.753778i
\(177\) 12.1244i 0.911322i
\(178\) 0.732051 2.73205i 0.0548695 0.204776i
\(179\) 12.0000i 0.896922i −0.893802 0.448461i \(-0.851972\pi\)
0.893802 0.448461i \(-0.148028\pi\)
\(180\) −6.00000 −0.447214
\(181\) 2.00000i 0.148659i 0.997234 + 0.0743294i \(0.0236816\pi\)
−0.997234 + 0.0743294i \(0.976318\pi\)
\(182\) 32.7846 + 8.78461i 2.43016 + 0.651159i
\(183\) −6.00000 3.46410i −0.443533 0.256074i
\(184\) −1.46410 5.46410i −0.107935 0.402819i
\(185\) 1.00000 1.73205i 0.0735215 0.127343i
\(186\) −2.53590 + 9.46410i −0.185941 + 0.693942i
\(187\) −12.9904 + 7.50000i −0.949951 + 0.548454i
\(188\) 4.00000i 0.291730i
\(189\) −10.3923 18.0000i −0.755929 1.30931i
\(190\) 7.00000 + 7.00000i 0.507833 + 0.507833i
\(191\) 4.00000 + 6.92820i 0.289430 + 0.501307i 0.973674 0.227946i \(-0.0732010\pi\)
−0.684244 + 0.729253i \(0.739868\pi\)
\(192\) 12.0000 6.92820i 0.866025 0.500000i
\(193\) 11.5000 19.9186i 0.827788 1.43377i −0.0719816 0.997406i \(-0.522932\pi\)
0.899770 0.436365i \(-0.143734\pi\)
\(194\) 9.56218 2.56218i 0.686524 0.183954i
\(195\) 5.19615 9.00000i 0.372104 0.644503i
\(196\) 15.5885 9.00000i 1.11346 0.642857i
\(197\) 8.00000i 0.569976i −0.958531 0.284988i \(-0.908010\pi\)
0.958531 0.284988i \(-0.0919897\pi\)
\(198\) 20.4904 + 5.49038i 1.45619 + 0.390184i
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −2.73205 0.732051i −0.193185 0.0517638i
\(201\) 5.19615i 0.366508i
\(202\) 5.12436 + 19.1244i 0.360548 + 1.34558i
\(203\) 0 0
\(204\) 10.3923i 0.727607i
\(205\) −4.33013 + 2.50000i −0.302429 + 0.174608i
\(206\) −14.0000 14.0000i −0.975426 0.975426i
\(207\) −3.00000 5.19615i −0.208514 0.361158i
\(208\) 24.0000i 1.66410i
\(209\) −17.5000 30.3109i −1.21050 2.09665i
\(210\) −2.53590 9.46410i −0.174994 0.653085i
\(211\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) −8.00000 + 13.8564i −0.549442 + 0.951662i
\(213\) 1.73205 + 3.00000i 0.118678 + 0.205557i
\(214\) −17.7583 4.75833i −1.21393 0.325273i
\(215\) 5.00000 0.340997
\(216\) 10.3923 10.3923i 0.707107 0.707107i
\(217\) −16.0000 −1.08615
\(218\) −5.46410 1.46410i −0.370076 0.0991615i
\(219\) 0.866025 + 1.50000i 0.0585206 + 0.101361i
\(220\) 8.66025 + 5.00000i 0.583874 + 0.337100i
\(221\) −15.5885 9.00000i −1.04859 0.605406i
\(222\) 1.26795 + 4.73205i 0.0850992 + 0.317594i
\(223\) 7.00000 + 12.1244i 0.468755 + 0.811907i 0.999362 0.0357107i \(-0.0113695\pi\)
−0.530607 + 0.847618i \(0.678036\pi\)
\(224\) 16.0000 + 16.0000i 1.06904 + 1.06904i
\(225\) −3.00000 −0.200000
\(226\) 6.00000 + 6.00000i 0.399114 + 0.399114i
\(227\) −7.79423 + 4.50000i −0.517321 + 0.298675i −0.735838 0.677158i \(-0.763211\pi\)
0.218517 + 0.975833i \(0.429878\pi\)
\(228\) −24.2487 −1.60591
\(229\) −3.46410 2.00000i −0.228914 0.132164i 0.381157 0.924510i \(-0.375526\pi\)
−0.610071 + 0.792347i \(0.708859\pi\)
\(230\) −0.732051 2.73205i −0.0482700 0.180146i
\(231\) 34.6410i 2.27921i
\(232\) 0 0
\(233\) −27.0000 −1.76883 −0.884414 0.466702i \(-0.845442\pi\)
−0.884414 + 0.466702i \(0.845442\pi\)
\(234\) 6.58846 + 24.5885i 0.430701 + 1.60740i
\(235\) 2.00000i 0.130466i
\(236\) 7.00000 + 12.1244i 0.455661 + 0.789228i
\(237\) 8.66025 15.0000i 0.562544 0.974355i
\(238\) −16.3923 + 4.39230i −1.06256 + 0.284711i
\(239\) 7.00000 12.1244i 0.452792 0.784259i −0.545766 0.837938i \(-0.683761\pi\)
0.998558 + 0.0536783i \(0.0170946\pi\)
\(240\) 6.00000 3.46410i 0.387298 0.223607i
\(241\) 7.50000 + 12.9904i 0.483117 + 0.836784i 0.999812 0.0193858i \(-0.00617107\pi\)
−0.516695 + 0.856170i \(0.672838\pi\)
\(242\) −14.0000 14.0000i −0.899954 0.899954i
\(243\) 7.79423 13.5000i 0.500000 0.866025i
\(244\) 8.00000 0.512148
\(245\) 7.79423 4.50000i 0.497955 0.287494i
\(246\) 3.16987 11.8301i 0.202104 0.754261i
\(247\) 21.0000 36.3731i 1.33620 2.31436i
\(248\) −2.92820 10.9282i −0.185941 0.693942i
\(249\) 18.0000 + 10.3923i 1.14070 + 0.658586i
\(250\) −1.36603 0.366025i −0.0863950 0.0231495i
\(251\) 9.00000i 0.568075i 0.958813 + 0.284037i \(0.0916740\pi\)
−0.958813 + 0.284037i \(0.908326\pi\)
\(252\) 20.7846 + 12.0000i 1.30931 + 0.755929i
\(253\) 10.0000i 0.628695i
\(254\) −6.58846 + 24.5885i −0.413397 + 1.54282i
\(255\) 5.19615i 0.325396i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −3.50000 + 6.06218i −0.218324 + 0.378148i −0.954296 0.298864i \(-0.903392\pi\)
0.735972 + 0.677012i \(0.236726\pi\)
\(258\) −8.66025 + 8.66025i −0.539164 + 0.539164i
\(259\) −6.92820 + 4.00000i −0.430498 + 0.248548i
\(260\) 12.0000i 0.744208i
\(261\) 0 0
\(262\) −12.0000 + 12.0000i −0.741362 + 0.741362i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) −23.6603 + 6.33975i −1.45619 + 0.390184i
\(265\) −4.00000 + 6.92820i −0.245718 + 0.425596i
\(266\) −10.2487 38.2487i −0.628389 2.34518i
\(267\) 1.73205 + 3.00000i 0.106000 + 0.183597i
\(268\) 3.00000 + 5.19615i 0.183254 + 0.317406i
\(269\) 20.0000i 1.21942i 0.792624 + 0.609711i \(0.208714\pi\)
−0.792624 + 0.609711i \(0.791286\pi\)
\(270\) 5.19615 5.19615i 0.316228 0.316228i
\(271\) 28.0000 1.70088 0.850439 0.526073i \(-0.176336\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) −6.00000 10.3923i −0.363803 0.630126i
\(273\) −36.0000 + 20.7846i −2.17882 + 1.25794i
\(274\) 23.2224 6.22243i 1.40292 0.375911i
\(275\) 4.33013 + 2.50000i 0.261116 + 0.150756i
\(276\) 6.00000 + 3.46410i 0.361158 + 0.208514i
\(277\) −1.73205 + 1.00000i −0.104069 + 0.0600842i −0.551131 0.834419i \(-0.685804\pi\)
0.447062 + 0.894503i \(0.352470\pi\)
\(278\) 11.0000 11.0000i 0.659736 0.659736i
\(279\) −6.00000 10.3923i −0.359211 0.622171i
\(280\) 8.00000 + 8.00000i 0.478091 + 0.478091i
\(281\) 11.0000 + 19.0526i 0.656205 + 1.13658i 0.981590 + 0.190999i \(0.0611727\pi\)
−0.325385 + 0.945582i \(0.605494\pi\)
\(282\) −3.46410 3.46410i −0.206284 0.206284i
\(283\) −3.46410 2.00000i −0.205919 0.118888i 0.393494 0.919327i \(-0.371266\pi\)
−0.599414 + 0.800439i \(0.704600\pi\)
\(284\) −3.46410 2.00000i −0.205557 0.118678i
\(285\) −12.1244 −0.718185
\(286\) 10.9808 40.9808i 0.649306 2.42324i
\(287\) 20.0000 1.18056
\(288\) −4.39230 + 16.3923i −0.258819 + 0.965926i
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −6.06218 + 10.5000i −0.355371 + 0.615521i
\(292\) −1.73205 1.00000i −0.101361 0.0585206i
\(293\) 3.46410 + 2.00000i 0.202375 + 0.116841i 0.597763 0.801673i \(-0.296056\pi\)
−0.395388 + 0.918514i \(0.629390\pi\)
\(294\) −5.70577 + 21.2942i −0.332767 + 1.24190i
\(295\) 3.50000 + 6.06218i 0.203778 + 0.352954i
\(296\) −4.00000 4.00000i −0.232495 0.232495i
\(297\) −22.5000 + 12.9904i −1.30558 + 0.753778i
\(298\) 6.00000 6.00000i 0.347571 0.347571i
\(299\) −10.3923 + 6.00000i −0.601003 + 0.346989i
\(300\) 3.00000 1.73205i 0.173205 0.100000i
\(301\) −17.3205 10.0000i −0.998337 0.576390i
\(302\) −13.6603 + 3.66025i −0.786059 + 0.210624i
\(303\) −21.0000 12.1244i −1.20642 0.696526i
\(304\) 24.2487 14.0000i 1.39076 0.802955i
\(305\) 4.00000 0.229039
\(306\) −9.00000 9.00000i −0.514496 0.514496i
\(307\) 23.0000i 1.31268i 0.754466 + 0.656340i \(0.227896\pi\)
−0.754466 + 0.656340i \(0.772104\pi\)
\(308\) −20.0000 34.6410i −1.13961 1.97386i
\(309\) 24.2487 1.37946
\(310\) −1.46410 5.46410i −0.0831554 0.310340i
\(311\) −10.0000 + 17.3205i −0.567048 + 0.982156i 0.429808 + 0.902920i \(0.358581\pi\)
−0.996856 + 0.0792356i \(0.974752\pi\)
\(312\) −20.7846 20.7846i −1.17670 1.17670i
\(313\) 4.50000 + 7.79423i 0.254355 + 0.440556i 0.964720 0.263278i \(-0.0848035\pi\)
−0.710365 + 0.703833i \(0.751470\pi\)
\(314\) 20.0000 20.0000i 1.12867 1.12867i
\(315\) 10.3923 + 6.00000i 0.585540 + 0.338062i
\(316\) 20.0000i 1.12509i
\(317\) −15.5885 + 9.00000i −0.875535 + 0.505490i −0.869184 0.494489i \(-0.835355\pi\)
−0.00635137 + 0.999980i \(0.502022\pi\)
\(318\) −5.07180 18.9282i −0.284412 1.06144i
\(319\) 0 0
\(320\) −4.00000 + 6.92820i −0.223607 + 0.387298i
\(321\) 19.5000 11.2583i 1.08838 0.628379i
\(322\) −2.92820 + 10.9282i −0.163182 + 0.609005i
\(323\) 21.0000i 1.16847i
\(324\) 18.0000i 1.00000i
\(325\) 6.00000i 0.332820i
\(326\) −27.3205 7.32051i −1.51314 0.405445i
\(327\) 6.00000 3.46410i 0.331801 0.191565i
\(328\) 3.66025 + 13.6603i 0.202104 + 0.754261i
\(329\) 4.00000 6.92820i 0.220527 0.381964i
\(330\) −11.8301 + 3.16987i −0.651227 + 0.174496i
\(331\) 17.3205 10.0000i 0.952021 0.549650i 0.0583130 0.998298i \(-0.481428\pi\)
0.893708 + 0.448649i \(0.148095\pi\)
\(332\) −24.0000 −1.31717
\(333\) −5.19615 3.00000i −0.284747 0.164399i
\(334\) 6.00000 + 6.00000i 0.328305 + 0.328305i
\(335\) 1.50000 + 2.59808i 0.0819538 + 0.141948i
\(336\) −27.7128 −1.51186
\(337\) −7.50000 + 12.9904i −0.408551 + 0.707631i −0.994728 0.102552i \(-0.967299\pi\)
0.586177 + 0.810183i \(0.300632\pi\)
\(338\) 31.4186 8.41858i 1.70895 0.457911i
\(339\) −10.3923 −0.564433
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) 20.0000i 1.08306i
\(342\) 21.0000 21.0000i 1.13555 1.13555i
\(343\) −8.00000 −0.431959
\(344\) 3.66025 13.6603i 0.197348 0.736512i
\(345\) 3.00000 + 1.73205i 0.161515 + 0.0932505i
\(346\) 2.92820 + 10.9282i 0.157421 + 0.587504i
\(347\) 16.4545 + 9.50000i 0.883323 + 0.509987i 0.871753 0.489946i \(-0.162984\pi\)
0.0115703 + 0.999933i \(0.496317\pi\)
\(348\) 0 0
\(349\) 13.8564 8.00000i 0.741716 0.428230i −0.0809766 0.996716i \(-0.525804\pi\)
0.822693 + 0.568486i \(0.192471\pi\)
\(350\) 4.00000 + 4.00000i 0.213809 + 0.213809i
\(351\) −27.0000 15.5885i −1.44115 0.832050i
\(352\) 20.0000 20.0000i 1.06600 1.06600i
\(353\) 4.50000 + 7.79423i 0.239511 + 0.414845i 0.960574 0.278024i \(-0.0896796\pi\)
−0.721063 + 0.692869i \(0.756346\pi\)
\(354\) −16.5622 4.43782i −0.880270 0.235868i
\(355\) −1.73205 1.00000i −0.0919277 0.0530745i
\(356\) −3.46410 2.00000i −0.183597 0.106000i
\(357\) 10.3923 18.0000i 0.550019 0.952661i
\(358\) −16.3923 4.39230i −0.866360 0.232141i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) −2.19615 + 8.19615i −0.115747 + 0.431975i
\(361\) −30.0000 −1.57895
\(362\) 2.73205 + 0.732051i 0.143593 + 0.0384757i
\(363\) 24.2487 1.27273
\(364\) 24.0000 41.5692i 1.25794 2.17882i
\(365\) −0.866025 0.500000i −0.0453298 0.0261712i
\(366\) −6.92820 + 6.92820i −0.362143 + 0.362143i
\(367\) −9.00000 15.5885i −0.469796 0.813711i 0.529607 0.848243i \(-0.322339\pi\)
−0.999404 + 0.0345320i \(0.989006\pi\)
\(368\) −8.00000 −0.417029
\(369\) 7.50000 + 12.9904i 0.390434 + 0.676252i
\(370\) −2.00000 2.00000i −0.103975 0.103975i
\(371\) 27.7128 16.0000i 1.43878 0.830679i
\(372\) 12.0000 + 6.92820i 0.622171 + 0.359211i
\(373\) −19.0526 11.0000i −0.986504 0.569558i −0.0822766 0.996610i \(-0.526219\pi\)
−0.904227 + 0.427051i \(0.859552\pi\)
\(374\) 5.49038 + 20.4904i 0.283901 + 1.05953i
\(375\) 1.50000 0.866025i 0.0774597 0.0447214i
\(376\) 5.46410 + 1.46410i 0.281790 + 0.0755053i
\(377\) 0 0
\(378\) −28.3923 + 7.60770i −1.46034 + 0.391298i
\(379\) 3.00000i 0.154100i 0.997027 + 0.0770498i \(0.0245501\pi\)
−0.997027 + 0.0770498i \(0.975450\pi\)
\(380\) 12.1244 7.00000i 0.621966 0.359092i
\(381\) −15.5885 27.0000i −0.798621 1.38325i
\(382\) 10.9282 2.92820i 0.559136 0.149820i
\(383\) −9.00000 + 15.5885i −0.459879 + 0.796533i −0.998954 0.0457244i \(-0.985440\pi\)
0.539076 + 0.842257i \(0.318774\pi\)
\(384\) −5.07180 18.9282i −0.258819 0.965926i
\(385\) −10.0000 17.3205i −0.509647 0.882735i
\(386\) −23.0000 23.0000i −1.17067 1.17067i
\(387\) 15.0000i 0.762493i
\(388\) 14.0000i 0.710742i
\(389\) −13.8564 + 8.00000i −0.702548 + 0.405616i −0.808296 0.588777i \(-0.799610\pi\)
0.105748 + 0.994393i \(0.466276\pi\)
\(390\) −10.3923 10.3923i −0.526235 0.526235i
\(391\) 3.00000 5.19615i 0.151717 0.262781i
\(392\) −6.58846 24.5885i −0.332767 1.24190i
\(393\) 20.7846i 1.04844i
\(394\) −10.9282 2.92820i −0.550555 0.147521i
\(395\) 10.0000i 0.503155i
\(396\) 15.0000 25.9808i 0.753778 1.30558i
\(397\) 26.0000i 1.30490i −0.757831 0.652451i \(-0.773741\pi\)
0.757831 0.652451i \(-0.226259\pi\)
\(398\) 0 0
\(399\) 42.0000 + 24.2487i 2.10263 + 1.21395i
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 7.50000 12.9904i 0.374532 0.648709i −0.615725 0.787961i \(-0.711137\pi\)
0.990257 + 0.139253i \(0.0444700\pi\)
\(402\) −7.09808 1.90192i −0.354020 0.0948593i
\(403\) −20.7846 + 12.0000i −1.03536 + 0.597763i
\(404\) 28.0000 1.39305
\(405\) 9.00000i 0.447214i
\(406\) 0 0
\(407\) 5.00000 + 8.66025i 0.247841 + 0.429273i
\(408\) 14.1962 + 3.80385i 0.702814 + 0.188319i
\(409\) −7.50000 + 12.9904i −0.370851 + 0.642333i −0.989697 0.143180i \(-0.954267\pi\)
0.618846 + 0.785513i \(0.287601\pi\)
\(410\) 1.83013 + 6.83013i 0.0903835 + 0.337316i
\(411\) −14.7224 + 25.5000i −0.726204 + 1.25782i
\(412\) −24.2487 + 14.0000i −1.19465 + 0.689730i
\(413\) 28.0000i 1.37779i
\(414\) −8.19615 + 2.19615i −0.402819 + 0.107935i
\(415\) −12.0000 −0.589057
\(416\) 32.7846 + 8.78461i 1.60740 + 0.430701i
\(417\) 19.0526i 0.933008i
\(418\) −47.8109 + 12.8109i −2.33851 + 0.626601i
\(419\) −3.46410 2.00000i −0.169232 0.0977064i 0.412991 0.910735i \(-0.364484\pi\)
−0.582224 + 0.813029i \(0.697817\pi\)
\(420\) −13.8564 −0.676123
\(421\) −1.73205 + 1.00000i −0.0844150 + 0.0487370i −0.541613 0.840628i \(-0.682186\pi\)
0.457198 + 0.889365i \(0.348853\pi\)
\(422\) 0 0
\(423\) 6.00000 0.291730
\(424\) 16.0000 + 16.0000i 0.777029 + 0.777029i
\(425\) −1.50000 2.59808i −0.0727607 0.126025i
\(426\) 4.73205 1.26795i 0.229269 0.0614323i
\(427\) −13.8564 8.00000i −0.670559 0.387147i
\(428\) −13.0000 + 22.5167i −0.628379 + 1.08838i
\(429\) 25.9808 + 45.0000i 1.25436 + 2.17262i
\(430\) 1.83013 6.83013i 0.0882566 0.329378i
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) −10.3923 18.0000i −0.500000 0.866025i
\(433\) 29.0000 1.39365 0.696826 0.717241i \(-0.254595\pi\)
0.696826 + 0.717241i \(0.254595\pi\)
\(434\) −5.85641 + 21.8564i −0.281117 + 1.04914i
\(435\) 0 0
\(436\) −4.00000 + 6.92820i −0.191565 + 0.331801i
\(437\) 12.1244 + 7.00000i 0.579987 + 0.334855i
\(438\) 2.36603 0.633975i 0.113053 0.0302925i
\(439\) 20.0000 + 34.6410i 0.954548 + 1.65333i 0.735399 + 0.677634i \(0.236995\pi\)
0.219149 + 0.975691i \(0.429672\pi\)
\(440\) 10.0000 10.0000i 0.476731 0.476731i
\(441\) −13.5000 23.3827i −0.642857 1.11346i
\(442\) −18.0000 + 18.0000i −0.856173 + 0.856173i
\(443\) −21.6506 + 12.5000i −1.02865 + 0.593893i −0.916598 0.399809i \(-0.869076\pi\)
−0.112054 + 0.993702i \(0.535743\pi\)
\(444\) 6.92820 0.328798
\(445\) −1.73205 1.00000i −0.0821071 0.0474045i
\(446\) 19.1244 5.12436i 0.905564 0.242645i
\(447\) 10.3923i 0.491539i
\(448\) 27.7128 16.0000i 1.30931 0.755929i
\(449\) −27.0000 −1.27421 −0.637104 0.770778i \(-0.719868\pi\)
−0.637104 + 0.770778i \(0.719868\pi\)
\(450\) −1.09808 + 4.09808i −0.0517638 + 0.193185i
\(451\) 25.0000i 1.17720i
\(452\) 10.3923 6.00000i 0.488813 0.282216i
\(453\) 8.66025 15.0000i 0.406894 0.704761i
\(454\) 3.29423 + 12.2942i 0.154606 + 0.576997i
\(455\) 12.0000 20.7846i 0.562569 0.974398i
\(456\) −8.87564 + 33.1244i −0.415640 + 1.55119i
\(457\) −1.50000 2.59808i −0.0701670 0.121533i 0.828807 0.559534i \(-0.189020\pi\)
−0.898974 + 0.438001i \(0.855687\pi\)
\(458\) −4.00000 + 4.00000i −0.186908 + 0.186908i
\(459\) 15.5885 0.727607
\(460\) −4.00000 −0.186501
\(461\) −12.1244 + 7.00000i −0.564688 + 0.326023i −0.755025 0.655696i \(-0.772375\pi\)
0.190337 + 0.981719i \(0.439042\pi\)
\(462\) 47.3205 + 12.6795i 2.20155 + 0.589903i
\(463\) −13.0000 + 22.5167i −0.604161 + 1.04644i 0.388022 + 0.921650i \(0.373158\pi\)
−0.992183 + 0.124788i \(0.960175\pi\)
\(464\) 0 0
\(465\) 6.00000 + 3.46410i 0.278243 + 0.160644i
\(466\) −9.88269 + 36.8827i −0.457807 + 1.70856i
\(467\) 13.0000i 0.601568i −0.953692 0.300784i \(-0.902752\pi\)
0.953692 0.300784i \(-0.0972484\pi\)
\(468\) 36.0000 1.66410
\(469\) 12.0000i 0.554109i
\(470\) 2.73205 + 0.732051i 0.126020 + 0.0337670i
\(471\) 34.6410i 1.59617i
\(472\) 19.1244 5.12436i 0.880270 0.235868i
\(473\) −12.5000 + 21.6506i −0.574751 + 0.995497i
\(474\) −17.3205 17.3205i −0.795557 0.795557i
\(475\) 6.06218 3.50000i 0.278152 0.160591i
\(476\) 24.0000i 1.10004i
\(477\) 20.7846 + 12.0000i 0.951662 + 0.549442i
\(478\) −14.0000 14.0000i −0.640345 0.640345i
\(479\) −8.00000 13.8564i −0.365529 0.633115i 0.623332 0.781958i \(-0.285779\pi\)
−0.988861 + 0.148842i \(0.952445\pi\)
\(480\) −2.53590 9.46410i −0.115747 0.431975i
\(481\) −6.00000 + 10.3923i −0.273576 + 0.473848i
\(482\) 20.4904 5.49038i 0.933311 0.250080i
\(483\) −6.92820 12.0000i −0.315244 0.546019i
\(484\) −24.2487 + 14.0000i −1.10221 + 0.636364i
\(485\) 7.00000i 0.317854i
\(486\) −15.5885 15.5885i −0.707107 0.707107i
\(487\) −12.0000 −0.543772 −0.271886 0.962329i \(-0.587647\pi\)
−0.271886 + 0.962329i \(0.587647\pi\)
\(488\) 2.92820 10.9282i 0.132554 0.494697i
\(489\) 30.0000 17.3205i 1.35665 0.783260i
\(490\) −3.29423 12.2942i −0.148818 0.555397i
\(491\) 9.52628 + 5.50000i 0.429915 + 0.248212i 0.699310 0.714818i \(-0.253491\pi\)
−0.269395 + 0.963030i \(0.586824\pi\)
\(492\) −15.0000 8.66025i −0.676252 0.390434i
\(493\) 0 0
\(494\) −42.0000 42.0000i −1.88967 1.88967i
\(495\) 7.50000 12.9904i 0.337100 0.583874i
\(496\) −16.0000 −0.718421
\(497\) 4.00000 + 6.92820i 0.179425 + 0.310772i
\(498\) 20.7846 20.7846i 0.931381 0.931381i
\(499\) −35.5070 20.5000i −1.58951 0.917706i −0.993387 0.114816i \(-0.963372\pi\)
−0.596127 0.802890i \(-0.703294\pi\)
\(500\) −1.00000 + 1.73205i −0.0447214 + 0.0774597i
\(501\) −10.3923 −0.464294
\(502\) 12.2942 + 3.29423i 0.548718 + 0.147029i
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 24.0000 24.0000i 1.06904 1.06904i
\(505\) 14.0000 0.622992
\(506\) 13.6603 + 3.66025i 0.607272 + 0.162718i
\(507\) −19.9186 + 34.5000i −0.884615 + 1.53220i
\(508\) 31.1769 + 18.0000i 1.38325 + 0.798621i
\(509\) −10.3923 6.00000i −0.460631 0.265945i 0.251679 0.967811i \(-0.419017\pi\)
−0.712309 + 0.701866i \(0.752351\pi\)
\(510\) 7.09808 + 1.90192i 0.314308 + 0.0842186i
\(511\) 2.00000 + 3.46410i 0.0884748 + 0.153243i
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 36.3731i 1.60591i
\(514\) 7.00000 + 7.00000i 0.308757 + 0.308757i
\(515\) −12.1244 + 7.00000i −0.534263 + 0.308457i
\(516\) 8.66025 + 15.0000i 0.381246 + 0.660338i
\(517\) −8.66025 5.00000i −0.380878 0.219900i
\(518\) 2.92820 + 10.9282i 0.128658 + 0.480158i
\(519\) −12.0000 6.92820i −0.526742 0.304114i
\(520\) 16.3923 + 4.39230i 0.718850 + 0.192615i
\(521\) 15.0000 0.657162 0.328581 0.944476i \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) 0 0
\(523\) 4.00000i 0.174908i −0.996169 0.0874539i \(-0.972127\pi\)
0.996169 0.0874539i \(-0.0278730\pi\)
\(524\) 12.0000 + 20.7846i 0.524222 + 0.907980i
\(525\) −6.92820 −0.302372
\(526\) 0 0
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 34.6410i 1.50756i
\(529\) 9.50000 + 16.4545i 0.413043 + 0.715412i
\(530\) 8.00000 + 8.00000i 0.347498 + 0.347498i
\(531\) 18.1865 10.5000i 0.789228 0.455661i
\(532\) −56.0000 −2.42791
\(533\) 25.9808 15.0000i 1.12535 0.649722i
\(534\) 4.73205 1.26795i 0.204776 0.0548695i
\(535\) −6.50000 + 11.2583i −0.281020 + 0.486740i
\(536\) 8.19615 2.19615i 0.354020 0.0948593i
\(537\) 18.0000 10.3923i 0.776757 0.448461i
\(538\) 27.3205 + 7.32051i 1.17787 + 0.315610i
\(539\) 45.0000i 1.93829i
\(540\) −5.19615 9.00000i −0.223607 0.387298i
\(541\) 22.0000i 0.945854i −0.881102 0.472927i \(-0.843197\pi\)
0.881102 0.472927i \(-0.156803\pi\)
\(542\) 10.2487 38.2487i 0.440220 1.64292i
\(543\) −3.00000 + 1.73205i −0.128742 + 0.0743294i
\(544\) −16.3923 + 4.39230i −0.702814 + 0.188319i
\(545\) −2.00000 + 3.46410i −0.0856706 + 0.148386i
\(546\) 15.2154 + 56.7846i 0.651159 + 2.43016i
\(547\) 11.2583 6.50000i 0.481371 0.277920i −0.239616 0.970868i \(-0.577022\pi\)
0.720988 + 0.692948i \(0.243688\pi\)
\(548\) 34.0000i 1.45241i
\(549\) 12.0000i 0.512148i
\(550\) 5.00000 5.00000i 0.213201 0.213201i
\(551\) 0 0
\(552\) 6.92820 6.92820i 0.294884 0.294884i
\(553\) 20.0000 34.6410i 0.850487 1.47309i
\(554\) 0.732051 + 2.73205i 0.0311019 + 0.116074i
\(555\) 3.46410 0.147043
\(556\) −11.0000 19.0526i −0.466504 0.808008i
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) −16.3923 + 4.39230i −0.693942 + 0.185941i
\(559\) −30.0000 −1.26886
\(560\) 13.8564 8.00000i 0.585540 0.338062i
\(561\) −22.5000 12.9904i −0.949951 0.548454i
\(562\) 30.0526 8.05256i 1.26769 0.339677i
\(563\) −33.7750 19.5000i −1.42345 0.821827i −0.426855 0.904320i \(-0.640378\pi\)
−0.996592 + 0.0824933i \(0.973712\pi\)
\(564\) −6.00000 + 3.46410i −0.252646 + 0.145865i
\(565\) 5.19615 3.00000i 0.218604 0.126211i
\(566\) −4.00000 + 4.00000i −0.168133 + 0.168133i
\(567\) 18.0000 31.1769i 0.755929 1.30931i
\(568\) −4.00000 + 4.00000i −0.167836 + 0.167836i
\(569\) 12.5000 + 21.6506i 0.524027 + 0.907642i 0.999609 + 0.0279702i \(0.00890434\pi\)
−0.475581 + 0.879672i \(0.657762\pi\)
\(570\) −4.43782 + 16.5622i −0.185880 + 0.693713i
\(571\) 11.2583 + 6.50000i 0.471146 + 0.272017i 0.716720 0.697362i \(-0.245643\pi\)
−0.245573 + 0.969378i \(0.578976\pi\)
\(572\) −51.9615 30.0000i −2.17262 1.25436i
\(573\) −6.92820 + 12.0000i −0.289430 + 0.501307i
\(574\) 7.32051 27.3205i 0.305552 1.14034i
\(575\) −2.00000 −0.0834058
\(576\) 20.7846 + 12.0000i 0.866025 + 0.500000i
\(577\) 7.00000 0.291414 0.145707 0.989328i \(-0.453454\pi\)
0.145707 + 0.989328i \(0.453454\pi\)
\(578\) −2.92820 + 10.9282i −0.121797 + 0.454553i
\(579\) 39.8372 1.65558
\(580\) 0 0
\(581\) 41.5692 + 24.0000i 1.72458 + 0.995688i
\(582\) 12.1244 + 12.1244i 0.502571 + 0.502571i
\(583\) −20.0000 34.6410i −0.828315 1.43468i
\(584\) −2.00000 + 2.00000i −0.0827606 + 0.0827606i
\(585\) 18.0000 0.744208
\(586\) 4.00000 4.00000i 0.165238 0.165238i
\(587\) 23.3827 13.5000i 0.965107 0.557205i 0.0673658 0.997728i \(-0.478541\pi\)
0.897741 + 0.440524i \(0.145207\pi\)
\(588\) 27.0000 + 15.5885i 1.11346 + 0.642857i
\(589\) 24.2487 + 14.0000i 0.999151 + 0.576860i
\(590\) 9.56218 2.56218i 0.393669 0.105483i
\(591\) 12.0000 6.92820i 0.493614 0.284988i
\(592\) −6.92820 + 4.00000i −0.284747 + 0.164399i
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) 9.50962 + 35.4904i 0.390184 + 1.45619i
\(595\) 12.0000i 0.491952i
\(596\) −6.00000 10.3923i −0.245770 0.425685i
\(597\) 0 0
\(598\) 4.39230 + 16.3923i 0.179615 + 0.670331i
\(599\) 21.0000 36.3731i 0.858037 1.48616i −0.0157622 0.999876i \(-0.505017\pi\)
0.873799 0.486287i \(-0.161649\pi\)
\(600\) −1.26795 4.73205i −0.0517638 0.193185i
\(601\) −18.5000 32.0429i −0.754631 1.30706i −0.945558 0.325455i \(-0.894483\pi\)
0.190927 0.981604i \(-0.438851\pi\)
\(602\) −20.0000 + 20.0000i −0.815139 + 0.815139i
\(603\) 7.79423 4.50000i 0.317406 0.183254i
\(604\) 20.0000i 0.813788i
\(605\) −12.1244 + 7.00000i −0.492925 + 0.284590i
\(606\) −24.2487 + 24.2487i −0.985037 + 0.985037i
\(607\) 2.00000 3.46410i 0.0811775 0.140604i −0.822578 0.568652i \(-0.807465\pi\)
0.903756 + 0.428048i \(0.140799\pi\)
\(608\) −10.2487 38.2487i −0.415640 1.55119i
\(609\) 0 0
\(610\) 1.46410 5.46410i 0.0592797 0.221235i
\(611\) 12.0000i 0.485468i
\(612\) −15.5885 + 9.00000i −0.630126 + 0.363803i
\(613\) 26.0000i 1.05013i 0.851062 + 0.525065i \(0.175959\pi\)
−0.851062 + 0.525065i \(0.824041\pi\)
\(614\) 31.4186 + 8.41858i 1.26795 + 0.339746i
\(615\) −7.50000 4.33013i −0.302429 0.174608i
\(616\) −54.6410 + 14.6410i −2.20155 + 0.589903i
\(617\) 1.50000 2.59808i 0.0603877 0.104595i −0.834251 0.551385i \(-0.814100\pi\)
0.894639 + 0.446790i \(0.147433\pi\)
\(618\) 8.87564 33.1244i 0.357031 1.33246i
\(619\) −4.33013 + 2.50000i −0.174042 + 0.100483i −0.584491 0.811400i \(-0.698706\pi\)
0.410448 + 0.911884i \(0.365372\pi\)
\(620\) −8.00000 −0.321288
\(621\) 5.19615 9.00000i 0.208514 0.361158i
\(622\) 20.0000 + 20.0000i 0.801927 + 0.801927i
\(623\) 4.00000 + 6.92820i 0.160257 + 0.277573i
\(624\) −36.0000 + 20.7846i −1.44115 + 0.832050i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 12.2942 3.29423i 0.491376 0.131664i
\(627\) 30.3109 52.5000i 1.21050 2.09665i
\(628\) −20.0000 34.6410i −0.798087 1.38233i
\(629\) 6.00000i 0.239236i
\(630\) 12.0000 12.0000i 0.478091 0.478091i
\(631\) −6.00000 −0.238856 −0.119428 0.992843i \(-0.538106\pi\)
−0.119428 + 0.992843i \(0.538106\pi\)
\(632\) 27.3205 + 7.32051i 1.08675 + 0.291194i
\(633\) 0 0
\(634\) 6.58846 + 24.5885i 0.261661 + 0.976532i
\(635\) 15.5885 + 9.00000i 0.618609 + 0.357154i
\(636\) −27.7128 −1.09888
\(637\) −46.7654 + 27.0000i −1.85291 + 1.06978i
\(638\) 0 0
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 8.00000 + 8.00000i 0.316228 + 0.316228i
\(641\) −8.50000 14.7224i −0.335730 0.581501i 0.647895 0.761730i \(-0.275650\pi\)
−0.983625 + 0.180229i \(0.942316\pi\)
\(642\) −8.24167 30.7583i −0.325273 1.21393i
\(643\) −18.1865 10.5000i −0.717207 0.414080i 0.0965169 0.995331i \(-0.469230\pi\)
−0.813724 + 0.581252i \(0.802563\pi\)
\(644\) 13.8564 + 8.00000i 0.546019 + 0.315244i
\(645\) 4.33013 + 7.50000i 0.170499 + 0.295312i
\(646\) 28.6865 + 7.68653i 1.12866 + 0.302423i
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) 24.5885 + 6.58846i 0.965926 + 0.258819i
\(649\) −35.0000 −1.37387
\(650\) 8.19615 + 2.19615i 0.321480 + 0.0861402i
\(651\) −13.8564 24.0000i −0.543075 0.940634i
\(652\) −20.0000 + 34.6410i −0.783260 + 1.35665i
\(653\) 10.3923 + 6.00000i 0.406682 + 0.234798i 0.689363 0.724416i \(-0.257890\pi\)
−0.282681 + 0.959214i \(0.591224\pi\)
\(654\) −2.53590 9.46410i −0.0991615 0.370076i
\(655\) 6.00000 + 10.3923i 0.234439 + 0.406061i
\(656\) 20.0000 0.780869
\(657\) −1.50000 + 2.59808i −0.0585206 + 0.101361i
\(658\) −8.00000 8.00000i −0.311872 0.311872i
\(659\) 31.1769 18.0000i 1.21448 0.701180i 0.250748 0.968052i \(-0.419323\pi\)
0.963732 + 0.266872i \(0.0859901\pi\)
\(660\) 17.3205i 0.674200i
\(661\) −39.8372 23.0000i −1.54949 0.894596i −0.998181 0.0602929i \(-0.980797\pi\)
−0.551306 0.834303i \(-0.685870\pi\)
\(662\) −7.32051 27.3205i −0.284520 1.06184i
\(663\) 31.1769i 1.21081i
\(664\) −8.78461 + 32.7846i −0.340909 + 1.27229i
\(665\) −28.0000 −1.08579
\(666\) −6.00000 + 6.00000i −0.232495 + 0.232495i
\(667\) 0 0
\(668\) 10.3923 6.00000i 0.402090 0.232147i
\(669\) −12.1244 + 21.0000i −0.468755 + 0.811907i
\(670\) 4.09808 1.09808i 0.158322 0.0424224i
\(671\) −10.0000 + 17.3205i −0.386046 + 0.668651i
\(672\) −10.1436 + 37.8564i −0.391298 + 1.46034i
\(673\) −5.00000 8.66025i −0.192736 0.333828i 0.753420 0.657539i \(-0.228403\pi\)
−0.946156 + 0.323711i \(0.895069\pi\)
\(674\) 15.0000 + 15.0000i 0.577778 + 0.577778i
\(675\) −2.59808 4.50000i −0.100000 0.173205i
\(676\) 46.0000i 1.76923i
\(677\) −13.8564 + 8.00000i −0.532545 + 0.307465i −0.742052 0.670342i \(-0.766147\pi\)
0.209507 + 0.977807i \(0.432814\pi\)
\(678\) −3.80385 + 14.1962i −0.146086 + 0.545200i
\(679\) −14.0000 + 24.2487i −0.537271 + 0.930580i
\(680\) −8.19615 + 2.19615i −0.314308 + 0.0842186i
\(681\) −13.5000 7.79423i −0.517321 0.298675i
\(682\) 27.3205 + 7.32051i 1.04616 + 0.280317i
\(683\) 51.0000i 1.95146i 0.218975 + 0.975730i \(0.429729\pi\)
−0.218975 + 0.975730i \(0.570271\pi\)
\(684\) −21.0000 36.3731i −0.802955 1.39076i
\(685\) 17.0000i 0.649537i
\(686\) −2.92820 + 10.9282i −0.111799 + 0.417241i
\(687\) 6.92820i 0.264327i
\(688\) −17.3205 10.0000i −0.660338 0.381246i
\(689\) 24.0000 41.5692i 0.914327 1.58366i
\(690\) 3.46410 3.46410i 0.131876 0.131876i
\(691\) 10.3923 6.00000i 0.395342 0.228251i −0.289130 0.957290i \(-0.593366\pi\)
0.684472 + 0.729039i \(0.260033\pi\)
\(692\) 16.0000 0.608229
\(693\) −51.9615 + 30.0000i −1.97386 + 1.13961i
\(694\) 19.0000 19.0000i 0.721230 0.721230i
\(695\) −5.50000 9.52628i −0.208627 0.361352i
\(696\) 0 0
\(697\) −7.50000 + 12.9904i −0.284083 + 0.492046i
\(698\) −5.85641 21.8564i −0.221668 0.827277i
\(699\) −23.3827 40.5000i −0.884414 1.53185i
\(700\) 6.92820 4.00000i 0.261861 0.151186i
\(701\) 10.0000i 0.377695i 0.982006 + 0.188847i \(0.0604752\pi\)
−0.982006 + 0.188847i \(0.939525\pi\)
\(702\) −31.1769 + 31.1769i −1.17670 + 1.17670i
\(703\) 14.0000 0.528020
\(704\) −20.0000 34.6410i −0.753778 1.30558i
\(705\) −3.00000 + 1.73205i −0.112987 + 0.0652328i
\(706\) 12.2942 3.29423i 0.462699 0.123980i
\(707\) −48.4974 28.0000i −1.82393 1.05305i
\(708\) −12.1244 + 21.0000i −0.455661 + 0.789228i
\(709\) −27.7128 + 16.0000i −1.04078 + 0.600893i −0.920053 0.391794i \(-0.871855\pi\)
−0.120723 + 0.992686i \(0.538521\pi\)
\(710\) −2.00000 + 2.00000i −0.0750587 + 0.0750587i
\(711\) 30.0000 1.12509
\(712\) −4.00000 + 4.00000i −0.149906 + 0.149906i
\(713\) −4.00000 6.92820i −0.149801 0.259463i
\(714\) −20.7846 20.7846i −0.777844 0.777844i
\(715\) −25.9808 15.0000i −0.971625 0.560968i
\(716\) −12.0000 + 20.7846i −0.448461 + 0.776757i
\(717\) 24.2487 0.905585
\(718\) −4.39230 + 16.3923i −0.163919 + 0.611755i
\(719\) −18.0000 −0.671287 −0.335643 0.941989i \(-0.608954\pi\)
−0.335643 + 0.941989i \(0.608954\pi\)
\(720\) 10.3923 + 6.00000i 0.387298 + 0.223607i
\(721\) 56.0000 2.08555
\(722\) −10.9808 + 40.9808i −0.408662 + 1.52515i
\(723\) −12.9904 + 22.5000i −0.483117 + 0.836784i
\(724\) 2.00000 3.46410i 0.0743294 0.128742i
\(725\) 0 0
\(726\) 8.87564 33.1244i 0.329406 1.22936i
\(727\) 25.0000 + 43.3013i 0.927199 + 1.60596i 0.787986 + 0.615693i \(0.211124\pi\)
0.139212 + 0.990263i \(0.455543\pi\)
\(728\) −48.0000 48.0000i −1.77900 1.77900i
\(729\) 27.0000 1.00000
\(730\) −1.00000 + 1.00000i −0.0370117 + 0.0370117i
\(731\) 12.9904 7.50000i 0.480467 0.277398i
\(732\) 6.92820 + 12.0000i 0.256074 + 0.443533i
\(733\) 31.1769 + 18.0000i 1.15155 + 0.664845i 0.949263 0.314482i \(-0.101831\pi\)
0.202282 + 0.979327i \(0.435164\pi\)
\(734\) −24.5885 + 6.58846i −0.907577 + 0.243184i
\(735\) 13.5000 + 7.79423i 0.497955 + 0.287494i
\(736\) −2.92820 + 10.9282i −0.107935 + 0.402819i
\(737\) −15.0000 −0.552532
\(738\) 20.4904 5.49038i 0.754261 0.202104i
\(739\) 15.0000i 0.551784i −0.961189 0.275892i \(-0.911027\pi\)
0.961189 0.275892i \(-0.0889732\pi\)
\(740\) −3.46410 + 2.00000i −0.127343 + 0.0735215i
\(741\) 72.7461 2.67240
\(742\) −11.7128 43.7128i −0.429991 1.60475i
\(743\) −18.0000 + 31.1769i −0.660356 + 1.14377i 0.320166 + 0.947361i \(0.396261\pi\)
−0.980522 + 0.196409i \(0.937072\pi\)
\(744\) 13.8564 13.8564i 0.508001 0.508001i
\(745\) −3.00000 5.19615i −0.109911 0.190372i
\(746\) −22.0000 + 22.0000i −0.805477 + 0.805477i
\(747\) 36.0000i 1.31717i
\(748\) 30.0000 1.09691
\(749\) 45.0333 26.0000i 1.64548 0.950019i
\(750\) −0.633975 2.36603i −0.0231495 0.0863950i
\(751\) 23.0000 39.8372i 0.839282 1.45368i −0.0512140 0.998688i \(-0.516309\pi\)
0.890496 0.454991i \(-0.150358\pi\)
\(752\) 4.00000 6.92820i 0.145865 0.252646i
\(753\) −13.5000 + 7.79423i −0.491967 + 0.284037i
\(754\) 0 0
\(755\) 10.0000i 0.363937i
\(756\) 41.5692i 1.51186i
\(757\) 4.00000i 0.145382i −0.997354 0.0726912i \(-0.976841\pi\)
0.997354 0.0726912i \(-0.0231588\pi\)
\(758\) 4.09808 + 1.09808i 0.148849 + 0.0398839i
\(759\) −15.0000 + 8.66025i −0.544466 + 0.314347i
\(760\) −5.12436 19.1244i −0.185880 0.693713i
\(761\) 25.0000 43.3013i 0.906249 1.56967i 0.0870179 0.996207i \(-0.472266\pi\)
0.819231 0.573463i \(-0.194400\pi\)
\(762\) −42.5885 + 11.4115i −1.54282 + 0.413397i
\(763\) 13.8564 8.00000i 0.501636 0.289619i
\(764\) 16.0000i 0.578860i
\(765\) −7.79423 + 4.50000i −0.281801 + 0.162698i
\(766\) 18.0000 + 18.0000i 0.650366 + 0.650366i
\(767\) −21.0000 36.3731i −0.758266 1.31336i
\(768\) −27.7128 −1.00000
\(769\) 15.0000 25.9808i 0.540914 0.936890i −0.457938 0.888984i \(-0.651412\pi\)
0.998852 0.0479061i \(-0.0152548\pi\)
\(770\) −27.3205 + 7.32051i −0.984563 + 0.263813i
\(771\) −12.1244 −0.436648
\(772\) −39.8372 + 23.0000i −1.43377 + 0.827788i
\(773\) 42.0000i 1.51064i 0.655359 + 0.755318i \(0.272517\pi\)
−0.655359 + 0.755318i \(0.727483\pi\)
\(774\) −20.4904 5.49038i −0.736512 0.197348i
\(775\) −4.00000 −0.143684
\(776\) −19.1244 5.12436i −0.686524 0.183954i
\(777\) −12.0000 6.92820i −0.430498 0.248548i
\(778\) 5.85641 + 21.8564i 0.209962 + 0.783590i
\(779\) −30.3109 17.5000i −1.08600 0.627003i
\(780\) −18.0000 + 10.3923i −0.644503 + 0.372104i
\(781\) 8.66025 5.00000i 0.309888 0.178914i
\(782\) −6.00000 6.00000i −0.214560 0.214560i
\(783\) 0 0
\(784\) −36.0000 −1.28571
\(785\) −10.0000 17.3205i −0.356915 0.618195i
\(786\) −28.3923 7.60770i −1.01272 0.271357i
\(787\) 45.0333 + 26.0000i 1.60526 + 0.926800i 0.990410 + 0.138159i \(0.0441186\pi\)
0.614855 + 0.788641i \(0.289215\pi\)
\(788\) −8.00000 + 13.8564i −0.284988 + 0.493614i
\(789\) 0 0
\(790\) 13.6603 + 3.66025i 0.486010 + 0.130226i
\(791\) −24.0000 −0.853342
\(792\) −30.0000 30.0000i −1.06600 1.06600i
\(793\) −24.0000 −0.852265
\(794\) −35.5167 9.51666i −1.26044 0.337734i
\(795\) −13.8564 −0.491436
\(796\) 0 0
\(797\) 5.19615 + 3.00000i 0.184057 + 0.106265i 0.589197 0.807989i \(-0.299444\pi\)
−0.405140 + 0.914255i \(0.632777\pi\)
\(798\) 48.4974 48.4974i 1.71679 1.71679i
\(799\) 3.00000 + 5.19615i 0.106132 + 0.183827i
\(800\) 4.00000 + 4.00000i 0.141421 + 0.141421i
\(801\) −3.00000 + 5.19615i −0.106000 + 0.183597i
\(802\) −15.0000 15.0000i −0.529668 0.529668i
\(803\) 4.33013 2.50000i 0.152807 0.0882231i
\(804\) −5.19615 + 9.00000i −0.183254 + 0.317406i
\(805\) 6.92820 + 4.00000i 0.244187 + 0.140981i
\(806\) 8.78461 + 32.7846i 0.309425 + 1.15479i
\(807\) −30.0000 + 17.3205i −1.05605 + 0.609711i
\(808\) 10.2487 38.2487i 0.360548 1.34558i
\(809\) 7.00000 0.246107 0.123053 0.992400i \(-0.460731\pi\)
0.123053 + 0.992400i \(0.460731\pi\)
\(810\) 12.2942 + 3.29423i 0.431975 + 0.115747i
\(811\) 1.00000i 0.0351147i 0.999846 + 0.0175574i \(0.00558897\pi\)
−0.999846 + 0.0175574i \(0.994411\pi\)
\(812\) 0 0
\(813\) 24.2487 + 42.0000i 0.850439 + 1.47300i
\(814\) 13.6603 3.66025i 0.478792 0.128292i
\(815\) −10.0000 + 17.3205i −0.350285 + 0.606711i
\(816\) 10.3923 18.0000i 0.363803 0.630126i
\(817\) 17.5000 + 30.3109i 0.612247 + 1.06044i
\(818\) 15.0000 + 15.0000i 0.524463 + 0.524463i
\(819\) −62.3538 36.0000i −2.17882 1.25794i
\(820\) 10.0000 0.349215
\(821\) 3.46410 2.00000i 0.120898 0.0698005i −0.438331 0.898813i \(-0.644430\pi\)
0.559229 + 0.829013i \(0.311097\pi\)
\(822\) 29.4449 + 29.4449i 1.02701 + 1.02701i
\(823\) 3.00000 5.19615i 0.104573 0.181126i −0.808990 0.587822i \(-0.799986\pi\)
0.913564 + 0.406695i \(0.133319\pi\)
\(824\) 10.2487 + 38.2487i 0.357031 + 1.33246i
\(825\) 8.66025i 0.301511i
\(826\) −38.2487 10.2487i −1.33084 0.356598i
\(827\) 16.0000i 0.556375i 0.960527 + 0.278187i \(0.0897336\pi\)
−0.960527 + 0.278187i \(0.910266\pi\)
\(828\) 12.0000i 0.417029i
\(829\) 8.00000i 0.277851i 0.990303 + 0.138926i \(0.0443649\pi\)
−0.990303 + 0.138926i \(0.955635\pi\)
\(830\) −4.39230 + 16.3923i −0.152459 + 0.568985i
\(831\) −3.00000 1.73205i −0.104069 0.0600842i
\(832\) 24.0000 41.5692i 0.832050 1.44115i
\(833\) 13.5000 23.3827i 0.467747 0.810162i
\(834\) 26.0263 + 6.97372i 0.901216 + 0.241480i
\(835\) 5.19615 3.00000i 0.179820 0.103819i
\(836\) 70.0000i 2.42100i
\(837\) 10.3923 18.0000i 0.359211 0.622171i
\(838\) −4.00000 + 4.00000i −0.138178 + 0.138178i
\(839\) −14.0000 24.2487i −0.483334 0.837158i 0.516483 0.856297i \(-0.327241\pi\)
−0.999817 + 0.0191389i \(0.993908\pi\)
\(840\) −5.07180 + 18.9282i −0.174994 + 0.653085i
\(841\) −14.5000 + 25.1147i −0.500000 + 0.866025i
\(842\) 0.732051 + 2.73205i 0.0252281 + 0.0941527i
\(843\) −19.0526 + 33.0000i −0.656205 + 1.13658i
\(844\) 0 0
\(845\) 23.0000i 0.791224i
\(846\) 2.19615 8.19615i 0.0755053 0.281790i
\(847\) 56.0000 1.92418
\(848\) 27.7128 16.0000i 0.951662 0.549442i
\(849\) 6.92820i 0.237775i
\(850\) −4.09808 + 1.09808i −0.140563 + 0.0376637i
\(851\) −3.46410 2.00000i −0.118748 0.0685591i
\(852\) 6.92820i 0.237356i
\(853\) −39.8372 + 23.0000i −1.36400 + 0.787505i −0.990153 0.139986i \(-0.955294\pi\)
−0.373845 + 0.927491i \(0.621961\pi\)
\(854\) −16.0000 + 16.0000i −0.547509 + 0.547509i
\(855\) −10.5000 18.1865i −0.359092 0.621966i
\(856\) 26.0000 + 26.0000i 0.888662 + 0.888662i
\(857\) 21.0000 + 36.3731i 0.717346 + 1.24248i 0.962048 + 0.272882i \(0.0879768\pi\)
−0.244701 + 0.969599i \(0.578690\pi\)
\(858\) 70.9808 19.0192i 2.42324 0.649306i
\(859\) 32.0429 + 18.5000i 1.09329 + 0.631212i 0.934451 0.356092i \(-0.115891\pi\)
0.158840 + 0.987304i \(0.449225\pi\)
\(860\) −8.66025 5.00000i −0.295312 0.170499i
\(861\) 17.3205 + 30.0000i 0.590281 + 1.02240i
\(862\) −4.39230 + 16.3923i −0.149602 + 0.558324i
\(863\) 30.0000 1.02121 0.510606 0.859815i \(-0.329421\pi\)
0.510606 + 0.859815i \(0.329421\pi\)
\(864\) −28.3923 + 7.60770i −0.965926 + 0.258819i
\(865\) 8.00000 0.272008
\(866\) 10.6147 39.6147i 0.360703 1.34616i
\(867\) −6.92820 12.0000i −0.235294 0.407541i
\(868\) 27.7128 + 16.0000i 0.940634 + 0.543075i
\(869\) −43.3013 25.0000i −1.46889 0.848067i
\(870\) 0 0
\(871\) −9.00000 15.5885i −0.304953 0.528195i
\(872\) 8.00000 + 8.00000i 0.270914 + 0.270914i
\(873\) −21.0000 −0.710742
\(874\) 14.0000 14.0000i 0.473557 0.473557i
\(875\) 3.46410 2.00000i 0.117108 0.0676123i
\(876\) 3.46410i 0.117041i
\(877\) 27.7128 + 16.0000i 0.935795 + 0.540282i 0.888640 0.458606i \(-0.151651\pi\)
0.0471555 + 0.998888i \(0.484984\pi\)
\(878\) 54.6410 14.6410i 1.84404 0.494110i
\(879\) 6.92820i 0.233682i
\(880\) −10.0000 17.3205i −0.337100 0.583874i
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) −36.8827 + 9.88269i −1.24190 + 0.332767i
\(883\) 41.0000i 1.37976i −0.723924 0.689880i \(-0.757663\pi\)
0.723924 0.689880i \(-0.242337\pi\)
\(884\) 18.0000 + 31.1769i 0.605406 + 1.04859i
\(885\) −6.06218 + 10.5000i −0.203778 + 0.352954i
\(886\) 9.15064 + 34.1506i 0.307422 + 1.14731i
\(887\) −11.0000 + 19.0526i −0.369344 + 0.639722i −0.989463 0.144785i \(-0.953751\pi\)
0.620119 + 0.784508i \(0.287084\pi\)
\(888\) 2.53590 9.46410i 0.0850992 0.317594i
\(889\) −36.0000 62.3538i −1.20740 2.09128i
\(890\) −2.00000 + 2.00000i −0.0670402 + 0.0670402i
\(891\) −38.9711 22.5000i −1.30558 0.753778i
\(892\) 28.0000i 0.937509i
\(893\) −12.1244 + 7.00000i −0.405726 + 0.234246i
\(894\) 14.1962 + 3.80385i 0.474790 + 0.127220i
\(895\) −6.00000 + 10.3923i −0.200558 + 0.347376i
\(896\) −11.7128 43.7128i −0.391298 1.46034i
\(897\) −18.0000 10.3923i −0.601003 0.346989i
\(898\) −9.88269 + 36.8827i −0.329789 + 1.23079i
\(899\) 0 0
\(900\) 5.19615 + 3.00000i 0.173205 + 0.100000i
\(901\) 24.0000i 0.799556i
\(902\) −34.1506 9.15064i −1.13709 0.304683i
\(903\) 34.6410i 1.15278i
\(904\) −4.39230 16.3923i −0.146086 0.545200i
\(905\) 1.00000 1.73205i 0.0332411 0.0575753i
\(906\) −17.3205 17.3205i −0.575435 0.575435i
\(907\) 21.6506 12.5000i 0.718898 0.415056i −0.0954492 0.995434i \(-0.530429\pi\)
0.814347 + 0.580379i \(0.197095\pi\)
\(908\) 18.0000 0.597351
\(909\) 42.0000i 1.39305i
\(910\) −24.0000 24.0000i −0.795592 0.795592i
\(911\) −18.0000 31.1769i −0.596367 1.03294i −0.993352 0.115113i \(-0.963277\pi\)
0.396986 0.917825i \(-0.370056\pi\)
\(912\) 42.0000 + 24.2487i 1.39076 + 0.802955i
\(913\) 30.0000 51.9615i 0.992855 1.71968i
\(914\) −4.09808 + 1.09808i −0.135552 + 0.0363211i
\(915\) 3.46410 + 6.00000i 0.114520 + 0.198354i
\(916\) 4.00000 + 6.92820i 0.132164 + 0.228914i
\(917\) 48.0000i 1.58510i
\(918\) 5.70577 21.2942i 0.188319 0.702814i
\(919\) −26.0000 −0.857661 −0.428830 0.903385i \(-0.641074\pi\)
−0.428830 + 0.903385i \(0.641074\pi\)
\(920\) −1.46410 + 5.46410i −0.0482700 + 0.180146i
\(921\) −34.5000 + 19.9186i −1.13681 + 0.656340i
\(922\) 5.12436 + 19.1244i 0.168762 + 0.629827i
\(923\) 10.3923 + 6.00000i 0.342067 + 0.197492i
\(924\) 34.6410 60.0000i 1.13961 1.97386i
\(925\) −1.73205 + 1.00000i −0.0569495 + 0.0328798i
\(926\) 26.0000 + 26.0000i 0.854413 + 0.854413i
\(927\) 21.0000 + 36.3731i 0.689730 + 1.19465i
\(928\) 0 0
\(929\) 25.0000 + 43.3013i 0.820223 + 1.42067i 0.905516 + 0.424313i \(0.139484\pi\)
−0.0852924 + 0.996356i \(0.527182\pi\)
\(930\) 6.92820 6.92820i 0.227185 0.227185i
\(931\) 54.5596 + 31.5000i 1.78812 + 1.03237i
\(932\) 46.7654 + 27.0000i 1.53185 + 0.884414i
\(933\) −34.6410 −1.13410
\(934\) −17.7583 4.75833i −0.581070 0.155697i
\(935\) 15.0000 0.490552
\(936\) 13.1769 49.1769i 0.430701 1.60740i
\(937\) −14.0000 −0.457360 −0.228680 0.973502i \(-0.573441\pi\)
−0.228680 + 0.973502i \(0.573441\pi\)
\(938\) −16.3923 4.39230i −0.535228 0.143414i
\(939\) −7.79423 + 13.5000i −0.254355 + 0.440556i
\(940\) 2.00000 3.46410i 0.0652328 0.112987i
\(941\) −6.92820 4.00000i −0.225853 0.130396i 0.382804 0.923829i \(-0.374958\pi\)
−0.608657 + 0.793433i \(0.708292\pi\)
\(942\) 47.3205 + 12.6795i 1.54179 + 0.413120i
\(943\) 5.00000 + 8.66025i 0.162822 + 0.282017i
\(944\) 28.0000i 0.911322i
\(945\) 20.7846i 0.676123i
\(946\) 25.0000 + 25.0000i 0.812820 + 0.812820i
\(947\) −44.1673 + 25.5000i −1.43524 + 0.828639i −0.997514 0.0704677i \(-0.977551\pi\)
−0.437730 + 0.899106i \(0.644217\pi\)
\(948\) −30.0000 + 17.3205i −0.974355 + 0.562544i
\(949\) 5.19615 + 3.00000i 0.168674 + 0.0973841i
\(950\) −2.56218 9.56218i −0.0831280 0.310238i
\(951\) −27.0000 15.5885i −0.875535 0.505490i
\(952\) 32.7846 + 8.78461i 1.06256 + 0.284711i
\(953\) −29.0000 −0.939402 −0.469701 0.882826i \(-0.655638\pi\)
−0.469701 + 0.882826i \(0.655638\pi\)
\(954\) 24.0000 24.0000i 0.777029 0.777029i
\(955\) 8.00000i 0.258874i
\(956\) −24.2487 + 14.0000i −0.784259 + 0.452792i
\(957\) 0 0
\(958\) −21.8564 + 5.85641i −0.706148 + 0.189212i
\(959\) −34.0000 + 58.8897i −1.09792 + 1.90165i
\(960\) −13.8564 −0.447214
\(961\) 7.50000 + 12.9904i 0.241935 + 0.419045i
\(962\) 12.0000 + 12.0000i 0.386896 + 0.386896i
\(963\) 33.7750 + 19.5000i 1.08838 + 0.628379i
\(964\) 30.0000i 0.966235i
\(965\) −19.9186 + 11.5000i −0.641202 + 0.370198i
\(966\) −18.9282 + 5.07180i −0.609005 + 0.163182i
\(967\) −14.0000 + 24.2487i −0.450210 + 0.779786i −0.998399 0.0565684i \(-0.981984\pi\)
0.548189 + 0.836354i \(0.315317\pi\)
\(968\) 10.2487 + 38.2487i 0.329406 + 1.22936i
\(969\) −31.5000 + 18.1865i −1.01193 + 0.584236i
\(970\) −9.56218 2.56218i −0.307023 0.0822666i
\(971\) 36.0000i 1.15529i −0.816286 0.577647i \(-0.803971\pi\)
0.816286 0.577647i \(-0.196029\pi\)
\(972\) −27.0000 + 15.5885i −0.866025 + 0.500000i
\(973\) 44.0000i 1.41058i
\(974\) −4.39230 + 16.3923i −0.140739 + 0.525243i
\(975\) −9.00000 + 5.19615i −0.288231 + 0.166410i
\(976\) −13.8564 8.00000i −0.443533 0.256074i
\(977\) 27.5000 47.6314i 0.879803 1.52386i 0.0282462 0.999601i \(-0.491008\pi\)
0.851557 0.524262i \(-0.175659\pi\)
\(978\) −12.6795 47.3205i −0.405445 1.51314i
\(979\) 8.66025 5.00000i 0.276783 0.159801i
\(980\) −18.0000 −0.574989
\(981\) 10.3923 + 6.00000i 0.331801 + 0.191565i
\(982\) 11.0000 11.0000i 0.351024 0.351024i
\(983\) 25.0000 + 43.3013i 0.797376 + 1.38110i 0.921319 + 0.388807i \(0.127113\pi\)
−0.123943 + 0.992289i \(0.539554\pi\)
\(984\) −17.3205 + 17.3205i −0.552158 + 0.552158i
\(985\) −4.00000 + 6.92820i −0.127451 + 0.220751i
\(986\) 0 0
\(987\) 13.8564 0.441054
\(988\) −72.7461 + 42.0000i −2.31436 + 1.33620i
\(989\) 10.0000i 0.317982i
\(990\) −15.0000 15.0000i −0.476731 0.476731i
\(991\) 8.00000 0.254128 0.127064 0.991894i \(-0.459445\pi\)
0.127064 + 0.991894i \(0.459445\pi\)
\(992\) −5.85641 + 21.8564i −0.185941 + 0.693942i
\(993\) 30.0000 + 17.3205i 0.952021 + 0.549650i
\(994\) 10.9282 2.92820i 0.346622 0.0928770i
\(995\) 0 0
\(996\) −20.7846 36.0000i −0.658586 1.14070i
\(997\) 24.2487 14.0000i 0.767964 0.443384i −0.0641836 0.997938i \(-0.520444\pi\)
0.832148 + 0.554554i \(0.187111\pi\)
\(998\) −41.0000 + 41.0000i −1.29783 + 1.29783i
\(999\) 10.3923i 0.328798i
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.bf.a.301.2 yes 4
3.2 odd 2 1080.2.bf.a.901.1 4
4.3 odd 2 1440.2.bv.a.1201.1 4
8.3 odd 2 1440.2.bv.a.1201.2 4
8.5 even 2 inner 360.2.bf.a.301.1 yes 4
9.2 odd 6 1080.2.bf.a.181.2 4
9.7 even 3 inner 360.2.bf.a.61.1 4
12.11 even 2 4320.2.bv.a.3601.2 4
24.5 odd 2 1080.2.bf.a.901.2 4
24.11 even 2 4320.2.bv.a.3601.1 4
36.7 odd 6 1440.2.bv.a.241.2 4
36.11 even 6 4320.2.bv.a.721.1 4
72.11 even 6 4320.2.bv.a.721.2 4
72.29 odd 6 1080.2.bf.a.181.1 4
72.43 odd 6 1440.2.bv.a.241.1 4
72.61 even 6 inner 360.2.bf.a.61.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bf.a.61.1 4 9.7 even 3 inner
360.2.bf.a.61.2 yes 4 72.61 even 6 inner
360.2.bf.a.301.1 yes 4 8.5 even 2 inner
360.2.bf.a.301.2 yes 4 1.1 even 1 trivial
1080.2.bf.a.181.1 4 72.29 odd 6
1080.2.bf.a.181.2 4 9.2 odd 6
1080.2.bf.a.901.1 4 3.2 odd 2
1080.2.bf.a.901.2 4 24.5 odd 2
1440.2.bv.a.241.1 4 72.43 odd 6
1440.2.bv.a.241.2 4 36.7 odd 6
1440.2.bv.a.1201.1 4 4.3 odd 2
1440.2.bv.a.1201.2 4 8.3 odd 2
4320.2.bv.a.721.1 4 36.11 even 6
4320.2.bv.a.721.2 4 72.11 even 6
4320.2.bv.a.3601.1 4 24.11 even 2
4320.2.bv.a.3601.2 4 12.11 even 2