Properties

Label 165.2.k.b.122.1
Level $165$
Weight $2$
Character 165.122
Analytic conductor $1.318$
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] = [165,2,Mod(23,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.k (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 122.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 165.122
Dual form 165.2.k.b.23.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.292893 - 0.292893i) q^{2} +(1.41421 + 1.00000i) q^{3} +1.82843i q^{4} +(2.00000 - 1.00000i) q^{5} +(0.707107 - 0.121320i) q^{6} +(-3.41421 - 3.41421i) q^{7} +(1.12132 + 1.12132i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(0.292893 - 0.292893i) q^{2} +(1.41421 + 1.00000i) q^{3} +1.82843i q^{4} +(2.00000 - 1.00000i) q^{5} +(0.707107 - 0.121320i) q^{6} +(-3.41421 - 3.41421i) q^{7} +(1.12132 + 1.12132i) q^{8} +(1.00000 + 2.82843i) q^{9} +(0.292893 - 0.878680i) q^{10} +1.00000i q^{11} +(-1.82843 + 2.58579i) q^{12} +(-2.00000 + 2.00000i) q^{13} -2.00000 q^{14} +(3.82843 + 0.585786i) q^{15} -3.00000 q^{16} +(2.82843 - 2.82843i) q^{17} +(1.12132 + 0.535534i) q^{18} -2.82843i q^{19} +(1.82843 + 3.65685i) q^{20} +(-1.41421 - 8.24264i) q^{21} +(0.292893 + 0.292893i) q^{22} +(-3.24264 - 3.24264i) q^{23} +(0.464466 + 2.70711i) q^{24} +(3.00000 - 4.00000i) q^{25} +1.17157i q^{26} +(-1.41421 + 5.00000i) q^{27} +(6.24264 - 6.24264i) q^{28} -0.828427 q^{29} +(1.29289 - 0.949747i) q^{30} -3.17157 q^{31} +(-3.12132 + 3.12132i) q^{32} +(-1.00000 + 1.41421i) q^{33} -1.65685i q^{34} +(-10.2426 - 3.41421i) q^{35} +(-5.17157 + 1.82843i) q^{36} +(-0.171573 - 0.171573i) q^{37} +(-0.828427 - 0.828427i) q^{38} +(-4.82843 + 0.828427i) q^{39} +(3.36396 + 1.12132i) q^{40} +7.65685i q^{41} +(-2.82843 - 2.00000i) q^{42} +(0.242641 - 0.242641i) q^{43} -1.82843 q^{44} +(4.82843 + 4.65685i) q^{45} -1.89949 q^{46} +(7.24264 - 7.24264i) q^{47} +(-4.24264 - 3.00000i) q^{48} +16.3137i q^{49} +(-0.292893 - 2.05025i) q^{50} +(6.82843 - 1.17157i) q^{51} +(-3.65685 - 3.65685i) q^{52} +(-1.00000 - 1.00000i) q^{53} +(1.05025 + 1.87868i) q^{54} +(1.00000 + 2.00000i) q^{55} -7.65685i q^{56} +(2.82843 - 4.00000i) q^{57} +(-0.242641 + 0.242641i) q^{58} +4.00000 q^{59} +(-1.07107 + 7.00000i) q^{60} -6.48528 q^{61} +(-0.928932 + 0.928932i) q^{62} +(6.24264 - 13.0711i) q^{63} -4.17157i q^{64} +(-2.00000 + 6.00000i) q^{65} +(0.121320 + 0.707107i) q^{66} +(-6.41421 - 6.41421i) q^{67} +(5.17157 + 5.17157i) q^{68} +(-1.34315 - 7.82843i) q^{69} +(-4.00000 + 2.00000i) q^{70} +2.48528i q^{71} +(-2.05025 + 4.29289i) q^{72} -0.100505 q^{74} +(8.24264 - 2.65685i) q^{75} +5.17157 q^{76} +(3.41421 - 3.41421i) q^{77} +(-1.17157 + 1.65685i) q^{78} +10.8284i q^{79} +(-6.00000 + 3.00000i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(2.24264 + 2.24264i) q^{82} +(9.07107 + 9.07107i) q^{83} +(15.0711 - 2.58579i) q^{84} +(2.82843 - 8.48528i) q^{85} -0.142136i q^{86} +(-1.17157 - 0.828427i) q^{87} +(-1.12132 + 1.12132i) q^{88} +9.65685 q^{89} +(2.77817 - 0.0502525i) q^{90} +13.6569 q^{91} +(5.92893 - 5.92893i) q^{92} +(-4.48528 - 3.17157i) q^{93} -4.24264i q^{94} +(-2.82843 - 5.65685i) q^{95} +(-7.53553 + 1.29289i) q^{96} +(10.6569 + 10.6569i) q^{97} +(4.77817 + 4.77817i) q^{98} +(-2.82843 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 8 q^{5} - 8 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 8 q^{5} - 8 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 8 q^{14} + 4 q^{15} - 12 q^{16} - 4 q^{18} - 4 q^{20} + 4 q^{22} + 4 q^{23} + 16 q^{24} + 12 q^{25} + 8 q^{28} + 8 q^{29} + 8 q^{30} - 24 q^{31} - 4 q^{32} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 12 q^{37} + 8 q^{38} - 8 q^{39} - 12 q^{40} - 16 q^{43} + 4 q^{44} + 8 q^{45} + 32 q^{46} + 12 q^{47} - 4 q^{50} + 16 q^{51} + 8 q^{52} - 4 q^{53} + 24 q^{54} + 4 q^{55} + 16 q^{58} + 16 q^{59} + 24 q^{60} + 8 q^{61} - 32 q^{62} + 8 q^{63} - 8 q^{65} - 8 q^{66} - 20 q^{67} + 32 q^{68} - 28 q^{69} - 16 q^{70} - 28 q^{72} - 40 q^{74} + 16 q^{75} + 32 q^{76} + 8 q^{77} - 16 q^{78} - 24 q^{80} - 28 q^{81} - 8 q^{82} + 8 q^{83} + 32 q^{84} - 16 q^{87} + 4 q^{88} + 16 q^{89} - 20 q^{90} + 32 q^{91} + 52 q^{92} + 16 q^{93} - 16 q^{96} + 20 q^{97} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.292893 0.292893i 0.207107 0.207107i −0.595930 0.803037i \(-0.703216\pi\)
0.803037 + 0.595930i \(0.203216\pi\)
\(3\) 1.41421 + 1.00000i 0.816497 + 0.577350i
\(4\) 1.82843i 0.914214i
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) 0.707107 0.121320i 0.288675 0.0495288i
\(7\) −3.41421 3.41421i −1.29045 1.29045i −0.934507 0.355944i \(-0.884159\pi\)
−0.355944 0.934507i \(-0.615841\pi\)
\(8\) 1.12132 + 1.12132i 0.396447 + 0.396447i
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) 0.292893 0.878680i 0.0926210 0.277863i
\(11\) 1.00000i 0.301511i
\(12\) −1.82843 + 2.58579i −0.527821 + 0.746452i
\(13\) −2.00000 + 2.00000i −0.554700 + 0.554700i −0.927794 0.373094i \(-0.878297\pi\)
0.373094 + 0.927794i \(0.378297\pi\)
\(14\) −2.00000 −0.534522
\(15\) 3.82843 + 0.585786i 0.988496 + 0.151249i
\(16\) −3.00000 −0.750000
\(17\) 2.82843 2.82843i 0.685994 0.685994i −0.275350 0.961344i \(-0.588794\pi\)
0.961344 + 0.275350i \(0.0887937\pi\)
\(18\) 1.12132 + 0.535534i 0.264298 + 0.126227i
\(19\) 2.82843i 0.648886i −0.945905 0.324443i \(-0.894823\pi\)
0.945905 0.324443i \(-0.105177\pi\)
\(20\) 1.82843 + 3.65685i 0.408849 + 0.817697i
\(21\) −1.41421 8.24264i −0.308607 1.79869i
\(22\) 0.292893 + 0.292893i 0.0624450 + 0.0624450i
\(23\) −3.24264 3.24264i −0.676137 0.676137i 0.282987 0.959124i \(-0.408675\pi\)
−0.959124 + 0.282987i \(0.908675\pi\)
\(24\) 0.464466 + 2.70711i 0.0948087 + 0.552586i
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 1.17157i 0.229764i
\(27\) −1.41421 + 5.00000i −0.272166 + 0.962250i
\(28\) 6.24264 6.24264i 1.17975 1.17975i
\(29\) −0.828427 −0.153835 −0.0769175 0.997037i \(-0.524508\pi\)
−0.0769175 + 0.997037i \(0.524508\pi\)
\(30\) 1.29289 0.949747i 0.236049 0.173399i
\(31\) −3.17157 −0.569631 −0.284816 0.958582i \(-0.591932\pi\)
−0.284816 + 0.958582i \(0.591932\pi\)
\(32\) −3.12132 + 3.12132i −0.551777 + 0.551777i
\(33\) −1.00000 + 1.41421i −0.174078 + 0.246183i
\(34\) 1.65685i 0.284148i
\(35\) −10.2426 3.41421i −1.73132 0.577107i
\(36\) −5.17157 + 1.82843i −0.861929 + 0.304738i
\(37\) −0.171573 0.171573i −0.0282064 0.0282064i 0.692863 0.721069i \(-0.256349\pi\)
−0.721069 + 0.692863i \(0.756349\pi\)
\(38\) −0.828427 0.828427i −0.134389 0.134389i
\(39\) −4.82843 + 0.828427i −0.773167 + 0.132655i
\(40\) 3.36396 + 1.12132i 0.531889 + 0.177296i
\(41\) 7.65685i 1.19580i 0.801571 + 0.597900i \(0.203998\pi\)
−0.801571 + 0.597900i \(0.796002\pi\)
\(42\) −2.82843 2.00000i −0.436436 0.308607i
\(43\) 0.242641 0.242641i 0.0370024 0.0370024i −0.688364 0.725366i \(-0.741671\pi\)
0.725366 + 0.688364i \(0.241671\pi\)
\(44\) −1.82843 −0.275646
\(45\) 4.82843 + 4.65685i 0.719779 + 0.694203i
\(46\) −1.89949 −0.280065
\(47\) 7.24264 7.24264i 1.05645 1.05645i 0.0581392 0.998308i \(-0.481483\pi\)
0.998308 0.0581392i \(-0.0185167\pi\)
\(48\) −4.24264 3.00000i −0.612372 0.433013i
\(49\) 16.3137i 2.33053i
\(50\) −0.292893 2.05025i −0.0414214 0.289949i
\(51\) 6.82843 1.17157i 0.956171 0.164053i
\(52\) −3.65685 3.65685i −0.507114 0.507114i
\(53\) −1.00000 1.00000i −0.137361 0.137361i 0.635083 0.772444i \(-0.280966\pi\)
−0.772444 + 0.635083i \(0.780966\pi\)
\(54\) 1.05025 + 1.87868i 0.142921 + 0.255656i
\(55\) 1.00000 + 2.00000i 0.134840 + 0.269680i
\(56\) 7.65685i 1.02319i
\(57\) 2.82843 4.00000i 0.374634 0.529813i
\(58\) −0.242641 + 0.242641i −0.0318603 + 0.0318603i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) −1.07107 + 7.00000i −0.138274 + 0.903696i
\(61\) −6.48528 −0.830355 −0.415178 0.909740i \(-0.636281\pi\)
−0.415178 + 0.909740i \(0.636281\pi\)
\(62\) −0.928932 + 0.928932i −0.117975 + 0.117975i
\(63\) 6.24264 13.0711i 0.786499 1.64680i
\(64\) 4.17157i 0.521447i
\(65\) −2.00000 + 6.00000i −0.248069 + 0.744208i
\(66\) 0.121320 + 0.707107i 0.0149335 + 0.0870388i
\(67\) −6.41421 6.41421i −0.783621 0.783621i 0.196819 0.980440i \(-0.436939\pi\)
−0.980440 + 0.196819i \(0.936939\pi\)
\(68\) 5.17157 + 5.17157i 0.627145 + 0.627145i
\(69\) −1.34315 7.82843i −0.161696 0.942432i
\(70\) −4.00000 + 2.00000i −0.478091 + 0.239046i
\(71\) 2.48528i 0.294949i 0.989066 + 0.147474i \(0.0471144\pi\)
−0.989066 + 0.147474i \(0.952886\pi\)
\(72\) −2.05025 + 4.29289i −0.241625 + 0.505922i
\(73\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(74\) −0.100505 −0.0116835
\(75\) 8.24264 2.65685i 0.951778 0.306787i
\(76\) 5.17157 0.593220
\(77\) 3.41421 3.41421i 0.389086 0.389086i
\(78\) −1.17157 + 1.65685i −0.132655 + 0.187602i
\(79\) 10.8284i 1.21829i 0.793058 + 0.609147i \(0.208488\pi\)
−0.793058 + 0.609147i \(0.791512\pi\)
\(80\) −6.00000 + 3.00000i −0.670820 + 0.335410i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 2.24264 + 2.24264i 0.247658 + 0.247658i
\(83\) 9.07107 + 9.07107i 0.995679 + 0.995679i 0.999991 0.00431166i \(-0.00137245\pi\)
−0.00431166 + 0.999991i \(0.501372\pi\)
\(84\) 15.0711 2.58579i 1.64439 0.282132i
\(85\) 2.82843 8.48528i 0.306786 0.920358i
\(86\) 0.142136i 0.0153269i
\(87\) −1.17157 0.828427i −0.125606 0.0888167i
\(88\) −1.12132 + 1.12132i −0.119533 + 0.119533i
\(89\) 9.65685 1.02362 0.511812 0.859097i \(-0.328974\pi\)
0.511812 + 0.859097i \(0.328974\pi\)
\(90\) 2.77817 0.0502525i 0.292845 0.00529708i
\(91\) 13.6569 1.43163
\(92\) 5.92893 5.92893i 0.618134 0.618134i
\(93\) −4.48528 3.17157i −0.465102 0.328877i
\(94\) 4.24264i 0.437595i
\(95\) −2.82843 5.65685i −0.290191 0.580381i
\(96\) −7.53553 + 1.29289i −0.769092 + 0.131955i
\(97\) 10.6569 + 10.6569i 1.08204 + 1.08204i 0.996319 + 0.0857204i \(0.0273192\pi\)
0.0857204 + 0.996319i \(0.472681\pi\)
\(98\) 4.77817 + 4.77817i 0.482669 + 0.482669i
\(99\) −2.82843 + 1.00000i −0.284268 + 0.100504i
\(100\) 7.31371 + 5.48528i 0.731371 + 0.548528i
\(101\) 7.17157i 0.713598i 0.934181 + 0.356799i \(0.116132\pi\)
−0.934181 + 0.356799i \(0.883868\pi\)
\(102\) 1.65685 2.34315i 0.164053 0.232006i
\(103\) −6.41421 + 6.41421i −0.632011 + 0.632011i −0.948572 0.316561i \(-0.897472\pi\)
0.316561 + 0.948572i \(0.397472\pi\)
\(104\) −4.48528 −0.439818
\(105\) −11.0711 15.0711i −1.08043 1.47079i
\(106\) −0.585786 −0.0568966
\(107\) −0.242641 + 0.242641i −0.0234570 + 0.0234570i −0.718738 0.695281i \(-0.755280\pi\)
0.695281 + 0.718738i \(0.255280\pi\)
\(108\) −9.14214 2.58579i −0.879702 0.248817i
\(109\) 3.17157i 0.303782i 0.988397 + 0.151891i \(0.0485362\pi\)
−0.988397 + 0.151891i \(0.951464\pi\)
\(110\) 0.878680 + 0.292893i 0.0837788 + 0.0279263i
\(111\) −0.0710678 0.414214i −0.00674546 0.0393154i
\(112\) 10.2426 + 10.2426i 0.967839 + 0.967839i
\(113\) 5.82843 + 5.82843i 0.548292 + 0.548292i 0.925947 0.377654i \(-0.123269\pi\)
−0.377654 + 0.925947i \(0.623269\pi\)
\(114\) −0.343146 2.00000i −0.0321385 0.187317i
\(115\) −9.72792 3.24264i −0.907133 0.302378i
\(116\) 1.51472i 0.140638i
\(117\) −7.65685 3.65685i −0.707876 0.338076i
\(118\) 1.17157 1.17157i 0.107852 0.107852i
\(119\) −19.3137 −1.77048
\(120\) 3.63604 + 4.94975i 0.331923 + 0.451848i
\(121\) −1.00000 −0.0909091
\(122\) −1.89949 + 1.89949i −0.171972 + 0.171972i
\(123\) −7.65685 + 10.8284i −0.690395 + 0.976366i
\(124\) 5.79899i 0.520765i
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) −2.00000 5.65685i −0.178174 0.503953i
\(127\) 1.41421 + 1.41421i 0.125491 + 0.125491i 0.767063 0.641572i \(-0.221717\pi\)
−0.641572 + 0.767063i \(0.721717\pi\)
\(128\) −7.46447 7.46447i −0.659772 0.659772i
\(129\) 0.585786 0.100505i 0.0515756 0.00884898i
\(130\) 1.17157 + 2.34315i 0.102754 + 0.205507i
\(131\) 6.82843i 0.596602i −0.954472 0.298301i \(-0.903580\pi\)
0.954472 0.298301i \(-0.0964200\pi\)
\(132\) −2.58579 1.82843i −0.225064 0.159144i
\(133\) −9.65685 + 9.65685i −0.837355 + 0.837355i
\(134\) −3.75736 −0.324586
\(135\) 2.17157 + 11.4142i 0.186899 + 0.982379i
\(136\) 6.34315 0.543920
\(137\) −0.171573 + 0.171573i −0.0146585 + 0.0146585i −0.714398 0.699740i \(-0.753299\pi\)
0.699740 + 0.714398i \(0.253299\pi\)
\(138\) −2.68629 1.89949i −0.228672 0.161696i
\(139\) 17.6569i 1.49763i −0.662776 0.748817i \(-0.730622\pi\)
0.662776 0.748817i \(-0.269378\pi\)
\(140\) 6.24264 18.7279i 0.527599 1.58280i
\(141\) 17.4853 3.00000i 1.47253 0.252646i
\(142\) 0.727922 + 0.727922i 0.0610859 + 0.0610859i
\(143\) −2.00000 2.00000i −0.167248 0.167248i
\(144\) −3.00000 8.48528i −0.250000 0.707107i
\(145\) −1.65685 + 0.828427i −0.137594 + 0.0687971i
\(146\) 0 0
\(147\) −16.3137 + 23.0711i −1.34553 + 1.90287i
\(148\) 0.313708 0.313708i 0.0257867 0.0257867i
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 1.63604 3.19239i 0.133582 0.260657i
\(151\) 10.1421 0.825355 0.412678 0.910877i \(-0.364594\pi\)
0.412678 + 0.910877i \(0.364594\pi\)
\(152\) 3.17157 3.17157i 0.257249 0.257249i
\(153\) 10.8284 + 5.17157i 0.875426 + 0.418097i
\(154\) 2.00000i 0.161165i
\(155\) −6.34315 + 3.17157i −0.509494 + 0.254747i
\(156\) −1.51472 8.82843i −0.121275 0.706840i
\(157\) −9.48528 9.48528i −0.757008 0.757008i 0.218769 0.975777i \(-0.429796\pi\)
−0.975777 + 0.218769i \(0.929796\pi\)
\(158\) 3.17157 + 3.17157i 0.252317 + 0.252317i
\(159\) −0.414214 2.41421i −0.0328493 0.191460i
\(160\) −3.12132 + 9.36396i −0.246762 + 0.740286i
\(161\) 22.1421i 1.74504i
\(162\) −0.393398 + 3.70711i −0.0309083 + 0.291258i
\(163\) 3.58579 3.58579i 0.280860 0.280860i −0.552592 0.833452i \(-0.686361\pi\)
0.833452 + 0.552592i \(0.186361\pi\)
\(164\) −14.0000 −1.09322
\(165\) −0.585786 + 3.82843i −0.0456034 + 0.298043i
\(166\) 5.31371 0.412424
\(167\) −14.7279 + 14.7279i −1.13968 + 1.13968i −0.151174 + 0.988507i \(0.548305\pi\)
−0.988507 + 0.151174i \(0.951695\pi\)
\(168\) 7.65685 10.8284i 0.590739 0.835431i
\(169\) 5.00000i 0.384615i
\(170\) −1.65685 3.31371i −0.127075 0.254150i
\(171\) 8.00000 2.82843i 0.611775 0.216295i
\(172\) 0.443651 + 0.443651i 0.0338281 + 0.0338281i
\(173\) −8.48528 8.48528i −0.645124 0.645124i 0.306687 0.951811i \(-0.400780\pi\)
−0.951811 + 0.306687i \(0.900780\pi\)
\(174\) −0.585786 + 0.100505i −0.0444084 + 0.00761927i
\(175\) −23.8995 + 3.41421i −1.80663 + 0.258090i
\(176\) 3.00000i 0.226134i
\(177\) 5.65685 + 4.00000i 0.425195 + 0.300658i
\(178\) 2.82843 2.82843i 0.212000 0.212000i
\(179\) −24.1421 −1.80447 −0.902234 0.431247i \(-0.858074\pi\)
−0.902234 + 0.431247i \(0.858074\pi\)
\(180\) −8.51472 + 8.82843i −0.634650 + 0.658032i
\(181\) 5.65685 0.420471 0.210235 0.977651i \(-0.432577\pi\)
0.210235 + 0.977651i \(0.432577\pi\)
\(182\) 4.00000 4.00000i 0.296500 0.296500i
\(183\) −9.17157 6.48528i −0.677982 0.479406i
\(184\) 7.27208i 0.536105i
\(185\) −0.514719 0.171573i −0.0378429 0.0126143i
\(186\) −2.24264 + 0.384776i −0.164438 + 0.0282132i
\(187\) 2.82843 + 2.82843i 0.206835 + 0.206835i
\(188\) 13.2426 + 13.2426i 0.965819 + 0.965819i
\(189\) 21.8995 12.2426i 1.59295 0.890521i
\(190\) −2.48528 0.828427i −0.180301 0.0601004i
\(191\) 11.3137i 0.818631i −0.912393 0.409316i \(-0.865768\pi\)
0.912393 0.409316i \(-0.134232\pi\)
\(192\) 4.17157 5.89949i 0.301057 0.425759i
\(193\) 8.00000 8.00000i 0.575853 0.575853i −0.357905 0.933758i \(-0.616509\pi\)
0.933758 + 0.357905i \(0.116509\pi\)
\(194\) 6.24264 0.448195
\(195\) −8.82843 + 6.48528i −0.632217 + 0.464421i
\(196\) −29.8284 −2.13060
\(197\) 14.1421 14.1421i 1.00759 1.00759i 0.00761443 0.999971i \(-0.497576\pi\)
0.999971 0.00761443i \(-0.00242377\pi\)
\(198\) −0.535534 + 1.12132i −0.0380587 + 0.0796888i
\(199\) 14.4853i 1.02683i −0.858139 0.513417i \(-0.828379\pi\)
0.858139 0.513417i \(-0.171621\pi\)
\(200\) 7.84924 1.12132i 0.555025 0.0792893i
\(201\) −2.65685 15.4853i −0.187400 1.09225i
\(202\) 2.10051 + 2.10051i 0.147791 + 0.147791i
\(203\) 2.82843 + 2.82843i 0.198517 + 0.198517i
\(204\) 2.14214 + 12.4853i 0.149979 + 0.874145i
\(205\) 7.65685 + 15.3137i 0.534778 + 1.06956i
\(206\) 3.75736i 0.261788i
\(207\) 5.92893 12.4142i 0.412089 0.862847i
\(208\) 6.00000 6.00000i 0.416025 0.416025i
\(209\) 2.82843 0.195646
\(210\) −7.65685 1.17157i −0.528373 0.0808462i
\(211\) −4.48528 −0.308780 −0.154390 0.988010i \(-0.549341\pi\)
−0.154390 + 0.988010i \(0.549341\pi\)
\(212\) 1.82843 1.82843i 0.125577 0.125577i
\(213\) −2.48528 + 3.51472i −0.170289 + 0.240825i
\(214\) 0.142136i 0.00971619i
\(215\) 0.242641 0.727922i 0.0165480 0.0496439i
\(216\) −7.19239 + 4.02082i −0.489380 + 0.273582i
\(217\) 10.8284 + 10.8284i 0.735082 + 0.735082i
\(218\) 0.928932 + 0.928932i 0.0629152 + 0.0629152i
\(219\) 0 0
\(220\) −3.65685 + 1.82843i −0.246545 + 0.123273i
\(221\) 11.3137i 0.761042i
\(222\) −0.142136 0.100505i −0.00953952 0.00674546i
\(223\) −16.5563 + 16.5563i −1.10870 + 1.10870i −0.115373 + 0.993322i \(0.536806\pi\)
−0.993322 + 0.115373i \(0.963194\pi\)
\(224\) 21.3137 1.42408
\(225\) 14.3137 + 4.48528i 0.954247 + 0.299019i
\(226\) 3.41421 0.227110
\(227\) −10.2426 + 10.2426i −0.679828 + 0.679828i −0.959961 0.280133i \(-0.909621\pi\)
0.280133 + 0.959961i \(0.409621\pi\)
\(228\) 7.31371 + 5.17157i 0.484362 + 0.342496i
\(229\) 9.65685i 0.638143i −0.947731 0.319071i \(-0.896629\pi\)
0.947731 0.319071i \(-0.103371\pi\)
\(230\) −3.79899 + 1.89949i −0.250498 + 0.125249i
\(231\) 8.24264 1.41421i 0.542326 0.0930484i
\(232\) −0.928932 0.928932i −0.0609874 0.0609874i
\(233\) −19.6569 19.6569i −1.28776 1.28776i −0.936143 0.351621i \(-0.885631\pi\)
−0.351621 0.936143i \(-0.614369\pi\)
\(234\) −3.31371 + 1.17157i −0.216624 + 0.0765881i
\(235\) 7.24264 21.7279i 0.472458 1.41737i
\(236\) 7.31371i 0.476082i
\(237\) −10.8284 + 15.3137i −0.703382 + 0.994732i
\(238\) −5.65685 + 5.65685i −0.366679 + 0.366679i
\(239\) 23.7990 1.53943 0.769714 0.638388i \(-0.220399\pi\)
0.769714 + 0.638388i \(0.220399\pi\)
\(240\) −11.4853 1.75736i −0.741372 0.113437i
\(241\) 0.142136 0.00915576 0.00457788 0.999990i \(-0.498543\pi\)
0.00457788 + 0.999990i \(0.498543\pi\)
\(242\) −0.292893 + 0.292893i −0.0188279 + 0.0188279i
\(243\) −15.5563 + 1.00000i −0.997940 + 0.0641500i
\(244\) 11.8579i 0.759122i
\(245\) 16.3137 + 32.6274i 1.04224 + 2.08449i
\(246\) 0.928932 + 5.41421i 0.0592266 + 0.345198i
\(247\) 5.65685 + 5.65685i 0.359937 + 0.359937i
\(248\) −3.55635 3.55635i −0.225828 0.225828i
\(249\) 3.75736 + 21.8995i 0.238113 + 1.38782i
\(250\) −2.63604 3.80761i −0.166718 0.240815i
\(251\) 16.1421i 1.01888i 0.860505 + 0.509441i \(0.170148\pi\)
−0.860505 + 0.509441i \(0.829852\pi\)
\(252\) 23.8995 + 11.4142i 1.50553 + 0.719028i
\(253\) 3.24264 3.24264i 0.203863 0.203863i
\(254\) 0.828427 0.0519801
\(255\) 12.4853 9.17157i 0.781859 0.574346i
\(256\) 3.97056 0.248160
\(257\) 1.82843 1.82843i 0.114054 0.114054i −0.647776 0.761831i \(-0.724301\pi\)
0.761831 + 0.647776i \(0.224301\pi\)
\(258\) 0.142136 0.201010i 0.00884898 0.0125143i
\(259\) 1.17157i 0.0727980i
\(260\) −10.9706 3.65685i −0.680365 0.226788i
\(261\) −0.828427 2.34315i −0.0512784 0.145037i
\(262\) −2.00000 2.00000i −0.123560 0.123560i
\(263\) 1.75736 + 1.75736i 0.108363 + 0.108363i 0.759210 0.650846i \(-0.225586\pi\)
−0.650846 + 0.759210i \(0.725586\pi\)
\(264\) −2.70711 + 0.464466i −0.166611 + 0.0285859i
\(265\) −3.00000 1.00000i −0.184289 0.0614295i
\(266\) 5.65685i 0.346844i
\(267\) 13.6569 + 9.65685i 0.835786 + 0.590990i
\(268\) 11.7279 11.7279i 0.716397 0.716397i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 3.97918 + 2.70711i 0.242165 + 0.164749i
\(271\) 8.48528 0.515444 0.257722 0.966219i \(-0.417028\pi\)
0.257722 + 0.966219i \(0.417028\pi\)
\(272\) −8.48528 + 8.48528i −0.514496 + 0.514496i
\(273\) 19.3137 + 13.6569i 1.16892 + 0.826550i
\(274\) 0.100505i 0.00607173i
\(275\) 4.00000 + 3.00000i 0.241209 + 0.180907i
\(276\) 14.3137 2.45584i 0.861584 0.147824i
\(277\) −18.4853 18.4853i −1.11067 1.11067i −0.993059 0.117613i \(-0.962476\pi\)
−0.117613 0.993059i \(-0.537524\pi\)
\(278\) −5.17157 5.17157i −0.310170 0.310170i
\(279\) −3.17157 8.97056i −0.189877 0.537054i
\(280\) −7.65685 15.3137i −0.457585 0.915169i
\(281\) 28.6274i 1.70777i −0.520463 0.853884i \(-0.674241\pi\)
0.520463 0.853884i \(-0.325759\pi\)
\(282\) 4.24264 6.00000i 0.252646 0.357295i
\(283\) −15.0711 + 15.0711i −0.895882 + 0.895882i −0.995069 0.0991868i \(-0.968376\pi\)
0.0991868 + 0.995069i \(0.468376\pi\)
\(284\) −4.54416 −0.269646
\(285\) 1.65685 10.8284i 0.0981436 0.641421i
\(286\) −1.17157 −0.0692766
\(287\) 26.1421 26.1421i 1.54312 1.54312i
\(288\) −11.9497 5.70711i −0.704146 0.336294i
\(289\) 1.00000i 0.0588235i
\(290\) −0.242641 + 0.727922i −0.0142484 + 0.0427451i
\(291\) 4.41421 + 25.7279i 0.258766 + 1.50820i
\(292\) 0 0
\(293\) 3.65685 + 3.65685i 0.213636 + 0.213636i 0.805810 0.592174i \(-0.201730\pi\)
−0.592174 + 0.805810i \(0.701730\pi\)
\(294\) 1.97918 + 11.5355i 0.115428 + 0.672766i
\(295\) 8.00000 4.00000i 0.465778 0.232889i
\(296\) 0.384776i 0.0223647i
\(297\) −5.00000 1.41421i −0.290129 0.0820610i
\(298\) 2.92893 2.92893i 0.169668 0.169668i
\(299\) 12.9706 0.750107
\(300\) 4.85786 + 15.0711i 0.280469 + 0.870129i
\(301\) −1.65685 −0.0954995
\(302\) 2.97056 2.97056i 0.170937 0.170937i
\(303\) −7.17157 + 10.1421i −0.411996 + 0.582650i
\(304\) 8.48528i 0.486664i
\(305\) −12.9706 + 6.48528i −0.742692 + 0.371346i
\(306\) 4.68629 1.65685i 0.267897 0.0947161i
\(307\) −11.8995 11.8995i −0.679140 0.679140i 0.280666 0.959806i \(-0.409445\pi\)
−0.959806 + 0.280666i \(0.909445\pi\)
\(308\) 6.24264 + 6.24264i 0.355707 + 0.355707i
\(309\) −15.4853 + 2.65685i −0.880927 + 0.151143i
\(310\) −0.928932 + 2.78680i −0.0527598 + 0.158279i
\(311\) 28.1421i 1.59579i −0.602794 0.797897i \(-0.705946\pi\)
0.602794 0.797897i \(-0.294054\pi\)
\(312\) −6.34315 4.48528i −0.359110 0.253929i
\(313\) 12.6569 12.6569i 0.715408 0.715408i −0.252253 0.967661i \(-0.581172\pi\)
0.967661 + 0.252253i \(0.0811717\pi\)
\(314\) −5.55635 −0.313563
\(315\) −0.585786 32.3848i −0.0330053 1.82468i
\(316\) −19.7990 −1.11378
\(317\) −2.31371 + 2.31371i −0.129951 + 0.129951i −0.769091 0.639140i \(-0.779291\pi\)
0.639140 + 0.769091i \(0.279291\pi\)
\(318\) −0.828427 0.585786i −0.0464559 0.0328493i
\(319\) 0.828427i 0.0463830i
\(320\) −4.17157 8.34315i −0.233198 0.466396i
\(321\) −0.585786 + 0.100505i −0.0326954 + 0.00560965i
\(322\) 6.48528 + 6.48528i 0.361411 + 0.361411i
\(323\) −8.00000 8.00000i −0.445132 0.445132i
\(324\) −10.3431 12.7990i −0.574619 0.711055i
\(325\) 2.00000 + 14.0000i 0.110940 + 0.776580i
\(326\) 2.10051i 0.116336i
\(327\) −3.17157 + 4.48528i −0.175388 + 0.248037i
\(328\) −8.58579 + 8.58579i −0.474071 + 0.474071i
\(329\) −49.4558 −2.72659
\(330\) 0.949747 + 1.29289i 0.0522819 + 0.0711714i
\(331\) −6.48528 −0.356463 −0.178232 0.983989i \(-0.557038\pi\)
−0.178232 + 0.983989i \(0.557038\pi\)
\(332\) −16.5858 + 16.5858i −0.910263 + 0.910263i
\(333\) 0.313708 0.656854i 0.0171911 0.0359954i
\(334\) 8.62742i 0.472071i
\(335\) −19.2426 6.41421i −1.05134 0.350446i
\(336\) 4.24264 + 24.7279i 0.231455 + 1.34902i
\(337\) −10.8284 10.8284i −0.589862 0.589862i 0.347732 0.937594i \(-0.386952\pi\)
−0.937594 + 0.347732i \(0.886952\pi\)
\(338\) 1.46447 + 1.46447i 0.0796565 + 0.0796565i
\(339\) 2.41421 + 14.0711i 0.131122 + 0.764235i
\(340\) 15.5147 + 5.17157i 0.841404 + 0.280468i
\(341\) 3.17157i 0.171750i
\(342\) 1.51472 3.17157i 0.0819066 0.171499i
\(343\) 31.7990 31.7990i 1.71698 1.71698i
\(344\) 0.544156 0.0293389
\(345\) −10.5147 14.3137i −0.566093 0.770624i
\(346\) −4.97056 −0.267219
\(347\) −1.89949 + 1.89949i −0.101970 + 0.101970i −0.756251 0.654281i \(-0.772971\pi\)
0.654281 + 0.756251i \(0.272971\pi\)
\(348\) 1.51472 2.14214i 0.0811974 0.114831i
\(349\) 30.0000i 1.60586i 0.596071 + 0.802932i \(0.296728\pi\)
−0.596071 + 0.802932i \(0.703272\pi\)
\(350\) −6.00000 + 8.00000i −0.320713 + 0.427618i
\(351\) −7.17157 12.8284i −0.382790 0.684731i
\(352\) −3.12132 3.12132i −0.166367 0.166367i
\(353\) −7.82843 7.82843i −0.416665 0.416665i 0.467387 0.884053i \(-0.345195\pi\)
−0.884053 + 0.467387i \(0.845195\pi\)
\(354\) 2.82843 0.485281i 0.150329 0.0257924i
\(355\) 2.48528 + 4.97056i 0.131905 + 0.263810i
\(356\) 17.6569i 0.935811i
\(357\) −27.3137 19.3137i −1.44559 1.02219i
\(358\) −7.07107 + 7.07107i −0.373718 + 0.373718i
\(359\) 22.1421 1.16862 0.584309 0.811532i \(-0.301366\pi\)
0.584309 + 0.811532i \(0.301366\pi\)
\(360\) 0.192388 + 10.6360i 0.0101397 + 0.560568i
\(361\) 11.0000 0.578947
\(362\) 1.65685 1.65685i 0.0870823 0.0870823i
\(363\) −1.41421 1.00000i −0.0742270 0.0524864i
\(364\) 24.9706i 1.30881i
\(365\) 0 0
\(366\) −4.58579 + 0.786797i −0.239703 + 0.0411265i
\(367\) −1.10051 1.10051i −0.0574459 0.0574459i 0.677800 0.735246i \(-0.262933\pi\)
−0.735246 + 0.677800i \(0.762933\pi\)
\(368\) 9.72792 + 9.72792i 0.507103 + 0.507103i
\(369\) −21.6569 + 7.65685i −1.12741 + 0.398600i
\(370\) −0.201010 + 0.100505i −0.0104500 + 0.00522501i
\(371\) 6.82843i 0.354514i
\(372\) 5.79899 8.20101i 0.300664 0.425203i
\(373\) 3.51472 3.51472i 0.181985 0.181985i −0.610235 0.792220i \(-0.708925\pi\)
0.792220 + 0.610235i \(0.208925\pi\)
\(374\) 1.65685 0.0856739
\(375\) 13.8284 13.5563i 0.714097 0.700047i
\(376\) 16.2426 0.837650
\(377\) 1.65685 1.65685i 0.0853323 0.0853323i
\(378\) 2.82843 10.0000i 0.145479 0.514344i
\(379\) 28.1421i 1.44556i −0.691076 0.722782i \(-0.742863\pi\)
0.691076 0.722782i \(-0.257137\pi\)
\(380\) 10.3431 5.17157i 0.530592 0.265296i
\(381\) 0.585786 + 3.41421i 0.0300107 + 0.174915i
\(382\) −3.31371 3.31371i −0.169544 0.169544i
\(383\) 6.07107 + 6.07107i 0.310217 + 0.310217i 0.844994 0.534776i \(-0.179604\pi\)
−0.534776 + 0.844994i \(0.679604\pi\)
\(384\) −3.09188 18.0208i −0.157782 0.919621i
\(385\) 3.41421 10.2426i 0.174004 0.522013i
\(386\) 4.68629i 0.238526i
\(387\) 0.928932 + 0.443651i 0.0472203 + 0.0225520i
\(388\) −19.4853 + 19.4853i −0.989215 + 0.989215i
\(389\) 17.3137 0.877840 0.438920 0.898526i \(-0.355361\pi\)
0.438920 + 0.898526i \(0.355361\pi\)
\(390\) −0.686292 + 4.48528i −0.0347517 + 0.227121i
\(391\) −18.3431 −0.927653
\(392\) −18.2929 + 18.2929i −0.923931 + 0.923931i
\(393\) 6.82843 9.65685i 0.344449 0.487124i
\(394\) 8.28427i 0.417356i
\(395\) 10.8284 + 21.6569i 0.544837 + 1.08967i
\(396\) −1.82843 5.17157i −0.0918819 0.259881i
\(397\) 6.17157 + 6.17157i 0.309742 + 0.309742i 0.844810 0.535067i \(-0.179714\pi\)
−0.535067 + 0.844810i \(0.679714\pi\)
\(398\) −4.24264 4.24264i −0.212664 0.212664i
\(399\) −23.3137 + 4.00000i −1.16715 + 0.200250i
\(400\) −9.00000 + 12.0000i −0.450000 + 0.600000i
\(401\) 35.6569i 1.78062i −0.455357 0.890309i \(-0.650488\pi\)
0.455357 0.890309i \(-0.349512\pi\)
\(402\) −5.31371 3.75736i −0.265024 0.187400i
\(403\) 6.34315 6.34315i 0.315975 0.315975i
\(404\) −13.1127 −0.652381
\(405\) −8.34315 + 18.3137i −0.414574 + 0.910015i
\(406\) 1.65685 0.0822283
\(407\) 0.171573 0.171573i 0.00850455 0.00850455i
\(408\) 8.97056 + 6.34315i 0.444109 + 0.314033i
\(409\) 18.4853i 0.914038i 0.889457 + 0.457019i \(0.151083\pi\)
−0.889457 + 0.457019i \(0.848917\pi\)
\(410\) 6.72792 + 2.24264i 0.332268 + 0.110756i
\(411\) −0.414214 + 0.0710678i −0.0204316 + 0.00350552i
\(412\) −11.7279 11.7279i −0.577793 0.577793i
\(413\) −13.6569 13.6569i −0.672010 0.672010i
\(414\) −1.89949 5.37258i −0.0933551 0.264048i
\(415\) 27.2132 + 9.07107i 1.33584 + 0.445281i
\(416\) 12.4853i 0.612141i
\(417\) 17.6569 24.9706i 0.864660 1.22281i
\(418\) 0.828427 0.828427i 0.0405197 0.0405197i
\(419\) −15.4558 −0.755067 −0.377534 0.925996i \(-0.623228\pi\)
−0.377534 + 0.925996i \(0.623228\pi\)
\(420\) 27.5563 20.2426i 1.34461 0.987740i
\(421\) −4.00000 −0.194948 −0.0974740 0.995238i \(-0.531076\pi\)
−0.0974740 + 0.995238i \(0.531076\pi\)
\(422\) −1.31371 + 1.31371i −0.0639503 + 0.0639503i
\(423\) 27.7279 + 13.2426i 1.34818 + 0.643879i
\(424\) 2.24264i 0.108912i
\(425\) −2.82843 19.7990i −0.137199 0.960392i
\(426\) 0.301515 + 1.75736i 0.0146085 + 0.0851443i
\(427\) 22.1421 + 22.1421i 1.07153 + 1.07153i
\(428\) −0.443651 0.443651i −0.0214447 0.0214447i
\(429\) −0.828427 4.82843i −0.0399968 0.233119i
\(430\) −0.142136 0.284271i −0.00685439 0.0137088i
\(431\) 6.34315i 0.305539i 0.988262 + 0.152769i \(0.0488191\pi\)
−0.988262 + 0.152769i \(0.951181\pi\)
\(432\) 4.24264 15.0000i 0.204124 0.721688i
\(433\) −0.313708 + 0.313708i −0.0150759 + 0.0150759i −0.714605 0.699529i \(-0.753393\pi\)
0.699529 + 0.714605i \(0.253393\pi\)
\(434\) 6.34315 0.304481
\(435\) −3.17157 0.485281i −0.152065 0.0232675i
\(436\) −5.79899 −0.277721
\(437\) −9.17157 + 9.17157i −0.438736 + 0.438736i
\(438\) 0 0
\(439\) 7.31371i 0.349064i 0.984651 + 0.174532i \(0.0558413\pi\)
−0.984651 + 0.174532i \(0.944159\pi\)
\(440\) −1.12132 + 3.36396i −0.0534568 + 0.160371i
\(441\) −46.1421 + 16.3137i −2.19724 + 0.776843i
\(442\) 3.31371 + 3.31371i 0.157617 + 0.157617i
\(443\) 20.7574 + 20.7574i 0.986212 + 0.986212i 0.999906 0.0136943i \(-0.00435918\pi\)
−0.0136943 + 0.999906i \(0.504359\pi\)
\(444\) 0.757359 0.129942i 0.0359427 0.00616679i
\(445\) 19.3137 9.65685i 0.915558 0.457779i
\(446\) 9.69848i 0.459237i
\(447\) 14.1421 + 10.0000i 0.668900 + 0.472984i
\(448\) −14.2426 + 14.2426i −0.672902 + 0.672902i
\(449\) 3.02944 0.142968 0.0714840 0.997442i \(-0.477227\pi\)
0.0714840 + 0.997442i \(0.477227\pi\)
\(450\) 5.50610 2.87868i 0.259560 0.135702i
\(451\) −7.65685 −0.360547
\(452\) −10.6569 + 10.6569i −0.501256 + 0.501256i
\(453\) 14.3431 + 10.1421i 0.673900 + 0.476519i
\(454\) 6.00000i 0.281594i
\(455\) 27.3137 13.6569i 1.28049 0.640243i
\(456\) 7.65685 1.31371i 0.358565 0.0615200i
\(457\) −6.48528 6.48528i −0.303369 0.303369i 0.538962 0.842330i \(-0.318817\pi\)
−0.842330 + 0.538962i \(0.818817\pi\)
\(458\) −2.82843 2.82843i −0.132164 0.132164i
\(459\) 10.1421 + 18.1421i 0.473394 + 0.846802i
\(460\) 5.92893 17.7868i 0.276438 0.829314i
\(461\) 13.5147i 0.629443i 0.949184 + 0.314722i \(0.101911\pi\)
−0.949184 + 0.314722i \(0.898089\pi\)
\(462\) 2.00000 2.82843i 0.0930484 0.131590i
\(463\) 11.7279 11.7279i 0.545043 0.545043i −0.379960 0.925003i \(-0.624062\pi\)
0.925003 + 0.379960i \(0.124062\pi\)
\(464\) 2.48528 0.115376
\(465\) −12.1421 1.85786i −0.563078 0.0861564i
\(466\) −11.5147 −0.533409
\(467\) 0.414214 0.414214i 0.0191675 0.0191675i −0.697458 0.716626i \(-0.745686\pi\)
0.716626 + 0.697458i \(0.245686\pi\)
\(468\) 6.68629 14.0000i 0.309074 0.647150i
\(469\) 43.7990i 2.02245i
\(470\) −4.24264 8.48528i −0.195698 0.391397i
\(471\) −3.92893 22.8995i −0.181036 1.05515i
\(472\) 4.48528 + 4.48528i 0.206452 + 0.206452i
\(473\) 0.242641 + 0.242641i 0.0111566 + 0.0111566i
\(474\) 1.31371 + 7.65685i 0.0603406 + 0.351691i
\(475\) −11.3137 8.48528i −0.519109 0.389331i
\(476\) 35.3137i 1.61860i
\(477\) 1.82843 3.82843i 0.0837179 0.175292i
\(478\) 6.97056 6.97056i 0.318826 0.318826i
\(479\) 30.1421 1.37723 0.688615 0.725127i \(-0.258219\pi\)
0.688615 + 0.725127i \(0.258219\pi\)
\(480\) −13.7782 + 10.1213i −0.628885 + 0.461973i
\(481\) 0.686292 0.0312922
\(482\) 0.0416306 0.0416306i 0.00189622 0.00189622i
\(483\) −22.1421 + 31.3137i −1.00750 + 1.42482i
\(484\) 1.82843i 0.0831103i
\(485\) 31.9706 + 10.6569i 1.45171 + 0.483903i
\(486\) −4.26346 + 4.84924i −0.193394 + 0.219966i
\(487\) 11.7279 + 11.7279i 0.531443 + 0.531443i 0.921002 0.389559i \(-0.127372\pi\)
−0.389559 + 0.921002i \(0.627372\pi\)
\(488\) −7.27208 7.27208i −0.329192 0.329192i
\(489\) 8.65685 1.48528i 0.391476 0.0671667i
\(490\) 14.3345 + 4.77817i 0.647568 + 0.215856i
\(491\) 20.0000i 0.902587i 0.892375 + 0.451294i \(0.149037\pi\)
−0.892375 + 0.451294i \(0.850963\pi\)
\(492\) −19.7990 14.0000i −0.892607 0.631169i
\(493\) −2.34315 + 2.34315i −0.105530 + 0.105530i
\(494\) 3.31371 0.149091
\(495\) −4.65685 + 4.82843i −0.209310 + 0.217022i
\(496\) 9.51472 0.427223
\(497\) 8.48528 8.48528i 0.380617 0.380617i
\(498\) 7.51472 + 5.31371i 0.336743 + 0.238113i
\(499\) 24.8284i 1.11147i −0.831358 0.555737i \(-0.812436\pi\)
0.831358 0.555737i \(-0.187564\pi\)
\(500\) 20.1127 + 3.65685i 0.899467 + 0.163539i
\(501\) −35.5563 + 6.10051i −1.58854 + 0.272550i
\(502\) 4.72792 + 4.72792i 0.211017 + 0.211017i
\(503\) −0.928932 0.928932i −0.0414190 0.0414190i 0.686094 0.727513i \(-0.259324\pi\)
−0.727513 + 0.686094i \(0.759324\pi\)
\(504\) 21.6569 7.65685i 0.964673 0.341063i
\(505\) 7.17157 + 14.3431i 0.319131 + 0.638262i
\(506\) 1.89949i 0.0844428i
\(507\) −5.00000 + 7.07107i −0.222058 + 0.314037i
\(508\) −2.58579 + 2.58579i −0.114726 + 0.114726i
\(509\) −35.6569 −1.58046 −0.790231 0.612809i \(-0.790040\pi\)
−0.790231 + 0.612809i \(0.790040\pi\)
\(510\) 0.970563 6.34315i 0.0429772 0.280879i
\(511\) 0 0
\(512\) 16.0919 16.0919i 0.711167 0.711167i
\(513\) 14.1421 + 4.00000i 0.624391 + 0.176604i
\(514\) 1.07107i 0.0472428i
\(515\) −6.41421 + 19.2426i −0.282644 + 0.847932i
\(516\) 0.183766 + 1.07107i 0.00808986 + 0.0471511i
\(517\) 7.24264 + 7.24264i 0.318531 + 0.318531i
\(518\) 0.343146 + 0.343146i 0.0150770 + 0.0150770i
\(519\) −3.51472 20.4853i −0.154279 0.899204i
\(520\) −8.97056 + 4.48528i −0.393385 + 0.196693i
\(521\) 27.6569i 1.21167i 0.795591 + 0.605834i \(0.207161\pi\)
−0.795591 + 0.605834i \(0.792839\pi\)
\(522\) −0.928932 0.443651i −0.0406583 0.0194181i
\(523\) −27.2132 + 27.2132i −1.18995 + 1.18995i −0.212870 + 0.977081i \(0.568281\pi\)
−0.977081 + 0.212870i \(0.931719\pi\)
\(524\) 12.4853 0.545422
\(525\) −37.2132 19.0711i −1.62412 0.832330i
\(526\) 1.02944 0.0448856
\(527\) −8.97056 + 8.97056i −0.390764 + 0.390764i
\(528\) 3.00000 4.24264i 0.130558 0.184637i
\(529\) 1.97056i 0.0856766i
\(530\) −1.17157 + 0.585786i −0.0508899 + 0.0254449i
\(531\) 4.00000 + 11.3137i 0.173585 + 0.490973i
\(532\) −17.6569 17.6569i −0.765522 0.765522i
\(533\) −15.3137 15.3137i −0.663310 0.663310i
\(534\) 6.82843 1.17157i 0.295495 0.0506989i
\(535\) −0.242641 + 0.727922i −0.0104903 + 0.0314708i
\(536\) 14.3848i 0.621328i
\(537\) −34.1421 24.1421i −1.47334 1.04181i
\(538\) 4.10051 4.10051i 0.176785 0.176785i
\(539\) −16.3137 −0.702681
\(540\) −20.8701 + 3.97056i −0.898104 + 0.170866i
\(541\) −10.6863 −0.459440 −0.229720 0.973257i \(-0.573781\pi\)
−0.229720 + 0.973257i \(0.573781\pi\)
\(542\) 2.48528 2.48528i 0.106752 0.106752i
\(543\) 8.00000 + 5.65685i 0.343313 + 0.242759i
\(544\) 17.6569i 0.757031i
\(545\) 3.17157 + 6.34315i 0.135855 + 0.271711i
\(546\) 9.65685 1.65685i 0.413275 0.0709068i
\(547\) 2.10051 + 2.10051i 0.0898111 + 0.0898111i 0.750585 0.660774i \(-0.229772\pi\)
−0.660774 + 0.750585i \(0.729772\pi\)
\(548\) −0.313708 0.313708i −0.0134010 0.0134010i
\(549\) −6.48528 18.3431i −0.276785 0.782866i
\(550\) 2.05025 0.292893i 0.0874231 0.0124890i
\(551\) 2.34315i 0.0998214i
\(552\) 7.27208 10.2843i 0.309520 0.437728i
\(553\) 36.9706 36.9706i 1.57215 1.57215i
\(554\) −10.8284 −0.460056
\(555\) −0.556349 0.757359i −0.0236157 0.0321481i
\(556\) 32.2843 1.36916
\(557\) −8.97056 + 8.97056i −0.380095 + 0.380095i −0.871136 0.491041i \(-0.836616\pi\)
0.491041 + 0.871136i \(0.336616\pi\)
\(558\) −3.55635 1.69848i −0.150552 0.0719026i
\(559\) 0.970563i 0.0410504i
\(560\) 30.7279 + 10.2426i 1.29849 + 0.432831i
\(561\) 1.17157 + 6.82843i 0.0494638 + 0.288296i
\(562\) −8.38478 8.38478i −0.353690 0.353690i
\(563\) 9.89949 + 9.89949i 0.417214 + 0.417214i 0.884242 0.467028i \(-0.154675\pi\)
−0.467028 + 0.884242i \(0.654675\pi\)
\(564\) 5.48528 + 31.9706i 0.230972 + 1.34620i
\(565\) 17.4853 + 5.82843i 0.735611 + 0.245204i
\(566\) 8.82843i 0.371086i
\(567\) 43.2132 + 4.58579i 1.81478 + 0.192585i
\(568\) −2.78680 + 2.78680i −0.116931 + 0.116931i
\(569\) 28.3431 1.18821 0.594103 0.804389i \(-0.297507\pi\)
0.594103 + 0.804389i \(0.297507\pi\)
\(570\) −2.68629 3.65685i −0.112516 0.153169i
\(571\) 29.6569 1.24110 0.620550 0.784167i \(-0.286909\pi\)
0.620550 + 0.784167i \(0.286909\pi\)
\(572\) 3.65685 3.65685i 0.152901 0.152901i
\(573\) 11.3137 16.0000i 0.472637 0.668410i
\(574\) 15.3137i 0.639182i
\(575\) −22.6985 + 3.24264i −0.946592 + 0.135227i
\(576\) 11.7990 4.17157i 0.491625 0.173816i
\(577\) 17.0000 + 17.0000i 0.707719 + 0.707719i 0.966055 0.258336i \(-0.0831741\pi\)
−0.258336 + 0.966055i \(0.583174\pi\)
\(578\) 0.292893 + 0.292893i 0.0121828 + 0.0121828i
\(579\) 19.3137 3.31371i 0.802650 0.137713i
\(580\) −1.51472 3.02944i −0.0628953 0.125791i
\(581\) 61.9411i 2.56975i
\(582\) 8.82843 + 6.24264i 0.365950 + 0.258766i
\(583\) 1.00000 1.00000i 0.0414158 0.0414158i
\(584\) 0 0
\(585\) −18.9706 + 0.343146i −0.784336 + 0.0141873i
\(586\) 2.14214 0.0884908
\(587\) 0.414214 0.414214i 0.0170964 0.0170964i −0.698507 0.715603i \(-0.746152\pi\)
0.715603 + 0.698507i \(0.246152\pi\)
\(588\) −42.1838 29.8284i −1.73963 1.23010i
\(589\) 8.97056i 0.369626i
\(590\) 1.17157 3.51472i 0.0482329 0.144699i
\(591\) 34.1421 5.85786i 1.40442 0.240960i
\(592\) 0.514719 + 0.514719i 0.0211548 + 0.0211548i
\(593\) −5.85786 5.85786i −0.240554 0.240554i 0.576525 0.817079i \(-0.304408\pi\)
−0.817079 + 0.576525i \(0.804408\pi\)
\(594\) −1.87868 + 1.05025i −0.0770832 + 0.0430924i
\(595\) −38.6274 + 19.3137i −1.58357 + 0.791785i
\(596\) 18.2843i 0.748953i
\(597\) 14.4853 20.4853i 0.592843 0.838407i
\(598\) 3.79899 3.79899i 0.155352 0.155352i
\(599\) 3.45584 0.141202 0.0706010 0.997505i \(-0.477508\pi\)
0.0706010 + 0.997505i \(0.477508\pi\)
\(600\) 12.2218 + 6.26346i 0.498954 + 0.255705i
\(601\) −27.4558 −1.11995 −0.559974 0.828510i \(-0.689189\pi\)
−0.559974 + 0.828510i \(0.689189\pi\)
\(602\) −0.485281 + 0.485281i −0.0197786 + 0.0197786i
\(603\) 11.7279 24.5563i 0.477598 1.00001i
\(604\) 18.5442i 0.754551i
\(605\) −2.00000 + 1.00000i −0.0813116 + 0.0406558i
\(606\) 0.870058 + 5.07107i 0.0353437 + 0.205998i
\(607\) −21.8995 21.8995i −0.888873 0.888873i 0.105542 0.994415i \(-0.466342\pi\)
−0.994415 + 0.105542i \(0.966342\pi\)
\(608\) 8.82843 + 8.82843i 0.358040 + 0.358040i
\(609\) 1.17157 + 6.82843i 0.0474745 + 0.276702i
\(610\) −1.89949 + 5.69848i −0.0769083 + 0.230725i
\(611\) 28.9706i 1.17202i
\(612\) −9.45584 + 19.7990i −0.382230 + 0.800327i
\(613\) −16.0000 + 16.0000i −0.646234 + 0.646234i −0.952081 0.305847i \(-0.901060\pi\)
0.305847 + 0.952081i \(0.401060\pi\)
\(614\) −6.97056 −0.281309
\(615\) −4.48528 + 29.3137i −0.180864 + 1.18204i
\(616\) 7.65685 0.308503
\(617\) −29.8284 + 29.8284i −1.20085 + 1.20085i −0.226938 + 0.973909i \(0.572871\pi\)
−0.973909 + 0.226938i \(0.927129\pi\)
\(618\) −3.75736 + 5.31371i −0.151143 + 0.213749i
\(619\) 0.686292i 0.0275844i 0.999905 + 0.0137922i \(0.00439033\pi\)
−0.999905 + 0.0137922i \(0.995610\pi\)
\(620\) −5.79899 11.5980i −0.232893 0.465786i
\(621\) 20.7990 11.6274i 0.834635 0.466592i
\(622\) −8.24264 8.24264i −0.330500 0.330500i
\(623\) −32.9706 32.9706i −1.32094 1.32094i
\(624\) 14.4853 2.48528i 0.579875 0.0994909i
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 7.41421i 0.296332i
\(627\) 4.00000 + 2.82843i 0.159745 + 0.112956i
\(628\) 17.3431 17.3431i 0.692067 0.692067i
\(629\) −0.970563 −0.0386989
\(630\) −9.65685 9.31371i −0.384738 0.371067i
\(631\) −16.9706 −0.675587 −0.337794 0.941220i \(-0.609681\pi\)
−0.337794 + 0.941220i \(0.609681\pi\)
\(632\) −12.1421 + 12.1421i −0.482988 + 0.482988i
\(633\) −6.34315 4.48528i −0.252117 0.178274i
\(634\) 1.35534i 0.0538274i
\(635\) 4.24264 + 1.41421i 0.168364 + 0.0561214i
\(636\) 4.41421 0.757359i 0.175035 0.0300313i
\(637\) −32.6274 32.6274i −1.29275 1.29275i
\(638\) −0.242641 0.242641i −0.00960624 0.00960624i
\(639\) −7.02944 + 2.48528i −0.278080 + 0.0983162i
\(640\) −22.3934 7.46447i −0.885177 0.295059i
\(641\) 32.6274i 1.28871i 0.764728 + 0.644353i \(0.222873\pi\)
−0.764728 + 0.644353i \(0.777127\pi\)
\(642\) −0.142136 + 0.201010i −0.00560965 + 0.00793324i
\(643\) −9.24264 + 9.24264i −0.364494 + 0.364494i −0.865464 0.500970i \(-0.832977\pi\)
0.500970 + 0.865464i \(0.332977\pi\)
\(644\) −40.4853 −1.59534
\(645\) 1.07107 0.786797i 0.0421733 0.0309801i
\(646\) −4.68629 −0.184380
\(647\) −11.7279 + 11.7279i −0.461072 + 0.461072i −0.899007 0.437935i \(-0.855710\pi\)
0.437935 + 0.899007i \(0.355710\pi\)
\(648\) −14.1924 1.50610i −0.557530 0.0591651i
\(649\) 4.00000i 0.157014i
\(650\) 4.68629 + 3.51472i 0.183811 + 0.137859i
\(651\) 4.48528 + 26.1421i 0.175792 + 1.02459i
\(652\) 6.55635 + 6.55635i 0.256766 + 0.256766i
\(653\) −8.65685 8.65685i −0.338769 0.338769i 0.517135 0.855904i \(-0.326999\pi\)
−0.855904 + 0.517135i \(0.826999\pi\)
\(654\) 0.384776 + 2.24264i 0.0150459 + 0.0876942i
\(655\) −6.82843 13.6569i −0.266809 0.533617i
\(656\) 22.9706i 0.896850i
\(657\) 0 0
\(658\) −14.4853 + 14.4853i −0.564695 + 0.564695i
\(659\) 24.9706 0.972715 0.486358 0.873760i \(-0.338325\pi\)
0.486358 + 0.873760i \(0.338325\pi\)
\(660\) −7.00000 1.07107i −0.272475 0.0416913i
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) −1.89949 + 1.89949i −0.0738260 + 0.0738260i
\(663\) −11.3137 + 16.0000i −0.439388 + 0.621389i
\(664\) 20.3431i 0.789467i
\(665\) −9.65685 + 28.9706i −0.374477 + 1.12343i
\(666\) −0.100505 0.284271i −0.00389449 0.0110153i
\(667\) 2.68629 + 2.68629i 0.104014 + 0.104014i
\(668\) −26.9289 26.9289i −1.04191 1.04191i
\(669\) −39.9706 + 6.85786i −1.54535 + 0.265140i
\(670\) −7.51472 + 3.75736i −0.290319 + 0.145159i
\(671\) 6.48528i 0.250362i
\(672\) 30.1421 + 21.3137i 1.16276 + 0.822194i
\(673\) −22.3431 + 22.3431i −0.861265 + 0.861265i −0.991485 0.130220i \(-0.958432\pi\)
0.130220 + 0.991485i \(0.458432\pi\)
\(674\) −6.34315 −0.244329
\(675\) 15.7574 + 20.6569i 0.606501 + 0.795083i
\(676\) −9.14214 −0.351621
\(677\) −19.6569 + 19.6569i −0.755474 + 0.755474i −0.975495 0.220021i \(-0.929387\pi\)
0.220021 + 0.975495i \(0.429387\pi\)
\(678\) 4.82843 + 3.41421i 0.185435 + 0.131122i
\(679\) 72.7696i 2.79264i
\(680\) 12.6863 6.34315i 0.486497 0.243249i
\(681\) −24.7279 + 4.24264i −0.947576 + 0.162578i
\(682\) −0.928932 0.928932i −0.0355707 0.0355707i
\(683\) −7.72792 7.72792i −0.295701 0.295701i 0.543627 0.839327i \(-0.317051\pi\)
−0.839327 + 0.543627i \(0.817051\pi\)
\(684\) 5.17157 + 14.6274i 0.197740 + 0.559293i
\(685\) −0.171573 + 0.514719i −0.00655546 + 0.0196664i
\(686\) 18.6274i 0.711198i
\(687\) 9.65685 13.6569i 0.368432 0.521041i
\(688\) −0.727922 + 0.727922i −0.0277518 + 0.0277518i
\(689\) 4.00000 0.152388
\(690\) −7.27208 1.11270i −0.276843 0.0423597i
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 15.5147 15.5147i 0.589781 0.589781i
\(693\) 13.0711 + 6.24264i 0.496529 + 0.237138i
\(694\) 1.11270i 0.0422375i
\(695\) −17.6569 35.3137i −0.669763 1.33953i
\(696\) −0.384776 2.24264i −0.0145849 0.0850071i
\(697\) 21.6569 + 21.6569i 0.820312 + 0.820312i
\(698\) 8.78680 + 8.78680i 0.332585 + 0.332585i
\(699\) −8.14214 47.4558i −0.307964 1.79494i
\(700\) −6.24264 43.6985i −0.235950 1.65165i
\(701\) 1.31371i 0.0496181i −0.999692 0.0248090i \(-0.992102\pi\)
0.999692 0.0248090i \(-0.00789777\pi\)
\(702\) −5.85786 1.65685i −0.221091 0.0625339i
\(703\) −0.485281 + 0.485281i −0.0183027 + 0.0183027i
\(704\) 4.17157 0.157222
\(705\) 31.9706 23.4853i 1.20408 0.884507i
\(706\) −4.58579 −0.172588
\(707\) 24.4853 24.4853i 0.920864 0.920864i
\(708\) −7.31371 + 10.3431i −0.274866 + 0.388719i
\(709\) 29.3137i 1.10090i −0.834868 0.550450i \(-0.814456\pi\)
0.834868 0.550450i \(-0.185544\pi\)
\(710\) 2.18377 + 0.727922i 0.0819553 + 0.0273184i
\(711\) −30.6274 + 10.8284i −1.14862 + 0.406098i
\(712\) 10.8284 + 10.8284i 0.405812 + 0.405812i
\(713\) 10.2843 + 10.2843i 0.385149 + 0.385149i
\(714\) −13.6569 + 2.34315i −0.511095 + 0.0876900i
\(715\) −6.00000 2.00000i −0.224387 0.0747958i
\(716\) 44.1421i 1.64967i
\(717\) 33.6569 + 23.7990i 1.25694 + 0.888790i
\(718\) 6.48528 6.48528i 0.242029 0.242029i
\(719\) 22.7696 0.849161 0.424581 0.905390i \(-0.360422\pi\)
0.424581 + 0.905390i \(0.360422\pi\)
\(720\) −14.4853 13.9706i −0.539835 0.520652i
\(721\) 43.7990 1.63116
\(722\) 3.22183 3.22183i 0.119904 0.119904i
\(723\) 0.201010 + 0.142136i 0.00747565 + 0.00528608i
\(724\) 10.3431i 0.384400i
\(725\) −2.48528 + 3.31371i −0.0923010 + 0.123068i
\(726\) −0.707107 + 0.121320i −0.0262432 + 0.00450262i
\(727\) 20.2132 + 20.2132i 0.749666 + 0.749666i 0.974416 0.224750i \(-0.0721566\pi\)
−0.224750 + 0.974416i \(0.572157\pi\)
\(728\) 15.3137 + 15.3137i 0.567564 + 0.567564i
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 0 0
\(731\) 1.37258i 0.0507668i
\(732\) 11.8579 16.7696i 0.438279 0.619821i
\(733\) 3.79899 3.79899i 0.140319 0.140319i −0.633458 0.773777i \(-0.718365\pi\)
0.773777 + 0.633458i \(0.218365\pi\)
\(734\) −0.644661 −0.0237949
\(735\) −9.55635 + 62.4558i −0.352491 + 2.30372i
\(736\) 20.2426 0.746154
\(737\) 6.41421 6.41421i 0.236271 0.236271i
\(738\) −4.10051 + 8.58579i −0.150942 + 0.316047i
\(739\) 14.6274i 0.538078i 0.963129 + 0.269039i \(0.0867061\pi\)
−0.963129 + 0.269039i \(0.913294\pi\)
\(740\) 0.313708 0.941125i 0.0115322 0.0345965i
\(741\) 2.34315 + 13.6569i 0.0860776 + 0.501697i
\(742\) 2.00000 + 2.00000i 0.0734223 + 0.0734223i
\(743\) 26.0416 + 26.0416i 0.955375 + 0.955375i 0.999046 0.0436712i \(-0.0139054\pi\)
−0.0436712 + 0.999046i \(0.513905\pi\)
\(744\) −1.47309 8.58579i −0.0540060 0.314770i
\(745\) 20.0000 10.0000i 0.732743 0.366372i
\(746\) 2.05887i 0.0753808i
\(747\) −16.5858 + 34.7279i −0.606842 + 1.27063i
\(748\) −5.17157 + 5.17157i −0.189091 + 0.189091i
\(749\) 1.65685 0.0605401
\(750\) 0.0796898 8.02082i 0.00290986 0.292879i
\(751\) −46.6274 −1.70146 −0.850729 0.525604i \(-0.823839\pi\)
−0.850729 + 0.525604i \(0.823839\pi\)
\(752\) −21.7279 + 21.7279i −0.792336 + 0.792336i
\(753\) −16.1421 + 22.8284i −0.588252 + 0.831914i
\(754\) 0.970563i 0.0353458i
\(755\) 20.2843 10.1421i 0.738220 0.369110i
\(756\) 22.3848 + 40.0416i 0.814126 + 1.45630i
\(757\) 0.171573 + 0.171573i 0.00623592 + 0.00623592i 0.710218 0.703982i \(-0.248596\pi\)
−0.703982 + 0.710218i \(0.748596\pi\)
\(758\) −8.24264 8.24264i −0.299386 0.299386i
\(759\) 7.82843 1.34315i 0.284154 0.0487531i
\(760\) 3.17157 9.51472i 0.115045 0.345135i
\(761\) 1.51472i 0.0549085i −0.999623 0.0274543i \(-0.991260\pi\)
0.999623 0.0274543i \(-0.00874006\pi\)
\(762\) 1.17157 + 0.828427i 0.0424416 + 0.0300107i
\(763\) 10.8284 10.8284i 0.392015 0.392015i
\(764\) 20.6863 0.748404
\(765\) 26.8284 0.485281i 0.969984 0.0175454i
\(766\) 3.55635 0.128496
\(767\) −8.00000 + 8.00000i −0.288863 + 0.288863i
\(768\) 5.61522 + 3.97056i 0.202622 + 0.143275i
\(769\) 52.6274i 1.89779i −0.315587 0.948897i \(-0.602201\pi\)
0.315587 0.948897i \(-0.397799\pi\)
\(770\) −2.00000 4.00000i −0.0720750 0.144150i
\(771\) 4.41421 0.757359i 0.158974 0.0272756i
\(772\) 14.6274 + 14.6274i 0.526452 + 0.526452i
\(773\) −10.6569 10.6569i −0.383300 0.383300i 0.488989 0.872290i \(-0.337366\pi\)
−0.872290 + 0.488989i \(0.837366\pi\)
\(774\) 0.402020 0.142136i 0.0144503 0.00510896i
\(775\) −9.51472 + 12.6863i −0.341779 + 0.455705i
\(776\) 23.8995i 0.857942i
\(777\) −1.17157 + 1.65685i −0.0420299 + 0.0594393i
\(778\) 5.07107 5.07107i 0.181807 0.181807i
\(779\) 21.6569 0.775937
\(780\) −11.8579 16.1421i −0.424580 0.577981i
\(781\) −2.48528 −0.0889304
\(782\) −5.37258 + 5.37258i −0.192123 + 0.192123i
\(783\) 1.17157 4.14214i 0.0418686 0.148028i
\(784\) 48.9411i 1.74790i
\(785\) −28.4558 9.48528i −1.01563 0.338544i
\(786\) −0.828427 4.82843i −0.0295490 0.172224i
\(787\) −28.5858 28.5858i −1.01897 1.01897i −0.999816 0.0191567i \(-0.993902\pi\)
−0.0191567 0.999816i \(-0.506098\pi\)
\(788\) 25.8579 + 25.8579i 0.921148 + 0.921148i
\(789\) 0.727922 + 4.24264i 0.0259147 + 0.151042i
\(790\) 9.51472 + 3.17157i 0.338518 + 0.112839i
\(791\) 39.7990i 1.41509i
\(792\) −4.29289 2.05025i −0.152541 0.0728526i
\(793\) 12.9706 12.9706i 0.460598 0.460598i
\(794\) 3.61522 0.128299
\(795\) −3.24264 4.41421i −0.115005 0.156556i
\(796\) 26.4853 0.938746
\(797\) −25.9706 + 25.9706i −0.919925 + 0.919925i −0.997023 0.0770989i \(-0.975434\pi\)
0.0770989 + 0.997023i \(0.475434\pi\)
\(798\) −5.65685 + 8.00000i −0.200250 + 0.283197i
\(799\) 40.9706i 1.44943i
\(800\) 3.12132 + 21.8492i 0.110355 + 0.772487i
\(801\) 9.65685 + 27.3137i 0.341208 + 0.965082i
\(802\) −10.4437 10.4437i −0.368778 0.368778i
\(803\) 0 0
\(804\) 28.3137 4.85786i 0.998548 0.171324i
\(805\) 22.1421 + 44.2843i 0.780408 + 1.56082i
\(806\) 3.71573i 0.130881i
\(807\) 19.7990 + 14.0000i 0.696957 + 0.492823i
\(808\) −8.04163 + 8.04163i −0.282904 + 0.282904i
\(809\) 15.8579 0.557533 0.278766 0.960359i \(-0.410074\pi\)
0.278766 + 0.960359i \(0.410074\pi\)
\(810\) 2.92031 + 7.80761i 0.102609 + 0.274332i
\(811\) −41.6569 −1.46277 −0.731385 0.681965i \(-0.761126\pi\)
−0.731385 + 0.681965i \(0.761126\pi\)
\(812\) −5.17157 + 5.17157i −0.181487 + 0.181487i
\(813\) 12.0000 + 8.48528i 0.420858 + 0.297592i
\(814\) 0.100505i 0.00352270i
\(815\) 3.58579 10.7574i 0.125605 0.376814i
\(816\) −20.4853 + 3.51472i −0.717128 + 0.123040i
\(817\) −0.686292 0.686292i −0.0240103 0.0240103i
\(818\) 5.41421 + 5.41421i 0.189304 + 0.189304i
\(819\) 13.6569 + 38.6274i 0.477209 + 1.34975i
\(820\) −28.0000 + 14.0000i −0.977802 + 0.488901i
\(821\) 0.343146i 0.0119759i 0.999982 + 0.00598793i \(0.00190603\pi\)
−0.999982 + 0.00598793i \(0.998094\pi\)
\(822\) −0.100505 + 0.142136i −0.00350552 + 0.00495755i
\(823\) −18.4142 + 18.4142i −0.641879 + 0.641879i −0.951017 0.309138i \(-0.899959\pi\)
0.309138 + 0.951017i \(0.399959\pi\)
\(824\) −14.3848 −0.501117
\(825\) 2.65685 + 8.24264i 0.0924998 + 0.286972i
\(826\) −8.00000 −0.278356
\(827\) 28.0416 28.0416i 0.975103 0.975103i −0.0245945 0.999698i \(-0.507829\pi\)
0.999698 + 0.0245945i \(0.00782945\pi\)
\(828\) 22.6985 + 10.8406i 0.788827 + 0.376738i
\(829\) 10.9706i 0.381023i 0.981685 + 0.190512i \(0.0610147\pi\)
−0.981685 + 0.190512i \(0.938985\pi\)
\(830\) 10.6274 5.31371i 0.368883 0.184442i
\(831\) −7.65685 44.6274i −0.265613 1.54811i
\(832\) 8.34315 + 8.34315i 0.289247 + 0.289247i
\(833\) 46.1421 + 46.1421i 1.59873 + 1.59873i
\(834\) −2.14214 12.4853i −0.0741761 0.432330i
\(835\) −14.7279 + 44.1838i −0.509681 + 1.52904i
\(836\) 5.17157i 0.178863i
\(837\) 4.48528 15.8579i 0.155034 0.548128i
\(838\) −4.52691 + 4.52691i −0.156380 + 0.156380i
\(839\) 21.6569 0.747678 0.373839 0.927494i \(-0.378041\pi\)
0.373839 + 0.927494i \(0.378041\pi\)
\(840\) 4.48528 29.3137i 0.154757 1.01142i
\(841\) −28.3137 −0.976335
\(842\) −1.17157 + 1.17157i −0.0403751 + 0.0403751i
\(843\) 28.6274 40.4853i 0.985981 1.39439i
\(844\) 8.20101i 0.282290i
\(845\) 5.00000 + 10.0000i 0.172005 + 0.344010i
\(846\) 12.0000 4.24264i 0.412568 0.145865i
\(847\) 3.41421 + 3.41421i 0.117314 + 0.117314i
\(848\) 3.00000 + 3.00000i 0.103020 + 0.103020i
\(849\) −36.3848 + 6.24264i −1.24872 + 0.214247i
\(850\) −6.62742 4.97056i −0.227319 0.170489i
\(851\) 1.11270i 0.0381428i
\(852\) −6.42641 4.54416i −0.220165 0.155680i
\(853\) 18.1421 18.1421i 0.621175 0.621175i −0.324657 0.945832i \(-0.605249\pi\)
0.945832 + 0.324657i \(0.105249\pi\)
\(854\) 12.9706 0.443844
\(855\) 13.1716 13.6569i 0.450458 0.467055i
\(856\) −0.544156 −0.0185989
\(857\) 16.4853 16.4853i 0.563126 0.563126i −0.367068 0.930194i \(-0.619638\pi\)
0.930194 + 0.367068i \(0.119638\pi\)
\(858\) −1.65685 1.17157i −0.0565641 0.0399968i
\(859\) 36.0000i 1.22830i 0.789188 + 0.614152i \(0.210502\pi\)
−0.789188 + 0.614152i \(0.789498\pi\)
\(860\) 1.33095 + 0.443651i 0.0453851 + 0.0151284i
\(861\) 63.1127 10.8284i 2.15088 0.369032i
\(862\) 1.85786 + 1.85786i 0.0632791 + 0.0632791i
\(863\) −12.5563 12.5563i −0.427423 0.427423i 0.460327 0.887750i \(-0.347732\pi\)
−0.887750 + 0.460327i \(0.847732\pi\)
\(864\) −11.1924 20.0208i −0.380773 0.681122i
\(865\) −25.4558 8.48528i −0.865525 0.288508i
\(866\) 0.183766i 0.00624463i
\(867\) −1.00000 + 1.41421i −0.0339618 + 0.0480292i
\(868\) −19.7990 + 19.7990i −0.672022 + 0.672022i
\(869\) −10.8284 −0.367329
\(870\) −1.07107 + 0.786797i −0.0363126 + 0.0266749i
\(871\) 25.6569 0.869349
\(872\) −3.55635 + 3.55635i −0.120433 + 0.120433i
\(873\) −19.4853 + 40.7990i −0.659477 + 1.38084i
\(874\) 5.37258i 0.181730i
\(875\) −44.3848 + 30.7279i −1.50048 + 1.03879i
\(876\) 0 0
\(877\) 6.62742 + 6.62742i 0.223792 + 0.223792i 0.810093 0.586301i \(-0.199416\pi\)
−0.586301 + 0.810093i \(0.699416\pi\)
\(878\) 2.14214 + 2.14214i 0.0722936 + 0.0722936i
\(879\) 1.51472 + 8.82843i 0.0510902 + 0.297775i
\(880\) −3.00000 6.00000i −0.101130 0.202260i
\(881\) 12.9706i 0.436989i −0.975838 0.218495i \(-0.929885\pi\)
0.975838 0.218495i \(-0.0701146\pi\)
\(882\) −8.73654 + 18.2929i −0.294175 + 0.615954i
\(883\) −3.58579 + 3.58579i −0.120671 + 0.120671i −0.764864 0.644192i \(-0.777194\pi\)
0.644192 + 0.764864i \(0.277194\pi\)
\(884\) −20.6863 −0.695755
\(885\) 15.3137 + 2.34315i 0.514765 + 0.0787640i
\(886\) 12.1594 0.408502
\(887\) 9.75736 9.75736i 0.327620 0.327620i −0.524061 0.851681i \(-0.675584\pi\)
0.851681 + 0.524061i \(0.175584\pi\)
\(888\) 0.384776 0.544156i 0.0129122 0.0182607i
\(889\) 9.65685i 0.323880i
\(890\) 2.82843 8.48528i 0.0948091 0.284427i
\(891\) −5.65685 7.00000i −0.189512 0.234509i
\(892\) −30.2721 30.2721i −1.01358 1.01358i
\(893\) −20.4853 20.4853i −0.685514 0.685514i
\(894\) 7.07107 1.21320i 0.236492 0.0405756i
\(895\) −48.2843 + 24.1421i −1.61397 + 0.806983i
\(896\) 50.9706i 1.70281i
\(897\) 18.3431 + 12.9706i 0.612460 + 0.433074i
\(898\) 0.887302 0.887302i 0.0296096 0.0296096i
\(899\) 2.62742 0.0876293
\(900\) −8.20101 + 26.1716i −0.273367 + 0.872386i
\(901\) −5.65685 −0.188457
\(902\) −2.24264 + 2.24264i −0.0746718 + 0.0746718i
\(903\) −2.34315 1.65685i −0.0779750 0.0551367i
\(904\) 13.0711i 0.434737i
\(905\) 11.3137 5.65685i 0.376080 0.188040i
\(906\) 7.17157 1.23045i 0.238260 0.0408789i
\(907\) 29.0416 + 29.0416i 0.964312 + 0.964312i 0.999385 0.0350732i \(-0.0111664\pi\)
−0.0350732 + 0.999385i \(0.511166\pi\)
\(908\) −18.7279 18.7279i −0.621508 0.621508i
\(909\) −20.2843 + 7.17157i −0.672787 + 0.237866i
\(910\) 4.00000 12.0000i 0.132599 0.397796i
\(911\) 56.0000i 1.85536i 0.373373 + 0.927681i \(0.378201\pi\)
−0.373373 + 0.927681i \(0.621799\pi\)
\(912\) −8.48528 + 12.0000i −0.280976 + 0.397360i
\(913\) −9.07107 + 9.07107i −0.300209 + 0.300209i
\(914\) −3.79899 −0.125659
\(915\) −24.8284 3.79899i −0.820802 0.125591i
\(916\) 17.6569 0.583399
\(917\) −23.3137 + 23.3137i −0.769886 + 0.769886i
\(918\) 8.28427 + 2.34315i 0.273422 + 0.0773353i
\(919\) 14.6274i 0.482514i −0.970461 0.241257i \(-0.922440\pi\)
0.970461 0.241257i \(-0.0775597\pi\)
\(920\) −7.27208 14.5442i −0.239753 0.479507i
\(921\) −4.92893 28.7279i −0.162414 0.946617i
\(922\) 3.95837 + 3.95837i 0.130362 + 0.130362i
\(923\) −4.97056 4.97056i −0.163608 0.163608i
\(924\) 2.58579 + 15.0711i 0.0850661 + 0.495802i
\(925\) −1.20101 + 0.171573i −0.0394890 + 0.00564128i
\(926\) 6.87006i 0.225764i
\(927\) −24.5563 11.7279i −0.806536 0.385195i
\(928\) 2.58579 2.58579i 0.0848826 0.0848826i
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) −4.10051 + 3.01219i −0.134461 + 0.0987737i
\(931\) 46.1421 1.51225
\(932\) 35.9411 35.9411i 1.17729 1.17729i
\(933\) 28.1421 39.7990i 0.921332 1.30296i
\(934\) 0.242641i 0.00793945i
\(935\) 8.48528 + 2.82843i 0.277498 + 0.0924995i
\(936\) −4.48528 12.6863i −0.146606 0.414664i
\(937\) −10.9706 10.9706i −0.358393 0.358393i 0.504828 0.863220i \(-0.331556\pi\)
−0.863220 + 0.504828i \(0.831556\pi\)
\(938\) 12.8284 + 12.8284i 0.418863 + 0.418863i
\(939\) 30.5563 5.24264i 0.997169 0.171087i
\(940\) 39.7279 + 13.2426i 1.29578 + 0.431927i
\(941\) 37.1127i 1.20984i −0.796286 0.604920i \(-0.793205\pi\)
0.796286 0.604920i \(-0.206795\pi\)
\(942\) −7.85786 5.55635i −0.256023 0.181036i
\(943\) 24.8284 24.8284i 0.808525 0.808525i
\(944\) −12.0000 −0.390567
\(945\) 31.5563 46.3848i 1.02653 1.50890i
\(946\) 0.142136 0.00462123
\(947\) 17.2426 17.2426i 0.560311 0.560311i −0.369085 0.929396i \(-0.620329\pi\)
0.929396 + 0.369085i \(0.120329\pi\)
\(948\) −28.0000 19.7990i −0.909398 0.643041i
\(949\) 0 0
\(950\) −5.79899 + 0.828427i −0.188144 + 0.0268777i
\(951\) −5.58579 + 0.958369i −0.181132 + 0.0310773i
\(952\) −21.6569 21.6569i −0.701903 0.701903i
\(953\) −5.79899 5.79899i −0.187848 0.187848i 0.606917 0.794765i \(-0.292406\pi\)
−0.794765 + 0.606917i \(0.792406\pi\)
\(954\) −0.585786 1.65685i −0.0189655 0.0536426i
\(955\) −11.3137 22.6274i −0.366103 0.732206i
\(956\) 43.5147i 1.40737i
\(957\) 0.828427 1.17157i 0.0267792 0.0378716i
\(958\) 8.82843 8.82843i 0.285234 0.285234i
\(959\) 1.17157 0.0378321
\(960\) 2.44365 15.9706i 0.0788685 0.515448i
\(961\) −20.9411 −0.675520
\(962\) 0.201010 0.201010i 0.00648083 0.00648083i
\(963\) −0.928932 0.443651i −0.0299344 0.0142964i
\(964\) 0.259885i 0.00837032i
\(965\) 8.00000 24.0000i 0.257529 0.772587i
\(966\) 2.68629 + 15.6569i 0.0864300 + 0.503751i
\(967\) 38.3848 + 38.3848i 1.23437 + 1.23437i 0.962268 + 0.272103i \(0.0877192\pi\)
0.272103 + 0.962268i \(0.412281\pi\)
\(968\) −1.12132 1.12132i −0.0360406 0.0360406i
\(969\) −3.31371 19.3137i −0.106452 0.620446i
\(970\) 12.4853 6.24264i 0.400878 0.200439i
\(971\) 20.0000i 0.641831i 0.947108 + 0.320915i \(0.103990\pi\)
−0.947108 + 0.320915i \(0.896010\pi\)
\(972\) −1.82843 28.4437i −0.0586468 0.912331i
\(973\) −60.2843 + 60.2843i −1.93263 + 1.93263i
\(974\) 6.87006 0.220131
\(975\) −11.1716 + 21.7990i −0.357777 + 0.698126i
\(976\) 19.4558 0.622766
\(977\) 38.1127 38.1127i 1.21933 1.21933i 0.251468 0.967866i \(-0.419087\pi\)
0.967866 0.251468i \(-0.0809132\pi\)
\(978\) 2.10051 2.97056i 0.0671667 0.0949881i
\(979\) 9.65685i 0.308634i
\(980\) −59.6569 + 29.8284i −1.90567 + 0.952834i
\(981\) −8.97056 + 3.17157i −0.286408 + 0.101261i
\(982\) 5.85786 + 5.85786i 0.186932 + 0.186932i
\(983\) −23.7279 23.7279i −0.756803 0.756803i 0.218936 0.975739i \(-0.429741\pi\)
−0.975739 + 0.218936i \(0.929741\pi\)
\(984\) −20.7279 + 3.55635i −0.660782 + 0.113372i
\(985\) 14.1421 42.4264i 0.450606 1.35182i
\(986\) 1.37258i 0.0437119i
\(987\) −69.9411 49.4558i −2.22625 1.57420i
\(988\) −10.3431 + 10.3431i −0.329059 + 0.329059i
\(989\) −1.57359 −0.0500374
\(990\) 0.0502525 + 2.77817i 0.00159713 + 0.0882962i
\(991\) 24.8284 0.788701 0.394350 0.918960i \(-0.370970\pi\)
0.394350 + 0.918960i \(0.370970\pi\)
\(992\) 9.89949 9.89949i 0.314309 0.314309i
\(993\) −9.17157 6.48528i −0.291051 0.205804i
\(994\) 4.97056i 0.157657i
\(995\) −14.4853 28.9706i −0.459214 0.918429i
\(996\) −40.0416 + 6.87006i −1.26877 + 0.217686i
\(997\) 36.7696 + 36.7696i 1.16450 + 1.16450i 0.983479 + 0.181025i \(0.0579415\pi\)
0.181025 + 0.983479i \(0.442059\pi\)
\(998\) −7.27208 7.27208i −0.230194 0.230194i
\(999\) 1.10051 0.615224i 0.0348184 0.0194648i
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 165.2.k.b.122.1 yes 4
3.2 odd 2 165.2.k.a.122.2 yes 4
5.2 odd 4 825.2.k.f.518.1 4
5.3 odd 4 165.2.k.a.23.2 4
5.4 even 2 825.2.k.c.782.2 4
15.2 even 4 825.2.k.c.518.2 4
15.8 even 4 inner 165.2.k.b.23.1 yes 4
15.14 odd 2 825.2.k.f.782.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.k.a.23.2 4 5.3 odd 4
165.2.k.a.122.2 yes 4 3.2 odd 2
165.2.k.b.23.1 yes 4 15.8 even 4 inner
165.2.k.b.122.1 yes 4 1.1 even 1 trivial
825.2.k.c.518.2 4 15.2 even 4
825.2.k.c.782.2 4 5.4 even 2
825.2.k.f.518.1 4 5.2 odd 4
825.2.k.f.782.1 4 15.14 odd 2