Properties

Label 930.2.o.c.161.2
Level $930$
Weight $2$
Character 930.161
Analytic conductor $7.426$
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] = [930,2,Mod(161,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.o (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: \(7.42608738798\)
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 161.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 930.161
Dual form 930.2.o.c.491.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.866025 - 1.50000i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.866025 - 1.50000i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(2.59808 - 4.50000i) q^{11} +(0.866025 + 1.50000i) q^{12} +(-3.00000 - 1.73205i) q^{13} +(-0.866025 + 0.500000i) q^{14} -1.73205i q^{15} +1.00000 q^{16} +(1.73205 + 3.00000i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.866025 - 1.50000i) q^{21} +(4.50000 + 2.59808i) q^{22} +6.92820 q^{23} +(-1.50000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(1.73205 - 3.00000i) q^{26} +5.19615 q^{27} +(-0.500000 - 0.866025i) q^{28} -1.73205 q^{29} +1.73205 q^{30} +(-5.50000 + 0.866025i) q^{31} +1.00000i q^{32} -9.00000 q^{33} +(-3.00000 + 1.73205i) q^{34} +1.00000i q^{35} +(1.50000 - 2.59808i) q^{36} +(6.00000 - 3.46410i) q^{37} +(3.46410 - 2.00000i) q^{38} +6.00000i q^{39} +(0.500000 - 0.866025i) q^{40} +(-5.19615 - 3.00000i) q^{41} +(1.50000 + 0.866025i) q^{42} +(3.00000 - 1.73205i) q^{43} +(-2.59808 + 4.50000i) q^{44} +(-2.59808 + 1.50000i) q^{45} +6.92820i q^{46} -12.0000i q^{47} +(-0.866025 - 1.50000i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.00000 - 5.19615i) q^{51} +(3.00000 + 1.73205i) q^{52} +(6.06218 - 10.5000i) q^{53} +5.19615i q^{54} +(4.50000 - 2.59808i) q^{55} +(0.866025 - 0.500000i) q^{56} +(-3.46410 + 6.00000i) q^{57} -1.73205i q^{58} +(12.9904 - 7.50000i) q^{59} +1.73205i q^{60} +3.46410i q^{61} +(-0.866025 - 5.50000i) q^{62} -3.00000 q^{63} -1.00000 q^{64} +(-1.73205 - 3.00000i) q^{65} -9.00000i q^{66} +(1.00000 - 1.73205i) q^{67} +(-1.73205 - 3.00000i) q^{68} +(-6.00000 - 10.3923i) q^{69} -1.00000 q^{70} +(10.3923 + 6.00000i) q^{71} +(2.59808 + 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(3.46410 + 6.00000i) q^{74} +(0.866025 - 1.50000i) q^{75} +(2.00000 + 3.46410i) q^{76} +5.19615 q^{77} -6.00000 q^{78} +(-9.00000 + 5.19615i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(3.00000 - 5.19615i) q^{82} +(-2.59808 + 4.50000i) q^{83} +(-0.866025 + 1.50000i) q^{84} +3.46410i q^{85} +(1.73205 + 3.00000i) q^{86} +(1.50000 + 2.59808i) q^{87} +(-4.50000 - 2.59808i) q^{88} -10.3923 q^{89} +(-1.50000 - 2.59808i) q^{90} -3.46410i q^{91} -6.92820 q^{92} +(6.06218 + 7.50000i) q^{93} +12.0000 q^{94} -4.00000i q^{95} +(1.50000 - 0.866025i) q^{96} -1.00000 q^{97} +(5.19615 + 3.00000i) q^{98} +(7.79423 + 13.5000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + 6 q^{6} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} + 6 q^{6} + 2 q^{7} - 6 q^{9} - 2 q^{10} - 12 q^{13} + 4 q^{16} - 8 q^{19} + 18 q^{22} - 6 q^{24} + 2 q^{25} - 2 q^{28} - 22 q^{31} - 36 q^{33} - 12 q^{34} + 6 q^{36} + 24 q^{37} + 2 q^{40} + 6 q^{42} + 12 q^{43} + 12 q^{49} + 12 q^{51} + 12 q^{52} + 18 q^{55} - 12 q^{63} - 4 q^{64} + 4 q^{67} - 24 q^{69} - 4 q^{70} + 24 q^{73} + 8 q^{76} - 24 q^{78} - 36 q^{79} - 18 q^{81} + 12 q^{82} + 6 q^{87} - 18 q^{88} - 6 q^{90} + 48 q^{94} + 6 q^{96} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.866025 1.50000i −0.500000 0.866025i
\(4\) −1.00000 −0.500000
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) 1.50000 0.866025i 0.612372 0.353553i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i \(-0.106148\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) 2.59808 4.50000i 0.783349 1.35680i −0.146631 0.989191i \(-0.546843\pi\)
0.929980 0.367610i \(-0.119824\pi\)
\(12\) 0.866025 + 1.50000i 0.250000 + 0.433013i
\(13\) −3.00000 1.73205i −0.832050 0.480384i 0.0225039 0.999747i \(-0.492836\pi\)
−0.854554 + 0.519362i \(0.826170\pi\)
\(14\) −0.866025 + 0.500000i −0.231455 + 0.133631i
\(15\) 1.73205i 0.447214i
\(16\) 1.00000 0.250000
\(17\) 1.73205 + 3.00000i 0.420084 + 0.727607i 0.995947 0.0899392i \(-0.0286673\pi\)
−0.575863 + 0.817546i \(0.695334\pi\)
\(18\) −2.59808 1.50000i −0.612372 0.353553i
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 0.866025 1.50000i 0.188982 0.327327i
\(22\) 4.50000 + 2.59808i 0.959403 + 0.553912i
\(23\) 6.92820 1.44463 0.722315 0.691564i \(-0.243078\pi\)
0.722315 + 0.691564i \(0.243078\pi\)
\(24\) −1.50000 + 0.866025i −0.306186 + 0.176777i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 1.73205 3.00000i 0.339683 0.588348i
\(27\) 5.19615 1.00000
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) −1.73205 −0.321634 −0.160817 0.986984i \(-0.551413\pi\)
−0.160817 + 0.986984i \(0.551413\pi\)
\(30\) 1.73205 0.316228
\(31\) −5.50000 + 0.866025i −0.987829 + 0.155543i
\(32\) 1.00000i 0.176777i
\(33\) −9.00000 −1.56670
\(34\) −3.00000 + 1.73205i −0.514496 + 0.297044i
\(35\) 1.00000i 0.169031i
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) 6.00000 3.46410i 0.986394 0.569495i 0.0821995 0.996616i \(-0.473806\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 3.46410 2.00000i 0.561951 0.324443i
\(39\) 6.00000i 0.960769i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −5.19615 3.00000i −0.811503 0.468521i 0.0359748 0.999353i \(-0.488546\pi\)
−0.847477 + 0.530831i \(0.821880\pi\)
\(42\) 1.50000 + 0.866025i 0.231455 + 0.133631i
\(43\) 3.00000 1.73205i 0.457496 0.264135i −0.253495 0.967337i \(-0.581580\pi\)
0.710991 + 0.703201i \(0.248247\pi\)
\(44\) −2.59808 + 4.50000i −0.391675 + 0.678401i
\(45\) −2.59808 + 1.50000i −0.387298 + 0.223607i
\(46\) 6.92820i 1.02151i
\(47\) 12.0000i 1.75038i −0.483779 0.875190i \(-0.660736\pi\)
0.483779 0.875190i \(-0.339264\pi\)
\(48\) −0.866025 1.50000i −0.125000 0.216506i
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) 3.00000 + 1.73205i 0.416025 + 0.240192i
\(53\) 6.06218 10.5000i 0.832704 1.44229i −0.0631819 0.998002i \(-0.520125\pi\)
0.895886 0.444284i \(-0.146542\pi\)
\(54\) 5.19615i 0.707107i
\(55\) 4.50000 2.59808i 0.606780 0.350325i
\(56\) 0.866025 0.500000i 0.115728 0.0668153i
\(57\) −3.46410 + 6.00000i −0.458831 + 0.794719i
\(58\) 1.73205i 0.227429i
\(59\) 12.9904 7.50000i 1.69120 0.976417i 0.737655 0.675178i \(-0.235933\pi\)
0.953549 0.301239i \(-0.0974001\pi\)
\(60\) 1.73205i 0.223607i
\(61\) 3.46410i 0.443533i 0.975100 + 0.221766i \(0.0711822\pi\)
−0.975100 + 0.221766i \(0.928818\pi\)
\(62\) −0.866025 5.50000i −0.109985 0.698501i
\(63\) −3.00000 −0.377964
\(64\) −1.00000 −0.125000
\(65\) −1.73205 3.00000i −0.214834 0.372104i
\(66\) 9.00000i 1.10782i
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) −1.73205 3.00000i −0.210042 0.363803i
\(69\) −6.00000 10.3923i −0.722315 1.25109i
\(70\) −1.00000 −0.119523
\(71\) 10.3923 + 6.00000i 1.23334 + 0.712069i 0.967725 0.252010i \(-0.0810916\pi\)
0.265615 + 0.964079i \(0.414425\pi\)
\(72\) 2.59808 + 1.50000i 0.306186 + 0.176777i
\(73\) 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i \(-0.200451\pi\)
−0.105937 + 0.994373i \(0.533784\pi\)
\(74\) 3.46410 + 6.00000i 0.402694 + 0.697486i
\(75\) 0.866025 1.50000i 0.100000 0.173205i
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) 5.19615 0.592157
\(78\) −6.00000 −0.679366
\(79\) −9.00000 + 5.19615i −1.01258 + 0.584613i −0.911946 0.410311i \(-0.865420\pi\)
−0.100633 + 0.994924i \(0.532087\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) −2.59808 + 4.50000i −0.285176 + 0.493939i −0.972652 0.232268i \(-0.925385\pi\)
0.687476 + 0.726207i \(0.258719\pi\)
\(84\) −0.866025 + 1.50000i −0.0944911 + 0.163663i
\(85\) 3.46410i 0.375735i
\(86\) 1.73205 + 3.00000i 0.186772 + 0.323498i
\(87\) 1.50000 + 2.59808i 0.160817 + 0.278543i
\(88\) −4.50000 2.59808i −0.479702 0.276956i
\(89\) −10.3923 −1.10158 −0.550791 0.834643i \(-0.685674\pi\)
−0.550791 + 0.834643i \(0.685674\pi\)
\(90\) −1.50000 2.59808i −0.158114 0.273861i
\(91\) 3.46410i 0.363137i
\(92\) −6.92820 −0.722315
\(93\) 6.06218 + 7.50000i 0.628619 + 0.777714i
\(94\) 12.0000 1.23771
\(95\) 4.00000i 0.410391i
\(96\) 1.50000 0.866025i 0.153093 0.0883883i
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) 5.19615 + 3.00000i 0.524891 + 0.303046i
\(99\) 7.79423 + 13.5000i 0.783349 + 1.35680i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 15.0000i 1.49256i −0.665635 0.746278i \(-0.731839\pi\)
0.665635 0.746278i \(-0.268161\pi\)
\(102\) 5.19615 + 3.00000i 0.514496 + 0.297044i
\(103\) −3.50000 + 6.06218i −0.344865 + 0.597324i −0.985329 0.170664i \(-0.945409\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) −1.73205 + 3.00000i −0.169842 + 0.294174i
\(105\) 1.50000 0.866025i 0.146385 0.0845154i
\(106\) 10.5000 + 6.06218i 1.01985 + 0.588811i
\(107\) −2.59808 + 1.50000i −0.251166 + 0.145010i −0.620298 0.784366i \(-0.712988\pi\)
0.369132 + 0.929377i \(0.379655\pi\)
\(108\) −5.19615 −0.500000
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 2.59808 + 4.50000i 0.247717 + 0.429058i
\(111\) −10.3923 6.00000i −0.986394 0.569495i
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) −6.00000 3.46410i −0.561951 0.324443i
\(115\) 6.00000 + 3.46410i 0.559503 + 0.323029i
\(116\) 1.73205 0.160817
\(117\) 9.00000 5.19615i 0.832050 0.480384i
\(118\) 7.50000 + 12.9904i 0.690431 + 1.19586i
\(119\) −1.73205 + 3.00000i −0.158777 + 0.275010i
\(120\) −1.73205 −0.158114
\(121\) −8.00000 13.8564i −0.727273 1.25967i
\(122\) −3.46410 −0.313625
\(123\) 10.3923i 0.937043i
\(124\) 5.50000 0.866025i 0.493915 0.0777714i
\(125\) 1.00000i 0.0894427i
\(126\) 3.00000i 0.267261i
\(127\) 10.5000 6.06218i 0.931724 0.537931i 0.0443678 0.999015i \(-0.485873\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −5.19615 3.00000i −0.457496 0.264135i
\(130\) 3.00000 1.73205i 0.263117 0.151911i
\(131\) −10.3923 + 6.00000i −0.907980 + 0.524222i −0.879781 0.475380i \(-0.842311\pi\)
−0.0281993 + 0.999602i \(0.508977\pi\)
\(132\) 9.00000 0.783349
\(133\) 2.00000 3.46410i 0.173422 0.300376i
\(134\) 1.73205 + 1.00000i 0.149626 + 0.0863868i
\(135\) 4.50000 + 2.59808i 0.387298 + 0.223607i
\(136\) 3.00000 1.73205i 0.257248 0.148522i
\(137\) −6.92820 + 12.0000i −0.591916 + 1.02523i 0.402058 + 0.915614i \(0.368295\pi\)
−0.993974 + 0.109615i \(0.965038\pi\)
\(138\) 10.3923 6.00000i 0.884652 0.510754i
\(139\) 20.7846i 1.76293i 0.472252 + 0.881464i \(0.343441\pi\)
−0.472252 + 0.881464i \(0.656559\pi\)
\(140\) 1.00000i 0.0845154i
\(141\) −18.0000 + 10.3923i −1.51587 + 0.875190i
\(142\) −6.00000 + 10.3923i −0.503509 + 0.872103i
\(143\) −15.5885 + 9.00000i −1.30357 + 0.752618i
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) −1.50000 0.866025i −0.124568 0.0719195i
\(146\) −3.46410 + 6.00000i −0.286691 + 0.496564i
\(147\) −10.3923 −0.857143
\(148\) −6.00000 + 3.46410i −0.493197 + 0.284747i
\(149\) −12.9904 + 7.50000i −1.06421 + 0.614424i −0.926595 0.376061i \(-0.877278\pi\)
−0.137619 + 0.990485i \(0.543945\pi\)
\(150\) 1.50000 + 0.866025i 0.122474 + 0.0707107i
\(151\) 8.66025i 0.704761i 0.935857 + 0.352381i \(0.114628\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) −3.46410 + 2.00000i −0.280976 + 0.162221i
\(153\) −10.3923 −0.840168
\(154\) 5.19615i 0.418718i
\(155\) −5.19615 2.00000i −0.417365 0.160644i
\(156\) 6.00000i 0.480384i
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) −5.19615 9.00000i −0.413384 0.716002i
\(159\) −21.0000 −1.66541
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 3.46410 + 6.00000i 0.273009 + 0.472866i
\(162\) 7.79423 4.50000i 0.612372 0.353553i
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) 5.19615 + 3.00000i 0.405751 + 0.234261i
\(165\) −7.79423 4.50000i −0.606780 0.350325i
\(166\) −4.50000 2.59808i −0.349268 0.201650i
\(167\) 5.19615 + 9.00000i 0.402090 + 0.696441i 0.993978 0.109580i \(-0.0349504\pi\)
−0.591888 + 0.806020i \(0.701617\pi\)
\(168\) −1.50000 0.866025i −0.115728 0.0668153i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) −3.46410 −0.265684
\(171\) 12.0000 0.917663
\(172\) −3.00000 + 1.73205i −0.228748 + 0.132068i
\(173\) 2.59808 + 1.50000i 0.197528 + 0.114043i 0.595502 0.803354i \(-0.296953\pi\)
−0.397974 + 0.917397i \(0.630287\pi\)
\(174\) −2.59808 + 1.50000i −0.196960 + 0.113715i
\(175\) −0.500000 + 0.866025i −0.0377964 + 0.0654654i
\(176\) 2.59808 4.50000i 0.195837 0.339200i
\(177\) −22.5000 12.9904i −1.69120 0.976417i
\(178\) 10.3923i 0.778936i
\(179\) −7.79423 13.5000i −0.582568 1.00904i −0.995174 0.0981277i \(-0.968715\pi\)
0.412606 0.910910i \(-0.364619\pi\)
\(180\) 2.59808 1.50000i 0.193649 0.111803i
\(181\) 3.00000 + 1.73205i 0.222988 + 0.128742i 0.607333 0.794447i \(-0.292239\pi\)
−0.384345 + 0.923190i \(0.625573\pi\)
\(182\) 3.46410 0.256776
\(183\) 5.19615 3.00000i 0.384111 0.221766i
\(184\) 6.92820i 0.510754i
\(185\) 6.92820 0.509372
\(186\) −7.50000 + 6.06218i −0.549927 + 0.444500i
\(187\) 18.0000 1.31629
\(188\) 12.0000i 0.875190i
\(189\) 2.59808 + 4.50000i 0.188982 + 0.327327i
\(190\) 4.00000 0.290191
\(191\) 10.3923 + 6.00000i 0.751961 + 0.434145i 0.826402 0.563081i \(-0.190384\pi\)
−0.0744412 + 0.997225i \(0.523717\pi\)
\(192\) 0.866025 + 1.50000i 0.0625000 + 0.108253i
\(193\) 5.50000 + 9.52628i 0.395899 + 0.685717i 0.993215 0.116289i \(-0.0370998\pi\)
−0.597317 + 0.802005i \(0.703766\pi\)
\(194\) 1.00000i 0.0717958i
\(195\) −3.00000 + 5.19615i −0.214834 + 0.372104i
\(196\) −3.00000 + 5.19615i −0.214286 + 0.371154i
\(197\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(198\) −13.5000 + 7.79423i −0.959403 + 0.553912i
\(199\) −10.5000 6.06218i −0.744325 0.429736i 0.0793146 0.996850i \(-0.474727\pi\)
−0.823640 + 0.567113i \(0.808060\pi\)
\(200\) 0.866025 0.500000i 0.0612372 0.0353553i
\(201\) −3.46410 −0.244339
\(202\) 15.0000 1.05540
\(203\) −0.866025 1.50000i −0.0607831 0.105279i
\(204\) −3.00000 + 5.19615i −0.210042 + 0.363803i
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) −6.06218 3.50000i −0.422372 0.243857i
\(207\) −10.3923 + 18.0000i −0.722315 + 1.25109i
\(208\) −3.00000 1.73205i −0.208013 0.120096i
\(209\) −20.7846 −1.43770
\(210\) 0.866025 + 1.50000i 0.0597614 + 0.103510i
\(211\) 5.00000 + 8.66025i 0.344214 + 0.596196i 0.985211 0.171347i \(-0.0548120\pi\)
−0.640996 + 0.767544i \(0.721479\pi\)
\(212\) −6.06218 + 10.5000i −0.416352 + 0.721143i
\(213\) 20.7846i 1.42414i
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) 3.46410 0.236250
\(216\) 5.19615i 0.353553i
\(217\) −3.50000 4.33013i −0.237595 0.293948i
\(218\) 4.00000i 0.270914i
\(219\) 12.0000i 0.810885i
\(220\) −4.50000 + 2.59808i −0.303390 + 0.175162i
\(221\) 12.0000i 0.807207i
\(222\) 6.00000 10.3923i 0.402694 0.697486i
\(223\) 13.5000 7.79423i 0.904027 0.521940i 0.0255224 0.999674i \(-0.491875\pi\)
0.878504 + 0.477734i \(0.158542\pi\)
\(224\) −0.866025 + 0.500000i −0.0578638 + 0.0334077i
\(225\) −3.00000 −0.200000
\(226\) 0 0
\(227\) 12.9904 + 7.50000i 0.862202 + 0.497792i 0.864749 0.502204i \(-0.167477\pi\)
−0.00254715 + 0.999997i \(0.500811\pi\)
\(228\) 3.46410 6.00000i 0.229416 0.397360i
\(229\) −24.0000 + 13.8564i −1.58596 + 0.915657i −0.592002 + 0.805936i \(0.701662\pi\)
−0.993962 + 0.109721i \(0.965004\pi\)
\(230\) −3.46410 + 6.00000i −0.228416 + 0.395628i
\(231\) −4.50000 7.79423i −0.296078 0.512823i
\(232\) 1.73205i 0.113715i
\(233\) 18.0000i 1.17922i 0.807688 + 0.589610i \(0.200718\pi\)
−0.807688 + 0.589610i \(0.799282\pi\)
\(234\) 5.19615 + 9.00000i 0.339683 + 0.588348i
\(235\) 6.00000 10.3923i 0.391397 0.677919i
\(236\) −12.9904 + 7.50000i −0.845602 + 0.488208i
\(237\) 15.5885 + 9.00000i 1.01258 + 0.584613i
\(238\) −3.00000 1.73205i −0.194461 0.112272i
\(239\) 13.8564 24.0000i 0.896296 1.55243i 0.0641045 0.997943i \(-0.479581\pi\)
0.832192 0.554488i \(-0.187086\pi\)
\(240\) 1.73205i 0.111803i
\(241\) −13.5000 + 7.79423i −0.869611 + 0.502070i −0.867219 0.497927i \(-0.834095\pi\)
−0.00239235 + 0.999997i \(0.500762\pi\)
\(242\) 13.8564 8.00000i 0.890724 0.514259i
\(243\) −7.79423 + 13.5000i −0.500000 + 0.866025i
\(244\) 3.46410i 0.221766i
\(245\) 5.19615 3.00000i 0.331970 0.191663i
\(246\) −10.3923 −0.662589
\(247\) 13.8564i 0.881662i
\(248\) 0.866025 + 5.50000i 0.0549927 + 0.349250i
\(249\) 9.00000 0.570352
\(250\) −1.00000 −0.0632456
\(251\) 5.19615 + 9.00000i 0.327978 + 0.568075i 0.982111 0.188305i \(-0.0602994\pi\)
−0.654132 + 0.756380i \(0.726966\pi\)
\(252\) 3.00000 0.188982
\(253\) 18.0000 31.1769i 1.13165 1.96008i
\(254\) 6.06218 + 10.5000i 0.380375 + 0.658829i
\(255\) 5.19615 3.00000i 0.325396 0.187867i
\(256\) 1.00000 0.0625000
\(257\) −20.7846 12.0000i −1.29651 0.748539i −0.316709 0.948523i \(-0.602578\pi\)
−0.979799 + 0.199983i \(0.935911\pi\)
\(258\) 3.00000 5.19615i 0.186772 0.323498i
\(259\) 6.00000 + 3.46410i 0.372822 + 0.215249i
\(260\) 1.73205 + 3.00000i 0.107417 + 0.186052i
\(261\) 2.59808 4.50000i 0.160817 0.278543i
\(262\) −6.00000 10.3923i −0.370681 0.642039i
\(263\) −3.46410 −0.213606 −0.106803 0.994280i \(-0.534061\pi\)
−0.106803 + 0.994280i \(0.534061\pi\)
\(264\) 9.00000i 0.553912i
\(265\) 10.5000 6.06218i 0.645010 0.372397i
\(266\) 3.46410 + 2.00000i 0.212398 + 0.122628i
\(267\) 9.00000 + 15.5885i 0.550791 + 0.953998i
\(268\) −1.00000 + 1.73205i −0.0610847 + 0.105802i
\(269\) 13.8564 24.0000i 0.844840 1.46331i −0.0409201 0.999162i \(-0.513029\pi\)
0.885760 0.464143i \(-0.153638\pi\)
\(270\) −2.59808 + 4.50000i −0.158114 + 0.273861i
\(271\) 12.1244i 0.736502i −0.929726 0.368251i \(-0.879957\pi\)
0.929726 0.368251i \(-0.120043\pi\)
\(272\) 1.73205 + 3.00000i 0.105021 + 0.181902i
\(273\) −5.19615 + 3.00000i −0.314485 + 0.181568i
\(274\) −12.0000 6.92820i −0.724947 0.418548i
\(275\) 5.19615 0.313340
\(276\) 6.00000 + 10.3923i 0.361158 + 0.625543i
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −20.7846 −1.24658
\(279\) 6.00000 15.5885i 0.359211 0.933257i
\(280\) 1.00000 0.0597614
\(281\) 12.0000i 0.715860i 0.933748 + 0.357930i \(0.116517\pi\)
−0.933748 + 0.357930i \(0.883483\pi\)
\(282\) −10.3923 18.0000i −0.618853 1.07188i
\(283\) −22.0000 −1.30776 −0.653882 0.756596i \(-0.726861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) −10.3923 6.00000i −0.616670 0.356034i
\(285\) −6.00000 + 3.46410i −0.355409 + 0.205196i
\(286\) −9.00000 15.5885i −0.532181 0.921765i
\(287\) 6.00000i 0.354169i
\(288\) −2.59808 1.50000i −0.153093 0.0883883i
\(289\) 2.50000 4.33013i 0.147059 0.254713i
\(290\) 0.866025 1.50000i 0.0508548 0.0880830i
\(291\) 0.866025 + 1.50000i 0.0507673 + 0.0879316i
\(292\) −6.00000 3.46410i −0.351123 0.202721i
\(293\) −7.79423 + 4.50000i −0.455344 + 0.262893i −0.710084 0.704117i \(-0.751343\pi\)
0.254741 + 0.967009i \(0.418010\pi\)
\(294\) 10.3923i 0.606092i
\(295\) 15.0000 0.873334
\(296\) −3.46410 6.00000i −0.201347 0.348743i
\(297\) 13.5000 23.3827i 0.783349 1.35680i
\(298\) −7.50000 12.9904i −0.434463 0.752513i
\(299\) −20.7846 12.0000i −1.20201 0.693978i
\(300\) −0.866025 + 1.50000i −0.0500000 + 0.0866025i
\(301\) 3.00000 + 1.73205i 0.172917 + 0.0998337i
\(302\) −8.66025 −0.498342
\(303\) −22.5000 + 12.9904i −1.29259 + 0.746278i
\(304\) −2.00000 3.46410i −0.114708 0.198680i
\(305\) −1.73205 + 3.00000i −0.0991769 + 0.171780i
\(306\) 10.3923i 0.594089i
\(307\) 7.00000 + 12.1244i 0.399511 + 0.691974i 0.993666 0.112377i \(-0.0358466\pi\)
−0.594154 + 0.804351i \(0.702513\pi\)
\(308\) −5.19615 −0.296078
\(309\) 12.1244 0.689730
\(310\) 2.00000 5.19615i 0.113592 0.295122i
\(311\) 30.0000i 1.70114i 0.525859 + 0.850572i \(0.323744\pi\)
−0.525859 + 0.850572i \(0.676256\pi\)
\(312\) 6.00000 0.339683
\(313\) −22.5000 + 12.9904i −1.27178 + 0.734260i −0.975322 0.220788i \(-0.929137\pi\)
−0.296453 + 0.955047i \(0.595804\pi\)
\(314\) 10.0000i 0.564333i
\(315\) −2.59808 1.50000i −0.146385 0.0845154i
\(316\) 9.00000 5.19615i 0.506290 0.292306i
\(317\) −2.59808 + 1.50000i −0.145922 + 0.0842484i −0.571184 0.820822i \(-0.693516\pi\)
0.425261 + 0.905071i \(0.360182\pi\)
\(318\) 21.0000i 1.17762i
\(319\) −4.50000 + 7.79423i −0.251952 + 0.436393i
\(320\) −0.866025 0.500000i −0.0484123 0.0279508i
\(321\) 4.50000 + 2.59808i 0.251166 + 0.145010i
\(322\) −6.00000 + 3.46410i −0.334367 + 0.193047i
\(323\) 6.92820 12.0000i 0.385496 0.667698i
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) 3.46410i 0.192154i
\(326\) 8.00000i 0.443079i
\(327\) 3.46410 + 6.00000i 0.191565 + 0.331801i
\(328\) −3.00000 + 5.19615i −0.165647 + 0.286910i
\(329\) 10.3923 6.00000i 0.572946 0.330791i
\(330\) 4.50000 7.79423i 0.247717 0.429058i
\(331\) −15.0000 8.66025i −0.824475 0.476011i 0.0274825 0.999622i \(-0.491251\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 2.59808 4.50000i 0.142588 0.246970i
\(333\) 20.7846i 1.13899i
\(334\) −9.00000 + 5.19615i −0.492458 + 0.284321i
\(335\) 1.73205 1.00000i 0.0946320 0.0546358i
\(336\) 0.866025 1.50000i 0.0472456 0.0818317i
\(337\) 12.1244i 0.660456i −0.943901 0.330228i \(-0.892874\pi\)
0.943901 0.330228i \(-0.107126\pi\)
\(338\) 0.866025 0.500000i 0.0471056 0.0271964i
\(339\) 0 0
\(340\) 3.46410i 0.187867i
\(341\) −10.3923 + 27.0000i −0.562775 + 1.46213i
\(342\) 12.0000i 0.648886i
\(343\) 13.0000 0.701934
\(344\) −1.73205 3.00000i −0.0933859 0.161749i
\(345\) 12.0000i 0.646058i
\(346\) −1.50000 + 2.59808i −0.0806405 + 0.139673i
\(347\) −9.52628 16.5000i −0.511397 0.885766i −0.999913 0.0132111i \(-0.995795\pi\)
0.488515 0.872555i \(-0.337539\pi\)
\(348\) −1.50000 2.59808i −0.0804084 0.139272i
\(349\) −8.00000 −0.428230 −0.214115 0.976808i \(-0.568687\pi\)
−0.214115 + 0.976808i \(0.568687\pi\)
\(350\) −0.866025 0.500000i −0.0462910 0.0267261i
\(351\) −15.5885 9.00000i −0.832050 0.480384i
\(352\) 4.50000 + 2.59808i 0.239851 + 0.138478i
\(353\) 17.3205 + 30.0000i 0.921878 + 1.59674i 0.796507 + 0.604629i \(0.206679\pi\)
0.125370 + 0.992110i \(0.459988\pi\)
\(354\) 12.9904 22.5000i 0.690431 1.19586i
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) 10.3923 0.550791
\(357\) 6.00000 0.317554
\(358\) 13.5000 7.79423i 0.713497 0.411938i
\(359\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(360\) 1.50000 + 2.59808i 0.0790569 + 0.136931i
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −1.73205 + 3.00000i −0.0910346 + 0.157676i
\(363\) −13.8564 + 24.0000i −0.727273 + 1.25967i
\(364\) 3.46410i 0.181568i
\(365\) 3.46410 + 6.00000i 0.181319 + 0.314054i
\(366\) 3.00000 + 5.19615i 0.156813 + 0.271607i
\(367\) 9.00000 + 5.19615i 0.469796 + 0.271237i 0.716154 0.697942i \(-0.245901\pi\)
−0.246358 + 0.969179i \(0.579234\pi\)
\(368\) 6.92820 0.361158
\(369\) 15.5885 9.00000i 0.811503 0.468521i
\(370\) 6.92820i 0.360180i
\(371\) 12.1244 0.629465
\(372\) −6.06218 7.50000i −0.314309 0.388857i
\(373\) −28.0000 −1.44979 −0.724893 0.688862i \(-0.758111\pi\)
−0.724893 + 0.688862i \(0.758111\pi\)
\(374\) 18.0000i 0.930758i
\(375\) 1.50000 0.866025i 0.0774597 0.0447214i
\(376\) −12.0000 −0.618853
\(377\) 5.19615 + 3.00000i 0.267615 + 0.154508i
\(378\) −4.50000 + 2.59808i −0.231455 + 0.133631i
\(379\) −7.00000 12.1244i −0.359566 0.622786i 0.628322 0.777953i \(-0.283742\pi\)
−0.987888 + 0.155167i \(0.950409\pi\)
\(380\) 4.00000i 0.205196i
\(381\) −18.1865 10.5000i −0.931724 0.537931i
\(382\) −6.00000 + 10.3923i −0.306987 + 0.531717i
\(383\) 5.19615 9.00000i 0.265511 0.459879i −0.702186 0.711993i \(-0.747793\pi\)
0.967697 + 0.252115i \(0.0811260\pi\)
\(384\) −1.50000 + 0.866025i −0.0765466 + 0.0441942i
\(385\) 4.50000 + 2.59808i 0.229341 + 0.132410i
\(386\) −9.52628 + 5.50000i −0.484875 + 0.279943i
\(387\) 10.3923i 0.528271i
\(388\) 1.00000 0.0507673
\(389\) 13.8564 + 24.0000i 0.702548 + 1.21685i 0.967569 + 0.252606i \(0.0812876\pi\)
−0.265022 + 0.964242i \(0.585379\pi\)
\(390\) −5.19615 3.00000i −0.263117 0.151911i
\(391\) 12.0000 + 20.7846i 0.606866 + 1.05112i
\(392\) −5.19615 3.00000i −0.262445 0.151523i
\(393\) 18.0000 + 10.3923i 0.907980 + 0.524222i
\(394\) 0 0
\(395\) −10.3923 −0.522894
\(396\) −7.79423 13.5000i −0.391675 0.678401i
\(397\) 14.0000 + 24.2487i 0.702640 + 1.21701i 0.967537 + 0.252731i \(0.0813288\pi\)
−0.264897 + 0.964277i \(0.585338\pi\)
\(398\) 6.06218 10.5000i 0.303870 0.526317i
\(399\) −6.92820 −0.346844
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 6.92820 0.345978 0.172989 0.984924i \(-0.444657\pi\)
0.172989 + 0.984924i \(0.444657\pi\)
\(402\) 3.46410i 0.172774i
\(403\) 18.0000 + 6.92820i 0.896644 + 0.345118i
\(404\) 15.0000i 0.746278i
\(405\) 9.00000i 0.447214i
\(406\) 1.50000 0.866025i 0.0744438 0.0429801i
\(407\) 36.0000i 1.78445i
\(408\) −5.19615 3.00000i −0.257248 0.148522i
\(409\) −10.5000 + 6.06218i −0.519192 + 0.299755i −0.736604 0.676324i \(-0.763572\pi\)
0.217412 + 0.976080i \(0.430238\pi\)
\(410\) 5.19615 3.00000i 0.256620 0.148159i
\(411\) 24.0000 1.18383
\(412\) 3.50000 6.06218i 0.172433 0.298662i
\(413\) 12.9904 + 7.50000i 0.639215 + 0.369051i
\(414\) −18.0000 10.3923i −0.884652 0.510754i
\(415\) −4.50000 + 2.59808i −0.220896 + 0.127535i
\(416\) 1.73205 3.00000i 0.0849208 0.147087i
\(417\) 31.1769 18.0000i 1.52674 0.881464i
\(418\) 20.7846i 1.01661i
\(419\) 33.0000i 1.61216i −0.591810 0.806078i \(-0.701586\pi\)
0.591810 0.806078i \(-0.298414\pi\)
\(420\) −1.50000 + 0.866025i −0.0731925 + 0.0422577i
\(421\) 10.0000 17.3205i 0.487370 0.844150i −0.512524 0.858673i \(-0.671290\pi\)
0.999895 + 0.0145228i \(0.00462290\pi\)
\(422\) −8.66025 + 5.00000i −0.421575 + 0.243396i
\(423\) 31.1769 + 18.0000i 1.51587 + 0.875190i
\(424\) −10.5000 6.06218i −0.509925 0.294405i
\(425\) −1.73205 + 3.00000i −0.0840168 + 0.145521i
\(426\) 20.7846 1.00702
\(427\) −3.00000 + 1.73205i −0.145180 + 0.0838198i
\(428\) 2.59808 1.50000i 0.125583 0.0725052i
\(429\) 27.0000 + 15.5885i 1.30357 + 0.752618i
\(430\) 3.46410i 0.167054i
\(431\) 25.9808 15.0000i 1.25145 0.722525i 0.280052 0.959985i \(-0.409648\pi\)
0.971397 + 0.237460i \(0.0763149\pi\)
\(432\) 5.19615 0.250000
\(433\) 27.7128i 1.33179i 0.746044 + 0.665896i \(0.231951\pi\)
−0.746044 + 0.665896i \(0.768049\pi\)
\(434\) 4.33013 3.50000i 0.207853 0.168005i
\(435\) 3.00000i 0.143839i
\(436\) 4.00000 0.191565
\(437\) −13.8564 24.0000i −0.662842 1.14808i
\(438\) 12.0000 0.573382
\(439\) 8.50000 14.7224i 0.405683 0.702663i −0.588718 0.808339i \(-0.700367\pi\)
0.994401 + 0.105675i \(0.0337004\pi\)
\(440\) −2.59808 4.50000i −0.123858 0.214529i
\(441\) 9.00000 + 15.5885i 0.428571 + 0.742307i
\(442\) 12.0000 0.570782
\(443\) 10.3923 + 6.00000i 0.493753 + 0.285069i 0.726130 0.687557i \(-0.241317\pi\)
−0.232377 + 0.972626i \(0.574650\pi\)
\(444\) 10.3923 + 6.00000i 0.493197 + 0.284747i
\(445\) −9.00000 5.19615i −0.426641 0.246321i
\(446\) 7.79423 + 13.5000i 0.369067 + 0.639244i
\(447\) 22.5000 + 12.9904i 1.06421 + 0.614424i
\(448\) −0.500000 0.866025i −0.0236228 0.0409159i
\(449\) −6.92820 −0.326962 −0.163481 0.986546i \(-0.552272\pi\)
−0.163481 + 0.986546i \(0.552272\pi\)
\(450\) 3.00000i 0.141421i
\(451\) −27.0000 + 15.5885i −1.27138 + 0.734032i
\(452\) 0 0
\(453\) 12.9904 7.50000i 0.610341 0.352381i
\(454\) −7.50000 + 12.9904i −0.351992 + 0.609669i
\(455\) 1.73205 3.00000i 0.0811998 0.140642i
\(456\) 6.00000 + 3.46410i 0.280976 + 0.162221i
\(457\) 6.92820i 0.324088i −0.986784 0.162044i \(-0.948191\pi\)
0.986784 0.162044i \(-0.0518086\pi\)
\(458\) −13.8564 24.0000i −0.647467 1.12145i
\(459\) 9.00000 + 15.5885i 0.420084 + 0.727607i
\(460\) −6.00000 3.46410i −0.279751 0.161515i
\(461\) 39.8372 1.85540 0.927701 0.373324i \(-0.121782\pi\)
0.927701 + 0.373324i \(0.121782\pi\)
\(462\) 7.79423 4.50000i 0.362620 0.209359i
\(463\) 12.1244i 0.563467i 0.959493 + 0.281733i \(0.0909093\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(464\) −1.73205 −0.0804084
\(465\) 1.50000 + 9.52628i 0.0695608 + 0.441771i
\(466\) −18.0000 −0.833834
\(467\) 27.0000i 1.24941i −0.780860 0.624705i \(-0.785219\pi\)
0.780860 0.624705i \(-0.214781\pi\)
\(468\) −9.00000 + 5.19615i −0.416025 + 0.240192i
\(469\) 2.00000 0.0923514
\(470\) 10.3923 + 6.00000i 0.479361 + 0.276759i
\(471\) −8.66025 15.0000i −0.399043 0.691164i
\(472\) −7.50000 12.9904i −0.345215 0.597931i
\(473\) 18.0000i 0.827641i
\(474\) −9.00000 + 15.5885i −0.413384 + 0.716002i
\(475\) 2.00000 3.46410i 0.0917663 0.158944i
\(476\) 1.73205 3.00000i 0.0793884 0.137505i
\(477\) 18.1865 + 31.5000i 0.832704 + 1.44229i
\(478\) 24.0000 + 13.8564i 1.09773 + 0.633777i
\(479\) 10.3923 6.00000i 0.474837 0.274147i −0.243426 0.969920i \(-0.578271\pi\)
0.718262 + 0.695773i \(0.244938\pi\)
\(480\) 1.73205 0.0790569
\(481\) −24.0000 −1.09431
\(482\) −7.79423 13.5000i −0.355017 0.614908i
\(483\) 6.00000 10.3923i 0.273009 0.472866i
\(484\) 8.00000 + 13.8564i 0.363636 + 0.629837i
\(485\) −0.866025 0.500000i −0.0393242 0.0227038i
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) 31.5000 + 18.1865i 1.42740 + 0.824110i 0.996915 0.0784867i \(-0.0250088\pi\)
0.430486 + 0.902597i \(0.358342\pi\)
\(488\) 3.46410 0.156813
\(489\) −6.92820 12.0000i −0.313304 0.542659i
\(490\) 3.00000 + 5.19615i 0.135526 + 0.234738i
\(491\) −18.1865 + 31.5000i −0.820747 + 1.42158i 0.0843802 + 0.996434i \(0.473109\pi\)
−0.905127 + 0.425141i \(0.860224\pi\)
\(492\) 10.3923i 0.468521i
\(493\) −3.00000 5.19615i −0.135113 0.234023i
\(494\) −13.8564 −0.623429
\(495\) 15.5885i 0.700649i
\(496\) −5.50000 + 0.866025i −0.246957 + 0.0388857i
\(497\) 12.0000i 0.538274i
\(498\) 9.00000i 0.403300i
\(499\) −21.0000 + 12.1244i −0.940089 + 0.542761i −0.889988 0.455983i \(-0.849288\pi\)
−0.0501009 + 0.998744i \(0.515954\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 9.00000 15.5885i 0.402090 0.696441i
\(502\) −9.00000 + 5.19615i −0.401690 + 0.231916i
\(503\) −31.1769 + 18.0000i −1.39011 + 0.802580i −0.993327 0.115332i \(-0.963207\pi\)
−0.396783 + 0.917912i \(0.629873\pi\)
\(504\) 3.00000i 0.133631i
\(505\) 7.50000 12.9904i 0.333746 0.578064i
\(506\) 31.1769 + 18.0000i 1.38598 + 0.800198i
\(507\) −0.866025 + 1.50000i −0.0384615 + 0.0666173i
\(508\) −10.5000 + 6.06218i −0.465862 + 0.268966i
\(509\) 12.9904 22.5000i 0.575789 0.997295i −0.420167 0.907447i \(-0.638028\pi\)
0.995955 0.0898481i \(-0.0286382\pi\)
\(510\) 3.00000 + 5.19615i 0.132842 + 0.230089i
\(511\) 6.92820i 0.306486i
\(512\) 1.00000i 0.0441942i
\(513\) −10.3923 18.0000i −0.458831 0.794719i
\(514\) 12.0000 20.7846i 0.529297 0.916770i
\(515\) −6.06218 + 3.50000i −0.267131 + 0.154228i
\(516\) 5.19615 + 3.00000i 0.228748 + 0.132068i
\(517\) −54.0000 31.1769i −2.37492 1.37116i
\(518\) −3.46410 + 6.00000i −0.152204 + 0.263625i
\(519\) 5.19615i 0.228086i
\(520\) −3.00000 + 1.73205i −0.131559 + 0.0759555i
\(521\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 4.50000 + 2.59808i 0.196960 + 0.113715i
\(523\) 17.3205i 0.757373i 0.925525 + 0.378686i \(0.123624\pi\)
−0.925525 + 0.378686i \(0.876376\pi\)
\(524\) 10.3923 6.00000i 0.453990 0.262111i
\(525\) 1.73205 0.0755929
\(526\) 3.46410i 0.151042i
\(527\) −12.1244 15.0000i −0.528145 0.653410i
\(528\) −9.00000 −0.391675
\(529\) 25.0000 1.08696
\(530\) 6.06218 + 10.5000i 0.263324 + 0.456091i
\(531\) 45.0000i 1.95283i
\(532\) −2.00000 + 3.46410i −0.0867110 + 0.150188i
\(533\) 10.3923 + 18.0000i 0.450141 + 0.779667i
\(534\) −15.5885 + 9.00000i −0.674579 + 0.389468i
\(535\) −3.00000 −0.129701
\(536\) −1.73205 1.00000i −0.0748132 0.0431934i
\(537\) −13.5000 + 23.3827i −0.582568 + 1.00904i
\(538\) 24.0000 + 13.8564i 1.03471 + 0.597392i
\(539\) −15.5885 27.0000i −0.671442 1.16297i
\(540\) −4.50000 2.59808i −0.193649 0.111803i
\(541\) 4.00000 + 6.92820i 0.171973 + 0.297867i 0.939110 0.343617i \(-0.111652\pi\)
−0.767136 + 0.641484i \(0.778319\pi\)
\(542\) 12.1244 0.520786
\(543\) 6.00000i 0.257485i
\(544\) −3.00000 + 1.73205i −0.128624 + 0.0742611i
\(545\) −3.46410 2.00000i −0.148386 0.0856706i
\(546\) −3.00000 5.19615i −0.128388 0.222375i
\(547\) 13.0000 22.5167i 0.555840 0.962743i −0.441998 0.897016i \(-0.645730\pi\)
0.997838 0.0657267i \(-0.0209366\pi\)
\(548\) 6.92820 12.0000i 0.295958 0.512615i
\(549\) −9.00000 5.19615i −0.384111 0.221766i
\(550\) 5.19615i 0.221565i
\(551\) 3.46410 + 6.00000i 0.147576 + 0.255609i
\(552\) −10.3923 + 6.00000i −0.442326 + 0.255377i
\(553\) −9.00000 5.19615i −0.382719 0.220963i
\(554\) 0 0
\(555\) −6.00000 10.3923i −0.254686 0.441129i
\(556\) 20.7846i 0.881464i
\(557\) 5.19615 0.220168 0.110084 0.993922i \(-0.464888\pi\)
0.110084 + 0.993922i \(0.464888\pi\)
\(558\) 15.5885 + 6.00000i 0.659912 + 0.254000i
\(559\) −12.0000 −0.507546
\(560\) 1.00000i 0.0422577i
\(561\) −15.5885 27.0000i −0.658145 1.13994i
\(562\) −12.0000 −0.506189
\(563\) −28.5788 16.5000i −1.20445 0.695392i −0.242912 0.970048i \(-0.578103\pi\)
−0.961542 + 0.274656i \(0.911436\pi\)
\(564\) 18.0000 10.3923i 0.757937 0.437595i
\(565\) 0 0
\(566\) 22.0000i 0.924729i
\(567\) 4.50000 7.79423i 0.188982 0.327327i
\(568\) 6.00000 10.3923i 0.251754 0.436051i
\(569\) 20.7846 36.0000i 0.871336 1.50920i 0.0107211 0.999943i \(-0.496587\pi\)
0.860615 0.509256i \(-0.170079\pi\)
\(570\) −3.46410 6.00000i −0.145095 0.251312i
\(571\) 36.0000 + 20.7846i 1.50655 + 0.869809i 0.999971 + 0.00761713i \(0.00242463\pi\)
0.506582 + 0.862192i \(0.330909\pi\)
\(572\) 15.5885 9.00000i 0.651786 0.376309i
\(573\) 20.7846i 0.868290i
\(574\) 6.00000 0.250435
\(575\) 3.46410 + 6.00000i 0.144463 + 0.250217i
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) 1.00000 + 1.73205i 0.0416305 + 0.0721062i 0.886090 0.463513i \(-0.153411\pi\)
−0.844459 + 0.535620i \(0.820078\pi\)
\(578\) 4.33013 + 2.50000i 0.180110 + 0.103986i
\(579\) 9.52628 16.5000i 0.395899 0.685717i
\(580\) 1.50000 + 0.866025i 0.0622841 + 0.0359597i
\(581\) −5.19615 −0.215573
\(582\) −1.50000 + 0.866025i −0.0621770 + 0.0358979i
\(583\) −31.5000 54.5596i −1.30460 2.25963i
\(584\) 3.46410 6.00000i 0.143346 0.248282i
\(585\) 10.3923 0.429669
\(586\) −4.50000 7.79423i −0.185893 0.321977i
\(587\) 25.9808 1.07234 0.536170 0.844110i \(-0.319870\pi\)
0.536170 + 0.844110i \(0.319870\pi\)
\(588\) 10.3923 0.428571
\(589\) 14.0000 + 17.3205i 0.576860 + 0.713679i
\(590\) 15.0000i 0.617540i
\(591\) 0 0
\(592\) 6.00000 3.46410i 0.246598 0.142374i
\(593\) 6.00000i 0.246390i −0.992382 0.123195i \(-0.960686\pi\)
0.992382 0.123195i \(-0.0393141\pi\)
\(594\) 23.3827 + 13.5000i 0.959403 + 0.553912i
\(595\) −3.00000 + 1.73205i −0.122988 + 0.0710072i
\(596\) 12.9904 7.50000i 0.532107 0.307212i
\(597\) 21.0000i 0.859473i
\(598\) 12.0000 20.7846i 0.490716 0.849946i
\(599\) 5.19615 + 3.00000i 0.212309 + 0.122577i 0.602384 0.798206i \(-0.294218\pi\)
−0.390075 + 0.920783i \(0.627551\pi\)
\(600\) −1.50000 0.866025i −0.0612372 0.0353553i
\(601\) −12.0000 + 6.92820i −0.489490 + 0.282607i −0.724363 0.689419i \(-0.757866\pi\)
0.234873 + 0.972026i \(0.424533\pi\)
\(602\) −1.73205 + 3.00000i −0.0705931 + 0.122271i
\(603\) 3.00000 + 5.19615i 0.122169 + 0.211604i
\(604\) 8.66025i 0.352381i
\(605\) 16.0000i 0.650493i
\(606\) −12.9904 22.5000i −0.527698 0.914000i
\(607\) 16.0000 27.7128i 0.649420 1.12483i −0.333842 0.942629i \(-0.608345\pi\)
0.983262 0.182199i \(-0.0583216\pi\)
\(608\) 3.46410 2.00000i 0.140488 0.0811107i
\(609\) −1.50000 + 2.59808i −0.0607831 + 0.105279i
\(610\) −3.00000 1.73205i −0.121466 0.0701287i
\(611\) −20.7846 + 36.0000i −0.840855 + 1.45640i
\(612\) 10.3923 0.420084
\(613\) 3.00000 1.73205i 0.121169 0.0699569i −0.438191 0.898882i \(-0.644380\pi\)
0.559359 + 0.828925i \(0.311047\pi\)
\(614\) −12.1244 + 7.00000i −0.489299 + 0.282497i
\(615\) −5.19615 + 9.00000i −0.209529 + 0.362915i
\(616\) 5.19615i 0.209359i
\(617\) −36.3731 + 21.0000i −1.46432 + 0.845428i −0.999207 0.0398207i \(-0.987321\pi\)
−0.465118 + 0.885249i \(0.653988\pi\)
\(618\) 12.1244i 0.487713i
\(619\) 20.7846i 0.835404i 0.908584 + 0.417702i \(0.137164\pi\)
−0.908584 + 0.417702i \(0.862836\pi\)
\(620\) 5.19615 + 2.00000i 0.208683 + 0.0803219i
\(621\) 36.0000 1.44463
\(622\) −30.0000 −1.20289
\(623\) −5.19615 9.00000i −0.208179 0.360577i
\(624\) 6.00000i 0.240192i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −12.9904 22.5000i −0.519200 0.899281i
\(627\) 18.0000 + 31.1769i 0.718851 + 1.24509i
\(628\) −10.0000 −0.399043
\(629\) 20.7846 + 12.0000i 0.828737 + 0.478471i
\(630\) 1.50000 2.59808i 0.0597614 0.103510i
\(631\) 10.5000 + 6.06218i 0.417998 + 0.241331i 0.694221 0.719762i \(-0.255749\pi\)
−0.276222 + 0.961094i \(0.589083\pi\)
\(632\) 5.19615 + 9.00000i 0.206692 + 0.358001i
\(633\) 8.66025 15.0000i 0.344214 0.596196i
\(634\) −1.50000 2.59808i −0.0595726 0.103183i
\(635\) 12.1244 0.481140
\(636\) 21.0000 0.832704
\(637\) −18.0000 + 10.3923i −0.713186 + 0.411758i
\(638\) −7.79423 4.50000i −0.308576 0.178157i
\(639\) −31.1769 + 18.0000i −1.23334 + 0.712069i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 1.73205 3.00000i 0.0684119 0.118493i −0.829790 0.558075i \(-0.811540\pi\)
0.898202 + 0.439582i \(0.144873\pi\)
\(642\) −2.59808 + 4.50000i −0.102538 + 0.177601i
\(643\) 3.46410i 0.136611i 0.997664 + 0.0683054i \(0.0217592\pi\)
−0.997664 + 0.0683054i \(0.978241\pi\)
\(644\) −3.46410 6.00000i −0.136505 0.236433i
\(645\) −3.00000 5.19615i −0.118125 0.204598i
\(646\) 12.0000 + 6.92820i 0.472134 + 0.272587i
\(647\) −17.3205 −0.680939 −0.340470 0.940255i \(-0.610586\pi\)
−0.340470 + 0.940255i \(0.610586\pi\)
\(648\) −7.79423 + 4.50000i −0.306186 + 0.176777i
\(649\) 77.9423i 3.05950i
\(650\) 3.46410 0.135873
\(651\) −3.46410 + 9.00000i −0.135769 + 0.352738i
\(652\) −8.00000 −0.313304
\(653\) 9.00000i 0.352197i −0.984373 0.176099i \(-0.943652\pi\)
0.984373 0.176099i \(-0.0563478\pi\)
\(654\) −6.00000 + 3.46410i −0.234619 + 0.135457i
\(655\) −12.0000 −0.468879
\(656\) −5.19615 3.00000i −0.202876 0.117130i
\(657\) −18.0000 + 10.3923i −0.702247 + 0.405442i
\(658\) 6.00000 + 10.3923i 0.233904 + 0.405134i
\(659\) 21.0000i 0.818044i 0.912525 + 0.409022i \(0.134130\pi\)
−0.912525 + 0.409022i \(0.865870\pi\)
\(660\) 7.79423 + 4.50000i 0.303390 + 0.175162i
\(661\) 2.00000 3.46410i 0.0777910 0.134738i −0.824506 0.565854i \(-0.808547\pi\)
0.902297 + 0.431116i \(0.141880\pi\)
\(662\) 8.66025 15.0000i 0.336590 0.582992i
\(663\) −18.0000 + 10.3923i −0.699062 + 0.403604i
\(664\) 4.50000 + 2.59808i 0.174634 + 0.100825i
\(665\) 3.46410 2.00000i 0.134332 0.0775567i
\(666\) −20.7846 −0.805387
\(667\) −12.0000 −0.464642
\(668\) −5.19615 9.00000i −0.201045 0.348220i
\(669\) −23.3827 13.5000i −0.904027 0.521940i
\(670\) 1.00000 + 1.73205i 0.0386334 + 0.0669150i
\(671\) 15.5885 + 9.00000i 0.601786 + 0.347441i
\(672\) 1.50000 + 0.866025i 0.0578638 + 0.0334077i
\(673\) 4.50000 + 2.59808i 0.173462 + 0.100148i 0.584217 0.811597i \(-0.301402\pi\)
−0.410755 + 0.911746i \(0.634735\pi\)
\(674\) 12.1244 0.467013
\(675\) 2.59808 + 4.50000i 0.100000 + 0.173205i
\(676\) 0.500000 + 0.866025i 0.0192308 + 0.0333087i
\(677\) 16.4545 28.5000i 0.632397 1.09534i −0.354663 0.934994i \(-0.615404\pi\)
0.987060 0.160350i \(-0.0512622\pi\)
\(678\) 0 0
\(679\) −0.500000 0.866025i −0.0191882 0.0332350i
\(680\) 3.46410 0.132842
\(681\) 25.9808i 0.995585i
\(682\) −27.0000 10.3923i −1.03388 0.397942i
\(683\) 9.00000i 0.344375i −0.985064 0.172188i \(-0.944916\pi\)
0.985064 0.172188i \(-0.0550836\pi\)
\(684\) −12.0000 −0.458831
\(685\) −12.0000 + 6.92820i −0.458496 + 0.264713i
\(686\) 13.0000i 0.496342i
\(687\) 41.5692 + 24.0000i 1.58596 + 0.915657i
\(688\) 3.00000 1.73205i 0.114374 0.0660338i
\(689\) −36.3731 + 21.0000i −1.38570 + 0.800036i
\(690\) 12.0000 0.456832
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) −2.59808 1.50000i −0.0987640 0.0570214i
\(693\) −7.79423 + 13.5000i −0.296078 + 0.512823i
\(694\) 16.5000 9.52628i 0.626331 0.361613i
\(695\) −10.3923 + 18.0000i −0.394203 + 0.682779i
\(696\) 2.59808 1.50000i 0.0984798 0.0568574i
\(697\) 20.7846i 0.787273i
\(698\) 8.00000i 0.302804i
\(699\) 27.0000 15.5885i 1.02123 0.589610i
\(700\) 0.500000 0.866025i 0.0188982 0.0327327i
\(701\) −12.9904 + 7.50000i −0.490640 + 0.283271i −0.724840 0.688917i \(-0.758086\pi\)
0.234200 + 0.972188i \(0.424753\pi\)
\(702\) 9.00000 15.5885i 0.339683 0.588348i
\(703\) −24.0000 13.8564i −0.905177 0.522604i
\(704\) −2.59808 + 4.50000i −0.0979187 + 0.169600i
\(705\) −20.7846 −0.782794
\(706\) −30.0000 + 17.3205i −1.12906 + 0.651866i
\(707\) 12.9904 7.50000i 0.488554 0.282067i
\(708\) 22.5000 + 12.9904i 0.845602 + 0.488208i
\(709\) 24.2487i 0.910679i 0.890318 + 0.455340i \(0.150482\pi\)
−0.890318 + 0.455340i \(0.849518\pi\)
\(710\) −10.3923 + 6.00000i −0.390016 + 0.225176i
\(711\) 31.1769i 1.16923i
\(712\) 10.3923i 0.389468i
\(713\) −38.1051 + 6.00000i −1.42705 + 0.224702i
\(714\) 6.00000i 0.224544i
\(715\) −18.0000 −0.673162
\(716\) 7.79423 + 13.5000i 0.291284 + 0.504519i
\(717\) −48.0000 −1.79259
\(718\) 0 0
\(719\) 3.46410 + 6.00000i 0.129189 + 0.223762i 0.923363 0.383929i \(-0.125429\pi\)
−0.794173 + 0.607691i \(0.792096\pi\)
\(720\) −2.59808 + 1.50000i −0.0968246 + 0.0559017i
\(721\) −7.00000 −0.260694
\(722\) 2.59808 + 1.50000i 0.0966904 + 0.0558242i
\(723\) 23.3827 + 13.5000i 0.869611 + 0.502070i
\(724\) −3.00000 1.73205i −0.111494 0.0643712i
\(725\) −0.866025 1.50000i −0.0321634 0.0557086i
\(726\) −24.0000 13.8564i −0.890724 0.514259i
\(727\) −17.5000 30.3109i −0.649039 1.12417i −0.983353 0.181707i \(-0.941838\pi\)
0.334314 0.942462i \(-0.391496\pi\)
\(728\) −3.46410 −0.128388
\(729\) 27.0000 1.00000
\(730\) −6.00000 + 3.46410i −0.222070 + 0.128212i
\(731\) 10.3923 + 6.00000i 0.384373 + 0.221918i
\(732\) −5.19615 + 3.00000i −0.192055 + 0.110883i
\(733\) 7.00000 12.1244i 0.258551 0.447823i −0.707303 0.706910i \(-0.750088\pi\)
0.965854 + 0.259087i \(0.0834217\pi\)
\(734\) −5.19615 + 9.00000i −0.191793 + 0.332196i
\(735\) −9.00000 5.19615i −0.331970 0.191663i
\(736\) 6.92820i 0.255377i
\(737\) −5.19615 9.00000i −0.191403 0.331519i
\(738\) 9.00000 + 15.5885i 0.331295 + 0.573819i
\(739\) −3.00000 1.73205i −0.110357 0.0637145i 0.443806 0.896123i \(-0.353628\pi\)
−0.554162 + 0.832409i \(0.686961\pi\)
\(740\) −6.92820 −0.254686
\(741\) 20.7846 12.0000i 0.763542 0.440831i
\(742\) 12.1244i 0.445099i
\(743\) 20.7846 0.762513 0.381257 0.924469i \(-0.375491\pi\)
0.381257 + 0.924469i \(0.375491\pi\)
\(744\) 7.50000 6.06218i 0.274963 0.222250i
\(745\) −15.0000 −0.549557
\(746\) 28.0000i 1.02515i
\(747\) −7.79423 13.5000i −0.285176 0.493939i
\(748\) −18.0000 −0.658145
\(749\) −2.59808 1.50000i −0.0949316 0.0548088i
\(750\) 0.866025 + 1.50000i 0.0316228 + 0.0547723i
\(751\) −15.5000 26.8468i −0.565603 0.979653i −0.996993 0.0774878i \(-0.975310\pi\)
0.431390 0.902165i \(-0.358023\pi\)
\(752\) 12.0000i 0.437595i
\(753\) 9.00000 15.5885i 0.327978 0.568075i
\(754\) −3.00000 + 5.19615i −0.109254 + 0.189233i
\(755\) −4.33013 + 7.50000i −0.157589 + 0.272953i
\(756\) −2.59808 4.50000i −0.0944911 0.163663i
\(757\) −3.00000 1.73205i −0.109037 0.0629525i 0.444490 0.895784i \(-0.353385\pi\)
−0.553527 + 0.832831i \(0.686718\pi\)
\(758\) 12.1244 7.00000i 0.440376 0.254251i
\(759\) −62.3538 −2.26330
\(760\) −4.00000 −0.145095
\(761\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 10.5000 18.1865i 0.380375 0.658829i
\(763\) −2.00000 3.46410i −0.0724049 0.125409i
\(764\) −10.3923 6.00000i −0.375980 0.217072i
\(765\) −9.00000 5.19615i −0.325396 0.187867i
\(766\) 9.00000 + 5.19615i 0.325183 + 0.187745i
\(767\) −51.9615 −1.87622
\(768\) −0.866025 1.50000i −0.0312500 0.0541266i
\(769\) 11.5000 + 19.9186i 0.414701 + 0.718283i 0.995397 0.0958377i \(-0.0305530\pi\)
−0.580696 + 0.814120i \(0.697220\pi\)
\(770\) −2.59808 + 4.50000i −0.0936282 + 0.162169i
\(771\) 41.5692i 1.49708i
\(772\) −5.50000 9.52628i −0.197949 0.342858i
\(773\) 27.7128 0.996761 0.498380 0.866959i \(-0.333928\pi\)
0.498380 + 0.866959i \(0.333928\pi\)
\(774\) −10.3923 −0.373544
\(775\) −3.50000 4.33013i −0.125724 0.155543i
\(776\) 1.00000i 0.0358979i
\(777\) 12.0000i 0.430498i
\(778\) −24.0000 + 13.8564i −0.860442 + 0.496776i
\(779\) 24.0000i 0.859889i
\(780\) 3.00000 5.19615i 0.107417 0.186052i
\(781\) 54.0000 31.1769i 1.93227 1.11560i
\(782\) −20.7846 + 12.0000i −0.743256 + 0.429119i
\(783\) −9.00000 −0.321634
\(784\) 3.00000 5.19615i 0.107143 0.185577i
\(785\) 8.66025 + 5.00000i 0.309098 + 0.178458i
\(786\) −10.3923 + 18.0000i −0.370681 + 0.642039i
\(787\) −9.00000 + 5.19615i −0.320815 + 0.185223i −0.651756 0.758429i \(-0.725967\pi\)
0.330941 + 0.943652i \(0.392634\pi\)
\(788\) 0 0
\(789\) 3.00000 + 5.19615i 0.106803 + 0.184988i
\(790\) 10.3923i 0.369742i
\(791\) 0 0
\(792\) 13.5000 7.79423i 0.479702 0.276956i
\(793\) 6.00000 10.3923i 0.213066 0.369042i
\(794\) −24.2487 + 14.0000i −0.860555 + 0.496841i
\(795\) −18.1865 10.5000i −0.645010 0.372397i
\(796\) 10.5000 + 6.06218i 0.372163 + 0.214868i
\(797\) −19.9186 + 34.5000i −0.705552 + 1.22205i 0.260939 + 0.965355i \(0.415968\pi\)
−0.966492 + 0.256697i \(0.917366\pi\)
\(798\) 6.92820i 0.245256i
\(799\) 36.0000 20.7846i 1.27359 0.735307i
\(800\) −0.866025 + 0.500000i −0.0306186 + 0.0176777i
\(801\) 15.5885 27.0000i 0.550791 0.953998i
\(802\) 6.92820i 0.244643i
\(803\) 31.1769 18.0000i 1.10021 0.635206i
\(804\) 3.46410 0.122169
\(805\) 6.92820i 0.244187i
\(806\) −6.92820 + 18.0000i −0.244036 + 0.634023i
\(807\) −48.0000 −1.68968
\(808\) −15.0000 −0.527698
\(809\) 13.8564 + 24.0000i 0.487165 + 0.843795i 0.999891 0.0147574i \(-0.00469758\pi\)
−0.512726 + 0.858552i \(0.671364\pi\)
\(810\) 9.00000 0.316228
\(811\) −20.0000 + 34.6410i −0.702295 + 1.21641i 0.265364 + 0.964148i \(0.414508\pi\)
−0.967659 + 0.252262i \(0.918825\pi\)
\(812\) 0.866025 + 1.50000i 0.0303915 + 0.0526397i
\(813\) −18.1865 + 10.5000i −0.637830 + 0.368251i
\(814\) 36.0000 1.26180
\(815\) 6.92820 + 4.00000i 0.242684 + 0.140114i
\(816\) 3.00000 5.19615i 0.105021 0.181902i
\(817\) −12.0000 6.92820i −0.419827 0.242387i
\(818\) −6.06218 10.5000i −0.211959 0.367124i
\(819\) 9.00000 + 5.19615i 0.314485 + 0.181568i
\(820\) 3.00000 + 5.19615i 0.104765 + 0.181458i
\(821\) −12.1244 −0.423143 −0.211571 0.977363i \(-0.567858\pi\)
−0.211571 + 0.977363i \(0.567858\pi\)
\(822\) 24.0000i 0.837096i
\(823\) 1.50000 0.866025i 0.0522867 0.0301877i −0.473629 0.880725i \(-0.657056\pi\)
0.525915 + 0.850537i \(0.323723\pi\)
\(824\) 6.06218 + 3.50000i 0.211186 + 0.121928i
\(825\) −4.50000 7.79423i −0.156670 0.271360i
\(826\) −7.50000 + 12.9904i −0.260958 + 0.451993i
\(827\) 19.0526 33.0000i 0.662522 1.14752i −0.317428 0.948282i \(-0.602819\pi\)
0.979951 0.199240i \(-0.0638474\pi\)
\(828\) 10.3923 18.0000i 0.361158 0.625543i
\(829\) 3.46410i 0.120313i −0.998189 0.0601566i \(-0.980840\pi\)
0.998189 0.0601566i \(-0.0191600\pi\)
\(830\) −2.59808 4.50000i −0.0901805 0.156197i
\(831\) 0 0
\(832\) 3.00000 + 1.73205i 0.104006 + 0.0600481i
\(833\) 20.7846 0.720144
\(834\) 18.0000 + 31.1769i 0.623289 + 1.07957i
\(835\) 10.3923i 0.359641i
\(836\) 20.7846 0.718851
\(837\) −28.5788 + 4.50000i −0.987829 + 0.155543i
\(838\) 33.0000 1.13997
\(839\) 12.0000i 0.414286i −0.978311 0.207143i \(-0.933583\pi\)
0.978311 0.207143i \(-0.0664165\pi\)
\(840\) −0.866025 1.50000i −0.0298807 0.0517549i
\(841\) −26.0000 −0.896552
\(842\) 17.3205 + 10.0000i 0.596904 + 0.344623i
\(843\) 18.0000 10.3923i 0.619953 0.357930i
\(844\) −5.00000 8.66025i −0.172107 0.298098i
\(845\) 1.00000i 0.0344010i
\(846\) −18.0000 + 31.1769i −0.618853 + 1.07188i
\(847\) 8.00000 13.8564i 0.274883 0.476112i
\(848\) 6.06218 10.5000i 0.208176 0.360571i
\(849\) 19.0526 + 33.0000i 0.653882 + 1.13256i
\(850\) −3.00000 1.73205i −0.102899 0.0594089i
\(851\) 41.5692 24.0000i 1.42497 0.822709i
\(852\) 20.7846i 0.712069i
\(853\) −2.00000 −0.0684787 −0.0342393 0.999414i \(-0.510901\pi\)
−0.0342393 + 0.999414i \(0.510901\pi\)
\(854\) −1.73205 3.00000i −0.0592696 0.102658i
\(855\) 10.3923 + 6.00000i 0.355409 + 0.205196i
\(856\) 1.50000 + 2.59808i 0.0512689 + 0.0888004i
\(857\) 25.9808 + 15.0000i 0.887486 + 0.512390i 0.873119 0.487507i \(-0.162093\pi\)
0.0143666 + 0.999897i \(0.495427\pi\)
\(858\) −15.5885 + 27.0000i −0.532181 + 0.921765i
\(859\) −3.00000 1.73205i −0.102359 0.0590968i 0.447947 0.894060i \(-0.352155\pi\)
−0.550305 + 0.834963i \(0.685489\pi\)
\(860\) −3.46410 −0.118125
\(861\) −9.00000 + 5.19615i −0.306719 + 0.177084i
\(862\) 15.0000 + 25.9808i 0.510902 + 0.884908i
\(863\) 6.92820 12.0000i 0.235839 0.408485i −0.723677 0.690138i \(-0.757550\pi\)
0.959516 + 0.281654i \(0.0908829\pi\)
\(864\) 5.19615i 0.176777i
\(865\) 1.50000 + 2.59808i 0.0510015 + 0.0883372i
\(866\) −27.7128 −0.941720
\(867\) −8.66025 −0.294118
\(868\) 3.50000 + 4.33013i 0.118798 + 0.146974i
\(869\) 54.0000i 1.83182i
\(870\) −3.00000 −0.101710
\(871\) −6.00000 + 3.46410i −0.203302 + 0.117377i
\(872\) 4.00000i 0.135457i
\(873\) 1.50000 2.59808i 0.0507673 0.0879316i
\(874\) 24.0000 13.8564i 0.811812 0.468700i
\(875\) −0.866025 + 0.500000i −0.0292770 + 0.0169031i
\(876\) 12.0000i 0.405442i
\(877\) −17.0000 + 29.4449i −0.574049 + 0.994282i 0.422095 + 0.906552i \(0.361295\pi\)
−0.996144 + 0.0877308i \(0.972038\pi\)
\(878\) 14.7224 + 8.50000i 0.496858 + 0.286861i
\(879\) 13.5000 + 7.79423i 0.455344 + 0.262893i
\(880\) 4.50000 2.59808i 0.151695 0.0875811i
\(881\) 3.46410 6.00000i 0.116709 0.202145i −0.801753 0.597656i \(-0.796099\pi\)
0.918461 + 0.395511i \(0.129432\pi\)
\(882\) −15.5885 + 9.00000i −0.524891 + 0.303046i
\(883\) 20.7846i 0.699458i 0.936851 + 0.349729i \(0.113726\pi\)
−0.936851 + 0.349729i \(0.886274\pi\)
\(884\) 12.0000i 0.403604i
\(885\) −12.9904 22.5000i −0.436667 0.756329i
\(886\) −6.00000 + 10.3923i −0.201574 + 0.349136i
\(887\) −20.7846 + 12.0000i −0.697879 + 0.402921i −0.806557 0.591156i \(-0.798672\pi\)
0.108678 + 0.994077i \(0.465338\pi\)
\(888\) −6.00000 + 10.3923i −0.201347 + 0.348743i
\(889\) 10.5000 + 6.06218i 0.352159 + 0.203319i
\(890\) 5.19615 9.00000i 0.174175 0.301681i
\(891\) −46.7654 −1.56670
\(892\) −13.5000 + 7.79423i −0.452013 + 0.260970i
\(893\) −41.5692 + 24.0000i −1.39106 + 0.803129i
\(894\) −12.9904 + 22.5000i −0.434463 + 0.752513i
\(895\) 15.5885i 0.521065i
\(896\) 0.866025 0.500000i 0.0289319 0.0167038i
\(897\) 41.5692i 1.38796i
\(898\) 6.92820i 0.231197i
\(899\) 9.52628 1.50000i 0.317719 0.0500278i
\(900\) 3.00000 0.100000
\(901\) 42.0000 1.39922
\(902\) −15.5885 27.0000i −0.519039 0.899002i
\(903\) 6.00000i 0.199667i
\(904\) 0 0
\(905\) 1.73205 + 3.00000i 0.0575753 + 0.0997234i
\(906\) 7.50000 + 12.9904i 0.249171 + 0.431577i
\(907\) 16.0000 0.531271 0.265636 0.964073i \(-0.414418\pi\)
0.265636 + 0.964073i \(0.414418\pi\)
\(908\) −12.9904 7.50000i −0.431101 0.248896i
\(909\) 38.9711 + 22.5000i 1.29259 + 0.746278i
\(910\) 3.00000 + 1.73205i 0.0994490 + 0.0574169i
\(911\) −8.66025 15.0000i −0.286927 0.496972i 0.686148 0.727462i \(-0.259300\pi\)
−0.973075 + 0.230490i \(0.925967\pi\)
\(912\) −3.46410 + 6.00000i −0.114708 + 0.198680i
\(913\) 13.5000 + 23.3827i 0.446785 + 0.773854i
\(914\) 6.92820 0.229165
\(915\) 6.00000 0.198354
\(916\) 24.0000 13.8564i 0.792982 0.457829i
\(917\) −10.3923 6.00000i −0.343184 0.198137i
\(918\) −15.5885 + 9.00000i −0.514496 + 0.297044i
\(919\) 8.50000 14.7224i 0.280389 0.485648i −0.691091 0.722767i \(-0.742870\pi\)
0.971481 + 0.237119i \(0.0762032\pi\)
\(920\) 3.46410 6.00000i 0.114208 0.197814i
\(921\) 12.1244 21.0000i 0.399511 0.691974i
\(922\) 39.8372i 1.31197i
\(923\) −20.7846 36.0000i −0.684134 1.18495i
\(924\) 4.50000 + 7.79423i 0.148039 + 0.256411i
\(925\) 6.00000 + 3.46410i 0.197279 + 0.113899i
\(926\) −12.1244 −0.398431
\(927\) −10.5000 18.1865i −0.344865 0.597324i
\(928\) 1.73205i 0.0568574i
\(929\) −45.0333 −1.47750 −0.738748 0.673982i \(-0.764582\pi\)
−0.738748 + 0.673982i \(0.764582\pi\)
\(930\) −9.52628 + 1.50000i −0.312379 + 0.0491869i
\(931\) −24.0000 −0.786568
\(932\) 18.0000i 0.589610i
\(933\) 45.0000 25.9808i 1.47323 0.850572i
\(934\) 27.0000 0.883467
\(935\) 15.5885 + 9.00000i 0.509797 + 0.294331i
\(936\) −5.19615 9.00000i −0.169842 0.294174i
\(937\) −5.00000 8.66025i −0.163343 0.282918i 0.772723 0.634744i \(-0.218894\pi\)
−0.936066 + 0.351826i \(0.885561\pi\)
\(938\) 2.00000i 0.0653023i
\(939\) 38.9711 + 22.5000i 1.27178 + 0.734260i
\(940\) −6.00000 + 10.3923i −0.195698 + 0.338960i
\(941\) 6.06218 10.5000i 0.197621 0.342290i −0.750135 0.661284i \(-0.770012\pi\)
0.947757 + 0.318994i \(0.103345\pi\)
\(942\) 15.0000 8.66025i 0.488726 0.282166i
\(943\) −36.0000 20.7846i −1.17232 0.676840i
\(944\) 12.9904 7.50000i 0.422801 0.244104i
\(945\) 5.19615i 0.169031i
\(946\) 18.0000 0.585230
\(947\) 12.1244 + 21.0000i 0.393989 + 0.682408i 0.992972 0.118354i \(-0.0377616\pi\)
−0.598983 + 0.800762i \(0.704428\pi\)
\(948\) −15.5885 9.00000i −0.506290 0.292306i
\(949\) −12.0000 20.7846i −0.389536 0.674697i
\(950\) 3.46410 + 2.00000i 0.112390 + 0.0648886i
\(951\) 4.50000 + 2.59808i 0.145922 + 0.0842484i
\(952\) 3.00000 + 1.73205i 0.0972306 + 0.0561361i
\(953\) 10.3923 0.336640 0.168320 0.985732i \(-0.446166\pi\)
0.168320 + 0.985732i \(0.446166\pi\)
\(954\) −31.5000 + 18.1865i −1.01985 + 0.588811i
\(955\) 6.00000 + 10.3923i 0.194155 + 0.336287i
\(956\) −13.8564 + 24.0000i −0.448148 + 0.776215i
\(957\) 15.5885 0.503903
\(958\) 6.00000 + 10.3923i 0.193851 + 0.335760i
\(959\) −13.8564 −0.447447
\(960\) 1.73205i 0.0559017i
\(961\) 29.5000 9.52628i 0.951613 0.307299i
\(962\) 24.0000i 0.773791i
\(963\) 9.00000i 0.290021i
\(964\) 13.5000 7.79423i 0.434806 0.251035i
\(965\) 11.0000i 0.354103i
\(966\) 10.3923 + 6.00000i 0.334367 + 0.193047i
\(967\) −27.0000 + 15.5885i −0.868261 + 0.501291i −0.866770 0.498708i \(-0.833808\pi\)
−0.00149135 + 0.999999i \(0.500475\pi\)
\(968\) −13.8564 + 8.00000i −0.445362 + 0.257130i
\(969\) −24.0000 −0.770991
\(970\) 0.500000 0.866025i 0.0160540 0.0278064i
\(971\) 23.3827 + 13.5000i 0.750386 + 0.433236i 0.825833 0.563914i \(-0.190705\pi\)
−0.0754473 + 0.997150i \(0.524038\pi\)
\(972\) 7.79423 13.5000i 0.250000 0.433013i
\(973\) −18.0000 + 10.3923i −0.577054 + 0.333162i
\(974\) −18.1865 + 31.5000i −0.582734 + 1.00933i
\(975\) −5.19615 + 3.00000i −0.166410 + 0.0960769i
\(976\) 3.46410i 0.110883i
\(977\) 12.0000i 0.383914i −0.981403 0.191957i \(-0.938517\pi\)
0.981403 0.191957i \(-0.0614834\pi\)
\(978\) 12.0000 6.92820i 0.383718 0.221540i
\(979\) −27.0000 + 46.7654i −0.862924 + 1.49463i
\(980\) −5.19615 + 3.00000i −0.165985 + 0.0958315i
\(981\) 6.00000 10.3923i 0.191565 0.331801i
\(982\) −31.5000 18.1865i −1.00521 0.580356i
\(983\) −8.66025 + 15.0000i −0.276219 + 0.478426i −0.970442 0.241334i \(-0.922415\pi\)
0.694223 + 0.719760i \(0.255748\pi\)
\(984\) 10.3923 0.331295
\(985\) 0 0
\(986\) 5.19615 3.00000i 0.165479 0.0955395i
\(987\) −18.0000 10.3923i −0.572946 0.330791i
\(988\) 13.8564i 0.440831i
\(989\) 20.7846 12.0000i 0.660912 0.381578i
\(990\) −15.5885 −0.495434
\(991\) 24.2487i 0.770286i −0.922857 0.385143i \(-0.874152\pi\)
0.922857 0.385143i \(-0.125848\pi\)
\(992\) −0.866025 5.50000i −0.0274963 0.174625i
\(993\) 30.0000i 0.952021i
\(994\) −12.0000 −0.380617
\(995\) −6.06218 10.5000i −0.192184 0.332872i
\(996\) −9.00000 −0.285176
\(997\) −1.00000 + 1.73205i −0.0316703 + 0.0548546i −0.881426 0.472322i \(-0.843416\pi\)
0.849756 + 0.527176i \(0.176749\pi\)
\(998\) −12.1244 21.0000i −0.383790 0.664743i
\(999\) 31.1769 18.0000i 0.986394 0.569495i
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 930.2.o.c.161.2 yes 4
3.2 odd 2 inner 930.2.o.c.161.1 4
31.26 odd 6 inner 930.2.o.c.491.2 yes 4
93.26 even 6 inner 930.2.o.c.491.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.o.c.161.1 4 3.2 odd 2 inner
930.2.o.c.161.2 yes 4 1.1 even 1 trivial
930.2.o.c.491.1 yes 4 93.26 even 6 inner
930.2.o.c.491.2 yes 4 31.26 odd 6 inner