Properties

Label 845.2.m.b.316.1
Level $845$
Weight $2$
Character 845.316
Analytic conductor $6.747$
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] = [845,2,Mod(316,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.316");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.m (of order \(6\), degree \(2\), not 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: \(6.74735897080\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 845.316
Dual form 845.2.m.b.361.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-1.73205 + 1.00000i) q^{6} +(-3.46410 + 2.00000i) q^{7} +3.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-1.73205 + 1.00000i) q^{6} +(-3.46410 + 2.00000i) q^{7} +3.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.73205 - 1.00000i) q^{11} -2.00000 q^{12} +4.00000 q^{14} +(1.73205 + 1.00000i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +1.00000i q^{18} +(5.19615 - 3.00000i) q^{19} +(0.866025 - 0.500000i) q^{20} +8.00000i q^{21} +(1.00000 + 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(5.19615 + 3.00000i) q^{24} -1.00000 q^{25} +4.00000 q^{27} +(3.46410 + 2.00000i) q^{28} +(-1.00000 + 1.73205i) q^{29} +(-1.00000 - 1.73205i) q^{30} +10.0000i q^{31} +(4.33013 - 2.50000i) q^{32} +(-3.46410 + 2.00000i) q^{33} -2.00000i q^{34} +(-2.00000 - 3.46410i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.73205 + 1.00000i) q^{37} -6.00000 q^{38} -3.00000 q^{40} +(-5.19615 - 3.00000i) q^{41} +(4.00000 - 6.92820i) q^{42} +(5.00000 + 8.66025i) q^{43} +2.00000i q^{44} +(0.866025 - 0.500000i) q^{45} +(5.19615 - 3.00000i) q^{46} +4.00000i q^{47} +(-1.00000 - 1.73205i) q^{48} +(4.50000 - 7.79423i) q^{49} +(0.866025 + 0.500000i) q^{50} +4.00000 q^{51} +2.00000 q^{53} +(-3.46410 - 2.00000i) q^{54} +(1.00000 - 1.73205i) q^{55} +(-6.00000 - 10.3923i) q^{56} -12.0000i q^{57} +(1.73205 - 1.00000i) q^{58} +(5.19615 - 3.00000i) q^{59} -2.00000i q^{60} +(-1.00000 - 1.73205i) q^{61} +(5.00000 - 8.66025i) q^{62} +(3.46410 + 2.00000i) q^{63} -7.00000 q^{64} +4.00000 q^{66} +(-3.46410 - 2.00000i) q^{67} +(1.00000 - 1.73205i) q^{68} +(6.00000 + 10.3923i) q^{69} +4.00000i q^{70} +(-5.19615 + 3.00000i) q^{71} +(2.59808 - 1.50000i) q^{72} -6.00000i q^{73} +(-1.00000 - 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{75} +(-5.19615 - 3.00000i) q^{76} +8.00000 q^{77} -12.0000 q^{79} +(0.866025 + 0.500000i) q^{80} +(5.50000 - 9.52628i) q^{81} +(3.00000 + 5.19615i) q^{82} +16.0000i q^{83} +(6.92820 - 4.00000i) q^{84} +(-1.73205 + 1.00000i) q^{85} -10.0000i q^{86} +(2.00000 + 3.46410i) q^{87} +(3.00000 - 5.19615i) q^{88} +(-1.73205 - 1.00000i) q^{89} -1.00000 q^{90} +6.00000 q^{92} +(17.3205 + 10.0000i) q^{93} +(2.00000 - 3.46410i) q^{94} +(3.00000 + 5.19615i) q^{95} -10.0000i q^{96} +(1.73205 - 1.00000i) q^{97} +(-7.79423 + 4.50000i) q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} - 2 q^{4} - 2 q^{9} + 2 q^{10} - 8 q^{12} + 16 q^{14} + 2 q^{16} + 4 q^{17} + 4 q^{22} - 12 q^{23} - 4 q^{25} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 8 q^{35} - 2 q^{36} - 24 q^{38} - 12 q^{40} + 16 q^{42} + 20 q^{43} - 4 q^{48} + 18 q^{49} + 16 q^{51} + 8 q^{53} + 4 q^{55} - 24 q^{56} - 4 q^{61} + 20 q^{62} - 28 q^{64} + 16 q^{66} + 4 q^{68} + 24 q^{69} - 4 q^{74} - 4 q^{75} + 32 q^{77} - 48 q^{79} + 22 q^{81} + 12 q^{82} + 8 q^{87} + 12 q^{88} - 4 q^{90} + 24 q^{92} + 8 q^{94} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i 0.161521 0.986869i \(-0.448360\pi\)
−0.773893 + 0.633316i \(0.781693\pi\)
\(3\) 1.00000 1.73205i 0.577350 1.00000i −0.418432 0.908248i \(-0.637420\pi\)
0.995782 0.0917517i \(-0.0292466\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) −1.73205 + 1.00000i −0.707107 + 0.408248i
\(7\) −3.46410 + 2.00000i −1.30931 + 0.755929i −0.981981 0.188982i \(-0.939481\pi\)
−0.327327 + 0.944911i \(0.606148\pi\)
\(8\) 3.00000i 1.06066i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −1.73205 1.00000i −0.522233 0.301511i 0.215615 0.976478i \(-0.430824\pi\)
−0.737848 + 0.674967i \(0.764158\pi\)
\(12\) −2.00000 −0.577350
\(13\) 0 0
\(14\) 4.00000 1.06904
\(15\) 1.73205 + 1.00000i 0.447214 + 0.258199i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 5.19615 3.00000i 1.19208 0.688247i 0.233301 0.972404i \(-0.425047\pi\)
0.958778 + 0.284157i \(0.0917138\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 8.00000i 1.74574i
\(22\) 1.00000 + 1.73205i 0.213201 + 0.369274i
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 5.19615 + 3.00000i 1.06066 + 0.612372i
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) 3.46410 + 2.00000i 0.654654 + 0.377964i
\(29\) −1.00000 + 1.73205i −0.185695 + 0.321634i −0.943811 0.330487i \(-0.892787\pi\)
0.758115 + 0.652121i \(0.226120\pi\)
\(30\) −1.00000 1.73205i −0.182574 0.316228i
\(31\) 10.0000i 1.79605i 0.439941 + 0.898027i \(0.354999\pi\)
−0.439941 + 0.898027i \(0.645001\pi\)
\(32\) 4.33013 2.50000i 0.765466 0.441942i
\(33\) −3.46410 + 2.00000i −0.603023 + 0.348155i
\(34\) 2.00000i 0.342997i
\(35\) −2.00000 3.46410i −0.338062 0.585540i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 1.73205 + 1.00000i 0.284747 + 0.164399i 0.635571 0.772043i \(-0.280765\pi\)
−0.350823 + 0.936442i \(0.614098\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) −3.00000 −0.474342
\(41\) −5.19615 3.00000i −0.811503 0.468521i 0.0359748 0.999353i \(-0.488546\pi\)
−0.847477 + 0.530831i \(0.821880\pi\)
\(42\) 4.00000 6.92820i 0.617213 1.06904i
\(43\) 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i \(0.109358\pi\)
−0.179069 + 0.983836i \(0.557309\pi\)
\(44\) 2.00000i 0.301511i
\(45\) 0.866025 0.500000i 0.129099 0.0745356i
\(46\) 5.19615 3.00000i 0.766131 0.442326i
\(47\) 4.00000i 0.583460i 0.956501 + 0.291730i \(0.0942309\pi\)
−0.956501 + 0.291730i \(0.905769\pi\)
\(48\) −1.00000 1.73205i −0.144338 0.250000i
\(49\) 4.50000 7.79423i 0.642857 1.11346i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 4.00000 0.560112
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) −3.46410 2.00000i −0.471405 0.272166i
\(55\) 1.00000 1.73205i 0.134840 0.233550i
\(56\) −6.00000 10.3923i −0.801784 1.38873i
\(57\) 12.0000i 1.58944i
\(58\) 1.73205 1.00000i 0.227429 0.131306i
\(59\) 5.19615 3.00000i 0.676481 0.390567i −0.122047 0.992524i \(-0.538946\pi\)
0.798528 + 0.601958i \(0.205612\pi\)
\(60\) 2.00000i 0.258199i
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) 5.00000 8.66025i 0.635001 1.09985i
\(63\) 3.46410 + 2.00000i 0.436436 + 0.251976i
\(64\) −7.00000 −0.875000
\(65\) 0 0
\(66\) 4.00000 0.492366
\(67\) −3.46410 2.00000i −0.423207 0.244339i 0.273241 0.961946i \(-0.411904\pi\)
−0.696449 + 0.717607i \(0.745238\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 6.00000 + 10.3923i 0.722315 + 1.25109i
\(70\) 4.00000i 0.478091i
\(71\) −5.19615 + 3.00000i −0.616670 + 0.356034i −0.775571 0.631260i \(-0.782538\pi\)
0.158901 + 0.987294i \(0.449205\pi\)
\(72\) 2.59808 1.50000i 0.306186 0.176777i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) −1.00000 + 1.73205i −0.115470 + 0.200000i
\(76\) −5.19615 3.00000i −0.596040 0.344124i
\(77\) 8.00000 0.911685
\(78\) 0 0
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 3.00000 + 5.19615i 0.331295 + 0.573819i
\(83\) 16.0000i 1.75623i 0.478451 + 0.878114i \(0.341198\pi\)
−0.478451 + 0.878114i \(0.658802\pi\)
\(84\) 6.92820 4.00000i 0.755929 0.436436i
\(85\) −1.73205 + 1.00000i −0.187867 + 0.108465i
\(86\) 10.0000i 1.07833i
\(87\) 2.00000 + 3.46410i 0.214423 + 0.371391i
\(88\) 3.00000 5.19615i 0.319801 0.553912i
\(89\) −1.73205 1.00000i −0.183597 0.106000i 0.405385 0.914146i \(-0.367138\pi\)
−0.588982 + 0.808146i \(0.700471\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 17.3205 + 10.0000i 1.79605 + 1.03695i
\(94\) 2.00000 3.46410i 0.206284 0.357295i
\(95\) 3.00000 + 5.19615i 0.307794 + 0.533114i
\(96\) 10.0000i 1.02062i
\(97\) 1.73205 1.00000i 0.175863 0.101535i −0.409484 0.912317i \(-0.634291\pi\)
0.585348 + 0.810782i \(0.300958\pi\)
\(98\) −7.79423 + 4.50000i −0.787336 + 0.454569i
\(99\) 2.00000i 0.201008i
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i \(0.519872\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(102\) −3.46410 2.00000i −0.342997 0.198030i
\(103\) −2.00000 −0.197066 −0.0985329 0.995134i \(-0.531415\pi\)
−0.0985329 + 0.995134i \(0.531415\pi\)
\(104\) 0 0
\(105\) −8.00000 −0.780720
\(106\) −1.73205 1.00000i −0.168232 0.0971286i
\(107\) −5.00000 + 8.66025i −0.483368 + 0.837218i −0.999818 0.0190994i \(-0.993920\pi\)
0.516449 + 0.856318i \(0.327253\pi\)
\(108\) −2.00000 3.46410i −0.192450 0.333333i
\(109\) 10.0000i 0.957826i −0.877862 0.478913i \(-0.841031\pi\)
0.877862 0.478913i \(-0.158969\pi\)
\(110\) −1.73205 + 1.00000i −0.165145 + 0.0953463i
\(111\) 3.46410 2.00000i 0.328798 0.189832i
\(112\) 4.00000i 0.377964i
\(113\) 7.00000 + 12.1244i 0.658505 + 1.14056i 0.981003 + 0.193993i \(0.0621440\pi\)
−0.322498 + 0.946570i \(0.604523\pi\)
\(114\) −6.00000 + 10.3923i −0.561951 + 0.973329i
\(115\) −5.19615 3.00000i −0.484544 0.279751i
\(116\) 2.00000 0.185695
\(117\) 0 0
\(118\) −6.00000 −0.552345
\(119\) −6.92820 4.00000i −0.635107 0.366679i
\(120\) −3.00000 + 5.19615i −0.273861 + 0.474342i
\(121\) −3.50000 6.06218i −0.318182 0.551107i
\(122\) 2.00000i 0.181071i
\(123\) −10.3923 + 6.00000i −0.937043 + 0.541002i
\(124\) 8.66025 5.00000i 0.777714 0.449013i
\(125\) 1.00000i 0.0894427i
\(126\) −2.00000 3.46410i −0.178174 0.308607i
\(127\) −1.00000 + 1.73205i −0.0887357 + 0.153695i −0.906977 0.421180i \(-0.861616\pi\)
0.818241 + 0.574875i \(0.194949\pi\)
\(128\) −2.59808 1.50000i −0.229640 0.132583i
\(129\) 20.0000 1.76090
\(130\) 0 0
\(131\) 20.0000 1.74741 0.873704 0.486458i \(-0.161711\pi\)
0.873704 + 0.486458i \(0.161711\pi\)
\(132\) 3.46410 + 2.00000i 0.301511 + 0.174078i
\(133\) −12.0000 + 20.7846i −1.04053 + 1.80225i
\(134\) 2.00000 + 3.46410i 0.172774 + 0.299253i
\(135\) 4.00000i 0.344265i
\(136\) −5.19615 + 3.00000i −0.445566 + 0.257248i
\(137\) −1.73205 + 1.00000i −0.147979 + 0.0854358i −0.572161 0.820141i \(-0.693895\pi\)
0.424182 + 0.905577i \(0.360562\pi\)
\(138\) 12.0000i 1.02151i
\(139\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(140\) −2.00000 + 3.46410i −0.169031 + 0.292770i
\(141\) 6.92820 + 4.00000i 0.583460 + 0.336861i
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) −1.73205 1.00000i −0.143839 0.0830455i
\(146\) −3.00000 + 5.19615i −0.248282 + 0.430037i
\(147\) −9.00000 15.5885i −0.742307 1.28571i
\(148\) 2.00000i 0.164399i
\(149\) −15.5885 + 9.00000i −1.27706 + 0.737309i −0.976306 0.216394i \(-0.930570\pi\)
−0.300750 + 0.953703i \(0.597237\pi\)
\(150\) 1.73205 1.00000i 0.141421 0.0816497i
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 9.00000 + 15.5885i 0.729996 + 1.26439i
\(153\) 1.00000 1.73205i 0.0808452 0.140028i
\(154\) −6.92820 4.00000i −0.558291 0.322329i
\(155\) −10.0000 −0.803219
\(156\) 0 0
\(157\) −6.00000 −0.478852 −0.239426 0.970915i \(-0.576959\pi\)
−0.239426 + 0.970915i \(0.576959\pi\)
\(158\) 10.3923 + 6.00000i 0.826767 + 0.477334i
\(159\) 2.00000 3.46410i 0.158610 0.274721i
\(160\) 2.50000 + 4.33013i 0.197642 + 0.342327i
\(161\) 24.0000i 1.89146i
\(162\) −9.52628 + 5.50000i −0.748455 + 0.432121i
\(163\) −10.3923 + 6.00000i −0.813988 + 0.469956i −0.848339 0.529454i \(-0.822397\pi\)
0.0343508 + 0.999410i \(0.489064\pi\)
\(164\) 6.00000i 0.468521i
\(165\) −2.00000 3.46410i −0.155700 0.269680i
\(166\) 8.00000 13.8564i 0.620920 1.07547i
\(167\) 10.3923 + 6.00000i 0.804181 + 0.464294i 0.844931 0.534875i \(-0.179641\pi\)
−0.0407502 + 0.999169i \(0.512975\pi\)
\(168\) −24.0000 −1.85164
\(169\) 0 0
\(170\) 2.00000 0.153393
\(171\) −5.19615 3.00000i −0.397360 0.229416i
\(172\) 5.00000 8.66025i 0.381246 0.660338i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 4.00000i 0.303239i
\(175\) 3.46410 2.00000i 0.261861 0.151186i
\(176\) −1.73205 + 1.00000i −0.130558 + 0.0753778i
\(177\) 12.0000i 0.901975i
\(178\) 1.00000 + 1.73205i 0.0749532 + 0.129823i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) −0.866025 0.500000i −0.0645497 0.0372678i
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) −4.00000 −0.295689
\(184\) −15.5885 9.00000i −1.14920 0.663489i
\(185\) −1.00000 + 1.73205i −0.0735215 + 0.127343i
\(186\) −10.0000 17.3205i −0.733236 1.27000i
\(187\) 4.00000i 0.292509i
\(188\) 3.46410 2.00000i 0.252646 0.145865i
\(189\) −13.8564 + 8.00000i −1.00791 + 0.581914i
\(190\) 6.00000i 0.435286i
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) −7.00000 + 12.1244i −0.505181 + 0.875000i
\(193\) 1.73205 + 1.00000i 0.124676 + 0.0719816i 0.561041 0.827788i \(-0.310401\pi\)
−0.436365 + 0.899770i \(0.643734\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) −9.00000 −0.642857
\(197\) −5.19615 3.00000i −0.370211 0.213741i 0.303340 0.952882i \(-0.401898\pi\)
−0.673550 + 0.739141i \(0.735232\pi\)
\(198\) 1.00000 1.73205i 0.0710669 0.123091i
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 3.00000i 0.212132i
\(201\) −6.92820 + 4.00000i −0.488678 + 0.282138i
\(202\) 15.5885 9.00000i 1.09680 0.633238i
\(203\) 8.00000i 0.561490i
\(204\) −2.00000 3.46410i −0.140028 0.242536i
\(205\) 3.00000 5.19615i 0.209529 0.362915i
\(206\) 1.73205 + 1.00000i 0.120678 + 0.0696733i
\(207\) 6.00000 0.417029
\(208\) 0 0
\(209\) −12.0000 −0.830057
\(210\) 6.92820 + 4.00000i 0.478091 + 0.276026i
\(211\) −6.00000 + 10.3923i −0.413057 + 0.715436i −0.995222 0.0976347i \(-0.968872\pi\)
0.582165 + 0.813070i \(0.302206\pi\)
\(212\) −1.00000 1.73205i −0.0686803 0.118958i
\(213\) 12.0000i 0.822226i
\(214\) 8.66025 5.00000i 0.592003 0.341793i
\(215\) −8.66025 + 5.00000i −0.590624 + 0.340997i
\(216\) 12.0000i 0.816497i
\(217\) −20.0000 34.6410i −1.35769 2.35159i
\(218\) −5.00000 + 8.66025i −0.338643 + 0.586546i
\(219\) −10.3923 6.00000i −0.702247 0.405442i
\(220\) −2.00000 −0.134840
\(221\) 0 0
\(222\) −4.00000 −0.268462
\(223\) 3.46410 + 2.00000i 0.231973 + 0.133930i 0.611482 0.791258i \(-0.290574\pi\)
−0.379509 + 0.925188i \(0.623907\pi\)
\(224\) −10.0000 + 17.3205i −0.668153 + 1.15728i
\(225\) 0.500000 + 0.866025i 0.0333333 + 0.0577350i
\(226\) 14.0000i 0.931266i
\(227\) −3.46410 + 2.00000i −0.229920 + 0.132745i −0.610535 0.791989i \(-0.709046\pi\)
0.380615 + 0.924734i \(0.375712\pi\)
\(228\) −10.3923 + 6.00000i −0.688247 + 0.397360i
\(229\) 22.0000i 1.45380i −0.686743 0.726900i \(-0.740960\pi\)
0.686743 0.726900i \(-0.259040\pi\)
\(230\) 3.00000 + 5.19615i 0.197814 + 0.342624i
\(231\) 8.00000 13.8564i 0.526361 0.911685i
\(232\) −5.19615 3.00000i −0.341144 0.196960i
\(233\) −10.0000 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) 0 0
\(235\) −4.00000 −0.260931
\(236\) −5.19615 3.00000i −0.338241 0.195283i
\(237\) −12.0000 + 20.7846i −0.779484 + 1.35011i
\(238\) 4.00000 + 6.92820i 0.259281 + 0.449089i
\(239\) 6.00000i 0.388108i 0.980991 + 0.194054i \(0.0621637\pi\)
−0.980991 + 0.194054i \(0.937836\pi\)
\(240\) 1.73205 1.00000i 0.111803 0.0645497i
\(241\) 8.66025 5.00000i 0.557856 0.322078i −0.194429 0.980917i \(-0.562285\pi\)
0.752285 + 0.658838i \(0.228952\pi\)
\(242\) 7.00000i 0.449977i
\(243\) −5.00000 8.66025i −0.320750 0.555556i
\(244\) −1.00000 + 1.73205i −0.0640184 + 0.110883i
\(245\) 7.79423 + 4.50000i 0.497955 + 0.287494i
\(246\) 12.0000 0.765092
\(247\) 0 0
\(248\) −30.0000 −1.90500
\(249\) 27.7128 + 16.0000i 1.75623 + 1.01396i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 12.0000 + 20.7846i 0.757433 + 1.31191i 0.944156 + 0.329500i \(0.106880\pi\)
−0.186722 + 0.982413i \(0.559786\pi\)
\(252\) 4.00000i 0.251976i
\(253\) 10.3923 6.00000i 0.653359 0.377217i
\(254\) 1.73205 1.00000i 0.108679 0.0627456i
\(255\) 4.00000i 0.250490i
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 1.00000 1.73205i 0.0623783 0.108042i −0.833150 0.553047i \(-0.813465\pi\)
0.895528 + 0.445005i \(0.146798\pi\)
\(258\) −17.3205 10.0000i −1.07833 0.622573i
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) −17.3205 10.0000i −1.07006 0.617802i
\(263\) −7.00000 + 12.1244i −0.431638 + 0.747620i −0.997015 0.0772134i \(-0.975398\pi\)
0.565376 + 0.824833i \(0.308731\pi\)
\(264\) −6.00000 10.3923i −0.369274 0.639602i
\(265\) 2.00000i 0.122859i
\(266\) 20.7846 12.0000i 1.27439 0.735767i
\(267\) −3.46410 + 2.00000i −0.212000 + 0.122398i
\(268\) 4.00000i 0.244339i
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 2.00000 3.46410i 0.121716 0.210819i
\(271\) −1.73205 1.00000i −0.105215 0.0607457i 0.446469 0.894799i \(-0.352681\pi\)
−0.551684 + 0.834053i \(0.686015\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 1.73205 + 1.00000i 0.104447 + 0.0603023i
\(276\) 6.00000 10.3923i 0.361158 0.625543i
\(277\) −7.00000 12.1244i −0.420589 0.728482i 0.575408 0.817867i \(-0.304843\pi\)
−0.995997 + 0.0893846i \(0.971510\pi\)
\(278\) 0 0
\(279\) 8.66025 5.00000i 0.518476 0.299342i
\(280\) 10.3923 6.00000i 0.621059 0.358569i
\(281\) 6.00000i 0.357930i −0.983855 0.178965i \(-0.942725\pi\)
0.983855 0.178965i \(-0.0572749\pi\)
\(282\) −4.00000 6.92820i −0.238197 0.412568i
\(283\) 1.00000 1.73205i 0.0594438 0.102960i −0.834772 0.550596i \(-0.814401\pi\)
0.894216 + 0.447636i \(0.147734\pi\)
\(284\) 5.19615 + 3.00000i 0.308335 + 0.178017i
\(285\) 12.0000 0.710819
\(286\) 0 0
\(287\) 24.0000 1.41668
\(288\) −4.33013 2.50000i −0.255155 0.147314i
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 1.00000 + 1.73205i 0.0587220 + 0.101710i
\(291\) 4.00000i 0.234484i
\(292\) −5.19615 + 3.00000i −0.304082 + 0.175562i
\(293\) 19.0526 11.0000i 1.11306 0.642627i 0.173442 0.984844i \(-0.444511\pi\)
0.939621 + 0.342217i \(0.111178\pi\)
\(294\) 18.0000i 1.04978i
\(295\) 3.00000 + 5.19615i 0.174667 + 0.302532i
\(296\) −3.00000 + 5.19615i −0.174371 + 0.302020i
\(297\) −6.92820 4.00000i −0.402015 0.232104i
\(298\) 18.0000 1.04271
\(299\) 0 0
\(300\) 2.00000 0.115470
\(301\) −34.6410 20.0000i −1.99667 1.15278i
\(302\) 5.00000 8.66025i 0.287718 0.498342i
\(303\) 18.0000 + 31.1769i 1.03407 + 1.79107i
\(304\) 6.00000i 0.344124i
\(305\) 1.73205 1.00000i 0.0991769 0.0572598i
\(306\) −1.73205 + 1.00000i −0.0990148 + 0.0571662i
\(307\) 8.00000i 0.456584i 0.973593 + 0.228292i \(0.0733141\pi\)
−0.973593 + 0.228292i \(0.926686\pi\)
\(308\) −4.00000 6.92820i −0.227921 0.394771i
\(309\) −2.00000 + 3.46410i −0.113776 + 0.197066i
\(310\) 8.66025 + 5.00000i 0.491869 + 0.283981i
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 5.19615 + 3.00000i 0.293236 + 0.169300i
\(315\) −2.00000 + 3.46410i −0.112687 + 0.195180i
\(316\) 6.00000 + 10.3923i 0.337526 + 0.584613i
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) −3.46410 + 2.00000i −0.194257 + 0.112154i
\(319\) 3.46410 2.00000i 0.193952 0.111979i
\(320\) 7.00000i 0.391312i
\(321\) 10.0000 + 17.3205i 0.558146 + 0.966736i
\(322\) −12.0000 + 20.7846i −0.668734 + 1.15828i
\(323\) 10.3923 + 6.00000i 0.578243 + 0.333849i
\(324\) −11.0000 −0.611111
\(325\) 0 0
\(326\) 12.0000 0.664619
\(327\) −17.3205 10.0000i −0.957826 0.553001i
\(328\) 9.00000 15.5885i 0.496942 0.860729i
\(329\) −8.00000 13.8564i −0.441054 0.763928i
\(330\) 4.00000i 0.220193i
\(331\) 15.5885 9.00000i 0.856819 0.494685i −0.00612670 0.999981i \(-0.501950\pi\)
0.862946 + 0.505296i \(0.168617\pi\)
\(332\) 13.8564 8.00000i 0.760469 0.439057i
\(333\) 2.00000i 0.109599i
\(334\) −6.00000 10.3923i −0.328305 0.568642i
\(335\) 2.00000 3.46410i 0.109272 0.189264i
\(336\) 6.92820 + 4.00000i 0.377964 + 0.218218i
\(337\) −26.0000 −1.41631 −0.708155 0.706057i \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) 0 0
\(339\) 28.0000 1.52075
\(340\) 1.73205 + 1.00000i 0.0939336 + 0.0542326i
\(341\) 10.0000 17.3205i 0.541530 0.937958i
\(342\) 3.00000 + 5.19615i 0.162221 + 0.280976i
\(343\) 8.00000i 0.431959i
\(344\) −25.9808 + 15.0000i −1.40079 + 0.808746i
\(345\) −10.3923 + 6.00000i −0.559503 + 0.323029i
\(346\) 6.00000i 0.322562i
\(347\) 11.0000 + 19.0526i 0.590511 + 1.02279i 0.994164 + 0.107883i \(0.0344071\pi\)
−0.403653 + 0.914912i \(0.632260\pi\)
\(348\) 2.00000 3.46410i 0.107211 0.185695i
\(349\) 25.9808 + 15.0000i 1.39072 + 0.802932i 0.993395 0.114747i \(-0.0366057\pi\)
0.397324 + 0.917679i \(0.369939\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) −10.0000 −0.533002
\(353\) 15.5885 + 9.00000i 0.829690 + 0.479022i 0.853746 0.520689i \(-0.174325\pi\)
−0.0240566 + 0.999711i \(0.507658\pi\)
\(354\) −6.00000 + 10.3923i −0.318896 + 0.552345i
\(355\) −3.00000 5.19615i −0.159223 0.275783i
\(356\) 2.00000i 0.106000i
\(357\) −13.8564 + 8.00000i −0.733359 + 0.423405i
\(358\) −10.3923 + 6.00000i −0.549250 + 0.317110i
\(359\) 10.0000i 0.527780i −0.964553 0.263890i \(-0.914994\pi\)
0.964553 0.263890i \(-0.0850056\pi\)
\(360\) 1.50000 + 2.59808i 0.0790569 + 0.136931i
\(361\) 8.50000 14.7224i 0.447368 0.774865i
\(362\) −19.0526 11.0000i −1.00138 0.578147i
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 3.46410 + 2.00000i 0.181071 + 0.104542i
\(367\) 7.00000 12.1244i 0.365397 0.632886i −0.623443 0.781869i \(-0.714267\pi\)
0.988840 + 0.148983i \(0.0475999\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 6.00000i 0.312348i
\(370\) 1.73205 1.00000i 0.0900450 0.0519875i
\(371\) −6.92820 + 4.00000i −0.359694 + 0.207670i
\(372\) 20.0000i 1.03695i
\(373\) −17.0000 29.4449i −0.880227 1.52460i −0.851089 0.525022i \(-0.824057\pi\)
−0.0291379 0.999575i \(-0.509276\pi\)
\(374\) −2.00000 + 3.46410i −0.103418 + 0.179124i
\(375\) −1.73205 1.00000i −0.0894427 0.0516398i
\(376\) −12.0000 −0.618853
\(377\) 0 0
\(378\) 16.0000 0.822951
\(379\) 8.66025 + 5.00000i 0.444847 + 0.256833i 0.705652 0.708559i \(-0.250654\pi\)
−0.260804 + 0.965392i \(0.583988\pi\)
\(380\) 3.00000 5.19615i 0.153897 0.266557i
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) 0 0
\(383\) −10.3923 + 6.00000i −0.531022 + 0.306586i −0.741433 0.671027i \(-0.765853\pi\)
0.210411 + 0.977613i \(0.432520\pi\)
\(384\) −5.19615 + 3.00000i −0.265165 + 0.153093i
\(385\) 8.00000i 0.407718i
\(386\) −1.00000 1.73205i −0.0508987 0.0881591i
\(387\) 5.00000 8.66025i 0.254164 0.440225i
\(388\) −1.73205 1.00000i −0.0879316 0.0507673i
\(389\) 10.0000 0.507020 0.253510 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 23.3827 + 13.5000i 1.18100 + 0.681853i
\(393\) 20.0000 34.6410i 1.00887 1.74741i
\(394\) 3.00000 + 5.19615i 0.151138 + 0.261778i
\(395\) 12.0000i 0.603786i
\(396\) 1.73205 1.00000i 0.0870388 0.0502519i
\(397\) 5.19615 3.00000i 0.260787 0.150566i −0.363906 0.931436i \(-0.618557\pi\)
0.624694 + 0.780870i \(0.285224\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 24.0000 + 41.5692i 1.20150 + 2.08106i
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −8.66025 5.00000i −0.432472 0.249688i 0.267927 0.963439i \(-0.413661\pi\)
−0.700399 + 0.713751i \(0.746995\pi\)
\(402\) 8.00000 0.399004
\(403\) 0 0
\(404\) 18.0000 0.895533
\(405\) 9.52628 + 5.50000i 0.473365 + 0.273297i
\(406\) −4.00000 + 6.92820i −0.198517 + 0.343841i
\(407\) −2.00000 3.46410i −0.0991363 0.171709i
\(408\) 12.0000i 0.594089i
\(409\) −15.5885 + 9.00000i −0.770800 + 0.445021i −0.833160 0.553032i \(-0.813471\pi\)
0.0623602 + 0.998054i \(0.480137\pi\)
\(410\) −5.19615 + 3.00000i −0.256620 + 0.148159i
\(411\) 4.00000i 0.197305i
\(412\) 1.00000 + 1.73205i 0.0492665 + 0.0853320i
\(413\) −12.0000 + 20.7846i −0.590481 + 1.02274i
\(414\) −5.19615 3.00000i −0.255377 0.147442i
\(415\) −16.0000 −0.785409
\(416\) 0 0
\(417\) 0 0
\(418\) 10.3923 + 6.00000i 0.508304 + 0.293470i
\(419\) 20.0000 34.6410i 0.977064 1.69232i 0.304115 0.952635i \(-0.401639\pi\)
0.672949 0.739689i \(-0.265027\pi\)
\(420\) 4.00000 + 6.92820i 0.195180 + 0.338062i
\(421\) 10.0000i 0.487370i −0.969854 0.243685i \(-0.921644\pi\)
0.969854 0.243685i \(-0.0783563\pi\)
\(422\) 10.3923 6.00000i 0.505889 0.292075i
\(423\) 3.46410 2.00000i 0.168430 0.0972433i
\(424\) 6.00000i 0.291386i
\(425\) −1.00000 1.73205i −0.0485071 0.0840168i
\(426\) 6.00000 10.3923i 0.290701 0.503509i
\(427\) 6.92820 + 4.00000i 0.335279 + 0.193574i
\(428\) 10.0000 0.483368
\(429\) 0 0
\(430\) 10.0000 0.482243
\(431\) 12.1244 + 7.00000i 0.584010 + 0.337178i 0.762725 0.646723i \(-0.223861\pi\)
−0.178716 + 0.983901i \(0.557194\pi\)
\(432\) 2.00000 3.46410i 0.0962250 0.166667i
\(433\) 5.00000 + 8.66025i 0.240285 + 0.416185i 0.960795 0.277259i \(-0.0894259\pi\)
−0.720511 + 0.693444i \(0.756093\pi\)
\(434\) 40.0000i 1.92006i
\(435\) −3.46410 + 2.00000i −0.166091 + 0.0958927i
\(436\) −8.66025 + 5.00000i −0.414751 + 0.239457i
\(437\) 36.0000i 1.72211i
\(438\) 6.00000 + 10.3923i 0.286691 + 0.496564i
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 5.19615 + 3.00000i 0.247717 + 0.143019i
\(441\) −9.00000 −0.428571
\(442\) 0 0
\(443\) 14.0000 0.665160 0.332580 0.943075i \(-0.392081\pi\)
0.332580 + 0.943075i \(0.392081\pi\)
\(444\) −3.46410 2.00000i −0.164399 0.0949158i
\(445\) 1.00000 1.73205i 0.0474045 0.0821071i
\(446\) −2.00000 3.46410i −0.0947027 0.164030i
\(447\) 36.0000i 1.70274i
\(448\) 24.2487 14.0000i 1.14564 0.661438i
\(449\) −5.19615 + 3.00000i −0.245222 + 0.141579i −0.617574 0.786513i \(-0.711885\pi\)
0.372353 + 0.928091i \(0.378551\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 6.00000 + 10.3923i 0.282529 + 0.489355i
\(452\) 7.00000 12.1244i 0.329252 0.570282i
\(453\) 17.3205 + 10.0000i 0.813788 + 0.469841i
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) 36.0000 1.68585
\(457\) 32.9090 + 19.0000i 1.53942 + 0.888783i 0.998873 + 0.0474665i \(0.0151147\pi\)
0.540544 + 0.841316i \(0.318219\pi\)
\(458\) −11.0000 + 19.0526i −0.513996 + 0.890268i
\(459\) 4.00000 + 6.92820i 0.186704 + 0.323381i
\(460\) 6.00000i 0.279751i
\(461\) −8.66025 + 5.00000i −0.403348 + 0.232873i −0.687928 0.725779i \(-0.741479\pi\)
0.284579 + 0.958652i \(0.408146\pi\)
\(462\) −13.8564 + 8.00000i −0.644658 + 0.372194i
\(463\) 24.0000i 1.11537i −0.830051 0.557687i \(-0.811689\pi\)
0.830051 0.557687i \(-0.188311\pi\)
\(464\) 1.00000 + 1.73205i 0.0464238 + 0.0804084i
\(465\) −10.0000 + 17.3205i −0.463739 + 0.803219i
\(466\) 8.66025 + 5.00000i 0.401179 + 0.231621i
\(467\) 10.0000 0.462745 0.231372 0.972865i \(-0.425678\pi\)
0.231372 + 0.972865i \(0.425678\pi\)
\(468\) 0 0
\(469\) 16.0000 0.738811
\(470\) 3.46410 + 2.00000i 0.159787 + 0.0922531i
\(471\) −6.00000 + 10.3923i −0.276465 + 0.478852i
\(472\) 9.00000 + 15.5885i 0.414259 + 0.717517i
\(473\) 20.0000i 0.919601i
\(474\) 20.7846 12.0000i 0.954669 0.551178i
\(475\) −5.19615 + 3.00000i −0.238416 + 0.137649i
\(476\) 8.00000i 0.366679i
\(477\) −1.00000 1.73205i −0.0457869 0.0793052i
\(478\) 3.00000 5.19615i 0.137217 0.237666i
\(479\) −25.9808 15.0000i −1.18709 0.685367i −0.229447 0.973321i \(-0.573692\pi\)
−0.957644 + 0.287954i \(0.907025\pi\)
\(480\) 10.0000 0.456435
\(481\) 0 0
\(482\) −10.0000 −0.455488
\(483\) −41.5692 24.0000i −1.89146 1.09204i
\(484\) −3.50000 + 6.06218i −0.159091 + 0.275554i
\(485\) 1.00000 + 1.73205i 0.0454077 + 0.0786484i
\(486\) 10.0000i 0.453609i
\(487\) 34.6410 20.0000i 1.56973 0.906287i 0.573535 0.819181i \(-0.305572\pi\)
0.996199 0.0871056i \(-0.0277618\pi\)
\(488\) 5.19615 3.00000i 0.235219 0.135804i
\(489\) 24.0000i 1.08532i
\(490\) −4.50000 7.79423i −0.203289 0.352107i
\(491\) −12.0000 + 20.7846i −0.541552 + 0.937996i 0.457263 + 0.889332i \(0.348830\pi\)
−0.998815 + 0.0486647i \(0.984503\pi\)
\(492\) 10.3923 + 6.00000i 0.468521 + 0.270501i
\(493\) −4.00000 −0.180151
\(494\) 0 0
\(495\) −2.00000 −0.0898933
\(496\) 8.66025 + 5.00000i 0.388857 + 0.224507i
\(497\) 12.0000 20.7846i 0.538274 0.932317i
\(498\) −16.0000 27.7128i −0.716977 1.24184i
\(499\) 10.0000i 0.447661i −0.974628 0.223831i \(-0.928144\pi\)
0.974628 0.223831i \(-0.0718563\pi\)
\(500\) −0.866025 + 0.500000i −0.0387298 + 0.0223607i
\(501\) 20.7846 12.0000i 0.928588 0.536120i
\(502\) 24.0000i 1.07117i
\(503\) 9.00000 + 15.5885i 0.401290 + 0.695055i 0.993882 0.110448i \(-0.0352286\pi\)
−0.592592 + 0.805503i \(0.701895\pi\)
\(504\) −6.00000 + 10.3923i −0.267261 + 0.462910i
\(505\) −15.5885 9.00000i −0.693677 0.400495i
\(506\) −12.0000 −0.533465
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) −5.19615 3.00000i −0.230315 0.132973i 0.380402 0.924821i \(-0.375786\pi\)
−0.610718 + 0.791849i \(0.709119\pi\)
\(510\) 2.00000 3.46410i 0.0885615 0.153393i
\(511\) 12.0000 + 20.7846i 0.530849 + 0.919457i
\(512\) 11.0000i 0.486136i
\(513\) 20.7846 12.0000i 0.917663 0.529813i
\(514\) −1.73205 + 1.00000i −0.0763975 + 0.0441081i
\(515\) 2.00000i 0.0881305i
\(516\) −10.0000 17.3205i −0.440225 0.762493i
\(517\) 4.00000 6.92820i 0.175920 0.304702i
\(518\) 6.92820 + 4.00000i 0.304408 + 0.175750i
\(519\) −12.0000 −0.526742
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) −1.73205 1.00000i −0.0758098 0.0437688i
\(523\) −3.00000 + 5.19615i −0.131181 + 0.227212i −0.924132 0.382073i \(-0.875210\pi\)
0.792951 + 0.609285i \(0.208544\pi\)
\(524\) −10.0000 17.3205i −0.436852 0.756650i
\(525\) 8.00000i 0.349149i
\(526\) 12.1244 7.00000i 0.528647 0.305215i
\(527\) −17.3205 + 10.0000i −0.754493 + 0.435607i
\(528\) 4.00000i 0.174078i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 1.00000 1.73205i 0.0434372 0.0752355i
\(531\) −5.19615 3.00000i −0.225494 0.130189i
\(532\) 24.0000 1.04053
\(533\) 0 0
\(534\) 4.00000 0.173097
\(535\) −8.66025 5.00000i −0.374415 0.216169i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) −12.0000 20.7846i −0.517838 0.896922i
\(538\) 6.00000i 0.258678i
\(539\) −15.5885 + 9.00000i −0.671442 + 0.387657i
\(540\) 3.46410 2.00000i 0.149071 0.0860663i
\(541\) 22.0000i 0.945854i −0.881102 0.472927i \(-0.843197\pi\)
0.881102 0.472927i \(-0.156803\pi\)
\(542\) 1.00000 + 1.73205i 0.0429537 + 0.0743980i
\(543\) 22.0000 38.1051i 0.944110 1.63525i
\(544\) 8.66025 + 5.00000i 0.371305 + 0.214373i
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) −6.00000 −0.256541 −0.128271 0.991739i \(-0.540943\pi\)
−0.128271 + 0.991739i \(0.540943\pi\)
\(548\) 1.73205 + 1.00000i 0.0739895 + 0.0427179i
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) −1.00000 1.73205i −0.0426401 0.0738549i
\(551\) 12.0000i 0.511217i
\(552\) −31.1769 + 18.0000i −1.32698 + 0.766131i
\(553\) 41.5692 24.0000i 1.76770 1.02058i
\(554\) 14.0000i 0.594803i
\(555\) 2.00000 + 3.46410i 0.0848953 + 0.147043i
\(556\) 0 0
\(557\) 22.5167 + 13.0000i 0.954062 + 0.550828i 0.894340 0.447387i \(-0.147645\pi\)
0.0597213 + 0.998215i \(0.480979\pi\)
\(558\) −10.0000 −0.423334
\(559\) 0 0
\(560\) −4.00000 −0.169031
\(561\) −6.92820 4.00000i −0.292509 0.168880i
\(562\) −3.00000 + 5.19615i −0.126547 + 0.219186i
\(563\) −11.0000 19.0526i −0.463595 0.802970i 0.535542 0.844508i \(-0.320107\pi\)
−0.999137 + 0.0415389i \(0.986774\pi\)
\(564\) 8.00000i 0.336861i
\(565\) −12.1244 + 7.00000i −0.510075 + 0.294492i
\(566\) −1.73205 + 1.00000i −0.0728035 + 0.0420331i
\(567\) 44.0000i 1.84783i
\(568\) −9.00000 15.5885i −0.377632 0.654077i
\(569\) −13.0000 + 22.5167i −0.544988 + 0.943948i 0.453619 + 0.891196i \(0.350133\pi\)
−0.998608 + 0.0527519i \(0.983201\pi\)
\(570\) −10.3923 6.00000i −0.435286 0.251312i
\(571\) −24.0000 −1.00437 −0.502184 0.864761i \(-0.667470\pi\)
−0.502184 + 0.864761i \(0.667470\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −20.7846 12.0000i −0.867533 0.500870i
\(575\) 3.00000 5.19615i 0.125109 0.216695i
\(576\) 3.50000 + 6.06218i 0.145833 + 0.252591i
\(577\) 2.00000i 0.0832611i −0.999133 0.0416305i \(-0.986745\pi\)
0.999133 0.0416305i \(-0.0132552\pi\)
\(578\) −11.2583 + 6.50000i −0.468285 + 0.270364i
\(579\) 3.46410 2.00000i 0.143963 0.0831172i
\(580\) 2.00000i 0.0830455i
\(581\) −32.0000 55.4256i −1.32758 2.29944i
\(582\) −2.00000 + 3.46410i −0.0829027 + 0.143592i
\(583\) −3.46410 2.00000i −0.143468 0.0828315i
\(584\) 18.0000 0.744845
\(585\) 0 0
\(586\) −22.0000 −0.908812
\(587\) −38.1051 22.0000i −1.57277 0.908037i −0.995828 0.0912496i \(-0.970914\pi\)
−0.576938 0.816788i \(-0.695753\pi\)
\(588\) −9.00000 + 15.5885i −0.371154 + 0.642857i
\(589\) 30.0000 + 51.9615i 1.23613 + 2.14104i
\(590\) 6.00000i 0.247016i
\(591\) −10.3923 + 6.00000i −0.427482 + 0.246807i
\(592\) 1.73205 1.00000i 0.0711868 0.0410997i
\(593\) 14.0000i 0.574911i 0.957794 + 0.287456i \(0.0928094\pi\)
−0.957794 + 0.287456i \(0.907191\pi\)
\(594\) 4.00000 + 6.92820i 0.164122 + 0.284268i
\(595\) 4.00000 6.92820i 0.163984 0.284029i
\(596\) 15.5885 + 9.00000i 0.638528 + 0.368654i
\(597\) −32.0000 −1.30967
\(598\) 0 0
\(599\) −4.00000 −0.163436 −0.0817178 0.996656i \(-0.526041\pi\)
−0.0817178 + 0.996656i \(0.526041\pi\)
\(600\) −5.19615 3.00000i −0.212132 0.122474i
\(601\) −5.00000 + 8.66025i −0.203954 + 0.353259i −0.949799 0.312861i \(-0.898713\pi\)
0.745845 + 0.666120i \(0.232046\pi\)
\(602\) 20.0000 + 34.6410i 0.815139 + 1.41186i
\(603\) 4.00000i 0.162893i
\(604\) 8.66025 5.00000i 0.352381 0.203447i
\(605\) 6.06218 3.50000i 0.246463 0.142295i
\(606\) 36.0000i 1.46240i
\(607\) −17.0000 29.4449i −0.690009 1.19513i −0.971834 0.235665i \(-0.924273\pi\)
0.281826 0.959466i \(-0.409060\pi\)
\(608\) 15.0000 25.9808i 0.608330 1.05366i
\(609\) −13.8564 8.00000i −0.561490 0.324176i
\(610\) −2.00000 −0.0809776
\(611\) 0 0
\(612\) −2.00000 −0.0808452
\(613\) −5.19615 3.00000i −0.209871 0.121169i 0.391381 0.920229i \(-0.371998\pi\)
−0.601251 + 0.799060i \(0.705331\pi\)
\(614\) 4.00000 6.92820i 0.161427 0.279600i
\(615\) −6.00000 10.3923i −0.241943 0.419058i
\(616\) 24.0000i 0.966988i
\(617\) 36.3731 21.0000i 1.46432 0.845428i 0.465118 0.885249i \(-0.346012\pi\)
0.999207 + 0.0398207i \(0.0126787\pi\)
\(618\) 3.46410 2.00000i 0.139347 0.0804518i
\(619\) 2.00000i 0.0803868i −0.999192 0.0401934i \(-0.987203\pi\)
0.999192 0.0401934i \(-0.0127974\pi\)
\(620\) 5.00000 + 8.66025i 0.200805 + 0.347804i
\(621\) −12.0000 + 20.7846i −0.481543 + 0.834058i
\(622\) −3.46410 2.00000i −0.138898 0.0801927i
\(623\) 8.00000 0.320513
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 19.0526 + 11.0000i 0.761493 + 0.439648i
\(627\) −12.0000 + 20.7846i −0.479234 + 0.830057i
\(628\) 3.00000 + 5.19615i 0.119713 + 0.207349i
\(629\) 4.00000i 0.159490i
\(630\) 3.46410 2.00000i 0.138013 0.0796819i
\(631\) −12.1244 + 7.00000i −0.482663 + 0.278666i −0.721526 0.692388i \(-0.756559\pi\)
0.238863 + 0.971053i \(0.423225\pi\)
\(632\) 36.0000i 1.43200i
\(633\) 12.0000 + 20.7846i 0.476957 + 0.826114i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) −1.73205 1.00000i −0.0687343 0.0396838i
\(636\) −4.00000 −0.158610
\(637\) 0 0
\(638\) −4.00000 −0.158362
\(639\) 5.19615 + 3.00000i 0.205557 + 0.118678i
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) −23.0000 39.8372i −0.908445 1.57347i −0.816224 0.577735i \(-0.803937\pi\)
−0.0922210 0.995739i \(-0.529397\pi\)
\(642\) 20.0000i 0.789337i
\(643\) 13.8564 8.00000i 0.546443 0.315489i −0.201243 0.979541i \(-0.564498\pi\)
0.747686 + 0.664052i \(0.231165\pi\)
\(644\) −20.7846 + 12.0000i −0.819028 + 0.472866i
\(645\) 20.0000i 0.787499i
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) 19.0000 32.9090i 0.746967 1.29378i −0.202303 0.979323i \(-0.564843\pi\)
0.949270 0.314462i \(-0.101824\pi\)
\(648\) 28.5788 + 16.5000i 1.12268 + 0.648181i
\(649\) −12.0000 −0.471041
\(650\) 0 0
\(651\) −80.0000 −3.13545
\(652\) 10.3923 + 6.00000i 0.406994 + 0.234978i
\(653\) 3.00000 5.19615i 0.117399 0.203341i −0.801337 0.598213i \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) 10.0000 + 17.3205i 0.391031 + 0.677285i
\(655\) 20.0000i 0.781465i
\(656\) −5.19615 + 3.00000i −0.202876 + 0.117130i
\(657\) −5.19615 + 3.00000i −0.202721 + 0.117041i
\(658\) 16.0000i 0.623745i
\(659\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(660\) −2.00000 + 3.46410i −0.0778499 + 0.134840i
\(661\) −1.73205 1.00000i −0.0673690 0.0388955i 0.465937 0.884818i \(-0.345717\pi\)
−0.533306 + 0.845922i \(0.679051\pi\)
\(662\) −18.0000 −0.699590
\(663\) 0 0
\(664\) −48.0000 −1.86276
\(665\) −20.7846 12.0000i −0.805993 0.465340i
\(666\) −1.00000 + 1.73205i −0.0387492 + 0.0671156i
\(667\) −6.00000 10.3923i −0.232321 0.402392i
\(668\) 12.0000i 0.464294i
\(669\) 6.92820 4.00000i 0.267860 0.154649i
\(670\) −3.46410 + 2.00000i −0.133830 + 0.0772667i
\(671\) 4.00000i 0.154418i
\(672\) 20.0000 + 34.6410i 0.771517 + 1.33631i
\(673\) −15.0000 + 25.9808i −0.578208 + 1.00148i 0.417477 + 0.908687i \(0.362914\pi\)
−0.995685 + 0.0927975i \(0.970419\pi\)
\(674\) 22.5167 + 13.0000i 0.867309 + 0.500741i
\(675\) −4.00000 −0.153960
\(676\) 0 0
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) −24.2487 14.0000i −0.931266 0.537667i
\(679\) −4.00000 + 6.92820i −0.153506 + 0.265880i
\(680\) −3.00000 5.19615i −0.115045 0.199263i
\(681\) 8.00000i 0.306561i
\(682\) −17.3205 + 10.0000i −0.663237 + 0.382920i
\(683\) −17.3205 + 10.0000i −0.662751 + 0.382639i −0.793324 0.608799i \(-0.791651\pi\)
0.130573 + 0.991439i \(0.458318\pi\)
\(684\) 6.00000i 0.229416i
\(685\) −1.00000 1.73205i −0.0382080 0.0661783i
\(686\) 4.00000 6.92820i 0.152721 0.264520i
\(687\) −38.1051 22.0000i −1.45380 0.839352i
\(688\) 10.0000 0.381246
\(689\) 0 0
\(690\) 12.0000 0.456832
\(691\) 19.0526 + 11.0000i 0.724793 + 0.418460i 0.816514 0.577325i \(-0.195903\pi\)
−0.0917209 + 0.995785i \(0.529237\pi\)
\(692\) −3.00000 + 5.19615i −0.114043 + 0.197528i
\(693\) −4.00000 6.92820i −0.151947 0.263181i
\(694\) 22.0000i 0.835109i
\(695\) 0 0
\(696\) −10.3923 + 6.00000i −0.393919 + 0.227429i
\(697\) 12.0000i 0.454532i
\(698\) −15.0000 25.9808i −0.567758 0.983386i
\(699\) −10.0000 + 17.3205i −0.378235 + 0.655122i
\(700\) −3.46410 2.00000i −0.130931 0.0755929i
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) 12.0000 0.452589
\(704\) 12.1244 + 7.00000i 0.456954 + 0.263822i
\(705\) −4.00000 + 6.92820i −0.150649 + 0.260931i
\(706\) −9.00000 15.5885i −0.338719 0.586679i
\(707\) 72.0000i 2.70784i
\(708\) −10.3923 + 6.00000i −0.390567 + 0.225494i
\(709\) 8.66025 5.00000i 0.325243 0.187779i −0.328484 0.944509i \(-0.606538\pi\)
0.653727 + 0.756730i \(0.273204\pi\)
\(710\) 6.00000i 0.225176i
\(711\) 6.00000 + 10.3923i 0.225018 + 0.389742i
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) −51.9615 30.0000i −1.94597 1.12351i
\(714\) 16.0000 0.598785
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) 10.3923 + 6.00000i 0.388108 + 0.224074i
\(718\) −5.00000 + 8.66025i −0.186598 + 0.323198i
\(719\) −16.0000 27.7128i −0.596699 1.03351i −0.993305 0.115524i \(-0.963145\pi\)
0.396605 0.917989i \(-0.370188\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 6.92820 4.00000i 0.258020 0.148968i
\(722\) −14.7224 + 8.50000i −0.547912 + 0.316337i
\(723\) 20.0000i 0.743808i
\(724\) −11.0000 19.0526i −0.408812 0.708083i
\(725\) 1.00000 1.73205i 0.0371391 0.0643268i
\(726\) 12.1244 + 7.00000i 0.449977 + 0.259794i
\(727\) 18.0000 0.667583 0.333792 0.942647i \(-0.391672\pi\)
0.333792 + 0.942647i \(0.391672\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −5.19615 3.00000i −0.192318 0.111035i
\(731\) −10.0000 + 17.3205i −0.369863 + 0.640622i
\(732\) 2.00000 + 3.46410i 0.0739221 + 0.128037i
\(733\) 34.0000i 1.25582i −0.778287 0.627909i \(-0.783911\pi\)
0.778287 0.627909i \(-0.216089\pi\)
\(734\) −12.1244 + 7.00000i −0.447518 + 0.258375i
\(735\) 15.5885 9.00000i 0.574989 0.331970i
\(736\) 30.0000i 1.10581i
\(737\) 4.00000 + 6.92820i 0.147342 + 0.255204i
\(738\) 3.00000 5.19615i 0.110432 0.191273i
\(739\) −5.19615 3.00000i −0.191144 0.110357i 0.401374 0.915914i \(-0.368533\pi\)
−0.592518 + 0.805557i \(0.701866\pi\)
\(740\) 2.00000 0.0735215
\(741\) 0 0
\(742\) 8.00000 0.293689
\(743\) −10.3923 6.00000i −0.381257 0.220119i 0.297108 0.954844i \(-0.403978\pi\)
−0.678365 + 0.734725i \(0.737311\pi\)
\(744\) −30.0000 + 51.9615i −1.09985 + 1.90500i
\(745\) −9.00000 15.5885i −0.329734 0.571117i
\(746\) 34.0000i 1.24483i
\(747\) 13.8564 8.00000i 0.506979 0.292705i
\(748\) −3.46410 + 2.00000i −0.126660 + 0.0731272i
\(749\) 40.0000i 1.46157i
\(750\) 1.00000 + 1.73205i 0.0365148 + 0.0632456i
\(751\) −14.0000 + 24.2487i −0.510867 + 0.884848i 0.489053 + 0.872254i \(0.337342\pi\)
−0.999921 + 0.0125942i \(0.995991\pi\)
\(752\) 3.46410 + 2.00000i 0.126323 + 0.0729325i
\(753\) 48.0000 1.74922
\(754\) 0 0
\(755\) −10.0000 −0.363937
\(756\) 13.8564 + 8.00000i 0.503953 + 0.290957i
\(757\) −1.00000 + 1.73205i −0.0363456 + 0.0629525i −0.883626 0.468193i \(-0.844905\pi\)
0.847280 + 0.531146i \(0.178238\pi\)
\(758\) −5.00000 8.66025i −0.181608 0.314555i
\(759\) 24.0000i 0.871145i
\(760\) −15.5885 + 9.00000i −0.565453 + 0.326464i
\(761\) 15.5885 9.00000i 0.565081 0.326250i −0.190101 0.981764i \(-0.560882\pi\)
0.755182 + 0.655515i \(0.227548\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 20.0000 + 34.6410i 0.724049 + 1.25409i
\(764\) 0 0
\(765\) 1.73205 + 1.00000i 0.0626224 + 0.0361551i
\(766\) 12.0000 0.433578
\(767\) 0 0
\(768\) 34.0000 1.22687
\(769\) 22.5167 + 13.0000i 0.811972 + 0.468792i 0.847640 0.530572i \(-0.178023\pi\)
−0.0356685 + 0.999364i \(0.511356\pi\)
\(770\) 4.00000 6.92820i 0.144150 0.249675i
\(771\) −2.00000 3.46410i −0.0720282 0.124757i
\(772\) 2.00000i 0.0719816i
\(773\) 1.73205 1.00000i 0.0622975 0.0359675i −0.468528 0.883449i \(-0.655215\pi\)
0.530825 + 0.847481i \(0.321882\pi\)
\(774\) −8.66025 + 5.00000i −0.311286 + 0.179721i
\(775\) 10.0000i 0.359211i
\(776\) 3.00000 + 5.19615i 0.107694 + 0.186531i
\(777\) −8.00000 + 13.8564i −0.286998 + 0.497096i
\(778\) −8.66025 5.00000i −0.310485 0.179259i
\(779\) −36.0000 −1.28983
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 10.3923 + 6.00000i 0.371628 + 0.214560i
\(783\) −4.00000 + 6.92820i −0.142948 + 0.247594i
\(784\) −4.50000 7.79423i −0.160714 0.278365i
\(785\) 6.00000i 0.214149i
\(786\) −34.6410 + 20.0000i −1.23560 + 0.713376i
\(787\) 6.92820 4.00000i 0.246964 0.142585i −0.371409 0.928469i \(-0.621125\pi\)
0.618373 + 0.785885i \(0.287792\pi\)
\(788\) 6.00000i 0.213741i
\(789\) 14.0000 + 24.2487i 0.498413 + 0.863277i
\(790\) −6.00000 + 10.3923i −0.213470 + 0.369742i
\(791\) −48.4974 28.0000i −1.72437 0.995565i
\(792\) −6.00000 −0.213201
\(793\) 0 0
\(794\) −6.00000 −0.212932
\(795\) 3.46410 + 2.00000i 0.122859 + 0.0709327i
\(796\) −8.00000 + 13.8564i −0.283552 + 0.491127i
\(797\) 21.0000 + 36.3731i 0.743858 + 1.28840i 0.950726 + 0.310031i \(0.100340\pi\)
−0.206868 + 0.978369i \(0.566327\pi\)
\(798\) 48.0000i 1.69918i
\(799\) −6.92820 + 4.00000i −0.245102 + 0.141510i
\(800\) −4.33013 + 2.50000i −0.153093 + 0.0883883i
\(801\) 2.00000i 0.0706665i
\(802\) 5.00000 + 8.66025i 0.176556 + 0.305804i
\(803\) −6.00000 + 10.3923i −0.211735 + 0.366736i
\(804\) 6.92820 + 4.00000i 0.244339 + 0.141069i
\(805\) 24.0000 0.845889
\(806\) 0 0
\(807\) −12.0000 −0.422420
\(808\) −46.7654 27.0000i −1.64520 0.949857i
\(809\) 1.00000 1.73205i 0.0351581 0.0608957i −0.847911 0.530139i \(-0.822140\pi\)
0.883069 + 0.469243i \(0.155473\pi\)
\(810\) −5.50000 9.52628i −0.193250 0.334719i
\(811\) 42.0000i 1.47482i 0.675446 + 0.737410i \(0.263951\pi\)
−0.675446 + 0.737410i \(0.736049\pi\)
\(812\) −6.92820 + 4.00000i −0.243132 + 0.140372i
\(813\) −3.46410 + 2.00000i −0.121491 + 0.0701431i
\(814\) 4.00000i 0.140200i
\(815\) −6.00000 10.3923i −0.210171 0.364027i
\(816\) 2.00000 3.46410i 0.0700140 0.121268i
\(817\) 51.9615 + 30.0000i 1.81790 + 1.04957i
\(818\) 18.0000 0.629355
\(819\) 0 0
\(820\) −6.00000 −0.209529
\(821\) 43.3013 + 25.0000i 1.51122 + 0.872506i 0.999914 + 0.0131101i \(0.00417319\pi\)
0.511311 + 0.859396i \(0.329160\pi\)
\(822\) 2.00000 3.46410i 0.0697580 0.120824i
\(823\) −23.0000 39.8372i −0.801730 1.38864i −0.918477 0.395475i \(-0.870580\pi\)
0.116747 0.993162i \(-0.462753\pi\)
\(824\) 6.00000i 0.209020i
\(825\) 3.46410 2.00000i 0.120605 0.0696311i
\(826\) 20.7846 12.0000i 0.723189 0.417533i
\(827\) 32.0000i 1.11275i −0.830932 0.556375i \(-0.812192\pi\)
0.830932 0.556375i \(-0.187808\pi\)
\(828\) −3.00000 5.19615i −0.104257 0.180579i
\(829\) 17.0000 29.4449i 0.590434 1.02266i −0.403739 0.914874i \(-0.632290\pi\)
0.994174 0.107788i \(-0.0343769\pi\)
\(830\) 13.8564 + 8.00000i 0.480963 + 0.277684i
\(831\) −28.0000 −0.971309
\(832\) 0 0
\(833\) 18.0000 0.623663
\(834\) 0 0
\(835\) −6.00000 + 10.3923i −0.207639 + 0.359641i
\(836\) 6.00000 + 10.3923i 0.207514 + 0.359425i
\(837\) 40.0000i 1.38260i
\(838\) −34.6410 + 20.0000i −1.19665 + 0.690889i
\(839\) 32.9090 19.0000i 1.13614 0.655953i 0.190671 0.981654i \(-0.438934\pi\)
0.945473 + 0.325701i \(0.105600\pi\)
\(840\) 24.0000i 0.828079i
\(841\) 12.5000 + 21.6506i 0.431034 + 0.746574i
\(842\) −5.00000 + 8.66025i −0.172311 + 0.298452i
\(843\) −10.3923 6.00000i −0.357930 0.206651i
\(844\) 12.0000 0.413057
\(845\) 0 0
\(846\) −4.00000 −0.137523
\(847\) 24.2487 + 14.0000i 0.833196 + 0.481046i
\(848\) 1.00000 1.73205i 0.0343401 0.0594789i
\(849\) −2.00000 3.46410i −0.0686398 0.118888i
\(850\) 2.00000i 0.0685994i
\(851\) −10.3923 + 6.00000i −0.356244 + 0.205677i
\(852\) 10.3923 6.00000i 0.356034 0.205557i
\(853\) 6.00000i 0.205436i 0.994711 + 0.102718i \(0.0327539\pi\)
−0.994711 + 0.102718i \(0.967246\pi\)
\(854\) −4.00000 6.92820i −0.136877 0.237078i
\(855\) 3.00000 5.19615i 0.102598 0.177705i
\(856\) −25.9808 15.0000i −0.888004 0.512689i
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) 40.0000 1.36478 0.682391 0.730987i \(-0.260940\pi\)
0.682391 + 0.730987i \(0.260940\pi\)
\(860\) 8.66025 + 5.00000i 0.295312 + 0.170499i
\(861\) 24.0000 41.5692i 0.817918 1.41668i
\(862\) −7.00000 12.1244i −0.238421 0.412957i
\(863\) 12.0000i 0.408485i −0.978920 0.204242i \(-0.934527\pi\)
0.978920 0.204242i \(-0.0654731\pi\)
\(864\) 17.3205 10.0000i 0.589256 0.340207i
\(865\) 5.19615 3.00000i 0.176674 0.102003i
\(866\) 10.0000i 0.339814i
\(867\) −13.0000 22.5167i −0.441503 0.764706i
\(868\) −20.0000 + 34.6410i −0.678844 + 1.17579i
\(869\) 20.7846 + 12.0000i 0.705070 + 0.407072i
\(870\) 4.00000 0.135613
\(871\) 0 0
\(872\) 30.0000 1.01593
\(873\) −1.73205 1.00000i −0.0586210 0.0338449i
\(874\) 18.0000 31.1769i 0.608859 1.05457i
\(875\) 2.00000 + 3.46410i 0.0676123 + 0.117108i
\(876\) 12.0000i 0.405442i
\(877\) −15.5885 + 9.00000i −0.526385 + 0.303908i −0.739543 0.673109i \(-0.764958\pi\)
0.213158 + 0.977018i \(0.431625\pi\)
\(878\) 0 0
\(879\) 44.0000i 1.48408i
\(880\) −1.00000 1.73205i −0.0337100 0.0583874i
\(881\) 19.0000 32.9090i 0.640126 1.10873i −0.345278 0.938500i \(-0.612215\pi\)
0.985404 0.170231i \(-0.0544513\pi\)
\(882\) 7.79423 + 4.50000i 0.262445 + 0.151523i
\(883\) 22.0000 0.740359 0.370179 0.928960i \(-0.379296\pi\)
0.370179 + 0.928960i \(0.379296\pi\)
\(884\) 0 0
\(885\) 12.0000 0.403376
\(886\) −12.1244 7.00000i −0.407326 0.235170i
\(887\) −29.0000 + 50.2295i −0.973725 + 1.68654i −0.289644 + 0.957135i \(0.593537\pi\)
−0.684081 + 0.729406i \(0.739796\pi\)
\(888\) 6.00000 + 10.3923i 0.201347 + 0.348743i
\(889\) 8.00000i 0.268311i
\(890\) −1.73205 + 1.00000i −0.0580585 + 0.0335201i
\(891\) −19.0526 + 11.0000i −0.638285 + 0.368514i
\(892\) 4.00000i 0.133930i
\(893\) 12.0000 + 20.7846i 0.401565 + 0.695530i
\(894\) 18.0000 31.1769i 0.602010 1.04271i
\(895\) 10.3923 + 6.00000i 0.347376 + 0.200558i
\(896\) 12.0000 0.400892
\(897\) 0 0
\(898\) 6.00000 0.200223
\(899\) −17.3205 10.0000i −0.577671 0.333519i
\(900\) 0.500000 0.866025i 0.0166667 0.0288675i
\(901\) 2.00000 + 3.46410i 0.0666297 + 0.115406i
\(902\) 12.0000i 0.399556i
\(903\) −69.2820 + 40.0000i −2.30556 + 1.33112i
\(904\) −36.3731 + 21.0000i −1.20975 + 0.698450i
\(905\) 22.0000i 0.731305i
\(906\) −10.0000 17.3205i −0.332228 0.575435i
\(907\) −17.0000 + 29.4449i −0.564476 + 0.977701i 0.432623 + 0.901575i \(0.357588\pi\)
−0.997098 + 0.0761255i \(0.975745\pi\)
\(908\) 3.46410 + 2.00000i 0.114960 + 0.0663723i
\(909\) 18.0000 0.597022
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) −10.3923 6.00000i −0.344124 0.198680i
\(913\) 16.0000 27.7128i 0.529523 0.917160i
\(914\) −19.0000 32.9090i −0.628464 1.08853i
\(915\) 4.00000i 0.132236i
\(916\) −19.0526 + 11.0000i −0.629514 + 0.363450i
\(917\) −69.2820 + 40.0000i −2.28789 + 1.32092i
\(918\) 8.00000i 0.264039i
\(919\) 26.0000 + 45.0333i 0.857661 + 1.48551i 0.874154 + 0.485648i \(0.161416\pi\)
−0.0164935 + 0.999864i \(0.505250\pi\)
\(920\) 9.00000 15.5885i 0.296721 0.513936i
\(921\) 13.8564 + 8.00000i 0.456584 + 0.263609i
\(922\) 10.0000 0.329332
\(923\) 0 0
\(924\) −16.0000 −0.526361
\(925\) −1.73205 1.00000i −0.0569495 0.0328798i
\(926\) −12.0000 + 20.7846i −0.394344 + 0.683025i
\(927\) 1.00000 + 1.73205i 0.0328443 + 0.0568880i
\(928\) 10.0000i 0.328266i
\(929\) 32.9090 19.0000i 1.07971 0.623370i 0.148890 0.988854i \(-0.452430\pi\)
0.930818 + 0.365484i \(0.119096\pi\)
\(930\) 17.3205 10.0000i 0.567962 0.327913i
\(931\) 54.0000i 1.76978i
\(932\) 5.00000 + 8.66025i 0.163780 + 0.283676i
\(933\) 4.00000 6.92820i 0.130954 0.226819i
\(934\) −8.66025 5.00000i −0.283372 0.163605i
\(935\) 4.00000 0.130814
\(936\) 0 0
\(937\) −30.0000 −0.980057 −0.490029 0.871706i \(-0.663014\pi\)
−0.490029 + 0.871706i \(0.663014\pi\)
\(938\) −13.8564 8.00000i −0.452428 0.261209i
\(939\) −22.0000 + 38.1051i −0.717943 + 1.24351i
\(940\) 2.00000 + 3.46410i 0.0652328 + 0.112987i
\(941\) 18.0000i 0.586783i −0.955992 0.293392i \(-0.905216\pi\)
0.955992 0.293392i \(-0.0947840\pi\)
\(942\) 10.3923 6.00000i 0.338600 0.195491i
\(943\) 31.1769 18.0000i 1.01526 0.586161i
\(944\) 6.00000i 0.195283i
\(945\) −8.00000 13.8564i −0.260240 0.450749i
\(946\) −10.0000 + 17.3205i −0.325128 + 0.563138i
\(947\) −20.7846 12.0000i −0.675409 0.389948i 0.122714 0.992442i \(-0.460840\pi\)
−0.798123 + 0.602494i \(0.794174\pi\)
\(948\) 24.0000 0.779484
\(949\) 0 0
\(950\) 6.00000 0.194666
\(951\) 31.1769 + 18.0000i 1.01098 + 0.583690i
\(952\) 12.0000 20.7846i 0.388922 0.673633i
\(953\) 9.00000 + 15.5885i 0.291539 + 0.504960i 0.974174 0.225800i \(-0.0724995\pi\)
−0.682635 + 0.730759i \(0.739166\pi\)
\(954\) 2.00000i 0.0647524i
\(955\) 0 0
\(956\) 5.19615 3.00000i 0.168056 0.0970269i
\(957\) 8.00000i 0.258603i
\(958\) 15.0000 + 25.9808i 0.484628 + 0.839400i
\(959\) 4.00000 6.92820i 0.129167 0.223723i
\(960\) −12.1244 7.00000i −0.391312 0.225924i
\(961\) −69.0000 −2.22581
\(962\) 0 0
\(963\) 10.0000 0.322245
\(964\) −8.66025 5.00000i −0.278928 0.161039i
\(965\) −1.00000 + 1.73205i −0.0321911 + 0.0557567i
\(966\) 24.0000 + 41.5692i 0.772187 + 1.33747i
\(967\) 8.00000i 0.257263i 0.991692 + 0.128631i \(0.0410584\pi\)
−0.991692 + 0.128631i \(0.958942\pi\)
\(968\) 18.1865 10.5000i 0.584537 0.337483i
\(969\) 20.7846 12.0000i 0.667698 0.385496i
\(970\) 2.00000i 0.0642161i
\(971\) 14.0000 + 24.2487i 0.449281 + 0.778178i 0.998339 0.0576061i \(-0.0183467\pi\)
−0.549058 + 0.835784i \(0.685013\pi\)
\(972\) −5.00000 + 8.66025i −0.160375 + 0.277778i
\(973\) 0 0
\(974\) −40.0000 −1.28168
\(975\) 0 0
\(976\) −2.00000 −0.0640184
\(977\) 15.5885 + 9.00000i 0.498719 + 0.287936i 0.728184 0.685381i \(-0.240364\pi\)
−0.229465 + 0.973317i \(0.573698\pi\)
\(978\) 12.0000 20.7846i 0.383718 0.664619i
\(979\) 2.00000 + 3.46410i 0.0639203 + 0.110713i
\(980\) 9.00000i 0.287494i
\(981\) −8.66025 + 5.00000i −0.276501 + 0.159638i
\(982\) 20.7846 12.0000i 0.663264 0.382935i
\(983\) 56.0000i 1.78612i 0.449935 + 0.893061i \(0.351447\pi\)
−0.449935 + 0.893061i \(0.648553\pi\)
\(984\) −18.0000 31.1769i −0.573819 0.993884i
\(985\) 3.00000 5.19615i 0.0955879 0.165563i
\(986\) 3.46410 + 2.00000i 0.110319 + 0.0636930i
\(987\) −32.0000 −1.01857
\(988\) 0 0
\(989\) −60.0000 −1.90789
\(990\) 1.73205 + 1.00000i 0.0550482 + 0.0317821i
\(991\) −24.0000 + 41.5692i −0.762385 + 1.32049i 0.179233 + 0.983807i \(0.442638\pi\)
−0.941618 + 0.336683i \(0.890695\pi\)
\(992\) 25.0000 + 43.3013i 0.793751 + 1.37482i
\(993\) 36.0000i 1.14243i
\(994\) −20.7846 + 12.0000i −0.659248 + 0.380617i
\(995\) 13.8564 8.00000i 0.439278 0.253617i
\(996\) 32.0000i 1.01396i
\(997\) 11.0000 + 19.0526i 0.348373 + 0.603401i 0.985961 0.166978i \(-0.0534008\pi\)
−0.637587 + 0.770378i \(0.720067\pi\)
\(998\) −5.00000 + 8.66025i −0.158272 + 0.274136i
\(999\) 6.92820 + 4.00000i 0.219199 + 0.126554i
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 845.2.m.b.316.1 4
13.2 odd 12 845.2.e.a.146.1 2
13.3 even 3 inner 845.2.m.b.361.2 4
13.4 even 6 845.2.c.a.506.1 2
13.5 odd 4 845.2.e.a.191.1 2
13.6 odd 12 845.2.a.a.1.1 1
13.7 odd 12 65.2.a.a.1.1 1
13.8 odd 4 845.2.e.b.191.1 2
13.9 even 3 845.2.c.a.506.2 2
13.10 even 6 inner 845.2.m.b.361.1 4
13.11 odd 12 845.2.e.b.146.1 2
13.12 even 2 inner 845.2.m.b.316.2 4
39.20 even 12 585.2.a.h.1.1 1
39.32 even 12 7605.2.a.f.1.1 1
52.7 even 12 1040.2.a.f.1.1 1
65.7 even 12 325.2.b.b.274.1 2
65.19 odd 12 4225.2.a.g.1.1 1
65.33 even 12 325.2.b.b.274.2 2
65.59 odd 12 325.2.a.d.1.1 1
91.20 even 12 3185.2.a.e.1.1 1
104.59 even 12 4160.2.a.f.1.1 1
104.85 odd 12 4160.2.a.q.1.1 1
143.98 even 12 7865.2.a.c.1.1 1
156.59 odd 12 9360.2.a.ca.1.1 1
195.59 even 12 2925.2.a.f.1.1 1
195.98 odd 12 2925.2.c.h.2224.1 2
195.137 odd 12 2925.2.c.h.2224.2 2
260.59 even 12 5200.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.a.a.1.1 1 13.7 odd 12
325.2.a.d.1.1 1 65.59 odd 12
325.2.b.b.274.1 2 65.7 even 12
325.2.b.b.274.2 2 65.33 even 12
585.2.a.h.1.1 1 39.20 even 12
845.2.a.a.1.1 1 13.6 odd 12
845.2.c.a.506.1 2 13.4 even 6
845.2.c.a.506.2 2 13.9 even 3
845.2.e.a.146.1 2 13.2 odd 12
845.2.e.a.191.1 2 13.5 odd 4
845.2.e.b.146.1 2 13.11 odd 12
845.2.e.b.191.1 2 13.8 odd 4
845.2.m.b.316.1 4 1.1 even 1 trivial
845.2.m.b.316.2 4 13.12 even 2 inner
845.2.m.b.361.1 4 13.10 even 6 inner
845.2.m.b.361.2 4 13.3 even 3 inner
1040.2.a.f.1.1 1 52.7 even 12
2925.2.a.f.1.1 1 195.59 even 12
2925.2.c.h.2224.1 2 195.98 odd 12
2925.2.c.h.2224.2 2 195.137 odd 12
3185.2.a.e.1.1 1 91.20 even 12
4160.2.a.f.1.1 1 104.59 even 12
4160.2.a.q.1.1 1 104.85 odd 12
4225.2.a.g.1.1 1 65.19 odd 12
5200.2.a.d.1.1 1 260.59 even 12
7605.2.a.f.1.1 1 39.32 even 12
7865.2.a.c.1.1 1 143.98 even 12
9360.2.a.ca.1.1 1 156.59 odd 12