Properties

Label 50.3.c.c.43.1
Level $50$
Weight $3$
Character 50.43
Analytic conductor $1.362$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [50,3,Mod(7,50)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(50, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("50.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 50.c (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.36240132180\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 10)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 50.43
Dual form 50.3.c.c.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(2.00000 + 2.00000i) q^{3} -2.00000i q^{4} +4.00000 q^{6} +(-2.00000 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(2.00000 + 2.00000i) q^{3} -2.00000i q^{4} +4.00000 q^{6} +(-2.00000 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -1.00000i q^{9} -8.00000 q^{11} +(4.00000 - 4.00000i) q^{12} +(-3.00000 - 3.00000i) q^{13} +4.00000i q^{14} -4.00000 q^{16} +(-7.00000 + 7.00000i) q^{17} +(-1.00000 - 1.00000i) q^{18} +20.0000i q^{19} -8.00000 q^{21} +(-8.00000 + 8.00000i) q^{22} +(2.00000 + 2.00000i) q^{23} -8.00000i q^{24} -6.00000 q^{26} +(20.0000 - 20.0000i) q^{27} +(4.00000 + 4.00000i) q^{28} -40.0000i q^{29} +52.0000 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-16.0000 - 16.0000i) q^{33} +14.0000i q^{34} -2.00000 q^{36} +(3.00000 - 3.00000i) q^{37} +(20.0000 + 20.0000i) q^{38} -12.0000i q^{39} -8.00000 q^{41} +(-8.00000 + 8.00000i) q^{42} +(42.0000 + 42.0000i) q^{43} +16.0000i q^{44} +4.00000 q^{46} +(18.0000 - 18.0000i) q^{47} +(-8.00000 - 8.00000i) q^{48} +41.0000i q^{49} -28.0000 q^{51} +(-6.00000 + 6.00000i) q^{52} +(-53.0000 - 53.0000i) q^{53} -40.0000i q^{54} +8.00000 q^{56} +(-40.0000 + 40.0000i) q^{57} +(-40.0000 - 40.0000i) q^{58} +20.0000i q^{59} -48.0000 q^{61} +(52.0000 - 52.0000i) q^{62} +(2.00000 + 2.00000i) q^{63} +8.00000i q^{64} -32.0000 q^{66} +(-62.0000 + 62.0000i) q^{67} +(14.0000 + 14.0000i) q^{68} +8.00000i q^{69} -28.0000 q^{71} +(-2.00000 + 2.00000i) q^{72} +(47.0000 + 47.0000i) q^{73} -6.00000i q^{74} +40.0000 q^{76} +(16.0000 - 16.0000i) q^{77} +(-12.0000 - 12.0000i) q^{78} +71.0000 q^{81} +(-8.00000 + 8.00000i) q^{82} +(-18.0000 - 18.0000i) q^{83} +16.0000i q^{84} +84.0000 q^{86} +(80.0000 - 80.0000i) q^{87} +(16.0000 + 16.0000i) q^{88} -80.0000i q^{89} +12.0000 q^{91} +(4.00000 - 4.00000i) q^{92} +(104.000 + 104.000i) q^{93} -36.0000i q^{94} -16.0000 q^{96} +(63.0000 - 63.0000i) q^{97} +(41.0000 + 41.0000i) q^{98} +8.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 4 q^{3} + 8 q^{6} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 4 q^{3} + 8 q^{6} - 4 q^{7} - 4 q^{8} - 16 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} - 14 q^{17} - 2 q^{18} - 16 q^{21} - 16 q^{22} + 4 q^{23} - 12 q^{26} + 40 q^{27} + 8 q^{28} + 104 q^{31} - 8 q^{32} - 32 q^{33} - 4 q^{36} + 6 q^{37} + 40 q^{38} - 16 q^{41} - 16 q^{42} + 84 q^{43} + 8 q^{46} + 36 q^{47} - 16 q^{48} - 56 q^{51} - 12 q^{52} - 106 q^{53} + 16 q^{56} - 80 q^{57} - 80 q^{58} - 96 q^{61} + 104 q^{62} + 4 q^{63} - 64 q^{66} - 124 q^{67} + 28 q^{68} - 56 q^{71} - 4 q^{72} + 94 q^{73} + 80 q^{76} + 32 q^{77} - 24 q^{78} + 142 q^{81} - 16 q^{82} - 36 q^{83} + 168 q^{86} + 160 q^{87} + 32 q^{88} + 24 q^{91} + 8 q^{92} + 208 q^{93} - 32 q^{96} + 126 q^{97} + 82 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).

\(n\) \(27\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.500000 0.500000i
\(3\) 2.00000 + 2.00000i 0.666667 + 0.666667i 0.956943 0.290276i \(-0.0937472\pi\)
−0.290276 + 0.956943i \(0.593747\pi\)
\(4\) 2.00000i 0.500000i
\(5\) 0 0
\(6\) 4.00000 0.666667
\(7\) −2.00000 + 2.00000i −0.285714 + 0.285714i −0.835383 0.549669i \(-0.814754\pi\)
0.549669 + 0.835383i \(0.314754\pi\)
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 1.00000i 0.111111i
\(10\) 0 0
\(11\) −8.00000 −0.727273 −0.363636 0.931541i \(-0.618465\pi\)
−0.363636 + 0.931541i \(0.618465\pi\)
\(12\) 4.00000 4.00000i 0.333333 0.333333i
\(13\) −3.00000 3.00000i −0.230769 0.230769i 0.582245 0.813014i \(-0.302175\pi\)
−0.813014 + 0.582245i \(0.802175\pi\)
\(14\) 4.00000i 0.285714i
\(15\) 0 0
\(16\) −4.00000 −0.250000
\(17\) −7.00000 + 7.00000i −0.411765 + 0.411765i −0.882353 0.470588i \(-0.844042\pi\)
0.470588 + 0.882353i \(0.344042\pi\)
\(18\) −1.00000 1.00000i −0.0555556 0.0555556i
\(19\) 20.0000i 1.05263i 0.850289 + 0.526316i \(0.176427\pi\)
−0.850289 + 0.526316i \(0.823573\pi\)
\(20\) 0 0
\(21\) −8.00000 −0.380952
\(22\) −8.00000 + 8.00000i −0.363636 + 0.363636i
\(23\) 2.00000 + 2.00000i 0.0869565 + 0.0869565i 0.749247 0.662291i \(-0.230416\pi\)
−0.662291 + 0.749247i \(0.730416\pi\)
\(24\) 8.00000i 0.333333i
\(25\) 0 0
\(26\) −6.00000 −0.230769
\(27\) 20.0000 20.0000i 0.740741 0.740741i
\(28\) 4.00000 + 4.00000i 0.142857 + 0.142857i
\(29\) 40.0000i 1.37931i −0.724138 0.689655i \(-0.757762\pi\)
0.724138 0.689655i \(-0.242238\pi\)
\(30\) 0 0
\(31\) 52.0000 1.67742 0.838710 0.544579i \(-0.183310\pi\)
0.838710 + 0.544579i \(0.183310\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) −16.0000 16.0000i −0.484848 0.484848i
\(34\) 14.0000i 0.411765i
\(35\) 0 0
\(36\) −2.00000 −0.0555556
\(37\) 3.00000 3.00000i 0.0810811 0.0810811i −0.665403 0.746484i \(-0.731740\pi\)
0.746484 + 0.665403i \(0.231740\pi\)
\(38\) 20.0000 + 20.0000i 0.526316 + 0.526316i
\(39\) 12.0000i 0.307692i
\(40\) 0 0
\(41\) −8.00000 −0.195122 −0.0975610 0.995230i \(-0.531104\pi\)
−0.0975610 + 0.995230i \(0.531104\pi\)
\(42\) −8.00000 + 8.00000i −0.190476 + 0.190476i
\(43\) 42.0000 + 42.0000i 0.976744 + 0.976744i 0.999736 0.0229915i \(-0.00731906\pi\)
−0.0229915 + 0.999736i \(0.507319\pi\)
\(44\) 16.0000i 0.363636i
\(45\) 0 0
\(46\) 4.00000 0.0869565
\(47\) 18.0000 18.0000i 0.382979 0.382979i −0.489195 0.872174i \(-0.662710\pi\)
0.872174 + 0.489195i \(0.162710\pi\)
\(48\) −8.00000 8.00000i −0.166667 0.166667i
\(49\) 41.0000i 0.836735i
\(50\) 0 0
\(51\) −28.0000 −0.549020
\(52\) −6.00000 + 6.00000i −0.115385 + 0.115385i
\(53\) −53.0000 53.0000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(54\) 40.0000i 0.740741i
\(55\) 0 0
\(56\) 8.00000 0.142857
\(57\) −40.0000 + 40.0000i −0.701754 + 0.701754i
\(58\) −40.0000 40.0000i −0.689655 0.689655i
\(59\) 20.0000i 0.338983i 0.985532 + 0.169492i \(0.0542125\pi\)
−0.985532 + 0.169492i \(0.945787\pi\)
\(60\) 0 0
\(61\) −48.0000 −0.786885 −0.393443 0.919349i \(-0.628716\pi\)
−0.393443 + 0.919349i \(0.628716\pi\)
\(62\) 52.0000 52.0000i 0.838710 0.838710i
\(63\) 2.00000 + 2.00000i 0.0317460 + 0.0317460i
\(64\) 8.00000i 0.125000i
\(65\) 0 0
\(66\) −32.0000 −0.484848
\(67\) −62.0000 + 62.0000i −0.925373 + 0.925373i −0.997403 0.0720294i \(-0.977052\pi\)
0.0720294 + 0.997403i \(0.477052\pi\)
\(68\) 14.0000 + 14.0000i 0.205882 + 0.205882i
\(69\) 8.00000i 0.115942i
\(70\) 0 0
\(71\) −28.0000 −0.394366 −0.197183 0.980367i \(-0.563179\pi\)
−0.197183 + 0.980367i \(0.563179\pi\)
\(72\) −2.00000 + 2.00000i −0.0277778 + 0.0277778i
\(73\) 47.0000 + 47.0000i 0.643836 + 0.643836i 0.951496 0.307661i \(-0.0995461\pi\)
−0.307661 + 0.951496i \(0.599546\pi\)
\(74\) 6.00000i 0.0810811i
\(75\) 0 0
\(76\) 40.0000 0.526316
\(77\) 16.0000 16.0000i 0.207792 0.207792i
\(78\) −12.0000 12.0000i −0.153846 0.153846i
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 71.0000 0.876543
\(82\) −8.00000 + 8.00000i −0.0975610 + 0.0975610i
\(83\) −18.0000 18.0000i −0.216867 0.216867i 0.590310 0.807177i \(-0.299006\pi\)
−0.807177 + 0.590310i \(0.799006\pi\)
\(84\) 16.0000i 0.190476i
\(85\) 0 0
\(86\) 84.0000 0.976744
\(87\) 80.0000 80.0000i 0.919540 0.919540i
\(88\) 16.0000 + 16.0000i 0.181818 + 0.181818i
\(89\) 80.0000i 0.898876i −0.893311 0.449438i \(-0.851624\pi\)
0.893311 0.449438i \(-0.148376\pi\)
\(90\) 0 0
\(91\) 12.0000 0.131868
\(92\) 4.00000 4.00000i 0.0434783 0.0434783i
\(93\) 104.000 + 104.000i 1.11828 + 1.11828i
\(94\) 36.0000i 0.382979i
\(95\) 0 0
\(96\) −16.0000 −0.166667
\(97\) 63.0000 63.0000i 0.649485 0.649485i −0.303384 0.952868i \(-0.598116\pi\)
0.952868 + 0.303384i \(0.0981164\pi\)
\(98\) 41.0000 + 41.0000i 0.418367 + 0.418367i
\(99\) 8.00000i 0.0808081i
\(100\) 0 0
\(101\) 62.0000 0.613861 0.306931 0.951732i \(-0.400698\pi\)
0.306931 + 0.951732i \(0.400698\pi\)
\(102\) −28.0000 + 28.0000i −0.274510 + 0.274510i
\(103\) −118.000 118.000i −1.14563 1.14563i −0.987403 0.158229i \(-0.949422\pi\)
−0.158229 0.987403i \(-0.550578\pi\)
\(104\) 12.0000i 0.115385i
\(105\) 0 0
\(106\) −106.000 −1.00000
\(107\) −142.000 + 142.000i −1.32710 + 1.32710i −0.419217 + 0.907886i \(0.637695\pi\)
−0.907886 + 0.419217i \(0.862305\pi\)
\(108\) −40.0000 40.0000i −0.370370 0.370370i
\(109\) 10.0000i 0.0917431i 0.998947 + 0.0458716i \(0.0146065\pi\)
−0.998947 + 0.0458716i \(0.985394\pi\)
\(110\) 0 0
\(111\) 12.0000 0.108108
\(112\) 8.00000 8.00000i 0.0714286 0.0714286i
\(113\) −23.0000 23.0000i −0.203540 0.203540i 0.597975 0.801515i \(-0.295972\pi\)
−0.801515 + 0.597975i \(0.795972\pi\)
\(114\) 80.0000i 0.701754i
\(115\) 0 0
\(116\) −80.0000 −0.689655
\(117\) −3.00000 + 3.00000i −0.0256410 + 0.0256410i
\(118\) 20.0000 + 20.0000i 0.169492 + 0.169492i
\(119\) 28.0000i 0.235294i
\(120\) 0 0
\(121\) −57.0000 −0.471074
\(122\) −48.0000 + 48.0000i −0.393443 + 0.393443i
\(123\) −16.0000 16.0000i −0.130081 0.130081i
\(124\) 104.000i 0.838710i
\(125\) 0 0
\(126\) 4.00000 0.0317460
\(127\) 118.000 118.000i 0.929134 0.929134i −0.0685161 0.997650i \(-0.521826\pi\)
0.997650 + 0.0685161i \(0.0218265\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 168.000i 1.30233i
\(130\) 0 0
\(131\) −128.000 −0.977099 −0.488550 0.872536i \(-0.662474\pi\)
−0.488550 + 0.872536i \(0.662474\pi\)
\(132\) −32.0000 + 32.0000i −0.242424 + 0.242424i
\(133\) −40.0000 40.0000i −0.300752 0.300752i
\(134\) 124.000i 0.925373i
\(135\) 0 0
\(136\) 28.0000 0.205882
\(137\) 63.0000 63.0000i 0.459854 0.459854i −0.438753 0.898607i \(-0.644580\pi\)
0.898607 + 0.438753i \(0.144580\pi\)
\(138\) 8.00000 + 8.00000i 0.0579710 + 0.0579710i
\(139\) 140.000i 1.00719i −0.863939 0.503597i \(-0.832010\pi\)
0.863939 0.503597i \(-0.167990\pi\)
\(140\) 0 0
\(141\) 72.0000 0.510638
\(142\) −28.0000 + 28.0000i −0.197183 + 0.197183i
\(143\) 24.0000 + 24.0000i 0.167832 + 0.167832i
\(144\) 4.00000i 0.0277778i
\(145\) 0 0
\(146\) 94.0000 0.643836
\(147\) −82.0000 + 82.0000i −0.557823 + 0.557823i
\(148\) −6.00000 6.00000i −0.0405405 0.0405405i
\(149\) 150.000i 1.00671i 0.864079 + 0.503356i \(0.167901\pi\)
−0.864079 + 0.503356i \(0.832099\pi\)
\(150\) 0 0
\(151\) 52.0000 0.344371 0.172185 0.985065i \(-0.444917\pi\)
0.172185 + 0.985065i \(0.444917\pi\)
\(152\) 40.0000 40.0000i 0.263158 0.263158i
\(153\) 7.00000 + 7.00000i 0.0457516 + 0.0457516i
\(154\) 32.0000i 0.207792i
\(155\) 0 0
\(156\) −24.0000 −0.153846
\(157\) −27.0000 + 27.0000i −0.171975 + 0.171975i −0.787846 0.615872i \(-0.788804\pi\)
0.615872 + 0.787846i \(0.288804\pi\)
\(158\) 0 0
\(159\) 212.000i 1.33333i
\(160\) 0 0
\(161\) −8.00000 −0.0496894
\(162\) 71.0000 71.0000i 0.438272 0.438272i
\(163\) 82.0000 + 82.0000i 0.503067 + 0.503067i 0.912390 0.409322i \(-0.134235\pi\)
−0.409322 + 0.912390i \(0.634235\pi\)
\(164\) 16.0000i 0.0975610i
\(165\) 0 0
\(166\) −36.0000 −0.216867
\(167\) −62.0000 + 62.0000i −0.371257 + 0.371257i −0.867935 0.496678i \(-0.834553\pi\)
0.496678 + 0.867935i \(0.334553\pi\)
\(168\) 16.0000 + 16.0000i 0.0952381 + 0.0952381i
\(169\) 151.000i 0.893491i
\(170\) 0 0
\(171\) 20.0000 0.116959
\(172\) 84.0000 84.0000i 0.488372 0.488372i
\(173\) 107.000 + 107.000i 0.618497 + 0.618497i 0.945146 0.326649i \(-0.105919\pi\)
−0.326649 + 0.945146i \(0.605919\pi\)
\(174\) 160.000i 0.919540i
\(175\) 0 0
\(176\) 32.0000 0.181818
\(177\) −40.0000 + 40.0000i −0.225989 + 0.225989i
\(178\) −80.0000 80.0000i −0.449438 0.449438i
\(179\) 220.000i 1.22905i 0.788897 + 0.614525i \(0.210652\pi\)
−0.788897 + 0.614525i \(0.789348\pi\)
\(180\) 0 0
\(181\) 2.00000 0.0110497 0.00552486 0.999985i \(-0.498241\pi\)
0.00552486 + 0.999985i \(0.498241\pi\)
\(182\) 12.0000 12.0000i 0.0659341 0.0659341i
\(183\) −96.0000 96.0000i −0.524590 0.524590i
\(184\) 8.00000i 0.0434783i
\(185\) 0 0
\(186\) 208.000 1.11828
\(187\) 56.0000 56.0000i 0.299465 0.299465i
\(188\) −36.0000 36.0000i −0.191489 0.191489i
\(189\) 80.0000i 0.423280i
\(190\) 0 0
\(191\) 212.000 1.10995 0.554974 0.831868i \(-0.312728\pi\)
0.554974 + 0.831868i \(0.312728\pi\)
\(192\) −16.0000 + 16.0000i −0.0833333 + 0.0833333i
\(193\) 57.0000 + 57.0000i 0.295337 + 0.295337i 0.839184 0.543847i \(-0.183033\pi\)
−0.543847 + 0.839184i \(0.683033\pi\)
\(194\) 126.000i 0.649485i
\(195\) 0 0
\(196\) 82.0000 0.418367
\(197\) 3.00000 3.00000i 0.0152284 0.0152284i −0.699452 0.714680i \(-0.746572\pi\)
0.714680 + 0.699452i \(0.246572\pi\)
\(198\) 8.00000 + 8.00000i 0.0404040 + 0.0404040i
\(199\) 120.000i 0.603015i 0.953464 + 0.301508i \(0.0974898\pi\)
−0.953464 + 0.301508i \(0.902510\pi\)
\(200\) 0 0
\(201\) −248.000 −1.23383
\(202\) 62.0000 62.0000i 0.306931 0.306931i
\(203\) 80.0000 + 80.0000i 0.394089 + 0.394089i
\(204\) 56.0000i 0.274510i
\(205\) 0 0
\(206\) −236.000 −1.14563
\(207\) 2.00000 2.00000i 0.00966184 0.00966184i
\(208\) 12.0000 + 12.0000i 0.0576923 + 0.0576923i
\(209\) 160.000i 0.765550i
\(210\) 0 0
\(211\) −328.000 −1.55450 −0.777251 0.629190i \(-0.783387\pi\)
−0.777251 + 0.629190i \(0.783387\pi\)
\(212\) −106.000 + 106.000i −0.500000 + 0.500000i
\(213\) −56.0000 56.0000i −0.262911 0.262911i
\(214\) 284.000i 1.32710i
\(215\) 0 0
\(216\) −80.0000 −0.370370
\(217\) −104.000 + 104.000i −0.479263 + 0.479263i
\(218\) 10.0000 + 10.0000i 0.0458716 + 0.0458716i
\(219\) 188.000i 0.858447i
\(220\) 0 0
\(221\) 42.0000 0.190045
\(222\) 12.0000 12.0000i 0.0540541 0.0540541i
\(223\) −138.000 138.000i −0.618834 0.618834i 0.326398 0.945232i \(-0.394165\pi\)
−0.945232 + 0.326398i \(0.894165\pi\)
\(224\) 16.0000i 0.0714286i
\(225\) 0 0
\(226\) −46.0000 −0.203540
\(227\) −2.00000 + 2.00000i −0.00881057 + 0.00881057i −0.711498 0.702688i \(-0.751983\pi\)
0.702688 + 0.711498i \(0.251983\pi\)
\(228\) 80.0000 + 80.0000i 0.350877 + 0.350877i
\(229\) 120.000i 0.524017i −0.965066 0.262009i \(-0.915615\pi\)
0.965066 0.262009i \(-0.0843849\pi\)
\(230\) 0 0
\(231\) 64.0000 0.277056
\(232\) −80.0000 + 80.0000i −0.344828 + 0.344828i
\(233\) −183.000 183.000i −0.785408 0.785408i 0.195330 0.980738i \(-0.437422\pi\)
−0.980738 + 0.195330i \(0.937422\pi\)
\(234\) 6.00000i 0.0256410i
\(235\) 0 0
\(236\) 40.0000 0.169492
\(237\) 0 0
\(238\) −28.0000 28.0000i −0.117647 0.117647i
\(239\) 120.000i 0.502092i −0.967975 0.251046i \(-0.919225\pi\)
0.967975 0.251046i \(-0.0807746\pi\)
\(240\) 0 0
\(241\) 232.000 0.962656 0.481328 0.876541i \(-0.340155\pi\)
0.481328 + 0.876541i \(0.340155\pi\)
\(242\) −57.0000 + 57.0000i −0.235537 + 0.235537i
\(243\) −38.0000 38.0000i −0.156379 0.156379i
\(244\) 96.0000i 0.393443i
\(245\) 0 0
\(246\) −32.0000 −0.130081
\(247\) 60.0000 60.0000i 0.242915 0.242915i
\(248\) −104.000 104.000i −0.419355 0.419355i
\(249\) 72.0000i 0.289157i
\(250\) 0 0
\(251\) −48.0000 −0.191235 −0.0956175 0.995418i \(-0.530483\pi\)
−0.0956175 + 0.995418i \(0.530483\pi\)
\(252\) 4.00000 4.00000i 0.0158730 0.0158730i
\(253\) −16.0000 16.0000i −0.0632411 0.0632411i
\(254\) 236.000i 0.929134i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 313.000 313.000i 1.21790 1.21790i 0.249532 0.968366i \(-0.419723\pi\)
0.968366 0.249532i \(-0.0802769\pi\)
\(258\) 168.000 + 168.000i 0.651163 + 0.651163i
\(259\) 12.0000i 0.0463320i
\(260\) 0 0
\(261\) −40.0000 −0.153257
\(262\) −128.000 + 128.000i −0.488550 + 0.488550i
\(263\) 262.000 + 262.000i 0.996198 + 0.996198i 0.999993 0.00379508i \(-0.00120801\pi\)
−0.00379508 + 0.999993i \(0.501208\pi\)
\(264\) 64.0000i 0.242424i
\(265\) 0 0
\(266\) −80.0000 −0.300752
\(267\) 160.000 160.000i 0.599251 0.599251i
\(268\) 124.000 + 124.000i 0.462687 + 0.462687i
\(269\) 10.0000i 0.0371747i −0.999827 0.0185874i \(-0.994083\pi\)
0.999827 0.0185874i \(-0.00591688\pi\)
\(270\) 0 0
\(271\) 252.000 0.929889 0.464945 0.885340i \(-0.346074\pi\)
0.464945 + 0.885340i \(0.346074\pi\)
\(272\) 28.0000 28.0000i 0.102941 0.102941i
\(273\) 24.0000 + 24.0000i 0.0879121 + 0.0879121i
\(274\) 126.000i 0.459854i
\(275\) 0 0
\(276\) 16.0000 0.0579710
\(277\) −267.000 + 267.000i −0.963899 + 0.963899i −0.999371 0.0354718i \(-0.988707\pi\)
0.0354718 + 0.999371i \(0.488707\pi\)
\(278\) −140.000 140.000i −0.503597 0.503597i
\(279\) 52.0000i 0.186380i
\(280\) 0 0
\(281\) 312.000 1.11032 0.555160 0.831743i \(-0.312657\pi\)
0.555160 + 0.831743i \(0.312657\pi\)
\(282\) 72.0000 72.0000i 0.255319 0.255319i
\(283\) 262.000 + 262.000i 0.925795 + 0.925795i 0.997431 0.0716358i \(-0.0228219\pi\)
−0.0716358 + 0.997431i \(0.522822\pi\)
\(284\) 56.0000i 0.197183i
\(285\) 0 0
\(286\) 48.0000 0.167832
\(287\) 16.0000 16.0000i 0.0557491 0.0557491i
\(288\) 4.00000 + 4.00000i 0.0138889 + 0.0138889i
\(289\) 191.000i 0.660900i
\(290\) 0 0
\(291\) 252.000 0.865979
\(292\) 94.0000 94.0000i 0.321918 0.321918i
\(293\) −243.000 243.000i −0.829352 0.829352i 0.158075 0.987427i \(-0.449471\pi\)
−0.987427 + 0.158075i \(0.949471\pi\)
\(294\) 164.000i 0.557823i
\(295\) 0 0
\(296\) −12.0000 −0.0405405
\(297\) −160.000 + 160.000i −0.538721 + 0.538721i
\(298\) 150.000 + 150.000i 0.503356 + 0.503356i
\(299\) 12.0000i 0.0401338i
\(300\) 0 0
\(301\) −168.000 −0.558140
\(302\) 52.0000 52.0000i 0.172185 0.172185i
\(303\) 124.000 + 124.000i 0.409241 + 0.409241i
\(304\) 80.0000i 0.263158i
\(305\) 0 0
\(306\) 14.0000 0.0457516
\(307\) 18.0000 18.0000i 0.0586319 0.0586319i −0.677183 0.735815i \(-0.736799\pi\)
0.735815 + 0.677183i \(0.236799\pi\)
\(308\) −32.0000 32.0000i −0.103896 0.103896i
\(309\) 472.000i 1.52751i
\(310\) 0 0
\(311\) −388.000 −1.24759 −0.623794 0.781589i \(-0.714410\pi\)
−0.623794 + 0.781589i \(0.714410\pi\)
\(312\) −24.0000 + 24.0000i −0.0769231 + 0.0769231i
\(313\) −183.000 183.000i −0.584665 0.584665i 0.351517 0.936182i \(-0.385666\pi\)
−0.936182 + 0.351517i \(0.885666\pi\)
\(314\) 54.0000i 0.171975i
\(315\) 0 0
\(316\) 0 0
\(317\) 213.000 213.000i 0.671924 0.671924i −0.286235 0.958159i \(-0.592404\pi\)
0.958159 + 0.286235i \(0.0924038\pi\)
\(318\) −212.000 212.000i −0.666667 0.666667i
\(319\) 320.000i 1.00313i
\(320\) 0 0
\(321\) −568.000 −1.76947
\(322\) −8.00000 + 8.00000i −0.0248447 + 0.0248447i
\(323\) −140.000 140.000i −0.433437 0.433437i
\(324\) 142.000i 0.438272i
\(325\) 0 0
\(326\) 164.000 0.503067
\(327\) −20.0000 + 20.0000i −0.0611621 + 0.0611621i
\(328\) 16.0000 + 16.0000i 0.0487805 + 0.0487805i
\(329\) 72.0000i 0.218845i
\(330\) 0 0
\(331\) 232.000 0.700906 0.350453 0.936580i \(-0.386028\pi\)
0.350453 + 0.936580i \(0.386028\pi\)
\(332\) −36.0000 + 36.0000i −0.108434 + 0.108434i
\(333\) −3.00000 3.00000i −0.00900901 0.00900901i
\(334\) 124.000i 0.371257i
\(335\) 0 0
\(336\) 32.0000 0.0952381
\(337\) −417.000 + 417.000i −1.23739 + 1.23739i −0.276324 + 0.961064i \(0.589116\pi\)
−0.961064 + 0.276324i \(0.910884\pi\)
\(338\) −151.000 151.000i −0.446746 0.446746i
\(339\) 92.0000i 0.271386i
\(340\) 0 0
\(341\) −416.000 −1.21994
\(342\) 20.0000 20.0000i 0.0584795 0.0584795i
\(343\) −180.000 180.000i −0.524781 0.524781i
\(344\) 168.000i 0.488372i
\(345\) 0 0
\(346\) 214.000 0.618497
\(347\) −202.000 + 202.000i −0.582133 + 0.582133i −0.935489 0.353356i \(-0.885040\pi\)
0.353356 + 0.935489i \(0.385040\pi\)
\(348\) −160.000 160.000i −0.459770 0.459770i
\(349\) 440.000i 1.26074i 0.776293 + 0.630372i \(0.217098\pi\)
−0.776293 + 0.630372i \(0.782902\pi\)
\(350\) 0 0
\(351\) −120.000 −0.341880
\(352\) 32.0000 32.0000i 0.0909091 0.0909091i
\(353\) 447.000 + 447.000i 1.26629 + 1.26629i 0.947991 + 0.318298i \(0.103111\pi\)
0.318298 + 0.947991i \(0.396889\pi\)
\(354\) 80.0000i 0.225989i
\(355\) 0 0
\(356\) −160.000 −0.449438
\(357\) 56.0000 56.0000i 0.156863 0.156863i
\(358\) 220.000 + 220.000i 0.614525 + 0.614525i
\(359\) 400.000i 1.11421i 0.830443 + 0.557103i \(0.188087\pi\)
−0.830443 + 0.557103i \(0.811913\pi\)
\(360\) 0 0
\(361\) −39.0000 −0.108033
\(362\) 2.00000 2.00000i 0.00552486 0.00552486i
\(363\) −114.000 114.000i −0.314050 0.314050i
\(364\) 24.0000i 0.0659341i
\(365\) 0 0
\(366\) −192.000 −0.524590
\(367\) 118.000 118.000i 0.321526 0.321526i −0.527826 0.849352i \(-0.676993\pi\)
0.849352 + 0.527826i \(0.176993\pi\)
\(368\) −8.00000 8.00000i −0.0217391 0.0217391i
\(369\) 8.00000i 0.0216802i
\(370\) 0 0
\(371\) 212.000 0.571429
\(372\) 208.000 208.000i 0.559140 0.559140i
\(373\) 107.000 + 107.000i 0.286863 + 0.286863i 0.835839 0.548975i \(-0.184982\pi\)
−0.548975 + 0.835839i \(0.684982\pi\)
\(374\) 112.000i 0.299465i
\(375\) 0 0
\(376\) −72.0000 −0.191489
\(377\) −120.000 + 120.000i −0.318302 + 0.318302i
\(378\) 80.0000 + 80.0000i 0.211640 + 0.211640i
\(379\) 340.000i 0.897098i −0.893758 0.448549i \(-0.851941\pi\)
0.893758 0.448549i \(-0.148059\pi\)
\(380\) 0 0
\(381\) 472.000 1.23885
\(382\) 212.000 212.000i 0.554974 0.554974i
\(383\) 342.000 + 342.000i 0.892950 + 0.892950i 0.994800 0.101849i \(-0.0324760\pi\)
−0.101849 + 0.994800i \(0.532476\pi\)
\(384\) 32.0000i 0.0833333i
\(385\) 0 0
\(386\) 114.000 0.295337
\(387\) 42.0000 42.0000i 0.108527 0.108527i
\(388\) −126.000 126.000i −0.324742 0.324742i
\(389\) 390.000i 1.00257i −0.865282 0.501285i \(-0.832861\pi\)
0.865282 0.501285i \(-0.167139\pi\)
\(390\) 0 0
\(391\) −28.0000 −0.0716113
\(392\) 82.0000 82.0000i 0.209184 0.209184i
\(393\) −256.000 256.000i −0.651399 0.651399i
\(394\) 6.00000i 0.0152284i
\(395\) 0 0
\(396\) 16.0000 0.0404040
\(397\) 323.000 323.000i 0.813602 0.813602i −0.171570 0.985172i \(-0.554884\pi\)
0.985172 + 0.171570i \(0.0548839\pi\)
\(398\) 120.000 + 120.000i 0.301508 + 0.301508i
\(399\) 160.000i 0.401003i
\(400\) 0 0
\(401\) 642.000 1.60100 0.800499 0.599334i \(-0.204568\pi\)
0.800499 + 0.599334i \(0.204568\pi\)
\(402\) −248.000 + 248.000i −0.616915 + 0.616915i
\(403\) −156.000 156.000i −0.387097 0.387097i
\(404\) 124.000i 0.306931i
\(405\) 0 0
\(406\) 160.000 0.394089
\(407\) −24.0000 + 24.0000i −0.0589681 + 0.0589681i
\(408\) 56.0000 + 56.0000i 0.137255 + 0.137255i
\(409\) 150.000i 0.366748i 0.983043 + 0.183374i \(0.0587020\pi\)
−0.983043 + 0.183374i \(0.941298\pi\)
\(410\) 0 0
\(411\) 252.000 0.613139
\(412\) −236.000 + 236.000i −0.572816 + 0.572816i
\(413\) −40.0000 40.0000i −0.0968523 0.0968523i
\(414\) 4.00000i 0.00966184i
\(415\) 0 0
\(416\) 24.0000 0.0576923
\(417\) 280.000 280.000i 0.671463 0.671463i
\(418\) −160.000 160.000i −0.382775 0.382775i
\(419\) 300.000i 0.715990i −0.933723 0.357995i \(-0.883460\pi\)
0.933723 0.357995i \(-0.116540\pi\)
\(420\) 0 0
\(421\) −208.000 −0.494062 −0.247031 0.969008i \(-0.579455\pi\)
−0.247031 + 0.969008i \(0.579455\pi\)
\(422\) −328.000 + 328.000i −0.777251 + 0.777251i
\(423\) −18.0000 18.0000i −0.0425532 0.0425532i
\(424\) 212.000i 0.500000i
\(425\) 0 0
\(426\) −112.000 −0.262911
\(427\) 96.0000 96.0000i 0.224824 0.224824i
\(428\) 284.000 + 284.000i 0.663551 + 0.663551i
\(429\) 96.0000i 0.223776i
\(430\) 0 0
\(431\) −788.000 −1.82831 −0.914153 0.405369i \(-0.867143\pi\)
−0.914153 + 0.405369i \(0.867143\pi\)
\(432\) −80.0000 + 80.0000i −0.185185 + 0.185185i
\(433\) 367.000 + 367.000i 0.847575 + 0.847575i 0.989830 0.142255i \(-0.0454353\pi\)
−0.142255 + 0.989830i \(0.545435\pi\)
\(434\) 208.000i 0.479263i
\(435\) 0 0
\(436\) 20.0000 0.0458716
\(437\) −40.0000 + 40.0000i −0.0915332 + 0.0915332i
\(438\) 188.000 + 188.000i 0.429224 + 0.429224i
\(439\) 560.000i 1.27563i −0.770191 0.637813i \(-0.779839\pi\)
0.770191 0.637813i \(-0.220161\pi\)
\(440\) 0 0
\(441\) 41.0000 0.0929705
\(442\) 42.0000 42.0000i 0.0950226 0.0950226i
\(443\) −378.000 378.000i −0.853273 0.853273i 0.137262 0.990535i \(-0.456170\pi\)
−0.990535 + 0.137262i \(0.956170\pi\)
\(444\) 24.0000i 0.0540541i
\(445\) 0 0
\(446\) −276.000 −0.618834
\(447\) −300.000 + 300.000i −0.671141 + 0.671141i
\(448\) −16.0000 16.0000i −0.0357143 0.0357143i
\(449\) 410.000i 0.913140i 0.889687 + 0.456570i \(0.150922\pi\)
−0.889687 + 0.456570i \(0.849078\pi\)
\(450\) 0 0
\(451\) 64.0000 0.141907
\(452\) −46.0000 + 46.0000i −0.101770 + 0.101770i
\(453\) 104.000 + 104.000i 0.229581 + 0.229581i
\(454\) 4.00000i 0.00881057i
\(455\) 0 0
\(456\) 160.000 0.350877
\(457\) 393.000 393.000i 0.859956 0.859956i −0.131376 0.991333i \(-0.541940\pi\)
0.991333 + 0.131376i \(0.0419396\pi\)
\(458\) −120.000 120.000i −0.262009 0.262009i
\(459\) 280.000i 0.610022i
\(460\) 0 0
\(461\) 622.000 1.34924 0.674620 0.738165i \(-0.264307\pi\)
0.674620 + 0.738165i \(0.264307\pi\)
\(462\) 64.0000 64.0000i 0.138528 0.138528i
\(463\) −278.000 278.000i −0.600432 0.600432i 0.339995 0.940427i \(-0.389575\pi\)
−0.940427 + 0.339995i \(0.889575\pi\)
\(464\) 160.000i 0.344828i
\(465\) 0 0
\(466\) −366.000 −0.785408
\(467\) 38.0000 38.0000i 0.0813704 0.0813704i −0.665250 0.746621i \(-0.731675\pi\)
0.746621 + 0.665250i \(0.231675\pi\)
\(468\) 6.00000 + 6.00000i 0.0128205 + 0.0128205i
\(469\) 248.000i 0.528785i
\(470\) 0 0
\(471\) −108.000 −0.229299
\(472\) 40.0000 40.0000i 0.0847458 0.0847458i
\(473\) −336.000 336.000i −0.710359 0.710359i
\(474\) 0 0
\(475\) 0 0
\(476\) −56.0000 −0.117647
\(477\) −53.0000 + 53.0000i −0.111111 + 0.111111i
\(478\) −120.000 120.000i −0.251046 0.251046i
\(479\) 440.000i 0.918580i 0.888286 + 0.459290i \(0.151896\pi\)
−0.888286 + 0.459290i \(0.848104\pi\)
\(480\) 0 0
\(481\) −18.0000 −0.0374220
\(482\) 232.000 232.000i 0.481328 0.481328i
\(483\) −16.0000 16.0000i −0.0331263 0.0331263i
\(484\) 114.000i 0.235537i
\(485\) 0 0
\(486\) −76.0000 −0.156379
\(487\) −522.000 + 522.000i −1.07187 + 1.07187i −0.0746595 + 0.997209i \(0.523787\pi\)
−0.997209 + 0.0746595i \(0.976213\pi\)
\(488\) 96.0000 + 96.0000i 0.196721 + 0.196721i
\(489\) 328.000i 0.670757i
\(490\) 0 0
\(491\) −328.000 −0.668024 −0.334012 0.942569i \(-0.608403\pi\)
−0.334012 + 0.942569i \(0.608403\pi\)
\(492\) −32.0000 + 32.0000i −0.0650407 + 0.0650407i
\(493\) 280.000 + 280.000i 0.567951 + 0.567951i
\(494\) 120.000i 0.242915i
\(495\) 0 0
\(496\) −208.000 −0.419355
\(497\) 56.0000 56.0000i 0.112676 0.112676i
\(498\) −72.0000 72.0000i −0.144578 0.144578i
\(499\) 380.000i 0.761523i −0.924673 0.380762i \(-0.875662\pi\)
0.924673 0.380762i \(-0.124338\pi\)
\(500\) 0 0
\(501\) −248.000 −0.495010
\(502\) −48.0000 + 48.0000i −0.0956175 + 0.0956175i
\(503\) 42.0000 + 42.0000i 0.0834990 + 0.0834990i 0.747623 0.664124i \(-0.231195\pi\)
−0.664124 + 0.747623i \(0.731195\pi\)
\(504\) 8.00000i 0.0158730i
\(505\) 0 0
\(506\) −32.0000 −0.0632411
\(507\) 302.000 302.000i 0.595661 0.595661i
\(508\) −236.000 236.000i −0.464567 0.464567i
\(509\) 440.000i 0.864440i 0.901768 + 0.432220i \(0.142270\pi\)
−0.901768 + 0.432220i \(0.857730\pi\)
\(510\) 0 0
\(511\) −188.000 −0.367906
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) 400.000 + 400.000i 0.779727 + 0.779727i
\(514\) 626.000i 1.21790i
\(515\) 0 0
\(516\) 336.000 0.651163
\(517\) −144.000 + 144.000i −0.278530 + 0.278530i
\(518\) 12.0000 + 12.0000i 0.0231660 + 0.0231660i
\(519\) 428.000i 0.824663i
\(520\) 0 0
\(521\) −258.000 −0.495202 −0.247601 0.968862i \(-0.579642\pi\)
−0.247601 + 0.968862i \(0.579642\pi\)
\(522\) −40.0000 + 40.0000i −0.0766284 + 0.0766284i
\(523\) −258.000 258.000i −0.493308 0.493308i 0.416039 0.909347i \(-0.363418\pi\)
−0.909347 + 0.416039i \(0.863418\pi\)
\(524\) 256.000i 0.488550i
\(525\) 0 0
\(526\) 524.000 0.996198
\(527\) −364.000 + 364.000i −0.690702 + 0.690702i
\(528\) 64.0000 + 64.0000i 0.121212 + 0.121212i
\(529\) 521.000i 0.984877i
\(530\) 0 0
\(531\) 20.0000 0.0376648
\(532\) −80.0000 + 80.0000i −0.150376 + 0.150376i
\(533\) 24.0000 + 24.0000i 0.0450281 + 0.0450281i
\(534\) 320.000i 0.599251i
\(535\) 0 0
\(536\) 248.000 0.462687
\(537\) −440.000 + 440.000i −0.819367 + 0.819367i
\(538\) −10.0000 10.0000i −0.0185874 0.0185874i
\(539\) 328.000i 0.608534i
\(540\) 0 0
\(541\) −338.000 −0.624769 −0.312384 0.949956i \(-0.601128\pi\)
−0.312384 + 0.949956i \(0.601128\pi\)
\(542\) 252.000 252.000i 0.464945 0.464945i
\(543\) 4.00000 + 4.00000i 0.00736648 + 0.00736648i
\(544\) 56.0000i 0.102941i
\(545\) 0 0
\(546\) 48.0000 0.0879121
\(547\) 558.000 558.000i 1.02011 1.02011i 0.0203161 0.999794i \(-0.493533\pi\)
0.999794 0.0203161i \(-0.00646725\pi\)
\(548\) −126.000 126.000i −0.229927 0.229927i
\(549\) 48.0000i 0.0874317i
\(550\) 0 0
\(551\) 800.000 1.45191
\(552\) 16.0000 16.0000i 0.0289855 0.0289855i
\(553\) 0 0
\(554\) 534.000i 0.963899i
\(555\) 0 0
\(556\) −280.000 −0.503597
\(557\) 3.00000 3.00000i 0.00538600 0.00538600i −0.704409 0.709795i \(-0.748788\pi\)
0.709795 + 0.704409i \(0.248788\pi\)
\(558\) −52.0000 52.0000i −0.0931900 0.0931900i
\(559\) 252.000i 0.450805i
\(560\) 0 0
\(561\) 224.000 0.399287
\(562\) 312.000 312.000i 0.555160 0.555160i
\(563\) 42.0000 + 42.0000i 0.0746004 + 0.0746004i 0.743422 0.668822i \(-0.233201\pi\)
−0.668822 + 0.743422i \(0.733201\pi\)
\(564\) 144.000i 0.255319i
\(565\) 0 0
\(566\) 524.000 0.925795
\(567\) −142.000 + 142.000i −0.250441 + 0.250441i
\(568\) 56.0000 + 56.0000i 0.0985915 + 0.0985915i
\(569\) 950.000i 1.66960i −0.550557 0.834798i \(-0.685584\pi\)
0.550557 0.834798i \(-0.314416\pi\)
\(570\) 0 0
\(571\) 392.000 0.686515 0.343257 0.939241i \(-0.388470\pi\)
0.343257 + 0.939241i \(0.388470\pi\)
\(572\) 48.0000 48.0000i 0.0839161 0.0839161i
\(573\) 424.000 + 424.000i 0.739965 + 0.739965i
\(574\) 32.0000i 0.0557491i
\(575\) 0 0
\(576\) 8.00000 0.0138889
\(577\) 473.000 473.000i 0.819757 0.819757i −0.166315 0.986073i \(-0.553187\pi\)
0.986073 + 0.166315i \(0.0531869\pi\)
\(578\) 191.000 + 191.000i 0.330450 + 0.330450i
\(579\) 228.000i 0.393782i
\(580\) 0 0
\(581\) 72.0000 0.123924
\(582\) 252.000 252.000i 0.432990 0.432990i
\(583\) 424.000 + 424.000i 0.727273 + 0.727273i
\(584\) 188.000i 0.321918i
\(585\) 0 0
\(586\) −486.000 −0.829352
\(587\) 198.000 198.000i 0.337308 0.337308i −0.518045 0.855353i \(-0.673340\pi\)
0.855353 + 0.518045i \(0.173340\pi\)
\(588\) 164.000 + 164.000i 0.278912 + 0.278912i
\(589\) 1040.00i 1.76570i
\(590\) 0 0
\(591\) 12.0000 0.0203046
\(592\) −12.0000 + 12.0000i −0.0202703 + 0.0202703i
\(593\) 47.0000 + 47.0000i 0.0792580 + 0.0792580i 0.745624 0.666366i \(-0.232151\pi\)
−0.666366 + 0.745624i \(0.732151\pi\)
\(594\) 320.000i 0.538721i
\(595\) 0 0
\(596\) 300.000 0.503356
\(597\) −240.000 + 240.000i −0.402010 + 0.402010i
\(598\) −12.0000 12.0000i −0.0200669 0.0200669i
\(599\) 520.000i 0.868114i −0.900886 0.434057i \(-0.857082\pi\)
0.900886 0.434057i \(-0.142918\pi\)
\(600\) 0 0
\(601\) −328.000 −0.545757 −0.272879 0.962048i \(-0.587976\pi\)
−0.272879 + 0.962048i \(0.587976\pi\)
\(602\) −168.000 + 168.000i −0.279070 + 0.279070i
\(603\) 62.0000 + 62.0000i 0.102819 + 0.102819i
\(604\) 104.000i 0.172185i
\(605\) 0 0
\(606\) 248.000 0.409241
\(607\) −462.000 + 462.000i −0.761120 + 0.761120i −0.976525 0.215405i \(-0.930893\pi\)
0.215405 + 0.976525i \(0.430893\pi\)
\(608\) −80.0000 80.0000i −0.131579 0.131579i
\(609\) 320.000i 0.525452i
\(610\) 0 0
\(611\) −108.000 −0.176759
\(612\) 14.0000 14.0000i 0.0228758 0.0228758i
\(613\) −723.000 723.000i −1.17945 1.17945i −0.979886 0.199560i \(-0.936049\pi\)
−0.199560 0.979886i \(-0.563951\pi\)
\(614\) 36.0000i 0.0586319i
\(615\) 0 0
\(616\) −64.0000 −0.103896
\(617\) −327.000 + 327.000i −0.529984 + 0.529984i −0.920567 0.390584i \(-0.872273\pi\)
0.390584 + 0.920567i \(0.372273\pi\)
\(618\) −472.000 472.000i −0.763754 0.763754i
\(619\) 660.000i 1.06624i 0.846041 + 0.533118i \(0.178980\pi\)
−0.846041 + 0.533118i \(0.821020\pi\)
\(620\) 0 0
\(621\) 80.0000 0.128824
\(622\) −388.000 + 388.000i −0.623794 + 0.623794i
\(623\) 160.000 + 160.000i 0.256822 + 0.256822i
\(624\) 48.0000i 0.0769231i
\(625\) 0 0
\(626\) −366.000 −0.584665
\(627\) 320.000 320.000i 0.510367 0.510367i
\(628\) 54.0000 + 54.0000i 0.0859873 + 0.0859873i
\(629\) 42.0000i 0.0667727i
\(630\) 0 0
\(631\) −548.000 −0.868463 −0.434231 0.900801i \(-0.642980\pi\)
−0.434231 + 0.900801i \(0.642980\pi\)
\(632\) 0 0
\(633\) −656.000 656.000i −1.03633 1.03633i
\(634\) 426.000i 0.671924i
\(635\) 0 0
\(636\) −424.000 −0.666667
\(637\) 123.000 123.000i 0.193093 0.193093i
\(638\) 320.000 + 320.000i 0.501567 + 0.501567i
\(639\) 28.0000i 0.0438185i
\(640\) 0 0
\(641\) −568.000 −0.886115 −0.443058 0.896493i \(-0.646106\pi\)
−0.443058 + 0.896493i \(0.646106\pi\)
\(642\) −568.000 + 568.000i −0.884735 + 0.884735i
\(643\) 342.000 + 342.000i 0.531882 + 0.531882i 0.921132 0.389250i \(-0.127266\pi\)
−0.389250 + 0.921132i \(0.627266\pi\)
\(644\) 16.0000i 0.0248447i
\(645\) 0 0
\(646\) −280.000 −0.433437
\(647\) 118.000 118.000i 0.182380 0.182380i −0.610012 0.792392i \(-0.708835\pi\)
0.792392 + 0.610012i \(0.208835\pi\)
\(648\) −142.000 142.000i −0.219136 0.219136i
\(649\) 160.000i 0.246533i
\(650\) 0 0
\(651\) −416.000 −0.639017
\(652\) 164.000 164.000i 0.251534 0.251534i
\(653\) −453.000 453.000i −0.693721 0.693721i 0.269327 0.963049i \(-0.413199\pi\)
−0.963049 + 0.269327i \(0.913199\pi\)
\(654\) 40.0000i 0.0611621i
\(655\) 0 0
\(656\) 32.0000 0.0487805
\(657\) 47.0000 47.0000i 0.0715373 0.0715373i
\(658\) 72.0000 + 72.0000i 0.109422 + 0.109422i
\(659\) 140.000i 0.212443i −0.994342 0.106222i \(-0.966125\pi\)
0.994342 0.106222i \(-0.0338753\pi\)
\(660\) 0 0
\(661\) 512.000 0.774584 0.387292 0.921957i \(-0.373411\pi\)
0.387292 + 0.921957i \(0.373411\pi\)
\(662\) 232.000 232.000i 0.350453 0.350453i
\(663\) 84.0000 + 84.0000i 0.126697 + 0.126697i
\(664\) 72.0000i 0.108434i
\(665\) 0 0
\(666\) −6.00000 −0.00900901
\(667\) 80.0000 80.0000i 0.119940 0.119940i
\(668\) 124.000 + 124.000i 0.185629 + 0.185629i
\(669\) 552.000i 0.825112i
\(670\) 0 0
\(671\) 384.000 0.572280
\(672\) 32.0000 32.0000i 0.0476190 0.0476190i
\(673\) −193.000 193.000i −0.286776 0.286776i 0.549028 0.835804i \(-0.314998\pi\)
−0.835804 + 0.549028i \(0.814998\pi\)
\(674\) 834.000i 1.23739i
\(675\) 0 0
\(676\) −302.000 −0.446746
\(677\) −157.000 + 157.000i −0.231905 + 0.231905i −0.813488 0.581582i \(-0.802434\pi\)
0.581582 + 0.813488i \(0.302434\pi\)
\(678\) −92.0000 92.0000i −0.135693 0.135693i
\(679\) 252.000i 0.371134i
\(680\) 0 0
\(681\) −8.00000 −0.0117474
\(682\) −416.000 + 416.000i −0.609971 + 0.609971i
\(683\) −438.000 438.000i −0.641288 0.641288i 0.309584 0.950872i \(-0.399810\pi\)
−0.950872 + 0.309584i \(0.899810\pi\)
\(684\) 40.0000i 0.0584795i
\(685\) 0 0
\(686\) −360.000 −0.524781
\(687\) 240.000 240.000i 0.349345 0.349345i
\(688\) −168.000 168.000i −0.244186 0.244186i
\(689\) 318.000i 0.461538i
\(690\) 0 0
\(691\) 1032.00 1.49349 0.746744 0.665112i \(-0.231616\pi\)
0.746744 + 0.665112i \(0.231616\pi\)
\(692\) 214.000 214.000i 0.309249 0.309249i
\(693\) −16.0000 16.0000i −0.0230880 0.0230880i
\(694\) 404.000i 0.582133i
\(695\) 0 0
\(696\) −320.000 −0.459770
\(697\) 56.0000 56.0000i 0.0803443 0.0803443i
\(698\) 440.000 + 440.000i 0.630372 + 0.630372i
\(699\) 732.000i 1.04721i
\(700\) 0 0
\(701\) −128.000 −0.182596 −0.0912981 0.995824i \(-0.529102\pi\)
−0.0912981 + 0.995824i \(0.529102\pi\)
\(702\) −120.000 + 120.000i −0.170940 + 0.170940i
\(703\) 60.0000 + 60.0000i 0.0853485 + 0.0853485i
\(704\) 64.0000i 0.0909091i
\(705\) 0 0
\(706\) 894.000 1.26629
\(707\) −124.000 + 124.000i −0.175389 + 0.175389i
\(708\) 80.0000 + 80.0000i 0.112994 + 0.112994i
\(709\) 760.000i 1.07193i −0.844239 0.535966i \(-0.819947\pi\)
0.844239 0.535966i \(-0.180053\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −160.000 + 160.000i −0.224719 + 0.224719i
\(713\) 104.000 + 104.000i 0.145863 + 0.145863i
\(714\) 112.000i 0.156863i
\(715\) 0 0
\(716\) 440.000 0.614525
\(717\) 240.000 240.000i 0.334728 0.334728i
\(718\) 400.000 + 400.000i 0.557103 + 0.557103i
\(719\) 1160.00i 1.61335i 0.590994 + 0.806676i \(0.298736\pi\)
−0.590994 + 0.806676i \(0.701264\pi\)
\(720\) 0 0
\(721\) 472.000 0.654646
\(722\) −39.0000 + 39.0000i −0.0540166 + 0.0540166i
\(723\) 464.000 + 464.000i 0.641770 + 0.641770i
\(724\) 4.00000i 0.00552486i
\(725\) 0 0
\(726\) −228.000 −0.314050
\(727\) 558.000 558.000i 0.767538 0.767538i −0.210135 0.977672i \(-0.567390\pi\)
0.977672 + 0.210135i \(0.0673902\pi\)
\(728\) −24.0000 24.0000i −0.0329670 0.0329670i
\(729\) 791.000i 1.08505i
\(730\) 0 0
\(731\) −588.000 −0.804378
\(732\) −192.000 + 192.000i −0.262295 + 0.262295i
\(733\) 827.000 + 827.000i 1.12824 + 1.12824i 0.990463 + 0.137777i \(0.0439957\pi\)
0.137777 + 0.990463i \(0.456004\pi\)
\(734\) 236.000i 0.321526i
\(735\) 0 0
\(736\) −16.0000 −0.0217391
\(737\) 496.000 496.000i 0.672999 0.672999i
\(738\) 8.00000 + 8.00000i 0.0108401 + 0.0108401i
\(739\) 700.000i 0.947226i 0.880733 + 0.473613i \(0.157050\pi\)
−0.880733 + 0.473613i \(0.842950\pi\)
\(740\) 0 0
\(741\) 240.000 0.323887
\(742\) 212.000 212.000i 0.285714 0.285714i
\(743\) 382.000 + 382.000i 0.514132 + 0.514132i 0.915790 0.401658i \(-0.131566\pi\)
−0.401658 + 0.915790i \(0.631566\pi\)
\(744\) 416.000i 0.559140i
\(745\) 0 0
\(746\) 214.000 0.286863
\(747\) −18.0000 + 18.0000i −0.0240964 + 0.0240964i
\(748\) −112.000 112.000i −0.149733 0.149733i
\(749\) 568.000i 0.758344i
\(750\) 0 0
\(751\) −588.000 −0.782956 −0.391478 0.920187i \(-0.628036\pi\)
−0.391478 + 0.920187i \(0.628036\pi\)
\(752\) −72.0000 + 72.0000i −0.0957447 + 0.0957447i
\(753\) −96.0000 96.0000i −0.127490 0.127490i
\(754\) 240.000i 0.318302i
\(755\) 0 0
\(756\) 160.000 0.211640
\(757\) −987.000 + 987.000i −1.30383 + 1.30383i −0.378043 + 0.925788i \(0.623403\pi\)
−0.925788 + 0.378043i \(0.876597\pi\)
\(758\) −340.000 340.000i −0.448549 0.448549i
\(759\) 64.0000i 0.0843215i
\(760\) 0 0
\(761\) −158.000 −0.207622 −0.103811 0.994597i \(-0.533104\pi\)
−0.103811 + 0.994597i \(0.533104\pi\)
\(762\) 472.000 472.000i 0.619423 0.619423i
\(763\) −20.0000 20.0000i −0.0262123 0.0262123i
\(764\) 424.000i 0.554974i
\(765\) 0 0
\(766\) 684.000 0.892950
\(767\) 60.0000 60.0000i 0.0782269 0.0782269i
\(768\) 32.0000 + 32.0000i 0.0416667 + 0.0416667i
\(769\) 80.0000i 0.104031i −0.998646 0.0520156i \(-0.983435\pi\)
0.998646 0.0520156i \(-0.0165646\pi\)
\(770\) 0 0
\(771\) 1252.00 1.62387
\(772\) 114.000 114.000i 0.147668 0.147668i
\(773\) −243.000 243.000i −0.314360 0.314360i 0.532236 0.846596i \(-0.321352\pi\)
−0.846596 + 0.532236i \(0.821352\pi\)
\(774\) 84.0000i 0.108527i
\(775\) 0 0
\(776\) −252.000 −0.324742
\(777\) −24.0000 + 24.0000i −0.0308880 + 0.0308880i
\(778\) −390.000 390.000i −0.501285 0.501285i
\(779\) 160.000i