Properties

Label 320.3.p.h.257.1
Level $320$
Weight $3$
Character 320.257
Analytic conductor $8.719$
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] = [320,3,Mod(193,320)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(320, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("320.193");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 320.p (of order \(4\), 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: \(8.71936845953\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 10)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 257.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 320.257
Dual form 320.3.p.h.193.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 - 2.00000i) q^{3} +5.00000i q^{5} +(2.00000 + 2.00000i) q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(2.00000 - 2.00000i) q^{3} +5.00000i q^{5} +(2.00000 + 2.00000i) q^{7} +1.00000i q^{9} +8.00000 q^{11} +(-3.00000 + 3.00000i) q^{13} +(10.0000 + 10.0000i) q^{15} +(7.00000 + 7.00000i) q^{17} +20.0000i q^{19} +8.00000 q^{21} +(-2.00000 + 2.00000i) q^{23} -25.0000 q^{25} +(20.0000 + 20.0000i) q^{27} -40.0000i q^{29} +52.0000 q^{31} +(16.0000 - 16.0000i) q^{33} +(-10.0000 + 10.0000i) q^{35} +(3.00000 + 3.00000i) q^{37} +12.0000i q^{39} -8.00000 q^{41} +(42.0000 - 42.0000i) q^{43} -5.00000 q^{45} +(-18.0000 - 18.0000i) q^{47} -41.0000i q^{49} +28.0000 q^{51} +(-53.0000 + 53.0000i) q^{53} +40.0000i q^{55} +(40.0000 + 40.0000i) q^{57} +20.0000i q^{59} +48.0000 q^{61} +(-2.00000 + 2.00000i) q^{63} +(-15.0000 - 15.0000i) q^{65} +(-62.0000 - 62.0000i) q^{67} +8.00000i q^{69} -28.0000 q^{71} +(-47.0000 + 47.0000i) q^{73} +(-50.0000 + 50.0000i) q^{75} +(16.0000 + 16.0000i) q^{77} +71.0000 q^{81} +(-18.0000 + 18.0000i) q^{83} +(-35.0000 + 35.0000i) q^{85} +(-80.0000 - 80.0000i) q^{87} +80.0000i q^{89} -12.0000 q^{91} +(104.000 - 104.000i) q^{93} -100.000 q^{95} +(-63.0000 - 63.0000i) q^{97} +8.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 4 q^{3} + 4 q^{7} + 16 q^{11} - 6 q^{13} + 20 q^{15} + 14 q^{17} + 16 q^{21} - 4 q^{23} - 50 q^{25} + 40 q^{27} + 104 q^{31} + 32 q^{33} - 20 q^{35} + 6 q^{37} - 16 q^{41} + 84 q^{43} - 10 q^{45} - 36 q^{47} + 56 q^{51} - 106 q^{53} + 80 q^{57} + 96 q^{61} - 4 q^{63} - 30 q^{65} - 124 q^{67} - 56 q^{71} - 94 q^{73} - 100 q^{75} + 32 q^{77} + 142 q^{81} - 36 q^{83} - 70 q^{85} - 160 q^{87} - 24 q^{91} + 208 q^{93} - 200 q^{95} - 126 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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 0
\(3\) 2.00000 2.00000i 0.666667 0.666667i −0.290276 0.956943i \(-0.593747\pi\)
0.956943 + 0.290276i \(0.0937472\pi\)
\(4\) 0 0
\(5\) 5.00000i 1.00000i
\(6\) 0 0
\(7\) 2.00000 + 2.00000i 0.285714 + 0.285714i 0.835383 0.549669i \(-0.185246\pi\)
−0.549669 + 0.835383i \(0.685246\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.111111i
\(10\) 0 0
\(11\) 8.00000 0.727273 0.363636 0.931541i \(-0.381535\pi\)
0.363636 + 0.931541i \(0.381535\pi\)
\(12\) 0 0
\(13\) −3.00000 + 3.00000i −0.230769 + 0.230769i −0.813014 0.582245i \(-0.802175\pi\)
0.582245 + 0.813014i \(0.302175\pi\)
\(14\) 0 0
\(15\) 10.0000 + 10.0000i 0.666667 + 0.666667i
\(16\) 0 0
\(17\) 7.00000 + 7.00000i 0.411765 + 0.411765i 0.882353 0.470588i \(-0.155958\pi\)
−0.470588 + 0.882353i \(0.655958\pi\)
\(18\) 0 0
\(19\) 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
\(22\) 0 0
\(23\) −2.00000 + 2.00000i −0.0869565 + 0.0869565i −0.749247 0.662291i \(-0.769584\pi\)
0.662291 + 0.749247i \(0.269584\pi\)
\(24\) 0 0
\(25\) −25.0000 −1.00000
\(26\) 0 0
\(27\) 20.0000 + 20.0000i 0.740741 + 0.740741i
\(28\) 0 0
\(29\) 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 \(0.183310\pi\)
\(32\) 0 0
\(33\) 16.0000 16.0000i 0.484848 0.484848i
\(34\) 0 0
\(35\) −10.0000 + 10.0000i −0.285714 + 0.285714i
\(36\) 0 0
\(37\) 3.00000 + 3.00000i 0.0810811 + 0.0810811i 0.746484 0.665403i \(-0.231740\pi\)
−0.665403 + 0.746484i \(0.731740\pi\)
\(38\) 0 0
\(39\) 12.0000i 0.307692i
\(40\) 0 0
\(41\) −8.00000 −0.195122 −0.0975610 0.995230i \(-0.531104\pi\)
−0.0975610 + 0.995230i \(0.531104\pi\)
\(42\) 0 0
\(43\) 42.0000 42.0000i 0.976744 0.976744i −0.0229915 0.999736i \(-0.507319\pi\)
0.999736 + 0.0229915i \(0.00731906\pi\)
\(44\) 0 0
\(45\) −5.00000 −0.111111
\(46\) 0 0
\(47\) −18.0000 18.0000i −0.382979 0.382979i 0.489195 0.872174i \(-0.337290\pi\)
−0.872174 + 0.489195i \(0.837290\pi\)
\(48\) 0 0
\(49\) 41.0000i 0.836735i
\(50\) 0 0
\(51\) 28.0000 0.549020
\(52\) 0 0
\(53\) −53.0000 + 53.0000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 40.0000i 0.727273i
\(56\) 0 0
\(57\) 40.0000 + 40.0000i 0.701754 + 0.701754i
\(58\) 0 0
\(59\) 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 \(-0.371284\pi\)
0.393443 + 0.919349i \(0.371284\pi\)
\(62\) 0 0
\(63\) −2.00000 + 2.00000i −0.0317460 + 0.0317460i
\(64\) 0 0
\(65\) −15.0000 15.0000i −0.230769 0.230769i
\(66\) 0 0
\(67\) −62.0000 62.0000i −0.925373 0.925373i 0.0720294 0.997403i \(-0.477052\pi\)
−0.997403 + 0.0720294i \(0.977052\pi\)
\(68\) 0 0
\(69\) 8.00000i 0.115942i
\(70\) 0 0
\(71\) −28.0000 −0.394366 −0.197183 0.980367i \(-0.563179\pi\)
−0.197183 + 0.980367i \(0.563179\pi\)
\(72\) 0 0
\(73\) −47.0000 + 47.0000i −0.643836 + 0.643836i −0.951496 0.307661i \(-0.900454\pi\)
0.307661 + 0.951496i \(0.400454\pi\)
\(74\) 0 0
\(75\) −50.0000 + 50.0000i −0.666667 + 0.666667i
\(76\) 0 0
\(77\) 16.0000 + 16.0000i 0.207792 + 0.207792i
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 71.0000 0.876543
\(82\) 0 0
\(83\) −18.0000 + 18.0000i −0.216867 + 0.216867i −0.807177 0.590310i \(-0.799006\pi\)
0.590310 + 0.807177i \(0.299006\pi\)
\(84\) 0 0
\(85\) −35.0000 + 35.0000i −0.411765 + 0.411765i
\(86\) 0 0
\(87\) −80.0000 80.0000i −0.919540 0.919540i
\(88\) 0 0
\(89\) 80.0000i 0.898876i 0.893311 + 0.449438i \(0.148376\pi\)
−0.893311 + 0.449438i \(0.851624\pi\)
\(90\) 0 0
\(91\) −12.0000 −0.131868
\(92\) 0 0
\(93\) 104.000 104.000i 1.11828 1.11828i
\(94\) 0 0
\(95\) −100.000 −1.05263
\(96\) 0 0
\(97\) −63.0000 63.0000i −0.649485 0.649485i 0.303384 0.952868i \(-0.401884\pi\)
−0.952868 + 0.303384i \(0.901884\pi\)
\(98\) 0 0
\(99\) 8.00000i 0.0808081i
\(100\) 0 0
\(101\) −62.0000 −0.613861 −0.306931 0.951732i \(-0.599302\pi\)
−0.306931 + 0.951732i \(0.599302\pi\)
\(102\) 0 0
\(103\) 118.000 118.000i 1.14563 1.14563i 0.158229 0.987403i \(-0.449422\pi\)
0.987403 0.158229i \(-0.0505783\pi\)
\(104\) 0 0
\(105\) 40.0000i 0.380952i
\(106\) 0 0
\(107\) −142.000 142.000i −1.32710 1.32710i −0.907886 0.419217i \(-0.862305\pi\)
−0.419217 0.907886i \(-0.637695\pi\)
\(108\) 0 0
\(109\) 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
\(112\) 0 0
\(113\) 23.0000 23.0000i 0.203540 0.203540i −0.597975 0.801515i \(-0.704028\pi\)
0.801515 + 0.597975i \(0.204028\pi\)
\(114\) 0 0
\(115\) −10.0000 10.0000i −0.0869565 0.0869565i
\(116\) 0 0
\(117\) −3.00000 3.00000i −0.0256410 0.0256410i
\(118\) 0 0
\(119\) 28.0000i 0.235294i
\(120\) 0 0
\(121\) −57.0000 −0.471074
\(122\) 0 0
\(123\) −16.0000 + 16.0000i −0.130081 + 0.130081i
\(124\) 0 0
\(125\) 125.000i 1.00000i
\(126\) 0 0
\(127\) −118.000 118.000i −0.929134 0.929134i 0.0685161 0.997650i \(-0.478174\pi\)
−0.997650 + 0.0685161i \(0.978174\pi\)
\(128\) 0 0
\(129\) 168.000i 1.30233i
\(130\) 0 0
\(131\) 128.000 0.977099 0.488550 0.872536i \(-0.337526\pi\)
0.488550 + 0.872536i \(0.337526\pi\)
\(132\) 0 0
\(133\) −40.0000 + 40.0000i −0.300752 + 0.300752i
\(134\) 0 0
\(135\) −100.000 + 100.000i −0.740741 + 0.740741i
\(136\) 0 0
\(137\) −63.0000 63.0000i −0.459854 0.459854i 0.438753 0.898607i \(-0.355420\pi\)
−0.898607 + 0.438753i \(0.855420\pi\)
\(138\) 0 0
\(139\) 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
\(142\) 0 0
\(143\) −24.0000 + 24.0000i −0.167832 + 0.167832i
\(144\) 0 0
\(145\) 200.000 1.37931
\(146\) 0 0
\(147\) −82.0000 82.0000i −0.557823 0.557823i
\(148\) 0 0
\(149\) 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 \(0.444917\pi\)
\(152\) 0 0
\(153\) −7.00000 + 7.00000i −0.0457516 + 0.0457516i
\(154\) 0 0
\(155\) 260.000i 1.67742i
\(156\) 0 0
\(157\) −27.0000 27.0000i −0.171975 0.171975i 0.615872 0.787846i \(-0.288804\pi\)
−0.787846 + 0.615872i \(0.788804\pi\)
\(158\) 0 0
\(159\) 212.000i 1.33333i
\(160\) 0 0
\(161\) −8.00000 −0.0496894
\(162\) 0 0
\(163\) 82.0000 82.0000i 0.503067 0.503067i −0.409322 0.912390i \(-0.634235\pi\)
0.912390 + 0.409322i \(0.134235\pi\)
\(164\) 0 0
\(165\) 80.0000 + 80.0000i 0.484848 + 0.484848i
\(166\) 0 0
\(167\) 62.0000 + 62.0000i 0.371257 + 0.371257i 0.867935 0.496678i \(-0.165447\pi\)
−0.496678 + 0.867935i \(0.665447\pi\)
\(168\) 0 0
\(169\) 151.000i 0.893491i
\(170\) 0 0
\(171\) −20.0000 −0.116959
\(172\) 0 0
\(173\) 107.000 107.000i 0.618497 0.618497i −0.326649 0.945146i \(-0.605919\pi\)
0.945146 + 0.326649i \(0.105919\pi\)
\(174\) 0 0
\(175\) −50.0000 50.0000i −0.285714 0.285714i
\(176\) 0 0
\(177\) 40.0000 + 40.0000i 0.225989 + 0.225989i
\(178\) 0 0
\(179\) 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 \(-0.501759\pi\)
−0.00552486 + 0.999985i \(0.501759\pi\)
\(182\) 0 0
\(183\) 96.0000 96.0000i 0.524590 0.524590i
\(184\) 0 0
\(185\) −15.0000 + 15.0000i −0.0810811 + 0.0810811i
\(186\) 0 0
\(187\) 56.0000 + 56.0000i 0.299465 + 0.299465i
\(188\) 0 0
\(189\) 80.0000i 0.423280i
\(190\) 0 0
\(191\) 212.000 1.10995 0.554974 0.831868i \(-0.312728\pi\)
0.554974 + 0.831868i \(0.312728\pi\)
\(192\) 0 0
\(193\) −57.0000 + 57.0000i −0.295337 + 0.295337i −0.839184 0.543847i \(-0.816967\pi\)
0.543847 + 0.839184i \(0.316967\pi\)
\(194\) 0 0
\(195\) −60.0000 −0.307692
\(196\) 0 0
\(197\) 3.00000 + 3.00000i 0.0152284 + 0.0152284i 0.714680 0.699452i \(-0.246572\pi\)
−0.699452 + 0.714680i \(0.746572\pi\)
\(198\) 0 0
\(199\) 120.000i 0.603015i −0.953464 0.301508i \(-0.902510\pi\)
0.953464 0.301508i \(-0.0974898\pi\)
\(200\) 0 0
\(201\) −248.000 −1.23383
\(202\) 0 0
\(203\) 80.0000 80.0000i 0.394089 0.394089i
\(204\) 0 0
\(205\) 40.0000i 0.195122i
\(206\) 0 0
\(207\) −2.00000 2.00000i −0.00966184 0.00966184i
\(208\) 0 0
\(209\) 160.000i 0.765550i
\(210\) 0 0
\(211\) 328.000 1.55450 0.777251 0.629190i \(-0.216613\pi\)
0.777251 + 0.629190i \(0.216613\pi\)
\(212\) 0 0
\(213\) −56.0000 + 56.0000i −0.262911 + 0.262911i
\(214\) 0 0
\(215\) 210.000 + 210.000i 0.976744 + 0.976744i
\(216\) 0 0
\(217\) 104.000 + 104.000i 0.479263 + 0.479263i
\(218\) 0 0
\(219\) 188.000i 0.858447i
\(220\) 0 0
\(221\) −42.0000 −0.190045
\(222\) 0 0
\(223\) 138.000 138.000i 0.618834 0.618834i −0.326398 0.945232i \(-0.605835\pi\)
0.945232 + 0.326398i \(0.105835\pi\)
\(224\) 0 0
\(225\) 25.0000i 0.111111i
\(226\) 0 0
\(227\) −2.00000 2.00000i −0.00881057 0.00881057i 0.702688 0.711498i \(-0.251983\pi\)
−0.711498 + 0.702688i \(0.751983\pi\)
\(228\) 0 0
\(229\) 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
\(232\) 0 0
\(233\) 183.000 183.000i 0.785408 0.785408i −0.195330 0.980738i \(-0.562578\pi\)
0.980738 + 0.195330i \(0.0625777\pi\)
\(234\) 0 0
\(235\) 90.0000 90.0000i 0.382979 0.382979i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 120.000i 0.502092i 0.967975 + 0.251046i \(0.0807746\pi\)
−0.967975 + 0.251046i \(0.919225\pi\)
\(240\) 0 0
\(241\) 232.000 0.962656 0.481328 0.876541i \(-0.340155\pi\)
0.481328 + 0.876541i \(0.340155\pi\)
\(242\) 0 0
\(243\) −38.0000 + 38.0000i −0.156379 + 0.156379i
\(244\) 0 0
\(245\) 205.000 0.836735
\(246\) 0 0
\(247\) −60.0000 60.0000i −0.242915 0.242915i
\(248\) 0 0
\(249\) 72.0000i 0.289157i
\(250\) 0 0
\(251\) 48.0000 0.191235 0.0956175 0.995418i \(-0.469517\pi\)
0.0956175 + 0.995418i \(0.469517\pi\)
\(252\) 0 0
\(253\) −16.0000 + 16.0000i −0.0632411 + 0.0632411i
\(254\) 0 0
\(255\) 140.000i 0.549020i
\(256\) 0 0
\(257\) −313.000 313.000i −1.21790 1.21790i −0.968366 0.249532i \(-0.919723\pi\)
−0.249532 0.968366i \(-0.580277\pi\)
\(258\) 0 0
\(259\) 12.0000i 0.0463320i
\(260\) 0 0
\(261\) 40.0000 0.153257
\(262\) 0 0
\(263\) −262.000 + 262.000i −0.996198 + 0.996198i −0.999993 0.00379508i \(-0.998792\pi\)
0.00379508 + 0.999993i \(0.498792\pi\)
\(264\) 0 0
\(265\) −265.000 265.000i −1.00000 1.00000i
\(266\) 0 0
\(267\) 160.000 + 160.000i 0.599251 + 0.599251i
\(268\) 0 0
\(269\) 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 \(0.346074\pi\)
\(272\) 0 0
\(273\) −24.0000 + 24.0000i −0.0879121 + 0.0879121i
\(274\) 0 0
\(275\) −200.000 −0.727273
\(276\) 0 0
\(277\) −267.000 267.000i −0.963899 0.963899i 0.0354718 0.999371i \(-0.488707\pi\)
−0.999371 + 0.0354718i \(0.988707\pi\)
\(278\) 0 0
\(279\) 52.0000i 0.186380i
\(280\) 0 0
\(281\) 312.000 1.11032 0.555160 0.831743i \(-0.312657\pi\)
0.555160 + 0.831743i \(0.312657\pi\)
\(282\) 0 0
\(283\) 262.000 262.000i 0.925795 0.925795i −0.0716358 0.997431i \(-0.522822\pi\)
0.997431 + 0.0716358i \(0.0228219\pi\)
\(284\) 0 0
\(285\) −200.000 + 200.000i −0.701754 + 0.701754i
\(286\) 0 0
\(287\) −16.0000 16.0000i −0.0557491 0.0557491i
\(288\) 0 0
\(289\) 191.000i 0.660900i
\(290\) 0 0
\(291\) −252.000 −0.865979
\(292\) 0 0
\(293\) −243.000 + 243.000i −0.829352 + 0.829352i −0.987427 0.158075i \(-0.949471\pi\)
0.158075 + 0.987427i \(0.449471\pi\)
\(294\) 0 0
\(295\) −100.000 −0.338983
\(296\) 0 0
\(297\) 160.000 + 160.000i 0.538721 + 0.538721i
\(298\) 0 0
\(299\) 12.0000i 0.0401338i
\(300\) 0 0
\(301\) 168.000 0.558140
\(302\) 0 0
\(303\) −124.000 + 124.000i −0.409241 + 0.409241i
\(304\) 0 0
\(305\) 240.000i 0.786885i
\(306\) 0 0
\(307\) 18.0000 + 18.0000i 0.0586319 + 0.0586319i 0.735815 0.677183i \(-0.236799\pi\)
−0.677183 + 0.735815i \(0.736799\pi\)
\(308\) 0 0
\(309\) 472.000i 1.52751i
\(310\) 0 0
\(311\) −388.000 −1.24759 −0.623794 0.781589i \(-0.714410\pi\)
−0.623794 + 0.781589i \(0.714410\pi\)
\(312\) 0 0
\(313\) 183.000 183.000i 0.584665 0.584665i −0.351517 0.936182i \(-0.614334\pi\)
0.936182 + 0.351517i \(0.114334\pi\)
\(314\) 0 0
\(315\) −10.0000 10.0000i −0.0317460 0.0317460i
\(316\) 0 0
\(317\) 213.000 + 213.000i 0.671924 + 0.671924i 0.958159 0.286235i \(-0.0924038\pi\)
−0.286235 + 0.958159i \(0.592404\pi\)
\(318\) 0 0
\(319\) 320.000i 1.00313i
\(320\) 0 0
\(321\) −568.000 −1.76947
\(322\) 0 0
\(323\) −140.000 + 140.000i −0.433437 + 0.433437i
\(324\) 0 0
\(325\) 75.0000 75.0000i 0.230769 0.230769i
\(326\) 0 0
\(327\) 20.0000 + 20.0000i 0.0611621 + 0.0611621i
\(328\) 0 0
\(329\) 72.0000i 0.218845i
\(330\) 0 0
\(331\) −232.000 −0.700906 −0.350453 0.936580i \(-0.613972\pi\)
−0.350453 + 0.936580i \(0.613972\pi\)
\(332\) 0 0
\(333\) −3.00000 + 3.00000i −0.00900901 + 0.00900901i
\(334\) 0 0
\(335\) 310.000 310.000i 0.925373 0.925373i
\(336\) 0 0
\(337\) 417.000 + 417.000i 1.23739 + 1.23739i 0.961064 + 0.276324i \(0.0891164\pi\)
0.276324 + 0.961064i \(0.410884\pi\)
\(338\) 0 0
\(339\) 92.0000i 0.271386i
\(340\) 0 0
\(341\) 416.000 1.21994
\(342\) 0 0
\(343\) 180.000 180.000i 0.524781 0.524781i
\(344\) 0 0
\(345\) −40.0000 −0.115942
\(346\) 0 0
\(347\) −202.000 202.000i −0.582133 0.582133i 0.353356 0.935489i \(-0.385040\pi\)
−0.935489 + 0.353356i \(0.885040\pi\)
\(348\) 0 0
\(349\) 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
\(352\) 0 0
\(353\) −447.000 + 447.000i −1.26629 + 1.26629i −0.318298 + 0.947991i \(0.603111\pi\)
−0.947991 + 0.318298i \(0.896889\pi\)
\(354\) 0 0
\(355\) 140.000i 0.394366i
\(356\) 0 0
\(357\) 56.0000 + 56.0000i 0.156863 + 0.156863i
\(358\) 0 0
\(359\) 400.000i 1.11421i −0.830443 0.557103i \(-0.811913\pi\)
0.830443 0.557103i \(-0.188087\pi\)
\(360\) 0 0
\(361\) −39.0000 −0.108033
\(362\) 0 0
\(363\) −114.000 + 114.000i −0.314050 + 0.314050i
\(364\) 0 0
\(365\) −235.000 235.000i −0.643836 0.643836i
\(366\) 0 0
\(367\) −118.000 118.000i −0.321526 0.321526i 0.527826 0.849352i \(-0.323007\pi\)
−0.849352 + 0.527826i \(0.823007\pi\)
\(368\) 0 0
\(369\) 8.00000i 0.0216802i
\(370\) 0 0
\(371\) −212.000 −0.571429
\(372\) 0 0
\(373\) 107.000 107.000i 0.286863 0.286863i −0.548975 0.835839i \(-0.684982\pi\)
0.835839 + 0.548975i \(0.184982\pi\)
\(374\) 0 0
\(375\) −250.000 250.000i −0.666667 0.666667i
\(376\) 0 0
\(377\) 120.000 + 120.000i 0.318302 + 0.318302i
\(378\) 0 0
\(379\) 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
\(382\) 0 0
\(383\) −342.000 + 342.000i −0.892950 + 0.892950i −0.994800 0.101849i \(-0.967524\pi\)
0.101849 + 0.994800i \(0.467524\pi\)
\(384\) 0 0
\(385\) −80.0000 + 80.0000i −0.207792 + 0.207792i
\(386\) 0 0
\(387\) 42.0000 + 42.0000i 0.108527 + 0.108527i
\(388\) 0 0
\(389\) 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
\(392\) 0 0
\(393\) 256.000 256.000i 0.651399 0.651399i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 323.000 + 323.000i 0.813602 + 0.813602i 0.985172 0.171570i \(-0.0548839\pi\)
−0.171570 + 0.985172i \(0.554884\pi\)
\(398\) 0 0
\(399\) 160.000i 0.401003i
\(400\) 0 0
\(401\) 642.000 1.60100 0.800499 0.599334i \(-0.204568\pi\)
0.800499 + 0.599334i \(0.204568\pi\)
\(402\) 0 0
\(403\) −156.000 + 156.000i −0.387097 + 0.387097i
\(404\) 0 0
\(405\) 355.000i 0.876543i
\(406\) 0 0
\(407\) 24.0000 + 24.0000i 0.0589681 + 0.0589681i
\(408\) 0 0
\(409\) 150.000i 0.366748i −0.983043 0.183374i \(-0.941298\pi\)
0.983043 0.183374i \(-0.0587020\pi\)
\(410\) 0 0
\(411\) −252.000 −0.613139
\(412\) 0 0
\(413\) −40.0000 + 40.0000i −0.0968523 + 0.0968523i
\(414\) 0 0
\(415\) −90.0000 90.0000i −0.216867 0.216867i
\(416\) 0 0
\(417\) −280.000 280.000i −0.671463 0.671463i
\(418\) 0 0
\(419\) 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 \(-0.420545\pi\)
0.247031 + 0.969008i \(0.420545\pi\)
\(422\) 0 0
\(423\) 18.0000 18.0000i 0.0425532 0.0425532i
\(424\) 0 0
\(425\) −175.000 175.000i −0.411765 0.411765i
\(426\) 0 0
\(427\) 96.0000 + 96.0000i 0.224824 + 0.224824i
\(428\) 0 0
\(429\) 96.0000i 0.223776i
\(430\) 0 0
\(431\) −788.000 −1.82831 −0.914153 0.405369i \(-0.867143\pi\)
−0.914153 + 0.405369i \(0.867143\pi\)
\(432\) 0 0
\(433\) −367.000 + 367.000i −0.847575 + 0.847575i −0.989830 0.142255i \(-0.954565\pi\)
0.142255 + 0.989830i \(0.454565\pi\)
\(434\) 0 0
\(435\) 400.000 400.000i 0.919540 0.919540i
\(436\) 0 0
\(437\) −40.0000 40.0000i −0.0915332 0.0915332i
\(438\) 0 0
\(439\) 560.000i 1.27563i 0.770191 + 0.637813i \(0.220161\pi\)
−0.770191 + 0.637813i \(0.779839\pi\)
\(440\) 0 0
\(441\) 41.0000 0.0929705
\(442\) 0 0
\(443\) −378.000 + 378.000i −0.853273 + 0.853273i −0.990535 0.137262i \(-0.956170\pi\)
0.137262 + 0.990535i \(0.456170\pi\)
\(444\) 0 0
\(445\) −400.000 −0.898876
\(446\) 0 0
\(447\) 300.000 + 300.000i 0.671141 + 0.671141i
\(448\) 0 0
\(449\) 410.000i 0.913140i −0.889687 0.456570i \(-0.849078\pi\)
0.889687 0.456570i \(-0.150922\pi\)
\(450\) 0 0
\(451\) −64.0000 −0.141907
\(452\) 0 0
\(453\) 104.000 104.000i 0.229581 0.229581i
\(454\) 0 0
\(455\) 60.0000i 0.131868i
\(456\) 0 0
\(457\) −393.000 393.000i −0.859956 0.859956i 0.131376 0.991333i \(-0.458060\pi\)
−0.991333 + 0.131376i \(0.958060\pi\)
\(458\) 0 0
\(459\) 280.000i 0.610022i
\(460\) 0 0
\(461\) −622.000 −1.34924 −0.674620 0.738165i \(-0.735693\pi\)
−0.674620 + 0.738165i \(0.735693\pi\)
\(462\) 0 0
\(463\) 278.000 278.000i 0.600432 0.600432i −0.339995 0.940427i \(-0.610425\pi\)
0.940427 + 0.339995i \(0.110425\pi\)
\(464\) 0 0
\(465\) 520.000 + 520.000i 1.11828 + 1.11828i
\(466\) 0 0
\(467\) 38.0000 + 38.0000i 0.0813704 + 0.0813704i 0.746621 0.665250i \(-0.231675\pi\)
−0.665250 + 0.746621i \(0.731675\pi\)
\(468\) 0 0
\(469\) 248.000i 0.528785i
\(470\) 0 0
\(471\) −108.000 −0.229299
\(472\) 0 0
\(473\) 336.000 336.000i 0.710359 0.710359i
\(474\) 0 0
\(475\) 500.000i 1.05263i
\(476\) 0 0
\(477\) −53.0000 53.0000i −0.111111 0.111111i
\(478\) 0 0
\(479\) 440.000i 0.918580i −0.888286 0.459290i \(-0.848104\pi\)
0.888286 0.459290i \(-0.151896\pi\)
\(480\) 0 0
\(481\) −18.0000 −0.0374220
\(482\) 0 0
\(483\) −16.0000 + 16.0000i −0.0331263 + 0.0331263i
\(484\) 0 0
\(485\) 315.000 315.000i 0.649485 0.649485i
\(486\) 0 0
\(487\) 522.000 + 522.000i 1.07187 + 1.07187i 0.997209 + 0.0746595i \(0.0237870\pi\)
0.0746595 + 0.997209i \(0.476213\pi\)
\(488\) 0 0
\(489\) 328.000i 0.670757i
\(490\) 0 0
\(491\) 328.000 0.668024 0.334012 0.942569i \(-0.391597\pi\)
0.334012 + 0.942569i \(0.391597\pi\)
\(492\) 0 0
\(493\) 280.000 280.000i 0.567951 0.567951i
\(494\) 0 0
\(495\) −40.0000 −0.0808081
\(496\) 0 0
\(497\) −56.0000 56.0000i −0.112676 0.112676i
\(498\) 0 0
\(499\) 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
\(502\) 0 0
\(503\) −42.0000 + 42.0000i −0.0834990 + 0.0834990i −0.747623 0.664124i \(-0.768805\pi\)
0.664124 + 0.747623i \(0.268805\pi\)
\(504\) 0 0
\(505\) 310.000i 0.613861i
\(506\) 0 0
\(507\) 302.000 + 302.000i 0.595661 + 0.595661i
\(508\) 0 0
\(509\) 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
\(512\) 0 0
\(513\) −400.000 + 400.000i −0.779727 + 0.779727i
\(514\) 0 0
\(515\) 590.000 + 590.000i 1.14563 + 1.14563i
\(516\) 0 0
\(517\) −144.000 144.000i −0.278530 0.278530i
\(518\) 0 0
\(519\) 428.000i 0.824663i
\(520\) 0 0
\(521\) −258.000 −0.495202 −0.247601 0.968862i \(-0.579642\pi\)
−0.247601 + 0.968862i \(0.579642\pi\)
\(522\) 0 0
\(523\) −258.000 + 258.000i −0.493308 + 0.493308i −0.909347 0.416039i \(-0.863418\pi\)
0.416039 + 0.909347i \(0.363418\pi\)
\(524\) 0 0
\(525\) −200.000 −0.380952
\(526\) 0 0
\(527\) 364.000 + 364.000i 0.690702 + 0.690702i
\(528\) 0 0
\(529\) 521.000i 0.984877i
\(530\) 0 0
\(531\) −20.0000 −0.0376648
\(532\) 0 0
\(533\) 24.0000 24.0000i 0.0450281 0.0450281i
\(534\) 0 0
\(535\) 710.000 710.000i 1.32710 1.32710i
\(536\) 0 0
\(537\) 440.000 + 440.000i 0.819367 + 0.819367i
\(538\) 0 0
\(539\) 328.000i 0.608534i
\(540\) 0 0
\(541\) 338.000 0.624769 0.312384 0.949956i \(-0.398872\pi\)
0.312384 + 0.949956i \(0.398872\pi\)
\(542\) 0 0
\(543\) −4.00000 + 4.00000i −0.00736648 + 0.00736648i
\(544\) 0 0
\(545\) −50.0000 −0.0917431
\(546\) 0 0
\(547\) 558.000 + 558.000i 1.02011 + 1.02011i 0.999794 + 0.0203161i \(0.00646725\pi\)
0.0203161 + 0.999794i \(0.493533\pi\)
\(548\) 0 0
\(549\) 48.0000i 0.0874317i
\(550\) 0 0
\(551\) 800.000 1.45191
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 60.0000i 0.108108i
\(556\) 0 0
\(557\) 3.00000 + 3.00000i 0.00538600 + 0.00538600i 0.709795 0.704409i \(-0.248788\pi\)
−0.704409 + 0.709795i \(0.748788\pi\)
\(558\) 0 0
\(559\) 252.000i 0.450805i
\(560\) 0 0
\(561\) 224.000 0.399287
\(562\) 0 0
\(563\) 42.0000 42.0000i 0.0746004 0.0746004i −0.668822 0.743422i \(-0.733201\pi\)
0.743422 + 0.668822i \(0.233201\pi\)
\(564\) 0 0
\(565\) 115.000 + 115.000i 0.203540 + 0.203540i
\(566\) 0 0
\(567\) 142.000 + 142.000i 0.250441 + 0.250441i
\(568\) 0 0
\(569\) 950.000i 1.66960i 0.550557 + 0.834798i \(0.314416\pi\)
−0.550557 + 0.834798i \(0.685584\pi\)
\(570\) 0 0
\(571\) −392.000 −0.686515 −0.343257 0.939241i \(-0.611530\pi\)
−0.343257 + 0.939241i \(0.611530\pi\)
\(572\) 0 0
\(573\) 424.000 424.000i 0.739965 0.739965i
\(574\) 0 0
\(575\) 50.0000 50.0000i 0.0869565 0.0869565i
\(576\) 0 0
\(577\) −473.000 473.000i −0.819757 0.819757i 0.166315 0.986073i \(-0.446813\pi\)
−0.986073 + 0.166315i \(0.946813\pi\)
\(578\) 0 0
\(579\) 228.000i 0.393782i
\(580\) 0 0
\(581\) −72.0000 −0.123924
\(582\) 0 0
\(583\) −424.000 + 424.000i −0.727273 + 0.727273i
\(584\) 0 0
\(585\) 15.0000 15.0000i 0.0256410 0.0256410i
\(586\) 0 0
\(587\) 198.000 + 198.000i 0.337308 + 0.337308i 0.855353 0.518045i \(-0.173340\pi\)
−0.518045 + 0.855353i \(0.673340\pi\)
\(588\) 0 0
\(589\) 1040.00i 1.76570i
\(590\) 0 0
\(591\) 12.0000 0.0203046
\(592\) 0 0
\(593\) −47.0000 + 47.0000i −0.0792580 + 0.0792580i −0.745624 0.666366i \(-0.767849\pi\)
0.666366 + 0.745624i \(0.267849\pi\)
\(594\) 0 0
\(595\) −140.000 −0.235294
\(596\) 0 0
\(597\) −240.000 240.000i −0.402010 0.402010i
\(598\) 0 0
\(599\) 520.000i 0.868114i 0.900886 + 0.434057i \(0.142918\pi\)
−0.900886 + 0.434057i \(0.857082\pi\)
\(600\) 0 0
\(601\) −328.000 −0.545757 −0.272879 0.962048i \(-0.587976\pi\)
−0.272879 + 0.962048i \(0.587976\pi\)
\(602\) 0 0
\(603\) 62.0000 62.0000i 0.102819 0.102819i
\(604\) 0 0
\(605\) 285.000i 0.471074i
\(606\) 0 0
\(607\) 462.000 + 462.000i 0.761120 + 0.761120i 0.976525 0.215405i \(-0.0691070\pi\)
−0.215405 + 0.976525i \(0.569107\pi\)
\(608\) 0 0
\(609\) 320.000i 0.525452i
\(610\) 0 0
\(611\) 108.000 0.176759
\(612\) 0 0
\(613\) −723.000 + 723.000i −1.17945 + 1.17945i −0.199560 + 0.979886i \(0.563951\pi\)
−0.979886 + 0.199560i \(0.936049\pi\)
\(614\) 0 0
\(615\) −80.0000 80.0000i −0.130081 0.130081i
\(616\) 0 0
\(617\) 327.000 + 327.000i 0.529984 + 0.529984i 0.920567 0.390584i \(-0.127727\pi\)
−0.390584 + 0.920567i \(0.627727\pi\)
\(618\) 0 0
\(619\) 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
\(622\) 0 0
\(623\) −160.000 + 160.000i −0.256822 + 0.256822i
\(624\) 0 0
\(625\) 625.000 1.00000
\(626\) 0 0
\(627\) 320.000 + 320.000i 0.510367 + 0.510367i
\(628\) 0 0
\(629\) 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
\(634\) 0 0
\(635\) 590.000 590.000i 0.929134 0.929134i
\(636\) 0 0
\(637\) 123.000 + 123.000i 0.193093 + 0.193093i
\(638\) 0 0
\(639\) 28.0000i 0.0438185i
\(640\) 0 0
\(641\) −568.000 −0.886115 −0.443058 0.896493i \(-0.646106\pi\)
−0.443058 + 0.896493i \(0.646106\pi\)
\(642\) 0 0
\(643\) 342.000 342.000i 0.531882 0.531882i −0.389250 0.921132i \(-0.627266\pi\)
0.921132 + 0.389250i \(0.127266\pi\)
\(644\) 0 0
\(645\) 840.000 1.30233
\(646\) 0 0
\(647\) −118.000 118.000i −0.182380 0.182380i 0.610012 0.792392i \(-0.291165\pi\)
−0.792392 + 0.610012i \(0.791165\pi\)
\(648\) 0 0
\(649\) 160.000i 0.246533i
\(650\) 0 0
\(651\) 416.000 0.639017
\(652\) 0 0
\(653\) −453.000 + 453.000i −0.693721 + 0.693721i −0.963049 0.269327i \(-0.913199\pi\)
0.269327 + 0.963049i \(0.413199\pi\)
\(654\) 0 0
\(655\) 640.000i 0.977099i
\(656\) 0 0
\(657\) −47.0000 47.0000i −0.0715373 0.0715373i
\(658\) 0 0
\(659\) 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 \(-0.626589\pi\)
−0.387292 + 0.921957i \(0.626589\pi\)
\(662\) 0 0
\(663\) −84.0000 + 84.0000i −0.126697 + 0.126697i
\(664\) 0 0
\(665\) −200.000 200.000i −0.300752 0.300752i
\(666\) 0 0
\(667\) 80.0000 + 80.0000i 0.119940 + 0.119940i
\(668\) 0 0
\(669\) 552.000i 0.825112i
\(670\) 0 0
\(671\) 384.000 0.572280
\(672\) 0 0
\(673\) 193.000 193.000i 0.286776 0.286776i −0.549028 0.835804i \(-0.685002\pi\)
0.835804 + 0.549028i \(0.185002\pi\)
\(674\) 0 0
\(675\) −500.000 500.000i −0.740741 0.740741i
\(676\) 0 0
\(677\) −157.000 157.000i −0.231905 0.231905i 0.581582 0.813488i \(-0.302434\pi\)
−0.813488 + 0.581582i \(0.802434\pi\)
\(678\) 0 0
\(679\) 252.000i 0.371134i
\(680\) 0 0
\(681\) −8.00000 −0.0117474
\(682\) 0 0
\(683\) −438.000 + 438.000i −0.641288 + 0.641288i −0.950872 0.309584i \(-0.899810\pi\)
0.309584 + 0.950872i \(0.399810\pi\)
\(684\) 0 0
\(685\) 315.000 315.000i 0.459854 0.459854i
\(686\) 0 0
\(687\) −240.000 240.000i −0.349345 0.349345i
\(688\) 0 0
\(689\) 318.000i 0.461538i
\(690\) 0 0
\(691\) −1032.00 −1.49349 −0.746744 0.665112i \(-0.768384\pi\)
−0.746744 + 0.665112i \(0.768384\pi\)
\(692\) 0 0
\(693\) −16.0000 + 16.0000i −0.0230880 + 0.0230880i
\(694\) 0 0
\(695\) 700.000 1.00719
\(696\) 0 0
\(697\) −56.0000 56.0000i −0.0803443 0.0803443i
\(698\) 0 0
\(699\) 732.000i 1.04721i
\(700\) 0 0
\(701\) 128.000 0.182596 0.0912981 0.995824i \(-0.470898\pi\)
0.0912981 + 0.995824i \(0.470898\pi\)
\(702\) 0 0
\(703\) −60.0000 + 60.0000i −0.0853485 + 0.0853485i
\(704\) 0 0
\(705\) 360.000i 0.510638i
\(706\) 0 0
\(707\) −124.000 124.000i −0.175389 0.175389i
\(708\) 0 0
\(709\) 760.000i 1.07193i −0.844239 0.535966i \(-0.819947\pi\)
0.844239 0.535966i \(-0.180053\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −104.000 + 104.000i −0.145863 + 0.145863i
\(714\) 0 0
\(715\) −120.000 120.000i −0.167832 0.167832i
\(716\) 0 0
\(717\) 240.000 + 240.000i 0.334728 + 0.334728i
\(718\) 0 0
\(719\) 1160.00i 1.61335i −0.590994 0.806676i \(-0.701264\pi\)
0.590994 0.806676i \(-0.298736\pi\)
\(720\) 0 0
\(721\) 472.000 0.654646
\(722\) 0 0
\(723\) 464.000 464.000i 0.641770 0.641770i
\(724\) 0 0
\(725\) 1000.00i 1.37931i
\(726\) 0 0
\(727\) −558.000 558.000i −0.767538 0.767538i 0.210135 0.977672i \(-0.432610\pi\)
−0.977672 + 0.210135i \(0.932610\pi\)
\(728\) 0 0
\(729\) 791.000i 1.08505i
\(730\) 0 0
\(731\) 588.000 0.804378
\(732\) 0 0
\(733\) 827.000 827.000i 1.12824 1.12824i 0.137777 0.990463i \(-0.456004\pi\)
0.990463 0.137777i \(-0.0439957\pi\)
\(734\) 0 0
\(735\) 410.000 410.000i 0.557823 0.557823i
\(736\) 0 0
\(737\) −496.000 496.000i −0.672999 0.672999i
\(738\) 0 0
\(739\) 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
\(742\) 0 0
\(743\) −382.000 + 382.000i −0.514132 + 0.514132i −0.915790 0.401658i \(-0.868434\pi\)
0.401658 + 0.915790i \(0.368434\pi\)
\(744\) 0 0
\(745\) −750.000 −1.00671
\(746\) 0 0
\(747\) −18.0000 18.0000i −0.0240964 0.0240964i
\(748\) 0 0
\(749\) 568.000i 0.758344i
\(750\) 0 0
\(751\) −588.000 −0.782956 −0.391478 0.920187i \(-0.628036\pi\)
−0.391478 + 0.920187i \(0.628036\pi\)
\(752\) 0 0
\(753\) 96.0000 96.0000i 0.127490 0.127490i
\(754\) 0 0
\(755\) 260.000i 0.344371i
\(756\) 0 0
\(757\) −987.000 987.000i −1.30383 1.30383i −0.925788 0.378043i \(-0.876597\pi\)
−0.378043 0.925788i \(-0.623403\pi\)
\(758\) 0 0
\(759\) 64.0000i 0.0843215i
\(760\) 0 0
\(761\) −158.000 −0.207622 −0.103811 0.994597i \(-0.533104\pi\)
−0.103811 + 0.994597i \(0.533104\pi\)
\(762\) 0 0
\(763\) −20.0000 + 20.0000i −0.0262123 + 0.0262123i
\(764\) 0 0
\(765\) −35.0000 35.0000i −0.0457516 0.0457516i
\(766\) 0 0
\(767\) −60.0000 60.0000i −0.0782269 0.0782269i
\(768\) 0 0
\(769\) 80.0000i 0.104031i 0.998646 + 0.0520156i \(0.0165646\pi\)
−0.998646 + 0.0520156i \(0.983435\pi\)
\(770\) 0 0
\(771\) −1252.00 −1.62387
\(772\) 0 0
\(773\) −243.000 + 243.000i −0.314360 + 0.314360i −0.846596 0.532236i \(-0.821352\pi\)
0.532236 + 0.846596i \(0.321352\pi\)
\(774\) 0 0
\(775\) −1300.00 −1.67742
\(776\) 0 0
\(777\) 24.0000 + 24.0000i 0.0308880 + 0.0308880i
\(778\) 0 0
\(779\) 160.000i 0.205392i
\(780\) 0 0
\(781\) −224.000 −0.286812
\(782\) 0 0
\(783\) 800.000 800.000i 1.02171 1.02171i
\(784\) 0 0
\(785\) 135.000 135.000i 0.171975 0.171975i
\(786\) 0 0
\(787\) −262.000 262.000i −0.332910 0.332910i 0.520781 0.853690i \(-0.325641\pi\)
−0.853690 + 0.520781i \(0.825641\pi\)
\(788\) 0 0
\(789\) 1048.00i 1.32826i
\(790\)