Properties

Label 450.3.g.e.343.1
Level $450$
Weight $3$
Character 450.343
Analytic conductor $12.262$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [450,3,Mod(307,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.307");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 450.g (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: \(12.2616118962\)
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 50)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 343.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 450.343
Dual form 450.3.g.e.307.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-3.00000 + 3.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-3.00000 + 3.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -12.0000 q^{11} +(-12.0000 - 12.0000i) q^{13} +6.00000i q^{14} -4.00000 q^{16} +(-12.0000 + 12.0000i) q^{17} -20.0000i q^{19} +(-12.0000 + 12.0000i) q^{22} +(-3.00000 - 3.00000i) q^{23} -24.0000 q^{26} +(6.00000 + 6.00000i) q^{28} -30.0000i q^{29} -8.00000 q^{31} +(-4.00000 + 4.00000i) q^{32} +24.0000i q^{34} +(-48.0000 + 48.0000i) q^{37} +(-20.0000 - 20.0000i) q^{38} +48.0000 q^{41} +(-27.0000 - 27.0000i) q^{43} +24.0000i q^{44} -6.00000 q^{46} +(-27.0000 + 27.0000i) q^{47} +31.0000i q^{49} +(-24.0000 + 24.0000i) q^{52} +(12.0000 + 12.0000i) q^{53} +12.0000 q^{56} +(-30.0000 - 30.0000i) q^{58} -60.0000i q^{59} +32.0000 q^{61} +(-8.00000 + 8.00000i) q^{62} +8.00000i q^{64} +(-3.00000 + 3.00000i) q^{67} +(24.0000 + 24.0000i) q^{68} +48.0000 q^{71} +(-12.0000 - 12.0000i) q^{73} +96.0000i q^{74} -40.0000 q^{76} +(36.0000 - 36.0000i) q^{77} -40.0000i q^{79} +(48.0000 - 48.0000i) q^{82} +(-93.0000 - 93.0000i) q^{83} -54.0000 q^{86} +(24.0000 + 24.0000i) q^{88} +30.0000i q^{89} +72.0000 q^{91} +(-6.00000 + 6.00000i) q^{92} +54.0000i q^{94} +(12.0000 - 12.0000i) q^{97} +(31.0000 + 31.0000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 6 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 6 q^{7} - 4 q^{8} - 24 q^{11} - 24 q^{13} - 8 q^{16} - 24 q^{17} - 24 q^{22} - 6 q^{23} - 48 q^{26} + 12 q^{28} - 16 q^{31} - 8 q^{32} - 96 q^{37} - 40 q^{38} + 96 q^{41} - 54 q^{43} - 12 q^{46} - 54 q^{47} - 48 q^{52} + 24 q^{53} + 24 q^{56} - 60 q^{58} + 64 q^{61} - 16 q^{62} - 6 q^{67} + 48 q^{68} + 96 q^{71} - 24 q^{73} - 80 q^{76} + 72 q^{77} + 96 q^{82} - 186 q^{83} - 108 q^{86} + 48 q^{88} + 144 q^{91} - 12 q^{92} + 24 q^{97} + 62 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 0 0
\(4\) 2.00000i 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) −3.00000 + 3.00000i −0.428571 + 0.428571i −0.888142 0.459570i \(-0.848004\pi\)
0.459570 + 0.888142i \(0.348004\pi\)
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) −12.0000 −1.09091 −0.545455 0.838140i \(-0.683643\pi\)
−0.545455 + 0.838140i \(0.683643\pi\)
\(12\) 0 0
\(13\) −12.0000 12.0000i −0.923077 0.923077i 0.0741688 0.997246i \(-0.476370\pi\)
−0.997246 + 0.0741688i \(0.976370\pi\)
\(14\) 6.00000i 0.428571i
\(15\) 0 0
\(16\) −4.00000 −0.250000
\(17\) −12.0000 + 12.0000i −0.705882 + 0.705882i −0.965667 0.259784i \(-0.916349\pi\)
0.259784 + 0.965667i \(0.416349\pi\)
\(18\) 0 0
\(19\) 20.0000i 1.05263i −0.850289 0.526316i \(-0.823573\pi\)
0.850289 0.526316i \(-0.176427\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −12.0000 + 12.0000i −0.545455 + 0.545455i
\(23\) −3.00000 3.00000i −0.130435 0.130435i 0.638875 0.769310i \(-0.279400\pi\)
−0.769310 + 0.638875i \(0.779400\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −24.0000 −0.923077
\(27\) 0 0
\(28\) 6.00000 + 6.00000i 0.214286 + 0.214286i
\(29\) 30.0000i 1.03448i −0.855840 0.517241i \(-0.826959\pi\)
0.855840 0.517241i \(-0.173041\pi\)
\(30\) 0 0
\(31\) −8.00000 −0.258065 −0.129032 0.991640i \(-0.541187\pi\)
−0.129032 + 0.991640i \(0.541187\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) 0 0
\(34\) 24.0000i 0.705882i
\(35\) 0 0
\(36\) 0 0
\(37\) −48.0000 + 48.0000i −1.29730 + 1.29730i −0.367126 + 0.930171i \(0.619658\pi\)
−0.930171 + 0.367126i \(0.880342\pi\)
\(38\) −20.0000 20.0000i −0.526316 0.526316i
\(39\) 0 0
\(40\) 0 0
\(41\) 48.0000 1.17073 0.585366 0.810769i \(-0.300951\pi\)
0.585366 + 0.810769i \(0.300951\pi\)
\(42\) 0 0
\(43\) −27.0000 27.0000i −0.627907 0.627907i 0.319634 0.947541i \(-0.396440\pi\)
−0.947541 + 0.319634i \(0.896440\pi\)
\(44\) 24.0000i 0.545455i
\(45\) 0 0
\(46\) −6.00000 −0.130435
\(47\) −27.0000 + 27.0000i −0.574468 + 0.574468i −0.933374 0.358906i \(-0.883150\pi\)
0.358906 + 0.933374i \(0.383150\pi\)
\(48\) 0 0
\(49\) 31.0000i 0.632653i
\(50\) 0 0
\(51\) 0 0
\(52\) −24.0000 + 24.0000i −0.461538 + 0.461538i
\(53\) 12.0000 + 12.0000i 0.226415 + 0.226415i 0.811193 0.584778i \(-0.198818\pi\)
−0.584778 + 0.811193i \(0.698818\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 12.0000 0.214286
\(57\) 0 0
\(58\) −30.0000 30.0000i −0.517241 0.517241i
\(59\) 60.0000i 1.01695i −0.861077 0.508475i \(-0.830210\pi\)
0.861077 0.508475i \(-0.169790\pi\)
\(60\) 0 0
\(61\) 32.0000 0.524590 0.262295 0.964988i \(-0.415521\pi\)
0.262295 + 0.964988i \(0.415521\pi\)
\(62\) −8.00000 + 8.00000i −0.129032 + 0.129032i
\(63\) 0 0
\(64\) 8.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) −3.00000 + 3.00000i −0.0447761 + 0.0447761i −0.729140 0.684364i \(-0.760080\pi\)
0.684364 + 0.729140i \(0.260080\pi\)
\(68\) 24.0000 + 24.0000i 0.352941 + 0.352941i
\(69\) 0 0
\(70\) 0 0
\(71\) 48.0000 0.676056 0.338028 0.941136i \(-0.390240\pi\)
0.338028 + 0.941136i \(0.390240\pi\)
\(72\) 0 0
\(73\) −12.0000 12.0000i −0.164384 0.164384i 0.620122 0.784505i \(-0.287083\pi\)
−0.784505 + 0.620122i \(0.787083\pi\)
\(74\) 96.0000i 1.29730i
\(75\) 0 0
\(76\) −40.0000 −0.526316
\(77\) 36.0000 36.0000i 0.467532 0.467532i
\(78\) 0 0
\(79\) 40.0000i 0.506329i −0.967423 0.253165i \(-0.918529\pi\)
0.967423 0.253165i \(-0.0814714\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 48.0000 48.0000i 0.585366 0.585366i
\(83\) −93.0000 93.0000i −1.12048 1.12048i −0.991669 0.128813i \(-0.958883\pi\)
−0.128813 0.991669i \(-0.541117\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −54.0000 −0.627907
\(87\) 0 0
\(88\) 24.0000 + 24.0000i 0.272727 + 0.272727i
\(89\) 30.0000i 0.337079i 0.985695 + 0.168539i \(0.0539050\pi\)
−0.985695 + 0.168539i \(0.946095\pi\)
\(90\) 0 0
\(91\) 72.0000 0.791209
\(92\) −6.00000 + 6.00000i −0.0652174 + 0.0652174i
\(93\) 0 0
\(94\) 54.0000i 0.574468i
\(95\) 0 0
\(96\) 0 0
\(97\) 12.0000 12.0000i 0.123711 0.123711i −0.642540 0.766252i \(-0.722120\pi\)
0.766252 + 0.642540i \(0.222120\pi\)
\(98\) 31.0000 + 31.0000i 0.316327 + 0.316327i
\(99\) 0 0
\(100\) 0 0
\(101\) 78.0000 0.772277 0.386139 0.922441i \(-0.373809\pi\)
0.386139 + 0.922441i \(0.373809\pi\)
\(102\) 0 0
\(103\) 93.0000 + 93.0000i 0.902913 + 0.902913i 0.995687 0.0927745i \(-0.0295736\pi\)
−0.0927745 + 0.995687i \(0.529574\pi\)
\(104\) 48.0000i 0.461538i
\(105\) 0 0
\(106\) 24.0000 0.226415
\(107\) −27.0000 + 27.0000i −0.252336 + 0.252336i −0.821928 0.569591i \(-0.807101\pi\)
0.569591 + 0.821928i \(0.307101\pi\)
\(108\) 0 0
\(109\) 160.000i 1.46789i −0.679209 0.733945i \(-0.737677\pi\)
0.679209 0.733945i \(-0.262323\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 12.0000 12.0000i 0.107143 0.107143i
\(113\) 72.0000 + 72.0000i 0.637168 + 0.637168i 0.949856 0.312688i \(-0.101229\pi\)
−0.312688 + 0.949856i \(0.601229\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −60.0000 −0.517241
\(117\) 0 0
\(118\) −60.0000 60.0000i −0.508475 0.508475i
\(119\) 72.0000i 0.605042i
\(120\) 0 0
\(121\) 23.0000 0.190083
\(122\) 32.0000 32.0000i 0.262295 0.262295i
\(123\) 0 0
\(124\) 16.0000i 0.129032i
\(125\) 0 0
\(126\) 0 0
\(127\) 117.000 117.000i 0.921260 0.921260i −0.0758587 0.997119i \(-0.524170\pi\)
0.997119 + 0.0758587i \(0.0241698\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) −132.000 −1.00763 −0.503817 0.863811i \(-0.668071\pi\)
−0.503817 + 0.863811i \(0.668071\pi\)
\(132\) 0 0
\(133\) 60.0000 + 60.0000i 0.451128 + 0.451128i
\(134\) 6.00000i 0.0447761i
\(135\) 0 0
\(136\) 48.0000 0.352941
\(137\) 168.000 168.000i 1.22628 1.22628i 0.260916 0.965362i \(-0.415975\pi\)
0.965362 0.260916i \(-0.0840245\pi\)
\(138\) 0 0
\(139\) 100.000i 0.719424i 0.933063 + 0.359712i \(0.117125\pi\)
−0.933063 + 0.359712i \(0.882875\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 48.0000 48.0000i 0.338028 0.338028i
\(143\) 144.000 + 144.000i 1.00699 + 1.00699i
\(144\) 0 0
\(145\) 0 0
\(146\) −24.0000 −0.164384
\(147\) 0 0
\(148\) 96.0000 + 96.0000i 0.648649 + 0.648649i
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −248.000 −1.64238 −0.821192 0.570652i \(-0.806691\pi\)
−0.821192 + 0.570652i \(0.806691\pi\)
\(152\) −40.0000 + 40.0000i −0.263158 + 0.263158i
\(153\) 0 0
\(154\) 72.0000i 0.467532i
\(155\) 0 0
\(156\) 0 0
\(157\) 72.0000 72.0000i 0.458599 0.458599i −0.439597 0.898195i \(-0.644879\pi\)
0.898195 + 0.439597i \(0.144879\pi\)
\(158\) −40.0000 40.0000i −0.253165 0.253165i
\(159\) 0 0
\(160\) 0 0
\(161\) 18.0000 0.111801
\(162\) 0 0
\(163\) 93.0000 + 93.0000i 0.570552 + 0.570552i 0.932283 0.361731i \(-0.117814\pi\)
−0.361731 + 0.932283i \(0.617814\pi\)
\(164\) 96.0000i 0.585366i
\(165\) 0 0
\(166\) −186.000 −1.12048
\(167\) 3.00000 3.00000i 0.0179641 0.0179641i −0.698068 0.716032i \(-0.745957\pi\)
0.716032 + 0.698068i \(0.245957\pi\)
\(168\) 0 0
\(169\) 119.000i 0.704142i
\(170\) 0 0
\(171\) 0 0
\(172\) −54.0000 + 54.0000i −0.313953 + 0.313953i
\(173\) −168.000 168.000i −0.971098 0.971098i 0.0284957 0.999594i \(-0.490928\pi\)
−0.999594 + 0.0284957i \(0.990928\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 48.0000 0.272727
\(177\) 0 0
\(178\) 30.0000 + 30.0000i 0.168539 + 0.168539i
\(179\) 300.000i 1.67598i −0.545687 0.837989i \(-0.683731\pi\)
0.545687 0.837989i \(-0.316269\pi\)
\(180\) 0 0
\(181\) 142.000 0.784530 0.392265 0.919852i \(-0.371692\pi\)
0.392265 + 0.919852i \(0.371692\pi\)
\(182\) 72.0000 72.0000i 0.395604 0.395604i
\(183\) 0 0
\(184\) 12.0000i 0.0652174i
\(185\) 0 0
\(186\) 0 0
\(187\) 144.000 144.000i 0.770053 0.770053i
\(188\) 54.0000 + 54.0000i 0.287234 + 0.287234i
\(189\) 0 0
\(190\) 0 0
\(191\) −192.000 −1.00524 −0.502618 0.864509i \(-0.667630\pi\)
−0.502618 + 0.864509i \(0.667630\pi\)
\(192\) 0 0
\(193\) −132.000 132.000i −0.683938 0.683938i 0.276947 0.960885i \(-0.410677\pi\)
−0.960885 + 0.276947i \(0.910677\pi\)
\(194\) 24.0000i 0.123711i
\(195\) 0 0
\(196\) 62.0000 0.316327
\(197\) −132.000 + 132.000i −0.670051 + 0.670051i −0.957728 0.287677i \(-0.907117\pi\)
0.287677 + 0.957728i \(0.407117\pi\)
\(198\) 0 0
\(199\) 160.000i 0.804020i −0.915635 0.402010i \(-0.868312\pi\)
0.915635 0.402010i \(-0.131688\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 78.0000 78.0000i 0.386139 0.386139i
\(203\) 90.0000 + 90.0000i 0.443350 + 0.443350i
\(204\) 0 0
\(205\) 0 0
\(206\) 186.000 0.902913
\(207\) 0 0
\(208\) 48.0000 + 48.0000i 0.230769 + 0.230769i
\(209\) 240.000i 1.14833i
\(210\) 0 0
\(211\) −28.0000 −0.132701 −0.0663507 0.997796i \(-0.521136\pi\)
−0.0663507 + 0.997796i \(0.521136\pi\)
\(212\) 24.0000 24.0000i 0.113208 0.113208i
\(213\) 0 0
\(214\) 54.0000i 0.252336i
\(215\) 0 0
\(216\) 0 0
\(217\) 24.0000 24.0000i 0.110599 0.110599i
\(218\) −160.000 160.000i −0.733945 0.733945i
\(219\) 0 0
\(220\) 0 0
\(221\) 288.000 1.30317
\(222\) 0 0
\(223\) −117.000 117.000i −0.524664 0.524664i 0.394313 0.918976i \(-0.370983\pi\)
−0.918976 + 0.394313i \(0.870983\pi\)
\(224\) 24.0000i 0.107143i
\(225\) 0 0
\(226\) 144.000 0.637168
\(227\) 93.0000 93.0000i 0.409692 0.409692i −0.471939 0.881631i \(-0.656446\pi\)
0.881631 + 0.471939i \(0.156446\pi\)
\(228\) 0 0
\(229\) 370.000i 1.61572i 0.589374 + 0.807860i \(0.299374\pi\)
−0.589374 + 0.807860i \(0.700626\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −60.0000 + 60.0000i −0.258621 + 0.258621i
\(233\) 252.000 + 252.000i 1.08155 + 1.08155i 0.996366 + 0.0851794i \(0.0271464\pi\)
0.0851794 + 0.996366i \(0.472854\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −120.000 −0.508475
\(237\) 0 0
\(238\) −72.0000 72.0000i −0.302521 0.302521i
\(239\) 360.000i 1.50628i 0.657862 + 0.753138i \(0.271461\pi\)
−0.657862 + 0.753138i \(0.728539\pi\)
\(240\) 0 0
\(241\) 32.0000 0.132780 0.0663900 0.997794i \(-0.478852\pi\)
0.0663900 + 0.997794i \(0.478852\pi\)
\(242\) 23.0000 23.0000i 0.0950413 0.0950413i
\(243\) 0 0
\(244\) 64.0000i 0.262295i
\(245\) 0 0
\(246\) 0 0
\(247\) −240.000 + 240.000i −0.971660 + 0.971660i
\(248\) 16.0000 + 16.0000i 0.0645161 + 0.0645161i
\(249\) 0 0
\(250\) 0 0
\(251\) −252.000 −1.00398 −0.501992 0.864872i \(-0.667399\pi\)
−0.501992 + 0.864872i \(0.667399\pi\)
\(252\) 0 0
\(253\) 36.0000 + 36.0000i 0.142292 + 0.142292i
\(254\) 234.000i 0.921260i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) −192.000 + 192.000i −0.747082 + 0.747082i −0.973930 0.226848i \(-0.927158\pi\)
0.226848 + 0.973930i \(0.427158\pi\)
\(258\) 0 0
\(259\) 288.000i 1.11197i
\(260\) 0 0
\(261\) 0 0
\(262\) −132.000 + 132.000i −0.503817 + 0.503817i
\(263\) −333.000 333.000i −1.26616 1.26616i −0.948056 0.318104i \(-0.896954\pi\)
−0.318104 0.948056i \(-0.603046\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 120.000 0.451128
\(267\) 0 0
\(268\) 6.00000 + 6.00000i 0.0223881 + 0.0223881i
\(269\) 480.000i 1.78439i 0.451654 + 0.892193i \(0.350834\pi\)
−0.451654 + 0.892193i \(0.649166\pi\)
\(270\) 0 0
\(271\) −88.0000 −0.324723 −0.162362 0.986731i \(-0.551911\pi\)
−0.162362 + 0.986731i \(0.551911\pi\)
\(272\) 48.0000 48.0000i 0.176471 0.176471i
\(273\) 0 0
\(274\) 336.000i 1.22628i
\(275\) 0 0
\(276\) 0 0
\(277\) −288.000 + 288.000i −1.03971 + 1.03971i −0.0405330 + 0.999178i \(0.512906\pi\)
−0.999178 + 0.0405330i \(0.987094\pi\)
\(278\) 100.000 + 100.000i 0.359712 + 0.359712i
\(279\) 0 0
\(280\) 0 0
\(281\) 288.000 1.02491 0.512456 0.858714i \(-0.328736\pi\)
0.512456 + 0.858714i \(0.328736\pi\)
\(282\) 0 0
\(283\) −117.000 117.000i −0.413428 0.413428i 0.469503 0.882931i \(-0.344433\pi\)
−0.882931 + 0.469503i \(0.844433\pi\)
\(284\) 96.0000i 0.338028i
\(285\) 0 0
\(286\) 288.000 1.00699
\(287\) −144.000 + 144.000i −0.501742 + 0.501742i
\(288\) 0 0
\(289\) 1.00000i 0.00346021i
\(290\) 0 0
\(291\) 0 0
\(292\) −24.0000 + 24.0000i −0.0821918 + 0.0821918i
\(293\) −168.000 168.000i −0.573379 0.573379i 0.359692 0.933071i \(-0.382882\pi\)
−0.933071 + 0.359692i \(0.882882\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 192.000 0.648649
\(297\) 0 0
\(298\) 0 0
\(299\) 72.0000i 0.240803i
\(300\) 0 0
\(301\) 162.000 0.538206
\(302\) −248.000 + 248.000i −0.821192 + 0.821192i
\(303\) 0 0
\(304\) 80.0000i 0.263158i
\(305\) 0 0
\(306\) 0 0
\(307\) −243.000 + 243.000i −0.791531 + 0.791531i −0.981743 0.190212i \(-0.939082\pi\)
0.190212 + 0.981743i \(0.439082\pi\)
\(308\) −72.0000 72.0000i −0.233766 0.233766i
\(309\) 0 0
\(310\) 0 0
\(311\) −552.000 −1.77492 −0.887460 0.460885i \(-0.847532\pi\)
−0.887460 + 0.460885i \(0.847532\pi\)
\(312\) 0 0
\(313\) 48.0000 + 48.0000i 0.153355 + 0.153355i 0.779614 0.626260i \(-0.215415\pi\)
−0.626260 + 0.779614i \(0.715415\pi\)
\(314\) 144.000i 0.458599i
\(315\) 0 0
\(316\) −80.0000 −0.253165
\(317\) 228.000 228.000i 0.719243 0.719243i −0.249207 0.968450i \(-0.580170\pi\)
0.968450 + 0.249207i \(0.0801700\pi\)
\(318\) 0 0
\(319\) 360.000i 1.12853i
\(320\) 0 0
\(321\) 0 0
\(322\) 18.0000 18.0000i 0.0559006 0.0559006i
\(323\) 240.000 + 240.000i 0.743034 + 0.743034i
\(324\) 0 0
\(325\) 0 0
\(326\) 186.000 0.570552
\(327\) 0 0
\(328\) −96.0000 96.0000i −0.292683 0.292683i
\(329\) 162.000i 0.492401i
\(330\) 0 0
\(331\) −148.000 −0.447130 −0.223565 0.974689i \(-0.571769\pi\)
−0.223565 + 0.974689i \(0.571769\pi\)
\(332\) −186.000 + 186.000i −0.560241 + 0.560241i
\(333\) 0 0
\(334\) 6.00000i 0.0179641i
\(335\) 0 0
\(336\) 0 0
\(337\) 192.000 192.000i 0.569733 0.569733i −0.362321 0.932054i \(-0.618015\pi\)
0.932054 + 0.362321i \(0.118015\pi\)
\(338\) 119.000 + 119.000i 0.352071 + 0.352071i
\(339\) 0 0
\(340\) 0 0
\(341\) 96.0000 0.281525
\(342\) 0 0
\(343\) −240.000 240.000i −0.699708 0.699708i
\(344\) 108.000i 0.313953i
\(345\) 0 0
\(346\) −336.000 −0.971098
\(347\) −117.000 + 117.000i −0.337176 + 0.337176i −0.855303 0.518128i \(-0.826629\pi\)
0.518128 + 0.855303i \(0.326629\pi\)
\(348\) 0 0
\(349\) 130.000i 0.372493i 0.982503 + 0.186246i \(0.0596323\pi\)
−0.982503 + 0.186246i \(0.940368\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 48.0000 48.0000i 0.136364 0.136364i
\(353\) −288.000 288.000i −0.815864 0.815864i 0.169642 0.985506i \(-0.445739\pi\)
−0.985506 + 0.169642i \(0.945739\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 60.0000 0.168539
\(357\) 0 0
\(358\) −300.000 300.000i −0.837989 0.837989i
\(359\) 120.000i 0.334262i −0.985935 0.167131i \(-0.946550\pi\)
0.985935 0.167131i \(-0.0534503\pi\)
\(360\) 0 0
\(361\) −39.0000 −0.108033
\(362\) 142.000 142.000i 0.392265 0.392265i
\(363\) 0 0
\(364\) 144.000i 0.395604i
\(365\) 0 0
\(366\) 0 0
\(367\) −213.000 + 213.000i −0.580381 + 0.580381i −0.935008 0.354627i \(-0.884608\pi\)
0.354627 + 0.935008i \(0.384608\pi\)
\(368\) 12.0000 + 12.0000i 0.0326087 + 0.0326087i
\(369\) 0 0
\(370\) 0 0
\(371\) −72.0000 −0.194070
\(372\) 0 0
\(373\) 168.000 + 168.000i 0.450402 + 0.450402i 0.895488 0.445086i \(-0.146827\pi\)
−0.445086 + 0.895488i \(0.646827\pi\)
\(374\) 288.000i 0.770053i
\(375\) 0 0
\(376\) 108.000 0.287234
\(377\) −360.000 + 360.000i −0.954907 + 0.954907i
\(378\) 0 0
\(379\) 20.0000i 0.0527704i −0.999652 0.0263852i \(-0.991600\pi\)
0.999652 0.0263852i \(-0.00839965\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −192.000 + 192.000i −0.502618 + 0.502618i
\(383\) −123.000 123.000i −0.321149 0.321149i 0.528059 0.849208i \(-0.322920\pi\)
−0.849208 + 0.528059i \(0.822920\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −264.000 −0.683938
\(387\) 0 0
\(388\) −24.0000 24.0000i −0.0618557 0.0618557i
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 72.0000 0.184143
\(392\) 62.0000 62.0000i 0.158163 0.158163i
\(393\) 0 0
\(394\) 264.000i 0.670051i
\(395\) 0 0
\(396\) 0 0
\(397\) −108.000 + 108.000i −0.272040 + 0.272040i −0.829921 0.557881i \(-0.811615\pi\)
0.557881 + 0.829921i \(0.311615\pi\)
\(398\) −160.000 160.000i −0.402010 0.402010i
\(399\) 0 0
\(400\) 0 0
\(401\) 18.0000 0.0448878 0.0224439 0.999748i \(-0.492855\pi\)
0.0224439 + 0.999748i \(0.492855\pi\)
\(402\) 0 0
\(403\) 96.0000 + 96.0000i 0.238213 + 0.238213i
\(404\) 156.000i 0.386139i
\(405\) 0 0
\(406\) 180.000 0.443350
\(407\) 576.000 576.000i 1.41523 1.41523i
\(408\) 0 0
\(409\) 80.0000i 0.195599i −0.995206 0.0977995i \(-0.968820\pi\)
0.995206 0.0977995i \(-0.0311804\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 186.000 186.000i 0.451456 0.451456i
\(413\) 180.000 + 180.000i 0.435835 + 0.435835i
\(414\) 0 0
\(415\) 0 0
\(416\) 96.0000 0.230769
\(417\) 0 0
\(418\) 240.000 + 240.000i 0.574163 + 0.574163i
\(419\) 540.000i 1.28878i −0.764696 0.644391i \(-0.777111\pi\)
0.764696 0.644391i \(-0.222889\pi\)
\(420\) 0 0
\(421\) −608.000 −1.44418 −0.722090 0.691799i \(-0.756818\pi\)
−0.722090 + 0.691799i \(0.756818\pi\)
\(422\) −28.0000 + 28.0000i −0.0663507 + 0.0663507i
\(423\) 0 0
\(424\) 48.0000i 0.113208i
\(425\) 0 0
\(426\) 0 0
\(427\) −96.0000 + 96.0000i −0.224824 + 0.224824i
\(428\) 54.0000 + 54.0000i 0.126168 + 0.126168i
\(429\) 0 0
\(430\) 0 0
\(431\) −312.000 −0.723898 −0.361949 0.932198i \(-0.617889\pi\)
−0.361949 + 0.932198i \(0.617889\pi\)
\(432\) 0 0
\(433\) −252.000 252.000i −0.581986 0.581986i 0.353463 0.935449i \(-0.385004\pi\)
−0.935449 + 0.353463i \(0.885004\pi\)
\(434\) 48.0000i 0.110599i
\(435\) 0 0
\(436\) −320.000 −0.733945
\(437\) −60.0000 + 60.0000i −0.137300 + 0.137300i
\(438\) 0 0
\(439\) 40.0000i 0.0911162i −0.998962 0.0455581i \(-0.985493\pi\)
0.998962 0.0455581i \(-0.0145066\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 288.000 288.000i 0.651584 0.651584i
\(443\) −213.000 213.000i −0.480813 0.480813i 0.424578 0.905391i \(-0.360422\pi\)
−0.905391 + 0.424578i \(0.860422\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −234.000 −0.524664
\(447\) 0 0
\(448\) −24.0000 24.0000i −0.0535714 0.0535714i
\(449\) 480.000i 1.06904i 0.845155 + 0.534521i \(0.179508\pi\)
−0.845155 + 0.534521i \(0.820492\pi\)
\(450\) 0 0
\(451\) −576.000 −1.27716
\(452\) 144.000 144.000i 0.318584 0.318584i
\(453\) 0 0
\(454\) 186.000i 0.409692i
\(455\) 0 0
\(456\) 0 0
\(457\) 432.000 432.000i 0.945295 0.945295i −0.0532840 0.998579i \(-0.516969\pi\)
0.998579 + 0.0532840i \(0.0169689\pi\)
\(458\) 370.000 + 370.000i 0.807860 + 0.807860i
\(459\) 0 0
\(460\) 0 0
\(461\) −222.000 −0.481562 −0.240781 0.970579i \(-0.577404\pi\)
−0.240781 + 0.970579i \(0.577404\pi\)
\(462\) 0 0
\(463\) 213.000 + 213.000i 0.460043 + 0.460043i 0.898670 0.438626i \(-0.144535\pi\)
−0.438626 + 0.898670i \(0.644535\pi\)
\(464\) 120.000i 0.258621i
\(465\) 0 0
\(466\) 504.000 1.08155
\(467\) 3.00000 3.00000i 0.00642398 0.00642398i −0.703887 0.710311i \(-0.748554\pi\)
0.710311 + 0.703887i \(0.248554\pi\)
\(468\) 0 0
\(469\) 18.0000i 0.0383795i
\(470\) 0 0
\(471\) 0 0
\(472\) −120.000 + 120.000i −0.254237 + 0.254237i
\(473\) 324.000 + 324.000i 0.684989 + 0.684989i
\(474\) 0 0
\(475\) 0 0
\(476\) −144.000 −0.302521
\(477\) 0 0
\(478\) 360.000 + 360.000i 0.753138 + 0.753138i
\(479\) 240.000i 0.501044i −0.968111 0.250522i \(-0.919398\pi\)
0.968111 0.250522i \(-0.0806022\pi\)
\(480\) 0 0
\(481\) 1152.00 2.39501
\(482\) 32.0000 32.0000i 0.0663900 0.0663900i
\(483\) 0 0
\(484\) 46.0000i 0.0950413i
\(485\) 0 0
\(486\) 0 0
\(487\) 627.000 627.000i 1.28747 1.28747i 0.351158 0.936316i \(-0.385788\pi\)
0.936316 0.351158i \(-0.114212\pi\)
\(488\) −64.0000 64.0000i −0.131148 0.131148i
\(489\) 0 0
\(490\) 0 0
\(491\) 588.000 1.19756 0.598778 0.800915i \(-0.295653\pi\)
0.598778 + 0.800915i \(0.295653\pi\)
\(492\) 0 0
\(493\) 360.000 + 360.000i 0.730223 + 0.730223i
\(494\) 480.000i 0.971660i
\(495\) 0 0
\(496\) 32.0000 0.0645161
\(497\) −144.000 + 144.000i −0.289738 + 0.289738i
\(498\) 0 0
\(499\) 460.000i 0.921844i −0.887441 0.460922i \(-0.847519\pi\)
0.887441 0.460922i \(-0.152481\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −252.000 + 252.000i −0.501992 + 0.501992i
\(503\) 627.000 + 627.000i 1.24652 + 1.24652i 0.957246 + 0.289275i \(0.0934141\pi\)
0.289275 + 0.957246i \(0.406586\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 72.0000 0.142292
\(507\) 0 0
\(508\) −234.000 234.000i −0.460630 0.460630i
\(509\) 450.000i 0.884086i 0.896994 + 0.442043i \(0.145746\pi\)
−0.896994 + 0.442043i \(0.854254\pi\)
\(510\) 0 0
\(511\) 72.0000 0.140900
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 384.000i 0.747082i
\(515\) 0 0
\(516\) 0 0
\(517\) 324.000 324.000i 0.626692 0.626692i
\(518\) −288.000 288.000i −0.555985 0.555985i
\(519\) 0 0
\(520\) 0 0
\(521\) 558.000 1.07102 0.535509 0.844530i \(-0.320120\pi\)
0.535509 + 0.844530i \(0.320120\pi\)
\(522\) 0 0
\(523\) 123.000 + 123.000i 0.235182 + 0.235182i 0.814851 0.579670i \(-0.196818\pi\)
−0.579670 + 0.814851i \(0.696818\pi\)
\(524\) 264.000i 0.503817i
\(525\) 0 0
\(526\) −666.000 −1.26616
\(527\) 96.0000 96.0000i 0.182163 0.182163i
\(528\) 0 0
\(529\) 511.000i 0.965974i
\(530\) 0 0
\(531\) 0 0
\(532\) 120.000 120.000i 0.225564 0.225564i
\(533\) −576.000 576.000i −1.08068 1.08068i
\(534\) 0 0
\(535\) 0 0
\(536\) 12.0000 0.0223881
\(537\) 0 0
\(538\) 480.000 + 480.000i 0.892193 + 0.892193i
\(539\) 372.000i 0.690167i
\(540\) 0 0
\(541\) 542.000 1.00185 0.500924 0.865491i \(-0.332994\pi\)
0.500924 + 0.865491i \(0.332994\pi\)
\(542\) −88.0000 + 88.0000i −0.162362 + 0.162362i
\(543\) 0 0
\(544\) 96.0000i 0.176471i
\(545\) 0 0
\(546\) 0 0
\(547\) 147.000 147.000i 0.268739 0.268739i −0.559853 0.828592i \(-0.689142\pi\)
0.828592 + 0.559853i \(0.189142\pi\)
\(548\) −336.000 336.000i −0.613139 0.613139i
\(549\) 0 0
\(550\) 0 0
\(551\) −600.000 −1.08893
\(552\) 0 0
\(553\) 120.000 + 120.000i 0.216998 + 0.216998i
\(554\) 576.000i 1.03971i
\(555\) 0 0
\(556\) 200.000 0.359712
\(557\) 288.000 288.000i 0.517056 0.517056i −0.399624 0.916679i \(-0.630859\pi\)
0.916679 + 0.399624i \(0.130859\pi\)
\(558\) 0 0
\(559\) 648.000i 1.15921i
\(560\) 0 0
\(561\) 0 0
\(562\) 288.000 288.000i 0.512456 0.512456i
\(563\) 477.000 + 477.000i 0.847247 + 0.847247i 0.989789 0.142542i \(-0.0455276\pi\)
−0.142542 + 0.989789i \(0.545528\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −234.000 −0.413428
\(567\) 0 0
\(568\) −96.0000 96.0000i −0.169014 0.169014i
\(569\) 240.000i 0.421793i −0.977508 0.210896i \(-0.932362\pi\)
0.977508 0.210896i \(-0.0676382\pi\)
\(570\) 0 0
\(571\) 692.000 1.21191 0.605954 0.795499i \(-0.292791\pi\)
0.605954 + 0.795499i \(0.292791\pi\)
\(572\) 288.000 288.000i 0.503497 0.503497i
\(573\) 0 0
\(574\) 288.000i 0.501742i
\(575\) 0 0
\(576\) 0 0
\(577\) −168.000 + 168.000i −0.291161 + 0.291161i −0.837539 0.546378i \(-0.816006\pi\)
0.546378 + 0.837539i \(0.316006\pi\)
\(578\) 1.00000 + 1.00000i 0.00173010 + 0.00173010i
\(579\) 0 0
\(580\) 0 0
\(581\) 558.000 0.960413
\(582\) 0 0
\(583\) −144.000 144.000i −0.246998 0.246998i
\(584\) 48.0000i 0.0821918i
\(585\) 0 0
\(586\) −336.000 −0.573379
\(587\) 213.000 213.000i 0.362862 0.362862i −0.502004 0.864866i \(-0.667404\pi\)
0.864866 + 0.502004i \(0.167404\pi\)
\(588\) 0 0
\(589\) 160.000i 0.271647i
\(590\) 0 0
\(591\) 0 0
\(592\) 192.000 192.000i 0.324324 0.324324i
\(593\) 312.000 + 312.000i 0.526138 + 0.526138i 0.919419 0.393280i \(-0.128660\pi\)
−0.393280 + 0.919419i \(0.628660\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 72.0000 + 72.0000i 0.120401 + 0.120401i
\(599\) 240.000i 0.400668i 0.979728 + 0.200334i \(0.0642027\pi\)
−0.979728 + 0.200334i \(0.935797\pi\)
\(600\) 0 0
\(601\) −608.000 −1.01165 −0.505824 0.862637i \(-0.668811\pi\)
−0.505824 + 0.862637i \(0.668811\pi\)
\(602\) 162.000 162.000i 0.269103 0.269103i
\(603\) 0 0
\(604\) 496.000i 0.821192i
\(605\) 0 0
\(606\) 0 0
\(607\) 267.000 267.000i 0.439868 0.439868i −0.452099 0.891968i \(-0.649325\pi\)
0.891968 + 0.452099i \(0.149325\pi\)
\(608\) 80.0000 + 80.0000i 0.131579 + 0.131579i
\(609\) 0 0
\(610\) 0 0
\(611\) 648.000 1.06056
\(612\) 0 0
\(613\) 228.000 + 228.000i 0.371941 + 0.371941i 0.868184 0.496243i \(-0.165287\pi\)
−0.496243 + 0.868184i \(0.665287\pi\)
\(614\) 486.000i 0.791531i
\(615\) 0 0
\(616\) −144.000 −0.233766
\(617\) 348.000 348.000i 0.564019 0.564019i −0.366427 0.930447i \(-0.619419\pi\)
0.930447 + 0.366427i \(0.119419\pi\)
\(618\) 0 0
\(619\) 940.000i 1.51858i −0.650753 0.759289i \(-0.725547\pi\)
0.650753 0.759289i \(-0.274453\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −552.000 + 552.000i −0.887460 + 0.887460i
\(623\) −90.0000 90.0000i −0.144462 0.144462i
\(624\) 0 0
\(625\) 0 0
\(626\) 96.0000 0.153355
\(627\) 0 0
\(628\) −144.000 144.000i −0.229299 0.229299i
\(629\) 1152.00i 1.83148i
\(630\) 0 0
\(631\) −808.000 −1.28051 −0.640254 0.768164i \(-0.721171\pi\)
−0.640254 + 0.768164i \(0.721171\pi\)
\(632\) −80.0000 + 80.0000i −0.126582 + 0.126582i
\(633\) 0 0
\(634\) 456.000i 0.719243i
\(635\) 0 0
\(636\) 0 0
\(637\) 372.000 372.000i 0.583987 0.583987i
\(638\) 360.000 + 360.000i 0.564263 + 0.564263i
\(639\) 0 0
\(640\) 0 0
\(641\) 768.000 1.19813 0.599064 0.800701i \(-0.295540\pi\)
0.599064 + 0.800701i \(0.295540\pi\)
\(642\) 0 0
\(643\) −477.000 477.000i −0.741835 0.741835i 0.231096 0.972931i \(-0.425769\pi\)
−0.972931 + 0.231096i \(0.925769\pi\)
\(644\) 36.0000i 0.0559006i
\(645\) 0 0
\(646\) 480.000 0.743034
\(647\) −627.000 + 627.000i −0.969088 + 0.969088i −0.999536 0.0304482i \(-0.990307\pi\)
0.0304482 + 0.999536i \(0.490307\pi\)
\(648\) 0 0
\(649\) 720.000i 1.10940i
\(650\) 0 0
\(651\) 0 0
\(652\) 186.000 186.000i 0.285276 0.285276i
\(653\) 12.0000 + 12.0000i 0.0183767 + 0.0183767i 0.716235 0.697859i \(-0.245864\pi\)
−0.697859 + 0.716235i \(0.745864\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −192.000 −0.292683
\(657\) 0 0
\(658\) −162.000 162.000i −0.246201 0.246201i
\(659\) 540.000i 0.819423i −0.912215 0.409712i \(-0.865629\pi\)
0.912215 0.409712i \(-0.134371\pi\)
\(660\) 0 0
\(661\) 352.000 0.532526 0.266263 0.963900i \(-0.414211\pi\)
0.266263 + 0.963900i \(0.414211\pi\)
\(662\) −148.000 + 148.000i −0.223565 + 0.223565i
\(663\) 0 0
\(664\) 372.000i 0.560241i
\(665\) 0 0
\(666\) 0 0
\(667\) −90.0000 + 90.0000i −0.134933 + 0.134933i
\(668\) −6.00000 6.00000i −0.00898204 0.00898204i
\(669\) 0 0
\(670\) 0 0
\(671\) −384.000 −0.572280
\(672\) 0 0
\(673\) −732.000 732.000i −1.08767 1.08767i −0.995768 0.0918988i \(-0.970706\pi\)
−0.0918988 0.995768i \(-0.529294\pi\)
\(674\) 384.000i 0.569733i
\(675\) 0 0
\(676\) 238.000 0.352071
\(677\) 108.000 108.000i 0.159527 0.159527i −0.622830 0.782357i \(-0.714017\pi\)
0.782357 + 0.622830i \(0.214017\pi\)
\(678\) 0 0
\(679\) 72.0000i 0.106038i
\(680\) 0 0
\(681\) 0 0
\(682\) 96.0000 96.0000i 0.140762 0.140762i
\(683\) −933.000 933.000i −1.36603 1.36603i −0.866016 0.500016i \(-0.833327\pi\)
−0.500016 0.866016i \(-0.666673\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −480.000 −0.699708
\(687\) 0 0
\(688\) 108.000 + 108.000i 0.156977 + 0.156977i
\(689\) 288.000i 0.417997i
\(690\) 0 0
\(691\) −68.0000 −0.0984081 −0.0492041 0.998789i \(-0.515668\pi\)
−0.0492041 + 0.998789i \(0.515668\pi\)
\(692\) −336.000 + 336.000i −0.485549 + 0.485549i
\(693\) 0 0
\(694\) 234.000i 0.337176i
\(695\) 0 0
\(696\) 0 0
\(697\) −576.000 + 576.000i −0.826399 + 0.826399i
\(698\) 130.000 + 130.000i 0.186246 + 0.186246i
\(699\) 0 0
\(700\) 0 0
\(701\) −192.000 −0.273894 −0.136947 0.990578i \(-0.543729\pi\)
−0.136947 + 0.990578i \(0.543729\pi\)
\(702\) 0 0
\(703\) 960.000 + 960.000i 1.36558 + 1.36558i
\(704\) 96.0000i 0.136364i
\(705\) 0 0
\(706\) −576.000 −0.815864
\(707\) −234.000 + 234.000i −0.330976 + 0.330976i
\(708\) 0 0
\(709\) 50.0000i 0.0705219i −0.999378 0.0352609i \(-0.988774\pi\)
0.999378 0.0352609i \(-0.0112262\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 60.0000 60.0000i 0.0842697 0.0842697i
\(713\) 24.0000 + 24.0000i 0.0336606 + 0.0336606i
\(714\) 0 0
\(715\) 0 0
\(716\) −600.000 −0.837989
\(717\) 0 0
\(718\) −120.000 120.000i −0.167131 0.167131i
\(719\) 840.000i 1.16829i 0.811650 + 0.584145i \(0.198570\pi\)
−0.811650 + 0.584145i \(0.801430\pi\)
\(720\) 0 0
\(721\) −558.000 −0.773925
\(722\) −39.0000 + 39.0000i −0.0540166 + 0.0540166i
\(723\) 0 0
\(724\) 284.000i 0.392265i
\(725\) 0 0
\(726\) 0 0
\(727\) −963.000 + 963.000i −1.32462 + 1.32462i −0.414633 + 0.909989i \(0.636090\pi\)
−0.909989 + 0.414633i \(0.863910\pi\)
\(728\) −144.000 144.000i −0.197802 0.197802i
\(729\) 0 0
\(730\) 0 0
\(731\) 648.000 0.886457
\(732\) 0 0
\(733\) −72.0000 72.0000i −0.0982265 0.0982265i 0.656286 0.754512i \(-0.272127\pi\)
−0.754512 + 0.656286i \(0.772127\pi\)
\(734\) 426.000i 0.580381i
\(735\) 0 0
\(736\) 24.0000 0.0326087
\(737\) 36.0000 36.0000i 0.0488467 0.0488467i
\(738\) 0 0
\(739\) 20.0000i 0.0270636i −0.999908 0.0135318i \(-0.995693\pi\)
0.999908 0.0135318i \(-0.00430744\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −72.0000 + 72.0000i −0.0970350 + 0.0970350i
\(743\) −243.000 243.000i −0.327052 0.327052i 0.524412 0.851465i \(-0.324285\pi\)
−0.851465 + 0.524412i \(0.824285\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 336.000 0.450402
\(747\) 0 0
\(748\) −288.000 288.000i −0.385027 0.385027i
\(749\) 162.000i 0.216288i
\(750\) 0 0
\(751\) 1072.00 1.42743 0.713715 0.700436i \(-0.247011\pi\)
0.713715 + 0.700436i \(0.247011\pi\)
\(752\) 108.000 108.000i 0.143617 0.143617i
\(753\) 0 0
\(754\) 720.000i 0.954907i
\(755\) 0 0
\(756\) 0 0
\(757\) −408.000 + 408.000i −0.538970 + 0.538970i −0.923226 0.384257i \(-0.874458\pi\)
0.384257 + 0.923226i \(0.374458\pi\)
\(758\) −20.0000 20.0000i −0.0263852 0.0263852i
\(759\) 0 0
\(760\) 0 0
\(761\) −1362.00 −1.78975 −0.894875 0.446317i \(-0.852736\pi\)
−0.894875 + 0.446317i \(0.852736\pi\)
\(762\) 0 0
\(763\) 480.000 + 480.000i 0.629096 + 0.629096i
\(764\) 384.000i 0.502618i
\(765\) 0 0
\(766\) −246.000 −0.321149
\(767\) −720.000 + 720.000i −0.938722 + 0.938722i
\(768\) 0 0
\(769\) 370.000i 0.481144i −0.970631 0.240572i \(-0.922665\pi\)
0.970631 0.240572i \(-0.0773351\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −264.000 + 264.000i −0.341969 + 0.341969i
\(773\) 132.000 + 132.000i 0.170763 + 0.170763i 0.787315 0.616551i \(-0.211471\pi\)
−0.616551 + 0.787315i \(0.711471\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −48.0000 −0.0618557
\(777\) 0 0
\(778\) 0 0
\(779\) 960.000i 1.23235i
\(780\) 0 0
\(781\) −576.000 −0.737516
\(782\) 72.0000 72.0000i 0.0920716 0.0920716i
\(783\) 0 0
\(784\) 124.000i 0.158163i
\(785\) 0 0
\(786\) 0 0
\(787\) −93.0000 + 93.0000i −0.118170 + 0.118170i −0.763719 0.645549i \(-0.776629\pi\)
0.645549 + 0.763719i \(0.276629\pi\)
\(788\) 264.000 + 264.000i 0.335025 + 0.335025i