Properties

Label 370.2.b.a.149.1
Level $370$
Weight $2$
Character 370.149
Analytic conductor $2.954$
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] = [370,2,Mod(149,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.b (of order \(2\), degree \(1\), 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: \(2.95446487479\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 149.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 370.149
Dual form 370.2.b.a.149.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{8} +3.00000 q^{9} +(1.00000 + 2.00000i) q^{10} +2.00000i q^{13} +2.00000 q^{14} +1.00000 q^{16} +6.00000i q^{17} -3.00000i q^{18} +6.00000 q^{19} +(2.00000 - 1.00000i) q^{20} +4.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -2.00000i q^{28} -4.00000 q^{31} -1.00000i q^{32} +6.00000 q^{34} +(-2.00000 - 4.00000i) q^{35} -3.00000 q^{36} +1.00000i q^{37} -6.00000i q^{38} +(-1.00000 - 2.00000i) q^{40} -10.0000 q^{41} -4.00000i q^{43} +(-6.00000 + 3.00000i) q^{45} +4.00000 q^{46} +2.00000i q^{47} +3.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -2.00000i q^{52} +2.00000i q^{53} -2.00000 q^{56} +6.00000 q^{59} +4.00000i q^{62} +6.00000i q^{63} -1.00000 q^{64} +(-2.00000 - 4.00000i) q^{65} -8.00000i q^{67} -6.00000i q^{68} +(-4.00000 + 2.00000i) q^{70} +3.00000i q^{72} +8.00000i q^{73} +1.00000 q^{74} -6.00000 q^{76} -4.00000 q^{79} +(-2.00000 + 1.00000i) q^{80} +9.00000 q^{81} +10.0000i q^{82} -12.0000i q^{83} +(-6.00000 - 12.0000i) q^{85} -4.00000 q^{86} -6.00000 q^{89} +(3.00000 + 6.00000i) q^{90} -4.00000 q^{91} -4.00000i q^{92} +2.00000 q^{94} +(-12.0000 + 6.00000i) q^{95} +10.0000i q^{97} -3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} - 4 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} - 4 q^{5} + 6 q^{9} + 2 q^{10} + 4 q^{14} + 2 q^{16} + 12 q^{19} + 4 q^{20} + 6 q^{25} + 4 q^{26} - 8 q^{31} + 12 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{40} - 20 q^{41} - 12 q^{45} + 8 q^{46} + 6 q^{49} - 8 q^{50} - 4 q^{56} + 12 q^{59} - 2 q^{64} - 4 q^{65} - 8 q^{70} + 2 q^{74} - 12 q^{76} - 8 q^{79} - 4 q^{80} + 18 q^{81} - 12 q^{85} - 8 q^{86} - 12 q^{89} + 6 q^{90} - 8 q^{91} + 4 q^{94} - 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 0 0
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 3.00000 1.00000
\(10\) 1.00000 + 2.00000i 0.316228 + 0.632456i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.00000i 1.45521i 0.685994 + 0.727607i \(0.259367\pi\)
−0.685994 + 0.727607i \(0.740633\pi\)
\(18\) 3.00000i 0.707107i
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 2.00000 1.00000i 0.447214 0.223607i
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 0 0
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 2.00000i 0.377964i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) −2.00000 4.00000i −0.338062 0.676123i
\(36\) −3.00000 −0.500000
\(37\) 1.00000i 0.164399i
\(38\) 6.00000i 0.973329i
\(39\) 0 0
\(40\) −1.00000 2.00000i −0.158114 0.316228i
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 0 0
\(45\) −6.00000 + 3.00000i −0.894427 + 0.447214i
\(46\) 4.00000 0.589768
\(47\) 2.00000i 0.291730i 0.989305 + 0.145865i \(0.0465965\pi\)
−0.989305 + 0.145865i \(0.953403\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) −4.00000 3.00000i −0.565685 0.424264i
\(51\) 0 0
\(52\) 2.00000i 0.277350i
\(53\) 2.00000i 0.274721i 0.990521 + 0.137361i \(0.0438619\pi\)
−0.990521 + 0.137361i \(0.956138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) 0 0
\(58\) 0 0
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 6.00000i 0.755929i
\(64\) −1.00000 −0.125000
\(65\) −2.00000 4.00000i −0.248069 0.496139i
\(66\) 0 0
\(67\) 8.00000i 0.977356i −0.872464 0.488678i \(-0.837479\pi\)
0.872464 0.488678i \(-0.162521\pi\)
\(68\) 6.00000i 0.727607i
\(69\) 0 0
\(70\) −4.00000 + 2.00000i −0.478091 + 0.239046i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 8.00000i 0.936329i 0.883641 + 0.468165i \(0.155085\pi\)
−0.883641 + 0.468165i \(0.844915\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) 0 0
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) −2.00000 + 1.00000i −0.223607 + 0.111803i
\(81\) 9.00000 1.00000
\(82\) 10.0000i 1.10432i
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 0 0
\(85\) −6.00000 12.0000i −0.650791 1.30158i
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 3.00000 + 6.00000i 0.316228 + 0.632456i
\(91\) −4.00000 −0.419314
\(92\) 4.00000i 0.417029i
\(93\) 0 0
\(94\) 2.00000 0.206284
\(95\) −12.0000 + 6.00000i −1.23117 + 0.615587i
\(96\) 0 0
\(97\) 10.0000i 1.01535i 0.861550 + 0.507673i \(0.169494\pi\)
−0.861550 + 0.507673i \(0.830506\pi\)
\(98\) 3.00000i 0.303046i
\(99\) 0 0
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 8.00000i 0.773389i −0.922208 0.386695i \(-0.873617\pi\)
0.922208 0.386695i \(-0.126383\pi\)
\(108\) 0 0
\(109\) 20.0000 1.91565 0.957826 0.287348i \(-0.0927736\pi\)
0.957826 + 0.287348i \(0.0927736\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.00000i 0.188982i
\(113\) 2.00000i 0.188144i 0.995565 + 0.0940721i \(0.0299884\pi\)
−0.995565 + 0.0940721i \(0.970012\pi\)
\(114\) 0 0
\(115\) −4.00000 8.00000i −0.373002 0.746004i
\(116\) 0 0
\(117\) 6.00000i 0.554700i
\(118\) 6.00000i 0.552345i
\(119\) −12.0000 −1.10004
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 4.00000 0.359211
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 6.00000 0.534522
\(127\) 22.0000i 1.95218i −0.217357 0.976092i \(-0.569744\pi\)
0.217357 0.976092i \(-0.430256\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −4.00000 + 2.00000i −0.350823 + 0.175412i
\(131\) 14.0000 1.22319 0.611593 0.791173i \(-0.290529\pi\)
0.611593 + 0.791173i \(0.290529\pi\)
\(132\) 0 0
\(133\) 12.0000i 1.04053i
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 2.00000 + 4.00000i 0.169031 + 0.338062i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) 0 0
\(146\) 8.00000 0.662085
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) −14.0000 −1.14692 −0.573462 0.819232i \(-0.694400\pi\)
−0.573462 + 0.819232i \(0.694400\pi\)
\(150\) 0 0
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 18.0000i 1.45521i
\(154\) 0 0
\(155\) 8.00000 4.00000i 0.642575 0.321288i
\(156\) 0 0
\(157\) 22.0000i 1.75579i −0.478852 0.877896i \(-0.658947\pi\)
0.478852 0.877896i \(-0.341053\pi\)
\(158\) 4.00000i 0.318223i
\(159\) 0 0
\(160\) 1.00000 + 2.00000i 0.0790569 + 0.158114i
\(161\) −8.00000 −0.630488
\(162\) 9.00000i 0.707107i
\(163\) 12.0000i 0.939913i −0.882690 0.469956i \(-0.844270\pi\)
0.882690 0.469956i \(-0.155730\pi\)
\(164\) 10.0000 0.780869
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) 16.0000i 1.23812i −0.785345 0.619059i \(-0.787514\pi\)
0.785345 0.619059i \(-0.212486\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −12.0000 + 6.00000i −0.920358 + 0.460179i
\(171\) 18.0000 1.37649
\(172\) 4.00000i 0.304997i
\(173\) 2.00000i 0.152057i 0.997106 + 0.0760286i \(0.0242240\pi\)
−0.997106 + 0.0760286i \(0.975776\pi\)
\(174\) 0 0
\(175\) 8.00000 + 6.00000i 0.604743 + 0.453557i
\(176\) 0 0
\(177\) 0 0
\(178\) 6.00000i 0.449719i
\(179\) 14.0000 1.04641 0.523205 0.852207i \(-0.324736\pi\)
0.523205 + 0.852207i \(0.324736\pi\)
\(180\) 6.00000 3.00000i 0.447214 0.223607i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) −1.00000 2.00000i −0.0735215 0.147043i
\(186\) 0 0
\(187\) 0 0
\(188\) 2.00000i 0.145865i
\(189\) 0 0
\(190\) 6.00000 + 12.0000i 0.435286 + 0.870572i
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 0 0
\(193\) 10.0000i 0.719816i 0.932988 + 0.359908i \(0.117192\pi\)
−0.932988 + 0.359908i \(0.882808\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 10.0000i 0.712470i 0.934396 + 0.356235i \(0.115940\pi\)
−0.934396 + 0.356235i \(0.884060\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 4.00000 + 3.00000i 0.282843 + 0.212132i
\(201\) 0 0
\(202\) 10.0000i 0.703598i
\(203\) 0 0
\(204\) 0 0
\(205\) 20.0000 10.0000i 1.39686 0.698430i
\(206\) 0 0
\(207\) 12.0000i 0.834058i
\(208\) 2.00000i 0.138675i
\(209\) 0 0
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 2.00000i 0.137361i
\(213\) 0 0
\(214\) −8.00000 −0.546869
\(215\) 4.00000 + 8.00000i 0.272798 + 0.545595i
\(216\) 0 0
\(217\) 8.00000i 0.543075i
\(218\) 20.0000i 1.35457i
\(219\) 0 0
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) 14.0000i 0.937509i 0.883328 + 0.468755i \(0.155297\pi\)
−0.883328 + 0.468755i \(0.844703\pi\)
\(224\) 2.00000 0.133631
\(225\) 9.00000 12.0000i 0.600000 0.800000i
\(226\) 2.00000 0.133038
\(227\) 20.0000i 1.32745i −0.747978 0.663723i \(-0.768975\pi\)
0.747978 0.663723i \(-0.231025\pi\)
\(228\) 0 0
\(229\) −2.00000 −0.132164 −0.0660819 0.997814i \(-0.521050\pi\)
−0.0660819 + 0.997814i \(0.521050\pi\)
\(230\) −8.00000 + 4.00000i −0.527504 + 0.263752i
\(231\) 0 0
\(232\) 0 0
\(233\) 24.0000i 1.57229i −0.618041 0.786146i \(-0.712073\pi\)
0.618041 0.786146i \(-0.287927\pi\)
\(234\) 6.00000 0.392232
\(235\) −2.00000 4.00000i −0.130466 0.260931i
\(236\) −6.00000 −0.390567
\(237\) 0 0
\(238\) 12.0000i 0.777844i
\(239\) −28.0000 −1.81117 −0.905585 0.424165i \(-0.860568\pi\)
−0.905585 + 0.424165i \(0.860568\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 11.0000i 0.707107i
\(243\) 0 0
\(244\) 0 0
\(245\) −6.00000 + 3.00000i −0.383326 + 0.191663i
\(246\) 0 0
\(247\) 12.0000i 0.763542i
\(248\) 4.00000i 0.254000i
\(249\) 0 0
\(250\) 11.0000 + 2.00000i 0.695701 + 0.126491i
\(251\) 2.00000 0.126239 0.0631194 0.998006i \(-0.479895\pi\)
0.0631194 + 0.998006i \(0.479895\pi\)
\(252\) 6.00000i 0.377964i
\(253\) 0 0
\(254\) −22.0000 −1.38040
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 30.0000i 1.87135i 0.352865 + 0.935674i \(0.385208\pi\)
−0.352865 + 0.935674i \(0.614792\pi\)
\(258\) 0 0
\(259\) −2.00000 −0.124274
\(260\) 2.00000 + 4.00000i 0.124035 + 0.248069i
\(261\) 0 0
\(262\) 14.0000i 0.864923i
\(263\) 2.00000i 0.123325i −0.998097 0.0616626i \(-0.980360\pi\)
0.998097 0.0616626i \(-0.0196403\pi\)
\(264\) 0 0
\(265\) −2.00000 4.00000i −0.122859 0.245718i
\(266\) 12.0000 0.735767
\(267\) 0 0
\(268\) 8.00000i 0.488678i
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 6.00000i 0.363803i
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 18.0000i 1.08152i 0.841178 + 0.540758i \(0.181862\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 20.0000i 1.19952i
\(279\) −12.0000 −0.718421
\(280\) 4.00000 2.00000i 0.239046 0.119523i
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 28.0000i 1.66443i 0.554455 + 0.832214i \(0.312927\pi\)
−0.554455 + 0.832214i \(0.687073\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 20.0000i 1.18056i
\(288\) 3.00000i 0.176777i
\(289\) −19.0000 −1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) 8.00000i 0.468165i
\(293\) 6.00000i 0.350524i 0.984522 + 0.175262i \(0.0560772\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(294\) 0 0
\(295\) −12.0000 + 6.00000i −0.698667 + 0.349334i
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 14.0000i 0.810998i
\(299\) −8.00000 −0.462652
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 16.0000i 0.920697i
\(303\) 0 0
\(304\) 6.00000 0.344124
\(305\) 0 0
\(306\) 18.0000 1.02899
\(307\) 4.00000i 0.228292i −0.993464 0.114146i \(-0.963587\pi\)
0.993464 0.114146i \(-0.0364132\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.00000 8.00000i −0.227185 0.454369i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 14.0000i 0.791327i −0.918396 0.395663i \(-0.870515\pi\)
0.918396 0.395663i \(-0.129485\pi\)
\(314\) −22.0000 −1.24153
\(315\) −6.00000 12.0000i −0.338062 0.676123i
\(316\) 4.00000 0.225018
\(317\) 6.00000i 0.336994i 0.985702 + 0.168497i \(0.0538913\pi\)
−0.985702 + 0.168497i \(0.946109\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 2.00000 1.00000i 0.111803 0.0559017i
\(321\) 0 0
\(322\) 8.00000i 0.445823i
\(323\) 36.0000i 2.00309i
\(324\) −9.00000 −0.500000
\(325\) 8.00000 + 6.00000i 0.443760 + 0.332820i
\(326\) −12.0000 −0.664619
\(327\) 0 0
\(328\) 10.0000i 0.552158i
\(329\) −4.00000 −0.220527
\(330\) 0 0
\(331\) −34.0000 −1.86881 −0.934405 0.356214i \(-0.884068\pi\)
−0.934405 + 0.356214i \(0.884068\pi\)
\(332\) 12.0000i 0.658586i
\(333\) 3.00000i 0.164399i
\(334\) −16.0000 −0.875481
\(335\) 8.00000 + 16.0000i 0.437087 + 0.874173i
\(336\) 0 0
\(337\) 8.00000i 0.435788i −0.975972 0.217894i \(-0.930081\pi\)
0.975972 0.217894i \(-0.0699187\pi\)
\(338\) 9.00000i 0.489535i
\(339\) 0 0
\(340\) 6.00000 + 12.0000i 0.325396 + 0.650791i
\(341\) 0 0
\(342\) 18.0000i 0.973329i
\(343\) 20.0000i 1.07990i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) 36.0000i 1.93258i −0.257454 0.966291i \(-0.582883\pi\)
0.257454 0.966291i \(-0.417117\pi\)
\(348\) 0 0
\(349\) −30.0000 −1.60586 −0.802932 0.596071i \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) 6.00000 8.00000i 0.320713 0.427618i
\(351\) 0 0
\(352\) 0 0
\(353\) 18.0000i 0.958043i −0.877803 0.479022i \(-0.840992\pi\)
0.877803 0.479022i \(-0.159008\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 14.0000i 0.739923i
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) −3.00000 6.00000i −0.158114 0.316228i
\(361\) 17.0000 0.894737
\(362\) 2.00000i 0.105118i
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) −8.00000 16.0000i −0.418739 0.837478i
\(366\) 0 0
\(367\) 26.0000i 1.35719i 0.734513 + 0.678594i \(0.237411\pi\)
−0.734513 + 0.678594i \(0.762589\pi\)
\(368\) 4.00000i 0.208514i
\(369\) −30.0000 −1.56174
\(370\) −2.00000 + 1.00000i −0.103975 + 0.0519875i
\(371\) −4.00000 −0.207670
\(372\) 0 0
\(373\) 34.0000i 1.76045i −0.474554 0.880227i \(-0.657390\pi\)
0.474554 0.880227i \(-0.342610\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −2.00000 −0.103142
\(377\) 0 0
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 12.0000 6.00000i 0.615587 0.307794i
\(381\) 0 0
\(382\) 4.00000i 0.204658i
\(383\) 28.0000i 1.43073i −0.698749 0.715367i \(-0.746260\pi\)
0.698749 0.715367i \(-0.253740\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 12.0000i 0.609994i
\(388\) 10.0000i 0.507673i
\(389\) 16.0000 0.811232 0.405616 0.914044i \(-0.367057\pi\)
0.405616 + 0.914044i \(0.367057\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) 3.00000i 0.151523i
\(393\) 0 0
\(394\) 10.0000 0.503793
\(395\) 8.00000 4.00000i 0.402524 0.201262i
\(396\) 0 0
\(397\) 2.00000i 0.100377i −0.998740 0.0501886i \(-0.984018\pi\)
0.998740 0.0501886i \(-0.0159822\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 0 0
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) −2.00000 −0.0998752 −0.0499376 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 0 0
\(403\) 8.00000i 0.398508i
\(404\) 10.0000 0.497519
\(405\) −18.0000 + 9.00000i −0.894427 + 0.447214i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) −10.0000 20.0000i −0.493865 0.987730i
\(411\) 0 0
\(412\) 0 0
\(413\) 12.0000i 0.590481i
\(414\) 12.0000 0.589768
\(415\) 12.0000 + 24.0000i 0.589057 + 1.17811i
\(416\) 2.00000 0.0980581
\(417\) 0 0
\(418\) 0 0
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0 0
\(421\) 36.0000 1.75453 0.877266 0.480004i \(-0.159365\pi\)
0.877266 + 0.480004i \(0.159365\pi\)
\(422\) 16.0000i 0.778868i
\(423\) 6.00000i 0.291730i
\(424\) −2.00000 −0.0971286
\(425\) 24.0000 + 18.0000i 1.16417 + 0.873128i
\(426\) 0 0
\(427\) 0 0
\(428\) 8.00000i 0.386695i
\(429\) 0 0
\(430\) 8.00000 4.00000i 0.385794 0.192897i
\(431\) 20.0000 0.963366 0.481683 0.876346i \(-0.340026\pi\)
0.481683 + 0.876346i \(0.340026\pi\)
\(432\) 0 0
\(433\) 16.0000i 0.768911i −0.923144 0.384455i \(-0.874389\pi\)
0.923144 0.384455i \(-0.125611\pi\)
\(434\) −8.00000 −0.384012
\(435\) 0 0
\(436\) −20.0000 −0.957826
\(437\) 24.0000i 1.14808i
\(438\) 0 0
\(439\) −4.00000 −0.190910 −0.0954548 0.995434i \(-0.530431\pi\)
−0.0954548 + 0.995434i \(0.530431\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 12.0000i 0.570782i
\(443\) 16.0000i 0.760183i 0.924949 + 0.380091i \(0.124107\pi\)
−0.924949 + 0.380091i \(0.875893\pi\)
\(444\) 0 0
\(445\) 12.0000 6.00000i 0.568855 0.284427i
\(446\) 14.0000 0.662919
\(447\) 0 0
\(448\) 2.00000i 0.0944911i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −12.0000 9.00000i −0.565685 0.424264i
\(451\) 0 0
\(452\) 2.00000i 0.0940721i
\(453\) 0 0
\(454\) −20.0000 −0.938647
\(455\) 8.00000 4.00000i 0.375046 0.187523i
\(456\) 0 0
\(457\) 10.0000i 0.467780i 0.972263 + 0.233890i \(0.0751456\pi\)
−0.972263 + 0.233890i \(0.924854\pi\)
\(458\) 2.00000i 0.0934539i
\(459\) 0 0
\(460\) 4.00000 + 8.00000i 0.186501 + 0.373002i
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 4.00000i 0.185896i −0.995671 0.0929479i \(-0.970371\pi\)
0.995671 0.0929479i \(-0.0296290\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −24.0000 −1.11178
\(467\) 36.0000i 1.66588i 0.553362 + 0.832941i \(0.313345\pi\)
−0.553362 + 0.832941i \(0.686655\pi\)
\(468\) 6.00000i 0.277350i
\(469\) 16.0000 0.738811
\(470\) −4.00000 + 2.00000i −0.184506 + 0.0922531i
\(471\) 0 0
\(472\) 6.00000i 0.276172i
\(473\) 0 0
\(474\) 0 0
\(475\) 18.0000 24.0000i 0.825897 1.10120i
\(476\) 12.0000 0.550019
\(477\) 6.00000i 0.274721i
\(478\) 28.0000i 1.28069i
\(479\) −12.0000 −0.548294 −0.274147 0.961688i \(-0.588395\pi\)
−0.274147 + 0.961688i \(0.588395\pi\)
\(480\) 0 0
\(481\) −2.00000 −0.0911922
\(482\) 10.0000i 0.455488i
\(483\) 0 0
\(484\) 11.0000 0.500000
\(485\) −10.0000 20.0000i −0.454077 0.908153i
\(486\) 0 0
\(487\) 24.0000i 1.08754i −0.839233 0.543772i \(-0.816996\pi\)
0.839233 0.543772i \(-0.183004\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 3.00000 + 6.00000i 0.135526 + 0.271052i
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 12.0000 0.539906
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) −30.0000 −1.34298 −0.671492 0.741012i \(-0.734346\pi\)
−0.671492 + 0.741012i \(0.734346\pi\)
\(500\) 2.00000 11.0000i 0.0894427 0.491935i
\(501\) 0 0
\(502\) 2.00000i 0.0892644i
\(503\) 40.0000i 1.78351i 0.452517 + 0.891756i \(0.350526\pi\)
−0.452517 + 0.891756i \(0.649474\pi\)
\(504\) −6.00000 −0.267261
\(505\) 20.0000 10.0000i 0.889988 0.444994i
\(506\) 0 0
\(507\) 0 0
\(508\) 22.0000i 0.976092i
\(509\) 18.0000 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 0 0
\(511\) −16.0000 −0.707798
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 30.0000 1.32324
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 2.00000i 0.0878750i
\(519\) 0 0
\(520\) 4.00000 2.00000i 0.175412 0.0877058i
\(521\) 26.0000 1.13908 0.569540 0.821963i \(-0.307121\pi\)
0.569540 + 0.821963i \(0.307121\pi\)
\(522\) 0 0
\(523\) 4.00000i 0.174908i 0.996169 + 0.0874539i \(0.0278730\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(524\) −14.0000 −0.611593
\(525\) 0 0
\(526\) −2.00000 −0.0872041
\(527\) 24.0000i 1.04546i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) −4.00000 + 2.00000i −0.173749 + 0.0868744i
\(531\) 18.0000 0.781133
\(532\) 12.0000i 0.520266i
\(533\) 20.0000i 0.866296i
\(534\) 0 0
\(535\) 8.00000 + 16.0000i 0.345870 + 0.691740i
\(536\) 8.00000 0.345547
\(537\) 0 0
\(538\) 10.0000i 0.431131i
\(539\) 0 0
\(540\) 0 0
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) 8.00000i 0.343629i
\(543\) 0 0
\(544\) 6.00000 0.257248
\(545\) −40.0000 + 20.0000i −1.71341 + 0.856706i
\(546\) 0 0
\(547\) 28.0000i 1.19719i 0.801050 + 0.598597i \(0.204275\pi\)
−0.801050 + 0.598597i \(0.795725\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 8.00000i 0.340195i
\(554\) 18.0000 0.764747
\(555\) 0 0
\(556\) −20.0000 −0.848189
\(557\) 30.0000i 1.27114i 0.772043 + 0.635570i \(0.219235\pi\)
−0.772043 + 0.635570i \(0.780765\pi\)
\(558\) 12.0000i 0.508001i
\(559\) 8.00000 0.338364
\(560\) −2.00000 4.00000i −0.0845154 0.169031i
\(561\) 0 0
\(562\) 6.00000i 0.253095i
\(563\) 4.00000i 0.168580i −0.996441 0.0842900i \(-0.973138\pi\)
0.996441 0.0842900i \(-0.0268622\pi\)
\(564\) 0 0
\(565\) −2.00000 4.00000i −0.0841406 0.168281i
\(566\) 28.0000 1.17693
\(567\) 18.0000i 0.755929i
\(568\) 0 0
\(569\) 34.0000 1.42535 0.712677 0.701492i \(-0.247483\pi\)
0.712677 + 0.701492i \(0.247483\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −20.0000 −0.834784
\(575\) 16.0000 + 12.0000i 0.667246 + 0.500435i
\(576\) −3.00000 −0.125000
\(577\) 38.0000i 1.58196i 0.611842 + 0.790980i \(0.290429\pi\)
−0.611842 + 0.790980i \(0.709571\pi\)
\(578\) 19.0000i 0.790296i
\(579\) 0 0
\(580\) 0 0
\(581\) 24.0000 0.995688
\(582\) 0 0
\(583\) 0 0
\(584\) −8.00000 −0.331042
\(585\) −6.00000 12.0000i −0.248069 0.496139i
\(586\) 6.00000 0.247858
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 0 0
\(589\) −24.0000 −0.988903
\(590\) 6.00000 + 12.0000i 0.247016 + 0.494032i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 24.0000i 0.985562i 0.870153 + 0.492781i \(0.164020\pi\)
−0.870153 + 0.492781i \(0.835980\pi\)
\(594\) 0 0
\(595\) 24.0000 12.0000i 0.983904 0.491952i
\(596\) 14.0000 0.573462
\(597\) 0 0
\(598\) 8.00000i 0.327144i
\(599\) 8.00000 0.326871 0.163436 0.986554i \(-0.447742\pi\)
0.163436 + 0.986554i \(0.447742\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 24.0000i 0.977356i
\(604\) −16.0000 −0.651031
\(605\) 22.0000 11.0000i 0.894427 0.447214i
\(606\) 0 0
\(607\) 36.0000i 1.46119i 0.682808 + 0.730597i \(0.260758\pi\)
−0.682808 + 0.730597i \(0.739242\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 0 0
\(610\) 0 0
\(611\) −4.00000 −0.161823
\(612\) 18.0000i 0.727607i
\(613\) 30.0000i 1.21169i −0.795583 0.605844i \(-0.792835\pi\)
0.795583 0.605844i \(-0.207165\pi\)
\(614\) −4.00000 −0.161427
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000i 0.483102i −0.970388 0.241551i \(-0.922344\pi\)
0.970388 0.241551i \(-0.0776561\pi\)
\(618\) 0 0
\(619\) 32.0000 1.28619 0.643094 0.765787i \(-0.277650\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) −8.00000 + 4.00000i −0.321288 + 0.160644i
\(621\) 0 0
\(622\) 0 0
\(623\) 12.0000i 0.480770i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) −14.0000 −0.559553
\(627\) 0 0
\(628\) 22.0000i 0.877896i
\(629\) −6.00000 −0.239236
\(630\) −12.0000 + 6.00000i −0.478091 + 0.239046i
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 4.00000i 0.159111i
\(633\) 0 0
\(634\) 6.00000 0.238290
\(635\) 22.0000 + 44.0000i 0.873043 + 1.74609i
\(636\) 0 0
\(637\) 6.00000i 0.237729i
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 2.00000i −0.0395285 0.0790569i
\(641\) 14.0000 0.552967 0.276483 0.961019i \(-0.410831\pi\)
0.276483 + 0.961019i \(0.410831\pi\)
\(642\) 0 0
\(643\) 44.0000i 1.73519i −0.497271 0.867595i \(-0.665665\pi\)
0.497271 0.867595i \(-0.334335\pi\)
\(644\) 8.00000 0.315244
\(645\) 0 0
\(646\) 36.0000 1.41640
\(647\) 16.0000i 0.629025i 0.949253 + 0.314512i \(0.101841\pi\)
−0.949253 + 0.314512i \(0.898159\pi\)
\(648\) 9.00000i 0.353553i
\(649\) 0 0
\(650\) 6.00000 8.00000i 0.235339 0.313786i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) 14.0000i 0.547862i 0.961749 + 0.273931i \(0.0883240\pi\)
−0.961749 + 0.273931i \(0.911676\pi\)
\(654\) 0 0
\(655\) −28.0000 + 14.0000i −1.09405 + 0.547025i
\(656\) −10.0000 −0.390434
\(657\) 24.0000i 0.936329i
\(658\) 4.00000i 0.155936i
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) −28.0000 −1.08907 −0.544537 0.838737i \(-0.683295\pi\)
−0.544537 + 0.838737i \(0.683295\pi\)
\(662\) 34.0000i 1.32145i
\(663\) 0 0
\(664\) 12.0000 0.465690
\(665\) −12.0000 24.0000i −0.465340 0.930680i
\(666\) 3.00000 0.116248
\(667\) 0 0
\(668\) 16.0000i 0.619059i
\(669\) 0 0
\(670\) 16.0000 8.00000i 0.618134 0.309067i
\(671\) 0 0
\(672\) 0 0
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) −8.00000 −0.308148
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 30.0000i 1.15299i −0.817099 0.576497i \(-0.804419\pi\)
0.817099 0.576497i \(-0.195581\pi\)
\(678\) 0 0
\(679\) −20.0000 −0.767530
\(680\) 12.0000 6.00000i 0.460179 0.230089i
\(681\) 0 0
\(682\) 0 0
\(683\) 20.0000i 0.765279i −0.923898 0.382639i \(-0.875015\pi\)
0.923898 0.382639i \(-0.124985\pi\)
\(684\) −18.0000 −0.688247
\(685\) 0 0
\(686\) 20.0000 0.763604
\(687\) 0 0
\(688\) 4.00000i 0.152499i
\(689\) −4.00000 −0.152388
\(690\) 0 0
\(691\) 4.00000 0.152167 0.0760836 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) 2.00000i 0.0760286i
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) −40.0000 + 20.0000i −1.51729 + 0.758643i
\(696\) 0 0
\(697\) 60.0000i 2.27266i
\(698\) 30.0000i 1.13552i
\(699\) 0 0
\(700\) −8.00000 6.00000i −0.302372 0.226779i
\(701\) −4.00000 −0.151078 −0.0755390 0.997143i \(-0.524068\pi\)
−0.0755390 + 0.997143i \(0.524068\pi\)
\(702\) 0 0
\(703\) 6.00000i 0.226294i
\(704\) 0 0
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 20.0000i 0.752177i
\(708\) 0 0
\(709\) 40.0000 1.50223 0.751116 0.660171i \(-0.229516\pi\)
0.751116 + 0.660171i \(0.229516\pi\)
\(710\) 0 0
\(711\) −12.0000 −0.450035
\(712\) 6.00000i 0.224860i
\(713\) 16.0000i 0.599205i
\(714\) 0 0
\(715\) 0 0
\(716\) −14.0000 −0.523205
\(717\) 0 0
\(718\) 8.00000i 0.298557i
\(719\) 16.0000 0.596699 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) −6.00000 + 3.00000i −0.223607 + 0.111803i
\(721\) 0 0
\(722\) 17.0000i 0.632674i
\(723\) 0 0
\(724\) −2.00000 −0.0743294
\(725\) 0 0
\(726\) 0 0
\(727\) 28.0000i 1.03846i −0.854634 0.519231i \(-0.826218\pi\)
0.854634 0.519231i \(-0.173782\pi\)
\(728\) 4.00000i 0.148250i
\(729\) 27.0000 1.00000
\(730\) −16.0000 + 8.00000i −0.592187 + 0.296093i
\(731\) 24.0000 0.887672
\(732\) 0 0
\(733\) 38.0000i 1.40356i −0.712393 0.701781i \(-0.752388\pi\)
0.712393 0.701781i \(-0.247612\pi\)
\(734\) 26.0000 0.959678
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 0 0
\(738\) 30.0000i 1.10432i
\(739\) 36.0000 1.32428 0.662141 0.749380i \(-0.269648\pi\)
0.662141 + 0.749380i \(0.269648\pi\)
\(740\) 1.00000 + 2.00000i 0.0367607 + 0.0735215i
\(741\) 0 0
\(742\) 4.00000i 0.146845i
\(743\) 26.0000i 0.953847i 0.878945 + 0.476924i \(0.158248\pi\)
−0.878945 + 0.476924i \(0.841752\pi\)
\(744\) 0 0
\(745\) 28.0000 14.0000i 1.02584 0.512920i
\(746\) −34.0000 −1.24483
\(747\) 36.0000i 1.31717i
\(748\) 0 0
\(749\) 16.0000 0.584627
\(750\) 0 0
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 2.00000i 0.0729325i
\(753\) 0 0
\(754\) 0 0
\(755\) −32.0000 + 16.0000i −1.16460 + 0.582300i
\(756\) 0 0
\(757\) 14.0000i 0.508839i −0.967094 0.254419i \(-0.918116\pi\)
0.967094 0.254419i \(-0.0818843\pi\)
\(758\) 12.0000i 0.435860i
\(759\) 0 0
\(760\) −6.00000 12.0000i −0.217643 0.435286i
\(761\) 34.0000 1.23250 0.616250 0.787551i \(-0.288651\pi\)
0.616250 + 0.787551i \(0.288651\pi\)
\(762\) 0 0
\(763\) 40.0000i 1.44810i
\(764\) −4.00000 −0.144715
\(765\) −18.0000 36.0000i −0.650791 1.30158i
\(766\) −28.0000 −1.01168
\(767\) 12.0000i 0.433295i
\(768\) 0 0
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.0000i 0.359908i
\(773\) 54.0000i 1.94225i −0.238581 0.971123i \(-0.576682\pi\)
0.238581 0.971123i \(-0.423318\pi\)
\(774\) −12.0000 −0.431331
\(775\) −12.0000 + 16.0000i −0.431053 + 0.574737i
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) 16.0000i 0.573628i
\(779\) −60.0000 −2.14972
\(780\) 0 0
\(781\) 0 0
\(782\) 24.0000i 0.858238i
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) 22.0000 + 44.0000i 0.785214 + 1.57043i
\(786\) 0 0
\(787\) 40.0000i 1.42585i −0.701242 0.712923i \(-0.747371\pi\)
0.701242 0.712923i \(-0.252629\pi\)
\(788\) 10.0000i 0.356235i
\(789\) 0 0
\(790\) −4.00000 8.00000i −0.142314 0.284627i
\(791\) −4.00000 −0.142224