Properties

Label 416.2.u.a.47.2
Level $416$
Weight $2$
Character 416.47
Analytic conductor $3.322$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [416,2,Mod(47,416)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(416, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 416 = 2^{5} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 416.u (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: \(3.32177672409\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{26})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 169 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 104)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.2
Root \(2.54951 - 2.54951i\) of defining polynomial
Character \(\chi\) \(=\) 416.47
Dual form 416.2.u.a.239.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} +(2.54951 - 2.54951i) q^{5} +(2.54951 + 2.54951i) q^{7} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +(2.54951 - 2.54951i) q^{5} +(2.54951 + 2.54951i) q^{7} -2.00000 q^{9} +(-1.00000 + 1.00000i) q^{11} +(2.54951 - 2.54951i) q^{13} +(2.54951 - 2.54951i) q^{15} +3.00000i q^{17} +(-2.00000 - 2.00000i) q^{19} +(2.54951 + 2.54951i) q^{21} -5.09902 q^{23} -8.00000i q^{25} -5.00000 q^{27} +5.09902i q^{29} +(5.09902 - 5.09902i) q^{31} +(-1.00000 + 1.00000i) q^{33} +13.0000 q^{35} +(-2.54951 - 2.54951i) q^{37} +(2.54951 - 2.54951i) q^{39} +(6.00000 + 6.00000i) q^{41} -1.00000i q^{43} +(-5.09902 + 5.09902i) q^{45} +(2.54951 + 2.54951i) q^{47} +6.00000i q^{49} +3.00000i q^{51} -5.09902i q^{53} +5.09902i q^{55} +(-2.00000 - 2.00000i) q^{57} +(-8.00000 + 8.00000i) q^{59} +(-5.09902 - 5.09902i) q^{63} -13.0000i q^{65} +(-3.00000 - 3.00000i) q^{67} -5.09902 q^{69} +(-7.64853 + 7.64853i) q^{71} +(-6.00000 + 6.00000i) q^{73} -8.00000i q^{75} -5.09902 q^{77} -5.09902i q^{79} +1.00000 q^{81} +(-5.00000 - 5.00000i) q^{83} +(7.64853 + 7.64853i) q^{85} +5.09902i q^{87} +(-2.00000 + 2.00000i) q^{89} +13.0000 q^{91} +(5.09902 - 5.09902i) q^{93} -10.1980 q^{95} +(-7.00000 - 7.00000i) q^{97} +(2.00000 - 2.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} - 8 q^{9} - 4 q^{11} - 8 q^{19} - 20 q^{27} - 4 q^{33} + 52 q^{35} + 24 q^{41} - 8 q^{57} - 32 q^{59} - 12 q^{67} - 24 q^{73} + 4 q^{81} - 20 q^{83} - 8 q^{89} + 52 q^{91} - 28 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(287\) \(353\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 0 0
\(5\) 2.54951 2.54951i 1.14018 1.14018i 0.151758 0.988418i \(-0.451507\pi\)
0.988418 0.151758i \(-0.0484933\pi\)
\(6\) 0 0
\(7\) 2.54951 + 2.54951i 0.963624 + 0.963624i 0.999361 0.0357371i \(-0.0113779\pi\)
−0.0357371 + 0.999361i \(0.511378\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) −1.00000 + 1.00000i −0.301511 + 0.301511i −0.841605 0.540094i \(-0.818389\pi\)
0.540094 + 0.841605i \(0.318389\pi\)
\(12\) 0 0
\(13\) 2.54951 2.54951i 0.707107 0.707107i
\(14\) 0 0
\(15\) 2.54951 2.54951i 0.658281 0.658281i
\(16\) 0 0
\(17\) 3.00000i 0.727607i 0.931476 + 0.363803i \(0.118522\pi\)
−0.931476 + 0.363803i \(0.881478\pi\)
\(18\) 0 0
\(19\) −2.00000 2.00000i −0.458831 0.458831i 0.439440 0.898272i \(-0.355177\pi\)
−0.898272 + 0.439440i \(0.855177\pi\)
\(20\) 0 0
\(21\) 2.54951 + 2.54951i 0.556349 + 0.556349i
\(22\) 0 0
\(23\) −5.09902 −1.06322 −0.531610 0.846990i \(-0.678413\pi\)
−0.531610 + 0.846990i \(0.678413\pi\)
\(24\) 0 0
\(25\) 8.00000i 1.60000i
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 5.09902i 0.946864i 0.880830 + 0.473432i \(0.156985\pi\)
−0.880830 + 0.473432i \(0.843015\pi\)
\(30\) 0 0
\(31\) 5.09902 5.09902i 0.915811 0.915811i −0.0809104 0.996721i \(-0.525783\pi\)
0.996721 + 0.0809104i \(0.0257828\pi\)
\(32\) 0 0
\(33\) −1.00000 + 1.00000i −0.174078 + 0.174078i
\(34\) 0 0
\(35\) 13.0000 2.19740
\(36\) 0 0
\(37\) −2.54951 2.54951i −0.419137 0.419137i 0.465769 0.884906i \(-0.345778\pi\)
−0.884906 + 0.465769i \(0.845778\pi\)
\(38\) 0 0
\(39\) 2.54951 2.54951i 0.408248 0.408248i
\(40\) 0 0
\(41\) 6.00000 + 6.00000i 0.937043 + 0.937043i 0.998132 0.0610897i \(-0.0194576\pi\)
−0.0610897 + 0.998132i \(0.519458\pi\)
\(42\) 0 0
\(43\) 1.00000i 0.152499i −0.997089 0.0762493i \(-0.975706\pi\)
0.997089 0.0762493i \(-0.0242945\pi\)
\(44\) 0 0
\(45\) −5.09902 + 5.09902i −0.760117 + 0.760117i
\(46\) 0 0
\(47\) 2.54951 + 2.54951i 0.371884 + 0.371884i 0.868163 0.496279i \(-0.165301\pi\)
−0.496279 + 0.868163i \(0.665301\pi\)
\(48\) 0 0
\(49\) 6.00000i 0.857143i
\(50\) 0 0
\(51\) 3.00000i 0.420084i
\(52\) 0 0
\(53\) 5.09902i 0.700404i −0.936674 0.350202i \(-0.886113\pi\)
0.936674 0.350202i \(-0.113887\pi\)
\(54\) 0 0
\(55\) 5.09902i 0.687552i
\(56\) 0 0
\(57\) −2.00000 2.00000i −0.264906 0.264906i
\(58\) 0 0
\(59\) −8.00000 + 8.00000i −1.04151 + 1.04151i −0.0424110 + 0.999100i \(0.513504\pi\)
−0.999100 + 0.0424110i \(0.986496\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) −5.09902 5.09902i −0.642416 0.642416i
\(64\) 0 0
\(65\) 13.0000i 1.61245i
\(66\) 0 0
\(67\) −3.00000 3.00000i −0.366508 0.366508i 0.499694 0.866202i \(-0.333446\pi\)
−0.866202 + 0.499694i \(0.833446\pi\)
\(68\) 0 0
\(69\) −5.09902 −0.613850
\(70\) 0 0
\(71\) −7.64853 + 7.64853i −0.907713 + 0.907713i −0.996087 0.0883739i \(-0.971833\pi\)
0.0883739 + 0.996087i \(0.471833\pi\)
\(72\) 0 0
\(73\) −6.00000 + 6.00000i −0.702247 + 0.702247i −0.964892 0.262646i \(-0.915405\pi\)
0.262646 + 0.964892i \(0.415405\pi\)
\(74\) 0 0
\(75\) 8.00000i 0.923760i
\(76\) 0 0
\(77\) −5.09902 −0.581087
\(78\) 0 0
\(79\) 5.09902i 0.573685i −0.957978 0.286842i \(-0.907394\pi\)
0.957978 0.286842i \(-0.0926056\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −5.00000 5.00000i −0.548821 0.548821i 0.377279 0.926100i \(-0.376860\pi\)
−0.926100 + 0.377279i \(0.876860\pi\)
\(84\) 0 0
\(85\) 7.64853 + 7.64853i 0.829599 + 0.829599i
\(86\) 0 0
\(87\) 5.09902i 0.546672i
\(88\) 0 0
\(89\) −2.00000 + 2.00000i −0.212000 + 0.212000i −0.805116 0.593117i \(-0.797897\pi\)
0.593117 + 0.805116i \(0.297897\pi\)
\(90\) 0 0
\(91\) 13.0000 1.36277
\(92\) 0 0
\(93\) 5.09902 5.09902i 0.528744 0.528744i
\(94\) 0 0
\(95\) −10.1980 −1.04630
\(96\) 0 0
\(97\) −7.00000 7.00000i −0.710742 0.710742i 0.255948 0.966691i \(-0.417612\pi\)
−0.966691 + 0.255948i \(0.917612\pi\)
\(98\) 0 0
\(99\) 2.00000 2.00000i 0.201008 0.201008i
\(100\) 0 0
\(101\) −10.1980 −1.01474 −0.507371 0.861727i \(-0.669383\pi\)
−0.507371 + 0.861727i \(0.669383\pi\)
\(102\) 0 0
\(103\) −5.09902 −0.502421 −0.251211 0.967932i \(-0.580829\pi\)
−0.251211 + 0.967932i \(0.580829\pi\)
\(104\) 0 0
\(105\) 13.0000 1.26867
\(106\) 0 0
\(107\) 2.00000 0.193347 0.0966736 0.995316i \(-0.469180\pi\)
0.0966736 + 0.995316i \(0.469180\pi\)
\(108\) 0 0
\(109\) −2.54951 + 2.54951i −0.244199 + 0.244199i −0.818585 0.574386i \(-0.805241\pi\)
0.574386 + 0.818585i \(0.305241\pi\)
\(110\) 0 0
\(111\) −2.54951 2.54951i −0.241989 0.241989i
\(112\) 0 0
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 0 0
\(115\) −13.0000 + 13.0000i −1.21226 + 1.21226i
\(116\) 0 0
\(117\) −5.09902 + 5.09902i −0.471405 + 0.471405i
\(118\) 0 0
\(119\) −7.64853 + 7.64853i −0.701140 + 0.701140i
\(120\) 0 0
\(121\) 9.00000i 0.818182i
\(122\) 0 0
\(123\) 6.00000 + 6.00000i 0.541002 + 0.541002i
\(124\) 0 0
\(125\) −7.64853 7.64853i −0.684105 0.684105i
\(126\) 0 0
\(127\) 15.2971 1.35739 0.678697 0.734418i \(-0.262545\pi\)
0.678697 + 0.734418i \(0.262545\pi\)
\(128\) 0 0
\(129\) 1.00000i 0.0880451i
\(130\) 0 0
\(131\) −7.00000 −0.611593 −0.305796 0.952097i \(-0.598923\pi\)
−0.305796 + 0.952097i \(0.598923\pi\)
\(132\) 0 0
\(133\) 10.1980i 0.884282i
\(134\) 0 0
\(135\) −12.7475 + 12.7475i −1.09713 + 1.09713i
\(136\) 0 0
\(137\) −5.00000 + 5.00000i −0.427179 + 0.427179i −0.887666 0.460487i \(-0.847675\pi\)
0.460487 + 0.887666i \(0.347675\pi\)
\(138\) 0 0
\(139\) 15.0000 1.27228 0.636142 0.771572i \(-0.280529\pi\)
0.636142 + 0.771572i \(0.280529\pi\)
\(140\) 0 0
\(141\) 2.54951 + 2.54951i 0.214707 + 0.214707i
\(142\) 0 0
\(143\) 5.09902i 0.426401i
\(144\) 0 0
\(145\) 13.0000 + 13.0000i 1.07959 + 1.07959i
\(146\) 0 0
\(147\) 6.00000i 0.494872i
\(148\) 0 0
\(149\) 10.1980 10.1980i 0.835456 0.835456i −0.152801 0.988257i \(-0.548829\pi\)
0.988257 + 0.152801i \(0.0488294\pi\)
\(150\) 0 0
\(151\) −7.64853 7.64853i −0.622428 0.622428i 0.323723 0.946152i \(-0.395065\pi\)
−0.946152 + 0.323723i \(0.895065\pi\)
\(152\) 0 0
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 26.0000i 2.08837i
\(156\) 0 0
\(157\) 10.1980i 0.813892i 0.913452 + 0.406946i \(0.133406\pi\)
−0.913452 + 0.406946i \(0.866594\pi\)
\(158\) 0 0
\(159\) 5.09902i 0.404379i
\(160\) 0 0
\(161\) −13.0000 13.0000i −1.02454 1.02454i
\(162\) 0 0
\(163\) −9.00000 + 9.00000i −0.704934 + 0.704934i −0.965465 0.260531i \(-0.916102\pi\)
0.260531 + 0.965465i \(0.416102\pi\)
\(164\) 0 0
\(165\) 5.09902i 0.396958i
\(166\) 0 0
\(167\) 15.2971 + 15.2971i 1.18372 + 1.18372i 0.978773 + 0.204949i \(0.0657030\pi\)
0.204949 + 0.978773i \(0.434297\pi\)
\(168\) 0 0
\(169\) 13.0000i 1.00000i
\(170\) 0 0
\(171\) 4.00000 + 4.00000i 0.305888 + 0.305888i
\(172\) 0 0
\(173\) 5.09902 0.387671 0.193836 0.981034i \(-0.437907\pi\)
0.193836 + 0.981034i \(0.437907\pi\)
\(174\) 0 0
\(175\) 20.3961 20.3961i 1.54180 1.54180i
\(176\) 0 0
\(177\) −8.00000 + 8.00000i −0.601317 + 0.601317i
\(178\) 0 0
\(179\) 9.00000i 0.672692i −0.941739 0.336346i \(-0.890809\pi\)
0.941739 0.336346i \(-0.109191\pi\)
\(180\) 0 0
\(181\) 15.2971 1.13702 0.568511 0.822676i \(-0.307520\pi\)
0.568511 + 0.822676i \(0.307520\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −13.0000 −0.955779
\(186\) 0 0
\(187\) −3.00000 3.00000i −0.219382 0.219382i
\(188\) 0 0
\(189\) −12.7475 12.7475i −0.927248 0.927248i
\(190\) 0 0
\(191\) 25.4951i 1.84476i −0.386283 0.922380i \(-0.626241\pi\)
0.386283 0.922380i \(-0.373759\pi\)
\(192\) 0 0
\(193\) 9.00000 9.00000i 0.647834 0.647834i −0.304635 0.952469i \(-0.598534\pi\)
0.952469 + 0.304635i \(0.0985345\pi\)
\(194\) 0 0
\(195\) 13.0000i 0.930949i
\(196\) 0 0
\(197\) −12.7475 + 12.7475i −0.908225 + 0.908225i −0.996129 0.0879037i \(-0.971983\pi\)
0.0879037 + 0.996129i \(0.471983\pi\)
\(198\) 0 0
\(199\) 25.4951 1.80730 0.903650 0.428272i \(-0.140878\pi\)
0.903650 + 0.428272i \(0.140878\pi\)
\(200\) 0 0
\(201\) −3.00000 3.00000i −0.211604 0.211604i
\(202\) 0 0
\(203\) −13.0000 + 13.0000i −0.912421 + 0.912421i
\(204\) 0 0
\(205\) 30.5941 2.13679
\(206\) 0 0
\(207\) 10.1980 0.708813
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) −7.00000 −0.481900 −0.240950 0.970538i \(-0.577459\pi\)
−0.240950 + 0.970538i \(0.577459\pi\)
\(212\) 0 0
\(213\) −7.64853 + 7.64853i −0.524069 + 0.524069i
\(214\) 0 0
\(215\) −2.54951 2.54951i −0.173875 0.173875i
\(216\) 0 0
\(217\) 26.0000 1.76500
\(218\) 0 0
\(219\) −6.00000 + 6.00000i −0.405442 + 0.405442i
\(220\) 0 0
\(221\) 7.64853 + 7.64853i 0.514496 + 0.514496i
\(222\) 0 0
\(223\) 7.64853 7.64853i 0.512183 0.512183i −0.403012 0.915195i \(-0.632037\pi\)
0.915195 + 0.403012i \(0.132037\pi\)
\(224\) 0 0
\(225\) 16.0000i 1.06667i
\(226\) 0 0
\(227\) 12.0000 + 12.0000i 0.796468 + 0.796468i 0.982537 0.186069i \(-0.0595747\pi\)
−0.186069 + 0.982537i \(0.559575\pi\)
\(228\) 0 0
\(229\) 2.54951 + 2.54951i 0.168476 + 0.168476i 0.786309 0.617833i \(-0.211989\pi\)
−0.617833 + 0.786309i \(0.711989\pi\)
\(230\) 0 0
\(231\) −5.09902 −0.335491
\(232\) 0 0
\(233\) 11.0000i 0.720634i 0.932830 + 0.360317i \(0.117331\pi\)
−0.932830 + 0.360317i \(0.882669\pi\)
\(234\) 0 0
\(235\) 13.0000 0.848026
\(236\) 0 0
\(237\) 5.09902i 0.331217i
\(238\) 0 0
\(239\) 2.54951 2.54951i 0.164914 0.164914i −0.619826 0.784740i \(-0.712797\pi\)
0.784740 + 0.619826i \(0.212797\pi\)
\(240\) 0 0
\(241\) −14.0000 + 14.0000i −0.901819 + 0.901819i −0.995593 0.0937742i \(-0.970107\pi\)
0.0937742 + 0.995593i \(0.470107\pi\)
\(242\) 0 0
\(243\) 16.0000 1.02640
\(244\) 0 0
\(245\) 15.2971 + 15.2971i 0.977293 + 0.977293i
\(246\) 0 0
\(247\) −10.1980 −0.648886
\(248\) 0 0
\(249\) −5.00000 5.00000i −0.316862 0.316862i
\(250\) 0 0
\(251\) 10.0000i 0.631194i 0.948893 + 0.315597i \(0.102205\pi\)
−0.948893 + 0.315597i \(0.897795\pi\)
\(252\) 0 0
\(253\) 5.09902 5.09902i 0.320573 0.320573i
\(254\) 0 0
\(255\) 7.64853 + 7.64853i 0.478969 + 0.478969i
\(256\) 0 0
\(257\) 3.00000i 0.187135i 0.995613 + 0.0935674i \(0.0298271\pi\)
−0.995613 + 0.0935674i \(0.970173\pi\)
\(258\) 0 0
\(259\) 13.0000i 0.807781i
\(260\) 0 0
\(261\) 10.1980i 0.631243i
\(262\) 0 0
\(263\) 20.3961i 1.25768i −0.777536 0.628838i \(-0.783531\pi\)
0.777536 0.628838i \(-0.216469\pi\)
\(264\) 0 0
\(265\) −13.0000 13.0000i −0.798584 0.798584i
\(266\) 0 0
\(267\) −2.00000 + 2.00000i −0.122398 + 0.122398i
\(268\) 0 0
\(269\) 20.3961i 1.24357i −0.783188 0.621785i \(-0.786408\pi\)
0.783188 0.621785i \(-0.213592\pi\)
\(270\) 0 0
\(271\) −7.64853 7.64853i −0.464615 0.464615i 0.435550 0.900165i \(-0.356554\pi\)
−0.900165 + 0.435550i \(0.856554\pi\)
\(272\) 0 0
\(273\) 13.0000 0.786796
\(274\) 0 0
\(275\) 8.00000 + 8.00000i 0.482418 + 0.482418i
\(276\) 0 0
\(277\) 10.1980 0.612741 0.306370 0.951912i \(-0.400885\pi\)
0.306370 + 0.951912i \(0.400885\pi\)
\(278\) 0 0
\(279\) −10.1980 + 10.1980i −0.610541 + 0.610541i
\(280\) 0 0
\(281\) 16.0000 16.0000i 0.954480 0.954480i −0.0445282 0.999008i \(-0.514178\pi\)
0.999008 + 0.0445282i \(0.0141784\pi\)
\(282\) 0 0
\(283\) 16.0000i 0.951101i −0.879688 0.475551i \(-0.842249\pi\)
0.879688 0.475551i \(-0.157751\pi\)
\(284\) 0 0
\(285\) −10.1980 −0.604080
\(286\) 0 0
\(287\) 30.5941i 1.80591i
\(288\) 0 0
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) −7.00000 7.00000i −0.410347 0.410347i
\(292\) 0 0
\(293\) −12.7475 12.7475i −0.744720 0.744720i 0.228763 0.973482i \(-0.426532\pi\)
−0.973482 + 0.228763i \(0.926532\pi\)
\(294\) 0 0
\(295\) 40.7922i 2.37501i
\(296\) 0 0
\(297\) 5.00000 5.00000i 0.290129 0.290129i
\(298\) 0 0
\(299\) −13.0000 + 13.0000i −0.751809 + 0.751809i
\(300\) 0 0
\(301\) 2.54951 2.54951i 0.146951 0.146951i
\(302\) 0 0
\(303\) −10.1980 −0.585862
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 10.0000 10.0000i 0.570730 0.570730i −0.361602 0.932332i \(-0.617770\pi\)
0.932332 + 0.361602i \(0.117770\pi\)
\(308\) 0 0
\(309\) −5.09902 −0.290073
\(310\) 0 0
\(311\) 10.1980 0.578278 0.289139 0.957287i \(-0.406631\pi\)
0.289139 + 0.957287i \(0.406631\pi\)
\(312\) 0 0
\(313\) −31.0000 −1.75222 −0.876112 0.482108i \(-0.839871\pi\)
−0.876112 + 0.482108i \(0.839871\pi\)
\(314\) 0 0
\(315\) −26.0000 −1.46493
\(316\) 0 0
\(317\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(318\) 0 0
\(319\) −5.09902 5.09902i −0.285490 0.285490i
\(320\) 0 0
\(321\) 2.00000 0.111629
\(322\) 0 0
\(323\) 6.00000 6.00000i 0.333849 0.333849i
\(324\) 0 0
\(325\) −20.3961 20.3961i −1.13137 1.13137i
\(326\) 0 0
\(327\) −2.54951 + 2.54951i −0.140988 + 0.140988i
\(328\) 0 0
\(329\) 13.0000i 0.716713i
\(330\) 0 0
\(331\) −21.0000 21.0000i −1.15426 1.15426i −0.985689 0.168576i \(-0.946083\pi\)
−0.168576 0.985689i \(-0.553917\pi\)
\(332\) 0 0
\(333\) 5.09902 + 5.09902i 0.279425 + 0.279425i
\(334\) 0 0
\(335\) −15.2971 −0.835768
\(336\) 0 0
\(337\) 17.0000i 0.926049i −0.886345 0.463025i \(-0.846764\pi\)
0.886345 0.463025i \(-0.153236\pi\)
\(338\) 0 0
\(339\) 4.00000 0.217250
\(340\) 0 0
\(341\) 10.1980i 0.552255i
\(342\) 0 0
\(343\) 2.54951 2.54951i 0.137661 0.137661i
\(344\) 0 0
\(345\) −13.0000 + 13.0000i −0.699896 + 0.699896i
\(346\) 0 0
\(347\) 7.00000 0.375780 0.187890 0.982190i \(-0.439835\pi\)
0.187890 + 0.982190i \(0.439835\pi\)
\(348\) 0 0
\(349\) −22.9456 22.9456i −1.22825 1.22825i −0.964626 0.263624i \(-0.915082\pi\)
−0.263624 0.964626i \(-0.584918\pi\)
\(350\) 0 0
\(351\) −12.7475 + 12.7475i −0.680414 + 0.680414i
\(352\) 0 0
\(353\) 5.00000 + 5.00000i 0.266123 + 0.266123i 0.827536 0.561413i \(-0.189742\pi\)
−0.561413 + 0.827536i \(0.689742\pi\)
\(354\) 0 0
\(355\) 39.0000i 2.06991i
\(356\) 0 0
\(357\) −7.64853 + 7.64853i −0.404803 + 0.404803i
\(358\) 0 0
\(359\) −15.2971 15.2971i −0.807348 0.807348i 0.176884 0.984232i \(-0.443398\pi\)
−0.984232 + 0.176884i \(0.943398\pi\)
\(360\) 0 0
\(361\) 11.0000i 0.578947i
\(362\) 0 0
\(363\) 9.00000i 0.472377i
\(364\) 0 0
\(365\) 30.5941i 1.60137i
\(366\) 0 0
\(367\) 15.2971i 0.798500i 0.916842 + 0.399250i \(0.130729\pi\)
−0.916842 + 0.399250i \(0.869271\pi\)
\(368\) 0 0
\(369\) −12.0000 12.0000i −0.624695 0.624695i
\(370\) 0 0
\(371\) 13.0000 13.0000i 0.674926 0.674926i
\(372\) 0 0
\(373\) 20.3961i 1.05607i 0.849223 + 0.528034i \(0.177071\pi\)
−0.849223 + 0.528034i \(0.822929\pi\)
\(374\) 0 0
\(375\) −7.64853 7.64853i −0.394968 0.394968i
\(376\) 0 0
\(377\) 13.0000 + 13.0000i 0.669534 + 0.669534i
\(378\) 0 0
\(379\) 23.0000 + 23.0000i 1.18143 + 1.18143i 0.979374 + 0.202057i \(0.0647626\pi\)
0.202057 + 0.979374i \(0.435237\pi\)
\(380\) 0 0
\(381\) 15.2971 0.783692
\(382\) 0 0
\(383\) 7.64853 7.64853i 0.390822 0.390822i −0.484159 0.874980i \(-0.660874\pi\)
0.874980 + 0.484159i \(0.160874\pi\)
\(384\) 0 0
\(385\) −13.0000 + 13.0000i −0.662541 + 0.662541i
\(386\) 0 0
\(387\) 2.00000i 0.101666i
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 15.2971i 0.773606i
\(392\) 0 0
\(393\) −7.00000 −0.353103
\(394\) 0 0
\(395\) −13.0000 13.0000i −0.654101 0.654101i
\(396\) 0 0
\(397\) 10.1980 + 10.1980i 0.511825 + 0.511825i 0.915085 0.403260i \(-0.132123\pi\)
−0.403260 + 0.915085i \(0.632123\pi\)
\(398\) 0 0
\(399\) 10.1980i 0.510541i
\(400\) 0 0
\(401\) 1.00000 1.00000i 0.0499376 0.0499376i −0.681697 0.731635i \(-0.738758\pi\)
0.731635 + 0.681697i \(0.238758\pi\)
\(402\) 0 0
\(403\) 26.0000i 1.29515i
\(404\) 0 0
\(405\) 2.54951 2.54951i 0.126686 0.126686i
\(406\) 0 0
\(407\) 5.09902 0.252749
\(408\) 0 0
\(409\) 27.0000 + 27.0000i 1.33506 + 1.33506i 0.900772 + 0.434292i \(0.143001\pi\)
0.434292 + 0.900772i \(0.356999\pi\)
\(410\) 0 0
\(411\) −5.00000 + 5.00000i −0.246632 + 0.246632i
\(412\) 0 0
\(413\) −40.7922 −2.00725
\(414\) 0 0
\(415\) −25.4951 −1.25151
\(416\) 0 0
\(417\) 15.0000 0.734553
\(418\) 0 0
\(419\) −5.00000 −0.244266 −0.122133 0.992514i \(-0.538973\pi\)
−0.122133 + 0.992514i \(0.538973\pi\)
\(420\) 0 0
\(421\) 7.64853 7.64853i 0.372767 0.372767i −0.495717 0.868484i \(-0.665095\pi\)
0.868484 + 0.495717i \(0.165095\pi\)
\(422\) 0 0
\(423\) −5.09902 5.09902i −0.247923 0.247923i
\(424\) 0 0
\(425\) 24.0000 1.16417
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 5.09902i 0.246183i
\(430\) 0 0
\(431\) −7.64853 + 7.64853i −0.368417 + 0.368417i −0.866900 0.498483i \(-0.833891\pi\)
0.498483 + 0.866900i \(0.333891\pi\)
\(432\) 0 0
\(433\) 19.0000i 0.913082i −0.889702 0.456541i \(-0.849088\pi\)
0.889702 0.456541i \(-0.150912\pi\)
\(434\) 0 0
\(435\) 13.0000 + 13.0000i 0.623302 + 0.623302i
\(436\) 0 0
\(437\) 10.1980 + 10.1980i 0.487838 + 0.487838i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 12.0000i 0.571429i
\(442\) 0 0
\(443\) 31.0000 1.47285 0.736427 0.676517i \(-0.236511\pi\)
0.736427 + 0.676517i \(0.236511\pi\)
\(444\) 0 0
\(445\) 10.1980i 0.483433i
\(446\) 0 0
\(447\) 10.1980 10.1980i 0.482351 0.482351i
\(448\) 0 0
\(449\) 3.00000 3.00000i 0.141579 0.141579i −0.632765 0.774344i \(-0.718080\pi\)
0.774344 + 0.632765i \(0.218080\pi\)
\(450\) 0 0
\(451\) −12.0000 −0.565058
\(452\) 0 0
\(453\) −7.64853 7.64853i −0.359359 0.359359i
\(454\) 0 0
\(455\) 33.1436 33.1436i 1.55380 1.55380i
\(456\) 0 0
\(457\) −2.00000 2.00000i −0.0935561 0.0935561i 0.658780 0.752336i \(-0.271073\pi\)
−0.752336 + 0.658780i \(0.771073\pi\)
\(458\) 0 0
\(459\) 15.0000i 0.700140i
\(460\) 0 0
\(461\) −17.8466 + 17.8466i −0.831198 + 0.831198i −0.987681 0.156483i \(-0.949984\pi\)
0.156483 + 0.987681i \(0.449984\pi\)
\(462\) 0 0
\(463\) 25.4951 + 25.4951i 1.18486 + 1.18486i 0.978470 + 0.206387i \(0.0661707\pi\)
0.206387 + 0.978470i \(0.433829\pi\)
\(464\) 0 0
\(465\) 26.0000i 1.20572i
\(466\) 0 0
\(467\) 2.00000i 0.0925490i 0.998929 + 0.0462745i \(0.0147349\pi\)
−0.998929 + 0.0462745i \(0.985265\pi\)
\(468\) 0 0
\(469\) 15.2971i 0.706353i
\(470\) 0 0
\(471\) 10.1980i 0.469901i
\(472\) 0 0
\(473\) 1.00000 + 1.00000i 0.0459800 + 0.0459800i
\(474\) 0 0
\(475\) −16.0000 + 16.0000i −0.734130 + 0.734130i
\(476\) 0 0
\(477\) 10.1980i 0.466936i
\(478\) 0 0
\(479\) −2.54951 2.54951i −0.116490 0.116490i 0.646459 0.762949i \(-0.276249\pi\)
−0.762949 + 0.646459i \(0.776249\pi\)
\(480\) 0 0
\(481\) −13.0000 −0.592749
\(482\) 0 0
\(483\) −13.0000 13.0000i −0.591520 0.591520i
\(484\) 0 0
\(485\) −35.6931 −1.62074
\(486\) 0 0
\(487\) −25.4951 + 25.4951i −1.15529 + 1.15529i −0.169818 + 0.985476i \(0.554318\pi\)
−0.985476 + 0.169818i \(0.945682\pi\)
\(488\) 0 0
\(489\) −9.00000 + 9.00000i −0.406994 + 0.406994i
\(490\) 0 0
\(491\) 5.00000i 0.225647i 0.993615 + 0.112823i \(0.0359894\pi\)
−0.993615 + 0.112823i \(0.964011\pi\)
\(492\) 0 0
\(493\) −15.2971 −0.688945
\(494\) 0 0
\(495\) 10.1980i 0.458368i
\(496\) 0 0
\(497\) −39.0000 −1.74939
\(498\) 0 0
\(499\) −2.00000 2.00000i −0.0895323 0.0895323i 0.660922 0.750454i \(-0.270165\pi\)
−0.750454 + 0.660922i \(0.770165\pi\)
\(500\) 0 0
\(501\) 15.2971 + 15.2971i 0.683422 + 0.683422i
\(502\) 0 0
\(503\) 20.3961i 0.909416i −0.890641 0.454708i \(-0.849744\pi\)
0.890641 0.454708i \(-0.150256\pi\)
\(504\) 0 0
\(505\) −26.0000 + 26.0000i −1.15698 + 1.15698i
\(506\) 0 0
\(507\) 13.0000i 0.577350i
\(508\) 0 0
\(509\) 10.1980 10.1980i 0.452020 0.452020i −0.444004 0.896025i \(-0.646443\pi\)
0.896025 + 0.444004i \(0.146443\pi\)
\(510\) 0 0
\(511\) −30.5941 −1.35340
\(512\) 0 0
\(513\) 10.0000 + 10.0000i 0.441511 + 0.441511i
\(514\) 0 0
\(515\) −13.0000 + 13.0000i −0.572848 + 0.572848i
\(516\) 0 0
\(517\) −5.09902 −0.224255
\(518\) 0 0
\(519\) 5.09902 0.223822
\(520\) 0 0
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 0 0
\(523\) 6.00000 0.262362 0.131181 0.991358i \(-0.458123\pi\)
0.131181 + 0.991358i \(0.458123\pi\)
\(524\) 0 0
\(525\) 20.3961 20.3961i 0.890158 0.890158i
\(526\) 0 0
\(527\) 15.2971 + 15.2971i 0.666350 + 0.666350i
\(528\) 0 0
\(529\) 3.00000 0.130435
\(530\) 0 0
\(531\) 16.0000 16.0000i 0.694341 0.694341i
\(532\) 0 0
\(533\) 30.5941 1.32518
\(534\) 0 0
\(535\) 5.09902 5.09902i 0.220450 0.220450i
\(536\) 0 0
\(537\) 9.00000i 0.388379i
\(538\) 0 0
\(539\) −6.00000 6.00000i −0.258438 0.258438i
\(540\) 0 0
\(541\) −17.8466 17.8466i −0.767284 0.767284i 0.210344 0.977628i \(-0.432542\pi\)
−0.977628 + 0.210344i \(0.932542\pi\)
\(542\) 0 0
\(543\) 15.2971 0.656460
\(544\) 0 0
\(545\) 13.0000i 0.556859i
\(546\) 0 0
\(547\) −23.0000 −0.983409 −0.491704 0.870762i \(-0.663626\pi\)
−0.491704 + 0.870762i \(0.663626\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 10.1980 10.1980i 0.434451 0.434451i
\(552\) 0 0
\(553\) 13.0000 13.0000i 0.552816 0.552816i
\(554\) 0 0
\(555\) −13.0000 −0.551819
\(556\) 0 0
\(557\) 22.9456 + 22.9456i 0.972236 + 0.972236i 0.999625 0.0273891i \(-0.00871931\pi\)
−0.0273891 + 0.999625i \(0.508719\pi\)
\(558\) 0 0
\(559\) −2.54951 2.54951i −0.107833 0.107833i
\(560\) 0 0
\(561\) −3.00000 3.00000i −0.126660 0.126660i
\(562\) 0 0
\(563\) 9.00000i 0.379305i 0.981851 + 0.189652i \(0.0607361\pi\)
−0.981851 + 0.189652i \(0.939264\pi\)
\(564\) 0 0
\(565\) 10.1980 10.1980i 0.429035 0.429035i
\(566\) 0 0
\(567\) 2.54951 + 2.54951i 0.107069 + 0.107069i
\(568\) 0 0
\(569\) 31.0000i 1.29959i −0.760111 0.649794i \(-0.774855\pi\)
0.760111 0.649794i \(-0.225145\pi\)
\(570\) 0 0
\(571\) 15.0000i 0.627730i 0.949468 + 0.313865i \(0.101624\pi\)
−0.949468 + 0.313865i \(0.898376\pi\)
\(572\) 0 0
\(573\) 25.4951i 1.06507i
\(574\) 0 0
\(575\) 40.7922i 1.70115i
\(576\) 0 0
\(577\) 18.0000 + 18.0000i 0.749350 + 0.749350i 0.974357 0.225007i \(-0.0722406\pi\)
−0.225007 + 0.974357i \(0.572241\pi\)
\(578\) 0 0
\(579\) 9.00000 9.00000i 0.374027 0.374027i
\(580\) 0 0
\(581\) 25.4951i 1.05771i
\(582\) 0 0
\(583\) 5.09902 + 5.09902i 0.211180 + 0.211180i
\(584\) 0 0
\(585\) 26.0000i 1.07497i
\(586\) 0 0
\(587\) 7.00000 + 7.00000i 0.288921 + 0.288921i 0.836653 0.547733i \(-0.184509\pi\)
−0.547733 + 0.836653i \(0.684509\pi\)
\(588\) 0 0
\(589\) −20.3961 −0.840406
\(590\) 0 0
\(591\) −12.7475 + 12.7475i −0.524364 + 0.524364i
\(592\) 0 0
\(593\) 29.0000 29.0000i 1.19089 1.19089i 0.214069 0.976819i \(-0.431328\pi\)
0.976819 0.214069i \(-0.0686716\pi\)
\(594\) 0 0
\(595\) 39.0000i 1.59884i
\(596\) 0 0
\(597\) 25.4951 1.04344
\(598\) 0 0
\(599\) 30.5941i 1.25004i −0.780608 0.625021i \(-0.785090\pi\)
0.780608 0.625021i \(-0.214910\pi\)
\(600\) 0 0
\(601\) 37.0000 1.50926 0.754631 0.656150i \(-0.227816\pi\)
0.754631 + 0.656150i \(0.227816\pi\)
\(602\) 0 0
\(603\) 6.00000 + 6.00000i 0.244339 + 0.244339i
\(604\) 0 0
\(605\) 22.9456 + 22.9456i 0.932871 + 0.932871i
\(606\) 0 0
\(607\) 10.1980i 0.413926i −0.978349 0.206963i \(-0.933642\pi\)
0.978349 0.206963i \(-0.0663579\pi\)
\(608\) 0 0
\(609\) −13.0000 + 13.0000i −0.526787 + 0.526787i
\(610\) 0 0
\(611\) 13.0000 0.525924
\(612\) 0 0
\(613\) 5.09902 5.09902i 0.205947 0.205947i −0.596595 0.802542i \(-0.703480\pi\)
0.802542 + 0.596595i \(0.203480\pi\)
\(614\) 0 0
\(615\) 30.5941 1.23367
\(616\) 0 0
\(617\) −12.0000 12.0000i −0.483102 0.483102i 0.423019 0.906121i \(-0.360970\pi\)
−0.906121 + 0.423019i \(0.860970\pi\)
\(618\) 0 0
\(619\) 22.0000 22.0000i 0.884255 0.884255i −0.109709 0.993964i \(-0.534992\pi\)
0.993964 + 0.109709i \(0.0349919\pi\)
\(620\) 0 0
\(621\) 25.4951 1.02308
\(622\) 0 0
\(623\) −10.1980 −0.408576
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 4.00000 0.159745
\(628\) 0 0
\(629\) 7.64853 7.64853i 0.304967 0.304967i
\(630\) 0 0
\(631\) 17.8466 + 17.8466i 0.710461 + 0.710461i 0.966632 0.256171i \(-0.0824610\pi\)
−0.256171 + 0.966632i \(0.582461\pi\)
\(632\) 0 0
\(633\) −7.00000 −0.278225
\(634\) 0 0
\(635\) 39.0000 39.0000i 1.54767 1.54767i
\(636\) 0 0
\(637\) 15.2971 + 15.2971i 0.606092 + 0.606092i
\(638\) 0 0
\(639\) 15.2971 15.2971i 0.605142 0.605142i
\(640\) 0 0
\(641\) 40.0000i 1.57991i 0.613168 + 0.789953i \(0.289895\pi\)
−0.613168 + 0.789953i \(0.710105\pi\)
\(642\) 0 0
\(643\) −15.0000 15.0000i −0.591542 0.591542i 0.346506 0.938048i \(-0.387368\pi\)
−0.938048 + 0.346506i \(0.887368\pi\)
\(644\) 0 0
\(645\) −2.54951 2.54951i −0.100387 0.100387i
\(646\) 0 0
\(647\) −10.1980 −0.400926 −0.200463 0.979701i \(-0.564245\pi\)
−0.200463 + 0.979701i \(0.564245\pi\)
\(648\) 0 0
\(649\) 16.0000i 0.628055i
\(650\) 0 0
\(651\) 26.0000 1.01902
\(652\) 0 0
\(653\) 30.5941i 1.19724i −0.801033 0.598620i \(-0.795716\pi\)
0.801033 0.598620i \(-0.204284\pi\)
\(654\) 0 0
\(655\) −17.8466 + 17.8466i −0.697323 + 0.697323i
\(656\) 0 0
\(657\) 12.0000 12.0000i 0.468165 0.468165i
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) −5.09902 5.09902i −0.198329 0.198329i 0.600954 0.799283i \(-0.294787\pi\)
−0.799283 + 0.600954i \(0.794787\pi\)
\(662\) 0 0
\(663\) 7.64853 + 7.64853i 0.297044 + 0.297044i
\(664\) 0 0
\(665\) −26.0000 26.0000i −1.00824 1.00824i
\(666\) 0 0
\(667\) 26.0000i 1.00672i
\(668\) 0 0
\(669\) 7.64853 7.64853i 0.295709 0.295709i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 21.0000i 0.809491i 0.914429 + 0.404745i \(0.132640\pi\)
−0.914429 + 0.404745i \(0.867360\pi\)
\(674\) 0 0
\(675\) 40.0000i 1.53960i
\(676\) 0 0
\(677\) 15.2971i 0.587914i −0.955819 0.293957i \(-0.905028\pi\)
0.955819 0.293957i \(-0.0949722\pi\)
\(678\) 0 0
\(679\) 35.6931i 1.36978i
\(680\) 0 0
\(681\) 12.0000 + 12.0000i 0.459841 + 0.459841i
\(682\) 0 0
\(683\) −29.0000 + 29.0000i −1.10965 + 1.10965i −0.116459 + 0.993196i \(0.537154\pi\)
−0.993196 + 0.116459i \(0.962846\pi\)
\(684\) 0 0
\(685\) 25.4951i 0.974118i
\(686\) 0 0
\(687\) 2.54951 + 2.54951i 0.0972699 + 0.0972699i
\(688\) 0 0
\(689\) −13.0000 13.0000i −0.495261 0.495261i
\(690\) 0 0
\(691\) −6.00000 6.00000i −0.228251 0.228251i 0.583711 0.811962i \(-0.301600\pi\)
−0.811962 + 0.583711i \(0.801600\pi\)
\(692\) 0 0
\(693\) 10.1980 0.387391
\(694\) 0 0
\(695\) 38.2426 38.2426i 1.45063 1.45063i
\(696\) 0 0
\(697\) −18.0000 + 18.0000i −0.681799 + 0.681799i
\(698\) 0 0
\(699\) 11.0000i 0.416058i
\(700\) 0 0
\(701\) 15.2971 0.577762 0.288881 0.957365i \(-0.406717\pi\)
0.288881 + 0.957365i \(0.406717\pi\)
\(702\) 0 0
\(703\) 10.1980i 0.384626i
\(704\) 0 0
\(705\) 13.0000 0.489608
\(706\) 0 0
\(707\) −26.0000 26.0000i −0.977831 0.977831i
\(708\) 0 0
\(709\) −10.1980 10.1980i −0.382995 0.382995i 0.489185 0.872180i \(-0.337294\pi\)
−0.872180 + 0.489185i \(0.837294\pi\)
\(710\) 0 0
\(711\) 10.1980i 0.382456i
\(712\) 0 0
\(713\) −26.0000 + 26.0000i −0.973708 + 0.973708i
\(714\) 0 0
\(715\) 13.0000 + 13.0000i 0.486172 + 0.486172i
\(716\) 0 0
\(717\) 2.54951 2.54951i 0.0952132 0.0952132i
\(718\) 0 0
\(719\) −25.4951 −0.950807 −0.475403 0.879768i \(-0.657698\pi\)
−0.475403 + 0.879768i \(0.657698\pi\)
\(720\) 0 0
\(721\) −13.0000 13.0000i −0.484145 0.484145i
\(722\) 0 0
\(723\) −14.0000 + 14.0000i −0.520666 + 0.520666i
\(724\) 0 0
\(725\) 40.7922 1.51498
\(726\) 0 0
\(727\) 15.2971 0.567336 0.283668 0.958922i \(-0.408449\pi\)
0.283668 + 0.958922i \(0.408449\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 3.00000 0.110959
\(732\) 0 0
\(733\) −33.1436 + 33.1436i −1.22419 + 1.22419i −0.258058 + 0.966129i \(0.583083\pi\)
−0.966129 + 0.258058i \(0.916917\pi\)
\(734\) 0 0
\(735\) 15.2971 + 15.2971i 0.564241 + 0.564241i
\(736\) 0 0
\(737\) 6.00000 0.221013
\(738\) 0 0
\(739\) 2.00000 2.00000i 0.0735712 0.0735712i −0.669364 0.742935i \(-0.733433\pi\)
0.742935 + 0.669364i \(0.233433\pi\)
\(740\) 0 0
\(741\) −10.1980 −0.374634
\(742\) 0 0
\(743\) 7.64853 7.64853i 0.280597 0.280597i −0.552750 0.833347i \(-0.686422\pi\)
0.833347 + 0.552750i \(0.186422\pi\)
\(744\) 0 0
\(745\) 52.0000i 1.90513i
\(746\) 0 0
\(747\) 10.0000 + 10.0000i 0.365881 + 0.365881i
\(748\) 0 0
\(749\) 5.09902 + 5.09902i 0.186314 + 0.186314i
\(750\) 0 0
\(751\) 10.1980 0.372132 0.186066 0.982537i \(-0.440426\pi\)
0.186066 + 0.982537i \(0.440426\pi\)
\(752\) 0 0
\(753\) 10.0000i 0.364420i
\(754\) 0 0
\(755\) −39.0000 −1.41936
\(756\) 0 0
\(757\) 35.6931i 1.29729i 0.761091 + 0.648645i \(0.224664\pi\)
−0.761091 + 0.648645i \(0.775336\pi\)
\(758\) 0 0
\(759\) 5.09902 5.09902i 0.185083 0.185083i
\(760\) 0 0
\(761\) −4.00000 + 4.00000i −0.145000 + 0.145000i −0.775880 0.630880i \(-0.782694\pi\)
0.630880 + 0.775880i \(0.282694\pi\)
\(762\) 0 0
\(763\) −13.0000 −0.470632
\(764\) 0 0
\(765\) −15.2971 15.2971i −0.553066 0.553066i
\(766\) 0 0
\(767\) 40.7922i 1.47292i
\(768\) 0 0
\(769\) −8.00000 8.00000i −0.288487 0.288487i 0.547995 0.836482i \(-0.315391\pi\)
−0.836482 + 0.547995i \(0.815391\pi\)
\(770\) 0 0
\(771\) 3.00000i 0.108042i
\(772\) 0 0
\(773\) −7.64853 + 7.64853i −0.275098 + 0.275098i −0.831149 0.556050i \(-0.812316\pi\)
0.556050 + 0.831149i \(0.312316\pi\)
\(774\) 0 0
\(775\) −40.7922 40.7922i −1.46530 1.46530i
\(776\) 0 0
\(777\) 13.0000i 0.466372i
\(778\) 0 0
\(779\) 24.0000i 0.859889i
\(780\) 0 0
\(781\) 15.2971i 0.547372i
\(782\) 0 0
\(783\) 25.4951i 0.911120i
\(784\) 0 0
\(785\) 26.0000 + 26.0000i 0.927980 + 0.927980i
\(786\) 0 0
\(787\) 30.0000 30.0000i 1.06938 1.06938i 0.0719783 0.997406i \(-0.477069\pi\)
0.997406 0.0719783i \(-0.0229312\pi\)
\(788\) 0 0
\(789\) 20.3961i 0.726120i
\(790\) 0 0
\(791\) 10.1980 + 10.1980i 0.362601 + 0.362601i
\(792\) 0 0