Properties

Label 416.2.k.b.255.1
Level $416$
Weight $2$
Character 416.255
Analytic conductor $3.322$
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] = [416,2,Mod(31,416)]
 
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, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 416 = 2^{5} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 416.k (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: \(3.32177672409\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 255.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 416.255
Dual form 416.2.k.b.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000i q^{3} +(-1.00000 - 1.00000i) q^{5} +(1.00000 + 1.00000i) q^{7} -1.00000 q^{9} +O(q^{10})\) \(q+2.00000i q^{3} +(-1.00000 - 1.00000i) q^{5} +(1.00000 + 1.00000i) q^{7} -1.00000 q^{9} +(3.00000 + 3.00000i) q^{11} +(-3.00000 + 2.00000i) q^{13} +(2.00000 - 2.00000i) q^{15} +4.00000i q^{17} +(-3.00000 + 3.00000i) q^{19} +(-2.00000 + 2.00000i) q^{21} -3.00000i q^{25} +4.00000i q^{27} -6.00000 q^{29} +(3.00000 - 3.00000i) q^{31} +(-6.00000 + 6.00000i) q^{33} -2.00000i q^{35} +(3.00000 - 3.00000i) q^{37} +(-4.00000 - 6.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} -4.00000 q^{43} +(1.00000 + 1.00000i) q^{45} +(5.00000 + 5.00000i) q^{47} -5.00000i q^{49} -8.00000 q^{51} +6.00000 q^{53} -6.00000i q^{55} +(-6.00000 - 6.00000i) q^{57} +(7.00000 + 7.00000i) q^{59} +14.0000 q^{61} +(-1.00000 - 1.00000i) q^{63} +(5.00000 + 1.00000i) q^{65} +(5.00000 - 5.00000i) q^{67} +(-5.00000 + 5.00000i) q^{71} +(9.00000 - 9.00000i) q^{73} +6.00000 q^{75} +6.00000i q^{77} -6.00000i q^{79} -11.0000 q^{81} +(-7.00000 + 7.00000i) q^{83} +(4.00000 - 4.00000i) q^{85} -12.0000i q^{87} +(5.00000 - 5.00000i) q^{89} +(-5.00000 - 1.00000i) q^{91} +(6.00000 + 6.00000i) q^{93} +6.00000 q^{95} +(13.0000 + 13.0000i) q^{97} +(-3.00000 - 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{5} + 2 q^{7} - 2 q^{9} + 6 q^{11} - 6 q^{13} + 4 q^{15} - 6 q^{19} - 4 q^{21} - 12 q^{29} + 6 q^{31} - 12 q^{33} + 6 q^{37} - 8 q^{39} + 2 q^{41} - 8 q^{43} + 2 q^{45} + 10 q^{47} - 16 q^{51} + 12 q^{53} - 12 q^{57} + 14 q^{59} + 28 q^{61} - 2 q^{63} + 10 q^{65} + 10 q^{67} - 10 q^{71} + 18 q^{73} + 12 q^{75} - 22 q^{81} - 14 q^{83} + 8 q^{85} + 10 q^{89} - 10 q^{91} + 12 q^{93} + 12 q^{95} + 26 q^{97} - 6 q^{99}+O(q^{100}) \) 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
\(3\) 2.00000i 1.15470i 0.816497 + 0.577350i \(0.195913\pi\)
−0.816497 + 0.577350i \(0.804087\pi\)
\(4\) 0 0
\(5\) −1.00000 1.00000i −0.447214 0.447214i 0.447214 0.894427i \(-0.352416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 0 0
\(7\) 1.00000 + 1.00000i 0.377964 + 0.377964i 0.870367 0.492403i \(-0.163881\pi\)
−0.492403 + 0.870367i \(0.663881\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.00000 + 3.00000i 0.904534 + 0.904534i 0.995824 0.0912903i \(-0.0290991\pi\)
−0.0912903 + 0.995824i \(0.529099\pi\)
\(12\) 0 0
\(13\) −3.00000 + 2.00000i −0.832050 + 0.554700i
\(14\) 0 0
\(15\) 2.00000 2.00000i 0.516398 0.516398i
\(16\) 0 0
\(17\) 4.00000i 0.970143i 0.874475 + 0.485071i \(0.161206\pi\)
−0.874475 + 0.485071i \(0.838794\pi\)
\(18\) 0 0
\(19\) −3.00000 + 3.00000i −0.688247 + 0.688247i −0.961844 0.273597i \(-0.911786\pi\)
0.273597 + 0.961844i \(0.411786\pi\)
\(20\) 0 0
\(21\) −2.00000 + 2.00000i −0.436436 + 0.436436i
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 3.00000i 0.600000i
\(26\) 0 0
\(27\) 4.00000i 0.769800i
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 3.00000 3.00000i 0.538816 0.538816i −0.384365 0.923181i \(-0.625580\pi\)
0.923181 + 0.384365i \(0.125580\pi\)
\(32\) 0 0
\(33\) −6.00000 + 6.00000i −1.04447 + 1.04447i
\(34\) 0 0
\(35\) 2.00000i 0.338062i
\(36\) 0 0
\(37\) 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i \(-0.636609\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(38\) 0 0
\(39\) −4.00000 6.00000i −0.640513 0.960769i
\(40\) 0 0
\(41\) 1.00000 + 1.00000i 0.156174 + 0.156174i 0.780869 0.624695i \(-0.214777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 1.00000 + 1.00000i 0.149071 + 0.149071i
\(46\) 0 0
\(47\) 5.00000 + 5.00000i 0.729325 + 0.729325i 0.970485 0.241160i \(-0.0775280\pi\)
−0.241160 + 0.970485i \(0.577528\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) −8.00000 −1.12022
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 6.00000i 0.809040i
\(56\) 0 0
\(57\) −6.00000 6.00000i −0.794719 0.794719i
\(58\) 0 0
\(59\) 7.00000 + 7.00000i 0.911322 + 0.911322i 0.996376 0.0850540i \(-0.0271063\pi\)
−0.0850540 + 0.996376i \(0.527106\pi\)
\(60\) 0 0
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) −1.00000 1.00000i −0.125988 0.125988i
\(64\) 0 0
\(65\) 5.00000 + 1.00000i 0.620174 + 0.124035i
\(66\) 0 0
\(67\) 5.00000 5.00000i 0.610847 0.610847i −0.332320 0.943167i \(-0.607831\pi\)
0.943167 + 0.332320i \(0.107831\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.00000 + 5.00000i −0.593391 + 0.593391i −0.938546 0.345155i \(-0.887826\pi\)
0.345155 + 0.938546i \(0.387826\pi\)
\(72\) 0 0
\(73\) 9.00000 9.00000i 1.05337 1.05337i 0.0548772 0.998493i \(-0.482523\pi\)
0.998493 0.0548772i \(-0.0174767\pi\)
\(74\) 0 0
\(75\) 6.00000 0.692820
\(76\) 0 0
\(77\) 6.00000i 0.683763i
\(78\) 0 0
\(79\) 6.00000i 0.675053i −0.941316 0.337526i \(-0.890410\pi\)
0.941316 0.337526i \(-0.109590\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) −7.00000 + 7.00000i −0.768350 + 0.768350i −0.977816 0.209466i \(-0.932827\pi\)
0.209466 + 0.977816i \(0.432827\pi\)
\(84\) 0 0
\(85\) 4.00000 4.00000i 0.433861 0.433861i
\(86\) 0 0
\(87\) 12.0000i 1.28654i
\(88\) 0 0
\(89\) 5.00000 5.00000i 0.529999 0.529999i −0.390573 0.920572i \(-0.627723\pi\)
0.920572 + 0.390573i \(0.127723\pi\)
\(90\) 0 0
\(91\) −5.00000 1.00000i −0.524142 0.104828i
\(92\) 0 0
\(93\) 6.00000 + 6.00000i 0.622171 + 0.622171i
\(94\) 0 0
\(95\) 6.00000 0.615587
\(96\) 0 0
\(97\) 13.0000 + 13.0000i 1.31995 + 1.31995i 0.913812 + 0.406138i \(0.133125\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 0 0
\(99\) −3.00000 3.00000i −0.301511 0.301511i
\(100\) 0 0
\(101\) 16.0000i 1.59206i −0.605257 0.796030i \(-0.706930\pi\)
0.605257 0.796030i \(-0.293070\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) 4.00000 0.390360
\(106\) 0 0
\(107\) 14.0000i 1.35343i −0.736245 0.676716i \(-0.763403\pi\)
0.736245 0.676716i \(-0.236597\pi\)
\(108\) 0 0
\(109\) −9.00000 9.00000i −0.862044 0.862044i 0.129532 0.991575i \(-0.458653\pi\)
−0.991575 + 0.129532i \(0.958653\pi\)
\(110\) 0 0
\(111\) 6.00000 + 6.00000i 0.569495 + 0.569495i
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.00000 2.00000i 0.277350 0.184900i
\(118\) 0 0
\(119\) −4.00000 + 4.00000i −0.366679 + 0.366679i
\(120\) 0 0
\(121\) 7.00000i 0.636364i
\(122\) 0 0
\(123\) −2.00000 + 2.00000i −0.180334 + 0.180334i
\(124\) 0 0
\(125\) −8.00000 + 8.00000i −0.715542 + 0.715542i
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) 8.00000i 0.704361i
\(130\) 0 0
\(131\) 14.0000i 1.22319i −0.791173 0.611593i \(-0.790529\pi\)
0.791173 0.611593i \(-0.209471\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 0 0
\(135\) 4.00000 4.00000i 0.344265 0.344265i
\(136\) 0 0
\(137\) −3.00000 + 3.00000i −0.256307 + 0.256307i −0.823550 0.567243i \(-0.808010\pi\)
0.567243 + 0.823550i \(0.308010\pi\)
\(138\) 0 0
\(139\) 22.0000i 1.86602i −0.359856 0.933008i \(-0.617174\pi\)
0.359856 0.933008i \(-0.382826\pi\)
\(140\) 0 0
\(141\) −10.0000 + 10.0000i −0.842152 + 0.842152i
\(142\) 0 0
\(143\) −15.0000 3.00000i −1.25436 0.250873i
\(144\) 0 0
\(145\) 6.00000 + 6.00000i 0.498273 + 0.498273i
\(146\) 0 0
\(147\) 10.0000 0.824786
\(148\) 0 0
\(149\) −13.0000 13.0000i −1.06500 1.06500i −0.997735 0.0672664i \(-0.978572\pi\)
−0.0672664 0.997735i \(-0.521428\pi\)
\(150\) 0 0
\(151\) 9.00000 + 9.00000i 0.732410 + 0.732410i 0.971097 0.238687i \(-0.0767170\pi\)
−0.238687 + 0.971097i \(0.576717\pi\)
\(152\) 0 0
\(153\) 4.00000i 0.323381i
\(154\) 0 0
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) 12.0000i 0.951662i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 3.00000 + 3.00000i 0.234978 + 0.234978i 0.814767 0.579789i \(-0.196865\pi\)
−0.579789 + 0.814767i \(0.696865\pi\)
\(164\) 0 0
\(165\) 12.0000 0.934199
\(166\) 0 0
\(167\) 13.0000 + 13.0000i 1.00597 + 1.00597i 0.999982 + 0.00598813i \(0.00190609\pi\)
0.00598813 + 0.999982i \(0.498094\pi\)
\(168\) 0 0
\(169\) 5.00000 12.0000i 0.384615 0.923077i
\(170\) 0 0
\(171\) 3.00000 3.00000i 0.229416 0.229416i
\(172\) 0 0
\(173\) 24.0000i 1.82469i 0.409426 + 0.912343i \(0.365729\pi\)
−0.409426 + 0.912343i \(0.634271\pi\)
\(174\) 0 0
\(175\) 3.00000 3.00000i 0.226779 0.226779i
\(176\) 0 0
\(177\) −14.0000 + 14.0000i −1.05230 + 1.05230i
\(178\) 0 0
\(179\) 20.0000 1.49487 0.747435 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(180\) 0 0
\(181\) 4.00000i 0.297318i −0.988889 0.148659i \(-0.952504\pi\)
0.988889 0.148659i \(-0.0474956\pi\)
\(182\) 0 0
\(183\) 28.0000i 2.06982i
\(184\) 0 0
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) −12.0000 + 12.0000i −0.877527 + 0.877527i
\(188\) 0 0
\(189\) −4.00000 + 4.00000i −0.290957 + 0.290957i
\(190\) 0 0
\(191\) 10.0000i 0.723575i 0.932261 + 0.361787i \(0.117833\pi\)
−0.932261 + 0.361787i \(0.882167\pi\)
\(192\) 0 0
\(193\) 5.00000 5.00000i 0.359908 0.359908i −0.503871 0.863779i \(-0.668091\pi\)
0.863779 + 0.503871i \(0.168091\pi\)
\(194\) 0 0
\(195\) −2.00000 + 10.0000i −0.143223 + 0.716115i
\(196\) 0 0
\(197\) 7.00000 + 7.00000i 0.498729 + 0.498729i 0.911042 0.412313i \(-0.135279\pi\)
−0.412313 + 0.911042i \(0.635279\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 0 0
\(201\) 10.0000 + 10.0000i 0.705346 + 0.705346i
\(202\) 0 0
\(203\) −6.00000 6.00000i −0.421117 0.421117i
\(204\) 0 0
\(205\) 2.00000i 0.139686i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −18.0000 −1.24509
\(210\) 0 0
\(211\) 10.0000i 0.688428i 0.938891 + 0.344214i \(0.111855\pi\)
−0.938891 + 0.344214i \(0.888145\pi\)
\(212\) 0 0
\(213\) −10.0000 10.0000i −0.685189 0.685189i
\(214\) 0 0
\(215\) 4.00000 + 4.00000i 0.272798 + 0.272798i
\(216\) 0 0
\(217\) 6.00000 0.407307
\(218\) 0 0
\(219\) 18.0000 + 18.0000i 1.21633 + 1.21633i
\(220\) 0 0
\(221\) −8.00000 12.0000i −0.538138 0.807207i
\(222\) 0 0
\(223\) 7.00000 7.00000i 0.468755 0.468755i −0.432756 0.901511i \(-0.642459\pi\)
0.901511 + 0.432756i \(0.142459\pi\)
\(224\) 0 0
\(225\) 3.00000i 0.200000i
\(226\) 0 0
\(227\) 13.0000 13.0000i 0.862840 0.862840i −0.128827 0.991667i \(-0.541121\pi\)
0.991667 + 0.128827i \(0.0411211\pi\)
\(228\) 0 0
\(229\) 3.00000 3.00000i 0.198246 0.198246i −0.601002 0.799248i \(-0.705232\pi\)
0.799248 + 0.601002i \(0.205232\pi\)
\(230\) 0 0
\(231\) −12.0000 −0.789542
\(232\) 0 0
\(233\) 16.0000i 1.04819i −0.851658 0.524097i \(-0.824403\pi\)
0.851658 0.524097i \(-0.175597\pi\)
\(234\) 0 0
\(235\) 10.0000i 0.652328i
\(236\) 0 0
\(237\) 12.0000 0.779484
\(238\) 0 0
\(239\) −17.0000 + 17.0000i −1.09964 + 1.09964i −0.105186 + 0.994453i \(0.533544\pi\)
−0.994453 + 0.105186i \(0.966456\pi\)
\(240\) 0 0
\(241\) −15.0000 + 15.0000i −0.966235 + 0.966235i −0.999448 0.0332133i \(-0.989426\pi\)
0.0332133 + 0.999448i \(0.489426\pi\)
\(242\) 0 0
\(243\) 10.0000i 0.641500i
\(244\) 0 0
\(245\) −5.00000 + 5.00000i −0.319438 + 0.319438i
\(246\) 0 0
\(247\) 3.00000 15.0000i 0.190885 0.954427i
\(248\) 0 0
\(249\) −14.0000 14.0000i −0.887214 0.887214i
\(250\) 0 0
\(251\) −4.00000 −0.252478 −0.126239 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 8.00000 + 8.00000i 0.500979 + 0.500979i
\(256\) 0 0
\(257\) 24.0000i 1.49708i 0.663090 + 0.748539i \(0.269245\pi\)
−0.663090 + 0.748539i \(0.730755\pi\)
\(258\) 0 0
\(259\) 6.00000 0.372822
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) 18.0000i 1.10993i 0.831875 + 0.554964i \(0.187268\pi\)
−0.831875 + 0.554964i \(0.812732\pi\)
\(264\) 0 0
\(265\) −6.00000 6.00000i −0.368577 0.368577i
\(266\) 0 0
\(267\) 10.0000 + 10.0000i 0.611990 + 0.611990i
\(268\) 0 0
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) −19.0000 19.0000i −1.15417 1.15417i −0.985709 0.168459i \(-0.946121\pi\)
−0.168459 0.985709i \(-0.553879\pi\)
\(272\) 0 0
\(273\) 2.00000 10.0000i 0.121046 0.605228i
\(274\) 0 0
\(275\) 9.00000 9.00000i 0.542720 0.542720i
\(276\) 0 0
\(277\) 16.0000i 0.961347i 0.876900 + 0.480673i \(0.159608\pi\)
−0.876900 + 0.480673i \(0.840392\pi\)
\(278\) 0 0
\(279\) −3.00000 + 3.00000i −0.179605 + 0.179605i
\(280\) 0 0
\(281\) 1.00000 1.00000i 0.0596550 0.0596550i −0.676650 0.736305i \(-0.736569\pi\)
0.736305 + 0.676650i \(0.236569\pi\)
\(282\) 0 0
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 0 0
\(285\) 12.0000i 0.710819i
\(286\) 0 0
\(287\) 2.00000i 0.118056i
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −26.0000 + 26.0000i −1.52415 + 1.52415i
\(292\) 0 0
\(293\) −9.00000 + 9.00000i −0.525786 + 0.525786i −0.919313 0.393527i \(-0.871255\pi\)
0.393527 + 0.919313i \(0.371255\pi\)
\(294\) 0 0
\(295\) 14.0000i 0.815112i
\(296\) 0 0
\(297\) −12.0000 + 12.0000i −0.696311 + 0.696311i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −4.00000 4.00000i −0.230556 0.230556i
\(302\) 0 0
\(303\) 32.0000 1.83835
\(304\) 0 0
\(305\) −14.0000 14.0000i −0.801638 0.801638i
\(306\) 0 0
\(307\) −5.00000 5.00000i −0.285365 0.285365i 0.549879 0.835244i \(-0.314674\pi\)
−0.835244 + 0.549879i \(0.814674\pi\)
\(308\) 0 0
\(309\) 16.0000i 0.910208i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 0 0
\(315\) 2.00000i 0.112687i
\(316\) 0 0
\(317\) 3.00000 + 3.00000i 0.168497 + 0.168497i 0.786318 0.617822i \(-0.211985\pi\)
−0.617822 + 0.786318i \(0.711985\pi\)
\(318\) 0 0
\(319\) −18.0000 18.0000i −1.00781 1.00781i
\(320\) 0 0
\(321\) 28.0000 1.56281
\(322\) 0 0
\(323\) −12.0000 12.0000i −0.667698 0.667698i
\(324\) 0 0
\(325\) 6.00000 + 9.00000i 0.332820 + 0.499230i
\(326\) 0 0
\(327\) 18.0000 18.0000i 0.995402 0.995402i
\(328\) 0 0
\(329\) 10.0000i 0.551318i
\(330\) 0 0
\(331\) 17.0000 17.0000i 0.934405 0.934405i −0.0635727 0.997977i \(-0.520249\pi\)
0.997977 + 0.0635727i \(0.0202495\pi\)
\(332\) 0 0
\(333\) −3.00000 + 3.00000i −0.164399 + 0.164399i
\(334\) 0 0
\(335\) −10.0000 −0.546358
\(336\) 0 0
\(337\) 20.0000i 1.08947i −0.838608 0.544735i \(-0.816630\pi\)
0.838608 0.544735i \(-0.183370\pi\)
\(338\) 0 0
\(339\) 4.00000i 0.217250i
\(340\) 0 0
\(341\) 18.0000 0.974755
\(342\) 0 0
\(343\) 12.0000 12.0000i 0.647939 0.647939i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.00000i 0.322097i −0.986947 0.161048i \(-0.948512\pi\)
0.986947 0.161048i \(-0.0514875\pi\)
\(348\) 0 0
\(349\) 3.00000 3.00000i 0.160586 0.160586i −0.622240 0.782826i \(-0.713777\pi\)
0.782826 + 0.622240i \(0.213777\pi\)
\(350\) 0 0
\(351\) −8.00000 12.0000i −0.427008 0.640513i
\(352\) 0 0
\(353\) 17.0000 + 17.0000i 0.904819 + 0.904819i 0.995848 0.0910295i \(-0.0290158\pi\)
−0.0910295 + 0.995848i \(0.529016\pi\)
\(354\) 0 0
\(355\) 10.0000 0.530745
\(356\) 0 0
\(357\) −8.00000 8.00000i −0.423405 0.423405i
\(358\) 0 0
\(359\) 1.00000 + 1.00000i 0.0527780 + 0.0527780i 0.733003 0.680225i \(-0.238118\pi\)
−0.680225 + 0.733003i \(0.738118\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 0 0
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) −18.0000 −0.942163
\(366\) 0 0
\(367\) 10.0000i 0.521996i 0.965339 + 0.260998i \(0.0840516\pi\)
−0.965339 + 0.260998i \(0.915948\pi\)
\(368\) 0 0
\(369\) −1.00000 1.00000i −0.0520579 0.0520579i
\(370\) 0 0
\(371\) 6.00000 + 6.00000i 0.311504 + 0.311504i
\(372\) 0 0
\(373\) 10.0000 0.517780 0.258890 0.965907i \(-0.416643\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(374\) 0 0
\(375\) −16.0000 16.0000i −0.826236 0.826236i
\(376\) 0 0
\(377\) 18.0000 12.0000i 0.927047 0.618031i
\(378\) 0 0
\(379\) −23.0000 + 23.0000i −1.18143 + 1.18143i −0.202057 + 0.979374i \(0.564763\pi\)
−0.979374 + 0.202057i \(0.935237\pi\)
\(380\) 0 0
\(381\) 32.0000i 1.63941i
\(382\) 0 0
\(383\) −9.00000 + 9.00000i −0.459879 + 0.459879i −0.898616 0.438737i \(-0.855426\pi\)
0.438737 + 0.898616i \(0.355426\pi\)
\(384\) 0 0
\(385\) 6.00000 6.00000i 0.305788 0.305788i
\(386\) 0 0
\(387\) 4.00000 0.203331
\(388\) 0 0
\(389\) 20.0000i 1.01404i −0.861934 0.507020i \(-0.830747\pi\)
0.861934 0.507020i \(-0.169253\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 28.0000 1.41241
\(394\) 0 0
\(395\) −6.00000 + 6.00000i −0.301893 + 0.301893i
\(396\) 0 0
\(397\) 7.00000 7.00000i 0.351320 0.351320i −0.509281 0.860601i \(-0.670088\pi\)
0.860601 + 0.509281i \(0.170088\pi\)
\(398\) 0 0
\(399\) 12.0000i 0.600751i
\(400\) 0 0
\(401\) −7.00000 + 7.00000i −0.349563 + 0.349563i −0.859947 0.510384i \(-0.829503\pi\)
0.510384 + 0.859947i \(0.329503\pi\)
\(402\) 0 0
\(403\) −3.00000 + 15.0000i −0.149441 + 0.747203i
\(404\) 0 0
\(405\) 11.0000 + 11.0000i 0.546594 + 0.546594i
\(406\) 0 0
\(407\) 18.0000 0.892227
\(408\) 0 0
\(409\) −3.00000 3.00000i −0.148340 0.148340i 0.629036 0.777376i \(-0.283450\pi\)
−0.777376 + 0.629036i \(0.783450\pi\)
\(410\) 0 0
\(411\) −6.00000 6.00000i −0.295958 0.295958i
\(412\) 0 0
\(413\) 14.0000i 0.688895i
\(414\) 0 0
\(415\) 14.0000 0.687233
\(416\) 0 0
\(417\) 44.0000 2.15469
\(418\) 0 0
\(419\) 2.00000i 0.0977064i 0.998806 + 0.0488532i \(0.0155566\pi\)
−0.998806 + 0.0488532i \(0.984443\pi\)
\(420\) 0 0
\(421\) 3.00000 + 3.00000i 0.146211 + 0.146211i 0.776423 0.630212i \(-0.217032\pi\)
−0.630212 + 0.776423i \(0.717032\pi\)
\(422\) 0 0
\(423\) −5.00000 5.00000i −0.243108 0.243108i
\(424\) 0 0
\(425\) 12.0000 0.582086
\(426\) 0 0
\(427\) 14.0000 + 14.0000i 0.677507 + 0.677507i
\(428\) 0 0
\(429\) 6.00000 30.0000i 0.289683 1.44841i
\(430\) 0 0
\(431\) 11.0000 11.0000i 0.529851 0.529851i −0.390677 0.920528i \(-0.627759\pi\)
0.920528 + 0.390677i \(0.127759\pi\)
\(432\) 0 0
\(433\) 24.0000i 1.15337i −0.816968 0.576683i \(-0.804347\pi\)
0.816968 0.576683i \(-0.195653\pi\)
\(434\) 0 0
\(435\) −12.0000 + 12.0000i −0.575356 + 0.575356i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −40.0000 −1.90910 −0.954548 0.298057i \(-0.903661\pi\)
−0.954548 + 0.298057i \(0.903661\pi\)
\(440\) 0 0
\(441\) 5.00000i 0.238095i
\(442\) 0 0
\(443\) 30.0000i 1.42534i −0.701498 0.712672i \(-0.747485\pi\)
0.701498 0.712672i \(-0.252515\pi\)
\(444\) 0 0
\(445\) −10.0000 −0.474045
\(446\) 0 0
\(447\) 26.0000 26.0000i 1.22976 1.22976i
\(448\) 0 0
\(449\) 1.00000 1.00000i 0.0471929 0.0471929i −0.683117 0.730309i \(-0.739376\pi\)
0.730309 + 0.683117i \(0.239376\pi\)
\(450\) 0 0
\(451\) 6.00000i 0.282529i
\(452\) 0 0
\(453\) −18.0000 + 18.0000i −0.845714 + 0.845714i
\(454\) 0 0
\(455\) 4.00000 + 6.00000i 0.187523 + 0.281284i
\(456\) 0 0
\(457\) 13.0000 + 13.0000i 0.608114 + 0.608114i 0.942453 0.334339i \(-0.108513\pi\)
−0.334339 + 0.942453i \(0.608513\pi\)
\(458\) 0 0
\(459\) −16.0000 −0.746816
\(460\) 0 0
\(461\) 11.0000 + 11.0000i 0.512321 + 0.512321i 0.915237 0.402916i \(-0.132003\pi\)
−0.402916 + 0.915237i \(0.632003\pi\)
\(462\) 0 0
\(463\) 5.00000 + 5.00000i 0.232370 + 0.232370i 0.813681 0.581311i \(-0.197460\pi\)
−0.581311 + 0.813681i \(0.697460\pi\)
\(464\) 0 0
\(465\) 12.0000i 0.556487i
\(466\) 0 0
\(467\) 4.00000 0.185098 0.0925490 0.995708i \(-0.470499\pi\)
0.0925490 + 0.995708i \(0.470499\pi\)
\(468\) 0 0
\(469\) 10.0000 0.461757
\(470\) 0 0
\(471\) 4.00000i 0.184310i
\(472\) 0 0
\(473\) −12.0000 12.0000i −0.551761 0.551761i
\(474\) 0 0
\(475\) 9.00000 + 9.00000i 0.412948 + 0.412948i
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) −23.0000 23.0000i −1.05090 1.05090i −0.998633 0.0522635i \(-0.983356\pi\)
−0.0522635 0.998633i \(-0.516644\pi\)
\(480\) 0 0
\(481\) −3.00000 + 15.0000i −0.136788 + 0.683941i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 26.0000i 1.18060i
\(486\) 0 0
\(487\) 23.0000 23.0000i 1.04223 1.04223i 0.0431614 0.999068i \(-0.486257\pi\)
0.999068 0.0431614i \(-0.0137430\pi\)
\(488\) 0 0
\(489\) −6.00000 + 6.00000i −0.271329 + 0.271329i
\(490\) 0 0
\(491\) 4.00000 0.180517 0.0902587 0.995918i \(-0.471231\pi\)
0.0902587 + 0.995918i \(0.471231\pi\)
\(492\) 0 0
\(493\) 24.0000i 1.08091i
\(494\) 0 0
\(495\) 6.00000i 0.269680i
\(496\) 0 0
\(497\) −10.0000 −0.448561
\(498\) 0 0
\(499\) −27.0000 + 27.0000i −1.20869 + 1.20869i −0.237233 + 0.971453i \(0.576241\pi\)
−0.971453 + 0.237233i \(0.923759\pi\)
\(500\) 0 0
\(501\) −26.0000 + 26.0000i −1.16159 + 1.16159i
\(502\) 0 0
\(503\) 14.0000i 0.624229i −0.950044 0.312115i \(-0.898963\pi\)
0.950044 0.312115i \(-0.101037\pi\)
\(504\) 0 0
\(505\) −16.0000 + 16.0000i −0.711991 + 0.711991i
\(506\) 0 0
\(507\) 24.0000 + 10.0000i 1.06588 + 0.444116i
\(508\) 0 0
\(509\) 11.0000 + 11.0000i 0.487566 + 0.487566i 0.907537 0.419971i \(-0.137960\pi\)
−0.419971 + 0.907537i \(0.637960\pi\)
\(510\) 0 0
\(511\) 18.0000 0.796273
\(512\) 0 0
\(513\) −12.0000 12.0000i −0.529813 0.529813i
\(514\) 0 0
\(515\) 8.00000 + 8.00000i 0.352522 + 0.352522i
\(516\) 0 0
\(517\) 30.0000i 1.31940i
\(518\) 0 0
\(519\) −48.0000 −2.10697
\(520\) 0 0
\(521\) −10.0000 −0.438108 −0.219054 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 0 0
\(523\) 34.0000i 1.48672i 0.668894 + 0.743358i \(0.266768\pi\)
−0.668894 + 0.743358i \(0.733232\pi\)
\(524\) 0 0
\(525\) 6.00000 + 6.00000i 0.261861 + 0.261861i
\(526\) 0 0
\(527\) 12.0000 + 12.0000i 0.522728 + 0.522728i
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) −7.00000 7.00000i −0.303774 0.303774i
\(532\) 0 0
\(533\) −5.00000 1.00000i −0.216574 0.0433148i
\(534\) 0 0
\(535\) −14.0000 + 14.0000i −0.605273 + 0.605273i
\(536\) 0 0
\(537\) 40.0000i 1.72613i
\(538\) 0 0
\(539\) 15.0000 15.0000i 0.646096 0.646096i
\(540\) 0 0
\(541\) −1.00000 + 1.00000i −0.0429934 + 0.0429934i −0.728277 0.685283i \(-0.759678\pi\)
0.685283 + 0.728277i \(0.259678\pi\)
\(542\) 0 0
\(543\) 8.00000 0.343313
\(544\) 0 0
\(545\) 18.0000i 0.771035i
\(546\) 0 0
\(547\) 30.0000i 1.28271i −0.767245 0.641354i \(-0.778373\pi\)
0.767245 0.641354i \(-0.221627\pi\)
\(548\) 0 0
\(549\) −14.0000 −0.597505
\(550\) 0 0
\(551\) 18.0000 18.0000i 0.766826 0.766826i
\(552\) 0 0
\(553\) 6.00000 6.00000i 0.255146 0.255146i
\(554\) 0 0
\(555\) 12.0000i 0.509372i
\(556\) 0 0
\(557\) 15.0000 15.0000i 0.635570 0.635570i −0.313889 0.949460i \(-0.601632\pi\)
0.949460 + 0.313889i \(0.101632\pi\)
\(558\) 0 0
\(559\) 12.0000 8.00000i 0.507546 0.338364i
\(560\) 0 0
\(561\) −24.0000 24.0000i −1.01328 1.01328i
\(562\) 0 0
\(563\) −20.0000 −0.842900 −0.421450 0.906852i \(-0.638479\pi\)
−0.421450 + 0.906852i \(0.638479\pi\)
\(564\) 0 0
\(565\) 2.00000 + 2.00000i 0.0841406 + 0.0841406i
\(566\) 0 0
\(567\) −11.0000 11.0000i −0.461957 0.461957i
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) −20.0000 −0.835512
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 5.00000 + 5.00000i 0.208153 + 0.208153i 0.803482 0.595329i \(-0.202978\pi\)
−0.595329 + 0.803482i \(0.702978\pi\)
\(578\) 0 0
\(579\) 10.0000 + 10.0000i 0.415586 + 0.415586i
\(580\) 0 0
\(581\) −14.0000 −0.580818
\(582\) 0 0
\(583\) 18.0000 + 18.0000i 0.745484 + 0.745484i
\(584\) 0 0
\(585\) −5.00000 1.00000i −0.206725 0.0413449i
\(586\) 0 0
\(587\) −7.00000 + 7.00000i −0.288921 + 0.288921i −0.836653 0.547733i \(-0.815491\pi\)
0.547733 + 0.836653i \(0.315491\pi\)
\(588\) 0 0
\(589\) 18.0000i 0.741677i
\(590\) 0 0
\(591\) −14.0000 + 14.0000i −0.575883 + 0.575883i
\(592\) 0 0
\(593\) −3.00000 + 3.00000i −0.123195 + 0.123195i −0.766016 0.642821i \(-0.777764\pi\)
0.642821 + 0.766016i \(0.277764\pi\)
\(594\) 0 0
\(595\) 8.00000 0.327968
\(596\) 0 0
\(597\) 16.0000i 0.654836i
\(598\) 0 0
\(599\) 26.0000i 1.06233i 0.847268 + 0.531166i \(0.178246\pi\)
−0.847268 + 0.531166i \(0.821754\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) −5.00000 + 5.00000i −0.203616 + 0.203616i
\(604\) 0 0
\(605\) 7.00000 7.00000i 0.284590 0.284590i
\(606\) 0 0
\(607\) 42.0000i 1.70473i 0.522949 + 0.852364i \(0.324832\pi\)
−0.522949 + 0.852364i \(0.675168\pi\)
\(608\) 0 0
\(609\) 12.0000 12.0000i 0.486265 0.486265i
\(610\) 0 0
\(611\) −25.0000 5.00000i −1.01139 0.202278i
\(612\) 0 0
\(613\) −9.00000 9.00000i −0.363507 0.363507i 0.501596 0.865102i \(-0.332747\pi\)
−0.865102 + 0.501596i \(0.832747\pi\)
\(614\) 0 0
\(615\) 4.00000 0.161296
\(616\) 0 0
\(617\) −23.0000 23.0000i −0.925945 0.925945i 0.0714958 0.997441i \(-0.477223\pi\)
−0.997441 + 0.0714958i \(0.977223\pi\)
\(618\) 0 0
\(619\) 3.00000 + 3.00000i 0.120580 + 0.120580i 0.764822 0.644242i \(-0.222827\pi\)
−0.644242 + 0.764822i \(0.722827\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 10.0000 0.400642
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 36.0000i 1.43770i
\(628\) 0 0
\(629\) 12.0000 + 12.0000i 0.478471 + 0.478471i
\(630\) 0 0
\(631\) 1.00000 + 1.00000i 0.0398094 + 0.0398094i 0.726731 0.686922i \(-0.241039\pi\)
−0.686922 + 0.726731i \(0.741039\pi\)
\(632\) 0 0
\(633\) −20.0000 −0.794929
\(634\) 0 0
\(635\) 16.0000 + 16.0000i 0.634941 + 0.634941i
\(636\) 0 0
\(637\) 10.0000 + 15.0000i 0.396214 + 0.594322i
\(638\) 0 0
\(639\) 5.00000 5.00000i 0.197797 0.197797i
\(640\) 0 0
\(641\) 36.0000i 1.42191i −0.703235 0.710957i \(-0.748262\pi\)
0.703235 0.710957i \(-0.251738\pi\)
\(642\) 0 0
\(643\) −7.00000 + 7.00000i −0.276053 + 0.276053i −0.831531 0.555478i \(-0.812535\pi\)
0.555478 + 0.831531i \(0.312535\pi\)
\(644\) 0 0
\(645\) −8.00000 + 8.00000i −0.315000 + 0.315000i
\(646\) 0 0
\(647\) −32.0000 −1.25805 −0.629025 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) 0 0
\(649\) 42.0000i 1.64864i
\(650\) 0 0
\(651\) 12.0000i 0.470317i
\(652\) 0 0
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 0 0
\(655\) −14.0000 + 14.0000i −0.547025 + 0.547025i
\(656\) 0 0
\(657\) −9.00000 + 9.00000i −0.351123 + 0.351123i
\(658\) 0 0
\(659\) 34.0000i 1.32445i 0.749304 + 0.662226i \(0.230388\pi\)
−0.749304 + 0.662226i \(0.769612\pi\)
\(660\) 0 0
\(661\) 19.0000 19.0000i 0.739014 0.739014i −0.233373 0.972387i \(-0.574976\pi\)
0.972387 + 0.233373i \(0.0749763\pi\)
\(662\) 0 0
\(663\) 24.0000 16.0000i 0.932083 0.621389i
\(664\) 0 0
\(665\) 6.00000 + 6.00000i 0.232670 + 0.232670i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 14.0000 + 14.0000i 0.541271 + 0.541271i
\(670\) 0 0
\(671\) 42.0000 + 42.0000i 1.62139 + 1.62139i
\(672\) 0 0
\(673\) 44.0000i 1.69608i −0.529936 0.848038i \(-0.677784\pi\)
0.529936 0.848038i \(-0.322216\pi\)
\(674\) 0 0
\(675\) 12.0000 0.461880
\(676\) 0 0
\(677\) 22.0000 0.845529 0.422764 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(678\) 0 0
\(679\) 26.0000i 0.997788i
\(680\) 0 0
\(681\) 26.0000 + 26.0000i 0.996322 + 0.996322i
\(682\) 0 0
\(683\) −5.00000 5.00000i −0.191320 0.191320i 0.604946 0.796266i \(-0.293195\pi\)
−0.796266 + 0.604946i \(0.793195\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) 0 0
\(687\) 6.00000 + 6.00000i 0.228914 + 0.228914i
\(688\) 0 0
\(689\) −18.0000 + 12.0000i −0.685745 + 0.457164i
\(690\) 0 0
\(691\) 21.0000 21.0000i 0.798878 0.798878i −0.184041 0.982919i \(-0.558918\pi\)
0.982919 + 0.184041i \(0.0589179\pi\)
\(692\) 0 0
\(693\) 6.00000i 0.227921i
\(694\) 0 0
\(695\) −22.0000 + 22.0000i −0.834508 + 0.834508i
\(696\) 0 0
\(697\) −4.00000 + 4.00000i −0.151511 + 0.151511i
\(698\) 0 0
\(699\) 32.0000 1.21035
\(700\) 0 0
\(701\) 28.0000i 1.05755i −0.848763 0.528773i \(-0.822652\pi\)
0.848763 0.528773i \(-0.177348\pi\)
\(702\) 0 0
\(703\) 18.0000i 0.678883i
\(704\) 0 0
\(705\) 20.0000 0.753244
\(706\) 0 0
\(707\) 16.0000 16.0000i 0.601742 0.601742i
\(708\) 0 0
\(709\) −33.0000 + 33.0000i −1.23934 + 1.23934i −0.279070 + 0.960271i \(0.590026\pi\)
−0.960271 + 0.279070i \(0.909974\pi\)
\(710\) 0 0
\(711\) 6.00000i 0.225018i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 12.0000 + 18.0000i 0.448775 + 0.673162i
\(716\) 0 0
\(717\) −34.0000 34.0000i −1.26975 1.26975i
\(718\) 0 0
\(719\) −40.0000 −1.49175 −0.745874 0.666087i \(-0.767968\pi\)
−0.745874 + 0.666087i \(0.767968\pi\)
\(720\) 0 0
\(721\) −8.00000 8.00000i −0.297936 0.297936i
\(722\) 0 0
\(723\) −30.0000 30.0000i −1.11571 1.11571i
\(724\) 0 0
\(725\) 18.0000i 0.668503i
\(726\) 0 0
\(727\) 48.0000 1.78022 0.890111 0.455744i \(-0.150627\pi\)
0.890111 + 0.455744i \(0.150627\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 16.0000i 0.591781i
\(732\) 0 0
\(733\) −17.0000 17.0000i −0.627909 0.627909i 0.319632 0.947542i \(-0.396441\pi\)
−0.947542 + 0.319632i \(0.896441\pi\)
\(734\) 0 0
\(735\) −10.0000 10.0000i −0.368856 0.368856i
\(736\) 0 0
\(737\) 30.0000 1.10506
\(738\) 0 0
\(739\) 7.00000 + 7.00000i 0.257499 + 0.257499i 0.824036 0.566537i \(-0.191717\pi\)
−0.566537 + 0.824036i \(0.691717\pi\)
\(740\) 0 0
\(741\) 30.0000 + 6.00000i 1.10208 + 0.220416i
\(742\) 0 0
\(743\) −13.0000 + 13.0000i −0.476924 + 0.476924i −0.904146 0.427223i \(-0.859492\pi\)
0.427223 + 0.904146i \(0.359492\pi\)
\(744\) 0 0
\(745\) 26.0000i 0.952566i
\(746\) 0 0
\(747\) 7.00000 7.00000i 0.256117 0.256117i
\(748\) 0 0
\(749\) 14.0000 14.0000i 0.511549 0.511549i
\(750\) 0 0
\(751\) 48.0000 1.75154 0.875772 0.482724i \(-0.160353\pi\)
0.875772 + 0.482724i \(0.160353\pi\)
\(752\) 0 0
\(753\) 8.00000i 0.291536i
\(754\) 0 0
\(755\) 18.0000i 0.655087i
\(756\) 0 0
\(757\) −42.0000 −1.52652 −0.763258 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 29.0000 29.0000i 1.05125 1.05125i 0.0526354 0.998614i \(-0.483238\pi\)
0.998614 0.0526354i \(-0.0167621\pi\)
\(762\) 0 0
\(763\) 18.0000i 0.651644i
\(764\) 0 0
\(765\) −4.00000 + 4.00000i −0.144620 + 0.144620i
\(766\) 0 0
\(767\) −35.0000 7.00000i −1.26378 0.252755i
\(768\) 0 0
\(769\) 17.0000 + 17.0000i 0.613036 + 0.613036i 0.943736 0.330700i \(-0.107285\pi\)
−0.330700 + 0.943736i \(0.607285\pi\)
\(770\) 0 0
\(771\) −48.0000 −1.72868
\(772\) 0 0
\(773\) 7.00000 + 7.00000i 0.251773 + 0.251773i 0.821697 0.569925i \(-0.193028\pi\)
−0.569925 + 0.821697i \(0.693028\pi\)
\(774\) 0 0
\(775\) −9.00000 9.00000i −0.323290 0.323290i
\(776\) 0 0
\(777\) 12.0000i 0.430498i
\(778\) 0 0
\(779\) −6.00000 −0.214972
\(780\) 0 0
\(781\) −30.0000 −1.07348
\(782\) 0 0
\(783\) 24.0000i 0.857690i
\(784\) 0 0
\(785\) −2.00000 2.00000i −0.0713831 0.0713831i
\(786\) 0 0
\(787\) 3.00000 + 3.00000i 0.106938 + 0.106938i 0.758552 0.651613i \(-0.225907\pi\)
−0.651613 + 0.758552i \(0.725907\pi\)
\(788\) 0 0
\(789\) −36.0000 −1.28163
\(790\) 0 0
\(791\) −2.00000 2.00000i −0.0711118 0.0711118i
\(792\)