Properties

Label 3024.2.r.g.2017.2
Level $3024$
Weight $2$
Character 3024.2017
Analytic conductor $24.147$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3024,2,Mod(1009,3024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.1009");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.r (of order \(3\), 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: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2017.2
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2017
Dual form 3024.2.r.g.1009.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.29679 - 2.24611i) q^{5} +(-0.500000 + 0.866025i) q^{7} +O(q^{10})\) \(q+(-1.29679 - 2.24611i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.25729 + 3.90975i) q^{11} +(-0.500000 - 0.866025i) q^{13} +0.945916 q^{17} +4.05408 q^{19} +(0.136673 + 0.236725i) q^{23} +(-0.863327 + 1.49533i) q^{25} +(1.23025 - 2.13086i) q^{29} +(1.16372 + 2.01561i) q^{31} +2.59358 q^{35} +1.78074 q^{37} +(-3.20321 - 5.54812i) q^{41} +(-5.21780 + 9.03749i) q^{43} +(6.08113 - 10.5328i) q^{47} +(-0.500000 - 0.866025i) q^{49} +6.27335 q^{53} +11.7089 q^{55} +(1.36333 + 2.36135i) q^{59} +(1.13667 - 1.96878i) q^{61} +(-1.29679 + 2.24611i) q^{65} +(-7.90856 - 13.6980i) q^{67} +3.27335 q^{71} -1.50739 q^{73} +(-2.25729 - 3.90975i) q^{77} +(7.35447 - 12.7383i) q^{79} +(0.472958 - 0.819187i) q^{83} +(-1.22665 - 2.12463i) q^{85} +14.3566 q^{89} +1.00000 q^{91} +(-5.25729 - 9.10590i) q^{95} +(5.74484 - 9.95036i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 5 q^{5} - 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 5 q^{5} - 3 q^{7} + 2 q^{11} - 3 q^{13} + 24 q^{17} + 6 q^{19} - 6 q^{25} + q^{29} - 3 q^{31} + 10 q^{35} - 6 q^{37} - 22 q^{41} - 3 q^{43} + 9 q^{47} - 3 q^{49} + 36 q^{53} + 12 q^{55} + 9 q^{59} + 6 q^{61} - 5 q^{65} + 18 q^{71} + 6 q^{73} + 2 q^{77} + 15 q^{79} + 12 q^{83} - 9 q^{85} + 4 q^{89} + 6 q^{91} - 16 q^{95} - 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.29679 2.24611i −0.579942 1.00449i −0.995485 0.0949156i \(-0.969742\pi\)
0.415543 0.909573i \(-0.363591\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.25729 + 3.90975i −0.680600 + 1.17883i 0.294198 + 0.955744i \(0.404947\pi\)
−0.974798 + 0.223089i \(0.928386\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.945916 0.229418 0.114709 0.993399i \(-0.463406\pi\)
0.114709 + 0.993399i \(0.463406\pi\)
\(18\) 0 0
\(19\) 4.05408 0.930071 0.465035 0.885292i \(-0.346042\pi\)
0.465035 + 0.885292i \(0.346042\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.136673 + 0.236725i 0.0284983 + 0.0493605i 0.879923 0.475117i \(-0.157594\pi\)
−0.851425 + 0.524477i \(0.824261\pi\)
\(24\) 0 0
\(25\) −0.863327 + 1.49533i −0.172665 + 0.299065i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.23025 2.13086i 0.228452 0.395691i −0.728897 0.684623i \(-0.759967\pi\)
0.957350 + 0.288932i \(0.0933002\pi\)
\(30\) 0 0
\(31\) 1.16372 + 2.01561i 0.209009 + 0.362015i 0.951403 0.307949i \(-0.0996427\pi\)
−0.742393 + 0.669964i \(0.766309\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.59358 0.438395
\(36\) 0 0
\(37\) 1.78074 0.292752 0.146376 0.989229i \(-0.453239\pi\)
0.146376 + 0.989229i \(0.453239\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.20321 5.54812i −0.500257 0.866471i −1.00000 0.000297253i \(-0.999905\pi\)
0.499743 0.866174i \(-0.333428\pi\)
\(42\) 0 0
\(43\) −5.21780 + 9.03749i −0.795707 + 1.37820i 0.126682 + 0.991943i \(0.459567\pi\)
−0.922389 + 0.386262i \(0.873766\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.08113 10.5328i 0.887023 1.53637i 0.0436467 0.999047i \(-0.486102\pi\)
0.843377 0.537323i \(-0.180564\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.27335 0.861710 0.430855 0.902421i \(-0.358212\pi\)
0.430855 + 0.902421i \(0.358212\pi\)
\(54\) 0 0
\(55\) 11.7089 1.57883
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.36333 + 2.36135i 0.177490 + 0.307422i 0.941020 0.338350i \(-0.109869\pi\)
−0.763530 + 0.645772i \(0.776536\pi\)
\(60\) 0 0
\(61\) 1.13667 1.96878i 0.145536 0.252076i −0.784037 0.620714i \(-0.786843\pi\)
0.929573 + 0.368639i \(0.120176\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.29679 + 2.24611i −0.160847 + 0.278595i
\(66\) 0 0
\(67\) −7.90856 13.6980i −0.966184 1.67348i −0.706400 0.707813i \(-0.749682\pi\)
−0.259784 0.965667i \(-0.583651\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.27335 0.388475 0.194237 0.980955i \(-0.437777\pi\)
0.194237 + 0.980955i \(0.437777\pi\)
\(72\) 0 0
\(73\) −1.50739 −0.176427 −0.0882134 0.996102i \(-0.528116\pi\)
−0.0882134 + 0.996102i \(0.528116\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.25729 3.90975i −0.257243 0.445557i
\(78\) 0 0
\(79\) 7.35447 12.7383i 0.827443 1.43317i −0.0725952 0.997361i \(-0.523128\pi\)
0.900038 0.435811i \(-0.143539\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.472958 0.819187i 0.0519139 0.0899175i −0.838901 0.544285i \(-0.816801\pi\)
0.890815 + 0.454367i \(0.150135\pi\)
\(84\) 0 0
\(85\) −1.22665 2.12463i −0.133049 0.230448i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.3566 1.52180 0.760899 0.648871i \(-0.224758\pi\)
0.760899 + 0.648871i \(0.224758\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.25729 9.10590i −0.539387 0.934246i
\(96\) 0 0
\(97\) 5.74484 9.95036i 0.583300 1.01031i −0.411785 0.911281i \(-0.635094\pi\)
0.995085 0.0990246i \(-0.0315722\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.83988 + 3.18677i −0.183075 + 0.317096i −0.942926 0.333002i \(-0.891939\pi\)
0.759851 + 0.650097i \(0.225272\pi\)
\(102\) 0 0
\(103\) −4.86333 8.42353i −0.479198 0.829995i 0.520518 0.853851i \(-0.325739\pi\)
−0.999715 + 0.0238560i \(0.992406\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.37432 −0.132860 −0.0664301 0.997791i \(-0.521161\pi\)
−0.0664301 + 0.997791i \(0.521161\pi\)
\(108\) 0 0
\(109\) −3.39922 −0.325587 −0.162793 0.986660i \(-0.552050\pi\)
−0.162793 + 0.986660i \(0.552050\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 5.19436 + 8.99689i 0.488644 + 0.846356i 0.999915 0.0130636i \(-0.00415840\pi\)
−0.511271 + 0.859420i \(0.670825\pi\)
\(114\) 0 0
\(115\) 0.354473 0.613964i 0.0330547 0.0572525i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.472958 + 0.819187i −0.0433560 + 0.0750948i
\(120\) 0 0
\(121\) −4.69076 8.12463i −0.426432 0.738603i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −8.48968 −0.759340
\(126\) 0 0
\(127\) −0.672570 −0.0596809 −0.0298405 0.999555i \(-0.509500\pi\)
−0.0298405 + 0.999555i \(0.509500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.95691 6.85356i −0.345717 0.598799i 0.639767 0.768569i \(-0.279031\pi\)
−0.985484 + 0.169770i \(0.945697\pi\)
\(132\) 0 0
\(133\) −2.02704 + 3.51094i −0.175767 + 0.304437i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.83628 + 3.18054i −0.156884 + 0.271732i −0.933744 0.357943i \(-0.883478\pi\)
0.776859 + 0.629674i \(0.216812\pi\)
\(138\) 0 0
\(139\) −1.02704 1.77889i −0.0871126 0.150883i 0.819177 0.573541i \(-0.194431\pi\)
−0.906289 + 0.422658i \(0.861097\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.51459 0.377529
\(144\) 0 0
\(145\) −6.38151 −0.529956
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.77188 11.7292i −0.554774 0.960897i −0.997921 0.0644482i \(-0.979471\pi\)
0.443147 0.896449i \(-0.353862\pi\)
\(150\) 0 0
\(151\) 4.96410 8.59808i 0.403973 0.699702i −0.590228 0.807236i \(-0.700962\pi\)
0.994201 + 0.107535i \(0.0342956\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.01819 5.22765i 0.242427 0.419895i
\(156\) 0 0
\(157\) −3.02704 5.24299i −0.241584 0.418436i 0.719581 0.694408i \(-0.244334\pi\)
−0.961166 + 0.275972i \(0.911000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.273346 −0.0215427
\(162\) 0 0
\(163\) −17.8171 −1.39554 −0.697772 0.716320i \(-0.745825\pi\)
−0.697772 + 0.716320i \(0.745825\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.23385 + 7.33325i 0.327625 + 0.567464i 0.982040 0.188672i \(-0.0604183\pi\)
−0.654415 + 0.756136i \(0.727085\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 8.67830 15.0313i 0.659799 1.14281i −0.320868 0.947124i \(-0.603975\pi\)
0.980667 0.195682i \(-0.0626920\pi\)
\(174\) 0 0
\(175\) −0.863327 1.49533i −0.0652614 0.113036i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −11.3494 −0.848295 −0.424147 0.905593i \(-0.639426\pi\)
−0.424147 + 0.905593i \(0.639426\pi\)
\(180\) 0 0
\(181\) 21.8889 1.62699 0.813495 0.581572i \(-0.197562\pi\)
0.813495 + 0.581572i \(0.197562\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.30924 3.99973i −0.169779 0.294066i
\(186\) 0 0
\(187\) −2.13521 + 3.69829i −0.156142 + 0.270446i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.350874 0.607731i 0.0253883 0.0439739i −0.853052 0.521826i \(-0.825251\pi\)
0.878440 + 0.477852i \(0.158584\pi\)
\(192\) 0 0
\(193\) −6.07227 10.5175i −0.437092 0.757065i 0.560372 0.828241i \(-0.310658\pi\)
−0.997464 + 0.0711760i \(0.977325\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.4107 1.16921 0.584607 0.811317i \(-0.301249\pi\)
0.584607 + 0.811317i \(0.301249\pi\)
\(198\) 0 0
\(199\) −22.7060 −1.60959 −0.804794 0.593555i \(-0.797724\pi\)
−0.804794 + 0.593555i \(0.797724\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.23025 + 2.13086i 0.0863468 + 0.149557i
\(204\) 0 0
\(205\) −8.30778 + 14.3895i −0.580241 + 1.00501i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −9.15126 + 15.8505i −0.633006 + 1.09640i
\(210\) 0 0
\(211\) 2.28074 + 3.95035i 0.157012 + 0.271954i 0.933790 0.357822i \(-0.116480\pi\)
−0.776778 + 0.629775i \(0.783147\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 27.0656 1.84586
\(216\) 0 0
\(217\) −2.32743 −0.157996
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.472958 0.819187i −0.0318146 0.0551045i
\(222\) 0 0
\(223\) 6.66225 11.5394i 0.446137 0.772733i −0.551993 0.833849i \(-0.686133\pi\)
0.998131 + 0.0611159i \(0.0194659\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.690757 + 1.19643i −0.0458472 + 0.0794096i −0.888038 0.459769i \(-0.847932\pi\)
0.842191 + 0.539179i \(0.181265\pi\)
\(228\) 0 0
\(229\) 8.98968 + 15.5706i 0.594055 + 1.02893i 0.993679 + 0.112254i \(0.0358072\pi\)
−0.399625 + 0.916679i \(0.630859\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 18.9823 1.24357 0.621786 0.783187i \(-0.286408\pi\)
0.621786 + 0.783187i \(0.286408\pi\)
\(234\) 0 0
\(235\) −31.5438 −2.05769
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.44592 4.23645i −0.158213 0.274033i 0.776011 0.630719i \(-0.217240\pi\)
−0.934224 + 0.356686i \(0.883907\pi\)
\(240\) 0 0
\(241\) 13.0797 22.6546i 0.842535 1.45931i −0.0452094 0.998978i \(-0.514396\pi\)
0.887745 0.460336i \(-0.152271\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.29679 + 2.24611i −0.0828489 + 0.143498i
\(246\) 0 0
\(247\) −2.02704 3.51094i −0.128978 0.223396i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 18.4576 1.16503 0.582516 0.812819i \(-0.302068\pi\)
0.582516 + 0.812819i \(0.302068\pi\)
\(252\) 0 0
\(253\) −1.23405 −0.0775838
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.86693 10.1618i −0.365969 0.633876i 0.622962 0.782252i \(-0.285929\pi\)
−0.988931 + 0.148375i \(0.952596\pi\)
\(258\) 0 0
\(259\) −0.890369 + 1.54216i −0.0553248 + 0.0958254i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3.76089 6.51406i 0.231907 0.401674i −0.726463 0.687206i \(-0.758837\pi\)
0.958369 + 0.285532i \(0.0921703\pi\)
\(264\) 0 0
\(265\) −8.13521 14.0906i −0.499742 0.865579i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 18.8348 1.14838 0.574190 0.818722i \(-0.305317\pi\)
0.574190 + 0.818722i \(0.305317\pi\)
\(270\) 0 0
\(271\) 23.9823 1.45682 0.728410 0.685141i \(-0.240260\pi\)
0.728410 + 0.685141i \(0.240260\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.89757 6.75078i −0.235032 0.407088i
\(276\) 0 0
\(277\) −3.58113 + 6.20269i −0.215169 + 0.372684i −0.953325 0.301947i \(-0.902364\pi\)
0.738156 + 0.674630i \(0.235697\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7.44085 12.8879i 0.443884 0.768830i −0.554090 0.832457i \(-0.686933\pi\)
0.997974 + 0.0636271i \(0.0202668\pi\)
\(282\) 0 0
\(283\) 9.99854 + 17.3180i 0.594351 + 1.02945i 0.993638 + 0.112621i \(0.0359245\pi\)
−0.399287 + 0.916826i \(0.630742\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.40642 0.378159
\(288\) 0 0
\(289\) −16.1052 −0.947367
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7.53278 + 13.0472i 0.440070 + 0.762223i 0.997694 0.0678705i \(-0.0216205\pi\)
−0.557625 + 0.830093i \(0.688287\pi\)
\(294\) 0 0
\(295\) 3.53590 6.12435i 0.205868 0.356574i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.136673 0.236725i 0.00790401 0.0136901i
\(300\) 0 0
\(301\) −5.21780 9.03749i −0.300749 0.520912i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5.89610 −0.337610
\(306\) 0 0
\(307\) 27.2704 1.55641 0.778203 0.628013i \(-0.216132\pi\)
0.778203 + 0.628013i \(0.216132\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7.99115 + 13.8411i 0.453136 + 0.784855i 0.998579 0.0532931i \(-0.0169718\pi\)
−0.545443 + 0.838148i \(0.683638\pi\)
\(312\) 0 0
\(313\) −5.79893 + 10.0440i −0.327775 + 0.567722i −0.982070 0.188517i \(-0.939632\pi\)
0.654295 + 0.756239i \(0.272965\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.00885 + 1.74739i −0.0566629 + 0.0981430i −0.892965 0.450125i \(-0.851379\pi\)
0.836303 + 0.548268i \(0.184713\pi\)
\(318\) 0 0
\(319\) 5.55408 + 9.61996i 0.310969 + 0.538614i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.83482 0.213375
\(324\) 0 0
\(325\) 1.72665 0.0957775
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.08113 + 10.5328i 0.335263 + 0.580693i
\(330\) 0 0
\(331\) −9.85447 + 17.0684i −0.541651 + 0.938167i 0.457159 + 0.889385i \(0.348867\pi\)
−0.998809 + 0.0487815i \(0.984466\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −20.5115 + 35.5269i −1.12066 + 1.94104i
\(336\) 0 0
\(337\) 14.5256 + 25.1590i 0.791259 + 1.37050i 0.925188 + 0.379509i \(0.123907\pi\)
−0.133929 + 0.990991i \(0.542759\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −10.5074 −0.569007
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −14.5416 25.1868i −0.780636 1.35210i −0.931572 0.363557i \(-0.881562\pi\)
0.150936 0.988544i \(-0.451771\pi\)
\(348\) 0 0
\(349\) −12.3815 + 21.4454i −0.662767 + 1.14795i 0.317118 + 0.948386i \(0.397285\pi\)
−0.979885 + 0.199561i \(0.936049\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −16.6513 + 28.8408i −0.886257 + 1.53504i −0.0419914 + 0.999118i \(0.513370\pi\)
−0.844266 + 0.535925i \(0.819963\pi\)
\(354\) 0 0
\(355\) −4.24484 7.35228i −0.225293 0.390219i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 25.5366 1.34777 0.673884 0.738837i \(-0.264625\pi\)
0.673884 + 0.738837i \(0.264625\pi\)
\(360\) 0 0
\(361\) −2.56440 −0.134968
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.95477 + 3.38576i 0.102317 + 0.177219i
\(366\) 0 0
\(367\) 13.7252 23.7727i 0.716449 1.24093i −0.245949 0.969283i \(-0.579100\pi\)
0.962398 0.271644i \(-0.0875672\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3.13667 + 5.43288i −0.162848 + 0.282061i
\(372\) 0 0
\(373\) −8.16372 14.1400i −0.422701 0.732140i 0.573502 0.819204i \(-0.305585\pi\)
−0.996203 + 0.0870646i \(0.972251\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.46050 −0.126722
\(378\) 0 0
\(379\) −12.0364 −0.618267 −0.309134 0.951019i \(-0.600039\pi\)
−0.309134 + 0.951019i \(0.600039\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6.21780 + 10.7695i 0.317715 + 0.550298i 0.980011 0.198944i \(-0.0637512\pi\)
−0.662296 + 0.749242i \(0.730418\pi\)
\(384\) 0 0
\(385\) −5.85447 + 10.1402i −0.298372 + 0.516795i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10.3004 17.8408i 0.522250 0.904564i −0.477414 0.878678i \(-0.658426\pi\)
0.999665 0.0258860i \(-0.00824070\pi\)
\(390\) 0 0
\(391\) 0.129281 + 0.223922i 0.00653803 + 0.0113242i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −38.1488 −1.91948
\(396\) 0 0
\(397\) −23.6372 −1.18631 −0.593157 0.805087i \(-0.702119\pi\)
−0.593157 + 0.805087i \(0.702119\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.28220 2.22084i −0.0640300 0.110903i 0.832233 0.554426i \(-0.187062\pi\)
−0.896263 + 0.443522i \(0.853729\pi\)
\(402\) 0 0
\(403\) 1.16372 2.01561i 0.0579688 0.100405i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.01965 + 6.96224i −0.199247 + 0.345105i
\(408\) 0 0
\(409\) 17.1623 + 29.7259i 0.848619 + 1.46985i 0.882441 + 0.470423i \(0.155899\pi\)
−0.0338223 + 0.999428i \(0.510768\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.72665 −0.134170
\(414\) 0 0
\(415\) −2.45331 −0.120428
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.02850 3.51347i −0.0990989 0.171644i 0.812213 0.583361i \(-0.198263\pi\)
−0.911312 + 0.411717i \(0.864929\pi\)
\(420\) 0 0
\(421\) 10.5344 18.2462i 0.513417 0.889264i −0.486462 0.873702i \(-0.661713\pi\)
0.999879 0.0155624i \(-0.00495387\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.816635 + 1.41445i −0.0396126 + 0.0686110i
\(426\) 0 0
\(427\) 1.13667 + 1.96878i 0.0550075 + 0.0952757i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 22.6185 1.08949 0.544747 0.838600i \(-0.316626\pi\)
0.544747 + 0.838600i \(0.316626\pi\)
\(432\) 0 0
\(433\) 2.41789 0.116196 0.0580982 0.998311i \(-0.481496\pi\)
0.0580982 + 0.998311i \(0.481496\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.554084 + 0.959702i 0.0265054 + 0.0459088i
\(438\) 0 0
\(439\) −11.7448 + 20.3427i −0.560551 + 0.970902i 0.436898 + 0.899511i \(0.356077\pi\)
−0.997448 + 0.0713911i \(0.977256\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.70895 11.6202i 0.318752 0.552094i −0.661476 0.749966i \(-0.730070\pi\)
0.980228 + 0.197872i \(0.0634031\pi\)
\(444\) 0 0
\(445\) −18.6175 32.2465i −0.882554 1.52863i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9.16225 0.432393 0.216197 0.976350i \(-0.430635\pi\)
0.216197 + 0.976350i \(0.430635\pi\)
\(450\) 0 0
\(451\) 28.9224 1.36190
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.29679 2.24611i −0.0607944 0.105299i
\(456\) 0 0
\(457\) −4.40856 + 7.63584i −0.206224 + 0.357190i −0.950522 0.310658i \(-0.899451\pi\)
0.744298 + 0.667847i \(0.232784\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.82957 + 4.90095i −0.131786 + 0.228260i −0.924365 0.381509i \(-0.875405\pi\)
0.792579 + 0.609769i \(0.208738\pi\)
\(462\) 0 0
\(463\) 7.86333 + 13.6197i 0.365440 + 0.632960i 0.988847 0.148937i \(-0.0475853\pi\)
−0.623407 + 0.781898i \(0.714252\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −21.9971 −1.01790 −0.508952 0.860795i \(-0.669967\pi\)
−0.508952 + 0.860795i \(0.669967\pi\)
\(468\) 0 0
\(469\) 15.8171 0.730366
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −23.5562 40.8006i −1.08312 1.87601i
\(474\) 0 0
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.4875 + 21.6291i −0.570571 + 0.988257i 0.425937 + 0.904753i \(0.359945\pi\)
−0.996507 + 0.0835043i \(0.973389\pi\)
\(480\) 0 0
\(481\) −0.890369 1.54216i −0.0405973 0.0703166i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −29.7994 −1.35312
\(486\) 0 0
\(487\) 17.5979 0.797435 0.398717 0.917074i \(-0.369455\pi\)
0.398717 + 0.917074i \(0.369455\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.89757 11.9469i −0.311283 0.539158i 0.667358 0.744737i \(-0.267425\pi\)
−0.978640 + 0.205580i \(0.934092\pi\)
\(492\) 0 0
\(493\) 1.16372 2.01561i 0.0524111 0.0907787i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.63667 + 2.83480i −0.0734148 + 0.127158i
\(498\) 0 0
\(499\) 6.54377 + 11.3341i 0.292939 + 0.507386i 0.974503 0.224373i \(-0.0720333\pi\)
−0.681564 + 0.731758i \(0.738700\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.3068 −0.994611 −0.497305 0.867576i \(-0.665677\pi\)
−0.497305 + 0.867576i \(0.665677\pi\)
\(504\) 0 0
\(505\) 9.54377 0.424692
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −7.94659 13.7639i −0.352226 0.610074i 0.634413 0.772994i \(-0.281242\pi\)
−0.986639 + 0.162920i \(0.947909\pi\)
\(510\) 0 0
\(511\) 0.753696 1.30544i 0.0333415 0.0577492i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12.6134 + 21.8471i −0.555814 + 0.962698i
\(516\) 0 0
\(517\) 27.4538 + 47.5514i 1.20742 + 2.09131i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4.41789 −0.193551 −0.0967756 0.995306i \(-0.530853\pi\)
−0.0967756 + 0.995306i \(0.530853\pi\)
\(522\) 0 0
\(523\) −25.2733 −1.10513 −0.552563 0.833471i \(-0.686350\pi\)
−0.552563 + 0.833471i \(0.686350\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.10078 + 1.90660i 0.0479506 + 0.0830528i
\(528\) 0 0
\(529\) 11.4626 19.8539i 0.498376 0.863212i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.20321 + 5.54812i −0.138746 + 0.240316i
\(534\) 0 0
\(535\) 1.78220 + 3.08686i 0.0770513 + 0.133457i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.51459 0.194457
\(540\) 0 0
\(541\) −3.43852 −0.147834 −0.0739168 0.997264i \(-0.523550\pi\)
−0.0739168 + 0.997264i \(0.523550\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.40808 + 7.63501i 0.188821 + 0.327048i
\(546\) 0 0
\(547\) −3.46410 + 6.00000i −0.148114 + 0.256542i −0.930531 0.366214i \(-0.880654\pi\)
0.782416 + 0.622756i \(0.213987\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.98755 8.63868i 0.212477 0.368020i
\(552\) 0 0
\(553\) 7.35447 + 12.7383i 0.312744 + 0.541688i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −33.5835 −1.42298 −0.711488 0.702698i \(-0.751979\pi\)
−0.711488 + 0.702698i \(0.751979\pi\)
\(558\) 0 0
\(559\) 10.4356 0.441379
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −21.2396 36.7880i −0.895142 1.55043i −0.833629 0.552325i \(-0.813741\pi\)
−0.0615128 0.998106i \(-0.519593\pi\)
\(564\) 0 0
\(565\) 13.4720 23.3341i 0.566770 0.981675i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.20175 9.00969i 0.218069 0.377706i −0.736149 0.676820i \(-0.763358\pi\)
0.954217 + 0.299114i \(0.0966910\pi\)
\(570\) 0 0
\(571\) 8.92480 + 15.4582i 0.373491 + 0.646906i 0.990100 0.140364i \(-0.0448272\pi\)
−0.616609 + 0.787270i \(0.711494\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.471974 −0.0196827
\(576\) 0 0
\(577\) 11.9430 0.497193 0.248597 0.968607i \(-0.420031\pi\)
0.248597 + 0.968607i \(0.420031\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.472958 + 0.819187i 0.0196216 + 0.0339856i
\(582\) 0 0
\(583\) −14.1608 + 24.5272i −0.586480 + 1.01581i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −11.9299 + 20.6631i −0.492398 + 0.852859i −0.999962 0.00875568i \(-0.997213\pi\)
0.507563 + 0.861614i \(0.330546\pi\)
\(588\) 0 0
\(589\) 4.71780 + 8.17147i 0.194394 + 0.336699i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −19.5801 −0.804060 −0.402030 0.915626i \(-0.631695\pi\)
−0.402030 + 0.915626i \(0.631695\pi\)
\(594\) 0 0
\(595\) 2.45331 0.100576
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9.27335 16.0619i −0.378899 0.656272i 0.612004 0.790855i \(-0.290364\pi\)
−0.990902 + 0.134583i \(0.957030\pi\)
\(600\) 0 0
\(601\) 9.09931 15.7605i 0.371169 0.642883i −0.618577 0.785724i \(-0.712290\pi\)
0.989746 + 0.142841i \(0.0456238\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −12.1659 + 21.0719i −0.494612 + 0.856693i
\(606\) 0 0
\(607\) −11.1549 19.3208i −0.452762 0.784206i 0.545795 0.837919i \(-0.316228\pi\)
−0.998556 + 0.0537125i \(0.982895\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.1623 −0.492032
\(612\) 0 0
\(613\) 10.2370 0.413467 0.206734 0.978397i \(-0.433717\pi\)
0.206734 + 0.978397i \(0.433717\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.66372 9.80984i −0.228013 0.394929i 0.729206 0.684294i \(-0.239889\pi\)
−0.957219 + 0.289364i \(0.906556\pi\)
\(618\) 0 0
\(619\) 4.31663 7.47663i 0.173500 0.300511i −0.766141 0.642672i \(-0.777826\pi\)
0.939641 + 0.342161i \(0.111159\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.17830 + 12.4332i −0.287593 + 0.498125i
\(624\) 0 0
\(625\) 15.3260 + 26.5454i 0.613039 + 1.06181i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.68443 0.0671626
\(630\) 0 0
\(631\) 14.8535 0.591308 0.295654 0.955295i \(-0.404462\pi\)
0.295654 + 0.955295i \(0.404462\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.872181 + 1.51066i 0.0346115 + 0.0599488i
\(636\) 0 0
\(637\) −0.500000 + 0.866025i −0.0198107 + 0.0343132i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −17.0797 + 29.5828i −0.674606 + 1.16845i 0.301978 + 0.953315i \(0.402353\pi\)
−0.976584 + 0.215137i \(0.930980\pi\)
\(642\) 0 0
\(643\) −5.41741 9.38323i −0.213642 0.370039i 0.739210 0.673475i \(-0.235199\pi\)
−0.952852 + 0.303437i \(0.901866\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 32.9692 1.29615 0.648077 0.761575i \(-0.275573\pi\)
0.648077 + 0.761575i \(0.275573\pi\)
\(648\) 0 0
\(649\) −12.3097 −0.483199
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.96557 3.40446i −0.0769185 0.133227i 0.825000 0.565132i \(-0.191175\pi\)
−0.901919 + 0.431905i \(0.857841\pi\)
\(654\) 0 0
\(655\) −10.2626 + 17.7753i −0.400991 + 0.694537i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −8.40856 + 14.5640i −0.327551 + 0.567335i −0.982025 0.188749i \(-0.939557\pi\)
0.654474 + 0.756084i \(0.272890\pi\)
\(660\) 0 0
\(661\) 8.51080 + 14.7411i 0.331032 + 0.573364i 0.982714 0.185128i \(-0.0592700\pi\)
−0.651683 + 0.758492i \(0.725937\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 10.5146 0.407738
\(666\) 0 0
\(667\) 0.672570 0.0260420
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.13161 + 8.88821i 0.198104 + 0.343126i
\(672\) 0 0
\(673\) −14.3727 + 24.8942i −0.554025 + 0.959600i 0.443953 + 0.896050i \(0.353576\pi\)
−0.997979 + 0.0635501i \(0.979758\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.01819 + 5.22765i −0.115998 + 0.200915i −0.918178 0.396167i \(-0.870340\pi\)
0.802180 + 0.597082i \(0.203673\pi\)
\(678\) 0 0
\(679\) 5.74484 + 9.95036i 0.220467 + 0.381860i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 20.5113 0.784842 0.392421 0.919786i \(-0.371638\pi\)
0.392421 + 0.919786i \(0.371638\pi\)
\(684\) 0 0
\(685\) 9.52510 0.363935
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3.13667 5.43288i −0.119498 0.206976i
\(690\) 0 0
\(691\) −7.50146 + 12.9929i −0.285369 + 0.494274i −0.972699 0.232072i \(-0.925450\pi\)
0.687330 + 0.726346i \(0.258783\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.66372 + 4.61369i −0.101040 + 0.175007i
\(696\) 0 0
\(697\) −3.02997 5.24806i −0.114768 0.198784i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −38.5113 −1.45455 −0.727275 0.686346i \(-0.759214\pi\)
−0.727275 + 0.686346i \(0.759214\pi\)
\(702\) 0 0
\(703\) 7.21926 0.272280
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.83988 3.18677i −0.0691959 0.119851i
\(708\) 0 0
\(709\) −3.82004 + 6.61650i −0.143465 + 0.248488i −0.928799 0.370584i \(-0.879158\pi\)
0.785334 + 0.619072i \(0.212491\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.318097 + 0.550960i −0.0119128 + 0.0206336i
\(714\) 0 0
\(715\) −5.85447 10.1402i −0.218945 0.379224i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −30.0364 −1.12017 −0.560084 0.828436i \(-0.689231\pi\)
−0.560084 + 0.828436i \(0.689231\pi\)
\(720\) 0 0
\(721\) 9.72665 0.362240
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.12422 + 3.67926i 0.0788916 + 0.136644i
\(726\) 0 0
\(727\) 1.72812 2.99319i 0.0640923 0.111011i −0.832199 0.554478i \(-0.812918\pi\)
0.896291 + 0.443466i \(0.146251\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.93560 + 8.54871i −0.182550 + 0.316185i
\(732\) 0 0
\(733\) −19.2630 33.3645i −0.711496 1.23235i −0.964295 0.264829i \(-0.914685\pi\)
0.252799 0.967519i \(-0.418649\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 71.4078 2.63034
\(738\) 0 0
\(739\) −45.1239 −1.65991 −0.829955 0.557830i \(-0.811634\pi\)
−0.829955 + 0.557830i \(0.811634\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.74338 8.21577i −0.174018 0.301407i 0.765803 0.643075i \(-0.222342\pi\)
−0.939821 + 0.341668i \(0.889008\pi\)
\(744\) 0 0
\(745\) −17.5634 + 30.4207i −0.643474 + 1.11453i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.687159 1.19019i 0.0251082 0.0434887i
\(750\) 0 0
\(751\) −4.91595 8.51467i −0.179386 0.310705i 0.762285 0.647242i \(-0.224078\pi\)
−0.941670 + 0.336537i \(0.890744\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −25.7496 −0.937124
\(756\) 0 0
\(757\) −41.8171 −1.51987 −0.759934 0.650000i \(-0.774769\pi\)
−0.759934 + 0.650000i \(0.774769\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11.4897 + 19.9007i 0.416501 + 0.721400i 0.995585 0.0938675i \(-0.0299230\pi\)
−0.579084 + 0.815268i \(0.696590\pi\)
\(762\) 0 0
\(763\) 1.69961 2.94381i 0.0615301 0.106573i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.36333 2.36135i 0.0492269 0.0852635i
\(768\) 0 0
\(769\) −3.04329 5.27113i −0.109744 0.190082i 0.805923 0.592021i \(-0.201670\pi\)
−0.915666 + 0.401939i \(0.868336\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 41.8214 1.50421 0.752105 0.659043i \(-0.229038\pi\)
0.752105 + 0.659043i \(0.229038\pi\)
\(774\) 0 0
\(775\) −4.01867 −0.144355
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −12.9861 22.4926i −0.465275 0.805880i
\(780\) 0 0
\(781\) −7.38891 + 12.7980i −0.264396 + 0.457947i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.85087 + 13.5981i −0.280210 + 0.485337i
\(786\) 0 0
\(787\) 16.1460 + 27.9657i 0.575543 + 0.996870i 0.995982 + 0.0895491i \(0.0285426\pi\)
−0.420439 + 0.907321i \(0.638124\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −10.3887 −0.369380
\(792\) 0 0
\(793\) −2.27335 −0.0807289
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\)