Properties

Label 3024.2.r.g.1009.3
Level $3024$
Weight $2$
Character 3024.1009
Analytic conductor $24.147$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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 1009.3
Root \(0.500000 - 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 3024.1009
Dual form 3024.2.r.g.2017.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.590972 - 1.02359i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})\) \(q+(0.590972 - 1.02359i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.85185 + 3.20750i) q^{11} +(-0.500000 + 0.866025i) q^{13} +6.94282 q^{17} -1.94282 q^{19} +(2.80150 - 4.85235i) q^{23} +(1.80150 + 3.12030i) q^{25} +(0.119562 + 0.207087i) q^{29} +(0.830095 - 1.43777i) q^{31} -1.18194 q^{35} -9.54583 q^{37} +(-5.09097 + 8.81782i) q^{41} +(1.11273 + 1.92730i) q^{43} +(-2.91423 - 5.04759i) q^{47} +(-0.500000 + 0.866025i) q^{49} +11.6030 q^{53} +4.37756 q^{55} +(-1.30150 + 2.25427i) q^{59} +(3.80150 + 6.58440i) q^{61} +(0.590972 + 1.02359i) q^{65} +(1.75404 - 3.03809i) q^{67} +8.60301 q^{71} +15.1488 q^{73} +(1.85185 - 3.20750i) q^{77} +(3.68878 + 6.38915i) q^{79} +(3.47141 + 6.01266i) q^{83} +(4.10301 - 7.10662i) q^{85} -2.74720 q^{89} +1.00000 q^{91} +(-1.14815 + 1.98866i) q^{95} +(-3.58414 - 6.20790i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 5 q^{5} - 3 q^{7}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

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

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
\(5\) 0.590972 1.02359i 0.264291 0.457765i −0.703087 0.711104i \(-0.748196\pi\)
0.967378 + 0.253339i \(0.0815289\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.85185 + 3.20750i 0.558353 + 0.967096i 0.997634 + 0.0687465i \(0.0219000\pi\)
−0.439281 + 0.898350i \(0.644767\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.94282 1.68388 0.841941 0.539570i \(-0.181413\pi\)
0.841941 + 0.539570i \(0.181413\pi\)
\(18\) 0 0
\(19\) −1.94282 −0.445713 −0.222857 0.974851i \(-0.571538\pi\)
−0.222857 + 0.974851i \(0.571538\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.80150 4.85235i 0.584154 1.01178i −0.410826 0.911714i \(-0.634760\pi\)
0.994980 0.100071i \(-0.0319070\pi\)
\(24\) 0 0
\(25\) 1.80150 + 3.12030i 0.360301 + 0.624060i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.119562 + 0.207087i 0.0222020 + 0.0384551i 0.876913 0.480649i \(-0.159599\pi\)
−0.854711 + 0.519104i \(0.826266\pi\)
\(30\) 0 0
\(31\) 0.830095 1.43777i 0.149089 0.258231i −0.781802 0.623527i \(-0.785699\pi\)
0.930891 + 0.365297i \(0.119032\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.18194 −0.199785
\(36\) 0 0
\(37\) −9.54583 −1.56932 −0.784662 0.619923i \(-0.787164\pi\)
−0.784662 + 0.619923i \(0.787164\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.09097 + 8.81782i −0.795076 + 1.37711i 0.127715 + 0.991811i \(0.459236\pi\)
−0.922791 + 0.385301i \(0.874097\pi\)
\(42\) 0 0
\(43\) 1.11273 + 1.92730i 0.169689 + 0.293910i 0.938311 0.345794i \(-0.112390\pi\)
−0.768622 + 0.639704i \(0.779057\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.91423 5.04759i −0.425084 0.736267i 0.571344 0.820711i \(-0.306422\pi\)
−0.996428 + 0.0844432i \(0.973089\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11.6030 1.59380 0.796898 0.604114i \(-0.206473\pi\)
0.796898 + 0.604114i \(0.206473\pi\)
\(54\) 0 0
\(55\) 4.37756 0.590270
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.30150 + 2.25427i −0.169442 + 0.293481i −0.938224 0.346029i \(-0.887530\pi\)
0.768782 + 0.639511i \(0.220863\pi\)
\(60\) 0 0
\(61\) 3.80150 + 6.58440i 0.486733 + 0.843046i 0.999884 0.0152524i \(-0.00485519\pi\)
−0.513151 + 0.858298i \(0.671522\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.590972 + 1.02359i 0.0733010 + 0.126961i
\(66\) 0 0
\(67\) 1.75404 3.03809i 0.214290 0.371161i −0.738763 0.673966i \(-0.764590\pi\)
0.953053 + 0.302804i \(0.0979229\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.60301 1.02099 0.510495 0.859881i \(-0.329462\pi\)
0.510495 + 0.859881i \(0.329462\pi\)
\(72\) 0 0
\(73\) 15.1488 1.77304 0.886519 0.462693i \(-0.153117\pi\)
0.886519 + 0.462693i \(0.153117\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.85185 3.20750i 0.211038 0.365528i
\(78\) 0 0
\(79\) 3.68878 + 6.38915i 0.415020 + 0.718836i 0.995431 0.0954881i \(-0.0304412\pi\)
−0.580410 + 0.814324i \(0.697108\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.47141 + 6.01266i 0.381037 + 0.659975i 0.991211 0.132292i \(-0.0422338\pi\)
−0.610174 + 0.792267i \(0.708900\pi\)
\(84\) 0 0
\(85\) 4.10301 7.10662i 0.445034 0.770821i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.74720 −0.291203 −0.145602 0.989343i \(-0.546512\pi\)
−0.145602 + 0.989343i \(0.546512\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.14815 + 1.98866i −0.117798 + 0.204032i
\(96\) 0 0
\(97\) −3.58414 6.20790i −0.363914 0.630317i 0.624687 0.780875i \(-0.285226\pi\)
−0.988601 + 0.150558i \(0.951893\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.39248 11.0721i −0.636075 1.10171i −0.986286 0.165044i \(-0.947223\pi\)
0.350211 0.936671i \(-0.386110\pi\)
\(102\) 0 0
\(103\) −2.19850 + 3.80791i −0.216624 + 0.375204i −0.953774 0.300526i \(-0.902838\pi\)
0.737150 + 0.675730i \(0.236171\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.7278 1.32711 0.663557 0.748126i \(-0.269046\pi\)
0.663557 + 0.748126i \(0.269046\pi\)
\(108\) 0 0
\(109\) 1.26320 0.120993 0.0604963 0.998168i \(-0.480732\pi\)
0.0604963 + 0.998168i \(0.480732\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.08126 10.5330i 0.572076 0.990866i −0.424276 0.905533i \(-0.639471\pi\)
0.996353 0.0853326i \(-0.0271953\pi\)
\(114\) 0 0
\(115\) −3.31122 5.73520i −0.308773 0.534810i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.47141 6.01266i −0.318224 0.551180i
\(120\) 0 0
\(121\) −1.35868 + 2.35331i −0.123517 + 0.213937i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10.1683 0.909478
\(126\) 0 0
\(127\) −1.33981 −0.118889 −0.0594445 0.998232i \(-0.518933\pi\)
−0.0594445 + 0.998232i \(0.518933\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.48345 4.30146i 0.216980 0.375820i −0.736903 0.675998i \(-0.763713\pi\)
0.953883 + 0.300178i \(0.0970461\pi\)
\(132\) 0 0
\(133\) 0.971410 + 1.68253i 0.0842319 + 0.145894i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.16991 3.75839i −0.185387 0.321101i 0.758320 0.651883i \(-0.226021\pi\)
−0.943707 + 0.330782i \(0.892687\pi\)
\(138\) 0 0
\(139\) 1.97141 3.41458i 0.167213 0.289621i −0.770226 0.637771i \(-0.779857\pi\)
0.937439 + 0.348150i \(0.113190\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.70370 −0.309719
\(144\) 0 0
\(145\) 0.282630 0.0234712
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.55555 9.62249i 0.455128 0.788305i −0.543568 0.839365i \(-0.682927\pi\)
0.998696 + 0.0510606i \(0.0162602\pi\)
\(150\) 0 0
\(151\) 6.96169 + 12.0580i 0.566535 + 0.981267i 0.996905 + 0.0786145i \(0.0250496\pi\)
−0.430370 + 0.902652i \(0.641617\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.981125 1.69936i −0.0788059 0.136496i
\(156\) 0 0
\(157\) −0.0285900 + 0.0495193i −0.00228173 + 0.00395207i −0.867164 0.498023i \(-0.834060\pi\)
0.864882 + 0.501975i \(0.167393\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5.60301 −0.441579
\(162\) 0 0
\(163\) 1.50808 0.118122 0.0590610 0.998254i \(-0.481189\pi\)
0.0590610 + 0.998254i \(0.481189\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.34213 12.7169i 0.568151 0.984067i −0.428598 0.903496i \(-0.640992\pi\)
0.996749 0.0805714i \(-0.0256745\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.126398 + 0.218928i 0.00960987 + 0.0166448i 0.870790 0.491655i \(-0.163608\pi\)
−0.861180 + 0.508299i \(0.830274\pi\)
\(174\) 0 0
\(175\) 1.80150 3.12030i 0.136181 0.235872i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.1923 1.06079 0.530393 0.847752i \(-0.322044\pi\)
0.530393 + 0.847752i \(0.322044\pi\)
\(180\) 0 0
\(181\) −1.43147 −0.106400 −0.0532002 0.998584i \(-0.516942\pi\)
−0.0532002 + 0.998584i \(0.516942\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.64132 + 9.77104i −0.414758 + 0.718381i
\(186\) 0 0
\(187\) 12.8571 + 22.2691i 0.940201 + 1.62848i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.53379 13.0489i −0.545126 0.944186i −0.998599 0.0529159i \(-0.983148\pi\)
0.453473 0.891270i \(-0.350185\pi\)
\(192\) 0 0
\(193\) 3.92395 6.79647i 0.282452 0.489221i −0.689536 0.724251i \(-0.742186\pi\)
0.971988 + 0.235030i \(0.0755190\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.69002 −0.476644 −0.238322 0.971186i \(-0.576597\pi\)
−0.238322 + 0.971186i \(0.576597\pi\)
\(198\) 0 0
\(199\) 19.9396 1.41348 0.706739 0.707475i \(-0.250166\pi\)
0.706739 + 0.707475i \(0.250166\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.119562 0.207087i 0.00839158 0.0145346i
\(204\) 0 0
\(205\) 6.01724 + 10.4222i 0.420262 + 0.727916i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3.59781 6.23159i −0.248866 0.431048i
\(210\) 0 0
\(211\) −9.04583 + 15.6678i −0.622741 + 1.07862i 0.366233 + 0.930523i \(0.380647\pi\)
−0.988973 + 0.148095i \(0.952686\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.63036 0.179389
\(216\) 0 0
\(217\) −1.66019 −0.112701
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.47141 + 6.01266i −0.233512 + 0.404455i
\(222\) 0 0
\(223\) −11.3285 19.6215i −0.758610 1.31395i −0.943560 0.331203i \(-0.892546\pi\)
0.184950 0.982748i \(-0.440788\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.64132 + 4.57489i 0.175310 + 0.303646i 0.940269 0.340433i \(-0.110574\pi\)
−0.764958 + 0.644080i \(0.777240\pi\)
\(228\) 0 0
\(229\) −9.66827 + 16.7459i −0.638897 + 1.10660i 0.346778 + 0.937947i \(0.387276\pi\)
−0.985675 + 0.168655i \(0.946058\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 16.9806 1.11243 0.556217 0.831037i \(-0.312252\pi\)
0.556217 + 0.831037i \(0.312252\pi\)
\(234\) 0 0
\(235\) −6.88891 −0.449383
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.44282 + 14.6234i −0.546121 + 0.945909i 0.452415 + 0.891808i \(0.350563\pi\)
−0.998535 + 0.0541011i \(0.982771\pi\)
\(240\) 0 0
\(241\) −13.5728 23.5088i −0.874300 1.51433i −0.857507 0.514473i \(-0.827988\pi\)
−0.0167933 0.999859i \(-0.505346\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.590972 + 1.02359i 0.0377558 + 0.0653950i
\(246\) 0 0
\(247\) 0.971410 1.68253i 0.0618093 0.107057i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −19.0780 −1.20419 −0.602096 0.798424i \(-0.705668\pi\)
−0.602096 + 0.798424i \(0.705668\pi\)
\(252\) 0 0
\(253\) 20.7518 1.30466
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −7.42107 + 12.8537i −0.462913 + 0.801790i −0.999105 0.0423070i \(-0.986529\pi\)
0.536191 + 0.844097i \(0.319863\pi\)
\(258\) 0 0
\(259\) 4.77292 + 8.26693i 0.296575 + 0.513682i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3.87072 + 6.70429i 0.238679 + 0.413404i 0.960335 0.278847i \(-0.0899523\pi\)
−0.721656 + 0.692251i \(0.756619\pi\)
\(264\) 0 0
\(265\) 6.85705 11.8768i 0.421225 0.729584i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.51135 0.0921486 0.0460743 0.998938i \(-0.485329\pi\)
0.0460743 + 0.998938i \(0.485329\pi\)
\(270\) 0 0
\(271\) 21.9806 1.33522 0.667612 0.744509i \(-0.267316\pi\)
0.667612 + 0.744509i \(0.267316\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.67223 + 11.5566i −0.402350 + 0.696892i
\(276\) 0 0
\(277\) 5.41423 + 9.37772i 0.325310 + 0.563453i 0.981575 0.191077i \(-0.0611982\pi\)
−0.656265 + 0.754530i \(0.727865\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.43831 14.6156i −0.503387 0.871892i −0.999992 0.00391559i \(-0.998754\pi\)
0.496605 0.867977i \(-0.334580\pi\)
\(282\) 0 0
\(283\) −7.65856 + 13.2650i −0.455254 + 0.788523i −0.998703 0.0509194i \(-0.983785\pi\)
0.543449 + 0.839442i \(0.317118\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.1819 0.601021
\(288\) 0 0
\(289\) 31.2028 1.83546
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.68482 + 8.11435i −0.273690 + 0.474045i −0.969804 0.243886i \(-0.921578\pi\)
0.696114 + 0.717932i \(0.254911\pi\)
\(294\) 0 0
\(295\) 1.53831 + 2.66442i 0.0895636 + 0.155129i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.80150 + 4.85235i 0.162015 + 0.280619i
\(300\) 0 0
\(301\) 1.11273 1.92730i 0.0641364 0.111088i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.98633 0.514556
\(306\) 0 0
\(307\) −2.71410 −0.154902 −0.0774509 0.996996i \(-0.524678\pi\)
−0.0774509 + 0.996996i \(0.524678\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 6.99028 12.1075i 0.396383 0.686555i −0.596894 0.802320i \(-0.703599\pi\)
0.993277 + 0.115765i \(0.0369320\pi\)
\(312\) 0 0
\(313\) 9.52696 + 16.5012i 0.538495 + 0.932701i 0.998985 + 0.0450364i \(0.0143404\pi\)
−0.460490 + 0.887665i \(0.652326\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.00972 3.48093i −0.112877 0.195508i 0.804052 0.594559i \(-0.202673\pi\)
−0.916929 + 0.399050i \(0.869340\pi\)
\(318\) 0 0
\(319\) −0.442820 + 0.766987i −0.0247932 + 0.0429430i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −13.4887 −0.750529
\(324\) 0 0
\(325\) −3.60301 −0.199859
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.91423 + 5.04759i −0.160667 + 0.278283i
\(330\) 0 0
\(331\) −6.18878 10.7193i −0.340166 0.589185i 0.644297 0.764775i \(-0.277150\pi\)
−0.984463 + 0.175590i \(0.943817\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2.07318 3.59085i −0.113270 0.196189i
\(336\) 0 0
\(337\) −6.12997 + 10.6174i −0.333920 + 0.578367i −0.983277 0.182117i \(-0.941705\pi\)
0.649356 + 0.760484i \(0.275038\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.14884 0.332978
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.32489 + 5.75888i −0.178490 + 0.309153i −0.941363 0.337394i \(-0.890454\pi\)
0.762874 + 0.646547i \(0.223788\pi\)
\(348\) 0 0
\(349\) −5.71737 9.90278i −0.306044 0.530083i 0.671449 0.741050i \(-0.265672\pi\)
−0.977493 + 0.210967i \(0.932339\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −11.0978 19.2220i −0.590677 1.02308i −0.994141 0.108087i \(-0.965528\pi\)
0.403465 0.914995i \(-0.367806\pi\)
\(354\) 0 0
\(355\) 5.08414 8.80598i 0.269838 0.467373i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.55623 −0.398803 −0.199401 0.979918i \(-0.563900\pi\)
−0.199401 + 0.979918i \(0.563900\pi\)
\(360\) 0 0
\(361\) −15.2255 −0.801339
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 8.95254 15.5062i 0.468597 0.811634i
\(366\) 0 0
\(367\) −9.26157 16.0415i −0.483450 0.837360i 0.516370 0.856366i \(-0.327283\pi\)
−0.999819 + 0.0190063i \(0.993950\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.80150 10.0485i −0.301199 0.521692i
\(372\) 0 0
\(373\) −7.83009 + 13.5621i −0.405427 + 0.702220i −0.994371 0.105954i \(-0.966210\pi\)
0.588944 + 0.808174i \(0.299544\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.239123 −0.0123155
\(378\) 0 0
\(379\) −4.03775 −0.207405 −0.103703 0.994608i \(-0.533069\pi\)
−0.103703 + 0.994608i \(0.533069\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −0.112725 + 0.195246i −0.00575998 + 0.00997659i −0.868891 0.495003i \(-0.835167\pi\)
0.863131 + 0.504980i \(0.168500\pi\)
\(384\) 0 0
\(385\) −2.18878 3.79108i −0.111551 0.193211i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12.6316 + 21.8786i 0.640448 + 1.10929i 0.985333 + 0.170643i \(0.0545844\pi\)
−0.344885 + 0.938645i \(0.612082\pi\)
\(390\) 0 0
\(391\) 19.4503 33.6890i 0.983646 1.70373i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.71986 0.438744
\(396\) 0 0
\(397\) −20.3009 −1.01888 −0.509438 0.860508i \(-0.670147\pi\)
−0.509438 + 0.860508i \(0.670147\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −7.61273 + 13.1856i −0.380161 + 0.658459i −0.991085 0.133231i \(-0.957465\pi\)
0.610924 + 0.791689i \(0.290798\pi\)
\(402\) 0 0
\(403\) 0.830095 + 1.43777i 0.0413500 + 0.0716203i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −17.6774 30.6182i −0.876238 1.51769i
\(408\) 0 0
\(409\) −0.828460 + 1.43494i −0.0409647 + 0.0709530i −0.885781 0.464104i \(-0.846376\pi\)
0.844816 + 0.535057i \(0.179710\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.60301 0.128086
\(414\) 0 0
\(415\) 8.20602 0.402818
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −16.6871 + 28.9030i −0.815220 + 1.41200i 0.0939492 + 0.995577i \(0.470051\pi\)
−0.909170 + 0.416426i \(0.863282\pi\)
\(420\) 0 0
\(421\) −9.12025 15.7967i −0.444494 0.769886i 0.553523 0.832834i \(-0.313283\pi\)
−0.998017 + 0.0629481i \(0.979950\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 12.5075 + 21.6637i 0.606704 + 1.05084i
\(426\) 0 0
\(427\) 3.80150 6.58440i 0.183968 0.318641i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 29.2826 1.41049 0.705247 0.708961i \(-0.250836\pi\)
0.705247 + 0.708961i \(0.250836\pi\)
\(432\) 0 0
\(433\) −12.2449 −0.588451 −0.294226 0.955736i \(-0.595062\pi\)
−0.294226 + 0.955736i \(0.595062\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.44282 + 9.42724i −0.260365 + 0.450966i
\(438\) 0 0
\(439\) −2.41586 4.18440i −0.115303 0.199711i 0.802598 0.596520i \(-0.203451\pi\)
−0.917901 + 0.396810i \(0.870117\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −0.622440 1.07810i −0.0295730 0.0512220i 0.850860 0.525392i \(-0.176081\pi\)
−0.880433 + 0.474170i \(0.842748\pi\)
\(444\) 0 0
\(445\) −1.62352 + 2.81202i −0.0769622 + 0.133302i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −8.82846 −0.416641 −0.208320 0.978061i \(-0.566800\pi\)
−0.208320 + 0.978061i \(0.566800\pi\)
\(450\) 0 0
\(451\) −37.7108 −1.77573
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.590972 1.02359i 0.0277052 0.0479868i
\(456\) 0 0
\(457\) 5.25404 + 9.10026i 0.245774 + 0.425692i 0.962349 0.271817i \(-0.0876247\pi\)
−0.716575 + 0.697510i \(0.754291\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.2758 + 19.5302i 0.525166 + 0.909614i 0.999570 + 0.0293073i \(0.00933013\pi\)
−0.474404 + 0.880307i \(0.657337\pi\)
\(462\) 0 0
\(463\) 5.19850 9.00406i 0.241595 0.418454i −0.719574 0.694416i \(-0.755663\pi\)
0.961169 + 0.275962i \(0.0889963\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13.3171 0.616242 0.308121 0.951347i \(-0.400300\pi\)
0.308121 + 0.951347i \(0.400300\pi\)
\(468\) 0 0
\(469\) −3.50808 −0.161988
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.12120 + 7.13812i −0.189493 + 0.328211i
\(474\) 0 0
\(475\) −3.50000 6.06218i −0.160591 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.26771 12.5880i −0.332070 0.575163i 0.650847 0.759209i \(-0.274414\pi\)
−0.982918 + 0.184046i \(0.941080\pi\)
\(480\) 0 0
\(481\) 4.77292 8.26693i 0.217626 0.376940i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.47249 −0.384716
\(486\) 0 0
\(487\) −13.0539 −0.591529 −0.295765 0.955261i \(-0.595574\pi\)
−0.295765 + 0.955261i \(0.595574\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −9.67223 + 16.7528i −0.436502 + 0.756043i −0.997417 0.0718303i \(-0.977116\pi\)
0.560915 + 0.827873i \(0.310449\pi\)
\(492\) 0 0
\(493\) 0.830095 + 1.43777i 0.0373856 + 0.0647538i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.30150 7.45043i −0.192949 0.334197i
\(498\) 0 0
\(499\) −18.1111 + 31.3693i −0.810764 + 1.40428i 0.101566 + 0.994829i \(0.467615\pi\)
−0.912330 + 0.409455i \(0.865719\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 15.6764 0.698974 0.349487 0.936941i \(-0.386356\pi\)
0.349487 + 0.936941i \(0.386356\pi\)
\(504\) 0 0
\(505\) −15.1111 −0.672435
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 17.1517 29.7076i 0.760237 1.31677i −0.182492 0.983207i \(-0.558416\pi\)
0.942729 0.333561i \(-0.108250\pi\)
\(510\) 0 0
\(511\) −7.57442 13.1193i −0.335073 0.580363i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.59850 + 4.50073i 0.114503 + 0.198326i
\(516\) 0 0
\(517\) 10.7934 18.6948i 0.474694 0.822195i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 10.2449 0.448836 0.224418 0.974493i \(-0.427952\pi\)
0.224418 + 0.974493i \(0.427952\pi\)
\(522\) 0 0
\(523\) −30.6030 −1.33818 −0.669088 0.743183i \(-0.733315\pi\)
−0.669088 + 0.743183i \(0.733315\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.76320 9.98215i 0.251049 0.434829i
\(528\) 0 0
\(529\) −4.19686 7.26918i −0.182472 0.316051i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5.09097 8.81782i −0.220514 0.381942i
\(534\) 0 0
\(535\) 8.11273 14.0517i 0.350744 0.607506i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3.70370 −0.159530
\(540\) 0 0
\(541\) −26.0917 −1.12177 −0.560884 0.827894i \(-0.689539\pi\)
−0.560884 + 0.827894i \(0.689539\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.746515 1.29300i 0.0319772 0.0553861i
\(546\) 0 0
\(547\) −5.46169 9.45993i −0.233525 0.404478i 0.725318 0.688414i \(-0.241693\pi\)
−0.958843 + 0.283937i \(0.908359\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.232287 0.402332i −0.00989575 0.0171399i
\(552\) 0 0
\(553\) 3.68878 6.38915i 0.156863 0.271694i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 13.9442 0.590835 0.295417 0.955368i \(-0.404541\pi\)
0.295417 + 0.955368i \(0.404541\pi\)
\(558\) 0 0
\(559\) −2.22545 −0.0941265
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −15.1287 + 26.2037i −0.637600 + 1.10435i 0.348358 + 0.937361i \(0.386739\pi\)
−0.985958 + 0.166993i \(0.946594\pi\)
\(564\) 0 0
\(565\) −7.18770 12.4495i −0.302389 0.523753i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.5676 18.3036i −0.443016 0.767326i 0.554896 0.831920i \(-0.312758\pi\)
−0.997912 + 0.0645936i \(0.979425\pi\)
\(570\) 0 0
\(571\) −16.3932 + 28.3938i −0.686033 + 1.18824i 0.287078 + 0.957907i \(0.407316\pi\)
−0.973111 + 0.230336i \(0.926017\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 20.1877 0.841885
\(576\) 0 0
\(577\) −17.3743 −0.723301 −0.361651 0.932314i \(-0.617787\pi\)
−0.361651 + 0.932314i \(0.617787\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.47141 6.01266i 0.144018 0.249447i
\(582\) 0 0
\(583\) 21.4870 + 37.2166i 0.889901 + 1.54135i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8.48796 14.7016i −0.350336 0.606799i 0.635973 0.771712i \(-0.280599\pi\)
−0.986308 + 0.164913i \(0.947266\pi\)
\(588\) 0 0
\(589\) −1.61273 + 2.79332i −0.0664512 + 0.115097i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 13.0733 0.536858 0.268429 0.963300i \(-0.413496\pi\)
0.268429 + 0.963300i \(0.413496\pi\)
\(594\) 0 0
\(595\) −8.20602 −0.336414
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −14.6030 + 25.2932i −0.596663 + 1.03345i 0.396647 + 0.917971i \(0.370174\pi\)
−0.993310 + 0.115479i \(0.963160\pi\)
\(600\) 0 0
\(601\) −3.89536 6.74695i −0.158895 0.275214i 0.775576 0.631255i \(-0.217460\pi\)
−0.934470 + 0.356041i \(0.884126\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.60589 + 2.78148i 0.0652887 + 0.113083i
\(606\) 0 0
\(607\) −9.82038 + 17.0094i −0.398597 + 0.690390i −0.993553 0.113368i \(-0.963836\pi\)
0.594956 + 0.803758i \(0.297169\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.82846 0.235794
\(612\) 0 0
\(613\) 23.5653 0.951792 0.475896 0.879502i \(-0.342124\pi\)
0.475896 + 0.879502i \(0.342124\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.33009 + 9.23200i −0.214582 + 0.371666i −0.953143 0.302520i \(-0.902172\pi\)
0.738562 + 0.674186i \(0.235505\pi\)
\(618\) 0 0
\(619\) −9.00752 15.6015i −0.362043 0.627077i 0.626254 0.779619i \(-0.284587\pi\)
−0.988297 + 0.152542i \(0.951254\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.37360 + 2.37915i 0.0550322 + 0.0953186i
\(624\) 0 0
\(625\) −2.99837 + 5.19332i −0.119935 + 0.207733i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −66.2750 −2.64256
\(630\) 0 0
\(631\) −12.4703 −0.496436 −0.248218 0.968704i \(-0.579845\pi\)
−0.248218 + 0.968704i \(0.579845\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.791790 + 1.37142i −0.0314212 + 0.0544232i
\(636\) 0 0
\(637\) −0.500000 0.866025i −0.0198107 0.0343132i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 9.57279 + 16.5806i 0.378102 + 0.654892i 0.990786 0.135436i \(-0.0432434\pi\)
−0.612684 + 0.790328i \(0.709910\pi\)
\(642\) 0 0
\(643\) 3.24433 5.61934i 0.127944 0.221605i −0.794936 0.606693i \(-0.792496\pi\)
0.922880 + 0.385088i \(0.125829\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −48.0988 −1.89096 −0.945479 0.325682i \(-0.894406\pi\)
−0.945479 + 0.325682i \(0.894406\pi\)
\(648\) 0 0
\(649\) −9.64076 −0.378433
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −21.6202 + 37.4474i −0.846066 + 1.46543i 0.0386267 + 0.999254i \(0.487702\pi\)
−0.884692 + 0.466175i \(0.845632\pi\)
\(654\) 0 0
\(655\) −2.93530 5.08408i −0.114691 0.198651i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.25404 + 2.17206i 0.0488505 + 0.0846115i 0.889417 0.457097i \(-0.151111\pi\)
−0.840566 + 0.541709i \(0.817778\pi\)
\(660\) 0 0
\(661\) 21.1677 36.6636i 0.823329 1.42605i −0.0798613 0.996806i \(-0.525448\pi\)
0.903190 0.429241i \(-0.141219\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.29630 0.0890468
\(666\) 0 0
\(667\) 1.33981 0.0518777
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −14.0796 + 24.3866i −0.543538 + 0.941435i
\(672\) 0 0
\(673\) −6.70765 11.6180i −0.258561 0.447841i 0.707296 0.706918i \(-0.249915\pi\)
−0.965857 + 0.259077i \(0.916582\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0.981125 + 1.69936i 0.0377077 + 0.0653117i 0.884263 0.466989i \(-0.154661\pi\)
−0.846556 + 0.532300i \(0.821328\pi\)
\(678\) 0 0
\(679\) −3.58414 + 6.20790i −0.137546 + 0.238237i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 27.1672 1.03952 0.519761 0.854312i \(-0.326021\pi\)
0.519761 + 0.854312i \(0.326021\pi\)
\(684\) 0 0
\(685\) −5.12941 −0.195985
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5.80150 + 10.0485i −0.221020 + 0.382817i
\(690\) 0 0
\(691\) −25.1586 43.5759i −0.957077 1.65771i −0.729543 0.683935i \(-0.760267\pi\)
−0.227534 0.973770i \(-0.573066\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.33009 4.03584i −0.0883855 0.153088i
\(696\) 0 0
\(697\) −35.3457 + 61.2205i −1.33881 + 2.31889i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −45.1672 −1.70594 −0.852970 0.521960i \(-0.825201\pi\)
−0.852970 + 0.521960i \(0.825201\pi\)
\(702\) 0 0
\(703\) 18.5458 0.699469
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.39248 + 11.0721i −0.240414 + 0.416409i
\(708\) 0 0
\(709\) −19.8090 34.3102i −0.743944 1.28855i −0.950687 0.310153i \(-0.899620\pi\)
0.206743 0.978395i \(-0.433714\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.65103 8.05582i −0.174182 0.301693i
\(714\) 0 0
\(715\) −2.18878 + 3.79108i −0.0818557 + 0.141778i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −22.0377 −0.821869 −0.410935 0.911665i \(-0.634798\pi\)
−0.410935 + 0.911665i \(0.634798\pi\)
\(720\) 0 0
\(721\) 4.39699 0.163752
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.430782 + 0.746136i −0.0159988 + 0.0277108i
\(726\) 0 0
\(727\) 14.0555 + 24.3449i 0.521291 + 0.902903i 0.999693 + 0.0247621i \(0.00788284\pi\)
−0.478402 + 0.878141i \(0.658784\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 7.72545 + 13.3809i 0.285736 + 0.494909i
\(732\) 0 0
\(733\) −5.93474 + 10.2793i −0.219205 + 0.379674i −0.954565 0.298003i \(-0.903680\pi\)
0.735360 + 0.677676i \(0.237013\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12.9929 0.478598
\(738\) 0 0
\(739\) 12.1844 0.448212 0.224106 0.974565i \(-0.428054\pi\)
0.224106 + 0.974565i \(0.428054\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 22.2427 38.5255i 0.816005 1.41336i −0.0925987 0.995704i \(-0.529517\pi\)
0.908604 0.417659i \(-0.137149\pi\)
\(744\) 0 0
\(745\) −6.56634 11.3732i −0.240572 0.416683i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6.86389 11.8886i −0.250801 0.434400i
\(750\) 0 0
\(751\) 21.4029 37.0709i 0.781002 1.35274i −0.150356 0.988632i \(-0.548042\pi\)
0.931358 0.364104i \(-0.118625\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.4567 0.598919
\(756\) 0 0
\(757\) −22.4919 −0.817483 −0.408741 0.912650i \(-0.634032\pi\)
−0.408741 + 0.912650i \(0.634032\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −7.16827 + 12.4158i −0.259850 + 0.450073i −0.966201 0.257788i \(-0.917006\pi\)
0.706352 + 0.707861i \(0.250340\pi\)
\(762\) 0 0
\(763\) −0.631600 1.09396i −0.0228655 0.0396041i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.30150 2.25427i −0.0469946 0.0813971i
\(768\) 0 0
\(769\) 15.6105 27.0382i 0.562930 0.975024i −0.434309 0.900764i \(-0.643007\pi\)
0.997239 0.0742597i \(-0.0236594\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −4.38005 −0.157539 −0.0787697 0.996893i \(-0.525099\pi\)
−0.0787697 + 0.996893i \(0.525099\pi\)
\(774\) 0 0
\(775\) 5.98168 0.214868
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 9.89084 17.1314i 0.354376 0.613798i
\(780\) 0 0
\(781\) 15.9315 + 27.5941i 0.570073 + 0.987395i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.0337917 + 0.0585290i 0.00120608 + 0.00208899i
\(786\) 0 0
\(787\) 13.8107 23.9208i 0.492297 0.852683i −0.507664 0.861555i \(-0.669491\pi\)
0.999961 + 0.00887191i \(0.00282405\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12.1625 −0.432449
\(792\) 0 0
\(793\) −7.60301 −0.269991
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\)