Properties

Label 3240.2.q.w.1081.1
Level $3240$
Weight $2$
Character 3240.1081
Analytic conductor $25.872$
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] = [3240,2,Mod(1081,3240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3240, 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("3240.1081");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.q (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: \(25.8715302549\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1080)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1081.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 3240.1081
Dual form 3240.2.q.w.2161.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +(2.00000 + 3.46410i) q^{7} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(2.00000 + 3.46410i) q^{7} +(-1.00000 - 1.73205i) q^{11} +(-2.00000 + 3.46410i) q^{13} +1.00000 q^{17} -5.00000 q^{19} +(-2.50000 + 4.33013i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-4.00000 - 6.92820i) q^{29} +(-3.50000 + 6.06218i) q^{31} +4.00000 q^{35} -6.00000 q^{37} +(-3.00000 + 5.19615i) q^{41} +(1.00000 + 1.73205i) q^{43} +(-4.00000 - 6.92820i) q^{47} +(-4.50000 + 7.79423i) q^{49} +9.00000 q^{53} -2.00000 q^{55} +(-2.00000 + 3.46410i) q^{59} +(-6.50000 - 11.2583i) q^{61} +(2.00000 + 3.46410i) q^{65} +(5.00000 - 8.66025i) q^{67} -6.00000 q^{71} -6.00000 q^{73} +(4.00000 - 6.92820i) q^{77} +(-4.50000 - 7.79423i) q^{79} +(8.50000 + 14.7224i) q^{83} +(0.500000 - 0.866025i) q^{85} -6.00000 q^{89} -16.0000 q^{91} +(-2.50000 + 4.33013i) q^{95} +(4.00000 + 6.92820i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{5} + 4 q^{7} - 2 q^{11} - 4 q^{13} + 2 q^{17} - 10 q^{19} - 5 q^{23} - q^{25} - 8 q^{29} - 7 q^{31} + 8 q^{35} - 12 q^{37} - 6 q^{41} + 2 q^{43} - 8 q^{47} - 9 q^{49} + 18 q^{53} - 4 q^{55} - 4 q^{59} - 13 q^{61} + 4 q^{65} + 10 q^{67} - 12 q^{71} - 12 q^{73} + 8 q^{77} - 9 q^{79} + 17 q^{83} + q^{85} - 12 q^{89} - 32 q^{91} - 5 q^{95} + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).

\(n\) \(1297\) \(1621\) \(2431\) \(3161\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i \(0.106148\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) −2.00000 + 3.46410i −0.554700 + 0.960769i 0.443227 + 0.896410i \(0.353834\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0 0
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.50000 + 4.33013i −0.521286 + 0.902894i 0.478407 + 0.878138i \(0.341214\pi\)
−0.999694 + 0.0247559i \(0.992119\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.00000 6.92820i −0.742781 1.28654i −0.951224 0.308500i \(-0.900173\pi\)
0.208443 0.978035i \(-0.433160\pi\)
\(30\) 0 0
\(31\) −3.50000 + 6.06218i −0.628619 + 1.08880i 0.359211 + 0.933257i \(0.383046\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 0 0
\(43\) 1.00000 + 1.73205i 0.152499 + 0.264135i 0.932145 0.362084i \(-0.117935\pi\)
−0.779647 + 0.626219i \(0.784601\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(48\) 0 0
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) −6.50000 11.2583i −0.832240 1.44148i −0.896258 0.443533i \(-0.853725\pi\)
0.0640184 0.997949i \(-0.479608\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.00000 + 3.46410i 0.248069 + 0.429669i
\(66\) 0 0
\(67\) 5.00000 8.66025i 0.610847 1.05802i −0.380251 0.924883i \(-0.624162\pi\)
0.991098 0.133135i \(-0.0425044\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.00000 6.92820i 0.455842 0.789542i
\(78\) 0 0
\(79\) −4.50000 7.79423i −0.506290 0.876919i −0.999974 0.00727784i \(-0.997683\pi\)
0.493684 0.869641i \(-0.335650\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.50000 + 14.7224i 0.932996 + 1.61600i 0.778169 + 0.628055i \(0.216149\pi\)
0.154828 + 0.987942i \(0.450518\pi\)
\(84\) 0 0
\(85\) 0.500000 0.866025i 0.0542326 0.0939336i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −16.0000 −1.67726
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.50000 + 4.33013i −0.256495 + 0.444262i
\(96\) 0 0
\(97\) 4.00000 + 6.92820i 0.406138 + 0.703452i 0.994453 0.105180i \(-0.0335417\pi\)
−0.588315 + 0.808632i \(0.700208\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 0 0
\(103\) −2.00000 + 3.46410i −0.197066 + 0.341328i −0.947576 0.319531i \(-0.896475\pi\)
0.750510 + 0.660859i \(0.229808\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 17.0000 1.62830 0.814152 0.580651i \(-0.197202\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i \(-0.924403\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(114\) 0 0
\(115\) 2.50000 + 4.33013i 0.233126 + 0.403786i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.00000 + 3.46410i 0.183340 + 0.317554i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −18.0000 −1.59724 −0.798621 0.601834i \(-0.794437\pi\)
−0.798621 + 0.601834i \(0.794437\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i \(-0.917752\pi\)
0.704692 + 0.709514i \(0.251085\pi\)
\(132\) 0 0
\(133\) −10.0000 17.3205i −0.867110 1.50188i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.50000 9.52628i −0.469897 0.813885i 0.529511 0.848303i \(-0.322376\pi\)
−0.999408 + 0.0344182i \(0.989042\pi\)
\(138\) 0 0
\(139\) −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i \(0.336619\pi\)
−0.999947 + 0.0103230i \(0.996714\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) −8.00000 −0.664364
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.00000 12.1244i 0.573462 0.993266i −0.422744 0.906249i \(-0.638933\pi\)
0.996207 0.0870170i \(-0.0277334\pi\)
\(150\) 0 0
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.50000 + 6.06218i 0.281127 + 0.486926i
\(156\) 0 0
\(157\) −11.0000 + 19.0526i −0.877896 + 1.52056i −0.0242497 + 0.999706i \(0.507720\pi\)
−0.853646 + 0.520854i \(0.825614\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −20.0000 −1.57622
\(162\) 0 0
\(163\) −2.00000 −0.156652 −0.0783260 0.996928i \(-0.524958\pi\)
−0.0783260 + 0.996928i \(0.524958\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.50000 12.9904i 0.580367 1.00523i −0.415068 0.909790i \(-0.636242\pi\)
0.995436 0.0954356i \(-0.0304244\pi\)
\(168\) 0 0
\(169\) −1.50000 2.59808i −0.115385 0.199852i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.50000 6.06218i −0.266100 0.460899i 0.701751 0.712422i \(-0.252402\pi\)
−0.967851 + 0.251523i \(0.919068\pi\)
\(174\) 0 0
\(175\) 2.00000 3.46410i 0.151186 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 16.0000 1.19590 0.597948 0.801535i \(-0.295983\pi\)
0.597948 + 0.801535i \(0.295983\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) −1.00000 1.73205i −0.0731272 0.126660i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 13.0000 + 22.5167i 0.940647 + 1.62925i 0.764241 + 0.644931i \(0.223114\pi\)
0.176406 + 0.984317i \(0.443553\pi\)
\(192\) 0 0
\(193\) −8.00000 + 13.8564i −0.575853 + 0.997406i 0.420096 + 0.907480i \(0.361996\pi\)
−0.995948 + 0.0899262i \(0.971337\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −25.0000 −1.78118 −0.890588 0.454811i \(-0.849707\pi\)
−0.890588 + 0.454811i \(0.849707\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 16.0000 27.7128i 1.12298 1.94506i
\(204\) 0 0
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.00000 + 8.66025i 0.345857 + 0.599042i
\(210\) 0 0
\(211\) −8.50000 + 14.7224i −0.585164 + 1.01353i 0.409691 + 0.912224i \(0.365637\pi\)
−0.994855 + 0.101310i \(0.967697\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.00000 0.136399
\(216\) 0 0
\(217\) −28.0000 −1.90076
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.00000 + 3.46410i −0.134535 + 0.233021i
\(222\) 0 0
\(223\) −1.00000 1.73205i −0.0669650 0.115987i 0.830599 0.556871i \(-0.187998\pi\)
−0.897564 + 0.440884i \(0.854665\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.50000 + 7.79423i 0.298675 + 0.517321i 0.975833 0.218517i \(-0.0701218\pi\)
−0.677158 + 0.735838i \(0.736789\pi\)
\(228\) 0 0
\(229\) −9.50000 + 16.4545i −0.627778 + 1.08734i 0.360219 + 0.932868i \(0.382702\pi\)
−0.987997 + 0.154475i \(0.950631\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3.00000 + 5.19615i −0.194054 + 0.336111i −0.946590 0.322440i \(-0.895497\pi\)
0.752536 + 0.658551i \(0.228830\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.50000 + 7.79423i 0.287494 + 0.497955i
\(246\) 0 0
\(247\) 10.0000 17.3205i 0.636285 1.10208i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 10.0000 0.628695
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 0 0
\(259\) −12.0000 20.7846i −0.745644 1.29149i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 0 0
\(265\) 4.50000 7.79423i 0.276433 0.478796i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −26.0000 −1.58525 −0.792624 0.609711i \(-0.791286\pi\)
−0.792624 + 0.609711i \(0.791286\pi\)
\(270\) 0 0
\(271\) 15.0000 0.911185 0.455593 0.890188i \(-0.349427\pi\)
0.455593 + 0.890188i \(0.349427\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) 0 0
\(277\) 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i \(0.0631696\pi\)
−0.319447 + 0.947604i \(0.603497\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.00000 + 13.8564i 0.477240 + 0.826604i 0.999660 0.0260845i \(-0.00830391\pi\)
−0.522420 + 0.852688i \(0.674971\pi\)
\(282\) 0 0
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.500000 0.866025i 0.0292103 0.0505937i −0.851051 0.525084i \(-0.824034\pi\)
0.880261 + 0.474490i \(0.157367\pi\)
\(294\) 0 0
\(295\) 2.00000 + 3.46410i 0.116445 + 0.201688i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −10.0000 17.3205i −0.578315 1.00167i
\(300\) 0 0
\(301\) −4.00000 + 6.92820i −0.230556 + 0.399335i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −13.0000 −0.744378
\(306\) 0 0
\(307\) 10.0000 0.570730 0.285365 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8.00000 + 13.8564i −0.453638 + 0.785725i −0.998609 0.0527306i \(-0.983208\pi\)
0.544970 + 0.838455i \(0.316541\pi\)
\(312\) 0 0
\(313\) 14.0000 + 24.2487i 0.791327 + 1.37062i 0.925146 + 0.379612i \(0.123943\pi\)
−0.133819 + 0.991006i \(0.542724\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −16.5000 28.5788i −0.926732 1.60515i −0.788751 0.614713i \(-0.789272\pi\)
−0.137981 0.990435i \(-0.544061\pi\)
\(318\) 0 0
\(319\) −8.00000 + 13.8564i −0.447914 + 0.775810i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.00000 −0.278207
\(324\) 0 0
\(325\) 4.00000 0.221880
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 16.0000 27.7128i 0.882109 1.52786i
\(330\) 0 0
\(331\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.00000 8.66025i −0.273179 0.473160i
\(336\) 0 0
\(337\) 10.0000 17.3205i 0.544735 0.943508i −0.453889 0.891058i \(-0.649964\pi\)
0.998624 0.0524499i \(-0.0167030\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 14.0000 0.758143
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10.0000 17.3205i 0.536828 0.929814i −0.462244 0.886753i \(-0.652956\pi\)
0.999072 0.0430610i \(-0.0137110\pi\)
\(348\) 0 0
\(349\) −4.50000 7.79423i −0.240879 0.417215i 0.720086 0.693885i \(-0.244103\pi\)
−0.960965 + 0.276670i \(0.910769\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −17.0000 29.4449i −0.904819 1.56719i −0.821160 0.570697i \(-0.806673\pi\)
−0.0836583 0.996495i \(-0.526660\pi\)
\(354\) 0 0
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 30.0000 1.58334 0.791670 0.610949i \(-0.209212\pi\)
0.791670 + 0.610949i \(0.209212\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.00000 + 5.19615i −0.157027 + 0.271979i
\(366\) 0 0
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 18.0000 + 31.1769i 0.934513 + 1.61862i
\(372\) 0 0
\(373\) 10.0000 17.3205i 0.517780 0.896822i −0.482006 0.876168i \(-0.660092\pi\)
0.999787 0.0206542i \(-0.00657489\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 32.0000 1.64808
\(378\) 0 0
\(379\) 13.0000 0.667765 0.333883 0.942615i \(-0.391641\pi\)
0.333883 + 0.942615i \(0.391641\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −10.5000 + 18.1865i −0.536525 + 0.929288i 0.462563 + 0.886586i \(0.346930\pi\)
−0.999088 + 0.0427020i \(0.986403\pi\)
\(384\) 0 0
\(385\) −4.00000 6.92820i −0.203859 0.353094i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.00000 + 5.19615i 0.152106 + 0.263455i 0.932002 0.362454i \(-0.118061\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(390\) 0 0
\(391\) −2.50000 + 4.33013i −0.126430 + 0.218984i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −9.00000 −0.452839
\(396\) 0 0
\(397\) −32.0000 −1.60603 −0.803017 0.595956i \(-0.796773\pi\)
−0.803017 + 0.595956i \(0.796773\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.0000 + 25.9808i −0.749064 + 1.29742i 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) 0 0
\(403\) −14.0000 24.2487i −0.697390 1.20791i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 + 10.3923i 0.297409 + 0.515127i
\(408\) 0 0
\(409\) 11.5000 19.9186i 0.568638 0.984911i −0.428063 0.903749i \(-0.640804\pi\)
0.996701 0.0811615i \(-0.0258630\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −16.0000 −0.787309
\(414\) 0 0
\(415\) 17.0000 0.834497
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.00000 5.19615i 0.146560 0.253849i −0.783394 0.621525i \(-0.786513\pi\)
0.929954 + 0.367677i \(0.119847\pi\)
\(420\) 0 0
\(421\) −7.50000 12.9904i −0.365528 0.633112i 0.623333 0.781956i \(-0.285778\pi\)
−0.988861 + 0.148844i \(0.952445\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.500000 0.866025i −0.0242536 0.0420084i
\(426\) 0 0
\(427\) 26.0000 45.0333i 1.25823 2.17932i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −20.0000 −0.963366 −0.481683 0.876346i \(-0.659974\pi\)
−0.481683 + 0.876346i \(0.659974\pi\)
\(432\) 0 0
\(433\) 20.0000 0.961139 0.480569 0.876957i \(-0.340430\pi\)
0.480569 + 0.876957i \(0.340430\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 12.5000 21.6506i 0.597956 1.03569i
\(438\) 0 0
\(439\) 2.50000 + 4.33013i 0.119318 + 0.206666i 0.919498 0.393095i \(-0.128596\pi\)
−0.800179 + 0.599761i \(0.795262\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.50000 2.59808i −0.0712672 0.123438i 0.828190 0.560448i \(-0.189371\pi\)
−0.899457 + 0.437009i \(0.856038\pi\)
\(444\) 0 0
\(445\) −3.00000 + 5.19615i −0.142214 + 0.246321i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 12.0000 0.565058
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8.00000 + 13.8564i −0.375046 + 0.649598i
\(456\) 0 0
\(457\) 4.00000 + 6.92820i 0.187112 + 0.324088i 0.944286 0.329125i \(-0.106754\pi\)
−0.757174 + 0.653213i \(0.773421\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.00000 + 5.19615i 0.139724 + 0.242009i 0.927392 0.374091i \(-0.122045\pi\)
−0.787668 + 0.616100i \(0.788712\pi\)
\(462\) 0 0
\(463\) −3.00000 + 5.19615i −0.139422 + 0.241486i −0.927278 0.374374i \(-0.877858\pi\)
0.787856 + 0.615859i \(0.211191\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 31.0000 1.43451 0.717254 0.696811i \(-0.245399\pi\)
0.717254 + 0.696811i \(0.245399\pi\)
\(468\) 0 0
\(469\) 40.0000 1.84703
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.00000 3.46410i 0.0919601 0.159280i
\(474\) 0 0
\(475\) 2.50000 + 4.33013i 0.114708 + 0.198680i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −13.0000 22.5167i −0.593985 1.02881i −0.993689 0.112168i \(-0.964220\pi\)
0.399704 0.916644i \(-0.369113\pi\)
\(480\) 0 0
\(481\) 12.0000 20.7846i 0.547153 0.947697i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.00000 0.363261
\(486\) 0 0
\(487\) 34.0000 1.54069 0.770344 0.637629i \(-0.220085\pi\)
0.770344 + 0.637629i \(0.220085\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −15.0000 + 25.9808i −0.676941 + 1.17250i 0.298957 + 0.954267i \(0.403361\pi\)
−0.975898 + 0.218229i \(0.929972\pi\)
\(492\) 0 0
\(493\) −4.00000 6.92820i −0.180151 0.312031i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −12.0000 20.7846i −0.538274 0.932317i
\(498\) 0 0
\(499\) 0.500000 0.866025i 0.0223831 0.0387686i −0.854617 0.519259i \(-0.826208\pi\)
0.877000 + 0.480490i \(0.159541\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −27.0000 −1.20387 −0.601935 0.798545i \(-0.705603\pi\)
−0.601935 + 0.798545i \(0.705603\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 14.0000 24.2487i 0.620539 1.07481i −0.368846 0.929490i \(-0.620247\pi\)
0.989385 0.145315i \(-0.0464195\pi\)
\(510\) 0 0
\(511\) −12.0000 20.7846i −0.530849 0.919457i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.00000 + 3.46410i 0.0881305 + 0.152647i
\(516\) 0 0
\(517\) −8.00000 + 13.8564i −0.351840 + 0.609404i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 14.0000 0.613351 0.306676 0.951814i \(-0.400783\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(522\) 0 0
\(523\) −8.00000 −0.349816 −0.174908 0.984585i \(-0.555963\pi\)
−0.174908 + 0.984585i \(0.555963\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.50000 + 6.06218i −0.152462 + 0.264073i
\(528\) 0 0
\(529\) −1.00000 1.73205i −0.0434783 0.0753066i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 20.7846i −0.519778 0.900281i
\(534\) 0 0
\(535\) 6.00000 10.3923i 0.259403 0.449299i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 8.50000 14.7224i 0.364100 0.630640i
\(546\) 0 0
\(547\) 5.00000 + 8.66025i 0.213785 + 0.370286i 0.952896 0.303298i \(-0.0980876\pi\)
−0.739111 + 0.673583i \(0.764754\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 20.0000 + 34.6410i 0.852029 + 1.47576i
\(552\) 0 0
\(553\) 18.0000 31.1769i 0.765438 1.32578i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.0000 0.932170 0.466085 0.884740i \(-0.345664\pi\)
0.466085 + 0.884740i \(0.345664\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i \(-0.806471\pi\)
0.905088 + 0.425223i \(0.139804\pi\)
\(564\) 0 0
\(565\) 3.00000 + 5.19615i 0.126211 + 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −14.0000 24.2487i −0.586911 1.01656i −0.994634 0.103454i \(-0.967011\pi\)
0.407724 0.913105i \(-0.366323\pi\)
\(570\) 0 0
\(571\) 2.50000 4.33013i 0.104622 0.181210i −0.808962 0.587861i \(-0.799970\pi\)
0.913584 + 0.406651i \(0.133303\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.00000 0.208514
\(576\) 0 0
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −34.0000 + 58.8897i −1.41056 + 2.44316i
\(582\) 0 0
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.5000 28.5788i −0.681028 1.17957i −0.974668 0.223659i \(-0.928200\pi\)
0.293640 0.955916i \(-0.405133\pi\)
\(588\) 0 0
\(589\) 17.5000 30.3109i 0.721075 1.24894i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15.0000 0.615976 0.307988 0.951390i \(-0.400344\pi\)
0.307988 + 0.951390i \(0.400344\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −18.0000 + 31.1769i −0.735460 + 1.27385i 0.219061 + 0.975711i \(0.429701\pi\)
−0.954521 + 0.298143i \(0.903633\pi\)
\(600\) 0 0
\(601\) 23.5000 + 40.7032i 0.958585 + 1.66032i 0.725942 + 0.687756i \(0.241404\pi\)
0.232643 + 0.972562i \(0.425263\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.50000 6.06218i −0.142295 0.246463i
\(606\) 0 0
\(607\) −15.0000 + 25.9808i −0.608831 + 1.05453i 0.382602 + 0.923913i \(0.375028\pi\)
−0.991433 + 0.130613i \(0.958305\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 32.0000 1.29458
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 13.5000 23.3827i 0.543490 0.941351i −0.455211 0.890384i \(-0.650436\pi\)
0.998700 0.0509678i \(-0.0162306\pi\)
\(618\) 0 0
\(619\) 14.0000 + 24.2487i 0.562708 + 0.974638i 0.997259 + 0.0739910i \(0.0235736\pi\)
−0.434551 + 0.900647i \(0.643093\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −12.0000 20.7846i −0.480770 0.832718i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 1.00000 0.0398094 0.0199047 0.999802i \(-0.493664\pi\)
0.0199047 + 0.999802i \(0.493664\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.00000 + 15.5885i −0.357154 + 0.618609i
\(636\) 0 0
\(637\) −18.0000 31.1769i −0.713186 1.23527i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 24.0000 + 41.5692i 0.947943 + 1.64189i 0.749749 + 0.661723i \(0.230174\pi\)
0.198194 + 0.980163i \(0.436492\pi\)
\(642\) 0 0
\(643\) −6.00000 + 10.3923i −0.236617 + 0.409832i −0.959741 0.280885i \(-0.909372\pi\)
0.723124 + 0.690718i \(0.242705\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 33.0000 1.29736 0.648682 0.761060i \(-0.275321\pi\)
0.648682 + 0.761060i \(0.275321\pi\)
\(648\) 0 0
\(649\) 8.00000 0.314027
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −12.5000 + 21.6506i −0.489163 + 0.847255i −0.999922 0.0124688i \(-0.996031\pi\)
0.510759 + 0.859724i \(0.329364\pi\)
\(654\) 0 0
\(655\) 3.00000 + 5.19615i 0.117220 + 0.203030i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(660\) 0 0
\(661\) 9.00000 15.5885i 0.350059 0.606321i −0.636200 0.771524i \(-0.719495\pi\)
0.986260 + 0.165203i \(0.0528281\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −20.0000 −0.775567
\(666\) 0 0
\(667\) 40.0000 1.54881
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −13.0000 + 22.5167i −0.501859 + 0.869246i
\(672\) 0 0
\(673\) 18.0000 + 31.1769i 0.693849 + 1.20178i 0.970567 + 0.240831i \(0.0774198\pi\)
−0.276718 + 0.960951i \(0.589247\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 17.0000 + 29.4449i 0.653363 + 1.13166i 0.982301 + 0.187307i \(0.0599758\pi\)
−0.328938 + 0.944351i \(0.606691\pi\)
\(678\) 0 0
\(679\) −16.0000 + 27.7128i −0.614024 + 1.06352i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) 0 0
\(685\) −11.0000 −0.420288
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −18.0000 + 31.1769i −0.685745 + 1.18775i
\(690\) 0 0
\(691\) −8.50000 14.7224i −0.323355 0.560068i 0.657823 0.753173i \(-0.271478\pi\)
−0.981178 + 0.193105i \(0.938144\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.00000 + 10.3923i 0.227593 + 0.394203i
\(696\) 0 0
\(697\) −3.00000 + 5.19615i −0.113633 + 0.196818i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) 30.0000 1.13147
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 24.0000 41.5692i 0.902613 1.56337i
\(708\) 0 0
\(709\) 23.0000 + 39.8372i 0.863783 + 1.49612i 0.868250 + 0.496126i \(0.165245\pi\)
−0.00446726 + 0.999990i \(0.501422\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −17.5000 30.3109i −0.655380 1.13515i
\(714\) 0 0
\(715\) 4.00000 6.92820i 0.149592 0.259100i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −34.0000 −1.26799 −0.633993 0.773339i \(-0.718585\pi\)
−0.633993 + 0.773339i \(0.718585\pi\)
\(720\) 0 0
\(721\) −16.0000 −0.595871
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.00000 + 6.92820i −0.148556 + 0.257307i
\(726\) 0 0
\(727\) 2.00000 + 3.46410i 0.0741759 + 0.128476i 0.900728 0.434384i \(-0.143034\pi\)
−0.826552 + 0.562861i \(0.809701\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.00000 + 1.73205i 0.0369863 + 0.0640622i
\(732\) 0 0
\(733\) −12.0000 + 20.7846i −0.443230 + 0.767697i −0.997927 0.0643554i \(-0.979501\pi\)
0.554697 + 0.832052i \(0.312834\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −20.0000 −0.736709
\(738\) 0 0
\(739\) 9.00000 0.331070 0.165535 0.986204i \(-0.447065\pi\)
0.165535 + 0.986204i \(0.447065\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000 41.5692i 0.880475 1.52503i 0.0296605 0.999560i \(-0.490557\pi\)
0.850814 0.525467i \(-0.176109\pi\)
\(744\) 0 0
\(745\) −7.00000 12.1244i −0.256460 0.444202i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 24.0000 + 41.5692i 0.876941 + 1.51891i
\(750\) 0 0
\(751\) 19.5000 33.7750i 0.711565 1.23247i −0.252704 0.967544i \(-0.581320\pi\)
0.964269 0.264923i \(-0.0853467\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 12.0000 20.7846i 0.435000 0.753442i −0.562296 0.826936i \(-0.690082\pi\)
0.997296 + 0.0734946i \(0.0234152\pi\)
\(762\) 0 0
\(763\) 34.0000 + 58.8897i 1.23088 + 2.13195i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.00000 13.8564i −0.288863 0.500326i
\(768\) 0 0
\(769\) 17.5000 30.3109i 0.631066 1.09304i −0.356268 0.934384i \(-0.615951\pi\)
0.987334 0.158655i \(-0.0507157\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 33.0000 1.18693 0.593464 0.804861i \(-0.297760\pi\)
0.593464 + 0.804861i \(0.297760\pi\)
\(774\) 0 0
\(775\) 7.00000 0.251447
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 15.0000 25.9808i 0.537431 0.930857i
\(780\) 0 0
\(781\) 6.00000 + 10.3923i 0.214697 + 0.371866i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 11.0000 + 19.0526i 0.392607 + 0.680015i
\(786\) 0 0
\(787\) −19.0000 + 32.9090i −0.677277 + 1.17308i 0.298521 + 0.954403i \(0.403507\pi\)
−0.975798 + 0.218675i \(0.929827\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −24.0000 −0.853342
\(792\) 0 0
\(793\) 52.0000 1.84657
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 10.5000 18.1865i 0.371929 0.644200i