Properties

Label 400.3.p.d.193.1
Level $400$
Weight $3$
Character 400.193
Analytic conductor $10.899$
Analytic rank $0$
Dimension $2$
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] = [400,3,Mod(193,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.193");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 400.p (of order \(4\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.8992105744\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 193.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 400.193
Dual form 400.3.p.d.257.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{3} +(-7.00000 + 7.00000i) q^{7} -7.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{3} +(-7.00000 + 7.00000i) q^{7} -7.00000i q^{9} -10.0000 q^{11} +(-9.00000 - 9.00000i) q^{13} +(-1.00000 + 1.00000i) q^{17} -8.00000i q^{19} -14.0000 q^{21} +(-23.0000 - 23.0000i) q^{23} +(16.0000 - 16.0000i) q^{27} +8.00000i q^{29} +14.0000 q^{31} +(-10.0000 - 10.0000i) q^{33} +(-33.0000 + 33.0000i) q^{37} -18.0000i q^{39} -14.0000 q^{41} +(-15.0000 - 15.0000i) q^{43} +(-39.0000 + 39.0000i) q^{47} -49.0000i q^{49} -2.00000 q^{51} +(7.00000 + 7.00000i) q^{53} +(8.00000 - 8.00000i) q^{57} -56.0000i q^{59} +42.0000 q^{61} +(49.0000 + 49.0000i) q^{63} +(-7.00000 + 7.00000i) q^{67} -46.0000i q^{69} -98.0000 q^{71} +(-49.0000 - 49.0000i) q^{73} +(70.0000 - 70.0000i) q^{77} +96.0000i q^{79} -31.0000 q^{81} +(-63.0000 - 63.0000i) q^{83} +(-8.00000 + 8.00000i) q^{87} +112.000i q^{89} +126.000 q^{91} +(14.0000 + 14.0000i) q^{93} +(-33.0000 + 33.0000i) q^{97} +70.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - 14 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} - 14 q^{7} - 20 q^{11} - 18 q^{13} - 2 q^{17} - 28 q^{21} - 46 q^{23} + 32 q^{27} + 28 q^{31} - 20 q^{33} - 66 q^{37} - 28 q^{41} - 30 q^{43} - 78 q^{47} - 4 q^{51} + 14 q^{53} + 16 q^{57} + 84 q^{61} + 98 q^{63} - 14 q^{67} - 196 q^{71} - 98 q^{73} + 140 q^{77} - 62 q^{81} - 126 q^{83} - 16 q^{87} + 252 q^{91} + 28 q^{93} - 66 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) 1.00000 + 1.00000i 0.333333 + 0.333333i 0.853851 0.520518i \(-0.174261\pi\)
−0.520518 + 0.853851i \(0.674261\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −7.00000 + 7.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) 7.00000i 0.777778i
\(10\) 0 0
\(11\) −10.0000 −0.909091 −0.454545 0.890724i \(-0.650198\pi\)
−0.454545 + 0.890724i \(0.650198\pi\)
\(12\) 0 0
\(13\) −9.00000 9.00000i −0.692308 0.692308i 0.270432 0.962739i \(-0.412834\pi\)
−0.962739 + 0.270432i \(0.912834\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.00000 + 1.00000i −0.0588235 + 0.0588235i −0.735907 0.677083i \(-0.763244\pi\)
0.677083 + 0.735907i \(0.263244\pi\)
\(18\) 0 0
\(19\) 8.00000i 0.421053i −0.977588 0.210526i \(-0.932482\pi\)
0.977588 0.210526i \(-0.0675178\pi\)
\(20\) 0 0
\(21\) −14.0000 −0.666667
\(22\) 0 0
\(23\) −23.0000 23.0000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 16.0000 16.0000i 0.592593 0.592593i
\(28\) 0 0
\(29\) 8.00000i 0.275862i 0.990442 + 0.137931i \(0.0440452\pi\)
−0.990442 + 0.137931i \(0.955955\pi\)
\(30\) 0 0
\(31\) 14.0000 0.451613 0.225806 0.974172i \(-0.427498\pi\)
0.225806 + 0.974172i \(0.427498\pi\)
\(32\) 0 0
\(33\) −10.0000 10.0000i −0.303030 0.303030i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −33.0000 + 33.0000i −0.891892 + 0.891892i −0.994701 0.102809i \(-0.967217\pi\)
0.102809 + 0.994701i \(0.467217\pi\)
\(38\) 0 0
\(39\) 18.0000i 0.461538i
\(40\) 0 0
\(41\) −14.0000 −0.341463 −0.170732 0.985318i \(-0.554613\pi\)
−0.170732 + 0.985318i \(0.554613\pi\)
\(42\) 0 0
\(43\) −15.0000 15.0000i −0.348837 0.348837i 0.510839 0.859676i \(-0.329335\pi\)
−0.859676 + 0.510839i \(0.829335\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −39.0000 + 39.0000i −0.829787 + 0.829787i −0.987487 0.157700i \(-0.949592\pi\)
0.157700 + 0.987487i \(0.449592\pi\)
\(48\) 0 0
\(49\) 49.0000i 1.00000i
\(50\) 0 0
\(51\) −2.00000 −0.0392157
\(52\) 0 0
\(53\) 7.00000 + 7.00000i 0.132075 + 0.132075i 0.770054 0.637979i \(-0.220229\pi\)
−0.637979 + 0.770054i \(0.720229\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.00000 8.00000i 0.140351 0.140351i
\(58\) 0 0
\(59\) 56.0000i 0.949153i −0.880214 0.474576i \(-0.842601\pi\)
0.880214 0.474576i \(-0.157399\pi\)
\(60\) 0 0
\(61\) 42.0000 0.688525 0.344262 0.938874i \(-0.388129\pi\)
0.344262 + 0.938874i \(0.388129\pi\)
\(62\) 0 0
\(63\) 49.0000 + 49.0000i 0.777778 + 0.777778i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.00000 + 7.00000i −0.104478 + 0.104478i −0.757413 0.652936i \(-0.773537\pi\)
0.652936 + 0.757413i \(0.273537\pi\)
\(68\) 0 0
\(69\) 46.0000i 0.666667i
\(70\) 0 0
\(71\) −98.0000 −1.38028 −0.690141 0.723675i \(-0.742451\pi\)
−0.690141 + 0.723675i \(0.742451\pi\)
\(72\) 0 0
\(73\) −49.0000 49.0000i −0.671233 0.671233i 0.286767 0.958000i \(-0.407419\pi\)
−0.958000 + 0.286767i \(0.907419\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 70.0000 70.0000i 0.909091 0.909091i
\(78\) 0 0
\(79\) 96.0000i 1.21519i 0.794247 + 0.607595i \(0.207866\pi\)
−0.794247 + 0.607595i \(0.792134\pi\)
\(80\) 0 0
\(81\) −31.0000 −0.382716
\(82\) 0 0
\(83\) −63.0000 63.0000i −0.759036 0.759036i 0.217111 0.976147i \(-0.430337\pi\)
−0.976147 + 0.217111i \(0.930337\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −8.00000 + 8.00000i −0.0919540 + 0.0919540i
\(88\) 0 0
\(89\) 112.000i 1.25843i 0.777233 + 0.629213i \(0.216623\pi\)
−0.777233 + 0.629213i \(0.783377\pi\)
\(90\) 0 0
\(91\) 126.000 1.38462
\(92\) 0 0
\(93\) 14.0000 + 14.0000i 0.150538 + 0.150538i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −33.0000 + 33.0000i −0.340206 + 0.340206i −0.856445 0.516239i \(-0.827332\pi\)
0.516239 + 0.856445i \(0.327332\pi\)
\(98\) 0 0
\(99\) 70.0000i 0.707071i
\(100\) 0 0
\(101\) 26.0000 0.257426 0.128713 0.991682i \(-0.458915\pi\)
0.128713 + 0.991682i \(0.458915\pi\)
\(102\) 0 0
\(103\) 73.0000 + 73.0000i 0.708738 + 0.708738i 0.966270 0.257532i \(-0.0829093\pi\)
−0.257532 + 0.966270i \(0.582909\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 121.000 121.000i 1.13084 1.13084i 0.140804 0.990038i \(-0.455031\pi\)
0.990038 0.140804i \(-0.0449686\pi\)
\(108\) 0 0
\(109\) 136.000i 1.24771i 0.781542 + 0.623853i \(0.214434\pi\)
−0.781542 + 0.623853i \(0.785566\pi\)
\(110\) 0 0
\(111\) −66.0000 −0.594595
\(112\) 0 0
\(113\) 127.000 + 127.000i 1.12389 + 1.12389i 0.991150 + 0.132743i \(0.0423786\pi\)
0.132743 + 0.991150i \(0.457621\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −63.0000 + 63.0000i −0.538462 + 0.538462i
\(118\) 0 0
\(119\) 14.0000i 0.117647i
\(120\) 0 0
\(121\) −21.0000 −0.173554
\(122\) 0 0
\(123\) −14.0000 14.0000i −0.113821 0.113821i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −7.00000 + 7.00000i −0.0551181 + 0.0551181i −0.734129 0.679010i \(-0.762409\pi\)
0.679010 + 0.734129i \(0.262409\pi\)
\(128\) 0 0
\(129\) 30.0000i 0.232558i
\(130\) 0 0
\(131\) 230.000 1.75573 0.877863 0.478913i \(-0.158969\pi\)
0.877863 + 0.478913i \(0.158969\pi\)
\(132\) 0 0
\(133\) 56.0000 + 56.0000i 0.421053 + 0.421053i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 63.0000 63.0000i 0.459854 0.459854i −0.438753 0.898607i \(-0.644580\pi\)
0.898607 + 0.438753i \(0.144580\pi\)
\(138\) 0 0
\(139\) 88.0000i 0.633094i −0.948577 0.316547i \(-0.897477\pi\)
0.948577 0.316547i \(-0.102523\pi\)
\(140\) 0 0
\(141\) −78.0000 −0.553191
\(142\) 0 0
\(143\) 90.0000 + 90.0000i 0.629371 + 0.629371i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 49.0000 49.0000i 0.333333 0.333333i
\(148\) 0 0
\(149\) 168.000i 1.12752i −0.825940 0.563758i \(-0.809355\pi\)
0.825940 0.563758i \(-0.190645\pi\)
\(150\) 0 0
\(151\) −130.000 −0.860927 −0.430464 0.902608i \(-0.641650\pi\)
−0.430464 + 0.902608i \(0.641650\pi\)
\(152\) 0 0
\(153\) 7.00000 + 7.00000i 0.0457516 + 0.0457516i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 63.0000 63.0000i 0.401274 0.401274i −0.477408 0.878682i \(-0.658424\pi\)
0.878682 + 0.477408i \(0.158424\pi\)
\(158\) 0 0
\(159\) 14.0000i 0.0880503i
\(160\) 0 0
\(161\) 322.000 2.00000
\(162\) 0 0
\(163\) 65.0000 + 65.0000i 0.398773 + 0.398773i 0.877800 0.479027i \(-0.159010\pi\)
−0.479027 + 0.877800i \(0.659010\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −103.000 + 103.000i −0.616766 + 0.616766i −0.944701 0.327934i \(-0.893648\pi\)
0.327934 + 0.944701i \(0.393648\pi\)
\(168\) 0 0
\(169\) 7.00000i 0.0414201i
\(170\) 0 0
\(171\) −56.0000 −0.327485
\(172\) 0 0
\(173\) −73.0000 73.0000i −0.421965 0.421965i 0.463915 0.885880i \(-0.346444\pi\)
−0.885880 + 0.463915i \(0.846444\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 56.0000 56.0000i 0.316384 0.316384i
\(178\) 0 0
\(179\) 56.0000i 0.312849i 0.987690 + 0.156425i \(0.0499968\pi\)
−0.987690 + 0.156425i \(0.950003\pi\)
\(180\) 0 0
\(181\) −70.0000 −0.386740 −0.193370 0.981126i \(-0.561942\pi\)
−0.193370 + 0.981126i \(0.561942\pi\)
\(182\) 0 0
\(183\) 42.0000 + 42.0000i 0.229508 + 0.229508i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 10.0000 10.0000i 0.0534759 0.0534759i
\(188\) 0 0
\(189\) 224.000i 1.18519i
\(190\) 0 0
\(191\) 142.000 0.743455 0.371728 0.928342i \(-0.378765\pi\)
0.371728 + 0.928342i \(0.378765\pi\)
\(192\) 0 0
\(193\) 63.0000 + 63.0000i 0.326425 + 0.326425i 0.851225 0.524800i \(-0.175860\pi\)
−0.524800 + 0.851225i \(0.675860\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 63.0000 63.0000i 0.319797 0.319797i −0.528892 0.848689i \(-0.677392\pi\)
0.848689 + 0.528892i \(0.177392\pi\)
\(198\) 0 0
\(199\) 336.000i 1.68844i 0.535995 + 0.844221i \(0.319937\pi\)
−0.535995 + 0.844221i \(0.680063\pi\)
\(200\) 0 0
\(201\) −14.0000 −0.0696517
\(202\) 0 0
\(203\) −56.0000 56.0000i −0.275862 0.275862i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −161.000 + 161.000i −0.777778 + 0.777778i
\(208\) 0 0
\(209\) 80.0000i 0.382775i
\(210\) 0 0
\(211\) −314.000 −1.48815 −0.744076 0.668095i \(-0.767110\pi\)
−0.744076 + 0.668095i \(0.767110\pi\)
\(212\) 0 0
\(213\) −98.0000 98.0000i −0.460094 0.460094i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −98.0000 + 98.0000i −0.451613 + 0.451613i
\(218\) 0 0
\(219\) 98.0000i 0.447489i
\(220\) 0 0
\(221\) 18.0000 0.0814480
\(222\) 0 0
\(223\) −135.000 135.000i −0.605381 0.605381i 0.336354 0.941736i \(-0.390806\pi\)
−0.941736 + 0.336354i \(0.890806\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 281.000 281.000i 1.23789 1.23789i 0.277022 0.960864i \(-0.410653\pi\)
0.960864 0.277022i \(-0.0893474\pi\)
\(228\) 0 0
\(229\) 168.000i 0.733624i −0.930295 0.366812i \(-0.880449\pi\)
0.930295 0.366812i \(-0.119551\pi\)
\(230\) 0 0
\(231\) 140.000 0.606061
\(232\) 0 0
\(233\) −273.000 273.000i −1.17167 1.17167i −0.981811 0.189863i \(-0.939196\pi\)
−0.189863 0.981811i \(-0.560804\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −96.0000 + 96.0000i −0.405063 + 0.405063i
\(238\) 0 0
\(239\) 288.000i 1.20502i −0.798111 0.602510i \(-0.794167\pi\)
0.798111 0.602510i \(-0.205833\pi\)
\(240\) 0 0
\(241\) −446.000 −1.85062 −0.925311 0.379209i \(-0.876196\pi\)
−0.925311 + 0.379209i \(0.876196\pi\)
\(242\) 0 0
\(243\) −175.000 175.000i −0.720165 0.720165i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −72.0000 + 72.0000i −0.291498 + 0.291498i
\(248\) 0 0
\(249\) 126.000i 0.506024i
\(250\) 0 0
\(251\) 150.000 0.597610 0.298805 0.954314i \(-0.403412\pi\)
0.298805 + 0.954314i \(0.403412\pi\)
\(252\) 0 0
\(253\) 230.000 + 230.000i 0.909091 + 0.909091i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −161.000 + 161.000i −0.626459 + 0.626459i −0.947175 0.320716i \(-0.896076\pi\)
0.320716 + 0.947175i \(0.396076\pi\)
\(258\) 0 0
\(259\) 462.000i 1.78378i
\(260\) 0 0
\(261\) 56.0000 0.214559
\(262\) 0 0
\(263\) −151.000 151.000i −0.574144 0.574144i 0.359139 0.933284i \(-0.383070\pi\)
−0.933284 + 0.359139i \(0.883070\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −112.000 + 112.000i −0.419476 + 0.419476i
\(268\) 0 0
\(269\) 376.000i 1.39777i −0.715234 0.698885i \(-0.753680\pi\)
0.715234 0.698885i \(-0.246320\pi\)
\(270\) 0 0
\(271\) −210.000 −0.774908 −0.387454 0.921889i \(-0.626645\pi\)
−0.387454 + 0.921889i \(0.626645\pi\)
\(272\) 0 0
\(273\) 126.000 + 126.000i 0.461538 + 0.461538i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −129.000 + 129.000i −0.465704 + 0.465704i −0.900520 0.434816i \(-0.856814\pi\)
0.434816 + 0.900520i \(0.356814\pi\)
\(278\) 0 0
\(279\) 98.0000i 0.351254i
\(280\) 0 0
\(281\) −174.000 −0.619217 −0.309609 0.950864i \(-0.600198\pi\)
−0.309609 + 0.950864i \(0.600198\pi\)
\(282\) 0 0
\(283\) 113.000 + 113.000i 0.399293 + 0.399293i 0.877984 0.478690i \(-0.158888\pi\)
−0.478690 + 0.877984i \(0.658888\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 98.0000 98.0000i 0.341463 0.341463i
\(288\) 0 0
\(289\) 287.000i 0.993080i
\(290\) 0 0
\(291\) −66.0000 −0.226804
\(292\) 0 0
\(293\) −345.000 345.000i −1.17747 1.17747i −0.980386 0.197089i \(-0.936851\pi\)
−0.197089 0.980386i \(-0.563149\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −160.000 + 160.000i −0.538721 + 0.538721i
\(298\) 0 0
\(299\) 414.000i 1.38462i
\(300\) 0 0
\(301\) 210.000 0.697674
\(302\) 0 0
\(303\) 26.0000 + 26.0000i 0.0858086 + 0.0858086i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −327.000 + 327.000i −1.06515 + 1.06515i −0.0674220 + 0.997725i \(0.521477\pi\)
−0.997725 + 0.0674220i \(0.978523\pi\)
\(308\) 0 0
\(309\) 146.000i 0.472492i
\(310\) 0 0
\(311\) −2.00000 −0.00643087 −0.00321543 0.999995i \(-0.501024\pi\)
−0.00321543 + 0.999995i \(0.501024\pi\)
\(312\) 0 0
\(313\) −81.0000 81.0000i −0.258786 0.258786i 0.565774 0.824560i \(-0.308577\pi\)
−0.824560 + 0.565774i \(0.808577\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 159.000 159.000i 0.501577 0.501577i −0.410351 0.911928i \(-0.634594\pi\)
0.911928 + 0.410351i \(0.134594\pi\)
\(318\) 0 0
\(319\) 80.0000i 0.250784i
\(320\) 0 0
\(321\) 242.000 0.753894
\(322\) 0 0
\(323\) 8.00000 + 8.00000i 0.0247678 + 0.0247678i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −136.000 + 136.000i −0.415902 + 0.415902i
\(328\) 0 0
\(329\) 546.000i 1.65957i
\(330\) 0 0
\(331\) 182.000 0.549849 0.274924 0.961466i \(-0.411347\pi\)
0.274924 + 0.961466i \(0.411347\pi\)
\(332\) 0 0
\(333\) 231.000 + 231.000i 0.693694 + 0.693694i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 447.000 447.000i 1.32641 1.32641i 0.417930 0.908479i \(-0.362756\pi\)
0.908479 0.417930i \(-0.137244\pi\)
\(338\) 0 0
\(339\) 254.000i 0.749263i
\(340\) 0 0
\(341\) −140.000 −0.410557
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 25.0000 25.0000i 0.0720461 0.0720461i −0.670166 0.742212i \(-0.733777\pi\)
0.742212 + 0.670166i \(0.233777\pi\)
\(348\) 0 0
\(349\) 200.000i 0.573066i 0.958070 + 0.286533i \(0.0925028\pi\)
−0.958070 + 0.286533i \(0.907497\pi\)
\(350\) 0 0
\(351\) −288.000 −0.820513
\(352\) 0 0
\(353\) −321.000 321.000i −0.909348 0.909348i 0.0868711 0.996220i \(-0.472313\pi\)
−0.996220 + 0.0868711i \(0.972313\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 14.0000 14.0000i 0.0392157 0.0392157i
\(358\) 0 0
\(359\) 112.000i 0.311978i −0.987759 0.155989i \(-0.950144\pi\)
0.987759 0.155989i \(-0.0498564\pi\)
\(360\) 0 0
\(361\) 297.000 0.822715
\(362\) 0 0
\(363\) −21.0000 21.0000i −0.0578512 0.0578512i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 377.000 377.000i 1.02725 1.02725i 0.0276297 0.999618i \(-0.491204\pi\)
0.999618 0.0276297i \(-0.00879594\pi\)
\(368\) 0 0
\(369\) 98.0000i 0.265583i
\(370\) 0 0
\(371\) −98.0000 −0.264151
\(372\) 0 0
\(373\) −217.000 217.000i −0.581769 0.581769i 0.353620 0.935389i \(-0.384951\pi\)
−0.935389 + 0.353620i \(0.884951\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 72.0000 72.0000i 0.190981 0.190981i
\(378\) 0 0
\(379\) 56.0000i 0.147757i −0.997267 0.0738786i \(-0.976462\pi\)
0.997267 0.0738786i \(-0.0235377\pi\)
\(380\) 0 0
\(381\) −14.0000 −0.0367454
\(382\) 0 0
\(383\) 57.0000 + 57.0000i 0.148825 + 0.148825i 0.777593 0.628768i \(-0.216440\pi\)
−0.628768 + 0.777593i \(0.716440\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −105.000 + 105.000i −0.271318 + 0.271318i
\(388\) 0 0
\(389\) 312.000i 0.802057i 0.916066 + 0.401028i \(0.131347\pi\)
−0.916066 + 0.401028i \(0.868653\pi\)
\(390\) 0 0
\(391\) 46.0000 0.117647
\(392\) 0 0
\(393\) 230.000 + 230.000i 0.585242 + 0.585242i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −193.000 + 193.000i −0.486146 + 0.486146i −0.907088 0.420942i \(-0.861700\pi\)
0.420942 + 0.907088i \(0.361700\pi\)
\(398\) 0 0
\(399\) 112.000i 0.280702i
\(400\) 0 0
\(401\) −30.0000 −0.0748130 −0.0374065 0.999300i \(-0.511910\pi\)
−0.0374065 + 0.999300i \(0.511910\pi\)
\(402\) 0 0
\(403\) −126.000 126.000i −0.312655 0.312655i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 330.000 330.000i 0.810811 0.810811i
\(408\) 0 0
\(409\) 432.000i 1.05623i −0.849171 0.528117i \(-0.822898\pi\)
0.849171 0.528117i \(-0.177102\pi\)
\(410\) 0 0
\(411\) 126.000 0.306569
\(412\) 0 0
\(413\) 392.000 + 392.000i 0.949153 + 0.949153i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 88.0000 88.0000i 0.211031 0.211031i
\(418\) 0 0
\(419\) 168.000i 0.400955i −0.979698 0.200477i \(-0.935751\pi\)
0.979698 0.200477i \(-0.0642493\pi\)
\(420\) 0 0
\(421\) −454.000 −1.07838 −0.539192 0.842183i \(-0.681270\pi\)
−0.539192 + 0.842183i \(0.681270\pi\)
\(422\) 0 0
\(423\) 273.000 + 273.000i 0.645390 + 0.645390i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −294.000 + 294.000i −0.688525 + 0.688525i
\(428\) 0 0
\(429\) 180.000i 0.419580i
\(430\) 0 0
\(431\) 494.000 1.14617 0.573086 0.819495i \(-0.305746\pi\)
0.573086 + 0.819495i \(0.305746\pi\)
\(432\) 0 0
\(433\) 511.000 + 511.000i 1.18014 + 1.18014i 0.979708 + 0.200431i \(0.0642341\pi\)
0.200431 + 0.979708i \(0.435766\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −184.000 + 184.000i −0.421053 + 0.421053i
\(438\) 0 0
\(439\) 176.000i 0.400911i 0.979703 + 0.200456i \(0.0642422\pi\)
−0.979703 + 0.200456i \(0.935758\pi\)
\(440\) 0 0
\(441\) −343.000 −0.777778
\(442\) 0 0
\(443\) 177.000 + 177.000i 0.399549 + 0.399549i 0.878074 0.478525i \(-0.158828\pi\)
−0.478525 + 0.878074i \(0.658828\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 168.000 168.000i 0.375839 0.375839i
\(448\) 0 0
\(449\) 608.000i 1.35412i 0.735928 + 0.677060i \(0.236746\pi\)
−0.735928 + 0.677060i \(0.763254\pi\)
\(450\) 0 0
\(451\) 140.000 0.310421
\(452\) 0 0
\(453\) −130.000 130.000i −0.286976 0.286976i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −609.000 + 609.000i −1.33260 + 1.33260i −0.429571 + 0.903033i \(0.641335\pi\)
−0.903033 + 0.429571i \(0.858665\pi\)
\(458\) 0 0
\(459\) 32.0000i 0.0697168i
\(460\) 0 0
\(461\) 490.000 1.06291 0.531453 0.847088i \(-0.321646\pi\)
0.531453 + 0.847088i \(0.321646\pi\)
\(462\) 0 0
\(463\) −7.00000 7.00000i −0.0151188 0.0151188i 0.699507 0.714626i \(-0.253403\pi\)
−0.714626 + 0.699507i \(0.753403\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 25.0000 25.0000i 0.0535332 0.0535332i −0.679833 0.733367i \(-0.737948\pi\)
0.733367 + 0.679833i \(0.237948\pi\)
\(468\) 0 0
\(469\) 98.0000i 0.208955i
\(470\) 0 0
\(471\) 126.000 0.267516
\(472\) 0 0
\(473\) 150.000 + 150.000i 0.317125 + 0.317125i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 49.0000 49.0000i 0.102725 0.102725i
\(478\) 0 0
\(479\) 128.000i 0.267223i −0.991034 0.133612i \(-0.957343\pi\)
0.991034 0.133612i \(-0.0426575\pi\)
\(480\) 0 0
\(481\) 594.000 1.23493
\(482\) 0 0
\(483\) 322.000 + 322.000i 0.666667 + 0.666667i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 249.000 249.000i 0.511294 0.511294i −0.403629 0.914923i \(-0.632251\pi\)
0.914923 + 0.403629i \(0.132251\pi\)
\(488\) 0 0
\(489\) 130.000i 0.265849i
\(490\) 0 0
\(491\) −650.000 −1.32383 −0.661914 0.749579i \(-0.730256\pi\)
−0.661914 + 0.749579i \(0.730256\pi\)
\(492\) 0 0
\(493\) −8.00000 8.00000i −0.0162272 0.0162272i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 686.000 686.000i 1.38028 1.38028i
\(498\) 0 0
\(499\) 632.000i 1.26653i 0.773934 + 0.633267i \(0.218286\pi\)
−0.773934 + 0.633267i \(0.781714\pi\)
\(500\) 0 0
\(501\) −206.000 −0.411178
\(502\) 0 0
\(503\) −471.000 471.000i −0.936382 0.936382i 0.0617123 0.998094i \(-0.480344\pi\)
−0.998094 + 0.0617123i \(0.980344\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 7.00000 7.00000i 0.0138067 0.0138067i
\(508\) 0 0
\(509\) 8.00000i 0.0157171i 0.999969 + 0.00785855i \(0.00250148\pi\)
−0.999969 + 0.00785855i \(0.997499\pi\)
\(510\) 0 0
\(511\) 686.000 1.34247
\(512\) 0 0
\(513\) −128.000 128.000i −0.249513 0.249513i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 390.000 390.000i 0.754352 0.754352i
\(518\) 0 0
\(519\) 146.000i 0.281310i
\(520\) 0 0
\(521\) −366.000 −0.702495 −0.351248 0.936283i \(-0.614242\pi\)
−0.351248 + 0.936283i \(0.614242\pi\)
\(522\) 0 0
\(523\) 273.000 + 273.000i 0.521989 + 0.521989i 0.918172 0.396183i \(-0.129665\pi\)
−0.396183 + 0.918172i \(0.629665\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −14.0000 + 14.0000i −0.0265655 + 0.0265655i
\(528\) 0 0
\(529\) 529.000i 1.00000i
\(530\) 0 0
\(531\) −392.000 −0.738230
\(532\) 0 0
\(533\) 126.000 + 126.000i 0.236398 + 0.236398i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −56.0000 + 56.0000i −0.104283 + 0.104283i
\(538\) 0 0
\(539\) 490.000i 0.909091i
\(540\) 0 0
\(541\) 394.000 0.728281 0.364140 0.931344i \(-0.381363\pi\)
0.364140 + 0.931344i \(0.381363\pi\)
\(542\) 0 0
\(543\) −70.0000 70.0000i −0.128913 0.128913i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −231.000 + 231.000i −0.422303 + 0.422303i −0.885996 0.463693i \(-0.846524\pi\)
0.463693 + 0.885996i \(0.346524\pi\)
\(548\) 0 0
\(549\) 294.000i 0.535519i
\(550\) 0 0
\(551\) 64.0000 0.116152
\(552\) 0 0
\(553\) −672.000 672.000i −1.21519 1.21519i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 735.000 735.000i 1.31957 1.31957i 0.405453 0.914116i \(-0.367114\pi\)
0.914116 0.405453i \(-0.132886\pi\)
\(558\) 0 0
\(559\) 270.000i 0.483005i
\(560\) 0 0
\(561\) 20.0000 0.0356506
\(562\) 0 0
\(563\) 609.000 + 609.000i 1.08171 + 1.08171i 0.996351 + 0.0853545i \(0.0272023\pi\)
0.0853545 + 0.996351i \(0.472798\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 217.000 217.000i 0.382716 0.382716i
\(568\) 0 0
\(569\) 560.000i 0.984183i −0.870544 0.492091i \(-0.836233\pi\)
0.870544 0.492091i \(-0.163767\pi\)
\(570\) 0 0
\(571\) −938.000 −1.64273 −0.821366 0.570401i \(-0.806788\pi\)
−0.821366 + 0.570401i \(0.806788\pi\)
\(572\) 0 0
\(573\) 142.000 + 142.000i 0.247818 + 0.247818i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −97.0000 + 97.0000i −0.168111 + 0.168111i −0.786149 0.618038i \(-0.787928\pi\)
0.618038 + 0.786149i \(0.287928\pi\)
\(578\) 0 0
\(579\) 126.000i 0.217617i
\(580\) 0 0
\(581\) 882.000 1.51807
\(582\) 0 0
\(583\) −70.0000 70.0000i −0.120069 0.120069i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −39.0000 + 39.0000i −0.0664395 + 0.0664395i −0.739546 0.673106i \(-0.764960\pi\)
0.673106 + 0.739546i \(0.264960\pi\)
\(588\) 0 0
\(589\) 112.000i 0.190153i
\(590\) 0 0
\(591\) 126.000 0.213198
\(592\) 0 0
\(593\) 479.000 + 479.000i 0.807757 + 0.807757i 0.984294 0.176537i \(-0.0564895\pi\)
−0.176537 + 0.984294i \(0.556489\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −336.000 + 336.000i −0.562814 + 0.562814i
\(598\) 0 0
\(599\) 1040.00i 1.73623i −0.496366 0.868114i \(-0.665332\pi\)
0.496366 0.868114i \(-0.334668\pi\)
\(600\) 0 0
\(601\) −430.000 −0.715474 −0.357737 0.933822i \(-0.616452\pi\)
−0.357737 + 0.933822i \(0.616452\pi\)
\(602\) 0 0
\(603\) 49.0000 + 49.0000i 0.0812604 + 0.0812604i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −423.000 + 423.000i −0.696870 + 0.696870i −0.963734 0.266864i \(-0.914012\pi\)
0.266864 + 0.963734i \(0.414012\pi\)
\(608\) 0 0
\(609\) 112.000i 0.183908i
\(610\) 0 0
\(611\) 702.000 1.14894
\(612\) 0 0
\(613\) −249.000 249.000i −0.406199 0.406199i 0.474212 0.880411i \(-0.342733\pi\)
−0.880411 + 0.474212i \(0.842733\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −321.000 + 321.000i −0.520259 + 0.520259i −0.917650 0.397390i \(-0.869916\pi\)
0.397390 + 0.917650i \(0.369916\pi\)
\(618\) 0 0
\(619\) 600.000i 0.969305i −0.874707 0.484653i \(-0.838946\pi\)
0.874707 0.484653i \(-0.161054\pi\)
\(620\) 0 0
\(621\) −736.000 −1.18519
\(622\) 0 0
\(623\) −784.000 784.000i −1.25843 1.25843i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −80.0000 + 80.0000i −0.127592 + 0.127592i
\(628\) 0 0
\(629\) 66.0000i 0.104928i
\(630\) 0 0
\(631\) 638.000 1.01109 0.505547 0.862799i \(-0.331291\pi\)
0.505547 + 0.862799i \(0.331291\pi\)
\(632\) 0 0
\(633\) −314.000 314.000i −0.496051 0.496051i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −441.000 + 441.000i −0.692308 + 0.692308i
\(638\) 0 0
\(639\) 686.000i 1.07355i
\(640\) 0 0
\(641\) 482.000 0.751950 0.375975 0.926630i \(-0.377308\pi\)
0.375975 + 0.926630i \(0.377308\pi\)
\(642\) 0 0
\(643\) 33.0000 + 33.0000i 0.0513219 + 0.0513219i 0.732302 0.680980i \(-0.238446\pi\)
−0.680980 + 0.732302i \(0.738446\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7.00000 + 7.00000i −0.0108192 + 0.0108192i −0.712496 0.701677i \(-0.752435\pi\)
0.701677 + 0.712496i \(0.252435\pi\)
\(648\) 0 0
\(649\) 560.000i 0.862866i
\(650\) 0 0
\(651\) −196.000 −0.301075
\(652\) 0 0
\(653\) 471.000 + 471.000i 0.721286 + 0.721286i 0.968867 0.247581i \(-0.0796356\pi\)
−0.247581 + 0.968867i \(0.579636\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −343.000 + 343.000i −0.522070 + 0.522070i
\(658\) 0 0
\(659\) 328.000i 0.497724i −0.968539 0.248862i \(-0.919943\pi\)
0.968539 0.248862i \(-0.0800565\pi\)
\(660\) 0 0
\(661\) −742.000 −1.12254 −0.561271 0.827632i \(-0.689687\pi\)
−0.561271 + 0.827632i \(0.689687\pi\)
\(662\) 0 0
\(663\) 18.0000 + 18.0000i 0.0271493 + 0.0271493i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 184.000 184.000i 0.275862 0.275862i
\(668\) 0 0
\(669\) 270.000i 0.403587i
\(670\) 0 0
\(671\) −420.000 −0.625931
\(672\) 0 0
\(673\) 287.000 + 287.000i 0.426449 + 0.426449i 0.887417 0.460968i \(-0.152498\pi\)
−0.460968 + 0.887417i \(0.652498\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −577.000 + 577.000i −0.852290 + 0.852290i −0.990415 0.138125i \(-0.955892\pi\)
0.138125 + 0.990415i \(0.455892\pi\)
\(678\) 0 0
\(679\) 462.000i 0.680412i
\(680\) 0 0
\(681\) 562.000 0.825257
\(682\) 0 0
\(683\) −399.000 399.000i −0.584187 0.584187i 0.351864 0.936051i \(-0.385548\pi\)
−0.936051 + 0.351864i \(0.885548\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 168.000 168.000i 0.244541 0.244541i
\(688\) 0 0
\(689\) 126.000i 0.182874i
\(690\) 0 0
\(691\) −378.000 −0.547033 −0.273517 0.961867i \(-0.588187\pi\)
−0.273517 + 0.961867i \(0.588187\pi\)
\(692\) 0 0
\(693\) −490.000 490.000i −0.707071 0.707071i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 14.0000 14.0000i 0.0200861 0.0200861i
\(698\) 0 0
\(699\) 546.000i 0.781116i
\(700\) 0 0
\(701\) −470.000 −0.670471 −0.335235 0.942134i \(-0.608816\pi\)
−0.335235 + 0.942134i \(0.608816\pi\)
\(702\) 0 0
\(703\) 264.000 + 264.000i 0.375533 + 0.375533i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −182.000 + 182.000i −0.257426 + 0.257426i
\(708\) 0 0
\(709\) 1192.00i 1.68124i −0.541624 0.840621i \(-0.682190\pi\)
0.541624 0.840621i \(-0.317810\pi\)
\(710\) 0 0
\(711\) 672.000 0.945148
\(712\) 0 0
\(713\) −322.000 322.000i −0.451613 0.451613i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 288.000 288.000i 0.401674 0.401674i
\(718\) 0 0
\(719\) 608.000i 0.845619i −0.906219 0.422809i \(-0.861044\pi\)
0.906219 0.422809i \(-0.138956\pi\)
\(720\) 0 0
\(721\) −1022.00 −1.41748
\(722\) 0 0
\(723\) −446.000 446.000i −0.616874 0.616874i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 441.000 441.000i 0.606602 0.606602i −0.335454 0.942057i \(-0.608890\pi\)
0.942057 + 0.335454i \(0.108890\pi\)
\(728\) 0 0
\(729\) 71.0000i 0.0973937i
\(730\) 0 0
\(731\) 30.0000 0.0410397
\(732\) 0 0
\(733\) −361.000 361.000i −0.492497 0.492497i 0.416595 0.909092i \(-0.363223\pi\)
−0.909092 + 0.416595i \(0.863223\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 70.0000 70.0000i 0.0949796 0.0949796i
\(738\) 0 0
\(739\) 920.000i 1.24493i 0.782649 + 0.622463i \(0.213868\pi\)
−0.782649 + 0.622463i \(0.786132\pi\)
\(740\) 0 0
\(741\) −144.000 −0.194332
\(742\) 0 0
\(743\) −343.000 343.000i −0.461642 0.461642i 0.437551 0.899193i \(-0.355846\pi\)
−0.899193 + 0.437551i \(0.855846\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −441.000 + 441.000i −0.590361 + 0.590361i
\(748\) 0 0
\(749\) 1694.00i 2.26168i
\(750\) 0 0
\(751\) −786.000 −1.04660 −0.523302 0.852147i \(-0.675300\pi\)
−0.523302 + 0.852147i \(0.675300\pi\)
\(752\) 0 0
\(753\) 150.000 + 150.000i 0.199203 + 0.199203i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 63.0000 63.0000i 0.0832232 0.0832232i −0.664270 0.747493i \(-0.731257\pi\)
0.747493 + 0.664270i \(0.231257\pi\)
\(758\) 0 0
\(759\) 460.000i 0.606061i
\(760\) 0 0
\(761\) −398.000 −0.522996 −0.261498 0.965204i \(-0.584216\pi\)
−0.261498 + 0.965204i \(0.584216\pi\)
\(762\) 0 0
\(763\) −952.000 952.000i −1.24771 1.24771i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −504.000 + 504.000i −0.657106 + 0.657106i
\(768\) 0 0
\(769\) 704.000i 0.915475i −0.889087 0.457737i \(-0.848660\pi\)
0.889087 0.457737i \(-0.151340\pi\)
\(770\) 0 0
\(771\) −322.000 −0.417639
\(772\) 0 0
\(773\) −825.000 825.000i −1.06727 1.06727i −0.997568 0.0697026i \(-0.977795\pi\)
−0.0697026 0.997568i \(-0.522205\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 462.000 462.000i 0.594595 0.594595i
\(778\) 0 0
\(779\) 112.000i 0.143774i
\(780\) 0 0
\(781\) 980.000 1.25480
\(782\) 0 0
\(783\) 128.000 + 128.000i 0.163474 + 0.163474i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −71.0000 + 71.0000i −0.0902160 + 0.0902160i −0.750775 0.660559i \(-0.770320\pi\)
0.660559 + 0.750775i \(0.270320\pi\)
\(788\) 0 0
\(789\) 302.000i 0.382763i
\(790\) 0 0
\(791\) −1778.00 −2.24779
\(792\) 0 0
\(793\)