Properties

Label 120.4.f.a.49.1
Level $120$
Weight $4$
Character 120.49
Analytic conductor $7.080$
Analytic rank $1$
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] = [120,4,Mod(49,120)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(120, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("120.49");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 120.f (of order \(2\), degree \(1\), 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: \(7.08022920069\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 49.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 120.49
Dual form 120.4.f.a.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000i q^{3} +(-10.0000 - 5.00000i) q^{5} +10.0000i q^{7} -9.00000 q^{9} +O(q^{10})\) \(q-3.00000i q^{3} +(-10.0000 - 5.00000i) q^{5} +10.0000i q^{7} -9.00000 q^{9} -46.0000 q^{11} +34.0000i q^{13} +(-15.0000 + 30.0000i) q^{15} +66.0000i q^{17} -104.000 q^{19} +30.0000 q^{21} -164.000i q^{23} +(75.0000 + 100.000i) q^{25} +27.0000i q^{27} -224.000 q^{29} -72.0000 q^{31} +138.000i q^{33} +(50.0000 - 100.000i) q^{35} -22.0000i q^{37} +102.000 q^{39} +194.000 q^{41} -108.000i q^{43} +(90.0000 + 45.0000i) q^{45} -480.000i q^{47} +243.000 q^{49} +198.000 q^{51} -286.000i q^{53} +(460.000 + 230.000i) q^{55} +312.000i q^{57} -426.000 q^{59} +698.000 q^{61} -90.0000i q^{63} +(170.000 - 340.000i) q^{65} +328.000i q^{67} -492.000 q^{69} +188.000 q^{71} +740.000i q^{73} +(300.000 - 225.000i) q^{75} -460.000i q^{77} -1168.00 q^{79} +81.0000 q^{81} -412.000i q^{83} +(330.000 - 660.000i) q^{85} +672.000i q^{87} -1206.00 q^{89} -340.000 q^{91} +216.000i q^{93} +(1040.00 + 520.000i) q^{95} -1384.00i q^{97} +414.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 20 q^{5} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 20 q^{5} - 18 q^{9} - 92 q^{11} - 30 q^{15} - 208 q^{19} + 60 q^{21} + 150 q^{25} - 448 q^{29} - 144 q^{31} + 100 q^{35} + 204 q^{39} + 388 q^{41} + 180 q^{45} + 486 q^{49} + 396 q^{51} + 920 q^{55} - 852 q^{59} + 1396 q^{61} + 340 q^{65} - 984 q^{69} + 376 q^{71} + 600 q^{75} - 2336 q^{79} + 162 q^{81} + 660 q^{85} - 2412 q^{89} - 680 q^{91} + 2080 q^{95} + 828 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 3.00000i 0.577350i
\(4\) 0 0
\(5\) −10.0000 5.00000i −0.894427 0.447214i
\(6\) 0 0
\(7\) 10.0000i 0.539949i 0.962867 + 0.269975i \(0.0870153\pi\)
−0.962867 + 0.269975i \(0.912985\pi\)
\(8\) 0 0
\(9\) −9.00000 −0.333333
\(10\) 0 0
\(11\) −46.0000 −1.26087 −0.630433 0.776244i \(-0.717123\pi\)
−0.630433 + 0.776244i \(0.717123\pi\)
\(12\) 0 0
\(13\) 34.0000i 0.725377i 0.931910 + 0.362689i \(0.118141\pi\)
−0.931910 + 0.362689i \(0.881859\pi\)
\(14\) 0 0
\(15\) −15.0000 + 30.0000i −0.258199 + 0.516398i
\(16\) 0 0
\(17\) 66.0000i 0.941609i 0.882238 + 0.470804i \(0.156036\pi\)
−0.882238 + 0.470804i \(0.843964\pi\)
\(18\) 0 0
\(19\) −104.000 −1.25575 −0.627875 0.778314i \(-0.716075\pi\)
−0.627875 + 0.778314i \(0.716075\pi\)
\(20\) 0 0
\(21\) 30.0000 0.311740
\(22\) 0 0
\(23\) 164.000i 1.48680i −0.668848 0.743399i \(-0.733212\pi\)
0.668848 0.743399i \(-0.266788\pi\)
\(24\) 0 0
\(25\) 75.0000 + 100.000i 0.600000 + 0.800000i
\(26\) 0 0
\(27\) 27.0000i 0.192450i
\(28\) 0 0
\(29\) −224.000 −1.43434 −0.717168 0.696900i \(-0.754562\pi\)
−0.717168 + 0.696900i \(0.754562\pi\)
\(30\) 0 0
\(31\) −72.0000 −0.417148 −0.208574 0.978007i \(-0.566882\pi\)
−0.208574 + 0.978007i \(0.566882\pi\)
\(32\) 0 0
\(33\) 138.000i 0.727961i
\(34\) 0 0
\(35\) 50.0000 100.000i 0.241473 0.482945i
\(36\) 0 0
\(37\) 22.0000i 0.0977507i −0.998805 0.0488754i \(-0.984436\pi\)
0.998805 0.0488754i \(-0.0155637\pi\)
\(38\) 0 0
\(39\) 102.000 0.418797
\(40\) 0 0
\(41\) 194.000 0.738969 0.369484 0.929237i \(-0.379534\pi\)
0.369484 + 0.929237i \(0.379534\pi\)
\(42\) 0 0
\(43\) 108.000i 0.383020i −0.981491 0.191510i \(-0.938662\pi\)
0.981491 0.191510i \(-0.0613384\pi\)
\(44\) 0 0
\(45\) 90.0000 + 45.0000i 0.298142 + 0.149071i
\(46\) 0 0
\(47\) 480.000i 1.48969i −0.667240 0.744843i \(-0.732525\pi\)
0.667240 0.744843i \(-0.267475\pi\)
\(48\) 0 0
\(49\) 243.000 0.708455
\(50\) 0 0
\(51\) 198.000 0.543638
\(52\) 0 0
\(53\) 286.000i 0.741229i −0.928787 0.370614i \(-0.879147\pi\)
0.928787 0.370614i \(-0.120853\pi\)
\(54\) 0 0
\(55\) 460.000 + 230.000i 1.12775 + 0.563876i
\(56\) 0 0
\(57\) 312.000i 0.725007i
\(58\) 0 0
\(59\) −426.000 −0.940008 −0.470004 0.882664i \(-0.655748\pi\)
−0.470004 + 0.882664i \(0.655748\pi\)
\(60\) 0 0
\(61\) 698.000 1.46508 0.732539 0.680725i \(-0.238335\pi\)
0.732539 + 0.680725i \(0.238335\pi\)
\(62\) 0 0
\(63\) 90.0000i 0.179983i
\(64\) 0 0
\(65\) 170.000 340.000i 0.324399 0.648797i
\(66\) 0 0
\(67\) 328.000i 0.598083i 0.954240 + 0.299042i \(0.0966669\pi\)
−0.954240 + 0.299042i \(0.903333\pi\)
\(68\) 0 0
\(69\) −492.000 −0.858403
\(70\) 0 0
\(71\) 188.000 0.314246 0.157123 0.987579i \(-0.449778\pi\)
0.157123 + 0.987579i \(0.449778\pi\)
\(72\) 0 0
\(73\) 740.000i 1.18644i 0.805039 + 0.593222i \(0.202144\pi\)
−0.805039 + 0.593222i \(0.797856\pi\)
\(74\) 0 0
\(75\) 300.000 225.000i 0.461880 0.346410i
\(76\) 0 0
\(77\) 460.000i 0.680803i
\(78\) 0 0
\(79\) −1168.00 −1.66342 −0.831711 0.555209i \(-0.812638\pi\)
−0.831711 + 0.555209i \(0.812638\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 412.000i 0.544854i −0.962176 0.272427i \(-0.912174\pi\)
0.962176 0.272427i \(-0.0878263\pi\)
\(84\) 0 0
\(85\) 330.000 660.000i 0.421100 0.842201i
\(86\) 0 0
\(87\) 672.000i 0.828115i
\(88\) 0 0
\(89\) −1206.00 −1.43636 −0.718178 0.695859i \(-0.755024\pi\)
−0.718178 + 0.695859i \(0.755024\pi\)
\(90\) 0 0
\(91\) −340.000 −0.391667
\(92\) 0 0
\(93\) 216.000i 0.240840i
\(94\) 0 0
\(95\) 1040.00 + 520.000i 1.12318 + 0.561588i
\(96\) 0 0
\(97\) 1384.00i 1.44870i −0.689432 0.724350i \(-0.742140\pi\)
0.689432 0.724350i \(-0.257860\pi\)
\(98\) 0 0
\(99\) 414.000 0.420289
\(100\) 0 0
\(101\) −1128.00 −1.11129 −0.555645 0.831420i \(-0.687528\pi\)
−0.555645 + 0.831420i \(0.687528\pi\)
\(102\) 0 0
\(103\) 758.000i 0.725126i 0.931959 + 0.362563i \(0.118098\pi\)
−0.931959 + 0.362563i \(0.881902\pi\)
\(104\) 0 0
\(105\) −300.000 150.000i −0.278829 0.139414i
\(106\) 0 0
\(107\) 1324.00i 1.19622i 0.801413 + 0.598112i \(0.204082\pi\)
−0.801413 + 0.598112i \(0.795918\pi\)
\(108\) 0 0
\(109\) −1602.00 −1.40774 −0.703871 0.710328i \(-0.748546\pi\)
−0.703871 + 0.710328i \(0.748546\pi\)
\(110\) 0 0
\(111\) −66.0000 −0.0564364
\(112\) 0 0
\(113\) 2074.00i 1.72660i 0.504693 + 0.863299i \(0.331606\pi\)
−0.504693 + 0.863299i \(0.668394\pi\)
\(114\) 0 0
\(115\) −820.000 + 1640.00i −0.664916 + 1.32983i
\(116\) 0 0
\(117\) 306.000i 0.241792i
\(118\) 0 0
\(119\) −660.000 −0.508421
\(120\) 0 0
\(121\) 785.000 0.589782
\(122\) 0 0
\(123\) 582.000i 0.426644i
\(124\) 0 0
\(125\) −250.000 1375.00i −0.178885 0.983870i
\(126\) 0 0
\(127\) 534.000i 0.373109i −0.982445 0.186554i \(-0.940268\pi\)
0.982445 0.186554i \(-0.0597321\pi\)
\(128\) 0 0
\(129\) −324.000 −0.221137
\(130\) 0 0
\(131\) 1806.00 1.20451 0.602256 0.798303i \(-0.294269\pi\)
0.602256 + 0.798303i \(0.294269\pi\)
\(132\) 0 0
\(133\) 1040.00i 0.678041i
\(134\) 0 0
\(135\) 135.000 270.000i 0.0860663 0.172133i
\(136\) 0 0
\(137\) 1822.00i 1.13623i 0.822948 + 0.568117i \(0.192328\pi\)
−0.822948 + 0.568117i \(0.807672\pi\)
\(138\) 0 0
\(139\) −532.000 −0.324631 −0.162315 0.986739i \(-0.551896\pi\)
−0.162315 + 0.986739i \(0.551896\pi\)
\(140\) 0 0
\(141\) −1440.00 −0.860070
\(142\) 0 0
\(143\) 1564.00i 0.914603i
\(144\) 0 0
\(145\) 2240.00 + 1120.00i 1.28291 + 0.641455i
\(146\) 0 0
\(147\) 729.000i 0.409027i
\(148\) 0 0
\(149\) 1284.00 0.705969 0.352984 0.935629i \(-0.385167\pi\)
0.352984 + 0.935629i \(0.385167\pi\)
\(150\) 0 0
\(151\) 184.000 0.0991636 0.0495818 0.998770i \(-0.484211\pi\)
0.0495818 + 0.998770i \(0.484211\pi\)
\(152\) 0 0
\(153\) 594.000i 0.313870i
\(154\) 0 0
\(155\) 720.000 + 360.000i 0.373108 + 0.186554i
\(156\) 0 0
\(157\) 3746.00i 1.90423i −0.305748 0.952113i \(-0.598906\pi\)
0.305748 0.952113i \(-0.401094\pi\)
\(158\) 0 0
\(159\) −858.000 −0.427949
\(160\) 0 0
\(161\) 1640.00 0.802796
\(162\) 0 0
\(163\) 1504.00i 0.722714i −0.932428 0.361357i \(-0.882314\pi\)
0.932428 0.361357i \(-0.117686\pi\)
\(164\) 0 0
\(165\) 690.000 1380.00i 0.325554 0.651108i
\(166\) 0 0
\(167\) 3012.00i 1.39566i 0.716262 + 0.697831i \(0.245851\pi\)
−0.716262 + 0.697831i \(0.754149\pi\)
\(168\) 0 0
\(169\) 1041.00 0.473828
\(170\) 0 0
\(171\) 936.000 0.418583
\(172\) 0 0
\(173\) 438.000i 0.192489i 0.995358 + 0.0962443i \(0.0306830\pi\)
−0.995358 + 0.0962443i \(0.969317\pi\)
\(174\) 0 0
\(175\) −1000.00 + 750.000i −0.431959 + 0.323970i
\(176\) 0 0
\(177\) 1278.00i 0.542714i
\(178\) 0 0
\(179\) 1462.00 0.610475 0.305237 0.952276i \(-0.401264\pi\)
0.305237 + 0.952276i \(0.401264\pi\)
\(180\) 0 0
\(181\) 586.000 0.240647 0.120323 0.992735i \(-0.461607\pi\)
0.120323 + 0.992735i \(0.461607\pi\)
\(182\) 0 0
\(183\) 2094.00i 0.845863i
\(184\) 0 0
\(185\) −110.000 + 220.000i −0.0437155 + 0.0874309i
\(186\) 0 0
\(187\) 3036.00i 1.18724i
\(188\) 0 0
\(189\) −270.000 −0.103913
\(190\) 0 0
\(191\) 60.0000 0.0227301 0.0113650 0.999935i \(-0.496382\pi\)
0.0113650 + 0.999935i \(0.496382\pi\)
\(192\) 0 0
\(193\) 4676.00i 1.74397i 0.489534 + 0.871984i \(0.337167\pi\)
−0.489534 + 0.871984i \(0.662833\pi\)
\(194\) 0 0
\(195\) −1020.00 510.000i −0.374583 0.187292i
\(196\) 0 0
\(197\) 2286.00i 0.826755i 0.910560 + 0.413378i \(0.135651\pi\)
−0.910560 + 0.413378i \(0.864349\pi\)
\(198\) 0 0
\(199\) 3536.00 1.25960 0.629800 0.776757i \(-0.283137\pi\)
0.629800 + 0.776757i \(0.283137\pi\)
\(200\) 0 0
\(201\) 984.000 0.345304
\(202\) 0 0
\(203\) 2240.00i 0.774469i
\(204\) 0 0
\(205\) −1940.00 970.000i −0.660954 0.330477i
\(206\) 0 0
\(207\) 1476.00i 0.495599i
\(208\) 0 0
\(209\) 4784.00 1.58333
\(210\) 0 0
\(211\) −3500.00 −1.14194 −0.570971 0.820970i \(-0.693433\pi\)
−0.570971 + 0.820970i \(0.693433\pi\)
\(212\) 0 0
\(213\) 564.000i 0.181430i
\(214\) 0 0
\(215\) −540.000 + 1080.00i −0.171292 + 0.342583i
\(216\) 0 0
\(217\) 720.000i 0.225239i
\(218\) 0 0
\(219\) 2220.00 0.684994
\(220\) 0 0
\(221\) −2244.00 −0.683022
\(222\) 0 0
\(223\) 5874.00i 1.76391i −0.471333 0.881955i \(-0.656227\pi\)
0.471333 0.881955i \(-0.343773\pi\)
\(224\) 0 0
\(225\) −675.000 900.000i −0.200000 0.266667i
\(226\) 0 0
\(227\) 124.000i 0.0362563i −0.999836 0.0181281i \(-0.994229\pi\)
0.999836 0.0181281i \(-0.00577068\pi\)
\(228\) 0 0
\(229\) 1362.00 0.393028 0.196514 0.980501i \(-0.437038\pi\)
0.196514 + 0.980501i \(0.437038\pi\)
\(230\) 0 0
\(231\) −1380.00 −0.393062
\(232\) 0 0
\(233\) 3870.00i 1.08812i 0.839046 + 0.544060i \(0.183114\pi\)
−0.839046 + 0.544060i \(0.816886\pi\)
\(234\) 0 0
\(235\) −2400.00 + 4800.00i −0.666207 + 1.33241i
\(236\) 0 0
\(237\) 3504.00i 0.960377i
\(238\) 0 0
\(239\) −6116.00 −1.65528 −0.827638 0.561262i \(-0.810316\pi\)
−0.827638 + 0.561262i \(0.810316\pi\)
\(240\) 0 0
\(241\) −5962.00 −1.59355 −0.796776 0.604274i \(-0.793463\pi\)
−0.796776 + 0.604274i \(0.793463\pi\)
\(242\) 0 0
\(243\) 243.000i 0.0641500i
\(244\) 0 0
\(245\) −2430.00 1215.00i −0.633661 0.316831i
\(246\) 0 0
\(247\) 3536.00i 0.910892i
\(248\) 0 0
\(249\) −1236.00 −0.314572
\(250\) 0 0
\(251\) −1490.00 −0.374693 −0.187347 0.982294i \(-0.559989\pi\)
−0.187347 + 0.982294i \(0.559989\pi\)
\(252\) 0 0
\(253\) 7544.00i 1.87465i
\(254\) 0 0
\(255\) −1980.00 990.000i −0.486245 0.243122i
\(256\) 0 0
\(257\) 5394.00i 1.30922i −0.755969 0.654608i \(-0.772834\pi\)
0.755969 0.654608i \(-0.227166\pi\)
\(258\) 0 0
\(259\) 220.000 0.0527804
\(260\) 0 0
\(261\) 2016.00 0.478112
\(262\) 0 0
\(263\) 636.000i 0.149116i 0.997217 + 0.0745579i \(0.0237546\pi\)
−0.997217 + 0.0745579i \(0.976245\pi\)
\(264\) 0 0
\(265\) −1430.00 + 2860.00i −0.331488 + 0.662975i
\(266\) 0 0
\(267\) 3618.00i 0.829281i
\(268\) 0 0
\(269\) 3360.00 0.761572 0.380786 0.924663i \(-0.375653\pi\)
0.380786 + 0.924663i \(0.375653\pi\)
\(270\) 0 0
\(271\) 5768.00 1.29292 0.646459 0.762948i \(-0.276249\pi\)
0.646459 + 0.762948i \(0.276249\pi\)
\(272\) 0 0
\(273\) 1020.00i 0.226129i
\(274\) 0 0
\(275\) −3450.00 4600.00i −0.756519 1.00869i
\(276\) 0 0
\(277\) 1398.00i 0.303241i −0.988439 0.151620i \(-0.951551\pi\)
0.988439 0.151620i \(-0.0484491\pi\)
\(278\) 0 0
\(279\) 648.000 0.139049
\(280\) 0 0
\(281\) −4194.00 −0.890367 −0.445183 0.895439i \(-0.646862\pi\)
−0.445183 + 0.895439i \(0.646862\pi\)
\(282\) 0 0
\(283\) 8256.00i 1.73416i 0.498166 + 0.867082i \(0.334007\pi\)
−0.498166 + 0.867082i \(0.665993\pi\)
\(284\) 0 0
\(285\) 1560.00 3120.00i 0.324233 0.648466i
\(286\) 0 0
\(287\) 1940.00i 0.399006i
\(288\) 0 0
\(289\) 557.000 0.113373
\(290\) 0 0
\(291\) −4152.00 −0.836407
\(292\) 0 0
\(293\) 5534.00i 1.10341i −0.834039 0.551706i \(-0.813977\pi\)
0.834039 0.551706i \(-0.186023\pi\)
\(294\) 0 0
\(295\) 4260.00 + 2130.00i 0.840769 + 0.420384i
\(296\) 0 0
\(297\) 1242.00i 0.242654i
\(298\) 0 0
\(299\) 5576.00 1.07849
\(300\) 0 0
\(301\) 1080.00 0.206811
\(302\) 0 0
\(303\) 3384.00i 0.641603i
\(304\) 0 0
\(305\) −6980.00 3490.00i −1.31041 0.655203i
\(306\) 0 0
\(307\) 484.000i 0.0899783i −0.998987 0.0449892i \(-0.985675\pi\)
0.998987 0.0449892i \(-0.0143253\pi\)
\(308\) 0 0
\(309\) 2274.00 0.418652
\(310\) 0 0
\(311\) −2724.00 −0.496668 −0.248334 0.968674i \(-0.579883\pi\)
−0.248334 + 0.968674i \(0.579883\pi\)
\(312\) 0 0
\(313\) 5308.00i 0.958549i −0.877665 0.479275i \(-0.840900\pi\)
0.877665 0.479275i \(-0.159100\pi\)
\(314\) 0 0
\(315\) −450.000 + 900.000i −0.0804909 + 0.160982i
\(316\) 0 0
\(317\) 4218.00i 0.747339i 0.927562 + 0.373670i \(0.121901\pi\)
−0.927562 + 0.373670i \(0.878099\pi\)
\(318\) 0 0
\(319\) 10304.0 1.80851
\(320\) 0 0
\(321\) 3972.00 0.690640
\(322\) 0 0
\(323\) 6864.00i 1.18242i
\(324\) 0 0
\(325\) −3400.00 + 2550.00i −0.580302 + 0.435226i
\(326\) 0 0
\(327\) 4806.00i 0.812760i
\(328\) 0 0
\(329\) 4800.00 0.804354
\(330\) 0 0
\(331\) −4640.00 −0.770506 −0.385253 0.922811i \(-0.625886\pi\)
−0.385253 + 0.922811i \(0.625886\pi\)
\(332\) 0 0
\(333\) 198.000i 0.0325836i
\(334\) 0 0
\(335\) 1640.00 3280.00i 0.267471 0.534942i
\(336\) 0 0
\(337\) 8156.00i 1.31835i −0.751987 0.659177i \(-0.770905\pi\)
0.751987 0.659177i \(-0.229095\pi\)
\(338\) 0 0
\(339\) 6222.00 0.996851
\(340\) 0 0
\(341\) 3312.00 0.525967
\(342\) 0 0
\(343\) 5860.00i 0.922479i
\(344\) 0 0
\(345\) 4920.00 + 2460.00i 0.767779 + 0.383890i
\(346\) 0 0
\(347\) 4124.00i 0.638006i 0.947754 + 0.319003i \(0.103348\pi\)
−0.947754 + 0.319003i \(0.896652\pi\)
\(348\) 0 0
\(349\) −3650.00 −0.559828 −0.279914 0.960025i \(-0.590306\pi\)
−0.279914 + 0.960025i \(0.590306\pi\)
\(350\) 0 0
\(351\) −918.000 −0.139599
\(352\) 0 0
\(353\) 6834.00i 1.03042i −0.857065 0.515208i \(-0.827715\pi\)
0.857065 0.515208i \(-0.172285\pi\)
\(354\) 0 0
\(355\) −1880.00 940.000i −0.281071 0.140535i
\(356\) 0 0
\(357\) 1980.00i 0.293537i
\(358\) 0 0
\(359\) −3904.00 −0.573942 −0.286971 0.957939i \(-0.592648\pi\)
−0.286971 + 0.957939i \(0.592648\pi\)
\(360\) 0 0
\(361\) 3957.00 0.576906
\(362\) 0 0
\(363\) 2355.00i 0.340511i
\(364\) 0 0
\(365\) 3700.00 7400.00i 0.530594 1.06119i
\(366\) 0 0
\(367\) 13174.0i 1.87378i −0.349624 0.936890i \(-0.613691\pi\)
0.349624 0.936890i \(-0.386309\pi\)
\(368\) 0 0
\(369\) −1746.00 −0.246323
\(370\) 0 0
\(371\) 2860.00 0.400226
\(372\) 0 0
\(373\) 1090.00i 0.151308i 0.997134 + 0.0756542i \(0.0241045\pi\)
−0.997134 + 0.0756542i \(0.975895\pi\)
\(374\) 0 0
\(375\) −4125.00 + 750.000i −0.568038 + 0.103280i
\(376\) 0 0
\(377\) 7616.00i 1.04043i
\(378\) 0 0
\(379\) 9220.00 1.24960 0.624802 0.780784i \(-0.285180\pi\)
0.624802 + 0.780784i \(0.285180\pi\)
\(380\) 0 0
\(381\) −1602.00 −0.215415
\(382\) 0 0
\(383\) 3960.00i 0.528320i 0.964479 + 0.264160i \(0.0850947\pi\)
−0.964479 + 0.264160i \(0.914905\pi\)
\(384\) 0 0
\(385\) −2300.00 + 4600.00i −0.304465 + 0.608929i
\(386\) 0 0
\(387\) 972.000i 0.127673i
\(388\) 0 0
\(389\) 1788.00 0.233047 0.116523 0.993188i \(-0.462825\pi\)
0.116523 + 0.993188i \(0.462825\pi\)
\(390\) 0 0
\(391\) 10824.0 1.39998
\(392\) 0 0
\(393\) 5418.00i 0.695425i
\(394\) 0 0
\(395\) 11680.0 + 5840.00i 1.48781 + 0.743905i
\(396\) 0 0
\(397\) 9642.00i 1.21894i 0.792810 + 0.609469i \(0.208617\pi\)
−0.792810 + 0.609469i \(0.791383\pi\)
\(398\) 0 0
\(399\) −3120.00 −0.391467
\(400\) 0 0
\(401\) −410.000 −0.0510584 −0.0255292 0.999674i \(-0.508127\pi\)
−0.0255292 + 0.999674i \(0.508127\pi\)
\(402\) 0 0
\(403\) 2448.00i 0.302589i
\(404\) 0 0
\(405\) −810.000 405.000i −0.0993808 0.0496904i
\(406\) 0 0
\(407\) 1012.00i 0.123251i
\(408\) 0 0
\(409\) −13766.0 −1.66427 −0.832133 0.554576i \(-0.812880\pi\)
−0.832133 + 0.554576i \(0.812880\pi\)
\(410\) 0 0
\(411\) 5466.00 0.656005
\(412\) 0 0
\(413\) 4260.00i 0.507557i
\(414\) 0 0
\(415\) −2060.00 + 4120.00i −0.243666 + 0.487332i
\(416\) 0 0
\(417\) 1596.00i 0.187426i
\(418\) 0 0
\(419\) −16998.0 −1.98188 −0.990939 0.134315i \(-0.957117\pi\)
−0.990939 + 0.134315i \(0.957117\pi\)
\(420\) 0 0
\(421\) −2450.00 −0.283624 −0.141812 0.989894i \(-0.545293\pi\)
−0.141812 + 0.989894i \(0.545293\pi\)
\(422\) 0 0
\(423\) 4320.00i 0.496562i
\(424\) 0 0
\(425\) −6600.00 + 4950.00i −0.753287 + 0.564965i
\(426\) 0 0
\(427\) 6980.00i 0.791068i
\(428\) 0 0
\(429\) −4692.00 −0.528046
\(430\) 0 0
\(431\) −9248.00 −1.03355 −0.516776 0.856121i \(-0.672868\pi\)
−0.516776 + 0.856121i \(0.672868\pi\)
\(432\) 0 0
\(433\) 5028.00i 0.558038i 0.960286 + 0.279019i \(0.0900092\pi\)
−0.960286 + 0.279019i \(0.909991\pi\)
\(434\) 0 0
\(435\) 3360.00 6720.00i 0.370344 0.740688i
\(436\) 0 0
\(437\) 17056.0i 1.86705i
\(438\) 0 0
\(439\) −3120.00 −0.339202 −0.169601 0.985513i \(-0.554248\pi\)
−0.169601 + 0.985513i \(0.554248\pi\)
\(440\) 0 0
\(441\) −2187.00 −0.236152
\(442\) 0 0
\(443\) 8220.00i 0.881589i 0.897608 + 0.440795i \(0.145303\pi\)
−0.897608 + 0.440795i \(0.854697\pi\)
\(444\) 0 0
\(445\) 12060.0 + 6030.00i 1.28472 + 0.642358i
\(446\) 0 0
\(447\) 3852.00i 0.407591i
\(448\) 0 0
\(449\) 5826.00 0.612352 0.306176 0.951975i \(-0.400950\pi\)
0.306176 + 0.951975i \(0.400950\pi\)
\(450\) 0 0
\(451\) −8924.00 −0.931740
\(452\) 0 0
\(453\) 552.000i 0.0572521i
\(454\) 0 0
\(455\) 3400.00 + 1700.00i 0.350317 + 0.175159i
\(456\) 0 0
\(457\) 16896.0i 1.72946i −0.502240 0.864728i \(-0.667491\pi\)
0.502240 0.864728i \(-0.332509\pi\)
\(458\) 0 0
\(459\) −1782.00 −0.181213
\(460\) 0 0
\(461\) −996.000 −0.100625 −0.0503127 0.998734i \(-0.516022\pi\)
−0.0503127 + 0.998734i \(0.516022\pi\)
\(462\) 0 0
\(463\) 10046.0i 1.00837i −0.863594 0.504187i \(-0.831792\pi\)
0.863594 0.504187i \(-0.168208\pi\)
\(464\) 0 0
\(465\) 1080.00 2160.00i 0.107707 0.215414i
\(466\) 0 0
\(467\) 8388.00i 0.831157i −0.909557 0.415579i \(-0.863579\pi\)
0.909557 0.415579i \(-0.136421\pi\)
\(468\) 0 0
\(469\) −3280.00 −0.322935
\(470\) 0 0
\(471\) −11238.0 −1.09940
\(472\) 0 0
\(473\) 4968.00i 0.482936i
\(474\) 0 0
\(475\) −7800.00 10400.0i −0.753450 1.00460i
\(476\) 0 0
\(477\) 2574.00i 0.247076i
\(478\) 0 0
\(479\) −11396.0 −1.08705 −0.543525 0.839393i \(-0.682911\pi\)
−0.543525 + 0.839393i \(0.682911\pi\)
\(480\) 0 0
\(481\) 748.000 0.0709062
\(482\) 0 0
\(483\) 4920.00i 0.463494i
\(484\) 0 0
\(485\) −6920.00 + 13840.0i −0.647878 + 1.29576i
\(486\) 0 0
\(487\) 6454.00i 0.600531i 0.953856 + 0.300266i \(0.0970753\pi\)
−0.953856 + 0.300266i \(0.902925\pi\)
\(488\) 0 0
\(489\) −4512.00 −0.417259
\(490\) 0 0
\(491\) 18638.0 1.71308 0.856539 0.516083i \(-0.172610\pi\)
0.856539 + 0.516083i \(0.172610\pi\)
\(492\) 0 0
\(493\) 14784.0i 1.35058i
\(494\) 0 0
\(495\) −4140.00 2070.00i −0.375917 0.187959i
\(496\) 0 0
\(497\) 1880.00i 0.169677i
\(498\) 0 0
\(499\) −17768.0 −1.59400 −0.796999 0.603981i \(-0.793580\pi\)
−0.796999 + 0.603981i \(0.793580\pi\)
\(500\) 0 0
\(501\) 9036.00 0.805786
\(502\) 0 0
\(503\) 7952.00i 0.704895i 0.935832 + 0.352447i \(0.114650\pi\)
−0.935832 + 0.352447i \(0.885350\pi\)
\(504\) 0 0
\(505\) 11280.0 + 5640.00i 0.993967 + 0.496984i
\(506\) 0 0
\(507\) 3123.00i 0.273565i
\(508\) 0 0
\(509\) 12896.0 1.12300 0.561498 0.827478i \(-0.310225\pi\)
0.561498 + 0.827478i \(0.310225\pi\)
\(510\) 0 0
\(511\) −7400.00 −0.640620
\(512\) 0 0
\(513\) 2808.00i 0.241669i
\(514\) 0 0
\(515\) 3790.00 7580.00i 0.324286 0.648572i
\(516\) 0 0
\(517\) 22080.0i 1.87829i
\(518\) 0 0
\(519\) 1314.00 0.111133
\(520\) 0 0
\(521\) −2714.00 −0.228220 −0.114110 0.993468i \(-0.536402\pi\)
−0.114110 + 0.993468i \(0.536402\pi\)
\(522\) 0 0
\(523\) 13792.0i 1.15312i 0.817055 + 0.576560i \(0.195605\pi\)
−0.817055 + 0.576560i \(0.804395\pi\)
\(524\) 0 0
\(525\) 2250.00 + 3000.00i 0.187044 + 0.249392i
\(526\) 0 0
\(527\) 4752.00i 0.392790i
\(528\) 0 0
\(529\) −14729.0 −1.21057
\(530\) 0 0
\(531\) 3834.00 0.313336
\(532\) 0 0
\(533\) 6596.00i 0.536031i
\(534\) 0 0
\(535\) 6620.00 13240.0i 0.534967 1.06993i
\(536\) 0 0
\(537\) 4386.00i 0.352458i
\(538\) 0 0
\(539\) −11178.0 −0.893266
\(540\) 0 0
\(541\) 6802.00 0.540556 0.270278 0.962782i \(-0.412884\pi\)
0.270278 + 0.962782i \(0.412884\pi\)
\(542\) 0 0
\(543\) 1758.00i 0.138937i
\(544\) 0 0
\(545\) 16020.0 + 8010.00i 1.25912 + 0.629561i
\(546\) 0 0
\(547\) 18188.0i 1.42169i −0.703350 0.710843i \(-0.748313\pi\)
0.703350 0.710843i \(-0.251687\pi\)
\(548\) 0 0
\(549\) −6282.00 −0.488359
\(550\) 0 0
\(551\) 23296.0 1.80117
\(552\) 0 0
\(553\) 11680.0i 0.898163i
\(554\) 0 0
\(555\) 660.000 + 330.000i 0.0504783 + 0.0252391i
\(556\) 0 0
\(557\) 21462.0i 1.63263i 0.577608 + 0.816314i \(0.303986\pi\)
−0.577608 + 0.816314i \(0.696014\pi\)
\(558\) 0 0
\(559\) 3672.00 0.277834
\(560\) 0 0
\(561\) −9108.00 −0.685455
\(562\) 0 0
\(563\) 17244.0i 1.29085i 0.763824 + 0.645424i \(0.223319\pi\)
−0.763824 + 0.645424i \(0.776681\pi\)
\(564\) 0 0
\(565\) 10370.0 20740.0i 0.772158 1.54432i
\(566\) 0 0
\(567\) 810.000i 0.0599944i
\(568\) 0 0
\(569\) −8790.00 −0.647620 −0.323810 0.946122i \(-0.604964\pi\)
−0.323810 + 0.946122i \(0.604964\pi\)
\(570\) 0 0
\(571\) −5984.00 −0.438568 −0.219284 0.975661i \(-0.570372\pi\)
−0.219284 + 0.975661i \(0.570372\pi\)
\(572\) 0 0
\(573\) 180.000i 0.0131232i
\(574\) 0 0
\(575\) 16400.0 12300.0i 1.18944 0.892079i
\(576\) 0 0
\(577\) 9344.00i 0.674170i −0.941474 0.337085i \(-0.890559\pi\)
0.941474 0.337085i \(-0.109441\pi\)
\(578\) 0 0
\(579\) 14028.0 1.00688
\(580\) 0 0
\(581\) 4120.00 0.294193
\(582\) 0 0
\(583\) 13156.0i 0.934590i
\(584\) 0 0
\(585\) −1530.00 + 3060.00i −0.108133 + 0.216266i
\(586\) 0 0
\(587\) 6932.00i 0.487418i −0.969848 0.243709i \(-0.921636\pi\)
0.969848 0.243709i \(-0.0783642\pi\)
\(588\) 0 0
\(589\) 7488.00 0.523833
\(590\) 0 0
\(591\) 6858.00 0.477327
\(592\) 0 0
\(593\) 9382.00i 0.649701i −0.945765 0.324850i \(-0.894686\pi\)
0.945765 0.324850i \(-0.105314\pi\)
\(594\) 0 0
\(595\) 6600.00 + 3300.00i 0.454746 + 0.227373i
\(596\) 0 0
\(597\) 10608.0i 0.727230i
\(598\) 0 0
\(599\) −4096.00 −0.279396 −0.139698 0.990194i \(-0.544613\pi\)
−0.139698 + 0.990194i \(0.544613\pi\)
\(600\) 0 0
\(601\) 22962.0 1.55847 0.779234 0.626733i \(-0.215608\pi\)
0.779234 + 0.626733i \(0.215608\pi\)
\(602\) 0 0
\(603\) 2952.00i 0.199361i
\(604\) 0 0
\(605\) −7850.00 3925.00i −0.527517 0.263759i
\(606\) 0 0
\(607\) 3490.00i 0.233369i −0.993169 0.116684i \(-0.962773\pi\)
0.993169 0.116684i \(-0.0372266\pi\)
\(608\) 0 0
\(609\) −6720.00 −0.447140
\(610\) 0 0
\(611\) 16320.0 1.08058
\(612\) 0 0
\(613\) 6386.00i 0.420764i −0.977619 0.210382i \(-0.932529\pi\)
0.977619 0.210382i \(-0.0674707\pi\)
\(614\) 0 0
\(615\) −2910.00 + 5820.00i −0.190801 + 0.381602i
\(616\) 0 0
\(617\) 19534.0i 1.27457i −0.770629 0.637285i \(-0.780058\pi\)
0.770629 0.637285i \(-0.219942\pi\)
\(618\) 0 0
\(619\) −8764.00 −0.569071 −0.284535 0.958666i \(-0.591839\pi\)
−0.284535 + 0.958666i \(0.591839\pi\)
\(620\) 0 0
\(621\) 4428.00 0.286134
\(622\) 0 0
\(623\) 12060.0i 0.775560i
\(624\) 0 0
\(625\) −4375.00 + 15000.0i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) 14352.0i 0.914137i
\(628\) 0 0
\(629\) 1452.00 0.0920430
\(630\) 0 0
\(631\) 7856.00 0.495630 0.247815 0.968807i \(-0.420288\pi\)
0.247815 + 0.968807i \(0.420288\pi\)
\(632\) 0 0
\(633\) 10500.0i 0.659301i
\(634\) 0 0
\(635\) −2670.00 + 5340.00i −0.166859 + 0.333719i
\(636\) 0 0
\(637\) 8262.00i 0.513897i
\(638\) 0 0
\(639\) −1692.00 −0.104749
\(640\) 0 0
\(641\) −22974.0 −1.41563 −0.707815 0.706398i \(-0.750319\pi\)
−0.707815 + 0.706398i \(0.750319\pi\)
\(642\) 0 0
\(643\) 6216.00i 0.381237i 0.981664 + 0.190618i \(0.0610493\pi\)
−0.981664 + 0.190618i \(0.938951\pi\)
\(644\) 0 0
\(645\) 3240.00 + 1620.00i 0.197791 + 0.0988953i
\(646\) 0 0
\(647\) 13384.0i 0.813260i 0.913593 + 0.406630i \(0.133296\pi\)
−0.913593 + 0.406630i \(0.866704\pi\)
\(648\) 0 0
\(649\) 19596.0 1.18522
\(650\) 0 0
\(651\) −2160.00 −0.130042
\(652\) 0 0
\(653\) 12882.0i 0.771993i −0.922500 0.385997i \(-0.873858\pi\)
0.922500 0.385997i \(-0.126142\pi\)
\(654\) 0 0
\(655\) −18060.0 9030.00i −1.07735 0.538674i
\(656\) 0 0
\(657\) 6660.00i 0.395482i
\(658\) 0 0
\(659\) 2082.00 0.123070 0.0615351 0.998105i \(-0.480400\pi\)
0.0615351 + 0.998105i \(0.480400\pi\)
\(660\) 0 0
\(661\) −9430.00 −0.554893 −0.277447 0.960741i \(-0.589488\pi\)
−0.277447 + 0.960741i \(0.589488\pi\)
\(662\) 0 0
\(663\) 6732.00i 0.394343i
\(664\) 0 0
\(665\) −5200.00 + 10400.0i −0.303229 + 0.606458i
\(666\) 0 0
\(667\) 36736.0i 2.13257i
\(668\) 0 0
\(669\) −17622.0 −1.01839
\(670\) 0 0
\(671\) −32108.0 −1.84727
\(672\) 0 0
\(673\) 3268.00i 0.187180i −0.995611 0.0935900i \(-0.970166\pi\)
0.995611 0.0935900i \(-0.0298343\pi\)
\(674\) 0 0
\(675\) −2700.00 + 2025.00i −0.153960 + 0.115470i
\(676\) 0 0
\(677\) 15606.0i 0.885949i −0.896534 0.442974i \(-0.853923\pi\)
0.896534 0.442974i \(-0.146077\pi\)
\(678\) 0 0
\(679\) 13840.0 0.782225
\(680\) 0 0
\(681\) −372.000 −0.0209326
\(682\) 0 0
\(683\) 428.000i 0.0239780i −0.999928 0.0119890i \(-0.996184\pi\)
0.999928 0.0119890i \(-0.00381631\pi\)
\(684\) 0 0
\(685\) 9110.00 18220.0i 0.508139 1.01628i
\(686\) 0 0
\(687\) 4086.00i 0.226915i
\(688\) 0 0
\(689\) 9724.00 0.537670
\(690\) 0 0
\(691\) −6384.00 −0.351460 −0.175730 0.984438i \(-0.556229\pi\)
−0.175730 + 0.984438i \(0.556229\pi\)
\(692\) 0 0
\(693\) 4140.00i 0.226934i
\(694\) 0 0
\(695\) 5320.00 + 2660.00i 0.290358 + 0.145179i
\(696\) 0 0
\(697\) 12804.0i 0.695819i
\(698\) 0 0
\(699\) 11610.0 0.628227
\(700\) 0 0
\(701\) −12224.0 −0.658622 −0.329311 0.944221i \(-0.606816\pi\)
−0.329311 + 0.944221i \(0.606816\pi\)
\(702\) 0 0
\(703\) 2288.00i 0.122750i
\(704\) 0 0
\(705\) 14400.0 + 7200.00i 0.769270 + 0.384635i
\(706\) 0 0
\(707\) 11280.0i 0.600040i
\(708\) 0 0
\(709\) −19510.0 −1.03345 −0.516723 0.856153i \(-0.672848\pi\)
−0.516723 + 0.856153i \(0.672848\pi\)
\(710\) 0 0
\(711\) 10512.0 0.554474
\(712\) 0 0
\(713\) 11808.0i 0.620215i
\(714\) 0 0
\(715\) −7820.00 + 15640.0i −0.409023 + 0.818046i
\(716\) 0 0
\(717\) 18348.0i 0.955674i
\(718\) 0 0
\(719\) 3368.00 0.174694 0.0873472 0.996178i \(-0.472161\pi\)
0.0873472 + 0.996178i \(0.472161\pi\)
\(720\) 0 0
\(721\) −7580.00 −0.391531
\(722\) 0 0
\(723\) 17886.0i 0.920038i
\(724\) 0 0
\(725\) −16800.0 22400.0i −0.860602 1.14747i
\(726\) 0 0
\(727\) 22134.0i 1.12917i 0.825376 + 0.564584i \(0.190963\pi\)
−0.825376 + 0.564584i \(0.809037\pi\)
\(728\) 0 0
\(729\) −729.000 −0.0370370
\(730\) 0 0
\(731\) 7128.00 0.360655
\(732\) 0 0
\(733\) 32298.0i 1.62750i −0.581219 0.813748i \(-0.697424\pi\)
0.581219 0.813748i \(-0.302576\pi\)
\(734\) 0 0
\(735\) −3645.00 + 7290.00i −0.182922 + 0.365844i
\(736\) 0 0
\(737\) 15088.0i 0.754103i
\(738\) 0 0
\(739\) −25104.0 −1.24962 −0.624808 0.780779i \(-0.714823\pi\)
−0.624808 + 0.780779i \(0.714823\pi\)
\(740\) 0 0
\(741\) −10608.0 −0.525904
\(742\) 0 0
\(743\) 27696.0i 1.36752i 0.729707 + 0.683760i \(0.239657\pi\)
−0.729707 + 0.683760i \(0.760343\pi\)
\(744\) 0 0
\(745\) −12840.0 6420.00i −0.631438 0.315719i
\(746\) 0 0
\(747\) 3708.00i 0.181618i
\(748\) 0 0
\(749\) −13240.0 −0.645900
\(750\) 0 0
\(751\) −2176.00 −0.105730 −0.0528651 0.998602i \(-0.516835\pi\)
−0.0528651 + 0.998602i \(0.516835\pi\)
\(752\) 0 0
\(753\) 4470.00i 0.216329i
\(754\) 0 0
\(755\) −1840.00 920.000i −0.0886946 0.0443473i
\(756\) 0 0
\(757\) 25514.0i 1.22500i 0.790472 + 0.612498i \(0.209835\pi\)
−0.790472 + 0.612498i \(0.790165\pi\)
\(758\) 0 0
\(759\) 22632.0 1.08233
\(760\) 0 0
\(761\) 18238.0 0.868761 0.434380 0.900730i \(-0.356967\pi\)
0.434380 + 0.900730i \(0.356967\pi\)
\(762\) 0 0
\(763\) 16020.0i 0.760109i
\(764\) 0 0
\(765\) −2970.00 + 5940.00i −0.140367 + 0.280734i
\(766\) 0 0
\(767\) 14484.0i 0.681860i
\(768\) 0 0
\(769\) 14462.0 0.678170 0.339085 0.940756i \(-0.389882\pi\)
0.339085 + 0.940756i \(0.389882\pi\)
\(770\) 0 0
\(771\) −16182.0 −0.755876
\(772\) 0 0
\(773\) 34034.0i 1.58359i −0.610785 0.791797i \(-0.709146\pi\)
0.610785 0.791797i \(-0.290854\pi\)
\(774\) 0 0
\(775\) −5400.00 7200.00i −0.250289 0.333718i
\(776\) 0 0
\(777\) 660.000i 0.0304728i
\(778\) 0 0
\(779\) −20176.0 −0.927959
\(780\) 0 0
\(781\) −8648.00 −0.396222
\(782\) 0 0
\(783\) 6048.00i 0.276038i
\(784\) 0 0
\(785\) −18730.0 + 37460.0i −0.851595 + 1.70319i
\(786\) 0 0
\(787\) 22064.0i 0.999360i 0.866210 + 0.499680i \(0.166549\pi\)
−0.866210 + 0.499680i \(0.833451\pi\)
\(788\) 0 0
\(789\) 1908.00 0.0860920
\(790\) 0 0