Properties

Label 2640.2.d.h.529.4
Level $2640$
Weight $2$
Character 2640.529
Analytic conductor $21.081$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2640,2,Mod(529,2640)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2640, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2640.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2640.d (of order \(2\), degree \(1\), 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: \(21.0805061336\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 529.4
Root \(0.403032 - 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 2640.529
Dual form 2640.2.d.h.529.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{3} +(-1.48119 - 1.67513i) q^{5} -1.19394i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{3} +(-1.48119 - 1.67513i) q^{5} -1.19394i q^{7} -1.00000 q^{9} -1.00000 q^{11} -0.806063i q^{13} +(1.67513 - 1.48119i) q^{15} +3.76845i q^{17} -5.35026 q^{19} +1.19394 q^{21} +4.00000i q^{23} +(-0.612127 + 4.96239i) q^{25} -1.00000i q^{27} +4.31265 q^{29} -0.962389 q^{31} -1.00000i q^{33} +(-2.00000 + 1.76845i) q^{35} +1.61213i q^{37} +0.806063 q^{39} +9.08840 q^{41} +4.41819i q^{43} +(1.48119 + 1.67513i) q^{45} -12.3127i q^{47} +5.57452 q^{49} -3.76845 q^{51} -1.42548i q^{53} +(1.48119 + 1.67513i) q^{55} -5.35026i q^{57} +13.2750 q^{59} -0.0752228 q^{61} +1.19394i q^{63} +(-1.35026 + 1.19394i) q^{65} +2.70052i q^{67} -4.00000 q^{69} +14.0508 q^{71} +10.7308i q^{73} +(-4.96239 - 0.612127i) q^{75} +1.19394i q^{77} +13.9756 q^{79} +1.00000 q^{81} -9.89446i q^{83} +(6.31265 - 5.58181i) q^{85} +4.31265i q^{87} -16.8872 q^{89} -0.962389 q^{91} -0.962389i q^{93} +(7.92478 + 8.96239i) q^{95} +11.4763i q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{5} - 6 q^{9} - 6 q^{11} - 12 q^{19} + 8 q^{21} - 2 q^{25} - 16 q^{29} + 16 q^{31} - 12 q^{35} + 4 q^{39} + 16 q^{41} - 2 q^{45} + 10 q^{49} - 2 q^{55} + 16 q^{59} - 44 q^{61} + 12 q^{65} - 24 q^{69} + 24 q^{71} - 8 q^{75} - 20 q^{79} + 6 q^{81} - 4 q^{85} - 36 q^{89} + 16 q^{91} + 4 q^{95} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2640\mathbb{Z}\right)^\times\).

\(n\) \(661\) \(881\) \(991\) \(1057\) \(1201\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\) \(1\)

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
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) −1.48119 1.67513i −0.662410 0.749141i
\(6\) 0 0
\(7\) 1.19394i 0.451266i −0.974212 0.225633i \(-0.927555\pi\)
0.974212 0.225633i \(-0.0724450\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 0.806063i 0.223562i −0.993733 0.111781i \(-0.964345\pi\)
0.993733 0.111781i \(-0.0356555\pi\)
\(14\) 0 0
\(15\) 1.67513 1.48119i 0.432517 0.382443i
\(16\) 0 0
\(17\) 3.76845i 0.913984i 0.889471 + 0.456992i \(0.151073\pi\)
−0.889471 + 0.456992i \(0.848927\pi\)
\(18\) 0 0
\(19\) −5.35026 −1.22743 −0.613717 0.789526i \(-0.710326\pi\)
−0.613717 + 0.789526i \(0.710326\pi\)
\(20\) 0 0
\(21\) 1.19394 0.260538
\(22\) 0 0
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 0 0
\(25\) −0.612127 + 4.96239i −0.122425 + 0.992478i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 4.31265 0.800839 0.400420 0.916332i \(-0.368864\pi\)
0.400420 + 0.916332i \(0.368864\pi\)
\(30\) 0 0
\(31\) −0.962389 −0.172850 −0.0864250 0.996258i \(-0.527544\pi\)
−0.0864250 + 0.996258i \(0.527544\pi\)
\(32\) 0 0
\(33\) 1.00000i 0.174078i
\(34\) 0 0
\(35\) −2.00000 + 1.76845i −0.338062 + 0.298923i
\(36\) 0 0
\(37\) 1.61213i 0.265032i 0.991181 + 0.132516i \(0.0423056\pi\)
−0.991181 + 0.132516i \(0.957694\pi\)
\(38\) 0 0
\(39\) 0.806063 0.129073
\(40\) 0 0
\(41\) 9.08840 1.41937 0.709685 0.704520i \(-0.248837\pi\)
0.709685 + 0.704520i \(0.248837\pi\)
\(42\) 0 0
\(43\) 4.41819i 0.673768i 0.941546 + 0.336884i \(0.109373\pi\)
−0.941546 + 0.336884i \(0.890627\pi\)
\(44\) 0 0
\(45\) 1.48119 + 1.67513i 0.220803 + 0.249714i
\(46\) 0 0
\(47\) 12.3127i 1.79598i −0.440011 0.897992i \(-0.645026\pi\)
0.440011 0.897992i \(-0.354974\pi\)
\(48\) 0 0
\(49\) 5.57452 0.796359
\(50\) 0 0
\(51\) −3.76845 −0.527689
\(52\) 0 0
\(53\) 1.42548i 0.195805i −0.995196 0.0979027i \(-0.968787\pi\)
0.995196 0.0979027i \(-0.0312134\pi\)
\(54\) 0 0
\(55\) 1.48119 + 1.67513i 0.199724 + 0.225875i
\(56\) 0 0
\(57\) 5.35026i 0.708659i
\(58\) 0 0
\(59\) 13.2750 1.72826 0.864131 0.503266i \(-0.167868\pi\)
0.864131 + 0.503266i \(0.167868\pi\)
\(60\) 0 0
\(61\) −0.0752228 −0.00963129 −0.00481565 0.999988i \(-0.501533\pi\)
−0.00481565 + 0.999988i \(0.501533\pi\)
\(62\) 0 0
\(63\) 1.19394i 0.150422i
\(64\) 0 0
\(65\) −1.35026 + 1.19394i −0.167479 + 0.148090i
\(66\) 0 0
\(67\) 2.70052i 0.329921i 0.986300 + 0.164961i \(0.0527497\pi\)
−0.986300 + 0.164961i \(0.947250\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 14.0508 1.66752 0.833761 0.552126i \(-0.186183\pi\)
0.833761 + 0.552126i \(0.186183\pi\)
\(72\) 0 0
\(73\) 10.7308i 1.25595i 0.778234 + 0.627975i \(0.216116\pi\)
−0.778234 + 0.627975i \(0.783884\pi\)
\(74\) 0 0
\(75\) −4.96239 0.612127i −0.573007 0.0706823i
\(76\) 0 0
\(77\) 1.19394i 0.136062i
\(78\) 0 0
\(79\) 13.9756 1.57237 0.786187 0.617989i \(-0.212052\pi\)
0.786187 + 0.617989i \(0.212052\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 9.89446i 1.08606i −0.839714 0.543029i \(-0.817277\pi\)
0.839714 0.543029i \(-0.182723\pi\)
\(84\) 0 0
\(85\) 6.31265 5.58181i 0.684703 0.605432i
\(86\) 0 0
\(87\) 4.31265i 0.462365i
\(88\) 0 0
\(89\) −16.8872 −1.79004 −0.895018 0.446030i \(-0.852837\pi\)
−0.895018 + 0.446030i \(0.852837\pi\)
\(90\) 0 0
\(91\) −0.962389 −0.100886
\(92\) 0 0
\(93\) 0.962389i 0.0997950i
\(94\) 0 0
\(95\) 7.92478 + 8.96239i 0.813065 + 0.919522i
\(96\) 0 0
\(97\) 11.4763i 1.16524i 0.812745 + 0.582619i \(0.197972\pi\)
−0.812745 + 0.582619i \(0.802028\pi\)
\(98\) 0 0
\(99\) 1.00000 0.100504
\(100\) 0 0
\(101\) 10.7612 1.07078 0.535388 0.844606i \(-0.320166\pi\)
0.535388 + 0.844606i \(0.320166\pi\)
\(102\) 0 0
\(103\) 16.9380i 1.66895i 0.551049 + 0.834473i \(0.314228\pi\)
−0.551049 + 0.834473i \(0.685772\pi\)
\(104\) 0 0
\(105\) −1.76845 2.00000i −0.172583 0.195180i
\(106\) 0 0
\(107\) 8.28233i 0.800683i −0.916366 0.400342i \(-0.868891\pi\)
0.916366 0.400342i \(-0.131109\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) −1.61213 −0.153016
\(112\) 0 0
\(113\) 2.26187i 0.212778i −0.994325 0.106389i \(-0.966071\pi\)
0.994325 0.106389i \(-0.0339289\pi\)
\(114\) 0 0
\(115\) 6.70052 5.92478i 0.624827 0.552488i
\(116\) 0 0
\(117\) 0.806063i 0.0745206i
\(118\) 0 0
\(119\) 4.49929 0.412449
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 9.08840i 0.819473i
\(124\) 0 0
\(125\) 9.21933 6.32487i 0.824602 0.565713i
\(126\) 0 0
\(127\) 13.8192i 1.22626i 0.789982 + 0.613130i \(0.210090\pi\)
−0.789982 + 0.613130i \(0.789910\pi\)
\(128\) 0 0
\(129\) −4.41819 −0.389000
\(130\) 0 0
\(131\) 5.92478 0.517650 0.258825 0.965924i \(-0.416665\pi\)
0.258825 + 0.965924i \(0.416665\pi\)
\(132\) 0 0
\(133\) 6.38787i 0.553899i
\(134\) 0 0
\(135\) −1.67513 + 1.48119i −0.144172 + 0.127481i
\(136\) 0 0
\(137\) 3.35026i 0.286232i 0.989706 + 0.143116i \(0.0457122\pi\)
−0.989706 + 0.143116i \(0.954288\pi\)
\(138\) 0 0
\(139\) −21.1998 −1.79814 −0.899072 0.437800i \(-0.855758\pi\)
−0.899072 + 0.437800i \(0.855758\pi\)
\(140\) 0 0
\(141\) 12.3127 1.03691
\(142\) 0 0
\(143\) 0.806063i 0.0674064i
\(144\) 0 0
\(145\) −6.38787 7.22425i −0.530484 0.599942i
\(146\) 0 0
\(147\) 5.57452i 0.459778i
\(148\) 0 0
\(149\) −6.38787 −0.523315 −0.261657 0.965161i \(-0.584269\pi\)
−0.261657 + 0.965161i \(0.584269\pi\)
\(150\) 0 0
\(151\) 2.64974 0.215633 0.107816 0.994171i \(-0.465614\pi\)
0.107816 + 0.994171i \(0.465614\pi\)
\(152\) 0 0
\(153\) 3.76845i 0.304661i
\(154\) 0 0
\(155\) 1.42548 + 1.61213i 0.114498 + 0.129489i
\(156\) 0 0
\(157\) 1.61213i 0.128662i 0.997929 + 0.0643309i \(0.0204913\pi\)
−0.997929 + 0.0643309i \(0.979509\pi\)
\(158\) 0 0
\(159\) 1.42548 0.113048
\(160\) 0 0
\(161\) 4.77575 0.376382
\(162\) 0 0
\(163\) 0.312650i 0.0244887i −0.999925 0.0122443i \(-0.996102\pi\)
0.999925 0.0122443i \(-0.00389759\pi\)
\(164\) 0 0
\(165\) −1.67513 + 1.48119i −0.130409 + 0.115311i
\(166\) 0 0
\(167\) 0.493413i 0.0381815i −0.999818 0.0190907i \(-0.993923\pi\)
0.999818 0.0190907i \(-0.00607714\pi\)
\(168\) 0 0
\(169\) 12.3503 0.950020
\(170\) 0 0
\(171\) 5.35026 0.409145
\(172\) 0 0
\(173\) 23.3054i 1.77187i 0.463806 + 0.885937i \(0.346483\pi\)
−0.463806 + 0.885937i \(0.653517\pi\)
\(174\) 0 0
\(175\) 5.92478 + 0.730841i 0.447871 + 0.0552464i
\(176\) 0 0
\(177\) 13.2750i 0.997813i
\(178\) 0 0
\(179\) −10.7005 −0.799795 −0.399897 0.916560i \(-0.630954\pi\)
−0.399897 + 0.916560i \(0.630954\pi\)
\(180\) 0 0
\(181\) −7.79877 −0.579678 −0.289839 0.957075i \(-0.593602\pi\)
−0.289839 + 0.957075i \(0.593602\pi\)
\(182\) 0 0
\(183\) 0.0752228i 0.00556063i
\(184\) 0 0
\(185\) 2.70052 2.38787i 0.198546 0.175560i
\(186\) 0 0
\(187\) 3.76845i 0.275577i
\(188\) 0 0
\(189\) −1.19394 −0.0868461
\(190\) 0 0
\(191\) −1.29948 −0.0940268 −0.0470134 0.998894i \(-0.514970\pi\)
−0.0470134 + 0.998894i \(0.514970\pi\)
\(192\) 0 0
\(193\) 8.59498i 0.618680i −0.950951 0.309340i \(-0.899892\pi\)
0.950951 0.309340i \(-0.100108\pi\)
\(194\) 0 0
\(195\) −1.19394 1.35026i −0.0854996 0.0966943i
\(196\) 0 0
\(197\) 20.7064i 1.47527i −0.675200 0.737635i \(-0.735943\pi\)
0.675200 0.737635i \(-0.264057\pi\)
\(198\) 0 0
\(199\) 5.55149 0.393535 0.196767 0.980450i \(-0.436956\pi\)
0.196767 + 0.980450i \(0.436956\pi\)
\(200\) 0 0
\(201\) −2.70052 −0.190480
\(202\) 0 0
\(203\) 5.14903i 0.361391i
\(204\) 0 0
\(205\) −13.4617 15.2243i −0.940205 1.06331i
\(206\) 0 0
\(207\) 4.00000i 0.278019i
\(208\) 0 0
\(209\) 5.35026 0.370085
\(210\) 0 0
\(211\) 18.4993 1.27354 0.636772 0.771052i \(-0.280269\pi\)
0.636772 + 0.771052i \(0.280269\pi\)
\(212\) 0 0
\(213\) 14.0508i 0.962744i
\(214\) 0 0
\(215\) 7.40105 6.54420i 0.504747 0.446311i
\(216\) 0 0
\(217\) 1.14903i 0.0780013i
\(218\) 0 0
\(219\) −10.7308 −0.725123
\(220\) 0 0
\(221\) 3.03761 0.204332
\(222\) 0 0
\(223\) 17.6121i 1.17940i 0.807624 + 0.589698i \(0.200753\pi\)
−0.807624 + 0.589698i \(0.799247\pi\)
\(224\) 0 0
\(225\) 0.612127 4.96239i 0.0408085 0.330826i
\(226\) 0 0
\(227\) 17.4314i 1.15696i 0.815696 + 0.578480i \(0.196354\pi\)
−0.815696 + 0.578480i \(0.803646\pi\)
\(228\) 0 0
\(229\) −13.0738 −0.863942 −0.431971 0.901888i \(-0.642182\pi\)
−0.431971 + 0.901888i \(0.642182\pi\)
\(230\) 0 0
\(231\) −1.19394 −0.0785553
\(232\) 0 0
\(233\) 13.8437i 0.906929i 0.891274 + 0.453465i \(0.149812\pi\)
−0.891274 + 0.453465i \(0.850188\pi\)
\(234\) 0 0
\(235\) −20.6253 + 18.2374i −1.34545 + 1.18968i
\(236\) 0 0
\(237\) 13.9756i 0.907810i
\(238\) 0 0
\(239\) −12.3733 −0.800361 −0.400181 0.916436i \(-0.631053\pi\)
−0.400181 + 0.916436i \(0.631053\pi\)
\(240\) 0 0
\(241\) −24.5501 −1.58141 −0.790705 0.612198i \(-0.790286\pi\)
−0.790705 + 0.612198i \(0.790286\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −8.25694 9.33804i −0.527517 0.596586i
\(246\) 0 0
\(247\) 4.31265i 0.274407i
\(248\) 0 0
\(249\) 9.89446 0.627036
\(250\) 0 0
\(251\) −13.9003 −0.877382 −0.438691 0.898638i \(-0.644558\pi\)
−0.438691 + 0.898638i \(0.644558\pi\)
\(252\) 0 0
\(253\) 4.00000i 0.251478i
\(254\) 0 0
\(255\) 5.58181 + 6.31265i 0.349546 + 0.395313i
\(256\) 0 0
\(257\) 18.8872i 1.17815i −0.808079 0.589075i \(-0.799492\pi\)
0.808079 0.589075i \(-0.200508\pi\)
\(258\) 0 0
\(259\) 1.92478 0.119600
\(260\) 0 0
\(261\) −4.31265 −0.266946
\(262\) 0 0
\(263\) 20.8061i 1.28296i 0.767141 + 0.641478i \(0.221679\pi\)
−0.767141 + 0.641478i \(0.778321\pi\)
\(264\) 0 0
\(265\) −2.38787 + 2.11142i −0.146686 + 0.129703i
\(266\) 0 0
\(267\) 16.8872i 1.03348i
\(268\) 0 0
\(269\) 32.3996 1.97544 0.987720 0.156233i \(-0.0499351\pi\)
0.987720 + 0.156233i \(0.0499351\pi\)
\(270\) 0 0
\(271\) 16.8265 1.02214 0.511069 0.859539i \(-0.329249\pi\)
0.511069 + 0.859539i \(0.329249\pi\)
\(272\) 0 0
\(273\) 0.962389i 0.0582464i
\(274\) 0 0
\(275\) 0.612127 4.96239i 0.0369126 0.299243i
\(276\) 0 0
\(277\) 16.9076i 1.01588i 0.861392 + 0.507941i \(0.169593\pi\)
−0.861392 + 0.507941i \(0.830407\pi\)
\(278\) 0 0
\(279\) 0.962389 0.0576167
\(280\) 0 0
\(281\) 5.61213 0.334791 0.167396 0.985890i \(-0.446464\pi\)
0.167396 + 0.985890i \(0.446464\pi\)
\(282\) 0 0
\(283\) 5.81924i 0.345918i 0.984929 + 0.172959i \(0.0553328\pi\)
−0.984929 + 0.172959i \(0.944667\pi\)
\(284\) 0 0
\(285\) −8.96239 + 7.92478i −0.530886 + 0.469423i
\(286\) 0 0
\(287\) 10.8510i 0.640512i
\(288\) 0 0
\(289\) 2.79877 0.164633
\(290\) 0 0
\(291\) −11.4763 −0.672751
\(292\) 0 0
\(293\) 8.29218i 0.484434i 0.970222 + 0.242217i \(0.0778747\pi\)
−0.970222 + 0.242217i \(0.922125\pi\)
\(294\) 0 0
\(295\) −19.6629 22.2374i −1.14482 1.29471i
\(296\) 0 0
\(297\) 1.00000i 0.0580259i
\(298\) 0 0
\(299\) 3.22425 0.186463
\(300\) 0 0
\(301\) 5.27504 0.304048
\(302\) 0 0
\(303\) 10.7612i 0.618212i
\(304\) 0 0
\(305\) 0.111420 + 0.126008i 0.00637987 + 0.00721520i
\(306\) 0 0
\(307\) 25.6688i 1.46500i −0.680770 0.732498i \(-0.738354\pi\)
0.680770 0.732498i \(-0.261646\pi\)
\(308\) 0 0
\(309\) −16.9380 −0.963566
\(310\) 0 0
\(311\) 15.7235 0.891601 0.445800 0.895132i \(-0.352919\pi\)
0.445800 + 0.895132i \(0.352919\pi\)
\(312\) 0 0
\(313\) 26.8627i 1.51837i 0.650874 + 0.759186i \(0.274403\pi\)
−0.650874 + 0.759186i \(0.725597\pi\)
\(314\) 0 0
\(315\) 2.00000 1.76845i 0.112687 0.0996410i
\(316\) 0 0
\(317\) 0.710373i 0.0398985i 0.999801 + 0.0199492i \(0.00635046\pi\)
−0.999801 + 0.0199492i \(0.993650\pi\)
\(318\) 0 0
\(319\) −4.31265 −0.241462
\(320\) 0 0
\(321\) 8.28233 0.462275
\(322\) 0 0
\(323\) 20.1622i 1.12186i
\(324\) 0 0
\(325\) 4.00000 + 0.493413i 0.221880 + 0.0273696i
\(326\) 0 0
\(327\) 10.0000i 0.553001i
\(328\) 0 0
\(329\) −14.7005 −0.810466
\(330\) 0 0
\(331\) −0.962389 −0.0528977 −0.0264488 0.999650i \(-0.508420\pi\)
−0.0264488 + 0.999650i \(0.508420\pi\)
\(332\) 0 0
\(333\) 1.61213i 0.0883440i
\(334\) 0 0
\(335\) 4.52373 4.00000i 0.247158 0.218543i
\(336\) 0 0
\(337\) 19.8192i 1.07962i 0.841786 + 0.539811i \(0.181504\pi\)
−0.841786 + 0.539811i \(0.818496\pi\)
\(338\) 0 0
\(339\) 2.26187 0.122848
\(340\) 0 0
\(341\) 0.962389 0.0521163
\(342\) 0 0
\(343\) 15.0132i 0.810635i
\(344\) 0 0
\(345\) 5.92478 + 6.70052i 0.318979 + 0.360744i
\(346\) 0 0
\(347\) 6.20711i 0.333215i −0.986023 0.166608i \(-0.946719\pi\)
0.986023 0.166608i \(-0.0532813\pi\)
\(348\) 0 0
\(349\) −4.44851 −0.238123 −0.119062 0.992887i \(-0.537989\pi\)
−0.119062 + 0.992887i \(0.537989\pi\)
\(350\) 0 0
\(351\) −0.806063 −0.0430245
\(352\) 0 0
\(353\) 6.57452i 0.349926i −0.984575 0.174963i \(-0.944019\pi\)
0.984575 0.174963i \(-0.0559806\pi\)
\(354\) 0 0
\(355\) −20.8119 23.5369i −1.10458 1.24921i
\(356\) 0 0
\(357\) 4.49929i 0.238128i
\(358\) 0 0
\(359\) 8.62530 0.455226 0.227613 0.973752i \(-0.426908\pi\)
0.227613 + 0.973752i \(0.426908\pi\)
\(360\) 0 0
\(361\) 9.62530 0.506595
\(362\) 0 0
\(363\) 1.00000i 0.0524864i
\(364\) 0 0
\(365\) 17.9756 15.8945i 0.940884 0.831954i
\(366\) 0 0
\(367\) 23.0132i 1.20128i −0.799520 0.600639i \(-0.794913\pi\)
0.799520 0.600639i \(-0.205087\pi\)
\(368\) 0 0
\(369\) −9.08840 −0.473123
\(370\) 0 0
\(371\) −1.70194 −0.0883602
\(372\) 0 0
\(373\) 28.1925i 1.45975i −0.683579 0.729877i \(-0.739577\pi\)
0.683579 0.729877i \(-0.260423\pi\)
\(374\) 0 0
\(375\) 6.32487 + 9.21933i 0.326615 + 0.476084i
\(376\) 0 0
\(377\) 3.47627i 0.179037i
\(378\) 0 0
\(379\) 3.74798 0.192521 0.0962605 0.995356i \(-0.469312\pi\)
0.0962605 + 0.995356i \(0.469312\pi\)
\(380\) 0 0
\(381\) −13.8192 −0.707981
\(382\) 0 0
\(383\) 1.76257i 0.0900632i 0.998986 + 0.0450316i \(0.0143389\pi\)
−0.998986 + 0.0450316i \(0.985661\pi\)
\(384\) 0 0
\(385\) 2.00000 1.76845i 0.101929 0.0901287i
\(386\) 0 0
\(387\) 4.41819i 0.224589i
\(388\) 0 0
\(389\) −6.52373 −0.330766 −0.165383 0.986229i \(-0.552886\pi\)
−0.165383 + 0.986229i \(0.552886\pi\)
\(390\) 0 0
\(391\) −15.0738 −0.762315
\(392\) 0 0
\(393\) 5.92478i 0.298865i
\(394\) 0 0
\(395\) −20.7005 23.4109i −1.04156 1.17793i
\(396\) 0 0
\(397\) 23.6991i 1.18942i −0.803939 0.594712i \(-0.797266\pi\)
0.803939 0.594712i \(-0.202734\pi\)
\(398\) 0 0
\(399\) −6.38787 −0.319794
\(400\) 0 0
\(401\) 8.88717 0.443804 0.221902 0.975069i \(-0.428774\pi\)
0.221902 + 0.975069i \(0.428774\pi\)
\(402\) 0 0
\(403\) 0.775746i 0.0386427i
\(404\) 0 0
\(405\) −1.48119 1.67513i −0.0736011 0.0832379i
\(406\) 0 0
\(407\) 1.61213i 0.0799102i
\(408\) 0 0
\(409\) 4.85097 0.239865 0.119932 0.992782i \(-0.461732\pi\)
0.119932 + 0.992782i \(0.461732\pi\)
\(410\) 0 0
\(411\) −3.35026 −0.165256
\(412\) 0 0
\(413\) 15.8496i 0.779906i
\(414\) 0 0
\(415\) −16.5745 + 14.6556i −0.813611 + 0.719416i
\(416\) 0 0
\(417\) 21.1998i 1.03816i
\(418\) 0 0
\(419\) −10.7005 −0.522755 −0.261377 0.965237i \(-0.584177\pi\)
−0.261377 + 0.965237i \(0.584177\pi\)
\(420\) 0 0
\(421\) −30.6009 −1.49139 −0.745697 0.666285i \(-0.767884\pi\)
−0.745697 + 0.666285i \(0.767884\pi\)
\(422\) 0 0
\(423\) 12.3127i 0.598662i
\(424\) 0 0
\(425\) −18.7005 2.30677i −0.907109 0.111895i
\(426\) 0 0
\(427\) 0.0898112i 0.00434627i
\(428\) 0 0
\(429\) −0.806063 −0.0389171
\(430\) 0 0
\(431\) 5.92478 0.285386 0.142693 0.989767i \(-0.454424\pi\)
0.142693 + 0.989767i \(0.454424\pi\)
\(432\) 0 0
\(433\) 16.0000i 0.768911i 0.923144 + 0.384455i \(0.125611\pi\)
−0.923144 + 0.384455i \(0.874389\pi\)
\(434\) 0 0
\(435\) 7.22425 6.38787i 0.346376 0.306275i
\(436\) 0 0
\(437\) 21.4010i 1.02375i
\(438\) 0 0
\(439\) 5.35026 0.255354 0.127677 0.991816i \(-0.459248\pi\)
0.127677 + 0.991816i \(0.459248\pi\)
\(440\) 0 0
\(441\) −5.57452 −0.265453
\(442\) 0 0
\(443\) 19.6873i 0.935374i 0.883894 + 0.467687i \(0.154913\pi\)
−0.883894 + 0.467687i \(0.845087\pi\)
\(444\) 0 0
\(445\) 25.0132 + 28.2882i 1.18574 + 1.34099i
\(446\) 0 0
\(447\) 6.38787i 0.302136i
\(448\) 0 0
\(449\) 31.3357 1.47882 0.739411 0.673254i \(-0.235104\pi\)
0.739411 + 0.673254i \(0.235104\pi\)
\(450\) 0 0
\(451\) −9.08840 −0.427956
\(452\) 0 0
\(453\) 2.64974i 0.124496i
\(454\) 0 0
\(455\) 1.42548 + 1.61213i 0.0668277 + 0.0755777i
\(456\) 0 0
\(457\) 37.5936i 1.75855i −0.476312 0.879276i \(-0.658027\pi\)
0.476312 0.879276i \(-0.341973\pi\)
\(458\) 0 0
\(459\) 3.76845 0.175896
\(460\) 0 0
\(461\) 17.9854 0.837664 0.418832 0.908064i \(-0.362440\pi\)
0.418832 + 0.908064i \(0.362440\pi\)
\(462\) 0 0
\(463\) 39.0132i 1.81310i 0.422103 + 0.906548i \(0.361292\pi\)
−0.422103 + 0.906548i \(0.638708\pi\)
\(464\) 0 0
\(465\) −1.61213 + 1.42548i −0.0747606 + 0.0661053i
\(466\) 0 0
\(467\) 14.5501i 0.673297i −0.941630 0.336649i \(-0.890707\pi\)
0.941630 0.336649i \(-0.109293\pi\)
\(468\) 0 0
\(469\) 3.22425 0.148882
\(470\) 0 0
\(471\) −1.61213 −0.0742829
\(472\) 0 0
\(473\) 4.41819i 0.203149i
\(474\) 0 0
\(475\) 3.27504 26.5501i 0.150269 1.21820i
\(476\) 0 0
\(477\) 1.42548i 0.0652685i
\(478\) 0 0
\(479\) 28.6253 1.30792 0.653962 0.756528i \(-0.273106\pi\)
0.653962 + 0.756528i \(0.273106\pi\)
\(480\) 0 0
\(481\) 1.29948 0.0592510
\(482\) 0 0
\(483\) 4.77575i 0.217304i
\(484\) 0 0
\(485\) 19.2243 16.9986i 0.872928 0.771866i
\(486\) 0 0
\(487\) 1.44992i 0.0657022i −0.999460 0.0328511i \(-0.989541\pi\)
0.999460 0.0328511i \(-0.0104587\pi\)
\(488\) 0 0
\(489\) 0.312650 0.0141385
\(490\) 0 0
\(491\) 8.00000 0.361035 0.180517 0.983572i \(-0.442223\pi\)
0.180517 + 0.983572i \(0.442223\pi\)
\(492\) 0 0
\(493\) 16.2520i 0.731954i
\(494\) 0 0
\(495\) −1.48119 1.67513i −0.0665747 0.0752915i
\(496\) 0 0
\(497\) 16.7757i 0.752495i
\(498\) 0 0
\(499\) 30.7005 1.37434 0.687172 0.726495i \(-0.258852\pi\)
0.687172 + 0.726495i \(0.258852\pi\)
\(500\) 0 0
\(501\) 0.493413 0.0220441
\(502\) 0 0
\(503\) 19.7586i 0.880993i −0.897754 0.440496i \(-0.854802\pi\)
0.897754 0.440496i \(-0.145198\pi\)
\(504\) 0 0
\(505\) −15.9394 18.0263i −0.709292 0.802162i
\(506\) 0 0
\(507\) 12.3503i 0.548494i
\(508\) 0 0
\(509\) −22.1016 −0.979635 −0.489817 0.871825i \(-0.662937\pi\)
−0.489817 + 0.871825i \(0.662937\pi\)
\(510\) 0 0
\(511\) 12.8119 0.566767
\(512\) 0 0
\(513\) 5.35026i 0.236220i
\(514\) 0 0
\(515\) 28.3733 25.0884i 1.25028 1.10553i
\(516\) 0 0
\(517\) 12.3127i 0.541510i
\(518\) 0 0
\(519\) −23.3054 −1.02299
\(520\) 0 0
\(521\) −22.8119 −0.999409 −0.499705 0.866196i \(-0.666558\pi\)
−0.499705 + 0.866196i \(0.666558\pi\)
\(522\) 0 0
\(523\) 12.2677i 0.536431i −0.963359 0.268216i \(-0.913566\pi\)
0.963359 0.268216i \(-0.0864339\pi\)
\(524\) 0 0
\(525\) −0.730841 + 5.92478i −0.0318965 + 0.258578i
\(526\) 0 0
\(527\) 3.62672i 0.157982i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) −13.2750 −0.576088
\(532\) 0 0
\(533\) 7.32582i 0.317317i
\(534\) 0 0
\(535\) −13.8740 + 12.2677i −0.599825 + 0.530381i
\(536\) 0 0
\(537\) 10.7005i 0.461762i
\(538\) 0 0
\(539\) −5.57452 −0.240111
\(540\) 0 0
\(541\) −5.22425 −0.224608 −0.112304 0.993674i \(-0.535823\pi\)
−0.112304 + 0.993674i \(0.535823\pi\)
\(542\) 0 0
\(543\) 7.79877i 0.334677i
\(544\) 0 0
\(545\) −14.8119 16.7513i −0.634474 0.717547i
\(546\) 0 0
\(547\) 17.9697i 0.768328i 0.923265 + 0.384164i \(0.125510\pi\)
−0.923265 + 0.384164i \(0.874490\pi\)
\(548\) 0 0
\(549\) 0.0752228 0.00321043
\(550\) 0 0
\(551\) −23.0738 −0.982977
\(552\) 0 0
\(553\) 16.6859i 0.709558i
\(554\) 0 0
\(555\) 2.38787 + 2.70052i 0.101360 + 0.114631i
\(556\) 0 0
\(557\) 15.8700i 0.672434i 0.941784 + 0.336217i \(0.109148\pi\)
−0.941784 + 0.336217i \(0.890852\pi\)
\(558\) 0 0
\(559\) 3.56134 0.150629
\(560\) 0 0
\(561\) 3.76845 0.159104
\(562\) 0 0
\(563\) 31.6688i 1.33468i 0.744753 + 0.667340i \(0.232567\pi\)
−0.744753 + 0.667340i \(0.767433\pi\)
\(564\) 0 0
\(565\) −3.78892 + 3.35026i −0.159401 + 0.140947i
\(566\) 0 0
\(567\) 1.19394i 0.0501406i
\(568\) 0 0
\(569\) 24.3127 1.01924 0.509620 0.860400i \(-0.329786\pi\)
0.509620 + 0.860400i \(0.329786\pi\)
\(570\) 0 0
\(571\) −8.05079 −0.336915 −0.168457 0.985709i \(-0.553879\pi\)
−0.168457 + 0.985709i \(0.553879\pi\)
\(572\) 0 0
\(573\) 1.29948i 0.0542864i
\(574\) 0 0
\(575\) −19.8496 2.44851i −0.827784 0.102110i
\(576\) 0 0
\(577\) 44.5355i 1.85404i −0.375016 0.927018i \(-0.622363\pi\)
0.375016 0.927018i \(-0.377637\pi\)
\(578\) 0 0
\(579\) 8.59498 0.357195
\(580\) 0 0
\(581\) −11.8134 −0.490101
\(582\) 0 0
\(583\) 1.42548i 0.0590375i
\(584\) 0 0
\(585\) 1.35026 1.19394i 0.0558265 0.0493632i
\(586\) 0 0
\(587\) 15.4763i 0.638774i 0.947624 + 0.319387i \(0.103477\pi\)
−0.947624 + 0.319387i \(0.896523\pi\)
\(588\) 0 0
\(589\) 5.14903 0.212162
\(590\) 0 0
\(591\) 20.7064 0.851748
\(592\) 0 0
\(593\) 9.53102i 0.391392i 0.980665 + 0.195696i \(0.0626966\pi\)
−0.980665 + 0.195696i \(0.937303\pi\)
\(594\) 0 0
\(595\) −6.66433 7.53690i −0.273211 0.308983i
\(596\) 0 0
\(597\) 5.55149i 0.227207i
\(598\) 0 0
\(599\) −25.5515 −1.04401 −0.522003 0.852944i \(-0.674815\pi\)
−0.522003 + 0.852944i \(0.674815\pi\)
\(600\) 0 0
\(601\) 12.0263 0.490565 0.245282 0.969452i \(-0.421119\pi\)
0.245282 + 0.969452i \(0.421119\pi\)
\(602\) 0 0
\(603\) 2.70052i 0.109974i
\(604\) 0 0
\(605\) −1.48119 1.67513i −0.0602191 0.0681038i
\(606\) 0 0
\(607\) 6.86670i 0.278711i 0.990242 + 0.139355i \(0.0445030\pi\)
−0.990242 + 0.139355i \(0.955497\pi\)
\(608\) 0 0
\(609\) 5.14903 0.208649
\(610\) 0 0
\(611\) −9.92478 −0.401514
\(612\) 0 0
\(613\) 7.25457i 0.293009i 0.989210 + 0.146505i \(0.0468023\pi\)
−0.989210 + 0.146505i \(0.953198\pi\)
\(614\) 0 0
\(615\) 15.2243 13.4617i 0.613901 0.542827i
\(616\) 0 0
\(617\) 38.3634i 1.54445i 0.635347 + 0.772227i \(0.280857\pi\)
−0.635347 + 0.772227i \(0.719143\pi\)
\(618\) 0 0
\(619\) −29.6893 −1.19331 −0.596656 0.802497i \(-0.703504\pi\)
−0.596656 + 0.802497i \(0.703504\pi\)
\(620\) 0 0
\(621\) 4.00000 0.160514
\(622\) 0 0
\(623\) 20.1622i 0.807782i
\(624\) 0 0
\(625\) −24.2506 6.07522i −0.970024 0.243009i
\(626\) 0 0
\(627\) 5.35026i 0.213669i
\(628\) 0 0
\(629\) −6.07522 −0.242235
\(630\) 0 0
\(631\) 19.6991 0.784209 0.392105 0.919921i \(-0.371747\pi\)
0.392105 + 0.919921i \(0.371747\pi\)
\(632\) 0 0
\(633\) 18.4993i 0.735281i
\(634\) 0 0
\(635\) 23.1490 20.4690i 0.918641 0.812287i
\(636\) 0 0
\(637\) 4.49341i 0.178036i
\(638\) 0 0
\(639\) −14.0508 −0.555840
\(640\) 0 0
\(641\) −31.4372 −1.24170 −0.620848 0.783931i \(-0.713212\pi\)
−0.620848 + 0.783931i \(0.713212\pi\)
\(642\) 0 0
\(643\) 34.4894i 1.36013i −0.733151 0.680065i \(-0.761951\pi\)
0.733151 0.680065i \(-0.238049\pi\)
\(644\) 0 0
\(645\) 6.54420 + 7.40105i 0.257678 + 0.291416i
\(646\) 0 0
\(647\) 5.61213i 0.220635i 0.993896 + 0.110318i \(0.0351868\pi\)
−0.993896 + 0.110318i \(0.964813\pi\)
\(648\) 0 0
\(649\) −13.2750 −0.521091
\(650\) 0 0
\(651\) −1.14903 −0.0450341
\(652\) 0 0
\(653\) 4.06537i 0.159090i −0.996831 0.0795452i \(-0.974653\pi\)
0.996831 0.0795452i \(-0.0253468\pi\)
\(654\) 0 0
\(655\) −8.77575 9.92478i −0.342897 0.387793i
\(656\) 0 0
\(657\) 10.7308i 0.418650i
\(658\) 0 0
\(659\) 11.3747 0.443095 0.221548 0.975150i \(-0.428889\pi\)
0.221548 + 0.975150i \(0.428889\pi\)
\(660\) 0 0
\(661\) −42.4749 −1.65208 −0.826040 0.563611i \(-0.809412\pi\)
−0.826040 + 0.563611i \(0.809412\pi\)
\(662\) 0 0
\(663\) 3.03761i 0.117971i
\(664\) 0 0
\(665\) 10.7005 9.46168i 0.414949 0.366908i
\(666\) 0 0
\(667\) 17.2506i 0.667946i
\(668\) 0 0
\(669\) −17.6121 −0.680924
\(670\) 0 0
\(671\) 0.0752228 0.00290394
\(672\) 0 0
\(673\) 14.8813i 0.573631i 0.957986 + 0.286816i \(0.0925967\pi\)
−0.957986 + 0.286816i \(0.907403\pi\)
\(674\) 0 0
\(675\) 4.96239 + 0.612127i 0.191002 + 0.0235608i
\(676\) 0 0
\(677\) 27.7685i 1.06723i −0.845728 0.533614i \(-0.820833\pi\)
0.845728 0.533614i \(-0.179167\pi\)
\(678\) 0 0
\(679\) 13.7019 0.525832
\(680\) 0 0
\(681\) −17.4314 −0.667971
\(682\) 0 0
\(683\) 25.4617i 0.974264i −0.873328 0.487132i \(-0.838043\pi\)
0.873328 0.487132i \(-0.161957\pi\)
\(684\) 0 0
\(685\) 5.61213 4.96239i 0.214428 0.189603i
\(686\) 0 0
\(687\) 13.0738i 0.498797i
\(688\) 0 0
\(689\) −1.14903 −0.0437746
\(690\) 0 0
\(691\) −43.6991 −1.66239 −0.831196 0.555979i \(-0.812343\pi\)
−0.831196 + 0.555979i \(0.812343\pi\)
\(692\) 0 0
\(693\) 1.19394i 0.0453539i
\(694\) 0 0
\(695\) 31.4010 + 35.5125i 1.19111 + 1.34706i
\(696\) 0 0
\(697\) 34.2492i 1.29728i
\(698\) 0 0
\(699\) −13.8437 −0.523616
\(700\) 0 0
\(701\) 7.01317 0.264884 0.132442 0.991191i \(-0.457718\pi\)
0.132442 + 0.991191i \(0.457718\pi\)
\(702\) 0 0
\(703\) 8.62530i 0.325309i
\(704\) 0 0
\(705\) −18.2374 20.6253i −0.686861 0.776794i
\(706\) 0 0
\(707\) 12.8481i 0.483204i
\(708\) 0 0
\(709\) −45.6747 −1.71535 −0.857674 0.514194i \(-0.828091\pi\)
−0.857674 + 0.514194i \(0.828091\pi\)
\(710\) 0 0
\(711\) −13.9756 −0.524125
\(712\) 0 0
\(713\) 3.84955i 0.144167i
\(714\) 0 0
\(715\) 1.35026 1.19394i 0.0504969 0.0446507i
\(716\) 0 0
\(717\) 12.3733i 0.462089i
\(718\) 0 0
\(719\) 16.2520 0.606098 0.303049 0.952975i \(-0.401995\pi\)
0.303049 + 0.952975i \(0.401995\pi\)
\(720\) 0 0
\(721\) 20.2228 0.753138
\(722\) 0 0
\(723\) 24.5501i 0.913027i
\(724\) 0 0
\(725\) −2.63989 + 21.4010i −0.0980430 + 0.794815i
\(726\) 0 0
\(727\) 15.2243i 0.564636i −0.959321 0.282318i \(-0.908897\pi\)
0.959321 0.282318i \(-0.0911034\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −16.6497 −0.615813
\(732\) 0 0
\(733\) 43.5066i 1.60695i 0.595337 + 0.803476i \(0.297019\pi\)
−0.595337 + 0.803476i \(0.702981\pi\)
\(734\) 0 0
\(735\) 9.33804 8.25694i 0.344439 0.304562i
\(736\) 0 0
\(737\) 2.70052i 0.0994751i
\(738\) 0 0
\(739\) −7.02302 −0.258346 −0.129173 0.991622i \(-0.541232\pi\)
−0.129173 + 0.991622i \(0.541232\pi\)
\(740\) 0 0
\(741\) −4.31265 −0.158429
\(742\) 0 0
\(743\) 2.94192i 0.107929i −0.998543 0.0539643i \(-0.982814\pi\)
0.998543 0.0539643i \(-0.0171857\pi\)
\(744\) 0 0
\(745\) 9.46168 + 10.7005i 0.346649 + 0.392037i
\(746\) 0 0
\(747\) 9.89446i 0.362019i
\(748\) 0 0
\(749\) −9.88858 −0.361321
\(750\) 0 0
\(751\) −24.1016 −0.879479 −0.439739 0.898125i \(-0.644929\pi\)
−0.439739 + 0.898125i \(0.644929\pi\)
\(752\) 0 0
\(753\) 13.9003i 0.506557i
\(754\) 0 0
\(755\) −3.92478 4.43866i −0.142837 0.161539i
\(756\) 0 0
\(757\) 16.3127i 0.592893i −0.955049 0.296447i \(-0.904198\pi\)
0.955049 0.296447i \(-0.0958017\pi\)
\(758\) 0 0
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) −5.08840 −0.184454 −0.0922271 0.995738i \(-0.529399\pi\)
−0.0922271 + 0.995738i \(0.529399\pi\)
\(762\) 0 0
\(763\) 11.9394i 0.432234i
\(764\) 0 0
\(765\) −6.31265 + 5.58181i −0.228234 + 0.201811i
\(766\) 0 0
\(767\) 10.7005i 0.386374i
\(768\) 0 0
\(769\) −2.10157 −0.0757846 −0.0378923 0.999282i \(-0.512064\pi\)
−0.0378923 + 0.999282i \(0.512064\pi\)
\(770\) 0 0
\(771\) 18.8872 0.680205
\(772\) 0 0
\(773\) 46.0625i 1.65675i −0.560171 0.828377i \(-0.689264\pi\)
0.560171 0.828377i \(-0.310736\pi\)
\(774\) 0 0
\(775\) 0.589104 4.77575i 0.0211612 0.171550i
\(776\) 0 0
\(777\) 1.92478i 0.0690510i
\(778\) 0 0
\(779\) −48.6253 −1.74218
\(780\) 0 0
\(781\) −14.0508 −0.502777
\(782\) 0 0
\(783\) 4.31265i 0.154122i
\(784\) 0 0
\(785\) 2.70052 2.38787i 0.0963858 0.0852268i
\(786\) 0 0
\(787\) 26.0303i 0.927881i 0.885866 + 0.463940i \(0.153565\pi\)
−0.885866 + 0.463940i \(0.846435\pi\)
\(788\) 0 0
\(789\) −20.8061 −0.740715
\(790\) 0 0
\(791\) −2.70052 −0.0960196
\(792\) 0 0
\(793\) 0.0606343i 0.00215319i
\(794\) 0 0
\(795\) −2.11142 2.38787i −0.0748843 0.0846891i
\(796\) 0 0