Properties

Label 1386.2.g.a.881.9
Level $1386$
Weight $2$
Character 1386.881
Analytic conductor $11.067$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{14} + 8 x^{12} + 80 x^{10} + 1189 x^{8} - 2028 x^{6} + 1800 x^{4} + 1080 x^{2} + 324\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{9}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 881.9
Root \(-0.876932 + 2.11710i\) of defining polynomial
Character \(\chi\) \(=\) 1386.881
Dual form 1386.2.g.a.881.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} -4.23420 q^{5} +(-2.59178 - 0.531652i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} -4.23420 q^{5} +(-2.59178 - 0.531652i) q^{7} -1.00000i q^{8} -4.23420i q^{10} -1.00000i q^{11} +(0.531652 - 2.59178i) q^{14} +1.00000 q^{16} -5.29751 q^{17} +0.250123i q^{19} +4.23420 q^{20} +1.00000 q^{22} +4.50225i q^{23} +12.9285 q^{25} +(2.59178 + 0.531652i) q^{28} +1.05907i q^{29} -6.32489i q^{31} +1.00000i q^{32} -5.29751i q^{34} +(10.9741 + 2.25112i) q^{35} +2.50225 q^{37} -0.250123 q^{38} +4.23420i q^{40} -1.31343 q^{41} +7.18357 q^{43} +1.00000i q^{44} -4.50225 q^{46} +7.15497 q^{47} +(6.43469 + 2.75586i) q^{49} +12.9285i q^{50} -4.68132i q^{53} +4.23420i q^{55} +(-0.531652 + 2.59178i) q^{56} -1.05907 q^{58} -8.46840 q^{59} +14.8102i q^{61} +6.32489 q^{62} -1.00000 q^{64} +9.42621 q^{67} +5.29751 q^{68} +(-2.25112 + 10.9741i) q^{70} +12.9875i q^{71} -7.15497i q^{73} +2.50225i q^{74} -0.250123i q^{76} +(-0.531652 + 2.59178i) q^{77} -0.377749 q^{79} -4.23420 q^{80} -1.31343i q^{82} +1.84057 q^{83} +22.4307 q^{85} +7.18357i q^{86} -1.00000 q^{88} -1.56355 q^{89} -4.50225i q^{92} +7.15497i q^{94} -1.05907i q^{95} -7.96815i q^{97} +(-2.75586 + 6.43469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{4} - 8q^{7} + O(q^{10}) \) \( 16q - 16q^{4} - 8q^{7} + 16q^{16} + 16q^{22} + 16q^{25} + 8q^{28} - 16q^{37} + 48q^{43} - 16q^{46} + 8q^{49} - 16q^{58} - 16q^{64} + 16q^{67} - 8q^{70} - 16q^{79} + 112q^{85} - 16q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −4.23420 −1.89359 −0.946796 0.321834i \(-0.895701\pi\)
−0.946796 + 0.321834i \(0.895701\pi\)
\(6\) 0 0
\(7\) −2.59178 0.531652i −0.979602 0.200946i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 4.23420i 1.33897i
\(11\) 1.00000i 0.301511i
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0.531652 2.59178i 0.142090 0.692683i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −5.29751 −1.28483 −0.642417 0.766355i \(-0.722068\pi\)
−0.642417 + 0.766355i \(0.722068\pi\)
\(18\) 0 0
\(19\) 0.250123i 0.0573822i 0.999588 + 0.0286911i \(0.00913392\pi\)
−0.999588 + 0.0286911i \(0.990866\pi\)
\(20\) 4.23420 0.946796
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 4.50225i 0.938783i 0.882990 + 0.469392i \(0.155527\pi\)
−0.882990 + 0.469392i \(0.844473\pi\)
\(24\) 0 0
\(25\) 12.9285 2.58569
\(26\) 0 0
\(27\) 0 0
\(28\) 2.59178 + 0.531652i 0.489801 + 0.100473i
\(29\) 1.05907i 0.196665i 0.995154 + 0.0983324i \(0.0313508\pi\)
−0.995154 + 0.0983324i \(0.968649\pi\)
\(30\) 0 0
\(31\) 6.32489i 1.13598i −0.823034 0.567992i \(-0.807720\pi\)
0.823034 0.567992i \(-0.192280\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 5.29751i 0.908515i
\(35\) 10.9741 + 2.25112i 1.85497 + 0.380509i
\(36\) 0 0
\(37\) 2.50225 0.411367 0.205683 0.978619i \(-0.434058\pi\)
0.205683 + 0.978619i \(0.434058\pi\)
\(38\) −0.250123 −0.0405754
\(39\) 0 0
\(40\) 4.23420i 0.669486i
\(41\) −1.31343 −0.205123 −0.102562 0.994727i \(-0.532704\pi\)
−0.102562 + 0.994727i \(0.532704\pi\)
\(42\) 0 0
\(43\) 7.18357 1.09548 0.547742 0.836647i \(-0.315488\pi\)
0.547742 + 0.836647i \(0.315488\pi\)
\(44\) 1.00000i 0.150756i
\(45\) 0 0
\(46\) −4.50225 −0.663820
\(47\) 7.15497 1.04366 0.521830 0.853049i \(-0.325250\pi\)
0.521830 + 0.853049i \(0.325250\pi\)
\(48\) 0 0
\(49\) 6.43469 + 2.75586i 0.919242 + 0.393694i
\(50\) 12.9285i 1.82836i
\(51\) 0 0
\(52\) 0 0
\(53\) 4.68132i 0.643029i −0.946905 0.321515i \(-0.895808\pi\)
0.946905 0.321515i \(-0.104192\pi\)
\(54\) 0 0
\(55\) 4.23420i 0.570939i
\(56\) −0.531652 + 2.59178i −0.0710450 + 0.346342i
\(57\) 0 0
\(58\) −1.05907 −0.139063
\(59\) −8.46840 −1.10249 −0.551246 0.834343i \(-0.685847\pi\)
−0.551246 + 0.834343i \(0.685847\pi\)
\(60\) 0 0
\(61\) 14.8102i 1.89625i 0.317896 + 0.948125i \(0.397024\pi\)
−0.317896 + 0.948125i \(0.602976\pi\)
\(62\) 6.32489 0.803262
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 9.42621 1.15159 0.575797 0.817592i \(-0.304692\pi\)
0.575797 + 0.817592i \(0.304692\pi\)
\(68\) 5.29751 0.642417
\(69\) 0 0
\(70\) −2.25112 + 10.9741i −0.269061 + 1.31166i
\(71\) 12.9875i 1.54134i 0.637237 + 0.770668i \(0.280077\pi\)
−0.637237 + 0.770668i \(0.719923\pi\)
\(72\) 0 0
\(73\) 7.15497i 0.837426i −0.908119 0.418713i \(-0.862481\pi\)
0.908119 0.418713i \(-0.137519\pi\)
\(74\) 2.50225i 0.290880i
\(75\) 0 0
\(76\) 0.250123i 0.0286911i
\(77\) −0.531652 + 2.59178i −0.0605874 + 0.295361i
\(78\) 0 0
\(79\) −0.377749 −0.0425001 −0.0212501 0.999774i \(-0.506765\pi\)
−0.0212501 + 0.999774i \(0.506765\pi\)
\(80\) −4.23420 −0.473398
\(81\) 0 0
\(82\) 1.31343i 0.145044i
\(83\) 1.84057 0.202029 0.101014 0.994885i \(-0.467791\pi\)
0.101014 + 0.994885i \(0.467791\pi\)
\(84\) 0 0
\(85\) 22.4307 2.43295
\(86\) 7.18357i 0.774624i
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) −1.56355 −0.165736 −0.0828681 0.996561i \(-0.526408\pi\)
−0.0828681 + 0.996561i \(0.526408\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.50225i 0.469392i
\(93\) 0 0
\(94\) 7.15497i 0.737979i
\(95\) 1.05907i 0.108659i
\(96\) 0 0
\(97\) 7.96815i 0.809044i −0.914528 0.404522i \(-0.867438\pi\)
0.914528 0.404522i \(-0.132562\pi\)
\(98\) −2.75586 + 6.43469i −0.278384 + 0.650002i
\(99\) 0 0
\(100\) −12.9285 −1.29285
\(101\) 15.6065 1.55290 0.776451 0.630177i \(-0.217018\pi\)
0.776451 + 0.630177i \(0.217018\pi\)
\(102\) 0 0
\(103\) 1.84057i 0.181357i 0.995880 + 0.0906784i \(0.0289035\pi\)
−0.995880 + 0.0906784i \(0.971096\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 4.68132 0.454690
\(107\) 17.2365i 1.66632i −0.553034 0.833159i \(-0.686530\pi\)
0.553034 0.833159i \(-0.313470\pi\)
\(108\) 0 0
\(109\) −17.8103 −1.70592 −0.852959 0.521978i \(-0.825194\pi\)
−0.852959 + 0.521978i \(0.825194\pi\)
\(110\) −4.23420 −0.403715
\(111\) 0 0
\(112\) −2.59178 0.531652i −0.244901 0.0502364i
\(113\) 9.80396i 0.922279i 0.887328 + 0.461139i \(0.152559\pi\)
−0.887328 + 0.461139i \(0.847441\pi\)
\(114\) 0 0
\(115\) 19.0634i 1.77767i
\(116\) 1.05907i 0.0983324i
\(117\) 0 0
\(118\) 8.46840i 0.779580i
\(119\) 13.7300 + 2.81643i 1.25863 + 0.258182i
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) −14.8102 −1.34085
\(123\) 0 0
\(124\) 6.32489i 0.567992i
\(125\) −33.5707 −3.00265
\(126\) 0 0
\(127\) −13.1120 −1.16350 −0.581752 0.813366i \(-0.697633\pi\)
−0.581752 + 0.813366i \(0.697633\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 0 0
\(131\) 16.3928 1.43224 0.716121 0.697976i \(-0.245916\pi\)
0.716121 + 0.697976i \(0.245916\pi\)
\(132\) 0 0
\(133\) 0.132979 0.648266i 0.0115307 0.0562118i
\(134\) 9.42621i 0.814300i
\(135\) 0 0
\(136\) 5.29751i 0.454257i
\(137\) 17.6688i 1.50955i −0.655983 0.754776i \(-0.727746\pi\)
0.655983 0.754776i \(-0.272254\pi\)
\(138\) 0 0
\(139\) 16.8840i 1.43208i −0.698059 0.716041i \(-0.745952\pi\)
0.698059 0.716041i \(-0.254048\pi\)
\(140\) −10.9741 2.25112i −0.927484 0.190255i
\(141\) 0 0
\(142\) −12.9875 −1.08989
\(143\) 0 0
\(144\) 0 0
\(145\) 4.48432i 0.372403i
\(146\) 7.15497 0.592150
\(147\) 0 0
\(148\) −2.50225 −0.205683
\(149\) 10.8694i 0.890455i 0.895418 + 0.445227i \(0.146877\pi\)
−0.895418 + 0.445227i \(0.853123\pi\)
\(150\) 0 0
\(151\) 8.17110 0.664954 0.332477 0.943111i \(-0.392116\pi\)
0.332477 + 0.943111i \(0.392116\pi\)
\(152\) 0.250123 0.0202877
\(153\) 0 0
\(154\) −2.59178 0.531652i −0.208852 0.0428418i
\(155\) 26.7809i 2.15109i
\(156\) 0 0
\(157\) 20.6348i 1.64684i −0.567433 0.823420i \(-0.692063\pi\)
0.567433 0.823420i \(-0.307937\pi\)
\(158\) 0.377749i 0.0300521i
\(159\) 0 0
\(160\) 4.23420i 0.334743i
\(161\) 2.39363 11.6688i 0.188644 0.919634i
\(162\) 0 0
\(163\) 8.62039 0.675201 0.337601 0.941289i \(-0.390385\pi\)
0.337601 + 0.941289i \(0.390385\pi\)
\(164\) 1.31343 0.102562
\(165\) 0 0
\(166\) 1.84057i 0.142856i
\(167\) −2.88486 −0.223237 −0.111618 0.993751i \(-0.535603\pi\)
−0.111618 + 0.993751i \(0.535603\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 22.4307i 1.72036i
\(171\) 0 0
\(172\) −7.18357 −0.547742
\(173\) 11.8535 0.901205 0.450603 0.892725i \(-0.351209\pi\)
0.450603 + 0.892725i \(0.351209\pi\)
\(174\) 0 0
\(175\) −33.5078 6.87344i −2.53295 0.519584i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) 1.56355i 0.117193i
\(179\) 13.4262i 1.00352i −0.865006 0.501761i \(-0.832686\pi\)
0.865006 0.501761i \(-0.167314\pi\)
\(180\) 0 0
\(181\) 19.8766i 1.47742i 0.674026 + 0.738708i \(0.264564\pi\)
−0.674026 + 0.738708i \(0.735436\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.50225 0.331910
\(185\) −10.5950 −0.778961
\(186\) 0 0
\(187\) 5.29751i 0.387392i
\(188\) −7.15497 −0.521830
\(189\) 0 0
\(190\) 1.05907 0.0768332
\(191\) 0.253253i 0.0183247i −0.999958 0.00916237i \(-0.997083\pi\)
0.999958 0.00916237i \(-0.00291651\pi\)
\(192\) 0 0
\(193\) 12.8524 0.925137 0.462569 0.886583i \(-0.346928\pi\)
0.462569 + 0.886583i \(0.346928\pi\)
\(194\) 7.96815 0.572080
\(195\) 0 0
\(196\) −6.43469 2.75586i −0.459621 0.196847i
\(197\) 25.4352i 1.81218i −0.423082 0.906091i \(-0.639052\pi\)
0.423082 0.906091i \(-0.360948\pi\)
\(198\) 0 0
\(199\) 22.7615i 1.61352i 0.590882 + 0.806758i \(0.298780\pi\)
−0.590882 + 0.806758i \(0.701220\pi\)
\(200\) 12.9285i 0.914180i
\(201\) 0 0
\(202\) 15.6065i 1.09807i
\(203\) 0.563058 2.74489i 0.0395189 0.192653i
\(204\) 0 0
\(205\) 5.56132 0.388419
\(206\) −1.84057 −0.128239
\(207\) 0 0
\(208\) 0 0
\(209\) 0.250123 0.0173014
\(210\) 0 0
\(211\) −16.6733 −1.14784 −0.573920 0.818911i \(-0.694578\pi\)
−0.573920 + 0.818911i \(0.694578\pi\)
\(212\) 4.68132i 0.321515i
\(213\) 0 0
\(214\) 17.2365 1.17826
\(215\) −30.4167 −2.07440
\(216\) 0 0
\(217\) −3.36265 + 16.3928i −0.228271 + 1.11281i
\(218\) 17.8103i 1.20627i
\(219\) 0 0
\(220\) 4.23420i 0.285470i
\(221\) 0 0
\(222\) 0 0
\(223\) 19.0085i 1.27290i 0.771317 + 0.636451i \(0.219598\pi\)
−0.771317 + 0.636451i \(0.780402\pi\)
\(224\) 0.531652 2.59178i 0.0355225 0.173171i
\(225\) 0 0
\(226\) −9.80396 −0.652150
\(227\) 11.1122 0.737540 0.368770 0.929521i \(-0.379779\pi\)
0.368770 + 0.929521i \(0.379779\pi\)
\(228\) 0 0
\(229\) 1.34032i 0.0885711i −0.999019 0.0442856i \(-0.985899\pi\)
0.999019 0.0442856i \(-0.0141011\pi\)
\(230\) 19.0634 1.25700
\(231\) 0 0
\(232\) 1.05907 0.0695315
\(233\) 14.4853i 0.948962i 0.880266 + 0.474481i \(0.157364\pi\)
−0.880266 + 0.474481i \(0.842636\pi\)
\(234\) 0 0
\(235\) −30.2956 −1.97627
\(236\) 8.46840 0.551246
\(237\) 0 0
\(238\) −2.81643 + 13.7300i −0.182562 + 0.889983i
\(239\) 2.01696i 0.130467i −0.997870 0.0652333i \(-0.979221\pi\)
0.997870 0.0652333i \(-0.0207792\pi\)
\(240\) 0 0
\(241\) 12.1395i 0.781977i −0.920396 0.390988i \(-0.872133\pi\)
0.920396 0.390988i \(-0.127867\pi\)
\(242\) 1.00000i 0.0642824i
\(243\) 0 0
\(244\) 14.8102i 0.948125i
\(245\) −27.2458 11.6688i −1.74067 0.745495i
\(246\) 0 0
\(247\) 0 0
\(248\) −6.32489 −0.401631
\(249\) 0 0
\(250\) 33.5707i 2.12320i
\(251\) 6.34179 0.400290 0.200145 0.979766i \(-0.435859\pi\)
0.200145 + 0.979766i \(0.435859\pi\)
\(252\) 0 0
\(253\) 4.50225 0.283054
\(254\) 13.1120i 0.822722i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 1.56355 0.0975317 0.0487658 0.998810i \(-0.484471\pi\)
0.0487658 + 0.998810i \(0.484471\pi\)
\(258\) 0 0
\(259\) −6.48528 1.33032i −0.402976 0.0826624i
\(260\) 0 0
\(261\) 0 0
\(262\) 16.3928i 1.01275i
\(263\) 6.18171i 0.381180i −0.981670 0.190590i \(-0.938960\pi\)
0.981670 0.190590i \(-0.0610402\pi\)
\(264\) 0 0
\(265\) 19.8217i 1.21763i
\(266\) 0.648266 + 0.132979i 0.0397477 + 0.00815344i
\(267\) 0 0
\(268\) −9.42621 −0.575797
\(269\) 25.0832 1.52935 0.764676 0.644415i \(-0.222899\pi\)
0.764676 + 0.644415i \(0.222899\pi\)
\(270\) 0 0
\(271\) 3.15188i 0.191463i −0.995407 0.0957315i \(-0.969481\pi\)
0.995407 0.0957315i \(-0.0305190\pi\)
\(272\) −5.29751 −0.321208
\(273\) 0 0
\(274\) 17.6688 1.06741
\(275\) 12.9285i 0.779615i
\(276\) 0 0
\(277\) 1.04211 0.0626142 0.0313071 0.999510i \(-0.490033\pi\)
0.0313071 + 0.999510i \(0.490033\pi\)
\(278\) 16.8840 1.01263
\(279\) 0 0
\(280\) 2.25112 10.9741i 0.134530 0.655830i
\(281\) 22.9706i 1.37031i 0.728398 + 0.685154i \(0.240265\pi\)
−0.728398 + 0.685154i \(0.759735\pi\)
\(282\) 0 0
\(283\) 23.7979i 1.41464i 0.706896 + 0.707318i \(0.250095\pi\)
−0.706896 + 0.707318i \(0.749905\pi\)
\(284\) 12.9875i 0.770668i
\(285\) 0 0
\(286\) 0 0
\(287\) 3.40412 + 0.698287i 0.200939 + 0.0412186i
\(288\) 0 0
\(289\) 11.0636 0.650798
\(290\) 4.48432 0.263329
\(291\) 0 0
\(292\) 7.15497i 0.418713i
\(293\) 13.9801 0.816727 0.408364 0.912819i \(-0.366100\pi\)
0.408364 + 0.912819i \(0.366100\pi\)
\(294\) 0 0
\(295\) 35.8569 2.08767
\(296\) 2.50225i 0.145440i
\(297\) 0 0
\(298\) −10.8694 −0.629646
\(299\) 0 0
\(300\) 0 0
\(301\) −18.6183 3.81916i −1.07314 0.220133i
\(302\) 8.17110i 0.470194i
\(303\) 0 0
\(304\) 0.250123i 0.0143456i
\(305\) 62.7093i 3.59073i
\(306\) 0 0
\(307\) 33.5897i 1.91706i 0.284984 + 0.958532i \(0.408012\pi\)
−0.284984 + 0.958532i \(0.591988\pi\)
\(308\) 0.531652 2.59178i 0.0302937 0.147681i
\(309\) 0 0
\(310\) −26.7809 −1.52105
\(311\) −11.6393 −0.660004 −0.330002 0.943980i \(-0.607049\pi\)
−0.330002 + 0.943980i \(0.607049\pi\)
\(312\) 0 0
\(313\) 1.83057i 0.103470i 0.998661 + 0.0517350i \(0.0164751\pi\)
−0.998661 + 0.0517350i \(0.983525\pi\)
\(314\) 20.6348 1.16449
\(315\) 0 0
\(316\) 0.377749 0.0212501
\(317\) 29.9348i 1.68131i −0.541574 0.840653i \(-0.682171\pi\)
0.541574 0.840653i \(-0.317829\pi\)
\(318\) 0 0
\(319\) 1.05907 0.0592967
\(320\) 4.23420 0.236699
\(321\) 0 0
\(322\) 11.6688 + 2.39363i 0.650280 + 0.133392i
\(323\) 1.32503i 0.0737266i
\(324\) 0 0
\(325\) 0 0
\(326\) 8.62039i 0.477439i
\(327\) 0 0
\(328\) 1.31343i 0.0725219i
\(329\) −18.5441 3.80396i −1.02237 0.209719i
\(330\) 0 0
\(331\) −5.69643 −0.313104 −0.156552 0.987670i \(-0.550038\pi\)
−0.156552 + 0.987670i \(0.550038\pi\)
\(332\) −1.84057 −0.101014
\(333\) 0 0
\(334\) 2.88486i 0.157852i
\(335\) −39.9125 −2.18065
\(336\) 0 0
\(337\) 0.637355 0.0347189 0.0173595 0.999849i \(-0.494474\pi\)
0.0173595 + 0.999849i \(0.494474\pi\)
\(338\) 13.0000i 0.707107i
\(339\) 0 0
\(340\) −22.4307 −1.21648
\(341\) −6.32489 −0.342512
\(342\) 0 0
\(343\) −15.2122 10.5636i −0.821380 0.570381i
\(344\) 7.18357i 0.387312i
\(345\) 0 0
\(346\) 11.8535i 0.637248i
\(347\) 21.4728i 1.15272i −0.817196 0.576360i \(-0.804472\pi\)
0.817196 0.576360i \(-0.195528\pi\)
\(348\) 0 0
\(349\) 9.52269i 0.509738i −0.966976 0.254869i \(-0.917968\pi\)
0.966976 0.254869i \(-0.0820323\pi\)
\(350\) 6.87344 33.5078i 0.367401 1.79107i
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) 32.3101 1.71969 0.859845 0.510555i \(-0.170560\pi\)
0.859845 + 0.510555i \(0.170560\pi\)
\(354\) 0 0
\(355\) 54.9918i 2.91866i
\(356\) 1.56355 0.0828681
\(357\) 0 0
\(358\) 13.4262 0.709597
\(359\) 3.07604i 0.162347i −0.996700 0.0811735i \(-0.974133\pi\)
0.996700 0.0811735i \(-0.0258668\pi\)
\(360\) 0 0
\(361\) 18.9374 0.996707
\(362\) −19.8766 −1.04469
\(363\) 0 0
\(364\) 0 0
\(365\) 30.2956i 1.58574i
\(366\) 0 0
\(367\) 16.6508i 0.869163i 0.900633 + 0.434581i \(0.143104\pi\)
−0.900633 + 0.434581i \(0.856896\pi\)
\(368\) 4.50225i 0.234696i
\(369\) 0 0
\(370\) 10.5950i 0.550808i
\(371\) −2.48884 + 12.1330i −0.129214 + 0.629913i
\(372\) 0 0
\(373\) −7.37163 −0.381688 −0.190844 0.981620i \(-0.561123\pi\)
−0.190844 + 0.981620i \(0.561123\pi\)
\(374\) −5.29751 −0.273927
\(375\) 0 0
\(376\) 7.15497i 0.368990i
\(377\) 0 0
\(378\) 0 0
\(379\) 4.62039 0.237333 0.118667 0.992934i \(-0.462138\pi\)
0.118667 + 0.992934i \(0.462138\pi\)
\(380\) 1.05907i 0.0543293i
\(381\) 0 0
\(382\) 0.253253 0.0129576
\(383\) −26.9159 −1.37534 −0.687670 0.726023i \(-0.741366\pi\)
−0.687670 + 0.726023i \(0.741366\pi\)
\(384\) 0 0
\(385\) 2.25112 10.9741i 0.114728 0.559294i
\(386\) 12.8524i 0.654171i
\(387\) 0 0
\(388\) 7.96815i 0.404522i
\(389\) 5.20053i 0.263677i 0.991271 + 0.131839i \(0.0420881\pi\)
−0.991271 + 0.131839i \(0.957912\pi\)
\(390\) 0 0
\(391\) 23.8507i 1.20618i
\(392\) 2.75586 6.43469i 0.139192 0.325001i
\(393\) 0 0
\(394\) 25.4352 1.28141
\(395\) 1.59947 0.0804779
\(396\) 0 0
\(397\) 7.38608i 0.370697i −0.982673 0.185348i \(-0.940659\pi\)
0.982673 0.185348i \(-0.0593413\pi\)
\(398\) −22.7615 −1.14093
\(399\) 0 0
\(400\) 12.9285 0.646423
\(401\) 16.0699i 0.802493i −0.915970 0.401247i \(-0.868577\pi\)
0.915970 0.401247i \(-0.131423\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −15.6065 −0.776451
\(405\) 0 0
\(406\) 2.74489 + 0.563058i 0.136226 + 0.0279441i
\(407\) 2.50225i 0.124032i
\(408\) 0 0
\(409\) 22.1625i 1.09586i 0.836523 + 0.547932i \(0.184585\pi\)
−0.836523 + 0.547932i \(0.815415\pi\)
\(410\) 5.56132i 0.274654i
\(411\) 0 0
\(412\) 1.84057i 0.0906784i
\(413\) 21.9483 + 4.50225i 1.08000 + 0.221541i
\(414\) 0 0
\(415\) −7.79335 −0.382560
\(416\) 0 0
\(417\) 0 0
\(418\) 0.250123i 0.0122339i
\(419\) 24.9050 1.21669 0.608343 0.793674i \(-0.291834\pi\)
0.608343 + 0.793674i \(0.291834\pi\)
\(420\) 0 0
\(421\) −7.47281 −0.364202 −0.182101 0.983280i \(-0.558290\pi\)
−0.182101 + 0.983280i \(0.558290\pi\)
\(422\) 16.6733i 0.811646i
\(423\) 0 0
\(424\) −4.68132 −0.227345
\(425\) −68.4886 −3.32218
\(426\) 0 0
\(427\) 7.87387 38.3848i 0.381043 1.85757i
\(428\) 17.2365i 0.833159i
\(429\) 0 0
\(430\) 30.4167i 1.46682i
\(431\) 14.6797i 0.707096i 0.935416 + 0.353548i \(0.115025\pi\)
−0.935416 + 0.353548i \(0.884975\pi\)
\(432\) 0 0
\(433\) 32.4714i 1.56048i −0.625481 0.780239i \(-0.715097\pi\)
0.625481 0.780239i \(-0.284903\pi\)
\(434\) −16.3928 3.36265i −0.786878 0.161412i
\(435\) 0 0
\(436\) 17.8103 0.852959
\(437\) −1.12612 −0.0538695
\(438\) 0 0
\(439\) 33.3643i 1.59239i 0.605038 + 0.796197i \(0.293158\pi\)
−0.605038 + 0.796197i \(0.706842\pi\)
\(440\) 4.23420 0.201858
\(441\) 0 0
\(442\) 0 0
\(443\) 27.9205i 1.32654i 0.748379 + 0.663271i \(0.230832\pi\)
−0.748379 + 0.663271i \(0.769168\pi\)
\(444\) 0 0
\(445\) 6.62039 0.313837
\(446\) −19.0085 −0.900078
\(447\) 0 0
\(448\) 2.59178 + 0.531652i 0.122450 + 0.0251182i
\(449\) 12.4413i 0.587142i 0.955937 + 0.293571i \(0.0948437\pi\)
−0.955937 + 0.293571i \(0.905156\pi\)
\(450\) 0 0
\(451\) 1.31343i 0.0618469i
\(452\) 9.80396i 0.461139i
\(453\) 0 0
\(454\) 11.1122i 0.521519i
\(455\) 0 0
\(456\) 0 0
\(457\) 6.48528 0.303369 0.151684 0.988429i \(-0.451530\pi\)
0.151684 + 0.988429i \(0.451530\pi\)
\(458\) 1.34032 0.0626292
\(459\) 0 0
\(460\) 19.0634i 0.888836i
\(461\) −2.38461 −0.111062 −0.0555312 0.998457i \(-0.517685\pi\)
−0.0555312 + 0.998457i \(0.517685\pi\)
\(462\) 0 0
\(463\) 8.35815 0.388436 0.194218 0.980958i \(-0.437783\pi\)
0.194218 + 0.980958i \(0.437783\pi\)
\(464\) 1.05907i 0.0491662i
\(465\) 0 0
\(466\) −14.4853 −0.671018
\(467\) 25.8336 1.19544 0.597719 0.801706i \(-0.296074\pi\)
0.597719 + 0.801706i \(0.296074\pi\)
\(468\) 0 0
\(469\) −24.4307 5.01147i −1.12810 0.231408i
\(470\) 30.2956i 1.39743i
\(471\) 0 0
\(472\) 8.46840i 0.389790i
\(473\) 7.18357i 0.330301i
\(474\) 0 0
\(475\) 3.23371i 0.148373i
\(476\) −13.7300 2.81643i −0.629313 0.129091i
\(477\) 0 0
\(478\) 2.01696 0.0922538
\(479\) −21.9102 −1.00110 −0.500552 0.865706i \(-0.666870\pi\)
−0.500552 + 0.865706i \(0.666870\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 12.1395 0.552941
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 33.7388i 1.53200i
\(486\) 0 0
\(487\) −25.4898 −1.15505 −0.577526 0.816372i \(-0.695982\pi\)
−0.577526 + 0.816372i \(0.695982\pi\)
\(488\) 14.8102 0.670426
\(489\) 0 0
\(490\) 11.6688 27.2458i 0.527145 1.23084i
\(491\) 13.5067i 0.609551i −0.952424 0.304775i \(-0.901419\pi\)
0.952424 0.304775i \(-0.0985814\pi\)
\(492\) 0 0
\(493\) 5.61044i 0.252682i
\(494\) 0 0
\(495\) 0 0
\(496\) 6.32489i 0.283996i
\(497\) 6.90485 33.6609i 0.309725 1.50990i
\(498\) 0 0
\(499\) 4.90700 0.219667 0.109834 0.993950i \(-0.464968\pi\)
0.109834 + 0.993950i \(0.464968\pi\)
\(500\) 33.5707 1.50133
\(501\) 0 0
\(502\) 6.34179i 0.283048i
\(503\) −14.0519 −0.626545 −0.313273 0.949663i \(-0.601425\pi\)
−0.313273 + 0.949663i \(0.601425\pi\)
\(504\) 0 0
\(505\) −66.0810 −2.94056
\(506\) 4.50225i 0.200149i
\(507\) 0 0
\(508\) 13.1120 0.581752
\(509\) 42.0201 1.86251 0.931253 0.364373i \(-0.118717\pi\)
0.931253 + 0.364373i \(0.118717\pi\)
\(510\) 0 0
\(511\) −3.80396 + 18.5441i −0.168277 + 0.820345i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 1.56355i 0.0689653i
\(515\) 7.79335i 0.343416i
\(516\) 0 0
\(517\) 7.15497i 0.314675i
\(518\) 1.33032 6.48528i 0.0584511 0.284947i
\(519\) 0 0
\(520\) 0 0
\(521\) 43.4053 1.90162 0.950811 0.309773i \(-0.100253\pi\)
0.950811 + 0.309773i \(0.100253\pi\)
\(522\) 0 0
\(523\) 1.60734i 0.0702843i 0.999382 + 0.0351421i \(0.0111884\pi\)
−0.999382 + 0.0351421i \(0.988812\pi\)
\(524\) −16.3928 −0.716121
\(525\) 0 0
\(526\) 6.18171 0.269535
\(527\) 33.5062i 1.45955i
\(528\) 0 0
\(529\) 2.72978 0.118686
\(530\) −19.8217 −0.860998
\(531\) 0 0
\(532\) −0.132979 + 0.648266i −0.00576536 + 0.0281059i
\(533\) 0 0
\(534\) 0 0
\(535\) 72.9829i 3.15533i
\(536\) 9.42621i 0.407150i
\(537\) 0 0
\(538\) 25.0832i 1.08142i
\(539\) 2.75586 6.43469i 0.118703 0.277162i
\(540\) 0 0
\(541\) 10.9955 0.472734 0.236367 0.971664i \(-0.424043\pi\)
0.236367 + 0.971664i \(0.424043\pi\)
\(542\) 3.15188 0.135385
\(543\) 0 0
\(544\) 5.29751i 0.227129i
\(545\) 75.4124 3.23031
\(546\) 0 0
\(547\) 28.6733 1.22598 0.612992 0.790089i \(-0.289966\pi\)
0.612992 + 0.790089i \(0.289966\pi\)
\(548\) 17.6688i 0.754776i
\(549\) 0 0
\(550\) 12.9285 0.551271
\(551\) −0.264899 −0.0112851
\(552\) 0 0
\(553\) 0.979045 + 0.200831i 0.0416332 + 0.00854022i
\(554\) 1.04211i 0.0442749i
\(555\) 0 0
\(556\) 16.8840i 0.716041i
\(557\) 25.4352i 1.07772i −0.842394 0.538862i \(-0.818854\pi\)
0.842394 0.538862i \(-0.181146\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 10.9741 + 2.25112i 0.463742 + 0.0951273i
\(561\) 0 0
\(562\) −22.9706 −0.968955
\(563\) −14.4973 −0.610987 −0.305493 0.952194i \(-0.598821\pi\)
−0.305493 + 0.952194i \(0.598821\pi\)
\(564\) 0 0
\(565\) 41.5119i 1.74642i
\(566\) −23.7979 −1.00030
\(567\) 0 0
\(568\) 12.9875 0.544945
\(569\) 2.48528i 0.104188i 0.998642 + 0.0520942i \(0.0165896\pi\)
−0.998642 + 0.0520942i \(0.983410\pi\)
\(570\) 0 0
\(571\) −37.9141 −1.58666 −0.793328 0.608794i \(-0.791654\pi\)
−0.793328 + 0.608794i \(0.791654\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −0.698287 + 3.40412i −0.0291459 + 0.142085i
\(575\) 58.2071i 2.42740i
\(576\) 0 0
\(577\) 0.572077i 0.0238159i 0.999929 + 0.0119079i \(0.00379051\pi\)
−0.999929 + 0.0119079i \(0.996209\pi\)
\(578\) 11.0636i 0.460184i
\(579\) 0 0
\(580\) 4.48432i 0.186201i
\(581\) −4.77036 0.978544i −0.197908 0.0405968i
\(582\) 0 0
\(583\) −4.68132 −0.193881
\(584\) −7.15497 −0.296075
\(585\) 0 0
\(586\) 13.9801i 0.577513i
\(587\) 19.0296 0.785436 0.392718 0.919659i \(-0.371535\pi\)
0.392718 + 0.919659i \(0.371535\pi\)
\(588\) 0 0
\(589\) 1.58200 0.0651853
\(590\) 35.8569i 1.47621i
\(591\) 0 0
\(592\) 2.50225 0.102842
\(593\) −7.58339 −0.311412 −0.155706 0.987803i \(-0.549765\pi\)
−0.155706 + 0.987803i \(0.549765\pi\)
\(594\) 0 0
\(595\) −58.1355 11.9253i −2.38332 0.488891i
\(596\) 10.8694i 0.445227i
\(597\) 0 0
\(598\) 0 0
\(599\) 25.5067i 1.04218i 0.853503 + 0.521089i \(0.174474\pi\)
−0.853503 + 0.521089i \(0.825526\pi\)
\(600\) 0 0
\(601\) 32.8631i 1.34051i −0.742129 0.670257i \(-0.766184\pi\)
0.742129 0.670257i \(-0.233816\pi\)
\(602\) 3.81916 18.6183i 0.155657 0.758824i
\(603\) 0 0
\(604\) −8.17110 −0.332477
\(605\) 4.23420 0.172145
\(606\) 0 0
\(607\) 33.8646i 1.37452i 0.726411 + 0.687261i \(0.241187\pi\)
−0.726411 + 0.687261i \(0.758813\pi\)
\(608\) −0.250123 −0.0101438
\(609\) 0 0
\(610\) 62.7093 2.53903
\(611\) 0 0
\(612\) 0 0
\(613\) 28.4434 1.14882 0.574408 0.818569i \(-0.305232\pi\)
0.574408 + 0.818569i \(0.305232\pi\)
\(614\) −33.5897 −1.35557
\(615\) 0 0
\(616\) 2.59178 + 0.531652i 0.104426 + 0.0214209i
\(617\) 12.0064i 0.483358i −0.970356 0.241679i \(-0.922302\pi\)
0.970356 0.241679i \(-0.0776980\pi\)
\(618\) 0 0
\(619\) 3.71494i 0.149316i 0.997209 + 0.0746579i \(0.0237865\pi\)
−0.997209 + 0.0746579i \(0.976214\pi\)
\(620\) 26.7809i 1.07555i
\(621\) 0 0
\(622\) 11.6393i 0.466693i
\(623\) 4.05239 + 0.831266i 0.162355 + 0.0333040i
\(624\) 0 0
\(625\) 77.5027 3.10011
\(626\) −1.83057 −0.0731644
\(627\) 0 0
\(628\) 20.6348i 0.823420i
\(629\) −13.2557 −0.528538
\(630\) 0 0
\(631\) −26.9795 −1.07404 −0.537019 0.843570i \(-0.680450\pi\)
−0.537019 + 0.843570i \(0.680450\pi\)
\(632\) 0.377749i 0.0150261i
\(633\) 0 0
\(634\) 29.9348 1.18886
\(635\) 55.5189 2.20320
\(636\) 0 0
\(637\) 0 0
\(638\) 1.05907i 0.0419291i
\(639\) 0 0
\(640\) 4.23420i 0.167371i
\(641\) 20.4916i 0.809371i 0.914456 + 0.404685i \(0.132619\pi\)
−0.914456 + 0.404685i \(0.867381\pi\)
\(642\) 0 0
\(643\) 9.59452i 0.378371i −0.981941 0.189185i \(-0.939415\pi\)
0.981941 0.189185i \(-0.0605847\pi\)
\(644\) −2.39363 + 11.6688i −0.0943222 + 0.459817i
\(645\) 0 0
\(646\) 1.32503 0.0521326
\(647\) −37.5110 −1.47471 −0.737354 0.675507i \(-0.763925\pi\)
−0.737354 + 0.675507i \(0.763925\pi\)
\(648\) 0 0
\(649\) 8.46840i 0.332414i
\(650\) 0 0
\(651\) 0 0
\(652\) −8.62039 −0.337601
\(653\) 28.8964i 1.13080i −0.824816 0.565401i \(-0.808721\pi\)
0.824816 0.565401i \(-0.191279\pi\)
\(654\) 0 0
\(655\) −69.4102 −2.71208
\(656\) −1.31343 −0.0512808
\(657\) 0 0
\(658\) 3.80396 18.5441i 0.148294 0.722926i
\(659\) 45.5957i 1.77616i 0.459693 + 0.888078i \(0.347959\pi\)
−0.459693 + 0.888078i \(0.652041\pi\)
\(660\) 0 0
\(661\) 3.42890i 0.133369i 0.997774 + 0.0666843i \(0.0212420\pi\)
−0.997774 + 0.0666843i \(0.978758\pi\)
\(662\) 5.69643i 0.221398i
\(663\) 0 0
\(664\) 1.84057i 0.0714280i
\(665\) −0.563058 + 2.74489i −0.0218345 + 0.106442i
\(666\) 0 0
\(667\) −4.76820 −0.184626
\(668\) 2.88486 0.111618
\(669\) 0 0
\(670\) 39.9125i 1.54195i
\(671\) 14.8102 0.571741
\(672\) 0 0
\(673\) −23.2069 −0.894558 −0.447279 0.894394i \(-0.647607\pi\)
−0.447279 + 0.894394i \(0.647607\pi\)
\(674\) 0.637355i 0.0245500i
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) −8.06674 −0.310030 −0.155015 0.987912i \(-0.549543\pi\)
−0.155015 + 0.987912i \(0.549543\pi\)
\(678\) 0 0
\(679\) −4.23629 + 20.6517i −0.162574 + 0.792541i
\(680\) 22.4307i 0.860178i
\(681\) 0 0
\(682\) 6.32489i 0.242193i
\(683\) 34.2876i 1.31198i 0.754770 + 0.655989i \(0.227748\pi\)
−0.754770 + 0.655989i \(0.772252\pi\)
\(684\) 0 0
\(685\) 74.8135i 2.85848i
\(686\) 10.5636 15.2122i 0.403320 0.580804i
\(687\) 0 0
\(688\) 7.18357 0.273871
\(689\) 0 0
\(690\) 0 0
\(691\) 49.1840i 1.87105i 0.353261 + 0.935525i \(0.385073\pi\)
−0.353261 + 0.935525i \(0.614927\pi\)
\(692\) −11.8535 −0.450603
\(693\) 0 0
\(694\) 21.4728 0.815097
\(695\) 71.4902i 2.71178i
\(696\) 0 0
\(697\) 6.95789 0.263549
\(698\) 9.52269 0.360439
\(699\) 0 0
\(700\) 33.5078 + 6.87344i 1.26647 + 0.259792i
\(701\) 37.6079i 1.42043i 0.703984 + 0.710216i \(0.251403\pi\)
−0.703984 + 0.710216i \(0.748597\pi\)
\(702\) 0 0
\(703\) 0.625870i 0.0236051i
\(704\) 1.00000i 0.0376889i
\(705\) 0 0
\(706\) 32.3101i 1.21600i
\(707\) −40.4486 8.29722i −1.52123 0.312049i
\(708\) 0 0
\(709\) 36.7093 1.37865 0.689324 0.724453i \(-0.257908\pi\)
0.689324 + 0.724453i \(0.257908\pi\)
\(710\) 54.9918 2.06381
\(711\) 0 0
\(712\) 1.56355i 0.0585966i
\(713\) 28.4762 1.06644
\(714\) 0 0
\(715\) 0 0
\(716\) 13.4262i 0.501761i
\(717\) 0 0
\(718\) 3.07604 0.114797
\(719\) 50.7486 1.89260 0.946301 0.323286i \(-0.104788\pi\)
0.946301 + 0.323286i \(0.104788\pi\)
\(720\) 0 0
\(721\) 0.978544 4.77036i 0.0364429 0.177658i
\(722\) 18.9374i 0.704778i
\(723\) 0 0
\(724\) 19.8766i 0.738708i
\(725\) 13.6922i 0.508514i
\(726\) 0 0
\(727\) 0.570936i 0.0211748i 0.999944 + 0.0105874i \(0.00337014\pi\)
−0.999944 + 0.0105874i \(0.996630\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −30.2956 −1.12129
\(731\) −38.0550 −1.40751
\(732\) 0 0
\(733\) 12.6836i 0.468479i 0.972179 + 0.234239i \(0.0752600\pi\)
−0.972179 + 0.234239i \(0.924740\pi\)
\(734\) −16.6508 −0.614591
\(735\) 0 0
\(736\) −4.50225 −0.165955
\(737\) 9.42621i 0.347219i
\(738\) 0 0
\(739\) 26.0360 0.957749 0.478875 0.877883i \(-0.341045\pi\)
0.478875 + 0.877883i \(0.341045\pi\)
\(740\) 10.5950 0.389480
\(741\) 0 0
\(742\) −12.1330 2.48884i −0.445416 0.0913681i
\(743\) 30.8355i 1.13124i 0.824665 + 0.565622i \(0.191364\pi\)
−0.824665 + 0.565622i \(0.808636\pi\)
\(744\) 0 0
\(745\) 46.0231i 1.68616i
\(746\) 7.37163i 0.269895i
\(747\) 0 0
\(748\) 5.29751i 0.193696i
\(749\) −9.16384 + 44.6733i −0.334839 + 1.63233i
\(750\) 0 0
\(751\) 14.9616 0.545956 0.272978 0.962020i \(-0.411991\pi\)
0.272978 + 0.962020i \(0.411991\pi\)
\(752\) 7.15497 0.260915
\(753\) 0 0
\(754\) 0 0
\(755\) −34.5981 −1.25915
\(756\) 0 0
\(757\) 22.6294 0.822479 0.411239 0.911527i \(-0.365096\pi\)
0.411239 + 0.911527i \(0.365096\pi\)
\(758\) 4.62039i 0.167820i
\(759\) 0 0
\(760\) −1.05907 −0.0384166
\(761\) −35.1870 −1.27553 −0.637764 0.770231i \(-0.720141\pi\)
−0.637764 + 0.770231i \(0.720141\pi\)
\(762\) 0 0
\(763\) 46.1605 + 9.46889i 1.67112 + 0.342797i
\(764\) 0.253253i 0.00916237i
\(765\) 0 0
\(766\) 26.9159i 0.972513i
\(767\) 0 0
\(768\) 0 0
\(769\) 31.4721i 1.13491i −0.823403 0.567456i \(-0.807928\pi\)
0.823403 0.567456i \(-0.192072\pi\)
\(770\) 10.9741 + 2.25112i 0.395480 + 0.0811248i
\(771\) 0 0
\(772\) −12.8524 −0.462569
\(773\) 29.3365 1.05516 0.527580 0.849506i \(-0.323100\pi\)
0.527580 + 0.849506i \(0.323100\pi\)
\(774\) 0 0
\(775\) 81.7711i 2.93731i
\(776\) −7.96815 −0.286040
\(777\) 0 0
\(778\) −5.20053 −0.186448
\(779\) 0.328519i 0.0117704i
\(780\) 0 0
\(781\) 12.9875 0.464730
\(782\) 23.8507 0.852898
\(783\) 0 0
\(784\) 6.43469 + 2.75586i 0.229810 + 0.0984235i
\(785\) 87.3721i 3.11844i
\(786\) 0 0
\(787\) 27.7101i 0.987759i −0.869530 0.493879i \(-0.835578\pi\)
0.869530 0.493879i \(-0.164422\pi\)
\(788\) 25.4352i 0.906091i
\(789\) 0 0
\(790\) 1.59947i 0.0569065i
\(791\) 5.21230 25.4097i 0.185328 0.903467i
\(792\) 0 0
\(793\) 0 0
\(794\) 7.38608 0.262122
\(795\) 0 0
\(796\) 22.7615i 0.806758i
\(797\) 21.4739 0.760646 0.380323 0.924854i \(-0.375813\pi\)
0.380323 + 0.924854i \(0.375813\pi\)
\(798\) 0 0
\(799\) −37.9035 −1.34093
\(800\) 12.9285i 0.457090i
\(801\) 0