Properties

Label 1386.2.g.a.881.15
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 881.15
Root \(-2.43348 - 1.00798i\) of defining polynomial
Character \(\chi\) \(=\) 1386.881
Dual form 1386.2.g.a.881.7

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +2.01596 q^{5} +(1.78450 + 1.95335i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +2.01596 q^{5} +(1.78450 + 1.95335i) q^{7} -1.00000i q^{8} +2.01596i q^{10} -1.00000i q^{11} +(-1.95335 + 1.78450i) q^{14} +1.00000 q^{16} +5.92266 q^{17} -0.657927i q^{19} -2.01596 q^{20} +1.00000 q^{22} +7.87575i q^{23} -0.935886 q^{25} +(-1.78450 - 1.95335i) q^{28} +1.32636i q^{29} -10.6942i q^{31} +1.00000i q^{32} +5.92266i q^{34} +(3.59749 + 3.93788i) q^{35} +5.87575 q^{37} +0.657927 q^{38} -2.01596i q^{40} +4.56462 q^{41} -1.56900 q^{43} +1.00000i q^{44} -7.87575 q^{46} +0.532690 q^{47} +(-0.631122 + 6.97149i) q^{49} -0.935886i q^{50} +7.44475i q^{53} -2.01596i q^{55} +(1.95335 - 1.78450i) q^{56} -1.32636 q^{58} +4.03193 q^{59} -0.250475i q^{61} +10.6942 q^{62} -1.00000 q^{64} -7.81164 q^{67} -5.92266 q^{68} +(-3.93788 + 3.59749i) q^{70} -0.609527i q^{71} -0.532690i q^{73} +5.87575i q^{74} +0.657927i q^{76} +(1.95335 - 1.78450i) q^{77} -12.7711 q^{79} +2.01596 q^{80} +4.56462i q^{82} +13.3681 q^{83} +11.9399 q^{85} -1.56900i q^{86} -1.00000 q^{88} +5.22255 q^{89} -7.87575i q^{92} +0.532690i q^{94} -1.32636i q^{95} +2.71607i q^{97} +(-6.97149 - 0.631122i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{4} - 8q^{7} + O(q^{10}) \) \( 16q - 16q^{4} - 8q^{7} + 16q^{16} + 16q^{22} + 16q^{25} + 8q^{28} - 16q^{37} + 48q^{43} - 16q^{46} + 8q^{49} - 16q^{58} - 16q^{64} + 16q^{67} - 8q^{70} - 16q^{79} + 112q^{85} - 16q^{88} + O(q^{100}) \)

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
\(5\) 2.01596 0.901567 0.450783 0.892633i \(-0.351145\pi\)
0.450783 + 0.892633i \(0.351145\pi\)
\(6\) 0 0
\(7\) 1.78450 + 1.95335i 0.674477 + 0.738295i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.01596i 0.637504i
\(11\) 1.00000i 0.301511i
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −1.95335 + 1.78450i −0.522054 + 0.476928i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 5.92266 1.43646 0.718228 0.695808i \(-0.244954\pi\)
0.718228 + 0.695808i \(0.244954\pi\)
\(18\) 0 0
\(19\) 0.657927i 0.150939i −0.997148 0.0754695i \(-0.975954\pi\)
0.997148 0.0754695i \(-0.0240455\pi\)
\(20\) −2.01596 −0.450783
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 7.87575i 1.64221i 0.570778 + 0.821104i \(0.306642\pi\)
−0.570778 + 0.821104i \(0.693358\pi\)
\(24\) 0 0
\(25\) −0.935886 −0.187177
\(26\) 0 0
\(27\) 0 0
\(28\) −1.78450 1.95335i −0.337239 0.369148i
\(29\) 1.32636i 0.246299i 0.992388 + 0.123149i \(0.0392994\pi\)
−0.992388 + 0.123149i \(0.960701\pi\)
\(30\) 0 0
\(31\) 10.6942i 1.92074i −0.278732 0.960369i \(-0.589914\pi\)
0.278732 0.960369i \(-0.410086\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 5.92266i 1.01573i
\(35\) 3.59749 + 3.93788i 0.608087 + 0.665623i
\(36\) 0 0
\(37\) 5.87575 0.965968 0.482984 0.875629i \(-0.339553\pi\)
0.482984 + 0.875629i \(0.339553\pi\)
\(38\) 0.657927 0.106730
\(39\) 0 0
\(40\) 2.01596i 0.318752i
\(41\) 4.56462 0.712874 0.356437 0.934319i \(-0.383991\pi\)
0.356437 + 0.934319i \(0.383991\pi\)
\(42\) 0 0
\(43\) −1.56900 −0.239270 −0.119635 0.992818i \(-0.538172\pi\)
−0.119635 + 0.992818i \(0.538172\pi\)
\(44\) 1.00000i 0.150756i
\(45\) 0 0
\(46\) −7.87575 −1.16122
\(47\) 0.532690 0.0777008 0.0388504 0.999245i \(-0.487630\pi\)
0.0388504 + 0.999245i \(0.487630\pi\)
\(48\) 0 0
\(49\) −0.631122 + 6.97149i −0.0901603 + 0.995927i
\(50\) 0.935886i 0.132354i
\(51\) 0 0
\(52\) 0 0
\(53\) 7.44475i 1.02262i 0.859398 + 0.511308i \(0.170839\pi\)
−0.859398 + 0.511308i \(0.829161\pi\)
\(54\) 0 0
\(55\) 2.01596i 0.271833i
\(56\) 1.95335 1.78450i 0.261027 0.238464i
\(57\) 0 0
\(58\) −1.32636 −0.174159
\(59\) 4.03193 0.524913 0.262456 0.964944i \(-0.415467\pi\)
0.262456 + 0.964944i \(0.415467\pi\)
\(60\) 0 0
\(61\) 0.250475i 0.0320700i −0.999871 0.0160350i \(-0.994896\pi\)
0.999871 0.0160350i \(-0.00510432\pi\)
\(62\) 10.6942 1.35817
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −7.81164 −0.954344 −0.477172 0.878810i \(-0.658338\pi\)
−0.477172 + 0.878810i \(0.658338\pi\)
\(68\) −5.92266 −0.718228
\(69\) 0 0
\(70\) −3.93788 + 3.59749i −0.470666 + 0.429982i
\(71\) 0.609527i 0.0723376i −0.999346 0.0361688i \(-0.988485\pi\)
0.999346 0.0361688i \(-0.0115154\pi\)
\(72\) 0 0
\(73\) 0.532690i 0.0623466i −0.999514 0.0311733i \(-0.990076\pi\)
0.999514 0.0311733i \(-0.00992438\pi\)
\(74\) 5.87575i 0.683043i
\(75\) 0 0
\(76\) 0.657927i 0.0754695i
\(77\) 1.95335 1.78450i 0.222604 0.203363i
\(78\) 0 0
\(79\) −12.7711 −1.43686 −0.718431 0.695598i \(-0.755139\pi\)
−0.718431 + 0.695598i \(0.755139\pi\)
\(80\) 2.01596 0.225392
\(81\) 0 0
\(82\) 4.56462i 0.504078i
\(83\) 13.3681 1.46734 0.733670 0.679506i \(-0.237806\pi\)
0.733670 + 0.679506i \(0.237806\pi\)
\(84\) 0 0
\(85\) 11.9399 1.29506
\(86\) 1.56900i 0.169190i
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) 5.22255 0.553589 0.276794 0.960929i \(-0.410728\pi\)
0.276794 + 0.960929i \(0.410728\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 7.87575i 0.821104i
\(93\) 0 0
\(94\) 0.532690i 0.0549428i
\(95\) 1.32636i 0.136082i
\(96\) 0 0
\(97\) 2.71607i 0.275776i 0.990448 + 0.137888i \(0.0440313\pi\)
−0.990448 + 0.137888i \(0.955969\pi\)
\(98\) −6.97149 0.631122i −0.704227 0.0637530i
\(99\) 0 0
\(100\) 0.935886 0.0935886
\(101\) 3.41352 0.339658 0.169829 0.985474i \(-0.445678\pi\)
0.169829 + 0.985474i \(0.445678\pi\)
\(102\) 0 0
\(103\) 13.3681i 1.31720i 0.752494 + 0.658599i \(0.228851\pi\)
−0.752494 + 0.658599i \(0.771149\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −7.44475 −0.723098
\(107\) 14.4002i 1.39212i 0.717982 + 0.696062i \(0.245066\pi\)
−0.717982 + 0.696062i \(0.754934\pi\)
\(108\) 0 0
\(109\) −3.41140 −0.326753 −0.163376 0.986564i \(-0.552238\pi\)
−0.163376 + 0.986564i \(0.552238\pi\)
\(110\) 2.01596 0.192215
\(111\) 0 0
\(112\) 1.78450 + 1.95335i 0.168619 + 0.184574i
\(113\) 4.95947i 0.466548i 0.972411 + 0.233274i \(0.0749439\pi\)
−0.972411 + 0.233274i \(0.925056\pi\)
\(114\) 0 0
\(115\) 15.8772i 1.48056i
\(116\) 1.32636i 0.123149i
\(117\) 0 0
\(118\) 4.03193i 0.371169i
\(119\) 10.5690 + 11.5690i 0.968857 + 1.06053i
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) 0.250475 0.0226769
\(123\) 0 0
\(124\) 10.6942i 0.960369i
\(125\) −11.9665 −1.07032
\(126\) 0 0
\(127\) 9.50488 0.843422 0.421711 0.906730i \(-0.361430\pi\)
0.421711 + 0.906730i \(0.361430\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 0 0
\(131\) −19.0838 −1.66736 −0.833681 0.552247i \(-0.813771\pi\)
−0.833681 + 0.552247i \(0.813771\pi\)
\(132\) 0 0
\(133\) 1.28516 1.17407i 0.111438 0.101805i
\(134\) 7.81164i 0.674823i
\(135\) 0 0
\(136\) 5.92266i 0.507864i
\(137\) 8.05428i 0.688124i 0.938947 + 0.344062i \(0.111803\pi\)
−0.938947 + 0.344062i \(0.888197\pi\)
\(138\) 0 0
\(139\) 19.3725i 1.64315i −0.570099 0.821576i \(-0.693095\pi\)
0.570099 0.821576i \(-0.306905\pi\)
\(140\) −3.59749 3.93788i −0.304043 0.332811i
\(141\) 0 0
\(142\) 0.609527 0.0511504
\(143\) 0 0
\(144\) 0 0
\(145\) 2.67389i 0.222055i
\(146\) 0.532690 0.0440857
\(147\) 0 0
\(148\) −5.87575 −0.482984
\(149\) 3.26224i 0.267253i −0.991032 0.133627i \(-0.957338\pi\)
0.991032 0.133627i \(-0.0426623\pi\)
\(150\) 0 0
\(151\) −14.1785 −1.15383 −0.576916 0.816803i \(-0.695744\pi\)
−0.576916 + 0.816803i \(0.695744\pi\)
\(152\) −0.657927 −0.0533650
\(153\) 0 0
\(154\) 1.78450 + 1.95335i 0.143799 + 0.157405i
\(155\) 21.5592i 1.73167i
\(156\) 0 0
\(157\) 11.7596i 0.938518i −0.883061 0.469259i \(-0.844521\pi\)
0.883061 0.469259i \(-0.155479\pi\)
\(158\) 12.7711i 1.01602i
\(159\) 0 0
\(160\) 2.01596i 0.159376i
\(161\) −15.3841 + 14.0543i −1.21243 + 1.10763i
\(162\) 0 0
\(163\) 12.5285 0.981306 0.490653 0.871355i \(-0.336758\pi\)
0.490653 + 0.871355i \(0.336758\pi\)
\(164\) −4.56462 −0.356437
\(165\) 0 0
\(166\) 13.3681i 1.03757i
\(167\) −23.0722 −1.78538 −0.892691 0.450669i \(-0.851185\pi\)
−0.892691 + 0.450669i \(0.851185\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 11.9399i 0.915746i
\(171\) 0 0
\(172\) 1.56900 0.119635
\(173\) 17.7244 1.34756 0.673782 0.738930i \(-0.264669\pi\)
0.673782 + 0.738930i \(0.264669\pi\)
\(174\) 0 0
\(175\) −1.67009 1.82811i −0.126247 0.138192i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) 5.22255i 0.391446i
\(179\) 3.81164i 0.284895i 0.989802 + 0.142448i \(0.0454973\pi\)
−0.989802 + 0.142448i \(0.954503\pi\)
\(180\) 0 0
\(181\) 19.1260i 1.42163i −0.703382 0.710813i \(-0.748327\pi\)
0.703382 0.710813i \(-0.251673\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 7.87575 0.580608
\(185\) 11.8453 0.870885
\(186\) 0 0
\(187\) 5.92266i 0.433108i
\(188\) −0.532690 −0.0388504
\(189\) 0 0
\(190\) 1.32636 0.0962242
\(191\) 21.6665i 1.56773i −0.620931 0.783865i \(-0.713245\pi\)
0.620931 0.783865i \(-0.286755\pi\)
\(192\) 0 0
\(193\) −21.6233 −1.55648 −0.778239 0.627968i \(-0.783887\pi\)
−0.778239 + 0.627968i \(0.783887\pi\)
\(194\) −2.71607 −0.195003
\(195\) 0 0
\(196\) 0.631122 6.97149i 0.0450802 0.497964i
\(197\) 21.6914i 1.54545i −0.634743 0.772723i \(-0.718894\pi\)
0.634743 0.772723i \(-0.281106\pi\)
\(198\) 0 0
\(199\) 3.94621i 0.279740i 0.990170 + 0.139870i \(0.0446684\pi\)
−0.990170 + 0.139870i \(0.955332\pi\)
\(200\) 0.935886i 0.0661771i
\(201\) 0 0
\(202\) 3.41352i 0.240175i
\(203\) −2.59084 + 2.36689i −0.181841 + 0.166123i
\(204\) 0 0
\(205\) 9.20211 0.642703
\(206\) −13.3681 −0.931400
\(207\) 0 0
\(208\) 0 0
\(209\) −0.657927 −0.0455098
\(210\) 0 0
\(211\) 2.30277 0.158529 0.0792647 0.996854i \(-0.474743\pi\)
0.0792647 + 0.996854i \(0.474743\pi\)
\(212\) 7.44475i 0.511308i
\(213\) 0 0
\(214\) −14.4002 −0.984380
\(215\) −3.16305 −0.215718
\(216\) 0 0
\(217\) 20.8895 19.0838i 1.41807 1.29549i
\(218\) 3.41140i 0.231049i
\(219\) 0 0
\(220\) 2.01596i 0.135916i
\(221\) 0 0
\(222\) 0 0
\(223\) 18.2571i 1.22259i 0.791404 + 0.611294i \(0.209351\pi\)
−0.791404 + 0.611294i \(0.790649\pi\)
\(224\) −1.95335 + 1.78450i −0.130513 + 0.119232i
\(225\) 0 0
\(226\) −4.95947 −0.329899
\(227\) −20.0739 −1.33235 −0.666177 0.745794i \(-0.732070\pi\)
−0.666177 + 0.745794i \(0.732070\pi\)
\(228\) 0 0
\(229\) 14.6840i 0.970344i −0.874419 0.485172i \(-0.838757\pi\)
0.874419 0.485172i \(-0.161243\pi\)
\(230\) −15.8772 −1.04691
\(231\) 0 0
\(232\) 1.32636 0.0870797
\(233\) 2.48528i 0.162816i −0.996681 0.0814081i \(-0.974058\pi\)
0.996681 0.0814081i \(-0.0259417\pi\)
\(234\) 0 0
\(235\) 1.07388 0.0700525
\(236\) −4.03193 −0.262456
\(237\) 0 0
\(238\) −11.5690 + 10.5690i −0.749907 + 0.685085i
\(239\) 22.3610i 1.44642i −0.690631 0.723208i \(-0.742667\pi\)
0.690631 0.723208i \(-0.257333\pi\)
\(240\) 0 0
\(241\) 3.45706i 0.222689i 0.993782 + 0.111344i \(0.0355156\pi\)
−0.993782 + 0.111344i \(0.964484\pi\)
\(242\) 1.00000i 0.0642824i
\(243\) 0 0
\(244\) 0.250475i 0.0160350i
\(245\) −1.27232 + 14.0543i −0.0812855 + 0.897895i
\(246\) 0 0
\(247\) 0 0
\(248\) −10.6942 −0.679083
\(249\) 0 0
\(250\) 11.9665i 0.756830i
\(251\) 3.78145 0.238683 0.119342 0.992853i \(-0.461922\pi\)
0.119342 + 0.992853i \(0.461922\pi\)
\(252\) 0 0
\(253\) 7.87575 0.495144
\(254\) 9.50488i 0.596390i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −5.22255 −0.325774 −0.162887 0.986645i \(-0.552081\pi\)
−0.162887 + 0.986645i \(0.552081\pi\)
\(258\) 0 0
\(259\) 10.4853 + 11.4774i 0.651524 + 0.713170i
\(260\) 0 0
\(261\) 0 0
\(262\) 19.0838i 1.17900i
\(263\) 13.7306i 0.846664i −0.905975 0.423332i \(-0.860860\pi\)
0.905975 0.423332i \(-0.139140\pi\)
\(264\) 0 0
\(265\) 15.0084i 0.921956i
\(266\) 1.17407 + 1.28516i 0.0719869 + 0.0787982i
\(267\) 0 0
\(268\) 7.81164 0.477172
\(269\) 29.6093 1.80531 0.902655 0.430366i \(-0.141615\pi\)
0.902655 + 0.430366i \(0.141615\pi\)
\(270\) 0 0
\(271\) 15.5015i 0.941651i −0.882226 0.470825i \(-0.843956\pi\)
0.882226 0.470825i \(-0.156044\pi\)
\(272\) 5.92266 0.359114
\(273\) 0 0
\(274\) −8.05428 −0.486577
\(275\) 0.935886i 0.0564360i
\(276\) 0 0
\(277\) −19.0347 −1.14368 −0.571841 0.820364i \(-0.693771\pi\)
−0.571841 + 0.820364i \(0.693771\pi\)
\(278\) 19.3725 1.16188
\(279\) 0 0
\(280\) 3.93788 3.59749i 0.235333 0.214991i
\(281\) 10.9706i 0.654449i −0.944947 0.327224i \(-0.893887\pi\)
0.944947 0.327224i \(-0.106113\pi\)
\(282\) 0 0
\(283\) 19.2091i 1.14186i −0.820999 0.570930i \(-0.806583\pi\)
0.820999 0.570930i \(-0.193417\pi\)
\(284\) 0.609527i 0.0361688i
\(285\) 0 0
\(286\) 0 0
\(287\) 8.14556 + 8.91628i 0.480817 + 0.526311i
\(288\) 0 0
\(289\) 18.0779 1.06340
\(290\) −2.67389 −0.157016
\(291\) 0 0
\(292\) 0.532690i 0.0311733i
\(293\) 9.91105 0.579010 0.289505 0.957177i \(-0.406509\pi\)
0.289505 + 0.957177i \(0.406509\pi\)
\(294\) 0 0
\(295\) 8.12823 0.473244
\(296\) 5.87575i 0.341521i
\(297\) 0 0
\(298\) 3.26224 0.188977
\(299\) 0 0
\(300\) 0 0
\(301\) −2.79988 3.06480i −0.161382 0.176652i
\(302\) 14.1785i 0.815883i
\(303\) 0 0
\(304\) 0.657927i 0.0377347i
\(305\) 0.504949i 0.0289133i
\(306\) 0 0
\(307\) 1.64427i 0.0938433i −0.998899 0.0469216i \(-0.985059\pi\)
0.998899 0.0469216i \(-0.0149411\pi\)
\(308\) −1.95335 + 1.78450i −0.111302 + 0.101681i
\(309\) 0 0
\(310\) 21.5592 1.22448
\(311\) 2.14120 0.121416 0.0607082 0.998156i \(-0.480664\pi\)
0.0607082 + 0.998156i \(0.480664\pi\)
\(312\) 0 0
\(313\) 12.7932i 0.723116i −0.932350 0.361558i \(-0.882245\pi\)
0.932350 0.361558i \(-0.117755\pi\)
\(314\) 11.7596 0.663632
\(315\) 0 0
\(316\) 12.7711 0.718431
\(317\) 6.51604i 0.365977i −0.983115 0.182989i \(-0.941423\pi\)
0.983115 0.182989i \(-0.0585771\pi\)
\(318\) 0 0
\(319\) 1.32636 0.0742618
\(320\) −2.01596 −0.112696
\(321\) 0 0
\(322\) −14.0543 15.3841i −0.783214 0.857321i
\(323\) 3.89668i 0.216817i
\(324\) 0 0
\(325\) 0 0
\(326\) 12.5285i 0.693888i
\(327\) 0 0
\(328\) 4.56462i 0.252039i
\(329\) 0.950585 + 1.04053i 0.0524074 + 0.0573662i
\(330\) 0 0
\(331\) −30.2159 −1.66081 −0.830407 0.557157i \(-0.811892\pi\)
−0.830407 + 0.557157i \(0.811892\pi\)
\(332\) −13.3681 −0.733670
\(333\) 0 0
\(334\) 23.0722i 1.26246i
\(335\) −15.7480 −0.860405
\(336\) 0 0
\(337\) 24.8895 1.35582 0.677909 0.735146i \(-0.262886\pi\)
0.677909 + 0.735146i \(0.262886\pi\)
\(338\) 13.0000i 0.707107i
\(339\) 0 0
\(340\) −11.9399 −0.647530
\(341\) −10.6942 −0.579124
\(342\) 0 0
\(343\) −14.7440 + 11.2078i −0.796100 + 0.605166i
\(344\) 1.56900i 0.0845948i
\(345\) 0 0
\(346\) 17.7244i 0.952872i
\(347\) 9.09481i 0.488235i 0.969746 + 0.244117i \(0.0784982\pi\)
−0.969746 + 0.244117i \(0.921502\pi\)
\(348\) 0 0
\(349\) 31.8335i 1.70401i −0.523534 0.852005i \(-0.675387\pi\)
0.523534 0.852005i \(-0.324613\pi\)
\(350\) 1.82811 1.67009i 0.0977165 0.0892699i
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) −10.9052 −0.580424 −0.290212 0.956962i \(-0.593726\pi\)
−0.290212 + 0.956962i \(0.593726\pi\)
\(354\) 0 0
\(355\) 1.22879i 0.0652171i
\(356\) −5.22255 −0.276794
\(357\) 0 0
\(358\) −3.81164 −0.201451
\(359\) 23.6874i 1.25017i −0.780556 0.625086i \(-0.785064\pi\)
0.780556 0.625086i \(-0.214936\pi\)
\(360\) 0 0
\(361\) 18.5671 0.977217
\(362\) 19.1260 1.00524
\(363\) 0 0
\(364\) 0 0
\(365\) 1.07388i 0.0562097i
\(366\) 0 0
\(367\) 13.1176i 0.684735i 0.939566 + 0.342367i \(0.111229\pi\)
−0.939566 + 0.342367i \(0.888771\pi\)
\(368\) 7.87575i 0.410552i
\(369\) 0 0
\(370\) 11.8453i 0.615809i
\(371\) −14.5422 + 13.2852i −0.754992 + 0.689731i
\(372\) 0 0
\(373\) 3.38649 0.175346 0.0876729 0.996149i \(-0.472057\pi\)
0.0876729 + 0.996149i \(0.472057\pi\)
\(374\) 5.92266 0.306253
\(375\) 0 0
\(376\) 0.532690i 0.0274714i
\(377\) 0 0
\(378\) 0 0
\(379\) 8.52847 0.438078 0.219039 0.975716i \(-0.429708\pi\)
0.219039 + 0.975716i \(0.429708\pi\)
\(380\) 1.32636i 0.0680408i
\(381\) 0 0
\(382\) 21.6665 1.10855
\(383\) −10.1180 −0.517005 −0.258503 0.966011i \(-0.583229\pi\)
−0.258503 + 0.966011i \(0.583229\pi\)
\(384\) 0 0
\(385\) 3.93788 3.59749i 0.200693 0.183345i
\(386\) 21.6233i 1.10060i
\(387\) 0 0
\(388\) 2.71607i 0.137888i
\(389\) 16.7920i 0.851390i 0.904867 + 0.425695i \(0.139970\pi\)
−0.904867 + 0.425695i \(0.860030\pi\)
\(390\) 0 0
\(391\) 46.6454i 2.35896i
\(392\) 6.97149 + 0.631122i 0.352113 + 0.0318765i
\(393\) 0 0
\(394\) 21.6914 1.09280
\(395\) −25.7461 −1.29543
\(396\) 0 0
\(397\) 13.4856i 0.676821i −0.940999 0.338411i \(-0.890111\pi\)
0.940999 0.338411i \(-0.109889\pi\)
\(398\) −3.94621 −0.197806
\(399\) 0 0
\(400\) −0.935886 −0.0467943
\(401\) 13.5298i 0.675646i −0.941210 0.337823i \(-0.890310\pi\)
0.941210 0.337823i \(-0.109690\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −3.41352 −0.169829
\(405\) 0 0
\(406\) −2.36689 2.59084i −0.117467 0.128581i
\(407\) 5.87575i 0.291250i
\(408\) 0 0
\(409\) 27.0606i 1.33806i 0.743235 + 0.669031i \(0.233291\pi\)
−0.743235 + 0.669031i \(0.766709\pi\)
\(410\) 9.20211i 0.454460i
\(411\) 0 0
\(412\) 13.3681i 0.658599i
\(413\) 7.19498 + 7.87575i 0.354042 + 0.387541i
\(414\) 0 0
\(415\) 26.9496 1.32291
\(416\) 0 0
\(417\) 0 0
\(418\) 0.657927i 0.0321803i
\(419\) −10.7799 −0.526634 −0.263317 0.964709i \(-0.584817\pi\)
−0.263317 + 0.964709i \(0.584817\pi\)
\(420\) 0 0
\(421\) 23.0948 1.12557 0.562786 0.826603i \(-0.309729\pi\)
0.562786 + 0.826603i \(0.309729\pi\)
\(422\) 2.30277i 0.112097i
\(423\) 0 0
\(424\) 7.44475 0.361549
\(425\) −5.54293 −0.268872
\(426\) 0 0
\(427\) 0.489264 0.446973i 0.0236772 0.0216305i
\(428\) 14.4002i 0.696062i
\(429\) 0 0
\(430\) 3.16305i 0.152536i
\(431\) 13.8508i 0.667172i −0.942720 0.333586i \(-0.891741\pi\)
0.942720 0.333586i \(-0.108259\pi\)
\(432\) 0 0
\(433\) 36.3968i 1.74912i −0.484919 0.874559i \(-0.661151\pi\)
0.484919 0.874559i \(-0.338849\pi\)
\(434\) 19.0838 + 20.8895i 0.916053 + 1.00273i
\(435\) 0 0
\(436\) 3.41140 0.163376
\(437\) 5.18167 0.247873
\(438\) 0 0
\(439\) 24.9603i 1.19129i 0.803248 + 0.595645i \(0.203103\pi\)
−0.803248 + 0.595645i \(0.796897\pi\)
\(440\) −2.01596 −0.0961074
\(441\) 0 0
\(442\) 0 0
\(443\) 7.20610i 0.342372i 0.985239 + 0.171186i \(0.0547599\pi\)
−0.985239 + 0.171186i \(0.945240\pi\)
\(444\) 0 0
\(445\) 10.5285 0.499097
\(446\) −18.2571 −0.864500
\(447\) 0 0
\(448\) −1.78450 1.95335i −0.0843097 0.0922869i
\(449\) 31.8490i 1.50305i 0.659707 + 0.751523i \(0.270680\pi\)
−0.659707 + 0.751523i \(0.729320\pi\)
\(450\) 0 0
\(451\) 4.56462i 0.214940i
\(452\) 4.95947i 0.233274i
\(453\) 0 0
\(454\) 20.0739i 0.942116i
\(455\) 0 0
\(456\) 0 0
\(457\) −10.4853 −0.490481 −0.245240 0.969462i \(-0.578867\pi\)
−0.245240 + 0.969462i \(0.578867\pi\)
\(458\) 14.6840 0.686137
\(459\) 0 0
\(460\) 15.8772i 0.740280i
\(461\) −24.3881 −1.13587 −0.567933 0.823075i \(-0.692257\pi\)
−0.567933 + 0.823075i \(0.692257\pi\)
\(462\) 0 0
\(463\) −22.6410 −1.05222 −0.526109 0.850417i \(-0.676349\pi\)
−0.526109 + 0.850417i \(0.676349\pi\)
\(464\) 1.32636i 0.0615747i
\(465\) 0 0
\(466\) 2.48528 0.115128
\(467\) 27.6355 1.27882 0.639409 0.768867i \(-0.279179\pi\)
0.639409 + 0.768867i \(0.279179\pi\)
\(468\) 0 0
\(469\) −13.9399 15.2588i −0.643683 0.704588i
\(470\) 1.07388i 0.0495346i
\(471\) 0 0
\(472\) 4.03193i 0.185585i
\(473\) 1.56900i 0.0721427i
\(474\) 0 0
\(475\) 0.615745i 0.0282523i
\(476\) −10.5690 11.5690i −0.484428 0.530264i
\(477\) 0 0
\(478\) 22.3610 1.02277
\(479\) −34.4166 −1.57253 −0.786267 0.617887i \(-0.787989\pi\)
−0.786267 + 0.617887i \(0.787989\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −3.45706 −0.157465
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 5.47551i 0.248630i
\(486\) 0 0
\(487\) −15.2662 −0.691779 −0.345889 0.938275i \(-0.612423\pi\)
−0.345889 + 0.938275i \(0.612423\pi\)
\(488\) −0.250475 −0.0113385
\(489\) 0 0
\(490\) −14.0543 1.27232i −0.634908 0.0574776i
\(491\) 23.6273i 1.06628i −0.846026 0.533142i \(-0.821011\pi\)
0.846026 0.533142i \(-0.178989\pi\)
\(492\) 0 0
\(493\) 7.85557i 0.353797i
\(494\) 0 0
\(495\) 0 0
\(496\) 10.6942i 0.480185i
\(497\) 1.19062 1.08770i 0.0534065 0.0487901i
\(498\) 0 0
\(499\) −36.0484 −1.61375 −0.806875 0.590723i \(-0.798843\pi\)
−0.806875 + 0.590723i \(0.798843\pi\)
\(500\) 11.9665 0.535160
\(501\) 0 0
\(502\) 3.78145i 0.168775i
\(503\) 31.1361 1.38829 0.694145 0.719836i \(-0.255783\pi\)
0.694145 + 0.719836i \(0.255783\pi\)
\(504\) 0 0
\(505\) 6.88154 0.306225
\(506\) 7.87575i 0.350120i
\(507\) 0 0
\(508\) −9.50488 −0.421711
\(509\) 21.5454 0.954984 0.477492 0.878636i \(-0.341546\pi\)
0.477492 + 0.878636i \(0.341546\pi\)
\(510\) 0 0
\(511\) 1.04053 0.950585i 0.0460302 0.0420514i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 5.22255i 0.230357i
\(515\) 26.9496i 1.18754i
\(516\) 0 0
\(517\) 0.532690i 0.0234277i
\(518\) −11.4774 + 10.4853i −0.504287 + 0.460697i
\(519\) 0 0
\(520\) 0 0
\(521\) −24.0663 −1.05437 −0.527183 0.849752i \(-0.676752\pi\)
−0.527183 + 0.849752i \(0.676752\pi\)
\(522\) 0 0
\(523\) 7.11327i 0.311042i 0.987833 + 0.155521i \(0.0497056\pi\)
−0.987833 + 0.155521i \(0.950294\pi\)
\(524\) 19.0838 0.833681
\(525\) 0 0
\(526\) 13.7306 0.598682
\(527\) 63.3382i 2.75905i
\(528\) 0 0
\(529\) −39.0275 −1.69685
\(530\) −15.0084 −0.651922
\(531\) 0 0
\(532\) −1.28516 + 1.17407i −0.0557188 + 0.0509024i
\(533\) 0 0
\(534\) 0 0
\(535\) 29.0304i 1.25509i
\(536\) 7.81164i 0.337411i
\(537\) 0 0
\(538\) 29.6093i 1.27655i
\(539\) 6.97149 + 0.631122i 0.300283 + 0.0271844i
\(540\) 0 0
\(541\) 4.24849 0.182657 0.0913285 0.995821i \(-0.470889\pi\)
0.0913285 + 0.995821i \(0.470889\pi\)
\(542\) 15.5015 0.665848
\(543\) 0 0
\(544\) 5.92266i 0.253932i
\(545\) −6.87726 −0.294589
\(546\) 0 0
\(547\) 9.69723 0.414624 0.207312 0.978275i \(-0.433529\pi\)
0.207312 + 0.978275i \(0.433529\pi\)
\(548\) 8.05428i 0.344062i
\(549\) 0 0
\(550\) −0.935886 −0.0399063
\(551\) 0.872648 0.0371760
\(552\) 0 0
\(553\) −22.7900 24.9464i −0.969131 1.06083i
\(554\) 19.0347i 0.808706i
\(555\) 0 0
\(556\) 19.3725i 0.821576i
\(557\) 21.6914i 0.919093i −0.888154 0.459547i \(-0.848012\pi\)
0.888154 0.459547i \(-0.151988\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 3.59749 + 3.93788i 0.152022 + 0.166406i
\(561\) 0 0
\(562\) 10.9706 0.462765
\(563\) −1.68243 −0.0709062 −0.0354531 0.999371i \(-0.511287\pi\)
−0.0354531 + 0.999371i \(0.511287\pi\)
\(564\) 0 0
\(565\) 9.99812i 0.420624i
\(566\) 19.2091 0.807417
\(567\) 0 0
\(568\) −0.609527 −0.0255752
\(569\) 14.4853i 0.607255i −0.952791 0.303627i \(-0.901802\pi\)
0.952791 0.303627i \(-0.0981978\pi\)
\(570\) 0 0
\(571\) −26.7542 −1.11963 −0.559814 0.828619i \(-0.689127\pi\)
−0.559814 + 0.828619i \(0.689127\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −8.91628 + 8.14556i −0.372158 + 0.339989i
\(575\) 7.37081i 0.307384i
\(576\) 0 0
\(577\) 42.3630i 1.76359i −0.471629 0.881797i \(-0.656334\pi\)
0.471629 0.881797i \(-0.343666\pi\)
\(578\) 18.0779i 0.751940i
\(579\) 0 0
\(580\) 2.67389i 0.111027i
\(581\) 23.8554 + 26.1125i 0.989688 + 1.08333i
\(582\) 0 0
\(583\) 7.44475 0.308330
\(584\) −0.532690 −0.0220429
\(585\) 0 0
\(586\) 9.91105i 0.409422i
\(587\) −2.05172 −0.0846835 −0.0423418 0.999103i \(-0.513482\pi\)
−0.0423418 + 0.999103i \(0.513482\pi\)
\(588\) 0 0
\(589\) −7.03602 −0.289914
\(590\) 8.12823i 0.334634i
\(591\) 0 0
\(592\) 5.87575 0.241492
\(593\) −40.2640 −1.65344 −0.826721 0.562611i \(-0.809797\pi\)
−0.826721 + 0.562611i \(0.809797\pi\)
\(594\) 0 0
\(595\) 21.3067 + 23.3227i 0.873489 + 0.956137i
\(596\) 3.26224i 0.133627i
\(597\) 0 0
\(598\) 0 0
\(599\) 35.6273i 1.45569i 0.685741 + 0.727845i \(0.259478\pi\)
−0.685741 + 0.727845i \(0.740522\pi\)
\(600\) 0 0
\(601\) 39.6574i 1.61766i 0.588044 + 0.808829i \(0.299898\pi\)
−0.588044 + 0.808829i \(0.700102\pi\)
\(602\) 3.06480 2.79988i 0.124912 0.114115i
\(603\) 0 0
\(604\) 14.1785 0.576916
\(605\) −2.01596 −0.0819606
\(606\) 0 0
\(607\) 23.6444i 0.959698i 0.877351 + 0.479849i \(0.159309\pi\)
−0.877351 + 0.479849i \(0.840691\pi\)
\(608\) 0.657927 0.0266825
\(609\) 0 0
\(610\) 0.504949 0.0204448
\(611\) 0 0
\(612\) 0 0
\(613\) −36.0654 −1.45667 −0.728333 0.685223i \(-0.759705\pi\)
−0.728333 + 0.685223i \(0.759705\pi\)
\(614\) 1.64427 0.0663572
\(615\) 0 0
\(616\) −1.78450 1.95335i −0.0718995 0.0787026i
\(617\) 2.45192i 0.0987108i −0.998781 0.0493554i \(-0.984283\pi\)
0.998781 0.0493554i \(-0.0157167\pi\)
\(618\) 0 0
\(619\) 12.9107i 0.518925i 0.965753 + 0.259462i \(0.0835453\pi\)
−0.965753 + 0.259462i \(0.916455\pi\)
\(620\) 21.5592i 0.865837i
\(621\) 0 0
\(622\) 2.14120i 0.0858544i
\(623\) 9.31963 + 10.2014i 0.373383 + 0.408712i
\(624\) 0 0
\(625\) −19.4447 −0.777788
\(626\) 12.7932 0.511321
\(627\) 0 0
\(628\) 11.7596i 0.469259i
\(629\) 34.8001 1.38757
\(630\) 0 0
\(631\) −6.53245 −0.260053 −0.130026 0.991511i \(-0.541506\pi\)
−0.130026 + 0.991511i \(0.541506\pi\)
\(632\) 12.7711i 0.508008i
\(633\) 0 0
\(634\) 6.51604 0.258785
\(635\) 19.1615 0.760401
\(636\) 0 0
\(637\) 0 0
\(638\) 1.32636i 0.0525110i
\(639\) 0 0
\(640\) 2.01596i 0.0796880i
\(641\) 6.03336i 0.238303i −0.992876 0.119152i \(-0.961983\pi\)
0.992876 0.119152i \(-0.0380175\pi\)
\(642\) 0 0
\(643\) 9.21360i 0.363349i 0.983359 + 0.181675i \(0.0581517\pi\)
−0.983359 + 0.181675i \(0.941848\pi\)
\(644\) 15.3841 14.0543i 0.606217 0.553816i
\(645\) 0 0
\(646\) 3.89668 0.153313
\(647\) 1.72732 0.0679080 0.0339540 0.999423i \(-0.489190\pi\)
0.0339540 + 0.999423i \(0.489190\pi\)
\(648\) 0 0
\(649\) 4.03193i 0.158267i
\(650\) 0 0
\(651\) 0 0
\(652\) −12.5285 −0.490653
\(653\) 41.9575i 1.64193i 0.570982 + 0.820963i \(0.306563\pi\)
−0.570982 + 0.820963i \(0.693437\pi\)
\(654\) 0 0
\(655\) −38.4723 −1.50324
\(656\) 4.56462 0.178218
\(657\) 0 0
\(658\) −1.04053 + 0.950585i −0.0405640 + 0.0370577i
\(659\) 10.3963i 0.404981i −0.979284 0.202490i \(-0.935097\pi\)
0.979284 0.202490i \(-0.0649035\pi\)
\(660\) 0 0
\(661\) 34.0922i 1.32603i 0.748605 + 0.663016i \(0.230724\pi\)
−0.748605 + 0.663016i \(0.769276\pi\)
\(662\) 30.2159i 1.17437i
\(663\) 0 0
\(664\) 13.3681i 0.518783i
\(665\) 2.59084 2.36689i 0.100468 0.0917839i
\(666\) 0 0
\(667\) −10.4461 −0.404474
\(668\) 23.0722 0.892691
\(669\) 0 0
\(670\) 15.7480i 0.608398i
\(671\) −0.250475 −0.00966948
\(672\) 0 0
\(673\) 9.66513 0.372563 0.186282 0.982496i \(-0.440356\pi\)
0.186282 + 0.982496i \(0.440356\pi\)
\(674\) 24.8895i 0.958708i
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) −45.8609 −1.76258 −0.881288 0.472579i \(-0.843323\pi\)
−0.881288 + 0.472579i \(0.843323\pi\)
\(678\) 0 0
\(679\) −5.30543 + 4.84683i −0.203604 + 0.186004i
\(680\) 11.9399i 0.457873i
\(681\) 0 0
\(682\) 10.6942i 0.409503i
\(683\) 3.93190i 0.150450i −0.997167 0.0752250i \(-0.976032\pi\)
0.997167 0.0752250i \(-0.0239675\pi\)
\(684\) 0 0
\(685\) 16.2371i 0.620389i
\(686\) −11.2078 14.7440i −0.427917 0.562927i
\(687\) 0 0
\(688\) −1.56900 −0.0598175
\(689\) 0 0
\(690\) 0 0
\(691\) 17.6940i 0.673113i −0.941663 0.336557i \(-0.890738\pi\)
0.941663 0.336557i \(-0.109262\pi\)
\(692\) −17.7244 −0.673782
\(693\) 0 0
\(694\) −9.09481 −0.345234
\(695\) 39.0542i 1.48141i
\(696\) 0 0
\(697\) 27.0347 1.02401
\(698\) 31.8335 1.20492
\(699\) 0 0
\(700\) 1.67009 + 1.82811i 0.0631234 + 0.0690960i
\(701\) 27.9189i 1.05448i 0.849715 + 0.527242i \(0.176774\pi\)
−0.849715 + 0.527242i \(0.823226\pi\)
\(702\) 0 0
\(703\) 3.86582i 0.145802i
\(704\) 1.00000i 0.0376889i
\(705\) 0 0
\(706\) 10.9052i 0.410422i
\(707\) 6.09143 + 6.66779i 0.229092 + 0.250768i
\(708\) 0 0
\(709\) −25.4951 −0.957487 −0.478743 0.877955i \(-0.658908\pi\)
−0.478743 + 0.877955i \(0.658908\pi\)
\(710\) 1.22879 0.0461155
\(711\) 0 0
\(712\) 5.22255i 0.195723i
\(713\) 84.2250 3.15425
\(714\) 0 0
\(715\) 0 0
\(716\) 3.81164i 0.142448i
\(717\) 0 0
\(718\) 23.6874 0.884006
\(719\) 43.0169 1.60426 0.802130 0.597150i \(-0.203700\pi\)
0.802130 + 0.597150i \(0.203700\pi\)
\(720\) 0 0
\(721\) −26.1125 + 23.8554i −0.972482 + 0.888421i
\(722\) 18.5671i 0.690997i
\(723\) 0 0
\(724\) 19.1260i 0.710813i
\(725\) 1.24132i 0.0461015i
\(726\) 0 0
\(727\) 30.2686i 1.12260i 0.827613 + 0.561299i \(0.189698\pi\)
−0.827613 + 0.561299i \(0.810302\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1.07388 0.0397462
\(731\) −9.29264 −0.343701
\(732\) 0 0
\(733\) 7.56291i 0.279342i 0.990198 + 0.139671i \(0.0446046\pi\)
−0.990198 + 0.139671i \(0.955395\pi\)
\(734\) −13.1176 −0.484181
\(735\) 0 0
\(736\) −7.87575 −0.290304
\(737\) 7.81164i 0.287745i
\(738\) 0 0
\(739\) −17.1923 −0.632428 −0.316214 0.948688i \(-0.602412\pi\)
−0.316214 + 0.948688i \(0.602412\pi\)
\(740\) −11.8453 −0.435442
\(741\) 0 0
\(742\) −13.2852 14.5422i −0.487714 0.533860i
\(743\) 23.9843i 0.879899i −0.898022 0.439950i \(-0.854996\pi\)
0.898022 0.439950i \(-0.145004\pi\)
\(744\) 0 0
\(745\) 6.57657i 0.240947i
\(746\) 3.38649i 0.123988i
\(747\) 0 0
\(748\) 5.92266i 0.216554i
\(749\) −28.1287 + 25.6972i −1.02780 + 0.938956i
\(750\) 0 0
\(751\) −32.4736 −1.18498 −0.592489 0.805579i \(-0.701855\pi\)
−0.592489 + 0.805579i \(0.701855\pi\)
\(752\) 0.532690 0.0194252
\(753\) 0 0
\(754\) 0 0
\(755\) −28.5834 −1.04026
\(756\) 0 0
\(757\) 40.0315 1.45497 0.727485 0.686124i \(-0.240689\pi\)
0.727485 + 0.686124i \(0.240689\pi\)
\(758\) 8.52847i 0.309768i
\(759\) 0 0
\(760\) −1.32636 −0.0481121
\(761\) 20.6923 0.750097 0.375048 0.927005i \(-0.377626\pi\)
0.375048 + 0.927005i \(0.377626\pi\)
\(762\) 0 0
\(763\) −6.08764 6.66364i −0.220387 0.241240i
\(764\) 21.6665i 0.783865i
\(765\) 0 0
\(766\) 10.1180i 0.365578i
\(767\) 0 0
\(768\) 0 0
\(769\) 33.6030i 1.21176i 0.795557 + 0.605878i \(0.207178\pi\)
−0.795557 + 0.605878i \(0.792822\pi\)
\(770\) 3.59749 + 3.93788i 0.129644 + 0.141911i
\(771\) 0 0
\(772\) 21.6233 0.778239
\(773\) 13.9825 0.502916 0.251458 0.967868i \(-0.419090\pi\)
0.251458 + 0.967868i \(0.419090\pi\)
\(774\) 0 0
\(775\) 10.0086i 0.359518i
\(776\) 2.71607 0.0975014
\(777\) 0 0
\(778\) −16.7920 −0.602024
\(779\) 3.00319i 0.107600i
\(780\) 0 0
\(781\) −0.609527 −0.0218106
\(782\) −46.6454 −1.66804
\(783\) 0 0
\(784\) −0.631122 + 6.97149i −0.0225401 + 0.248982i
\(785\) 23.7069i 0.846137i
\(786\) 0 0
\(787\) 20.4800i 0.730034i −0.931001 0.365017i \(-0.881063\pi\)
0.931001 0.365017i \(-0.118937\pi\)
\(788\) 21.6914i 0.772723i
\(789\) 0 0
\(790\) 25.7461i 0.916006i
\(791\) −9.68757 + 8.85018i −0.344450 + 0.314676i
\(792\) 0 0
\(793\) 0 0
\(794\) 13.4856 0.478585
\(795\) 0 0
\(796\) 3.94621i 0.139870i
\(797\) −38.1741 −1.35220 −0.676098 0.736812i \(-0.736330\pi\)
−0.676098 + 0.736812i \(0.736330\pi\)
\(798\) 0 0
\(799\) 3.15494 0.111614
\(800\) 0.935886i 0.0330886i