Properties

Label 336.4.h.b.239.23
Level $336$
Weight $4$
Character 336.239
Analytic conductor $19.825$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.23
Character \(\chi\) \(=\) 336.239
Dual form 336.4.h.b.239.24

$q$-expansion

\(f(q)\) \(=\) \(q+(5.19367 - 0.160438i) q^{3} -7.59851i q^{5} +7.00000i q^{7} +(26.9485 - 1.66652i) q^{9} +O(q^{10})\) \(q+(5.19367 - 0.160438i) q^{3} -7.59851i q^{5} +7.00000i q^{7} +(26.9485 - 1.66652i) q^{9} -0.0298576 q^{11} +40.1686 q^{13} +(-1.21909 - 39.4642i) q^{15} -0.439999i q^{17} -0.434338i q^{19} +(1.12306 + 36.3557i) q^{21} +139.817 q^{23} +67.2627 q^{25} +(139.694 - 12.9789i) q^{27} -273.309i q^{29} -149.527i q^{31} +(-0.155070 + 0.00479027i) q^{33} +53.1896 q^{35} -290.284 q^{37} +(208.622 - 6.44454i) q^{39} -57.4908i q^{41} +432.992i q^{43} +(-12.6631 - 204.769i) q^{45} +317.042 q^{47} -49.0000 q^{49} +(-0.0705924 - 2.28521i) q^{51} -147.100i q^{53} +0.226873i q^{55} +(-0.0696841 - 2.25581i) q^{57} +488.249 q^{59} -441.188 q^{61} +(11.6656 + 188.640i) q^{63} -305.221i q^{65} +440.204i q^{67} +(726.166 - 22.4319i) q^{69} +202.974 q^{71} -542.719 q^{73} +(349.341 - 10.7915i) q^{75} -0.209003i q^{77} -325.250i q^{79} +(723.445 - 89.8205i) q^{81} +376.536 q^{83} -3.34334 q^{85} +(-43.8491 - 1419.48i) q^{87} +496.611i q^{89} +281.180i q^{91} +(-23.9898 - 776.595i) q^{93} -3.30032 q^{95} +373.344 q^{97} +(-0.804617 + 0.0497582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 136q^{9} + O(q^{10}) \) \( 24q - 136q^{9} + 96q^{13} - 112q^{21} + 168q^{25} - 320q^{33} - 864q^{37} + 592q^{45} - 1176q^{49} - 1120q^{57} - 2304q^{61} + 1168q^{69} + 3312q^{73} - 968q^{81} - 5808q^{85} + 1776q^{93} + 6480q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 5.19367 0.160438i 0.999523 0.0308762i
\(4\) 0 0
\(5\) 7.59851i 0.679631i −0.940492 0.339816i \(-0.889635\pi\)
0.940492 0.339816i \(-0.110365\pi\)
\(6\) 0 0
\(7\) 7.00000i 0.377964i
\(8\) 0 0
\(9\) 26.9485 1.66652i 0.998093 0.0617230i
\(10\) 0 0
\(11\) −0.0298576 −0.000818399 −0.000409200 1.00000i \(-0.500130\pi\)
−0.000409200 1.00000i \(0.500130\pi\)
\(12\) 0 0
\(13\) 40.1686 0.856981 0.428490 0.903546i \(-0.359046\pi\)
0.428490 + 0.903546i \(0.359046\pi\)
\(14\) 0 0
\(15\) −1.21909 39.4642i −0.0209844 0.679307i
\(16\) 0 0
\(17\) 0.439999i 0.00627738i −0.999995 0.00313869i \(-0.999001\pi\)
0.999995 0.00313869i \(-0.000999078\pi\)
\(18\) 0 0
\(19\) 0.434338i 0.00524441i −0.999997 0.00262221i \(-0.999165\pi\)
0.999997 0.00262221i \(-0.000834675\pi\)
\(20\) 0 0
\(21\) 1.12306 + 36.3557i 0.0116701 + 0.377784i
\(22\) 0 0
\(23\) 139.817 1.26756 0.633781 0.773513i \(-0.281502\pi\)
0.633781 + 0.773513i \(0.281502\pi\)
\(24\) 0 0
\(25\) 67.2627 0.538101
\(26\) 0 0
\(27\) 139.694 12.9789i 0.995712 0.0925109i
\(28\) 0 0
\(29\) 273.309i 1.75008i −0.484053 0.875039i \(-0.660836\pi\)
0.484053 0.875039i \(-0.339164\pi\)
\(30\) 0 0
\(31\) 149.527i 0.866318i −0.901318 0.433159i \(-0.857399\pi\)
0.901318 0.433159i \(-0.142601\pi\)
\(32\) 0 0
\(33\) −0.155070 + 0.00479027i −0.000818009 + 2.52691e-5i
\(34\) 0 0
\(35\) 53.1896 0.256876
\(36\) 0 0
\(37\) −290.284 −1.28979 −0.644897 0.764269i \(-0.723100\pi\)
−0.644897 + 0.764269i \(0.723100\pi\)
\(38\) 0 0
\(39\) 208.622 6.44454i 0.856572 0.0264603i
\(40\) 0 0
\(41\) 57.4908i 0.218989i −0.993987 0.109495i \(-0.965077\pi\)
0.993987 0.109495i \(-0.0349232\pi\)
\(42\) 0 0
\(43\) 432.992i 1.53560i 0.640692 + 0.767798i \(0.278648\pi\)
−0.640692 + 0.767798i \(0.721352\pi\)
\(44\) 0 0
\(45\) −12.6631 204.769i −0.0419489 0.678335i
\(46\) 0 0
\(47\) 317.042 0.983942 0.491971 0.870612i \(-0.336277\pi\)
0.491971 + 0.870612i \(0.336277\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 0 0
\(51\) −0.0705924 2.28521i −0.000193822 0.00627439i
\(52\) 0 0
\(53\) 147.100i 0.381239i −0.981664 0.190620i \(-0.938950\pi\)
0.981664 0.190620i \(-0.0610497\pi\)
\(54\) 0 0
\(55\) 0.226873i 0.000556210i
\(56\) 0 0
\(57\) −0.0696841 2.25581i −0.000161928 0.00524191i
\(58\) 0 0
\(59\) 488.249 1.07737 0.538683 0.842508i \(-0.318922\pi\)
0.538683 + 0.842508i \(0.318922\pi\)
\(60\) 0 0
\(61\) −441.188 −0.926038 −0.463019 0.886348i \(-0.653234\pi\)
−0.463019 + 0.886348i \(0.653234\pi\)
\(62\) 0 0
\(63\) 11.6656 + 188.640i 0.0233291 + 0.377244i
\(64\) 0 0
\(65\) 305.221i 0.582431i
\(66\) 0 0
\(67\) 440.204i 0.802678i 0.915930 + 0.401339i \(0.131455\pi\)
−0.915930 + 0.401339i \(0.868545\pi\)
\(68\) 0 0
\(69\) 726.166 22.4319i 1.26696 0.0391375i
\(70\) 0 0
\(71\) 202.974 0.339275 0.169638 0.985507i \(-0.445740\pi\)
0.169638 + 0.985507i \(0.445740\pi\)
\(72\) 0 0
\(73\) −542.719 −0.870144 −0.435072 0.900396i \(-0.643277\pi\)
−0.435072 + 0.900396i \(0.643277\pi\)
\(74\) 0 0
\(75\) 349.341 10.7915i 0.537845 0.0166145i
\(76\) 0 0
\(77\) 0.209003i 0.000309326i
\(78\) 0 0
\(79\) 325.250i 0.463209i −0.972810 0.231605i \(-0.925602\pi\)
0.972810 0.231605i \(-0.0743976\pi\)
\(80\) 0 0
\(81\) 723.445 89.8205i 0.992381 0.123211i
\(82\) 0 0
\(83\) 376.536 0.497955 0.248977 0.968509i \(-0.419906\pi\)
0.248977 + 0.968509i \(0.419906\pi\)
\(84\) 0 0
\(85\) −3.34334 −0.00426631
\(86\) 0 0
\(87\) −43.8491 1419.48i −0.0540358 1.74924i
\(88\) 0 0
\(89\) 496.611i 0.591468i 0.955270 + 0.295734i \(0.0955641\pi\)
−0.955270 + 0.295734i \(0.904436\pi\)
\(90\) 0 0
\(91\) 281.180i 0.323908i
\(92\) 0 0
\(93\) −23.9898 776.595i −0.0267486 0.865905i
\(94\) 0 0
\(95\) −3.30032 −0.00356427
\(96\) 0 0
\(97\) 373.344 0.390797 0.195398 0.980724i \(-0.437400\pi\)
0.195398 + 0.980724i \(0.437400\pi\)
\(98\) 0 0
\(99\) −0.804617 + 0.0497582i −0.000816839 + 5.05141e-5i
\(100\) 0 0
\(101\) 336.295i 0.331313i 0.986183 + 0.165657i \(0.0529743\pi\)
−0.986183 + 0.165657i \(0.947026\pi\)
\(102\) 0 0
\(103\) 372.072i 0.355936i −0.984036 0.177968i \(-0.943048\pi\)
0.984036 0.177968i \(-0.0569523\pi\)
\(104\) 0 0
\(105\) 276.249 8.53360i 0.256754 0.00793137i
\(106\) 0 0
\(107\) −1350.90 −1.22053 −0.610263 0.792199i \(-0.708936\pi\)
−0.610263 + 0.792199i \(0.708936\pi\)
\(108\) 0 0
\(109\) 171.760 0.150932 0.0754662 0.997148i \(-0.475955\pi\)
0.0754662 + 0.997148i \(0.475955\pi\)
\(110\) 0 0
\(111\) −1507.64 + 46.5725i −1.28918 + 0.0398240i
\(112\) 0 0
\(113\) 1132.11i 0.942479i 0.882005 + 0.471240i \(0.156193\pi\)
−0.882005 + 0.471240i \(0.843807\pi\)
\(114\) 0 0
\(115\) 1062.40i 0.861475i
\(116\) 0 0
\(117\) 1082.48 66.9417i 0.855347 0.0528954i
\(118\) 0 0
\(119\) 3.08000 0.00237263
\(120\) 0 0
\(121\) −1331.00 −0.999999
\(122\) 0 0
\(123\) −9.22368 298.588i −0.00676156 0.218885i
\(124\) 0 0
\(125\) 1460.91i 1.04534i
\(126\) 0 0
\(127\) 2285.26i 1.59673i 0.602177 + 0.798363i \(0.294300\pi\)
−0.602177 + 0.798363i \(0.705700\pi\)
\(128\) 0 0
\(129\) 69.4682 + 2248.82i 0.0474134 + 1.53486i
\(130\) 0 0
\(131\) −1583.22 −1.05593 −0.527963 0.849267i \(-0.677044\pi\)
−0.527963 + 0.849267i \(0.677044\pi\)
\(132\) 0 0
\(133\) 3.04036 0.00198220
\(134\) 0 0
\(135\) −98.6204 1061.47i −0.0628733 0.676717i
\(136\) 0 0
\(137\) 2999.39i 1.87047i 0.354023 + 0.935237i \(0.384814\pi\)
−0.354023 + 0.935237i \(0.615186\pi\)
\(138\) 0 0
\(139\) 1324.48i 0.808210i 0.914712 + 0.404105i \(0.132417\pi\)
−0.914712 + 0.404105i \(0.867583\pi\)
\(140\) 0 0
\(141\) 1646.61 50.8654i 0.983473 0.0303804i
\(142\) 0 0
\(143\) −1.19933 −0.000701353
\(144\) 0 0
\(145\) −2076.74 −1.18941
\(146\) 0 0
\(147\) −254.490 + 7.86144i −0.142789 + 0.00441089i
\(148\) 0 0
\(149\) 2415.47i 1.32808i −0.747699 0.664038i \(-0.768841\pi\)
0.747699 0.664038i \(-0.231159\pi\)
\(150\) 0 0
\(151\) 2734.78i 1.47386i 0.675967 + 0.736932i \(0.263726\pi\)
−0.675967 + 0.736932i \(0.736274\pi\)
\(152\) 0 0
\(153\) −0.733268 11.8573i −0.000387459 0.00626541i
\(154\) 0 0
\(155\) −1136.18 −0.588777
\(156\) 0 0
\(157\) −2957.87 −1.50359 −0.751794 0.659398i \(-0.770811\pi\)
−0.751794 + 0.659398i \(0.770811\pi\)
\(158\) 0 0
\(159\) −23.6003 763.987i −0.0117712 0.381057i
\(160\) 0 0
\(161\) 978.721i 0.479093i
\(162\) 0 0
\(163\) 691.183i 0.332133i −0.986115 0.166066i \(-0.946893\pi\)
0.986115 0.166066i \(-0.0531066\pi\)
\(164\) 0 0
\(165\) 0.0363989 + 1.17830i 1.71737e−5 + 0.000555945i
\(166\) 0 0
\(167\) −1944.18 −0.900868 −0.450434 0.892810i \(-0.648731\pi\)
−0.450434 + 0.892810i \(0.648731\pi\)
\(168\) 0 0
\(169\) −583.488 −0.265584
\(170\) 0 0
\(171\) −0.723833 11.7048i −0.000323701 0.00523441i
\(172\) 0 0
\(173\) 1459.20i 0.641275i 0.947202 + 0.320637i \(0.103897\pi\)
−0.947202 + 0.320637i \(0.896103\pi\)
\(174\) 0 0
\(175\) 470.839i 0.203383i
\(176\) 0 0
\(177\) 2535.81 78.3335i 1.07685 0.0332650i
\(178\) 0 0
\(179\) −2398.75 −1.00163 −0.500813 0.865555i \(-0.666966\pi\)
−0.500813 + 0.865555i \(0.666966\pi\)
\(180\) 0 0
\(181\) −2169.01 −0.890724 −0.445362 0.895351i \(-0.646925\pi\)
−0.445362 + 0.895351i \(0.646925\pi\)
\(182\) 0 0
\(183\) −2291.39 + 70.7831i −0.925596 + 0.0285925i
\(184\) 0 0
\(185\) 2205.73i 0.876585i
\(186\) 0 0
\(187\) 0.0131373i 5.13741e-6i
\(188\) 0 0
\(189\) 90.8525 + 977.861i 0.0349658 + 0.376344i
\(190\) 0 0
\(191\) −3345.58 −1.26742 −0.633712 0.773569i \(-0.718470\pi\)
−0.633712 + 0.773569i \(0.718470\pi\)
\(192\) 0 0
\(193\) −1400.64 −0.522383 −0.261192 0.965287i \(-0.584115\pi\)
−0.261192 + 0.965287i \(0.584115\pi\)
\(194\) 0 0
\(195\) −48.9689 1585.22i −0.0179833 0.582153i
\(196\) 0 0
\(197\) 3747.32i 1.35526i −0.735405 0.677628i \(-0.763008\pi\)
0.735405 0.677628i \(-0.236992\pi\)
\(198\) 0 0
\(199\) 1160.47i 0.413385i −0.978406 0.206692i \(-0.933730\pi\)
0.978406 0.206692i \(-0.0662699\pi\)
\(200\) 0 0
\(201\) 70.6252 + 2286.27i 0.0247837 + 0.802295i
\(202\) 0 0
\(203\) 1913.16 0.661467
\(204\) 0 0
\(205\) −436.844 −0.148832
\(206\) 0 0
\(207\) 3767.87 233.008i 1.26515 0.0782377i
\(208\) 0 0
\(209\) 0.0129683i 4.29203e-6i
\(210\) 0 0
\(211\) 3860.25i 1.25948i −0.776806 0.629740i \(-0.783161\pi\)
0.776806 0.629740i \(-0.216839\pi\)
\(212\) 0 0
\(213\) 1054.18 32.5646i 0.339114 0.0104755i
\(214\) 0 0
\(215\) 3290.09 1.04364
\(216\) 0 0
\(217\) 1046.69 0.327437
\(218\) 0 0
\(219\) −2818.71 + 87.0725i −0.869729 + 0.0268667i
\(220\) 0 0
\(221\) 17.6741i 0.00537960i
\(222\) 0 0
\(223\) 4974.72i 1.49386i 0.664901 + 0.746932i \(0.268474\pi\)
−0.664901 + 0.746932i \(0.731526\pi\)
\(224\) 0 0
\(225\) 1812.63 112.095i 0.537076 0.0332132i
\(226\) 0 0
\(227\) 3501.02 1.02366 0.511830 0.859087i \(-0.328968\pi\)
0.511830 + 0.859087i \(0.328968\pi\)
\(228\) 0 0
\(229\) 4196.81 1.21106 0.605530 0.795822i \(-0.292961\pi\)
0.605530 + 0.795822i \(0.292961\pi\)
\(230\) 0 0
\(231\) −0.0335319 1.08549i −9.55081e−6 0.000309178i
\(232\) 0 0
\(233\) 4918.36i 1.38288i −0.722432 0.691442i \(-0.756976\pi\)
0.722432 0.691442i \(-0.243024\pi\)
\(234\) 0 0
\(235\) 2409.04i 0.668717i
\(236\) 0 0
\(237\) −52.1824 1689.24i −0.0143022 0.462988i
\(238\) 0 0
\(239\) 1041.63 0.281913 0.140957 0.990016i \(-0.454982\pi\)
0.140957 + 0.990016i \(0.454982\pi\)
\(240\) 0 0
\(241\) 2047.75 0.547332 0.273666 0.961825i \(-0.411764\pi\)
0.273666 + 0.961825i \(0.411764\pi\)
\(242\) 0 0
\(243\) 3742.93 582.567i 0.988103 0.153793i
\(244\) 0 0
\(245\) 372.327i 0.0970902i
\(246\) 0 0
\(247\) 17.4467i 0.00449436i
\(248\) 0 0
\(249\) 1955.61 60.4106i 0.497717 0.0153750i
\(250\) 0 0
\(251\) 741.223 0.186397 0.0931983 0.995648i \(-0.470291\pi\)
0.0931983 + 0.995648i \(0.470291\pi\)
\(252\) 0 0
\(253\) −4.17460 −0.00103737
\(254\) 0 0
\(255\) −17.3642 + 0.536397i −0.00426427 + 0.000131727i
\(256\) 0 0
\(257\) 7849.47i 1.90520i 0.304225 + 0.952600i \(0.401602\pi\)
−0.304225 + 0.952600i \(0.598398\pi\)
\(258\) 0 0
\(259\) 2031.99i 0.487497i
\(260\) 0 0
\(261\) −455.475 7365.28i −0.108020 1.74674i
\(262\) 0 0
\(263\) 1518.51 0.356029 0.178014 0.984028i \(-0.443033\pi\)
0.178014 + 0.984028i \(0.443033\pi\)
\(264\) 0 0
\(265\) −1117.74 −0.259102
\(266\) 0 0
\(267\) 79.6750 + 2579.23i 0.0182623 + 0.591186i
\(268\) 0 0
\(269\) 2768.04i 0.627398i 0.949522 + 0.313699i \(0.101568\pi\)
−0.949522 + 0.313699i \(0.898432\pi\)
\(270\) 0 0
\(271\) 2789.15i 0.625199i 0.949885 + 0.312599i \(0.101200\pi\)
−0.949885 + 0.312599i \(0.898800\pi\)
\(272\) 0 0
\(273\) 45.1118 + 1460.36i 0.0100011 + 0.323754i
\(274\) 0 0
\(275\) −2.00830 −0.000440382
\(276\) 0 0
\(277\) −2896.05 −0.628184 −0.314092 0.949393i \(-0.601700\pi\)
−0.314092 + 0.949393i \(0.601700\pi\)
\(278\) 0 0
\(279\) −249.190 4029.53i −0.0534717 0.864666i
\(280\) 0 0
\(281\) 4683.57i 0.994300i −0.867665 0.497150i \(-0.834380\pi\)
0.867665 0.497150i \(-0.165620\pi\)
\(282\) 0 0
\(283\) 8527.52i 1.79120i 0.444864 + 0.895598i \(0.353252\pi\)
−0.444864 + 0.895598i \(0.646748\pi\)
\(284\) 0 0
\(285\) −17.1408 + 0.529495i −0.00356257 + 0.000110051i
\(286\) 0 0
\(287\) 402.436 0.0827701
\(288\) 0 0
\(289\) 4912.81 0.999961
\(290\) 0 0
\(291\) 1939.03 59.8983i 0.390611 0.0120663i
\(292\) 0 0
\(293\) 8621.57i 1.71904i −0.511106 0.859518i \(-0.670764\pi\)
0.511106 0.859518i \(-0.329236\pi\)
\(294\) 0 0
\(295\) 3709.96i 0.732212i
\(296\) 0 0
\(297\) −4.17094 + 0.387519i −0.000814890 + 7.57109e-5i
\(298\) 0 0
\(299\) 5616.26 1.08628
\(300\) 0 0
\(301\) −3030.94 −0.580401
\(302\) 0 0
\(303\) 53.9544 + 1746.61i 0.0102297 + 0.331155i
\(304\) 0 0
\(305\) 3352.37i 0.629364i
\(306\) 0 0
\(307\) 4270.07i 0.793830i −0.917855 0.396915i \(-0.870081\pi\)
0.917855 0.396915i \(-0.129919\pi\)
\(308\) 0 0
\(309\) −59.6944 1932.42i −0.0109900 0.355766i
\(310\) 0 0
\(311\) 8868.46 1.61699 0.808496 0.588502i \(-0.200282\pi\)
0.808496 + 0.588502i \(0.200282\pi\)
\(312\) 0 0
\(313\) −6273.41 −1.13289 −0.566444 0.824100i \(-0.691681\pi\)
−0.566444 + 0.824100i \(0.691681\pi\)
\(314\) 0 0
\(315\) 1433.38 88.6415i 0.256387 0.0158552i
\(316\) 0 0
\(317\) 11021.1i 1.95271i −0.216178 0.976354i \(-0.569359\pi\)
0.216178 0.976354i \(-0.430641\pi\)
\(318\) 0 0
\(319\) 8.16034i 0.00143226i
\(320\) 0 0
\(321\) −7016.13 + 216.735i −1.21994 + 0.0376852i
\(322\) 0 0
\(323\) −0.191108 −3.29212e−5
\(324\) 0 0
\(325\) 2701.84 0.461143
\(326\) 0 0
\(327\) 892.066 27.5568i 0.150860 0.00466022i
\(328\) 0 0
\(329\) 2219.29i 0.371895i
\(330\) 0 0
\(331\) 1923.51i 0.319414i 0.987164 + 0.159707i \(0.0510549\pi\)
−0.987164 + 0.159707i \(0.948945\pi\)
\(332\) 0 0
\(333\) −7822.73 + 483.765i −1.28734 + 0.0796100i
\(334\) 0 0
\(335\) 3344.89 0.545525
\(336\) 0 0
\(337\) −7227.06 −1.16820 −0.584100 0.811682i \(-0.698552\pi\)
−0.584100 + 0.811682i \(0.698552\pi\)
\(338\) 0 0
\(339\) 181.633 + 5879.82i 0.0291002 + 0.942030i
\(340\) 0 0
\(341\) 4.46451i 0.000708994i
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) 0 0
\(345\) −170.449 5517.78i −0.0265991 0.861064i
\(346\) 0 0
\(347\) 7023.96 1.08665 0.543323 0.839524i \(-0.317166\pi\)
0.543323 + 0.839524i \(0.317166\pi\)
\(348\) 0 0
\(349\) 10241.7 1.57085 0.785425 0.618957i \(-0.212444\pi\)
0.785425 + 0.618957i \(0.212444\pi\)
\(350\) 0 0
\(351\) 5611.32 521.345i 0.853306 0.0792801i
\(352\) 0 0
\(353\) 10999.2i 1.65843i 0.558930 + 0.829215i \(0.311212\pi\)
−0.558930 + 0.829215i \(0.688788\pi\)
\(354\) 0 0
\(355\) 1542.30i 0.230582i
\(356\) 0 0
\(357\) 15.9965 0.494147i 0.00237150 7.32578e-5i
\(358\) 0 0
\(359\) −10462.6 −1.53815 −0.769076 0.639157i \(-0.779283\pi\)
−0.769076 + 0.639157i \(0.779283\pi\)
\(360\) 0 0
\(361\) 6858.81 0.999972
\(362\) 0 0
\(363\) −6912.78 + 213.542i −0.999523 + 0.0308762i
\(364\) 0 0
\(365\) 4123.86i 0.591377i
\(366\) 0 0
\(367\) 2957.89i 0.420711i 0.977625 + 0.210355i \(0.0674621\pi\)
−0.977625 + 0.210355i \(0.932538\pi\)
\(368\) 0 0
\(369\) −95.8096 1549.29i −0.0135167 0.218572i
\(370\) 0 0
\(371\) 1029.70 0.144095
\(372\) 0 0
\(373\) −4947.61 −0.686803 −0.343402 0.939189i \(-0.611579\pi\)
−0.343402 + 0.939189i \(0.611579\pi\)
\(374\) 0 0
\(375\) −234.385 7587.49i −0.0322762 1.04484i
\(376\) 0 0
\(377\) 10978.4i 1.49978i
\(378\) 0 0
\(379\) 7756.85i 1.05130i −0.850701 0.525650i \(-0.823822\pi\)
0.850701 0.525650i \(-0.176178\pi\)
\(380\) 0 0
\(381\) 366.642 + 11868.9i 0.0493009 + 1.59596i
\(382\) 0 0
\(383\) −7742.65 −1.03298 −0.516489 0.856294i \(-0.672761\pi\)
−0.516489 + 0.856294i \(0.672761\pi\)
\(384\) 0 0
\(385\) −1.58811 −0.000210228
\(386\) 0 0
\(387\) 721.590 + 11668.5i 0.0947816 + 1.53267i
\(388\) 0 0
\(389\) 7875.98i 1.02655i 0.858224 + 0.513275i \(0.171568\pi\)
−0.858224 + 0.513275i \(0.828432\pi\)
\(390\) 0 0
\(391\) 61.5195i 0.00795697i
\(392\) 0 0
\(393\) −8222.72 + 254.008i −1.05542 + 0.0326030i
\(394\) 0 0
\(395\) −2471.42 −0.314811
\(396\) 0 0
\(397\) 10206.3 1.29028 0.645140 0.764065i \(-0.276799\pi\)
0.645140 + 0.764065i \(0.276799\pi\)
\(398\) 0 0
\(399\) 15.7907 0.487788i 0.00198126 6.12029e-5i
\(400\) 0 0
\(401\) 11841.0i 1.47459i −0.675570 0.737296i \(-0.736103\pi\)
0.675570 0.737296i \(-0.263897\pi\)
\(402\) 0 0
\(403\) 6006.28i 0.742418i
\(404\) 0 0
\(405\) −682.502 5497.11i −0.0837378 0.674453i
\(406\) 0 0
\(407\) 8.66717 0.00105557
\(408\) 0 0
\(409\) 13143.7 1.58903 0.794517 0.607241i \(-0.207724\pi\)
0.794517 + 0.607241i \(0.207724\pi\)
\(410\) 0 0
\(411\) 481.214 + 15577.8i 0.0577532 + 1.86958i
\(412\) 0 0
\(413\) 3417.74i 0.407206i
\(414\) 0 0
\(415\) 2861.11i 0.338426i
\(416\) 0 0
\(417\) 212.497 + 6878.94i 0.0249545 + 0.807825i
\(418\) 0 0
\(419\) −9151.59 −1.06703 −0.533514 0.845791i \(-0.679129\pi\)
−0.533514 + 0.845791i \(0.679129\pi\)
\(420\) 0 0
\(421\) 4546.98 0.526380 0.263190 0.964744i \(-0.415225\pi\)
0.263190 + 0.964744i \(0.415225\pi\)
\(422\) 0 0
\(423\) 8543.80 528.356i 0.982066 0.0607318i
\(424\) 0 0
\(425\) 29.5955i 0.00337787i
\(426\) 0 0
\(427\) 3088.31i 0.350009i
\(428\) 0 0
\(429\) −6.22896 + 0.192418i −0.000701018 + 2.16551e-5i
\(430\) 0 0
\(431\) −1673.79 −0.187061 −0.0935307 0.995616i \(-0.529815\pi\)
−0.0935307 + 0.995616i \(0.529815\pi\)
\(432\) 0 0
\(433\) 7444.60 0.826246 0.413123 0.910675i \(-0.364438\pi\)
0.413123 + 0.910675i \(0.364438\pi\)
\(434\) 0 0
\(435\) −10785.9 + 333.187i −1.18884 + 0.0367244i
\(436\) 0 0
\(437\) 60.7279i 0.00664762i
\(438\) 0 0
\(439\) 7622.30i 0.828685i −0.910121 0.414343i \(-0.864012\pi\)
0.910121 0.414343i \(-0.135988\pi\)
\(440\) 0 0
\(441\) −1320.48 + 81.6595i −0.142585 + 0.00881757i
\(442\) 0 0
\(443\) −11283.3 −1.21012 −0.605062 0.796178i \(-0.706852\pi\)
−0.605062 + 0.796178i \(0.706852\pi\)
\(444\) 0 0
\(445\) 3773.50 0.401980
\(446\) 0 0
\(447\) −387.533 12545.2i −0.0410060 1.32744i
\(448\) 0 0
\(449\) 1115.19i 0.117214i −0.998281 0.0586072i \(-0.981334\pi\)
0.998281 0.0586072i \(-0.0186660\pi\)
\(450\) 0 0
\(451\) 1.71653i 0.000179221i
\(452\) 0 0
\(453\) 438.762 + 14203.6i 0.0455074 + 1.47316i
\(454\) 0 0
\(455\) 2136.55 0.220138
\(456\) 0 0
\(457\) 5761.30 0.589720 0.294860 0.955540i \(-0.404727\pi\)
0.294860 + 0.955540i \(0.404727\pi\)
\(458\) 0 0
\(459\) −5.71072 61.4655i −0.000580727 0.00625046i
\(460\) 0 0
\(461\) 13482.7i 1.36215i 0.732212 + 0.681077i \(0.238488\pi\)
−0.732212 + 0.681077i \(0.761512\pi\)
\(462\) 0 0
\(463\) 2543.21i 0.255276i 0.991821 + 0.127638i \(0.0407396\pi\)
−0.991821 + 0.127638i \(0.959260\pi\)
\(464\) 0 0
\(465\) −5900.96 + 182.286i −0.588496 + 0.0181792i
\(466\) 0 0
\(467\) 10843.8 1.07450 0.537248 0.843424i \(-0.319464\pi\)
0.537248 + 0.843424i \(0.319464\pi\)
\(468\) 0 0
\(469\) −3081.43 −0.303384
\(470\) 0 0
\(471\) −15362.2 + 474.553i −1.50287 + 0.0464251i
\(472\) 0 0
\(473\) 12.9281i 0.00125673i
\(474\) 0 0
\(475\) 29.2147i 0.00282203i
\(476\) 0 0
\(477\) −245.144 3964.11i −0.0235312 0.380512i
\(478\) 0 0
\(479\) −3170.33 −0.302414 −0.151207 0.988502i \(-0.548316\pi\)
−0.151207 + 0.988502i \(0.548316\pi\)
\(480\) 0 0
\(481\) −11660.3 −1.10533
\(482\) 0 0
\(483\) 157.024 + 5083.16i 0.0147926 + 0.478865i
\(484\) 0 0
\(485\) 2836.85i 0.265598i
\(486\) 0 0
\(487\) 5722.95i 0.532509i 0.963903 + 0.266254i \(0.0857861\pi\)
−0.963903 + 0.266254i \(0.914214\pi\)
\(488\) 0 0
\(489\) −110.892 3589.78i −0.0102550 0.331974i
\(490\) 0 0
\(491\) −13139.2 −1.20767 −0.603834 0.797110i \(-0.706361\pi\)
−0.603834 + 0.797110i \(0.706361\pi\)
\(492\) 0 0
\(493\) −120.256 −0.0109859
\(494\) 0 0
\(495\) 0.378088 + 6.11389i 3.43309e−5 + 0.000555149i
\(496\) 0 0
\(497\) 1420.82i 0.128234i
\(498\) 0 0
\(499\) 13089.1i 1.17425i −0.809498 0.587123i \(-0.800261\pi\)
0.809498 0.587123i \(-0.199739\pi\)
\(500\) 0 0
\(501\) −10097.4 + 311.919i −0.900439 + 0.0278154i
\(502\) 0 0
\(503\) −17972.9 −1.59318 −0.796592 0.604518i \(-0.793366\pi\)
−0.796592 + 0.604518i \(0.793366\pi\)
\(504\) 0 0
\(505\) 2555.34 0.225171
\(506\) 0 0
\(507\) −3030.44 + 93.6133i −0.265457 + 0.00820022i
\(508\) 0 0
\(509\) 18517.0i 1.61248i 0.591588 + 0.806240i \(0.298501\pi\)
−0.591588 + 0.806240i \(0.701499\pi\)
\(510\) 0 0
\(511\) 3799.03i 0.328883i
\(512\) 0 0
\(513\) −5.63723 60.6746i −0.000485166 0.00522192i
\(514\) 0 0
\(515\) −2827.20 −0.241905
\(516\) 0 0
\(517\) −9.46609 −0.000805257
\(518\) 0 0
\(519\) 234.110 + 7578.59i 0.0198001 + 0.640969i
\(520\) 0 0
\(521\) 5545.36i 0.466308i 0.972440 + 0.233154i \(0.0749047\pi\)
−0.972440 + 0.233154i \(0.925095\pi\)
\(522\) 0 0
\(523\) 10763.5i 0.899912i −0.893051 0.449956i \(-0.851440\pi\)
0.893051 0.449956i \(-0.148560\pi\)
\(524\) 0 0
\(525\) 75.5402 + 2445.38i 0.00627971 + 0.203286i
\(526\) 0 0
\(527\) −65.7918 −0.00543821
\(528\) 0 0
\(529\) 7381.88 0.606714
\(530\) 0 0
\(531\) 13157.6 813.677i 1.07531 0.0664983i
\(532\) 0 0
\(533\) 2309.32i 0.187669i
\(534\) 0 0
\(535\) 10264.8i 0.829508i
\(536\) 0 0
\(537\) −12458.3 + 384.850i −1.00115 + 0.0309264i
\(538\) 0 0
\(539\) 1.46302 0.000116914
\(540\) 0 0
\(541\) −9149.30 −0.727097 −0.363548 0.931575i \(-0.618435\pi\)
−0.363548 + 0.931575i \(0.618435\pi\)
\(542\) 0 0
\(543\) −11265.1 + 347.990i −0.890300 + 0.0275022i
\(544\) 0 0
\(545\) 1305.12i 0.102578i
\(546\) 0 0
\(547\) 4297.91i 0.335951i −0.985791 0.167976i \(-0.946277\pi\)
0.985791 0.167976i \(-0.0537230\pi\)
\(548\) 0 0
\(549\) −11889.4 + 735.249i −0.924272 + 0.0571578i
\(550\) 0 0
\(551\) −118.708 −0.00917813
\(552\) 0 0
\(553\) 2276.75 0.175077
\(554\) 0 0
\(555\) 353.881 + 11455.8i 0.0270656 + 0.876167i
\(556\) 0 0
\(557\) 1753.57i 0.133395i 0.997773 + 0.0666975i \(0.0212462\pi\)
−0.997773 + 0.0666975i \(0.978754\pi\)
\(558\) 0 0
\(559\) 17392.7i 1.31598i
\(560\) 0 0
\(561\) 0.00210772 + 0.0682309i 1.58624e−7 + 5.13496e-6i
\(562\) 0 0
\(563\) −10323.1 −0.772764 −0.386382 0.922339i \(-0.626275\pi\)
−0.386382 + 0.922339i \(0.626275\pi\)
\(564\) 0 0
\(565\) 8602.36 0.640538
\(566\) 0 0
\(567\) 628.744 + 5064.12i 0.0465692 + 0.375085i
\(568\) 0 0
\(569\) 15103.5i 1.11278i −0.830920 0.556391i \(-0.812186\pi\)
0.830920 0.556391i \(-0.187814\pi\)
\(570\) 0 0
\(571\) 9072.75i 0.664944i 0.943113 + 0.332472i \(0.107883\pi\)
−0.943113 + 0.332472i \(0.892117\pi\)
\(572\) 0 0
\(573\) −17375.9 + 536.757i −1.26682 + 0.0391333i
\(574\) 0 0
\(575\) 9404.49 0.682077
\(576\) 0 0
\(577\) 3540.84 0.255472 0.127736 0.991808i \(-0.459229\pi\)
0.127736 + 0.991808i \(0.459229\pi\)
\(578\) 0 0
\(579\) −7274.45 + 224.715i −0.522134 + 0.0161292i
\(580\) 0 0
\(581\) 2635.75i 0.188209i
\(582\) 0 0
\(583\) 4.39203i 0.000312006i
\(584\) 0 0
\(585\) −508.657 8225.25i −0.0359494 0.581320i
\(586\) 0 0
\(587\) 11465.3 0.806171 0.403085 0.915162i \(-0.367938\pi\)
0.403085 + 0.915162i \(0.367938\pi\)
\(588\) 0 0
\(589\) −64.9452 −0.00454333
\(590\) 0 0
\(591\) −601.210 19462.3i −0.0418452 1.35461i
\(592\) 0 0
\(593\) 4829.33i 0.334430i 0.985920 + 0.167215i \(0.0534774\pi\)
−0.985920 + 0.167215i \(0.946523\pi\)
\(594\) 0 0
\(595\) 23.4034i 0.00161251i
\(596\) 0 0
\(597\) −186.183 6027.10i −0.0127638 0.413188i
\(598\) 0 0
\(599\) 9235.49 0.629970 0.314985 0.949097i \(-0.398001\pi\)
0.314985 + 0.949097i \(0.398001\pi\)
\(600\) 0 0
\(601\) 7969.74 0.540919 0.270460 0.962731i \(-0.412824\pi\)
0.270460 + 0.962731i \(0.412824\pi\)
\(602\) 0 0
\(603\) 733.609 + 11862.8i 0.0495437 + 0.801148i
\(604\) 0 0
\(605\) 10113.6i 0.679631i
\(606\) 0 0
\(607\) 12277.3i 0.820953i 0.911871 + 0.410477i \(0.134638\pi\)
−0.911871 + 0.410477i \(0.865362\pi\)
\(608\) 0 0
\(609\) 9936.35 306.943i 0.661152 0.0204236i
\(610\) 0 0
\(611\) 12735.1 0.843219
\(612\) 0 0
\(613\) 2671.59 0.176027 0.0880135 0.996119i \(-0.471948\pi\)
0.0880135 + 0.996119i \(0.471948\pi\)
\(614\) 0 0
\(615\) −2268.83 + 70.0862i −0.148761 + 0.00459536i
\(616\) 0 0
\(617\) 16638.0i 1.08561i −0.839860 0.542803i \(-0.817363\pi\)
0.839860 0.542803i \(-0.182637\pi\)
\(618\) 0 0
\(619\) 30122.8i 1.95596i −0.208698 0.977980i \(-0.566923\pi\)
0.208698 0.977980i \(-0.433077\pi\)
\(620\) 0 0
\(621\) 19531.7 1814.68i 1.26213 0.117263i
\(622\) 0 0
\(623\) −3476.27 −0.223554
\(624\) 0 0
\(625\) −2692.90 −0.172345
\(626\) 0 0
\(627\) 0.00208060 + 0.0673529i 1.32522e−7 + 4.28998e-6i
\(628\) 0 0
\(629\) 127.725i 0.00809654i
\(630\) 0 0
\(631\) 4373.21i 0.275903i −0.990439 0.137952i \(-0.955948\pi\)
0.990439 0.137952i \(-0.0440518\pi\)
\(632\) 0 0
\(633\) −619.329 20048.9i −0.0388880 1.25888i
\(634\) 0 0
\(635\) 17364.6 1.08518
\(636\) 0 0
\(637\) −1968.26 −0.122426
\(638\) 0 0
\(639\) 5469.84 338.260i 0.338628 0.0209411i
\(640\) 0 0
\(641\) 9337.02i 0.575335i −0.957730 0.287668i \(-0.907120\pi\)
0.957730 0.287668i \(-0.0928799\pi\)
\(642\) 0 0
\(643\) 22548.8i 1.38295i 0.722400 + 0.691476i \(0.243039\pi\)
−0.722400 + 0.691476i \(0.756961\pi\)
\(644\) 0 0
\(645\) 17087.7 527.854i 1.04314 0.0322236i
\(646\) 0 0
\(647\) 21092.7 1.28167 0.640834 0.767680i \(-0.278589\pi\)
0.640834 + 0.767680i \(0.278589\pi\)
\(648\) 0 0
\(649\) −14.5779 −0.000881716
\(650\) 0 0
\(651\) 5436.16 167.928i 0.327281 0.0101100i
\(652\) 0 0
\(653\) 23059.3i 1.38190i 0.722902 + 0.690951i \(0.242808\pi\)
−0.722902 + 0.690951i \(0.757192\pi\)
\(654\) 0 0
\(655\) 12030.1i 0.717641i
\(656\) 0 0
\(657\) −14625.5 + 904.453i −0.868485 + 0.0537079i
\(658\) 0 0
\(659\) −22080.3 −1.30520 −0.652601 0.757702i \(-0.726322\pi\)
−0.652601 + 0.757702i \(0.726322\pi\)
\(660\) 0 0
\(661\) −22653.9 −1.33303 −0.666516 0.745491i \(-0.732215\pi\)
−0.666516 + 0.745491i \(0.732215\pi\)
\(662\) 0 0
\(663\) −2.83560 91.7937i −0.000166102 0.00537703i
\(664\) 0 0
\(665\) 23.1022i 0.00134717i
\(666\) 0 0
\(667\) 38213.4i 2.21833i
\(668\) 0 0
\(669\) 798.131 + 25837.1i 0.0461249 + 1.49315i
\(670\) 0 0
\(671\) 13.1728 0.000757869
\(672\) 0 0
\(673\) 3686.80 0.211168 0.105584 0.994410i \(-0.466329\pi\)
0.105584 + 0.994410i \(0.466329\pi\)
\(674\) 0 0
\(675\) 9396.23 872.997i 0.535794 0.0497803i
\(676\) 0 0
\(677\) 23120.2i 1.31253i −0.754531 0.656264i \(-0.772136\pi\)
0.754531 0.656264i \(-0.227864\pi\)
\(678\) 0 0
\(679\) 2613.41i 0.147707i
\(680\) 0 0
\(681\) 18183.2 561.695i 1.02317 0.0316068i
\(682\) 0 0
\(683\) 14836.8 0.831207 0.415603 0.909546i \(-0.363570\pi\)
0.415603 + 0.909546i \(0.363570\pi\)
\(684\) 0 0
\(685\) 22790.9 1.27123
\(686\) 0 0
\(687\) 21796.9 673.326i 1.21048 0.0373930i
\(688\) 0 0
\(689\) 5908.77i 0.326715i
\(690\) 0 0
\(691\) 25813.4i 1.42111i −0.703642 0.710555i \(-0.748444\pi\)
0.703642 0.710555i \(-0.251556\pi\)
\(692\) 0 0
\(693\) −0.348308 5.63232i −1.90925e−5 0.000308736i
\(694\) 0 0
\(695\) 10064.1 0.549285
\(696\) 0 0
\(697\) −25.2959 −0.00137468
\(698\) 0 0
\(699\) −789.089 25544.3i −0.0426983 1.38223i
\(700\) 0 0
\(701\) 16480.0i 0.887931i 0.896044 + 0.443965i \(0.146429\pi\)
−0.896044 + 0.443965i \(0.853571\pi\)
\(702\) 0 0
\(703\) 126.081i 0.00676422i
\(704\) 0 0
\(705\) −386.501 12511.8i −0.0206475 0.668399i
\(706\) 0 0
\(707\) −2354.07 −0.125225
\(708\) 0 0
\(709\) 2993.67 0.158575 0.0792875 0.996852i \(-0.474735\pi\)
0.0792875 + 0.996852i \(0.474735\pi\)
\(710\) 0 0
\(711\) −542.037 8765.02i −0.0285907 0.462326i
\(712\) 0 0
\(713\) 20906.5i 1.09811i
\(714\) 0 0
\(715\) 9.11316i 0.000476661i
\(716\) 0 0
\(717\) 5409.87 167.116i 0.281779 0.00870442i
\(718\) 0 0
\(719\) −17596.5 −0.912711 −0.456355 0.889798i \(-0.650845\pi\)
−0.456355 + 0.889798i \(0.650845\pi\)
\(720\) 0 0
\(721\) 2604.51 0.134531
\(722\) 0 0
\(723\) 10635.3 328.535i 0.547071 0.0168995i
\(724\) 0 0
\(725\) 18383.5i 0.941719i
\(726\) 0 0
\(727\) 33368.5i 1.70229i 0.524927 + 0.851147i \(0.324093\pi\)
−0.524927 + 0.851147i \(0.675907\pi\)
\(728\) 0 0
\(729\) 19346.1 3626.17i 0.982883 0.184228i
\(730\) 0 0
\(731\) 190.516 0.00963953
\(732\) 0 0
\(733\) −23542.7 −1.18632 −0.593158 0.805086i \(-0.702119\pi\)
−0.593158 + 0.805086i \(0.702119\pi\)
\(734\) 0 0
\(735\) 59.7352 + 1933.74i 0.00299778 + 0.0970439i
\(736\) 0 0
\(737\) 13.1434i 0.000656911i
\(738\) 0 0
\(739\) 23280.9i 1.15886i 0.815021 + 0.579432i \(0.196726\pi\)
−0.815021 + 0.579432i \(0.803274\pi\)
\(740\) 0 0
\(741\) −2.79911 90.6125i −0.000138769 0.00449222i
\(742\) 0 0
\(743\) 35371.0 1.74648 0.873242 0.487287i \(-0.162013\pi\)
0.873242 + 0.487287i \(0.162013\pi\)
\(744\) 0 0
\(745\) −18354.0 −0.902602
\(746\) 0 0
\(747\) 10147.1 627.506i 0.497005 0.0307353i
\(748\) 0 0
\(749\) 9456.29i 0.461316i
\(750\) 0 0
\(751\) 8592.26i 0.417492i −0.977970 0.208746i \(-0.933062\pi\)
0.977970 0.208746i \(-0.0669381\pi\)
\(752\) 0 0
\(753\) 3849.67 118.920i 0.186308 0.00575522i
\(754\) 0 0
\(755\) 20780.3 1.00168
\(756\) 0 0
\(757\) 5401.34 0.259333 0.129666 0.991558i \(-0.458609\pi\)
0.129666 + 0.991558i \(0.458609\pi\)
\(758\) 0 0
\(759\) −21.6815 + 0.669763i −0.00103688 + 3.20301e-5i
\(760\) 0 0
\(761\) 34301.0i 1.63391i −0.576698 0.816957i \(-0.695659\pi\)
0.576698 0.816957i \(-0.304341\pi\)
\(762\) 0 0
\(763\) 1202.32i 0.0570471i
\(764\) 0 0
\(765\) −90.0980 + 5.57174i −0.00425817 + 0.000263329i
\(766\) 0 0
\(767\) 19612.3 0.923282
\(768\) 0 0
\(769\) −23217.6 −1.08875 −0.544375 0.838842i \(-0.683233\pi\)
−0.544375 + 0.838842i \(0.683233\pi\)
\(770\) 0 0
\(771\) 1259.35 + 40767.6i 0.0588254 + 1.90429i
\(772\) 0 0
\(773\) 9655.19i 0.449254i −0.974445 0.224627i \(-0.927884\pi\)
0.974445 0.224627i \(-0.0721163\pi\)
\(774\) 0 0
\(775\) 10057.6i 0.466167i
\(776\) 0 0
\(777\) −326.007 10553.5i −0.0150521 0.487264i
\(778\) 0 0
\(779\) −24.9704 −0.00114847
\(780\) 0 0
\(781\) −6.06030 −0.000277663
\(782\) 0 0
\(783\) −3547.26 38179.8i −0.161901 1.74257i
\(784\) 0 0
\(785\) 22475.4i 1.02189i
\(786\) 0 0
\(787\) 7935.72i 0.359438i −0.983718 0.179719i \(-0.942481\pi\)
0.983718 0.179719i \(-0.0575189\pi\)
\(788\) 0 0
\(789\) 7886.66 243.626i 0.355859 0.0109928i
\(790\) 0 0
\(791\) −7924.79 −0.356224
\(792\) 0 0
\(793\) −17721.9 −0.793597
\(794\) 0 0
\(795\) −5805.16 + 179.327i −0.258978 + 0.00800009i
\(796\) 0 0
\(797\) 13066.5i 0.580726i 0.956917 + 0.290363i \(0.0937760\pi\)
−0.956917 + 0.290363i \(0.906224\pi\)
\(798\) 0 0
\(799\)