Properties

Label 3024.2.q.k.2305.5
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.5
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.k.2881.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.790938 - 1.36994i) q^{5} +(-2.57645 + 0.601597i) q^{7} +O(q^{10})\) \(q+(-0.790938 - 1.36994i) q^{5} +(-2.57645 + 0.601597i) q^{7} +(-2.58569 + 4.47855i) q^{11} +(-0.681985 + 1.18123i) q^{13} +(2.30781 + 3.99724i) q^{17} +(-0.0321742 + 0.0557274i) q^{19} +(-3.37197 - 5.84043i) q^{23} +(1.24883 - 2.16305i) q^{25} +(-4.70787 - 8.15427i) q^{29} +2.66278 q^{31} +(2.86196 + 3.05376i) q^{35} +(0.880766 - 1.52553i) q^{37} +(0.858924 - 1.48770i) q^{41} +(5.12012 + 8.86831i) q^{43} +5.20834 q^{47} +(6.27616 - 3.09997i) q^{49} +(0.479996 + 0.831377i) q^{53} +8.18049 q^{55} -9.33353 q^{59} +14.3902 q^{61} +2.15763 q^{65} +12.4981 q^{67} -4.49160 q^{71} +(-0.941655 - 1.63099i) q^{73} +(3.96762 - 13.0943i) q^{77} -6.53504 q^{79} +(-5.08661 - 8.81026i) q^{83} +(3.65066 - 6.32314i) q^{85} +(4.12369 - 7.14243i) q^{89} +(1.04647 - 3.45366i) q^{91} +0.101791 q^{95} +(-7.26638 - 12.5857i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{5} + 5q^{7} + O(q^{10}) \) \( 22q - 3q^{5} + 5q^{7} - 3q^{11} - 3q^{13} - 7q^{17} + q^{19} + 2q^{23} - 10q^{25} - 9q^{29} - 8q^{31} + 14q^{35} + 2q^{37} - 16q^{41} - 10q^{47} + 15q^{49} - 11q^{53} - 22q^{55} + 38q^{59} + 26q^{61} + 26q^{65} + 52q^{67} - 48q^{71} - 35q^{73} - 17q^{77} + 20q^{79} - 28q^{83} - 20q^{85} - 6q^{89} + 37q^{91} - 24q^{95} - 29q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −0.790938 1.36994i −0.353718 0.612658i 0.633180 0.774005i \(-0.281749\pi\)
−0.986898 + 0.161347i \(0.948416\pi\)
\(6\) 0 0
\(7\) −2.57645 + 0.601597i −0.973806 + 0.227382i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.58569 + 4.47855i −0.779616 + 1.35033i 0.152548 + 0.988296i \(0.451252\pi\)
−0.932163 + 0.362038i \(0.882081\pi\)
\(12\) 0 0
\(13\) −0.681985 + 1.18123i −0.189149 + 0.327615i −0.944967 0.327167i \(-0.893906\pi\)
0.755818 + 0.654782i \(0.227239\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.30781 + 3.99724i 0.559726 + 0.969473i 0.997519 + 0.0703975i \(0.0224268\pi\)
−0.437794 + 0.899076i \(0.644240\pi\)
\(18\) 0 0
\(19\) −0.0321742 + 0.0557274i −0.00738128 + 0.0127847i −0.869692 0.493594i \(-0.835683\pi\)
0.862311 + 0.506379i \(0.169016\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.37197 5.84043i −0.703105 1.21781i −0.967371 0.253364i \(-0.918463\pi\)
0.264266 0.964450i \(-0.414870\pi\)
\(24\) 0 0
\(25\) 1.24883 2.16305i 0.249767 0.432609i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.70787 8.15427i −0.874229 1.51421i −0.857582 0.514348i \(-0.828034\pi\)
−0.0166475 0.999861i \(-0.505299\pi\)
\(30\) 0 0
\(31\) 2.66278 0.478250 0.239125 0.970989i \(-0.423139\pi\)
0.239125 + 0.970989i \(0.423139\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.86196 + 3.05376i 0.483760 + 0.516180i
\(36\) 0 0
\(37\) 0.880766 1.52553i 0.144797 0.250796i −0.784500 0.620129i \(-0.787080\pi\)
0.929297 + 0.369333i \(0.120414\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.858924 1.48770i 0.134141 0.232340i −0.791128 0.611651i \(-0.790506\pi\)
0.925269 + 0.379311i \(0.123839\pi\)
\(42\) 0 0
\(43\) 5.12012 + 8.86831i 0.780811 + 1.35240i 0.931470 + 0.363819i \(0.118527\pi\)
−0.150658 + 0.988586i \(0.548139\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.20834 0.759715 0.379857 0.925045i \(-0.375973\pi\)
0.379857 + 0.925045i \(0.375973\pi\)
\(48\) 0 0
\(49\) 6.27616 3.09997i 0.896594 0.442853i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.479996 + 0.831377i 0.0659325 + 0.114198i 0.897107 0.441813i \(-0.145664\pi\)
−0.831175 + 0.556011i \(0.812331\pi\)
\(54\) 0 0
\(55\) 8.18049 1.10306
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −9.33353 −1.21512 −0.607561 0.794273i \(-0.707852\pi\)
−0.607561 + 0.794273i \(0.707852\pi\)
\(60\) 0 0
\(61\) 14.3902 1.84248 0.921241 0.388993i \(-0.127177\pi\)
0.921241 + 0.388993i \(0.127177\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.15763 0.267621
\(66\) 0 0
\(67\) 12.4981 1.52688 0.763441 0.645878i \(-0.223509\pi\)
0.763441 + 0.645878i \(0.223509\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.49160 −0.533055 −0.266527 0.963827i \(-0.585876\pi\)
−0.266527 + 0.963827i \(0.585876\pi\)
\(72\) 0 0
\(73\) −0.941655 1.63099i −0.110212 0.190893i 0.805643 0.592401i \(-0.201820\pi\)
−0.915856 + 0.401507i \(0.868486\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.96762 13.0943i 0.452152 1.49223i
\(78\) 0 0
\(79\) −6.53504 −0.735250 −0.367625 0.929974i \(-0.619829\pi\)
−0.367625 + 0.929974i \(0.619829\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.08661 8.81026i −0.558328 0.967052i −0.997636 0.0687156i \(-0.978110\pi\)
0.439309 0.898336i \(-0.355223\pi\)
\(84\) 0 0
\(85\) 3.65066 6.32314i 0.395970 0.685840i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.12369 7.14243i 0.437110 0.757096i −0.560355 0.828252i \(-0.689335\pi\)
0.997465 + 0.0711559i \(0.0226688\pi\)
\(90\) 0 0
\(91\) 1.04647 3.45366i 0.109700 0.362042i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.101791 0.0104436
\(96\) 0 0
\(97\) −7.26638 12.5857i −0.737789 1.27789i −0.953489 0.301428i \(-0.902537\pi\)
0.215700 0.976460i \(-0.430797\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.12310 5.40937i 0.310760 0.538252i −0.667767 0.744370i \(-0.732750\pi\)
0.978527 + 0.206118i \(0.0660831\pi\)
\(102\) 0 0
\(103\) −2.88881 5.00357i −0.284643 0.493016i 0.687879 0.725825i \(-0.258542\pi\)
−0.972523 + 0.232809i \(0.925208\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.251126 + 0.434963i −0.0242773 + 0.0420494i −0.877909 0.478828i \(-0.841062\pi\)
0.853632 + 0.520877i \(0.174395\pi\)
\(108\) 0 0
\(109\) −2.37218 4.10874i −0.227214 0.393546i 0.729767 0.683696i \(-0.239628\pi\)
−0.956981 + 0.290149i \(0.906295\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.11328 1.92825i 0.104728 0.181395i −0.808899 0.587948i \(-0.799936\pi\)
0.913627 + 0.406553i \(0.133269\pi\)
\(114\) 0 0
\(115\) −5.33404 + 9.23883i −0.497402 + 0.861526i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −8.35067 8.91031i −0.765505 0.816806i
\(120\) 0 0
\(121\) −7.87162 13.6340i −0.715601 1.23946i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.8604 −1.06082
\(126\) 0 0
\(127\) 18.6057 1.65099 0.825494 0.564410i \(-0.190896\pi\)
0.825494 + 0.564410i \(0.190896\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.77020 11.7263i −0.591515 1.02453i −0.994029 0.109120i \(-0.965197\pi\)
0.402514 0.915414i \(-0.368137\pi\)
\(132\) 0 0
\(133\) 0.0493698 0.162935i 0.00428090 0.0141282i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.87100 11.9009i 0.587029 1.01676i −0.407590 0.913165i \(-0.633631\pi\)
0.994619 0.103599i \(-0.0330358\pi\)
\(138\) 0 0
\(139\) −6.79328 + 11.7663i −0.576198 + 0.998005i 0.419712 + 0.907657i \(0.362131\pi\)
−0.995910 + 0.0903476i \(0.971202\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.52681 6.10861i −0.294927 0.510828i
\(144\) 0 0
\(145\) −7.44726 + 12.8990i −0.618461 + 1.07121i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.98033 + 5.16209i 0.244158 + 0.422895i 0.961895 0.273420i \(-0.0881550\pi\)
−0.717736 + 0.696315i \(0.754822\pi\)
\(150\) 0 0
\(151\) 4.27071 7.39709i 0.347546 0.601967i −0.638267 0.769815i \(-0.720349\pi\)
0.985813 + 0.167848i \(0.0536819\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.10610 3.64786i −0.169166 0.293004i
\(156\) 0 0
\(157\) −2.63992 −0.210688 −0.105344 0.994436i \(-0.533594\pi\)
−0.105344 + 0.994436i \(0.533594\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 12.2013 + 13.0190i 0.961597 + 1.02604i
\(162\) 0 0
\(163\) 8.87875 15.3785i 0.695438 1.20453i −0.274595 0.961560i \(-0.588544\pi\)
0.970033 0.242973i \(-0.0781228\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.98937 6.90979i 0.308706 0.534695i −0.669373 0.742926i \(-0.733437\pi\)
0.978080 + 0.208231i \(0.0667706\pi\)
\(168\) 0 0
\(169\) 5.56979 + 9.64716i 0.428446 + 0.742090i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −7.66341 −0.582638 −0.291319 0.956626i \(-0.594094\pi\)
−0.291319 + 0.956626i \(0.594094\pi\)
\(174\) 0 0
\(175\) −1.91627 + 6.32427i −0.144857 + 0.478070i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.7864 + 20.4147i 0.880958 + 1.52586i 0.850277 + 0.526335i \(0.176434\pi\)
0.0306808 + 0.999529i \(0.490232\pi\)
\(180\) 0 0
\(181\) 17.3700 1.29110 0.645551 0.763717i \(-0.276628\pi\)
0.645551 + 0.763717i \(0.276628\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.78653 −0.204869
\(186\) 0 0
\(187\) −23.8691 −1.74548
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.84660 0.350687 0.175344 0.984507i \(-0.443896\pi\)
0.175344 + 0.984507i \(0.443896\pi\)
\(192\) 0 0
\(193\) −14.6418 −1.05394 −0.526970 0.849884i \(-0.676672\pi\)
−0.526970 + 0.849884i \(0.676672\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 19.1996 1.36791 0.683957 0.729522i \(-0.260257\pi\)
0.683957 + 0.729522i \(0.260257\pi\)
\(198\) 0 0
\(199\) −6.50796 11.2721i −0.461337 0.799060i 0.537691 0.843142i \(-0.319297\pi\)
−0.999028 + 0.0440825i \(0.985964\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 17.0352 + 18.1768i 1.19563 + 1.27576i
\(204\) 0 0
\(205\) −2.71742 −0.189793
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.166385 0.288188i −0.0115091 0.0199344i
\(210\) 0 0
\(211\) 7.43389 12.8759i 0.511770 0.886412i −0.488137 0.872767i \(-0.662323\pi\)
0.999907 0.0136450i \(-0.00434348\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.09940 14.0286i 0.552374 0.956740i
\(216\) 0 0
\(217\) −6.86052 + 1.60192i −0.465722 + 0.108746i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6.29556 −0.423485
\(222\) 0 0
\(223\) −11.2085 19.4136i −0.750574 1.30003i −0.947545 0.319623i \(-0.896444\pi\)
0.196971 0.980409i \(-0.436890\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.94725 + 3.37273i −0.129243 + 0.223856i −0.923384 0.383878i \(-0.874588\pi\)
0.794140 + 0.607735i \(0.207922\pi\)
\(228\) 0 0
\(229\) 0.693586 + 1.20133i 0.0458334 + 0.0793858i 0.888032 0.459782i \(-0.152072\pi\)
−0.842199 + 0.539167i \(0.818739\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.99057 + 15.5721i −0.588992 + 1.02016i 0.405373 + 0.914151i \(0.367142\pi\)
−0.994365 + 0.106013i \(0.966192\pi\)
\(234\) 0 0
\(235\) −4.11947 7.13514i −0.268725 0.465445i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.68043 + 4.64264i −0.173382 + 0.300307i −0.939600 0.342274i \(-0.888803\pi\)
0.766218 + 0.642581i \(0.222136\pi\)
\(240\) 0 0
\(241\) −0.208296 + 0.360779i −0.0134175 + 0.0232398i −0.872656 0.488335i \(-0.837604\pi\)
0.859239 + 0.511575i \(0.170938\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −9.21084 6.14611i −0.588459 0.392661i
\(246\) 0 0
\(247\) −0.0438847 0.0760106i −0.00279232 0.00483644i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 22.5606 1.42401 0.712006 0.702173i \(-0.247787\pi\)
0.712006 + 0.702173i \(0.247787\pi\)
\(252\) 0 0
\(253\) 34.8756 2.19261
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.52307 9.56624i −0.344520 0.596726i 0.640747 0.767752i \(-0.278625\pi\)
−0.985266 + 0.171027i \(0.945292\pi\)
\(258\) 0 0
\(259\) −1.35149 + 4.46032i −0.0839776 + 0.277151i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.7310 22.0508i 0.785028 1.35971i −0.143954 0.989584i \(-0.545982\pi\)
0.928982 0.370124i \(-0.120685\pi\)
\(264\) 0 0
\(265\) 0.759294 1.31514i 0.0466430 0.0807881i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.78957 4.83168i −0.170083 0.294593i 0.768366 0.640011i \(-0.221070\pi\)
−0.938449 + 0.345419i \(0.887737\pi\)
\(270\) 0 0
\(271\) 1.46645 2.53997i 0.0890806 0.154292i −0.818042 0.575158i \(-0.804940\pi\)
0.907123 + 0.420866i \(0.138274\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.45821 + 11.1859i 0.389445 + 0.674538i
\(276\) 0 0
\(277\) −11.0458 + 19.1320i −0.663680 + 1.14953i 0.315961 + 0.948772i \(0.397673\pi\)
−0.979641 + 0.200756i \(0.935660\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2.81009 + 4.86721i 0.167636 + 0.290354i 0.937588 0.347748i \(-0.113053\pi\)
−0.769952 + 0.638101i \(0.779720\pi\)
\(282\) 0 0
\(283\) −21.3003 −1.26617 −0.633086 0.774082i \(-0.718212\pi\)
−0.633086 + 0.774082i \(0.718212\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.31798 + 4.34971i −0.0777977 + 0.256755i
\(288\) 0 0
\(289\) −2.15195 + 3.72729i −0.126585 + 0.219252i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −14.1128 + 24.4440i −0.824477 + 1.42804i 0.0778418 + 0.996966i \(0.475197\pi\)
−0.902319 + 0.431070i \(0.858136\pi\)
\(294\) 0 0
\(295\) 7.38224 + 12.7864i 0.429811 + 0.744454i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 9.19854 0.531966
\(300\) 0 0
\(301\) −18.5269 19.7685i −1.06787 1.13944i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −11.3818 19.7138i −0.651719 1.12881i
\(306\) 0 0
\(307\) 2.41329 0.137734 0.0688669 0.997626i \(-0.478062\pi\)
0.0688669 + 0.997626i \(0.478062\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9.53680 0.540782 0.270391 0.962751i \(-0.412847\pi\)
0.270391 + 0.962751i \(0.412847\pi\)
\(312\) 0 0
\(313\) 32.6020 1.84277 0.921386 0.388650i \(-0.127058\pi\)
0.921386 + 0.388650i \(0.127058\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.09954 0.174088 0.0870438 0.996204i \(-0.472258\pi\)
0.0870438 + 0.996204i \(0.472258\pi\)
\(318\) 0 0
\(319\) 48.6924 2.72625
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.297008 −0.0165260
\(324\) 0 0
\(325\) 1.70337 + 2.95033i 0.0944862 + 0.163655i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −13.4190 + 3.13332i −0.739814 + 0.172746i
\(330\) 0 0
\(331\) 3.67650 0.202079 0.101039 0.994882i \(-0.467783\pi\)
0.101039 + 0.994882i \(0.467783\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −9.88519 17.1216i −0.540086 0.935456i
\(336\) 0 0
\(337\) 6.15866 10.6671i 0.335483 0.581074i −0.648094 0.761560i \(-0.724434\pi\)
0.983578 + 0.180486i \(0.0577670\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6.88514 + 11.9254i −0.372851 + 0.645797i
\(342\) 0 0
\(343\) −14.3053 + 11.7626i −0.772412 + 0.635122i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −17.7016 −0.950269 −0.475135 0.879913i \(-0.657601\pi\)
−0.475135 + 0.879913i \(0.657601\pi\)
\(348\) 0 0
\(349\) 0.562639 + 0.974519i 0.0301174 + 0.0521648i 0.880691 0.473691i \(-0.157079\pi\)
−0.850574 + 0.525856i \(0.823745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5.48125 + 9.49381i −0.291738 + 0.505304i −0.974221 0.225597i \(-0.927567\pi\)
0.682483 + 0.730901i \(0.260900\pi\)
\(354\) 0 0
\(355\) 3.55257 + 6.15324i 0.188551 + 0.326580i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −13.4733 + 23.3364i −0.711092 + 1.23165i 0.253356 + 0.967373i \(0.418466\pi\)
−0.964448 + 0.264274i \(0.914868\pi\)
\(360\) 0 0
\(361\) 9.49793 + 16.4509i 0.499891 + 0.865837i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.48958 + 2.58003i −0.0779682 + 0.135045i
\(366\) 0 0
\(367\) 17.4137 30.1614i 0.908986 1.57441i 0.0935112 0.995618i \(-0.470191\pi\)
0.815475 0.578792i \(-0.196476\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.73684 1.85324i −0.0901722 0.0962152i
\(372\) 0 0
\(373\) 11.5793 + 20.0559i 0.599551 + 1.03845i 0.992887 + 0.119058i \(0.0379876\pi\)
−0.393336 + 0.919395i \(0.628679\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.8428 0.661437
\(378\) 0 0
\(379\) −22.7259 −1.16735 −0.583676 0.811987i \(-0.698386\pi\)
−0.583676 + 0.811987i \(0.698386\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −11.6021 20.0954i −0.592837 1.02682i −0.993848 0.110751i \(-0.964674\pi\)
0.401011 0.916073i \(-0.368659\pi\)
\(384\) 0 0
\(385\) −21.0766 + 4.92136i −1.07416 + 0.250816i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.56737 + 7.91091i −0.231575 + 0.401099i −0.958272 0.285859i \(-0.907721\pi\)
0.726697 + 0.686958i \(0.241054\pi\)
\(390\) 0 0
\(391\) 15.5637 26.9572i 0.787092 1.36328i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 5.16881 + 8.95265i 0.260071 + 0.450456i
\(396\) 0 0
\(397\) −19.2126 + 33.2773i −0.964255 + 1.67014i −0.252652 + 0.967557i \(0.581303\pi\)
−0.711603 + 0.702582i \(0.752031\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.47348 + 2.55214i 0.0735821 + 0.127448i 0.900469 0.434921i \(-0.143224\pi\)
−0.826887 + 0.562369i \(0.809890\pi\)
\(402\) 0 0
\(403\) −1.81598 + 3.14537i −0.0904603 + 0.156682i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.55478 + 7.88912i 0.225772 + 0.391049i
\(408\) 0 0
\(409\) 6.60591 0.326641 0.163321 0.986573i \(-0.447779\pi\)
0.163321 + 0.986573i \(0.447779\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 24.0473 5.61503i 1.18329 0.276297i
\(414\) 0 0
\(415\) −8.04638 + 13.9367i −0.394981 + 0.684127i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.381961 + 0.661576i −0.0186600 + 0.0323201i −0.875205 0.483753i \(-0.839273\pi\)
0.856545 + 0.516073i \(0.172607\pi\)
\(420\) 0 0
\(421\) −2.48798 4.30931i −0.121257 0.210023i 0.799007 0.601322i \(-0.205359\pi\)
−0.920264 + 0.391299i \(0.872026\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 11.5283 0.559204
\(426\) 0 0
\(427\) −37.0757 + 8.65713i −1.79422 + 0.418948i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.01856 6.96035i −0.193567 0.335268i 0.752863 0.658178i \(-0.228672\pi\)
−0.946430 + 0.322909i \(0.895339\pi\)
\(432\) 0 0
\(433\) −10.8006 −0.519043 −0.259522 0.965737i \(-0.583565\pi\)
−0.259522 + 0.965737i \(0.583565\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.433963 0.0207593
\(438\) 0 0
\(439\) 20.1194 0.960244 0.480122 0.877202i \(-0.340592\pi\)
0.480122 + 0.877202i \(0.340592\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.21245 −0.437697 −0.218848 0.975759i \(-0.570230\pi\)
−0.218848 + 0.975759i \(0.570230\pi\)
\(444\) 0 0
\(445\) −13.0463 −0.618455
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.4840 1.06109 0.530544 0.847658i \(-0.321988\pi\)
0.530544 + 0.847658i \(0.321988\pi\)
\(450\) 0 0
\(451\) 4.44183 + 7.69347i 0.209158 + 0.362271i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −5.55902 + 1.29803i −0.260611 + 0.0608524i
\(456\) 0 0
\(457\) 18.7955 0.879218 0.439609 0.898189i \(-0.355117\pi\)
0.439609 + 0.898189i \(0.355117\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.3773 17.9739i −0.483317 0.837129i 0.516500 0.856287i \(-0.327235\pi\)
−0.999816 + 0.0191582i \(0.993901\pi\)
\(462\) 0 0
\(463\) −10.0414 + 17.3922i −0.466663 + 0.808284i −0.999275 0.0380753i \(-0.987877\pi\)
0.532612 + 0.846360i \(0.321211\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 14.6015 25.2905i 0.675676 1.17030i −0.300595 0.953752i \(-0.597185\pi\)
0.976271 0.216553i \(-0.0694813\pi\)
\(468\) 0 0
\(469\) −32.2006 + 7.51880i −1.48689 + 0.347186i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −52.9563 −2.43493
\(474\) 0 0
\(475\) 0.0803606 + 0.139189i 0.00368720 + 0.00638642i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 20.0327 34.6977i 0.915319 1.58538i 0.108884 0.994054i \(-0.465272\pi\)
0.806434 0.591324i \(-0.201394\pi\)
\(480\) 0 0
\(481\) 1.20134 + 2.08078i 0.0547763 + 0.0948754i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −11.4945 + 19.9091i −0.521939 + 0.904024i
\(486\) 0 0
\(487\) −9.32801 16.1566i −0.422692 0.732125i 0.573509 0.819199i \(-0.305582\pi\)
−0.996202 + 0.0870742i \(0.972248\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.285132 + 0.493864i −0.0128678 + 0.0222878i −0.872388 0.488815i \(-0.837429\pi\)
0.859520 + 0.511102i \(0.170763\pi\)
\(492\) 0 0
\(493\) 21.7297 37.6370i 0.978657 1.69508i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 11.5724 2.70213i 0.519092 0.121207i
\(498\) 0 0
\(499\) −0.464297 0.804185i −0.0207848 0.0360003i 0.855446 0.517892i \(-0.173283\pi\)
−0.876231 + 0.481892i \(0.839950\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.27170 −0.145878 −0.0729389 0.997336i \(-0.523238\pi\)
−0.0729389 + 0.997336i \(0.523238\pi\)
\(504\) 0 0
\(505\) −9.88071 −0.439686
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.48391 + 7.76635i 0.198746 + 0.344238i 0.948122 0.317907i \(-0.102980\pi\)
−0.749376 + 0.662144i \(0.769647\pi\)
\(510\) 0 0
\(511\) 3.40733 + 3.63567i 0.150731 + 0.160833i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4.56974 + 7.91502i −0.201367 + 0.348778i
\(516\) 0 0
\(517\) −13.4672 + 23.3258i −0.592286 + 1.02587i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.37649 + 9.31235i 0.235548 + 0.407982i 0.959432 0.281940i \(-0.0909781\pi\)
−0.723884 + 0.689922i \(0.757645\pi\)
\(522\) 0 0
\(523\) 16.2796 28.1970i 0.711856 1.23297i −0.252304 0.967648i \(-0.581188\pi\)
0.964160 0.265322i \(-0.0854784\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.14519 + 10.6438i 0.267689 + 0.463650i
\(528\) 0 0
\(529\) −11.2404 + 19.4690i −0.488714 + 0.846477i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.17155 + 2.02918i 0.0507453 + 0.0878935i
\(534\) 0 0
\(535\) 0.794500 0.0343492
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.34486 + 36.1237i −0.101000 + 1.55596i
\(540\) 0 0
\(541\) −3.46359 + 5.99911i −0.148911 + 0.257922i −0.930825 0.365464i \(-0.880910\pi\)
0.781914 + 0.623386i \(0.214244\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.75250 + 6.49952i −0.160739 + 0.278409i
\(546\) 0 0
\(547\) 15.8974 + 27.5351i 0.679725 + 1.17732i 0.975064 + 0.221925i \(0.0712340\pi\)
−0.295339 + 0.955392i \(0.595433\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.605888 0.0258117
\(552\) 0 0
\(553\) 16.8372 3.93147i 0.715990 0.167183i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.1679 24.5395i −0.600314 1.03977i −0.992773 0.120005i \(-0.961709\pi\)
0.392460 0.919769i \(-0.371624\pi\)
\(558\) 0 0
\(559\) −13.9674 −0.590758
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −44.6541 −1.88194 −0.940972 0.338484i \(-0.890086\pi\)
−0.940972 + 0.338484i \(0.890086\pi\)
\(564\) 0 0
\(565\) −3.52213 −0.148177
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 21.2205 0.889608 0.444804 0.895628i \(-0.353273\pi\)
0.444804 + 0.895628i \(0.353273\pi\)
\(570\) 0 0
\(571\) −11.8957 −0.497820 −0.248910 0.968527i \(-0.580072\pi\)
−0.248910 + 0.968527i \(0.580072\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −16.8442 −0.702450
\(576\) 0 0
\(577\) −19.3490 33.5135i −0.805511 1.39519i −0.915946 0.401302i \(-0.868558\pi\)
0.110435 0.993883i \(-0.464776\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 18.4056 + 19.6391i 0.763593 + 0.814766i
\(582\) 0 0
\(583\) −4.96449 −0.205608
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.92138 + 17.1843i 0.409499 + 0.709274i 0.994834 0.101518i \(-0.0323701\pi\)
−0.585334 + 0.810792i \(0.699037\pi\)
\(588\) 0 0
\(589\) −0.0856730 + 0.148390i −0.00353010 + 0.00611431i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −10.9566 + 18.9774i −0.449933 + 0.779307i −0.998381 0.0568775i \(-0.981886\pi\)
0.548448 + 0.836185i \(0.315219\pi\)
\(594\) 0 0
\(595\) −5.60176 + 18.4875i −0.229650 + 0.757912i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 33.0445 1.35016 0.675081 0.737743i \(-0.264108\pi\)
0.675081 + 0.737743i \(0.264108\pi\)
\(600\) 0 0
\(601\) 11.4951 + 19.9100i 0.468893 + 0.812147i 0.999368 0.0355541i \(-0.0113196\pi\)
−0.530475 + 0.847701i \(0.677986\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −12.4519 + 21.5674i −0.506242 + 0.876838i
\(606\) 0 0
\(607\) 13.8282 + 23.9511i 0.561269 + 0.972146i 0.997386 + 0.0722559i \(0.0230198\pi\)
−0.436118 + 0.899890i \(0.643647\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.55201 + 6.15226i −0.143699 + 0.248894i
\(612\) 0 0
\(613\) −15.7684 27.3116i −0.636879 1.10311i −0.986114 0.166072i \(-0.946892\pi\)
0.349235 0.937035i \(-0.386442\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 10.7513 18.6217i 0.432830 0.749683i −0.564286 0.825580i \(-0.690848\pi\)
0.997116 + 0.0758961i \(0.0241817\pi\)
\(618\) 0 0
\(619\) 14.1261 24.4671i 0.567776 0.983417i −0.429009 0.903300i \(-0.641137\pi\)
0.996785 0.0801169i \(-0.0255294\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.32759 + 20.8829i −0.253509 + 0.836656i
\(624\) 0 0
\(625\) 3.13665 + 5.43283i 0.125466 + 0.217313i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 8.13056 0.324187
\(630\) 0 0
\(631\) 9.12550 0.363281 0.181640 0.983365i \(-0.441859\pi\)
0.181640 + 0.983365i \(0.441859\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −14.7159 25.4888i −0.583985 1.01149i
\(636\) 0 0
\(637\) −0.618464 + 9.52774i −0.0245044 + 0.377503i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 16.4489 28.4904i 0.649693 1.12530i −0.333503 0.942749i \(-0.608231\pi\)
0.983196 0.182552i \(-0.0584359\pi\)
\(642\) 0 0
\(643\) −10.1276 + 17.5415i −0.399392 + 0.691767i −0.993651 0.112506i \(-0.964112\pi\)
0.594259 + 0.804274i \(0.297445\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.67441 9.82837i −0.223084 0.386393i 0.732659 0.680596i \(-0.238279\pi\)
−0.955743 + 0.294203i \(0.904946\pi\)
\(648\) 0 0
\(649\) 24.1336 41.8007i 0.947328 1.64082i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.79018 + 3.10069i 0.0700552 + 0.121339i 0.898925 0.438102i \(-0.144349\pi\)
−0.828870 + 0.559441i \(0.811016\pi\)
\(654\) 0 0
\(655\) −10.7096 + 18.5496i −0.418459 + 0.724792i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9.13582 + 15.8237i 0.355881 + 0.616404i 0.987268 0.159064i \(-0.0508475\pi\)
−0.631387 + 0.775468i \(0.717514\pi\)
\(660\) 0 0
\(661\) 2.23391 0.0868891 0.0434446 0.999056i \(-0.486167\pi\)
0.0434446 + 0.999056i \(0.486167\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.262260 + 0.0612374i −0.0101700 + 0.00237468i
\(666\) 0 0
\(667\) −31.7496 + 54.9919i −1.22935 + 2.12930i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −37.2087 + 64.4474i −1.43643 + 2.48797i
\(672\) 0 0
\(673\) −12.4804 21.6166i −0.481083 0.833260i 0.518681 0.854968i \(-0.326423\pi\)
−0.999764 + 0.0217074i \(0.993090\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19.8127 0.761463 0.380731 0.924686i \(-0.375672\pi\)
0.380731 + 0.924686i \(0.375672\pi\)
\(678\) 0 0
\(679\) 26.2930 + 28.0551i 1.00903 + 1.07665i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5.72871 + 9.92242i 0.219203 + 0.379671i 0.954565 0.298004i \(-0.0963209\pi\)
−0.735361 + 0.677675i \(0.762988\pi\)
\(684\) 0 0
\(685\) −21.7381 −0.830571
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.30940 −0.0498842
\(690\) 0 0
\(691\) −40.5105 −1.54109 −0.770545 0.637385i \(-0.780016\pi\)
−0.770545 + 0.637385i \(0.780016\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 21.4922 0.815247
\(696\) 0 0
\(697\) 7.92893 0.300330
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 29.5416 1.11577 0.557885 0.829918i \(-0.311613\pi\)
0.557885 + 0.829918i \(0.311613\pi\)
\(702\) 0 0
\(703\) 0.0566760 + 0.0981657i 0.00213758 + 0.00370239i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.79224 + 15.8158i −0.180231 + 0.594814i
\(708\) 0 0
\(709\) −37.4814 −1.40764 −0.703822 0.710376i \(-0.748525\pi\)
−0.703822 + 0.710376i \(0.748525\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8.97883 15.5518i −0.336260 0.582419i
\(714\) 0 0
\(715\) −5.57897 + 9.66306i −0.208642 + 0.361378i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.35418 11.0058i 0.236971 0.410445i −0.722873 0.690981i \(-0.757179\pi\)
0.959844 + 0.280536i \(0.0905121\pi\)
\(720\) 0 0
\(721\) 10.4530 + 11.1535i 0.389290 + 0.415379i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −23.5174 −0.873414
\(726\) 0 0
\(727\) −19.9463 34.5480i −0.739768 1.28132i −0.952600 0.304227i \(-0.901602\pi\)
0.212832 0.977089i \(-0.431731\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −23.6325 + 40.9327i −0.874080 + 1.51395i
\(732\) 0 0
\(733\) 22.4091 + 38.8137i 0.827699 + 1.43362i 0.899839 + 0.436222i \(0.143684\pi\)
−0.0721400 + 0.997395i \(0.522983\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −32.3162 + 55.9732i −1.19038 + 2.06180i
\(738\) 0 0
\(739\) 6.64954 + 11.5173i 0.244607 + 0.423672i 0.962021 0.272975i \(-0.0880076\pi\)
−0.717414 + 0.696647i \(0.754674\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.15562 3.73365i 0.0790822 0.136974i −0.823772 0.566921i \(-0.808134\pi\)
0.902854 + 0.429947i \(0.141468\pi\)
\(744\) 0 0
\(745\) 4.71451 8.16578i 0.172726 0.299171i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.385340 1.27174i 0.0140800 0.0464682i
\(750\) 0 0
\(751\) −21.7651 37.6983i −0.794221 1.37563i −0.923333 0.384001i \(-0.874546\pi\)
0.129112 0.991630i \(-0.458787\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −13.5115 −0.491733
\(756\) 0 0
\(757\) 34.6790 1.26043 0.630215 0.776420i \(-0.282967\pi\)
0.630215 + 0.776420i \(0.282967\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.75973 3.04794i −0.0637902 0.110488i 0.832367 0.554226i \(-0.186986\pi\)
−0.896157 + 0.443738i \(0.853652\pi\)
\(762\) 0 0
\(763\) 8.58362 + 9.15886i 0.310748 + 0.331573i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.36533 11.0251i 0.229839 0.398092i
\(768\) 0 0
\(769\) −19.5075 + 33.7879i −0.703457 + 1.21842i 0.263788 + 0.964581i \(0.415028\pi\)
−0.967245 + 0.253843i \(0.918305\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −23.2169 40.2128i −0.835054 1.44636i −0.893987 0.448094i \(-0.852103\pi\)
0.0589329 0.998262i \(-0.481230\pi\)
\(774\) 0 0
\(775\) 3.32538 5.75972i 0.119451 0.206895i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.0552705 + 0.0957313i 0.00198027 + 0.00342993i
\(780\) 0 0
\(781\) 11.6139 20.1159i 0.415578 0.719802i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.08801 + 3.61654i 0.0745242 + 0.129080i
\(786\) 0 0
\(787\) −47.4424 −1.69114 −0.845569 0.533866i \(-0.820739\pi\)
−0.845569 + 0.533866i \(0.820739\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.70827 + 5.63778i −0.0607390 + 0.200456i
\(792\) 0 0
\(793\) −9.81393 + 16.9982i −0.348503 + 0.603625i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.69773 + 13.3329i −0.272668 + 0.472274i −0.969544 0.244917i \(-0.921239\pi\)
0.696876 + 0.717191i \(0.254573\pi\)
\(798\)