Properties

Label 2394.2.b.i.1709.7
Level $2394$
Weight $2$
Character 2394.1709
Analytic conductor $19.116$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1161862439\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \( x^{8} + 10x^{6} + 30x^{4} + 24x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{5}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1709.7
Root \(2.03530i\) of defining polynomial
Character \(\chi\) \(=\) 2394.1709
Dual form 2394.2.b.i.1709.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +3.02986i q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +3.02986i q^{5} -1.00000 q^{7} -1.00000 q^{8} -3.02986i q^{10} -4.70358i q^{11} +6.26603i q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.70358i q^{17} +(4.28832 + 0.781225i) q^{19} +3.02986i q^{20} +4.70358i q^{22} +0.460942i q^{23} -4.18005 q^{25} -6.26603i q^{26} -1.00000 q^{28} +3.18005 q^{29} +7.73344i q^{31} -1.00000 q^{32} +4.70358i q^{34} -3.02986i q^{35} -1.81708i q^{37} +(-4.28832 - 0.781225i) q^{38} -3.02986i q^{40} +8.40856 q^{41} +4.86151 q^{43} -4.70358i q^{44} -0.460942i q^{46} +12.5321i q^{47} +1.00000 q^{49} +4.18005 q^{50} +6.26603i q^{52} -11.3897 q^{53} +14.2512 q^{55} +1.00000 q^{56} -3.18005 q^{58} +5.46492 q^{61} -7.73344i q^{62} +1.00000 q^{64} -18.9852 q^{65} +12.0711i q^{67} -4.70358i q^{68} +3.02986i q^{70} -2.20964 q^{71} -13.2216 q^{73} +1.81708i q^{74} +(4.28832 + 0.781225i) q^{76} +4.70358i q^{77} +8.69159i q^{79} +3.02986i q^{80} -8.40856 q^{82} +8.37401i q^{83} +14.2512 q^{85} -4.86151 q^{86} +4.70358i q^{88} -6.19892 q^{89} -6.26603i q^{91} +0.460942i q^{92} -12.5321i q^{94} +(-2.36700 + 12.9930i) q^{95} +9.50221i q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{7} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{7} - 8 q^{8} + 8 q^{14} + 8 q^{16} + 12 q^{19} - 24 q^{25} - 8 q^{28} + 16 q^{29} - 8 q^{32} - 12 q^{38} - 24 q^{41} - 32 q^{43} + 8 q^{49} + 24 q^{50} - 48 q^{53} + 8 q^{56} - 16 q^{58} + 8 q^{61} + 8 q^{64} - 16 q^{65} + 16 q^{71} - 16 q^{73} + 12 q^{76} + 24 q^{82} + 32 q^{86} + 8 q^{89} - 8 q^{95} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(1009\) \(1711\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 3.02986i 1.35499i 0.735525 + 0.677497i \(0.236935\pi\)
−0.735525 + 0.677497i \(0.763065\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 3.02986i 0.958126i
\(11\) 4.70358i 1.41818i −0.705116 0.709092i \(-0.749105\pi\)
0.705116 0.709092i \(-0.250895\pi\)
\(12\) 0 0
\(13\) 6.26603i 1.73788i 0.494913 + 0.868942i \(0.335200\pi\)
−0.494913 + 0.868942i \(0.664800\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.70358i 1.14079i −0.821372 0.570393i \(-0.806791\pi\)
0.821372 0.570393i \(-0.193209\pi\)
\(18\) 0 0
\(19\) 4.28832 + 0.781225i 0.983808 + 0.179225i
\(20\) 3.02986i 0.677497i
\(21\) 0 0
\(22\) 4.70358i 1.00281i
\(23\) 0.460942i 0.0961131i 0.998845 + 0.0480565i \(0.0153028\pi\)
−0.998845 + 0.0480565i \(0.984697\pi\)
\(24\) 0 0
\(25\) −4.18005 −0.836010
\(26\) 6.26603i 1.22887i
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 3.18005 0.590520 0.295260 0.955417i \(-0.404594\pi\)
0.295260 + 0.955417i \(0.404594\pi\)
\(30\) 0 0
\(31\) 7.73344i 1.38897i 0.719508 + 0.694484i \(0.244367\pi\)
−0.719508 + 0.694484i \(0.755633\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.70358i 0.806658i
\(35\) 3.02986i 0.512140i
\(36\) 0 0
\(37\) 1.81708i 0.298726i −0.988782 0.149363i \(-0.952278\pi\)
0.988782 0.149363i \(-0.0477223\pi\)
\(38\) −4.28832 0.781225i −0.695657 0.126731i
\(39\) 0 0
\(40\) 3.02986i 0.479063i
\(41\) 8.40856 1.31320 0.656598 0.754241i \(-0.271995\pi\)
0.656598 + 0.754241i \(0.271995\pi\)
\(42\) 0 0
\(43\) 4.86151 0.741373 0.370687 0.928758i \(-0.379122\pi\)
0.370687 + 0.928758i \(0.379122\pi\)
\(44\) 4.70358i 0.709092i
\(45\) 0 0
\(46\) 0.460942i 0.0679622i
\(47\) 12.5321i 1.82799i 0.405726 + 0.913995i \(0.367019\pi\)
−0.405726 + 0.913995i \(0.632981\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 4.18005 0.591148
\(51\) 0 0
\(52\) 6.26603i 0.868942i
\(53\) −11.3897 −1.56449 −0.782247 0.622968i \(-0.785926\pi\)
−0.782247 + 0.622968i \(0.785926\pi\)
\(54\) 0 0
\(55\) 14.2512 1.92163
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −3.18005 −0.417561
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 5.46492 0.699711 0.349856 0.936804i \(-0.386231\pi\)
0.349856 + 0.936804i \(0.386231\pi\)
\(62\) 7.73344i 0.982148i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −18.9852 −2.35482
\(66\) 0 0
\(67\) 12.0711i 1.47472i 0.675499 + 0.737361i \(0.263928\pi\)
−0.675499 + 0.737361i \(0.736072\pi\)
\(68\) 4.70358i 0.570393i
\(69\) 0 0
\(70\) 3.02986i 0.362137i
\(71\) −2.20964 −0.262236 −0.131118 0.991367i \(-0.541857\pi\)
−0.131118 + 0.991367i \(0.541857\pi\)
\(72\) 0 0
\(73\) −13.2216 −1.54747 −0.773736 0.633508i \(-0.781614\pi\)
−0.773736 + 0.633508i \(0.781614\pi\)
\(74\) 1.81708i 0.211231i
\(75\) 0 0
\(76\) 4.28832 + 0.781225i 0.491904 + 0.0896126i
\(77\) 4.70358i 0.536023i
\(78\) 0 0
\(79\) 8.69159i 0.977881i 0.872317 + 0.488940i \(0.162616\pi\)
−0.872317 + 0.488940i \(0.837384\pi\)
\(80\) 3.02986i 0.338749i
\(81\) 0 0
\(82\) −8.40856 −0.928570
\(83\) 8.37401i 0.919167i 0.888135 + 0.459583i \(0.152001\pi\)
−0.888135 + 0.459583i \(0.847999\pi\)
\(84\) 0 0
\(85\) 14.2512 1.54576
\(86\) −4.86151 −0.524230
\(87\) 0 0
\(88\) 4.70358i 0.501404i
\(89\) −6.19892 −0.657084 −0.328542 0.944489i \(-0.606557\pi\)
−0.328542 + 0.944489i \(0.606557\pi\)
\(90\) 0 0
\(91\) 6.26603i 0.656859i
\(92\) 0.460942i 0.0480565i
\(93\) 0 0
\(94\) 12.5321i 1.29258i
\(95\) −2.36700 + 12.9930i −0.242849 + 1.33305i
\(96\) 0 0
\(97\) 9.50221i 0.964803i 0.875950 + 0.482401i \(0.160235\pi\)
−0.875950 + 0.482401i \(0.839765\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −4.18005 −0.418005
\(101\) 15.5619i 1.54847i −0.632899 0.774235i \(-0.718135\pi\)
0.632899 0.774235i \(-0.281865\pi\)
\(102\) 0 0
\(103\) 12.2307i 1.20513i −0.798071 0.602564i \(-0.794146\pi\)
0.798071 0.602564i \(-0.205854\pi\)
\(104\) 6.26603i 0.614435i
\(105\) 0 0
\(106\) 11.3897 1.10626
\(107\) −6.29177 −0.608248 −0.304124 0.952632i \(-0.598364\pi\)
−0.304124 + 0.952632i \(0.598364\pi\)
\(108\) 0 0
\(109\) 17.9245i 1.71686i −0.512932 0.858429i \(-0.671441\pi\)
0.512932 0.858429i \(-0.328559\pi\)
\(110\) −14.2512 −1.35880
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) −18.0831 −1.70112 −0.850558 0.525881i \(-0.823736\pi\)
−0.850558 + 0.525881i \(0.823736\pi\)
\(114\) 0 0
\(115\) −1.39659 −0.130233
\(116\) 3.18005 0.295260
\(117\) 0 0
\(118\) 0 0
\(119\) 4.70358i 0.431177i
\(120\) 0 0
\(121\) −11.1237 −1.01124
\(122\) −5.46492 −0.494770
\(123\) 0 0
\(124\) 7.73344i 0.694484i
\(125\) 2.48433i 0.222206i
\(126\) 0 0
\(127\) 7.18792i 0.637824i −0.947784 0.318912i \(-0.896682\pi\)
0.947784 0.318912i \(-0.103318\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 18.9852 1.66511
\(131\) 16.6314i 1.45309i 0.687120 + 0.726544i \(0.258875\pi\)
−0.687120 + 0.726544i \(0.741125\pi\)
\(132\) 0 0
\(133\) −4.28832 0.781225i −0.371844 0.0677408i
\(134\) 12.0711i 1.04279i
\(135\) 0 0
\(136\) 4.70358i 0.403329i
\(137\) 5.16452i 0.441235i −0.975360 0.220618i \(-0.929193\pi\)
0.975360 0.220618i \(-0.0708073\pi\)
\(138\) 0 0
\(139\) −20.9890 −1.78026 −0.890132 0.455702i \(-0.849388\pi\)
−0.890132 + 0.455702i \(0.849388\pi\)
\(140\) 3.02986i 0.256070i
\(141\) 0 0
\(142\) 2.20964 0.185429
\(143\) 29.4728 2.46464
\(144\) 0 0
\(145\) 9.63510i 0.800152i
\(146\) 13.2216 1.09423
\(147\) 0 0
\(148\) 1.81708i 0.149363i
\(149\) 0.921884i 0.0755237i −0.999287 0.0377619i \(-0.987977\pi\)
0.999287 0.0377619i \(-0.0120228\pi\)
\(150\) 0 0
\(151\) 16.3725i 1.33238i 0.745783 + 0.666189i \(0.232076\pi\)
−0.745783 + 0.666189i \(0.767924\pi\)
\(152\) −4.28832 0.781225i −0.347829 0.0633657i
\(153\) 0 0
\(154\) 4.70358i 0.379026i
\(155\) −23.4312 −1.88204
\(156\) 0 0
\(157\) −8.69343 −0.693811 −0.346906 0.937900i \(-0.612768\pi\)
−0.346906 + 0.937900i \(0.612768\pi\)
\(158\) 8.69159i 0.691466i
\(159\) 0 0
\(160\) 3.02986i 0.239531i
\(161\) 0.460942i 0.0363273i
\(162\) 0 0
\(163\) 8.12750 0.636595 0.318298 0.947991i \(-0.396889\pi\)
0.318298 + 0.947991i \(0.396889\pi\)
\(164\) 8.40856 0.656598
\(165\) 0 0
\(166\) 8.37401i 0.649949i
\(167\) 23.1127 1.78851 0.894257 0.447553i \(-0.147704\pi\)
0.894257 + 0.447553i \(0.147704\pi\)
\(168\) 0 0
\(169\) −26.2632 −2.02024
\(170\) −14.2512 −1.09302
\(171\) 0 0
\(172\) 4.86151 0.370687
\(173\) −6.29177 −0.478355 −0.239177 0.970976i \(-0.576878\pi\)
−0.239177 + 0.970976i \(0.576878\pi\)
\(174\) 0 0
\(175\) 4.18005 0.315982
\(176\) 4.70358i 0.354546i
\(177\) 0 0
\(178\) 6.19892 0.464629
\(179\) −4.15046 −0.310220 −0.155110 0.987897i \(-0.549573\pi\)
−0.155110 + 0.987897i \(0.549573\pi\)
\(180\) 0 0
\(181\) 24.6677i 1.83354i 0.399417 + 0.916769i \(0.369212\pi\)
−0.399417 + 0.916769i \(0.630788\pi\)
\(182\) 6.26603i 0.464469i
\(183\) 0 0
\(184\) 0.460942i 0.0339811i
\(185\) 5.50549 0.404772
\(186\) 0 0
\(187\) −22.1237 −1.61784
\(188\) 12.5321i 0.913995i
\(189\) 0 0
\(190\) 2.36700 12.9930i 0.171720 0.942612i
\(191\) 1.51413i 0.109559i 0.998498 + 0.0547795i \(0.0174456\pi\)
−0.998498 + 0.0547795i \(0.982554\pi\)
\(192\) 0 0
\(193\) 13.3952i 0.964206i 0.876115 + 0.482103i \(0.160127\pi\)
−0.876115 + 0.482103i \(0.839873\pi\)
\(194\) 9.50221i 0.682219i
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 12.5321i 0.892873i −0.894815 0.446436i \(-0.852693\pi\)
0.894815 0.446436i \(-0.147307\pi\)
\(198\) 0 0
\(199\) 21.3453 1.51313 0.756564 0.653920i \(-0.226877\pi\)
0.756564 + 0.653920i \(0.226877\pi\)
\(200\) 4.18005 0.295574
\(201\) 0 0
\(202\) 15.5619i 1.09493i
\(203\) −3.18005 −0.223196
\(204\) 0 0
\(205\) 25.4768i 1.77937i
\(206\) 12.2307i 0.852154i
\(207\) 0 0
\(208\) 6.26603i 0.434471i
\(209\) 3.67456 20.1705i 0.254174 1.39522i
\(210\) 0 0
\(211\) 2.02339i 0.139296i 0.997572 + 0.0696480i \(0.0221876\pi\)
−0.997572 + 0.0696480i \(0.977812\pi\)
\(212\) −11.3897 −0.782247
\(213\) 0 0
\(214\) 6.29177 0.430097
\(215\) 14.7297i 1.00456i
\(216\) 0 0
\(217\) 7.73344i 0.524980i
\(218\) 17.9245i 1.21400i
\(219\) 0 0
\(220\) 14.2512 0.960815
\(221\) 29.4728 1.98256
\(222\) 0 0
\(223\) 3.04609i 0.203981i −0.994785 0.101991i \(-0.967479\pi\)
0.994785 0.101991i \(-0.0325212\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 18.0831 1.20287
\(227\) 7.89110 0.523750 0.261875 0.965102i \(-0.415659\pi\)
0.261875 + 0.965102i \(0.415659\pi\)
\(228\) 0 0
\(229\) 8.12369 0.536829 0.268414 0.963304i \(-0.413500\pi\)
0.268414 + 0.963304i \(0.413500\pi\)
\(230\) 1.39659 0.0920884
\(231\) 0 0
\(232\) −3.18005 −0.208780
\(233\) 12.2774i 0.804322i 0.915569 + 0.402161i \(0.131741\pi\)
−0.915569 + 0.402161i \(0.868259\pi\)
\(234\) 0 0
\(235\) −37.9704 −2.47692
\(236\) 0 0
\(237\) 0 0
\(238\) 4.70358i 0.304888i
\(239\) 15.0647i 0.974455i 0.873275 + 0.487228i \(0.161992\pi\)
−0.873275 + 0.487228i \(0.838008\pi\)
\(240\) 0 0
\(241\) 4.53354i 0.292031i −0.989282 0.146015i \(-0.953355\pi\)
0.989282 0.146015i \(-0.0466449\pi\)
\(242\) 11.1237 0.715058
\(243\) 0 0
\(244\) 5.46492 0.349856
\(245\) 3.02986i 0.193571i
\(246\) 0 0
\(247\) −4.89518 + 26.8708i −0.311473 + 1.70975i
\(248\) 7.73344i 0.491074i
\(249\) 0 0
\(250\) 2.48433i 0.157123i
\(251\) 25.4033i 1.60344i 0.597697 + 0.801722i \(0.296083\pi\)
−0.597697 + 0.801722i \(0.703917\pi\)
\(252\) 0 0
\(253\) 2.16808 0.136306
\(254\) 7.18792i 0.451010i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 23.9219 1.49221 0.746105 0.665829i \(-0.231922\pi\)
0.746105 + 0.665829i \(0.231922\pi\)
\(258\) 0 0
\(259\) 1.81708i 0.112908i
\(260\) −18.9852 −1.17741
\(261\) 0 0
\(262\) 16.6314i 1.02749i
\(263\) 11.9398i 0.736241i −0.929778 0.368120i \(-0.880001\pi\)
0.929778 0.368120i \(-0.119999\pi\)
\(264\) 0 0
\(265\) 34.5092i 2.11988i
\(266\) 4.28832 + 0.781225i 0.262934 + 0.0479000i
\(267\) 0 0
\(268\) 12.0711i 0.737361i
\(269\) −7.91787 −0.482761 −0.241380 0.970431i \(-0.577600\pi\)
−0.241380 + 0.970431i \(0.577600\pi\)
\(270\) 0 0
\(271\) 5.87348 0.356788 0.178394 0.983959i \(-0.442910\pi\)
0.178394 + 0.983959i \(0.442910\pi\)
\(272\) 4.70358i 0.285197i
\(273\) 0 0
\(274\) 5.16452i 0.312000i
\(275\) 19.6612i 1.18562i
\(276\) 0 0
\(277\) 15.4542 0.928553 0.464277 0.885690i \(-0.346314\pi\)
0.464277 + 0.885690i \(0.346314\pi\)
\(278\) 20.9890 1.25884
\(279\) 0 0
\(280\) 3.02986i 0.181069i
\(281\) 16.7794 1.00097 0.500487 0.865744i \(-0.333154\pi\)
0.500487 + 0.865744i \(0.333154\pi\)
\(282\) 0 0
\(283\) −1.63300 −0.0970717 −0.0485358 0.998821i \(-0.515456\pi\)
−0.0485358 + 0.998821i \(0.515456\pi\)
\(284\) −2.20964 −0.131118
\(285\) 0 0
\(286\) −29.4728 −1.74276
\(287\) −8.40856 −0.496342
\(288\) 0 0
\(289\) −5.12369 −0.301394
\(290\) 9.63510i 0.565793i
\(291\) 0 0
\(292\) −13.2216 −0.773736
\(293\) −29.7913 −1.74043 −0.870214 0.492673i \(-0.836020\pi\)
−0.870214 + 0.492673i \(0.836020\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.81708i 0.105616i
\(297\) 0 0
\(298\) 0.921884i 0.0534033i
\(299\) −2.88828 −0.167033
\(300\) 0 0
\(301\) −4.86151 −0.280213
\(302\) 16.3725i 0.942134i
\(303\) 0 0
\(304\) 4.28832 + 0.781225i 0.245952 + 0.0448063i
\(305\) 16.5579i 0.948105i
\(306\) 0 0
\(307\) 12.2454i 0.698879i 0.936959 + 0.349440i \(0.113628\pi\)
−0.936959 + 0.349440i \(0.886372\pi\)
\(308\) 4.70358i 0.268012i
\(309\) 0 0
\(310\) 23.4312 1.33081
\(311\) 17.4798i 0.991190i 0.868554 + 0.495595i \(0.165050\pi\)
−0.868554 + 0.495595i \(0.834950\pi\)
\(312\) 0 0
\(313\) −11.1533 −0.630421 −0.315210 0.949022i \(-0.602075\pi\)
−0.315210 + 0.949022i \(0.602075\pi\)
\(314\) 8.69343 0.490599
\(315\) 0 0
\(316\) 8.69159i 0.488940i
\(317\) −4.01380 −0.225438 −0.112719 0.993627i \(-0.535956\pi\)
−0.112719 + 0.993627i \(0.535956\pi\)
\(318\) 0 0
\(319\) 14.9576i 0.837466i
\(320\) 3.02986i 0.169374i
\(321\) 0 0
\(322\) 0.460942i 0.0256873i
\(323\) 3.67456 20.1705i 0.204458 1.12231i
\(324\) 0 0
\(325\) 26.1923i 1.45289i
\(326\) −8.12750 −0.450141
\(327\) 0 0
\(328\) −8.40856 −0.464285
\(329\) 12.5321i 0.690915i
\(330\) 0 0
\(331\) 9.45548i 0.519720i −0.965646 0.259860i \(-0.916324\pi\)
0.965646 0.259860i \(-0.0836765\pi\)
\(332\) 8.37401i 0.459583i
\(333\) 0 0
\(334\) −23.1127 −1.26467
\(335\) −36.5738 −1.99824
\(336\) 0 0
\(337\) 30.2932i 1.65018i 0.565004 + 0.825088i \(0.308875\pi\)
−0.565004 + 0.825088i \(0.691125\pi\)
\(338\) 26.2632 1.42853
\(339\) 0 0
\(340\) 14.2512 0.772880
\(341\) 36.3749 1.96981
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −4.86151 −0.262115
\(345\) 0 0
\(346\) 6.29177 0.338248
\(347\) 13.6015i 0.730166i 0.930975 + 0.365083i \(0.118959\pi\)
−0.930975 + 0.365083i \(0.881041\pi\)
\(348\) 0 0
\(349\) 6.61820 0.354264 0.177132 0.984187i \(-0.443318\pi\)
0.177132 + 0.984187i \(0.443318\pi\)
\(350\) −4.18005 −0.223433
\(351\) 0 0
\(352\) 4.70358i 0.250702i
\(353\) 6.20726i 0.330379i −0.986262 0.165190i \(-0.947176\pi\)
0.986262 0.165190i \(-0.0528236\pi\)
\(354\) 0 0
\(355\) 6.69489i 0.355328i
\(356\) −6.19892 −0.328542
\(357\) 0 0
\(358\) 4.15046 0.219359
\(359\) 24.1906i 1.27673i 0.769734 + 0.638365i \(0.220389\pi\)
−0.769734 + 0.638365i \(0.779611\pi\)
\(360\) 0 0
\(361\) 17.7794 + 6.70028i 0.935757 + 0.352647i
\(362\) 24.6677i 1.29651i
\(363\) 0 0
\(364\) 6.26603i 0.328429i
\(365\) 40.0596i 2.09682i
\(366\) 0 0
\(367\) 4.88447 0.254967 0.127484 0.991841i \(-0.459310\pi\)
0.127484 + 0.991841i \(0.459310\pi\)
\(368\) 0.460942i 0.0240283i
\(369\) 0 0
\(370\) −5.50549 −0.286217
\(371\) 11.3897 0.591323
\(372\) 0 0
\(373\) 7.08083i 0.366631i 0.983054 + 0.183316i \(0.0586831\pi\)
−0.983054 + 0.183316i \(0.941317\pi\)
\(374\) 22.1237 1.14399
\(375\) 0 0
\(376\) 12.5321i 0.646292i
\(377\) 19.9263i 1.02626i
\(378\) 0 0
\(379\) 31.1134i 1.59819i −0.601206 0.799094i \(-0.705313\pi\)
0.601206 0.799094i \(-0.294687\pi\)
\(380\) −2.36700 + 12.9930i −0.121425 + 0.666527i
\(381\) 0 0
\(382\) 1.51413i 0.0774699i
\(383\) −23.6569 −1.20881 −0.604407 0.796676i \(-0.706590\pi\)
−0.604407 + 0.796676i \(0.706590\pi\)
\(384\) 0 0
\(385\) −14.2512 −0.726308
\(386\) 13.3952i 0.681797i
\(387\) 0 0
\(388\) 9.50221i 0.482401i
\(389\) 0.731804i 0.0371039i 0.999828 + 0.0185520i \(0.00590561\pi\)
−0.999828 + 0.0185520i \(0.994094\pi\)
\(390\) 0 0
\(391\) 2.16808 0.109644
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) 12.5321i 0.631356i
\(395\) −26.3343 −1.32502
\(396\) 0 0
\(397\) −5.59933 −0.281022 −0.140511 0.990079i \(-0.544875\pi\)
−0.140511 + 0.990079i \(0.544875\pi\)
\(398\) −21.3453 −1.06994
\(399\) 0 0
\(400\) −4.18005 −0.209002
\(401\) −5.77274 −0.288277 −0.144139 0.989558i \(-0.546041\pi\)
−0.144139 + 0.989558i \(0.546041\pi\)
\(402\) 0 0
\(403\) −48.4580 −2.41387
\(404\) 15.5619i 0.774235i
\(405\) 0 0
\(406\) 3.18005 0.157823
\(407\) −8.54678 −0.423648
\(408\) 0 0
\(409\) 10.7779i 0.532935i −0.963844 0.266468i \(-0.914143\pi\)
0.963844 0.266468i \(-0.0858565\pi\)
\(410\) 25.4768i 1.25821i
\(411\) 0 0
\(412\) 12.2307i 0.602564i
\(413\) 0 0
\(414\) 0 0
\(415\) −25.3721 −1.24547
\(416\) 6.26603i 0.307218i
\(417\) 0 0
\(418\) −3.67456 + 20.1705i −0.179728 + 0.986570i
\(419\) 2.53684i 0.123933i 0.998078 + 0.0619663i \(0.0197371\pi\)
−0.998078 + 0.0619663i \(0.980263\pi\)
\(420\) 0 0
\(421\) 11.6956i 0.570011i −0.958526 0.285005i \(-0.908005\pi\)
0.958526 0.285005i \(-0.0919954\pi\)
\(422\) 2.02339i 0.0984972i
\(423\) 0 0
\(424\) 11.3897 0.553132
\(425\) 19.6612i 0.953709i
\(426\) 0 0
\(427\) −5.46492 −0.264466
\(428\) −6.29177 −0.304124
\(429\) 0 0
\(430\) 14.7297i 0.710329i
\(431\) 35.4690 1.70848 0.854241 0.519878i \(-0.174023\pi\)
0.854241 + 0.519878i \(0.174023\pi\)
\(432\) 0 0
\(433\) 15.1493i 0.728029i 0.931393 + 0.364014i \(0.118594\pi\)
−0.931393 + 0.364014i \(0.881406\pi\)
\(434\) 7.73344i 0.371217i
\(435\) 0 0
\(436\) 17.9245i 0.858429i
\(437\) −0.360100 + 1.97667i −0.0172259 + 0.0945568i
\(438\) 0 0
\(439\) 25.5293i 1.21845i −0.792999 0.609223i \(-0.791482\pi\)
0.792999 0.609223i \(-0.208518\pi\)
\(440\) −14.2512 −0.679399
\(441\) 0 0
\(442\) −29.4728 −1.40188
\(443\) 4.29096i 0.203869i −0.994791 0.101935i \(-0.967497\pi\)
0.994791 0.101935i \(-0.0325033\pi\)
\(444\) 0 0
\(445\) 18.7819i 0.890346i
\(446\) 3.04609i 0.144237i
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) 11.4542 0.540557 0.270279 0.962782i \(-0.412884\pi\)
0.270279 + 0.962782i \(0.412884\pi\)
\(450\) 0 0
\(451\) 39.5504i 1.86235i
\(452\) −18.0831 −0.850558
\(453\) 0 0
\(454\) −7.89110 −0.370348
\(455\) 18.9852 0.890040
\(456\) 0 0
\(457\) −2.04058 −0.0954541 −0.0477270 0.998860i \(-0.515198\pi\)
−0.0477270 + 0.998860i \(0.515198\pi\)
\(458\) −8.12369 −0.379595
\(459\) 0 0
\(460\) −1.39659 −0.0651163
\(461\) 12.0244i 0.560032i 0.959995 + 0.280016i \(0.0903398\pi\)
−0.959995 + 0.280016i \(0.909660\pi\)
\(462\) 0 0
\(463\) 36.2484 1.68460 0.842302 0.539006i \(-0.181200\pi\)
0.842302 + 0.539006i \(0.181200\pi\)
\(464\) 3.18005 0.147630
\(465\) 0 0
\(466\) 12.2774i 0.568741i
\(467\) 25.4621i 1.17825i −0.808043 0.589123i \(-0.799473\pi\)
0.808043 0.589123i \(-0.200527\pi\)
\(468\) 0 0
\(469\) 12.0711i 0.557393i
\(470\) 37.9704 1.75144
\(471\) 0 0
\(472\) 0 0
\(473\) 22.8665i 1.05140i
\(474\) 0 0
\(475\) −17.9254 3.26556i −0.822473 0.149834i
\(476\) 4.70358i 0.215588i
\(477\) 0 0
\(478\) 15.0647i 0.689044i
\(479\) 11.6102i 0.530483i −0.964182 0.265241i \(-0.914548\pi\)
0.964182 0.265241i \(-0.0854516\pi\)
\(480\) 0 0
\(481\) 11.3859 0.519151
\(482\) 4.53354i 0.206497i
\(483\) 0 0
\(484\) −11.1237 −0.505622
\(485\) −28.7904 −1.30730
\(486\) 0 0
\(487\) 9.10422i 0.412552i −0.978494 0.206276i \(-0.933866\pi\)
0.978494 0.206276i \(-0.0661344\pi\)
\(488\) −5.46492 −0.247385
\(489\) 0 0
\(490\) 3.02986i 0.136875i
\(491\) 10.5408i 0.475698i −0.971302 0.237849i \(-0.923558\pi\)
0.971302 0.237849i \(-0.0764423\pi\)
\(492\) 0 0
\(493\) 14.9576i 0.673658i
\(494\) 4.89518 26.8708i 0.220245 1.20897i
\(495\) 0 0
\(496\) 7.73344i 0.347242i
\(497\) 2.20964 0.0991158
\(498\) 0 0
\(499\) 34.4432 1.54189 0.770945 0.636902i \(-0.219784\pi\)
0.770945 + 0.636902i \(0.219784\pi\)
\(500\) 2.48433i 0.111103i
\(501\) 0 0
\(502\) 25.4033i 1.13381i
\(503\) 15.9174i 0.709720i −0.934919 0.354860i \(-0.884528\pi\)
0.934919 0.354860i \(-0.115472\pi\)
\(504\) 0 0
\(505\) 47.1504 2.09817
\(506\) −2.16808 −0.0963829
\(507\) 0 0
\(508\) 7.18792i 0.318912i
\(509\) 36.9436 1.63750 0.818749 0.574152i \(-0.194668\pi\)
0.818749 + 0.574152i \(0.194668\pi\)
\(510\) 0 0
\(511\) 13.2216 0.584890
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −23.9219 −1.05515
\(515\) 37.0573 1.63294
\(516\) 0 0
\(517\) 58.9456 2.59242
\(518\) 1.81708i 0.0798379i
\(519\) 0 0
\(520\) 18.9852 0.832556
\(521\) −23.7952 −1.04248 −0.521242 0.853409i \(-0.674531\pi\)
−0.521242 + 0.853409i \(0.674531\pi\)
\(522\) 0 0
\(523\) 0.980657i 0.0428811i 0.999770 + 0.0214406i \(0.00682526\pi\)
−0.999770 + 0.0214406i \(0.993175\pi\)
\(524\) 16.6314i 0.726544i
\(525\) 0 0
\(526\) 11.9398i 0.520601i
\(527\) 36.3749 1.58451
\(528\) 0 0
\(529\) 22.7875 0.990762
\(530\) 34.5092i 1.49898i
\(531\) 0 0
\(532\) −4.28832 0.781225i −0.185922 0.0338704i
\(533\) 52.6883i 2.28218i
\(534\) 0 0
\(535\) 19.0632i 0.824173i
\(536\) 12.0711i 0.521393i
\(537\) 0 0
\(538\) 7.91787 0.341363
\(539\) 4.70358i 0.202598i
\(540\) 0 0
\(541\) −16.0869 −0.691631 −0.345816 0.938303i \(-0.612398\pi\)
−0.345816 + 0.938303i \(0.612398\pi\)
\(542\) −5.87348 −0.252288
\(543\) 0 0
\(544\) 4.70358i 0.201664i
\(545\) 54.3088 2.32633
\(546\) 0 0
\(547\) 18.3534i 0.784734i −0.919809 0.392367i \(-0.871656\pi\)
0.919809 0.392367i \(-0.128344\pi\)
\(548\) 5.16452i 0.220618i
\(549\) 0 0
\(550\) 19.6612i 0.838357i
\(551\) 13.6371 + 2.48433i 0.580959 + 0.105836i
\(552\) 0 0
\(553\) 8.69159i 0.369604i
\(554\) −15.4542 −0.656586
\(555\) 0 0
\(556\) −20.9890 −0.890132
\(557\) 29.1109i 1.23347i 0.787171 + 0.616735i \(0.211545\pi\)
−0.787171 + 0.616735i \(0.788455\pi\)
\(558\) 0 0
\(559\) 30.4624i 1.28842i
\(560\) 3.02986i 0.128035i
\(561\) 0 0
\(562\) −16.7794 −0.707795
\(563\) 34.8625 1.46928 0.734639 0.678458i \(-0.237351\pi\)
0.734639 + 0.678458i \(0.237351\pi\)
\(564\) 0 0
\(565\) 54.7893i 2.30500i
\(566\) 1.63300 0.0686400
\(567\) 0 0
\(568\) 2.20964 0.0927143
\(569\) −20.5736 −0.862488 −0.431244 0.902235i \(-0.641925\pi\)
−0.431244 + 0.902235i \(0.641925\pi\)
\(570\) 0 0
\(571\) −18.5014 −0.774260 −0.387130 0.922025i \(-0.626534\pi\)
−0.387130 + 0.922025i \(0.626534\pi\)
\(572\) 29.4728 1.23232
\(573\) 0 0
\(574\) 8.40856 0.350967
\(575\) 1.92676i 0.0803515i
\(576\) 0 0
\(577\) 30.5392 1.27136 0.635681 0.771952i \(-0.280719\pi\)
0.635681 + 0.771952i \(0.280719\pi\)
\(578\) 5.12369 0.213117
\(579\) 0 0
\(580\) 9.63510i 0.400076i
\(581\) 8.37401i 0.347412i
\(582\) 0 0
\(583\) 53.5723i 2.21874i
\(584\) 13.2216 0.547114
\(585\) 0 0
\(586\) 29.7913 1.23067
\(587\) 13.3427i 0.550711i −0.961342 0.275356i \(-0.911204\pi\)
0.961342 0.275356i \(-0.0887956\pi\)
\(588\) 0 0
\(589\) −6.04156 + 33.1635i −0.248938 + 1.36648i
\(590\) 0 0
\(591\) 0 0
\(592\) 1.81708i 0.0746815i
\(593\) 12.8938i 0.529484i 0.964319 + 0.264742i \(0.0852868\pi\)
−0.964319 + 0.264742i \(0.914713\pi\)
\(594\) 0 0
\(595\) −14.2512 −0.584242
\(596\) 0.921884i 0.0377619i
\(597\) 0 0
\(598\) 2.88828 0.118110
\(599\) 1.48944 0.0608568 0.0304284 0.999537i \(-0.490313\pi\)
0.0304284 + 0.999537i \(0.490313\pi\)
\(600\) 0 0
\(601\) 30.1603i 1.23026i −0.788424 0.615132i \(-0.789103\pi\)
0.788424 0.615132i \(-0.210897\pi\)
\(602\) 4.86151 0.198140
\(603\) 0 0
\(604\) 16.3725i 0.666189i
\(605\) 33.7032i 1.37023i
\(606\) 0 0
\(607\) 9.64975i 0.391671i −0.980637 0.195836i \(-0.937258\pi\)
0.980637 0.195836i \(-0.0627419\pi\)
\(608\) −4.28832 0.781225i −0.173914 0.0316829i
\(609\) 0 0
\(610\) 16.5579i 0.670411i
\(611\) −78.5263 −3.17684
\(612\) 0 0
\(613\) 44.5401 1.79896 0.899480 0.436963i \(-0.143946\pi\)
0.899480 + 0.436963i \(0.143946\pi\)
\(614\) 12.2454i 0.494182i
\(615\) 0 0
\(616\) 4.70358i 0.189513i
\(617\) 22.9603i 0.924349i −0.886789 0.462174i \(-0.847069\pi\)
0.886789 0.462174i \(-0.152931\pi\)
\(618\) 0 0
\(619\) 2.36293 0.0949741 0.0474871 0.998872i \(-0.484879\pi\)
0.0474871 + 0.998872i \(0.484879\pi\)
\(620\) −23.4312 −0.941021
\(621\) 0 0
\(622\) 17.4798i 0.700877i
\(623\) 6.19892 0.248355
\(624\) 0 0
\(625\) −28.4274 −1.13710
\(626\) 11.1533 0.445775
\(627\) 0 0
\(628\) −8.69343 −0.346906
\(629\) −8.54678 −0.340782
\(630\) 0 0
\(631\) 10.2234 0.406989 0.203494 0.979076i \(-0.434770\pi\)
0.203494 + 0.979076i \(0.434770\pi\)
\(632\) 8.69159i 0.345733i
\(633\) 0 0
\(634\) 4.01380 0.159409
\(635\) 21.7784 0.864249
\(636\) 0 0
\(637\) 6.26603i 0.248269i
\(638\) 14.9576i 0.592178i
\(639\) 0 0
\(640\) 3.02986i 0.119766i
\(641\) −41.2603 −1.62969 −0.814843 0.579682i \(-0.803177\pi\)
−0.814843 + 0.579682i \(0.803177\pi\)
\(642\) 0 0
\(643\) −46.7765 −1.84469 −0.922343 0.386371i \(-0.873728\pi\)
−0.922343 + 0.386371i \(0.873728\pi\)
\(644\) 0.460942i 0.0181637i
\(645\) 0 0
\(646\) −3.67456 + 20.1705i −0.144573 + 0.793596i
\(647\) 10.1065i 0.397328i 0.980068 + 0.198664i \(0.0636602\pi\)
−0.980068 + 0.198664i \(0.936340\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 26.1923i 1.02735i
\(651\) 0 0
\(652\) 8.12750 0.318298
\(653\) 5.13784i 0.201059i 0.994934 + 0.100530i \(0.0320537\pi\)
−0.994934 + 0.100530i \(0.967946\pi\)
\(654\) 0 0
\(655\) −50.3907 −1.96893
\(656\) 8.40856 0.328299
\(657\) 0 0
\(658\) 12.5321i 0.488551i
\(659\) 43.3639 1.68922 0.844609 0.535384i \(-0.179833\pi\)
0.844609 + 0.535384i \(0.179833\pi\)
\(660\) 0 0
\(661\) 44.0314i 1.71262i −0.516460 0.856311i \(-0.672750\pi\)
0.516460 0.856311i \(-0.327250\pi\)
\(662\) 9.45548i 0.367498i
\(663\) 0 0
\(664\) 8.37401i 0.324975i
\(665\) 2.36700 12.9930i 0.0917884 0.503847i
\(666\) 0 0
\(667\) 1.46582i 0.0567567i
\(668\) 23.1127 0.894257
\(669\) 0 0
\(670\) 36.5738 1.41297
\(671\) 25.7047i 0.992319i
\(672\) 0 0
\(673\) 21.8133i 0.840842i −0.907329 0.420421i \(-0.861882\pi\)
0.907329 0.420421i \(-0.138118\pi\)
\(674\) 30.2932i 1.16685i
\(675\) 0 0
\(676\) −26.2632 −1.01012
\(677\) −8.81614 −0.338832 −0.169416 0.985545i \(-0.554188\pi\)
−0.169416 + 0.985545i \(0.554188\pi\)
\(678\) 0 0
\(679\) 9.50221i 0.364661i
\(680\) −14.2512 −0.546508
\(681\) 0 0
\(682\) −36.3749 −1.39287
\(683\) 0.254026 0.00972003 0.00486002 0.999988i \(-0.498453\pi\)
0.00486002 + 0.999988i \(0.498453\pi\)
\(684\) 0 0
\(685\) 15.6478 0.597871
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) 4.86151 0.185343
\(689\) 71.3682i 2.71891i
\(690\) 0 0
\(691\) −12.4331 −0.472977 −0.236488 0.971634i \(-0.575997\pi\)
−0.236488 + 0.971634i \(0.575997\pi\)
\(692\) −6.29177 −0.239177
\(693\) 0 0
\(694\) 13.6015i 0.516306i
\(695\) 63.5938i 2.41225i
\(696\) 0 0
\(697\) 39.5504i 1.49808i
\(698\) −6.61820 −0.250502
\(699\) 0 0
\(700\) 4.18005 0.157991
\(701\) 23.1215i 0.873288i −0.899634 0.436644i \(-0.856167\pi\)
0.899634 0.436644i \(-0.143833\pi\)
\(702\) 0 0
\(703\) 1.41955 7.79221i 0.0535392 0.293889i
\(704\) 4.70358i 0.177273i
\(705\) 0 0
\(706\) 6.20726i 0.233613i
\(707\) 15.5619i 0.585266i
\(708\) 0 0
\(709\) −18.3425 −0.688866 −0.344433 0.938811i \(-0.611929\pi\)
−0.344433 + 0.938811i \(0.611929\pi\)
\(710\) 6.69489i 0.251255i
\(711\) 0 0
\(712\) 6.19892 0.232314
\(713\) −3.56467 −0.133498
\(714\) 0 0
\(715\) 89.2985i 3.33957i
\(716\) −4.15046 −0.155110
\(717\) 0 0
\(718\) 24.1906i 0.902784i
\(719\) 35.7903i 1.33475i 0.744721 + 0.667376i \(0.232583\pi\)
−0.744721 + 0.667376i \(0.767417\pi\)
\(720\) 0 0
\(721\) 12.2307i 0.455496i
\(722\) −17.7794 6.70028i −0.661680 0.249359i
\(723\) 0 0
\(724\) 24.6677i 0.916769i
\(725\) −13.2928 −0.493681
\(726\) 0 0
\(727\) 3.98620 0.147840 0.0739199 0.997264i \(-0.476449\pi\)
0.0739199 + 0.997264i \(0.476449\pi\)
\(728\) 6.26603i 0.232235i
\(729\) 0 0
\(730\) 40.0596i 1.48267i
\(731\) 22.8665i 0.845748i
\(732\) 0 0
\(733\) −28.3274 −1.04630 −0.523148 0.852242i \(-0.675243\pi\)
−0.523148 + 0.852242i \(0.675243\pi\)
\(734\) −4.88447 −0.180289
\(735\) 0 0
\(736\) 0.460942i 0.0169906i
\(737\) 56.7775 2.09143
\(738\) 0 0
\(739\) −48.4794 −1.78334 −0.891672 0.452681i \(-0.850468\pi\)
−0.891672 + 0.452681i \(0.850468\pi\)
\(740\) 5.50549 0.202386
\(741\) 0 0
\(742\) −11.3897 −0.418129
\(743\) 9.17624 0.336643 0.168322 0.985732i \(-0.446165\pi\)
0.168322 + 0.985732i \(0.446165\pi\)
\(744\) 0 0
\(745\) 2.79318 0.102334
\(746\) 7.08083i 0.259248i
\(747\) 0 0
\(748\) −22.1237 −0.808922
\(749\) 6.29177 0.229896
\(750\) 0 0
\(751\) 33.8848i 1.23647i −0.785991 0.618237i \(-0.787847\pi\)
0.785991 0.618237i \(-0.212153\pi\)
\(752\) 12.5321i 0.456997i
\(753\) 0 0
\(754\) 19.9263i 0.725673i
\(755\) −49.6065 −1.80536
\(756\) 0 0
\(757\) 15.3175 0.556726 0.278363 0.960476i \(-0.410208\pi\)
0.278363 + 0.960476i \(0.410208\pi\)
\(758\) 31.1134i 1.13009i
\(759\) 0 0
\(760\) 2.36700 12.9930i 0.0858602 0.471306i
\(761\) 21.8967i 0.793754i 0.917872 + 0.396877i \(0.129906\pi\)
−0.917872 + 0.396877i \(0.870094\pi\)
\(762\) 0 0
\(763\) 17.9245i 0.648912i
\(764\) 1.51413i 0.0547795i
\(765\) 0 0
\(766\) 23.6569 0.854760
\(767\) 0 0
\(768\) 0 0
\(769\) 6.43308 0.231983 0.115991 0.993250i \(-0.462995\pi\)
0.115991 + 0.993250i \(0.462995\pi\)
\(770\) 14.2512 0.513577
\(771\) 0 0
\(772\) 13.3952i 0.482103i
\(773\) −5.68527 −0.204485 −0.102243 0.994760i \(-0.532602\pi\)
−0.102243 + 0.994760i \(0.532602\pi\)
\(774\) 0 0
\(775\) 32.3262i 1.16119i
\(776\) 9.50221i 0.341109i
\(777\) 0 0
\(778\) 0.731804i 0.0262364i
\(779\) 36.0586 + 6.56898i 1.29193 + 0.235358i
\(780\) 0 0
\(781\) 10.3932i 0.371898i
\(782\) −2.16808 −0.0775304
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 26.3399i 0.940110i
\(786\) 0 0
\(787\) 1.08566i 0.0386995i 0.999813 + 0.0193498i \(0.00615961\pi\)
−0.999813 + 0.0193498i \(0.993840\pi\)
\(788\) 12.5321i 0.446436i
\(789\) 0 0
\(790\) 26.3343 0.936933
\(791\) 18.0831 0.642962
\(792\) 0 0
\(793\) 34.2434i 1.21602i
\(794\) 5.59933 0.198713
\(795\) 0 0
\(796\) 21.3453 0.756564
\(797\) −40.9456 −1.45037 −0.725184 0.688555i \(-0.758245\pi\)