Properties

Label 2205.2.d.l.1324.6
Level $2205$
Weight $2$
Character 2205.1324
Analytic conductor $17.607$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2205.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.6070136457\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1324.6
Root \(-0.854638 - 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 2205.1324
Dual form 2205.2.d.l.1324.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.70928i q^{2} -5.34017 q^{4} +(2.17009 - 0.539189i) q^{5} -9.04945i q^{8} +O(q^{10})\) \(q+2.70928i q^{2} -5.34017 q^{4} +(2.17009 - 0.539189i) q^{5} -9.04945i q^{8} +(1.46081 + 5.87936i) q^{10} -2.00000 q^{11} +0.921622i q^{13} +13.8371 q^{16} +1.07838i q^{17} +3.07838 q^{19} +(-11.5886 + 2.87936i) q^{20} -5.41855i q^{22} +2.34017i q^{23} +(4.41855 - 2.34017i) q^{25} -2.49693 q^{26} -6.68035 q^{29} +7.75872 q^{31} +19.3896i q^{32} -2.92162 q^{34} +10.8371i q^{37} +8.34017i q^{38} +(-4.87936 - 19.6381i) q^{40} +6.49693 q^{41} +6.52359i q^{43} +10.6803 q^{44} -6.34017 q^{46} +4.68035i q^{47} +(6.34017 + 11.9711i) q^{50} -4.92162i q^{52} +3.75872i q^{53} +(-4.34017 + 1.07838i) q^{55} -18.0989i q^{58} -10.5236 q^{59} +4.15676 q^{61} +21.0205i q^{62} -24.8576 q^{64} +(0.496928 + 2.00000i) q^{65} +4.68035i q^{67} -5.75872i q^{68} -2.00000 q^{71} +7.07838i q^{73} -29.3607 q^{74} -16.4391 q^{76} -6.15676 q^{79} +(30.0277 - 7.46081i) q^{80} +17.6020i q^{82} -6.83710i q^{83} +(0.581449 + 2.34017i) q^{85} -17.6742 q^{86} +18.0989i q^{88} -8.34017 q^{89} -12.4969i q^{92} -12.6803 q^{94} +(6.68035 - 1.65983i) q^{95} +8.43907i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 10 q^{4} + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 10 q^{4} + 2 q^{5} + 12 q^{10} - 12 q^{11} + 26 q^{16} + 12 q^{19} - 30 q^{20} - 2 q^{25} + 20 q^{26} + 4 q^{29} - 4 q^{31} - 24 q^{34} - 4 q^{40} + 4 q^{41} + 20 q^{44} - 16 q^{46} + 16 q^{50} - 4 q^{55} - 32 q^{59} + 12 q^{61} - 26 q^{64} - 32 q^{65} - 12 q^{71} - 88 q^{74} - 4 q^{76} - 24 q^{79} + 46 q^{80} + 32 q^{85} + 8 q^{86} - 28 q^{89} - 32 q^{94} - 4 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times\).

\(n\) \(442\) \(1081\) \(1226\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.70928i 1.91575i 0.287190 + 0.957873i \(0.407279\pi\)
−0.287190 + 0.957873i \(0.592721\pi\)
\(3\) 0 0
\(4\) −5.34017 −2.67009
\(5\) 2.17009 0.539189i 0.970492 0.241133i
\(6\) 0 0
\(7\) 0 0
\(8\) 9.04945i 3.19946i
\(9\) 0 0
\(10\) 1.46081 + 5.87936i 0.461949 + 1.85922i
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 0.921622i 0.255612i 0.991799 + 0.127806i \(0.0407935\pi\)
−0.991799 + 0.127806i \(0.959207\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 13.8371 3.45928
\(17\) 1.07838i 0.261545i 0.991412 + 0.130773i \(0.0417457\pi\)
−0.991412 + 0.130773i \(0.958254\pi\)
\(18\) 0 0
\(19\) 3.07838 0.706228 0.353114 0.935580i \(-0.385123\pi\)
0.353114 + 0.935580i \(0.385123\pi\)
\(20\) −11.5886 + 2.87936i −2.59130 + 0.643845i
\(21\) 0 0
\(22\) 5.41855i 1.15524i
\(23\) 2.34017i 0.487960i 0.969780 + 0.243980i \(0.0784531\pi\)
−0.969780 + 0.243980i \(0.921547\pi\)
\(24\) 0 0
\(25\) 4.41855 2.34017i 0.883710 0.468035i
\(26\) −2.49693 −0.489688
\(27\) 0 0
\(28\) 0 0
\(29\) −6.68035 −1.24051 −0.620255 0.784401i \(-0.712971\pi\)
−0.620255 + 0.784401i \(0.712971\pi\)
\(30\) 0 0
\(31\) 7.75872 1.39351 0.696754 0.717310i \(-0.254627\pi\)
0.696754 + 0.717310i \(0.254627\pi\)
\(32\) 19.3896i 3.42763i
\(33\) 0 0
\(34\) −2.92162 −0.501054
\(35\) 0 0
\(36\) 0 0
\(37\) 10.8371i 1.78161i 0.454387 + 0.890804i \(0.349858\pi\)
−0.454387 + 0.890804i \(0.650142\pi\)
\(38\) 8.34017i 1.35295i
\(39\) 0 0
\(40\) −4.87936 19.6381i −0.771495 3.10505i
\(41\) 6.49693 1.01465 0.507325 0.861755i \(-0.330634\pi\)
0.507325 + 0.861755i \(0.330634\pi\)
\(42\) 0 0
\(43\) 6.52359i 0.994838i 0.867510 + 0.497419i \(0.165719\pi\)
−0.867510 + 0.497419i \(0.834281\pi\)
\(44\) 10.6803 1.61012
\(45\) 0 0
\(46\) −6.34017 −0.934808
\(47\) 4.68035i 0.682699i 0.939937 + 0.341349i \(0.110884\pi\)
−0.939937 + 0.341349i \(0.889116\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 6.34017 + 11.9711i 0.896636 + 1.69297i
\(51\) 0 0
\(52\) 4.92162i 0.682506i
\(53\) 3.75872i 0.516300i 0.966105 + 0.258150i \(0.0831129\pi\)
−0.966105 + 0.258150i \(0.916887\pi\)
\(54\) 0 0
\(55\) −4.34017 + 1.07838i −0.585229 + 0.145408i
\(56\) 0 0
\(57\) 0 0
\(58\) 18.0989i 2.37650i
\(59\) −10.5236 −1.37005 −0.685027 0.728517i \(-0.740210\pi\)
−0.685027 + 0.728517i \(0.740210\pi\)
\(60\) 0 0
\(61\) 4.15676 0.532218 0.266109 0.963943i \(-0.414262\pi\)
0.266109 + 0.963943i \(0.414262\pi\)
\(62\) 21.0205i 2.66961i
\(63\) 0 0
\(64\) −24.8576 −3.10720
\(65\) 0.496928 + 2.00000i 0.0616364 + 0.248069i
\(66\) 0 0
\(67\) 4.68035i 0.571795i 0.958260 + 0.285898i \(0.0922917\pi\)
−0.958260 + 0.285898i \(0.907708\pi\)
\(68\) 5.75872i 0.698348i
\(69\) 0 0
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 7.07838i 0.828461i 0.910172 + 0.414231i \(0.135949\pi\)
−0.910172 + 0.414231i \(0.864051\pi\)
\(74\) −29.3607 −3.41311
\(75\) 0 0
\(76\) −16.4391 −1.88569
\(77\) 0 0
\(78\) 0 0
\(79\) −6.15676 −0.692689 −0.346345 0.938107i \(-0.612577\pi\)
−0.346345 + 0.938107i \(0.612577\pi\)
\(80\) 30.0277 7.46081i 3.35720 0.834144i
\(81\) 0 0
\(82\) 17.6020i 1.94381i
\(83\) 6.83710i 0.750469i −0.926930 0.375235i \(-0.877562\pi\)
0.926930 0.375235i \(-0.122438\pi\)
\(84\) 0 0
\(85\) 0.581449 + 2.34017i 0.0630670 + 0.253827i
\(86\) −17.6742 −1.90586
\(87\) 0 0
\(88\) 18.0989i 1.92935i
\(89\) −8.34017 −0.884057 −0.442028 0.897001i \(-0.645741\pi\)
−0.442028 + 0.897001i \(0.645741\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 12.4969i 1.30289i
\(93\) 0 0
\(94\) −12.6803 −1.30788
\(95\) 6.68035 1.65983i 0.685389 0.170295i
\(96\) 0 0
\(97\) 8.43907i 0.856858i 0.903576 + 0.428429i \(0.140933\pi\)
−0.903576 + 0.428429i \(0.859067\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −23.5958 + 12.4969i −2.35958 + 1.24969i
\(101\) −5.81658 −0.578772 −0.289386 0.957213i \(-0.593451\pi\)
−0.289386 + 0.957213i \(0.593451\pi\)
\(102\) 0 0
\(103\) 2.15676i 0.212511i −0.994339 0.106256i \(-0.966114\pi\)
0.994339 0.106256i \(-0.0338862\pi\)
\(104\) 8.34017 0.817821
\(105\) 0 0
\(106\) −10.1834 −0.989101
\(107\) 16.4969i 1.59482i 0.603439 + 0.797409i \(0.293797\pi\)
−0.603439 + 0.797409i \(0.706203\pi\)
\(108\) 0 0
\(109\) 12.8371 1.22957 0.614786 0.788694i \(-0.289243\pi\)
0.614786 + 0.788694i \(0.289243\pi\)
\(110\) −2.92162 11.7587i −0.278566 1.12115i
\(111\) 0 0
\(112\) 0 0
\(113\) 5.23513i 0.492480i −0.969209 0.246240i \(-0.920805\pi\)
0.969209 0.246240i \(-0.0791951\pi\)
\(114\) 0 0
\(115\) 1.26180 + 5.07838i 0.117663 + 0.473561i
\(116\) 35.6742 3.31227
\(117\) 0 0
\(118\) 28.5113i 2.62468i
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 11.2618i 1.01960i
\(123\) 0 0
\(124\) −41.4329 −3.72079
\(125\) 8.32684 7.46081i 0.744775 0.667315i
\(126\) 0 0
\(127\) 1.84324i 0.163562i 0.996650 + 0.0817808i \(0.0260607\pi\)
−0.996650 + 0.0817808i \(0.973939\pi\)
\(128\) 28.5669i 2.52498i
\(129\) 0 0
\(130\) −5.41855 + 1.34632i −0.475238 + 0.118080i
\(131\) 1.47641 0.128995 0.0644973 0.997918i \(-0.479456\pi\)
0.0644973 + 0.997918i \(0.479456\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −12.6803 −1.09542
\(135\) 0 0
\(136\) 9.75872 0.836804
\(137\) 4.43907i 0.379255i −0.981856 0.189628i \(-0.939272\pi\)
0.981856 0.189628i \(-0.0607281\pi\)
\(138\) 0 0
\(139\) 13.6020 1.15370 0.576852 0.816849i \(-0.304281\pi\)
0.576852 + 0.816849i \(0.304281\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 5.41855i 0.454715i
\(143\) 1.84324i 0.154140i
\(144\) 0 0
\(145\) −14.4969 + 3.60197i −1.20390 + 0.299127i
\(146\) −19.1773 −1.58712
\(147\) 0 0
\(148\) 57.8720i 4.75705i
\(149\) 15.6742 1.28408 0.642040 0.766671i \(-0.278088\pi\)
0.642040 + 0.766671i \(0.278088\pi\)
\(150\) 0 0
\(151\) 5.84324 0.475516 0.237758 0.971324i \(-0.423587\pi\)
0.237758 + 0.971324i \(0.423587\pi\)
\(152\) 27.8576i 2.25955i
\(153\) 0 0
\(154\) 0 0
\(155\) 16.8371 4.18342i 1.35239 0.336020i
\(156\) 0 0
\(157\) 4.92162i 0.392788i −0.980525 0.196394i \(-0.937077\pi\)
0.980525 0.196394i \(-0.0629232\pi\)
\(158\) 16.6803i 1.32702i
\(159\) 0 0
\(160\) 10.4547 + 42.0772i 0.826514 + 3.32649i
\(161\) 0 0
\(162\) 0 0
\(163\) 9.84324i 0.770982i 0.922712 + 0.385491i \(0.125968\pi\)
−0.922712 + 0.385491i \(0.874032\pi\)
\(164\) −34.6947 −2.70920
\(165\) 0 0
\(166\) 18.5236 1.43771
\(167\) 19.2039i 1.48605i −0.669266 0.743023i \(-0.733391\pi\)
0.669266 0.743023i \(-0.266609\pi\)
\(168\) 0 0
\(169\) 12.1506 0.934662
\(170\) −6.34017 + 1.57531i −0.486269 + 0.120820i
\(171\) 0 0
\(172\) 34.8371i 2.65630i
\(173\) 22.4391i 1.70601i 0.521902 + 0.853005i \(0.325223\pi\)
−0.521902 + 0.853005i \(0.674777\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −27.6742 −2.08602
\(177\) 0 0
\(178\) 22.5958i 1.69363i
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 0 0
\(181\) 8.52359 0.633553 0.316777 0.948500i \(-0.397399\pi\)
0.316777 + 0.948500i \(0.397399\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 21.1773 1.56121
\(185\) 5.84324 + 23.5174i 0.429604 + 1.72904i
\(186\) 0 0
\(187\) 2.15676i 0.157718i
\(188\) 24.9939i 1.82286i
\(189\) 0 0
\(190\) 4.49693 + 18.0989i 0.326241 + 1.31303i
\(191\) −15.3607 −1.11146 −0.555730 0.831363i \(-0.687561\pi\)
−0.555730 + 0.831363i \(0.687561\pi\)
\(192\) 0 0
\(193\) 8.36683i 0.602258i −0.953583 0.301129i \(-0.902637\pi\)
0.953583 0.301129i \(-0.0973635\pi\)
\(194\) −22.8638 −1.64152
\(195\) 0 0
\(196\) 0 0
\(197\) 11.7587i 0.837774i 0.908038 + 0.418887i \(0.137580\pi\)
−0.908038 + 0.418887i \(0.862420\pi\)
\(198\) 0 0
\(199\) −22.5958 −1.60178 −0.800888 0.598814i \(-0.795639\pi\)
−0.800888 + 0.598814i \(0.795639\pi\)
\(200\) −21.1773 39.9854i −1.49746 2.82740i
\(201\) 0 0
\(202\) 15.7587i 1.10878i
\(203\) 0 0
\(204\) 0 0
\(205\) 14.0989 3.50307i 0.984710 0.244665i
\(206\) 5.84324 0.407118
\(207\) 0 0
\(208\) 12.7526i 0.884232i
\(209\) −6.15676 −0.425872
\(210\) 0 0
\(211\) −13.6742 −0.941371 −0.470685 0.882301i \(-0.655993\pi\)
−0.470685 + 0.882301i \(0.655993\pi\)
\(212\) 20.0722i 1.37857i
\(213\) 0 0
\(214\) −44.6947 −3.05527
\(215\) 3.51745 + 14.1568i 0.239888 + 0.965483i
\(216\) 0 0
\(217\) 0 0
\(218\) 34.7792i 2.35555i
\(219\) 0 0
\(220\) 23.1773 5.75872i 1.56261 0.388253i
\(221\) −0.993857 −0.0668541
\(222\) 0 0
\(223\) 21.6742i 1.45141i −0.688005 0.725706i \(-0.741513\pi\)
0.688005 0.725706i \(-0.258487\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 14.1834 0.943467
\(227\) 11.5174i 0.764440i −0.924071 0.382220i \(-0.875160\pi\)
0.924071 0.382220i \(-0.124840\pi\)
\(228\) 0 0
\(229\) 12.8371 0.848300 0.424150 0.905592i \(-0.360573\pi\)
0.424150 + 0.905592i \(0.360573\pi\)
\(230\) −13.7587 + 3.41855i −0.907223 + 0.225413i
\(231\) 0 0
\(232\) 60.4534i 3.96896i
\(233\) 6.76487i 0.443181i −0.975140 0.221591i \(-0.928875\pi\)
0.975140 0.221591i \(-0.0711248\pi\)
\(234\) 0 0
\(235\) 2.52359 + 10.1568i 0.164621 + 0.662554i
\(236\) 56.1978 3.65816
\(237\) 0 0
\(238\) 0 0
\(239\) −23.3607 −1.51108 −0.755539 0.655104i \(-0.772625\pi\)
−0.755539 + 0.655104i \(0.772625\pi\)
\(240\) 0 0
\(241\) 14.6803 0.945644 0.472822 0.881158i \(-0.343235\pi\)
0.472822 + 0.881158i \(0.343235\pi\)
\(242\) 18.9649i 1.21911i
\(243\) 0 0
\(244\) −22.1978 −1.42107
\(245\) 0 0
\(246\) 0 0
\(247\) 2.83710i 0.180520i
\(248\) 70.2122i 4.45848i
\(249\) 0 0
\(250\) 20.2134 + 22.5597i 1.27841 + 1.42680i
\(251\) 9.16290 0.578357 0.289179 0.957275i \(-0.406618\pi\)
0.289179 + 0.957275i \(0.406618\pi\)
\(252\) 0 0
\(253\) 4.68035i 0.294251i
\(254\) −4.99386 −0.313342
\(255\) 0 0
\(256\) 27.6803 1.73002
\(257\) 5.07838i 0.316781i −0.987377 0.158390i \(-0.949370\pi\)
0.987377 0.158390i \(-0.0506304\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2.65368 10.6803i −0.164574 0.662367i
\(261\) 0 0
\(262\) 4.00000i 0.247121i
\(263\) 5.65983i 0.349000i 0.984657 + 0.174500i \(0.0558309\pi\)
−0.984657 + 0.174500i \(0.944169\pi\)
\(264\) 0 0
\(265\) 2.02666 + 8.15676i 0.124497 + 0.501066i
\(266\) 0 0
\(267\) 0 0
\(268\) 24.9939i 1.52674i
\(269\) 27.8576 1.69851 0.849255 0.527984i \(-0.177052\pi\)
0.849255 + 0.527984i \(0.177052\pi\)
\(270\) 0 0
\(271\) −25.1194 −1.52590 −0.762948 0.646460i \(-0.776249\pi\)
−0.762948 + 0.646460i \(0.776249\pi\)
\(272\) 14.9216i 0.904756i
\(273\) 0 0
\(274\) 12.0267 0.726557
\(275\) −8.83710 + 4.68035i −0.532897 + 0.282235i
\(276\) 0 0
\(277\) 28.1978i 1.69424i −0.531401 0.847121i \(-0.678334\pi\)
0.531401 0.847121i \(-0.321666\pi\)
\(278\) 36.8515i 2.21020i
\(279\) 0 0
\(280\) 0 0
\(281\) 20.3545 1.21425 0.607125 0.794606i \(-0.292323\pi\)
0.607125 + 0.794606i \(0.292323\pi\)
\(282\) 0 0
\(283\) 23.5174i 1.39797i 0.715138 + 0.698984i \(0.246364\pi\)
−0.715138 + 0.698984i \(0.753636\pi\)
\(284\) 10.6803 0.633762
\(285\) 0 0
\(286\) 4.99386 0.295293
\(287\) 0 0
\(288\) 0 0
\(289\) 15.8371 0.931594
\(290\) −9.75872 39.2762i −0.573052 2.30638i
\(291\) 0 0
\(292\) 37.7998i 2.21206i
\(293\) 2.92162i 0.170683i 0.996352 + 0.0853415i \(0.0271981\pi\)
−0.996352 + 0.0853415i \(0.972802\pi\)
\(294\) 0 0
\(295\) −22.8371 + 5.67420i −1.32963 + 0.330365i
\(296\) 98.0698 5.70019
\(297\) 0 0
\(298\) 42.4657i 2.45997i
\(299\) −2.15676 −0.124728
\(300\) 0 0
\(301\) 0 0
\(302\) 15.8310i 0.910969i
\(303\) 0 0
\(304\) 42.5958 2.44304
\(305\) 9.02052 2.24128i 0.516513 0.128335i
\(306\) 0 0
\(307\) 10.4703i 0.597570i 0.954321 + 0.298785i \(0.0965813\pi\)
−0.954321 + 0.298785i \(0.903419\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 11.3340 + 45.6163i 0.643730 + 2.59083i
\(311\) 23.8310 1.35133 0.675665 0.737209i \(-0.263857\pi\)
0.675665 + 0.737209i \(0.263857\pi\)
\(312\) 0 0
\(313\) 32.7526i 1.85129i 0.378399 + 0.925643i \(0.376475\pi\)
−0.378399 + 0.925643i \(0.623525\pi\)
\(314\) 13.3340 0.752483
\(315\) 0 0
\(316\) 32.8781 1.84954
\(317\) 17.9155i 1.00623i 0.864218 + 0.503117i \(0.167813\pi\)
−0.864218 + 0.503117i \(0.832187\pi\)
\(318\) 0 0
\(319\) 13.3607 0.748055
\(320\) −53.9432 + 13.4030i −3.01552 + 0.749248i
\(321\) 0 0
\(322\) 0 0
\(323\) 3.31965i 0.184710i
\(324\) 0 0
\(325\) 2.15676 + 4.07223i 0.119635 + 0.225887i
\(326\) −26.6681 −1.47701
\(327\) 0 0
\(328\) 58.7936i 3.24633i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.36069 −0.0747904 −0.0373952 0.999301i \(-0.511906\pi\)
−0.0373952 + 0.999301i \(0.511906\pi\)
\(332\) 36.5113i 2.00382i
\(333\) 0 0
\(334\) 52.0288 2.84689
\(335\) 2.52359 + 10.1568i 0.137878 + 0.554923i
\(336\) 0 0
\(337\) 25.3607i 1.38148i −0.723101 0.690742i \(-0.757284\pi\)
0.723101 0.690742i \(-0.242716\pi\)
\(338\) 32.9194i 1.79058i
\(339\) 0 0
\(340\) −3.10504 12.4969i −0.168394 0.677741i
\(341\) −15.5174 −0.840317
\(342\) 0 0
\(343\) 0 0
\(344\) 59.0349 3.18295
\(345\) 0 0
\(346\) −60.7936 −3.26829
\(347\) 16.8638i 0.905294i −0.891690 0.452647i \(-0.850480\pi\)
0.891690 0.452647i \(-0.149520\pi\)
\(348\) 0 0
\(349\) 9.51745 0.509457 0.254729 0.967013i \(-0.418014\pi\)
0.254729 + 0.967013i \(0.418014\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 38.7792i 2.06694i
\(353\) 35.7998i 1.90543i 0.303867 + 0.952715i \(0.401722\pi\)
−0.303867 + 0.952715i \(0.598278\pi\)
\(354\) 0 0
\(355\) −4.34017 + 1.07838i −0.230352 + 0.0572343i
\(356\) 44.5380 2.36051
\(357\) 0 0
\(358\) 27.0928i 1.43190i
\(359\) −22.3135 −1.17766 −0.588831 0.808256i \(-0.700412\pi\)
−0.588831 + 0.808256i \(0.700412\pi\)
\(360\) 0 0
\(361\) −9.52359 −0.501242
\(362\) 23.0928i 1.21373i
\(363\) 0 0
\(364\) 0 0
\(365\) 3.81658 + 15.3607i 0.199769 + 0.804015i
\(366\) 0 0
\(367\) 20.3135i 1.06036i −0.847886 0.530178i \(-0.822125\pi\)
0.847886 0.530178i \(-0.177875\pi\)
\(368\) 32.3812i 1.68799i
\(369\) 0 0
\(370\) −63.7152 + 15.8310i −3.31240 + 0.823012i
\(371\) 0 0
\(372\) 0 0
\(373\) 16.0000i 0.828449i 0.910175 + 0.414224i \(0.135947\pi\)
−0.910175 + 0.414224i \(0.864053\pi\)
\(374\) 5.84324 0.302147
\(375\) 0 0
\(376\) 42.3545 2.18427
\(377\) 6.15676i 0.317089i
\(378\) 0 0
\(379\) −6.15676 −0.316251 −0.158126 0.987419i \(-0.550545\pi\)
−0.158126 + 0.987419i \(0.550545\pi\)
\(380\) −35.6742 + 8.86376i −1.83005 + 0.454701i
\(381\) 0 0
\(382\) 41.6163i 2.12928i
\(383\) 26.8371i 1.37131i −0.727926 0.685656i \(-0.759515\pi\)
0.727926 0.685656i \(-0.240485\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 22.6681 1.15377
\(387\) 0 0
\(388\) 45.0661i 2.28788i
\(389\) −5.63317 −0.285613 −0.142806 0.989751i \(-0.545613\pi\)
−0.142806 + 0.989751i \(0.545613\pi\)
\(390\) 0 0
\(391\) −2.52359 −0.127623
\(392\) 0 0
\(393\) 0 0
\(394\) −31.8576 −1.60496
\(395\) −13.3607 + 3.31965i −0.672249 + 0.167030i
\(396\) 0 0
\(397\) 37.7998i 1.89712i −0.316604 0.948558i \(-0.602543\pi\)
0.316604 0.948558i \(-0.397457\pi\)
\(398\) 61.2183i 3.06860i
\(399\) 0 0
\(400\) 61.1399 32.3812i 3.05700 1.61906i
\(401\) 13.6332 0.680808 0.340404 0.940279i \(-0.389436\pi\)
0.340404 + 0.940279i \(0.389436\pi\)
\(402\) 0 0
\(403\) 7.15061i 0.356197i
\(404\) 31.0616 1.54537
\(405\) 0 0
\(406\) 0 0
\(407\) 21.6742i 1.07435i
\(408\) 0 0
\(409\) 12.3545 0.610893 0.305447 0.952209i \(-0.401194\pi\)
0.305447 + 0.952209i \(0.401194\pi\)
\(410\) 9.49079 + 38.1978i 0.468716 + 1.88645i
\(411\) 0 0
\(412\) 11.5174i 0.567424i
\(413\) 0 0
\(414\) 0 0
\(415\) −3.68649 14.8371i −0.180963 0.728325i
\(416\) −17.8699 −0.876144
\(417\) 0 0
\(418\) 16.6803i 0.815862i
\(419\) −28.9939 −1.41644 −0.708221 0.705991i \(-0.750502\pi\)
−0.708221 + 0.705991i \(0.750502\pi\)
\(420\) 0 0
\(421\) −15.1629 −0.738994 −0.369497 0.929232i \(-0.620470\pi\)
−0.369497 + 0.929232i \(0.620470\pi\)
\(422\) 37.0472i 1.80343i
\(423\) 0 0
\(424\) 34.0144 1.65188
\(425\) 2.52359 + 4.76487i 0.122412 + 0.231130i
\(426\) 0 0
\(427\) 0 0
\(428\) 88.0965i 4.25830i
\(429\) 0 0
\(430\) −38.3545 + 9.52973i −1.84962 + 0.459565i
\(431\) 10.3135 0.496784 0.248392 0.968660i \(-0.420098\pi\)
0.248392 + 0.968660i \(0.420098\pi\)
\(432\) 0 0
\(433\) 20.4391i 0.982239i 0.871092 + 0.491120i \(0.163412\pi\)
−0.871092 + 0.491120i \(0.836588\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −68.5523 −3.28306
\(437\) 7.20394i 0.344611i
\(438\) 0 0
\(439\) −16.9216 −0.807625 −0.403812 0.914842i \(-0.632315\pi\)
−0.403812 + 0.914842i \(0.632315\pi\)
\(440\) 9.75872 + 39.2762i 0.465229 + 1.87242i
\(441\) 0 0
\(442\) 2.69263i 0.128075i
\(443\) 12.8104i 0.608642i −0.952569 0.304321i \(-0.901570\pi\)
0.952569 0.304321i \(-0.0984296\pi\)
\(444\) 0 0
\(445\) −18.0989 + 4.49693i −0.857970 + 0.213175i
\(446\) 58.7214 2.78054
\(447\) 0 0
\(448\) 0 0
\(449\) −14.6270 −0.690292 −0.345146 0.938549i \(-0.612171\pi\)
−0.345146 + 0.938549i \(0.612171\pi\)
\(450\) 0 0
\(451\) −12.9939 −0.611857
\(452\) 27.9565i 1.31496i
\(453\) 0 0
\(454\) 31.2039 1.46447
\(455\) 0 0
\(456\) 0 0
\(457\) 14.1568i 0.662225i 0.943591 + 0.331113i \(0.107424\pi\)
−0.943591 + 0.331113i \(0.892576\pi\)
\(458\) 34.7792i 1.62513i
\(459\) 0 0
\(460\) −6.73820 27.1194i −0.314170 1.26445i
\(461\) 0.340173 0.0158434 0.00792172 0.999969i \(-0.497478\pi\)
0.00792172 + 0.999969i \(0.497478\pi\)
\(462\) 0 0
\(463\) 9.84324i 0.457454i 0.973491 + 0.228727i \(0.0734564\pi\)
−0.973491 + 0.228727i \(0.926544\pi\)
\(464\) −92.4366 −4.29126
\(465\) 0 0
\(466\) 18.3279 0.849023
\(467\) 11.5174i 0.532964i −0.963840 0.266482i \(-0.914139\pi\)
0.963840 0.266482i \(-0.0858613\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −27.5174 + 6.83710i −1.26929 + 0.315372i
\(471\) 0 0
\(472\) 95.2327i 4.38344i
\(473\) 13.0472i 0.599910i
\(474\) 0 0
\(475\) 13.6020 7.20394i 0.624101 0.330539i
\(476\) 0 0
\(477\) 0 0
\(478\) 63.2905i 2.89484i
\(479\) 19.5174 0.891775 0.445887 0.895089i \(-0.352888\pi\)
0.445887 + 0.895089i \(0.352888\pi\)
\(480\) 0 0
\(481\) −9.98771 −0.455401
\(482\) 39.7731i 1.81162i
\(483\) 0 0
\(484\) 37.3812 1.69915
\(485\) 4.55025 + 18.3135i 0.206616 + 0.831574i
\(486\) 0 0
\(487\) 23.1506i 1.04905i 0.851394 + 0.524527i \(0.175758\pi\)
−0.851394 + 0.524527i \(0.824242\pi\)
\(488\) 37.6163i 1.70281i
\(489\) 0 0
\(490\) 0 0
\(491\) −2.00000 −0.0902587 −0.0451294 0.998981i \(-0.514370\pi\)
−0.0451294 + 0.998981i \(0.514370\pi\)
\(492\) 0 0
\(493\) 7.20394i 0.324449i
\(494\) −7.68649 −0.345831
\(495\) 0 0
\(496\) 107.358 4.82053
\(497\) 0 0
\(498\) 0 0
\(499\) −27.2039 −1.21782 −0.608908 0.793241i \(-0.708392\pi\)
−0.608908 + 0.793241i \(0.708392\pi\)
\(500\) −44.4668 + 39.8420i −1.98861 + 1.78179i
\(501\) 0 0
\(502\) 24.8248i 1.10799i
\(503\) 18.8371i 0.839905i 0.907546 + 0.419952i \(0.137953\pi\)
−0.907546 + 0.419952i \(0.862047\pi\)
\(504\) 0 0
\(505\) −12.6225 + 3.13624i −0.561693 + 0.139561i
\(506\) 12.6803 0.563710
\(507\) 0 0
\(508\) 9.84324i 0.436723i
\(509\) −6.81044 −0.301867 −0.150934 0.988544i \(-0.548228\pi\)
−0.150934 + 0.988544i \(0.548228\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 17.8599i 0.789303i
\(513\) 0 0
\(514\) 13.7587 0.606871
\(515\) −1.16290 4.68035i −0.0512434 0.206241i
\(516\) 0 0
\(517\) 9.36069i 0.411683i
\(518\) 0 0
\(519\) 0 0
\(520\) 18.0989 4.49693i 0.793689 0.197203i
\(521\) −25.8166 −1.13105 −0.565523 0.824733i \(-0.691325\pi\)
−0.565523 + 0.824733i \(0.691325\pi\)
\(522\) 0 0
\(523\) 4.00000i 0.174908i 0.996169 + 0.0874539i \(0.0278730\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(524\) −7.88428 −0.344426
\(525\) 0 0
\(526\) −15.3340 −0.668595
\(527\) 8.36683i 0.364465i
\(528\) 0 0
\(529\) 17.5236 0.761895
\(530\) −22.0989 + 5.49079i −0.959915 + 0.238504i
\(531\) 0 0
\(532\) 0 0
\(533\) 5.98771i 0.259357i
\(534\) 0 0
\(535\) 8.89496 + 35.7998i 0.384563 + 1.54776i
\(536\) 42.3545 1.82944
\(537\) 0 0
\(538\) 75.4740i 3.25391i
\(539\) 0 0
\(540\) 0 0
\(541\) 25.8843 1.11285 0.556426 0.830897i \(-0.312172\pi\)
0.556426 + 0.830897i \(0.312172\pi\)
\(542\) 68.0554i 2.92323i
\(543\) 0 0
\(544\) −20.9093 −0.896480
\(545\) 27.8576 6.92162i 1.19329 0.296490i
\(546\) 0 0
\(547\) 11.3197i 0.483993i 0.970277 + 0.241997i \(0.0778023\pi\)
−0.970277 + 0.241997i \(0.922198\pi\)
\(548\) 23.7054i 1.01264i
\(549\) 0 0
\(550\) −12.6803 23.9421i −0.540692 1.02090i
\(551\) −20.5646 −0.876083
\(552\) 0 0
\(553\) 0 0
\(554\) 76.3956 3.24574
\(555\) 0 0
\(556\) −72.6369 −3.08049
\(557\) 26.6491i 1.12916i 0.825378 + 0.564580i \(0.190962\pi\)
−0.825378 + 0.564580i \(0.809038\pi\)
\(558\) 0 0
\(559\) −6.01229 −0.254293
\(560\) 0 0
\(561\) 0 0
\(562\) 55.1461i 2.32620i
\(563\) 46.3545i 1.95361i −0.214128 0.976806i \(-0.568691\pi\)
0.214128 0.976806i \(-0.431309\pi\)
\(564\) 0 0
\(565\) −2.82273 11.3607i −0.118753 0.477948i
\(566\) −63.7152 −2.67815
\(567\) 0 0
\(568\) 18.0989i 0.759413i
\(569\) −14.3668 −0.602289 −0.301145 0.953579i \(-0.597369\pi\)
−0.301145 + 0.953579i \(0.597369\pi\)
\(570\) 0 0
\(571\) 38.7214 1.62044 0.810220 0.586126i \(-0.199348\pi\)
0.810220 + 0.586126i \(0.199348\pi\)
\(572\) 9.84324i 0.411567i
\(573\) 0 0
\(574\) 0 0
\(575\) 5.47641 + 10.3402i 0.228382 + 0.431215i
\(576\) 0 0
\(577\) 43.4740i 1.80984i −0.425577 0.904922i \(-0.639929\pi\)
0.425577 0.904922i \(-0.360071\pi\)
\(578\) 42.9071i 1.78470i
\(579\) 0 0
\(580\) 77.4161 19.2351i 3.21453 0.798695i
\(581\) 0 0
\(582\) 0 0
\(583\) 7.51745i 0.311341i
\(584\) 64.0554 2.65063
\(585\) 0 0
\(586\) −7.91548 −0.326985
\(587\) 36.0288i 1.48707i 0.668699 + 0.743533i \(0.266851\pi\)
−0.668699 + 0.743533i \(0.733149\pi\)
\(588\) 0 0
\(589\) 23.8843 0.984135
\(590\) −15.3730 61.8720i −0.632895 2.54723i
\(591\) 0 0
\(592\) 149.954i 6.16307i
\(593\) 31.4863i 1.29299i −0.762920 0.646493i \(-0.776235\pi\)
0.762920 0.646493i \(-0.223765\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −83.7030 −3.42861
\(597\) 0 0
\(598\) 5.84324i 0.238948i
\(599\) 29.0349 1.18633 0.593167 0.805080i \(-0.297877\pi\)
0.593167 + 0.805080i \(0.297877\pi\)
\(600\) 0 0
\(601\) −15.3607 −0.626576 −0.313288 0.949658i \(-0.601430\pi\)
−0.313288 + 0.949658i \(0.601430\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −31.2039 −1.26967
\(605\) −15.1906 + 3.77432i −0.617586 + 0.153448i
\(606\) 0 0
\(607\) 13.0472i 0.529569i 0.964308 + 0.264784i \(0.0853008\pi\)
−0.964308 + 0.264784i \(0.914699\pi\)
\(608\) 59.6886i 2.42069i
\(609\) 0 0
\(610\) 6.07223 + 24.4391i 0.245858 + 0.989509i
\(611\) −4.31351 −0.174506
\(612\) 0 0
\(613\) 15.5174i 0.626744i 0.949630 + 0.313372i \(0.101459\pi\)
−0.949630 + 0.313372i \(0.898541\pi\)
\(614\) −28.3668 −1.14479
\(615\) 0 0
\(616\) 0 0
\(617\) 22.7649i 0.916479i 0.888829 + 0.458240i \(0.151520\pi\)
−0.888829 + 0.458240i \(0.848480\pi\)
\(618\) 0 0
\(619\) 7.92777 0.318644 0.159322 0.987227i \(-0.449069\pi\)
0.159322 + 0.987227i \(0.449069\pi\)
\(620\) −89.9130 + 22.3402i −3.61099 + 0.897203i
\(621\) 0 0
\(622\) 64.5646i 2.58881i
\(623\) 0 0
\(624\) 0 0
\(625\) 14.0472 20.6803i 0.561887 0.827214i
\(626\) −88.7358 −3.54659
\(627\) 0 0
\(628\) 26.2823i 1.04878i
\(629\) −11.6865 −0.465971
\(630\) 0 0
\(631\) 19.2039 0.764497 0.382248 0.924060i \(-0.375150\pi\)
0.382248 + 0.924060i \(0.375150\pi\)
\(632\) 55.7152i 2.21623i
\(633\) 0 0
\(634\) −48.5380 −1.92769
\(635\) 0.993857 + 4.00000i 0.0394400 + 0.158735i
\(636\) 0 0
\(637\) 0 0
\(638\) 36.1978i 1.43308i
\(639\) 0 0
\(640\) −15.4030 61.9926i −0.608855 2.45047i
\(641\) 5.94668 0.234880 0.117440 0.993080i \(-0.462531\pi\)
0.117440 + 0.993080i \(0.462531\pi\)
\(642\) 0 0
\(643\) 30.8904i 1.21820i −0.793094 0.609100i \(-0.791531\pi\)
0.793094 0.609100i \(-0.208469\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −8.99386 −0.353859
\(647\) 19.2039i 0.754985i −0.926013 0.377492i \(-0.876786\pi\)
0.926013 0.377492i \(-0.123214\pi\)
\(648\) 0 0
\(649\) 21.0472 0.826174
\(650\) −11.0328 + 5.84324i −0.432742 + 0.229191i
\(651\) 0 0
\(652\) 52.5646i 2.05859i
\(653\) 28.5548i 1.11744i −0.829358 0.558718i \(-0.811294\pi\)
0.829358 0.558718i \(-0.188706\pi\)
\(654\) 0 0
\(655\) 3.20394 0.796064i 0.125188 0.0311048i
\(656\) 89.8987 3.50995
\(657\) 0 0
\(658\) 0 0
\(659\) −27.9877 −1.09025 −0.545123 0.838356i \(-0.683517\pi\)
−0.545123 + 0.838356i \(0.683517\pi\)
\(660\) 0 0
\(661\) 22.1445 0.861320 0.430660 0.902514i \(-0.358281\pi\)
0.430660 + 0.902514i \(0.358281\pi\)
\(662\) 3.68649i 0.143279i
\(663\) 0 0
\(664\) −61.8720 −2.40110
\(665\) 0 0
\(666\) 0 0
\(667\) 15.6332i 0.605319i
\(668\) 102.552i 3.96787i
\(669\) 0 0
\(670\) −27.5174 + 6.83710i −1.06309 + 0.264140i
\(671\) −8.31351 −0.320940
\(672\) 0 0
\(673\) 2.21008i 0.0851923i −0.999092 0.0425962i \(-0.986437\pi\)
0.999092 0.0425962i \(-0.0135629\pi\)
\(674\) 68.7091 2.64658
\(675\) 0 0
\(676\) −64.8864 −2.49563
\(677\) 19.5486i 0.751315i 0.926758 + 0.375658i \(0.122583\pi\)
−0.926758 + 0.375658i \(0.877417\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 21.1773 5.26180i 0.812111 0.201781i
\(681\) 0 0
\(682\) 42.0410i 1.60983i
\(683\) 11.8166i 0.452149i 0.974110 + 0.226074i \(0.0725893\pi\)
−0.974110 + 0.226074i \(0.927411\pi\)
\(684\) 0 0
\(685\) −2.39350 9.63317i −0.0914508 0.368064i
\(686\) 0 0
\(687\) 0 0
\(688\) 90.2676i 3.44142i
\(689\) −3.46412 −0.131973
\(690\) 0 0
\(691\) −11.7587 −0.447323 −0.223661 0.974667i \(-0.571801\pi\)
−0.223661 + 0.974667i \(0.571801\pi\)
\(692\) 119.829i 4.55520i
\(693\) 0 0
\(694\) 45.6886 1.73431
\(695\) 29.5174 7.33403i 1.11966 0.278196i
\(696\) 0 0
\(697\) 7.00614i 0.265377i
\(698\) 25.7854i 0.975991i
\(699\) 0 0
\(700\) 0 0
\(701\) −9.94668 −0.375681 −0.187840 0.982200i \(-0.560149\pi\)
−0.187840 + 0.982200i \(0.560149\pi\)
\(702\) 0 0
\(703\) 33.3607i 1.25822i
\(704\) 49.7152 1.87371
\(705\) 0 0
\(706\) −96.9914 −3.65032
\(707\) 0 0
\(708\) 0 0
\(709\) 11.0472 0.414886 0.207443 0.978247i \(-0.433486\pi\)
0.207443 + 0.978247i \(0.433486\pi\)
\(710\) −2.92162 11.7587i −0.109647 0.441297i
\(711\) 0 0
\(712\) 75.4740i 2.82851i
\(713\) 18.1568i 0.679976i
\(714\) 0 0
\(715\) −0.993857 4.00000i −0.0371681 0.149592i
\(716\) −53.4017 −1.99572
\(717\) 0 0
\(718\) 60.4534i 2.25610i
\(719\) 6.15676 0.229608 0.114804 0.993388i \(-0.463376\pi\)
0.114804 + 0.993388i \(0.463376\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 25.8020i 0.960252i
\(723\) 0 0
\(724\) −45.5174 −1.69164
\(725\) −29.5174 + 15.6332i −1.09625 + 0.580601i
\(726\) 0 0
\(727\) 2.89043i 0.107200i −0.998562 0.0536000i \(-0.982930\pi\)
0.998562 0.0536000i \(-0.0170696\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −41.6163 + 10.3402i −1.54029 + 0.382707i
\(731\) −7.03489 −0.260195
\(732\) 0 0
\(733\) 25.7998i 0.952936i −0.879192 0.476468i \(-0.841917\pi\)
0.879192 0.476468i \(-0.158083\pi\)
\(734\) 55.0349 2.03138
\(735\) 0 0
\(736\) −45.3751 −1.67255
\(737\) 9.36069i 0.344806i
\(738\) 0 0
\(739\) 1.04718 0.0385212 0.0192606 0.999814i \(-0.493869\pi\)
0.0192606 + 0.999814i \(0.493869\pi\)
\(740\) −31.2039 125.587i −1.14708 4.61668i
\(741\) 0 0
\(742\) 0 0
\(743\) 9.97334i 0.365886i −0.983123 0.182943i \(-0.941438\pi\)
0.983123 0.182943i \(-0.0585624\pi\)
\(744\) 0 0
\(745\) 34.0144 8.45136i 1.24619 0.309634i
\(746\) −43.3484 −1.58710
\(747\) 0 0
\(748\) 11.5174i 0.421120i
\(749\) 0 0
\(750\) 0 0
\(751\) 3.26633 0.119190 0.0595950 0.998223i \(-0.481019\pi\)
0.0595950 + 0.998223i \(0.481019\pi\)
\(752\) 64.7624i 2.36164i
\(753\) 0 0
\(754\) 16.6803 0.607462
\(755\) 12.6803 3.15061i 0.461485 0.114663i
\(756\) 0 0
\(757\) 49.9877i 1.81683i −0.418065 0.908417i \(-0.637292\pi\)
0.418065 0.908417i \(-0.362708\pi\)
\(758\) 16.6803i 0.605857i
\(759\) 0 0
\(760\) −15.0205 60.4534i −0.544851 2.19288i
\(761\) 2.61265 0.0947083 0.0473542 0.998878i \(-0.484921\pi\)
0.0473542 + 0.998878i \(0.484921\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 82.0288 2.96770
\(765\) 0 0
\(766\) 72.7091 2.62709
\(767\) 9.69878i 0.350202i
\(768\) 0 0
\(769\) −15.6742 −0.565226 −0.282613 0.959234i \(-0.591201\pi\)
−0.282613 + 0.959234i \(0.591201\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 44.6803i 1.60808i
\(773\) 5.81205i 0.209045i −0.994523 0.104522i \(-0.966669\pi\)
0.994523 0.104522i \(-0.0333314\pi\)
\(774\) 0 0
\(775\) 34.2823 18.1568i 1.23146 0.652210i
\(776\) 76.3689 2.74148
\(777\) 0 0
\(778\) 15.2618i 0.547162i
\(779\) 20.0000 0.716574
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 6.83710i 0.244494i
\(783\) 0 0
\(784\) 0 0
\(785\) −2.65368 10.6803i −0.0947140 0.381198i
\(786\) 0 0
\(787\) 39.3484i 1.40262i −0.712857 0.701310i \(-0.752599\pi\)
0.712857 0.701310i \(-0.247401\pi\)
\(788\) 62.7936i 2.23693i
\(789\) 0 0
\(790\) −8.99386 36.1978i −0.319987 1.28786i
\(791\) 0 0
\(792\) 0 0
\(793\) 3.83096i 0.136041i
\(794\) 102.410 3.63439
\(795\) 0 0
\(796\) 120.666 4.27688
\(797\) 28.2823i 1.00181i 0.865502 + 0.500905i \(0.167000\pi\)
−0.865502 + 0.500905i \(0.833000\pi\)