Properties

Label 1400.2.x.c.993.11
Level $1400$
Weight $2$
Character 1400.993
Analytic conductor $11.179$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.x (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 993.11
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.c.657.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.923076 - 0.923076i) q^{3} +(0.915096 + 2.48246i) q^{7} +1.29586i q^{9} +O(q^{10})\) \(q+(0.923076 - 0.923076i) q^{3} +(0.915096 + 2.48246i) q^{7} +1.29586i q^{9} +1.21658 q^{11} +(0.996254 - 0.996254i) q^{13} +(0.567852 + 0.567852i) q^{17} +0.103488 q^{19} +(3.13620 + 1.44679i) q^{21} +(-1.43395 - 1.43395i) q^{23} +(3.96541 + 3.96541i) q^{27} +4.97655i q^{29} +4.35159i q^{31} +(1.12300 - 1.12300i) q^{33} +(2.54187 - 2.54187i) q^{37} -1.83924i q^{39} +7.06593i q^{41} +(-3.11342 - 3.11342i) q^{43} +(7.23621 + 7.23621i) q^{47} +(-5.32520 + 4.54338i) q^{49} +1.04834 q^{51} +(-0.882128 - 0.882128i) q^{53} +(0.0955275 - 0.0955275i) q^{57} +8.28584 q^{59} +10.0630i q^{61} +(-3.21692 + 1.18584i) q^{63} +(7.07422 - 7.07422i) q^{67} -2.64729 q^{69} +0.329005 q^{71} +(11.3569 - 11.3569i) q^{73} +(1.11329 + 3.02012i) q^{77} -13.6882i q^{79} +3.43317 q^{81} +(4.61538 - 4.61538i) q^{83} +(4.59373 + 4.59373i) q^{87} -13.1942 q^{89} +(3.38483 + 1.56149i) q^{91} +(4.01685 + 4.01685i) q^{93} +(-2.40130 - 2.40130i) q^{97} +1.57652i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q - 16q^{11} - 40q^{21} + 32q^{51} + 128q^{71} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 0.923076 0.923076i 0.532938 0.532938i −0.388507 0.921446i \(-0.627009\pi\)
0.921446 + 0.388507i \(0.127009\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.915096 + 2.48246i 0.345874 + 0.938281i
\(8\) 0 0
\(9\) 1.29586i 0.431953i
\(10\) 0 0
\(11\) 1.21658 0.366814 0.183407 0.983037i \(-0.441287\pi\)
0.183407 + 0.983037i \(0.441287\pi\)
\(12\) 0 0
\(13\) 0.996254 0.996254i 0.276311 0.276311i −0.555323 0.831634i \(-0.687406\pi\)
0.831634 + 0.555323i \(0.187406\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.567852 + 0.567852i 0.137724 + 0.137724i 0.772608 0.634883i \(-0.218952\pi\)
−0.634883 + 0.772608i \(0.718952\pi\)
\(18\) 0 0
\(19\) 0.103488 0.0237418 0.0118709 0.999930i \(-0.496221\pi\)
0.0118709 + 0.999930i \(0.496221\pi\)
\(20\) 0 0
\(21\) 3.13620 + 1.44679i 0.684376 + 0.315717i
\(22\) 0 0
\(23\) −1.43395 1.43395i −0.298999 0.298999i 0.541623 0.840622i \(-0.317810\pi\)
−0.840622 + 0.541623i \(0.817810\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.96541 + 3.96541i 0.763143 + 0.763143i
\(28\) 0 0
\(29\) 4.97655i 0.924121i 0.886848 + 0.462061i \(0.152890\pi\)
−0.886848 + 0.462061i \(0.847110\pi\)
\(30\) 0 0
\(31\) 4.35159i 0.781569i 0.920482 + 0.390784i \(0.127796\pi\)
−0.920482 + 0.390784i \(0.872204\pi\)
\(32\) 0 0
\(33\) 1.12300 1.12300i 0.195489 0.195489i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.54187 2.54187i 0.417880 0.417880i −0.466592 0.884473i \(-0.654518\pi\)
0.884473 + 0.466592i \(0.154518\pi\)
\(38\) 0 0
\(39\) 1.83924i 0.294514i
\(40\) 0 0
\(41\) 7.06593i 1.10351i 0.834005 + 0.551757i \(0.186042\pi\)
−0.834005 + 0.551757i \(0.813958\pi\)
\(42\) 0 0
\(43\) −3.11342 3.11342i −0.474793 0.474793i 0.428669 0.903462i \(-0.358983\pi\)
−0.903462 + 0.428669i \(0.858983\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.23621 + 7.23621i 1.05551 + 1.05551i 0.998366 + 0.0571445i \(0.0181996\pi\)
0.0571445 + 0.998366i \(0.481800\pi\)
\(48\) 0 0
\(49\) −5.32520 + 4.54338i −0.760742 + 0.649054i
\(50\) 0 0
\(51\) 1.04834 0.146797
\(52\) 0 0
\(53\) −0.882128 0.882128i −0.121170 0.121170i 0.643922 0.765091i \(-0.277306\pi\)
−0.765091 + 0.643922i \(0.777306\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.0955275 0.0955275i 0.0126529 0.0126529i
\(58\) 0 0
\(59\) 8.28584 1.07872 0.539362 0.842074i \(-0.318665\pi\)
0.539362 + 0.842074i \(0.318665\pi\)
\(60\) 0 0
\(61\) 10.0630i 1.28844i 0.764842 + 0.644218i \(0.222817\pi\)
−0.764842 + 0.644218i \(0.777183\pi\)
\(62\) 0 0
\(63\) −3.21692 + 1.18584i −0.405294 + 0.149401i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 7.07422 7.07422i 0.864253 0.864253i −0.127575 0.991829i \(-0.540720\pi\)
0.991829 + 0.127575i \(0.0407195\pi\)
\(68\) 0 0
\(69\) −2.64729 −0.318696
\(70\) 0 0
\(71\) 0.329005 0.0390457 0.0195229 0.999809i \(-0.493785\pi\)
0.0195229 + 0.999809i \(0.493785\pi\)
\(72\) 0 0
\(73\) 11.3569 11.3569i 1.32923 1.32923i 0.423183 0.906044i \(-0.360913\pi\)
0.906044 0.423183i \(-0.139087\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.11329 + 3.02012i 0.126871 + 0.344175i
\(78\) 0 0
\(79\) 13.6882i 1.54004i −0.638020 0.770019i \(-0.720246\pi\)
0.638020 0.770019i \(-0.279754\pi\)
\(80\) 0 0
\(81\) 3.43317 0.381463
\(82\) 0 0
\(83\) 4.61538 4.61538i 0.506604 0.506604i −0.406878 0.913482i \(-0.633383\pi\)
0.913482 + 0.406878i \(0.133383\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 4.59373 + 4.59373i 0.492500 + 0.492500i
\(88\) 0 0
\(89\) −13.1942 −1.39858 −0.699291 0.714837i \(-0.746501\pi\)
−0.699291 + 0.714837i \(0.746501\pi\)
\(90\) 0 0
\(91\) 3.38483 + 1.56149i 0.354826 + 0.163689i
\(92\) 0 0
\(93\) 4.01685 + 4.01685i 0.416528 + 0.416528i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.40130 2.40130i −0.243815 0.243815i 0.574611 0.818426i \(-0.305153\pi\)
−0.818426 + 0.574611i \(0.805153\pi\)
\(98\) 0 0
\(99\) 1.57652i 0.158446i
\(100\) 0 0
\(101\) 8.77555i 0.873200i 0.899656 + 0.436600i \(0.143817\pi\)
−0.899656 + 0.436600i \(0.856183\pi\)
\(102\) 0 0
\(103\) −0.710448 + 0.710448i −0.0700025 + 0.0700025i −0.741241 0.671239i \(-0.765763\pi\)
0.671239 + 0.741241i \(0.265763\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.2829 13.2829i 1.28411 1.28411i 0.345796 0.938310i \(-0.387609\pi\)
0.938310 0.345796i \(-0.112391\pi\)
\(108\) 0 0
\(109\) 7.13731i 0.683630i −0.939767 0.341815i \(-0.888958\pi\)
0.939767 0.341815i \(-0.111042\pi\)
\(110\) 0 0
\(111\) 4.69267i 0.445409i
\(112\) 0 0
\(113\) −4.35947 4.35947i −0.410104 0.410104i 0.471671 0.881775i \(-0.343651\pi\)
−0.881775 + 0.471671i \(0.843651\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.29100 + 1.29100i 0.119353 + 0.119353i
\(118\) 0 0
\(119\) −0.890030 + 1.92931i −0.0815889 + 0.176860i
\(120\) 0 0
\(121\) −9.51992 −0.865448
\(122\) 0 0
\(123\) 6.52240 + 6.52240i 0.588105 + 0.588105i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −3.07395 + 3.07395i −0.272769 + 0.272769i −0.830214 0.557445i \(-0.811782\pi\)
0.557445 + 0.830214i \(0.311782\pi\)
\(128\) 0 0
\(129\) −5.74786 −0.506070
\(130\) 0 0
\(131\) 6.12826i 0.535429i −0.963498 0.267714i \(-0.913732\pi\)
0.963498 0.267714i \(-0.0862684\pi\)
\(132\) 0 0
\(133\) 0.0947017 + 0.256905i 0.00821168 + 0.0222765i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.69973 + 2.69973i −0.230654 + 0.230654i −0.812965 0.582312i \(-0.802148\pi\)
0.582312 + 0.812965i \(0.302148\pi\)
\(138\) 0 0
\(139\) 8.95480 0.759536 0.379768 0.925082i \(-0.376004\pi\)
0.379768 + 0.925082i \(0.376004\pi\)
\(140\) 0 0
\(141\) 13.3592 1.12504
\(142\) 0 0
\(143\) 1.21203 1.21203i 0.101355 0.101355i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.721680 + 9.10945i −0.0595232 + 0.751335i
\(148\) 0 0
\(149\) 9.15227i 0.749783i −0.927069 0.374891i \(-0.877680\pi\)
0.927069 0.374891i \(-0.122320\pi\)
\(150\) 0 0
\(151\) −10.4406 −0.849648 −0.424824 0.905276i \(-0.639664\pi\)
−0.424824 + 0.905276i \(0.639664\pi\)
\(152\) 0 0
\(153\) −0.735857 + 0.735857i −0.0594905 + 0.0594905i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −13.3298 13.3298i −1.06384 1.06384i −0.997818 0.0660171i \(-0.978971\pi\)
−0.0660171 0.997818i \(-0.521029\pi\)
\(158\) 0 0
\(159\) −1.62854 −0.129152
\(160\) 0 0
\(161\) 2.24752 4.87192i 0.177129 0.383961i
\(162\) 0 0
\(163\) −3.31503 3.31503i −0.259653 0.259653i 0.565260 0.824913i \(-0.308776\pi\)
−0.824913 + 0.565260i \(0.808776\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.75278 + 3.75278i 0.290399 + 0.290399i 0.837238 0.546839i \(-0.184169\pi\)
−0.546839 + 0.837238i \(0.684169\pi\)
\(168\) 0 0
\(169\) 11.0150i 0.847304i
\(170\) 0 0
\(171\) 0.134106i 0.0102554i
\(172\) 0 0
\(173\) −13.8850 + 13.8850i −1.05565 + 1.05565i −0.0572975 + 0.998357i \(0.518248\pi\)
−0.998357 + 0.0572975i \(0.981752\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 7.64846 7.64846i 0.574894 0.574894i
\(178\) 0 0
\(179\) 9.64006i 0.720532i 0.932850 + 0.360266i \(0.117314\pi\)
−0.932850 + 0.360266i \(0.882686\pi\)
\(180\) 0 0
\(181\) 15.6258i 1.16146i 0.814097 + 0.580728i \(0.197232\pi\)
−0.814097 + 0.580728i \(0.802768\pi\)
\(182\) 0 0
\(183\) 9.28893 + 9.28893i 0.686657 + 0.686657i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.690840 + 0.690840i 0.0505192 + 0.0505192i
\(188\) 0 0
\(189\) −6.21523 + 13.4727i −0.452091 + 0.979994i
\(190\) 0 0
\(191\) −18.4481 −1.33486 −0.667430 0.744673i \(-0.732606\pi\)
−0.667430 + 0.744673i \(0.732606\pi\)
\(192\) 0 0
\(193\) −15.3732 15.3732i −1.10659 1.10659i −0.993596 0.112990i \(-0.963957\pi\)
−0.112990 0.993596i \(-0.536043\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −15.7687 + 15.7687i −1.12347 + 1.12347i −0.132258 + 0.991215i \(0.542223\pi\)
−0.991215 + 0.132258i \(0.957777\pi\)
\(198\) 0 0
\(199\) 24.6117 1.74468 0.872339 0.488901i \(-0.162602\pi\)
0.872339 + 0.488901i \(0.162602\pi\)
\(200\) 0 0
\(201\) 13.0601i 0.921188i
\(202\) 0 0
\(203\) −12.3541 + 4.55402i −0.867085 + 0.319629i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.85820 1.85820i 0.129154 0.129154i
\(208\) 0 0
\(209\) 0.125902 0.00870883
\(210\) 0 0
\(211\) 7.49647 0.516078 0.258039 0.966134i \(-0.416924\pi\)
0.258039 + 0.966134i \(0.416924\pi\)
\(212\) 0 0
\(213\) 0.303697 0.303697i 0.0208090 0.0208090i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −10.8026 + 3.98213i −0.733331 + 0.270324i
\(218\) 0 0
\(219\) 20.9666i 1.41679i
\(220\) 0 0
\(221\) 1.13145 0.0761096
\(222\) 0 0
\(223\) 7.88619 7.88619i 0.528098 0.528098i −0.391907 0.920005i \(-0.628184\pi\)
0.920005 + 0.391907i \(0.128184\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.54162 6.54162i −0.434182 0.434182i 0.455866 0.890048i \(-0.349330\pi\)
−0.890048 + 0.455866i \(0.849330\pi\)
\(228\) 0 0
\(229\) 6.01657 0.397586 0.198793 0.980041i \(-0.436298\pi\)
0.198793 + 0.980041i \(0.436298\pi\)
\(230\) 0 0
\(231\) 3.81545 + 1.76015i 0.251039 + 0.115809i
\(232\) 0 0
\(233\) 8.74138 + 8.74138i 0.572667 + 0.572667i 0.932873 0.360206i \(-0.117294\pi\)
−0.360206 + 0.932873i \(0.617294\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −12.6352 12.6352i −0.820746 0.820746i
\(238\) 0 0
\(239\) 23.0398i 1.49032i 0.666884 + 0.745162i \(0.267628\pi\)
−0.666884 + 0.745162i \(0.732372\pi\)
\(240\) 0 0
\(241\) 22.8987i 1.47504i −0.675328 0.737518i \(-0.735998\pi\)
0.675328 0.737518i \(-0.264002\pi\)
\(242\) 0 0
\(243\) −8.72714 + 8.72714i −0.559847 + 0.559847i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.103101 0.103101i 0.00656013 0.00656013i
\(248\) 0 0
\(249\) 8.52070i 0.539978i
\(250\) 0 0
\(251\) 24.5447i 1.54925i −0.632423 0.774623i \(-0.717940\pi\)
0.632423 0.774623i \(-0.282060\pi\)
\(252\) 0 0
\(253\) −1.74452 1.74452i −0.109677 0.109677i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −7.22931 7.22931i −0.450952 0.450952i 0.444718 0.895670i \(-0.353304\pi\)
−0.895670 + 0.444718i \(0.853304\pi\)
\(258\) 0 0
\(259\) 8.63613 + 3.98402i 0.536623 + 0.247555i
\(260\) 0 0
\(261\) −6.44890 −0.399177
\(262\) 0 0
\(263\) 12.0746 + 12.0746i 0.744550 + 0.744550i 0.973450 0.228900i \(-0.0735130\pi\)
−0.228900 + 0.973450i \(0.573513\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −12.1793 + 12.1793i −0.745358 + 0.745358i
\(268\) 0 0
\(269\) 0.430862 0.0262701 0.0131351 0.999914i \(-0.495819\pi\)
0.0131351 + 0.999914i \(0.495819\pi\)
\(270\) 0 0
\(271\) 10.1612i 0.617248i −0.951184 0.308624i \(-0.900132\pi\)
0.951184 0.308624i \(-0.0998685\pi\)
\(272\) 0 0
\(273\) 4.56583 1.68308i 0.276336 0.101865i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −11.9353 + 11.9353i −0.717123 + 0.717123i −0.968015 0.250892i \(-0.919276\pi\)
0.250892 + 0.968015i \(0.419276\pi\)
\(278\) 0 0
\(279\) −5.63905 −0.337601
\(280\) 0 0
\(281\) 1.47379 0.0879191 0.0439596 0.999033i \(-0.486003\pi\)
0.0439596 + 0.999033i \(0.486003\pi\)
\(282\) 0 0
\(283\) −2.68335 + 2.68335i −0.159508 + 0.159508i −0.782349 0.622840i \(-0.785979\pi\)
0.622840 + 0.782349i \(0.285979\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −17.5409 + 6.46601i −1.03541 + 0.381677i
\(288\) 0 0
\(289\) 16.3551i 0.962064i
\(290\) 0 0
\(291\) −4.43317 −0.259877
\(292\) 0 0
\(293\) −20.8195 + 20.8195i −1.21629 + 1.21629i −0.247368 + 0.968921i \(0.579566\pi\)
−0.968921 + 0.247368i \(0.920434\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 4.82425 + 4.82425i 0.279931 + 0.279931i
\(298\) 0 0
\(299\) −2.85715 −0.165234
\(300\) 0 0
\(301\) 4.87986 10.5780i 0.281271 0.609707i
\(302\) 0 0
\(303\) 8.10050 + 8.10050i 0.465362 + 0.465362i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −10.0501 10.0501i −0.573588 0.573588i 0.359541 0.933129i \(-0.382933\pi\)
−0.933129 + 0.359541i \(0.882933\pi\)
\(308\) 0 0
\(309\) 1.31160i 0.0746141i
\(310\) 0 0
\(311\) 6.48676i 0.367830i −0.982942 0.183915i \(-0.941123\pi\)
0.982942 0.183915i \(-0.0588771\pi\)
\(312\) 0 0
\(313\) 11.7441 11.7441i 0.663814 0.663814i −0.292463 0.956277i \(-0.594475\pi\)
0.956277 + 0.292463i \(0.0944748\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 18.1787 18.1787i 1.02102 1.02102i 0.0212445 0.999774i \(-0.493237\pi\)
0.999774 0.0212445i \(-0.00676284\pi\)
\(318\) 0 0
\(319\) 6.05439i 0.338981i
\(320\) 0 0
\(321\) 24.5223i 1.36870i
\(322\) 0 0
\(323\) 0.0587660 + 0.0587660i 0.00326983 + 0.00326983i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −6.58828 6.58828i −0.364333 0.364333i
\(328\) 0 0
\(329\) −11.3418 + 24.5854i −0.625292 + 1.35544i
\(330\) 0 0
\(331\) −2.57796 −0.141697 −0.0708486 0.997487i \(-0.522571\pi\)
−0.0708486 + 0.997487i \(0.522571\pi\)
\(332\) 0 0
\(333\) 3.29390 + 3.29390i 0.180505 + 0.180505i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −16.8387 + 16.8387i −0.917264 + 0.917264i −0.996830 0.0795652i \(-0.974647\pi\)
0.0795652 + 0.996830i \(0.474647\pi\)
\(338\) 0 0
\(339\) −8.04825 −0.437121
\(340\) 0 0
\(341\) 5.29408i 0.286690i
\(342\) 0 0
\(343\) −16.1518 9.06195i −0.872116 0.489299i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.2400 12.2400i 0.657079 0.657079i −0.297609 0.954688i \(-0.596189\pi\)
0.954688 + 0.297609i \(0.0961892\pi\)
\(348\) 0 0
\(349\) 27.3348 1.46320 0.731598 0.681736i \(-0.238775\pi\)
0.731598 + 0.681736i \(0.238775\pi\)
\(350\) 0 0
\(351\) 7.90110 0.421730
\(352\) 0 0
\(353\) −3.42987 + 3.42987i −0.182553 + 0.182553i −0.792468 0.609914i \(-0.791204\pi\)
0.609914 + 0.792468i \(0.291204\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0.959334 + 2.60247i 0.0507734 + 0.137737i
\(358\) 0 0
\(359\) 30.4578i 1.60750i −0.594966 0.803751i \(-0.702834\pi\)
0.594966 0.803751i \(-0.297166\pi\)
\(360\) 0 0
\(361\) −18.9893 −0.999436
\(362\) 0 0
\(363\) −8.78762 + 8.78762i −0.461230 + 0.461230i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −17.6219 17.6219i −0.919856 0.919856i 0.0771629 0.997019i \(-0.475414\pi\)
−0.997019 + 0.0771629i \(0.975414\pi\)
\(368\) 0 0
\(369\) −9.15646 −0.476666
\(370\) 0 0
\(371\) 1.38261 2.99708i 0.0717817 0.155601i
\(372\) 0 0
\(373\) 13.1403 + 13.1403i 0.680379 + 0.680379i 0.960086 0.279707i \(-0.0902372\pi\)
−0.279707 + 0.960086i \(0.590237\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.95790 + 4.95790i 0.255345 + 0.255345i
\(378\) 0 0
\(379\) 9.88955i 0.507992i 0.967205 + 0.253996i \(0.0817450\pi\)
−0.967205 + 0.253996i \(0.918255\pi\)
\(380\) 0 0
\(381\) 5.67499i 0.290738i
\(382\) 0 0
\(383\) 1.61392 1.61392i 0.0824673 0.0824673i −0.664670 0.747137i \(-0.731428\pi\)
0.747137 + 0.664670i \(0.231428\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.03456 4.03456i 0.205088 0.205088i
\(388\) 0 0
\(389\) 33.9003i 1.71881i −0.511292 0.859407i \(-0.670833\pi\)
0.511292 0.859407i \(-0.329167\pi\)
\(390\) 0 0
\(391\) 1.62854i 0.0823590i
\(392\) 0 0
\(393\) −5.65685 5.65685i −0.285351 0.285351i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.67961 4.67961i −0.234863 0.234863i 0.579856 0.814719i \(-0.303109\pi\)
−0.814719 + 0.579856i \(0.803109\pi\)
\(398\) 0 0
\(399\) 0.324560 + 0.149726i 0.0162483 + 0.00749569i
\(400\) 0 0
\(401\) −31.2427 −1.56018 −0.780092 0.625665i \(-0.784828\pi\)
−0.780092 + 0.625665i \(0.784828\pi\)
\(402\) 0 0
\(403\) 4.33529 + 4.33529i 0.215956 + 0.215956i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.09239 3.09239i 0.153284 0.153284i
\(408\) 0 0
\(409\) 15.5228 0.767554 0.383777 0.923426i \(-0.374623\pi\)
0.383777 + 0.923426i \(0.374623\pi\)
\(410\) 0 0
\(411\) 4.98411i 0.245848i
\(412\) 0 0
\(413\) 7.58234 + 20.5693i 0.373103 + 1.01215i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 8.26596 8.26596i 0.404786 0.404786i
\(418\) 0 0
\(419\) −29.0634 −1.41984 −0.709920 0.704282i \(-0.751269\pi\)
−0.709920 + 0.704282i \(0.751269\pi\)
\(420\) 0 0
\(421\) 2.76601 0.134807 0.0674034 0.997726i \(-0.478529\pi\)
0.0674034 + 0.997726i \(0.478529\pi\)
\(422\) 0 0
\(423\) −9.37712 + 9.37712i −0.455931 + 0.455931i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −24.9810 + 9.20863i −1.20892 + 0.445637i
\(428\) 0 0
\(429\) 2.23759i 0.108032i
\(430\) 0 0
\(431\) −6.31931 −0.304391 −0.152195 0.988350i \(-0.548634\pi\)
−0.152195 + 0.988350i \(0.548634\pi\)
\(432\) 0 0
\(433\) 12.4583 12.4583i 0.598706 0.598706i −0.341262 0.939968i \(-0.610854\pi\)
0.939968 + 0.341262i \(0.110854\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.148397 0.148397i −0.00709878 0.00709878i
\(438\) 0 0
\(439\) 16.9890 0.810842 0.405421 0.914130i \(-0.367125\pi\)
0.405421 + 0.914130i \(0.367125\pi\)
\(440\) 0 0
\(441\) −5.88758 6.90071i −0.280361 0.328605i
\(442\) 0 0
\(443\) −16.8935 16.8935i −0.802633 0.802633i 0.180873 0.983506i \(-0.442108\pi\)
−0.983506 + 0.180873i \(0.942108\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −8.44824 8.44824i −0.399588 0.399588i
\(448\) 0 0
\(449\) 4.85641i 0.229188i 0.993412 + 0.114594i \(0.0365567\pi\)
−0.993412 + 0.114594i \(0.963443\pi\)
\(450\) 0 0
\(451\) 8.59630i 0.404784i
\(452\) 0 0
\(453\) −9.63752 + 9.63752i −0.452810 + 0.452810i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 27.2995 27.2995i 1.27702 1.27702i 0.334686 0.942330i \(-0.391370\pi\)
0.942330 0.334686i \(-0.108630\pi\)
\(458\) 0 0
\(459\) 4.50353i 0.210207i
\(460\) 0 0
\(461\) 33.0098i 1.53742i 0.639599 + 0.768709i \(0.279100\pi\)
−0.639599 + 0.768709i \(0.720900\pi\)
\(462\) 0 0
\(463\) −11.5774 11.5774i −0.538048 0.538048i 0.384908 0.922955i \(-0.374233\pi\)
−0.922955 + 0.384908i \(0.874233\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.90541 7.90541i −0.365819 0.365819i 0.500131 0.865950i \(-0.333285\pi\)
−0.865950 + 0.500131i \(0.833285\pi\)
\(468\) 0 0
\(469\) 24.0350 + 11.0879i 1.10984 + 0.511990i
\(470\) 0 0
\(471\) −24.6089 −1.13392
\(472\) 0 0
\(473\) −3.78774 3.78774i −0.174161 0.174161i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.14311 1.14311i 0.0523396 0.0523396i
\(478\) 0 0
\(479\) −39.6277 −1.81064 −0.905319 0.424733i \(-0.860368\pi\)
−0.905319 + 0.424733i \(0.860368\pi\)
\(480\) 0 0
\(481\) 5.06469i 0.230930i
\(482\) 0 0
\(483\) −2.42253 6.57179i −0.110229 0.299027i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 7.44241 7.44241i 0.337248 0.337248i −0.518083 0.855331i \(-0.673354\pi\)
0.855331 + 0.518083i \(0.173354\pi\)
\(488\) 0 0
\(489\) −6.12006 −0.276759
\(490\) 0 0
\(491\) −0.423477 −0.0191113 −0.00955563 0.999954i \(-0.503042\pi\)
−0.00955563 + 0.999954i \(0.503042\pi\)
\(492\) 0 0
\(493\) −2.82594 + 2.82594i −0.127274 + 0.127274i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.301072 + 0.816742i 0.0135049 + 0.0366359i
\(498\) 0 0
\(499\) 42.5173i 1.90334i −0.307130 0.951668i \(-0.599369\pi\)
0.307130 0.951668i \(-0.400631\pi\)
\(500\) 0 0
\(501\) 6.92820 0.309529
\(502\) 0 0
\(503\) 6.94351 6.94351i 0.309596 0.309596i −0.535157 0.844753i \(-0.679748\pi\)
0.844753 + 0.535157i \(0.179748\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 10.1676 + 10.1676i 0.451561 + 0.451561i
\(508\) 0 0
\(509\) 38.8912 1.72382 0.861911 0.507059i \(-0.169267\pi\)
0.861911 + 0.507059i \(0.169267\pi\)
\(510\) 0 0
\(511\) 38.5858 + 17.8004i 1.70693 + 0.787444i
\(512\) 0 0
\(513\) 0.410373 + 0.410373i 0.0181184 + 0.0181184i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 8.80347 + 8.80347i 0.387176 + 0.387176i
\(518\) 0 0
\(519\) 25.6338i 1.12520i
\(520\) 0 0
\(521\) 31.1879i 1.36637i −0.730246 0.683184i \(-0.760595\pi\)
0.730246 0.683184i \(-0.239405\pi\)
\(522\) 0 0
\(523\) 19.0273 19.0273i 0.832007 0.832007i −0.155784 0.987791i \(-0.549790\pi\)
0.987791 + 0.155784i \(0.0497903\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.47106 + 2.47106i −0.107641 + 0.107641i
\(528\) 0 0
\(529\) 18.8876i 0.821199i
\(530\) 0 0
\(531\) 10.7373i 0.465959i
\(532\) 0 0
\(533\) 7.03946 + 7.03946i 0.304913 + 0.304913i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 8.89851 + 8.89851i 0.383999 + 0.383999i
\(538\) 0 0
\(539\) −6.47855 + 5.52740i −0.279051 + 0.238082i
\(540\) 0 0
\(541\) 2.48151 0.106688 0.0533442 0.998576i \(-0.483012\pi\)
0.0533442 + 0.998576i \(0.483012\pi\)
\(542\) 0 0
\(543\) 14.4238 + 14.4238i 0.618985 + 0.618985i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −20.6132 + 20.6132i −0.881356 + 0.881356i −0.993673 0.112316i \(-0.964173\pi\)
0.112316 + 0.993673i \(0.464173\pi\)
\(548\) 0 0
\(549\) −13.0403 −0.556544
\(550\) 0 0
\(551\) 0.515014i 0.0219403i
\(552\) 0 0
\(553\) 33.9803 12.5260i 1.44499 0.532659i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.10076 5.10076i 0.216126 0.216126i −0.590738 0.806864i \(-0.701163\pi\)
0.806864 + 0.590738i \(0.201163\pi\)
\(558\) 0 0
\(559\) −6.20352 −0.262381
\(560\) 0 0
\(561\) 1.27540 0.0538473
\(562\) 0 0
\(563\) −7.13112 + 7.13112i −0.300541 + 0.300541i −0.841225 0.540685i \(-0.818165\pi\)
0.540685 + 0.841225i \(0.318165\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 3.14168 + 8.52270i 0.131938 + 0.357920i
\(568\) 0 0
\(569\) 8.16848i 0.342441i 0.985233 + 0.171220i \(0.0547710\pi\)
−0.985233 + 0.171220i \(0.945229\pi\)
\(570\) 0 0
\(571\) −6.66328 −0.278849 −0.139425 0.990233i \(-0.544525\pi\)
−0.139425 + 0.990233i \(0.544525\pi\)
\(572\) 0 0
\(573\) −17.0290 + 17.0290i −0.711398 + 0.711398i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 22.2531 + 22.2531i 0.926410 + 0.926410i 0.997472 0.0710620i \(-0.0226388\pi\)
−0.0710620 + 0.997472i \(0.522639\pi\)
\(578\) 0 0
\(579\) −28.3812 −1.17948
\(580\) 0 0
\(581\) 15.6810 + 7.23397i 0.650558 + 0.300116i
\(582\) 0 0
\(583\) −1.07318 1.07318i −0.0444467 0.0444467i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 16.6776 + 16.6776i 0.688357 + 0.688357i 0.961869 0.273512i \(-0.0881853\pi\)
−0.273512 + 0.961869i \(0.588185\pi\)
\(588\) 0 0
\(589\) 0.450338i 0.0185559i
\(590\) 0 0
\(591\) 29.1114i 1.19748i
\(592\) 0 0
\(593\) 6.56327 6.56327i 0.269521 0.269521i −0.559386 0.828907i \(-0.688963\pi\)
0.828907 + 0.559386i \(0.188963\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 22.7185 22.7185i 0.929806 0.929806i
\(598\) 0 0
\(599\) 9.55935i 0.390585i 0.980745 + 0.195292i \(0.0625655\pi\)
−0.980745 + 0.195292i \(0.937434\pi\)
\(600\) 0 0
\(601\) 20.1897i 0.823555i −0.911285 0.411777i \(-0.864908\pi\)
0.911285 0.411777i \(-0.135092\pi\)
\(602\) 0 0
\(603\) 9.16719 + 9.16719i 0.373317 + 0.373317i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −9.55854 9.55854i −0.387969 0.387969i 0.485993 0.873962i \(-0.338458\pi\)
−0.873962 + 0.485993i \(0.838458\pi\)
\(608\) 0 0
\(609\) −7.20004 + 15.6075i −0.291760 + 0.632446i
\(610\) 0 0
\(611\) 14.4182 0.583298
\(612\) 0 0
\(613\) −27.0641 27.0641i −1.09311 1.09311i −0.995195 0.0979135i \(-0.968783\pi\)
−0.0979135 0.995195i \(-0.531217\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.331871 + 0.331871i −0.0133606 + 0.0133606i −0.713756 0.700395i \(-0.753007\pi\)
0.700395 + 0.713756i \(0.253007\pi\)
\(618\) 0 0
\(619\) −2.99126 −0.120229 −0.0601145 0.998191i \(-0.519147\pi\)
−0.0601145 + 0.998191i \(0.519147\pi\)
\(620\) 0 0
\(621\) 11.3724i 0.456358i
\(622\) 0 0
\(623\) −12.0740 32.7540i −0.483733 1.31226i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0.116217 0.116217i 0.00464127 0.00464127i
\(628\) 0 0
\(629\) 2.88681 0.115105
\(630\) 0 0
\(631\) 28.0573 1.11694 0.558471 0.829524i \(-0.311388\pi\)
0.558471 + 0.829524i \(0.311388\pi\)
\(632\) 0 0
\(633\) 6.91981 6.91981i 0.275038 0.275038i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −0.778891 + 9.83160i −0.0308608 + 0.389542i
\(638\) 0 0
\(639\) 0.426345i 0.0168659i
\(640\) 0 0
\(641\) 26.1153 1.03149 0.515746 0.856742i \(-0.327515\pi\)
0.515746 + 0.856742i \(0.327515\pi\)
\(642\) 0 0
\(643\) 20.4107 20.4107i 0.804921 0.804921i −0.178939 0.983860i \(-0.557267\pi\)
0.983860 + 0.178939i \(0.0572666\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18.2719 + 18.2719i 0.718342 + 0.718342i 0.968265 0.249924i \(-0.0804056\pi\)
−0.249924 + 0.968265i \(0.580406\pi\)
\(648\) 0 0
\(649\) 10.0804 0.395691
\(650\) 0 0
\(651\) −6.29586 + 13.6475i −0.246754 + 0.534887i
\(652\) 0 0
\(653\) 24.0558 + 24.0558i 0.941376 + 0.941376i 0.998374 0.0569981i \(-0.0181529\pi\)
−0.0569981 + 0.998374i \(0.518153\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 14.7170 + 14.7170i 0.574164 + 0.574164i
\(658\) 0 0
\(659\) 30.6949i 1.19570i 0.801607 + 0.597851i \(0.203979\pi\)
−0.801607 + 0.597851i \(0.796021\pi\)
\(660\) 0 0
\(661\) 30.4577i 1.18467i 0.805692 + 0.592335i \(0.201794\pi\)
−0.805692 + 0.592335i \(0.798206\pi\)
\(662\) 0 0
\(663\) 1.04441 1.04441i 0.0405617 0.0405617i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.13611 7.13611i 0.276311 0.276311i
\(668\) 0 0
\(669\) 14.5591i 0.562888i
\(670\) 0 0
\(671\) 12.2425i 0.472617i
\(672\) 0 0
\(673\) −24.7437 24.7437i −0.953801 0.953801i 0.0451778 0.998979i \(-0.485615\pi\)
−0.998979 + 0.0451778i \(0.985615\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 23.6461 + 23.6461i 0.908793 + 0.908793i 0.996175 0.0873819i \(-0.0278500\pi\)
−0.0873819 + 0.996175i \(0.527850\pi\)
\(678\) 0 0
\(679\) 3.76371 8.15855i 0.144438 0.313096i
\(680\) 0 0
\(681\) −12.0768 −0.462785
\(682\) 0 0
\(683\) 25.8548 + 25.8548i 0.989307 + 0.989307i 0.999943 0.0106366i \(-0.00338580\pi\)
−0.0106366 + 0.999943i \(0.503386\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 5.55375 5.55375i 0.211889 0.211889i
\(688\) 0 0
\(689\) −1.75765 −0.0669610
\(690\) 0 0
\(691\) 40.5649i 1.54316i 0.636131 + 0.771581i \(0.280534\pi\)
−0.636131 + 0.771581i \(0.719466\pi\)
\(692\) 0 0
\(693\) −3.91365 + 1.44267i −0.148667 + 0.0548025i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −4.01241 + 4.01241i −0.151981 + 0.151981i
\(698\) 0 0
\(699\) 16.1379 0.610393
\(700\) 0 0
\(701\) 12.4481 0.470159 0.235080 0.971976i \(-0.424465\pi\)
0.235080 + 0.971976i \(0.424465\pi\)
\(702\) 0 0
\(703\) 0.263053 0.263053i 0.00992124 0.00992124i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −21.7849 + 8.03048i −0.819307 + 0.302017i
\(708\) 0 0
\(709\) 23.9211i 0.898377i −0.893437 0.449189i \(-0.851713\pi\)
0.893437 0.449189i \(-0.148287\pi\)
\(710\) 0 0
\(711\) 17.7379 0.665225
\(712\) 0 0
\(713\) 6.23996 6.23996i 0.233688 0.233688i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 21.2675 + 21.2675i 0.794251 + 0.794251i
\(718\) 0 0
\(719\) −32.4190 −1.20902 −0.604512 0.796596i \(-0.706632\pi\)
−0.604512 + 0.796596i \(0.706632\pi\)
\(720\) 0 0
\(721\) −2.41379 1.11353i −0.0898941 0.0414700i
\(722\) 0 0
\(723\) −21.1373 21.1373i −0.786103 0.786103i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.14090 + 2.14090i 0.0794017 + 0.0794017i 0.745692 0.666291i \(-0.232119\pi\)
−0.666291 + 0.745692i \(0.732119\pi\)
\(728\) 0 0
\(729\) 26.4111i 0.978191i
\(730\) 0 0
\(731\) 3.53593i 0.130781i
\(732\) 0 0
\(733\) 18.1647 18.1647i 0.670930 0.670930i −0.287001 0.957930i \(-0.592658\pi\)
0.957930 + 0.287001i \(0.0926582\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.60638 8.60638i 0.317020 0.317020i
\(738\) 0 0
\(739\) 42.7086i 1.57106i 0.618822 + 0.785531i \(0.287610\pi\)
−0.618822 + 0.785531i \(0.712390\pi\)
\(740\) 0 0
\(741\) 0.190339i 0.00699229i
\(742\) 0 0
\(743\) −15.2579 15.2579i −0.559759 0.559759i 0.369480 0.929239i \(-0.379536\pi\)
−0.929239 + 0.369480i \(0.879536\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 5.98089 + 5.98089i 0.218829 + 0.218829i
\(748\) 0 0
\(749\) 45.1294 + 20.8191i 1.64899 + 0.760713i
\(750\) 0 0
\(751\) 8.87908 0.324002 0.162001 0.986791i \(-0.448205\pi\)
0.162001 + 0.986791i \(0.448205\pi\)
\(752\) 0 0
\(753\) −22.6566 22.6566i −0.825653 0.825653i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −7.15917 + 7.15917i −0.260204 + 0.260204i −0.825137 0.564933i \(-0.808902\pi\)
0.564933 + 0.825137i \(0.308902\pi\)
\(758\) 0 0
\(759\) −3.22065 −0.116902
\(760\) 0 0
\(761\) 36.7681i 1.33284i 0.745575 + 0.666422i \(0.232175\pi\)
−0.745575 + 0.666422i \(0.767825\pi\)
\(762\) 0 0
\(763\) 17.7181 6.53133i 0.641437 0.236450i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.25480 8.25480i 0.298064 0.298064i
\(768\) 0 0
\(769\) 0.372202 0.0134220 0.00671098 0.999977i \(-0.497864\pi\)
0.00671098 + 0.999977i \(0.497864\pi\)
\(770\) 0 0
\(771\) −13.3464 −0.480659
\(772\) 0 0
\(773\) −28.1925 + 28.1925i −1.01402 + 1.01402i −0.0141148 + 0.999900i \(0.504493\pi\)
−0.999900 + 0.0141148i \(0.995507\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 11.6494 4.29425i 0.417919 0.154055i
\(778\) 0 0
\(779\) 0.731241i 0.0261994i
\(780\) 0 0
\(781\) 0.400263 0.0143225
\(782\) 0 0
\(783\) −19.7340 + 19.7340i −0.705237 + 0.705237i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −2.61707 2.61707i −0.0932886 0.0932886i 0.658922 0.752211i \(-0.271013\pi\)
−0.752211 + 0.658922i \(0.771013\pi\)
\(788\) 0 0
\(789\) 22.2915 0.793598
\(790\) 0 0
\(791\) 6.83286 14.8115i 0.242949 0.526637i
\(792\) 0 0
\(793\) 10.0253 + 10.0253i 0.356009 + 0.356009i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 13.2158 + 13.2158i 0.468127 + 0.468127i 0.901307 0.433180i \(-0.142609\pi\)
−0.433180 + 0.901307i \(0.642609\pi\)
\(798\) 0 0
\(799\) 8.21820i 0.290739i
\(800\) 0 0
\(801\) 17.0978i 0.604122i
\(802\) 0 0
\(803\) 13.8167 13.8167i 0.487579 0.487579i
\(804\) 0 0