Properties

Label 1400.2.x.c.993.6
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 993.6
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.c.657.5

$q$-expansion

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

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 −0.921446 0.388507i \(-0.872991\pi\)
0.388507 + 0.921446i \(0.372991\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.48246 0.915096i −0.938281 0.345874i
\(8\) 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 −0.831634 0.555323i \(-0.812594\pi\)
0.555323 + 0.831634i \(0.312594\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.567852 0.567852i −0.137724 0.137724i 0.634883 0.772608i \(-0.281048\pi\)
−0.772608 + 0.634883i \(0.781048\pi\)
\(18\) 0 0
\(19\) −0.103488 −0.0237418 −0.0118709 0.999930i \(-0.503779\pi\)
−0.0118709 + 0.999930i \(0.503779\pi\)
\(20\) 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 \(-0.872204\pi\)
0.920482 0.390784i \(-0.127796\pi\)
\(32\) 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 \(-0.813958\pi\)
0.834005 0.551757i \(-0.186042\pi\)
\(42\) 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 \(-0.981800\pi\)
−0.0571445 0.998366i \(-0.518200\pi\)
\(48\) 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 \(-0.681335\pi\)
−0.539362 + 0.842074i \(0.681335\pi\)
\(60\) 0 0
\(61\) 10.0630i 1.28844i −0.764842 0.644218i \(-0.777183\pi\)
0.764842 0.644218i \(-0.222817\pi\)
\(62\) 0 0
\(63\) 1.18584 3.21692i 0.149401 0.405294i
\(64\) 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 \(0.639087\pi\)
−0.906044 + 0.423183i \(0.860913\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.02012 1.11329i −0.344175 0.126871i
\(78\) 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 −0.913482 0.406878i \(-0.866617\pi\)
0.406878 + 0.913482i \(0.366617\pi\)
\(84\) 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 \(-0.253499\pi\)
0.699291 + 0.714837i \(0.253499\pi\)
\(90\) 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 0.818426 0.574611i \(-0.194847\pi\)
−0.574611 + 0.818426i \(0.694847\pi\)
\(98\) 0 0
\(99\) 1.57652i 0.158446i
\(100\) 0 0
\(101\) 8.77555i 0.873200i −0.899656 0.436600i \(-0.856183\pi\)
0.899656 0.436600i \(-0.143817\pi\)
\(102\) 0 0
\(103\) 0.710448 0.710448i 0.0700025 0.0700025i −0.671239 0.741241i \(-0.734237\pi\)
0.741241 + 0.671239i \(0.234237\pi\)
\(104\) 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 \(0.0862684\pi\)
−0.963498 + 0.267714i \(0.913732\pi\)
\(132\) 0 0
\(133\) 0.256905 + 0.0947017i 0.0222765 + 0.00821168i
\(134\) 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 \(-0.623996\pi\)
−0.379768 + 0.925082i \(0.623996\pi\)
\(140\) 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
\(147\) −9.10945 + 0.721680i −0.751335 + 0.0595232i
\(148\) 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 \(0.0210292\pi\)
0.0660171 + 0.997818i \(0.478971\pi\)
\(158\) 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 0.546839 0.837238i \(-0.315831\pi\)
−0.837238 + 0.546839i \(0.815831\pi\)
\(168\) 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 \(-0.481752\pi\)
0.998357 0.0572975i \(-0.0182484\pi\)
\(174\) 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 \(-0.802768\pi\)
0.814097 0.580728i \(-0.197232\pi\)
\(182\) 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 \(-0.837398\pi\)
−0.872339 + 0.488901i \(0.837398\pi\)
\(200\) 0 0
\(201\) 13.0601i 0.921188i
\(202\) 0 0
\(203\) 4.55402 12.3541i 0.319629 0.867085i
\(204\) 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
\(217\) −3.98213 + 10.8026i −0.270324 + 0.733331i
\(218\) 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 −0.920005 0.391907i \(-0.871816\pi\)
0.391907 + 0.920005i \(0.371816\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.54162 + 6.54162i 0.434182 + 0.434182i 0.890048 0.455866i \(-0.150670\pi\)
−0.455866 + 0.890048i \(0.650670\pi\)
\(228\) 0 0
\(229\) −6.01657 −0.397586 −0.198793 0.980041i \(-0.563702\pi\)
−0.198793 + 0.980041i \(0.563702\pi\)
\(230\) 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 \(0.264002\pi\)
−0.675328 + 0.737518i \(0.735998\pi\)
\(242\) 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 \(0.282060\pi\)
−0.632423 + 0.774623i \(0.717940\pi\)
\(252\) 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 0.895670 0.444718i \(-0.146696\pi\)
−0.444718 + 0.895670i \(0.646696\pi\)
\(258\) 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 \(-0.504181\pi\)
−0.0131351 + 0.999914i \(0.504181\pi\)
\(270\) 0 0
\(271\) 10.1612i 0.617248i 0.951184 + 0.308624i \(0.0998685\pi\)
−0.951184 + 0.308624i \(0.900132\pi\)
\(272\) 0 0
\(273\) −1.68308 + 4.56583i −0.101865 + 0.276336i
\(274\) 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 −0.622840 0.782349i \(-0.714021\pi\)
0.782349 + 0.622840i \(0.214021\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.46601 + 17.5409i −0.381677 + 1.03541i
\(288\) 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 \(-0.420434\pi\)
0.968921 0.247368i \(-0.0795658\pi\)
\(294\) 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 0.933129 0.359541i \(-0.117067\pi\)
−0.359541 + 0.933129i \(0.617067\pi\)
\(308\) 0 0
\(309\) 1.31160i 0.0746141i
\(310\) 0 0
\(311\) 6.48676i 0.367830i 0.982942 + 0.183915i \(0.0588771\pi\)
−0.982942 + 0.183915i \(0.941123\pi\)
\(312\) 0 0
\(313\) −11.7441 + 11.7441i −0.663814 + 0.663814i −0.956277 0.292463i \(-0.905525\pi\)
0.292463 + 0.956277i \(0.405525\pi\)
\(314\) 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
\(343\) −9.06195 16.1518i −0.489299 0.872116i
\(344\) 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 \(-0.761225\pi\)
−0.731598 + 0.681736i \(0.761225\pi\)
\(350\) 0 0
\(351\) 7.90110 0.421730
\(352\) 0 0
\(353\) 3.42987 3.42987i 0.182553 0.182553i −0.609914 0.792468i \(-0.708796\pi\)
0.792468 + 0.609914i \(0.208796\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2.60247 0.959334i −0.137737 0.0507734i
\(358\) 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 0.997019 0.0771629i \(-0.0245861\pi\)
−0.0771629 + 0.997019i \(0.524586\pi\)
\(368\) 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 −0.747137 0.664670i \(-0.768572\pi\)
0.664670 + 0.747137i \(0.268572\pi\)
\(384\) 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 0.814719 0.579856i \(-0.196891\pi\)
−0.579856 + 0.814719i \(0.696891\pi\)
\(398\) 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 \(-0.625377\pi\)
−0.383777 + 0.923426i \(0.625377\pi\)
\(410\) 0 0
\(411\) 4.98411i 0.245848i
\(412\) 0 0
\(413\) 20.5693 + 7.58234i 1.01215 + 0.373103i
\(414\) 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 \(-0.248731\pi\)
0.709920 + 0.704282i \(0.248731\pi\)
\(420\) 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
\(427\) −9.20863 + 24.9810i −0.445637 + 1.20892i
\(428\) 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 −0.939968 0.341262i \(-0.889146\pi\)
0.341262 + 0.939968i \(0.389146\pi\)
\(434\) 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 \(-0.632875\pi\)
−0.405421 + 0.914130i \(0.632875\pi\)
\(440\) 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 \(-0.720900\pi\)
0.639599 0.768709i \(-0.279100\pi\)
\(462\) 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 0.865950 0.500131i \(-0.166715\pi\)
−0.500131 + 0.865950i \(0.666715\pi\)
\(468\) 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 \(-0.139632\pi\)
0.905319 + 0.424733i \(0.139632\pi\)
\(480\) 0 0
\(481\) 5.06469i 0.230930i
\(482\) 0 0
\(483\) −6.57179 2.42253i −0.299027 0.110229i
\(484\) 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
\(497\) −0.816742 0.301072i −0.0366359 0.0135049i
\(498\) 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 −0.844753 0.535157i \(-0.820252\pi\)
0.535157 + 0.844753i \(0.320252\pi\)
\(504\) 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 \(-0.830733\pi\)
−0.861911 + 0.507059i \(0.830733\pi\)
\(510\) 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 \(0.239405\pi\)
−0.730246 + 0.683184i \(0.760595\pi\)
\(522\) 0 0
\(523\) −19.0273 + 19.0273i −0.832007 + 0.832007i −0.987791 0.155784i \(-0.950210\pi\)
0.155784 + 0.987791i \(0.450210\pi\)
\(524\) 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
\(553\) −12.5260 + 33.9803i −0.532659 + 1.44499i
\(554\) 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 −0.540685 0.841225i \(-0.681835\pi\)
0.841225 + 0.540685i \(0.181835\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −8.52270 3.14168i −0.357920 0.131938i
\(568\) 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 0.0710620 0.997472i \(-0.477361\pi\)
−0.997472 + 0.0710620i \(0.977361\pi\)
\(578\) 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 0.273512 0.961869i \(-0.411815\pi\)
−0.961869 + 0.273512i \(0.911815\pi\)
\(588\) 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 −0.828907 0.559386i \(-0.811037\pi\)
0.559386 + 0.828907i \(0.311037\pi\)
\(594\) 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 \(0.135092\pi\)
−0.911285 + 0.411777i \(0.864908\pi\)
\(602\) 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 0.873962 0.485993i \(-0.161542\pi\)
−0.485993 + 0.873962i \(0.661542\pi\)
\(608\) 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 \(-0.480853\pi\)
0.0601145 + 0.998191i \(0.480853\pi\)
\(620\) 0 0
\(621\) 11.3724i 0.456358i
\(622\) 0 0
\(623\) −32.7540 12.0740i −1.31226 0.483733i
\(624\) 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
\(637\) −9.83160 + 0.778891i −0.389542 + 0.0308608i
\(638\) 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 −0.983860 0.178939i \(-0.942733\pi\)
0.178939 + 0.983860i \(0.442733\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.2719 18.2719i −0.718342 0.718342i 0.249924 0.968265i \(-0.419594\pi\)
−0.968265 + 0.249924i \(0.919594\pi\)
\(648\) 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 \(-0.798206\pi\)
0.805692 0.592335i \(-0.201794\pi\)
\(662\) 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 0.0873819 0.996175i \(-0.472150\pi\)
−0.996175 + 0.0873819i \(0.972150\pi\)
\(678\) 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 \(-0.719466\pi\)
0.636131 0.771581i \(-0.280534\pi\)
\(692\) 0 0
\(693\) 1.44267 3.91365i 0.0548025 0.148667i
\(694\) 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
\(707\) −8.03048 + 21.7849i −0.302017 + 0.819307i
\(708\) 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 \(-0.293368\pi\)
0.604512 + 0.796596i \(0.293368\pi\)
\(720\) 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 0.666291 0.745692i \(-0.267881\pi\)
−0.745692 + 0.666291i \(0.767881\pi\)
\(728\) 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 −0.957930 0.287001i \(-0.907342\pi\)
0.287001 + 0.957930i \(0.407342\pi\)
\(734\) 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 \(-0.767825\pi\)
0.745575 0.666422i \(-0.232175\pi\)
\(762\) 0 0
\(763\) −6.53133 + 17.7181i −0.236450 + 0.641437i
\(764\) 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 \(-0.502136\pi\)
−0.00671098 + 0.999977i \(0.502136\pi\)
\(770\) 0 0
\(771\) −13.3464 −0.480659
\(772\) 0 0
\(773\) 28.1925 28.1925i 1.01402 1.01402i 0.0141148 0.999900i \(-0.495507\pi\)
0.999900 0.0141148i \(-0.00449302\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 4.29425 11.6494i 0.154055 0.417919i
\(778\) 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 0.752211 0.658922i \(-0.228987\pi\)
−0.658922 + 0.752211i \(0.728987\pi\)
\(788\) 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 0.433180 0.901307i \(-0.357391\pi\)
−0.901307 + 0.433180i \(0.857391\pi\)
\(798\) 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
\(804\)