Properties

Label 1400.2.x.c.993.12
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 993.12
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.c.657.12

$q$-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 −0.388507 0.921446i \(-0.627009\pi\)
0.921446 + 0.388507i \(0.127009\pi\)
\(4\) 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 −0.555323 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 \(-0.503779\pi\)
−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 0.840622 0.541623i \(-0.182190\pi\)
−0.541623 + 0.840622i \(0.682190\pi\)
\(24\) 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 −0.884473 0.466592i \(-0.845482\pi\)
0.466592 + 0.884473i \(0.345482\pi\)
\(38\) 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 0.903462 0.428669i \(-0.141017\pi\)
−0.428669 + 0.903462i \(0.641017\pi\)
\(44\) 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 0.765091 0.643922i \(-0.222694\pi\)
−0.643922 + 0.765091i \(0.722694\pi\)
\(54\) 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 −0.991829 0.127575i \(-0.959280\pi\)
0.127575 + 0.991829i \(0.459280\pi\)
\(68\) 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
\(77\) 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 −0.406878 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 \(-0.253499\pi\)
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 0.574611 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 \(-0.856183\pi\)
0.899656 0.436600i \(-0.143817\pi\)
\(102\) 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 \(0.612391\pi\)
−0.938310 + 0.345796i \(0.887609\pi\)
\(108\) 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 0.881775 0.471671i \(-0.156349\pi\)
−0.471671 + 0.881775i \(0.656349\pi\)
\(114\) 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 −0.557445 0.830214i \(-0.688218\pi\)
0.830214 + 0.557445i \(0.188218\pi\)
\(128\) 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 −0.582312 0.812965i \(-0.697852\pi\)
0.812965 + 0.582312i \(0.197852\pi\)
\(138\) 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 \(-0.978971\pi\)
−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 0.824913 0.565260i \(-0.191224\pi\)
−0.565260 + 0.824913i \(0.691224\pi\)
\(164\) 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 \(-0.802768\pi\)
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 \(0.0360427\pi\)
0.112990 + 0.993596i \(0.463957\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.7687 15.7687i 1.12347 1.12347i 0.132258 0.991215i \(-0.457777\pi\)
0.991215 0.132258i \(-0.0422229\pi\)
\(198\) 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 −0.391907 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 \(-0.563702\pi\)
−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 0.360206 0.932873i \(-0.382706\pi\)
−0.932873 + 0.360206i \(0.882706\pi\)
\(234\) 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 0.444718 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 0.228900 0.973450i \(-0.426487\pi\)
−0.973450 + 0.228900i \(0.926487\pi\)
\(264\) 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 −0.250892 0.968015i \(-0.580724\pi\)
0.968015 + 0.250892i \(0.0807238\pi\)
\(278\) 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
\(287\) 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 \(0.579566\pi\)
−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 \(0.0588771\pi\)
−0.982942 + 0.183915i \(0.941123\pi\)
\(312\) 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 \(0.506763\pi\)
−0.999774 + 0.0212445i \(0.993237\pi\)
\(318\) 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 −0.0795652 0.996830i \(-0.525353\pi\)
0.996830 + 0.0795652i \(0.0253532\pi\)
\(338\) 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 −0.954688 0.297609i \(-0.903811\pi\)
0.297609 + 0.954688i \(0.403811\pi\)
\(348\) 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 −0.792468 0.609914i \(-0.791204\pi\)
0.609914 + 0.792468i \(0.291204\pi\)
\(354\) 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 0.0771629 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 0.279707 0.960086i \(-0.409763\pi\)
−0.960086 + 0.279707i \(0.909763\pi\)
\(374\) 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 \(-0.625377\pi\)
−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 −0.341262 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 \(-0.632875\pi\)
−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 0.983506 0.180873i \(-0.0578923\pi\)
−0.180873 + 0.983506i \(0.557892\pi\)
\(444\) 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 \(0.608630\pi\)
−0.942330 + 0.334686i \(0.891370\pi\)
\(458\) 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 0.922955 0.384908i \(-0.125767\pi\)
−0.384908 + 0.922955i \(0.625767\pi\)
\(464\) 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 \(-0.139632\pi\)
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 −0.855331 0.518083i \(-0.826646\pi\)
0.518083 + 0.855331i \(0.326646\pi\)
\(488\) 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 −0.535157 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 \(-0.830733\pi\)
−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 −0.155784 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 −0.112316 0.993673i \(-0.535827\pi\)
0.993673 + 0.112316i \(0.0358269\pi\)
\(548\) 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 −0.806864 0.590738i \(-0.798837\pi\)
0.590738 + 0.806864i \(0.298837\pi\)
\(558\) 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
\(567\) 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 0.997472 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 \(0.135092\pi\)
−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 0.485993 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 \(0.0312169\pi\)
0.0979135 + 0.995195i \(0.468783\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.331871 0.331871i 0.0133606 0.0133606i −0.700395 0.713756i \(-0.746993\pi\)
0.713756 + 0.700395i \(0.246993\pi\)
\(618\) 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 −0.178939 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 0.0569981 0.998374i \(-0.481847\pi\)
−0.998374 + 0.0569981i \(0.981847\pi\)
\(654\) 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 0.998979 0.0451778i \(-0.0143854\pi\)
−0.0451778 + 0.998979i \(0.514385\pi\)
\(674\) 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 0.0106366 0.999943i \(-0.496614\pi\)
−0.999943 + 0.0106366i \(0.996614\pi\)
\(684\) 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 0.745692 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 0.929239 0.369480i \(-0.120464\pi\)
−0.369480 + 0.929239i \(0.620464\pi\)
\(744\) 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 −0.564933 0.825137i \(-0.691098\pi\)
0.825137 + 0.564933i \(0.191098\pi\)
\(758\) 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 \(0.504493\pi\)
−0.999900 + 0.0141148i \(0.995507\pi\)
\(774\) 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 0.658922 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