Properties

Label 2520.2.bi.r.361.5
Level $2520$
Weight $2$
Character 2520.361
Analytic conductor $20.122$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.bi (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.1223013094\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 29 x^{8} + 247 x^{6} + 855 x^{4} + 1212 x^{2} + 588\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.5
Root \(1.22977i\) of defining polynomial
Character \(\chi\) \(=\) 2520.361
Dual form 2520.2.bi.r.1801.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{5} +(1.87518 + 1.86646i) q^{7} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{5} +(1.87518 + 1.86646i) q^{7} +(-1.56501 + 2.71069i) q^{11} -3.53916 q^{13} +(2.76138 - 4.78286i) q^{17} +(2.94839 + 5.10677i) q^{19} +(-0.0732100 - 0.126804i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.91882 q^{29} +(-2.54580 + 4.40946i) q^{31} +(0.678814 - 2.55719i) q^{35} +(-0.321186 - 0.556310i) q^{37} -8.63076 q^{41} -5.93189 q^{43} +(0.704564 + 1.22034i) q^{47} +(0.0326205 + 6.99992i) q^{49} +(-4.83459 + 8.37376i) q^{53} +3.13003 q^{55} +(1.67062 - 2.89360i) q^{59} +(6.19876 + 10.7366i) q^{61} +(1.76958 + 3.06500i) q^{65} +(-6.62555 + 11.4758i) q^{67} -0.658762 q^{71} +(2.34561 - 4.06272i) q^{73} +(-7.99409 + 2.16199i) q^{77} +(-2.67499 - 4.63322i) q^{79} +13.4787 q^{83} -5.52277 q^{85} +(-7.20978 - 12.4877i) q^{89} +(-6.63657 - 6.60571i) q^{91} +(2.94839 - 5.10677i) q^{95} -2.86400 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 5q^{5} - q^{7} + O(q^{10}) \) \( 10q - 5q^{5} - q^{7} - 2q^{11} + 6q^{13} + 2q^{17} + q^{19} + 8q^{23} - 5q^{25} + 7q^{31} - q^{35} - 11q^{37} + 20q^{41} + 6q^{43} - 23q^{49} - 14q^{53} + 4q^{55} + 4q^{59} - 6q^{61} - 3q^{65} - 7q^{67} - 32q^{71} + 3q^{73} + 8q^{77} - 19q^{79} + 28q^{83} - 4q^{85} - 18q^{89} - 21q^{91} + q^{95} + 48q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 1.87518 + 1.86646i 0.708752 + 0.705457i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.56501 + 2.71069i −0.471870 + 0.817302i −0.999482 0.0321830i \(-0.989754\pi\)
0.527612 + 0.849485i \(0.323087\pi\)
\(12\) 0 0
\(13\) −3.53916 −0.981586 −0.490793 0.871276i \(-0.663293\pi\)
−0.490793 + 0.871276i \(0.663293\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.76138 4.78286i 0.669734 1.16001i −0.308245 0.951307i \(-0.599742\pi\)
0.977978 0.208706i \(-0.0669251\pi\)
\(18\) 0 0
\(19\) 2.94839 + 5.10677i 0.676408 + 1.17157i 0.976055 + 0.217523i \(0.0697976\pi\)
−0.299648 + 0.954050i \(0.596869\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.0732100 0.126804i −0.0152653 0.0264404i 0.858292 0.513162i \(-0.171526\pi\)
−0.873557 + 0.486722i \(0.838193\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.91882 0.542011 0.271006 0.962578i \(-0.412644\pi\)
0.271006 + 0.962578i \(0.412644\pi\)
\(30\) 0 0
\(31\) −2.54580 + 4.40946i −0.457239 + 0.791962i −0.998814 0.0486908i \(-0.984495\pi\)
0.541574 + 0.840653i \(0.317828\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.678814 2.55719i 0.114741 0.432244i
\(36\) 0 0
\(37\) −0.321186 0.556310i −0.0528026 0.0914568i 0.838416 0.545031i \(-0.183482\pi\)
−0.891219 + 0.453574i \(0.850149\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.63076 −1.34790 −0.673949 0.738778i \(-0.735403\pi\)
−0.673949 + 0.738778i \(0.735403\pi\)
\(42\) 0 0
\(43\) −5.93189 −0.904605 −0.452303 0.891865i \(-0.649397\pi\)
−0.452303 + 0.891865i \(0.649397\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.704564 + 1.22034i 0.102771 + 0.178005i 0.912825 0.408350i \(-0.133896\pi\)
−0.810054 + 0.586355i \(0.800562\pi\)
\(48\) 0 0
\(49\) 0.0326205 + 6.99992i 0.00466007 + 0.999989i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.83459 + 8.37376i −0.664082 + 1.15022i 0.315451 + 0.948942i \(0.397844\pi\)
−0.979533 + 0.201283i \(0.935489\pi\)
\(54\) 0 0
\(55\) 3.13003 0.422053
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.67062 2.89360i 0.217496 0.376714i −0.736546 0.676388i \(-0.763544\pi\)
0.954042 + 0.299673i \(0.0968777\pi\)
\(60\) 0 0
\(61\) 6.19876 + 10.7366i 0.793670 + 1.37468i 0.923680 + 0.383164i \(0.125165\pi\)
−0.130011 + 0.991513i \(0.541501\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.76958 + 3.06500i 0.219489 + 0.380166i
\(66\) 0 0
\(67\) −6.62555 + 11.4758i −0.809440 + 1.40199i 0.103813 + 0.994597i \(0.466896\pi\)
−0.913253 + 0.407394i \(0.866438\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.658762 −0.0781807 −0.0390903 0.999236i \(-0.512446\pi\)
−0.0390903 + 0.999236i \(0.512446\pi\)
\(72\) 0 0
\(73\) 2.34561 4.06272i 0.274533 0.475505i −0.695484 0.718541i \(-0.744810\pi\)
0.970017 + 0.243036i \(0.0781434\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.99409 + 2.16199i −0.911011 + 0.246381i
\(78\) 0 0
\(79\) −2.67499 4.63322i −0.300960 0.521278i 0.675394 0.737457i \(-0.263974\pi\)
−0.976354 + 0.216179i \(0.930640\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 13.4787 1.47948 0.739740 0.672893i \(-0.234949\pi\)
0.739740 + 0.672893i \(0.234949\pi\)
\(84\) 0 0
\(85\) −5.52277 −0.599028
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.20978 12.4877i −0.764235 1.32369i −0.940650 0.339378i \(-0.889784\pi\)
0.176416 0.984316i \(-0.443550\pi\)
\(90\) 0 0
\(91\) −6.63657 6.60571i −0.695701 0.692467i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.94839 5.10677i 0.302499 0.523943i
\(96\) 0 0
\(97\) −2.86400 −0.290796 −0.145398 0.989373i \(-0.546446\pi\)
−0.145398 + 0.989373i \(0.546446\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.77861 + 11.7409i −0.674497 + 1.16826i 0.302118 + 0.953270i \(0.402306\pi\)
−0.976616 + 0.214993i \(0.931027\pi\)
\(102\) 0 0
\(103\) 2.93084 + 5.07636i 0.288784 + 0.500189i 0.973520 0.228603i \(-0.0734157\pi\)
−0.684736 + 0.728792i \(0.740082\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.76138 + 6.51491i 0.363627 + 0.629820i 0.988555 0.150862i \(-0.0482051\pi\)
−0.624928 + 0.780682i \(0.714872\pi\)
\(108\) 0 0
\(109\) −2.86417 + 4.96088i −0.274337 + 0.475166i −0.969968 0.243234i \(-0.921792\pi\)
0.695630 + 0.718400i \(0.255125\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.50073 0.893754 0.446877 0.894596i \(-0.352536\pi\)
0.446877 + 0.894596i \(0.352536\pi\)
\(114\) 0 0
\(115\) −0.0732100 + 0.126804i −0.00682687 + 0.0118245i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 14.1051 3.81471i 1.29302 0.349693i
\(120\) 0 0
\(121\) 0.601458 + 1.04176i 0.0546780 + 0.0947050i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 10.5145 0.933009 0.466504 0.884519i \(-0.345513\pi\)
0.466504 + 0.884519i \(0.345513\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.105604 + 0.182912i 0.00922669 + 0.0159811i 0.870602 0.491988i \(-0.163730\pi\)
−0.861375 + 0.507969i \(0.830396\pi\)
\(132\) 0 0
\(133\) −4.00282 + 15.0792i −0.347089 + 1.30753i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.57985 + 6.20049i −0.305848 + 0.529744i −0.977450 0.211168i \(-0.932273\pi\)
0.671602 + 0.740912i \(0.265606\pi\)
\(138\) 0 0
\(139\) −3.27313 −0.277623 −0.138812 0.990319i \(-0.544328\pi\)
−0.138812 + 0.990319i \(0.544328\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5.53883 9.59354i 0.463180 0.802252i
\(144\) 0 0
\(145\) −1.45941 2.52777i −0.121197 0.209920i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.50405 + 6.06919i 0.287063 + 0.497207i 0.973107 0.230352i \(-0.0739878\pi\)
−0.686044 + 0.727560i \(0.740654\pi\)
\(150\) 0 0
\(151\) −9.57842 + 16.5903i −0.779481 + 1.35010i 0.152760 + 0.988263i \(0.451184\pi\)
−0.932241 + 0.361837i \(0.882150\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.09160 0.408967
\(156\) 0 0
\(157\) −3.00239 + 5.20029i −0.239617 + 0.415028i −0.960604 0.277920i \(-0.910355\pi\)
0.720988 + 0.692948i \(0.243688\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.0993920 0.374424i 0.00783319 0.0295087i
\(162\) 0 0
\(163\) 6.41955 + 11.1190i 0.502818 + 0.870907i 0.999995 + 0.00325713i \(0.00103678\pi\)
−0.497177 + 0.867649i \(0.665630\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.14642 0.166095 0.0830475 0.996546i \(-0.473535\pi\)
0.0830475 + 0.996546i \(0.473535\pi\)
\(168\) 0 0
\(169\) −0.474368 −0.0364899
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.08423 1.87794i −0.0824323 0.142777i 0.821862 0.569687i \(-0.192935\pi\)
−0.904294 + 0.426910i \(0.859602\pi\)
\(174\) 0 0
\(175\) −2.55400 + 0.690724i −0.193064 + 0.0522138i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.46323 2.53439i 0.109367 0.189429i −0.806147 0.591715i \(-0.798451\pi\)
0.915514 + 0.402286i \(0.131784\pi\)
\(180\) 0 0
\(181\) 21.4630 1.59533 0.797665 0.603101i \(-0.206068\pi\)
0.797665 + 0.603101i \(0.206068\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.321186 + 0.556310i −0.0236140 + 0.0409007i
\(186\) 0 0
\(187\) 8.64321 + 14.9705i 0.632054 + 1.09475i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −10.2731 17.7936i −0.743338 1.28750i −0.950967 0.309291i \(-0.899908\pi\)
0.207630 0.978208i \(-0.433425\pi\)
\(192\) 0 0
\(193\) −8.68120 + 15.0363i −0.624887 + 1.08234i 0.363676 + 0.931526i \(0.381522\pi\)
−0.988563 + 0.150810i \(0.951812\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −24.9087 −1.77467 −0.887335 0.461126i \(-0.847446\pi\)
−0.887335 + 0.461126i \(0.847446\pi\)
\(198\) 0 0
\(199\) −5.97116 + 10.3424i −0.423284 + 0.733150i −0.996258 0.0864236i \(-0.972456\pi\)
0.572974 + 0.819573i \(0.305789\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.47332 + 5.44788i 0.384152 + 0.382366i
\(204\) 0 0
\(205\) 4.31538 + 7.47446i 0.301399 + 0.522039i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −18.4571 −1.27671
\(210\) 0 0
\(211\) 0.0571436 0.00393393 0.00196696 0.999998i \(-0.499374\pi\)
0.00196696 + 0.999998i \(0.499374\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.96595 + 5.13717i 0.202276 + 0.350352i
\(216\) 0 0
\(217\) −13.0039 + 3.51689i −0.882765 + 0.238742i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −9.77297 + 16.9273i −0.657401 + 1.13865i
\(222\) 0 0
\(223\) 26.5790 1.77986 0.889932 0.456093i \(-0.150751\pi\)
0.889932 + 0.456093i \(0.150751\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −7.43057 + 12.8701i −0.493184 + 0.854220i −0.999969 0.00785238i \(-0.997500\pi\)
0.506785 + 0.862073i \(0.330834\pi\)
\(228\) 0 0
\(229\) −2.59730 4.49866i −0.171634 0.297280i 0.767357 0.641220i \(-0.221571\pi\)
−0.938991 + 0.343941i \(0.888238\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.25441 10.8330i −0.409740 0.709691i 0.585120 0.810947i \(-0.301047\pi\)
−0.994860 + 0.101256i \(0.967714\pi\)
\(234\) 0 0
\(235\) 0.704564 1.22034i 0.0459607 0.0796062i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −14.5201 −0.939228 −0.469614 0.882872i \(-0.655607\pi\)
−0.469614 + 0.882872i \(0.655607\pi\)
\(240\) 0 0
\(241\) −6.31809 + 10.9433i −0.406984 + 0.704917i −0.994550 0.104259i \(-0.966753\pi\)
0.587566 + 0.809176i \(0.300086\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.04580 3.52821i 0.386252 0.225409i
\(246\) 0 0
\(247\) −10.4348 18.0736i −0.663952 1.15000i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 25.7531 1.62552 0.812762 0.582596i \(-0.197963\pi\)
0.812762 + 0.582596i \(0.197963\pi\)
\(252\) 0 0
\(253\) 0.458299 0.0288130
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.82662 + 8.35996i 0.301077 + 0.521480i 0.976380 0.216060i \(-0.0693207\pi\)
−0.675304 + 0.737540i \(0.735987\pi\)
\(258\) 0 0
\(259\) 0.436051 1.64266i 0.0270949 0.102070i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 11.8069 20.4501i 0.728042 1.26101i −0.229667 0.973269i \(-0.573764\pi\)
0.957709 0.287737i \(-0.0929029\pi\)
\(264\) 0 0
\(265\) 9.66919 0.593973
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7.44923 + 12.9024i −0.454188 + 0.786676i −0.998641 0.0521149i \(-0.983404\pi\)
0.544453 + 0.838791i \(0.316737\pi\)
\(270\) 0 0
\(271\) −11.2256 19.4433i −0.681905 1.18109i −0.974399 0.224827i \(-0.927818\pi\)
0.292494 0.956267i \(-0.405515\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.56501 2.71069i −0.0943739 0.163460i
\(276\) 0 0
\(277\) 9.33400 16.1670i 0.560826 0.971379i −0.436599 0.899656i \(-0.643817\pi\)
0.997425 0.0717224i \(-0.0228496\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −19.9279 −1.18880 −0.594400 0.804169i \(-0.702610\pi\)
−0.594400 + 0.804169i \(0.702610\pi\)
\(282\) 0 0
\(283\) 9.73835 16.8673i 0.578885 1.00266i −0.416723 0.909034i \(-0.636821\pi\)
0.995608 0.0936241i \(-0.0298452\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −16.1843 16.1090i −0.955326 0.950885i
\(288\) 0 0
\(289\) −6.75047 11.6922i −0.397087 0.687774i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 24.4381 1.42769 0.713844 0.700305i \(-0.246953\pi\)
0.713844 + 0.700305i \(0.246953\pi\)
\(294\) 0 0
\(295\) −3.34124 −0.194534
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.259102 + 0.448778i 0.0149842 + 0.0259535i
\(300\) 0 0
\(301\) −11.1234 11.0717i −0.641141 0.638160i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.19876 10.7366i 0.354940 0.614774i
\(306\) 0 0
\(307\) −3.63208 −0.207294 −0.103647 0.994614i \(-0.533051\pi\)
−0.103647 + 0.994614i \(0.533051\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6.89822 + 11.9481i −0.391162 + 0.677513i −0.992603 0.121405i \(-0.961260\pi\)
0.601441 + 0.798917i \(0.294593\pi\)
\(312\) 0 0
\(313\) −7.45360 12.9100i −0.421303 0.729718i 0.574765 0.818319i \(-0.305094\pi\)
−0.996067 + 0.0886012i \(0.971760\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.17616 2.03716i −0.0660595 0.114418i 0.831104 0.556117i \(-0.187709\pi\)
−0.897163 + 0.441699i \(0.854376\pi\)
\(318\) 0 0
\(319\) −4.56800 + 7.91200i −0.255759 + 0.442987i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 32.5666 1.81205
\(324\) 0 0
\(325\) 1.76958 3.06500i 0.0981586 0.170016i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −0.956536 + 3.60340i −0.0527355 + 0.198662i
\(330\) 0 0
\(331\) −16.3584 28.3335i −0.899137 1.55735i −0.828600 0.559841i \(-0.810862\pi\)
−0.0705370 0.997509i \(-0.522471\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 13.2511 0.723985
\(336\) 0 0
\(337\) 2.65676 0.144723 0.0723615 0.997378i \(-0.476946\pi\)
0.0723615 + 0.997378i \(0.476946\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −7.96843 13.8017i −0.431515 0.747406i
\(342\) 0 0
\(343\) −13.0039 + 13.1870i −0.702147 + 0.712032i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 17.7311 30.7112i 0.951856 1.64866i 0.210451 0.977604i \(-0.432507\pi\)
0.741405 0.671058i \(-0.234160\pi\)
\(348\) 0 0
\(349\) 19.8638 1.06328 0.531642 0.846969i \(-0.321575\pi\)
0.531642 + 0.846969i \(0.321575\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 14.8473 25.7164i 0.790244 1.36874i −0.135571 0.990768i \(-0.543287\pi\)
0.925816 0.377976i \(-0.123380\pi\)
\(354\) 0 0
\(355\) 0.329381 + 0.570505i 0.0174817 + 0.0302792i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 17.5641 + 30.4219i 0.926997 + 1.60561i 0.788317 + 0.615269i \(0.210952\pi\)
0.138680 + 0.990337i \(0.455714\pi\)
\(360\) 0 0
\(361\) −7.88604 + 13.6590i −0.415055 + 0.718896i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.69122 −0.245550
\(366\) 0 0
\(367\) 5.94568 10.2982i 0.310362 0.537563i −0.668079 0.744091i \(-0.732883\pi\)
0.978441 + 0.206528i \(0.0662164\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −24.6951 + 6.67874i −1.28210 + 0.346743i
\(372\) 0 0
\(373\) −12.7884 22.1501i −0.662156 1.14689i −0.980048 0.198761i \(-0.936308\pi\)
0.317892 0.948127i \(-0.397025\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10.3302 −0.532031
\(378\) 0 0
\(379\) 26.9174 1.38265 0.691327 0.722542i \(-0.257026\pi\)
0.691327 + 0.722542i \(0.257026\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.99973 + 17.3200i 0.510962 + 0.885013i 0.999919 + 0.0127049i \(0.00404419\pi\)
−0.488957 + 0.872308i \(0.662622\pi\)
\(384\) 0 0
\(385\) 5.86938 + 5.84209i 0.299131 + 0.297740i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −16.7269 + 28.9718i −0.848087 + 1.46893i 0.0348254 + 0.999393i \(0.488912\pi\)
−0.882913 + 0.469537i \(0.844421\pi\)
\(390\) 0 0
\(391\) −0.808644 −0.0408949
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.67499 + 4.63322i −0.134593 + 0.233123i
\(396\) 0 0
\(397\) 1.36765 + 2.36883i 0.0686402 + 0.118888i 0.898303 0.439377i \(-0.144801\pi\)
−0.829663 + 0.558265i \(0.811467\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.53112 9.58018i −0.276211 0.478412i 0.694229 0.719754i \(-0.255746\pi\)
−0.970440 + 0.241343i \(0.922412\pi\)
\(402\) 0 0
\(403\) 9.00999 15.6058i 0.448820 0.777378i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.01064 0.0996638
\(408\) 0 0
\(409\) 13.6241 23.5977i 0.673669 1.16683i −0.303187 0.952931i \(-0.598051\pi\)
0.976856 0.213898i \(-0.0686160\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.53351 2.30787i 0.419907 0.113563i
\(414\) 0 0
\(415\) −6.73935 11.6729i −0.330822 0.573000i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −17.9126 −0.875090 −0.437545 0.899197i \(-0.644152\pi\)
−0.437545 + 0.899197i \(0.644152\pi\)
\(420\) 0 0
\(421\) 36.4906 1.77844 0.889221 0.457478i \(-0.151247\pi\)
0.889221 + 0.457478i \(0.151247\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.76138 + 4.78286i 0.133947 + 0.232003i
\(426\) 0 0
\(427\) −8.41561 + 31.7028i −0.407260 + 1.53421i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.52755 + 7.84194i −0.218084 + 0.377733i −0.954222 0.299099i \(-0.903314\pi\)
0.736138 + 0.676831i \(0.236647\pi\)
\(432\) 0 0
\(433\) 3.24154 0.155778 0.0778892 0.996962i \(-0.475182\pi\)
0.0778892 + 0.996962i \(0.475182\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.431704 0.747733i 0.0206512 0.0357689i
\(438\) 0 0
\(439\) 9.61353 + 16.6511i 0.458829 + 0.794715i 0.998899 0.0469050i \(-0.0149358\pi\)
−0.540071 + 0.841620i \(0.681602\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.57427 + 2.72671i 0.0747956 + 0.129550i 0.900997 0.433825i \(-0.142836\pi\)
−0.826202 + 0.563374i \(0.809503\pi\)
\(444\) 0 0
\(445\) −7.20978 + 12.4877i −0.341776 + 0.591974i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 20.8343 0.983233 0.491616 0.870812i \(-0.336406\pi\)
0.491616 + 0.870812i \(0.336406\pi\)
\(450\) 0 0
\(451\) 13.5073 23.3953i 0.636032 1.10164i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.40243 + 9.05029i −0.112628 + 0.424284i
\(456\) 0 0
\(457\) −17.4872 30.2888i −0.818018 1.41685i −0.907140 0.420828i \(-0.861740\pi\)
0.0891226 0.996021i \(-0.471594\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −36.4665 −1.69842 −0.849208 0.528058i \(-0.822920\pi\)
−0.849208 + 0.528058i \(0.822920\pi\)
\(462\) 0 0
\(463\) −28.6711 −1.33246 −0.666230 0.745747i \(-0.732093\pi\)
−0.666230 + 0.745747i \(0.732093\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.0975696 + 0.168996i 0.00451498 + 0.00782018i 0.868274 0.496085i \(-0.165229\pi\)
−0.863759 + 0.503905i \(0.831896\pi\)
\(468\) 0 0
\(469\) −33.8433 + 9.15285i −1.56274 + 0.422639i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9.28350 16.0795i 0.426856 0.739336i
\(474\) 0 0
\(475\) −5.89679 −0.270563
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.78547 10.0207i 0.264345 0.457859i −0.703047 0.711144i \(-0.748178\pi\)
0.967392 + 0.253285i \(0.0815109\pi\)
\(480\) 0 0
\(481\) 1.13673 + 1.96887i 0.0518303 + 0.0897727i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.43200 + 2.48030i 0.0650239 + 0.112625i
\(486\) 0 0
\(487\) 14.7824 25.6039i 0.669854 1.16022i −0.308090 0.951357i \(-0.599690\pi\)
0.977945 0.208864i \(-0.0669767\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −39.0817 −1.76373 −0.881866 0.471501i \(-0.843712\pi\)
−0.881866 + 0.471501i \(0.843712\pi\)
\(492\) 0 0
\(493\) 8.05998 13.9603i 0.363003 0.628740i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.23530 1.22956i −0.0554107 0.0551531i
\(498\) 0 0
\(499\) −8.43216 14.6049i −0.377475 0.653807i 0.613219 0.789913i \(-0.289874\pi\)
−0.990694 + 0.136106i \(0.956541\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 17.2768 0.770335 0.385167 0.922847i \(-0.374144\pi\)
0.385167 + 0.922847i \(0.374144\pi\)
\(504\) 0 0
\(505\) 13.5572 0.603289
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0.189173 + 0.327657i 0.00838495 + 0.0145232i 0.870187 0.492721i \(-0.163998\pi\)
−0.861802 + 0.507244i \(0.830664\pi\)
\(510\) 0 0
\(511\) 11.9814 3.24034i 0.530024 0.143344i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.93084 5.07636i 0.129148 0.223691i
\(516\) 0 0
\(517\) −4.41061 −0.193978
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.39844 + 16.2786i −0.411753 + 0.713178i −0.995082 0.0990588i \(-0.968417\pi\)
0.583328 + 0.812237i \(0.301750\pi\)
\(522\) 0 0
\(523\) 3.76719 + 6.52496i 0.164728 + 0.285317i 0.936559 0.350511i \(-0.113992\pi\)
−0.771831 + 0.635828i \(0.780659\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.0599 + 24.3524i 0.612457 + 1.06081i
\(528\) 0 0
\(529\) 11.4893 19.9000i 0.499534 0.865218i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 30.5456 1.32308
\(534\) 0 0
\(535\) 3.76138 6.51491i 0.162619 0.281664i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −19.0256 10.8666i −0.819492 0.468056i
\(540\) 0 0
\(541\) 0.347666 + 0.602175i 0.0149473 + 0.0258895i 0.873402 0.486999i \(-0.161909\pi\)
−0.858455 + 0.512889i \(0.828575\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.72833 0.245375
\(546\) 0 0
\(547\) 21.8791 0.935482 0.467741 0.883866i \(-0.345068\pi\)
0.467741 + 0.883866i \(0.345068\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 8.60583 + 14.9057i 0.366621 + 0.635006i
\(552\) 0 0
\(553\) 3.63165 13.6809i 0.154433 0.581772i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18.4950 + 32.0343i −0.783660 + 1.35734i 0.146137 + 0.989264i \(0.453316\pi\)
−0.929796 + 0.368074i \(0.880017\pi\)
\(558\) 0 0
\(559\) 20.9939 0.887947
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 20.8040 36.0336i 0.876784 1.51863i 0.0219336 0.999759i \(-0.493018\pi\)
0.854850 0.518875i \(-0.173649\pi\)
\(564\) 0 0
\(565\) −4.75037 8.22787i −0.199849 0.346149i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.42337 16.3218i −0.395048 0.684244i 0.598059 0.801452i \(-0.295939\pi\)
−0.993107 + 0.117208i \(0.962606\pi\)
\(570\) 0 0
\(571\) −9.33875 + 16.1752i −0.390815 + 0.676911i −0.992557 0.121779i \(-0.961140\pi\)
0.601743 + 0.798690i \(0.294473\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.146420 0.00610614
\(576\) 0 0
\(577\) 13.9151 24.1016i 0.579292 1.00336i −0.416269 0.909242i \(-0.636662\pi\)
0.995561 0.0941215i \(-0.0300042\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 25.2750 + 25.1575i 1.04858 + 1.04371i
\(582\) 0 0
\(583\) −15.1324 26.2101i −0.626721 1.08551i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.4459 −0.720070 −0.360035 0.932939i \(-0.617235\pi\)
−0.360035 + 0.932939i \(0.617235\pi\)
\(588\) 0 0
\(589\) −30.0241 −1.23712
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8.44153 14.6212i −0.346652 0.600419i 0.639000 0.769206i \(-0.279348\pi\)
−0.985653 + 0.168787i \(0.946015\pi\)
\(594\) 0 0
\(595\) −10.3562 10.3080i −0.424563 0.422589i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.76198 4.78388i 0.112851 0.195464i −0.804067 0.594538i \(-0.797335\pi\)
0.916919 + 0.399074i \(0.130668\pi\)
\(600\) 0 0
\(601\) 41.7051 1.70119 0.850593 0.525824i \(-0.176243\pi\)
0.850593 + 0.525824i \(0.176243\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.601458 1.04176i 0.0244527 0.0423534i
\(606\) 0 0
\(607\) 14.3356 + 24.8299i 0.581862 + 1.00781i 0.995259 + 0.0972636i \(0.0310090\pi\)
−0.413397 + 0.910551i \(0.635658\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.49356 4.31898i −0.100879 0.174727i
\(612\) 0 0
\(613\) 3.10644 5.38052i 0.125468 0.217317i −0.796448 0.604707i \(-0.793290\pi\)
0.921916 + 0.387390i \(0.126623\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.6550 0.589988 0.294994 0.955499i \(-0.404682\pi\)
0.294994 + 0.955499i \(0.404682\pi\)
\(618\) 0 0
\(619\) 15.4589 26.7756i 0.621347 1.07620i −0.367889 0.929870i \(-0.619919\pi\)
0.989235 0.146334i \(-0.0467475\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 9.78820 36.8735i 0.392156 1.47731i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3.54767 −0.141455
\(630\) 0 0
\(631\) −23.4514 −0.933584 −0.466792 0.884367i \(-0.654590\pi\)
−0.466792 + 0.884367i \(0.654590\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.25724 9.10580i −0.208627 0.361353i
\(636\) 0 0
\(637\) −0.115449 24.7738i −0.00457426 0.981575i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 10.6564 18.4574i 0.420903 0.729025i −0.575125 0.818065i \(-0.695047\pi\)
0.996028 + 0.0890406i \(0.0283801\pi\)
\(642\) 0 0
\(643\) −0.958256 −0.0377899 −0.0188950 0.999821i \(-0.506015\pi\)
−0.0188950 + 0.999821i \(0.506015\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.836865 + 1.44949i −0.0329006 + 0.0569855i −0.882007 0.471237i \(-0.843808\pi\)
0.849106 + 0.528222i \(0.177141\pi\)
\(648\) 0 0
\(649\) 5.22909 + 9.05704i 0.205260 + 0.355520i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 18.2047 + 31.5315i 0.712405 + 1.23392i 0.963952 + 0.266077i \(0.0857274\pi\)
−0.251547 + 0.967845i \(0.580939\pi\)
\(654\) 0 0
\(655\) 0.105604 0.182912i 0.00412630 0.00714696i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 17.6686 0.688273 0.344136 0.938920i \(-0.388172\pi\)
0.344136 + 0.938920i \(0.388172\pi\)
\(660\) 0 0
\(661\) 0.772562 1.33812i 0.0300492 0.0520467i −0.850610 0.525798i \(-0.823767\pi\)
0.880659 + 0.473751i \(0.157100\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 15.0604 4.07305i 0.584016 0.157946i
\(666\) 0 0
\(667\) −0.213687 0.370117i −0.00827399 0.0143310i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −38.8046 −1.49803
\(672\) 0 0
\(673\) 45.0768 1.73758 0.868792 0.495178i \(-0.164897\pi\)
0.868792 + 0.495178i \(0.164897\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.3864 + 26.6501i 0.591349 + 1.02425i 0.994051 + 0.108916i \(0.0347378\pi\)
−0.402702 + 0.915331i \(0.631929\pi\)
\(678\) 0 0
\(679\) −5.37053 5.34556i −0.206102 0.205144i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 2.48261 4.30000i 0.0949943 0.164535i −0.814612 0.580006i \(-0.803050\pi\)
0.909606 + 0.415471i \(0.136383\pi\)
\(684\) 0 0
\(685\) 7.15971 0.273558
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 17.1104 29.6361i 0.651854 1.12904i
\(690\) 0 0
\(691\) −7.58026 13.1294i −0.288367 0.499466i 0.685053 0.728493i \(-0.259779\pi\)
−0.973420 + 0.229027i \(0.926446\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.63657 + 2.83462i 0.0620785 + 0.107523i
\(696\) 0 0
\(697\) −23.8328 + 41.2797i −0.902733 + 1.56358i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −16.9545 −0.640364 −0.320182 0.947356i \(-0.603744\pi\)
−0.320182 + 0.947356i \(0.603744\pi\)
\(702\) 0 0
\(703\) 1.89396 3.28044i 0.0714322 0.123724i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −34.6251 + 9.36430i −1.30221 + 0.352181i
\(708\) 0 0
\(709\) −23.1603 40.1149i −0.869805 1.50655i −0.862196 0.506575i \(-0.830911\pi\)
−0.00760839 0.999971i \(-0.502422\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.745513 0.0279197
\(714\) 0 0
\(715\) −11.0777 −0.414281
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.2544 + 17.7612i 0.382425 + 0.662380i 0.991408 0.130803i \(-0.0417557\pi\)
−0.608983 + 0.793183i \(0.708422\pi\)
\(720\) 0 0
\(721\) −3.97899 + 14.9894i −0.148185 + 0.558235i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.45941 + 2.52777i −0.0542011 + 0.0938791i
\(726\) 0 0
\(727\) 42.7056 1.58386 0.791931 0.610611i \(-0.209076\pi\)
0.791931 + 0.610611i \(0.209076\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −16.3802 + 28.3714i −0.605845 + 1.04935i
\(732\) 0 0
\(733\) 9.31438 + 16.1330i 0.344034 + 0.595885i 0.985178 0.171536i \(-0.0548730\pi\)
−0.641143 + 0.767421i \(0.721540\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −20.7382 35.9195i −0.763900 1.32311i
\(738\) 0 0
\(739\) −7.39263 + 12.8044i −0.271942 + 0.471018i −0.969359 0.245648i \(-0.920999\pi\)
0.697417 + 0.716666i \(0.254333\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −13.3016 −0.487988 −0.243994 0.969777i \(-0.578458\pi\)
−0.243994 + 0.969777i \(0.578458\pi\)
\(744\) 0 0
\(745\) 3.50405 6.06919i 0.128378 0.222358i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.10656 + 19.2371i −0.186590 + 0.702909i
\(750\) 0 0
\(751\) −14.1441 24.4983i −0.516126 0.893956i −0.999825 0.0187215i \(-0.994040\pi\)
0.483699 0.875234i \(-0.339293\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 19.1568 0.697189
\(756\) 0 0
\(757\) −29.8800 −1.08601 −0.543003 0.839731i \(-0.682713\pi\)
−0.543003 + 0.839731i \(0.682713\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −25.7487 44.5980i −0.933389 1.61668i −0.777482 0.628905i \(-0.783503\pi\)
−0.155906 0.987772i \(-0.549830\pi\)
\(762\) 0 0
\(763\) −14.6301 + 3.95669i −0.529647 + 0.143242i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.91258 + 10.2409i −0.213491 + 0.369777i
\(768\) 0 0
\(769\) −32.9959 −1.18986 −0.594932 0.803776i \(-0.702821\pi\)
−0.594932 + 0.803776i \(0.702821\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −7.56630 + 13.1052i −0.272141 + 0.471362i −0.969410 0.245448i \(-0.921065\pi\)
0.697269 + 0.716810i \(0.254398\pi\)
\(774\) 0 0
\(775\) −2.54580 4.40946i −0.0914479 0.158392i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −25.4469 44.0753i −0.911729 1.57916i
\(780\) 0 0
\(781\) 1.03097 1.78570i 0.0368911 0.0638972i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.00478 0.214320
\(786\) 0 0
\(787\) 6.70761 11.6179i 0.239101 0.414134i −0.721356 0.692565i \(-0.756481\pi\)
0.960456 + 0.278430i \(0.0898141\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 17.8156 + 17.7328i 0.633450 + 0.630505i
\(792\) 0 0
\(793\) −21.9384 37.9984i −0.779055 1.34936i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −26.8075 −0.949571 −0.474785 0.880102i \(-0.657474\pi\)
−0.474785 + 0.880102i \(0.657474\pi\)
\(798\) 0 0
\(799\) 7.78228 0.275317
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 7.34183 + 12.7164i 0.259088 + 0.448753i
\(804\) 0