Properties

Label 1840.2.e.g.369.11
Level $1840$
Weight $2$
Character 1840.369
Analytic conductor $14.692$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} - 20 x^{3} + 64 x^{2} - 32 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 920)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.11
Root \(-1.71470 + 1.71470i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.g.369.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.58319i q^{3} +(-2.09277 - 0.787606i) q^{5} -2.84620i q^{7} +0.493499 q^{9} +O(q^{10})\) \(q+1.58319i q^{3} +(-2.09277 - 0.787606i) q^{5} -2.84620i q^{7} +0.493499 q^{9} -1.98637 q^{11} +4.69204i q^{13} +(1.24693 - 3.31326i) q^{15} -3.16675i q^{17} -6.16110 q^{19} +4.50609 q^{21} -1.00000i q^{23} +(3.75935 + 3.29655i) q^{25} +5.53088i q^{27} +6.61816 q^{29} +8.29732 q^{31} -3.14481i q^{33} +(-2.24169 + 5.95644i) q^{35} +1.71181i q^{37} -7.42840 q^{39} +6.72440 q^{41} +0.177968i q^{43} +(-1.03278 - 0.388683i) q^{45} +11.4749i q^{47} -1.10086 q^{49} +5.01358 q^{51} +6.18762i q^{53} +(4.15701 + 1.56448i) q^{55} -9.75422i q^{57} -7.61559 q^{59} +11.8577 q^{61} -1.40460i q^{63} +(3.69548 - 9.81934i) q^{65} +3.07554i q^{67} +1.58319 q^{69} +1.96195 q^{71} +4.94732i q^{73} +(-5.21908 + 5.95178i) q^{75} +5.65361i q^{77} +8.53182 q^{79} -7.27596 q^{81} -3.49429i q^{83} +(-2.49415 + 6.62728i) q^{85} +10.4778i q^{87} -7.07506 q^{89} +13.3545 q^{91} +13.1363i q^{93} +(12.8938 + 4.85252i) q^{95} +7.00705i q^{97} -0.980272 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{5} - 4q^{9} + O(q^{10}) \) \( 14q + 2q^{5} - 4q^{9} + 14q^{11} + 6q^{15} - 14q^{19} - 12q^{21} - 14q^{25} + 22q^{29} + 20q^{31} + 2q^{35} - 48q^{39} - 32q^{41} - 26q^{45} + 34q^{49} + 14q^{51} + 38q^{55} - 22q^{59} + 10q^{61} - 38q^{65} + 6q^{69} + 28q^{71} + 24q^{75} - 64q^{79} - 10q^{81} - 50q^{85} + 48q^{89} + 14q^{91} + 30q^{95} - 122q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.58319i 0.914057i 0.889452 + 0.457029i \(0.151086\pi\)
−0.889452 + 0.457029i \(0.848914\pi\)
\(4\) 0 0
\(5\) −2.09277 0.787606i −0.935914 0.352228i
\(6\) 0 0
\(7\) 2.84620i 1.07576i −0.843020 0.537881i \(-0.819225\pi\)
0.843020 0.537881i \(-0.180775\pi\)
\(8\) 0 0
\(9\) 0.493499 0.164500
\(10\) 0 0
\(11\) −1.98637 −0.598913 −0.299457 0.954110i \(-0.596805\pi\)
−0.299457 + 0.954110i \(0.596805\pi\)
\(12\) 0 0
\(13\) 4.69204i 1.30134i 0.759362 + 0.650668i \(0.225511\pi\)
−0.759362 + 0.650668i \(0.774489\pi\)
\(14\) 0 0
\(15\) 1.24693 3.31326i 0.321957 0.855479i
\(16\) 0 0
\(17\) 3.16675i 0.768050i −0.923323 0.384025i \(-0.874538\pi\)
0.923323 0.384025i \(-0.125462\pi\)
\(18\) 0 0
\(19\) −6.16110 −1.41345 −0.706727 0.707486i \(-0.749829\pi\)
−0.706727 + 0.707486i \(0.749829\pi\)
\(20\) 0 0
\(21\) 4.50609 0.983309
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 3.75935 + 3.29655i 0.751871 + 0.659311i
\(26\) 0 0
\(27\) 5.53088i 1.06442i
\(28\) 0 0
\(29\) 6.61816 1.22896 0.614481 0.788932i \(-0.289365\pi\)
0.614481 + 0.788932i \(0.289365\pi\)
\(30\) 0 0
\(31\) 8.29732 1.49024 0.745121 0.666929i \(-0.232392\pi\)
0.745121 + 0.666929i \(0.232392\pi\)
\(32\) 0 0
\(33\) 3.14481i 0.547441i
\(34\) 0 0
\(35\) −2.24169 + 5.95644i −0.378914 + 1.00682i
\(36\) 0 0
\(37\) 1.71181i 0.281420i 0.990051 + 0.140710i \(0.0449386\pi\)
−0.990051 + 0.140710i \(0.955061\pi\)
\(38\) 0 0
\(39\) −7.42840 −1.18950
\(40\) 0 0
\(41\) 6.72440 1.05018 0.525088 0.851048i \(-0.324033\pi\)
0.525088 + 0.851048i \(0.324033\pi\)
\(42\) 0 0
\(43\) 0.177968i 0.0271399i 0.999908 + 0.0135700i \(0.00431958\pi\)
−0.999908 + 0.0135700i \(0.995680\pi\)
\(44\) 0 0
\(45\) −1.03278 0.388683i −0.153958 0.0579414i
\(46\) 0 0
\(47\) 11.4749i 1.67378i 0.547369 + 0.836891i \(0.315629\pi\)
−0.547369 + 0.836891i \(0.684371\pi\)
\(48\) 0 0
\(49\) −1.10086 −0.157266
\(50\) 0 0
\(51\) 5.01358 0.702042
\(52\) 0 0
\(53\) 6.18762i 0.849934i 0.905209 + 0.424967i \(0.139714\pi\)
−0.905209 + 0.424967i \(0.860286\pi\)
\(54\) 0 0
\(55\) 4.15701 + 1.56448i 0.560531 + 0.210954i
\(56\) 0 0
\(57\) 9.75422i 1.29198i
\(58\) 0 0
\(59\) −7.61559 −0.991465 −0.495733 0.868475i \(-0.665100\pi\)
−0.495733 + 0.868475i \(0.665100\pi\)
\(60\) 0 0
\(61\) 11.8577 1.51822 0.759109 0.650964i \(-0.225635\pi\)
0.759109 + 0.650964i \(0.225635\pi\)
\(62\) 0 0
\(63\) 1.40460i 0.176963i
\(64\) 0 0
\(65\) 3.69548 9.81934i 0.458367 1.21794i
\(66\) 0 0
\(67\) 3.07554i 0.375737i 0.982194 + 0.187868i \(0.0601579\pi\)
−0.982194 + 0.187868i \(0.939842\pi\)
\(68\) 0 0
\(69\) 1.58319 0.190594
\(70\) 0 0
\(71\) 1.96195 0.232840 0.116420 0.993200i \(-0.462858\pi\)
0.116420 + 0.993200i \(0.462858\pi\)
\(72\) 0 0
\(73\) 4.94732i 0.579041i 0.957172 + 0.289520i \(0.0934958\pi\)
−0.957172 + 0.289520i \(0.906504\pi\)
\(74\) 0 0
\(75\) −5.21908 + 5.95178i −0.602647 + 0.687253i
\(76\) 0 0
\(77\) 5.65361i 0.644289i
\(78\) 0 0
\(79\) 8.53182 0.959905 0.479952 0.877295i \(-0.340654\pi\)
0.479952 + 0.877295i \(0.340654\pi\)
\(80\) 0 0
\(81\) −7.27596 −0.808440
\(82\) 0 0
\(83\) 3.49429i 0.383548i −0.981439 0.191774i \(-0.938576\pi\)
0.981439 0.191774i \(-0.0614241\pi\)
\(84\) 0 0
\(85\) −2.49415 + 6.62728i −0.270529 + 0.718829i
\(86\) 0 0
\(87\) 10.4778i 1.12334i
\(88\) 0 0
\(89\) −7.07506 −0.749954 −0.374977 0.927034i \(-0.622349\pi\)
−0.374977 + 0.927034i \(0.622349\pi\)
\(90\) 0 0
\(91\) 13.3545 1.39993
\(92\) 0 0
\(93\) 13.1363i 1.36217i
\(94\) 0 0
\(95\) 12.8938 + 4.85252i 1.32287 + 0.497858i
\(96\) 0 0
\(97\) 7.00705i 0.711458i 0.934589 + 0.355729i \(0.115767\pi\)
−0.934589 + 0.355729i \(0.884233\pi\)
\(98\) 0 0
\(99\) −0.980272 −0.0985210
\(100\) 0 0
\(101\) 7.22362 0.718777 0.359389 0.933188i \(-0.382985\pi\)
0.359389 + 0.933188i \(0.382985\pi\)
\(102\) 0 0
\(103\) 12.8178i 1.26297i 0.775386 + 0.631487i \(0.217555\pi\)
−0.775386 + 0.631487i \(0.782445\pi\)
\(104\) 0 0
\(105\) −9.43019 3.54902i −0.920293 0.346349i
\(106\) 0 0
\(107\) 11.6841i 1.12954i −0.825247 0.564772i \(-0.808964\pi\)
0.825247 0.564772i \(-0.191036\pi\)
\(108\) 0 0
\(109\) 13.6019 1.30283 0.651413 0.758723i \(-0.274176\pi\)
0.651413 + 0.758723i \(0.274176\pi\)
\(110\) 0 0
\(111\) −2.71013 −0.257234
\(112\) 0 0
\(113\) 1.44526i 0.135959i 0.997687 + 0.0679795i \(0.0216553\pi\)
−0.997687 + 0.0679795i \(0.978345\pi\)
\(114\) 0 0
\(115\) −0.787606 + 2.09277i −0.0734446 + 0.195152i
\(116\) 0 0
\(117\) 2.31552i 0.214069i
\(118\) 0 0
\(119\) −9.01322 −0.826240
\(120\) 0 0
\(121\) −7.05433 −0.641303
\(122\) 0 0
\(123\) 10.6460i 0.959920i
\(124\) 0 0
\(125\) −5.27107 9.85981i −0.471459 0.881888i
\(126\) 0 0
\(127\) 9.12328i 0.809561i −0.914414 0.404780i \(-0.867348\pi\)
0.914414 0.404780i \(-0.132652\pi\)
\(128\) 0 0
\(129\) −0.281758 −0.0248074
\(130\) 0 0
\(131\) −9.33180 −0.815323 −0.407661 0.913133i \(-0.633656\pi\)
−0.407661 + 0.913133i \(0.633656\pi\)
\(132\) 0 0
\(133\) 17.5357i 1.52054i
\(134\) 0 0
\(135\) 4.35616 11.5749i 0.374918 0.996205i
\(136\) 0 0
\(137\) 21.0013i 1.79426i 0.441768 + 0.897129i \(0.354351\pi\)
−0.441768 + 0.897129i \(0.645649\pi\)
\(138\) 0 0
\(139\) −16.1299 −1.36812 −0.684061 0.729425i \(-0.739788\pi\)
−0.684061 + 0.729425i \(0.739788\pi\)
\(140\) 0 0
\(141\) −18.1669 −1.52993
\(142\) 0 0
\(143\) 9.32012i 0.779388i
\(144\) 0 0
\(145\) −13.8503 5.21251i −1.15020 0.432875i
\(146\) 0 0
\(147\) 1.74288i 0.143750i
\(148\) 0 0
\(149\) 9.57227 0.784191 0.392096 0.919925i \(-0.371750\pi\)
0.392096 + 0.919925i \(0.371750\pi\)
\(150\) 0 0
\(151\) −3.04120 −0.247489 −0.123745 0.992314i \(-0.539490\pi\)
−0.123745 + 0.992314i \(0.539490\pi\)
\(152\) 0 0
\(153\) 1.56279i 0.126344i
\(154\) 0 0
\(155\) −17.3644 6.53502i −1.39474 0.524905i
\(156\) 0 0
\(157\) 12.4786i 0.995900i 0.867206 + 0.497950i \(0.165914\pi\)
−0.867206 + 0.497950i \(0.834086\pi\)
\(158\) 0 0
\(159\) −9.79619 −0.776889
\(160\) 0 0
\(161\) −2.84620 −0.224312
\(162\) 0 0
\(163\) 16.3939i 1.28407i 0.766676 + 0.642034i \(0.221909\pi\)
−0.766676 + 0.642034i \(0.778091\pi\)
\(164\) 0 0
\(165\) −2.47687 + 6.58135i −0.192824 + 0.512358i
\(166\) 0 0
\(167\) 8.13265i 0.629323i −0.949204 0.314662i \(-0.898109\pi\)
0.949204 0.314662i \(-0.101891\pi\)
\(168\) 0 0
\(169\) −9.01521 −0.693477
\(170\) 0 0
\(171\) −3.04050 −0.232513
\(172\) 0 0
\(173\) 10.5256i 0.800250i −0.916461 0.400125i \(-0.868967\pi\)
0.916461 0.400125i \(-0.131033\pi\)
\(174\) 0 0
\(175\) 9.38265 10.6999i 0.709262 0.808835i
\(176\) 0 0
\(177\) 12.0570i 0.906256i
\(178\) 0 0
\(179\) 20.5421 1.53539 0.767695 0.640816i \(-0.221404\pi\)
0.767695 + 0.640816i \(0.221404\pi\)
\(180\) 0 0
\(181\) −22.0754 −1.64085 −0.820424 0.571756i \(-0.806263\pi\)
−0.820424 + 0.571756i \(0.806263\pi\)
\(182\) 0 0
\(183\) 18.7730i 1.38774i
\(184\) 0 0
\(185\) 1.34823 3.58243i 0.0991242 0.263385i
\(186\) 0 0
\(187\) 6.29034i 0.459995i
\(188\) 0 0
\(189\) 15.7420 1.14506
\(190\) 0 0
\(191\) 4.50910 0.326267 0.163133 0.986604i \(-0.447840\pi\)
0.163133 + 0.986604i \(0.447840\pi\)
\(192\) 0 0
\(193\) 21.1534i 1.52266i 0.648366 + 0.761329i \(0.275453\pi\)
−0.648366 + 0.761329i \(0.724547\pi\)
\(194\) 0 0
\(195\) 15.5459 + 5.85065i 1.11327 + 0.418974i
\(196\) 0 0
\(197\) 10.1475i 0.722980i −0.932376 0.361490i \(-0.882268\pi\)
0.932376 0.361490i \(-0.117732\pi\)
\(198\) 0 0
\(199\) 6.57598 0.466159 0.233079 0.972458i \(-0.425120\pi\)
0.233079 + 0.972458i \(0.425120\pi\)
\(200\) 0 0
\(201\) −4.86917 −0.343445
\(202\) 0 0
\(203\) 18.8366i 1.32207i
\(204\) 0 0
\(205\) −14.0726 5.29618i −0.982874 0.369901i
\(206\) 0 0
\(207\) 0.493499i 0.0343005i
\(208\) 0 0
\(209\) 12.2382 0.846536
\(210\) 0 0
\(211\) 26.5357 1.82680 0.913398 0.407069i \(-0.133449\pi\)
0.913398 + 0.407069i \(0.133449\pi\)
\(212\) 0 0
\(213\) 3.10614i 0.212829i
\(214\) 0 0
\(215\) 0.140169 0.372446i 0.00955944 0.0254006i
\(216\) 0 0
\(217\) 23.6158i 1.60315i
\(218\) 0 0
\(219\) −7.83257 −0.529276
\(220\) 0 0
\(221\) 14.8585 0.999492
\(222\) 0 0
\(223\) 20.9231i 1.40111i 0.713597 + 0.700557i \(0.247065\pi\)
−0.713597 + 0.700557i \(0.752935\pi\)
\(224\) 0 0
\(225\) 1.85524 + 1.62685i 0.123682 + 0.108456i
\(226\) 0 0
\(227\) 9.32581i 0.618975i −0.950903 0.309488i \(-0.899842\pi\)
0.950903 0.309488i \(-0.100158\pi\)
\(228\) 0 0
\(229\) −29.5189 −1.95066 −0.975332 0.220742i \(-0.929152\pi\)
−0.975332 + 0.220742i \(0.929152\pi\)
\(230\) 0 0
\(231\) −8.95076 −0.588917
\(232\) 0 0
\(233\) 28.9849i 1.89886i −0.313974 0.949431i \(-0.601661\pi\)
0.313974 0.949431i \(-0.398339\pi\)
\(234\) 0 0
\(235\) 9.03768 24.0142i 0.589553 1.56652i
\(236\) 0 0
\(237\) 13.5075i 0.877408i
\(238\) 0 0
\(239\) −9.62209 −0.622401 −0.311201 0.950344i \(-0.600731\pi\)
−0.311201 + 0.950344i \(0.600731\pi\)
\(240\) 0 0
\(241\) 15.5745 1.00324 0.501621 0.865088i \(-0.332737\pi\)
0.501621 + 0.865088i \(0.332737\pi\)
\(242\) 0 0
\(243\) 5.07340i 0.325459i
\(244\) 0 0
\(245\) 2.30385 + 0.867045i 0.147187 + 0.0553935i
\(246\) 0 0
\(247\) 28.9081i 1.83938i
\(248\) 0 0
\(249\) 5.53214 0.350585
\(250\) 0 0
\(251\) 22.8066 1.43954 0.719770 0.694213i \(-0.244247\pi\)
0.719770 + 0.694213i \(0.244247\pi\)
\(252\) 0 0
\(253\) 1.98637i 0.124882i
\(254\) 0 0
\(255\) −10.4923 3.94873i −0.657051 0.247279i
\(256\) 0 0
\(257\) 11.5591i 0.721038i −0.932752 0.360519i \(-0.882600\pi\)
0.932752 0.360519i \(-0.117400\pi\)
\(258\) 0 0
\(259\) 4.87216 0.302742
\(260\) 0 0
\(261\) 3.26606 0.202164
\(262\) 0 0
\(263\) 6.57534i 0.405453i −0.979235 0.202726i \(-0.935020\pi\)
0.979235 0.202726i \(-0.0649802\pi\)
\(264\) 0 0
\(265\) 4.87340 12.9492i 0.299371 0.795466i
\(266\) 0 0
\(267\) 11.2012i 0.685501i
\(268\) 0 0
\(269\) 16.6536 1.01539 0.507694 0.861537i \(-0.330498\pi\)
0.507694 + 0.861537i \(0.330498\pi\)
\(270\) 0 0
\(271\) 23.8675 1.44985 0.724925 0.688828i \(-0.241874\pi\)
0.724925 + 0.688828i \(0.241874\pi\)
\(272\) 0 0
\(273\) 21.1427i 1.27962i
\(274\) 0 0
\(275\) −7.46747 6.54817i −0.450305 0.394870i
\(276\) 0 0
\(277\) 5.65369i 0.339697i −0.985470 0.169849i \(-0.945672\pi\)
0.985470 0.169849i \(-0.0543279\pi\)
\(278\) 0 0
\(279\) 4.09472 0.245144
\(280\) 0 0
\(281\) −31.7408 −1.89350 −0.946750 0.321971i \(-0.895655\pi\)
−0.946750 + 0.321971i \(0.895655\pi\)
\(282\) 0 0
\(283\) 0.998092i 0.0593304i 0.999560 + 0.0296652i \(0.00944412\pi\)
−0.999560 + 0.0296652i \(0.990556\pi\)
\(284\) 0 0
\(285\) −7.68248 + 20.4133i −0.455071 + 1.20918i
\(286\) 0 0
\(287\) 19.1390i 1.12974i
\(288\) 0 0
\(289\) 6.97168 0.410099
\(290\) 0 0
\(291\) −11.0935 −0.650314
\(292\) 0 0
\(293\) 13.8947i 0.811739i 0.913931 + 0.405869i \(0.133031\pi\)
−0.913931 + 0.405869i \(0.866969\pi\)
\(294\) 0 0
\(295\) 15.9377 + 5.99808i 0.927927 + 0.349222i
\(296\) 0 0
\(297\) 10.9864i 0.637495i
\(298\) 0 0
\(299\) 4.69204 0.271347
\(300\) 0 0
\(301\) 0.506534 0.0291961
\(302\) 0 0
\(303\) 11.4364i 0.657003i
\(304\) 0 0
\(305\) −24.8153 9.33916i −1.42092 0.534759i
\(306\) 0 0
\(307\) 3.66633i 0.209249i 0.994512 + 0.104624i \(0.0333640\pi\)
−0.994512 + 0.104624i \(0.966636\pi\)
\(308\) 0 0
\(309\) −20.2930 −1.15443
\(310\) 0 0
\(311\) 14.4210 0.817741 0.408870 0.912593i \(-0.365923\pi\)
0.408870 + 0.912593i \(0.365923\pi\)
\(312\) 0 0
\(313\) 10.5046i 0.593754i −0.954916 0.296877i \(-0.904055\pi\)
0.954916 0.296877i \(-0.0959451\pi\)
\(314\) 0 0
\(315\) −1.10627 + 2.93950i −0.0623312 + 0.165622i
\(316\) 0 0
\(317\) 32.0818i 1.80189i −0.433931 0.900946i \(-0.642874\pi\)
0.433931 0.900946i \(-0.357126\pi\)
\(318\) 0 0
\(319\) −13.1461 −0.736042
\(320\) 0 0
\(321\) 18.4982 1.03247
\(322\) 0 0
\(323\) 19.5107i 1.08560i
\(324\) 0 0
\(325\) −15.4675 + 17.6390i −0.857985 + 0.978437i
\(326\) 0 0
\(327\) 21.5344i 1.19086i
\(328\) 0 0
\(329\) 32.6598 1.80059
\(330\) 0 0
\(331\) −9.71307 −0.533879 −0.266939 0.963713i \(-0.586012\pi\)
−0.266939 + 0.963713i \(0.586012\pi\)
\(332\) 0 0
\(333\) 0.844778i 0.0462935i
\(334\) 0 0
\(335\) 2.42231 6.43639i 0.132345 0.351657i
\(336\) 0 0
\(337\) 0.131832i 0.00718136i −0.999994 0.00359068i \(-0.998857\pi\)
0.999994 0.00359068i \(-0.00114295\pi\)
\(338\) 0 0
\(339\) −2.28813 −0.124274
\(340\) 0 0
\(341\) −16.4815 −0.892526
\(342\) 0 0
\(343\) 16.7901i 0.906582i
\(344\) 0 0
\(345\) −3.31326 1.24693i −0.178380 0.0671326i
\(346\) 0 0
\(347\) 13.1981i 0.708512i 0.935148 + 0.354256i \(0.115266\pi\)
−0.935148 + 0.354256i \(0.884734\pi\)
\(348\) 0 0
\(349\) 34.0451 1.82239 0.911197 0.411971i \(-0.135159\pi\)
0.911197 + 0.411971i \(0.135159\pi\)
\(350\) 0 0
\(351\) −25.9511 −1.38517
\(352\) 0 0
\(353\) 10.8593i 0.577984i −0.957331 0.288992i \(-0.906680\pi\)
0.957331 0.288992i \(-0.0933201\pi\)
\(354\) 0 0
\(355\) −4.10590 1.54524i −0.217919 0.0820129i
\(356\) 0 0
\(357\) 14.2697i 0.755231i
\(358\) 0 0
\(359\) −20.3091 −1.07188 −0.535938 0.844257i \(-0.680042\pi\)
−0.535938 + 0.844257i \(0.680042\pi\)
\(360\) 0 0
\(361\) 18.9592 0.997853
\(362\) 0 0
\(363\) 11.1684i 0.586188i
\(364\) 0 0
\(365\) 3.89654 10.3536i 0.203954 0.541932i
\(366\) 0 0
\(367\) 18.6731i 0.974727i 0.873199 + 0.487364i \(0.162041\pi\)
−0.873199 + 0.487364i \(0.837959\pi\)
\(368\) 0 0
\(369\) 3.31848 0.172753
\(370\) 0 0
\(371\) 17.6112 0.914328
\(372\) 0 0
\(373\) 9.51979i 0.492916i −0.969153 0.246458i \(-0.920733\pi\)
0.969153 0.246458i \(-0.0792667\pi\)
\(374\) 0 0
\(375\) 15.6100 8.34512i 0.806096 0.430940i
\(376\) 0 0
\(377\) 31.0527i 1.59929i
\(378\) 0 0
\(379\) 18.8304 0.967251 0.483625 0.875275i \(-0.339320\pi\)
0.483625 + 0.875275i \(0.339320\pi\)
\(380\) 0 0
\(381\) 14.4439 0.739985
\(382\) 0 0
\(383\) 10.9401i 0.559015i −0.960144 0.279507i \(-0.909829\pi\)
0.960144 0.279507i \(-0.0901712\pi\)
\(384\) 0 0
\(385\) 4.45282 11.8317i 0.226937 0.602999i
\(386\) 0 0
\(387\) 0.0878272i 0.00446451i
\(388\) 0 0
\(389\) −22.2830 −1.12979 −0.564896 0.825162i \(-0.691084\pi\)
−0.564896 + 0.825162i \(0.691084\pi\)
\(390\) 0 0
\(391\) −3.16675 −0.160150
\(392\) 0 0
\(393\) 14.7740i 0.745252i
\(394\) 0 0
\(395\) −17.8551 6.71971i −0.898389 0.338105i
\(396\) 0 0
\(397\) 10.8388i 0.543983i −0.962300 0.271991i \(-0.912318\pi\)
0.962300 0.271991i \(-0.0876822\pi\)
\(398\) 0 0
\(399\) −27.7625 −1.38986
\(400\) 0 0
\(401\) −2.71329 −0.135495 −0.0677476 0.997702i \(-0.521581\pi\)
−0.0677476 + 0.997702i \(0.521581\pi\)
\(402\) 0 0
\(403\) 38.9313i 1.93931i
\(404\) 0 0
\(405\) 15.2269 + 5.73059i 0.756631 + 0.284755i
\(406\) 0 0
\(407\) 3.40029i 0.168546i
\(408\) 0 0
\(409\) −21.6271 −1.06939 −0.534696 0.845044i \(-0.679574\pi\)
−0.534696 + 0.845044i \(0.679574\pi\)
\(410\) 0 0
\(411\) −33.2490 −1.64005
\(412\) 0 0
\(413\) 21.6755i 1.06658i
\(414\) 0 0
\(415\) −2.75212 + 7.31274i −0.135097 + 0.358968i
\(416\) 0 0
\(417\) 25.5368i 1.25054i
\(418\) 0 0
\(419\) 4.00587 0.195700 0.0978498 0.995201i \(-0.468804\pi\)
0.0978498 + 0.995201i \(0.468804\pi\)
\(420\) 0 0
\(421\) 25.4251 1.23914 0.619572 0.784940i \(-0.287306\pi\)
0.619572 + 0.784940i \(0.287306\pi\)
\(422\) 0 0
\(423\) 5.66284i 0.275337i
\(424\) 0 0
\(425\) 10.4394 11.9049i 0.506384 0.577475i
\(426\) 0 0
\(427\) 33.7493i 1.63324i
\(428\) 0 0
\(429\) 14.7556 0.712405
\(430\) 0 0
\(431\) −1.07679 −0.0518673 −0.0259336 0.999664i \(-0.508256\pi\)
−0.0259336 + 0.999664i \(0.508256\pi\)
\(432\) 0 0
\(433\) 3.93871i 0.189283i 0.995511 + 0.0946413i \(0.0301704\pi\)
−0.995511 + 0.0946413i \(0.969830\pi\)
\(434\) 0 0
\(435\) 8.25240 21.9277i 0.395672 1.05135i
\(436\) 0 0
\(437\) 6.16110i 0.294726i
\(438\) 0 0
\(439\) 13.1539 0.627802 0.313901 0.949456i \(-0.398364\pi\)
0.313901 + 0.949456i \(0.398364\pi\)
\(440\) 0 0
\(441\) −0.543274 −0.0258702
\(442\) 0 0
\(443\) 8.95394i 0.425415i −0.977116 0.212707i \(-0.931772\pi\)
0.977116 0.212707i \(-0.0682281\pi\)
\(444\) 0 0
\(445\) 14.8064 + 5.57236i 0.701893 + 0.264155i
\(446\) 0 0
\(447\) 15.1548i 0.716795i
\(448\) 0 0
\(449\) −8.23267 −0.388524 −0.194262 0.980950i \(-0.562231\pi\)
−0.194262 + 0.980950i \(0.562231\pi\)
\(450\) 0 0
\(451\) −13.3571 −0.628964
\(452\) 0 0
\(453\) 4.81480i 0.226219i
\(454\) 0 0
\(455\) −27.9478 10.5181i −1.31021 0.493095i
\(456\) 0 0
\(457\) 36.3473i 1.70026i 0.526576 + 0.850128i \(0.323476\pi\)
−0.526576 + 0.850128i \(0.676524\pi\)
\(458\) 0 0
\(459\) 17.5149 0.817527
\(460\) 0 0
\(461\) −15.2421 −0.709894 −0.354947 0.934886i \(-0.615501\pi\)
−0.354947 + 0.934886i \(0.615501\pi\)
\(462\) 0 0
\(463\) 5.57424i 0.259057i −0.991576 0.129528i \(-0.958654\pi\)
0.991576 0.129528i \(-0.0413463\pi\)
\(464\) 0 0
\(465\) 10.3462 27.4911i 0.479793 1.27487i
\(466\) 0 0
\(467\) 6.21488i 0.287590i 0.989607 + 0.143795i \(0.0459306\pi\)
−0.989607 + 0.143795i \(0.954069\pi\)
\(468\) 0 0
\(469\) 8.75360 0.404204
\(470\) 0 0
\(471\) −19.7560 −0.910309
\(472\) 0 0
\(473\) 0.353511i 0.0162545i
\(474\) 0 0
\(475\) −23.1618 20.3104i −1.06273 0.931905i
\(476\) 0 0
\(477\) 3.05358i 0.139814i
\(478\) 0 0
\(479\) −34.4168 −1.57254 −0.786272 0.617880i \(-0.787992\pi\)
−0.786272 + 0.617880i \(0.787992\pi\)
\(480\) 0 0
\(481\) −8.03189 −0.366223
\(482\) 0 0
\(483\) 4.50609i 0.205034i
\(484\) 0 0
\(485\) 5.51880 14.6641i 0.250596 0.665864i
\(486\) 0 0
\(487\) 22.7752i 1.03204i −0.856576 0.516021i \(-0.827413\pi\)
0.856576 0.516021i \(-0.172587\pi\)
\(488\) 0 0
\(489\) −25.9547 −1.17371
\(490\) 0 0
\(491\) −3.16911 −0.143020 −0.0715099 0.997440i \(-0.522782\pi\)
−0.0715099 + 0.997440i \(0.522782\pi\)
\(492\) 0 0
\(493\) 20.9581i 0.943905i
\(494\) 0 0
\(495\) 2.05148 + 0.772068i 0.0922072 + 0.0347019i
\(496\) 0 0
\(497\) 5.58410i 0.250481i
\(498\) 0 0
\(499\) −14.0809 −0.630346 −0.315173 0.949034i \(-0.602063\pi\)
−0.315173 + 0.949034i \(0.602063\pi\)
\(500\) 0 0
\(501\) 12.8756 0.575237
\(502\) 0 0
\(503\) 21.4946i 0.958399i 0.877706 + 0.479199i \(0.159073\pi\)
−0.877706 + 0.479199i \(0.840927\pi\)
\(504\) 0 0
\(505\) −15.1174 5.68937i −0.672714 0.253173i
\(506\) 0 0
\(507\) 14.2728i 0.633878i
\(508\) 0 0
\(509\) 34.0952 1.51124 0.755622 0.655008i \(-0.227335\pi\)
0.755622 + 0.655008i \(0.227335\pi\)
\(510\) 0 0
\(511\) 14.0811 0.622910
\(512\) 0 0
\(513\) 34.0764i 1.50451i
\(514\) 0 0
\(515\) 10.0954 26.8247i 0.444855 1.18204i
\(516\) 0 0
\(517\) 22.7933i 1.00245i
\(518\) 0 0
\(519\) 16.6641 0.731474
\(520\) 0 0
\(521\) −14.1367 −0.619339 −0.309669 0.950844i \(-0.600218\pi\)
−0.309669 + 0.950844i \(0.600218\pi\)
\(522\) 0 0
\(523\) 11.2020i 0.489828i −0.969545 0.244914i \(-0.921240\pi\)
0.969545 0.244914i \(-0.0787598\pi\)
\(524\) 0 0
\(525\) 16.9400 + 14.8546i 0.739321 + 0.648306i
\(526\) 0 0
\(527\) 26.2756i 1.14458i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) −3.75829 −0.163096
\(532\) 0 0
\(533\) 31.5511i 1.36663i
\(534\) 0 0
\(535\) −9.20247 + 24.4521i −0.397857 + 1.05716i
\(536\) 0 0
\(537\) 32.5221i 1.40343i
\(538\) 0 0
\(539\) 2.18672 0.0941887
\(540\) 0 0
\(541\) −33.6704 −1.44760 −0.723802 0.690008i \(-0.757607\pi\)
−0.723802 + 0.690008i \(0.757607\pi\)
\(542\) 0 0
\(543\) 34.9496i 1.49983i
\(544\) 0 0
\(545\) −28.4656 10.7129i −1.21933 0.458892i
\(546\) 0 0
\(547\) 23.1062i 0.987949i −0.869476 0.493975i \(-0.835544\pi\)
0.869476 0.493975i \(-0.164456\pi\)
\(548\) 0 0
\(549\) 5.85174 0.249746
\(550\) 0 0
\(551\) −40.7752 −1.73708
\(552\) 0 0
\(553\) 24.2833i 1.03263i
\(554\) 0 0
\(555\) 5.67167 + 2.13452i 0.240749 + 0.0906051i
\(556\) 0 0
\(557\) 3.48937i 0.147849i −0.997264 0.0739246i \(-0.976448\pi\)
0.997264 0.0739246i \(-0.0235524\pi\)
\(558\) 0 0
\(559\) −0.835034 −0.0353182
\(560\) 0 0
\(561\) −9.95883 −0.420462
\(562\) 0 0
\(563\) 38.8593i 1.63772i 0.573991 + 0.818862i \(0.305394\pi\)
−0.573991 + 0.818862i \(0.694606\pi\)
\(564\) 0 0
\(565\) 1.13830 3.02460i 0.0478886 0.127246i
\(566\) 0 0
\(567\) 20.7089i 0.869690i
\(568\) 0 0
\(569\) 23.2055 0.972823 0.486412 0.873730i \(-0.338306\pi\)
0.486412 + 0.873730i \(0.338306\pi\)
\(570\) 0 0
\(571\) 5.39836 0.225914 0.112957 0.993600i \(-0.463968\pi\)
0.112957 + 0.993600i \(0.463968\pi\)
\(572\) 0 0
\(573\) 7.13877i 0.298226i
\(574\) 0 0
\(575\) 3.29655 3.75935i 0.137476 0.156776i
\(576\) 0 0
\(577\) 13.1082i 0.545701i 0.962056 + 0.272850i \(0.0879664\pi\)
−0.962056 + 0.272850i \(0.912034\pi\)
\(578\) 0 0
\(579\) −33.4900 −1.39180
\(580\) 0 0
\(581\) −9.94546 −0.412607
\(582\) 0 0
\(583\) 12.2909i 0.509037i
\(584\) 0 0
\(585\) 1.82371 4.84584i 0.0754013 0.200351i
\(586\) 0 0
\(587\) 12.9646i 0.535108i 0.963543 + 0.267554i \(0.0862154\pi\)
−0.963543 + 0.267554i \(0.913785\pi\)
\(588\) 0 0
\(589\) −51.1206 −2.10639
\(590\) 0 0
\(591\) 16.0655 0.660845
\(592\) 0 0
\(593\) 17.0225i 0.699030i −0.936931 0.349515i \(-0.886346\pi\)
0.936931 0.349515i \(-0.113654\pi\)
\(594\) 0 0
\(595\) 18.8626 + 7.09886i 0.773290 + 0.291025i
\(596\) 0 0
\(597\) 10.4110i 0.426096i
\(598\) 0 0
\(599\) −5.98111 −0.244381 −0.122191 0.992507i \(-0.538992\pi\)
−0.122191 + 0.992507i \(0.538992\pi\)
\(600\) 0 0
\(601\) −21.3680 −0.871617 −0.435809 0.900039i \(-0.643538\pi\)
−0.435809 + 0.900039i \(0.643538\pi\)
\(602\) 0 0
\(603\) 1.51778i 0.0618086i
\(604\) 0 0
\(605\) 14.7631 + 5.55604i 0.600205 + 0.225885i
\(606\) 0 0
\(607\) 17.5464i 0.712186i 0.934450 + 0.356093i \(0.115891\pi\)
−0.934450 + 0.356093i \(0.884109\pi\)
\(608\) 0 0
\(609\) 29.8220 1.20845
\(610\) 0 0
\(611\) −53.8405 −2.17815
\(612\) 0 0
\(613\) 45.4601i 1.83612i 0.396444 + 0.918059i \(0.370244\pi\)
−0.396444 + 0.918059i \(0.629756\pi\)
\(614\) 0 0
\(615\) 8.38487 22.2797i 0.338111 0.898403i
\(616\) 0 0
\(617\) 25.8720i 1.04157i −0.853688 0.520785i \(-0.825640\pi\)
0.853688 0.520785i \(-0.174360\pi\)
\(618\) 0 0
\(619\) −3.20381 −0.128772 −0.0643859 0.997925i \(-0.520509\pi\)
−0.0643859 + 0.997925i \(0.520509\pi\)
\(620\) 0 0
\(621\) 5.53088 0.221947
\(622\) 0 0
\(623\) 20.1370i 0.806773i
\(624\) 0 0
\(625\) 3.26548 + 24.7858i 0.130619 + 0.991433i
\(626\) 0 0
\(627\) 19.3755i 0.773783i
\(628\) 0 0
\(629\) 5.42089 0.216145
\(630\) 0 0
\(631\) −0.0248650 −0.000989858 −0.000494929 1.00000i \(-0.500158\pi\)
−0.000494929 1.00000i \(0.500158\pi\)
\(632\) 0 0
\(633\) 42.0112i 1.66980i
\(634\) 0 0
\(635\) −7.18555 + 19.0929i −0.285150 + 0.757679i
\(636\) 0 0
\(637\) 5.16528i 0.204656i
\(638\) 0 0
\(639\) 0.968219 0.0383022
\(640\) 0 0
\(641\) −9.77145 −0.385949 −0.192975 0.981204i \(-0.561813\pi\)
−0.192975 + 0.981204i \(0.561813\pi\)
\(642\) 0 0
\(643\) 36.8211i 1.45208i 0.687651 + 0.726041i \(0.258642\pi\)
−0.687651 + 0.726041i \(0.741358\pi\)
\(644\) 0 0
\(645\) 0.589655 + 0.221914i 0.0232176 + 0.00873787i
\(646\) 0 0
\(647\) 46.5570i 1.83034i 0.403064 + 0.915172i \(0.367945\pi\)
−0.403064 + 0.915172i \(0.632055\pi\)
\(648\) 0 0
\(649\) 15.1274 0.593802
\(650\) 0 0
\(651\) 37.3884 1.46537
\(652\) 0 0
\(653\) 2.76029i 0.108018i 0.998540 + 0.0540092i \(0.0172000\pi\)
−0.998540 + 0.0540092i \(0.982800\pi\)
\(654\) 0 0
\(655\) 19.5293 + 7.34978i 0.763072 + 0.287180i
\(656\) 0 0
\(657\) 2.44150i 0.0952520i
\(658\) 0 0
\(659\) 39.3922 1.53450 0.767252 0.641346i \(-0.221624\pi\)
0.767252 + 0.641346i \(0.221624\pi\)
\(660\) 0 0
\(661\) −17.7641 −0.690943 −0.345472 0.938429i \(-0.612281\pi\)
−0.345472 + 0.938429i \(0.612281\pi\)
\(662\) 0 0
\(663\) 23.5239i 0.913593i
\(664\) 0 0
\(665\) 13.8113 36.6982i 0.535578 1.42310i
\(666\) 0 0
\(667\) 6.61816i 0.256256i
\(668\) 0 0
\(669\) −33.1253 −1.28070
\(670\) 0 0
\(671\) −23.5537 −0.909280
\(672\) 0 0
\(673\) 23.7072i 0.913847i −0.889506 0.456923i \(-0.848951\pi\)
0.889506 0.456923i \(-0.151049\pi\)
\(674\) 0 0
\(675\) −18.2329 + 20.7925i −0.701783 + 0.800306i
\(676\) 0 0
\(677\) 49.3507i 1.89670i −0.317221 0.948352i \(-0.602750\pi\)
0.317221 0.948352i \(-0.397250\pi\)
\(678\) 0 0
\(679\) 19.9435 0.765361
\(680\) 0 0
\(681\) 14.7646 0.565779
\(682\) 0 0
\(683\) 15.6461i 0.598682i −0.954146 0.299341i \(-0.903233\pi\)
0.954146 0.299341i \(-0.0967669\pi\)
\(684\) 0 0
\(685\) 16.5407 43.9507i 0.631988 1.67927i
\(686\) 0 0
\(687\) 46.7341i 1.78302i
\(688\) 0 0
\(689\) −29.0325 −1.10605
\(690\) 0 0
\(691\) −3.79498 −0.144368 −0.0721839 0.997391i \(-0.522997\pi\)
−0.0721839 + 0.997391i \(0.522997\pi\)
\(692\) 0 0
\(693\) 2.79005i 0.105985i
\(694\) 0 0
\(695\) 33.7562 + 12.7040i 1.28044 + 0.481891i
\(696\) 0 0
\(697\) 21.2945i 0.806587i
\(698\) 0 0
\(699\) 45.8887 1.73567
\(700\) 0 0
\(701\) 0.751725 0.0283923 0.0141961 0.999899i \(-0.495481\pi\)
0.0141961 + 0.999899i \(0.495481\pi\)
\(702\) 0 0
\(703\) 10.5467i 0.397775i
\(704\) 0 0
\(705\) 38.0192 + 14.3084i 1.43189 + 0.538885i
\(706\) 0 0
\(707\) 20.5599i 0.773234i
\(708\) 0 0
\(709\) −4.52035 −0.169765 −0.0848827 0.996391i \(-0.527052\pi\)
−0.0848827 + 0.996391i \(0.527052\pi\)
\(710\) 0 0
\(711\) 4.21044 0.157904
\(712\) 0 0
\(713\) 8.29732i 0.310737i
\(714\) 0 0
\(715\) −7.34058 + 19.5048i −0.274522 + 0.729440i
\(716\) 0 0
\(717\) 15.2336i 0.568910i
\(718\) 0 0
\(719\) −36.6742 −1.36772 −0.683859 0.729614i \(-0.739700\pi\)
−0.683859 + 0.729614i \(0.739700\pi\)
\(720\) 0 0
\(721\) 36.4820 1.35866
\(722\) 0 0
\(723\) 24.6574i 0.917020i
\(724\) 0 0
\(725\) 24.8800 + 21.8171i 0.924021 + 0.810268i
\(726\) 0 0
\(727\) 33.6449i 1.24782i −0.781496 0.623910i \(-0.785543\pi\)
0.781496 0.623910i \(-0.214457\pi\)
\(728\) 0 0
\(729\) −29.8601 −1.10593
\(730\) 0 0
\(731\) 0.563582 0.0208448
\(732\) 0 0
\(733\) 47.5745i 1.75720i 0.477555 + 0.878602i \(0.341523\pi\)
−0.477555 + 0.878602i \(0.658477\pi\)
\(734\) 0 0
\(735\) −1.37270 + 3.64744i −0.0506328 + 0.134538i
\(736\) 0 0
\(737\) 6.10916i 0.225034i
\(738\) 0 0
\(739\) 28.8914 1.06279 0.531395 0.847124i \(-0.321668\pi\)
0.531395 + 0.847124i \(0.321668\pi\)
\(740\) 0 0
\(741\) 45.7672 1.68130
\(742\) 0 0
\(743\) 3.61970i 0.132794i −0.997793 0.0663969i \(-0.978850\pi\)
0.997793 0.0663969i \(-0.0211504\pi\)
\(744\) 0 0
\(745\) −20.0325 7.53918i −0.733936 0.276214i
\(746\) 0 0
\(747\) 1.72443i 0.0630936i
\(748\) 0 0
\(749\) −33.2553 −1.21512
\(750\) 0 0
\(751\) −19.2050 −0.700801 −0.350401 0.936600i \(-0.613955\pi\)
−0.350401 + 0.936600i \(0.613955\pi\)
\(752\) 0 0
\(753\) 36.1073i 1.31582i
\(754\) 0 0
\(755\) 6.36452 + 2.39527i 0.231629 + 0.0871726i
\(756\) 0 0
\(757\) 12.6638i 0.460275i 0.973158 + 0.230137i \(0.0739176\pi\)
−0.973158 + 0.230137i \(0.926082\pi\)
\(758\) 0 0
\(759\) −3.14481 −0.114149
\(760\) 0 0
\(761\) −38.9053 −1.41032 −0.705159 0.709050i \(-0.749124\pi\)
−0.705159 + 0.709050i \(0.749124\pi\)
\(762\) 0 0
\(763\) 38.7138i 1.40153i
\(764\) 0 0
\(765\) −1.23086 + 3.27055i −0.0445019 + 0.118247i
\(766\) 0 0
\(767\) 35.7326i 1.29023i
\(768\) 0 0
\(769\) −4.16816 −0.150308 −0.0751539 0.997172i \(-0.523945\pi\)
−0.0751539 + 0.997172i \(0.523945\pi\)
\(770\) 0 0
\(771\) 18.3003 0.659070
\(772\) 0 0
\(773\) 26.6030i 0.956842i 0.878131 + 0.478421i \(0.158791\pi\)
−0.878131 + 0.478421i \(0.841209\pi\)
\(774\) 0 0
\(775\) 31.1926 + 27.3525i 1.12047 + 0.982533i
\(776\) 0 0
\(777\) 7.71358i 0.276723i
\(778\) 0 0
\(779\) −41.4297 −1.48437
\(780\) 0 0
\(781\) −3.89716 −0.139451
\(782\) 0 0
\(783\) 36.6043i 1.30813i
\(784\) 0 0
\(785\) 9.82821 26.1148i 0.350784 0.932077i
\(786\) 0 0
\(787\) 21.7538i 0.775440i 0.921777 + 0.387720i \(0.126737\pi\)
−0.921777 + 0.387720i \(0.873263\pi\)
\(788\) 0 0
\(789\) 10.4100 0.370607
\(790\) 0 0
\(791\) 4.11351 0.146260
\(792\) 0 0
\(793\) 55.6366i 1.97571i
\(794\) 0 0
\(795\) 20.5012 + 7.71554i 0.727101 + 0.273642i
\(796\) 0 0
\(797\) 10.2490i 0.363039i −0.983387 0.181519i \(-0.941898\pi\)
0.983387 0.181519i \(-0.0581015\pi\)
\(798\) 0 0
\(799\) 36.3381 1.28555
\(800\) 0 0
\(801\) −3.49153 −0.123367
\(802\) 0 0
\(803\) 9.82722i