Properties

Label 1512.2.s.n.865.3
Level $1512$
Weight $2$
Character 1512.865
Analytic conductor $12.073$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 3 x^{7} + 4 x^{6} + 28 x^{5} + 14 x^{4} - 52 x^{3} + 306 x^{2} + 1052 x + 1051\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.3
Root \(1.89574 + 2.48951i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.n.1297.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0144658 - 0.0250554i) q^{5} +(-1.70811 + 2.02048i) q^{7} +O(q^{10})\) \(q+(-0.0144658 - 0.0250554i) q^{5} +(-1.70811 + 2.02048i) q^{7} +(-1.88127 + 3.25845i) q^{11} -2.97107 q^{13} +(0.708111 - 1.22648i) q^{17} +(-3.81196 - 6.60250i) q^{19} +(-2.98512 - 5.17037i) q^{23} +(2.49958 - 4.32940i) q^{25} +9.99916 q^{29} +(4.27700 - 7.40799i) q^{31} +(0.0753332 + 0.0135696i) q^{35} +(-0.737043 - 1.27660i) q^{37} -4.38729 q^{41} +3.76254 q^{43} +(2.07491 + 3.59386i) q^{47} +(-1.16471 - 6.90242i) q^{49} +(3.60385 - 6.24204i) q^{53} +0.108856 q^{55} +(-6.93027 + 12.0036i) q^{59} +(-5.61831 - 9.73120i) q^{61} +(0.0429788 + 0.0744414i) q^{65} +(-2.77742 + 4.81064i) q^{67} -11.5661 q^{71} +(2.17918 - 3.77445i) q^{73} +(-3.37024 - 9.36688i) q^{77} +(-7.04556 - 12.2033i) q^{79} +6.62475 q^{83} -0.0409735 q^{85} +(2.14423 + 3.71391i) q^{89} +(5.07491 - 6.00300i) q^{91} +(-0.110286 + 0.191020i) q^{95} -6.77458 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{5} - 4q^{7} + O(q^{10}) \) \( 8q - 2q^{5} - 4q^{7} - q^{11} - 20q^{13} - 4q^{17} + q^{19} + 12q^{23} - 14q^{25} + 12q^{29} + 8q^{31} + 9q^{35} - 12q^{41} + 2q^{43} - 9q^{47} + 6q^{49} + 7q^{53} - 36q^{55} - 4q^{59} - 25q^{61} - 28q^{65} - 30q^{67} - 22q^{71} + 4q^{73} - 37q^{77} + 7q^{79} + 58q^{83} + 14q^{85} + 9q^{89} + 15q^{91} - 4q^{95} - 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −0.0144658 0.0250554i −0.00646928 0.0112051i 0.862773 0.505592i \(-0.168726\pi\)
−0.869242 + 0.494387i \(0.835393\pi\)
\(6\) 0 0
\(7\) −1.70811 + 2.02048i −0.645605 + 0.763671i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.88127 + 3.25845i −0.567224 + 0.982461i 0.429615 + 0.903012i \(0.358649\pi\)
−0.996839 + 0.0794487i \(0.974684\pi\)
\(12\) 0 0
\(13\) −2.97107 −0.824026 −0.412013 0.911178i \(-0.635174\pi\)
−0.412013 + 0.911178i \(0.635174\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.708111 1.22648i 0.171742 0.297466i −0.767287 0.641304i \(-0.778394\pi\)
0.939029 + 0.343838i \(0.111727\pi\)
\(18\) 0 0
\(19\) −3.81196 6.60250i −0.874523 1.51472i −0.857270 0.514867i \(-0.827841\pi\)
−0.0172529 0.999851i \(-0.505492\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.98512 5.17037i −0.622440 1.07810i −0.989030 0.147715i \(-0.952808\pi\)
0.366590 0.930382i \(-0.380525\pi\)
\(24\) 0 0
\(25\) 2.49958 4.32940i 0.499916 0.865880i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 9.99916 1.85680 0.928399 0.371585i \(-0.121186\pi\)
0.928399 + 0.371585i \(0.121186\pi\)
\(30\) 0 0
\(31\) 4.27700 7.40799i 0.768173 1.33051i −0.170380 0.985378i \(-0.554500\pi\)
0.938553 0.345136i \(-0.112167\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.0753332 + 0.0135696i 0.0127336 + 0.00229368i
\(36\) 0 0
\(37\) −0.737043 1.27660i −0.121169 0.209871i 0.799060 0.601251i \(-0.205331\pi\)
−0.920229 + 0.391380i \(0.871998\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.38729 −0.685180 −0.342590 0.939485i \(-0.611304\pi\)
−0.342590 + 0.939485i \(0.611304\pi\)
\(42\) 0 0
\(43\) 3.76254 0.573782 0.286891 0.957963i \(-0.407378\pi\)
0.286891 + 0.957963i \(0.407378\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.07491 + 3.59386i 0.302657 + 0.524218i 0.976737 0.214441i \(-0.0687929\pi\)
−0.674080 + 0.738659i \(0.735460\pi\)
\(48\) 0 0
\(49\) −1.16471 6.90242i −0.166388 0.986060i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.60385 6.24204i 0.495026 0.857411i −0.504957 0.863144i \(-0.668492\pi\)
0.999984 + 0.00573358i \(0.00182507\pi\)
\(54\) 0 0
\(55\) 0.108856 0.0146781
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −6.93027 + 12.0036i −0.902244 + 1.56273i −0.0776699 + 0.996979i \(0.524748\pi\)
−0.824574 + 0.565754i \(0.808585\pi\)
\(60\) 0 0
\(61\) −5.61831 9.73120i −0.719351 1.24595i −0.961257 0.275653i \(-0.911106\pi\)
0.241906 0.970300i \(-0.422227\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.0429788 + 0.0744414i 0.00533086 + 0.00923332i
\(66\) 0 0
\(67\) −2.77742 + 4.81064i −0.339316 + 0.587713i −0.984304 0.176480i \(-0.943529\pi\)
0.644988 + 0.764193i \(0.276862\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −11.5661 −1.37264 −0.686319 0.727301i \(-0.740775\pi\)
−0.686319 + 0.727301i \(0.740775\pi\)
\(72\) 0 0
\(73\) 2.17918 3.77445i 0.255054 0.441766i −0.709856 0.704346i \(-0.751240\pi\)
0.964910 + 0.262580i \(0.0845735\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.37024 9.36688i −0.384074 1.06745i
\(78\) 0 0
\(79\) −7.04556 12.2033i −0.792688 1.37298i −0.924297 0.381674i \(-0.875348\pi\)
0.131609 0.991302i \(-0.457986\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.62475 0.727161 0.363580 0.931563i \(-0.381554\pi\)
0.363580 + 0.931563i \(0.381554\pi\)
\(84\) 0 0
\(85\) −0.0409735 −0.00444420
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.14423 + 3.71391i 0.227288 + 0.393674i 0.957003 0.290077i \(-0.0936809\pi\)
−0.729716 + 0.683751i \(0.760348\pi\)
\(90\) 0 0
\(91\) 5.07491 6.00300i 0.531996 0.629285i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.110286 + 0.191020i −0.0113151 + 0.0195983i
\(96\) 0 0
\(97\) −6.77458 −0.687854 −0.343927 0.938996i \(-0.611757\pi\)
−0.343927 + 0.938996i \(0.611757\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.37282 5.84190i 0.335609 0.581291i −0.647993 0.761646i \(-0.724391\pi\)
0.983602 + 0.180355i \(0.0577247\pi\)
\(102\) 0 0
\(103\) −1.38169 2.39315i −0.136142 0.235804i 0.789891 0.613247i \(-0.210137\pi\)
−0.926033 + 0.377442i \(0.876804\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.90134 + 15.4176i 0.860525 + 1.49047i 0.871423 + 0.490532i \(0.163198\pi\)
−0.0108984 + 0.999941i \(0.503469\pi\)
\(108\) 0 0
\(109\) −5.41622 + 9.38117i −0.518780 + 0.898553i 0.480982 + 0.876731i \(0.340280\pi\)
−0.999762 + 0.0218227i \(0.993053\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.879102 0.0826990 0.0413495 0.999145i \(-0.486834\pi\)
0.0413495 + 0.999145i \(0.486834\pi\)
\(114\) 0 0
\(115\) −0.0863639 + 0.149587i −0.00805348 + 0.0139490i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.26856 + 3.52570i 0.116289 + 0.323200i
\(120\) 0 0
\(121\) −1.57835 2.73378i −0.143486 0.248526i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −0.289291 −0.0258750
\(126\) 0 0
\(127\) −1.27156 −0.112833 −0.0564165 0.998407i \(-0.517967\pi\)
−0.0564165 + 0.998407i \(0.517967\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −8.31998 14.4106i −0.726920 1.25906i −0.958179 0.286171i \(-0.907618\pi\)
0.231258 0.972892i \(-0.425716\pi\)
\(132\) 0 0
\(133\) 19.8515 + 3.57581i 1.72134 + 0.310062i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.44515 4.23513i 0.208904 0.361832i −0.742466 0.669884i \(-0.766344\pi\)
0.951369 + 0.308052i \(0.0996772\pi\)
\(138\) 0 0
\(139\) −8.61187 −0.730449 −0.365225 0.930919i \(-0.619008\pi\)
−0.365225 + 0.930919i \(0.619008\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5.58938 9.68109i 0.467407 0.809573i
\(144\) 0 0
\(145\) −0.144645 0.250533i −0.0120122 0.0208057i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.95920 8.58959i −0.406274 0.703686i 0.588195 0.808719i \(-0.299839\pi\)
−0.994469 + 0.105033i \(0.966505\pi\)
\(150\) 0 0
\(151\) −4.73704 + 8.20480i −0.385495 + 0.667697i −0.991838 0.127506i \(-0.959303\pi\)
0.606343 + 0.795203i \(0.292636\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.247481 −0.0198781
\(156\) 0 0
\(157\) 5.83745 10.1108i 0.465880 0.806927i −0.533361 0.845888i \(-0.679071\pi\)
0.999241 + 0.0389606i \(0.0124047\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 15.5456 + 2.80019i 1.22516 + 0.220686i
\(162\) 0 0
\(163\) −6.36680 11.0276i −0.498687 0.863750i 0.501312 0.865266i \(-0.332851\pi\)
−0.999999 + 0.00151597i \(0.999517\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −19.8597 −1.53679 −0.768395 0.639976i \(-0.778944\pi\)
−0.768395 + 0.639976i \(0.778944\pi\)
\(168\) 0 0
\(169\) −4.17275 −0.320981
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.55443 + 4.42440i 0.194210 + 0.336381i 0.946641 0.322290i \(-0.104452\pi\)
−0.752432 + 0.658670i \(0.771119\pi\)
\(174\) 0 0
\(175\) 4.47793 + 12.4455i 0.338499 + 0.940789i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.98470 + 15.5620i −0.671548 + 1.16315i 0.305917 + 0.952058i \(0.401037\pi\)
−0.977465 + 0.211097i \(0.932296\pi\)
\(180\) 0 0
\(181\) −3.72157 −0.276622 −0.138311 0.990389i \(-0.544167\pi\)
−0.138311 + 0.990389i \(0.544167\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.0213238 + 0.0369338i −0.00156775 + 0.00271543i
\(186\) 0 0
\(187\) 2.66430 + 4.61469i 0.194833 + 0.337460i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2.88127 + 4.99051i 0.208481 + 0.361100i 0.951236 0.308463i \(-0.0998146\pi\)
−0.742755 + 0.669563i \(0.766481\pi\)
\(192\) 0 0
\(193\) −1.80635 + 3.12870i −0.130024 + 0.225209i −0.923686 0.383151i \(-0.874839\pi\)
0.793661 + 0.608360i \(0.208172\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.44432 0.459139 0.229569 0.973292i \(-0.426268\pi\)
0.229569 + 0.973292i \(0.426268\pi\)
\(198\) 0 0
\(199\) 1.29147 2.23689i 0.0915499 0.158569i −0.816614 0.577185i \(-0.804151\pi\)
0.908163 + 0.418616i \(0.137485\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −17.0797 + 20.2032i −1.19876 + 1.41798i
\(204\) 0 0
\(205\) 0.0634655 + 0.109925i 0.00443262 + 0.00767753i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 28.6853 1.98420
\(210\) 0 0
\(211\) 19.4162 1.33667 0.668334 0.743861i \(-0.267008\pi\)
0.668334 + 0.743861i \(0.267008\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.0544280 0.0942720i −0.00371196 0.00642930i
\(216\) 0 0
\(217\) 7.66213 + 21.2953i 0.520139 + 1.44562i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.10385 + 3.64397i −0.141520 + 0.245120i
\(222\) 0 0
\(223\) 11.5074 0.770589 0.385295 0.922794i \(-0.374100\pi\)
0.385295 + 0.922794i \(0.374100\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.48595 2.57375i 0.0986261 0.170826i −0.812490 0.582975i \(-0.801889\pi\)
0.911116 + 0.412150i \(0.135222\pi\)
\(228\) 0 0
\(229\) −11.0775 19.1868i −0.732023 1.26790i −0.956017 0.293310i \(-0.905243\pi\)
0.223995 0.974590i \(-0.428090\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.0056 17.3302i −0.655489 1.13534i −0.981771 0.190068i \(-0.939129\pi\)
0.326282 0.945272i \(-0.394204\pi\)
\(234\) 0 0
\(235\) 0.0600304 0.103976i 0.00391595 0.00678263i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −23.6930 −1.53257 −0.766286 0.642500i \(-0.777897\pi\)
−0.766286 + 0.642500i \(0.777897\pi\)
\(240\) 0 0
\(241\) −5.64983 + 9.78579i −0.363938 + 0.630358i −0.988605 0.150533i \(-0.951901\pi\)
0.624668 + 0.780891i \(0.285234\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.156095 + 0.129031i −0.00997253 + 0.00824350i
\(246\) 0 0
\(247\) 11.3256 + 19.6165i 0.720630 + 1.24817i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4.76254 0.300609 0.150304 0.988640i \(-0.451975\pi\)
0.150304 + 0.988640i \(0.451975\pi\)
\(252\) 0 0
\(253\) 22.4632 1.41225
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.3230 21.3440i −0.768687 1.33140i −0.938275 0.345890i \(-0.887577\pi\)
0.169588 0.985515i \(-0.445756\pi\)
\(258\) 0 0
\(259\) 3.83829 + 0.691383i 0.238500 + 0.0429605i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 5.33787 9.24547i 0.329147 0.570100i −0.653196 0.757189i \(-0.726572\pi\)
0.982343 + 0.187089i \(0.0599054\pi\)
\(264\) 0 0
\(265\) −0.208530 −0.0128099
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.653264 + 1.13149i −0.0398302 + 0.0689880i −0.885253 0.465109i \(-0.846015\pi\)
0.845423 + 0.534097i \(0.179348\pi\)
\(270\) 0 0
\(271\) −9.83787 17.0397i −0.597608 1.03509i −0.993173 0.116650i \(-0.962785\pi\)
0.395565 0.918438i \(-0.370549\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 9.40477 + 16.2895i 0.567129 + 0.982296i
\(276\) 0 0
\(277\) −14.3774 + 24.9024i −0.863855 + 1.49624i 0.00432421 + 0.999991i \(0.498624\pi\)
−0.868179 + 0.496250i \(0.834710\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.20853 0.549335 0.274667 0.961539i \(-0.411432\pi\)
0.274667 + 0.961539i \(0.411432\pi\)
\(282\) 0 0
\(283\) −11.2613 + 19.5051i −0.669414 + 1.15946i 0.308654 + 0.951174i \(0.400121\pi\)
−0.978068 + 0.208285i \(0.933212\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7.49398 8.86445i 0.442356 0.523252i
\(288\) 0 0
\(289\) 7.49716 + 12.9855i 0.441009 + 0.763850i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3.30534 0.193100 0.0965501 0.995328i \(-0.469219\pi\)
0.0965501 + 0.995328i \(0.469219\pi\)
\(294\) 0 0
\(295\) 0.401006 0.0233475
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 8.86898 + 15.3615i 0.512907 + 0.888380i
\(300\) 0 0
\(301\) −6.42683 + 7.60215i −0.370437 + 0.438181i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.162546 + 0.281538i −0.00930737 + 0.0161208i
\(306\) 0 0
\(307\) −14.2358 −0.812479 −0.406240 0.913767i \(-0.633160\pi\)
−0.406240 + 0.913767i \(0.633160\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 14.9694 25.9278i 0.848836 1.47023i −0.0334108 0.999442i \(-0.510637\pi\)
0.882247 0.470786i \(-0.156030\pi\)
\(312\) 0 0
\(313\) −5.47107 9.47617i −0.309243 0.535625i 0.668954 0.743304i \(-0.266742\pi\)
−0.978197 + 0.207679i \(0.933409\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.27700 + 9.14004i 0.296386 + 0.513356i 0.975306 0.220856i \(-0.0708851\pi\)
−0.678920 + 0.734212i \(0.737552\pi\)
\(318\) 0 0
\(319\) −18.8111 + 32.5818i −1.05322 + 1.82423i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −10.7972 −0.600770
\(324\) 0 0
\(325\) −7.42643 + 12.8630i −0.411944 + 0.713508i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −10.8055 1.94638i −0.595727 0.107307i
\(330\) 0 0
\(331\) 15.1319 + 26.2093i 0.831727 + 1.44059i 0.896668 + 0.442704i \(0.145981\pi\)
−0.0649412 + 0.997889i \(0.520686\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.160710 0.00878053
\(336\) 0 0
\(337\) 26.8428 1.46222 0.731111 0.682259i \(-0.239002\pi\)
0.731111 + 0.682259i \(0.239002\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 16.0924 + 27.8728i 0.871452 + 1.50940i
\(342\) 0 0
\(343\) 15.9357 + 9.43682i 0.860447 + 0.509540i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.08938 15.7433i 0.487944 0.845143i −0.511960 0.859009i \(-0.671081\pi\)
0.999904 + 0.0138661i \(0.00441387\pi\)
\(348\) 0 0
\(349\) 5.15586 0.275987 0.137993 0.990433i \(-0.455935\pi\)
0.137993 + 0.990433i \(0.455935\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −14.1838 + 24.5670i −0.754926 + 1.30757i 0.190485 + 0.981690i \(0.438994\pi\)
−0.945411 + 0.325880i \(0.894339\pi\)
\(354\) 0 0
\(355\) 0.167312 + 0.289792i 0.00887998 + 0.0153806i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −12.9793 22.4808i −0.685020 1.18649i −0.973431 0.228982i \(-0.926460\pi\)
0.288411 0.957507i \(-0.406873\pi\)
\(360\) 0 0
\(361\) −19.5620 + 33.8824i −1.02958 + 1.78329i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.126094 −0.00660006
\(366\) 0 0
\(367\) 9.91062 17.1657i 0.517330 0.896042i −0.482467 0.875914i \(-0.660259\pi\)
0.999797 0.0201281i \(-0.00640740\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6.45618 + 17.9436i 0.335188 + 0.931586i
\(372\) 0 0
\(373\) −4.58294 7.93789i −0.237296 0.411008i 0.722642 0.691223i \(-0.242928\pi\)
−0.959937 + 0.280215i \(0.909594\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −29.7082 −1.53005
\(378\) 0 0
\(379\) 6.12575 0.314658 0.157329 0.987546i \(-0.449712\pi\)
0.157329 + 0.987546i \(0.449712\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.25795 7.37498i −0.217571 0.376844i 0.736494 0.676444i \(-0.236480\pi\)
−0.954065 + 0.299600i \(0.903147\pi\)
\(384\) 0 0
\(385\) −0.185938 + 0.219942i −0.00947628 + 0.0112093i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.16773 5.48667i 0.160610 0.278185i −0.774477 0.632602i \(-0.781987\pi\)
0.935088 + 0.354416i \(0.115320\pi\)
\(390\) 0 0
\(391\) −8.45517 −0.427596
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −0.203839 + 0.353059i −0.0102562 + 0.0177643i
\(396\) 0 0
\(397\) 15.6401 + 27.0895i 0.784956 + 1.35958i 0.929026 + 0.370015i \(0.120648\pi\)
−0.144070 + 0.989567i \(0.546019\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.31454 + 2.27686i 0.0656452 + 0.113701i 0.896980 0.442071i \(-0.145756\pi\)
−0.831335 + 0.555772i \(0.812423\pi\)
\(402\) 0 0
\(403\) −12.7073 + 22.0096i −0.632994 + 1.09638i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.54630 0.274920
\(408\) 0 0
\(409\) 6.89574 11.9438i 0.340972 0.590581i −0.643641 0.765327i \(-0.722577\pi\)
0.984614 + 0.174746i \(0.0559105\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −12.4154 34.5059i −0.610921 1.69793i
\(414\) 0 0
\(415\) −0.0958321 0.165986i −0.00470421 0.00814793i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.84532 0.139003 0.0695016 0.997582i \(-0.477859\pi\)
0.0695016 + 0.997582i \(0.477859\pi\)
\(420\) 0 0
\(421\) 29.4374 1.43469 0.717347 0.696716i \(-0.245356\pi\)
0.717347 + 0.696716i \(0.245356\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.53996 6.13139i −0.171713 0.297416i
\(426\) 0 0
\(427\) 29.2584 + 5.27026i 1.41592 + 0.255046i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.36096 4.08930i 0.113723 0.196975i −0.803545 0.595243i \(-0.797056\pi\)
0.917269 + 0.398269i \(0.130389\pi\)
\(432\) 0 0
\(433\) −3.83813 −0.184449 −0.0922243 0.995738i \(-0.529398\pi\)
−0.0922243 + 0.995738i \(0.529398\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −22.7583 + 39.4185i −1.08868 + 1.88564i
\(438\) 0 0
\(439\) −9.23018 15.9871i −0.440533 0.763025i 0.557196 0.830381i \(-0.311877\pi\)
−0.997729 + 0.0673558i \(0.978544\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11.3001 + 19.5723i 0.536883 + 0.929908i 0.999070 + 0.0431258i \(0.0137316\pi\)
−0.462187 + 0.886783i \(0.652935\pi\)
\(444\) 0 0
\(445\) 0.0620357 0.107449i 0.00294078 0.00509357i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 20.0043 0.944063 0.472031 0.881582i \(-0.343521\pi\)
0.472031 + 0.881582i \(0.343521\pi\)
\(450\) 0 0
\(451\) 8.25368 14.2958i 0.388650 0.673162i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.223820 0.0403163i −0.0104929 0.00189006i
\(456\) 0 0
\(457\) −13.5196 23.4167i −0.632423 1.09539i −0.987055 0.160382i \(-0.948727\pi\)
0.354632 0.935006i \(-0.384606\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −30.9557 −1.44175 −0.720875 0.693065i \(-0.756260\pi\)
−0.720875 + 0.693065i \(0.756260\pi\)
\(462\) 0 0
\(463\) 3.96105 0.184086 0.0920428 0.995755i \(-0.470660\pi\)
0.0920428 + 0.995755i \(0.470660\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13.5834 + 23.5271i 0.628563 + 1.08870i 0.987840 + 0.155472i \(0.0496899\pi\)
−0.359277 + 0.933231i \(0.616977\pi\)
\(468\) 0 0
\(469\) −4.97567 13.8288i −0.229755 0.638557i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −7.07835 + 12.2601i −0.325463 + 0.563718i
\(474\) 0 0
\(475\) −38.1132 −1.74875
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.83788 15.3077i 0.403813 0.699425i −0.590369 0.807133i \(-0.701018\pi\)
0.994183 + 0.107708i \(0.0343512\pi\)
\(480\) 0 0
\(481\) 2.18980 + 3.79285i 0.0998465 + 0.172939i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.0979995 + 0.169740i 0.00444993 + 0.00770750i
\(486\) 0 0
\(487\) 6.79665 11.7722i 0.307986 0.533447i −0.669936 0.742419i \(-0.733678\pi\)
0.977922 + 0.208972i \(0.0670117\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 21.8256 0.984974 0.492487 0.870320i \(-0.336088\pi\)
0.492487 + 0.870320i \(0.336088\pi\)
\(492\) 0 0
\(493\) 7.08052 12.2638i 0.318890 0.552334i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 19.7561 23.3690i 0.886182 1.04824i
\(498\) 0 0
\(499\) −10.6374 18.4245i −0.476194 0.824792i 0.523434 0.852066i \(-0.324651\pi\)
−0.999628 + 0.0272740i \(0.991317\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.2281 1.21404 0.607020 0.794687i \(-0.292365\pi\)
0.607020 + 0.794687i \(0.292365\pi\)
\(504\) 0 0
\(505\) −0.195162 −0.00868459
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −9.23879 16.0021i −0.409502 0.709279i 0.585332 0.810794i \(-0.300964\pi\)
−0.994834 + 0.101515i \(0.967631\pi\)
\(510\) 0 0
\(511\) 3.90394 + 10.8502i 0.172700 + 0.479984i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.0399743 + 0.0692376i −0.00176148 + 0.00305097i
\(516\) 0 0
\(517\) −15.6139 −0.686698
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.93913 5.09073i 0.128766 0.223029i −0.794433 0.607352i \(-0.792232\pi\)
0.923199 + 0.384323i \(0.125565\pi\)
\(522\) 0 0
\(523\) −6.22258 10.7778i −0.272094 0.471281i 0.697304 0.716776i \(-0.254383\pi\)
−0.969398 + 0.245495i \(0.921050\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.05719 10.4914i −0.263855 0.457011i
\(528\) 0 0
\(529\) −6.32183 + 10.9497i −0.274862 + 0.476075i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 13.0349 0.564606
\(534\) 0 0
\(535\) 0.257529 0.446054i 0.0111340 0.0192846i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 24.6824 + 9.19015i 1.06314 + 0.395848i
\(540\) 0 0
\(541\) 10.7362 + 18.5957i 0.461586 + 0.799490i 0.999040 0.0438031i \(-0.0139474\pi\)
−0.537455 + 0.843293i \(0.680614\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.313399 0.0134245
\(546\) 0 0
\(547\) 30.6741 1.31153 0.655764 0.754966i \(-0.272347\pi\)
0.655764 + 0.754966i \(0.272347\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −38.1164 66.0195i −1.62381 2.81253i
\(552\) 0 0
\(553\) 36.6911 + 6.60910i 1.56027 + 0.281047i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −20.5857 + 35.6555i −0.872244 + 1.51077i −0.0125744 + 0.999921i \(0.504003\pi\)
−0.859670 + 0.510850i \(0.829331\pi\)
\(558\) 0 0
\(559\) −11.1788 −0.472811
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.56848 + 7.91283i −0.192538 + 0.333486i −0.946091 0.323902i \(-0.895005\pi\)
0.753552 + 0.657388i \(0.228339\pi\)
\(564\) 0 0
\(565\) −0.0127169 0.0220263i −0.000535003 0.000926653i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11.7123 20.2863i −0.491004 0.850445i 0.508942 0.860801i \(-0.330037\pi\)
−0.999946 + 0.0103562i \(0.996703\pi\)
\(570\) 0 0
\(571\) −9.91580 + 17.1747i −0.414963 + 0.718738i −0.995425 0.0955501i \(-0.969539\pi\)
0.580461 + 0.814288i \(0.302872\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −29.8462 −1.24467
\(576\) 0 0
\(577\) 15.2800 26.4658i 0.636116 1.10178i −0.350162 0.936689i \(-0.613873\pi\)
0.986278 0.165095i \(-0.0527932\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −11.3158 + 13.3852i −0.469459 + 0.555312i
\(582\) 0 0
\(583\) 13.5596 + 23.4859i 0.561582 + 0.972688i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.37643 0.180635 0.0903174 0.995913i \(-0.471212\pi\)
0.0903174 + 0.995913i \(0.471212\pi\)
\(588\) 0 0
\(589\) −65.2150 −2.68714
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 22.2762 + 38.5835i 0.914773 + 1.58443i 0.807234 + 0.590232i \(0.200964\pi\)
0.107539 + 0.994201i \(0.465703\pi\)
\(594\) 0 0
\(595\) 0.0699872 0.0827862i 0.00286920 0.00339390i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 6.85577 11.8745i 0.280119 0.485181i −0.691295 0.722573i \(-0.742959\pi\)
0.971414 + 0.237392i \(0.0762926\pi\)
\(600\) 0 0
\(601\) −2.21373 −0.0902997 −0.0451499 0.998980i \(-0.514377\pi\)
−0.0451499 + 0.998980i \(0.514377\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.0456641 + 0.0790925i −0.00185651 + 0.00321557i
\(606\) 0 0
\(607\) 1.58980 + 2.75361i 0.0645280 + 0.111766i 0.896484 0.443075i \(-0.146113\pi\)
−0.831957 + 0.554841i \(0.812779\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.16471 10.6776i −0.249398 0.431969i
\(612\) 0 0
\(613\) −6.15827 + 10.6664i −0.248730 + 0.430814i −0.963174 0.268880i \(-0.913347\pi\)
0.714443 + 0.699693i \(0.246680\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 45.9405 1.84949 0.924747 0.380583i \(-0.124277\pi\)
0.924747 + 0.380583i \(0.124277\pi\)
\(618\) 0 0
\(619\) 6.79648 11.7718i 0.273174 0.473151i −0.696499 0.717558i \(-0.745260\pi\)
0.969673 + 0.244407i \(0.0785933\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −11.1665 2.01139i −0.447375 0.0805848i
\(624\) 0 0
\(625\) −12.4937 21.6398i −0.499749 0.865590i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.08763 −0.0832393
\(630\) 0 0
\(631\) 0.682615 0.0271745 0.0135872 0.999908i \(-0.495675\pi\)
0.0135872 + 0.999908i \(0.495675\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.0183941 + 0.0318596i 0.000729949 + 0.00126431i
\(636\) 0 0
\(637\) 3.46044 + 20.5076i 0.137108 + 0.812540i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −23.7325 + 41.1059i −0.937378 + 1.62359i −0.167042 + 0.985950i \(0.553421\pi\)
−0.770337 + 0.637637i \(0.779912\pi\)
\(642\) 0 0
\(643\) 34.4928 1.36026 0.680132 0.733090i \(-0.261923\pi\)
0.680132 + 0.733090i \(0.261923\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.6587 21.9255i 0.497665 0.861980i −0.502332 0.864675i \(-0.667524\pi\)
0.999996 + 0.00269463i \(0.000857729\pi\)
\(648\) 0 0
\(649\) −26.0754 45.1639i −1.02355 1.77284i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.19122 + 7.25941i 0.164015 + 0.284083i 0.936305 0.351188i \(-0.114222\pi\)
−0.772290 + 0.635270i \(0.780889\pi\)
\(654\) 0 0
\(655\) −0.240710 + 0.416922i −0.00940531 + 0.0162905i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −19.4114 −0.756160 −0.378080 0.925773i \(-0.623416\pi\)
−0.378080 + 0.925773i \(0.623416\pi\)
\(660\) 0 0
\(661\) 5.39833 9.35019i 0.209971 0.363680i −0.741734 0.670694i \(-0.765996\pi\)
0.951705 + 0.307014i \(0.0993298\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.197574 0.549115i −0.00766158 0.0212938i
\(666\) 0 0
\(667\) −29.8487 51.6994i −1.15574 2.00181i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 42.2782 1.63213
\(672\) 0 0
\(673\) −5.07074 −0.195463 −0.0977314 0.995213i \(-0.531159\pi\)
−0.0977314 + 0.995213i \(0.531159\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.2737 + 31.6511i 0.702317 + 1.21645i 0.967651 + 0.252292i \(0.0811844\pi\)
−0.265334 + 0.964157i \(0.585482\pi\)
\(678\) 0 0
\(679\) 11.5717 13.6879i 0.444082 0.525295i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5.34590 9.25937i 0.204555 0.354300i −0.745436 0.666577i \(-0.767759\pi\)
0.949991 + 0.312278i \(0.101092\pi\)
\(684\) 0 0
\(685\) −0.141484 −0.00540583
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −10.7073 + 18.5455i −0.407915 + 0.706529i
\(690\) 0 0
\(691\) −11.4686 19.8643i −0.436288 0.755673i 0.561112 0.827740i \(-0.310374\pi\)
−0.997400 + 0.0720673i \(0.977040\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.124577 + 0.215774i 0.00472549 + 0.00818478i
\(696\) 0 0
\(697\) −3.10669 + 5.38094i −0.117674 + 0.203818i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −47.9789 −1.81214 −0.906069 0.423129i \(-0.860932\pi\)
−0.906069 + 0.423129i \(0.860932\pi\)
\(702\) 0 0
\(703\) −5.61915 + 9.73265i −0.211930 + 0.367074i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.04232 + 16.7934i 0.227245 + 0.631579i
\(708\) 0 0
\(709\) −10.3095 17.8566i −0.387183 0.670620i 0.604887 0.796312i \(-0.293218\pi\)
−0.992069 + 0.125692i \(0.959885\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −51.0694 −1.91256
\(714\) 0 0
\(715\) −0.323419 −0.0120952
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.59498 4.49464i −0.0967765 0.167622i 0.813572 0.581464i \(-0.197520\pi\)
−0.910349 + 0.413842i \(0.864187\pi\)
\(720\) 0 0
\(721\) 7.19541 + 1.29609i 0.267971 + 0.0482690i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 24.9937 43.2904i 0.928244 1.60776i
\(726\) 0 0
\(727\) −39.9339 −1.48107 −0.740534 0.672019i \(-0.765427\pi\)
−0.740534 + 0.672019i \(0.765427\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.66430 4.61469i 0.0985425 0.170681i
\(732\) 0 0
\(733\) −24.6661 42.7229i −0.911062 1.57800i −0.812567 0.582867i \(-0.801931\pi\)
−0.0984942 0.995138i \(-0.531403\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −10.4502 18.1002i −0.384937 0.666730i
\(738\) 0 0
\(739\) −16.5576 + 28.6786i −0.609081 + 1.05496i 0.382311 + 0.924034i \(0.375128\pi\)
−0.991392 + 0.130926i \(0.958205\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 23.4157 0.859040 0.429520 0.903057i \(-0.358683\pi\)
0.429520 + 0.903057i \(0.358683\pi\)
\(744\) 0 0
\(745\) −0.143477 + 0.248510i −0.00525660 + 0.00910470i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −46.3554 8.34991i −1.69379 0.305099i
\(750\) 0 0
\(751\) −9.41364 16.3049i −0.343508 0.594974i 0.641573 0.767062i \(-0.278282\pi\)
−0.985082 + 0.172088i \(0.944949\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.274100 0.00997551
\(756\) 0 0
\(757\) 27.0156 0.981897 0.490949 0.871188i \(-0.336650\pi\)
0.490949 + 0.871188i \(0.336650\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9.64356 + 16.7031i 0.349579 + 0.605488i 0.986175 0.165709i \(-0.0529913\pi\)
−0.636596 + 0.771198i \(0.719658\pi\)
\(762\) 0 0
\(763\) −9.70300 26.9675i −0.351272 0.976288i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 20.5903 35.6635i 0.743473 1.28773i
\(768\) 0 0
\(769\) −3.26639 −0.117789 −0.0588946 0.998264i \(-0.518758\pi\)
−0.0588946 + 0.998264i \(0.518758\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 10.9963 19.0462i 0.395510 0.685044i −0.597656 0.801753i \(-0.703901\pi\)
0.993166 + 0.116709i \(0.0372345\pi\)
\(774\) 0 0
\(775\) −21.3814 37.0337i −0.768044 1.33029i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 16.7242 + 28.9671i 0.599205 + 1.03785i
\(780\) 0 0
\(781\) 21.7589 37.6875i 0.778593 1.34856i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.337773 −0.0120556
\(786\) 0 0
\(787\) −4.64724 + 8.04926i −0.165656 + 0.286925i −0.936888 0.349629i \(-0.886308\pi\)
0.771232 + 0.636554i \(0.219641\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.50160 + 1.77621i −0.0533909 + 0.0631548i
\(792\) 0 0
\(793\) 16.6924 + 28.9121i 0.592764 + 1.02670i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 28.4137 1.00647 0.503233 0.864151i \(-0.332144\pi\)
0.503233 + 0.864151i \(0.332144\pi\)
\(798\) 0 0
\(799\) 5.87708 0.207916
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 8.19925 + 14.2015i 0.289345 + 0.501161i
\(804\) 0 0
\(805\) −0.154718 0.430008i −0.00545311 0.0151558i