Properties

Label 1512.2.s.n.1297.3
Level $1512$
Weight $2$
Character 1512.1297
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 1297.3
Root \(1.89574 - 2.48951i\) of defining polynomial
Character \(\chi\) \(=\) 1512.1297
Dual form 1512.2.s.n.865.3

$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

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

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 −0.869242 0.494387i \(-0.835393\pi\)
0.862773 + 0.505592i \(0.168726\pi\)
\(6\) 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 −0.996839 0.0794487i \(-0.974684\pi\)
0.429615 0.903012i \(-0.358649\pi\)
\(12\) 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 0.939029 0.343838i \(-0.111727\pi\)
−0.767287 + 0.641304i \(0.778394\pi\)
\(18\) 0 0
\(19\) −3.81196 + 6.60250i −0.874523 + 1.51472i −0.0172529 + 0.999851i \(0.505492\pi\)
−0.857270 + 0.514867i \(0.827841\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.98512 + 5.17037i −0.622440 + 1.07810i 0.366590 + 0.930382i \(0.380525\pi\)
−0.989030 + 0.147715i \(0.952808\pi\)
\(24\) 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 0.938553 + 0.345136i \(0.112167\pi\)
−0.170380 + 0.985378i \(0.554500\pi\)
\(32\) 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 −0.920229 0.391380i \(-0.871998\pi\)
0.799060 + 0.601251i \(0.205331\pi\)
\(38\) 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 −0.674080 0.738659i \(-0.735460\pi\)
0.976737 + 0.214441i \(0.0687929\pi\)
\(48\) 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 0.999984 0.00573358i \(-0.00182507\pi\)
−0.504957 + 0.863144i \(0.668492\pi\)
\(54\) 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 −0.824574 0.565754i \(-0.808585\pi\)
−0.0776699 0.996979i \(-0.524748\pi\)
\(60\) 0 0
\(61\) −5.61831 + 9.73120i −0.719351 + 1.24595i 0.241906 + 0.970300i \(0.422227\pi\)
−0.961257 + 0.275653i \(0.911106\pi\)
\(62\) 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 0.644988 0.764193i \(-0.276862\pi\)
−0.984304 + 0.176480i \(0.943529\pi\)
\(68\) 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 0.964910 0.262580i \(-0.0845735\pi\)
−0.709856 + 0.704346i \(0.751240\pi\)
\(74\) 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 0.131609 + 0.991302i \(0.457986\pi\)
−0.924297 + 0.381674i \(0.875348\pi\)
\(80\) 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 −0.729716 0.683751i \(-0.760348\pi\)
0.957003 + 0.290077i \(0.0936809\pi\)
\(90\) 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 0.983602 0.180355i \(-0.0577247\pi\)
−0.647993 + 0.761646i \(0.724391\pi\)
\(102\) 0 0
\(103\) −1.38169 + 2.39315i −0.136142 + 0.235804i −0.926033 0.377442i \(-0.876804\pi\)
0.789891 + 0.613247i \(0.210137\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.90134 15.4176i 0.860525 1.49047i −0.0108984 0.999941i \(-0.503469\pi\)
0.871423 0.490532i \(-0.163198\pi\)
\(108\) 0 0
\(109\) −5.41622 9.38117i −0.518780 0.898553i −0.999762 0.0218227i \(-0.993053\pi\)
0.480982 0.876731i \(-0.340280\pi\)
\(110\) 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 0.231258 + 0.972892i \(0.425716\pi\)
−0.958179 + 0.286171i \(0.907618\pi\)
\(132\) 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 0.951369 0.308052i \(-0.0996772\pi\)
−0.742466 + 0.669884i \(0.766344\pi\)
\(138\) 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 −0.994469 0.105033i \(-0.966505\pi\)
0.588195 + 0.808719i \(0.299839\pi\)
\(150\) 0 0
\(151\) −4.73704 8.20480i −0.385495 0.667697i 0.606343 0.795203i \(-0.292636\pi\)
−0.991838 + 0.127506i \(0.959303\pi\)
\(152\) 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 0.999241 0.0389606i \(-0.0124047\pi\)
−0.533361 + 0.845888i \(0.679071\pi\)
\(158\) 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 −0.999999 0.00151597i \(-0.999517\pi\)
0.501312 + 0.865266i \(0.332851\pi\)
\(164\) 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 −0.752432 0.658670i \(-0.771119\pi\)
0.946641 + 0.322290i \(0.104452\pi\)
\(174\) 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 −0.977465 0.211097i \(-0.932296\pi\)
0.305917 0.952058i \(-0.401037\pi\)
\(180\) 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 −0.742755 0.669563i \(-0.766481\pi\)
0.951236 + 0.308463i \(0.0998146\pi\)
\(192\) 0 0
\(193\) −1.80635 3.12870i −0.130024 0.225209i 0.793661 0.608360i \(-0.208172\pi\)
−0.923686 + 0.383151i \(0.874839\pi\)
\(194\) 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 0.908163 0.418616i \(-0.137485\pi\)
−0.816614 + 0.577185i \(0.804151\pi\)
\(200\) 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 0.911116 0.412150i \(-0.135222\pi\)
−0.812490 + 0.582975i \(0.801889\pi\)
\(228\) 0 0
\(229\) −11.0775 + 19.1868i −0.732023 + 1.26790i 0.223995 + 0.974590i \(0.428090\pi\)
−0.956017 + 0.293310i \(0.905243\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.0056 + 17.3302i −0.655489 + 1.13534i 0.326282 + 0.945272i \(0.394204\pi\)
−0.981771 + 0.190068i \(0.939129\pi\)
\(234\) 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 0.624668 0.780891i \(-0.285234\pi\)
−0.988605 + 0.150533i \(0.951901\pi\)
\(242\) 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 0.169588 + 0.985515i \(0.445756\pi\)
−0.938275 + 0.345890i \(0.887577\pi\)
\(258\) 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 0.982343 0.187089i \(-0.0599054\pi\)
−0.653196 + 0.757189i \(0.726572\pi\)
\(264\) 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 0.845423 0.534097i \(-0.179348\pi\)
−0.885253 + 0.465109i \(0.846015\pi\)
\(270\) 0 0
\(271\) −9.83787 + 17.0397i −0.597608 + 1.03509i 0.395565 + 0.918438i \(0.370549\pi\)
−0.993173 + 0.116650i \(0.962785\pi\)
\(272\) 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 −0.868179 0.496250i \(-0.834710\pi\)
0.00432421 0.999991i \(-0.498624\pi\)
\(278\) 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 −0.978068 0.208285i \(-0.933212\pi\)
0.308654 0.951174i \(-0.400121\pi\)
\(284\) 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 0.882247 + 0.470786i \(0.156030\pi\)
−0.0334108 + 0.999442i \(0.510637\pi\)
\(312\) 0 0
\(313\) −5.47107 + 9.47617i −0.309243 + 0.535625i −0.978197 0.207679i \(-0.933409\pi\)
0.668954 + 0.743304i \(0.266742\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.27700 9.14004i 0.296386 0.513356i −0.678920 0.734212i \(-0.737552\pi\)
0.975306 + 0.220856i \(0.0708851\pi\)
\(318\) 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 −0.0649412 0.997889i \(-0.520686\pi\)
0.896668 0.442704i \(-0.145981\pi\)
\(332\) 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 0.999904 0.0138661i \(-0.00441387\pi\)
−0.511960 + 0.859009i \(0.671081\pi\)
\(348\) 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 −0.945411 0.325880i \(-0.894339\pi\)
0.190485 0.981690i \(-0.438994\pi\)
\(354\) 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 0.288411 + 0.957507i \(0.406873\pi\)
−0.973431 + 0.228982i \(0.926460\pi\)
\(360\) 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 0.999797 + 0.0201281i \(0.00640740\pi\)
−0.482467 + 0.875914i \(0.660259\pi\)
\(368\) 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 −0.959937 0.280215i \(-0.909594\pi\)
0.722642 + 0.691223i \(0.242928\pi\)
\(374\) 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 −0.954065 0.299600i \(-0.903147\pi\)
0.736494 + 0.676444i \(0.236480\pi\)
\(384\) 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 0.935088 0.354416i \(-0.115320\pi\)
−0.774477 + 0.632602i \(0.781987\pi\)
\(390\) 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 −0.144070 0.989567i \(-0.546019\pi\)
0.929026 0.370015i \(-0.120648\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.31454 2.27686i 0.0656452 0.113701i −0.831335 0.555772i \(-0.812423\pi\)
0.896980 + 0.442071i \(0.145756\pi\)
\(402\) 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 0.984614 0.174746i \(-0.0559105\pi\)
−0.643641 + 0.765327i \(0.722577\pi\)
\(410\) 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 0.917269 0.398269i \(-0.130389\pi\)
−0.803545 + 0.595243i \(0.797056\pi\)
\(432\) 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 −0.997729 0.0673558i \(-0.978544\pi\)
0.557196 + 0.830381i \(0.311877\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11.3001 19.5723i 0.536883 0.929908i −0.462187 0.886783i \(-0.652935\pi\)
0.999070 0.0431258i \(-0.0137316\pi\)
\(444\) 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 0.354632 + 0.935006i \(0.384606\pi\)
−0.987055 + 0.160382i \(0.948727\pi\)
\(458\) 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 −0.359277 0.933231i \(-0.616977\pi\)
0.987840 0.155472i \(-0.0496899\pi\)
\(468\) 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 0.994183 0.107708i \(-0.0343512\pi\)
−0.590369 + 0.807133i \(0.701018\pi\)
\(480\) 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 0.977922 0.208972i \(-0.0670117\pi\)
−0.669936 + 0.742419i \(0.733678\pi\)
\(488\) 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 −0.999628 0.0272740i \(-0.991317\pi\)
0.523434 + 0.852066i \(0.324651\pi\)
\(500\) 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 −0.994834 0.101515i \(-0.967631\pi\)
0.585332 + 0.810794i \(0.300964\pi\)
\(510\) 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 0.923199 0.384323i \(-0.125565\pi\)
−0.794433 + 0.607352i \(0.792232\pi\)
\(522\) 0 0
\(523\) −6.22258 + 10.7778i −0.272094 + 0.471281i −0.969398 0.245495i \(-0.921050\pi\)
0.697304 + 0.716776i \(0.254383\pi\)
\(524\) 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 −0.537455 0.843293i \(-0.680614\pi\)
0.999040 + 0.0438031i \(0.0139474\pi\)
\(542\) 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 −0.859670 0.510850i \(-0.829331\pi\)
−0.0125744 0.999921i \(-0.504003\pi\)
\(558\) 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 0.753552 0.657388i \(-0.228339\pi\)
−0.946091 + 0.323902i \(0.895005\pi\)
\(564\) 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 −0.999946 0.0103562i \(-0.996703\pi\)
0.508942 + 0.860801i \(0.330037\pi\)
\(570\) 0 0
\(571\) −9.91580 17.1747i −0.414963 0.718738i 0.580461 0.814288i \(-0.302872\pi\)
−0.995425 + 0.0955501i \(0.969539\pi\)
\(572\) 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 0.986278 + 0.165095i \(0.0527932\pi\)
−0.350162 + 0.936689i \(0.613873\pi\)
\(578\) 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 0.107539 0.994201i \(-0.465703\pi\)
0.807234 0.590232i \(-0.200964\pi\)
\(594\) 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 0.971414 0.237392i \(-0.0762926\pi\)
−0.691295 + 0.722573i \(0.742959\pi\)
\(600\) 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 −0.831957 0.554841i \(-0.812779\pi\)
0.896484 + 0.443075i \(0.146113\pi\)
\(608\) 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 0.714443 0.699693i \(-0.246680\pi\)
−0.963174 + 0.268880i \(0.913347\pi\)
\(614\) 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 0.969673 0.244407i \(-0.0785933\pi\)
−0.696499 + 0.717558i \(0.745260\pi\)
\(620\) 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 −0.770337 0.637637i \(-0.779912\pi\)
−0.167042 0.985950i \(-0.553421\pi\)
\(642\) 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 0.999996 0.00269463i \(-0.000857729\pi\)
−0.502332 + 0.864675i \(0.667524\pi\)
\(648\) 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 −0.772290 0.635270i \(-0.780889\pi\)
0.936305 + 0.351188i \(0.114222\pi\)
\(654\) 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 0.951705 0.307014i \(-0.0993298\pi\)
−0.741734 + 0.670694i \(0.765996\pi\)
\(662\) 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 −0.265334 0.964157i \(-0.585482\pi\)
0.967651 0.252292i \(-0.0811844\pi\)
\(678\) 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 0.949991 0.312278i \(-0.101092\pi\)
−0.745436 + 0.666577i \(0.767759\pi\)
\(684\) 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 −0.997400 0.0720673i \(-0.977040\pi\)
0.561112 + 0.827740i \(0.310374\pi\)
\(692\) 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 −0.992069 0.125692i \(-0.959885\pi\)
0.604887 + 0.796312i \(0.293218\pi\)
\(710\) 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 −0.910349 0.413842i \(-0.864187\pi\)
0.813572 + 0.581464i \(0.197520\pi\)
\(720\) 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 −0.0984942 + 0.995138i \(0.531403\pi\)
−0.812567 + 0.582867i \(0.801931\pi\)
\(734\) 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 −0.991392 0.130926i \(-0.958205\pi\)
0.382311 0.924034i \(-0.375128\pi\)
\(740\) 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 −0.985082 0.172088i \(-0.944949\pi\)
0.641573 + 0.767062i \(0.278282\pi\)
\(752\) 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 −0.636596 0.771198i \(-0.719658\pi\)
0.986175 + 0.165709i \(0.0529913\pi\)
\(762\) 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 0.993166 0.116709i \(-0.0372345\pi\)
−0.597656 + 0.801753i \(0.703901\pi\)
\(774\) 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 0.771232 0.636554i \(-0.219641\pi\)
−0.936888 + 0.349629i \(0.886308\pi\)
\(788\) 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