Properties

Label 1512.2.s.o.1297.2
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 1297.2
Root \(1.89574 - 2.48951i\) of defining polynomial
Character \(\chi\) \(=\) 1512.1297
Dual form 1512.2.s.o.865.2

$q$-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 −0.862773 0.505592i \(-0.831274\pi\)
0.869242 + 0.494387i \(0.164607\pi\)
\(6\) 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 \(0.0253160\pi\)
−0.429615 + 0.903012i \(0.641351\pi\)
\(12\) 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 \(-0.221606\pi\)
−0.939029 + 0.343838i \(0.888273\pi\)
\(18\) 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 \(-0.619475\pi\)
0.989030 0.147715i \(-0.0471917\pi\)
\(24\) 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 \(-0.878814\pi\)
−0.928399 + 0.371585i \(0.878814\pi\)
\(30\) 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 \(-0.388696\pi\)
0.342590 + 0.939485i \(0.388696\pi\)
\(42\) 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 \(-0.931207\pi\)
0.674080 + 0.738659i \(0.264540\pi\)
\(48\) 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 \(-0.331508\pi\)
−0.999984 + 0.00573358i \(0.998175\pi\)
\(54\) 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 \(0.191415\pi\)
0.0776699 + 0.996979i \(0.475252\pi\)
\(60\) 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 \(-0.259225\pi\)
0.686319 + 0.727301i \(0.259225\pi\)
\(72\) 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 \(-0.618446\pi\)
−0.363580 + 0.931563i \(0.618446\pi\)
\(84\) 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 \(-0.906319\pi\)
0.729716 + 0.683751i \(0.239652\pi\)
\(90\) 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 \(-0.275609\pi\)
−0.983602 + 0.180355i \(0.942275\pi\)
\(102\) 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 \(0.496531\pi\)
−0.871423 + 0.490532i \(0.836802\pi\)
\(108\) 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 \(-0.513166\pi\)
−0.0413495 + 0.999145i \(0.513166\pi\)
\(114\) 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 \(-0.574284\pi\)
0.958179 0.286171i \(-0.0923824\pi\)
\(132\) 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 \(-0.233656\pi\)
−0.951369 + 0.308052i \(0.900323\pi\)
\(138\) 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 \(-0.700161\pi\)
0.994469 + 0.105033i \(0.0334947\pi\)
\(150\) 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 \(-0.221056\pi\)
0.768395 + 0.639976i \(0.221056\pi\)
\(168\) 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 \(-0.895548\pi\)
0.752432 + 0.658670i \(0.228881\pi\)
\(174\) 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 \(0.0677035\pi\)
−0.305917 + 0.952058i \(0.598963\pi\)
\(180\) 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 \(-0.900185\pi\)
0.742755 + 0.669563i \(0.233519\pi\)
\(192\) 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 \(-0.573732\pi\)
−0.229569 + 0.973292i \(0.573732\pi\)
\(198\) 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 0.812490 0.582975i \(-0.198111\pi\)
−0.911116 + 0.412150i \(0.864778\pi\)
\(228\) 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 \(-0.605796\pi\)
0.981771 0.190068i \(-0.0608707\pi\)
\(234\) 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 \(-0.222103\pi\)
0.766286 + 0.642500i \(0.222103\pi\)
\(240\) 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 \(-0.548025\pi\)
−0.150304 + 0.988640i \(0.548025\pi\)
\(252\) 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 \(-0.554244\pi\)
0.938275 0.345890i \(-0.112423\pi\)
\(258\) 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 \(-0.273428\pi\)
−0.982343 + 0.187089i \(0.940095\pi\)
\(264\) 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 \(-0.153985\pi\)
−0.845423 + 0.534097i \(0.820652\pi\)
\(270\) 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 \(-0.588568\pi\)
−0.274667 + 0.961539i \(0.588568\pi\)
\(282\) 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 \(-0.530781\pi\)
−0.0965501 + 0.995328i \(0.530781\pi\)
\(294\) 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 \(-0.843970\pi\)
0.0334108 0.999442i \(-0.489363\pi\)
\(312\) 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 −0.975306 0.220856i \(-0.929115\pi\)
0.678920 + 0.734212i \(0.262448\pi\)
\(318\) 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 0.511960 0.859009i \(-0.328919\pi\)
−0.999904 + 0.0138661i \(0.995586\pi\)
\(348\) 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 \(0.105661\pi\)
−0.190485 + 0.981690i \(0.561006\pi\)
\(354\) 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 \(-0.593127\pi\)
0.973431 0.228982i \(-0.0735397\pi\)
\(360\) 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 −0.736494 0.676444i \(-0.763520\pi\)
0.954065 + 0.299600i \(0.0968533\pi\)
\(384\) 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 \(-0.218013\pi\)
−0.935088 + 0.354416i \(0.884680\pi\)
\(390\) 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 −0.896980 0.442071i \(-0.854244\pi\)
0.831335 + 0.555772i \(0.187577\pi\)
\(402\) 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 \(-0.522141\pi\)
−0.0695016 + 0.997582i \(0.522141\pi\)
\(420\) 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 \(-0.202944\pi\)
−0.917269 + 0.398269i \(0.869611\pi\)
\(432\) 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 \(0.347065\pi\)
−0.999070 + 0.0431258i \(0.986268\pi\)
\(444\) 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 \(-0.656479\pi\)
−0.472031 + 0.881582i \(0.656479\pi\)
\(450\) 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 \(-0.243740\pi\)
0.720875 + 0.693065i \(0.243740\pi\)
\(462\) 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 \(0.383023\pi\)
−0.987840 + 0.155472i \(0.950310\pi\)
\(468\) 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 \(-0.298982\pi\)
−0.994183 + 0.107708i \(0.965649\pi\)
\(480\) 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 \(-0.663912\pi\)
−0.492487 + 0.870320i \(0.663912\pi\)
\(492\) 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 \(-0.707635\pi\)
−0.607020 + 0.794687i \(0.707635\pi\)
\(504\) 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 \(-0.699036\pi\)
0.994834 + 0.101515i \(0.0323691\pi\)
\(510\) 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 \(-0.207768\pi\)
−0.923199 + 0.384323i \(0.874435\pi\)
\(522\) 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 \(0.170669\pi\)
0.0125744 + 0.999921i \(0.495997\pi\)
\(558\) 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 \(-0.104995\pi\)
−0.753552 + 0.657388i \(0.771661\pi\)
\(564\) 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 \(-0.669963\pi\)
0.999946 + 0.0103562i \(0.00329653\pi\)
\(570\) 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 \(-0.528788\pi\)
−0.0903174 + 0.995913i \(0.528788\pi\)
\(588\) 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 \(0.534297\pi\)
−0.807234 + 0.590232i \(0.799036\pi\)
\(594\) 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 \(-0.257041\pi\)
−0.971414 + 0.237392i \(0.923707\pi\)
\(600\) 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 \(-0.875723\pi\)
−0.924747 + 0.380583i \(0.875723\pi\)
\(618\) 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 \(0.220088\pi\)
0.167042 + 0.985950i \(0.446579\pi\)
\(642\) 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 \(-0.332476\pi\)
−0.999996 + 0.00269463i \(0.999142\pi\)
\(648\) 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 \(-0.885778\pi\)
0.772290 + 0.635270i \(0.219111\pi\)
\(654\) 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 \(-0.376584\pi\)
0.378080 + 0.925773i \(0.376584\pi\)
\(660\) 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 \(0.414518\pi\)
−0.967651 + 0.252292i \(0.918816\pi\)
\(678\) 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 \(-0.232241\pi\)
−0.949991 + 0.312278i \(0.898908\pi\)
\(684\) 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 \(-0.139068\pi\)
0.906069 + 0.423129i \(0.139068\pi\)
\(702\) 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 −0.813572 0.581464i \(-0.802480\pi\)
0.910349 + 0.413842i \(0.135813\pi\)
\(720\) 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 \(-0.641317\pi\)
−0.429520 + 0.903057i \(0.641317\pi\)
\(744\) 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 −0.986175 0.165709i \(-0.947009\pi\)
0.636596 + 0.771198i \(0.280342\pi\)
\(762\) 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 \(-0.296099\pi\)
−0.993166 + 0.116709i \(0.962766\pi\)
\(774\) 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 \(-0.667856\pi\)
−0.503233 + 0.864151i \(0.667856\pi\)
\(798\) 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