Properties

Label 2268.2.t.b.2105.8
Level $2268$
Weight $2$
Character 2268.2105
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 2105.8
Root \(-0.213160 - 1.71888i\) of defining polynomial
Character \(\chi\) \(=\) 2268.2105
Dual form 2268.2.t.b.1781.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.43402 - 2.48379i) q^{5} +(-0.736590 + 2.54115i) q^{7} +O(q^{10})\) \(q+(1.43402 - 2.48379i) q^{5} +(-0.736590 + 2.54115i) q^{7} +(2.34941 - 1.35643i) q^{11} +3.68335i q^{13} +(3.22192 + 5.58052i) q^{17} +(2.73867 + 1.58117i) q^{19} +(-2.59068 - 1.49573i) q^{23} +(-1.61282 - 2.79348i) q^{25} -2.86749i q^{29} +(-8.26739 + 4.77318i) q^{31} +(5.25540 + 5.47359i) q^{35} +(-1.70640 + 2.95556i) q^{37} +1.58908 q^{41} +9.35656 q^{43} +(-5.65372 + 9.79254i) q^{47} +(-5.91487 - 3.74357i) q^{49} +(2.16419 - 1.24950i) q^{53} -7.78058i q^{55} +(4.33680 + 7.51156i) q^{59} +(0.566915 + 0.327308i) q^{61} +(9.14867 + 5.28199i) q^{65} +(-3.86146 - 6.68825i) q^{67} +7.86582i q^{71} +(11.0769 - 6.39527i) q^{73} +(1.71634 + 6.96932i) q^{77} +(-2.59566 + 4.49581i) q^{79} +15.8590 q^{83} +18.4811 q^{85} +(3.14826 - 5.45295i) q^{89} +(-9.35993 - 2.71312i) q^{91} +(7.85460 - 4.53486i) q^{95} -15.2495i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{7} + O(q^{10}) \) \( 16 q + 2 q^{7} + 6 q^{11} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{31} - 15 q^{35} + q^{37} + 12 q^{41} + 4 q^{43} + 18 q^{47} - 8 q^{49} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - 48 q^{77} - q^{79} - 12 q^{85} + 21 q^{89} + 9 q^{91} + 6 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.43402 2.48379i 0.641312 1.11079i −0.343828 0.939033i \(-0.611724\pi\)
0.985140 0.171753i \(-0.0549431\pi\)
\(6\) 0 0
\(7\) −0.736590 + 2.54115i −0.278405 + 0.960464i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.34941 1.35643i 0.708373 0.408979i −0.102086 0.994776i \(-0.532552\pi\)
0.810458 + 0.585797i \(0.199218\pi\)
\(12\) 0 0
\(13\) 3.68335i 1.02158i 0.859706 + 0.510789i \(0.170646\pi\)
−0.859706 + 0.510789i \(0.829354\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.22192 + 5.58052i 0.781429 + 1.35348i 0.931109 + 0.364741i \(0.118842\pi\)
−0.149680 + 0.988735i \(0.547824\pi\)
\(18\) 0 0
\(19\) 2.73867 + 1.58117i 0.628294 + 0.362746i 0.780091 0.625666i \(-0.215173\pi\)
−0.151797 + 0.988412i \(0.548506\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.59068 1.49573i −0.540195 0.311882i 0.204963 0.978770i \(-0.434293\pi\)
−0.745158 + 0.666888i \(0.767626\pi\)
\(24\) 0 0
\(25\) −1.61282 2.79348i −0.322563 0.558696i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.86749i 0.532480i −0.963907 0.266240i \(-0.914219\pi\)
0.963907 0.266240i \(-0.0857814\pi\)
\(30\) 0 0
\(31\) −8.26739 + 4.77318i −1.48487 + 0.857289i −0.999852 0.0172169i \(-0.994519\pi\)
−0.485016 + 0.874506i \(0.661186\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 5.25540 + 5.47359i 0.888325 + 0.925205i
\(36\) 0 0
\(37\) −1.70640 + 2.95556i −0.280530 + 0.485892i −0.971515 0.236977i \(-0.923843\pi\)
0.690986 + 0.722868i \(0.257177\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.58908 0.248172 0.124086 0.992271i \(-0.460400\pi\)
0.124086 + 0.992271i \(0.460400\pi\)
\(42\) 0 0
\(43\) 9.35656 1.42686 0.713431 0.700726i \(-0.247140\pi\)
0.713431 + 0.700726i \(0.247140\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.65372 + 9.79254i −0.824680 + 1.42839i 0.0774831 + 0.996994i \(0.475312\pi\)
−0.902163 + 0.431394i \(0.858022\pi\)
\(48\) 0 0
\(49\) −5.91487 3.74357i −0.844981 0.534796i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.16419 1.24950i 0.297275 0.171632i −0.343943 0.938990i \(-0.611763\pi\)
0.641218 + 0.767359i \(0.278429\pi\)
\(54\) 0 0
\(55\) 7.78058i 1.04913i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.33680 + 7.51156i 0.564604 + 0.977922i 0.997086 + 0.0762801i \(0.0243043\pi\)
−0.432483 + 0.901642i \(0.642362\pi\)
\(60\) 0 0
\(61\) 0.566915 + 0.327308i 0.0725860 + 0.0419075i 0.535854 0.844311i \(-0.319990\pi\)
−0.463268 + 0.886218i \(0.653323\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 9.14867 + 5.28199i 1.13475 + 0.655150i
\(66\) 0 0
\(67\) −3.86146 6.68825i −0.471752 0.817099i 0.527725 0.849415i \(-0.323045\pi\)
−0.999478 + 0.0323159i \(0.989712\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.86582i 0.933501i 0.884389 + 0.466750i \(0.154575\pi\)
−0.884389 + 0.466750i \(0.845425\pi\)
\(72\) 0 0
\(73\) 11.0769 6.39527i 1.29646 0.748510i 0.316667 0.948537i \(-0.397436\pi\)
0.979790 + 0.200027i \(0.0641028\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.71634 + 6.96932i 0.195595 + 0.794228i
\(78\) 0 0
\(79\) −2.59566 + 4.49581i −0.292034 + 0.505819i −0.974291 0.225295i \(-0.927666\pi\)
0.682256 + 0.731113i \(0.260999\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 15.8590 1.74075 0.870373 0.492393i \(-0.163878\pi\)
0.870373 + 0.492393i \(0.163878\pi\)
\(84\) 0 0
\(85\) 18.4811 2.00456
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.14826 5.45295i 0.333715 0.578012i −0.649522 0.760343i \(-0.725031\pi\)
0.983237 + 0.182331i \(0.0583643\pi\)
\(90\) 0 0
\(91\) −9.35993 2.71312i −0.981188 0.284412i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 7.85460 4.53486i 0.805865 0.465267i
\(96\) 0 0
\(97\) 15.2495i 1.54836i −0.632968 0.774178i \(-0.718163\pi\)
0.632968 0.774178i \(-0.281837\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.74451 3.02158i −0.173585 0.300658i 0.766086 0.642739i \(-0.222202\pi\)
−0.939671 + 0.342080i \(0.888869\pi\)
\(102\) 0 0
\(103\) 2.89161 + 1.66947i 0.284919 + 0.164498i 0.635648 0.771979i \(-0.280733\pi\)
−0.350729 + 0.936477i \(0.614066\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.10776 1.79427i −0.300439 0.173458i 0.342201 0.939627i \(-0.388828\pi\)
−0.642640 + 0.766168i \(0.722161\pi\)
\(108\) 0 0
\(109\) 6.89673 + 11.9455i 0.660587 + 1.14417i 0.980462 + 0.196710i \(0.0630258\pi\)
−0.319875 + 0.947460i \(0.603641\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.10383i 0.574200i 0.957901 + 0.287100i \(0.0926911\pi\)
−0.957901 + 0.287100i \(0.907309\pi\)
\(114\) 0 0
\(115\) −7.43018 + 4.28981i −0.692867 + 0.400027i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −16.5542 + 4.07681i −1.51752 + 0.373720i
\(120\) 0 0
\(121\) −1.82019 + 3.15267i −0.165472 + 0.286606i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 5.08895 0.455170
\(126\) 0 0
\(127\) −13.3819 −1.18745 −0.593727 0.804666i \(-0.702344\pi\)
−0.593727 + 0.804666i \(0.702344\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −0.388964 + 0.673705i −0.0339839 + 0.0588619i −0.882517 0.470280i \(-0.844153\pi\)
0.848533 + 0.529142i \(0.177486\pi\)
\(132\) 0 0
\(133\) −6.03527 + 5.79469i −0.523324 + 0.502463i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.3082 8.26083i 1.22243 0.705771i 0.256995 0.966413i \(-0.417268\pi\)
0.965435 + 0.260642i \(0.0839343\pi\)
\(138\) 0 0
\(139\) 11.4526i 0.971399i −0.874126 0.485699i \(-0.838565\pi\)
0.874126 0.485699i \(-0.161435\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.99620 + 8.65368i 0.417804 + 0.723657i
\(144\) 0 0
\(145\) −7.12226 4.11204i −0.591472 0.341486i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.24781 + 2.45247i 0.347994 + 0.200914i 0.663801 0.747909i \(-0.268942\pi\)
−0.315807 + 0.948823i \(0.602275\pi\)
\(150\) 0 0
\(151\) −4.92814 8.53579i −0.401047 0.694633i 0.592806 0.805345i \(-0.298020\pi\)
−0.993852 + 0.110712i \(0.964687\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 27.3793i 2.19916i
\(156\) 0 0
\(157\) 13.3514 7.70843i 1.06556 0.615200i 0.138593 0.990349i \(-0.455742\pi\)
0.926964 + 0.375149i \(0.122409\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.70915 5.48157i 0.449944 0.432008i
\(162\) 0 0
\(163\) −5.72053 + 9.90825i −0.448066 + 0.776074i −0.998260 0.0589632i \(-0.981221\pi\)
0.550194 + 0.835037i \(0.314554\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.9821 1.00458 0.502291 0.864699i \(-0.332491\pi\)
0.502291 + 0.864699i \(0.332491\pi\)
\(168\) 0 0
\(169\) −0.567055 −0.0436196
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 9.79984 16.9738i 0.745068 1.29050i −0.205095 0.978742i \(-0.565750\pi\)
0.950163 0.311754i \(-0.100916\pi\)
\(174\) 0 0
\(175\) 8.28663 2.04075i 0.626410 0.154267i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −16.2630 + 9.38942i −1.21555 + 0.701799i −0.963963 0.266036i \(-0.914286\pi\)
−0.251588 + 0.967835i \(0.580953\pi\)
\(180\) 0 0
\(181\) 4.47775i 0.332829i 0.986056 + 0.166414i \(0.0532190\pi\)
−0.986056 + 0.166414i \(0.946781\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.89400 + 8.47666i 0.359814 + 0.623217i
\(186\) 0 0
\(187\) 15.1392 + 8.74061i 1.10709 + 0.639177i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.90050 3.40665i −0.426945 0.246497i 0.271099 0.962551i \(-0.412613\pi\)
−0.698044 + 0.716055i \(0.745946\pi\)
\(192\) 0 0
\(193\) 7.97694 + 13.8165i 0.574193 + 0.994531i 0.996129 + 0.0879053i \(0.0280173\pi\)
−0.421936 + 0.906626i \(0.638649\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 25.9511i 1.84894i −0.381254 0.924470i \(-0.624508\pi\)
0.381254 0.924470i \(-0.375492\pi\)
\(198\) 0 0
\(199\) 2.75706 1.59179i 0.195443 0.112839i −0.399085 0.916914i \(-0.630672\pi\)
0.594528 + 0.804075i \(0.297339\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 7.28673 + 2.11217i 0.511428 + 0.148245i
\(204\) 0 0
\(205\) 2.27876 3.94693i 0.159156 0.275666i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 8.57900 0.593422
\(210\) 0 0
\(211\) 0.110482 0.00760591 0.00380295 0.999993i \(-0.498789\pi\)
0.00380295 + 0.999993i \(0.498789\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 13.4175 23.2397i 0.915064 1.58494i
\(216\) 0 0
\(217\) −6.03968 24.5245i −0.410000 1.66483i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −20.5550 + 11.8674i −1.38268 + 0.798290i
\(222\) 0 0
\(223\) 13.0555i 0.874261i 0.899398 + 0.437130i \(0.144005\pi\)
−0.899398 + 0.437130i \(0.855995\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.63392 + 8.02618i 0.307564 + 0.532716i 0.977829 0.209406i \(-0.0671529\pi\)
−0.670265 + 0.742122i \(0.733820\pi\)
\(228\) 0 0
\(229\) −11.6204 6.70902i −0.767895 0.443344i 0.0642281 0.997935i \(-0.479541\pi\)
−0.832123 + 0.554591i \(0.812875\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.3415 10.5895i −1.20159 0.693738i −0.240681 0.970604i \(-0.577371\pi\)
−0.960909 + 0.276866i \(0.910704\pi\)
\(234\) 0 0
\(235\) 16.2151 + 28.0853i 1.05776 + 1.83209i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.92978i 0.577620i 0.957386 + 0.288810i \(0.0932595\pi\)
−0.957386 + 0.288810i \(0.906740\pi\)
\(240\) 0 0
\(241\) −15.9430 + 9.20469i −1.02698 + 0.592926i −0.916117 0.400910i \(-0.868694\pi\)
−0.110860 + 0.993836i \(0.535361\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −17.7803 + 9.32296i −1.13594 + 0.595622i
\(246\) 0 0
\(247\) −5.82401 + 10.0875i −0.370573 + 0.641851i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −6.33194 −0.399669 −0.199834 0.979830i \(-0.564040\pi\)
−0.199834 + 0.979830i \(0.564040\pi\)
\(252\) 0 0
\(253\) −8.11542 −0.510212
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.19283 14.1904i 0.511054 0.885172i −0.488863 0.872360i \(-0.662588\pi\)
0.999918 0.0128120i \(-0.00407829\pi\)
\(258\) 0 0
\(259\) −6.25361 6.51324i −0.388580 0.404713i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 10.4663 6.04270i 0.645377 0.372609i −0.141306 0.989966i \(-0.545130\pi\)
0.786683 + 0.617357i \(0.211797\pi\)
\(264\) 0 0
\(265\) 7.16721i 0.440278i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.6652 + 21.9368i 0.772212 + 1.33751i 0.936348 + 0.351072i \(0.114183\pi\)
−0.164136 + 0.986438i \(0.552484\pi\)
\(270\) 0 0
\(271\) −0.195591 0.112924i −0.0118813 0.00685967i 0.494048 0.869435i \(-0.335517\pi\)
−0.505929 + 0.862575i \(0.668850\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7.57832 4.37534i −0.456990 0.263843i
\(276\) 0 0
\(277\) 10.2170 + 17.6963i 0.613878 + 1.06327i 0.990580 + 0.136934i \(0.0437248\pi\)
−0.376702 + 0.926335i \(0.622942\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 10.3534i 0.617635i 0.951121 + 0.308817i \(0.0999332\pi\)
−0.951121 + 0.308817i \(0.900067\pi\)
\(282\) 0 0
\(283\) −11.8781 + 6.85783i −0.706080 + 0.407656i −0.809608 0.586971i \(-0.800320\pi\)
0.103528 + 0.994627i \(0.466987\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.17050 + 4.03808i −0.0690923 + 0.238360i
\(288\) 0 0
\(289\) −12.2615 + 21.2375i −0.721264 + 1.24927i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −8.43053 −0.492517 −0.246258 0.969204i \(-0.579201\pi\)
−0.246258 + 0.969204i \(0.579201\pi\)
\(294\) 0 0
\(295\) 24.8762 1.44835
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.50930 9.54239i 0.318611 0.551851i
\(300\) 0 0
\(301\) −6.89195 + 23.7764i −0.397245 + 1.37045i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.62593 0.938732i 0.0931006 0.0537516i
\(306\) 0 0
\(307\) 5.34345i 0.304967i −0.988306 0.152484i \(-0.951273\pi\)
0.988306 0.152484i \(-0.0487271\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.70867 + 8.15565i 0.267004 + 0.462465i 0.968087 0.250615i \(-0.0806329\pi\)
−0.701083 + 0.713080i \(0.747300\pi\)
\(312\) 0 0
\(313\) −14.3347 8.27614i −0.810245 0.467795i 0.0367961 0.999323i \(-0.488285\pi\)
−0.847041 + 0.531528i \(0.821618\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −22.9725 13.2632i −1.29026 0.744934i −0.311563 0.950225i \(-0.600853\pi\)
−0.978701 + 0.205291i \(0.934186\pi\)
\(318\) 0 0
\(319\) −3.88956 6.73691i −0.217773 0.377194i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 20.3776i 1.13384i
\(324\) 0 0
\(325\) 10.2894 5.94056i 0.570751 0.329523i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −20.7198 21.5800i −1.14232 1.18975i
\(330\) 0 0
\(331\) 8.82000 15.2767i 0.484791 0.839682i −0.515056 0.857156i \(-0.672229\pi\)
0.999847 + 0.0174739i \(0.00556238\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −22.1496 −1.21016
\(336\) 0 0
\(337\) −14.6234 −0.796586 −0.398293 0.917258i \(-0.630397\pi\)
−0.398293 + 0.917258i \(0.630397\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −12.9490 + 22.4283i −0.701226 + 1.21456i
\(342\) 0 0
\(343\) 13.8698 12.2731i 0.748899 0.662684i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.05563 0.609467i 0.0566691 0.0327179i −0.471398 0.881921i \(-0.656250\pi\)
0.528067 + 0.849203i \(0.322917\pi\)
\(348\) 0 0
\(349\) 12.3388i 0.660483i −0.943897 0.330241i \(-0.892870\pi\)
0.943897 0.330241i \(-0.107130\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −11.1484 19.3097i −0.593372 1.02775i −0.993774 0.111411i \(-0.964463\pi\)
0.400402 0.916339i \(-0.368870\pi\)
\(354\) 0 0
\(355\) 19.5371 + 11.2797i 1.03692 + 0.598666i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.4819 + 6.05173i 0.553214 + 0.319398i 0.750417 0.660965i \(-0.229853\pi\)
−0.197204 + 0.980363i \(0.563186\pi\)
\(360\) 0 0
\(361\) −4.49979 7.79387i −0.236831 0.410204i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 36.6838i 1.92012i
\(366\) 0 0
\(367\) −12.7544 + 7.36375i −0.665774 + 0.384385i −0.794473 0.607299i \(-0.792253\pi\)
0.128700 + 0.991684i \(0.458920\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.58103 + 6.41990i 0.0820832 + 0.333305i
\(372\) 0 0
\(373\) 4.54279 7.86834i 0.235217 0.407407i −0.724119 0.689675i \(-0.757753\pi\)
0.959336 + 0.282268i \(0.0910867\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10.5620 0.543970
\(378\) 0 0
\(379\) 21.2298 1.09050 0.545250 0.838273i \(-0.316435\pi\)
0.545250 + 0.838273i \(0.316435\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.35227 5.80630i 0.171293 0.296688i −0.767579 0.640954i \(-0.778539\pi\)
0.938872 + 0.344266i \(0.111872\pi\)
\(384\) 0 0
\(385\) 19.7716 + 5.73110i 1.00765 + 0.292084i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.66661 3.84897i 0.338011 0.195151i −0.321381 0.946950i \(-0.604147\pi\)
0.659392 + 0.751799i \(0.270814\pi\)
\(390\) 0 0
\(391\) 19.2765i 0.974854i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.44444 + 12.8942i 0.374571 + 0.648775i
\(396\) 0 0
\(397\) −0.0428112 0.0247170i −0.00214863 0.00124051i 0.498925 0.866645i \(-0.333728\pi\)
−0.501074 + 0.865404i \(0.667062\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −17.6039 10.1636i −0.879096 0.507546i −0.00873572 0.999962i \(-0.502781\pi\)
−0.870360 + 0.492416i \(0.836114\pi\)
\(402\) 0 0
\(403\) −17.5813 30.4517i −0.875786 1.51691i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.25842i 0.458923i
\(408\) 0 0
\(409\) −12.1144 + 6.99428i −0.599021 + 0.345845i −0.768656 0.639662i \(-0.779074\pi\)
0.169636 + 0.985507i \(0.445741\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −22.2824 + 5.48752i −1.09645 + 0.270023i
\(414\) 0 0
\(415\) 22.7420 39.3903i 1.11636 1.93360i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −21.3437 −1.04271 −0.521353 0.853341i \(-0.674573\pi\)
−0.521353 + 0.853341i \(0.674573\pi\)
\(420\) 0 0
\(421\) −7.94574 −0.387252 −0.193626 0.981075i \(-0.562025\pi\)
−0.193626 + 0.981075i \(0.562025\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 10.3927 18.0007i 0.504121 0.873163i
\(426\) 0 0
\(427\) −1.24932 + 1.19952i −0.0604590 + 0.0580489i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −27.6515 + 15.9646i −1.33193 + 0.768989i −0.985595 0.169123i \(-0.945907\pi\)
−0.346333 + 0.938112i \(0.612573\pi\)
\(432\) 0 0
\(433\) 18.5300i 0.890493i 0.895408 + 0.445247i \(0.146884\pi\)
−0.895408 + 0.445247i \(0.853116\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.73002 8.19263i −0.226267 0.391907i
\(438\) 0 0
\(439\) −1.80316 1.04106i −0.0860603 0.0496869i 0.456352 0.889799i \(-0.349156\pi\)
−0.542413 + 0.840112i \(0.682489\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.13895 + 1.23493i 0.101625 + 0.0586731i 0.549951 0.835197i \(-0.314646\pi\)
−0.448326 + 0.893870i \(0.647980\pi\)
\(444\) 0 0
\(445\) −9.02933 15.6393i −0.428031 0.741372i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 37.5094i 1.77018i −0.465424 0.885088i \(-0.654098\pi\)
0.465424 0.885088i \(-0.345902\pi\)
\(450\) 0 0
\(451\) 3.73338 2.15547i 0.175798 0.101497i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −20.1611 + 19.3575i −0.945169 + 0.907492i
\(456\) 0 0
\(457\) −2.92345 + 5.06356i −0.136753 + 0.236864i −0.926266 0.376871i \(-0.877000\pi\)
0.789513 + 0.613734i \(0.210333\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.65659 −0.356603 −0.178302 0.983976i \(-0.557060\pi\)
−0.178302 + 0.983976i \(0.557060\pi\)
\(462\) 0 0
\(463\) −9.78899 −0.454933 −0.227466 0.973786i \(-0.573044\pi\)
−0.227466 + 0.973786i \(0.573044\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 14.0806 24.3883i 0.651572 1.12856i −0.331169 0.943571i \(-0.607443\pi\)
0.982741 0.184985i \(-0.0592235\pi\)
\(468\) 0 0
\(469\) 19.8401 4.88605i 0.916132 0.225617i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 21.9824 12.6915i 1.01075 0.583557i
\(474\) 0 0
\(475\) 10.2006i 0.468033i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −14.8053 25.6435i −0.676470 1.17168i −0.976037 0.217605i \(-0.930175\pi\)
0.299567 0.954075i \(-0.403158\pi\)
\(480\) 0 0
\(481\) −10.8864 6.28525i −0.496376 0.286583i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −37.8767 21.8681i −1.71989 0.992980i
\(486\) 0 0
\(487\) −14.6701 25.4094i −0.664767 1.15141i −0.979348 0.202180i \(-0.935198\pi\)
0.314582 0.949230i \(-0.398136\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 9.97367i 0.450105i 0.974347 + 0.225053i \(0.0722554\pi\)
−0.974347 + 0.225053i \(0.927745\pi\)
\(492\) 0 0
\(493\) 16.0021 9.23883i 0.720699 0.416096i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −19.9882 5.79388i −0.896594 0.259891i
\(498\) 0 0
\(499\) 9.79784 16.9704i 0.438611 0.759697i −0.558971 0.829187i \(-0.688804\pi\)
0.997583 + 0.0694898i \(0.0221371\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 21.2907 0.949304 0.474652 0.880174i \(-0.342574\pi\)
0.474652 + 0.880174i \(0.342574\pi\)
\(504\) 0 0
\(505\) −10.0066 −0.445289
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 21.8307 37.8119i 0.967630 1.67598i 0.265252 0.964179i \(-0.414545\pi\)
0.702378 0.711804i \(-0.252122\pi\)
\(510\) 0 0
\(511\) 8.09217 + 32.8588i 0.357977 + 1.45359i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8.29324 4.78810i 0.365444 0.210989i
\(516\) 0 0
\(517\) 30.6755i 1.34911i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.60043 + 4.50408i 0.113927 + 0.197327i 0.917350 0.398081i \(-0.130324\pi\)
−0.803423 + 0.595408i \(0.796990\pi\)
\(522\) 0 0
\(523\) −34.7043 20.0365i −1.51751 0.876137i −0.999788 0.0205902i \(-0.993445\pi\)
−0.517726 0.855547i \(-0.673221\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −53.2737 30.7576i −2.32064 1.33982i
\(528\) 0 0
\(529\) −7.02557 12.1686i −0.305460 0.529072i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.85312i 0.253527i
\(534\) 0 0
\(535\) −8.91317 + 5.14602i −0.385350 + 0.222482i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −18.9743 0.772057i −0.817282 0.0332549i
\(540\) 0 0
\(541\) −4.12096 + 7.13771i −0.177174 + 0.306874i −0.940911 0.338653i \(-0.890029\pi\)
0.763738 + 0.645527i \(0.223362\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 39.5601 1.69457
\(546\) 0 0
\(547\) 5.07512 0.216997 0.108498 0.994097i \(-0.465396\pi\)
0.108498 + 0.994097i \(0.465396\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.53400 7.85312i 0.193155 0.334554i
\(552\) 0 0
\(553\) −9.51259 9.90753i −0.404517 0.421311i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 37.6102 21.7142i 1.59359 0.920062i 0.600910 0.799316i \(-0.294805\pi\)
0.992684 0.120745i \(-0.0385285\pi\)
\(558\) 0 0
\(559\) 34.4635i 1.45765i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.99118 + 8.64498i 0.210353 + 0.364343i 0.951825 0.306641i \(-0.0992052\pi\)
−0.741472 + 0.670984i \(0.765872\pi\)
\(564\) 0 0
\(565\) 15.1606 + 8.75300i 0.637813 + 0.368241i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −14.0597 8.11739i −0.589415 0.340299i 0.175451 0.984488i \(-0.443862\pi\)
−0.764866 + 0.644189i \(0.777195\pi\)
\(570\) 0 0
\(571\) 6.31028 + 10.9297i 0.264077 + 0.457395i 0.967321 0.253553i \(-0.0815994\pi\)
−0.703244 + 0.710948i \(0.748266\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.64936i 0.402406i
\(576\) 0 0
\(577\) −4.18012 + 2.41339i −0.174020 + 0.100471i −0.584480 0.811408i \(-0.698702\pi\)
0.410460 + 0.911879i \(0.365368\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −11.6815 + 40.2999i −0.484632 + 1.67192i
\(582\) 0 0
\(583\) 3.38971 5.87115i 0.140387 0.243158i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.5206 −0.434233 −0.217117 0.976146i \(-0.569665\pi\)
−0.217117 + 0.976146i \(0.569665\pi\)
\(588\) 0 0
\(589\) −30.1889 −1.24391
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.7342 25.5205i 0.605063 1.04800i −0.386979 0.922089i \(-0.626481\pi\)
0.992042 0.125911i \(-0.0401853\pi\)
\(594\) 0 0
\(595\) −13.6130 + 46.9633i −0.558080 + 1.92531i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.11658 + 4.10876i −0.290776 + 0.167879i −0.638292 0.769795i \(-0.720359\pi\)
0.347516 + 0.937674i \(0.387025\pi\)
\(600\) 0 0
\(601\) 37.7738i 1.54083i 0.637545 + 0.770413i \(0.279950\pi\)
−0.637545 + 0.770413i \(0.720050\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.22038 + 9.04197i 0.212239 + 0.367608i
\(606\) 0 0
\(607\) 30.8497 + 17.8111i 1.25215 + 0.722929i 0.971536 0.236892i \(-0.0761289\pi\)
0.280613 + 0.959821i \(0.409462\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −36.0693 20.8246i −1.45921 0.842474i
\(612\) 0 0
\(613\) 11.9660 + 20.7256i 0.483301 + 0.837101i 0.999816 0.0191767i \(-0.00610451\pi\)
−0.516516 + 0.856278i \(0.672771\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.29349i 0.0923325i 0.998934 + 0.0461663i \(0.0147004\pi\)
−0.998934 + 0.0461663i \(0.985300\pi\)
\(618\) 0 0
\(619\) 9.10806 5.25854i 0.366084 0.211359i −0.305662 0.952140i \(-0.598878\pi\)
0.671746 + 0.740781i \(0.265545\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.5378 + 12.0168i 0.462251 + 0.481443i
\(624\) 0 0
\(625\) 15.3617 26.6073i 0.614469 1.06429i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −21.9914 −0.876856
\(630\) 0 0
\(631\) −2.02836 −0.0807477 −0.0403739 0.999185i \(-0.512855\pi\)
−0.0403739 + 0.999185i \(0.512855\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −19.1899 + 33.2380i −0.761530 + 1.31901i
\(636\) 0 0
\(637\) 13.7889 21.7865i 0.546335 0.863214i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −10.7778 + 6.22257i −0.425698 + 0.245777i −0.697512 0.716573i \(-0.745710\pi\)
0.271814 + 0.962350i \(0.412376\pi\)
\(642\) 0 0
\(643\) 14.2442i 0.561735i 0.959746 + 0.280868i \(0.0906222\pi\)
−0.959746 + 0.280868i \(0.909378\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.1910 17.6513i −0.400649 0.693945i 0.593155 0.805088i \(-0.297882\pi\)
−0.993804 + 0.111143i \(0.964549\pi\)
\(648\) 0 0
\(649\) 20.3778 + 11.7651i 0.799899 + 0.461822i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.55335 4.36093i −0.295585 0.170656i 0.344873 0.938650i \(-0.387922\pi\)
−0.640458 + 0.767993i \(0.721255\pi\)
\(654\) 0 0
\(655\) 1.11556 + 1.93221i 0.0435887 + 0.0754978i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 19.3440i 0.753535i −0.926308 0.376768i \(-0.877036\pi\)
0.926308 0.376768i \(-0.122964\pi\)
\(660\) 0 0
\(661\) 31.8948 18.4145i 1.24056 0.716240i 0.271355 0.962479i \(-0.412528\pi\)
0.969209 + 0.246239i \(0.0791949\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.73812 + 23.3000i 0.222515 + 0.903537i
\(666\) 0 0
\(667\) −4.28900 + 7.42877i −0.166071 + 0.287643i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.77588 0.0685572
\(672\) 0 0
\(673\) −17.5841 −0.677816 −0.338908 0.940819i \(-0.610058\pi\)
−0.338908 + 0.940819i \(0.610058\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −20.4146 + 35.3590i −0.784595 + 1.35896i 0.144646 + 0.989484i \(0.453796\pi\)
−0.929241 + 0.369475i \(0.879538\pi\)
\(678\) 0 0
\(679\) 38.7514 + 11.2327i 1.48714 + 0.431070i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8.56287 + 4.94377i −0.327649 + 0.189168i −0.654797 0.755805i \(-0.727246\pi\)
0.327148 + 0.944973i \(0.393912\pi\)
\(684\) 0 0
\(685\) 47.3847i 1.81048i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4.60233 + 7.97148i 0.175335 + 0.303689i
\(690\) 0 0
\(691\) −37.9217 21.8941i −1.44261 0.832891i −0.444587 0.895736i \(-0.646649\pi\)
−0.998023 + 0.0628444i \(0.979983\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −28.4459 16.4233i −1.07902 0.622970i
\(696\) 0 0
\(697\) 5.11987 + 8.86787i 0.193929 + 0.335894i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 29.6742i 1.12078i 0.828229 + 0.560389i \(0.189349\pi\)
−0.828229 + 0.560389i \(0.810651\pi\)
\(702\) 0 0
\(703\) −9.34651 + 5.39621i −0.352510 + 0.203522i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.96327 2.20739i 0.337099 0.0830175i
\(708\) 0 0
\(709\) −23.5269 + 40.7498i −0.883572 + 1.53039i −0.0362296 + 0.999343i \(0.511535\pi\)
−0.847342 + 0.531048i \(0.821799\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 28.5576 1.06949
\(714\) 0 0
\(715\) 28.6586 1.07177
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.909148 1.57469i 0.0339055 0.0587261i −0.848575 0.529076i \(-0.822539\pi\)
0.882480 + 0.470349i \(0.155872\pi\)
\(720\) 0 0
\(721\) −6.37230 + 6.11829i −0.237317 + 0.227857i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8.01029 + 4.62474i −0.297495 + 0.171759i
\(726\) 0 0
\(727\) 25.1556i 0.932970i 0.884529 + 0.466485i \(0.154480\pi\)
−0.884529 + 0.466485i \(0.845520\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 30.1460 + 52.2145i 1.11499 + 1.93122i
\(732\) 0 0
\(733\) 3.84543 + 2.22016i 0.142034 + 0.0820034i 0.569333 0.822107i \(-0.307201\pi\)
−0.427299 + 0.904110i \(0.640535\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −18.1443 10.4756i −0.668353 0.385874i
\(738\) 0 0
\(739\) −8.97608 15.5470i −0.330191 0.571907i 0.652358 0.757911i \(-0.273780\pi\)
−0.982549 + 0.186004i \(0.940446\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 36.2244i 1.32894i 0.747313 + 0.664472i \(0.231343\pi\)
−0.747313 + 0.664472i \(0.768657\pi\)
\(744\) 0 0
\(745\) 12.1829 7.03378i 0.446345 0.257698i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.84864 6.57564i 0.250244 0.240269i
\(750\) 0 0
\(751\) −5.98210 + 10.3613i −0.218290 + 0.378089i −0.954285 0.298897i \(-0.903381\pi\)
0.735995 + 0.676986i \(0.236714\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −28.2682 −1.02878
\(756\) 0 0
\(757\) −49.4440 −1.79707 −0.898537 0.438898i \(-0.855369\pi\)
−0.898537 + 0.438898i \(0.855369\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 14.6192 25.3212i 0.529945 0.917892i −0.469445 0.882962i \(-0.655546\pi\)
0.999390 0.0349300i \(-0.0111208\pi\)
\(762\) 0 0
\(763\) −35.4353 + 8.72668i −1.28284 + 0.315927i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −27.6677 + 15.9740i −0.999023 + 0.576786i
\(768\) 0 0
\(769\) 5.25030i 0.189331i 0.995509 + 0.0946653i \(0.0301781\pi\)
−0.995509 + 0.0946653i \(0.969822\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −15.6829 27.1635i −0.564073 0.977003i −0.997135 0.0756393i \(-0.975900\pi\)
0.433062 0.901364i \(-0.357433\pi\)
\(774\) 0 0
\(775\) 26.6676 + 15.3965i 0.957927 + 0.553059i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.35195 + 2.51260i 0.155925 + 0.0900233i
\(780\) 0 0
\(781\) 10.6694 + 18.4800i 0.381782 + 0.661266i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 44.2161i 1.57814i
\(786\) 0 0
\(787\) 1.59324 0.919855i 0.0567927 0.0327893i −0.471335 0.881954i \(-0.656228\pi\)
0.528128 + 0.849165i \(0.322894\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −15.5107 4.49602i −0.551498 0.159860i
\(792\) 0 0
\(793\) −1.20559 + 2.08814i −0.0428118 + 0.0741522i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.7932 0.453158 0.226579 0.973993i \(-0.427246\pi\)
0.226579 + 0.973993i \(0.427246\pi\)
\(798\) 0 0
\(799\) −72.8633 −2.57772
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 17.3495 30.0502i 0.612250 1.06045i