Properties

Label 1764.2.e.j.1079.13
Level $1764$
Weight $2$
Character 1764.1079
Analytic conductor $14.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 8 x^{14} + 49 x^{12} - 104 x^{10} + 160 x^{8} - 104 x^{6} + 49 x^{4} - 8 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1079.13
Root \(-0.367543 + 0.212201i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1079
Dual form 1764.2.e.j.1079.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.39033 - 0.258819i) q^{2} +(1.86603 - 0.719687i) q^{4} -0.732051i q^{5} +(2.40812 - 1.48356i) q^{8} +O(q^{10})\) \(q+(1.39033 - 0.258819i) q^{2} +(1.86603 - 0.719687i) q^{4} -0.732051i q^{5} +(2.40812 - 1.48356i) q^{8} +(-0.189469 - 1.01779i) q^{10} +2.03558 q^{11} +1.41421 q^{13} +(2.96410 - 2.68591i) q^{16} +4.19615i q^{17} +5.56131i q^{19} +(-0.526847 - 1.36603i) q^{20} +(2.83013 - 0.526847i) q^{22} +2.03558 q^{23} +4.46410 q^{25} +(1.96622 - 0.366025i) q^{26} -5.27792i q^{29} -9.63248i q^{31} +(3.42591 - 4.50146i) q^{32} +(1.08604 + 5.83403i) q^{34} +3.46410 q^{37} +(1.43937 + 7.73205i) q^{38} +(-1.08604 - 1.76287i) q^{40} -8.73205i q^{41} +7.86488i q^{43} +(3.79845 - 1.46498i) q^{44} +(2.83013 - 0.526847i) q^{46} -10.7436 q^{47} +(6.20657 - 1.15539i) q^{50} +(2.63896 - 1.01779i) q^{52} -9.14162i q^{53} -1.49015i q^{55} +(-1.36603 - 7.33804i) q^{58} +4.98614 q^{59} -9.41902 q^{61} +(-2.49307 - 13.3923i) q^{62} +(3.59808 - 7.14520i) q^{64} -1.03528i q^{65} +2.87875i q^{67} +(3.01992 + 7.83013i) q^{68} -9.08704 q^{71} +1.69161 q^{73} +(4.81624 - 0.896575i) q^{74} +(4.00240 + 10.3776i) q^{76} +4.98614i q^{79} +(-1.96622 - 2.16987i) q^{80} +(-2.26002 - 12.1404i) q^{82} +13.6224 q^{83} +3.07180 q^{85} +(2.03558 + 10.9348i) q^{86} +(4.90192 - 3.01992i) q^{88} +8.73205i q^{89} +(3.79845 - 1.46498i) q^{92} +(-14.9372 + 2.78066i) q^{94} +4.07116 q^{95} +15.0759 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{4} + O(q^{10}) \) \( 16 q + 16 q^{4} - 8 q^{16} - 24 q^{22} + 16 q^{25} - 24 q^{46} - 8 q^{58} + 16 q^{64} + 160 q^{85} + 120 q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39033 0.258819i 0.983111 0.183013i
\(3\) 0 0
\(4\) 1.86603 0.719687i 0.933013 0.359843i
\(5\) 0.732051i 0.327383i −0.986512 0.163692i \(-0.947660\pi\)
0.986512 0.163692i \(-0.0523402\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.40812 1.48356i 0.851399 0.524519i
\(9\) 0 0
\(10\) −0.189469 1.01779i −0.0599153 0.321854i
\(11\) 2.03558 0.613751 0.306876 0.951750i \(-0.400716\pi\)
0.306876 + 0.951750i \(0.400716\pi\)
\(12\) 0 0
\(13\) 1.41421 0.392232 0.196116 0.980581i \(-0.437167\pi\)
0.196116 + 0.980581i \(0.437167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.96410 2.68591i 0.741025 0.671477i
\(17\) 4.19615i 1.01772i 0.860850 + 0.508858i \(0.169932\pi\)
−0.860850 + 0.508858i \(0.830068\pi\)
\(18\) 0 0
\(19\) 5.56131i 1.27585i 0.770097 + 0.637926i \(0.220208\pi\)
−0.770097 + 0.637926i \(0.779792\pi\)
\(20\) −0.526847 1.36603i −0.117807 0.305453i
\(21\) 0 0
\(22\) 2.83013 0.526847i 0.603385 0.112324i
\(23\) 2.03558 0.424448 0.212224 0.977221i \(-0.431929\pi\)
0.212224 + 0.977221i \(0.431929\pi\)
\(24\) 0 0
\(25\) 4.46410 0.892820
\(26\) 1.96622 0.366025i 0.385608 0.0717835i
\(27\) 0 0
\(28\) 0 0
\(29\) 5.27792i 0.980085i −0.871699 0.490042i \(-0.836981\pi\)
0.871699 0.490042i \(-0.163019\pi\)
\(30\) 0 0
\(31\) 9.63248i 1.73004i −0.501734 0.865022i \(-0.667304\pi\)
0.501734 0.865022i \(-0.332696\pi\)
\(32\) 3.42591 4.50146i 0.605621 0.795753i
\(33\) 0 0
\(34\) 1.08604 + 5.83403i 0.186255 + 1.00053i
\(35\) 0 0
\(36\) 0 0
\(37\) 3.46410 0.569495 0.284747 0.958603i \(-0.408090\pi\)
0.284747 + 0.958603i \(0.408090\pi\)
\(38\) 1.43937 + 7.73205i 0.233497 + 1.25430i
\(39\) 0 0
\(40\) −1.08604 1.76287i −0.171719 0.278734i
\(41\) 8.73205i 1.36372i −0.731484 0.681859i \(-0.761172\pi\)
0.731484 0.681859i \(-0.238828\pi\)
\(42\) 0 0
\(43\) 7.86488i 1.19938i 0.800231 + 0.599692i \(0.204710\pi\)
−0.800231 + 0.599692i \(0.795290\pi\)
\(44\) 3.79845 1.46498i 0.572638 0.220854i
\(45\) 0 0
\(46\) 2.83013 0.526847i 0.417279 0.0776794i
\(47\) −10.7436 −1.56712 −0.783560 0.621316i \(-0.786598\pi\)
−0.783560 + 0.621316i \(0.786598\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 6.20657 1.15539i 0.877741 0.163397i
\(51\) 0 0
\(52\) 2.63896 1.01779i 0.365958 0.141142i
\(53\) 9.14162i 1.25570i −0.778335 0.627849i \(-0.783936\pi\)
0.778335 0.627849i \(-0.216064\pi\)
\(54\) 0 0
\(55\) 1.49015i 0.200932i
\(56\) 0 0
\(57\) 0 0
\(58\) −1.36603 7.33804i −0.179368 0.963531i
\(59\) 4.98614 0.649140 0.324570 0.945862i \(-0.394780\pi\)
0.324570 + 0.945862i \(0.394780\pi\)
\(60\) 0 0
\(61\) −9.41902 −1.20598 −0.602991 0.797748i \(-0.706025\pi\)
−0.602991 + 0.797748i \(0.706025\pi\)
\(62\) −2.49307 13.3923i −0.316620 1.70082i
\(63\) 0 0
\(64\) 3.59808 7.14520i 0.449760 0.893150i
\(65\) 1.03528i 0.128410i
\(66\) 0 0
\(67\) 2.87875i 0.351695i 0.984417 + 0.175847i \(0.0562666\pi\)
−0.984417 + 0.175847i \(0.943733\pi\)
\(68\) 3.01992 + 7.83013i 0.366219 + 0.949542i
\(69\) 0 0
\(70\) 0 0
\(71\) −9.08704 −1.07843 −0.539217 0.842167i \(-0.681280\pi\)
−0.539217 + 0.842167i \(0.681280\pi\)
\(72\) 0 0
\(73\) 1.69161 0.197989 0.0989943 0.995088i \(-0.468437\pi\)
0.0989943 + 0.995088i \(0.468437\pi\)
\(74\) 4.81624 0.896575i 0.559876 0.104225i
\(75\) 0 0
\(76\) 4.00240 + 10.3776i 0.459107 + 1.19039i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.98614i 0.560984i 0.959856 + 0.280492i \(0.0904977\pi\)
−0.959856 + 0.280492i \(0.909502\pi\)
\(80\) −1.96622 2.16987i −0.219830 0.242599i
\(81\) 0 0
\(82\) −2.26002 12.1404i −0.249578 1.34068i
\(83\) 13.6224 1.49525 0.747625 0.664121i \(-0.231194\pi\)
0.747625 + 0.664121i \(0.231194\pi\)
\(84\) 0 0
\(85\) 3.07180 0.333183
\(86\) 2.03558 + 10.9348i 0.219502 + 1.17913i
\(87\) 0 0
\(88\) 4.90192 3.01992i 0.522547 0.321924i
\(89\) 8.73205i 0.925596i 0.886464 + 0.462798i \(0.153154\pi\)
−0.886464 + 0.462798i \(0.846846\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.79845 1.46498i 0.396016 0.152735i
\(93\) 0 0
\(94\) −14.9372 + 2.78066i −1.54065 + 0.286803i
\(95\) 4.07116 0.417693
\(96\) 0 0
\(97\) 15.0759 1.53072 0.765362 0.643600i \(-0.222560\pi\)
0.765362 + 0.643600i \(0.222560\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 8.33013 3.21276i 0.833013 0.321276i
\(101\) 5.26795i 0.524181i 0.965043 + 0.262090i \(0.0844118\pi\)
−0.965043 + 0.262090i \(0.915588\pi\)
\(102\) 0 0
\(103\) 16.6839i 1.64392i 0.569547 + 0.821959i \(0.307119\pi\)
−0.569547 + 0.821959i \(0.692881\pi\)
\(104\) 3.40559 2.09808i 0.333946 0.205733i
\(105\) 0 0
\(106\) −2.36603 12.7099i −0.229809 1.23449i
\(107\) −13.1582 −1.27205 −0.636026 0.771668i \(-0.719423\pi\)
−0.636026 + 0.771668i \(0.719423\pi\)
\(108\) 0 0
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) −0.385679 2.07180i −0.0367731 0.197538i
\(111\) 0 0
\(112\) 0 0
\(113\) 0.656339i 0.0617432i −0.999523 0.0308716i \(-0.990172\pi\)
0.999523 0.0308716i \(-0.00982829\pi\)
\(114\) 0 0
\(115\) 1.49015i 0.138957i
\(116\) −3.79845 9.84873i −0.352677 0.914431i
\(117\) 0 0
\(118\) 6.93237 1.29051i 0.638176 0.118801i
\(119\) 0 0
\(120\) 0 0
\(121\) −6.85641 −0.623310
\(122\) −13.0955 + 2.43782i −1.18561 + 0.220710i
\(123\) 0 0
\(124\) −6.93237 17.9744i −0.622545 1.61415i
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 18.6085i 1.65124i 0.564227 + 0.825619i \(0.309174\pi\)
−0.564227 + 0.825619i \(0.690826\pi\)
\(128\) 3.15319 10.8654i 0.278706 0.960377i
\(129\) 0 0
\(130\) −0.267949 1.43937i −0.0235007 0.126241i
\(131\) −15.7298 −1.37432 −0.687158 0.726508i \(-0.741142\pi\)
−0.687158 + 0.726508i \(0.741142\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.745075 + 4.00240i 0.0643646 + 0.345755i
\(135\) 0 0
\(136\) 6.22526 + 10.1048i 0.533812 + 0.866482i
\(137\) 5.27792i 0.450923i −0.974252 0.225461i \(-0.927611\pi\)
0.974252 0.225461i \(-0.0723890\pi\)
\(138\) 0 0
\(139\) 11.1226i 0.943409i −0.881757 0.471704i \(-0.843639\pi\)
0.881757 0.471704i \(-0.156361\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −12.6340 + 2.35190i −1.06022 + 0.197367i
\(143\) 2.87875 0.240733
\(144\) 0 0
\(145\) −3.86370 −0.320863
\(146\) 2.35190 0.437822i 0.194645 0.0362344i
\(147\) 0 0
\(148\) 6.46410 2.49307i 0.531346 0.204929i
\(149\) 4.24264i 0.347571i −0.984784 0.173785i \(-0.944400\pi\)
0.984784 0.173785i \(-0.0555999\pi\)
\(150\) 0 0
\(151\) 7.86488i 0.640035i 0.947412 + 0.320018i \(0.103689\pi\)
−0.947412 + 0.320018i \(0.896311\pi\)
\(152\) 8.25056 + 13.3923i 0.669209 + 1.08626i
\(153\) 0 0
\(154\) 0 0
\(155\) −7.05146 −0.566387
\(156\) 0 0
\(157\) −15.0759 −1.20319 −0.601593 0.798803i \(-0.705467\pi\)
−0.601593 + 0.798803i \(0.705467\pi\)
\(158\) 1.29051 + 6.93237i 0.102667 + 0.551510i
\(159\) 0 0
\(160\) −3.29530 2.50794i −0.260516 0.198270i
\(161\) 0 0
\(162\) 0 0
\(163\) 24.3660i 1.90849i 0.299021 + 0.954247i \(0.403340\pi\)
−0.299021 + 0.954247i \(0.596660\pi\)
\(164\) −6.28434 16.2942i −0.490725 1.27237i
\(165\) 0 0
\(166\) 18.9396 3.52573i 1.47000 0.273650i
\(167\) 10.7436 0.831367 0.415684 0.909509i \(-0.363542\pi\)
0.415684 + 0.909509i \(0.363542\pi\)
\(168\) 0 0
\(169\) −11.0000 −0.846154
\(170\) 4.27081 0.795040i 0.327556 0.0609767i
\(171\) 0 0
\(172\) 5.66025 + 14.6761i 0.431590 + 1.11904i
\(173\) 9.66025i 0.734456i −0.930131 0.367228i \(-0.880307\pi\)
0.930131 0.367228i \(-0.119693\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.03367 5.46739i 0.454805 0.412120i
\(177\) 0 0
\(178\) 2.26002 + 12.1404i 0.169396 + 0.909963i
\(179\) −17.2294 −1.28778 −0.643892 0.765117i \(-0.722681\pi\)
−0.643892 + 0.765117i \(0.722681\pi\)
\(180\) 0 0
\(181\) −5.00052 −0.371685 −0.185843 0.982580i \(-0.559501\pi\)
−0.185843 + 0.982580i \(0.559501\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.90192 3.01992i 0.361375 0.222631i
\(185\) 2.53590i 0.186443i
\(186\) 0 0
\(187\) 8.54161i 0.624625i
\(188\) −20.0479 + 7.73205i −1.46214 + 0.563918i
\(189\) 0 0
\(190\) 5.66025 1.05369i 0.410638 0.0764430i
\(191\) −13.1582 −0.952095 −0.476047 0.879420i \(-0.657931\pi\)
−0.476047 + 0.879420i \(0.657931\pi\)
\(192\) 0 0
\(193\) −9.85641 −0.709480 −0.354740 0.934965i \(-0.615431\pi\)
−0.354740 + 0.934965i \(0.615431\pi\)
\(194\) 20.9604 3.90192i 1.50487 0.280142i
\(195\) 0 0
\(196\) 0 0
\(197\) 15.3533i 1.09388i −0.837173 0.546938i \(-0.815793\pi\)
0.837173 0.546938i \(-0.184207\pi\)
\(198\) 0 0
\(199\) 4.07116i 0.288597i 0.989534 + 0.144299i \(0.0460926\pi\)
−0.989534 + 0.144299i \(0.953907\pi\)
\(200\) 10.7501 6.62278i 0.760146 0.468301i
\(201\) 0 0
\(202\) 1.36345 + 7.32418i 0.0959317 + 0.515327i
\(203\) 0 0
\(204\) 0 0
\(205\) −6.39230 −0.446458
\(206\) 4.31812 + 23.1962i 0.300858 + 1.61615i
\(207\) 0 0
\(208\) 4.19187 3.79845i 0.290654 0.263375i
\(209\) 11.3205i 0.783056i
\(210\) 0 0
\(211\) 21.4873i 1.47924i 0.673022 + 0.739622i \(0.264996\pi\)
−0.673022 + 0.739622i \(0.735004\pi\)
\(212\) −6.57910 17.0585i −0.451855 1.17158i
\(213\) 0 0
\(214\) −18.2942 + 3.40559i −1.25057 + 0.232802i
\(215\) 5.75749 0.392658
\(216\) 0 0
\(217\) 0 0
\(218\) 8.34197 1.55291i 0.564989 0.105177i
\(219\) 0 0
\(220\) −1.07244 2.78066i −0.0723040 0.187472i
\(221\) 5.93426i 0.399181i
\(222\) 0 0
\(223\) 15.1938i 1.01745i −0.860929 0.508726i \(-0.830117\pi\)
0.860929 0.508726i \(-0.169883\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −0.169873 0.912526i −0.0112998 0.0607004i
\(227\) −10.7436 −0.713080 −0.356540 0.934280i \(-0.616044\pi\)
−0.356540 + 0.934280i \(0.616044\pi\)
\(228\) 0 0
\(229\) 25.3543 1.67546 0.837730 0.546085i \(-0.183882\pi\)
0.837730 + 0.546085i \(0.183882\pi\)
\(230\) −0.385679 2.07180i −0.0254309 0.136610i
\(231\) 0 0
\(232\) −7.83013 12.7099i −0.514073 0.834443i
\(233\) 5.83272i 0.382114i −0.981579 0.191057i \(-0.938808\pi\)
0.981579 0.191057i \(-0.0611916\pi\)
\(234\) 0 0
\(235\) 7.86488i 0.513048i
\(236\) 9.30426 3.58846i 0.605656 0.233589i
\(237\) 0 0
\(238\) 0 0
\(239\) −2.03558 −0.131671 −0.0658354 0.997830i \(-0.520971\pi\)
−0.0658354 + 0.997830i \(0.520971\pi\)
\(240\) 0 0
\(241\) 13.0053 0.837747 0.418873 0.908045i \(-0.362425\pi\)
0.418873 + 0.908045i \(0.362425\pi\)
\(242\) −9.53266 + 1.77457i −0.612782 + 0.114074i
\(243\) 0 0
\(244\) −17.5761 + 6.77875i −1.12520 + 0.433965i
\(245\) 0 0
\(246\) 0 0
\(247\) 7.86488i 0.500431i
\(248\) −14.2904 23.1962i −0.907441 1.47296i
\(249\) 0 0
\(250\) −1.79315 9.63248i −0.113409 0.609211i
\(251\) −8.63624 −0.545115 −0.272557 0.962140i \(-0.587869\pi\)
−0.272557 + 0.962140i \(0.587869\pi\)
\(252\) 0 0
\(253\) 4.14359 0.260505
\(254\) 4.81624 + 25.8719i 0.302198 + 1.62335i
\(255\) 0 0
\(256\) 1.57180 15.9226i 0.0982373 0.995163i
\(257\) 1.12436i 0.0701354i −0.999385 0.0350677i \(-0.988835\pi\)
0.999385 0.0350677i \(-0.0111647\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.745075 1.93185i −0.0462076 0.119808i
\(261\) 0 0
\(262\) −21.8695 + 4.07116i −1.35110 + 0.251517i
\(263\) −2.03558 −0.125519 −0.0627597 0.998029i \(-0.519990\pi\)
−0.0627597 + 0.998029i \(0.519990\pi\)
\(264\) 0 0
\(265\) −6.69213 −0.411094
\(266\) 0 0
\(267\) 0 0
\(268\) 2.07180 + 5.37182i 0.126555 + 0.328136i
\(269\) 3.66025i 0.223170i −0.993755 0.111585i \(-0.964407\pi\)
0.993755 0.111585i \(-0.0355927\pi\)
\(270\) 0 0
\(271\) 13.7036i 0.832437i 0.909265 + 0.416218i \(0.136645\pi\)
−0.909265 + 0.416218i \(0.863355\pi\)
\(272\) 11.2705 + 12.4378i 0.683373 + 0.754154i
\(273\) 0 0
\(274\) −1.36603 7.33804i −0.0825246 0.443307i
\(275\) 9.08704 0.547969
\(276\) 0 0
\(277\) −7.07180 −0.424903 −0.212452 0.977172i \(-0.568145\pi\)
−0.212452 + 0.977172i \(0.568145\pi\)
\(278\) −2.87875 15.4641i −0.172656 0.927475i
\(279\) 0 0
\(280\) 0 0
\(281\) 23.5612i 1.40554i 0.711417 + 0.702770i \(0.248054\pi\)
−0.711417 + 0.702770i \(0.751946\pi\)
\(282\) 0 0
\(283\) 5.56131i 0.330586i −0.986245 0.165293i \(-0.947143\pi\)
0.986245 0.165293i \(-0.0528569\pi\)
\(284\) −16.9567 + 6.53983i −1.00619 + 0.388067i
\(285\) 0 0
\(286\) 4.00240 0.745075i 0.236667 0.0440572i
\(287\) 0 0
\(288\) 0 0
\(289\) −0.607695 −0.0357468
\(290\) −5.37182 + 1.00000i −0.315444 + 0.0587220i
\(291\) 0 0
\(292\) 3.15660 1.21743i 0.184726 0.0712449i
\(293\) 31.1244i 1.81830i 0.416464 + 0.909152i \(0.363269\pi\)
−0.416464 + 0.909152i \(0.636731\pi\)
\(294\) 0 0
\(295\) 3.65011i 0.212517i
\(296\) 8.34197 5.13922i 0.484867 0.298711i
\(297\) 0 0
\(298\) −1.09808 5.89866i −0.0636098 0.341700i
\(299\) 2.87875 0.166482
\(300\) 0 0
\(301\) 0 0
\(302\) 2.03558 + 10.9348i 0.117135 + 0.629225i
\(303\) 0 0
\(304\) 14.9372 + 16.4843i 0.856706 + 0.945439i
\(305\) 6.89520i 0.394818i
\(306\) 0 0
\(307\) 9.63248i 0.549754i −0.961479 0.274877i \(-0.911363\pi\)
0.961479 0.274877i \(-0.0886372\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −9.80385 + 1.82505i −0.556821 + 0.103656i
\(311\) 20.7159 1.17469 0.587346 0.809336i \(-0.300173\pi\)
0.587346 + 0.809336i \(0.300173\pi\)
\(312\) 0 0
\(313\) −30.2533 −1.71002 −0.855008 0.518614i \(-0.826448\pi\)
−0.855008 + 0.518614i \(0.826448\pi\)
\(314\) −20.9604 + 3.90192i −1.18286 + 0.220198i
\(315\) 0 0
\(316\) 3.58846 + 9.30426i 0.201866 + 0.523405i
\(317\) 4.24264i 0.238290i −0.992877 0.119145i \(-0.961985\pi\)
0.992877 0.119145i \(-0.0380154\pi\)
\(318\) 0 0
\(319\) 10.7436i 0.601528i
\(320\) −5.23065 2.63397i −0.292402 0.147244i
\(321\) 0 0
\(322\) 0 0
\(323\) −23.3361 −1.29846
\(324\) 0 0
\(325\) 6.31319 0.350193
\(326\) 6.30639 + 33.8768i 0.349279 + 1.87626i
\(327\) 0 0
\(328\) −12.9546 21.0278i −0.715296 1.16107i
\(329\) 0 0
\(330\) 0 0
\(331\) 11.5150i 0.632921i −0.948606 0.316461i \(-0.897506\pi\)
0.948606 0.316461i \(-0.102494\pi\)
\(332\) 25.4197 9.80385i 1.39509 0.538056i
\(333\) 0 0
\(334\) 14.9372 2.78066i 0.817326 0.152151i
\(335\) 2.10739 0.115139
\(336\) 0 0
\(337\) −1.60770 −0.0875767 −0.0437884 0.999041i \(-0.513943\pi\)
−0.0437884 + 0.999041i \(0.513943\pi\)
\(338\) −15.2936 + 2.84701i −0.831863 + 0.154857i
\(339\) 0 0
\(340\) 5.73205 2.21073i 0.310864 0.119894i
\(341\) 19.6077i 1.06182i
\(342\) 0 0
\(343\) 0 0
\(344\) 11.6681 + 18.9396i 0.629100 + 1.02115i
\(345\) 0 0
\(346\) −2.50026 13.4309i −0.134415 0.722051i
\(347\) 20.2097 1.08491 0.542456 0.840084i \(-0.317495\pi\)
0.542456 + 0.840084i \(0.317495\pi\)
\(348\) 0 0
\(349\) −11.4896 −0.615023 −0.307511 0.951544i \(-0.599496\pi\)
−0.307511 + 0.951544i \(0.599496\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6.97372 9.16309i 0.371701 0.488394i
\(353\) 28.1962i 1.50073i −0.661024 0.750365i \(-0.729878\pi\)
0.661024 0.750365i \(-0.270122\pi\)
\(354\) 0 0
\(355\) 6.65218i 0.353061i
\(356\) 6.28434 + 16.2942i 0.333069 + 0.863592i
\(357\) 0 0
\(358\) −23.9545 + 4.45929i −1.26603 + 0.235681i
\(359\) −9.08704 −0.479596 −0.239798 0.970823i \(-0.577081\pi\)
−0.239798 + 0.970823i \(0.577081\pi\)
\(360\) 0 0
\(361\) −11.9282 −0.627800
\(362\) −6.95236 + 1.29423i −0.365408 + 0.0680231i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.23835i 0.0648181i
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 6.03367 5.46739i 0.314527 0.285007i
\(369\) 0 0
\(370\) −0.656339 3.52573i −0.0341214 0.183294i
\(371\) 0 0
\(372\) 0 0
\(373\) 16.9282 0.876509 0.438255 0.898851i \(-0.355597\pi\)
0.438255 + 0.898851i \(0.355597\pi\)
\(374\) 2.21073 + 11.8756i 0.114314 + 0.614075i
\(375\) 0 0
\(376\) −25.8719 + 15.9389i −1.33424 + 0.821984i
\(377\) 7.46410i 0.384421i
\(378\) 0 0
\(379\) 27.2448i 1.39947i −0.714403 0.699735i \(-0.753302\pi\)
0.714403 0.699735i \(-0.246698\pi\)
\(380\) 7.59689 2.92996i 0.389712 0.150304i
\(381\) 0 0
\(382\) −18.2942 + 3.40559i −0.936014 + 0.174245i
\(383\) −21.4873 −1.09795 −0.548974 0.835839i \(-0.684981\pi\)
−0.548974 + 0.835839i \(0.684981\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −13.7036 + 2.55103i −0.697497 + 0.129844i
\(387\) 0 0
\(388\) 28.1320 10.8499i 1.42818 0.550821i
\(389\) 32.6012i 1.65295i 0.562974 + 0.826474i \(0.309657\pi\)
−0.562974 + 0.826474i \(0.690343\pi\)
\(390\) 0 0
\(391\) 8.54161i 0.431968i
\(392\) 0 0
\(393\) 0 0
\(394\) −3.97372 21.3461i −0.200193 1.07540i
\(395\) 3.65011 0.183657
\(396\) 0 0
\(397\) 17.3495 0.870746 0.435373 0.900250i \(-0.356616\pi\)
0.435373 + 0.900250i \(0.356616\pi\)
\(398\) 1.05369 + 5.66025i 0.0528169 + 0.283723i
\(399\) 0 0
\(400\) 13.2321 11.9902i 0.661603 0.599508i
\(401\) 38.2581i 1.91052i 0.295770 + 0.955259i \(0.404424\pi\)
−0.295770 + 0.955259i \(0.595576\pi\)
\(402\) 0 0
\(403\) 13.6224i 0.678579i
\(404\) 3.79127 + 9.83013i 0.188623 + 0.489067i
\(405\) 0 0
\(406\) 0 0
\(407\) 7.05146 0.349528
\(408\) 0 0
\(409\) 10.1769 0.503215 0.251608 0.967829i \(-0.419041\pi\)
0.251608 + 0.967829i \(0.419041\pi\)
\(410\) −8.88740 + 1.65445i −0.438918 + 0.0817075i
\(411\) 0 0
\(412\) 12.0072 + 31.1327i 0.591553 + 1.53380i
\(413\) 0 0
\(414\) 0 0
\(415\) 9.97227i 0.489520i
\(416\) 4.84497 6.36603i 0.237544 0.312120i
\(417\) 0 0
\(418\) 2.92996 + 15.7392i 0.143309 + 0.769831i
\(419\) −24.3660 −1.19036 −0.595179 0.803593i \(-0.702919\pi\)
−0.595179 + 0.803593i \(0.702919\pi\)
\(420\) 0 0
\(421\) −29.7128 −1.44811 −0.724057 0.689740i \(-0.757725\pi\)
−0.724057 + 0.689740i \(0.757725\pi\)
\(422\) 5.56131 + 29.8744i 0.270720 + 1.45426i
\(423\) 0 0
\(424\) −13.5622 22.0141i −0.658638 1.06910i
\(425\) 18.7321i 0.908638i
\(426\) 0 0
\(427\) 0 0
\(428\) −24.5536 + 9.46979i −1.18684 + 0.457740i
\(429\) 0 0
\(430\) 8.00481 1.49015i 0.386026 0.0718614i
\(431\) −32.4232 −1.56177 −0.780884 0.624676i \(-0.785231\pi\)
−0.780884 + 0.624676i \(0.785231\pi\)
\(432\) 0 0
\(433\) −14.7985 −0.711169 −0.355585 0.934644i \(-0.615718\pi\)
−0.355585 + 0.934644i \(0.615718\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 11.1962 4.31812i 0.536198 0.206801i
\(437\) 11.3205i 0.541533i
\(438\) 0 0
\(439\) 27.4073i 1.30808i −0.756461 0.654039i \(-0.773073\pi\)
0.756461 0.654039i \(-0.226927\pi\)
\(440\) −2.21073 3.58846i −0.105393 0.171073i
\(441\) 0 0
\(442\) 1.53590 + 8.25056i 0.0730552 + 0.392439i
\(443\) 10.1779 0.483567 0.241784 0.970330i \(-0.422268\pi\)
0.241784 + 0.970330i \(0.422268\pi\)
\(444\) 0 0
\(445\) 6.39230 0.303024
\(446\) −3.93244 21.1244i −0.186207 1.00027i
\(447\) 0 0
\(448\) 0 0
\(449\) 32.3238i 1.52546i 0.646719 + 0.762728i \(0.276141\pi\)
−0.646719 + 0.762728i \(0.723859\pi\)
\(450\) 0 0
\(451\) 17.7748i 0.836983i
\(452\) −0.472358 1.22474i −0.0222179 0.0576072i
\(453\) 0 0
\(454\) −14.9372 + 2.78066i −0.701036 + 0.130503i
\(455\) 0 0
\(456\) 0 0
\(457\) −22.9282 −1.07254 −0.536268 0.844048i \(-0.680166\pi\)
−0.536268 + 0.844048i \(0.680166\pi\)
\(458\) 35.2508 6.56218i 1.64716 0.306630i
\(459\) 0 0
\(460\) −1.07244 2.78066i −0.0500028 0.129649i
\(461\) 9.26795i 0.431651i 0.976432 + 0.215826i \(0.0692443\pi\)
−0.976432 + 0.215826i \(0.930756\pi\)
\(462\) 0 0
\(463\) 7.09353i 0.329664i −0.986322 0.164832i \(-0.947292\pi\)
0.986322 0.164832i \(-0.0527082\pi\)
\(464\) −14.1760 15.6443i −0.658104 0.726268i
\(465\) 0 0
\(466\) −1.50962 8.10940i −0.0699317 0.375660i
\(467\) 12.8510 0.594674 0.297337 0.954773i \(-0.403901\pi\)
0.297337 + 0.954773i \(0.403901\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 2.03558 + 10.9348i 0.0938944 + 0.504383i
\(471\) 0 0
\(472\) 12.0072 7.39725i 0.552677 0.340486i
\(473\) 16.0096i 0.736123i
\(474\) 0 0
\(475\) 24.8263i 1.13911i
\(476\) 0 0
\(477\) 0 0
\(478\) −2.83013 + 0.526847i −0.129447 + 0.0240974i
\(479\) −12.8510 −0.587178 −0.293589 0.955932i \(-0.594850\pi\)
−0.293589 + 0.955932i \(0.594850\pi\)
\(480\) 0 0
\(481\) 4.89898 0.223374
\(482\) 18.0817 3.36603i 0.823597 0.153318i
\(483\) 0 0
\(484\) −12.7942 + 4.93447i −0.581556 + 0.224294i
\(485\) 11.0363i 0.501133i
\(486\) 0 0
\(487\) 13.6224i 0.617289i −0.951177 0.308644i \(-0.900125\pi\)
0.951177 0.308644i \(-0.0998753\pi\)
\(488\) −22.6821 + 13.9737i −1.02677 + 0.632561i
\(489\) 0 0
\(490\) 0 0
\(491\) 13.1582 0.593822 0.296911 0.954905i \(-0.404044\pi\)
0.296911 + 0.954905i \(0.404044\pi\)
\(492\) 0 0
\(493\) 22.1469 0.997448
\(494\) 2.03558 + 10.9348i 0.0915852 + 0.491979i
\(495\) 0 0
\(496\) −25.8719 28.5516i −1.16168 1.28201i
\(497\) 0 0
\(498\) 0 0
\(499\) 29.3521i 1.31398i −0.753898 0.656991i \(-0.771829\pi\)
0.753898 0.656991i \(-0.228171\pi\)
\(500\) −4.98614 12.9282i −0.222987 0.578167i
\(501\) 0 0
\(502\) −12.0072 + 2.23522i −0.535908 + 0.0997629i
\(503\) −19.3799 −0.864106 −0.432053 0.901848i \(-0.642211\pi\)
−0.432053 + 0.901848i \(0.642211\pi\)
\(504\) 0 0
\(505\) 3.85641 0.171608
\(506\) 5.76096 1.07244i 0.256106 0.0476758i
\(507\) 0 0
\(508\) 13.3923 + 34.7240i 0.594187 + 1.54063i
\(509\) 27.6603i 1.22602i −0.790075 0.613010i \(-0.789959\pi\)
0.790075 0.613010i \(-0.210041\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.93576 22.5445i −0.0855493 0.996334i
\(513\) 0 0
\(514\) −0.291005 1.56322i −0.0128357 0.0689508i
\(515\) 12.2135 0.538191
\(516\) 0 0
\(517\) −21.8695 −0.961821
\(518\) 0 0
\(519\) 0 0
\(520\) −1.53590 2.49307i −0.0673536 0.109328i
\(521\) 9.66025i 0.423223i 0.977354 + 0.211612i \(0.0678712\pi\)
−0.977354 + 0.211612i \(0.932129\pi\)
\(522\) 0 0
\(523\) 2.98030i 0.130319i −0.997875 0.0651597i \(-0.979244\pi\)
0.997875 0.0651597i \(-0.0207557\pi\)
\(524\) −29.3521 + 11.3205i −1.28225 + 0.494539i
\(525\) 0 0
\(526\) −2.83013 + 0.526847i −0.123399 + 0.0229716i
\(527\) 40.4193 1.76069
\(528\) 0 0
\(529\) −18.8564 −0.819844
\(530\) −9.30426 + 1.73205i −0.404151 + 0.0752355i
\(531\) 0 0
\(532\) 0 0
\(533\) 12.3490i 0.534894i
\(534\) 0 0
\(535\) 9.63248i 0.416448i
\(536\) 4.27081 + 6.93237i 0.184471 + 0.299433i
\(537\) 0 0
\(538\) −0.947343 5.08895i −0.0408429 0.219400i
\(539\) 0 0
\(540\) 0 0
\(541\) 15.8564 0.681720 0.340860 0.940114i \(-0.389282\pi\)
0.340860 + 0.940114i \(0.389282\pi\)
\(542\) 3.54676 + 19.0526i 0.152347 + 0.818377i
\(543\) 0 0
\(544\) 18.8888 + 14.3756i 0.809851 + 0.616351i
\(545\) 4.39230i 0.188146i
\(546\) 0 0
\(547\) 26.4734i 1.13192i −0.824432 0.565960i \(-0.808505\pi\)
0.824432 0.565960i \(-0.191495\pi\)
\(548\) −3.79845 9.84873i −0.162262 0.420717i
\(549\) 0 0
\(550\) 12.6340 2.35190i 0.538714 0.100285i
\(551\) 29.3521 1.25044
\(552\) 0 0
\(553\) 0 0
\(554\) −9.83212 + 1.83032i −0.417727 + 0.0777627i
\(555\) 0 0
\(556\) −8.00481 20.7551i −0.339479 0.880212i
\(557\) 18.9396i 0.802496i −0.915970 0.401248i \(-0.868577\pi\)
0.915970 0.401248i \(-0.131423\pi\)
\(558\) 0 0
\(559\) 11.1226i 0.470437i
\(560\) 0 0
\(561\) 0 0
\(562\) 6.09808 + 32.7577i 0.257232 + 1.38180i
\(563\) 37.9884 1.60102 0.800510 0.599320i \(-0.204562\pi\)
0.800510 + 0.599320i \(0.204562\pi\)
\(564\) 0 0
\(565\) −0.480473 −0.0202137
\(566\) −1.43937 7.73205i −0.0605014 0.325002i
\(567\) 0 0
\(568\) −21.8827 + 13.4812i −0.918177 + 0.565659i
\(569\) 16.5916i 0.695557i 0.937577 + 0.347779i \(0.113064\pi\)
−0.937577 + 0.347779i \(0.886936\pi\)
\(570\) 0 0
\(571\) 0.771358i 0.0322803i −0.999870 0.0161402i \(-0.994862\pi\)
0.999870 0.0161402i \(-0.00513780\pi\)
\(572\) 5.37182 2.07180i 0.224607 0.0866262i
\(573\) 0 0
\(574\) 0 0
\(575\) 9.08704 0.378956
\(576\) 0 0
\(577\) −7.62587 −0.317469 −0.158735 0.987321i \(-0.550741\pi\)
−0.158735 + 0.987321i \(0.550741\pi\)
\(578\) −0.844896 + 0.157283i −0.0351430 + 0.00654211i
\(579\) 0 0
\(580\) −7.20977 + 2.78066i −0.299369 + 0.115460i
\(581\) 0 0
\(582\) 0 0
\(583\) 18.6085i 0.770686i
\(584\) 4.07361 2.50962i 0.168567 0.103849i
\(585\) 0 0
\(586\) 8.05558 + 43.2731i 0.332773 + 1.78759i
\(587\) 16.5011 0.681074 0.340537 0.940231i \(-0.389391\pi\)
0.340537 + 0.940231i \(0.389391\pi\)
\(588\) 0 0
\(589\) 53.5692 2.20728
\(590\) −0.944717 5.07484i −0.0388934 0.208928i
\(591\) 0 0
\(592\) 10.2679 9.30426i 0.422010 0.382403i
\(593\) 28.1962i 1.15788i 0.815371 + 0.578939i \(0.196533\pi\)
−0.815371 + 0.578939i \(0.803467\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.05337 7.91688i −0.125071 0.324288i
\(597\) 0 0
\(598\) 4.00240 0.745075i 0.163670 0.0304684i
\(599\) 31.3323 1.28020 0.640101 0.768290i \(-0.278892\pi\)
0.640101 + 0.768290i \(0.278892\pi\)
\(600\) 0 0
\(601\) 30.4564 1.24234 0.621170 0.783676i \(-0.286657\pi\)
0.621170 + 0.783676i \(0.286657\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5.66025 + 14.6761i 0.230312 + 0.597161i
\(605\) 5.01924i 0.204061i
\(606\) 0 0
\(607\) 14.1029i 0.572420i −0.958167 0.286210i \(-0.907604\pi\)
0.958167 0.286210i \(-0.0923955\pi\)
\(608\) 25.0340 + 19.0526i 1.01526 + 0.772683i
\(609\) 0 0
\(610\) 1.78461 + 9.58659i 0.0722567 + 0.388150i
\(611\) −15.1938 −0.614675
\(612\) 0 0
\(613\) 16.3923 0.662079 0.331039 0.943617i \(-0.392601\pi\)
0.331039 + 0.943617i \(0.392601\pi\)
\(614\) −2.49307 13.3923i −0.100612 0.540469i
\(615\) 0 0
\(616\) 0 0
\(617\) 10.3800i 0.417882i 0.977928 + 0.208941i \(0.0670016\pi\)
−0.977928 + 0.208941i \(0.932998\pi\)
\(618\) 0 0
\(619\) 26.3164i 1.05775i 0.848701 + 0.528873i \(0.177385\pi\)
−0.848701 + 0.528873i \(0.822615\pi\)
\(620\) −13.1582 + 5.07484i −0.528446 + 0.203811i
\(621\) 0 0
\(622\) 28.8019 5.36167i 1.15485 0.214983i
\(623\) 0 0
\(624\) 0 0
\(625\) 17.2487 0.689948
\(626\) −42.0620 + 7.83013i −1.68114 + 0.312955i
\(627\) 0 0
\(628\) −28.1320 + 10.8499i −1.12259 + 0.432959i
\(629\) 14.5359i 0.579584i
\(630\) 0 0
\(631\) 7.09353i 0.282389i −0.989982 0.141194i \(-0.954906\pi\)
0.989982 0.141194i \(-0.0450943\pi\)
\(632\) 7.39725 + 12.0072i 0.294247 + 0.477621i
\(633\) 0 0
\(634\) −1.09808 5.89866i −0.0436102 0.234266i
\(635\) 13.6224 0.540588
\(636\) 0 0
\(637\) 0 0
\(638\) −2.78066 14.9372i −0.110087 0.591368i
\(639\) 0 0
\(640\) −7.95404 2.30830i −0.314411 0.0912435i
\(641\) 3.96524i 0.156618i 0.996929 + 0.0783088i \(0.0249520\pi\)
−0.996929 + 0.0783088i \(0.975048\pi\)
\(642\) 0 0
\(643\) 2.58101i 0.101785i −0.998704 0.0508926i \(-0.983793\pi\)
0.998704 0.0508926i \(-0.0162066\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −32.4449 + 6.03983i −1.27653 + 0.237634i
\(647\) −47.9607 −1.88553 −0.942764 0.333460i \(-0.891784\pi\)
−0.942764 + 0.333460i \(0.891784\pi\)
\(648\) 0 0
\(649\) 10.1497 0.398410
\(650\) 8.77741 1.63397i 0.344278 0.0640898i
\(651\) 0 0
\(652\) 17.5359 + 45.4676i 0.686759 + 1.78065i
\(653\) 39.2190i 1.53476i −0.641193 0.767380i \(-0.721560\pi\)
0.641193 0.767380i \(-0.278440\pi\)
\(654\) 0 0
\(655\) 11.5150i 0.449928i
\(656\) −23.4535 25.8827i −0.915705 1.01055i
\(657\) 0 0
\(658\) 0 0
\(659\) 47.6170 1.85489 0.927447 0.373956i \(-0.121999\pi\)
0.927447 + 0.373956i \(0.121999\pi\)
\(660\) 0 0
\(661\) −30.7338 −1.19540 −0.597702 0.801718i \(-0.703920\pi\)
−0.597702 + 0.801718i \(0.703920\pi\)
\(662\) −2.98030 16.0096i −0.115833 0.622231i
\(663\) 0 0
\(664\) 32.8043 20.2097i 1.27305 0.784287i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.7436i 0.415995i
\(668\) 20.0479 7.73205i 0.775676 0.299162i
\(669\) 0 0
\(670\) 2.92996 0.545433i 0.113194 0.0210719i
\(671\) −19.1732 −0.740173
\(672\) 0 0
\(673\) −42.0000 −1.61898 −0.809491 0.587133i \(-0.800257\pi\)
−0.809491 + 0.587133i \(0.800257\pi\)
\(674\) −2.23522 + 0.416102i −0.0860976 + 0.0160277i
\(675\) 0 0
\(676\) −20.5263 + 7.91656i −0.789472 + 0.304483i
\(677\) 24.8756i 0.956049i −0.878347 0.478024i \(-0.841353\pi\)
0.878347 0.478024i \(-0.158647\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 7.39725 4.55721i 0.283672 0.174761i
\(681\) 0 0
\(682\) −5.07484 27.2611i −0.194326 1.04388i
\(683\) −24.2808 −0.929080 −0.464540 0.885552i \(-0.653780\pi\)
−0.464540 + 0.885552i \(0.653780\pi\)
\(684\) 0 0
\(685\) −3.86370 −0.147625
\(686\) 0 0
\(687\) 0 0
\(688\) 21.1244 + 23.3123i 0.805359 + 0.888774i
\(689\) 12.9282i 0.492525i
\(690\) 0 0
\(691\) 37.4390i 1.42425i −0.702054 0.712124i \(-0.747733\pi\)
0.702054 0.712124i \(-0.252267\pi\)
\(692\) −6.95236 18.0263i −0.264289 0.685256i
\(693\) 0 0
\(694\) 28.0981 5.23065i 1.06659 0.198553i
\(695\) −8.14233 −0.308856
\(696\) 0 0
\(697\) 36.6410 1.38788
\(698\) −15.9743 + 2.97372i −0.604635 + 0.112557i
\(699\) 0 0
\(700\) 0 0
\(701\) 48.2591i 1.82272i −0.411608 0.911361i \(-0.635033\pi\)
0.411608 0.911361i \(-0.364967\pi\)
\(702\) 0 0
\(703\) 19.2650i 0.726591i
\(704\) 7.32418 14.5446i 0.276040 0.548172i
\(705\) 0 0
\(706\) −7.29770 39.2019i −0.274653 1.47538i
\(707\) 0 0
\(708\) 0 0
\(709\) −0.928203 −0.0348594 −0.0174297 0.999848i \(-0.505548\pi\)
−0.0174297 + 0.999848i \(0.505548\pi\)
\(710\) 1.72171 + 9.24871i 0.0646146 + 0.347098i
\(711\) 0 0
\(712\) 12.9546 + 21.0278i 0.485492 + 0.788051i
\(713\) 19.6077i 0.734314i
\(714\) 0 0
\(715\) 2.10739i 0.0788119i
\(716\) −32.1504 + 12.3998i −1.20152 + 0.463401i
\(717\) 0 0
\(718\) −12.6340 + 2.35190i −0.471496 + 0.0877721i
\(719\) 52.9468 1.97458 0.987291 0.158921i \(-0.0508016\pi\)
0.987291 + 0.158921i \(0.0508016\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −16.5841 + 3.08725i −0.617197 + 0.114895i
\(723\) 0 0
\(724\) −9.33109 + 3.59881i −0.346787 + 0.133749i
\(725\) 23.5612i 0.875039i
\(726\) 0 0
\(727\) 10.7233i 0.397707i 0.980029 + 0.198853i \(0.0637218\pi\)
−0.980029 + 0.198853i \(0.936278\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −0.320508 1.72171i −0.0118625 0.0637234i
\(731\) −33.0023 −1.22063
\(732\) 0 0
\(733\) 19.1427 0.707050 0.353525 0.935425i \(-0.384983\pi\)
0.353525 + 0.935425i \(0.384983\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 6.97372 9.16309i 0.257055 0.337756i
\(737\) 5.85993i 0.215853i
\(738\) 0 0
\(739\) 12.8510i 0.472732i −0.971664 0.236366i \(-0.924043\pi\)
0.971664 0.236366i \(-0.0759565\pi\)
\(740\) −1.82505 4.73205i −0.0670903 0.173954i
\(741\) 0 0
\(742\) 0 0
\(743\) 25.3717 0.930797 0.465399 0.885101i \(-0.345911\pi\)
0.465399 + 0.885101i \(0.345911\pi\)
\(744\) 0 0
\(745\) −3.10583 −0.113789
\(746\) 23.5358 4.38134i 0.861705 0.160412i
\(747\) 0 0
\(748\) 6.14729 + 15.9389i 0.224767 + 0.582783i
\(749\) 0 0
\(750\) 0 0
\(751\) 33.0023i 1.20427i 0.798395 + 0.602135i \(0.205683\pi\)
−0.798395 + 0.602135i \(0.794317\pi\)
\(752\) −31.8452 + 28.8564i −1.16128 + 1.05228i
\(753\) 0 0
\(754\) −1.93185 10.3776i −0.0703539 0.377928i
\(755\) 5.75749 0.209537
\(756\) 0 0
\(757\) 40.6410 1.47712 0.738561 0.674186i \(-0.235505\pi\)
0.738561 + 0.674186i \(0.235505\pi\)
\(758\) −7.05146 37.8792i −0.256121 1.37583i
\(759\) 0 0
\(760\) 9.80385 6.03983i 0.355623 0.219088i
\(761\) 37.1244i 1.34576i 0.739753 + 0.672878i \(0.234942\pi\)
−0.739753 + 0.672878i \(0.765058\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −24.5536 + 9.46979i −0.888316 + 0.342605i
\(765\) 0 0
\(766\) −29.8744 + 5.56131i −1.07940 + 0.200938i
\(767\) 7.05146 0.254614
\(768\) 0 0
\(769\) −2.72689 −0.0983342 −0.0491671 0.998791i \(-0.515657\pi\)
−0.0491671 + 0.998791i \(0.515657\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −18.3923 + 7.09353i −0.661954 + 0.255302i
\(773\) 11.5167i 0.414225i −0.978317 0.207113i \(-0.933593\pi\)
0.978317 0.207113i \(-0.0664067\pi\)
\(774\) 0 0
\(775\) 43.0004i 1.54462i
\(776\) 36.3045 22.3660i 1.30326 0.802894i
\(777\) 0 0
\(778\) 8.43782 + 45.3264i 0.302511 + 1.62503i
\(779\) 48.5617 1.73990
\(780\) 0 0
\(781\) −18.4974 −0.661890
\(782\) 2.21073 + 11.8756i 0.0790556 + 0.424672i
\(783\) 0 0
\(784\) 0 0
\(785\) 11.0363i 0.393903i
\(786\) 0 0
\(787\) 29.2967i 1.04432i 0.852849 + 0.522158i \(0.174873\pi\)
−0.852849 + 0.522158i \(0.825127\pi\)
\(788\) −11.0496 28.6496i −0.393624 1.02060i
\(789\) 0 0
\(790\) 5.07484 0.944717i 0.180555 0.0336115i
\(791\) 0 0
\(792\) 0 0
\(793\) −13.3205 −0.473025
\(794\) 24.1215 4.49038i 0.856040 0.159358i
\(795\) 0 0
\(796\) 2.92996 + 7.59689i 0.103850 + 0.269265i