Properties

Label 1800.2.k.u.901.10
Level $1800$
Weight $2$
Character 1800.901
Analytic conductor $14.373$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.k (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.3730723638\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.180227832610816.1
Defining polynomial: \( x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 901.10
Root \(0.806504 - 1.16170i\) of defining polynomial
Character \(\chi\) \(=\) 1800.901
Dual form 1800.2.k.u.901.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.806504 + 1.16170i) q^{2} +(-0.699104 + 1.87383i) q^{4} -0.746175 q^{7} +(-2.74067 + 0.699104i) q^{8} +O(q^{10})\) \(q+(0.806504 + 1.16170i) q^{2} +(-0.699104 + 1.87383i) q^{4} -0.746175 q^{7} +(-2.74067 + 0.699104i) q^{8} -5.36068i q^{11} -2.92520i q^{13} +(-0.601793 - 0.866833i) q^{14} +(-3.02251 - 2.62001i) q^{16} +2.13466 q^{17} +1.73367i q^{19} +(6.22751 - 4.32340i) q^{22} +7.49534 q^{23} +(3.39821 - 2.35918i) q^{26} +(0.521653 - 1.39821i) q^{28} -6.74916i q^{29} +2.64681 q^{31} +(0.606006 - 5.62430i) q^{32} +(1.72161 + 2.47984i) q^{34} +1.07480i q^{37} +(-2.01400 + 1.39821i) q^{38} +11.2936 q^{41} +7.44322i q^{43} +(10.0450 + 3.74767i) q^{44} +(6.04502 + 8.70735i) q^{46} +1.73367 q^{47} -6.44322 q^{49} +(5.48133 + 2.04502i) q^{52} -7.72161i q^{53} +(2.04502 - 0.521653i) q^{56} +(7.84052 - 5.44322i) q^{58} -6.85302i q^{59} -6.45203i q^{61} +(2.13466 + 3.07480i) q^{62} +(7.02251 - 3.83202i) q^{64} +7.44322i q^{67} +(-1.49235 + 4.00000i) q^{68} -13.2936 q^{71} +0.690358 q^{73} +(-1.24860 + 0.866833i) q^{74} +(-3.24860 - 1.21201i) q^{76} +4.00000i q^{77} +2.64681 q^{79} +(9.10834 + 13.1198i) q^{82} +5.85039i q^{83} +(-8.64681 + 6.00299i) q^{86} +(3.74767 + 14.6918i) q^{88} -7.59283 q^{89} +2.18271i q^{91} +(-5.24002 + 14.0450i) q^{92} +(1.39821 + 2.01400i) q^{94} +14.1887 q^{97} +(-5.19648 - 7.48511i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{4} - 20 q^{14} + 2 q^{16} + 28 q^{26} - 32 q^{31} - 24 q^{34} + 8 q^{41} + 44 q^{44} - 4 q^{46} + 12 q^{49} - 52 q^{56} + 46 q^{64} - 32 q^{71} + 36 q^{74} + 12 q^{76} - 32 q^{79} - 40 q^{86} - 40 q^{89} + 4 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1001\) \(1351\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.806504 + 1.16170i 0.570284 + 0.821447i
\(3\) 0 0
\(4\) −0.699104 + 1.87383i −0.349552 + 0.936917i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.746175 −0.282028 −0.141014 0.990008i \(-0.545036\pi\)
−0.141014 + 0.990008i \(0.545036\pi\)
\(8\) −2.74067 + 0.699104i −0.968972 + 0.247170i
\(9\) 0 0
\(10\) 0 0
\(11\) 5.36068i 1.61630i −0.588974 0.808152i \(-0.700468\pi\)
0.588974 0.808152i \(-0.299532\pi\)
\(12\) 0 0
\(13\) 2.92520i 0.811304i −0.914028 0.405652i \(-0.867045\pi\)
0.914028 0.405652i \(-0.132955\pi\)
\(14\) −0.601793 0.866833i −0.160836 0.231671i
\(15\) 0 0
\(16\) −3.02251 2.62001i −0.755627 0.655002i
\(17\) 2.13466 0.517731 0.258866 0.965913i \(-0.416651\pi\)
0.258866 + 0.965913i \(0.416651\pi\)
\(18\) 0 0
\(19\) 1.73367i 0.397730i 0.980027 + 0.198865i \(0.0637255\pi\)
−0.980027 + 0.198865i \(0.936274\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 6.22751 4.32340i 1.32771 0.921753i
\(23\) 7.49534 1.56289 0.781443 0.623977i \(-0.214484\pi\)
0.781443 + 0.623977i \(0.214484\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.39821 2.35918i 0.666443 0.462674i
\(27\) 0 0
\(28\) 0.521653 1.39821i 0.0985832 0.264236i
\(29\) 6.74916i 1.25329i −0.779306 0.626644i \(-0.784428\pi\)
0.779306 0.626644i \(-0.215572\pi\)
\(30\) 0 0
\(31\) 2.64681 0.475381 0.237690 0.971341i \(-0.423610\pi\)
0.237690 + 0.971341i \(0.423610\pi\)
\(32\) 0.606006 5.62430i 0.107128 0.994245i
\(33\) 0 0
\(34\) 1.72161 + 2.47984i 0.295254 + 0.425289i
\(35\) 0 0
\(36\) 0 0
\(37\) 1.07480i 0.176697i 0.996090 + 0.0883483i \(0.0281588\pi\)
−0.996090 + 0.0883483i \(0.971841\pi\)
\(38\) −2.01400 + 1.39821i −0.326714 + 0.226819i
\(39\) 0 0
\(40\) 0 0
\(41\) 11.2936 1.76377 0.881883 0.471468i \(-0.156276\pi\)
0.881883 + 0.471468i \(0.156276\pi\)
\(42\) 0 0
\(43\) 7.44322i 1.13508i 0.823346 + 0.567540i \(0.192105\pi\)
−0.823346 + 0.567540i \(0.807895\pi\)
\(44\) 10.0450 + 3.74767i 1.51434 + 0.564982i
\(45\) 0 0
\(46\) 6.04502 + 8.70735i 0.891289 + 1.28383i
\(47\) 1.73367 0.252881 0.126441 0.991974i \(-0.459645\pi\)
0.126441 + 0.991974i \(0.459645\pi\)
\(48\) 0 0
\(49\) −6.44322 −0.920460
\(50\) 0 0
\(51\) 0 0
\(52\) 5.48133 + 2.04502i 0.760124 + 0.283593i
\(53\) 7.72161i 1.06064i −0.847796 0.530322i \(-0.822071\pi\)
0.847796 0.530322i \(-0.177929\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.04502 0.521653i 0.273277 0.0697089i
\(57\) 0 0
\(58\) 7.84052 5.44322i 1.02951 0.714730i
\(59\) 6.85302i 0.892188i −0.894986 0.446094i \(-0.852815\pi\)
0.894986 0.446094i \(-0.147185\pi\)
\(60\) 0 0
\(61\) 6.45203i 0.826098i −0.910709 0.413049i \(-0.864464\pi\)
0.910709 0.413049i \(-0.135536\pi\)
\(62\) 2.13466 + 3.07480i 0.271102 + 0.390500i
\(63\) 0 0
\(64\) 7.02251 3.83202i 0.877813 0.479003i
\(65\) 0 0
\(66\) 0 0
\(67\) 7.44322i 0.909334i 0.890661 + 0.454667i \(0.150242\pi\)
−0.890661 + 0.454667i \(0.849758\pi\)
\(68\) −1.49235 + 4.00000i −0.180974 + 0.485071i
\(69\) 0 0
\(70\) 0 0
\(71\) −13.2936 −1.57766 −0.788831 0.614610i \(-0.789313\pi\)
−0.788831 + 0.614610i \(0.789313\pi\)
\(72\) 0 0
\(73\) 0.690358 0.0808003 0.0404002 0.999184i \(-0.487137\pi\)
0.0404002 + 0.999184i \(0.487137\pi\)
\(74\) −1.24860 + 0.866833i −0.145147 + 0.100767i
\(75\) 0 0
\(76\) −3.24860 1.21201i −0.372640 0.139027i
\(77\) 4.00000i 0.455842i
\(78\) 0 0
\(79\) 2.64681 0.297789 0.148895 0.988853i \(-0.452428\pi\)
0.148895 + 0.988853i \(0.452428\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 9.10834 + 13.1198i 1.00585 + 1.44884i
\(83\) 5.85039i 0.642164i 0.947051 + 0.321082i \(0.104047\pi\)
−0.947051 + 0.321082i \(0.895953\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −8.64681 + 6.00299i −0.932409 + 0.647319i
\(87\) 0 0
\(88\) 3.74767 + 14.6918i 0.399503 + 1.56615i
\(89\) −7.59283 −0.804838 −0.402419 0.915456i \(-0.631831\pi\)
−0.402419 + 0.915456i \(0.631831\pi\)
\(90\) 0 0
\(91\) 2.18271i 0.228810i
\(92\) −5.24002 + 14.0450i −0.546310 + 1.46429i
\(93\) 0 0
\(94\) 1.39821 + 2.01400i 0.144214 + 0.207729i
\(95\) 0 0
\(96\) 0 0
\(97\) 14.1887 1.44064 0.720321 0.693641i \(-0.243994\pi\)
0.720321 + 0.693641i \(0.243994\pi\)
\(98\) −5.19648 7.48511i −0.524924 0.756110i
\(99\) 0 0
\(100\) 0 0
\(101\) 7.43952i 0.740260i 0.928980 + 0.370130i \(0.120687\pi\)
−0.928980 + 0.370130i \(0.879313\pi\)
\(102\) 0 0
\(103\) −7.19820 −0.709260 −0.354630 0.935007i \(-0.615393\pi\)
−0.354630 + 0.935007i \(0.615393\pi\)
\(104\) 2.04502 + 8.01699i 0.200530 + 0.786131i
\(105\) 0 0
\(106\) 8.97021 6.22751i 0.871264 0.604869i
\(107\) 4.00000i 0.386695i −0.981130 0.193347i \(-0.938066\pi\)
0.981130 0.193347i \(-0.0619344\pi\)
\(108\) 0 0
\(109\) 19.9504i 1.91090i −0.295158 0.955449i \(-0.595372\pi\)
0.295158 0.955449i \(-0.404628\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.25532 + 1.95498i 0.213108 + 0.184729i
\(113\) 12.0540 1.13395 0.566973 0.823736i \(-0.308114\pi\)
0.566973 + 0.823736i \(0.308114\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 12.6468 + 4.71836i 1.17423 + 0.438089i
\(117\) 0 0
\(118\) 7.96117 5.52699i 0.732885 0.508801i
\(119\) −1.59283 −0.146014
\(120\) 0 0
\(121\) −17.7368 −1.61244
\(122\) 7.49534 5.20359i 0.678596 0.471110i
\(123\) 0 0
\(124\) −1.85039 + 4.95968i −0.166170 + 0.445392i
\(125\) 0 0
\(126\) 0 0
\(127\) 4.21351 0.373888 0.186944 0.982371i \(-0.440142\pi\)
0.186944 + 0.982371i \(0.440142\pi\)
\(128\) 10.1153 + 5.06752i 0.894079 + 0.447910i
\(129\) 0 0
\(130\) 0 0
\(131\) 10.3204i 0.901694i −0.892601 0.450847i \(-0.851122\pi\)
0.892601 0.450847i \(-0.148878\pi\)
\(132\) 0 0
\(133\) 1.29362i 0.112171i
\(134\) −8.64681 + 6.00299i −0.746970 + 0.518579i
\(135\) 0 0
\(136\) −5.85039 + 1.49235i −0.501667 + 0.127968i
\(137\) 15.0387 1.28484 0.642422 0.766351i \(-0.277930\pi\)
0.642422 + 0.766351i \(0.277930\pi\)
\(138\) 0 0
\(139\) 9.47032i 0.803262i −0.915802 0.401631i \(-0.868443\pi\)
0.915802 0.401631i \(-0.131557\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −10.7214 15.4432i −0.899716 1.29597i
\(143\) −15.6810 −1.31131
\(144\) 0 0
\(145\) 0 0
\(146\) 0.556777 + 0.801991i 0.0460792 + 0.0663732i
\(147\) 0 0
\(148\) −2.01400 0.751399i −0.165550 0.0617646i
\(149\) 1.78948i 0.146600i −0.997310 0.0733000i \(-0.976647\pi\)
0.997310 0.0733000i \(-0.0233531\pi\)
\(150\) 0 0
\(151\) 10.6468 0.866425 0.433212 0.901292i \(-0.357380\pi\)
0.433212 + 0.901292i \(0.357380\pi\)
\(152\) −1.21201 4.75140i −0.0983071 0.385389i
\(153\) 0 0
\(154\) −4.64681 + 3.22601i −0.374451 + 0.259960i
\(155\) 0 0
\(156\) 0 0
\(157\) 6.92520i 0.552691i −0.961058 0.276345i \(-0.910877\pi\)
0.961058 0.276345i \(-0.0891234\pi\)
\(158\) 2.13466 + 3.07480i 0.169824 + 0.244618i
\(159\) 0 0
\(160\) 0 0
\(161\) −5.59283 −0.440777
\(162\) 0 0
\(163\) 7.70079i 0.603172i 0.953439 + 0.301586i \(0.0975161\pi\)
−0.953439 + 0.301586i \(0.902484\pi\)
\(164\) −7.89541 + 21.1624i −0.616528 + 1.65250i
\(165\) 0 0
\(166\) −6.79641 + 4.71836i −0.527504 + 0.366216i
\(167\) −3.22601 −0.249637 −0.124818 0.992180i \(-0.539835\pi\)
−0.124818 + 0.992180i \(0.539835\pi\)
\(168\) 0 0
\(169\) 4.44322 0.341786
\(170\) 0 0
\(171\) 0 0
\(172\) −13.9474 5.20359i −1.06348 0.396770i
\(173\) 6.42799i 0.488711i 0.969686 + 0.244356i \(0.0785764\pi\)
−0.969686 + 0.244356i \(0.921424\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −14.0450 + 16.2027i −1.05868 + 1.22132i
\(177\) 0 0
\(178\) −6.12364 8.82061i −0.458987 0.661132i
\(179\) 8.13765i 0.608236i −0.952634 0.304118i \(-0.901638\pi\)
0.952634 0.304118i \(-0.0983618\pi\)
\(180\) 0 0
\(181\) 1.49235i 0.110925i −0.998461 0.0554627i \(-0.982337\pi\)
0.998461 0.0554627i \(-0.0176634\pi\)
\(182\) −2.53566 + 1.76036i −0.187955 + 0.130487i
\(183\) 0 0
\(184\) −20.5422 + 5.24002i −1.51439 + 0.386299i
\(185\) 0 0
\(186\) 0 0
\(187\) 11.4432i 0.836811i
\(188\) −1.21201 + 3.24860i −0.0883951 + 0.236929i
\(189\) 0 0
\(190\) 0 0
\(191\) −6.88645 −0.498286 −0.249143 0.968467i \(-0.580149\pi\)
−0.249143 + 0.968467i \(0.580149\pi\)
\(192\) 0 0
\(193\) 16.4830 1.18647 0.593237 0.805028i \(-0.297850\pi\)
0.593237 + 0.805028i \(0.297850\pi\)
\(194\) 11.4432 + 16.4830i 0.821576 + 1.18341i
\(195\) 0 0
\(196\) 4.50448 12.0735i 0.321749 0.862395i
\(197\) 13.5720i 0.966965i −0.875354 0.483483i \(-0.839372\pi\)
0.875354 0.483483i \(-0.160628\pi\)
\(198\) 0 0
\(199\) 9.05398 0.641820 0.320910 0.947110i \(-0.396011\pi\)
0.320910 + 0.947110i \(0.396011\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −8.64251 + 6.00000i −0.608085 + 0.422159i
\(203\) 5.03605i 0.353462i
\(204\) 0 0
\(205\) 0 0
\(206\) −5.80538 8.36217i −0.404480 0.582620i
\(207\) 0 0
\(208\) −7.66404 + 8.84143i −0.531406 + 0.613043i
\(209\) 9.29362 0.642853
\(210\) 0 0
\(211\) 2.53566i 0.174562i 0.996184 + 0.0872809i \(0.0278178\pi\)
−0.996184 + 0.0872809i \(0.972182\pi\)
\(212\) 14.4690 + 5.39821i 0.993736 + 0.370750i
\(213\) 0 0
\(214\) 4.64681 3.22601i 0.317649 0.220526i
\(215\) 0 0
\(216\) 0 0
\(217\) −1.97498 −0.134070
\(218\) 23.1764 16.0900i 1.56970 1.08975i
\(219\) 0 0
\(220\) 0 0
\(221\) 6.24430i 0.420037i
\(222\) 0 0
\(223\) −12.1579 −0.814152 −0.407076 0.913394i \(-0.633452\pi\)
−0.407076 + 0.913394i \(0.633452\pi\)
\(224\) −0.452186 + 4.19671i −0.0302130 + 0.280405i
\(225\) 0 0
\(226\) 9.72161 + 14.0032i 0.646672 + 0.931478i
\(227\) 20.7368i 1.37635i 0.725544 + 0.688176i \(0.241588\pi\)
−0.725544 + 0.688176i \(0.758412\pi\)
\(228\) 0 0
\(229\) 19.9504i 1.31836i 0.751987 + 0.659178i \(0.229096\pi\)
−0.751987 + 0.659178i \(0.770904\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.71836 + 18.4972i 0.309776 + 1.21440i
\(233\) −13.3386 −0.873844 −0.436922 0.899499i \(-0.643931\pi\)
−0.436922 + 0.899499i \(0.643931\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 12.8414 + 4.79097i 0.835906 + 0.311866i
\(237\) 0 0
\(238\) −1.28462 1.85039i −0.0832697 0.119943i
\(239\) −22.8864 −1.48040 −0.740201 0.672386i \(-0.765269\pi\)
−0.740201 + 0.672386i \(0.765269\pi\)
\(240\) 0 0
\(241\) 3.59283 0.231435 0.115717 0.993282i \(-0.463083\pi\)
0.115717 + 0.993282i \(0.463083\pi\)
\(242\) −14.3048 20.6049i −0.919549 1.32453i
\(243\) 0 0
\(244\) 12.0900 + 4.51064i 0.773985 + 0.288764i
\(245\) 0 0
\(246\) 0 0
\(247\) 5.07131 0.322680
\(248\) −7.25402 + 1.85039i −0.460631 + 0.117500i
\(249\) 0 0
\(250\) 0 0
\(251\) 8.82801i 0.557219i 0.960404 + 0.278609i \(0.0898735\pi\)
−0.960404 + 0.278609i \(0.910127\pi\)
\(252\) 0 0
\(253\) 40.1801i 2.52610i
\(254\) 3.39821 + 4.89484i 0.213222 + 0.307129i
\(255\) 0 0
\(256\) 2.27111 + 15.8380i 0.141944 + 0.989875i
\(257\) −22.2927 −1.39058 −0.695291 0.718728i \(-0.744725\pi\)
−0.695291 + 0.718728i \(0.744725\pi\)
\(258\) 0 0
\(259\) 0.801991i 0.0498333i
\(260\) 0 0
\(261\) 0 0
\(262\) 11.9892 8.32340i 0.740694 0.514222i
\(263\) −21.2014 −1.30733 −0.653667 0.756783i \(-0.726770\pi\)
−0.653667 + 0.756783i \(0.726770\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.50280 1.04331i 0.0921424 0.0639693i
\(267\) 0 0
\(268\) −13.9474 5.20359i −0.851971 0.317860i
\(269\) 14.6935i 0.895881i −0.894063 0.447940i \(-0.852158\pi\)
0.894063 0.447940i \(-0.147842\pi\)
\(270\) 0 0
\(271\) −20.2396 −1.22947 −0.614735 0.788734i \(-0.710737\pi\)
−0.614735 + 0.788734i \(0.710737\pi\)
\(272\) −6.45203 5.59283i −0.391212 0.339115i
\(273\) 0 0
\(274\) 12.1288 + 17.4705i 0.732727 + 1.05543i
\(275\) 0 0
\(276\) 0 0
\(277\) 0.518027i 0.0311252i −0.999879 0.0155626i \(-0.995046\pi\)
0.999879 0.0155626i \(-0.00495393\pi\)
\(278\) 11.0017 7.63785i 0.659837 0.458088i
\(279\) 0 0
\(280\) 0 0
\(281\) −13.7008 −0.817320 −0.408660 0.912687i \(-0.634004\pi\)
−0.408660 + 0.912687i \(0.634004\pi\)
\(282\) 0 0
\(283\) 18.0305i 1.07180i 0.844282 + 0.535900i \(0.180027\pi\)
−0.844282 + 0.535900i \(0.819973\pi\)
\(284\) 9.29362 24.9100i 0.551475 1.47814i
\(285\) 0 0
\(286\) −12.6468 18.2167i −0.747821 1.07718i
\(287\) −8.42701 −0.497431
\(288\) 0 0
\(289\) −12.4432 −0.731954
\(290\) 0 0
\(291\) 0 0
\(292\) −0.482632 + 1.29362i −0.0282439 + 0.0757032i
\(293\) 15.9792i 0.933513i −0.884386 0.466757i \(-0.845422\pi\)
0.884386 0.466757i \(-0.154578\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.751399 2.94568i −0.0436742 0.171214i
\(297\) 0 0
\(298\) 2.07884 1.44322i 0.120424 0.0836037i
\(299\) 21.9253i 1.26797i
\(300\) 0 0
\(301\) 5.55394i 0.320124i
\(302\) 8.58669 + 12.3684i 0.494108 + 0.711723i
\(303\) 0 0
\(304\) 4.54222 5.24002i 0.260514 0.300536i
\(305\) 0 0
\(306\) 0 0
\(307\) 22.5872i 1.28912i 0.764553 + 0.644561i \(0.222960\pi\)
−0.764553 + 0.644561i \(0.777040\pi\)
\(308\) −7.49534 2.79641i −0.427086 0.159341i
\(309\) 0 0
\(310\) 0 0
\(311\) 18.5872 1.05399 0.526993 0.849870i \(-0.323320\pi\)
0.526993 + 0.849870i \(0.323320\pi\)
\(312\) 0 0
\(313\) 29.3871 1.66106 0.830528 0.556977i \(-0.188039\pi\)
0.830528 + 0.556977i \(0.188039\pi\)
\(314\) 8.04502 5.58520i 0.454007 0.315191i
\(315\) 0 0
\(316\) −1.85039 + 4.95968i −0.104093 + 0.279004i
\(317\) 5.57201i 0.312955i −0.987682 0.156478i \(-0.949986\pi\)
0.987682 0.156478i \(-0.0500139\pi\)
\(318\) 0 0
\(319\) −36.1801 −2.02569
\(320\) 0 0
\(321\) 0 0
\(322\) −4.51064 6.49720i −0.251368 0.362075i
\(323\) 3.70079i 0.205917i
\(324\) 0 0
\(325\) 0 0
\(326\) −8.94602 + 6.21071i −0.495474 + 0.343980i
\(327\) 0 0
\(328\) −30.9520 + 7.89541i −1.70904 + 0.435951i
\(329\) −1.29362 −0.0713194
\(330\) 0 0
\(331\) 13.7396i 0.755199i 0.925969 + 0.377599i \(0.123250\pi\)
−0.925969 + 0.377599i \(0.876750\pi\)
\(332\) −10.9627 4.09003i −0.601655 0.224470i
\(333\) 0 0
\(334\) −2.60179 3.74767i −0.142364 0.205063i
\(335\) 0 0
\(336\) 0 0
\(337\) −20.7523 −1.13045 −0.565226 0.824936i \(-0.691211\pi\)
−0.565226 + 0.824936i \(0.691211\pi\)
\(338\) 3.58348 + 5.16170i 0.194915 + 0.280760i
\(339\) 0 0
\(340\) 0 0
\(341\) 14.1887i 0.768360i
\(342\) 0 0
\(343\) 10.0310 0.541623
\(344\) −5.20359 20.3994i −0.280559 1.09986i
\(345\) 0 0
\(346\) −7.46742 + 5.18420i −0.401451 + 0.278704i
\(347\) 4.73684i 0.254287i −0.991884 0.127143i \(-0.959419\pi\)
0.991884 0.127143i \(-0.0405809\pi\)
\(348\) 0 0
\(349\) 0.482632i 0.0258347i 0.999917 + 0.0129174i \(0.00411184\pi\)
−0.999917 + 0.0129174i \(0.995888\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −30.1500 3.24860i −1.60700 0.173151i
\(353\) −2.13466 −0.113617 −0.0568083 0.998385i \(-0.518092\pi\)
−0.0568083 + 0.998385i \(0.518092\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 5.30818 14.2277i 0.281333 0.754067i
\(357\) 0 0
\(358\) 9.45352 6.56304i 0.499634 0.346868i
\(359\) 9.59283 0.506290 0.253145 0.967428i \(-0.418535\pi\)
0.253145 + 0.967428i \(0.418535\pi\)
\(360\) 0 0
\(361\) 15.9944 0.841811
\(362\) 1.73367 1.20359i 0.0911194 0.0632590i
\(363\) 0 0
\(364\) −4.09003 1.52594i −0.214376 0.0799809i
\(365\) 0 0
\(366\) 0 0
\(367\) −34.0832 −1.77913 −0.889565 0.456809i \(-0.848992\pi\)
−0.889565 + 0.456809i \(0.848992\pi\)
\(368\) −22.6547 19.6378i −1.18096 1.02369i
\(369\) 0 0
\(370\) 0 0
\(371\) 5.76167i 0.299131i
\(372\) 0 0
\(373\) 4.33796i 0.224611i 0.993674 + 0.112306i \(0.0358236\pi\)
−0.993674 + 0.112306i \(0.964176\pi\)
\(374\) 13.2936 9.22900i 0.687397 0.477220i
\(375\) 0 0
\(376\) −4.75140 + 1.21201i −0.245035 + 0.0625047i
\(377\) −19.7426 −1.01680
\(378\) 0 0
\(379\) 6.90107i 0.354484i −0.984167 0.177242i \(-0.943282\pi\)
0.984167 0.177242i \(-0.0567176\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −5.55394 8.00000i −0.284165 0.409316i
\(383\) 22.3744 1.14328 0.571639 0.820506i \(-0.306308\pi\)
0.571639 + 0.820506i \(0.306308\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 13.2936 + 19.1484i 0.676627 + 0.974626i
\(387\) 0 0
\(388\) −9.91936 + 26.5872i −0.503579 + 1.34976i
\(389\) 11.0185i 0.558659i 0.960195 + 0.279330i \(0.0901122\pi\)
−0.960195 + 0.279330i \(0.909888\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 17.6587 4.50448i 0.891900 0.227511i
\(393\) 0 0
\(394\) 15.7666 10.9459i 0.794311 0.551445i
\(395\) 0 0
\(396\) 0 0
\(397\) 25.2549i 1.26751i −0.773536 0.633753i \(-0.781514\pi\)
0.773536 0.633753i \(-0.218486\pi\)
\(398\) 7.30207 + 10.5180i 0.366020 + 0.527221i
\(399\) 0 0
\(400\) 0 0
\(401\) −7.29362 −0.364226 −0.182113 0.983278i \(-0.558294\pi\)
−0.182113 + 0.983278i \(0.558294\pi\)
\(402\) 0 0
\(403\) 7.74244i 0.385678i
\(404\) −13.9404 5.20100i −0.693562 0.258759i
\(405\) 0 0
\(406\) −5.85039 + 4.06160i −0.290350 + 0.201574i
\(407\) 5.76167 0.285595
\(408\) 0 0
\(409\) 15.8504 0.783752 0.391876 0.920018i \(-0.371826\pi\)
0.391876 + 0.920018i \(0.371826\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 5.03229 13.4882i 0.247923 0.664518i
\(413\) 5.11355i 0.251622i
\(414\) 0 0
\(415\) 0 0
\(416\) −16.4522 1.77269i −0.806635 0.0869131i
\(417\) 0 0
\(418\) 7.49534 + 10.7964i 0.366609 + 0.528070i
\(419\) 8.02602i 0.392097i 0.980594 + 0.196048i \(0.0628109\pi\)
−0.980594 + 0.196048i \(0.937189\pi\)
\(420\) 0 0
\(421\) 22.9351i 1.11779i 0.829240 + 0.558893i \(0.188774\pi\)
−0.829240 + 0.558893i \(0.811226\pi\)
\(422\) −2.94568 + 2.04502i −0.143393 + 0.0995498i
\(423\) 0 0
\(424\) 5.39821 + 21.1624i 0.262160 + 1.02774i
\(425\) 0 0
\(426\) 0 0
\(427\) 4.81434i 0.232982i
\(428\) 7.49534 + 2.79641i 0.362301 + 0.135170i
\(429\) 0 0
\(430\) 0 0
\(431\) 35.0665 1.68909 0.844547 0.535481i \(-0.179870\pi\)
0.844547 + 0.535481i \(0.179870\pi\)
\(432\) 0 0
\(433\) −17.0773 −0.820682 −0.410341 0.911932i \(-0.634590\pi\)
−0.410341 + 0.911932i \(0.634590\pi\)
\(434\) −1.59283 2.29434i −0.0764583 0.110132i
\(435\) 0 0
\(436\) 37.3836 + 13.9474i 1.79035 + 0.667958i
\(437\) 12.9944i 0.621607i
\(438\) 0 0
\(439\) 8.53885 0.407537 0.203769 0.979019i \(-0.434681\pi\)
0.203769 + 0.979019i \(0.434681\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 7.25402 5.03605i 0.345039 0.239541i
\(443\) 20.7368i 0.985237i 0.870245 + 0.492619i \(0.163960\pi\)
−0.870245 + 0.492619i \(0.836040\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −9.80538 14.1238i −0.464298 0.668783i
\(447\) 0 0
\(448\) −5.24002 + 2.85936i −0.247568 + 0.135092i
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) 60.5414i 2.85078i
\(452\) −8.42701 + 22.5872i −0.396373 + 1.06241i
\(453\) 0 0
\(454\) −24.0900 + 16.7243i −1.13060 + 0.784912i
\(455\) 0 0
\(456\) 0 0
\(457\) −1.28462 −0.0600921 −0.0300461 0.999549i \(-0.509565\pi\)
−0.0300461 + 0.999549i \(0.509565\pi\)
\(458\) −23.1764 + 16.0900i −1.08296 + 0.751838i
\(459\) 0 0
\(460\) 0 0
\(461\) 15.7033i 0.731374i −0.930738 0.365687i \(-0.880834\pi\)
0.930738 0.365687i \(-0.119166\pi\)
\(462\) 0 0
\(463\) −18.7215 −0.870064 −0.435032 0.900415i \(-0.643263\pi\)
−0.435032 + 0.900415i \(0.643263\pi\)
\(464\) −17.6829 + 20.3994i −0.820906 + 0.947018i
\(465\) 0 0
\(466\) −10.7577 15.4955i −0.498339 0.717817i
\(467\) 2.14961i 0.0994719i −0.998762 0.0497360i \(-0.984162\pi\)
0.998762 0.0497360i \(-0.0158380\pi\)
\(468\) 0 0
\(469\) 5.55394i 0.256457i
\(470\) 0 0
\(471\) 0 0
\(472\) 4.79097 + 18.7819i 0.220522 + 0.864505i
\(473\) 39.9007 1.83464
\(474\) 0 0
\(475\) 0 0
\(476\) 1.11355 2.98470i 0.0510396 0.136803i
\(477\) 0 0
\(478\) −18.4580 26.5872i −0.844249 1.21607i
\(479\) 12.1801 0.556521 0.278261 0.960506i \(-0.410242\pi\)
0.278261 + 0.960506i \(0.410242\pi\)
\(480\) 0 0
\(481\) 3.14401 0.143355
\(482\) 2.89763 + 4.17380i 0.131983 + 0.190111i
\(483\) 0 0
\(484\) 12.3999 33.2359i 0.563631 1.51072i
\(485\) 0 0
\(486\) 0 0
\(487\) −25.7678 −1.16765 −0.583826 0.811879i \(-0.698445\pi\)
−0.583826 + 0.811879i \(0.698445\pi\)
\(488\) 4.51064 + 17.6829i 0.204187 + 0.800466i
\(489\) 0 0
\(490\) 0 0
\(491\) 16.7724i 0.756927i 0.925616 + 0.378464i \(0.123547\pi\)
−0.925616 + 0.378464i \(0.876453\pi\)
\(492\) 0 0
\(493\) 14.4072i 0.648866i
\(494\) 4.09003 + 5.89135i 0.184019 + 0.265065i
\(495\) 0 0
\(496\) −8.00000 6.93466i −0.359211 0.311375i
\(497\) 9.91936 0.444944
\(498\) 0 0
\(499\) 17.6224i 0.788888i 0.918920 + 0.394444i \(0.129063\pi\)
−0.918920 + 0.394444i \(0.870937\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −10.2555 + 7.11982i −0.457726 + 0.317773i
\(503\) −27.1263 −1.20950 −0.604752 0.796414i \(-0.706728\pi\)
−0.604752 + 0.796414i \(0.706728\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 46.6773 32.4054i 2.07506 1.44059i
\(507\) 0 0
\(508\) −2.94568 + 7.89541i −0.130693 + 0.350302i
\(509\) 15.9782i 0.708220i 0.935204 + 0.354110i \(0.115216\pi\)
−0.935204 + 0.354110i \(0.884784\pi\)
\(510\) 0 0
\(511\) −0.515128 −0.0227879
\(512\) −16.5674 + 15.4118i −0.732181 + 0.681110i
\(513\) 0 0
\(514\) −17.9792 25.8975i −0.793027 1.14229i
\(515\) 0 0
\(516\) 0 0
\(517\) 9.29362i 0.408733i
\(518\) 0.931674 0.646809i 0.0409354 0.0284191i
\(519\) 0 0
\(520\) 0 0
\(521\) −0.886447 −0.0388359 −0.0194180 0.999811i \(-0.506181\pi\)
−0.0194180 + 0.999811i \(0.506181\pi\)
\(522\) 0 0
\(523\) 41.7729i 1.82660i 0.407286 + 0.913301i \(0.366475\pi\)
−0.407286 + 0.913301i \(0.633525\pi\)
\(524\) 19.3386 + 7.21500i 0.844812 + 0.315189i
\(525\) 0 0
\(526\) −17.0990 24.6297i −0.745552 1.07391i
\(527\) 5.65004 0.246120
\(528\) 0 0
\(529\) 33.1801 1.44261
\(530\) 0 0
\(531\) 0 0
\(532\) 2.42402 + 0.904373i 0.105095 + 0.0392095i
\(533\) 33.0361i 1.43095i
\(534\) 0 0
\(535\) 0 0
\(536\) −5.20359 20.3994i −0.224761 0.881120i
\(537\) 0 0
\(538\) 17.0695 11.8504i 0.735919 0.510907i
\(539\) 34.5400i 1.48774i
\(540\) 0 0
\(541\) 4.47705i 0.192483i −0.995358 0.0962417i \(-0.969318\pi\)
0.995358 0.0962417i \(-0.0306822\pi\)
\(542\) −16.3233 23.5124i −0.701148 1.00995i
\(543\) 0 0
\(544\) 1.29362 12.0060i 0.0554634 0.514752i
\(545\) 0 0
\(546\) 0 0
\(547\) 14.3297i 0.612692i 0.951920 + 0.306346i \(0.0991065\pi\)
−0.951920 + 0.306346i \(0.900893\pi\)
\(548\) −10.5136 + 28.1801i −0.449120 + 1.20379i
\(549\) 0 0
\(550\) 0 0
\(551\) 11.7008 0.498470
\(552\) 0 0
\(553\) −1.97498 −0.0839848
\(554\) 0.601793 0.417790i 0.0255677 0.0177502i
\(555\) 0 0
\(556\) 17.7458 + 6.62073i 0.752590 + 0.280782i
\(557\) 2.68556i 0.113791i 0.998380 + 0.0568954i \(0.0181201\pi\)
−0.998380 + 0.0568954i \(0.981880\pi\)
\(558\) 0 0
\(559\) 21.7729 0.920895
\(560\) 0 0
\(561\) 0 0
\(562\) −11.0497 15.9162i −0.466105 0.671386i
\(563\) 20.7368i 0.873954i −0.899473 0.436977i \(-0.856049\pi\)
0.899473 0.436977i \(-0.143951\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −20.9460 + 14.5416i −0.880427 + 0.611230i
\(567\) 0 0
\(568\) 36.4334 9.29362i 1.52871 0.389952i
\(569\) −4.40717 −0.184758 −0.0923791 0.995724i \(-0.529447\pi\)
−0.0923791 + 0.995724i \(0.529447\pi\)
\(570\) 0 0
\(571\) 23.6590i 0.990098i 0.868865 + 0.495049i \(0.164850\pi\)
−0.868865 + 0.495049i \(0.835150\pi\)
\(572\) 10.9627 29.3836i 0.458372 1.22859i
\(573\) 0 0
\(574\) −6.79641 9.78968i −0.283677 0.408613i
\(575\) 0 0
\(576\) 0 0
\(577\) 6.56366 0.273249 0.136624 0.990623i \(-0.456375\pi\)
0.136624 + 0.990623i \(0.456375\pi\)
\(578\) −10.0355 14.4553i −0.417422 0.601262i
\(579\) 0 0
\(580\) 0 0
\(581\) 4.36542i 0.181108i
\(582\) 0 0
\(583\) −41.3931 −1.71433
\(584\) −1.89204 + 0.482632i −0.0782933 + 0.0199715i
\(585\) 0 0
\(586\) 18.5630 12.8873i 0.766832 0.532368i
\(587\) 16.2992i 0.672741i −0.941730 0.336370i \(-0.890801\pi\)
0.941730 0.336370i \(-0.109199\pi\)
\(588\) 0 0
\(589\) 4.58868i 0.189073i
\(590\) 0 0
\(591\) 0 0
\(592\) 2.81599 3.24860i 0.115737 0.133517i
\(593\) −16.3233 −0.670319 −0.335160 0.942161i \(-0.608790\pi\)
−0.335160 + 0.942161i \(0.608790\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.35319 + 1.25103i 0.137352 + 0.0512443i
\(597\) 0 0
\(598\) 25.4707 17.6829i 1.04157 0.723106i
\(599\) 25.5928 1.04569 0.522847 0.852426i \(-0.324870\pi\)
0.522847 + 0.852426i \(0.324870\pi\)
\(600\) 0 0
\(601\) 29.9225 1.22056 0.610282 0.792184i \(-0.291056\pi\)
0.610282 + 0.792184i \(0.291056\pi\)
\(602\) 6.45203 4.47928i 0.262965 0.182562i
\(603\) 0 0
\(604\) −7.44322 + 19.9504i −0.302860 + 0.811768i
\(605\) 0 0
\(606\) 0 0
\(607\) 20.6965 0.840046 0.420023 0.907513i \(-0.362022\pi\)
0.420023 + 0.907513i \(0.362022\pi\)
\(608\) 9.75065 + 1.05061i 0.395441 + 0.0426079i
\(609\) 0 0
\(610\) 0 0
\(611\) 5.07131i 0.205163i
\(612\) 0 0
\(613\) 22.6676i 0.915537i 0.889071 + 0.457769i \(0.151351\pi\)
−0.889071 + 0.457769i \(0.848649\pi\)
\(614\) −26.2396 + 18.2167i −1.05895 + 0.735166i
\(615\) 0 0
\(616\) −2.79641 10.9627i −0.112671 0.441698i
\(617\) 22.1966 0.893603 0.446802 0.894633i \(-0.352563\pi\)
0.446802 + 0.894633i \(0.352563\pi\)
\(618\) 0 0
\(619\) 16.8204i 0.676070i −0.941133 0.338035i \(-0.890238\pi\)
0.941133 0.338035i \(-0.109762\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 14.9907 + 21.5928i 0.601071 + 0.865794i
\(623\) 5.66558 0.226987
\(624\) 0 0
\(625\) 0 0
\(626\) 23.7008 + 34.1390i 0.947274 + 1.36447i
\(627\) 0 0
\(628\) 12.9767 + 4.84143i 0.517825 + 0.193194i
\(629\) 2.29434i 0.0914813i
\(630\) 0 0
\(631\) −44.1205 −1.75641 −0.878204 0.478285i \(-0.841258\pi\)
−0.878204 + 0.478285i \(0.841258\pi\)
\(632\) −7.25402 + 1.85039i −0.288549 + 0.0736047i
\(633\) 0 0
\(634\) 6.47301 4.49384i 0.257076 0.178473i
\(635\) 0 0
\(636\) 0 0
\(637\) 18.8477i 0.746773i
\(638\) −29.1794 42.0305i −1.15522 1.66400i
\(639\) 0 0
\(640\) 0 0
\(641\) 1.18566 0.0468307 0.0234154 0.999726i \(-0.492546\pi\)
0.0234154 + 0.999726i \(0.492546\pi\)
\(642\) 0 0
\(643\) 22.5872i 0.890754i −0.895343 0.445377i \(-0.853070\pi\)
0.895343 0.445377i \(-0.146930\pi\)
\(644\) 3.90997 10.4800i 0.154074 0.412971i
\(645\) 0 0
\(646\) −4.29921 + 2.98470i −0.169150 + 0.117431i
\(647\) −19.7090 −0.774842 −0.387421 0.921903i \(-0.626634\pi\)
−0.387421 + 0.921903i \(0.626634\pi\)
\(648\) 0 0
\(649\) −36.7368 −1.44205
\(650\) 0 0
\(651\) 0 0
\(652\) −14.4300 5.38365i −0.565122 0.210840i
\(653\) 44.4585i 1.73979i 0.493234 + 0.869897i \(0.335815\pi\)
−0.493234 + 0.869897i \(0.664185\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −34.1350 29.5894i −1.33275 1.15527i
\(657\) 0 0
\(658\) −1.04331 1.50280i −0.0406723 0.0585852i
\(659\) 41.5863i 1.61997i 0.586448 + 0.809987i \(0.300526\pi\)
−0.586448 + 0.809987i \(0.699474\pi\)
\(660\) 0 0
\(661\) 12.0060i 0.466978i −0.972359 0.233489i \(-0.924986\pi\)
0.972359 0.233489i \(-0.0750143\pi\)
\(662\) −15.9614 + 11.0811i −0.620356 + 0.430678i
\(663\) 0 0
\(664\) −4.09003 16.0340i −0.158724 0.622239i
\(665\) 0 0
\(666\) 0 0
\(667\) 50.5872i 1.95875i
\(668\) 2.25532 6.04502i 0.0872609 0.233889i
\(669\) 0 0
\(670\) 0 0
\(671\) −34.5872 −1.33523
\(672\) 0 0
\(673\) −14.5080 −0.559244 −0.279622 0.960110i \(-0.590209\pi\)
−0.279622 + 0.960110i \(0.590209\pi\)
\(674\) −16.7368 24.1080i −0.644679 0.928607i
\(675\) 0 0
\(676\) −3.10627 + 8.32586i −0.119472 + 0.320226i
\(677\) 43.8600i 1.68568i −0.538166 0.842839i \(-0.680883\pi\)
0.538166 0.842839i \(-0.319117\pi\)
\(678\) 0 0
\(679\) −10.5872 −0.406301
\(680\) 0 0
\(681\) 0 0
\(682\) 16.4830 11.4432i 0.631168 0.438184i
\(683\) 5.33527i 0.204148i −0.994777 0.102074i \(-0.967452\pi\)
0.994777 0.102074i \(-0.0325479\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 8.09003 + 11.6530i 0.308879 + 0.444915i
\(687\) 0 0
\(688\) 19.5013 22.4972i 0.743480 0.857698i
\(689\) −22.5872 −0.860505
\(690\) 0 0
\(691\) 39.7710i 1.51296i 0.654016 + 0.756480i \(0.273083\pi\)
−0.654016 + 0.756480i \(0.726917\pi\)
\(692\) −12.0450 4.49383i −0.457882 0.170830i
\(693\) 0 0
\(694\) 5.50280 3.82028i 0.208883 0.145016i
\(695\) 0 0
\(696\) 0 0
\(697\) 24.1080 0.913157
\(698\) −0.560675 + 0.389245i −0.0212219 + 0.0147331i
\(699\) 0 0
\(700\) 0 0
\(701\) 27.5015i 1.03872i 0.854556 + 0.519359i \(0.173829\pi\)
−0.854556 + 0.519359i \(0.826171\pi\)
\(702\) 0 0
\(703\) −1.86335 −0.0702775
\(704\) −20.5422 37.6454i −0.774214 1.41881i
\(705\) 0 0
\(706\) −1.72161 2.47984i −0.0647937 0.0933300i
\(707\) 5.55118i 0.208774i
\(708\) 0 0
\(709\) 0.111632i 0.00419244i 0.999998 + 0.00209622i \(0.000667249\pi\)
−0.999998 + 0.00209622i \(0.999333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 20.8094 5.30818i 0.779866 0.198932i
\(713\) 19.8387 0.742966
\(714\) 0 0
\(715\) 0 0
\(716\) 15.2486 + 5.68906i 0.569867 + 0.212610i
\(717\) 0 0
\(718\) 7.73665 + 11.1440i 0.288729 + 0.415891i
\(719\) −10.7064 −0.399281 −0.199640 0.979869i \(-0.563977\pi\)
−0.199640 + 0.979869i \(0.563977\pi\)
\(720\) 0 0
\(721\) 5.37112 0.200031
\(722\) 12.8995 + 18.5807i 0.480071 + 0.691503i
\(723\) 0 0
\(724\) 2.79641 + 1.04331i 0.103928 + 0.0387742i
\(725\) 0 0
\(726\) 0 0
\(727\) 25.6562 0.951536 0.475768 0.879571i \(-0.342170\pi\)
0.475768 + 0.879571i \(0.342170\pi\)
\(728\) −1.52594 5.98207i −0.0565551 0.221710i
\(729\) 0 0
\(730\) 0 0
\(731\) 15.8888i 0.587667i
\(732\) 0 0
\(733\) 30.3684i 1.12168i −0.827923 0.560842i \(-0.810478\pi\)
0.827923 0.560842i \(-0.189522\pi\)
\(734\) −27.4882 39.5945i −1.01461 1.46146i
\(735\) 0 0
\(736\) 4.54222 42.1560i 0.167428 1.55389i
\(737\) 39.9007 1.46976
\(738\) 0 0
\(739\) 20.1917i 0.742763i 0.928480 + 0.371381i \(0.121116\pi\)
−0.928480 + 0.371381i \(0.878884\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −6.69335 + 4.64681i −0.245720 + 0.170590i
\(743\) 46.3863 1.70175 0.850875 0.525369i \(-0.176073\pi\)
0.850875 + 0.525369i \(0.176073\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −5.03942 + 3.49858i −0.184506 + 0.128092i
\(747\) 0 0
\(748\) 21.4427 + 8.00000i 0.784023 + 0.292509i
\(749\) 2.98470i 0.109059i
\(750\) 0 0
\(751\) −27.1261 −0.989845 −0.494922 0.868937i \(-0.664804\pi\)
−0.494922 + 0.868937i \(0.664804\pi\)
\(752\) −5.24002 4.54222i −0.191084 0.165638i
\(753\) 0 0
\(754\) −15.9225 22.9351i −0.579863 0.835245i
\(755\) 0 0
\(756\) 0 0
\(757\) 45.2549i 1.64482i 0.568898 + 0.822408i \(0.307370\pi\)
−0.568898 + 0.822408i \(0.692630\pi\)
\(758\) 8.01699 5.56574i 0.291190 0.202157i
\(759\) 0 0
\(760\) 0 0
\(761\) −16.8864 −0.612133 −0.306067 0.952010i \(-0.599013\pi\)
−0.306067 + 0.952010i \(0.599013\pi\)
\(762\) 0 0
\(763\) 14.8864i 0.538926i
\(764\) 4.81434 12.9041i 0.174177 0.466852i
\(765\) 0 0
\(766\) 18.0450 + 25.9924i 0.651993 + 0.939142i
\(767\) −20.0464 −0.723835
\(768\) 0 0
\(769\) 16.3297 0.588863 0.294431 0.955673i \(-0.404870\pi\)
0.294431 + 0.955673i \(0.404870\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −11.5233 + 30.8864i −0.414734 + 1.11163i
\(773\) 41.3144i 1.48598i −0.669304 0.742989i \(-0.733408\pi\)
0.669304 0.742989i \(-0.266592\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −38.8864 + 9.91936i −1.39594 + 0.356084i
\(777\) 0 0
\(778\) −12.8002 + 8.88645i −0.458909 + 0.318595i
\(779\) 19.5794i 0.701503i
\(780\) 0 0
\(781\) 71.2628i 2.54998i
\(782\) 12.9041 + 18.5872i 0.461448 + 0.664678i
\(783\) 0 0
\(784\) 19.4747 + 16.8813i 0.695525 + 0.602904i
\(785\) 0 0
\(786\) 0 0
\(787\) 11.4849i 0.409391i 0.978826 + 0.204696i \(0.0656205\pi\)
−0.978826 + 0.204696i \(0.934380\pi\)
\(788\) 25.4317 + 9.48824i 0.905966 + 0.338005i
\(789\) 0 0
\(790\) 0 0
\(791\) −8.99440 −0.319804
\(792\) 0 0
\(793\) −18.8735 −0.670216
\(794\) 29.3386 20.3681i 1.04119 0.722838i
\(795\) 0 0
\(796\) −6.32967 + 16.9657i −0.224349 + 0.601332i
\(797\) 45.4945i