Properties

Label 1800.2.k.u.901.7
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 901.7
Root \(0.450129 + 1.34067i\) of defining polynomial
Character \(\chi\) \(=\) 1800.901
Dual form 1800.2.k.u.901.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.450129 - 1.34067i) q^{2} +(-1.59477 - 1.20695i) q^{4} +2.64265 q^{7} +(-2.33596 + 1.59477i) q^{8} +O(q^{10})\) \(q+(0.450129 - 1.34067i) q^{2} +(-1.59477 - 1.20695i) q^{4} +2.64265 q^{7} +(-2.33596 + 1.59477i) q^{8} +1.51363i q^{11} +3.87086i q^{13} +(1.18953 - 3.54291i) q^{14} +(1.08656 + 3.84959i) q^{16} -3.31415 q^{17} +7.08582i q^{19} +(2.02927 + 0.681331i) q^{22} -4.82778 q^{23} +(5.18953 + 1.74239i) q^{26} +(-4.21441 - 3.18953i) q^{28} +2.18513i q^{29} -7.36266 q^{31} +(5.65011 + 0.276098i) q^{32} +(-1.49180 + 4.44317i) q^{34} +7.87086i q^{37} +(9.49971 + 3.18953i) q^{38} -8.72532 q^{41} +1.01641i q^{43} +(1.82687 - 2.41389i) q^{44} +(-2.17313 + 6.47244i) q^{46} +7.08582 q^{47} -0.0164068 q^{49} +(4.67192 - 6.17313i) q^{52} -4.50820i q^{53} +(-6.17313 + 4.21441i) q^{56} +(2.92953 + 0.983593i) q^{58} +6.79893i q^{59} -3.60104i q^{61} +(-3.31415 + 9.87086i) q^{62} +(2.91344 - 7.45063i) q^{64} +1.01641i q^{67} +(5.28530 + 4.00000i) q^{68} +6.72532 q^{71} +15.5146 q^{73} +(10.5522 + 3.54291i) q^{74} +(8.55220 - 11.3002i) q^{76} +4.00000i q^{77} -7.36266 q^{79} +(-3.92752 + 11.6977i) q^{82} -7.74173i q^{83} +(1.36266 + 0.457515i) q^{86} +(-2.41389 - 3.53579i) q^{88} -14.7581 q^{89} +10.2293i q^{91} +(7.69919 + 5.82687i) q^{92} +(3.18953 - 9.49971i) q^{94} +11.1444 q^{97} +(-0.00738516 + 0.0219960i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{4}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.450129 1.34067i 0.318290 0.947994i
\(3\) 0 0
\(4\) −1.59477 1.20695i −0.797384 0.603473i
\(5\) 0 0
\(6\) 0 0
\(7\) 2.64265 0.998827 0.499414 0.866364i \(-0.333549\pi\)
0.499414 + 0.866364i \(0.333549\pi\)
\(8\) −2.33596 + 1.59477i −0.825887 + 0.563835i
\(9\) 0 0
\(10\) 0 0
\(11\) 1.51363i 0.456377i 0.973617 + 0.228189i \(0.0732803\pi\)
−0.973617 + 0.228189i \(0.926720\pi\)
\(12\) 0 0
\(13\) 3.87086i 1.07358i 0.843714 + 0.536792i \(0.180364\pi\)
−0.843714 + 0.536792i \(0.819636\pi\)
\(14\) 1.18953 3.54291i 0.317916 0.946882i
\(15\) 0 0
\(16\) 1.08656 + 3.84959i 0.271641 + 0.962399i
\(17\) −3.31415 −0.803800 −0.401900 0.915684i \(-0.631650\pi\)
−0.401900 + 0.915684i \(0.631650\pi\)
\(18\) 0 0
\(19\) 7.08582i 1.62560i 0.582545 + 0.812799i \(0.302057\pi\)
−0.582545 + 0.812799i \(0.697943\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.02927 + 0.681331i 0.432643 + 0.145260i
\(23\) −4.82778 −1.00666 −0.503331 0.864094i \(-0.667892\pi\)
−0.503331 + 0.864094i \(0.667892\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 5.18953 + 1.74239i 1.01775 + 0.341711i
\(27\) 0 0
\(28\) −4.21441 3.18953i −0.796448 0.602765i
\(29\) 2.18513i 0.405769i 0.979203 + 0.202885i \(0.0650316\pi\)
−0.979203 + 0.202885i \(0.934968\pi\)
\(30\) 0 0
\(31\) −7.36266 −1.32237 −0.661187 0.750222i \(-0.729947\pi\)
−0.661187 + 0.750222i \(0.729947\pi\)
\(32\) 5.65011 + 0.276098i 0.998808 + 0.0488076i
\(33\) 0 0
\(34\) −1.49180 + 4.44317i −0.255841 + 0.761997i
\(35\) 0 0
\(36\) 0 0
\(37\) 7.87086i 1.29396i 0.762506 + 0.646981i \(0.223969\pi\)
−0.762506 + 0.646981i \(0.776031\pi\)
\(38\) 9.49971 + 3.18953i 1.54106 + 0.517411i
\(39\) 0 0
\(40\) 0 0
\(41\) −8.72532 −1.36267 −0.681333 0.731973i \(-0.738600\pi\)
−0.681333 + 0.731973i \(0.738600\pi\)
\(42\) 0 0
\(43\) 1.01641i 0.155001i 0.996992 + 0.0775003i \(0.0246939\pi\)
−0.996992 + 0.0775003i \(0.975306\pi\)
\(44\) 1.82687 2.41389i 0.275411 0.363908i
\(45\) 0 0
\(46\) −2.17313 + 6.47244i −0.320410 + 0.954309i
\(47\) 7.08582 1.03357 0.516786 0.856114i \(-0.327128\pi\)
0.516786 + 0.856114i \(0.327128\pi\)
\(48\) 0 0
\(49\) −0.0164068 −0.00234382
\(50\) 0 0
\(51\) 0 0
\(52\) 4.67192 6.17313i 0.647879 0.856059i
\(53\) 4.50820i 0.619249i −0.950859 0.309625i \(-0.899797\pi\)
0.950859 0.309625i \(-0.100203\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −6.17313 + 4.21441i −0.824919 + 0.563174i
\(57\) 0 0
\(58\) 2.92953 + 0.983593i 0.384667 + 0.129152i
\(59\) 6.79893i 0.885145i 0.896733 + 0.442573i \(0.145934\pi\)
−0.896733 + 0.442573i \(0.854066\pi\)
\(60\) 0 0
\(61\) 3.60104i 0.461065i −0.973065 0.230533i \(-0.925953\pi\)
0.973065 0.230533i \(-0.0740469\pi\)
\(62\) −3.31415 + 9.87086i −0.420898 + 1.25360i
\(63\) 0 0
\(64\) 2.91344 7.45063i 0.364180 0.931329i
\(65\) 0 0
\(66\) 0 0
\(67\) 1.01641i 0.124174i 0.998071 + 0.0620869i \(0.0197756\pi\)
−0.998071 + 0.0620869i \(0.980224\pi\)
\(68\) 5.28530 + 4.00000i 0.640937 + 0.485071i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.72532 0.798149 0.399074 0.916919i \(-0.369331\pi\)
0.399074 + 0.916919i \(0.369331\pi\)
\(72\) 0 0
\(73\) 15.5146 1.81585 0.907925 0.419132i \(-0.137666\pi\)
0.907925 + 0.419132i \(0.137666\pi\)
\(74\) 10.5522 + 3.54291i 1.22667 + 0.411855i
\(75\) 0 0
\(76\) 8.55220 11.3002i 0.981004 1.29622i
\(77\) 4.00000i 0.455842i
\(78\) 0 0
\(79\) −7.36266 −0.828364 −0.414182 0.910194i \(-0.635932\pi\)
−0.414182 + 0.910194i \(0.635932\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.92752 + 11.6977i −0.433723 + 1.29180i
\(83\) 7.74173i 0.849765i −0.905248 0.424883i \(-0.860315\pi\)
0.905248 0.424883i \(-0.139685\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.36266 + 0.457515i 0.146940 + 0.0493351i
\(87\) 0 0
\(88\) −2.41389 3.53579i −0.257322 0.376916i
\(89\) −14.7581 −1.56436 −0.782180 0.623053i \(-0.785892\pi\)
−0.782180 + 0.623053i \(0.785892\pi\)
\(90\) 0 0
\(91\) 10.2293i 1.07233i
\(92\) 7.69919 + 5.82687i 0.802696 + 0.607493i
\(93\) 0 0
\(94\) 3.18953 9.49971i 0.328975 0.979820i
\(95\) 0 0
\(96\) 0 0
\(97\) 11.1444 1.13154 0.565769 0.824563i \(-0.308579\pi\)
0.565769 + 0.824563i \(0.308579\pi\)
\(98\) −0.00738516 + 0.0219960i −0.000746014 + 0.00222193i
\(99\) 0 0
\(100\) 0 0
\(101\) 13.3295i 1.32633i 0.748471 + 0.663167i \(0.230788\pi\)
−0.748471 + 0.663167i \(0.769212\pi\)
\(102\) 0 0
\(103\) −0.958386 −0.0944326 −0.0472163 0.998885i \(-0.515035\pi\)
−0.0472163 + 0.998885i \(0.515035\pi\)
\(104\) −6.17313 9.04219i −0.605325 0.886660i
\(105\) 0 0
\(106\) −6.04399 2.02927i −0.587044 0.197101i
\(107\) 4.00000i 0.386695i −0.981130 0.193347i \(-0.938066\pi\)
0.981130 0.193347i \(-0.0619344\pi\)
\(108\) 0 0
\(109\) 0.769233i 0.0736792i 0.999321 + 0.0368396i \(0.0117291\pi\)
−0.999321 + 0.0368396i \(0.988271\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.87141 + 10.1731i 0.271322 + 0.961270i
\(113\) 14.4585 1.36014 0.680071 0.733146i \(-0.261949\pi\)
0.680071 + 0.733146i \(0.261949\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 2.63734 3.48478i 0.244871 0.323554i
\(117\) 0 0
\(118\) 9.11509 + 3.06040i 0.839112 + 0.281733i
\(119\) −8.75814 −0.802857
\(120\) 0 0
\(121\) 8.70892 0.791720
\(122\) −4.82778 1.62093i −0.437087 0.146752i
\(123\) 0 0
\(124\) 11.7417 + 8.88633i 1.05444 + 0.798016i
\(125\) 0 0
\(126\) 0 0
\(127\) 11.5290 1.02303 0.511516 0.859274i \(-0.329084\pi\)
0.511516 + 0.859274i \(0.329084\pi\)
\(128\) −8.67738 7.25969i −0.766979 0.641672i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.37270i 0.644156i −0.946713 0.322078i \(-0.895619\pi\)
0.946713 0.322078i \(-0.104381\pi\)
\(132\) 0 0
\(133\) 18.7253i 1.62369i
\(134\) 1.36266 + 0.457515i 0.117716 + 0.0395232i
\(135\) 0 0
\(136\) 7.74173 5.28530i 0.663848 0.453211i
\(137\) 3.88792 0.332167 0.166084 0.986112i \(-0.446888\pi\)
0.166084 + 0.986112i \(0.446888\pi\)
\(138\) 0 0
\(139\) 14.6291i 1.24083i −0.784275 0.620414i \(-0.786965\pi\)
0.784275 0.620414i \(-0.213035\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.02727 9.01641i 0.254042 0.756640i
\(143\) −5.85907 −0.489960
\(144\) 0 0
\(145\) 0 0
\(146\) 6.98359 20.7999i 0.577966 1.72141i
\(147\) 0 0
\(148\) 9.49971 12.5522i 0.780871 1.03178i
\(149\) 11.0715i 0.907010i 0.891254 + 0.453505i \(0.149827\pi\)
−0.891254 + 0.453505i \(0.850173\pi\)
\(150\) 0 0
\(151\) 0.637339 0.0518659 0.0259329 0.999664i \(-0.491744\pi\)
0.0259329 + 0.999664i \(0.491744\pi\)
\(152\) −11.3002 16.5522i −0.916569 1.34256i
\(153\) 0 0
\(154\) 5.36266 + 1.80052i 0.432136 + 0.145090i
\(155\) 0 0
\(156\) 0 0
\(157\) 0.129135i 0.0103061i −0.999987 0.00515306i \(-0.998360\pi\)
0.999987 0.00515306i \(-0.00164028\pi\)
\(158\) −3.31415 + 9.87086i −0.263660 + 0.785284i
\(159\) 0 0
\(160\) 0 0
\(161\) −12.7581 −1.00548
\(162\) 0 0
\(163\) 19.4835i 1.52606i −0.646362 0.763031i \(-0.723710\pi\)
0.646362 0.763031i \(-0.276290\pi\)
\(164\) 13.9149 + 10.5310i 1.08657 + 0.822332i
\(165\) 0 0
\(166\) −10.3791 3.48478i −0.805572 0.270471i
\(167\) −1.80052 −0.139328 −0.0696641 0.997571i \(-0.522193\pi\)
−0.0696641 + 0.997571i \(0.522193\pi\)
\(168\) 0 0
\(169\) −1.98359 −0.152584
\(170\) 0 0
\(171\) 0 0
\(172\) 1.22675 1.62093i 0.0935386 0.123595i
\(173\) 23.2335i 1.76641i 0.468985 + 0.883206i \(0.344620\pi\)
−0.468985 + 0.883206i \(0.655380\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −5.82687 + 1.64466i −0.439217 + 0.123971i
\(177\) 0 0
\(178\) −6.64307 + 19.7857i −0.497919 + 1.48300i
\(179\) 2.85664i 0.213515i 0.994285 + 0.106757i \(0.0340468\pi\)
−0.994285 + 0.106757i \(0.965953\pi\)
\(180\) 0 0
\(181\) 5.28530i 0.392853i 0.980519 + 0.196427i \(0.0629337\pi\)
−0.980519 + 0.196427i \(0.937066\pi\)
\(182\) 13.7141 + 4.60453i 1.01656 + 0.341310i
\(183\) 0 0
\(184\) 11.2775 7.69919i 0.831390 0.567592i
\(185\) 0 0
\(186\) 0 0
\(187\) 5.01641i 0.366836i
\(188\) −11.3002 8.55220i −0.824154 0.623733i
\(189\) 0 0
\(190\) 0 0
\(191\) 5.96719 0.431770 0.215885 0.976419i \(-0.430736\pi\)
0.215885 + 0.976419i \(0.430736\pi\)
\(192\) 0 0
\(193\) −14.9409 −1.07547 −0.537733 0.843115i \(-0.680719\pi\)
−0.537733 + 0.843115i \(0.680719\pi\)
\(194\) 5.01641 14.9409i 0.360157 1.07269i
\(195\) 0 0
\(196\) 0.0261649 + 0.0198021i 0.00186892 + 0.00141443i
\(197\) 3.23353i 0.230379i 0.993344 + 0.115190i \(0.0367476\pi\)
−0.993344 + 0.115190i \(0.963252\pi\)
\(198\) 0 0
\(199\) −8.12080 −0.575668 −0.287834 0.957680i \(-0.592935\pi\)
−0.287834 + 0.957680i \(0.592935\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 17.8704 + 6.00000i 1.25736 + 0.422159i
\(203\) 5.77454i 0.405293i
\(204\) 0 0
\(205\) 0 0
\(206\) −0.431398 + 1.28488i −0.0300569 + 0.0895215i
\(207\) 0 0
\(208\) −14.9013 + 4.20594i −1.03322 + 0.291630i
\(209\) −10.7253 −0.741886
\(210\) 0 0
\(211\) 13.7141i 0.944119i −0.881567 0.472059i \(-0.843511\pi\)
0.881567 0.472059i \(-0.156489\pi\)
\(212\) −5.44116 + 7.18953i −0.373700 + 0.493779i
\(213\) 0 0
\(214\) −5.36266 1.80052i −0.366584 0.123081i
\(215\) 0 0
\(216\) 0 0
\(217\) −19.4569 −1.32082
\(218\) 1.03128 + 0.346255i 0.0698474 + 0.0234513i
\(219\) 0 0
\(220\) 0 0
\(221\) 12.8286i 0.862947i
\(222\) 0 0
\(223\) −9.84472 −0.659251 −0.329626 0.944112i \(-0.606923\pi\)
−0.329626 + 0.944112i \(0.606923\pi\)
\(224\) 14.9313 + 0.729629i 0.997637 + 0.0487504i
\(225\) 0 0
\(226\) 6.50820 19.3840i 0.432919 1.28941i
\(227\) 5.70892i 0.378914i −0.981889 0.189457i \(-0.939327\pi\)
0.981889 0.189457i \(-0.0606728\pi\)
\(228\) 0 0
\(229\) 0.769233i 0.0508324i −0.999677 0.0254162i \(-0.991909\pi\)
0.999677 0.0254162i \(-0.00809109\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.48478 5.10439i −0.228787 0.335120i
\(233\) −18.4008 −1.20548 −0.602739 0.797939i \(-0.705924\pi\)
−0.602739 + 0.797939i \(0.705924\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 8.20594 10.8427i 0.534161 0.705800i
\(237\) 0 0
\(238\) −3.94229 + 11.7417i −0.255541 + 0.761103i
\(239\) −10.0328 −0.648969 −0.324484 0.945891i \(-0.605191\pi\)
−0.324484 + 0.945891i \(0.605191\pi\)
\(240\) 0 0
\(241\) 10.7581 0.692992 0.346496 0.938051i \(-0.387371\pi\)
0.346496 + 0.938051i \(0.387371\pi\)
\(242\) 3.92014 11.6757i 0.251996 0.750545i
\(243\) 0 0
\(244\) −4.34625 + 5.74281i −0.278240 + 0.367646i
\(245\) 0 0
\(246\) 0 0
\(247\) −27.4282 −1.74522
\(248\) 17.1989 11.7417i 1.09213 0.745601i
\(249\) 0 0
\(250\) 0 0
\(251\) 12.6580i 0.798966i 0.916741 + 0.399483i \(0.130810\pi\)
−0.916741 + 0.399483i \(0.869190\pi\)
\(252\) 0 0
\(253\) 7.30749i 0.459418i
\(254\) 5.18953 15.4565i 0.325620 0.969827i
\(255\) 0 0
\(256\) −13.6388 + 8.36566i −0.852422 + 0.522854i
\(257\) 13.3110 0.830316 0.415158 0.909749i \(-0.363726\pi\)
0.415158 + 0.909749i \(0.363726\pi\)
\(258\) 0 0
\(259\) 20.7999i 1.29244i
\(260\) 0 0
\(261\) 0 0
\(262\) −9.88432 3.31867i −0.610656 0.205028i
\(263\) 18.4256 1.13617 0.568087 0.822969i \(-0.307684\pi\)
0.568087 + 0.822969i \(0.307684\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 25.1044 + 8.42882i 1.53925 + 0.516804i
\(267\) 0 0
\(268\) 1.22675 1.62093i 0.0749356 0.0990142i
\(269\) 3.86940i 0.235921i 0.993018 + 0.117961i \(0.0376357\pi\)
−0.993018 + 0.117961i \(0.962364\pi\)
\(270\) 0 0
\(271\) −17.3955 −1.05670 −0.528350 0.849027i \(-0.677189\pi\)
−0.528350 + 0.849027i \(0.677189\pi\)
\(272\) −3.60104 12.7581i −0.218345 0.773576i
\(273\) 0 0
\(274\) 1.75007 5.21240i 0.105725 0.314893i
\(275\) 0 0
\(276\) 0 0
\(277\) 0.887271i 0.0533110i −0.999645 0.0266555i \(-0.991514\pi\)
0.999645 0.0266555i \(-0.00848571\pi\)
\(278\) −19.6128 6.58501i −1.17630 0.394943i
\(279\) 0 0
\(280\) 0 0
\(281\) 13.4835 0.804356 0.402178 0.915562i \(-0.368253\pi\)
0.402178 + 0.915562i \(0.368253\pi\)
\(282\) 0 0
\(283\) 28.4342i 1.69024i −0.534577 0.845120i \(-0.679529\pi\)
0.534577 0.845120i \(-0.320471\pi\)
\(284\) −10.7253 8.11710i −0.636431 0.481661i
\(285\) 0 0
\(286\) −2.63734 + 7.85505i −0.155949 + 0.464479i
\(287\) −23.0580 −1.36107
\(288\) 0 0
\(289\) −6.01641 −0.353906
\(290\) 0 0
\(291\) 0 0
\(292\) −24.7422 18.7253i −1.44793 1.09582i
\(293\) 7.99166i 0.466878i 0.972371 + 0.233439i \(0.0749979\pi\)
−0.972371 + 0.233439i \(0.925002\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −12.5522 18.3860i −0.729582 1.06867i
\(297\) 0 0
\(298\) 14.8431 + 4.98359i 0.859840 + 0.288692i
\(299\) 18.6877i 1.08074i
\(300\) 0 0
\(301\) 2.68601i 0.154819i
\(302\) 0.286885 0.854458i 0.0165084 0.0491685i
\(303\) 0 0
\(304\) −27.2775 + 7.69919i −1.56447 + 0.441579i
\(305\) 0 0
\(306\) 0 0
\(307\) 17.4506i 0.995961i −0.867188 0.497980i \(-0.834075\pi\)
0.867188 0.497980i \(-0.165925\pi\)
\(308\) 4.82778 6.37907i 0.275088 0.363481i
\(309\) 0 0
\(310\) 0 0
\(311\) −21.4506 −1.21635 −0.608177 0.793801i \(-0.708099\pi\)
−0.608177 + 0.793801i \(0.708099\pi\)
\(312\) 0 0
\(313\) −7.73879 −0.437422 −0.218711 0.975790i \(-0.570185\pi\)
−0.218711 + 0.975790i \(0.570185\pi\)
\(314\) −0.173127 0.0581276i −0.00977014 0.00328033i
\(315\) 0 0
\(316\) 11.7417 + 8.88633i 0.660524 + 0.499895i
\(317\) 11.2335i 0.630938i 0.948936 + 0.315469i \(0.102162\pi\)
−0.948936 + 0.315469i \(0.897838\pi\)
\(318\) 0 0
\(319\) −3.30749 −0.185184
\(320\) 0 0
\(321\) 0 0
\(322\) −5.74281 + 17.1044i −0.320034 + 0.953190i
\(323\) 23.4835i 1.30665i
\(324\) 0 0
\(325\) 0 0
\(326\) −26.1208 8.77008i −1.44670 0.485730i
\(327\) 0 0
\(328\) 20.3820 13.9149i 1.12541 0.768319i
\(329\) 18.7253 1.03236
\(330\) 0 0
\(331\) 8.00084i 0.439766i 0.975526 + 0.219883i \(0.0705676\pi\)
−0.975526 + 0.219883i \(0.929432\pi\)
\(332\) −9.34385 + 12.3463i −0.512810 + 0.677589i
\(333\) 0 0
\(334\) −0.810466 + 2.41389i −0.0443467 + 0.132082i
\(335\) 0 0
\(336\) 0 0
\(337\) 21.5692 1.17495 0.587474 0.809243i \(-0.300123\pi\)
0.587474 + 0.809243i \(0.300123\pi\)
\(338\) −0.892874 + 2.65933i −0.0485659 + 0.144649i
\(339\) 0 0
\(340\) 0 0
\(341\) 11.1444i 0.603501i
\(342\) 0 0
\(343\) −18.5419 −1.00117
\(344\) −1.62093 2.37429i −0.0873948 0.128013i
\(345\) 0 0
\(346\) 31.1484 + 10.4581i 1.67455 + 0.562231i
\(347\) 21.7089i 1.16540i 0.812689 + 0.582698i \(0.198003\pi\)
−0.812689 + 0.582698i \(0.801997\pi\)
\(348\) 0 0
\(349\) 24.7422i 1.32442i 0.749318 + 0.662211i \(0.230382\pi\)
−0.749318 + 0.662211i \(0.769618\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.417910 + 8.55220i −0.0222747 + 0.455834i
\(353\) 3.31415 0.176394 0.0881972 0.996103i \(-0.471889\pi\)
0.0881972 + 0.996103i \(0.471889\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 23.5358 + 17.8123i 1.24739 + 0.944048i
\(357\) 0 0
\(358\) 3.82979 + 1.28586i 0.202411 + 0.0679596i
\(359\) 16.7581 0.884461 0.442230 0.896902i \(-0.354187\pi\)
0.442230 + 0.896902i \(0.354187\pi\)
\(360\) 0 0
\(361\) −31.2088 −1.64257
\(362\) 7.08582 + 2.37907i 0.372422 + 0.125041i
\(363\) 0 0
\(364\) 12.3463 16.3134i 0.647120 0.855055i
\(365\) 0 0
\(366\) 0 0
\(367\) −28.5324 −1.48938 −0.744690 0.667411i \(-0.767403\pi\)
−0.744690 + 0.667411i \(0.767403\pi\)
\(368\) −5.24569 18.5850i −0.273451 0.968811i
\(369\) 0 0
\(370\) 0 0
\(371\) 11.9136i 0.618523i
\(372\) 0 0
\(373\) 37.5798i 1.94581i 0.231211 + 0.972904i \(0.425731\pi\)
−0.231211 + 0.972904i \(0.574269\pi\)
\(374\) −6.72532 2.25803i −0.347758 0.116760i
\(375\) 0 0
\(376\) −16.5522 + 11.3002i −0.853614 + 0.582765i
\(377\) −8.45836 −0.435628
\(378\) 0 0
\(379\) 6.74456i 0.346445i −0.984883 0.173222i \(-0.944582\pi\)
0.984883 0.173222i \(-0.0554179\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 2.68601 8.00000i 0.137428 0.409316i
\(383\) 21.8312 1.11552 0.557762 0.830001i \(-0.311660\pi\)
0.557762 + 0.830001i \(0.311660\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −6.72532 + 20.0307i −0.342310 + 1.01954i
\(387\) 0 0
\(388\) −17.7727 13.4506i −0.902270 0.682853i
\(389\) 8.81344i 0.446859i −0.974720 0.223429i \(-0.928275\pi\)
0.974720 0.223429i \(-0.0717252\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0.0383256 0.0261649i 0.00193573 0.00132153i
\(393\) 0 0
\(394\) 4.33508 + 1.45551i 0.218398 + 0.0733273i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.821644i 0.0412372i 0.999787 + 0.0206186i \(0.00656356\pi\)
−0.999787 + 0.0206186i \(0.993436\pi\)
\(398\) −3.65541 + 10.8873i −0.183229 + 0.545730i
\(399\) 0 0
\(400\) 0 0
\(401\) 12.7253 0.635472 0.317736 0.948179i \(-0.397077\pi\)
0.317736 + 0.948179i \(0.397077\pi\)
\(402\) 0 0
\(403\) 28.4999i 1.41968i
\(404\) 16.0880 21.2574i 0.800407 1.05760i
\(405\) 0 0
\(406\) 7.74173 + 2.59929i 0.384216 + 0.129001i
\(407\) −11.9136 −0.590535
\(408\) 0 0
\(409\) 2.25827 0.111664 0.0558321 0.998440i \(-0.482219\pi\)
0.0558321 + 0.998440i \(0.482219\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.52840 + 1.15672i 0.0752990 + 0.0569875i
\(413\) 17.9672i 0.884107i
\(414\) 0 0
\(415\) 0 0
\(416\) −1.06874 + 21.8708i −0.0523991 + 1.07231i
\(417\) 0 0
\(418\) −4.82778 + 14.3791i −0.236135 + 0.703303i
\(419\) 33.4579i 1.63453i 0.576264 + 0.817263i \(0.304510\pi\)
−0.576264 + 0.817263i \(0.695490\pi\)
\(420\) 0 0
\(421\) 11.3398i 0.552669i −0.961061 0.276335i \(-0.910880\pi\)
0.961061 0.276335i \(-0.0891198\pi\)
\(422\) −18.3860 6.17313i −0.895018 0.300503i
\(423\) 0 0
\(424\) 7.18953 + 10.5310i 0.349155 + 0.511430i
\(425\) 0 0
\(426\) 0 0
\(427\) 9.51627i 0.460525i
\(428\) −4.82778 + 6.37907i −0.233360 + 0.308344i
\(429\) 0 0
\(430\) 0 0
\(431\) −10.6597 −0.513459 −0.256730 0.966483i \(-0.582645\pi\)
−0.256730 + 0.966483i \(0.582645\pi\)
\(432\) 0 0
\(433\) 26.5132 1.27414 0.637072 0.770805i \(-0.280146\pi\)
0.637072 + 0.770805i \(0.280146\pi\)
\(434\) −8.75814 + 26.0852i −0.420404 + 1.25213i
\(435\) 0 0
\(436\) 0.928423 1.22675i 0.0444634 0.0587506i
\(437\) 34.2088i 1.63643i
\(438\) 0 0
\(439\) 32.8789 1.56923 0.784613 0.619986i \(-0.212862\pi\)
0.784613 + 0.619986i \(0.212862\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −17.1989 5.77454i −0.818068 0.274667i
\(443\) 5.70892i 0.271239i −0.990761 0.135619i \(-0.956698\pi\)
0.990761 0.135619i \(-0.0433024\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −4.43140 + 13.1985i −0.209833 + 0.624966i
\(447\) 0 0
\(448\) 7.69919 19.6894i 0.363753 0.930237i
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) 13.2069i 0.621890i
\(452\) −23.0580 17.4506i −1.08456 0.820809i
\(453\) 0 0
\(454\) −7.65375 2.56975i −0.359208 0.120604i
\(455\) 0 0
\(456\) 0 0
\(457\) −3.94229 −0.184413 −0.0922064 0.995740i \(-0.529392\pi\)
−0.0922064 + 0.995740i \(0.529392\pi\)
\(458\) −1.03128 0.346255i −0.0481888 0.0161794i
\(459\) 0 0
\(460\) 0 0
\(461\) 33.8969i 1.57874i 0.613920 + 0.789369i \(0.289592\pi\)
−0.613920 + 0.789369i \(0.710408\pi\)
\(462\) 0 0
\(463\) 22.8688 1.06280 0.531402 0.847120i \(-0.321665\pi\)
0.531402 + 0.847120i \(0.321665\pi\)
\(464\) −8.41188 + 2.37429i −0.390512 + 0.110224i
\(465\) 0 0
\(466\) −8.28275 + 24.6693i −0.383691 + 1.14278i
\(467\) 15.7417i 0.728440i −0.931313 0.364220i \(-0.881336\pi\)
0.931313 0.364220i \(-0.118664\pi\)
\(468\) 0 0
\(469\) 2.68601i 0.124028i
\(470\) 0 0
\(471\) 0 0
\(472\) −10.8427 15.8820i −0.499076 0.731030i
\(473\) −1.53847 −0.0707388
\(474\) 0 0
\(475\) 0 0
\(476\) 13.9672 + 10.5706i 0.640185 + 0.484502i
\(477\) 0 0
\(478\) −4.51606 + 13.4506i −0.206560 + 0.615218i
\(479\) −20.6925 −0.945465 −0.472732 0.881206i \(-0.656732\pi\)
−0.472732 + 0.881206i \(0.656732\pi\)
\(480\) 0 0
\(481\) −30.4671 −1.38918
\(482\) 4.84255 14.4231i 0.220572 0.656952i
\(483\) 0 0
\(484\) −13.8887 10.5112i −0.631304 0.477781i
\(485\) 0 0
\(486\) 0 0
\(487\) 30.8401 1.39750 0.698750 0.715366i \(-0.253740\pi\)
0.698750 + 0.715366i \(0.253740\pi\)
\(488\) 5.74281 + 8.41188i 0.259965 + 0.380788i
\(489\) 0 0
\(490\) 0 0
\(491\) 10.9737i 0.495238i 0.968858 + 0.247619i \(0.0796481\pi\)
−0.968858 + 0.247619i \(0.920352\pi\)
\(492\) 0 0
\(493\) 7.24186i 0.326157i
\(494\) −12.3463 + 36.7721i −0.555484 + 1.65445i
\(495\) 0 0
\(496\) −8.00000 28.3433i −0.359211 1.27265i
\(497\) 17.7727 0.797213
\(498\) 0 0
\(499\) 3.71729i 0.166409i 0.996533 + 0.0832044i \(0.0265154\pi\)
−0.996533 + 0.0832044i \(0.973485\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 16.9701 + 5.69774i 0.757414 + 0.254302i
\(503\) −39.9451 −1.78107 −0.890533 0.454919i \(-0.849668\pi\)
−0.890533 + 0.454919i \(0.849668\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −9.79690 3.28932i −0.435525 0.146228i
\(507\) 0 0
\(508\) −18.3860 13.9149i −0.815749 0.617372i
\(509\) 0.0728979i 0.00323114i 0.999999 + 0.00161557i \(0.000514253\pi\)
−0.999999 + 0.00161557i \(0.999486\pi\)
\(510\) 0 0
\(511\) 40.9997 1.81372
\(512\) 5.07634 + 22.0506i 0.224345 + 0.974510i
\(513\) 0 0
\(514\) 5.99166 17.8456i 0.264281 0.787134i
\(515\) 0 0
\(516\) 0 0
\(517\) 10.7253i 0.471699i
\(518\) 27.8857 + 9.36266i 1.22523 + 0.411372i
\(519\) 0 0
\(520\) 0 0
\(521\) 11.9672 0.524292 0.262146 0.965028i \(-0.415570\pi\)
0.262146 + 0.965028i \(0.415570\pi\)
\(522\) 0 0
\(523\) 16.0656i 0.702501i 0.936282 + 0.351250i \(0.114243\pi\)
−0.936282 + 0.351250i \(0.885757\pi\)
\(524\) −8.89845 + 11.7577i −0.388731 + 0.513639i
\(525\) 0 0
\(526\) 8.29392 24.7026i 0.361632 1.07709i
\(527\) 24.4010 1.06292
\(528\) 0 0
\(529\) 0.307491 0.0133692
\(530\) 0 0
\(531\) 0 0
\(532\) 22.6004 29.8625i 0.979854 1.29470i
\(533\) 33.7745i 1.46294i
\(534\) 0 0
\(535\) 0 0
\(536\) −1.62093 2.37429i −0.0700136 0.102554i
\(537\) 0 0
\(538\) 5.18757 + 1.74173i 0.223652 + 0.0750913i
\(539\) 0.0248338i 0.00106967i
\(540\) 0 0
\(541\) 15.8559i 0.681698i 0.940118 + 0.340849i \(0.110715\pi\)
−0.940118 + 0.340849i \(0.889285\pi\)
\(542\) −7.83021 + 23.3215i −0.336337 + 1.00174i
\(543\) 0 0
\(544\) −18.7253 0.915029i −0.802842 0.0392316i
\(545\) 0 0
\(546\) 0 0
\(547\) 4.95078i 0.211680i −0.994383 0.105840i \(-0.966247\pi\)
0.994383 0.105840i \(-0.0337531\pi\)
\(548\) −6.20033 4.69251i −0.264865 0.200454i
\(549\) 0 0
\(550\) 0 0
\(551\) −15.4835 −0.659618
\(552\) 0 0
\(553\) −19.4569 −0.827393
\(554\) −1.18953 0.399387i −0.0505385 0.0169683i
\(555\) 0 0
\(556\) −17.6566 + 23.3301i −0.748806 + 0.989416i
\(557\) 1.26634i 0.0536565i −0.999640 0.0268283i \(-0.991459\pi\)
0.999640 0.0268283i \(-0.00854073\pi\)
\(558\) 0 0
\(559\) −3.93437 −0.166406
\(560\) 0 0
\(561\) 0 0
\(562\) 6.06930 18.0768i 0.256018 0.762524i
\(563\) 5.70892i 0.240602i 0.992737 + 0.120301i \(0.0383860\pi\)
−0.992737 + 0.120301i \(0.961614\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −38.1208 12.7991i −1.60234 0.537986i
\(567\) 0 0
\(568\) −15.7101 + 10.7253i −0.659181 + 0.450025i
\(569\) 2.75814 0.115627 0.0578135 0.998327i \(-0.481587\pi\)
0.0578135 + 0.998327i \(0.481587\pi\)
\(570\) 0 0
\(571\) 25.7735i 1.07859i 0.842118 + 0.539294i \(0.181309\pi\)
−0.842118 + 0.539294i \(0.818691\pi\)
\(572\) 9.34385 + 7.07158i 0.390686 + 0.295677i
\(573\) 0 0
\(574\) −10.3791 + 30.9130i −0.433214 + 1.29028i
\(575\) 0 0
\(576\) 0 0
\(577\) −32.7135 −1.36188 −0.680941 0.732338i \(-0.738429\pi\)
−0.680941 + 0.732338i \(0.738429\pi\)
\(578\) −2.70816 + 8.06599i −0.112645 + 0.335501i
\(579\) 0 0
\(580\) 0 0
\(581\) 20.4587i 0.848769i
\(582\) 0 0
\(583\) 6.82376 0.282611
\(584\) −36.2416 + 24.7422i −1.49969 + 1.02384i
\(585\) 0 0
\(586\) 10.7141 + 3.59728i 0.442597 + 0.148602i
\(587\) 43.4835i 1.79475i −0.441264 0.897377i \(-0.645470\pi\)
0.441264 0.897377i \(-0.354530\pi\)
\(588\) 0 0
\(589\) 52.1705i 2.14965i
\(590\) 0 0
\(591\) 0 0
\(592\) −30.2996 + 8.55220i −1.24531 + 0.351493i
\(593\) −7.83021 −0.321548 −0.160774 0.986991i \(-0.551399\pi\)
−0.160774 + 0.986991i \(0.551399\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 13.3627 17.6564i 0.547356 0.723235i
\(597\) 0 0
\(598\) −25.0539 8.41188i −1.02453 0.343987i
\(599\) 32.7581 1.33846 0.669231 0.743055i \(-0.266624\pi\)
0.669231 + 0.743055i \(0.266624\pi\)
\(600\) 0 0
\(601\) 17.8074 0.726377 0.363189 0.931716i \(-0.381688\pi\)
0.363189 + 0.931716i \(0.381688\pi\)
\(602\) 3.60104 + 1.20905i 0.146767 + 0.0492772i
\(603\) 0 0
\(604\) −1.01641 0.769233i −0.0413570 0.0312997i
\(605\) 0 0
\(606\) 0 0
\(607\) −3.41188 −0.138484 −0.0692420 0.997600i \(-0.522058\pi\)
−0.0692420 + 0.997600i \(0.522058\pi\)
\(608\) −1.95638 + 40.0357i −0.0793416 + 1.62366i
\(609\) 0 0
\(610\) 0 0
\(611\) 27.4282i 1.10963i
\(612\) 0 0
\(613\) 36.6290i 1.47943i 0.672920 + 0.739716i \(0.265040\pi\)
−0.672920 + 0.739716i \(0.734960\pi\)
\(614\) −23.3955 7.85505i −0.944165 0.317004i
\(615\) 0 0
\(616\) −6.37907 9.34385i −0.257020 0.376474i
\(617\) −40.3979 −1.62636 −0.813180 0.582012i \(-0.802266\pi\)
−0.813180 + 0.582012i \(0.802266\pi\)
\(618\) 0 0
\(619\) 24.5172i 0.985430i −0.870191 0.492715i \(-0.836004\pi\)
0.870191 0.492715i \(-0.163996\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −9.65557 + 28.7581i −0.387153 + 1.15310i
\(623\) −39.0006 −1.56252
\(624\) 0 0
\(625\) 0 0
\(626\) −3.48346 + 10.3751i −0.139227 + 0.414674i
\(627\) 0 0
\(628\) −0.155859 + 0.205941i −0.00621947 + 0.00821793i
\(629\) 26.0852i 1.04009i
\(630\) 0 0
\(631\) 18.7805 0.747640 0.373820 0.927501i \(-0.378048\pi\)
0.373820 + 0.927501i \(0.378048\pi\)
\(632\) 17.1989 11.7417i 0.684135 0.467061i
\(633\) 0 0
\(634\) 15.0604 + 5.05654i 0.598125 + 0.200821i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.0635083i 0.00251629i
\(638\) −1.48880 + 4.43424i −0.0589421 + 0.175553i
\(639\) 0 0
\(640\) 0 0
\(641\) 15.5163 0.612856 0.306428 0.951894i \(-0.400866\pi\)
0.306428 + 0.951894i \(0.400866\pi\)
\(642\) 0 0
\(643\) 17.4506i 0.688186i 0.938936 + 0.344093i \(0.111814\pi\)
−0.938936 + 0.344093i \(0.888186\pi\)
\(644\) 20.3463 + 15.3984i 0.801755 + 0.606781i
\(645\) 0 0
\(646\) −31.4835 10.5706i −1.23870 0.415895i
\(647\) 13.1403 0.516600 0.258300 0.966065i \(-0.416838\pi\)
0.258300 + 0.966065i \(0.416838\pi\)
\(648\) 0 0
\(649\) −10.2911 −0.403960
\(650\) 0 0
\(651\) 0 0
\(652\) −23.5155 + 31.0716i −0.920937 + 1.21686i
\(653\) 14.7993i 0.579141i 0.957157 + 0.289570i \(0.0935124\pi\)
−0.957157 + 0.289570i \(0.906488\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −9.48062 33.5890i −0.370156 1.31143i
\(657\) 0 0
\(658\) 8.42882 25.1044i 0.328590 0.978671i
\(659\) 7.99614i 0.311485i −0.987798 0.155743i \(-0.950223\pi\)
0.987798 0.155743i \(-0.0497771\pi\)
\(660\) 0 0
\(661\) 0.915029i 0.0355905i −0.999842 0.0177953i \(-0.994335\pi\)
0.999842 0.0177953i \(-0.00566470\pi\)
\(662\) 10.7265 + 3.60142i 0.416896 + 0.139973i
\(663\) 0 0
\(664\) 12.3463 + 18.0844i 0.479128 + 0.701810i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.5494i 0.408473i
\(668\) 2.87141 + 2.17313i 0.111098 + 0.0840808i
\(669\) 0 0
\(670\) 0 0
\(671\) 5.45065 0.210420
\(672\) 0 0
\(673\) 34.3978 1.32594 0.662969 0.748647i \(-0.269296\pi\)
0.662969 + 0.748647i \(0.269296\pi\)
\(674\) 9.70892 28.9170i 0.373973 1.11384i
\(675\) 0 0
\(676\) 3.16337 + 2.39409i 0.121668 + 0.0920804i
\(677\) 40.1676i 1.54377i 0.635764 + 0.771884i \(0.280685\pi\)
−0.635764 + 0.771884i \(0.719315\pi\)
\(678\) 0 0
\(679\) 29.4506 1.13021
\(680\) 0 0
\(681\) 0 0
\(682\) −14.9409 5.01641i −0.572115 0.192088i
\(683\) 33.2580i 1.27258i −0.771449 0.636291i \(-0.780468\pi\)
0.771449 0.636291i \(-0.219532\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −8.34625 + 24.8585i −0.318661 + 0.949101i
\(687\) 0 0
\(688\) −3.91275 + 1.10439i −0.149172 + 0.0421045i
\(689\) 17.4506 0.664817
\(690\) 0 0
\(691\) 50.2241i 1.91062i −0.295611 0.955308i \(-0.595523\pi\)
0.295611 0.955308i \(-0.404477\pi\)
\(692\) 28.0416 37.0521i 1.06598 1.40851i
\(693\) 0 0
\(694\) 29.1044 + 9.77182i 1.10479 + 0.370933i
\(695\) 0 0
\(696\) 0 0
\(697\) 28.9170 1.09531
\(698\) 33.1710 + 11.1372i 1.25554 + 0.421549i
\(699\) 0 0
\(700\) 0 0
\(701\) 23.7543i 0.897188i −0.893736 0.448594i \(-0.851925\pi\)
0.893736 0.448594i \(-0.148075\pi\)
\(702\) 0 0
\(703\) −55.7715 −2.10346
\(704\) 11.2775 + 4.40987i 0.425037 + 0.166203i
\(705\) 0 0
\(706\) 1.49180 4.44317i 0.0561445 0.167221i
\(707\) 35.2252i 1.32478i
\(708\) 0 0
\(709\) 36.3146i 1.36382i −0.731435 0.681911i \(-0.761149\pi\)
0.731435 0.681911i \(-0.238851\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 34.4744 23.5358i 1.29198 0.882041i
\(713\) 35.5453 1.33118
\(714\) 0 0
\(715\) 0 0
\(716\) 3.44780 4.55567i 0.128851 0.170253i
\(717\) 0 0
\(718\) 7.54333 22.4671i 0.281515 0.838463i
\(719\) −30.7253 −1.14586 −0.572931 0.819604i \(-0.694194\pi\)
−0.572931 + 0.819604i \(0.694194\pi\)
\(720\) 0 0
\(721\) −2.53268 −0.0943219
\(722\) −14.0480 + 41.8405i −0.522812 + 1.55714i
\(723\) 0 0
\(724\) 6.37907 8.42882i 0.237076 0.313255i
\(725\) 0 0
\(726\) 0 0
\(727\) 5.47445 0.203036 0.101518 0.994834i \(-0.467630\pi\)
0.101518 + 0.994834i \(0.467630\pi\)
\(728\) −16.3134 23.8953i −0.604615 0.885620i
\(729\) 0 0
\(730\) 0 0
\(731\) 3.36852i 0.124589i
\(732\) 0 0
\(733\) 17.1455i 0.633285i −0.948545 0.316643i \(-0.897444\pi\)
0.948545 0.316643i \(-0.102556\pi\)
\(734\) −12.8433 + 38.2524i −0.474054 + 1.41192i
\(735\) 0 0
\(736\) −27.2775 1.33294i −1.00546 0.0491328i
\(737\) −1.53847 −0.0566701
\(738\) 0 0
\(739\) 11.6019i 0.426782i 0.976967 + 0.213391i \(0.0684508\pi\)
−0.976967 + 0.213391i \(0.931549\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −15.9721 5.36266i −0.586356 0.196869i
\(743\) 23.6613 0.868048 0.434024 0.900901i \(-0.357093\pi\)
0.434024 + 0.900901i \(0.357093\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 50.3819 + 16.9158i 1.84461 + 0.619330i
\(747\) 0 0
\(748\) −6.05453 + 8.00000i −0.221376 + 0.292509i
\(749\) 10.5706i 0.386241i
\(750\) 0 0
\(751\) −11.4283 −0.417024 −0.208512 0.978020i \(-0.566862\pi\)
−0.208512 + 0.978020i \(0.566862\pi\)
\(752\) 7.69919 + 27.2775i 0.280761 + 0.994709i
\(753\) 0 0
\(754\) −3.80736 + 11.3398i −0.138656 + 0.412972i
\(755\) 0 0
\(756\) 0 0
\(757\) 19.1784i 0.697049i 0.937300 + 0.348525i \(0.113317\pi\)
−0.937300 + 0.348525i \(0.886683\pi\)
\(758\) −9.04219 3.03592i −0.328427 0.110270i
\(759\) 0 0
\(760\) 0 0
\(761\) −4.03281 −0.146189 −0.0730947 0.997325i \(-0.523288\pi\)
−0.0730947 + 0.997325i \(0.523288\pi\)
\(762\) 0 0
\(763\) 2.03281i 0.0735928i
\(764\) −9.51627 7.20207i −0.344287 0.260562i
\(765\) 0 0
\(766\) 9.82687 29.2684i 0.355059 1.05751i
\(767\) −26.3177 −0.950279
\(768\) 0 0
\(769\) −2.95078 −0.106408 −0.0532039 0.998584i \(-0.516943\pi\)
−0.0532039 + 0.998584i \(0.516943\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 23.8272 + 18.0328i 0.857560 + 0.649015i
\(773\) 45.2663i 1.62812i −0.580783 0.814059i \(-0.697253\pi\)
0.580783 0.814059i \(-0.302747\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −26.0328 + 17.7727i −0.934524 + 0.638002i
\(777\) 0 0
\(778\) −11.8159 3.96719i −0.423619 0.142231i
\(779\) 61.8260i 2.21515i
\(780\) 0 0
\(781\) 10.1797i 0.364257i
\(782\) 7.20207 21.4506i 0.257546 0.767074i
\(783\) 0 0
\(784\) −0.0178270 0.0631594i −0.000636678 0.00225569i
\(785\) 0 0
\(786\) 0 0
\(787\) 52.9997i 1.88924i 0.328171 + 0.944618i \(0.393568\pi\)
−0.328171 + 0.944618i \(0.606432\pi\)
\(788\) 3.90269 5.15672i 0.139028 0.183701i
\(789\) 0 0
\(790\) 0 0
\(791\) 38.2088 1.35855
\(792\) 0 0
\(793\) 13.9391 0.494993
\(794\) 1.10155 + 0.369846i 0.0390926 + 0.0131254i
\(795\) 0 0
\(796\) 12.9508 + 9.80136i 0.459028 + 0.347400i
\(797\) 16.5738i