Properties

Label 1792.2.m.h.449.4
Level $1792$
Weight $2$
Character 1792.449
Analytic conductor $14.309$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.3091920422\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 449.4
Root \(0.277956 + 0.213283i\) of defining polynomial
Character \(\chi\) \(=\) 1792.449
Dual form 1792.2.m.h.1345.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.328027 + 0.328027i) q^{3} +(-1.40197 - 1.40197i) q^{5} +1.00000i q^{7} +2.78480i q^{9} +O(q^{10})\) \(q+(-0.328027 + 0.328027i) q^{3} +(-1.40197 - 1.40197i) q^{5} +1.00000i q^{7} +2.78480i q^{9} +(-0.444087 - 0.444087i) q^{11} +(-2.25590 + 2.25590i) q^{13} +0.919765 q^{15} +4.85578 q^{17} +(0.114004 - 0.114004i) q^{19} +(-0.328027 - 0.328027i) q^{21} -3.20529i q^{23} -1.06898i q^{25} +(-1.89757 - 1.89757i) q^{27} +(0.997091 - 0.997091i) q^{29} -5.34435 q^{31} +0.291345 q^{33} +(1.40197 - 1.40197i) q^{35} +(-2.03472 - 2.03472i) q^{37} -1.47999i q^{39} +9.57673i q^{41} +(-6.86758 - 6.86758i) q^{43} +(3.90419 - 3.90419i) q^{45} -9.70703 q^{47} -1.00000 q^{49} +(-1.59282 + 1.59282i) q^{51} +(-7.64426 - 7.64426i) q^{53} +1.24519i q^{55} +0.0747927i q^{57} +(-1.50266 - 1.50266i) q^{59} +(1.74157 - 1.74157i) q^{61} -2.78480 q^{63} +6.32541 q^{65} +(-8.96491 + 8.96491i) q^{67} +(1.05142 + 1.05142i) q^{69} +7.18356i q^{71} +9.04029i q^{73} +(0.350652 + 0.350652i) q^{75} +(0.444087 - 0.444087i) q^{77} -9.58806 q^{79} -7.10949 q^{81} +(-5.30245 + 5.30245i) q^{83} +(-6.80764 - 6.80764i) q^{85} +0.654145i q^{87} -2.49938i q^{89} +(-2.25590 - 2.25590i) q^{91} +(1.75309 - 1.75309i) q^{93} -0.319660 q^{95} +5.89073 q^{97} +(1.23669 - 1.23669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{3} + 4q^{5} + O(q^{10}) \) \( 16q + 4q^{3} + 4q^{5} - 8q^{11} - 12q^{13} - 8q^{17} + 4q^{19} + 4q^{21} - 56q^{27} - 8q^{31} + 16q^{33} - 4q^{35} + 8q^{37} - 24q^{43} + 36q^{45} - 40q^{47} - 16q^{49} + 24q^{51} + 32q^{53} - 4q^{59} + 20q^{61} + 24q^{63} + 72q^{65} + 32q^{67} - 56q^{69} - 28q^{75} + 8q^{77} - 40q^{81} + 36q^{83} - 12q^{91} - 8q^{93} - 80q^{95} - 72q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.328027 + 0.328027i −0.189386 + 0.189386i −0.795431 0.606044i \(-0.792755\pi\)
0.606044 + 0.795431i \(0.292755\pi\)
\(4\) 0 0
\(5\) −1.40197 1.40197i −0.626979 0.626979i 0.320328 0.947307i \(-0.396207\pi\)
−0.947307 + 0.320328i \(0.896207\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 2.78480i 0.928266i
\(10\) 0 0
\(11\) −0.444087 0.444087i −0.133897 0.133897i 0.636982 0.770879i \(-0.280183\pi\)
−0.770879 + 0.636982i \(0.780183\pi\)
\(12\) 0 0
\(13\) −2.25590 + 2.25590i −0.625675 + 0.625675i −0.946977 0.321302i \(-0.895880\pi\)
0.321302 + 0.946977i \(0.395880\pi\)
\(14\) 0 0
\(15\) 0.919765 0.237482
\(16\) 0 0
\(17\) 4.85578 1.17770 0.588849 0.808243i \(-0.299581\pi\)
0.588849 + 0.808243i \(0.299581\pi\)
\(18\) 0 0
\(19\) 0.114004 0.114004i 0.0261543 0.0261543i −0.693909 0.720063i \(-0.744113\pi\)
0.720063 + 0.693909i \(0.244113\pi\)
\(20\) 0 0
\(21\) −0.328027 0.328027i −0.0715813 0.0715813i
\(22\) 0 0
\(23\) 3.20529i 0.668350i −0.942511 0.334175i \(-0.891542\pi\)
0.942511 0.334175i \(-0.108458\pi\)
\(24\) 0 0
\(25\) 1.06898i 0.213795i
\(26\) 0 0
\(27\) −1.89757 1.89757i −0.365187 0.365187i
\(28\) 0 0
\(29\) 0.997091 0.997091i 0.185155 0.185155i −0.608443 0.793598i \(-0.708205\pi\)
0.793598 + 0.608443i \(0.208205\pi\)
\(30\) 0 0
\(31\) −5.34435 −0.959874 −0.479937 0.877303i \(-0.659340\pi\)
−0.479937 + 0.877303i \(0.659340\pi\)
\(32\) 0 0
\(33\) 0.291345 0.0507167
\(34\) 0 0
\(35\) 1.40197 1.40197i 0.236976 0.236976i
\(36\) 0 0
\(37\) −2.03472 2.03472i −0.334507 0.334507i 0.519788 0.854295i \(-0.326011\pi\)
−0.854295 + 0.519788i \(0.826011\pi\)
\(38\) 0 0
\(39\) 1.47999i 0.236989i
\(40\) 0 0
\(41\) 9.57673i 1.49563i 0.663905 + 0.747817i \(0.268898\pi\)
−0.663905 + 0.747817i \(0.731102\pi\)
\(42\) 0 0
\(43\) −6.86758 6.86758i −1.04730 1.04730i −0.998825 0.0484714i \(-0.984565\pi\)
−0.0484714 0.998825i \(-0.515435\pi\)
\(44\) 0 0
\(45\) 3.90419 3.90419i 0.582003 0.582003i
\(46\) 0 0
\(47\) −9.70703 −1.41592 −0.707958 0.706255i \(-0.750383\pi\)
−0.707958 + 0.706255i \(0.750383\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −1.59282 + 1.59282i −0.223040 + 0.223040i
\(52\) 0 0
\(53\) −7.64426 7.64426i −1.05002 1.05002i −0.998681 0.0513390i \(-0.983651\pi\)
−0.0513390 0.998681i \(-0.516349\pi\)
\(54\) 0 0
\(55\) 1.24519i 0.167902i
\(56\) 0 0
\(57\) 0.0747927i 0.00990653i
\(58\) 0 0
\(59\) −1.50266 1.50266i −0.195630 0.195630i 0.602494 0.798123i \(-0.294174\pi\)
−0.798123 + 0.602494i \(0.794174\pi\)
\(60\) 0 0
\(61\) 1.74157 1.74157i 0.222985 0.222985i −0.586769 0.809754i \(-0.699601\pi\)
0.809754 + 0.586769i \(0.199601\pi\)
\(62\) 0 0
\(63\) −2.78480 −0.350851
\(64\) 0 0
\(65\) 6.32541 0.784571
\(66\) 0 0
\(67\) −8.96491 + 8.96491i −1.09524 + 1.09524i −0.100279 + 0.994959i \(0.531973\pi\)
−0.994959 + 0.100279i \(0.968027\pi\)
\(68\) 0 0
\(69\) 1.05142 + 1.05142i 0.126576 + 0.126576i
\(70\) 0 0
\(71\) 7.18356i 0.852532i 0.904598 + 0.426266i \(0.140171\pi\)
−0.904598 + 0.426266i \(0.859829\pi\)
\(72\) 0 0
\(73\) 9.04029i 1.05809i 0.848595 + 0.529043i \(0.177449\pi\)
−0.848595 + 0.529043i \(0.822551\pi\)
\(74\) 0 0
\(75\) 0.350652 + 0.350652i 0.0404898 + 0.0404898i
\(76\) 0 0
\(77\) 0.444087 0.444087i 0.0506085 0.0506085i
\(78\) 0 0
\(79\) −9.58806 −1.07874 −0.539370 0.842069i \(-0.681338\pi\)
−0.539370 + 0.842069i \(0.681338\pi\)
\(80\) 0 0
\(81\) −7.10949 −0.789943
\(82\) 0 0
\(83\) −5.30245 + 5.30245i −0.582020 + 0.582020i −0.935458 0.353438i \(-0.885012\pi\)
0.353438 + 0.935458i \(0.385012\pi\)
\(84\) 0 0
\(85\) −6.80764 6.80764i −0.738392 0.738392i
\(86\) 0 0
\(87\) 0.654145i 0.0701317i
\(88\) 0 0
\(89\) 2.49938i 0.264934i −0.991187 0.132467i \(-0.957710\pi\)
0.991187 0.132467i \(-0.0422898\pi\)
\(90\) 0 0
\(91\) −2.25590 2.25590i −0.236483 0.236483i
\(92\) 0 0
\(93\) 1.75309 1.75309i 0.181787 0.181787i
\(94\) 0 0
\(95\) −0.319660 −0.0327964
\(96\) 0 0
\(97\) 5.89073 0.598113 0.299057 0.954235i \(-0.403328\pi\)
0.299057 + 0.954235i \(0.403328\pi\)
\(98\) 0 0
\(99\) 1.23669 1.23669i 0.124292 0.124292i
\(100\) 0 0
\(101\) 7.00499 + 7.00499i 0.697022 + 0.697022i 0.963767 0.266745i \(-0.0859482\pi\)
−0.266745 + 0.963767i \(0.585948\pi\)
\(102\) 0 0
\(103\) 8.10887i 0.798991i −0.916735 0.399496i \(-0.869185\pi\)
0.916735 0.399496i \(-0.130815\pi\)
\(104\) 0 0
\(105\) 0.919765i 0.0897599i
\(106\) 0 0
\(107\) 2.24367 + 2.24367i 0.216904 + 0.216904i 0.807192 0.590288i \(-0.200986\pi\)
−0.590288 + 0.807192i \(0.700986\pi\)
\(108\) 0 0
\(109\) −0.299413 + 0.299413i −0.0286786 + 0.0286786i −0.721301 0.692622i \(-0.756455\pi\)
0.692622 + 0.721301i \(0.256455\pi\)
\(110\) 0 0
\(111\) 1.33489 0.126702
\(112\) 0 0
\(113\) 4.67432 0.439723 0.219862 0.975531i \(-0.429439\pi\)
0.219862 + 0.975531i \(0.429439\pi\)
\(114\) 0 0
\(115\) −4.49372 + 4.49372i −0.419041 + 0.419041i
\(116\) 0 0
\(117\) −6.28224 6.28224i −0.580793 0.580793i
\(118\) 0 0
\(119\) 4.85578i 0.445128i
\(120\) 0 0
\(121\) 10.6056i 0.964143i
\(122\) 0 0
\(123\) −3.14142 3.14142i −0.283252 0.283252i
\(124\) 0 0
\(125\) −8.50850 + 8.50850i −0.761024 + 0.761024i
\(126\) 0 0
\(127\) −13.7602 −1.22102 −0.610509 0.792009i \(-0.709035\pi\)
−0.610509 + 0.792009i \(0.709035\pi\)
\(128\) 0 0
\(129\) 4.50550 0.396687
\(130\) 0 0
\(131\) −6.91851 + 6.91851i −0.604473 + 0.604473i −0.941496 0.337023i \(-0.890580\pi\)
0.337023 + 0.941496i \(0.390580\pi\)
\(132\) 0 0
\(133\) 0.114004 + 0.114004i 0.00988539 + 0.00988539i
\(134\) 0 0
\(135\) 5.32066i 0.457929i
\(136\) 0 0
\(137\) 7.10937i 0.607395i 0.952769 + 0.303697i \(0.0982211\pi\)
−0.952769 + 0.303697i \(0.901779\pi\)
\(138\) 0 0
\(139\) −10.8171 10.8171i −0.917496 0.917496i 0.0793508 0.996847i \(-0.474715\pi\)
−0.996847 + 0.0793508i \(0.974715\pi\)
\(140\) 0 0
\(141\) 3.18416 3.18416i 0.268155 0.268155i
\(142\) 0 0
\(143\) 2.00364 0.167553
\(144\) 0 0
\(145\) −2.79578 −0.232177
\(146\) 0 0
\(147\) 0.328027 0.328027i 0.0270552 0.0270552i
\(148\) 0 0
\(149\) −15.3257 15.3257i −1.25553 1.25553i −0.953205 0.302325i \(-0.902237\pi\)
−0.302325 0.953205i \(-0.597763\pi\)
\(150\) 0 0
\(151\) 21.5070i 1.75022i −0.483925 0.875109i \(-0.660789\pi\)
0.483925 0.875109i \(-0.339211\pi\)
\(152\) 0 0
\(153\) 13.5224i 1.09322i
\(154\) 0 0
\(155\) 7.49260 + 7.49260i 0.601821 + 0.601821i
\(156\) 0 0
\(157\) −7.72626 + 7.72626i −0.616623 + 0.616623i −0.944664 0.328041i \(-0.893612\pi\)
0.328041 + 0.944664i \(0.393612\pi\)
\(158\) 0 0
\(159\) 5.01504 0.397719
\(160\) 0 0
\(161\) 3.20529 0.252612
\(162\) 0 0
\(163\) 16.9336 16.9336i 1.32634 1.32634i 0.417802 0.908538i \(-0.362801\pi\)
0.908538 0.417802i \(-0.137199\pi\)
\(164\) 0 0
\(165\) −0.408456 0.408456i −0.0317983 0.0317983i
\(166\) 0 0
\(167\) 8.57678i 0.663691i −0.943334 0.331846i \(-0.892329\pi\)
0.943334 0.331846i \(-0.107671\pi\)
\(168\) 0 0
\(169\) 2.82179i 0.217061i
\(170\) 0 0
\(171\) 0.317478 + 0.317478i 0.0242781 + 0.0242781i
\(172\) 0 0
\(173\) 5.44032 5.44032i 0.413620 0.413620i −0.469378 0.882997i \(-0.655522\pi\)
0.882997 + 0.469378i \(0.155522\pi\)
\(174\) 0 0
\(175\) 1.06898 0.0808069
\(176\) 0 0
\(177\) 0.985825 0.0740991
\(178\) 0 0
\(179\) −8.32748 + 8.32748i −0.622425 + 0.622425i −0.946151 0.323726i \(-0.895064\pi\)
0.323726 + 0.946151i \(0.395064\pi\)
\(180\) 0 0
\(181\) 6.24148 + 6.24148i 0.463926 + 0.463926i 0.899940 0.436014i \(-0.143610\pi\)
−0.436014 + 0.899940i \(0.643610\pi\)
\(182\) 0 0
\(183\) 1.14256i 0.0844605i
\(184\) 0 0
\(185\) 5.70524i 0.419457i
\(186\) 0 0
\(187\) −2.15639 2.15639i −0.157691 0.157691i
\(188\) 0 0
\(189\) 1.89757 1.89757i 0.138028 0.138028i
\(190\) 0 0
\(191\) 1.57521 0.113979 0.0569893 0.998375i \(-0.481850\pi\)
0.0569893 + 0.998375i \(0.481850\pi\)
\(192\) 0 0
\(193\) 0.649369 0.0467426 0.0233713 0.999727i \(-0.492560\pi\)
0.0233713 + 0.999727i \(0.492560\pi\)
\(194\) 0 0
\(195\) −2.07490 + 2.07490i −0.148587 + 0.148587i
\(196\) 0 0
\(197\) 1.16865 + 1.16865i 0.0832632 + 0.0832632i 0.747512 0.664249i \(-0.231248\pi\)
−0.664249 + 0.747512i \(0.731248\pi\)
\(198\) 0 0
\(199\) 4.09013i 0.289942i −0.989436 0.144971i \(-0.953691\pi\)
0.989436 0.144971i \(-0.0463088\pi\)
\(200\) 0 0
\(201\) 5.88146i 0.414846i
\(202\) 0 0
\(203\) 0.997091 + 0.997091i 0.0699821 + 0.0699821i
\(204\) 0 0
\(205\) 13.4263 13.4263i 0.937731 0.937731i
\(206\) 0 0
\(207\) 8.92609 0.620406
\(208\) 0 0
\(209\) −0.101255 −0.00700398
\(210\) 0 0
\(211\) 19.0421 19.0421i 1.31091 1.31091i 0.390164 0.920745i \(-0.372418\pi\)
0.920745 0.390164i \(-0.127582\pi\)
\(212\) 0 0
\(213\) −2.35640 2.35640i −0.161458 0.161458i
\(214\) 0 0
\(215\) 19.2562i 1.31326i
\(216\) 0 0
\(217\) 5.34435i 0.362798i
\(218\) 0 0
\(219\) −2.96546 2.96546i −0.200387 0.200387i
\(220\) 0 0
\(221\) −10.9542 + 10.9542i −0.736857 + 0.736857i
\(222\) 0 0
\(223\) 26.0121 1.74190 0.870950 0.491372i \(-0.163504\pi\)
0.870950 + 0.491372i \(0.163504\pi\)
\(224\) 0 0
\(225\) 2.97688 0.198459
\(226\) 0 0
\(227\) −0.181612 + 0.181612i −0.0120540 + 0.0120540i −0.713108 0.701054i \(-0.752713\pi\)
0.701054 + 0.713108i \(0.252713\pi\)
\(228\) 0 0
\(229\) 0.679595 + 0.679595i 0.0449089 + 0.0449089i 0.729205 0.684296i \(-0.239890\pi\)
−0.684296 + 0.729205i \(0.739890\pi\)
\(230\) 0 0
\(231\) 0.291345i 0.0191691i
\(232\) 0 0
\(233\) 19.6676i 1.28847i −0.764828 0.644235i \(-0.777176\pi\)
0.764828 0.644235i \(-0.222824\pi\)
\(234\) 0 0
\(235\) 13.6089 + 13.6089i 0.887749 + 0.887749i
\(236\) 0 0
\(237\) 3.14514 3.14514i 0.204299 0.204299i
\(238\) 0 0
\(239\) −9.44846 −0.611170 −0.305585 0.952165i \(-0.598852\pi\)
−0.305585 + 0.952165i \(0.598852\pi\)
\(240\) 0 0
\(241\) −22.8233 −1.47018 −0.735088 0.677971i \(-0.762859\pi\)
−0.735088 + 0.677971i \(0.762859\pi\)
\(242\) 0 0
\(243\) 8.02480 8.02480i 0.514791 0.514791i
\(244\) 0 0
\(245\) 1.40197 + 1.40197i 0.0895684 + 0.0895684i
\(246\) 0 0
\(247\) 0.514364i 0.0327282i
\(248\) 0 0
\(249\) 3.47869i 0.220453i
\(250\) 0 0
\(251\) 12.2670 + 12.2670i 0.774287 + 0.774287i 0.978853 0.204566i \(-0.0655782\pi\)
−0.204566 + 0.978853i \(0.565578\pi\)
\(252\) 0 0
\(253\) −1.42343 + 1.42343i −0.0894903 + 0.0894903i
\(254\) 0 0
\(255\) 4.46618 0.279683
\(256\) 0 0
\(257\) 7.71213 0.481070 0.240535 0.970641i \(-0.422677\pi\)
0.240535 + 0.970641i \(0.422677\pi\)
\(258\) 0 0
\(259\) 2.03472 2.03472i 0.126432 0.126432i
\(260\) 0 0
\(261\) 2.77670 + 2.77670i 0.171873 + 0.171873i
\(262\) 0 0
\(263\) 9.24972i 0.570362i 0.958474 + 0.285181i \(0.0920538\pi\)
−0.958474 + 0.285181i \(0.907946\pi\)
\(264\) 0 0
\(265\) 21.4340i 1.31668i
\(266\) 0 0
\(267\) 0.819863 + 0.819863i 0.0501748 + 0.0501748i
\(268\) 0 0
\(269\) −8.36587 + 8.36587i −0.510076 + 0.510076i −0.914550 0.404474i \(-0.867455\pi\)
0.404474 + 0.914550i \(0.367455\pi\)
\(270\) 0 0
\(271\) −1.15740 −0.0703071 −0.0351535 0.999382i \(-0.511192\pi\)
−0.0351535 + 0.999382i \(0.511192\pi\)
\(272\) 0 0
\(273\) 1.47999 0.0895733
\(274\) 0 0
\(275\) −0.474718 + 0.474718i −0.0286266 + 0.0286266i
\(276\) 0 0
\(277\) 16.6925 + 16.6925i 1.00296 + 1.00296i 0.999996 + 0.00295975i \(0.000942120\pi\)
0.00295975 + 0.999996i \(0.499058\pi\)
\(278\) 0 0
\(279\) 14.8829i 0.891018i
\(280\) 0 0
\(281\) 29.3656i 1.75180i −0.482490 0.875902i \(-0.660268\pi\)
0.482490 0.875902i \(-0.339732\pi\)
\(282\) 0 0
\(283\) −13.0502 13.0502i −0.775752 0.775752i 0.203354 0.979105i \(-0.434816\pi\)
−0.979105 + 0.203354i \(0.934816\pi\)
\(284\) 0 0
\(285\) 0.104857 0.104857i 0.00621118 0.00621118i
\(286\) 0 0
\(287\) −9.57673 −0.565296
\(288\) 0 0
\(289\) 6.57857 0.386975
\(290\) 0 0
\(291\) −1.93232 + 1.93232i −0.113274 + 0.113274i
\(292\) 0 0
\(293\) 19.4435 + 19.4435i 1.13590 + 1.13590i 0.989178 + 0.146723i \(0.0468727\pi\)
0.146723 + 0.989178i \(0.453127\pi\)
\(294\) 0 0
\(295\) 4.21336i 0.245311i
\(296\) 0 0
\(297\) 1.68537i 0.0977952i
\(298\) 0 0
\(299\) 7.23084 + 7.23084i 0.418170 + 0.418170i
\(300\) 0 0
\(301\) 6.86758 6.86758i 0.395841 0.395841i
\(302\) 0 0
\(303\) −4.59564 −0.264013
\(304\) 0 0
\(305\) −4.88324 −0.279613
\(306\) 0 0
\(307\) −19.5562 + 19.5562i −1.11613 + 1.11613i −0.123830 + 0.992303i \(0.539518\pi\)
−0.992303 + 0.123830i \(0.960482\pi\)
\(308\) 0 0
\(309\) 2.65993 + 2.65993i 0.151318 + 0.151318i
\(310\) 0 0
\(311\) 24.5927i 1.39453i 0.716815 + 0.697263i \(0.245599\pi\)
−0.716815 + 0.697263i \(0.754401\pi\)
\(312\) 0 0
\(313\) 18.0125i 1.01812i −0.860730 0.509062i \(-0.829992\pi\)
0.860730 0.509062i \(-0.170008\pi\)
\(314\) 0 0
\(315\) 3.90419 + 3.90419i 0.219976 + 0.219976i
\(316\) 0 0
\(317\) −9.70483 + 9.70483i −0.545078 + 0.545078i −0.925013 0.379935i \(-0.875946\pi\)
0.379935 + 0.925013i \(0.375946\pi\)
\(318\) 0 0
\(319\) −0.885591 −0.0495836
\(320\) 0 0
\(321\) −1.47197 −0.0821573
\(322\) 0 0
\(323\) 0.553578 0.553578i 0.0308019 0.0308019i
\(324\) 0 0
\(325\) 2.41151 + 2.41151i 0.133766 + 0.133766i
\(326\) 0 0
\(327\) 0.196431i 0.0108627i
\(328\) 0 0
\(329\) 9.70703i 0.535166i
\(330\) 0 0
\(331\) −1.50341 1.50341i −0.0826349 0.0826349i 0.664581 0.747216i \(-0.268610\pi\)
−0.747216 + 0.664581i \(0.768610\pi\)
\(332\) 0 0
\(333\) 5.66630 5.66630i 0.310511 0.310511i
\(334\) 0 0
\(335\) 25.1370 1.37338
\(336\) 0 0
\(337\) −17.7244 −0.965512 −0.482756 0.875755i \(-0.660364\pi\)
−0.482756 + 0.875755i \(0.660364\pi\)
\(338\) 0 0
\(339\) −1.53330 + 1.53330i −0.0832776 + 0.0832776i
\(340\) 0 0
\(341\) 2.37336 + 2.37336i 0.128525 + 0.128525i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 2.94812i 0.158721i
\(346\) 0 0
\(347\) −4.92098 4.92098i −0.264172 0.264172i 0.562574 0.826747i \(-0.309811\pi\)
−0.826747 + 0.562574i \(0.809811\pi\)
\(348\) 0 0
\(349\) −24.8975 + 24.8975i −1.33274 + 1.33274i −0.429821 + 0.902914i \(0.641423\pi\)
−0.902914 + 0.429821i \(0.858577\pi\)
\(350\) 0 0
\(351\) 8.56146 0.456977
\(352\) 0 0
\(353\) −5.71306 −0.304075 −0.152038 0.988375i \(-0.548584\pi\)
−0.152038 + 0.988375i \(0.548584\pi\)
\(354\) 0 0
\(355\) 10.0711 10.0711i 0.534519 0.534519i
\(356\) 0 0
\(357\) −1.59282 1.59282i −0.0843012 0.0843012i
\(358\) 0 0
\(359\) 25.2978i 1.33516i 0.744536 + 0.667582i \(0.232671\pi\)
−0.744536 + 0.667582i \(0.767329\pi\)
\(360\) 0 0
\(361\) 18.9740i 0.998632i
\(362\) 0 0
\(363\) 3.47891 + 3.47891i 0.182595 + 0.182595i
\(364\) 0 0
\(365\) 12.6742 12.6742i 0.663398 0.663398i
\(366\) 0 0
\(367\) 13.9944 0.730499 0.365250 0.930910i \(-0.380984\pi\)
0.365250 + 0.930910i \(0.380984\pi\)
\(368\) 0 0
\(369\) −26.6692 −1.38835
\(370\) 0 0
\(371\) 7.64426 7.64426i 0.396870 0.396870i
\(372\) 0 0
\(373\) 6.44242 + 6.44242i 0.333576 + 0.333576i 0.853943 0.520367i \(-0.174205\pi\)
−0.520367 + 0.853943i \(0.674205\pi\)
\(374\) 0 0
\(375\) 5.58203i 0.288255i
\(376\) 0 0
\(377\) 4.49869i 0.231694i
\(378\) 0 0
\(379\) 20.0039 + 20.0039i 1.02753 + 1.02753i 0.999610 + 0.0279235i \(0.00888948\pi\)
0.0279235 + 0.999610i \(0.491111\pi\)
\(380\) 0 0
\(381\) 4.51371 4.51371i 0.231244 0.231244i
\(382\) 0 0
\(383\) −8.23256 −0.420664 −0.210332 0.977630i \(-0.567455\pi\)
−0.210332 + 0.977630i \(0.567455\pi\)
\(384\) 0 0
\(385\) −1.24519 −0.0634609
\(386\) 0 0
\(387\) 19.1248 19.1248i 0.972169 0.972169i
\(388\) 0 0
\(389\) 22.8204 + 22.8204i 1.15704 + 1.15704i 0.985109 + 0.171930i \(0.0550003\pi\)
0.171930 + 0.985109i \(0.445000\pi\)
\(390\) 0 0
\(391\) 15.5642i 0.787115i
\(392\) 0 0
\(393\) 4.53891i 0.228958i
\(394\) 0 0
\(395\) 13.4421 + 13.4421i 0.676348 + 0.676348i
\(396\) 0 0
\(397\) 20.2540 20.2540i 1.01652 1.01652i 0.0166562 0.999861i \(-0.494698\pi\)
0.999861 0.0166562i \(-0.00530208\pi\)
\(398\) 0 0
\(399\) −0.0747927 −0.00374432
\(400\) 0 0
\(401\) −20.9844 −1.04791 −0.523956 0.851745i \(-0.675544\pi\)
−0.523956 + 0.851745i \(0.675544\pi\)
\(402\) 0 0
\(403\) 12.0563 12.0563i 0.600569 0.600569i
\(404\) 0 0
\(405\) 9.96727 + 9.96727i 0.495277 + 0.495277i
\(406\) 0 0
\(407\) 1.80719i 0.0895791i
\(408\) 0 0
\(409\) 22.9268i 1.13366i −0.823836 0.566828i \(-0.808170\pi\)
0.823836 0.566828i \(-0.191830\pi\)
\(410\) 0 0
\(411\) −2.33206 2.33206i −0.115032 0.115032i
\(412\) 0 0
\(413\) 1.50266 1.50266i 0.0739410 0.0739410i
\(414\) 0 0
\(415\) 14.8677 0.729828
\(416\) 0 0
\(417\) 7.09661 0.347522
\(418\) 0 0
\(419\) −27.8867 + 27.8867i −1.36235 + 1.36235i −0.491444 + 0.870909i \(0.663531\pi\)
−0.870909 + 0.491444i \(0.836469\pi\)
\(420\) 0 0
\(421\) 3.93087 + 3.93087i 0.191579 + 0.191579i 0.796378 0.604799i \(-0.206747\pi\)
−0.604799 + 0.796378i \(0.706747\pi\)
\(422\) 0 0
\(423\) 27.0321i 1.31435i
\(424\) 0 0
\(425\) 5.19071i 0.251786i
\(426\) 0 0
\(427\) 1.74157 + 1.74157i 0.0842803 + 0.0842803i
\(428\) 0 0
\(429\) −0.657247 + 0.657247i −0.0317322 + 0.0317322i
\(430\) 0 0
\(431\) 30.8494 1.48596 0.742981 0.669313i \(-0.233411\pi\)
0.742981 + 0.669313i \(0.233411\pi\)
\(432\) 0 0
\(433\) −22.5480 −1.08359 −0.541794 0.840511i \(-0.682255\pi\)
−0.541794 + 0.840511i \(0.682255\pi\)
\(434\) 0 0
\(435\) 0.917090 0.917090i 0.0439711 0.0439711i
\(436\) 0 0
\(437\) −0.365416 0.365416i −0.0174802 0.0174802i
\(438\) 0 0
\(439\) 20.4983i 0.978329i 0.872192 + 0.489164i \(0.162698\pi\)
−0.872192 + 0.489164i \(0.837302\pi\)
\(440\) 0 0
\(441\) 2.78480i 0.132609i
\(442\) 0 0
\(443\) 15.8801 + 15.8801i 0.754485 + 0.754485i 0.975313 0.220828i \(-0.0708758\pi\)
−0.220828 + 0.975313i \(0.570876\pi\)
\(444\) 0 0
\(445\) −3.50405 + 3.50405i −0.166108 + 0.166108i
\(446\) 0 0
\(447\) 10.0545 0.475560
\(448\) 0 0
\(449\) 28.3273 1.33685 0.668423 0.743781i \(-0.266969\pi\)
0.668423 + 0.743781i \(0.266969\pi\)
\(450\) 0 0
\(451\) 4.25290 4.25290i 0.200261 0.200261i
\(452\) 0 0
\(453\) 7.05488 + 7.05488i 0.331467 + 0.331467i
\(454\) 0 0
\(455\) 6.32541i 0.296540i
\(456\) 0 0
\(457\) 0.979734i 0.0458300i −0.999737 0.0229150i \(-0.992705\pi\)
0.999737 0.0229150i \(-0.00729472\pi\)
\(458\) 0 0
\(459\) −9.21417 9.21417i −0.430080 0.430080i
\(460\) 0 0
\(461\) −25.7845 + 25.7845i −1.20091 + 1.20091i −0.227014 + 0.973891i \(0.572896\pi\)
−0.973891 + 0.227014i \(0.927104\pi\)
\(462\) 0 0
\(463\) −1.56380 −0.0726760 −0.0363380 0.999340i \(-0.511569\pi\)
−0.0363380 + 0.999340i \(0.511569\pi\)
\(464\) 0 0
\(465\) −4.91555 −0.227953
\(466\) 0 0
\(467\) 28.6856 28.6856i 1.32741 1.32741i 0.419792 0.907620i \(-0.362103\pi\)
0.907620 0.419792i \(-0.137897\pi\)
\(468\) 0 0
\(469\) −8.96491 8.96491i −0.413961 0.413961i
\(470\) 0 0
\(471\) 5.06884i 0.233560i
\(472\) 0 0
\(473\) 6.09961i 0.280460i
\(474\) 0 0
\(475\) −0.121867 0.121867i −0.00559166 0.00559166i
\(476\) 0 0
\(477\) 21.2877 21.2877i 0.974698 0.974698i
\(478\) 0 0
\(479\) 25.8040 1.17902 0.589508 0.807762i \(-0.299322\pi\)
0.589508 + 0.807762i \(0.299322\pi\)
\(480\) 0 0
\(481\) 9.18029 0.418585
\(482\) 0 0
\(483\) −1.05142 + 1.05142i −0.0478413 + 0.0478413i
\(484\) 0 0
\(485\) −8.25861 8.25861i −0.375004 0.375004i
\(486\) 0 0
\(487\) 2.56961i 0.116440i 0.998304 + 0.0582201i \(0.0185425\pi\)
−0.998304 + 0.0582201i \(0.981457\pi\)
\(488\) 0 0
\(489\) 11.1093i 0.502381i
\(490\) 0 0
\(491\) −2.11127 2.11127i −0.0952804 0.0952804i 0.657860 0.753140i \(-0.271462\pi\)
−0.753140 + 0.657860i \(0.771462\pi\)
\(492\) 0 0
\(493\) 4.84165 4.84165i 0.218057 0.218057i
\(494\) 0 0
\(495\) −3.46761 −0.155857
\(496\) 0 0
\(497\) −7.18356 −0.322227
\(498\) 0 0
\(499\) 5.30410 5.30410i 0.237444 0.237444i −0.578347 0.815791i \(-0.696302\pi\)
0.815791 + 0.578347i \(0.196302\pi\)
\(500\) 0 0
\(501\) 2.81341 + 2.81341i 0.125694 + 0.125694i
\(502\) 0 0
\(503\) 37.3432i 1.66505i −0.553987 0.832525i \(-0.686894\pi\)
0.553987 0.832525i \(-0.313106\pi\)
\(504\) 0 0
\(505\) 19.6415i 0.874036i
\(506\) 0 0
\(507\) −0.925621 0.925621i −0.0411083 0.0411083i
\(508\) 0 0
\(509\) −21.7303 + 21.7303i −0.963178 + 0.963178i −0.999346 0.0361674i \(-0.988485\pi\)
0.0361674 + 0.999346i \(0.488485\pi\)
\(510\) 0 0
\(511\) −9.04029 −0.399919
\(512\) 0 0
\(513\) −0.432660 −0.0191024
\(514\) 0 0
\(515\) −11.3684 + 11.3684i −0.500951 + 0.500951i
\(516\) 0 0
\(517\) 4.31077 + 4.31077i 0.189587 + 0.189587i
\(518\) 0 0
\(519\) 3.56914i 0.156668i
\(520\) 0 0
\(521\) 4.96517i 0.217528i −0.994068 0.108764i \(-0.965311\pi\)
0.994068 0.108764i \(-0.0346893\pi\)
\(522\) 0 0
\(523\) −0.922937 0.922937i −0.0403572 0.0403572i 0.686640 0.726997i \(-0.259085\pi\)
−0.726997 + 0.686640i \(0.759085\pi\)
\(524\) 0 0
\(525\) −0.350652 + 0.350652i −0.0153037 + 0.0153037i
\(526\) 0 0
\(527\) −25.9510 −1.13044
\(528\) 0 0
\(529\) 12.7261 0.553309
\(530\) 0 0
\(531\) 4.18460 4.18460i 0.181596 0.181596i
\(532\) 0 0
\(533\) −21.6042 21.6042i −0.935781 0.935781i
\(534\) 0 0
\(535\) 6.29111i 0.271989i
\(536\) 0 0
\(537\) 5.46327i 0.235757i
\(538\) 0 0
\(539\) 0.444087 + 0.444087i 0.0191282 + 0.0191282i
\(540\) 0 0
\(541\) 20.1027 20.1027i 0.864281 0.864281i −0.127551 0.991832i \(-0.540712\pi\)
0.991832 + 0.127551i \(0.0407116\pi\)
\(542\) 0 0
\(543\) −4.09474 −0.175722
\(544\) 0 0
\(545\) 0.839535 0.0359617
\(546\) 0 0
\(547\) 16.7415 16.7415i 0.715813 0.715813i −0.251932 0.967745i \(-0.581066\pi\)
0.967745 + 0.251932i \(0.0810659\pi\)
\(548\) 0 0
\(549\) 4.84991 + 4.84991i 0.206989 + 0.206989i
\(550\) 0 0
\(551\) 0.227345i 0.00968521i
\(552\) 0 0
\(553\) 9.58806i 0.407726i
\(554\) 0 0
\(555\) −1.87147 1.87147i −0.0794394 0.0794394i
\(556\) 0 0
\(557\) −22.1766 + 22.1766i −0.939655 + 0.939655i −0.998280 0.0586254i \(-0.981328\pi\)
0.0586254 + 0.998280i \(0.481328\pi\)
\(558\) 0 0
\(559\) 30.9852 1.31053
\(560\) 0 0
\(561\) 1.41471 0.0597290
\(562\) 0 0
\(563\) −24.2669 + 24.2669i −1.02273 + 1.02273i −0.0229924 + 0.999736i \(0.507319\pi\)
−0.999736 + 0.0229924i \(0.992681\pi\)
\(564\) 0 0
\(565\) −6.55325 6.55325i −0.275697 0.275697i
\(566\) 0 0
\(567\) 7.10949i 0.298570i
\(568\) 0 0
\(569\) 42.8086i 1.79463i −0.441392 0.897315i \(-0.645515\pi\)
0.441392 0.897315i \(-0.354485\pi\)
\(570\) 0 0
\(571\) 6.89908 + 6.89908i 0.288717 + 0.288717i 0.836573 0.547856i \(-0.184556\pi\)
−0.547856 + 0.836573i \(0.684556\pi\)
\(572\) 0 0
\(573\) −0.516712 + 0.516712i −0.0215860 + 0.0215860i
\(574\) 0 0
\(575\) −3.42638 −0.142890
\(576\) 0 0
\(577\) −2.38332 −0.0992189 −0.0496094 0.998769i \(-0.515798\pi\)
−0.0496094 + 0.998769i \(0.515798\pi\)
\(578\) 0 0
\(579\) −0.213010 + 0.213010i −0.00885240 + 0.00885240i
\(580\) 0 0
\(581\) −5.30245 5.30245i −0.219983 0.219983i
\(582\) 0 0
\(583\) 6.78944i 0.281190i
\(584\) 0 0
\(585\) 17.6150i 0.728290i
\(586\) 0 0
\(587\) 2.70993 + 2.70993i 0.111851 + 0.111851i 0.760817 0.648966i \(-0.224798\pi\)
−0.648966 + 0.760817i \(0.724798\pi\)
\(588\) 0 0
\(589\) −0.609277 + 0.609277i −0.0251048 + 0.0251048i
\(590\) 0 0
\(591\) −0.766700 −0.0315378
\(592\) 0 0
\(593\) 29.3573 1.20556 0.602780 0.797907i \(-0.294060\pi\)
0.602780 + 0.797907i \(0.294060\pi\)
\(594\) 0 0
\(595\) 6.80764 6.80764i 0.279086 0.279086i
\(596\) 0 0
\(597\) 1.34167 + 1.34167i 0.0549110 + 0.0549110i
\(598\) 0 0
\(599\) 40.3716i 1.64954i 0.565468 + 0.824770i \(0.308696\pi\)
−0.565468 + 0.824770i \(0.691304\pi\)
\(600\) 0 0
\(601\) 30.9931i 1.26424i 0.774872 + 0.632118i \(0.217814\pi\)
−0.774872 + 0.632118i \(0.782186\pi\)
\(602\) 0 0
\(603\) −24.9655 24.9655i −1.01667 1.01667i
\(604\) 0 0
\(605\) −14.8687 + 14.8687i −0.604497 + 0.604497i
\(606\) 0 0
\(607\) −9.81876 −0.398531 −0.199265 0.979946i \(-0.563856\pi\)
−0.199265 + 0.979946i \(0.563856\pi\)
\(608\) 0 0
\(609\) −0.654145 −0.0265073
\(610\) 0 0
\(611\) 21.8981 21.8981i 0.885904 0.885904i
\(612\) 0 0
\(613\) 5.05548 + 5.05548i 0.204189 + 0.204189i 0.801792 0.597603i \(-0.203880\pi\)
−0.597603 + 0.801792i \(0.703880\pi\)
\(614\) 0 0
\(615\) 8.80834i 0.355187i
\(616\) 0 0
\(617\) 34.8190i 1.40176i −0.713279 0.700881i \(-0.752791\pi\)
0.713279 0.700881i \(-0.247209\pi\)
\(618\) 0 0
\(619\) 34.1722 + 34.1722i 1.37350 + 1.37350i 0.855203 + 0.518294i \(0.173433\pi\)
0.518294 + 0.855203i \(0.326567\pi\)
\(620\) 0 0
\(621\) −6.08226 + 6.08226i −0.244073 + 0.244073i
\(622\) 0 0
\(623\) 2.49938 0.100135
\(624\) 0 0
\(625\) 18.5124 0.740497
\(626\) 0 0
\(627\) 0.0332145 0.0332145i 0.00132646 0.00132646i
\(628\) 0 0
\(629\) −9.88017 9.88017i −0.393948 0.393948i
\(630\) 0 0
\(631\) 1.37799i 0.0548569i 0.999624 + 0.0274285i \(0.00873184\pi\)
−0.999624 + 0.0274285i \(0.991268\pi\)
\(632\) 0 0
\(633\) 12.4926i 0.496537i
\(634\) 0 0
\(635\) 19.2913 + 19.2913i 0.765553 + 0.765553i
\(636\) 0 0
\(637\) 2.25590 2.25590i 0.0893822 0.0893822i
\(638\) 0 0
\(639\) −20.0048 −0.791376
\(640\) 0 0
\(641\) −1.24423 −0.0491440 −0.0245720 0.999698i \(-0.507822\pi\)
−0.0245720 + 0.999698i \(0.507822\pi\)
\(642\) 0 0
\(643\) −25.0773 + 25.0773i −0.988954 + 0.988954i −0.999940 0.0109861i \(-0.996503\pi\)
0.0109861 + 0.999940i \(0.496503\pi\)
\(644\) 0 0
\(645\) −6.31656 6.31656i −0.248714 0.248714i
\(646\) 0 0
\(647\) 28.0343i 1.10214i −0.834458 0.551071i \(-0.814219\pi\)
0.834458 0.551071i \(-0.185781\pi\)
\(648\) 0 0
\(649\) 1.33462i 0.0523886i
\(650\) 0 0
\(651\) 1.75309 + 1.75309i 0.0687090 + 0.0687090i
\(652\) 0 0
\(653\) 18.5604 18.5604i 0.726324 0.726324i −0.243561 0.969886i \(-0.578316\pi\)
0.969886 + 0.243561i \(0.0783157\pi\)
\(654\) 0 0
\(655\) 19.3991 0.757984
\(656\) 0 0
\(657\) −25.1754 −0.982185
\(658\) 0 0
\(659\) −2.92378 + 2.92378i −0.113894 + 0.113894i −0.761757 0.647863i \(-0.775663\pi\)
0.647863 + 0.761757i \(0.275663\pi\)
\(660\) 0 0
\(661\) 1.13234 + 1.13234i 0.0440428 + 0.0440428i 0.728785 0.684742i \(-0.240085\pi\)
−0.684742 + 0.728785i \(0.740085\pi\)
\(662\) 0 0
\(663\) 7.18652i 0.279101i
\(664\) 0 0
\(665\) 0.319660i 0.0123959i
\(666\) 0 0
\(667\) −3.19597 3.19597i −0.123748 0.123748i
\(668\) 0 0
\(669\) −8.53267 + 8.53267i −0.329892 + 0.329892i
\(670\) 0 0
\(671\) −1.54681 −0.0597141
\(672\) 0 0
\(673\) −50.3603 −1.94125 −0.970623 0.240607i \(-0.922654\pi\)
−0.970623 + 0.240607i \(0.922654\pi\)
\(674\) 0 0
\(675\) −2.02845 + 2.02845i −0.0780752 + 0.0780752i
\(676\) 0 0
\(677\) 7.37404 + 7.37404i 0.283407 + 0.283407i 0.834466 0.551059i \(-0.185776\pi\)
−0.551059 + 0.834466i \(0.685776\pi\)
\(678\) 0 0
\(679\) 5.89073i 0.226065i
\(680\) 0 0
\(681\) 0.119147i 0.00456573i
\(682\) 0 0
\(683\) −23.3569 23.3569i −0.893726 0.893726i 0.101146 0.994872i \(-0.467749\pi\)
−0.994872 + 0.101146i \(0.967749\pi\)
\(684\) 0 0
\(685\) 9.96711 9.96711i 0.380824 0.380824i
\(686\) 0 0
\(687\) −0.445851 −0.0170103
\(688\) 0 0
\(689\) 34.4895 1.31394
\(690\) 0 0
\(691\) −12.1302 + 12.1302i −0.461453 + 0.461453i −0.899132 0.437679i \(-0.855801\pi\)
0.437679 + 0.899132i \(0.355801\pi\)
\(692\) 0 0
\(693\) 1.23669 + 1.23669i 0.0469781 + 0.0469781i
\(694\) 0 0
\(695\) 30.3305i 1.15050i
\(696\) 0 0
\(697\) 46.5025i 1.76141i
\(698\) 0 0
\(699\) 6.45151 + 6.45151i 0.244019 + 0.244019i
\(700\) 0 0
\(701\) −4.41607 + 4.41607i −0.166793 + 0.166793i −0.785568 0.618775i \(-0.787629\pi\)
0.618775 + 0.785568i \(0.287629\pi\)
\(702\) 0 0
\(703\) −0.463933 −0.0174976
\(704\) 0 0
\(705\) −8.92819 −0.336255
\(706\) 0 0
\(707\) −7.00499 + 7.00499i −0.263450 + 0.263450i
\(708\) 0 0
\(709\) −2.70925 2.70925i −0.101748 0.101748i 0.654400 0.756148i \(-0.272921\pi\)
−0.756148 + 0.654400i \(0.772921\pi\)
\(710\) 0 0
\(711\) 26.7008i 1.00136i
\(712\) 0 0
\(713\) 17.1302i 0.641531i
\(714\) 0 0
\(715\) −2.80903 2.80903i −0.105052 0.105052i
\(716\) 0 0
\(717\) 3.09935 3.09935i 0.115747 0.115747i
\(718\) 0 0
\(719\) −8.99485 −0.335451 −0.167726 0.985834i \(-0.553642\pi\)
−0.167726 + 0.985834i \(0.553642\pi\)
\(720\) 0 0
\(721\) 8.10887 0.301990
\(722\) 0 0
\(723\) 7.48664 7.48664i 0.278431 0.278431i
\(724\) 0 0
\(725\) −1.06587 1.06587i −0.0395853 0.0395853i
\(726\) 0 0
\(727\) 33.6636i 1.24851i −0.781219 0.624256i \(-0.785402\pi\)
0.781219 0.624256i \(-0.214598\pi\)
\(728\) 0 0
\(729\) 16.0638i 0.594954i
\(730\) 0 0
\(731\) −33.3474 33.3474i −1.23340 1.23340i
\(732\) 0 0
\(733\) 29.0542 29.0542i 1.07314 1.07314i 0.0760379 0.997105i \(-0.475773\pi\)
0.997105 0.0760379i \(-0.0242270\pi\)
\(734\) 0 0
\(735\) −0.919765 −0.0339261
\(736\) 0 0
\(737\) 7.96241 0.293299
\(738\) 0 0
\(739\) −5.63034 + 5.63034i −0.207115 + 0.207115i −0.803040 0.595925i \(-0.796786\pi\)
0.595925 + 0.803040i \(0.296786\pi\)
\(740\) 0 0
\(741\) −0.168725 0.168725i −0.00619827 0.00619827i
\(742\) 0 0
\(743\) 27.7688i 1.01874i 0.860548 + 0.509369i \(0.170121\pi\)
−0.860548 + 0.509369i \(0.829879\pi\)
\(744\) 0 0
\(745\) 42.9723i 1.57438i
\(746\) 0 0
\(747\) −14.7663 14.7663i −0.540269 0.540269i
\(748\) 0 0
\(749\) −2.24367 + 2.24367i −0.0819820 + 0.0819820i
\(750\) 0 0
\(751\) −45.5138 −1.66082 −0.830410 0.557153i \(-0.811894\pi\)
−0.830410 + 0.557153i \(0.811894\pi\)
\(752\) 0 0
\(753\) −8.04781 −0.293279
\(754\) 0 0
\(755\) −30.1522 + 30.1522i −1.09735 + 1.09735i
\(756\) 0 0
\(757\) −20.7637 20.7637i −0.754671 0.754671i 0.220676 0.975347i \(-0.429174\pi\)
−0.975347 + 0.220676i \(0.929174\pi\)
\(758\) 0 0
\(759\) 0.933846i 0.0338965i
\(760\) 0 0
\(761\) 3.64393i 0.132092i 0.997817 + 0.0660461i \(0.0210384\pi\)
−0.997817 + 0.0660461i \(0.978962\pi\)
\(762\) 0 0
\(763\) −0.299413 0.299413i −0.0108395 0.0108395i
\(764\) 0 0
\(765\) 18.9579 18.9579i 0.685424 0.685424i
\(766\) 0 0
\(767\) 6.77971 0.244801
\(768\) 0 0
\(769\) −6.23588 −0.224872 −0.112436 0.993659i \(-0.535865\pi\)
−0.112436 + 0.993659i \(0.535865\pi\)
\(770\) 0 0
\(771\) −2.52979 + 2.52979i −0.0911080 + 0.0911080i
\(772\) 0 0
\(773\) 1.49286 + 1.49286i 0.0536943 + 0.0536943i 0.733444 0.679750i \(-0.237912\pi\)
−0.679750 + 0.733444i \(0.737912\pi\)
\(774\) 0 0
\(775\) 5.71298i 0.205216i
\(776\) 0 0
\(777\) 1.33489i 0.0478888i
\(778\) 0 0
\(779\) 1.09178 + 1.09178i 0.0391172 + 0.0391172i
\(780\) 0 0
\(781\) 3.19013 3.19013i 0.114152 0.114152i
\(782\) 0 0
\(783\) −3.78410 −0.135233
\(784\) 0 0
\(785\) 21.6639 0.773219
\(786\) 0 0
\(787\) −8.76929 + 8.76929i −0.312591 + 0.312591i −0.845913 0.533321i \(-0.820944\pi\)
0.533321 + 0.845913i \(0.320944\pi\)
\(788\) 0 0
\(789\) −3.03416 3.03416i −0.108019 0.108019i
\(790\) 0 0
\(791\) 4.67432i 0.166200i
\(792\) 0 0
\(793\) 7.85761i 0.279032i
\(794\) 0 0
\(795\) −7.03093 7.03093i −0.249361 0.249361i
\(796\) 0 0
\(797\) −22.7473 + 22.7473i −0.805750 + 0.805750i −0.983987 0.178238i \(-0.942960\pi\)
0.178238 + 0.983987i \(0.442960\pi\)
\(798\) 0 0
\(799\)