Properties

Label 1792.2.m.h.449.6
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 449.6
Root \(2.69978 + 0.355433i\) of defining polynomial
Character \(\chi\) \(=\) 1792.449
Dual form 1792.2.m.h.1345.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.62602 - 1.62602i) q^{3} +(-1.16900 - 1.16900i) q^{5} +1.00000i q^{7} -2.28788i q^{9} +O(q^{10})\) \(q+(1.62602 - 1.62602i) q^{3} +(-1.16900 - 1.16900i) q^{5} +1.00000i q^{7} -2.28788i q^{9} +(4.39956 + 4.39956i) q^{11} +(0.448377 - 0.448377i) q^{13} -3.80163 q^{15} +5.02326 q^{17} +(-1.49851 + 1.49851i) q^{19} +(1.62602 + 1.62602i) q^{21} -8.89958i q^{23} -2.26688i q^{25} +(1.15793 + 1.15793i) q^{27} +(-0.803165 + 0.803165i) q^{29} +8.27524 q^{31} +14.3075 q^{33} +(1.16900 - 1.16900i) q^{35} +(1.55173 + 1.55173i) q^{37} -1.45814i q^{39} +4.93020i q^{41} +(-3.73291 - 3.73291i) q^{43} +(-2.67453 + 2.67453i) q^{45} -6.68692 q^{47} -1.00000 q^{49} +(8.16791 - 8.16791i) q^{51} +(4.53424 + 4.53424i) q^{53} -10.2862i q^{55} +4.87321i q^{57} +(1.06717 + 1.06717i) q^{59} +(-5.11346 + 5.11346i) q^{61} +2.28788 q^{63} -1.04830 q^{65} +(7.47532 - 7.47532i) q^{67} +(-14.4709 - 14.4709i) q^{69} -4.07354i q^{71} -13.5063i q^{73} +(-3.68600 - 3.68600i) q^{75} +(-4.39956 + 4.39956i) q^{77} +9.19701 q^{79} +10.6293 q^{81} +(2.62248 - 2.62248i) q^{83} +(-5.87218 - 5.87218i) q^{85} +2.61192i q^{87} +1.60040i q^{89} +(0.448377 + 0.448377i) q^{91} +(13.4557 - 13.4557i) q^{93} +3.50351 q^{95} -13.0167 q^{97} +(10.0657 - 10.0657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{3} + 4q^{5} + O(q^{10}) \) \( 16q + 4q^{3} + 4q^{5} - 8q^{11} - 12q^{13} - 8q^{17} + 4q^{19} + 4q^{21} - 56q^{27} - 8q^{31} + 16q^{33} - 4q^{35} + 8q^{37} - 24q^{43} + 36q^{45} - 40q^{47} - 16q^{49} + 24q^{51} + 32q^{53} - 4q^{59} + 20q^{61} + 24q^{63} + 72q^{65} + 32q^{67} - 56q^{69} - 28q^{75} + 8q^{77} - 40q^{81} + 36q^{83} - 12q^{91} - 8q^{93} - 80q^{95} - 72q^{97} - 8q^{99} + O(q^{100}) \)

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
\(3\) 1.62602 1.62602i 0.938783 0.938783i −0.0594487 0.998231i \(-0.518934\pi\)
0.998231 + 0.0594487i \(0.0189343\pi\)
\(4\) 0 0
\(5\) −1.16900 1.16900i −0.522792 0.522792i 0.395621 0.918414i \(-0.370529\pi\)
−0.918414 + 0.395621i \(0.870529\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 2.28788i 0.762626i
\(10\) 0 0
\(11\) 4.39956 + 4.39956i 1.32652 + 1.32652i 0.908387 + 0.418130i \(0.137314\pi\)
0.418130 + 0.908387i \(0.362686\pi\)
\(12\) 0 0
\(13\) 0.448377 0.448377i 0.124357 0.124357i −0.642189 0.766546i \(-0.721974\pi\)
0.766546 + 0.642189i \(0.221974\pi\)
\(14\) 0 0
\(15\) −3.80163 −0.981576
\(16\) 0 0
\(17\) 5.02326 1.21832 0.609159 0.793048i \(-0.291507\pi\)
0.609159 + 0.793048i \(0.291507\pi\)
\(18\) 0 0
\(19\) −1.49851 + 1.49851i −0.343782 + 0.343782i −0.857787 0.514005i \(-0.828161\pi\)
0.514005 + 0.857787i \(0.328161\pi\)
\(20\) 0 0
\(21\) 1.62602 + 1.62602i 0.354826 + 0.354826i
\(22\) 0 0
\(23\) 8.89958i 1.85569i −0.372965 0.927845i \(-0.621659\pi\)
0.372965 0.927845i \(-0.378341\pi\)
\(24\) 0 0
\(25\) 2.26688i 0.453377i
\(26\) 0 0
\(27\) 1.15793 + 1.15793i 0.222843 + 0.222843i
\(28\) 0 0
\(29\) −0.803165 + 0.803165i −0.149144 + 0.149144i −0.777736 0.628592i \(-0.783632\pi\)
0.628592 + 0.777736i \(0.283632\pi\)
\(30\) 0 0
\(31\) 8.27524 1.48628 0.743139 0.669137i \(-0.233336\pi\)
0.743139 + 0.669137i \(0.233336\pi\)
\(32\) 0 0
\(33\) 14.3075 2.49062
\(34\) 0 0
\(35\) 1.16900 1.16900i 0.197597 0.197597i
\(36\) 0 0
\(37\) 1.55173 + 1.55173i 0.255102 + 0.255102i 0.823059 0.567956i \(-0.192266\pi\)
−0.567956 + 0.823059i \(0.692266\pi\)
\(38\) 0 0
\(39\) 1.45814i 0.233489i
\(40\) 0 0
\(41\) 4.93020i 0.769968i 0.922923 + 0.384984i \(0.125793\pi\)
−0.922923 + 0.384984i \(0.874207\pi\)
\(42\) 0 0
\(43\) −3.73291 3.73291i −0.569263 0.569263i 0.362659 0.931922i \(-0.381869\pi\)
−0.931922 + 0.362659i \(0.881869\pi\)
\(44\) 0 0
\(45\) −2.67453 + 2.67453i −0.398695 + 0.398695i
\(46\) 0 0
\(47\) −6.68692 −0.975387 −0.487693 0.873015i \(-0.662162\pi\)
−0.487693 + 0.873015i \(0.662162\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 8.16791 8.16791i 1.14374 1.14374i
\(52\) 0 0
\(53\) 4.53424 + 4.53424i 0.622826 + 0.622826i 0.946253 0.323427i \(-0.104835\pi\)
−0.323427 + 0.946253i \(0.604835\pi\)
\(54\) 0 0
\(55\) 10.2862i 1.38699i
\(56\) 0 0
\(57\) 4.87321i 0.645473i
\(58\) 0 0
\(59\) 1.06717 + 1.06717i 0.138934 + 0.138934i 0.773153 0.634219i \(-0.218678\pi\)
−0.634219 + 0.773153i \(0.718678\pi\)
\(60\) 0 0
\(61\) −5.11346 + 5.11346i −0.654711 + 0.654711i −0.954124 0.299413i \(-0.903209\pi\)
0.299413 + 0.954124i \(0.403209\pi\)
\(62\) 0 0
\(63\) 2.28788 0.288245
\(64\) 0 0
\(65\) −1.04830 −0.130026
\(66\) 0 0
\(67\) 7.47532 7.47532i 0.913256 0.913256i −0.0832712 0.996527i \(-0.526537\pi\)
0.996527 + 0.0832712i \(0.0265368\pi\)
\(68\) 0 0
\(69\) −14.4709 14.4709i −1.74209 1.74209i
\(70\) 0 0
\(71\) 4.07354i 0.483440i −0.970346 0.241720i \(-0.922288\pi\)
0.970346 0.241720i \(-0.0777116\pi\)
\(72\) 0 0
\(73\) 13.5063i 1.58079i −0.612595 0.790397i \(-0.709874\pi\)
0.612595 0.790397i \(-0.290126\pi\)
\(74\) 0 0
\(75\) −3.68600 3.68600i −0.425622 0.425622i
\(76\) 0 0
\(77\) −4.39956 + 4.39956i −0.501376 + 0.501376i
\(78\) 0 0
\(79\) 9.19701 1.03474 0.517372 0.855760i \(-0.326910\pi\)
0.517372 + 0.855760i \(0.326910\pi\)
\(80\) 0 0
\(81\) 10.6293 1.18103
\(82\) 0 0
\(83\) 2.62248 2.62248i 0.287855 0.287855i −0.548377 0.836231i \(-0.684754\pi\)
0.836231 + 0.548377i \(0.184754\pi\)
\(84\) 0 0
\(85\) −5.87218 5.87218i −0.636928 0.636928i
\(86\) 0 0
\(87\) 2.61192i 0.280028i
\(88\) 0 0
\(89\) 1.60040i 0.169642i 0.996396 + 0.0848209i \(0.0270318\pi\)
−0.996396 + 0.0848209i \(0.972968\pi\)
\(90\) 0 0
\(91\) 0.448377 + 0.448377i 0.0470027 + 0.0470027i
\(92\) 0 0
\(93\) 13.4557 13.4557i 1.39529 1.39529i
\(94\) 0 0
\(95\) 3.50351 0.359453
\(96\) 0 0
\(97\) −13.0167 −1.32164 −0.660822 0.750543i \(-0.729792\pi\)
−0.660822 + 0.750543i \(0.729792\pi\)
\(98\) 0 0
\(99\) 10.0657 10.0657i 1.01164 1.01164i
\(100\) 0 0
\(101\) −3.76253 3.76253i −0.374386 0.374386i 0.494686 0.869072i \(-0.335283\pi\)
−0.869072 + 0.494686i \(0.835283\pi\)
\(102\) 0 0
\(103\) 7.91886i 0.780268i 0.920758 + 0.390134i \(0.127571\pi\)
−0.920758 + 0.390134i \(0.872429\pi\)
\(104\) 0 0
\(105\) 3.80163i 0.371001i
\(106\) 0 0
\(107\) −13.5961 13.5961i −1.31438 1.31438i −0.918152 0.396228i \(-0.870319\pi\)
−0.396228 0.918152i \(-0.629681\pi\)
\(108\) 0 0
\(109\) −7.03367 + 7.03367i −0.673704 + 0.673704i −0.958568 0.284864i \(-0.908052\pi\)
0.284864 + 0.958568i \(0.408052\pi\)
\(110\) 0 0
\(111\) 5.04627 0.478971
\(112\) 0 0
\(113\) 5.62753 0.529394 0.264697 0.964332i \(-0.414728\pi\)
0.264697 + 0.964332i \(0.414728\pi\)
\(114\) 0 0
\(115\) −10.4036 + 10.4036i −0.970141 + 0.970141i
\(116\) 0 0
\(117\) −1.02583 1.02583i −0.0948381 0.0948381i
\(118\) 0 0
\(119\) 5.02326i 0.460481i
\(120\) 0 0
\(121\) 27.7123i 2.51930i
\(122\) 0 0
\(123\) 8.01660 + 8.01660i 0.722833 + 0.722833i
\(124\) 0 0
\(125\) −8.49498 + 8.49498i −0.759814 + 0.759814i
\(126\) 0 0
\(127\) 13.5320 1.20077 0.600386 0.799710i \(-0.295013\pi\)
0.600386 + 0.799710i \(0.295013\pi\)
\(128\) 0 0
\(129\) −12.1396 −1.06883
\(130\) 0 0
\(131\) −1.48631 + 1.48631i −0.129859 + 0.129859i −0.769049 0.639190i \(-0.779270\pi\)
0.639190 + 0.769049i \(0.279270\pi\)
\(132\) 0 0
\(133\) −1.49851 1.49851i −0.129937 0.129937i
\(134\) 0 0
\(135\) 2.70723i 0.233001i
\(136\) 0 0
\(137\) 11.7463i 1.00355i −0.864998 0.501776i \(-0.832680\pi\)
0.864998 0.501776i \(-0.167320\pi\)
\(138\) 0 0
\(139\) −8.00812 8.00812i −0.679240 0.679240i 0.280588 0.959828i \(-0.409470\pi\)
−0.959828 + 0.280588i \(0.909470\pi\)
\(140\) 0 0
\(141\) −10.8731 + 10.8731i −0.915676 + 0.915676i
\(142\) 0 0
\(143\) 3.94532 0.329924
\(144\) 0 0
\(145\) 1.87780 0.155943
\(146\) 0 0
\(147\) −1.62602 + 1.62602i −0.134112 + 0.134112i
\(148\) 0 0
\(149\) 3.63681 + 3.63681i 0.297939 + 0.297939i 0.840206 0.542267i \(-0.182434\pi\)
−0.542267 + 0.840206i \(0.682434\pi\)
\(150\) 0 0
\(151\) 15.9697i 1.29959i −0.760108 0.649797i \(-0.774854\pi\)
0.760108 0.649797i \(-0.225146\pi\)
\(152\) 0 0
\(153\) 11.4926i 0.929121i
\(154\) 0 0
\(155\) −9.67375 9.67375i −0.777014 0.777014i
\(156\) 0 0
\(157\) −14.0481 + 14.0481i −1.12116 + 1.12116i −0.129589 + 0.991568i \(0.541366\pi\)
−0.991568 + 0.129589i \(0.958634\pi\)
\(158\) 0 0
\(159\) 14.7455 1.16940
\(160\) 0 0
\(161\) 8.89958 0.701385
\(162\) 0 0
\(163\) 10.2797 10.2797i 0.805169 0.805169i −0.178729 0.983898i \(-0.557199\pi\)
0.983898 + 0.178729i \(0.0571985\pi\)
\(164\) 0 0
\(165\) −16.7255 16.7255i −1.30208 1.30208i
\(166\) 0 0
\(167\) 19.4131i 1.50223i −0.660172 0.751115i \(-0.729517\pi\)
0.660172 0.751115i \(-0.270483\pi\)
\(168\) 0 0
\(169\) 12.5979i 0.969071i
\(170\) 0 0
\(171\) 3.42841 + 3.42841i 0.262177 + 0.262177i
\(172\) 0 0
\(173\) −4.56281 + 4.56281i −0.346904 + 0.346904i −0.858955 0.512051i \(-0.828886\pi\)
0.512051 + 0.858955i \(0.328886\pi\)
\(174\) 0 0
\(175\) 2.26688 0.171360
\(176\) 0 0
\(177\) 3.47048 0.260857
\(178\) 0 0
\(179\) −16.8129 + 16.8129i −1.25665 + 1.25665i −0.303970 + 0.952682i \(0.598312\pi\)
−0.952682 + 0.303970i \(0.901688\pi\)
\(180\) 0 0
\(181\) 6.25856 + 6.25856i 0.465195 + 0.465195i 0.900354 0.435159i \(-0.143308\pi\)
−0.435159 + 0.900354i \(0.643308\pi\)
\(182\) 0 0
\(183\) 16.6292i 1.22926i
\(184\) 0 0
\(185\) 3.62793i 0.266731i
\(186\) 0 0
\(187\) 22.1001 + 22.1001i 1.61612 + 1.61612i
\(188\) 0 0
\(189\) −1.15793 + 1.15793i −0.0842267 + 0.0842267i
\(190\) 0 0
\(191\) −15.8222 −1.14486 −0.572428 0.819955i \(-0.693999\pi\)
−0.572428 + 0.819955i \(0.693999\pi\)
\(192\) 0 0
\(193\) −7.50630 −0.540315 −0.270158 0.962816i \(-0.587076\pi\)
−0.270158 + 0.962816i \(0.587076\pi\)
\(194\) 0 0
\(195\) −1.70456 + 1.70456i −0.122066 + 0.122066i
\(196\) 0 0
\(197\) 17.2320 + 17.2320i 1.22773 + 1.22773i 0.964822 + 0.262905i \(0.0846807\pi\)
0.262905 + 0.964822i \(0.415319\pi\)
\(198\) 0 0
\(199\) 21.8653i 1.54999i 0.631967 + 0.774995i \(0.282248\pi\)
−0.631967 + 0.774995i \(0.717752\pi\)
\(200\) 0 0
\(201\) 24.3100i 1.71470i
\(202\) 0 0
\(203\) −0.803165 0.803165i −0.0563712 0.0563712i
\(204\) 0 0
\(205\) 5.76340 5.76340i 0.402533 0.402533i
\(206\) 0 0
\(207\) −20.3611 −1.41520
\(208\) 0 0
\(209\) −13.1856 −0.912065
\(210\) 0 0
\(211\) 2.78563 2.78563i 0.191771 0.191771i −0.604690 0.796461i \(-0.706703\pi\)
0.796461 + 0.604690i \(0.206703\pi\)
\(212\) 0 0
\(213\) −6.62366 6.62366i −0.453845 0.453845i
\(214\) 0 0
\(215\) 8.72753i 0.595212i
\(216\) 0 0
\(217\) 8.27524i 0.561760i
\(218\) 0 0
\(219\) −21.9615 21.9615i −1.48402 1.48402i
\(220\) 0 0
\(221\) 2.25231 2.25231i 0.151507 0.151507i
\(222\) 0 0
\(223\) −4.64913 −0.311329 −0.155665 0.987810i \(-0.549752\pi\)
−0.155665 + 0.987810i \(0.549752\pi\)
\(224\) 0 0
\(225\) −5.18635 −0.345757
\(226\) 0 0
\(227\) −4.41312 + 4.41312i −0.292909 + 0.292909i −0.838228 0.545319i \(-0.816408\pi\)
0.545319 + 0.838228i \(0.316408\pi\)
\(228\) 0 0
\(229\) 14.4119 + 14.4119i 0.952362 + 0.952362i 0.998916 0.0465535i \(-0.0148238\pi\)
−0.0465535 + 0.998916i \(0.514824\pi\)
\(230\) 0 0
\(231\) 14.3075i 0.941367i
\(232\) 0 0
\(233\) 11.2765i 0.738746i 0.929281 + 0.369373i \(0.120428\pi\)
−0.929281 + 0.369373i \(0.879572\pi\)
\(234\) 0 0
\(235\) 7.81700 + 7.81700i 0.509925 + 0.509925i
\(236\) 0 0
\(237\) 14.9545 14.9545i 0.971400 0.971400i
\(238\) 0 0
\(239\) 0.994605 0.0643356 0.0321678 0.999482i \(-0.489759\pi\)
0.0321678 + 0.999482i \(0.489759\pi\)
\(240\) 0 0
\(241\) 27.1158 1.74669 0.873343 0.487107i \(-0.161948\pi\)
0.873343 + 0.487107i \(0.161948\pi\)
\(242\) 0 0
\(243\) 13.8096 13.8096i 0.885885 0.885885i
\(244\) 0 0
\(245\) 1.16900 + 1.16900i 0.0746846 + 0.0746846i
\(246\) 0 0
\(247\) 1.34379i 0.0855036i
\(248\) 0 0
\(249\) 8.52841i 0.540466i
\(250\) 0 0
\(251\) 4.47591 + 4.47591i 0.282517 + 0.282517i 0.834112 0.551595i \(-0.185981\pi\)
−0.551595 + 0.834112i \(0.685981\pi\)
\(252\) 0 0
\(253\) 39.1542 39.1542i 2.46161 2.46161i
\(254\) 0 0
\(255\) −19.0966 −1.19587
\(256\) 0 0
\(257\) −7.08743 −0.442102 −0.221051 0.975262i \(-0.570949\pi\)
−0.221051 + 0.975262i \(0.570949\pi\)
\(258\) 0 0
\(259\) −1.55173 + 1.55173i −0.0964196 + 0.0964196i
\(260\) 0 0
\(261\) 1.83754 + 1.83754i 0.113741 + 0.113741i
\(262\) 0 0
\(263\) 6.95421i 0.428815i 0.976744 + 0.214408i \(0.0687821\pi\)
−0.976744 + 0.214408i \(0.931218\pi\)
\(264\) 0 0
\(265\) 10.6010i 0.651217i
\(266\) 0 0
\(267\) 2.60228 + 2.60228i 0.159257 + 0.159257i
\(268\) 0 0
\(269\) −13.2606 + 13.2606i −0.808516 + 0.808516i −0.984409 0.175893i \(-0.943719\pi\)
0.175893 + 0.984409i \(0.443719\pi\)
\(270\) 0 0
\(271\) 14.2967 0.868463 0.434231 0.900801i \(-0.357020\pi\)
0.434231 + 0.900801i \(0.357020\pi\)
\(272\) 0 0
\(273\) 1.45814 0.0882506
\(274\) 0 0
\(275\) 9.97329 9.97329i 0.601412 0.601412i
\(276\) 0 0
\(277\) 1.56248 + 1.56248i 0.0938806 + 0.0938806i 0.752487 0.658607i \(-0.228854\pi\)
−0.658607 + 0.752487i \(0.728854\pi\)
\(278\) 0 0
\(279\) 18.9327i 1.13347i
\(280\) 0 0
\(281\) 6.06619i 0.361879i −0.983494 0.180939i \(-0.942086\pi\)
0.983494 0.180939i \(-0.0579138\pi\)
\(282\) 0 0
\(283\) 20.3191 + 20.3191i 1.20785 + 1.20785i 0.971723 + 0.236125i \(0.0758774\pi\)
0.236125 + 0.971723i \(0.424123\pi\)
\(284\) 0 0
\(285\) 5.69678 5.69678i 0.337448 0.337448i
\(286\) 0 0
\(287\) −4.93020 −0.291021
\(288\) 0 0
\(289\) 8.23311 0.484301
\(290\) 0 0
\(291\) −21.1654 + 21.1654i −1.24074 + 1.24074i
\(292\) 0 0
\(293\) −22.2357 22.2357i −1.29903 1.29903i −0.929036 0.369989i \(-0.879361\pi\)
−0.369989 0.929036i \(-0.620639\pi\)
\(294\) 0 0
\(295\) 2.49504i 0.145267i
\(296\) 0 0
\(297\) 10.1887i 0.591210i
\(298\) 0 0
\(299\) −3.99036 3.99036i −0.230769 0.230769i
\(300\) 0 0
\(301\) 3.73291 3.73291i 0.215161 0.215161i
\(302\) 0 0
\(303\) −12.2359 −0.702934
\(304\) 0 0
\(305\) 11.9553 0.684556
\(306\) 0 0
\(307\) −17.7656 + 17.7656i −1.01393 + 1.01393i −0.0140326 + 0.999902i \(0.504467\pi\)
−0.999902 + 0.0140326i \(0.995533\pi\)
\(308\) 0 0
\(309\) 12.8762 + 12.8762i 0.732502 + 0.732502i
\(310\) 0 0
\(311\) 31.2698i 1.77315i −0.462588 0.886574i \(-0.653079\pi\)
0.462588 0.886574i \(-0.346921\pi\)
\(312\) 0 0
\(313\) 18.0095i 1.01796i 0.860778 + 0.508980i \(0.169977\pi\)
−0.860778 + 0.508980i \(0.830023\pi\)
\(314\) 0 0
\(315\) −2.67453 2.67453i −0.150692 0.150692i
\(316\) 0 0
\(317\) 12.2418 12.2418i 0.687567 0.687567i −0.274127 0.961694i \(-0.588389\pi\)
0.961694 + 0.274127i \(0.0883888\pi\)
\(318\) 0 0
\(319\) −7.06715 −0.395684
\(320\) 0 0
\(321\) −44.2149 −2.46783
\(322\) 0 0
\(323\) −7.52740 + 7.52740i −0.418836 + 0.418836i
\(324\) 0 0
\(325\) −1.01642 1.01642i −0.0563807 0.0563807i
\(326\) 0 0
\(327\) 22.8738i 1.26492i
\(328\) 0 0
\(329\) 6.68692i 0.368662i
\(330\) 0 0
\(331\) 11.7456 + 11.7456i 0.645599 + 0.645599i 0.951926 0.306328i \(-0.0991003\pi\)
−0.306328 + 0.951926i \(0.599100\pi\)
\(332\) 0 0
\(333\) 3.55016 3.55016i 0.194548 0.194548i
\(334\) 0 0
\(335\) −17.4773 −0.954886
\(336\) 0 0
\(337\) 6.23237 0.339499 0.169750 0.985487i \(-0.445704\pi\)
0.169750 + 0.985487i \(0.445704\pi\)
\(338\) 0 0
\(339\) 9.15047 9.15047i 0.496986 0.496986i
\(340\) 0 0
\(341\) 36.4074 + 36.4074i 1.97157 + 1.97157i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 33.8329i 1.82150i
\(346\) 0 0
\(347\) −6.62041 6.62041i −0.355402 0.355402i 0.506713 0.862115i \(-0.330860\pi\)
−0.862115 + 0.506713i \(0.830860\pi\)
\(348\) 0 0
\(349\) 14.7958 14.7958i 0.792001 0.792001i −0.189819 0.981819i \(-0.560790\pi\)
0.981819 + 0.189819i \(0.0607900\pi\)
\(350\) 0 0
\(351\) 1.03837 0.0554243
\(352\) 0 0
\(353\) −17.7098 −0.942599 −0.471300 0.881973i \(-0.656215\pi\)
−0.471300 + 0.881973i \(0.656215\pi\)
\(354\) 0 0
\(355\) −4.76196 + 4.76196i −0.252739 + 0.252739i
\(356\) 0 0
\(357\) 8.16791 + 8.16791i 0.432292 + 0.432292i
\(358\) 0 0
\(359\) 8.53643i 0.450535i −0.974297 0.225268i \(-0.927674\pi\)
0.974297 0.225268i \(-0.0723257\pi\)
\(360\) 0 0
\(361\) 14.5089i 0.763628i
\(362\) 0 0
\(363\) 45.0607 + 45.0607i 2.36507 + 2.36507i
\(364\) 0 0
\(365\) −15.7889 + 15.7889i −0.826427 + 0.826427i
\(366\) 0 0
\(367\) −11.3226 −0.591037 −0.295519 0.955337i \(-0.595492\pi\)
−0.295519 + 0.955337i \(0.595492\pi\)
\(368\) 0 0
\(369\) 11.2797 0.587198
\(370\) 0 0
\(371\) −4.53424 + 4.53424i −0.235406 + 0.235406i
\(372\) 0 0
\(373\) 7.88728 + 7.88728i 0.408388 + 0.408388i 0.881176 0.472788i \(-0.156752\pi\)
−0.472788 + 0.881176i \(0.656752\pi\)
\(374\) 0 0
\(375\) 27.6260i 1.42660i
\(376\) 0 0
\(377\) 0.720241i 0.0370943i
\(378\) 0 0
\(379\) −9.53241 9.53241i −0.489647 0.489647i 0.418548 0.908195i \(-0.362539\pi\)
−0.908195 + 0.418548i \(0.862539\pi\)
\(380\) 0 0
\(381\) 22.0033 22.0033i 1.12726 1.12726i
\(382\) 0 0
\(383\) −18.9261 −0.967077 −0.483539 0.875323i \(-0.660649\pi\)
−0.483539 + 0.875323i \(0.660649\pi\)
\(384\) 0 0
\(385\) 10.2862 0.524231
\(386\) 0 0
\(387\) −8.54043 + 8.54043i −0.434134 + 0.434134i
\(388\) 0 0
\(389\) 6.78034 + 6.78034i 0.343777 + 0.343777i 0.857785 0.514008i \(-0.171840\pi\)
−0.514008 + 0.857785i \(0.671840\pi\)
\(390\) 0 0
\(391\) 44.7049i 2.26082i
\(392\) 0 0
\(393\) 4.83352i 0.243819i
\(394\) 0 0
\(395\) −10.7513 10.7513i −0.540956 0.540956i
\(396\) 0 0
\(397\) −1.93608 + 1.93608i −0.0971692 + 0.0971692i −0.754020 0.656851i \(-0.771888\pi\)
0.656851 + 0.754020i \(0.271888\pi\)
\(398\) 0 0
\(399\) −4.87321 −0.243966
\(400\) 0 0
\(401\) −16.6483 −0.831378 −0.415689 0.909507i \(-0.636460\pi\)
−0.415689 + 0.909507i \(0.636460\pi\)
\(402\) 0 0
\(403\) 3.71043 3.71043i 0.184829 0.184829i
\(404\) 0 0
\(405\) −12.4256 12.4256i −0.617432 0.617432i
\(406\) 0 0
\(407\) 13.6538i 0.676795i
\(408\) 0 0
\(409\) 16.8706i 0.834199i −0.908861 0.417100i \(-0.863047\pi\)
0.908861 0.417100i \(-0.136953\pi\)
\(410\) 0 0
\(411\) −19.0997 19.0997i −0.942117 0.942117i
\(412\) 0 0
\(413\) −1.06717 + 1.06717i −0.0525120 + 0.0525120i
\(414\) 0 0
\(415\) −6.13136 −0.300976
\(416\) 0 0
\(417\) −26.0427 −1.27532
\(418\) 0 0
\(419\) −20.1511 + 20.1511i −0.984444 + 0.984444i −0.999881 0.0154368i \(-0.995086\pi\)
0.0154368 + 0.999881i \(0.495086\pi\)
\(420\) 0 0
\(421\) 6.44015 + 6.44015i 0.313874 + 0.313874i 0.846408 0.532535i \(-0.178760\pi\)
−0.532535 + 0.846408i \(0.678760\pi\)
\(422\) 0 0
\(423\) 15.2988i 0.743855i
\(424\) 0 0
\(425\) 11.3871i 0.552357i
\(426\) 0 0
\(427\) −5.11346 5.11346i −0.247458 0.247458i
\(428\) 0 0
\(429\) 6.41517 6.41517i 0.309727 0.309727i
\(430\) 0 0
\(431\) 28.6481 1.37993 0.689965 0.723843i \(-0.257626\pi\)
0.689965 + 0.723843i \(0.257626\pi\)
\(432\) 0 0
\(433\) −4.69574 −0.225663 −0.112832 0.993614i \(-0.535992\pi\)
−0.112832 + 0.993614i \(0.535992\pi\)
\(434\) 0 0
\(435\) 3.05334 3.05334i 0.146396 0.146396i
\(436\) 0 0
\(437\) 13.3361 + 13.3361i 0.637953 + 0.637953i
\(438\) 0 0
\(439\) 22.6652i 1.08175i 0.841103 + 0.540874i \(0.181907\pi\)
−0.841103 + 0.540874i \(0.818093\pi\)
\(440\) 0 0
\(441\) 2.28788i 0.108947i
\(442\) 0 0
\(443\) −17.7935 17.7935i −0.845394 0.845394i 0.144160 0.989554i \(-0.453952\pi\)
−0.989554 + 0.144160i \(0.953952\pi\)
\(444\) 0 0
\(445\) 1.87086 1.87086i 0.0886875 0.0886875i
\(446\) 0 0
\(447\) 11.8270 0.559400
\(448\) 0 0
\(449\) −11.2262 −0.529799 −0.264900 0.964276i \(-0.585339\pi\)
−0.264900 + 0.964276i \(0.585339\pi\)
\(450\) 0 0
\(451\) −21.6907 + 21.6907i −1.02138 + 1.02138i
\(452\) 0 0
\(453\) −25.9670 25.9670i −1.22004 1.22004i
\(454\) 0 0
\(455\) 1.04830i 0.0491452i
\(456\) 0 0
\(457\) 20.8858i 0.976998i −0.872564 0.488499i \(-0.837545\pi\)
0.872564 0.488499i \(-0.162455\pi\)
\(458\) 0 0
\(459\) 5.81656 + 5.81656i 0.271494 + 0.271494i
\(460\) 0 0
\(461\) 1.78650 1.78650i 0.0832056 0.0832056i −0.664279 0.747485i \(-0.731261\pi\)
0.747485 + 0.664279i \(0.231261\pi\)
\(462\) 0 0
\(463\) −21.0754 −0.979457 −0.489728 0.871875i \(-0.662904\pi\)
−0.489728 + 0.871875i \(0.662904\pi\)
\(464\) 0 0
\(465\) −31.4594 −1.45889
\(466\) 0 0
\(467\) −8.05590 + 8.05590i −0.372783 + 0.372783i −0.868490 0.495707i \(-0.834909\pi\)
0.495707 + 0.868490i \(0.334909\pi\)
\(468\) 0 0
\(469\) 7.47532 + 7.47532i 0.345178 + 0.345178i
\(470\) 0 0
\(471\) 45.6848i 2.10505i
\(472\) 0 0
\(473\) 32.8463i 1.51027i
\(474\) 0 0
\(475\) 3.39695 + 3.39695i 0.155863 + 0.155863i
\(476\) 0 0
\(477\) 10.3738 10.3738i 0.474983 0.474983i
\(478\) 0 0
\(479\) −19.8741 −0.908070 −0.454035 0.890984i \(-0.650016\pi\)
−0.454035 + 0.890984i \(0.650016\pi\)
\(480\) 0 0
\(481\) 1.39152 0.0634477
\(482\) 0 0
\(483\) 14.4709 14.4709i 0.658448 0.658448i
\(484\) 0 0
\(485\) 15.2165 + 15.2165i 0.690945 + 0.690945i
\(486\) 0 0
\(487\) 19.2744i 0.873406i −0.899606 0.436703i \(-0.856146\pi\)
0.899606 0.436703i \(-0.143854\pi\)
\(488\) 0 0
\(489\) 33.4300i 1.51176i
\(490\) 0 0
\(491\) −4.01202 4.01202i −0.181060 0.181060i 0.610758 0.791818i \(-0.290865\pi\)
−0.791818 + 0.610758i \(0.790865\pi\)
\(492\) 0 0
\(493\) −4.03451 + 4.03451i −0.181705 + 0.181705i
\(494\) 0 0
\(495\) −23.5335 −1.05775
\(496\) 0 0
\(497\) 4.07354 0.182723
\(498\) 0 0
\(499\) −4.10545 + 4.10545i −0.183785 + 0.183785i −0.793003 0.609218i \(-0.791484\pi\)
0.609218 + 0.793003i \(0.291484\pi\)
\(500\) 0 0
\(501\) −31.5660 31.5660i −1.41027 1.41027i
\(502\) 0 0
\(503\) 19.8588i 0.885460i 0.896655 + 0.442730i \(0.145990\pi\)
−0.896655 + 0.442730i \(0.854010\pi\)
\(504\) 0 0
\(505\) 8.79680i 0.391452i
\(506\) 0 0
\(507\) 20.4845 + 20.4845i 0.909747 + 0.909747i
\(508\) 0 0
\(509\) −8.11547 + 8.11547i −0.359712 + 0.359712i −0.863707 0.503995i \(-0.831863\pi\)
0.503995 + 0.863707i \(0.331863\pi\)
\(510\) 0 0
\(511\) 13.5063 0.597484
\(512\) 0 0
\(513\) −3.47033 −0.153219
\(514\) 0 0
\(515\) 9.25714 9.25714i 0.407918 0.407918i
\(516\) 0 0
\(517\) −29.4195 29.4195i −1.29387 1.29387i
\(518\) 0 0
\(519\) 14.8384i 0.651335i
\(520\) 0 0
\(521\) 11.8477i 0.519059i 0.965735 + 0.259530i \(0.0835675\pi\)
−0.965735 + 0.259530i \(0.916432\pi\)
\(522\) 0 0
\(523\) −19.5435 19.5435i −0.854575 0.854575i 0.136117 0.990693i \(-0.456538\pi\)
−0.990693 + 0.136117i \(0.956538\pi\)
\(524\) 0 0
\(525\) 3.68600 3.68600i 0.160870 0.160870i
\(526\) 0 0
\(527\) 41.5687 1.81076
\(528\) 0 0
\(529\) −56.2025 −2.44359
\(530\) 0 0
\(531\) 2.44155 2.44155i 0.105954 0.105954i
\(532\) 0 0
\(533\) 2.21059 + 2.21059i 0.0957512 + 0.0957512i
\(534\) 0 0
\(535\) 31.7876i 1.37430i
\(536\) 0 0
\(537\) 54.6760i 2.35945i
\(538\) 0 0
\(539\) −4.39956 4.39956i −0.189502 0.189502i
\(540\) 0 0
\(541\) −29.1223 + 29.1223i −1.25207 + 1.25207i −0.297274 + 0.954792i \(0.596078\pi\)
−0.954792 + 0.297274i \(0.903922\pi\)
\(542\) 0 0
\(543\) 20.3531 0.873434
\(544\) 0 0
\(545\) 16.4447 0.704414
\(546\) 0 0
\(547\) 12.7023 12.7023i 0.543111 0.543111i −0.381329 0.924440i \(-0.624533\pi\)
0.924440 + 0.381329i \(0.124533\pi\)
\(548\) 0 0
\(549\) 11.6990 + 11.6990i 0.499299 + 0.499299i
\(550\) 0 0
\(551\) 2.40710i 0.102546i
\(552\) 0 0
\(553\) 9.19701i 0.391097i
\(554\) 0 0
\(555\) −5.89909 5.89909i −0.250402 0.250402i
\(556\) 0 0
\(557\) −18.2855 + 18.2855i −0.774780 + 0.774780i −0.978938 0.204158i \(-0.934554\pi\)
0.204158 + 0.978938i \(0.434554\pi\)
\(558\) 0 0
\(559\) −3.34750 −0.141584
\(560\) 0 0
\(561\) 71.8704 3.03437
\(562\) 0 0
\(563\) −0.721510 + 0.721510i −0.0304080 + 0.0304080i −0.722147 0.691739i \(-0.756845\pi\)
0.691739 + 0.722147i \(0.256845\pi\)
\(564\) 0 0
\(565\) −6.57858 6.57858i −0.276763 0.276763i
\(566\) 0 0
\(567\) 10.6293i 0.446387i
\(568\) 0 0
\(569\) 33.5555i 1.40672i −0.710834 0.703360i \(-0.751682\pi\)
0.710834 0.703360i \(-0.248318\pi\)
\(570\) 0 0
\(571\) 3.80134 + 3.80134i 0.159081 + 0.159081i 0.782159 0.623078i \(-0.214118\pi\)
−0.623078 + 0.782159i \(0.714118\pi\)
\(572\) 0 0
\(573\) −25.7273 + 25.7273i −1.07477 + 1.07477i
\(574\) 0 0
\(575\) −20.1743 −0.841327
\(576\) 0 0
\(577\) −2.22515 −0.0926344 −0.0463172 0.998927i \(-0.514748\pi\)
−0.0463172 + 0.998927i \(0.514748\pi\)
\(578\) 0 0
\(579\) −12.2054 + 12.2054i −0.507238 + 0.507238i
\(580\) 0 0
\(581\) 2.62248 + 2.62248i 0.108799 + 0.108799i
\(582\) 0 0
\(583\) 39.8973i 1.65238i
\(584\) 0 0
\(585\) 2.39839i 0.0991612i
\(586\) 0 0
\(587\) 4.33373 + 4.33373i 0.178872 + 0.178872i 0.790864 0.611992i \(-0.209631\pi\)
−0.611992 + 0.790864i \(0.709631\pi\)
\(588\) 0 0
\(589\) −12.4005 + 12.4005i −0.510955 + 0.510955i
\(590\) 0 0
\(591\) 56.0390 2.30514
\(592\) 0 0
\(593\) −16.8460 −0.691784 −0.345892 0.938274i \(-0.612424\pi\)
−0.345892 + 0.938274i \(0.612424\pi\)
\(594\) 0 0
\(595\) 5.87218 5.87218i 0.240736 0.240736i
\(596\) 0 0
\(597\) 35.5534 + 35.5534i 1.45510 + 1.45510i
\(598\) 0 0
\(599\) 43.9075i 1.79401i −0.442018 0.897006i \(-0.645737\pi\)
0.442018 0.897006i \(-0.354263\pi\)
\(600\) 0 0
\(601\) 35.5257i 1.44912i 0.689210 + 0.724562i \(0.257958\pi\)
−0.689210 + 0.724562i \(0.742042\pi\)
\(602\) 0 0
\(603\) −17.1026 17.1026i −0.696472 0.696472i
\(604\) 0 0
\(605\) 32.3956 32.3956i 1.31707 1.31707i
\(606\) 0 0
\(607\) 15.7700 0.640084 0.320042 0.947403i \(-0.396303\pi\)
0.320042 + 0.947403i \(0.396303\pi\)
\(608\) 0 0
\(609\) −2.61192 −0.105841
\(610\) 0 0
\(611\) −2.99826 + 2.99826i −0.121297 + 0.121297i
\(612\) 0 0
\(613\) −8.17171 8.17171i −0.330052 0.330052i 0.522554 0.852606i \(-0.324979\pi\)
−0.852606 + 0.522554i \(0.824979\pi\)
\(614\) 0 0
\(615\) 18.7428i 0.755783i
\(616\) 0 0
\(617\) 23.3938i 0.941800i 0.882187 + 0.470900i \(0.156071\pi\)
−0.882187 + 0.470900i \(0.843929\pi\)
\(618\) 0 0
\(619\) −2.73711 2.73711i −0.110014 0.110014i 0.649957 0.759971i \(-0.274787\pi\)
−0.759971 + 0.649957i \(0.774787\pi\)
\(620\) 0 0
\(621\) 10.3051 10.3051i 0.413528 0.413528i
\(622\) 0 0
\(623\) −1.60040 −0.0641186
\(624\) 0 0
\(625\) 8.52682 0.341073
\(626\) 0 0
\(627\) −21.4400 + 21.4400i −0.856231 + 0.856231i
\(628\) 0 0
\(629\) 7.79472 + 7.79472i 0.310796 + 0.310796i
\(630\) 0 0
\(631\) 34.9200i 1.39014i 0.718941 + 0.695071i \(0.244627\pi\)
−0.718941 + 0.695071i \(0.755373\pi\)
\(632\) 0 0
\(633\) 9.05897i 0.360062i
\(634\) 0 0
\(635\) −15.8189 15.8189i −0.627755 0.627755i
\(636\) 0 0
\(637\) −0.448377 + 0.448377i −0.0177653 + 0.0177653i
\(638\) 0 0
\(639\) −9.31976 −0.368684
\(640\) 0 0
\(641\) −42.9662 −1.69706 −0.848532 0.529144i \(-0.822513\pi\)
−0.848532 + 0.529144i \(0.822513\pi\)
\(642\) 0 0
\(643\) −17.5924 + 17.5924i −0.693777 + 0.693777i −0.963061 0.269284i \(-0.913213\pi\)
0.269284 + 0.963061i \(0.413213\pi\)
\(644\) 0 0
\(645\) 14.1911 + 14.1911i 0.558775 + 0.558775i
\(646\) 0 0
\(647\) 33.5883i 1.32049i −0.751049 0.660246i \(-0.770452\pi\)
0.751049 0.660246i \(-0.229548\pi\)
\(648\) 0 0
\(649\) 9.39016i 0.368596i
\(650\) 0 0
\(651\) 13.4557 + 13.4557i 0.527371 + 0.527371i
\(652\) 0 0
\(653\) −0.281193 + 0.281193i −0.0110039 + 0.0110039i −0.712587 0.701583i \(-0.752477\pi\)
0.701583 + 0.712587i \(0.252477\pi\)
\(654\) 0 0
\(655\) 3.47498 0.135779
\(656\) 0 0
\(657\) −30.9008 −1.20555
\(658\) 0 0
\(659\) 1.25405 1.25405i 0.0488508 0.0488508i −0.682259 0.731110i \(-0.739003\pi\)
0.731110 + 0.682259i \(0.239003\pi\)
\(660\) 0 0
\(661\) −30.7505 30.7505i −1.19605 1.19605i −0.975338 0.220717i \(-0.929160\pi\)
−0.220717 0.975338i \(-0.570840\pi\)
\(662\) 0 0
\(663\) 7.32460i 0.284464i
\(664\) 0 0
\(665\) 3.50351i 0.135860i
\(666\) 0 0
\(667\) 7.14783 + 7.14783i 0.276765 + 0.276765i
\(668\) 0 0
\(669\) −7.55958 + 7.55958i −0.292270 + 0.292270i
\(670\) 0 0
\(671\) −44.9939 −1.73697
\(672\) 0 0
\(673\) −22.2711 −0.858486 −0.429243 0.903189i \(-0.641220\pi\)
−0.429243 + 0.903189i \(0.641220\pi\)
\(674\) 0 0
\(675\) 2.62488 2.62488i 0.101032 0.101032i
\(676\) 0 0
\(677\) −29.3508 29.3508i −1.12804 1.12804i −0.990495 0.137547i \(-0.956078\pi\)
−0.137547 0.990495i \(-0.543922\pi\)
\(678\) 0 0
\(679\) 13.0167i 0.499535i
\(680\) 0 0
\(681\) 14.3516i 0.549956i
\(682\) 0 0
\(683\) 1.79560 + 1.79560i 0.0687066 + 0.0687066i 0.740625 0.671918i \(-0.234529\pi\)
−0.671918 + 0.740625i \(0.734529\pi\)
\(684\) 0 0
\(685\) −13.7314 + 13.7314i −0.524649 + 0.524649i
\(686\) 0 0
\(687\) 46.8679 1.78812
\(688\) 0 0
\(689\) 4.06610 0.154906
\(690\) 0 0
\(691\) −11.7289 + 11.7289i −0.446188 + 0.446188i −0.894085 0.447897i \(-0.852173\pi\)
0.447897 + 0.894085i \(0.352173\pi\)
\(692\) 0 0
\(693\) 10.0657 + 10.0657i 0.382363 + 0.382363i
\(694\) 0 0
\(695\) 18.7230i 0.710202i
\(696\) 0 0
\(697\) 24.7657i 0.938067i
\(698\) 0 0
\(699\) 18.3358 + 18.3358i 0.693522 + 0.693522i
\(700\) 0 0
\(701\) −23.5050 + 23.5050i −0.887772 + 0.887772i −0.994309 0.106536i \(-0.966024\pi\)
0.106536 + 0.994309i \(0.466024\pi\)
\(702\) 0 0
\(703\) −4.65056 −0.175399
\(704\) 0 0
\(705\) 25.4212 0.957417
\(706\) 0 0
\(707\) 3.76253 3.76253i 0.141505 0.141505i
\(708\) 0 0
\(709\) 1.55617 + 1.55617i 0.0584430 + 0.0584430i 0.735724 0.677281i \(-0.236842\pi\)
−0.677281 + 0.735724i \(0.736842\pi\)
\(710\) 0 0
\(711\) 21.0416i 0.789123i
\(712\) 0 0
\(713\) 73.6462i 2.75807i
\(714\) 0 0
\(715\) −4.61208 4.61208i −0.172482 0.172482i
\(716\) 0 0
\(717\) 1.61725 1.61725i 0.0603972 0.0603972i
\(718\) 0 0
\(719\) −6.97452 −0.260106 −0.130053 0.991507i \(-0.541515\pi\)
−0.130053 + 0.991507i \(0.541515\pi\)
\(720\) 0 0
\(721\) −7.91886 −0.294914
\(722\) 0 0
\(723\) 44.0909 44.0909i 1.63976 1.63976i
\(724\) 0 0
\(725\) 1.82068 + 1.82068i 0.0676184 + 0.0676184i
\(726\) 0 0
\(727\) 12.7285i 0.472073i −0.971744 0.236037i \(-0.924151\pi\)
0.971744 0.236037i \(-0.0758485\pi\)
\(728\) 0 0
\(729\) 13.0216i 0.482280i
\(730\) 0 0
\(731\) −18.7513 18.7513i −0.693544 0.693544i
\(732\) 0 0
\(733\) 14.0786 14.0786i 0.520006 0.520006i −0.397567 0.917573i \(-0.630145\pi\)
0.917573 + 0.397567i \(0.130145\pi\)
\(734\) 0 0
\(735\) 3.80163 0.140225
\(736\) 0 0
\(737\) 65.7762 2.42290
\(738\) 0 0
\(739\) 36.9779 36.9779i 1.36026 1.36026i 0.486669 0.873587i \(-0.338212\pi\)
0.873587 0.486669i \(-0.161788\pi\)
\(740\) 0 0
\(741\) 2.18504 + 2.18504i 0.0802693 + 0.0802693i
\(742\) 0 0
\(743\) 10.0453i 0.368527i 0.982877 + 0.184263i \(0.0589900\pi\)
−0.982877 + 0.184263i \(0.941010\pi\)
\(744\) 0 0
\(745\) 8.50285i 0.311520i
\(746\) 0 0
\(747\) −5.99992 5.99992i −0.219525 0.219525i
\(748\) 0 0
\(749\) 13.5961 13.5961i 0.496789 0.496789i
\(750\) 0 0
\(751\) 42.4776 1.55003 0.775014 0.631944i \(-0.217743\pi\)
0.775014 + 0.631944i \(0.217743\pi\)
\(752\) 0 0
\(753\) 14.5558 0.530443
\(754\) 0 0
\(755\) −18.6685 + 18.6685i −0.679417 + 0.679417i
\(756\) 0 0
\(757\) −29.7792 29.7792i −1.08234 1.08234i −0.996291 0.0860518i \(-0.972575\pi\)
−0.0860518 0.996291i \(-0.527425\pi\)
\(758\) 0 0
\(759\) 127.331i 4.62183i
\(760\) 0 0
\(761\) 6.54784i 0.237359i −0.992933 0.118679i \(-0.962134\pi\)
0.992933 0.118679i \(-0.0378661\pi\)
\(762\) 0 0
\(763\) −7.03367 7.03367i −0.254636 0.254636i
\(764\) 0 0
\(765\) −13.4348 + 13.4348i −0.485737 + 0.485737i
\(766\) 0 0
\(767\) 0.956988 0.0345549
\(768\) 0 0
\(769\) 31.6203 1.14026 0.570129 0.821555i \(-0.306893\pi\)
0.570129 + 0.821555i \(0.306893\pi\)
\(770\) 0 0
\(771\) −11.5243 + 11.5243i −0.415037 + 0.415037i
\(772\) 0 0
\(773\) −10.6240 10.6240i −0.382118 0.382118i 0.489747 0.871865i \(-0.337089\pi\)
−0.871865 + 0.489747i \(0.837089\pi\)
\(774\) 0 0
\(775\) 18.7590i 0.673843i
\(776\) 0 0
\(777\) 5.04627i 0.181034i
\(778\) 0 0
\(779\) −7.38796 7.38796i −0.264701 0.264701i
\(780\) 0 0
\(781\) 17.9218 17.9218i 0.641292 0.641292i
\(782\) 0 0
\(783\) −1.86001 −0.0664714
\(784\) 0 0
\(785\) 32.8443 1.17226
\(786\) 0 0
\(787\) 34.2598 34.2598i 1.22123 1.22123i 0.254035 0.967195i \(-0.418242\pi\)
0.967195 0.254035i \(-0.0817580\pi\)
\(788\) 0 0
\(789\) 11.3077 + 11.3077i 0.402564 + 0.402564i
\(790\) 0 0
\(791\) 5.62753i 0.200092i
\(792\) 0 0
\(793\) 4.58551i 0.162836i
\(794\) 0 0
\(795\) −17.2375 17.2375i −0.611351 0.611351i
\(796\) 0 0
\(797\) −8.55176 + 8.55176i −0.302919 + 0.302919i −0.842155 0.539236i \(-0.818713\pi\)
0.539236 + 0.842155i \(0.318713\pi\)
\(798\) 0 0
\(799\) −33.5901