Properties

Label 1792.2.m.e.449.7
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 449.7
Root \(-1.09227 - 0.838128i\) of defining polynomial
Character \(\chi\) \(=\) 1792.449
Dual form 1792.2.m.e.1345.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.26274 - 1.26274i) q^{3} +(-2.95746 - 2.95746i) q^{5} +1.00000i q^{7} -0.189043i q^{9} +O(q^{10})\) \(q+(1.26274 - 1.26274i) q^{3} +(-2.95746 - 2.95746i) q^{5} +1.00000i q^{7} -0.189043i q^{9} +(3.18454 + 3.18454i) q^{11} +(-3.42541 + 3.42541i) q^{13} -7.46903 q^{15} -5.13834 q^{17} +(1.50497 - 1.50497i) q^{19} +(1.26274 + 1.26274i) q^{21} +7.11888i q^{23} +12.4932i q^{25} +(3.54952 + 3.54952i) q^{27} +(3.84618 - 3.84618i) q^{29} -0.831138 q^{31} +8.04251 q^{33} +(2.95746 - 2.95746i) q^{35} +(5.64619 + 5.64619i) q^{37} +8.65084i q^{39} +2.22639i q^{41} +(-1.61789 - 1.61789i) q^{43} +(-0.559087 + 0.559087i) q^{45} -7.83759 q^{47} -1.00000 q^{49} +(-6.48840 + 6.48840i) q^{51} +(-5.58781 - 5.58781i) q^{53} -18.8363i q^{55} -3.80079i q^{57} +(-1.85835 - 1.85835i) q^{59} +(1.65017 - 1.65017i) q^{61} +0.189043 q^{63} +20.2611 q^{65} +(-5.77581 + 5.77581i) q^{67} +(8.98933 + 8.98933i) q^{69} -6.04851i q^{71} +7.67177i q^{73} +(15.7757 + 15.7757i) q^{75} +(-3.18454 + 3.18454i) q^{77} +1.90198 q^{79} +9.53139 q^{81} +(7.97920 - 7.97920i) q^{83} +(15.1964 + 15.1964i) q^{85} -9.71349i q^{87} -2.49938i q^{89} +(-3.42541 - 3.42541i) q^{91} +(-1.04951 + 1.04951i) q^{93} -8.90180 q^{95} -1.98784 q^{97} +(0.602015 - 0.602015i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{3} - 4q^{5} + O(q^{10}) \) \( 16q - 4q^{3} - 4q^{5} + 8q^{11} + 12q^{13} - 8q^{17} - 4q^{19} - 4q^{21} + 56q^{27} - 8q^{31} + 16q^{33} + 4q^{35} - 8q^{37} + 24q^{43} - 36q^{45} - 40q^{47} - 16q^{49} - 24q^{51} - 32q^{53} + 4q^{59} - 20q^{61} + 24q^{63} + 72q^{65} - 32q^{67} + 56q^{69} + 28q^{75} - 8q^{77} - 40q^{81} - 36q^{83} + 12q^{91} + 8q^{93} - 80q^{95} - 72q^{97} + 8q^{99} + O(q^{100}) \)

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
\(3\) 1.26274 1.26274i 0.729045 0.729045i −0.241384 0.970430i \(-0.577601\pi\)
0.970430 + 0.241384i \(0.0776014\pi\)
\(4\) 0 0
\(5\) −2.95746 2.95746i −1.32262 1.32262i −0.911650 0.410967i \(-0.865191\pi\)
−0.410967 0.911650i \(-0.634809\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0.189043i 0.0630143i
\(10\) 0 0
\(11\) 3.18454 + 3.18454i 0.960175 + 0.960175i 0.999237 0.0390622i \(-0.0124370\pi\)
−0.0390622 + 0.999237i \(0.512437\pi\)
\(12\) 0 0
\(13\) −3.42541 + 3.42541i −0.950039 + 0.950039i −0.998810 0.0487712i \(-0.984469\pi\)
0.0487712 + 0.998810i \(0.484469\pi\)
\(14\) 0 0
\(15\) −7.46903 −1.92850
\(16\) 0 0
\(17\) −5.13834 −1.24623 −0.623115 0.782130i \(-0.714133\pi\)
−0.623115 + 0.782130i \(0.714133\pi\)
\(18\) 0 0
\(19\) 1.50497 1.50497i 0.345265 0.345265i −0.513078 0.858342i \(-0.671495\pi\)
0.858342 + 0.513078i \(0.171495\pi\)
\(20\) 0 0
\(21\) 1.26274 + 1.26274i 0.275553 + 0.275553i
\(22\) 0 0
\(23\) 7.11888i 1.48439i 0.670184 + 0.742195i \(0.266215\pi\)
−0.670184 + 0.742195i \(0.733785\pi\)
\(24\) 0 0
\(25\) 12.4932i 2.49863i
\(26\) 0 0
\(27\) 3.54952 + 3.54952i 0.683105 + 0.683105i
\(28\) 0 0
\(29\) 3.84618 3.84618i 0.714218 0.714218i −0.253197 0.967415i \(-0.581482\pi\)
0.967415 + 0.253197i \(0.0814820\pi\)
\(30\) 0 0
\(31\) −0.831138 −0.149277 −0.0746384 0.997211i \(-0.523780\pi\)
−0.0746384 + 0.997211i \(0.523780\pi\)
\(32\) 0 0
\(33\) 8.04251 1.40002
\(34\) 0 0
\(35\) 2.95746 2.95746i 0.499902 0.499902i
\(36\) 0 0
\(37\) 5.64619 + 5.64619i 0.928229 + 0.928229i 0.997591 0.0693630i \(-0.0220967\pi\)
−0.0693630 + 0.997591i \(0.522097\pi\)
\(38\) 0 0
\(39\) 8.65084i 1.38524i
\(40\) 0 0
\(41\) 2.22639i 0.347704i 0.984772 + 0.173852i \(0.0556214\pi\)
−0.984772 + 0.173852i \(0.944379\pi\)
\(42\) 0 0
\(43\) −1.61789 1.61789i −0.246726 0.246726i 0.572900 0.819626i \(-0.305818\pi\)
−0.819626 + 0.572900i \(0.805818\pi\)
\(44\) 0 0
\(45\) −0.559087 + 0.559087i −0.0833438 + 0.0833438i
\(46\) 0 0
\(47\) −7.83759 −1.14323 −0.571615 0.820522i \(-0.693683\pi\)
−0.571615 + 0.820522i \(0.693683\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −6.48840 + 6.48840i −0.908558 + 0.908558i
\(52\) 0 0
\(53\) −5.58781 5.58781i −0.767544 0.767544i 0.210129 0.977674i \(-0.432612\pi\)
−0.977674 + 0.210129i \(0.932612\pi\)
\(54\) 0 0
\(55\) 18.8363i 2.53989i
\(56\) 0 0
\(57\) 3.80079i 0.503427i
\(58\) 0 0
\(59\) −1.85835 1.85835i −0.241937 0.241937i 0.575714 0.817651i \(-0.304724\pi\)
−0.817651 + 0.575714i \(0.804724\pi\)
\(60\) 0 0
\(61\) 1.65017 1.65017i 0.211283 0.211283i −0.593529 0.804812i \(-0.702266\pi\)
0.804812 + 0.593529i \(0.202266\pi\)
\(62\) 0 0
\(63\) 0.189043 0.0238172
\(64\) 0 0
\(65\) 20.2611 2.51307
\(66\) 0 0
\(67\) −5.77581 + 5.77581i −0.705627 + 0.705627i −0.965613 0.259985i \(-0.916282\pi\)
0.259985 + 0.965613i \(0.416282\pi\)
\(68\) 0 0
\(69\) 8.98933 + 8.98933i 1.08219 + 1.08219i
\(70\) 0 0
\(71\) 6.04851i 0.717826i −0.933371 0.358913i \(-0.883147\pi\)
0.933371 0.358913i \(-0.116853\pi\)
\(72\) 0 0
\(73\) 7.67177i 0.897913i 0.893554 + 0.448957i \(0.148204\pi\)
−0.893554 + 0.448957i \(0.851796\pi\)
\(74\) 0 0
\(75\) 15.7757 + 15.7757i 1.82162 + 1.82162i
\(76\) 0 0
\(77\) −3.18454 + 3.18454i −0.362912 + 0.362912i
\(78\) 0 0
\(79\) 1.90198 0.213989 0.106995 0.994260i \(-0.465877\pi\)
0.106995 + 0.994260i \(0.465877\pi\)
\(80\) 0 0
\(81\) 9.53139 1.05904
\(82\) 0 0
\(83\) 7.97920 7.97920i 0.875831 0.875831i −0.117269 0.993100i \(-0.537414\pi\)
0.993100 + 0.117269i \(0.0374139\pi\)
\(84\) 0 0
\(85\) 15.1964 + 15.1964i 1.64829 + 1.64829i
\(86\) 0 0
\(87\) 9.71349i 1.04139i
\(88\) 0 0
\(89\) 2.49938i 0.264934i −0.991187 0.132467i \(-0.957710\pi\)
0.991187 0.132467i \(-0.0422898\pi\)
\(90\) 0 0
\(91\) −3.42541 3.42541i −0.359081 0.359081i
\(92\) 0 0
\(93\) −1.04951 + 1.04951i −0.108830 + 0.108830i
\(94\) 0 0
\(95\) −8.90180 −0.913306
\(96\) 0 0
\(97\) −1.98784 −0.201834 −0.100917 0.994895i \(-0.532178\pi\)
−0.100917 + 0.994895i \(0.532178\pi\)
\(98\) 0 0
\(99\) 0.602015 0.602015i 0.0605047 0.0605047i
\(100\) 0 0
\(101\) 11.1341 + 11.1341i 1.10788 + 1.10788i 0.993429 + 0.114451i \(0.0365110\pi\)
0.114451 + 0.993429i \(0.463489\pi\)
\(102\) 0 0
\(103\) 15.2106i 1.49874i 0.662150 + 0.749371i \(0.269644\pi\)
−0.662150 + 0.749371i \(0.730356\pi\)
\(104\) 0 0
\(105\) 7.46903i 0.728903i
\(106\) 0 0
\(107\) 0.897608 + 0.897608i 0.0867751 + 0.0867751i 0.749162 0.662387i \(-0.230456\pi\)
−0.662387 + 0.749162i \(0.730456\pi\)
\(108\) 0 0
\(109\) −2.84528 + 2.84528i −0.272528 + 0.272528i −0.830117 0.557589i \(-0.811727\pi\)
0.557589 + 0.830117i \(0.311727\pi\)
\(110\) 0 0
\(111\) 14.2594 1.35344
\(112\) 0 0
\(113\) −1.66487 −0.156618 −0.0783089 0.996929i \(-0.524952\pi\)
−0.0783089 + 0.996929i \(0.524952\pi\)
\(114\) 0 0
\(115\) 21.0538 21.0538i 1.96328 1.96328i
\(116\) 0 0
\(117\) 0.647550 + 0.647550i 0.0598660 + 0.0598660i
\(118\) 0 0
\(119\) 5.13834i 0.471031i
\(120\) 0 0
\(121\) 9.28258i 0.843871i
\(122\) 0 0
\(123\) 2.81136 + 2.81136i 0.253492 + 0.253492i
\(124\) 0 0
\(125\) 22.1607 22.1607i 1.98212 1.98212i
\(126\) 0 0
\(127\) 7.86069 0.697523 0.348762 0.937211i \(-0.386602\pi\)
0.348762 + 0.937211i \(0.386602\pi\)
\(128\) 0 0
\(129\) −4.08596 −0.359749
\(130\) 0 0
\(131\) −5.44479 + 5.44479i −0.475713 + 0.475713i −0.903758 0.428045i \(-0.859203\pi\)
0.428045 + 0.903758i \(0.359203\pi\)
\(132\) 0 0
\(133\) 1.50497 + 1.50497i 0.130498 + 0.130498i
\(134\) 0 0
\(135\) 20.9951i 1.80697i
\(136\) 0 0
\(137\) 17.6977i 1.51201i 0.654564 + 0.756007i \(0.272852\pi\)
−0.654564 + 0.756007i \(0.727148\pi\)
\(138\) 0 0
\(139\) −11.4502 11.4502i −0.971194 0.971194i 0.0284022 0.999597i \(-0.490958\pi\)
−0.999597 + 0.0284022i \(0.990958\pi\)
\(140\) 0 0
\(141\) −9.89687 + 9.89687i −0.833467 + 0.833467i
\(142\) 0 0
\(143\) −21.8167 −1.82441
\(144\) 0 0
\(145\) −22.7499 −1.88927
\(146\) 0 0
\(147\) −1.26274 + 1.26274i −0.104149 + 0.104149i
\(148\) 0 0
\(149\) 8.61299 + 8.61299i 0.705604 + 0.705604i 0.965608 0.260004i \(-0.0837239\pi\)
−0.260004 + 0.965608i \(0.583724\pi\)
\(150\) 0 0
\(151\) 17.7449i 1.44406i 0.691863 + 0.722029i \(0.256790\pi\)
−0.691863 + 0.722029i \(0.743210\pi\)
\(152\) 0 0
\(153\) 0.971366i 0.0785303i
\(154\) 0 0
\(155\) 2.45806 + 2.45806i 0.197436 + 0.197436i
\(156\) 0 0
\(157\) −9.88456 + 9.88456i −0.788873 + 0.788873i −0.981310 0.192436i \(-0.938361\pi\)
0.192436 + 0.981310i \(0.438361\pi\)
\(158\) 0 0
\(159\) −14.1119 −1.11915
\(160\) 0 0
\(161\) −7.11888 −0.561047
\(162\) 0 0
\(163\) −9.61397 + 9.61397i −0.753024 + 0.753024i −0.975042 0.222019i \(-0.928735\pi\)
0.222019 + 0.975042i \(0.428735\pi\)
\(164\) 0 0
\(165\) −23.7854 23.7854i −1.85169 1.85169i
\(166\) 0 0
\(167\) 6.70735i 0.519030i −0.965739 0.259515i \(-0.916437\pi\)
0.965739 0.259515i \(-0.0835627\pi\)
\(168\) 0 0
\(169\) 10.4669i 0.805147i
\(170\) 0 0
\(171\) −0.284505 0.284505i −0.0217566 0.0217566i
\(172\) 0 0
\(173\) −14.7331 + 14.7331i −1.12014 + 1.12014i −0.128417 + 0.991720i \(0.540990\pi\)
−0.991720 + 0.128417i \(0.959010\pi\)
\(174\) 0 0
\(175\) −12.4932 −0.944394
\(176\) 0 0
\(177\) −4.69325 −0.352766
\(178\) 0 0
\(179\) 15.8453 15.8453i 1.18433 1.18433i 0.205719 0.978611i \(-0.434047\pi\)
0.978611 0.205719i \(-0.0659533\pi\)
\(180\) 0 0
\(181\) 3.13208 + 3.13208i 0.232805 + 0.232805i 0.813863 0.581057i \(-0.197361\pi\)
−0.581057 + 0.813863i \(0.697361\pi\)
\(182\) 0 0
\(183\) 4.16749i 0.308070i
\(184\) 0 0
\(185\) 33.3968i 2.45538i
\(186\) 0 0
\(187\) −16.3632 16.3632i −1.19660 1.19660i
\(188\) 0 0
\(189\) −3.54952 + 3.54952i −0.258189 + 0.258189i
\(190\) 0 0
\(191\) −7.38976 −0.534704 −0.267352 0.963599i \(-0.586149\pi\)
−0.267352 + 0.963599i \(0.586149\pi\)
\(192\) 0 0
\(193\) 0.139138 0.0100154 0.00500769 0.999987i \(-0.498406\pi\)
0.00500769 + 0.999987i \(0.498406\pi\)
\(194\) 0 0
\(195\) 25.5845 25.5845i 1.83215 1.83215i
\(196\) 0 0
\(197\) −7.35796 7.35796i −0.524233 0.524233i 0.394614 0.918847i \(-0.370878\pi\)
−0.918847 + 0.394614i \(0.870878\pi\)
\(198\) 0 0
\(199\) 5.09550i 0.361211i 0.983556 + 0.180605i \(0.0578057\pi\)
−0.983556 + 0.180605i \(0.942194\pi\)
\(200\) 0 0
\(201\) 14.5867i 1.02887i
\(202\) 0 0
\(203\) 3.84618 + 3.84618i 0.269949 + 0.269949i
\(204\) 0 0
\(205\) 6.58447 6.58447i 0.459879 0.459879i
\(206\) 0 0
\(207\) 1.34577 0.0935378
\(208\) 0 0
\(209\) 9.58529 0.663029
\(210\) 0 0
\(211\) −8.88050 + 8.88050i −0.611359 + 0.611359i −0.943300 0.331941i \(-0.892296\pi\)
0.331941 + 0.943300i \(0.392296\pi\)
\(212\) 0 0
\(213\) −7.63772 7.63772i −0.523328 0.523328i
\(214\) 0 0
\(215\) 9.56970i 0.652648i
\(216\) 0 0
\(217\) 0.831138i 0.0564213i
\(218\) 0 0
\(219\) 9.68748 + 9.68748i 0.654619 + 0.654619i
\(220\) 0 0
\(221\) 17.6009 17.6009i 1.18397 1.18397i
\(222\) 0 0
\(223\) 9.66949 0.647517 0.323758 0.946140i \(-0.395054\pi\)
0.323758 + 0.946140i \(0.395054\pi\)
\(224\) 0 0
\(225\) 2.36174 0.157450
\(226\) 0 0
\(227\) −2.11845 + 2.11845i −0.140606 + 0.140606i −0.773906 0.633300i \(-0.781700\pi\)
0.633300 + 0.773906i \(0.281700\pi\)
\(228\) 0 0
\(229\) −6.36091 6.36091i −0.420341 0.420341i 0.464980 0.885321i \(-0.346061\pi\)
−0.885321 + 0.464980i \(0.846061\pi\)
\(230\) 0 0
\(231\) 8.04251i 0.529158i
\(232\) 0 0
\(233\) 7.53066i 0.493350i −0.969098 0.246675i \(-0.920662\pi\)
0.969098 0.246675i \(-0.0793380\pi\)
\(234\) 0 0
\(235\) 23.1794 + 23.1794i 1.51206 + 1.51206i
\(236\) 0 0
\(237\) 2.40171 2.40171i 0.156008 0.156008i
\(238\) 0 0
\(239\) 1.87072 0.121007 0.0605034 0.998168i \(-0.480729\pi\)
0.0605034 + 0.998168i \(0.480729\pi\)
\(240\) 0 0
\(241\) −14.4911 −0.933454 −0.466727 0.884401i \(-0.654567\pi\)
−0.466727 + 0.884401i \(0.654567\pi\)
\(242\) 0 0
\(243\) 1.38715 1.38715i 0.0889857 0.0889857i
\(244\) 0 0
\(245\) 2.95746 + 2.95746i 0.188945 + 0.188945i
\(246\) 0 0
\(247\) 10.3103i 0.656029i
\(248\) 0 0
\(249\) 20.1514i 1.27704i
\(250\) 0 0
\(251\) −4.48287 4.48287i −0.282956 0.282956i 0.551330 0.834287i \(-0.314120\pi\)
−0.834287 + 0.551330i \(0.814120\pi\)
\(252\) 0 0
\(253\) −22.6704 + 22.6704i −1.42527 + 1.42527i
\(254\) 0 0
\(255\) 38.3784 2.40335
\(256\) 0 0
\(257\) 12.1594 0.758483 0.379241 0.925298i \(-0.376185\pi\)
0.379241 + 0.925298i \(0.376185\pi\)
\(258\) 0 0
\(259\) −5.64619 + 5.64619i −0.350837 + 0.350837i
\(260\) 0 0
\(261\) −0.727094 0.727094i −0.0450060 0.0450060i
\(262\) 0 0
\(263\) 0.0299529i 0.00184698i 1.00000 0.000923488i \(0.000293955\pi\)
−1.00000 0.000923488i \(0.999706\pi\)
\(264\) 0 0
\(265\) 33.0514i 2.03033i
\(266\) 0 0
\(267\) −3.15607 3.15607i −0.193149 0.193149i
\(268\) 0 0
\(269\) 12.7719 12.7719i 0.778718 0.778718i −0.200895 0.979613i \(-0.564385\pi\)
0.979613 + 0.200895i \(0.0643849\pi\)
\(270\) 0 0
\(271\) −10.0906 −0.612958 −0.306479 0.951877i \(-0.599151\pi\)
−0.306479 + 0.951877i \(0.599151\pi\)
\(272\) 0 0
\(273\) −8.65084 −0.523573
\(274\) 0 0
\(275\) −39.7849 + 39.7849i −2.39912 + 2.39912i
\(276\) 0 0
\(277\) 6.26957 + 6.26957i 0.376702 + 0.376702i 0.869911 0.493209i \(-0.164176\pi\)
−0.493209 + 0.869911i \(0.664176\pi\)
\(278\) 0 0
\(279\) 0.157121i 0.00940657i
\(280\) 0 0
\(281\) 11.6731i 0.696356i −0.937428 0.348178i \(-0.886800\pi\)
0.937428 0.348178i \(-0.113200\pi\)
\(282\) 0 0
\(283\) 8.87749 + 8.87749i 0.527712 + 0.527712i 0.919890 0.392178i \(-0.128278\pi\)
−0.392178 + 0.919890i \(0.628278\pi\)
\(284\) 0 0
\(285\) −11.2407 + 11.2407i −0.665841 + 0.665841i
\(286\) 0 0
\(287\) −2.22639 −0.131420
\(288\) 0 0
\(289\) 9.40252 0.553090
\(290\) 0 0
\(291\) −2.51013 + 2.51013i −0.147146 + 0.147146i
\(292\) 0 0
\(293\) −17.1935 17.1935i −1.00445 1.00445i −0.999990 0.00446326i \(-0.998579\pi\)
−0.00446326 0.999990i \(-0.501421\pi\)
\(294\) 0 0
\(295\) 10.9920i 0.639980i
\(296\) 0 0
\(297\) 22.6072i 1.31180i
\(298\) 0 0
\(299\) −24.3851 24.3851i −1.41023 1.41023i
\(300\) 0 0
\(301\) 1.61789 1.61789i 0.0932536 0.0932536i
\(302\) 0 0
\(303\) 28.1189 1.61539
\(304\) 0 0
\(305\) −9.76065 −0.558893
\(306\) 0 0
\(307\) −19.2712 + 19.2712i −1.09987 + 1.09987i −0.105440 + 0.994426i \(0.533625\pi\)
−0.994426 + 0.105440i \(0.966375\pi\)
\(308\) 0 0
\(309\) 19.2071 + 19.2071i 1.09265 + 1.09265i
\(310\) 0 0
\(311\) 5.78650i 0.328122i 0.986450 + 0.164061i \(0.0524595\pi\)
−0.986450 + 0.164061i \(0.947541\pi\)
\(312\) 0 0
\(313\) 3.03673i 0.171646i 0.996310 + 0.0858231i \(0.0273520\pi\)
−0.996310 + 0.0858231i \(0.972648\pi\)
\(314\) 0 0
\(315\) −0.559087 0.559087i −0.0315010 0.0315010i
\(316\) 0 0
\(317\) 3.32219 3.32219i 0.186593 0.186593i −0.607629 0.794221i \(-0.707879\pi\)
0.794221 + 0.607629i \(0.207879\pi\)
\(318\) 0 0
\(319\) 24.4966 1.37155
\(320\) 0 0
\(321\) 2.26690 0.126526
\(322\) 0 0
\(323\) −7.73306 + 7.73306i −0.430279 + 0.430279i
\(324\) 0 0
\(325\) −42.7942 42.7942i −2.37380 2.37380i
\(326\) 0 0
\(327\) 7.18572i 0.397371i
\(328\) 0 0
\(329\) 7.83759i 0.432101i
\(330\) 0 0
\(331\) −25.5017 25.5017i −1.40170 1.40170i −0.794710 0.606990i \(-0.792377\pi\)
−0.606990 0.794710i \(-0.707623\pi\)
\(332\) 0 0
\(333\) 1.06737 1.06737i 0.0584917 0.0584917i
\(334\) 0 0
\(335\) 34.1634 1.86655
\(336\) 0 0
\(337\) 31.3282 1.70656 0.853279 0.521454i \(-0.174610\pi\)
0.853279 + 0.521454i \(0.174610\pi\)
\(338\) 0 0
\(339\) −2.10230 + 2.10230i −0.114182 + 0.114182i
\(340\) 0 0
\(341\) −2.64679 2.64679i −0.143332 0.143332i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 53.1712i 2.86264i
\(346\) 0 0
\(347\) −24.1128 24.1128i −1.29444 1.29444i −0.932011 0.362429i \(-0.881947\pi\)
−0.362429 0.932011i \(-0.618053\pi\)
\(348\) 0 0
\(349\) 20.9731 20.9731i 1.12266 1.12266i 0.131324 0.991340i \(-0.458077\pi\)
0.991340 0.131324i \(-0.0419228\pi\)
\(350\) 0 0
\(351\) −24.3171 −1.29795
\(352\) 0 0
\(353\) −0.605671 −0.0322366 −0.0161183 0.999870i \(-0.505131\pi\)
−0.0161183 + 0.999870i \(0.505131\pi\)
\(354\) 0 0
\(355\) −17.8882 + 17.8882i −0.949409 + 0.949409i
\(356\) 0 0
\(357\) −6.48840 6.48840i −0.343403 0.343403i
\(358\) 0 0
\(359\) 11.6214i 0.613354i 0.951814 + 0.306677i \(0.0992171\pi\)
−0.951814 + 0.306677i \(0.900783\pi\)
\(360\) 0 0
\(361\) 14.4701i 0.761585i
\(362\) 0 0
\(363\) 11.7215 + 11.7215i 0.615220 + 0.615220i
\(364\) 0 0
\(365\) 22.6890 22.6890i 1.18760 1.18760i
\(366\) 0 0
\(367\) −13.1299 −0.685376 −0.342688 0.939449i \(-0.611337\pi\)
−0.342688 + 0.939449i \(0.611337\pi\)
\(368\) 0 0
\(369\) 0.420883 0.0219103
\(370\) 0 0
\(371\) 5.58781 5.58781i 0.290104 0.290104i
\(372\) 0 0
\(373\) 13.0674 + 13.0674i 0.676604 + 0.676604i 0.959230 0.282626i \(-0.0912056\pi\)
−0.282626 + 0.959230i \(0.591206\pi\)
\(374\) 0 0
\(375\) 55.9666i 2.89010i
\(376\) 0 0
\(377\) 26.3495i 1.35707i
\(378\) 0 0
\(379\) −2.92702 2.92702i −0.150351 0.150351i 0.627924 0.778275i \(-0.283905\pi\)
−0.778275 + 0.627924i \(0.783905\pi\)
\(380\) 0 0
\(381\) 9.92603 9.92603i 0.508526 0.508526i
\(382\) 0 0
\(383\) 34.3667 1.75606 0.878029 0.478608i \(-0.158858\pi\)
0.878029 + 0.478608i \(0.158858\pi\)
\(384\) 0 0
\(385\) 18.8363 0.959987
\(386\) 0 0
\(387\) −0.305851 + 0.305851i −0.0155473 + 0.0155473i
\(388\) 0 0
\(389\) 7.44858 + 7.44858i 0.377658 + 0.377658i 0.870257 0.492599i \(-0.163953\pi\)
−0.492599 + 0.870257i \(0.663953\pi\)
\(390\) 0 0
\(391\) 36.5792i 1.84989i
\(392\) 0 0
\(393\) 13.7507i 0.693633i
\(394\) 0 0
\(395\) −5.62503 5.62503i −0.283026 0.283026i
\(396\) 0 0
\(397\) 7.92582 7.92582i 0.397786 0.397786i −0.479666 0.877451i \(-0.659242\pi\)
0.877451 + 0.479666i \(0.159242\pi\)
\(398\) 0 0
\(399\) 3.80079 0.190278
\(400\) 0 0
\(401\) 15.4031 0.769192 0.384596 0.923085i \(-0.374341\pi\)
0.384596 + 0.923085i \(0.374341\pi\)
\(402\) 0 0
\(403\) 2.84699 2.84699i 0.141819 0.141819i
\(404\) 0 0
\(405\) −28.1887 28.1887i −1.40071 1.40071i
\(406\) 0 0
\(407\) 35.9610i 1.78252i
\(408\) 0 0
\(409\) 22.6029i 1.11764i 0.829289 + 0.558820i \(0.188746\pi\)
−0.829289 + 0.558820i \(0.811254\pi\)
\(410\) 0 0
\(411\) 22.3476 + 22.3476i 1.10233 + 1.10233i
\(412\) 0 0
\(413\) 1.85835 1.85835i 0.0914436 0.0914436i
\(414\) 0 0
\(415\) −47.1964 −2.31678
\(416\) 0 0
\(417\) −28.9174 −1.41609
\(418\) 0 0
\(419\) 9.01333 9.01333i 0.440330 0.440330i −0.451793 0.892123i \(-0.649215\pi\)
0.892123 + 0.451793i \(0.149215\pi\)
\(420\) 0 0
\(421\) −21.8788 21.8788i −1.06631 1.06631i −0.997640 0.0686687i \(-0.978125\pi\)
−0.0686687 0.997640i \(-0.521875\pi\)
\(422\) 0 0
\(423\) 1.48164i 0.0720399i
\(424\) 0 0
\(425\) 64.1941i 3.11387i
\(426\) 0 0
\(427\) 1.65017 + 1.65017i 0.0798575 + 0.0798575i
\(428\) 0 0
\(429\) −27.5489 + 27.5489i −1.33007 + 1.33007i
\(430\) 0 0
\(431\) 13.1089 0.631434 0.315717 0.948853i \(-0.397755\pi\)
0.315717 + 0.948853i \(0.397755\pi\)
\(432\) 0 0
\(433\) −35.1859 −1.69093 −0.845463 0.534033i \(-0.820676\pi\)
−0.845463 + 0.534033i \(0.820676\pi\)
\(434\) 0 0
\(435\) −28.7273 + 28.7273i −1.37737 + 1.37737i
\(436\) 0 0
\(437\) 10.7137 + 10.7137i 0.512507 + 0.512507i
\(438\) 0 0
\(439\) 4.82251i 0.230166i −0.993356 0.115083i \(-0.963287\pi\)
0.993356 0.115083i \(-0.0367134\pi\)
\(440\) 0 0
\(441\) 0.189043i 0.00900204i
\(442\) 0 0
\(443\) 12.5595 + 12.5595i 0.596719 + 0.596719i 0.939438 0.342719i \(-0.111348\pi\)
−0.342719 + 0.939438i \(0.611348\pi\)
\(444\) 0 0
\(445\) −7.39181 + 7.39181i −0.350406 + 0.350406i
\(446\) 0 0
\(447\) 21.7520 1.02883
\(448\) 0 0
\(449\) −29.9204 −1.41203 −0.706015 0.708197i \(-0.749509\pi\)
−0.706015 + 0.708197i \(0.749509\pi\)
\(450\) 0 0
\(451\) −7.09003 + 7.09003i −0.333856 + 0.333856i
\(452\) 0 0
\(453\) 22.4072 + 22.4072i 1.05278 + 1.05278i
\(454\) 0 0
\(455\) 20.2611i 0.949853i
\(456\) 0 0
\(457\) 29.1293i 1.36261i −0.732000 0.681305i \(-0.761413\pi\)
0.732000 0.681305i \(-0.238587\pi\)
\(458\) 0 0
\(459\) −18.2386 18.2386i −0.851306 0.851306i
\(460\) 0 0
\(461\) −7.15458 + 7.15458i −0.333222 + 0.333222i −0.853809 0.520587i \(-0.825713\pi\)
0.520587 + 0.853809i \(0.325713\pi\)
\(462\) 0 0
\(463\) 40.1547 1.86615 0.933074 0.359686i \(-0.117116\pi\)
0.933074 + 0.359686i \(0.117116\pi\)
\(464\) 0 0
\(465\) 6.20779 0.287880
\(466\) 0 0
\(467\) 28.5054 28.5054i 1.31907 1.31907i 0.404563 0.914510i \(-0.367423\pi\)
0.914510 0.404563i \(-0.132577\pi\)
\(468\) 0 0
\(469\) −5.77581 5.77581i −0.266702 0.266702i
\(470\) 0 0
\(471\) 24.9633i 1.15025i
\(472\) 0 0
\(473\) 10.3045i 0.473800i
\(474\) 0 0
\(475\) 18.8019 + 18.8019i 0.862689 + 0.862689i
\(476\) 0 0
\(477\) −1.05634 + 1.05634i −0.0483663 + 0.0483663i
\(478\) 0 0
\(479\) 12.6994 0.580249 0.290124 0.956989i \(-0.406303\pi\)
0.290124 + 0.956989i \(0.406303\pi\)
\(480\) 0 0
\(481\) −38.6811 −1.76371
\(482\) 0 0
\(483\) −8.98933 + 8.98933i −0.409028 + 0.409028i
\(484\) 0 0
\(485\) 5.87895 + 5.87895i 0.266949 + 0.266949i
\(486\) 0 0
\(487\) 34.2373i 1.55144i −0.631076 0.775721i \(-0.717386\pi\)
0.631076 0.775721i \(-0.282614\pi\)
\(488\) 0 0
\(489\) 24.2799i 1.09798i
\(490\) 0 0
\(491\) −21.4142 21.4142i −0.966412 0.966412i 0.0330424 0.999454i \(-0.489480\pi\)
−0.999454 + 0.0330424i \(0.989480\pi\)
\(492\) 0 0
\(493\) −19.7630 + 19.7630i −0.890080 + 0.890080i
\(494\) 0 0
\(495\) −3.56087 −0.160049
\(496\) 0 0
\(497\) 6.04851 0.271313
\(498\) 0 0
\(499\) 15.7099 15.7099i 0.703270 0.703270i −0.261841 0.965111i \(-0.584330\pi\)
0.965111 + 0.261841i \(0.0843296\pi\)
\(500\) 0 0
\(501\) −8.46966 8.46966i −0.378397 0.378397i
\(502\) 0 0
\(503\) 28.6238i 1.27627i 0.769923 + 0.638137i \(0.220294\pi\)
−0.769923 + 0.638137i \(0.779706\pi\)
\(504\) 0 0
\(505\) 65.8571i 2.93060i
\(506\) 0 0
\(507\) −13.2170 13.2170i −0.586989 0.586989i
\(508\) 0 0
\(509\) 15.0347 15.0347i 0.666399 0.666399i −0.290481 0.956881i \(-0.593815\pi\)
0.956881 + 0.290481i \(0.0938154\pi\)
\(510\) 0 0
\(511\) −7.67177 −0.339379
\(512\) 0 0
\(513\) 10.6839 0.471704
\(514\) 0 0
\(515\) 44.9847 44.9847i 1.98226 1.98226i
\(516\) 0 0
\(517\) −24.9591 24.9591i −1.09770 1.09770i
\(518\) 0 0
\(519\) 37.2083i 1.63326i
\(520\) 0 0
\(521\) 23.7033i 1.03846i 0.854635 + 0.519230i \(0.173781\pi\)
−0.854635 + 0.519230i \(0.826219\pi\)
\(522\) 0 0
\(523\) 13.9046 + 13.9046i 0.608004 + 0.608004i 0.942424 0.334420i \(-0.108541\pi\)
−0.334420 + 0.942424i \(0.608541\pi\)
\(524\) 0 0
\(525\) −15.7757 + 15.7757i −0.688506 + 0.688506i
\(526\) 0 0
\(527\) 4.27067 0.186033
\(528\) 0 0
\(529\) −27.6785 −1.20341
\(530\) 0 0
\(531\) −0.351308 + 0.351308i −0.0152455 + 0.0152455i
\(532\) 0 0
\(533\) −7.62631 7.62631i −0.330332 0.330332i
\(534\) 0 0
\(535\) 5.30928i 0.229540i
\(536\) 0 0
\(537\) 40.0170i 1.72686i
\(538\) 0 0
\(539\) −3.18454 3.18454i −0.137168 0.137168i
\(540\) 0 0
\(541\) −8.66926 + 8.66926i −0.372721 + 0.372721i −0.868467 0.495747i \(-0.834894\pi\)
0.495747 + 0.868467i \(0.334894\pi\)
\(542\) 0 0
\(543\) 7.91002 0.339451
\(544\) 0 0
\(545\) 16.8296 0.720901
\(546\) 0 0
\(547\) −4.07284 + 4.07284i −0.174142 + 0.174142i −0.788796 0.614655i \(-0.789295\pi\)
0.614655 + 0.788796i \(0.289295\pi\)
\(548\) 0 0
\(549\) −0.311954 0.311954i −0.0133139 0.0133139i
\(550\) 0 0
\(551\) 11.5768i 0.493188i
\(552\) 0 0
\(553\) 1.90198i 0.0808804i
\(554\) 0 0
\(555\) −42.1716 42.1716i −1.79008 1.79008i
\(556\) 0 0
\(557\) −1.82388 + 1.82388i −0.0772805 + 0.0772805i −0.744690 0.667410i \(-0.767403\pi\)
0.667410 + 0.744690i \(0.267403\pi\)
\(558\) 0 0
\(559\) 11.0839 0.468798
\(560\) 0 0
\(561\) −41.3252 −1.74475
\(562\) 0 0
\(563\) 10.6911 10.6911i 0.450577 0.450577i −0.444969 0.895546i \(-0.646785\pi\)
0.895546 + 0.444969i \(0.146785\pi\)
\(564\) 0 0
\(565\) 4.92379 + 4.92379i 0.207145 + 0.207145i
\(566\) 0 0
\(567\) 9.53139i 0.400281i
\(568\) 0 0
\(569\) 11.0034i 0.461288i 0.973038 + 0.230644i \(0.0740833\pi\)
−0.973038 + 0.230644i \(0.925917\pi\)
\(570\) 0 0
\(571\) −28.9901 28.9901i −1.21320 1.21320i −0.969968 0.243231i \(-0.921793\pi\)
−0.243231 0.969968i \(-0.578207\pi\)
\(572\) 0 0
\(573\) −9.33137 + 9.33137i −0.389824 + 0.389824i
\(574\) 0 0
\(575\) −88.9373 −3.70894
\(576\) 0 0
\(577\) 2.85596 0.118895 0.0594476 0.998231i \(-0.481066\pi\)
0.0594476 + 0.998231i \(0.481066\pi\)
\(578\) 0 0
\(579\) 0.175696 0.175696i 0.00730167 0.00730167i
\(580\) 0 0
\(581\) 7.97920 + 7.97920i 0.331033 + 0.331033i
\(582\) 0 0
\(583\) 35.5892i 1.47395i
\(584\) 0 0
\(585\) 3.83021i 0.158360i
\(586\) 0 0
\(587\) 17.5561 + 17.5561i 0.724617 + 0.724617i 0.969542 0.244925i \(-0.0787635\pi\)
−0.244925 + 0.969542i \(0.578763\pi\)
\(588\) 0 0
\(589\) −1.25084 + 1.25084i −0.0515400 + 0.0515400i
\(590\) 0 0
\(591\) −18.5824 −0.764379
\(592\) 0 0
\(593\) 7.72713 0.317315 0.158658 0.987334i \(-0.449283\pi\)
0.158658 + 0.987334i \(0.449283\pi\)
\(594\) 0 0
\(595\) −15.1964 + 15.1964i −0.622993 + 0.622993i
\(596\) 0 0
\(597\) 6.43431 + 6.43431i 0.263339 + 0.263339i
\(598\) 0 0
\(599\) 7.28771i 0.297768i −0.988855 0.148884i \(-0.952432\pi\)
0.988855 0.148884i \(-0.0475681\pi\)
\(600\) 0 0
\(601\) 20.0313i 0.817095i 0.912737 + 0.408547i \(0.133965\pi\)
−0.912737 + 0.408547i \(0.866035\pi\)
\(602\) 0 0
\(603\) 1.09188 + 1.09188i 0.0444646 + 0.0444646i
\(604\) 0 0
\(605\) 27.4529 27.4529i 1.11612 1.11612i
\(606\) 0 0
\(607\) −17.2219 −0.699014 −0.349507 0.936934i \(-0.613651\pi\)
−0.349507 + 0.936934i \(0.613651\pi\)
\(608\) 0 0
\(609\) 9.71349 0.393610
\(610\) 0 0
\(611\) 26.8470 26.8470i 1.08611 1.08611i
\(612\) 0 0
\(613\) 26.4453 + 26.4453i 1.06811 + 1.06811i 0.997504 + 0.0706108i \(0.0224948\pi\)
0.0706108 + 0.997504i \(0.477505\pi\)
\(614\) 0 0
\(615\) 16.6290i 0.670545i
\(616\) 0 0
\(617\) 22.1036i 0.889856i 0.895566 + 0.444928i \(0.146771\pi\)
−0.895566 + 0.444928i \(0.853229\pi\)
\(618\) 0 0
\(619\) 21.5602 + 21.5602i 0.866579 + 0.866579i 0.992092 0.125513i \(-0.0400576\pi\)
−0.125513 + 0.992092i \(0.540058\pi\)
\(620\) 0 0
\(621\) −25.2686 + 25.2686i −1.01399 + 1.01399i
\(622\) 0 0
\(623\) 2.49938 0.100135
\(624\) 0 0
\(625\) −68.6132 −2.74453
\(626\) 0 0
\(627\) 12.1038 12.1038i 0.483378 0.483378i
\(628\) 0 0
\(629\) −29.0121 29.0121i −1.15679 1.15679i
\(630\) 0 0
\(631\) 40.3151i 1.60492i −0.596708 0.802458i \(-0.703525\pi\)
0.596708 0.802458i \(-0.296475\pi\)
\(632\) 0 0
\(633\) 22.4276i 0.891417i
\(634\) 0 0
\(635\) −23.2477 23.2477i −0.922556 0.922556i
\(636\) 0 0
\(637\) 3.42541 3.42541i 0.135720 0.135720i
\(638\) 0 0
\(639\) −1.14343 −0.0452333
\(640\) 0 0
\(641\) −0.875535 −0.0345815 −0.0172908 0.999851i \(-0.505504\pi\)
−0.0172908 + 0.999851i \(0.505504\pi\)
\(642\) 0 0
\(643\) 28.5976 28.5976i 1.12778 1.12778i 0.137240 0.990538i \(-0.456177\pi\)
0.990538 0.137240i \(-0.0438230\pi\)
\(644\) 0 0
\(645\) 12.0841 + 12.0841i 0.475810 + 0.475810i
\(646\) 0 0
\(647\) 3.32973i 0.130905i 0.997856 + 0.0654526i \(0.0208491\pi\)
−0.997856 + 0.0654526i \(0.979151\pi\)
\(648\) 0 0
\(649\) 11.8360i 0.464603i
\(650\) 0 0
\(651\) −1.04951 1.04951i −0.0411337 0.0411337i
\(652\) 0 0
\(653\) −20.7599 + 20.7599i −0.812397 + 0.812397i −0.984993 0.172596i \(-0.944785\pi\)
0.172596 + 0.984993i \(0.444785\pi\)
\(654\) 0 0
\(655\) 32.2055 1.25837
\(656\) 0 0
\(657\) 1.45029 0.0565814
\(658\) 0 0
\(659\) −20.7066 + 20.7066i −0.806616 + 0.806616i −0.984120 0.177504i \(-0.943198\pi\)
0.177504 + 0.984120i \(0.443198\pi\)
\(660\) 0 0
\(661\) 9.70914 + 9.70914i 0.377642 + 0.377642i 0.870251 0.492609i \(-0.163957\pi\)
−0.492609 + 0.870251i \(0.663957\pi\)
\(662\) 0 0
\(663\) 44.4509i 1.72633i
\(664\) 0 0
\(665\) 8.90180i 0.345197i
\(666\) 0 0
\(667\) 27.3805 + 27.3805i 1.06018 + 1.06018i
\(668\) 0 0
\(669\) 12.2101 12.2101i 0.472069 0.472069i
\(670\) 0 0
\(671\) 10.5101 0.405737
\(672\) 0 0
\(673\) 49.3202 1.90115 0.950577 0.310490i \(-0.100493\pi\)
0.950577 + 0.310490i \(0.100493\pi\)
\(674\) 0 0
\(675\) −44.3447 + 44.3447i −1.70683 + 1.70683i
\(676\) 0 0
\(677\) 12.2329 + 12.2329i 0.470149 + 0.470149i 0.901963 0.431813i \(-0.142126\pi\)
−0.431813 + 0.901963i \(0.642126\pi\)
\(678\) 0 0
\(679\) 1.98784i 0.0762861i
\(680\) 0 0
\(681\) 5.35011i 0.205017i
\(682\) 0 0
\(683\) −3.79812 3.79812i −0.145331 0.145331i 0.630698 0.776029i \(-0.282769\pi\)
−0.776029 + 0.630698i \(0.782769\pi\)
\(684\) 0 0
\(685\) 52.3402 52.3402i 1.99981 1.99981i
\(686\) 0 0
\(687\) −16.0644 −0.612895
\(688\) 0 0
\(689\) 38.2811 1.45839
\(690\) 0 0
\(691\) −31.7387 + 31.7387i −1.20740 + 1.20740i −0.235531 + 0.971867i \(0.575683\pi\)
−0.971867 + 0.235531i \(0.924317\pi\)
\(692\) 0 0
\(693\) 0.602015 + 0.602015i 0.0228686 + 0.0228686i
\(694\) 0 0
\(695\) 67.7271i 2.56904i
\(696\) 0 0
\(697\) 11.4399i 0.433319i
\(698\) 0 0
\(699\) −9.50930 9.50930i −0.359675 0.359675i
\(700\) 0 0
\(701\) −6.08828 + 6.08828i −0.229951 + 0.229951i −0.812672 0.582721i \(-0.801988\pi\)
0.582721 + 0.812672i \(0.301988\pi\)
\(702\) 0 0
\(703\) 16.9947 0.640969
\(704\) 0 0
\(705\) 58.5392 2.20472
\(706\) 0 0
\(707\) −11.1341 + 11.1341i −0.418739 + 0.418739i
\(708\) 0 0
\(709\) −2.17748 2.17748i −0.0817769 0.0817769i 0.665035 0.746812i \(-0.268417\pi\)
−0.746812 + 0.665035i \(0.768417\pi\)
\(710\) 0 0
\(711\) 0.359556i 0.0134844i
\(712\) 0 0
\(713\) 5.91677i 0.221585i
\(714\) 0 0
\(715\) 64.5221 + 64.5221i 2.41299 + 2.41299i
\(716\) 0 0
\(717\) 2.36224 2.36224i 0.0882195 0.0882195i
\(718\) 0 0
\(719\) −42.5677 −1.58751 −0.793754 0.608239i \(-0.791876\pi\)
−0.793754 + 0.608239i \(0.791876\pi\)
\(720\) 0 0
\(721\) −15.2106 −0.566471
\(722\) 0 0
\(723\) −18.2986 + 18.2986i −0.680531 + 0.680531i
\(724\) 0 0
\(725\) 48.0510 + 48.0510i 1.78457 + 1.78457i
\(726\) 0 0
\(727\) 3.44163i 0.127643i 0.997961 + 0.0638214i \(0.0203288\pi\)
−0.997961 + 0.0638214i \(0.979671\pi\)
\(728\) 0 0
\(729\) 25.0909i 0.929294i
\(730\) 0 0
\(731\) 8.31327 + 8.31327i 0.307477 + 0.307477i
\(732\) 0 0
\(733\) 8.59144 8.59144i 0.317332 0.317332i −0.530410 0.847742i \(-0.677962\pi\)
0.847742 + 0.530410i \(0.177962\pi\)
\(734\) 0 0
\(735\) 7.46903 0.275499
\(736\) 0 0
\(737\) −36.7866 −1.35505
\(738\) 0 0
\(739\) 19.7676 19.7676i 0.727161 0.727161i −0.242892 0.970053i \(-0.578096\pi\)
0.970053 + 0.242892i \(0.0780960\pi\)
\(740\) 0 0
\(741\) 13.0193 + 13.0193i 0.478275 + 0.478275i
\(742\) 0 0
\(743\) 14.0786i 0.516495i −0.966079 0.258248i \(-0.916855\pi\)
0.966079 0.258248i \(-0.0831450\pi\)
\(744\) 0 0
\(745\) 50.9452i 1.86649i
\(746\) 0 0
\(747\) −1.50841 1.50841i −0.0551899 0.0551899i
\(748\) 0 0
\(749\) −0.897608 + 0.897608i −0.0327979 + 0.0327979i
\(750\) 0 0
\(751\) −27.6318 −1.00830 −0.504148 0.863617i \(-0.668194\pi\)
−0.504148 + 0.863617i \(0.668194\pi\)
\(752\) 0 0
\(753\) −11.3214 −0.412576
\(754\) 0 0
\(755\) 52.4798 52.4798i 1.90994 1.90994i
\(756\) 0 0
\(757\) −1.95221 1.95221i −0.0709542 0.0709542i 0.670739 0.741693i \(-0.265977\pi\)
−0.741693 + 0.670739i \(0.765977\pi\)
\(758\) 0 0
\(759\) 57.2537i 2.07818i
\(760\) 0 0
\(761\) 34.5598i 1.25279i 0.779505 + 0.626396i \(0.215471\pi\)
−0.779505 + 0.626396i \(0.784529\pi\)
\(762\) 0 0
\(763\) −2.84528 2.84528i −0.103006 0.103006i
\(764\) 0 0
\(765\) 2.87278 2.87278i 0.103866 0.103866i
\(766\) 0 0
\(767\) 12.7313 0.459699
\(768\) 0 0
\(769\) 49.7370 1.79356 0.896781 0.442474i \(-0.145899\pi\)
0.896781 + 0.442474i \(0.145899\pi\)
\(770\) 0 0
\(771\) 15.3542 15.3542i 0.552968 0.552968i
\(772\) 0 0
\(773\) −10.0261 10.0261i −0.360614 0.360614i 0.503425 0.864039i \(-0.332073\pi\)
−0.864039 + 0.503425i \(0.832073\pi\)
\(774\) 0 0
\(775\) 10.3835i 0.372988i
\(776\) 0 0
\(777\) 14.2594i 0.511553i
\(778\) 0 0
\(779\) 3.35066 + 3.35066i 0.120050 + 0.120050i
\(780\) 0 0
\(781\) 19.2617 19.2617i 0.689238 0.689238i
\(782\) 0 0
\(783\) 27.3042 0.975772
\(784\) 0 0
\(785\) 58.4664 2.08675
\(786\) 0 0
\(787\) 9.26586 9.26586i 0.330292 0.330292i −0.522405 0.852697i \(-0.674965\pi\)
0.852697 + 0.522405i \(0.174965\pi\)
\(788\) 0 0
\(789\) 0.0378229 + 0.0378229i 0.00134653 + 0.00134653i
\(790\) 0 0
\(791\) 1.66487i 0.0591960i
\(792\) 0 0
\(793\) 11.3050i 0.401454i
\(794\) 0 0
\(795\) 41.7355 + 41.7355i 1.48021 + 1.48021i
\(796\) 0 0
\(797\) 21.3858 21.3858i 0.757525 0.757525i −0.218346 0.975871i \(-0.570066\pi\)
0.975871 + 0.218346i \(0.0700663\pi\)
\(798\) 0 0