Properties

Label 1792.2.m.h.449.2
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 449.2
Root \(-1.09227 - 0.838128i\) of defining polynomial
Character \(\chi\) \(=\) 1792.449
Dual form 1792.2.m.h.1345.2

$q$-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 −0.970430 0.241384i \(-0.922399\pi\)
0.241384 + 0.970430i \(0.422399\pi\)
\(4\) 0 0
\(5\) 2.95746 + 2.95746i 1.32262 + 1.32262i 0.911650 + 0.410967i \(0.134809\pi\)
0.410967 + 0.911650i \(0.365191\pi\)
\(6\) 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 0.0390622 0.999237i \(-0.487563\pi\)
−0.999237 + 0.0390622i \(0.987563\pi\)
\(12\) 0 0
\(13\) 3.42541 3.42541i 0.950039 0.950039i −0.0487712 0.998810i \(-0.515531\pi\)
0.998810 + 0.0487712i \(0.0155305\pi\)
\(14\) 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 −0.858342 0.513078i \(-0.828505\pi\)
0.513078 + 0.858342i \(0.328505\pi\)
\(20\) 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 −0.967415 0.253197i \(-0.918518\pi\)
0.253197 + 0.967415i \(0.418518\pi\)
\(30\) 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 0.0693630 0.997591i \(-0.477903\pi\)
−0.997591 + 0.0693630i \(0.977903\pi\)
\(38\) 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 0.819626 0.572900i \(-0.194182\pi\)
−0.572900 + 0.819626i \(0.694182\pi\)
\(44\) 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 0.977674 0.210129i \(-0.0673885\pi\)
−0.210129 + 0.977674i \(0.567388\pi\)
\(54\) 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 0.817651 0.575714i \(-0.195276\pi\)
−0.575714 + 0.817651i \(0.695276\pi\)
\(60\) 0 0
\(61\) −1.65017 + 1.65017i −0.211283 + 0.211283i −0.804812 0.593529i \(-0.797734\pi\)
0.593529 + 0.804812i \(0.297734\pi\)
\(62\) 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 −0.259985 0.965613i \(-0.583718\pi\)
0.965613 + 0.259985i \(0.0837178\pi\)
\(68\) 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 −0.993100 0.117269i \(-0.962586\pi\)
0.117269 + 0.993100i \(0.462586\pi\)
\(84\) 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 \(-0.963489\pi\)
−0.114451 0.993429i \(-0.536511\pi\)
\(102\) 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 0.662387 0.749162i \(-0.269544\pi\)
−0.749162 + 0.662387i \(0.769544\pi\)
\(108\) 0 0
\(109\) 2.84528 2.84528i 0.272528 0.272528i −0.557589 0.830117i \(-0.688273\pi\)
0.830117 + 0.557589i \(0.188273\pi\)
\(110\) 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 −0.428045 0.903758i \(-0.640797\pi\)
0.903758 + 0.428045i \(0.140797\pi\)
\(132\) 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 0.999597 0.0284022i \(-0.00904192\pi\)
−0.0284022 + 0.999597i \(0.509042\pi\)
\(140\) 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 0.260004 0.965608i \(-0.416276\pi\)
−0.965608 + 0.260004i \(0.916276\pi\)
\(150\) 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 −0.192436 0.981310i \(-0.561639\pi\)
0.981310 + 0.192436i \(0.0616388\pi\)
\(158\) 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 −0.222019 0.975042i \(-0.571265\pi\)
0.975042 + 0.222019i \(0.0712646\pi\)
\(164\) 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 \(-0.459010\pi\)
0.991720 0.128417i \(-0.0409896\pi\)
\(174\) 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 \(0.565953\pi\)
−0.978611 + 0.205719i \(0.934047\pi\)
\(180\) 0 0
\(181\) −3.13208 3.13208i −0.232805 0.232805i 0.581057 0.813863i \(-0.302639\pi\)
−0.813863 + 0.581057i \(0.802639\pi\)
\(182\) 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 0.918847 0.394614i \(-0.129122\pi\)
−0.394614 + 0.918847i \(0.629122\pi\)
\(198\) 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 −0.331941 0.943300i \(-0.607704\pi\)
0.943300 + 0.331941i \(0.107704\pi\)
\(212\) 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 −0.633300 0.773906i \(-0.718300\pi\)
0.773906 + 0.633300i \(0.218300\pi\)
\(228\) 0 0
\(229\) 6.36091 + 6.36091i 0.420341 + 0.420341i 0.885321 0.464980i \(-0.153939\pi\)
−0.464980 + 0.885321i \(0.653939\pi\)
\(230\) 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 0.834287 0.551330i \(-0.185880\pi\)
−0.551330 + 0.834287i \(0.685880\pi\)
\(252\) 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 −0.979613 0.200895i \(-0.935615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(270\) 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 0.493209 0.869911i \(-0.335824\pi\)
−0.869911 + 0.493209i \(0.835824\pi\)
\(278\) 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 0.392178 0.919890i \(-0.371722\pi\)
−0.919890 + 0.392178i \(0.871722\pi\)
\(284\) 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 \(0.00142070\pi\)
0.00446326 + 0.999990i \(0.498579\pi\)
\(294\) 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 \(-0.466375\pi\)
0.994426 0.105440i \(-0.0336251\pi\)
\(308\) 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 −0.794221 0.607629i \(-0.792121\pi\)
0.607629 + 0.794221i \(0.292121\pi\)
\(318\) 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 \(0.207623\pi\)
0.606990 + 0.794710i \(0.292377\pi\)
\(332\) 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 \(0.118053\pi\)
0.362429 + 0.932011i \(0.381947\pi\)
\(348\) 0 0
\(349\) −20.9731 + 20.9731i −1.12266 + 1.12266i −0.131324 + 0.991340i \(0.541923\pi\)
−0.991340 + 0.131324i \(0.958077\pi\)
\(350\) 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 0.282626 0.959230i \(-0.408794\pi\)
−0.959230 + 0.282626i \(0.908794\pi\)
\(374\) 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 0.778275 0.627924i \(-0.216095\pi\)
−0.627924 + 0.778275i \(0.716095\pi\)
\(380\) 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 0.492599 0.870257i \(-0.336047\pi\)
−0.870257 + 0.492599i \(0.836047\pi\)
\(390\) 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 −0.877451 0.479666i \(-0.840758\pi\)
0.479666 + 0.877451i \(0.340758\pi\)
\(398\) 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 −0.892123 0.451793i \(-0.850785\pi\)
0.451793 + 0.892123i \(0.350785\pi\)
\(420\) 0 0
\(421\) 21.8788 + 21.8788i 1.06631 + 1.06631i 0.997640 + 0.0686687i \(0.0218751\pi\)
0.0686687 + 0.997640i \(0.478125\pi\)
\(422\) 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 0.342719 0.939438i \(-0.388652\pi\)
−0.939438 + 0.342719i \(0.888652\pi\)
\(444\) 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 −0.520587 0.853809i \(-0.674287\pi\)
0.853809 + 0.520587i \(0.174287\pi\)
\(462\) 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 \(0.632577\pi\)
−0.914510 + 0.404563i \(0.867423\pi\)
\(468\) 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 0.999454 0.0330424i \(-0.0105196\pi\)
−0.0330424 + 0.999454i \(0.510520\pi\)
\(492\) 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 −0.965111 0.261841i \(-0.915670\pi\)
0.261841 + 0.965111i \(0.415670\pi\)
\(500\) 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 −0.956881 0.290481i \(-0.906185\pi\)
0.290481 + 0.956881i \(0.406185\pi\)
\(510\) 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 0.334420 0.942424i \(-0.391459\pi\)
−0.942424 + 0.334420i \(0.891459\pi\)
\(524\) 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 −0.495747 0.868467i \(-0.665106\pi\)
0.868467 + 0.495747i \(0.165106\pi\)
\(542\) 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 −0.614655 0.788796i \(-0.710705\pi\)
0.788796 + 0.614655i \(0.210705\pi\)
\(548\) 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 −0.667410 0.744690i \(-0.732597\pi\)
0.744690 + 0.667410i \(0.232597\pi\)
\(558\) 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 −0.895546 0.444969i \(-0.853215\pi\)
0.444969 + 0.895546i \(0.353215\pi\)
\(564\) 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 \(0.0782073\pi\)
0.243231 + 0.969968i \(0.421793\pi\)
\(572\) 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 0.244925 0.969542i \(-0.421237\pi\)
−0.969542 + 0.244925i \(0.921237\pi\)
\(588\) 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 \(-0.977505\pi\)
−0.0706108 0.997504i \(-0.522495\pi\)
\(614\) 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 0.125513 0.992092i \(-0.459942\pi\)
−0.992092 + 0.125513i \(0.959942\pi\)
\(620\) 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 \(0.543823\pi\)
−0.990538 + 0.137240i \(0.956177\pi\)
\(644\) 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 −0.172596 0.984993i \(-0.555215\pi\)
0.984993 + 0.172596i \(0.0552154\pi\)
\(654\) 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 −0.177504 0.984120i \(-0.556802\pi\)
0.984120 + 0.177504i \(0.0568022\pi\)
\(660\) 0 0
\(661\) −9.70914 9.70914i −0.377642 0.377642i 0.492609 0.870251i \(-0.336043\pi\)
−0.870251 + 0.492609i \(0.836043\pi\)
\(662\) 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 0.431813 0.901963i \(-0.357874\pi\)
−0.901963 + 0.431813i \(0.857874\pi\)
\(678\) 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 0.776029 0.630698i \(-0.217231\pi\)
−0.630698 + 0.776029i \(0.717231\pi\)
\(684\) 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 \(-0.424317\pi\)
0.971867 0.235531i \(-0.0756830\pi\)
\(692\) 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 −0.582721 0.812672i \(-0.698012\pi\)
0.812672 + 0.582721i \(0.198012\pi\)
\(702\) 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 0.746812 0.665035i \(-0.231583\pi\)
−0.665035 + 0.746812i \(0.731583\pi\)
\(710\) 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 −0.847742 0.530410i \(-0.822038\pi\)
0.530410 + 0.847742i \(0.322038\pi\)
\(734\) 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 −0.970053 0.242892i \(-0.921904\pi\)
0.242892 + 0.970053i \(0.421904\pi\)
\(740\) 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 0.741693 0.670739i \(-0.234023\pi\)
−0.670739 + 0.741693i \(0.734023\pi\)
\(758\) 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 0.864039 0.503425i \(-0.167927\pi\)
−0.503425 + 0.864039i \(0.667927\pi\)
\(774\) 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 −0.852697 0.522405i \(-0.825035\pi\)
0.522405 + 0.852697i \(0.325035\pi\)
\(788\) 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 −0.975871 0.218346i \(-0.929934\pi\)
0.218346 + 0.975871i \(0.429934\pi\)
\(798\) 0 0
\(799\) 40.2722 1.42473