Properties

Label 2352.2.bl.t.31.3
Level $2352$
Weight $2$
Character 2352.31
Analytic conductor $18.781$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.bl (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.339738624.1
Defining polynomial: \(x^{8} - 4 x^{6} + 14 x^{4} - 8 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.3
Root \(0.662827 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 2352.31
Dual form 2352.2.bl.t.607.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(0.521114 - 0.300865i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(0.521114 - 0.300865i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-0.141713 - 0.0818181i) q^{11} -3.37849i q^{13} -0.601731i q^{15} +(-1.84677 - 1.06623i) q^{17} +(0.476834 + 0.825901i) q^{19} +(6.05870 - 3.49799i) q^{23} +(-2.31896 + 4.01656i) q^{25} -1.00000 q^{27} -1.28897 q^{29} +(1.67725 - 2.90508i) q^{31} +(-0.141713 + 0.0818181i) q^{33} +(-2.58187 - 4.47192i) q^{37} +(-2.92586 - 1.68925i) q^{39} -6.67896i q^{41} -6.09172i q^{43} +(-0.521114 - 0.300865i) q^{45} +(-1.84882 - 3.20225i) q^{47} +(-1.84677 + 1.06623i) q^{51} +(-6.94028 + 12.0209i) q^{53} -0.0984649 q^{55} +0.953669 q^{57} +(4.02594 - 6.97313i) q^{59} +(-0.157153 + 0.0907323i) q^{61} +(-1.01647 - 1.76058i) q^{65} +(-7.87476 - 4.54649i) q^{67} -6.99598i q^{69} +3.36066i q^{71} +(-10.5172 - 6.07210i) q^{73} +(2.31896 + 4.01656i) q^{75} +(6.05213 - 3.49420i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.9788 q^{83} -1.28317 q^{85} +(-0.644486 + 1.11628i) q^{87} +(12.8911 - 7.44266i) q^{89} +(-1.67725 - 2.90508i) q^{93} +(0.496970 + 0.286926i) q^{95} -9.08274i q^{97} +0.163636i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{3} - 4q^{9} + 24q^{23} + 12q^{25} - 8q^{27} + 16q^{29} - 16q^{31} - 8q^{47} - 8q^{53} + 64q^{55} + 24q^{59} - 48q^{61} + 8q^{65} - 48q^{67} - 48q^{73} - 12q^{75} - 24q^{79} - 4q^{81} - 64q^{85} + 8q^{87} - 48q^{89} + 16q^{93} + 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) 0.521114 0.300865i 0.233049 0.134551i −0.378929 0.925426i \(-0.623707\pi\)
0.611978 + 0.790875i \(0.290374\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −0.141713 0.0818181i −0.0427281 0.0246691i 0.478484 0.878096i \(-0.341187\pi\)
−0.521212 + 0.853427i \(0.674520\pi\)
\(12\) 0 0
\(13\) 3.37849i 0.937025i −0.883457 0.468513i \(-0.844790\pi\)
0.883457 0.468513i \(-0.155210\pi\)
\(14\) 0 0
\(15\) 0.601731i 0.155366i
\(16\) 0 0
\(17\) −1.84677 1.06623i −0.447907 0.258599i 0.259039 0.965867i \(-0.416594\pi\)
−0.706946 + 0.707268i \(0.749928\pi\)
\(18\) 0 0
\(19\) 0.476834 + 0.825901i 0.109393 + 0.189475i 0.915525 0.402262i \(-0.131776\pi\)
−0.806131 + 0.591737i \(0.798443\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.05870 3.49799i 1.26333 0.729382i 0.289610 0.957145i \(-0.406475\pi\)
0.973717 + 0.227763i \(0.0731412\pi\)
\(24\) 0 0
\(25\) −2.31896 + 4.01656i −0.463792 + 0.803311i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.28897 −0.239356 −0.119678 0.992813i \(-0.538186\pi\)
−0.119678 + 0.992813i \(0.538186\pi\)
\(30\) 0 0
\(31\) 1.67725 2.90508i 0.301242 0.521767i −0.675175 0.737657i \(-0.735932\pi\)
0.976418 + 0.215890i \(0.0692653\pi\)
\(32\) 0 0
\(33\) −0.141713 + 0.0818181i −0.0246691 + 0.0142427i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.58187 4.47192i −0.424456 0.735179i 0.571913 0.820314i \(-0.306201\pi\)
−0.996369 + 0.0851346i \(0.972868\pi\)
\(38\) 0 0
\(39\) −2.92586 1.68925i −0.468513 0.270496i
\(40\) 0 0
\(41\) 6.67896i 1.04308i −0.853227 0.521539i \(-0.825358\pi\)
0.853227 0.521539i \(-0.174642\pi\)
\(42\) 0 0
\(43\) 6.09172i 0.928978i −0.885579 0.464489i \(-0.846238\pi\)
0.885579 0.464489i \(-0.153762\pi\)
\(44\) 0 0
\(45\) −0.521114 0.300865i −0.0776831 0.0448504i
\(46\) 0 0
\(47\) −1.84882 3.20225i −0.269678 0.467096i 0.699101 0.715023i \(-0.253584\pi\)
−0.968779 + 0.247927i \(0.920251\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −1.84677 + 1.06623i −0.258599 + 0.149302i
\(52\) 0 0
\(53\) −6.94028 + 12.0209i −0.953321 + 1.65120i −0.215156 + 0.976580i \(0.569026\pi\)
−0.738165 + 0.674620i \(0.764307\pi\)
\(54\) 0 0
\(55\) −0.0984649 −0.0132770
\(56\) 0 0
\(57\) 0.953669 0.126317
\(58\) 0 0
\(59\) 4.02594 6.97313i 0.524133 0.907824i −0.475473 0.879730i \(-0.657723\pi\)
0.999605 0.0280937i \(-0.00894369\pi\)
\(60\) 0 0
\(61\) −0.157153 + 0.0907323i −0.0201214 + 0.0116171i −0.510027 0.860158i \(-0.670365\pi\)
0.489906 + 0.871776i \(0.337031\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.01647 1.76058i −0.126078 0.218373i
\(66\) 0 0
\(67\) −7.87476 4.54649i −0.962055 0.555443i −0.0652500 0.997869i \(-0.520784\pi\)
−0.896805 + 0.442426i \(0.854118\pi\)
\(68\) 0 0
\(69\) 6.99598i 0.842217i
\(70\) 0 0
\(71\) 3.36066i 0.398837i 0.979914 + 0.199419i \(0.0639054\pi\)
−0.979914 + 0.199419i \(0.936095\pi\)
\(72\) 0 0
\(73\) −10.5172 6.07210i −1.23094 0.710686i −0.263717 0.964600i \(-0.584949\pi\)
−0.967227 + 0.253914i \(0.918282\pi\)
\(74\) 0 0
\(75\) 2.31896 + 4.01656i 0.267770 + 0.463792i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 6.05213 3.49420i 0.680918 0.393128i −0.119283 0.992860i \(-0.538059\pi\)
0.800201 + 0.599732i \(0.204726\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 12.9788 1.42460 0.712302 0.701873i \(-0.247652\pi\)
0.712302 + 0.701873i \(0.247652\pi\)
\(84\) 0 0
\(85\) −1.28317 −0.139179
\(86\) 0 0
\(87\) −0.644486 + 1.11628i −0.0690961 + 0.119678i
\(88\) 0 0
\(89\) 12.8911 7.44266i 1.36645 0.788920i 0.375977 0.926629i \(-0.377307\pi\)
0.990473 + 0.137709i \(0.0439739\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −1.67725 2.90508i −0.173922 0.301242i
\(94\) 0 0
\(95\) 0.496970 + 0.286926i 0.0509881 + 0.0294380i
\(96\) 0 0
\(97\) 9.08274i 0.922213i −0.887345 0.461106i \(-0.847453\pi\)
0.887345 0.461106i \(-0.152547\pi\)
\(98\) 0 0
\(99\) 0.163636i 0.0164461i
\(100\) 0 0
\(101\) −7.37548 4.25824i −0.733888 0.423710i 0.0859551 0.996299i \(-0.472606\pi\)
−0.819843 + 0.572589i \(0.805939\pi\)
\(102\) 0 0
\(103\) 8.38043 + 14.5153i 0.825749 + 1.43024i 0.901346 + 0.433100i \(0.142580\pi\)
−0.0755973 + 0.997138i \(0.524086\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.80822 2.19867i 0.368154 0.212554i −0.304498 0.952513i \(-0.598489\pi\)
0.672652 + 0.739959i \(0.265155\pi\)
\(108\) 0 0
\(109\) −5.77263 + 9.99849i −0.552918 + 0.957681i 0.445145 + 0.895459i \(0.353152\pi\)
−0.998062 + 0.0622227i \(0.980181\pi\)
\(110\) 0 0
\(111\) −5.16373 −0.490120
\(112\) 0 0
\(113\) −1.09821 −0.103311 −0.0516554 0.998665i \(-0.516450\pi\)
−0.0516554 + 0.998665i \(0.516450\pi\)
\(114\) 0 0
\(115\) 2.10485 3.64571i 0.196278 0.339964i
\(116\) 0 0
\(117\) −2.92586 + 1.68925i −0.270496 + 0.156171i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −5.48661 9.50309i −0.498783 0.863917i
\(122\) 0 0
\(123\) −5.78415 3.33948i −0.521539 0.301111i
\(124\) 0 0
\(125\) 5.79943i 0.518717i
\(126\) 0 0
\(127\) 5.22625i 0.463755i 0.972745 + 0.231877i \(0.0744868\pi\)
−0.972745 + 0.231877i \(0.925513\pi\)
\(128\) 0 0
\(129\) −5.27558 3.04586i −0.464489 0.268173i
\(130\) 0 0
\(131\) −11.2659 19.5132i −0.984309 1.70487i −0.644966 0.764211i \(-0.723129\pi\)
−0.339343 0.940663i \(-0.610205\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.521114 + 0.300865i −0.0448504 + 0.0258944i
\(136\) 0 0
\(137\) −7.29579 + 12.6367i −0.623322 + 1.07963i 0.365541 + 0.930795i \(0.380884\pi\)
−0.988863 + 0.148830i \(0.952449\pi\)
\(138\) 0 0
\(139\) 8.30816 0.704689 0.352345 0.935870i \(-0.385385\pi\)
0.352345 + 0.935870i \(0.385385\pi\)
\(140\) 0 0
\(141\) −3.69764 −0.311397
\(142\) 0 0
\(143\) −0.276422 + 0.478777i −0.0231156 + 0.0400373i
\(144\) 0 0
\(145\) −0.671701 + 0.387807i −0.0557818 + 0.0322056i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.40083 9.35450i −0.442453 0.766351i 0.555418 0.831571i \(-0.312558\pi\)
−0.997871 + 0.0652205i \(0.979225\pi\)
\(150\) 0 0
\(151\) −12.2618 7.07937i −0.997854 0.576111i −0.0902412 0.995920i \(-0.528764\pi\)
−0.907613 + 0.419809i \(0.862097\pi\)
\(152\) 0 0
\(153\) 2.13246i 0.172400i
\(154\) 0 0
\(155\) 2.01850i 0.162130i
\(156\) 0 0
\(157\) 0.946253 + 0.546320i 0.0755192 + 0.0436011i 0.537284 0.843401i \(-0.319450\pi\)
−0.461765 + 0.887002i \(0.652784\pi\)
\(158\) 0 0
\(159\) 6.94028 + 12.0209i 0.550400 + 0.953321i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −15.6627 + 9.04284i −1.22679 + 0.708290i −0.966358 0.257201i \(-0.917200\pi\)
−0.260436 + 0.965491i \(0.583866\pi\)
\(164\) 0 0
\(165\) −0.0492325 + 0.0852731i −0.00383274 + 0.00663850i
\(166\) 0 0
\(167\) 19.0196 1.47178 0.735889 0.677103i \(-0.236765\pi\)
0.735889 + 0.677103i \(0.236765\pi\)
\(168\) 0 0
\(169\) 1.58579 0.121984
\(170\) 0 0
\(171\) 0.476834 0.825901i 0.0364644 0.0631583i
\(172\) 0 0
\(173\) 7.14939 4.12770i 0.543558 0.313823i −0.202962 0.979187i \(-0.565057\pi\)
0.746520 + 0.665363i \(0.231723\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.02594 6.97313i −0.302608 0.524133i
\(178\) 0 0
\(179\) 4.76008 + 2.74823i 0.355785 + 0.205413i 0.667230 0.744852i \(-0.267480\pi\)
−0.311445 + 0.950264i \(0.600813\pi\)
\(180\) 0 0
\(181\) 11.8519i 0.880946i −0.897766 0.440473i \(-0.854811\pi\)
0.897766 0.440473i \(-0.145189\pi\)
\(182\) 0 0
\(183\) 0.181465i 0.0134143i
\(184\) 0 0
\(185\) −2.69089 1.55359i −0.197838 0.114222i
\(186\) 0 0
\(187\) 0.174474 + 0.302198i 0.0127588 + 0.0220989i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 20.0470 11.5741i 1.45055 0.837476i 0.452038 0.891999i \(-0.350697\pi\)
0.998513 + 0.0545227i \(0.0173637\pi\)
\(192\) 0 0
\(193\) 0.256029 0.443455i 0.0184294 0.0319206i −0.856664 0.515875i \(-0.827467\pi\)
0.875093 + 0.483955i \(0.160800\pi\)
\(194\) 0 0
\(195\) −2.03294 −0.145582
\(196\) 0 0
\(197\) −12.7934 −0.911495 −0.455748 0.890109i \(-0.650628\pi\)
−0.455748 + 0.890109i \(0.650628\pi\)
\(198\) 0 0
\(199\) −7.90360 + 13.6894i −0.560271 + 0.970418i 0.437201 + 0.899364i \(0.355970\pi\)
−0.997472 + 0.0710545i \(0.977364\pi\)
\(200\) 0 0
\(201\) −7.87476 + 4.54649i −0.555443 + 0.320685i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.00947 3.48050i −0.140347 0.243089i
\(206\) 0 0
\(207\) −6.05870 3.49799i −0.421109 0.243127i
\(208\) 0 0
\(209\) 0.156055i 0.0107945i
\(210\) 0 0
\(211\) 0.191712i 0.0131980i 0.999978 + 0.00659899i \(0.00210054\pi\)
−0.999978 + 0.00659899i \(0.997899\pi\)
\(212\) 0 0
\(213\) 2.91042 + 1.68033i 0.199419 + 0.115134i
\(214\) 0 0
\(215\) −1.83279 3.17448i −0.124995 0.216498i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −10.5172 + 6.07210i −0.710686 + 0.410315i
\(220\) 0 0
\(221\) −3.60226 + 6.23929i −0.242314 + 0.419700i
\(222\) 0 0
\(223\) −10.0111 −0.670392 −0.335196 0.942148i \(-0.608803\pi\)
−0.335196 + 0.942148i \(0.608803\pi\)
\(224\) 0 0
\(225\) 4.63792 0.309195
\(226\) 0 0
\(227\) 3.06817 5.31422i 0.203641 0.352717i −0.746058 0.665881i \(-0.768056\pi\)
0.949699 + 0.313164i \(0.101389\pi\)
\(228\) 0 0
\(229\) −8.17961 + 4.72250i −0.540524 + 0.312072i −0.745291 0.666739i \(-0.767690\pi\)
0.204767 + 0.978811i \(0.434356\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.1108 + 19.2445i 0.727895 + 1.26075i 0.957771 + 0.287531i \(0.0928345\pi\)
−0.229876 + 0.973220i \(0.573832\pi\)
\(234\) 0 0
\(235\) −1.92689 1.11249i −0.125697 0.0725710i
\(236\) 0 0
\(237\) 6.98840i 0.453945i
\(238\) 0 0
\(239\) 20.7962i 1.34520i 0.740008 + 0.672598i \(0.234822\pi\)
−0.740008 + 0.672598i \(0.765178\pi\)
\(240\) 0 0
\(241\) −11.3063 6.52769i −0.728302 0.420486i 0.0894984 0.995987i \(-0.471474\pi\)
−0.817801 + 0.575501i \(0.804807\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.79030 1.61098i 0.177543 0.102504i
\(248\) 0 0
\(249\) 6.48938 11.2399i 0.411248 0.712302i
\(250\) 0 0
\(251\) 17.8975 1.12968 0.564839 0.825201i \(-0.308938\pi\)
0.564839 + 0.825201i \(0.308938\pi\)
\(252\) 0 0
\(253\) −1.14480 −0.0719727
\(254\) 0 0
\(255\) −0.641585 + 1.11126i −0.0401776 + 0.0695896i
\(256\) 0 0
\(257\) 5.78415 3.33948i 0.360805 0.208311i −0.308629 0.951183i \(-0.599870\pi\)
0.669434 + 0.742872i \(0.266537\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.644486 + 1.11628i 0.0398927 + 0.0690961i
\(262\) 0 0
\(263\) 21.1452 + 12.2082i 1.30387 + 0.752790i 0.981066 0.193676i \(-0.0620410\pi\)
0.322804 + 0.946466i \(0.395374\pi\)
\(264\) 0 0
\(265\) 8.35236i 0.513081i
\(266\) 0 0
\(267\) 14.8853i 0.910966i
\(268\) 0 0
\(269\) −0.992403 0.572964i −0.0605079 0.0349342i 0.469441 0.882964i \(-0.344456\pi\)
−0.529949 + 0.848030i \(0.677789\pi\)
\(270\) 0 0
\(271\) 2.82578 + 4.89440i 0.171654 + 0.297314i 0.938998 0.343922i \(-0.111756\pi\)
−0.767344 + 0.641235i \(0.778422\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.657254 0.379466i 0.0396339 0.0228826i
\(276\) 0 0
\(277\) 9.63792 16.6934i 0.579087 1.00301i −0.416498 0.909137i \(-0.636743\pi\)
0.995584 0.0938706i \(-0.0299240\pi\)
\(278\) 0 0
\(279\) −3.35449 −0.200828
\(280\) 0 0
\(281\) 8.80369 0.525184 0.262592 0.964907i \(-0.415423\pi\)
0.262592 + 0.964907i \(0.415423\pi\)
\(282\) 0 0
\(283\) 13.0725 22.6423i 0.777081 1.34594i −0.156536 0.987672i \(-0.550033\pi\)
0.933617 0.358272i \(-0.116634\pi\)
\(284\) 0 0
\(285\) 0.496970 0.286926i 0.0294380 0.0169960i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −6.22630 10.7843i −0.366253 0.634368i
\(290\) 0 0
\(291\) −7.86588 4.54137i −0.461106 0.266220i
\(292\) 0 0
\(293\) 18.2640i 1.06699i 0.845802 + 0.533497i \(0.179123\pi\)
−0.845802 + 0.533497i \(0.820877\pi\)
\(294\) 0 0
\(295\) 4.84506i 0.282090i
\(296\) 0 0
\(297\) 0.141713 + 0.0818181i 0.00822303 + 0.00474757i
\(298\) 0 0
\(299\) −11.8179 20.4693i −0.683449 1.18377i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −7.37548 + 4.25824i −0.423710 + 0.244629i
\(304\) 0 0
\(305\) −0.0545964 + 0.0945638i −0.00312618 + 0.00541471i
\(306\) 0 0
\(307\) −21.4472 −1.22405 −0.612027 0.790837i \(-0.709646\pi\)
−0.612027 + 0.790837i \(0.709646\pi\)
\(308\) 0 0
\(309\) 16.7609 0.953492
\(310\) 0 0
\(311\) −7.24000 + 12.5400i −0.410543 + 0.711081i −0.994949 0.100380i \(-0.967994\pi\)
0.584407 + 0.811461i \(0.301327\pi\)
\(312\) 0 0
\(313\) −1.28590 + 0.742415i −0.0726834 + 0.0419638i −0.535901 0.844281i \(-0.680028\pi\)
0.463218 + 0.886244i \(0.346695\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.74541 + 9.95135i 0.322695 + 0.558923i 0.981043 0.193790i \(-0.0620780\pi\)
−0.658348 + 0.752713i \(0.728745\pi\)
\(318\) 0 0
\(319\) 0.182664 + 0.105461i 0.0102272 + 0.00590469i
\(320\) 0 0
\(321\) 4.39735i 0.245436i
\(322\) 0 0
\(323\) 2.03366i 0.113156i
\(324\) 0 0
\(325\) 13.5699 + 7.83459i 0.752723 + 0.434585i
\(326\) 0 0
\(327\) 5.77263 + 9.99849i 0.319227 + 0.552918i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −18.2703 + 10.5484i −1.00423 + 0.579790i −0.909496 0.415713i \(-0.863532\pi\)
−0.0947302 + 0.995503i \(0.530199\pi\)
\(332\) 0 0
\(333\) −2.58187 + 4.47192i −0.141485 + 0.245060i
\(334\) 0 0
\(335\) −5.47153 −0.298942
\(336\) 0 0
\(337\) −5.62683 −0.306513 −0.153256 0.988186i \(-0.548976\pi\)
−0.153256 + 0.988186i \(0.548976\pi\)
\(338\) 0 0
\(339\) −0.549104 + 0.951076i −0.0298232 + 0.0516554i
\(340\) 0 0
\(341\) −0.475376 + 0.274458i −0.0257430 + 0.0148628i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.10485 3.64571i −0.113321 0.196278i
\(346\) 0 0
\(347\) 21.1108 + 12.1883i 1.13329 + 0.654305i 0.944760 0.327763i \(-0.106295\pi\)
0.188529 + 0.982068i \(0.439628\pi\)
\(348\) 0 0
\(349\) 2.84502i 0.152290i 0.997097 + 0.0761451i \(0.0242612\pi\)
−0.997097 + 0.0761451i \(0.975739\pi\)
\(350\) 0 0
\(351\) 3.37849i 0.180331i
\(352\) 0 0
\(353\) 21.3545 + 12.3290i 1.13659 + 0.656208i 0.945583 0.325381i \(-0.105493\pi\)
0.191003 + 0.981589i \(0.438826\pi\)
\(354\) 0 0
\(355\) 1.01111 + 1.75129i 0.0536640 + 0.0929488i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 30.8472 17.8096i 1.62805 0.939957i 0.643381 0.765546i \(-0.277531\pi\)
0.984673 0.174411i \(-0.0558022\pi\)
\(360\) 0 0
\(361\) 9.04526 15.6668i 0.476066 0.824571i
\(362\) 0 0
\(363\) −10.9732 −0.575945
\(364\) 0 0
\(365\) −7.30754 −0.382494
\(366\) 0 0
\(367\) −11.6338 + 20.1504i −0.607280 + 1.05184i 0.384406 + 0.923164i \(0.374406\pi\)
−0.991687 + 0.128676i \(0.958927\pi\)
\(368\) 0 0
\(369\) −5.78415 + 3.33948i −0.301111 + 0.173846i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.9866 + 19.0294i 0.568865 + 0.985303i 0.996679 + 0.0814363i \(0.0259507\pi\)
−0.427813 + 0.903867i \(0.640716\pi\)
\(374\) 0 0
\(375\) 5.02246 + 2.89972i 0.259358 + 0.149741i
\(376\) 0 0
\(377\) 4.35478i 0.224283i
\(378\) 0 0
\(379\) 19.7876i 1.01642i −0.861233 0.508211i \(-0.830307\pi\)
0.861233 0.508211i \(-0.169693\pi\)
\(380\) 0 0
\(381\) 4.52607 + 2.61313i 0.231877 + 0.133874i
\(382\) 0 0
\(383\) −6.82843 11.8272i −0.348916 0.604341i 0.637141 0.770747i \(-0.280117\pi\)
−0.986057 + 0.166407i \(0.946784\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −5.27558 + 3.04586i −0.268173 + 0.154830i
\(388\) 0 0
\(389\) 6.52505 11.3017i 0.330833 0.573020i −0.651842 0.758354i \(-0.726004\pi\)
0.982675 + 0.185335i \(0.0593370\pi\)
\(390\) 0 0
\(391\) −14.9187 −0.754470
\(392\) 0 0
\(393\) −22.5319 −1.13658
\(394\) 0 0
\(395\) 2.10257 3.64175i 0.105792 0.183237i
\(396\) 0 0
\(397\) −5.65172 + 3.26302i −0.283652 + 0.163766i −0.635075 0.772450i \(-0.719031\pi\)
0.351424 + 0.936217i \(0.385698\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15.7156 + 27.2201i 0.784797 + 1.35931i 0.929120 + 0.369778i \(0.120566\pi\)
−0.144323 + 0.989531i \(0.546100\pi\)
\(402\) 0 0
\(403\) −9.81478 5.66657i −0.488909 0.282272i
\(404\) 0 0
\(405\) 0.601731i 0.0299002i
\(406\) 0 0
\(407\) 0.844973i 0.0418838i
\(408\) 0 0
\(409\) 30.1568 + 17.4110i 1.49116 + 0.860921i 0.999949 0.0101207i \(-0.00322157\pi\)
0.491210 + 0.871041i \(0.336555\pi\)
\(410\) 0 0
\(411\) 7.29579 + 12.6367i 0.359875 + 0.623322i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 6.76342 3.90486i 0.332003 0.191682i
\(416\) 0 0
\(417\) 4.15408 7.19508i 0.203426 0.352345i
\(418\) 0 0
\(419\) −11.9597 −0.584271 −0.292135 0.956377i \(-0.594366\pi\)
−0.292135 + 0.956377i \(0.594366\pi\)
\(420\) 0 0
\(421\) 22.6274 1.10279 0.551396 0.834243i \(-0.314095\pi\)
0.551396 + 0.834243i \(0.314095\pi\)
\(422\) 0 0
\(423\) −1.84882 + 3.20225i −0.0898927 + 0.155699i
\(424\) 0 0
\(425\) 8.56516 4.94510i 0.415471 0.239873i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0.276422 + 0.478777i 0.0133458 + 0.0231156i
\(430\) 0 0
\(431\) 16.5809 + 9.57300i 0.798675 + 0.461115i 0.843008 0.537902i \(-0.180783\pi\)
−0.0443327 + 0.999017i \(0.514116\pi\)
\(432\) 0 0
\(433\) 1.66205i 0.0798730i 0.999202 + 0.0399365i \(0.0127156\pi\)
−0.999202 + 0.0399365i \(0.987284\pi\)
\(434\) 0 0
\(435\) 0.775614i 0.0371878i
\(436\) 0 0
\(437\) 5.77799 + 3.33593i 0.276399 + 0.159579i
\(438\) 0 0
\(439\) 8.27932 + 14.3402i 0.395151 + 0.684421i 0.993120 0.117098i \(-0.0373591\pi\)
−0.597970 + 0.801519i \(0.704026\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −15.8781 + 9.16722i −0.754391 + 0.435548i −0.827278 0.561792i \(-0.810112\pi\)
0.0728872 + 0.997340i \(0.476779\pi\)
\(444\) 0 0
\(445\) 4.47847 7.75695i 0.212300 0.367715i
\(446\) 0 0
\(447\) −10.8017 −0.510901
\(448\) 0 0
\(449\) 18.9899 0.896187 0.448093 0.893987i \(-0.352103\pi\)
0.448093 + 0.893987i \(0.352103\pi\)
\(450\) 0 0
\(451\) −0.546460 + 0.946496i −0.0257318 + 0.0445687i
\(452\) 0 0
\(453\) −12.2618 + 7.07937i −0.576111 + 0.332618i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.41976 + 14.5835i 0.393860 + 0.682185i 0.992955 0.118493i \(-0.0378062\pi\)
−0.599095 + 0.800678i \(0.704473\pi\)
\(458\) 0 0
\(459\) 1.84677 + 1.06623i 0.0861998 + 0.0497675i
\(460\) 0 0
\(461\) 36.8939i 1.71832i 0.511708 + 0.859160i \(0.329013\pi\)
−0.511708 + 0.859160i \(0.670987\pi\)
\(462\) 0 0
\(463\) 35.2394i 1.63771i 0.573997 + 0.818857i \(0.305392\pi\)
−0.573997 + 0.818857i \(0.694608\pi\)
\(464\) 0 0
\(465\) −1.74807 1.00925i −0.0810650 0.0468029i
\(466\) 0 0
\(467\) −17.9123 31.0250i −0.828882 1.43567i −0.898916 0.438122i \(-0.855644\pi\)
0.0700331 0.997545i \(-0.477690\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0.946253 0.546320i 0.0436011 0.0251731i
\(472\) 0 0
\(473\) −0.498413 + 0.863276i −0.0229170 + 0.0396935i
\(474\) 0 0
\(475\) −4.42304 −0.202943
\(476\) 0 0
\(477\) 13.8806 0.635547
\(478\) 0 0
\(479\) −3.05297 + 5.28790i −0.139494 + 0.241610i −0.927305 0.374306i \(-0.877881\pi\)
0.787811 + 0.615917i \(0.211214\pi\)
\(480\) 0 0
\(481\) −15.1084 + 8.72281i −0.688882 + 0.397726i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.73268 4.73314i −0.124085 0.214921i
\(486\) 0 0
\(487\) 14.7285 + 8.50353i 0.667414 + 0.385332i 0.795096 0.606484i \(-0.207420\pi\)
−0.127682 + 0.991815i \(0.540754\pi\)
\(488\) 0 0
\(489\) 18.0857i 0.817863i
\(490\) 0 0
\(491\) 31.2897i 1.41209i −0.708169 0.706043i \(-0.750479\pi\)
0.708169 0.706043i \(-0.249521\pi\)
\(492\) 0 0
\(493\) 2.38043 + 1.37434i 0.107209 + 0.0618973i
\(494\) 0 0
\(495\) 0.0492325 + 0.0852731i 0.00221283 + 0.00383274i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −18.4043 + 10.6257i −0.823891 + 0.475674i −0.851756 0.523938i \(-0.824462\pi\)
0.0278654 + 0.999612i \(0.491129\pi\)
\(500\) 0 0
\(501\) 9.50978 16.4714i 0.424866 0.735889i
\(502\) 0 0
\(503\) 0.728285 0.0324726 0.0162363 0.999868i \(-0.494832\pi\)
0.0162363 + 0.999868i \(0.494832\pi\)
\(504\) 0 0
\(505\) −5.12462 −0.228043
\(506\) 0 0
\(507\) 0.792893 1.37333i 0.0352136 0.0609918i
\(508\) 0 0
\(509\) 27.4031 15.8212i 1.21462 0.701263i 0.250860 0.968023i \(-0.419287\pi\)
0.963763 + 0.266761i \(0.0859534\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −0.476834 0.825901i −0.0210528 0.0364644i
\(514\) 0 0
\(515\) 8.73432 + 5.04276i 0.384880 + 0.222211i
\(516\) 0 0
\(517\) 0.605068i 0.0266108i
\(518\) 0 0
\(519\) 8.25540i 0.362372i
\(520\) 0 0
\(521\) 16.4836 + 9.51681i 0.722159 + 0.416939i 0.815547 0.578691i \(-0.196436\pi\)
−0.0933876 + 0.995630i \(0.529770\pi\)
\(522\) 0 0
\(523\) −2.45644 4.25468i −0.107413 0.186044i 0.807309 0.590129i \(-0.200923\pi\)
−0.914721 + 0.404085i \(0.867590\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.19497 + 3.57667i −0.269857 + 0.155802i
\(528\) 0 0
\(529\) 12.9719 22.4680i 0.563995 0.976869i
\(530\) 0 0
\(531\) −8.05188 −0.349422
\(532\) 0 0
\(533\) −22.5648 −0.977391
\(534\) 0 0
\(535\) 1.32301 2.29152i 0.0571987 0.0990711i
\(536\) 0 0
\(537\) 4.76008 2.74823i 0.205413 0.118595i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 14.0443 + 24.3254i 0.603811 + 1.04583i 0.992238 + 0.124352i \(0.0396853\pi\)
−0.388427 + 0.921480i \(0.626981\pi\)
\(542\) 0 0
\(543\) −10.2641 5.92596i −0.440473 0.254307i
\(544\) 0 0
\(545\) 6.94714i 0.297583i
\(546\) 0 0
\(547\) 18.5886i 0.794792i −0.917647 0.397396i \(-0.869914\pi\)
0.917647 0.397396i \(-0.130086\pi\)
\(548\) 0 0
\(549\) 0.157153 + 0.0907323i 0.00670713 + 0.00387236i
\(550\) 0 0
\(551\) −0.614626 1.06456i −0.0261840 0.0453519i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2.69089 + 1.55359i −0.114222 + 0.0659461i
\(556\) 0 0
\(557\) 17.9939 31.1663i 0.762424 1.32056i −0.179174 0.983817i \(-0.557342\pi\)
0.941598 0.336740i \(-0.109324\pi\)
\(558\) 0 0
\(559\) −20.5808 −0.870476
\(560\) 0 0
\(561\) 0.348948 0.0147326
\(562\) 0 0
\(563\) 12.6731 21.9505i 0.534109 0.925105i −0.465097 0.885260i \(-0.653980\pi\)
0.999206 0.0398445i \(-0.0126863\pi\)
\(564\) 0 0
\(565\) −0.572292 + 0.330413i −0.0240765 + 0.0139006i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.82160 + 15.2795i 0.369821 + 0.640549i 0.989537 0.144277i \(-0.0460857\pi\)
−0.619716 + 0.784826i \(0.712752\pi\)
\(570\) 0 0
\(571\) 25.9138 + 14.9613i 1.08446 + 0.626112i 0.932095 0.362213i \(-0.117979\pi\)
0.152362 + 0.988325i \(0.451312\pi\)
\(572\) 0 0
\(573\) 23.1483i 0.967034i
\(574\) 0 0
\(575\) 32.4468i 1.35313i
\(576\) 0 0
\(577\) −7.36021 4.24942i −0.306410 0.176906i 0.338909 0.940819i \(-0.389942\pi\)
−0.645319 + 0.763913i \(0.723275\pi\)
\(578\) 0 0
\(579\) −0.256029 0.443455i −0.0106402 0.0184294i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.96706 1.13568i 0.0814672 0.0470351i
\(584\) 0 0
\(585\) −1.01647 + 1.76058i −0.0420259 + 0.0727910i
\(586\) 0 0
\(587\) 21.1156 0.871535 0.435767 0.900059i \(-0.356477\pi\)
0.435767 + 0.900059i \(0.356477\pi\)
\(588\) 0 0
\(589\) 3.19908 0.131816
\(590\) 0 0
\(591\) −6.39672 + 11.0794i −0.263126 + 0.455748i
\(592\) 0 0
\(593\) −31.0085 + 17.9027i −1.27336 + 0.735177i −0.975620 0.219468i \(-0.929568\pi\)
−0.297745 + 0.954645i \(0.596235\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 7.90360 + 13.6894i 0.323473 + 0.560271i
\(598\) 0 0
\(599\) 8.73895 + 5.04544i 0.357064 + 0.206151i 0.667792 0.744348i \(-0.267240\pi\)
−0.310728 + 0.950499i \(0.600573\pi\)
\(600\) 0 0
\(601\) 31.0913i 1.26824i 0.773234 + 0.634120i \(0.218638\pi\)
−0.773234 + 0.634120i \(0.781362\pi\)
\(602\) 0 0
\(603\) 9.09299i 0.370295i
\(604\) 0 0
\(605\) −5.71830 3.30146i −0.232482 0.134224i
\(606\) 0 0
\(607\) 10.8573 + 18.8053i 0.440683 + 0.763285i 0.997740 0.0671889i \(-0.0214030\pi\)
−0.557057 + 0.830474i \(0.688070\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −10.8188 + 6.24622i −0.437681 + 0.252695i
\(612\) 0 0
\(613\) 10.1405 17.5639i 0.409571 0.709398i −0.585270 0.810838i \(-0.699012\pi\)
0.994842 + 0.101440i \(0.0323449\pi\)
\(614\) 0 0
\(615\) −4.01893 −0.162059
\(616\) 0 0
\(617\) 14.1442 0.569423 0.284712 0.958613i \(-0.408102\pi\)
0.284712 + 0.958613i \(0.408102\pi\)
\(618\) 0 0
\(619\) −21.2581 + 36.8201i −0.854435 + 1.47992i 0.0227335 + 0.999742i \(0.492763\pi\)
−0.877168 + 0.480183i \(0.840570\pi\)
\(620\) 0 0
\(621\) −6.05870 + 3.49799i −0.243127 + 0.140370i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −9.84995 17.0606i −0.393998 0.682425i
\(626\) 0 0
\(627\) −0.135147 0.0780274i −0.00539727 0.00311611i
\(628\) 0 0
\(629\) 11.0115i 0.439056i
\(630\) 0 0
\(631\) 11.2426i 0.447561i −0.974640 0.223781i \(-0.928160\pi\)
0.974640 0.223781i \(-0.0718399\pi\)
\(632\) 0 0
\(633\) 0.166027 + 0.0958559i 0.00659899 + 0.00380993i
\(634\) 0 0
\(635\) 1.57240 + 2.72347i 0.0623987 + 0.108078i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2.91042 1.68033i 0.115134 0.0664729i
\(640\) 0 0
\(641\) −0.235818 + 0.408449i −0.00931425 + 0.0161328i −0.870645 0.491912i \(-0.836298\pi\)
0.861331 + 0.508045i \(0.169632\pi\)
\(642\) 0 0
\(643\) −1.10040 −0.0433955 −0.0216977 0.999765i \(-0.506907\pi\)
−0.0216977 + 0.999765i \(0.506907\pi\)
\(644\) 0 0
\(645\) −3.66557 −0.144332
\(646\) 0 0
\(647\) −15.8657 + 27.4802i −0.623746 + 1.08036i 0.365036 + 0.930993i \(0.381057\pi\)
−0.988782 + 0.149366i \(0.952277\pi\)
\(648\) 0 0
\(649\) −1.14106 + 0.658789i −0.0447904 + 0.0258597i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.49210 + 7.78055i 0.175790 + 0.304477i 0.940434 0.339976i \(-0.110419\pi\)
−0.764645 + 0.644452i \(0.777085\pi\)
\(654\) 0 0
\(655\) −11.7417 6.77906i −0.458785 0.264880i
\(656\) 0 0
\(657\) 12.1442i 0.473791i
\(658\) 0 0
\(659\) 26.0679i 1.01546i 0.861516 + 0.507731i \(0.169516\pi\)
−0.861516 + 0.507731i \(0.830484\pi\)
\(660\) 0 0
\(661\) 1.18105 + 0.681880i 0.0459376 + 0.0265221i 0.522793 0.852460i \(-0.324890\pi\)
−0.476855 + 0.878982i \(0.658223\pi\)
\(662\) 0 0
\(663\) 3.60226 + 6.23929i 0.139900 + 0.242314i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −7.80949 + 4.50881i −0.302385 + 0.174582i
\(668\) 0 0
\(669\) −5.00555 + 8.66986i −0.193526 + 0.335196i
\(670\) 0 0
\(671\) 0.0296942 0.00114633
\(672\) 0 0
\(673\) −17.6874 −0.681799 −0.340899 0.940100i \(-0.610732\pi\)
−0.340899 + 0.940100i \(0.610732\pi\)
\(674\) 0 0
\(675\) 2.31896 4.01656i 0.0892568 0.154597i
\(676\) 0 0
\(677\) −6.88562 + 3.97541i −0.264636 + 0.152788i −0.626447 0.779464i \(-0.715492\pi\)
0.361812 + 0.932251i \(0.382158\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −3.06817 5.31422i −0.117572 0.203641i
\(682\) 0 0
\(683\) 15.6132 + 9.01431i 0.597424 + 0.344923i 0.768028 0.640417i \(-0.221238\pi\)
−0.170603 + 0.985340i \(0.554572\pi\)
\(684\) 0 0
\(685\) 8.78021i 0.335474i
\(686\) 0 0
\(687\) 9.44500i 0.360349i
\(688\) 0 0
\(689\) 40.6126 + 23.4477i 1.54722 + 0.893286i
\(690\) 0 0
\(691\) −22.2488 38.5361i −0.846384 1.46598i −0.884413 0.466704i \(-0.845441\pi\)
0.0380289 0.999277i \(-0.487892\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.32950 2.49964i 0.164227 0.0948167i
\(696\) 0 0
\(697\) −7.12132 + 12.3345i −0.269739 + 0.467202i
\(698\) 0 0
\(699\) 22.2217 0.840501
\(700\) 0 0
\(701\) −11.8785 −0.448646 −0.224323 0.974515i \(-0.572017\pi\)
−0.224323 + 0.974515i \(0.572017\pi\)
\(702\) 0 0
\(703\) 2.46224 4.26473i 0.0928653 0.160847i
\(704\) 0 0
\(705\) −1.92689 + 1.11249i −0.0725710 + 0.0418989i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −12.4321 21.5331i −0.466899 0.808693i 0.532386 0.846502i \(-0.321295\pi\)
−0.999285 + 0.0378090i \(0.987962\pi\)
\(710\) 0 0
\(711\) −6.05213 3.49420i −0.226973 0.131043i
\(712\) 0 0
\(713\) 23.4680i 0.878883i
\(714\) 0 0
\(715\) 0.332663i 0.0124409i
\(716\) 0 0
\(717\) 18.0101 + 10.3981i 0.672598 + 0.388325i
\(718\) 0 0
\(719\) 0.302360 + 0.523703i 0.0112761 + 0.0195308i 0.871608 0.490203i \(-0.163077\pi\)
−0.860332 + 0.509734i \(0.829744\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −11.3063 + 6.52769i −0.420486 + 0.242767i
\(724\) 0 0
\(725\) 2.98907 5.17723i 0.111011 0.192277i
\(726\) 0 0
\(727\) 17.7628 0.658786 0.329393 0.944193i \(-0.393156\pi\)
0.329393 + 0.944193i \(0.393156\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −6.49519 + 11.2500i −0.240233 + 0.416096i
\(732\) 0 0
\(733\) −13.4467 + 7.76347i −0.496666 + 0.286750i −0.727336 0.686282i \(-0.759242\pi\)
0.230670 + 0.973032i \(0.425908\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.743971 + 1.28860i 0.0274045 + 0.0474660i
\(738\) 0 0
\(739\) −14.8992 8.60208i −0.548077 0.316433i 0.200269 0.979741i \(-0.435818\pi\)
−0.748346 + 0.663308i \(0.769152\pi\)
\(740\) 0 0
\(741\) 3.22196i 0.118362i
\(742\) 0 0
\(743\) 13.1996i 0.484247i −0.970245 0.242123i \(-0.922156\pi\)
0.970245 0.242123i \(-0.0778439\pi\)
\(744\) 0 0
\(745\) −5.62889 3.24984i −0.206227 0.119065i
\(746\) 0 0
\(747\) −6.48938 11.2399i −0.237434 0.411248i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −17.5756 + 10.1473i −0.641344 + 0.370280i −0.785132 0.619328i \(-0.787405\pi\)
0.143788 + 0.989609i \(0.454072\pi\)
\(752\) 0 0
\(753\) 8.94873 15.4997i 0.326110 0.564839i
\(754\) 0 0
\(755\) −8.51975 −0.310065
\(756\) 0 0
\(757\) 24.7011 0.897778 0.448889 0.893587i \(-0.351820\pi\)
0.448889 + 0.893587i \(0.351820\pi\)
\(758\) 0 0
\(759\) −0.572398 + 0.991422i −0.0207767 + 0.0359864i
\(760\) 0 0
\(761\) 4.13548 2.38762i 0.149911 0.0865512i −0.423168 0.906051i \(-0.639082\pi\)
0.573079 + 0.819500i \(0.305749\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.641585 + 1.11126i 0.0231965 + 0.0401776i
\(766\) 0 0
\(767\) −23.5587 13.6016i −0.850654 0.491125i
\(768\) 0 0
\(769\) 14.7721i 0.532696i 0.963877 + 0.266348i \(0.0858170\pi\)
−0.963877 + 0.266348i \(0.914183\pi\)
\(770\) 0 0
\(771\) 6.67896i 0.240537i
\(772\) 0 0
\(773\) −31.9715 18.4588i −1.14994 0.663916i −0.201064 0.979578i \(-0.564440\pi\)
−0.948872 + 0.315662i \(0.897773\pi\)
\(774\) 0 0
\(775\) 7.77894 + 13.4735i 0.279428 + 0.483983i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.51616 3.18476i 0.197637 0.114106i
\(780\) 0 0
\(781\) 0.274963 0.476250i 0.00983895 0.0170416i
\(782\) 0 0
\(783\) 1.28897 0.0460641
\(784\) 0 0
\(785\) 0.657475 0.0234663
\(786\) 0 0
\(787\) 18.5199 32.0774i 0.660164 1.14344i −0.320408 0.947280i \(-0.603820\pi\)
0.980572 0.196158i \(-0.0628466\pi\)
\(788\) 0 0
\(789\) 21.1452 12.2082i 0.752790 0.434623i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0.306539 + 0.530940i 0.0108855 + 0.0188542i
\(794\) 0 0
\(795\) 7.23336 + 4.17618i 0.256541 + 0.148114i
\(796\) 0 0
\(797\) 36.9752i 1.30973i 0.755746 + 0.654865i \(0.227275\pi\)
−0.755746 + 0.654865i \(0.772725\pi\)
\(798\) 0 0
\(799\) 7.88509i 0.278954i
\(800\) 0 0