Properties

Label 1078.2.i.d.901.1
Level $1078$
Weight $2$
Character 1078.901
Analytic conductor $8.608$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.1
Character \(\chi\) \(=\) 1078.901
Dual form 1078.2.i.d.1011.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.662827 + 0.382683i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-3.37695 - 1.94969i) q^{5} +0.765367 q^{6} -1.00000i q^{8} +(-1.20711 + 2.09077i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.662827 + 0.382683i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-3.37695 - 1.94969i) q^{5} +0.765367 q^{6} -1.00000i q^{8} +(-1.20711 + 2.09077i) q^{9} +(1.94969 + 3.37695i) q^{10} +(-2.97369 + 1.46874i) q^{11} +(-0.662827 - 0.382683i) q^{12} +1.81903 q^{13} +2.98445 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.03803 - 5.26202i) q^{17} +(2.09077 - 1.20711i) q^{18} +(-3.41476 + 5.91454i) q^{19} -3.89937i q^{20} +(3.30966 + 0.214882i) q^{22} +(2.18834 - 3.79031i) q^{23} +(0.382683 + 0.662827i) q^{24} +(5.10255 + 8.83788i) q^{25} +(-1.57532 - 0.909513i) q^{26} -4.14386i q^{27} +9.36112i q^{29} +(-2.58461 - 1.49222i) q^{30} +(6.82704 - 3.94159i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.40898 - 2.11150i) q^{33} +6.07606i q^{34} -2.41421 q^{36} +(2.30389 - 3.99045i) q^{37} +(5.91454 - 3.41476i) q^{38} +(-1.20570 + 0.696111i) q^{39} +(-1.94969 + 3.37695i) q^{40} -3.58235 q^{41} -3.25819i q^{43} +(-2.75881 - 1.84092i) q^{44} +(8.15269 - 4.70696i) q^{45} +(-3.79031 + 2.18834i) q^{46} +(-0.176542 - 0.101927i) q^{47} -0.765367i q^{48} -10.2051i q^{50} +(4.02738 + 2.32521i) q^{51} +(0.909513 + 1.57532i) q^{52} +(-2.49222 - 4.31666i) q^{53} +(-2.07193 + 3.58869i) q^{54} +(12.9056 + 0.837904i) q^{55} -5.22709i q^{57} +(4.68056 - 8.10697i) q^{58} +(4.50118 - 2.59876i) q^{59} +(1.49222 + 2.58461i) q^{60} +(4.49186 - 7.78013i) q^{61} -7.88318 q^{62} -1.00000 q^{64} +(-6.14277 - 3.54653i) q^{65} +(-2.27596 + 1.12412i) q^{66} +(4.01676 + 6.95724i) q^{67} +(3.03803 - 5.26202i) q^{68} +3.34976i q^{69} +8.86195 q^{71} +(2.09077 + 1.20711i) q^{72} +(0.0278530 + 0.0482428i) q^{73} +(-3.99045 + 2.30389i) q^{74} +(-6.76422 - 3.90532i) q^{75} -6.82952 q^{76} +1.39222 q^{78} +(7.34847 + 4.24264i) q^{79} +(3.37695 - 1.94969i) q^{80} +(-2.03553 - 3.52565i) q^{81} +(3.10240 + 1.79117i) q^{82} +10.4676 q^{83} +23.6928i q^{85} +(-1.62910 + 2.82168i) q^{86} +(-3.58235 - 6.20481i) q^{87} +(1.46874 + 2.97369i) q^{88} +(1.46160 + 0.843855i) q^{89} -9.41392 q^{90} +4.37667 q^{92} +(-3.01676 + 5.22519i) q^{93} +(0.101927 + 0.176542i) q^{94} +(23.0630 - 13.3154i) q^{95} +(-0.382683 + 0.662827i) q^{96} +9.23880i q^{97} +(0.518771 - 7.99022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{9} + O(q^{10}) \) \( 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.662827 + 0.382683i −0.382683 + 0.220942i −0.678985 0.734152i \(-0.737580\pi\)
0.296302 + 0.955094i \(0.404247\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −3.37695 1.94969i −1.51022 0.871926i −0.999929 0.0119244i \(-0.996204\pi\)
−0.510291 0.860002i \(-0.670462\pi\)
\(6\) 0.765367 0.312460
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.20711 + 2.09077i −0.402369 + 0.696923i
\(10\) 1.94969 + 3.37695i 0.616545 + 1.06789i
\(11\) −2.97369 + 1.46874i −0.896601 + 0.442840i
\(12\) −0.662827 0.382683i −0.191342 0.110471i
\(13\) 1.81903 0.504507 0.252254 0.967661i \(-0.418828\pi\)
0.252254 + 0.967661i \(0.418828\pi\)
\(14\) 0 0
\(15\) 2.98445 0.770582
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.03803 5.26202i −0.736830 1.27623i −0.953916 0.300075i \(-0.902988\pi\)
0.217085 0.976153i \(-0.430345\pi\)
\(18\) 2.09077 1.20711i 0.492799 0.284518i
\(19\) −3.41476 + 5.91454i −0.783400 + 1.35689i 0.146550 + 0.989203i \(0.453183\pi\)
−0.929950 + 0.367685i \(0.880150\pi\)
\(20\) 3.89937i 0.871926i
\(21\) 0 0
\(22\) 3.30966 + 0.214882i 0.705621 + 0.0458130i
\(23\) 2.18834 3.79031i 0.456300 0.790334i −0.542462 0.840080i \(-0.682508\pi\)
0.998762 + 0.0497460i \(0.0158412\pi\)
\(24\) 0.382683 + 0.662827i 0.0781149 + 0.135299i
\(25\) 5.10255 + 8.83788i 1.02051 + 1.76758i
\(26\) −1.57532 0.909513i −0.308946 0.178370i
\(27\) 4.14386i 0.797486i
\(28\) 0 0
\(29\) 9.36112i 1.73832i 0.494534 + 0.869158i \(0.335339\pi\)
−0.494534 + 0.869158i \(0.664661\pi\)
\(30\) −2.58461 1.49222i −0.471883 0.272442i
\(31\) 6.82704 3.94159i 1.22617 0.707931i 0.259945 0.965623i \(-0.416296\pi\)
0.966227 + 0.257693i \(0.0829622\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 1.40898 2.11150i 0.245272 0.367565i
\(34\) 6.07606i 1.04204i
\(35\) 0 0
\(36\) −2.41421 −0.402369
\(37\) 2.30389 3.99045i 0.378757 0.656026i −0.612125 0.790761i \(-0.709685\pi\)
0.990882 + 0.134735i \(0.0430183\pi\)
\(38\) 5.91454 3.41476i 0.959465 0.553947i
\(39\) −1.20570 + 0.696111i −0.193067 + 0.111467i
\(40\) −1.94969 + 3.37695i −0.308272 + 0.533943i
\(41\) −3.58235 −0.559469 −0.279734 0.960077i \(-0.590246\pi\)
−0.279734 + 0.960077i \(0.590246\pi\)
\(42\) 0 0
\(43\) 3.25819i 0.496869i −0.968649 0.248435i \(-0.920084\pi\)
0.968649 0.248435i \(-0.0799161\pi\)
\(44\) −2.75881 1.84092i −0.415906 0.277529i
\(45\) 8.15269 4.70696i 1.21533 0.701672i
\(46\) −3.79031 + 2.18834i −0.558851 + 0.322653i
\(47\) −0.176542 0.101927i −0.0257513 0.0148675i 0.487069 0.873363i \(-0.338066\pi\)
−0.512820 + 0.858496i \(0.671399\pi\)
\(48\) 0.765367i 0.110471i
\(49\) 0 0
\(50\) 10.2051i 1.44322i
\(51\) 4.02738 + 2.32521i 0.563945 + 0.325594i
\(52\) 0.909513 + 1.57532i 0.126127 + 0.218458i
\(53\) −2.49222 4.31666i −0.342333 0.592939i 0.642532 0.766259i \(-0.277884\pi\)
−0.984866 + 0.173320i \(0.944551\pi\)
\(54\) −2.07193 + 3.58869i −0.281954 + 0.488359i
\(55\) 12.9056 + 0.837904i 1.74019 + 0.112983i
\(56\) 0 0
\(57\) 5.22709i 0.692345i
\(58\) 4.68056 8.10697i 0.614588 1.06450i
\(59\) 4.50118 2.59876i 0.586004 0.338330i −0.177512 0.984119i \(-0.556805\pi\)
0.763516 + 0.645789i \(0.223471\pi\)
\(60\) 1.49222 + 2.58461i 0.192645 + 0.333672i
\(61\) 4.49186 7.78013i 0.575124 0.996143i −0.420905 0.907105i \(-0.638287\pi\)
0.996028 0.0890385i \(-0.0283794\pi\)
\(62\) −7.88318 −1.00117
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −6.14277 3.54653i −0.761917 0.439893i
\(66\) −2.27596 + 1.12412i −0.280152 + 0.138370i
\(67\) 4.01676 + 6.95724i 0.490726 + 0.849962i 0.999943 0.0106761i \(-0.00339837\pi\)
−0.509217 + 0.860638i \(0.670065\pi\)
\(68\) 3.03803 5.26202i 0.368415 0.638114i
\(69\) 3.34976i 0.403264i
\(70\) 0 0
\(71\) 8.86195 1.05172 0.525860 0.850571i \(-0.323744\pi\)
0.525860 + 0.850571i \(0.323744\pi\)
\(72\) 2.09077 + 1.20711i 0.246400 + 0.142259i
\(73\) 0.0278530 + 0.0482428i 0.00325995 + 0.00564639i 0.867651 0.497174i \(-0.165629\pi\)
−0.864391 + 0.502821i \(0.832296\pi\)
\(74\) −3.99045 + 2.30389i −0.463881 + 0.267822i
\(75\) −6.76422 3.90532i −0.781064 0.450948i
\(76\) −6.82952 −0.783400
\(77\) 0 0
\(78\) 1.39222 0.157638
\(79\) 7.34847 + 4.24264i 0.826767 + 0.477334i 0.852745 0.522328i \(-0.174936\pi\)
−0.0259772 + 0.999663i \(0.508270\pi\)
\(80\) 3.37695 1.94969i 0.377555 0.217982i
\(81\) −2.03553 3.52565i −0.226170 0.391739i
\(82\) 3.10240 + 1.79117i 0.342603 + 0.197802i
\(83\) 10.4676 1.14897 0.574483 0.818517i \(-0.305203\pi\)
0.574483 + 0.818517i \(0.305203\pi\)
\(84\) 0 0
\(85\) 23.6928i 2.56985i
\(86\) −1.62910 + 2.82168i −0.175670 + 0.304269i
\(87\) −3.58235 6.20481i −0.384068 0.665225i
\(88\) 1.46874 + 2.97369i 0.156568 + 0.316996i
\(89\) 1.46160 + 0.843855i 0.154929 + 0.0894484i 0.575460 0.817830i \(-0.304823\pi\)
−0.420531 + 0.907278i \(0.638156\pi\)
\(90\) −9.41392 −0.992314
\(91\) 0 0
\(92\) 4.37667 0.456300
\(93\) −3.01676 + 5.22519i −0.312824 + 0.541827i
\(94\) 0.101927 + 0.176542i 0.0105129 + 0.0182090i
\(95\) 23.0630 13.3154i 2.36621 1.36613i
\(96\) −0.382683 + 0.662827i −0.0390575 + 0.0676495i
\(97\) 9.23880i 0.938058i 0.883183 + 0.469029i \(0.155396\pi\)
−0.883183 + 0.469029i \(0.844604\pi\)
\(98\) 0 0
\(99\) 0.518771 7.99022i 0.0521384 0.803047i
\(100\) −5.10255 + 8.83788i −0.510255 + 0.883788i
\(101\) 2.67283 + 4.62948i 0.265957 + 0.460651i 0.967814 0.251667i \(-0.0809788\pi\)
−0.701857 + 0.712318i \(0.747645\pi\)
\(102\) −2.32521 4.02738i −0.230230 0.398770i
\(103\) −3.67639 2.12256i −0.362246 0.209143i 0.307820 0.951445i \(-0.400401\pi\)
−0.670065 + 0.742302i \(0.733734\pi\)
\(104\) 1.81903i 0.178370i
\(105\) 0 0
\(106\) 4.98445i 0.484133i
\(107\) 6.26883 + 3.61931i 0.606031 + 0.349892i 0.771411 0.636338i \(-0.219552\pi\)
−0.165379 + 0.986230i \(0.552885\pi\)
\(108\) 3.58869 2.07193i 0.345322 0.199372i
\(109\) 5.19615 3.00000i 0.497701 0.287348i −0.230063 0.973176i \(-0.573893\pi\)
0.727764 + 0.685828i \(0.240560\pi\)
\(110\) −10.7576 7.17844i −1.02570 0.684437i
\(111\) 3.52664i 0.334734i
\(112\) 0 0
\(113\) 16.8400 1.58417 0.792085 0.610411i \(-0.208996\pi\)
0.792085 + 0.610411i \(0.208996\pi\)
\(114\) −2.61355 + 4.52679i −0.244781 + 0.423973i
\(115\) −14.7798 + 8.53314i −1.37823 + 0.795719i
\(116\) −8.10697 + 4.68056i −0.752713 + 0.434579i
\(117\) −2.19576 + 3.80317i −0.202998 + 0.351603i
\(118\) −5.19752 −0.478470
\(119\) 0 0
\(120\) 2.98445i 0.272442i
\(121\) 6.68563 8.73512i 0.607785 0.794102i
\(122\) −7.78013 + 4.49186i −0.704380 + 0.406674i
\(123\) 2.37448 1.37090i 0.214099 0.123610i
\(124\) 6.82704 + 3.94159i 0.613086 + 0.353965i
\(125\) 20.2966i 1.81538i
\(126\) 0 0
\(127\) 17.3300i 1.53779i −0.639375 0.768895i \(-0.720807\pi\)
0.639375 0.768895i \(-0.279193\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 1.24686 + 2.15962i 0.109780 + 0.190144i
\(130\) 3.54653 + 6.14277i 0.311051 + 0.538757i
\(131\) −3.17776 + 5.50404i −0.277642 + 0.480890i −0.970798 0.239897i \(-0.922886\pi\)
0.693156 + 0.720788i \(0.256220\pi\)
\(132\) 2.53310 + 0.164463i 0.220478 + 0.0143147i
\(133\) 0 0
\(134\) 8.03353i 0.693991i
\(135\) −8.07922 + 13.9936i −0.695349 + 1.20438i
\(136\) −5.26202 + 3.03803i −0.451215 + 0.260509i
\(137\) −0.674793 1.16878i −0.0576515 0.0998553i 0.835759 0.549096i \(-0.185028\pi\)
−0.893411 + 0.449241i \(0.851695\pi\)
\(138\) 1.67488 2.90098i 0.142575 0.246948i
\(139\) −11.8957 −1.00898 −0.504491 0.863417i \(-0.668320\pi\)
−0.504491 + 0.863417i \(0.668320\pi\)
\(140\) 0 0
\(141\) 0.156023 0.0131395
\(142\) −7.67468 4.43098i −0.644045 0.371839i
\(143\) −5.40922 + 2.67167i −0.452341 + 0.223416i
\(144\) −1.20711 2.09077i −0.100592 0.174231i
\(145\) 18.2512 31.6121i 1.51568 2.62524i
\(146\) 0.0557060i 0.00461026i
\(147\) 0 0
\(148\) 4.60778 0.378757
\(149\) 5.69557 + 3.28834i 0.466599 + 0.269391i 0.714815 0.699314i \(-0.246511\pi\)
−0.248216 + 0.968705i \(0.579844\pi\)
\(150\) 3.90532 + 6.76422i 0.318868 + 0.552296i
\(151\) −7.48149 + 4.31944i −0.608835 + 0.351511i −0.772509 0.635003i \(-0.780999\pi\)
0.163674 + 0.986514i \(0.447665\pi\)
\(152\) 5.91454 + 3.41476i 0.479733 + 0.276974i
\(153\) 14.6689 1.18591
\(154\) 0 0
\(155\) −30.7395 −2.46905
\(156\) −1.20570 0.696111i −0.0965333 0.0557335i
\(157\) 2.12168 1.22495i 0.169329 0.0977619i −0.412941 0.910758i \(-0.635498\pi\)
0.582269 + 0.812996i \(0.302165\pi\)
\(158\) −4.24264 7.34847i −0.337526 0.584613i
\(159\) 3.30383 + 1.90747i 0.262011 + 0.151272i
\(160\) −3.89937 −0.308272
\(161\) 0 0
\(162\) 4.07107i 0.319853i
\(163\) −1.14503 + 1.98325i −0.0896854 + 0.155340i −0.907378 0.420315i \(-0.861920\pi\)
0.817693 + 0.575655i \(0.195253\pi\)
\(164\) −1.79117 3.10240i −0.139867 0.242257i
\(165\) −8.87482 + 4.38337i −0.690904 + 0.341245i
\(166\) −9.06519 5.23379i −0.703595 0.406221i
\(167\) −8.51406 −0.658838 −0.329419 0.944184i \(-0.606853\pi\)
−0.329419 + 0.944184i \(0.606853\pi\)
\(168\) 0 0
\(169\) −9.69114 −0.745473
\(170\) 11.8464 20.5186i 0.908578 1.57370i
\(171\) −8.24396 14.2790i −0.630432 1.09194i
\(172\) 2.82168 1.62910i 0.215151 0.124217i
\(173\) −11.9961 + 20.7778i −0.912044 + 1.57971i −0.100872 + 0.994899i \(0.532163\pi\)
−0.811172 + 0.584807i \(0.801170\pi\)
\(174\) 7.16469i 0.543154i
\(175\) 0 0
\(176\) 0.214882 3.30966i 0.0161973 0.249475i
\(177\) −1.98900 + 3.44506i −0.149503 + 0.258946i
\(178\) −0.843855 1.46160i −0.0632496 0.109552i
\(179\) −10.0792 17.4577i −0.753357 1.30485i −0.946187 0.323620i \(-0.895100\pi\)
0.192831 0.981232i \(-0.438233\pi\)
\(180\) 8.15269 + 4.70696i 0.607666 + 0.350836i
\(181\) 11.1135i 0.826062i 0.910717 + 0.413031i \(0.135530\pi\)
−0.910717 + 0.413031i \(0.864470\pi\)
\(182\) 0 0
\(183\) 6.87584i 0.508277i
\(184\) −3.79031 2.18834i −0.279425 0.161326i
\(185\) −15.5603 + 8.98372i −1.14401 + 0.660496i
\(186\) 5.22519 3.01676i 0.383129 0.221200i
\(187\) 16.7627 + 11.1855i 1.22581 + 0.817968i
\(188\) 0.203854i 0.0148675i
\(189\) 0 0
\(190\) −26.6308 −1.93200
\(191\) 12.2542 21.2249i 0.886681 1.53578i 0.0429063 0.999079i \(-0.486338\pi\)
0.843775 0.536698i \(-0.180328\pi\)
\(192\) 0.662827 0.382683i 0.0478354 0.0276178i
\(193\) −10.9286 + 6.30966i −0.786661 + 0.454179i −0.838786 0.544462i \(-0.816734\pi\)
0.0521247 + 0.998641i \(0.483401\pi\)
\(194\) 4.61940 8.00103i 0.331653 0.574441i
\(195\) 5.42879 0.388764
\(196\) 0 0
\(197\) 17.2697i 1.23042i 0.788364 + 0.615209i \(0.210928\pi\)
−0.788364 + 0.615209i \(0.789072\pi\)
\(198\) −4.44438 + 6.66035i −0.315848 + 0.473330i
\(199\) 7.95279 4.59154i 0.563758 0.325486i −0.190894 0.981611i \(-0.561139\pi\)
0.754653 + 0.656125i \(0.227805\pi\)
\(200\) 8.83788 5.10255i 0.624932 0.360805i
\(201\) −5.32484 3.07430i −0.375585 0.216844i
\(202\) 5.34567i 0.376120i
\(203\) 0 0
\(204\) 4.65041i 0.325594i
\(205\) 12.0974 + 6.98445i 0.844921 + 0.487815i
\(206\) 2.12256 + 3.67639i 0.147886 + 0.256146i
\(207\) 5.28311 + 9.15062i 0.367202 + 0.636012i
\(208\) −0.909513 + 1.57532i −0.0630634 + 0.109229i
\(209\) 1.46754 22.6034i 0.101512 1.56351i
\(210\) 0 0
\(211\) 2.12250i 0.146119i 0.997328 + 0.0730593i \(0.0232762\pi\)
−0.997328 + 0.0730593i \(0.976724\pi\)
\(212\) 2.49222 4.31666i 0.171167 0.296469i
\(213\) −5.87394 + 3.39132i −0.402476 + 0.232370i
\(214\) −3.61931 6.26883i −0.247411 0.428529i
\(215\) −6.35245 + 11.0028i −0.433233 + 0.750382i
\(216\) −4.14386 −0.281954
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) −0.0369234 0.0213178i −0.00249505 0.00144052i
\(220\) 5.72714 + 11.5955i 0.386124 + 0.781769i
\(221\) −5.52625 9.57175i −0.371736 0.643866i
\(222\) 1.76332 3.05416i 0.118346 0.204982i
\(223\) 5.77586i 0.386780i −0.981122 0.193390i \(-0.938052\pi\)
0.981122 0.193390i \(-0.0619483\pi\)
\(224\) 0 0
\(225\) −24.6373 −1.64249
\(226\) −14.5838 8.41998i −0.970102 0.560089i
\(227\) 0.605269 + 1.04836i 0.0401731 + 0.0695819i 0.885413 0.464805i \(-0.153876\pi\)
−0.845240 + 0.534387i \(0.820542\pi\)
\(228\) 4.52679 2.61355i 0.299794 0.173086i
\(229\) 16.8020 + 9.70062i 1.11031 + 0.641035i 0.938909 0.344167i \(-0.111839\pi\)
0.171397 + 0.985202i \(0.445172\pi\)
\(230\) 17.0663 1.12532
\(231\) 0 0
\(232\) 9.36112 0.614588
\(233\) 17.0714 + 9.85619i 1.11839 + 0.645700i 0.940988 0.338439i \(-0.109899\pi\)
0.177397 + 0.984139i \(0.443232\pi\)
\(234\) 3.80317 2.19576i 0.248621 0.143541i
\(235\) 0.397450 + 0.688404i 0.0259268 + 0.0449065i
\(236\) 4.50118 + 2.59876i 0.293002 + 0.169165i
\(237\) −6.49435 −0.421854
\(238\) 0 0
\(239\) 11.6292i 0.752229i −0.926573 0.376115i \(-0.877260\pi\)
0.926573 0.376115i \(-0.122740\pi\)
\(240\) −1.49222 + 2.58461i −0.0963227 + 0.166836i
\(241\) 13.6869 + 23.7064i 0.881651 + 1.52706i 0.849505 + 0.527581i \(0.176901\pi\)
0.0321456 + 0.999483i \(0.489766\pi\)
\(242\) −10.1575 + 4.22202i −0.652948 + 0.271402i
\(243\) 13.4645 + 7.77372i 0.863747 + 0.498684i
\(244\) 8.98372 0.575124
\(245\) 0 0
\(246\) −2.74181 −0.174811
\(247\) −6.21154 + 10.7587i −0.395231 + 0.684560i
\(248\) −3.94159 6.82704i −0.250291 0.433517i
\(249\) −6.93819 + 4.00577i −0.439690 + 0.253855i
\(250\) −10.1483 + 17.5774i −0.641835 + 1.11169i
\(251\) 13.5021i 0.852243i 0.904666 + 0.426122i \(0.140120\pi\)
−0.904666 + 0.426122i \(0.859880\pi\)
\(252\) 0 0
\(253\) −0.940467 + 14.4853i −0.0591267 + 0.910682i
\(254\) −8.66501 + 15.0082i −0.543691 + 0.941701i
\(255\) −9.06684 15.7042i −0.567788 0.983437i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 2.43041 + 1.40320i 0.151605 + 0.0875289i 0.573883 0.818937i \(-0.305436\pi\)
−0.422279 + 0.906466i \(0.638770\pi\)
\(258\) 2.49371i 0.155252i
\(259\) 0 0
\(260\) 7.09306i 0.439893i
\(261\) −19.5720 11.2999i −1.21147 0.699445i
\(262\) 5.50404 3.17776i 0.340041 0.196323i
\(263\) −7.34847 + 4.24264i −0.453126 + 0.261612i −0.709150 0.705058i \(-0.750921\pi\)
0.256023 + 0.966671i \(0.417588\pi\)
\(264\) −2.11150 1.40898i −0.129954 0.0867167i
\(265\) 19.4362i 1.19396i
\(266\) 0 0
\(267\) −1.29172 −0.0790518
\(268\) −4.01676 + 6.95724i −0.245363 + 0.424981i
\(269\) −18.1498 + 10.4788i −1.10662 + 0.638905i −0.937951 0.346768i \(-0.887279\pi\)
−0.168665 + 0.985673i \(0.553946\pi\)
\(270\) 13.9936 8.07922i 0.851625 0.491686i
\(271\) 7.30660 12.6554i 0.443844 0.768761i −0.554127 0.832432i \(-0.686948\pi\)
0.997971 + 0.0636717i \(0.0202810\pi\)
\(272\) 6.07606 0.368415
\(273\) 0 0
\(274\) 1.34959i 0.0815315i
\(275\) −28.1539 18.7868i −1.69774 1.13289i
\(276\) −2.90098 + 1.67488i −0.174618 + 0.100816i
\(277\) 9.63380 5.56208i 0.578839 0.334193i −0.181833 0.983329i \(-0.558203\pi\)
0.760672 + 0.649136i \(0.224870\pi\)
\(278\) 10.3020 + 5.94786i 0.617873 + 0.356729i
\(279\) 19.0317i 1.13940i
\(280\) 0 0
\(281\) 7.28929i 0.434843i −0.976078 0.217421i \(-0.930235\pi\)
0.976078 0.217421i \(-0.0697646\pi\)
\(282\) −0.135120 0.0780114i −0.00804626 0.00464551i
\(283\) −8.00696 13.8685i −0.475965 0.824395i 0.523656 0.851930i \(-0.324568\pi\)
−0.999621 + 0.0275349i \(0.991234\pi\)
\(284\) 4.43098 + 7.67468i 0.262930 + 0.455408i
\(285\) −10.1912 + 17.6516i −0.603674 + 1.04559i
\(286\) 6.02035 + 0.390876i 0.355991 + 0.0231130i
\(287\) 0 0
\(288\) 2.41421i 0.142259i
\(289\) −9.95924 + 17.2499i −0.585838 + 1.01470i
\(290\) −31.6121 + 18.2512i −1.85633 + 1.07175i
\(291\) −3.53553 6.12372i −0.207257 0.358979i
\(292\) −0.0278530 + 0.0482428i −0.00162997 + 0.00282320i
\(293\) −14.2550 −0.832783 −0.416392 0.909185i \(-0.636705\pi\)
−0.416392 + 0.909185i \(0.636705\pi\)
\(294\) 0 0
\(295\) −20.2671 −1.17999
\(296\) −3.99045 2.30389i −0.231940 0.133911i
\(297\) 6.08623 + 12.3225i 0.353159 + 0.715027i
\(298\) −3.28834 5.69557i −0.190488 0.329935i
\(299\) 3.98064 6.89467i 0.230206 0.398729i
\(300\) 7.81064i 0.450948i
\(301\) 0 0
\(302\) 8.63888 0.497112
\(303\) −3.54325 2.04570i −0.203555 0.117522i
\(304\) −3.41476 5.91454i −0.195850 0.339222i
\(305\) −30.3376 + 17.5154i −1.73713 + 1.00293i
\(306\) −12.7036 7.33445i −0.726219 0.419283i
\(307\) 6.75074 0.385285 0.192643 0.981269i \(-0.438294\pi\)
0.192643 + 0.981269i \(0.438294\pi\)
\(308\) 0 0
\(309\) 3.24908 0.184834
\(310\) 26.6212 + 15.3697i 1.51198 + 0.872942i
\(311\) −15.4763 + 8.93526i −0.877581 + 0.506672i −0.869860 0.493298i \(-0.835791\pi\)
−0.00772127 + 0.999970i \(0.502458\pi\)
\(312\) 0.696111 + 1.20570i 0.0394095 + 0.0682593i
\(313\) −13.0188 7.51640i −0.735865 0.424852i 0.0846986 0.996407i \(-0.473007\pi\)
−0.820564 + 0.571554i \(0.806341\pi\)
\(314\) −2.44991 −0.138256
\(315\) 0 0
\(316\) 8.48528i 0.477334i
\(317\) −4.86597 + 8.42810i −0.273300 + 0.473370i −0.969705 0.244280i \(-0.921449\pi\)
0.696405 + 0.717649i \(0.254782\pi\)
\(318\) −1.90747 3.30383i −0.106965 0.185270i
\(319\) −13.7490 27.8371i −0.769797 1.55858i
\(320\) 3.37695 + 1.94969i 0.188778 + 0.108991i
\(321\) −5.54020 −0.309224
\(322\) 0 0
\(323\) 41.4966 2.30893
\(324\) 2.03553 3.52565i 0.113085 0.195869i
\(325\) 9.28167 + 16.0763i 0.514854 + 0.891754i
\(326\) 1.98325 1.14503i 0.109842 0.0634172i
\(327\) −2.29610 + 3.97696i −0.126975 + 0.219927i
\(328\) 3.58235i 0.197802i
\(329\) 0 0
\(330\) 9.87750 + 0.641304i 0.543739 + 0.0353026i
\(331\) −9.12993 + 15.8135i −0.501826 + 0.869188i 0.498172 + 0.867078i \(0.334005\pi\)
−0.999998 + 0.00210996i \(0.999328\pi\)
\(332\) 5.23379 + 9.06519i 0.287241 + 0.497517i
\(333\) 5.56208 + 9.63380i 0.304800 + 0.527929i
\(334\) 7.37339 + 4.25703i 0.403454 + 0.232934i
\(335\) 31.3257i 1.71151i
\(336\) 0 0
\(337\) 29.6928i 1.61747i −0.588173 0.808735i \(-0.700153\pi\)
0.588173 0.808735i \(-0.299847\pi\)
\(338\) 8.39278 + 4.84557i 0.456507 + 0.263564i
\(339\) −11.1620 + 6.44437i −0.606236 + 0.350010i
\(340\) −20.5186 + 11.8464i −1.11278 + 0.642461i
\(341\) −14.5123 + 21.7482i −0.785886 + 1.17773i
\(342\) 16.4879i 0.891565i
\(343\) 0 0
\(344\) −3.25819 −0.175670
\(345\) 6.53098 11.3120i 0.351616 0.609017i
\(346\) 20.7778 11.9961i 1.11702 0.644913i
\(347\) 16.6981 9.64063i 0.896399 0.517536i 0.0203688 0.999793i \(-0.493516\pi\)
0.876030 + 0.482256i \(0.160183\pi\)
\(348\) 3.58235 6.20481i 0.192034 0.332613i
\(349\) 23.9921 1.28427 0.642135 0.766592i \(-0.278049\pi\)
0.642135 + 0.766592i \(0.278049\pi\)
\(350\) 0 0
\(351\) 7.53779i 0.402337i
\(352\) −1.84092 + 2.75881i −0.0981214 + 0.147045i
\(353\) 13.9844 8.07391i 0.744316 0.429731i −0.0793204 0.996849i \(-0.525275\pi\)
0.823636 + 0.567118i \(0.191942\pi\)
\(354\) 3.44506 1.98900i 0.183103 0.105714i
\(355\) −29.9264 17.2780i −1.58833 0.917022i
\(356\) 1.68771i 0.0894484i
\(357\) 0 0
\(358\) 20.1584i 1.06541i
\(359\) −15.7145 9.07278i −0.829381 0.478843i 0.0242599 0.999706i \(-0.492277\pi\)
−0.853641 + 0.520862i \(0.825610\pi\)
\(360\) −4.70696 8.15269i −0.248078 0.429685i
\(361\) −13.8212 23.9390i −0.727431 1.25995i
\(362\) 5.55676 9.62460i 0.292057 0.505858i
\(363\) −1.08864 + 8.34836i −0.0571385 + 0.438175i
\(364\) 0 0
\(365\) 0.217218i 0.0113697i
\(366\) 3.43792 5.95465i 0.179703 0.311255i
\(367\) 4.25692 2.45773i 0.222209 0.128293i −0.384763 0.923015i \(-0.625717\pi\)
0.606973 + 0.794723i \(0.292384\pi\)
\(368\) 2.18834 + 3.79031i 0.114075 + 0.197584i
\(369\) 4.32427 7.48986i 0.225113 0.389907i
\(370\) 17.9674 0.934083
\(371\) 0 0
\(372\) −6.03353 −0.312824
\(373\) 1.96420 + 1.13403i 0.101702 + 0.0587179i 0.549989 0.835172i \(-0.314632\pi\)
−0.448286 + 0.893890i \(0.647965\pi\)
\(374\) −8.92412 18.0683i −0.461455 0.934289i
\(375\) 7.76718 + 13.4531i 0.401095 + 0.694718i
\(376\) −0.101927 + 0.176542i −0.00525647 + 0.00910448i
\(377\) 17.0281i 0.876993i
\(378\) 0 0
\(379\) 14.7984 0.760143 0.380072 0.924957i \(-0.375899\pi\)
0.380072 + 0.924957i \(0.375899\pi\)
\(380\) 23.0630 + 13.3154i 1.18311 + 0.683067i
\(381\) 6.63191 + 11.4868i 0.339763 + 0.588487i
\(382\) −21.2249 + 12.2542i −1.08596 + 0.626978i
\(383\) 6.29627 + 3.63515i 0.321724 + 0.185748i 0.652161 0.758081i \(-0.273863\pi\)
−0.330437 + 0.943828i \(0.607196\pi\)
\(384\) −0.765367 −0.0390575
\(385\) 0 0
\(386\) 12.6193 0.642306
\(387\) 6.81213 + 3.93298i 0.346280 + 0.199925i
\(388\) −8.00103 + 4.61940i −0.406191 + 0.234514i
\(389\) 17.5968 + 30.4786i 0.892194 + 1.54533i 0.837239 + 0.546837i \(0.184168\pi\)
0.0549549 + 0.998489i \(0.482498\pi\)
\(390\) −4.70147 2.71440i −0.238068 0.137449i
\(391\) −26.5929 −1.34486
\(392\) 0 0
\(393\) 4.86431i 0.245372i
\(394\) 8.63486 14.9560i 0.435018 0.753473i
\(395\) −16.5436 28.6544i −0.832401 1.44176i
\(396\) 7.17912 3.54584i 0.360764 0.178185i
\(397\) 16.3081 + 9.41550i 0.818481 + 0.472550i 0.849893 0.526956i \(-0.176667\pi\)
−0.0314111 + 0.999507i \(0.510000\pi\)
\(398\) −9.18309 −0.460307
\(399\) 0 0
\(400\) −10.2051 −0.510255
\(401\) 3.55347 6.15480i 0.177452 0.307356i −0.763555 0.645743i \(-0.776548\pi\)
0.941007 + 0.338387i \(0.109881\pi\)
\(402\) 3.07430 + 5.32484i 0.153332 + 0.265579i
\(403\) 12.4186 7.16986i 0.618612 0.357156i
\(404\) −2.67283 + 4.62948i −0.132978 + 0.230325i
\(405\) 15.8746i 0.788816i
\(406\) 0 0
\(407\) −0.990128 + 15.2502i −0.0490788 + 0.755922i
\(408\) 2.32521 4.02738i 0.115115 0.199385i
\(409\) 4.85705 + 8.41267i 0.240166 + 0.415980i 0.960761 0.277376i \(-0.0894648\pi\)
−0.720595 + 0.693356i \(0.756131\pi\)
\(410\) −6.98445 12.0974i −0.344937 0.597449i
\(411\) 0.894543 + 0.516465i 0.0441245 + 0.0254753i
\(412\) 4.24513i 0.209143i
\(413\) 0 0
\(414\) 10.5662i 0.519301i
\(415\) −35.3485 20.4085i −1.73519 1.00181i
\(416\) 1.57532 0.909513i 0.0772366 0.0445925i
\(417\) 7.88481 4.55230i 0.386121 0.222927i
\(418\) −12.5726 + 18.8413i −0.614947 + 0.921559i
\(419\) 23.0474i 1.12594i −0.826478 0.562970i \(-0.809659\pi\)
0.826478 0.562970i \(-0.190341\pi\)
\(420\) 0 0
\(421\) −1.67074 −0.0814270 −0.0407135 0.999171i \(-0.512963\pi\)
−0.0407135 + 0.999171i \(0.512963\pi\)
\(422\) 1.06125 1.83814i 0.0516608 0.0894790i
\(423\) 0.426211 0.246073i 0.0207231 0.0119645i
\(424\) −4.31666 + 2.49222i −0.209636 + 0.121033i
\(425\) 31.0034 53.6994i 1.50389 2.60481i
\(426\) 6.78265 0.328620
\(427\) 0 0
\(428\) 7.23863i 0.349892i
\(429\) 2.56297 3.84087i 0.123741 0.185439i
\(430\) 11.0028 6.35245i 0.530600 0.306342i
\(431\) 33.6434 19.4240i 1.62055 0.935623i 0.633772 0.773520i \(-0.281506\pi\)
0.986774 0.162103i \(-0.0518277\pi\)
\(432\) 3.58869 + 2.07193i 0.172661 + 0.0996858i
\(433\) 31.8479i 1.53051i −0.643726 0.765256i \(-0.722612\pi\)
0.643726 0.765256i \(-0.277388\pi\)
\(434\) 0 0
\(435\) 27.9378i 1.33951i
\(436\) 5.19615 + 3.00000i 0.248851 + 0.143674i
\(437\) 14.9453 + 25.8860i 0.714930 + 1.23830i
\(438\) 0.0213178 + 0.0369234i 0.00101860 + 0.00176427i
\(439\) −6.02035 + 10.4276i −0.287336 + 0.497680i −0.973173 0.230075i \(-0.926103\pi\)
0.685837 + 0.727755i \(0.259436\pi\)
\(440\) 0.837904 12.9056i 0.0399455 0.615249i
\(441\) 0 0
\(442\) 11.0525i 0.525714i
\(443\) 15.2762 26.4591i 0.725793 1.25711i −0.232854 0.972512i \(-0.574807\pi\)
0.958647 0.284598i \(-0.0918601\pi\)
\(444\) −3.05416 + 1.76332i −0.144944 + 0.0836835i
\(445\) −3.29050 5.69932i −0.155985 0.270174i
\(446\) −2.88793 + 5.00204i −0.136748 + 0.236854i
\(447\) −5.03357 −0.238080
\(448\) 0 0
\(449\) 15.7378 0.742712 0.371356 0.928490i \(-0.378893\pi\)
0.371356 + 0.928490i \(0.378893\pi\)
\(450\) 21.3365 + 12.3186i 1.00581 + 0.580706i
\(451\) 10.6528 5.26152i 0.501620 0.247755i
\(452\) 8.41998 + 14.5838i 0.396043 + 0.685966i
\(453\) 3.30596 5.72608i 0.155327 0.269035i
\(454\) 1.21054i 0.0568134i
\(455\) 0 0
\(456\) −5.22709 −0.244781
\(457\) 14.8669 + 8.58340i 0.695443 + 0.401514i 0.805648 0.592395i \(-0.201817\pi\)
−0.110205 + 0.993909i \(0.535151\pi\)
\(458\) −9.70062 16.8020i −0.453280 0.785105i
\(459\) −21.8051 + 12.5892i −1.01777 + 0.587612i
\(460\) −14.7798 8.53314i −0.689113 0.397860i
\(461\) −0.312096 −0.0145357 −0.00726787 0.999974i \(-0.502313\pi\)
−0.00726787 + 0.999974i \(0.502313\pi\)
\(462\) 0 0
\(463\) −31.9402 −1.48439 −0.742194 0.670185i \(-0.766215\pi\)
−0.742194 + 0.670185i \(0.766215\pi\)
\(464\) −8.10697 4.68056i −0.376357 0.217290i
\(465\) 20.3749 11.7635i 0.944866 0.545518i
\(466\) −9.85619 17.0714i −0.456579 0.790818i
\(467\) 16.3264 + 9.42604i 0.755495 + 0.436185i 0.827676 0.561206i \(-0.189663\pi\)
−0.0721810 + 0.997392i \(0.522996\pi\)
\(468\) −4.39152 −0.202998
\(469\) 0 0
\(470\) 0.794901i 0.0366660i
\(471\) −0.937539 + 1.62386i −0.0431995 + 0.0748237i
\(472\) −2.59876 4.50118i −0.119618 0.207184i
\(473\) 4.78542 + 9.68884i 0.220034 + 0.445493i
\(474\) 5.62427 + 3.24718i 0.258331 + 0.149148i
\(475\) −69.6960 −3.19787
\(476\) 0 0
\(477\) 12.0335 0.550977
\(478\) −5.81459 + 10.0712i −0.265953 + 0.460645i
\(479\) 14.5270 + 25.1615i 0.663755 + 1.14966i 0.979621 + 0.200854i \(0.0643717\pi\)
−0.315866 + 0.948804i \(0.602295\pi\)
\(480\) 2.58461 1.49222i 0.117971 0.0681104i
\(481\) 4.19083 7.25874i 0.191086 0.330970i
\(482\) 27.3738i 1.24684i
\(483\) 0 0
\(484\) 10.9077 + 1.42237i 0.495802 + 0.0646532i
\(485\) 18.0127 31.1990i 0.817917 1.41667i
\(486\) −7.77372 13.4645i −0.352623 0.610761i
\(487\) 16.5674 + 28.6956i 0.750742 + 1.30032i 0.947463 + 0.319864i \(0.103637\pi\)
−0.196721 + 0.980459i \(0.563029\pi\)
\(488\) −7.78013 4.49186i −0.352190 0.203337i
\(489\) 1.75273i 0.0792613i
\(490\) 0 0
\(491\) 42.4151i 1.91416i −0.289817 0.957082i \(-0.593594\pi\)
0.289817 0.957082i \(-0.406406\pi\)
\(492\) 2.37448 + 1.37090i 0.107050 + 0.0618052i
\(493\) 49.2584 28.4394i 2.21849 1.28084i
\(494\) 10.7587 6.21154i 0.484057 0.279470i
\(495\) −17.3303 + 25.9712i −0.778938 + 1.16732i
\(496\) 7.88318i 0.353965i
\(497\) 0 0
\(498\) 8.01154 0.359005
\(499\) −7.72103 + 13.3732i −0.345641 + 0.598667i −0.985470 0.169850i \(-0.945672\pi\)
0.639829 + 0.768517i \(0.279005\pi\)
\(500\) 17.5774 10.1483i 0.786085 0.453846i
\(501\) 5.64335 3.25819i 0.252126 0.145565i
\(502\) 6.75103 11.6931i 0.301313 0.521890i
\(503\) 39.5816 1.76486 0.882429 0.470446i \(-0.155907\pi\)
0.882429 + 0.470446i \(0.155907\pi\)
\(504\) 0 0
\(505\) 20.8447i 0.927579i
\(506\) 8.05711 12.0744i 0.358182 0.536772i
\(507\) 6.42355 3.70864i 0.285280 0.164706i
\(508\) 15.0082 8.66501i 0.665883 0.384448i
\(509\) 4.57165 + 2.63944i 0.202635 + 0.116991i 0.597884 0.801583i \(-0.296008\pi\)
−0.395249 + 0.918574i \(0.629342\pi\)
\(510\) 18.1337i 0.802973i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 24.5090 + 14.1503i 1.08210 + 0.624751i
\(514\) −1.40320 2.43041i −0.0618923 0.107201i
\(515\) 8.27667 + 14.3356i 0.364714 + 0.631703i
\(516\) −1.24686 + 2.15962i −0.0548898 + 0.0950719i
\(517\) 0.674685 + 0.0438044i 0.0296726 + 0.00192652i
\(518\) 0 0
\(519\) 18.3628i 0.806037i
\(520\) −3.54653 + 6.14277i −0.155526 + 0.269378i
\(521\) 23.6500 13.6543i 1.03613 0.598207i 0.117392 0.993086i \(-0.462547\pi\)
0.918733 + 0.394878i \(0.129213\pi\)
\(522\) 11.2999 + 19.5720i 0.494582 + 0.856641i
\(523\) 4.32645 7.49363i 0.189182 0.327673i −0.755796 0.654808i \(-0.772750\pi\)
0.944978 + 0.327134i \(0.106083\pi\)
\(524\) −6.35552 −0.277642
\(525\) 0 0
\(526\) 8.48528 0.369976
\(527\) −41.4815 23.9493i −1.80696 1.04325i
\(528\) 1.12412 + 2.27596i 0.0489211 + 0.0990485i
\(529\) 1.92237 + 3.32964i 0.0835813 + 0.144767i
\(530\) 9.71811 16.8323i 0.422128 0.731147i
\(531\) 12.5479i 0.544533i
\(532\) 0 0
\(533\) −6.51638 −0.282256
\(534\) 1.11866 + 0.645859i 0.0484092 + 0.0279490i
\(535\) −14.1130 24.4445i −0.610160 1.05683i
\(536\) 6.95724 4.01676i 0.300507 0.173498i
\(537\) 13.3616 + 7.71430i 0.576594 + 0.332897i
\(538\) 20.9576 0.903548
\(539\) 0 0
\(540\) −16.1584 −0.695349
\(541\) 0.447200 + 0.258191i 0.0192266 + 0.0111005i 0.509583 0.860422i \(-0.329800\pi\)
−0.490356 + 0.871522i \(0.663133\pi\)
\(542\) −12.6554 + 7.30660i −0.543596 + 0.313845i
\(543\) −4.25296 7.36635i −0.182512 0.316120i
\(544\) −5.26202 3.03803i −0.225607 0.130254i
\(545\) −23.3962 −1.00218
\(546\) 0 0
\(547\) 28.0407i 1.19894i −0.800399 0.599468i \(-0.795379\pi\)
0.800399 0.599468i \(-0.204621\pi\)
\(548\) 0.674793 1.16878i 0.0288257 0.0499277i
\(549\) 10.8443 + 18.7829i 0.462824 + 0.801634i
\(550\) 14.9886 + 30.3468i 0.639116 + 1.29399i
\(551\) −55.3667 31.9660i −2.35870 1.36180i
\(552\) 3.34976 0.142575
\(553\) 0 0
\(554\) −11.1242 −0.472620
\(555\) 6.87584 11.9093i 0.291863 0.505522i
\(556\) −5.94786 10.3020i −0.252246 0.436902i
\(557\) −24.8942 + 14.3727i −1.05480 + 0.608989i −0.923989 0.382418i \(-0.875091\pi\)
−0.130811 + 0.991407i \(0.541758\pi\)
\(558\) 9.51584 16.4819i 0.402838 0.697735i
\(559\) 5.92673i 0.250674i
\(560\) 0 0
\(561\) −15.3913 0.999289i −0.649820 0.0421900i
\(562\) −3.64465 + 6.31271i −0.153740 + 0.266286i
\(563\) −3.37537 5.84631i −0.142255 0.246393i 0.786090 0.618111i \(-0.212102\pi\)
−0.928345 + 0.371719i \(0.878769\pi\)
\(564\) 0.0780114 + 0.135120i 0.00328487 + 0.00568956i
\(565\) −56.8678 32.8326i −2.39245 1.38128i
\(566\) 16.0139i 0.673115i
\(567\) 0 0
\(568\) 8.86195i 0.371839i
\(569\) 8.41827 + 4.86029i 0.352912 + 0.203754i 0.665967 0.745981i \(-0.268019\pi\)
−0.313055 + 0.949735i \(0.601352\pi\)
\(570\) 17.6516 10.1912i 0.739346 0.426862i
\(571\) −17.6516 + 10.1912i −0.738698 + 0.426487i −0.821596 0.570071i \(-0.806916\pi\)
0.0828978 + 0.996558i \(0.473582\pi\)
\(572\) −5.01834 3.34868i −0.209827 0.140016i
\(573\) 18.7579i 0.783622i
\(574\) 0 0
\(575\) 44.6644 1.86263
\(576\) 1.20711 2.09077i 0.0502961 0.0871154i
\(577\) −10.5781 + 6.10726i −0.440371 + 0.254248i −0.703755 0.710443i \(-0.748495\pi\)
0.263384 + 0.964691i \(0.415161\pi\)
\(578\) 17.2499 9.95924i 0.717502 0.414250i
\(579\) 4.82920 8.36442i 0.200695 0.347614i
\(580\) 36.5025 1.51568
\(581\) 0 0
\(582\) 7.07107i 0.293105i
\(583\) 13.7511 + 9.17598i 0.569514 + 0.380030i
\(584\) 0.0482428 0.0278530i 0.00199630 0.00115257i
\(585\) 14.8300 8.56208i 0.613143 0.353998i
\(586\) 12.3451 + 7.12748i 0.509973 + 0.294433i
\(587\) 22.5689i 0.931519i −0.884911 0.465759i \(-0.845781\pi\)
0.884911 0.465759i \(-0.154219\pi\)
\(588\) 0 0
\(589\) 53.8384i 2.21837i
\(590\) 17.5518 + 10.1335i 0.722596 + 0.417191i
\(591\) −6.60884 11.4468i −0.271851 0.470860i
\(592\) 2.30389 + 3.99045i 0.0946892 + 0.164007i
\(593\) 18.3348 31.7568i 0.752920 1.30410i −0.193481 0.981104i \(-0.561978\pi\)
0.946402 0.322992i \(-0.104689\pi\)
\(594\) 0.890440 13.7148i 0.0365352 0.562723i
\(595\) 0 0
\(596\) 6.57668i 0.269391i
\(597\) −3.51422 + 6.08680i −0.143827 + 0.249116i
\(598\) −6.89467 + 3.98064i −0.281944 + 0.162780i
\(599\) −3.17279 5.49543i −0.129637 0.224537i 0.793899 0.608049i \(-0.208048\pi\)
−0.923536 + 0.383512i \(0.874714\pi\)
\(600\) −3.90532 + 6.76422i −0.159434 + 0.276148i
\(601\) 1.60141 0.0653230 0.0326615 0.999466i \(-0.489602\pi\)
0.0326615 + 0.999466i \(0.489602\pi\)
\(602\) 0 0
\(603\) −19.3946 −0.789811
\(604\) −7.48149 4.31944i −0.304417 0.175755i
\(605\) −39.6078 + 16.4632i −1.61029 + 0.669325i
\(606\) 2.04570 + 3.54325i 0.0831008 + 0.143935i
\(607\) 8.37216 14.5010i 0.339815 0.588578i −0.644582 0.764535i \(-0.722969\pi\)
0.984398 + 0.175957i \(0.0563021\pi\)
\(608\) 6.82952i 0.276974i
\(609\) 0 0
\(610\) 35.0309 1.41836
\(611\) −0.321135 0.185407i −0.0129917 0.00750078i
\(612\) 7.33445 + 12.7036i 0.296478 + 0.513514i
\(613\) 1.57905 0.911666i 0.0637773 0.0368219i −0.467772 0.883849i \(-0.654943\pi\)
0.531550 + 0.847027i \(0.321610\pi\)
\(614\) −5.84631 3.37537i −0.235938 0.136219i
\(615\) −10.6913 −0.431116
\(616\) 0 0
\(617\) 46.7616 1.88255 0.941276 0.337638i \(-0.109628\pi\)
0.941276 + 0.337638i \(0.109628\pi\)
\(618\) −2.81379 1.62454i −0.113187 0.0653486i
\(619\) 35.0519 20.2372i 1.40885 0.813402i 0.413576 0.910470i \(-0.364280\pi\)
0.995278 + 0.0970680i \(0.0309464\pi\)
\(620\) −15.3697 26.6212i −0.617263 1.06913i
\(621\) −15.7065 9.06816i −0.630281 0.363893i
\(622\) 17.8705 0.716542
\(623\) 0 0
\(624\) 1.39222i 0.0557335i
\(625\) −14.0593 + 24.3514i −0.562371 + 0.974055i
\(626\) 7.51640 + 13.0188i 0.300416 + 0.520335i
\(627\) 7.67721 + 15.5437i 0.306598 + 0.620757i
\(628\) 2.12168 + 1.22495i 0.0846643 + 0.0488810i
\(629\) −27.9971 −1.11632
\(630\) 0 0
\(631\) 12.6619 0.504064 0.252032 0.967719i \(-0.418901\pi\)
0.252032 + 0.967719i \(0.418901\pi\)
\(632\) 4.24264 7.34847i 0.168763 0.292306i
\(633\) −0.812244 1.40685i −0.0322838 0.0559172i
\(634\) 8.42810 4.86597i 0.334723 0.193252i
\(635\) −33.7881 + 58.5227i −1.34084 + 2.32240i
\(636\) 3.81493i 0.151272i
\(637\) 0 0
\(638\) −2.01154 + 30.9821i −0.0796374 + 1.22659i
\(639\) −10.6973 + 18.5283i −0.423180 + 0.732969i
\(640\) −1.94969 3.37695i −0.0770681 0.133486i
\(641\) 0.653476 + 1.13185i 0.0258107 + 0.0447055i 0.878642 0.477481i \(-0.158450\pi\)
−0.852832 + 0.522186i \(0.825117\pi\)
\(642\) 4.79796 + 2.77010i 0.189360 + 0.109327i
\(643\) 39.1745i 1.54489i 0.635081 + 0.772446i \(0.280967\pi\)
−0.635081 + 0.772446i \(0.719033\pi\)
\(644\) 0 0
\(645\) 9.72391i 0.382878i
\(646\) −35.9371 20.7483i −1.41393 0.816330i
\(647\) −14.3245 + 8.27023i −0.563153 + 0.325136i −0.754410 0.656404i \(-0.772077\pi\)
0.191257 + 0.981540i \(0.438744\pi\)
\(648\) −3.52565 + 2.03553i −0.138501 + 0.0799633i
\(649\) −9.56822 + 14.3389i −0.375586 + 0.562853i
\(650\) 18.5633i 0.728114i
\(651\) 0 0
\(652\) −2.29005 −0.0896854
\(653\) −17.3853 + 30.1122i −0.680339 + 1.17838i 0.294539 + 0.955639i \(0.404834\pi\)
−0.974878 + 0.222741i \(0.928499\pi\)
\(654\) 3.97696 2.29610i 0.155512 0.0897846i
\(655\) 21.4623 12.3913i 0.838602 0.484167i
\(656\) 1.79117 3.10240i 0.0699336 0.121128i
\(657\) −0.134486 −0.00524680
\(658\) 0 0
\(659\) 22.4888i 0.876039i 0.898966 + 0.438019i \(0.144320\pi\)
−0.898966 + 0.438019i \(0.855680\pi\)
\(660\) −8.23352 5.49414i −0.320489 0.213859i
\(661\) −22.7587 + 13.1398i −0.885212 + 0.511077i −0.872373 0.488840i \(-0.837420\pi\)
−0.0128383 + 0.999918i \(0.504087\pi\)
\(662\) 15.8135 9.12993i 0.614609 0.354845i
\(663\) 7.32590 + 4.22961i 0.284514 + 0.164265i
\(664\) 10.4676i 0.406221i
\(665\) 0 0
\(666\) 11.1242i 0.431052i
\(667\) 35.4815 + 20.4853i 1.37385 + 0.793193i
\(668\) −4.25703 7.37339i −0.164709 0.285285i
\(669\) 2.21033 + 3.82840i 0.0854562 + 0.148014i
\(670\) −15.6629 + 27.1289i −0.605109 + 1.04808i
\(671\) −1.93044 + 29.7330i −0.0745237 + 1.14783i
\(672\) 0 0
\(673\) 3.77457i 0.145499i −0.997350 0.0727495i \(-0.976823\pi\)
0.997350 0.0727495i \(-0.0231774\pi\)
\(674\) −14.8464 + 25.7147i −0.571862 + 0.990494i
\(675\) 36.6229 21.1442i 1.40962 0.813843i
\(676\) −4.84557 8.39278i −0.186368 0.322799i
\(677\) −15.7129 + 27.2155i −0.603896 + 1.04598i 0.388329 + 0.921521i \(0.373052\pi\)
−0.992225 + 0.124457i \(0.960281\pi\)
\(678\) 12.8887 0.494989
\(679\) 0 0
\(680\) 23.6928 0.908578
\(681\) −0.802378 0.463253i −0.0307472 0.0177519i
\(682\) 23.4421 11.5783i 0.897645 0.443356i
\(683\) 9.95029 + 17.2344i 0.380737 + 0.659456i 0.991168 0.132614i \(-0.0423369\pi\)
−0.610431 + 0.792070i \(0.709004\pi\)
\(684\) 8.24396 14.2790i 0.315216 0.545970i
\(685\) 5.26254i 0.201071i
\(686\) 0 0
\(687\) −14.8491 −0.566527
\(688\) 2.82168 + 1.62910i 0.107575 + 0.0621087i
\(689\) −4.53342 7.85212i −0.172710 0.299142i
\(690\) −11.3120 + 6.53098i −0.430640 + 0.248630i
\(691\) −24.7690 14.3004i −0.942255 0.544011i −0.0515887 0.998668i \(-0.516428\pi\)
−0.890667 + 0.454657i \(0.849762\pi\)
\(692\) −23.9921 −0.912044
\(693\) 0 0
\(694\) −19.2813 −0.731907
\(695\) 40.1713 + 23.1929i 1.52379 + 0.879758i
\(696\) −6.20481 + 3.58235i −0.235193 + 0.135788i
\(697\) 10.8833 + 18.8504i 0.412233 + 0.714009i
\(698\) −20.7778 11.9961i −0.786451 0.454058i
\(699\) −15.0872 −0.570650
\(700\) 0 0
\(701\) 21.2928i 0.804218i −0.915592 0.402109i \(-0.868277\pi\)
0.915592 0.402109i \(-0.131723\pi\)
\(702\) −3.76889 + 6.52792i −0.142248 + 0.246380i
\(703\) 15.7345 + 27.2529i 0.593436 + 1.02786i
\(704\) 2.97369 1.46874i 0.112075 0.0553550i
\(705\) −0.526882 0.304195i −0.0198435 0.0114567i
\(706\) −16.1478 −0.607731
\(707\) 0 0
\(708\) −3.97801 −0.149503
\(709\) 8.43913 14.6170i 0.316938 0.548953i −0.662909 0.748700i \(-0.730679\pi\)
0.979848 + 0.199746i \(0.0640118\pi\)
\(710\) 17.2780 + 29.9264i 0.648433 + 1.12312i
\(711\) −17.7408 + 10.2426i −0.665331 + 0.384129i
\(712\) 0.843855 1.46160i 0.0316248 0.0547758i
\(713\) 34.5021i 1.29211i
\(714\) 0 0
\(715\) 23.4756 + 1.52417i 0.877937 + 0.0570007i
\(716\) 10.0792 17.4577i 0.376678 0.652426i
\(717\) 4.45030 + 7.70814i 0.166199 + 0.287866i
\(718\) 9.07278 + 15.7145i 0.338593 + 0.586461i
\(719\) 31.3046 + 18.0737i 1.16746 + 0.674036i 0.953081 0.302714i \(-0.0978927\pi\)
0.214383 + 0.976750i \(0.431226\pi\)
\(720\) 9.41392i 0.350836i
\(721\) 0 0
\(722\) 27.6424i 1.02874i
\(723\) −18.1441 10.4755i −0.674786 0.389588i
\(724\) −9.62460 + 5.55676i −0.357695 + 0.206515i
\(725\) −82.7324 + 47.7656i −3.07261 + 1.77397i
\(726\) 5.11696 6.68557i 0.189908 0.248125i
\(727\) 8.74172i 0.324212i −0.986773 0.162106i \(-0.948171\pi\)
0.986773 0.162106i \(-0.0518287\pi\)
\(728\) 0 0
\(729\) 0.313708 0.0116188
\(730\) −0.108609 + 0.188117i −0.00401981 + 0.00696251i
\(731\) −17.1447 + 9.89848i −0.634118 + 0.366108i
\(732\) −5.95465 + 3.43792i −0.220090 + 0.127069i
\(733\) 6.73225 11.6606i 0.248661 0.430694i −0.714493 0.699642i \(-0.753343\pi\)
0.963155 + 0.268948i \(0.0866760\pi\)
\(734\) −4.91547 −0.181433
\(735\) 0 0
\(736\) 4.37667i 0.161326i
\(737\) −22.1629 14.7891i −0.816382 0.544763i
\(738\) −7.48986 + 4.32427i −0.275706 + 0.159179i
\(739\) 32.3387 18.6708i 1.18960 0.686816i 0.231384 0.972862i \(-0.425675\pi\)
0.958216 + 0.286047i \(0.0923413\pi\)
\(740\) −15.5603 8.98372i −0.572006 0.330248i
\(741\) 9.50821i 0.349293i
\(742\) 0 0
\(743\) 17.5472i 0.643746i −0.946783 0.321873i \(-0.895688\pi\)
0.946783 0.321873i \(-0.104312\pi\)
\(744\) 5.22519 + 3.01676i 0.191565 + 0.110600i
\(745\) −12.8225 22.2091i −0.469778 0.813680i
\(746\) −1.13403 1.96420i −0.0415198 0.0719145i
\(747\) −12.6355 + 21.8853i −0.462308 + 0.800741i
\(748\) −1.30563 + 20.1097i −0.0477387 + 0.735282i
\(749\) 0 0
\(750\) 15.5344i 0.567235i
\(751\) 17.3623 30.0724i 0.633561 1.09736i −0.353258 0.935526i \(-0.614926\pi\)
0.986818 0.161833i \(-0.0517406\pi\)
\(752\) 0.176542 0.101927i 0.00643784 0.00371689i
\(753\) −5.16702 8.94954i −0.188297 0.326139i
\(754\) 8.51406 14.7468i 0.310064 0.537046i
\(755\) 33.6862 1.22597
\(756\) 0 0
\(757\) 28.0627 1.01996 0.509978 0.860187i \(-0.329653\pi\)
0.509978 + 0.860187i \(0.329653\pi\)
\(758\) −12.8158 7.39920i −0.465491 0.268751i
\(759\) −4.91991 9.96114i −0.178581 0.361566i
\(760\) −13.3154 23.0630i −0.483001 0.836583i
\(761\) 3.79149 6.56706i 0.137442 0.238056i −0.789086 0.614283i \(-0.789445\pi\)
0.926527 + 0.376227i \(0.122779\pi\)
\(762\) 13.2638i 0.480498i
\(763\) 0 0
\(764\) 24.5084 0.886681
\(765\) −49.5362 28.5997i −1.79099 1.03403i
\(766\) −3.63515 6.29627i −0.131343 0.227494i
\(767\) 8.18777 4.72721i 0.295643 0.170690i
\(768\) 0.662827 + 0.382683i 0.0239177 + 0.0138089i
\(769\) 1.95786 0.0706022 0.0353011 0.999377i \(-0.488761\pi\)
0.0353011 + 0.999377i \(0.488761\pi\)
\(770\) 0 0
\(771\) −2.14792 −0.0773554
\(772\) −10.9286 6.30966i −0.393331 0.227090i
\(773\) 8.18023 4.72286i 0.294223 0.169869i −0.345622 0.938374i \(-0.612332\pi\)
0.639845 + 0.768504i \(0.278999\pi\)
\(774\) −3.93298 6.81213i −0.141368 0.244857i
\(775\) 69.6706 + 40.2243i 2.50264 + 1.44490i
\(776\) 9.23880 0.331653
\(777\) 0 0
\(778\) 35.1936i 1.26175i
\(779\) 12.2329 21.1879i 0.438288 0.759136i
\(780\) 2.71440 + 4.70147i 0.0971910 + 0.168340i
\(781\) −26.3527 + 13.0159i −0.942973 + 0.465744i
\(782\) 23.0301 + 13.2965i 0.823556 + 0.475480i
\(783\) 38.7912 1.38628
\(784\) 0