Properties

Label 1323.2.o.e.440.6
Level $1323$
Weight $2$
Character 1323.440
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 440.6
Character \(\chi\) \(=\) 1323.440
Dual form 1323.2.o.e.881.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.61855 - 0.934468i) q^{2} +(0.746462 + 1.29291i) q^{4} +(1.25287 + 2.17003i) q^{5} +0.947692i q^{8} +O(q^{10})\) \(q+(-1.61855 - 0.934468i) q^{2} +(0.746462 + 1.29291i) q^{4} +(1.25287 + 2.17003i) q^{5} +0.947692i q^{8} -4.68306i q^{10} +(4.85803 + 2.80479i) q^{11} +(-0.384312 + 0.221883i) q^{13} +(2.37851 - 4.11970i) q^{16} +3.07770 q^{17} +2.57419i q^{19} +(-1.87044 + 3.23969i) q^{20} +(-5.24197 - 9.07935i) q^{22} +(-6.83476 + 3.94605i) q^{23} +(-0.639351 + 1.10739i) q^{25} +0.829370 q^{26} +(-2.71041 - 1.56485i) q^{29} +(9.06457 - 5.23343i) q^{31} +(-6.05802 + 3.49760i) q^{32} +(-4.98140 - 2.87601i) q^{34} -1.41634 q^{37} +(2.40550 - 4.16645i) q^{38} +(-2.05652 + 1.18733i) q^{40} +(1.64665 + 2.85208i) q^{41} +(-4.75676 + 8.23894i) q^{43} +8.37467i q^{44} +14.7498 q^{46} +(-1.07190 + 1.85659i) q^{47} +(2.06964 - 1.19491i) q^{50} +(-0.573749 - 0.331254i) q^{52} +4.85412i q^{53} +14.0561i q^{55} +(2.92461 + 5.06558i) q^{58} +(-3.65496 - 6.33057i) q^{59} +(-7.40950 - 4.27788i) q^{61} -19.5619 q^{62} +3.55953 q^{64} +(-0.962984 - 0.555979i) q^{65} +(0.934442 + 1.61850i) q^{67} +(2.29739 + 3.97919i) q^{68} +2.95338i q^{71} +8.51943i q^{73} +(2.29241 + 1.32352i) q^{74} +(-3.32820 + 1.92154i) q^{76} +(0.287130 - 0.497324i) q^{79} +11.9198 q^{80} -6.15497i q^{82} +(4.23521 - 7.33560i) q^{83} +(3.85595 + 6.67870i) q^{85} +(15.3981 - 8.89008i) q^{86} +(-2.65807 + 4.60392i) q^{88} -7.57858 q^{89} +(-10.2038 - 5.89115i) q^{92} +(3.46984 - 2.00332i) q^{94} +(-5.58607 + 3.22512i) q^{95} +(3.22662 + 1.86289i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{4} + O(q^{10}) \) \( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61855 0.934468i −1.14449 0.660769i −0.196948 0.980414i \(-0.563103\pi\)
−0.947537 + 0.319645i \(0.896436\pi\)
\(3\) 0 0
\(4\) 0.746462 + 1.29291i 0.373231 + 0.646455i
\(5\) 1.25287 + 2.17003i 0.560299 + 0.970467i 0.997470 + 0.0710881i \(0.0226472\pi\)
−0.437171 + 0.899378i \(0.644020\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.947692i 0.335060i
\(9\) 0 0
\(10\) 4.68306i 1.48091i
\(11\) 4.85803 + 2.80479i 1.46475 + 0.845675i 0.999225 0.0393590i \(-0.0125316\pi\)
0.465527 + 0.885034i \(0.345865\pi\)
\(12\) 0 0
\(13\) −0.384312 + 0.221883i −0.106589 + 0.0615392i −0.552347 0.833614i \(-0.686268\pi\)
0.445758 + 0.895154i \(0.352934\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.37851 4.11970i 0.594628 1.02993i
\(17\) 3.07770 0.746451 0.373226 0.927741i \(-0.378252\pi\)
0.373226 + 0.927741i \(0.378252\pi\)
\(18\) 0 0
\(19\) 2.57419i 0.590560i 0.955411 + 0.295280i \(0.0954130\pi\)
−0.955411 + 0.295280i \(0.904587\pi\)
\(20\) −1.87044 + 3.23969i −0.418242 + 0.724417i
\(21\) 0 0
\(22\) −5.24197 9.07935i −1.11759 1.93572i
\(23\) −6.83476 + 3.94605i −1.42515 + 0.822808i −0.996732 0.0807749i \(-0.974261\pi\)
−0.428413 + 0.903583i \(0.640927\pi\)
\(24\) 0 0
\(25\) −0.639351 + 1.10739i −0.127870 + 0.221478i
\(26\) 0.829370 0.162653
\(27\) 0 0
\(28\) 0 0
\(29\) −2.71041 1.56485i −0.503310 0.290586i 0.226770 0.973948i \(-0.427184\pi\)
−0.730079 + 0.683362i \(0.760517\pi\)
\(30\) 0 0
\(31\) 9.06457 5.23343i 1.62805 0.939952i 0.643370 0.765556i \(-0.277536\pi\)
0.984675 0.174397i \(-0.0557975\pi\)
\(32\) −6.05802 + 3.49760i −1.07092 + 0.618294i
\(33\) 0 0
\(34\) −4.98140 2.87601i −0.854303 0.493232i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.41634 −0.232844 −0.116422 0.993200i \(-0.537143\pi\)
−0.116422 + 0.993200i \(0.537143\pi\)
\(38\) 2.40550 4.16645i 0.390224 0.675887i
\(39\) 0 0
\(40\) −2.05652 + 1.18733i −0.325164 + 0.187734i
\(41\) 1.64665 + 2.85208i 0.257163 + 0.445420i 0.965481 0.260474i \(-0.0838788\pi\)
−0.708318 + 0.705894i \(0.750545\pi\)
\(42\) 0 0
\(43\) −4.75676 + 8.23894i −0.725398 + 1.25643i 0.233411 + 0.972378i \(0.425011\pi\)
−0.958810 + 0.284049i \(0.908322\pi\)
\(44\) 8.37467i 1.26253i
\(45\) 0 0
\(46\) 14.7498 2.17474
\(47\) −1.07190 + 1.85659i −0.156353 + 0.270811i −0.933551 0.358445i \(-0.883307\pi\)
0.777198 + 0.629256i \(0.216640\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.06964 1.19491i 0.292691 0.168985i
\(51\) 0 0
\(52\) −0.573749 0.331254i −0.0795647 0.0459367i
\(53\) 4.85412i 0.666764i 0.942792 + 0.333382i \(0.108190\pi\)
−0.942792 + 0.333382i \(0.891810\pi\)
\(54\) 0 0
\(55\) 14.0561i 1.89532i
\(56\) 0 0
\(57\) 0 0
\(58\) 2.92461 + 5.06558i 0.384020 + 0.665143i
\(59\) −3.65496 6.33057i −0.475835 0.824170i 0.523782 0.851852i \(-0.324521\pi\)
−0.999617 + 0.0276824i \(0.991187\pi\)
\(60\) 0 0
\(61\) −7.40950 4.27788i −0.948690 0.547726i −0.0560160 0.998430i \(-0.517840\pi\)
−0.892674 + 0.450704i \(0.851173\pi\)
\(62\) −19.5619 −2.48437
\(63\) 0 0
\(64\) 3.55953 0.444941
\(65\) −0.962984 0.555979i −0.119443 0.0689607i
\(66\) 0 0
\(67\) 0.934442 + 1.61850i 0.114160 + 0.197731i 0.917444 0.397865i \(-0.130249\pi\)
−0.803284 + 0.595597i \(0.796916\pi\)
\(68\) 2.29739 + 3.97919i 0.278599 + 0.482548i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.95338i 0.350501i 0.984524 + 0.175251i \(0.0560736\pi\)
−0.984524 + 0.175251i \(0.943926\pi\)
\(72\) 0 0
\(73\) 8.51943i 0.997124i 0.866854 + 0.498562i \(0.166138\pi\)
−0.866854 + 0.498562i \(0.833862\pi\)
\(74\) 2.29241 + 1.32352i 0.266487 + 0.153856i
\(75\) 0 0
\(76\) −3.32820 + 1.92154i −0.381771 + 0.220415i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.287130 0.497324i 0.0323047 0.0559533i −0.849421 0.527716i \(-0.823049\pi\)
0.881726 + 0.471762i \(0.156382\pi\)
\(80\) 11.9198 1.33268
\(81\) 0 0
\(82\) 6.15497i 0.679702i
\(83\) 4.23521 7.33560i 0.464875 0.805186i −0.534321 0.845281i \(-0.679433\pi\)
0.999196 + 0.0400951i \(0.0127661\pi\)
\(84\) 0 0
\(85\) 3.85595 + 6.67870i 0.418236 + 0.724406i
\(86\) 15.3981 8.89008i 1.66042 0.958642i
\(87\) 0 0
\(88\) −2.65807 + 4.60392i −0.283352 + 0.490779i
\(89\) −7.57858 −0.803328 −0.401664 0.915787i \(-0.631568\pi\)
−0.401664 + 0.915787i \(0.631568\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −10.2038 5.89115i −1.06382 0.614195i
\(93\) 0 0
\(94\) 3.46984 2.00332i 0.357887 0.206626i
\(95\) −5.58607 + 3.22512i −0.573119 + 0.330890i
\(96\) 0 0
\(97\) 3.22662 + 1.86289i 0.327614 + 0.189148i 0.654781 0.755818i \(-0.272761\pi\)
−0.327167 + 0.944966i \(0.606094\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.90901 −0.190901
\(101\) −3.76725 + 6.52506i −0.374855 + 0.649268i −0.990305 0.138908i \(-0.955641\pi\)
0.615450 + 0.788176i \(0.288974\pi\)
\(102\) 0 0
\(103\) 12.4045 7.16173i 1.22225 0.705666i 0.256853 0.966451i \(-0.417315\pi\)
0.965397 + 0.260784i \(0.0839812\pi\)
\(104\) −0.210276 0.364210i −0.0206193 0.0357137i
\(105\) 0 0
\(106\) 4.53602 7.85662i 0.440577 0.763102i
\(107\) 13.4866i 1.30380i 0.758305 + 0.651900i \(0.226028\pi\)
−0.758305 + 0.651900i \(0.773972\pi\)
\(108\) 0 0
\(109\) −0.918695 −0.0879950 −0.0439975 0.999032i \(-0.514009\pi\)
−0.0439975 + 0.999032i \(0.514009\pi\)
\(110\) 13.1350 22.7504i 1.25237 2.16917i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.10412 + 2.36952i −0.386083 + 0.222905i −0.680462 0.732784i \(-0.738221\pi\)
0.294378 + 0.955689i \(0.404887\pi\)
\(114\) 0 0
\(115\) −17.1261 9.88775i −1.59702 0.922037i
\(116\) 4.67242i 0.433823i
\(117\) 0 0
\(118\) 13.6618i 1.25767i
\(119\) 0 0
\(120\) 0 0
\(121\) 10.2337 + 17.7252i 0.930332 + 1.61138i
\(122\) 7.99508 + 13.8479i 0.723841 + 1.25373i
\(123\) 0 0
\(124\) 13.5327 + 7.81312i 1.21527 + 0.701639i
\(125\) 9.32458 0.834016
\(126\) 0 0
\(127\) 7.37245 0.654200 0.327100 0.944990i \(-0.393929\pi\)
0.327100 + 0.944990i \(0.393929\pi\)
\(128\) 6.35477 + 3.66893i 0.561688 + 0.324291i
\(129\) 0 0
\(130\) 1.03909 + 1.79976i 0.0911342 + 0.157849i
\(131\) 3.93150 + 6.80955i 0.343497 + 0.594953i 0.985079 0.172100i \(-0.0550553\pi\)
−0.641583 + 0.767054i \(0.721722\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.49283i 0.301734i
\(135\) 0 0
\(136\) 2.91671i 0.250106i
\(137\) 10.0198 + 5.78491i 0.856046 + 0.494238i 0.862686 0.505740i \(-0.168780\pi\)
−0.00664016 + 0.999978i \(0.502114\pi\)
\(138\) 0 0
\(139\) 16.9741 9.79999i 1.43972 0.831224i 0.441893 0.897068i \(-0.354307\pi\)
0.997830 + 0.0658437i \(0.0209739\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.75984 4.78018i 0.231600 0.401144i
\(143\) −2.48933 −0.208169
\(144\) 0 0
\(145\) 7.84221i 0.651260i
\(146\) 7.96114 13.7891i 0.658868 1.14119i
\(147\) 0 0
\(148\) −1.05724 1.83120i −0.0869047 0.150523i
\(149\) 13.6315 7.87012i 1.11673 0.644746i 0.176167 0.984360i \(-0.443630\pi\)
0.940565 + 0.339615i \(0.110297\pi\)
\(150\) 0 0
\(151\) 0.991353 1.71707i 0.0806752 0.139734i −0.822865 0.568237i \(-0.807626\pi\)
0.903540 + 0.428503i \(0.140959\pi\)
\(152\) −2.43954 −0.197873
\(153\) 0 0
\(154\) 0 0
\(155\) 22.7134 + 13.1136i 1.82438 + 1.05331i
\(156\) 0 0
\(157\) −7.26790 + 4.19612i −0.580041 + 0.334887i −0.761150 0.648576i \(-0.775365\pi\)
0.181108 + 0.983463i \(0.442031\pi\)
\(158\) −0.929468 + 0.536628i −0.0739445 + 0.0426919i
\(159\) 0 0
\(160\) −15.1798 8.76405i −1.20007 0.692859i
\(161\) 0 0
\(162\) 0 0
\(163\) −1.07411 −0.0841306 −0.0420653 0.999115i \(-0.513394\pi\)
−0.0420653 + 0.999115i \(0.513394\pi\)
\(164\) −2.45832 + 4.25794i −0.191963 + 0.332489i
\(165\) 0 0
\(166\) −13.7098 + 7.91534i −1.06408 + 0.614349i
\(167\) −3.99731 6.92354i −0.309321 0.535760i 0.668893 0.743359i \(-0.266768\pi\)
−0.978214 + 0.207599i \(0.933435\pi\)
\(168\) 0 0
\(169\) −6.40154 + 11.0878i −0.492426 + 0.852907i
\(170\) 14.4130i 1.10543i
\(171\) 0 0
\(172\) −14.2030 −1.08297
\(173\) −0.501744 + 0.869046i −0.0381469 + 0.0660723i −0.884468 0.466600i \(-0.845479\pi\)
0.846322 + 0.532672i \(0.178812\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 23.1098 13.3424i 1.74197 1.00572i
\(177\) 0 0
\(178\) 12.2663 + 7.08195i 0.919398 + 0.530814i
\(179\) 1.47539i 0.110276i −0.998479 0.0551379i \(-0.982440\pi\)
0.998479 0.0551379i \(-0.0175599\pi\)
\(180\) 0 0
\(181\) 15.0440i 1.11821i −0.829096 0.559106i \(-0.811145\pi\)
0.829096 0.559106i \(-0.188855\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.73964 6.47724i −0.275690 0.477509i
\(185\) −1.77448 3.07349i −0.130462 0.225967i
\(186\) 0 0
\(187\) 14.9516 + 8.63229i 1.09337 + 0.631255i
\(188\) −3.20054 −0.233423
\(189\) 0 0
\(190\) 12.0551 0.874568
\(191\) −11.4521 6.61187i −0.828644 0.478418i 0.0247439 0.999694i \(-0.492123\pi\)
−0.853388 + 0.521276i \(0.825456\pi\)
\(192\) 0 0
\(193\) 0.777855 + 1.34728i 0.0559912 + 0.0969796i 0.892662 0.450726i \(-0.148835\pi\)
−0.836671 + 0.547705i \(0.815501\pi\)
\(194\) −3.48163 6.03035i −0.249966 0.432954i
\(195\) 0 0
\(196\) 0 0
\(197\) 4.96185i 0.353517i 0.984254 + 0.176759i \(0.0565612\pi\)
−0.984254 + 0.176759i \(0.943439\pi\)
\(198\) 0 0
\(199\) 11.1922i 0.793394i 0.917950 + 0.396697i \(0.129844\pi\)
−0.917950 + 0.396697i \(0.870156\pi\)
\(200\) −1.04946 0.605908i −0.0742083 0.0428442i
\(201\) 0 0
\(202\) 12.1949 7.04074i 0.858032 0.495385i
\(203\) 0 0
\(204\) 0 0
\(205\) −4.12606 + 7.14655i −0.288177 + 0.499137i
\(206\) −26.7696 −1.86513
\(207\) 0 0
\(208\) 2.11100i 0.146372i
\(209\) −7.22006 + 12.5055i −0.499422 + 0.865024i
\(210\) 0 0
\(211\) 7.68026 + 13.3026i 0.528731 + 0.915789i 0.999439 + 0.0334999i \(0.0106654\pi\)
−0.470708 + 0.882289i \(0.656001\pi\)
\(212\) −6.27594 + 3.62342i −0.431033 + 0.248857i
\(213\) 0 0
\(214\) 12.6028 21.8287i 0.861511 1.49218i
\(215\) −23.8383 −1.62576
\(216\) 0 0
\(217\) 0 0
\(218\) 1.48695 + 0.858492i 0.100709 + 0.0581444i
\(219\) 0 0
\(220\) −18.1733 + 10.4923i −1.22524 + 0.707394i
\(221\) −1.18280 + 0.682888i −0.0795635 + 0.0459360i
\(222\) 0 0
\(223\) −2.76845 1.59837i −0.185389 0.107034i 0.404433 0.914568i \(-0.367469\pi\)
−0.589822 + 0.807533i \(0.700802\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 8.85695 0.589156
\(227\) 7.33494 12.7045i 0.486837 0.843227i −0.513048 0.858360i \(-0.671484\pi\)
0.999885 + 0.0151329i \(0.00481714\pi\)
\(228\) 0 0
\(229\) 2.92550 1.68904i 0.193322 0.111615i −0.400215 0.916421i \(-0.631064\pi\)
0.593537 + 0.804807i \(0.297731\pi\)
\(230\) 18.4796 + 32.0076i 1.21851 + 2.11052i
\(231\) 0 0
\(232\) 1.48300 2.56863i 0.0973637 0.168639i
\(233\) 4.88009i 0.319706i 0.987141 + 0.159853i \(0.0511020\pi\)
−0.987141 + 0.159853i \(0.948898\pi\)
\(234\) 0 0
\(235\) −5.37180 −0.350418
\(236\) 5.45657 9.45106i 0.355193 0.615212i
\(237\) 0 0
\(238\) 0 0
\(239\) −13.6253 + 7.86657i −0.881347 + 0.508846i −0.871102 0.491101i \(-0.836594\pi\)
−0.0102448 + 0.999948i \(0.503261\pi\)
\(240\) 0 0
\(241\) −0.666305 0.384691i −0.0429205 0.0247801i 0.478386 0.878150i \(-0.341222\pi\)
−0.521307 + 0.853369i \(0.674555\pi\)
\(242\) 38.2521i 2.45894i
\(243\) 0 0
\(244\) 12.7731i 0.817714i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.571169 0.989293i −0.0363426 0.0629472i
\(248\) 4.95968 + 8.59042i 0.314940 + 0.545492i
\(249\) 0 0
\(250\) −15.0923 8.71353i −0.954519 0.551092i
\(251\) −1.14544 −0.0722996 −0.0361498 0.999346i \(-0.511509\pi\)
−0.0361498 + 0.999346i \(0.511509\pi\)
\(252\) 0 0
\(253\) −44.2713 −2.78331
\(254\) −11.9327 6.88933i −0.748722 0.432275i
\(255\) 0 0
\(256\) −10.4165 18.0420i −0.651033 1.12762i
\(257\) 14.4917 + 25.1004i 0.903969 + 1.56572i 0.822295 + 0.569061i \(0.192693\pi\)
0.0816738 + 0.996659i \(0.473973\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.66007i 0.102953i
\(261\) 0 0
\(262\) 14.6954i 0.907887i
\(263\) −11.8643 6.84988i −0.731586 0.422381i 0.0874160 0.996172i \(-0.472139\pi\)
−0.819002 + 0.573790i \(0.805472\pi\)
\(264\) 0 0
\(265\) −10.5336 + 6.08156i −0.647072 + 0.373587i
\(266\) 0 0
\(267\) 0 0
\(268\) −1.39505 + 2.41630i −0.0852163 + 0.147599i
\(269\) −10.4795 −0.638944 −0.319472 0.947596i \(-0.603506\pi\)
−0.319472 + 0.947596i \(0.603506\pi\)
\(270\) 0 0
\(271\) 6.54607i 0.397646i 0.980035 + 0.198823i \(0.0637118\pi\)
−0.980035 + 0.198823i \(0.936288\pi\)
\(272\) 7.32034 12.6792i 0.443861 0.768790i
\(273\) 0 0
\(274\) −10.8116 18.7263i −0.653155 1.13130i
\(275\) −6.21198 + 3.58649i −0.374596 + 0.216273i
\(276\) 0 0
\(277\) −11.2156 + 19.4261i −0.673883 + 1.16720i 0.302911 + 0.953019i \(0.402041\pi\)
−0.976794 + 0.214181i \(0.931292\pi\)
\(278\) −36.6311 −2.19699
\(279\) 0 0
\(280\) 0 0
\(281\) −19.3552 11.1747i −1.15463 0.666627i −0.204621 0.978841i \(-0.565596\pi\)
−0.950012 + 0.312214i \(0.898929\pi\)
\(282\) 0 0
\(283\) 16.4296 9.48563i 0.976638 0.563862i 0.0753848 0.997155i \(-0.475981\pi\)
0.901254 + 0.433292i \(0.142648\pi\)
\(284\) −3.81845 + 2.20459i −0.226584 + 0.130818i
\(285\) 0 0
\(286\) 4.02910 + 2.32620i 0.238246 + 0.137551i
\(287\) 0 0
\(288\) 0 0
\(289\) −7.52777 −0.442810
\(290\) −7.32830 + 12.6930i −0.430333 + 0.745358i
\(291\) 0 0
\(292\) −11.0149 + 6.35943i −0.644596 + 0.372158i
\(293\) 4.41136 + 7.64069i 0.257714 + 0.446374i 0.965629 0.259924i \(-0.0836974\pi\)
−0.707915 + 0.706298i \(0.750364\pi\)
\(294\) 0 0
\(295\) 9.15835 15.8627i 0.533220 0.923563i
\(296\) 1.34225i 0.0780167i
\(297\) 0 0
\(298\) −29.4175 −1.70411
\(299\) 1.75112 3.03303i 0.101270 0.175405i
\(300\) 0 0
\(301\) 0 0
\(302\) −3.20910 + 1.85278i −0.184663 + 0.106615i
\(303\) 0 0
\(304\) 10.6049 + 6.12275i 0.608233 + 0.351164i
\(305\) 21.4385i 1.22756i
\(306\) 0 0
\(307\) 28.7533i 1.64104i −0.571620 0.820519i \(-0.693685\pi\)
0.571620 0.820519i \(-0.306315\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −24.5085 42.4499i −1.39199 2.41099i
\(311\) −6.64294 11.5059i −0.376687 0.652441i 0.613891 0.789391i \(-0.289603\pi\)
−0.990578 + 0.136950i \(0.956270\pi\)
\(312\) 0 0
\(313\) −27.3227 15.7748i −1.54437 0.891643i −0.998555 0.0537372i \(-0.982887\pi\)
−0.545815 0.837905i \(-0.683780\pi\)
\(314\) 15.6846 0.885132
\(315\) 0 0
\(316\) 0.857328 0.0482285
\(317\) −17.3819 10.0354i −0.976264 0.563646i −0.0751236 0.997174i \(-0.523935\pi\)
−0.901140 + 0.433528i \(0.857268\pi\)
\(318\) 0 0
\(319\) −8.77816 15.2042i −0.491483 0.851273i
\(320\) 4.45961 + 7.72428i 0.249300 + 0.431800i
\(321\) 0 0
\(322\) 0 0
\(323\) 7.92259i 0.440824i
\(324\) 0 0
\(325\) 0.567444i 0.0314761i
\(326\) 1.73849 + 1.00372i 0.0962862 + 0.0555909i
\(327\) 0 0
\(328\) −2.70289 + 1.56052i −0.149242 + 0.0861651i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.623957 + 1.08073i −0.0342958 + 0.0594020i −0.882664 0.470005i \(-0.844252\pi\)
0.848368 + 0.529407i \(0.177585\pi\)
\(332\) 12.6457 0.694023
\(333\) 0 0
\(334\) 14.9414i 0.817559i
\(335\) −2.34146 + 4.05553i −0.127928 + 0.221577i
\(336\) 0 0
\(337\) 6.58745 + 11.4098i 0.358842 + 0.621532i 0.987768 0.155933i \(-0.0498385\pi\)
−0.628926 + 0.777465i \(0.716505\pi\)
\(338\) 20.7224 11.9641i 1.12715 0.650759i
\(339\) 0 0
\(340\) −5.75664 + 9.97079i −0.312198 + 0.540742i
\(341\) 58.7146 3.17958
\(342\) 0 0
\(343\) 0 0
\(344\) −7.80798 4.50794i −0.420978 0.243052i
\(345\) 0 0
\(346\) 1.62419 0.937727i 0.0873171 0.0504125i
\(347\) 23.4411 13.5337i 1.25838 0.726529i 0.285624 0.958342i \(-0.407799\pi\)
0.972760 + 0.231813i \(0.0744658\pi\)
\(348\) 0 0
\(349\) 30.3413 + 17.5176i 1.62413 + 0.937694i 0.985798 + 0.167936i \(0.0537101\pi\)
0.638336 + 0.769758i \(0.279623\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −39.2401 −2.09150
\(353\) −1.26256 + 2.18682i −0.0671992 + 0.116392i −0.897667 0.440674i \(-0.854740\pi\)
0.830468 + 0.557066i \(0.188073\pi\)
\(354\) 0 0
\(355\) −6.40892 + 3.70019i −0.340150 + 0.196386i
\(356\) −5.65713 9.79843i −0.299827 0.519316i
\(357\) 0 0
\(358\) −1.37871 + 2.38799i −0.0728669 + 0.126209i
\(359\) 7.26762i 0.383570i 0.981437 + 0.191785i \(0.0614277\pi\)
−0.981437 + 0.191785i \(0.938572\pi\)
\(360\) 0 0
\(361\) 12.3735 0.651239
\(362\) −14.0581 + 24.3494i −0.738880 + 1.27978i
\(363\) 0 0
\(364\) 0 0
\(365\) −18.4874 + 10.6737i −0.967675 + 0.558688i
\(366\) 0 0
\(367\) −11.6714 6.73848i −0.609242 0.351746i 0.163427 0.986555i \(-0.447745\pi\)
−0.772669 + 0.634809i \(0.781079\pi\)
\(368\) 37.5429i 1.95706i
\(369\) 0 0
\(370\) 6.63278i 0.344822i
\(371\) 0 0
\(372\) 0 0
\(373\) −11.8820 20.5801i −0.615224 1.06560i −0.990345 0.138624i \(-0.955732\pi\)
0.375121 0.926976i \(-0.377601\pi\)
\(374\) −16.1332 27.9435i −0.834228 1.44492i
\(375\) 0 0
\(376\) −1.75947 1.01583i −0.0907379 0.0523875i
\(377\) 1.38886 0.0715297
\(378\) 0 0
\(379\) 21.2283 1.09042 0.545211 0.838299i \(-0.316449\pi\)
0.545211 + 0.838299i \(0.316449\pi\)
\(380\) −8.33958 4.81486i −0.427812 0.246997i
\(381\) 0 0
\(382\) 12.3572 + 21.4032i 0.632248 + 1.09509i
\(383\) −6.47930 11.2225i −0.331077 0.573442i 0.651646 0.758523i \(-0.274079\pi\)
−0.982723 + 0.185081i \(0.940745\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.90752i 0.147989i
\(387\) 0 0
\(388\) 5.56231i 0.282384i
\(389\) −9.48037 5.47350i −0.480674 0.277517i 0.240023 0.970767i \(-0.422845\pi\)
−0.720697 + 0.693250i \(0.756178\pi\)
\(390\) 0 0
\(391\) −21.0353 + 12.1447i −1.06380 + 0.614186i
\(392\) 0 0
\(393\) 0 0
\(394\) 4.63669 8.03098i 0.233593 0.404595i
\(395\) 1.43894 0.0724011
\(396\) 0 0
\(397\) 29.8901i 1.50014i 0.661358 + 0.750071i \(0.269981\pi\)
−0.661358 + 0.750071i \(0.730019\pi\)
\(398\) 10.4588 18.1151i 0.524250 0.908028i
\(399\) 0 0
\(400\) 3.04141 + 5.26788i 0.152071 + 0.263394i
\(401\) −16.6233 + 9.59744i −0.830126 + 0.479273i −0.853896 0.520444i \(-0.825766\pi\)
0.0237698 + 0.999717i \(0.492433\pi\)
\(402\) 0 0
\(403\) −2.32242 + 4.02254i −0.115688 + 0.200377i
\(404\) −11.2484 −0.559630
\(405\) 0 0
\(406\) 0 0
\(407\) −6.88060 3.97252i −0.341059 0.196910i
\(408\) 0 0
\(409\) −24.9737 + 14.4186i −1.23487 + 0.712953i −0.968041 0.250790i \(-0.919309\pi\)
−0.266830 + 0.963744i \(0.585976\pi\)
\(410\) 13.3565 7.71135i 0.659628 0.380837i
\(411\) 0 0
\(412\) 18.5190 + 10.6919i 0.912363 + 0.526753i
\(413\) 0 0
\(414\) 0 0
\(415\) 21.2246 1.04188
\(416\) 1.55211 2.68834i 0.0760986 0.131807i
\(417\) 0 0
\(418\) 23.3720 13.4938i 1.14316 0.660005i
\(419\) −5.06390 8.77094i −0.247388 0.428488i 0.715412 0.698702i \(-0.246239\pi\)
−0.962800 + 0.270214i \(0.912906\pi\)
\(420\) 0 0
\(421\) 12.7094 22.0134i 0.619419 1.07287i −0.370173 0.928963i \(-0.620702\pi\)
0.989592 0.143902i \(-0.0459651\pi\)
\(422\) 28.7079i 1.39748i
\(423\) 0 0
\(424\) −4.60021 −0.223406
\(425\) −1.96773 + 3.40821i −0.0954490 + 0.165322i
\(426\) 0 0
\(427\) 0 0
\(428\) −17.4370 + 10.0673i −0.842849 + 0.486619i
\(429\) 0 0
\(430\) 38.5834 + 22.2762i 1.86066 + 1.07425i
\(431\) 10.8434i 0.522308i −0.965297 0.261154i \(-0.915897\pi\)
0.965297 0.261154i \(-0.0841031\pi\)
\(432\) 0 0
\(433\) 13.0519i 0.627233i 0.949550 + 0.313616i \(0.101541\pi\)
−0.949550 + 0.313616i \(0.898459\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.685771 1.18779i −0.0328425 0.0568849i
\(437\) −10.1579 17.5940i −0.485918 0.841634i
\(438\) 0 0
\(439\) 27.6736 + 15.9773i 1.32079 + 0.762557i 0.983854 0.178972i \(-0.0572772\pi\)
0.336933 + 0.941529i \(0.390611\pi\)
\(440\) −13.3208 −0.635046
\(441\) 0 0
\(442\) 2.55255 0.121412
\(443\) −21.4748 12.3985i −1.02030 0.589068i −0.106107 0.994355i \(-0.533838\pi\)
−0.914190 + 0.405286i \(0.867172\pi\)
\(444\) 0 0
\(445\) −9.49496 16.4458i −0.450104 0.779603i
\(446\) 2.98724 + 5.17406i 0.141450 + 0.244999i
\(447\) 0 0
\(448\) 0 0
\(449\) 13.7710i 0.649892i −0.945733 0.324946i \(-0.894654\pi\)
0.945733 0.324946i \(-0.105346\pi\)
\(450\) 0 0
\(451\) 18.4740i 0.869906i
\(452\) −6.12715 3.53751i −0.288197 0.166390i
\(453\) 0 0
\(454\) −23.7439 + 13.7085i −1.11436 + 0.643374i
\(455\) 0 0
\(456\) 0 0
\(457\) −13.6554 + 23.6518i −0.638771 + 1.10638i 0.346931 + 0.937890i \(0.387224\pi\)
−0.985703 + 0.168494i \(0.946110\pi\)
\(458\) −6.31340 −0.295006
\(459\) 0 0
\(460\) 29.5233i 1.37653i
\(461\) 5.51822 9.55784i 0.257009 0.445153i −0.708430 0.705781i \(-0.750596\pi\)
0.965439 + 0.260628i \(0.0839296\pi\)
\(462\) 0 0
\(463\) −12.2346 21.1910i −0.568591 0.984829i −0.996706 0.0811042i \(-0.974155\pi\)
0.428115 0.903724i \(-0.359178\pi\)
\(464\) −12.8935 + 7.44405i −0.598564 + 0.345581i
\(465\) 0 0
\(466\) 4.56029 7.89866i 0.211251 0.365898i
\(467\) −15.9048 −0.735988 −0.367994 0.929828i \(-0.619955\pi\)
−0.367994 + 0.929828i \(0.619955\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8.69451 + 5.01978i 0.401048 + 0.231545i
\(471\) 0 0
\(472\) 5.99943 3.46377i 0.276146 0.159433i
\(473\) −46.2169 + 26.6834i −2.12506 + 1.22690i
\(474\) 0 0
\(475\) −2.85063 1.64581i −0.130796 0.0755151i
\(476\) 0 0
\(477\) 0 0
\(478\) 29.4042 1.34492
\(479\) 6.92685 11.9976i 0.316496 0.548187i −0.663259 0.748390i \(-0.730827\pi\)
0.979754 + 0.200204i \(0.0641604\pi\)
\(480\) 0 0
\(481\) 0.544315 0.314261i 0.0248186 0.0143290i
\(482\) 0.718964 + 1.24528i 0.0327479 + 0.0567210i
\(483\) 0 0
\(484\) −15.2781 + 26.4624i −0.694458 + 1.20284i
\(485\) 9.33582i 0.423918i
\(486\) 0 0
\(487\) 28.7987 1.30499 0.652496 0.757792i \(-0.273722\pi\)
0.652496 + 0.757792i \(0.273722\pi\)
\(488\) 4.05411 7.02193i 0.183521 0.317868i
\(489\) 0 0
\(490\) 0 0
\(491\) 33.5627 19.3774i 1.51466 0.874492i 0.514812 0.857303i \(-0.327862\pi\)
0.999852 0.0171884i \(-0.00547151\pi\)
\(492\) 0 0
\(493\) −8.34181 4.81615i −0.375696 0.216908i
\(494\) 2.13496i 0.0960562i
\(495\) 0 0
\(496\) 49.7911i 2.23569i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.73333 + 3.00222i 0.0775946 + 0.134398i 0.902212 0.431294i \(-0.141943\pi\)
−0.824617 + 0.565691i \(0.808609\pi\)
\(500\) 6.96045 + 12.0558i 0.311281 + 0.539154i
\(501\) 0 0
\(502\) 1.85395 + 1.07038i 0.0827458 + 0.0477733i
\(503\) 28.2202 1.25828 0.629138 0.777293i \(-0.283408\pi\)
0.629138 + 0.777293i \(0.283408\pi\)
\(504\) 0 0
\(505\) −18.8794 −0.840124
\(506\) 71.6552 + 41.3701i 3.18546 + 1.83913i
\(507\) 0 0
\(508\) 5.50326 + 9.53193i 0.244168 + 0.422911i
\(509\) −17.9062 31.0144i −0.793678 1.37469i −0.923675 0.383176i \(-0.874830\pi\)
0.129997 0.991514i \(-0.458503\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 24.2599i 1.07215i
\(513\) 0 0
\(514\) 54.1682i 2.38926i
\(515\) 31.0823 + 17.9454i 1.36965 + 0.790768i
\(516\) 0 0
\(517\) −10.4147 + 6.01291i −0.458036 + 0.264447i
\(518\) 0 0
\(519\) 0 0
\(520\) 0.526897 0.912612i 0.0231060 0.0400207i
\(521\) 26.9216 1.17946 0.589729 0.807601i \(-0.299234\pi\)
0.589729 + 0.807601i \(0.299234\pi\)
\(522\) 0 0
\(523\) 9.03185i 0.394935i 0.980309 + 0.197468i \(0.0632717\pi\)
−0.980309 + 0.197468i \(0.936728\pi\)
\(524\) −5.86943 + 10.1662i −0.256407 + 0.444110i
\(525\) 0 0
\(526\) 12.8020 + 22.1737i 0.558193 + 0.966819i
\(527\) 27.8980 16.1069i 1.21526 0.701629i
\(528\) 0 0
\(529\) 19.6426 34.0220i 0.854026 1.47922i
\(530\) 22.7321 0.987420
\(531\) 0 0
\(532\) 0 0
\(533\) −1.26565 0.730726i −0.0548216 0.0316513i
\(534\) 0 0
\(535\) −29.2664 + 16.8969i −1.26530 + 0.730518i
\(536\) −1.53384 + 0.885563i −0.0662518 + 0.0382505i
\(537\) 0 0
\(538\) 16.9615 + 9.79273i 0.731262 + 0.422195i
\(539\) 0 0
\(540\) 0 0
\(541\) 11.3358 0.487366 0.243683 0.969855i \(-0.421644\pi\)
0.243683 + 0.969855i \(0.421644\pi\)
\(542\) 6.11710 10.5951i 0.262752 0.455100i
\(543\) 0 0
\(544\) −18.6447 + 10.7646i −0.799387 + 0.461526i
\(545\) −1.15100 1.99360i −0.0493035 0.0853962i
\(546\) 0 0
\(547\) 19.4246 33.6444i 0.830537 1.43853i −0.0670762 0.997748i \(-0.521367\pi\)
0.897613 0.440784i \(-0.145300\pi\)
\(548\) 17.2729i 0.737861i
\(549\) 0 0
\(550\) 13.4058 0.571627
\(551\) 4.02823 6.97711i 0.171609 0.297235i
\(552\) 0 0
\(553\) 0 0
\(554\) 36.3061 20.9613i 1.54250 0.890562i
\(555\) 0 0
\(556\) 25.3410 + 14.6306i 1.07470 + 0.620478i
\(557\) 7.26499i 0.307827i −0.988084 0.153914i \(-0.950812\pi\)
0.988084 0.153914i \(-0.0491878\pi\)
\(558\) 0 0
\(559\) 4.22177i 0.178562i
\(560\) 0 0
\(561\) 0 0
\(562\) 20.8848 + 36.1736i 0.880973 + 1.52589i
\(563\) 11.5409 + 19.9894i 0.486390 + 0.842453i 0.999878 0.0156446i \(-0.00498004\pi\)
−0.513487 + 0.858097i \(0.671647\pi\)
\(564\) 0 0
\(565\) −10.2838 5.93738i −0.432644 0.249787i
\(566\) −35.4561 −1.49033
\(567\) 0 0
\(568\) −2.79889 −0.117439
\(569\) 15.5482 + 8.97677i 0.651815 + 0.376326i 0.789151 0.614199i \(-0.210521\pi\)
−0.137336 + 0.990525i \(0.543854\pi\)
\(570\) 0 0
\(571\) 7.04234 + 12.1977i 0.294713 + 0.510457i 0.974918 0.222564i \(-0.0714427\pi\)
−0.680205 + 0.733022i \(0.738109\pi\)
\(572\) −1.85819 3.21849i −0.0776950 0.134572i
\(573\) 0 0
\(574\) 0 0
\(575\) 10.0916i 0.420851i
\(576\) 0 0
\(577\) 30.0675i 1.25172i −0.779934 0.625862i \(-0.784747\pi\)
0.779934 0.625862i \(-0.215253\pi\)
\(578\) 12.1841 + 7.03447i 0.506790 + 0.292595i
\(579\) 0 0
\(580\) 10.1393 5.85392i 0.421011 0.243071i
\(581\) 0 0
\(582\) 0 0
\(583\) −13.6148 + 23.5815i −0.563866 + 0.976644i
\(584\) −8.07379 −0.334096
\(585\) 0 0
\(586\) 16.4891i 0.681158i
\(587\) −18.0979 + 31.3465i −0.746981 + 1.29381i 0.202283 + 0.979327i \(0.435164\pi\)
−0.949264 + 0.314481i \(0.898169\pi\)
\(588\) 0 0
\(589\) 13.4719 + 23.3339i 0.555098 + 0.961459i
\(590\) −29.6464 + 17.1164i −1.22052 + 0.704670i
\(591\) 0 0
\(592\) −3.36877 + 5.83489i −0.138456 + 0.239812i
\(593\) 2.04317 0.0839028 0.0419514 0.999120i \(-0.486643\pi\)
0.0419514 + 0.999120i \(0.486643\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 20.3507 + 11.7495i 0.833598 + 0.481278i
\(597\) 0 0
\(598\) −5.66854 + 3.27273i −0.231804 + 0.133832i
\(599\) 15.7873 9.11478i 0.645050 0.372420i −0.141507 0.989937i \(-0.545195\pi\)
0.786557 + 0.617517i \(0.211861\pi\)
\(600\) 0 0
\(601\) −32.1713 18.5741i −1.31230 0.757654i −0.329820 0.944044i \(-0.606988\pi\)
−0.982476 + 0.186390i \(0.940321\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2.96003 0.120442
\(605\) −25.6428 + 44.4146i −1.04253 + 1.80571i
\(606\) 0 0
\(607\) 17.1730 9.91482i 0.697030 0.402430i −0.109211 0.994019i \(-0.534832\pi\)
0.806240 + 0.591588i \(0.201499\pi\)
\(608\) −9.00349 15.5945i −0.365140 0.632440i
\(609\) 0 0
\(610\) −20.0336 + 34.6991i −0.811135 + 1.40493i
\(611\) 0.951346i 0.0384873i
\(612\) 0 0
\(613\) −12.6882 −0.512473 −0.256237 0.966614i \(-0.582483\pi\)
−0.256237 + 0.966614i \(0.582483\pi\)
\(614\) −26.8690 + 46.5385i −1.08435 + 1.87814i
\(615\) 0 0
\(616\) 0 0
\(617\) −4.37247 + 2.52445i −0.176029 + 0.101630i −0.585426 0.810726i \(-0.699073\pi\)
0.409397 + 0.912357i \(0.365739\pi\)
\(618\) 0 0
\(619\) 0.231999 + 0.133945i 0.00932485 + 0.00538370i 0.504655 0.863321i \(-0.331620\pi\)
−0.495330 + 0.868705i \(0.664953\pi\)
\(620\) 39.1552i 1.57251i
\(621\) 0 0
\(622\) 24.8305i 0.995611i
\(623\) 0 0
\(624\) 0 0
\(625\) 14.8792 + 25.7716i 0.595169 + 1.03086i
\(626\) 29.4820 + 51.0644i 1.17834 + 2.04094i
\(627\) 0 0
\(628\) −10.8504 6.26449i −0.432979 0.249981i
\(629\) −4.35905 −0.173807
\(630\) 0 0
\(631\) 37.7899 1.50439 0.752197 0.658938i \(-0.228994\pi\)
0.752197 + 0.658938i \(0.228994\pi\)
\(632\) 0.471310 + 0.272111i 0.0187477 + 0.0108240i
\(633\) 0 0
\(634\) 18.7556 + 32.4856i 0.744880 + 1.29017i
\(635\) 9.23671 + 15.9984i 0.366547 + 0.634879i
\(636\) 0 0
\(637\) 0 0
\(638\) 32.8117i 1.29903i
\(639\) 0 0
\(640\) 18.3867i 0.726799i
\(641\) −29.7991 17.2045i −1.17699 0.679537i −0.221676 0.975120i \(-0.571153\pi\)
−0.955317 + 0.295583i \(0.904486\pi\)
\(642\) 0 0
\(643\) 0.676278 0.390449i 0.0266698 0.0153978i −0.486606 0.873622i \(-0.661765\pi\)
0.513276 + 0.858224i \(0.328432\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 7.40341 12.8231i 0.291283 0.504517i
\(647\) 19.6436 0.772271 0.386136 0.922442i \(-0.373810\pi\)
0.386136 + 0.922442i \(0.373810\pi\)
\(648\) 0 0
\(649\) 41.0055i 1.60961i
\(650\) −0.530259 + 0.918435i −0.0207985 + 0.0360240i
\(651\) 0 0
\(652\) −0.801781 1.38872i −0.0314001 0.0543867i
\(653\) −2.77600 + 1.60272i −0.108633 + 0.0627194i −0.553332 0.832961i \(-0.686644\pi\)
0.444699 + 0.895680i \(0.353311\pi\)
\(654\) 0 0
\(655\) −9.85129 + 17.0629i −0.384922 + 0.666704i
\(656\) 15.6663 0.611666
\(657\) 0 0
\(658\) 0 0
\(659\) 24.2959 + 14.0273i 0.946435 + 0.546425i 0.891972 0.452091i \(-0.149322\pi\)
0.0544636 + 0.998516i \(0.482655\pi\)
\(660\) 0 0
\(661\) 28.0490 16.1941i 1.09098 0.629878i 0.157143 0.987576i \(-0.449772\pi\)
0.933837 + 0.357698i \(0.116438\pi\)
\(662\) 2.01981 1.16614i 0.0785020 0.0453232i
\(663\) 0 0
\(664\) 6.95189 + 4.01367i 0.269785 + 0.155761i
\(665\) 0 0
\(666\) 0 0
\(667\) 24.7000 0.956386
\(668\) 5.96768 10.3363i 0.230897 0.399925i
\(669\) 0 0
\(670\) 7.57953 4.37605i 0.292823 0.169061i
\(671\) −23.9971 41.5641i −0.926397 1.60457i
\(672\) 0 0
\(673\) −10.3088 + 17.8554i −0.397375 + 0.688273i −0.993401 0.114692i \(-0.963412\pi\)
0.596026 + 0.802965i \(0.296745\pi\)
\(674\) 24.6231i 0.948445i
\(675\) 0 0
\(676\) −19.1140 −0.735155
\(677\) 25.1655 43.5880i 0.967190 1.67522i 0.263578 0.964638i \(-0.415097\pi\)
0.703612 0.710585i \(-0.251569\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −6.32935 + 3.65425i −0.242719 + 0.140134i
\(681\) 0 0
\(682\) −95.0324 54.8670i −3.63898 2.10097i
\(683\) 13.7445i 0.525920i 0.964807 + 0.262960i \(0.0846987\pi\)
−0.964807 + 0.262960i \(0.915301\pi\)
\(684\) 0 0
\(685\) 28.9909i 1.10769i
\(686\) 0 0
\(687\) 0 0
\(688\) 22.6280 + 39.1929i 0.862685 + 1.49421i
\(689\) −1.07705 1.86550i −0.0410321 0.0710698i
\(690\) 0 0
\(691\) 25.4328 + 14.6837i 0.967511 + 0.558593i 0.898476 0.439022i \(-0.144675\pi\)
0.0690343 + 0.997614i \(0.478008\pi\)
\(692\) −1.49813 −0.0569504
\(693\) 0 0
\(694\) −50.5874 −1.92027
\(695\) 42.5325 + 24.5562i 1.61335 + 0.931468i
\(696\) 0 0
\(697\) 5.06789 + 8.77784i 0.191960 + 0.332484i
\(698\) −32.7392 56.7060i −1.23920 2.14635i
\(699\) 0 0
\(700\) 0 0
\(701\) 44.2011i 1.66945i −0.550666 0.834726i \(-0.685626\pi\)
0.550666 0.834726i \(-0.314374\pi\)
\(702\) 0 0
\(703\) 3.64592i 0.137508i
\(704\) 17.2923 + 9.98371i 0.651728 + 0.376275i
\(705\) 0 0
\(706\) 4.08702 2.35964i 0.153817 0.0888063i
\(707\) 0 0
\(708\) 0 0
\(709\) 5.66629 9.81430i 0.212802 0.368584i −0.739788 0.672840i \(-0.765074\pi\)
0.952590 + 0.304256i \(0.0984077\pi\)
\(710\) 13.8308 0.519062
\(711\) 0 0
\(712\) 7.18216i 0.269163i
\(713\) −41.3028 + 71.5385i −1.54680 + 2.67914i
\(714\) 0 0
\(715\) −3.11881 5.40193i −0.116637 0.202021i
\(716\) 1.90755 1.10132i 0.0712884 0.0411584i
\(717\) 0 0
\(718\) 6.79136 11.7630i 0.253451 0.438991i
\(719\) 36.1294 1.34740 0.673700 0.739005i \(-0.264704\pi\)
0.673700 + 0.739005i \(0.264704\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −20.0271 11.5627i −0.745333 0.430318i
\(723\) 0 0
\(724\) 19.4505 11.2298i 0.722874 0.417351i
\(725\) 3.46580 2.00098i 0.128717 0.0743146i
\(726\) 0 0
\(727\) −6.20547 3.58273i −0.230148 0.132876i 0.380492 0.924784i \(-0.375755\pi\)
−0.610640 + 0.791908i \(0.709088\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 39.8970 1.47665
\(731\) −14.6399 + 25.3570i −0.541475 + 0.937862i
\(732\) 0 0
\(733\) 41.4391 23.9249i 1.53059 0.883685i 0.531253 0.847213i \(-0.321721\pi\)
0.999335 0.0364726i \(-0.0116122\pi\)
\(734\) 12.5938 + 21.8131i 0.464846 + 0.805136i
\(735\) 0 0
\(736\) 27.6034 47.8105i 1.01747 1.76232i
\(737\) 10.4836i 0.386170i
\(738\) 0 0
\(739\) 15.3483 0.564597 0.282299 0.959327i \(-0.408903\pi\)
0.282299 + 0.959327i \(0.408903\pi\)
\(740\) 2.64917 4.58849i 0.0973853 0.168676i
\(741\) 0 0
\(742\) 0 0
\(743\) −34.9422 + 20.1739i −1.28191 + 0.740109i −0.977197 0.212337i \(-0.931893\pi\)
−0.304709 + 0.952445i \(0.598559\pi\)
\(744\) 0 0
\(745\) 34.1568 + 19.7204i 1.25141 + 0.722501i
\(746\) 44.4132i 1.62608i
\(747\) 0 0
\(748\) 25.7747i 0.942417i
\(749\) 0 0
\(750\) 0 0
\(751\) −16.9449 29.3494i −0.618327 1.07097i −0.989791 0.142527i \(-0.954477\pi\)
0.371463 0.928448i \(-0.378856\pi\)
\(752\) 5.09906 + 8.83183i 0.185944 + 0.322064i
\(753\) 0 0
\(754\) −2.24793 1.29784i −0.0818647 0.0472646i
\(755\) 4.96814 0.180809
\(756\) 0 0
\(757\) −5.73237 −0.208346 −0.104173 0.994559i \(-0.533220\pi\)
−0.104173 + 0.994559i \(0.533220\pi\)
\(758\) −34.3589 19.8371i −1.24797 0.720517i
\(759\) 0 0
\(760\) −3.05642 5.29387i −0.110868 0.192029i
\(761\) −13.2666 22.9784i −0.480914 0.832968i 0.518846 0.854868i \(-0.326362\pi\)
−0.999760 + 0.0218999i \(0.993028\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 19.7420i 0.714242i
\(765\) 0 0
\(766\) 24.2188i 0.875061i
\(767\) 2.80929 + 1.62194i 0.101438 + 0.0585650i
\(768\) 0 0
\(769\) 23.3944 13.5068i 0.843623 0.487066i −0.0148711 0.999889i \(-0.504734\pi\)
0.858494 + 0.512823i \(0.171400\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.16128 + 2.01139i −0.0417953 + 0.0723916i
\(773\) 22.6017 0.812927 0.406464 0.913667i \(-0.366762\pi\)
0.406464 + 0.913667i \(0.366762\pi\)
\(774\) 0 0
\(775\) 13.3840i 0.480768i
\(776\) −1.76545 + 3.05784i −0.0633758 + 0.109770i
\(777\) 0 0
\(778\) 10.2296 + 17.7182i 0.366750 + 0.635229i
\(779\) −7.34180 + 4.23879i −0.263047 + 0.151870i
\(780\) 0 0
\(781\) −8.28359 + 14.3476i −0.296410 + 0.513398i
\(782\) 45.3955 1.62334
\(783\) 0 0
\(784\) 0 0
\(785\) −18.2114 10.5144i −0.649993 0.375274i
\(786\) 0 0
\(787\) 22.6864 13.0980i 0.808683 0.466893i −0.0378153 0.999285i \(-0.512040\pi\)
0.846498 + 0.532391i \(0.178707\pi\)
\(788\) −6.41523 + 3.70383i −0.228533 + 0.131944i
\(789\) 0 0
\(790\) −2.32900 1.34465i −0.0828620 0.0478404i
\(791\) 0 0
\(792\) 0 0
\(793\) 3.79675 0.134827
\(794\) 27.9314 48.3785i 0.991247 1.71689i
\(795\) 0 0
\(796\) −14.4705 + 8.35456i −0.512894 + 0.296120i