Properties

Label 288.2.w.a.35.3
Level $288$
Weight $2$
Character 288.35
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 35.3
Character \(\chi\) \(=\) 288.35
Dual form 288.2.w.a.107.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19734 + 0.752583i) q^{2} +(0.867238 - 1.80219i) q^{4} +(-0.0913223 + 0.0378270i) q^{5} +(-3.05457 - 3.05457i) q^{7} +(0.317923 + 2.81050i) q^{8} +O(q^{10})\) \(q+(-1.19734 + 0.752583i) q^{2} +(0.867238 - 1.80219i) q^{4} +(-0.0913223 + 0.0378270i) q^{5} +(-3.05457 - 3.05457i) q^{7} +(0.317923 + 2.81050i) q^{8} +(0.0808758 - 0.114019i) q^{10} +(-5.25649 + 2.17731i) q^{11} +(-1.57202 + 3.79519i) q^{13} +(5.95618 + 1.35854i) q^{14} +(-2.49580 - 3.12586i) q^{16} -2.56471 q^{17} +(2.64058 + 1.09376i) q^{19} +(-0.0110267 + 0.197385i) q^{20} +(4.65519 - 6.56292i) q^{22} +(-4.03079 - 4.03079i) q^{23} +(-3.52863 + 3.52863i) q^{25} +(-0.973958 - 5.72721i) q^{26} +(-8.15397 + 2.85589i) q^{28} +(2.06984 - 4.99704i) q^{29} +1.44203i q^{31} +(5.34078 + 1.86442i) q^{32} +(3.07083 - 1.93016i) q^{34} +(0.394496 + 0.163406i) q^{35} +(-2.07758 - 5.01573i) q^{37} +(-3.98482 + 0.677651i) q^{38} +(-0.135346 - 0.244636i) q^{40} +(0.296726 - 0.296726i) q^{41} +(-2.72382 - 6.57588i) q^{43} +(-0.634695 + 11.3615i) q^{44} +(7.85972 + 1.79271i) q^{46} -7.42367i q^{47} +11.6608i q^{49} +(1.56937 - 6.88054i) q^{50} +(5.47636 + 6.12442i) q^{52} +(1.53235 + 3.69941i) q^{53} +(0.397674 - 0.397674i) q^{55} +(7.61376 - 9.55600i) q^{56} +(1.28239 + 7.54087i) q^{58} +(0.988255 + 2.38586i) q^{59} +(10.4346 + 4.32215i) q^{61} +(-1.08525 - 1.72660i) q^{62} +(-7.79785 + 1.78705i) q^{64} -0.406051i q^{65} +(-0.690522 + 1.66707i) q^{67} +(-2.22421 + 4.62211i) q^{68} +(-0.595321 + 0.101239i) q^{70} +(-2.97957 + 2.97957i) q^{71} +(9.22401 + 9.22401i) q^{73} +(6.26232 + 4.44197i) q^{74} +(4.26119 - 3.81028i) q^{76} +(22.7071 + 9.40558i) q^{77} -1.12181 q^{79} +(0.346164 + 0.191052i) q^{80} +(-0.131971 + 0.578593i) q^{82} +(-4.13529 + 9.98348i) q^{83} +(0.234216 - 0.0970152i) q^{85} +(8.21022 + 5.82365i) q^{86} +(-7.79049 - 14.0812i) q^{88} +(-12.0590 - 12.0590i) q^{89} +(16.3945 - 6.79084i) q^{91} +(-10.7599 + 3.76861i) q^{92} +(5.58693 + 8.88865i) q^{94} -0.282518 q^{95} -18.5545 q^{97} +(-8.77574 - 13.9619i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19734 + 0.752583i −0.846646 + 0.532157i
\(3\) 0 0
\(4\) 0.867238 1.80219i 0.433619 0.901096i
\(5\) −0.0913223 + 0.0378270i −0.0408406 + 0.0169167i −0.403010 0.915195i \(-0.632036\pi\)
0.362170 + 0.932112i \(0.382036\pi\)
\(6\) 0 0
\(7\) −3.05457 3.05457i −1.15452 1.15452i −0.985636 0.168884i \(-0.945984\pi\)
−0.168884 0.985636i \(-0.554016\pi\)
\(8\) 0.317923 + 2.81050i 0.112403 + 0.993663i
\(9\) 0 0
\(10\) 0.0808758 0.114019i 0.0255752 0.0360561i
\(11\) −5.25649 + 2.17731i −1.58489 + 0.656483i −0.989179 0.146715i \(-0.953130\pi\)
−0.595712 + 0.803198i \(0.703130\pi\)
\(12\) 0 0
\(13\) −1.57202 + 3.79519i −0.436000 + 1.05260i 0.541317 + 0.840818i \(0.317926\pi\)
−0.977318 + 0.211779i \(0.932074\pi\)
\(14\) 5.95618 + 1.35854i 1.59185 + 0.363084i
\(15\) 0 0
\(16\) −2.49580 3.12586i −0.623949 0.781465i
\(17\) −2.56471 −0.622034 −0.311017 0.950404i \(-0.600670\pi\)
−0.311017 + 0.950404i \(0.600670\pi\)
\(18\) 0 0
\(19\) 2.64058 + 1.09376i 0.605791 + 0.250927i 0.664428 0.747353i \(-0.268675\pi\)
−0.0586367 + 0.998279i \(0.518675\pi\)
\(20\) −0.0110267 + 0.197385i −0.00246565 + 0.0441367i
\(21\) 0 0
\(22\) 4.65519 6.56292i 0.992490 1.39922i
\(23\) −4.03079 4.03079i −0.840477 0.840477i 0.148443 0.988921i \(-0.452574\pi\)
−0.988921 + 0.148443i \(0.952574\pi\)
\(24\) 0 0
\(25\) −3.52863 + 3.52863i −0.705725 + 0.705725i
\(26\) −0.973958 5.72721i −0.191009 1.12320i
\(27\) 0 0
\(28\) −8.15397 + 2.85589i −1.54096 + 0.539712i
\(29\) 2.06984 4.99704i 0.384360 0.927927i −0.606752 0.794892i \(-0.707528\pi\)
0.991111 0.133035i \(-0.0424723\pi\)
\(30\) 0 0
\(31\) 1.44203i 0.258996i 0.991580 + 0.129498i \(0.0413366\pi\)
−0.991580 + 0.129498i \(0.958663\pi\)
\(32\) 5.34078 + 1.86442i 0.944126 + 0.329585i
\(33\) 0 0
\(34\) 3.07083 1.93016i 0.526643 0.331019i
\(35\) 0.394496 + 0.163406i 0.0666820 + 0.0276206i
\(36\) 0 0
\(37\) −2.07758 5.01573i −0.341552 0.824581i −0.997559 0.0698256i \(-0.977756\pi\)
0.656007 0.754755i \(-0.272244\pi\)
\(38\) −3.98482 + 0.677651i −0.646423 + 0.109929i
\(39\) 0 0
\(40\) −0.135346 0.244636i −0.0214001 0.0386803i
\(41\) 0.296726 0.296726i 0.0463409 0.0463409i −0.683557 0.729897i \(-0.739568\pi\)
0.729897 + 0.683557i \(0.239568\pi\)
\(42\) 0 0
\(43\) −2.72382 6.57588i −0.415378 1.00281i −0.983669 0.179984i \(-0.942395\pi\)
0.568291 0.822828i \(-0.307605\pi\)
\(44\) −0.634695 + 11.3615i −0.0956838 + 1.71280i
\(45\) 0 0
\(46\) 7.85972 + 1.79271i 1.15885 + 0.264321i
\(47\) 7.42367i 1.08285i −0.840748 0.541427i \(-0.817884\pi\)
0.840748 0.541427i \(-0.182116\pi\)
\(48\) 0 0
\(49\) 11.6608i 1.66583i
\(50\) 1.56937 6.88054i 0.221943 0.973055i
\(51\) 0 0
\(52\) 5.47636 + 6.12442i 0.759434 + 0.849304i
\(53\) 1.53235 + 3.69941i 0.210484 + 0.508153i 0.993498 0.113851i \(-0.0363187\pi\)
−0.783014 + 0.622004i \(0.786319\pi\)
\(54\) 0 0
\(55\) 0.397674 0.397674i 0.0536223 0.0536223i
\(56\) 7.61376 9.55600i 1.01743 1.27697i
\(57\) 0 0
\(58\) 1.28239 + 7.54087i 0.168386 + 0.990165i
\(59\) 0.988255 + 2.38586i 0.128660 + 0.310612i 0.975062 0.221931i \(-0.0712361\pi\)
−0.846402 + 0.532544i \(0.821236\pi\)
\(60\) 0 0
\(61\) 10.4346 + 4.32215i 1.33601 + 0.553395i 0.932365 0.361519i \(-0.117742\pi\)
0.403649 + 0.914914i \(0.367742\pi\)
\(62\) −1.08525 1.72660i −0.137827 0.219278i
\(63\) 0 0
\(64\) −7.79785 + 1.78705i −0.974731 + 0.223381i
\(65\) 0.406051i 0.0503644i
\(66\) 0 0
\(67\) −0.690522 + 1.66707i −0.0843606 + 0.203665i −0.960431 0.278519i \(-0.910156\pi\)
0.876070 + 0.482184i \(0.160156\pi\)
\(68\) −2.22421 + 4.62211i −0.269726 + 0.560513i
\(69\) 0 0
\(70\) −0.595321 + 0.101239i −0.0711545 + 0.0121004i
\(71\) −2.97957 + 2.97957i −0.353610 + 0.353610i −0.861451 0.507841i \(-0.830444\pi\)
0.507841 + 0.861451i \(0.330444\pi\)
\(72\) 0 0
\(73\) 9.22401 + 9.22401i 1.07959 + 1.07959i 0.996546 + 0.0830429i \(0.0264638\pi\)
0.0830429 + 0.996546i \(0.473536\pi\)
\(74\) 6.26232 + 4.44197i 0.727980 + 0.516368i
\(75\) 0 0
\(76\) 4.26119 3.81028i 0.488792 0.437070i
\(77\) 22.7071 + 9.40558i 2.58771 + 1.07187i
\(78\) 0 0
\(79\) −1.12181 −0.126213 −0.0631065 0.998007i \(-0.520101\pi\)
−0.0631065 + 0.998007i \(0.520101\pi\)
\(80\) 0.346164 + 0.191052i 0.0387023 + 0.0213603i
\(81\) 0 0
\(82\) −0.131971 + 0.578593i −0.0145737 + 0.0638949i
\(83\) −4.13529 + 9.98348i −0.453907 + 1.09583i 0.516916 + 0.856036i \(0.327080\pi\)
−0.970824 + 0.239794i \(0.922920\pi\)
\(84\) 0 0
\(85\) 0.234216 0.0970152i 0.0254042 0.0105228i
\(86\) 8.21022 + 5.82365i 0.885331 + 0.627980i
\(87\) 0 0
\(88\) −7.79049 14.0812i −0.830469 1.50106i
\(89\) −12.0590 12.0590i −1.27825 1.27825i −0.941644 0.336609i \(-0.890720\pi\)
−0.336609 0.941644i \(-0.609280\pi\)
\(90\) 0 0
\(91\) 16.3945 6.79084i 1.71862 0.711874i
\(92\) −10.7599 + 3.76861i −1.12180 + 0.392904i
\(93\) 0 0
\(94\) 5.58693 + 8.88865i 0.576248 + 0.916794i
\(95\) −0.282518 −0.0289857
\(96\) 0 0
\(97\) −18.5545 −1.88393 −0.941963 0.335717i \(-0.891022\pi\)
−0.941963 + 0.335717i \(0.891022\pi\)
\(98\) −8.77574 13.9619i −0.886483 1.41037i
\(99\) 0 0
\(100\) 3.29911 + 9.41942i 0.329911 + 0.941942i
\(101\) 5.24603 2.17298i 0.521999 0.216219i −0.106096 0.994356i \(-0.533835\pi\)
0.628095 + 0.778137i \(0.283835\pi\)
\(102\) 0 0
\(103\) −11.0095 11.0095i −1.08479 1.08479i −0.996055 0.0887398i \(-0.971716\pi\)
−0.0887398 0.996055i \(-0.528284\pi\)
\(104\) −11.1662 3.21159i −1.09493 0.314922i
\(105\) 0 0
\(106\) −4.61885 3.27623i −0.448622 0.318215i
\(107\) 0.182628 0.0756468i 0.0176553 0.00731305i −0.373838 0.927494i \(-0.621959\pi\)
0.391494 + 0.920181i \(0.371959\pi\)
\(108\) 0 0
\(109\) 2.10265 5.07626i 0.201398 0.486217i −0.790621 0.612305i \(-0.790242\pi\)
0.992019 + 0.126088i \(0.0402423\pi\)
\(110\) −0.176868 + 0.775433i −0.0168637 + 0.0739346i
\(111\) 0 0
\(112\) −1.92457 + 17.1718i −0.181855 + 1.62258i
\(113\) 5.91777 0.556697 0.278348 0.960480i \(-0.410213\pi\)
0.278348 + 0.960480i \(0.410213\pi\)
\(114\) 0 0
\(115\) 0.520573 + 0.215629i 0.0485437 + 0.0201075i
\(116\) −7.21058 8.06387i −0.669486 0.748712i
\(117\) 0 0
\(118\) −2.97883 2.11294i −0.274224 0.194512i
\(119\) 7.83410 + 7.83410i 0.718151 + 0.718151i
\(120\) 0 0
\(121\) 15.1118 15.1118i 1.37380 1.37380i
\(122\) −15.7465 + 2.67782i −1.42562 + 0.242439i
\(123\) 0 0
\(124\) 2.59882 + 1.25058i 0.233381 + 0.112306i
\(125\) 0.377900 0.912331i 0.0338004 0.0816014i
\(126\) 0 0
\(127\) 9.70061i 0.860790i −0.902641 0.430395i \(-0.858374\pi\)
0.902641 0.430395i \(-0.141626\pi\)
\(128\) 7.99176 8.00823i 0.706379 0.707834i
\(129\) 0 0
\(130\) 0.305587 + 0.486180i 0.0268017 + 0.0426408i
\(131\) 12.7327 + 5.27407i 1.11246 + 0.460798i 0.861786 0.507273i \(-0.169346\pi\)
0.250678 + 0.968070i \(0.419346\pi\)
\(132\) 0 0
\(133\) −4.72486 11.4068i −0.409698 0.989098i
\(134\) −0.427818 2.51572i −0.0369579 0.217325i
\(135\) 0 0
\(136\) −0.815381 7.20813i −0.0699183 0.618092i
\(137\) −5.62861 + 5.62861i −0.480884 + 0.480884i −0.905414 0.424530i \(-0.860439\pi\)
0.424530 + 0.905414i \(0.360439\pi\)
\(138\) 0 0
\(139\) 0.202389 + 0.488610i 0.0171664 + 0.0414434i 0.932230 0.361865i \(-0.117860\pi\)
−0.915064 + 0.403309i \(0.867860\pi\)
\(140\) 0.636610 0.569246i 0.0538034 0.0481101i
\(141\) 0 0
\(142\) 1.32518 5.80993i 0.111207 0.487559i
\(143\) 23.3722i 1.95448i
\(144\) 0 0
\(145\) 0.534637i 0.0443992i
\(146\) −17.9861 4.10243i −1.48854 0.339519i
\(147\) 0 0
\(148\) −10.8411 0.605624i −0.891130 0.0497820i
\(149\) 1.35052 + 3.26046i 0.110639 + 0.267107i 0.969495 0.245110i \(-0.0788242\pi\)
−0.858856 + 0.512217i \(0.828824\pi\)
\(150\) 0 0
\(151\) −13.6492 + 13.6492i −1.11076 + 1.11076i −0.117709 + 0.993048i \(0.537555\pi\)
−0.993048 + 0.117709i \(0.962445\pi\)
\(152\) −2.23453 + 7.76910i −0.181244 + 0.630157i
\(153\) 0 0
\(154\) −34.2665 + 5.82730i −2.76128 + 0.469577i
\(155\) −0.0545476 0.131690i −0.00438137 0.0105776i
\(156\) 0 0
\(157\) −15.4587 6.40321i −1.23374 0.511032i −0.331987 0.943284i \(-0.607719\pi\)
−0.901753 + 0.432252i \(0.857719\pi\)
\(158\) 1.34318 0.844252i 0.106858 0.0671651i
\(159\) 0 0
\(160\) −0.558258 + 0.0317627i −0.0441342 + 0.00251106i
\(161\) 24.6247i 1.94070i
\(162\) 0 0
\(163\) −6.04288 + 14.5888i −0.473315 + 1.14268i 0.489374 + 0.872074i \(0.337225\pi\)
−0.962689 + 0.270609i \(0.912775\pi\)
\(164\) −0.277426 0.792090i −0.0216633 0.0618519i
\(165\) 0 0
\(166\) −2.56205 15.0658i −0.198854 1.16933i
\(167\) 6.58872 6.58872i 0.509850 0.509850i −0.404630 0.914480i \(-0.632600\pi\)
0.914480 + 0.404630i \(0.132600\pi\)
\(168\) 0 0
\(169\) −2.73986 2.73986i −0.210759 0.210759i
\(170\) −0.207423 + 0.292427i −0.0159086 + 0.0224281i
\(171\) 0 0
\(172\) −14.2132 0.794004i −1.08375 0.0605422i
\(173\) −17.8204 7.38143i −1.35486 0.561200i −0.417216 0.908807i \(-0.636994\pi\)
−0.937640 + 0.347608i \(0.886994\pi\)
\(174\) 0 0
\(175\) 21.5569 1.62955
\(176\) 19.9251 + 10.9969i 1.50191 + 0.828924i
\(177\) 0 0
\(178\) 23.5141 + 5.36331i 1.76246 + 0.401997i
\(179\) −4.07369 + 9.83475i −0.304482 + 0.735084i 0.695383 + 0.718639i \(0.255235\pi\)
−0.999865 + 0.0164446i \(0.994765\pi\)
\(180\) 0 0
\(181\) 8.06280 3.33972i 0.599303 0.248239i −0.0623442 0.998055i \(-0.519858\pi\)
0.661647 + 0.749815i \(0.269858\pi\)
\(182\) −14.5191 + 20.4692i −1.07623 + 1.51728i
\(183\) 0 0
\(184\) 10.0471 12.6100i 0.740679 0.929623i
\(185\) 0.379459 + 0.379459i 0.0278984 + 0.0278984i
\(186\) 0 0
\(187\) 13.4814 5.58417i 0.985856 0.408355i
\(188\) −13.3789 6.43809i −0.975756 0.469546i
\(189\) 0 0
\(190\) 0.338270 0.212618i 0.0245406 0.0154249i
\(191\) 13.0520 0.944411 0.472205 0.881489i \(-0.343458\pi\)
0.472205 + 0.881489i \(0.343458\pi\)
\(192\) 0 0
\(193\) −3.05926 −0.220210 −0.110105 0.993920i \(-0.535119\pi\)
−0.110105 + 0.993920i \(0.535119\pi\)
\(194\) 22.2160 13.9638i 1.59502 1.00254i
\(195\) 0 0
\(196\) 21.0151 + 10.1127i 1.50108 + 0.722336i
\(197\) −5.46774 + 2.26481i −0.389560 + 0.161361i −0.568862 0.822433i \(-0.692616\pi\)
0.179302 + 0.983794i \(0.442616\pi\)
\(198\) 0 0
\(199\) −4.48835 4.48835i −0.318170 0.318170i 0.529894 0.848064i \(-0.322232\pi\)
−0.848064 + 0.529894i \(0.822232\pi\)
\(200\) −11.0390 8.79538i −0.780578 0.621927i
\(201\) 0 0
\(202\) −4.64593 + 6.54986i −0.326886 + 0.460846i
\(203\) −21.5863 + 8.94133i −1.51506 + 0.627559i
\(204\) 0 0
\(205\) −0.0158735 + 0.0383220i −0.00110865 + 0.00267652i
\(206\) 21.4676 + 4.89652i 1.49572 + 0.341156i
\(207\) 0 0
\(208\) 15.7867 4.55812i 1.09461 0.316049i
\(209\) −16.2617 −1.12484
\(210\) 0 0
\(211\) 0.322439 + 0.133558i 0.0221976 + 0.00919454i 0.393755 0.919216i \(-0.371176\pi\)
−0.371557 + 0.928410i \(0.621176\pi\)
\(212\) 7.99596 + 0.446685i 0.549165 + 0.0306785i
\(213\) 0 0
\(214\) −0.161736 + 0.228017i −0.0110561 + 0.0155869i
\(215\) 0.497491 + 0.497491i 0.0339286 + 0.0339286i
\(216\) 0 0
\(217\) 4.40478 4.40478i 0.299016 0.299016i
\(218\) 1.30272 + 7.66042i 0.0882311 + 0.518829i
\(219\) 0 0
\(220\) −0.371807 1.06156i −0.0250672 0.0715706i
\(221\) 4.03178 9.73358i 0.271207 0.654752i
\(222\) 0 0
\(223\) 19.1612i 1.28313i 0.767068 + 0.641566i \(0.221715\pi\)
−0.767068 + 0.641566i \(0.778285\pi\)
\(224\) −10.6188 22.0088i −0.709499 1.47052i
\(225\) 0 0
\(226\) −7.08557 + 4.45361i −0.471325 + 0.296250i
\(227\) 19.4451 + 8.05441i 1.29061 + 0.534590i 0.919169 0.393864i \(-0.128862\pi\)
0.371446 + 0.928455i \(0.378862\pi\)
\(228\) 0 0
\(229\) −6.97193 16.8317i −0.460718 1.11227i −0.968103 0.250552i \(-0.919388\pi\)
0.507385 0.861719i \(-0.330612\pi\)
\(230\) −0.785581 + 0.133594i −0.0517997 + 0.00880895i
\(231\) 0 0
\(232\) 14.7022 + 4.22862i 0.965249 + 0.277623i
\(233\) 16.7768 16.7768i 1.09909 1.09909i 0.104569 0.994518i \(-0.466654\pi\)
0.994518 0.104569i \(-0.0333462\pi\)
\(234\) 0 0
\(235\) 0.280815 + 0.677947i 0.0183183 + 0.0442244i
\(236\) 5.15683 + 0.288080i 0.335681 + 0.0187524i
\(237\) 0 0
\(238\) −15.2759 3.48426i −0.990188 0.225851i
\(239\) 9.10976i 0.589261i 0.955611 + 0.294631i \(0.0951966\pi\)
−0.955611 + 0.294631i \(0.904803\pi\)
\(240\) 0 0
\(241\) 7.39995i 0.476673i 0.971183 + 0.238336i \(0.0766020\pi\)
−0.971183 + 0.238336i \(0.923398\pi\)
\(242\) −6.72106 + 29.4669i −0.432046 + 1.89420i
\(243\) 0 0
\(244\) 16.8386 15.0568i 1.07798 0.963914i
\(245\) −0.441093 1.06489i −0.0281804 0.0680336i
\(246\) 0 0
\(247\) −8.30210 + 8.30210i −0.528250 + 0.528250i
\(248\) −4.05283 + 0.458454i −0.257355 + 0.0291119i
\(249\) 0 0
\(250\) 0.234131 + 1.37677i 0.0148077 + 0.0870746i
\(251\) −4.84250 11.6908i −0.305656 0.737919i −0.999836 0.0181174i \(-0.994233\pi\)
0.694180 0.719802i \(-0.255767\pi\)
\(252\) 0 0
\(253\) 29.9641 + 12.4115i 1.88382 + 0.780306i
\(254\) 7.30051 + 11.6149i 0.458075 + 0.728784i
\(255\) 0 0
\(256\) −3.54199 + 15.6030i −0.221374 + 0.975189i
\(257\) 6.02571i 0.375873i −0.982181 0.187937i \(-0.939820\pi\)
0.982181 0.187937i \(-0.0601800\pi\)
\(258\) 0 0
\(259\) −8.97478 + 21.6670i −0.557666 + 1.34632i
\(260\) −0.731782 0.352143i −0.0453832 0.0218390i
\(261\) 0 0
\(262\) −19.2146 + 3.26759i −1.18708 + 0.201872i
\(263\) −6.79218 + 6.79218i −0.418824 + 0.418824i −0.884798 0.465974i \(-0.845704\pi\)
0.465974 + 0.884798i \(0.345704\pi\)
\(264\) 0 0
\(265\) −0.279875 0.279875i −0.0171926 0.0171926i
\(266\) 14.2418 + 10.1020i 0.873224 + 0.619392i
\(267\) 0 0
\(268\) 2.40553 + 2.69020i 0.146941 + 0.164330i
\(269\) 13.8548 + 5.73883i 0.844740 + 0.349903i 0.762721 0.646728i \(-0.223863\pi\)
0.0820193 + 0.996631i \(0.473863\pi\)
\(270\) 0 0
\(271\) 5.62497 0.341692 0.170846 0.985298i \(-0.445350\pi\)
0.170846 + 0.985298i \(0.445350\pi\)
\(272\) 6.40100 + 8.01693i 0.388118 + 0.486098i
\(273\) 0 0
\(274\) 2.50335 10.9753i 0.151233 0.663045i
\(275\) 10.8653 26.2311i 0.655201 1.58179i
\(276\) 0 0
\(277\) −1.00843 + 0.417706i −0.0605908 + 0.0250975i −0.412773 0.910834i \(-0.635440\pi\)
0.352182 + 0.935931i \(0.385440\pi\)
\(278\) −0.610048 0.432717i −0.0365883 0.0259527i
\(279\) 0 0
\(280\) −0.333832 + 1.16068i −0.0199503 + 0.0693640i
\(281\) −21.7589 21.7589i −1.29803 1.29803i −0.929693 0.368335i \(-0.879928\pi\)
−0.368335 0.929693i \(-0.620072\pi\)
\(282\) 0 0
\(283\) −22.3614 + 9.26239i −1.32925 + 0.550592i −0.930441 0.366443i \(-0.880576\pi\)
−0.398807 + 0.917035i \(0.630576\pi\)
\(284\) 2.78577 + 7.95376i 0.165305 + 0.471969i
\(285\) 0 0
\(286\) 17.5895 + 27.9844i 1.04009 + 1.65475i
\(287\) −1.81274 −0.107003
\(288\) 0 0
\(289\) −10.4223 −0.613074
\(290\) −0.402359 0.640141i −0.0236273 0.0375904i
\(291\) 0 0
\(292\) 24.6229 8.62404i 1.44094 0.504684i
\(293\) −29.2423 + 12.1126i −1.70835 + 0.707623i −0.708355 + 0.705856i \(0.750562\pi\)
−0.999998 + 0.00176683i \(0.999438\pi\)
\(294\) 0 0
\(295\) −0.180500 0.180500i −0.0105091 0.0105091i
\(296\) 13.4362 7.43367i 0.780964 0.432073i
\(297\) 0 0
\(298\) −4.07080 2.88749i −0.235815 0.167268i
\(299\) 21.6341 8.96114i 1.25113 0.518236i
\(300\) 0 0
\(301\) −11.7664 + 28.4066i −0.678204 + 1.63733i
\(302\) 6.07056 26.6149i 0.349322 1.53152i
\(303\) 0 0
\(304\) −3.17140 10.9839i −0.181892 0.629970i
\(305\) −1.11641 −0.0639252
\(306\) 0 0
\(307\) 13.7854 + 5.71009i 0.786773 + 0.325892i 0.739645 0.672997i \(-0.234993\pi\)
0.0471275 + 0.998889i \(0.484993\pi\)
\(308\) 36.6431 32.7657i 2.08793 1.86700i
\(309\) 0 0
\(310\) 0.164419 + 0.116625i 0.00933838 + 0.00662387i
\(311\) −11.4220 11.4220i −0.647684 0.647684i 0.304749 0.952433i \(-0.401427\pi\)
−0.952433 + 0.304749i \(0.901427\pi\)
\(312\) 0 0
\(313\) 2.24707 2.24707i 0.127012 0.127012i −0.640743 0.767755i \(-0.721374\pi\)
0.767755 + 0.640743i \(0.221374\pi\)
\(314\) 23.3283 3.96716i 1.31649 0.223880i
\(315\) 0 0
\(316\) −0.972872 + 2.02171i −0.0547283 + 0.113730i
\(317\) −1.05906 + 2.55679i −0.0594826 + 0.143604i −0.950826 0.309724i \(-0.899763\pi\)
0.891344 + 0.453328i \(0.149763\pi\)
\(318\) 0 0
\(319\) 30.7736i 1.72299i
\(320\) 0.644519 0.458166i 0.0360297 0.0256123i
\(321\) 0 0
\(322\) −18.5321 29.4841i −1.03275 1.64308i
\(323\) −6.77233 2.80519i −0.376823 0.156085i
\(324\) 0 0
\(325\) −7.84475 18.9389i −0.435148 1.05054i
\(326\) −3.74391 22.0155i −0.207356 1.21933i
\(327\) 0 0
\(328\) 0.928286 + 0.739614i 0.0512560 + 0.0408384i
\(329\) −22.6761 + 22.6761i −1.25018 + 1.25018i
\(330\) 0 0
\(331\) −0.123439 0.298008i −0.00678481 0.0163800i 0.920451 0.390858i \(-0.127822\pi\)
−0.927236 + 0.374478i \(0.877822\pi\)
\(332\) 14.4059 + 16.1106i 0.790625 + 0.884187i
\(333\) 0 0
\(334\) −2.93037 + 12.8475i −0.160343 + 0.702983i
\(335\) 0.178361i 0.00974489i
\(336\) 0 0
\(337\) 16.5067i 0.899179i −0.893235 0.449590i \(-0.851570\pi\)
0.893235 0.449590i \(-0.148430\pi\)
\(338\) 5.34252 + 1.21857i 0.290595 + 0.0662814i
\(339\) 0 0
\(340\) 0.0282803 0.506237i 0.00153372 0.0274545i
\(341\) −3.13974 7.58001i −0.170027 0.410481i
\(342\) 0 0
\(343\) 14.2368 14.2368i 0.768716 0.768716i
\(344\) 17.6156 9.74592i 0.949767 0.525465i
\(345\) 0 0
\(346\) 26.8921 4.57322i 1.44573 0.245858i
\(347\) −5.96248 14.3947i −0.320083 0.772748i −0.999248 0.0387633i \(-0.987658\pi\)
0.679166 0.733985i \(-0.262342\pi\)
\(348\) 0 0
\(349\) 1.57618 + 0.652873i 0.0843707 + 0.0349475i 0.424470 0.905442i \(-0.360461\pi\)
−0.340099 + 0.940390i \(0.610461\pi\)
\(350\) −25.8109 + 16.2233i −1.37965 + 0.867174i
\(351\) 0 0
\(352\) −32.1332 + 1.82825i −1.71270 + 0.0974463i
\(353\) 18.7091i 0.995786i −0.867239 0.497893i \(-0.834107\pi\)
0.867239 0.497893i \(-0.165893\pi\)
\(354\) 0 0
\(355\) 0.159393 0.384810i 0.00845972 0.0204236i
\(356\) −32.1907 + 11.2746i −1.70610 + 0.597555i
\(357\) 0 0
\(358\) −2.52388 14.8413i −0.133391 0.784388i
\(359\) −23.5065 + 23.5065i −1.24062 + 1.24062i −0.280882 + 0.959742i \(0.590627\pi\)
−0.959742 + 0.280882i \(0.909373\pi\)
\(360\) 0 0
\(361\) −7.65868 7.65868i −0.403088 0.403088i
\(362\) −7.14048 + 10.0667i −0.375295 + 0.529094i
\(363\) 0 0
\(364\) 1.97956 35.4354i 0.103757 1.85732i
\(365\) −1.19127 0.493442i −0.0623542 0.0258279i
\(366\) 0 0
\(367\) −2.95190 −0.154088 −0.0770440 0.997028i \(-0.524548\pi\)
−0.0770440 + 0.997028i \(0.524548\pi\)
\(368\) −2.53964 + 22.6597i −0.132388 + 1.18122i
\(369\) 0 0
\(370\) −0.739916 0.168767i −0.0384664 0.00877376i
\(371\) 6.61945 15.9808i 0.343665 0.829680i
\(372\) 0 0
\(373\) −19.7552 + 8.18287i −1.02289 + 0.423693i −0.830140 0.557556i \(-0.811739\pi\)
−0.192746 + 0.981249i \(0.561739\pi\)
\(374\) −11.9392 + 16.8320i −0.617362 + 0.870362i
\(375\) 0 0
\(376\) 20.8643 2.36016i 1.07599 0.121716i
\(377\) 15.7109 + 15.7109i 0.809152 + 0.809152i
\(378\) 0 0
\(379\) 4.26476 1.76652i 0.219066 0.0907402i −0.270451 0.962734i \(-0.587173\pi\)
0.489518 + 0.871993i \(0.337173\pi\)
\(380\) −0.245010 + 0.509152i −0.0125688 + 0.0261189i
\(381\) 0 0
\(382\) −15.6277 + 9.82273i −0.799582 + 0.502574i
\(383\) 9.45328 0.483040 0.241520 0.970396i \(-0.422354\pi\)
0.241520 + 0.970396i \(0.422354\pi\)
\(384\) 0 0
\(385\) −2.42945 −0.123816
\(386\) 3.66296 2.30234i 0.186440 0.117186i
\(387\) 0 0
\(388\) −16.0912 + 33.4388i −0.816906 + 1.69760i
\(389\) −20.8554 + 8.63860i −1.05741 + 0.437994i −0.842532 0.538646i \(-0.818936\pi\)
−0.214880 + 0.976640i \(0.568936\pi\)
\(390\) 0 0
\(391\) 10.3378 + 10.3378i 0.522806 + 0.522806i
\(392\) −32.7728 + 3.70724i −1.65527 + 0.187244i
\(393\) 0 0
\(394\) 4.84228 6.82667i 0.243950 0.343923i
\(395\) 0.102446 0.0424345i 0.00515461 0.00213511i
\(396\) 0 0
\(397\) 3.29268 7.94922i 0.165255 0.398960i −0.819460 0.573137i \(-0.805726\pi\)
0.984714 + 0.174177i \(0.0557264\pi\)
\(398\) 8.75192 + 1.99622i 0.438694 + 0.100061i
\(399\) 0 0
\(400\) 19.8367 + 2.22325i 0.991836 + 0.111162i
\(401\) 32.5903 1.62748 0.813740 0.581229i \(-0.197428\pi\)
0.813740 + 0.581229i \(0.197428\pi\)
\(402\) 0 0
\(403\) −5.47278 2.26690i −0.272619 0.112922i
\(404\) 0.633431 11.3388i 0.0315144 0.564128i
\(405\) 0 0
\(406\) 19.1170 26.9513i 0.948760 1.33757i
\(407\) 21.8416 + 21.8416i 1.08265 + 1.08265i
\(408\) 0 0
\(409\) 5.41708 5.41708i 0.267858 0.267858i −0.560379 0.828236i \(-0.689344\pi\)
0.828236 + 0.560379i \(0.189344\pi\)
\(410\) −0.00983455 0.0578305i −0.000485694 0.00285605i
\(411\) 0 0
\(412\) −29.3890 + 10.2934i −1.44789 + 0.507117i
\(413\) 4.26908 10.3065i 0.210068 0.507149i
\(414\) 0 0
\(415\) 1.06814i 0.0524329i
\(416\) −15.4716 + 17.3384i −0.758560 + 0.850085i
\(417\) 0 0
\(418\) 19.4707 12.2382i 0.952343 0.598592i
\(419\) −22.0298 9.12504i −1.07623 0.445787i −0.227042 0.973885i \(-0.572906\pi\)
−0.849184 + 0.528097i \(0.822906\pi\)
\(420\) 0 0
\(421\) 2.82553 + 6.82144i 0.137708 + 0.332457i 0.977656 0.210210i \(-0.0674147\pi\)
−0.839948 + 0.542667i \(0.817415\pi\)
\(422\) −0.486582 + 0.0827472i −0.0236864 + 0.00402807i
\(423\) 0 0
\(424\) −9.91003 + 5.48279i −0.481274 + 0.266268i
\(425\) 9.04991 9.04991i 0.438985 0.438985i
\(426\) 0 0
\(427\) −18.6709 45.0756i −0.903549 2.18136i
\(428\) 0.0220514 0.394734i 0.00106589 0.0190802i
\(429\) 0 0
\(430\) −0.970068 0.221262i −0.0467808 0.0106702i
\(431\) 6.73112i 0.324226i 0.986772 + 0.162113i \(0.0518310\pi\)
−0.986772 + 0.162113i \(0.948169\pi\)
\(432\) 0 0
\(433\) 12.1160i 0.582257i −0.956684 0.291129i \(-0.905969\pi\)
0.956684 0.291129i \(-0.0940308\pi\)
\(434\) −1.95905 + 8.58898i −0.0940374 + 0.412284i
\(435\) 0 0
\(436\) −7.32489 8.19171i −0.350799 0.392312i
\(437\) −6.23489 15.0524i −0.298255 0.720052i
\(438\) 0 0
\(439\) 14.0767 14.0767i 0.671843 0.671843i −0.286298 0.958141i \(-0.592425\pi\)
0.958141 + 0.286298i \(0.0924246\pi\)
\(440\) 1.24409 + 0.991234i 0.0593098 + 0.0472552i
\(441\) 0 0
\(442\) 2.49792 + 14.6886i 0.118814 + 0.698667i
\(443\) 14.5313 + 35.0817i 0.690404 + 1.66678i 0.743965 + 0.668218i \(0.232943\pi\)
−0.0535615 + 0.998565i \(0.517057\pi\)
\(444\) 0 0
\(445\) 1.55741 + 0.645102i 0.0738285 + 0.0305808i
\(446\) −14.4204 22.9425i −0.682827 1.08636i
\(447\) 0 0
\(448\) 29.2778 + 18.3604i 1.38324 + 0.867449i
\(449\) 25.9809i 1.22611i 0.790039 + 0.613056i \(0.210060\pi\)
−0.790039 + 0.613056i \(0.789940\pi\)
\(450\) 0 0
\(451\) −0.913674 + 2.20580i −0.0430232 + 0.103867i
\(452\) 5.13211 10.6650i 0.241394 0.501638i
\(453\) 0 0
\(454\) −29.3439 + 4.99017i −1.37718 + 0.234200i
\(455\) −1.24031 + 1.24031i −0.0581467 + 0.0581467i
\(456\) 0 0
\(457\) 6.23785 + 6.23785i 0.291794 + 0.291794i 0.837789 0.545994i \(-0.183848\pi\)
−0.545994 + 0.837789i \(0.683848\pi\)
\(458\) 21.0150 + 14.9063i 0.981968 + 0.696526i
\(459\) 0 0
\(460\) 0.840065 0.751172i 0.0391682 0.0350236i
\(461\) −23.3278 9.66269i −1.08648 0.450036i −0.233704 0.972308i \(-0.575085\pi\)
−0.852779 + 0.522271i \(0.825085\pi\)
\(462\) 0 0
\(463\) 3.99595 0.185707 0.0928537 0.995680i \(-0.470401\pi\)
0.0928537 + 0.995680i \(0.470401\pi\)
\(464\) −20.7859 + 6.00156i −0.964963 + 0.278616i
\(465\) 0 0
\(466\) −7.46158 + 32.7135i −0.345651 + 1.51542i
\(467\) −7.26272 + 17.5338i −0.336079 + 0.811366i 0.662006 + 0.749499i \(0.269706\pi\)
−0.998084 + 0.0618671i \(0.980294\pi\)
\(468\) 0 0
\(469\) 7.20142 2.98293i 0.332531 0.137739i
\(470\) −0.846442 0.600396i −0.0390435 0.0276942i
\(471\) 0 0
\(472\) −6.39127 + 3.53601i −0.294182 + 0.162758i
\(473\) 28.6354 + 28.6354i 1.31666 + 1.31666i
\(474\) 0 0
\(475\) −13.1771 + 5.45814i −0.604607 + 0.250437i
\(476\) 20.9126 7.32453i 0.958527 0.335719i
\(477\) 0 0
\(478\) −6.85585 10.9075i −0.313579 0.498896i
\(479\) −21.7665 −0.994537 −0.497268 0.867597i \(-0.665664\pi\)
−0.497268 + 0.867597i \(0.665664\pi\)
\(480\) 0 0
\(481\) 22.3017 1.01687
\(482\) −5.56908 8.86024i −0.253664 0.403573i
\(483\) 0 0
\(484\) −14.1289 40.3400i −0.642222 1.83364i
\(485\) 1.69444 0.701861i 0.0769407 0.0318699i
\(486\) 0 0
\(487\) −9.10128 9.10128i −0.412419 0.412419i 0.470162 0.882580i \(-0.344196\pi\)
−0.882580 + 0.470162i \(0.844196\pi\)
\(488\) −8.83002 + 30.7006i −0.399716 + 1.38975i
\(489\) 0 0
\(490\) 1.32956 + 0.943078i 0.0600633 + 0.0426039i
\(491\) −15.2645 + 6.32276i −0.688876 + 0.285342i −0.699532 0.714601i \(-0.746608\pi\)
0.0106556 + 0.999943i \(0.496608\pi\)
\(492\) 0 0
\(493\) −5.30855 + 12.8160i −0.239085 + 0.577202i
\(494\) 3.69240 16.1884i 0.166129 0.728352i
\(495\) 0 0
\(496\) 4.50758 3.59901i 0.202396 0.161601i
\(497\) 18.2026 0.816500
\(498\) 0 0
\(499\) −32.2595 13.3623i −1.44413 0.598180i −0.483337 0.875434i \(-0.660575\pi\)
−0.960796 + 0.277255i \(0.910575\pi\)
\(500\) −1.31647 1.47226i −0.0588742 0.0658413i
\(501\) 0 0
\(502\) 14.5964 + 10.3535i 0.651471 + 0.462099i
\(503\) 7.34111 + 7.34111i 0.327324 + 0.327324i 0.851568 0.524244i \(-0.175652\pi\)
−0.524244 + 0.851568i \(0.675652\pi\)
\(504\) 0 0
\(505\) −0.396882 + 0.396882i −0.0176610 + 0.0176610i
\(506\) −45.2178 + 7.68966i −2.01018 + 0.341847i
\(507\) 0 0
\(508\) −17.4824 8.41273i −0.775654 0.373255i
\(509\) −7.55299 + 18.2345i −0.334780 + 0.808231i 0.663419 + 0.748248i \(0.269105\pi\)
−0.998199 + 0.0599832i \(0.980895\pi\)
\(510\) 0 0
\(511\) 56.3508i 2.49281i
\(512\) −7.50161 21.3477i −0.331528 0.943446i
\(513\) 0 0
\(514\) 4.53485 + 7.21481i 0.200024 + 0.318232i
\(515\) 1.42186 + 0.588955i 0.0626548 + 0.0259525i
\(516\) 0 0
\(517\) 16.1636 + 39.0225i 0.710876 + 1.71621i
\(518\) −5.56039 32.6970i −0.244310 1.43662i
\(519\) 0 0
\(520\) 1.14121 0.129093i 0.0500452 0.00566109i
\(521\) 26.3209 26.3209i 1.15314 1.15314i 0.167218 0.985920i \(-0.446522\pi\)
0.985920 0.167218i \(-0.0534785\pi\)
\(522\) 0 0
\(523\) 5.50275 + 13.2848i 0.240619 + 0.580905i 0.997345 0.0728276i \(-0.0232023\pi\)
−0.756726 + 0.653732i \(0.773202\pi\)
\(524\) 20.5472 18.3730i 0.897608 0.802627i
\(525\) 0 0
\(526\) 3.02086 13.2442i 0.131716 0.577475i
\(527\) 3.69839i 0.161104i
\(528\) 0 0
\(529\) 9.49450i 0.412805i
\(530\) 0.545734 + 0.124476i 0.0237052 + 0.00540688i
\(531\) 0 0
\(532\) −24.6549 1.37732i −1.06893 0.0597143i
\(533\) 0.659674 + 1.59259i 0.0285737 + 0.0689829i
\(534\) 0 0
\(535\) −0.0138165 + 0.0138165i −0.000597339 + 0.000597339i
\(536\) −4.90483 1.41071i −0.211856 0.0609336i
\(537\) 0 0
\(538\) −20.9078 + 3.55554i −0.901399 + 0.153290i
\(539\) −25.3892 61.2950i −1.09359 2.64016i
\(540\) 0 0
\(541\) 1.34772 + 0.558245i 0.0579431 + 0.0240008i 0.411467 0.911425i \(-0.365017\pi\)
−0.353524 + 0.935426i \(0.615017\pi\)
\(542\) −6.73499 + 4.23325i −0.289292 + 0.181834i
\(543\) 0 0
\(544\) −13.6976 4.78169i −0.587278 0.205013i
\(545\) 0.543113i 0.0232644i
\(546\) 0 0
\(547\) 3.11417 7.51828i 0.133152 0.321458i −0.843215 0.537577i \(-0.819340\pi\)
0.976367 + 0.216119i \(0.0693398\pi\)
\(548\) 5.26250 + 15.0252i 0.224803 + 0.641844i
\(549\) 0 0
\(550\) 6.73166 + 39.5845i 0.287039 + 1.68789i
\(551\) 10.9312 10.9312i 0.465683 0.465683i
\(552\) 0 0
\(553\) 3.42664 + 3.42664i 0.145715 + 0.145715i
\(554\) 0.893076 1.25906i 0.0379431 0.0534925i
\(555\) 0 0
\(556\) 1.05609 + 0.0589973i 0.0447882 + 0.00250204i
\(557\) 10.3810 + 4.29993i 0.439855 + 0.182194i 0.591610 0.806224i \(-0.298492\pi\)
−0.151755 + 0.988418i \(0.548492\pi\)
\(558\) 0 0
\(559\) 29.2386 1.23666
\(560\) −0.473799 1.64097i −0.0200217 0.0693434i
\(561\) 0 0
\(562\) 42.4282 + 9.67739i 1.78972 + 0.408216i
\(563\) 1.95005 4.70784i 0.0821848 0.198412i −0.877445 0.479677i \(-0.840754\pi\)
0.959630 + 0.281265i \(0.0907540\pi\)
\(564\) 0 0
\(565\) −0.540424 + 0.223851i −0.0227358 + 0.00941749i
\(566\) 19.8034 27.9190i 0.832400 1.17352i
\(567\) 0 0
\(568\) −9.32137 7.42682i −0.391116 0.311623i
\(569\) 3.12423 + 3.12423i 0.130974 + 0.130974i 0.769555 0.638581i \(-0.220478\pi\)
−0.638581 + 0.769555i \(0.720478\pi\)
\(570\) 0 0
\(571\) 33.4029 13.8360i 1.39787 0.579017i 0.448672 0.893697i \(-0.351897\pi\)
0.949198 + 0.314680i \(0.101897\pi\)
\(572\) −42.1212 20.2692i −1.76117 0.847499i
\(573\) 0 0
\(574\) 2.17047 1.36424i 0.0905936 0.0569423i
\(575\) 28.4463 1.18629
\(576\) 0 0
\(577\) −14.0315 −0.584141 −0.292070 0.956397i \(-0.594344\pi\)
−0.292070 + 0.956397i \(0.594344\pi\)
\(578\) 12.4790 7.84361i 0.519056 0.326251i
\(579\) 0 0
\(580\) 0.963519 + 0.463657i 0.0400079 + 0.0192523i
\(581\) 43.1268 17.8637i 1.78920 0.741112i
\(582\) 0 0
\(583\) −16.1095 16.1095i −0.667188 0.667188i
\(584\) −22.9916 + 28.8566i −0.951398 + 1.19410i
\(585\) 0 0
\(586\) 25.8972 36.5101i 1.06980 1.50822i
\(587\) 12.0165 4.97740i 0.495975 0.205439i −0.120652 0.992695i \(-0.538499\pi\)
0.616627 + 0.787255i \(0.288499\pi\)
\(588\) 0 0
\(589\) −1.57724 + 3.80780i −0.0649891 + 0.156898i
\(590\) 0.351960 + 0.0802781i 0.0144900 + 0.00330500i
\(591\) 0 0
\(592\) −10.4932 + 19.0125i −0.431269 + 0.781408i
\(593\) 17.6528 0.724914 0.362457 0.932000i \(-0.381938\pi\)
0.362457 + 0.932000i \(0.381938\pi\)
\(594\) 0 0
\(595\) −1.01177 0.419088i −0.0414785 0.0171809i
\(596\) 7.04719 + 0.393684i 0.288664 + 0.0161259i
\(597\) 0 0
\(598\) −19.1593 + 27.0110i −0.783484 + 1.10456i
\(599\) −5.25995 5.25995i −0.214916 0.214916i 0.591436 0.806352i \(-0.298561\pi\)
−0.806352 + 0.591436i \(0.798561\pi\)
\(600\) 0 0
\(601\) 6.54574 6.54574i 0.267006 0.267006i −0.560886 0.827893i \(-0.689540\pi\)
0.827893 + 0.560886i \(0.189540\pi\)
\(602\) −7.28996 42.8675i −0.297117 1.74715i
\(603\) 0 0
\(604\) 12.7614 + 36.4356i 0.519254 + 1.48255i
\(605\) −0.808413 + 1.95168i −0.0328667 + 0.0793472i
\(606\) 0 0
\(607\) 1.72276i 0.0699248i −0.999389 0.0349624i \(-0.988869\pi\)
0.999389 0.0349624i \(-0.0111311\pi\)
\(608\) 12.0635 + 10.7647i 0.489241 + 0.436566i
\(609\) 0 0
\(610\) 1.33672 0.840188i 0.0541220 0.0340182i
\(611\) 28.1743 + 11.6702i 1.13981 + 0.472125i
\(612\) 0 0
\(613\) 16.6267 + 40.1405i 0.671547 + 1.62126i 0.778982 + 0.627046i \(0.215736\pi\)
−0.107435 + 0.994212i \(0.534264\pi\)
\(614\) −20.8031 + 3.53773i −0.839544 + 0.142771i
\(615\) 0 0
\(616\) −19.2153 + 66.8085i −0.774207 + 2.69179i
\(617\) 7.78933 7.78933i 0.313587 0.313587i −0.532711 0.846297i \(-0.678827\pi\)
0.846297 + 0.532711i \(0.178827\pi\)
\(618\) 0 0
\(619\) 11.0171 + 26.5976i 0.442814 + 1.06905i 0.974957 + 0.222394i \(0.0713871\pi\)
−0.532143 + 0.846655i \(0.678613\pi\)
\(620\) −0.284636 0.0159008i −0.0114312 0.000638593i
\(621\) 0 0
\(622\) 22.2721 + 5.08001i 0.893028 + 0.203690i
\(623\) 73.6703i 2.95154i
\(624\) 0 0
\(625\) 24.8535i 0.994141i
\(626\) −0.999396 + 4.38161i −0.0399439 + 0.175124i
\(627\) 0 0
\(628\) −24.9462 + 22.3065i −0.995461 + 0.890125i
\(629\) 5.32840 + 12.8639i 0.212457 + 0.512917i
\(630\) 0 0
\(631\) −21.0548 + 21.0548i −0.838177 + 0.838177i −0.988619 0.150442i \(-0.951930\pi\)
0.150442 + 0.988619i \(0.451930\pi\)
\(632\) −0.356648 3.15284i −0.0141867 0.125413i
\(633\) 0 0
\(634\) −0.656147 3.85837i −0.0260589 0.153235i
\(635\) 0.366944 + 0.885882i 0.0145617 + 0.0351552i
\(636\) 0 0
\(637\) −44.2551 18.3311i −1.75345 0.726303i
\(638\) −23.1597 36.8464i −0.916900 1.45876i
\(639\) 0 0
\(640\) −0.426900 + 1.03363i −0.0168747 + 0.0408580i
\(641\) 5.65123i 0.223210i 0.993753 + 0.111605i \(0.0355992\pi\)
−0.993753 + 0.111605i \(0.964401\pi\)
\(642\) 0 0
\(643\) 17.0022 41.0470i 0.670502 1.61874i −0.110256 0.993903i \(-0.535167\pi\)
0.780759 0.624833i \(-0.214833\pi\)
\(644\) 44.3784 + 21.3554i 1.74875 + 0.841522i
\(645\) 0 0
\(646\) 10.2199 1.73798i 0.402097 0.0683799i
\(647\) 0.0151270 0.0151270i 0.000594703 0.000594703i −0.706809 0.707404i \(-0.749866\pi\)
0.707404 + 0.706809i \(0.249866\pi\)
\(648\) 0 0
\(649\) −10.3895 10.3895i −0.407824 0.407824i
\(650\) 23.6459 + 16.7724i 0.927469 + 0.657869i
\(651\) 0 0
\(652\) 21.0512 + 23.5424i 0.824429 + 0.921991i
\(653\) −28.8575 11.9531i −1.12928 0.467763i −0.261744 0.965137i \(-0.584297\pi\)
−0.867536 + 0.497375i \(0.834297\pi\)
\(654\) 0 0
\(655\) −1.36228 −0.0532289
\(656\) −1.66809 0.186956i −0.0651281 0.00729940i
\(657\) 0 0
\(658\) 10.0853 44.2167i 0.393167 1.72375i
\(659\) 7.25678 17.5194i 0.282684 0.682459i −0.717212 0.696855i \(-0.754582\pi\)
0.999896 + 0.0143952i \(0.00458229\pi\)
\(660\) 0 0
\(661\) −15.6310 + 6.47456i −0.607974 + 0.251831i −0.665362 0.746521i \(-0.731723\pi\)
0.0573877 + 0.998352i \(0.481723\pi\)
\(662\) 0.372074 + 0.263918i 0.0144611 + 0.0102575i
\(663\) 0 0
\(664\) −29.3733 8.44828i −1.13991 0.327857i
\(665\) 0.862971 + 0.862971i 0.0334646 + 0.0334646i
\(666\) 0 0
\(667\) −28.4851 + 11.7989i −1.10295 + 0.456856i
\(668\) −6.16016 17.5881i −0.238344 0.680505i
\(669\) 0 0
\(670\) 0.134231 + 0.213558i 0.00518581 + 0.00825047i
\(671\) −64.2600 −2.48073
\(672\) 0 0
\(673\) 26.5987 1.02530 0.512652 0.858596i \(-0.328663\pi\)
0.512652 + 0.858596i \(0.328663\pi\)
\(674\) 12.4227 + 19.7641i 0.478504 + 0.761287i
\(675\) 0 0
\(676\) −7.31387 + 2.56165i −0.281303 + 0.0985249i
\(677\) 26.3000 10.8938i 1.01079 0.418683i 0.185047 0.982730i \(-0.440756\pi\)
0.825743 + 0.564047i \(0.190756\pi\)
\(678\) 0 0
\(679\) 56.6761 + 56.6761i 2.17503 + 2.17503i
\(680\) 0.347124 + 0.627420i 0.0133116 + 0.0240605i
\(681\) 0 0
\(682\) 9.46392 + 6.71292i 0.362392 + 0.257051i
\(683\) 29.9528 12.4069i 1.14611 0.474735i 0.272884 0.962047i \(-0.412022\pi\)
0.873228 + 0.487312i \(0.162022\pi\)
\(684\) 0 0
\(685\) 0.301105 0.726931i 0.0115046 0.0277746i
\(686\) −6.33190 + 27.7607i −0.241753 + 1.05991i
\(687\) 0 0
\(688\) −13.7572 + 24.9263i −0.524487 + 0.950307i
\(689\) −16.4489 −0.626652
\(690\) 0 0
\(691\) −9.94272 4.11841i −0.378239 0.156672i 0.185460 0.982652i \(-0.440622\pi\)
−0.563699 + 0.825980i \(0.690622\pi\)
\(692\) −28.7572 + 25.7143i −1.09319 + 0.977509i
\(693\) 0 0
\(694\) 17.9723 + 12.7481i 0.682220 + 0.483910i
\(695\) −0.0369653 0.0369653i −0.00140217 0.00140217i
\(696\) 0 0
\(697\) −0.761018 + 0.761018i −0.0288256 + 0.0288256i
\(698\) −2.37856 + 0.404493i −0.0900297 + 0.0153103i
\(699\) 0 0
\(700\) 18.6949 38.8497i 0.706602 1.46838i
\(701\) −5.59430 + 13.5058i −0.211294 + 0.510108i −0.993623 0.112757i \(-0.964032\pi\)
0.782329 + 0.622866i \(0.214032\pi\)
\(702\) 0 0
\(703\) 15.5168i 0.585228i
\(704\) 37.0984 26.3719i 1.39820 0.993929i
\(705\) 0 0
\(706\) 14.0802 + 22.4011i 0.529914 + 0.843078i
\(707\) −22.6619 9.38686i −0.852288 0.353029i
\(708\) 0 0
\(709\) 4.92207 + 11.8829i 0.184852 + 0.446273i 0.988955 0.148218i \(-0.0473537\pi\)
−0.804102 + 0.594491i \(0.797354\pi\)
\(710\) 0.0987534 + 0.580704i 0.00370615 + 0.0217934i
\(711\) 0 0
\(712\) 30.0581 37.7258i 1.12647 1.41383i
\(713\) 5.81252 5.81252i 0.217680 0.217680i
\(714\) 0 0
\(715\) 0.884098 + 2.13440i 0.0330634 + 0.0798221i
\(716\) 14.1913 + 15.8706i 0.530352 + 0.593114i
\(717\) 0 0
\(718\) 10.4546 45.8358i 0.390163 1.71058i
\(719\) 16.1029i 0.600537i −0.953855 0.300268i \(-0.902924\pi\)
0.953855 0.300268i \(-0.0970762\pi\)
\(720\) 0 0
\(721\) 67.2584i 2.50483i
\(722\) 14.9338 + 3.40624i 0.555779 + 0.126767i
\(723\) 0 0
\(724\) 0.973542 17.4270i 0.0361814 0.647671i
\(725\) 10.3290 + 24.9364i 0.383609 + 0.926113i
\(726\) 0 0
\(727\) 21.0560 21.0560i 0.780923 0.780923i −0.199064 0.979987i \(-0.563790\pi\)
0.979987 + 0.199064i \(0.0637900\pi\)
\(728\) 24.2979 + 43.9180i 0.900540 + 1.62771i
\(729\) 0 0
\(730\) 1.79771 0.305716i 0.0665364 0.0113151i
\(731\) 6.98581 + 16.8652i 0.258379 + 0.623783i
\(732\) 0 0
\(733\) 41.2426 + 17.0832i 1.52333 + 0.630984i 0.978255 0.207404i \(-0.0665015\pi\)
0.545074 + 0.838388i \(0.316501\pi\)
\(734\) 3.53443 2.22155i 0.130458 0.0819990i
\(735\) 0 0
\(736\) −14.0125 29.0426i −0.516508 1.07053i
\(737\) 10.2664i 0.378168i
\(738\) 0 0
\(739\) 11.2262 27.1024i 0.412962 0.996977i −0.571377 0.820688i \(-0.693591\pi\)
0.984338 0.176290i \(-0.0564095\pi\)
\(740\) 1.01294 0.354778i 0.0372364 0.0130419i
\(741\) 0 0
\(742\) 4.10113 + 24.1161i 0.150557 + 0.885329i
\(743\) −15.8059 + 15.8059i −0.579863 + 0.579863i −0.934865 0.355003i \(-0.884480\pi\)
0.355003 + 0.934865i \(0.384480\pi\)
\(744\) 0 0
\(745\) −0.246666 0.246666i −0.00903715 0.00903715i
\(746\) 17.4954 24.6651i 0.640551 0.903053i
\(747\) 0 0
\(748\) 1.62781 29.1389i 0.0595186 1.06542i
\(749\) −0.788918 0.326780i −0.0288264 0.0119403i
\(750\) 0 0
\(751\) −12.4955 −0.455969 −0.227984 0.973665i \(-0.573213\pi\)
−0.227984 + 0.973665i \(0.573213\pi\)
\(752\) −23.2054 + 18.5280i −0.846212 + 0.675646i
\(753\) 0 0
\(754\) −30.6350 6.98750i −1.11566 0.254470i
\(755\) 0.730170 1.76279i 0.0265736 0.0641544i
\(756\) 0 0
\(757\) 30.0398 12.4429i 1.09182 0.452245i 0.237176 0.971467i \(-0.423778\pi\)
0.854639 + 0.519222i \(0.173778\pi\)
\(758\) −3.77691 + 5.32471i −0.137184 + 0.193402i
\(759\) 0 0
\(760\) −0.0898189 0.794017i −0.00325807 0.0288020i
\(761\) −15.5032 15.5032i −0.561992 0.561992i 0.367881 0.929873i \(-0.380083\pi\)
−0.929873 + 0.367881i \(0.880083\pi\)
\(762\) 0 0
\(763\) −21.9285 + 9.08308i −0.793865 + 0.328830i
\(764\) 11.3192 23.5223i 0.409514 0.851005i
\(765\) 0 0
\(766\) −11.3188 + 7.11438i −0.408964 + 0.257053i
\(767\) −10.6084 −0.383046
\(768\) 0 0
\(769\) −7.08253 −0.255403 −0.127701 0.991813i \(-0.540760\pi\)
−0.127701 + 0.991813i \(0.540760\pi\)
\(770\) 2.90887 1.82836i 0.104828 0.0658896i
\(771\) 0 0
\(772\) −2.65310 + 5.51337i −0.0954872 + 0.198430i
\(773\) −30.3534 + 12.5728i −1.09173 + 0.452211i −0.854611 0.519268i \(-0.826204\pi\)
−0.237123 + 0.971480i \(0.576204\pi\)
\(774\) 0 0
\(775\) −5.08838 5.08838i −0.182780 0.182780i
\(776\) −5.89891 52.1475i −0.211758 1.87199i
\(777\) 0 0
\(778\) 18.4697 26.0388i 0.662172 0.933535i
\(779\) 1.10808 0.458981i 0.0397011 0.0164447i
\(780\) 0 0
\(781\) 9.17464 22.1495i 0.328294 0.792573i
\(782\) −20.1579 4.59780i −0.720846 0.164417i
\(783\) 0 0
\(784\) 36.4501 29.1031i 1.30179 1.03939i
\(785\) 1.65394 0.0590316
\(786\) 0 0
\(787\) −37.1276 15.3788i −1.32346 0.548194i −0.394675 0.918821i \(-0.629143\pi\)