Properties

Label 280.2.bo.a.33.3
Level $280$
Weight $2$
Character 280.33
Analytic conductor $2.236$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bo (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 33.3
Character \(\chi\) \(=\) 280.33
Dual form 280.2.bo.a.17.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00047 - 0.536025i) q^{3} +(1.38383 - 1.75642i) q^{5} +(1.24986 + 2.33192i) q^{7} +(1.11649 + 0.644605i) q^{9} +O(q^{10})\) \(q+(-2.00047 - 0.536025i) q^{3} +(1.38383 - 1.75642i) q^{5} +(1.24986 + 2.33192i) q^{7} +(1.11649 + 0.644605i) q^{9} +(-3.09606 - 5.36253i) q^{11} +(0.782930 - 0.782930i) q^{13} +(-3.70979 + 2.77191i) q^{15} +(1.18027 - 4.40483i) q^{17} +(2.37523 - 4.11401i) q^{19} +(-1.25033 - 5.33490i) q^{21} +(-6.52089 + 1.74727i) q^{23} +(-1.17005 - 4.86117i) q^{25} +(2.50536 + 2.50536i) q^{27} -5.30715i q^{29} +(2.16657 - 1.25087i) q^{31} +(3.31913 + 12.3871i) q^{33} +(5.82543 + 1.03170i) q^{35} +(1.77376 + 6.61976i) q^{37} +(-1.98590 + 1.14656i) q^{39} +2.51428i q^{41} +(0.404551 + 0.404551i) q^{43} +(2.67723 - 1.06901i) q^{45} +(8.63838 - 2.31465i) q^{47} +(-3.87572 + 5.82913i) q^{49} +(-4.72220 + 8.17909i) q^{51} +(-2.66008 + 9.92755i) q^{53} +(-13.7033 - 1.98282i) q^{55} +(-6.95679 + 6.95679i) q^{57} +(0.0710796 + 0.123113i) q^{59} +(2.67752 + 1.54587i) q^{61} +(-0.107719 + 3.40923i) q^{63} +(-0.291718 - 2.45860i) q^{65} +(-4.34482 - 1.16419i) q^{67} +13.9814 q^{69} +10.3517 q^{71} +(-1.80614 - 0.483952i) q^{73} +(-0.265056 + 10.3518i) q^{75} +(8.63537 - 13.9221i) q^{77} +(5.42390 + 3.13149i) q^{79} +(-5.60278 - 9.70431i) q^{81} +(5.82768 - 5.82768i) q^{83} +(-6.10346 - 8.16858i) q^{85} +(-2.84477 + 10.6168i) q^{87} +(-4.58578 + 7.94281i) q^{89} +(2.80428 + 0.847183i) q^{91} +(-5.00466 + 1.34100i) q^{93} +(-3.93905 - 9.86498i) q^{95} +(2.64580 + 2.64580i) q^{97} -7.98294i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 4q^{7} + O(q^{10}) \) \( 48q - 4q^{7} + 4q^{11} + 8q^{15} - 4q^{21} - 4q^{23} - 8q^{25} - 36q^{33} + 24q^{35} + 8q^{37} - 16q^{43} + 48q^{45} + 24q^{51} + 16q^{53} - 96q^{57} - 36q^{61} - 68q^{63} + 12q^{65} - 16q^{67} - 64q^{71} - 48q^{73} - 48q^{75} + 4q^{77} - 40q^{85} - 12q^{87} - 80q^{91} + 24q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.00047 0.536025i −1.15497 0.309474i −0.370017 0.929025i \(-0.620648\pi\)
−0.784956 + 0.619551i \(0.787315\pi\)
\(4\) 0 0
\(5\) 1.38383 1.75642i 0.618866 0.785497i
\(6\) 0 0
\(7\) 1.24986 + 2.33192i 0.472401 + 0.881384i
\(8\) 0 0
\(9\) 1.11649 + 0.644605i 0.372163 + 0.214868i
\(10\) 0 0
\(11\) −3.09606 5.36253i −0.933496 1.61686i −0.777294 0.629138i \(-0.783408\pi\)
−0.156202 0.987725i \(-0.549925\pi\)
\(12\) 0 0
\(13\) 0.782930 0.782930i 0.217146 0.217146i −0.590149 0.807294i \(-0.700931\pi\)
0.807294 + 0.590149i \(0.200931\pi\)
\(14\) 0 0
\(15\) −3.70979 + 2.77191i −0.957864 + 0.715705i
\(16\) 0 0
\(17\) 1.18027 4.40483i 0.286258 1.06833i −0.661658 0.749806i \(-0.730147\pi\)
0.947915 0.318522i \(-0.103187\pi\)
\(18\) 0 0
\(19\) 2.37523 4.11401i 0.544914 0.943819i −0.453698 0.891156i \(-0.649895\pi\)
0.998612 0.0526638i \(-0.0167712\pi\)
\(20\) 0 0
\(21\) −1.25033 5.33490i −0.272845 1.16417i
\(22\) 0 0
\(23\) −6.52089 + 1.74727i −1.35970 + 0.364330i −0.863706 0.503996i \(-0.831863\pi\)
−0.495993 + 0.868326i \(0.665196\pi\)
\(24\) 0 0
\(25\) −1.17005 4.86117i −0.234010 0.972234i
\(26\) 0 0
\(27\) 2.50536 + 2.50536i 0.482157 + 0.482157i
\(28\) 0 0
\(29\) 5.30715i 0.985514i −0.870167 0.492757i \(-0.835989\pi\)
0.870167 0.492757i \(-0.164011\pi\)
\(30\) 0 0
\(31\) 2.16657 1.25087i 0.389128 0.224663i −0.292654 0.956218i \(-0.594539\pi\)
0.681782 + 0.731555i \(0.261205\pi\)
\(32\) 0 0
\(33\) 3.31913 + 12.3871i 0.577786 + 2.15633i
\(34\) 0 0
\(35\) 5.82543 + 1.03170i 0.984677 + 0.174389i
\(36\) 0 0
\(37\) 1.77376 + 6.61976i 0.291604 + 1.08828i 0.943877 + 0.330298i \(0.107149\pi\)
−0.652273 + 0.757984i \(0.726184\pi\)
\(38\) 0 0
\(39\) −1.98590 + 1.14656i −0.317998 + 0.183596i
\(40\) 0 0
\(41\) 2.51428i 0.392665i 0.980537 + 0.196333i \(0.0629032\pi\)
−0.980537 + 0.196333i \(0.937097\pi\)
\(42\) 0 0
\(43\) 0.404551 + 0.404551i 0.0616934 + 0.0616934i 0.737280 0.675587i \(-0.236110\pi\)
−0.675587 + 0.737280i \(0.736110\pi\)
\(44\) 0 0
\(45\) 2.67723 1.06901i 0.399097 0.159358i
\(46\) 0 0
\(47\) 8.63838 2.31465i 1.26004 0.337626i 0.433832 0.900994i \(-0.357161\pi\)
0.826206 + 0.563368i \(0.190495\pi\)
\(48\) 0 0
\(49\) −3.87572 + 5.82913i −0.553675 + 0.832733i
\(50\) 0 0
\(51\) −4.72220 + 8.17909i −0.661240 + 1.14530i
\(52\) 0 0
\(53\) −2.66008 + 9.92755i −0.365390 + 1.36365i 0.501502 + 0.865157i \(0.332781\pi\)
−0.866892 + 0.498497i \(0.833886\pi\)
\(54\) 0 0
\(55\) −13.7033 1.98282i −1.84775 0.267363i
\(56\) 0 0
\(57\) −6.95679 + 6.95679i −0.921449 + 0.921449i
\(58\) 0 0
\(59\) 0.0710796 + 0.123113i 0.00925377 + 0.0160280i 0.870615 0.491965i \(-0.163721\pi\)
−0.861361 + 0.507993i \(0.830388\pi\)
\(60\) 0 0
\(61\) 2.67752 + 1.54587i 0.342822 + 0.197928i 0.661519 0.749928i \(-0.269912\pi\)
−0.318697 + 0.947856i \(0.603245\pi\)
\(62\) 0 0
\(63\) −0.107719 + 3.40923i −0.0135714 + 0.429523i
\(64\) 0 0
\(65\) −0.291718 2.45860i −0.0361832 0.304951i
\(66\) 0 0
\(67\) −4.34482 1.16419i −0.530804 0.142228i −0.0165444 0.999863i \(-0.505266\pi\)
−0.514259 + 0.857635i \(0.671933\pi\)
\(68\) 0 0
\(69\) 13.9814 1.68317
\(70\) 0 0
\(71\) 10.3517 1.22852 0.614258 0.789105i \(-0.289455\pi\)
0.614258 + 0.789105i \(0.289455\pi\)
\(72\) 0 0
\(73\) −1.80614 0.483952i −0.211392 0.0566424i 0.151569 0.988447i \(-0.451567\pi\)
−0.362961 + 0.931804i \(0.618234\pi\)
\(74\) 0 0
\(75\) −0.265056 + 10.3518i −0.0306060 + 1.19532i
\(76\) 0 0
\(77\) 8.63537 13.9221i 0.984092 1.58658i
\(78\) 0 0
\(79\) 5.42390 + 3.13149i 0.610236 + 0.352320i 0.773058 0.634336i \(-0.218726\pi\)
−0.162822 + 0.986655i \(0.552060\pi\)
\(80\) 0 0
\(81\) −5.60278 9.70431i −0.622532 1.07826i
\(82\) 0 0
\(83\) 5.82768 5.82768i 0.639671 0.639671i −0.310803 0.950474i \(-0.600598\pi\)
0.950474 + 0.310803i \(0.100598\pi\)
\(84\) 0 0
\(85\) −6.10346 8.16858i −0.662013 0.886007i
\(86\) 0 0
\(87\) −2.84477 + 10.6168i −0.304991 + 1.13824i
\(88\) 0 0
\(89\) −4.58578 + 7.94281i −0.486092 + 0.841936i −0.999872 0.0159859i \(-0.994911\pi\)
0.513780 + 0.857922i \(0.328245\pi\)
\(90\) 0 0
\(91\) 2.80428 + 0.847183i 0.293969 + 0.0888089i
\(92\) 0 0
\(93\) −5.00466 + 1.34100i −0.518960 + 0.139055i
\(94\) 0 0
\(95\) −3.93905 9.86498i −0.404138 1.01213i
\(96\) 0 0
\(97\) 2.64580 + 2.64580i 0.268641 + 0.268641i 0.828552 0.559912i \(-0.189165\pi\)
−0.559912 + 0.828552i \(0.689165\pi\)
\(98\) 0 0
\(99\) 7.98294i 0.802315i
\(100\) 0 0
\(101\) −4.36323 + 2.51911i −0.434157 + 0.250661i −0.701116 0.713047i \(-0.747315\pi\)
0.266959 + 0.963708i \(0.413981\pi\)
\(102\) 0 0
\(103\) 0.710053 + 2.64995i 0.0699636 + 0.261108i 0.992044 0.125890i \(-0.0401787\pi\)
−0.922081 + 0.386998i \(0.873512\pi\)
\(104\) 0 0
\(105\) −11.1006 5.18646i −1.08331 0.506147i
\(106\) 0 0
\(107\) −3.79590 14.1665i −0.366963 1.36953i −0.864740 0.502221i \(-0.832517\pi\)
0.497776 0.867306i \(-0.334150\pi\)
\(108\) 0 0
\(109\) 13.0388 7.52797i 1.24889 0.721049i 0.278005 0.960580i \(-0.410327\pi\)
0.970889 + 0.239531i \(0.0769936\pi\)
\(110\) 0 0
\(111\) 14.1934i 1.34718i
\(112\) 0 0
\(113\) 1.41309 + 1.41309i 0.132932 + 0.132932i 0.770442 0.637510i \(-0.220035\pi\)
−0.637510 + 0.770442i \(0.720035\pi\)
\(114\) 0 0
\(115\) −5.95483 + 13.8714i −0.555291 + 1.29351i
\(116\) 0 0
\(117\) 1.37881 0.369452i 0.127471 0.0341558i
\(118\) 0 0
\(119\) 11.7469 2.75310i 1.07684 0.252376i
\(120\) 0 0
\(121\) −13.6711 + 23.6791i −1.24283 + 2.15264i
\(122\) 0 0
\(123\) 1.34772 5.02976i 0.121520 0.453518i
\(124\) 0 0
\(125\) −10.1574 4.67191i −0.908508 0.417868i
\(126\) 0 0
\(127\) −4.61249 + 4.61249i −0.409292 + 0.409292i −0.881492 0.472200i \(-0.843460\pi\)
0.472200 + 0.881492i \(0.343460\pi\)
\(128\) 0 0
\(129\) −0.592443 1.02614i −0.0521617 0.0903467i
\(130\) 0 0
\(131\) 17.5930 + 10.1573i 1.53711 + 0.887448i 0.999006 + 0.0445661i \(0.0141905\pi\)
0.538099 + 0.842882i \(0.319143\pi\)
\(132\) 0 0
\(133\) 12.5622 + 0.396922i 1.08929 + 0.0344175i
\(134\) 0 0
\(135\) 7.86746 0.933492i 0.677123 0.0803422i
\(136\) 0 0
\(137\) 6.84734 + 1.83474i 0.585008 + 0.156752i 0.539171 0.842197i \(-0.318738\pi\)
0.0458371 + 0.998949i \(0.485404\pi\)
\(138\) 0 0
\(139\) −7.94314 −0.673728 −0.336864 0.941553i \(-0.609366\pi\)
−0.336864 + 0.941553i \(0.609366\pi\)
\(140\) 0 0
\(141\) −18.5216 −1.55980
\(142\) 0 0
\(143\) −6.62248 1.77449i −0.553799 0.148390i
\(144\) 0 0
\(145\) −9.32161 7.34418i −0.774118 0.609901i
\(146\) 0 0
\(147\) 10.8778 9.58353i 0.897189 0.790436i
\(148\) 0 0
\(149\) −2.61568 1.51016i −0.214285 0.123717i 0.389016 0.921231i \(-0.372815\pi\)
−0.603301 + 0.797514i \(0.706148\pi\)
\(150\) 0 0
\(151\) 2.00848 + 3.47878i 0.163447 + 0.283099i 0.936103 0.351726i \(-0.114405\pi\)
−0.772655 + 0.634826i \(0.781072\pi\)
\(152\) 0 0
\(153\) 4.15714 4.15714i 0.336085 0.336085i
\(154\) 0 0
\(155\) 0.801099 5.53641i 0.0643459 0.444695i
\(156\) 0 0
\(157\) 0.989145 3.69154i 0.0789424 0.294617i −0.915156 0.403100i \(-0.867933\pi\)
0.994098 + 0.108483i \(0.0345993\pi\)
\(158\) 0 0
\(159\) 10.6428 18.4339i 0.844031 1.46190i
\(160\) 0 0
\(161\) −12.2247 13.0224i −0.963438 1.02631i
\(162\) 0 0
\(163\) −8.52498 + 2.28426i −0.667728 + 0.178917i −0.576731 0.816934i \(-0.695672\pi\)
−0.0909967 + 0.995851i \(0.529005\pi\)
\(164\) 0 0
\(165\) 26.3502 + 11.3119i 2.05136 + 0.880628i
\(166\) 0 0
\(167\) 5.91156 + 5.91156i 0.457450 + 0.457450i 0.897818 0.440367i \(-0.145152\pi\)
−0.440367 + 0.897818i \(0.645152\pi\)
\(168\) 0 0
\(169\) 11.7740i 0.905695i
\(170\) 0 0
\(171\) 5.30383 3.06217i 0.405594 0.234170i
\(172\) 0 0
\(173\) −5.80426 21.6618i −0.441290 1.64692i −0.725550 0.688170i \(-0.758414\pi\)
0.284260 0.958747i \(-0.408252\pi\)
\(174\) 0 0
\(175\) 9.87348 8.80423i 0.746365 0.665537i
\(176\) 0 0
\(177\) −0.0762008 0.284385i −0.00572760 0.0213757i
\(178\) 0 0
\(179\) −9.81825 + 5.66857i −0.733850 + 0.423689i −0.819829 0.572608i \(-0.805932\pi\)
0.0859789 + 0.996297i \(0.472598\pi\)
\(180\) 0 0
\(181\) 8.90901i 0.662201i −0.943595 0.331101i \(-0.892580\pi\)
0.943595 0.331101i \(-0.107420\pi\)
\(182\) 0 0
\(183\) −4.52768 4.52768i −0.334696 0.334696i
\(184\) 0 0
\(185\) 14.0817 + 6.04512i 1.03531 + 0.444446i
\(186\) 0 0
\(187\) −27.2752 + 7.30837i −1.99456 + 0.534441i
\(188\) 0 0
\(189\) −2.71097 + 8.97364i −0.197194 + 0.652737i
\(190\) 0 0
\(191\) 8.07475 13.9859i 0.584268 1.01198i −0.410698 0.911771i \(-0.634715\pi\)
0.994966 0.100211i \(-0.0319517\pi\)
\(192\) 0 0
\(193\) −0.102134 + 0.381168i −0.00735174 + 0.0274371i −0.969504 0.245074i \(-0.921188\pi\)
0.962153 + 0.272511i \(0.0878543\pi\)
\(194\) 0 0
\(195\) −0.734295 + 5.07472i −0.0525839 + 0.363408i
\(196\) 0 0
\(197\) −8.65729 + 8.65729i −0.616806 + 0.616806i −0.944711 0.327904i \(-0.893658\pi\)
0.327904 + 0.944711i \(0.393658\pi\)
\(198\) 0 0
\(199\) −4.96288 8.59596i −0.351809 0.609351i 0.634757 0.772711i \(-0.281100\pi\)
−0.986566 + 0.163360i \(0.947767\pi\)
\(200\) 0 0
\(201\) 8.06765 + 4.65786i 0.569048 + 0.328540i
\(202\) 0 0
\(203\) 12.3759 6.63318i 0.868616 0.465558i
\(204\) 0 0
\(205\) 4.41615 + 3.47933i 0.308437 + 0.243007i
\(206\) 0 0
\(207\) −8.40680 2.25259i −0.584313 0.156566i
\(208\) 0 0
\(209\) −29.4153 −2.03470
\(210\) 0 0
\(211\) 9.25891 0.637410 0.318705 0.947854i \(-0.396752\pi\)
0.318705 + 0.947854i \(0.396752\pi\)
\(212\) 0 0
\(213\) −20.7082 5.54875i −1.41890 0.380194i
\(214\) 0 0
\(215\) 1.27039 0.150735i 0.0866399 0.0102800i
\(216\) 0 0
\(217\) 5.62484 + 3.48887i 0.381839 + 0.236840i
\(218\) 0 0
\(219\) 3.35371 + 1.93627i 0.226623 + 0.130841i
\(220\) 0 0
\(221\) −2.52461 4.37274i −0.169823 0.294143i
\(222\) 0 0
\(223\) 2.26542 2.26542i 0.151703 0.151703i −0.627175 0.778878i \(-0.715789\pi\)
0.778878 + 0.627175i \(0.215789\pi\)
\(224\) 0 0
\(225\) 1.82719 6.18167i 0.121813 0.412111i
\(226\) 0 0
\(227\) −5.72434 + 21.3635i −0.379938 + 1.41795i 0.466057 + 0.884755i \(0.345674\pi\)
−0.845994 + 0.533192i \(0.820992\pi\)
\(228\) 0 0
\(229\) −3.16366 + 5.47963i −0.209061 + 0.362104i −0.951419 0.307899i \(-0.900374\pi\)
0.742358 + 0.670003i \(0.233707\pi\)
\(230\) 0 0
\(231\) −24.7374 + 23.2221i −1.62760 + 1.52790i
\(232\) 0 0
\(233\) 10.1387 2.71667i 0.664211 0.177975i 0.0890650 0.996026i \(-0.471612\pi\)
0.575145 + 0.818051i \(0.304945\pi\)
\(234\) 0 0
\(235\) 7.88852 18.3757i 0.514590 1.19870i
\(236\) 0 0
\(237\) −9.17180 9.17180i −0.595772 0.595772i
\(238\) 0 0
\(239\) 2.87268i 0.185818i 0.995675 + 0.0929091i \(0.0296166\pi\)
−0.995675 + 0.0929091i \(0.970383\pi\)
\(240\) 0 0
\(241\) 25.6935 14.8342i 1.65507 0.955553i 0.680124 0.733097i \(-0.261926\pi\)
0.974943 0.222456i \(-0.0714074\pi\)
\(242\) 0 0
\(243\) 3.25539 + 12.1493i 0.208833 + 0.779376i
\(244\) 0 0
\(245\) 4.87510 + 14.8739i 0.311459 + 0.950260i
\(246\) 0 0
\(247\) −1.36135 5.08062i −0.0866205 0.323272i
\(248\) 0 0
\(249\) −14.7819 + 8.53433i −0.936764 + 0.540841i
\(250\) 0 0
\(251\) 15.0696i 0.951182i 0.879667 + 0.475591i \(0.157766\pi\)
−0.879667 + 0.475591i \(0.842234\pi\)
\(252\) 0 0
\(253\) 29.5588 + 29.5588i 1.85835 + 1.85835i
\(254\) 0 0
\(255\) 7.83124 + 19.6126i 0.490412 + 1.22819i
\(256\) 0 0
\(257\) 22.7927 6.10728i 1.42177 0.380962i 0.535658 0.844435i \(-0.320064\pi\)
0.886111 + 0.463474i \(0.153397\pi\)
\(258\) 0 0
\(259\) −13.2198 + 12.4100i −0.821440 + 0.771121i
\(260\) 0 0
\(261\) 3.42102 5.92538i 0.211756 0.366772i
\(262\) 0 0
\(263\) −5.21774 + 19.4729i −0.321739 + 1.20075i 0.595810 + 0.803126i \(0.296831\pi\)
−0.917549 + 0.397622i \(0.869835\pi\)
\(264\) 0 0
\(265\) 13.7559 + 18.4102i 0.845018 + 1.13093i
\(266\) 0 0
\(267\) 13.4313 13.4313i 0.821980 0.821980i
\(268\) 0 0
\(269\) −6.41634 11.1134i −0.391211 0.677597i 0.601399 0.798949i \(-0.294610\pi\)
−0.992610 + 0.121352i \(0.961277\pi\)
\(270\) 0 0
\(271\) 1.51548 + 0.874961i 0.0920587 + 0.0531501i 0.545323 0.838226i \(-0.316407\pi\)
−0.453264 + 0.891376i \(0.649740\pi\)
\(272\) 0 0
\(273\) −5.15577 3.19793i −0.312042 0.193547i
\(274\) 0 0
\(275\) −22.4456 + 21.3249i −1.35352 + 1.28594i
\(276\) 0 0
\(277\) 5.44886 + 1.46002i 0.327390 + 0.0877240i 0.418770 0.908092i \(-0.362461\pi\)
−0.0913802 + 0.995816i \(0.529128\pi\)
\(278\) 0 0
\(279\) 3.22527 0.193092
\(280\) 0 0
\(281\) 18.7713 1.11980 0.559901 0.828560i \(-0.310839\pi\)
0.559901 + 0.828560i \(0.310839\pi\)
\(282\) 0 0
\(283\) −12.0479 3.22822i −0.716172 0.191898i −0.117709 0.993048i \(-0.537555\pi\)
−0.598463 + 0.801150i \(0.704222\pi\)
\(284\) 0 0
\(285\) 2.59208 + 21.8461i 0.153542 + 1.29405i
\(286\) 0 0
\(287\) −5.86312 + 3.14249i −0.346089 + 0.185495i
\(288\) 0 0
\(289\) −3.28707 1.89779i −0.193357 0.111635i
\(290\) 0 0
\(291\) −3.87464 6.71107i −0.227135 0.393410i
\(292\) 0 0
\(293\) 0.810657 0.810657i 0.0473591 0.0473591i −0.683031 0.730390i \(-0.739338\pi\)
0.730390 + 0.683031i \(0.239338\pi\)
\(294\) 0 0
\(295\) 0.314601 + 0.0455217i 0.0183168 + 0.00265038i
\(296\) 0 0
\(297\) 5.67833 21.1918i 0.329490 1.22967i
\(298\) 0 0
\(299\) −3.73741 + 6.47339i −0.216140 + 0.374366i
\(300\) 0 0
\(301\) −0.437751 + 1.44901i −0.0252315 + 0.0835196i
\(302\) 0 0
\(303\) 10.0788 2.70061i 0.579013 0.155146i
\(304\) 0 0
\(305\) 6.42042 2.56365i 0.367632 0.146794i
\(306\) 0 0
\(307\) 4.68380 + 4.68380i 0.267319 + 0.267319i 0.828019 0.560700i \(-0.189468\pi\)
−0.560700 + 0.828019i \(0.689468\pi\)
\(308\) 0 0
\(309\) 5.68177i 0.323224i
\(310\) 0 0
\(311\) 5.90190 3.40747i 0.334666 0.193220i −0.323245 0.946315i \(-0.604774\pi\)
0.657911 + 0.753096i \(0.271440\pi\)
\(312\) 0 0
\(313\) −6.97836 26.0436i −0.394440 1.47207i −0.822731 0.568430i \(-0.807551\pi\)
0.428291 0.903641i \(-0.359116\pi\)
\(314\) 0 0
\(315\) 5.83899 + 4.90698i 0.328990 + 0.276477i
\(316\) 0 0
\(317\) −4.81685 17.9767i −0.270541 1.00967i −0.958771 0.284180i \(-0.908279\pi\)
0.688230 0.725493i \(-0.258388\pi\)
\(318\) 0 0
\(319\) −28.4598 + 16.4313i −1.59344 + 0.919973i
\(320\) 0 0
\(321\) 30.3744i 1.69533i
\(322\) 0 0
\(323\) −15.3181 15.3181i −0.852323 0.852323i
\(324\) 0 0
\(325\) −4.72202 2.88989i −0.261931 0.160302i
\(326\) 0 0
\(327\) −30.1190 + 8.07036i −1.66558 + 0.446292i
\(328\) 0 0
\(329\) 16.1943 + 17.2511i 0.892821 + 0.951082i
\(330\) 0 0
\(331\) 7.03546 12.1858i 0.386704 0.669791i −0.605300 0.795997i \(-0.706947\pi\)
0.992004 + 0.126206i \(0.0402802\pi\)
\(332\) 0 0
\(333\) −2.28675 + 8.53427i −0.125313 + 0.467675i
\(334\) 0 0
\(335\) −8.05728 + 6.02030i −0.440216 + 0.328924i
\(336\) 0 0
\(337\) −21.1500 + 21.1500i −1.15212 + 1.15212i −0.165988 + 0.986128i \(0.553081\pi\)
−0.986128 + 0.165988i \(0.946919\pi\)
\(338\) 0 0
\(339\) −2.06940 3.58430i −0.112394 0.194673i
\(340\) 0 0
\(341\) −13.4157 7.74553i −0.726499 0.419444i
\(342\) 0 0
\(343\) −18.4372 1.75231i −0.995514 0.0946160i
\(344\) 0 0
\(345\) 19.3479 24.5573i 1.04165 1.32212i
\(346\) 0 0
\(347\) −4.07182 1.09104i −0.218587 0.0585701i 0.147864 0.989008i \(-0.452760\pi\)
−0.366450 + 0.930438i \(0.619427\pi\)
\(348\) 0 0
\(349\) 37.0391 1.98266 0.991329 0.131407i \(-0.0419495\pi\)
0.991329 + 0.131407i \(0.0419495\pi\)
\(350\) 0 0
\(351\) 3.92304 0.209397
\(352\) 0 0
\(353\) 22.7295 + 6.09034i 1.20977 + 0.324156i 0.806671 0.591001i \(-0.201267\pi\)
0.403096 + 0.915157i \(0.367934\pi\)
\(354\) 0 0
\(355\) 14.3249 18.1819i 0.760287 0.964995i
\(356\) 0 0
\(357\) −24.9751 0.789123i −1.32182 0.0417648i
\(358\) 0 0
\(359\) 17.5695 + 10.1437i 0.927281 + 0.535366i 0.885951 0.463780i \(-0.153507\pi\)
0.0413304 + 0.999146i \(0.486840\pi\)
\(360\) 0 0
\(361\) −1.78340 3.08894i −0.0938633 0.162576i
\(362\) 0 0
\(363\) 40.0413 40.0413i 2.10162 2.10162i
\(364\) 0 0
\(365\) −3.34940 + 2.50263i −0.175316 + 0.130994i
\(366\) 0 0
\(367\) 2.92561 10.9185i 0.152715 0.569942i −0.846575 0.532270i \(-0.821339\pi\)
0.999290 0.0376718i \(-0.0119941\pi\)
\(368\) 0 0
\(369\) −1.62072 + 2.80717i −0.0843714 + 0.146136i
\(370\) 0 0
\(371\) −26.4750 + 6.20490i −1.37451 + 0.322142i
\(372\) 0 0
\(373\) 12.8568 3.44497i 0.665700 0.178374i 0.0898828 0.995952i \(-0.471351\pi\)
0.575817 + 0.817579i \(0.304684\pi\)
\(374\) 0 0
\(375\) 17.8154 + 14.7907i 0.919982 + 0.763786i
\(376\) 0 0
\(377\) −4.15513 4.15513i −0.214000 0.214000i
\(378\) 0 0
\(379\) 11.7429i 0.603191i −0.953436 0.301595i \(-0.902481\pi\)
0.953436 0.301595i \(-0.0975191\pi\)
\(380\) 0 0
\(381\) 11.6996 6.75474i 0.599387 0.346056i
\(382\) 0 0
\(383\) −8.49569 31.7063i −0.434109 1.62012i −0.743188 0.669082i \(-0.766687\pi\)
0.309079 0.951036i \(-0.399979\pi\)
\(384\) 0 0
\(385\) −12.5033 34.4332i −0.637229 1.75488i
\(386\) 0 0
\(387\) 0.190901 + 0.712452i 0.00970404 + 0.0362160i
\(388\) 0 0
\(389\) −14.7903 + 8.53916i −0.749895 + 0.432952i −0.825656 0.564174i \(-0.809195\pi\)
0.0757607 + 0.997126i \(0.475862\pi\)
\(390\) 0 0
\(391\) 30.7857i 1.55690i
\(392\) 0 0
\(393\) −29.7497 29.7497i −1.50067 1.50067i
\(394\) 0 0
\(395\) 13.0060 5.19323i 0.654400 0.261300i
\(396\) 0 0
\(397\) −11.6115 + 3.11129i −0.582764 + 0.156151i −0.538144 0.842853i \(-0.680874\pi\)
−0.0446201 + 0.999004i \(0.514208\pi\)
\(398\) 0 0
\(399\) −24.9177 7.52771i −1.24744 0.376857i
\(400\) 0 0
\(401\) −12.4166 + 21.5062i −0.620055 + 1.07397i 0.369420 + 0.929263i \(0.379556\pi\)
−0.989475 + 0.144704i \(0.953777\pi\)
\(402\) 0 0
\(403\) 0.716930 2.67562i 0.0357128 0.133282i
\(404\) 0 0
\(405\) −24.7982 3.58821i −1.23223 0.178300i
\(406\) 0 0
\(407\) 30.0070 30.0070i 1.48739 1.48739i
\(408\) 0 0
\(409\) −15.8290 27.4166i −0.782692 1.35566i −0.930368 0.366626i \(-0.880513\pi\)
0.147676 0.989036i \(-0.452821\pi\)
\(410\) 0 0
\(411\) −12.7144 7.34069i −0.627157 0.362089i
\(412\) 0 0
\(413\) −0.198252 + 0.319626i −0.00975533 + 0.0157278i
\(414\) 0 0
\(415\) −2.17138 18.3004i −0.106589 0.898330i
\(416\) 0 0
\(417\) 15.8900 + 4.25772i 0.778138 + 0.208501i
\(418\) 0 0
\(419\) 6.53217 0.319118 0.159559 0.987188i \(-0.448993\pi\)
0.159559 + 0.987188i \(0.448993\pi\)
\(420\) 0 0
\(421\) 23.0995 1.12580 0.562899 0.826525i \(-0.309686\pi\)
0.562899 + 0.826525i \(0.309686\pi\)
\(422\) 0 0
\(423\) 11.1367 + 2.98407i 0.541485 + 0.145090i
\(424\) 0 0
\(425\) −22.7936 0.583625i −1.10565 0.0283100i
\(426\) 0 0
\(427\) −0.258329 + 8.17588i −0.0125014 + 0.395659i
\(428\) 0 0
\(429\) 12.2969 + 7.09963i 0.593701 + 0.342773i
\(430\) 0 0
\(431\) −5.53350 9.58430i −0.266539 0.461660i 0.701427 0.712742i \(-0.252547\pi\)
−0.967966 + 0.251082i \(0.919214\pi\)
\(432\) 0 0
\(433\) 4.53425 4.53425i 0.217902 0.217902i −0.589712 0.807614i \(-0.700759\pi\)
0.807614 + 0.589712i \(0.200759\pi\)
\(434\) 0 0
\(435\) 14.7110 + 19.6884i 0.705337 + 0.943989i
\(436\) 0 0
\(437\) −8.30031 + 30.9772i −0.397058 + 1.48184i
\(438\) 0 0
\(439\) 9.10949 15.7781i 0.434772 0.753047i −0.562505 0.826794i \(-0.690162\pi\)
0.997277 + 0.0737466i \(0.0234956\pi\)
\(440\) 0 0
\(441\) −8.08469 + 4.00985i −0.384985 + 0.190945i
\(442\) 0 0
\(443\) 17.9720 4.81558i 0.853875 0.228795i 0.194773 0.980848i \(-0.437603\pi\)
0.659102 + 0.752053i \(0.270936\pi\)
\(444\) 0 0
\(445\) 7.60501 + 19.0460i 0.360512 + 0.902869i
\(446\) 0 0
\(447\) 4.42311 + 4.42311i 0.209206 + 0.209206i
\(448\) 0 0
\(449\) 32.4548i 1.53164i −0.643056 0.765819i \(-0.722334\pi\)
0.643056 0.765819i \(-0.277666\pi\)
\(450\) 0 0
\(451\) 13.4829 7.78437i 0.634886 0.366552i
\(452\) 0 0
\(453\) −2.15319 8.03580i −0.101165 0.377555i
\(454\) 0 0
\(455\) 5.36865 3.75315i 0.251686 0.175951i
\(456\) 0 0
\(457\) −2.40043 8.95853i −0.112287 0.419062i 0.886782 0.462187i \(-0.152935\pi\)
−0.999070 + 0.0431250i \(0.986269\pi\)
\(458\) 0 0
\(459\) 13.9927 8.07869i 0.653123 0.377081i
\(460\) 0 0
\(461\) 36.2380i 1.68777i 0.536521 + 0.843887i \(0.319738\pi\)
−0.536521 + 0.843887i \(0.680262\pi\)
\(462\) 0 0
\(463\) 6.39137 + 6.39137i 0.297032 + 0.297032i 0.839850 0.542818i \(-0.182643\pi\)
−0.542818 + 0.839850i \(0.682643\pi\)
\(464\) 0 0
\(465\) −4.57023 + 10.6460i −0.211939 + 0.493697i
\(466\) 0 0
\(467\) −3.18040 + 0.852186i −0.147171 + 0.0394345i −0.331653 0.943402i \(-0.607606\pi\)
0.184481 + 0.982836i \(0.440940\pi\)
\(468\) 0 0
\(469\) −2.71559 11.5868i −0.125394 0.535031i
\(470\) 0 0
\(471\) −3.95752 + 6.85462i −0.182353 + 0.315844i
\(472\) 0 0
\(473\) 0.916902 3.42193i 0.0421592 0.157340i
\(474\) 0 0
\(475\) −22.7781 6.73278i −1.04513 0.308921i
\(476\) 0 0
\(477\) −9.36930 + 9.36930i −0.428991 + 0.428991i
\(478\) 0 0
\(479\) 15.1734 + 26.2811i 0.693292 + 1.20082i 0.970753 + 0.240079i \(0.0771735\pi\)
−0.277462 + 0.960737i \(0.589493\pi\)
\(480\) 0 0
\(481\) 6.57154 + 3.79408i 0.299636 + 0.172995i
\(482\) 0 0
\(483\) 17.4748 + 32.6036i 0.795129 + 1.48352i
\(484\) 0 0
\(485\) 8.30848 0.985820i 0.377269 0.0447638i
\(486\) 0 0
\(487\) 28.1791 + 7.55058i 1.27692 + 0.342149i 0.832678 0.553758i \(-0.186807\pi\)
0.444241 + 0.895907i \(0.353473\pi\)
\(488\) 0 0
\(489\) 18.2784 0.826578
\(490\) 0 0
\(491\) −25.5532 −1.15320 −0.576600 0.817027i \(-0.695621\pi\)
−0.576600 + 0.817027i \(0.695621\pi\)
\(492\) 0 0
\(493\) −23.3771 6.26388i −1.05285 0.282111i
\(494\) 0 0
\(495\) −14.0214 11.0470i −0.630216 0.496526i
\(496\) 0 0
\(497\) 12.9381 + 24.1393i 0.580352 + 1.08279i
\(498\) 0 0
\(499\) −25.9209 14.9655i −1.16038 0.669946i −0.208985 0.977919i \(-0.567016\pi\)
−0.951395 + 0.307973i \(0.900349\pi\)
\(500\) 0 0
\(501\) −8.65717 14.9947i −0.386774 0.669912i
\(502\) 0 0
\(503\) −10.5316 + 10.5316i −0.469582 + 0.469582i −0.901779 0.432197i \(-0.857738\pi\)
0.432197 + 0.901779i \(0.357738\pi\)
\(504\) 0 0
\(505\) −1.61332 + 11.1497i −0.0717919 + 0.496154i
\(506\) 0 0
\(507\) 6.31118 23.5536i 0.280289 1.04605i
\(508\) 0 0
\(509\) −7.10159 + 12.3003i −0.314772 + 0.545202i −0.979389 0.201983i \(-0.935261\pi\)
0.664617 + 0.747184i \(0.268595\pi\)
\(510\) 0 0
\(511\) −1.12887 4.81664i −0.0499382 0.213075i
\(512\) 0 0
\(513\) 16.2579 4.35629i 0.717803 0.192335i
\(514\) 0 0
\(515\) 5.63703 + 2.41992i 0.248397 + 0.106635i
\(516\) 0 0
\(517\) −39.1573 39.1573i −1.72214 1.72214i
\(518\) 0 0
\(519\) 46.4451i 2.03871i
\(520\) 0 0
\(521\) −21.2944 + 12.2943i −0.932924 + 0.538624i −0.887735 0.460355i \(-0.847722\pi\)
−0.0451888 + 0.998978i \(0.514389\pi\)
\(522\) 0 0
\(523\) 8.19527 + 30.5852i 0.358354 + 1.33740i 0.876211 + 0.481929i \(0.160064\pi\)
−0.517856 + 0.855468i \(0.673270\pi\)
\(524\) 0 0
\(525\) −24.4709 + 12.3202i −1.06800 + 0.537697i
\(526\) 0 0
\(527\) −2.95273 11.0198i −0.128623 0.480028i
\(528\) 0 0
\(529\) 19.5505 11.2875i 0.850020 0.490759i
\(530\) 0 0
\(531\) 0.183273i 0.00795337i
\(532\) 0 0
\(533\) 1.96851 + 1.96851i 0.0852656 + 0.0852656i
\(534\) 0 0
\(535\) −30.1352 12.9367i −1.30286 0.559304i
\(536\) 0 0
\(537\) 22.6796 6.07699i 0.978698 0.262241i
\(538\) 0 0
\(539\) 43.2583 + 2.73635i 1.86327 + 0.117863i
\(540\) 0 0
\(541\) 10.8368 18.7700i 0.465912 0.806984i −0.533330 0.845907i \(-0.679060\pi\)
0.999242 + 0.0389236i \(0.0123929\pi\)
\(542\) 0 0
\(543\) −4.77545 + 17.8222i −0.204934 + 0.764824i
\(544\) 0 0
\(545\) 4.82116 33.3191i 0.206516 1.42723i
\(546\) 0 0
\(547\) −7.94707 + 7.94707i −0.339792 + 0.339792i −0.856289 0.516497i \(-0.827236\pi\)
0.516497 + 0.856289i \(0.327236\pi\)
\(548\) 0 0
\(549\) 1.99295 + 3.45189i 0.0850570 + 0.147323i
\(550\) 0 0
\(551\) −21.8337 12.6057i −0.930147 0.537021i
\(552\) 0 0
\(553\) −0.523300 + 16.5620i −0.0222530 + 0.704288i
\(554\) 0 0
\(555\) −24.9297 19.6412i −1.05821 0.833724i
\(556\) 0 0
\(557\) −14.1578 3.79358i −0.599886 0.160739i −0.0539186 0.998545i \(-0.517171\pi\)
−0.545968 + 0.837806i \(0.683838\pi\)
\(558\) 0 0
\(559\) 0.633470 0.0267929
\(560\) 0 0
\(561\) 58.4808 2.46906
\(562\) 0 0
\(563\) −22.8910 6.13364i −0.964742 0.258502i −0.258136 0.966109i \(-0.583108\pi\)
−0.706607 + 0.707607i \(0.749775\pi\)
\(564\) 0 0
\(565\) 4.43746 0.526515i 0.186685 0.0221506i
\(566\) 0 0
\(567\) 15.6270 25.1942i 0.656273 1.05806i
\(568\) 0 0
\(569\) −20.3034 11.7221i −0.851161 0.491418i 0.00988157 0.999951i \(-0.496855\pi\)
−0.861042 + 0.508533i \(0.830188\pi\)
\(570\) 0 0
\(571\) −1.81550 3.14454i −0.0759764 0.131595i 0.825534 0.564352i \(-0.190874\pi\)
−0.901510 + 0.432757i \(0.857541\pi\)
\(572\) 0 0
\(573\) −23.6501 + 23.6501i −0.987996 + 0.987996i
\(574\) 0 0
\(575\) 16.1235 + 29.6548i 0.672398 + 1.23669i
\(576\) 0 0
\(577\) −8.92952 + 33.3254i −0.371741 + 1.38736i 0.486308 + 0.873788i \(0.338343\pi\)
−0.858049 + 0.513568i \(0.828323\pi\)
\(578\) 0 0
\(579\) 0.408631 0.707769i 0.0169821 0.0294139i
\(580\) 0 0
\(581\) 20.8734 + 6.30594i 0.865977 + 0.261614i
\(582\) 0 0
\(583\) 61.4725 16.4715i 2.54593 0.682180i
\(584\) 0 0
\(585\) 1.25912 2.93304i 0.0520584 0.121266i
\(586\) 0 0
\(587\) −13.1856 13.1856i −0.544227 0.544227i 0.380538 0.924765i \(-0.375739\pi\)
−0.924765 + 0.380538i \(0.875739\pi\)
\(588\) 0 0
\(589\) 11.8844i 0.489688i
\(590\) 0 0
\(591\) 21.9592 12.6781i 0.903280 0.521509i
\(592\) 0 0
\(593\) −5.19125 19.3740i −0.213179 0.795595i −0.986800 0.161946i \(-0.948223\pi\)
0.773621 0.633649i \(-0.218444\pi\)
\(594\) 0 0
\(595\) 11.4200 24.4423i 0.468176 1.00204i
\(596\) 0 0
\(597\) 5.32045 + 19.8562i 0.217752 + 0.812660i
\(598\) 0 0
\(599\) −29.2830 + 16.9065i −1.19647 + 0.690783i −0.959767 0.280799i \(-0.909401\pi\)
−0.236704 + 0.971582i \(0.576067\pi\)
\(600\) 0 0
\(601\) 6.43168i 0.262354i 0.991359 + 0.131177i \(0.0418756\pi\)
−0.991359 + 0.131177i \(0.958124\pi\)
\(602\) 0 0
\(603\) −4.10050 4.10050i −0.166985 0.166985i
\(604\) 0 0
\(605\) 22.6721 + 56.7801i 0.921750 + 2.30844i
\(606\) 0 0
\(607\) −3.68755 + 0.988075i −0.149673 + 0.0401047i −0.332878 0.942970i \(-0.608020\pi\)
0.183205 + 0.983075i \(0.441353\pi\)
\(608\) 0 0
\(609\) −28.3131 + 6.63571i −1.14731 + 0.268892i
\(610\) 0 0
\(611\) 4.95104 8.57546i 0.200298 0.346926i
\(612\) 0 0
\(613\) −11.8572 + 44.2518i −0.478909 + 1.78731i 0.127138 + 0.991885i \(0.459421\pi\)
−0.606047 + 0.795429i \(0.707246\pi\)
\(614\) 0 0
\(615\) −6.96938 9.32747i −0.281032 0.376120i
\(616\) 0 0
\(617\) 15.0385 15.0385i 0.605429 0.605429i −0.336319 0.941748i \(-0.609182\pi\)
0.941748 + 0.336319i \(0.109182\pi\)
\(618\) 0 0
\(619\) −0.630180 1.09150i −0.0253291 0.0438712i 0.853083 0.521775i \(-0.174730\pi\)
−0.878412 + 0.477904i \(0.841397\pi\)
\(620\) 0 0
\(621\) −20.7147 11.9596i −0.831253 0.479924i
\(622\) 0 0
\(623\) −24.2536 0.766326i −0.971699 0.0307022i
\(624\) 0 0
\(625\) −22.2620 + 11.3756i −0.890479 + 0.455025i
\(626\) 0 0
\(627\) 58.8446 + 15.7674i 2.35003 + 0.629688i
\(628\) 0 0
\(629\) 31.2525 1.24612
\(630\) 0 0
\(631\) −28.6052 −1.13876 −0.569378 0.822076i \(-0.692816\pi\)
−0.569378 + 0.822076i \(0.692816\pi\)
\(632\) 0 0
\(633\) −18.5222 4.96301i −0.736191 0.197262i
\(634\) 0 0
\(635\) 1.71860 + 14.4844i 0.0682007 + 0.574794i
\(636\) 0 0
\(637\) 1.52938 + 7.59822i 0.0605963 + 0.301052i
\(638\) 0 0
\(639\) 11.5575 + 6.67274i 0.457208 + 0.263969i
\(640\) 0 0
\(641\) 5.62256 + 9.73856i 0.222078 + 0.384650i 0.955439 0.295190i \(-0.0953828\pi\)
−0.733361 + 0.679839i \(0.762049\pi\)
\(642\) 0 0
\(643\) −34.9847 + 34.9847i −1.37966 + 1.37966i −0.534485 + 0.845178i \(0.679494\pi\)
−0.845178 + 0.534485i \(0.820506\pi\)
\(644\) 0 0
\(645\) −2.62218 0.379420i −0.103248 0.0149397i
\(646\) 0 0
\(647\) −4.92794 + 18.3913i −0.193737 + 0.723038i 0.798853 + 0.601527i \(0.205441\pi\)
−0.992590 + 0.121511i \(0.961226\pi\)
\(648\) 0 0
\(649\) 0.440133 0.762332i 0.0172767 0.0299242i
\(650\) 0 0
\(651\) −9.38220 9.99444i −0.367718 0.391713i
\(652\) 0 0
\(653\) −35.7631 + 9.58269i −1.39952 + 0.375000i −0.878171 0.478346i \(-0.841237\pi\)
−0.521346 + 0.853345i \(0.674570\pi\)
\(654\) 0 0
\(655\) 42.1862 16.8448i 1.64835 0.658180i
\(656\) 0 0
\(657\) −1.70457 1.70457i −0.0665017 0.0665017i
\(658\) 0 0
\(659\) 43.8946i 1.70989i 0.518719 + 0.854945i \(0.326409\pi\)
−0.518719 + 0.854945i \(0.673591\pi\)
\(660\) 0 0
\(661\) 31.7743 18.3449i 1.23588 0.713534i 0.267629 0.963522i \(-0.413760\pi\)
0.968249 + 0.249988i \(0.0804266\pi\)
\(662\) 0 0
\(663\) 2.70650 + 10.1008i 0.105112 + 0.392283i
\(664\) 0 0
\(665\) 18.0811 21.5154i 0.701156 0.834330i
\(666\) 0 0
\(667\) 9.27301 + 34.6074i 0.359053 + 1.34000i
\(668\) 0 0
\(669\) −5.74622 + 3.31758i −0.222162 + 0.128265i
\(670\) 0 0
\(671\) 19.1444i 0.739061i
\(672\) 0 0
\(673\) 4.16595 + 4.16595i 0.160586 + 0.160586i 0.782826 0.622240i \(-0.213777\pi\)
−0.622240 + 0.782826i \(0.713777\pi\)
\(674\) 0 0
\(675\) 9.24759 15.1104i 0.355940 0.581599i
\(676\) 0 0
\(677\) −17.5741 + 4.70896i −0.675427 + 0.180980i −0.580198 0.814475i \(-0.697025\pi\)
−0.0952289 + 0.995455i \(0.530358\pi\)
\(678\) 0 0
\(679\) −2.86294 + 9.47668i −0.109869 + 0.363682i
\(680\) 0 0
\(681\) 22.9028 39.6687i 0.877635 1.52011i
\(682\) 0 0
\(683\) −12.5644 + 46.8911i −0.480765 + 1.79424i 0.117652 + 0.993055i \(0.462463\pi\)
−0.598417 + 0.801185i \(0.704203\pi\)
\(684\) 0 0
\(685\) 12.6981 9.48787i 0.485170 0.362513i
\(686\) 0 0
\(687\) 9.26604 9.26604i 0.353521 0.353521i
\(688\) 0 0
\(689\) 5.68992 + 9.85523i 0.216769 + 0.375454i
\(690\) 0 0
\(691\) 28.7175 + 16.5800i 1.09246 + 0.630734i 0.934231 0.356668i \(-0.116087\pi\)
0.158233 + 0.987402i \(0.449420\pi\)
\(692\) 0 0
\(693\) 18.6156 9.97752i 0.707148 0.379015i
\(694\) 0 0
\(695\) −10.9919 + 13.9515i −0.416947 + 0.529211i
\(696\) 0 0
\(697\) 11.0750 + 2.96754i 0.419496 + 0.112404i
\(698\) 0 0
\(699\) −21.7385 −0.822224
\(700\) 0 0
\(701\) −49.8387 −1.88238 −0.941191 0.337874i \(-0.890292\pi\)
−0.941191 + 0.337874i \(0.890292\pi\)
\(702\) 0 0
\(703\) 31.4469 + 8.42616i 1.18604 + 0.317799i
\(704\) 0 0
\(705\) −25.6306 + 32.5317i −0.965305 + 1.22521i
\(706\) 0 0
\(707\) −11.3278 7.02618i −0.426025 0.264247i
\(708\) 0 0
\(709\) −14.8597 8.57923i −0.558066 0.322200i 0.194303 0.980942i \(-0.437756\pi\)
−0.752369 + 0.658742i \(0.771089\pi\)
\(710\) 0 0
\(711\) 4.03715 + 6.99255i 0.151405 + 0.262241i
\(712\) 0 0
\(713\) −11.9424 + 11.9424i −0.447245 + 0.447245i
\(714\) 0 0
\(715\) −12.2811 + 9.17630i −0.459288 + 0.343174i
\(716\) 0 0
\(717\) 1.53983 5.74671i 0.0575059 0.214615i
\(718\) 0 0
\(719\) 16.7860 29.0742i 0.626012 1.08429i −0.362332 0.932049i \(-0.618019\pi\)
0.988344 0.152236i \(-0.0486474\pi\)
\(720\) 0 0
\(721\) −5.29202 + 4.96785i −0.197085 + 0.185012i
\(722\) 0 0
\(723\) −59.3507 + 15.9030i −2.20728 + 0.591438i
\(724\) 0 0
\(725\) −25.7990 + 6.20964i −0.958150 + 0.230620i
\(726\) 0 0
\(727\) −1.55262 1.55262i −0.0575835 0.0575835i 0.677729 0.735312i \(-0.262964\pi\)
−0.735312 + 0.677729i \(0.762964\pi\)
\(728\) 0 0
\(729\) 7.56747i 0.280277i
\(730\) 0 0
\(731\) 2.25946 1.30450i 0.0835691 0.0482486i
\(732\) 0 0
\(733\) 4.45750 + 16.6356i 0.164641 + 0.614450i 0.998086 + 0.0618467i \(0.0196990\pi\)
−0.833444 + 0.552604i \(0.813634\pi\)
\(734\) 0 0
\(735\) −1.77971 32.3680i −0.0656456 1.19391i
\(736\) 0 0
\(737\) 7.20880 + 26.9036i 0.265539 + 0.991007i
\(738\) 0 0
\(739\) 40.9386 23.6359i 1.50595 0.869461i 0.505974 0.862549i \(-0.331133\pi\)
0.999976 0.00691159i \(-0.00220004\pi\)
\(740\) 0 0
\(741\) 10.8934i 0.400177i
\(742\) 0 0
\(743\) −2.52069 2.52069i −0.0924753 0.0924753i 0.659356 0.751831i \(-0.270829\pi\)
−0.751831 + 0.659356i \(0.770829\pi\)
\(744\) 0 0
\(745\) −6.27213 + 2.50444i −0.229793 + 0.0917555i
\(746\) 0 0
\(747\) 10.2631 2.74999i 0.375507 0.100617i
\(748\) 0 0
\(749\) 28.2908 26.5578i 1.03372 0.970401i
\(750\) 0 0
\(751\) 6.40069 11.0863i 0.233564 0.404546i −0.725290 0.688443i \(-0.758294\pi\)
0.958855 + 0.283898i \(0.0916277\pi\)
\(752\) 0 0
\(753\) 8.07766 30.1462i 0.294366 1.09859i
\(754\) 0 0
\(755\) 8.88960 + 1.28629i 0.323526 + 0.0468131i
\(756\) 0 0
\(757\) 22.6605 22.6605i 0.823609 0.823609i −0.163014 0.986624i \(-0.552122\pi\)
0.986624 + 0.163014i \(0.0521217\pi\)
\(758\) 0 0
\(759\) −43.2873 74.9758i −1.57123 2.72145i
\(760\) 0 0
\(761\) 9.29607 + 5.36709i 0.336982 + 0.194557i 0.658937 0.752198i \(-0.271007\pi\)
−0.321955 + 0.946755i \(0.604340\pi\)
\(762\) 0 0
\(763\) 33.8513 + 20.9967i 1.22550 + 0.760130i
\(764\) 0 0
\(765\) −1.54894 13.0545i −0.0560021 0.471985i
\(766\) 0 0
\(767\) 0.152040 + 0.0407389i 0.00548983 + 0.00147100i
\(768\) 0 0
\(769\) 10.4824 0.378005 0.189002 0.981977i \(-0.439475\pi\)
0.189002 + 0.981977i \(0.439475\pi\)
\(770\) 0 0
\(771\) −48.8698 −1.76000
\(772\) 0 0
\(773\) 16.3424 + 4.37894i 0.587796 + 0.157499i 0.540446 0.841379i \(-0.318256\pi\)
0.0473503 + 0.998878i \(0.484922\pi\)
\(774\) 0 0
\(775\) −8.61570 9.06849i −0.309485 0.325750i
\(776\) 0 0
\(777\) 33.0980 17.7397i 1.18738 0.636409i
\(778\) 0 0
\(779\) 10.3438 + 5.97200i 0.370605 + 0.213969i
\(780\) 0 0
\(781\) −32.0493 55.5111i −1.14682 1.98634i
\(782\) 0 0
\(783\) 13.2963 13.2963i 0.475172 0.475172i
\(784\) 0 0
\(785\) −5.11511 6.84581i −0.182566 0.244337i
\(786\) 0 0
\(787\) −9.55515 + 35.6603i −0.340604 + 1.27115i 0.557060 + 0.830472i \(0.311929\pi\)
−0.897664 + 0.440680i \(0.854737\pi\)
\(788\) 0 0
\(789\) 20.8759 36.1581i 0.743201 1.28726i
\(790\) 0 0
\(791\) −1.52906 + 5.06138i −0.0543671 + 0.179962i
\(792\) 0 0
\(793\) 3.30662 0.886006i 0.117421 0.0314630i
\(794\) 0 0
\(795\) −17.6499 44.2026i −0.625979 1.56771i
\(796\) 0 0
\(797\) 10.9328 + 10.9328i