Properties

Label 280.2.bo.a.17.3
Level $280$
Weight $2$
Character 280.17
Analytic conductor $2.236$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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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 17.3
Character \(\chi\) \(=\) 280.17
Dual form 280.2.bo.a.33.3

$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.00047 + 0.536025i −1.15497 + 0.309474i −0.784956 0.619551i \(-0.787315\pi\)
−0.370017 + 0.929025i \(0.620648\pi\)
\(4\) 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 −0.156202 + 0.987725i \(0.549925\pi\)
−0.777294 + 0.629138i \(0.783408\pi\)
\(12\) 0 0
\(13\) 0.782930 + 0.782930i 0.217146 + 0.217146i 0.807294 0.590149i \(-0.200931\pi\)
−0.590149 + 0.807294i \(0.700931\pi\)
\(14\) 0 0
\(15\) −3.70979 2.77191i −0.957864 0.715705i
\(16\) 0 0
\(17\) 1.18027 + 4.40483i 0.286258 + 1.06833i 0.947915 + 0.318522i \(0.103187\pi\)
−0.661658 + 0.749806i \(0.730147\pi\)
\(18\) 0 0
\(19\) 2.37523 + 4.11401i 0.544914 + 0.943819i 0.998612 + 0.0526638i \(0.0167712\pi\)
−0.453698 + 0.891156i \(0.649895\pi\)
\(20\) 0 0
\(21\) −1.25033 + 5.33490i −0.272845 + 1.16417i
\(22\) 0 0
\(23\) −6.52089 1.74727i −1.35970 0.364330i −0.495993 0.868326i \(-0.665196\pi\)
−0.863706 + 0.503996i \(0.831863\pi\)
\(24\) 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 \(0.164011\pi\)
−0.870167 + 0.492757i \(0.835989\pi\)
\(30\) 0 0
\(31\) 2.16657 + 1.25087i 0.389128 + 0.224663i 0.681782 0.731555i \(-0.261205\pi\)
−0.292654 + 0.956218i \(0.594539\pi\)
\(32\) 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 −0.652273 0.757984i \(-0.726184\pi\)
0.943877 0.330298i \(-0.107149\pi\)
\(38\) 0 0
\(39\) −1.98590 1.14656i −0.317998 0.183596i
\(40\) 0 0
\(41\) 2.51428i 0.392665i −0.980537 0.196333i \(-0.937097\pi\)
0.980537 0.196333i \(-0.0629032\pi\)
\(42\) 0 0
\(43\) 0.404551 0.404551i 0.0616934 0.0616934i −0.675587 0.737280i \(-0.736110\pi\)
0.737280 + 0.675587i \(0.236110\pi\)
\(44\) 0 0
\(45\) 2.67723 + 1.06901i 0.399097 + 0.159358i
\(46\) 0 0
\(47\) 8.63838 + 2.31465i 1.26004 + 0.337626i 0.826206 0.563368i \(-0.190495\pi\)
0.433832 + 0.900994i \(0.357161\pi\)
\(48\) 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 −0.866892 0.498497i \(-0.833886\pi\)
0.501502 0.865157i \(-0.332781\pi\)
\(54\) 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 −0.861361 0.507993i \(-0.830388\pi\)
0.870615 + 0.491965i \(0.163721\pi\)
\(60\) 0 0
\(61\) 2.67752 1.54587i 0.342822 0.197928i −0.318697 0.947856i \(-0.603245\pi\)
0.661519 + 0.749928i \(0.269912\pi\)
\(62\) 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 −0.514259 0.857635i \(-0.671933\pi\)
−0.0165444 + 0.999863i \(0.505266\pi\)
\(68\) 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 −0.362961 0.931804i \(-0.618234\pi\)
0.151569 + 0.988447i \(0.451567\pi\)
\(74\) 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 −0.162822 0.986655i \(-0.552060\pi\)
0.773058 + 0.634336i \(0.218726\pi\)
\(80\) 0 0
\(81\) −5.60278 + 9.70431i −0.622532 + 1.07826i
\(82\) 0 0
\(83\) 5.82768 + 5.82768i 0.639671 + 0.639671i 0.950474 0.310803i \(-0.100598\pi\)
−0.310803 + 0.950474i \(0.600598\pi\)
\(84\) 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 0.513780 0.857922i \(-0.328245\pi\)
−0.999872 + 0.0159859i \(0.994911\pi\)
\(90\) 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 −0.559912 0.828552i \(-0.689165\pi\)
0.828552 + 0.559912i \(0.189165\pi\)
\(98\) 0 0
\(99\) 7.98294i 0.802315i
\(100\) 0 0
\(101\) −4.36323 2.51911i −0.434157 0.250661i 0.266959 0.963708i \(-0.413981\pi\)
−0.701116 + 0.713047i \(0.747315\pi\)
\(102\) 0 0
\(103\) 0.710053 2.64995i 0.0699636 0.261108i −0.922081 0.386998i \(-0.873512\pi\)
0.992044 + 0.125890i \(0.0401787\pi\)
\(104\) 0 0
\(105\) −11.1006 + 5.18646i −1.08331 + 0.506147i
\(106\) 0 0
\(107\) −3.79590 + 14.1665i −0.366963 + 1.36953i 0.497776 + 0.867306i \(0.334150\pi\)
−0.864740 + 0.502221i \(0.832517\pi\)
\(108\) 0 0
\(109\) 13.0388 + 7.52797i 1.24889 + 0.721049i 0.970889 0.239531i \(-0.0769936\pi\)
0.278005 + 0.960580i \(0.410327\pi\)
\(110\) 0 0
\(111\) 14.1934i 1.34718i
\(112\) 0 0
\(113\) 1.41309 1.41309i 0.132932 0.132932i −0.637510 0.770442i \(-0.720035\pi\)
0.770442 + 0.637510i \(0.220035\pi\)
\(114\) 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 0.472200 0.881492i \(-0.343460\pi\)
−0.881492 + 0.472200i \(0.843460\pi\)
\(128\) 0 0
\(129\) −0.592443 + 1.02614i −0.0521617 + 0.0903467i
\(130\) 0 0
\(131\) 17.5930 10.1573i 1.53711 0.887448i 0.538099 0.842882i \(-0.319143\pi\)
0.999006 0.0445661i \(-0.0141905\pi\)
\(132\) 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 0.0458371 0.998949i \(-0.485404\pi\)
0.539171 + 0.842197i \(0.318738\pi\)
\(138\) 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 −0.603301 0.797514i \(-0.706148\pi\)
0.389016 + 0.921231i \(0.372815\pi\)
\(150\) 0 0
\(151\) 2.00848 3.47878i 0.163447 0.283099i −0.772655 0.634826i \(-0.781072\pi\)
0.936103 + 0.351726i \(0.114405\pi\)
\(152\) 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 0.994098 0.108483i \(-0.0345993\pi\)
−0.915156 + 0.403100i \(0.867933\pi\)
\(158\) 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 −0.0909967 0.995851i \(-0.529005\pi\)
−0.576731 + 0.816934i \(0.695672\pi\)
\(164\) 0 0
\(165\) 26.3502 11.3119i 2.05136 0.880628i
\(166\) 0 0
\(167\) 5.91156 5.91156i 0.457450 0.457450i −0.440367 0.897818i \(-0.645152\pi\)
0.897818 + 0.440367i \(0.145152\pi\)
\(168\) 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 0.284260 + 0.958747i \(0.408252\pi\)
−0.725550 + 0.688170i \(0.758414\pi\)
\(174\) 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 0.0859789 0.996297i \(-0.472598\pi\)
−0.819829 + 0.572608i \(0.805932\pi\)
\(180\) 0 0
\(181\) 8.90901i 0.662201i 0.943595 + 0.331101i \(0.107420\pi\)
−0.943595 + 0.331101i \(0.892580\pi\)
\(182\) 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 0.994966 + 0.100211i \(0.0319517\pi\)
−0.410698 + 0.911771i \(0.634715\pi\)
\(192\) 0 0
\(193\) −0.102134 0.381168i −0.00735174 0.0274371i 0.962153 0.272511i \(-0.0878543\pi\)
−0.969504 + 0.245074i \(0.921188\pi\)
\(194\) 0 0
\(195\) −0.734295 5.07472i −0.0525839 0.363408i
\(196\) 0 0
\(197\) −8.65729 8.65729i −0.616806 0.616806i 0.327904 0.944711i \(-0.393658\pi\)
−0.944711 + 0.327904i \(0.893658\pi\)
\(198\) 0 0
\(199\) −4.96288 + 8.59596i −0.351809 + 0.609351i −0.986566 0.163360i \(-0.947767\pi\)
0.634757 + 0.772711i \(0.281100\pi\)
\(200\) 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 0.778878 0.627175i \(-0.215789\pi\)
−0.627175 + 0.778878i \(0.715789\pi\)
\(224\) 0 0
\(225\) 1.82719 + 6.18167i 0.121813 + 0.412111i
\(226\) 0 0
\(227\) −5.72434 21.3635i −0.379938 1.41795i −0.845994 0.533192i \(-0.820992\pi\)
0.466057 0.884755i \(-0.345674\pi\)
\(228\) 0 0
\(229\) −3.16366 5.47963i −0.209061 0.362104i 0.742358 0.670003i \(-0.233707\pi\)
−0.951419 + 0.307899i \(0.900374\pi\)
\(230\) 0 0
\(231\) −24.7374 23.2221i −1.62760 1.52790i
\(232\) 0 0
\(233\) 10.1387 + 2.71667i 0.664211 + 0.177975i 0.575145 0.818051i \(-0.304945\pi\)
0.0890650 + 0.996026i \(0.471612\pi\)
\(234\) 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 \(-0.970383\pi\)
0.995675 0.0929091i \(-0.0296166\pi\)
\(240\) 0 0
\(241\) 25.6935 + 14.8342i 1.65507 + 0.955553i 0.974943 + 0.222456i \(0.0714074\pi\)
0.680124 + 0.733097i \(0.261926\pi\)
\(242\) 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 \(-0.842234\pi\)
0.879667 0.475591i \(-0.157766\pi\)
\(252\) 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 0.886111 0.463474i \(-0.153397\pi\)
0.535658 + 0.844435i \(0.320064\pi\)
\(258\) 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 −0.917549 0.397622i \(-0.869835\pi\)
0.595810 0.803126i \(-0.296831\pi\)
\(264\) 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 −0.992610 0.121352i \(-0.961277\pi\)
0.601399 + 0.798949i \(0.294610\pi\)
\(270\) 0 0
\(271\) 1.51548 0.874961i 0.0920587 0.0531501i −0.453264 0.891376i \(-0.649740\pi\)
0.545323 + 0.838226i \(0.316407\pi\)
\(272\) 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 −0.0913802 0.995816i \(-0.529128\pi\)
0.418770 + 0.908092i \(0.362461\pi\)
\(278\) 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 −0.598463 0.801150i \(-0.704222\pi\)
−0.117709 + 0.993048i \(0.537555\pi\)
\(284\) 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 0.730390 0.683031i \(-0.239338\pi\)
−0.683031 + 0.730390i \(0.739338\pi\)
\(294\) 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 −0.560700 0.828019i \(-0.689468\pi\)
0.828019 + 0.560700i \(0.189468\pi\)
\(308\) 0 0
\(309\) 5.68177i 0.323224i
\(310\) 0 0
\(311\) 5.90190 + 3.40747i 0.334666 + 0.193220i 0.657911 0.753096i \(-0.271440\pi\)
−0.323245 + 0.946315i \(0.604774\pi\)
\(312\) 0 0
\(313\) −6.97836 + 26.0436i −0.394440 + 1.47207i 0.428291 + 0.903641i \(0.359116\pi\)
−0.822731 + 0.568430i \(0.807551\pi\)
\(314\) 0 0
\(315\) 5.83899 4.90698i 0.328990 0.276477i
\(316\) 0 0
\(317\) −4.81685 + 17.9767i −0.270541 + 1.00967i 0.688230 + 0.725493i \(0.258388\pi\)
−0.958771 + 0.284180i \(0.908279\pi\)
\(318\) 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 0.992004 0.126206i \(-0.0402802\pi\)
−0.605300 + 0.795997i \(0.706947\pi\)
\(332\) 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 −0.986128 0.165988i \(-0.946919\pi\)
−0.165988 0.986128i \(-0.553081\pi\)
\(338\) 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 −0.366450 0.930438i \(-0.619427\pi\)
0.147864 + 0.989008i \(0.452760\pi\)
\(348\) 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 0.403096 0.915157i \(-0.367934\pi\)
0.806671 + 0.591001i \(0.201267\pi\)
\(354\) 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 0.0413304 0.999146i \(-0.486840\pi\)
0.885951 + 0.463780i \(0.153507\pi\)
\(360\) 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 0.999290 + 0.0376718i \(0.0119941\pi\)
−0.846575 + 0.532270i \(0.821339\pi\)
\(368\) 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 0.575817 0.817579i \(-0.304684\pi\)
0.0898828 + 0.995952i \(0.471351\pi\)
\(374\) 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 \(0.0975191\pi\)
−0.953436 + 0.301595i \(0.902481\pi\)
\(380\) 0 0
\(381\) 11.6996 + 6.75474i 0.599387 + 0.346056i
\(382\) 0 0
\(383\) −8.49569 + 31.7063i −0.434109 + 1.62012i 0.309079 + 0.951036i \(0.399979\pi\)
−0.743188 + 0.669082i \(0.766687\pi\)
\(384\) 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 0.0757607 0.997126i \(-0.475862\pi\)
−0.825656 + 0.564174i \(0.809195\pi\)
\(390\) 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 −0.0446201 0.999004i \(-0.514208\pi\)
−0.538144 + 0.842853i \(0.680874\pi\)
\(398\) 0 0
\(399\) −24.9177 + 7.52771i −1.24744 + 0.376857i
\(400\) 0 0
\(401\) −12.4166 21.5062i −0.620055 1.07397i −0.989475 0.144704i \(-0.953777\pi\)
0.369420 0.929263i \(-0.379556\pi\)
\(402\) 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 0.147676 + 0.989036i \(0.452821\pi\)
−0.930368 + 0.366626i \(0.880513\pi\)
\(410\) 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 −0.967966 0.251082i \(-0.919214\pi\)
0.701427 + 0.712742i \(0.252547\pi\)
\(432\) 0 0
\(433\) 4.53425 + 4.53425i 0.217902 + 0.217902i 0.807614 0.589712i \(-0.200759\pi\)
−0.589712 + 0.807614i \(0.700759\pi\)
\(434\) 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 0.997277 0.0737466i \(-0.0234956\pi\)
−0.562505 + 0.826794i \(0.690162\pi\)
\(440\) 0 0
\(441\) −8.08469 4.00985i −0.384985 0.190945i
\(442\) 0 0
\(443\) 17.9720 + 4.81558i 0.853875 + 0.228795i 0.659102 0.752053i \(-0.270936\pi\)
0.194773 + 0.980848i \(0.437603\pi\)
\(444\) 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 \(0.277666\pi\)
−0.643056 + 0.765819i \(0.722334\pi\)
\(450\) 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 −0.999070 0.0431250i \(-0.986269\pi\)
0.886782 + 0.462187i \(0.152935\pi\)
\(458\) 0 0
\(459\) 13.9927 + 8.07869i 0.653123 + 0.377081i
\(460\) 0 0
\(461\) 36.2380i 1.68777i −0.536521 0.843887i \(-0.680262\pi\)
0.536521 0.843887i \(-0.319738\pi\)
\(462\) 0 0
\(463\) 6.39137 6.39137i 0.297032 0.297032i −0.542818 0.839850i \(-0.682643\pi\)
0.839850 + 0.542818i \(0.182643\pi\)
\(464\) 0 0
\(465\) −4.57023 10.6460i −0.211939 0.493697i
\(466\) 0 0
\(467\) −3.18040 0.852186i −0.147171 0.0394345i 0.184481 0.982836i \(-0.440940\pi\)
−0.331653 + 0.943402i \(0.607606\pi\)
\(468\) 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 −0.277462 0.960737i \(-0.589493\pi\)
0.970753 0.240079i \(-0.0771735\pi\)
\(480\) 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 0.444241 0.895907i \(-0.353473\pi\)
0.832678 + 0.553758i \(0.186807\pi\)
\(488\) 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 −0.951395 0.307973i \(-0.900349\pi\)
−0.208985 + 0.977919i \(0.567016\pi\)
\(500\) 0 0
\(501\) −8.65717 + 14.9947i −0.386774 + 0.669912i
\(502\) 0 0
\(503\) −10.5316 10.5316i −0.469582 0.469582i 0.432197 0.901779i \(-0.357738\pi\)
−0.901779 + 0.432197i \(0.857738\pi\)
\(504\) 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 0.664617 0.747184i \(-0.268595\pi\)
−0.979389 + 0.201983i \(0.935261\pi\)
\(510\) 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 −0.0451888 0.998978i \(-0.514389\pi\)
−0.887735 + 0.460355i \(0.847722\pi\)
\(522\) 0 0
\(523\) 8.19527 30.5852i 0.358354 1.33740i −0.517856 0.855468i \(-0.673270\pi\)
0.876211 0.481929i \(-0.160064\pi\)
\(524\) 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 0.999242 0.0389236i \(-0.0123929\pi\)
−0.533330 + 0.845907i \(0.679060\pi\)
\(542\) 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 0.516497 0.856289i \(-0.327236\pi\)
−0.856289 + 0.516497i \(0.827236\pi\)
\(548\) 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 −0.545968 0.837806i \(-0.683838\pi\)
−0.0539186 + 0.998545i \(0.517171\pi\)
\(558\) 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 −0.706607 0.707607i \(-0.749775\pi\)
−0.258136 + 0.966109i \(0.583108\pi\)
\(564\) 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 −0.861042 0.508533i \(-0.830188\pi\)
0.00988157 + 0.999951i \(0.496855\pi\)
\(570\) 0 0
\(571\) −1.81550 + 3.14454i −0.0759764 + 0.131595i −0.901510 0.432757i \(-0.857541\pi\)
0.825534 + 0.564352i \(0.190874\pi\)
\(572\) 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 −0.858049 0.513568i \(-0.828323\pi\)
0.486308 0.873788i \(-0.338343\pi\)
\(578\) 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 −0.924765 0.380538i \(-0.875739\pi\)
0.380538 + 0.924765i \(0.375739\pi\)
\(588\) 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 0.773621 + 0.633649i \(0.218444\pi\)
−0.986800 + 0.161946i \(0.948223\pi\)
\(594\) 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 −0.236704 0.971582i \(-0.576067\pi\)
−0.959767 + 0.280799i \(0.909401\pi\)
\(600\) 0 0
\(601\) 6.43168i 0.262354i −0.991359 0.131177i \(-0.958124\pi\)
0.991359 0.131177i \(-0.0418756\pi\)
\(602\) 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 0.183205 0.983075i \(-0.441353\pi\)
−0.332878 + 0.942970i \(0.608020\pi\)
\(608\) 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 −0.606047 0.795429i \(-0.707246\pi\)
0.127138 0.991885i \(-0.459421\pi\)
\(614\) 0 0
\(615\) −6.96938 + 9.32747i −0.281032 + 0.376120i
\(616\) 0 0
\(617\) 15.0385 + 15.0385i 0.605429 + 0.605429i 0.941748 0.336319i \(-0.109182\pi\)
−0.336319 + 0.941748i \(0.609182\pi\)
\(618\) 0 0
\(619\) −0.630180 + 1.09150i −0.0253291 + 0.0438712i −0.878412 0.477904i \(-0.841397\pi\)
0.853083 + 0.521775i \(0.174730\pi\)
\(620\) 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 −0.733361 0.679839i \(-0.762049\pi\)
0.955439 + 0.295190i \(0.0953828\pi\)
\(642\) 0 0
\(643\) −34.9847 34.9847i −1.37966 1.37966i −0.845178 0.534485i \(-0.820506\pi\)
−0.534485 0.845178i \(-0.679494\pi\)
\(644\) 0 0
\(645\) −2.62218 + 0.379420i −0.103248 + 0.0149397i
\(646\) 0 0
\(647\) −4.92794 18.3913i −0.193737 0.723038i −0.992590 0.121511i \(-0.961226\pi\)
0.798853 0.601527i \(-0.205441\pi\)
\(648\) 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 −0.521346 0.853345i \(-0.674570\pi\)
−0.878171 + 0.478346i \(0.841237\pi\)
\(654\) 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 \(-0.673591\pi\)
0.518719 0.854945i \(-0.326409\pi\)
\(660\) 0 0
\(661\) 31.7743 + 18.3449i 1.23588 + 0.713534i 0.968249 0.249988i \(-0.0804266\pi\)
0.267629 + 0.963522i \(0.413760\pi\)
\(662\) 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 −0.622240 0.782826i \(-0.713777\pi\)
0.782826 + 0.622240i \(0.213777\pi\)
\(674\) 0 0
\(675\) 9.24759 + 15.1104i 0.355940 + 0.581599i
\(676\) 0 0
\(677\) −17.5741 4.70896i −0.675427 0.180980i −0.0952289 0.995455i \(-0.530358\pi\)
−0.580198 + 0.814475i \(0.697025\pi\)
\(678\) 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 −0.598417 0.801185i \(-0.704203\pi\)
0.117652 0.993055i \(-0.462463\pi\)
\(684\) 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 0.158233 0.987402i \(-0.449420\pi\)
0.934231 + 0.356668i \(0.116087\pi\)
\(692\) 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 −0.752369 0.658742i \(-0.771089\pi\)
0.194303 + 0.980942i \(0.437756\pi\)
\(710\) 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 0.988344 + 0.152236i \(0.0486474\pi\)
−0.362332 + 0.932049i \(0.618019\pi\)
\(720\) 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 −0.735312 0.677729i \(-0.762964\pi\)
0.677729 + 0.735312i \(0.262964\pi\)
\(728\) 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 −0.833444 0.552604i \(-0.813634\pi\)
0.998086 0.0618467i \(-0.0196990\pi\)
\(734\) 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 0.999976 + 0.00691159i \(0.00220004\pi\)
0.505974 + 0.862549i \(0.331133\pi\)
\(740\) 0 0
\(741\) 10.8934i 0.400177i
\(742\) 0 0
\(743\) −2.52069 + 2.52069i −0.0924753 + 0.0924753i −0.751831 0.659356i \(-0.770829\pi\)
0.659356 + 0.751831i \(0.270829\pi\)
\(744\) 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 0.958855 0.283898i \(-0.0916277\pi\)
−0.725290 + 0.688443i \(0.758294\pi\)
\(752\) 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 0.986624 0.163014i \(-0.0521217\pi\)
−0.163014 + 0.986624i \(0.552122\pi\)
\(758\) 0 0
\(759\) −43.2873 + 74.9758i −1.57123 + 2.72145i
\(760\) 0 0
\(761\) 9.29607 5.36709i 0.336982 0.194557i −0.321955 0.946755i \(-0.604340\pi\)
0.658937 + 0.752198i \(0.271007\pi\)
\(762\) 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 0.0473503 0.998878i \(-0.484922\pi\)
0.540446 + 0.841379i \(0.318256\pi\)
\(774\) 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 −0.897664 0.440680i \(-0.854737\pi\)
0.557060 0.830472i \(-0.311929\pi\)
\(788\) 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 0.387258 0.387258i