Properties

Label 720.2.u.a.179.13
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 179.13
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.956592 + 1.04160i) q^{2} +(-0.169864 - 1.99277i) q^{4} +(1.11222 - 1.93984i) q^{5} -1.78786i q^{7} +(2.23816 + 1.72934i) q^{8} +O(q^{10})\) \(q+(-0.956592 + 1.04160i) q^{2} +(-0.169864 - 1.99277i) q^{4} +(1.11222 - 1.93984i) q^{5} -1.78786i q^{7} +(2.23816 + 1.72934i) q^{8} +(0.956594 + 3.01412i) q^{10} +(-3.34421 + 3.34421i) q^{11} +(2.90349 - 2.90349i) q^{13} +(1.86224 + 1.71025i) q^{14} +(-3.94229 + 0.676999i) q^{16} +4.56733 q^{17} +(0.0693845 - 0.0693845i) q^{19} +(-4.05458 - 1.88690i) q^{20} +(-0.284286 - 6.68237i) q^{22} -1.07695 q^{23} +(-2.52593 - 4.31505i) q^{25} +(0.246821 + 5.80172i) q^{26} +(-3.56280 + 0.303692i) q^{28} +(1.23988 - 1.23988i) q^{29} -8.56612i q^{31} +(3.06600 - 4.75391i) q^{32} +(-4.36907 + 4.75733i) q^{34} +(-3.46816 - 1.98849i) q^{35} +(-7.62458 - 7.62458i) q^{37} +(0.00589828 + 0.138644i) q^{38} +(5.84397 - 2.41826i) q^{40} -7.91601 q^{41} +(2.35179 - 2.35179i) q^{43} +(7.23230 + 6.09619i) q^{44} +(1.03020 - 1.12175i) q^{46} -6.32188i q^{47} +3.80356 q^{49} +(6.91085 + 1.49673i) q^{50} +(-6.27919 - 5.29279i) q^{52} +(3.61429 - 3.61429i) q^{53} +(2.76772 + 10.2067i) q^{55} +(3.09182 - 4.00152i) q^{56} +(0.105400 + 2.47751i) q^{58} +(-2.25080 + 2.25080i) q^{59} +(4.29893 + 4.29893i) q^{61} +(8.92248 + 8.19429i) q^{62} +(2.01876 + 7.74110i) q^{64} +(-2.40297 - 8.86160i) q^{65} +(5.85271 + 5.85271i) q^{67} +(-0.775822 - 9.10164i) q^{68} +(5.38883 - 1.71026i) q^{70} -15.1431i q^{71} +6.88118 q^{73} +(15.2354 - 0.648155i) q^{74} +(-0.150054 - 0.126482i) q^{76} +(5.97897 + 5.97897i) q^{77} +12.9721i q^{79} +(-3.07143 + 8.40038i) q^{80} +(7.57239 - 8.24532i) q^{82} +(-6.88840 + 6.88840i) q^{83} +(5.07987 - 8.85986i) q^{85} +(0.199923 + 4.69933i) q^{86} +(-13.2682 + 1.70161i) q^{88} -6.31609 q^{89} +(-5.19103 - 5.19103i) q^{91} +(0.182935 + 2.14612i) q^{92} +(6.58487 + 6.04746i) q^{94} +(-0.0574238 - 0.211766i) q^{95} -4.56728i q^{97} +(-3.63845 + 3.96179i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.956592 + 1.04160i −0.676413 + 0.736523i
\(3\) 0 0
\(4\) −0.169864 1.99277i −0.0849318 0.996387i
\(5\) 1.11222 1.93984i 0.497400 0.867521i
\(6\) 0 0
\(7\) 1.78786i 0.675747i −0.941191 0.337874i \(-0.890292\pi\)
0.941191 0.337874i \(-0.109708\pi\)
\(8\) 2.23816 + 1.72934i 0.791311 + 0.611414i
\(9\) 0 0
\(10\) 0.956594 + 3.01412i 0.302502 + 0.953149i
\(11\) −3.34421 + 3.34421i −1.00832 + 1.00832i −0.00835103 + 0.999965i \(0.502658\pi\)
−0.999965 + 0.00835103i \(0.997342\pi\)
\(12\) 0 0
\(13\) 2.90349 2.90349i 0.805282 0.805282i −0.178634 0.983916i \(-0.557168\pi\)
0.983916 + 0.178634i \(0.0571677\pi\)
\(14\) 1.86224 + 1.71025i 0.497703 + 0.457084i
\(15\) 0 0
\(16\) −3.94229 + 0.676999i −0.985573 + 0.169250i
\(17\) 4.56733 1.10774 0.553870 0.832603i \(-0.313151\pi\)
0.553870 + 0.832603i \(0.313151\pi\)
\(18\) 0 0
\(19\) 0.0693845 0.0693845i 0.0159179 0.0159179i −0.699103 0.715021i \(-0.746417\pi\)
0.715021 + 0.699103i \(0.246417\pi\)
\(20\) −4.05458 1.88690i −0.906632 0.421923i
\(21\) 0 0
\(22\) −0.284286 6.68237i −0.0606100 1.42469i
\(23\) −1.07695 −0.224560 −0.112280 0.993677i \(-0.535815\pi\)
−0.112280 + 0.993677i \(0.535815\pi\)
\(24\) 0 0
\(25\) −2.52593 4.31505i −0.505186 0.863010i
\(26\) 0.246821 + 5.80172i 0.0484056 + 1.13781i
\(27\) 0 0
\(28\) −3.56280 + 0.303692i −0.673306 + 0.0573924i
\(29\) 1.23988 1.23988i 0.230239 0.230239i −0.582553 0.812792i \(-0.697946\pi\)
0.812792 + 0.582553i \(0.197946\pi\)
\(30\) 0 0
\(31\) 8.56612i 1.53852i −0.638935 0.769261i \(-0.720625\pi\)
0.638935 0.769261i \(-0.279375\pi\)
\(32\) 3.06600 4.75391i 0.541998 0.840380i
\(33\) 0 0
\(34\) −4.36907 + 4.75733i −0.749289 + 0.815875i
\(35\) −3.46816 1.98849i −0.586225 0.336117i
\(36\) 0 0
\(37\) −7.62458 7.62458i −1.25347 1.25347i −0.954153 0.299321i \(-0.903240\pi\)
−0.299321 0.954153i \(-0.596760\pi\)
\(38\) 0.00589828 + 0.138644i 0.000956828 + 0.0224910i
\(39\) 0 0
\(40\) 5.84397 2.41826i 0.924013 0.382361i
\(41\) −7.91601 −1.23627 −0.618137 0.786071i \(-0.712112\pi\)
−0.618137 + 0.786071i \(0.712112\pi\)
\(42\) 0 0
\(43\) 2.35179 2.35179i 0.358645 0.358645i −0.504668 0.863313i \(-0.668385\pi\)
0.863313 + 0.504668i \(0.168385\pi\)
\(44\) 7.23230 + 6.09619i 1.09031 + 0.919035i
\(45\) 0 0
\(46\) 1.03020 1.12175i 0.151895 0.165394i
\(47\) 6.32188i 0.922141i −0.887364 0.461070i \(-0.847466\pi\)
0.887364 0.461070i \(-0.152534\pi\)
\(48\) 0 0
\(49\) 3.80356 0.543365
\(50\) 6.91085 + 1.49673i 0.977341 + 0.211670i
\(51\) 0 0
\(52\) −6.27919 5.29279i −0.870766 0.733978i
\(53\) 3.61429 3.61429i 0.496461 0.496461i −0.413874 0.910334i \(-0.635824\pi\)
0.910334 + 0.413874i \(0.135824\pi\)
\(54\) 0 0
\(55\) 2.76772 + 10.2067i 0.373199 + 1.37627i
\(56\) 3.09182 4.00152i 0.413162 0.534726i
\(57\) 0 0
\(58\) 0.105400 + 2.47751i 0.0138397 + 0.325313i
\(59\) −2.25080 + 2.25080i −0.293030 + 0.293030i −0.838276 0.545246i \(-0.816436\pi\)
0.545246 + 0.838276i \(0.316436\pi\)
\(60\) 0 0
\(61\) 4.29893 + 4.29893i 0.550421 + 0.550421i 0.926562 0.376141i \(-0.122749\pi\)
−0.376141 + 0.926562i \(0.622749\pi\)
\(62\) 8.92248 + 8.19429i 1.13316 + 1.04068i
\(63\) 0 0
\(64\) 2.01876 + 7.74110i 0.252345 + 0.967637i
\(65\) −2.40297 8.86160i −0.298052 1.09915i
\(66\) 0 0
\(67\) 5.85271 + 5.85271i 0.715022 + 0.715022i 0.967581 0.252559i \(-0.0812722\pi\)
−0.252559 + 0.967581i \(0.581272\pi\)
\(68\) −0.775822 9.10164i −0.0940822 1.10374i
\(69\) 0 0
\(70\) 5.38883 1.71026i 0.644088 0.204415i
\(71\) 15.1431i 1.79716i −0.438812 0.898579i \(-0.644601\pi\)
0.438812 0.898579i \(-0.355399\pi\)
\(72\) 0 0
\(73\) 6.88118 0.805381 0.402691 0.915336i \(-0.368075\pi\)
0.402691 + 0.915336i \(0.368075\pi\)
\(74\) 15.2354 0.648155i 1.77108 0.0753465i
\(75\) 0 0
\(76\) −0.150054 0.126482i −0.0172123 0.0145085i
\(77\) 5.97897 + 5.97897i 0.681367 + 0.681367i
\(78\) 0 0
\(79\) 12.9721i 1.45947i 0.683730 + 0.729735i \(0.260357\pi\)
−0.683730 + 0.729735i \(0.739643\pi\)
\(80\) −3.07143 + 8.40038i −0.343396 + 0.939191i
\(81\) 0 0
\(82\) 7.57239 8.24532i 0.836231 0.910544i
\(83\) −6.88840 + 6.88840i −0.756100 + 0.756100i −0.975610 0.219510i \(-0.929554\pi\)
0.219510 + 0.975610i \(0.429554\pi\)
\(84\) 0 0
\(85\) 5.07987 8.85986i 0.550989 0.960987i
\(86\) 0.199923 + 4.69933i 0.0215582 + 0.506742i
\(87\) 0 0
\(88\) −13.2682 + 1.70161i −1.41439 + 0.181392i
\(89\) −6.31609 −0.669504 −0.334752 0.942306i \(-0.608653\pi\)
−0.334752 + 0.942306i \(0.608653\pi\)
\(90\) 0 0
\(91\) −5.19103 5.19103i −0.544167 0.544167i
\(92\) 0.182935 + 2.14612i 0.0190723 + 0.223749i
\(93\) 0 0
\(94\) 6.58487 + 6.04746i 0.679178 + 0.623748i
\(95\) −0.0574238 0.211766i −0.00589155 0.0217267i
\(96\) 0 0
\(97\) 4.56728i 0.463737i −0.972747 0.231869i \(-0.925516\pi\)
0.972747 0.231869i \(-0.0744839\pi\)
\(98\) −3.63845 + 3.96179i −0.367539 + 0.400201i
\(99\) 0 0
\(100\) −8.16986 + 5.76658i −0.816986 + 0.576658i
\(101\) 6.24690 + 6.24690i 0.621589 + 0.621589i 0.945938 0.324348i \(-0.105145\pi\)
−0.324348 + 0.945938i \(0.605145\pi\)
\(102\) 0 0
\(103\) 13.8548i 1.36515i 0.730815 + 0.682576i \(0.239140\pi\)
−0.730815 + 0.682576i \(0.760860\pi\)
\(104\) 11.5196 1.47736i 1.12959 0.144867i
\(105\) 0 0
\(106\) 0.307245 + 7.22204i 0.0298423 + 0.701467i
\(107\) 0.922209 + 0.922209i 0.0891533 + 0.0891533i 0.750277 0.661124i \(-0.229920\pi\)
−0.661124 + 0.750277i \(0.729920\pi\)
\(108\) 0 0
\(109\) −2.28662 2.28662i −0.219019 0.219019i 0.589066 0.808085i \(-0.299496\pi\)
−0.808085 + 0.589066i \(0.799496\pi\)
\(110\) −13.2789 6.88080i −1.26609 0.656058i
\(111\) 0 0
\(112\) 1.21038 + 7.04827i 0.114370 + 0.665999i
\(113\) 7.53772 0.709089 0.354544 0.935039i \(-0.384636\pi\)
0.354544 + 0.935039i \(0.384636\pi\)
\(114\) 0 0
\(115\) −1.19781 + 2.08911i −0.111696 + 0.194811i
\(116\) −2.68140 2.26018i −0.248962 0.209853i
\(117\) 0 0
\(118\) −0.191338 4.49754i −0.0176141 0.414032i
\(119\) 8.16574i 0.748552i
\(120\) 0 0
\(121\) 11.3674i 1.03340i
\(122\) −8.59008 + 0.365446i −0.777710 + 0.0330859i
\(123\) 0 0
\(124\) −17.0703 + 1.45507i −1.53296 + 0.130669i
\(125\) −11.1799 + 0.100608i −0.999960 + 0.00899866i
\(126\) 0 0
\(127\) −0.00277854 −0.000246555 −0.000123278 1.00000i \(-0.500039\pi\)
−0.000123278 1.00000i \(0.500039\pi\)
\(128\) −9.99426 5.30233i −0.883376 0.468665i
\(129\) 0 0
\(130\) 11.5289 + 5.97400i 1.01115 + 0.523955i
\(131\) −8.71989 8.71989i −0.761860 0.761860i 0.214798 0.976658i \(-0.431091\pi\)
−0.976658 + 0.214798i \(0.931091\pi\)
\(132\) 0 0
\(133\) −0.124050 0.124050i −0.0107565 0.0107565i
\(134\) −11.6948 + 0.497531i −1.01028 + 0.0429801i
\(135\) 0 0
\(136\) 10.2224 + 7.89846i 0.876566 + 0.677288i
\(137\) 23.1771i 1.98016i −0.140516 0.990078i \(-0.544876\pi\)
0.140516 0.990078i \(-0.455124\pi\)
\(138\) 0 0
\(139\) −7.85331 7.85331i −0.666109 0.666109i 0.290704 0.956813i \(-0.406111\pi\)
−0.956813 + 0.290704i \(0.906111\pi\)
\(140\) −3.37350 + 7.24902i −0.285113 + 0.612654i
\(141\) 0 0
\(142\) 15.7731 + 14.4858i 1.32365 + 1.21562i
\(143\) 19.4197i 1.62396i
\(144\) 0 0
\(145\) −1.02614 3.78417i −0.0852164 0.314258i
\(146\) −6.58248 + 7.16744i −0.544770 + 0.593182i
\(147\) 0 0
\(148\) −13.8989 + 16.4892i −1.14248 + 1.35540i
\(149\) 13.6076 + 13.6076i 1.11478 + 1.11478i 0.992495 + 0.122285i \(0.0390222\pi\)
0.122285 + 0.992495i \(0.460978\pi\)
\(150\) 0 0
\(151\) 15.2447 1.24059 0.620297 0.784367i \(-0.287012\pi\)
0.620297 + 0.784367i \(0.287012\pi\)
\(152\) 0.275284 0.0353044i 0.0223284 0.00286357i
\(153\) 0 0
\(154\) −11.9471 + 0.508264i −0.962728 + 0.0409571i
\(155\) −16.6169 9.52742i −1.33470 0.765261i
\(156\) 0 0
\(157\) 5.76894 5.76894i 0.460411 0.460411i −0.438379 0.898790i \(-0.644447\pi\)
0.898790 + 0.438379i \(0.144447\pi\)
\(158\) −13.5117 12.4090i −1.07493 0.987204i
\(159\) 0 0
\(160\) −5.81173 11.2349i −0.459458 0.888200i
\(161\) 1.92544i 0.151746i
\(162\) 0 0
\(163\) 10.4511 + 10.4511i 0.818594 + 0.818594i 0.985904 0.167311i \(-0.0535083\pi\)
−0.167311 + 0.985904i \(0.553508\pi\)
\(164\) 1.34464 + 15.7748i 0.104999 + 1.23181i
\(165\) 0 0
\(166\) −0.585573 13.7644i −0.0454493 1.06832i
\(167\) −9.41872 −0.728842 −0.364421 0.931234i \(-0.618733\pi\)
−0.364421 + 0.931234i \(0.618733\pi\)
\(168\) 0 0
\(169\) 3.86046i 0.296958i
\(170\) 4.36908 + 13.7665i 0.335093 + 1.05584i
\(171\) 0 0
\(172\) −5.08607 4.28711i −0.387810 0.326889i
\(173\) 6.21995 + 6.21995i 0.472894 + 0.472894i 0.902850 0.429956i \(-0.141471\pi\)
−0.429956 + 0.902850i \(0.641471\pi\)
\(174\) 0 0
\(175\) −7.71471 + 4.51601i −0.583177 + 0.341378i
\(176\) 10.9198 15.4479i 0.823112 1.16443i
\(177\) 0 0
\(178\) 6.04192 6.57884i 0.452861 0.493105i
\(179\) 18.4020 + 18.4020i 1.37543 + 1.37543i 0.852179 + 0.523251i \(0.175281\pi\)
0.523251 + 0.852179i \(0.324719\pi\)
\(180\) 0 0
\(181\) −18.5731 + 18.5731i −1.38053 + 1.38053i −0.536851 + 0.843677i \(0.680386\pi\)
−0.843677 + 0.536851i \(0.819614\pi\)
\(182\) 10.3727 0.441282i 0.768873 0.0327100i
\(183\) 0 0
\(184\) −2.41040 1.86242i −0.177697 0.137299i
\(185\) −23.2707 + 6.31023i −1.71089 + 0.463937i
\(186\) 0 0
\(187\) −15.2741 + 15.2741i −1.11695 + 1.11695i
\(188\) −12.5981 + 1.07386i −0.918809 + 0.0783190i
\(189\) 0 0
\(190\) 0.275506 + 0.142761i 0.0199873 + 0.0103569i
\(191\) −4.73383 −0.342528 −0.171264 0.985225i \(-0.554785\pi\)
−0.171264 + 0.985225i \(0.554785\pi\)
\(192\) 0 0
\(193\) 16.7218i 1.20366i −0.798625 0.601829i \(-0.794439\pi\)
0.798625 0.601829i \(-0.205561\pi\)
\(194\) 4.75728 + 4.36902i 0.341553 + 0.313678i
\(195\) 0 0
\(196\) −0.646086 7.57963i −0.0461490 0.541402i
\(197\) −7.93066 + 7.93066i −0.565036 + 0.565036i −0.930734 0.365698i \(-0.880830\pi\)
0.365698 + 0.930734i \(0.380830\pi\)
\(198\) 0 0
\(199\) −2.34717 −0.166386 −0.0831932 0.996533i \(-0.526512\pi\)
−0.0831932 + 0.996533i \(0.526512\pi\)
\(200\) 1.80875 14.0260i 0.127898 0.991787i
\(201\) 0 0
\(202\) −12.4825 + 0.531040i −0.878266 + 0.0373638i
\(203\) −2.21672 2.21672i −0.155583 0.155583i
\(204\) 0 0
\(205\) −8.80435 + 15.3558i −0.614922 + 1.07249i
\(206\) −14.4311 13.2534i −1.00547 0.923406i
\(207\) 0 0
\(208\) −9.48073 + 13.4120i −0.657371 + 0.929958i
\(209\) 0.464072i 0.0321006i
\(210\) 0 0
\(211\) −3.00077 + 3.00077i −0.206581 + 0.206581i −0.802813 0.596231i \(-0.796664\pi\)
0.596231 + 0.802813i \(0.296664\pi\)
\(212\) −7.81639 6.58852i −0.536832 0.452502i
\(213\) 0 0
\(214\) −1.84275 + 0.0783956i −0.125968 + 0.00535902i
\(215\) −1.94638 7.17781i −0.132742 0.489522i
\(216\) 0 0
\(217\) −15.3150 −1.03965
\(218\) 4.56911 0.194382i 0.309459 0.0131652i
\(219\) 0 0
\(220\) 19.8695 7.24919i 1.33960 0.488740i
\(221\) 13.2612 13.2612i 0.892042 0.892042i
\(222\) 0 0
\(223\) 24.6842 1.65298 0.826489 0.562952i \(-0.190335\pi\)
0.826489 + 0.562952i \(0.190335\pi\)
\(224\) −8.49932 5.48158i −0.567885 0.366254i
\(225\) 0 0
\(226\) −7.21052 + 7.85129i −0.479637 + 0.522260i
\(227\) −5.05360 + 5.05360i −0.335419 + 0.335419i −0.854640 0.519221i \(-0.826222\pi\)
0.519221 + 0.854640i \(0.326222\pi\)
\(228\) 0 0
\(229\) −13.4816 + 13.4816i −0.890886 + 0.890886i −0.994606 0.103720i \(-0.966925\pi\)
0.103720 + 0.994606i \(0.466925\pi\)
\(230\) −1.03021 3.24606i −0.0679298 0.214039i
\(231\) 0 0
\(232\) 4.91921 0.630877i 0.322962 0.0414191i
\(233\) 11.8466i 0.776096i 0.921639 + 0.388048i \(0.126851\pi\)
−0.921639 + 0.388048i \(0.873149\pi\)
\(234\) 0 0
\(235\) −12.2634 7.03132i −0.799977 0.458673i
\(236\) 4.86767 + 4.10301i 0.316858 + 0.267083i
\(237\) 0 0
\(238\) 8.50544 + 7.81128i 0.551326 + 0.506330i
\(239\) 24.8620 1.60819 0.804093 0.594503i \(-0.202651\pi\)
0.804093 + 0.594503i \(0.202651\pi\)
\(240\) 0 0
\(241\) 18.8396 1.21356 0.606782 0.794868i \(-0.292460\pi\)
0.606782 + 0.794868i \(0.292460\pi\)
\(242\) 11.8403 + 10.8740i 0.761125 + 0.699007i
\(243\) 0 0
\(244\) 7.83656 9.29702i 0.501684 0.595181i
\(245\) 4.23039 7.37828i 0.270270 0.471381i
\(246\) 0 0
\(247\) 0.402914i 0.0256368i
\(248\) 14.8138 19.1724i 0.940674 1.21745i
\(249\) 0 0
\(250\) 10.5898 11.7412i 0.669758 0.742580i
\(251\) −21.6723 + 21.6723i −1.36795 + 1.36795i −0.504582 + 0.863364i \(0.668353\pi\)
−0.863364 + 0.504582i \(0.831647\pi\)
\(252\) 0 0
\(253\) 3.60155 3.60155i 0.226428 0.226428i
\(254\) 0.00265793 0.00289413i 0.000166773 0.000181594i
\(255\) 0 0
\(256\) 15.0833 5.33786i 0.942709 0.333616i
\(257\) 0.914423 0.0570402 0.0285201 0.999593i \(-0.490921\pi\)
0.0285201 + 0.999593i \(0.490921\pi\)
\(258\) 0 0
\(259\) −13.6317 + 13.6317i −0.847031 + 0.847031i
\(260\) −17.2510 + 6.29384i −1.06986 + 0.390328i
\(261\) 0 0
\(262\) 17.4240 0.741265i 1.07646 0.0457955i
\(263\) 1.19643 0.0737752 0.0368876 0.999319i \(-0.488256\pi\)
0.0368876 + 0.999319i \(0.488256\pi\)
\(264\) 0 0
\(265\) −2.99124 11.0310i −0.183751 0.677630i
\(266\) 0.247875 0.0105453i 0.0151982 0.000646574i
\(267\) 0 0
\(268\) 10.6690 12.6573i 0.651711 0.773167i
\(269\) 7.54542 7.54542i 0.460053 0.460053i −0.438620 0.898673i \(-0.644533\pi\)
0.898673 + 0.438620i \(0.144533\pi\)
\(270\) 0 0
\(271\) 4.45852i 0.270836i 0.990789 + 0.135418i \(0.0432377\pi\)
−0.990789 + 0.135418i \(0.956762\pi\)
\(272\) −18.0057 + 3.09207i −1.09176 + 0.187485i
\(273\) 0 0
\(274\) 24.1413 + 22.1711i 1.45843 + 1.33940i
\(275\) 22.8777 + 5.98318i 1.37957 + 0.360800i
\(276\) 0 0
\(277\) 5.28152 + 5.28152i 0.317336 + 0.317336i 0.847743 0.530407i \(-0.177961\pi\)
−0.530407 + 0.847743i \(0.677961\pi\)
\(278\) 15.6924 0.667599i 0.941169 0.0400399i
\(279\) 0 0
\(280\) −4.32352 10.4482i −0.258380 0.624399i
\(281\) 26.3280 1.57060 0.785298 0.619118i \(-0.212510\pi\)
0.785298 + 0.619118i \(0.212510\pi\)
\(282\) 0 0
\(283\) 13.6186 13.6186i 0.809540 0.809540i −0.175024 0.984564i \(-0.556000\pi\)
0.984564 + 0.175024i \(0.0560005\pi\)
\(284\) −30.1768 + 2.57226i −1.79066 + 0.152636i
\(285\) 0 0
\(286\) −20.2276 18.5767i −1.19608 1.09847i
\(287\) 14.1527i 0.835409i
\(288\) 0 0
\(289\) 3.86046 0.227086
\(290\) 4.92319 + 2.55108i 0.289100 + 0.149804i
\(291\) 0 0
\(292\) −1.16886 13.7126i −0.0684024 0.802471i
\(293\) −9.23746 + 9.23746i −0.539658 + 0.539658i −0.923429 0.383770i \(-0.874625\pi\)
0.383770 + 0.923429i \(0.374625\pi\)
\(294\) 0 0
\(295\) 1.86280 + 6.86958i 0.108457 + 0.399962i
\(296\) −3.87956 30.2506i −0.225495 1.75828i
\(297\) 0 0
\(298\) −27.1907 + 1.15676i −1.57511 + 0.0670096i
\(299\) −3.12692 + 3.12692i −0.180834 + 0.180834i
\(300\) 0 0
\(301\) −4.20468 4.20468i −0.242353 0.242353i
\(302\) −14.5829 + 15.8789i −0.839153 + 0.913725i
\(303\) 0 0
\(304\) −0.226561 + 0.320507i −0.0129942 + 0.0183824i
\(305\) 13.1206 3.55786i 0.751282 0.203723i
\(306\) 0 0
\(307\) 2.37148 + 2.37148i 0.135348 + 0.135348i 0.771535 0.636187i \(-0.219489\pi\)
−0.636187 + 0.771535i \(0.719489\pi\)
\(308\) 10.8991 12.9303i 0.621035 0.736775i
\(309\) 0 0
\(310\) 25.8193 8.19430i 1.46644 0.465405i
\(311\) 14.5352i 0.824214i −0.911135 0.412107i \(-0.864793\pi\)
0.911135 0.412107i \(-0.135207\pi\)
\(312\) 0 0
\(313\) 21.2104 1.19888 0.599442 0.800418i \(-0.295389\pi\)
0.599442 + 0.800418i \(0.295389\pi\)
\(314\) 0.490409 + 11.5274i 0.0276754 + 0.650531i
\(315\) 0 0
\(316\) 25.8504 2.20348i 1.45420 0.123955i
\(317\) 0.575423 + 0.575423i 0.0323190 + 0.0323190i 0.723082 0.690763i \(-0.242725\pi\)
−0.690763 + 0.723082i \(0.742725\pi\)
\(318\) 0 0
\(319\) 8.29280i 0.464308i
\(320\) 17.2618 + 4.69375i 0.964962 + 0.262388i
\(321\) 0 0
\(322\) −2.00554 1.84186i −0.111764 0.102643i
\(323\) 0.316902 0.316902i 0.0176329 0.0176329i
\(324\) 0 0
\(325\) −19.8627 5.19468i −1.10178 0.288149i
\(326\) −20.8833 + 0.888433i −1.15662 + 0.0492058i
\(327\) 0 0
\(328\) −17.7173 13.6895i −0.978276 0.755875i
\(329\) −11.3026 −0.623134
\(330\) 0 0
\(331\) 5.54595 + 5.54595i 0.304833 + 0.304833i 0.842901 0.538068i \(-0.180846\pi\)
−0.538068 + 0.842901i \(0.680846\pi\)
\(332\) 14.8971 + 12.5569i 0.817585 + 0.689151i
\(333\) 0 0
\(334\) 9.00987 9.81054i 0.492998 0.536809i
\(335\) 17.8628 4.84380i 0.975949 0.264645i
\(336\) 0 0
\(337\) 16.3650i 0.891460i 0.895167 + 0.445730i \(0.147056\pi\)
−0.895167 + 0.445730i \(0.852944\pi\)
\(338\) 4.02106 + 3.69289i 0.218717 + 0.200866i
\(339\) 0 0
\(340\) −18.5186 8.61807i −1.00431 0.467380i
\(341\) 28.6469 + 28.6469i 1.55132 + 1.55132i
\(342\) 0 0
\(343\) 19.3152i 1.04293i
\(344\) 9.33075 1.19665i 0.503080 0.0645188i
\(345\) 0 0
\(346\) −12.4287 + 0.528749i −0.668168 + 0.0284257i
\(347\) −18.6768 18.6768i −1.00262 1.00262i −0.999997 0.00262421i \(-0.999165\pi\)
−0.00262421 0.999997i \(-0.500835\pi\)
\(348\) 0 0
\(349\) 15.2350 + 15.2350i 0.815511 + 0.815511i 0.985454 0.169943i \(-0.0543583\pi\)
−0.169943 + 0.985454i \(0.554358\pi\)
\(350\) 2.67595 12.3556i 0.143035 0.660436i
\(351\) 0 0
\(352\) 5.64470 + 26.1514i 0.300863 + 1.39387i
\(353\) 8.23255 0.438175 0.219087 0.975705i \(-0.429692\pi\)
0.219087 + 0.975705i \(0.429692\pi\)
\(354\) 0 0
\(355\) −29.3752 16.8425i −1.55907 0.893906i
\(356\) 1.07287 + 12.5865i 0.0568621 + 0.667085i
\(357\) 0 0
\(358\) −36.7707 + 1.56433i −1.94339 + 0.0826773i
\(359\) 4.96843i 0.262224i 0.991368 + 0.131112i \(0.0418547\pi\)
−0.991368 + 0.131112i \(0.958145\pi\)
\(360\) 0 0
\(361\) 18.9904i 0.999493i
\(362\) −1.57887 37.1126i −0.0829837 1.95060i
\(363\) 0 0
\(364\) −9.46277 + 11.2263i −0.495984 + 0.588418i
\(365\) 7.65339 13.3484i 0.400597 0.698685i
\(366\) 0 0
\(367\) −25.3790 −1.32477 −0.662385 0.749163i \(-0.730456\pi\)
−0.662385 + 0.749163i \(0.730456\pi\)
\(368\) 4.24566 0.729096i 0.221320 0.0380067i
\(369\) 0 0
\(370\) 15.6878 30.2750i 0.815569 1.57392i
\(371\) −6.46184 6.46184i −0.335482 0.335482i
\(372\) 0 0
\(373\) −2.85715 2.85715i −0.147938 0.147938i 0.629259 0.777196i \(-0.283359\pi\)
−0.777196 + 0.629259i \(0.783359\pi\)
\(374\) −1.29843 30.5205i −0.0671401 1.57818i
\(375\) 0 0
\(376\) 10.9327 14.1494i 0.563810 0.729700i
\(377\) 7.19992i 0.370815i
\(378\) 0 0
\(379\) −8.96148 8.96148i −0.460320 0.460320i 0.438440 0.898760i \(-0.355531\pi\)
−0.898760 + 0.438440i \(0.855531\pi\)
\(380\) −0.412247 + 0.150404i −0.0211478 + 0.00771555i
\(381\) 0 0
\(382\) 4.52834 4.93076i 0.231690 0.252280i
\(383\) 9.83688i 0.502641i −0.967904 0.251321i \(-0.919135\pi\)
0.967904 0.251321i \(-0.0808648\pi\)
\(384\) 0 0
\(385\) 18.2482 4.94829i 0.930012 0.252188i
\(386\) 17.4174 + 15.9959i 0.886522 + 0.814170i
\(387\) 0 0
\(388\) −9.10156 + 0.775814i −0.462062 + 0.0393860i
\(389\) 8.69886 + 8.69886i 0.441050 + 0.441050i 0.892365 0.451315i \(-0.149045\pi\)
−0.451315 + 0.892365i \(0.649045\pi\)
\(390\) 0 0
\(391\) −4.91879 −0.248754
\(392\) 8.51299 + 6.57765i 0.429971 + 0.332221i
\(393\) 0 0
\(394\) −0.674174 15.8470i −0.0339644 0.798359i
\(395\) 25.1637 + 14.4278i 1.26612 + 0.725941i
\(396\) 0 0
\(397\) 2.52696 2.52696i 0.126824 0.126824i −0.640845 0.767670i \(-0.721416\pi\)
0.767670 + 0.640845i \(0.221416\pi\)
\(398\) 2.24528 2.44481i 0.112546 0.122547i
\(399\) 0 0
\(400\) 12.8792 + 15.3011i 0.643962 + 0.765057i
\(401\) 11.5176i 0.575161i 0.957757 + 0.287580i \(0.0928508\pi\)
−0.957757 + 0.287580i \(0.907149\pi\)
\(402\) 0 0
\(403\) −24.8716 24.8716i −1.23894 1.23894i
\(404\) 11.3875 13.5098i 0.566551 0.672136i
\(405\) 0 0
\(406\) 4.42944 0.188441i 0.219829 0.00935215i
\(407\) 50.9963 2.52779
\(408\) 0 0
\(409\) 17.5055i 0.865591i −0.901492 0.432795i \(-0.857527\pi\)
0.901492 0.432795i \(-0.142473\pi\)
\(410\) −7.57241 23.8598i −0.373975 1.17835i
\(411\) 0 0
\(412\) 27.6094 2.35342i 1.36022 0.115945i
\(413\) 4.02412 + 4.02412i 0.198014 + 0.198014i
\(414\) 0 0
\(415\) 5.70095 + 21.0238i 0.279849 + 1.03202i
\(416\) −4.90080 22.7050i −0.240282 1.11320i
\(417\) 0 0
\(418\) −0.483378 0.443928i −0.0236428 0.0217132i
\(419\) 3.30068 + 3.30068i 0.161249 + 0.161249i 0.783120 0.621871i \(-0.213627\pi\)
−0.621871 + 0.783120i \(0.713627\pi\)
\(420\) 0 0
\(421\) −6.14311 + 6.14311i −0.299397 + 0.299397i −0.840778 0.541381i \(-0.817902\pi\)
0.541381 + 0.840778i \(0.317902\pi\)
\(422\) −0.255091 5.99611i −0.0124176 0.291886i
\(423\) 0 0
\(424\) 14.3397 1.83903i 0.696398 0.0893113i
\(425\) −11.5368 19.7082i −0.559615 0.955990i
\(426\) 0 0
\(427\) 7.68588 7.68588i 0.371946 0.371946i
\(428\) 1.68110 1.99440i 0.0812592 0.0964031i
\(429\) 0 0
\(430\) 9.33830 + 4.83888i 0.450333 + 0.233351i
\(431\) −8.73359 −0.420682 −0.210341 0.977628i \(-0.567457\pi\)
−0.210341 + 0.977628i \(0.567457\pi\)
\(432\) 0 0
\(433\) 2.28479i 0.109800i 0.998492 + 0.0548999i \(0.0174840\pi\)
−0.998492 + 0.0548999i \(0.982516\pi\)
\(434\) 14.6502 15.9521i 0.703234 0.765727i
\(435\) 0 0
\(436\) −4.16831 + 4.94513i −0.199626 + 0.236829i
\(437\) −0.0747238 + 0.0747238i −0.00357452 + 0.00357452i
\(438\) 0 0
\(439\) 27.7235 1.32317 0.661585 0.749870i \(-0.269884\pi\)
0.661585 + 0.749870i \(0.269884\pi\)
\(440\) −11.4563 + 27.6306i −0.546156 + 1.31724i
\(441\) 0 0
\(442\) 1.12731 + 26.4984i 0.0536208 + 1.26040i
\(443\) 15.8575 + 15.8575i 0.753410 + 0.753410i 0.975114 0.221704i \(-0.0711618\pi\)
−0.221704 + 0.975114i \(0.571162\pi\)
\(444\) 0 0
\(445\) −7.02488 + 12.2522i −0.333011 + 0.580809i
\(446\) −23.6127 + 25.7111i −1.11810 + 1.21746i
\(447\) 0 0
\(448\) 13.8400 3.60926i 0.653878 0.170521i
\(449\) 22.7098i 1.07174i −0.844301 0.535870i \(-0.819984\pi\)
0.844301 0.535870i \(-0.180016\pi\)
\(450\) 0 0
\(451\) 26.4728 26.4728i 1.24655 1.24655i
\(452\) −1.28038 15.0210i −0.0602242 0.706527i
\(453\) 0 0
\(454\) −0.429599 10.0981i −0.0201621 0.473925i
\(455\) −15.8433 + 4.29618i −0.742746 + 0.201408i
\(456\) 0 0
\(457\) −23.3185 −1.09079 −0.545397 0.838178i \(-0.683621\pi\)
−0.545397 + 0.838178i \(0.683621\pi\)
\(458\) −1.14605 26.9387i −0.0535513 1.25876i
\(459\) 0 0
\(460\) 4.36659 + 2.03210i 0.203593 + 0.0947470i
\(461\) −6.98422 + 6.98422i −0.325288 + 0.325288i −0.850791 0.525504i \(-0.823877\pi\)
0.525504 + 0.850791i \(0.323877\pi\)
\(462\) 0 0
\(463\) −0.177929 −0.00826905 −0.00413453 0.999991i \(-0.501316\pi\)
−0.00413453 + 0.999991i \(0.501316\pi\)
\(464\) −4.04856 + 5.72735i −0.187950 + 0.265885i
\(465\) 0 0
\(466\) −12.3394 11.3324i −0.571613 0.524961i
\(467\) −25.8586 + 25.8586i −1.19659 + 1.19659i −0.221414 + 0.975180i \(0.571067\pi\)
−0.975180 + 0.221414i \(0.928933\pi\)
\(468\) 0 0
\(469\) 10.4638 10.4638i 0.483175 0.483175i
\(470\) 19.0549 6.04747i 0.878937 0.278949i
\(471\) 0 0
\(472\) −8.93008 + 1.14526i −0.411040 + 0.0527149i
\(473\) 15.7298i 0.723255i
\(474\) 0 0
\(475\) −0.474658 0.124137i −0.0217788 0.00569581i
\(476\) −16.2725 + 1.38706i −0.745847 + 0.0635758i
\(477\) 0 0
\(478\) −23.7828 + 25.8962i −1.08780 + 1.18447i
\(479\) 6.74528 0.308200 0.154100 0.988055i \(-0.450752\pi\)
0.154100 + 0.988055i \(0.450752\pi\)
\(480\) 0 0
\(481\) −44.2757 −2.01880
\(482\) −18.0218 + 19.6233i −0.820870 + 0.893818i
\(483\) 0 0
\(484\) −22.6527 + 1.93091i −1.02967 + 0.0877687i
\(485\) −8.85978 5.07982i −0.402302 0.230663i
\(486\) 0 0
\(487\) 27.5084i 1.24652i −0.782014 0.623261i \(-0.785807\pi\)
0.782014 0.623261i \(-0.214193\pi\)
\(488\) 2.18739 + 17.0560i 0.0990186 + 0.772090i
\(489\) 0 0
\(490\) 3.63846 + 11.4644i 0.164369 + 0.517908i
\(491\) 1.96277 1.96277i 0.0885786 0.0885786i −0.661429 0.750008i \(-0.730050\pi\)
0.750008 + 0.661429i \(0.230050\pi\)
\(492\) 0 0
\(493\) 5.66291 5.66291i 0.255045 0.255045i
\(494\) 0.419675 + 0.385424i 0.0188821 + 0.0173411i
\(495\) 0 0
\(496\) 5.79926 + 33.7702i 0.260394 + 1.51633i
\(497\) −27.0738 −1.21442
\(498\) 0 0
\(499\) −10.0400 + 10.0400i −0.449452 + 0.449452i −0.895172 0.445720i \(-0.852948\pi\)
0.445720 + 0.895172i \(0.352948\pi\)
\(500\) 2.09954 + 22.2619i 0.0938945 + 0.995582i
\(501\) 0 0
\(502\) −1.84233 43.3055i −0.0822274 1.93282i
\(503\) 15.8104 0.704952 0.352476 0.935821i \(-0.385340\pi\)
0.352476 + 0.935821i \(0.385340\pi\)
\(504\) 0 0
\(505\) 19.0659 5.17003i 0.848421 0.230063i
\(506\) 0.306163 + 7.19659i 0.0136106 + 0.319927i
\(507\) 0 0
\(508\) 0.000471972 0.00553700i 2.09404e−5 0.000245664i
\(509\) −16.6015 + 16.6015i −0.735849 + 0.735849i −0.971772 0.235922i \(-0.924189\pi\)
0.235922 + 0.971772i \(0.424189\pi\)
\(510\) 0 0
\(511\) 12.3026i 0.544234i
\(512\) −8.86869 + 20.8170i −0.391945 + 0.919989i
\(513\) 0 0
\(514\) −0.874730 + 0.952464i −0.0385827 + 0.0420114i
\(515\) 26.8760 + 15.4096i 1.18430 + 0.679027i
\(516\) 0 0
\(517\) 21.1417 + 21.1417i 0.929809 + 0.929809i
\(518\) −1.15881 27.2387i −0.0509152 1.19680i
\(519\) 0 0
\(520\) 9.94649 23.9893i 0.436182 1.05200i
\(521\) −7.96468 −0.348939 −0.174469 0.984663i \(-0.555821\pi\)
−0.174469 + 0.984663i \(0.555821\pi\)
\(522\) 0 0
\(523\) 15.2514 15.2514i 0.666897 0.666897i −0.290099 0.956997i \(-0.593688\pi\)
0.956997 + 0.290099i \(0.0936883\pi\)
\(524\) −15.8956 + 18.8579i −0.694401 + 0.823813i
\(525\) 0 0
\(526\) −1.14450 + 1.24621i −0.0499025 + 0.0543372i
\(527\) 39.1243i 1.70428i
\(528\) 0 0
\(529\) −21.8402 −0.949573
\(530\) 14.3513 + 7.43650i 0.623381 + 0.323021i
\(531\) 0 0
\(532\) −0.226132 + 0.268275i −0.00980405 + 0.0116312i
\(533\) −22.9840 + 22.9840i −0.995549 + 0.995549i
\(534\) 0 0
\(535\) 2.81463 0.763235i 0.121687 0.0329975i
\(536\) 2.97799 + 23.2207i 0.128630 + 1.00298i
\(537\) 0 0
\(538\) 0.641426 + 15.0772i 0.0276538 + 0.650025i
\(539\) −12.7199 + 12.7199i −0.547884 + 0.547884i
\(540\) 0 0
\(541\) −6.80924 6.80924i −0.292752 0.292752i 0.545414 0.838167i \(-0.316372\pi\)
−0.838167 + 0.545414i \(0.816372\pi\)
\(542\) −4.64399 4.26498i −0.199477 0.183197i
\(543\) 0 0
\(544\) 14.0034 21.7126i 0.600392 0.930922i
\(545\) −6.97890 + 1.89245i −0.298943 + 0.0810635i
\(546\) 0 0
\(547\) 24.8809 + 24.8809i 1.06383 + 1.06383i 0.997819 + 0.0660132i \(0.0210279\pi\)
0.0660132 + 0.997819i \(0.478972\pi\)
\(548\) −46.1868 + 3.93695i −1.97300 + 0.168178i
\(549\) 0 0
\(550\) −28.1167 + 18.1059i −1.19890 + 0.772039i
\(551\) 0.172056i 0.00732985i
\(552\) 0 0
\(553\) 23.1922 0.986233
\(554\) −10.5535 + 0.448974i −0.448375 + 0.0190751i
\(555\) 0 0
\(556\) −14.3159 + 16.9839i −0.607129 + 0.720276i
\(557\) −3.05959 3.05959i −0.129639 0.129639i 0.639310 0.768949i \(-0.279220\pi\)
−0.768949 + 0.639310i \(0.779220\pi\)
\(558\) 0 0
\(559\) 13.6568i 0.577621i
\(560\) 15.0187 + 5.49129i 0.634656 + 0.232049i
\(561\) 0 0
\(562\) −25.1851 + 27.4232i −1.06237 + 1.15678i
\(563\) 32.0945 32.0945i 1.35262 1.35262i 0.469906 0.882716i \(-0.344288\pi\)
0.882716 0.469906i \(-0.155712\pi\)
\(564\) 0 0
\(565\) 8.38360 14.6219i 0.352701 0.615150i
\(566\) 1.15769 + 27.2125i 0.0486615 + 1.14383i
\(567\) 0 0
\(568\) 26.1876 33.8928i 1.09881 1.42211i
\(569\) −28.4585 −1.19304 −0.596521 0.802597i \(-0.703451\pi\)
−0.596521 + 0.802597i \(0.703451\pi\)
\(570\) 0 0
\(571\) −26.7837 26.7837i −1.12086 1.12086i −0.991612 0.129250i \(-0.958743\pi\)
−0.129250 0.991612i \(-0.541257\pi\)
\(572\) 38.6991 3.29870i 1.61809 0.137926i
\(573\) 0 0
\(574\) −14.7415 13.5384i −0.615297 0.565081i
\(575\) 2.72031 + 4.64710i 0.113445 + 0.193798i
\(576\) 0 0
\(577\) 33.4904i 1.39423i 0.716962 + 0.697113i \(0.245532\pi\)
−0.716962 + 0.697113i \(0.754468\pi\)
\(578\) −3.69289 + 4.02106i −0.153604 + 0.167254i
\(579\) 0 0
\(580\) −7.36669 + 2.68766i −0.305885 + 0.111599i
\(581\) 12.3155 + 12.3155i 0.510933 + 0.510933i
\(582\) 0 0
\(583\) 24.1738i 1.00118i
\(584\) 15.4012 + 11.8999i 0.637306 + 0.492422i
\(585\) 0 0
\(586\) −0.785264 18.4582i −0.0324389 0.762502i
\(587\) −12.3666 12.3666i −0.510425 0.510425i 0.404232 0.914657i \(-0.367539\pi\)
−0.914657 + 0.404232i \(0.867539\pi\)
\(588\) 0 0
\(589\) −0.594357 0.594357i −0.0244900 0.0244900i
\(590\) −8.93730 4.63109i −0.367943 0.190659i
\(591\) 0 0
\(592\) 35.2202 + 24.8965i 1.44754 + 1.02324i
\(593\) −24.1105 −0.990099 −0.495050 0.868865i \(-0.664850\pi\)
−0.495050 + 0.868865i \(0.664850\pi\)
\(594\) 0 0
\(595\) −15.8402 9.08210i −0.649385 0.372330i
\(596\) 24.8055 29.4284i 1.01607 1.20543i
\(597\) 0 0
\(598\) −0.265815 6.24818i −0.0108700 0.255507i
\(599\) 18.0184i 0.736213i −0.929784 0.368107i \(-0.880006\pi\)
0.929784 0.368107i \(-0.119994\pi\)
\(600\) 0 0
\(601\) 18.8361i 0.768342i 0.923262 + 0.384171i \(0.125513\pi\)
−0.923262 + 0.384171i \(0.874487\pi\)
\(602\) 8.40175 0.357433i 0.342430 0.0145679i
\(603\) 0 0
\(604\) −2.58951 30.3792i −0.105366 1.23611i
\(605\) −22.0510 12.6431i −0.896499 0.514015i
\(606\) 0 0
\(607\) −10.4336 −0.423486 −0.211743 0.977325i \(-0.567914\pi\)
−0.211743 + 0.977325i \(0.567914\pi\)
\(608\) −0.117114 0.542581i −0.00474962 0.0220046i
\(609\) 0 0
\(610\) −8.84516 + 17.0698i −0.358130 + 0.691137i
\(611\) −18.3555 18.3555i −0.742583 0.742583i
\(612\) 0 0
\(613\) 9.35631 + 9.35631i 0.377898 + 0.377898i 0.870343 0.492445i \(-0.163897\pi\)
−0.492445 + 0.870343i \(0.663897\pi\)
\(614\) −4.73868 + 0.201596i −0.191237 + 0.00813577i
\(615\) 0 0
\(616\) 3.04224 + 23.7216i 0.122575 + 0.955771i
\(617\) 22.8927i 0.921626i 0.887497 + 0.460813i \(0.152442\pi\)
−0.887497 + 0.460813i \(0.847558\pi\)
\(618\) 0 0
\(619\) 32.9542 + 32.9542i 1.32454 + 1.32454i 0.910057 + 0.414484i \(0.136038\pi\)
0.414484 + 0.910057i \(0.363962\pi\)
\(620\) −16.1634 + 34.7320i −0.649137 + 1.39487i
\(621\) 0 0
\(622\) 15.1398 + 13.9042i 0.607052 + 0.557509i
\(623\) 11.2923i 0.452415i
\(624\) 0 0
\(625\) −12.2393 + 21.7991i −0.489573 + 0.871962i
\(626\) −20.2897 + 22.0928i −0.810941 + 0.883006i
\(627\) 0 0
\(628\) −12.4761 10.5163i −0.497851 0.419644i
\(629\) −34.8239 34.8239i −1.38852 1.38852i
\(630\) 0 0
\(631\) 14.9668 0.595817 0.297908 0.954594i \(-0.403711\pi\)
0.297908 + 0.954594i \(0.403711\pi\)
\(632\) −22.4331 + 29.0336i −0.892341 + 1.15489i
\(633\) 0 0
\(634\) −1.14981 + 0.0489159i −0.0456646 + 0.00194270i
\(635\) −0.00309035 + 0.00538991i −0.000122637 + 0.000213892i
\(636\) 0 0
\(637\) 11.0436 11.0436i 0.437562 0.437562i
\(638\) −8.63778 7.93283i −0.341973 0.314064i
\(639\) 0 0
\(640\) −21.4015 + 13.4899i −0.845968 + 0.533234i
\(641\) 3.08889i 0.122004i −0.998138 0.0610019i \(-0.980570\pi\)
0.998138 0.0610019i \(-0.0194296\pi\)
\(642\) 0 0
\(643\) 18.1306 + 18.1306i 0.715001 + 0.715001i 0.967577 0.252576i \(-0.0812779\pi\)
−0.252576 + 0.967577i \(0.581278\pi\)
\(644\) 3.83696 0.327062i 0.151198 0.0128880i
\(645\) 0 0
\(646\) 0.0269394 + 0.633231i 0.00105992 + 0.0249141i
\(647\) 6.79255 0.267043 0.133521 0.991046i \(-0.457372\pi\)
0.133521 + 0.991046i \(0.457372\pi\)
\(648\) 0 0
\(649\) 15.0543i 0.590933i
\(650\) 24.4113 15.7198i 0.957489 0.616582i
\(651\) 0 0
\(652\) 19.0514 22.6019i 0.746111 0.885160i
\(653\) −12.2088 12.2088i −0.477769 0.477769i 0.426649 0.904417i \(-0.359694\pi\)
−0.904417 + 0.426649i \(0.859694\pi\)
\(654\) 0 0
\(655\) −26.6136 + 7.21672i −1.03988 + 0.281981i
\(656\) 31.2072 5.35913i 1.21844 0.209239i
\(657\) 0 0
\(658\) 10.8120 11.7728i 0.421496 0.458953i
\(659\) −24.8761 24.8761i −0.969034 0.969034i 0.0305007 0.999535i \(-0.490290\pi\)
−0.999535 + 0.0305007i \(0.990290\pi\)
\(660\) 0 0
\(661\) −21.1349 + 21.1349i −0.822052 + 0.822052i −0.986402 0.164350i \(-0.947447\pi\)
0.164350 + 0.986402i \(0.447447\pi\)
\(662\) −11.0819 + 0.471454i −0.430710 + 0.0183236i
\(663\) 0 0
\(664\) −27.3298 + 3.50498i −1.06060 + 0.136019i
\(665\) −0.378607 + 0.102666i −0.0146818 + 0.00398120i
\(666\) 0 0
\(667\) −1.33529 + 1.33529i −0.0517025 + 0.0517025i
\(668\) 1.59990 + 18.7694i 0.0619019 + 0.726209i
\(669\) 0 0
\(670\) −12.0421 + 23.2395i −0.465227 + 0.897818i
\(671\) −28.7530 −1.11000
\(672\) 0 0
\(673\) 48.6471i 1.87521i 0.347705 + 0.937604i \(0.386961\pi\)
−0.347705 + 0.937604i \(0.613039\pi\)
\(674\) −17.0458 15.6547i −0.656581 0.602995i
\(675\) 0 0
\(676\) −7.69302 + 0.655751i −0.295886 + 0.0252212i
\(677\) 8.69556 8.69556i 0.334197 0.334197i −0.519981 0.854178i \(-0.674061\pi\)
0.854178 + 0.519981i \(0.174061\pi\)
\(678\) 0 0
\(679\) −8.16566 −0.313369
\(680\) 26.6913 11.0450i 1.02357 0.423556i
\(681\) 0 0
\(682\) −57.2420 + 2.43523i −2.19191 + 0.0932498i
\(683\) 26.4514 + 26.4514i 1.01213 + 1.01213i 0.999925 + 0.0122093i \(0.00388645\pi\)
0.0122093 + 0.999925i \(0.496114\pi\)
\(684\) 0 0
\(685\) −44.9599 25.7781i −1.71783 0.984930i
\(686\) 20.1188 + 18.4768i 0.768138 + 0.705448i
\(687\) 0 0
\(688\) −7.67929 + 10.8636i −0.292770 + 0.414172i
\(689\) 20.9881i 0.799582i
\(690\) 0 0
\(691\) 8.89820 8.89820i 0.338503 0.338503i −0.517301 0.855804i \(-0.673063\pi\)
0.855804 + 0.517301i \(0.173063\pi\)
\(692\) 11.3384 13.4515i 0.431021 0.511349i
\(693\) 0 0
\(694\) 37.3198 1.58768i 1.41664 0.0602677i
\(695\) −23.9688 + 6.49953i −0.909187 + 0.246541i
\(696\) 0 0
\(697\) −36.1550 −1.36947
\(698\) −30.4425 + 1.29511i −1.15226 + 0.0490205i
\(699\) 0 0
\(700\) 10.3098 + 14.6066i 0.389675 + 0.552076i
\(701\) 15.7989 15.7989i 0.596716 0.596716i −0.342721 0.939437i \(-0.611349\pi\)
0.939437 + 0.342721i \(0.111349\pi\)
\(702\) 0 0
\(703\) −1.05806 −0.0399053
\(704\) −32.6390 19.1367i −1.23013 0.721241i
\(705\) 0 0
\(706\) −7.87519 + 8.57503i −0.296387 + 0.322726i
\(707\) 11.1686 11.1686i 0.420037 0.420037i
\(708\) 0 0
\(709\) 18.9259 18.9259i 0.710776 0.710776i −0.255922 0.966697i \(-0.582379\pi\)
0.966697 + 0.255922i \(0.0823790\pi\)
\(710\) 45.6432 14.4858i 1.71296 0.543643i
\(711\) 0 0
\(712\) −14.1364 10.9227i −0.529785 0.409344i
\(713\) 9.22531i 0.345490i
\(714\) 0 0
\(715\) 37.6711 + 21.5990i 1.40882 + 0.807757i
\(716\) 33.5452 39.7968i 1.25364 1.48728i
\(717\) 0 0
\(718\) −5.17512 4.75276i −0.193134 0.177372i
\(719\) −10.6789 −0.398256 −0.199128 0.979973i \(-0.563811\pi\)
−0.199128 + 0.979973i \(0.563811\pi\)
\(720\) 0 0
\(721\) 24.7704 0.922498
\(722\) −19.7804 18.1660i −0.736150 0.676070i
\(723\) 0 0
\(724\) 40.1669 + 33.8571i 1.49279 + 1.25829i
\(725\) −8.48197 2.21828i −0.315012 0.0823850i
\(726\) 0 0
\(727\) 32.2573i 1.19636i −0.801363 0.598179i \(-0.795891\pi\)
0.801363 0.598179i \(-0.204109\pi\)
\(728\) −2.64131 20.5954i −0.0978935 0.763317i
\(729\) 0 0
\(730\) 6.58249 + 20.7407i 0.243629 + 0.767648i
\(731\) 10.7414 10.7414i 0.397285 0.397285i
\(732\) 0 0
\(733\) −29.6986 + 29.6986i −1.09694 + 1.09694i −0.102175 + 0.994766i \(0.532580\pi\)
−0.994766 + 0.102175i \(0.967420\pi\)
\(734\) 24.2773 26.4347i 0.896092 0.975724i
\(735\) 0 0
\(736\) −3.30194 + 5.11973i −0.121711 + 0.188716i
\(737\) −39.1453 −1.44194
\(738\) 0 0
\(739\) 19.7806 19.7806i 0.727640 0.727640i −0.242509 0.970149i \(-0.577970\pi\)
0.970149 + 0.242509i \(0.0779704\pi\)
\(740\) 16.5277 + 45.3013i 0.607570 + 1.66531i
\(741\) 0 0
\(742\) 12.9120 0.549312i 0.474014 0.0201659i
\(743\) −34.3449 −1.25999 −0.629996 0.776598i \(-0.716944\pi\)
−0.629996 + 0.776598i \(0.716944\pi\)
\(744\) 0 0
\(745\) 41.5312 11.2619i 1.52159 0.412604i
\(746\) 5.70913 0.242882i 0.209026 0.00889255i
\(747\) 0 0
\(748\) 33.0323 + 27.8433i 1.20778 + 1.01805i
\(749\) 1.64878 1.64878i 0.0602451 0.0602451i
\(750\) 0 0
\(751\) 48.4556i 1.76817i −0.467326 0.884085i \(-0.654783\pi\)
0.467326 0.884085i \(-0.345217\pi\)
\(752\) 4.27991 + 24.9227i 0.156072 + 0.908837i
\(753\) 0 0
\(754\) 7.49944 + 6.88739i 0.273114 + 0.250824i
\(755\) 16.9554 29.5722i 0.617071 1.07624i
\(756\) 0 0
\(757\) 24.8358 + 24.8358i 0.902672 + 0.902672i 0.995667 0.0929947i \(-0.0296440\pi\)
−0.0929947 + 0.995667i \(0.529644\pi\)
\(758\) 17.9068 0.761803i 0.650403 0.0276699i
\(759\) 0 0
\(760\) 0.237691 0.573271i 0.00862196 0.0207947i
\(761\) 26.2421 0.951274 0.475637 0.879642i \(-0.342218\pi\)
0.475637 + 0.879642i \(0.342218\pi\)
\(762\) 0 0
\(763\) −4.08816 + 4.08816i −0.148001 + 0.148001i
\(764\) 0.804105 + 9.43345i 0.0290915 + 0.341290i
\(765\) 0 0
\(766\) 10.2461 + 9.40988i 0.370207 + 0.339993i
\(767\) 13.0704i 0.471943i
\(768\) 0 0
\(769\) 25.4168 0.916552 0.458276 0.888810i \(-0.348467\pi\)
0.458276 + 0.888810i \(0.348467\pi\)
\(770\) −12.3019 + 23.7408i −0.443330 + 0.855559i
\(771\) 0 0
\(772\) −33.3227 + 2.84042i −1.19931 + 0.102229i
\(773\) 30.1984 30.1984i 1.08616 1.08616i 0.0902412 0.995920i \(-0.471236\pi\)
0.995920 0.0902412i \(-0.0287638\pi\)
\(774\) 0 0
\(775\) −36.9633 + 21.6374i −1.32776 + 0.777240i
\(776\) 7.89839 10.2223i 0.283536 0.366960i
\(777\) 0 0
\(778\) −17.3820 + 0.739478i −0.623175 + 0.0265116i
\(779\) −0.549249 + 0.549249i −0.0196789 + 0.0196789i
\(780\) 0 0
\(781\) 50.6417 + 50.6417i 1.81210 + 1.81210i
\(782\) 4.70528 5.12341i 0.168260 0.183213i
\(783\) 0 0
\(784\) −14.9947 + 2.57501i −0.535526 + 0.0919645i
\(785\) −4.77447 17.6071i −0.170408 0.628425i
\(786\) 0 0
\(787\) −19.3428 19.3428i −0.689496 0.689496i 0.272625 0.962120i \(-0.412108\pi\)
−0.962120 + 0.272625i \(0.912108\pi\)
\(788\) 17.1511 + 14.4569i 0.610984 + 0.515005i
\(789\) 0 0
\(790\) −39.0994 + 12.4090i −1.39109 + 0.441492i
\(791\) 13.4764i 0.479165i