Properties

Label 720.2.u.a.179.14
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 179.14
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.14

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.956592 + 1.04160i) q^{2} +(-0.169864 - 1.99277i) q^{4} +(1.93984 - 1.11222i) q^{5} +1.78786i q^{7} +(2.23816 + 1.72934i) q^{8} +O(q^{10})\) \(q+(-0.956592 + 1.04160i) q^{2} +(-0.169864 - 1.99277i) q^{4} +(1.93984 - 1.11222i) q^{5} +1.78786i q^{7} +(2.23816 + 1.72934i) q^{8} +(-0.697143 + 3.08448i) q^{10} +(3.34421 - 3.34421i) q^{11} +(-2.90349 + 2.90349i) q^{13} +(-1.86224 - 1.71025i) q^{14} +(-3.94229 + 0.676999i) q^{16} +4.56733 q^{17} +(0.0693845 - 0.0693845i) q^{19} +(-2.54591 - 3.67673i) q^{20} +(0.284286 + 6.68237i) q^{22} -1.07695 q^{23} +(2.52593 - 4.31505i) q^{25} +(-0.246821 - 5.80172i) q^{26} +(3.56280 - 0.303692i) q^{28} +(-1.23988 + 1.23988i) q^{29} -8.56612i q^{31} +(3.06600 - 4.75391i) q^{32} +(-4.36907 + 4.75733i) q^{34} +(1.98849 + 3.46816i) q^{35} +(7.62458 + 7.62458i) q^{37} +(0.00589828 + 0.138644i) q^{38} +(6.26508 + 0.865308i) q^{40} +7.91601 q^{41} +(-2.35179 + 2.35179i) q^{43} +(-7.23230 - 6.09619i) q^{44} +(1.03020 - 1.12175i) q^{46} -6.32188i q^{47} +3.80356 q^{49} +(2.07827 + 6.75876i) q^{50} +(6.27919 + 5.29279i) q^{52} +(3.61429 - 3.61429i) q^{53} +(2.76772 - 10.2067i) q^{55} +(-3.09182 + 4.00152i) q^{56} +(-0.105400 - 2.47751i) q^{58} +(2.25080 - 2.25080i) q^{59} +(4.29893 + 4.29893i) q^{61} +(8.92248 + 8.19429i) q^{62} +(2.01876 + 7.74110i) q^{64} +(-2.40297 + 8.86160i) q^{65} +(-5.85271 - 5.85271i) q^{67} +(-0.775822 - 9.10164i) q^{68} +(-5.51461 - 1.24639i) q^{70} +15.1431i q^{71} -6.88118 q^{73} +(-15.2354 + 0.648155i) q^{74} +(-0.150054 - 0.126482i) q^{76} +(5.97897 + 5.97897i) q^{77} +12.9721i q^{79} +(-6.89443 + 5.69797i) q^{80} +(-7.57239 + 8.24532i) q^{82} +(-6.88840 + 6.88840i) q^{83} +(8.85986 - 5.07987i) q^{85} +(-0.199923 - 4.69933i) q^{86} +(13.2682 - 1.70161i) q^{88} +6.31609 q^{89} +(-5.19103 - 5.19103i) q^{91} +(0.182935 + 2.14612i) q^{92} +(6.58487 + 6.04746i) q^{94} +(0.0574238 - 0.211766i) q^{95} +4.56728i q^{97} +(-3.63845 + 3.96179i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

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
\(5\) 1.93984 1.11222i 0.867521 0.497400i
\(6\) 0 0
\(7\) 1.78786i 0.675747i 0.941191 + 0.337874i \(0.109708\pi\)
−0.941191 + 0.337874i \(0.890292\pi\)
\(8\) 2.23816 + 1.72934i 0.791311 + 0.611414i
\(9\) 0 0
\(10\) −0.697143 + 3.08448i −0.220456 + 0.975397i
\(11\) 3.34421 3.34421i 1.00832 1.00832i 0.00835103 0.999965i \(-0.497342\pi\)
0.999965 0.00835103i \(-0.00265824\pi\)
\(12\) 0 0
\(13\) −2.90349 + 2.90349i −0.805282 + 0.805282i −0.983916 0.178634i \(-0.942832\pi\)
0.178634 + 0.983916i \(0.442832\pi\)
\(14\) −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 \(0.246417\pi\)
\(20\) −2.54591 3.67673i −0.569283 0.822142i
\(21\) 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 −0.812792 0.582553i \(-0.802054\pi\)
0.582553 + 0.812792i \(0.302054\pi\)
\(30\) 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
\(35\) 1.98849 + 3.46816i 0.336117 + 0.586225i
\(36\) 0 0
\(37\) 7.62458 + 7.62458i 1.25347 + 1.25347i 0.954153 + 0.299321i \(0.0967600\pi\)
0.299321 + 0.954153i \(0.403240\pi\)
\(38\) 0.00589828 + 0.138644i 0.000956828 + 0.0224910i
\(39\) 0 0
\(40\) 6.26508 + 0.865308i 0.990596 + 0.136817i
\(41\) 7.91601 1.23627 0.618137 0.786071i \(-0.287888\pi\)
0.618137 + 0.786071i \(0.287888\pi\)
\(42\) 0 0
\(43\) −2.35179 + 2.35179i −0.358645 + 0.358645i −0.863313 0.504668i \(-0.831615\pi\)
0.504668 + 0.863313i \(0.331615\pi\)
\(44\) −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
\(50\) 2.07827 + 6.75876i 0.293912 + 0.955832i
\(51\) 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 −0.545246 0.838276i \(-0.683564\pi\)
0.838276 + 0.545246i \(0.183564\pi\)
\(60\) 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 0.252559 0.967581i \(-0.418728\pi\)
−0.967581 + 0.252559i \(0.918728\pi\)
\(68\) −0.775822 9.10164i −0.0940822 1.10374i
\(69\) 0 0
\(70\) −5.51461 1.24639i −0.659122 0.148973i
\(71\) 15.1431i 1.79716i 0.438812 + 0.898579i \(0.355399\pi\)
−0.438812 + 0.898579i \(0.644601\pi\)
\(72\) 0 0
\(73\) −6.88118 −0.805381 −0.402691 0.915336i \(-0.631925\pi\)
−0.402691 + 0.915336i \(0.631925\pi\)
\(74\) −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 \(0.739643\pi\)
\(80\) −6.89443 + 5.69797i −0.770821 + 0.637052i
\(81\) 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
\(85\) 8.85986 5.07987i 0.960987 0.550989i
\(86\) −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 \(-0.391347\pi\)
0.334752 + 0.942306i \(0.391347\pi\)
\(90\) 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 \(0.0744839\pi\)
−0.972747 + 0.231869i \(0.925516\pi\)
\(98\) −3.63845 + 3.96179i −0.367539 + 0.400201i
\(99\) 0 0
\(100\) −9.02798 4.30064i −0.902798 0.430064i
\(101\) −6.24690 6.24690i −0.621589 0.621589i 0.324348 0.945938i \(-0.394855\pi\)
−0.945938 + 0.324348i \(0.894855\pi\)
\(102\) 0 0
\(103\) 13.8548i 1.36515i −0.730815 0.682576i \(-0.760860\pi\)
0.730815 0.682576i \(-0.239140\pi\)
\(104\) −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 \(0.799496\pi\)
\(110\) 7.98373 + 12.6465i 0.761219 + 1.20580i
\(111\) 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
\(115\) −2.08911 + 1.19781i −0.194811 + 0.111696i
\(116\) 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
\(125\) 0.100608 11.1799i 0.00899866 0.999960i
\(126\) 0 0
\(127\) 0.00277854 0.000246555 0.000123278 1.00000i \(-0.499961\pi\)
0.000123278 1.00000i \(0.499961\pi\)
\(128\) −9.99426 5.30233i −0.883376 0.468665i
\(129\) 0 0
\(130\) −6.93159 10.9799i −0.607940 0.962999i
\(131\) 8.71989 + 8.71989i 0.761860 + 0.761860i 0.976658 0.214798i \(-0.0689095\pi\)
−0.214798 + 0.976658i \(0.568909\pi\)
\(132\) 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 \(0.906111\pi\)
\(140\) 6.57348 4.55173i 0.555560 0.384691i
\(141\) 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 \(-0.960978\pi\)
−0.122285 0.992495i \(-0.539022\pi\)
\(150\) 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
\(155\) −9.52742 16.6169i −0.765261 1.33470i
\(156\) 0 0
\(157\) −5.76894 + 5.76894i −0.460411 + 0.460411i −0.898790 0.438379i \(-0.855553\pi\)
0.438379 + 0.898790i \(0.355553\pi\)
\(158\) −13.5117 12.4090i −1.07493 0.987204i
\(159\) 0 0
\(160\) 0.660154 12.6319i 0.0521898 0.998637i
\(161\) 1.92544i 0.151746i
\(162\) 0 0
\(163\) −10.4511 10.4511i −0.818594 0.818594i 0.167311 0.985904i \(-0.446492\pi\)
−0.985904 + 0.167311i \(0.946492\pi\)
\(164\) −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
\(170\) −3.18408 + 14.0878i −0.244208 + 1.08049i
\(171\) 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 \(-0.824719\pi\)
−0.523251 0.852179i \(-0.675281\pi\)
\(180\) 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
\(190\) 0.165644 + 0.262386i 0.0120171 + 0.0190355i
\(191\) 4.73383 0.342528 0.171264 0.985225i \(-0.445215\pi\)
0.171264 + 0.985225i \(0.445215\pi\)
\(192\) 0 0
\(193\) 16.7218i 1.20366i 0.798625 + 0.601829i \(0.205561\pi\)
−0.798625 + 0.601829i \(0.794439\pi\)
\(194\) −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 \(0.526512\pi\)
\(200\) 13.1156 5.28959i 0.927416 0.374031i
\(201\) 0 0
\(202\) 12.4825 0.531040i 0.878266 0.0373638i
\(203\) −2.21672 2.21672i −0.155583 0.155583i
\(204\) 0 0
\(205\) 15.3558 8.80435i 1.07249 0.614922i
\(206\) 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
\(220\) −20.8098 3.78169i −1.40300 0.254962i
\(221\) −13.2612 + 13.2612i −0.892042 + 0.892042i
\(222\) 0 0
\(223\) −24.6842 −1.65298 −0.826489 0.562952i \(-0.809665\pi\)
−0.826489 + 0.562952i \(0.809665\pi\)
\(224\) 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 \(0.466925\pi\)
\(230\) 0.750789 3.32183i 0.0495056 0.219035i
\(231\) 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
\(235\) −7.03132 12.2634i −0.458673 0.799977i
\(236\) −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 \(-0.797349\pi\)
−0.804093 + 0.594503i \(0.797349\pi\)
\(240\) 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
\(245\) 7.37828 4.23039i 0.471381 0.270270i
\(246\) 0 0
\(247\) 0.402914i 0.0256368i
\(248\) 14.8138 19.1724i 0.940674 1.21745i
\(249\) 0 0
\(250\) 11.5487 + 10.7994i 0.730406 + 0.683013i
\(251\) 21.6723 21.6723i 1.36795 1.36795i 0.504582 0.863364i \(-0.331647\pi\)
0.863364 0.504582i \(-0.168353\pi\)
\(252\) 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
\(260\) 18.0673 + 3.28332i 1.12049 + 0.203623i
\(261\) 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 −0.898673 0.438620i \(-0.855467\pi\)
0.438620 + 0.898673i \(0.355467\pi\)
\(270\) 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
\(275\) −5.98318 22.8777i −0.360800 1.37957i
\(276\) 0 0
\(277\) −5.28152 5.28152i −0.317336 0.317336i 0.530407 0.847743i \(-0.322039\pi\)
−0.847743 + 0.530407i \(0.822039\pi\)
\(278\) 15.6924 0.667599i 0.941169 0.0400399i
\(279\) 0 0
\(280\) −1.54705 + 11.2011i −0.0924539 + 0.669393i
\(281\) −26.3280 −1.57060 −0.785298 0.619118i \(-0.787490\pi\)
−0.785298 + 0.619118i \(0.787490\pi\)
\(282\) 0 0
\(283\) −13.6186 + 13.6186i −0.809540 + 0.809540i −0.984564 0.175024i \(-0.944000\pi\)
0.175024 + 0.984564i \(0.444000\pi\)
\(284\) 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
\(290\) −2.96000 4.68874i −0.173817 0.275332i
\(291\) 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 0.636187 0.771535i \(-0.280511\pi\)
−0.771535 + 0.636187i \(0.780511\pi\)
\(308\) 10.8991 12.9303i 0.621035 0.736775i
\(309\) 0 0
\(310\) 26.4220 + 5.97181i 1.50067 + 0.339176i
\(311\) 14.5352i 0.824214i 0.911135 + 0.412107i \(0.135207\pi\)
−0.911135 + 0.412107i \(0.864793\pi\)
\(312\) 0 0
\(313\) −21.2104 −1.19888 −0.599442 0.800418i \(-0.704611\pi\)
−0.599442 + 0.800418i \(0.704611\pi\)
\(314\) −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
\(320\) 12.5259 + 12.7712i 0.700217 + 0.713930i
\(321\) 0 0
\(322\) 2.00554 + 1.84186i 0.111764 + 0.102643i
\(323\) 0.316902 0.316902i 0.0176329 0.0176329i
\(324\) 0 0
\(325\) 5.19468 + 19.8627i 0.288149 + 1.10178i
\(326\) 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 \(-0.852944\pi\)
0.895167 0.445730i \(-0.147056\pi\)
\(338\) 4.02106 + 3.69289i 0.218717 + 0.200866i
\(339\) 0 0
\(340\) −11.6280 16.7928i −0.630617 0.910718i
\(341\) −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 \(0.554358\pi\)
\(350\) −12.0837 + 3.71566i −0.645901 + 0.198610i
\(351\) 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
\(355\) 16.8425 + 29.3752i 0.893906 + 1.55907i
\(356\) −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 \(-0.958145\pi\)
0.991368 0.131112i \(-0.0418547\pi\)
\(360\) 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
\(365\) −13.3484 + 7.65339i −0.698685 + 0.400597i
\(366\) 0 0
\(367\) 25.3790 1.32477 0.662385 0.749163i \(-0.269544\pi\)
0.662385 + 0.749163i \(0.269544\pi\)
\(368\) 4.24566 0.729096i 0.221320 0.0380067i
\(369\) 0 0
\(370\) −28.8333 + 18.2024i −1.49897 + 0.946298i
\(371\) 6.46184 + 6.46184i 0.335482 + 0.335482i
\(372\) 0 0
\(373\) 2.85715 + 2.85715i 0.147938 + 0.147938i 0.777196 0.629259i \(-0.216641\pi\)
−0.629259 + 0.777196i \(0.716641\pi\)
\(374\) 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 \(0.855531\pi\)
\(380\) −0.431755 0.0784613i −0.0221486 0.00402498i
\(381\) 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 0.451315 0.892365i \(-0.350955\pi\)
−0.892365 + 0.451315i \(0.850955\pi\)
\(390\) 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
\(395\) 14.4278 + 25.1637i 0.725941 + 1.26612i
\(396\) 0 0
\(397\) −2.52696 + 2.52696i −0.126824 + 0.126824i −0.767670 0.640845i \(-0.778584\pi\)
0.640845 + 0.767670i \(0.278584\pi\)
\(398\) 2.24528 2.44481i 0.112546 0.122547i
\(399\) 0 0
\(400\) −7.03668 + 18.7212i −0.351834 + 0.936062i
\(401\) 11.5176i 0.575161i −0.957757 0.287580i \(-0.907149\pi\)
0.957757 0.287580i \(-0.0928508\pi\)
\(402\) 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 \(-0.142473\pi\)
\(410\) −5.51859 + 24.4167i −0.272544 + 1.20586i
\(411\) 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 0.621871 0.783120i \(-0.286373\pi\)
−0.783120 + 0.621871i \(0.786373\pi\)
\(420\) 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
\(430\) −5.61451 8.89358i −0.270756 0.428887i
\(431\) 8.73359 0.420682 0.210341 0.977628i \(-0.432543\pi\)
0.210341 + 0.977628i \(0.432543\pi\)
\(432\) 0 0
\(433\) 2.28479i 0.109800i −0.998492 0.0548999i \(-0.982516\pi\)
0.998492 0.0548999i \(-0.0174840\pi\)
\(434\) −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 \(0.269884\pi\)
\(440\) 23.8455 18.0580i 1.13679 0.860879i
\(441\) 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
\(445\) 12.2522 7.02488i 0.580809 0.333011i
\(446\) 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 \(0.180016\pi\)
−0.844301 + 0.535870i \(0.819984\pi\)
\(450\) 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 \(-0.316379\pi\)
0.545397 + 0.838178i \(0.316379\pi\)
\(458\) −1.14605 26.9387i −0.0535513 1.25876i
\(459\) 0 0
\(460\) 2.74182 + 3.95966i 0.127838 + 0.184620i
\(461\) 6.98422 6.98422i 0.325288 0.325288i −0.525504 0.850791i \(-0.676123\pi\)
0.850791 + 0.525504i \(0.176123\pi\)
\(462\) 0 0
\(463\) 0.177929 0.00826905 0.00413453 0.999991i \(-0.498684\pi\)
0.00413453 + 0.999991i \(0.498684\pi\)
\(464\) 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
\(470\) 19.4997 + 4.40725i 0.899453 + 0.203291i
\(471\) 0 0
\(472\) 8.93008 1.14526i 0.411040 0.0527149i
\(473\) 15.7298i 0.723255i
\(474\) 0 0
\(475\) −0.124137 0.474658i −0.00569581 0.0217788i
\(476\) 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 \(-0.549248\pi\)
−0.154100 + 0.988055i \(0.549248\pi\)
\(480\) 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
\(485\) 5.07982 + 8.85978i 0.230663 + 0.402302i
\(486\) 0 0
\(487\) 27.5084i 1.24652i 0.782014 + 0.623261i \(0.214193\pi\)
−0.782014 + 0.623261i \(0.785807\pi\)
\(488\) 2.18739 + 17.0560i 0.0990186 + 0.772090i
\(489\) 0 0
\(490\) −2.65162 + 11.7320i −0.119788 + 0.529997i
\(491\) −1.96277 + 1.96277i −0.0885786 + 0.0885786i −0.750008 0.661429i \(-0.769950\pi\)
0.661429 + 0.750008i \(0.269950\pi\)
\(492\) 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 \(0.352948\pi\)
\(500\) −22.2961 + 1.69857i −0.997111 + 0.0759622i
\(501\) 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 −0.235922 0.971772i \(-0.575811\pi\)
0.971772 + 0.235922i \(0.0758111\pi\)
\(510\) 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
\(515\) −15.4096 26.8760i −0.679027 1.18430i
\(516\) 0 0
\(517\) −21.1417 21.1417i −0.929809 0.929809i
\(518\) −1.15881 27.2387i −0.0509152 1.19680i
\(519\) 0 0
\(520\) −20.7030 + 15.6782i −0.907886 + 0.687533i
\(521\) 7.96468 0.348939 0.174469 0.984663i \(-0.444179\pi\)
0.174469 + 0.984663i \(0.444179\pi\)
\(522\) 0 0
\(523\) −15.2514 + 15.2514i −0.666897 + 0.666897i −0.956997 0.290099i \(-0.906312\pi\)
0.290099 + 0.956997i \(0.406312\pi\)
\(524\) 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
\(530\) 8.62851 + 13.6679i 0.374798 + 0.593694i
\(531\) 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 \(-0.978972\pi\)
−0.0660132 0.997819i \(-0.521028\pi\)
\(548\) −46.1868 + 3.93695i −1.97300 + 0.168178i
\(549\) 0 0
\(550\) 29.5528 + 15.6525i 1.26014 + 0.667425i
\(551\) 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
\(560\) −10.1872 12.3263i −0.430486 0.520880i
\(561\) 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
\(565\) 14.6219 8.38360i 0.615150 0.352701i
\(566\) −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 \(-0.296549\pi\)
0.596521 + 0.802597i \(0.296549\pi\)
\(570\) 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 \(-0.754468\pi\)
0.716962 0.697113i \(-0.245532\pi\)
\(578\) −3.69289 + 4.02106i −0.153604 + 0.167254i
\(579\) 0 0
\(580\) 7.71530 + 1.40207i 0.320360 + 0.0582180i
\(581\) −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
\(590\) 5.37342 + 8.51168i 0.221220 + 0.350420i
\(591\) 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
\(595\) 9.08210 + 15.8402i 0.372330 + 0.649385i
\(596\) −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 \(0.119994\pi\)
−0.929784 + 0.368107i \(0.880006\pi\)
\(600\) 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
\(605\) −12.6431 22.0510i −0.514015 0.896499i
\(606\) 0 0
\(607\) 10.4336 0.423486 0.211743 0.977325i \(-0.432086\pi\)
0.211743 + 0.977325i \(0.432086\pi\)
\(608\) −0.117114 0.542581i −0.00474962 0.0220046i
\(609\) 0 0
\(610\) −16.2569 + 10.2630i −0.658223 + 0.415536i
\(611\) 18.3555 + 18.3555i 0.742583 + 0.742583i
\(612\) 0 0
\(613\) −9.35631 9.35631i −0.377898 0.377898i 0.492445 0.870343i \(-0.336103\pi\)
−0.870343 + 0.492445i \(0.836103\pi\)
\(614\) 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 \(0.363962\pi\)
\(620\) −31.4953 + 21.8086i −1.26488 + 0.875854i
\(621\) 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
\(635\) 0.00538991 0.00309035i 0.000213892 0.000122637i
\(636\) 0 0
\(637\) −11.0436 + 11.0436i −0.437562 + 0.437562i
\(638\) −8.63778 7.93283i −0.341973 0.314064i
\(639\) 0 0
\(640\) −25.2846 + 0.830157i −0.999461 + 0.0328148i
\(641\) 3.08889i 0.122004i 0.998138 + 0.0610019i \(0.0194296\pi\)
−0.998138 + 0.0610019i \(0.980570\pi\)
\(642\) 0 0
\(643\) −18.1306 18.1306i −0.715001 0.715001i 0.252576 0.967577i \(-0.418722\pi\)
−0.967577 + 0.252576i \(0.918722\pi\)
\(644\) −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
\(650\) −25.6582 13.5897i −1.00640 0.533032i
\(651\) 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 0.999535 0.0305007i \(-0.00971017\pi\)
−0.0305007 + 0.999535i \(0.509710\pi\)
\(660\) 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
\(670\) 22.1327 13.9724i 0.855062 0.539800i
\(671\) 28.7530 1.11000
\(672\) 0 0
\(673\) 48.6471i 1.87521i −0.347705 0.937604i \(-0.613039\pi\)
0.347705 0.937604i \(-0.386961\pi\)
\(674\) 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
\(680\) 28.6147 + 3.95214i 1.09732 + 0.151558i
\(681\) 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
\(685\) −25.7781 44.9599i −0.984930 1.71783i
\(686\) −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
\(700\) 7.68894 16.1408i 0.290615 0.610064i
\(701\) −15.7989 + 15.7989i −0.596716 + 0.596716i −0.939437 0.342721i \(-0.888651\pi\)
0.342721 + 0.939437i \(0.388651\pi\)
\(702\) 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 \(0.0823790\pi\)
\(710\) −46.7086 10.5569i −1.75294 0.396194i
\(711\) 0 0
\(712\) 14.1364 + 10.9227i 0.529785 + 0.409344i
\(713\) 9.22531i 0.345490i
\(714\) 0 0
\(715\) 21.5990 + 37.6711i 0.807757 + 1.40882i
\(716\) −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 \(-0.436189\pi\)
0.199128 + 0.979973i \(0.436189\pi\)
\(720\) 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
\(725\) 2.21828 + 8.48197i 0.0823850 + 0.315012i
\(726\) 0 0
\(727\) 32.2573i 1.19636i 0.801363 + 0.598179i \(0.204109\pi\)
−0.801363 + 0.598179i \(0.795891\pi\)
\(728\) −2.64131 20.5954i −0.0978935 0.763317i
\(729\) 0 0
\(730\) 4.79716 21.2248i 0.177551 0.785566i
\(731\) −10.7414 + 10.7414i −0.397285 + 0.397285i
\(732\) 0 0
\(733\) 29.6986 29.6986i 1.09694 1.09694i 0.102175 0.994766i \(-0.467420\pi\)
0.994766 0.102175i \(-0.0325801\pi\)
\(734\) −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 \(0.0779704\pi\)
\(740\) 8.62202 47.4450i 0.316952 1.74411i
\(741\) 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
\(755\) 29.5722 16.9554i 1.07624 0.617071i
\(756\) 0 0
\(757\) −24.8358 24.8358i −0.902672 0.902672i 0.0929947 0.995667i \(-0.470356\pi\)
−0.995667 + 0.0929947i \(0.970356\pi\)
\(758\) 17.9068 0.761803i 0.650403 0.0276699i
\(759\) 0 0
\(760\) 0.494739 0.374661i 0.0179461 0.0135904i
\(761\) −26.2421 −0.951274 −0.475637 0.879642i \(-0.657782\pi\)
−0.475637 + 0.879642i \(0.657782\pi\)
\(762\) 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 \(0.348467\pi\)
\(770\) −22.6102 + 14.2738i −0.814815 + 0.514392i
\(771\) 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 0.962120 0.272625i \(-0.0878917\pi\)
−0.272625 + 0.962120i \(0.587892\pi\)
\(788\) 17.1511 + 14.4569i 0.610984 + 0.515005i
\(789\) 0 0
\(790\) −40.0120 9.04338i −1.42356 0.321749i
\(791\) 13.4764i 0.479165i</