Properties

Label 720.2.u.a.179.16
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 179.16
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.16

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.638599 - 1.26182i) q^{2} +(-1.18438 + 1.61160i) q^{4} +(0.646750 + 2.14049i) q^{5} +0.594230i q^{7} +(2.78989 + 0.465314i) q^{8} +O(q^{10})\) \(q+(-0.638599 - 1.26182i) q^{2} +(-1.18438 + 1.61160i) q^{4} +(0.646750 + 2.14049i) q^{5} +0.594230i q^{7} +(2.78989 + 0.465314i) q^{8} +(2.28790 - 2.18300i) q^{10} +(-3.48671 + 3.48671i) q^{11} +(3.41630 - 3.41630i) q^{13} +(0.749812 - 0.379475i) q^{14} +(-1.19448 - 3.81749i) q^{16} -5.22898 q^{17} +(-2.52907 + 2.52907i) q^{19} +(-4.21561 - 1.49286i) q^{20} +(6.62621 + 2.17299i) q^{22} -2.90543 q^{23} +(-4.16343 + 2.76873i) q^{25} +(-6.49240 - 2.12911i) q^{26} +(-0.957658 - 0.703795i) q^{28} +(0.201837 - 0.201837i) q^{29} +7.91354i q^{31} +(-4.05419 + 3.94506i) q^{32} +(3.33922 + 6.59803i) q^{34} +(-1.27195 + 0.384318i) q^{35} +(-3.40301 - 3.40301i) q^{37} +(4.80630 + 1.57617i) q^{38} +(0.808359 + 6.27268i) q^{40} -4.36373 q^{41} +(2.94210 - 2.94210i) q^{43} +(-1.48957 - 9.74875i) q^{44} +(1.85541 + 3.66613i) q^{46} +10.7533i q^{47} +6.64689 q^{49} +(6.15240 + 3.48539i) q^{50} +(1.45949 + 9.55189i) q^{52} +(-5.71919 + 5.71919i) q^{53} +(-9.71830 - 5.20824i) q^{55} +(-0.276504 + 1.65784i) q^{56} +(-0.383576 - 0.125789i) q^{58} +(3.56275 - 3.56275i) q^{59} +(-9.03433 - 9.03433i) q^{61} +(9.98547 - 5.05358i) q^{62} +(7.56697 + 2.59635i) q^{64} +(9.52206 + 5.10307i) q^{65} +(7.72594 + 7.72594i) q^{67} +(6.19311 - 8.42699i) q^{68} +(1.29720 + 1.35954i) q^{70} -2.31103i q^{71} -2.62944 q^{73} +(-2.12083 + 6.46715i) q^{74} +(-1.08045 - 7.07123i) q^{76} +(-2.07191 - 2.07191i) q^{77} +9.07044i q^{79} +(7.39878 - 5.02573i) q^{80} +(2.78667 + 5.50624i) q^{82} +(-3.75900 + 3.75900i) q^{83} +(-3.38184 - 11.1926i) q^{85} +(-5.59122 - 1.83358i) q^{86} +(-11.3499 + 8.10511i) q^{88} +17.3168 q^{89} +(2.03007 + 2.03007i) q^{91} +(3.44114 - 4.68238i) q^{92} +(13.5687 - 6.86704i) q^{94} +(-7.04915 - 3.77779i) q^{95} +2.43368i q^{97} +(-4.24470 - 8.38718i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.638599 1.26182i −0.451558 0.892242i
\(3\) 0 0
\(4\) −1.18438 + 1.61160i −0.592191 + 0.805798i
\(5\) 0.646750 + 2.14049i 0.289236 + 0.957258i
\(6\) 0 0
\(7\) 0.594230i 0.224598i 0.993674 + 0.112299i \(0.0358214\pi\)
−0.993674 + 0.112299i \(0.964179\pi\)
\(8\) 2.78989 + 0.465314i 0.986375 + 0.164513i
\(9\) 0 0
\(10\) 2.28790 2.18300i 0.723499 0.690325i
\(11\) −3.48671 + 3.48671i −1.05128 + 1.05128i −0.0526694 + 0.998612i \(0.516773\pi\)
−0.998612 + 0.0526694i \(0.983227\pi\)
\(12\) 0 0
\(13\) 3.41630 3.41630i 0.947511 0.947511i −0.0511786 0.998690i \(-0.516298\pi\)
0.998690 + 0.0511786i \(0.0162978\pi\)
\(14\) 0.749812 0.379475i 0.200396 0.101419i
\(15\) 0 0
\(16\) −1.19448 3.81749i −0.298619 0.954372i
\(17\) −5.22898 −1.26821 −0.634107 0.773246i \(-0.718632\pi\)
−0.634107 + 0.773246i \(0.718632\pi\)
\(18\) 0 0
\(19\) −2.52907 + 2.52907i −0.580209 + 0.580209i −0.934961 0.354751i \(-0.884566\pi\)
0.354751 + 0.934961i \(0.384566\pi\)
\(20\) −4.21561 1.49286i −0.942639 0.333814i
\(21\) 0 0
\(22\) 6.62621 + 2.17299i 1.41271 + 0.463283i
\(23\) −2.90543 −0.605824 −0.302912 0.953019i \(-0.597959\pi\)
−0.302912 + 0.953019i \(0.597959\pi\)
\(24\) 0 0
\(25\) −4.16343 + 2.76873i −0.832686 + 0.553746i
\(26\) −6.49240 2.12911i −1.27326 0.417553i
\(27\) 0 0
\(28\) −0.957658 0.703795i −0.180980 0.133005i
\(29\) 0.201837 0.201837i 0.0374802 0.0374802i −0.688118 0.725599i \(-0.741563\pi\)
0.725599 + 0.688118i \(0.241563\pi\)
\(30\) 0 0
\(31\) 7.91354i 1.42131i 0.703538 + 0.710657i \(0.251602\pi\)
−0.703538 + 0.710657i \(0.748398\pi\)
\(32\) −4.05419 + 3.94506i −0.716687 + 0.697395i
\(33\) 0 0
\(34\) 3.33922 + 6.59803i 0.572672 + 1.13155i
\(35\) −1.27195 + 0.384318i −0.214998 + 0.0649617i
\(36\) 0 0
\(37\) −3.40301 3.40301i −0.559452 0.559452i 0.369699 0.929151i \(-0.379461\pi\)
−0.929151 + 0.369699i \(0.879461\pi\)
\(38\) 4.80630 + 1.57617i 0.779685 + 0.255689i
\(39\) 0 0
\(40\) 0.808359 + 6.27268i 0.127813 + 0.991798i
\(41\) −4.36373 −0.681500 −0.340750 0.940154i \(-0.610681\pi\)
−0.340750 + 0.940154i \(0.610681\pi\)
\(42\) 0 0
\(43\) 2.94210 2.94210i 0.448666 0.448666i −0.446245 0.894911i \(-0.647239\pi\)
0.894911 + 0.446245i \(0.147239\pi\)
\(44\) −1.48957 9.74875i −0.224561 1.46968i
\(45\) 0 0
\(46\) 1.85541 + 3.66613i 0.273565 + 0.540542i
\(47\) 10.7533i 1.56853i 0.620427 + 0.784264i \(0.286959\pi\)
−0.620427 + 0.784264i \(0.713041\pi\)
\(48\) 0 0
\(49\) 6.64689 0.949556
\(50\) 6.15240 + 3.48539i 0.870081 + 0.492909i
\(51\) 0 0
\(52\) 1.45949 + 9.55189i 0.202394 + 1.32461i
\(53\) −5.71919 + 5.71919i −0.785591 + 0.785591i −0.980768 0.195177i \(-0.937472\pi\)
0.195177 + 0.980768i \(0.437472\pi\)
\(54\) 0 0
\(55\) −9.71830 5.20824i −1.31042 0.702280i
\(56\) −0.276504 + 1.65784i −0.0369494 + 0.221538i
\(57\) 0 0
\(58\) −0.383576 0.125789i −0.0503659 0.0165169i
\(59\) 3.56275 3.56275i 0.463831 0.463831i −0.436078 0.899909i \(-0.643633\pi\)
0.899909 + 0.436078i \(0.143633\pi\)
\(60\) 0 0
\(61\) −9.03433 9.03433i −1.15673 1.15673i −0.985175 0.171553i \(-0.945122\pi\)
−0.171553 0.985175i \(-0.554878\pi\)
\(62\) 9.98547 5.05358i 1.26816 0.641806i
\(63\) 0 0
\(64\) 7.56697 + 2.59635i 0.945871 + 0.324544i
\(65\) 9.52206 + 5.10307i 1.18107 + 0.632958i
\(66\) 0 0
\(67\) 7.72594 + 7.72594i 0.943874 + 0.943874i 0.998507 0.0546326i \(-0.0173988\pi\)
−0.0546326 + 0.998507i \(0.517399\pi\)
\(68\) 6.19311 8.42699i 0.751025 1.02192i
\(69\) 0 0
\(70\) 1.29720 + 1.35954i 0.155046 + 0.162496i
\(71\) 2.31103i 0.274269i −0.990552 0.137134i \(-0.956211\pi\)
0.990552 0.137134i \(-0.0437892\pi\)
\(72\) 0 0
\(73\) −2.62944 −0.307753 −0.153876 0.988090i \(-0.549176\pi\)
−0.153876 + 0.988090i \(0.549176\pi\)
\(74\) −2.12083 + 6.46715i −0.246542 + 0.751791i
\(75\) 0 0
\(76\) −1.08045 7.07123i −0.123936 0.811126i
\(77\) −2.07191 2.07191i −0.236116 0.236116i
\(78\) 0 0
\(79\) 9.07044i 1.02050i 0.860025 + 0.510252i \(0.170448\pi\)
−0.860025 + 0.510252i \(0.829552\pi\)
\(80\) 7.39878 5.02573i 0.827209 0.561894i
\(81\) 0 0
\(82\) 2.78667 + 5.50624i 0.307737 + 0.608063i
\(83\) −3.75900 + 3.75900i −0.412604 + 0.412604i −0.882645 0.470041i \(-0.844239\pi\)
0.470041 + 0.882645i \(0.344239\pi\)
\(84\) 0 0
\(85\) −3.38184 11.1926i −0.366812 1.21401i
\(86\) −5.59122 1.83358i −0.602917 0.197720i
\(87\) 0 0
\(88\) −11.3499 + 8.10511i −1.20991 + 0.864008i
\(89\) 17.3168 1.83558 0.917788 0.397070i \(-0.129973\pi\)
0.917788 + 0.397070i \(0.129973\pi\)
\(90\) 0 0
\(91\) 2.03007 + 2.03007i 0.212809 + 0.212809i
\(92\) 3.44114 4.68238i 0.358764 0.488172i
\(93\) 0 0
\(94\) 13.5687 6.86704i 1.39951 0.708281i
\(95\) −7.04915 3.77779i −0.723227 0.387593i
\(96\) 0 0
\(97\) 2.43368i 0.247103i 0.992338 + 0.123551i \(0.0394284\pi\)
−0.992338 + 0.123551i \(0.960572\pi\)
\(98\) −4.24470 8.38718i −0.428779 0.847233i
\(99\) 0 0
\(100\) 0.469017 9.98900i 0.0469017 0.998900i
\(101\) 9.22586 + 9.22586i 0.918007 + 0.918007i 0.996884 0.0788774i \(-0.0251336\pi\)
−0.0788774 + 0.996884i \(0.525134\pi\)
\(102\) 0 0
\(103\) 0.353806i 0.0348615i 0.999848 + 0.0174308i \(0.00554866\pi\)
−0.999848 + 0.0174308i \(0.994451\pi\)
\(104\) 11.1207 7.94144i 1.09048 0.778723i
\(105\) 0 0
\(106\) 10.8689 + 3.56432i 1.05568 + 0.346197i
\(107\) −7.83739 7.83739i −0.757670 0.757670i 0.218228 0.975898i \(-0.429972\pi\)
−0.975898 + 0.218228i \(0.929972\pi\)
\(108\) 0 0
\(109\) 5.04082 + 5.04082i 0.482823 + 0.482823i 0.906032 0.423209i \(-0.139096\pi\)
−0.423209 + 0.906032i \(0.639096\pi\)
\(110\) −0.365771 + 15.5887i −0.0348749 + 1.48633i
\(111\) 0 0
\(112\) 2.26847 0.709794i 0.214350 0.0670693i
\(113\) 13.6858 1.28745 0.643724 0.765257i \(-0.277388\pi\)
0.643724 + 0.765257i \(0.277388\pi\)
\(114\) 0 0
\(115\) −1.87909 6.21906i −0.175226 0.579930i
\(116\) 0.0862275 + 0.564333i 0.00800602 + 0.0523970i
\(117\) 0 0
\(118\) −6.77073 2.22038i −0.623296 0.204403i
\(119\) 3.10721i 0.284838i
\(120\) 0 0
\(121\) 13.3142i 1.21039i
\(122\) −5.63039 + 17.1690i −0.509751 + 1.55441i
\(123\) 0 0
\(124\) −12.7534 9.37266i −1.14529 0.841690i
\(125\) −8.61915 7.12111i −0.770920 0.636932i
\(126\) 0 0
\(127\) −21.2399 −1.88474 −0.942369 0.334575i \(-0.891407\pi\)
−0.942369 + 0.334575i \(0.891407\pi\)
\(128\) −1.55613 11.2062i −0.137544 0.990496i
\(129\) 0 0
\(130\) 0.358385 15.2739i 0.0314324 1.33961i
\(131\) −2.47505 2.47505i −0.216246 0.216246i 0.590668 0.806914i \(-0.298864\pi\)
−0.806914 + 0.590668i \(0.798864\pi\)
\(132\) 0 0
\(133\) −1.50285 1.50285i −0.130314 0.130314i
\(134\) 4.81497 14.6825i 0.415950 1.26838i
\(135\) 0 0
\(136\) −14.5883 2.43312i −1.25093 0.208638i
\(137\) 1.05127i 0.0898162i 0.998991 + 0.0449081i \(0.0142995\pi\)
−0.998991 + 0.0449081i \(0.985700\pi\)
\(138\) 0 0
\(139\) −2.76139 2.76139i −0.234218 0.234218i 0.580233 0.814451i \(-0.302962\pi\)
−0.814451 + 0.580233i \(0.802962\pi\)
\(140\) 0.887104 2.50504i 0.0749740 0.211715i
\(141\) 0 0
\(142\) −2.91610 + 1.47582i −0.244714 + 0.123848i
\(143\) 23.8233i 1.99220i
\(144\) 0 0
\(145\) 0.562570 + 0.301493i 0.0467189 + 0.0250376i
\(146\) 1.67916 + 3.31788i 0.138968 + 0.274590i
\(147\) 0 0
\(148\) 9.51475 1.45381i 0.782108 0.119503i
\(149\) 6.00428 + 6.00428i 0.491890 + 0.491890i 0.908901 0.417011i \(-0.136922\pi\)
−0.417011 + 0.908901i \(0.636922\pi\)
\(150\) 0 0
\(151\) −5.86656 −0.477414 −0.238707 0.971092i \(-0.576724\pi\)
−0.238707 + 0.971092i \(0.576724\pi\)
\(152\) −8.23265 + 5.87902i −0.667756 + 0.476852i
\(153\) 0 0
\(154\) −1.29126 + 3.93749i −0.104052 + 0.317292i
\(155\) −16.9389 + 5.11809i −1.36056 + 0.411095i
\(156\) 0 0
\(157\) −3.07654 + 3.07654i −0.245535 + 0.245535i −0.819135 0.573600i \(-0.805546\pi\)
0.573600 + 0.819135i \(0.305546\pi\)
\(158\) 11.4453 5.79238i 0.910537 0.460817i
\(159\) 0 0
\(160\) −11.0664 6.12651i −0.874878 0.484343i
\(161\) 1.72649i 0.136067i
\(162\) 0 0
\(163\) 11.6108 + 11.6108i 0.909426 + 0.909426i 0.996226 0.0867995i \(-0.0276639\pi\)
−0.0867995 + 0.996226i \(0.527664\pi\)
\(164\) 5.16832 7.03257i 0.403578 0.549151i
\(165\) 0 0
\(166\) 7.14368 + 2.34269i 0.554457 + 0.181828i
\(167\) −15.2444 −1.17965 −0.589823 0.807533i \(-0.700802\pi\)
−0.589823 + 0.807533i \(0.700802\pi\)
\(168\) 0 0
\(169\) 10.3422i 0.795554i
\(170\) −11.9634 + 11.4149i −0.917551 + 0.875480i
\(171\) 0 0
\(172\) 1.25690 + 8.22604i 0.0958380 + 0.627230i
\(173\) −8.88472 8.88472i −0.675493 0.675493i 0.283484 0.958977i \(-0.408510\pi\)
−0.958977 + 0.283484i \(0.908510\pi\)
\(174\) 0 0
\(175\) −1.64526 2.47403i −0.124370 0.187019i
\(176\) 17.4753 + 9.14567i 1.31725 + 0.689381i
\(177\) 0 0
\(178\) −11.0585 21.8507i −0.828869 1.63778i
\(179\) −16.3484 16.3484i −1.22193 1.22193i −0.966944 0.254990i \(-0.917928\pi\)
−0.254990 0.966944i \(-0.582072\pi\)
\(180\) 0 0
\(181\) 7.64457 7.64457i 0.568216 0.568216i −0.363412 0.931628i \(-0.618388\pi\)
0.931628 + 0.363412i \(0.118388\pi\)
\(182\) 1.26518 3.85798i 0.0937815 0.285972i
\(183\) 0 0
\(184\) −8.10583 1.35194i −0.597570 0.0996662i
\(185\) 5.08323 9.48503i 0.373726 0.697353i
\(186\) 0 0
\(187\) 18.2319 18.2319i 1.33325 1.33325i
\(188\) −17.3299 12.7360i −1.26392 0.928869i
\(189\) 0 0
\(190\) −0.265311 + 11.3072i −0.0192477 + 0.820314i
\(191\) 23.6358 1.71023 0.855113 0.518442i \(-0.173488\pi\)
0.855113 + 0.518442i \(0.173488\pi\)
\(192\) 0 0
\(193\) 11.6874i 0.841281i 0.907227 + 0.420640i \(0.138195\pi\)
−0.907227 + 0.420640i \(0.861805\pi\)
\(194\) 3.07087 1.55415i 0.220475 0.111581i
\(195\) 0 0
\(196\) −7.87246 + 10.7121i −0.562318 + 0.765150i
\(197\) 7.52719 7.52719i 0.536290 0.536290i −0.386147 0.922437i \(-0.626194\pi\)
0.922437 + 0.386147i \(0.126194\pi\)
\(198\) 0 0
\(199\) 9.24585 0.655421 0.327710 0.944778i \(-0.393723\pi\)
0.327710 + 0.944778i \(0.393723\pi\)
\(200\) −12.9038 + 5.78715i −0.912439 + 0.409213i
\(201\) 0 0
\(202\) 5.74975 17.5330i 0.404551 1.23362i
\(203\) 0.119938 + 0.119938i 0.00841798 + 0.00841798i
\(204\) 0 0
\(205\) −2.82224 9.34054i −0.197114 0.652371i
\(206\) 0.446439 0.225940i 0.0311049 0.0157420i
\(207\) 0 0
\(208\) −17.1224 8.96099i −1.18722 0.621333i
\(209\) 17.6363i 1.21993i
\(210\) 0 0
\(211\) −13.2934 + 13.2934i −0.915154 + 0.915154i −0.996672 0.0815182i \(-0.974023\pi\)
0.0815182 + 0.996672i \(0.474023\pi\)
\(212\) −2.44331 15.9907i −0.167807 1.09825i
\(213\) 0 0
\(214\) −4.88443 + 14.8943i −0.333893 + 1.01816i
\(215\) 8.20035 + 4.39474i 0.559259 + 0.299719i
\(216\) 0 0
\(217\) −4.70246 −0.319224
\(218\) 3.14155 9.57968i 0.212772 0.648818i
\(219\) 0 0
\(220\) 19.9038 9.49342i 1.34191 0.640046i
\(221\) −17.8637 + 17.8637i −1.20165 + 1.20165i
\(222\) 0 0
\(223\) 22.4740 1.50497 0.752487 0.658607i \(-0.228854\pi\)
0.752487 + 0.658607i \(0.228854\pi\)
\(224\) −2.34427 2.40912i −0.156633 0.160966i
\(225\) 0 0
\(226\) −8.73972 17.2690i −0.581357 1.14872i
\(227\) 20.4123 20.4123i 1.35481 1.35481i 0.474622 0.880190i \(-0.342585\pi\)
0.880190 0.474622i \(-0.157415\pi\)
\(228\) 0 0
\(229\) −1.13042 + 1.13042i −0.0747005 + 0.0747005i −0.743470 0.668769i \(-0.766821\pi\)
0.668769 + 0.743470i \(0.266821\pi\)
\(230\) −6.64735 + 6.34256i −0.438313 + 0.418216i
\(231\) 0 0
\(232\) 0.657022 0.469186i 0.0431356 0.0308036i
\(233\) 6.91098i 0.452753i 0.974040 + 0.226377i \(0.0726880\pi\)
−0.974040 + 0.226377i \(0.927312\pi\)
\(234\) 0 0
\(235\) −23.0174 + 6.95469i −1.50149 + 0.453674i
\(236\) 1.52205 + 9.96138i 0.0990773 + 0.648430i
\(237\) 0 0
\(238\) −3.92075 + 1.98426i −0.254144 + 0.128621i
\(239\) 3.97843 0.257343 0.128672 0.991687i \(-0.458929\pi\)
0.128672 + 0.991687i \(0.458929\pi\)
\(240\) 0 0
\(241\) 12.1568 0.783086 0.391543 0.920160i \(-0.371941\pi\)
0.391543 + 0.920160i \(0.371941\pi\)
\(242\) −16.8002 + 8.50246i −1.07996 + 0.546559i
\(243\) 0 0
\(244\) 25.2598 3.85958i 1.61709 0.247085i
\(245\) 4.29888 + 14.2276i 0.274645 + 0.908970i
\(246\) 0 0
\(247\) 17.2801i 1.09951i
\(248\) −3.68229 + 22.0779i −0.233825 + 1.40195i
\(249\) 0 0
\(250\) −3.48139 + 15.4234i −0.220182 + 0.975459i
\(251\) 9.68497 9.68497i 0.611310 0.611310i −0.331977 0.943287i \(-0.607716\pi\)
0.943287 + 0.331977i \(0.107716\pi\)
\(252\) 0 0
\(253\) 10.1304 10.1304i 0.636892 0.636892i
\(254\) 13.5638 + 26.8010i 0.851068 + 1.68164i
\(255\) 0 0
\(256\) −13.1464 + 9.11981i −0.821653 + 0.569988i
\(257\) 22.8387 1.42464 0.712320 0.701855i \(-0.247644\pi\)
0.712320 + 0.701855i \(0.247644\pi\)
\(258\) 0 0
\(259\) 2.02217 2.02217i 0.125652 0.125652i
\(260\) −19.5018 + 9.30171i −1.20945 + 0.576868i
\(261\) 0 0
\(262\) −1.54250 + 4.70363i −0.0952962 + 0.290591i
\(263\) 7.69609 0.474562 0.237281 0.971441i \(-0.423744\pi\)
0.237281 + 0.971441i \(0.423744\pi\)
\(264\) 0 0
\(265\) −15.9408 8.54300i −0.979234 0.524792i
\(266\) −0.936609 + 2.85605i −0.0574272 + 0.175116i
\(267\) 0 0
\(268\) −21.6016 + 3.30062i −1.31953 + 0.201618i
\(269\) 10.3047 10.3047i 0.628286 0.628286i −0.319351 0.947637i \(-0.603465\pi\)
0.947637 + 0.319351i \(0.103465\pi\)
\(270\) 0 0
\(271\) 11.2542i 0.683642i 0.939765 + 0.341821i \(0.111044\pi\)
−0.939765 + 0.341821i \(0.888956\pi\)
\(272\) 6.24590 + 19.9616i 0.378713 + 1.21035i
\(273\) 0 0
\(274\) 1.32652 0.671342i 0.0801378 0.0405572i
\(275\) 4.86290 24.1704i 0.293244 1.45753i
\(276\) 0 0
\(277\) −17.5560 17.5560i −1.05484 1.05484i −0.998407 0.0564290i \(-0.982029\pi\)
−0.0564290 0.998407i \(-0.517971\pi\)
\(278\) −1.72096 + 5.24780i −0.103216 + 0.314742i
\(279\) 0 0
\(280\) −3.72742 + 0.480351i −0.222756 + 0.0287065i
\(281\) −13.7416 −0.819753 −0.409876 0.912141i \(-0.634428\pi\)
−0.409876 + 0.912141i \(0.634428\pi\)
\(282\) 0 0
\(283\) 4.27900 4.27900i 0.254360 0.254360i −0.568395 0.822756i \(-0.692436\pi\)
0.822756 + 0.568395i \(0.192436\pi\)
\(284\) 3.72444 + 2.73714i 0.221005 + 0.162420i
\(285\) 0 0
\(286\) 30.0607 15.2135i 1.77753 0.899594i
\(287\) 2.59306i 0.153063i
\(288\) 0 0
\(289\) 10.3422 0.608365
\(290\) 0.0211736 0.902396i 0.00124336 0.0529905i
\(291\) 0 0
\(292\) 3.11426 4.23759i 0.182248 0.247986i
\(293\) −11.6595 + 11.6595i −0.681153 + 0.681153i −0.960260 0.279107i \(-0.909962\pi\)
0.279107 + 0.960260i \(0.409962\pi\)
\(294\) 0 0
\(295\) 9.93026 + 5.32184i 0.578162 + 0.309849i
\(296\) −7.91056 11.0775i −0.459792 0.643867i
\(297\) 0 0
\(298\) 3.74200 11.4107i 0.216768 0.661002i
\(299\) −9.92582 + 9.92582i −0.574025 + 0.574025i
\(300\) 0 0
\(301\) 1.74828 + 1.74828i 0.100769 + 0.100769i
\(302\) 3.74638 + 7.40255i 0.215580 + 0.425969i
\(303\) 0 0
\(304\) 12.6756 + 6.63379i 0.726997 + 0.380474i
\(305\) 13.4950 25.1809i 0.772720 1.44185i
\(306\) 0 0
\(307\) −4.64313 4.64313i −0.264997 0.264997i 0.562083 0.827081i \(-0.310000\pi\)
−0.827081 + 0.562083i \(0.810000\pi\)
\(308\) 5.79300 0.885145i 0.330087 0.0504358i
\(309\) 0 0
\(310\) 17.2753 + 18.1054i 0.981169 + 1.02832i
\(311\) 0.760850i 0.0431438i −0.999767 0.0215719i \(-0.993133\pi\)
0.999767 0.0215719i \(-0.00686709\pi\)
\(312\) 0 0
\(313\) 31.2608 1.76697 0.883483 0.468464i \(-0.155192\pi\)
0.883483 + 0.468464i \(0.155192\pi\)
\(314\) 5.84672 + 1.91737i 0.329950 + 0.108203i
\(315\) 0 0
\(316\) −14.6179 10.7429i −0.822320 0.604334i
\(317\) −3.38359 3.38359i −0.190041 0.190041i 0.605673 0.795714i \(-0.292904\pi\)
−0.795714 + 0.605673i \(0.792904\pi\)
\(318\) 0 0
\(319\) 1.40749i 0.0788046i
\(320\) −0.663537 + 17.8762i −0.0370928 + 0.999312i
\(321\) 0 0
\(322\) −2.17853 + 1.10254i −0.121404 + 0.0614420i
\(323\) 13.2245 13.2245i 0.735829 0.735829i
\(324\) 0 0
\(325\) −4.76470 + 23.6823i −0.264298 + 1.31366i
\(326\) 7.23608 22.0654i 0.400770 1.22209i
\(327\) 0 0
\(328\) −12.1743 2.03051i −0.672215 0.112116i
\(329\) −6.38993 −0.352288
\(330\) 0 0
\(331\) −0.0840779 0.0840779i −0.00462134 0.00462134i 0.704792 0.709414i \(-0.251040\pi\)
−0.709414 + 0.704792i \(0.751040\pi\)
\(332\) −1.60589 10.5101i −0.0881348 0.576815i
\(333\) 0 0
\(334\) 9.73504 + 19.2357i 0.532678 + 1.05253i
\(335\) −11.5406 + 21.5341i −0.630529 + 1.17653i
\(336\) 0 0
\(337\) 27.7179i 1.50989i 0.655787 + 0.754946i \(0.272337\pi\)
−0.655787 + 0.754946i \(0.727663\pi\)
\(338\) −13.0500 + 6.60452i −0.709826 + 0.359238i
\(339\) 0 0
\(340\) 22.0433 + 7.80615i 1.19547 + 0.423348i
\(341\) −27.5922 27.5922i −1.49420 1.49420i
\(342\) 0 0
\(343\) 8.10939i 0.437866i
\(344\) 9.57713 6.83913i 0.516364 0.368741i
\(345\) 0 0
\(346\) −5.53715 + 16.8847i −0.297679 + 0.907727i
\(347\) 11.7819 + 11.7819i 0.632487 + 0.632487i 0.948691 0.316204i \(-0.102408\pi\)
−0.316204 + 0.948691i \(0.602408\pi\)
\(348\) 0 0
\(349\) 1.41586 + 1.41586i 0.0757895 + 0.0757895i 0.743985 0.668196i \(-0.232933\pi\)
−0.668196 + 0.743985i \(0.732933\pi\)
\(350\) −2.07112 + 3.65594i −0.110706 + 0.195418i
\(351\) 0 0
\(352\) 0.380509 27.8911i 0.0202812 1.48660i
\(353\) 12.4948 0.665031 0.332515 0.943098i \(-0.392103\pi\)
0.332515 + 0.943098i \(0.392103\pi\)
\(354\) 0 0
\(355\) 4.94674 1.49466i 0.262546 0.0793283i
\(356\) −20.5097 + 27.9077i −1.08701 + 1.47910i
\(357\) 0 0
\(358\) −10.1886 + 31.0687i −0.538487 + 1.64203i
\(359\) 1.11928i 0.0590733i −0.999564 0.0295366i \(-0.990597\pi\)
0.999564 0.0295366i \(-0.00940317\pi\)
\(360\) 0 0
\(361\) 6.20757i 0.326714i
\(362\) −14.5279 4.76426i −0.763569 0.250404i
\(363\) 0 0
\(364\) −5.67602 + 0.867271i −0.297504 + 0.0454574i
\(365\) −1.70059 5.62830i −0.0890130 0.294599i
\(366\) 0 0
\(367\) −12.5630 −0.655784 −0.327892 0.944715i \(-0.606338\pi\)
−0.327892 + 0.944715i \(0.606338\pi\)
\(368\) 3.47047 + 11.0915i 0.180911 + 0.578182i
\(369\) 0 0
\(370\) −15.2146 0.356991i −0.790967 0.0185591i
\(371\) −3.39851 3.39851i −0.176442 0.176442i
\(372\) 0 0
\(373\) 20.4047 + 20.4047i 1.05652 + 1.05652i 0.998304 + 0.0582111i \(0.0185397\pi\)
0.0582111 + 0.998304i \(0.481460\pi\)
\(374\) −34.6483 11.3625i −1.79162 0.587542i
\(375\) 0 0
\(376\) −5.00366 + 30.0005i −0.258044 + 1.54716i
\(377\) 1.37907i 0.0710259i
\(378\) 0 0
\(379\) 9.82205 + 9.82205i 0.504525 + 0.504525i 0.912841 0.408316i \(-0.133884\pi\)
−0.408316 + 0.912841i \(0.633884\pi\)
\(380\) 14.4371 6.88603i 0.740610 0.353246i
\(381\) 0 0
\(382\) −15.0938 29.8241i −0.772266 1.52593i
\(383\) 16.0018i 0.817655i 0.912612 + 0.408827i \(0.134062\pi\)
−0.912612 + 0.408827i \(0.865938\pi\)
\(384\) 0 0
\(385\) 3.09489 5.77491i 0.157730 0.294316i
\(386\) 14.7475 7.46360i 0.750626 0.379887i
\(387\) 0 0
\(388\) −3.92211 2.88241i −0.199115 0.146332i
\(389\) 1.41189 + 1.41189i 0.0715855 + 0.0715855i 0.741993 0.670408i \(-0.233881\pi\)
−0.670408 + 0.741993i \(0.733881\pi\)
\(390\) 0 0
\(391\) 15.1924 0.768314
\(392\) 18.5441 + 3.09289i 0.936618 + 0.156215i
\(393\) 0 0
\(394\) −14.3048 4.69110i −0.720666 0.236334i
\(395\) −19.4152 + 5.86631i −0.976886 + 0.295166i
\(396\) 0 0
\(397\) 11.3004 11.3004i 0.567153 0.567153i −0.364177 0.931330i \(-0.618650\pi\)
0.931330 + 0.364177i \(0.118650\pi\)
\(398\) −5.90439 11.6666i −0.295960 0.584794i
\(399\) 0 0
\(400\) 15.5427 + 12.5867i 0.777136 + 0.629333i
\(401\) 17.8120i 0.889491i 0.895657 + 0.444745i \(0.146706\pi\)
−0.895657 + 0.444745i \(0.853294\pi\)
\(402\) 0 0
\(403\) 27.0350 + 27.0350i 1.34671 + 1.34671i
\(404\) −25.7953 + 3.94141i −1.28336 + 0.196092i
\(405\) 0 0
\(406\) 0.0747478 0.227932i 0.00370967 0.0113121i
\(407\) 23.7306 1.17628
\(408\) 0 0
\(409\) 33.7224i 1.66747i 0.552168 + 0.833733i \(0.313801\pi\)
−0.552168 + 0.833733i \(0.686199\pi\)
\(410\) −9.98380 + 9.52602i −0.493065 + 0.470457i
\(411\) 0 0
\(412\) −0.570192 0.419041i −0.0280913 0.0206447i
\(413\) 2.11709 + 2.11709i 0.104175 + 0.104175i
\(414\) 0 0
\(415\) −10.4772 5.61498i −0.514308 0.275629i
\(416\) −0.372826 + 27.3278i −0.0182793 + 1.33986i
\(417\) 0 0
\(418\) −22.2538 + 11.2625i −1.08847 + 0.550867i
\(419\) 10.1570 + 10.1570i 0.496200 + 0.496200i 0.910253 0.414053i \(-0.135887\pi\)
−0.414053 + 0.910253i \(0.635887\pi\)
\(420\) 0 0
\(421\) 3.90653 3.90653i 0.190393 0.190393i −0.605473 0.795866i \(-0.707016\pi\)
0.795866 + 0.605473i \(0.207016\pi\)
\(422\) 25.2630 + 8.28471i 1.22978 + 0.403294i
\(423\) 0 0
\(424\) −18.6171 + 13.2947i −0.904128 + 0.645647i
\(425\) 21.7705 14.4776i 1.05602 0.702268i
\(426\) 0 0
\(427\) 5.36847 5.36847i 0.259798 0.259798i
\(428\) 21.9132 3.34824i 1.05921 0.161843i
\(429\) 0 0
\(430\) 0.308639 13.1538i 0.0148839 0.634335i
\(431\) 0.155915 0.00751015 0.00375507 0.999993i \(-0.498805\pi\)
0.00375507 + 0.999993i \(0.498805\pi\)
\(432\) 0 0
\(433\) 4.49972i 0.216243i 0.994138 + 0.108121i \(0.0344835\pi\)
−0.994138 + 0.108121i \(0.965517\pi\)
\(434\) 3.00299 + 5.93367i 0.144148 + 0.284825i
\(435\) 0 0
\(436\) −14.0940 + 2.15350i −0.674981 + 0.103134i
\(437\) 7.34805 7.34805i 0.351505 0.351505i
\(438\) 0 0
\(439\) −22.8807 −1.09204 −0.546018 0.837773i \(-0.683857\pi\)
−0.546018 + 0.837773i \(0.683857\pi\)
\(440\) −24.6895 19.0525i −1.17703 0.908292i
\(441\) 0 0
\(442\) 33.9486 + 11.1331i 1.61477 + 0.529546i
\(443\) −23.6054 23.6054i −1.12153 1.12153i −0.991512 0.130015i \(-0.958498\pi\)
−0.130015 0.991512i \(-0.541502\pi\)
\(444\) 0 0
\(445\) 11.1996 + 37.0665i 0.530914 + 1.75712i
\(446\) −14.3519 28.3582i −0.679583 1.34280i
\(447\) 0 0
\(448\) −1.54283 + 4.49652i −0.0728918 + 0.212440i
\(449\) 13.5006i 0.637132i −0.947901 0.318566i \(-0.896799\pi\)
0.947901 0.318566i \(-0.103201\pi\)
\(450\) 0 0
\(451\) 15.2150 15.2150i 0.716448 0.716448i
\(452\) −16.2092 + 22.0559i −0.762416 + 1.03742i
\(453\) 0 0
\(454\) −38.7919 12.7214i −1.82060 0.597044i
\(455\) −3.03240 + 5.65829i −0.142161 + 0.265265i
\(456\) 0 0
\(457\) 21.9008 1.02448 0.512238 0.858844i \(-0.328817\pi\)
0.512238 + 0.858844i \(0.328817\pi\)
\(458\) 2.14828 + 0.704504i 0.100382 + 0.0329193i
\(459\) 0 0
\(460\) 12.2482 + 4.33741i 0.571073 + 0.202233i
\(461\) −20.7061 + 20.7061i −0.964381 + 0.964381i −0.999387 0.0350065i \(-0.988855\pi\)
0.0350065 + 0.999387i \(0.488855\pi\)
\(462\) 0 0
\(463\) −15.1973 −0.706277 −0.353139 0.935571i \(-0.614886\pi\)
−0.353139 + 0.935571i \(0.614886\pi\)
\(464\) −1.01160 0.529422i −0.0469624 0.0245778i
\(465\) 0 0
\(466\) 8.72041 4.41335i 0.403965 0.204444i
\(467\) −10.4255 + 10.4255i −0.482432 + 0.482432i −0.905908 0.423475i \(-0.860810\pi\)
0.423475 + 0.905908i \(0.360810\pi\)
\(468\) 0 0
\(469\) −4.59099 + 4.59099i −0.211992 + 0.211992i
\(470\) 23.4744 + 24.6025i 1.08280 + 1.13483i
\(471\) 0 0
\(472\) 11.5975 8.28189i 0.533818 0.381205i
\(473\) 20.5165i 0.943349i
\(474\) 0 0
\(475\) 3.52729 17.5319i 0.161843 0.804421i
\(476\) 5.00757 + 3.68013i 0.229522 + 0.168678i
\(477\) 0 0
\(478\) −2.54062 5.02007i −0.116205 0.229613i
\(479\) 8.69764 0.397406 0.198703 0.980060i \(-0.436327\pi\)
0.198703 + 0.980060i \(0.436327\pi\)
\(480\) 0 0
\(481\) −23.2514 −1.06017
\(482\) −7.76330 15.3397i −0.353609 0.698702i
\(483\) 0 0
\(484\) 21.4572 + 15.7691i 0.975326 + 0.716779i
\(485\) −5.20928 + 1.57398i −0.236541 + 0.0714709i
\(486\) 0 0
\(487\) 18.9603i 0.859172i −0.903026 0.429586i \(-0.858659\pi\)
0.903026 0.429586i \(-0.141341\pi\)
\(488\) −21.0010 29.4086i −0.950670 1.33126i
\(489\) 0 0
\(490\) 15.2075 14.5102i 0.687003 0.655502i
\(491\) 30.6747 30.6747i 1.38433 1.38433i 0.547573 0.836758i \(-0.315552\pi\)
0.836758 0.547573i \(-0.184448\pi\)
\(492\) 0 0
\(493\) −1.05540 + 1.05540i −0.0475329 + 0.0475329i
\(494\) 21.8044 11.0351i 0.981028 0.496492i
\(495\) 0 0
\(496\) 30.2099 9.45255i 1.35646 0.424432i
\(497\) 1.37328 0.0616002
\(498\) 0 0
\(499\) 25.7124 25.7124i 1.15105 1.15105i 0.164704 0.986343i \(-0.447333\pi\)
0.986343 0.164704i \(-0.0526670\pi\)
\(500\) 21.6847 5.45646i 0.969770 0.244020i
\(501\) 0 0
\(502\) −18.4055 6.03588i −0.821478 0.269395i
\(503\) −8.27958 −0.369168 −0.184584 0.982817i \(-0.559094\pi\)
−0.184584 + 0.982817i \(0.559094\pi\)
\(504\) 0 0
\(505\) −13.7811 + 25.7147i −0.613249 + 1.14429i
\(506\) −19.2520 6.31347i −0.855855 0.280668i
\(507\) 0 0
\(508\) 25.1562 34.2301i 1.11612 1.51872i
\(509\) −9.07951 + 9.07951i −0.402442 + 0.402442i −0.879093 0.476651i \(-0.841851\pi\)
0.476651 + 0.879093i \(0.341851\pi\)
\(510\) 0 0
\(511\) 1.56249i 0.0691206i
\(512\) 19.9029 + 10.7646i 0.879591 + 0.475730i
\(513\) 0 0
\(514\) −14.5848 28.8184i −0.643308 1.27112i
\(515\) −0.757319 + 0.228824i −0.0333715 + 0.0100832i
\(516\) 0 0
\(517\) −37.4936 37.4936i −1.64896 1.64896i
\(518\) −3.84298 1.26026i −0.168851 0.0553727i
\(519\) 0 0
\(520\) 24.1910 + 18.6678i 1.06084 + 0.818636i
\(521\) −26.5377 −1.16264 −0.581320 0.813675i \(-0.697463\pi\)
−0.581320 + 0.813675i \(0.697463\pi\)
\(522\) 0 0
\(523\) −3.66089 + 3.66089i −0.160080 + 0.160080i −0.782602 0.622522i \(-0.786108\pi\)
0.622522 + 0.782602i \(0.286108\pi\)
\(524\) 6.92018 1.05737i 0.302310 0.0461916i
\(525\) 0 0
\(526\) −4.91472 9.71109i −0.214292 0.423424i
\(527\) 41.3797i 1.80253i
\(528\) 0 0
\(529\) −14.5585 −0.632977
\(530\) −0.599968 + 25.5700i −0.0260609 + 1.11069i
\(531\) 0 0
\(532\) 4.20194 0.642038i 0.182177 0.0278359i
\(533\) −14.9078 + 14.9078i −0.645729 + 0.645729i
\(534\) 0 0
\(535\) 11.7071 21.8447i 0.506140 0.944430i
\(536\) 17.9595 + 25.1495i 0.775734 + 1.08629i
\(537\) 0 0
\(538\) −19.5832 6.42208i −0.844290 0.276876i
\(539\) −23.1758 + 23.1758i −0.998250 + 0.998250i
\(540\) 0 0
\(541\) −25.5381 25.5381i −1.09797 1.09797i −0.994648 0.103321i \(-0.967053\pi\)
−0.103321 0.994648i \(-0.532947\pi\)
\(542\) 14.2007 7.18690i 0.609974 0.308704i
\(543\) 0 0
\(544\) 21.1993 20.6286i 0.908912 0.884446i
\(545\) −7.52970 + 14.0500i −0.322537 + 0.601836i
\(546\) 0 0
\(547\) −10.4273 10.4273i −0.445837 0.445837i 0.448131 0.893968i \(-0.352090\pi\)
−0.893968 + 0.448131i \(0.852090\pi\)
\(548\) −1.69423 1.24511i −0.0723737 0.0531884i
\(549\) 0 0
\(550\) −33.6041 + 9.29909i −1.43289 + 0.396514i
\(551\) 1.02092i 0.0434928i
\(552\) 0 0
\(553\) −5.38993 −0.229203
\(554\) −10.9413 + 33.3637i −0.464849 + 1.41749i
\(555\) 0 0
\(556\) 7.72078 1.17970i 0.327434 0.0500305i
\(557\) −22.6374 22.6374i −0.959178 0.959178i 0.0400207 0.999199i \(-0.487258\pi\)
−0.999199 + 0.0400207i \(0.987258\pi\)
\(558\) 0 0
\(559\) 20.1022i 0.850232i
\(560\) 2.98644 + 4.39658i 0.126200 + 0.185789i
\(561\) 0 0
\(562\) 8.77535 + 17.3394i 0.370166 + 0.731418i
\(563\) −14.9776 + 14.9776i −0.631231 + 0.631231i −0.948377 0.317146i \(-0.897276\pi\)
0.317146 + 0.948377i \(0.397276\pi\)
\(564\) 0 0
\(565\) 8.85127 + 29.2943i 0.372376 + 1.23242i
\(566\) −8.13190 2.66677i −0.341809 0.112093i
\(567\) 0 0
\(568\) 1.07536 6.44752i 0.0451209 0.270532i
\(569\) −18.3967 −0.771229 −0.385615 0.922660i \(-0.626011\pi\)
−0.385615 + 0.922660i \(0.626011\pi\)
\(570\) 0 0
\(571\) 20.5645 + 20.5645i 0.860599 + 0.860599i 0.991408 0.130808i \(-0.0417573\pi\)
−0.130808 + 0.991408i \(0.541757\pi\)
\(572\) −38.3935 28.2158i −1.60531 1.17976i
\(573\) 0 0
\(574\) −3.27197 + 1.65593i −0.136570 + 0.0691170i
\(575\) 12.0966 8.04435i 0.504461 0.335473i
\(576\) 0 0
\(577\) 32.3657i 1.34740i 0.739004 + 0.673701i \(0.235297\pi\)
−0.739004 + 0.673701i \(0.764703\pi\)
\(578\) −6.60452 13.0500i −0.274712 0.542808i
\(579\) 0 0
\(580\) −1.15218 + 0.549552i −0.0478418 + 0.0228189i
\(581\) −2.23371 2.23371i −0.0926699 0.0926699i
\(582\) 0 0
\(583\) 39.8823i 1.65175i
\(584\) −7.33585 1.22352i −0.303560 0.0506295i
\(585\) 0 0
\(586\) 22.1579 + 7.26642i 0.915333 + 0.300173i
\(587\) 19.4315 + 19.4315i 0.802026 + 0.802026i 0.983412 0.181386i \(-0.0580584\pi\)
−0.181386 + 0.983412i \(0.558058\pi\)
\(588\) 0 0
\(589\) −20.0139 20.0139i −0.824660 0.824660i
\(590\) 0.373748 15.9287i 0.0153870 0.655775i
\(591\) 0 0
\(592\) −8.92614 + 17.0558i −0.366862 + 0.700989i
\(593\) −6.88255 −0.282633 −0.141316 0.989965i \(-0.545133\pi\)
−0.141316 + 0.989965i \(0.545133\pi\)
\(594\) 0 0
\(595\) 6.65097 2.00959i 0.272663 0.0823852i
\(596\) −16.7878 + 2.56511i −0.687657 + 0.105071i
\(597\) 0 0
\(598\) 18.8632 + 6.18598i 0.771375 + 0.252964i
\(599\) 9.77996i 0.399598i −0.979837 0.199799i \(-0.935971\pi\)
0.979837 0.199799i \(-0.0640290\pi\)
\(600\) 0 0
\(601\) 39.7298i 1.62061i −0.586008 0.810305i \(-0.699301\pi\)
0.586008 0.810305i \(-0.300699\pi\)
\(602\) 1.08957 3.32247i 0.0444075 0.135414i
\(603\) 0 0
\(604\) 6.94825 9.45452i 0.282720 0.384699i
\(605\) 28.4990 8.61099i 1.15865 0.350086i
\(606\) 0 0
\(607\) −39.5940 −1.60707 −0.803535 0.595257i \(-0.797050\pi\)
−0.803535 + 0.595257i \(0.797050\pi\)
\(608\) 0.276001 20.2307i 0.0111933 0.820463i
\(609\) 0 0
\(610\) −40.3916 0.947740i −1.63541 0.0383729i
\(611\) 36.7365 + 36.7365i 1.48620 + 1.48620i
\(612\) 0 0
\(613\) 22.7872 + 22.7872i 0.920367 + 0.920367i 0.997055 0.0766879i \(-0.0244345\pi\)
−0.0766879 + 0.997055i \(0.524435\pi\)
\(614\) −2.89370 + 8.82389i −0.116780 + 0.356103i
\(615\) 0 0
\(616\) −4.81630 6.74447i −0.194054 0.271743i
\(617\) 24.4206i 0.983136i 0.870839 + 0.491568i \(0.163576\pi\)
−0.870839 + 0.491568i \(0.836424\pi\)
\(618\) 0 0
\(619\) −33.1727 33.1727i −1.33332 1.33332i −0.902378 0.430945i \(-0.858180\pi\)
−0.430945 0.902378i \(-0.641820\pi\)
\(620\) 11.8138 33.3604i 0.474455 1.33979i
\(621\) 0 0
\(622\) −0.960056 + 0.485878i −0.0384947 + 0.0194819i
\(623\) 10.2902i 0.412267i
\(624\) 0 0
\(625\) 9.66826 23.0548i 0.386731 0.922193i
\(626\) −19.9631 39.4455i −0.797887 1.57656i
\(627\) 0 0
\(628\) −1.31434 8.60194i −0.0524478 0.343255i
\(629\) 17.7943 + 17.7943i 0.709504 + 0.709504i
\(630\) 0 0
\(631\) −1.09691 −0.0436675 −0.0218337 0.999762i \(-0.506950\pi\)
−0.0218337 + 0.999762i \(0.506950\pi\)
\(632\) −4.22061 + 25.3055i −0.167887 + 1.00660i
\(633\) 0 0
\(634\) −2.10872 + 6.43024i −0.0837481 + 0.255377i
\(635\) −13.7369 45.4639i −0.545133 1.80418i
\(636\) 0 0
\(637\) 22.7078 22.7078i 0.899714 0.899714i
\(638\) 1.77601 0.898825i 0.0703127 0.0355848i
\(639\) 0 0
\(640\) 22.9803 10.5785i 0.908377 0.418151i
\(641\) 37.4511i 1.47923i −0.673030 0.739615i \(-0.735007\pi\)
0.673030 0.739615i \(-0.264993\pi\)
\(642\) 0 0
\(643\) −33.6486 33.6486i −1.32697 1.32697i −0.907998 0.418973i \(-0.862390\pi\)
−0.418973 0.907998i \(-0.637610\pi\)
\(644\) 2.78241 + 2.04483i 0.109642 + 0.0805775i
\(645\) 0 0
\(646\) −25.1320 8.24177i −0.988807 0.324268i
\(647\) −35.0053 −1.37620 −0.688099 0.725617i \(-0.741555\pi\)
−0.688099 + 0.725617i \(0.741555\pi\)
\(648\) 0 0
\(649\) 24.8445i 0.975234i
\(650\) 32.9256 9.11131i 1.29145 0.357375i
\(651\) 0 0
\(652\) −32.4635 + 4.96028i −1.27137 + 0.194259i
\(653\) 29.4066 + 29.4066i 1.15077 + 1.15077i 0.986399 + 0.164370i \(0.0525590\pi\)
0.164370 + 0.986399i \(0.447441\pi\)
\(654\) 0 0
\(655\) 3.69709 6.89857i 0.144457 0.269549i
\(656\) 5.21238 + 16.6585i 0.203509 + 0.650405i
\(657\) 0 0
\(658\) 4.08060 + 8.06294i 0.159078 + 0.314326i
\(659\) 15.5185 + 15.5185i 0.604517 + 0.604517i 0.941508 0.336991i \(-0.109409\pi\)
−0.336991 + 0.941508i \(0.609409\pi\)
\(660\) 0 0
\(661\) −28.6602 + 28.6602i −1.11475 + 1.11475i −0.122253 + 0.992499i \(0.539012\pi\)
−0.992499 + 0.122253i \(0.960988\pi\)
\(662\) −0.0523992 + 0.159783i −0.00203655 + 0.00621016i
\(663\) 0 0
\(664\) −12.2363 + 8.73808i −0.474861 + 0.339103i
\(665\) 2.24487 4.18881i 0.0870525 0.162435i
\(666\) 0 0
\(667\) −0.586424 + 0.586424i −0.0227064 + 0.0227064i
\(668\) 18.0552 24.5678i 0.698575 0.950555i
\(669\) 0 0
\(670\) 34.5420 + 0.810485i 1.33447 + 0.0313118i
\(671\) 63.0001 2.43209
\(672\) 0 0
\(673\) 18.9415i 0.730143i −0.930979 0.365071i \(-0.881045\pi\)
0.930979 0.365071i \(-0.118955\pi\)
\(674\) 34.9751 17.7007i 1.34719 0.681804i
\(675\) 0 0
\(676\) 16.6674 + 12.2491i 0.641055 + 0.471120i
\(677\) −2.06741 + 2.06741i −0.0794572 + 0.0794572i −0.745718 0.666261i \(-0.767894\pi\)
0.666261 + 0.745718i \(0.267894\pi\)
\(678\) 0 0
\(679\) −1.44617 −0.0554987
\(680\) −4.22689 32.7997i −0.162094 1.25781i
\(681\) 0 0
\(682\) −17.1960 + 52.4368i −0.658471 + 2.00791i
\(683\) 16.5476 + 16.5476i 0.633174 + 0.633174i 0.948863 0.315688i \(-0.102235\pi\)
−0.315688 + 0.948863i \(0.602235\pi\)
\(684\) 0 0
\(685\) −2.25024 + 0.679911i −0.0859773 + 0.0259780i
\(686\) 10.2326 5.17865i 0.390682 0.197722i
\(687\) 0 0
\(688\) −14.7457 7.71716i −0.562175 0.294214i
\(689\) 39.0769i 1.48871i
\(690\) 0 0
\(691\) 2.10025 2.10025i 0.0798972 0.0798972i −0.666029 0.745926i \(-0.732007\pi\)
0.745926 + 0.666029i \(0.232007\pi\)
\(692\) 24.8415 3.79567i 0.944332 0.144290i
\(693\) 0 0
\(694\) 7.34275 22.3906i 0.278727 0.849936i
\(695\) 4.12481 7.69666i 0.156463 0.291951i
\(696\) 0 0
\(697\) 22.8178 0.864287
\(698\) 0.882397 2.69074i 0.0333992 0.101846i
\(699\) 0 0
\(700\) 5.93576 + 0.278704i 0.224351 + 0.0105340i
\(701\) 22.6892 22.6892i 0.856960 0.856960i −0.134018 0.990979i \(-0.542788\pi\)
0.990979 + 0.134018i \(0.0427881\pi\)
\(702\) 0 0
\(703\) 17.2129 0.649199
\(704\) −35.4365 + 17.3311i −1.33556 + 0.653189i
\(705\) 0 0
\(706\) −7.97917 15.7662i −0.300300 0.593368i
\(707\) −5.48228 + 5.48228i −0.206182 + 0.206182i
\(708\) 0 0
\(709\) −6.85782 + 6.85782i −0.257551 + 0.257551i −0.824057 0.566506i \(-0.808295\pi\)
0.566506 + 0.824057i \(0.308295\pi\)
\(710\) −5.04498 5.28742i −0.189335 0.198433i
\(711\) 0 0
\(712\) 48.3119 + 8.05775i 1.81057 + 0.301977i
\(713\) 22.9923i 0.861067i
\(714\) 0 0
\(715\) −50.9935 + 15.4077i −1.90705 + 0.576215i
\(716\) 45.7096 6.98423i 1.70825 0.261013i
\(717\) 0 0
\(718\) −1.41233 + 0.714771i −0.0527077 + 0.0266750i
\(719\) −44.1136 −1.64516 −0.822580 0.568649i \(-0.807466\pi\)
−0.822580 + 0.568649i \(0.807466\pi\)
\(720\) 0 0
\(721\) −0.210242 −0.00782982
\(722\) 7.83284 3.96415i 0.291508 0.147530i
\(723\) 0 0
\(724\) 3.26586 + 21.3740i 0.121375 + 0.794360i
\(725\) −0.281502 + 1.39917i −0.0104547 + 0.0519638i
\(726\) 0 0
\(727\) 49.5060i 1.83608i 0.396491 + 0.918039i \(0.370228\pi\)
−0.396491 + 0.918039i \(0.629772\pi\)
\(728\) 4.71904 + 6.60828i 0.174899 + 0.244919i
\(729\) 0 0
\(730\) −6.01591 + 5.74007i −0.222659 + 0.212450i
\(731\) −15.3842 + 15.3842i −0.569004 + 0.569004i
\(732\) 0 0
\(733\) −1.73352 + 1.73352i −0.0640290 + 0.0640290i −0.738396 0.674367i \(-0.764417\pi\)
0.674367 + 0.738396i \(0.264417\pi\)
\(734\) 8.02273 + 15.8523i 0.296124 + 0.585118i
\(735\) 0 0
\(736\) 11.7792 11.4621i 0.434186 0.422499i
\(737\) −53.8762 −1.98455
\(738\) 0 0
\(739\) 12.4907 12.4907i 0.459479 0.459479i −0.439005 0.898484i \(-0.644669\pi\)
0.898484 + 0.439005i \(0.144669\pi\)
\(740\) 9.26554 + 19.4260i 0.340608 + 0.714114i
\(741\) 0 0
\(742\) −2.11803 + 6.45860i −0.0777552 + 0.237103i
\(743\) 16.6402 0.610469 0.305235 0.952277i \(-0.401265\pi\)
0.305235 + 0.952277i \(0.401265\pi\)
\(744\) 0 0
\(745\) −8.96886 + 16.7354i −0.328593 + 0.613138i
\(746\) 12.7166 38.7775i 0.465589 1.41975i
\(747\) 0 0
\(748\) 7.78891 + 50.9760i 0.284791 + 1.86387i
\(749\) 4.65721 4.65721i 0.170171 0.170171i
\(750\) 0 0
\(751\) 40.3813i 1.47353i 0.676146 + 0.736767i \(0.263649\pi\)
−0.676146 + 0.736767i \(0.736351\pi\)
\(752\) 41.0506 12.8446i 1.49696 0.468393i
\(753\) 0 0
\(754\) −1.74014 + 0.880675i −0.0633723 + 0.0320723i
\(755\) −3.79420 12.5573i −0.138085 0.457008i
\(756\) 0 0
\(757\) −0.105334 0.105334i −0.00382842 0.00382842i 0.705190 0.709018i \(-0.250862\pi\)
−0.709018 + 0.705190i \(0.750862\pi\)
\(758\) 6.12131 18.6660i 0.222336 0.677981i
\(759\) 0 0
\(760\) −17.9085 13.8197i −0.649609 0.501292i
\(761\) −19.6399 −0.711944 −0.355972 0.934497i \(-0.615850\pi\)
−0.355972 + 0.934497i \(0.615850\pi\)
\(762\) 0 0
\(763\) −2.99541 + 2.99541i −0.108441 + 0.108441i
\(764\) −27.9938 + 38.0913i −1.01278 + 1.37810i
\(765\) 0 0
\(766\) 20.1914 10.2188i 0.729546 0.369218i
\(767\) 24.3429i 0.878970i
\(768\) 0 0
\(769\) 0.0910921 0.00328487 0.00164243 0.999999i \(-0.499477\pi\)
0.00164243 + 0.999999i \(0.499477\pi\)
\(770\) −9.26329 0.217352i −0.333826 0.00783282i
\(771\) 0 0
\(772\) −18.8354 13.8424i −0.677902 0.498199i
\(773\) −7.00151 + 7.00151i −0.251827 + 0.251827i −0.821719 0.569892i \(-0.806985\pi\)
0.569892 + 0.821719i \(0.306985\pi\)
\(774\) 0 0
\(775\) −21.9105 32.9475i −0.787047 1.18351i
\(776\) −1.13243 + 6.78970i −0.0406517 + 0.243736i
\(777\) 0 0
\(778\) 0.879918 2.68318i 0.0315466 0.0961966i
\(779\) 11.0362 11.0362i 0.395413 0.395413i
\(780\) 0 0
\(781\) 8.05788 + 8.05788i 0.288334 + 0.288334i
\(782\) −9.70187 19.1701i −0.346938 0.685522i
\(783\) 0 0
\(784\) −7.93956 25.3744i −0.283556 0.906230i
\(785\) −8.57507 4.59556i −0.306057 0.164023i
\(786\) 0 0
\(787\) −15.1938 15.1938i −0.541601 0.541601i 0.382397 0.923998i \(-0.375099\pi\)
−0.923998 + 0.382397i \(0.875099\pi\)
\(788\) 3.21571 + 21.0458i 0.114555 + 0.749727i
\(789\) 0 0
\(790\) 19.8008 + 20.7523i 0.704480 + 0.738334i
\(791\) 8.13249i