Properties

Label 720.2.u.a.179.15
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 179.15
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.15

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.638599 - 1.26182i) q^{2} +(-1.18438 + 1.61160i) q^{4} +(-2.14049 - 0.646750i) q^{5} -0.594230i q^{7} +(2.78989 + 0.465314i) q^{8} +O(q^{10})\) \(q+(-0.638599 - 1.26182i) q^{2} +(-1.18438 + 1.61160i) q^{4} +(-2.14049 - 0.646750i) q^{5} -0.594230i q^{7} +(2.78989 + 0.465314i) q^{8} +(0.550835 + 3.11393i) q^{10} +(3.48671 - 3.48671i) q^{11} +(-3.41630 + 3.41630i) q^{13} +(-0.749812 + 0.379475i) q^{14} +(-1.19448 - 3.81749i) q^{16} -5.22898 q^{17} +(-2.52907 + 2.52907i) q^{19} +(3.57746 - 2.68361i) q^{20} +(-6.62621 - 2.17299i) q^{22} -2.90543 q^{23} +(4.16343 + 2.76873i) q^{25} +(6.49240 + 2.12911i) q^{26} +(0.957658 + 0.703795i) q^{28} +(-0.201837 + 0.201837i) q^{29} +7.91354i q^{31} +(-4.05419 + 3.94506i) q^{32} +(3.33922 + 6.59803i) q^{34} +(-0.384318 + 1.27195i) q^{35} +(3.40301 + 3.40301i) q^{37} +(4.80630 + 1.57617i) q^{38} +(-5.67080 - 2.80036i) q^{40} +4.36373 q^{41} +(-2.94210 + 2.94210i) q^{43} +(1.48957 + 9.74875i) q^{44} +(1.85541 + 3.66613i) q^{46} +10.7533i q^{47} +6.64689 q^{49} +(0.834879 - 7.02161i) q^{50} +(-1.45949 - 9.55189i) q^{52} +(-5.71919 + 5.71919i) q^{53} +(-9.71830 + 5.20824i) q^{55} +(0.276504 - 1.65784i) q^{56} +(0.383576 + 0.125789i) q^{58} +(-3.56275 + 3.56275i) q^{59} +(-9.03433 - 9.03433i) q^{61} +(9.98547 - 5.05358i) q^{62} +(7.56697 + 2.59635i) q^{64} +(9.52206 - 5.10307i) q^{65} +(-7.72594 - 7.72594i) q^{67} +(6.19311 - 8.42699i) q^{68} +(1.85039 - 0.327323i) q^{70} +2.31103i q^{71} +2.62944 q^{73} +(2.12083 - 6.46715i) q^{74} +(-1.08045 - 7.07123i) q^{76} +(-2.07191 - 2.07191i) q^{77} +9.07044i q^{79} +(0.0878100 + 8.94384i) q^{80} +(-2.78667 - 5.50624i) q^{82} +(-3.75900 + 3.75900i) q^{83} +(11.1926 + 3.38184i) q^{85} +(5.59122 + 1.83358i) q^{86} +(11.3499 - 8.10511i) q^{88} -17.3168 q^{89} +(2.03007 + 2.03007i) q^{91} +(3.44114 - 4.68238i) q^{92} +(13.5687 - 6.86704i) q^{94} +(7.04915 - 3.77779i) q^{95} -2.43368i q^{97} +(-4.24470 - 8.38718i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

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
\(5\) −2.14049 0.646750i −0.957258 0.289236i
\(6\) 0 0
\(7\) 0.594230i 0.224598i −0.993674 0.112299i \(-0.964179\pi\)
0.993674 0.112299i \(-0.0358214\pi\)
\(8\) 2.78989 + 0.465314i 0.986375 + 0.164513i
\(9\) 0 0
\(10\) 0.550835 + 3.11393i 0.174189 + 0.984712i
\(11\) 3.48671 3.48671i 1.05128 1.05128i 0.0526694 0.998612i \(-0.483227\pi\)
0.998612 0.0526694i \(-0.0167730\pi\)
\(12\) 0 0
\(13\) −3.41630 + 3.41630i −0.947511 + 0.947511i −0.998690 0.0511786i \(-0.983702\pi\)
0.0511786 + 0.998690i \(0.483702\pi\)
\(14\) −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 \(0.384566\pi\)
\(20\) 3.57746 2.68361i 0.799945 0.600073i
\(21\) 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 −0.725599 0.688118i \(-0.758437\pi\)
0.688118 + 0.725599i \(0.258437\pi\)
\(30\) 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
\(35\) −0.384318 + 1.27195i −0.0649617 + 0.214998i
\(36\) 0 0
\(37\) 3.40301 + 3.40301i 0.559452 + 0.559452i 0.929151 0.369699i \(-0.120539\pi\)
−0.369699 + 0.929151i \(0.620539\pi\)
\(38\) 4.80630 + 1.57617i 0.779685 + 0.255689i
\(39\) 0 0
\(40\) −5.67080 2.80036i −0.896632 0.442777i
\(41\) 4.36373 0.681500 0.340750 0.940154i \(-0.389319\pi\)
0.340750 + 0.940154i \(0.389319\pi\)
\(42\) 0 0
\(43\) −2.94210 + 2.94210i −0.448666 + 0.448666i −0.894911 0.446245i \(-0.852761\pi\)
0.446245 + 0.894911i \(0.352761\pi\)
\(44\) 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
\(50\) 0.834879 7.02161i 0.118070 0.993005i
\(51\) 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 −0.899909 0.436078i \(-0.856367\pi\)
0.436078 + 0.899909i \(0.356367\pi\)
\(60\) 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 0.0546326 0.998507i \(-0.482601\pi\)
−0.998507 + 0.0546326i \(0.982601\pi\)
\(68\) 6.19311 8.42699i 0.751025 1.02192i
\(69\) 0 0
\(70\) 1.85039 0.327323i 0.221164 0.0391225i
\(71\) 2.31103i 0.274269i 0.990552 + 0.137134i \(0.0437892\pi\)
−0.990552 + 0.137134i \(0.956211\pi\)
\(72\) 0 0
\(73\) 2.62944 0.307753 0.153876 0.988090i \(-0.450824\pi\)
0.153876 + 0.988090i \(0.450824\pi\)
\(74\) 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 \(0.829552\pi\)
\(80\) 0.0878100 + 8.94384i 0.00981746 + 0.999952i
\(81\) 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
\(85\) 11.1926 + 3.38184i 1.21401 + 0.366812i
\(86\) 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 \(-0.870027\pi\)
−0.917788 + 0.397070i \(0.870027\pi\)
\(90\) 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 \(-0.960572\pi\)
0.992338 0.123551i \(-0.0394284\pi\)
\(98\) −4.24470 8.38718i −0.428779 0.847233i
\(99\) 0 0
\(100\) −9.39316 + 3.43053i −0.939316 + 0.343053i
\(101\) −9.22586 9.22586i −0.918007 0.918007i 0.0788774 0.996884i \(-0.474866\pi\)
−0.996884 + 0.0788774i \(0.974866\pi\)
\(102\) 0 0
\(103\) 0.353806i 0.0348615i −0.999848 0.0174308i \(-0.994451\pi\)
0.999848 0.0174308i \(-0.00554866\pi\)
\(104\) −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 \(0.639096\pi\)
\(110\) 12.7780 + 8.93677i 1.21833 + 0.852088i
\(111\) 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
\(115\) 6.21906 + 1.87909i 0.579930 + 0.175226i
\(116\) −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
\(125\) −7.12111 8.61915i −0.636932 0.770920i
\(126\) 0 0
\(127\) 21.2399 1.88474 0.942369 0.334575i \(-0.108593\pi\)
0.942369 + 0.334575i \(0.108593\pi\)
\(128\) −1.55613 11.2062i −0.137544 0.990496i
\(129\) 0 0
\(130\) −12.5199 8.75631i −1.09807 0.767979i
\(131\) 2.47505 + 2.47505i 0.216246 + 0.216246i 0.806914 0.590668i \(-0.201136\pi\)
−0.590668 + 0.806914i \(0.701136\pi\)
\(132\) 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 \(0.802962\pi\)
\(140\) −1.59468 2.12584i −0.134775 0.179666i
\(141\) 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 0.417011 0.908901i \(-0.363078\pi\)
−0.908901 + 0.417011i \(0.863078\pi\)
\(150\) 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
\(155\) 5.11809 16.9389i 0.411095 1.36056i
\(156\) 0 0
\(157\) 3.07654 3.07654i 0.245535 0.245535i −0.573600 0.819135i \(-0.694454\pi\)
0.819135 + 0.573600i \(0.194454\pi\)
\(158\) 11.4453 5.79238i 0.910537 0.460817i
\(159\) 0 0
\(160\) 11.2294 5.82233i 0.887766 0.460296i
\(161\) 1.72649i 0.136067i
\(162\) 0 0
\(163\) −11.6108 11.6108i −0.909426 0.909426i 0.0867995 0.996226i \(-0.472336\pi\)
−0.996226 + 0.0867995i \(0.972336\pi\)
\(164\) −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
\(170\) −2.88030 16.2827i −0.220909 1.24882i
\(171\) 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 \(0.0820721\pi\)
0.254990 + 0.966944i \(0.417928\pi\)
\(180\) 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
\(190\) −9.26847 6.48227i −0.672405 0.470273i
\(191\) −23.6358 −1.71023 −0.855113 0.518442i \(-0.826512\pi\)
−0.855113 + 0.518442i \(0.826512\pi\)
\(192\) 0 0
\(193\) 11.6874i 0.841281i −0.907227 0.420640i \(-0.861805\pi\)
0.907227 0.420640i \(-0.138195\pi\)
\(194\) −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 \(0.393723\pi\)
\(200\) 10.3272 + 9.66175i 0.730241 + 0.683189i
\(201\) 0 0
\(202\) −5.74975 + 17.5330i −0.404551 + 1.23362i
\(203\) 0.119938 + 0.119938i 0.00841798 + 0.00841798i
\(204\) 0 0
\(205\) −9.34054 2.82224i −0.652371 0.197114i
\(206\) −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
\(220\) 3.11660 21.8305i 0.210121 1.47181i
\(221\) 17.8637 17.8637i 1.20165 1.20165i
\(222\) 0 0
\(223\) −22.4740 −1.50497 −0.752487 0.658607i \(-0.771146\pi\)
−0.752487 + 0.658607i \(0.771146\pi\)
\(224\) 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 \(0.266821\pi\)
\(230\) −1.60041 9.04732i −0.105528 0.596562i
\(231\) 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
\(235\) 6.95469 23.0174i 0.453674 1.50149i
\(236\) −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 \(-0.541071\pi\)
−0.128672 + 0.991687i \(0.541071\pi\)
\(240\) 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
\(245\) −14.2276 4.29888i −0.908970 0.274645i
\(246\) 0 0
\(247\) 17.2801i 1.09951i
\(248\) −3.68229 + 22.0779i −0.233825 + 1.40195i
\(249\) 0 0
\(250\) −6.32828 + 14.4898i −0.400236 + 0.916412i
\(251\) −9.68497 + 9.68497i −0.611310 + 0.611310i −0.943287 0.331977i \(-0.892284\pi\)
0.331977 + 0.943287i \(0.392284\pi\)
\(252\) 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
\(260\) −3.05367 + 21.3897i −0.189380 + 1.32653i
\(261\) 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 −0.947637 0.319351i \(-0.896535\pi\)
0.319351 + 0.947637i \(0.396535\pi\)
\(270\) 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
\(275\) 24.1704 4.86290i 1.45753 0.293244i
\(276\) 0 0
\(277\) 17.5560 + 17.5560i 1.05484 + 1.05484i 0.998407 + 0.0564290i \(0.0179715\pi\)
0.0564290 + 0.998407i \(0.482029\pi\)
\(278\) −1.72096 + 5.24780i −0.103216 + 0.314742i
\(279\) 0 0
\(280\) −1.66406 + 3.36976i −0.0994466 + 0.201382i
\(281\) 13.7416 0.819753 0.409876 0.912141i \(-0.365572\pi\)
0.409876 + 0.912141i \(0.365572\pi\)
\(282\) 0 0
\(283\) −4.27900 + 4.27900i −0.254360 + 0.254360i −0.822756 0.568395i \(-0.807564\pi\)
0.568395 + 0.822756i \(0.307564\pi\)
\(284\) −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
\(290\) −0.739687 0.517329i −0.0434359 0.0303786i
\(291\) 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 0.827081 0.562083i \(-0.190000\pi\)
−0.562083 + 0.827081i \(0.690000\pi\)
\(308\) 5.79300 0.885145i 0.330087 0.0504358i
\(309\) 0 0
\(310\) −24.6422 + 4.35905i −1.39959 + 0.247578i
\(311\) 0.760850i 0.0431438i 0.999767 + 0.0215719i \(0.00686709\pi\)
−0.999767 + 0.0215719i \(0.993133\pi\)
\(312\) 0 0
\(313\) −31.2608 −1.76697 −0.883483 0.468464i \(-0.844808\pi\)
−0.883483 + 0.468464i \(0.844808\pi\)
\(314\) −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
\(320\) −14.5179 10.4514i −0.811573 0.584252i
\(321\) 0 0
\(322\) 2.17853 1.10254i 0.121404 0.0614420i
\(323\) 13.2245 13.2245i 0.735829 0.735829i
\(324\) 0 0
\(325\) −23.6823 + 4.76470i −1.31366 + 0.264298i
\(326\) −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 \(-0.727663\pi\)
0.655787 0.754946i \(-0.272337\pi\)
\(338\) −13.0500 + 6.60452i −0.709826 + 0.359238i
\(339\) 0 0
\(340\) −18.7065 + 14.0325i −1.01450 + 0.761021i
\(341\) 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 \(0.732933\pi\)
\(350\) −4.17245 0.496110i −0.223027 0.0265182i
\(351\) 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
\(355\) 1.49466 4.94674i 0.0793283 0.262546i
\(356\) 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 \(0.00940317\pi\)
−0.999564 + 0.0295366i \(0.990597\pi\)
\(360\) 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
\(365\) −5.62830 1.70059i −0.294599 0.0890130i
\(366\) 0 0
\(367\) 12.5630 0.655784 0.327892 0.944715i \(-0.393662\pi\)
0.327892 + 0.944715i \(0.393662\pi\)
\(368\) 3.47047 + 11.0915i 0.180911 + 0.578182i
\(369\) 0 0
\(370\) −8.72226 + 12.4713i −0.453449 + 0.648350i
\(371\) 3.39851 + 3.39851i 0.176442 + 0.176442i
\(372\) 0 0
\(373\) −20.4047 20.4047i −1.05652 1.05652i −0.998304 0.0582111i \(-0.981460\pi\)
−0.0582111 0.998304i \(-0.518540\pi\)
\(374\) 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 \(0.633884\pi\)
\(380\) −2.26062 + 15.8347i −0.115967 + 0.812304i
\(381\) 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 0.670408 0.741993i \(-0.266119\pi\)
−0.741993 + 0.670408i \(0.766119\pi\)
\(390\) 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
\(395\) 5.86631 19.4152i 0.295166 0.976886i
\(396\) 0 0
\(397\) −11.3004 + 11.3004i −0.567153 + 0.567153i −0.931330 0.364177i \(-0.881350\pi\)
0.364177 + 0.931330i \(0.381350\pi\)
\(398\) −5.90439 11.6666i −0.295960 0.584794i
\(399\) 0 0
\(400\) 5.59648 19.2010i 0.279824 0.960051i
\(401\) 17.8120i 0.889491i −0.895657 0.444745i \(-0.853294\pi\)
0.895657 0.444745i \(-0.146706\pi\)
\(402\) 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 \(0.686199\pi\)
\(410\) 2.40369 + 13.5884i 0.118710 + 0.671081i
\(411\) 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 0.414053 0.910253i \(-0.364113\pi\)
−0.910253 + 0.414053i \(0.864113\pi\)
\(420\) 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
\(430\) −10.7821 7.54089i −0.519960 0.363654i
\(431\) −0.155915 −0.00751015 −0.00375507 0.999993i \(-0.501195\pi\)
−0.00375507 + 0.999993i \(0.501195\pi\)
\(432\) 0 0
\(433\) 4.49972i 0.216243i −0.994138 0.108121i \(-0.965517\pi\)
0.994138 0.108121i \(-0.0344835\pi\)
\(434\) −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 \(0.683857\pi\)
\(440\) −29.5365 + 10.0084i −1.40810 + 0.477130i
\(441\) 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
\(445\) 37.0665 + 11.1996i 1.75712 + 0.530914i
\(446\) 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 \(0.103201\pi\)
−0.947901 + 0.318566i \(0.896799\pi\)
\(450\) 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 \(-0.671183\pi\)
−0.512238 + 0.858844i \(0.671183\pi\)
\(458\) 2.14828 + 0.704504i 0.100382 + 0.0329193i
\(459\) 0 0
\(460\) −10.3941 + 7.79704i −0.484626 + 0.363539i
\(461\) 20.7061 20.7061i 0.964381 0.964381i −0.0350065 0.999387i \(-0.511145\pi\)
0.999387 + 0.0350065i \(0.0111452\pi\)
\(462\) 0 0
\(463\) 15.1973 0.706277 0.353139 0.935571i \(-0.385114\pi\)
0.353139 + 0.935571i \(0.385114\pi\)
\(464\) 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
\(470\) −33.4850 + 5.92329i −1.54455 + 0.273221i
\(471\) 0 0
\(472\) −11.5975 + 8.28189i −0.533818 + 0.381205i
\(473\) 20.5165i 0.943349i
\(474\) 0 0
\(475\) −17.5319 + 3.52729i −0.804421 + 0.161843i
\(476\) −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 \(-0.563673\pi\)
−0.198703 + 0.980060i \(0.563673\pi\)
\(480\) 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
\(485\) −1.57398 + 5.20928i −0.0714709 + 0.236541i
\(486\) 0 0
\(487\) 18.9603i 0.859172i 0.903026 + 0.429586i \(0.141341\pi\)
−0.903026 + 0.429586i \(0.858659\pi\)
\(488\) −21.0010 29.4086i −0.950670 1.33126i
\(489\) 0 0
\(490\) 3.66134 + 20.6980i 0.165402 + 0.935039i
\(491\) −30.6747 + 30.6747i −1.38433 + 1.38433i −0.547573 + 0.836758i \(0.684448\pi\)
−0.836758 + 0.547573i \(0.815552\pi\)
\(492\) 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 \(-0.0526670\pi\)
\(500\) 22.3247 1.26799i 0.998391 0.0567061i
\(501\) 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 −0.476651 0.879093i \(-0.658149\pi\)
0.879093 + 0.476651i \(0.158149\pi\)
\(510\) 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
\(515\) −0.228824 + 0.757319i −0.0100832 + 0.0333715i
\(516\) 0 0
\(517\) 37.4936 + 37.4936i 1.64896 + 1.64896i
\(518\) −3.84298 1.26026i −0.168851 0.0553727i
\(519\) 0 0
\(520\) 28.9400 9.80626i 1.26910 0.430033i
\(521\) 26.5377 1.16264 0.581320 0.813675i \(-0.302537\pi\)
0.581320 + 0.813675i \(0.302537\pi\)
\(522\) 0 0
\(523\) 3.66089 3.66089i 0.160080 0.160080i −0.622522 0.782602i \(-0.713892\pi\)
0.782602 + 0.622522i \(0.213892\pi\)
\(524\) −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
\(530\) −20.9595 14.6588i −0.910423 0.636740i
\(531\) 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 0.893968 0.448131i \(-0.147910\pi\)
−0.448131 + 0.893968i \(0.647910\pi\)
\(548\) −1.69423 1.24511i −0.0723737 0.0531884i
\(549\) 0 0
\(550\) −21.5713 27.3933i −0.919804 1.16805i
\(551\) 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
\(560\) 5.31470 0.0521794i 0.224587 0.00220498i
\(561\) 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
\(565\) −29.2943 8.85127i −1.23242 0.372376i
\(566\) 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 \(-0.373989\pi\)
0.385615 + 0.922660i \(0.373989\pi\)
\(570\) 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 \(-0.764703\pi\)
0.739004 0.673701i \(-0.235297\pi\)
\(578\) −6.60452 13.0500i −0.274712 0.542808i
\(579\) 0 0
\(580\) −0.180413 + 1.26372i −0.00749123 + 0.0524730i
\(581\) 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
\(590\) −13.0567 9.13169i −0.537534 0.375946i
\(591\) 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
\(595\) 2.00959 6.65097i 0.0823852 0.272663i
\(596\) 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 \(0.0640290\pi\)
−0.979837 + 0.199799i \(0.935971\pi\)
\(600\) 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
\(605\) −8.61099 + 28.4990i −0.350086 + 1.15865i
\(606\) 0 0
\(607\) 39.5940 1.60707 0.803535 0.595257i \(-0.202950\pi\)
0.803535 + 0.595257i \(0.202950\pi\)
\(608\) 0.276001 20.2307i 0.0111933 0.820463i
\(609\) 0 0
\(610\) 23.1559 33.1087i 0.937554 1.34053i
\(611\) −36.7365 36.7365i −1.48620 1.48620i
\(612\) 0 0
\(613\) −22.7872 22.7872i −0.920367 0.920367i 0.0766879 0.997055i \(-0.475565\pi\)
−0.997055 + 0.0766879i \(0.975565\pi\)
\(614\) 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 \(-0.641820\pi\)
\(620\) 21.2369 + 28.3104i 0.852893 + 1.13697i
\(621\) 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
\(635\) −45.4639 13.7369i −1.80418 0.545133i
\(636\) 0 0
\(637\) −22.7078 + 22.7078i −0.899714 + 0.899714i
\(638\) 1.77601 0.898825i 0.0703127 0.0355848i
\(639\) 0 0
\(640\) −3.91672 + 24.9932i −0.154822 + 0.987942i
\(641\) 37.4511i 1.47923i 0.673030 + 0.739615i \(0.264993\pi\)
−0.673030 + 0.739615i \(0.735007\pi\)
\(642\) 0 0
\(643\) 33.6486 + 33.6486i 1.32697 + 1.32697i 0.907998 + 0.418973i \(0.137610\pi\)
0.418973 + 0.907998i \(0.362390\pi\)
\(644\) −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
\(650\) 21.1357 + 26.8401i 0.829011 + 1.05276i
\(651\) 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 0.336991 0.941508i \(-0.390591\pi\)
−0.941508 + 0.336991i \(0.890591\pi\)
\(660\) 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
\(670\) 19.8023 28.3138i 0.765031 1.09386i
\(671\) −63.0001 −2.43209
\(672\) 0 0
\(673\) 18.9415i 0.730143i 0.930979 + 0.365071i \(0.118955\pi\)
−0.930979 + 0.365071i \(0.881045\pi\)
\(674\) −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
\(680\) 29.6525 + 14.6430i 1.13712 + 0.561535i
\(681\) 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
\(685\) 0.679911 2.25024i 0.0259780 0.0859773i
\(686\) −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
\(700\) 2.03852 + 5.58170i 0.0770488 + 0.210968i
\(701\) −22.6892 + 22.6892i −0.856960 + 0.856960i −0.990979 0.134018i \(-0.957212\pi\)
0.134018 + 0.990979i \(0.457212\pi\)
\(702\) 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 \(0.308295\pi\)
\(710\) −7.19639 + 1.27300i −0.270076 + 0.0477747i
\(711\) 0 0
\(712\) −48.3119 8.05775i −1.81057 0.301977i
\(713\) 22.9923i 0.861067i
\(714\) 0 0
\(715\) 15.4077 50.9935i 0.576215 1.90705i
\(716\) −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 \(-0.192534\pi\)
0.822580 + 0.568649i \(0.192534\pi\)
\(720\) 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
\(725\) −1.39917 + 0.281502i −0.0519638 + 0.0104547i
\(726\) 0 0
\(727\) 49.5060i 1.83608i −0.396491 0.918039i \(-0.629772\pi\)
0.396491 0.918039i \(-0.370228\pi\)
\(728\) 4.71904 + 6.60828i 0.174899 + 0.244919i
\(729\) 0 0
\(730\) 1.44839 + 8.18790i 0.0536072 + 0.303048i
\(731\) 15.3842 15.3842i 0.569004 0.569004i
\(732\) 0 0
\(733\) 1.73352 1.73352i 0.0640290 0.0640290i −0.674367 0.738396i \(-0.735583\pi\)
0.738396 + 0.674367i \(0.235583\pi\)
\(734\) −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 \(0.144669\pi\)
\(740\) 21.3065 + 3.04179i 0.783243 + 0.111819i
\(741\) 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
\(755\) 12.5573 + 3.79420i 0.457008 + 0.138085i
\(756\) 0 0
\(757\) 0.105334 + 0.105334i 0.00382842 + 0.00382842i 0.709018 0.705190i \(-0.249138\pi\)
−0.705190 + 0.709018i \(0.749138\pi\)
\(758\) 6.12131 18.6660i 0.222336 0.677981i
\(759\) 0 0
\(760\) 21.4242 7.25954i 0.777137 0.263331i
\(761\) 19.6399 0.711944 0.355972 0.934497i \(-0.384150\pi\)
0.355972 + 0.934497i \(0.384150\pi\)
\(762\) 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 \(0.499477\pi\)
\(770\) 5.31050 7.59305i 0.191377 0.273635i
\(771\) 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 0.923998 0.382397i \(-0.124901\pi\)
−0.382397 + 0.923998i \(0.624901\pi\)
\(788\) 3.21571 + 21.0458i 0.114555 + 0.749727i
\(789\) 0 0
\(790\) −28.2448 + 4.99632i −1.00490 + 0.177761i
\(791\) 8.13249i 0.289158i