Properties

Label 1110.2.u.b.191.2
Level $1110$
Weight $2$
Character 1110.191
Analytic conductor $8.863$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 191.2
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1110.191
Dual form 1110.2.u.b.401.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} +4.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} +4.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +1.00000 q^{10} +4.24264 q^{11} +(1.00000 - 1.41421i) q^{12} +(-1.00000 - 1.00000i) q^{13} +(2.82843 + 2.82843i) q^{14} +(-1.70711 + 0.292893i) q^{15} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(-1.29289 + 2.70711i) q^{18} +(-2.00000 - 2.00000i) q^{19} +(0.707107 + 0.707107i) q^{20} +(-5.65685 - 4.00000i) q^{21} +(3.00000 + 3.00000i) q^{22} +(-4.24264 + 4.24264i) q^{23} +(1.70711 - 0.292893i) q^{24} -1.00000i q^{25} -1.41421i q^{26} +(1.41421 - 5.00000i) q^{27} +4.00000i q^{28} +(-1.41421 - 1.00000i) q^{30} +(5.00000 - 5.00000i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-6.00000 - 4.24264i) q^{33} -2.00000 q^{34} +(2.82843 - 2.82843i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(6.00000 - 1.00000i) q^{37} -2.82843i q^{38} +(0.414214 + 2.41421i) q^{39} +1.00000i q^{40} +5.65685 q^{41} +(-1.17157 - 6.82843i) q^{42} +(9.00000 + 9.00000i) q^{43} +4.24264i q^{44} +(2.70711 + 1.29289i) q^{45} -6.00000 q^{46} +1.41421i q^{47} +(1.41421 + 1.00000i) q^{48} +9.00000 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.41421 - 0.585786i) q^{51} +(1.00000 - 1.00000i) q^{52} +2.82843i q^{53} +(4.53553 - 2.53553i) q^{54} +(3.00000 - 3.00000i) q^{55} +(-2.82843 + 2.82843i) q^{56} +(0.828427 + 4.82843i) q^{57} +(-2.82843 + 2.82843i) q^{59} +(-0.292893 - 1.70711i) q^{60} +(4.00000 - 4.00000i) q^{61} +7.07107 q^{62} +(4.00000 + 11.3137i) q^{63} -1.00000i q^{64} -1.41421 q^{65} +(-1.24264 - 7.24264i) q^{66} +2.00000i q^{67} +(-1.41421 - 1.41421i) q^{68} +(10.2426 - 1.75736i) q^{69} +4.00000 q^{70} -2.82843i q^{71} +(-2.70711 - 1.29289i) q^{72} -6.00000i q^{73} +(4.94975 + 3.53553i) q^{74} +(-1.00000 + 1.41421i) q^{75} +(2.00000 - 2.00000i) q^{76} +16.9706 q^{77} +(-1.41421 + 2.00000i) q^{78} +(-3.00000 - 3.00000i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(4.00000 + 4.00000i) q^{82} -2.82843i q^{83} +(4.00000 - 5.65685i) q^{84} +2.00000i q^{85} +12.7279i q^{86} +(-3.00000 + 3.00000i) q^{88} +(-12.7279 - 12.7279i) q^{89} +(1.00000 + 2.82843i) q^{90} +(-4.00000 - 4.00000i) q^{91} +(-4.24264 - 4.24264i) q^{92} +(-12.0711 + 2.07107i) q^{93} +(-1.00000 + 1.00000i) q^{94} -2.82843 q^{95} +(0.292893 + 1.70711i) q^{96} +(-12.0000 - 12.0000i) q^{97} +(6.36396 + 6.36396i) q^{98} +(4.24264 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{6} + 16q^{7} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{6} + 16q^{7} + 4q^{9} + 4q^{10} + 4q^{12} - 4q^{13} - 4q^{15} - 4q^{16} - 8q^{18} - 8q^{19} + 12q^{22} + 4q^{24} + 20q^{31} - 24q^{33} - 8q^{34} + 24q^{37} - 4q^{39} - 16q^{42} + 36q^{43} + 8q^{45} - 24q^{46} + 36q^{49} + 8q^{51} + 4q^{52} + 4q^{54} + 12q^{55} - 8q^{57} - 4q^{60} + 16q^{61} + 16q^{63} + 12q^{66} + 24q^{69} + 16q^{70} - 8q^{72} - 4q^{75} + 8q^{76} - 12q^{79} - 28q^{81} + 16q^{82} + 16q^{84} - 12q^{88} + 4q^{90} - 16q^{91} - 20q^{93} - 4q^{94} + 4q^{96} - 48q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) −1.41421 1.00000i −0.816497 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) −0.292893 1.70711i −0.119573 0.696923i
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) 1.00000 0.316228
\(11\) 4.24264 1.27920 0.639602 0.768706i \(-0.279099\pi\)
0.639602 + 0.768706i \(0.279099\pi\)
\(12\) 1.00000 1.41421i 0.288675 0.408248i
\(13\) −1.00000 1.00000i −0.277350 0.277350i 0.554700 0.832050i \(-0.312833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 2.82843 + 2.82843i 0.755929 + 0.755929i
\(15\) −1.70711 + 0.292893i −0.440773 + 0.0756247i
\(16\) −1.00000 −0.250000
\(17\) −1.41421 + 1.41421i −0.342997 + 0.342997i −0.857493 0.514496i \(-0.827979\pi\)
0.514496 + 0.857493i \(0.327979\pi\)
\(18\) −1.29289 + 2.70711i −0.304738 + 0.638071i
\(19\) −2.00000 2.00000i −0.458831 0.458831i 0.439440 0.898272i \(-0.355177\pi\)
−0.898272 + 0.439440i \(0.855177\pi\)
\(20\) 0.707107 + 0.707107i 0.158114 + 0.158114i
\(21\) −5.65685 4.00000i −1.23443 0.872872i
\(22\) 3.00000 + 3.00000i 0.639602 + 0.639602i
\(23\) −4.24264 + 4.24264i −0.884652 + 0.884652i −0.994003 0.109351i \(-0.965123\pi\)
0.109351 + 0.994003i \(0.465123\pi\)
\(24\) 1.70711 0.292893i 0.348462 0.0597866i
\(25\) 1.00000i 0.200000i
\(26\) 1.41421i 0.277350i
\(27\) 1.41421 5.00000i 0.272166 0.962250i
\(28\) 4.00000i 0.755929i
\(29\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(30\) −1.41421 1.00000i −0.258199 0.182574i
\(31\) 5.00000 5.00000i 0.898027 0.898027i −0.0972349 0.995261i \(-0.531000\pi\)
0.995261 + 0.0972349i \(0.0309998\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −6.00000 4.24264i −1.04447 0.738549i
\(34\) −2.00000 −0.342997
\(35\) 2.82843 2.82843i 0.478091 0.478091i
\(36\) −2.82843 + 1.00000i −0.471405 + 0.166667i
\(37\) 6.00000 1.00000i 0.986394 0.164399i
\(38\) 2.82843i 0.458831i
\(39\) 0.414214 + 2.41421i 0.0663273 + 0.386584i
\(40\) 1.00000i 0.158114i
\(41\) 5.65685 0.883452 0.441726 0.897150i \(-0.354366\pi\)
0.441726 + 0.897150i \(0.354366\pi\)
\(42\) −1.17157 6.82843i −0.180778 1.05365i
\(43\) 9.00000 + 9.00000i 1.37249 + 1.37249i 0.856742 + 0.515745i \(0.172485\pi\)
0.515745 + 0.856742i \(0.327515\pi\)
\(44\) 4.24264i 0.639602i
\(45\) 2.70711 + 1.29289i 0.403552 + 0.192733i
\(46\) −6.00000 −0.884652
\(47\) 1.41421i 0.206284i 0.994667 + 0.103142i \(0.0328896\pi\)
−0.994667 + 0.103142i \(0.967110\pi\)
\(48\) 1.41421 + 1.00000i 0.204124 + 0.144338i
\(49\) 9.00000 1.28571
\(50\) 0.707107 0.707107i 0.100000 0.100000i
\(51\) 3.41421 0.585786i 0.478086 0.0820265i
\(52\) 1.00000 1.00000i 0.138675 0.138675i
\(53\) 2.82843i 0.388514i 0.980951 + 0.194257i \(0.0622296\pi\)
−0.980951 + 0.194257i \(0.937770\pi\)
\(54\) 4.53553 2.53553i 0.617208 0.345042i
\(55\) 3.00000 3.00000i 0.404520 0.404520i
\(56\) −2.82843 + 2.82843i −0.377964 + 0.377964i
\(57\) 0.828427 + 4.82843i 0.109728 + 0.639541i
\(58\) 0 0
\(59\) −2.82843 + 2.82843i −0.368230 + 0.368230i −0.866831 0.498601i \(-0.833847\pi\)
0.498601 + 0.866831i \(0.333847\pi\)
\(60\) −0.292893 1.70711i −0.0378124 0.220387i
\(61\) 4.00000 4.00000i 0.512148 0.512148i −0.403036 0.915184i \(-0.632045\pi\)
0.915184 + 0.403036i \(0.132045\pi\)
\(62\) 7.07107 0.898027
\(63\) 4.00000 + 11.3137i 0.503953 + 1.42539i
\(64\) 1.00000i 0.125000i
\(65\) −1.41421 −0.175412
\(66\) −1.24264 7.24264i −0.152958 0.891507i
\(67\) 2.00000i 0.244339i 0.992509 + 0.122169i \(0.0389851\pi\)
−0.992509 + 0.122169i \(0.961015\pi\)
\(68\) −1.41421 1.41421i −0.171499 0.171499i
\(69\) 10.2426 1.75736i 1.23307 0.211561i
\(70\) 4.00000 0.478091
\(71\) 2.82843i 0.335673i −0.985815 0.167836i \(-0.946322\pi\)
0.985815 0.167836i \(-0.0536780\pi\)
\(72\) −2.70711 1.29289i −0.319036 0.152369i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) 4.94975 + 3.53553i 0.575396 + 0.410997i
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) 2.00000 2.00000i 0.229416 0.229416i
\(77\) 16.9706 1.93398
\(78\) −1.41421 + 2.00000i −0.160128 + 0.226455i
\(79\) −3.00000 3.00000i −0.337526 0.337526i 0.517909 0.855436i \(-0.326710\pi\)
−0.855436 + 0.517909i \(0.826710\pi\)
\(80\) −0.707107 + 0.707107i −0.0790569 + 0.0790569i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 4.00000 + 4.00000i 0.441726 + 0.441726i
\(83\) 2.82843i 0.310460i −0.987878 0.155230i \(-0.950388\pi\)
0.987878 0.155230i \(-0.0496119\pi\)
\(84\) 4.00000 5.65685i 0.436436 0.617213i
\(85\) 2.00000i 0.216930i
\(86\) 12.7279i 1.37249i
\(87\) 0 0
\(88\) −3.00000 + 3.00000i −0.319801 + 0.319801i
\(89\) −12.7279 12.7279i −1.34916 1.34916i −0.886578 0.462579i \(-0.846924\pi\)
−0.462579 0.886578i \(-0.653076\pi\)
\(90\) 1.00000 + 2.82843i 0.105409 + 0.298142i
\(91\) −4.00000 4.00000i −0.419314 0.419314i
\(92\) −4.24264 4.24264i −0.442326 0.442326i
\(93\) −12.0711 + 2.07107i −1.25171 + 0.214760i
\(94\) −1.00000 + 1.00000i −0.103142 + 0.103142i
\(95\) −2.82843 −0.290191
\(96\) 0.292893 + 1.70711i 0.0298933 + 0.174231i
\(97\) −12.0000 12.0000i −1.21842 1.21842i −0.968187 0.250229i \(-0.919494\pi\)
−0.250229 0.968187i \(-0.580506\pi\)
\(98\) 6.36396 + 6.36396i 0.642857 + 0.642857i
\(99\) 4.24264 + 12.0000i 0.426401 + 1.20605i
\(100\) 1.00000 0.100000
\(101\) 15.5563 1.54791 0.773957 0.633238i \(-0.218274\pi\)
0.773957 + 0.633238i \(0.218274\pi\)
\(102\) 2.82843 + 2.00000i 0.280056 + 0.198030i
\(103\) −10.0000 + 10.0000i −0.985329 + 0.985329i −0.999894 0.0145647i \(-0.995364\pi\)
0.0145647 + 0.999894i \(0.495364\pi\)
\(104\) 1.41421 0.138675
\(105\) −6.82843 + 1.17157i −0.666386 + 0.114334i
\(106\) −2.00000 + 2.00000i −0.194257 + 0.194257i
\(107\) 14.1421i 1.36717i −0.729870 0.683586i \(-0.760419\pi\)
0.729870 0.683586i \(-0.239581\pi\)
\(108\) 5.00000 + 1.41421i 0.481125 + 0.136083i
\(109\) 12.0000 + 12.0000i 1.14939 + 1.14939i 0.986672 + 0.162719i \(0.0520264\pi\)
0.162719 + 0.986672i \(0.447974\pi\)
\(110\) 4.24264 0.404520
\(111\) −9.48528 4.58579i −0.900303 0.435264i
\(112\) −4.00000 −0.377964
\(113\) 4.24264 + 4.24264i 0.399114 + 0.399114i 0.877920 0.478806i \(-0.158930\pi\)
−0.478806 + 0.877920i \(0.658930\pi\)
\(114\) −2.82843 + 4.00000i −0.264906 + 0.374634i
\(115\) 6.00000i 0.559503i
\(116\) 0 0
\(117\) 1.82843 3.82843i 0.169038 0.353938i
\(118\) −4.00000 −0.368230
\(119\) −5.65685 + 5.65685i −0.518563 + 0.518563i
\(120\) 1.00000 1.41421i 0.0912871 0.129099i
\(121\) 7.00000 0.636364
\(122\) 5.65685 0.512148
\(123\) −8.00000 5.65685i −0.721336 0.510061i
\(124\) 5.00000 + 5.00000i 0.449013 + 0.449013i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) −5.17157 + 10.8284i −0.460720 + 0.964673i
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −3.72792 21.7279i −0.328225 1.91304i
\(130\) −1.00000 1.00000i −0.0877058 0.0877058i
\(131\) 8.48528 + 8.48528i 0.741362 + 0.741362i 0.972840 0.231478i \(-0.0743560\pi\)
−0.231478 + 0.972840i \(0.574356\pi\)
\(132\) 4.24264 6.00000i 0.369274 0.522233i
\(133\) −8.00000 8.00000i −0.693688 0.693688i
\(134\) −1.41421 + 1.41421i −0.122169 + 0.122169i
\(135\) −2.53553 4.53553i −0.218224 0.390357i
\(136\) 2.00000i 0.171499i
\(137\) 9.89949i 0.845771i 0.906183 + 0.422885i \(0.138983\pi\)
−0.906183 + 0.422885i \(0.861017\pi\)
\(138\) 8.48528 + 6.00000i 0.722315 + 0.510754i
\(139\) 16.0000i 1.35710i 0.734553 + 0.678551i \(0.237392\pi\)
−0.734553 + 0.678551i \(0.762608\pi\)
\(140\) 2.82843 + 2.82843i 0.239046 + 0.239046i
\(141\) 1.41421 2.00000i 0.119098 0.168430i
\(142\) 2.00000 2.00000i 0.167836 0.167836i
\(143\) −4.24264 4.24264i −0.354787 0.354787i
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) 0 0
\(146\) 4.24264 4.24264i 0.351123 0.351123i
\(147\) −12.7279 9.00000i −1.04978 0.742307i
\(148\) 1.00000 + 6.00000i 0.0821995 + 0.493197i
\(149\) 9.89949i 0.810998i −0.914095 0.405499i \(-0.867098\pi\)
0.914095 0.405499i \(-0.132902\pi\)
\(150\) −1.70711 + 0.292893i −0.139385 + 0.0239146i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 2.82843 0.229416
\(153\) −5.41421 2.58579i −0.437713 0.209048i
\(154\) 12.0000 + 12.0000i 0.966988 + 0.966988i
\(155\) 7.07107i 0.567962i
\(156\) −2.41421 + 0.414214i −0.193292 + 0.0331636i
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 4.24264i 0.337526i
\(159\) 2.82843 4.00000i 0.224309 0.317221i
\(160\) −1.00000 −0.0790569
\(161\) −16.9706 + 16.9706i −1.33747 + 1.33747i
\(162\) −8.94975 0.949747i −0.703159 0.0746192i
\(163\) −5.00000 + 5.00000i −0.391630 + 0.391630i −0.875268 0.483638i \(-0.839315\pi\)
0.483638 + 0.875268i \(0.339315\pi\)
\(164\) 5.65685i 0.441726i
\(165\) −7.24264 + 1.24264i −0.563839 + 0.0967394i
\(166\) 2.00000 2.00000i 0.155230 0.155230i
\(167\) −12.7279 + 12.7279i −0.984916 + 0.984916i −0.999888 0.0149717i \(-0.995234\pi\)
0.0149717 + 0.999888i \(0.495234\pi\)
\(168\) 6.82843 1.17157i 0.526825 0.0903888i
\(169\) 11.0000i 0.846154i
\(170\) −1.41421 + 1.41421i −0.108465 + 0.108465i
\(171\) 3.65685 7.65685i 0.279647 0.585534i
\(172\) −9.00000 + 9.00000i −0.686244 + 0.686244i
\(173\) −2.82843 −0.215041 −0.107521 0.994203i \(-0.534291\pi\)
−0.107521 + 0.994203i \(0.534291\pi\)
\(174\) 0 0
\(175\) 4.00000i 0.302372i
\(176\) −4.24264 −0.319801
\(177\) 6.82843 1.17157i 0.513256 0.0880608i
\(178\) 18.0000i 1.34916i
\(179\) −12.7279 12.7279i −0.951330 0.951330i 0.0475398 0.998869i \(-0.484862\pi\)
−0.998869 + 0.0475398i \(0.984862\pi\)
\(180\) −1.29289 + 2.70711i −0.0963666 + 0.201776i
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 5.65685i 0.419314i
\(183\) −9.65685 + 1.65685i −0.713855 + 0.122478i
\(184\) 6.00000i 0.442326i
\(185\) 3.53553 4.94975i 0.259938 0.363913i
\(186\) −10.0000 7.07107i −0.733236 0.518476i
\(187\) −6.00000 + 6.00000i −0.438763 + 0.438763i
\(188\) −1.41421 −0.103142
\(189\) 5.65685 20.0000i 0.411476 1.45479i
\(190\) −2.00000 2.00000i −0.145095 0.145095i
\(191\) 2.82843 2.82843i 0.204658 0.204658i −0.597334 0.801992i \(-0.703773\pi\)
0.801992 + 0.597334i \(0.203773\pi\)
\(192\) −1.00000 + 1.41421i −0.0721688 + 0.102062i
\(193\) 18.0000 + 18.0000i 1.29567 + 1.29567i 0.931226 + 0.364442i \(0.118740\pi\)
0.364442 + 0.931226i \(0.381260\pi\)
\(194\) 16.9706i 1.21842i
\(195\) 2.00000 + 1.41421i 0.143223 + 0.101274i
\(196\) 9.00000i 0.642857i
\(197\) 19.7990i 1.41062i −0.708899 0.705310i \(-0.750808\pi\)
0.708899 0.705310i \(-0.249192\pi\)
\(198\) −5.48528 + 11.4853i −0.389822 + 0.816223i
\(199\) −3.00000 + 3.00000i −0.212664 + 0.212664i −0.805398 0.592734i \(-0.798049\pi\)
0.592734 + 0.805398i \(0.298049\pi\)
\(200\) 0.707107 + 0.707107i 0.0500000 + 0.0500000i
\(201\) 2.00000 2.82843i 0.141069 0.199502i
\(202\) 11.0000 + 11.0000i 0.773957 + 0.773957i
\(203\) 0 0
\(204\) 0.585786 + 3.41421i 0.0410133 + 0.239043i
\(205\) 4.00000 4.00000i 0.279372 0.279372i
\(206\) −14.1421 −0.985329
\(207\) −16.2426 7.75736i −1.12894 0.539174i
\(208\) 1.00000 + 1.00000i 0.0693375 + 0.0693375i
\(209\) −8.48528 8.48528i −0.586939 0.586939i
\(210\) −5.65685 4.00000i −0.390360 0.276026i
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −2.82843 −0.194257
\(213\) −2.82843 + 4.00000i −0.193801 + 0.274075i
\(214\) 10.0000 10.0000i 0.683586 0.683586i
\(215\) 12.7279 0.868037
\(216\) 2.53553 + 4.53553i 0.172521 + 0.308604i
\(217\) 20.0000 20.0000i 1.35769 1.35769i
\(218\) 16.9706i 1.14939i
\(219\) −6.00000 + 8.48528i −0.405442 + 0.573382i
\(220\) 3.00000 + 3.00000i 0.202260 + 0.202260i
\(221\) 2.82843 0.190261
\(222\) −3.46447 9.94975i −0.232520 0.667783i
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) −2.82843 2.82843i −0.188982 0.188982i
\(225\) 2.82843 1.00000i 0.188562 0.0666667i
\(226\) 6.00000i 0.399114i
\(227\) −19.7990 + 19.7990i −1.31411 + 1.31411i −0.395744 + 0.918361i \(0.629513\pi\)
−0.918361 + 0.395744i \(0.870487\pi\)
\(228\) −4.82843 + 0.828427i −0.319770 + 0.0548639i
\(229\) 26.0000 1.71813 0.859064 0.511868i \(-0.171046\pi\)
0.859064 + 0.511868i \(0.171046\pi\)
\(230\) −4.24264 + 4.24264i −0.279751 + 0.279751i
\(231\) −24.0000 16.9706i −1.57908 1.11658i
\(232\) 0 0
\(233\) −7.07107 −0.463241 −0.231621 0.972806i \(-0.574403\pi\)
−0.231621 + 0.972806i \(0.574403\pi\)
\(234\) 4.00000 1.41421i 0.261488 0.0924500i
\(235\) 1.00000 + 1.00000i 0.0652328 + 0.0652328i
\(236\) −2.82843 2.82843i −0.184115 0.184115i
\(237\) 1.24264 + 7.24264i 0.0807182 + 0.470460i
\(238\) −8.00000 −0.518563
\(239\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(240\) 1.70711 0.292893i 0.110193 0.0189062i
\(241\) 3.00000 + 3.00000i 0.193247 + 0.193247i 0.797098 0.603851i \(-0.206368\pi\)
−0.603851 + 0.797098i \(0.706368\pi\)
\(242\) 4.94975 + 4.94975i 0.318182 + 0.318182i
\(243\) 15.5563 1.00000i 0.997940 0.0641500i
\(244\) 4.00000 + 4.00000i 0.256074 + 0.256074i
\(245\) 6.36396 6.36396i 0.406579 0.406579i
\(246\) −1.65685 9.65685i −0.105637 0.615699i
\(247\) 4.00000i 0.254514i
\(248\) 7.07107i 0.449013i
\(249\) −2.82843 + 4.00000i −0.179244 + 0.253490i
\(250\) 1.00000i 0.0632456i
\(251\) −2.82843 2.82843i −0.178529 0.178529i 0.612185 0.790714i \(-0.290291\pi\)
−0.790714 + 0.612185i \(0.790291\pi\)
\(252\) −11.3137 + 4.00000i −0.712697 + 0.251976i
\(253\) −18.0000 + 18.0000i −1.13165 + 1.13165i
\(254\) −8.48528 8.48528i −0.532414 0.532414i
\(255\) 2.00000 2.82843i 0.125245 0.177123i
\(256\) 1.00000 0.0625000
\(257\) 2.82843 2.82843i 0.176432 0.176432i −0.613366 0.789799i \(-0.710185\pi\)
0.789799 + 0.613366i \(0.210185\pi\)
\(258\) 12.7279 18.0000i 0.792406 1.12063i
\(259\) 24.0000 4.00000i 1.49129 0.248548i
\(260\) 1.41421i 0.0877058i
\(261\) 0 0
\(262\) 12.0000i 0.741362i
\(263\) −26.8701 −1.65688 −0.828439 0.560079i \(-0.810771\pi\)
−0.828439 + 0.560079i \(0.810771\pi\)
\(264\) 7.24264 1.24264i 0.445754 0.0764792i
\(265\) 2.00000 + 2.00000i 0.122859 + 0.122859i
\(266\) 11.3137i 0.693688i
\(267\) 5.27208 + 30.7279i 0.322646 + 1.88052i
\(268\) −2.00000 −0.122169
\(269\) 21.2132i 1.29339i −0.762748 0.646696i \(-0.776150\pi\)
0.762748 0.646696i \(-0.223850\pi\)
\(270\) 1.41421 5.00000i 0.0860663 0.304290i
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 1.41421 1.41421i 0.0857493 0.0857493i
\(273\) 1.65685 + 9.65685i 0.100277 + 0.584459i
\(274\) −7.00000 + 7.00000i −0.422885 + 0.422885i
\(275\) 4.24264i 0.255841i
\(276\) 1.75736 + 10.2426i 0.105781 + 0.616535i
\(277\) −15.0000 + 15.0000i −0.901263 + 0.901263i −0.995545 0.0942828i \(-0.969944\pi\)
0.0942828 + 0.995545i \(0.469944\pi\)
\(278\) −11.3137 + 11.3137i −0.678551 + 0.678551i
\(279\) 19.1421 + 9.14214i 1.14601 + 0.547325i
\(280\) 4.00000i 0.239046i
\(281\) −7.07107 + 7.07107i −0.421825 + 0.421825i −0.885832 0.464007i \(-0.846411\pi\)
0.464007 + 0.885832i \(0.346411\pi\)
\(282\) 2.41421 0.414214i 0.143764 0.0246661i
\(283\) −15.0000 + 15.0000i −0.891657 + 0.891657i −0.994679 0.103022i \(-0.967149\pi\)
0.103022 + 0.994679i \(0.467149\pi\)
\(284\) 2.82843 0.167836
\(285\) 4.00000 + 2.82843i 0.236940 + 0.167542i
\(286\) 6.00000i 0.354787i
\(287\) 22.6274 1.33565
\(288\) 1.29289 2.70711i 0.0761845 0.159518i
\(289\) 13.0000i 0.764706i
\(290\) 0 0
\(291\) 4.97056 + 28.9706i 0.291380 + 1.69828i
\(292\) 6.00000 0.351123
\(293\) 28.2843i 1.65238i −0.563388 0.826192i \(-0.690502\pi\)
0.563388 0.826192i \(-0.309498\pi\)
\(294\) −2.63604 15.3640i −0.153737 0.896044i
\(295\) 4.00000i 0.232889i
\(296\) −3.53553 + 4.94975i −0.205499 + 0.287698i
\(297\) 6.00000 21.2132i 0.348155 1.23091i
\(298\) 7.00000 7.00000i 0.405499 0.405499i
\(299\) 8.48528 0.490716
\(300\) −1.41421 1.00000i −0.0816497 0.0577350i
\(301\) 36.0000 + 36.0000i 2.07501 + 2.07501i
\(302\) 0 0
\(303\) −22.0000 15.5563i −1.26387 0.893689i
\(304\) 2.00000 + 2.00000i 0.114708 + 0.114708i
\(305\) 5.65685i 0.323911i
\(306\) −2.00000 5.65685i −0.114332 0.323381i
\(307\) 4.00000i 0.228292i −0.993464 0.114146i \(-0.963587\pi\)
0.993464 0.114146i \(-0.0364132\pi\)
\(308\) 16.9706i 0.966988i
\(309\) 24.1421 4.14214i 1.37340 0.235638i
\(310\) 5.00000 5.00000i 0.283981 0.283981i
\(311\) −8.48528 8.48528i −0.481156 0.481156i 0.424345 0.905501i \(-0.360505\pi\)
−0.905501 + 0.424345i \(0.860505\pi\)
\(312\) −2.00000 1.41421i −0.113228 0.0800641i
\(313\) 6.00000 + 6.00000i 0.339140 + 0.339140i 0.856044 0.516904i \(-0.172915\pi\)
−0.516904 + 0.856044i \(0.672915\pi\)
\(314\) −12.7279 12.7279i −0.718278 0.718278i
\(315\) 10.8284 + 5.17157i 0.610113 + 0.291385i
\(316\) 3.00000 3.00000i 0.168763 0.168763i
\(317\) 8.48528 0.476581 0.238290 0.971194i \(-0.423413\pi\)
0.238290 + 0.971194i \(0.423413\pi\)
\(318\) 4.82843 0.828427i 0.270765 0.0464559i
\(319\) 0 0
\(320\) −0.707107 0.707107i −0.0395285 0.0395285i
\(321\) −14.1421 + 20.0000i −0.789337 + 1.11629i
\(322\) −24.0000 −1.33747
\(323\) 5.65685 0.314756
\(324\) −5.65685 7.00000i −0.314270 0.388889i
\(325\) −1.00000 + 1.00000i −0.0554700 + 0.0554700i
\(326\) −7.07107 −0.391630
\(327\) −4.97056 28.9706i −0.274873 1.60208i
\(328\) −4.00000 + 4.00000i −0.220863 + 0.220863i
\(329\) 5.65685i 0.311872i
\(330\) −6.00000 4.24264i −0.330289 0.233550i
\(331\) −4.00000 4.00000i −0.219860 0.219860i 0.588579 0.808439i \(-0.299687\pi\)
−0.808439 + 0.588579i \(0.799687\pi\)
\(332\) 2.82843 0.155230
\(333\) 8.82843 + 15.9706i 0.483795 + 0.875181i
\(334\) −18.0000 −0.984916
\(335\) 1.41421 + 1.41421i 0.0772667 + 0.0772667i
\(336\) 5.65685 + 4.00000i 0.308607 + 0.218218i
\(337\) 2.00000i 0.108947i −0.998515 0.0544735i \(-0.982652\pi\)
0.998515 0.0544735i \(-0.0173480\pi\)
\(338\) 7.77817 7.77817i 0.423077 0.423077i
\(339\) −1.75736 10.2426i −0.0954467 0.556304i
\(340\) −2.00000 −0.108465
\(341\) 21.2132 21.2132i 1.14876 1.14876i
\(342\) 8.00000 2.82843i 0.432590 0.152944i
\(343\) 8.00000 0.431959
\(344\) −12.7279 −0.686244
\(345\) 6.00000 8.48528i 0.323029 0.456832i
\(346\) −2.00000 2.00000i −0.107521 0.107521i
\(347\) 8.48528 + 8.48528i 0.455514 + 0.455514i 0.897180 0.441666i \(-0.145612\pi\)
−0.441666 + 0.897180i \(0.645612\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 2.82843 2.82843i 0.151186 0.151186i
\(351\) −6.41421 + 3.58579i −0.342365 + 0.191395i
\(352\) −3.00000 3.00000i −0.159901 0.159901i
\(353\) −24.0416 24.0416i −1.27961 1.27961i −0.940887 0.338719i \(-0.890006\pi\)
−0.338719 0.940887i \(-0.609994\pi\)
\(354\) 5.65685 + 4.00000i 0.300658 + 0.212598i
\(355\) −2.00000 2.00000i −0.106149 0.106149i
\(356\) 12.7279 12.7279i 0.674579 0.674579i
\(357\) 13.6569 2.34315i 0.722797 0.124012i
\(358\) 18.0000i 0.951330i
\(359\) 11.3137i 0.597115i 0.954392 + 0.298557i \(0.0965054\pi\)
−0.954392 + 0.298557i \(0.903495\pi\)
\(360\) −2.82843 + 1.00000i −0.149071 + 0.0527046i
\(361\) 11.0000i 0.578947i
\(362\) 4.24264 + 4.24264i 0.222988 + 0.222988i
\(363\) −9.89949 7.00000i −0.519589 0.367405i
\(364\) 4.00000 4.00000i 0.209657 0.209657i
\(365\) −4.24264 4.24264i −0.222070 0.222070i
\(366\) −8.00000 5.65685i −0.418167 0.295689i
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 4.24264 4.24264i 0.221163 0.221163i
\(369\) 5.65685 + 16.0000i 0.294484 + 0.832927i
\(370\) 6.00000 1.00000i 0.311925 0.0519875i
\(371\) 11.3137i 0.587378i
\(372\) −2.07107 12.0711i −0.107380 0.625856i
\(373\) 34.0000i 1.76045i −0.474554 0.880227i \(-0.657390\pi\)
0.474554 0.880227i \(-0.342610\pi\)
\(374\) −8.48528 −0.438763
\(375\) 0.292893 + 1.70711i 0.0151249 + 0.0881546i
\(376\) −1.00000 1.00000i −0.0515711 0.0515711i
\(377\) 0 0
\(378\) 18.1421 10.1421i 0.933131 0.521655i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 2.82843i 0.145095i
\(381\) 16.9706 + 12.0000i 0.869428 + 0.614779i
\(382\) 4.00000 0.204658
\(383\) 11.3137 11.3137i 0.578103 0.578103i −0.356277 0.934380i \(-0.615954\pi\)
0.934380 + 0.356277i \(0.115954\pi\)
\(384\) −1.70711 + 0.292893i −0.0871154 + 0.0149466i
\(385\) 12.0000 12.0000i 0.611577 0.611577i
\(386\) 25.4558i 1.29567i
\(387\) −16.4558 + 34.4558i −0.836498 + 1.75149i
\(388\) 12.0000 12.0000i 0.609208 0.609208i
\(389\) −8.48528 + 8.48528i −0.430221 + 0.430221i −0.888703 0.458483i \(-0.848393\pi\)
0.458483 + 0.888703i \(0.348393\pi\)
\(390\) 0.414214 + 2.41421i 0.0209745 + 0.122248i
\(391\) 12.0000i 0.606866i
\(392\) −6.36396 + 6.36396i −0.321429 + 0.321429i
\(393\) −3.51472 20.4853i −0.177294 1.03335i
\(394\) 14.0000 14.0000i 0.705310 0.705310i
\(395\) −4.24264 −0.213470
\(396\) −12.0000 + 4.24264i −0.603023 + 0.213201i
\(397\) 18.0000i 0.903394i 0.892171 + 0.451697i \(0.149181\pi\)
−0.892171 + 0.451697i \(0.850819\pi\)
\(398\) −4.24264 −0.212664
\(399\) 3.31371 + 19.3137i 0.165893 + 0.966895i
\(400\) 1.00000i 0.0500000i
\(401\) −15.5563 15.5563i −0.776847 0.776847i 0.202446 0.979293i \(-0.435111\pi\)
−0.979293 + 0.202446i \(0.935111\pi\)
\(402\) 3.41421 0.585786i 0.170285 0.0292164i
\(403\) −10.0000 −0.498135
\(404\) 15.5563i 0.773957i
\(405\) −0.949747 + 8.94975i −0.0471933 + 0.444717i
\(406\) 0 0
\(407\) 25.4558 4.24264i 1.26180 0.210300i
\(408\) −2.00000 + 2.82843i −0.0990148 + 0.140028i
\(409\) 9.00000 9.00000i 0.445021 0.445021i −0.448674 0.893695i \(-0.648104\pi\)
0.893695 + 0.448674i \(0.148104\pi\)
\(410\) 5.65685 0.279372
\(411\) 9.89949 14.0000i 0.488306 0.690569i
\(412\) −10.0000 10.0000i −0.492665 0.492665i
\(413\) −11.3137 + 11.3137i −0.556711 + 0.556711i
\(414\) −6.00000 16.9706i −0.294884 0.834058i
\(415\) −2.00000 2.00000i −0.0981761 0.0981761i
\(416\) 1.41421i 0.0693375i
\(417\) 16.0000 22.6274i 0.783523 1.10807i
\(418\) 12.0000i 0.586939i
\(419\) 12.7279i 0.621800i 0.950443 + 0.310900i \(0.100630\pi\)
−0.950443 + 0.310900i \(0.899370\pi\)
\(420\) −1.17157 6.82843i −0.0571669 0.333193i
\(421\) −14.0000 + 14.0000i −0.682318 + 0.682318i −0.960522 0.278204i \(-0.910261\pi\)
0.278204 + 0.960522i \(0.410261\pi\)
\(422\) −11.3137 11.3137i −0.550743 0.550743i
\(423\) −4.00000 + 1.41421i −0.194487 + 0.0687614i
\(424\) −2.00000 2.00000i −0.0971286 0.0971286i
\(425\) 1.41421 + 1.41421i 0.0685994 + 0.0685994i
\(426\) −4.82843 + 0.828427i −0.233938 + 0.0401374i
\(427\) 16.0000 16.0000i 0.774294 0.774294i
\(428\) 14.1421 0.683586
\(429\) 1.75736 + 10.2426i 0.0848461 + 0.494519i
\(430\) 9.00000 + 9.00000i 0.434019 + 0.434019i
\(431\) 8.48528 + 8.48528i 0.408722 + 0.408722i 0.881293 0.472571i \(-0.156674\pi\)
−0.472571 + 0.881293i \(0.656674\pi\)
\(432\) −1.41421 + 5.00000i −0.0680414 + 0.240563i
\(433\) −6.00000 −0.288342 −0.144171 0.989553i \(-0.546051\pi\)
−0.144171 + 0.989553i \(0.546051\pi\)
\(434\) 28.2843 1.35769
\(435\) 0 0
\(436\) −12.0000 + 12.0000i −0.574696 + 0.574696i
\(437\) 16.9706 0.811812
\(438\) −10.2426 + 1.75736i −0.489412 + 0.0839699i
\(439\) 5.00000 5.00000i 0.238637 0.238637i −0.577649 0.816286i \(-0.696030\pi\)
0.816286 + 0.577649i \(0.196030\pi\)
\(440\) 4.24264i 0.202260i
\(441\) 9.00000 + 25.4558i 0.428571 + 1.21218i
\(442\) 2.00000 + 2.00000i 0.0951303 + 0.0951303i
\(443\) 2.82843 0.134383 0.0671913 0.997740i \(-0.478596\pi\)
0.0671913 + 0.997740i \(0.478596\pi\)
\(444\) 4.58579 9.48528i 0.217632 0.450152i
\(445\) −18.0000 −0.853282
\(446\) −8.48528 8.48528i −0.401790 0.401790i
\(447\) −9.89949 + 14.0000i −0.468230 + 0.662177i
\(448\) 4.00000i 0.188982i
\(449\) −12.7279 + 12.7279i −0.600668 + 0.600668i −0.940490 0.339822i \(-0.889633\pi\)
0.339822 + 0.940490i \(0.389633\pi\)
\(450\) 2.70711 + 1.29289i 0.127614 + 0.0609476i
\(451\) 24.0000 1.13012
\(452\) −4.24264 + 4.24264i −0.199557 + 0.199557i
\(453\) 0 0
\(454\) −28.0000 −1.31411
\(455\) −5.65685 −0.265197
\(456\) −4.00000 2.82843i −0.187317 0.132453i
\(457\) −12.0000 12.0000i −0.561336 0.561336i 0.368351 0.929687i \(-0.379923\pi\)
−0.929687 + 0.368351i \(0.879923\pi\)
\(458\) 18.3848 + 18.3848i 0.859064 + 0.859064i
\(459\) 5.07107 + 9.07107i 0.236697 + 0.423401i
\(460\) −6.00000 −0.279751
\(461\) −24.0416 + 24.0416i −1.11973 + 1.11973i −0.127950 + 0.991781i \(0.540840\pi\)
−0.991781 + 0.127950i \(0.959160\pi\)
\(462\) −4.97056 28.9706i −0.231252 1.34783i
\(463\) −22.0000 22.0000i −1.02243 1.02243i −0.999743 0.0226840i \(-0.992779\pi\)
−0.0226840 0.999743i \(-0.507221\pi\)
\(464\) 0 0
\(465\) −7.07107 + 10.0000i −0.327913 + 0.463739i
\(466\) −5.00000 5.00000i −0.231621 0.231621i
\(467\) 8.48528 8.48528i 0.392652 0.392652i −0.482980 0.875632i \(-0.660445\pi\)
0.875632 + 0.482980i \(0.160445\pi\)
\(468\) 3.82843 + 1.82843i 0.176969 + 0.0845191i
\(469\) 8.00000i 0.369406i
\(470\) 1.41421i 0.0652328i
\(471\) 25.4558 + 18.0000i 1.17294 + 0.829396i
\(472\) 4.00000i 0.184115i
\(473\) 38.1838 + 38.1838i 1.75569 + 1.75569i
\(474\) −4.24264 + 6.00000i −0.194871 + 0.275589i
\(475\) −2.00000 + 2.00000i −0.0917663 + 0.0917663i
\(476\) −5.65685 5.65685i −0.259281 0.259281i
\(477\) −8.00000 + 2.82843i −0.366295 + 0.129505i
\(478\) 0 0
\(479\) 25.4558 25.4558i 1.16311 1.16311i 0.179316 0.983792i \(-0.442612\pi\)
0.983792 0.179316i \(-0.0573883\pi\)
\(480\) 1.41421 + 1.00000i 0.0645497 + 0.0456435i
\(481\) −7.00000 5.00000i −0.319173 0.227980i
\(482\) 4.24264i 0.193247i
\(483\) 40.9706 7.02944i 1.86423 0.319850i
\(484\) 7.00000i 0.318182i
\(485\) −16.9706 −0.770594
\(486\) 11.7071 + 10.2929i 0.531045 + 0.466895i
\(487\) 22.0000 + 22.0000i 0.996915 + 0.996915i 0.999995 0.00308010i \(-0.000980427\pi\)
−0.00308010 + 0.999995i \(0.500980\pi\)
\(488\) 5.65685i 0.256074i
\(489\) 12.0711 2.07107i 0.545873 0.0936569i
\(490\) 9.00000 0.406579
\(491\) 21.2132i 0.957338i 0.877995 + 0.478669i \(0.158881\pi\)
−0.877995 + 0.478669i \(0.841119\pi\)
\(492\) 5.65685 8.00000i 0.255031 0.360668i
\(493\) 0 0
\(494\) −2.82843 + 2.82843i −0.127257 + 0.127257i
\(495\) 11.4853 + 5.48528i 0.516225 + 0.246545i
\(496\) −5.00000 + 5.00000i −0.224507 + 0.224507i
\(497\) 11.3137i 0.507489i
\(498\) −4.82843 + 0.828427i −0.216367 + 0.0371227i
\(499\) −12.0000 + 12.0000i −0.537194 + 0.537194i −0.922704 0.385510i \(-0.874026\pi\)
0.385510 + 0.922704i \(0.374026\pi\)
\(500\) 0.707107 0.707107i 0.0316228 0.0316228i
\(501\) 30.7279 5.27208i 1.37282 0.235539i
\(502\) 4.00000i 0.178529i
\(503\) −21.2132 + 21.2132i −0.945850 + 0.945850i −0.998607 0.0527574i \(-0.983199\pi\)
0.0527574 + 0.998607i \(0.483199\pi\)
\(504\) −10.8284 5.17157i −0.482336 0.230360i
\(505\) 11.0000 11.0000i 0.489494 0.489494i
\(506\) −25.4558 −1.13165
\(507\) −11.0000 + 15.5563i −0.488527 + 0.690882i
\(508\) 12.0000i 0.532414i
\(509\) −24.0416 −1.06563 −0.532813 0.846233i \(-0.678865\pi\)
−0.532813 + 0.846233i \(0.678865\pi\)
\(510\) 3.41421 0.585786i 0.151184 0.0259391i
\(511\) 24.0000i 1.06170i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −12.8284 + 7.17157i −0.566389 + 0.316633i
\(514\) 4.00000 0.176432
\(515\) 14.1421i 0.623177i
\(516\) 21.7279 3.72792i 0.956518 0.164113i
\(517\) 6.00000i 0.263880i
\(518\) 19.7990 + 14.1421i 0.869918 + 0.621370i
\(519\) 4.00000 + 2.82843i 0.175581 + 0.124154i
\(520\) 1.00000 1.00000i 0.0438529 0.0438529i
\(521\) 8.48528 0.371747 0.185873 0.982574i \(-0.440489\pi\)
0.185873 + 0.982574i \(0.440489\pi\)
\(522\) 0 0
\(523\) −9.00000 9.00000i −0.393543 0.393543i 0.482405 0.875948i \(-0.339763\pi\)
−0.875948 + 0.482405i \(0.839763\pi\)
\(524\) −8.48528 + 8.48528i −0.370681 + 0.370681i
\(525\) −4.00000 + 5.65685i −0.174574 + 0.246885i
\(526\) −19.0000 19.0000i −0.828439 0.828439i
\(527\) 14.1421i 0.616041i
\(528\) 6.00000 + 4.24264i 0.261116 + 0.184637i
\(529\) 13.0000i 0.565217i
\(530\) 2.82843i 0.122859i
\(531\) −10.8284 5.17157i −0.469914 0.224427i
\(532\) 8.00000 8.00000i 0.346844 0.346844i
\(533\) −5.65685 5.65685i −0.245026 0.245026i
\(534\) −18.0000 + 25.4558i −0.778936 + 1.10158i
\(535\) −10.0000 10.0000i −0.432338 0.432338i
\(536\) −1.41421 1.41421i −0.0610847 0.0610847i
\(537\) 5.27208 + 30.7279i 0.227507 + 1.32601i
\(538\) 15.0000 15.0000i 0.646696 0.646696i
\(539\) 38.1838 1.64469
\(540\) 4.53553 2.53553i 0.195178 0.109112i
\(541\) 2.00000 + 2.00000i 0.0859867 + 0.0859867i 0.748792 0.662805i \(-0.230634\pi\)
−0.662805 + 0.748792i \(0.730634\pi\)
\(542\) −5.65685 5.65685i −0.242983 0.242983i
\(543\) −8.48528 6.00000i −0.364138 0.257485i
\(544\) 2.00000 0.0857493
\(545\) 16.9706 0.726939
\(546\) −5.65685 + 8.00000i −0.242091 + 0.342368i
\(547\) −21.0000 + 21.0000i −0.897895 + 0.897895i −0.995250 0.0973546i \(-0.968962\pi\)
0.0973546 + 0.995250i \(0.468962\pi\)
\(548\) −9.89949 −0.422885
\(549\) 15.3137 + 7.31371i 0.653573 + 0.312141i
\(550\) 3.00000 3.00000i 0.127920 0.127920i
\(551\) 0 0
\(552\) −6.00000 + 8.48528i −0.255377 + 0.361158i
\(553\) −12.0000 12.0000i −0.510292 0.510292i
\(554\) −21.2132 −0.901263
\(555\) −9.94975 + 3.46447i −0.422343 + 0.147058i
\(556\) −16.0000 −0.678551
\(557\) −24.0416 24.0416i −1.01868 1.01868i −0.999822 0.0188543i \(-0.993998\pi\)
−0.0188543 0.999822i \(-0.506002\pi\)
\(558\) 7.07107 + 20.0000i 0.299342 + 0.846668i
\(559\) 18.0000i 0.761319i
\(560\) −2.82843 + 2.82843i −0.119523 + 0.119523i
\(561\) 14.4853 2.48528i 0.611569 0.104929i
\(562\) −10.0000 −0.421825
\(563\) 5.65685 5.65685i 0.238408 0.238408i −0.577783 0.816191i \(-0.696082\pi\)
0.816191 + 0.577783i \(0.196082\pi\)
\(564\) 2.00000 + 1.41421i 0.0842152 + 0.0595491i
\(565\) 6.00000 0.252422
\(566\) −21.2132 −0.891657
\(567\) −28.0000 + 22.6274i −1.17589 + 0.950262i
\(568\) 2.00000 + 2.00000i 0.0839181 + 0.0839181i
\(569\) 18.3848 + 18.3848i 0.770730 + 0.770730i 0.978234 0.207504i \(-0.0665341\pi\)
−0.207504 + 0.978234i \(0.566534\pi\)
\(570\) 0.828427 + 4.82843i 0.0346990 + 0.202241i
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 4.24264 4.24264i 0.177394 0.177394i
\(573\) −6.82843 + 1.17157i −0.285262 + 0.0489432i
\(574\) 16.0000 + 16.0000i 0.667827 + 0.667827i
\(575\) 4.24264 + 4.24264i 0.176930 + 0.176930i
\(576\) 2.82843 1.00000i 0.117851 0.0416667i
\(577\) 20.0000 + 20.0000i 0.832611 + 0.832611i 0.987873 0.155262i \(-0.0496223\pi\)
−0.155262 + 0.987873i \(0.549622\pi\)
\(578\) −9.19239 + 9.19239i −0.382353 + 0.382353i
\(579\) −7.45584 43.4558i −0.309854 1.80596i
\(580\) 0 0
\(581\) 11.3137i 0.469372i
\(582\) −16.9706 + 24.0000i −0.703452 + 0.994832i
\(583\) 12.0000i 0.496989i
\(584\) 4.24264 + 4.24264i 0.175562 + 0.175562i
\(585\) −1.41421 4.00000i −0.0584705 0.165380i
\(586\) 20.0000 20.0000i 0.826192 0.826192i
\(587\) 16.9706 + 16.9706i 0.700450 + 0.700450i 0.964507 0.264057i \(-0.0850607\pi\)
−0.264057 + 0.964507i \(0.585061\pi\)
\(588\) 9.00000 12.7279i 0.371154 0.524891i
\(589\) −20.0000 −0.824086
\(590\) −2.82843 + 2.82843i −0.116445 + 0.116445i
\(591\) −19.7990 + 28.0000i −0.814422 + 1.15177i
\(592\) −6.00000 + 1.00000i −0.246598 + 0.0410997i
\(593\) 15.5563i 0.638823i −0.947616 0.319411i \(-0.896515\pi\)
0.947616 0.319411i \(-0.103485\pi\)
\(594\) 19.2426 10.7574i 0.789535 0.441380i
\(595\) 8.00000i 0.327968i
\(596\) 9.89949 0.405499
\(597\) 7.24264 1.24264i 0.296422 0.0508579i
\(598\) 6.00000 + 6.00000i 0.245358 + 0.245358i
\(599\) 16.9706i 0.693398i −0.937976 0.346699i \(-0.887302\pi\)
0.937976 0.346699i \(-0.112698\pi\)
\(600\) −0.292893 1.70711i −0.0119573 0.0696923i
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 50.9117i 2.07501i
\(603\) −5.65685 + 2.00000i −0.230365 + 0.0814463i
\(604\) 0 0
\(605\) 4.94975 4.94975i 0.201236 0.201236i
\(606\) −4.55635 26.5563i −0.185089 1.07878i
\(607\) −22.0000 + 22.0000i −0.892952 + 0.892952i −0.994800 0.101848i \(-0.967525\pi\)
0.101848 + 0.994800i \(0.467525\pi\)
\(608\) 2.82843i 0.114708i
\(609\) 0 0
\(610\) 4.00000 4.00000i 0.161955 0.161955i
\(611\) 1.41421 1.41421i 0.0572130 0.0572130i
\(612\) 2.58579 5.41421i 0.104524 0.218857i
\(613\) 16.0000i 0.646234i 0.946359 + 0.323117i \(0.104731\pi\)
−0.946359 + 0.323117i \(0.895269\pi\)
\(614\) 2.82843 2.82843i 0.114146 0.114146i
\(615\) −9.65685 + 1.65685i −0.389402 + 0.0668108i
\(616\) −12.0000 + 12.0000i −0.483494 + 0.483494i
\(617\) −21.2132 −0.854011 −0.427006 0.904249i \(-0.640432\pi\)
−0.427006 + 0.904249i \(0.640432\pi\)
\(618\) 20.0000 + 14.1421i 0.804518 + 0.568880i
\(619\) 16.0000i 0.643094i −0.946894 0.321547i \(-0.895797\pi\)
0.946894 0.321547i \(-0.104203\pi\)
\(620\) 7.07107 0.283981
\(621\) 15.2132 + 27.2132i 0.610485 + 1.09203i
\(622\) 12.0000i 0.481156i
\(623\) −50.9117 50.9117i −2.03973 2.03973i
\(624\) −0.414214 2.41421i −0.0165818 0.0966459i
\(625\) −1.00000 −0.0400000
\(626\) 8.48528i 0.339140i
\(627\) 3.51472 + 20.4853i 0.140364 + 0.818103i
\(628\) 18.0000i 0.718278i
\(629\) −7.07107 + 9.89949i −0.281942 + 0.394719i
\(630\) 4.00000 + 11.3137i 0.159364 + 0.450749i
\(631\) 1.00000 1.00000i 0.0398094 0.0398094i −0.686922 0.726731i \(-0.741039\pi\)
0.726731 + 0.686922i \(0.241039\pi\)
\(632\) 4.24264 0.168763
\(633\) 22.6274 + 16.0000i 0.899359 + 0.635943i
\(634\) 6.00000 + 6.00000i 0.238290 + 0.238290i
\(635\) −8.48528 + 8.48528i −0.336728 + 0.336728i
\(636\) 4.00000 + 2.82843i 0.158610 + 0.112154i
\(637\) −9.00000 9.00000i −0.356593 0.356593i
\(638\) 0 0
\(639\) 8.00000 2.82843i 0.316475 0.111891i
\(640\) 1.00000i 0.0395285i
\(641\) 22.6274i 0.893729i −0.894602 0.446865i \(-0.852541\pi\)
0.894602 0.446865i \(-0.147459\pi\)
\(642\) −24.1421 + 4.14214i −0.952814 + 0.163477i
\(643\) 17.0000 17.0000i 0.670415 0.670415i −0.287397 0.957812i \(-0.592790\pi\)
0.957812 + 0.287397i \(0.0927899\pi\)
\(644\) −16.9706 16.9706i −0.668734 0.668734i
\(645\) −18.0000 12.7279i −0.708749 0.501161i
\(646\) 4.00000 + 4.00000i 0.157378 + 0.157378i
\(647\) 22.6274 + 22.6274i 0.889576 + 0.889576i 0.994482 0.104907i \(-0.0334543\pi\)
−0.104907 + 0.994482i \(0.533454\pi\)
\(648\) 0.949747 8.94975i 0.0373096 0.351579i
\(649\) −12.0000 + 12.0000i −0.471041 + 0.471041i
\(650\) −1.41421 −0.0554700
\(651\) −48.2843 + 8.28427i −1.89241 + 0.324686i
\(652\) −5.00000 5.00000i −0.195815 0.195815i
\(653\) −4.24264 4.24264i −0.166027 0.166027i 0.619203 0.785231i \(-0.287456\pi\)
−0.785231 + 0.619203i \(0.787456\pi\)
\(654\) 16.9706 24.0000i 0.663602 0.938474i
\(655\) 12.0000 0.468879
\(656\) −5.65685 −0.220863
\(657\) 16.9706 6.00000i 0.662085 0.234082i
\(658\) −4.00000 + 4.00000i −0.155936 + 0.155936i
\(659\) 9.89949 0.385630 0.192815 0.981235i \(-0.438238\pi\)
0.192815 + 0.981235i \(0.438238\pi\)
\(660\) −1.24264 7.24264i −0.0483697 0.281919i
\(661\) 10.0000 10.0000i 0.388955 0.388955i −0.485360 0.874315i \(-0.661311\pi\)
0.874315 + 0.485360i \(0.161311\pi\)
\(662\) 5.65685i 0.219860i
\(663\) −4.00000 2.82843i −0.155347 0.109847i
\(664\) 2.00000 + 2.00000i 0.0776151 + 0.0776151i
\(665\) −11.3137 −0.438727
\(666\) −5.05025 + 17.5355i −0.195693 + 0.679488i
\(667\) 0 0
\(668\) −12.7279 12.7279i −0.492458 0.492458i
\(669\) 16.9706 + 12.0000i 0.656120 + 0.463947i
\(670\) 2.00000i 0.0772667i
\(671\) 16.9706 16.9706i 0.655141 0.655141i
\(672\) 1.17157 + 6.82843i 0.0451944 + 0.263412i
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 1.41421 1.41421i 0.0544735 0.0544735i
\(675\) −5.00000 1.41421i −0.192450 0.0544331i
\(676\) 11.0000 0.423077
\(677\) 28.2843 1.08705 0.543526 0.839392i \(-0.317089\pi\)
0.543526 + 0.839392i \(0.317089\pi\)
\(678\) 6.00000 8.48528i 0.230429 0.325875i
\(679\) −48.0000 48.0000i −1.84207 1.84207i
\(680\) −1.41421 1.41421i −0.0542326 0.0542326i
\(681\) 47.7990 8.20101i 1.83166 0.314263i
\(682\) 30.0000 1.14876
\(683\) 22.6274 22.6274i 0.865814 0.865814i −0.126192 0.992006i \(-0.540275\pi\)
0.992006 + 0.126192i \(0.0402755\pi\)
\(684\) 7.65685 + 3.65685i 0.292767 + 0.139823i
\(685\) 7.00000 + 7.00000i 0.267456 + 0.267456i
\(686\) 5.65685 + 5.65685i 0.215980 + 0.215980i
\(687\) −36.7696 26.0000i −1.40285 0.991962i
\(688\) −9.00000 9.00000i −0.343122 0.343122i
\(689\) 2.82843 2.82843i 0.107754 0.107754i
\(690\) 10.2426 1.75736i 0.389931 0.0669015i
\(691\) 28.0000i 1.06517i −0.846376 0.532585i \(-0.821221\pi\)
0.846376 0.532585i \(-0.178779\pi\)
\(692\) 2.82843i 0.107521i
\(693\) 16.9706 + 48.0000i 0.644658 + 1.82337i
\(694\) 12.0000i 0.455514i
\(695\) 11.3137 + 11.3137i 0.429153 + 0.429153i
\(696\) 0 0
\(697\) −8.00000 + 8.00000i −0.303022 + 0.303022i
\(698\) −9.89949 9.89949i −0.374701 0.374701i
\(699\) 10.0000 + 7.07107i 0.378235 + 0.267452i
\(700\) 4.00000 0.151186
\(701\) −35.3553 + 35.3553i −1.33535 + 1.33535i −0.434850 + 0.900503i \(0.643198\pi\)
−0.900503 + 0.434850i \(0.856802\pi\)
\(702\) −7.07107 2.00000i −0.266880 0.0754851i
\(703\) −14.0000 10.0000i −0.528020 0.377157i
\(704\) 4.24264i 0.159901i
\(705\) −0.414214 2.41421i −0.0156002 0.0909245i
\(706\) 34.0000i 1.27961i
\(707\) 62.2254 2.34023
\(708\) 1.17157 + 6.82843i 0.0440304 + 0.256628i
\(709\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(710\) 2.82843i 0.106149i
\(711\) 5.48528 11.4853i 0.205714 0.430732i
\(712\) 18.0000 0.674579
\(713\) 42.4264i 1.58888i
\(714\) 11.3137 + 8.00000i 0.423405 + 0.299392i
\(715\) −6.00000 −0.224387
\(716\) 12.7279 12.7279i 0.475665 0.475665i
\(717\) 0 0
\(718\) −8.00000 + 8.00000i −0.298557 + 0.298557i
\(719\) 19.7990i 0.738378i 0.929354 + 0.369189i \(0.120364\pi\)
−0.929354 + 0.369189i \(0.879636\pi\)
\(720\) −2.70711 1.29289i −0.100888 0.0481833i
\(721\) −40.0000 + 40.0000i −1.48968 + 1.48968i
\(722\) 7.77817 7.77817i 0.289474 0.289474i
\(723\) −1.24264 7.24264i −0.0462143 0.269357i
\(724\) 6.00000i 0.222988i
\(725\) 0 0
\(726\) −2.05025 11.9497i −0.0760920 0.443497i
\(727\) 8.00000 8.00000i 0.296704 0.296704i −0.543018 0.839721i \(-0.682718\pi\)
0.839721 + 0.543018i \(0.182718\pi\)
\(728\) 5.65685 0.209657
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 6.00000i 0.222070i
\(731\) −25.4558 −0.941518
\(732\) −1.65685 9.65685i −0.0612391 0.356928i
\(733\) 24.0000i 0.886460i 0.896408 + 0.443230i \(0.146168\pi\)
−0.896408 + 0.443230i \(0.853832\pi\)
\(734\) 5.65685 + 5.65685i 0.208798 + 0.208798i
\(735\) −15.3640 + 2.63604i −0.566708 + 0.0972318i
\(736\) 6.00000 0.221163
\(737\) 8.48528i 0.312559i
\(738\) −7.31371 + 15.3137i −0.269221 + 0.563705i
\(739\) 40.0000i 1.47142i 0.677295 + 0.735712i \(0.263152\pi\)
−0.677295 + 0.735712i \(0.736848\pi\)
\(740\) 4.94975 + 3.53553i 0.181956 + 0.129969i
\(741\) 4.00000 5.65685i 0.146944 0.207810i
\(742\) −8.00000 + 8.00000i −0.293689 + 0.293689i
\(743\) 49.4975 1.81589 0.907943 0.419093i \(-0.137652\pi\)
0.907943 + 0.419093i \(0.137652\pi\)
\(744\) 7.07107 10.0000i 0.259238 0.366618i
\(745\) −7.00000 7.00000i −0.256460 0.256460i
\(746\) 24.0416 24.0416i 0.880227 0.880227i
\(747\) 8.00000 2.82843i 0.292705 0.103487i
\(748\) −6.00000 6.00000i −0.219382 0.219382i
\(749\) 56.5685i 2.06697i
\(750\) −1.00000 + 1.41421i −0.0365148 + 0.0516398i
\(751\) 2.00000i 0.0729810i −0.999334 0.0364905i \(-0.988382\pi\)
0.999334 0.0364905i \(-0.0116179\pi\)
\(752\) 1.41421i 0.0515711i
\(753\) 1.17157 + 6.82843i 0.0426945 + 0.248842i
\(754\) 0 0
\(755\) 0 0
\(756\) 20.0000 + 5.65685i 0.727393 + 0.205738i
\(757\) −5.00000 5.00000i −0.181728 0.181728i 0.610380 0.792108i \(-0.291017\pi\)
−0.792108 + 0.610380i \(0.791017\pi\)
\(758\) 0 0
\(759\) 43.4558 7.45584i 1.57735 0.270630i
\(760\) 2.00000 2.00000i 0.0725476 0.0725476i
\(761\) 22.6274 0.820243 0.410122 0.912031i \(-0.365486\pi\)
0.410122 + 0.912031i \(0.365486\pi\)
\(762\) 3.51472 + 20.4853i 0.127325 + 0.742103i
\(763\) 48.0000 + 48.0000i 1.73772 + 1.73772i
\(764\) 2.82843 + 2.82843i 0.102329 + 0.102329i
\(765\) −5.65685 + 2.00000i −0.204524 + 0.0723102i
\(766\) 16.0000 0.578103
\(767\) 5.65685 0.204257
\(768\) −1.41421 1.00000i −0.0510310 0.0360844i
\(769\) 19.0000 19.0000i 0.685158 0.685158i −0.276000 0.961158i \(-0.589009\pi\)
0.961158 + 0.276000i \(0.0890090\pi\)
\(770\) 16.9706 0.611577
\(771\) −6.82843 + 1.17157i −0.245920 + 0.0421932i
\(772\) −18.0000 + 18.0000i −0.647834 + 0.647834i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −36.0000 + 12.7279i −1.29399 + 0.457496i
\(775\) −5.00000 5.00000i −0.179605 0.179605i
\(776\) 16.9706 0.609208
\(777\) −37.9411 18.3431i −1.36113 0.658057i