Properties

Label 825.2.k.h.518.1
Level $825$
Weight $2$
Character 825.518
Analytic conductor $6.588$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 518.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 825.518
Dual form 825.2.k.h.782.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.292893 + 0.292893i) q^{2} +(1.70711 - 0.292893i) q^{3} -1.82843i q^{4} +(0.585786 + 0.414214i) q^{6} +(0.585786 - 0.585786i) q^{7} +(1.12132 - 1.12132i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(0.292893 + 0.292893i) q^{2} +(1.70711 - 0.292893i) q^{3} -1.82843i q^{4} +(0.585786 + 0.414214i) q^{6} +(0.585786 - 0.585786i) q^{7} +(1.12132 - 1.12132i) q^{8} +(2.82843 - 1.00000i) q^{9} -1.00000i q^{11} +(-0.535534 - 3.12132i) q^{12} +(3.41421 + 3.41421i) q^{13} +0.343146 q^{14} -3.00000 q^{16} +(-2.00000 - 2.00000i) q^{17} +(1.12132 + 0.535534i) q^{18} -0.828427i q^{19} +(0.828427 - 1.17157i) q^{21} +(0.292893 - 0.292893i) q^{22} +(-0.828427 + 0.828427i) q^{23} +(1.58579 - 2.24264i) q^{24} +2.00000i q^{26} +(4.53553 - 2.53553i) q^{27} +(-1.07107 - 1.07107i) q^{28} -8.82843 q^{29} +4.00000 q^{31} +(-3.12132 - 3.12132i) q^{32} +(-0.292893 - 1.70711i) q^{33} -1.17157i q^{34} +(-1.82843 - 5.17157i) q^{36} +(5.65685 - 5.65685i) q^{37} +(0.242641 - 0.242641i) q^{38} +(6.82843 + 4.82843i) q^{39} +4.82843i q^{41} +(0.585786 - 0.100505i) q^{42} +(4.58579 + 4.58579i) q^{43} -1.82843 q^{44} -0.485281 q^{46} +(-4.82843 - 4.82843i) q^{47} +(-5.12132 + 0.878680i) q^{48} +6.31371i q^{49} +(-4.00000 - 2.82843i) q^{51} +(6.24264 - 6.24264i) q^{52} +(8.48528 - 8.48528i) q^{53} +(2.07107 + 0.585786i) q^{54} -1.31371i q^{56} +(-0.242641 - 1.41421i) q^{57} +(-2.58579 - 2.58579i) q^{58} -2.34315 q^{59} -6.00000 q^{61} +(1.17157 + 1.17157i) q^{62} +(1.07107 - 2.24264i) q^{63} +4.17157i q^{64} +(0.414214 - 0.585786i) q^{66} +(-2.58579 + 2.58579i) q^{67} +(-3.65685 + 3.65685i) q^{68} +(-1.17157 + 1.65685i) q^{69} +9.65685i q^{71} +(2.05025 - 4.29289i) q^{72} +(4.58579 + 4.58579i) q^{73} +3.31371 q^{74} -1.51472 q^{76} +(-0.585786 - 0.585786i) q^{77} +(0.585786 + 3.41421i) q^{78} +4.82843i q^{79} +(7.00000 - 5.65685i) q^{81} +(-1.41421 + 1.41421i) q^{82} +(-4.24264 + 4.24264i) q^{83} +(-2.14214 - 1.51472i) q^{84} +2.68629i q^{86} +(-15.0711 + 2.58579i) q^{87} +(-1.12132 - 1.12132i) q^{88} -15.3137 q^{89} +4.00000 q^{91} +(1.51472 + 1.51472i) q^{92} +(6.82843 - 1.17157i) q^{93} -2.82843i q^{94} +(-6.24264 - 4.41421i) q^{96} +(-1.65685 + 1.65685i) q^{97} +(-1.84924 + 1.84924i) q^{98} +(-1.00000 - 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{7} - 4 q^{8} + O(q^{10}) \) \( 4 q + 4 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{7} - 4 q^{8} + 12 q^{12} + 8 q^{13} + 24 q^{14} - 12 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{21} + 4 q^{22} + 8 q^{23} + 12 q^{24} + 4 q^{27} + 24 q^{28} - 24 q^{29} + 16 q^{31} - 4 q^{32} - 4 q^{33} + 4 q^{36} - 16 q^{38} + 16 q^{39} + 8 q^{42} + 24 q^{43} + 4 q^{44} + 32 q^{46} - 8 q^{47} - 12 q^{48} - 16 q^{51} + 8 q^{52} - 20 q^{54} + 16 q^{57} - 16 q^{58} - 32 q^{59} - 24 q^{61} + 16 q^{62} - 24 q^{63} - 4 q^{66} - 16 q^{67} + 8 q^{68} - 16 q^{69} + 28 q^{72} + 24 q^{73} - 32 q^{74} - 40 q^{76} - 8 q^{77} + 8 q^{78} + 28 q^{81} + 48 q^{84} - 32 q^{87} + 4 q^{88} - 16 q^{89} + 16 q^{91} + 40 q^{92} + 16 q^{93} - 8 q^{96} + 16 q^{97} + 52 q^{98} - 4 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.292893 + 0.292893i 0.207107 + 0.207107i 0.803037 0.595930i \(-0.203216\pi\)
−0.595930 + 0.803037i \(0.703216\pi\)
\(3\) 1.70711 0.292893i 0.985599 0.169102i
\(4\) 1.82843i 0.914214i
\(5\) 0 0
\(6\) 0.585786 + 0.414214i 0.239146 + 0.169102i
\(7\) 0.585786 0.585786i 0.221406 0.221406i −0.587684 0.809091i \(-0.699960\pi\)
0.809091 + 0.587684i \(0.199960\pi\)
\(8\) 1.12132 1.12132i 0.396447 0.396447i
\(9\) 2.82843 1.00000i 0.942809 0.333333i
\(10\) 0 0
\(11\) 1.00000i 0.301511i
\(12\) −0.535534 3.12132i −0.154595 0.901048i
\(13\) 3.41421 + 3.41421i 0.946932 + 0.946932i 0.998661 0.0517287i \(-0.0164731\pi\)
−0.0517287 + 0.998661i \(0.516473\pi\)
\(14\) 0.343146 0.0917096
\(15\) 0 0
\(16\) −3.00000 −0.750000
\(17\) −2.00000 2.00000i −0.485071 0.485071i 0.421676 0.906747i \(-0.361442\pi\)
−0.906747 + 0.421676i \(0.861442\pi\)
\(18\) 1.12132 + 0.535534i 0.264298 + 0.126227i
\(19\) 0.828427i 0.190054i −0.995475 0.0950271i \(-0.969706\pi\)
0.995475 0.0950271i \(-0.0302938\pi\)
\(20\) 0 0
\(21\) 0.828427 1.17157i 0.180778 0.255658i
\(22\) 0.292893 0.292893i 0.0624450 0.0624450i
\(23\) −0.828427 + 0.828427i −0.172739 + 0.172739i −0.788182 0.615443i \(-0.788977\pi\)
0.615443 + 0.788182i \(0.288977\pi\)
\(24\) 1.58579 2.24264i 0.323697 0.457777i
\(25\) 0 0
\(26\) 2.00000i 0.392232i
\(27\) 4.53553 2.53553i 0.872864 0.487964i
\(28\) −1.07107 1.07107i −0.202413 0.202413i
\(29\) −8.82843 −1.63940 −0.819699 0.572795i \(-0.805859\pi\)
−0.819699 + 0.572795i \(0.805859\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −3.12132 3.12132i −0.551777 0.551777i
\(33\) −0.292893 1.70711i −0.0509862 0.297169i
\(34\) 1.17157i 0.200923i
\(35\) 0 0
\(36\) −1.82843 5.17157i −0.304738 0.861929i
\(37\) 5.65685 5.65685i 0.929981 0.929981i −0.0677230 0.997704i \(-0.521573\pi\)
0.997704 + 0.0677230i \(0.0215734\pi\)
\(38\) 0.242641 0.242641i 0.0393615 0.0393615i
\(39\) 6.82843 + 4.82843i 1.09342 + 0.773167i
\(40\) 0 0
\(41\) 4.82843i 0.754074i 0.926198 + 0.377037i \(0.123057\pi\)
−0.926198 + 0.377037i \(0.876943\pi\)
\(42\) 0.585786 0.100505i 0.0903888 0.0155083i
\(43\) 4.58579 + 4.58579i 0.699326 + 0.699326i 0.964265 0.264939i \(-0.0853519\pi\)
−0.264939 + 0.964265i \(0.585352\pi\)
\(44\) −1.82843 −0.275646
\(45\) 0 0
\(46\) −0.485281 −0.0715508
\(47\) −4.82843 4.82843i −0.704298 0.704298i 0.261032 0.965330i \(-0.415937\pi\)
−0.965330 + 0.261032i \(0.915937\pi\)
\(48\) −5.12132 + 0.878680i −0.739199 + 0.126826i
\(49\) 6.31371i 0.901958i
\(50\) 0 0
\(51\) −4.00000 2.82843i −0.560112 0.396059i
\(52\) 6.24264 6.24264i 0.865699 0.865699i
\(53\) 8.48528 8.48528i 1.16554 1.16554i 0.182300 0.983243i \(-0.441646\pi\)
0.983243 0.182300i \(-0.0583542\pi\)
\(54\) 2.07107 + 0.585786i 0.281837 + 0.0797154i
\(55\) 0 0
\(56\) 1.31371i 0.175552i
\(57\) −0.242641 1.41421i −0.0321385 0.187317i
\(58\) −2.58579 2.58579i −0.339530 0.339530i
\(59\) −2.34315 −0.305052 −0.152526 0.988299i \(-0.548741\pi\)
−0.152526 + 0.988299i \(0.548741\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 1.17157 + 1.17157i 0.148790 + 0.148790i
\(63\) 1.07107 2.24264i 0.134942 0.282546i
\(64\) 4.17157i 0.521447i
\(65\) 0 0
\(66\) 0.414214 0.585786i 0.0509862 0.0721053i
\(67\) −2.58579 + 2.58579i −0.315904 + 0.315904i −0.847192 0.531287i \(-0.821708\pi\)
0.531287 + 0.847192i \(0.321708\pi\)
\(68\) −3.65685 + 3.65685i −0.443459 + 0.443459i
\(69\) −1.17157 + 1.65685i −0.141041 + 0.199462i
\(70\) 0 0
\(71\) 9.65685i 1.14606i 0.819535 + 0.573029i \(0.194232\pi\)
−0.819535 + 0.573029i \(0.805768\pi\)
\(72\) 2.05025 4.29289i 0.241625 0.505922i
\(73\) 4.58579 + 4.58579i 0.536726 + 0.536726i 0.922566 0.385840i \(-0.126088\pi\)
−0.385840 + 0.922566i \(0.626088\pi\)
\(74\) 3.31371 0.385211
\(75\) 0 0
\(76\) −1.51472 −0.173750
\(77\) −0.585786 0.585786i −0.0667566 0.0667566i
\(78\) 0.585786 + 3.41421i 0.0663273 + 0.386584i
\(79\) 4.82843i 0.543240i 0.962405 + 0.271620i \(0.0875595\pi\)
−0.962405 + 0.271620i \(0.912441\pi\)
\(80\) 0 0
\(81\) 7.00000 5.65685i 0.777778 0.628539i
\(82\) −1.41421 + 1.41421i −0.156174 + 0.156174i
\(83\) −4.24264 + 4.24264i −0.465690 + 0.465690i −0.900515 0.434825i \(-0.856810\pi\)
0.434825 + 0.900515i \(0.356810\pi\)
\(84\) −2.14214 1.51472i −0.233726 0.165269i
\(85\) 0 0
\(86\) 2.68629i 0.289670i
\(87\) −15.0711 + 2.58579i −1.61579 + 0.277225i
\(88\) −1.12132 1.12132i −0.119533 0.119533i
\(89\) −15.3137 −1.62325 −0.811625 0.584179i \(-0.801417\pi\)
−0.811625 + 0.584179i \(0.801417\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 1.51472 + 1.51472i 0.157920 + 0.157920i
\(93\) 6.82843 1.17157i 0.708075 0.121486i
\(94\) 2.82843i 0.291730i
\(95\) 0 0
\(96\) −6.24264 4.41421i −0.637137 0.450524i
\(97\) −1.65685 + 1.65685i −0.168228 + 0.168228i −0.786200 0.617972i \(-0.787954\pi\)
0.617972 + 0.786200i \(0.287954\pi\)
\(98\) −1.84924 + 1.84924i −0.186802 + 0.186802i
\(99\) −1.00000 2.82843i −0.100504 0.284268i
\(100\) 0 0
\(101\) 0.828427i 0.0824316i 0.999150 + 0.0412158i \(0.0131231\pi\)
−0.999150 + 0.0412158i \(0.986877\pi\)
\(102\) −0.343146 2.00000i −0.0339765 0.198030i
\(103\) 4.24264 + 4.24264i 0.418040 + 0.418040i 0.884528 0.466488i \(-0.154481\pi\)
−0.466488 + 0.884528i \(0.654481\pi\)
\(104\) 7.65685 0.750816
\(105\) 0 0
\(106\) 4.97056 0.482784
\(107\) 13.8995 + 13.8995i 1.34371 + 1.34371i 0.892329 + 0.451386i \(0.149070\pi\)
0.451386 + 0.892329i \(0.350930\pi\)
\(108\) −4.63604 8.29289i −0.446103 0.797984i
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) 0 0
\(111\) 8.00000 11.3137i 0.759326 1.07385i
\(112\) −1.75736 + 1.75736i −0.166055 + 0.166055i
\(113\) 8.48528 8.48528i 0.798228 0.798228i −0.184588 0.982816i \(-0.559095\pi\)
0.982816 + 0.184588i \(0.0590950\pi\)
\(114\) 0.343146 0.485281i 0.0321385 0.0454508i
\(115\) 0 0
\(116\) 16.1421i 1.49876i
\(117\) 13.0711 + 6.24264i 1.20842 + 0.577132i
\(118\) −0.686292 0.686292i −0.0631783 0.0631783i
\(119\) −2.34315 −0.214796
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) −1.75736 1.75736i −0.159104 0.159104i
\(123\) 1.41421 + 8.24264i 0.127515 + 0.743214i
\(124\) 7.31371i 0.656790i
\(125\) 0 0
\(126\) 0.970563 0.343146i 0.0864646 0.0305699i
\(127\) −10.2426 + 10.2426i −0.908887 + 0.908887i −0.996182 0.0872951i \(-0.972178\pi\)
0.0872951 + 0.996182i \(0.472178\pi\)
\(128\) −7.46447 + 7.46447i −0.659772 + 0.659772i
\(129\) 9.17157 + 6.48528i 0.807512 + 0.570997i
\(130\) 0 0
\(131\) 17.6569i 1.54269i 0.636419 + 0.771343i \(0.280415\pi\)
−0.636419 + 0.771343i \(0.719585\pi\)
\(132\) −3.12132 + 0.535534i −0.271676 + 0.0466122i
\(133\) −0.485281 0.485281i −0.0420792 0.0420792i
\(134\) −1.51472 −0.130852
\(135\) 0 0
\(136\) −4.48528 −0.384610
\(137\) 1.65685 + 1.65685i 0.141555 + 0.141555i 0.774333 0.632778i \(-0.218086\pi\)
−0.632778 + 0.774333i \(0.718086\pi\)
\(138\) −0.828427 + 0.142136i −0.0705204 + 0.0120994i
\(139\) 16.8284i 1.42737i −0.700468 0.713684i \(-0.747025\pi\)
0.700468 0.713684i \(-0.252975\pi\)
\(140\) 0 0
\(141\) −9.65685 6.82843i −0.813254 0.575057i
\(142\) −2.82843 + 2.82843i −0.237356 + 0.237356i
\(143\) 3.41421 3.41421i 0.285511 0.285511i
\(144\) −8.48528 + 3.00000i −0.707107 + 0.250000i
\(145\) 0 0
\(146\) 2.68629i 0.222319i
\(147\) 1.84924 + 10.7782i 0.152523 + 0.888969i
\(148\) −10.3431 10.3431i −0.850201 0.850201i
\(149\) 17.7990 1.45815 0.729075 0.684434i \(-0.239951\pi\)
0.729075 + 0.684434i \(0.239951\pi\)
\(150\) 0 0
\(151\) 14.4853 1.17880 0.589398 0.807843i \(-0.299365\pi\)
0.589398 + 0.807843i \(0.299365\pi\)
\(152\) −0.928932 0.928932i −0.0753463 0.0753463i
\(153\) −7.65685 3.65685i −0.619020 0.295639i
\(154\) 0.343146i 0.0276515i
\(155\) 0 0
\(156\) 8.82843 12.4853i 0.706840 0.999623i
\(157\) −15.3137 + 15.3137i −1.22217 + 1.22217i −0.255307 + 0.966860i \(0.582177\pi\)
−0.966860 + 0.255307i \(0.917823\pi\)
\(158\) −1.41421 + 1.41421i −0.112509 + 0.112509i
\(159\) 12.0000 16.9706i 0.951662 1.34585i
\(160\) 0 0
\(161\) 0.970563i 0.0764911i
\(162\) 3.70711 + 0.393398i 0.291258 + 0.0309083i
\(163\) −9.89949 9.89949i −0.775388 0.775388i 0.203655 0.979043i \(-0.434718\pi\)
−0.979043 + 0.203655i \(0.934718\pi\)
\(164\) 8.82843 0.689384
\(165\) 0 0
\(166\) −2.48528 −0.192895
\(167\) 8.24264 + 8.24264i 0.637835 + 0.637835i 0.950021 0.312186i \(-0.101061\pi\)
−0.312186 + 0.950021i \(0.601061\pi\)
\(168\) −0.384776 2.24264i −0.0296861 0.173023i
\(169\) 10.3137i 0.793362i
\(170\) 0 0
\(171\) −0.828427 2.34315i −0.0633514 0.179185i
\(172\) 8.38478 8.38478i 0.639333 0.639333i
\(173\) −4.82843 + 4.82843i −0.367099 + 0.367099i −0.866418 0.499319i \(-0.833583\pi\)
0.499319 + 0.866418i \(0.333583\pi\)
\(174\) −5.17157 3.65685i −0.392056 0.277225i
\(175\) 0 0
\(176\) 3.00000i 0.226134i
\(177\) −4.00000 + 0.686292i −0.300658 + 0.0515848i
\(178\) −4.48528 4.48528i −0.336186 0.336186i
\(179\) −19.3137 −1.44357 −0.721787 0.692115i \(-0.756679\pi\)
−0.721787 + 0.692115i \(0.756679\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 1.17157 + 1.17157i 0.0868428 + 0.0868428i
\(183\) −10.2426 + 1.75736i −0.757158 + 0.129908i
\(184\) 1.85786i 0.136964i
\(185\) 0 0
\(186\) 2.34315 + 1.65685i 0.171808 + 0.121486i
\(187\) −2.00000 + 2.00000i −0.146254 + 0.146254i
\(188\) −8.82843 + 8.82843i −0.643879 + 0.643879i
\(189\) 1.17157 4.14214i 0.0852194 0.301296i
\(190\) 0 0
\(191\) 11.3137i 0.818631i −0.912393 0.409316i \(-0.865768\pi\)
0.912393 0.409316i \(-0.134232\pi\)
\(192\) 1.22183 + 7.12132i 0.0881777 + 0.513937i
\(193\) 9.07107 + 9.07107i 0.652950 + 0.652950i 0.953702 0.300752i \(-0.0972378\pi\)
−0.300752 + 0.953702i \(0.597238\pi\)
\(194\) −0.970563 −0.0696823
\(195\) 0 0
\(196\) 11.5442 0.824583
\(197\) −14.4853 14.4853i −1.03203 1.03203i −0.999470 0.0325639i \(-0.989633\pi\)
−0.0325639 0.999470i \(-0.510367\pi\)
\(198\) 0.535534 1.12132i 0.0380587 0.0796888i
\(199\) 12.9706i 0.919459i −0.888059 0.459729i \(-0.847946\pi\)
0.888059 0.459729i \(-0.152054\pi\)
\(200\) 0 0
\(201\) −3.65685 + 5.17157i −0.257935 + 0.364775i
\(202\) −0.242641 + 0.242641i −0.0170721 + 0.0170721i
\(203\) −5.17157 + 5.17157i −0.362973 + 0.362973i
\(204\) −5.17157 + 7.31371i −0.362083 + 0.512062i
\(205\) 0 0
\(206\) 2.48528i 0.173158i
\(207\) −1.51472 + 3.17157i −0.105280 + 0.220440i
\(208\) −10.2426 10.2426i −0.710199 0.710199i
\(209\) −0.828427 −0.0573035
\(210\) 0 0
\(211\) −10.4853 −0.721837 −0.360918 0.932597i \(-0.617537\pi\)
−0.360918 + 0.932597i \(0.617537\pi\)
\(212\) −15.5147 15.5147i −1.06556 1.06556i
\(213\) 2.82843 + 16.4853i 0.193801 + 1.12955i
\(214\) 8.14214i 0.556585i
\(215\) 0 0
\(216\) 2.24264 7.92893i 0.152592 0.539496i
\(217\) 2.34315 2.34315i 0.159063 0.159063i
\(218\) 0.585786 0.585786i 0.0396745 0.0396745i
\(219\) 9.17157 + 6.48528i 0.619757 + 0.438235i
\(220\) 0 0
\(221\) 13.6569i 0.918659i
\(222\) 5.65685 0.970563i 0.379663 0.0651399i
\(223\) −16.2426 16.2426i −1.08769 1.08769i −0.995766 0.0919214i \(-0.970699\pi\)
−0.0919214 0.995766i \(-0.529301\pi\)
\(224\) −3.65685 −0.244334
\(225\) 0 0
\(226\) 4.97056 0.330637
\(227\) 20.2426 + 20.2426i 1.34355 + 1.34355i 0.892496 + 0.451055i \(0.148952\pi\)
0.451055 + 0.892496i \(0.351048\pi\)
\(228\) −2.58579 + 0.443651i −0.171248 + 0.0293815i
\(229\) 18.0000i 1.18947i 0.803921 + 0.594737i \(0.202744\pi\)
−0.803921 + 0.594737i \(0.797256\pi\)
\(230\) 0 0
\(231\) −1.17157 0.828427i −0.0770838 0.0545065i
\(232\) −9.89949 + 9.89949i −0.649934 + 0.649934i
\(233\) −10.0000 + 10.0000i −0.655122 + 0.655122i −0.954222 0.299100i \(-0.903314\pi\)
0.299100 + 0.954222i \(0.403314\pi\)
\(234\) 2.00000 + 5.65685i 0.130744 + 0.369800i
\(235\) 0 0
\(236\) 4.28427i 0.278882i
\(237\) 1.41421 + 8.24264i 0.0918630 + 0.535417i
\(238\) −0.686292 0.686292i −0.0444857 0.0444857i
\(239\) 2.34315 0.151565 0.0757827 0.997124i \(-0.475854\pi\)
0.0757827 + 0.997124i \(0.475854\pi\)
\(240\) 0 0
\(241\) −26.9706 −1.73733 −0.868663 0.495403i \(-0.835020\pi\)
−0.868663 + 0.495403i \(0.835020\pi\)
\(242\) −0.292893 0.292893i −0.0188279 0.0188279i
\(243\) 10.2929 11.7071i 0.660289 0.751011i
\(244\) 10.9706i 0.702318i
\(245\) 0 0
\(246\) −2.00000 + 2.82843i −0.127515 + 0.180334i
\(247\) 2.82843 2.82843i 0.179969 0.179969i
\(248\) 4.48528 4.48528i 0.284816 0.284816i
\(249\) −6.00000 + 8.48528i −0.380235 + 0.537733i
\(250\) 0 0
\(251\) 1.65685i 0.104580i 0.998632 + 0.0522899i \(0.0166520\pi\)
−0.998632 + 0.0522899i \(0.983348\pi\)
\(252\) −4.10051 1.95837i −0.258308 0.123366i
\(253\) 0.828427 + 0.828427i 0.0520828 + 0.0520828i
\(254\) −6.00000 −0.376473
\(255\) 0 0
\(256\) 3.97056 0.248160
\(257\) 16.0000 + 16.0000i 0.998053 + 0.998053i 0.999998 0.00194553i \(-0.000619281\pi\)
−0.00194553 + 0.999998i \(0.500619\pi\)
\(258\) 0.786797 + 4.58579i 0.0489838 + 0.285499i
\(259\) 6.62742i 0.411808i
\(260\) 0 0
\(261\) −24.9706 + 8.82843i −1.54564 + 0.546466i
\(262\) −5.17157 + 5.17157i −0.319501 + 0.319501i
\(263\) 16.2426 16.2426i 1.00156 1.00156i 0.00156536 0.999999i \(-0.499502\pi\)
0.999999 0.00156536i \(-0.000498269\pi\)
\(264\) −2.24264 1.58579i −0.138025 0.0975984i
\(265\) 0 0
\(266\) 0.284271i 0.0174298i
\(267\) −26.1421 + 4.48528i −1.59987 + 0.274495i
\(268\) 4.72792 + 4.72792i 0.288804 + 0.288804i
\(269\) −13.6569 −0.832673 −0.416337 0.909211i \(-0.636686\pi\)
−0.416337 + 0.909211i \(0.636686\pi\)
\(270\) 0 0
\(271\) −9.51472 −0.577978 −0.288989 0.957332i \(-0.593319\pi\)
−0.288989 + 0.957332i \(0.593319\pi\)
\(272\) 6.00000 + 6.00000i 0.363803 + 0.363803i
\(273\) 6.82843 1.17157i 0.413275 0.0709068i
\(274\) 0.970563i 0.0586338i
\(275\) 0 0
\(276\) 3.02944 + 2.14214i 0.182351 + 0.128941i
\(277\) 17.0711 17.0711i 1.02570 1.02570i 0.0260402 0.999661i \(-0.491710\pi\)
0.999661 0.0260402i \(-0.00828978\pi\)
\(278\) 4.92893 4.92893i 0.295618 0.295618i
\(279\) 11.3137 4.00000i 0.677334 0.239474i
\(280\) 0 0
\(281\) 8.14214i 0.485719i −0.970061 0.242860i \(-0.921915\pi\)
0.970061 0.242860i \(-0.0780854\pi\)
\(282\) −0.828427 4.82843i −0.0493321 0.287529i
\(283\) 4.58579 + 4.58579i 0.272597 + 0.272597i 0.830145 0.557548i \(-0.188258\pi\)
−0.557548 + 0.830145i \(0.688258\pi\)
\(284\) 17.6569 1.04774
\(285\) 0 0
\(286\) 2.00000 0.118262
\(287\) 2.82843 + 2.82843i 0.166957 + 0.166957i
\(288\) −11.9497 5.70711i −0.704146 0.336294i
\(289\) 9.00000i 0.529412i
\(290\) 0 0
\(291\) −2.34315 + 3.31371i −0.137358 + 0.194253i
\(292\) 8.38478 8.38478i 0.490682 0.490682i
\(293\) −2.48528 + 2.48528i −0.145192 + 0.145192i −0.775966 0.630775i \(-0.782737\pi\)
0.630775 + 0.775966i \(0.282737\pi\)
\(294\) −2.61522 + 3.69848i −0.152523 + 0.215700i
\(295\) 0 0
\(296\) 12.6863i 0.737376i
\(297\) −2.53553 4.53553i −0.147127 0.263178i
\(298\) 5.21320 + 5.21320i 0.301993 + 0.301993i
\(299\) −5.65685 −0.327144
\(300\) 0 0
\(301\) 5.37258 0.309671
\(302\) 4.24264 + 4.24264i 0.244137 + 0.244137i
\(303\) 0.242641 + 1.41421i 0.0139393 + 0.0812444i
\(304\) 2.48528i 0.142541i
\(305\) 0 0
\(306\) −1.17157 3.31371i −0.0669744 0.189432i
\(307\) −18.7279 + 18.7279i −1.06886 + 1.06886i −0.0714121 + 0.997447i \(0.522751\pi\)
−0.997447 + 0.0714121i \(0.977249\pi\)
\(308\) −1.07107 + 1.07107i −0.0610298 + 0.0610298i
\(309\) 8.48528 + 6.00000i 0.482711 + 0.341328i
\(310\) 0 0
\(311\) 10.3431i 0.586506i −0.956035 0.293253i \(-0.905262\pi\)
0.956035 0.293253i \(-0.0947378\pi\)
\(312\) 13.0711 2.24264i 0.740003 0.126965i
\(313\) 18.8284 + 18.8284i 1.06425 + 1.06425i 0.997789 + 0.0664563i \(0.0211693\pi\)
0.0664563 + 0.997789i \(0.478831\pi\)
\(314\) −8.97056 −0.506238
\(315\) 0 0
\(316\) 8.82843 0.496638
\(317\) −18.1421 18.1421i −1.01896 1.01896i −0.999817 0.0191472i \(-0.993905\pi\)
−0.0191472 0.999817i \(-0.506095\pi\)
\(318\) 8.48528 1.45584i 0.475831 0.0816397i
\(319\) 8.82843i 0.494297i
\(320\) 0 0
\(321\) 27.7990 + 19.6569i 1.55159 + 1.09714i
\(322\) −0.284271 + 0.284271i −0.0158418 + 0.0158418i
\(323\) −1.65685 + 1.65685i −0.0921898 + 0.0921898i
\(324\) −10.3431 12.7990i −0.574619 0.711055i
\(325\) 0 0
\(326\) 5.79899i 0.321176i
\(327\) −0.585786 3.41421i −0.0323941 0.188806i
\(328\) 5.41421 + 5.41421i 0.298950 + 0.298950i
\(329\) −5.65685 −0.311872
\(330\) 0 0
\(331\) 1.65685 0.0910689 0.0455345 0.998963i \(-0.485501\pi\)
0.0455345 + 0.998963i \(0.485501\pi\)
\(332\) 7.75736 + 7.75736i 0.425740 + 0.425740i
\(333\) 10.3431 21.6569i 0.566801 1.18679i
\(334\) 4.82843i 0.264200i
\(335\) 0 0
\(336\) −2.48528 + 3.51472i −0.135583 + 0.191744i
\(337\) 15.8995 15.8995i 0.866101 0.866101i −0.125938 0.992038i \(-0.540194\pi\)
0.992038 + 0.125938i \(0.0401939\pi\)
\(338\) −3.02082 + 3.02082i −0.164311 + 0.164311i
\(339\) 12.0000 16.9706i 0.651751 0.921714i
\(340\) 0 0
\(341\) 4.00000i 0.216612i
\(342\) 0.443651 0.928932i 0.0239899 0.0502309i
\(343\) 7.79899 + 7.79899i 0.421106 + 0.421106i
\(344\) 10.2843 0.554491
\(345\) 0 0
\(346\) −2.82843 −0.152057
\(347\) −7.75736 7.75736i −0.416437 0.416437i 0.467537 0.883974i \(-0.345142\pi\)
−0.883974 + 0.467537i \(0.845142\pi\)
\(348\) 4.72792 + 27.5563i 0.253443 + 1.47718i
\(349\) 10.9706i 0.587241i −0.955922 0.293620i \(-0.905140\pi\)
0.955922 0.293620i \(-0.0948602\pi\)
\(350\) 0 0
\(351\) 24.1421 + 6.82843i 1.28861 + 0.364474i
\(352\) −3.12132 + 3.12132i −0.166367 + 0.166367i
\(353\) 12.4853 12.4853i 0.664524 0.664524i −0.291919 0.956443i \(-0.594294\pi\)
0.956443 + 0.291919i \(0.0942937\pi\)
\(354\) −1.37258 0.970563i −0.0729520 0.0515848i
\(355\) 0 0
\(356\) 28.0000i 1.48400i
\(357\) −4.00000 + 0.686292i −0.211702 + 0.0363224i
\(358\) −5.65685 5.65685i −0.298974 0.298974i
\(359\) −16.9706 −0.895672 −0.447836 0.894116i \(-0.647805\pi\)
−0.447836 + 0.894116i \(0.647805\pi\)
\(360\) 0 0
\(361\) 18.3137 0.963879
\(362\) −1.75736 1.75736i −0.0923648 0.0923648i
\(363\) −1.70711 + 0.292893i −0.0895999 + 0.0153729i
\(364\) 7.31371i 0.383342i
\(365\) 0 0
\(366\) −3.51472 2.48528i −0.183717 0.129908i
\(367\) 7.75736 7.75736i 0.404931 0.404931i −0.475036 0.879967i \(-0.657565\pi\)
0.879967 + 0.475036i \(0.157565\pi\)
\(368\) 2.48528 2.48528i 0.129554 0.129554i
\(369\) 4.82843 + 13.6569i 0.251358 + 0.710947i
\(370\) 0 0
\(371\) 9.94113i 0.516118i
\(372\) −2.14214 12.4853i −0.111065 0.647332i
\(373\) −15.8995 15.8995i −0.823245 0.823245i 0.163327 0.986572i \(-0.447777\pi\)
−0.986572 + 0.163327i \(0.947777\pi\)
\(374\) −1.17157 −0.0605806
\(375\) 0 0
\(376\) −10.8284 −0.558433
\(377\) −30.1421 30.1421i −1.55240 1.55240i
\(378\) 1.55635 0.870058i 0.0800500 0.0447509i
\(379\) 18.6274i 0.956826i 0.878135 + 0.478413i \(0.158788\pi\)
−0.878135 + 0.478413i \(0.841212\pi\)
\(380\) 0 0
\(381\) −14.4853 + 20.4853i −0.742103 + 1.04949i
\(382\) 3.31371 3.31371i 0.169544 0.169544i
\(383\) −9.31371 + 9.31371i −0.475908 + 0.475908i −0.903820 0.427912i \(-0.859249\pi\)
0.427912 + 0.903820i \(0.359249\pi\)
\(384\) −10.5563 + 14.9289i −0.538701 + 0.761839i
\(385\) 0 0
\(386\) 5.31371i 0.270461i
\(387\) 17.5563 + 8.38478i 0.892439 + 0.426222i
\(388\) 3.02944 + 3.02944i 0.153796 + 0.153796i
\(389\) 12.0000 0.608424 0.304212 0.952604i \(-0.401607\pi\)
0.304212 + 0.952604i \(0.401607\pi\)
\(390\) 0 0
\(391\) 3.31371 0.167581
\(392\) 7.07969 + 7.07969i 0.357578 + 0.357578i
\(393\) 5.17157 + 30.1421i 0.260871 + 1.52047i
\(394\) 8.48528i 0.427482i
\(395\) 0 0
\(396\) −5.17157 + 1.82843i −0.259881 + 0.0918819i
\(397\) 22.8284 22.8284i 1.14573 1.14573i 0.158342 0.987384i \(-0.449385\pi\)
0.987384 0.158342i \(-0.0506147\pi\)
\(398\) 3.79899 3.79899i 0.190426 0.190426i
\(399\) −0.970563 0.686292i −0.0485889 0.0343575i
\(400\) 0 0
\(401\) 20.2843i 1.01295i −0.862255 0.506474i \(-0.830949\pi\)
0.862255 0.506474i \(-0.169051\pi\)
\(402\) −2.58579 + 0.443651i −0.128967 + 0.0221273i
\(403\) 13.6569 + 13.6569i 0.680296 + 0.680296i
\(404\) 1.51472 0.0753601
\(405\) 0 0
\(406\) −3.02944 −0.150348
\(407\) −5.65685 5.65685i −0.280400 0.280400i
\(408\) −7.65685 + 1.31371i −0.379071 + 0.0650383i
\(409\) 16.3431i 0.808117i −0.914733 0.404058i \(-0.867599\pi\)
0.914733 0.404058i \(-0.132401\pi\)
\(410\) 0 0
\(411\) 3.31371 + 2.34315i 0.163453 + 0.115579i
\(412\) 7.75736 7.75736i 0.382178 0.382178i
\(413\) −1.37258 + 1.37258i −0.0675404 + 0.0675404i
\(414\) −1.37258 + 0.485281i −0.0674588 + 0.0238503i
\(415\) 0 0
\(416\) 21.3137i 1.04499i
\(417\) −4.92893 28.7279i −0.241371 1.40681i
\(418\) −0.242641 0.242641i −0.0118679 0.0118679i
\(419\) 35.3137 1.72519 0.862594 0.505897i \(-0.168838\pi\)
0.862594 + 0.505897i \(0.168838\pi\)
\(420\) 0 0
\(421\) 13.3137 0.648870 0.324435 0.945908i \(-0.394826\pi\)
0.324435 + 0.945908i \(0.394826\pi\)
\(422\) −3.07107 3.07107i −0.149497 0.149497i
\(423\) −18.4853 8.82843i −0.898785 0.429253i
\(424\) 19.0294i 0.924151i
\(425\) 0 0
\(426\) −4.00000 + 5.65685i −0.193801 + 0.274075i
\(427\) −3.51472 + 3.51472i −0.170089 + 0.170089i
\(428\) 25.4142 25.4142i 1.22844 1.22844i
\(429\) 4.82843 6.82843i 0.233119 0.329680i
\(430\) 0 0
\(431\) 5.65685i 0.272481i 0.990676 + 0.136241i \(0.0435020\pi\)
−0.990676 + 0.136241i \(0.956498\pi\)
\(432\) −13.6066 + 7.60660i −0.654648 + 0.365973i
\(433\) −7.31371 7.31371i −0.351474 0.351474i 0.509184 0.860658i \(-0.329947\pi\)
−0.860658 + 0.509184i \(0.829947\pi\)
\(434\) 1.37258 0.0658861
\(435\) 0 0
\(436\) −3.65685 −0.175132
\(437\) 0.686292 + 0.686292i 0.0328298 + 0.0328298i
\(438\) 0.786797 + 4.58579i 0.0375946 + 0.219117i
\(439\) 24.1421i 1.15224i −0.817365 0.576121i \(-0.804566\pi\)
0.817365 0.576121i \(-0.195434\pi\)
\(440\) 0 0
\(441\) 6.31371 + 17.8579i 0.300653 + 0.850374i
\(442\) 4.00000 4.00000i 0.190261 0.190261i
\(443\) 13.3137 13.3137i 0.632553 0.632553i −0.316154 0.948708i \(-0.602392\pi\)
0.948708 + 0.316154i \(0.102392\pi\)
\(444\) −20.6863 14.6274i −0.981728 0.694186i
\(445\) 0 0
\(446\) 9.51472i 0.450535i
\(447\) 30.3848 5.21320i 1.43715 0.246576i
\(448\) 2.44365 + 2.44365i 0.115452 + 0.115452i
\(449\) −14.3431 −0.676895 −0.338447 0.940985i \(-0.609902\pi\)
−0.338447 + 0.940985i \(0.609902\pi\)
\(450\) 0 0
\(451\) 4.82843 0.227362
\(452\) −15.5147 15.5147i −0.729751 0.729751i
\(453\) 24.7279 4.24264i 1.16182 0.199337i
\(454\) 11.8579i 0.556517i
\(455\) 0 0
\(456\) −1.85786 1.31371i −0.0870025 0.0615200i
\(457\) 19.4142 19.4142i 0.908159 0.908159i −0.0879650 0.996124i \(-0.528036\pi\)
0.996124 + 0.0879650i \(0.0280364\pi\)
\(458\) −5.27208 + 5.27208i −0.246348 + 0.246348i
\(459\) −14.1421 4.00000i −0.660098 0.186704i
\(460\) 0 0
\(461\) 23.1716i 1.07921i −0.841919 0.539604i \(-0.818574\pi\)
0.841919 0.539604i \(-0.181426\pi\)
\(462\) −0.100505 0.585786i −0.00467592 0.0272533i
\(463\) −22.3848 22.3848i −1.04031 1.04031i −0.999153 0.0411560i \(-0.986896\pi\)
−0.0411560 0.999153i \(-0.513104\pi\)
\(464\) 26.4853 1.22955
\(465\) 0 0
\(466\) −5.85786 −0.271360
\(467\) −12.8284 12.8284i −0.593629 0.593629i 0.344981 0.938610i \(-0.387885\pi\)
−0.938610 + 0.344981i \(0.887885\pi\)
\(468\) 11.4142 23.8995i 0.527622 1.10475i
\(469\) 3.02944i 0.139886i
\(470\) 0 0
\(471\) −21.6569 + 30.6274i −0.997895 + 1.41124i
\(472\) −2.62742 + 2.62742i −0.120937 + 0.120937i
\(473\) 4.58579 4.58579i 0.210855 0.210855i
\(474\) −2.00000 + 2.82843i −0.0918630 + 0.129914i
\(475\) 0 0
\(476\) 4.28427i 0.196369i
\(477\) 15.5147 32.4853i 0.710370 1.48740i
\(478\) 0.686292 + 0.686292i 0.0313902 + 0.0313902i
\(479\) −26.3431 −1.20365 −0.601825 0.798628i \(-0.705559\pi\)
−0.601825 + 0.798628i \(0.705559\pi\)
\(480\) 0 0
\(481\) 38.6274 1.76126
\(482\) −7.89949 7.89949i −0.359812 0.359812i
\(483\) 0.284271 + 1.65685i 0.0129348 + 0.0753895i
\(484\) 1.82843i 0.0831103i
\(485\) 0 0
\(486\) 6.44365 0.414214i 0.292290 0.0187891i
\(487\) −10.5858 + 10.5858i −0.479688 + 0.479688i −0.905032 0.425344i \(-0.860153\pi\)
0.425344 + 0.905032i \(0.360153\pi\)
\(488\) −6.72792 + 6.72792i −0.304559 + 0.304559i
\(489\) −19.7990 14.0000i −0.895341 0.633102i
\(490\) 0 0
\(491\) 18.6274i 0.840644i 0.907375 + 0.420322i \(0.138083\pi\)
−0.907375 + 0.420322i \(0.861917\pi\)
\(492\) 15.0711 2.58579i 0.679456 0.116576i
\(493\) 17.6569 + 17.6569i 0.795225 + 0.795225i
\(494\) 1.65685 0.0745454
\(495\) 0 0
\(496\) −12.0000 −0.538816
\(497\) 5.65685 + 5.65685i 0.253745 + 0.253745i
\(498\) −4.24264 + 0.727922i −0.190117 + 0.0326190i
\(499\) 2.34315i 0.104894i −0.998624 0.0524468i \(-0.983298\pi\)
0.998624 0.0524468i \(-0.0167020\pi\)
\(500\) 0 0
\(501\) 16.4853 + 11.6569i 0.736508 + 0.520790i
\(502\) −0.485281 + 0.485281i −0.0216592 + 0.0216592i
\(503\) −26.3848 + 26.3848i −1.17644 + 1.17644i −0.195794 + 0.980645i \(0.562728\pi\)
−0.980645 + 0.195794i \(0.937272\pi\)
\(504\) −1.31371 3.71573i −0.0585172 0.165512i
\(505\) 0 0
\(506\) 0.485281i 0.0215734i
\(507\) 3.02082 + 17.6066i 0.134159 + 0.781937i
\(508\) 18.7279 + 18.7279i 0.830917 + 0.830917i
\(509\) 35.3137 1.56525 0.782626 0.622492i \(-0.213880\pi\)
0.782626 + 0.622492i \(0.213880\pi\)
\(510\) 0 0
\(511\) 5.37258 0.237669
\(512\) 16.0919 + 16.0919i 0.711167 + 0.711167i
\(513\) −2.10051 3.75736i −0.0927396 0.165891i
\(514\) 9.37258i 0.413407i
\(515\) 0 0
\(516\) 11.8579 16.7696i 0.522013 0.738238i
\(517\) −4.82843 + 4.82843i −0.212354 + 0.212354i
\(518\) 1.94113 1.94113i 0.0852882 0.0852882i
\(519\) −6.82843 + 9.65685i −0.299735 + 0.423889i
\(520\) 0 0
\(521\) 40.9706i 1.79495i −0.441062 0.897476i \(-0.645398\pi\)
0.441062 0.897476i \(-0.354602\pi\)
\(522\) −9.89949 4.72792i −0.433289 0.206936i
\(523\) −2.92893 2.92893i −0.128073 0.128073i 0.640165 0.768238i \(-0.278866\pi\)
−0.768238 + 0.640165i \(0.778866\pi\)
\(524\) 32.2843 1.41034
\(525\) 0 0
\(526\) 9.51472 0.414861
\(527\) −8.00000 8.00000i −0.348485 0.348485i
\(528\) 0.878680 + 5.12132i 0.0382396 + 0.222877i
\(529\) 21.6274i 0.940322i
\(530\) 0 0
\(531\) −6.62742 + 2.34315i −0.287605 + 0.101684i
\(532\) −0.887302 + 0.887302i −0.0384694 + 0.0384694i
\(533\) −16.4853 + 16.4853i −0.714057 + 0.714057i
\(534\) −8.97056 6.34315i −0.388194 0.274495i
\(535\) 0 0
\(536\) 5.79899i 0.250478i
\(537\) −32.9706 + 5.65685i −1.42278 + 0.244111i
\(538\) −4.00000 4.00000i −0.172452 0.172452i
\(539\) 6.31371 0.271951
\(540\) 0 0
\(541\) −34.9706 −1.50350 −0.751751 0.659447i \(-0.770790\pi\)
−0.751751 + 0.659447i \(0.770790\pi\)
\(542\) −2.78680 2.78680i −0.119703 0.119703i
\(543\) −10.2426 + 1.75736i −0.439554 + 0.0754155i
\(544\) 12.4853i 0.535302i
\(545\) 0 0
\(546\) 2.34315 + 1.65685i 0.100277 + 0.0709068i
\(547\) 6.72792 6.72792i 0.287665 0.287665i −0.548491 0.836156i \(-0.684798\pi\)
0.836156 + 0.548491i \(0.184798\pi\)
\(548\) 3.02944 3.02944i 0.129411 0.129411i
\(549\) −16.9706 + 6.00000i −0.724286 + 0.256074i
\(550\) 0 0
\(551\) 7.31371i 0.311574i
\(552\) 0.544156 + 3.17157i 0.0231608 + 0.134991i
\(553\) 2.82843 + 2.82843i 0.120277 + 0.120277i
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) −30.7696 −1.30492
\(557\) 19.4558 + 19.4558i 0.824371 + 0.824371i 0.986731 0.162361i \(-0.0519109\pi\)
−0.162361 + 0.986731i \(0.551911\pi\)
\(558\) 4.48528 + 2.14214i 0.189877 + 0.0906838i
\(559\) 31.3137i 1.32443i
\(560\) 0 0
\(561\) −2.82843 + 4.00000i −0.119416 + 0.168880i
\(562\) 2.38478 2.38478i 0.100596 0.100596i
\(563\) −0.242641 + 0.242641i −0.0102261 + 0.0102261i −0.712201 0.701975i \(-0.752302\pi\)
0.701975 + 0.712201i \(0.252302\pi\)
\(564\) −12.4853 + 17.6569i −0.525725 + 0.743488i
\(565\) 0 0
\(566\) 2.68629i 0.112913i
\(567\) 0.786797 7.41421i 0.0330423 0.311368i
\(568\) 10.8284 + 10.8284i 0.454351 + 0.454351i
\(569\) −12.8284 −0.537796 −0.268898 0.963169i \(-0.586659\pi\)
−0.268898 + 0.963169i \(0.586659\pi\)
\(570\) 0 0
\(571\) −21.5147 −0.900363 −0.450181 0.892937i \(-0.648641\pi\)
−0.450181 + 0.892937i \(0.648641\pi\)
\(572\) −6.24264 6.24264i −0.261018 0.261018i
\(573\) −3.31371 19.3137i −0.138432 0.806842i
\(574\) 1.65685i 0.0691558i
\(575\) 0 0
\(576\) 4.17157 + 11.7990i 0.173816 + 0.491625i
\(577\) 3.51472 3.51472i 0.146320 0.146320i −0.630152 0.776472i \(-0.717007\pi\)
0.776472 + 0.630152i \(0.217007\pi\)
\(578\) 2.63604 2.63604i 0.109645 0.109645i
\(579\) 18.1421 + 12.8284i 0.753961 + 0.533131i
\(580\) 0 0
\(581\) 4.97056i 0.206214i
\(582\) −1.65685 + 0.284271i −0.0686788 + 0.0117834i
\(583\) −8.48528 8.48528i −0.351424 0.351424i
\(584\) 10.2843 0.425566
\(585\) 0 0
\(586\) −1.45584 −0.0601404
\(587\) 22.4853 + 22.4853i 0.928067 + 0.928067i 0.997581 0.0695141i \(-0.0221449\pi\)
−0.0695141 + 0.997581i \(0.522145\pi\)
\(588\) 19.7071 3.38120i 0.812707 0.139439i
\(589\) 3.31371i 0.136539i
\(590\) 0 0
\(591\) −28.9706 20.4853i −1.19169 0.842652i
\(592\) −16.9706 + 16.9706i −0.697486 + 0.697486i
\(593\) 19.6569 19.6569i 0.807210 0.807210i −0.177001 0.984211i \(-0.556639\pi\)
0.984211 + 0.177001i \(0.0566394\pi\)
\(594\) 0.585786 2.07107i 0.0240351 0.0849769i
\(595\) 0 0
\(596\) 32.5442i 1.33306i
\(597\) −3.79899 22.1421i −0.155482 0.906217i
\(598\) −1.65685 1.65685i −0.0677538 0.0677538i
\(599\) 23.3137 0.952572 0.476286 0.879290i \(-0.341983\pi\)
0.476286 + 0.879290i \(0.341983\pi\)
\(600\) 0 0
\(601\) 22.9706 0.936989 0.468494 0.883466i \(-0.344797\pi\)
0.468494 + 0.883466i \(0.344797\pi\)
\(602\) 1.57359 + 1.57359i 0.0641349 + 0.0641349i
\(603\) −4.72792 + 9.89949i −0.192536 + 0.403139i
\(604\) 26.4853i 1.07767i
\(605\) 0 0
\(606\) −0.343146 + 0.485281i −0.0139393 + 0.0197132i
\(607\) −8.10051 + 8.10051i −0.328789 + 0.328789i −0.852126 0.523337i \(-0.824687\pi\)
0.523337 + 0.852126i \(0.324687\pi\)
\(608\) −2.58579 + 2.58579i −0.104867 + 0.104867i
\(609\) −7.31371 + 10.3431i −0.296366 + 0.419125i
\(610\) 0 0
\(611\) 32.9706i 1.33385i
\(612\) −6.68629 + 14.0000i −0.270277 + 0.565916i
\(613\) 18.0416 + 18.0416i 0.728695 + 0.728695i 0.970360 0.241665i \(-0.0776935\pi\)
−0.241665 + 0.970360i \(0.577694\pi\)
\(614\) −10.9706 −0.442736
\(615\) 0 0
\(616\) −1.31371 −0.0529308
\(617\) 7.51472 + 7.51472i 0.302531 + 0.302531i 0.842003 0.539472i \(-0.181376\pi\)
−0.539472 + 0.842003i \(0.681376\pi\)
\(618\) 0.727922 + 4.24264i 0.0292813 + 0.170664i
\(619\) 4.97056i 0.199784i 0.994998 + 0.0998919i \(0.0318497\pi\)
−0.994998 + 0.0998919i \(0.968150\pi\)
\(620\) 0 0
\(621\) −1.65685 + 5.85786i −0.0664873 + 0.235068i
\(622\) 3.02944 3.02944i 0.121469 0.121469i
\(623\) −8.97056 + 8.97056i −0.359398 + 0.359398i
\(624\) −20.4853 14.4853i −0.820068 0.579875i
\(625\) 0 0
\(626\) 11.0294i 0.440825i
\(627\) −1.41421 + 0.242641i −0.0564782 + 0.00969014i
\(628\) 28.0000 + 28.0000i 1.11732 + 1.11732i
\(629\) −22.6274 −0.902214
\(630\) 0 0
\(631\) 1.65685 0.0659583 0.0329792 0.999456i \(-0.489501\pi\)
0.0329792 + 0.999456i \(0.489501\pi\)
\(632\) 5.41421 + 5.41421i 0.215366 + 0.215366i
\(633\) −17.8995 + 3.07107i −0.711441 + 0.122064i
\(634\) 10.6274i 0.422069i
\(635\) 0 0
\(636\) −31.0294 21.9411i −1.23040 0.870022i
\(637\) −21.5563 + 21.5563i −0.854094 + 0.854094i
\(638\) −2.58579 + 2.58579i −0.102372 + 0.102372i
\(639\) 9.65685 + 27.3137i 0.382019 + 1.08051i
\(640\) 0 0
\(641\) 6.34315i 0.250539i 0.992123 + 0.125270i \(0.0399796\pi\)
−0.992123 + 0.125270i \(0.960020\pi\)
\(642\) 2.38478 + 13.8995i 0.0941196 + 0.548569i
\(643\) 1.41421 + 1.41421i 0.0557711 + 0.0557711i 0.734442 0.678671i \(-0.237444\pi\)
−0.678671 + 0.734442i \(0.737444\pi\)
\(644\) 1.77460 0.0699292
\(645\) 0 0
\(646\) −0.970563 −0.0381863
\(647\) −6.00000 6.00000i −0.235884 0.235884i 0.579259 0.815143i \(-0.303342\pi\)
−0.815143 + 0.579259i \(0.803342\pi\)
\(648\) 1.50610 14.1924i 0.0591651 0.557530i
\(649\) 2.34315i 0.0919765i
\(650\) 0 0
\(651\) 3.31371 4.68629i 0.129874 0.183670i
\(652\) −18.1005 + 18.1005i −0.708870 + 0.708870i
\(653\) −4.00000 + 4.00000i −0.156532 + 0.156532i −0.781028 0.624496i \(-0.785304\pi\)
0.624496 + 0.781028i \(0.285304\pi\)
\(654\) 0.828427 1.17157i 0.0323941 0.0458121i
\(655\) 0 0
\(656\) 14.4853i 0.565555i
\(657\) 17.5563 + 8.38478i 0.684938 + 0.327121i
\(658\) −1.65685 1.65685i −0.0645909 0.0645909i
\(659\) −30.3431 −1.18200 −0.591001 0.806671i \(-0.701267\pi\)
−0.591001 + 0.806671i \(0.701267\pi\)
\(660\) 0 0
\(661\) −44.6274 −1.73581 −0.867903 0.496734i \(-0.834532\pi\)
−0.867903 + 0.496734i \(0.834532\pi\)
\(662\) 0.485281 + 0.485281i 0.0188610 + 0.0188610i
\(663\) −4.00000 23.3137i −0.155347 0.905429i
\(664\) 9.51472i 0.369243i
\(665\) 0 0
\(666\) 9.37258 3.31371i 0.363180 0.128404i
\(667\) 7.31371 7.31371i 0.283188 0.283188i
\(668\) 15.0711 15.0711i 0.583117 0.583117i
\(669\) −32.4853 22.9706i −1.25595 0.888093i
\(670\) 0 0
\(671\) 6.00000i 0.231627i
\(672\) −6.24264 + 1.07107i −0.240815 + 0.0413173i
\(673\) −30.7279 30.7279i −1.18447 1.18447i −0.978573 0.205902i \(-0.933987\pi\)
−0.205902 0.978573i \(-0.566013\pi\)
\(674\) 9.31371 0.358751
\(675\) 0 0
\(676\) 18.8579 0.725302
\(677\) −14.4853 14.4853i −0.556715 0.556715i 0.371656 0.928371i \(-0.378790\pi\)
−0.928371 + 0.371656i \(0.878790\pi\)
\(678\) 8.48528 1.45584i 0.325875 0.0559114i
\(679\) 1.94113i 0.0744936i
\(680\) 0 0
\(681\) 40.4853 + 28.6274i 1.55140 + 1.09701i
\(682\) 1.17157 1.17157i 0.0448618 0.0448618i
\(683\) 10.4853 10.4853i 0.401208 0.401208i −0.477451 0.878659i \(-0.658439\pi\)
0.878659 + 0.477451i \(0.158439\pi\)
\(684\) −4.28427 + 1.51472i −0.163813 + 0.0579167i
\(685\) 0 0
\(686\) 4.56854i 0.174428i
\(687\) 5.27208 + 30.7279i 0.201142 + 1.17234i
\(688\) −13.7574 13.7574i −0.524494 0.524494i
\(689\) 57.9411 2.20738
\(690\) 0 0
\(691\) 29.9411 1.13901 0.569507 0.821986i \(-0.307134\pi\)
0.569507 + 0.821986i \(0.307134\pi\)
\(692\) 8.82843 + 8.82843i 0.335606 + 0.335606i
\(693\) −2.24264 1.07107i −0.0851909 0.0406865i
\(694\) 4.54416i 0.172494i
\(695\) 0 0
\(696\) −14.0000 + 19.7990i −0.530669 + 0.750479i
\(697\) 9.65685 9.65685i 0.365779 0.365779i
\(698\) 3.21320 3.21320i 0.121622 0.121622i
\(699\) −14.1421 + 20.0000i −0.534905 + 0.756469i
\(700\) 0 0
\(701\) 33.5147i 1.26583i −0.774220 0.632917i \(-0.781858\pi\)
0.774220 0.632917i \(-0.218142\pi\)
\(702\) 5.07107 + 9.07107i 0.191395 + 0.342365i
\(703\) −4.68629 4.68629i −0.176747 0.176747i
\(704\) 4.17157 0.157222
\(705\) 0 0
\(706\) 7.31371 0.275255
\(707\) 0.485281 + 0.485281i 0.0182509 + 0.0182509i
\(708\) 1.25483 + 7.31371i 0.0471595 + 0.274866i
\(709\) 10.0000i 0.375558i −0.982211 0.187779i \(-0.939871\pi\)
0.982211 0.187779i \(-0.0601289\pi\)
\(710\) 0 0
\(711\) 4.82843 + 13.6569i 0.181080 + 0.512172i
\(712\) −17.1716 + 17.1716i −0.643532 + 0.643532i
\(713\) −3.31371 + 3.31371i −0.124099 + 0.124099i
\(714\) −1.37258 0.970563i −0.0513676 0.0363224i
\(715\) 0 0
\(716\) 35.3137i 1.31974i
\(717\) 4.00000 0.686292i 0.149383 0.0256300i
\(718\) −4.97056 4.97056i −0.185500 0.185500i
\(719\) −4.68629 −0.174769 −0.0873846 0.996175i \(-0.527851\pi\)
−0.0873846 + 0.996175i \(0.527851\pi\)
\(720\) 0 0
\(721\) 4.97056 0.185113
\(722\) 5.36396 + 5.36396i 0.199626 + 0.199626i
\(723\) −46.0416 + 7.89949i −1.71231 + 0.293785i
\(724\) 10.9706i 0.407718i
\(725\) 0 0
\(726\) −0.585786 0.414214i −0.0217406 0.0153729i
\(727\) −9.89949 + 9.89949i −0.367152 + 0.367152i −0.866437 0.499286i \(-0.833596\pi\)
0.499286 + 0.866437i \(0.333596\pi\)
\(728\) 4.48528 4.48528i 0.166236 0.166236i
\(729\) 14.1421 23.0000i 0.523783 0.851852i
\(730\) 0 0
\(731\) 18.3431i 0.678446i
\(732\) 3.21320 + 18.7279i 0.118763 + 0.692204i
\(733\) −7.89949 7.89949i −0.291775 0.291775i 0.546006 0.837781i \(-0.316147\pi\)
−0.837781 + 0.546006i \(0.816147\pi\)
\(734\) 4.54416 0.167728
\(735\) 0 0
\(736\) 5.17157 0.190627
\(737\) 2.58579 + 2.58579i 0.0952487 + 0.0952487i
\(738\) −2.58579 + 5.41421i −0.0951841 + 0.199300i
\(739\) 5.51472i 0.202862i 0.994843 + 0.101431i \(0.0323421\pi\)
−0.994843 + 0.101431i \(0.967658\pi\)
\(740\) 0 0
\(741\) 4.00000 5.65685i 0.146944 0.207810i
\(742\) 2.91169 2.91169i 0.106891 0.106891i
\(743\) −16.7279 + 16.7279i −0.613688 + 0.613688i −0.943905 0.330217i \(-0.892878\pi\)
0.330217 + 0.943905i \(0.392878\pi\)
\(744\) 6.34315 8.97056i 0.232551 0.328877i
\(745\) 0 0
\(746\) 9.31371i 0.340999i
\(747\) −7.75736 + 16.2426i −0.283827 + 0.594287i
\(748\) 3.65685 + 3.65685i 0.133708 + 0.133708i
\(749\) 16.2843 0.595014
\(750\) 0 0
\(751\) −32.2843 −1.17807 −0.589035 0.808108i \(-0.700492\pi\)
−0.589035 + 0.808108i \(0.700492\pi\)
\(752\) 14.4853 + 14.4853i 0.528224 + 0.528224i
\(753\) 0.485281 + 2.82843i 0.0176846 + 0.103074i
\(754\) 17.6569i 0.643025i
\(755\) 0 0
\(756\) −7.57359 2.14214i −0.275449 0.0779087i
\(757\) 0.686292 0.686292i 0.0249437 0.0249437i −0.694525 0.719469i \(-0.744385\pi\)
0.719469 + 0.694525i \(0.244385\pi\)
\(758\) −5.45584 + 5.45584i −0.198165 + 0.198165i
\(759\) 1.65685 + 1.17157i 0.0601400 + 0.0425254i
\(760\) 0 0
\(761\) 13.7990i 0.500213i 0.968218 + 0.250106i \(0.0804656\pi\)
−0.968218 + 0.250106i \(0.919534\pi\)
\(762\) −10.2426 + 1.75736i −0.371052 + 0.0636624i
\(763\) −1.17157 1.17157i −0.0424138 0.0424138i
\(764\) −20.6863 −0.748404
\(765\) 0 0
\(766\) −5.45584 −0.197128
\(767\) −8.00000 8.00000i −0.288863 0.288863i
\(768\) 6.77817 1.16295i 0.244586 0.0419644i
\(769\) 1.31371i 0.0473735i −0.999719 0.0236868i \(-0.992460\pi\)
0.999719 0.0236868i \(-0.00754044\pi\)
\(770\) 0 0
\(771\) 32.0000 + 22.6274i 1.15245 + 0.814907i
\(772\) 16.5858 16.5858i 0.596936 0.596936i
\(773\) −4.97056 + 4.97056i −0.178779 + 0.178779i −0.790823 0.612045i \(-0.790347\pi\)
0.612045 + 0.790823i \(0.290347\pi\)
\(774\) 2.68629 + 7.59798i 0.0965568 + 0.273104i
\(775\) 0 0
\(776\) 3.71573i 0.133387i
\(777\) −1.94113 11.3137i −0.0696375 0.405877i
\(778\) 3.51472 + 3.51472i 0.126009 + 0.126009i
\(779\) 4.00000 0.143315
\(780\) 0 0
\(781\) 9.65685 0.345549
\(782\) 0.970563 + 0.970563i 0.0347073 + 0.0347073i
\(783\) −40.0416 + 22.3848i −1.43097 +