Properties

Label 1110.2.u.e.401.7
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
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: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.7
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.e.191.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.544013 + 1.64440i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.54744 - 0.778090i) q^{6} -1.56844 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.40810 + 1.78915i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.544013 + 1.64440i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.54744 - 0.778090i) q^{6} -1.56844 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.40810 + 1.78915i) q^{9} +1.00000 q^{10} +1.64384 q^{11} +(1.64440 - 0.544013i) q^{12} +(-0.629176 + 0.629176i) q^{13} +(1.10905 - 1.10905i) q^{14} +(0.778090 - 1.54744i) q^{15} -1.00000 q^{16} +(4.46856 + 4.46856i) q^{17} +(0.437662 - 2.96790i) q^{18} +(-4.49720 + 4.49720i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(-0.853250 - 2.57914i) q^{21} +(-1.16237 + 1.16237i) q^{22} +(-1.08064 - 1.08064i) q^{23} +(-0.778090 + 1.54744i) q^{24} +1.00000i q^{25} -0.889790i q^{26} +(-4.25212 - 2.98655i) q^{27} +1.56844i q^{28} +(0.289296 - 0.289296i) q^{29} +(0.544013 + 1.64440i) q^{30} +(-5.62866 - 5.62866i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.894273 + 2.70314i) q^{33} -6.31950 q^{34} +(1.10905 + 1.10905i) q^{35} +(1.78915 + 2.40810i) q^{36} +(-5.36910 - 2.85880i) q^{37} -6.36001i q^{38} +(-1.37690 - 0.692337i) q^{39} -1.00000i q^{40} -10.6225 q^{41} +(2.42706 + 1.22039i) q^{42} +(-0.834374 + 0.834374i) q^{43} -1.64384i q^{44} +(2.96790 + 0.437662i) q^{45} +1.52825 q^{46} -13.1074i q^{47} +(-0.544013 - 1.64440i) q^{48} -4.54001 q^{49} +(-0.707107 - 0.707107i) q^{50} +(-4.91714 + 9.77905i) q^{51} +(0.629176 + 0.629176i) q^{52} +4.14299i q^{53} +(5.11851 - 0.894888i) q^{54} +(-1.16237 - 1.16237i) q^{55} +(-1.10905 - 1.10905i) q^{56} +(-9.84174 - 4.94866i) q^{57} +0.409126i q^{58} +(8.55319 + 8.55319i) q^{59} +(-1.54744 - 0.778090i) q^{60} +(-9.70779 - 9.70779i) q^{61} +7.96013 q^{62} +(3.77695 - 2.80617i) q^{63} +1.00000i q^{64} +0.889790 q^{65} +(-2.54375 - 1.27906i) q^{66} +4.75260i q^{67} +(4.46856 - 4.46856i) q^{68} +(1.18912 - 2.36488i) q^{69} -1.56844 q^{70} +3.82480i q^{71} +(-2.96790 - 0.437662i) q^{72} +12.7222i q^{73} +(5.81801 - 1.77505i) q^{74} +(-1.64440 + 0.544013i) q^{75} +(4.49720 + 4.49720i) q^{76} -2.57826 q^{77} +(1.46317 - 0.484058i) q^{78} +(-0.689395 + 0.689395i) q^{79} +(0.707107 + 0.707107i) q^{80} +(2.59788 - 8.61690i) q^{81} +(7.51125 - 7.51125i) q^{82} +2.00378i q^{83} +(-2.57914 + 0.853250i) q^{84} -6.31950i q^{85} -1.17998i q^{86} +(0.633098 + 0.318337i) q^{87} +(1.16237 + 1.16237i) q^{88} +(-7.48295 + 7.48295i) q^{89} +(-2.40810 + 1.78915i) q^{90} +(0.986823 - 0.986823i) q^{91} +(-1.08064 + 1.08064i) q^{92} +(6.19370 - 12.3178i) q^{93} +(9.26833 + 9.26833i) q^{94} +6.36001 q^{95} +(1.54744 + 0.778090i) q^{96} +(3.88735 - 3.88735i) q^{97} +(3.21027 - 3.21027i) q^{98} +(-3.95854 + 2.94108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q - 24q^{7} - 8q^{9} + 40q^{10} - 8q^{12} - 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 24q^{31} + 24q^{33} - 8q^{34} + 16q^{39} - 20q^{42} - 32q^{43} - 8q^{45} + 72q^{46} + 96q^{49} + 20q^{51} + 16q^{52} + 24q^{54} - 16q^{57} + 40q^{61} - 24q^{63} - 44q^{66} - 24q^{70} + 8q^{72} + 8q^{75} - 16q^{76} + 48q^{79} + 24q^{81} - 56q^{82} - 8q^{84} + 12q^{87} - 8q^{90} - 64q^{91} + 12q^{93} + 24q^{94} + 8q^{97} + O(q^{100}) \)

Character values

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

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

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
\(3\) 0.544013 + 1.64440i 0.314086 + 0.949394i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) −1.54744 0.778090i −0.631740 0.317654i
\(7\) −1.56844 −0.592813 −0.296407 0.955062i \(-0.595788\pi\)
−0.296407 + 0.955062i \(0.595788\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.40810 + 1.78915i −0.802700 + 0.596384i
\(10\) 1.00000 0.316228
\(11\) 1.64384 0.495638 0.247819 0.968806i \(-0.420286\pi\)
0.247819 + 0.968806i \(0.420286\pi\)
\(12\) 1.64440 0.544013i 0.474697 0.157043i
\(13\) −0.629176 + 0.629176i −0.174502 + 0.174502i −0.788954 0.614452i \(-0.789377\pi\)
0.614452 + 0.788954i \(0.289377\pi\)
\(14\) 1.10905 1.10905i 0.296407 0.296407i
\(15\) 0.778090 1.54744i 0.200902 0.399548i
\(16\) −1.00000 −0.250000
\(17\) 4.46856 + 4.46856i 1.08378 + 1.08378i 0.996153 + 0.0876320i \(0.0279300\pi\)
0.0876320 + 0.996153i \(0.472070\pi\)
\(18\) 0.437662 2.96790i 0.103158 0.699542i
\(19\) −4.49720 + 4.49720i −1.03173 + 1.03173i −0.0322497 + 0.999480i \(0.510267\pi\)
−0.999480 + 0.0322497i \(0.989733\pi\)
\(20\) −0.707107 + 0.707107i −0.158114 + 0.158114i
\(21\) −0.853250 2.57914i −0.186195 0.562814i
\(22\) −1.16237 + 1.16237i −0.247819 + 0.247819i
\(23\) −1.08064 1.08064i −0.225328 0.225328i 0.585410 0.810738i \(-0.300934\pi\)
−0.810738 + 0.585410i \(0.800934\pi\)
\(24\) −0.778090 + 1.54744i −0.158827 + 0.315870i
\(25\) 1.00000i 0.200000i
\(26\) 0.889790i 0.174502i
\(27\) −4.25212 2.98655i −0.818320 0.574763i
\(28\) 1.56844i 0.296407i
\(29\) 0.289296 0.289296i 0.0537209 0.0537209i −0.679736 0.733457i \(-0.737906\pi\)
0.733457 + 0.679736i \(0.237906\pi\)
\(30\) 0.544013 + 1.64440i 0.0993228 + 0.300225i
\(31\) −5.62866 5.62866i −1.01094 1.01094i −0.999940 0.0109977i \(-0.996499\pi\)
−0.0109977 0.999940i \(-0.503501\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0.894273 + 2.70314i 0.155673 + 0.470556i
\(34\) −6.31950 −1.08378
\(35\) 1.10905 + 1.10905i 0.187464 + 0.187464i
\(36\) 1.78915 + 2.40810i 0.298192 + 0.401350i
\(37\) −5.36910 2.85880i −0.882675 0.469983i
\(38\) 6.36001i 1.03173i
\(39\) −1.37690 0.692337i −0.220480 0.110863i
\(40\) 1.00000i 0.158114i
\(41\) −10.6225 −1.65896 −0.829479 0.558537i \(-0.811363\pi\)
−0.829479 + 0.558537i \(0.811363\pi\)
\(42\) 2.42706 + 1.22039i 0.374504 + 0.188310i
\(43\) −0.834374 + 0.834374i −0.127241 + 0.127241i −0.767859 0.640618i \(-0.778678\pi\)
0.640618 + 0.767859i \(0.278678\pi\)
\(44\) 1.64384i 0.247819i
\(45\) 2.96790 + 0.437662i 0.442429 + 0.0652429i
\(46\) 1.52825 0.225328
\(47\) 13.1074i 1.91191i −0.293511 0.955956i \(-0.594824\pi\)
0.293511 0.955956i \(-0.405176\pi\)
\(48\) −0.544013 1.64440i −0.0785216 0.237349i
\(49\) −4.54001 −0.648572
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) −4.91714 + 9.77905i −0.688537 + 1.36934i
\(52\) 0.629176 + 0.629176i 0.0872511 + 0.0872511i
\(53\) 4.14299i 0.569084i 0.958664 + 0.284542i \(0.0918415\pi\)
−0.958664 + 0.284542i \(0.908159\pi\)
\(54\) 5.11851 0.894888i 0.696541 0.121779i
\(55\) −1.16237 1.16237i −0.156734 0.156734i
\(56\) −1.10905 1.10905i −0.148203 0.148203i
\(57\) −9.84174 4.94866i −1.30357 0.655466i
\(58\) 0.409126i 0.0537209i
\(59\) 8.55319 + 8.55319i 1.11353 + 1.11353i 0.992669 + 0.120861i \(0.0385655\pi\)
0.120861 + 0.992669i \(0.461435\pi\)
\(60\) −1.54744 0.778090i −0.199774 0.100451i
\(61\) −9.70779 9.70779i −1.24296 1.24296i −0.958769 0.284186i \(-0.908277\pi\)
−0.284186 0.958769i \(-0.591723\pi\)
\(62\) 7.96013 1.01094
\(63\) 3.77695 2.80617i 0.475851 0.353544i
\(64\) 1.00000i 0.125000i
\(65\) 0.889790 0.110365
\(66\) −2.54375 1.27906i −0.313114 0.157441i
\(67\) 4.75260i 0.580622i 0.956932 + 0.290311i \(0.0937588\pi\)
−0.956932 + 0.290311i \(0.906241\pi\)
\(68\) 4.46856 4.46856i 0.541892 0.541892i
\(69\) 1.18912 2.36488i 0.143153 0.284698i
\(70\) −1.56844 −0.187464
\(71\) 3.82480i 0.453920i 0.973904 + 0.226960i \(0.0728786\pi\)
−0.973904 + 0.226960i \(0.927121\pi\)
\(72\) −2.96790 0.437662i −0.349771 0.0515790i
\(73\) 12.7222i 1.48902i 0.667611 + 0.744510i \(0.267317\pi\)
−0.667611 + 0.744510i \(0.732683\pi\)
\(74\) 5.81801 1.77505i 0.676329 0.206346i
\(75\) −1.64440 + 0.544013i −0.189879 + 0.0628173i
\(76\) 4.49720 + 4.49720i 0.515865 + 0.515865i
\(77\) −2.57826 −0.293821
\(78\) 1.46317 0.484058i 0.165671 0.0548087i
\(79\) −0.689395 + 0.689395i −0.0775630 + 0.0775630i −0.744824 0.667261i \(-0.767467\pi\)
0.667261 + 0.744824i \(0.267467\pi\)
\(80\) 0.707107 + 0.707107i 0.0790569 + 0.0790569i
\(81\) 2.59788 8.61690i 0.288653 0.957434i
\(82\) 7.51125 7.51125i 0.829479 0.829479i
\(83\) 2.00378i 0.219943i 0.993935 + 0.109972i \(0.0350760\pi\)
−0.993935 + 0.109972i \(0.964924\pi\)
\(84\) −2.57914 + 0.853250i −0.281407 + 0.0930973i
\(85\) 6.31950i 0.685446i
\(86\) 1.17998i 0.127241i
\(87\) 0.633098 + 0.318337i 0.0678753 + 0.0341293i
\(88\) 1.16237 + 1.16237i 0.123909 + 0.123909i
\(89\) −7.48295 + 7.48295i −0.793191 + 0.793191i −0.982012 0.188820i \(-0.939534\pi\)
0.188820 + 0.982012i \(0.439534\pi\)
\(90\) −2.40810 + 1.78915i −0.253836 + 0.188593i
\(91\) 0.986823 0.986823i 0.103447 0.103447i
\(92\) −1.08064 + 1.08064i −0.112664 + 0.112664i
\(93\) 6.19370 12.3178i 0.642257 1.27730i
\(94\) 9.26833 + 9.26833i 0.955956 + 0.955956i
\(95\) 6.36001 0.652523
\(96\) 1.54744 + 0.778090i 0.157935 + 0.0794135i
\(97\) 3.88735 3.88735i 0.394701 0.394701i −0.481658 0.876359i \(-0.659965\pi\)
0.876359 + 0.481658i \(0.159965\pi\)
\(98\) 3.21027 3.21027i 0.324286 0.324286i
\(99\) −3.95854 + 2.94108i −0.397848 + 0.295590i
\(100\) 1.00000 0.100000
\(101\) −4.85174 −0.482767 −0.241383 0.970430i \(-0.577601\pi\)
−0.241383 + 0.970430i \(0.577601\pi\)
\(102\) −3.43789 10.3918i −0.340402 1.02894i
\(103\) 7.40422 + 7.40422i 0.729559 + 0.729559i 0.970532 0.240973i \(-0.0774664\pi\)
−0.240973 + 0.970532i \(0.577466\pi\)
\(104\) −0.889790 −0.0872511
\(105\) −1.22039 + 2.42706i −0.119097 + 0.236857i
\(106\) −2.92954 2.92954i −0.284542 0.284542i
\(107\) 10.1894i 0.985049i −0.870299 0.492524i \(-0.836074\pi\)
0.870299 0.492524i \(-0.163926\pi\)
\(108\) −2.98655 + 4.25212i −0.287381 + 0.409160i
\(109\) −9.85790 + 9.85790i −0.944216 + 0.944216i −0.998524 0.0543083i \(-0.982705\pi\)
0.0543083 + 0.998524i \(0.482705\pi\)
\(110\) 1.64384 0.156734
\(111\) 1.78014 10.3842i 0.168964 0.985622i
\(112\) 1.56844 0.148203
\(113\) 13.0116 13.0116i 1.22403 1.22403i 0.257839 0.966188i \(-0.416990\pi\)
0.966188 0.257839i \(-0.0830104\pi\)
\(114\) 10.4584 3.45993i 0.979518 0.324052i
\(115\) 1.52825i 0.142510i
\(116\) −0.289296 0.289296i −0.0268604 0.0268604i
\(117\) 0.389427 2.64081i 0.0360026 0.244143i
\(118\) −12.0960 −1.11353
\(119\) −7.00865 7.00865i −0.642482 0.642482i
\(120\) 1.64440 0.544013i 0.150112 0.0496614i
\(121\) −8.29778 −0.754343
\(122\) 13.7289 1.24296
\(123\) −5.77879 17.4677i −0.521056 1.57501i
\(124\) −5.62866 + 5.62866i −0.505469 + 0.505469i
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) −0.686446 + 4.65497i −0.0611534 + 0.414697i
\(127\) 11.4287 1.01414 0.507068 0.861906i \(-0.330729\pi\)
0.507068 + 0.861906i \(0.330729\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −1.82596 0.918134i −0.160766 0.0808372i
\(130\) −0.629176 + 0.629176i −0.0551824 + 0.0551824i
\(131\) 3.48311 3.48311i 0.304320 0.304320i −0.538381 0.842702i \(-0.680964\pi\)
0.842702 + 0.538381i \(0.180964\pi\)
\(132\) 2.70314 0.894273i 0.235278 0.0778365i
\(133\) 7.05358 7.05358i 0.611623 0.611623i
\(134\) −3.36059 3.36059i −0.290311 0.290311i
\(135\) 0.894888 + 5.11851i 0.0770197 + 0.440531i
\(136\) 6.31950i 0.541892i
\(137\) 4.49515i 0.384047i 0.981390 + 0.192023i \(0.0615049\pi\)
−0.981390 + 0.192023i \(0.938495\pi\)
\(138\) 0.831388 + 2.51305i 0.0707725 + 0.213925i
\(139\) 21.9294i 1.86002i −0.367529 0.930012i \(-0.619796\pi\)
0.367529 0.930012i \(-0.380204\pi\)
\(140\) 1.10905 1.10905i 0.0937320 0.0937320i
\(141\) 21.5538 7.13060i 1.81516 0.600505i
\(142\) −2.70454 2.70454i −0.226960 0.226960i
\(143\) −1.03427 + 1.03427i −0.0864898 + 0.0864898i
\(144\) 2.40810 1.78915i 0.200675 0.149096i
\(145\) −0.409126 −0.0339761
\(146\) −8.99595 8.99595i −0.744510 0.744510i
\(147\) −2.46983 7.46559i −0.203708 0.615751i
\(148\) −2.85880 + 5.36910i −0.234992 + 0.441338i
\(149\) 22.3567i 1.83153i 0.401716 + 0.915764i \(0.368414\pi\)
−0.401716 + 0.915764i \(0.631586\pi\)
\(150\) 0.778090 1.54744i 0.0635308 0.126348i
\(151\) 22.5415i 1.83440i 0.398426 + 0.917201i \(0.369557\pi\)
−0.398426 + 0.917201i \(0.630443\pi\)
\(152\) −6.36001 −0.515865
\(153\) −18.7557 2.76581i −1.51631 0.223602i
\(154\) 1.82311 1.82311i 0.146910 0.146910i
\(155\) 7.96013i 0.639373i
\(156\) −0.692337 + 1.37690i −0.0554313 + 0.110240i
\(157\) −2.37029 −0.189170 −0.0945848 0.995517i \(-0.530152\pi\)
−0.0945848 + 0.995517i \(0.530152\pi\)
\(158\) 0.974951i 0.0775630i
\(159\) −6.81273 + 2.25384i −0.540285 + 0.178741i
\(160\) −1.00000 −0.0790569
\(161\) 1.69491 + 1.69491i 0.133577 + 0.133577i
\(162\) 4.25609 + 7.93005i 0.334390 + 0.623043i
\(163\) 8.06627 + 8.06627i 0.631799 + 0.631799i 0.948519 0.316720i \(-0.102582\pi\)
−0.316720 + 0.948519i \(0.602582\pi\)
\(164\) 10.6225i 0.829479i
\(165\) 1.27906 2.54375i 0.0995746 0.198031i
\(166\) −1.41689 1.41689i −0.109972 0.109972i
\(167\) −5.21464 5.21464i −0.403521 0.403521i 0.475951 0.879472i \(-0.342104\pi\)
−0.879472 + 0.475951i \(0.842104\pi\)
\(168\) 1.22039 2.42706i 0.0941548 0.187252i
\(169\) 12.2083i 0.939098i
\(170\) 4.46856 + 4.46856i 0.342723 + 0.342723i
\(171\) 2.78354 18.8759i 0.212862 1.44348i
\(172\) 0.834374 + 0.834374i 0.0636204 + 0.0636204i
\(173\) −18.5616 −1.41121 −0.705605 0.708606i \(-0.749324\pi\)
−0.705605 + 0.708606i \(0.749324\pi\)
\(174\) −0.672766 + 0.222570i −0.0510023 + 0.0168730i
\(175\) 1.56844i 0.118563i
\(176\) −1.64384 −0.123909
\(177\) −9.41181 + 18.7179i −0.707435 + 1.40692i
\(178\) 10.5825i 0.793191i
\(179\) 4.75163 4.75163i 0.355153 0.355153i −0.506869 0.862023i \(-0.669197\pi\)
0.862023 + 0.506869i \(0.169197\pi\)
\(180\) 0.437662 2.96790i 0.0326214 0.221214i
\(181\) 1.37431 0.102152 0.0510759 0.998695i \(-0.483735\pi\)
0.0510759 + 0.998695i \(0.483735\pi\)
\(182\) 1.39558i 0.103447i
\(183\) 10.6823 21.2447i 0.789660 1.57045i
\(184\) 1.52825i 0.112664i
\(185\) 1.77505 + 5.81801i 0.130505 + 0.427748i
\(186\) 4.33042 + 13.0896i 0.317522 + 0.959778i
\(187\) 7.34562 + 7.34562i 0.537165 + 0.537165i
\(188\) −13.1074 −0.955956
\(189\) 6.66917 + 4.68422i 0.485111 + 0.340727i
\(190\) −4.49720 + 4.49720i −0.326262 + 0.326262i
\(191\) −8.07560 8.07560i −0.584330 0.584330i 0.351760 0.936090i \(-0.385583\pi\)
−0.936090 + 0.351760i \(0.885583\pi\)
\(192\) −1.64440 + 0.544013i −0.118674 + 0.0392608i
\(193\) −10.3501 + 10.3501i −0.745016 + 0.745016i −0.973539 0.228523i \(-0.926611\pi\)
0.228523 + 0.973539i \(0.426611\pi\)
\(194\) 5.49755i 0.394701i
\(195\) 0.484058 + 1.46317i 0.0346641 + 0.104780i
\(196\) 4.54001i 0.324286i
\(197\) 9.80467i 0.698554i 0.937020 + 0.349277i \(0.113573\pi\)
−0.937020 + 0.349277i \(0.886427\pi\)
\(198\) 0.719449 4.87877i 0.0511290 0.346719i
\(199\) 5.14958 + 5.14958i 0.365044 + 0.365044i 0.865666 0.500622i \(-0.166895\pi\)
−0.500622 + 0.865666i \(0.666895\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) −7.81517 + 2.58548i −0.551240 + 0.182366i
\(202\) 3.43070 3.43070i 0.241383 0.241383i
\(203\) −0.453742 + 0.453742i −0.0318464 + 0.0318464i
\(204\) 9.77905 + 4.91714i 0.684671 + 0.344269i
\(205\) 7.51125 + 7.51125i 0.524609 + 0.524609i
\(206\) −10.4711 −0.729559
\(207\) 4.53570 + 0.668857i 0.315253 + 0.0464888i
\(208\) 0.629176 0.629176i 0.0436255 0.0436255i
\(209\) −7.39270 + 7.39270i −0.511364 + 0.511364i
\(210\) −0.853250 2.57914i −0.0588799 0.177977i
\(211\) −0.591484 −0.0407194 −0.0203597 0.999793i \(-0.506481\pi\)
−0.0203597 + 0.999793i \(0.506481\pi\)
\(212\) 4.14299 0.284542
\(213\) −6.28949 + 2.08074i −0.430949 + 0.142570i
\(214\) 7.20501 + 7.20501i 0.492524 + 0.492524i
\(215\) 1.17998 0.0804742
\(216\) −0.894888 5.11851i −0.0608894 0.348271i
\(217\) 8.82820 + 8.82820i 0.599297 + 0.599297i
\(218\) 13.9412i 0.944216i
\(219\) −20.9204 + 6.92104i −1.41367 + 0.467681i
\(220\) −1.16237 + 1.16237i −0.0783672 + 0.0783672i
\(221\) −5.62302 −0.378246
\(222\) 6.08397 + 8.60147i 0.408329 + 0.577293i
\(223\) −0.315113 −0.0211015 −0.0105508 0.999944i \(-0.503358\pi\)
−0.0105508 + 0.999944i \(0.503358\pi\)
\(224\) −1.10905 + 1.10905i −0.0741017 + 0.0741017i
\(225\) −1.78915 2.40810i −0.119277 0.160540i
\(226\) 18.4012i 1.22403i
\(227\) 9.38302 + 9.38302i 0.622773 + 0.622773i 0.946240 0.323467i \(-0.104848\pi\)
−0.323467 + 0.946240i \(0.604848\pi\)
\(228\) −4.94866 + 9.84174i −0.327733 + 0.651785i
\(229\) 25.4498 1.68177 0.840884 0.541216i \(-0.182036\pi\)
0.840884 + 0.541216i \(0.182036\pi\)
\(230\) −1.08064 1.08064i −0.0712550 0.0712550i
\(231\) −1.40261 4.23970i −0.0922850 0.278952i
\(232\) 0.409126 0.0268604
\(233\) −7.54603 −0.494357 −0.247178 0.968970i \(-0.579503\pi\)
−0.247178 + 0.968970i \(0.579503\pi\)
\(234\) 1.59197 + 2.14270i 0.104070 + 0.140073i
\(235\) −9.26833 + 9.26833i −0.604599 + 0.604599i
\(236\) 8.55319 8.55319i 0.556765 0.556765i
\(237\) −1.50868 0.758600i −0.0979993 0.0492764i
\(238\) 9.91173 0.642482
\(239\) −2.13485 2.13485i −0.138092 0.138092i 0.634682 0.772774i \(-0.281131\pi\)
−0.772774 + 0.634682i \(0.781131\pi\)
\(240\) −0.778090 + 1.54744i −0.0502255 + 0.0998869i
\(241\) 12.4422 12.4422i 0.801472 0.801472i −0.181854 0.983326i \(-0.558210\pi\)
0.983326 + 0.181854i \(0.0582097\pi\)
\(242\) 5.86741 5.86741i 0.377172 0.377172i
\(243\) 15.5829 0.415759i 0.999644 0.0266710i
\(244\) −9.70779 + 9.70779i −0.621478 + 0.621478i
\(245\) 3.21027 + 3.21027i 0.205097 + 0.205097i
\(246\) 16.4377 + 8.26528i 1.04803 + 0.526975i
\(247\) 5.65907i 0.360078i
\(248\) 7.96013i 0.505469i
\(249\) −3.29501 + 1.09008i −0.208813 + 0.0690812i
\(250\) 1.00000i 0.0632456i
\(251\) 1.93314 1.93314i 0.122019 0.122019i −0.643460 0.765479i \(-0.722502\pi\)
0.765479 + 0.643460i \(0.222502\pi\)
\(252\) −2.80617 3.77695i −0.176772 0.237925i
\(253\) −1.77640 1.77640i −0.111681 0.111681i
\(254\) −8.08133 + 8.08133i −0.507068 + 0.507068i
\(255\) 10.3918 3.43789i 0.650758 0.215289i
\(256\) 1.00000 0.0625000
\(257\) −0.00157497 0.00157497i −9.82441e−5 9.82441e-5i 0.707058 0.707156i \(-0.250022\pi\)
−0.707156 + 0.707058i \(0.750022\pi\)
\(258\) 1.94036 0.641927i 0.120802 0.0399646i
\(259\) 8.42110 + 4.48384i 0.523262 + 0.278612i
\(260\) 0.889790i 0.0551824i
\(261\) −0.179059 + 1.21425i −0.0110835 + 0.0751600i
\(262\) 4.92586i 0.304320i
\(263\) 10.5582 0.651043 0.325522 0.945535i \(-0.394460\pi\)
0.325522 + 0.945535i \(0.394460\pi\)
\(264\) −1.27906 + 2.54375i −0.0787207 + 0.156557i
\(265\) 2.92954 2.92954i 0.179960 0.179960i
\(266\) 9.97527i 0.611623i
\(267\) −16.3758 8.23413i −1.00218 0.503921i
\(268\) 4.75260 0.290311
\(269\) 9.40474i 0.573417i 0.958018 + 0.286708i \(0.0925611\pi\)
−0.958018 + 0.286708i \(0.907439\pi\)
\(270\) −4.25212 2.98655i −0.258776 0.181756i
\(271\) −6.28538 −0.381810 −0.190905 0.981609i \(-0.561142\pi\)
−0.190905 + 0.981609i \(0.561142\pi\)
\(272\) −4.46856 4.46856i −0.270946 0.270946i
\(273\) 2.15958 + 1.08589i 0.130703 + 0.0657208i
\(274\) −3.17855 3.17855i −0.192023 0.192023i
\(275\) 1.64384i 0.0991275i
\(276\) −2.36488 1.18912i −0.142349 0.0715764i
\(277\) −17.7788 17.7788i −1.06822 1.06822i −0.997496 0.0707289i \(-0.977467\pi\)
−0.0707289 0.997496i \(-0.522533\pi\)
\(278\) 15.5064 + 15.5064i 0.930012 + 0.930012i
\(279\) 23.6249 + 3.48385i 1.41439 + 0.208573i
\(280\) 1.56844i 0.0937320i
\(281\) 15.9903 + 15.9903i 0.953902 + 0.953902i 0.998983 0.0450817i \(-0.0143548\pi\)
−0.0450817 + 0.998983i \(0.514355\pi\)
\(282\) −10.1987 + 20.2829i −0.607326 + 1.20783i
\(283\) 5.52382 + 5.52382i 0.328357 + 0.328357i 0.851962 0.523604i \(-0.175413\pi\)
−0.523604 + 0.851962i \(0.675413\pi\)
\(284\) 3.82480 0.226960
\(285\) 3.45993 + 10.4584i 0.204949 + 0.619502i
\(286\) 1.46268i 0.0864898i
\(287\) 16.6607 0.983453
\(288\) −0.437662 + 2.96790i −0.0257895 + 0.174885i
\(289\) 22.9361i 1.34918i
\(290\) 0.289296 0.289296i 0.0169880 0.0169880i
\(291\) 8.50713 + 4.27759i 0.498697 + 0.250757i
\(292\) 12.7222 0.744510
\(293\) 13.9882i 0.817202i 0.912713 + 0.408601i \(0.133983\pi\)
−0.912713 + 0.408601i \(0.866017\pi\)
\(294\) 7.02540 + 3.53254i 0.409729 + 0.206022i
\(295\) 12.0960i 0.704258i
\(296\) −1.77505 5.81801i −0.103173 0.338165i
\(297\) −6.98982 4.90943i −0.405590 0.284874i
\(298\) −15.8085 15.8085i −0.915764 0.915764i
\(299\) 1.35982 0.0786405
\(300\) 0.544013 + 1.64440i 0.0314086 + 0.0949394i
\(301\) 1.30866 1.30866i 0.0754301 0.0754301i
\(302\) −15.9392 15.9392i −0.917201 0.917201i
\(303\) −2.63941 7.97821i −0.151630 0.458336i
\(304\) 4.49720 4.49720i 0.257932 0.257932i
\(305\) 13.7289i 0.786114i
\(306\) 15.2180 11.3065i 0.869954 0.646352i
\(307\) 10.1886i 0.581493i 0.956800 + 0.290746i \(0.0939036\pi\)
−0.956800 + 0.290746i \(0.906096\pi\)
\(308\) 2.57826i 0.146910i
\(309\) −8.14750 + 16.2035i −0.463495 + 0.921784i
\(310\) −5.62866 5.62866i −0.319686 0.319686i
\(311\) 10.4912 10.4912i 0.594899 0.594899i −0.344052 0.938951i \(-0.611800\pi\)
0.938951 + 0.344052i \(0.111800\pi\)
\(312\) −0.484058 1.46317i −0.0274044 0.0828357i
\(313\) 24.4934 24.4934i 1.38445 1.38445i 0.547922 0.836529i \(-0.315419\pi\)
0.836529 0.547922i \(-0.184581\pi\)
\(314\) 1.67605 1.67605i 0.0945848 0.0945848i
\(315\) −4.65497 0.686446i −0.262278 0.0386768i
\(316\) 0.689395 + 0.689395i 0.0387815 + 0.0387815i
\(317\) 18.8817 1.06050 0.530250 0.847841i \(-0.322098\pi\)
0.530250 + 0.847841i \(0.322098\pi\)
\(318\) 3.22362 6.41104i 0.180772 0.359513i
\(319\) 0.475557 0.475557i 0.0266261 0.0266261i
\(320\) 0.707107 0.707107i 0.0395285 0.0395285i
\(321\) 16.7555 5.54318i 0.935200 0.309390i
\(322\) −2.39696 −0.133577
\(323\) −40.1921 −2.23635
\(324\) −8.61690 2.59788i −0.478717 0.144327i
\(325\) −0.629176 0.629176i −0.0349004 0.0349004i
\(326\) −11.4074 −0.631799
\(327\) −21.5732 10.8475i −1.19300 0.599868i
\(328\) −7.51125 7.51125i −0.414740 0.414740i
\(329\) 20.5581i 1.13341i
\(330\) 0.894273 + 2.70314i 0.0492281 + 0.148803i
\(331\) −16.7777 + 16.7777i −0.922187 + 0.922187i −0.997184 0.0749970i \(-0.976105\pi\)
0.0749970 + 0.997184i \(0.476105\pi\)
\(332\) 2.00378 0.109972
\(333\) 18.0442 2.72187i 0.988813 0.149157i
\(334\) 7.37462 0.403521
\(335\) 3.36059 3.36059i 0.183609 0.183609i
\(336\) 0.853250 + 2.57914i 0.0465486 + 0.140703i
\(337\) 18.2617i 0.994779i 0.867527 + 0.497390i \(0.165708\pi\)
−0.867527 + 0.497390i \(0.834292\pi\)
\(338\) −8.63255 8.63255i −0.469549 0.469549i
\(339\) 28.4747 + 14.3178i 1.54653 + 0.777634i
\(340\) −6.31950 −0.342723
\(341\) −9.25264 9.25264i −0.501059 0.501059i
\(342\) 11.3790 + 15.3155i 0.615307 + 0.828169i
\(343\) 18.0998 0.977296
\(344\) −1.17998 −0.0636204
\(345\) −2.51305 + 0.831388i −0.135298 + 0.0447604i
\(346\) 13.1250 13.1250i 0.705605 0.705605i
\(347\) −8.03823 + 8.03823i −0.431515 + 0.431515i −0.889144 0.457628i \(-0.848699\pi\)
0.457628 + 0.889144i \(0.348699\pi\)
\(348\) 0.318337 0.633098i 0.0170647 0.0339376i
\(349\) −8.68067 −0.464665 −0.232333 0.972636i \(-0.574636\pi\)
−0.232333 + 0.972636i \(0.574636\pi\)
\(350\) 1.10905 + 1.10905i 0.0592813 + 0.0592813i
\(351\) 4.55440 0.796262i 0.243096 0.0425013i
\(352\) 1.16237 1.16237i 0.0619547 0.0619547i
\(353\) −4.36437 + 4.36437i −0.232292 + 0.232292i −0.813649 0.581357i \(-0.802522\pi\)
0.581357 + 0.813649i \(0.302522\pi\)
\(354\) −6.58041 19.8907i −0.349745 1.05718i
\(355\) 2.70454 2.70454i 0.143542 0.143542i
\(356\) 7.48295 + 7.48295i 0.396596 + 0.396596i
\(357\) 7.71222 15.3378i 0.408174 0.811764i
\(358\) 6.71982i 0.355153i
\(359\) 20.7643i 1.09590i 0.836511 + 0.547950i \(0.184591\pi\)
−0.836511 + 0.547950i \(0.815409\pi\)
\(360\) 1.78915 + 2.40810i 0.0942965 + 0.126918i
\(361\) 21.4497i 1.12893i
\(362\) −0.971785 + 0.971785i −0.0510759 + 0.0510759i
\(363\) −4.51410 13.6449i −0.236929 0.716169i
\(364\) −0.986823 0.986823i −0.0517236 0.0517236i
\(365\) 8.99595 8.99595i 0.470870 0.470870i
\(366\) 7.46870 + 22.5758i 0.390395 + 1.18005i
\(367\) −22.0692 −1.15200 −0.576002 0.817448i \(-0.695388\pi\)
−0.576002 + 0.817448i \(0.695388\pi\)
\(368\) 1.08064 + 1.08064i 0.0563320 + 0.0563320i
\(369\) 25.5801 19.0053i 1.33165 0.989376i
\(370\) −5.36910 2.85880i −0.279126 0.148622i
\(371\) 6.49802i 0.337360i
\(372\) −12.3178 6.19370i −0.638650 0.321128i
\(373\) 12.9551i 0.670787i 0.942078 + 0.335394i \(0.108869\pi\)
−0.942078 + 0.335394i \(0.891131\pi\)
\(374\) −10.3883 −0.537165
\(375\) 1.54744 + 0.778090i 0.0799095 + 0.0401804i
\(376\) 9.26833 9.26833i 0.477978 0.477978i
\(377\) 0.364036i 0.0187488i
\(378\) −8.02806 + 1.40357i −0.412919 + 0.0721921i
\(379\) −9.36563 −0.481080 −0.240540 0.970639i \(-0.577325\pi\)
−0.240540 + 0.970639i \(0.577325\pi\)
\(380\) 6.36001i 0.326262i
\(381\) 6.21738 + 18.7934i 0.318526 + 0.962814i
\(382\) 11.4206 0.584330
\(383\) 1.18802 + 1.18802i 0.0607051 + 0.0607051i 0.736808 0.676103i \(-0.236332\pi\)
−0.676103 + 0.736808i \(0.736332\pi\)
\(384\) 0.778090 1.54744i 0.0397068 0.0789675i
\(385\) 1.82311 + 1.82311i 0.0929142 + 0.0929142i
\(386\) 14.6372i 0.745016i
\(387\) 0.516434 3.50208i 0.0262518 0.178021i
\(388\) −3.88735 3.88735i −0.197350 0.197350i
\(389\) 22.0352 + 22.0352i 1.11723 + 1.11723i 0.992146 + 0.125085i \(0.0399204\pi\)
0.125085 + 0.992146i \(0.460080\pi\)
\(390\) −1.37690 0.692337i −0.0697219 0.0350578i
\(391\) 9.65777i 0.488414i
\(392\) −3.21027 3.21027i −0.162143 0.162143i
\(393\) 7.62248 + 3.83276i 0.384503 + 0.193337i
\(394\) −6.93295 6.93295i −0.349277 0.349277i
\(395\) 0.974951 0.0490551
\(396\) 2.94108 + 3.95854i 0.147795 + 0.198924i
\(397\) 19.3715i 0.972229i 0.873895 + 0.486115i \(0.161586\pi\)
−0.873895 + 0.486115i \(0.838414\pi\)
\(398\) −7.28261 −0.365044
\(399\) 15.4361 + 7.76166i 0.772774 + 0.388569i
\(400\) 1.00000i 0.0500000i
\(401\) 15.3652 15.3652i 0.767300 0.767300i −0.210331 0.977630i \(-0.567454\pi\)
0.977630 + 0.210331i \(0.0674540\pi\)
\(402\) 3.69795 7.35437i 0.184437 0.366803i
\(403\) 7.08284 0.352821
\(404\) 4.85174i 0.241383i
\(405\) −7.93005 + 4.25609i −0.394047 + 0.211487i
\(406\) 0.641688i 0.0318464i
\(407\) −8.82597 4.69942i −0.437487 0.232942i
\(408\) −10.3918 + 3.43789i −0.514470 + 0.170201i
\(409\) −14.2762 14.2762i −0.705914 0.705914i 0.259759 0.965673i \(-0.416357\pi\)
−0.965673 + 0.259759i \(0.916357\pi\)
\(410\) −10.6225 −0.524609
\(411\) −7.39182 + 2.44542i −0.364612 + 0.120624i
\(412\) 7.40422 7.40422i 0.364780 0.364780i
\(413\) −13.4151 13.4151i −0.660115 0.660115i
\(414\) −3.68018 + 2.73427i −0.180871 + 0.134382i
\(415\) 1.41689 1.41689i 0.0695522 0.0695522i
\(416\) 0.889790i 0.0436255i
\(417\) 36.0606 11.9299i 1.76590 0.584208i
\(418\) 10.4549i 0.511364i
\(419\) 0.599281i 0.0292768i 0.999893 + 0.0146384i \(0.00465972\pi\)
−0.999893 + 0.0146384i \(0.995340\pi\)
\(420\) 2.42706 + 1.22039i 0.118429 + 0.0595487i
\(421\) 2.61990 + 2.61990i 0.127686 + 0.127686i 0.768062 0.640376i \(-0.221221\pi\)
−0.640376 + 0.768062i \(0.721221\pi\)
\(422\) 0.418242 0.418242i 0.0203597 0.0203597i
\(423\) 23.4511 + 31.5639i 1.14023 + 1.53469i
\(424\) −2.92954 + 2.92954i −0.142271 + 0.142271i
\(425\) −4.46856 + 4.46856i −0.216757 + 0.216757i
\(426\) 2.97604 5.91865i 0.144189 0.286759i
\(427\) 15.2261 + 15.2261i 0.736840 + 0.736840i
\(428\) −10.1894 −0.492524
\(429\) −2.26340 1.13809i −0.109278 0.0549477i
\(430\) −0.834374 + 0.834374i −0.0402371 + 0.0402371i
\(431\) 26.5760 26.5760i 1.28012 1.28012i 0.339523 0.940598i \(-0.389734\pi\)
0.940598 0.339523i \(-0.110266\pi\)
\(432\) 4.25212 + 2.98655i 0.204580 + 0.143691i
\(433\) −35.9427 −1.72730 −0.863649 0.504094i \(-0.831826\pi\)
−0.863649 + 0.504094i \(0.831826\pi\)
\(434\) −12.4850 −0.599297
\(435\) −0.222570 0.672766i −0.0106714 0.0322567i
\(436\) 9.85790 + 9.85790i 0.472108 + 0.472108i
\(437\) 9.71968 0.464955
\(438\) 9.89902 19.6869i 0.472993 0.940674i
\(439\) −18.6711 18.6711i −0.891124 0.891124i 0.103505 0.994629i \(-0.466994\pi\)
−0.994629 + 0.103505i \(0.966994\pi\)
\(440\) 1.64384i 0.0783672i
\(441\) 10.9328 8.12276i 0.520609 0.386798i
\(442\) 3.97608 3.97608i 0.189123 0.189123i
\(443\) −11.8103 −0.561123 −0.280562 0.959836i \(-0.590521\pi\)
−0.280562 + 0.959836i \(0.590521\pi\)
\(444\) −10.3842 1.78014i −0.492811 0.0844818i
\(445\) 10.5825 0.501658
\(446\) 0.222819 0.222819i 0.0105508 0.0105508i
\(447\) −36.7633 + 12.1623i −1.73884 + 0.575258i
\(448\) 1.56844i 0.0741017i
\(449\) −23.8504 23.8504i −1.12557 1.12557i −0.990889 0.134681i \(-0.956999\pi\)
−0.134681 0.990889i \(-0.543001\pi\)
\(450\) 2.96790 + 0.437662i 0.139908 + 0.0206316i
\(451\) −17.4618 −0.822242
\(452\) −13.0116 13.0116i −0.612013 0.612013i
\(453\) −37.0672 + 12.2629i −1.74157 + 0.576160i
\(454\) −13.2696 −0.622773
\(455\) −1.39558 −0.0654257
\(456\) −3.45993 10.4584i −0.162026 0.489759i
\(457\) 5.62384 5.62384i 0.263072 0.263072i −0.563229 0.826301i \(-0.690441\pi\)
0.826301 + 0.563229i \(0.190441\pi\)
\(458\) −17.9957 + 17.9957i −0.840884 + 0.840884i
\(459\) −5.65524 32.3464i −0.263964 1.50980i
\(460\) 1.52825 0.0712550
\(461\) 16.5535 + 16.5535i 0.770972 + 0.770972i 0.978276 0.207305i \(-0.0664692\pi\)
−0.207305 + 0.978276i \(0.566469\pi\)
\(462\) 3.98971 + 2.00612i 0.185618 + 0.0933333i
\(463\) 1.55048 1.55048i 0.0720571 0.0720571i −0.670160 0.742217i \(-0.733774\pi\)
0.742217 + 0.670160i \(0.233774\pi\)
\(464\) −0.289296 + 0.289296i −0.0134302 + 0.0134302i
\(465\) −13.0896 + 4.33042i −0.607017 + 0.200818i
\(466\) 5.33585 5.33585i 0.247178 0.247178i
\(467\) 14.2943 + 14.2943i 0.661461 + 0.661461i 0.955724 0.294263i \(-0.0950743\pi\)
−0.294263 + 0.955724i \(0.595074\pi\)
\(468\) −2.64081 0.389427i −0.122071 0.0180013i
\(469\) 7.45415i 0.344201i
\(470\) 13.1074i 0.604599i
\(471\) −1.28947 3.89770i −0.0594156 0.179597i
\(472\) 12.0960i 0.556765i
\(473\) −1.37158 + 1.37158i −0.0630654 + 0.0630654i
\(474\) 1.60321 0.530387i 0.0736379 0.0243615i
\(475\) −4.49720 4.49720i −0.206346 0.206346i
\(476\) −7.00865 + 7.00865i −0.321241 + 0.321241i
\(477\) −7.41244 9.97673i −0.339392 0.456803i
\(478\) 3.01914 0.138092
\(479\) −2.65048 2.65048i −0.121103 0.121103i 0.643958 0.765061i \(-0.277291\pi\)
−0.765061 + 0.643958i \(0.777291\pi\)
\(480\) −0.544013 1.64440i −0.0248307 0.0750562i
\(481\) 5.17680 1.57942i 0.236042 0.0720156i
\(482\) 17.5959i 0.801472i
\(483\) −1.86505 + 3.70916i −0.0848629 + 0.168773i
\(484\) 8.29778i 0.377172i
\(485\) −5.49755 −0.249631
\(486\) −10.7248 + 11.3128i −0.486487 + 0.513158i
\(487\) −5.77603 + 5.77603i −0.261737 + 0.261737i −0.825759 0.564023i \(-0.809253\pi\)
0.564023 + 0.825759i \(0.309253\pi\)
\(488\) 13.7289i 0.621478i
\(489\) −8.87601 + 17.6523i −0.401387 + 0.798266i
\(490\) −4.54001 −0.205097
\(491\) 0.605121i 0.0273087i 0.999907 + 0.0136544i \(0.00434645\pi\)
−0.999907 + 0.0136544i \(0.995654\pi\)
\(492\) −17.4677 + 5.77879i −0.787503 + 0.260528i
\(493\) 2.58547 0.116444
\(494\) 4.00157 + 4.00157i 0.180039 + 0.180039i
\(495\) 4.87877 + 0.719449i 0.219284 + 0.0323368i
\(496\) 5.62866 + 5.62866i 0.252734 + 0.252734i
\(497\) 5.99895i 0.269090i
\(498\) 1.55912 3.10073i 0.0698659 0.138947i
\(499\) −11.7173 11.7173i −0.524539 0.524539i 0.394400 0.918939i \(-0.370952\pi\)
−0.918939 + 0.394400i \(0.870952\pi\)
\(500\) −0.707107 0.707107i −0.0316228 0.0316228i
\(501\) 5.73812 11.4118i 0.256360 0.509841i
\(502\) 2.73388i 0.122019i
\(503\) −15.1330 15.1330i −0.674748 0.674748i 0.284059 0.958807i \(-0.408319\pi\)
−0.958807 + 0.284059i \(0.908319\pi\)
\(504\) 4.65497 + 0.686446i 0.207349 + 0.0305767i
\(505\) 3.43070 + 3.43070i 0.152664 + 0.152664i
\(506\) 2.51220 0.111681
\(507\) −20.0753 + 6.64147i −0.891574 + 0.294958i
\(508\) 11.4287i 0.507068i
\(509\) 20.4200 0.905101 0.452551 0.891739i \(-0.350514\pi\)
0.452551 + 0.891739i \(0.350514\pi\)
\(510\) −4.91714 + 9.77905i −0.217735 + 0.433024i
\(511\) 19.9540i 0.882711i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 32.5538 5.69149i 1.43728 0.251286i
\(514\) 0.00222735 9.82441e−5
\(515\) 10.4711i 0.461414i
\(516\) −0.918134 + 1.82596i −0.0404186 + 0.0803832i
\(517\) 21.5465i 0.947615i
\(518\) −9.12517 + 2.78406i −0.400937 + 0.122325i
\(519\) −10.0977 30.5226i −0.443241 1.33979i
\(520\) 0.629176 + 0.629176i 0.0275912 + 0.0275912i
\(521\) −27.5843 −1.20849 −0.604246 0.796798i \(-0.706525\pi\)
−0.604246 + 0.796798i \(0.706525\pi\)
\(522\) −0.731988 0.985216i −0.0320382 0.0431217i
\(523\) 24.4745 24.4745i 1.07019 1.07019i 0.0728501 0.997343i \(-0.476791\pi\)
0.997343 0.0728501i \(-0.0232095\pi\)
\(524\) −3.48311 3.48311i −0.152160 0.152160i
\(525\) 2.57914 0.853250i 0.112563 0.0372389i
\(526\) −7.46574 + 7.46574i −0.325522 + 0.325522i
\(527\) 50.3040i 2.19128i
\(528\) −0.894273 2.70314i −0.0389182 0.117639i
\(529\) 20.6645i 0.898455i
\(530\) 4.14299i 0.179960i
\(531\) −35.8999 5.29398i −1.55792 0.229739i
\(532\) −7.05358 7.05358i −0.305811 0.305811i
\(533\) 6.68344 6.68344i 0.289492 0.289492i
\(534\) 17.4018 5.75702i 0.753051 0.249130i
\(535\) −7.20501 + 7.20501i −0.311500 + 0.311500i
\(536\) −3.36059 + 3.36059i −0.145156 + 0.145156i
\(537\) 10.3985 + 5.22862i 0.448729 + 0.225632i
\(538\) −6.65015 6.65015i −0.286708 0.286708i
\(539\) −7.46306 −0.321457
\(540\) 5.11851 0.894888i 0.220266 0.0385098i
\(541\) −25.8071 + 25.8071i −1.10953 + 1.10953i −0.116323 + 0.993211i \(0.537111\pi\)
−0.993211 + 0.116323i \(0.962889\pi\)
\(542\) 4.44443 4.44443i 0.190905 0.190905i
\(543\) 0.747644 + 2.25992i 0.0320845 + 0.0969823i
\(544\) 6.31950 0.270946
\(545\) 13.9412 0.597175
\(546\) −2.29489 + 0.759213i −0.0982122 + 0.0324913i
\(547\) 11.6788 + 11.6788i 0.499350 + 0.499350i 0.911236 0.411886i \(-0.135130\pi\)
−0.411886 + 0.911236i \(0.635130\pi\)
\(548\) 4.49515 0.192023
\(549\) 40.7460 + 6.00862i 1.73900 + 0.256442i
\(550\) −1.16237 1.16237i −0.0495638 0.0495638i
\(551\) 2.60204i 0.110851i
\(552\) 2.51305 0.831388i 0.106963 0.0353862i
\(553\) 1.08127 1.08127i 0.0459804 0.0459804i
\(554\) 25.1430 1.06822
\(555\) −8.60147 + 6.08397i −0.365112 + 0.258250i
\(556\) −21.9294 −0.930012
\(557\) 14.2831 14.2831i 0.605195 0.605195i −0.336491 0.941687i \(-0.609240\pi\)
0.941687 + 0.336491i \(0.109240\pi\)
\(558\) −19.1688 + 14.2419i −0.811479 + 0.602906i
\(559\) 1.04994i 0.0444076i
\(560\) −1.10905 1.10905i −0.0468660 0.0468660i
\(561\) −8.08301 + 16.0752i −0.341265 + 0.678697i
\(562\) −22.6137 −0.953902
\(563\) 28.5674 + 28.5674i 1.20397 + 1.20397i 0.972947 + 0.231027i \(0.0742086\pi\)
0.231027 + 0.972947i \(0.425791\pi\)
\(564\) −7.13060 21.5538i −0.300253 0.907579i
\(565\) −18.4012 −0.774143
\(566\) −7.81186 −0.328357
\(567\) −4.07461 + 13.5151i −0.171117 + 0.567579i
\(568\) −2.70454 + 2.70454i −0.113480 + 0.113480i
\(569\) −28.2760 + 28.2760i −1.18539 + 1.18539i −0.207065 + 0.978327i \(0.566391\pi\)
−0.978327 + 0.207065i \(0.933609\pi\)
\(570\) −9.84174 4.94866i −0.412225 0.207277i
\(571\) 4.49985 0.188313 0.0941563 0.995557i \(-0.469985\pi\)
0.0941563 + 0.995557i \(0.469985\pi\)
\(572\) 1.03427 + 1.03427i 0.0432449 + 0.0432449i
\(573\) 8.88627 17.6727i 0.371229 0.738289i
\(574\) −11.7809 + 11.7809i −0.491726 + 0.491726i
\(575\) 1.08064 1.08064i 0.0450656 0.0450656i
\(576\) −1.78915 2.40810i −0.0745479 0.100337i
\(577\) −18.3521 + 18.3521i −0.764009 + 0.764009i −0.977044 0.213036i \(-0.931665\pi\)
0.213036 + 0.977044i \(0.431665\pi\)
\(578\) −16.2182 16.2182i −0.674590 0.674590i
\(579\) −22.6503 11.3891i −0.941313 0.473315i
\(580\) 0.409126i 0.0169880i
\(581\) 3.14280i 0.130385i
\(582\) −9.04017 + 2.99074i −0.374727 + 0.123970i
\(583\) 6.81043i 0.282059i
\(584\) −8.99595 + 8.99595i −0.372255 + 0.372255i
\(585\) −2.14270 + 1.59197i −0.0885898 + 0.0658198i
\(586\) −9.89119 9.89119i −0.408601 0.408601i
\(587\) 11.8937 11.8937i 0.490908 0.490908i −0.417685 0.908592i \(-0.637158\pi\)
0.908592 + 0.417685i \(0.137158\pi\)
\(588\) −7.46559 + 2.46983i −0.307876 + 0.101854i
\(589\) 50.6265 2.08603
\(590\) 8.55319 + 8.55319i 0.352129 + 0.352129i
\(591\) −16.1228 + 5.33387i −0.663203 + 0.219406i
\(592\) 5.36910 + 2.85880i 0.220669 + 0.117496i
\(593\) 13.6712i 0.561409i 0.959794 + 0.280705i \(0.0905681\pi\)
−0.959794 + 0.280705i \(0.909432\pi\)
\(594\) 8.41404 1.47106i 0.345232 0.0603582i
\(595\) 9.91173i 0.406341i
\(596\) 22.3567 0.915764
\(597\) −5.66653 + 11.2694i −0.231915 + 0.461226i
\(598\) −0.961538 + 0.961538i −0.0393202 + 0.0393202i
\(599\) 16.0843i 0.657186i −0.944472 0.328593i \(-0.893426\pi\)
0.944472 0.328593i \(-0.106574\pi\)
\(600\) −1.54744 0.778090i −0.0631740 0.0317654i
\(601\) −24.8780 −1.01479 −0.507397 0.861713i \(-0.669392\pi\)
−0.507397 + 0.861713i \(0.669392\pi\)
\(602\) 1.85073i 0.0754301i
\(603\) −8.50312 11.4447i −0.346274 0.466065i
\(604\) 22.5415 0.917201
\(605\) 5.86741 + 5.86741i 0.238544 + 0.238544i
\(606\) 7.50779 + 3.77510i 0.304983 + 0.153353i
\(607\) 9.34830 + 9.34830i 0.379436 + 0.379436i 0.870899 0.491463i \(-0.163538\pi\)
−0.491463 + 0.870899i \(0.663538\pi\)
\(608\) 6.36001i 0.257932i
\(609\) −0.992975 0.499291i −0.0402374 0.0202323i
\(610\) −9.70779 9.70779i −0.393057 0.393057i
\(611\) 8.24687 + 8.24687i 0.333633 + 0.333633i
\(612\) −2.76581 + 18.7557i −0.111801 + 0.758153i
\(613\) 26.4265i 1.06736i 0.845688 + 0.533678i \(0.179190\pi\)
−0.845688 + 0.533678i \(0.820810\pi\)
\(614\) −7.20441 7.20441i −0.290746 0.290746i
\(615\) −8.26528 + 16.4377i −0.333288 + 0.662833i
\(616\) −1.82311 1.82311i −0.0734551 0.0734551i
\(617\) 14.1919 0.571346 0.285673 0.958327i \(-0.407783\pi\)
0.285673 + 0.958327i \(0.407783\pi\)
\(618\) −5.69644 17.2187i −0.229145 0.692639i
\(619\) 44.4517i 1.78666i −0.449398 0.893332i \(-0.648362\pi\)
0.449398 0.893332i \(-0.351638\pi\)
\(620\) 7.96013 0.319686
\(621\) 1.36761 + 7.82236i 0.0548804 + 0.313901i
\(622\) 14.8367i 0.594899i
\(623\) 11.7365 11.7365i 0.470214 0.470214i
\(624\) 1.37690 + 0.692337i 0.0551200 + 0.0277157i
\(625\) −1.00000 −0.0400000
\(626\) 34.6390i 1.38445i
\(627\) −16.1783 8.13483i −0.646099 0.324874i
\(628\) 2.37029i 0.0945848i
\(629\) −11.2175 36.7669i −0.447269 1.46599i
\(630\) 3.77695 2.80617i 0.150477 0.111800i
\(631\) 4.17746 + 4.17746i 0.166302 + 0.166302i 0.785352 0.619050i \(-0.212482\pi\)
−0.619050 + 0.785352i \(0.712482\pi\)
\(632\) −0.974951 −0.0387815
\(633\) −0.321775 0.972636i −0.0127894 0.0386588i
\(634\) −13.3514 + 13.3514i −0.530250 + 0.530250i
\(635\) −8.08133 8.08133i −0.320698 0.320698i
\(636\) 2.25384 + 6.81273i 0.0893707 + 0.270142i
\(637\) 2.85647 2.85647i 0.113177 0.113177i
\(638\) 0.672539i 0.0266261i
\(639\) −6.84314 9.21049i −0.270710 0.364361i
\(640\) 1.00000i 0.0395285i
\(641\) 27.7886i 1.09758i 0.835960 + 0.548791i \(0.184912\pi\)
−0.835960 + 0.548791i \(0.815088\pi\)
\(642\) −7.92829 + 15.7675i −0.312905 + 0.622295i
\(643\) −3.14293 3.14293i −0.123945 0.123945i 0.642413 0.766358i \(-0.277933\pi\)
−0.766358 + 0.642413i \(0.777933\pi\)
\(644\) 1.69491 1.69491i 0.0667887 0.0667887i
\(645\) 0.641927 + 1.94036i 0.0252758 + 0.0764018i
\(646\) 28.4201 28.4201i 1.11817 1.11817i
\(647\) 10.4437 10.4437i 0.410582 0.410582i −0.471359 0.881941i \(-0.656236\pi\)
0.881941 + 0.471359i \(0.156236\pi\)
\(648\) 7.93005 4.25609i 0.311522 0.167195i
\(649\) 14.0601 + 14.0601i 0.551908 + 0.551908i
\(650\) 0.889790 0.0349004
\(651\) −9.71442 + 19.3197i −0.380738 + 0.757200i
\(652\) 8.06627 8.06627i 0.315899 0.315899i
\(653\) 7.10309 7.10309i 0.277965 0.277965i −0.554331 0.832296i \(-0.687026\pi\)
0.832296 + 0.554331i \(0.187026\pi\)
\(654\) 22.9249 7.58419i 0.896433 0.296565i
\(655\) −4.92586 −0.192469
\(656\) 10.6225 0.414740
\(657\) −22.7619 30.6363i −0.888027 1.19524i
\(658\) −14.5368 14.5368i −0.566703 0.566703i
\(659\) −9.05248 −0.352635 −0.176317 0.984333i \(-0.556418\pi\)
−0.176317 + 0.984333i \(0.556418\pi\)
\(660\) −2.54375 1.27906i −0.0990154 0.0497873i
\(661\) −20.1666 20.1666i −0.784391 0.784391i 0.196177 0.980568i \(-0.437147\pi\)
−0.980568 + 0.196177i \(0.937147\pi\)
\(662\) 23.7273i 0.922187i
\(663\) −3.05900 9.24650i −0.118802 0.359104i
\(664\) −1.41689 + 1.41689i −0.0549858 + 0.0549858i
\(665\) −9.97527 −0.386824
\(666\) −10.8345 + 14.6838i −0.419828 + 0.568985i
\(667\) −0.625246 −0.0242096
\(668\) −5.21464 + 5.21464i −0.201761 + 0.201761i
\(669\) −0.171426 0.518172i −0.00662770 0.0200337i
\(670\) 4.75260i 0.183609i
\(671\) −15.9581 15.9581i −0.616055 0.616055i
\(672\) −2.42706 1.22039i −0.0936260 0.0470774i
\(673\) −7.56707 −0.291689 −0.145845 0.989308i \(-0.546590\pi\)
−0.145845 + 0.989308i \(0.546590\pi\)
\(674\) −12.9130 12.9130i −0.497390 0.497390i
\(675\) 2.98655 4.25212i 0.114953 0.163664i
\(676\) 12.2083 0.469549
\(677\) −3.72965 −0.143342 −0.0716710 0.997428i \(-0.522833\pi\)
−0.0716710 + 0.997428i \(0.522833\pi\)
\(678\) −30.2589 + 10.0105i −1.16208 + 0.384450i
\(679\) −6.09707 + 6.09707i −0.233984 + 0.233984i
\(680\) 4.46856 4.46856i 0.171361 0.171361i
\(681\) −10.3249 + 20.5339i −0.395653 + 0.786861i
\(682\) 13.0852 0.501059
\(683\) −9.79474 9.79474i −0.374785 0.374785i 0.494431 0.869217i \(-0.335376\pi\)
−0.869217 + 0.494431i \(0.835376\pi\)
\(684\) −18.8759 2.78354i −0.721738 0.106431i
\(685\) 3.17855 3.17855i 0.121446 0.121446i
\(686\) −12.7985 + 12.7985i −0.488648 + 0.488648i
\(687\) 13.8450 + 41.8496i 0.528220 + 1.59666i
\(688\) 0.834374 0.834374i 0.0318102 0.0318102i
\(689\) −2.60667 2.60667i −0.0993063 0.0993063i
\(690\) 1.18912 2.36488i 0.0452689 0.0900293i
\(691\) 13.8014i 0.525029i −0.964928 0.262515i \(-0.915448\pi\)
0.964928 0.262515i \(-0.0845518\pi\)
\(692\) 18.5616i 0.705605i
\(693\) 6.20872 4.61290i 0.235850 0.175230i
\(694\) 11.3678i 0.431515i
\(695\) −15.5064 + 15.5064i −0.588191 + 0.588191i
\(696\) 0.222570 + 0.672766i 0.00843649 + 0.0255011i
\(697\) −47.4674 47.4674i −1.79795 1.79795i
\(698\) 6.13816 6.13816i 0.232333 0.232333i
\(699\) −4.10514 12.4087i −0.155271 0.469340i
\(700\) −1.56844 −0.0592813
\(701\) 5.58493 + 5.58493i 0.210940 + 0.210940i 0.804667 0.593727i \(-0.202344\pi\)
−0.593727 + 0.804667i \(0.702344\pi\)
\(702\) −2.65741 + 3.78349i −0.100297 + 0.142799i
\(703\) 37.0026 11.2894i 1.39558 0.425786i
\(704\) 1.64384i 0.0619547i
\(705\) −20.2829 10.1987i −0.763900 0.384107i
\(706\) 6.17215i 0.232292i
\(707\) 7.60965 0.286190
\(708\) 18.7179 + 9.41181i 0.703462 + 0.353717i
\(709\) −13.9927 + 13.9927i −0.525507 + 0.525507i −0.919229 0.393722i \(-0.871187\pi\)
0.393722 + 0.919229i \(0.371187\pi\)
\(710\) 3.82480i 0.143542i
\(711\) 0.426700 2.89356i 0.0160025 0.108517i
\(712\) −10.5825 −0.396596
\(713\) 12.1651i 0.455585i
\(714\) 5.39211 + 16.2988i 0.201795 + 0.609969i
\(715\) 1.46268 0.0547010
\(716\) −4.75163 4.75163i −0.177577 0.177577i
\(717\) 2.34916 4.67194i 0.0877311 0.174477i
\(718\) −14.6826 14.6826i −0.547950 0.547950i
\(719\) 26.6215i 0.992813i 0.868090 + 0.496407i \(0.165347\pi\)
−0.868090 + 0.496407i \(0.834653\pi\)
\(720\) −2.96790 0.437662i −0.110607 0.0163107i
\(721\) −11.6130 11.6130i −0.432492 0.432492i
\(722\) 15.1672 + 15.1672i 0.564466 + 0.564466i
\(723\) 27.2286 + 13.6912i 1.01264 + 0.509182i
\(724\) 1.37431i 0.0510759i
\(725\) 0.289296 + 0.289296i 0.0107442 + 0.0107442i
\(726\) 12.8403 + 6.45642i 0.476549 + 0.239620i
\(727\) −10.4677 10.4677i −0.388226 0.388226i 0.485828 0.874054i \(-0.338518\pi\)
−0.874054 + 0.485828i \(0.838518\pi\)
\(728\) 1.39558 0.0517236
\(729\) 9.16099 + 25.3984i 0.339296 + 0.940680i
\(730\) 12.7222i 0.470870i
\(731\) −7.45690 −0.275804
\(732\) −21.2447 10.6823i −0.785225 0.394830i
\(733\) 14.9277i 0.551369i −0.961248 0.275684i \(-0.911096\pi\)
0.961248 0.275684i \(-0.0889044\pi\)
\(734\) 15.6053 15.6053i 0.576002 0.576002i
\(735\) −3.53254 + 7.02540i −0.130300 + 0.259136i
\(736\) −1.52825 −0.0563320
\(737\) 7.81253i 0.287778i
\(738\) −4.64908 + 31.5266i −0.171135 + 1.16051i
\(739\) 14.3573i 0.528141i −0.964503 0.264071i \(-0.914935\pi\)
0.964503 0.264071i \(-0.0850652\pi\)
\(740\) 5.81801 1.77505i 0.213874 0.0652523i
\(741\) 9.30577 3.07861i 0.341856 0.113096i
\(742\) 4.59479 + 4.59479i 0.168680 + 0.168680i
\(743\) 34.5132 1.26617 0.633083 0.774084i \(-0.281789\pi\)
0.633083 + 0.774084i \(0.281789\pi\)
\(744\) 13.0896 4.33042i 0.479889 0.158761i
\(745\) 15.8085 15.8085i 0.579180 0.579180i
\(746\) −9.16060 9.16060i −0.335394 0.335394i
\(747\) −3.58506 4.82530i −0.131171 0.176548i
\(748\) 7.34562 7.34562i 0.268582 0.268582i
\(749\) 15.9815i 0.583950i
\(750\) −1.64440 + 0.544013i −0.0600450 + 0.0198646i
\(751\) 26.5644i 0.969350i −0.874694 0.484675i \(-0.838938\pi\)
0.874694 0.484675i \(-0.161062\pi\)
\(752\) 13.1074i 0.477978i
\(753\) 4.23051 + 2.12720i 0.154168 + 0.0775196i
\(754\) −0.257412 0.257412i −0.00937440 0.00937440i
\(755\) 15.9392 15.9392i 0.580089 0.580089i
\(756\) 4.68422 6.66917i 0.170363 0.242556i
\(757\) 26.5621 26.5621i 0.965417 0.965417i −0.0340046 0.999422i \(-0.510826\pi\)
0.999422 + 0.0340046i \(0.0108261\pi\)
\(758\) 6.62250 6.62250i 0.240540 0.240540i
\(759\) 1.95472 3.88749i 0.0709519 0.141107i
\(760\) 4.49720 + 4.49720i 0.163131 + 0.163131i
\(761\) −3.25195 −0.117883 −0.0589415 0.998261i \(-0.518773\pi\)
−0.0589415 + 0.998261i \(0.518773\pi\)
\(762\) −17.6853 8.89258i −0.640670 0.322144i
\(763\) 15.4615 15.4615i 0.559744 0.559744i
\(764\) −8.07560 + 8.07560i −0.292165 + 0.292165i
\(765\) 11.3065 + 15.2180i 0.408789 + 0.550207i
\(766\) −1.68012 −0.0607051
\(767\) −10.7629 −0.388627
\(768\) 0.544013 + 1.64440i 0.0196304 + 0.0593372i
\(769\) 28.6343 + 28.6343i 1.03258 + 1.03258i 0.999451 + 0.0331270i \(0.0105466\pi\)
0.0331270 + 0.999451i \(0.489453\pi\)
\(770\) −2.57826 −0.0929142
\(771\) 0.00173308 0.00344669i 6.24153e−5 0.000124130i
\(772\) 10.3501 + 10.3501i 0.372508 + 0.372508i
\(773\) 14.0416i 0.505041i −0.967591 0.252521i \(-0.918740\pi\)
0.967591 0.252521i \(-0.0812596\pi\)
\(774\) 2.11117 + 2.84152i 0.0758844 + 0.102136i
\(775\) 5.62866 5.62866i 0.202187 0.202187i
\(776\) 5.49755 0.197350
\(777\) −2.79204 + 16.2869i −0.100164 + 0.584290i
\(778\) −31.1625 −1.11723