Properties

Label 1110.2.u.e.401.13
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 401.13
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.e.191.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.544013 + 1.64440i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(0.778090 + 1.54744i) q^{6} -1.56844 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.40810 - 1.78915i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.544013 + 1.64440i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(0.778090 + 1.54744i) 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} +(-1.54744 + 0.778090i) q^{15} -1.00000 q^{16} +(-4.46856 - 4.46856i) q^{17} +(-2.96790 + 0.437662i) 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} +(1.54744 - 0.778090i) 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} +(-0.692337 - 1.37690i) q^{39} -1.00000i q^{40} +10.6225 q^{41} +(-1.22039 - 2.42706i) q^{42} +(-0.834374 + 0.834374i) q^{43} +1.64384i q^{44} +(-0.437662 - 2.96790i) 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} +(9.77905 - 4.91714i) q^{51} +(0.629176 + 0.629176i) q^{52} -4.14299i q^{53} +(0.894888 - 5.11851i) q^{54} +(-1.16237 - 1.16237i) q^{55} +(1.10905 + 1.10905i) q^{56} +(-4.94866 - 9.84174i) q^{57} +0.409126i q^{58} +(-8.55319 - 8.55319i) q^{59} +(0.778090 + 1.54744i) 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} +(-1.27906 - 2.54375i) q^{66} +4.75260i q^{67} +(-4.46856 + 4.46856i) q^{68} +(-2.36488 + 1.18912i) q^{69} -1.56844 q^{70} -3.82480i q^{71} +(0.437662 + 2.96790i) 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} +(-0.318337 - 0.633098i) 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} +(12.3178 - 6.19370i) q^{93} +(9.26833 + 9.26833i) q^{94} -6.36001 q^{95} +(-0.778090 - 1.54744i) 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
\(6\) 0.778090 + 1.54744i 0.317654 + 0.631740i
\(7\) −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 \(-0.579714\pi\)
−0.247819 + 0.968806i \(0.579714\pi\)
\(12\) 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
\(15\) −1.54744 + 0.778090i −0.399548 + 0.200902i
\(16\) −1.00000 −0.250000
\(17\) −4.46856 4.46856i −1.08378 1.08378i −0.996153 0.0876320i \(-0.972070\pi\)
−0.0876320 0.996153i \(-0.527930\pi\)
\(18\) −2.96790 + 0.437662i −0.699542 + 0.103158i
\(19\) −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 0.810738 0.585410i \(-0.199066\pi\)
−0.585410 + 0.810738i \(0.699066\pi\)
\(24\) 1.54744 0.778090i 0.315870 0.158827i
\(25\) 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 −0.733457 0.679736i \(-0.762094\pi\)
0.679736 + 0.733457i \(0.262094\pi\)
\(30\) −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
\(39\) −0.692337 1.37690i −0.110863 0.220480i
\(40\) 1.00000i 0.158114i
\(41\) 10.6225 1.65896 0.829479 0.558537i \(-0.188637\pi\)
0.829479 + 0.558537i \(0.188637\pi\)
\(42\) −1.22039 2.42706i −0.188310 0.374504i
\(43\) −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
\(45\) −0.437662 2.96790i −0.0652429 0.442429i
\(46\) 1.52825 0.225328
\(47\) 13.1074i 1.91191i 0.293511 + 0.955956i \(0.405176\pi\)
−0.293511 + 0.955956i \(0.594824\pi\)
\(48\) 0.544013 1.64440i 0.0785216 0.237349i
\(49\) −4.54001 −0.648572
\(50\) 0.707107 + 0.707107i 0.100000 + 0.100000i
\(51\) 9.77905 4.91714i 1.36934 0.688537i
\(52\) 0.629176 + 0.629176i 0.0872511 + 0.0872511i
\(53\) 4.14299i 0.569084i −0.958664 0.284542i \(-0.908159\pi\)
0.958664 0.284542i \(-0.0918415\pi\)
\(54\) 0.894888 5.11851i 0.121779 0.696541i
\(55\) −1.16237 1.16237i −0.156734 0.156734i
\(56\) 1.10905 + 1.10905i 0.148203 + 0.148203i
\(57\) −4.94866 9.84174i −0.655466 1.30357i
\(58\) 0.409126i 0.0537209i
\(59\) −8.55319 8.55319i −1.11353 1.11353i −0.992669 0.120861i \(-0.961435\pi\)
−0.120861 0.992669i \(-0.538565\pi\)
\(60\) 0.778090 + 1.54744i 0.100451 + 0.199774i
\(61\) −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
\(66\) −1.27906 2.54375i −0.157441 0.313114i
\(67\) 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
\(69\) −2.36488 + 1.18912i −0.284698 + 0.143153i
\(70\) −1.56844 −0.187464
\(71\) 3.82480i 0.453920i −0.973904 0.226960i \(-0.927121\pi\)
0.973904 0.226960i \(-0.0728786\pi\)
\(72\) 0.437662 + 2.96790i 0.0515790 + 0.349771i
\(73\) 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 \(-0.964924\pi\)
0.993935 0.109972i \(-0.0350760\pi\)
\(84\) −2.57914 0.853250i −0.281407 0.0930973i
\(85\) 6.31950i 0.685446i
\(86\) 1.17998i 0.127241i
\(87\) −0.318337 0.633098i −0.0341293 0.0678753i
\(88\) 1.16237 + 1.16237i 0.123909 + 0.123909i
\(89\) 7.48295 7.48295i 0.793191 0.793191i −0.188820 0.982012i \(-0.560466\pi\)
0.982012 + 0.188820i \(0.0604664\pi\)
\(90\) −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
\(93\) 12.3178 6.19370i 1.27730 0.642257i
\(94\) 9.26833 + 9.26833i 0.955956 + 0.955956i
\(95\) −6.36001 −0.652523
\(96\) −0.778090 1.54744i −0.0794135 0.157935i
\(97\) 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 \(-0.422399\pi\)
0.241383 + 0.970430i \(0.422399\pi\)
\(102\) 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
\(105\) 2.42706 1.22039i 0.236857 0.119097i
\(106\) −2.92954 2.92954i −0.284542 0.284542i
\(107\) 10.1894i 0.985049i 0.870299 + 0.492524i \(0.163926\pi\)
−0.870299 + 0.492524i \(0.836074\pi\)
\(108\) −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
\(111\) 7.62187 7.27373i 0.723436 0.690392i
\(112\) 1.56844 0.148203
\(113\) −13.0116 + 13.0116i −1.22403 + 1.22403i −0.257839 + 0.966188i \(0.583010\pi\)
−0.966188 + 0.257839i \(0.916990\pi\)
\(114\) −10.4584 3.45993i −0.979518 0.324052i
\(115\) 1.52825i 0.142510i
\(116\) 0.289296 + 0.289296i 0.0268604 + 0.0268604i
\(117\) 2.64081 0.389427i 0.244143 0.0360026i
\(118\) −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
\(126\) 4.65497 0.686446i 0.414697 0.0611534i
\(127\) 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
\(129\) −0.918134 1.82596i −0.0808372 0.160766i
\(130\) −0.629176 + 0.629176i −0.0551824 + 0.0551824i
\(131\) −3.48311 + 3.48311i −0.304320 + 0.304320i −0.842702 0.538381i \(-0.819036\pi\)
0.538381 + 0.842702i \(0.319036\pi\)
\(132\) −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
\(135\) 5.11851 + 0.894888i 0.440531 + 0.0770197i
\(136\) 6.31950i 0.541892i
\(137\) 4.49515i 0.384047i −0.981390 0.192023i \(-0.938495\pi\)
0.981390 0.192023i \(-0.0615049\pi\)
\(138\) −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 \(-0.631586\pi\)
0.401716 0.915764i \(-0.368414\pi\)
\(150\) −1.54744 + 0.778090i −0.126348 + 0.0635308i
\(151\) 22.5415i 1.83440i 0.398426 + 0.917201i \(0.369557\pi\)
−0.398426 + 0.917201i \(0.630443\pi\)
\(152\) 6.36001 0.515865
\(153\) 2.76581 + 18.7557i 0.223602 + 1.51631i
\(154\) 1.82311 1.82311i 0.146910 0.146910i
\(155\) 7.96013i 0.639373i
\(156\) −1.37690 + 0.692337i −0.110240 + 0.0554313i
\(157\) −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
\(162\) 7.93005 + 4.25609i 0.623043 + 0.334390i
\(163\) 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
\(165\) 2.54375 1.27906i 0.198031 0.0995746i
\(166\) −1.41689 1.41689i −0.109972 0.109972i
\(167\) 5.21464 + 5.21464i 0.403521 + 0.403521i 0.879472 0.475951i \(-0.157896\pi\)
−0.475951 + 0.879472i \(0.657896\pi\)
\(168\) −2.42706 + 1.22039i −0.187252 + 0.0941548i
\(169\) 12.2083i 0.939098i
\(170\) −4.46856 4.46856i −0.342723 0.342723i
\(171\) 18.8759 2.78354i 1.44348 0.212862i
\(172\) 0.834374 + 0.834374i 0.0636204 + 0.0636204i
\(173\) 18.5616 1.41121 0.705605 0.708606i \(-0.250676\pi\)
0.705605 + 0.708606i \(0.250676\pi\)
\(174\) −0.672766 0.222570i −0.0510023 0.0168730i
\(175\) 1.56844i 0.118563i
\(176\) 1.64384 0.123909
\(177\) 18.7179 9.41181i 1.40692 0.707435i
\(178\) 10.5825i 0.793191i
\(179\) −4.75163 + 4.75163i −0.355153 + 0.355153i −0.862023 0.506869i \(-0.830803\pi\)
0.506869 + 0.862023i \(0.330803\pi\)
\(180\) −2.96790 + 0.437662i −0.221214 + 0.0326214i
\(181\) 1.37431 0.102152 0.0510759 0.998695i \(-0.483735\pi\)
0.0510759 + 0.998695i \(0.483735\pi\)
\(182\) 1.39558i 0.103447i
\(183\) 21.2447 10.6823i 1.57045 0.789660i
\(184\) 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 0.936090 0.351760i \(-0.114417\pi\)
−0.351760 + 0.936090i \(0.614417\pi\)
\(192\) −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 \(-0.886427\pi\)
0.937020 0.349277i \(-0.113573\pi\)
\(198\) 4.87877 0.719449i 0.346719 0.0511290i
\(199\) 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
\(204\) −4.91714 9.77905i −0.344269 0.684671i
\(205\) 7.51125 + 7.51125i 0.524609 + 0.524609i
\(206\) 10.4711 0.729559
\(207\) −0.668857 4.53570i −0.0464888 0.315253i
\(208\) 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
\(216\) −5.11851 0.894888i −0.348271 0.0608894i
\(217\) 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
\(222\) 0.246175 10.5328i 0.0165222 0.706914i
\(223\) −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 0.323467 0.946240i \(-0.395152\pi\)
−0.946240 + 0.323467i \(0.895152\pi\)
\(228\) −9.84174 + 4.94866i −0.651785 + 0.327733i
\(229\) 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 \(-0.420497\pi\)
0.247178 + 0.968970i \(0.420497\pi\)
\(234\) 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
\(237\) −0.758600 1.50868i −0.0492764 0.0979993i
\(238\) 9.91173 0.642482
\(239\) 2.13485 + 2.13485i 0.138092 + 0.138092i 0.772774 0.634682i \(-0.218869\pi\)
−0.634682 + 0.772774i \(0.718869\pi\)
\(240\) 1.54744 0.778090i 0.0998869 0.0502255i
\(241\) 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
\(246\) 8.26528 + 16.4377i 0.526975 + 1.04803i
\(247\) 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 −0.765479 0.643460i \(-0.777498\pi\)
0.643460 + 0.765479i \(0.277498\pi\)
\(252\) 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 0.707156 0.707058i \(-0.249978\pi\)
−0.707058 + 0.707156i \(0.749978\pi\)
\(258\) −1.94036 0.641927i −0.120802 0.0399646i
\(259\) 8.42110 + 4.48384i 0.523262 + 0.278612i
\(260\) 0.889790i 0.0551824i
\(261\) 1.21425 0.179059i 0.0751600 0.0110835i
\(262\) 4.92586i 0.304320i
\(263\) −10.5582 −0.651043 −0.325522 0.945535i \(-0.605540\pi\)
−0.325522 + 0.945535i \(0.605540\pi\)
\(264\) −2.54375 + 1.27906i −0.156557 + 0.0787207i
\(265\) 2.92954 2.92954i 0.179960 0.179960i
\(266\) 9.97527i 0.611623i
\(267\) 8.23413 + 16.3758i 0.503921 + 1.00218i
\(268\) 4.75260 0.290311
\(269\) 9.40474i 0.573417i −0.958018 0.286708i \(-0.907439\pi\)
0.958018 0.286708i \(-0.0925611\pi\)
\(270\) 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
\(273\) 1.08589 + 2.15958i 0.0657208 + 0.130703i
\(274\) −3.17855 3.17855i −0.192023 0.192023i
\(275\) 1.64384i 0.0991275i
\(276\) 1.18912 + 2.36488i 0.0715764 + 0.142349i
\(277\) −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
\(279\) 3.48385 + 23.6249i 0.208573 + 1.41439i
\(280\) 1.56844i 0.0937320i
\(281\) −15.9903 15.9903i −0.953902 0.953902i 0.0450817 0.998983i \(-0.485645\pi\)
−0.998983 + 0.0450817i \(0.985645\pi\)
\(282\) −20.2829 + 10.1987i −1.20783 + 0.607326i
\(283\) 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
\(288\) 2.96790 0.437662i 0.174885 0.0257895i
\(289\) 22.9361i 1.34918i
\(290\) −0.289296 + 0.289296i −0.0169880 + 0.0169880i
\(291\) 4.27759 + 8.50713i 0.250757 + 0.498697i
\(292\) 12.7222 0.744510
\(293\) 13.9882i 0.817202i −0.912713 0.408601i \(-0.866017\pi\)
0.912713 0.408601i \(-0.133983\pi\)
\(294\) −3.53254 7.02540i −0.206022 0.409729i
\(295\) 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
\(309\) −16.2035 + 8.14750i −0.921784 + 0.463495i
\(310\) −5.62866 5.62866i −0.319686 0.319686i
\(311\) −10.4912 + 10.4912i −0.594899 + 0.594899i −0.938951 0.344052i \(-0.888200\pi\)
0.344052 + 0.938951i \(0.388200\pi\)
\(312\) −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
\(315\) 0.686446 + 4.65497i 0.0386768 + 0.262278i
\(316\) 0.689395 + 0.689395i 0.0387815 + 0.0387815i
\(317\) −18.8817 −1.06050 −0.530250 0.847841i \(-0.677902\pi\)
−0.530250 + 0.847841i \(0.677902\pi\)
\(318\) 6.41104 3.22362i 0.359513 0.180772i
\(319\) 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
\(327\) −10.8475 21.5732i −0.599868 1.19300i
\(328\) −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
\(333\) 7.81451 + 16.4904i 0.428233 + 0.903669i
\(334\) 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
\(339\) −14.3178 28.4747i −0.777634 1.54653i
\(340\) −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 −0.457628 0.889144i \(-0.651301\pi\)
0.889144 + 0.457628i \(0.151301\pi\)
\(348\) −0.633098 + 0.318337i −0.0339376 + 0.0170647i
\(349\) −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
\(351\) −0.796262 + 4.55440i −0.0425013 + 0.243096i
\(352\) 1.16237 1.16237i 0.0619547 0.0619547i
\(353\) 4.36437 4.36437i 0.232292 0.232292i −0.581357 0.813649i \(-0.697478\pi\)
0.813649 + 0.581357i \(0.197478\pi\)
\(354\) 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
\(357\) −15.3378 + 7.71222i −0.811764 + 0.408174i
\(358\) 6.71982i 0.355153i
\(359\) 20.7643i 1.09590i −0.836511 0.547950i \(-0.815409\pi\)
0.836511 0.547950i \(-0.184591\pi\)
\(360\) −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
\(372\) −6.19370 12.3178i −0.321128 0.638650i
\(373\) 12.9551i 0.670787i 0.942078 + 0.335394i \(0.108869\pi\)
−0.942078 + 0.335394i \(0.891131\pi\)
\(374\) 10.3883 0.537165
\(375\) −0.778090 1.54744i −0.0401804 0.0799095i
\(376\) 9.26833 9.26833i 0.477978 0.477978i
\(377\) 0.364036i 0.0187488i
\(378\) −1.40357 + 8.02806i −0.0721921 + 0.412919i
\(379\) −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 0.676103 0.736808i \(-0.263668\pi\)
−0.736808 + 0.676103i \(0.763668\pi\)
\(384\) −1.54744 + 0.778090i −0.0789675 + 0.0397068i
\(385\) 1.82311 + 1.82311i 0.0929142 + 0.0929142i
\(386\) 14.6372i 0.745016i
\(387\) 3.50208 0.516434i 0.178021 0.0262518i
\(388\) −3.88735 3.88735i −0.197350 0.197350i
\(389\) −22.0352 22.0352i −1.11723 1.11723i −0.992146 0.125085i \(-0.960080\pi\)
−0.125085 0.992146i \(-0.539920\pi\)
\(390\) −0.692337 1.37690i −0.0350578 0.0697219i
\(391\) 9.65777i 0.488414i
\(392\) 3.21027 + 3.21027i 0.162143 + 0.162143i
\(393\) −3.83276 7.62248i −0.193337 0.384503i
\(394\) −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
\(399\) 7.76166 + 15.4361i 0.388569 + 0.772774i
\(400\) 1.00000i 0.0500000i
\(401\) −15.3652 + 15.3652i −0.767300 + 0.767300i −0.977630 0.210331i \(-0.932546\pi\)
0.210331 + 0.977630i \(0.432546\pi\)
\(402\) −7.35437 + 3.69795i −0.366803 + 0.184437i
\(403\) 7.08284 0.352821
\(404\) 4.85174i 0.241383i
\(405\) −4.25609 + 7.93005i −0.211487 + 0.394047i
\(406\) 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 \(-0.995340\pi\)
0.999893 0.0146384i \(-0.00465972\pi\)
\(420\) −1.22039 2.42706i −0.0595487 0.118429i
\(421\) 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
\(426\) 5.91865 2.97604i 0.286759 0.144189i
\(427\) 15.2261 + 15.2261i 0.736840 + 0.736840i
\(428\) 10.1894 0.492524
\(429\) 1.13809 + 2.26340i 0.0549477 + 0.109278i
\(430\) −0.834374 + 0.834374i −0.0402371 + 0.0402371i
\(431\) −26.5760 + 26.5760i −1.28012 + 1.28012i −0.339523 + 0.940598i \(0.610266\pi\)
−0.940598 + 0.339523i \(0.889734\pi\)
\(432\) −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
\(438\) −19.6869 + 9.89902i −0.940674 + 0.472993i
\(439\) −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 \(-0.409479\pi\)
0.280562 + 0.959836i \(0.409479\pi\)
\(444\) −7.27373 7.62187i −0.345196 0.361718i
\(445\) 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 \(0.0430009\pi\)
0.134681 + 0.990889i \(0.456999\pi\)
\(450\) −0.437662 2.96790i −0.0206316 0.139908i
\(451\) −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
\(459\) −32.3464 5.65524i −1.50980 0.263964i
\(460\) 1.52825 0.0712550
\(461\) −16.5535 16.5535i −0.770972 0.770972i 0.207305 0.978276i \(-0.433531\pi\)
−0.978276 + 0.207305i \(0.933531\pi\)
\(462\) 2.00612 + 3.98971i 0.0933333 + 0.185618i
\(463\) 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 0.294263 0.955724i \(-0.404926\pi\)
−0.955724 + 0.294263i \(0.904926\pi\)
\(468\) −0.389427 2.64081i −0.0180013 0.122071i
\(469\) 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 0.765061 0.643958i \(-0.222709\pi\)
−0.643958 + 0.765061i \(0.722709\pi\)
\(480\) 0.544013 1.64440i 0.0248307 0.0750562i
\(481\) 5.17680 1.57942i 0.236042 0.0720156i
\(482\) 17.5959i 0.801472i
\(483\) 3.70916 1.86505i 0.168773 0.0848629i
\(484\) 8.29778i 0.377172i
\(485\) 5.49755 0.249631
\(486\) −11.3128 + 10.7248i −0.513158 + 0.486487i
\(487\) −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
\(489\) −17.6523 + 8.87601i −0.798266 + 0.401387i
\(490\) −4.54001 −0.205097
\(491\) 0.605121i 0.0273087i −0.999907 0.0136544i \(-0.995654\pi\)
0.999907 0.0136544i \(-0.00434645\pi\)
\(492\) 17.4677 + 5.77879i 0.787503 + 0.260528i
\(493\) 2.58547 0.116444
\(494\) −4.00157 4.00157i −0.180039 0.180039i
\(495\) 0.719449 + 4.87877i 0.0323368 + 0.219284i
\(496\) 5.62866 + 5.62866i 0.252734 + 0.252734i
\(497\) 5.99895i 0.269090i
\(498\) 3.10073 1.55912i 0.138947 0.0698659i
\(499\) −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
\(501\) −11.4118 + 5.73812i −0.509841 + 0.256360i
\(502\) 2.73388i 0.122019i
\(503\) 15.1330 + 15.1330i 0.674748 + 0.674748i 0.958807 0.284059i \(-0.0916810\pi\)
−0.284059 + 0.958807i \(0.591681\pi\)
\(504\) −0.686446 4.65497i −0.0305767 0.207349i
\(505\) 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 \(-0.649486\pi\)
−0.452551 + 0.891739i \(0.649486\pi\)
\(510\) 9.77905 4.91714i 0.433024 0.217735i
\(511\) 19.9540i 0.882711i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −5.69149 + 32.5538i −0.251286 + 1.43728i
\(514\) 0.00222735 9.82441e−5
\(515\) 10.4711i 0.461414i
\(516\) −1.82596 + 0.918134i −0.0803832 + 0.0404186i
\(517\) 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 \(-0.293475\pi\)
0.604246 + 0.796798i \(0.293475\pi\)
\(522\) 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
\(531\) 5.29398 + 35.8999i 0.229739 + 1.55792i
\(532\) −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
\(537\) −5.22862 10.3985i −0.225632 0.448729i
\(538\) −6.65015 6.65015i −0.286708 0.286708i
\(539\) 7.46306 0.321457
\(540\) 0.894888 5.11851i 0.0385098 0.220266i
\(541\) −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
\(549\) 6.00862 + 40.7460i 0.256442 + 1.73900i
\(550\) −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
\(555\) 10.5328 + 0.246175i 0.447091 + 0.0104495i
\(556\) −21.9294 −0.930012
\(557\) −14.2831 + 14.2831i −0.605195 + 0.605195i −0.941687 0.336491i \(-0.890760\pi\)
0.336491 + 0.941687i \(0.390760\pi\)
\(558\) 19.1688 + 14.2419i 0.811479 + 0.602906i
\(559\) 1.04994i 0.0444076i
\(560\) 1.10905 + 1.10905i 0.0468660 + 0.0468660i
\(561\) −16.0752 + 8.08301i −0.678697 + 0.341265i
\(562\) −22.6137 −0.953902
\(563\) −28.5674 28.5674i −1.20397 1.20397i −0.972947 0.231027i \(-0.925791\pi\)
−0.231027 0.972947i \(-0.574209\pi\)
\(564\) −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 \(-0.433609\pi\)
0.978327 0.207065i \(-0.0663913\pi\)
\(570\) −4.94866 9.84174i −0.207277 0.412225i
\(571\) 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
\(573\) −17.6727 + 8.88627i −0.738289 + 0.371229i
\(574\) −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
\(579\) −11.3891 22.6503i −0.473315 0.941313i
\(580\) 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 −0.908592 0.417685i \(-0.862842\pi\)
0.417685 + 0.908592i \(0.362842\pi\)
\(588\) −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 \(-0.909432\pi\)
0.959794 0.280705i \(-0.0905681\pi\)
\(594\) −1.47106 + 8.41404i −0.0603582 + 0.345232i
\(595\) 9.91173i 0.406341i
\(596\) −22.3567 −0.915764
\(597\) −11.2694 + 5.66653i −0.461226 + 0.231915i
\(598\) −0.961538 + 0.961538i −0.0393202 + 0.0393202i
\(599\) 16.0843i 0.657186i 0.944472 + 0.328593i \(0.106574\pi\)
−0.944472 + 0.328593i \(0.893426\pi\)
\(600\) 0.778090 + 1.54744i 0.0317654 + 0.0631740i
\(601\) −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
\(606\) 3.77510 + 7.50779i 0.153353 + 0.304983i
\(607\) 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
\(609\) 0.499291 + 0.992975i 0.0202323 + 0.0402374i
\(610\) −9.70779 9.70779i −0.393057 0.393057i
\(611\) −8.24687 8.24687i −0.333633 0.333633i
\(612\) 18.7557 2.76581i 0.758153 0.111801i
\(613\) 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
\(615\) −16.4377 + 8.26528i −0.662833 + 0.333288i
\(616\) −1.82311 1.82311i −0.0734551 0.0734551i
\(617\) −14.1919 −0.571346 −0.285673 0.958327i \(-0.592217\pi\)
−0.285673 + 0.958327i \(0.592217\pi\)
\(618\) −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
\(621\) 7.82236 + 1.36761i 0.313901 + 0.0548804i
\(622\) 14.8367i 0.594899i
\(623\) −11.7365 + 11.7365i −0.470214 + 0.470214i
\(624\) 0.692337 + 1.37690i 0.0277157 + 0.0551200i
\(625\) −1.00000 −0.0400000
\(626\) 34.6390i 1.38445i
\(627\) 8.13483 + 16.1783i 0.324874 + 0.646099i
\(628\) 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 \(-0.815088\pi\)
0.835960 0.548791i \(-0.184912\pi\)
\(642\) −15.7675 + 7.92829i −0.622295 + 0.312905i
\(643\) −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 −0.881941 0.471359i \(-0.843764\pi\)
0.471359 + 0.881941i \(0.343764\pi\)
\(648\) 4.25609 7.93005i 0.167195 0.311522i
\(649\) 14.0601 + 14.0601i 0.551908 + 0.551908i
\(650\) −0.889790 −0.0349004
\(651\) −19.3197 + 9.71442i −0.757200 + 0.380738i
\(652\) 8.06627 8.06627i 0.315899 0.315899i
\(653\) −7.10309 + 7.10309i −0.277965 + 0.277965i −0.832296 0.554331i \(-0.812974\pi\)
0.554331 + 0.832296i \(0.312974\pi\)
\(654\) −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 \(-0.443582\pi\)
0.176317 + 0.984333i \(0.443582\pi\)
\(660\) −1.27906 2.54375i −0.0497873 0.0990154i
\(661\) −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
\(666\) 17.1862 + 6.13478i 0.665951 + 0.237718i
\(667\) −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
\(672\) 1.22039 + 2.42706i 0.0470774 + 0.0936260i
\(673\) −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 \(-0.477167\pi\)
0.0716710 + 0.997428i \(0.477167\pi\)
\(678\) −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
\(681\) 20.5339 10.3249i 0.786861 0.395653i
\(682\) 13.0852 0.501059
\(683\) 9.79474 + 9.79474i 0.374785 + 0.374785i 0.869217 0.494431i \(-0.164624\pi\)
−0.494431 + 0.869217i \(0.664624\pi\)
\(684\) −2.78354 18.8759i −0.106431 0.721738i
\(685\) 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
\(690\) −2.36488 + 1.18912i −0.0900293 + 0.0452689i
\(691\) 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 0.593727 0.804667i \(-0.297656\pi\)
−0.804667 + 0.593727i \(0.797656\pi\)
\(702\) 2.65741 + 3.78349i 0.100297 + 0.142799i
\(703\) 37.0026 11.2894i 1.39558 0.425786i
\(704\) 1.64384i 0.0619547i
\(705\) −10.1987 20.2829i −0.384107 0.763900i
\(706\) 6.17215i 0.232292i
\(707\) −7.60965 −0.286190
\(708\) −9.41181 18.7179i −0.353717 0.703462i
\(709\) −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
\(711\) 2.89356 0.426700i 0.108517 0.0160025i
\(712\) −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
\(717\) −4.67194 + 2.34916i −0.174477 + 0.0877311i
\(718\) −14.6826 14.6826i −0.547950 0.547950i
\(719\) 26.6215i 0.992813i −0.868090 0.496407i \(-0.834653\pi\)
0.868090 0.496407i \(-0.165347\pi\)
\(720\) 0.437662 + 2.96790i 0.0163107 + 0.110607i
\(721\) −11.6130 11.6130i −0.432492 0.432492i
\(722\) −15.1672 15.1672i −0.564466 0.564466i
\(723\) 13.6912 + 27.2286i 0.509182 + 1.01264i
\(724\) 1.37431i 0.0510759i
\(725\) −0.289296 0.289296i −0.0107442 0.0107442i
\(726\) −6.45642 12.8403i −0.239620 0.476549i
\(727\) −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
\(732\) −10.6823 21.2447i −0.394830 0.785225i
\(733\) 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
\(735\) 7.02540 3.53254i 0.259136 0.130300i
\(736\) −1.52825 −0.0563320
\(737\) 7.81253i 0.287778i
\(738\) −31.5266 + 4.64908i −1.16051 + 0.171135i
\(739\) 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 \(-0.718211\pi\)
−0.633083 + 0.774084i \(0.718211\pi\)
\(744\) −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
\(753\) −2.12720 4.23051i −0.0775196 0.154168i
\(754\) −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
\(759\) 3.88749 1.95472i 0.141107 0.0709519i
\(760\) 4.49720 + 4.49720i 0.163131 + 0.163131i
\(761\) 3.25195 0.117883 0.0589415 0.998261i \(-0.481227\pi\)
0.0589415 + 0.998261i \(0.481227\pi\)
\(762\) 8.89258 + 17.6853i 0.322144 + 0.640670i
\(763\) 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
\(771\) −0.00344669 + 0.00173308i −0.000124130 + 6.24153e-5i
\(772\) 10.3501 + 10.3501i 0.372508 + 0.372508i
\(773\) 14.0416i 0.505041i 0.967591 + 0.252521i \(0.0812596\pi\)
−0.967591 + 0.252521i \(0.918740\pi\)
\(774\) 2.11117 2.84152i 0.0758844 0.102136i
\(775\) 5.62866 5.62866i 0.202187 0.202187i
\(776\) −5.49755 −0.197350
\(777\) −11.9544 + 11.4084i −0.428862 + 0.409273i
\(778\) −31.1625 −1.11723