Properties

Label 1110.2.u.e.191.8
Level $1110$
Weight $2$
Character 1110.191
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 191.8
Character \(\chi\) \(=\) 1110.191
Dual form 1110.2.u.e.401.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.59695 + 0.670623i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.60342 + 0.655016i) q^{6} +3.28633 q^{7} +(0.707107 - 0.707107i) q^{8} +(2.10053 - 2.14191i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.59695 + 0.670623i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.60342 + 0.655016i) q^{6} +3.28633 q^{7} +(0.707107 - 0.707107i) q^{8} +(2.10053 - 2.14191i) q^{9} +1.00000 q^{10} -1.74571 q^{11} +(-0.670623 - 1.59695i) q^{12} +(-3.25667 - 3.25667i) q^{13} +(-2.32379 - 2.32379i) q^{14} +(0.655016 - 1.60342i) q^{15} -1.00000 q^{16} +(-1.24108 + 1.24108i) q^{17} +(-2.99986 + 0.0292590i) q^{18} +(0.258976 + 0.258976i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-5.24812 + 2.20389i) q^{21} +(1.23440 + 1.23440i) q^{22} +(1.64920 - 1.64920i) q^{23} +(-0.655016 + 1.60342i) q^{24} -1.00000i q^{25} +4.60563i q^{26} +(-1.91804 + 4.82920i) q^{27} +3.28633i q^{28} +(0.378286 + 0.378286i) q^{29} +(-1.59695 + 0.670623i) q^{30} +(3.64796 - 3.64796i) q^{31} +(0.707107 + 0.707107i) q^{32} +(2.78782 - 1.17071i) q^{33} +1.75515 q^{34} +(-2.32379 + 2.32379i) q^{35} +(2.14191 + 2.10053i) q^{36} +(-4.68494 + 3.87960i) q^{37} -0.366248i q^{38} +(7.38476 + 3.01676i) q^{39} +1.00000i q^{40} +9.92643 q^{41} +(5.26937 + 2.15260i) q^{42} +(-4.35358 - 4.35358i) q^{43} -1.74571i q^{44} +(0.0292590 + 2.99986i) q^{45} -2.33232 q^{46} -2.28468i q^{47} +(1.59695 - 0.670623i) q^{48} +3.79996 q^{49} +(-0.707107 + 0.707107i) q^{50} +(1.14965 - 2.81424i) q^{51} +(3.25667 - 3.25667i) q^{52} -9.35271i q^{53} +(4.77102 - 2.05850i) q^{54} +(1.23440 - 1.23440i) q^{55} +(2.32379 - 2.32379i) q^{56} +(-0.587249 - 0.239898i) q^{57} -0.534977i q^{58} +(-0.666775 + 0.666775i) q^{59} +(1.60342 + 0.655016i) q^{60} +(-0.134354 + 0.134354i) q^{61} -5.15899 q^{62} +(6.90303 - 7.03902i) q^{63} -1.00000i q^{64} +4.60563 q^{65} +(-2.79911 - 1.14347i) q^{66} -8.70321i q^{67} +(-1.24108 - 1.24108i) q^{68} +(-1.52770 + 3.73968i) q^{69} +3.28633 q^{70} -7.14239i q^{71} +(-0.0292590 - 2.99986i) q^{72} -13.7212i q^{73} +(6.05605 + 0.569464i) q^{74} +(0.670623 + 1.59695i) q^{75} +(-0.258976 + 0.258976i) q^{76} -5.73698 q^{77} +(-3.08864 - 7.35498i) q^{78} +(6.38622 + 6.38622i) q^{79} +(0.707107 - 0.707107i) q^{80} +(-0.175546 - 8.99829i) q^{81} +(-7.01905 - 7.01905i) q^{82} -14.6153i q^{83} +(-2.20389 - 5.24812i) q^{84} -1.75515i q^{85} +6.15689i q^{86} +(-0.857793 - 0.350418i) q^{87} +(-1.23440 + 1.23440i) q^{88} +(0.495164 + 0.495164i) q^{89} +(2.10053 - 2.14191i) q^{90} +(-10.7025 - 10.7025i) q^{91} +(1.64920 + 1.64920i) q^{92} +(-3.37922 + 8.27203i) q^{93} +(-1.61551 + 1.61551i) q^{94} -0.366248 q^{95} +(-1.60342 - 0.655016i) q^{96} +(4.16187 + 4.16187i) q^{97} +(-2.68698 - 2.68698i) q^{98} +(-3.66692 + 3.73915i) 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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) −1.59695 + 0.670623i −0.922002 + 0.387184i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) 1.60342 + 0.655016i 0.654593 + 0.267409i
\(7\) 3.28633 1.24212 0.621058 0.783765i \(-0.286703\pi\)
0.621058 + 0.783765i \(0.286703\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 2.10053 2.14191i 0.700177 0.713970i
\(10\) 1.00000 0.316228
\(11\) −1.74571 −0.526352 −0.263176 0.964748i \(-0.584770\pi\)
−0.263176 + 0.964748i \(0.584770\pi\)
\(12\) −0.670623 1.59695i −0.193592 0.461001i
\(13\) −3.25667 3.25667i −0.903238 0.903238i 0.0924765 0.995715i \(-0.470522\pi\)
−0.995715 + 0.0924765i \(0.970522\pi\)
\(14\) −2.32379 2.32379i −0.621058 0.621058i
\(15\) 0.655016 1.60342i 0.169124 0.414001i
\(16\) −1.00000 −0.250000
\(17\) −1.24108 + 1.24108i −0.301005 + 0.301005i −0.841407 0.540402i \(-0.818272\pi\)
0.540402 + 0.841407i \(0.318272\pi\)
\(18\) −2.99986 + 0.0292590i −0.707073 + 0.00689642i
\(19\) 0.258976 + 0.258976i 0.0594133 + 0.0594133i 0.736189 0.676776i \(-0.236623\pi\)
−0.676776 + 0.736189i \(0.736623\pi\)
\(20\) −0.707107 0.707107i −0.158114 0.158114i
\(21\) −5.24812 + 2.20389i −1.14523 + 0.480928i
\(22\) 1.23440 + 1.23440i 0.263176 + 0.263176i
\(23\) 1.64920 1.64920i 0.343881 0.343881i −0.513943 0.857824i \(-0.671816\pi\)
0.857824 + 0.513943i \(0.171816\pi\)
\(24\) −0.655016 + 1.60342i −0.133705 + 0.327297i
\(25\) 1.00000i 0.200000i
\(26\) 4.60563i 0.903238i
\(27\) −1.91804 + 4.82920i −0.369127 + 0.929379i
\(28\) 3.28633i 0.621058i
\(29\) 0.378286 + 0.378286i 0.0702459 + 0.0702459i 0.741357 0.671111i \(-0.234183\pi\)
−0.671111 + 0.741357i \(0.734183\pi\)
\(30\) −1.59695 + 0.670623i −0.291563 + 0.122438i
\(31\) 3.64796 3.64796i 0.655193 0.655193i −0.299046 0.954239i \(-0.596668\pi\)
0.954239 + 0.299046i \(0.0966683\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 2.78782 1.17071i 0.485297 0.203795i
\(34\) 1.75515 0.301005
\(35\) −2.32379 + 2.32379i −0.392792 + 0.392792i
\(36\) 2.14191 + 2.10053i 0.356985 + 0.350088i
\(37\) −4.68494 + 3.87960i −0.770200 + 0.637802i
\(38\) 0.366248i 0.0594133i
\(39\) 7.38476 + 3.01676i 1.18251 + 0.483068i
\(40\) 1.00000i 0.158114i
\(41\) 9.92643 1.55025 0.775124 0.631809i \(-0.217687\pi\)
0.775124 + 0.631809i \(0.217687\pi\)
\(42\) 5.26937 + 2.15260i 0.813081 + 0.332153i
\(43\) −4.35358 4.35358i −0.663914 0.663914i 0.292386 0.956300i \(-0.405551\pi\)
−0.956300 + 0.292386i \(0.905551\pi\)
\(44\) 1.74571i 0.263176i
\(45\) 0.0292590 + 2.99986i 0.00436168 + 0.447192i
\(46\) −2.33232 −0.343881
\(47\) 2.28468i 0.333255i −0.986020 0.166627i \(-0.946712\pi\)
0.986020 0.166627i \(-0.0532877\pi\)
\(48\) 1.59695 0.670623i 0.230501 0.0967961i
\(49\) 3.79996 0.542852
\(50\) −0.707107 + 0.707107i −0.100000 + 0.100000i
\(51\) 1.14965 2.81424i 0.160983 0.394072i
\(52\) 3.25667 3.25667i 0.451619 0.451619i
\(53\) 9.35271i 1.28469i −0.766414 0.642347i \(-0.777961\pi\)
0.766414 0.642347i \(-0.222039\pi\)
\(54\) 4.77102 2.05850i 0.649253 0.280126i
\(55\) 1.23440 1.23440i 0.166447 0.166447i
\(56\) 2.32379 2.32379i 0.310529 0.310529i
\(57\) −0.587249 0.239898i −0.0777831 0.0317753i
\(58\) 0.534977i 0.0702459i
\(59\) −0.666775 + 0.666775i −0.0868068 + 0.0868068i −0.749177 0.662370i \(-0.769551\pi\)
0.662370 + 0.749177i \(0.269551\pi\)
\(60\) 1.60342 + 0.655016i 0.207001 + 0.0845622i
\(61\) −0.134354 + 0.134354i −0.0172022 + 0.0172022i −0.715656 0.698453i \(-0.753872\pi\)
0.698453 + 0.715656i \(0.253872\pi\)
\(62\) −5.15899 −0.655193
\(63\) 6.90303 7.03902i 0.869701 0.886833i
\(64\) 1.00000i 0.125000i
\(65\) 4.60563 0.571258
\(66\) −2.79911 1.14347i −0.344546 0.140751i
\(67\) 8.70321i 1.06327i −0.846975 0.531633i \(-0.821579\pi\)
0.846975 0.531633i \(-0.178421\pi\)
\(68\) −1.24108 1.24108i −0.150503 0.150503i
\(69\) −1.52770 + 3.73968i −0.183914 + 0.450205i
\(70\) 3.28633 0.392792
\(71\) 7.14239i 0.847645i −0.905745 0.423823i \(-0.860688\pi\)
0.905745 0.423823i \(-0.139312\pi\)
\(72\) −0.0292590 2.99986i −0.00344821 0.353537i
\(73\) 13.7212i 1.60595i −0.596014 0.802974i \(-0.703250\pi\)
0.596014 0.802974i \(-0.296750\pi\)
\(74\) 6.05605 + 0.569464i 0.704001 + 0.0661988i
\(75\) 0.670623 + 1.59695i 0.0774368 + 0.184400i
\(76\) −0.258976 + 0.258976i −0.0297066 + 0.0297066i
\(77\) −5.73698 −0.653790
\(78\) −3.08864 7.35498i −0.349720 0.832788i
\(79\) 6.38622 + 6.38622i 0.718506 + 0.718506i 0.968299 0.249793i \(-0.0803627\pi\)
−0.249793 + 0.968299i \(0.580363\pi\)
\(80\) 0.707107 0.707107i 0.0790569 0.0790569i
\(81\) −0.175546 8.99829i −0.0195051 0.999810i
\(82\) −7.01905 7.01905i −0.775124 0.775124i
\(83\) 14.6153i 1.60423i −0.597166 0.802117i \(-0.703707\pi\)
0.597166 0.802117i \(-0.296293\pi\)
\(84\) −2.20389 5.24812i −0.240464 0.572617i
\(85\) 1.75515i 0.190373i
\(86\) 6.15689i 0.663914i
\(87\) −0.857793 0.350418i −0.0919650 0.0375688i
\(88\) −1.23440 + 1.23440i −0.131588 + 0.131588i
\(89\) 0.495164 + 0.495164i 0.0524872 + 0.0524872i 0.732863 0.680376i \(-0.238184\pi\)
−0.680376 + 0.732863i \(0.738184\pi\)
\(90\) 2.10053 2.14191i 0.221415 0.225777i
\(91\) −10.7025 10.7025i −1.12193 1.12193i
\(92\) 1.64920 + 1.64920i 0.171941 + 0.171941i
\(93\) −3.37922 + 8.27203i −0.350409 + 0.857770i
\(94\) −1.61551 + 1.61551i −0.166627 + 0.166627i
\(95\) −0.366248 −0.0375762
\(96\) −1.60342 0.655016i −0.163648 0.0668523i
\(97\) 4.16187 + 4.16187i 0.422573 + 0.422573i 0.886089 0.463515i \(-0.153412\pi\)
−0.463515 + 0.886089i \(0.653412\pi\)
\(98\) −2.68698 2.68698i −0.271426 0.271426i
\(99\) −3.66692 + 3.73915i −0.368539 + 0.375799i
\(100\) 1.00000 0.100000
\(101\) 18.6620 1.85694 0.928471 0.371406i \(-0.121124\pi\)
0.928471 + 0.371406i \(0.121124\pi\)
\(102\) −2.80289 + 1.17704i −0.277528 + 0.116545i
\(103\) 6.60999 6.60999i 0.651301 0.651301i −0.302005 0.953306i \(-0.597656\pi\)
0.953306 + 0.302005i \(0.0976559\pi\)
\(104\) −4.60563 −0.451619
\(105\) 2.15260 5.26937i 0.210072 0.514237i
\(106\) −6.61336 + 6.61336i −0.642347 + 0.642347i
\(107\) 10.8073i 1.04479i −0.852705 0.522393i \(-0.825040\pi\)
0.852705 0.522393i \(-0.174960\pi\)
\(108\) −4.82920 1.91804i −0.464690 0.184563i
\(109\) 8.67304 + 8.67304i 0.830726 + 0.830726i 0.987616 0.156890i \(-0.0501467\pi\)
−0.156890 + 0.987616i \(0.550147\pi\)
\(110\) −1.74571 −0.166447
\(111\) 4.87990 9.33738i 0.463179 0.886265i
\(112\) −3.28633 −0.310529
\(113\) 11.6207 + 11.6207i 1.09318 + 1.09318i 0.995187 + 0.0979919i \(0.0312419\pi\)
0.0979919 + 0.995187i \(0.468758\pi\)
\(114\) 0.245614 + 0.584882i 0.0230039 + 0.0547792i
\(115\) 2.33232i 0.217490i
\(116\) −0.378286 + 0.378286i −0.0351230 + 0.0351230i
\(117\) −13.8162 + 0.134756i −1.27731 + 0.0124582i
\(118\) 0.942963 0.0868068
\(119\) −4.07859 + 4.07859i −0.373884 + 0.373884i
\(120\) −0.670623 1.59695i −0.0612192 0.145781i
\(121\) −7.95249 −0.722954
\(122\) 0.190005 0.0172022
\(123\) −15.8521 + 6.65689i −1.42933 + 0.600231i
\(124\) 3.64796 + 3.64796i 0.327597 + 0.327597i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) −9.85852 + 0.0961548i −0.878267 + 0.00856615i
\(127\) −8.70788 −0.772700 −0.386350 0.922352i \(-0.626264\pi\)
−0.386350 + 0.922352i \(0.626264\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 9.87207 + 4.03286i 0.869188 + 0.355073i
\(130\) −3.25667 3.25667i −0.285629 0.285629i
\(131\) 7.38432 + 7.38432i 0.645171 + 0.645171i 0.951822 0.306651i \(-0.0992084\pi\)
−0.306651 + 0.951822i \(0.599208\pi\)
\(132\) 1.17071 + 2.78782i 0.101898 + 0.242649i
\(133\) 0.851082 + 0.851082i 0.0737982 + 0.0737982i
\(134\) −6.15410 + 6.15410i −0.531633 + 0.531633i
\(135\) −2.05850 4.77102i −0.177167 0.410624i
\(136\) 1.75515i 0.150503i
\(137\) 9.66267i 0.825537i 0.910836 + 0.412769i \(0.135438\pi\)
−0.910836 + 0.412769i \(0.864562\pi\)
\(138\) 3.72460 1.56410i 0.317059 0.133145i
\(139\) 9.40917i 0.798076i −0.916934 0.399038i \(-0.869344\pi\)
0.916934 0.399038i \(-0.130656\pi\)
\(140\) −2.32379 2.32379i −0.196396 0.196396i
\(141\) 1.53216 + 3.64853i 0.129031 + 0.307262i
\(142\) −5.05043 + 5.05043i −0.423823 + 0.423823i
\(143\) 5.68521 + 5.68521i 0.475421 + 0.475421i
\(144\) −2.10053 + 2.14191i −0.175044 + 0.178492i
\(145\) −0.534977 −0.0444274
\(146\) −9.70237 + 9.70237i −0.802974 + 0.802974i
\(147\) −6.06837 + 2.54834i −0.500511 + 0.210184i
\(148\) −3.87960 4.68494i −0.318901 0.385100i
\(149\) 7.23397i 0.592630i −0.955090 0.296315i \(-0.904242\pi\)
0.955090 0.296315i \(-0.0957578\pi\)
\(150\) 0.655016 1.60342i 0.0534818 0.130919i
\(151\) 15.0674i 1.22617i −0.790018 0.613084i \(-0.789929\pi\)
0.790018 0.613084i \(-0.210071\pi\)
\(152\) 0.366248 0.0297066
\(153\) 0.0513539 + 5.26519i 0.00415172 + 0.425666i
\(154\) 4.05666 + 4.05666i 0.326895 + 0.326895i
\(155\) 5.15899i 0.414380i
\(156\) −3.01676 + 7.38476i −0.241534 + 0.591254i
\(157\) 8.06347 0.643535 0.321768 0.946819i \(-0.395723\pi\)
0.321768 + 0.946819i \(0.395723\pi\)
\(158\) 9.03148i 0.718506i
\(159\) 6.27214 + 14.9359i 0.497413 + 1.18449i
\(160\) −1.00000 −0.0790569
\(161\) 5.41980 5.41980i 0.427140 0.427140i
\(162\) −6.23862 + 6.48688i −0.490152 + 0.509657i
\(163\) 2.23140 2.23140i 0.174777 0.174777i −0.614298 0.789074i \(-0.710561\pi\)
0.789074 + 0.614298i \(0.210561\pi\)
\(164\) 9.92643i 0.775124i
\(165\) −1.14347 + 2.79911i −0.0890189 + 0.217910i
\(166\) −10.3346 + 10.3346i −0.802117 + 0.802117i
\(167\) −0.575837 + 0.575837i −0.0445596 + 0.0445596i −0.729035 0.684476i \(-0.760031\pi\)
0.684476 + 0.729035i \(0.260031\pi\)
\(168\) −2.15260 + 5.26937i −0.166077 + 0.406540i
\(169\) 8.21183i 0.631679i
\(170\) −1.24108 + 1.24108i −0.0951863 + 0.0951863i
\(171\) 1.09869 0.0107161i 0.0840191 0.000819478i
\(172\) 4.35358 4.35358i 0.331957 0.331957i
\(173\) −16.6885 −1.26880 −0.634400 0.773005i \(-0.718753\pi\)
−0.634400 + 0.773005i \(0.718753\pi\)
\(174\) 0.358768 + 0.854334i 0.0271981 + 0.0647669i
\(175\) 3.28633i 0.248423i
\(176\) 1.74571 0.131588
\(177\) 0.617655 1.51196i 0.0464258 0.113646i
\(178\) 0.700267i 0.0524872i
\(179\) 0.0776850 + 0.0776850i 0.00580645 + 0.00580645i 0.710004 0.704198i \(-0.248693\pi\)
−0.704198 + 0.710004i \(0.748693\pi\)
\(180\) −2.99986 + 0.0292590i −0.223596 + 0.00218084i
\(181\) 14.4452 1.07370 0.536852 0.843677i \(-0.319614\pi\)
0.536852 + 0.843677i \(0.319614\pi\)
\(182\) 15.1356i 1.12193i
\(183\) 0.124456 0.304657i 0.00920006 0.0225209i
\(184\) 2.33232i 0.171941i
\(185\) 0.569464 6.05605i 0.0418678 0.445249i
\(186\) 8.23868 3.45974i 0.604090 0.253680i
\(187\) 2.16656 2.16656i 0.158435 0.158435i
\(188\) 2.28468 0.166627
\(189\) −6.30331 + 15.8703i −0.458498 + 1.15440i
\(190\) 0.258976 + 0.258976i 0.0187881 + 0.0187881i
\(191\) −8.90023 + 8.90023i −0.643998 + 0.643998i −0.951536 0.307538i \(-0.900495\pi\)
0.307538 + 0.951536i \(0.400495\pi\)
\(192\) 0.670623 + 1.59695i 0.0483980 + 0.115250i
\(193\) −14.5654 14.5654i −1.04844 1.04844i −0.998765 0.0496763i \(-0.984181\pi\)
−0.0496763 0.998765i \(-0.515819\pi\)
\(194\) 5.88577i 0.422573i
\(195\) −7.35498 + 3.08864i −0.526701 + 0.221182i
\(196\) 3.79996i 0.271426i
\(197\) 3.22806i 0.229990i −0.993366 0.114995i \(-0.963315\pi\)
0.993366 0.114995i \(-0.0366851\pi\)
\(198\) 5.23688 0.0510778i 0.372169 0.00362994i
\(199\) 15.7523 15.7523i 1.11665 1.11665i 0.124424 0.992229i \(-0.460292\pi\)
0.992229 0.124424i \(-0.0397081\pi\)
\(200\) −0.707107 0.707107i −0.0500000 0.0500000i
\(201\) 5.83657 + 13.8986i 0.411680 + 0.980334i
\(202\) −13.1960 13.1960i −0.928471 0.928471i
\(203\) 1.24317 + 1.24317i 0.0872536 + 0.0872536i
\(204\) 2.81424 + 1.14965i 0.197036 + 0.0804916i
\(205\) −7.01905 + 7.01905i −0.490231 + 0.490231i
\(206\) −9.34793 −0.651301
\(207\) −0.0682413 6.99661i −0.00474310 0.486298i
\(208\) 3.25667 + 3.25667i 0.225810 + 0.225810i
\(209\) −0.452098 0.452098i −0.0312723 0.0312723i
\(210\) −5.24812 + 2.20389i −0.362155 + 0.152083i
\(211\) −13.6945 −0.942766 −0.471383 0.881929i \(-0.656245\pi\)
−0.471383 + 0.881929i \(0.656245\pi\)
\(212\) 9.35271 0.642347
\(213\) 4.78985 + 11.4061i 0.328195 + 0.781531i
\(214\) −7.64195 + 7.64195i −0.522393 + 0.522393i
\(215\) 6.15689 0.419896
\(216\) 2.05850 + 4.77102i 0.140063 + 0.324626i
\(217\) 11.9884 11.9884i 0.813826 0.813826i
\(218\) 12.2655i 0.830726i
\(219\) 9.20176 + 21.9122i 0.621798 + 1.48069i
\(220\) 1.23440 + 1.23440i 0.0832235 + 0.0832235i
\(221\) 8.08356 0.543759
\(222\) −10.0531 + 3.15192i −0.674722 + 0.211543i
\(223\) −17.3050 −1.15883 −0.579413 0.815034i \(-0.696718\pi\)
−0.579413 + 0.815034i \(0.696718\pi\)
\(224\) 2.32379 + 2.32379i 0.155264 + 0.155264i
\(225\) −2.14191 2.10053i −0.142794 0.140035i
\(226\) 16.4341i 1.09318i
\(227\) −0.729623 + 0.729623i −0.0484268 + 0.0484268i −0.730905 0.682479i \(-0.760902\pi\)
0.682479 + 0.730905i \(0.260902\pi\)
\(228\) 0.239898 0.587249i 0.0158876 0.0388915i
\(229\) 18.8546 1.24595 0.622973 0.782243i \(-0.285925\pi\)
0.622973 + 0.782243i \(0.285925\pi\)
\(230\) 1.64920 1.64920i 0.108745 0.108745i
\(231\) 9.16170 3.84735i 0.602796 0.253137i
\(232\) 0.534977 0.0351230
\(233\) 3.88220 0.254332 0.127166 0.991881i \(-0.459412\pi\)
0.127166 + 0.991881i \(0.459412\pi\)
\(234\) 9.86484 + 9.67426i 0.644885 + 0.632426i
\(235\) 1.61551 + 1.61551i 0.105384 + 0.105384i
\(236\) −0.666775 0.666775i −0.0434034 0.0434034i
\(237\) −14.4813 5.91576i −0.940658 0.384270i
\(238\) 5.76799 0.373884
\(239\) −8.52789 + 8.52789i −0.551623 + 0.551623i −0.926909 0.375286i \(-0.877545\pi\)
0.375286 + 0.926909i \(0.377545\pi\)
\(240\) −0.655016 + 1.60342i −0.0422811 + 0.103500i
\(241\) 14.3656 + 14.3656i 0.925369 + 0.925369i 0.997402 0.0720330i \(-0.0229487\pi\)
−0.0720330 + 0.997402i \(0.522949\pi\)
\(242\) 5.62326 + 5.62326i 0.361477 + 0.361477i
\(243\) 6.31480 + 14.2521i 0.405094 + 0.914275i
\(244\) −0.134354 0.134354i −0.00860111 0.00860111i
\(245\) −2.68698 + 2.68698i −0.171665 + 0.171665i
\(246\) 15.9162 + 6.50197i 1.01478 + 0.414550i
\(247\) 1.68680i 0.107329i
\(248\) 5.15899i 0.327597i
\(249\) 9.80134 + 23.3399i 0.621134 + 1.47911i
\(250\) 1.00000i 0.0632456i
\(251\) −13.7487 13.7487i −0.867811 0.867811i 0.124418 0.992230i \(-0.460294\pi\)
−0.992230 + 0.124418i \(0.960294\pi\)
\(252\) 7.03902 + 6.90303i 0.443416 + 0.434850i
\(253\) −2.87902 + 2.87902i −0.181002 + 0.181002i
\(254\) 6.15740 + 6.15740i 0.386350 + 0.386350i
\(255\) 1.17704 + 2.80289i 0.0737092 + 0.175524i
\(256\) 1.00000 0.0625000
\(257\) −14.8299 + 14.8299i −0.925062 + 0.925062i −0.997382 0.0723195i \(-0.976960\pi\)
0.0723195 + 0.997382i \(0.476960\pi\)
\(258\) −4.12895 9.83227i −0.257057 0.612131i
\(259\) −15.3963 + 12.7496i −0.956678 + 0.792224i
\(260\) 4.60563i 0.285629i
\(261\) 1.60485 0.0156529i 0.0993380 0.000968891i
\(262\) 10.4430i 0.645171i
\(263\) 9.08600 0.560267 0.280134 0.959961i \(-0.409621\pi\)
0.280134 + 0.959961i \(0.409621\pi\)
\(264\) 1.14347 2.79911i 0.0703756 0.172273i
\(265\) 6.61336 + 6.61336i 0.406256 + 0.406256i
\(266\) 1.20361i 0.0737982i
\(267\) −1.12282 0.458686i −0.0687156 0.0280711i
\(268\) 8.70321 0.531633
\(269\) 19.1471i 1.16742i −0.811962 0.583710i \(-0.801601\pi\)
0.811962 0.583710i \(-0.198399\pi\)
\(270\) −1.91804 + 4.82920i −0.116728 + 0.293895i
\(271\) −29.7365 −1.80636 −0.903180 0.429261i \(-0.858774\pi\)
−0.903180 + 0.429261i \(0.858774\pi\)
\(272\) 1.24108 1.24108i 0.0752513 0.0752513i
\(273\) 24.2687 + 9.91407i 1.46881 + 0.600027i
\(274\) 6.83254 6.83254i 0.412769 0.412769i
\(275\) 1.74571i 0.105270i
\(276\) −3.73968 1.52770i −0.225102 0.0919569i
\(277\) −0.963857 + 0.963857i −0.0579126 + 0.0579126i −0.735470 0.677557i \(-0.763039\pi\)
0.677557 + 0.735470i \(0.263039\pi\)
\(278\) −6.65329 + 6.65329i −0.399038 + 0.399038i
\(279\) −0.150947 15.4762i −0.00903697 0.926539i
\(280\) 3.28633i 0.196396i
\(281\) −14.7139 + 14.7139i −0.877757 + 0.877757i −0.993302 0.115546i \(-0.963138\pi\)
0.115546 + 0.993302i \(0.463138\pi\)
\(282\) 1.49650 3.66330i 0.0891153 0.218146i
\(283\) 0.747604 0.747604i 0.0444404 0.0444404i −0.684537 0.728978i \(-0.739996\pi\)
0.728978 + 0.684537i \(0.239996\pi\)
\(284\) 7.14239 0.423823
\(285\) 0.584882 0.245614i 0.0346454 0.0145489i
\(286\) 8.04010i 0.475421i
\(287\) 32.6215 1.92559
\(288\) 2.99986 0.0292590i 0.176768 0.00172411i
\(289\) 13.9195i 0.818792i
\(290\) 0.378286 + 0.378286i 0.0222137 + 0.0222137i
\(291\) −9.43736 3.85527i −0.553228 0.226000i
\(292\) 13.7212 0.802974
\(293\) 27.9875i 1.63505i 0.575893 + 0.817525i \(0.304654\pi\)
−0.575893 + 0.817525i \(0.695346\pi\)
\(294\) 6.09293 + 2.48904i 0.355347 + 0.145163i
\(295\) 0.942963i 0.0549014i
\(296\) −0.569464 + 6.05605i −0.0330994 + 0.352001i
\(297\) 3.34834 8.43038i 0.194290 0.489180i
\(298\) −5.11519 + 5.11519i −0.296315 + 0.296315i
\(299\) −10.7418 −0.621213
\(300\) −1.59695 + 0.670623i −0.0922002 + 0.0387184i
\(301\) −14.3073 14.3073i −0.824658 0.824658i
\(302\) −10.6543 + 10.6543i −0.613084 + 0.613084i
\(303\) −29.8024 + 12.5152i −1.71210 + 0.718978i
\(304\) −0.258976 0.258976i −0.0148533 0.0148533i
\(305\) 0.190005i 0.0108796i
\(306\) 3.68674 3.75937i 0.210757 0.214909i
\(307\) 3.09733i 0.176774i −0.996086 0.0883870i \(-0.971829\pi\)
0.996086 0.0883870i \(-0.0281712\pi\)
\(308\) 5.73698i 0.326895i
\(309\) −6.12304 + 14.9887i −0.348328 + 0.852675i
\(310\) 3.64796 3.64796i 0.207190 0.207190i
\(311\) −6.12907 6.12907i −0.347548 0.347548i 0.511648 0.859195i \(-0.329035\pi\)
−0.859195 + 0.511648i \(0.829035\pi\)
\(312\) 7.35498 3.08864i 0.416394 0.174860i
\(313\) −14.4360 14.4360i −0.815969 0.815969i 0.169552 0.985521i \(-0.445768\pi\)
−0.985521 + 0.169552i \(0.945768\pi\)
\(314\) −5.70174 5.70174i −0.321768 0.321768i
\(315\) 0.0961548 + 9.85852i 0.00541771 + 0.555465i
\(316\) −6.38622 + 6.38622i −0.359253 + 0.359253i
\(317\) −16.7549 −0.941048 −0.470524 0.882387i \(-0.655935\pi\)
−0.470524 + 0.882387i \(0.655935\pi\)
\(318\) 6.12617 14.9963i 0.343539 0.840952i
\(319\) −0.660378 0.660378i −0.0369741 0.0369741i
\(320\) 0.707107 + 0.707107i 0.0395285 + 0.0395285i
\(321\) 7.24765 + 17.2588i 0.404524 + 0.963294i
\(322\) −7.66476 −0.427140
\(323\) −0.642819 −0.0357674
\(324\) 8.99829 0.175546i 0.499905 0.00975255i
\(325\) −3.25667 + 3.25667i −0.180648 + 0.180648i
\(326\) −3.15568 −0.174777
\(327\) −19.6668 8.03411i −1.08758 0.444288i
\(328\) 7.01905 7.01905i 0.387562 0.387562i
\(329\) 7.50821i 0.413941i
\(330\) 2.78782 1.17071i 0.153465 0.0644457i
\(331\) 2.35068 + 2.35068i 0.129205 + 0.129205i 0.768752 0.639547i \(-0.220878\pi\)
−0.639547 + 0.768752i \(0.720878\pi\)
\(332\) 14.6153 0.802117
\(333\) −1.53112 + 18.1839i −0.0839047 + 0.996474i
\(334\) 0.814356 0.0445596
\(335\) 6.15410 + 6.15410i 0.336234 + 0.336234i
\(336\) 5.24812 2.20389i 0.286308 0.120232i
\(337\) 7.13984i 0.388932i 0.980909 + 0.194466i \(0.0622974\pi\)
−0.980909 + 0.194466i \(0.937703\pi\)
\(338\) 5.80664 5.80664i 0.315840 0.315840i
\(339\) −26.3507 10.7646i −1.43118 0.584652i
\(340\) 1.75515 0.0951863
\(341\) −6.36828 + 6.36828i −0.344862 + 0.344862i
\(342\) −0.784470 0.769315i −0.0424193 0.0415998i
\(343\) −10.5164 −0.567831
\(344\) −6.15689 −0.331957
\(345\) −1.56410 3.72460i −0.0842085 0.200526i
\(346\) 11.8005 + 11.8005i 0.634400 + 0.634400i
\(347\) 21.1695 + 21.1695i 1.13644 + 1.13644i 0.989084 + 0.147356i \(0.0470762\pi\)
0.147356 + 0.989084i \(0.452924\pi\)
\(348\) 0.350418 0.857793i 0.0187844 0.0459825i
\(349\) 6.55526 0.350895 0.175447 0.984489i \(-0.443863\pi\)
0.175447 + 0.984489i \(0.443863\pi\)
\(350\) −2.32379 + 2.32379i −0.124212 + 0.124212i
\(351\) 21.9735 9.48068i 1.17286 0.506041i
\(352\) −1.23440 1.23440i −0.0657939 0.0657939i
\(353\) 4.68774 + 4.68774i 0.249503 + 0.249503i 0.820767 0.571264i \(-0.193547\pi\)
−0.571264 + 0.820767i \(0.693547\pi\)
\(354\) −1.50587 + 0.632372i −0.0800360 + 0.0336102i
\(355\) 5.05043 + 5.05043i 0.268049 + 0.268049i
\(356\) −0.495164 + 0.495164i −0.0262436 + 0.0262436i
\(357\) 3.77813 9.24852i 0.199960 0.489483i
\(358\) 0.109863i 0.00580645i
\(359\) 13.7603i 0.726242i −0.931742 0.363121i \(-0.881711\pi\)
0.931742 0.363121i \(-0.118289\pi\)
\(360\) 2.14191 + 2.10053i 0.112889 + 0.110708i
\(361\) 18.8659i 0.992940i
\(362\) −10.2143 10.2143i −0.536852 0.536852i
\(363\) 12.6998 5.33312i 0.666565 0.279916i
\(364\) 10.7025 10.7025i 0.560963 0.560963i
\(365\) 9.70237 + 9.70237i 0.507845 + 0.507845i
\(366\) −0.303429 + 0.127422i −0.0158605 + 0.00666043i
\(367\) 22.8151 1.19094 0.595468 0.803379i \(-0.296966\pi\)
0.595468 + 0.803379i \(0.296966\pi\)
\(368\) −1.64920 + 1.64920i −0.0859703 + 0.0859703i
\(369\) 20.8508 21.2615i 1.08545 1.10683i
\(370\) −4.68494 + 3.87960i −0.243559 + 0.201691i
\(371\) 30.7361i 1.59574i
\(372\) −8.27203 3.37922i −0.428885 0.175205i
\(373\) 33.4109i 1.72995i 0.501813 + 0.864976i \(0.332667\pi\)
−0.501813 + 0.864976i \(0.667333\pi\)
\(374\) −3.06398 −0.158435
\(375\) −1.60342 0.655016i −0.0828002 0.0338249i
\(376\) −1.61551 1.61551i −0.0833137 0.0833137i
\(377\) 2.46391i 0.126898i
\(378\) 15.6791 6.76490i 0.806447 0.347949i
\(379\) 17.5721 0.902618 0.451309 0.892368i \(-0.350957\pi\)
0.451309 + 0.892368i \(0.350957\pi\)
\(380\) 0.366248i 0.0187881i
\(381\) 13.9061 5.83970i 0.712431 0.299177i
\(382\) 12.5868 0.643998
\(383\) 10.0177 10.0177i 0.511883 0.511883i −0.403220 0.915103i \(-0.632109\pi\)
0.915103 + 0.403220i \(0.132109\pi\)
\(384\) 0.655016 1.60342i 0.0334261 0.0818242i
\(385\) 4.05666 4.05666i 0.206746 0.206746i
\(386\) 20.5986i 1.04844i
\(387\) −18.4698 + 0.180145i −0.938872 + 0.00915726i
\(388\) −4.16187 + 4.16187i −0.211287 + 0.211287i
\(389\) 0.842156 0.842156i 0.0426990 0.0426990i −0.685435 0.728134i \(-0.740388\pi\)
0.728134 + 0.685435i \(0.240388\pi\)
\(390\) 7.38476 + 3.01676i 0.373942 + 0.152760i
\(391\) 4.09356i 0.207020i
\(392\) 2.68698 2.68698i 0.135713 0.135713i
\(393\) −16.7445 6.84034i −0.844650 0.345049i
\(394\) −2.28258 + 2.28258i −0.114995 + 0.114995i
\(395\) −9.03148 −0.454423
\(396\) −3.73915 3.66692i −0.187900 0.184270i
\(397\) 7.83011i 0.392982i 0.980506 + 0.196491i \(0.0629546\pi\)
−0.980506 + 0.196491i \(0.937045\pi\)
\(398\) −22.2772 −1.11665
\(399\) −1.92989 0.788385i −0.0966156 0.0394686i
\(400\) 1.00000i 0.0500000i
\(401\) −13.4140 13.4140i −0.669863 0.669863i 0.287821 0.957684i \(-0.407069\pi\)
−0.957684 + 0.287821i \(0.907069\pi\)
\(402\) 5.70074 13.9549i 0.284327 0.696007i
\(403\) −23.7604 −1.18359
\(404\) 18.6620i 0.928471i
\(405\) 6.48688 + 6.23862i 0.322336 + 0.310000i
\(406\) 1.75811i 0.0872536i
\(407\) 8.17856 6.77266i 0.405396 0.335708i
\(408\) −1.17704 2.80289i −0.0582723 0.138764i
\(409\) −6.10615 + 6.10615i −0.301930 + 0.301930i −0.841768 0.539839i \(-0.818485\pi\)
0.539839 + 0.841768i \(0.318485\pi\)
\(410\) 9.92643 0.490231
\(411\) −6.48001 15.4308i −0.319635 0.761147i
\(412\) 6.60999 + 6.60999i 0.325651 + 0.325651i
\(413\) −2.19124 + 2.19124i −0.107824 + 0.107824i
\(414\) −4.89910 + 4.99561i −0.240778 + 0.245521i
\(415\) 10.3346 + 10.3346i 0.507304 + 0.507304i
\(416\) 4.60563i 0.225810i
\(417\) 6.31001 + 15.0260i 0.309002 + 0.735828i
\(418\) 0.639363i 0.0312723i
\(419\) 10.4867i 0.512308i 0.966636 + 0.256154i \(0.0824554\pi\)
−0.966636 + 0.256154i \(0.917545\pi\)
\(420\) 5.26937 + 2.15260i 0.257119 + 0.105036i
\(421\) −23.4161 + 23.4161i −1.14123 + 1.14123i −0.153004 + 0.988226i \(0.548895\pi\)
−0.988226 + 0.153004i \(0.951105\pi\)
\(422\) 9.68345 + 9.68345i 0.471383 + 0.471383i
\(423\) −4.89357 4.79904i −0.237934 0.233337i
\(424\) −6.61336 6.61336i −0.321173 0.321173i
\(425\) 1.24108 + 1.24108i 0.0602011 + 0.0602011i
\(426\) 4.67838 11.4522i 0.226668 0.554863i
\(427\) −0.441531 + 0.441531i −0.0213672 + 0.0213672i
\(428\) 10.8073 0.522393
\(429\) −12.8917 5.26639i −0.622415 0.254264i
\(430\) −4.35358 4.35358i −0.209948 0.209948i
\(431\) −17.7076 17.7076i −0.852946 0.852946i 0.137549 0.990495i \(-0.456077\pi\)
−0.990495 + 0.137549i \(0.956077\pi\)
\(432\) 1.91804 4.82920i 0.0922817 0.232345i
\(433\) 6.23639 0.299702 0.149851 0.988709i \(-0.452121\pi\)
0.149851 + 0.988709i \(0.452121\pi\)
\(434\) −16.9542 −0.813826
\(435\) 0.854334 0.358768i 0.0409622 0.0172016i
\(436\) −8.67304 + 8.67304i −0.415363 + 0.415363i
\(437\) 0.854206 0.0408622
\(438\) 8.98762 22.0009i 0.429445 1.05124i
\(439\) 4.50777 4.50777i 0.215144 0.215144i −0.591304 0.806449i \(-0.701387\pi\)
0.806449 + 0.591304i \(0.201387\pi\)
\(440\) 1.74571i 0.0832235i
\(441\) 7.98194 8.13917i 0.380092 0.387580i
\(442\) −5.71594 5.71594i −0.271880 0.271880i
\(443\) −13.6288 −0.647524 −0.323762 0.946139i \(-0.604948\pi\)
−0.323762 + 0.946139i \(0.604948\pi\)
\(444\) 9.33738 + 4.87990i 0.443132 + 0.231590i
\(445\) −0.700267 −0.0331958
\(446\) 12.2365 + 12.2365i 0.579413 + 0.579413i
\(447\) 4.85127 + 11.5523i 0.229457 + 0.546406i
\(448\) 3.28633i 0.155264i
\(449\) −7.59604 + 7.59604i −0.358479 + 0.358479i −0.863252 0.504773i \(-0.831576\pi\)
0.504773 + 0.863252i \(0.331576\pi\)
\(450\) 0.0292590 + 2.99986i 0.00137928 + 0.141415i
\(451\) −17.3287 −0.815975
\(452\) −11.6207 + 11.6207i −0.546590 + 0.546590i
\(453\) 10.1045 + 24.0620i 0.474753 + 1.13053i
\(454\) 1.03184 0.0484268
\(455\) 15.1356 0.709569
\(456\) −0.584882 + 0.245614i −0.0273896 + 0.0115019i
\(457\) 11.5653 + 11.5653i 0.541001 + 0.541001i 0.923822 0.382822i \(-0.125048\pi\)
−0.382822 + 0.923822i \(0.625048\pi\)
\(458\) −13.3322 13.3322i −0.622973 0.622973i
\(459\) −3.61297 8.37384i −0.168639 0.390857i
\(460\) −2.33232 −0.108745
\(461\) 15.5874 15.5874i 0.725979 0.725979i −0.243837 0.969816i \(-0.578406\pi\)
0.969816 + 0.243837i \(0.0784062\pi\)
\(462\) −9.19879 3.75781i −0.427966 0.174829i
\(463\) −10.8674 10.8674i −0.505049 0.505049i 0.407954 0.913003i \(-0.366243\pi\)
−0.913003 + 0.407954i \(0.866243\pi\)
\(464\) −0.378286 0.378286i −0.0175615 0.0175615i
\(465\) −3.45974 8.23868i −0.160442 0.382060i
\(466\) −2.74513 2.74513i −0.127166 0.127166i
\(467\) 24.9944 24.9944i 1.15660 1.15660i 0.171404 0.985201i \(-0.445170\pi\)
0.985201 0.171404i \(-0.0548303\pi\)
\(468\) −0.134756 13.8162i −0.00622911 0.638656i
\(469\) 28.6016i 1.32070i
\(470\) 2.28468i 0.105384i
\(471\) −12.8770 + 5.40755i −0.593341 + 0.249167i
\(472\) 0.942963i 0.0434034i
\(473\) 7.60009 + 7.60009i 0.349452 + 0.349452i
\(474\) 6.05672 + 14.4229i 0.278194 + 0.662464i
\(475\) 0.258976 0.258976i 0.0118827 0.0118827i
\(476\) −4.07859 4.07859i −0.186942 0.186942i
\(477\) −20.0327 19.6457i −0.917232 0.899513i
\(478\) 12.0603 0.551623
\(479\) 10.7474 10.7474i 0.491062 0.491062i −0.417579 0.908641i \(-0.637121\pi\)
0.908641 + 0.417579i \(0.137121\pi\)
\(480\) 1.59695 0.670623i 0.0728907 0.0306096i
\(481\) 27.8919 + 2.62274i 1.27176 + 0.119587i
\(482\) 20.3160i 0.925369i
\(483\) −5.02054 + 12.2898i −0.228442 + 0.559206i
\(484\) 7.95249i 0.361477i
\(485\) −5.88577 −0.267259
\(486\) 5.61255 14.5430i 0.254590 0.659685i
\(487\) 5.16144 + 5.16144i 0.233887 + 0.233887i 0.814313 0.580426i \(-0.197114\pi\)
−0.580426 + 0.814313i \(0.697114\pi\)
\(488\) 0.190005i 0.00860111i
\(489\) −2.06702 + 5.05988i −0.0934739 + 0.228816i
\(490\) 3.79996 0.171665
\(491\) 22.5148i 1.01608i −0.861334 0.508039i \(-0.830371\pi\)
0.861334 0.508039i \(-0.169629\pi\)
\(492\) −6.65689 15.8521i −0.300116 0.714666i
\(493\) −0.938964 −0.0422888
\(494\) −1.19275 + 1.19275i −0.0536643 + 0.0536643i
\(495\) −0.0510778 5.23688i −0.00229578 0.235380i
\(496\) −3.64796 + 3.64796i −0.163798 + 0.163798i
\(497\) 23.4722i 1.05287i
\(498\) 9.57323 23.4344i 0.428987 1.05012i
\(499\) −17.6251 + 17.6251i −0.789008 + 0.789008i −0.981332 0.192323i \(-0.938398\pi\)
0.192323 + 0.981332i \(0.438398\pi\)
\(500\) −0.707107 + 0.707107i −0.0316228 + 0.0316228i
\(501\) 0.533416 1.30575i 0.0238313 0.0583368i
\(502\) 19.4436i 0.867811i
\(503\) 5.33267 5.33267i 0.237772 0.237772i −0.578155 0.815927i \(-0.696227\pi\)
0.815927 + 0.578155i \(0.196227\pi\)
\(504\) −0.0961548 9.85852i −0.00428308 0.439133i
\(505\) −13.1960 + 13.1960i −0.587216 + 0.587216i
\(506\) 4.07155 0.181002
\(507\) −5.50704 13.1139i −0.244576 0.582410i
\(508\) 8.70788i 0.386350i
\(509\) −42.0833 −1.86531 −0.932654 0.360772i \(-0.882513\pi\)
−0.932654 + 0.360772i \(0.882513\pi\)
\(510\) 1.14965 2.81424i 0.0509073 0.124617i
\(511\) 45.0925i 1.99477i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −1.74737 + 0.753921i −0.0771485 + 0.0332864i
\(514\) 20.9726 0.925062
\(515\) 9.34793i 0.411919i
\(516\) −4.03286 + 9.87207i −0.177537 + 0.434594i
\(517\) 3.98839i 0.175409i
\(518\) 19.9022 + 1.87145i 0.874451 + 0.0822266i
\(519\) 26.6507 11.1917i 1.16984 0.491259i
\(520\) 3.25667 3.25667i 0.142815 0.142815i
\(521\) −31.4829 −1.37929 −0.689645 0.724147i \(-0.742234\pi\)
−0.689645 + 0.724147i \(0.742234\pi\)
\(522\) −1.14587 1.12374i −0.0501534 0.0491846i
\(523\) −23.0706 23.0706i −1.00880 1.00880i −0.999961 0.00884384i \(-0.997185\pi\)
−0.00884384 0.999961i \(-0.502815\pi\)
\(524\) −7.38432 + 7.38432i −0.322586 + 0.322586i
\(525\) 2.20389 + 5.24812i 0.0961855 + 0.229047i
\(526\) −6.42478 6.42478i −0.280134 0.280134i
\(527\) 9.05480i 0.394433i
\(528\) −2.78782 + 1.17071i −0.121324 + 0.0509488i
\(529\) 17.5603i 0.763492i
\(530\) 9.35271i 0.406256i
\(531\) 0.0275902 + 2.82875i 0.00119731 + 0.122757i
\(532\) −0.851082 + 0.851082i −0.0368991 + 0.0368991i
\(533\) −32.3271 32.3271i −1.40024 1.40024i
\(534\) 0.469615 + 1.11829i 0.0203222 + 0.0483933i
\(535\) 7.64195 + 7.64195i 0.330390 + 0.330390i
\(536\) −6.15410 6.15410i −0.265816 0.265816i
\(537\) −0.176157 0.0719622i −0.00760173 0.00310540i
\(538\) −13.5390 + 13.5390i −0.583710 + 0.583710i
\(539\) −6.63364 −0.285731
\(540\) 4.77102 2.05850i 0.205312 0.0885836i
\(541\) 23.9583 + 23.9583i 1.03005 + 1.03005i 0.999534 + 0.0305122i \(0.00971385\pi\)
0.0305122 + 0.999534i \(0.490286\pi\)
\(542\) 21.0268 + 21.0268i 0.903180 + 0.903180i
\(543\) −23.0683 + 9.68728i −0.989957 + 0.415721i
\(544\) −1.75515 −0.0752513
\(545\) −12.2655 −0.525397
\(546\) −10.1503 24.1709i −0.434392 1.03442i
\(547\) −2.23881 + 2.23881i −0.0957245 + 0.0957245i −0.753347 0.657623i \(-0.771562\pi\)
0.657623 + 0.753347i \(0.271562\pi\)
\(548\) −9.66267 −0.412769
\(549\) 0.00555936 + 0.569987i 0.000237268 + 0.0243265i
\(550\) 1.23440 1.23440i 0.0526352 0.0526352i
\(551\) 0.195934i 0.00834708i
\(552\) 1.56410 + 3.72460i 0.0665727 + 0.158530i
\(553\) 20.9872 + 20.9872i 0.892468 + 0.892468i
\(554\) 1.36310 0.0579126
\(555\) 3.15192 + 10.0531i 0.133791 + 0.426732i
\(556\) 9.40917 0.399038
\(557\) −20.2197 20.2197i −0.856737 0.856737i 0.134215 0.990952i \(-0.457149\pi\)
−0.990952 + 0.134215i \(0.957149\pi\)
\(558\) −10.8366 + 11.0501i −0.458751 + 0.467788i
\(559\) 28.3563i 1.19935i
\(560\) 2.32379 2.32379i 0.0981979 0.0981979i
\(561\) −2.00696 + 4.91285i −0.0847337 + 0.207421i
\(562\) 20.8086 0.877757
\(563\) 8.96911 8.96911i 0.378003 0.378003i −0.492378 0.870381i \(-0.663872\pi\)
0.870381 + 0.492378i \(0.163872\pi\)
\(564\) −3.64853 + 1.53216i −0.153631 + 0.0645155i
\(565\) −16.4341 −0.691387
\(566\) −1.05727 −0.0444404
\(567\) −0.576902 29.5713i −0.0242276 1.24188i
\(568\) −5.05043 5.05043i −0.211911 0.211911i
\(569\) 1.66794 + 1.66794i 0.0699235 + 0.0699235i 0.741204 0.671280i \(-0.234255\pi\)
−0.671280 + 0.741204i \(0.734255\pi\)
\(570\) −0.587249 0.239898i −0.0245972 0.0100482i
\(571\) −23.6993 −0.991783 −0.495892 0.868384i \(-0.665159\pi\)
−0.495892 + 0.868384i \(0.665159\pi\)
\(572\) −5.68521 + 5.68521i −0.237710 + 0.237710i
\(573\) 8.24457 20.1820i 0.344422 0.843113i
\(574\) −23.0669 23.0669i −0.962794 0.962794i
\(575\) −1.64920 1.64920i −0.0687762 0.0687762i
\(576\) −2.14191 2.10053i −0.0892462 0.0875221i
\(577\) 10.0160 + 10.0160i 0.416973 + 0.416973i 0.884159 0.467186i \(-0.154732\pi\)
−0.467186 + 0.884159i \(0.654732\pi\)
\(578\) 9.84254 9.84254i 0.409396 0.409396i
\(579\) 33.0282 + 13.4924i 1.37261 + 0.560726i
\(580\) 0.534977i 0.0222137i
\(581\) 48.0306i 1.99265i
\(582\) 3.94713 + 9.39931i 0.163614 + 0.389614i
\(583\) 16.3271i 0.676201i
\(584\) −9.70237 9.70237i −0.401487 0.401487i
\(585\) 9.67426 9.86484i 0.399982 0.407861i
\(586\) 19.7902 19.7902i 0.817525 0.817525i
\(587\) 13.1493 + 13.1493i 0.542729 + 0.542729i 0.924328 0.381599i \(-0.124626\pi\)
−0.381599 + 0.924328i \(0.624626\pi\)
\(588\) −2.54834 6.06837i −0.105092 0.250255i
\(589\) 1.88947 0.0778543
\(590\) −0.666775 + 0.666775i −0.0274507 + 0.0274507i
\(591\) 2.16481 + 5.15506i 0.0890483 + 0.212051i
\(592\) 4.68494 3.87960i 0.192550 0.159451i
\(593\) 10.4729i 0.430072i −0.976606 0.215036i \(-0.931013\pi\)
0.976606 0.215036i \(-0.0689870\pi\)
\(594\) −8.32881 + 3.59354i −0.341735 + 0.147445i
\(595\) 5.76799i 0.236465i
\(596\) 7.23397 0.296315
\(597\) −14.5919 + 35.7196i −0.597206 + 1.46191i
\(598\) 7.59559 + 7.59559i 0.310607 + 0.310607i
\(599\) 26.9297i 1.10032i −0.835060 0.550159i \(-0.814567\pi\)
0.835060 0.550159i \(-0.185433\pi\)
\(600\) 1.60342 + 0.655016i 0.0654593 + 0.0267409i
\(601\) 3.63775 0.148387 0.0741934 0.997244i \(-0.476362\pi\)
0.0741934 + 0.997244i \(0.476362\pi\)
\(602\) 20.2336i 0.824658i
\(603\) −18.6415 18.2813i −0.759139 0.744474i
\(604\) 15.0674 0.613084
\(605\) 5.62326 5.62326i 0.228618 0.228618i
\(606\) 29.9231 + 12.2239i 1.21554 + 0.496563i
\(607\) −8.68800 + 8.68800i −0.352635 + 0.352635i −0.861089 0.508454i \(-0.830217\pi\)
0.508454 + 0.861089i \(0.330217\pi\)
\(608\) 0.366248i 0.0148533i
\(609\) −2.81899 1.15159i −0.114231 0.0466648i
\(610\) −0.134354 + 0.134354i −0.00543982 + 0.00543982i
\(611\) −7.44045 + 7.44045i −0.301008 + 0.301008i
\(612\) −5.26519 + 0.0513539i −0.212833 + 0.00207586i
\(613\) 9.16353i 0.370112i −0.982728 0.185056i \(-0.940753\pi\)
0.982728 0.185056i \(-0.0592466\pi\)
\(614\) −2.19014 + 2.19014i −0.0883870 + 0.0883870i
\(615\) 6.50197 15.9162i 0.262185 0.641804i
\(616\) −4.05666 + 4.05666i −0.163447 + 0.163447i
\(617\) 35.6832 1.43655 0.718275 0.695759i \(-0.244932\pi\)
0.718275 + 0.695759i \(0.244932\pi\)
\(618\) 14.9282 6.26894i 0.600502 0.252174i
\(619\) 13.9865i 0.562167i 0.959683 + 0.281083i \(0.0906937\pi\)
−0.959683 + 0.281083i \(0.909306\pi\)
\(620\) −5.15899 −0.207190
\(621\) 4.80107 + 11.1275i 0.192660 + 0.446532i
\(622\) 8.66781i 0.347548i
\(623\) 1.62727 + 1.62727i 0.0651952 + 0.0651952i
\(624\) −7.38476 3.01676i −0.295627 0.120767i
\(625\) −1.00000 −0.0400000
\(626\) 20.4155i 0.815969i
\(627\) 1.02517 + 0.418793i 0.0409412 + 0.0167250i
\(628\) 8.06347i 0.321768i
\(629\) 0.999493 10.6293i 0.0398524 0.423816i
\(630\) 6.90303 7.03902i 0.275023 0.280441i
\(631\) −0.282325 + 0.282325i −0.0112392 + 0.0112392i −0.712704 0.701465i \(-0.752530\pi\)
0.701465 + 0.712704i \(0.252530\pi\)
\(632\) 9.03148 0.359253
\(633\) 21.8695 9.18382i 0.869233 0.365024i
\(634\) 11.8475 + 11.8475i 0.470524 + 0.470524i
\(635\) 6.15740 6.15740i 0.244349 0.244349i
\(636\) −14.9359 + 6.27214i −0.592245 + 0.248707i
\(637\) −12.3752 12.3752i −0.490325 0.490325i
\(638\) 0.933915i 0.0369741i
\(639\) −15.2983 15.0028i −0.605193 0.593502i
\(640\) 1.00000i 0.0395285i
\(641\) 25.2386i 0.996866i −0.866928 0.498433i \(-0.833909\pi\)
0.866928 0.498433i \(-0.166091\pi\)
\(642\) 7.07898 17.3287i 0.279385 0.683909i
\(643\) −21.1632 + 21.1632i −0.834596 + 0.834596i −0.988142 0.153546i \(-0.950931\pi\)
0.153546 + 0.988142i \(0.450931\pi\)
\(644\) 5.41980 + 5.41980i 0.213570 + 0.213570i
\(645\) −9.83227 + 4.12895i −0.387145 + 0.162577i
\(646\) 0.454542 + 0.454542i 0.0178837 + 0.0178837i
\(647\) 26.0237 + 26.0237i 1.02310 + 1.02310i 0.999727 + 0.0233686i \(0.00743914\pi\)
0.0233686 + 0.999727i \(0.492561\pi\)
\(648\) −6.48688 6.23862i −0.254829 0.245076i
\(649\) 1.16400 1.16400i 0.0456909 0.0456909i
\(650\) 4.60563 0.180648
\(651\) −11.1052 + 27.1846i −0.435249 + 1.06545i
\(652\) 2.23140 + 2.23140i 0.0873885 + 0.0873885i
\(653\) 17.4422 + 17.4422i 0.682567 + 0.682567i 0.960578 0.278011i \(-0.0896751\pi\)
−0.278011 + 0.960578i \(0.589675\pi\)
\(654\) 8.22554 + 19.5875i 0.321644 + 0.765932i
\(655\) −10.4430 −0.408042
\(656\) −9.92643 −0.387562
\(657\) −29.3896 28.8218i −1.14660 1.12445i
\(658\) −5.30910 + 5.30910i −0.206970 + 0.206970i
\(659\) −10.4238 −0.406055 −0.203028 0.979173i \(-0.565078\pi\)
−0.203028 + 0.979173i \(0.565078\pi\)
\(660\) −2.79911 1.14347i −0.108955 0.0445094i
\(661\) 16.8687 16.8687i 0.656115 0.656115i −0.298343 0.954459i \(-0.596434\pi\)
0.954459 + 0.298343i \(0.0964340\pi\)
\(662\) 3.32436i 0.129205i
\(663\) −12.9091 + 5.42102i −0.501347 + 0.210535i
\(664\) −10.3346 10.3346i −0.401059 0.401059i
\(665\) −1.20361 −0.0466741
\(666\) 13.9407 11.7753i 0.540189 0.456285i
\(667\) 1.24773 0.0483125
\(668\) −0.575837 0.575837i −0.0222798 0.0222798i
\(669\) 27.6353 11.6051i 1.06844 0.448680i
\(670\) 8.70321i 0.336234i
\(671\) 0.234543 0.234543i 0.00905442 0.00905442i
\(672\) −5.26937 2.15260i −0.203270 0.0830383i
\(673\) 37.8385 1.45857 0.729284 0.684211i \(-0.239853\pi\)
0.729284 + 0.684211i \(0.239853\pi\)
\(674\) 5.04863 5.04863i 0.194466 0.194466i
\(675\) 4.82920 + 1.91804i 0.185876 + 0.0738254i
\(676\) −8.21183 −0.315840
\(677\) 11.3003 0.434306 0.217153 0.976138i \(-0.430323\pi\)
0.217153 + 0.976138i \(0.430323\pi\)
\(678\) 11.0211 + 26.2445i 0.423262 + 1.00791i
\(679\) 13.6773 + 13.6773i 0.524885 + 0.524885i
\(680\) −1.24108 1.24108i −0.0475931 0.0475931i
\(681\) 0.675873 1.65448i 0.0258995 0.0633997i
\(682\) 9.00611 0.344862
\(683\) −5.37507 + 5.37507i −0.205671 + 0.205671i −0.802425 0.596753i \(-0.796457\pi\)
0.596753 + 0.802425i \(0.296457\pi\)
\(684\) 0.0107161 + 1.09869i 0.000409739 + 0.0420095i
\(685\) −6.83254 6.83254i −0.261058 0.261058i
\(686\) 7.43620 + 7.43620i 0.283915 + 0.283915i
\(687\) −30.1099 + 12.6443i −1.14877 + 0.482411i
\(688\) 4.35358 + 4.35358i 0.165979 + 0.165979i
\(689\) −30.4587 + 30.4587i −1.16038 + 1.16038i
\(690\) −1.52770 + 3.73968i −0.0581587 + 0.142367i
\(691\) 35.6614i 1.35663i 0.734773 + 0.678313i \(0.237289\pi\)
−0.734773 + 0.678313i \(0.762711\pi\)
\(692\) 16.6885i 0.634400i
\(693\) −12.0507 + 12.2881i −0.457768 + 0.466786i
\(694\) 29.9382i 1.13644i
\(695\) 6.65329 + 6.65329i 0.252374 + 0.252374i
\(696\) −0.854334 + 0.358768i −0.0323835 + 0.0135991i
\(697\) −12.3195 + 12.3195i −0.466633 + 0.466633i
\(698\) −4.63527 4.63527i −0.175447 0.175447i
\(699\) −6.19970 + 2.60349i −0.234494 + 0.0984732i
\(700\) 3.28633 0.124212
\(701\) −7.81125 + 7.81125i −0.295027 + 0.295027i −0.839062 0.544035i \(-0.816896\pi\)
0.544035 + 0.839062i \(0.316896\pi\)
\(702\) −22.2415 8.83378i −0.839451 0.333410i
\(703\) −2.21802 0.208565i −0.0836540 0.00786618i
\(704\) 1.74571i 0.0657939i
\(705\) −3.66330 1.49650i −0.137968 0.0563615i
\(706\) 6.62946i 0.249503i
\(707\) 61.3296 2.30654
\(708\) 1.51196 + 0.617655i 0.0568231 + 0.0232129i
\(709\) 27.9441 + 27.9441i 1.04946 + 1.04946i 0.998711 + 0.0507522i \(0.0161619\pi\)
0.0507522 + 0.998711i \(0.483838\pi\)
\(710\) 7.14239i 0.268049i
\(711\) 27.0932 0.264252i 1.01607 0.00991024i
\(712\) 0.700267 0.0262436
\(713\) 12.0324i 0.450617i
\(714\) −9.21123 + 3.86815i −0.344722 + 0.144762i
\(715\) −8.04010 −0.300683
\(716\) −0.0776850 + 0.0776850i −0.00290323 + 0.00290323i
\(717\) 7.89966 19.3376i 0.295018 0.722178i
\(718\) −9.73002 + 9.73002i −0.363121 + 0.363121i
\(719\) 14.9574i 0.557817i 0.960318 + 0.278908i \(0.0899726\pi\)
−0.960318 + 0.278908i \(0.910027\pi\)
\(720\) −0.0292590 2.99986i −0.00109042 0.111798i
\(721\) 21.7226 21.7226i 0.808992 0.808992i
\(722\) −13.3402 + 13.3402i −0.496470 + 0.496470i
\(723\) −32.5751 13.3073i −1.21148 0.494904i
\(724\) 14.4452i 0.536852i
\(725\) 0.378286 0.378286i 0.0140492 0.0140492i
\(726\) −12.7512 5.20901i −0.473241 0.193324i
\(727\) −7.87230 + 7.87230i −0.291967 + 0.291967i −0.837857 0.545890i \(-0.816192\pi\)
0.545890 + 0.837857i \(0.316192\pi\)
\(728\) −15.1356 −0.560963
\(729\) −19.6423 18.5252i −0.727491 0.686117i
\(730\) 13.7212i 0.507845i
\(731\) 10.8062 0.399684
\(732\) 0.304657 + 0.124456i 0.0112605 + 0.00460003i
\(733\) 2.19338i 0.0810144i 0.999179 + 0.0405072i \(0.0128974\pi\)
−0.999179 + 0.0405072i \(0.987103\pi\)
\(734\) −16.1327 16.1327i −0.595468 0.595468i
\(735\) 2.48904 6.09293i 0.0918095 0.224741i
\(736\) 2.33232 0.0859703
\(737\) 15.1933i 0.559652i
\(738\) −29.7779 + 0.290438i −1.09614 + 0.0106912i
\(739\) 53.7157i 1.97597i −0.154565 0.987983i \(-0.549398\pi\)
0.154565 0.987983i \(-0.450602\pi\)
\(740\) 6.05605 + 0.569464i 0.222625 + 0.0209339i
\(741\) 1.13121 + 2.69375i 0.0415560 + 0.0989573i
\(742\) −21.7337 + 21.7337i −0.797869 + 0.797869i
\(743\) −6.02994 −0.221217 −0.110609 0.993864i \(-0.535280\pi\)
−0.110609 + 0.993864i \(0.535280\pi\)
\(744\) 3.45974 + 8.23868i 0.126840 + 0.302045i
\(745\) 5.11519 + 5.11519i 0.187406 + 0.187406i
\(746\) 23.6251 23.6251i 0.864976 0.864976i
\(747\) −31.3046 30.6998i −1.14537 1.12325i
\(748\) 2.16656 + 2.16656i 0.0792173 + 0.0792173i
\(749\) 35.5165i 1.29774i
\(750\) 0.670623 + 1.59695i 0.0244877 + 0.0583125i
\(751\) 45.2316i 1.65052i 0.564750 + 0.825262i \(0.308973\pi\)
−0.564750 + 0.825262i \(0.691027\pi\)
\(752\) 2.28468i 0.0833137i
\(753\) 31.1763 + 12.7359i 1.13613 + 0.464121i
\(754\) −1.74224 + 1.74224i −0.0634488 + 0.0634488i
\(755\) 10.6543 + 10.6543i 0.387748 + 0.387748i
\(756\) −15.8703 6.30331i −0.577198 0.229249i
\(757\) −37.4148 37.4148i −1.35986 1.35986i −0.874077 0.485787i \(-0.838533\pi\)
−0.485787 0.874077i \(-0.661467\pi\)
\(758\) −12.4254 12.4254i −0.451309 0.451309i
\(759\) 2.66693 6.52840i 0.0968034 0.236966i
\(760\) −0.258976 + 0.258976i −0.00939406 + 0.00939406i
\(761\) 0.131478 0.00476608 0.00238304 0.999997i \(-0.499241\pi\)
0.00238304 + 0.999997i \(0.499241\pi\)
\(762\) −13.9624 5.70380i −0.505804 0.206627i
\(763\) 28.5025 + 28.5025i 1.03186 + 1.03186i
\(764\) −8.90023 8.90023i −0.321999 0.321999i
\(765\) −3.75937 3.68674i −0.135920 0.133294i
\(766\) −14.1672 −0.511883
\(767\) 4.34294 0.156814
\(768\) −1.59695 + 0.670623i −0.0576251 + 0.0241990i
\(769\) 20.5578 20.5578i 0.741334 0.741334i −0.231500 0.972835i \(-0.574363\pi\)
0.972835 + 0.231500i \(0.0743634\pi\)
\(770\) −5.73698 −0.206746
\(771\) 13.7374 33.6279i 0.494740 1.21108i
\(772\) 14.5654 14.5654i 0.524221 0.524221i
\(773\) 6.89204i 0.247889i −0.992289 0.123945i \(-0.960445\pi\)
0.992289 0.123945i \(-0.0395545\pi\)
\(774\) 13.1875 + 12.9327i 0.474015 + 0.464857i
\(775\) −3.64796 3.64796i −0.131039 0.131039i
\(776\) 5.88577 0.211287
\(777\) 16.0369 30.6857i 0.575322 1.10084i
\(778\) −1.19099 −0.0426990