Properties

Label 105.3.k.d.83.2
Level 105
Weight 3
Character 105.83
Analytic conductor 2.861
Analytic rank 0
Dimension 32
CM no
Inner twists 8

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.2
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.d.62.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.63482 - 2.63482i) q^{2} +(2.54097 - 1.59482i) q^{3} +9.88460i q^{4} +(4.15332 - 2.78387i) q^{5} +(-10.8971 - 2.49295i) q^{6} +(6.57626 - 2.39850i) q^{7} +(15.5049 - 15.5049i) q^{8} +(3.91310 - 8.10479i) q^{9} +O(q^{10})\) \(q+(-2.63482 - 2.63482i) q^{2} +(2.54097 - 1.59482i) q^{3} +9.88460i q^{4} +(4.15332 - 2.78387i) q^{5} +(-10.8971 - 2.49295i) q^{6} +(6.57626 - 2.39850i) q^{7} +(15.5049 - 15.5049i) q^{8} +(3.91310 - 8.10479i) q^{9} +(-18.2783 - 3.60824i) q^{10} +5.66373i q^{11} +(15.7642 + 25.1165i) q^{12} +(1.68481 - 1.68481i) q^{13} +(-23.6469 - 11.0077i) q^{14} +(6.11370 - 13.6975i) q^{15} -42.1670 q^{16} +(-14.0118 + 14.0118i) q^{17} +(-31.6650 + 11.0444i) q^{18} -24.0066 q^{19} +(27.5175 + 41.0539i) q^{20} +(12.8849 - 16.5825i) q^{21} +(14.9229 - 14.9229i) q^{22} +(3.17641 - 3.17641i) q^{23} +(14.6700 - 64.1251i) q^{24} +(9.50008 - 23.1246i) q^{25} -8.87835 q^{26} +(-2.98258 - 26.8348i) q^{27} +(23.7082 + 65.0037i) q^{28} +24.1064 q^{29} +(-52.1991 + 19.9821i) q^{30} +23.8436i q^{31} +(49.0830 + 49.0830i) q^{32} +(9.03263 + 14.3914i) q^{33} +73.8374 q^{34} +(20.6362 - 28.2692i) q^{35} +(80.1127 + 38.6795i) q^{36} +(-13.8075 + 13.8075i) q^{37} +(63.2532 + 63.2532i) q^{38} +(1.59409 - 6.96802i) q^{39} +(21.2331 - 107.560i) q^{40} -53.4368 q^{41} +(-77.6415 + 9.74236i) q^{42} +(25.9017 + 25.9017i) q^{43} -55.9837 q^{44} +(-6.31036 - 44.5554i) q^{45} -16.7386 q^{46} +(27.3968 - 27.3968i) q^{47} +(-107.145 + 67.2487i) q^{48} +(37.4944 - 31.5463i) q^{49} +(-85.9604 + 35.8983i) q^{50} +(-13.2573 + 57.9500i) q^{51} +(16.6537 + 16.6537i) q^{52} +(22.4866 - 22.4866i) q^{53} +(-62.8463 + 78.5635i) q^{54} +(15.7671 + 23.5233i) q^{55} +(64.7758 - 139.153i) q^{56} +(-61.0002 + 38.2862i) q^{57} +(-63.5160 - 63.5160i) q^{58} +14.2975i q^{59} +(135.395 + 60.4315i) q^{60} +90.2799i q^{61} +(62.8237 - 62.8237i) q^{62} +(6.29425 - 62.6848i) q^{63} -89.9824i q^{64} +(2.30725 - 11.6878i) q^{65} +(14.1194 - 61.7182i) q^{66} +(-0.492023 + 0.492023i) q^{67} +(-138.501 - 138.501i) q^{68} +(3.00538 - 13.1370i) q^{69} +(-128.857 + 20.1117i) q^{70} +54.2705i q^{71} +(-64.9917 - 186.336i) q^{72} +(-30.4748 + 30.4748i) q^{73} +72.7609 q^{74} +(-12.7401 - 73.9100i) q^{75} -237.296i q^{76} +(13.5845 + 37.2462i) q^{77} +(-22.5597 + 14.1594i) q^{78} +58.3371i q^{79} +(-175.133 + 117.388i) q^{80} +(-50.3753 - 63.4298i) q^{81} +(140.796 + 140.796i) q^{82} +(55.7696 + 55.7696i) q^{83} +(163.911 + 127.363i) q^{84} +(-19.1884 + 97.2026i) q^{85} -136.493i q^{86} +(61.2536 - 38.4453i) q^{87} +(87.8156 + 87.8156i) q^{88} +109.444i q^{89} +(-100.769 + 134.022i) q^{90} +(7.03872 - 15.1207i) q^{91} +(31.3976 + 31.3976i) q^{92} +(38.0262 + 60.5860i) q^{93} -144.372 q^{94} +(-99.7071 + 66.8314i) q^{95} +(202.997 + 46.4402i) q^{96} +(-48.0651 - 48.0651i) q^{97} +(-181.910 - 15.6722i) q^{98} +(45.9034 + 22.1628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q - 48q^{15} - 24q^{16} - 92q^{18} - 60q^{21} + 112q^{22} - 72q^{25} + 88q^{28} - 108q^{30} + 416q^{36} + 72q^{37} + 300q^{42} - 328q^{43} + 32q^{46} + 148q^{51} - 748q^{57} - 392q^{58} + 544q^{60} - 220q^{63} - 648q^{67} - 8q^{70} - 8q^{72} + 500q^{78} - 948q^{81} + 672q^{85} + 1288q^{88} + 808q^{91} + 292q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63482 2.63482i −1.31741 1.31741i −0.915817 0.401595i \(-0.868456\pi\)
−0.401595 0.915817i \(-0.631544\pi\)
\(3\) 2.54097 1.59482i 0.846991 0.531606i
\(4\) 9.88460i 2.47115i
\(5\) 4.15332 2.78387i 0.830663 0.556775i
\(6\) −10.8971 2.49295i −1.81618 0.415492i
\(7\) 6.57626 2.39850i 0.939466 0.342643i
\(8\) 15.5049 15.5049i 1.93811 1.93811i
\(9\) 3.91310 8.10479i 0.434789 0.900532i
\(10\) −18.2783 3.60824i −1.82783 0.360824i
\(11\) 5.66373i 0.514885i 0.966294 + 0.257442i \(0.0828797\pi\)
−0.966294 + 0.257442i \(0.917120\pi\)
\(12\) 15.7642 + 25.1165i 1.31368 + 2.09304i
\(13\) 1.68481 1.68481i 0.129601 0.129601i −0.639331 0.768932i \(-0.720789\pi\)
0.768932 + 0.639331i \(0.220789\pi\)
\(14\) −23.6469 11.0077i −1.68907 0.786262i
\(15\) 6.11370 13.6975i 0.407580 0.913170i
\(16\) −42.1670 −2.63544
\(17\) −14.0118 + 14.0118i −0.824224 + 0.824224i −0.986711 0.162486i \(-0.948049\pi\)
0.162486 + 0.986711i \(0.448049\pi\)
\(18\) −31.6650 + 11.0444i −1.75917 + 0.613576i
\(19\) −24.0066 −1.26351 −0.631753 0.775170i \(-0.717664\pi\)
−0.631753 + 0.775170i \(0.717664\pi\)
\(20\) 27.5175 + 41.0539i 1.37588 + 2.05269i
\(21\) 12.8849 16.5825i 0.613568 0.789642i
\(22\) 14.9229 14.9229i 0.678315 0.678315i
\(23\) 3.17641 3.17641i 0.138105 0.138105i −0.634675 0.772780i \(-0.718866\pi\)
0.772780 + 0.634675i \(0.218866\pi\)
\(24\) 14.6700 64.1251i 0.611252 2.67188i
\(25\) 9.50008 23.1246i 0.380003 0.924985i
\(26\) −8.87835 −0.341475
\(27\) −2.98258 26.8348i −0.110466 0.993880i
\(28\) 23.7082 + 65.0037i 0.846722 + 2.32156i
\(29\) 24.1064 0.831254 0.415627 0.909535i \(-0.363562\pi\)
0.415627 + 0.909535i \(0.363562\pi\)
\(30\) −52.1991 + 19.9821i −1.73997 + 0.666070i
\(31\) 23.8436i 0.769148i 0.923094 + 0.384574i \(0.125652\pi\)
−0.923094 + 0.384574i \(0.874348\pi\)
\(32\) 49.0830 + 49.0830i 1.53384 + 1.53384i
\(33\) 9.03263 + 14.3914i 0.273716 + 0.436103i
\(34\) 73.8374 2.17169
\(35\) 20.6362 28.2692i 0.589605 0.807692i
\(36\) 80.1127 + 38.6795i 2.22535 + 1.07443i
\(37\) −13.8075 + 13.8075i −0.373177 + 0.373177i −0.868633 0.495456i \(-0.835001\pi\)
0.495456 + 0.868633i \(0.335001\pi\)
\(38\) 63.2532 + 63.2532i 1.66456 + 1.66456i
\(39\) 1.59409 6.96802i 0.0408741 0.178667i
\(40\) 21.2331 107.560i 0.530827 2.68901i
\(41\) −53.4368 −1.30334 −0.651668 0.758505i \(-0.725930\pi\)
−0.651668 + 0.758505i \(0.725930\pi\)
\(42\) −77.6415 + 9.74236i −1.84861 + 0.231961i
\(43\) 25.9017 + 25.9017i 0.602366 + 0.602366i 0.940940 0.338574i \(-0.109945\pi\)
−0.338574 + 0.940940i \(0.609945\pi\)
\(44\) −55.9837 −1.27236
\(45\) −6.31036 44.5554i −0.140230 0.990119i
\(46\) −16.7386 −0.363882
\(47\) 27.3968 27.3968i 0.582911 0.582911i −0.352791 0.935702i \(-0.614767\pi\)
0.935702 + 0.352791i \(0.114767\pi\)
\(48\) −107.145 + 67.2487i −2.23219 + 1.40102i
\(49\) 37.4944 31.5463i 0.765192 0.643802i
\(50\) −85.9604 + 35.8983i −1.71921 + 0.717966i
\(51\) −13.2573 + 57.9500i −0.259948 + 1.13627i
\(52\) 16.6537 + 16.6537i 0.320263 + 0.320263i
\(53\) 22.4866 22.4866i 0.424276 0.424276i −0.462397 0.886673i \(-0.653011\pi\)
0.886673 + 0.462397i \(0.153011\pi\)
\(54\) −62.8463 + 78.5635i −1.16382 + 1.45488i
\(55\) 15.7671 + 23.5233i 0.286675 + 0.427696i
\(56\) 64.7758 139.153i 1.15671 2.48487i
\(57\) −61.0002 + 38.2862i −1.07018 + 0.671688i
\(58\) −63.5160 63.5160i −1.09510 1.09510i
\(59\) 14.2975i 0.242330i 0.992632 + 0.121165i \(0.0386631\pi\)
−0.992632 + 0.121165i \(0.961337\pi\)
\(60\) 135.395 + 60.4315i 2.25658 + 1.00719i
\(61\) 90.2799i 1.48000i 0.672608 + 0.739999i \(0.265174\pi\)
−0.672608 + 0.739999i \(0.734826\pi\)
\(62\) 62.8237 62.8237i 1.01329 1.01329i
\(63\) 6.29425 62.6848i 0.0999087 0.994997i
\(64\) 89.9824i 1.40598i
\(65\) 2.30725 11.6878i 0.0354961 0.179813i
\(66\) 14.1194 61.7182i 0.213931 0.935124i
\(67\) −0.492023 + 0.492023i −0.00734362 + 0.00734362i −0.710769 0.703425i \(-0.751653\pi\)
0.703425 + 0.710769i \(0.251653\pi\)
\(68\) −138.501 138.501i −2.03678 2.03678i
\(69\) 3.00538 13.1370i 0.0435562 0.190391i
\(70\) −128.857 + 20.1117i −1.84082 + 0.287310i
\(71\) 54.2705i 0.764374i 0.924085 + 0.382187i \(0.124829\pi\)
−0.924085 + 0.382187i \(0.875171\pi\)
\(72\) −64.9917 186.336i −0.902663 2.58800i
\(73\) −30.4748 + 30.4748i −0.417464 + 0.417464i −0.884329 0.466865i \(-0.845383\pi\)
0.466865 + 0.884329i \(0.345383\pi\)
\(74\) 72.7609 0.983256
\(75\) −12.7401 73.9100i −0.169868 0.985467i
\(76\) 237.296i 3.12231i
\(77\) 13.5845 + 37.2462i 0.176422 + 0.483717i
\(78\) −22.5597 + 14.1594i −0.289226 + 0.181530i
\(79\) 58.3371i 0.738444i 0.929341 + 0.369222i \(0.120376\pi\)
−0.929341 + 0.369222i \(0.879624\pi\)
\(80\) −175.133 + 117.388i −2.18916 + 1.46735i
\(81\) −50.3753 63.4298i −0.621917 0.783083i
\(82\) 140.796 + 140.796i 1.71703 + 1.71703i
\(83\) 55.7696 + 55.7696i 0.671923 + 0.671923i 0.958159 0.286236i \(-0.0924042\pi\)
−0.286236 + 0.958159i \(0.592404\pi\)
\(84\) 163.911 + 127.363i 1.95132 + 1.51622i
\(85\) −19.1884 + 97.2026i −0.225746 + 1.14356i
\(86\) 136.493i 1.58713i
\(87\) 61.2536 38.4453i 0.704065 0.441900i
\(88\) 87.8156 + 87.8156i 0.997905 + 0.997905i
\(89\) 109.444i 1.22971i 0.788641 + 0.614854i \(0.210785\pi\)
−0.788641 + 0.614854i \(0.789215\pi\)
\(90\) −100.769 + 134.022i −1.11965 + 1.48914i
\(91\) 7.03872 15.1207i 0.0773486 0.166162i
\(92\) 31.3976 + 31.3976i 0.341278 + 0.341278i
\(93\) 38.0262 + 60.5860i 0.408884 + 0.651462i
\(94\) −144.372 −1.53587
\(95\) −99.7071 + 66.8314i −1.04955 + 0.703489i
\(96\) 202.997 + 46.4402i 2.11456 + 0.483752i
\(97\) −48.0651 48.0651i −0.495516 0.495516i 0.414523 0.910039i \(-0.363949\pi\)
−0.910039 + 0.414523i \(0.863949\pi\)
\(98\) −181.910 15.6722i −1.85623 0.159920i
\(99\) 45.9034 + 22.1628i 0.463670 + 0.223866i
\(100\) 228.578 + 93.9046i 2.28578 + 0.939046i
\(101\) −103.406 −1.02382 −0.511911 0.859039i \(-0.671062\pi\)
−0.511911 + 0.859039i \(0.671062\pi\)
\(102\) 187.619 117.757i 1.83940 1.15448i
\(103\) 59.9292 59.9292i 0.581837 0.581837i −0.353571 0.935408i \(-0.615033\pi\)
0.935408 + 0.353571i \(0.115033\pi\)
\(104\) 52.2456i 0.502361i
\(105\) 7.35170 104.742i 0.0700162 0.997546i
\(106\) −118.497 −1.11789
\(107\) 33.4736 + 33.4736i 0.312837 + 0.312837i 0.846008 0.533170i \(-0.179000\pi\)
−0.533170 + 0.846008i \(0.679000\pi\)
\(108\) 265.251 29.4816i 2.45603 0.272978i
\(109\) 188.925i 1.73326i −0.498954 0.866628i \(-0.666282\pi\)
0.498954 0.866628i \(-0.333718\pi\)
\(110\) 20.4361 103.523i 0.185783 0.941121i
\(111\) −13.0641 + 57.1052i −0.117694 + 0.514461i
\(112\) −277.301 + 101.138i −2.47590 + 0.903013i
\(113\) 112.042 112.042i 0.991524 0.991524i −0.00844052 0.999964i \(-0.502687\pi\)
0.999964 + 0.00844052i \(0.00268673\pi\)
\(114\) 261.602 + 59.8474i 2.29476 + 0.524977i
\(115\) 4.34991 22.0354i 0.0378253 0.191612i
\(116\) 238.282i 2.05415i
\(117\) −7.06219 20.2478i −0.0603606 0.173058i
\(118\) 37.6714 37.6714i 0.319249 0.319249i
\(119\) −58.5380 + 125.753i −0.491916 + 1.05675i
\(120\) −117.587 307.171i −0.979890 2.55976i
\(121\) 88.9221 0.734894
\(122\) 237.872 237.872i 1.94977 1.94977i
\(123\) −135.781 + 85.2220i −1.10391 + 0.692862i
\(124\) −235.684 −1.90068
\(125\) −24.9192 122.491i −0.199354 0.979928i
\(126\) −181.748 + 148.579i −1.44244 + 1.17920i
\(127\) −27.2567 + 27.2567i −0.214620 + 0.214620i −0.806227 0.591607i \(-0.798494\pi\)
0.591607 + 0.806227i \(0.298494\pi\)
\(128\) −40.7558 + 40.7558i −0.318405 + 0.318405i
\(129\) 107.124 + 24.5071i 0.830420 + 0.189977i
\(130\) −36.8746 + 24.7162i −0.283651 + 0.190125i
\(131\) −22.2009 −0.169472 −0.0847362 0.996403i \(-0.527005\pi\)
−0.0847362 + 0.996403i \(0.527005\pi\)
\(132\) −142.253 + 89.2840i −1.07768 + 0.676394i
\(133\) −157.874 + 57.5799i −1.18702 + 0.432931i
\(134\) 2.59279 0.0193492
\(135\) −87.0922 103.150i −0.645127 0.764075i
\(136\) 434.504i 3.19488i
\(137\) −87.8267 87.8267i −0.641071 0.641071i 0.309748 0.950819i \(-0.399755\pi\)
−0.950819 + 0.309748i \(0.899755\pi\)
\(138\) −42.5323 + 26.6950i −0.308205 + 0.193442i
\(139\) 55.5125 0.399371 0.199685 0.979860i \(-0.436008\pi\)
0.199685 + 0.979860i \(0.436008\pi\)
\(140\) 279.430 + 203.980i 1.99593 + 1.45700i
\(141\) 25.9216 113.308i 0.183841 0.803600i
\(142\) 142.993 142.993i 1.00700 1.00700i
\(143\) 9.54230 + 9.54230i 0.0667294 + 0.0667294i
\(144\) −165.004 + 341.755i −1.14586 + 2.37330i
\(145\) 100.121 67.1091i 0.690492 0.462821i
\(146\) 160.592 1.09994
\(147\) 44.9616 139.955i 0.305862 0.952076i
\(148\) −136.482 136.482i −0.922177 0.922177i
\(149\) −267.880 −1.79785 −0.898925 0.438103i \(-0.855651\pi\)
−0.898925 + 0.438103i \(0.855651\pi\)
\(150\) −161.172 + 228.308i −1.07448 + 1.52205i
\(151\) 149.076 0.987261 0.493631 0.869672i \(-0.335670\pi\)
0.493631 + 0.869672i \(0.335670\pi\)
\(152\) −372.220 + 372.220i −2.44882 + 2.44882i
\(153\) 58.7331 + 168.392i 0.383877 + 1.10060i
\(154\) 62.3445 133.930i 0.404834 0.869674i
\(155\) 66.3776 + 99.0300i 0.428242 + 0.638903i
\(156\) 68.8761 + 15.7569i 0.441513 + 0.101006i
\(157\) −137.160 137.160i −0.873632 0.873632i 0.119235 0.992866i \(-0.461956\pi\)
−0.992866 + 0.119235i \(0.961956\pi\)
\(158\) 153.708 153.708i 0.972835 0.972835i
\(159\) 21.2758 93.0000i 0.133810 0.584906i
\(160\) 340.498 + 67.2164i 2.12811 + 0.420102i
\(161\) 13.2703 28.5075i 0.0824242 0.177066i
\(162\) −34.3963 + 299.856i −0.212323 + 1.85096i
\(163\) 30.1699 + 30.1699i 0.185091 + 0.185091i 0.793570 0.608479i \(-0.208220\pi\)
−0.608479 + 0.793570i \(0.708220\pi\)
\(164\) 528.201i 3.22074i
\(165\) 77.5792 + 34.6263i 0.470177 + 0.209857i
\(166\) 293.886i 1.77040i
\(167\) −138.915 + 138.915i −0.831827 + 0.831827i −0.987767 0.155939i \(-0.950160\pi\)
0.155939 + 0.987767i \(0.450160\pi\)
\(168\) −57.3299 456.889i −0.341250 2.71958i
\(169\) 163.323i 0.966407i
\(170\) 306.670 205.554i 1.80394 1.20914i
\(171\) −93.9404 + 194.569i −0.549359 + 1.13783i
\(172\) −256.028 + 256.028i −1.48854 + 1.48854i
\(173\) −91.9689 91.9689i −0.531612 0.531612i 0.389440 0.921052i \(-0.372669\pi\)
−0.921052 + 0.389440i \(0.872669\pi\)
\(174\) −262.689 60.0960i −1.50971 0.345379i
\(175\) 7.01062 174.860i 0.0400607 0.999197i
\(176\) 238.823i 1.35695i
\(177\) 22.8019 + 36.3295i 0.128824 + 0.205252i
\(178\) 288.366 288.366i 1.62003 1.62003i
\(179\) 138.994 0.776504 0.388252 0.921553i \(-0.373079\pi\)
0.388252 + 0.921553i \(0.373079\pi\)
\(180\) 440.412 62.3755i 2.44673 0.346530i
\(181\) 15.4468i 0.0853414i −0.999089 0.0426707i \(-0.986413\pi\)
0.999089 0.0426707i \(-0.0135866\pi\)
\(182\) −58.3863 + 21.2947i −0.320804 + 0.117004i
\(183\) 143.980 + 229.399i 0.786777 + 1.25355i
\(184\) 98.5000i 0.535326i
\(185\) −18.9086 + 95.7856i −0.102209 + 0.517760i
\(186\) 59.4410 259.826i 0.319575 1.39691i
\(187\) −79.3591 79.3591i −0.424380 0.424380i
\(188\) 270.807 + 270.807i 1.44046 + 1.44046i
\(189\) −83.9774 169.319i −0.444325 0.895866i
\(190\) 438.800 + 86.6217i 2.30947 + 0.455903i
\(191\) 269.579i 1.41141i 0.708508 + 0.705703i \(0.249369\pi\)
−0.708508 + 0.705703i \(0.750631\pi\)
\(192\) −143.506 228.643i −0.747426 1.19085i
\(193\) −81.8078 81.8078i −0.423875 0.423875i 0.462661 0.886535i \(-0.346895\pi\)
−0.886535 + 0.462661i \(0.846895\pi\)
\(194\) 253.286i 1.30560i
\(195\) −12.7773 33.3781i −0.0655248 0.171170i
\(196\) 311.823 + 370.617i 1.59093 + 1.89090i
\(197\) −114.419 114.419i −0.580805 0.580805i 0.354319 0.935125i \(-0.384713\pi\)
−0.935125 + 0.354319i \(0.884713\pi\)
\(198\) −62.5523 179.342i −0.315921 0.905769i
\(199\) −88.3996 −0.444219 −0.222110 0.975022i \(-0.571294\pi\)
−0.222110 + 0.975022i \(0.571294\pi\)
\(200\) −211.247 505.843i −1.05624 2.52922i
\(201\) −0.465530 + 2.03490i −0.00231607 + 0.0101239i
\(202\) 272.457 + 272.457i 1.34880 + 1.34880i
\(203\) 158.530 57.8191i 0.780934 0.284823i
\(204\) −572.813 131.044i −2.80790 0.642371i
\(205\) −221.940 + 148.761i −1.08263 + 0.725665i
\(206\) −315.806 −1.53304
\(207\) −13.3145 38.1738i −0.0643214 0.184414i
\(208\) −71.0433 + 71.0433i −0.341554 + 0.341554i
\(209\) 135.967i 0.650560i
\(210\) −295.348 + 256.607i −1.40642 + 1.22194i
\(211\) −167.468 −0.793685 −0.396842 0.917887i \(-0.629894\pi\)
−0.396842 + 0.917887i \(0.629894\pi\)
\(212\) 222.271 + 222.271i 1.04845 + 1.04845i
\(213\) 86.5517 + 137.900i 0.406346 + 0.647418i
\(214\) 176.394i 0.824272i
\(215\) 179.685 + 35.4709i 0.835745 + 0.164981i
\(216\) −462.315 369.826i −2.14035 1.71216i
\(217\) 57.1888 + 156.802i 0.263543 + 0.722588i
\(218\) −497.784 + 497.784i −2.28341 + 2.28341i
\(219\) −28.8339 + 126.038i −0.131662 + 0.575514i
\(220\) −232.518 + 155.852i −1.05690 + 0.708417i
\(221\) 47.2144i 0.213640i
\(222\) 184.884 116.041i 0.832809 0.522705i
\(223\) 14.5058 14.5058i 0.0650483 0.0650483i −0.673834 0.738883i \(-0.735354\pi\)
0.738883 + 0.673834i \(0.235354\pi\)
\(224\) 440.508 + 205.057i 1.96656 + 0.915434i
\(225\) −150.245 167.485i −0.667758 0.744379i
\(226\) −590.423 −2.61249
\(227\) 12.9045 12.9045i 0.0568479 0.0568479i −0.678111 0.734959i \(-0.737201\pi\)
0.734959 + 0.678111i \(0.237201\pi\)
\(228\) −378.444 602.963i −1.65984 2.64457i
\(229\) 325.906 1.42317 0.711585 0.702601i \(-0.247978\pi\)
0.711585 + 0.702601i \(0.247978\pi\)
\(230\) −69.5207 + 46.5981i −0.302264 + 0.202601i
\(231\) 93.9187 + 72.9768i 0.406574 + 0.315917i
\(232\) 373.767 373.767i 1.61106 1.61106i
\(233\) −66.9917 + 66.9917i −0.287518 + 0.287518i −0.836098 0.548580i \(-0.815169\pi\)
0.548580 + 0.836098i \(0.315169\pi\)
\(234\) −34.7419 + 71.9571i −0.148470 + 0.307509i
\(235\) 37.5184 190.057i 0.159653 0.808753i
\(236\) −141.325 −0.598835
\(237\) 93.0371 + 148.233i 0.392562 + 0.625456i
\(238\) 485.574 177.099i 2.04023 0.744113i
\(239\) 175.883 0.735912 0.367956 0.929843i \(-0.380058\pi\)
0.367956 + 0.929843i \(0.380058\pi\)
\(240\) −257.796 + 577.584i −1.07415 + 2.40660i
\(241\) 407.167i 1.68949i −0.535170 0.844745i \(-0.679752\pi\)
0.535170 0.844745i \(-0.320248\pi\)
\(242\) −234.294 234.294i −0.968158 0.968158i
\(243\) −229.161 80.8340i −0.943050 0.332650i
\(244\) −892.381 −3.65730
\(245\) 67.9052 235.402i 0.277164 0.960823i
\(246\) 582.305 + 133.215i 2.36709 + 0.541526i
\(247\) −40.4465 + 40.4465i −0.163751 + 0.163751i
\(248\) 369.693 + 369.693i 1.49070 + 1.49070i
\(249\) 230.652 + 52.7667i 0.926312 + 0.211914i
\(250\) −257.084 + 388.400i −1.02834 + 1.55360i
\(251\) 299.503 1.19324 0.596620 0.802524i \(-0.296510\pi\)
0.596620 + 0.802524i \(0.296510\pi\)
\(252\) 619.614 + 62.2161i 2.45879 + 0.246889i
\(253\) 17.9904 + 17.9904i 0.0711081 + 0.0711081i
\(254\) 143.634 0.565486
\(255\) 106.263 + 277.591i 0.416720 + 1.08859i
\(256\) −145.161 −0.567035
\(257\) 37.0235 37.0235i 0.144060 0.144060i −0.631398 0.775459i \(-0.717519\pi\)
0.775459 + 0.631398i \(0.217519\pi\)
\(258\) −217.682 346.825i −0.843728 1.34428i
\(259\) −57.6846 + 123.919i −0.222721 + 0.478453i
\(260\) 115.530 + 22.8062i 0.444345 + 0.0877163i
\(261\) 94.3307 195.377i 0.361420 0.748571i
\(262\) 58.4954 + 58.4954i 0.223265 + 0.223265i
\(263\) −108.381 + 108.381i −0.412093 + 0.412093i −0.882467 0.470374i \(-0.844119\pi\)
0.470374 + 0.882467i \(0.344119\pi\)
\(264\) 363.187 + 83.0872i 1.37571 + 0.314724i
\(265\) 30.7941 155.994i 0.116204 0.588657i
\(266\) 567.683 + 264.257i 2.13415 + 0.993447i
\(267\) 174.543 + 278.094i 0.653720 + 1.04155i
\(268\) −4.86345 4.86345i −0.0181472 0.0181472i
\(269\) 98.6945i 0.366894i −0.983030 0.183447i \(-0.941274\pi\)
0.983030 0.183447i \(-0.0587256\pi\)
\(270\) −42.3098 + 501.255i −0.156703 + 1.85650i
\(271\) 218.741i 0.807162i 0.914944 + 0.403581i \(0.132235\pi\)
−0.914944 + 0.403581i \(0.867765\pi\)
\(272\) 590.836 590.836i 2.17219 2.17219i
\(273\) −6.22964 49.6469i −0.0228192 0.181857i
\(274\) 462.816i 1.68911i
\(275\) 130.972 + 53.8059i 0.476261 + 0.195658i
\(276\) 129.854 + 29.7070i 0.470485 + 0.107634i
\(277\) −187.908 + 187.908i −0.678370 + 0.678370i −0.959631 0.281261i \(-0.909247\pi\)
0.281261 + 0.959631i \(0.409247\pi\)
\(278\) −146.266 146.266i −0.526136 0.526136i
\(279\) 193.247 + 93.3024i 0.692643 + 0.334417i
\(280\) −118.350 758.273i −0.422677 2.70812i
\(281\) 284.207i 1.01141i −0.862705 0.505707i \(-0.831232\pi\)
0.862705 0.505707i \(-0.168768\pi\)
\(282\) −366.845 + 230.247i −1.30087 + 0.816477i
\(283\) −67.0672 + 67.0672i −0.236986 + 0.236986i −0.815601 0.578615i \(-0.803594\pi\)
0.578615 + 0.815601i \(0.303594\pi\)
\(284\) −536.443 −1.88888
\(285\) −146.769 + 328.832i −0.514979 + 1.15380i
\(286\) 50.2846i 0.175820i
\(287\) −351.414 + 128.168i −1.22444 + 0.446578i
\(288\) 589.875 205.741i 2.04818 0.714378i
\(289\) 103.662i 0.358692i
\(290\) −440.623 86.9816i −1.51939 0.299936i
\(291\) −198.787 45.4770i −0.683118 0.156278i
\(292\) −301.232 301.232i −1.03162 1.03162i
\(293\) −290.821 290.821i −0.992563 0.992563i 0.00740994 0.999973i \(-0.497641\pi\)
−0.999973 + 0.00740994i \(0.997641\pi\)
\(294\) −487.223 + 250.291i −1.65722 + 0.851331i
\(295\) 39.8024 + 59.3820i 0.134923 + 0.201295i
\(296\) 428.169i 1.44652i
\(297\) 151.985 16.8925i 0.511734 0.0568773i
\(298\) 705.816 + 705.816i 2.36851 + 2.36851i
\(299\) 10.7033i 0.0357970i
\(300\) 730.571 125.931i 2.43524 0.419771i
\(301\) 232.462 + 108.211i 0.772298 + 0.359506i
\(302\) −392.790 392.790i −1.30063 1.30063i
\(303\) −262.752 + 164.914i −0.867168 + 0.544270i
\(304\) 1012.29 3.32989
\(305\) 251.328 + 374.961i 0.824026 + 1.22938i
\(306\) 288.933 598.436i 0.944226 1.95567i
\(307\) −107.588 107.588i −0.350451 0.350451i 0.509826 0.860277i \(-0.329710\pi\)
−0.860277 + 0.509826i \(0.829710\pi\)
\(308\) −368.164 + 134.277i −1.19534 + 0.435964i
\(309\) 56.7023 247.855i 0.183503 0.802119i
\(310\) 86.0334 435.820i 0.277527 1.40587i
\(311\) 537.149 1.72717 0.863583 0.504206i \(-0.168215\pi\)
0.863583 + 0.504206i \(0.168215\pi\)
\(312\) −83.3222 132.755i −0.267058 0.425496i
\(313\) −346.433 + 346.433i −1.10682 + 1.10682i −0.113249 + 0.993567i \(0.536126\pi\)
−0.993567 + 0.113249i \(0.963874\pi\)
\(314\) 722.786i 2.30187i
\(315\) −148.365 277.872i −0.470999 0.882134i
\(316\) −576.639 −1.82481
\(317\) 25.3251 + 25.3251i 0.0798898 + 0.0798898i 0.745923 0.666033i \(-0.232009\pi\)
−0.666033 + 0.745923i \(0.732009\pi\)
\(318\) −301.097 + 188.981i −0.946846 + 0.594279i
\(319\) 136.532i 0.428000i
\(320\) −250.500 373.726i −0.782812 1.16789i
\(321\) 138.440 + 31.6712i 0.431277 + 0.0986642i
\(322\) −110.077 + 40.1475i −0.341855 + 0.124682i
\(323\) 336.376 336.376i 1.04141 1.04141i
\(324\) 626.978 497.939i 1.93512 1.53685i
\(325\) −22.9547 54.9664i −0.0706300 0.169127i
\(326\) 158.985i 0.487683i
\(327\) −301.301 480.054i −0.921410 1.46805i
\(328\) −828.532 + 828.532i −2.52601 + 2.52601i
\(329\) 114.457 245.880i 0.347895 0.747355i
\(330\) −113.173 295.642i −0.342949 0.895885i
\(331\) 162.753 0.491702 0.245851 0.969308i \(-0.420933\pi\)
0.245851 + 0.969308i \(0.420933\pi\)
\(332\) −551.261 + 551.261i −1.66042 + 1.66042i
\(333\) 57.8769 + 165.938i 0.173805 + 0.498311i
\(334\) 732.034 2.19172
\(335\) −0.673796 + 3.41325i −0.00201133 + 0.0101888i
\(336\) −543.319 + 699.233i −1.61702 + 2.08105i
\(337\) 342.565 342.565i 1.01651 1.01651i 0.0166527 0.999861i \(-0.494699\pi\)
0.999861 0.0166527i \(-0.00530098\pi\)
\(338\) 430.327 430.327i 1.27316 1.27316i
\(339\) 106.009 463.383i 0.312712 1.36691i
\(340\) −960.810 189.669i −2.82591 0.557851i
\(341\) −135.044 −0.396023
\(342\) 760.171 265.138i 2.22272 0.775257i
\(343\) 170.909 297.387i 0.498277 0.867018i
\(344\) 803.208 2.33491
\(345\) −24.0894 62.9287i −0.0698245 0.182402i
\(346\) 484.644i 1.40070i
\(347\) −0.436435 0.436435i −0.00125774 0.00125774i 0.706478 0.707735i \(-0.250283\pi\)
−0.707735 + 0.706478i \(0.750283\pi\)
\(348\) 380.016 + 605.468i 1.09200 + 1.73985i
\(349\) −313.871 −0.899344 −0.449672 0.893194i \(-0.648459\pi\)
−0.449672 + 0.893194i \(0.648459\pi\)
\(350\) −479.196 + 442.252i −1.36913 + 1.26358i
\(351\) −50.2365 40.1863i −0.143124 0.114491i
\(352\) −277.993 + 277.993i −0.789753 + 0.789753i
\(353\) 12.4873 + 12.4873i 0.0353746 + 0.0353746i 0.724573 0.689198i \(-0.242037\pi\)
−0.689198 + 0.724573i \(0.742037\pi\)
\(354\) 35.6430 155.801i 0.100686 0.440116i
\(355\) 151.082 + 225.403i 0.425584 + 0.634937i
\(356\) −1081.81 −3.03879
\(357\) 51.8092 + 412.892i 0.145124 + 1.15656i
\(358\) −366.225 366.225i −1.02298 1.02298i
\(359\) −491.177 −1.36818 −0.684091 0.729397i \(-0.739801\pi\)
−0.684091 + 0.729397i \(0.739801\pi\)
\(360\) −788.668 592.985i −2.19074 1.64718i
\(361\) 215.318 0.596448
\(362\) −40.6996 + 40.6996i −0.112430 + 0.112430i
\(363\) 225.949 141.815i 0.622449 0.390674i
\(364\) 149.463 + 69.5750i 0.410612 + 0.191140i
\(365\) −41.7335 + 211.410i −0.114338 + 0.579205i
\(366\) 225.064 983.789i 0.614928 2.68795i
\(367\) −356.973 356.973i −0.972679 0.972679i 0.0269576 0.999637i \(-0.491418\pi\)
−0.999637 + 0.0269576i \(0.991418\pi\)
\(368\) −133.940 + 133.940i −0.363967 + 0.363967i
\(369\) −209.104 + 433.094i −0.566676 + 1.17370i
\(370\) 302.199 202.557i 0.816755 0.547452i
\(371\) 93.9437 201.812i 0.253218 0.543968i
\(372\) −598.868 + 375.874i −1.60986 + 1.01041i
\(373\) −71.3079 71.3079i −0.191174 0.191174i 0.605029 0.796203i \(-0.293161\pi\)
−0.796203 + 0.605029i \(0.793161\pi\)
\(374\) 418.195i 1.11817i
\(375\) −258.670 271.505i −0.689787 0.724013i
\(376\) 849.570i 2.25949i
\(377\) 40.6146 40.6146i 0.107731 0.107731i
\(378\) −224.859 + 667.391i −0.594866 + 1.76558i
\(379\) 730.407i 1.92720i −0.267356 0.963598i \(-0.586150\pi\)
0.267356 0.963598i \(-0.413850\pi\)
\(380\) −660.602 985.565i −1.73843 2.59359i
\(381\) −25.7891 + 112.728i −0.0676880 + 0.295875i
\(382\) 710.292 710.292i 1.85940 1.85940i
\(383\) −317.179 317.179i −0.828144 0.828144i 0.159116 0.987260i \(-0.449136\pi\)
−0.987260 + 0.159116i \(0.949136\pi\)
\(384\) −38.5613 + 168.558i −0.100420 + 0.438952i
\(385\) 160.109 + 116.878i 0.415868 + 0.303579i
\(386\) 431.099i 1.11684i
\(387\) 311.284 108.572i 0.804352 0.280548i
\(388\) 475.104 475.104i 1.22450 1.22450i
\(389\) −319.504 −0.821347 −0.410674 0.911782i \(-0.634706\pi\)
−0.410674 + 0.911782i \(0.634706\pi\)
\(390\) −54.2795 + 121.612i −0.139178 + 0.311825i
\(391\) 89.0146i 0.227659i
\(392\) 92.2245 1070.47i 0.235267 2.73079i
\(393\) −56.4119 + 35.4064i −0.143542 + 0.0900926i
\(394\) 602.946i 1.53032i
\(395\) 162.403 + 242.292i 0.411147 + 0.613398i
\(396\) −219.070 + 453.737i −0.553207 + 1.14580i
\(397\) 443.370 + 443.370i 1.11680 + 1.11680i 0.992208 + 0.124594i \(0.0397628\pi\)
0.124594 + 0.992208i \(0.460237\pi\)
\(398\) 232.918 + 232.918i 0.585220 + 0.585220i
\(399\) −309.324 + 398.089i −0.775247 + 0.997717i
\(400\) −400.590 + 975.096i −1.00147 + 2.43774i
\(401\) 462.240i 1.15272i 0.817197 + 0.576359i \(0.195527\pi\)
−0.817197 + 0.576359i \(0.804473\pi\)
\(402\) 6.58820 4.13503i 0.0163886 0.0102861i
\(403\) 40.1719 + 40.1719i 0.0996821 + 0.0996821i
\(404\) 1022.13i 2.53002i
\(405\) −385.805 123.205i −0.952605 0.304211i
\(406\) −570.041 265.355i −1.40404 0.653583i
\(407\) −78.2022 78.2022i −0.192143 0.192143i
\(408\) 692.955 + 1104.06i 1.69842 + 2.70604i
\(409\) 195.136 0.477106 0.238553 0.971130i \(-0.423327\pi\)
0.238553 + 0.971130i \(0.423327\pi\)
\(410\) 976.732 + 192.813i 2.38227 + 0.470275i
\(411\) −363.233 83.0977i −0.883779 0.202184i
\(412\) 592.376 + 592.376i 1.43781 + 1.43781i
\(413\) 34.2925 + 94.0240i 0.0830327 + 0.227661i
\(414\) −65.4998 + 135.663i −0.158212 + 0.327688i
\(415\) 386.884 + 76.3733i 0.932252 + 0.184032i
\(416\) 165.391 0.397574
\(417\) 141.056 88.5324i 0.338264 0.212308i
\(418\) −358.249 + 358.249i −0.857056 + 0.857056i
\(419\) 389.604i 0.929843i −0.885352 0.464922i \(-0.846083\pi\)
0.885352 0.464922i \(-0.153917\pi\)
\(420\) 1035.34 + 72.6687i 2.46509 + 0.173021i
\(421\) 22.7752 0.0540978 0.0270489 0.999634i \(-0.491389\pi\)
0.0270489 + 0.999634i \(0.491389\pi\)
\(422\) 441.248 + 441.248i 1.04561 + 1.04561i
\(423\) −114.839 329.252i −0.271487 0.778373i
\(424\) 697.306i 1.64459i
\(425\) 190.905 + 457.131i 0.449187 + 1.07560i
\(426\) 135.294 591.391i 0.317591 1.38824i
\(427\) 216.536 + 593.704i 0.507111 + 1.39041i
\(428\) −330.873 + 330.873i −0.773068 + 0.773068i
\(429\) 39.4650 + 9.02850i 0.0919930 + 0.0210454i
\(430\) −379.980 566.899i −0.883673 1.31837i
\(431\) 838.658i 1.94584i −0.231137 0.972921i \(-0.574244\pi\)
0.231137 0.972921i \(-0.425756\pi\)
\(432\) 125.767 + 1131.54i 0.291126 + 2.61931i
\(433\) −61.2050 + 61.2050i −0.141351 + 0.141351i −0.774241 0.632890i \(-0.781868\pi\)
0.632890 + 0.774241i \(0.281868\pi\)
\(434\) 262.462 563.828i 0.604752 1.29914i
\(435\) 147.379 330.198i 0.338802 0.759076i
\(436\) 1867.45 4.28314
\(437\) −76.2549 + 76.2549i −0.174496 + 0.174496i
\(438\) 408.060 256.115i 0.931643 0.584737i
\(439\) −452.142 −1.02994 −0.514968 0.857209i \(-0.672196\pi\)
−0.514968 + 0.857209i \(0.672196\pi\)
\(440\) 609.194 + 120.258i 1.38453 + 0.273315i
\(441\) −108.957 427.328i −0.247068 0.968998i
\(442\) 124.402 124.402i 0.281452 0.281452i
\(443\) 208.241 208.241i 0.470070 0.470070i −0.431867 0.901937i \(-0.642145\pi\)
0.901937 + 0.431867i \(0.142145\pi\)
\(444\) −564.462 129.133i −1.27131 0.290841i
\(445\) 304.678 + 454.555i 0.684670 + 1.02147i
\(446\) −76.4403 −0.171391
\(447\) −680.675 + 427.220i −1.52276 + 0.955749i
\(448\) −215.823 591.748i −0.481747 1.32087i
\(449\) −547.513 −1.21941 −0.609703 0.792630i \(-0.708711\pi\)
−0.609703 + 0.792630i \(0.708711\pi\)
\(450\) −45.4238 + 837.165i −0.100942 + 1.86037i
\(451\) 302.651i 0.671067i
\(452\) 1107.49 + 1107.49i 2.45021 + 2.45021i
\(453\) 378.799 237.750i 0.836202 0.524834i
\(454\) −68.0021 −0.149784
\(455\) −12.8602 82.3962i −0.0282642 0.181090i
\(456\) −352.178 + 1539.43i −0.772321 + 3.37594i
\(457\) 169.531 169.531i 0.370965 0.370965i −0.496864 0.867829i \(-0.665515\pi\)
0.867829 + 0.496864i \(0.165515\pi\)
\(458\) −858.704 858.704i −1.87490 1.87490i
\(459\) 417.795 + 334.212i 0.910229 + 0.728131i
\(460\) 217.811 + 42.9972i 0.473502 + 0.0934722i
\(461\) 668.267 1.44960 0.724801 0.688958i \(-0.241932\pi\)
0.724801 + 0.688958i \(0.241932\pi\)
\(462\) −55.1781 439.740i −0.119433 0.951819i
\(463\) −254.021 254.021i −0.548641 0.548641i 0.377407 0.926048i \(-0.376816\pi\)
−0.926048 + 0.377407i \(0.876816\pi\)
\(464\) −1016.49 −2.19072
\(465\) 326.599 + 145.772i 0.702363 + 0.313489i
\(466\) 353.023 0.757560
\(467\) 651.899 651.899i 1.39593 1.39593i 0.584629 0.811301i \(-0.301240\pi\)
0.811301 0.584629i \(-0.198760\pi\)
\(468\) 200.142 69.8069i 0.427654 0.149160i
\(469\) −2.05555 + 4.41578i −0.00438284 + 0.00941532i
\(470\) −599.621 + 401.912i −1.27579 + 0.855133i
\(471\) −567.266 129.775i −1.20439 0.275530i
\(472\) 221.681 + 221.681i 0.469663 + 0.469663i
\(473\) −146.700 + 146.700i −0.310149 + 0.310149i
\(474\) 145.432 635.704i 0.306818 1.34115i
\(475\) −228.065 + 555.144i −0.480137 + 1.16872i
\(476\) −1243.02 578.625i −2.61138 1.21560i
\(477\) −94.2569 270.242i −0.197604 0.566545i
\(478\) −463.421 463.421i −0.969500 0.969500i
\(479\) 686.172i 1.43251i 0.697839 + 0.716254i \(0.254145\pi\)
−0.697839 + 0.716254i \(0.745855\pi\)
\(480\) 972.396 372.238i 2.02582 0.775496i
\(481\) 46.5261i 0.0967279i
\(482\) −1072.81 + 1072.81i −2.22575 + 2.22575i
\(483\) −11.7449 93.6007i −0.0243166 0.193790i
\(484\) 878.960i 1.81603i
\(485\) −333.437 65.8224i −0.687498 0.135716i
\(486\) 390.816 + 816.783i 0.804149 + 1.68062i
\(487\) −642.848 + 642.848i −1.32002 + 1.32002i −0.406258 + 0.913758i \(0.633167\pi\)
−0.913758 + 0.406258i \(0.866833\pi\)
\(488\) 1399.78 + 1399.78i 2.86840 + 2.86840i
\(489\) 124.776 + 28.5454i 0.255166 + 0.0583750i
\(490\) −799.160 + 441.324i −1.63094 + 0.900661i
\(491\) 429.307i 0.874353i 0.899376 + 0.437176i \(0.144021\pi\)
−0.899376 + 0.437176i \(0.855979\pi\)
\(492\) −842.385 1342.15i −1.71217 2.72794i
\(493\) −337.774 + 337.774i −0.685140 + 0.685140i
\(494\) 213.139 0.431456
\(495\) 252.350 35.7402i 0.509797 0.0722024i
\(496\) 1005.41i 2.02704i
\(497\) 130.168 + 356.897i 0.261907 + 0.718103i
\(498\) −468.696 746.758i −0.941156 1.49951i
\(499\) 195.516i 0.391815i −0.980622 0.195908i \(-0.937235\pi\)
0.980622 0.195908i \(-0.0627653\pi\)
\(500\) 1210.77 246.316i 2.42155 0.492633i
\(501\) −131.435 + 574.525i −0.262346 + 1.14676i
\(502\) −789.138 789.138i −1.57199 1.57199i
\(503\) 328.382 + 328.382i 0.652846 + 0.652846i 0.953677 0.300831i \(-0.0972640\pi\)
−0.300831 + 0.953677i \(0.597264\pi\)
\(504\) −874.330 1069.51i −1.73478 2.12205i
\(505\) −429.478 + 287.869i −0.850451 + 0.570038i
\(506\) 94.8029i 0.187357i
\(507\) 260.470 + 414.999i 0.513748 + 0.818539i
\(508\) −269.422 269.422i −0.530359 0.530359i
\(509\) 16.1598i 0.0317481i 0.999874 + 0.0158740i \(0.00505308\pi\)
−0.999874 + 0.0158740i \(0.994947\pi\)
\(510\) 451.419 1011.39i 0.885135 1.98312i
\(511\) −127.317 + 273.504i −0.249152 + 0.535234i
\(512\) 545.497 + 545.497i 1.06542 + 1.06542i
\(513\) 71.6017 + 644.212i 0.139574 + 1.25577i
\(514\) −195.101 −0.379574
\(515\) 82.0696 415.740i 0.159358 0.807263i
\(516\) −242.243 + 1058.88i −0.469462 + 2.05209i
\(517\) 155.168 + 155.168i 0.300132 + 0.300132i
\(518\) 478.495 174.517i 0.923735 0.336905i
\(519\) −380.364 87.0168i −0.732879 0.167662i
\(520\) −145.445 216.992i −0.279702 0.417293i
\(521\) −656.049 −1.25921 −0.629605 0.776915i \(-0.716783\pi\)
−0.629605 + 0.776915i \(0.716783\pi\)
\(522\) −763.329 + 266.239i −1.46232 + 0.510037i
\(523\) 289.472 289.472i 0.553483 0.553483i −0.373961 0.927444i \(-0.622001\pi\)
0.927444 + 0.373961i \(0.122001\pi\)
\(524\) 219.447i 0.418792i
\(525\) −261.056 455.494i −0.497249 0.867608i
\(526\) 571.127 1.08579
\(527\) −334.092 334.092i −0.633951 0.633951i
\(528\) −380.879 606.842i −0.721361 1.14932i
\(529\) 508.821i 0.961854i
\(530\) −492.154 + 329.880i −0.928592 + 0.622415i
\(531\) 115.878 + 55.9475i 0.218226 + 0.105363i
\(532\) −569.154 1560.52i −1.06984 2.93331i
\(533\) −90.0307 + 90.0307i −0.168913 + 0.168913i
\(534\) 272.839 1192.62i 0.510934 2.23337i
\(535\) 232.213 + 45.8402i 0.434042 + 0.0856825i
\(536\) 15.2575i 0.0284655i
\(537\) 353.181 221.671i 0.657692 0.412794i
\(538\) −260.043 + 260.043i −0.483351 + 0.483351i
\(539\) 178.670 + 212.358i 0.331484 + 0.393986i
\(540\) 1019.60 860.872i 1.88814 1.59421i
\(541\) −210.543 −0.389174 −0.194587 0.980885i \(-0.562337\pi\)
−0.194587 + 0.980885i \(0.562337\pi\)
\(542\) 576.344 576.344i 1.06336 1.06336i
\(543\) −24.6349 39.2499i −0.0453680 0.0722835i
\(544\) −1375.48 −2.52846
\(545\) −525.944 784.665i −0.965034 1.43975i
\(546\) −114.397 + 147.225i −0.209518 + 0.269643i
\(547\) 81.9004 81.9004i 0.149727 0.149727i −0.628269 0.777996i \(-0.716236\pi\)
0.777996 + 0.628269i \(0.216236\pi\)
\(548\) 868.132 868.132i 1.58418 1.58418i
\(549\) 731.700 + 353.275i 1.33279 + 0.643487i
\(550\) −203.318 486.857i −0.369670 0.885194i
\(551\) −578.712 −1.05029
\(552\) −157.090 250.286i −0.284583 0.453416i
\(553\) 139.921 + 383.640i 0.253022 + 0.693743i
\(554\) 990.211 1.78739
\(555\) 104.714 + 273.545i 0.188674 + 0.492873i
\(556\) 548.719i 0.986905i
\(557\) 509.388 + 509.388i 0.914521 + 0.914521i 0.996624 0.0821026i \(-0.0261635\pi\)
−0.0821026 + 0.996624i \(0.526164\pi\)
\(558\) −263.337 755.008i −0.471931 1.35306i
\(559\) 87.2789 0.156134
\(560\) −870.165 + 1192.03i −1.55387 + 2.12862i
\(561\) −328.213 75.0861i −0.585050 0.133843i
\(562\) −748.837 + 748.837i −1.33245 + 1.33245i
\(563\) −345.404 345.404i −0.613507 0.613507i 0.330351 0.943858i \(-0.392833\pi\)
−0.943858 + 0.330351i \(0.892833\pi\)
\(564\) 1120.00 + 256.225i 1.98582 + 0.454300i
\(565\) 153.435 777.258i 0.271567 1.37568i
\(566\) 353.421 0.624418
\(567\) −483.417 296.306i −0.852587 0.522585i
\(568\) 841.459 + 841.459i 1.48144 + 1.48144i
\(569\) 304.242 0.534696 0.267348 0.963600i \(-0.413853\pi\)
0.267348 + 0.963600i \(0.413853\pi\)
\(570\) 1253.13 479.703i 2.19846 0.841584i
\(571\) 10.6264 0.0186101 0.00930507 0.999957i \(-0.497038\pi\)
0.00930507 + 0.999957i \(0.497038\pi\)
\(572\) −94.3219 + 94.3219i −0.164898 + 0.164898i
\(573\) 429.929 + 684.992i 0.750313 + 1.19545i
\(574\) 1263.61 + 588.214i 2.20142 + 1.02476i
\(575\) −43.2772 103.630i −0.0752647 0.180225i
\(576\) −729.289 352.110i −1.26613 0.611303i
\(577\) 21.8636 + 21.8636i 0.0378918 + 0.0378918i 0.725799 0.687907i \(-0.241470\pi\)
−0.687907 + 0.725799i \(0.741470\pi\)
\(578\) −273.131 + 273.131i −0.472545 + 0.472545i
\(579\) −338.340 77.4029i −0.584353 0.133684i
\(580\) 663.347 + 989.660i 1.14370 + 1.70631i
\(581\) 500.519 + 232.992i 0.861478 + 0.401019i
\(582\) 403.946 + 643.594i 0.694065 + 1.10583i
\(583\) 127.358 + 127.358i 0.218453 + 0.218453i
\(584\) 945.019i 1.61818i
\(585\) −85.6990 64.4355i −0.146494 0.110146i
\(586\) 1532.52i 2.61523i
\(587\) −229.516 + 229.516i −0.390999 + 0.390999i −0.875043 0.484045i \(-0.839167\pi\)
0.484045 + 0.875043i \(0.339167\pi\)
\(588\) 1383.40 + 444.428i 2.35272 + 0.755830i
\(589\) 572.404i 0.971823i
\(590\) 51.5888 261.334i 0.0874386 0.442938i
\(591\) −473.212 108.258i −0.800697 0.183177i
\(592\) 582.223 582.223i 0.983484 0.983484i
\(593\) −88.7036 88.7036i −0.149584 0.149584i 0.628348 0.777932i \(-0.283731\pi\)
−0.777932 + 0.628348i \(0.783731\pi\)
\(594\) −444.962 355.945i −0.749095 0.599233i
\(595\) 106.953 + 685.253i 0.179753 + 1.15169i
\(596\) 2647.88i 4.44276i
\(597\) −224.621 + 140.981i −0.376250 + 0.236150i
\(598\) −28.2013 + 28.2013i −0.0471594 + 0.0471594i
\(599\) −861.037 −1.43746 −0.718728 0.695291i \(-0.755276\pi\)
−0.718728 + 0.695291i \(0.755276\pi\)
\(600\) −1343.50 948.433i −2.23917 1.58072i
\(601\) 413.625i 0.688227i −0.938928 0.344114i \(-0.888179\pi\)
0.938928 0.344114i \(-0.111821\pi\)
\(602\) −327.378 897.614i −0.543818 1.49105i
\(603\) 2.06240 + 5.91307i 0.00342024 + 0.00980609i
\(604\) 1473.56i 2.43967i
\(605\) 369.322 247.548i 0.610449 0.409170i
\(606\) 1126.82 + 257.786i 1.85945 + 0.425390i
\(607\) 473.829 + 473.829i 0.780608 + 0.780608i 0.979933 0.199325i \(-0.0638749\pi\)
−0.199325 + 0.979933i \(0.563875\pi\)
\(608\) −1178.32 1178.32i −1.93802 1.93802i
\(609\) 310.609 399.743i 0.510031 0.656393i
\(610\) 325.752 1650.16i 0.534019 2.70518i
\(611\) 92.3167i 0.151091i
\(612\) −1664.49 + 580.554i −2.71976 + 0.948618i
\(613\) −298.846 298.846i −0.487514 0.487514i 0.420007 0.907521i \(-0.362028\pi\)
−0.907521 + 0.420007i \(0.862028\pi\)
\(614\) 566.954i 0.923377i
\(615\) −326.696 + 731.952i −0.531213 + 1.19017i
\(616\) 788.124 + 366.873i 1.27942 + 0.595572i
\(617\) −601.654 601.654i −0.975128 0.975128i 0.0245706 0.999698i \(-0.492178\pi\)
−0.999698 + 0.0245706i \(0.992178\pi\)
\(618\) −802.455 + 503.653i −1.29847 + 0.814973i
\(619\) −620.315 −1.00212 −0.501062 0.865411i \(-0.667057\pi\)
−0.501062 + 0.865411i \(0.667057\pi\)
\(620\) −978.872 + 656.116i −1.57883 + 1.05825i
\(621\) −94.7122 75.7644i −0.152516 0.122004i
\(622\) −1415.29 1415.29i −2.27539 2.27539i
\(623\) 262.501 + 719.732i 0.421350 + 1.15527i
\(624\) −67.2180 + 293.820i −0.107721 + 0.470866i
\(625\) −444.497 439.372i −0.711195 0.702995i
\(626\) 1825.58 2.91627
\(627\) −216.843 345.489i −0.345842 0.551019i
\(628\) 1355.77 1355.77i 2.15888 2.15888i
\(629\) 386.938i 0.615163i
\(630\) −341.230 + 1123.06i −0.541635 + 1.78263i
\(631\) 407.417 0.645669 0.322835 0.946455i \(-0.395364\pi\)
0.322835 + 0.946455i \(0.395364\pi\)
\(632\) 904.511 + 904.511i 1.43119 + 1.43119i
\(633\) −425.531 + 267.080i −0.672244 + 0.421928i
\(634\) 133.454i 0.210496i
\(635\) −37.3265 + 189.085i −0.0587820 + 0.297772i
\(636\) 919.268 + 210.303i 1.44539 + 0.330665i
\(637\) 10.0214 116.320i 0.0157322 0.182606i
\(638\) 359.738 359.738i 0.563852 0.563852i
\(639\) 439.851 + 212.366i 0.688343 + 0.332341i
\(640\) −55.8127 + 282.731i −0.0872074 + 0.441767i
\(641\) 715.610i 1.11640i 0.829708 + 0.558198i \(0.188507\pi\)
−0.829708 + 0.558198i \(0.811493\pi\)
\(642\) −281.317 448.213i −0.438188 0.698151i
\(643\) 562.981 562.981i 0.875554 0.875554i −0.117517 0.993071i \(-0.537494\pi\)
0.993071 + 0.117517i \(0.0374936\pi\)
\(644\) 281.786 + 131.172i 0.437556 + 0.203683i
\(645\) 513.145 196.435i 0.795574 0.304550i
\(646\) −1772.59 −2.74394
\(647\) 59.3647 59.3647i 0.0917537 0.0917537i −0.659740 0.751494i \(-0.729334\pi\)
0.751494 + 0.659740i \(0.229334\pi\)
\(648\) −1764.54 202.409i −2.72305 0.312359i
\(649\) −80.9771 −0.124772
\(650\) −84.3450 + 205.308i −0.129762 + 0.315859i
\(651\) 395.386 + 307.223i 0.607351 + 0.471925i
\(652\) −298.217 + 298.217i −0.457388 + 0.457388i
\(653\) 242.978 242.978i 0.372094 0.372094i −0.496145 0.868240i \(-0.665252\pi\)
0.868240 + 0.496145i \(0.165252\pi\)
\(654\) −470.981 + 2058.73i −0.720155 + 3.14791i
\(655\) −92.2073 + 61.8045i −0.140774 + 0.0943579i
\(656\) 2253.27 3.43486
\(657\) 127.741 + 366.243i 0.194431 + 0.557448i
\(658\) −949.425 + 346.275i −1.44290 + 0.526254i
\(659\) 1201.84 1.82373 0.911866 0.410489i \(-0.134642\pi\)
0.911866 + 0.410489i \(0.134642\pi\)
\(660\) −342.268 + 766.840i −0.518587 + 1.16188i
\(661\) 618.277i 0.935366i −0.883896 0.467683i \(-0.845089\pi\)
0.883896 0.467683i \(-0.154911\pi\)
\(662\) −428.827 428.827i −0.647775 0.647775i
\(663\) 75.2985 + 119.971i 0.113572 + 0.180951i
\(664\) 1729.40 2.60453
\(665\) −495.405 + 678.648i −0.744969 + 1.02052i
\(666\) 284.721 589.712i 0.427509 0.885454i
\(667\) 76.5718 76.5718i 0.114800 0.114800i
\(668\) −1373.12 1373.12i −2.05557 2.05557i
\(669\) 13.7247 59.9929i 0.0205153 0.0896754i
\(670\) 10.7687 7.21799i 0.0160726 0.0107731i
\(671\) −511.321 −0.762029
\(672\) 1446.35 181.486i 2.15231 0.270069i
\(673\) 172.954 + 172.954i 0.256990 + 0.256990i 0.823829 0.566839i \(-0.191834\pi\)
−0.566839 + 0.823829i \(0.691834\pi\)
\(674\) −1805.20 −2.67834
\(675\) −648.879 185.961i −0.961302 0.275498i
\(676\) −1614.38 −2.38814
\(677\) 785.544 785.544i 1.16033 1.16033i 0.175927 0.984403i \(-0.443708\pi\)
0.984403 0.175927i \(-0.0562923\pi\)
\(678\) −1500.25 + 941.618i −2.21276 + 1.38882i
\(679\) −431.373 200.804i −0.635306 0.295736i
\(680\) 1209.60 + 1804.63i 1.77883 + 2.65387i
\(681\) 12.2096 53.3702i 0.0179290 0.0783704i
\(682\) 355.816 + 355.816i 0.521725 + 0.521725i
\(683\) 510.988 510.988i 0.748152 0.748152i −0.225980 0.974132i \(-0.572558\pi\)
0.974132 + 0.225980i \(0.0725583\pi\)
\(684\) −1923.23 928.563i −2.81175 1.35755i
\(685\) −609.271 120.274i −0.889446 0.175582i
\(686\) −1233.88 + 333.247i −1.79866 + 0.485783i
\(687\) 828.118 519.761i 1.20541 0.756566i
\(688\) −1092.20 1092.20i −1.58750 1.58750i
\(689\) 75.7713i 0.109973i
\(690\) −102.335 + 229.278i −0.148311 + 0.332286i
\(691\) 93.1153i 0.134754i 0.997728 + 0.0673772i \(0.0214631\pi\)
−0.997728 + 0.0673772i \(0.978537\pi\)
\(692\) 909.076 909.076i 1.31369 1.31369i
\(693\) 355.030 + 35.6489i 0.512308 + 0.0514415i
\(694\) 2.29986i 0.00331392i
\(695\) 230.561 154.540i 0.331743 0.222360i
\(696\) 353.641 1545.82i 0.508105 2.22101i
\(697\) 748.746 748.746i 1.07424 1.07424i
\(698\) 826.995 + 826.995i 1.18481 + 1.18481i
\(699\) −63.3846 + 277.064i −0.0906789 + 0.396372i
\(700\) 1728.42 + 69.2972i 2.46917 + 0.0989960i
\(701\) 582.081i 0.830358i 0.909740 + 0.415179i \(0.136281\pi\)
−0.909740 + 0.415179i \(0.863719\pi\)
\(702\) 26.4804 + 238.248i 0.0377214 + 0.339385i
\(703\) 331.472 331.472i 0.471511 0.471511i
\(704\) 509.636 0.723915
\(705\) −207.773 542.765i −0.294714 0.769879i
\(706\) 65.8034i 0.0932060i
\(707\) −680.025 + 248.019i −0.961845 + 0.350805i
\(708\) −359.103 + 225.388i −0.507208 + 0.318344i
\(709\) 710.656i 1.00234i −0.865350 0.501168i \(-0.832904\pi\)
0.865350 0.501168i \(-0.167096\pi\)
\(710\) 195.821 991.972i 0.275804 1.39714i
\(711\) 472.810 + 228.279i 0.664993 + 0.321067i
\(712\) 1696.92 + 1696.92i 2.38331 + 2.38331i
\(713\) 75.7371 + 75.7371i 0.106223 + 0.106223i
\(714\) 951.390 1224.41i 1.33248 1.71485i
\(715\) 66.1968 + 13.0676i 0.0925829 + 0.0182764i
\(716\) 1373.90i 1.91886i
\(717\) 446.914 280.502i 0.623311 0.391216i
\(718\) 1294.17 + 1294.17i 1.80246 + 1.80246i
\(719\) 1307.80i 1.81892i 0.415790 + 0.909461i \(0.363505\pi\)
−0.415790 + 0.909461i \(0.636495\pi\)
\(720\) 266.089 + 1878.77i 0.369568 + 2.60940i
\(721\) 250.370 537.850i 0.347254 0.745978i
\(722\) −567.324 567.324i −0.785768 0.785768i
\(723\) −649.358 1034.60i −0.898143 1.43098i
\(724\) 152.685 0.210892
\(725\) 229.012 557.451i 0.315879 0.768897i
\(726\) −968.993 221.679i −1.33470 0.305343i
\(727\) −113.590 113.590i −0.156245 0.156245i 0.624655 0.780901i \(-0.285239\pi\)
−0.780901 + 0.624655i \(0.785239\pi\)
\(728\) −125.311 343.580i −0.172130 0.471951i
\(729\) −711.208 + 160.074i −0.975595 + 0.219580i
\(730\) 666.988 447.067i 0.913683 0.612421i
\(731\) −725.860 −0.992969
\(732\) −2267.52 + 1423.19i −3.09770 + 1.94424i
\(733\) 336.426 336.426i 0.458971 0.458971i −0.439346 0.898318i \(-0.644790\pi\)
0.898318 + 0.439346i \(0.144790\pi\)
\(734\) 1881.12i 2.56284i
\(735\) −202.878 706.446i −0.276024 0.961151i
\(736\) 311.816 0.423663
\(737\) −2.78668 2.78668i −0.00378112 0.00378112i
\(738\) 1692.08 590.175i 2.29279 0.799695i
\(739\) 290.721i 0.393398i 0.980464 + 0.196699i \(0.0630223\pi\)
−0.980464 + 0.196699i \(0.936978\pi\)
\(740\) −946.803 186.904i −1.27946 0.252574i
\(741\) −38.2687 + 167.279i −0.0516447 + 0.225747i
\(742\) −779.265 + 284.214i −1.05022 + 0.383038i
\(743\) −409.064 + 409.064i −0.550557 + 0.550557i −0.926602 0.376044i \(-0.877284\pi\)
0.376044 + 0.926602i \(0.377284\pi\)
\(744\) 1528.97 + 349.787i 2.05507 + 0.470143i
\(745\) −1112.59 + 745.743i −1.49341 + 1.00100i
\(746\) 375.768i 0.503710i
\(747\) 670.233 233.769i 0.897233 0.312943i
\(748\) 784.434 784.434i 1.04871 1.04871i
\(749\) 300.417 + 139.845i 0.401091 + 0.186709i
\(750\) −33.8173 + 1396.92i −0.0450898 + 1.86256i
\(751\) 220.161 0.293157 0.146579 0.989199i \(-0.453174\pi\)
0.146579 + 0.989199i \(0.453174\pi\)
\(752\) −1155.24 + 1155.24i −1.53622 + 1.53622i
\(753\) 761.029 477.653i 1.01066 0.634334i
\(754\) −214.025 −0.283852
\(755\) 619.162 415.010i 0.820082 0.549682i
\(756\) 1673.65 830.083i 2.21382 1.09799i
\(757\) −211.010 + 211.010i −0.278745 + 0.278745i −0.832608 0.553863i \(-0.813153\pi\)
0.553863 + 0.832608i \(0.313153\pi\)
\(758\) −1924.50 + 1924.50i −2.53891 + 2.53891i
\(759\) 74.4044 + 17.0217i 0.0980295 + 0.0224264i
\(760\) −509.734 + 2582.16i −0.670703 + 3.39758i
\(761\) −1091.43 −1.43420 −0.717100 0.696971i \(-0.754531\pi\)
−0.717100 + 0.696971i \(0.754531\pi\)
\(762\) 364.969 229.069i 0.478962 0.300616i
\(763\) −453.136 1242.42i −0.593888 1.62834i
\(764\) −2664.68 −3.48780
\(765\) 712.721 + 535.882i 0.931661 + 0.700499i
\(766\) 1671.42i 2.18201i
\(767\) 24.0885 + 24.0885i 0.0314061 + 0.0314061i