Properties

Label 105.3.k.d.62.15
Level 105
Weight 3
Character 105.62
Analytic conductor 2.861
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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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 62.15
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.15

$q$-expansion

\(f(q)\) \(=\) \(q+(2.63482 - 2.63482i) q^{2} +(-1.59482 - 2.54097i) q^{3} -9.88460i q^{4} +(4.15332 + 2.78387i) q^{5} +(-10.8971 - 2.49295i) q^{6} +(2.39850 + 6.57626i) q^{7} +(-15.5049 - 15.5049i) q^{8} +(-3.91310 + 8.10479i) q^{9} +O(q^{10})\) \(q+(2.63482 - 2.63482i) q^{2} +(-1.59482 - 2.54097i) q^{3} -9.88460i q^{4} +(4.15332 + 2.78387i) q^{5} +(-10.8971 - 2.49295i) q^{6} +(2.39850 + 6.57626i) q^{7} +(-15.5049 - 15.5049i) q^{8} +(-3.91310 + 8.10479i) q^{9} +(18.2783 - 3.60824i) q^{10} +5.66373i q^{11} +(-25.1165 + 15.7642i) q^{12} +(-1.68481 - 1.68481i) q^{13} +(23.6469 + 11.0077i) q^{14} +(0.449964 - 14.9932i) q^{15} -42.1670 q^{16} +(-14.0118 - 14.0118i) q^{17} +(11.0444 + 31.6650i) 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} +(26.8348 - 2.98258i) q^{27} +(65.0037 - 23.7082i) q^{28} -24.1064 q^{29} +(-38.3190 - 40.6902i) q^{30} +23.8436i q^{31} +(-49.0830 + 49.0830i) q^{32} +(14.3914 - 9.03263i) q^{33} -73.8374 q^{34} +(-8.34576 + 33.9904i) 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} +(-9.74236 - 77.6415i) q^{42} +(25.9017 - 25.9017i) q^{43} +55.9837 q^{44} +(-38.8151 + 22.7682i) q^{45} -16.7386 q^{46} +(27.3968 + 27.3968i) q^{47} +(67.2487 + 107.145i) 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} +(-38.2862 - 61.0002i) q^{57} +(-63.5160 + 63.5160i) q^{58} -14.2975i q^{59} +(-148.202 - 4.44772i) q^{60} +90.2799i q^{61} +(62.8237 + 62.8237i) q^{62} +(-62.6848 - 6.29425i) 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} +(67.5692 + 111.548i) q^{70} +54.2705i q^{71} +(186.336 - 64.9917i) q^{72} +(30.4748 + 30.4748i) q^{73} -72.7609 q^{74} +(43.6082 - 61.0191i) q^{75} -237.296i q^{76} +(-37.2462 + 13.5845i) q^{77} +(14.1594 + 22.5597i) 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} +(38.4453 + 61.2536i) q^{87} +(87.8156 - 87.8156i) q^{88} -109.444i q^{89} +(-42.2808 + 162.261i) q^{90} +(7.03872 - 15.1207i) q^{91} +(-31.3976 + 31.3976i) q^{92} +(60.5860 - 38.0262i) q^{93} +144.372 q^{94} +(99.7071 + 66.8314i) q^{95} +(202.997 + 46.4402i) q^{96} +(48.0651 - 48.0651i) q^{97} +(-15.6722 + 181.910i) 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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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 0.401595 0.915817i \(-0.368456\pi\)
0.915817 0.401595i \(-0.131544\pi\)
\(3\) −1.59482 2.54097i −0.531606 0.846991i
\(4\) 9.88460i 2.47115i
\(5\) 4.15332 + 2.78387i 0.830663 + 0.556775i
\(6\) −10.8971 2.49295i −1.81618 0.415492i
\(7\) 2.39850 + 6.57626i 0.342643 + 0.939466i
\(8\) −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 \(0.917120\pi\)
\(12\) −25.1165 + 15.7642i −2.09304 + 1.31368i
\(13\) −1.68481 1.68481i −0.129601 0.129601i 0.639331 0.768932i \(-0.279211\pi\)
−0.768932 + 0.639331i \(0.779211\pi\)
\(14\) 23.6469 + 11.0077i 1.68907 + 0.786262i
\(15\) 0.449964 14.9932i 0.0299976 0.999550i
\(16\) −42.1670 −2.63544
\(17\) −14.0118 14.0118i −0.824224 0.824224i 0.162486 0.986711i \(-0.448049\pi\)
−0.986711 + 0.162486i \(0.948049\pi\)
\(18\) 11.0444 + 31.6650i 0.613576 + 1.75917i
\(19\) 24.0066 1.26351 0.631753 0.775170i \(-0.282336\pi\)
0.631753 + 0.775170i \(0.282336\pi\)
\(20\) 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 \(-0.281134\pi\)
−0.772780 + 0.634675i \(0.781134\pi\)
\(24\) −14.6700 + 64.1251i −0.611252 + 2.67188i
\(25\) 9.50008 + 23.1246i 0.380003 + 0.924985i
\(26\) −8.87835 −0.341475
\(27\) 26.8348 2.98258i 0.993880 0.110466i
\(28\) 65.0037 23.7082i 2.32156 0.846722i
\(29\) −24.1064 −0.831254 −0.415627 0.909535i \(-0.636438\pi\)
−0.415627 + 0.909535i \(0.636438\pi\)
\(30\) −38.3190 40.6902i −1.27730 1.35634i
\(31\) 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
\(33\) 14.3914 9.03263i 0.436103 0.273716i
\(34\) −73.8374 −2.17169
\(35\) −8.34576 + 33.9904i −0.238450 + 0.971155i
\(36\) 80.1127 + 38.6795i 2.22535 + 1.07443i
\(37\) −13.8075 13.8075i −0.373177 0.373177i 0.495456 0.868633i \(-0.335001\pi\)
−0.868633 + 0.495456i \(0.835001\pi\)
\(38\) 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 \(0.725930\pi\)
\(42\) −9.74236 77.6415i −0.231961 1.84861i
\(43\) 25.9017 25.9017i 0.602366 0.602366i −0.338574 0.940940i \(-0.609945\pi\)
0.940940 + 0.338574i \(0.109945\pi\)
\(44\) 55.9837 1.27236
\(45\) −38.8151 + 22.7682i −0.862557 + 0.505959i
\(46\) −16.7386 −0.363882
\(47\) 27.3968 + 27.3968i 0.582911 + 0.582911i 0.935702 0.352791i \(-0.114767\pi\)
−0.352791 + 0.935702i \(0.614767\pi\)
\(48\) 67.2487 + 107.145i 1.40102 + 2.23219i
\(49\) −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 \(-0.346989\pi\)
−0.886673 + 0.462397i \(0.846989\pi\)
\(54\) 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
\(57\) −38.2862 61.0002i −0.671688 1.07018i
\(58\) −63.5160 + 63.5160i −1.09510 + 1.09510i
\(59\) 14.2975i 0.242330i −0.992632 0.121165i \(-0.961337\pi\)
0.992632 0.121165i \(-0.0386631\pi\)
\(60\) −148.202 4.44772i −2.47004 0.0741286i
\(61\) 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
\(63\) −62.6848 6.29425i −0.994997 0.0999087i
\(64\) 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 0.703425 0.710769i \(-0.251653\pi\)
−0.710769 + 0.703425i \(0.751653\pi\)
\(68\) −138.501 + 138.501i −2.03678 + 2.03678i
\(69\) −3.00538 + 13.1370i −0.0435562 + 0.190391i
\(70\) 67.5692 + 111.548i 0.965274 + 1.59355i
\(71\) 54.2705i 0.764374i 0.924085 + 0.382187i \(0.124829\pi\)
−0.924085 + 0.382187i \(0.875171\pi\)
\(72\) 186.336 64.9917i 2.58800 0.902663i
\(73\) 30.4748 + 30.4748i 0.417464 + 0.417464i 0.884329 0.466865i \(-0.154617\pi\)
−0.466865 + 0.884329i \(0.654617\pi\)
\(74\) −72.7609 −0.983256
\(75\) 43.6082 61.0191i 0.581442 0.813588i
\(76\) 237.296i 3.12231i
\(77\) −37.2462 + 13.5845i −0.483717 + 0.176422i
\(78\) 14.1594 + 22.5597i 0.181530 + 0.289226i
\(79\) 58.3371i 0.738444i −0.929341 0.369222i \(-0.879624\pi\)
0.929341 0.369222i \(-0.120376\pi\)
\(80\) −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 −0.286236 0.958159i \(-0.592404\pi\)
0.958159 + 0.286236i \(0.0924042\pi\)
\(84\) −163.911 127.363i −1.95132 1.51622i
\(85\) −19.1884 97.2026i −0.225746 1.14356i
\(86\) 136.493i 1.58713i
\(87\) 38.4453 + 61.2536i 0.441900 + 0.704065i
\(88\) 87.8156 87.8156i 0.997905 0.997905i
\(89\) 109.444i 1.22971i −0.788641 0.614854i \(-0.789215\pi\)
0.788641 0.614854i \(-0.210785\pi\)
\(90\) −42.2808 + 162.261i −0.469786 + 1.80290i
\(91\) 7.03872 15.1207i 0.0773486 0.166162i
\(92\) −31.3976 + 31.3976i −0.341278 + 0.341278i
\(93\) 60.5860 38.0262i 0.651462 0.408884i
\(94\) 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 \(-0.636051\pi\)
0.910039 + 0.414523i \(0.136051\pi\)
\(98\) −15.6722 + 181.910i −0.159920 + 1.85623i
\(99\) −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 \(0.671062\pi\)
\(102\) 117.757 + 187.619i 1.15448 + 1.83940i
\(103\) −59.9292 59.9292i −0.581837 0.581837i 0.353571 0.935408i \(-0.384967\pi\)
−0.935408 + 0.353571i \(0.884967\pi\)
\(104\) 52.2456i 0.502361i
\(105\) 99.6788 33.0022i 0.949321 0.314307i
\(106\) −118.497 −1.11789
\(107\) −33.4736 + 33.4736i −0.312837 + 0.312837i −0.846008 0.533170i \(-0.821000\pi\)
0.533170 + 0.846008i \(0.321000\pi\)
\(108\) −29.4816 265.251i −0.272978 2.45603i
\(109\) 188.925i 1.73326i 0.498954 + 0.866628i \(0.333718\pi\)
−0.498954 + 0.866628i \(0.666282\pi\)
\(110\) 20.4361 + 103.523i 0.185783 + 0.941121i
\(111\) −13.0641 + 57.1052i −0.117694 + 0.514461i
\(112\) −101.138 277.301i −0.903013 2.47590i
\(113\) −112.042 112.042i −0.991524 0.991524i 0.00844052 0.999964i \(-0.497313\pi\)
−0.999964 + 0.00844052i \(0.997313\pi\)
\(114\) −261.602 59.8474i −2.29476 0.524977i
\(115\) −4.34991 22.0354i −0.0378253 0.191612i
\(116\) 238.282i 2.05415i
\(117\) 20.2478 7.06219i 0.173058 0.0603606i
\(118\) −37.6714 37.6714i −0.319249 0.319249i
\(119\) 58.5380 125.753i 0.491916 1.05675i
\(120\) −239.446 + 225.492i −1.99538 + 1.87910i
\(121\) 88.9221 0.734894
\(122\) 237.872 + 237.872i 1.94977 + 1.94977i
\(123\) 85.2220 + 135.781i 0.692862 + 1.10391i
\(124\) 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 0.591607 0.806227i \(-0.298494\pi\)
−0.806227 + 0.591607i \(0.798494\pi\)
\(128\) 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 \(0.527005\pi\)
\(132\) −89.2840 142.253i −0.676394 1.07768i
\(133\) 57.5799 + 157.874i 0.432931 + 1.18702i
\(134\) −2.59279 −0.0193492
\(135\) 119.756 + 62.3170i 0.887084 + 0.461607i
\(136\) 434.504i 3.19488i
\(137\) 87.8267 87.8267i 0.641071 0.641071i −0.309748 0.950819i \(-0.600245\pi\)
0.950819 + 0.309748i \(0.100245\pi\)
\(138\) 26.6950 + 42.5323i 0.193442 + 0.308205i
\(139\) −55.5125 −0.399371 −0.199685 0.979860i \(-0.563992\pi\)
−0.199685 + 0.979860i \(0.563992\pi\)
\(140\) 335.982 + 82.4945i 2.39987 + 0.589246i
\(141\) 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
\(147\) 139.955 + 44.9616i 0.952076 + 0.305862i
\(148\) −136.482 + 136.482i −0.922177 + 0.922177i
\(149\) 267.880 1.79785 0.898925 0.438103i \(-0.144349\pi\)
0.898925 + 0.438103i \(0.144349\pi\)
\(150\) −45.8747 275.674i −0.305831 1.83783i
\(151\) 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
\(153\) 168.392 58.7331i 1.10060 0.383877i
\(154\) −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 \(-0.538044\pi\)
0.992866 + 0.119235i \(0.0380440\pi\)
\(158\) −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
\(162\) −299.856 34.3963i −1.85096 0.212323i
\(163\) 30.1699 30.1699i 0.185091 0.185091i −0.608479 0.793570i \(-0.708220\pi\)
0.793570 + 0.608479i \(0.208220\pi\)
\(164\) 528.201i 3.22074i
\(165\) 84.9177 + 2.54848i 0.514653 + 0.0154453i
\(166\) 293.886i 1.77040i
\(167\) −138.915 138.915i −0.831827 0.831827i 0.155939 0.987767i \(-0.450160\pi\)
−0.987767 + 0.155939i \(0.950160\pi\)
\(168\) −456.889 + 57.3299i −2.71958 + 0.341250i
\(169\) 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 −0.921052 0.389440i \(-0.872669\pi\)
0.389440 + 0.921052i \(0.372669\pi\)
\(174\) 262.689 + 60.0960i 1.50971 + 0.345379i
\(175\) −129.288 + 117.939i −0.738786 + 0.673940i
\(176\) 238.823i 1.35695i
\(177\) −36.3295 + 22.8019i −0.205252 + 0.128824i
\(178\) −288.366 288.366i −1.62003 1.62003i
\(179\) −138.994 −0.776504 −0.388252 0.921553i \(-0.626921\pi\)
−0.388252 + 0.921553i \(0.626921\pi\)
\(180\) 225.054 + 383.672i 1.25030 + 2.13151i
\(181\) 15.4468i 0.0853414i −0.999089 0.0426707i \(-0.986413\pi\)
0.999089 0.0426707i \(-0.0135866\pi\)
\(182\) −21.2947 58.3863i −0.117004 0.320804i
\(183\) 229.399 143.980i 1.25355 0.786777i
\(184\) 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 \(0.750631\pi\)
\(192\) 228.643 143.506i 1.19085 0.747426i
\(193\) −81.8078 + 81.8078i −0.423875 + 0.423875i −0.886535 0.462661i \(-0.846895\pi\)
0.462661 + 0.886535i \(0.346895\pi\)
\(194\) 253.286i 1.30560i
\(195\) −26.0188 + 24.5026i −0.133430 + 0.125655i
\(196\) 311.823 + 370.617i 1.59093 + 1.89090i
\(197\) 114.419 114.419i 0.580805 0.580805i −0.354319 0.935125i \(-0.615287\pi\)
0.935125 + 0.354319i \(0.115287\pi\)
\(198\) −179.342 + 62.5523i −0.905769 + 0.315921i
\(199\) 88.3996 0.444219 0.222110 0.975022i \(-0.428706\pi\)
0.222110 + 0.975022i \(0.428706\pi\)
\(200\) 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
\(203\) −57.8191 158.530i −0.284823 0.780934i
\(204\) 572.813 + 131.044i 2.80790 + 0.642371i
\(205\) −221.940 148.761i −1.08263 0.725665i
\(206\) −315.806 −1.53304
\(207\) 38.1738 13.3145i 0.184414 0.0643214i
\(208\) 71.0433 + 71.0433i 0.341554 + 0.341554i
\(209\) 135.967i 0.650560i
\(210\) 175.681 349.591i 0.836576 1.66472i
\(211\) −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
\(213\) 137.900 86.5517i 0.647418 0.406346i
\(214\) 176.394i 0.824272i
\(215\) 179.685 35.4709i 0.835745 0.164981i
\(216\) −462.315 369.826i −2.14035 1.71216i
\(217\) −156.802 + 57.1888i −0.722588 + 0.263543i
\(218\) 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
\(222\) 116.041 + 184.884i 0.522705 + 0.832809i
\(223\) −14.5058 14.5058i −0.0650483 0.0650483i 0.673834 0.738883i \(-0.264646\pi\)
−0.738883 + 0.673834i \(0.764646\pi\)
\(224\) −440.508 205.057i −1.96656 0.915434i
\(225\) −224.595 13.4929i −0.998200 0.0599682i
\(226\) −590.423 −2.61249
\(227\) 12.9045 + 12.9045i 0.0568479 + 0.0568479i 0.734959 0.678111i \(-0.237201\pi\)
−0.678111 + 0.734959i \(0.737201\pi\)
\(228\) −602.963 + 378.444i −2.64457 + 1.65984i
\(229\) −325.906 −1.42317 −0.711585 0.702601i \(-0.752022\pi\)
−0.711585 + 0.702601i \(0.752022\pi\)
\(230\) −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 \(-0.184831\pi\)
−0.548580 + 0.836098i \(0.684831\pi\)
\(234\) 34.7419 71.9571i 0.148470 0.307509i
\(235\) 37.5184 + 190.057i 0.159653 + 0.808753i
\(236\) −141.325 −0.598835
\(237\) −148.233 + 93.0371i −0.625456 + 0.392562i
\(238\) −177.099 485.574i −0.744113 2.04023i
\(239\) −175.883 −0.735912 −0.367956 0.929843i \(-0.619942\pi\)
−0.367956 + 0.929843i \(0.619942\pi\)
\(240\) −18.9736 + 632.220i −0.0790568 + 2.63425i
\(241\) 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
\(243\) −80.8340 + 229.161i −0.332650 + 0.943050i
\(244\) 892.381 3.65730
\(245\) −243.547 + 26.6421i −0.994070 + 0.108743i
\(246\) 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 \(0.296510\pi\)
\(252\) −62.2161 + 619.614i −0.246889 + 2.45879i
\(253\) 17.9904 17.9904i 0.0711081 0.0711081i
\(254\) −143.634 −0.565486
\(255\) −216.387 + 203.778i −0.848578 + 0.799129i
\(256\) −145.161 −0.567035
\(257\) 37.0235 + 37.0235i 0.144060 + 0.144060i 0.775459 0.631398i \(-0.217519\pi\)
−0.631398 + 0.775459i \(0.717519\pi\)
\(258\) −346.825 + 217.682i −1.34428 + 0.843728i
\(259\) 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 \(-0.155881\pi\)
−0.470374 + 0.882467i \(0.655881\pi\)
\(264\) −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
\(267\) −278.094 + 174.543i −1.04155 + 0.653720i
\(268\) −4.86345 + 4.86345i −0.0181472 + 0.0181472i
\(269\) 98.6945i 0.366894i 0.983030 + 0.183447i \(0.0587256\pi\)
−0.983030 + 0.183447i \(0.941274\pi\)
\(270\) 479.731 151.343i 1.77678 0.560529i
\(271\) 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
\(273\) −49.6469 + 6.22964i −0.181857 + 0.0228192i
\(274\) 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 0.281261 0.959631i \(-0.409247\pi\)
−0.959631 + 0.281261i \(0.909247\pi\)
\(278\) −146.266 + 146.266i −0.526136 + 0.526136i
\(279\) −193.247 93.3024i −0.692643 0.334417i
\(280\) 656.418 397.618i 2.34435 1.42006i
\(281\) 284.207i 1.01141i −0.862705 0.505707i \(-0.831232\pi\)
0.862705 0.505707i \(-0.168768\pi\)
\(282\) −230.247 366.845i −0.816477 1.30087i
\(283\) 67.0672 + 67.0672i 0.236986 + 0.236986i 0.815601 0.578615i \(-0.196406\pi\)
−0.578615 + 0.815601i \(0.696406\pi\)
\(284\) 536.443 1.88888
\(285\) 10.8021 359.937i 0.0379022 1.26294i
\(286\) 50.2846i 0.175820i
\(287\) −128.168 351.414i −0.446578 1.22444i
\(288\) −205.741 589.875i −0.714378 2.04818i
\(289\) 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 −0.999973 0.00740994i \(-0.997641\pi\)
0.00740994 + 0.999973i \(0.497641\pi\)
\(294\) 487.223 250.291i 1.65722 0.851331i
\(295\) 39.8024 59.3820i 0.134923 0.201295i
\(296\) 428.169i 1.44652i
\(297\) 16.8925 + 151.985i 0.0568773 + 0.511734i
\(298\) 705.816 705.816i 2.36851 2.36851i
\(299\) 10.7033i 0.0357970i
\(300\) −603.149 431.050i −2.01050 1.43683i
\(301\) 232.462 + 108.211i 0.772298 + 0.359506i
\(302\) 392.790 392.790i 1.30063 1.30063i
\(303\) 164.914 + 262.752i 0.544270 + 0.867168i
\(304\) −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 \(-0.670290\pi\)
0.860277 + 0.509826i \(0.170290\pi\)
\(308\) 134.277 + 368.164i 0.435964 + 1.19534i
\(309\) −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 \(0.168215\pi\)
\(312\) 132.755 83.3222i 0.425496 0.267058i
\(313\) 346.433 + 346.433i 1.10682 + 1.10682i 0.993567 + 0.113249i \(0.0361258\pi\)
0.113249 + 0.993567i \(0.463874\pi\)
\(314\) 722.786i 2.30187i
\(315\) −242.827 200.649i −0.770881 0.636980i
\(316\) −576.639 −1.82481
\(317\) −25.3251 + 25.3251i −0.0798898 + 0.0798898i −0.745923 0.666033i \(-0.767991\pi\)
0.666033 + 0.745923i \(0.267991\pi\)
\(318\) 188.981 + 301.097i 0.594279 + 0.946846i
\(319\) 136.532i 0.428000i
\(320\) −250.500 + 373.726i −0.782812 + 1.16789i
\(321\) 138.440 + 31.6712i 0.431277 + 0.0986642i
\(322\) −40.1475 110.077i −0.124682 0.341855i
\(323\) −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
\(327\) 480.054 301.301i 1.46805 0.921410i
\(328\) 828.532 + 828.532i 2.52601 + 2.52601i
\(329\) −114.457 + 245.880i −0.347895 + 0.747355i
\(330\) 230.458 217.029i 0.698358 0.657662i
\(331\) 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
\(333\) 165.938 57.8769i 0.498311 0.173805i
\(334\) −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 0.999861 + 0.0166527i \(0.00530098\pi\)
0.0166527 + 0.999861i \(0.494699\pi\)
\(338\) −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
\(342\) 265.138 + 760.171i 0.775257 + 2.22272i
\(343\) −297.387 170.909i −0.867018 0.498277i
\(344\) −803.208 −2.33491
\(345\) −49.0540 + 46.1955i −0.142186 + 0.133900i
\(346\) 484.644i 1.40070i
\(347\) 0.436435 0.436435i 0.00125774 0.00125774i −0.706478 0.707735i \(-0.749717\pi\)
0.707735 + 0.706478i \(0.249717\pi\)
\(348\) 605.468 380.016i 1.73985 1.09200i
\(349\) 313.871 0.899344 0.449672 0.893194i \(-0.351541\pi\)
0.449672 + 0.893194i \(0.351541\pi\)
\(350\) −29.9005 + 651.400i −0.0854300 + 1.86114i
\(351\) −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 −0.689198 0.724573i \(-0.742037\pi\)
0.724573 + 0.689198i \(0.242037\pi\)
\(354\) −35.6430 + 155.801i −0.100686 + 0.440116i
\(355\) −151.082 + 225.403i −0.425584 + 0.634937i
\(356\) −1081.81 −3.03879
\(357\) −412.892 + 51.8092i −1.15656 + 0.145124i
\(358\) −366.225 + 366.225i −1.02298 + 1.02298i
\(359\) 491.177 1.36818 0.684091 0.729397i \(-0.260199\pi\)
0.684091 + 0.729397i \(0.260199\pi\)
\(360\) 954.842 + 248.806i 2.65234 + 0.691127i
\(361\) 215.318 0.596448
\(362\) −40.6996 40.6996i −0.112430 0.112430i
\(363\) −141.815 225.949i −0.390674 0.622449i
\(364\) −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 \(-0.508582\pi\)
0.999637 + 0.0269576i \(0.00858191\pi\)
\(368\) 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
\(372\) −375.874 598.868i −1.01041 1.60986i
\(373\) −71.3079 + 71.3079i −0.191174 + 0.191174i −0.796203 0.605029i \(-0.793161\pi\)
0.605029 + 0.796203i \(0.293161\pi\)
\(374\) 418.195i 1.11817i
\(375\) 350.988 132.032i 0.935968 0.352085i
\(376\) 849.570i 2.25949i
\(377\) 40.6146 + 40.6146i 0.107731 + 0.107731i
\(378\) 667.391 + 224.859i 1.76558 + 0.594866i
\(379\) 730.407i 1.92720i 0.267356 + 0.963598i \(0.413850\pi\)
−0.267356 + 0.963598i \(0.586150\pi\)
\(380\) 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 −0.987260 0.159116i \(-0.949136\pi\)
0.159116 + 0.987260i \(0.449136\pi\)
\(384\) 38.5613 168.558i 0.100420 0.438952i
\(385\) −192.513 47.2681i −0.500033 0.122774i
\(386\) 431.099i 1.11684i
\(387\) 108.572 + 311.284i 0.280548 + 0.804352i
\(388\) −475.104 475.104i −1.22450 1.22450i
\(389\) 319.504 0.821347 0.410674 0.911782i \(-0.365294\pi\)
0.410674 + 0.911782i \(0.365294\pi\)
\(390\) −3.99494 + 133.115i −0.0102434 + 0.341321i
\(391\) 89.0146i 0.227659i
\(392\) 1070.47 + 92.2245i 2.73079 + 0.235267i
\(393\) 35.4064 + 56.4119i 0.0900926 + 0.143542i
\(394\) 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 −0.124594 + 0.992208i \(0.539763\pi\)
−0.992208 + 0.124594i \(0.960237\pi\)
\(398\) 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 \(0.804473\pi\)
\(402\) 4.13503 + 6.58820i 0.0102861 + 0.0163886i
\(403\) 40.1719 40.1719i 0.0996821 0.0996821i
\(404\) 1022.13i 2.53002i
\(405\) −32.6439 403.682i −0.0806023 0.996746i
\(406\) −570.041 265.355i −1.40404 0.653583i
\(407\) 78.2022 78.2022i 0.192143 0.192143i
\(408\) 1104.06 692.955i 2.70604 1.69842i
\(409\) −195.136 −0.477106 −0.238553 0.971130i \(-0.576673\pi\)
−0.238553 + 0.971130i \(0.576673\pi\)
\(410\) −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
\(413\) 94.0240 34.2925i 0.227661 0.0830327i
\(414\) 65.4998 135.663i 0.158212 0.327688i
\(415\) 386.884 76.3733i 0.932252 0.184032i
\(416\) 165.391 0.397574
\(417\) 88.5324 + 141.056i 0.212308 + 0.338264i
\(418\) 358.249 + 358.249i 0.857056 + 0.857056i
\(419\) 389.604i 0.929843i 0.885352 + 0.464922i \(0.153917\pi\)
−0.885352 + 0.464922i \(0.846083\pi\)
\(420\) −326.214 985.285i −0.776700 2.34592i
\(421\) 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
\(423\) −329.252 + 114.839i −0.778373 + 0.271487i
\(424\) 697.306i 1.64459i
\(425\) 190.905 457.131i 0.449187 1.07560i
\(426\) 135.294 591.391i 0.317591 1.38824i
\(427\) −593.704 + 216.536i −1.39041 + 0.507111i
\(428\) 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 \(-0.425756\pi\)
\(432\) −1131.54 + 125.767i −2.61931 + 0.291126i
\(433\) 61.2050 + 61.2050i 0.141351 + 0.141351i 0.774241 0.632890i \(-0.218132\pi\)
−0.632890 + 0.774241i \(0.718132\pi\)
\(434\) −262.462 + 563.828i −0.604752 + 1.29914i
\(435\) −10.8470 + 361.433i −0.0249356 + 0.830880i
\(436\) 1867.45 4.28314
\(437\) −76.2549 76.2549i −0.174496 0.174496i
\(438\) −256.115 408.060i −0.584737 0.931643i
\(439\) 452.142 1.02994 0.514968 0.857209i \(-0.327804\pi\)
0.514968 + 0.857209i \(0.327804\pi\)
\(440\) 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 \(-0.357855\pi\)
−0.901937 + 0.431867i \(0.857855\pi\)
\(444\) 564.462 + 129.133i 1.27131 + 0.290841i
\(445\) 304.678 454.555i 0.684670 1.02147i
\(446\) −76.4403 −0.171391
\(447\) −427.220 680.675i −0.955749 1.52276i
\(448\) −591.748 + 215.823i −1.32087 + 0.481747i
\(449\) 547.513 1.21941 0.609703 0.792630i \(-0.291289\pi\)
0.609703 + 0.792630i \(0.291289\pi\)
\(450\) −627.320 + 556.217i −1.39404 + 1.23604i
\(451\) 302.651i 0.671067i
\(452\) −1107.49 + 1107.49i −2.45021 + 2.45021i
\(453\) −237.750 378.799i −0.524834 0.836202i
\(454\) 68.0021 0.149784
\(455\) 71.3283 43.2063i 0.156766 0.0949589i
\(456\) −352.178 + 1539.43i −0.772321 + 3.37594i
\(457\) 169.531 + 169.531i 0.370965 + 0.370965i 0.867829 0.496864i \(-0.165515\pi\)
−0.496864 + 0.867829i \(0.665515\pi\)
\(458\) −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 \(0.241932\pi\)
\(462\) 439.740 55.1781i 0.951819 0.119433i
\(463\) −254.021 + 254.021i −0.548641 + 0.548641i −0.926048 0.377407i \(-0.876816\pi\)
0.377407 + 0.926048i \(0.376816\pi\)
\(464\) 1016.49 2.19072
\(465\) 357.493 + 10.7288i 0.768802 + 0.0230726i
\(466\) 353.023 0.757560
\(467\) 651.899 + 651.899i 1.39593 + 1.39593i 0.811301 + 0.584629i \(0.198760\pi\)
0.584629 + 0.811301i \(0.301240\pi\)
\(468\) −69.8069 200.142i −0.149160 0.427654i
\(469\) 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
\(477\) 270.242 94.2569i 0.566545 0.197604i
\(478\) −463.421 + 463.421i −0.969500 + 0.969500i
\(479\) 686.172i 1.43251i −0.697839 0.716254i \(-0.745855\pi\)
0.697839 0.716254i \(-0.254145\pi\)
\(480\) 713.829 + 758.000i 1.48714 + 1.57917i
\(481\) 46.5261i 0.0967279i
\(482\) −1072.81 1072.81i −2.22575 2.22575i
\(483\) −93.6007 + 11.7449i −0.193790 + 0.0243166i
\(484\) 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 −0.913758 0.406258i \(-0.866833\pi\)
−0.406258 0.913758i \(-0.633167\pi\)
\(488\) 1399.78 1399.78i 2.86840 2.86840i
\(489\) −124.776 28.5454i −0.255166 0.0583750i
\(490\) −571.507 + 711.901i −1.16634 + 1.45286i
\(491\) 429.307i 0.874353i 0.899376 + 0.437176i \(0.144021\pi\)
−0.899376 + 0.437176i \(0.855979\pi\)
\(492\) 1342.15 842.385i 2.72794 1.71217i
\(493\) 337.774 + 337.774i 0.685140 + 0.685140i
\(494\) −213.139 −0.431456
\(495\) −128.953 219.838i −0.260511 0.444117i
\(496\) 1005.41i 2.02704i
\(497\) −356.897 + 130.168i −0.718103 + 0.261907i
\(498\) −746.758 + 468.696i −1.49951 + 0.941156i
\(499\) 195.516i 0.391815i 0.980622 + 0.195908i \(0.0627653\pi\)
−0.980622 + 0.195908i \(0.937235\pi\)
\(500\) 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 −0.300831 0.953677i \(-0.597264\pi\)
0.953677 + 0.300831i \(0.0972640\pi\)
\(504\) 874.330 + 1069.51i 1.73478 + 2.12205i
\(505\) −429.478 287.869i −0.850451 0.570038i
\(506\) 94.8029i 0.187357i
\(507\) −414.999 + 260.470i −0.818539 + 0.513748i
\(508\) −269.422 + 269.422i −0.530359 + 0.530359i
\(509\) 16.1598i 0.0317481i −0.999874 0.0158740i \(-0.994947\pi\)
0.999874 0.0158740i \(-0.00505308\pi\)
\(510\) −33.2242 + 1107.06i −0.0651454 + 2.17071i
\(511\) −127.317 + 273.504i −0.249152 + 0.535234i
\(512\) −545.497 + 545.497i −1.06542 + 1.06542i
\(513\) 644.212 71.6017i 1.25577 0.139574i
\(514\) 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
\(518\) −174.517 478.495i −0.336905 0.923735i
\(519\) 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 \(0.716783\pi\)
\(522\) −266.239 763.329i −0.510037 1.46232i
\(523\) −289.472 289.472i −0.553483 0.553483i 0.373961 0.927444i \(-0.377999\pi\)
−0.927444 + 0.373961i \(0.877999\pi\)
\(524\) 219.447i 0.418792i
\(525\) 505.871 + 140.424i 0.963565 + 0.267475i
\(526\) 571.127 1.08579
\(527\) 334.092 334.092i 0.633951 0.633951i
\(528\) −606.842 + 380.879i −1.14932 + 0.721361i
\(529\) 508.821i 0.961854i
\(530\) −492.154 329.880i −0.928592 0.622415i
\(531\) 115.878 + 55.9475i 0.218226 + 0.105363i
\(532\) 1560.52 569.154i 2.93331 1.06984i
\(533\) 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
\(537\) 221.671 + 353.181i 0.412794 + 0.657692i
\(538\) 260.043 + 260.043i 0.483351 + 0.483351i
\(539\) −178.670 212.358i −0.331484 0.393986i
\(540\) 615.979 1183.74i 1.14070 2.19212i
\(541\) −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
\(543\) −39.2499 + 24.6349i −0.0722835 + 0.0453680i
\(544\) 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 0.777996 0.628269i \(-0.216236\pi\)
−0.628269 + 0.777996i \(0.716236\pi\)
\(548\) −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
\(552\) 250.286 157.090i 0.453416 0.284583i
\(553\) 383.640 139.921i 0.693743 0.253022i
\(554\) −990.211 −1.78739
\(555\) −213.233 + 200.807i −0.384203 + 0.361815i
\(556\) 548.719i 0.986905i
\(557\) −509.388 + 509.388i −0.914521 + 0.914521i −0.996624 0.0821026i \(-0.973836\pi\)
0.0821026 + 0.996624i \(0.473836\pi\)
\(558\) −755.008 + 263.337i −1.35306 + 0.471931i
\(559\) −87.2789 −0.156134
\(560\) 351.915 1433.27i 0.628420 2.55942i
\(561\) −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 −0.943858 0.330351i \(-0.892833\pi\)
0.330351 + 0.943858i \(0.392833\pi\)
\(564\) −1120.00 256.225i −1.98582 0.454300i
\(565\) −153.435 777.258i −0.271567 1.37568i
\(566\) 353.421 0.624418
\(567\) 296.306 483.417i 0.522585 0.852587i
\(568\) 841.459 841.459i 1.48144 1.48144i
\(569\) −304.242 −0.534696 −0.267348 0.963600i \(-0.586147\pi\)
−0.267348 + 0.963600i \(0.586147\pi\)
\(570\) −919.910 976.833i −1.61388 1.71374i
\(571\) 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
\(573\) 684.992 429.929i 1.19545 0.750313i
\(574\) −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 \(-0.758530\pi\)
0.687907 + 0.725799i \(0.258530\pi\)
\(578\) 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
\(582\) −643.594 + 403.946i −1.10583 + 0.694065i
\(583\) 127.358 127.358i 0.218453 0.218453i
\(584\) 945.019i 1.61818i
\(585\) 103.756 + 27.0359i 0.177361 + 0.0462153i
\(586\) 1532.52i 2.61523i
\(587\) −229.516 229.516i −0.390999 0.390999i 0.484045 0.875043i \(-0.339167\pi\)
−0.875043 + 0.484045i \(0.839167\pi\)
\(588\) 444.428 1383.40i 0.755830 2.35272i
\(589\) 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 −0.777932 0.628348i \(-0.783731\pi\)
0.628348 + 0.777932i \(0.283731\pi\)
\(594\) 444.962 + 355.945i 0.749095 + 0.599233i
\(595\) 593.207 359.328i 0.996986 0.603913i
\(596\) 2647.88i 4.44276i
\(597\) −140.981 224.621i −0.236150 0.376250i
\(598\) 28.2013 + 28.2013i 0.0471594 + 0.0471594i
\(599\) 861.037 1.43746 0.718728 0.695291i \(-0.244724\pi\)
0.718728 + 0.695291i \(0.244724\pi\)
\(600\) −1622.24 + 269.954i −2.70373 + 0.449924i
\(601\) 413.625i 0.688227i −0.938928 0.344114i \(-0.888179\pi\)
0.938928 0.344114i \(-0.111821\pi\)
\(602\) 897.614 327.378i 1.49105 0.543818i
\(603\) 5.91307 2.06240i 0.00980609 0.00342024i
\(604\) 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 \(-0.936125\pi\)
0.199325 + 0.979933i \(0.436125\pi\)
\(608\) −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
\(612\) −580.554 1664.49i −0.948618 2.71976i
\(613\) −298.846 + 298.846i −0.487514 + 0.487514i −0.907521 0.420007i \(-0.862028\pi\)
0.420007 + 0.907521i \(0.362028\pi\)
\(614\) 566.954i 0.923377i
\(615\) −24.0446 + 801.191i −0.0390970 + 1.30275i
\(616\) 788.124 + 366.873i 1.27942 + 0.595572i
\(617\) 601.654 601.654i 0.975128 0.975128i −0.0245706 0.999698i \(-0.507822\pi\)
0.999698 + 0.0245706i \(0.00782185\pi\)
\(618\) 503.653 + 802.455i 0.814973 + 1.29847i
\(619\) 620.315 1.00212 0.501062 0.865411i \(-0.332943\pi\)
0.501062 + 0.865411i \(0.332943\pi\)
\(620\) 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
\(623\) 719.732 262.501i 1.15527 0.421350i
\(624\) 67.2180 293.820i 0.107721 0.470866i
\(625\) −444.497 + 439.372i −0.711195 + 0.702995i
\(626\) 1825.58 2.91627
\(627\) 345.489 216.843i 0.551019 0.345842i
\(628\) −1355.77 1355.77i −2.15888 2.15888i
\(629\) 386.938i 0.615163i
\(630\) −1168.48 + 111.134i −1.85473 + 0.176403i
\(631\) 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
\(633\) 267.080 + 425.531i 0.421928 + 0.672244i
\(634\) 133.454i 0.210496i
\(635\) −37.3265 189.085i −0.0587820 0.297772i
\(636\) 919.268 + 210.303i 1.44539 + 0.330665i
\(637\) 116.320 + 10.0214i 0.182606 + 0.0157322i
\(638\) −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 \(0.811493\pi\)
\(642\) 448.213 281.317i 0.698151 0.438188i
\(643\) −562.981 562.981i −0.875554 0.875554i 0.117517 0.993071i \(-0.462506\pi\)
−0.993071 + 0.117517i \(0.962506\pi\)
\(644\) −281.786 131.172i −0.437556 0.203683i
\(645\) −376.696 400.006i −0.584025 0.620164i
\(646\) −1772.59 −2.74394
\(647\) 59.3647 + 59.3647i 0.0917537 + 0.0917537i 0.751494 0.659740i \(-0.229334\pi\)
−0.659740 + 0.751494i \(0.729334\pi\)
\(648\) −202.409 + 1764.54i −0.312359 + 2.72305i
\(649\) 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 \(-0.334748\pi\)
−0.868240 + 0.496145i \(0.834748\pi\)
\(654\) 470.981 2058.73i 0.720155 3.14791i
\(655\) −92.2073 61.8045i −0.140774 0.0943579i
\(656\) 2253.27 3.43486
\(657\) −366.243 + 127.741i −0.557448 + 0.194431i
\(658\) 346.275 + 949.425i 0.526254 + 1.44290i
\(659\) −1201.84 −1.82373 −0.911866 0.410489i \(-0.865358\pi\)
−0.911866 + 0.410489i \(0.865358\pi\)
\(660\) 25.1907 839.378i 0.0381677 1.27179i
\(661\) 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
\(663\) 119.971 75.2985i 0.180951 0.113572i
\(664\) −1729.40 −2.60453
\(665\) −200.353 + 815.995i −0.301283 + 1.22706i
\(666\) 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
\(672\) 181.486 + 1446.35i 0.270069 + 2.15231i
\(673\) 172.954 172.954i 0.256990 0.256990i −0.566839 0.823829i \(-0.691834\pi\)
0.823829 + 0.566839i \(0.191834\pi\)
\(674\) 1805.20 2.67834
\(675\) 323.904 + 592.209i 0.479857 + 0.877347i
\(676\) −1614.38 −2.38814
\(677\) 785.544 + 785.544i 1.16033 + 1.16033i 0.984403 + 0.175927i \(0.0562923\pi\)
0.175927 + 0.984403i \(0.443708\pi\)
\(678\) 941.618 + 1500.25i 1.38882 + 2.21276i
\(679\) 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 \(-0.427442\pi\)
−0.974132 + 0.225980i \(0.927442\pi\)
\(684\) 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
\(687\) 519.761 + 828.118i 0.756566 + 1.20541i
\(688\) −1092.20 + 1092.20i −1.58750 + 1.58750i
\(689\) 75.7713i 0.109973i
\(690\) −7.53176 + 250.966i −0.0109156 + 0.363719i
\(691\) 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
\(693\) 35.6489 355.030i 0.0514415 0.512308i
\(694\) 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
\(700\) 1165.78 + 1277.96i 1.66541 + 1.82565i
\(701\) 582.081i 0.830358i 0.909740 + 0.415179i \(0.136281\pi\)
−0.909740 + 0.415179i \(0.863719\pi\)
\(702\) −238.248 + 26.4804i −0.339385 + 0.0377214i
\(703\) −331.472 331.472i −0.471511 0.471511i
\(704\) −509.636 −0.723915
\(705\) 423.095 398.440i 0.600134 0.565163i
\(706\) 65.8034i 0.0932060i
\(707\) −248.019 680.025i −0.350805 0.961845i
\(708\) 225.388 + 359.103i 0.318344 + 0.507208i
\(709\) 710.656i 1.00234i 0.865350 + 0.501168i \(0.167096\pi\)
−0.865350 + 0.501168i \(0.832904\pi\)
\(710\) 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
\(717\) 280.502 + 446.914i 0.391216 + 0.623311i
\(718\) 1294.17 1294.17i 1.80246 1.80246i
\(719\) 1307.80i 1.81892i −0.415790 0.909461i \(-0.636495\pi\)
0.415790 0.909461i \(-0.363505\pi\)
\(720\) 1636.72 960.066i 2.27322 1.33342i
\(721\) 250.370 537.850i 0.347254 0.745978i
\(722\) 567.324 567.324i 0.785768 0.785768i
\(723\) −1034.60 + 649.358i −1.43098 + 0.898143i
\(724\) −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 \(-0.714761\pi\)
0.780901 + 0.624655i \(0.214761\pi\)
\(728\) −343.580 + 125.311i −0.471951 + 0.172130i
\(729\) 711.208 160.074i 0.975595 0.219580i
\(730\) 666.988 + 447.067i 0.913683 + 0.612421i
\(731\) −725.860 −0.992969
\(732\) −1423.19 2267.52i −1.94424 3.09770i
\(733\) −336.426 336.426i −0.458971 0.458971i 0.439346 0.898318i \(-0.355210\pi\)
−0.898318 + 0.439346i \(0.855210\pi\)
\(734\) 1881.12i 2.56284i
\(735\) 456.111 + 576.358i 0.620559 + 0.784160i
\(736\) 311.816 0.423663
\(737\) 2.78668 2.78668i 0.00378112 0.00378112i
\(738\) −590.175 1692.08i −0.799695 2.29279i
\(739\) 290.721i 0.393398i −0.980464 0.196699i \(-0.936978\pi\)
0.980464 0.196699i \(-0.0630223\pi\)
\(740\) −946.803 + 186.904i −1.27946 + 0.252574i
\(741\) −38.2687 + 167.279i −0.0516447 + 0.225747i
\(742\) −284.214 779.265i −0.383038 1.05022i
\(743\) 409.064 + 409.064i 0.550557 + 0.550557i 0.926602 0.376044i \(-0.122716\pi\)
−0.376044 + 0.926602i \(0.622716\pi\)
\(744\) −1528.97 349.787i −2.05507 0.470143i
\(745\) 1112.59 + 745.743i 1.49341 + 1.00100i
\(746\) 375.768i 0.503710i
\(747\) 233.769 + 670.233i 0.312943 + 0.897233i
\(748\) −784.434 784.434i −1.04871 1.04871i
\(749\) −300.417 139.845i −0.401091 0.186709i
\(750\) 576.911 1272.67i 0.769215 1.69690i
\(751\) 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
\(753\) −477.653 761.029i −0.634334 1.01066i
\(754\) 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 0.553863 0.832608i \(-0.313153\pi\)
−0.832608 + 0.553863i \(0.813153\pi\)
\(758\) 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 \(0.754531\pi\)
\(762\) 229.069 + 364.969i 0.300616 + 0.478962i
\(763\) −1242.42 + 453.136i −1.62834 + 0.593888i
\(764\) 2664.68 3.48780
\(765\) 862.893 + 224.846i 1.12796 + 0.293917i
\(766\) 1671.42i 2.18201i
\(767\) −24.0885 + 24.0885i −0.0314061 + 0.0314061i