Properties

Label 105.3.k.d.62.16
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 62.16
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.16

$q$-expansion

\(f(q)\) \(=\) \(q+(2.63482 - 2.63482i) q^{2} +(1.59482 + 2.54097i) q^{3} -9.88460i q^{4} +(-4.15332 - 2.78387i) q^{5} +(10.8971 + 2.49295i) q^{6} +(6.57626 + 2.39850i) q^{7} +(-15.5049 - 15.5049i) q^{8} +(-3.91310 + 8.10479i) q^{9} +O(q^{10})\) \(q+(2.63482 - 2.63482i) q^{2} +(1.59482 + 2.54097i) 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} +(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} +(4.39342 + 20.5353i) 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} +(23.7082 - 65.0037i) 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} +(-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} +(65.6828 + 42.5310i) 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} +(-45.1729 + 43.9136i) 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} +(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} +(-13.5845 + 37.2462i) 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} +(202.983 - 43.4272i) 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} +(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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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
\(7\) 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 \(0.917120\pi\)
\(12\) 25.1165 15.7642i 2.09304 1.31368i
\(13\) 1.68481 + 1.68481i 0.129601 + 0.129601i 0.768932 0.639331i \(-0.220789\pi\)
−0.639331 + 0.768932i \(0.720789\pi\)
\(14\) 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 0.986711 0.162486i \(-0.0519514\pi\)
−0.162486 + 0.986711i \(0.551951\pi\)
\(18\) 11.0444 + 31.6650i 0.613576 + 1.75917i
\(19\) −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
\(21\) 4.39342 + 20.5353i 0.209211 + 0.977871i
\(22\) 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
\(28\) 23.7082 65.0037i 0.846722 2.32156i
\(29\) −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 \(-0.874348\pi\)
0.923094 0.384574i \(-0.125652\pi\)
\(32\) −49.0830 + 49.0830i −1.53384 + 1.53384i
\(33\) −14.3914 + 9.03263i −0.436103 + 0.273716i
\(34\) 73.8374 2.17169
\(35\) −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 0.495456 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 \(-0.274070\pi\)
0.651668 + 0.758505i \(0.274070\pi\)
\(42\) 65.6828 + 42.5310i 1.56388 + 1.01264i
\(43\) 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 0.352791 0.935702i \(-0.385233\pi\)
−0.935702 + 0.352791i \(0.885233\pi\)
\(48\) −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 \(0.0386631\pi\)
−0.992632 + 0.121165i \(0.961337\pi\)
\(60\) −148.202 4.44772i −2.47004 0.0741286i
\(61\) 90.2799i 1.48000i −0.672608 0.739999i \(-0.734826\pi\)
0.672608 0.739999i \(-0.265174\pi\)
\(62\) −62.8237 62.8237i −1.01329 1.01329i
\(63\) −45.1729 + 43.9136i −0.717030 + 0.697042i
\(64\) 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
\(70\) −128.857 20.1117i −1.84082 0.287310i
\(71\) 54.2705i 0.764374i 0.924085 + 0.382187i \(0.124829\pi\)
−0.924085 + 0.382187i \(0.875171\pi\)
\(72\) 186.336 64.9917i 2.58800 0.902663i
\(73\) −30.4748 30.4748i −0.417464 0.417464i 0.466865 0.884329i \(-0.345383\pi\)
−0.884329 + 0.466865i \(0.845383\pi\)
\(74\) −72.7609 −0.983256
\(75\) −43.6082 + 61.0191i −0.581442 + 0.813588i
\(76\) 237.296i 3.12231i
\(77\) −13.5845 + 37.2462i −0.176422 + 0.483717i
\(78\) 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 −0.958159 0.286236i \(-0.907596\pi\)
0.286236 + 0.958159i \(0.407596\pi\)
\(84\) 202.983 43.4272i 2.41647 0.516991i
\(85\) −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 \(0.210785\pi\)
−0.788641 + 0.614854i \(0.789215\pi\)
\(90\) 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 −0.910039 0.414523i \(-0.863949\pi\)
0.414523 + 0.910039i \(0.363949\pi\)
\(98\) 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 \(-0.328938\pi\)
0.511911 + 0.859039i \(0.328938\pi\)
\(102\) 117.757 + 187.619i 1.15448 + 1.83940i
\(103\) 59.9292 + 59.9292i 0.581837 + 0.581837i 0.935408 0.353571i \(-0.115033\pi\)
−0.353571 + 0.935408i \(0.615033\pi\)
\(104\) 52.2456i 0.502361i
\(105\) 38.9204 97.5203i 0.370670 0.928765i
\(106\) −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
\(112\) −277.301 101.138i −2.47590 0.903013i
\(113\) −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
\(126\) −3.31798 + 234.727i −0.0263332 + 1.86292i
\(127\) −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 \(-0.472995\pi\)
0.0847362 + 0.996403i \(0.472995\pi\)
\(132\) 89.2840 + 142.253i 0.676394 + 1.07768i
\(133\) −157.874 57.5799i −1.18702 0.432931i
\(134\) −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 \(-0.436008\pi\)
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
\(147\) −20.3616 + 145.583i −0.138514 + 0.990360i
\(148\) −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 −0.992866 0.119235i \(-0.961956\pi\)
0.119235 + 0.992866i \(0.461956\pi\)
\(158\) −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 0.987767 0.155939i \(-0.0498404\pi\)
−0.155939 + 0.987767i \(0.549840\pi\)
\(168\) 250.278 386.517i 1.48975 2.30070i
\(169\) 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 \(-0.627331\pi\)
0.921052 + 0.389440i \(0.127331\pi\)
\(174\) −262.689 60.0960i −1.50971 0.345379i
\(175\) 7.01062 + 174.860i 0.0400607 + 0.999197i
\(176\) 238.823i 1.35695i
\(177\) −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 \(0.0135866\pi\)
−0.999089 + 0.0426707i \(0.986413\pi\)
\(182\) 58.3863 + 21.2947i 0.320804 + 0.117004i
\(183\) 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
\(189\) −183.626 44.7489i −0.971567 0.236767i
\(190\) 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 \(-0.571294\pi\)
−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
\(207\) 38.1738 13.3145i 0.184414 0.0643214i
\(208\) −71.0433 71.0433i −0.341554 0.341554i
\(209\) 135.967i 0.650560i
\(210\) −154.400 359.497i −0.735240 1.71189i
\(211\) −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
\(217\) 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
\(222\) −116.041 184.884i −0.522705 0.832809i
\(223\) 14.5058 + 14.5058i 0.0650483 + 0.0650483i 0.738883 0.673834i \(-0.235354\pi\)
−0.673834 + 0.738883i \(0.735354\pi\)
\(224\) −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 0.678111 0.734959i \(-0.262799\pi\)
−0.734959 + 0.678111i \(0.762799\pi\)
\(228\) −602.963 + 378.444i −2.64457 + 1.65984i
\(229\) 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
\(231\) −116.306 + 24.8832i −0.503491 + 0.107719i
\(232\) 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
\(238\) 485.574 + 177.099i 2.04023 + 0.744113i
\(239\) −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 \(0.320248\pi\)
−0.535170 + 0.844745i \(0.679752\pi\)
\(242\) 234.294 234.294i 0.968158 0.968158i
\(243\) 80.8340 229.161i 0.332650 0.943050i
\(244\) −892.381 −3.65730
\(245\) −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 \(-0.703490\pi\)
−0.596620 + 0.802524i \(0.703490\pi\)
\(252\) 434.069 + 446.516i 1.72250 + 1.77189i
\(253\) 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 0.631398 0.775459i \(-0.282481\pi\)
−0.775459 + 0.631398i \(0.782481\pi\)
\(258\) 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 \(-0.941274\pi\)
0.983030 0.183447i \(-0.0587256\pi\)
\(270\) 479.731 151.343i 1.77678 0.560529i
\(271\) 218.741i 0.807162i −0.914944 0.403581i \(-0.867765\pi\)
0.914944 0.403581i \(-0.132235\pi\)
\(272\) −590.836 590.836i −2.17219 2.17219i
\(273\) −27.1959 + 42.0001i −0.0996188 + 0.153846i
\(274\) 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
\(280\) −118.350 + 758.273i −0.422677 + 2.70812i
\(281\) 284.207i 1.01141i −0.862705 0.505707i \(-0.831232\pi\)
0.862705 0.505707i \(-0.168768\pi\)
\(282\) −230.247 366.845i −0.816477 1.30087i
\(283\) −67.0672 67.0672i −0.236986 0.236986i 0.578615 0.815601i \(-0.303594\pi\)
−0.815601 + 0.578615i \(0.803594\pi\)
\(284\) 536.443 1.88888
\(285\) −10.8021 + 359.937i −0.0379022 + 1.26294i
\(286\) 50.2846i 0.175820i
\(287\) 351.414 + 128.168i 1.22444 + 0.446578i
\(288\) −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 −0.00740994 0.999973i \(-0.502359\pi\)
0.999973 + 0.00740994i \(0.00235868\pi\)
\(294\) 329.936 + 437.235i 1.12223 + 1.48719i
\(295\) 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 −0.860277 0.509826i \(-0.829710\pi\)
0.509826 + 0.860277i \(0.329710\pi\)
\(308\) 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 \(-0.831785\pi\)
−0.863583 + 0.504206i \(0.831785\pi\)
\(312\) 132.755 83.3222i 0.425496 0.267058i
\(313\) −346.433 346.433i −1.10682 1.10682i −0.993567 0.113249i \(-0.963874\pi\)
−0.113249 0.993567i \(-0.536126\pi\)
\(314\) 722.786i 2.30187i
\(315\) 309.868 56.6315i 0.983706 0.179783i
\(316\) −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
\(322\) −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
\(327\) −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
\(336\) −185.257 865.911i −0.551361 2.57712i
\(337\) 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
\(343\) 170.909 + 297.387i 0.498277 + 0.867018i
\(344\) −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 \(-0.648459\pi\)
−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 \(-0.757963\pi\)
0.689198 + 0.724573i \(0.257963\pi\)
\(354\) −35.6430 + 155.801i −0.100686 + 0.440116i
\(355\) 151.082 225.403i 0.425584 0.634937i
\(356\) 1081.81 3.03879
\(357\) −226.177 + 349.296i −0.633548 + 0.978421i
\(358\) −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 −0.999637 0.0269576i \(-0.991418\pi\)
0.0269576 + 0.999637i \(0.491418\pi\)
\(368\) 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
\(378\) −601.728 + 365.917i −1.59187 + 0.968034i
\(379\) 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 −0.159116 0.987260i \(-0.550864\pi\)
0.987260 + 0.159116i \(0.0508644\pi\)
\(384\) −38.5613 + 168.558i −0.100420 + 0.438952i
\(385\) 160.109 116.878i 0.415868 0.303579i
\(386\) 431.099i 1.11684i
\(387\) 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
\(392\) −92.2245 1070.47i −0.235267 2.73079i
\(393\) 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 \(-0.460237\pi\)
0.992208 0.124594i \(-0.0397628\pi\)
\(398\) −232.918 + 232.918i −0.585220 + 0.585220i
\(399\) −105.471 492.983i −0.264339 1.23555i
\(400\) −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 \(-0.423327\pi\)
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
\(417\) 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 \(-0.846083\pi\)
0.885352 0.464922i \(-0.153917\pi\)
\(420\) −963.949 384.713i −2.29512 0.915982i
\(421\) 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
\(427\) 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 \(-0.425756\pi\)
\(432\) 1131.54 125.767i 2.61931 0.291126i
\(433\) −61.2050 61.2050i −0.141351 0.141351i 0.632890 0.774241i \(-0.281868\pi\)
−0.774241 + 0.632890i \(0.781868\pi\)
\(434\) −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 \(-0.672196\pi\)
−0.514968 + 0.857209i \(0.672196\pi\)
\(440\) −609.194 + 120.258i −1.38453 + 0.273315i
\(441\) −402.396 + 180.440i −0.912462 + 0.409162i
\(442\) 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
\(448\) −215.823 + 591.748i −0.481747 + 1.32087i
\(449\) 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
\(455\) 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 0.867829 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 \(-0.758068\pi\)
−0.724801 + 0.688958i \(0.758068\pi\)
\(462\) −240.884 + 372.010i −0.521394 + 0.805216i
\(463\) −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 \(-0.801240\pi\)
−0.584629 0.811301i \(-0.698760\pi\)
\(468\) 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 \(0.254145\pi\)
−0.697839 + 0.716254i \(0.745855\pi\)
\(480\) 713.829 + 758.000i 1.48714 + 1.57917i
\(481\) 46.5261i 0.0967279i
\(482\) 1072.81 + 1072.81i 2.22575 + 2.22575i
\(483\) 51.2732 79.1839i 0.106156 0.163942i
\(484\) 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
\(490\) −799.160 441.324i −1.63094 0.900661i
\(491\) 429.307i 0.874353i 0.899376 + 0.437176i \(0.144021\pi\)
−0.899376 + 0.437176i \(0.855979\pi\)
\(492\) 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
\(497\) −130.168 + 356.897i −0.261907 + 0.718103i
\(498\) −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 −0.953677 0.300831i \(-0.902736\pi\)
0.300831 + 0.953677i \(0.402736\pi\)
\(504\) 1381.28 + 19.5250i 2.74063 + 0.0387401i
\(505\) −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 \(0.00505308\pi\)
−0.999874 + 0.0158740i \(0.994947\pi\)
\(510\) 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
\(518\) −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 \(-0.283217\pi\)
0.629605 + 0.776915i \(0.283217\pi\)
\(522\) −266.239 763.329i −0.510037 1.46232i
\(523\) 289.472 + 289.472i 0.553483 + 0.553483i 0.927444 0.373961i \(-0.122001\pi\)
−0.373961 + 0.927444i \(0.622001\pi\)
\(524\) 219.447i 0.418792i
\(525\) −433.133 + 296.683i −0.825015 + 0.565111i
\(526\) 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
\(532\) −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
\(537\) −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
\(546\) 39.0063 + 182.319i 0.0714401 + 0.333918i
\(547\) 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
\(553\) 139.921 383.640i 0.253022 0.693743i
\(554\) −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
\(560\) 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 \(-0.607167\pi\)
0.943858 + 0.330351i \(0.107167\pi\)
\(564\) −1120.00 256.225i −1.98582 0.454300i
\(565\) 153.435 + 777.258i 0.271567 + 1.37568i
\(566\) −353.421 −0.624418
\(567\) −179.145 537.956i −0.315952 0.948775i
\(568\) 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 −0.687907 0.725799i \(-0.741470\pi\)
0.725799 + 0.687907i \(0.241470\pi\)
\(578\) 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 0.875043 0.484045i \(-0.160833\pi\)
−0.484045 + 0.875043i \(0.660833\pi\)
\(588\) 1439.03 + 201.266i 2.44733 + 0.342289i
\(589\) 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 \(-0.716269\pi\)
0.777932 + 0.628348i \(0.216269\pi\)
\(594\) −444.962 355.945i −0.749095 0.599233i
\(595\) 106.953 685.253i 0.179753 1.15169i
\(596\) 2647.88i 4.44276i
\(597\) −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 \(0.111821\pi\)
−0.938928 + 0.344114i \(0.888179\pi\)
\(602\) 327.378 897.614i 0.543818 1.49105i
\(603\) 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 −0.199325 0.979933i \(-0.563875\pi\)
0.979933 + 0.199325i \(0.0638749\pi\)
\(608\) 1178.32 1178.32i 1.93802 1.93802i
\(609\) −105.909 495.031i −0.173907 0.812859i
\(610\) 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 \(-0.667057\pi\)
−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
\(627\) 345.489 216.843i 0.551019 0.345842i
\(628\) 1355.77 + 1355.77i 2.15888 + 2.15888i
\(629\) 386.938i 0.615163i
\(630\) 667.232 965.661i 1.05910 1.53279i
\(631\) 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
\(637\) 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 \(0.811493\pi\)
\(642\) −448.213 + 281.317i −0.698151 + 0.438188i
\(643\) 562.981 + 562.981i 0.875554 + 0.875554i 0.993071 0.117517i \(-0.0374936\pi\)
−0.117517 + 0.993071i \(0.537494\pi\)
\(644\) −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 0.659740 0.751494i \(-0.270666\pi\)
−0.751494 + 0.659740i \(0.770666\pi\)
\(648\) −202.409 + 1764.54i −0.312359 + 2.72305i
\(649\) −80.9771 −0.124772
\(650\) 84.3450 + 205.308i 0.129762 + 0.315859i
\(651\) 489.635 104.755i 0.752127 0.160914i
\(652\) −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
\(658\) −949.425 346.275i −1.44290 0.526254i
\(659\) −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 \(0.154911\pi\)
−0.883896 + 0.467683i \(0.845089\pi\)
\(662\) 428.827 428.827i 0.647775 0.647775i
\(663\) −119.971 + 75.2985i −0.180951 + 0.113572i
\(664\) 1729.40 2.60453
\(665\) 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
\(672\) −1223.58 792.292i −1.82080 1.17901i
\(673\) 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 \(-0.943708\pi\)
−0.175927 0.984403i \(-0.556292\pi\)
\(678\) −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 \(-0.978537\pi\)
0.997728 0.0673772i \(-0.0214631\pi\)
\(692\) −909.076 909.076i −1.31369 1.31369i
\(693\) −248.715 255.847i −0.358896 0.369188i
\(694\) 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 \(0.863719\pi\)
\(702\) −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
\(707\) 680.025 + 248.019i 0.961845 + 0.350805i
\(708\) 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
\(714\) 324.399 + 1516.27i 0.454340 + 2.12363i
\(715\) 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 \(0.363505\pi\)
−0.415790 + 0.909461i \(0.636495\pi\)
\(720\) −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 −0.780901 0.624655i \(-0.785239\pi\)
0.624655 + 0.780901i \(0.285239\pi\)
\(728\) 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
\(732\) −1423.19 2267.52i −1.94424 3.09770i
\(733\) 336.426 + 336.426i 0.458971 + 0.458971i 0.898318 0.439346i \(-0.144790\pi\)
−0.439346 + 0.898318i \(0.644790\pi\)
\(734\) 1881.12i 2.56284i
\(735\) 489.853 547.968i 0.666467 0.745535i
\(736\) 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
\(742\) −779.265 284.214i −1.05022 0.383038i
\(743\) 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
\(756\) −442.325 + 1815.07i −0.585086 + 2.40089i
\(757\) −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 \(-0.245469\pi\)
0.717100 + 0.696971i \(0.245469\pi\)
\(762\) −229.069 364.969i −0.300616 0.478962i
\(763\) −453.136 + 1242.42i −0.593888 + 1.62834i
\(764\) 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