Properties

Label 105.3.k.d.62.1
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 62.1
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.63482 + 2.63482i) q^{2} +(-2.54097 - 1.59482i) q^{3} -9.88460i q^{4} +(-4.15332 - 2.78387i) q^{5} +(10.8971 - 2.49295i) q^{6} +(2.39850 + 6.57626i) q^{7} +(15.5049 + 15.5049i) q^{8} +(3.91310 + 8.10479i) q^{9} +O(q^{10})\) \(q+(-2.63482 + 2.63482i) q^{2} +(-2.54097 - 1.59482i) 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} +(-15.7642 + 25.1165i) q^{12} +(-1.68481 - 1.68481i) q^{13} +(-23.6469 - 11.0077i) q^{14} +(6.11370 + 13.6975i) q^{15} -42.1670 q^{16} +(14.0118 + 14.0118i) q^{17} +(-31.6650 - 11.0444i) q^{18} +24.0066 q^{19} +(-27.5175 + 41.0539i) q^{20} +(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} +(2.98258 - 26.8348i) q^{27} +(65.0037 - 23.7082i) q^{28} +24.1064 q^{29} +(-52.1991 - 19.9821i) q^{30} +23.8436i q^{31} +(49.0830 - 49.0830i) q^{32} +(-9.03263 + 14.3914i) q^{33} -73.8374 q^{34} +(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} +(42.5310 + 65.6828i) q^{42} +(25.9017 - 25.9017i) q^{43} -55.9837 q^{44} +(6.31036 - 44.5554i) q^{45} -16.7386 q^{46} +(-27.3968 - 27.3968i) q^{47} +(107.145 + 67.2487i) q^{48} +(-37.4944 + 31.5463i) q^{49} +(-85.9604 - 35.8983i) q^{50} +(-13.2573 - 57.9500i) q^{51} +(-16.6537 + 16.6537i) q^{52} +(22.4866 + 22.4866i) q^{53} +(62.8463 + 78.5635i) q^{54} +(-15.7671 + 23.5233i) q^{55} +(-64.7758 + 139.153i) q^{56} +(-61.0002 - 38.2862i) q^{57} +(-63.5160 + 63.5160i) q^{58} +14.2975i q^{59} +(135.395 - 60.4315i) q^{60} +90.2799i q^{61} +(-62.8237 - 62.8237i) q^{62} +(-43.9136 + 45.1729i) 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} +(-64.9917 + 186.336i) q^{72} +(30.4748 + 30.4748i) q^{73} +72.7609 q^{74} +(12.7401 - 73.9100i) q^{75} -237.296i q^{76} +(37.2462 - 13.5845i) q^{77} +(-22.5597 - 14.1594i) q^{78} -58.3371i q^{79} +(175.133 + 117.388i) q^{80} +(-50.3753 + 63.4298i) q^{81} +(-140.796 + 140.796i) q^{82} +(-55.7696 + 55.7696i) q^{83} +(-202.983 - 43.4272i) q^{84} +(-19.1884 - 97.2026i) q^{85} +136.493i q^{86} +(-61.2536 - 38.4453i) q^{87} +(87.8156 - 87.8156i) q^{88} +109.444i q^{89} +(100.769 + 134.022i) q^{90} +(7.03872 - 15.1207i) q^{91} +(31.3976 - 31.3976i) q^{92} +(38.0262 - 60.5860i) q^{93} +144.372 q^{94} +(-99.7071 - 66.8314i) q^{95} +(-202.997 + 46.4402i) q^{96} +(48.0651 - 48.0651i) q^{97} +(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 \(0.631544\pi\)
−0.915817 + 0.401595i \(0.868456\pi\)
\(3\) −2.54097 1.59482i −0.846991 0.531606i
\(4\) 9.88460i 2.47115i
\(5\) −4.15332 2.78387i −0.830663 0.556775i
\(6\) 10.8971 2.49295i 1.81618 0.415492i
\(7\) 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 \(-0.917120\pi\)
0.966294 0.257442i \(-0.0828797\pi\)
\(12\) −15.7642 + 25.1165i −1.31368 + 2.09304i
\(13\) −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
\(15\) 6.11370 + 13.6975i 0.407580 + 0.913170i
\(16\) −42.1670 −2.63544
\(17\) 14.0118 + 14.0118i 0.824224 + 0.824224i 0.986711 0.162486i \(-0.0519514\pi\)
−0.162486 + 0.986711i \(0.551951\pi\)
\(18\) −31.6650 11.0444i −1.75917 0.613576i
\(19\) 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
\(21\) 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 0.772780 0.634675i \(-0.218866\pi\)
−0.634675 + 0.772780i \(0.718866\pi\)
\(24\) −14.6700 64.1251i −0.611252 2.67188i
\(25\) 9.50008 + 23.1246i 0.380003 + 0.924985i
\(26\) 8.87835 0.341475
\(27\) 2.98258 26.8348i 0.110466 0.993880i
\(28\) 65.0037 23.7082i 2.32156 0.846722i
\(29\) 24.1064 0.831254 0.415627 0.909535i \(-0.363562\pi\)
0.415627 + 0.909535i \(0.363562\pi\)
\(30\) −52.1991 19.9821i −1.73997 0.666070i
\(31\) 23.8436i 0.769148i 0.923094 + 0.384574i \(0.125652\pi\)
−0.923094 + 0.384574i \(0.874348\pi\)
\(32\) 49.0830 49.0830i 1.53384 1.53384i
\(33\) −9.03263 + 14.3914i −0.273716 + 0.436103i
\(34\) −73.8374 −2.17169
\(35\) 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 \(-0.274070\pi\)
0.651668 + 0.758505i \(0.274070\pi\)
\(42\) 42.5310 + 65.6828i 1.01264 + 1.56388i
\(43\) 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
\(45\) 6.31036 44.5554i 0.140230 0.990119i
\(46\) −16.7386 −0.363882
\(47\) −27.3968 27.3968i −0.582911 0.582911i 0.352791 0.935702i \(-0.385233\pi\)
−0.935702 + 0.352791i \(0.885233\pi\)
\(48\) 107.145 + 67.2487i 2.23219 + 1.40102i
\(49\) −37.4944 + 31.5463i −0.765192 + 0.643802i
\(50\) −85.9604 35.8983i −1.71921 0.717966i
\(51\) −13.2573 57.9500i −0.259948 1.13627i
\(52\) −16.6537 + 16.6537i −0.320263 + 0.320263i
\(53\) 22.4866 + 22.4866i 0.424276 + 0.424276i 0.886673 0.462397i \(-0.153011\pi\)
−0.462397 + 0.886673i \(0.653011\pi\)
\(54\) 62.8463 + 78.5635i 1.16382 + 1.45488i
\(55\) −15.7671 + 23.5233i −0.286675 + 0.427696i
\(56\) −64.7758 + 139.153i −1.15671 + 2.48487i
\(57\) −61.0002 38.2862i −1.07018 0.671688i
\(58\) −63.5160 + 63.5160i −1.09510 + 1.09510i
\(59\) 14.2975i 0.242330i 0.992632 + 0.121165i \(0.0386631\pi\)
−0.992632 + 0.121165i \(0.961337\pi\)
\(60\) 135.395 60.4315i 2.25658 1.00719i
\(61\) 90.2799i 1.48000i 0.672608 + 0.739999i \(0.265174\pi\)
−0.672608 + 0.739999i \(0.734826\pi\)
\(62\) −62.8237 62.8237i −1.01329 1.01329i
\(63\) −43.9136 + 45.1729i −0.697042 + 0.717030i
\(64\) 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 \(-0.875171\pi\)
0.924085 0.382187i \(-0.124829\pi\)
\(72\) −64.9917 + 186.336i −0.902663 + 2.58800i
\(73\) 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
\(75\) 12.7401 73.9100i 0.169868 0.985467i
\(76\) 237.296i 3.12231i
\(77\) 37.2462 13.5845i 0.483717 0.176422i
\(78\) −22.5597 14.1594i −0.289226 0.181530i
\(79\) 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
\(87\) −61.2536 38.4453i −0.704065 0.441900i
\(88\) 87.8156 87.8156i 0.997905 0.997905i
\(89\) 109.444i 1.22971i 0.788641 + 0.614854i \(0.210785\pi\)
−0.788641 + 0.614854i \(0.789215\pi\)
\(90\) 100.769 + 134.022i 1.11965 + 1.48914i
\(91\) 7.03872 15.1207i 0.0773486 0.166162i
\(92\) 31.3976 31.3976i 0.341278 0.341278i
\(93\) 38.0262 60.5860i 0.408884 0.651462i
\(94\) 144.372 1.53587
\(95\) −99.7071 66.8314i −1.04955 0.703489i
\(96\) −202.997 + 46.4402i −2.11456 + 0.483752i
\(97\) 48.0651 48.0651i 0.495516 0.495516i −0.414523 0.910039i \(-0.636051\pi\)
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 \(-0.328938\pi\)
0.511911 + 0.859039i \(0.328938\pi\)
\(102\) 187.619 + 117.757i 1.83940 + 1.15448i
\(103\) −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
\(105\) −75.4149 + 73.0588i −0.718237 + 0.695798i
\(106\) −118.497 −1.11789
\(107\) 33.4736 33.4736i 0.312837 0.312837i −0.533170 0.846008i \(-0.679000\pi\)
0.846008 + 0.533170i \(0.179000\pi\)
\(108\) −265.251 29.4816i −2.45603 0.272978i
\(109\) 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 0.999964 0.00844052i \(-0.00268673\pi\)
−0.00844052 + 0.999964i \(0.502687\pi\)
\(114\) 261.602 59.8474i 2.29476 0.524977i
\(115\) −4.34991 22.0354i −0.0378253 0.191612i
\(116\) 238.282i 2.05415i
\(117\) 7.06219 20.2478i 0.0603606 0.173058i
\(118\) −37.6714 37.6714i −0.319249 0.319249i
\(119\) −58.5380 + 125.753i −0.491916 + 1.05675i
\(120\) −117.587 + 307.171i −0.979890 + 2.55976i
\(121\) 88.9221 0.734894
\(122\) −237.872 237.872i −1.94977 1.94977i
\(123\) −135.781 85.2220i −1.10391 0.692862i
\(124\) 235.684 1.90068
\(125\) 24.9192 122.491i 0.199354 0.979928i
\(126\) −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 \(0.472995\pi\)
\(132\) 142.253 + 89.2840i 1.07768 + 0.676394i
\(133\) 57.5799 + 157.874i 0.432931 + 1.18702i
\(134\) 2.59279 0.0193492
\(135\) −87.0922 + 103.150i −0.645127 + 0.764075i
\(136\) 434.504i 3.19488i
\(137\) −87.8267 + 87.8267i −0.641071 + 0.641071i −0.950819 0.309748i \(-0.899755\pi\)
0.309748 + 0.950819i \(0.399755\pi\)
\(138\) 42.5323 + 26.6950i 0.308205 + 0.193442i
\(139\) −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
\(147\) 145.583 20.3616i 0.990360 0.138514i
\(148\) −136.482 + 136.482i −0.922177 + 0.922177i
\(149\) −267.880 −1.79785 −0.898925 0.438103i \(-0.855651\pi\)
−0.898925 + 0.438103i \(0.855651\pi\)
\(150\) 161.172 + 228.308i 1.07448 + 1.52205i
\(151\) 149.076 0.987261 0.493631 0.869672i \(-0.335670\pi\)
0.493631 + 0.869672i \(0.335670\pi\)
\(152\) 372.220 + 372.220i 2.44882 + 2.44882i
\(153\) −58.7331 + 168.392i −0.383877 + 1.10060i
\(154\) −62.3445 + 133.930i −0.404834 + 0.869674i
\(155\) 66.3776 99.0300i 0.428242 0.638903i
\(156\) 68.8761 15.7569i 0.441513 0.101006i
\(157\) 137.160 137.160i 0.873632 0.873632i −0.119235 0.992866i \(-0.538044\pi\)
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
\(162\) −34.3963 299.856i −0.212323 1.85096i
\(163\) 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
\(165\) 77.5792 34.6263i 0.470177 0.209857i
\(166\) 293.886i 1.77040i
\(167\) 138.915 + 138.915i 0.831827 + 0.831827i 0.987767 0.155939i \(-0.0498404\pi\)
−0.155939 + 0.987767i \(0.549840\pi\)
\(168\) 386.517 250.278i 2.30070 1.48975i
\(169\) 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
\(175\) −129.288 + 117.939i −0.738786 + 0.673940i
\(176\) 238.823i 1.35695i
\(177\) 22.8019 36.3295i 0.128824 0.205252i
\(178\) −288.366 288.366i −1.62003 1.62003i
\(179\) 138.994 0.776504 0.388252 0.921553i \(-0.373079\pi\)
0.388252 + 0.921553i \(0.373079\pi\)
\(180\) −440.412 62.3755i −2.44673 0.346530i
\(181\) 15.4468i 0.0853414i −0.999089 0.0426707i \(-0.986413\pi\)
0.999089 0.0426707i \(-0.0135866\pi\)
\(182\) 21.2947 + 58.3863i 0.117004 + 0.320804i
\(183\) 143.980 229.399i 0.786777 1.25355i
\(184\) 98.5000i 0.535326i
\(185\) 18.9086 + 95.7856i 0.102209 + 0.517760i
\(186\) 59.4410 + 259.826i 0.319575 + 1.39691i
\(187\) 79.3591 79.3591i 0.424380 0.424380i
\(188\) −270.807 + 270.807i −1.44046 + 1.44046i
\(189\) 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 \(-0.750631\pi\)
0.708508 0.705703i \(-0.249369\pi\)
\(192\) 143.506 228.643i 0.747426 1.19085i
\(193\) −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
\(195\) 12.7773 33.3781i 0.0655248 0.171170i
\(196\) 311.823 + 370.617i 1.59093 + 1.89090i
\(197\) −114.419 + 114.419i −0.580805 + 0.580805i −0.935125 0.354319i \(-0.884713\pi\)
0.354319 + 0.935125i \(0.384713\pi\)
\(198\) −62.5523 + 179.342i −0.315921 + 0.905769i
\(199\) 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
\(207\) −13.3145 + 38.1738i −0.0643214 + 0.184414i
\(208\) 71.0433 + 71.0433i 0.341554 + 0.341554i
\(209\) 135.967i 0.650560i
\(210\) 6.20796 391.202i 0.0295617 1.86287i
\(211\) −167.468 −0.793685 −0.396842 0.917887i \(-0.629894\pi\)
−0.396842 + 0.917887i \(0.629894\pi\)
\(212\) 222.271 222.271i 1.04845 1.04845i
\(213\) −86.5517 + 137.900i −0.406346 + 0.647418i
\(214\) 176.394i 0.824272i
\(215\) −179.685 + 35.4709i −0.835745 + 0.164981i
\(216\) 462.315 369.826i 2.14035 1.71216i
\(217\) −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
\(222\) −184.884 116.041i −0.832809 0.522705i
\(223\) −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
\(225\) −150.245 + 167.485i −0.667758 + 0.744379i
\(226\) −590.423 −2.61249
\(227\) −12.9045 12.9045i −0.0568479 0.0568479i 0.678111 0.734959i \(-0.262799\pi\)
−0.734959 + 0.678111i \(0.762799\pi\)
\(228\) −378.444 + 602.963i −1.65984 + 2.64457i
\(229\) −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
\(231\) −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 0.548580 0.836098i \(-0.315169\pi\)
−0.836098 + 0.548580i \(0.815169\pi\)
\(234\) 34.7419 + 71.9571i 0.148470 + 0.307509i
\(235\) 37.5184 + 190.057i 0.159653 + 0.808753i
\(236\) 141.325 0.598835
\(237\) −93.0371 + 148.233i −0.392562 + 0.625456i
\(238\) −177.099 485.574i −0.744113 2.04023i
\(239\) 175.883 0.735912 0.367956 0.929843i \(-0.380058\pi\)
0.367956 + 0.929843i \(0.380058\pi\)
\(240\) −257.796 577.584i −1.07415 2.40660i
\(241\) 407.167i 1.68949i −0.535170 0.844745i \(-0.679752\pi\)
0.535170 0.844745i \(-0.320248\pi\)
\(242\) −234.294 + 234.294i −0.968158 + 0.968158i
\(243\) 229.161 80.8340i 0.943050 0.332650i
\(244\) 892.381 3.65730
\(245\) 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 \(-0.703490\pi\)
−0.596620 + 0.802524i \(0.703490\pi\)
\(252\) 446.516 + 434.069i 1.77189 + 1.72250i
\(253\) 17.9904 17.9904i 0.0711081 0.0711081i
\(254\) 143.634 0.565486
\(255\) −106.263 + 277.591i −0.416720 + 1.08859i
\(256\) −145.161 −0.567035
\(257\) −37.0235 37.0235i −0.144060 0.144060i 0.631398 0.775459i \(-0.282481\pi\)
−0.775459 + 0.631398i \(0.782481\pi\)
\(258\) 217.682 346.825i 0.843728 1.34428i
\(259\) 57.6846 123.919i 0.222721 0.478453i
\(260\) 115.530 22.8062i 0.444345 0.0877163i
\(261\) 94.3307 + 195.377i 0.361420 + 0.748571i
\(262\) −58.4954 + 58.4954i −0.223265 + 0.223265i
\(263\) −108.381 108.381i −0.412093 0.412093i 0.470374 0.882467i \(-0.344119\pi\)
−0.882467 + 0.470374i \(0.844119\pi\)
\(264\) −363.187 + 83.0872i −1.37571 + 0.314724i
\(265\) −30.7941 155.994i −0.116204 0.588657i
\(266\) −567.683 264.257i −2.13415 0.993447i
\(267\) 174.543 278.094i 0.653720 1.04155i
\(268\) −4.86345 + 4.86345i −0.0181472 + 0.0181472i
\(269\) 98.6945i 0.366894i −0.983030 0.183447i \(-0.941274\pi\)
0.983030 0.183447i \(-0.0587256\pi\)
\(270\) −42.3098 501.255i −0.156703 1.85650i
\(271\) 218.741i 0.807162i 0.914944 + 0.403581i \(0.132235\pi\)
−0.914944 + 0.403581i \(0.867765\pi\)
\(272\) −590.836 590.836i −2.17219 2.17219i
\(273\) −42.0001 + 27.1959i −0.153846 + 0.0996188i
\(274\) 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 \(0.168768\pi\)
−0.862705 + 0.505707i \(0.831232\pi\)
\(282\) −366.845 230.247i −1.30087 0.816477i
\(283\) 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
\(285\) 146.769 + 328.832i 0.514979 + 1.15380i
\(286\) 50.2846i 0.175820i
\(287\) 128.168 + 351.414i 0.446578 + 1.22444i
\(288\) 589.875 + 205.741i 2.04818 + 0.714378i
\(289\) 103.662i 0.358692i
\(290\) 440.623 86.9816i 1.51939 0.299936i
\(291\) −198.787 + 45.4770i −0.683118 + 0.156278i
\(292\) 301.232 301.232i 1.03162 1.03162i
\(293\) 290.821 290.821i 0.992563 0.992563i −0.00740994 0.999973i \(-0.502359\pi\)
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
\(297\) −151.985 16.8925i −0.511734 0.0568773i
\(298\) 705.816 705.816i 2.36851 2.36851i
\(299\) 10.7033i 0.0357970i
\(300\) −730.571 125.931i −2.43524 0.419771i
\(301\) 232.462 + 108.211i 0.772298 + 0.359506i
\(302\) −392.790 + 392.790i −1.30063 + 1.30063i
\(303\) −262.752 164.914i −0.867168 0.544270i
\(304\) −1012.29 −3.32989
\(305\) 251.328 374.961i 0.824026 1.22938i
\(306\) −288.933 598.436i −0.944226 1.95567i
\(307\) 107.588 107.588i 0.350451 0.350451i −0.509826 0.860277i \(-0.670290\pi\)
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 \(-0.831785\pi\)
−0.863583 + 0.504206i \(0.831785\pi\)
\(312\) −83.3222 + 132.755i −0.267058 + 0.425496i
\(313\) 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
\(315\) 308.143 65.3674i 0.978232 0.207515i
\(316\) −576.639 −1.82481
\(317\) 25.3251 25.3251i 0.0798898 0.0798898i −0.666033 0.745923i \(-0.732009\pi\)
0.745923 + 0.666033i \(0.232009\pi\)
\(318\) 301.097 + 188.981i 0.946846 + 0.594279i
\(319\) 136.532i 0.428000i
\(320\) 250.500 373.726i 0.782812 1.16789i
\(321\) −138.440 + 31.6712i −0.431277 + 0.0986642i
\(322\) −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
\(327\) 301.301 480.054i 0.921410 1.46805i
\(328\) 828.532 + 828.532i 2.52601 + 2.52601i
\(329\) 114.457 245.880i 0.347895 0.747355i
\(330\) −113.173 + 295.642i −0.342949 + 0.895885i
\(331\) 162.753 0.491702 0.245851 0.969308i \(-0.420933\pi\)
0.245851 + 0.969308i \(0.420933\pi\)
\(332\) 551.261 + 551.261i 1.66042 + 1.66042i
\(333\) 57.8769 165.938i 0.173805 0.498311i
\(334\) −732.034 −2.19172
\(335\) 0.673796 + 3.41325i 0.00201133 + 0.0101888i
\(336\) −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
\(342\) −760.171 265.138i −2.22272 0.775257i
\(343\) −297.387 170.909i −0.867018 0.498277i
\(344\) 803.208 2.33491
\(345\) −24.0894 + 62.9287i −0.0698245 + 0.182402i
\(346\) 484.644i 1.40070i
\(347\) −0.436435 + 0.436435i −0.00125774 + 0.00125774i −0.707735 0.706478i \(-0.750283\pi\)
0.706478 + 0.707735i \(0.250283\pi\)
\(348\) −380.016 + 605.468i −1.09200 + 1.73985i
\(349\) 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 −0.724573 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
\(357\) 349.296 226.177i 0.978421 0.633548i
\(358\) −366.225 + 366.225i −1.02298 + 1.02298i
\(359\) −491.177 −1.36818 −0.684091 0.729397i \(-0.739801\pi\)
−0.684091 + 0.729397i \(0.739801\pi\)
\(360\) 788.668 592.985i 2.19074 1.64718i
\(361\) 215.318 0.596448
\(362\) 40.6996 + 40.6996i 0.112430 + 0.112430i
\(363\) −225.949 141.815i −0.622449 0.390674i
\(364\) −149.463 69.5750i −0.410612 0.191140i
\(365\) −41.7335 211.410i −0.114338 0.579205i
\(366\) 225.064 + 983.789i 0.614928 + 2.68795i
\(367\) 356.973 356.973i 0.972679 0.972679i −0.0269576 0.999637i \(-0.508582\pi\)
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
\(372\) −598.868 375.874i −1.60986 1.01041i
\(373\) −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
\(375\) −258.670 + 271.505i −0.689787 + 0.724013i
\(376\) 849.570i 2.25949i
\(377\) −40.6146 40.6146i −0.107731 0.107731i
\(378\) −365.917 + 601.728i −0.968034 + 1.59187i
\(379\) 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
\(385\) −192.513 47.2681i −0.500033 0.122774i
\(386\) 431.099i 1.11684i
\(387\) 311.284 + 108.572i 0.804352 + 0.280548i
\(388\) −475.104 475.104i −1.22450 1.22450i
\(389\) −319.504 −0.821347 −0.410674 0.911782i \(-0.634706\pi\)
−0.410674 + 0.911782i \(0.634706\pi\)
\(390\) 54.2795 + 121.612i 0.139178 + 0.311825i
\(391\) 89.0146i 0.227659i
\(392\) −1070.47 92.2245i −2.73079 0.235267i
\(393\) −56.4119 35.4064i −0.143542 0.0900926i
\(394\) 602.946i 1.53032i
\(395\) −162.403 + 242.292i −0.411147 + 0.613398i
\(396\) −219.070 453.737i −0.553207 1.14580i
\(397\) −443.370 + 443.370i −1.11680 + 1.11680i −0.124594 + 0.992208i \(0.539763\pi\)
−0.992208 + 0.124594i \(0.960237\pi\)
\(398\) −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 \(-0.804473\pi\)
0.817197 0.576359i \(-0.195527\pi\)
\(402\) −6.58820 4.13503i −0.0163886 0.0102861i
\(403\) 40.1719 40.1719i 0.0996821 0.0996821i
\(404\) 1022.13i 2.53002i
\(405\) 385.805 123.205i 0.952605 0.304211i
\(406\) −570.041 265.355i −1.40404 0.653583i
\(407\) −78.2022 + 78.2022i −0.192143 + 0.192143i
\(408\) 692.955 1104.06i 1.69842 2.70604i
\(409\) −195.136 −0.477106 −0.238553 0.971130i \(-0.576673\pi\)
−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
\(417\) 141.056 + 88.5324i 0.338264 + 0.212308i
\(418\) 358.249 + 358.249i 0.857056 + 0.857056i
\(419\) 389.604i 0.929843i −0.885352 0.464922i \(-0.846083\pi\)
0.885352 0.464922i \(-0.153917\pi\)
\(420\) 722.157 + 745.447i 1.71942 + 1.77487i
\(421\) 22.7752 0.0540978 0.0270489 0.999634i \(-0.491389\pi\)
0.0270489 + 0.999634i \(0.491389\pi\)
\(422\) 441.248 441.248i 1.04561 1.04561i
\(423\) 114.839 329.252i 0.271487 0.778373i
\(424\) 697.306i 1.64459i
\(425\) −190.905 + 457.131i −0.449187 + 1.07560i
\(426\) −135.294 591.391i −0.317591 1.38824i
\(427\) −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 \(0.425756\pi\)
−0.231137 + 0.972921i \(0.574244\pi\)
\(432\) −125.767 + 1131.54i −0.291126 + 2.61931i
\(433\) 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
\(435\) 147.379 + 330.198i 0.338802 + 0.759076i
\(436\) 1867.45 4.28314
\(437\) 76.2549 + 76.2549i 0.174496 + 0.174496i
\(438\) 408.060 + 256.115i 0.931643 + 0.584737i
\(439\) 452.142 1.02994 0.514968 0.857209i \(-0.327804\pi\)
0.514968 + 0.857209i \(0.327804\pi\)
\(440\) −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 0.901937 0.431867i \(-0.142145\pi\)
−0.431867 + 0.901937i \(0.642145\pi\)
\(444\) 564.462 129.133i 1.27131 0.290841i
\(445\) 304.678 454.555i 0.684670 1.02147i
\(446\) 76.4403 0.171391
\(447\) 680.675 + 427.220i 1.52276 + 0.955749i
\(448\) −591.748 + 215.823i −1.32087 + 0.481747i
\(449\) −547.513 −1.21941 −0.609703 0.792630i \(-0.708711\pi\)
−0.609703 + 0.792630i \(0.708711\pi\)
\(450\) −45.4238 837.165i −0.100942 1.86037i
\(451\) 302.651i 0.671067i
\(452\) 1107.49 1107.49i 2.45021 2.45021i
\(453\) −378.799 237.750i −0.836202 0.524834i
\(454\) 68.0021 0.149784
\(455\) −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 \(-0.758068\pi\)
−0.724801 + 0.688958i \(0.758068\pi\)
\(462\) 372.010 240.884i 0.805216 0.521394i
\(463\) −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
\(465\) −326.599 + 145.772i −0.702363 + 0.313489i
\(466\) 353.023 0.757560
\(467\) −651.899 651.899i −1.39593 1.39593i −0.811301 0.584629i \(-0.801240\pi\)
−0.584629 0.811301i \(-0.698760\pi\)
\(468\) −200.142 69.8069i −0.427654 0.149160i
\(469\) 2.05555 4.41578i 0.00438284 0.00941532i
\(470\) −599.621 401.912i −1.27579 0.855133i
\(471\) −567.266 + 129.775i −1.20439 + 0.275530i
\(472\) −221.681 + 221.681i −0.469663 + 0.469663i
\(473\) −146.700 146.700i −0.310149 0.310149i
\(474\) −145.432 635.704i −0.306818 1.34115i
\(475\) 228.065 + 555.144i 0.480137 + 1.16872i
\(476\) 1243.02 + 578.625i 2.61138 + 1.21560i
\(477\) −94.2569 + 270.242i −0.197604 + 0.566545i
\(478\) −463.421 + 463.421i −0.969500 + 0.969500i
\(479\) 686.172i 1.43251i 0.697839 + 0.716254i \(0.254145\pi\)
−0.697839 + 0.716254i \(0.745855\pi\)
\(480\) 972.396 + 372.238i 2.02582 + 0.775496i
\(481\) 46.5261i 0.0967279i
\(482\) 1072.81 + 1072.81i 2.22575 + 2.22575i
\(483\) 79.1839 51.2732i 0.163942 0.106156i
\(484\) 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 \(-0.855979\pi\)
0.899376 0.437176i \(-0.144021\pi\)
\(492\) −842.385 + 1342.15i −1.71217 + 2.72794i
\(493\) 337.774 + 337.774i 0.685140 + 0.685140i
\(494\) 213.139 0.431456
\(495\) −252.350 35.7402i −0.509797 0.0722024i
\(496\) 1005.41i 2.02704i
\(497\) 356.897 130.168i 0.718103 0.261907i
\(498\) −468.696 + 746.758i −0.941156 + 1.49951i
\(499\) 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
\(507\) −260.470 + 414.999i −0.513748 + 0.818539i
\(508\) −269.422 + 269.422i −0.530359 + 0.530359i
\(509\) 16.1598i 0.0317481i 0.999874 + 0.0158740i \(0.00505308\pi\)
−0.999874 + 0.0158740i \(0.994947\pi\)
\(510\) −451.419 1011.39i −0.885135 1.98312i
\(511\) −127.317 + 273.504i −0.249152 + 0.535234i
\(512\) 545.497 545.497i 1.06542 1.06542i
\(513\) 71.6017 644.212i 0.139574 1.25577i
\(514\) 195.101 0.379574
\(515\) 82.0696 + 415.740i 0.159358 + 0.807263i
\(516\) 242.243 + 1058.88i 0.469462 + 2.05209i
\(517\) −155.168 + 155.168i −0.300132 + 0.300132i
\(518\) 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 \(-0.283217\pi\)
0.629605 + 0.776915i \(0.283217\pi\)
\(522\) −763.329 266.239i −1.46232 0.510037i
\(523\) −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
\(525\) 516.609 93.4907i 0.984016 0.178077i
\(526\) 571.127 1.08579
\(527\) −334.092 + 334.092i −0.633951 + 0.633951i
\(528\) 380.879 606.842i 0.721361 1.14932i
\(529\) 508.821i 0.961854i
\(530\) 492.154 + 329.880i 0.928592 + 0.622415i
\(531\) −115.878 + 55.9475i −0.218226 + 0.105363i
\(532\) 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
\(537\) −353.181 221.671i −0.657692 0.412794i
\(538\) 260.043 + 260.043i 0.483351 + 0.483351i
\(539\) 178.670 + 212.358i 0.331484 + 0.393986i
\(540\) 1019.60 + 860.872i 1.88814 + 1.59421i
\(541\) −210.543 −0.389174 −0.194587 0.980885i \(-0.562337\pi\)
−0.194587 + 0.980885i \(0.562337\pi\)
\(542\) −576.344 576.344i −1.06336 1.06336i
\(543\) −24.6349 + 39.2499i −0.0453680 + 0.0722835i
\(544\) 1375.48 2.52846
\(545\) 525.944 784.665i 0.965034 1.43975i
\(546\) 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
\(552\) 157.090 250.286i 0.284583 0.453416i
\(553\) 383.640 139.921i 0.693743 0.253022i
\(554\) 990.211 1.78739
\(555\) 104.714 273.545i 0.188674 0.492873i
\(556\) 548.719i 0.986905i
\(557\) 509.388 509.388i 0.914521 0.914521i −0.0821026 0.996624i \(-0.526164\pi\)
0.996624 + 0.0821026i \(0.0261635\pi\)
\(558\) 263.337 755.008i 0.471931 1.35306i
\(559\) −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 −0.330351 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
\(567\) −537.956 179.145i −0.948775 0.315952i
\(568\) 841.459 841.459i 1.48144 1.48144i
\(569\) 304.242 0.534696 0.267348 0.963600i \(-0.413853\pi\)
0.267348 + 0.963600i \(0.413853\pi\)
\(570\) −1253.13 479.703i −2.19846 0.841584i
\(571\) 10.6264 0.0186101 0.00930507 0.999957i \(-0.497038\pi\)
0.00930507 + 0.999957i \(0.497038\pi\)
\(572\) 94.3219 + 94.3219i 0.164898 + 0.164898i
\(573\) −429.929 + 684.992i −0.750313 + 1.19545i
\(574\) −1263.61 588.214i −2.20142 1.02476i
\(575\) −43.2772 + 103.630i −0.0752647 + 0.180225i
\(576\) −729.289 + 352.110i −1.26613 + 0.611303i
\(577\) −21.8636 + 21.8636i −0.0378918 + 0.0378918i −0.725799 0.687907i \(-0.758530\pi\)
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
\(582\) 403.946 643.594i 0.694065 1.10583i
\(583\) 127.358 127.358i 0.218453 0.218453i
\(584\) 945.019i 1.61818i
\(585\) −85.6990 + 64.4355i −0.146494 + 0.110146i
\(586\) 1532.52i 2.61523i
\(587\) 229.516 + 229.516i 0.390999 + 0.390999i 0.875043 0.484045i \(-0.160833\pi\)
−0.484045 + 0.875043i \(0.660833\pi\)
\(588\) −201.266 1439.03i −0.342289 2.44733i
\(589\) 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
\(595\) 593.207 359.328i 0.996986 0.603913i
\(596\) 2647.88i 4.44276i
\(597\) −224.621 140.981i −0.376250 0.236150i
\(598\) 28.2013 + 28.2013i 0.0471594 + 0.0471594i
\(599\) −861.037 −1.43746 −0.718728 0.695291i \(-0.755276\pi\)
−0.718728 + 0.695291i \(0.755276\pi\)
\(600\) 1343.50 948.433i 2.23917 1.58072i
\(601\) 413.625i 0.688227i −0.938928 0.344114i \(-0.888179\pi\)
0.938928 0.344114i \(-0.111821\pi\)
\(602\) −897.614 + 327.378i −1.49105 + 0.543818i
\(603\) 2.06240 5.91307i 0.00342024 0.00980609i
\(604\) 1473.56i 2.43967i
\(605\) −369.322 247.548i −0.610449 0.409170i
\(606\) 1126.82 257.786i 1.85945 0.425390i
\(607\) −473.829 + 473.829i −0.780608 + 0.780608i −0.979933 0.199325i \(-0.936125\pi\)
0.199325 + 0.979933i \(0.436125\pi\)
\(608\) 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
\(612\) 1664.49 + 580.554i 2.71976 + 0.948618i
\(613\) −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
\(615\) 326.696 + 731.952i 0.531213 + 1.19017i
\(616\) 788.124 + 366.873i 1.27942 + 0.595572i
\(617\) −601.654 + 601.654i −0.975128 + 0.975128i −0.999698 0.0245706i \(-0.992178\pi\)
0.0245706 + 0.999698i \(0.492178\pi\)
\(618\) −802.455 503.653i −1.29847 0.814973i
\(619\) 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
\(627\) −216.843 + 345.489i −0.345842 + 0.551019i
\(628\) −1355.77 1355.77i −2.15888 2.15888i
\(629\) 386.938i 0.615163i
\(630\) −639.671 + 984.134i −1.01535 + 1.56212i
\(631\) 407.417 0.645669 0.322835 0.946455i \(-0.395364\pi\)
0.322835 + 0.946455i \(0.395364\pi\)
\(632\) 904.511 904.511i 1.43119 1.43119i
\(633\) 425.531 + 267.080i 0.672244 + 0.421928i
\(634\) 133.454i 0.210496i
\(635\) 37.3265 + 189.085i 0.0587820 + 0.297772i
\(636\) −919.268 + 210.303i −1.44539 + 0.330665i
\(637\) 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 \(-0.811493\pi\)
0.829708 0.558198i \(-0.188507\pi\)
\(642\) 281.317 448.213i 0.438188 0.698151i
\(643\) −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
\(645\) 513.145 + 196.435i 0.795574 + 0.304550i
\(646\) −1772.59 −2.74394
\(647\) −59.3647 59.3647i −0.0917537 0.0917537i 0.659740 0.751494i \(-0.270666\pi\)
−0.751494 + 0.659740i \(0.770666\pi\)
\(648\) −1764.54 + 202.409i −2.72305 + 0.312359i
\(649\) 80.9771 0.124772
\(650\) 84.3450 + 205.308i 0.129762 + 0.315859i
\(651\) 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 0.868240 0.496145i \(-0.165252\pi\)
−0.496145 + 0.868240i \(0.665252\pi\)
\(654\) 470.981 + 2058.73i 0.720155 + 3.14791i
\(655\) −92.2073 61.8045i −0.140774 0.0943579i
\(656\) −2253.27 −3.43486
\(657\) −127.741 + 366.243i −0.194431 + 0.557448i
\(658\) 346.275 + 949.425i 0.526254 + 1.44290i
\(659\) 1201.84 1.82373 0.911866 0.410489i \(-0.134642\pi\)
0.911866 + 0.410489i \(0.134642\pi\)
\(660\) −342.268 766.840i −0.518587 1.16188i
\(661\) 618.277i 0.935366i −0.883896 0.467683i \(-0.845089\pi\)
0.883896 0.467683i \(-0.154911\pi\)
\(662\) −428.827 + 428.827i −0.647775 + 0.647775i
\(663\) −75.2985 + 119.971i −0.113572 + 0.180951i
\(664\) −1729.40 −2.60453
\(665\) 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
\(672\) −792.292 1223.58i −1.17901 1.82080i
\(673\) 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
\(675\) 648.879 185.961i 0.961302 0.275498i
\(676\) −1614.38 −2.38814
\(677\) −785.544 785.544i −1.16033 1.16033i −0.984403 0.175927i \(-0.943708\pi\)
−0.175927 0.984403i \(-0.556292\pi\)
\(678\) 1500.25 + 941.618i 2.21276 + 1.38882i
\(679\) 431.373 + 200.804i 0.635306 + 0.295736i
\(680\) 1209.60 1804.63i 1.77883 2.65387i
\(681\) 12.2096 + 53.3702i 0.0179290 + 0.0783704i
\(682\) −355.816 + 355.816i −0.521725 + 0.521725i
\(683\) 510.988 + 510.988i 0.748152 + 0.748152i 0.974132 0.225980i \(-0.0725583\pi\)
−0.225980 + 0.974132i \(0.572558\pi\)
\(684\) 1923.23 928.563i 2.81175 1.35755i
\(685\) 609.271 120.274i 0.889446 0.175582i
\(686\) 1233.88 333.247i 1.79866 0.485783i
\(687\) 828.118 + 519.761i 1.20541 + 0.756566i
\(688\) −1092.20 + 1092.20i −1.58750 + 1.58750i
\(689\) 75.7713i 0.109973i
\(690\) −102.335 229.278i −0.148311 0.332286i
\(691\) 93.1153i 0.134754i 0.997728 + 0.0673772i \(0.0214631\pi\)
−0.997728 + 0.0673772i \(0.978537\pi\)
\(692\) −909.076 909.076i −1.31369 1.31369i
\(693\) 255.847 + 248.715i 0.369188 + 0.358896i
\(694\) 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 \(-0.863719\pi\)
0.909740 0.415179i \(-0.136281\pi\)
\(702\) 26.4804 238.248i 0.0377214 0.339385i
\(703\) −331.472 331.472i −0.471511 0.471511i
\(704\) 509.636 0.723915
\(705\) 207.773 542.765i 0.294714 0.769879i
\(706\) 65.8034i 0.0932060i
\(707\) 248.019 + 680.025i 0.350805 + 0.961845i
\(708\) −359.103 225.388i −0.507208 0.318344i
\(709\) 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
\(717\) −446.914 280.502i −0.623311 0.391216i
\(718\) 1294.17 1294.17i 1.80246 1.80246i
\(719\) 1307.80i 1.81892i 0.415790 + 0.909461i \(0.363505\pi\)
−0.415790 + 0.909461i \(0.636495\pi\)
\(720\) −266.089 + 1878.77i −0.369568 + 2.60940i
\(721\) 250.370 537.850i 0.347254 0.745978i
\(722\) −567.324 + 567.324i −0.785768 + 0.785768i
\(723\) −649.358 + 1034.60i −0.898143 + 1.43098i
\(724\) −152.685 −0.210892
\(725\) 229.012 + 557.451i 0.315879 + 0.768897i
\(726\) 968.993 221.679i 1.33470 0.305343i
\(727\) 113.590 113.590i 0.156245 0.156245i −0.624655 0.780901i \(-0.714761\pi\)
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
\(732\) −2267.52 1423.19i −3.09770 1.94424i
\(733\) −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
\(735\) −661.336 320.717i −0.899777 0.436349i
\(736\) 311.816 0.423663
\(737\) −2.78668 + 2.78668i −0.00378112 + 0.00378112i
\(738\) −1692.08 590.175i −2.29279 0.799695i
\(739\) 290.721i 0.393398i −0.980464 0.196699i \(-0.936978\pi\)
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 0.376044 0.926602i \(-0.377284\pi\)
−0.926602 + 0.376044i \(0.877284\pi\)
\(744\) 1528.97 349.787i 2.05507 0.470143i
\(745\) 1112.59 + 745.743i 1.49341 + 1.00100i
\(746\) 375.768i 0.503710i
\(747\) −670.233 233.769i −0.897233 0.312943i
\(748\) −784.434 784.434i −1.04871 1.04871i
\(749\) 300.417 + 139.845i 0.401091 + 0.186709i
\(750\) −33.8173 1396.92i −0.0450898 1.86256i
\(751\) 220.161 0.293157 0.146579 0.989199i \(-0.453174\pi\)
0.146579 + 0.989199i \(0.453174\pi\)
\(752\) 1155.24 + 1155.24i 1.53622 + 1.53622i
\(753\) 761.029 + 477.653i 1.01066 + 0.634334i
\(754\) 214.025 0.283852
\(755\) −619.162 415.010i −0.820082 0.549682i
\(756\) −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 \(0.245469\pi\)
\(762\) −364.969 229.069i −0.478962 0.300616i
\(763\) −1242.42 + 453.136i −1.62834 + 0.593888i
\(764\) −2664.68 −3.48780
\(765\) 712.721 535.882i 0.931661 0.700499i
\(766\) 1671.42i 2.18201i
\(767\) 24.0885 24.0885i 0.0314061 0.0314061i