Properties

Label 48.3.l.a.19.7
Level 48
Weight 3
Character 48.19
Analytic conductor 1.308
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.30790526893\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.7
Root \(-1.87459 - 0.697079i\) of defining polynomial
Character \(\chi\) \(=\) 48.19
Dual form 48.3.l.a.43.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.87459 - 0.697079i) q^{2} +(1.22474 - 1.22474i) q^{3} +(3.02816 - 2.61347i) q^{4} +(-5.24354 + 5.24354i) q^{5} +(1.44215 - 3.14964i) q^{6} -5.32796 q^{7} +(3.85476 - 7.01005i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.87459 - 0.697079i) q^{2} +(1.22474 - 1.22474i) q^{3} +(3.02816 - 2.61347i) q^{4} +(-5.24354 + 5.24354i) q^{5} +(1.44215 - 3.14964i) q^{6} -5.32796 q^{7} +(3.85476 - 7.01005i) q^{8} -3.00000i q^{9} +(-6.17431 + 13.4846i) q^{10} +(12.2863 + 12.2863i) q^{11} +(0.507889 - 6.90956i) q^{12} +(-5.73657 - 5.73657i) q^{13} +(-9.98774 + 3.71401i) q^{14} +12.8440i q^{15} +(2.33953 - 15.8280i) q^{16} -23.3997 q^{17} +(-2.09124 - 5.62376i) q^{18} +(11.7492 - 11.7492i) q^{19} +(-2.17444 + 29.5821i) q^{20} +(-6.52540 + 6.52540i) q^{21} +(31.5962 + 14.4672i) q^{22} +5.80841 q^{23} +(-3.86443 - 13.3066i) q^{24} -29.9894i q^{25} +(-14.7526 - 6.75487i) q^{26} +(-3.67423 - 3.67423i) q^{27} +(-16.1339 + 13.9245i) q^{28} +(18.3914 + 18.3914i) q^{29} +(8.95328 + 24.0772i) q^{30} -16.9053i q^{31} +(-6.64774 - 31.3019i) q^{32} +30.0951 q^{33} +(-43.8648 + 16.3114i) q^{34} +(27.9374 - 27.9374i) q^{35} +(-7.84042 - 9.08449i) q^{36} +(15.3391 - 15.3391i) q^{37} +(13.8348 - 30.2151i) q^{38} -14.0517 q^{39} +(16.5449 + 56.9701i) q^{40} -29.2351i q^{41} +(-7.68371 + 16.7811i) q^{42} +(33.4099 + 33.4099i) q^{43} +(69.3146 + 5.09498i) q^{44} +(15.7306 + 15.7306i) q^{45} +(10.8884 - 4.04892i) q^{46} -18.2125i q^{47} +(-16.5200 - 22.2506i) q^{48} -20.6128 q^{49} +(-20.9050 - 56.2178i) q^{50} +(-28.6586 + 28.6586i) q^{51} +(-32.3637 - 2.37890i) q^{52} +(-66.9856 + 66.9856i) q^{53} +(-9.44891 - 4.32644i) q^{54} -128.847 q^{55} +(-20.5380 + 37.3493i) q^{56} -28.7796i q^{57} +(47.2965 + 21.6560i) q^{58} +(-27.1523 - 27.1523i) q^{59} +(33.5674 + 38.8937i) q^{60} +(65.2399 + 65.2399i) q^{61} +(-11.7843 - 31.6904i) q^{62} +15.9839i q^{63} +(-34.2817 - 54.0441i) q^{64} +60.1599 q^{65} +(56.4158 - 20.9786i) q^{66} +(-37.6951 + 37.6951i) q^{67} +(-70.8580 + 61.1544i) q^{68} +(7.11382 - 7.11382i) q^{69} +(32.8965 - 71.8456i) q^{70} +42.6559 q^{71} +(-21.0302 - 11.5643i) q^{72} +106.391i q^{73} +(18.0620 - 39.4471i) q^{74} +(-36.7294 - 36.7294i) q^{75} +(4.87228 - 66.2847i) q^{76} +(-65.4607 - 65.4607i) q^{77} +(-26.3411 + 9.79513i) q^{78} -21.2821i q^{79} +(70.7275 + 95.2623i) q^{80} -9.00000 q^{81} +(-20.3792 - 54.8038i) q^{82} +(24.1638 - 24.1638i) q^{83} +(-2.70601 + 36.8139i) q^{84} +(122.697 - 122.697i) q^{85} +(85.9192 + 39.3405i) q^{86} +45.0495 q^{87} +(133.488 - 38.7667i) q^{88} +52.8029i q^{89} +(40.4539 + 18.5229i) q^{90} +(30.5643 + 30.5643i) q^{91} +(17.5888 - 15.1801i) q^{92} +(-20.7047 - 20.7047i) q^{93} +(-12.6955 - 34.1409i) q^{94} +123.215i q^{95} +(-46.4786 - 30.1950i) q^{96} -21.0222 q^{97} +(-38.6405 + 14.3688i) q^{98} +(36.8588 - 36.8588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} - 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} - 12q^{8} - 56q^{10} + 32q^{11} - 24q^{12} - 44q^{14} + 32q^{16} + 12q^{18} - 32q^{19} + 80q^{20} + 32q^{22} - 128q^{23} + 36q^{24} - 100q^{26} - 120q^{28} + 32q^{29} + 72q^{30} + 160q^{32} + 96q^{34} + 96q^{35} + 12q^{36} - 96q^{37} + 168q^{38} + 48q^{40} - 60q^{42} + 160q^{43} + 88q^{44} + 136q^{46} - 144q^{48} + 112q^{49} - 236q^{50} - 96q^{51} - 48q^{52} - 160q^{53} - 36q^{54} - 256q^{55} - 224q^{56} + 144q^{58} - 128q^{59} - 72q^{60} - 32q^{61} - 276q^{62} - 408q^{64} - 32q^{65} + 72q^{66} + 320q^{67} - 448q^{68} + 96q^{69} - 384q^{70} + 512q^{71} + 60q^{72} + 348q^{74} + 192q^{75} + 72q^{76} + 224q^{77} + 396q^{78} + 552q^{80} - 144q^{81} - 40q^{82} - 160q^{83} + 72q^{84} + 160q^{85} + 528q^{86} + 480q^{88} - 24q^{90} - 480q^{91} + 496q^{92} + 312q^{94} - 480q^{96} - 440q^{98} + 96q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.87459 0.697079i 0.937294 0.348540i
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 3.02816 2.61347i 0.757040 0.653368i
\(5\) −5.24354 + 5.24354i −1.04871 + 1.04871i −0.0499563 + 0.998751i \(0.515908\pi\)
−0.998751 + 0.0499563i \(0.984092\pi\)
\(6\) 1.44215 3.14964i 0.240358 0.524939i
\(7\) −5.32796 −0.761138 −0.380569 0.924753i \(-0.624272\pi\)
−0.380569 + 0.924753i \(0.624272\pi\)
\(8\) 3.85476 7.01005i 0.481845 0.876256i
\(9\) 3.00000i 0.333333i
\(10\) −6.17431 + 13.4846i −0.617431 + 1.34846i
\(11\) 12.2863 + 12.2863i 1.11693 + 1.11693i 0.992189 + 0.124743i \(0.0398107\pi\)
0.124743 + 0.992189i \(0.460189\pi\)
\(12\) 0.507889 6.90956i 0.0423241 0.575797i
\(13\) −5.73657 5.73657i −0.441275 0.441275i 0.451165 0.892440i \(-0.351008\pi\)
−0.892440 + 0.451165i \(0.851008\pi\)
\(14\) −9.98774 + 3.71401i −0.713410 + 0.265287i
\(15\) 12.8440i 0.856266i
\(16\) 2.33953 15.8280i 0.146220 0.989252i
\(17\) −23.3997 −1.37645 −0.688226 0.725496i \(-0.741610\pi\)
−0.688226 + 0.725496i \(0.741610\pi\)
\(18\) −2.09124 5.62376i −0.116180 0.312431i
\(19\) 11.7492 11.7492i 0.618380 0.618380i −0.326736 0.945116i \(-0.605949\pi\)
0.945116 + 0.326736i \(0.105949\pi\)
\(20\) −2.17444 + 29.5821i −0.108722 + 1.47911i
\(21\) −6.52540 + 6.52540i −0.310733 + 0.310733i
\(22\) 31.5962 + 14.4672i 1.43619 + 0.657599i
\(23\) 5.80841 0.252540 0.126270 0.991996i \(-0.459699\pi\)
0.126270 + 0.991996i \(0.459699\pi\)
\(24\) −3.86443 13.3066i −0.161018 0.554443i
\(25\) 29.9894i 1.19958i
\(26\) −14.7526 6.75487i −0.567406 0.259803i
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −16.1339 + 13.9245i −0.576212 + 0.497303i
\(29\) 18.3914 + 18.3914i 0.634185 + 0.634185i 0.949115 0.314930i \(-0.101981\pi\)
−0.314930 + 0.949115i \(0.601981\pi\)
\(30\) 8.95328 + 24.0772i 0.298443 + 0.802573i
\(31\) 16.9053i 0.545332i −0.962109 0.272666i \(-0.912095\pi\)
0.962109 0.272666i \(-0.0879053\pi\)
\(32\) −6.64774 31.3019i −0.207742 0.978184i
\(33\) 30.0951 0.911971
\(34\) −43.8648 + 16.3114i −1.29014 + 0.479748i
\(35\) 27.9374 27.9374i 0.798211 0.798211i
\(36\) −7.84042 9.08449i −0.217789 0.252347i
\(37\) 15.3391 15.3391i 0.414571 0.414571i −0.468756 0.883327i \(-0.655298\pi\)
0.883327 + 0.468756i \(0.155298\pi\)
\(38\) 13.8348 30.2151i 0.364074 0.795133i
\(39\) −14.0517 −0.360299
\(40\) 16.5449 + 56.9701i 0.413622 + 1.42425i
\(41\) 29.2351i 0.713051i −0.934286 0.356526i \(-0.883961\pi\)
0.934286 0.356526i \(-0.116039\pi\)
\(42\) −7.68371 + 16.7811i −0.182946 + 0.399551i
\(43\) 33.4099 + 33.4099i 0.776975 + 0.776975i 0.979315 0.202340i \(-0.0648546\pi\)
−0.202340 + 0.979315i \(0.564855\pi\)
\(44\) 69.3146 + 5.09498i 1.57533 + 0.115795i
\(45\) 15.7306 + 15.7306i 0.349569 + 0.349569i
\(46\) 10.8884 4.04892i 0.236704 0.0880201i
\(47\) 18.2125i 0.387500i −0.981051 0.193750i \(-0.937935\pi\)
0.981051 0.193750i \(-0.0620650\pi\)
\(48\) −16.5200 22.2506i −0.344166 0.463555i
\(49\) −20.6128 −0.420670
\(50\) −20.9050 56.2178i −0.418100 1.12436i
\(51\) −28.6586 + 28.6586i −0.561934 + 0.561934i
\(52\) −32.3637 2.37890i −0.622378 0.0457480i
\(53\) −66.9856 + 66.9856i −1.26388 + 1.26388i −0.314681 + 0.949197i \(0.601898\pi\)
−0.949197 + 0.314681i \(0.898102\pi\)
\(54\) −9.44891 4.32644i −0.174980 0.0801194i
\(55\) −128.847 −2.34267
\(56\) −20.5380 + 37.3493i −0.366750 + 0.666952i
\(57\) 28.7796i 0.504905i
\(58\) 47.2965 + 21.6560i 0.815457 + 0.373380i
\(59\) −27.1523 27.1523i −0.460209 0.460209i 0.438515 0.898724i \(-0.355505\pi\)
−0.898724 + 0.438515i \(0.855505\pi\)
\(60\) 33.5674 + 38.8937i 0.559457 + 0.648228i
\(61\) 65.2399 + 65.2399i 1.06951 + 1.06951i 0.997397 + 0.0721103i \(0.0229733\pi\)
0.0721103 + 0.997397i \(0.477027\pi\)
\(62\) −11.7843 31.6904i −0.190070 0.511136i
\(63\) 15.9839i 0.253713i
\(64\) −34.2817 54.0441i −0.535651 0.844440i
\(65\) 60.1599 0.925537
\(66\) 56.4158 20.9786i 0.854785 0.317858i
\(67\) −37.6951 + 37.6951i −0.562614 + 0.562614i −0.930049 0.367435i \(-0.880236\pi\)
0.367435 + 0.930049i \(0.380236\pi\)
\(68\) −70.8580 + 61.1544i −1.04203 + 0.899330i
\(69\) 7.11382 7.11382i 0.103099 0.103099i
\(70\) 32.8965 71.8456i 0.469950 1.02637i
\(71\) 42.6559 0.600788 0.300394 0.953815i \(-0.402882\pi\)
0.300394 + 0.953815i \(0.402882\pi\)
\(72\) −21.0302 11.5643i −0.292085 0.160615i
\(73\) 106.391i 1.45742i 0.684825 + 0.728708i \(0.259879\pi\)
−0.684825 + 0.728708i \(0.740121\pi\)
\(74\) 18.0620 39.4471i 0.244081 0.533069i
\(75\) −36.7294 36.7294i −0.489725 0.489725i
\(76\) 4.87228 66.2847i 0.0641089 0.872168i
\(77\) −65.4607 65.4607i −0.850139 0.850139i
\(78\) −26.3411 + 9.79513i −0.337707 + 0.125579i
\(79\) 21.2821i 0.269394i −0.990887 0.134697i \(-0.956994\pi\)
0.990887 0.134697i \(-0.0430061\pi\)
\(80\) 70.7275 + 95.2623i 0.884094 + 1.19078i
\(81\) −9.00000 −0.111111
\(82\) −20.3792 54.8038i −0.248527 0.668339i
\(83\) 24.1638 24.1638i 0.291130 0.291130i −0.546396 0.837527i \(-0.684001\pi\)
0.837527 + 0.546396i \(0.184001\pi\)
\(84\) −2.70601 + 36.8139i −0.0322144 + 0.438261i
\(85\) 122.697 122.697i 1.44350 1.44350i
\(86\) 85.9192 + 39.3405i 0.999061 + 0.457448i
\(87\) 45.0495 0.517810
\(88\) 133.488 38.7667i 1.51691 0.440531i
\(89\) 52.8029i 0.593291i 0.954988 + 0.296645i \(0.0958679\pi\)
−0.954988 + 0.296645i \(0.904132\pi\)
\(90\) 40.4539 + 18.5229i 0.449488 + 0.205810i
\(91\) 30.5643 + 30.5643i 0.335871 + 0.335871i
\(92\) 17.5888 15.1801i 0.191183 0.165001i
\(93\) −20.7047 20.7047i −0.222631 0.222631i
\(94\) −12.6955 34.1409i −0.135059 0.363201i
\(95\) 123.215i 1.29700i
\(96\) −46.4786 30.1950i −0.484152 0.314532i
\(97\) −21.0222 −0.216724 −0.108362 0.994112i \(-0.534560\pi\)
−0.108362 + 0.994112i \(0.534560\pi\)
\(98\) −38.6405 + 14.3688i −0.394291 + 0.146620i
\(99\) 36.8588 36.8588i 0.372311 0.372311i
\(100\) −78.3764 90.8127i −0.783764 0.908127i
\(101\) −3.24960 + 3.24960i −0.0321743 + 0.0321743i −0.723011 0.690837i \(-0.757242\pi\)
0.690837 + 0.723011i \(0.257242\pi\)
\(102\) −33.7458 + 73.7005i −0.330841 + 0.722554i
\(103\) 105.112 1.02050 0.510252 0.860025i \(-0.329552\pi\)
0.510252 + 0.860025i \(0.329552\pi\)
\(104\) −62.3268 + 18.1006i −0.599296 + 0.174044i
\(105\) 68.4323i 0.651736i
\(106\) −78.8761 + 172.265i −0.744114 + 1.62514i
\(107\) −99.6160 99.6160i −0.930991 0.930991i 0.0667770 0.997768i \(-0.478728\pi\)
−0.997768 + 0.0667770i \(0.978728\pi\)
\(108\) −20.7287 1.52367i −0.191932 0.0141080i
\(109\) −108.050 108.050i −0.991282 0.991282i 0.00868078 0.999962i \(-0.497237\pi\)
−0.999962 + 0.00868078i \(0.997237\pi\)
\(110\) −241.535 + 89.8165i −2.19577 + 0.816513i
\(111\) 37.5730i 0.338496i
\(112\) −12.4649 + 84.3312i −0.111294 + 0.752957i
\(113\) −23.2835 −0.206048 −0.103024 0.994679i \(-0.532852\pi\)
−0.103024 + 0.994679i \(0.532852\pi\)
\(114\) −20.0616 53.9498i −0.175979 0.473244i
\(115\) −30.4566 + 30.4566i −0.264840 + 0.264840i
\(116\) 103.757 + 7.62671i 0.894460 + 0.0657475i
\(117\) −17.2097 + 17.2097i −0.147092 + 0.147092i
\(118\) −69.8268 31.9721i −0.591752 0.270950i
\(119\) 124.673 1.04767
\(120\) 90.0371 + 49.5105i 0.750309 + 0.412588i
\(121\) 180.904i 1.49508i
\(122\) 167.775 + 76.8206i 1.37521 + 0.629677i
\(123\) −35.8055 35.8055i −0.291102 0.291102i
\(124\) −44.1815 51.1919i −0.356302 0.412838i
\(125\) 26.1621 + 26.1621i 0.209297 + 0.209297i
\(126\) 11.1420 + 29.9632i 0.0884288 + 0.237803i
\(127\) 118.180i 0.930550i −0.885166 0.465275i \(-0.845955\pi\)
0.885166 0.465275i \(-0.154045\pi\)
\(128\) −101.937 77.4135i −0.796383 0.604793i
\(129\) 81.8373 0.634398
\(130\) 112.775 41.9362i 0.867500 0.322586i
\(131\) −69.2067 + 69.2067i −0.528296 + 0.528296i −0.920064 0.391768i \(-0.871863\pi\)
0.391768 + 0.920064i \(0.371863\pi\)
\(132\) 91.1327 78.6526i 0.690399 0.595853i
\(133\) −62.5994 + 62.5994i −0.470672 + 0.470672i
\(134\) −44.3864 + 96.9393i −0.331241 + 0.723428i
\(135\) 38.5320 0.285422
\(136\) −90.2002 + 164.033i −0.663237 + 1.20613i
\(137\) 124.474i 0.908572i −0.890856 0.454286i \(-0.849894\pi\)
0.890856 0.454286i \(-0.150106\pi\)
\(138\) 8.37659 18.2944i 0.0607000 0.132568i
\(139\) 169.014 + 169.014i 1.21593 + 1.21593i 0.969046 + 0.246881i \(0.0794057\pi\)
0.246881 + 0.969046i \(0.420594\pi\)
\(140\) 11.5853 157.612i 0.0827524 1.12580i
\(141\) −22.3057 22.3057i −0.158196 0.158196i
\(142\) 79.9623 29.7346i 0.563115 0.209398i
\(143\) 140.962i 0.985749i
\(144\) −47.4841 7.01858i −0.329751 0.0487401i
\(145\) −192.872 −1.33015
\(146\) 74.1632 + 199.440i 0.507967 + 1.36603i
\(147\) −25.2454 + 25.2454i −0.171738 + 0.171738i
\(148\) 6.36098 86.5377i 0.0429796 0.584714i
\(149\) 146.988 146.988i 0.986495 0.986495i −0.0134145 0.999910i \(-0.504270\pi\)
0.999910 + 0.0134145i \(0.00427011\pi\)
\(150\) −94.4557 43.2492i −0.629705 0.288328i
\(151\) 75.5456 0.500302 0.250151 0.968207i \(-0.419520\pi\)
0.250151 + 0.968207i \(0.419520\pi\)
\(152\) −37.0722 127.653i −0.243896 0.839822i
\(153\) 70.1991i 0.458817i
\(154\) −168.343 77.0806i −1.09314 0.500523i
\(155\) 88.6435 + 88.6435i 0.571893 + 0.571893i
\(156\) −42.5508 + 36.7237i −0.272761 + 0.235408i
\(157\) −81.5356 81.5356i −0.519335 0.519335i 0.398035 0.917370i \(-0.369692\pi\)
−0.917370 + 0.398035i \(0.869692\pi\)
\(158\) −14.8353 39.8952i −0.0938943 0.252501i
\(159\) 164.080i 1.03195i
\(160\) 198.990 + 129.275i 1.24369 + 0.807968i
\(161\) −30.9470 −0.192217
\(162\) −16.8713 + 6.27371i −0.104144 + 0.0387266i
\(163\) 55.8065 55.8065i 0.342371 0.342371i −0.514887 0.857258i \(-0.672166\pi\)
0.857258 + 0.514887i \(0.172166\pi\)
\(164\) −76.4051 88.5286i −0.465885 0.539809i
\(165\) −157.805 + 157.805i −0.956391 + 0.956391i
\(166\) 28.4531 62.1413i 0.171404 0.374345i
\(167\) −24.6339 −0.147508 −0.0737540 0.997276i \(-0.523498\pi\)
−0.0737540 + 0.997276i \(0.523498\pi\)
\(168\) 20.5895 + 70.8972i 0.122557 + 0.422007i
\(169\) 103.183i 0.610553i
\(170\) 144.477 315.536i 0.849865 1.85610i
\(171\) −35.2476 35.2476i −0.206127 0.206127i
\(172\) 188.487 + 13.8548i 1.09585 + 0.0805509i
\(173\) 4.88551 + 4.88551i 0.0282399 + 0.0282399i 0.721086 0.692846i \(-0.243643\pi\)
−0.692846 + 0.721086i \(0.743643\pi\)
\(174\) 84.4492 31.4030i 0.485340 0.180477i
\(175\) 159.782i 0.913042i
\(176\) 223.211 165.723i 1.26825 0.941609i
\(177\) −66.5094 −0.375759
\(178\) 36.8078 + 98.9836i 0.206785 + 0.556088i
\(179\) −229.504 + 229.504i −1.28215 + 1.28215i −0.342702 + 0.939444i \(0.611342\pi\)
−0.939444 + 0.342702i \(0.888658\pi\)
\(180\) 88.7464 + 6.52332i 0.493035 + 0.0362407i
\(181\) 116.607 116.607i 0.644238 0.644238i −0.307356 0.951595i \(-0.599444\pi\)
0.951595 + 0.307356i \(0.0994443\pi\)
\(182\) 78.6011 + 35.9897i 0.431874 + 0.197746i
\(183\) 159.805 0.873249
\(184\) 22.3900 40.7173i 0.121685 0.221290i
\(185\) 160.863i 0.869528i
\(186\) −53.2455 24.3799i −0.286266 0.131075i
\(187\) −287.495 287.495i −1.53740 1.53740i
\(188\) −47.5978 55.1504i −0.253180 0.293353i
\(189\) 19.5762 + 19.5762i 0.103578 + 0.103578i
\(190\) 85.8905 + 230.977i 0.452055 + 1.21567i
\(191\) 94.2316i 0.493359i 0.969097 + 0.246680i \(0.0793395\pi\)
−0.969097 + 0.246680i \(0.920660\pi\)
\(192\) −108.177 24.2040i −0.563420 0.126062i
\(193\) 84.2667 0.436615 0.218308 0.975880i \(-0.429946\pi\)
0.218308 + 0.975880i \(0.429946\pi\)
\(194\) −39.4079 + 14.6541i −0.203134 + 0.0755367i
\(195\) 73.6805 73.6805i 0.377849 0.377849i
\(196\) −62.4189 + 53.8710i −0.318464 + 0.274852i
\(197\) −56.9578 + 56.9578i −0.289126 + 0.289126i −0.836734 0.547609i \(-0.815538\pi\)
0.547609 + 0.836734i \(0.315538\pi\)
\(198\) 43.4015 94.7885i 0.219200 0.478730i
\(199\) −196.179 −0.985827 −0.492913 0.870078i \(-0.664068\pi\)
−0.492913 + 0.870078i \(0.664068\pi\)
\(200\) −210.227 115.602i −1.05114 0.578009i
\(201\) 92.3338i 0.459372i
\(202\) −3.82644 + 8.35690i −0.0189428 + 0.0413708i
\(203\) −97.9886 97.9886i −0.482702 0.482702i
\(204\) −11.8844 + 161.682i −0.0582571 + 0.792557i
\(205\) 153.295 + 153.295i 0.747782 + 0.747782i
\(206\) 197.042 73.2714i 0.956513 0.355686i
\(207\) 17.4252i 0.0841799i
\(208\) −104.220 + 77.3778i −0.501056 + 0.372009i
\(209\) 288.708 1.38138
\(210\) −47.7027 128.282i −0.227156 0.610869i
\(211\) 177.340 177.340i 0.840475 0.840475i −0.148445 0.988921i \(-0.547427\pi\)
0.988921 + 0.148445i \(0.0474269\pi\)
\(212\) −27.7782 + 377.908i −0.131029 + 1.78259i
\(213\) 52.2426 52.2426i 0.245271 0.245271i
\(214\) −256.179 117.299i −1.19710 0.548125i
\(215\) −350.373 −1.62964
\(216\) −39.9199 + 11.5933i −0.184814 + 0.0536726i
\(217\) 90.0707i 0.415072i
\(218\) −277.868 127.229i −1.27462 0.583622i
\(219\) 130.302 + 130.302i 0.594987 + 0.594987i
\(220\) −390.169 + 336.738i −1.77350 + 1.53063i
\(221\) 134.234 + 134.234i 0.607394 + 0.607394i
\(222\) −26.1914 70.4340i −0.117979 0.317270i
\(223\) 377.924i 1.69473i −0.531012 0.847364i \(-0.678188\pi\)
0.531012 0.847364i \(-0.321812\pi\)
\(224\) 35.4189 + 166.775i 0.158120 + 0.744532i
\(225\) −89.9682 −0.399859
\(226\) −43.6469 + 16.2304i −0.193128 + 0.0718160i
\(227\) 103.909 103.909i 0.457750 0.457750i −0.440166 0.897916i \(-0.645080\pi\)
0.897916 + 0.440166i \(0.145080\pi\)
\(228\) −75.2146 87.1492i −0.329889 0.382233i
\(229\) −101.055 + 101.055i −0.441290 + 0.441290i −0.892445 0.451156i \(-0.851012\pi\)
0.451156 + 0.892445i \(0.351012\pi\)
\(230\) −35.8630 + 78.3243i −0.155926 + 0.340541i
\(231\) −160.345 −0.694136
\(232\) 199.819 58.0302i 0.861288 0.250130i
\(233\) 287.259i 1.23287i −0.787405 0.616436i \(-0.788576\pi\)
0.787405 0.616436i \(-0.211424\pi\)
\(234\) −20.2646 + 44.2577i −0.0866009 + 0.189135i
\(235\) 95.4979 + 95.4979i 0.406374 + 0.406374i
\(236\) −153.184 11.2598i −0.649083 0.0477110i
\(237\) −26.0651 26.0651i −0.109980 0.109980i
\(238\) 233.710 86.9067i 0.981974 0.365154i
\(239\) 150.941i 0.631554i 0.948833 + 0.315777i \(0.102265\pi\)
−0.948833 + 0.315777i \(0.897735\pi\)
\(240\) 203.295 + 30.0489i 0.847063 + 0.125204i
\(241\) 37.7817 0.156771 0.0783853 0.996923i \(-0.475024\pi\)
0.0783853 + 0.996923i \(0.475024\pi\)
\(242\) 126.105 + 339.121i 0.521093 + 1.40133i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 368.060 + 27.0543i 1.50844 + 0.110878i
\(245\) 108.084 108.084i 0.441159 0.441159i
\(246\) −92.0799 42.1614i −0.374309 0.171388i
\(247\) −134.800 −0.545751
\(248\) −118.507 65.1658i −0.477850 0.262765i
\(249\) 59.1890i 0.237707i
\(250\) 67.2801 + 30.8061i 0.269121 + 0.123224i
\(251\) 100.915 + 100.915i 0.402050 + 0.402050i 0.878955 0.476905i \(-0.158241\pi\)
−0.476905 + 0.878955i \(0.658241\pi\)
\(252\) 41.7735 + 48.4018i 0.165768 + 0.192071i
\(253\) 71.3637 + 71.3637i 0.282070 + 0.282070i
\(254\) −82.3807 221.539i −0.324333 0.872199i
\(255\) 300.545i 1.17861i
\(256\) −245.053 74.0602i −0.957239 0.289298i
\(257\) 241.295 0.938891 0.469446 0.882961i \(-0.344454\pi\)
0.469446 + 0.882961i \(0.344454\pi\)
\(258\) 153.411 57.0471i 0.594617 0.221113i
\(259\) −81.7263 + 81.7263i −0.315546 + 0.315546i
\(260\) 182.174 157.226i 0.700669 0.604716i
\(261\) 55.1741 55.1741i 0.211395 0.211395i
\(262\) −81.4916 + 177.977i −0.311037 + 0.679300i
\(263\) −118.747 −0.451509 −0.225754 0.974184i \(-0.572485\pi\)
−0.225754 + 0.974184i \(0.572485\pi\)
\(264\) 116.009 210.968i 0.439429 0.799121i
\(265\) 702.483i 2.65088i
\(266\) −73.7113 + 160.985i −0.277110 + 0.605206i
\(267\) 64.6700 + 64.6700i 0.242210 + 0.242210i
\(268\) −15.6318 + 212.662i −0.0583275 + 0.793515i
\(269\) 7.74853 + 7.74853i 0.0288050 + 0.0288050i 0.721363 0.692558i \(-0.243516\pi\)
−0.692558 + 0.721363i \(0.743516\pi\)
\(270\) 72.2316 26.8598i 0.267524 0.0994809i
\(271\) 131.899i 0.486712i 0.969937 + 0.243356i \(0.0782484\pi\)
−0.969937 + 0.243356i \(0.921752\pi\)
\(272\) −54.7442 + 370.371i −0.201265 + 1.36166i
\(273\) 74.8668 0.274237
\(274\) −86.7685 233.338i −0.316673 0.851599i
\(275\) 368.457 368.457i 1.33984 1.33984i
\(276\) 2.95003 40.1336i 0.0106885 0.145412i
\(277\) −202.352 + 202.352i −0.730513 + 0.730513i −0.970721 0.240208i \(-0.922784\pi\)
0.240208 + 0.970721i \(0.422784\pi\)
\(278\) 434.647 + 199.015i 1.56348 + 0.715883i
\(279\) −50.7158 −0.181777
\(280\) −88.1506 303.534i −0.314824 1.08405i
\(281\) 68.8493i 0.245015i 0.992468 + 0.122508i \(0.0390936\pi\)
−0.992468 + 0.122508i \(0.960906\pi\)
\(282\) −57.3627 26.2651i −0.203414 0.0931387i
\(283\) 206.773 + 206.773i 0.730646 + 0.730646i 0.970748 0.240102i \(-0.0771808\pi\)
−0.240102 + 0.970748i \(0.577181\pi\)
\(284\) 129.169 111.480i 0.454821 0.392535i
\(285\) 150.907 + 150.907i 0.529498 + 0.529498i
\(286\) −98.2617 264.246i −0.343572 0.923936i
\(287\) 155.764i 0.542730i
\(288\) −93.9056 + 19.9432i −0.326061 + 0.0692473i
\(289\) 258.545 0.894620
\(290\) −361.555 + 134.447i −1.24674 + 0.463610i
\(291\) −25.7468 + 25.7468i −0.0884770 + 0.0884770i
\(292\) 278.051 + 322.170i 0.952229 + 1.10332i
\(293\) −361.237 + 361.237i −1.23289 + 1.23289i −0.270043 + 0.962848i \(0.587038\pi\)
−0.962848 + 0.270043i \(0.912962\pi\)
\(294\) −29.7267 + 64.9228i −0.101111 + 0.220826i
\(295\) 284.749 0.965250
\(296\) −48.3994 166.657i −0.163512 0.563029i
\(297\) 90.2852i 0.303990i
\(298\) 173.080 378.004i 0.580804 1.26847i
\(299\) −33.3204 33.3204i −0.111439 0.111439i
\(300\) −207.214 15.2313i −0.690712 0.0507709i
\(301\) −178.007 178.007i −0.591385 0.591385i
\(302\) 141.617 52.6613i 0.468930 0.174375i
\(303\) 7.95987i 0.0262702i
\(304\) −158.479 213.454i −0.521314 0.702153i
\(305\) −684.176 −2.24320
\(306\) 48.9343 + 131.594i 0.159916 + 0.430047i
\(307\) −10.9073 + 10.9073i −0.0355286 + 0.0355286i −0.724648 0.689119i \(-0.757998\pi\)
0.689119 + 0.724648i \(0.257998\pi\)
\(308\) −369.305 27.1459i −1.19904 0.0881360i
\(309\) 128.735 128.735i 0.416619 0.416619i
\(310\) 227.962 + 104.379i 0.735360 + 0.336705i
\(311\) −160.251 −0.515278 −0.257639 0.966241i \(-0.582945\pi\)
−0.257639 + 0.966241i \(0.582945\pi\)
\(312\) −54.1658 + 98.5030i −0.173608 + 0.315715i
\(313\) 355.500i 1.13578i 0.823103 + 0.567892i \(0.192241\pi\)
−0.823103 + 0.567892i \(0.807759\pi\)
\(314\) −209.682 96.0089i −0.667778 0.305761i
\(315\) −83.8121 83.8121i −0.266070 0.266070i
\(316\) −55.6202 64.4456i −0.176013 0.203942i
\(317\) 72.5192 + 72.5192i 0.228767 + 0.228767i 0.812178 0.583410i \(-0.198282\pi\)
−0.583410 + 0.812178i \(0.698282\pi\)
\(318\) 114.377 + 307.583i 0.359676 + 0.967243i
\(319\) 451.922i 1.41668i
\(320\) 463.140 + 103.625i 1.44731 + 0.323829i
\(321\) −244.008 −0.760151
\(322\) −58.0129 + 21.5725i −0.180164 + 0.0669954i
\(323\) −274.928 + 274.928i −0.851170 + 0.851170i
\(324\) −27.2535 + 23.5212i −0.0841156 + 0.0725964i
\(325\) −172.036 + 172.036i −0.529343 + 0.529343i
\(326\) 65.7127 143.516i 0.201573 0.440233i
\(327\) −264.667 −0.809378
\(328\) −204.940 112.694i −0.624816 0.343580i
\(329\) 97.0355i 0.294941i
\(330\) −185.816 + 405.821i −0.563080 + 1.22976i
\(331\) −248.096 248.096i −0.749536 0.749536i 0.224856 0.974392i \(-0.427809\pi\)
−0.974392 + 0.224856i \(0.927809\pi\)
\(332\) 10.0205 136.323i 0.0301822 0.410613i
\(333\) −46.0174 46.0174i −0.138190 0.138190i
\(334\) −46.1783 + 17.1717i −0.138258 + 0.0514124i
\(335\) 395.312i 1.18003i
\(336\) 88.0178 + 118.551i 0.261958 + 0.352829i
\(337\) −467.271 −1.38656 −0.693280 0.720668i \(-0.743835\pi\)
−0.693280 + 0.720668i \(0.743835\pi\)
\(338\) −71.9270 193.426i −0.212802 0.572268i
\(339\) −28.5163 + 28.5163i −0.0841189 + 0.0841189i
\(340\) 50.8812 692.212i 0.149651 2.03592i
\(341\) 207.703 207.703i 0.609098 0.609098i
\(342\) −90.6452 41.5044i −0.265044 0.121358i
\(343\) 370.894 1.08133
\(344\) 362.993 105.418i 1.05521 0.306448i
\(345\) 74.6032i 0.216241i
\(346\) 12.5639 + 5.75273i 0.0363118 + 0.0166264i
\(347\) 292.821 + 292.821i 0.843863 + 0.843863i 0.989359 0.145496i \(-0.0464776\pi\)
−0.145496 + 0.989359i \(0.546478\pi\)
\(348\) 136.417 117.736i 0.392003 0.338321i
\(349\) 346.260 + 346.260i 0.992150 + 0.992150i 0.999969 0.00781941i \(-0.00248902\pi\)
−0.00781941 + 0.999969i \(0.502489\pi\)
\(350\) 111.381 + 299.526i 0.318231 + 0.855789i
\(351\) 42.1550i 0.120100i
\(352\) 302.907 466.259i 0.860531 1.32460i
\(353\) 8.01816 0.0227143 0.0113572 0.999936i \(-0.496385\pi\)
0.0113572 + 0.999936i \(0.496385\pi\)
\(354\) −124.678 + 46.3623i −0.352197 + 0.130967i
\(355\) −223.668 + 223.668i −0.630051 + 0.630051i
\(356\) 137.999 + 159.896i 0.387637 + 0.449145i
\(357\) 152.692 152.692i 0.427709 0.427709i
\(358\) −270.243 + 590.208i −0.754869 + 1.64863i
\(359\) 590.403 1.64458 0.822289 0.569071i \(-0.192697\pi\)
0.822289 + 0.569071i \(0.192697\pi\)
\(360\) 170.910 49.6347i 0.474750 0.137874i
\(361\) 84.9121i 0.235213i
\(362\) 137.306 299.875i 0.379298 0.828383i
\(363\) 221.561 + 221.561i 0.610362 + 0.610362i
\(364\) 172.432 + 12.6747i 0.473715 + 0.0348205i
\(365\) −557.867 557.867i −1.52840 1.52840i
\(366\) 299.568 111.396i 0.818491 0.304362i
\(367\) 397.100i 1.08202i 0.841017 + 0.541008i \(0.181957\pi\)
−0.841017 + 0.541008i \(0.818043\pi\)
\(368\) 13.5889 91.9358i 0.0369265 0.249825i
\(369\) −87.7053 −0.237684
\(370\) 112.134 + 301.551i 0.303065 + 0.815003i
\(371\) 356.897 356.897i 0.961986 0.961986i
\(372\) −116.808 8.58600i −0.314000 0.0230807i
\(373\) −165.010 + 165.010i −0.442387 + 0.442387i −0.892814 0.450427i \(-0.851272\pi\)
0.450427 + 0.892814i \(0.351272\pi\)
\(374\) −739.340 338.527i −1.97685 0.905154i
\(375\) 64.0837 0.170890
\(376\) −127.671 70.2048i −0.339549 0.186715i
\(377\) 211.007i 0.559700i
\(378\) 50.3434 + 23.0511i 0.133184 + 0.0609819i
\(379\) −206.669 206.669i −0.545300 0.545300i 0.379778 0.925078i \(-0.376000\pi\)
−0.925078 + 0.379778i \(0.876000\pi\)
\(380\) 322.019 + 373.115i 0.847418 + 0.981881i
\(381\) −144.740 144.740i −0.379895 0.379895i
\(382\) 65.6869 + 176.645i 0.171955 + 0.462423i
\(383\) 598.414i 1.56244i −0.624257 0.781219i \(-0.714598\pi\)
0.624257 0.781219i \(-0.285402\pi\)
\(384\) −219.659 + 30.0351i −0.572028 + 0.0782164i
\(385\) 686.492 1.78310
\(386\) 157.965 58.7405i 0.409237 0.152178i
\(387\) 100.230 100.230i 0.258992 0.258992i
\(388\) −63.6586 + 54.9409i −0.164069 + 0.141600i
\(389\) 186.696 186.696i 0.479939 0.479939i −0.425173 0.905112i \(-0.639787\pi\)
0.905112 + 0.425173i \(0.139787\pi\)
\(390\) 86.7595 189.482i 0.222460 0.485851i
\(391\) −135.915 −0.347609
\(392\) −79.4574 + 144.497i −0.202697 + 0.368614i
\(393\) 169.521i 0.431352i
\(394\) −67.0683 + 146.476i −0.170224 + 0.371768i
\(395\) 111.594 + 111.594i 0.282515 + 0.282515i
\(396\) 15.2849 207.944i 0.0385984 0.525110i
\(397\) −57.3727 57.3727i −0.144516 0.144516i 0.631147 0.775663i \(-0.282584\pi\)
−0.775663 + 0.631147i \(0.782584\pi\)
\(398\) −367.756 + 136.753i −0.924009 + 0.343600i
\(399\) 153.337i 0.384302i
\(400\) −474.673 70.1610i −1.18668 0.175402i
\(401\) −466.082 −1.16230 −0.581149 0.813797i \(-0.697397\pi\)
−0.581149 + 0.813797i \(0.697397\pi\)
\(402\) 64.3640 + 173.088i 0.160109 + 0.430567i
\(403\) −96.9784 + 96.9784i −0.240641 + 0.240641i
\(404\) −1.34758 + 18.3331i −0.00333559 + 0.0453789i
\(405\) 47.1918 47.1918i 0.116523 0.116523i
\(406\) −251.994 115.382i −0.620675 0.284193i
\(407\) 376.921 0.926096
\(408\) 90.4264 + 311.371i 0.221633 + 0.763164i
\(409\) 597.952i 1.46198i −0.682386 0.730992i \(-0.739058\pi\)
0.682386 0.730992i \(-0.260942\pi\)
\(410\) 394.225 + 180.507i 0.961524 + 0.440260i
\(411\) −152.449 152.449i −0.370923 0.370923i
\(412\) 318.296 274.707i 0.772563 0.666765i
\(413\) 144.667 + 144.667i 0.350282 + 0.350282i
\(414\) −12.1468 32.6651i −0.0293400 0.0789013i
\(415\) 253.408i 0.610621i
\(416\) −141.430 + 217.701i −0.339977 + 0.523319i
\(417\) 413.998 0.992800
\(418\) 541.208 201.252i 1.29476 0.481464i
\(419\) −4.65301 + 4.65301i −0.0111050 + 0.0111050i −0.712638 0.701532i \(-0.752500\pi\)
0.701532 + 0.712638i \(0.252500\pi\)
\(420\) −178.846 207.224i −0.425824 0.493391i
\(421\) 34.3754 34.3754i 0.0816519 0.0816519i −0.665101 0.746753i \(-0.731612\pi\)
0.746753 + 0.665101i \(0.231612\pi\)
\(422\) 208.820 456.060i 0.494834 1.08071i
\(423\) −54.6375 −0.129167
\(424\) 211.359 + 727.786i 0.498488 + 1.71648i
\(425\) 701.742i 1.65116i
\(426\) 61.5162 134.351i 0.144404 0.315377i
\(427\) −347.596 347.596i −0.814042 0.814042i
\(428\) −561.997 41.3097i −1.31308 0.0965181i
\(429\) −172.643 172.643i −0.402430 0.402430i
\(430\) −656.804 + 244.237i −1.52745 + 0.567994i
\(431\) 423.823i 0.983347i −0.870780 0.491674i \(-0.836385\pi\)
0.870780 0.491674i \(-0.163615\pi\)
\(432\) −66.7519 + 49.5599i −0.154518 + 0.114722i
\(433\) 833.377 1.92466 0.962330 0.271885i \(-0.0876472\pi\)
0.962330 + 0.271885i \(0.0876472\pi\)
\(434\) 62.7864 + 168.845i 0.144669 + 0.389045i
\(435\) −236.219 + 236.219i −0.543031 + 0.543031i
\(436\) −609.577 44.8071i −1.39811 0.102769i
\(437\) 68.2443 68.2443i 0.156165 0.156165i
\(438\) 335.094 + 153.432i 0.765055 + 0.350301i
\(439\) 32.3193 0.0736203 0.0368102 0.999322i \(-0.488280\pi\)
0.0368102 + 0.999322i \(0.488280\pi\)
\(440\) −496.674 + 903.224i −1.12880 + 2.05278i
\(441\) 61.8384i 0.140223i
\(442\) 345.205 + 158.062i 0.781007 + 0.357606i
\(443\) 119.527 + 119.527i 0.269813 + 0.269813i 0.829025 0.559212i \(-0.188896\pi\)
−0.559212 + 0.829025i \(0.688896\pi\)
\(444\) −98.1961 113.777i −0.221162 0.256255i
\(445\) −276.874 276.874i −0.622189 0.622189i
\(446\) −263.443 708.453i −0.590680 1.58846i
\(447\) 360.045i 0.805470i
\(448\) 182.651 + 287.945i 0.407704 + 0.642735i
\(449\) −182.359 −0.406146 −0.203073 0.979164i \(-0.565093\pi\)
−0.203073 + 0.979164i \(0.565093\pi\)
\(450\) −168.653 + 62.7149i −0.374785 + 0.139367i
\(451\) 359.190 359.190i 0.796430 0.796430i
\(452\) −70.5061 + 60.8507i −0.155987 + 0.134625i
\(453\) 92.5241 92.5241i 0.204248 0.204248i
\(454\) 122.354 267.220i 0.269502 0.588591i
\(455\) −320.530 −0.704461
\(456\) −201.746 110.938i −0.442426 0.243286i
\(457\) 272.942i 0.597246i 0.954371 + 0.298623i \(0.0965274\pi\)
−0.954371 + 0.298623i \(0.903473\pi\)
\(458\) −118.994 + 259.881i −0.259811 + 0.567425i
\(459\) 85.9759 + 85.9759i 0.187311 + 0.187311i
\(460\) −12.6301 + 171.825i −0.0274566 + 0.373533i
\(461\) 188.323 + 188.323i 0.408510 + 0.408510i 0.881219 0.472709i \(-0.156724\pi\)
−0.472709 + 0.881219i \(0.656724\pi\)
\(462\) −300.582 + 111.773i −0.650609 + 0.241934i
\(463\) 116.023i 0.250590i −0.992120 0.125295i \(-0.960012\pi\)
0.992120 0.125295i \(-0.0399877\pi\)
\(464\) 334.126 248.072i 0.720100 0.534638i
\(465\) 217.131 0.466949
\(466\) −200.242 538.492i −0.429704 1.15556i
\(467\) −271.914 + 271.914i −0.582257 + 0.582257i −0.935523 0.353266i \(-0.885071\pi\)
0.353266 + 0.935523i \(0.385071\pi\)
\(468\) −7.13669 + 97.0910i −0.0152493 + 0.207459i
\(469\) 200.838 200.838i 0.428227 0.428227i
\(470\) 245.589 + 112.450i 0.522530 + 0.239255i
\(471\) −199.721 −0.424035
\(472\) −295.005 + 85.6736i −0.625011 + 0.181512i
\(473\) 820.966i 1.73566i
\(474\) −67.0309 30.6919i −0.141415 0.0647509i
\(475\) −352.352 352.352i −0.741793 0.741793i
\(476\) 377.529 325.829i 0.793128 0.684514i
\(477\) 200.957 + 200.957i 0.421293 + 0.421293i
\(478\) 105.218 + 282.953i 0.220121 + 0.591952i
\(479\) 775.808i 1.61964i 0.586678 + 0.809820i \(0.300435\pi\)
−0.586678 + 0.809820i \(0.699565\pi\)
\(480\) 402.041 85.3835i 0.837586 0.177882i
\(481\) −175.988 −0.365880
\(482\) 70.8252 26.3369i 0.146940 0.0546408i
\(483\) −37.9022 + 37.9022i −0.0784725 + 0.0784725i
\(484\) 472.788 + 547.807i 0.976835 + 1.13183i
\(485\) 110.231 110.231i 0.227280 0.227280i
\(486\) −12.9793 + 28.3467i −0.0267065 + 0.0583266i
\(487\) 174.891 0.359118 0.179559 0.983747i \(-0.442533\pi\)
0.179559 + 0.983747i \(0.442533\pi\)
\(488\) 708.819 205.851i 1.45250 0.421826i
\(489\) 136.697i 0.279545i
\(490\) 127.270 277.956i 0.259735 0.567258i
\(491\) −348.578 348.578i −0.709934 0.709934i 0.256587 0.966521i \(-0.417402\pi\)
−0.966521 + 0.256587i \(0.917402\pi\)
\(492\) −202.002 14.8482i −0.410573 0.0301792i
\(493\) −430.352 430.352i −0.872926 0.872926i
\(494\) −252.695 + 93.9666i −0.511529 + 0.190216i
\(495\) 386.541i 0.780890i
\(496\) −267.577 39.5503i −0.539470 0.0797386i
\(497\) −227.269 −0.457282
\(498\) −41.2594 110.955i −0.0828502 0.222801i
\(499\) −607.544 + 607.544i −1.21752 + 1.21752i −0.249027 + 0.968496i \(0.580111\pi\)
−0.968496 + 0.249027i \(0.919889\pi\)
\(500\) 147.597 + 10.8491i 0.295194 + 0.0216983i
\(501\) −30.1702 + 30.1702i −0.0602199 + 0.0602199i
\(502\) 259.519 + 118.828i 0.516969 + 0.236709i
\(503\) −130.935 −0.260309 −0.130154 0.991494i \(-0.541547\pi\)
−0.130154 + 0.991494i \(0.541547\pi\)
\(504\) 112.048 + 61.6141i 0.222317 + 0.122250i
\(505\) 34.0789i 0.0674829i
\(506\) 183.524 + 84.0314i 0.362695 + 0.166070i
\(507\) −126.373 126.373i −0.249257 0.249257i
\(508\) −308.860 357.868i −0.607992 0.704464i
\(509\) −61.5539 61.5539i −0.120931 0.120931i 0.644051 0.764982i \(-0.277252\pi\)
−0.764982 + 0.644051i \(0.777252\pi\)
\(510\) −209.504 563.399i −0.410792 1.10470i
\(511\) 566.849i 1.10929i
\(512\) −511.000 + 31.9891i −0.998046 + 0.0624786i
\(513\) −86.3387 −0.168302
\(514\) 452.329 168.202i 0.880017 0.327241i
\(515\) −551.159 + 551.159i −1.07021 + 1.07021i
\(516\) 247.817 213.880i 0.480265 0.414495i
\(517\) 223.763 223.763i 0.432811 0.432811i
\(518\) −96.2335 + 210.173i −0.185779 + 0.405739i
\(519\) 11.9670 0.0230578
\(520\) 231.902 421.724i 0.445965 0.811008i
\(521\) 32.5929i 0.0625584i 0.999511 + 0.0312792i \(0.00995810\pi\)
−0.999511 + 0.0312792i \(0.990042\pi\)
\(522\) 64.9680 141.889i 0.124460 0.271819i
\(523\) −226.407 226.407i −0.432900 0.432900i 0.456713 0.889614i \(-0.349026\pi\)
−0.889614 + 0.456713i \(0.849026\pi\)
\(524\) −28.6993 + 390.439i −0.0547697 + 0.745113i
\(525\) 195.693 + 195.693i 0.372748 + 0.372748i
\(526\) −222.601 + 82.7759i −0.423196 + 0.157369i
\(527\) 395.578i 0.750623i
\(528\) 70.4082 476.346i 0.133349 0.902170i
\(529\) −495.262 −0.936224
\(530\) −489.686 1316.87i −0.923936 2.48465i
\(531\) −81.4570 + 81.4570i −0.153403 + 0.153403i
\(532\) −25.9593 + 353.163i −0.0487957 + 0.663840i
\(533\) −167.709 + 167.709i −0.314652 + 0.314652i
\(534\) 166.310 + 76.1496i 0.311442 + 0.142602i
\(535\) 1044.68 1.95267
\(536\) 118.939 + 409.550i 0.221901 + 0.764087i
\(537\) 562.168i 1.04687i
\(538\) 19.9266 + 9.12397i 0.0370384 + 0.0169590i
\(539\) −253.254 253.254i −0.469859 0.469859i
\(540\) 116.681 100.702i 0.216076 0.186486i
\(541\) 510.912 + 510.912i 0.944385 + 0.944385i 0.998533 0.0541480i \(-0.0172443\pi\)
−0.0541480 + 0.998533i \(0.517244\pi\)
\(542\) 91.9440 + 247.256i 0.169638 + 0.456192i
\(543\) 285.628i 0.526018i
\(544\) 155.555 + 732.454i 0.285947 + 1.34642i
\(545\) 1133.13 2.07913
\(546\) 140.344 52.1881i 0.257041 0.0955826i
\(547\) 512.889 512.889i 0.937639 0.937639i −0.0605271 0.998167i \(-0.519278\pi\)
0.998167 + 0.0605271i \(0.0192782\pi\)
\(548\) −325.310 376.929i −0.593632 0.687826i
\(549\) 195.720 195.720i 0.356502 0.356502i
\(550\) 433.862 947.550i 0.788840 1.72282i
\(551\) 432.168 0.784334
\(552\) −22.4462 77.2904i −0.0406634 0.140019i
\(553\) 113.390i 0.205046i
\(554\) −238.272 + 520.382i −0.430093 + 0.939318i
\(555\) 197.016 + 197.016i 0.354983 + 0.354983i
\(556\) 953.514 + 70.0883i 1.71495 + 0.126058i
\(557\) 566.691 + 566.691i 1.01740 + 1.01740i 0.999846 + 0.0175529i \(0.00558754\pi\)
0.0175529 + 0.999846i \(0.494412\pi\)
\(558\) −95.0713 + 35.3529i −0.170379 + 0.0633565i
\(559\) 383.317i 0.685720i
\(560\) −376.834 507.554i −0.672917 0.906346i
\(561\) −704.215 −1.25529
\(562\) 47.9934 + 129.064i 0.0853975 + 0.229651i
\(563\) 548.653 548.653i 0.974517 0.974517i −0.0251665 0.999683i \(-0.508012\pi\)
0.999683 + 0.0251665i \(0.00801159\pi\)
\(564\) −125.840 9.24992i −0.223121 0.0164006i
\(565\) 122.088 122.088i 0.216085 0.216085i
\(566\) 531.751 + 243.477i 0.939489 + 0.430171i
\(567\) 47.9517 0.0845708
\(568\) 164.428 299.020i 0.289487 0.526444i
\(569\) 551.224i 0.968760i −0.874858 0.484380i \(-0.839045\pi\)
0.874858 0.484380i \(-0.160955\pi\)
\(570\) 388.082 + 177.694i 0.680846 + 0.311744i
\(571\) 458.387 + 458.387i 0.802780 + 0.802780i 0.983529 0.180749i \(-0.0578522\pi\)
−0.180749 + 0.983529i \(0.557852\pi\)
\(572\) −368.400 426.856i −0.644057 0.746251i
\(573\) 115.410 + 115.410i 0.201413 + 0.201413i
\(574\) 108.580 + 291.993i 0.189163 + 0.508698i
\(575\) 174.191i 0.302941i
\(576\) −162.132 + 102.845i −0.281480 + 0.178550i
\(577\) −718.488 −1.24521 −0.622607 0.782535i \(-0.713926\pi\)
−0.622607 + 0.782535i \(0.713926\pi\)
\(578\) 484.666 180.227i 0.838522 0.311811i
\(579\) 103.205 103.205i 0.178247 0.178247i
\(580\) −584.047 + 504.065i −1.00698 + 0.869078i
\(581\) −128.744 + 128.744i −0.221590 + 0.221590i
\(582\) −30.3171 + 66.2122i −0.0520913 + 0.113767i
\(583\) −1646.00 −2.82333
\(584\) 745.809 + 410.113i 1.27707 + 0.702248i
\(585\) 180.480i 0.308512i
\(586\) −425.360 + 928.982i −0.725870 + 1.58529i
\(587\) 3.02450 + 3.02450i 0.00515247 + 0.00515247i 0.709678 0.704526i \(-0.248840\pi\)
−0.704526 + 0.709678i \(0.748840\pi\)
\(588\) −10.4690 + 142.425i −0.0178044 + 0.242220i
\(589\) −198.624 198.624i −0.337222 0.337222i
\(590\) 533.786 198.492i 0.904723 0.336428i
\(591\) 139.517i 0.236070i
\(592\) −206.902 278.674i −0.349496 0.470734i
\(593\) 576.193 0.971657 0.485829 0.874054i \(-0.338518\pi\)
0.485829 + 0.874054i \(0.338518\pi\)
\(594\) −62.9359 169.248i −0.105953 0.284928i
\(595\) −653.726 + 653.726i −1.09870 + 1.09870i
\(596\) 60.9543 829.252i 0.102272 1.39136i
\(597\) −240.270 + 240.270i −0.402462 + 0.402462i
\(598\) −85.6890 39.2351i −0.143293 0.0656105i
\(599\) −1101.40 −1.83873 −0.919365 0.393406i \(-0.871297\pi\)
−0.919365 + 0.393406i \(0.871297\pi\)
\(600\) −399.058 + 115.892i −0.665096 + 0.193153i
\(601\) 7.11053i 0.0118312i −0.999983 0.00591558i \(-0.998117\pi\)
0.999983 0.00591558i \(-0.00188300\pi\)
\(602\) −457.775 209.605i −0.760423 0.348181i
\(603\) 113.085 + 113.085i 0.187538 + 0.187538i
\(604\) 228.764 197.436i 0.378749 0.326882i
\(605\) −948.578 948.578i −1.56790 1.56790i
\(606\) 5.54866 + 14.9215i 0.00915620 + 0.0246229i
\(607\) 528.384i 0.870485i 0.900313 + 0.435242i \(0.143337\pi\)
−0.900313 + 0.435242i \(0.856663\pi\)
\(608\) −445.878 289.667i −0.733352 0.476425i
\(609\) −240.022 −0.394125
\(610\) −1282.55 + 476.925i −2.10254 + 0.781844i
\(611\) −104.477 + 104.477i −0.170994 + 0.170994i
\(612\) 183.463 + 212.574i 0.299777 + 0.347343i
\(613\) −642.364 + 642.364i −1.04790 + 1.04790i −0.0491093 + 0.998793i \(0.515638\pi\)
−0.998793 + 0.0491093i \(0.984362\pi\)
\(614\) −12.8434 + 28.0499i −0.0209176 + 0.0456838i
\(615\) 375.496 0.610562
\(616\) −711.218 + 206.548i −1.15458 + 0.335305i
\(617\) 1068.16i 1.73122i −0.500717 0.865611i \(-0.666930\pi\)
0.500717 0.865611i \(-0.333070\pi\)
\(618\) 151.587 331.065i 0.245287 0.535703i
\(619\) 691.136 + 691.136i 1.11654 + 1.11654i 0.992246 + 0.124290i \(0.0396653\pi\)
0.124290 + 0.992246i \(0.460335\pi\)
\(620\) 500.094 + 36.7595i 0.806603 + 0.0592896i
\(621\) −21.3415 21.3415i −0.0343663 0.0343663i
\(622\) −300.405 + 111.708i −0.482967 + 0.179595i
\(623\) 281.332i 0.451576i
\(624\) −32.8743 + 222.410i −0.0526831 + 0.356427i
\(625\) 475.371 0.760594
\(626\) 247.812 + 666.417i 0.395866 + 1.06456i
\(627\) 353.593 353.593i 0.563945 0.563945i
\(628\) −459.994 33.8120i −0.732474 0.0538407i
\(629\) −358.931 + 358.931i −0.570637 + 0.570637i
\(630\) −215.537 98.6896i −0.342122 0.156650i
\(631\) 486.622 0.771191 0.385596 0.922668i \(-0.373996\pi\)
0.385596 + 0.922668i \(0.373996\pi\)
\(632\) −149.189 82.0374i −0.236058 0.129806i
\(633\) 434.393i 0.686245i
\(634\) 186.495 + 85.3920i 0.294156 + 0.134688i
\(635\) 619.681 + 619.681i 0.975875 + 0.975875i
\(636\) 428.820 + 496.862i 0.674245 + 0.781230i
\(637\) 118.247 + 118.247i 0.185631 + 0.185631i
\(638\) 315.026 + 847.168i 0.493770 + 1.32785i
\(639\) 127.968i 0.200263i
\(640\) 940.431 128.590i 1.46942 0.200922i
\(641\) −691.017 −1.07803 −0.539015 0.842296i \(-0.681203\pi\)
−0.539015 + 0.842296i \(0.681203\pi\)
\(642\) −457.415 + 170.093i −0.712485 + 0.264943i
\(643\) 652.605 652.605i 1.01494 1.01494i 0.0150512 0.999887i \(-0.495209\pi\)
0.999887 0.0150512i \(-0.00479113\pi\)
\(644\) −93.7126 + 80.8792i −0.145516 + 0.125589i
\(645\) −429.117 + 429.117i −0.665298 + 0.665298i
\(646\) −323.730 + 707.023i −0.501130 + 1.09446i
\(647\) 1156.72 1.78782 0.893911 0.448245i \(-0.147951\pi\)
0.893911 + 0.448245i \(0.147951\pi\)
\(648\) −34.6928 + 63.0905i −0.0535383 + 0.0973618i
\(649\) 667.201i 1.02804i
\(650\) −202.574 + 442.420i −0.311653 + 0.680647i
\(651\) 110.314 + 110.314i 0.169453 + 0.169453i
\(652\) 23.1424 314.840i 0.0354945 0.482883i
\(653\) −209.105 209.105i −0.320222 0.320222i 0.528630 0.848852i \(-0.322706\pi\)
−0.848852 + 0.528630i \(0.822706\pi\)
\(654\) −496.141 + 184.494i −0.758625 + 0.282100i
\(655\) 725.776i 1.10806i
\(656\) −462.734 68.3963i −0.705388 0.104263i
\(657\) 319.174 0.485805
\(658\) 67.6414 + 181.902i 0.102799 + 0.276446i
\(659\) 533.902 533.902i 0.810170 0.810170i −0.174489 0.984659i \(-0.555827\pi\)
0.984659 + 0.174489i \(0.0558274\pi\)
\(660\) −65.4399 + 890.276i −0.0991514 + 1.34890i
\(661\) 283.120 283.120i 0.428320 0.428320i −0.459736 0.888056i \(-0.652056\pi\)
0.888056 + 0.459736i \(0.152056\pi\)
\(662\) −638.021 292.136i −0.963779 0.441293i
\(663\) 328.805 0.495935
\(664\) −76.2439 262.535i −0.114825 0.395384i
\(665\) 656.484i 0.987195i
\(666\) −118.341 54.1859i −0.177690 0.0813602i
\(667\) 106.825 + 106.825i 0.160157 + 0.160157i
\(668\) −74.5953 + 64.3799i −0.111670 + 0.0963771i
\(669\) −462.861 462.861i −0.691870 0.691870i
\(670\) −275.563 741.047i −0.411289 1.10604i
\(671\) 1603.11i 2.38913i
\(672\) 247.636 + 160.878i 0.368506 + 0.239402i
\(673\) −397.854 −0.591164 −0.295582 0.955317i \(-0.595514\pi\)
−0.295582 + 0.955317i \(0.595514\pi\)
\(674\) −875.941 + 325.725i −1.29962 + 0.483271i
\(675\) −110.188 + 110.188i −0.163242 + 0.163242i
\(676\) −269.667 312.456i −0.398916 0.462213i
\(677\) 289.959 289.959i 0.428299 0.428299i −0.459749 0.888049i \(-0.652061\pi\)
0.888049 + 0.459749i \(0.152061\pi\)
\(678\) −33.5782 + 73.3345i −0.0495254 + 0.108163i
\(679\) 112.005 0.164956
\(680\) −387.145 1333.08i −0.569331 1.96041i
\(681\) 254.525i 0.373751i
\(682\) 244.572 534.142i 0.358609 0.783199i
\(683\) −150.197 150.197i −0.219908 0.219908i 0.588551 0.808460i \(-0.299698\pi\)
−0.808460 + 0.588551i \(0.799698\pi\)
\(684\) −198.854 14.6168i −0.290723 0.0213696i
\(685\) 652.686 + 652.686i 0.952826 + 0.952826i
\(686\) 695.274 258.543i 1.01352 0.376884i
\(687\) 247.534i 0.360312i
\(688\) 606.977 450.650i 0.882234 0.655015i
\(689\) 768.535 1.11544
\(690\) 52.0043 + 139.850i 0.0753686 + 0.202682i
\(691\) 791.212 791.212i 1.14502 1.14502i 0.157506 0.987518i \(-0.449655\pi\)
0.987518 0.157506i \(-0.0503453\pi\)
\(692\) 27.5622 + 2.02597i 0.0398298 + 0.00292770i
\(693\) −196.382 + 196.382i −0.283380 + 0.283380i
\(694\) 753.037 + 344.799i 1.08507 + 0.496828i
\(695\) −1772.46 −2.55030
\(696\) 173.655 315.799i 0.249504 0.453734i
\(697\) 684.092i 0.981481i
\(698\) 890.466 + 407.725i 1.27574 + 0.584133i
\(699\) −351.819 351.819i −0.503318 0.503318i
\(700\) 417.587 + 483.847i 0.596553 + 0.691210i
\(701\) 900.201 + 900.201i 1.28417 + 1.28417i 0.938274 + 0.345893i \(0.112424\pi\)
0.345893 + 0.938274i \(0.387576\pi\)
\(702\) 29.3854 + 79.0233i 0.0418595 + 0.112569i
\(703\) 360.445i 0.512724i
\(704\) 242.807 1085.19i 0.344896 1.54147i
\(705\) 233.921 0.331803
\(706\) 15.0308 5.58929i 0.0212900 0.00791685i
\(707\) 17.3138 17.3138i 0.0244891 0.0244891i
\(708\) −201.401 + 173.820i −0.284465 + 0.245509i
\(709\) 128.490 128.490i 0.181227 0.181227i −0.610663 0.791891i \(-0.709097\pi\)
0.791891 + 0.610663i \(0.209097\pi\)
\(710\) −263.371 + 575.200i −0.370945 + 0.810140i
\(711\) −63.8463 −0.0897979
\(712\) 370.151 + 203.542i 0.519875 + 0.285874i
\(713\) 98.1928i 0.137718i
\(714\) 179.796 392.674i 0.251816 0.549963i
\(715\) 739.140 + 739.140i 1.03376 + 1.03376i
\(716\) −95.1730 + 1294.78i −0.132923 + 1.80835i
\(717\) 184.865 + 184.865i 0.257831 + 0.257831i
\(718\) 1106.76 411.558i 1.54145 0.573200i
\(719\) 1246.14i 1.73315i −0.499045 0.866576i \(-0.666316\pi\)
0.499045 0.866576i \(-0.333684\pi\)
\(720\) 285.787 212.182i 0.396926 0.294698i
\(721\) −560.033 −0.776745
\(722\) 59.1904 + 159.175i 0.0819812 + 0.220464i
\(723\) 46.2730 46.2730i 0.0640014 0.0640014i
\(724\) 48.3558 657.855i 0.0667897 0.908639i
\(725\) 551.546 551.546i 0.760753 0.760753i
\(726\) 569.782 + 260.891i 0.784824 + 0.359354i
\(727\) −1130.07 −1.55443 −0.777216 0.629234i \(-0.783369\pi\)
−0.777216 + 0.629234i \(0.783369\pi\)
\(728\) 332.075 96.4392i 0.456147 0.132471i
\(729\) 27.0000i 0.0370370i
\(730\) −1434.65 656.893i −1.96527 0.899854i
\(731\) −781.782 781.782i −1.06947 1.06947i
\(732\) 483.914 417.645i 0.661085 0.570553i
\(733\) −708.087 708.087i −0.966012 0.966012i 0.0334292 0.999441i \(-0.489357\pi\)
−0.999441 + 0.0334292i \(0.989357\pi\)
\(734\) 276.810 + 744.399i 0.377126 + 1.01417i
\(735\) 264.751i 0.360205i
\(736\) −38.6128 181.814i −0.0524631 0.247030i
\(737\) −926.264 −1.25680
\(738\) −164.411 + 61.1375i −0.222780 + 0.0828422i
\(739\) −32.7516 + 32.7516i −0.0443188 + 0.0443188i −0.728919 0.684600i \(-0.759977\pi\)
0.684600 + 0.728919i \(0.259977\pi\)
\(740\) 420.410 + 487.118i 0.568122 + 0.658268i
\(741\) −165.096 + 165.096i −0.222802 + 0.222802i
\(742\) 420.249 917.819i 0.566373 1.23695i
\(743\) 708.128 0.953066 0.476533 0.879157i \(-0.341893\pi\)
0.476533 + 0.879157i \(0.341893\pi\)
\(744\) −224.952 + 65.3292i −0.302355 + 0.0878081i
\(745\) 1541.47i 2.06909i
\(746\) −194.301 + 424.352i −0.260457 + 0.568836i
\(747\) −72.4914 72.4914i −0.0970434 0.0970434i
\(748\) −1621.94 119.221i −2.16837 0.159386i
\(749\) 530.751 + 530.751i 0.708612 + 0.708612i
\(750\) 120.131 44.6714i 0.160174 0.0595619i
\(751\) 1242.37i 1.65429i 0.561990 + 0.827144i \(0.310036\pi\)
−0.561990 + 0.827144i \(0.689964\pi\)
\(752\) −288.268 42.6086i −0.383335 0.0566604i
\(753\) 247.189 0.328272
\(754\) −147.089 395.551i −0.195078 0.524604i
\(755\) −396.127 + 396.127i −0.524671 + 0.524671i
\(756\) 110.442 + 8.11804i 0.146087 + 0.0107381i
\(757\) −311.304 + 311.304i −0.411233 + 0.411233i −0.882168 0.470935i \(-0.843917\pi\)
0.470935 + 0.882168i \(0.343917\pi\)
\(758\) −531.483 243.354i −0.701165 0.321048i
\(759\) 174.805 0.230309
\(760\) 863.743 + 474.964i 1.13650 + 0.624952i
\(761\) 179.137i 0.235397i 0.993049 + 0.117699i \(0.0375517\pi\)
−0.993049 + 0.117699i \(0.962448\pi\)
\(762\) −372.224 170.433i −0.488482 0.223665i
\(763\) 575.685 + 575.685i 0.754502 + 0.754502i
\(764\) 246.272 + 285.348i 0.322345 + 0.373493i
\(765\) −368.091 368.091i −0.481165 0.481165i
\(766\) −417.142 1121.78i −0.544572 1.46446i
\(767\) 311.523i 0.406158i
\(768\) −390.833 + 209.423i −0.508897 + 0.272686i
\(769\) −967.409 −1.25801 −0.629005 0.777402i \(-0.716537\pi\)
−0.629005 + 0.777402i \(0.716537\pi\)
\(770\) 1286.89 478.539i 1.67128 0.621479i
\(771\) 295.525 295.525i 0.383301 0.383301i