Properties

Label 48.3.l.a.43.6
Level 48
Weight 3
Character 48.43
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 43.6
Root \(-1.25564 - 1.55672i\) of defining polynomial
Character \(\chi\) \(=\) 48.43
Dual form 48.3.l.a.19.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.25564 - 1.55672i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-0.846753 - 3.90935i) q^{4} +(0.909023 + 0.909023i) q^{5} +(3.44442 - 0.368750i) q^{6} -0.654713 q^{7} +(-7.14897 - 3.59057i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(1.25564 - 1.55672i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-0.846753 - 3.90935i) q^{4} +(0.909023 + 0.909023i) q^{5} +(3.44442 - 0.368750i) q^{6} -0.654713 q^{7} +(-7.14897 - 3.59057i) q^{8} +3.00000i q^{9} +(2.55650 - 0.273691i) q^{10} +(-13.3760 + 13.3760i) q^{11} +(3.75090 - 5.82501i) q^{12} +(8.32795 - 8.32795i) q^{13} +(-0.822082 + 1.01921i) q^{14} +2.22664i q^{15} +(-14.5660 + 6.62050i) q^{16} -3.93529 q^{17} +(4.67016 + 3.76691i) q^{18} +(16.8974 + 16.8974i) q^{19} +(2.78397 - 4.32340i) q^{20} +(-0.801857 - 0.801857i) q^{21} +(4.02729 + 37.6181i) q^{22} -23.1787 q^{23} +(-4.35814 - 13.1532i) q^{24} -23.3474i q^{25} +(-2.50740 - 23.4212i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(0.554380 + 2.55950i) q^{28} +(35.6105 - 35.6105i) q^{29} +(3.46626 + 2.79585i) q^{30} -45.5687i q^{31} +(-7.98336 + 30.9882i) q^{32} -32.7644 q^{33} +(-4.94130 + 6.12615i) q^{34} +(-0.595149 - 0.595149i) q^{35} +(11.7280 - 2.54026i) q^{36} +(10.1527 + 10.1527i) q^{37} +(47.5215 - 5.08752i) q^{38} +20.3992 q^{39} +(-3.23467 - 9.76249i) q^{40} +28.4661i q^{41} +(-2.25511 + 0.241425i) q^{42} +(22.7354 - 22.7354i) q^{43} +(63.6176 + 40.9653i) q^{44} +(-2.72707 + 2.72707i) q^{45} +(-29.1040 + 36.0827i) q^{46} -10.7746i q^{47} +(-25.9481 - 9.73123i) q^{48} -48.5714 q^{49} +(-36.3453 - 29.3158i) q^{50} +(-4.81973 - 4.81973i) q^{51} +(-39.6086 - 25.5051i) q^{52} +(41.5142 + 41.5142i) q^{53} +(1.10625 + 10.3333i) q^{54} -24.3182 q^{55} +(4.68053 + 2.35079i) q^{56} +41.3900i q^{57} +(-10.7217 - 100.149i) q^{58} +(-21.0646 + 21.0646i) q^{59} +(8.70472 - 1.88541i) q^{60} +(-68.7531 + 68.7531i) q^{61} +(-70.9377 - 57.2178i) q^{62} -1.96414i q^{63} +(38.2157 + 51.3377i) q^{64} +15.1406 q^{65} +(-41.1402 + 51.0050i) q^{66} +(67.8242 + 67.8242i) q^{67} +(3.33222 + 15.3844i) q^{68} +(-28.3880 - 28.3880i) q^{69} +(-1.67377 + 0.179189i) q^{70} +33.3094 q^{71} +(10.7717 - 21.4469i) q^{72} +18.6331i q^{73} +(28.5531 - 3.05682i) q^{74} +(28.5946 - 28.5946i) q^{75} +(51.7499 - 80.3657i) q^{76} +(8.75745 - 8.75745i) q^{77} +(25.6140 - 31.7559i) q^{78} -6.29222i q^{79} +(-19.2590 - 7.22265i) q^{80} -9.00000 q^{81} +(44.3137 + 35.7431i) q^{82} +(-72.0774 - 72.0774i) q^{83} +(-2.45576 + 3.81371i) q^{84} +(-3.57727 - 3.57727i) q^{85} +(-6.84524 - 63.9400i) q^{86} +87.2275 q^{87} +(143.652 - 47.5973i) q^{88} -10.6131i q^{89} +(0.821074 + 7.66949i) q^{90} +(-5.45242 + 5.45242i) q^{91} +(19.6266 + 90.6135i) q^{92} +(55.8101 - 55.8101i) q^{93} +(-16.7730 - 13.5290i) q^{94} +30.7202i q^{95} +(-47.7302 + 28.1750i) q^{96} +143.631 q^{97} +(-60.9880 + 75.6120i) q^{98} +(-40.1280 - 40.1280i) 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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.25564 1.55672i 0.627818 0.778360i
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) −0.846753 3.90935i −0.211688 0.977337i
\(5\) 0.909023 + 0.909023i 0.181805 + 0.181805i 0.792142 0.610337i \(-0.208966\pi\)
−0.610337 + 0.792142i \(0.708966\pi\)
\(6\) 3.44442 0.368750i 0.574070 0.0614583i
\(7\) −0.654713 −0.0935305 −0.0467652 0.998906i \(-0.514891\pi\)
−0.0467652 + 0.998906i \(0.514891\pi\)
\(8\) −7.14897 3.59057i −0.893622 0.448821i
\(9\) 3.00000i 0.333333i
\(10\) 2.55650 0.273691i 0.255650 0.0273691i
\(11\) −13.3760 + 13.3760i −1.21600 + 1.21600i −0.246980 + 0.969021i \(0.579438\pi\)
−0.969021 + 0.246980i \(0.920562\pi\)
\(12\) 3.75090 5.82501i 0.312575 0.485418i
\(13\) 8.32795 8.32795i 0.640612 0.640612i −0.310094 0.950706i \(-0.600361\pi\)
0.950706 + 0.310094i \(0.100361\pi\)
\(14\) −0.822082 + 1.01921i −0.0587202 + 0.0728004i
\(15\) 2.22664i 0.148443i
\(16\) −14.5660 + 6.62050i −0.910376 + 0.413781i
\(17\) −3.93529 −0.231488 −0.115744 0.993279i \(-0.536925\pi\)
−0.115744 + 0.993279i \(0.536925\pi\)
\(18\) 4.67016 + 3.76691i 0.259453 + 0.209273i
\(19\) 16.8974 + 16.8974i 0.889336 + 0.889336i 0.994459 0.105123i \(-0.0335236\pi\)
−0.105123 + 0.994459i \(0.533524\pi\)
\(20\) 2.78397 4.32340i 0.139198 0.216170i
\(21\) −0.801857 0.801857i −0.0381837 0.0381837i
\(22\) 4.02729 + 37.6181i 0.183059 + 1.70991i
\(23\) −23.1787 −1.00777 −0.503884 0.863771i \(-0.668096\pi\)
−0.503884 + 0.863771i \(0.668096\pi\)
\(24\) −4.35814 13.1532i −0.181589 0.548050i
\(25\) 23.3474i 0.933894i
\(26\) −2.50740 23.4212i −0.0964386 0.900814i
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 0.554380 + 2.55950i 0.0197993 + 0.0914108i
\(29\) 35.6105 35.6105i 1.22795 1.22795i 0.263209 0.964739i \(-0.415219\pi\)
0.964739 0.263209i \(-0.0847809\pi\)
\(30\) 3.46626 + 2.79585i 0.115542 + 0.0931951i
\(31\) 45.5687i 1.46996i −0.678089 0.734980i \(-0.737192\pi\)
0.678089 0.734980i \(-0.262808\pi\)
\(32\) −7.98336 + 30.9882i −0.249480 + 0.968380i
\(33\) −32.7644 −0.992860
\(34\) −4.94130 + 6.12615i −0.145332 + 0.180181i
\(35\) −0.595149 0.595149i −0.0170043 0.0170043i
\(36\) 11.7280 2.54026i 0.325779 0.0705627i
\(37\) 10.1527 + 10.1527i 0.274398 + 0.274398i 0.830868 0.556470i \(-0.187844\pi\)
−0.556470 + 0.830868i \(0.687844\pi\)
\(38\) 47.5215 5.08752i 1.25057 0.133882i
\(39\) 20.3992 0.523057
\(40\) −3.23467 9.76249i −0.0808669 0.244062i
\(41\) 28.4661i 0.694295i 0.937811 + 0.347148i \(0.112850\pi\)
−0.937811 + 0.347148i \(0.887150\pi\)
\(42\) −2.25511 + 0.241425i −0.0536930 + 0.00574823i
\(43\) 22.7354 22.7354i 0.528730 0.528730i −0.391464 0.920194i \(-0.628031\pi\)
0.920194 + 0.391464i \(0.128031\pi\)
\(44\) 63.6176 + 40.9653i 1.44586 + 0.931030i
\(45\) −2.72707 + 2.72707i −0.0606015 + 0.0606015i
\(46\) −29.1040 + 36.0827i −0.632696 + 0.784407i
\(47\) 10.7746i 0.229247i −0.993409 0.114623i \(-0.963434\pi\)
0.993409 0.114623i \(-0.0365661\pi\)
\(48\) −25.9481 9.73123i −0.540585 0.202734i
\(49\) −48.5714 −0.991252
\(50\) −36.3453 29.3158i −0.726906 0.586316i
\(51\) −4.81973 4.81973i −0.0945045 0.0945045i
\(52\) −39.6086 25.5051i −0.761703 0.490484i
\(53\) 41.5142 + 41.5142i 0.783287 + 0.783287i 0.980384 0.197097i \(-0.0631514\pi\)
−0.197097 + 0.980384i \(0.563151\pi\)
\(54\) 1.10625 + 10.3333i 0.0204861 + 0.191357i
\(55\) −24.3182 −0.442149
\(56\) 4.68053 + 2.35079i 0.0835809 + 0.0419784i
\(57\) 41.3900i 0.726140i
\(58\) −10.7217 100.149i −0.184857 1.72671i
\(59\) −21.0646 + 21.0646i −0.357027 + 0.357027i −0.862716 0.505689i \(-0.831238\pi\)
0.505689 + 0.862716i \(0.331238\pi\)
\(60\) 8.70472 1.88541i 0.145079 0.0314236i
\(61\) −68.7531 + 68.7531i −1.12710 + 1.12710i −0.136453 + 0.990647i \(0.543570\pi\)
−0.990647 + 0.136453i \(0.956430\pi\)
\(62\) −70.9377 57.2178i −1.14416 0.922867i
\(63\) 1.96414i 0.0311768i
\(64\) 38.2157 + 51.3377i 0.597120 + 0.802152i
\(65\) 15.1406 0.232932
\(66\) −41.1402 + 51.0050i −0.623336 + 0.772803i
\(67\) 67.8242 + 67.8242i 1.01230 + 1.01230i 0.999923 + 0.0123779i \(0.00394012\pi\)
0.0123779 + 0.999923i \(0.496060\pi\)
\(68\) 3.33222 + 15.3844i 0.0490033 + 0.226242i
\(69\) −28.3880 28.3880i −0.411420 0.411420i
\(70\) −1.67377 + 0.179189i −0.0239110 + 0.00255985i
\(71\) 33.3094 0.469147 0.234573 0.972098i \(-0.424631\pi\)
0.234573 + 0.972098i \(0.424631\pi\)
\(72\) 10.7717 21.4469i 0.149607 0.297874i
\(73\) 18.6331i 0.255248i 0.991823 + 0.127624i \(0.0407351\pi\)
−0.991823 + 0.127624i \(0.959265\pi\)
\(74\) 28.5531 3.05682i 0.385853 0.0413083i
\(75\) 28.5946 28.5946i 0.381261 0.381261i
\(76\) 51.7499 80.3657i 0.680920 1.05744i
\(77\) 8.75745 8.75745i 0.113733 0.113733i
\(78\) 25.6140 31.7559i 0.328385 0.407127i
\(79\) 6.29222i 0.0796483i −0.999207 0.0398242i \(-0.987320\pi\)
0.999207 0.0398242i \(-0.0126798\pi\)
\(80\) −19.2590 7.22265i −0.240738 0.0902832i
\(81\) −9.00000 −0.111111
\(82\) 44.3137 + 35.7431i 0.540411 + 0.435891i
\(83\) −72.0774 72.0774i −0.868402 0.868402i 0.123894 0.992296i \(-0.460462\pi\)
−0.992296 + 0.123894i \(0.960462\pi\)
\(84\) −2.45576 + 3.81371i −0.0292353 + 0.0454013i
\(85\) −3.57727 3.57727i −0.0420855 0.0420855i
\(86\) −6.84524 63.9400i −0.0795958 0.743489i
\(87\) 87.2275 1.00262
\(88\) 143.652 47.5973i 1.63241 0.540878i
\(89\) 10.6131i 0.119248i −0.998221 0.0596240i \(-0.981010\pi\)
0.998221 0.0596240i \(-0.0189902\pi\)
\(90\) 0.821074 + 7.66949i 0.00912304 + 0.0852165i
\(91\) −5.45242 + 5.45242i −0.0599167 + 0.0599167i
\(92\) 19.6266 + 90.6135i 0.213333 + 0.984930i
\(93\) 55.8101 55.8101i 0.600108 0.600108i
\(94\) −16.7730 13.5290i −0.178436 0.143925i
\(95\) 30.7202i 0.323371i
\(96\) −47.7302 + 28.1750i −0.497189 + 0.293490i
\(97\) 143.631 1.48073 0.740366 0.672204i \(-0.234652\pi\)
0.740366 + 0.672204i \(0.234652\pi\)
\(98\) −60.9880 + 75.6120i −0.622326 + 0.771551i
\(99\) −40.1280 40.1280i −0.405334 0.405334i
\(100\) −91.2730 + 19.7694i −0.912730 + 0.197694i
\(101\) −90.3100 90.3100i −0.894159 0.894159i 0.100753 0.994912i \(-0.467875\pi\)
−0.994912 + 0.100753i \(0.967875\pi\)
\(102\) −13.5548 + 1.45114i −0.132890 + 0.0142269i
\(103\) −95.1656 −0.923938 −0.461969 0.886896i \(-0.652857\pi\)
−0.461969 + 0.886896i \(0.652857\pi\)
\(104\) −89.4384 + 29.6343i −0.859984 + 0.284945i
\(105\) 1.45781i 0.0138839i
\(106\) 116.753 12.4992i 1.10144 0.117917i
\(107\) 27.2524 27.2524i 0.254695 0.254695i −0.568197 0.822892i \(-0.692359\pi\)
0.822892 + 0.568197i \(0.192359\pi\)
\(108\) 17.4750 + 11.2527i 0.161806 + 0.104192i
\(109\) −132.413 + 132.413i −1.21480 + 1.21480i −0.245366 + 0.969430i \(0.578908\pi\)
−0.969430 + 0.245366i \(0.921092\pi\)
\(110\) −30.5348 + 37.8566i −0.277589 + 0.344151i
\(111\) 24.8690i 0.224045i
\(112\) 9.53657 4.33453i 0.0851479 0.0387012i
\(113\) 37.9551 0.335886 0.167943 0.985797i \(-0.446288\pi\)
0.167943 + 0.985797i \(0.446288\pi\)
\(114\) 64.4326 + 51.9708i 0.565198 + 0.455884i
\(115\) −21.0699 21.0699i −0.183217 0.183217i
\(116\) −169.367 109.061i −1.46006 0.940177i
\(117\) 24.9838 + 24.9838i 0.213537 + 0.213537i
\(118\) 6.34219 + 59.2411i 0.0537474 + 0.502044i
\(119\) 2.57649 0.0216512
\(120\) 7.99490 15.9182i 0.0666242 0.132652i
\(121\) 236.835i 1.95731i
\(122\) 20.7004 + 193.358i 0.169675 + 1.58490i
\(123\) −34.8637 + 34.8637i −0.283445 + 0.283445i
\(124\) −178.144 + 38.5854i −1.43665 + 0.311173i
\(125\) 43.9488 43.9488i 0.351591 0.351591i
\(126\) −3.05762 2.46625i −0.0242668 0.0195734i
\(127\) 96.5399i 0.760157i 0.924954 + 0.380078i \(0.124103\pi\)
−0.924954 + 0.380078i \(0.875897\pi\)
\(128\) 127.903 + 4.97043i 0.999246 + 0.0388315i
\(129\) 55.6901 0.431706
\(130\) 19.0111 23.5697i 0.146239 0.181305i
\(131\) −54.5082 54.5082i −0.416093 0.416093i 0.467762 0.883855i \(-0.345061\pi\)
−0.883855 + 0.467762i \(0.845061\pi\)
\(132\) 27.7433 + 128.087i 0.210177 + 0.970359i
\(133\) −11.0629 11.0629i −0.0831801 0.0831801i
\(134\) 190.746 20.4207i 1.42348 0.152393i
\(135\) −6.67992 −0.0494809
\(136\) 28.1333 + 14.1299i 0.206863 + 0.103897i
\(137\) 25.9333i 0.189294i 0.995511 + 0.0946471i \(0.0301723\pi\)
−0.995511 + 0.0946471i \(0.969828\pi\)
\(138\) −79.8371 + 8.54713i −0.578530 + 0.0619358i
\(139\) 3.64066 3.64066i 0.0261918 0.0261918i −0.693890 0.720081i \(-0.744104\pi\)
0.720081 + 0.693890i \(0.244104\pi\)
\(140\) −1.82270 + 2.83059i −0.0130193 + 0.0202185i
\(141\) 13.1961 13.1961i 0.0935896 0.0935896i
\(142\) 41.8245 51.8534i 0.294539 0.365165i
\(143\) 222.789i 1.55797i
\(144\) −19.8615 43.6981i −0.137927 0.303459i
\(145\) 64.7415 0.446493
\(146\) 29.0066 + 23.3964i 0.198675 + 0.160250i
\(147\) −59.4875 59.4875i −0.404677 0.404677i
\(148\) 31.0937 48.2874i 0.210093 0.326266i
\(149\) −18.9718 18.9718i −0.127328 0.127328i 0.640571 0.767899i \(-0.278698\pi\)
−0.767899 + 0.640571i \(0.778698\pi\)
\(150\) −8.60933 80.4181i −0.0573956 0.536121i
\(151\) −103.209 −0.683503 −0.341751 0.939790i \(-0.611020\pi\)
−0.341751 + 0.939790i \(0.611020\pi\)
\(152\) −60.1278 181.470i −0.395578 1.19388i
\(153\) 11.8059i 0.0771626i
\(154\) −2.63672 24.6291i −0.0171216 0.159929i
\(155\) 41.4230 41.4230i 0.267245 0.267245i
\(156\) −17.2731 79.7477i −0.110725 0.511203i
\(157\) 88.2067 88.2067i 0.561826 0.561826i −0.368000 0.929826i \(-0.619957\pi\)
0.929826 + 0.368000i \(0.119957\pi\)
\(158\) −9.79522 7.90074i −0.0619951 0.0500047i
\(159\) 101.689i 0.639551i
\(160\) −35.4260 + 20.9119i −0.221412 + 0.130699i
\(161\) 15.1754 0.0942571
\(162\) −11.3007 + 14.0105i −0.0697576 + 0.0864844i
\(163\) 18.8038 + 18.8038i 0.115361 + 0.115361i 0.762431 0.647070i \(-0.224006\pi\)
−0.647070 + 0.762431i \(0.724006\pi\)
\(164\) 111.284 24.1037i 0.678561 0.146974i
\(165\) −29.7836 29.7836i −0.180507 0.180507i
\(166\) −202.707 + 21.7013i −1.22113 + 0.130731i
\(167\) 267.105 1.59943 0.799715 0.600380i \(-0.204984\pi\)
0.799715 + 0.600380i \(0.204984\pi\)
\(168\) 2.85333 + 8.61157i 0.0169841 + 0.0512594i
\(169\) 30.2905i 0.179234i
\(170\) −10.0606 + 1.07706i −0.0591798 + 0.00633562i
\(171\) −50.6922 + 50.6922i −0.296445 + 0.296445i
\(172\) −108.132 69.6293i −0.628673 0.404822i
\(173\) −153.520 + 153.520i −0.887396 + 0.887396i −0.994272 0.106876i \(-0.965915\pi\)
0.106876 + 0.994272i \(0.465915\pi\)
\(174\) 109.526 135.789i 0.629460 0.780396i
\(175\) 15.2858i 0.0873476i
\(176\) 106.279 283.391i 0.603859 1.61018i
\(177\) −51.5975 −0.291511
\(178\) −16.5216 13.3262i −0.0928179 0.0748661i
\(179\) 123.581 + 123.581i 0.690399 + 0.690399i 0.962320 0.271921i \(-0.0876589\pi\)
−0.271921 + 0.962320i \(0.587659\pi\)
\(180\) 12.9702 + 8.35191i 0.0720567 + 0.0463995i
\(181\) 122.965 + 122.965i 0.679364 + 0.679364i 0.959856 0.280493i \(-0.0904978\pi\)
−0.280493 + 0.959856i \(0.590498\pi\)
\(182\) 1.64163 + 15.3341i 0.00901995 + 0.0842536i
\(183\) −168.410 −0.920273
\(184\) 165.704 + 83.2246i 0.900564 + 0.452307i
\(185\) 18.4581i 0.0997737i
\(186\) −16.8035 156.958i −0.0903412 0.843859i
\(187\) 52.6385 52.6385i 0.281489 0.281489i
\(188\) −42.1217 + 9.12342i −0.224051 + 0.0485288i
\(189\) 2.40557 2.40557i 0.0127279 0.0127279i
\(190\) 47.8228 + 38.5734i 0.251699 + 0.203018i
\(191\) 193.992i 1.01566i −0.861456 0.507832i \(-0.830447\pi\)
0.861456 0.507832i \(-0.169553\pi\)
\(192\) −16.0712 + 109.680i −0.0837040 + 0.571250i
\(193\) 141.555 0.733444 0.366722 0.930331i \(-0.380480\pi\)
0.366722 + 0.930331i \(0.380480\pi\)
\(194\) 180.348 223.593i 0.929631 1.15254i
\(195\) 18.5434 + 18.5434i 0.0950942 + 0.0950942i
\(196\) 41.1279 + 189.882i 0.209836 + 0.968788i
\(197\) 28.9507 + 28.9507i 0.146958 + 0.146958i 0.776758 0.629800i \(-0.216863\pi\)
−0.629800 + 0.776758i \(0.716863\pi\)
\(198\) −112.854 + 12.0819i −0.569971 + 0.0610195i
\(199\) −27.6253 −0.138821 −0.0694104 0.997588i \(-0.522112\pi\)
−0.0694104 + 0.997588i \(0.522112\pi\)
\(200\) −83.8302 + 166.910i −0.419151 + 0.834548i
\(201\) 166.135i 0.826541i
\(202\) −253.984 + 27.1908i −1.25735 + 0.134608i
\(203\) −23.3147 + 23.3147i −0.114851 + 0.114851i
\(204\) −14.7609 + 22.9231i −0.0723573 + 0.112368i
\(205\) −25.8763 + 25.8763i −0.126226 + 0.126226i
\(206\) −119.493 + 148.146i −0.580065 + 0.719156i
\(207\) 69.5360i 0.335923i
\(208\) −66.1699 + 176.440i −0.318124 + 0.848271i
\(209\) −452.039 −2.16287
\(210\) −2.26940 1.83048i −0.0108067 0.00871658i
\(211\) 7.35041 + 7.35041i 0.0348361 + 0.0348361i 0.724310 0.689474i \(-0.242158\pi\)
−0.689474 + 0.724310i \(0.742158\pi\)
\(212\) 127.141 197.446i 0.599723 0.931348i
\(213\) 40.7955 + 40.7955i 0.191528 + 0.191528i
\(214\) −8.20523 76.6435i −0.0383422 0.358147i
\(215\) 41.3340 0.192251
\(216\) 39.4596 13.0744i 0.182683 0.0605298i
\(217\) 29.8345i 0.137486i
\(218\) 39.8673 + 372.392i 0.182877 + 1.70822i
\(219\) −22.8208 + 22.8208i −0.104205 + 0.104205i
\(220\) 20.5915 + 95.0683i 0.0935977 + 0.432129i
\(221\) −32.7729 + 32.7729i −0.148294 + 0.148294i
\(222\) 38.7141 + 31.2265i 0.174388 + 0.140660i
\(223\) 386.106i 1.73142i −0.500549 0.865708i \(-0.666869\pi\)
0.500549 0.865708i \(-0.333131\pi\)
\(224\) 5.22681 20.2884i 0.0233340 0.0905730i
\(225\) 70.0421 0.311298
\(226\) 47.6579 59.0855i 0.210875 0.261440i
\(227\) −49.7286 49.7286i −0.219069 0.219069i 0.589037 0.808106i \(-0.299507\pi\)
−0.808106 + 0.589037i \(0.799507\pi\)
\(228\) 161.808 35.0471i 0.709684 0.153715i
\(229\) −191.870 191.870i −0.837861 0.837861i 0.150716 0.988577i \(-0.451842\pi\)
−0.988577 + 0.150716i \(0.951842\pi\)
\(230\) −59.2562 + 6.34380i −0.257636 + 0.0275817i
\(231\) 21.4513 0.0928627
\(232\) −382.440 + 126.717i −1.64845 + 0.546193i
\(233\) 298.610i 1.28159i 0.767712 + 0.640795i \(0.221395\pi\)
−0.767712 + 0.640795i \(0.778605\pi\)
\(234\) 70.2635 7.52221i 0.300271 0.0321462i
\(235\) 9.79435 9.79435i 0.0416781 0.0416781i
\(236\) 100.185 + 64.5123i 0.424514 + 0.273357i
\(237\) 7.70636 7.70636i 0.0325163 0.0325163i
\(238\) 3.23514 4.01087i 0.0135930 0.0168524i
\(239\) 247.352i 1.03495i −0.855700 0.517473i \(-0.826873\pi\)
0.855700 0.517473i \(-0.173127\pi\)
\(240\) −14.7415 32.4333i −0.0614229 0.135139i
\(241\) −220.337 −0.914260 −0.457130 0.889400i \(-0.651123\pi\)
−0.457130 + 0.889400i \(0.651123\pi\)
\(242\) −368.686 297.379i −1.52350 1.22884i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 326.997 + 210.563i 1.34015 + 0.862963i
\(245\) −44.1525 44.1525i −0.180214 0.180214i
\(246\) 10.4969 + 98.0492i 0.0426702 + 0.398574i
\(247\) 281.441 1.13944
\(248\) −163.618 + 325.770i −0.659748 + 1.31359i
\(249\) 176.553i 0.709047i
\(250\) −13.2322 123.600i −0.0529290 0.494399i
\(251\) 162.716 162.716i 0.648272 0.648272i −0.304303 0.952575i \(-0.598424\pi\)
0.952575 + 0.304303i \(0.0984235\pi\)
\(252\) −7.67851 + 1.66314i −0.0304703 + 0.00659977i
\(253\) 310.038 310.038i 1.22545 1.22545i
\(254\) 150.286 + 121.219i 0.591675 + 0.477240i
\(255\) 8.76249i 0.0343627i
\(256\) 168.338 192.869i 0.657570 0.753394i
\(257\) 101.165 0.393637 0.196819 0.980440i \(-0.436939\pi\)
0.196819 + 0.980440i \(0.436939\pi\)
\(258\) 69.9265 86.6939i 0.271033 0.336023i
\(259\) −6.64713 6.64713i −0.0256646 0.0256646i
\(260\) −12.8203 59.1899i −0.0493090 0.227653i
\(261\) 106.831 + 106.831i 0.409316 + 0.409316i
\(262\) −153.296 + 16.4115i −0.585101 + 0.0626393i
\(263\) −323.635 −1.23055 −0.615276 0.788312i \(-0.710955\pi\)
−0.615276 + 0.788312i \(0.710955\pi\)
\(264\) 234.232 + 117.643i 0.887242 + 0.445616i
\(265\) 75.4747i 0.284810i
\(266\) −31.1130 + 3.33087i −0.116966 + 0.0125220i
\(267\) 12.9983 12.9983i 0.0486828 0.0486828i
\(268\) 207.718 322.579i 0.775068 1.20365i
\(269\) 1.51275 1.51275i 0.00562361 0.00562361i −0.704289 0.709913i \(-0.748734\pi\)
0.709913 + 0.704289i \(0.248734\pi\)
\(270\) −8.38756 + 10.3988i −0.0310650 + 0.0385140i
\(271\) 166.098i 0.612909i −0.951885 0.306454i \(-0.900857\pi\)
0.951885 0.306454i \(-0.0991427\pi\)
\(272\) 57.3216 26.0536i 0.210741 0.0957854i
\(273\) −13.3556 −0.0489218
\(274\) 40.3709 + 32.5628i 0.147339 + 0.118842i
\(275\) 312.294 + 312.294i 1.13562 + 1.13562i
\(276\) −86.9409 + 135.016i −0.315003 + 0.489189i
\(277\) 317.830 + 317.830i 1.14740 + 1.14740i 0.987062 + 0.160338i \(0.0512586\pi\)
0.160338 + 0.987062i \(0.448741\pi\)
\(278\) −1.09614 10.2388i −0.00394296 0.0368304i
\(279\) 136.706 0.489986
\(280\) 2.11778 + 6.39163i 0.00756352 + 0.0228272i
\(281\) 402.790i 1.43342i −0.697374 0.716708i \(-0.745648\pi\)
0.697374 0.716708i \(-0.254352\pi\)
\(282\) −3.97313 37.1122i −0.0140891 0.131604i
\(283\) −192.406 + 192.406i −0.679881 + 0.679881i −0.959973 0.280092i \(-0.909635\pi\)
0.280092 + 0.959973i \(0.409635\pi\)
\(284\) −28.2048 130.218i −0.0993128 0.458515i
\(285\) −37.6244 + 37.6244i −0.132016 + 0.132016i
\(286\) 346.821 + 279.743i 1.21266 + 0.978121i
\(287\) 18.6371i 0.0649378i
\(288\) −92.9645 23.9501i −0.322793 0.0831600i
\(289\) −273.513 −0.946413
\(290\) 81.2918 100.784i 0.280317 0.347532i
\(291\) 175.911 + 175.911i 0.604506 + 0.604506i
\(292\) 72.8434 15.7777i 0.249464 0.0540331i
\(293\) −75.3645 75.3645i −0.257217 0.257217i 0.566704 0.823921i \(-0.308218\pi\)
−0.823921 + 0.566704i \(0.808218\pi\)
\(294\) −167.300 + 17.9107i −0.569048 + 0.0609207i
\(295\) −38.2964 −0.129818
\(296\) −36.1276 109.036i −0.122053 0.368364i
\(297\) 98.2932i 0.330953i
\(298\) −53.3556 + 5.71210i −0.179046 + 0.0191681i
\(299\) −193.031 + 193.031i −0.645588 + 0.645588i
\(300\) −135.999 87.5736i −0.453329 0.291912i
\(301\) −14.8852 + 14.8852i −0.0494524 + 0.0494524i
\(302\) −129.593 + 160.667i −0.429116 + 0.532011i
\(303\) 221.214i 0.730078i
\(304\) −357.997 134.258i −1.17762 0.441640i
\(305\) −124.996 −0.409824
\(306\) −18.3785 14.8239i −0.0600603 0.0484441i
\(307\) −111.544 111.544i −0.363337 0.363337i 0.501703 0.865040i \(-0.332707\pi\)
−0.865040 + 0.501703i \(0.832707\pi\)
\(308\) −41.6513 26.8205i −0.135232 0.0870797i
\(309\) −116.554 116.554i −0.377196 0.377196i
\(310\) −12.4718 116.496i −0.0402315 0.375794i
\(311\) −224.484 −0.721813 −0.360906 0.932602i \(-0.617533\pi\)
−0.360906 + 0.932602i \(0.617533\pi\)
\(312\) −145.834 73.2448i −0.467415 0.234759i
\(313\) 488.339i 1.56019i 0.625661 + 0.780095i \(0.284829\pi\)
−0.625661 + 0.780095i \(0.715171\pi\)
\(314\) −26.5575 248.069i −0.0845781 0.790027i
\(315\) 1.78545 1.78545i 0.00566809 0.00566809i
\(316\) −24.5985 + 5.32795i −0.0778433 + 0.0168606i
\(317\) 257.361 257.361i 0.811863 0.811863i −0.173050 0.984913i \(-0.555362\pi\)
0.984913 + 0.173050i \(0.0553621\pi\)
\(318\) 158.301 + 127.684i 0.497801 + 0.401522i
\(319\) 952.652i 2.98637i
\(320\) −11.9282 + 81.4061i −0.0372757 + 0.254394i
\(321\) 66.7545 0.207958
\(322\) 19.0548 23.6238i 0.0591763 0.0733659i
\(323\) −66.4962 66.4962i −0.205871 0.205871i
\(324\) 7.62077 + 35.1841i 0.0235209 + 0.108593i
\(325\) −194.436 194.436i −0.598263 0.598263i
\(326\) 52.8829 5.66150i 0.162218 0.0173666i
\(327\) −324.344 −0.991877
\(328\) 102.209 203.503i 0.311614 0.620437i
\(329\) 7.05427i 0.0214416i
\(330\) −83.7620 + 8.96733i −0.253824 + 0.0271737i
\(331\) −123.553 + 123.553i −0.373271 + 0.373271i −0.868667 0.495396i \(-0.835023\pi\)
0.495396 + 0.868667i \(0.335023\pi\)
\(332\) −220.744 + 342.807i −0.664891 + 1.03255i
\(333\) −30.4582 + 30.4582i −0.0914661 + 0.0914661i
\(334\) 335.387 415.807i 1.00415 1.24493i
\(335\) 123.307i 0.368082i
\(336\) 16.9886 + 6.37117i 0.0505612 + 0.0189618i
\(337\) −246.234 −0.730665 −0.365333 0.930877i \(-0.619045\pi\)
−0.365333 + 0.930877i \(0.619045\pi\)
\(338\) 47.1538 + 38.0339i 0.139508 + 0.112526i
\(339\) 46.4853 + 46.4853i 0.137125 + 0.137125i
\(340\) −10.9557 + 17.0139i −0.0322228 + 0.0500408i
\(341\) 609.528 + 609.528i 1.78747 + 1.78747i
\(342\) 15.2626 + 142.564i 0.0446273 + 0.416855i
\(343\) 63.8813 0.186243
\(344\) −244.168 + 80.9018i −0.709790 + 0.235180i
\(345\) 51.6106i 0.149596i
\(346\) 46.2221 + 431.752i 0.133590 + 1.24784i
\(347\) −123.212 + 123.212i −0.355076 + 0.355076i −0.861994 0.506918i \(-0.830785\pi\)
0.506918 + 0.861994i \(0.330785\pi\)
\(348\) −73.8601 341.003i −0.212242 0.979893i
\(349\) 115.371 115.371i 0.330575 0.330575i −0.522230 0.852805i \(-0.674900\pi\)
0.852805 + 0.522230i \(0.174900\pi\)
\(350\) 23.7957 + 19.1934i 0.0679878 + 0.0548384i
\(351\) 61.1977i 0.174352i
\(352\) −307.712 521.283i −0.874183 1.48092i
\(353\) 650.544 1.84290 0.921451 0.388495i \(-0.127005\pi\)
0.921451 + 0.388495i \(0.127005\pi\)
\(354\) −64.7877 + 80.3228i −0.183016 + 0.226901i
\(355\) 30.2790 + 30.2790i 0.0852930 + 0.0852930i
\(356\) −41.4902 + 8.98665i −0.116546 + 0.0252434i
\(357\) 3.15554 + 3.15554i 0.00883906 + 0.00883906i
\(358\) 347.555 37.2083i 0.970824 0.103934i
\(359\) 94.4878 0.263197 0.131599 0.991303i \(-0.457989\pi\)
0.131599 + 0.991303i \(0.457989\pi\)
\(360\) 29.2875 9.70402i 0.0813540 0.0269556i
\(361\) 210.044i 0.581838i
\(362\) 345.821 37.0226i 0.955306 0.102272i
\(363\) 290.063 290.063i 0.799070 0.799070i
\(364\) 25.9323 + 16.6986i 0.0712425 + 0.0458752i
\(365\) −16.9379 + 16.9379i −0.0464053 + 0.0464053i
\(366\) −211.462 + 262.167i −0.577764 + 0.716304i
\(367\) 131.379i 0.357982i −0.983851 0.178991i \(-0.942717\pi\)
0.983851 0.178991i \(-0.0572832\pi\)
\(368\) 337.621 153.455i 0.917449 0.416996i
\(369\) −85.3983 −0.231432
\(370\) 28.7341 + 23.1767i 0.0776598 + 0.0626398i
\(371\) −27.1799 27.1799i −0.0732612 0.0732612i
\(372\) −265.438 170.924i −0.713544 0.459472i
\(373\) −275.796 275.796i −0.739400 0.739400i 0.233062 0.972462i \(-0.425126\pi\)
−0.972462 + 0.233062i \(0.925126\pi\)
\(374\) −15.8486 148.038i −0.0423758 0.395824i
\(375\) 107.652 0.287073
\(376\) −38.6869 + 77.0273i −0.102891 + 0.204860i
\(377\) 593.125i 1.57328i
\(378\) −0.724276 6.76532i −0.00191608 0.0178977i
\(379\) −13.0427 + 13.0427i −0.0344135 + 0.0344135i −0.724104 0.689691i \(-0.757747\pi\)
0.689691 + 0.724104i \(0.257747\pi\)
\(380\) 120.096 26.0124i 0.316042 0.0684538i
\(381\) −118.237 + 118.237i −0.310333 + 0.310333i
\(382\) −301.991 243.583i −0.790553 0.637653i
\(383\) 121.974i 0.318470i −0.987241 0.159235i \(-0.949097\pi\)
0.987241 0.159235i \(-0.0509027\pi\)
\(384\) 150.562 + 162.737i 0.392087 + 0.423793i
\(385\) 15.9214 0.0413544
\(386\) 177.741 220.361i 0.460470 0.570883i
\(387\) 68.2062 + 68.2062i 0.176243 + 0.176243i
\(388\) −121.620 561.504i −0.313454 1.44717i
\(389\) −233.267 233.267i −0.599659 0.599659i 0.340563 0.940222i \(-0.389382\pi\)
−0.940222 + 0.340563i \(0.889382\pi\)
\(390\) 52.1505 5.58309i 0.133719 0.0143156i
\(391\) 91.2149 0.233286
\(392\) 347.235 + 174.399i 0.885804 + 0.444894i
\(393\) 133.517i 0.339738i
\(394\) 81.4198 8.71657i 0.206649 0.0221233i
\(395\) 5.71977 5.71977i 0.0144804 0.0144804i
\(396\) −122.896 + 190.853i −0.310343 + 0.481952i
\(397\) −83.7693 + 83.7693i −0.211006 + 0.211006i −0.804695 0.593689i \(-0.797671\pi\)
0.593689 + 0.804695i \(0.297671\pi\)
\(398\) −34.6874 + 43.0049i −0.0871542 + 0.108053i
\(399\) 27.0986i 0.0679162i
\(400\) 154.571 + 340.078i 0.386428 + 0.850195i
\(401\) 589.134 1.46916 0.734581 0.678521i \(-0.237379\pi\)
0.734581 + 0.678521i \(0.237379\pi\)
\(402\) 258.625 + 208.605i 0.643346 + 0.518917i
\(403\) −379.494 379.494i −0.941673 0.941673i
\(404\) −276.583 + 429.524i −0.684612 + 1.06318i
\(405\) −8.18120 8.18120i −0.0202005 0.0202005i
\(406\) 7.01965 + 65.5691i 0.0172898 + 0.161500i
\(407\) −271.606 −0.667337
\(408\) 17.1506 + 51.7617i 0.0420357 + 0.126867i
\(409\) 449.285i 1.09850i −0.835659 0.549248i \(-0.814914\pi\)
0.835659 0.549248i \(-0.185086\pi\)
\(410\) 7.79092 + 72.7735i 0.0190023 + 0.177496i
\(411\) −31.7617 + 31.7617i −0.0772790 + 0.0772790i
\(412\) 80.5818 + 372.036i 0.195587 + 0.902999i
\(413\) 13.7913 13.7913i 0.0333929 0.0333929i
\(414\) −108.248 87.3120i −0.261469 0.210899i
\(415\) 131.040i 0.315759i
\(416\) 191.583 + 324.553i 0.460536 + 0.780175i
\(417\) 8.91777 0.0213855
\(418\) −567.597 + 703.698i −1.35789 + 1.68349i
\(419\) −218.639 218.639i −0.521811 0.521811i 0.396307 0.918118i \(-0.370292\pi\)
−0.918118 + 0.396307i \(0.870292\pi\)
\(420\) −5.69910 + 1.23441i −0.0135693 + 0.00293906i
\(421\) −61.2101 61.2101i −0.145392 0.145392i 0.630664 0.776056i \(-0.282783\pi\)
−0.776056 + 0.630664i \(0.782783\pi\)
\(422\) 20.6720 2.21308i 0.0489857 0.00524427i
\(423\) 32.3238 0.0764156
\(424\) −147.725 445.844i −0.348407 1.05152i
\(425\) 91.8787i 0.216185i
\(426\) 114.732 12.2828i 0.269323 0.0288330i
\(427\) 45.0136 45.0136i 0.105418 0.105418i
\(428\) −129.615 83.4631i −0.302839 0.195007i
\(429\) −272.860 + 272.860i −0.636038 + 0.636038i
\(430\) 51.9004 64.3454i 0.120699 0.149640i
\(431\) 501.119i 1.16269i 0.813657 + 0.581345i \(0.197473\pi\)
−0.813657 + 0.581345i \(0.802527\pi\)
\(432\) 29.1937 77.8443i 0.0675780 0.180195i
\(433\) 75.5505 0.174482 0.0872408 0.996187i \(-0.472195\pi\)
0.0872408 + 0.996187i \(0.472195\pi\)
\(434\) 46.4439 + 37.4612i 0.107014 + 0.0863162i
\(435\) 79.2918 + 79.2918i 0.182280 + 0.182280i
\(436\) 629.769 + 405.527i 1.44442 + 0.930108i
\(437\) −391.659 391.659i −0.896245 0.896245i
\(438\) 6.87096 + 64.1803i 0.0156871 + 0.146530i
\(439\) 717.251 1.63383 0.816915 0.576758i \(-0.195682\pi\)
0.816915 + 0.576758i \(0.195682\pi\)
\(440\) 173.850 + 87.3160i 0.395114 + 0.198446i
\(441\) 145.714i 0.330417i
\(442\) 9.86737 + 92.1692i 0.0223244 + 0.208528i
\(443\) 299.093 299.093i 0.675153 0.675153i −0.283746 0.958899i \(-0.591577\pi\)
0.958899 + 0.283746i \(0.0915773\pi\)
\(444\) 97.2217 21.0579i 0.218968 0.0474277i
\(445\) 9.64753 9.64753i 0.0216798 0.0216798i
\(446\) −601.059 484.809i −1.34767 1.08702i
\(447\) 46.4714i 0.103963i
\(448\) −25.0203 33.6115i −0.0558489 0.0750257i
\(449\) −44.5560 −0.0992339 −0.0496170 0.998768i \(-0.515800\pi\)
−0.0496170 + 0.998768i \(0.515800\pi\)
\(450\) 87.9474 109.036i 0.195439 0.242302i
\(451\) −380.763 380.763i −0.844263 0.844263i
\(452\) −32.1386 148.380i −0.0711031 0.328274i
\(453\) −126.405 126.405i −0.279039 0.279039i
\(454\) −139.855 + 14.9725i −0.308050 + 0.0329790i
\(455\) −9.91275 −0.0217863
\(456\) 148.613 295.896i 0.325907 0.648895i
\(457\) 641.227i 1.40312i 0.712609 + 0.701562i \(0.247514\pi\)
−0.712609 + 0.701562i \(0.752486\pi\)
\(458\) −539.607 + 57.7689i −1.17818 + 0.126133i
\(459\) 14.4592 14.4592i 0.0315015 0.0315015i
\(460\) −64.5287 + 100.211i −0.140280 + 0.217850i
\(461\) −393.690 + 393.690i −0.853991 + 0.853991i −0.990622 0.136631i \(-0.956373\pi\)
0.136631 + 0.990622i \(0.456373\pi\)
\(462\) 26.9350 33.3936i 0.0583009 0.0722806i
\(463\) 395.861i 0.854991i 0.904018 + 0.427495i \(0.140604\pi\)
−0.904018 + 0.427495i \(0.859396\pi\)
\(464\) −282.944 + 754.462i −0.609792 + 1.62600i
\(465\) 101.465 0.218205
\(466\) 464.853 + 374.946i 0.997538 + 0.804606i
\(467\) −83.1457 83.1457i −0.178042 0.178042i 0.612460 0.790502i \(-0.290180\pi\)
−0.790502 + 0.612460i \(0.790180\pi\)
\(468\) 76.5154 118.826i 0.163495 0.253901i
\(469\) −44.4054 44.4054i −0.0946810 0.0946810i
\(470\) −2.94891 27.5452i −0.00627428 0.0586068i
\(471\) 216.061 0.458729
\(472\) 226.224 74.9564i 0.479288 0.158806i
\(473\) 608.217i 1.28587i
\(474\) −2.32025 21.6730i −0.00489505 0.0457237i
\(475\) 394.509 394.509i 0.830546 0.830546i
\(476\) −2.18165 10.0724i −0.00458330 0.0211605i
\(477\) −124.543 + 124.543i −0.261096 + 0.261096i
\(478\) −385.058 310.584i −0.805560 0.649758i
\(479\) 430.043i 0.897793i −0.893584 0.448896i \(-0.851817\pi\)
0.893584 0.448896i \(-0.148183\pi\)
\(480\) −68.9995 17.7761i −0.143749 0.0370335i
\(481\) 169.103 0.351565
\(482\) −276.663 + 343.003i −0.573989 + 0.711624i
\(483\) 18.5860 + 18.5860i 0.0384803 + 0.0384803i
\(484\) −925.871 + 200.541i −1.91296 + 0.414340i
\(485\) 130.564 + 130.564i 0.269204 + 0.269204i
\(486\) −30.9998 + 3.31875i −0.0637855 + 0.00682870i
\(487\) 573.790 1.17821 0.589107 0.808055i \(-0.299480\pi\)
0.589107 + 0.808055i \(0.299480\pi\)
\(488\) 738.376 244.652i 1.51307 0.501335i
\(489\) 46.0597i 0.0941916i
\(490\) −124.172 + 13.2936i −0.253413 + 0.0271297i
\(491\) −489.133 + 489.133i −0.996197 + 0.996197i −0.999993 0.00379588i \(-0.998792\pi\)
0.00379588 + 0.999993i \(0.498792\pi\)
\(492\) 165.815 + 106.773i 0.337023 + 0.217019i
\(493\) −140.138 + 140.138i −0.284255 + 0.284255i
\(494\) 353.388 438.125i 0.715360 0.886893i
\(495\) 72.9546i 0.147383i
\(496\) 301.688 + 663.755i 0.608242 + 1.33822i
\(497\) −21.8081 −0.0438795
\(498\) −274.843 221.686i −0.551894 0.445153i
\(499\) 260.469 + 260.469i 0.521982 + 0.521982i 0.918170 0.396188i \(-0.129667\pi\)
−0.396188 + 0.918170i \(0.629667\pi\)
\(500\) −209.025 134.598i −0.418050 0.269195i
\(501\) 327.135 + 327.135i 0.652965 + 0.652965i
\(502\) −48.9911 457.616i −0.0975919 0.911586i
\(503\) −975.416 −1.93920 −0.969598 0.244701i \(-0.921310\pi\)
−0.969598 + 0.244701i \(0.921310\pi\)
\(504\) −7.05237 + 14.0416i −0.0139928 + 0.0278603i
\(505\) 164.188i 0.325124i
\(506\) −93.3472 871.938i −0.184481 1.72320i
\(507\) −37.0981 + 37.0981i −0.0731719 + 0.0731719i
\(508\) 377.408 81.7454i 0.742929 0.160916i
\(509\) −420.191 + 420.191i −0.825523 + 0.825523i −0.986894 0.161371i \(-0.948408\pi\)
0.161371 + 0.986894i \(0.448408\pi\)
\(510\) −13.6407 11.0025i −0.0267466 0.0215735i
\(511\) 12.1994i 0.0238735i
\(512\) −88.8714 504.228i −0.173577 0.984820i
\(513\) −124.170 −0.242047
\(514\) 127.026 157.485i 0.247133 0.306391i
\(515\) −86.5077 86.5077i −0.167976 0.167976i
\(516\) −47.1557 217.712i −0.0913871 0.421923i
\(517\) 144.121 + 144.121i 0.278764 + 0.278764i
\(518\) −18.6941 + 2.00134i −0.0360890 + 0.00386359i
\(519\) −376.044 −0.724556
\(520\) −108.240 54.3633i −0.208153 0.104545i
\(521\) 396.333i 0.760716i −0.924839 0.380358i \(-0.875801\pi\)
0.924839 0.380358i \(-0.124199\pi\)
\(522\) 300.448 32.1651i 0.575571 0.0616190i
\(523\) 564.600 564.600i 1.07954 1.07954i 0.0829913 0.996550i \(-0.473553\pi\)
0.996550 0.0829913i \(-0.0264474\pi\)
\(524\) −166.937 + 259.246i −0.318581 + 0.494745i
\(525\) −18.7212 + 18.7212i −0.0356595 + 0.0356595i
\(526\) −406.368 + 503.809i −0.772563 + 0.957812i
\(527\) 179.326i 0.340278i
\(528\) 477.247 216.917i 0.903876 0.410827i
\(529\) 8.25115 0.0155976
\(530\) 117.493 + 94.7688i 0.221685 + 0.178809i
\(531\) −63.1938 63.1938i −0.119009 0.119009i
\(532\) −33.8813 + 52.6165i −0.0636867 + 0.0989032i
\(533\) 237.064 + 237.064i 0.444773 + 0.444773i
\(534\) −3.91357 36.5559i −0.00732878 0.0684567i
\(535\) 49.5461 0.0926095
\(536\) −241.346 728.401i −0.450273 1.35896i
\(537\) 302.711i 0.563708i
\(538\) −0.455463 4.25439i −0.000846586 0.00790779i
\(539\) 649.691 649.691i 1.20536 1.20536i
\(540\) 5.65624 + 26.1142i 0.0104745 + 0.0483596i
\(541\) −29.5601 + 29.5601i −0.0546398 + 0.0546398i −0.733899 0.679259i \(-0.762301\pi\)
0.679259 + 0.733899i \(0.262301\pi\)
\(542\) −258.568 208.559i −0.477064 0.384795i
\(543\) 301.201i 0.554698i
\(544\) 31.4169 121.948i 0.0577516 0.224168i
\(545\) −240.733 −0.441711
\(546\) −16.7698 + 20.7910i −0.0307140 + 0.0380788i
\(547\) −138.608 138.608i −0.253397 0.253397i 0.568965 0.822362i \(-0.307344\pi\)
−0.822362 + 0.568965i \(0.807344\pi\)
\(548\) 101.382 21.9591i 0.185004 0.0400713i
\(549\) −206.259 206.259i −0.375700 0.375700i
\(550\) 878.283 94.0265i 1.59688 0.170957i
\(551\) 1203.45 2.18412
\(552\) 101.016 + 304.874i 0.183000 + 0.552307i
\(553\) 4.11960i 0.00744955i
\(554\) 893.851 95.6932i 1.61345 0.172731i
\(555\) −22.6065 + 22.6065i −0.0407324 + 0.0407324i
\(556\) −17.3154 11.1499i −0.0311428 0.0200538i
\(557\) 60.4400 60.4400i 0.108510 0.108510i −0.650767 0.759277i \(-0.725553\pi\)
0.759277 + 0.650767i \(0.225553\pi\)
\(558\) 171.653 212.813i 0.307622 0.381386i
\(559\) 378.678i 0.677421i
\(560\) 12.6091 + 4.72877i 0.0225163 + 0.00844423i
\(561\) 128.938 0.229835
\(562\) −627.031 505.758i −1.11571 0.899924i
\(563\) 267.325 + 267.325i 0.474822 + 0.474822i 0.903471 0.428649i \(-0.141010\pi\)
−0.428649 + 0.903471i \(0.641010\pi\)
\(564\) −62.7621 40.4144i −0.111280 0.0716568i
\(565\) 34.5021 + 34.5021i 0.0610656 + 0.0610656i
\(566\) 57.9303 + 541.115i 0.102350 + 0.956034i
\(567\) 5.89242 0.0103923
\(568\) −238.128 119.600i −0.419240 0.210563i
\(569\) 315.715i 0.554859i 0.960746 + 0.277429i \(0.0894825\pi\)
−0.960746 + 0.277429i \(0.910518\pi\)
\(570\) 11.3281 + 105.813i 0.0198738 + 0.185637i
\(571\) −670.572 + 670.572i −1.17438 + 1.17438i −0.193228 + 0.981154i \(0.561896\pi\)
−0.981154 + 0.193228i \(0.938104\pi\)
\(572\) 870.962 188.648i 1.52266 0.329803i
\(573\) 237.591 237.591i 0.414643 0.414643i
\(574\) −29.0128 23.4015i −0.0505449 0.0407691i
\(575\) 541.161i 0.941149i
\(576\) −154.013 + 114.647i −0.267384 + 0.199040i
\(577\) 413.628 0.716859 0.358430 0.933557i \(-0.383312\pi\)
0.358430 + 0.933557i \(0.383312\pi\)
\(578\) −343.434 + 425.784i −0.594176 + 0.736650i
\(579\) 173.368 + 173.368i 0.299427 + 0.299427i
\(580\) −54.8200 253.097i −0.0945173 0.436374i
\(581\) 47.1900 + 47.1900i 0.0812220 + 0.0812220i
\(582\) 494.726 52.9639i 0.850044 0.0910033i
\(583\) −1110.59 −1.90495
\(584\) 66.9035 133.208i 0.114561 0.228095i
\(585\) 45.4218i 0.0776441i
\(586\) −211.952 + 22.6910i −0.361693 + 0.0387218i
\(587\) −420.085 + 420.085i −0.715647 + 0.715647i −0.967711 0.252064i \(-0.918891\pi\)
0.252064 + 0.967711i \(0.418891\pi\)
\(588\) −182.186 + 282.929i −0.309841 + 0.481171i
\(589\) 769.993 769.993i 1.30729 1.30729i
\(590\) −48.0863 + 59.6167i −0.0815023 + 0.101045i
\(591\) 70.9145i 0.119991i
\(592\) −215.101 80.6687i −0.363347 0.136265i
\(593\) −740.798 −1.24924 −0.624619 0.780930i \(-0.714746\pi\)
−0.624619 + 0.780930i \(0.714746\pi\)
\(594\) −153.015 123.421i −0.257601 0.207779i
\(595\) 2.34209 + 2.34209i 0.00393628 + 0.00393628i
\(596\) −58.1031 + 90.2320i −0.0974885 + 0.151396i
\(597\) −33.8340 33.8340i −0.0566733 0.0566733i
\(598\) 58.1183 + 542.872i 0.0971878 + 0.907812i
\(599\) 435.161 0.726479 0.363240 0.931696i \(-0.381671\pi\)
0.363240 + 0.931696i \(0.381671\pi\)
\(600\) −307.092 + 101.751i −0.511821 + 0.169585i
\(601\) 380.001i 0.632280i −0.948712 0.316140i \(-0.897613\pi\)
0.948712 0.316140i \(-0.102387\pi\)
\(602\) 4.48167 + 41.8624i 0.00744463 + 0.0695388i
\(603\) −203.473 + 203.473i −0.337434 + 0.337434i
\(604\) 87.3924 + 403.480i 0.144689 + 0.668013i
\(605\) 215.288 215.288i 0.355849 0.355849i
\(606\) −344.367 277.764i −0.568263 0.458356i
\(607\) 181.813i 0.299527i −0.988722 0.149763i \(-0.952149\pi\)
0.988722 0.149763i \(-0.0478512\pi\)
\(608\) −658.517 + 388.721i −1.08309 + 0.639344i
\(609\) −57.1090 −0.0937751
\(610\) −156.950 + 194.584i −0.257295 + 0.318990i
\(611\) −89.7303 89.7303i −0.146858 0.146858i
\(612\) −46.1533 + 9.99666i −0.0754139 + 0.0163344i
\(613\) 55.1479 + 55.1479i 0.0899640 + 0.0899640i 0.750657 0.660693i \(-0.229737\pi\)
−0.660693 + 0.750657i \(0.729737\pi\)
\(614\) −313.703 + 33.5841i −0.510917 + 0.0546973i
\(615\) −63.3838 −0.103063
\(616\) −94.0510 + 31.1626i −0.152680 + 0.0505886i
\(617\) 579.674i 0.939504i −0.882798 0.469752i \(-0.844343\pi\)
0.882798 0.469752i \(-0.155657\pi\)
\(618\) −327.790 + 35.0923i −0.530405 + 0.0567837i
\(619\) 91.1070 91.1070i 0.147184 0.147184i −0.629675 0.776859i \(-0.716812\pi\)
0.776859 + 0.629675i \(0.216812\pi\)
\(620\) −197.012 126.862i −0.317761 0.204616i
\(621\) 85.1639 85.1639i 0.137140 0.137140i
\(622\) −281.870 + 349.458i −0.453167 + 0.561830i
\(623\) 6.94852i 0.0111533i
\(624\) −297.136 + 135.053i −0.476179 + 0.216431i
\(625\) −503.783 −0.806053
\(626\) 760.208 + 613.177i 1.21439 + 0.979516i
\(627\) −553.633 553.633i −0.882987 0.882987i
\(628\) −419.520 270.141i −0.668025 0.430162i
\(629\) −39.9540 39.9540i −0.0635199 0.0635199i
\(630\) −0.537568 5.02132i −0.000853283 0.00797034i
\(631\) −693.474 −1.09901 −0.549504 0.835491i \(-0.685183\pi\)
−0.549504 + 0.835491i \(0.685183\pi\)
\(632\) −22.5926 + 44.9829i −0.0357478 + 0.0711755i
\(633\) 18.0048i 0.0284435i
\(634\) −77.4869 723.790i −0.122219 1.14162i
\(635\) −87.7570 + 87.7570i −0.138200 + 0.138200i
\(636\) 397.536 86.1051i 0.625057 0.135385i
\(637\) −404.500 + 404.500i −0.635007 + 0.635007i
\(638\) 1483.01 + 1196.19i 2.32447 + 1.87490i
\(639\) 99.9283i 0.156382i
\(640\) 111.749 + 120.785i 0.174608 + 0.188727i
\(641\) −218.329 −0.340607 −0.170304 0.985392i \(-0.554475\pi\)
−0.170304 + 0.985392i \(0.554475\pi\)
\(642\) 83.8194 103.918i 0.130560 0.161866i
\(643\) 887.430 + 887.430i 1.38014 + 1.38014i 0.844353 + 0.535787i \(0.179985\pi\)
0.535787 + 0.844353i \(0.320015\pi\)
\(644\) −12.8498 59.3259i −0.0199531 0.0921210i
\(645\) 50.6236 + 50.6236i 0.0784861 + 0.0784861i
\(646\) −187.011 + 20.0209i −0.289491 + 0.0309921i
\(647\) −223.177 −0.344941 −0.172470 0.985015i \(-0.555175\pi\)
−0.172470 + 0.985015i \(0.555175\pi\)
\(648\) 64.3408 + 32.3151i 0.0992913 + 0.0498690i
\(649\) 563.520i 0.868290i
\(650\) −546.822 + 58.5413i −0.841265 + 0.0900635i
\(651\) −36.5396 + 36.5396i −0.0561284 + 0.0561284i
\(652\) 57.5884 89.4327i 0.0883258 0.137167i
\(653\) 539.691 539.691i 0.826479 0.826479i −0.160549 0.987028i \(-0.551326\pi\)
0.987028 + 0.160549i \(0.0513264\pi\)
\(654\) −407.258 + 504.913i −0.622719 + 0.772037i
\(655\) 99.0983i 0.151295i
\(656\) −188.460 414.638i −0.287286 0.632070i
\(657\) −55.8994 −0.0850828
\(658\) 10.9815 + 8.85760i 0.0166892 + 0.0134614i
\(659\) 625.166 + 625.166i 0.948659 + 0.948659i 0.998745 0.0500862i \(-0.0159496\pi\)
−0.0500862 + 0.998745i \(0.515950\pi\)
\(660\) −91.2151 + 141.654i −0.138205 + 0.214627i
\(661\) −326.893 326.893i −0.494544 0.494544i 0.415191 0.909734i \(-0.363715\pi\)
−0.909734 + 0.415191i \(0.863715\pi\)
\(662\) 37.1996 + 347.474i 0.0561928 + 0.524886i
\(663\) −80.2770 −0.121081
\(664\) 256.481 + 774.078i 0.386266 + 1.16578i
\(665\) 20.1129i 0.0302450i
\(666\) 9.17045 + 85.6593i 0.0137694 + 0.128618i
\(667\) −825.404 + 825.404i −1.23749 + 1.23749i
\(668\) −226.172 1044.21i −0.338581 1.56318i
\(669\) 472.881 472.881i 0.706848 0.706848i
\(670\) 191.955 + 154.829i 0.286500 + 0.231089i
\(671\) 1839.28i 2.74111i
\(672\) 31.2496 18.4466i 0.0465023 0.0274502i
\(673\) 422.147 0.627262 0.313631 0.949545i \(-0.398455\pi\)
0.313631 + 0.949545i \(0.398455\pi\)
\(674\) −309.181 + 383.318i −0.458725 + 0.568720i
\(675\) 85.7837 + 85.7837i 0.127087 + 0.127087i
\(676\) 118.416 25.6486i 0.175172 0.0379417i
\(677\) −126.017 126.017i −0.186140 0.186140i 0.607885 0.794025i \(-0.292018\pi\)
−0.794025 + 0.607885i \(0.792018\pi\)
\(678\) 130.733 13.9959i 0.192822 0.0206430i
\(679\) −94.0372 −0.138494
\(680\) 12.7294 + 38.4183i 0.0187197 + 0.0564974i
\(681\) 121.810i 0.178869i
\(682\) 1714.21 183.518i 2.51350 0.269089i
\(683\) 621.906 621.906i 0.910551 0.910551i −0.0857647 0.996315i \(-0.527333\pi\)
0.996315 + 0.0857647i \(0.0273333\pi\)
\(684\) 241.097 + 155.250i 0.352481 + 0.226973i
\(685\) −23.5740 + 23.5740i −0.0344145 + 0.0344145i
\(686\) 80.2117 99.4452i 0.116927 0.144964i
\(687\) 469.984i 0.684111i
\(688\) −180.644 + 481.684i −0.262564 + 0.700122i
\(689\) 691.456 1.00357
\(690\) −80.3433 64.8042i −0.116440 0.0939191i
\(691\) −403.376 403.376i −0.583758 0.583758i 0.352176 0.935934i \(-0.385442\pi\)
−0.935934 + 0.352176i \(0.885442\pi\)
\(692\) 730.154 + 470.168i 1.05514 + 0.679434i
\(693\) 26.2724 + 26.2724i 0.0379110 + 0.0379110i
\(694\) 37.0969 + 346.515i 0.0534537 + 0.499301i
\(695\) 6.61889 0.00952359
\(696\) −623.587 313.196i −0.895959 0.449995i
\(697\) 112.022i 0.160721i
\(698\) −34.7361 324.463i −0.0497652 0.464847i
\(699\) −365.722 + 365.722i −0.523207 + 0.523207i
\(700\) 59.7576 12.9433i 0.0853680 0.0184904i
\(701\) 466.593 466.593i 0.665611 0.665611i −0.291086 0.956697i \(-0.594017\pi\)
0.956697 + 0.291086i \(0.0940166\pi\)
\(702\) 95.2676 + 76.8421i 0.135709 + 0.109462i
\(703\) 343.109i 0.488065i
\(704\) −1197.87 175.521i −1.70152 0.249319i
\(705\) 23.9912 0.0340300
\(706\) 816.847 1012.72i 1.15701 1.43444i
\(707\) 59.1272 + 59.1272i 0.0836311 + 0.0836311i
\(708\) 43.6903 + 201.713i 0.0617095 + 0.284905i
\(709\) 822.764 + 822.764i 1.16046 + 1.16046i 0.984376 + 0.176081i \(0.0563422\pi\)
0.176081 + 0.984376i \(0.443658\pi\)
\(710\) 85.1554 9.11650i 0.119937 0.0128401i
\(711\) 18.8767 0.0265494
\(712\) −38.1069 + 75.8726i −0.0535210 + 0.106563i
\(713\) 1056.22i 1.48138i
\(714\) 8.87451 0.950080i 0.0124293 0.00133064i
\(715\) −202.521 + 202.521i −0.283246 + 0.283246i
\(716\) 378.480 587.766i 0.528603 0.820902i
\(717\) 302.943 302.943i 0.422515 0.422515i
\(718\) 118.642 147.091i 0.165240 0.204862i
\(719\) 710.142i 0.987681i 0.869553 + 0.493840i \(0.164407\pi\)
−0.869553 + 0.493840i \(0.835593\pi\)
\(720\) 21.6680 57.7771i 0.0300944 0.0802460i
\(721\) 62.3062 0.0864164
\(722\) 326.979 + 263.738i 0.452879 + 0.365289i
\(723\) −269.856 269.856i −0.373245 0.373245i
\(724\) 376.592 584.833i 0.520154 0.807781i
\(725\) −831.411 831.411i −1.14677 1.14677i
\(726\) −87.3329 815.759i −0.120293 1.12364i
\(727\) −214.095 −0.294490 −0.147245 0.989100i \(-0.547041\pi\)
−0.147245 + 0.989100i \(0.547041\pi\)
\(728\) 58.5565 19.4019i 0.0804347 0.0266510i
\(729\) 27.0000i 0.0370370i
\(730\) 5.09972 + 47.6355i 0.00698592 + 0.0652541i
\(731\) −89.4704 + 89.4704i −0.122395 + 0.122395i
\(732\) 142.602 + 658.373i 0.194811 + 0.899417i
\(733\) −96.1768 + 96.1768i −0.131210 + 0.131210i −0.769662 0.638452i \(-0.779575\pi\)
0.638452 + 0.769662i \(0.279575\pi\)
\(734\) −204.521 164.965i −0.278638 0.224747i
\(735\) 108.151i 0.147144i
\(736\) 185.044 718.265i 0.251418 0.975903i
\(737\) −1814.43 −2.46192
\(738\) −107.229 + 132.941i −0.145297 + 0.180137i
\(739\) 885.341 + 885.341i 1.19803 + 1.19803i 0.974757 + 0.223268i \(0.0716726\pi\)
0.223268 + 0.974757i \(0.428327\pi\)
\(740\) 72.1593 15.6295i 0.0975125 0.0211209i
\(741\) 344.694 + 344.694i 0.465174 + 0.465174i
\(742\) −76.4396 + 8.18341i −0.103018 + 0.0110289i
\(743\) 906.258 1.21973 0.609864 0.792506i \(-0.291224\pi\)
0.609864 + 0.792506i \(0.291224\pi\)
\(744\) −599.374 + 198.595i −0.805611 + 0.266929i
\(745\) 34.4917i 0.0462976i
\(746\) −775.637 + 83.0376i −1.03973 + 0.111310i
\(747\) 216.232 216.232i 0.289467 0.289467i
\(748\) −250.354 161.211i −0.334698 0.215522i
\(749\) −17.8425 + 17.8425i −0.0238218 + 0.0238218i
\(750\) 135.172 167.584i 0.180229 0.223446i
\(751\) 1147.02i 1.52732i −0.645618 0.763661i \(-0.723400\pi\)
0.645618 0.763661i \(-0.276600\pi\)
\(752\) 71.3333 + 156.943i 0.0948581 + 0.208701i
\(753\) 398.572 0.529312
\(754\) −923.329 744.749i −1.22457 0.987731i
\(755\) −93.8192 93.8192i −0.124264 0.124264i
\(756\) −11.4411 7.36729i −0.0151338 0.00974509i
\(757\) 525.591 + 525.591i 0.694308 + 0.694308i 0.963177 0.268869i \(-0.0866497\pi\)
−0.268869 + 0.963177i \(0.586650\pi\)
\(758\) 3.92694 + 36.6808i 0.00518066 + 0.0483915i
\(759\) 759.435 1.00057
\(760\) 110.303 219.618i 0.145135 0.288971i
\(761\) 788.107i 1.03562i 0.855495 + 0.517810i \(0.173253\pi\)
−0.855495 + 0.517810i \(0.826747\pi\)
\(762\) 35.5991 + 332.524i 0.0467179 + 0.436383i
\(763\) 86.6925 86.6925i 0.113621 0.113621i
\(764\) −758.382 + 164.263i −0.992647 + 0.215004i
\(765\) 10.7318 10.7318i 0.0140285 0.0140285i
\(766\) −189.879 153.155i −0.247884 0.199941i
\(767\) 350.850i 0.457431i
\(768\) 442.386 30.0441i 0.576023 0.0391199i
\(769\) −768.187 −0.998943 −0.499471 0.866330i \(-0.666472\pi\)
−0.499471 + 0.866330i \(0.666472\pi\)
\(770\) 19.9915 24.7852i 0.0259630 0.0321886i
\(771\) 123.901 + 123.901i 0.160702