Properties

Label 105.3.o.b.44.3
Level 105
Weight 3
Character 105.44
Analytic conductor 2.861
Analytic rank 0
Dimension 40
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 44.3
Character \(\chi\) \(=\) 105.44
Dual form 105.3.o.b.74.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.60486 + 2.77971i) q^{2} +(-2.69226 - 1.32352i) q^{3} +(-3.15118 - 5.45800i) q^{4} +(-4.78223 + 1.45954i) q^{5} +(7.99972 - 5.35963i) q^{6} +(6.02754 - 3.55932i) q^{7} +7.38994 q^{8} +(5.49658 + 7.12655i) q^{9} +O(q^{10})\) \(q+(-1.60486 + 2.77971i) q^{2} +(-2.69226 - 1.32352i) q^{3} +(-3.15118 - 5.45800i) q^{4} +(-4.78223 + 1.45954i) q^{5} +(7.99972 - 5.35963i) q^{6} +(6.02754 - 3.55932i) q^{7} +7.38994 q^{8} +(5.49658 + 7.12655i) q^{9} +(3.61773 - 15.6356i) q^{10} +(10.5523 - 6.09236i) q^{11} +(1.26002 + 18.8650i) q^{12} -8.47270i q^{13} +(0.220467 + 22.4670i) q^{14} +(14.8068 + 2.39992i) q^{15} +(0.744857 - 1.29013i) q^{16} +(-5.29476 - 9.17080i) q^{17} +(-28.6310 + 3.84173i) q^{18} +(-10.0823 + 17.4631i) q^{19} +(23.0359 + 21.5022i) q^{20} +(-20.9386 + 1.60503i) q^{21} +39.1096i q^{22} +(15.2706 - 26.4494i) q^{23} +(-19.8957 - 9.78076i) q^{24} +(20.7395 - 13.9597i) q^{25} +(23.5516 + 13.5975i) q^{26} +(-5.36609 - 26.4614i) q^{27} +(-38.4206 - 21.6823i) q^{28} -42.8910i q^{29} +(-30.4339 + 37.3069i) q^{30} +(-6.11033 - 10.5834i) q^{31} +(17.1707 + 29.7405i) q^{32} +(-36.4729 + 2.43607i) q^{33} +33.9895 q^{34} +(-23.6301 + 25.8189i) q^{35} +(21.5760 - 52.4573i) q^{36} +(-28.8063 - 16.6313i) q^{37} +(-32.3616 - 56.0519i) q^{38} +(-11.2138 + 22.8108i) q^{39} +(-35.3404 + 10.7859i) q^{40} -6.40934i q^{41} +(29.1420 - 60.7790i) q^{42} +20.0231i q^{43} +(-66.5042 - 38.3962i) q^{44} +(-36.6874 - 26.0583i) q^{45} +(49.0144 + 84.8955i) q^{46} +(11.8740 - 20.5664i) q^{47} +(-3.71287 + 2.48754i) q^{48} +(23.6625 - 42.9079i) q^{49} +(5.51992 + 80.0531i) q^{50} +(2.11714 + 31.6979i) q^{51} +(-46.2440 + 26.6990i) q^{52} +(43.9372 + 76.1014i) q^{53} +(82.1667 + 27.5508i) q^{54} +(-41.5714 + 44.5366i) q^{55} +(44.5432 - 26.3032i) q^{56} +(50.2571 - 33.6711i) q^{57} +(119.224 + 68.8342i) q^{58} +(-41.9905 + 24.2432i) q^{59} +(-33.5600 - 88.3779i) q^{60} +(10.4973 - 18.1819i) q^{61} +39.2250 q^{62} +(58.4965 + 23.3915i) q^{63} -104.268 q^{64} +(12.3663 + 40.5184i) q^{65} +(51.7625 - 105.294i) q^{66} +(-19.6174 + 11.3261i) q^{67} +(-33.3695 + 57.7976i) q^{68} +(-76.1189 + 50.9979i) q^{69} +(-33.8459 - 107.121i) q^{70} -2.44145i q^{71} +(40.6194 + 52.6648i) q^{72} +(76.5611 - 44.2026i) q^{73} +(92.4605 - 53.3821i) q^{74} +(-74.3122 + 10.1341i) q^{75} +127.085 q^{76} +(41.9197 - 74.2809i) q^{77} +(-45.4106 - 67.7793i) q^{78} +(-3.20270 + 5.54725i) q^{79} +(-1.67908 + 7.25685i) q^{80} +(-20.5753 + 78.3432i) q^{81} +(17.8161 + 10.2861i) q^{82} -103.557 q^{83} +(74.7415 + 109.225i) q^{84} +(38.7059 + 36.1289i) q^{85} +(-55.6583 - 32.1344i) q^{86} +(-56.7672 + 115.474i) q^{87} +(77.9808 - 45.0222i) q^{88} +(-54.2968 - 31.3483i) q^{89} +(131.313 - 60.1601i) q^{90} +(-30.1570 - 51.0696i) q^{91} -192.481 q^{92} +(2.44325 + 36.5805i) q^{93} +(38.1124 + 66.0126i) q^{94} +(22.7279 - 98.2282i) q^{95} +(-6.86580 - 102.795i) q^{96} -140.539i q^{97} +(81.2961 + 134.636i) q^{98} +(101.419 + 41.7142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + O(q^{10}) \) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + 62q^{10} + 84q^{15} - 116q^{16} - 56q^{19} + 36q^{21} - 12q^{24} - 6q^{25} - 20q^{30} - 444q^{31} + 256q^{34} - 688q^{36} + 168q^{39} + 54q^{40} - 40q^{45} + 304q^{46} + 156q^{49} + 156q^{51} - 140q^{54} - 500q^{55} - 130q^{60} + 288q^{61} + 472q^{64} + 340q^{66} - 272q^{69} + 710q^{70} - 524q^{75} + 400q^{76} - 340q^{79} + 496q^{84} + 896q^{85} + 1356q^{90} - 656q^{91} - 560q^{94} + 472q^{96} - 336q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.60486 + 2.77971i −0.802432 + 1.38985i 0.115579 + 0.993298i \(0.463128\pi\)
−0.918011 + 0.396555i \(0.870206\pi\)
\(3\) −2.69226 1.32352i −0.897421 0.441174i
\(4\) −3.15118 5.45800i −0.787795 1.36450i
\(5\) −4.78223 + 1.45954i −0.956446 + 0.291908i
\(6\) 7.99972 5.35963i 1.33329 0.893272i
\(7\) 6.02754 3.55932i 0.861077 0.508474i
\(8\) 7.38994 0.923743
\(9\) 5.49658 + 7.12655i 0.610731 + 0.791838i
\(10\) 3.61773 15.6356i 0.361773 1.56356i
\(11\) 10.5523 6.09236i 0.959298 0.553851i 0.0633411 0.997992i \(-0.479824\pi\)
0.895957 + 0.444141i \(0.146491\pi\)
\(12\) 1.26002 + 18.8650i 0.105002 + 1.57209i
\(13\) 8.47270i 0.651746i −0.945414 0.325873i \(-0.894342\pi\)
0.945414 0.325873i \(-0.105658\pi\)
\(14\) 0.220467 + 22.4670i 0.0157477 + 1.60479i
\(15\) 14.8068 + 2.39992i 0.987118 + 0.159995i
\(16\) 0.744857 1.29013i 0.0465536 0.0806332i
\(17\) −5.29476 9.17080i −0.311457 0.539459i 0.667221 0.744859i \(-0.267484\pi\)
−0.978678 + 0.205401i \(0.934150\pi\)
\(18\) −28.6310 + 3.84173i −1.59061 + 0.213429i
\(19\) −10.0823 + 17.4631i −0.530649 + 0.919111i 0.468711 + 0.883351i \(0.344718\pi\)
−0.999360 + 0.0357599i \(0.988615\pi\)
\(20\) 23.0359 + 21.5022i 1.15179 + 1.07511i
\(21\) −20.9386 + 1.60503i −0.997075 + 0.0764301i
\(22\) 39.1096i 1.77771i
\(23\) 15.2706 26.4494i 0.663939 1.14998i −0.315633 0.948881i \(-0.602217\pi\)
0.979572 0.201094i \(-0.0644497\pi\)
\(24\) −19.8957 9.78076i −0.828987 0.407532i
\(25\) 20.7395 13.9597i 0.829579 0.558389i
\(26\) 23.5516 + 13.5975i 0.905832 + 0.522982i
\(27\) −5.36609 26.4614i −0.198744 0.980051i
\(28\) −38.4206 21.6823i −1.37217 0.774368i
\(29\) 42.8910i 1.47900i −0.673157 0.739499i \(-0.735062\pi\)
0.673157 0.739499i \(-0.264938\pi\)
\(30\) −30.4339 + 37.3069i −1.01446 + 1.24356i
\(31\) −6.11033 10.5834i −0.197107 0.341400i 0.750482 0.660891i \(-0.229821\pi\)
−0.947589 + 0.319491i \(0.896488\pi\)
\(32\) 17.1707 + 29.7405i 0.536584 + 0.929390i
\(33\) −36.4729 + 2.43607i −1.10524 + 0.0738203i
\(34\) 33.9895 0.999691
\(35\) −23.6301 + 25.8189i −0.675147 + 0.737684i
\(36\) 21.5760 52.4573i 0.599333 1.45715i
\(37\) −28.8063 16.6313i −0.778550 0.449496i 0.0573663 0.998353i \(-0.481730\pi\)
−0.835916 + 0.548857i \(0.815063\pi\)
\(38\) −32.3616 56.0519i −0.851620 1.47505i
\(39\) −11.2138 + 22.8108i −0.287534 + 0.584891i
\(40\) −35.3404 + 10.7859i −0.883511 + 0.269648i
\(41\) 6.40934i 0.156325i −0.996941 0.0781627i \(-0.975095\pi\)
0.996941 0.0781627i \(-0.0249054\pi\)
\(42\) 29.1420 60.7790i 0.693858 1.44712i
\(43\) 20.0231i 0.465653i 0.972518 + 0.232827i \(0.0747975\pi\)
−0.972518 + 0.232827i \(0.925203\pi\)
\(44\) −66.5042 38.3962i −1.51146 0.872642i
\(45\) −36.6874 26.0583i −0.815275 0.579073i
\(46\) 49.0144 + 84.8955i 1.06553 + 1.84555i
\(47\) 11.8740 20.5664i 0.252639 0.437583i −0.711613 0.702572i \(-0.752035\pi\)
0.964251 + 0.264989i \(0.0853683\pi\)
\(48\) −3.71287 + 2.48754i −0.0773514 + 0.0518237i
\(49\) 23.6625 42.9079i 0.482909 0.875671i
\(50\) 5.51992 + 80.0531i 0.110398 + 1.60106i
\(51\) 2.11714 + 31.6979i 0.0415126 + 0.621528i
\(52\) −46.2440 + 26.6990i −0.889308 + 0.513442i
\(53\) 43.9372 + 76.1014i 0.829003 + 1.43588i 0.898821 + 0.438316i \(0.144425\pi\)
−0.0698177 + 0.997560i \(0.522242\pi\)
\(54\) 82.1667 + 27.5508i 1.52161 + 0.510199i
\(55\) −41.5714 + 44.5366i −0.755843 + 0.809756i
\(56\) 44.5432 26.3032i 0.795414 0.469699i
\(57\) 50.2571 33.6711i 0.881704 0.590722i
\(58\) 119.224 + 68.8342i 2.05559 + 1.18680i
\(59\) −41.9905 + 24.2432i −0.711703 + 0.410902i −0.811691 0.584087i \(-0.801453\pi\)
0.0999885 + 0.994989i \(0.468119\pi\)
\(60\) −33.5600 88.3779i −0.559334 1.47297i
\(61\) 10.4973 18.1819i 0.172087 0.298063i −0.767062 0.641573i \(-0.778282\pi\)
0.939149 + 0.343509i \(0.111616\pi\)
\(62\) 39.2250 0.632662
\(63\) 58.4965 + 23.3915i 0.928515 + 0.371294i
\(64\) −104.268 −1.62918
\(65\) 12.3663 + 40.5184i 0.190250 + 0.623360i
\(66\) 51.7625 105.294i 0.784280 1.59536i
\(67\) −19.6174 + 11.3261i −0.292798 + 0.169047i −0.639203 0.769038i \(-0.720736\pi\)
0.346405 + 0.938085i \(0.387402\pi\)
\(68\) −33.3695 + 57.7976i −0.490728 + 0.849965i
\(69\) −76.1189 + 50.9979i −1.10317 + 0.739100i
\(70\) −33.8459 107.121i −0.483513 1.53030i
\(71\) 2.44145i 0.0343867i −0.999852 0.0171933i \(-0.994527\pi\)
0.999852 0.0171933i \(-0.00547308\pi\)
\(72\) 40.6194 + 52.6648i 0.564158 + 0.731455i
\(73\) 76.5611 44.2026i 1.04878 0.605515i 0.126474 0.991970i \(-0.459634\pi\)
0.922308 + 0.386455i \(0.126301\pi\)
\(74\) 92.4605 53.3821i 1.24947 0.721380i
\(75\) −74.3122 + 10.1341i −0.990829 + 0.135122i
\(76\) 127.085 1.67217
\(77\) 41.9197 74.2809i 0.544411 0.964686i
\(78\) −45.4106 67.7793i −0.582187 0.868965i
\(79\) −3.20270 + 5.54725i −0.0405406 + 0.0702183i −0.885584 0.464480i \(-0.846241\pi\)
0.845043 + 0.534698i \(0.179575\pi\)
\(80\) −1.67908 + 7.25685i −0.0209885 + 0.0907107i
\(81\) −20.5753 + 78.3432i −0.254016 + 0.967200i
\(82\) 17.8161 + 10.2861i 0.217269 + 0.125440i
\(83\) −103.557 −1.24768 −0.623839 0.781553i \(-0.714428\pi\)
−0.623839 + 0.781553i \(0.714428\pi\)
\(84\) 74.7415 + 109.225i 0.889779 + 1.30030i
\(85\) 38.7059 + 36.1289i 0.455364 + 0.425046i
\(86\) −55.6583 32.1344i −0.647190 0.373655i
\(87\) −56.7672 + 115.474i −0.652496 + 1.32729i
\(88\) 77.9808 45.0222i 0.886145 0.511616i
\(89\) −54.2968 31.3483i −0.610077 0.352228i 0.162919 0.986639i \(-0.447909\pi\)
−0.772995 + 0.634412i \(0.781242\pi\)
\(90\) 131.313 60.1601i 1.45903 0.668446i
\(91\) −30.1570 51.0696i −0.331396 0.561204i
\(92\) −192.481 −2.09219
\(93\) 2.44325 + 36.5805i 0.0262716 + 0.393339i
\(94\) 38.1124 + 66.0126i 0.405451 + 0.702262i
\(95\) 22.7279 98.2282i 0.239241 1.03398i
\(96\) −6.86580 102.795i −0.0715188 1.07078i
\(97\) 140.539i 1.44886i −0.689348 0.724430i \(-0.742103\pi\)
0.689348 0.724430i \(-0.257897\pi\)
\(98\) 81.2961 + 134.636i 0.829552 + 1.37384i
\(99\) 101.419 + 41.7142i 1.02443 + 0.421355i
\(100\) −141.546 69.2065i −1.41546 0.692065i
\(101\) 132.859 76.7059i 1.31543 0.759465i 0.332442 0.943124i \(-0.392128\pi\)
0.982990 + 0.183659i \(0.0587942\pi\)
\(102\) −91.5087 44.9859i −0.897144 0.441038i
\(103\) 123.005 + 71.0169i 1.19422 + 0.689485i 0.959261 0.282520i \(-0.0911704\pi\)
0.234961 + 0.972005i \(0.424504\pi\)
\(104\) 62.6128i 0.602046i
\(105\) 97.7905 38.2364i 0.931338 0.364156i
\(106\) −282.053 −2.66088
\(107\) −28.5434 + 49.4386i −0.266761 + 0.462043i −0.968023 0.250860i \(-0.919287\pi\)
0.701263 + 0.712903i \(0.252620\pi\)
\(108\) −127.517 + 112.673i −1.18071 + 1.04327i
\(109\) −88.6354 153.521i −0.813169 1.40845i −0.910635 0.413211i \(-0.864407\pi\)
0.0974665 0.995239i \(-0.468926\pi\)
\(110\) −57.0822 187.031i −0.518929 1.70029i
\(111\) 55.5423 + 82.9018i 0.500381 + 0.746863i
\(112\) −0.102324 10.4275i −0.000913610 0.0931027i
\(113\) −8.70089 −0.0769990 −0.0384995 0.999259i \(-0.512258\pi\)
−0.0384995 + 0.999259i \(0.512258\pi\)
\(114\) 12.9400 + 193.738i 0.113509 + 1.69945i
\(115\) −34.4234 + 148.775i −0.299334 + 1.29370i
\(116\) −234.099 + 135.157i −2.01809 + 1.16515i
\(117\) 60.3811 46.5708i 0.516078 0.398041i
\(118\) 155.628i 1.31888i
\(119\) −64.5562 36.4316i −0.542489 0.306148i
\(120\) 109.421 + 17.7353i 0.911843 + 0.147794i
\(121\) 13.7337 23.7875i 0.113502 0.196591i
\(122\) 33.6935 + 58.3588i 0.276176 + 0.478351i
\(123\) −8.48290 + 17.2556i −0.0689667 + 0.140290i
\(124\) −38.5095 + 66.7004i −0.310560 + 0.537907i
\(125\) −78.8061 + 97.0288i −0.630449 + 0.776231i
\(126\) −158.900 + 125.063i −1.26111 + 0.992562i
\(127\) 58.7503i 0.462601i −0.972882 0.231300i \(-0.925702\pi\)
0.972882 0.231300i \(-0.0742980\pi\)
\(128\) 98.6526 170.871i 0.770724 1.33493i
\(129\) 26.5010 53.9075i 0.205434 0.417887i
\(130\) −132.475 30.6520i −1.01904 0.235784i
\(131\) 69.7084 + 40.2462i 0.532125 + 0.307223i 0.741881 0.670531i \(-0.233934\pi\)
−0.209756 + 0.977754i \(0.567267\pi\)
\(132\) 128.229 + 191.393i 0.971430 + 1.44994i
\(133\) 1.38505 + 141.146i 0.0104139 + 1.06125i
\(134\) 72.7076i 0.542594i
\(135\) 64.2834 + 118.712i 0.476173 + 0.879351i
\(136\) −39.1280 67.7717i −0.287706 0.498321i
\(137\) −5.95720 10.3182i −0.0434832 0.0753151i 0.843465 0.537185i \(-0.180512\pi\)
−0.886948 + 0.461870i \(0.847179\pi\)
\(138\) −19.5987 293.433i −0.142020 2.12633i
\(139\) 126.136 0.907450 0.453725 0.891142i \(-0.350095\pi\)
0.453725 + 0.891142i \(0.350095\pi\)
\(140\) 215.383 + 47.6132i 1.53845 + 0.340095i
\(141\) −59.1881 + 39.6547i −0.419774 + 0.281239i
\(142\) 6.78652 + 3.91820i 0.0477924 + 0.0275930i
\(143\) −51.6187 89.4063i −0.360970 0.625219i
\(144\) 13.2883 1.78304i 0.0922801 0.0123822i
\(145\) 62.6012 + 205.115i 0.431732 + 1.41458i
\(146\) 283.757i 1.94354i
\(147\) −120.495 + 84.2014i −0.819696 + 0.572799i
\(148\) 209.633i 1.41644i
\(149\) −99.8945 57.6741i −0.670433 0.387074i 0.125808 0.992055i \(-0.459848\pi\)
−0.796241 + 0.604980i \(0.793181\pi\)
\(150\) 91.0910 222.830i 0.607274 1.48553i
\(151\) 139.800 + 242.140i 0.925827 + 1.60358i 0.790226 + 0.612815i \(0.209963\pi\)
0.135600 + 0.990764i \(0.456704\pi\)
\(152\) −74.5079 + 129.051i −0.490184 + 0.849023i
\(153\) 36.2530 88.1413i 0.236948 0.576087i
\(154\) 139.204 + 235.735i 0.903920 + 1.53075i
\(155\) 44.6679 + 41.6940i 0.288180 + 0.268994i
\(156\) 159.838 10.6758i 1.02460 0.0684344i
\(157\) 23.3925 13.5057i 0.148997 0.0860235i −0.423648 0.905827i \(-0.639251\pi\)
0.572645 + 0.819803i \(0.305917\pi\)
\(158\) −10.2798 17.8052i −0.0650621 0.112691i
\(159\) −17.5686 263.037i −0.110494 1.65432i
\(160\) −125.522 117.165i −0.784510 0.732279i
\(161\) −2.09779 213.778i −0.0130297 1.32781i
\(162\) −184.751 182.924i −1.14044 1.12916i
\(163\) −238.591 137.750i −1.46375 0.845094i −0.464565 0.885539i \(-0.653789\pi\)
−0.999182 + 0.0404450i \(0.987122\pi\)
\(164\) −34.9822 + 20.1970i −0.213306 + 0.123152i
\(165\) 170.866 64.8836i 1.03555 0.393234i
\(166\) 166.195 287.859i 1.00118 1.73409i
\(167\) −8.17643 −0.0489607 −0.0244803 0.999700i \(-0.507793\pi\)
−0.0244803 + 0.999700i \(0.507793\pi\)
\(168\) −154.735 + 11.8611i −0.921041 + 0.0706018i
\(169\) 97.2133 0.575227
\(170\) −162.546 + 49.6091i −0.956151 + 0.291818i
\(171\) −179.870 + 24.1351i −1.05187 + 0.141141i
\(172\) 109.286 63.0964i 0.635384 0.366839i
\(173\) −42.5110 + 73.6312i −0.245728 + 0.425614i −0.962336 0.271862i \(-0.912360\pi\)
0.716608 + 0.697476i \(0.245694\pi\)
\(174\) −229.880 343.116i −1.32115 1.97193i
\(175\) 75.3209 157.961i 0.430405 0.902636i
\(176\) 18.1518i 0.103135i
\(177\) 145.136 9.69379i 0.819976 0.0547672i
\(178\) 174.278 100.619i 0.979090 0.565278i
\(179\) 107.239 61.9145i 0.599101 0.345891i −0.169587 0.985515i \(-0.554243\pi\)
0.768688 + 0.639624i \(0.220910\pi\)
\(180\) −26.6178 + 282.354i −0.147876 + 1.56863i
\(181\) −169.201 −0.934815 −0.467407 0.884042i \(-0.654812\pi\)
−0.467407 + 0.884042i \(0.654812\pi\)
\(182\) 190.356 1.86795i 1.04591 0.0102635i
\(183\) −52.3256 + 35.0570i −0.285932 + 0.191568i
\(184\) 112.849 195.460i 0.613309 1.06228i
\(185\) 162.033 + 37.4909i 0.875853 + 0.202653i
\(186\) −105.604 51.9152i −0.567764 0.279114i
\(187\) −111.744 64.5152i −0.597559 0.345001i
\(188\) −149.669 −0.796110
\(189\) −126.529 140.398i −0.669465 0.742844i
\(190\) 236.570 + 220.820i 1.24511 + 1.16221i
\(191\) 110.601 + 63.8554i 0.579062 + 0.334322i 0.760761 0.649033i \(-0.224826\pi\)
−0.181699 + 0.983354i \(0.558159\pi\)
\(192\) 280.716 + 138.000i 1.46206 + 0.718753i
\(193\) −107.040 + 61.7995i −0.554611 + 0.320205i −0.750980 0.660325i \(-0.770418\pi\)
0.196369 + 0.980530i \(0.437085\pi\)
\(194\) 390.658 + 225.547i 2.01370 + 1.16261i
\(195\) 20.3338 125.453i 0.104276 0.643350i
\(196\) −308.756 + 6.06019i −1.57529 + 0.0309193i
\(197\) 22.5579 0.114507 0.0572536 0.998360i \(-0.481766\pi\)
0.0572536 + 0.998360i \(0.481766\pi\)
\(198\) −278.717 + 214.969i −1.40766 + 1.08570i
\(199\) 17.2597 + 29.8946i 0.0867319 + 0.150224i 0.906128 0.423004i \(-0.139024\pi\)
−0.819396 + 0.573228i \(0.805691\pi\)
\(200\) 153.264 103.162i 0.766318 0.515808i
\(201\) 67.8057 4.52883i 0.337342 0.0225315i
\(202\) 492.411i 2.43768i
\(203\) −152.663 258.527i −0.752032 1.27353i
\(204\) 166.336 111.441i 0.815372 0.546281i
\(205\) 9.35470 + 30.6509i 0.0456327 + 0.149517i
\(206\) −394.812 + 227.945i −1.91657 + 1.10653i
\(207\) 272.429 36.5548i 1.31608 0.176593i
\(208\) −10.9309 6.31095i −0.0525524 0.0303411i
\(209\) 245.701i 1.17560i
\(210\) −50.6546 + 333.193i −0.241212 + 1.58663i
\(211\) 76.0725 0.360533 0.180267 0.983618i \(-0.442304\pi\)
0.180267 + 0.983618i \(0.442304\pi\)
\(212\) 276.908 479.618i 1.30617 2.26235i
\(213\) −3.23132 + 6.57304i −0.0151705 + 0.0308593i
\(214\) −91.6165 158.684i −0.428114 0.741516i
\(215\) −29.2246 95.7551i −0.135928 0.445372i
\(216\) −39.6551 195.548i −0.183589 0.905316i
\(217\) −74.5000 42.0433i −0.343318 0.193748i
\(218\) 568.991 2.61005
\(219\) −264.626 + 17.6747i −1.20834 + 0.0807063i
\(220\) 374.080 + 86.5540i 1.70036 + 0.393427i
\(221\) −77.7014 + 44.8609i −0.351590 + 0.202991i
\(222\) −319.581 + 21.3452i −1.43955 + 0.0961494i
\(223\) 312.738i 1.40241i 0.712959 + 0.701206i \(0.247355\pi\)
−0.712959 + 0.701206i \(0.752645\pi\)
\(224\) 209.353 + 118.146i 0.934611 + 0.527438i
\(225\) 213.481 + 71.0701i 0.948803 + 0.315867i
\(226\) 13.9638 24.1859i 0.0617865 0.107017i
\(227\) 34.4570 + 59.6813i 0.151793 + 0.262913i 0.931887 0.362750i \(-0.118162\pi\)
−0.780094 + 0.625663i \(0.784829\pi\)
\(228\) −342.146 168.200i −1.50064 0.737718i
\(229\) −172.075 + 298.043i −0.751419 + 1.30150i 0.195716 + 0.980661i \(0.437297\pi\)
−0.947135 + 0.320835i \(0.896036\pi\)
\(230\) −358.307 334.451i −1.55786 1.45414i
\(231\) −211.171 + 144.502i −0.914161 + 0.625550i
\(232\) 316.962i 1.36622i
\(233\) −20.0104 + 34.6590i −0.0858816 + 0.148751i −0.905767 0.423777i \(-0.860704\pi\)
0.819885 + 0.572528i \(0.194037\pi\)
\(234\) 32.5498 + 242.582i 0.139102 + 1.03667i
\(235\) −26.7668 + 115.684i −0.113901 + 0.492272i
\(236\) 264.639 + 152.789i 1.12135 + 0.647412i
\(237\) 15.9644 10.6958i 0.0673605 0.0451300i
\(238\) 204.873 120.979i 0.860811 0.508317i
\(239\) 341.734i 1.42985i 0.699201 + 0.714925i \(0.253539\pi\)
−0.699201 + 0.714925i \(0.746461\pi\)
\(240\) 14.1251 17.3151i 0.0588547 0.0721461i
\(241\) −64.0475 110.934i −0.265757 0.460305i 0.702004 0.712173i \(-0.252289\pi\)
−0.967762 + 0.251867i \(0.918955\pi\)
\(242\) 44.0815 + 76.3514i 0.182155 + 0.315502i
\(243\) 159.083 183.689i 0.654663 0.755921i
\(244\) −132.316 −0.542277
\(245\) −50.5339 + 239.732i −0.206261 + 0.978497i
\(246\) −34.3517 51.2729i −0.139641 0.208427i
\(247\) 147.960 + 85.4246i 0.599027 + 0.345849i
\(248\) −45.1550 78.2108i −0.182077 0.315366i
\(249\) 278.803 + 137.060i 1.11969 + 0.550443i
\(250\) −143.238 374.776i −0.572954 1.49910i
\(251\) 201.118i 0.801266i −0.916239 0.400633i \(-0.868790\pi\)
0.916239 0.400633i \(-0.131210\pi\)
\(252\) −56.6620 392.985i −0.224849 1.55946i
\(253\) 372.136i 1.47089i
\(254\) 163.309 + 94.2863i 0.642947 + 0.371206i
\(255\) −56.3891 148.497i −0.221134 0.582341i
\(256\) 108.113 + 187.257i 0.422316 + 0.731473i
\(257\) −126.605 + 219.286i −0.492626 + 0.853253i −0.999964 0.00849432i \(-0.997296\pi\)
0.507338 + 0.861747i \(0.330629\pi\)
\(258\) 107.316 + 160.179i 0.415955 + 0.620850i
\(259\) −232.828 + 2.28472i −0.898949 + 0.00882132i
\(260\) 182.181 195.176i 0.700697 0.750676i
\(261\) 305.664 235.753i 1.17113 0.903270i
\(262\) −223.745 + 129.179i −0.853989 + 0.493051i
\(263\) 90.9512 + 157.532i 0.345822 + 0.598982i 0.985503 0.169659i \(-0.0542667\pi\)
−0.639681 + 0.768641i \(0.720933\pi\)
\(264\) −269.533 + 18.0024i −1.02096 + 0.0681910i
\(265\) −321.191 299.806i −1.21204 1.13134i
\(266\) −394.567 222.670i −1.48333 0.837105i
\(267\) 104.691 + 156.261i 0.392102 + 0.585247i
\(268\) 123.636 + 71.3814i 0.461329 + 0.266348i
\(269\) −224.807 + 129.792i −0.835714 + 0.482499i −0.855805 0.517299i \(-0.826938\pi\)
0.0200914 + 0.999798i \(0.493604\pi\)
\(270\) −433.152 11.8284i −1.60427 0.0438087i
\(271\) −17.7512 + 30.7460i −0.0655026 + 0.113454i −0.896917 0.442199i \(-0.854198\pi\)
0.831414 + 0.555653i \(0.187532\pi\)
\(272\) −15.7754 −0.0579977
\(273\) 13.5990 + 177.406i 0.0498131 + 0.649840i
\(274\) 38.2420 0.139569
\(275\) 133.801 273.659i 0.486549 0.995125i
\(276\) 518.211 + 254.753i 1.87758 + 0.923020i
\(277\) −310.160 + 179.071i −1.11971 + 0.646466i −0.941327 0.337495i \(-0.890421\pi\)
−0.178385 + 0.983961i \(0.557087\pi\)
\(278\) −202.431 + 350.620i −0.728167 + 1.26122i
\(279\) 41.8372 101.718i 0.149954 0.364581i
\(280\) −174.625 + 190.800i −0.623662 + 0.681430i
\(281\) 193.923i 0.690117i −0.938581 0.345058i \(-0.887859\pi\)
0.938581 0.345058i \(-0.112141\pi\)
\(282\) −15.2395 228.166i −0.0540407 0.809099i
\(283\) 111.089 64.1371i 0.392539 0.226633i −0.290720 0.956808i \(-0.593895\pi\)
0.683260 + 0.730175i \(0.260562\pi\)
\(284\) −13.3255 + 7.69345i −0.0469206 + 0.0270896i
\(285\) −191.197 + 234.376i −0.670866 + 0.822370i
\(286\) 331.364 1.15862
\(287\) −22.8129 38.6326i −0.0794873 0.134608i
\(288\) −117.567 + 285.838i −0.408219 + 0.992495i
\(289\) 88.4310 153.167i 0.305990 0.529990i
\(290\) −670.625 155.168i −2.31250 0.535062i
\(291\) −186.007 + 378.369i −0.639200 + 1.30024i
\(292\) −482.516 278.581i −1.65245 0.954043i
\(293\) 430.914 1.47070 0.735348 0.677689i \(-0.237019\pi\)
0.735348 + 0.677689i \(0.237019\pi\)
\(294\) −40.6766 470.073i −0.138356 1.59889i
\(295\) 165.424 177.223i 0.560760 0.600757i
\(296\) −212.877 122.905i −0.719180 0.415219i
\(297\) −217.837 246.536i −0.733457 0.830087i
\(298\) 320.634 185.118i 1.07595 0.621202i
\(299\) −224.098 129.383i −0.749492 0.432719i
\(300\) 289.483 + 373.662i 0.964944 + 1.24554i
\(301\) 71.2685 + 120.690i 0.236773 + 0.400964i
\(302\) −897.439 −2.97165
\(303\) −459.213 + 30.6713i −1.51555 + 0.101226i
\(304\) 15.0198 + 26.0151i 0.0494072 + 0.0855758i
\(305\) −23.6633 + 102.271i −0.0775847 + 0.335315i
\(306\) 186.826 + 242.228i 0.610542 + 0.791594i
\(307\) 204.653i 0.666622i 0.942817 + 0.333311i \(0.108166\pi\)
−0.942817 + 0.333311i \(0.891834\pi\)
\(308\) −537.521 + 5.27466i −1.74520 + 0.0171255i
\(309\) −237.169 353.996i −0.767538 1.14562i
\(310\) −187.583 + 57.2506i −0.605107 + 0.184679i
\(311\) 338.495 195.430i 1.08841 0.628393i 0.155257 0.987874i \(-0.450379\pi\)
0.933153 + 0.359481i \(0.117046\pi\)
\(312\) −82.8694 + 168.570i −0.265607 + 0.540289i
\(313\) 222.263 + 128.323i 0.710104 + 0.409979i 0.811100 0.584908i \(-0.198869\pi\)
−0.100996 + 0.994887i \(0.532203\pi\)
\(314\) 86.6992i 0.276112i
\(315\) −313.885 26.4855i −0.996459 0.0840810i
\(316\) 40.3692 0.127751
\(317\) 159.906 276.965i 0.504435 0.873707i −0.495552 0.868578i \(-0.665034\pi\)
0.999987 0.00512853i \(-0.00163247\pi\)
\(318\) 759.361 + 373.303i 2.38793 + 1.17391i
\(319\) −261.307 452.597i −0.819145 1.41880i
\(320\) 498.632 152.183i 1.55822 0.475572i
\(321\) 142.279 95.3239i 0.443238 0.296959i
\(322\) 597.607 + 337.253i 1.85592 + 1.04737i
\(323\) 213.534 0.661097
\(324\) 492.434 134.573i 1.51986 0.415350i
\(325\) −118.277 175.719i −0.363928 0.540675i
\(326\) 765.811 442.141i 2.34911 1.35626i
\(327\) 35.4414 + 530.630i 0.108384 + 1.62272i
\(328\) 47.3647i 0.144404i
\(329\) −1.63119 166.228i −0.00495801 0.505253i
\(330\) −93.8599 + 579.088i −0.284424 + 1.75481i
\(331\) −144.224 + 249.804i −0.435723 + 0.754694i −0.997354 0.0726932i \(-0.976841\pi\)
0.561631 + 0.827388i \(0.310174\pi\)
\(332\) 326.327 + 565.215i 0.982914 + 1.70246i
\(333\) −39.8122 296.705i −0.119556 0.891007i
\(334\) 13.1221 22.7281i 0.0392876 0.0680482i
\(335\) 77.2842 82.7967i 0.230699 0.247154i
\(336\) −13.5255 + 28.2090i −0.0402546 + 0.0839554i
\(337\) 380.518i 1.12913i −0.825387 0.564567i \(-0.809043\pi\)
0.825387 0.564567i \(-0.190957\pi\)
\(338\) −156.014 + 270.225i −0.461581 + 0.799481i
\(339\) 23.4251 + 11.5158i 0.0691006 + 0.0339700i
\(340\) 75.2225 325.106i 0.221243 0.956194i
\(341\) −128.956 74.4527i −0.378170 0.218336i
\(342\) 221.578 538.719i 0.647890 1.57520i
\(343\) −10.0957 342.851i −0.0294336 0.999567i
\(344\) 147.970i 0.430144i
\(345\) 289.585 354.982i 0.839375 1.02893i
\(346\) −136.449 236.336i −0.394361 0.683053i
\(347\) 85.3529 + 147.836i 0.245974 + 0.426039i 0.962405 0.271619i \(-0.0875590\pi\)
−0.716431 + 0.697658i \(0.754226\pi\)
\(348\) 809.140 54.0434i 2.32511 0.155297i
\(349\) 549.147 1.57349 0.786744 0.617280i \(-0.211765\pi\)
0.786744 + 0.617280i \(0.211765\pi\)
\(350\) 318.206 + 462.877i 0.909160 + 1.32250i
\(351\) −224.199 + 45.4653i −0.638745 + 0.129531i
\(352\) 362.380 + 209.220i 1.02949 + 0.594375i
\(353\) −153.623 266.082i −0.435192 0.753775i 0.562119 0.827056i \(-0.309986\pi\)
−0.997311 + 0.0732815i \(0.976653\pi\)
\(354\) −205.977 + 418.992i −0.581857 + 1.18359i
\(355\) 3.56340 + 11.6756i 0.0100378 + 0.0328890i
\(356\) 395.136i 1.10993i
\(357\) 125.584 + 183.525i 0.351776 + 0.514076i
\(358\) 397.457i 1.11022i
\(359\) 94.3043 + 54.4466i 0.262686 + 0.151662i 0.625559 0.780177i \(-0.284871\pi\)
−0.362873 + 0.931839i \(0.618204\pi\)
\(360\) −271.118 192.569i −0.753105 0.534915i
\(361\) −22.8069 39.5027i −0.0631770 0.109426i
\(362\) 271.545 470.330i 0.750125 1.29926i
\(363\) −68.4581 + 45.8653i −0.188590 + 0.126351i
\(364\) −183.708 + 325.526i −0.504691 + 0.894303i
\(365\) −301.618 + 323.131i −0.826349 + 0.885291i
\(366\) −13.4726 201.712i −0.0368103 0.551124i
\(367\) −99.8081 + 57.6242i −0.271957 + 0.157014i −0.629776 0.776776i \(-0.716854\pi\)
0.357820 + 0.933791i \(0.383520\pi\)
\(368\) −22.7488 39.4021i −0.0618174 0.107071i
\(369\) 45.6764 35.2294i 0.123784 0.0954727i
\(370\) −364.254 + 390.236i −0.984471 + 1.05469i
\(371\) 535.702 + 302.318i 1.44394 + 0.814874i
\(372\) 191.957 128.607i 0.516014 0.345718i
\(373\) 77.4504 + 44.7160i 0.207642 + 0.119882i 0.600215 0.799839i \(-0.295082\pi\)
−0.392573 + 0.919721i \(0.628415\pi\)
\(374\) 358.667 207.076i 0.959002 0.553680i
\(375\) 340.587 156.926i 0.908232 0.418468i
\(376\) 87.7484 151.985i 0.233373 0.404214i
\(377\) −363.402 −0.963932
\(378\) 593.325 126.394i 1.56964 0.334376i
\(379\) 221.030 0.583193 0.291596 0.956541i \(-0.405814\pi\)
0.291596 + 0.956541i \(0.405814\pi\)
\(380\) −607.750 + 185.486i −1.59934 + 0.488121i
\(381\) −77.7574 + 158.171i −0.204088 + 0.415148i
\(382\) −354.999 + 204.959i −0.929316 + 0.536541i
\(383\) −93.5845 + 162.093i −0.244346 + 0.423220i −0.961948 0.273234i \(-0.911907\pi\)
0.717602 + 0.696454i \(0.245240\pi\)
\(384\) −491.751 + 329.462i −1.28060 + 0.857974i
\(385\) −92.0535 + 416.412i −0.239100 + 1.08159i
\(386\) 396.719i 1.02777i
\(387\) −142.696 + 110.058i −0.368722 + 0.284389i
\(388\) −767.065 + 442.865i −1.97697 + 1.14140i
\(389\) −183.652 + 106.032i −0.472113 + 0.272575i −0.717124 0.696946i \(-0.754542\pi\)
0.245011 + 0.969520i \(0.421209\pi\)
\(390\) 316.090 + 257.858i 0.810488 + 0.661173i
\(391\) −323.416 −0.827152
\(392\) 174.865 317.087i 0.446084 0.808895i
\(393\) −134.407 200.614i −0.342002 0.510468i
\(394\) −36.2024 + 62.7044i −0.0918843 + 0.159148i
\(395\) 7.21963 31.2027i 0.0182776 0.0789942i
\(396\) −91.9131 684.993i −0.232104 1.72978i
\(397\) 514.877 + 297.264i 1.29692 + 0.748776i 0.979871 0.199634i \(-0.0639752\pi\)
0.317048 + 0.948410i \(0.397308\pi\)
\(398\) −110.798 −0.278386
\(399\) 183.081 381.835i 0.458849 0.956980i
\(400\) −2.56193 37.1546i −0.00640483 0.0928866i
\(401\) −400.309 231.118i −0.998277 0.576355i −0.0905387 0.995893i \(-0.528859\pi\)
−0.907738 + 0.419538i \(0.862192\pi\)
\(402\) −96.2302 + 195.748i −0.239379 + 0.486936i
\(403\) −89.6700 + 51.7710i −0.222506 + 0.128464i
\(404\) −837.322 483.428i −2.07258 1.19660i
\(405\) −15.9493 404.686i −0.0393811 0.999224i
\(406\) 963.632 9.45606i 2.37348 0.0232908i
\(407\) −405.297 −0.995815
\(408\) 15.6456 + 234.246i 0.0383470 + 0.574132i
\(409\) −105.366 182.500i −0.257620 0.446211i 0.707984 0.706228i \(-0.249605\pi\)
−0.965604 + 0.260018i \(0.916272\pi\)
\(410\) −100.214 23.1873i −0.244424 0.0565544i
\(411\) 2.38202 + 35.6637i 0.00579567 + 0.0867730i
\(412\) 895.148i 2.17269i
\(413\) −166.810 + 295.584i −0.403898 + 0.715700i
\(414\) −335.600 + 815.938i −0.810628 + 1.97087i
\(415\) 495.235 151.146i 1.19334 0.364207i
\(416\) 251.982 145.482i 0.605727 0.349716i
\(417\) −339.590 166.943i −0.814365 0.400344i
\(418\) −682.976 394.317i −1.63391 0.943341i
\(419\) 97.7368i 0.233262i −0.993175 0.116631i \(-0.962791\pi\)
0.993175 0.116631i \(-0.0372095\pi\)
\(420\) −516.850 413.251i −1.23059 0.983931i
\(421\) 576.919 1.37035 0.685177 0.728376i \(-0.259725\pi\)
0.685177 + 0.728376i \(0.259725\pi\)
\(422\) −122.086 + 211.459i −0.289303 + 0.501088i
\(423\) 211.834 28.4241i 0.500789 0.0671964i
\(424\) 324.693 + 562.385i 0.765786 + 1.32638i
\(425\) −237.832 116.284i −0.559606 0.273609i
\(426\) −13.0853 19.5309i −0.0307166 0.0458473i
\(427\) −1.44206 146.955i −0.00337719 0.344157i
\(428\) 359.781 0.840610
\(429\) 20.6401 + 309.024i 0.0481121 + 0.720336i
\(430\) 313.072 + 72.4382i 0.728076 + 0.168461i
\(431\) −146.182 + 84.3983i −0.339170 + 0.195820i −0.659905 0.751349i \(-0.729403\pi\)
0.320735 + 0.947169i \(0.396070\pi\)
\(432\) −38.1356 12.7870i −0.0882769 0.0295995i
\(433\) 328.967i 0.759739i 0.925040 + 0.379870i \(0.124031\pi\)
−0.925040 + 0.379870i \(0.875969\pi\)
\(434\) 236.430 139.614i 0.544771 0.321692i
\(435\) 102.935 635.077i 0.236632 1.45995i
\(436\) −558.612 + 967.544i −1.28122 + 2.21914i
\(437\) 307.926 + 533.344i 0.704637 + 1.22047i
\(438\) 375.558 763.948i 0.857439 1.74417i
\(439\) 110.035 190.586i 0.250649 0.434136i −0.713056 0.701107i \(-0.752689\pi\)
0.963705 + 0.266971i \(0.0860228\pi\)
\(440\) −307.210 + 329.123i −0.698205 + 0.748006i
\(441\) 435.848 67.2142i 0.988317 0.152413i
\(442\) 287.983i 0.651545i
\(443\) 98.0040 169.748i 0.221228 0.383178i −0.733953 0.679200i \(-0.762327\pi\)
0.955181 + 0.296022i \(0.0956602\pi\)
\(444\) 277.455 564.389i 0.624898 1.27115i
\(445\) 305.414 + 70.6662i 0.686324 + 0.158801i
\(446\) −869.319 501.902i −1.94915 1.12534i
\(447\) 192.609 + 287.487i 0.430893 + 0.643147i
\(448\) −628.477 + 371.121i −1.40285 + 0.828396i
\(449\) 434.253i 0.967156i 0.875301 + 0.483578i \(0.160663\pi\)
−0.875301 + 0.483578i \(0.839337\pi\)
\(450\) −540.162 + 479.356i −1.20036 + 1.06524i
\(451\) −39.0480 67.6331i −0.0865809 0.149963i
\(452\) 27.4181 + 47.4895i 0.0606594 + 0.105065i
\(453\) −55.8998 836.934i −0.123399 1.84754i
\(454\) −221.195 −0.487214
\(455\) 218.756 + 200.211i 0.480782 + 0.440024i
\(456\) 371.397 248.828i 0.814468 0.545675i
\(457\) −18.5054 10.6841i −0.0404932 0.0233787i 0.479617 0.877478i \(-0.340776\pi\)
−0.520110 + 0.854099i \(0.674109\pi\)
\(458\) −552.314 956.636i −1.20593 2.08872i
\(459\) −214.260 + 189.318i −0.466797 + 0.412458i
\(460\) 920.491 280.935i 2.00107 0.610728i
\(461\) 759.274i 1.64702i −0.567305 0.823508i \(-0.692014\pi\)
0.567305 0.823508i \(-0.307986\pi\)
\(462\) −62.7723 818.900i −0.135871 1.77251i
\(463\) 242.225i 0.523164i −0.965181 0.261582i \(-0.915756\pi\)
0.965181 0.261582i \(-0.0842443\pi\)
\(464\) −55.3349 31.9476i −0.119256 0.0688527i
\(465\) −65.0750 171.370i −0.139946 0.368538i
\(466\) −64.2280 111.246i −0.137828 0.238726i
\(467\) 207.939 360.160i 0.445265 0.771221i −0.552806 0.833310i \(-0.686443\pi\)
0.998071 + 0.0620891i \(0.0197763\pi\)
\(468\) −444.455 182.807i −0.949691 0.390613i
\(469\) −77.9317 + 138.093i −0.166166 + 0.294442i
\(470\) −278.610 260.061i −0.592788 0.553321i
\(471\) −80.8540 + 5.40033i −0.171665 + 0.0114657i
\(472\) −310.307 + 179.156i −0.657430 + 0.379568i
\(473\) 121.988 + 211.289i 0.257903 + 0.446700i
\(474\) 4.11045 + 61.5418i 0.00867183 + 0.129835i
\(475\) 34.6781 + 502.923i 0.0730066 + 1.05878i
\(476\) 4.58411 + 467.150i 0.00963049 + 0.981408i
\(477\) −300.836 + 731.417i −0.630684 + 1.53337i
\(478\) −949.921 548.437i −1.98728 1.14736i
\(479\) 45.1496 26.0672i 0.0942581 0.0544199i −0.452130 0.891952i \(-0.649336\pi\)
0.546388 + 0.837532i \(0.316002\pi\)
\(480\) 182.868 + 481.569i 0.380974 + 1.00327i
\(481\) −140.912 + 244.067i −0.292957 + 0.507417i
\(482\) 411.150 0.853009
\(483\) −277.292 + 578.323i −0.574104 + 1.19736i
\(484\) −173.110 −0.357664
\(485\) 205.123 + 672.092i 0.422934 + 1.38576i
\(486\) 255.294 + 737.000i 0.525296 + 1.51646i
\(487\) 728.584 420.648i 1.49607 0.863754i 0.496075 0.868280i \(-0.334774\pi\)
0.999990 + 0.00452596i \(0.00144066\pi\)
\(488\) 77.5745 134.363i 0.158964 0.275334i
\(489\) 460.033 + 686.641i 0.940764 + 1.40417i
\(490\) −585.284 525.206i −1.19446 1.07185i
\(491\) 842.285i 1.71545i 0.514110 + 0.857724i \(0.328122\pi\)
−0.514110 + 0.857724i \(0.671878\pi\)
\(492\) 120.912 8.07589i 0.245757 0.0164144i
\(493\) −393.344 + 227.097i −0.797859 + 0.460644i
\(494\) −474.911 + 274.190i −0.961358 + 0.555040i
\(495\) −545.892 51.4617i −1.10281 0.103963i
\(496\) −18.2053 −0.0367042
\(497\) −8.68990 14.7160i −0.0174847 0.0296096i
\(498\) −828.429 + 555.028i −1.66351 + 1.11451i
\(499\) −430.078 + 744.916i −0.861879 + 1.49282i 0.00823367 + 0.999966i \(0.497379\pi\)
−0.870113 + 0.492852i \(0.835954\pi\)
\(500\) 777.916 + 124.369i 1.55583 + 0.248738i
\(501\) 22.0131 + 10.8217i 0.0439384 + 0.0216002i
\(502\) 559.048 + 322.767i 1.11364 + 0.642961i
\(503\) 639.911 1.27219 0.636095 0.771611i \(-0.280549\pi\)
0.636095 + 0.771611i \(0.280549\pi\)
\(504\) 432.286 + 172.862i 0.857710 + 0.342980i
\(505\) −523.405 + 560.738i −1.03645 + 1.11037i
\(506\) 1034.43 + 597.227i 2.04432 + 1.18029i
\(507\) −261.724 128.664i −0.516221 0.253775i
\(508\) −320.659 + 185.133i −0.631219 + 0.364435i
\(509\) 627.238 + 362.136i 1.23230 + 0.711466i 0.967508 0.252841i \(-0.0813649\pi\)
0.264787 + 0.964307i \(0.414698\pi\)
\(510\) 503.275 + 81.5720i 0.986813 + 0.159945i
\(511\) 304.144 538.938i 0.595195 1.05467i
\(512\) 95.1944 0.185927
\(513\) 516.201 + 173.084i 1.00624 + 0.337395i
\(514\) −406.367 703.848i −0.790597 1.36935i
\(515\) −691.890 160.089i −1.34348 0.310851i
\(516\) −377.737 + 25.2295i −0.732048 + 0.0488943i
\(517\) 289.363i 0.559697i
\(518\) 367.306 650.859i 0.709085 1.25649i
\(519\) 211.903 141.970i 0.408292 0.273546i
\(520\) 91.3860 + 299.429i 0.175742 + 0.575825i
\(521\) −426.309 + 246.130i −0.818251 + 0.472418i −0.849813 0.527084i \(-0.823285\pi\)
0.0315618 + 0.999502i \(0.489952\pi\)
\(522\) 164.776 + 1228.01i 0.315662 + 2.35251i
\(523\) 51.6590 + 29.8254i 0.0987744 + 0.0570274i 0.548574 0.836102i \(-0.315171\pi\)
−0.449799 + 0.893130i \(0.648504\pi\)
\(524\) 507.291i 0.968113i
\(525\) −411.849 + 325.584i −0.784475 + 0.620161i
\(526\) −583.858 −1.11000
\(527\) −64.7055 + 112.073i −0.122781 + 0.212663i
\(528\) −24.0243 + 48.8693i −0.0455005 + 0.0925555i
\(529\) −201.882 349.669i −0.381629 0.661001i
\(530\) 1348.84 411.668i 2.54498 0.776732i
\(531\) −403.574 165.992i −0.760026 0.312603i
\(532\) 766.010 452.336i 1.43987 0.850255i
\(533\) −54.3044 −0.101884
\(534\) −602.375 + 40.2333i −1.12804 + 0.0753433i
\(535\) 64.3434 278.087i 0.120268 0.519789i
\(536\) −144.972 + 83.6995i −0.270470 + 0.156156i
\(537\) −370.661 + 24.7569i −0.690244 + 0.0461022i
\(538\) 833.196i 1.54869i
\(539\) −11.7165 596.936i −0.0217375 1.10749i
\(540\) 445.364 724.943i 0.824749 1.34249i
\(541\) 276.972 479.729i 0.511962 0.886745i −0.487941 0.872876i \(-0.662252\pi\)
0.999904 0.0138685i \(-0.00441463\pi\)
\(542\) −56.9766 98.6863i −0.105123 0.182078i
\(543\) 455.535 + 223.942i 0.838923 + 0.412416i
\(544\) 181.829 314.938i 0.334245 0.578929i
\(545\) 647.945 + 604.806i 1.18889 + 1.10974i
\(546\) −514.962 246.912i −0.943154 0.452220i
\(547\) 109.968i 0.201039i −0.994935 0.100520i \(-0.967949\pi\)
0.994935 0.100520i \(-0.0320505\pi\)
\(548\) −37.5444 + 65.0288i −0.0685117 + 0.118666i
\(549\) 187.273 25.1285i 0.341117 0.0457714i
\(550\) 545.960 + 811.114i 0.992655 + 1.47475i
\(551\) 749.010 + 432.441i 1.35936 + 0.784830i
\(552\) −562.514 + 376.872i −1.01905 + 0.682739i
\(553\) 0.439970 + 44.8357i 0.000795605 + 0.0810772i
\(554\) 1149.54i 2.07498i
\(555\) −386.615 315.389i −0.696603 0.568269i
\(556\) −397.476 688.448i −0.714885 1.23822i
\(557\) −226.708 392.669i −0.407015 0.704971i 0.587538 0.809196i \(-0.300097\pi\)
−0.994554 + 0.104225i \(0.966764\pi\)
\(558\) 215.603 + 279.539i 0.386386 + 0.500966i
\(559\) 169.650 0.303488
\(560\) 15.7087 + 49.7174i 0.0280513 + 0.0887810i
\(561\) 215.456 + 321.587i 0.384057 + 0.573239i
\(562\) 539.049 + 311.220i 0.959161 + 0.553772i
\(563\) −25.2929 43.8087i −0.0449253 0.0778129i 0.842688 0.538402i \(-0.180972\pi\)
−0.887614 + 0.460589i \(0.847638\pi\)
\(564\) 402.948 + 198.090i 0.714446 + 0.351223i
\(565\) 41.6097 12.6993i 0.0736455 0.0224767i
\(566\) 411.725i 0.727430i
\(567\) 154.830 + 545.451i 0.273068 + 0.961995i
\(568\) 18.0422i 0.0317644i
\(569\) −767.186 442.935i −1.34831 0.778445i −0.360297 0.932838i \(-0.617325\pi\)
−0.988010 + 0.154392i \(0.950658\pi\)
\(570\) −344.650 907.612i −0.604649 1.59230i
\(571\) −479.840 831.107i −0.840350 1.45553i −0.889599 0.456742i \(-0.849016\pi\)
0.0492497 0.998786i \(-0.484317\pi\)
\(572\) −325.320 + 563.470i −0.568741 + 0.985088i
\(573\) −213.253 318.298i −0.372169 0.555495i
\(574\) 143.999 1.41305i 0.250869 0.00246176i
\(575\) −52.5231 761.721i −0.0913446 1.32473i
\(576\) −573.115 743.068i −0.994991 1.29005i
\(577\) −265.694 + 153.399i −0.460476 + 0.265856i −0.712244 0.701932i \(-0.752321\pi\)
0.251769 + 0.967787i \(0.418988\pi\)
\(578\) 283.840 + 491.624i 0.491072 + 0.850561i
\(579\) 369.973 24.7109i 0.638986 0.0426786i
\(580\) 922.248 988.030i 1.59008 1.70350i
\(581\) −624.195 + 368.593i −1.07435 + 0.634411i
\(582\) −753.240 1124.28i −1.29423 1.93175i
\(583\) 927.274 + 535.362i 1.59052 + 0.918288i
\(584\) 565.783 326.655i 0.968806 0.559340i
\(585\) −220.784 + 310.841i −0.377409 + 0.531353i
\(586\) −691.559 + 1197.81i −1.18013 + 2.04405i
\(587\) 336.767 0.573708 0.286854 0.957974i \(-0.407390\pi\)
0.286854 + 0.957974i \(0.407390\pi\)
\(588\) 839.274 + 392.330i 1.42734 + 0.667228i
\(589\) 246.426 0.418380
\(590\) 227.146 + 744.250i 0.384993 + 1.26144i
\(591\) −60.7319 29.8559i −0.102761 0.0505176i
\(592\) −42.9132 + 24.7760i −0.0724885 + 0.0418513i
\(593\) −556.222 + 963.405i −0.937980 + 1.62463i −0.168748 + 0.985659i \(0.553972\pi\)
−0.769232 + 0.638970i \(0.779361\pi\)
\(594\) 1034.90 209.866i 1.74225 0.353310i
\(595\) 361.896 + 80.0021i 0.608229 + 0.134457i
\(596\) 726.966i 1.21974i
\(597\) −6.90138 103.328i −0.0115601 0.173078i
\(598\) 719.294 415.285i 1.20283 0.694456i
\(599\) 514.713 297.170i 0.859287 0.496110i −0.00448642 0.999990i \(-0.501428\pi\)
0.863773 + 0.503880i \(0.168095\pi\)
\(600\) −549.163 + 74.8907i −0.915271 + 0.124818i
\(601\) 434.293 0.722617 0.361309 0.932446i \(-0.382330\pi\)
0.361309 + 0.932446i \(0.382330\pi\)
\(602\) −449.859 + 4.41444i −0.747275 + 0.00733295i
\(603\) −188.545 77.5496i −0.312678 0.128606i
\(604\) 881.069 1526.06i 1.45872 2.52658i
\(605\) −30.9590 + 133.802i −0.0511718 + 0.221161i
\(606\) 651.716 1325.70i 1.07544 2.18762i
\(607\) −783.964 452.622i −1.29154 0.745670i −0.312612 0.949881i \(-0.601204\pi\)
−0.978927 + 0.204211i \(0.934537\pi\)
\(608\) −692.482 −1.13895
\(609\) 68.8414 + 898.076i 0.113040 + 1.47467i
\(610\) −246.307 229.908i −0.403782 0.376899i
\(611\) −174.253 100.605i −0.285193 0.164656i
\(612\) −595.315 + 79.8800i −0.972738 + 0.130523i
\(613\) −595.512 + 343.819i −0.971472 + 0.560879i −0.899685 0.436541i \(-0.856204\pi\)
−0.0717871 + 0.997420i \(0.522870\pi\)
\(614\) −568.875 328.440i −0.926507 0.534919i
\(615\) 15.3819 94.9016i 0.0250112 0.154312i
\(616\) 309.784 548.931i 0.502896 0.891122i
\(617\) 205.651 0.333308 0.166654 0.986015i \(-0.446704\pi\)
0.166654 + 0.986015i \(0.446704\pi\)
\(618\) 1364.63 91.1452i 2.20814 0.147484i
\(619\) 428.521 + 742.221i 0.692280 + 1.19906i 0.971089 + 0.238718i \(0.0767271\pi\)
−0.278809 + 0.960347i \(0.589940\pi\)
\(620\) 86.8093 375.183i 0.140015 0.605134i
\(621\) −781.832 262.151i −1.25899 0.422143i
\(622\) 1254.56i 2.01697i
\(623\) −438.855 + 4.30645i −0.704422 + 0.00691244i
\(624\) 21.0762 + 31.4580i 0.0337759 + 0.0504135i
\(625\) 235.252 579.035i 0.376403 0.926456i
\(626\) −713.402 + 411.883i −1.13962 + 0.657960i
\(627\) 325.191 661.492i 0.518645 1.05501i
\(628\) −147.428 85.1177i −0.234758 0.135538i
\(629\) 352.236i 0.559994i
\(630\) 577.364 830.001i 0.916451 1.31746i
\(631\) −464.352 −0.735899 −0.367949 0.929846i \(-0.619940\pi\)
−0.367949 + 0.929846i \(0.619940\pi\)
\(632\) −23.6678 + 40.9938i −0.0374491 + 0.0648637i
\(633\) −204.807 100.684i −0.323550 0.159058i
\(634\) 513.254 + 888.983i 0.809550 + 1.40218i
\(635\) 85.7485 + 280.958i 0.135037 + 0.442453i
\(636\) −1380.29 + 924.766i −2.17027 + 1.45403i
\(637\) −363.545 200.486i −0.570715 0.314734i
\(638\) 1677.45 2.62923
\(639\) 17.3991 13.4196i 0.0272287 0.0210010i
\(640\) −222.386 + 961.134i −0.347478 + 1.50177i
\(641\) 144.334 83.3312i 0.225170 0.130002i −0.383172 0.923677i \(-0.625168\pi\)
0.608342 + 0.793675i \(0.291835\pi\)
\(642\) 36.6334 + 548.477i 0.0570614 + 0.854325i
\(643\) 643.063i 1.00010i −0.865997 0.500049i \(-0.833315\pi\)
0.865997 0.500049i \(-0.166685\pi\)
\(644\) −1160.19 + 685.102i −1.80154 + 1.06382i
\(645\) −48.0538 + 296.477i −0.0745020 + 0.459655i
\(646\) −342.693 + 593.562i −0.530485 + 0.918827i
\(647\) 86.4616 + 149.756i 0.133635 + 0.231462i 0.925075 0.379784i \(-0.124002\pi\)
−0.791440 + 0.611246i \(0.790668\pi\)
\(648\) −152.050 + 578.952i −0.234646 + 0.893444i
\(649\) −295.397 + 511.642i −0.455157 + 0.788354i
\(650\) 678.266 46.7687i 1.04349 0.0719518i
\(651\) 144.928 + 211.794i 0.222624 + 0.325337i
\(652\) 1736.30i 2.66304i
\(653\) 514.097 890.443i 0.787285 1.36362i −0.140339 0.990104i \(-0.544819\pi\)
0.927624 0.373515i \(-0.121847\pi\)
\(654\) −1531.87 753.073i −2.34232 1.15149i
\(655\) −392.103 90.7241i −0.598630 0.138510i
\(656\) −8.26888 4.77404i −0.0126050 0.00727750i
\(657\) 735.836 + 302.653i 1.11999 + 0.460660i
\(658\) 464.684 + 262.240i 0.706206 + 0.398540i
\(659\) 494.948i 0.751059i −0.926810 0.375530i \(-0.877461\pi\)
0.926810 0.375530i \(-0.122539\pi\)
\(660\) −892.565 728.129i −1.35237 1.10323i
\(661\) 190.532 + 330.011i 0.288248 + 0.499261i 0.973392 0.229147i \(-0.0735938\pi\)
−0.685143 + 0.728408i \(0.740260\pi\)
\(662\) −462.921 801.803i −0.699276 1.21118i
\(663\) 268.567 17.9379i 0.405079 0.0270557i
\(664\) −765.282 −1.15253
\(665\) −212.632 672.971i −0.319747 1.01199i
\(666\) 888.646 + 365.505i 1.33430 + 0.548807i
\(667\) −1134.44 654.970i −1.70081 0.981964i
\(668\) 25.7654 + 44.6270i 0.0385710 + 0.0668069i
\(669\) 413.915 841.973i 0.618708 1.25855i
\(670\) 106.120 + 347.705i 0.158388 + 0.518962i
\(671\) 255.813i 0.381242i
\(672\) −407.264 595.164i −0.606048 0.885661i
\(673\) 617.578i 0.917649i 0.888527 + 0.458825i \(0.151729\pi\)
−0.888527 + 0.458825i \(0.848271\pi\)
\(674\) 1057.73 + 610.680i 1.56933 + 0.906053i
\(675\) −480.684 473.886i −0.712124 0.702053i
\(676\) −306.337 530.591i −0.453161 0.784897i
\(677\) −150.968 + 261.485i −0.222996 + 0.386241i −0.955716 0.294289i \(-0.904917\pi\)
0.732720 + 0.680530i \(0.238250\pi\)
\(678\) −69.6047 + 46.6336i −0.102662 + 0.0687811i
\(679\) −500.224 847.107i −0.736707 1.24758i
\(680\) 286.035 + 266.991i 0.420639 + 0.392634i
\(681\) −13.7778 206.282i −0.0202318 0.302911i
\(682\) 413.913 238.973i 0.606911 0.350400i
\(683\) 45.4093 + 78.6511i 0.0664850 + 0.115155i 0.897352 0.441316i \(-0.145488\pi\)
−0.830867 + 0.556471i \(0.812155\pi\)
\(684\) 698.532 + 905.677i 1.02125 + 1.32409i
\(685\) 43.5485 + 40.6491i 0.0635744 + 0.0593417i
\(686\) 969.229 + 522.167i 1.41287 + 0.761176i
\(687\) 857.737 574.664i 1.24853 0.836484i
\(688\) 25.8324 + 14.9143i 0.0375471 + 0.0216778i
\(689\) 644.784 372.266i 0.935827 0.540300i
\(690\) 522.003 + 1374.66i 0.756526 + 1.99226i
\(691\) −492.003 + 852.173i −0.712015 + 1.23325i 0.252084 + 0.967705i \(0.418884\pi\)
−0.964099 + 0.265541i \(0.914449\pi\)
\(692\) 535.839 0.774334
\(693\) 759.781 109.548i 1.09636 0.158078i
\(694\) −547.919 −0.789509
\(695\) −603.210 + 184.100i −0.867927 + 0.264892i
\(696\) −419.506 + 853.345i −0.602739 + 1.22607i
\(697\) −58.7787 + 33.9359i −0.0843310 + 0.0486886i
\(698\) −881.307 + 1526.47i −1.26262 + 2.18692i
\(699\) 99.7454 66.8271i 0.142697 0.0956039i
\(700\) −1099.50 + 86.6623i −1.57072 + 0.123803i
\(701\) 446.823i 0.637408i −0.947854 0.318704i \(-0.896752\pi\)
0.947854 0.318704i \(-0.103248\pi\)
\(702\) 233.429 696.174i 0.332521 0.991701i
\(703\) 580.870 335.366i 0.826274 0.477049i
\(704\) −1100.26 + 635.236i −1.56287 + 0.902323i
\(705\) 225.174 276.025i 0.319395 0.391525i
\(706\) 986.175 1.39685
\(707\) 527.790 935.234i 0.746521 1.32282i
\(708\) −510.258 761.605i −0.720703 1.07571i
\(709\) −574.318 + 994.748i −0.810040 + 1.40303i 0.102796 + 0.994702i \(0.467221\pi\)
−0.912836 + 0.408327i \(0.866112\pi\)
\(710\) −38.1735 8.83253i −0.0537655 0.0124402i
\(711\) −57.1366 + 7.66665i −0.0803609 + 0.0107829i
\(712\) −401.250 231.662i −0.563554 0.325368i
\(713\) −373.233 −0.523469
\(714\) −711.692 + 54.5543i −0.996767 + 0.0764065i
\(715\) 377.345 + 352.222i 0.527755 + 0.492618i
\(716\) −675.859 390.207i −0.943937 0.544982i
\(717\) 452.293 920.039i 0.630813 1.28318i
\(718\) −302.691 + 174.759i −0.421576 + 0.243397i
\(719\) 867.476 + 500.837i 1.20650 + 0.696575i 0.961994 0.273072i \(-0.0880397\pi\)
0.244510 + 0.969647i \(0.421373\pi\)
\(720\) −60.9455 + 27.9218i −0.0846465 + 0.0387803i
\(721\) 994.189 9.75591i 1.37890 0.0135311i
\(722\) 146.408 0.202781
\(723\) 25.6098 + 383.431i 0.0354216 + 0.530333i
\(724\) 533.184 + 923.502i 0.736442 + 1.27556i
\(725\) −598.747 889.536i −0.825857 1.22695i
\(726\) −17.6263 263.901i −0.0242786 0.363500i
\(727\) 160.419i 0.220659i 0.993895 + 0.110330i \(0.0351906\pi\)
−0.993895 + 0.110330i \(0.964809\pi\)
\(728\) −222.859 377.401i −0.306125 0.518408i
\(729\) −671.410 + 283.989i −0.921001 + 0.389559i
\(730\) −414.155 1356.99i −0.567335 1.85889i
\(731\) 183.628 106.018i 0.251201 0.145031i
\(732\) 356.228 + 175.123i 0.486651 + 0.239238i
\(733\) 336.580 + 194.325i 0.459181 + 0.265109i 0.711700 0.702484i \(-0.247926\pi\)
−0.252519 + 0.967592i \(0.581259\pi\)
\(734\) 369.916i 0.503973i
\(735\) 453.341 578.539i 0.616790 0.787127i
\(736\) 1048.83 1.42503
\(737\) −138.006 + 239.033i −0.187253 + 0.324332i
\(738\) 24.6230 + 183.506i 0.0333644 + 0.248653i
\(739\) 599.057 + 1037.60i 0.810631 + 1.40405i 0.912423 + 0.409249i \(0.134209\pi\)
−0.101792 + 0.994806i \(0.532457\pi\)
\(740\) −305.969 1002.52i −0.413471 1.35475i
\(741\) −285.285 425.814i −0.385001 0.574647i
\(742\) −1700.09 + 1003.92i −2.29122 + 1.35299i
\(743\) −592.907 −0.797990 −0.398995 0.916953i \(-0.630641\pi\)
−0.398995 + 0.916953i \(0.630641\pi\)
\(744\) 18.0555 + 270.328i 0.0242682 + 0.363344i
\(745\) 561.896 + 130.011i 0.754223 + 0.174511i
\(746\) −248.595 + 143.526i −0.333237 + 0.192394i
\(747\) −569.210 738.005i −0.761995 0.987959i
\(748\) 813.196i 1.08716i
\(749\) 3.92113 + 399.588i 0.00523515 + 0.533495i
\(750\) −110.389 + 1198.58i −0.147185 + 1.59810i
\(751\) −86.7806 + 150.308i −0.115553 + 0.200144i −0.918001 0.396578i \(-0.870197\pi\)
0.802447 + 0.596723i \(0.203531\pi\)
\(752\) −17.6889 30.6381i −0.0235225 0.0407421i
\(753\) −266.184 + 541.462i −0.353498 + 0.719073i
\(754\) 583.211 1010.15i 0.773490 1.33972i
\(755\) −1021.97 953.928i −1.35360 1.26348i
\(756\) −367.575 + 1133.01i −0.486210 + 1.49869i
\(757\) 560.146i 0.739956i −0.929041 0.369978i \(-0.879365\pi\)
0.929041 0.369978i \(-0.120635\pi\)
\(758\) −354.723 + 614.399i −0.467973 + 0.810553i
\(759\) −492.530 + 1001.89i −0.648920 + 1.32001i
\(760\) 167.958 725.901i 0.220997 0.955133i
\(761\) −450.545 260.123i −0.592044 0.341817i 0.173861 0.984770i \(-0.444376\pi\)
−0.765905 + 0.642953i \(0.777709\pi\)
\(762\) −314.880 469.986i −0.413228 0.616780i
\(763\) −1080.68 609.873i −1.41636 0.799309i
\(764\)