Properties

Label 105.3.o.b.74.4
Level 105
Weight 3
Character 105.74
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 74.4
Character \(\chi\) \(=\) 105.74
Dual form 105.3.o.b.44.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.60486 - 2.77971i) q^{2} +(0.199928 + 2.99333i) q^{3} +(-3.15118 + 5.45800i) q^{4} +(1.12712 - 4.87130i) q^{5} +(7.99972 - 5.35963i) q^{6} +(-6.02754 - 3.55932i) q^{7} +7.38994 q^{8} +(-8.92006 + 1.19690i) q^{9} +O(q^{10})\) \(q+(-1.60486 - 2.77971i) q^{2} +(0.199928 + 2.99333i) q^{3} +(-3.15118 + 5.45800i) q^{4} +(1.12712 - 4.87130i) q^{5} +(7.99972 - 5.35963i) q^{6} +(-6.02754 - 3.55932i) q^{7} +7.38994 q^{8} +(-8.92006 + 1.19690i) q^{9} +(-15.3497 + 4.68473i) q^{10} +(-10.5523 - 6.09236i) q^{11} +(-16.9676 - 8.34131i) 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} +(17.6425 + 22.8743i) q^{18} +(-10.0823 - 17.4631i) q^{19} +(23.0359 + 21.5022i) q^{20} +(9.44914 - 18.7540i) q^{21} +39.1096i q^{22} +(15.2706 + 26.4494i) q^{23} +(1.47746 + 22.1205i) q^{24} +(-22.4592 - 10.9810i) q^{25} +(-23.5516 + 13.5975i) q^{26} +(-5.36609 - 26.4614i) q^{27} +(38.4206 - 21.6823i) q^{28} -42.8910i q^{29} +(-17.0918 - 45.0100i) q^{30} +(-6.11033 + 10.5834i) q^{31} +(17.1707 - 29.7405i) q^{32} +(16.1268 - 32.8045i) q^{33} +33.9895 q^{34} +(-24.1323 + 25.3502i) q^{35} +(21.5760 - 52.4573i) q^{36} +(28.8063 - 16.6313i) q^{37} +(-32.3616 + 56.0519i) q^{38} +(25.3616 - 1.69393i) q^{39} +(8.32932 - 35.9987i) q^{40} -6.40934i q^{41} +(-67.2953 + 3.83186i) q^{42} +20.0231i q^{43} +(66.5042 - 38.3962i) q^{44} +(-4.22346 + 44.8014i) 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} +(-28.5098 - 14.0155i) q^{51} +(46.2440 + 26.6990i) q^{52} +(43.9372 - 76.1014i) q^{53} +(-64.9430 + 57.3831i) 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} +(-59.7575 + 73.2528i) q^{60} +(10.4973 + 18.1819i) q^{61} +39.2250 q^{62} +(58.0262 + 24.5349i) q^{63} -104.268 q^{64} +(-41.2731 - 9.54971i) q^{65} +(-117.068 + 7.81912i) q^{66} +(19.6174 + 11.3261i) q^{67} +(-33.3695 - 57.7976i) q^{68} +(-76.1189 + 50.9979i) q^{69} +(109.195 + 26.3969i) q^{70} -2.44145i q^{71} +(-65.9187 + 8.84504i) q^{72} +(-76.5611 - 44.2026i) q^{73} +(-92.4605 - 53.3821i) q^{74} +(28.3797 - 69.4233i) q^{75} +127.085 q^{76} +(41.9197 + 74.2809i) q^{77} +(-45.4106 - 67.7793i) q^{78} +(-3.20270 - 5.54725i) q^{79} +(7.12416 - 2.17430i) q^{80} +(78.1349 - 21.3529i) q^{81} +(-17.8161 + 10.2861i) q^{82} -103.557 q^{83} +(72.5836 + 110.671i) q^{84} +(38.7059 + 36.1289i) q^{85} +(55.6583 - 32.1344i) q^{86} +(128.387 - 8.57511i) 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} +(-32.9013 - 16.1743i) q^{93} +(38.1124 - 66.0126i) q^{94} +(-96.4321 + 29.4312i) q^{95} +(92.4560 + 45.4516i) 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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 −0.918011 0.396555i \(-0.870206\pi\)
0.115579 0.993298i \(-0.463128\pi\)
\(3\) 0.199928 + 2.99333i 0.0666427 + 0.997777i
\(4\) −3.15118 + 5.45800i −0.787795 + 1.36450i
\(5\) 1.12712 4.87130i 0.225423 0.974261i
\(6\) 7.99972 5.35963i 1.33329 0.893272i
\(7\) −6.02754 3.55932i −0.861077 0.508474i
\(8\) 7.38994 0.923743
\(9\) −8.92006 + 1.19690i −0.991117 + 0.132989i
\(10\) −15.3497 + 4.68473i −1.53497 + 0.468473i
\(11\) −10.5523 6.09236i −0.959298 0.553851i −0.0633411 0.997992i \(-0.520176\pi\)
−0.895957 + 0.444141i \(0.853509\pi\)
\(12\) −16.9676 8.34131i −1.41397 0.695109i
\(13\) 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 −0.978678 0.205401i \(-0.934150\pi\)
0.667221 + 0.744859i \(0.267484\pi\)
\(18\) 17.6425 + 22.8743i 0.980140 + 1.27079i
\(19\) −10.0823 17.4631i −0.530649 0.919111i −0.999360 0.0357599i \(-0.988615\pi\)
0.468711 0.883351i \(-0.344718\pi\)
\(20\) 23.0359 + 21.5022i 1.15179 + 1.07511i
\(21\) 9.44914 18.7540i 0.449959 0.893049i
\(22\) 39.1096i 1.77771i
\(23\) 15.2706 + 26.4494i 0.663939 + 1.14998i 0.979572 + 0.201094i \(0.0644497\pi\)
−0.315633 + 0.948881i \(0.602217\pi\)
\(24\) 1.47746 + 22.1205i 0.0615607 + 0.921690i
\(25\) −22.4592 10.9810i −0.898369 0.439242i
\(26\) −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 \(-0.264938\pi\)
\(30\) −17.0918 45.0100i −0.569726 1.50033i
\(31\) −6.11033 + 10.5834i −0.197107 + 0.341400i −0.947589 0.319491i \(-0.896488\pi\)
0.750482 + 0.660891i \(0.229821\pi\)
\(32\) 17.1707 29.7405i 0.536584 0.929390i
\(33\) 16.1268 32.8045i 0.488689 0.994076i
\(34\) 33.9895 0.999691
\(35\) −24.1323 + 25.3502i −0.689493 + 0.724292i
\(36\) 21.5760 52.4573i 0.599333 1.45715i
\(37\) 28.8063 16.6313i 0.778550 0.449496i −0.0573663 0.998353i \(-0.518270\pi\)
0.835916 + 0.548857i \(0.184937\pi\)
\(38\) −32.3616 + 56.0519i −0.851620 + 1.47505i
\(39\) 25.3616 1.69393i 0.650297 0.0434341i
\(40\) 8.32932 35.9987i 0.208233 0.899967i
\(41\) 6.40934i 0.156325i −0.996941 0.0781627i \(-0.975095\pi\)
0.996941 0.0781627i \(-0.0249054\pi\)
\(42\) −67.2953 + 3.83186i −1.60227 + 0.0912347i
\(43\) 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
\(45\) −4.22346 + 44.8014i −0.0938546 + 0.995586i
\(46\) 49.0144 84.8955i 1.06553 1.84555i
\(47\) 11.8740 + 20.5664i 0.252639 + 0.437583i 0.964251 0.264989i \(-0.0853683\pi\)
−0.711613 + 0.702572i \(0.752035\pi\)
\(48\) −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
\(51\) −28.5098 14.0155i −0.559016 0.274813i
\(52\) 46.2440 + 26.6990i 0.889308 + 0.513442i
\(53\) 43.9372 76.1014i 0.829003 1.43588i −0.0698177 0.997560i \(-0.522242\pi\)
0.898821 0.438316i \(-0.144425\pi\)
\(54\) −64.9430 + 57.3831i −1.20265 + 1.06265i
\(55\) −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 \(-0.198547\pi\)
−0.0999885 + 0.994989i \(0.531881\pi\)
\(60\) −59.7575 + 73.2528i −0.995959 + 1.22088i
\(61\) 10.4973 + 18.1819i 0.172087 + 0.298063i 0.939149 0.343509i \(-0.111616\pi\)
−0.767062 + 0.641573i \(0.778282\pi\)
\(62\) 39.2250 0.632662
\(63\) 58.0262 + 24.5349i 0.921050 + 0.389443i
\(64\) −104.268 −1.62918
\(65\) −41.2731 9.54971i −0.634971 0.146919i
\(66\) −117.068 + 7.81912i −1.77376 + 0.118471i
\(67\) 19.6174 + 11.3261i 0.292798 + 0.169047i 0.639203 0.769038i \(-0.279264\pi\)
−0.346405 + 0.938085i \(0.612598\pi\)
\(68\) −33.3695 57.7976i −0.490728 0.849965i
\(69\) −76.1189 + 50.9979i −1.10317 + 0.739100i
\(70\) 109.195 + 26.3969i 1.55993 + 0.377098i
\(71\) 2.44145i 0.0343867i −0.999852 0.0171933i \(-0.994527\pi\)
0.999852 0.0171933i \(-0.00547308\pi\)
\(72\) −65.9187 + 8.84504i −0.915538 + 0.122848i
\(73\) −76.5611 44.2026i −1.04878 0.605515i −0.126474 0.991970i \(-0.540366\pi\)
−0.922308 + 0.386455i \(0.873699\pi\)
\(74\) −92.4605 53.3821i −1.24947 0.721380i
\(75\) 28.3797 69.4233i 0.378396 0.925644i
\(76\) 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 0.845043 0.534698i \(-0.179575\pi\)
−0.885584 + 0.464480i \(0.846241\pi\)
\(80\) 7.12416 2.17430i 0.0890520 0.0271788i
\(81\) 78.1349 21.3529i 0.964628 0.263616i
\(82\) −17.8161 + 10.2861i −0.217269 + 0.125440i
\(83\) −103.557 −1.24768 −0.623839 0.781553i \(-0.714428\pi\)
−0.623839 + 0.781553i \(0.714428\pi\)
\(84\) 72.5836 + 110.671i 0.864091 + 1.31751i
\(85\) 38.7059 + 36.1289i 0.455364 + 0.425046i
\(86\) 55.6583 32.1344i 0.647190 0.373655i
\(87\) 128.387 8.57511i 1.47571 0.0985645i
\(88\) −77.9808 45.0222i −0.886145 0.511616i
\(89\) 54.2968 31.3483i 0.610077 0.352228i −0.162919 0.986639i \(-0.552091\pi\)
0.772995 + 0.634412i \(0.218758\pi\)
\(90\) 131.313 60.1601i 1.45903 0.668446i
\(91\) −30.1570 + 51.0696i −0.331396 + 0.561204i
\(92\) −192.481 −2.09219
\(93\) −32.9013 16.1743i −0.353777 0.173917i
\(94\) 38.1124 66.0126i 0.405451 0.702262i
\(95\) −96.4321 + 29.4312i −1.01507 + 0.309802i
\(96\) 92.4560 + 45.4516i 0.963084 + 0.473454i
\(97\) 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
\(100\) 130.708 87.9792i 1.30708 0.879792i
\(101\) −132.859 76.7059i −1.31543 0.759465i −0.332442 0.943124i \(-0.607872\pi\)
−0.982990 + 0.183659i \(0.941206\pi\)
\(102\) 6.79546 + 101.742i 0.0666221 + 0.997469i
\(103\) −123.005 + 71.0169i −1.19422 + 0.689485i −0.959261 0.282520i \(-0.908830\pi\)
−0.234961 + 0.972005i \(0.575496\pi\)
\(104\) 62.6128i 0.602046i
\(105\) −80.7064 67.1676i −0.768632 0.639691i
\(106\) −282.053 −2.66088
\(107\) −28.5434 49.4386i −0.266761 0.462043i 0.701263 0.712903i \(-0.252620\pi\)
−0.968023 + 0.250860i \(0.919287\pi\)
\(108\) 161.336 + 54.0964i 1.49385 + 0.500893i
\(109\) −88.6354 + 153.521i −0.813169 + 1.40845i 0.0974665 + 0.995239i \(0.468926\pi\)
−0.910635 + 0.413211i \(0.864407\pi\)
\(110\) 190.515 + 44.0811i 1.73195 + 0.400737i
\(111\) 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 \(0.512258\pi\)
\(114\) −174.252 85.6625i −1.52852 0.751425i
\(115\) 146.055 44.5761i 1.27004 0.387618i
\(116\) 234.099 + 135.157i 2.01809 + 1.16515i
\(117\) 10.1410 + 75.5770i 0.0866751 + 0.645957i
\(118\) 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
\(123\) 19.1853 1.28141i 0.155978 0.0104179i
\(124\) −38.5095 66.7004i −0.310560 0.537907i
\(125\) −78.8061 + 97.0288i −0.630449 + 0.776231i
\(126\) −24.9242 200.671i −0.197811 1.59263i
\(127\) 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
\(129\) −59.9358 + 4.00318i −0.464618 + 0.0310324i
\(130\) 39.6923 + 130.053i 0.305326 + 1.00041i
\(131\) −69.7084 + 40.2462i −0.532125 + 0.307223i −0.741881 0.670531i \(-0.766066\pi\)
0.209756 + 0.977754i \(0.432733\pi\)
\(132\) 128.229 + 191.393i 0.971430 + 1.44994i
\(133\) −1.38505 + 141.146i −0.0104139 + 1.06125i
\(134\) 72.7076i 0.542594i
\(135\) −134.950 3.68516i −0.999627 0.0272975i
\(136\) −39.1280 + 67.7717i −0.287706 + 0.498321i
\(137\) −5.95720 + 10.3182i −0.0434832 + 0.0753151i −0.886948 0.461870i \(-0.847179\pi\)
0.843465 + 0.537185i \(0.180512\pi\)
\(138\) 263.920 + 129.743i 1.91246 + 0.940170i
\(139\) 126.136 0.907450 0.453725 0.891142i \(-0.350095\pi\)
0.453725 + 0.891142i \(0.350095\pi\)
\(140\) −62.3166 211.597i −0.445119 1.51141i
\(141\) −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
\(144\) −8.18833 10.6165i −0.0568634 0.0737258i
\(145\) −208.935 48.3431i −1.44093 0.333400i
\(146\) 283.757i 1.94354i
\(147\) −123.707 + 79.4083i −0.841542 + 0.540192i
\(148\) 209.633i 1.41644i
\(149\) 99.8945 57.6741i 0.670433 0.387074i −0.125808 0.992055i \(-0.540152\pi\)
0.796241 + 0.604980i \(0.206819\pi\)
\(150\) −238.522 + 32.5278i −1.59015 + 0.216852i
\(151\) 139.800 242.140i 0.925827 1.60358i 0.135600 0.990764i \(-0.456704\pi\)
0.790226 0.612815i \(-0.209963\pi\)
\(152\) −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
\(156\) −70.6734 + 143.762i −0.453035 + 0.921548i
\(157\) −23.3925 13.5057i −0.148997 0.0860235i 0.423648 0.905827i \(-0.360749\pi\)
−0.572645 + 0.819803i \(0.694083\pi\)
\(158\) −10.2798 + 17.8052i −0.0650621 + 0.112691i
\(159\) 236.581 + 116.304i 1.48793 + 0.731470i
\(160\) −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 \(-0.346211\pi\)
0.999182 + 0.0404450i \(0.0128776\pi\)
\(164\) 34.9822 + 20.1970i 0.213306 + 0.123152i
\(165\) −141.624 115.533i −0.858327 0.700199i
\(166\) 166.195 + 287.859i 1.00118 + 1.73409i
\(167\) −8.17643 −0.0489607 −0.0244803 0.999700i \(-0.507793\pi\)
−0.0244803 + 0.999700i \(0.507793\pi\)
\(168\) 69.8286 138.591i 0.415646 0.824948i
\(169\) 97.2133 0.575227
\(170\) 38.3101 165.573i 0.225353 0.973960i
\(171\) 110.837 + 143.704i 0.648167 + 0.840377i
\(172\) −109.286 63.0964i −0.635384 0.366839i
\(173\) −42.5110 73.6312i −0.245728 0.425614i 0.716608 0.697476i \(-0.245694\pi\)
−0.962336 + 0.271862i \(0.912360\pi\)
\(174\) −229.880 343.116i −1.32115 1.97193i
\(175\) 96.2889 + 146.128i 0.550222 + 0.835018i
\(176\) 18.1518i 0.103135i
\(177\) −64.1728 + 130.538i −0.362558 + 0.737504i
\(178\) −174.278 100.619i −0.979090 0.565278i
\(179\) −107.239 61.9145i −0.599101 0.345891i 0.169587 0.985515i \(-0.445757\pi\)
−0.768688 + 0.639624i \(0.779090\pi\)
\(180\) −231.217 164.229i −1.28454 0.912382i
\(181\) −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
\(185\) −48.5483 159.070i −0.262423 0.859837i
\(186\) 7.84218 + 117.413i 0.0421623 + 0.631255i
\(187\) 111.744 64.5152i 0.597559 0.345001i
\(188\) −149.669 −0.796110
\(189\) −61.8401 + 178.597i −0.327196 + 0.944956i
\(190\) 236.570 + 220.820i 1.24511 + 1.16221i
\(191\) −110.601 + 63.8554i −0.579062 + 0.334322i −0.760761 0.649033i \(-0.775174\pi\)
0.181699 + 0.983354i \(0.441841\pi\)
\(192\) −20.8460 312.107i −0.108573 1.62556i
\(193\) 107.040 + 61.7995i 0.554611 + 0.320205i 0.750980 0.660325i \(-0.229582\pi\)
−0.196369 + 0.980530i \(0.562915\pi\)
\(194\) −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 \(0.481766\pi\)
\(198\) −46.8104 348.860i −0.236416 1.76192i
\(199\) 17.2597 29.8946i 0.0867319 0.150224i −0.819396 0.573228i \(-0.805691\pi\)
0.906128 + 0.423004i \(0.139024\pi\)
\(200\) −165.972 81.1493i −0.829862 0.405747i
\(201\) −29.9808 + 60.9859i −0.149158 + 0.303412i
\(202\) 492.411i 2.43768i
\(203\) −152.663 + 258.527i −0.752032 + 1.27353i
\(204\) 166.336 111.441i 0.815372 0.546281i
\(205\) −31.2218 7.22406i −0.152302 0.0352393i
\(206\) 394.812 + 227.945i 1.91657 + 1.10653i
\(207\) −167.872 217.653i −0.810975 1.05146i
\(208\) 10.9309 6.31095i 0.0525524 0.0303411i
\(209\) 245.701i 1.17560i
\(210\) −57.1834 + 332.135i −0.272302 + 1.58159i
\(211\) 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
\(213\) 7.30808 0.488115i 0.0343102 0.00229162i
\(214\) −91.6165 + 158.684i −0.428114 + 0.741516i
\(215\) 97.5386 + 22.5683i 0.453668 + 0.104969i
\(216\) −39.6551 195.548i −0.183589 0.905316i
\(217\) 74.5000 42.0433i 0.343318 0.193748i
\(218\) 568.991 2.61005
\(219\) 117.006 238.010i 0.534275 1.08680i
\(220\) −112.082 367.239i −0.509463 1.66927i
\(221\) 77.7014 + 44.8609i 0.351590 + 0.202991i
\(222\) 141.305 287.438i 0.636508 1.29476i
\(223\) 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 −0.780094 0.625663i \(-0.784829\pi\)
0.931887 + 0.362750i \(0.118162\pi\)
\(228\) 25.4079 + 380.407i 0.111438 + 1.66845i
\(229\) −172.075 298.043i −0.751419 1.30150i −0.947135 0.320835i \(-0.896036\pi\)
0.195716 0.980661i \(-0.437297\pi\)
\(230\) −358.307 334.451i −1.55786 1.45414i
\(231\) −213.966 + 140.330i −0.926261 + 0.607490i
\(232\) 316.962i 1.36622i
\(233\) −20.0104 34.6590i −0.0858816 0.148751i 0.819885 0.572528i \(-0.194037\pi\)
−0.905767 + 0.423777i \(0.860704\pi\)
\(234\) 193.807 149.480i 0.828235 0.638802i
\(235\) 113.569 34.6613i 0.483271 0.147495i
\(236\) −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 \(0.746461\pi\)
\(240\) 7.93272 + 20.8903i 0.0330530 + 0.0870427i
\(241\) −64.0475 + 110.934i −0.265757 + 0.460305i −0.967762 0.251867i \(-0.918955\pi\)
0.702004 + 0.712173i \(0.252289\pi\)
\(242\) 44.0815 76.3514i 0.182155 0.315502i
\(243\) 79.5375 + 229.614i 0.327315 + 0.944915i
\(244\) −132.316 −0.542277
\(245\) 235.688 66.9053i 0.961991 0.273083i
\(246\) −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
\(249\) −20.7040 309.981i −0.0831486 1.24490i
\(250\) 396.185 + 63.3399i 1.58474 + 0.253360i
\(251\) 201.118i 0.801266i −0.916239 0.400633i \(-0.868790\pi\)
0.916239 0.400633i \(-0.131210\pi\)
\(252\) −316.763 + 239.393i −1.25699 + 0.949972i
\(253\) 372.136i 1.47089i
\(254\) −163.309 + 94.2863i −0.642947 + 0.371206i
\(255\) −100.407 + 123.083i −0.393755 + 0.482678i
\(256\) 108.113 187.257i 0.422316 0.731473i
\(257\) −126.605 219.286i −0.492626 0.853253i 0.507338 0.861747i \(-0.330629\pi\)
−0.999964 + 0.00849432i \(0.997296\pi\)
\(258\) 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
\(261\) 51.3363 + 382.590i 0.196691 + 1.46586i
\(262\) 223.745 + 129.179i 0.853989 + 0.493051i
\(263\) 90.9512 157.532i 0.345822 0.598982i −0.639681 0.768641i \(-0.720933\pi\)
0.985503 + 0.169659i \(0.0542667\pi\)
\(264\) 119.176 242.423i 0.451424 0.918270i
\(265\) −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 \(-0.173062\pi\)
−0.0200914 + 0.999798i \(0.506396\pi\)
\(270\) 206.332 + 381.035i 0.764194 + 1.41124i
\(271\) −17.7512 30.7460i −0.0655026 0.113454i 0.831414 0.555653i \(-0.187532\pi\)
−0.896917 + 0.442199i \(0.854198\pi\)
\(272\) −15.7754 −0.0579977
\(273\) −158.897 80.0597i −0.582041 0.293259i
\(274\) 38.2420 0.139569
\(275\) 170.095 + 252.705i 0.618529 + 0.918926i
\(276\) −38.4824 576.161i −0.139429 2.08754i
\(277\) 310.160 + 179.071i 1.11971 + 0.646466i 0.941327 0.337495i \(-0.109579\pi\)
0.178385 + 0.983961i \(0.442913\pi\)
\(278\) −202.431 350.620i −0.728167 1.26122i
\(279\) 41.8372 101.718i 0.149954 0.364581i
\(280\) −178.336 + 187.337i −0.636914 + 0.669060i
\(281\) 193.923i 0.690117i −0.938581 0.345058i \(-0.887859\pi\)
0.938581 0.345058i \(-0.112141\pi\)
\(282\) 205.217 + 100.885i 0.727721 + 0.357749i
\(283\) −111.089 64.1371i −0.392539 0.226633i 0.290720 0.956808i \(-0.406105\pi\)
−0.683260 + 0.730175i \(0.739438\pi\)
\(284\) 13.3255 + 7.69345i 0.0469206 + 0.0270896i
\(285\) −107.377 282.769i −0.376760 0.992172i
\(286\) 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
\(290\) 200.933 + 658.362i 0.692872 + 2.27021i
\(291\) 420.681 28.0978i 1.44564 0.0965560i
\(292\) 482.516 278.581i 1.65245 0.954043i
\(293\) 430.914 1.47070 0.735348 0.677689i \(-0.237019\pi\)
0.735348 + 0.677689i \(0.237019\pi\)
\(294\) 419.264 + 216.429i 1.42607 + 0.736152i
\(295\) 165.424 177.223i 0.560760 0.600757i
\(296\) 212.877 122.905i 0.719180 0.415219i
\(297\) −104.588 + 311.920i −0.352147 + 1.05024i
\(298\) −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
\(303\) 203.044 413.025i 0.670112 1.36312i
\(304\) 15.0198 26.0151i 0.0494072 0.0855758i
\(305\) 100.401 30.6425i 0.329184 0.100467i
\(306\) −303.188 + 40.6821i −0.990811 + 0.132948i
\(307\) 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
\(310\) 44.2111 191.077i 0.142616 0.616377i
\(311\) −338.495 195.430i −1.08841 0.628393i −0.155257 0.987874i \(-0.549621\pi\)
−0.933153 + 0.359481i \(0.882954\pi\)
\(312\) 187.421 12.5181i 0.600708 0.0401220i
\(313\) −222.263 + 128.323i −0.710104 + 0.409979i −0.811100 0.584908i \(-0.801131\pi\)
0.100996 + 0.994887i \(0.467797\pi\)
\(314\) 86.6992i 0.276112i
\(315\) 184.919 255.010i 0.587045 0.809554i
\(316\) 40.3692 0.127751
\(317\) 159.906 + 276.965i 0.504435 + 0.873707i 0.999987 + 0.00512853i \(0.00163247\pi\)
−0.495552 + 0.868578i \(0.665034\pi\)
\(318\) −56.3903 844.277i −0.177328 2.65496i
\(319\) −261.307 + 452.597i −0.819145 + 1.41880i
\(320\) −117.522 + 507.919i −0.367255 + 1.58725i
\(321\) 142.279 95.3239i 0.443238 0.296959i
\(322\) −597.607 + 337.253i −1.85592 + 1.04737i
\(323\) 213.534 0.661097
\(324\) −129.673 + 493.747i −0.400225 + 1.52391i
\(325\) −93.0391 + 190.290i −0.286274 + 0.585509i
\(326\) −765.811 442.141i −2.34911 1.35626i
\(327\) −477.260 234.622i −1.45951 0.717498i
\(328\) 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 0.561631 0.827388i \(-0.310174\pi\)
−0.997354 + 0.0726932i \(0.976841\pi\)
\(332\) 326.327 565.215i 0.982914 1.70246i
\(333\) −237.048 + 182.831i −0.711856 + 0.549042i
\(334\) 13.1221 + 22.7281i 0.0392876 + 0.0680482i
\(335\) 77.2842 82.7967i 0.230699 0.247154i
\(336\) 31.2334 1.77846i 0.0929566 0.00529303i
\(337\) 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
\(339\) −1.73955 26.0446i −0.00513142 0.0768279i
\(340\) −319.161 + 97.4083i −0.938709 + 0.286495i
\(341\) 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
\(345\) 162.632 + 428.279i 0.471396 + 1.24139i
\(346\) −136.449 + 236.336i −0.394361 + 0.683053i
\(347\) 85.3529 147.836i 0.245974 0.426039i −0.716431 0.697658i \(-0.754226\pi\)
0.962405 + 0.271619i \(0.0875590\pi\)
\(348\) −357.767 + 727.757i −1.02807 + 2.09126i
\(349\) 549.147 1.57349 0.786744 0.617280i \(-0.211765\pi\)
0.786744 + 0.617280i \(0.211765\pi\)
\(350\) 251.663 502.171i 0.719037 1.43477i
\(351\) −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 −0.997311 0.0732815i \(-0.976653\pi\)
0.562119 + 0.827056i \(0.309986\pi\)
\(354\) 465.847 31.1145i 1.31595 0.0878939i
\(355\) −11.8931 2.75180i −0.0335016 0.00775155i
\(356\) 395.136i 1.10993i
\(357\) 121.959 + 185.954i 0.341620 + 0.520880i
\(358\) 397.457i 1.11022i
\(359\) −94.3043 + 54.4466i −0.262686 + 0.151662i −0.625559 0.780177i \(-0.715129\pi\)
0.362873 + 0.931839i \(0.381796\pi\)
\(360\) −31.2111 + 331.080i −0.0866976 + 0.919666i
\(361\) −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
\(366\) 181.424 + 89.1882i 0.495693 + 0.243684i
\(367\) 99.8081 + 57.6242i 0.271957 + 0.157014i 0.629776 0.776776i \(-0.283146\pi\)
−0.357820 + 0.933791i \(0.616480\pi\)
\(368\) −22.7488 + 39.4021i −0.0618174 + 0.107071i
\(369\) 7.67135 + 57.1717i 0.0207896 + 0.154937i
\(370\) −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 \(-0.704918\pi\)
0.392573 + 0.919721i \(0.371585\pi\)
\(374\) −358.667 207.076i −0.959002 0.553680i
\(375\) −306.195 216.494i −0.816520 0.577318i
\(376\) 87.7484 + 151.985i 0.233373 + 0.404214i
\(377\) −363.402 −0.963932
\(378\) 595.692 114.726i 1.57590 0.303509i
\(379\) 221.030 0.583193 0.291596 0.956541i \(-0.405814\pi\)
0.291596 + 0.956541i \(0.405814\pi\)
\(380\) 143.239 619.070i 0.376946 1.62913i
\(381\) 175.859 11.7458i 0.461572 0.0308290i
\(382\) 354.999 + 204.959i 0.929316 + 0.536541i
\(383\) −93.5845 162.093i −0.244346 0.423220i 0.717602 0.696454i \(-0.245240\pi\)
−0.961948 + 0.273234i \(0.911907\pi\)
\(384\) −491.751 + 329.462i −1.28060 + 0.857974i
\(385\) 409.093 120.480i 1.06258 0.312936i
\(386\) 396.719i 1.02777i
\(387\) −23.9657 178.607i −0.0619268 0.461517i
\(388\) 767.065 + 442.865i 1.97697 + 1.14140i
\(389\) 183.652 + 106.032i 0.472113 + 0.272575i 0.717124 0.696946i \(-0.245458\pi\)
−0.245011 + 0.969520i \(0.578791\pi\)
\(390\) −381.356 + 144.814i −0.977837 + 0.371317i
\(391\) −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
\(395\) −30.6321 + 9.34896i −0.0775497 + 0.0236683i
\(396\) −547.265 + 422.096i −1.38198 + 1.06590i
\(397\) −514.877 + 297.264i −1.29692 + 0.748776i −0.979871 0.199634i \(-0.936025\pi\)
−0.317048 + 0.948410i \(0.602692\pi\)
\(398\) −110.798 −0.278386
\(399\) −422.773 + 24.0731i −1.05958 + 0.0603336i
\(400\) −2.56193 37.1546i −0.00640483 0.0928866i
\(401\) 400.309 231.118i 0.998277 0.576355i 0.0905387 0.995893i \(-0.471141\pi\)
0.907738 + 0.419538i \(0.137808\pi\)
\(402\) 217.638 14.5363i 0.541388 0.0361600i
\(403\) 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
\(408\) −210.686 103.574i −0.516387 0.253857i
\(409\) −105.366 + 182.500i −0.257620 + 0.446211i −0.965604 0.260018i \(-0.916272\pi\)
0.707984 + 0.706228i \(0.249605\pi\)
\(410\) 30.0260 + 98.3812i 0.0732343 + 0.239954i
\(411\) −32.0767 15.7690i −0.0780455 0.0383673i
\(412\) 895.148i 2.17269i
\(413\) −166.810 295.584i −0.403898 0.715700i
\(414\) −335.600 + 815.938i −0.810628 + 1.97087i
\(415\) −116.721 + 504.459i −0.281255 + 1.21556i
\(416\) −251.982 145.482i −0.605727 0.349716i
\(417\) 25.2181 + 377.566i 0.0604749 + 0.905433i
\(418\) 682.976 394.317i 1.63391 0.943341i
\(419\) 97.7368i 0.233262i −0.993175 0.116631i \(-0.962791\pi\)
0.993175 0.116631i \(-0.0372095\pi\)
\(420\) 620.921 228.838i 1.47838 0.544853i
\(421\) 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
\(423\) −130.533 169.241i −0.308588 0.400098i
\(424\) 324.693 562.385i 0.765786 1.32638i
\(425\) 219.621 147.827i 0.516756 0.347828i
\(426\) −13.0853 19.5309i −0.0307166 0.0458473i
\(427\) 1.44206 146.955i 0.00337719 0.344157i
\(428\) 359.781 0.840610
\(429\) −277.943 136.637i −0.647885 0.318502i
\(430\) −93.8029 307.348i −0.218146 0.714762i
\(431\) 146.182 + 84.3983i 0.339170 + 0.195820i 0.659905 0.751349i \(-0.270597\pi\)
−0.320735 + 0.947169i \(0.603930\pi\)
\(432\) 30.1417 26.6329i 0.0697724 0.0616503i
\(433\) 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
\(438\) −849.377 + 56.7309i −1.93922 + 0.129523i
\(439\) 110.035 + 190.586i 0.250649 + 0.434136i 0.963705 0.266971i \(-0.0860228\pi\)
−0.713056 + 0.701107i \(0.752689\pi\)
\(440\) −307.210 + 329.123i −0.698205 + 0.748006i
\(441\) −262.428 354.419i −0.595074 0.803671i
\(442\) 287.983i 0.651545i
\(443\) 98.0040 + 169.748i 0.221228 + 0.383178i 0.955181 0.296022i \(-0.0956602\pi\)
−0.733953 + 0.679200i \(0.762327\pi\)
\(444\) −627.502 + 41.9116i −1.41329 + 0.0943955i
\(445\) −91.5083 299.829i −0.205637 0.673774i
\(446\) 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 \(0.839337\pi\)
\(450\) −145.054 707.472i −0.322342 1.57216i
\(451\) −39.0480 + 67.6331i −0.0865809 + 0.149963i
\(452\) 27.4181 47.4895i 0.0606594 0.105065i
\(453\) 752.756 + 370.056i 1.66171 + 0.816902i
\(454\) −221.195 −0.487214
\(455\) 214.785 + 204.465i 0.472055 + 0.449374i
\(456\) 371.397 248.828i 0.814468 0.545675i
\(457\) 18.5054 10.6841i 0.0404932 0.0233787i −0.479617 0.877478i \(-0.659224\pi\)
0.520110 + 0.854099i \(0.325891\pi\)
\(458\) −552.314 + 956.636i −1.20593 + 2.08872i
\(459\) 271.084 + 90.8954i 0.590597 + 0.198029i
\(460\) −216.949 + 937.636i −0.471628 + 2.03834i
\(461\) 759.274i 1.64702i −0.567305 0.823508i \(-0.692014\pi\)
0.567305 0.823508i \(-0.307986\pi\)
\(462\) 733.464 + 369.552i 1.58758 + 0.799897i
\(463\) 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
\(465\) −115.874 + 142.042i −0.249190 + 0.305466i
\(466\) −64.2280 + 111.246i −0.137828 + 0.238726i
\(467\) 207.939 + 360.160i 0.445265 + 0.771221i 0.998071 0.0620891i \(-0.0197763\pi\)
−0.552806 + 0.833310i \(0.686443\pi\)
\(468\) −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
\(471\) 35.7502 72.7218i 0.0759027 0.154399i
\(472\) 310.307 + 179.156i 0.657430 + 0.379568i
\(473\) 121.988 211.289i 0.257903 0.446700i
\(474\) −55.3519 27.2111i −0.116776 0.0574074i
\(475\) 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 \(-0.350664\pi\)
−0.546388 + 0.837532i \(0.683998\pi\)
\(480\) 325.617 399.152i 0.678369 0.831567i
\(481\) −140.912 244.067i −0.292957 0.507417i
\(482\) 411.150 0.853009
\(483\) 640.327 36.4608i 1.32573 0.0754883i
\(484\) −173.110 −0.357664
\(485\) −684.610 158.404i −1.41157 0.326606i
\(486\) 510.614 589.591i 1.05065 1.21315i
\(487\) −728.584 420.648i −1.49607 0.863754i −0.496075 0.868280i \(-0.665226\pi\)
−0.999990 + 0.00452596i \(0.998559\pi\)
\(488\) 77.5745 + 134.363i 0.158964 + 0.275334i
\(489\) 460.033 + 686.641i 0.940764 + 1.40417i
\(490\) −564.224 547.769i −1.15148 1.11790i
\(491\) 842.285i 1.71545i 0.514110 + 0.857724i \(0.328122\pi\)
−0.514110 + 0.857724i \(0.671878\pi\)
\(492\) −53.4623 + 108.751i −0.108663 + 0.221039i
\(493\) 393.344 + 227.097i 0.797859 + 0.460644i
\(494\) 474.911 + 274.190i 0.961358 + 0.555040i
\(495\) 317.513 447.026i 0.641441 0.903082i
\(496\) −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 −0.870113 0.492852i \(-0.835954\pi\)
0.00823367 0.999966i \(-0.497379\pi\)
\(500\) −281.251 735.879i −0.562502 1.47176i
\(501\) −1.63470 24.4748i −0.00326287 0.0488518i
\(502\) −559.048 + 322.767i −1.11364 + 0.642961i
\(503\) 639.911 1.27219 0.636095 0.771611i \(-0.280549\pi\)
0.636095 + 0.771611i \(0.280549\pi\)
\(504\) 428.810 + 181.312i 0.850814 + 0.359746i
\(505\) −523.405 + 560.738i −1.03645 + 1.11037i
\(506\) −1034.43 + 597.227i −2.04432 + 1.18029i
\(507\) 19.4357 + 290.992i 0.0383347 + 0.573948i
\(508\) 320.659 + 185.133i 0.631219 + 0.364435i
\(509\) −627.238 + 362.136i −1.23230 + 0.711466i −0.967508 0.252841i \(-0.918635\pi\)
−0.264787 + 0.964307i \(0.585302\pi\)
\(510\) 503.275 + 81.5720i 0.986813 + 0.159945i
\(511\) 304.144 + 538.938i 0.595195 + 1.05467i
\(512\) 95.1944 0.185927
\(513\) −407.995 + 360.501i −0.795313 + 0.702731i
\(514\) −406.367 + 703.848i −0.790597 + 1.36935i
\(515\) 207.304 + 679.239i 0.402533 + 1.31891i
\(516\) 167.019 339.744i 0.323680 0.658419i
\(517\) 289.363i 0.559697i
\(518\) 367.306 + 650.859i 0.709085 + 1.25649i
\(519\) 211.903 141.970i 0.408292 0.273546i
\(520\) −305.006 70.5718i −0.586550 0.135715i
\(521\) 426.309 + 246.130i 0.818251 + 0.472418i 0.849813 0.527084i \(-0.176715\pi\)
−0.0315618 + 0.999502i \(0.510048\pi\)
\(522\) 981.100 756.705i 1.87950 1.44963i
\(523\) −51.6590 + 29.8254i −0.0987744 + 0.0570274i −0.548574 0.836102i \(-0.684829\pi\)
0.449799 + 0.893130i \(0.351496\pi\)
\(524\) 507.291i 0.968113i
\(525\) −418.159 + 317.440i −0.796494 + 0.604647i
\(526\) −583.858 −1.11000
\(527\) −64.7055 112.073i −0.122781 0.212663i
\(528\) 54.3342 3.62905i 0.102906 0.00687319i
\(529\) −201.882 + 349.669i −0.381629 + 0.661001i
\(530\) −317.906 + 1373.97i −0.599823 + 2.59239i
\(531\) −403.574 165.992i −0.760026 0.312603i
\(532\) −766.010 452.336i −1.43987 0.850255i
\(533\) −54.3044 −0.101884
\(534\) 266.344 541.788i 0.498772 1.01459i
\(535\) −273.002 + 83.3205i −0.510284 + 0.155739i
\(536\) 144.972 + 83.6995i 0.270470 + 0.156156i
\(537\) 163.890 333.380i 0.305196 0.620820i
\(538\) 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 0.999904 + 0.0138685i \(0.00441463\pi\)
−0.487941 + 0.872876i \(0.662252\pi\)
\(542\) −56.9766 + 98.6863i −0.105123 + 0.182078i
\(543\) −33.8281 506.476i −0.0622986 0.932737i
\(544\) 181.829 + 314.938i 0.334245 + 0.578929i
\(545\) 647.945 + 604.806i 1.18889 + 1.10974i
\(546\) 32.4662 + 570.173i 0.0594619 + 1.04427i
\(547\) 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
\(549\) −115.398 149.619i −0.210198 0.272530i
\(550\) 429.465 878.372i 0.780845 1.59704i
\(551\) −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
\(555\) 466.443 177.124i 0.840437 0.319142i
\(556\) −397.476 + 688.448i −0.714885 + 1.23822i
\(557\) −226.708 + 392.669i −0.407015 + 0.704971i −0.994554 0.104225i \(-0.966764\pi\)
0.587538 + 0.809196i \(0.300097\pi\)
\(558\) −349.889 + 46.9485i −0.627042 + 0.0841371i
\(559\) 169.650 0.303488
\(560\) −50.6802 12.2514i −0.0905003 0.0218776i
\(561\) 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 −0.887614 0.460589i \(-0.847638\pi\)
0.842688 + 0.538402i \(0.180972\pi\)
\(564\) −29.9230 448.008i −0.0530549 0.794340i
\(565\) −9.80691 + 42.3847i −0.0173574 + 0.0750172i
\(566\) 411.725i 0.727430i
\(567\) −546.963 149.401i −0.964661 0.263494i
\(568\) 18.0422i 0.0317644i
\(569\) 767.186 442.935i 1.34831 0.778445i 0.360297 0.932838i \(-0.382675\pi\)
0.988010 + 0.154392i \(0.0493420\pi\)
\(570\) −613.690 + 752.282i −1.07665 + 1.31979i
\(571\) −479.840 + 831.107i −0.840350 + 1.45553i 0.0492497 + 0.998786i \(0.484317\pi\)
−0.889599 + 0.456742i \(0.849016\pi\)
\(572\) −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
\(576\) 930.073 124.798i 1.61471 0.216663i
\(577\) 265.694 + 153.399i 0.460476 + 0.265856i 0.712244 0.701932i \(-0.247679\pi\)
−0.251769 + 0.967787i \(0.581012\pi\)
\(578\) 283.840 491.624i 0.491072 0.850561i
\(579\) −163.586 + 332.761i −0.282532 + 0.574717i
\(580\) 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
\(585\) 379.589 + 35.7841i 0.648869 + 0.0611694i
\(586\) −691.559 1197.81i −1.18013 2.04405i
\(587\) 336.767 0.573708 0.286854 0.957974i \(-0.407390\pi\)
0.286854 + 0.957974i \(0.407390\pi\)
\(588\) −43.5889 925.421i −0.0741307 1.57384i
\(589\) 246.426 0.418380
\(590\) −758.112 175.411i −1.28494 0.297307i
\(591\) 4.50996 + 67.5233i 0.00763107 + 0.114253i
\(592\) 42.9132 + 24.7760i 0.0724885 + 0.0418513i
\(593\) −556.222 963.405i −0.937980 1.62463i −0.769232 0.638970i \(-0.779361\pi\)
−0.168748 0.985659i \(-0.553972\pi\)
\(594\) 1034.90 209.866i 1.74225 0.353310i
\(595\) −104.707 355.535i −0.175979 0.597538i
\(596\) 726.966i 1.21974i
\(597\) 92.9351 + 45.6871i 0.155670 + 0.0765278i
\(598\) −719.294 415.285i −1.20283 0.694456i
\(599\) −514.713 297.170i −0.859287 0.496110i 0.00448642 0.999990i \(-0.498572\pi\)
−0.863773 + 0.503880i \(0.831905\pi\)
\(600\) 209.724 513.034i 0.349540 0.855057i
\(601\) 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
\(605\) 131.356 40.0899i 0.217117 0.0662642i
\(606\) −1473.95 + 98.4467i −2.43226 + 0.162453i
\(607\) 783.964 452.622i 1.29154 0.745670i 0.312612 0.949881i \(-0.398796\pi\)
0.978927 + 0.204211i \(0.0654628\pi\)
\(608\) −692.482 −1.13895
\(609\) −804.379 405.283i −1.32082 0.665489i
\(610\) −246.307 229.908i −0.403782 0.376899i
\(611\) 174.253 100.605i 0.285193 0.164656i
\(612\) 366.836 + 475.618i 0.599405 + 0.777154i
\(613\) 595.512 + 343.819i 0.971472 + 0.560879i 0.899685 0.436541i \(-0.143796\pi\)
0.0717871 + 0.997420i \(0.477130\pi\)
\(614\) 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 \(0.446704\pi\)
\(618\) −603.381 + 1227.38i −0.976344 + 1.98605i
\(619\) 428.521 742.221i 0.692280 1.19906i −0.278809 0.960347i \(-0.589940\pi\)
0.971089 0.238718i \(-0.0767271\pi\)
\(620\) −368.323 + 112.412i −0.594069 + 0.181310i
\(621\) 617.945 546.011i 0.995081 0.879245i
\(622\) 1254.56i 2.01697i
\(623\) −438.855 4.30645i −0.704422 0.00691244i
\(624\) 21.0762 + 31.4580i 0.0337759 + 0.0504135i
\(625\) 383.833 + 493.251i 0.614133 + 0.789202i
\(626\) 713.402 + 411.883i 1.13962 + 0.657960i
\(627\) −735.464 + 49.1225i −1.17299 + 0.0783453i
\(628\) 147.428 85.1177i 0.234758 0.135538i
\(629\) 352.236i 0.559994i
\(630\) −1005.62 104.766i −1.59623 0.166295i
\(631\) −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
\(633\) 15.2090 + 227.710i 0.0240269 + 0.359732i
\(634\) 513.254 888.983i 0.809550 1.40218i
\(635\) −286.191 66.2184i −0.450694 0.104281i
\(636\) −1380.29 + 924.766i −2.17027 + 1.45403i
\(637\) 363.545 200.486i 0.570715 0.314734i
\(638\) 1677.45 2.62923
\(639\) 2.92218 + 21.7779i 0.00457305 + 0.0340812i
\(640\) 943.559 287.975i 1.47431 0.449961i
\(641\) −144.334 83.3312i −0.225170 0.130002i 0.383172 0.923677i \(-0.374832\pi\)
−0.608342 + 0.793675i \(0.708165\pi\)
\(642\) −493.312 242.513i −0.768398 0.377746i
\(643\) 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 −0.791440 0.611246i \(-0.790668\pi\)
0.925075 + 0.379784i \(0.124002\pi\)
\(648\) 577.412 157.797i 0.891068 0.243513i
\(649\) −295.397 511.642i −0.455157 0.788354i
\(650\) 678.266 46.7687i 1.04349 0.0719518i
\(651\) 140.744 + 214.597i 0.216197 + 0.329643i
\(652\) 1736.30i 2.66304i
\(653\) 514.097 + 890.443i 0.787285 + 1.36362i 0.927624 + 0.373515i \(0.121847\pi\)
−0.140339 + 0.990104i \(0.544819\pi\)
\(654\) 113.757 + 1703.18i 0.173941 + 2.60425i
\(655\) 117.482 + 384.933i 0.179362 + 0.587684i
\(656\) 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 \(-0.122539\pi\)
\(660\) 1076.86 408.919i 1.63161 0.619575i
\(661\) 190.532 330.011i 0.288248 0.499261i −0.685143 0.728408i \(-0.740260\pi\)
0.973392 + 0.229147i \(0.0735938\pi\)
\(662\) −462.921 + 801.803i −0.699276 + 1.21118i
\(663\) −118.749 + 241.555i −0.179108 + 0.364336i
\(664\) −765.282 −1.15253
\(665\) 686.003 + 165.835i 1.03158 + 0.249375i
\(666\) 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
\(669\) −936.128 + 62.5251i −1.39929 + 0.0934605i
\(670\) −354.181 81.9499i −0.528628 0.122313i
\(671\) 255.813i 0.381242i
\(672\) −395.506 603.041i −0.588551 0.897383i
\(673\) 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
\(675\) −170.055 + 653.228i −0.251934 + 0.967744i
\(676\) −306.337 + 530.591i −0.453161 + 0.784897i
\(677\) −150.968 261.485i −0.222996 0.386241i 0.732720 0.680530i \(-0.238250\pi\)
−0.955716 + 0.294289i \(0.904917\pi\)
\(678\) −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
\(681\) 185.535 + 91.2092i 0.272445 + 0.133934i
\(682\) −413.913 238.973i −0.606911 0.350400i
\(683\) 45.4093 78.6511i 0.0664850 0.115155i −0.830867 0.556471i \(-0.812155\pi\)
0.897352 + 0.441316i \(0.145488\pi\)
\(684\) −1133.61 + 152.108i −1.65732 + 0.222380i
\(685\) 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
\(690\) 929.488 1139.40i 1.34708 1.65130i
\(691\) −492.003 852.173i −0.712015 1.23325i −0.964099 0.265541i \(-0.914449\pi\)
0.252084 0.967705i \(-0.418884\pi\)
\(692\) 535.839 0.774334
\(693\) −462.833 612.416i −0.667868 0.883717i
\(694\) −547.919 −0.789509
\(695\) 142.169 614.445i 0.204560 0.884093i
\(696\) 948.772 63.3696i 1.36318 0.0910483i
\(697\) 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
\(700\) −1100.99 + 65.0690i −1.57285 + 0.0929557i
\(701\) 446.823i 0.637408i −0.947854 0.318704i \(-0.896752\pi\)
0.947854 0.318704i \(-0.103248\pi\)
\(702\) 486.190 + 550.243i 0.692578 + 0.783822i
\(703\) −580.870 335.366i −0.826274 0.477049i
\(704\) 1100.26 + 635.236i 1.56287 + 0.902323i
\(705\) 126.458 + 333.019i 0.179373 + 0.472367i
\(706\) 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 −0.912836 0.408327i \(-0.866112\pi\)
0.102796 0.994702i \(-0.467221\pi\)
\(710\) 11.4376 + 37.4755i 0.0161092 + 0.0527824i
\(711\) 35.2078 + 45.6484i 0.0495187 + 0.0642031i
\(712\) 401.250 231.662i 0.563554 0.325368i
\(713\) −373.233 −0.523469
\(714\) 321.171 637.440i 0.449820 0.892773i
\(715\) 377.345 + 352.222i 0.527755 + 0.492618i
\(716\) 675.859 390.207i 0.943937 0.544982i
\(717\) −1022.92 + 68.3223i −1.42667 + 0.0952891i
\(718\) 302.691 + 174.759i 0.421576 + 0.243397i
\(719\) −867.476 + 500.837i −1.20650 + 0.696575i −0.961994 0.273072i \(-0.911960\pi\)
−0.244510 + 0.969647i \(0.578627\pi\)
\(720\) −60.9455 + 27.9218i −0.0846465 + 0.0387803i
\(721\) 994.189 + 9.75591i 1.37890 + 0.0135311i
\(722\) 146.408 0.202781
\(723\) −344.866 169.537i −0.476993 0.234491i
\(724\) 533.184 923.502i 0.736442 1.27556i
\(725\) −470.988 + 963.298i −0.649638 + 1.32869i
\(726\) 237.358 + 116.686i 0.326940 + 0.160724i
\(727\) 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
\(730\) 1382.27 + 319.826i 1.89351 + 0.438118i
\(731\) −183.628 106.018i −0.251201 0.145031i
\(732\) −26.4536 396.064i −0.0361388 0.541071i
\(733\) −336.580 + 194.325i −0.459181 + 0.265109i −0.711700 0.702484i \(-0.752074\pi\)
0.252519 + 0.967592i \(0.418741\pi\)
\(734\) 369.916i 0.503973i
\(735\) 247.390 + 692.115i 0.336585 + 0.941653i
\(736\) 1048.83 1.42503
\(737\) −138.006 239.033i −0.187253 0.324332i
\(738\) 146.609 113.077i 0.198657 0.153221i
\(739\) 599.057 1037.60i 0.810631 1.40405i −0.101792 0.994806i \(-0.532457\pi\)
0.912423 0.409249i \(-0.134209\pi\)
\(740\) 1021.19 + 236.281i 1.37998 + 0.319299i
\(741\) −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 \(0.630641\pi\)
\(744\) −243.138 119.527i −0.326799 0.160655i
\(745\) −168.356 551.622i −0.225981 0.740432i
\(746\) 248.595 + 143.526i 0.333237 + 0.192394i
\(747\) 923.736 123.948i 1.23659 0.165927i
\(748\) 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 0.802447 0.596723i \(-0.203531\pi\)
−0.918001 + 0.396578i \(0.870197\pi\)
\(752\) −17.6889 + 30.6381i −0.0235225 + 0.0407421i
\(753\) 602.012 40.2091i 0.799484 0.0533985i
\(754\) 583.211 + 1010.15i 0.773490 + 1.33972i
\(755\) −1021.97 953.928i −1.35360 1.26348i
\(756\) −779.912 900.314i −1.03163 1.19089i
\(757\) 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
\(759\) 1113.93 74.4004i 1.46762 0.0980242i
\(760\) −712.628 + 217.495i −0.937668 + 0.286177i
\(761\) 450.545 260.123i 0.592044 0.341817i −0.173861 0.984770i \(-0.555624\pi\)
0.765905 + 0.642953i \(0.222291\pi\)
\(762\) −314.880 469.986i −0.413228 0.616780i
\(763\) 1080.68 609.873i 1.41636 0.799309i
\(764\) 804.880i 1.05351i
\(765\) −388.502 275.945i