Properties

Label 105.3.o.b.44.4
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 44.4
Character \(\chi\) \(=\) 105.44
Dual form 105.3.o.b.74.4

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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 \(0.870206\pi\)
\(3\) 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 −0.895957 0.444141i \(-0.853509\pi\)
−0.0633411 + 0.997992i \(0.520176\pi\)
\(12\) −16.9676 + 8.34131i −1.41397 + 0.695109i
\(13\) 8.47270i 0.651746i 0.945414 + 0.325873i \(0.105658\pi\)
−0.945414 + 0.325873i \(0.894342\pi\)
\(14\) −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 \(0.934150\pi\)
\(18\) 17.6425 22.8743i 0.980140 1.27079i
\(19\) −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
\(21\) 9.44914 + 18.7540i 0.449959 + 0.893049i
\(22\) 39.1096i 1.77771i
\(23\) 15.2706 26.4494i 0.663939 1.14998i −0.315633 0.948881i \(-0.602217\pi\)
0.979572 0.201094i \(-0.0644497\pi\)
\(24\) 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 \(0.264938\pi\)
−0.673157 + 0.739499i \(0.735062\pi\)
\(30\) −17.0918 + 45.0100i −0.569726 + 1.50033i
\(31\) −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
\(33\) 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 0.835916 0.548857i \(-0.184937\pi\)
−0.0573663 + 0.998353i \(0.518270\pi\)
\(38\) −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 \(0.0249054\pi\)
−0.996941 + 0.0781627i \(0.975095\pi\)
\(42\) −67.2953 3.83186i −1.60227 0.0912347i
\(43\) 20.0231i 0.465653i −0.972518 0.232827i \(-0.925203\pi\)
0.972518 0.232827i \(-0.0747975\pi\)
\(44\) 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 −0.711613 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
\(51\) −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 0.898821 + 0.438316i \(0.144425\pi\)
−0.0698177 + 0.997560i \(0.522242\pi\)
\(54\) −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 −0.0999885 0.994989i \(-0.531881\pi\)
0.811691 + 0.584087i \(0.198547\pi\)
\(60\) −59.7575 73.2528i −0.995959 1.22088i
\(61\) 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
\(63\) 58.0262 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 −0.346405 0.938085i \(-0.612598\pi\)
0.639203 + 0.769038i \(0.279264\pi\)
\(68\) −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 \(0.00547308\pi\)
−0.999852 + 0.0171933i \(0.994527\pi\)
\(72\) −65.9187 8.84504i −0.915538 0.122848i
\(73\) −76.5611 + 44.2026i −1.04878 + 0.605515i −0.922308 0.386455i \(-0.873699\pi\)
−0.126474 + 0.991970i \(0.540366\pi\)
\(74\) −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 −0.885584 0.464480i \(-0.846241\pi\)
0.845043 + 0.534698i \(0.179575\pi\)
\(80\) 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 0.772995 0.634412i \(-0.218758\pi\)
−0.162919 + 0.986639i \(0.552091\pi\)
\(90\) 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 \(0.257897\pi\)
−0.689348 + 0.724430i \(0.742103\pi\)
\(98\) 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 −0.982990 0.183659i \(-0.941206\pi\)
−0.332442 + 0.943124i \(0.607872\pi\)
\(102\) 6.79546 101.742i 0.0666221 0.997469i
\(103\) −123.005 71.0169i −1.19422 0.689485i −0.234961 0.972005i \(-0.575496\pi\)
−0.959261 + 0.282520i \(0.908830\pi\)
\(104\) 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 −0.968023 0.250860i \(-0.919287\pi\)
0.701263 + 0.712903i \(0.252620\pi\)
\(108\) 161.336 54.0964i 1.49385 0.500893i
\(109\) −88.6354 153.521i −0.813169 1.40845i −0.910635 0.413211i \(-0.864407\pi\)
0.0974665 0.995239i \(-0.468926\pi\)
\(110\) 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 \(0.0742980\pi\)
−0.972882 + 0.231300i \(0.925702\pi\)
\(128\) 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 0.209756 0.977754i \(-0.432733\pi\)
−0.741881 + 0.670531i \(0.766066\pi\)
\(132\) 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 0.843465 0.537185i \(-0.180512\pi\)
−0.886948 + 0.461870i \(0.847179\pi\)
\(138\) 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 0.796241 0.604980i \(-0.206819\pi\)
−0.125808 + 0.992055i \(0.540152\pi\)
\(150\) −238.522 32.5278i −1.59015 0.216852i
\(151\) 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
\(156\) −70.6734 143.762i −0.453035 0.921548i
\(157\) −23.3925 + 13.5057i −0.148997 + 0.0860235i −0.572645 0.819803i \(-0.694083\pi\)
0.423648 + 0.905827i \(0.360749\pi\)
\(158\) −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 0.999182 0.0404450i \(-0.0128776\pi\)
0.464565 + 0.885539i \(0.346211\pi\)
\(164\) 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 −0.962336 0.271862i \(-0.912360\pi\)
0.716608 + 0.697476i \(0.245694\pi\)
\(174\) −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 −0.768688 0.639624i \(-0.779090\pi\)
0.169587 + 0.985515i \(0.445757\pi\)
\(180\) −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 0.181699 0.983354i \(-0.441841\pi\)
−0.760761 + 0.649033i \(0.775174\pi\)
\(192\) −20.8460 + 312.107i −0.108573 + 1.62556i
\(193\) 107.040 61.7995i 0.554611 0.320205i −0.196369 0.980530i \(-0.562915\pi\)
0.750980 + 0.660325i \(0.229582\pi\)
\(194\) −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 0.906128 0.423004i \(-0.139024\pi\)
−0.819396 + 0.573228i \(0.805691\pi\)
\(200\) −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 \(-0.752645\pi\)
0.712959 0.701206i \(-0.247355\pi\)
\(224\) −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 \(0.784829\pi\)
\(228\) 25.4079 380.407i 0.111438 1.66845i
\(229\) −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
\(231\) −213.966 140.330i −0.926261 0.607490i
\(232\) 316.962i 1.36622i
\(233\) −20.0104 + 34.6590i −0.0858816 + 0.148751i −0.905767 0.423777i \(-0.860704\pi\)
0.819885 + 0.572528i \(0.194037\pi\)
\(234\) 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 \(-0.746461\pi\)
0.699201 0.714925i \(-0.253539\pi\)
\(240\) 7.93272 20.8903i 0.0330530 0.0870427i
\(241\) −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
\(243\) 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 \(0.131210\pi\)
−0.916239 + 0.400633i \(0.868790\pi\)
\(252\) −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 −0.999964 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
\(261\) 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 0.985503 0.169659i \(-0.0542667\pi\)
−0.639681 + 0.768641i \(0.720933\pi\)
\(264\) 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 −0.0200914 0.999798i \(-0.506396\pi\)
0.855805 + 0.517299i \(0.173062\pi\)
\(270\) 206.332 381.035i 0.764194 1.41124i
\(271\) −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
\(273\) −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 0.178385 0.983961i \(-0.442913\pi\)
0.941327 + 0.337495i \(0.109579\pi\)
\(278\) −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 \(0.112141\pi\)
−0.938581 + 0.345058i \(0.887859\pi\)
\(282\) 205.217 100.885i 0.727721 0.357749i
\(283\) −111.089 + 64.1371i −0.392539 + 0.226633i −0.683260 0.730175i \(-0.739438\pi\)
0.290720 + 0.956808i \(0.406105\pi\)
\(284\) 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 \(-0.891834\pi\)
0.942817 0.333311i \(-0.108166\pi\)
\(308\) −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 −0.933153 0.359481i \(-0.882954\pi\)
−0.155257 + 0.987874i \(0.549621\pi\)
\(312\) 187.421 + 12.5181i 0.600708 + 0.0401220i
\(313\) −222.263 128.323i −0.710104 0.409979i 0.100996 0.994887i \(-0.467797\pi\)
−0.811100 + 0.584908i \(0.801131\pi\)
\(314\) 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 −0.495552 0.868578i \(-0.665034\pi\)
0.999987 0.00512853i \(-0.00163247\pi\)
\(318\) −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 −0.997354 0.0726932i \(-0.976841\pi\)
0.561631 + 0.827388i \(0.310174\pi\)
\(332\) 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 \(0.190957\pi\)
−0.825387 + 0.564567i \(0.809043\pi\)
\(338\) −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 0.962405 0.271619i \(-0.0875590\pi\)
−0.716431 + 0.697658i \(0.754226\pi\)
\(348\) −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 0.562119 0.827056i \(-0.309986\pi\)
−0.997311 + 0.0732815i \(0.976653\pi\)
\(354\) 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 0.362873 0.931839i \(-0.381796\pi\)
−0.625559 + 0.780177i \(0.715129\pi\)
\(360\) −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 −0.357820 0.933791i \(-0.616480\pi\)
0.629776 + 0.776776i \(0.283146\pi\)
\(368\) −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 0.392573 0.919721i \(-0.371585\pi\)
−0.600215 + 0.799839i \(0.704918\pi\)
\(374\) −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 −0.961948 0.273234i \(-0.911907\pi\)
0.717602 + 0.696454i \(0.245240\pi\)
\(384\) −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 −0.245011 0.969520i \(-0.578791\pi\)
0.717124 + 0.696946i \(0.245458\pi\)
\(390\) −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 −0.317048 0.948410i \(-0.602692\pi\)
−0.979871 + 0.199634i \(0.936025\pi\)
\(398\) −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 0.907738 0.419538i \(-0.137808\pi\)
0.0905387 + 0.995893i \(0.471141\pi\)
\(402\) 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 0.707984 0.706228i \(-0.249605\pi\)
−0.965604 + 0.260018i \(0.916272\pi\)
\(410\) 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 \(0.0372095\pi\)
−0.993175 + 0.116631i \(0.962791\pi\)
\(420\) 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 −0.320735 0.947169i \(-0.603930\pi\)
0.659905 + 0.751349i \(0.270597\pi\)
\(432\) 30.1417 + 26.6329i 0.0697724 + 0.0616503i
\(433\) 328.967i 0.759739i −0.925040 0.379870i \(-0.875969\pi\)
0.925040 0.379870i \(-0.124031\pi\)
\(434\) −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 −0.713056 0.701107i \(-0.752689\pi\)
0.963705 + 0.266971i \(0.0860228\pi\)
\(440\) −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 −0.733953 0.679200i \(-0.762327\pi\)
0.955181 + 0.296022i \(0.0956602\pi\)
\(444\) −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 \(-0.839337\pi\)
0.875301 0.483578i \(-0.160663\pi\)
\(450\) −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 0.520110 0.854099i \(-0.325891\pi\)
−0.479617 + 0.877478i \(0.659224\pi\)
\(458\) −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 \(0.307986\pi\)
−0.567305 + 0.823508i \(0.692014\pi\)
\(462\) 733.464 369.552i 1.58758 0.799897i
\(463\) 242.225i 0.523164i 0.965181 + 0.261582i \(0.0842443\pi\)
−0.965181 + 0.261582i \(0.915756\pi\)
\(464\) 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 −0.552806 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
\(471\) 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 −0.546388 0.837532i \(-0.683998\pi\)
0.452130 + 0.891952i \(0.350664\pi\)
\(480\) 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 −0.999990 0.00452596i \(-0.998559\pi\)
−0.496075 + 0.868280i \(0.665226\pi\)
\(488\) 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 \(-0.671878\pi\)
0.514110 0.857724i \(-0.328122\pi\)
\(492\) −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 0.00823367 + 0.999966i \(0.497379\pi\)
−0.870113 + 0.492852i \(0.835954\pi\)
\(500\) −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 −0.264787 0.964307i \(-0.585302\pi\)
−0.967508 + 0.252841i \(0.918635\pi\)
\(510\) 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 −0.0315618 0.999502i \(-0.510048\pi\)
0.849813 + 0.527084i \(0.176715\pi\)
\(522\) 981.100 + 756.705i 1.87950 + 1.44963i
\(523\) −51.6590 29.8254i −0.0987744 0.0570274i 0.449799 0.893130i \(-0.351496\pi\)
−0.548574 + 0.836102i \(0.684829\pi\)
\(524\) 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 −0.487941 0.872876i \(-0.662252\pi\)
0.999904 0.0138685i \(-0.00441463\pi\)
\(542\) −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 \(0.0320505\pi\)
−0.994935 + 0.100520i \(0.967949\pi\)
\(548\) −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 0.587538 0.809196i \(-0.300097\pi\)
−0.994554 + 0.104225i \(0.966764\pi\)
\(558\) −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 0.842688 0.538402i \(-0.180972\pi\)
−0.887614 + 0.460589i \(0.847638\pi\)
\(564\) −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 0.988010 0.154392i \(-0.0493420\pi\)
0.360297 + 0.932838i \(0.382675\pi\)
\(570\) −613.690 752.282i −1.07665 1.31979i
\(571\) −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
\(576\) 930.073 + 124.798i 1.61471 + 0.216663i
\(577\) 265.694 153.399i 0.460476 0.265856i −0.251769 0.967787i \(-0.581012\pi\)
0.712244 + 0.701932i \(0.247679\pi\)
\(578\) 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 −0.168748 + 0.985659i \(0.553972\pi\)
−0.769232 + 0.638970i \(0.779361\pi\)
\(594\) 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 −0.863773 0.503880i \(-0.831905\pi\)
0.00448642 + 0.999990i \(0.498572\pi\)
\(600\) 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 0.978927 0.204211i \(-0.0654628\pi\)
0.312612 + 0.949881i \(0.398796\pi\)
\(608\) −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 0.0717871 0.997420i \(-0.477130\pi\)
0.899685 + 0.436541i \(0.143796\pi\)
\(614\) 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 0.971089 + 0.238718i \(0.0767271\pi\)
−0.278809 + 0.960347i \(0.589940\pi\)
\(620\) −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 −0.608342 0.793675i \(-0.708165\pi\)
0.383172 + 0.923677i \(0.374832\pi\)
\(642\) −493.312 + 242.513i −0.768398 + 0.377746i
\(643\) 643.063i 1.00010i 0.865997 + 0.500049i \(0.166685\pi\)
−0.865997 + 0.500049i \(0.833315\pi\)
\(644\) 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 \(0.790668\pi\)
\(648\) 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 −0.140339 0.990104i \(-0.544819\pi\)
0.927624 0.373515i \(-0.121847\pi\)
\(654\) 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 \(0.122539\pi\)
−0.926810 + 0.375530i \(0.877461\pi\)
\(660\) 1076.86 + 408.919i 1.63161 + 0.619575i
\(661\) 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
\(663\) −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 \(-0.848271\pi\)
0.888527 0.458825i \(-0.151729\pi\)
\(674\) −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 −0.955716 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
\(681\) 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 0.897352 0.441316i \(-0.145488\pi\)
−0.830867 + 0.556471i \(0.812155\pi\)
\(684\) −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 0.252084 + 0.967705i \(0.418884\pi\)
−0.964099 + 0.265541i \(0.914449\pi\)
\(692\) 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 \(0.103248\pi\)
−0.947854 + 0.318704i \(0.896752\pi\)
\(702\) 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 0.102796 + 0.994702i \(0.467221\pi\)
−0.912836 + 0.408327i \(0.866112\pi\)
\(710\) 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 −0.244510 0.969647i \(-0.578627\pi\)
−0.961994 + 0.273072i \(0.911960\pi\)
\(720\) −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 \(-0.964809\pi\)
0.993895 0.110330i \(-0.0351906\pi\)
\(728\) −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 0.252519 0.967592i \(-0.418741\pi\)
−0.711700 + 0.702484i \(0.752074\pi\)
\(734\) 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 0.912423 + 0.409249i \(0.134209\pi\)
−0.101792 + 0.994806i \(0.532457\pi\)
\(740\) 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 −0.918001 0.396578i \(-0.870197\pi\)
0.802447 + 0.596723i \(0.203531\pi\)
\(752\) −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 \(0.120635\pi\)
−0.929041 + 0.369978i \(0.879365\pi\)
\(758\) −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 0.765905 0.642953i \(-0.222291\pi\)
−0.173861 + 0.984770i \(0.555624\pi\)
\(762\) −314.880 + 469.986i −0.413228 + 0.616780i
\(763\) 1080.68 + 609.873i 1.41636 + 0.799309i
\(764\) 804.880i