Properties

Label 105.3.o.b.74.17
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 74.17
Character \(\chi\) \(=\) 105.74
Dual form 105.3.o.b.44.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.60486 + 2.77971i) q^{2} +(-0.199928 - 2.99333i) q^{3} +(-3.15118 + 5.45800i) q^{4} +(4.78223 + 1.45954i) q^{5} +(7.99972 - 5.35963i) q^{6} +(6.02754 + 3.55932i) q^{7} -7.38994 q^{8} +(-8.92006 + 1.19690i) q^{9} +O(q^{10})\) \(q+(1.60486 + 2.77971i) q^{2} +(-0.199928 - 2.99333i) q^{3} +(-3.15118 + 5.45800i) q^{4} +(4.78223 + 1.45954i) q^{5} +(7.99972 - 5.35963i) q^{6} +(6.02754 + 3.55932i) q^{7} -7.38994 q^{8} +(-8.92006 + 1.19690i) q^{9} +(3.61773 + 15.6356i) q^{10} +(-10.5523 - 6.09236i) q^{11} +(16.9676 + 8.34131i) q^{12} +8.47270i q^{13} +(-0.220467 + 22.4670i) q^{14} +(3.41279 - 14.6066i) 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} +(20.7395 + 13.9597i) q^{25} +(-23.5516 + 13.5975i) q^{26} +(5.36609 + 26.4614i) q^{27} +(-38.4206 + 21.6823i) q^{28} -42.8910i q^{29} +(46.0791 - 13.9551i) q^{30} +(-6.11033 + 10.5834i) q^{31} +(-17.1707 + 29.7405i) q^{32} +(-16.1268 + 32.8045i) q^{33} +33.9895 q^{34} +(23.6301 + 25.8189i) q^{35} +(21.5760 - 52.4573i) q^{36} +(-28.8063 + 16.6313i) q^{37} +(32.3616 - 56.0519i) q^{38} +(25.3616 - 1.69393i) q^{39} +(-35.3404 - 10.7859i) q^{40} -6.40934i q^{41} +(67.2953 - 3.83186i) q^{42} -20.0231i q^{43} +(66.5042 - 38.3962i) q^{44} +(-44.4047 - 7.29534i) 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} +(68.9686 + 64.6550i) q^{60} +(10.4973 + 18.1819i) q^{61} -39.2250 q^{62} +(-58.0262 - 24.5349i) q^{63} -104.268 q^{64} +(-12.3663 + 40.5184i) 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} +(-33.8459 + 107.121i) q^{70} -2.44145i q^{71} +(65.9187 - 8.84504i) q^{72} +(76.5611 + 44.2026i) q^{73} +(-92.4605 - 53.3821i) q^{74} +(37.6397 - 64.8710i) q^{75} +127.085 q^{76} +(-41.9197 - 74.2809i) q^{77} +(45.4106 + 67.7793i) q^{78} +(-3.20270 - 5.54725i) q^{79} +(1.67908 + 7.25685i) q^{80} +(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} +(-50.9846 - 135.140i) q^{90} +(-30.1570 + 51.0696i) q^{91} +192.481 q^{92} +(32.9013 + 16.1743i) q^{93} +(38.1124 - 66.0126i) q^{94} +(-22.7279 - 98.2282i) 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 \(0.129794\pi\)
−0.115579 + 0.993298i \(0.536872\pi\)
\(3\) −0.199928 2.99333i −0.0666427 0.997777i
\(4\) −3.15118 + 5.45800i −0.787795 + 1.36450i
\(5\) 4.78223 + 1.45954i 0.956446 + 0.291908i
\(6\) 7.99972 5.35963i 1.33329 0.893272i
\(7\) 6.02754 + 3.55932i 0.861077 + 0.508474i
\(8\) −7.38994 −0.923743
\(9\) −8.92006 + 1.19690i −0.991117 + 0.132989i
\(10\) 3.61773 + 15.6356i 0.361773 + 1.56356i
\(11\) −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 \(0.105658\pi\)
−0.945414 + 0.325873i \(0.894342\pi\)
\(14\) −0.220467 + 22.4670i −0.0157477 + 1.60479i
\(15\) 3.41279 14.6066i 0.227519 0.973774i
\(16\) 0.744857 + 1.29013i 0.0465536 + 0.0806332i
\(17\) 5.29476 9.17080i 0.311457 0.539459i −0.667221 0.744859i \(-0.732516\pi\)
0.978678 + 0.205401i \(0.0658498\pi\)
\(18\) −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 \(-0.935550\pi\)
0.315633 0.948881i \(-0.397783\pi\)
\(24\) 1.47746 + 22.1205i 0.0615607 + 0.921690i
\(25\) 20.7395 + 13.9597i 0.829579 + 0.558389i
\(26\) −23.5516 + 13.5975i −0.905832 + 0.522982i
\(27\) 5.36609 + 26.4614i 0.198744 + 0.980051i
\(28\) −38.4206 + 21.6823i −1.37217 + 0.774368i
\(29\) 42.8910i 1.47900i −0.673157 0.739499i \(-0.735062\pi\)
0.673157 0.739499i \(-0.264938\pi\)
\(30\) 46.0791 13.9551i 1.53597 0.465169i
\(31\) −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
\(35\) 23.6301 + 25.8189i 0.675147 + 0.737684i
\(36\) 21.5760 52.4573i 0.599333 1.45715i
\(37\) −28.8063 + 16.6313i −0.778550 + 0.449496i −0.835916 0.548857i \(-0.815063\pi\)
0.0573663 + 0.998353i \(0.481730\pi\)
\(38\) 32.3616 56.0519i 0.851620 1.47505i
\(39\) 25.3616 1.69393i 0.650297 0.0434341i
\(40\) −35.3404 10.7859i −0.883511 0.269648i
\(41\) 6.40934i 0.156325i −0.996941 0.0781627i \(-0.975095\pi\)
0.996941 0.0781627i \(-0.0249054\pi\)
\(42\) 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
\(45\) −44.4047 7.29534i −0.986771 0.162119i
\(46\) 49.0144 84.8955i 1.06553 1.84555i
\(47\) −11.8740 20.5664i −0.252639 0.437583i 0.711613 0.702572i \(-0.247965\pi\)
−0.964251 + 0.264989i \(0.914632\pi\)
\(48\) 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 \(0.477758\pi\)
−0.898821 + 0.438316i \(0.855575\pi\)
\(54\) −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 \(0.531881\pi\)
\(60\) 68.9686 + 64.6550i 1.14948 + 1.07758i
\(61\) 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
\(65\) −12.3663 + 40.5184i −0.190250 + 0.623360i
\(66\) −117.068 + 7.81912i −1.77376 + 0.118471i
\(67\) −19.6174 11.3261i −0.292798 0.169047i 0.346405 0.938085i \(-0.387402\pi\)
−0.639203 + 0.769038i \(0.720736\pi\)
\(68\) 33.3695 + 57.7976i 0.490728 + 0.849965i
\(69\) −76.1189 + 50.9979i −1.10317 + 0.739100i
\(70\) −33.8459 + 107.121i −0.483513 + 1.53030i
\(71\) 2.44145i 0.0343867i −0.999852 0.0171933i \(-0.994527\pi\)
0.999852 0.0171933i \(-0.00547308\pi\)
\(72\) 65.9187 8.84504i 0.915538 0.122848i
\(73\) 76.5611 + 44.2026i 1.04878 + 0.605515i 0.922308 0.386455i \(-0.126301\pi\)
0.126474 + 0.991970i \(0.459634\pi\)
\(74\) −92.4605 53.3821i −1.24947 0.721380i
\(75\) 37.6397 64.8710i 0.501863 0.864947i
\(76\) 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 \(0.846241\pi\)
\(80\) 1.67908 + 7.25685i 0.0209885 + 0.0907107i
\(81\) 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 \(-0.285572\pi\)
0.623839 + 0.781553i \(0.285572\pi\)
\(84\) 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 \(0.218758\pi\)
\(90\) −50.9846 135.140i −0.566496 1.50156i
\(91\) −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
\(95\) −22.7279 98.2282i −0.239241 1.03398i
\(96\) 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
\(100\) −141.546 + 69.2065i −1.41546 + 0.692065i
\(101\) −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 0.234961 0.972005i \(-0.424504\pi\)
0.959261 + 0.282520i \(0.0911704\pi\)
\(104\) 62.6128i 0.602046i
\(105\) 72.5603 75.8947i 0.691050 0.722807i
\(106\) −282.053 −2.66088
\(107\) 28.5434 + 49.4386i 0.266761 + 0.462043i 0.968023 0.250860i \(-0.0807134\pi\)
−0.701263 + 0.712903i \(0.747380\pi\)
\(108\) −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 \(0.864407\pi\)
\(110\) 57.0822 187.031i 0.518929 1.70029i
\(111\) 55.5423 + 82.9018i 0.500381 + 0.746863i
\(112\) −0.102324 + 10.4275i −0.000913610 + 0.0931027i
\(113\) 8.70089 0.0769990 0.0384995 0.999259i \(-0.487742\pi\)
0.0384995 + 0.999259i \(0.487742\pi\)
\(114\) −174.252 85.6625i −1.52852 0.751425i
\(115\) −34.4234 148.775i −0.299334 1.29370i
\(116\) 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
\(120\) −25.2203 + 107.942i −0.210169 + 0.899517i
\(121\) 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
\(130\) −132.475 + 30.6520i −1.01904 + 0.235784i
\(131\) −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
\(135\) −12.9596 + 134.377i −0.0959971 + 0.995382i
\(136\) −39.1280 + 67.7717i −0.287706 + 0.498321i
\(137\) 5.95720 10.3182i 0.0434832 0.0753151i −0.843465 0.537185i \(-0.819488\pi\)
0.886948 + 0.461870i \(0.152821\pi\)
\(138\) −263.920 129.743i −1.91246 0.940170i
\(139\) 126.136 0.907450 0.453725 0.891142i \(-0.350095\pi\)
0.453725 + 0.891142i \(0.350095\pi\)
\(140\) −215.383 + 47.6132i −1.53845 + 0.340095i
\(141\) −59.1881 + 39.6547i −0.419774 + 0.281239i
\(142\) 6.78652 3.91820i 0.0477924 0.0275930i
\(143\) 51.6187 89.4063i 0.360970 0.625219i
\(144\) −8.18833 10.6165i −0.0568634 0.0737258i
\(145\) 62.6012 205.115i 0.431732 1.41458i
\(146\) 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 \(0.206819\pi\)
\(150\) 240.729 + 0.518085i 1.60486 + 0.00345390i
\(151\) 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 0.572645 0.819803i \(-0.305917\pi\)
−0.423648 + 0.905827i \(0.639251\pi\)
\(158\) 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 \(-0.987122\pi\)
−0.464565 + 0.885539i \(0.653789\pi\)
\(164\) 34.9822 + 20.1970i 0.213306 + 0.123152i
\(165\) −125.001 + 133.341i −0.757584 + 0.808127i
\(166\) 166.195 + 287.859i 1.00118 + 1.73409i
\(167\) 8.17643 0.0489607 0.0244803 0.999700i \(-0.492207\pi\)
0.0244803 + 0.999700i \(0.492207\pi\)
\(168\) −69.8286 + 138.591i −0.415646 + 0.824948i
\(169\) 97.2133 0.575227
\(170\) 162.546 + 49.6091i 0.956151 + 0.291818i
\(171\) 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 \(-0.0876395\pi\)
−0.716608 + 0.697476i \(0.754306\pi\)
\(174\) −229.880 343.116i −1.32115 1.97193i
\(175\) 75.3209 + 157.961i 0.430405 + 0.902636i
\(176\) 18.1518i 0.103135i
\(177\) 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 \(0.779090\pi\)
\(180\) 179.745 219.372i 0.998584 1.21873i
\(181\) −169.201 −0.934815 −0.467407 0.884042i \(-0.654812\pi\)
−0.467407 + 0.884042i \(0.654812\pi\)
\(182\) −190.356 1.86795i −1.04591 0.0102635i
\(183\) 52.3256 35.0570i 0.285932 0.191568i
\(184\) 112.849 + 195.460i 0.613309 + 1.06228i
\(185\) −162.033 + 37.4909i −0.875853 + 0.202653i
\(186\) 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 0.196369 0.980530i \(-0.437085\pi\)
−0.750980 + 0.660325i \(0.770418\pi\)
\(194\) −390.658 + 225.547i −2.01370 + 1.16261i
\(195\) 123.757 + 28.9155i 0.634653 + 0.148285i
\(196\) −308.756 6.06019i −1.57529 0.0309193i
\(197\) −22.5579 −0.114507 −0.0572536 0.998360i \(-0.518234\pi\)
−0.0572536 + 0.998360i \(0.518234\pi\)
\(198\) 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 \(0.139024\pi\)
\(200\) −153.264 103.162i −0.766318 0.515808i
\(201\) −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
\(205\) 9.35470 30.6509i 0.0456327 0.149517i
\(206\) 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
\(210\) 327.414 + 79.8955i 1.55912 + 0.380455i
\(211\) 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
\(215\) 29.2246 95.7551i 0.135928 0.445372i
\(216\) −39.6551 195.548i −0.183589 0.905316i
\(217\) −74.5000 + 42.0433i −0.343318 + 0.193748i
\(218\) −568.991 −2.61005
\(219\) 117.006 238.010i 0.534275 1.08680i
\(220\) 374.080 86.5540i 1.70036 0.393427i
\(221\) 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
\(225\) −201.706 99.6985i −0.896470 0.443105i
\(226\) 13.9638 + 24.1859i 0.0617865 + 0.107017i
\(227\) −34.4570 + 59.6813i −0.151793 + 0.262913i −0.931887 0.362750i \(-0.881838\pi\)
0.780094 + 0.625663i \(0.215171\pi\)
\(228\) −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 0.905767 0.423777i \(-0.139296\pi\)
−0.819885 + 0.572528i \(0.805963\pi\)
\(234\) 193.807 149.480i 0.828235 0.638802i
\(235\) −26.7668 115.684i −0.113901 0.492272i
\(236\) −264.639 + 152.789i −1.12135 + 0.647412i
\(237\) −15.9644 + 10.6958i −0.0673605 + 0.0451300i
\(238\) 204.873 + 120.979i 0.860811 + 0.508317i
\(239\) 341.734i 1.42985i 0.699201 + 0.714925i \(0.253539\pi\)
−0.699201 + 0.714925i \(0.746461\pi\)
\(240\) 21.3865 6.47689i 0.0891103 0.0269870i
\(241\) −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
\(245\) 50.5339 + 239.732i 0.206261 + 0.978497i
\(246\) −34.3517 51.2729i −0.139641 0.208427i
\(247\) 147.960 85.4246i 0.599027 0.345849i
\(248\) 45.1550 78.2108i 0.182077 0.315366i
\(249\) −20.7040 309.981i −0.0831486 1.24490i
\(250\) −143.238 + 374.776i −0.572954 + 1.49910i
\(251\) 201.118i 0.801266i −0.916239 0.400633i \(-0.868790\pi\)
0.916239 0.400633i \(-0.131210\pi\)
\(252\) 316.763 239.393i 1.25699 0.949972i
\(253\) 372.136i 1.47089i
\(254\) −163.309 + 94.2863i −0.642947 + 0.371206i
\(255\) −115.884 108.636i −0.454448 0.426025i
\(256\) 108.113 187.257i 0.422316 0.731473i
\(257\) 126.605 + 219.286i 0.492626 + 0.853253i 0.999964 0.00849432i \(-0.00270386\pi\)
−0.507338 + 0.861747i \(0.669371\pi\)
\(258\) −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 \(-0.945733\pi\)
0.639681 + 0.768641i \(0.279067\pi\)
\(264\) 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 \(0.506396\pi\)
\(270\) −394.326 + 179.632i −1.46047 + 0.665304i
\(271\) −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
\(275\) −133.801 273.659i −0.486549 0.995125i
\(276\) −38.4824 576.161i −0.139429 2.08754i
\(277\) −310.160 179.071i −1.11971 0.646466i −0.178385 0.983961i \(-0.557087\pi\)
−0.941327 + 0.337495i \(0.890421\pi\)
\(278\) 202.431 + 350.620i 0.728167 + 1.26122i
\(279\) 41.8372 101.718i 0.149954 0.364581i
\(280\) −174.625 190.800i −0.623662 0.681430i
\(281\) 193.923i 0.690117i −0.938581 0.345058i \(-0.887859\pi\)
0.938581 0.345058i \(-0.112141\pi\)
\(282\) −205.217 100.885i −0.727721 0.357749i
\(283\) 111.089 + 64.1371i 0.392539 + 0.226633i 0.683260 0.730175i \(-0.260562\pi\)
−0.290720 + 0.956808i \(0.593895\pi\)
\(284\) 13.3255 + 7.69345i 0.0469206 + 0.0270896i
\(285\) −289.486 + 87.6707i −1.01574 + 0.307617i
\(286\) 331.364 1.15862
\(287\) 22.8129 38.6326i 0.0794873 0.134608i
\(288\) 117.567 285.838i 0.408219 0.992495i
\(289\) 88.4310 + 153.167i 0.305990 + 0.529990i
\(290\) 670.625 155.168i 2.31250 0.535062i
\(291\) 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 \(-0.762981\pi\)
−0.735348 + 0.677689i \(0.762981\pi\)
\(294\) 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
\(300\) 235.457 + 409.858i 0.784856 + 1.36619i
\(301\) 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
\(305\) 23.6633 + 102.271i 0.0775847 + 0.335315i
\(306\) −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
\(310\) −187.583 57.2506i −0.605107 0.184679i
\(311\) −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 −0.100996 0.994887i \(-0.532203\pi\)
0.811100 + 0.584908i \(0.198869\pi\)
\(314\) 86.6992i 0.276112i
\(315\) −241.685 202.023i −0.767253 0.641344i
\(316\) 40.3692 0.127751
\(317\) −159.906 276.965i −0.504435 0.873707i −0.999987 0.00512853i \(-0.998368\pi\)
0.495552 0.868578i \(-0.334966\pi\)
\(318\) 56.3903 + 844.277i 0.177328 + 2.65496i
\(319\) −261.307 + 452.597i −0.819145 + 1.41880i
\(320\) −498.632 152.183i −1.55822 0.475572i
\(321\) 142.279 95.3239i 0.443238 0.296959i
\(322\) 597.607 337.253i 1.85592 1.04737i
\(323\) −213.534 −0.661097
\(324\) −129.673 + 493.747i −0.400225 + 1.52391i
\(325\) −118.277 + 175.719i −0.363928 + 0.540675i
\(326\) −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
\(330\) −571.259 133.473i −1.73109 0.404464i
\(331\) −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 \(0.190957\pi\)
−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
\(340\) 75.2225 + 325.106i 0.221243 + 0.956194i
\(341\) 128.956 74.4527i 0.378170 0.218336i
\(342\) −221.578 + 538.719i −0.647890 + 1.57520i
\(343\) −10.0957 + 342.851i −0.0294336 + 0.999567i
\(344\) 147.970i 0.430144i
\(345\) −438.452 + 132.785i −1.27087 + 0.384884i
\(346\) −136.449 + 236.336i −0.394361 + 0.683053i
\(347\) −85.3529 + 147.836i −0.245974 + 0.426039i −0.962405 0.271619i \(-0.912441\pi\)
0.716431 + 0.697658i \(0.245774\pi\)
\(348\) 357.767 727.757i 1.02807 2.09126i
\(349\) 549.147 1.57349 0.786744 0.617280i \(-0.211765\pi\)
0.786744 + 0.617280i \(0.211765\pi\)
\(350\) −318.206 + 462.877i −0.909160 + 1.32250i
\(351\) −224.199 + 45.4653i −0.638745 + 0.129531i
\(352\) 362.380 209.220i 1.02949 0.594375i
\(353\) 153.623 266.082i 0.435192 0.753775i −0.562119 0.827056i \(-0.690014\pi\)
0.997311 + 0.0732815i \(0.0233472\pi\)
\(354\) 465.847 31.1145i 1.31595 0.0878939i
\(355\) 3.56340 11.6756i 0.0100378 0.0328890i
\(356\) 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 \(0.381796\pi\)
\(360\) 328.148 + 53.9121i 0.911523 + 0.149756i
\(361\) −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 \(-0.383520\pi\)
−0.629776 + 0.776776i \(0.716854\pi\)
\(368\) 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 \(-0.628415\pi\)
0.600215 + 0.799839i \(0.295082\pi\)
\(374\) −358.667 207.076i −0.959002 0.553680i
\(375\) 274.684 255.292i 0.732490 0.680778i
\(376\) 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 \(0.405814\pi\)
\(380\) 607.750 + 185.486i 1.59934 + 0.488121i
\(381\) 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 \(-0.0880934\pi\)
−0.717602 + 0.696454i \(0.754760\pi\)
\(384\) −491.751 + 329.462i −1.28060 + 0.857974i
\(385\) −92.0535 416.412i −0.239100 1.08159i
\(386\) 396.719i 1.02777i
\(387\) 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 \(0.578791\pi\)
\(390\) 118.237 + 390.415i 0.303172 + 1.00106i
\(391\) −323.416 −0.827152
\(392\) −174.865 317.087i −0.446084 0.808895i
\(393\) 134.407 + 200.614i 0.342002 + 0.510468i
\(394\) −36.2024 62.7044i −0.0918843 0.159148i
\(395\) −7.21963 31.2027i −0.0182776 0.0789942i
\(396\) −547.265 + 422.096i −1.38198 + 1.06590i
\(397\) 514.877 297.264i 1.29692 0.748776i 0.317048 0.948410i \(-0.397308\pi\)
0.979871 + 0.199634i \(0.0639752\pi\)
\(398\) 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
\(405\) 404.824 + 11.9267i 0.999566 + 0.0294487i
\(406\) 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 \(0.249605\pi\)
\(410\) 100.214 23.1873i 0.244424 0.0565544i
\(411\) −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
\(415\) 495.235 + 151.146i 1.19334 + 0.364207i
\(416\) −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 \(-0.0372095\pi\)
\(420\) 185.583 + 635.192i 0.441865 + 1.51236i
\(421\) 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
\(425\) 237.832 116.284i 0.559606 0.273609i
\(426\) −13.0853 19.5309i −0.0307166 0.0458473i
\(427\) −1.44206 + 146.955i −0.00337719 + 0.344157i
\(428\) −359.781 −0.840610
\(429\) −277.943 136.637i −0.647885 0.318502i
\(430\) 313.072 72.4382i 0.728076 0.168461i
\(431\) 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 \(-0.875969\pi\)
0.925040 0.379870i \(-0.124031\pi\)
\(434\) −236.430 139.614i −0.544771 0.321692i
\(435\) −626.491 146.378i −1.44021 0.336501i
\(436\) −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 0.733953 0.679200i \(-0.237673\pi\)
−0.955181 + 0.296022i \(0.904340\pi\)
\(444\) −627.502 + 41.9116i −1.41329 + 0.0943955i
\(445\) 305.414 70.6662i 0.686324 0.158801i
\(446\) 869.319 501.902i 1.94915 1.12534i
\(447\) −192.609 287.487i −0.430893 0.643147i
\(448\) −628.477 371.121i −1.40285 0.828396i
\(449\) 434.253i 0.967156i 0.875301 + 0.483578i \(0.160663\pi\)
−0.875301 + 0.483578i \(0.839337\pi\)
\(450\) −46.5777 720.685i −0.103506 1.60152i
\(451\) −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
\(455\) −218.756 + 200.211i −0.480782 + 0.440024i
\(456\) 371.397 248.828i 0.814468 0.545675i
\(457\) −18.5054 + 10.6841i −0.0404932 + 0.0233787i −0.520110 0.854099i \(-0.674109\pi\)
0.479617 + 0.877478i \(0.340776\pi\)
\(458\) 552.314 956.636i 1.20593 2.08872i
\(459\) 271.084 + 90.8954i 0.590597 + 0.198029i
\(460\) 920.491 + 280.935i 2.00107 + 0.610728i
\(461\) 759.274i 1.64702i −0.567305 0.823508i \(-0.692014\pi\)
0.567305 0.823508i \(-0.307986\pi\)
\(462\) −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
\(465\) 133.734 + 125.370i 0.287601 + 0.269613i
\(466\) −64.2280 + 111.246i −0.137828 + 0.238726i
\(467\) −207.939 360.160i −0.445265 0.771221i 0.552806 0.833310i \(-0.313557\pi\)
−0.998071 + 0.0620891i \(0.980224\pi\)
\(468\) 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 \(0.683998\pi\)
\(480\) 375.808 + 352.303i 0.782933 + 0.733965i
\(481\) −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
\(485\) −205.123 + 672.092i −0.422934 + 1.38576i
\(486\) 510.614 589.591i 1.05065 1.21315i
\(487\) 728.584 + 420.648i 1.49607 + 0.863754i 0.999990 0.00452596i \(-0.00144066\pi\)
0.496075 + 0.868280i \(0.334774\pi\)
\(488\) −77.5745 134.363i −0.158964 0.275334i
\(489\) 460.033 + 686.641i 0.940764 + 1.40417i
\(490\) −585.284 + 525.206i −1.19446 + 1.07185i
\(491\) 842.285i 1.71545i 0.514110 + 0.857724i \(0.328122\pi\)
−0.514110 + 0.857724i \(0.671878\pi\)
\(492\) 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
\(495\) 424.125 + 347.512i 0.856818 + 0.702044i
\(496\) −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 \(-0.497379\pi\)
\(500\) −777.916 + 124.369i −1.55583 + 0.248738i
\(501\) −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 \(-0.719451\pi\)
−0.636095 + 0.771611i \(0.719451\pi\)
\(504\) 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 \(0.585302\pi\)
\(510\) 115.999 496.471i 0.227449 0.973473i
\(511\) 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
\(515\) 691.890 160.089i 1.34348 0.310851i
\(516\) 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
\(520\) 91.3860 299.429i 0.175742 0.575825i
\(521\) 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 −0.449799 0.893130i \(-0.648504\pi\)
0.548574 + 0.836102i \(0.315171\pi\)
\(524\) 507.291i 0.968113i
\(525\) 457.771 257.041i 0.871946 0.489603i
\(526\) −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
\(530\) −1348.84 411.668i −2.54498 0.776732i
\(531\) −403.574 165.992i −0.760026 0.312603i
\(532\) 766.010 + 452.336i 1.43987 + 0.850255i
\(533\) 54.3044 0.101884
\(534\) 266.344 541.788i 0.498772 1.01459i
\(535\) 64.3434 + 278.087i 0.120268 + 0.519789i
\(536\) 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
\(540\) −692.589 494.178i −1.28257 0.915144i
\(541\) 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 \(0.0320505\pi\)
−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
\(550\) 545.960 811.114i 0.992655 1.47475i
\(551\) −749.010 + 432.441i −1.35936 + 0.784830i
\(552\) 562.514 376.872i 1.01905 0.682739i
\(553\) 0.439970 44.8357i 0.000795605 0.0810772i
\(554\) 1149.54i 2.07498i
\(555\) 144.618 + 477.522i 0.260572 + 0.860400i
\(556\) −397.476 + 688.448i −0.714885 + 1.23822i
\(557\) 226.708 392.669i 0.407015 0.704971i −0.587538 0.809196i \(-0.699903\pi\)
0.994554 + 0.104225i \(0.0332362\pi\)
\(558\) 349.889 46.9485i 0.627042 0.0841371i
\(559\) 169.650 0.303488
\(560\) −15.7087 + 49.7174i −0.0280513 + 0.0887810i
\(561\) 215.456 + 321.587i 0.384057 + 0.573239i
\(562\) 539.049 311.220i 0.959161 0.553772i
\(563\) 25.2929 43.8087i 0.0449253 0.0778129i −0.842688 0.538402i \(-0.819028\pi\)
0.887614 + 0.460589i \(0.152362\pi\)
\(564\) −29.9230 448.008i −0.0530549 0.794340i
\(565\) 41.6097 + 12.6993i 0.0736455 + 0.0224767i
\(566\) 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 \(0.0493420\pi\)
\(570\) −708.284 663.986i −1.24260 1.16489i
\(571\) −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 0.251769 0.967787i \(-0.418988\pi\)
−0.712244 + 0.701932i \(0.752321\pi\)
\(578\) −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
\(585\) 61.8112 376.228i 0.105660 0.643124i
\(586\) −691.559 1197.81i −1.18013 2.04405i
\(587\) −336.767 −0.573708 −0.286854 0.957974i \(-0.592610\pi\)
−0.286854 + 0.957974i \(0.592610\pi\)
\(588\) 43.5889 + 925.421i 0.0741307 + 1.57384i
\(589\) 246.426 0.418380
\(590\) −227.146 + 744.250i −0.384993 + 1.26144i
\(591\) 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 \(0.220639\pi\)
0.168748 + 0.985659i \(0.446028\pi\)
\(594\) 1034.90 209.866i 1.74225 0.353310i
\(595\) 361.896 80.0021i 0.608229 0.134457i
\(596\) 726.966i 1.21974i
\(597\) −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 \(0.831905\pi\)
\(600\) −278.155 + 479.393i −0.463592 + 0.798989i
\(601\) 434.293 0.722617 0.361309 0.932446i \(-0.382330\pi\)
0.361309 + 0.932446i \(0.382330\pi\)
\(602\) 449.859 + 4.41444i 0.747275 + 0.00733295i
\(603\) 188.545 + 77.5496i 0.312678 + 0.128606i
\(604\) 881.069 + 1526.06i 1.45872 + 2.52658i
\(605\) 30.9590 + 133.802i 0.0511718 + 0.221161i
\(606\) −1473.95 + 98.4467i −2.43226 + 0.162453i
\(607\) −783.964 + 452.622i −1.29154 + 0.745670i −0.978927 0.204211i \(-0.934537\pi\)
−0.312612 + 0.949881i \(0.601204\pi\)
\(608\) 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 \(-0.522870\pi\)
−0.899685 + 0.436541i \(0.856204\pi\)
\(614\) 568.875 328.440i 0.926507 0.534919i
\(615\) −93.6187 21.8737i −0.152225 0.0355670i
\(616\) 309.784 + 548.931i 0.502896 + 0.891122i
\(617\) −205.651 −0.333308 −0.166654 0.986015i \(-0.553296\pi\)
−0.166654 + 0.986015i \(0.553296\pi\)
\(618\) 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 \(-0.0767271\pi\)
\(620\) −86.8093 375.183i −0.140015 0.605134i
\(621\) 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
\(625\) 235.252 + 579.035i 0.376403 + 0.926456i
\(626\) 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
\(630\) 173.694 996.033i 0.275705 1.58100i
\(631\) −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
\(635\) −85.7485 + 280.958i −0.135037 + 0.442453i
\(636\) −1380.29 + 924.766i −2.17027 + 1.45403i
\(637\) −363.545 + 200.486i −0.570715 + 0.314734i
\(638\) −1677.45 −2.62923
\(639\) 2.92218 + 21.7779i 0.00457305 + 0.0340812i
\(640\) −222.386 961.134i −0.347478 1.50177i
\(641\) −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 \(0.166685\pi\)
−0.865997 + 0.500049i \(0.833315\pi\)
\(644\) 1160.19 + 685.102i 1.80154 + 1.06382i
\(645\) −292.469 68.3346i −0.453441 0.105945i
\(646\) −342.693 593.562i −0.530485 0.918827i
\(647\) −86.4616 + 149.756i −0.133635 + 0.231462i −0.925075 0.379784i \(-0.875998\pi\)
0.791440 + 0.611246i \(0.209332\pi\)
\(648\) −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 \(-0.878153\pi\)
0.140339 0.990104i \(-0.455181\pi\)
\(654\) 113.757 + 1703.18i 0.173941 + 2.60425i
\(655\) −392.103 + 90.7241i −0.598630 + 0.138510i
\(656\) 8.26888 4.77404i 0.0126050 0.00727750i
\(657\) −735.836 302.653i −1.11999 0.460660i
\(658\) 464.684 262.240i 0.706206 0.398540i
\(659\) 494.948i 0.751059i −0.926810 0.375530i \(-0.877461\pi\)
0.926810 0.375530i \(-0.122539\pi\)
\(660\) −333.874 1102.44i −0.505869 1.67036i
\(661\) 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
\(665\) 212.632 672.971i 0.319747 1.01199i
\(666\) 888.646 + 365.505i 1.33430 + 0.548807i
\(667\) −1134.44 + 654.970i −1.70081 + 0.981964i
\(668\) −25.7654 + 44.6270i −0.0385710 + 0.0668069i
\(669\) −936.128 + 62.5251i −1.39929 + 0.0934605i
\(670\) 106.120 347.705i 0.158388 0.518962i
\(671\) 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
\(675\) −258.104 + 623.705i −0.382376 + 0.924007i
\(676\) −306.337 + 530.591i −0.453161 + 0.784897i
\(677\) 150.968 + 261.485i 0.222996 + 0.386241i 0.955716 0.294289i \(-0.0950829\pi\)
−0.732720 + 0.680530i \(0.761750\pi\)
\(678\) 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 \(-0.854512\pi\)
0.830867 + 0.556471i \(0.187845\pi\)
\(684\) −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
\(690\) −1072.76 1005.66i −1.55472 1.45749i
\(691\) −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
\(695\) 603.210 + 184.100i 0.867927 + 0.264892i
\(696\) 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
\(700\) −1099.50 86.6623i −1.57072 0.123803i
\(701\) 446.823i 0.637408i −0.947854 0.318704i \(-0.896752\pi\)
0.947854 0.318704i \(-0.103248\pi\)
\(702\) −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
\(705\) −340.929 + 103.250i −0.483587 + 0.146454i
\(706\) 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 \(-0.467221\pi\)
\(710\) 38.1735 8.83253i 0.0537655 0.0124402i
\(711\) 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 \(0.578627\pi\)
\(720\) −23.6632 62.7219i −0.0328656 0.0871137i
\(721\) 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
\(725\) 598.747 889.536i 0.825857 1.22695i
\(726\) 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
\(730\) −414.155 + 1356.99i −0.567335 + 1.85889i
\(731\) −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 \(-0.581259\pi\)
0.711700 + 0.702484i \(0.247926\pi\)
\(734\) 369.916i 0.503973i
\(735\) 707.493 199.194i 0.962576 0.271012i
\(736\) 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 \(-0.134209\pi\)
\(740\) 305.969 1002.52i 0.413471 1.35475i
\(741\) −285.285 425.814i −0.385001 0.574647i
\(742\) −1700.09 1003.92i −2.29122 1.35299i
\(743\) 592.907 0.797990 0.398995 0.916953i \(-0.369359\pi\)
0.398995 + 0.916953i \(0.369359\pi\)
\(744\) −243.138 119.527i −0.326799 0.160655i
\(745\) 561.896 130.011i 0.754223 0.174511i
\(746\) 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
\(750\) 1150.47 + 353.832i 1.53395 + 0.471776i
\(751\) −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 \(0.120635\pi\)
−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
\(760\) 167.958 + 725.901i 0.220997 + 0.955133i
\(761\) 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
\(765\) −302.016 + 368.599i −0.394793 + 0.481829i