Properties

Label 105.3.o.b.44.18
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 44.18
Character \(\chi\) \(=\) 105.44
Dual form 105.3.o.b.74.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.60486 - 2.77971i) q^{2} +(2.69226 + 1.32352i) q^{3} +(-3.15118 - 5.45800i) q^{4} +(-1.12712 - 4.87130i) q^{5} +(7.99972 - 5.35963i) q^{6} +(-6.02754 + 3.55932i) q^{7} -7.38994 q^{8} +(5.49658 + 7.12655i) q^{9} +O(q^{10})\) \(q+(1.60486 - 2.77971i) q^{2} +(2.69226 + 1.32352i) q^{3} +(-3.15118 - 5.45800i) q^{4} +(-1.12712 - 4.87130i) q^{5} +(7.99972 - 5.35963i) q^{6} +(-6.02754 + 3.55932i) q^{7} -7.38994 q^{8} +(5.49658 + 7.12655i) q^{9} +(-15.3497 - 4.68473i) q^{10} +(10.5523 - 6.09236i) q^{11} +(-1.26002 - 18.8650i) 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} +(28.6310 - 3.84173i) q^{18} +(-10.0823 + 17.4631i) q^{19} +(-23.0359 + 21.5022i) q^{20} +(-20.9386 + 1.60503i) q^{21} -39.1096i q^{22} +(-15.2706 + 26.4494i) q^{23} +(-19.8957 - 9.78076i) q^{24} +(-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} +(-35.1250 - 32.9282i) q^{30} +(-6.11033 - 10.5834i) q^{31} +(-17.1707 - 29.7405i) q^{32} +(36.4729 - 2.43607i) 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} +(-11.2138 + 22.8108i) q^{39} +(8.32932 + 35.9987i) q^{40} -6.40934i q^{41} +(-29.1420 + 60.7790i) q^{42} -20.0231i q^{43} +(-66.5042 - 38.3962i) q^{44} +(28.5203 - 34.8079i) q^{45} +(49.0144 + 84.8955i) q^{46} +(-11.8740 + 20.5664i) q^{47} +(3.71287 - 2.48754i) q^{48} +(23.6625 - 42.9079i) q^{49} +(-5.51992 + 80.0531i) q^{50} +(2.11714 + 31.6979i) q^{51} +(46.2440 - 26.6990i) q^{52} +(-43.9372 - 76.1014i) q^{53} +(82.1667 + 27.5508i) q^{54} +(-41.5714 - 44.5366i) q^{55} +(44.5432 - 26.3032i) q^{56} +(-50.2571 + 33.6711i) q^{57} +(-119.224 - 68.8342i) q^{58} +(-41.9905 + 24.2432i) q^{59} +(-90.4772 + 27.4010i) q^{60} +(10.4973 - 18.1819i) q^{61} -39.2250 q^{62} +(-58.4965 - 23.3915i) q^{63} -104.268 q^{64} +(41.2731 - 9.54971i) q^{65} +(51.7625 - 105.294i) q^{66} +(19.6174 - 11.3261i) q^{67} +(33.3695 - 57.7976i) q^{68} +(-76.1189 + 50.9979i) q^{69} +(109.195 - 26.3969i) q^{70} -2.44145i q^{71} +(-40.6194 - 52.6648i) q^{72} +(-76.5611 + 44.2026i) q^{73} +(92.4605 - 53.3821i) q^{74} +(-74.9998 - 0.161411i) 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} +(-20.5753 + 78.3432i) q^{81} +(-17.8161 - 10.2861i) q^{82} +103.557 q^{83} +(74.7415 + 109.225i) q^{84} +(38.7059 - 36.1289i) q^{85} +(-55.6583 - 32.1344i) q^{86} +(56.7672 - 115.474i) q^{87} +(-77.9808 + 45.0222i) q^{88} +(-54.2968 - 31.3483i) q^{89} +(-50.9846 - 135.140i) q^{90} +(-30.1570 - 51.0696i) q^{91} +192.481 q^{92} +(-2.44325 - 36.5805i) q^{93} +(38.1124 + 66.0126i) q^{94} +(96.4321 + 29.4312i) q^{95} +(-6.86580 - 102.795i) q^{96} +140.539i q^{97} +(-81.2961 - 134.636i) q^{98} +(101.419 + 41.7142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + O(q^{10}) \) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + 62q^{10} + 84q^{15} - 116q^{16} - 56q^{19} + 36q^{21} - 12q^{24} - 6q^{25} - 20q^{30} - 444q^{31} + 256q^{34} - 688q^{36} + 168q^{39} + 54q^{40} - 40q^{45} + 304q^{46} + 156q^{49} + 156q^{51} - 140q^{54} - 500q^{55} - 130q^{60} + 288q^{61} + 472q^{64} + 340q^{66} - 272q^{69} + 710q^{70} - 524q^{75} + 400q^{76} - 340q^{79} + 496q^{84} + 896q^{85} + 1356q^{90} - 656q^{91} - 560q^{94} + 472q^{96} - 336q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.60486 2.77971i 0.802432 1.38985i −0.115579 0.993298i \(-0.536872\pi\)
0.918011 0.396555i \(-0.129794\pi\)
\(3\) 2.69226 + 1.32352i 0.897421 + 0.441174i
\(4\) −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
\(9\) 5.49658 + 7.12655i 0.610731 + 0.791838i
\(10\) −15.3497 4.68473i −1.53497 0.468473i
\(11\) 10.5523 6.09236i 0.959298 0.553851i 0.0633411 0.997992i \(-0.479824\pi\)
0.895957 + 0.444141i \(0.146491\pi\)
\(12\) −1.26002 18.8650i −0.105002 1.57209i
\(13\) 8.47270i 0.651746i 0.945414 + 0.325873i \(0.105658\pi\)
−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 0.978678 0.205401i \(-0.0658498\pi\)
−0.667221 + 0.744859i \(0.732516\pi\)
\(18\) 28.6310 3.84173i 1.59061 0.213429i
\(19\) −10.0823 + 17.4631i −0.530649 + 0.919111i 0.468711 + 0.883351i \(0.344718\pi\)
−0.999360 + 0.0357599i \(0.988615\pi\)
\(20\) −23.0359 + 21.5022i −1.15179 + 1.07511i
\(21\) −20.9386 + 1.60503i −0.997075 + 0.0764301i
\(22\) 39.1096i 1.77771i
\(23\) −15.2706 + 26.4494i −0.663939 + 1.14998i 0.315633 + 0.948881i \(0.397783\pi\)
−0.979572 + 0.201094i \(0.935550\pi\)
\(24\) −19.8957 9.78076i −0.828987 0.407532i
\(25\) −22.4592 + 10.9810i −0.898369 + 0.439242i
\(26\) 23.5516 + 13.5975i 0.905832 + 0.522982i
\(27\) 5.36609 + 26.4614i 0.198744 + 0.980051i
\(28\) 38.4206 + 21.6823i 1.37217 + 0.774368i
\(29\) 42.8910i 1.47900i −0.673157 0.739499i \(-0.735062\pi\)
0.673157 0.739499i \(-0.264938\pi\)
\(30\) −35.1250 32.9282i −1.17083 1.09761i
\(31\) −6.11033 10.5834i −0.197107 0.341400i 0.750482 0.660891i \(-0.229821\pi\)
−0.947589 + 0.319491i \(0.896488\pi\)
\(32\) −17.1707 29.7405i −0.536584 0.929390i
\(33\) 36.4729 2.43607i 1.10524 0.0738203i
\(34\) 33.9895 0.999691
\(35\) 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
\(39\) −11.2138 + 22.8108i −0.287534 + 0.584891i
\(40\) 8.32932 + 35.9987i 0.208233 + 0.899967i
\(41\) 6.40934i 0.156325i −0.996941 0.0781627i \(-0.975095\pi\)
0.996941 0.0781627i \(-0.0249054\pi\)
\(42\) −29.1420 + 60.7790i −0.693858 + 1.44712i
\(43\) 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
\(45\) 28.5203 34.8079i 0.633784 0.773510i
\(46\) 49.0144 + 84.8955i 1.06553 + 1.84555i
\(47\) −11.8740 + 20.5664i −0.252639 + 0.437583i −0.964251 0.264989i \(-0.914632\pi\)
0.711613 + 0.702572i \(0.247965\pi\)
\(48\) 3.71287 2.48754i 0.0773514 0.0518237i
\(49\) 23.6625 42.9079i 0.482909 0.875671i
\(50\) −5.51992 + 80.0531i −0.110398 + 1.60106i
\(51\) 2.11714 + 31.6979i 0.0415126 + 0.621528i
\(52\) 46.2440 26.6990i 0.889308 0.513442i
\(53\) −43.9372 76.1014i −0.829003 1.43588i −0.898821 0.438316i \(-0.855575\pi\)
0.0698177 0.997560i \(-0.477758\pi\)
\(54\) 82.1667 + 27.5508i 1.52161 + 0.510199i
\(55\) −41.5714 44.5366i −0.755843 0.809756i
\(56\) 44.5432 26.3032i 0.795414 0.469699i
\(57\) −50.2571 + 33.6711i −0.881704 + 0.590722i
\(58\) −119.224 68.8342i −2.05559 1.18680i
\(59\) −41.9905 + 24.2432i −0.711703 + 0.410902i −0.811691 0.584087i \(-0.801453\pi\)
0.0999885 + 0.994989i \(0.468119\pi\)
\(60\) −90.4772 + 27.4010i −1.50795 + 0.456684i
\(61\) 10.4973 18.1819i 0.172087 0.298063i −0.767062 0.641573i \(-0.778282\pi\)
0.939149 + 0.343509i \(0.111616\pi\)
\(62\) −39.2250 −0.632662
\(63\) −58.4965 23.3915i −0.928515 0.371294i
\(64\) −104.268 −1.62918
\(65\) 41.2731 9.54971i 0.634971 0.146919i
\(66\) 51.7625 105.294i 0.784280 1.59536i
\(67\) 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 \(-0.994527\pi\)
0.999852 0.0171933i \(-0.00547308\pi\)
\(72\) −40.6194 52.6648i −0.564158 0.731455i
\(73\) −76.5611 + 44.2026i −1.04878 + 0.605515i −0.922308 0.386455i \(-0.873699\pi\)
−0.126474 + 0.991970i \(0.540366\pi\)
\(74\) 92.4605 53.3821i 1.24947 0.721380i
\(75\) −74.9998 0.161411i −0.999998 0.00215215i
\(76\) 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
\(81\) −20.5753 + 78.3432i −0.254016 + 0.967200i
\(82\) −17.8161 10.2861i −0.217269 0.125440i
\(83\) 103.557 1.24768 0.623839 0.781553i \(-0.285572\pi\)
0.623839 + 0.781553i \(0.285572\pi\)
\(84\) 74.7415 + 109.225i 0.889779 + 1.30030i
\(85\) 38.7059 36.1289i 0.455364 0.425046i
\(86\) −55.6583 32.1344i −0.647190 0.373655i
\(87\) 56.7672 115.474i 0.652496 1.32729i
\(88\) −77.9808 + 45.0222i −0.886145 + 0.511616i
\(89\) −54.2968 31.3483i −0.610077 0.352228i 0.162919 0.986639i \(-0.447909\pi\)
−0.772995 + 0.634412i \(0.781242\pi\)
\(90\) −50.9846 135.140i −0.566496 1.50156i
\(91\) −30.1570 51.0696i −0.331396 0.561204i
\(92\) 192.481 2.09219
\(93\) −2.44325 36.5805i −0.0262716 0.393339i
\(94\) 38.1124 + 66.0126i 0.405451 + 0.702262i
\(95\) 96.4321 + 29.4312i 1.01507 + 0.309802i
\(96\) −6.86580 102.795i −0.0715188 1.07078i
\(97\) 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 0.332442 0.943124i \(-0.392128\pi\)
0.982990 + 0.183659i \(0.0587942\pi\)
\(102\) 91.5087 + 44.9859i 0.897144 + 0.441038i
\(103\) −123.005 71.0169i −1.19422 0.689485i −0.234961 0.972005i \(-0.575496\pi\)
−0.959261 + 0.282520i \(0.908830\pi\)
\(104\) 62.6128i 0.602046i
\(105\) 31.4188 + 100.189i 0.299227 + 0.954182i
\(106\) −282.053 −2.66088
\(107\) 28.5434 49.4386i 0.266761 0.462043i −0.701263 0.712903i \(-0.747380\pi\)
0.968023 + 0.250860i \(0.0807134\pi\)
\(108\) 127.517 112.673i 1.18071 1.04327i
\(109\) −88.6354 153.521i −0.813169 1.40845i −0.910635 0.413211i \(-0.864407\pi\)
0.0974665 0.995239i \(-0.468926\pi\)
\(110\) −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 \(-0.487742\pi\)
0.0384995 + 0.999259i \(0.487742\pi\)
\(114\) 12.9400 + 193.738i 0.113509 + 1.69945i
\(115\) 146.055 + 44.5761i 1.27004 + 0.387618i
\(116\) −234.099 + 135.157i −2.01809 + 1.16515i
\(117\) −60.3811 + 46.5708i −0.516078 + 0.398041i
\(118\) 155.628i 1.31888i
\(119\) −64.5562 36.4316i −0.542489 0.306148i
\(120\) −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
\(123\) 8.48290 17.2556i 0.0689667 0.140290i
\(124\) −38.5095 + 66.7004i −0.310560 + 0.537907i
\(125\) 78.8061 + 97.0288i 0.630449 + 0.776231i
\(126\) −158.900 + 125.063i −1.26111 + 0.992562i
\(127\) 58.7503i 0.462601i 0.972882 + 0.231300i \(0.0742980\pi\)
−0.972882 + 0.231300i \(0.925702\pi\)
\(128\) −98.6526 + 170.871i −0.770724 + 1.33493i
\(129\) 26.5010 53.9075i 0.205434 0.417887i
\(130\) 39.6923 130.053i 0.305326 1.00041i
\(131\) 69.7084 + 40.2462i 0.532125 + 0.307223i 0.741881 0.670531i \(-0.233934\pi\)
−0.209756 + 0.977754i \(0.567267\pi\)
\(132\) −128.229 191.393i −0.971430 1.44994i
\(133\) −1.38505 141.146i −0.0104139 1.06125i
\(134\) 72.7076i 0.542594i
\(135\) 122.853 55.9649i 0.910024 0.414555i
\(136\) −39.1280 67.7717i −0.287706 0.498321i
\(137\) 5.95720 + 10.3182i 0.0434832 + 0.0753151i 0.886948 0.461870i \(-0.152821\pi\)
−0.843465 + 0.537185i \(0.819488\pi\)
\(138\) 19.5987 + 293.433i 0.142020 + 2.12633i
\(139\) 126.136 0.907450 0.453725 0.891142i \(-0.350095\pi\)
0.453725 + 0.891142i \(0.350095\pi\)
\(140\) 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
\(144\) 13.2883 1.78304i 0.0922801 0.0123822i
\(145\) −208.935 + 48.3431i −1.44093 + 0.333400i
\(146\) 283.757i 1.94354i
\(147\) 120.495 84.2014i 0.819696 0.572799i
\(148\) 209.633i 1.41644i
\(149\) −99.8945 57.6741i −0.670433 0.387074i 0.125808 0.992055i \(-0.459848\pi\)
−0.796241 + 0.604980i \(0.793181\pi\)
\(150\) −120.813 + 208.218i −0.805421 + 1.38812i
\(151\) 139.800 + 242.140i 0.925827 + 1.60358i 0.790226 + 0.612815i \(0.209963\pi\)
0.135600 + 0.990764i \(0.456704\pi\)
\(152\) 74.5079 129.051i 0.490184 0.849023i
\(153\) −36.2530 + 88.1413i −0.236948 + 0.576087i
\(154\) 139.204 + 235.735i 0.903920 + 1.53075i
\(155\) −44.6679 + 41.6940i −0.288180 + 0.268994i
\(156\) 159.838 10.6758i 1.02460 0.0684344i
\(157\) −23.3925 + 13.5057i −0.148997 + 0.0860235i −0.572645 0.819803i \(-0.694083\pi\)
0.423648 + 0.905827i \(0.360749\pi\)
\(158\) 10.2798 + 17.8052i 0.0650621 + 0.112691i
\(159\) −17.5686 263.037i −0.110494 1.65432i
\(160\) −125.522 + 117.165i −0.784510 + 0.732279i
\(161\) −2.09779 213.778i −0.0130297 1.32781i
\(162\) 184.751 + 182.924i 1.14044 + 1.12916i
\(163\) 238.591 + 137.750i 1.46375 + 0.845094i 0.999182 0.0404450i \(-0.0128776\pi\)
0.464565 + 0.885539i \(0.346211\pi\)
\(164\) −34.9822 + 20.1970i −0.213306 + 0.123152i
\(165\) −52.9760 174.925i −0.321067 1.06015i
\(166\) 166.195 287.859i 1.00118 1.73409i
\(167\) 8.17643 0.0489607 0.0244803 0.999700i \(-0.492207\pi\)
0.0244803 + 0.999700i \(0.492207\pi\)
\(168\) 154.735 11.8611i 0.921041 0.0706018i
\(169\) 97.2133 0.575227
\(170\) −38.3101 165.573i −0.225353 0.973960i
\(171\) −179.870 + 24.1351i −1.05187 + 0.141141i
\(172\) −109.286 + 63.0964i −0.635384 + 0.366839i
\(173\) 42.5110 73.6312i 0.245728 0.425614i −0.716608 0.697476i \(-0.754306\pi\)
0.962336 + 0.271862i \(0.0876395\pi\)
\(174\) −229.880 343.116i −1.32115 1.97193i
\(175\) 96.2889 146.128i 0.550222 0.835018i
\(176\) 18.1518i 0.103135i
\(177\) −145.136 + 9.69379i −0.819976 + 0.0547672i
\(178\) −174.278 + 100.619i −0.979090 + 0.565278i
\(179\) 107.239 61.9145i 0.599101 0.345891i −0.169587 0.985515i \(-0.554243\pi\)
0.768688 + 0.639624i \(0.220910\pi\)
\(180\) −279.854 45.9778i −1.55475 0.255432i
\(181\) −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
\(186\) −105.604 51.9152i −0.567764 0.279114i
\(187\) 111.744 + 64.5152i 0.597559 + 0.345001i
\(188\) 149.669 0.796110
\(189\) −126.529 140.398i −0.669465 0.742844i
\(190\) 236.570 220.820i 1.24511 1.16221i
\(191\) 110.601 + 63.8554i 0.579062 + 0.334322i 0.760761 0.649033i \(-0.224826\pi\)
−0.181699 + 0.983354i \(0.558159\pi\)
\(192\) −280.716 138.000i −1.46206 0.718753i
\(193\) 107.040 61.7995i 0.554611 0.320205i −0.196369 0.980530i \(-0.562915\pi\)
0.750980 + 0.660325i \(0.229582\pi\)
\(194\) 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 \(0.518234\pi\)
\(198\) 278.717 214.969i 1.40766 1.08570i
\(199\) 17.2597 + 29.8946i 0.0867319 + 0.150224i 0.906128 0.423004i \(-0.139024\pi\)
−0.819396 + 0.573228i \(0.805691\pi\)
\(200\) 165.972 81.1493i 0.829862 0.405747i
\(201\) 67.8057 4.52883i 0.337342 0.0225315i
\(202\) 492.411i 2.43768i
\(203\) 152.663 + 258.527i 0.752032 + 1.27353i
\(204\) 166.336 111.441i 0.815372 0.546281i
\(205\) −31.2218 + 7.22406i −0.152302 + 0.0352393i
\(206\) −394.812 + 227.945i −1.91657 + 1.10653i
\(207\) −272.429 + 36.5548i −1.31608 + 0.176593i
\(208\) 10.9309 + 6.31095i 0.0525524 + 0.0303411i
\(209\) 245.701i 1.17560i
\(210\) 328.919 + 73.4549i 1.56628 + 0.349785i
\(211\) 76.0725 0.360533 0.180267 0.983618i \(-0.442304\pi\)
0.180267 + 0.983618i \(0.442304\pi\)
\(212\) −276.908 + 479.618i −1.30617 + 2.26235i
\(213\) 3.23132 6.57304i 0.0151705 0.0308593i
\(214\) −91.6165 158.684i −0.428114 0.741516i
\(215\) −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
\(219\) −264.626 + 17.6747i −1.20834 + 0.0807063i
\(220\) −112.082 + 367.239i −0.509463 + 1.66927i
\(221\) −77.7014 + 44.8609i −0.351590 + 0.202991i
\(222\) 319.581 21.3452i 1.43955 0.0961494i
\(223\) 312.738i 1.40241i −0.712959 0.701206i \(-0.752645\pi\)
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 0.780094 0.625663i \(-0.215171\pi\)
−0.931887 + 0.362750i \(0.881838\pi\)
\(228\) 342.146 + 168.200i 1.50064 + 0.737718i
\(229\) −172.075 + 298.043i −0.751419 + 1.30150i 0.195716 + 0.980661i \(0.437297\pi\)
−0.947135 + 0.320835i \(0.896036\pi\)
\(230\) 358.307 334.451i 1.55786 1.45414i
\(231\) −211.171 + 144.502i −0.914161 + 0.625550i
\(232\) 316.962i 1.36622i
\(233\) 20.0104 34.6590i 0.0858816 0.148751i −0.819885 0.572528i \(-0.805963\pi\)
0.905767 + 0.423777i \(0.139296\pi\)
\(234\) 32.5498 + 242.582i 0.139102 + 1.03667i
\(235\) 113.569 + 34.6613i 0.483271 + 0.147495i
\(236\) 264.639 + 152.789i 1.12135 + 0.647412i
\(237\) −15.9644 + 10.6958i −0.0673605 + 0.0451300i
\(238\) −204.873 + 120.979i −0.860811 + 0.508317i
\(239\) 341.734i 1.42985i 0.699201 + 0.714925i \(0.253539\pi\)
−0.699201 + 0.714925i \(0.746461\pi\)
\(240\) −16.3024 15.2828i −0.0679266 0.0636782i
\(241\) −64.0475 110.934i −0.265757 0.460305i 0.702004 0.712173i \(-0.252289\pi\)
−0.967762 + 0.251867i \(0.918955\pi\)
\(242\) −44.0815 76.3514i −0.182155 0.315502i
\(243\) −159.083 + 183.689i −0.654663 + 0.755921i
\(244\) −132.316 −0.542277
\(245\) −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
\(249\) 278.803 + 137.060i 1.11969 + 0.550443i
\(250\) 396.185 63.3399i 1.58474 0.253360i
\(251\) 201.118i 0.801266i −0.916239 0.400633i \(-0.868790\pi\)
0.916239 0.400633i \(-0.131210\pi\)
\(252\) 56.6620 + 392.985i 0.224849 + 1.55946i
\(253\) 372.136i 1.47089i
\(254\) 163.309 + 94.2863i 0.642947 + 0.371206i
\(255\) 152.024 46.0405i 0.596173 0.180551i
\(256\) 108.113 + 187.257i 0.422316 + 0.731473i
\(257\) 126.605 219.286i 0.492626 0.853253i −0.507338 0.861747i \(-0.669371\pi\)
0.999964 + 0.00849432i \(0.00270386\pi\)
\(258\) −107.316 160.179i −0.415955 0.620850i
\(259\) −232.828 + 2.28472i −0.898949 + 0.00882132i
\(260\) −182.181 195.176i −0.700697 0.750676i
\(261\) 305.664 235.753i 1.17113 0.903270i
\(262\) 223.745 129.179i 0.853989 0.493051i
\(263\) −90.9512 157.532i −0.345822 0.598982i 0.639681 0.768641i \(-0.279067\pi\)
−0.985503 + 0.169659i \(0.945733\pi\)
\(264\) −269.533 + 18.0024i −1.02096 + 0.0681910i
\(265\) −321.191 + 299.806i −1.21204 + 1.13134i
\(266\) −394.567 222.670i −1.48333 0.837105i
\(267\) −104.691 156.261i −0.392102 0.585247i
\(268\) −123.636 71.3814i −0.461329 0.266348i
\(269\) −224.807 + 129.792i −0.835714 + 0.482499i −0.855805 0.517299i \(-0.826938\pi\)
0.0200914 + 0.999798i \(0.493604\pi\)
\(270\) 41.5968 431.312i 0.154062 1.59745i
\(271\) −17.7512 + 30.7460i −0.0655026 + 0.113454i −0.896917 0.442199i \(-0.854198\pi\)
0.831414 + 0.555653i \(0.187532\pi\)
\(272\) 15.7754 0.0579977
\(273\) −13.5990 177.406i −0.0498131 0.649840i
\(274\) 38.2420 0.139569
\(275\) −170.095 + 252.705i −0.618529 + 0.918926i
\(276\) 518.211 + 254.753i 1.87758 + 0.923020i
\(277\) 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 \(-0.887859\pi\)
0.938581 0.345058i \(-0.112141\pi\)
\(282\) 15.2395 + 228.166i 0.0540407 + 0.809099i
\(283\) −111.089 + 64.1371i −0.392539 + 0.226633i −0.683260 0.730175i \(-0.739438\pi\)
0.290720 + 0.956808i \(0.406105\pi\)
\(284\) −13.3255 + 7.69345i −0.0469206 + 0.0270896i
\(285\) 220.668 + 206.867i 0.774273 + 0.725848i
\(286\) 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
\(291\) −186.007 + 378.369i −0.639200 + 1.30024i
\(292\) 482.516 + 278.581i 1.65245 + 0.954043i
\(293\) −430.914 −1.47070 −0.735348 0.677689i \(-0.762981\pi\)
−0.735348 + 0.677689i \(0.762981\pi\)
\(294\) −40.6766 470.073i −0.138356 1.59889i
\(295\) 165.424 + 177.223i 0.560760 + 0.600757i
\(296\) −212.877 122.905i −0.719180 0.415219i
\(297\) 217.837 + 246.536i 0.733457 + 0.830087i
\(298\) −320.634 + 185.118i −1.07595 + 0.621202i
\(299\) −224.098 129.383i −0.749492 0.432719i
\(300\) 235.457 + 409.858i 0.784856 + 1.36619i
\(301\) 71.2685 + 120.690i 0.236773 + 0.400964i
\(302\) 897.439 2.97165
\(303\) 459.213 30.6713i 1.51555 0.101226i
\(304\) 15.0198 + 26.0151i 0.0494072 + 0.0855758i
\(305\) −100.401 30.6425i −0.329184 0.100467i
\(306\) 186.826 + 242.228i 0.610542 + 0.791594i
\(307\) 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 0.155257 0.987874i \(-0.450379\pi\)
0.933153 + 0.359481i \(0.117046\pi\)
\(312\) 82.8694 168.570i 0.265607 0.540289i
\(313\) −222.263 128.323i −0.710104 0.409979i 0.100996 0.994887i \(-0.467797\pi\)
−0.811100 + 0.584908i \(0.801131\pi\)
\(314\) 86.6992i 0.276112i
\(315\) −48.0149 + 311.319i −0.152428 + 0.988315i
\(316\) 40.3692 0.127751
\(317\) −159.906 + 276.965i −0.504435 + 0.873707i 0.495552 + 0.868578i \(0.334966\pi\)
−0.999987 + 0.00512853i \(0.998368\pi\)
\(318\) −759.361 373.303i −2.38793 1.17391i
\(319\) −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
\(324\) 492.434 134.573i 1.51986 0.415350i
\(325\) −93.0391 190.290i −0.286274 0.585509i
\(326\) 765.811 442.141i 2.34911 1.35626i
\(327\) −35.4414 530.630i −0.108384 1.62272i
\(328\) 47.3647i 0.144404i
\(329\) −1.63119 166.228i −0.00495801 0.505253i
\(330\) −571.259 133.473i −1.73109 0.404464i
\(331\) −144.224 + 249.804i −0.435723 + 0.754694i −0.997354 0.0726932i \(-0.976841\pi\)
0.561631 + 0.827388i \(0.310174\pi\)
\(332\) −326.327 565.215i −0.982914 1.70246i
\(333\) 39.8122 + 296.705i 0.119556 + 0.891007i
\(334\) 13.1221 22.7281i 0.0392876 0.0680482i
\(335\) −77.2842 82.7967i −0.230699 0.247154i
\(336\) −13.5255 + 28.2090i −0.0402546 + 0.0839554i
\(337\) 380.518i 1.12913i 0.825387 + 0.564567i \(0.190957\pi\)
−0.825387 + 0.564567i \(0.809043\pi\)
\(338\) 156.014 270.225i 0.461581 0.799481i
\(339\) 23.4251 + 11.5158i 0.0691006 + 0.0339700i
\(340\) −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
\(345\) 334.221 + 313.318i 0.968757 + 0.908167i
\(346\) −136.449 236.336i −0.394361 0.683053i
\(347\) −85.3529 147.836i −0.245974 0.426039i 0.716431 0.697658i \(-0.245774\pi\)
−0.962405 + 0.271619i \(0.912441\pi\)
\(348\) −809.140 + 54.0434i −2.32511 + 0.155297i
\(349\) 549.147 1.57349 0.786744 0.617280i \(-0.211765\pi\)
0.786744 + 0.617280i \(0.211765\pi\)
\(350\) −251.663 502.171i −0.719037 1.43477i
\(351\) −224.199 + 45.4653i −0.638745 + 0.129531i
\(352\) −362.380 209.220i −1.02949 0.594375i
\(353\) 153.623 + 266.082i 0.435192 + 0.753775i 0.997311 0.0732815i \(-0.0233472\pi\)
−0.562119 + 0.827056i \(0.690014\pi\)
\(354\) −205.977 + 418.992i −0.581857 + 1.18359i
\(355\) −11.8931 + 2.75180i −0.0335016 + 0.00775155i
\(356\) 395.136i 1.10993i
\(357\) −125.584 183.525i −0.351776 0.514076i
\(358\) 397.457i 1.11022i
\(359\) 94.3043 + 54.4466i 0.262686 + 0.151662i 0.625559 0.780177i \(-0.284871\pi\)
−0.362873 + 0.931839i \(0.618204\pi\)
\(360\) −210.763 + 257.229i −0.585454 + 0.714524i
\(361\) −22.8069 39.5027i −0.0631770 0.109426i
\(362\) −271.545 + 470.330i −0.750125 + 1.29926i
\(363\) 68.4581 45.8653i 0.188590 0.126351i
\(364\) −183.708 + 325.526i −0.504691 + 0.894303i
\(365\) 301.618 + 323.131i 0.826349 + 0.885291i
\(366\) −13.4726 201.712i −0.0368103 0.551124i
\(367\) 99.8081 57.6242i 0.271957 0.157014i −0.357820 0.933791i \(-0.616480\pi\)
0.629776 + 0.776776i \(0.283146\pi\)
\(368\) 22.7488 + 39.4021i 0.0618174 + 0.107071i
\(369\) 45.6764 35.2294i 0.123784 0.0954727i
\(370\) −364.254 390.236i −0.984471 1.05469i
\(371\) 535.702 + 302.318i 1.44394 + 0.814874i
\(372\) −191.957 + 128.607i −0.516014 + 0.345718i
\(373\) −77.4504 44.7160i −0.207642 0.119882i 0.392573 0.919721i \(-0.371585\pi\)
−0.600215 + 0.799839i \(0.704918\pi\)
\(374\) 358.667 207.076i 0.959002 0.553680i
\(375\) 83.7472 + 365.529i 0.223326 + 0.974744i
\(376\) 87.7484 151.985i 0.233373 0.404214i
\(377\) 363.402 0.963932
\(378\) −593.325 + 126.394i −1.56964 + 0.334376i
\(379\) 221.030 0.583193 0.291596 0.956541i \(-0.405814\pi\)
0.291596 + 0.956541i \(0.405814\pi\)
\(380\) −143.239 619.070i −0.376946 1.62913i
\(381\) −77.7574 + 158.171i −0.204088 + 0.415148i
\(382\) 354.999 204.959i 0.929316 0.536541i
\(383\) 93.5845 162.093i 0.244346 0.423220i −0.717602 0.696454i \(-0.754760\pi\)
0.961948 + 0.273234i \(0.0880934\pi\)
\(384\) −491.751 + 329.462i −1.28060 + 0.857974i
\(385\) 409.093 + 120.480i 1.06258 + 0.312936i
\(386\) 396.719i 1.02777i
\(387\) 142.696 110.058i 0.368722 0.284389i
\(388\) 767.065 442.865i 1.97697 1.14140i
\(389\) −183.652 + 106.032i −0.472113 + 0.272575i −0.717124 0.696946i \(-0.754542\pi\)
0.245011 + 0.969520i \(0.421209\pi\)
\(390\) 278.991 297.604i 0.715360 0.763086i
\(391\) −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
\(396\) −91.9131 684.993i −0.232104 1.72978i
\(397\) −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
\(399\) 183.081 381.835i 0.458849 0.956980i
\(400\) −2.56193 + 37.1546i −0.00640483 + 0.0928866i
\(401\) −400.309 231.118i −0.998277 0.576355i −0.0905387 0.995893i \(-0.528859\pi\)
−0.907738 + 0.419538i \(0.862192\pi\)
\(402\) 96.2302 195.748i 0.239379 0.486936i
\(403\) 89.6700 51.7710i 0.222506 0.128464i
\(404\) −837.322 483.428i −2.07258 1.19660i
\(405\) 404.824 + 11.9267i 0.999566 + 0.0294487i
\(406\) 963.632 9.45606i 2.37348 0.0232908i
\(407\) 405.297 0.995815
\(408\) −15.6456 234.246i −0.0383470 0.574132i
\(409\) −105.366 182.500i −0.257620 0.446211i 0.707984 0.706228i \(-0.249605\pi\)
−0.965604 + 0.260018i \(0.916272\pi\)
\(410\) −30.0260 + 98.3812i −0.0732343 + 0.239954i
\(411\) 2.38202 + 35.6637i 0.00579567 + 0.0867730i
\(412\) 895.148i 2.17269i
\(413\) 166.810 295.584i 0.403898 0.715700i
\(414\) −335.600 + 815.938i −0.810628 + 1.97087i
\(415\) −116.721 504.459i −0.281255 1.21556i
\(416\) 251.982 145.482i 0.605727 0.349716i
\(417\) 339.590 + 166.943i 0.814365 + 0.400344i
\(418\) 682.976 + 394.317i 1.63391 + 0.943341i
\(419\) 97.7368i 0.233262i −0.993175 0.116631i \(-0.962791\pi\)
0.993175 0.116631i \(-0.0372095\pi\)
\(420\) 447.826 487.198i 1.06625 1.15999i
\(421\) 576.919 1.37035 0.685177 0.728376i \(-0.259725\pi\)
0.685177 + 0.728376i \(0.259725\pi\)
\(422\) 122.086 211.459i 0.289303 0.501088i
\(423\) −211.834 + 28.4241i −0.500789 + 0.0671964i
\(424\) 324.693 + 562.385i 0.765786 + 1.32638i
\(425\) −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
\(429\) 20.6401 + 309.024i 0.0481121 + 0.720336i
\(430\) −93.8029 + 307.348i −0.218146 + 0.714762i
\(431\) −146.182 + 84.3983i −0.339170 + 0.195820i −0.659905 0.751349i \(-0.729403\pi\)
0.320735 + 0.947169i \(0.396070\pi\)
\(432\) 38.1356 + 12.7870i 0.0882769 + 0.0295995i
\(433\) 328.967i 0.759739i −0.925040 0.379870i \(-0.875969\pi\)
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
\(438\) −375.558 + 763.948i −0.857439 + 1.74417i
\(439\) 110.035 190.586i 0.250649 0.434136i −0.713056 0.701107i \(-0.752689\pi\)
0.963705 + 0.266971i \(0.0860228\pi\)
\(440\) 307.210 + 329.123i 0.698205 + 0.748006i
\(441\) 435.848 67.2142i 0.988317 0.152413i
\(442\) 287.983i 0.651545i
\(443\) −98.0040 + 169.748i −0.221228 + 0.383178i −0.955181 0.296022i \(-0.904340\pi\)
0.733953 + 0.679200i \(0.237673\pi\)
\(444\) 277.455 564.389i 0.624898 1.27115i
\(445\) −91.5083 + 299.829i −0.205637 + 0.673774i
\(446\) −869.319 501.902i −1.94915 1.12534i
\(447\) −192.609 287.487i −0.430893 0.643147i
\(448\) 628.477 371.121i 1.40285 0.828396i
\(449\) 434.253i 0.967156i 0.875301 + 0.483578i \(0.160663\pi\)
−0.875301 + 0.483578i \(0.839337\pi\)
\(450\) −600.843 + 400.680i −1.33521 + 0.890400i
\(451\) −39.0480 67.6331i −0.0865809 0.149963i
\(452\) −27.4181 47.4895i −0.0606594 0.105065i
\(453\) 55.8998 + 836.934i 0.123399 + 1.84754i
\(454\) −221.195 −0.487214
\(455\) −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
\(459\) −214.260 + 189.318i −0.466797 + 0.412458i
\(460\) −216.949 937.636i −0.471628 2.03834i
\(461\) 759.274i 1.64702i −0.567305 0.823508i \(-0.692014\pi\)
0.567305 0.823508i \(-0.307986\pi\)
\(462\) 62.7723 + 818.900i 0.135871 + 1.77251i
\(463\) 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
\(465\) −175.441 + 53.1323i −0.377292 + 0.114263i
\(466\) −64.2280 111.246i −0.137828 0.238726i
\(467\) −207.939 + 360.160i −0.445265 + 0.771221i −0.998071 0.0620891i \(-0.980224\pi\)
0.552806 + 0.833310i \(0.313557\pi\)
\(468\) 444.455 + 182.807i 0.949691 + 0.390613i
\(469\) −77.9317 + 138.093i −0.166166 + 0.294442i
\(470\) 278.610 260.061i 0.592788 0.553321i
\(471\) −80.8540 + 5.40033i −0.171665 + 0.0114657i
\(472\) 310.307 179.156i 0.657430 0.379568i
\(473\) −121.988 211.289i −0.257903 0.446700i
\(474\) 4.11045 + 61.5418i 0.00867183 + 0.129835i
\(475\) 34.6781 502.923i 0.0730066 1.05878i
\(476\) 4.58411 + 467.150i 0.00963049 + 0.981408i
\(477\) 300.836 731.417i 0.630684 1.53337i
\(478\) 949.921 + 548.437i 1.98728 + 1.14736i
\(479\) 45.1496 26.0672i 0.0942581 0.0544199i −0.452130 0.891952i \(-0.649336\pi\)
0.546388 + 0.837532i \(0.316002\pi\)
\(480\) −493.007 + 149.307i −1.02710 + 0.311057i
\(481\) −140.912 + 244.067i −0.292957 + 0.507417i
\(482\) −411.150 −0.853009
\(483\) 277.292 578.323i 0.574104 1.19736i
\(484\) −173.110 −0.357664
\(485\) 684.610 158.404i 1.41157 0.326606i
\(486\) 255.294 + 737.000i 0.525296 + 1.51646i
\(487\) −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 \(0.328122\pi\)
−0.514110 + 0.857724i \(0.671878\pi\)
\(492\) −120.912 + 8.07589i −0.245757 + 0.0164144i
\(493\) 393.344 227.097i 0.797859 0.460644i
\(494\) −474.911 + 274.190i −0.961358 + 0.555040i
\(495\) 88.8916 541.059i 0.179579 1.09305i
\(496\) −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
\(501\) 22.0131 + 10.8217i 0.0439384 + 0.0216002i
\(502\) −559.048 322.767i −1.11364 0.642961i
\(503\) −639.911 −1.27219 −0.636095 0.771611i \(-0.719451\pi\)
−0.636095 + 0.771611i \(0.719451\pi\)
\(504\) 432.286 + 172.862i 0.857710 + 0.342980i
\(505\) −523.405 560.738i −1.03645 1.11037i
\(506\) 1034.43 + 597.227i 2.04432 + 1.18029i
\(507\) 261.724 + 128.664i 0.516221 + 0.253775i
\(508\) 320.659 185.133i 0.631219 0.364435i
\(509\) 627.238 + 362.136i 1.23230 + 0.711466i 0.967508 0.252841i \(-0.0813649\pi\)
0.264787 + 0.964307i \(0.414698\pi\)
\(510\) 115.999 496.471i 0.227449 0.973473i
\(511\) 304.144 538.938i 0.595195 1.05467i
\(512\) −95.1944 −0.185927
\(513\) −516.201 173.084i −1.00624 0.337395i
\(514\) −406.367 703.848i −0.790597 1.36935i
\(515\) −207.304 + 679.239i −0.402533 + 1.31891i
\(516\) −377.737 + 25.2295i −0.732048 + 0.0488943i
\(517\) 289.363i 0.559697i
\(518\) −367.306 + 650.859i −0.709085 + 1.25649i
\(519\) 211.903 141.970i 0.408292 0.273546i
\(520\) −305.006 + 70.5718i −0.586550 + 0.135715i
\(521\) −426.309 + 246.130i −0.818251 + 0.472418i −0.849813 0.527084i \(-0.823285\pi\)
0.0315618 + 0.999502i \(0.489952\pi\)
\(522\) −164.776 1228.01i −0.315662 2.35251i
\(523\) −51.6590 29.8254i −0.0987744 0.0570274i 0.449799 0.893130i \(-0.351496\pi\)
−0.548574 + 0.836102i \(0.684829\pi\)
\(524\) 507.291i 0.968113i
\(525\) 452.639 265.975i 0.862170 0.506619i
\(526\) −583.858 −1.11000
\(527\) 64.7055 112.073i 0.122781 0.212663i
\(528\) 24.0243 48.8693i 0.0455005 0.0925555i
\(529\) −201.882 349.669i −0.381629 0.661001i
\(530\) 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
\(534\) −602.375 + 40.2333i −1.12804 + 0.0753433i
\(535\) −273.002 83.3205i −0.510284 0.155739i
\(536\) −144.972 + 83.6995i −0.270470 + 0.156156i
\(537\) 370.661 24.7569i 0.690244 0.0461022i
\(538\) 833.196i 1.54869i
\(539\) −11.7165 596.936i −0.0217375 1.10749i
\(540\) −692.589 494.178i −1.28257 0.915144i
\(541\) 276.972 479.729i 0.511962 0.886745i −0.487941 0.872876i \(-0.662252\pi\)
0.999904 0.0138685i \(-0.00441463\pi\)
\(542\) 56.9766 + 98.6863i 0.105123 + 0.182078i
\(543\) −455.535 223.942i −0.838923 0.412416i
\(544\) 181.829 314.938i 0.334245 0.578929i
\(545\) −647.945 + 604.806i −1.18889 + 1.10974i
\(546\) −514.962 246.912i −0.943154 0.452220i
\(547\) 109.968i 0.201039i 0.994935 + 0.100520i \(0.0320505\pi\)
−0.994935 + 0.100520i \(0.967949\pi\)
\(548\) 37.5444 65.0288i 0.0685117 0.118666i
\(549\) 187.273 25.1285i 0.341117 0.0457714i
\(550\) 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
\(555\) 341.237 364.004i 0.614842 0.655862i
\(556\) −397.476 688.448i −0.714885 1.23822i
\(557\) 226.708 + 392.669i 0.407015 + 0.704971i 0.994554 0.104225i \(-0.0332362\pi\)
−0.587538 + 0.809196i \(0.699903\pi\)
\(558\) −215.603 279.539i −0.386386 0.500966i
\(559\) 169.650 0.303488
\(560\) 50.6802 12.2514i 0.0905003 0.0218776i
\(561\) 215.456 + 321.587i 0.384057 + 0.573239i
\(562\) −539.049 311.220i −0.959161 0.553772i
\(563\) 25.2929 + 43.8087i 0.0449253 + 0.0778129i 0.887614 0.460589i \(-0.152362\pi\)
−0.842688 + 0.538402i \(0.819028\pi\)
\(564\) 402.948 + 198.090i 0.714446 + 0.351223i
\(565\) −9.80691 42.3847i −0.0173574 0.0750172i
\(566\) 411.725i 0.727430i
\(567\) −154.830 545.451i −0.273068 0.961995i
\(568\) 18.0422i 0.0317644i
\(569\) −767.186 442.935i −1.34831 0.778445i −0.360297 0.932838i \(-0.617325\pi\)
−0.988010 + 0.154392i \(0.950658\pi\)
\(570\) 929.170 281.399i 1.63012 0.493683i
\(571\) −479.840 831.107i −0.840350 1.45553i −0.889599 0.456742i \(-0.849016\pi\)
0.0492497 0.998786i \(-0.484317\pi\)
\(572\) 325.320 563.470i 0.568741 0.985088i
\(573\) 213.253 + 318.298i 0.372169 + 0.555495i
\(574\) 143.999 1.41305i 0.250869 0.00246176i
\(575\) 52.5231 761.721i 0.0913446 1.32473i
\(576\) −573.115 743.068i −0.994991 1.29005i
\(577\) 265.694 153.399i 0.460476 0.265856i −0.251769 0.967787i \(-0.581012\pi\)
0.712244 + 0.701932i \(0.247679\pi\)
\(578\) −283.840 491.624i −0.491072 0.850561i
\(579\) 369.973 24.7109i 0.638986 0.0426786i
\(580\) 922.248 + 988.030i 1.59008 + 1.70350i
\(581\) −624.195 + 368.593i −1.07435 + 0.634411i
\(582\) 753.240 + 1124.28i 1.29423 + 1.93175i
\(583\) −927.274 535.362i −1.59052 0.918288i
\(584\) 565.783 326.655i 0.968806 0.559340i
\(585\) 294.917 + 241.644i 0.504132 + 0.413067i
\(586\) −691.559 + 1197.81i −1.18013 + 2.04405i
\(587\) −336.767 −0.573708 −0.286854 0.957974i \(-0.592610\pi\)
−0.286854 + 0.957974i \(0.592610\pi\)
\(588\) −839.274 392.330i −1.42734 0.667228i
\(589\) 246.426 0.418380
\(590\) 758.112 175.411i 1.28494 0.297307i
\(591\) −60.7319 29.8559i −0.102761 0.0505176i
\(592\) 42.9132 24.7760i 0.0724885 0.0418513i
\(593\) 556.222 963.405i 0.937980 1.62463i 0.168748 0.985659i \(-0.446028\pi\)
0.769232 0.638970i \(-0.220639\pi\)
\(594\) 1034.90 209.866i 1.74225 0.353310i
\(595\) −104.707 + 355.535i −0.175979 + 0.597538i
\(596\) 726.966i 1.21974i
\(597\) 6.90138 + 103.328i 0.0115601 + 0.173078i
\(598\) −719.294 + 415.285i −1.20283 + 0.694456i
\(599\) 514.713 297.170i 0.859287 0.496110i −0.00448642 0.999990i \(-0.501428\pi\)
0.863773 + 0.503880i \(0.168095\pi\)
\(600\) 554.245 + 1.19282i 0.923741 + 0.00198803i
\(601\) 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
\(606\) 651.716 1325.70i 1.07544 2.18762i
\(607\) 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
\(609\) 68.8414 + 898.076i 0.113040 + 1.47467i
\(610\) −246.307 + 229.908i −0.403782 + 0.376899i
\(611\) −174.253 100.605i −0.285193 0.164656i
\(612\) 595.315 79.8800i 0.972738 0.130523i
\(613\) 595.512 343.819i 0.971472 0.560879i 0.0717871 0.997420i \(-0.477130\pi\)
0.899685 + 0.436541i \(0.143796\pi\)
\(614\) −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 \(0.553296\pi\)
\(618\) −1364.63 + 91.1452i −2.20814 + 0.147484i
\(619\) 428.521 + 742.221i 0.692280 + 1.19906i 0.971089 + 0.238718i \(0.0767271\pi\)
−0.278809 + 0.960347i \(0.589940\pi\)
\(620\) 368.323 + 112.412i 0.594069 + 0.181310i
\(621\) −781.832 262.151i −1.25899 0.422143i
\(622\) 1254.56i 2.01697i
\(623\) 438.855 4.30645i 0.704422 0.00691244i
\(624\) 21.0762 + 31.4580i 0.0337759 + 0.0504135i
\(625\) 383.833 493.251i 0.614133 0.789202i
\(626\) −713.402 + 411.883i −1.13962 + 0.657960i
\(627\) −325.191 + 661.492i −0.518645 + 1.05501i
\(628\) 147.428 + 85.1177i 0.234758 + 0.135538i
\(629\) 352.236i 0.559994i
\(630\) 788.318 + 633.092i 1.25130 + 1.00491i
\(631\) −464.352 −0.735899 −0.367949 0.929846i \(-0.619940\pi\)
−0.367949 + 0.929846i \(0.619940\pi\)
\(632\) 23.6678 40.9938i 0.0374491 0.0648637i
\(633\) 204.807 + 100.684i 0.323550 + 0.159058i
\(634\) 513.254 + 888.983i 0.809550 + 1.40218i
\(635\) 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
\(639\) 17.3991 13.4196i 0.0272287 0.0210010i
\(640\) 943.559 + 287.975i 1.47431 + 0.449961i
\(641\) 144.334 83.3312i 0.225170 0.130002i −0.383172 0.923677i \(-0.625168\pi\)
0.608342 + 0.793675i \(0.291835\pi\)
\(642\) −36.6334 548.477i −0.0570614 0.854325i
\(643\) 643.063i 1.00010i 0.865997 + 0.500049i \(0.166685\pi\)
−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 0.791440 0.611246i \(-0.209332\pi\)
−0.925075 + 0.379784i \(0.875998\pi\)
\(648\) 152.050 578.952i 0.234646 0.893444i
\(649\) −295.397 + 511.642i −0.455157 + 0.788354i
\(650\) −678.266 46.7687i −1.04349 0.0719518i
\(651\) 144.928 + 211.794i 0.222624 + 0.325337i
\(652\) 1736.30i 2.66304i
\(653\) −514.097 + 890.443i −0.787285 + 1.36362i 0.140339 + 0.990104i \(0.455181\pi\)
−0.927624 + 0.373515i \(0.878153\pi\)
\(654\) −1531.87 753.073i −2.34232 1.15149i
\(655\) 117.482 384.933i 0.179362 0.587684i
\(656\) −8.26888 4.77404i −0.0126050 0.00727750i
\(657\) −735.836 302.653i −1.11999 0.460660i
\(658\) −464.684 262.240i −0.706206 0.398540i
\(659\) 494.948i 0.751059i −0.926810 0.375530i \(-0.877461\pi\)
0.926810 0.375530i \(-0.122539\pi\)
\(660\) −787.804 + 840.363i −1.19364 + 1.27328i
\(661\) 190.532 + 330.011i 0.288248 + 0.499261i 0.973392 0.229147i \(-0.0735938\pi\)
−0.685143 + 0.728408i \(0.740260\pi\)
\(662\) 462.921 + 801.803i 0.699276 + 1.21118i
\(663\) −268.567 + 17.9379i −0.405079 + 0.0270557i
\(664\) −765.282 −1.15253
\(665\) −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
\(669\) 413.915 841.973i 0.618708 1.25855i
\(670\) −354.181 + 81.9499i −0.528628 + 0.122313i
\(671\) 255.813i 0.381242i
\(672\) 407.264 + 595.164i 0.606048 + 0.885661i
\(673\) 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
\(675\) −411.092 535.377i −0.609025 0.793151i
\(676\) −306.337 530.591i −0.453161 0.784897i
\(677\) 150.968 261.485i 0.222996 0.386241i −0.732720 0.680530i \(-0.761750\pi\)
0.955716 + 0.294289i \(0.0950829\pi\)
\(678\) 69.6047 46.6336i 0.102662 0.0687811i
\(679\) −500.224 847.107i −0.736707 1.24758i
\(680\) −286.035 + 266.991i −0.420639 + 0.392634i
\(681\) −13.7778 206.282i −0.0202318 0.302911i
\(682\) −413.913 + 238.973i −0.606911 + 0.350400i
\(683\) −45.4093 78.6511i −0.0664850 0.115155i 0.830867 0.556471i \(-0.187845\pi\)
−0.897352 + 0.441316i \(0.854512\pi\)
\(684\) 698.532 + 905.677i 1.02125 + 1.32409i
\(685\) 43.5485 40.6491i 0.0635744 0.0593417i
\(686\) 969.229 + 522.167i 1.41287 + 0.761176i
\(687\) −857.737 + 574.664i −1.24853 + 0.836484i
\(688\) −25.8324 14.9143i −0.0375471 0.0216778i
\(689\) 644.784 372.266i 0.935827 0.540300i
\(690\) 1407.31 426.204i 2.03958 0.617687i
\(691\) −492.003 + 852.173i −0.712015 + 1.23325i 0.252084 + 0.967705i \(0.418884\pi\)
−0.964099 + 0.265541i \(0.914449\pi\)
\(692\) −535.839 −0.774334
\(693\) −759.781 + 109.548i −1.09636 + 0.158078i
\(694\) −547.919 −0.789509
\(695\) −142.169 614.445i −0.204560 0.884093i
\(696\) −419.506 + 853.345i −0.602739 + 1.22607i
\(697\) 58.7787 33.9359i 0.0843310 0.0486886i
\(698\) 881.307 1526.47i 1.26262 2.18692i
\(699\) 99.7454 66.8271i 0.142697 0.0956039i
\(700\) −1100.99 65.0690i −1.57285 0.0929557i
\(701\) 446.823i 0.637408i −0.947854 0.318704i \(-0.896752\pi\)
0.947854 0.318704i \(-0.103248\pi\)
\(702\) −233.429 + 696.174i −0.332521 + 0.991701i
\(703\) −580.870 + 335.366i −0.826274 + 0.477049i
\(704\) −1100.26 + 635.236i −1.56287 + 0.902323i
\(705\) 259.882 + 243.628i 0.368627 + 0.345572i
\(706\) 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
\(711\) −57.1366 + 7.66665i −0.0803609 + 0.0107829i
\(712\) 401.250 + 231.662i 0.563554 + 0.325368i
\(713\) 373.233 0.523469
\(714\) −711.692 + 54.5543i −0.996767 + 0.0764065i
\(715\) 377.345 352.222i 0.527755 0.492618i
\(716\) −675.859 390.207i −0.943937 0.544982i
\(717\) −452.293 + 920.039i −0.630813 + 1.28318i
\(718\) 302.691 174.759i 0.421576 0.243397i
\(719\) 867.476 + 500.837i 1.20650 + 0.696575i 0.961994 0.273072i \(-0.0880397\pi\)
0.244510 + 0.969647i \(0.421373\pi\)
\(720\) −23.6632 62.7219i −0.0328656 0.0871137i
\(721\) 994.189 9.75591i 1.37890 0.0135311i
\(722\) −146.408 −0.202781
\(723\) −25.6098 383.431i −0.0354216 0.530333i
\(724\) 533.184 + 923.502i 0.736442 + 1.27556i
\(725\) 470.988 + 963.298i 0.649638 + 1.32869i
\(726\) −17.6263 263.901i −0.0242786 0.363500i
\(727\) 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
\(732\) −356.228 175.123i −0.486651 0.239238i
\(733\) −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
\(735\) −545.983 492.065i −0.742834 0.669476i
\(736\) 1048.83 1.42503
\(737\) 138.006 239.033i 0.187253 0.324332i
\(738\) −24.6230 183.506i −0.0333644 0.248653i
\(739\) 599.057 + 1037.60i 0.810631 + 1.40405i 0.912423 + 0.409249i \(0.134209\pi\)
−0.101792 + 0.994806i \(0.532457\pi\)
\(740\) −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 \(-0.369359\pi\)
0.398995 + 0.916953i \(0.369359\pi\)
\(744\) 18.0555 + 270.328i 0.0242682 + 0.363344i
\(745\) −168.356 + 551.622i −0.225981 + 0.740432i
\(746\) −248.595 + 143.526i −0.333237 + 0.192394i
\(747\) 569.210 + 738.005i 0.761995 + 0.987959i
\(748\) 813.196i 1.08716i
\(749\) 3.92113 + 399.588i 0.00523515 + 0.533495i
\(750\) 1150.47 + 353.832i 1.53395 + 0.471776i
\(751\) −86.7806 + 150.308i −0.115553 + 0.200144i −0.918001 0.396578i \(-0.870197\pi\)
0.802447 + 0.596723i \(0.203531\pi\)
\(752\) 17.6889 + 30.6381i 0.0235225 + 0.0407421i
\(753\) 266.184 541.462i 0.353498 0.719073i
\(754\) 583.211 1010.15i 0.773490 1.33972i
\(755\) 1021.97 953.928i 1.35360 1.26348i
\(756\) −367.575 + 1133.01i −0.486210 + 1.49869i
\(757\) 560.146i 0.739956i 0.929041 + 0.369978i \(0.120635\pi\)
−0.929041 + 0.369978i \(0.879365\pi\)
\(758\) 354.723 614.399i 0.467973 0.810553i
\(759\) −492.530 + 1001.89i −0.648920 + 1.32001i
\(760\) −712.628 217.495i −0.937668 0.286177i
\(761\) −450.545 260.123i −0.592044 0.341817i 0.173861 0.984770i \(-0.444376\pi\)
−0.765905 + 0.642953i \(0.777709\pi\)
\(762\) 314.880 + 469.986i 0.413228 + 0.616780i
\(763\) 1080.68 + 609.873i 1.41636 + 0.799309i
\(764\)