Properties

Label 57.3.g.b.31.1
Level $57$
Weight $3$
Character 57.31
Analytic conductor $1.553$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 57 = 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 57.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.55313750685\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.92607408.1
Defining polynomial: \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(0.500000 + 2.93068i\) of defining polynomial
Character \(\chi\) \(=\) 57.31
Dual form 57.3.g.b.46.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.78805 + 1.03233i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.131406 - 0.227602i) q^{4} +(-3.20750 - 5.55555i) q^{5} +(1.78805 - 3.09699i) q^{6} -2.26281 q^{7} -7.71601i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.78805 + 1.03233i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.131406 - 0.227602i) q^{4} +(-3.20750 - 5.55555i) q^{5} +(1.78805 - 3.09699i) q^{6} -2.26281 q^{7} -7.71601i q^{8} +(1.50000 - 2.59808i) q^{9} +(11.4703 + 6.62239i) q^{10} -20.0928 q^{11} +0.455204i q^{12} +(-0.135471 - 0.0782143i) q^{13} +(4.04601 - 2.33597i) q^{14} +(9.62250 + 5.55555i) q^{15} +(8.49109 + 14.7070i) q^{16} +(12.3133 + 21.3272i) q^{17} +6.19397i q^{18} +(-18.9317 - 1.60945i) q^{19} -1.68594 q^{20} +(3.39422 - 1.95965i) q^{21} +(35.9269 - 20.7424i) q^{22} +(-2.62250 + 4.54230i) q^{23} +(6.68226 + 11.5740i) q^{24} +(-8.07609 + 13.9882i) q^{25} +0.322972 q^{26} +5.19615i q^{27} +(-0.297347 + 0.515021i) q^{28} +(-31.4573 - 18.1619i) q^{29} -22.9406 q^{30} -17.1105i q^{31} +(-3.63586 - 2.09917i) q^{32} +(30.1392 - 17.4009i) q^{33} +(-44.0334 - 25.4227i) q^{34} +(7.25797 + 12.5712i) q^{35} +(-0.394218 - 0.682806i) q^{36} -42.7124i q^{37} +(35.5123 - 16.6660i) q^{38} +0.270942 q^{39} +(-42.8667 + 24.7491i) q^{40} +(30.0928 - 17.3741i) q^{41} +(-4.04601 + 7.00790i) q^{42} +(12.5553 + 21.7464i) q^{43} +(-2.64032 + 4.57316i) q^{44} -19.2450 q^{45} -10.8291i q^{46} +(-14.6778 + 25.4227i) q^{47} +(-25.4733 - 14.7070i) q^{48} -43.8797 q^{49} -33.3487i q^{50} +(-36.9398 - 21.3272i) q^{51} +(-0.0356035 + 0.0205557i) q^{52} +(48.4176 + 27.9539i) q^{53} +(-5.36414 - 9.29096i) q^{54} +(64.4476 + 111.627i) q^{55} +17.4599i q^{56} +(29.7914 - 13.9812i) q^{57} +74.9962 q^{58} +(-29.9269 + 17.2783i) q^{59} +(2.52891 - 1.46007i) q^{60} +(27.3805 - 47.4244i) q^{61} +(17.6637 + 30.5944i) q^{62} +(-3.39422 + 5.87896i) q^{63} -59.2606 q^{64} +1.00349i q^{65} +(-35.9269 + 62.2272i) q^{66} +(66.0698 + 38.1454i) q^{67} +6.47216 q^{68} -9.08459i q^{69} +(-25.9552 - 14.9852i) q^{70} +(63.6080 - 36.7241i) q^{71} +(-20.0468 - 11.5740i) q^{72} +(-45.9053 - 79.5103i) q^{73} +(44.0932 + 76.3717i) q^{74} -27.9764i q^{75} +(-2.85406 + 4.09740i) q^{76} +45.4662 q^{77} +(-0.484457 + 0.279702i) q^{78} +(-53.1300 + 30.6746i) q^{79} +(54.4703 - 94.3453i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-35.8716 + 62.1313i) q^{82} -148.793 q^{83} -1.03004i q^{84} +(78.9897 - 136.814i) q^{85} +(-44.8990 - 25.9224i) q^{86} +62.9147 q^{87} +155.036i q^{88} +(-62.7829 - 36.2477i) q^{89} +(34.4109 - 19.8672i) q^{90} +(0.306546 + 0.176984i) q^{91} +(0.689224 + 1.19377i) q^{92} +(14.8181 + 25.6657i) q^{93} -60.6093i q^{94} +(51.7820 + 110.338i) q^{95} +7.27172 q^{96} +(-70.0326 + 40.4334i) q^{97} +(78.4589 - 45.2983i) q^{98} +(-30.1392 + 52.2026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9} + 54 q^{10} - 36 q^{11} - 3 q^{13} - 57 q^{14} - 12 q^{15} - 23 q^{16} + 38 q^{17} - 10 q^{19} + 32 q^{20} + 33 q^{21} + 36 q^{22} + 54 q^{23} + 39 q^{24} - 21 q^{25} + 118 q^{26} - 101 q^{28} - 102 q^{29} - 108 q^{30} - 63 q^{32} + 54 q^{33} - 150 q^{34} - 24 q^{35} - 15 q^{36} + 119 q^{38} + 6 q^{39} + 30 q^{40} + 96 q^{41} + 57 q^{42} + 107 q^{43} - 94 q^{44} + 24 q^{45} - 50 q^{47} + 69 q^{48} - 48 q^{49} - 114 q^{51} + 399 q^{52} - 90 q^{53} + 9 q^{54} + 148 q^{55} - 3 q^{57} - 116 q^{58} - 48 q^{60} + 27 q^{61} - 121 q^{62} - 33 q^{63} + 46 q^{64} - 36 q^{66} - 39 q^{67} - 388 q^{68} - 354 q^{70} + 84 q^{71} - 117 q^{72} - 77 q^{73} + 219 q^{74} + 215 q^{76} + 260 q^{77} - 177 q^{78} + 9 q^{79} + 312 q^{80} - 27 q^{81} - 4 q^{82} - 348 q^{83} + 68 q^{85} + 249 q^{86} + 204 q^{87} - 72 q^{89} + 162 q^{90} - 393 q^{91} - 118 q^{92} + 129 q^{93} + 104 q^{95} + 126 q^{96} - 228 q^{97} + 540 q^{98} - 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/57\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(40\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.78805 + 1.03233i −0.894023 + 0.516164i −0.875256 0.483659i \(-0.839307\pi\)
−0.0187668 + 0.999824i \(0.505974\pi\)
\(3\) −1.50000 + 0.866025i −0.500000 + 0.288675i
\(4\) 0.131406 0.227602i 0.0328515 0.0569005i
\(5\) −3.20750 5.55555i −0.641500 1.11111i −0.985098 0.171993i \(-0.944979\pi\)
0.343598 0.939117i \(-0.388354\pi\)
\(6\) 1.78805 3.09699i 0.298008 0.516164i
\(7\) −2.26281 −0.323259 −0.161629 0.986852i \(-0.551675\pi\)
−0.161629 + 0.986852i \(0.551675\pi\)
\(8\) 7.71601i 0.964502i
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 11.4703 + 6.62239i 1.14703 + 0.662239i
\(11\) −20.0928 −1.82662 −0.913309 0.407267i \(-0.866482\pi\)
−0.913309 + 0.407267i \(0.866482\pi\)
\(12\) 0.455204i 0.0379337i
\(13\) −0.135471 0.0782143i −0.0104209 0.00601649i 0.494781 0.869018i \(-0.335248\pi\)
−0.505201 + 0.863001i \(0.668582\pi\)
\(14\) 4.04601 2.33597i 0.289001 0.166855i
\(15\) 9.62250 + 5.55555i 0.641500 + 0.370370i
\(16\) 8.49109 + 14.7070i 0.530693 + 0.919187i
\(17\) 12.3133 + 21.3272i 0.724311 + 1.25454i 0.959257 + 0.282534i \(0.0911752\pi\)
−0.234947 + 0.972008i \(0.575492\pi\)
\(18\) 6.19397i 0.344110i
\(19\) −18.9317 1.60945i −0.996406 0.0847081i
\(20\) −1.68594 −0.0842970
\(21\) 3.39422 1.95965i 0.161629 0.0933168i
\(22\) 35.9269 20.7424i 1.63304 0.942836i
\(23\) −2.62250 + 4.54230i −0.114022 + 0.197491i −0.917388 0.397994i \(-0.869707\pi\)
0.803367 + 0.595485i \(0.203040\pi\)
\(24\) 6.68226 + 11.5740i 0.278428 + 0.482251i
\(25\) −8.07609 + 13.9882i −0.323044 + 0.559528i
\(26\) 0.322972 0.0124220
\(27\) 5.19615i 0.192450i
\(28\) −0.297347 + 0.515021i −0.0106195 + 0.0183936i
\(29\) −31.4573 18.1619i −1.08474 0.626272i −0.152566 0.988293i \(-0.548754\pi\)
−0.932170 + 0.362021i \(0.882087\pi\)
\(30\) −22.9406 −0.764687
\(31\) 17.1105i 0.551952i −0.961165 0.275976i \(-0.910999\pi\)
0.961165 0.275976i \(-0.0890010\pi\)
\(32\) −3.63586 2.09917i −0.113621 0.0655989i
\(33\) 30.1392 17.4009i 0.913309 0.527299i
\(34\) −44.0334 25.4227i −1.29510 0.747727i
\(35\) 7.25797 + 12.5712i 0.207370 + 0.359176i
\(36\) −0.394218 0.682806i −0.0109505 0.0189668i
\(37\) 42.7124i 1.15439i −0.816607 0.577194i \(-0.804148\pi\)
0.816607 0.577194i \(-0.195852\pi\)
\(38\) 35.5123 16.6660i 0.934533 0.438578i
\(39\) 0.270942 0.00694724
\(40\) −42.8667 + 24.7491i −1.07167 + 0.618728i
\(41\) 30.0928 17.3741i 0.733971 0.423758i −0.0859022 0.996304i \(-0.527377\pi\)
0.819873 + 0.572545i \(0.194044\pi\)
\(42\) −4.04601 + 7.00790i −0.0963336 + 0.166855i
\(43\) 12.5553 + 21.7464i 0.291984 + 0.505731i 0.974279 0.225346i \(-0.0723512\pi\)
−0.682295 + 0.731077i \(0.739018\pi\)
\(44\) −2.64032 + 4.57316i −0.0600072 + 0.103936i
\(45\) −19.2450 −0.427666
\(46\) 10.8291i 0.235415i
\(47\) −14.6778 + 25.4227i −0.312294 + 0.540909i −0.978859 0.204538i \(-0.934431\pi\)
0.666565 + 0.745447i \(0.267764\pi\)
\(48\) −25.4733 14.7070i −0.530693 0.306396i
\(49\) −43.8797 −0.895504
\(50\) 33.3487i 0.666975i
\(51\) −36.9398 21.3272i −0.724311 0.418181i
\(52\) −0.0356035 + 0.0205557i −0.000684682 + 0.000395301i
\(53\) 48.4176 + 27.9539i 0.913540 + 0.527433i 0.881568 0.472056i \(-0.156488\pi\)
0.0319716 + 0.999489i \(0.489821\pi\)
\(54\) −5.36414 9.29096i −0.0993359 0.172055i
\(55\) 64.4476 + 111.627i 1.17178 + 2.02957i
\(56\) 17.4599i 0.311784i
\(57\) 29.7914 13.9812i 0.522656 0.245284i
\(58\) 74.9962 1.29304
\(59\) −29.9269 + 17.2783i −0.507235 + 0.292852i −0.731696 0.681631i \(-0.761271\pi\)
0.224461 + 0.974483i \(0.427938\pi\)
\(60\) 2.52891 1.46007i 0.0421485 0.0243344i
\(61\) 27.3805 47.4244i 0.448860 0.777448i −0.549452 0.835525i \(-0.685164\pi\)
0.998312 + 0.0580769i \(0.0184968\pi\)
\(62\) 17.6637 + 30.5944i 0.284898 + 0.493457i
\(63\) −3.39422 + 5.87896i −0.0538765 + 0.0933168i
\(64\) −59.2606 −0.925947
\(65\) 1.00349i 0.0154383i
\(66\) −35.9269 + 62.2272i −0.544346 + 0.942836i
\(67\) 66.0698 + 38.1454i 0.986117 + 0.569335i 0.904111 0.427297i \(-0.140534\pi\)
0.0820054 + 0.996632i \(0.473868\pi\)
\(68\) 6.47216 0.0951788
\(69\) 9.08459i 0.131661i
\(70\) −25.9552 14.9852i −0.370788 0.214075i
\(71\) 63.6080 36.7241i 0.895887 0.517240i 0.0200233 0.999800i \(-0.493626\pi\)
0.875863 + 0.482559i \(0.160293\pi\)
\(72\) −20.0468 11.5740i −0.278428 0.160750i
\(73\) −45.9053 79.5103i −0.628840 1.08918i −0.987785 0.155824i \(-0.950197\pi\)
0.358945 0.933359i \(-0.383137\pi\)
\(74\) 44.0932 + 76.3717i 0.595854 + 1.03205i
\(75\) 27.9764i 0.373019i
\(76\) −2.85406 + 4.09740i −0.0375534 + 0.0539132i
\(77\) 45.4662 0.590471
\(78\) −0.484457 + 0.279702i −0.00621099 + 0.00358592i
\(79\) −53.1300 + 30.6746i −0.672531 + 0.388286i −0.797035 0.603933i \(-0.793599\pi\)
0.124504 + 0.992219i \(0.460266\pi\)
\(80\) 54.4703 94.3453i 0.680879 1.17932i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) −35.8716 + 62.1313i −0.437458 + 0.757699i
\(83\) −148.793 −1.79268 −0.896342 0.443363i \(-0.853785\pi\)
−0.896342 + 0.443363i \(0.853785\pi\)
\(84\) 1.03004i 0.0122624i
\(85\) 78.9897 136.814i 0.929290 1.60958i
\(86\) −44.8990 25.9224i −0.522081 0.301424i
\(87\) 62.9147 0.723157
\(88\) 155.036i 1.76178i
\(89\) −62.7829 36.2477i −0.705426 0.407278i 0.103939 0.994584i \(-0.466855\pi\)
−0.809365 + 0.587306i \(0.800189\pi\)
\(90\) 34.4109 19.8672i 0.382344 0.220746i
\(91\) 0.306546 + 0.176984i 0.00336864 + 0.00194488i
\(92\) 0.689224 + 1.19377i 0.00749156 + 0.0129758i
\(93\) 14.8181 + 25.6657i 0.159335 + 0.275976i
\(94\) 60.6093i 0.644780i
\(95\) 51.7820 + 110.338i 0.545074 + 1.16146i
\(96\) 7.27172 0.0757471
\(97\) −70.0326 + 40.4334i −0.721986 + 0.416839i −0.815483 0.578781i \(-0.803529\pi\)
0.0934972 + 0.995620i \(0.470195\pi\)
\(98\) 78.4589 45.2983i 0.800601 0.462227i
\(99\) −30.1392 + 52.2026i −0.304436 + 0.527299i
\(100\) 2.12250 + 3.67627i 0.0212250 + 0.0367627i
\(101\) −76.6770 + 132.809i −0.759178 + 1.31494i 0.184092 + 0.982909i \(0.441066\pi\)
−0.943270 + 0.332027i \(0.892268\pi\)
\(102\) 88.0669 0.863401
\(103\) 168.948i 1.64027i −0.572169 0.820136i \(-0.693898\pi\)
0.572169 0.820136i \(-0.306102\pi\)
\(104\) −0.603503 + 1.04530i −0.00580291 + 0.0100509i
\(105\) −21.7739 12.5712i −0.207370 0.119725i
\(106\) −115.431 −1.08897
\(107\) 139.060i 1.29963i −0.760093 0.649815i \(-0.774846\pi\)
0.760093 0.649815i \(-0.225154\pi\)
\(108\) 1.18265 + 0.682806i 0.0109505 + 0.00632228i
\(109\) −9.15888 + 5.28788i −0.0840264 + 0.0485127i −0.541424 0.840749i \(-0.682115\pi\)
0.457398 + 0.889262i \(0.348781\pi\)
\(110\) −230.471 133.062i −2.09519 1.20966i
\(111\) 36.9900 + 64.0685i 0.333243 + 0.577194i
\(112\) −19.2137 33.2792i −0.171551 0.297135i
\(113\) 69.1581i 0.612018i 0.952029 + 0.306009i \(0.0989938\pi\)
−0.952029 + 0.306009i \(0.901006\pi\)
\(114\) −38.8352 + 55.7535i −0.340660 + 0.489066i
\(115\) 33.6466 0.292579
\(116\) −8.26737 + 4.77317i −0.0712704 + 0.0411480i
\(117\) −0.406413 + 0.234643i −0.00347362 + 0.00200550i
\(118\) 35.6737 61.7887i 0.302320 0.523633i
\(119\) −27.8626 48.2595i −0.234140 0.405542i
\(120\) 42.8667 74.2473i 0.357223 0.618728i
\(121\) 282.721 2.33654
\(122\) 113.063i 0.926742i
\(123\) −30.0928 + 52.1223i −0.244657 + 0.423758i
\(124\) −3.89438 2.24842i −0.0314063 0.0181324i
\(125\) −56.7587 −0.454070
\(126\) 14.0158i 0.111236i
\(127\) −25.6547 14.8118i −0.202006 0.116628i 0.395585 0.918429i \(-0.370542\pi\)
−0.597591 + 0.801801i \(0.703875\pi\)
\(128\) 120.504 69.5731i 0.941438 0.543540i
\(129\) −37.6659 21.7464i −0.291984 0.168577i
\(130\) −1.03593 1.79428i −0.00796870 0.0138022i
\(131\) −28.6526 49.6278i −0.218722 0.378838i 0.735695 0.677313i \(-0.236856\pi\)
−0.954418 + 0.298474i \(0.903522\pi\)
\(132\) 9.14633i 0.0692903i
\(133\) 42.8389 + 3.64189i 0.322097 + 0.0273826i
\(134\) −157.514 −1.17548
\(135\) 28.8675 16.6667i 0.213833 0.123457i
\(136\) 164.561 95.0094i 1.21001 0.698599i
\(137\) 47.4499 82.1856i 0.346349 0.599895i −0.639249 0.769000i \(-0.720755\pi\)
0.985598 + 0.169105i \(0.0540879\pi\)
\(138\) 9.37829 + 16.2437i 0.0679586 + 0.117708i
\(139\) −91.2747 + 158.092i −0.656652 + 1.13736i 0.324824 + 0.945774i \(0.394695\pi\)
−0.981477 + 0.191581i \(0.938639\pi\)
\(140\) 3.81496 0.0272497
\(141\) 50.8454i 0.360606i
\(142\) −75.8226 + 131.329i −0.533962 + 0.924850i
\(143\) 2.72200 + 1.57155i 0.0190349 + 0.0109898i
\(144\) 50.9465 0.353795
\(145\) 233.017i 1.60701i
\(146\) 164.162 + 94.7788i 1.12439 + 0.649170i
\(147\) 65.8195 38.0009i 0.447752 0.258510i
\(148\) −9.72142 5.61266i −0.0656852 0.0379234i
\(149\) −5.50439 9.53389i −0.0369422 0.0639858i 0.846963 0.531652i \(-0.178428\pi\)
−0.883905 + 0.467666i \(0.845095\pi\)
\(150\) 28.8809 + 50.0231i 0.192539 + 0.333487i
\(151\) 238.846i 1.58176i 0.611968 + 0.790882i \(0.290378\pi\)
−0.611968 + 0.790882i \(0.709622\pi\)
\(152\) −12.4186 + 146.077i −0.0817011 + 0.961035i
\(153\) 73.8797 0.482874
\(154\) −81.2957 + 46.9361i −0.527894 + 0.304780i
\(155\) −95.0582 + 54.8819i −0.613279 + 0.354077i
\(156\) 0.0356035 0.0616670i 0.000228227 0.000395301i
\(157\) 22.8125 + 39.5124i 0.145303 + 0.251671i 0.929486 0.368858i \(-0.120251\pi\)
−0.784183 + 0.620529i \(0.786918\pi\)
\(158\) 63.3326 109.695i 0.400839 0.694273i
\(159\) −96.8353 −0.609027
\(160\) 26.9323i 0.168327i
\(161\) 5.93421 10.2784i 0.0368585 0.0638407i
\(162\) 16.0924 + 9.29096i 0.0993359 + 0.0573516i
\(163\) 5.89159 0.0361447 0.0180724 0.999837i \(-0.494247\pi\)
0.0180724 + 0.999837i \(0.494247\pi\)
\(164\) 9.13224i 0.0556844i
\(165\) −193.343 111.627i −1.17178 0.676525i
\(166\) 266.048 153.603i 1.60270 0.925320i
\(167\) 142.140 + 82.0646i 0.851138 + 0.491405i 0.861035 0.508546i \(-0.169817\pi\)
−0.00989689 + 0.999951i \(0.503150\pi\)
\(168\) −15.1207 26.1898i −0.0900042 0.155892i
\(169\) −84.4878 146.337i −0.499928 0.865900i
\(170\) 326.173i 1.91867i
\(171\) −32.5790 + 46.7718i −0.190521 + 0.273520i
\(172\) 6.59938 0.0383685
\(173\) 234.355 135.305i 1.35465 0.782109i 0.365755 0.930711i \(-0.380811\pi\)
0.988897 + 0.148603i \(0.0474775\pi\)
\(174\) −112.494 + 64.9486i −0.646519 + 0.373268i
\(175\) 18.2747 31.6527i 0.104427 0.180872i
\(176\) −170.610 295.505i −0.969374 1.67900i
\(177\) 29.9269 51.8349i 0.169078 0.292852i
\(178\) 149.678 0.840890
\(179\) 186.439i 1.04156i −0.853691 0.520779i \(-0.825641\pi\)
0.853691 0.520779i \(-0.174359\pi\)
\(180\) −2.52891 + 4.38020i −0.0140495 + 0.0243344i
\(181\) −40.1939 23.2059i −0.222066 0.128210i 0.384841 0.922983i \(-0.374256\pi\)
−0.606906 + 0.794773i \(0.707590\pi\)
\(182\) −0.730824 −0.00401552
\(183\) 94.8487i 0.518299i
\(184\) 35.0484 + 20.2352i 0.190481 + 0.109974i
\(185\) −237.291 + 137.000i −1.28265 + 0.740539i
\(186\) −52.9910 30.5944i −0.284898 0.164486i
\(187\) −247.408 428.524i −1.32304 2.29157i
\(188\) 3.85751 + 6.68140i 0.0205187 + 0.0355393i
\(189\) 11.7579i 0.0622112i
\(190\) −206.494 143.834i −1.08681 0.757021i
\(191\) −36.7222 −0.192263 −0.0961315 0.995369i \(-0.530647\pi\)
−0.0961315 + 0.995369i \(0.530647\pi\)
\(192\) 88.8909 51.3212i 0.462973 0.267298i
\(193\) −173.472 + 100.154i −0.898817 + 0.518932i −0.876816 0.480826i \(-0.840337\pi\)
−0.0220009 + 0.999758i \(0.507004\pi\)
\(194\) 83.4811 144.593i 0.430315 0.745327i
\(195\) −0.869047 1.50523i −0.00445665 0.00771915i
\(196\) −5.76606 + 9.98710i −0.0294187 + 0.0509546i
\(197\) −171.512 −0.870620 −0.435310 0.900281i \(-0.643361\pi\)
−0.435310 + 0.900281i \(0.643361\pi\)
\(198\) 124.454i 0.628557i
\(199\) −43.7500 + 75.7772i −0.219849 + 0.380790i −0.954762 0.297372i \(-0.903890\pi\)
0.734913 + 0.678162i \(0.237223\pi\)
\(200\) 107.933 + 62.3152i 0.539666 + 0.311576i
\(201\) −132.140 −0.657411
\(202\) 316.624i 1.56744i
\(203\) 71.1820 + 41.0970i 0.350650 + 0.202448i
\(204\) −9.70824 + 5.60505i −0.0475894 + 0.0274758i
\(205\) −193.045 111.455i −0.941684 0.543682i
\(206\) 174.410 + 302.087i 0.846650 + 1.46644i
\(207\) 7.86749 + 13.6269i 0.0380072 + 0.0658304i
\(208\) 2.65650i 0.0127716i
\(209\) 380.391 + 32.3384i 1.82005 + 0.154729i
\(210\) 51.9103 0.247192
\(211\) 16.3950 9.46566i 0.0777014 0.0448609i −0.460646 0.887584i \(-0.652382\pi\)
0.538347 + 0.842723i \(0.319049\pi\)
\(212\) 12.7247 7.34663i 0.0600224 0.0346539i
\(213\) −63.6080 + 110.172i −0.298629 + 0.517240i
\(214\) 143.556 + 248.646i 0.670823 + 1.16190i
\(215\) 80.5423 139.503i 0.374615 0.648853i
\(216\) 40.0936 0.185618
\(217\) 38.7178i 0.178423i
\(218\) 10.9177 18.9100i 0.0500810 0.0867429i
\(219\) 137.716 + 79.5103i 0.628840 + 0.363061i
\(220\) 33.8752 0.153978
\(221\) 3.85230i 0.0174312i
\(222\) −132.280 76.3717i −0.595854 0.344016i
\(223\) −224.162 + 129.420i −1.00521 + 0.580358i −0.909786 0.415078i \(-0.863754\pi\)
−0.0954244 + 0.995437i \(0.530421\pi\)
\(224\) 8.22727 + 4.75002i 0.0367289 + 0.0212054i
\(225\) 24.2283 + 41.9646i 0.107681 + 0.186509i
\(226\) −71.3939 123.658i −0.315902 0.547159i
\(227\) 129.054i 0.568522i −0.958747 0.284261i \(-0.908252\pi\)
0.958747 0.284261i \(-0.0917482\pi\)
\(228\) 0.732630 8.61779i 0.00321329 0.0377973i
\(229\) −98.8946 −0.431854 −0.215927 0.976409i \(-0.569277\pi\)
−0.215927 + 0.976409i \(0.569277\pi\)
\(230\) −60.1617 + 34.7344i −0.261572 + 0.151019i
\(231\) −68.1994 + 39.3749i −0.295235 + 0.170454i
\(232\) −140.137 + 242.725i −0.604041 + 1.04623i
\(233\) 174.731 + 302.644i 0.749920 + 1.29890i 0.947861 + 0.318685i \(0.103241\pi\)
−0.197941 + 0.980214i \(0.563425\pi\)
\(234\) 0.484457 0.839105i 0.00207033 0.00358592i
\(235\) 188.316 0.801346
\(236\) 9.08189i 0.0384826i
\(237\) 53.1300 92.0238i 0.224177 0.388286i
\(238\) 99.6394 + 57.5268i 0.418653 + 0.241709i
\(239\) 301.091 1.25979 0.629897 0.776679i \(-0.283097\pi\)
0.629897 + 0.776679i \(0.283097\pi\)
\(240\) 188.691i 0.786211i
\(241\) 110.242 + 63.6485i 0.457438 + 0.264102i 0.710966 0.703226i \(-0.248258\pi\)
−0.253529 + 0.967328i \(0.581591\pi\)
\(242\) −505.518 + 291.861i −2.08892 + 1.20604i
\(243\) 13.5000 + 7.79423i 0.0555556 + 0.0320750i
\(244\) −7.19592 12.4637i −0.0294915 0.0510807i
\(245\) 140.744 + 243.776i 0.574465 + 0.995003i
\(246\) 124.263i 0.505133i
\(247\) 2.43882 + 1.69877i 0.00987376 + 0.00687759i
\(248\) −132.025 −0.532358
\(249\) 223.189 128.858i 0.896342 0.517503i
\(250\) 101.487 58.5937i 0.405949 0.234375i
\(251\) 177.023 306.613i 0.705271 1.22157i −0.261322 0.965252i \(-0.584159\pi\)
0.966594 0.256314i \(-0.0825081\pi\)
\(252\) 0.892042 + 1.54506i 0.00353985 + 0.00613120i
\(253\) 52.6933 91.2675i 0.208274 0.360741i
\(254\) 61.1625 0.240797
\(255\) 273.628i 1.07305i
\(256\) −25.1234 + 43.5151i −0.0981384 + 0.169981i
\(257\) −236.669 136.641i −0.920889 0.531676i −0.0369706 0.999316i \(-0.511771\pi\)
−0.883919 + 0.467641i \(0.845104\pi\)
\(258\) 89.7979 0.348054
\(259\) 96.6500i 0.373166i
\(260\) 0.228396 + 0.131865i 0.000878447 + 0.000507171i
\(261\) −94.3720 + 54.4857i −0.361579 + 0.208757i
\(262\) 102.464 + 59.1579i 0.391086 + 0.225793i
\(263\) −75.5642 130.881i −0.287316 0.497646i 0.685852 0.727741i \(-0.259430\pi\)
−0.973168 + 0.230095i \(0.926096\pi\)
\(264\) −134.265 232.555i −0.508581 0.880889i
\(265\) 358.649i 1.35339i
\(266\) −80.3576 + 37.7120i −0.302096 + 0.141774i
\(267\) 125.566 0.470284
\(268\) 17.3639 10.0251i 0.0647909 0.0374070i
\(269\) 58.9364 34.0269i 0.219094 0.126494i −0.386437 0.922316i \(-0.626294\pi\)
0.605531 + 0.795822i \(0.292961\pi\)
\(270\) −34.4109 + 59.6015i −0.127448 + 0.220746i
\(271\) 56.8991 + 98.5521i 0.209960 + 0.363661i 0.951702 0.307025i \(-0.0993334\pi\)
−0.741742 + 0.670685i \(0.766000\pi\)
\(272\) −209.106 + 362.183i −0.768773 + 1.33155i
\(273\) −0.613092 −0.00224576
\(274\) 195.935i 0.715093i
\(275\) 162.271 281.062i 0.590078 1.02204i
\(276\) −2.06767 1.19377i −0.00749156 0.00432526i
\(277\) 440.910 1.59173 0.795867 0.605472i \(-0.207016\pi\)
0.795867 + 0.605472i \(0.207016\pi\)
\(278\) 376.902i 1.35576i
\(279\) −44.4544 25.6657i −0.159335 0.0919919i
\(280\) 96.9993 56.0026i 0.346426 0.200009i
\(281\) 78.0928 + 45.0869i 0.277910 + 0.160452i 0.632477 0.774579i \(-0.282038\pi\)
−0.354567 + 0.935031i \(0.615372\pi\)
\(282\) 52.4892 + 90.9140i 0.186132 + 0.322390i
\(283\) 34.5331 + 59.8131i 0.122025 + 0.211354i 0.920566 0.390587i \(-0.127728\pi\)
−0.798541 + 0.601940i \(0.794394\pi\)
\(284\) 19.3031i 0.0679685i
\(285\) −173.229 120.663i −0.607821 0.423379i
\(286\) −6.48941 −0.0226902
\(287\) −68.0944 + 39.3143i −0.237263 + 0.136984i
\(288\) −10.9076 + 6.29750i −0.0378736 + 0.0218663i
\(289\) −158.734 + 274.935i −0.549252 + 0.951332i
\(290\) −240.550 416.645i −0.829484 1.43671i
\(291\) 70.0326 121.300i 0.240662 0.416839i
\(292\) −24.1289 −0.0826334
\(293\) 410.238i 1.40013i 0.714079 + 0.700065i \(0.246846\pi\)
−0.714079 + 0.700065i \(0.753154\pi\)
\(294\) −78.4589 + 135.895i −0.266867 + 0.462227i
\(295\) 191.981 + 110.840i 0.650782 + 0.375729i
\(296\) −329.569 −1.11341
\(297\) 104.405i 0.351533i
\(298\) 19.6842 + 11.3647i 0.0660544 + 0.0381365i
\(299\) 0.710545 0.410233i 0.00237640 0.00137202i
\(300\) −6.36749 3.67627i −0.0212250 0.0122542i
\(301\) −28.4103 49.2081i −0.0943864 0.163482i
\(302\) −246.568 427.068i −0.816451 1.41413i
\(303\) 265.617i 0.876624i
\(304\) −137.081 292.095i −0.450923 0.960838i
\(305\) −351.291 −1.15177
\(306\) −132.100 + 76.2681i −0.431700 + 0.249242i
\(307\) −201.882 + 116.556i −0.657595 + 0.379663i −0.791360 0.611350i \(-0.790627\pi\)
0.133765 + 0.991013i \(0.457293\pi\)
\(308\) 5.97454 10.3482i 0.0193979 0.0335981i
\(309\) 146.313 + 253.422i 0.473506 + 0.820136i
\(310\) 113.312 196.263i 0.365524 0.633106i
\(311\) −441.280 −1.41891 −0.709454 0.704752i \(-0.751058\pi\)
−0.709454 + 0.704752i \(0.751058\pi\)
\(312\) 2.09059i 0.00670062i
\(313\) −60.6339 + 105.021i −0.193719 + 0.335530i −0.946480 0.322763i \(-0.895388\pi\)
0.752761 + 0.658294i \(0.228722\pi\)
\(314\) −81.5796 47.1000i −0.259808 0.150000i
\(315\) 43.5478 0.138247
\(316\) 16.1233i 0.0510232i
\(317\) 286.409 + 165.358i 0.903499 + 0.521635i 0.878334 0.478048i \(-0.158656\pi\)
0.0251649 + 0.999683i \(0.491989\pi\)
\(318\) 173.146 99.9658i 0.544484 0.314358i
\(319\) 632.066 + 364.924i 1.98140 + 1.14396i
\(320\) 190.078 + 329.225i 0.593995 + 1.02883i
\(321\) 120.430 + 208.591i 0.375171 + 0.649815i
\(322\) 24.5042i 0.0761001i
\(323\) −198.786 423.579i −0.615437 1.31139i
\(324\) −2.36531 −0.00730034
\(325\) 2.18816 1.26333i 0.00673279 0.00388718i
\(326\) −10.5344 + 6.08206i −0.0323142 + 0.0186566i
\(327\) 9.15888 15.8636i 0.0280088 0.0485127i
\(328\) −134.059 232.197i −0.408716 0.707916i
\(329\) 33.2131 57.5268i 0.100952 0.174854i
\(330\) 460.941 1.39679
\(331\) 436.308i 1.31815i −0.752077 0.659075i \(-0.770948\pi\)
0.752077 0.659075i \(-0.229052\pi\)
\(332\) −19.5523 + 33.8655i −0.0588924 + 0.102005i
\(333\) −110.970 64.0685i −0.333243 0.192398i
\(334\) −338.870 −1.01458
\(335\) 489.406i 1.46091i
\(336\) 57.6412 + 33.2792i 0.171551 + 0.0990452i
\(337\) −217.027 + 125.301i −0.643997 + 0.371812i −0.786153 0.618033i \(-0.787930\pi\)
0.142156 + 0.989844i \(0.454597\pi\)
\(338\) 302.136 + 174.438i 0.893894 + 0.516090i
\(339\) −59.8927 103.737i −0.176675 0.306009i
\(340\) −20.7594 35.9564i −0.0610572 0.105754i
\(341\) 343.798i 1.00821i
\(342\) 9.96891 117.263i 0.0291489 0.342873i
\(343\) 210.169 0.612738
\(344\) 167.796 96.8770i 0.487779 0.281619i
\(345\) −50.4699 + 29.1388i −0.146290 + 0.0844603i
\(346\) −279.358 + 483.862i −0.807393 + 1.39845i
\(347\) −83.6670 144.915i −0.241115 0.417624i 0.719917 0.694060i \(-0.244180\pi\)
−0.961032 + 0.276436i \(0.910846\pi\)
\(348\) 8.26737 14.3195i 0.0237568 0.0411480i
\(349\) −486.776 −1.39477 −0.697387 0.716695i \(-0.745654\pi\)
−0.697387 + 0.716695i \(0.745654\pi\)
\(350\) 75.4619i 0.215605i
\(351\) 0.406413 0.703929i 0.00115787 0.00200550i
\(352\) 73.0547 + 42.1781i 0.207542 + 0.119824i
\(353\) 30.1507 0.0854128 0.0427064 0.999088i \(-0.486402\pi\)
0.0427064 + 0.999088i \(0.486402\pi\)
\(354\) 123.577i 0.349089i
\(355\) −408.045 235.585i −1.14942 0.663619i
\(356\) −16.5001 + 9.52635i −0.0463486 + 0.0267594i
\(357\) 83.5879 + 48.2595i 0.234140 + 0.135181i
\(358\) 192.466 + 333.361i 0.537615 + 0.931177i
\(359\) −75.0088 129.919i −0.208938 0.361891i 0.742442 0.669910i \(-0.233667\pi\)
−0.951380 + 0.308019i \(0.900334\pi\)
\(360\) 148.495i 0.412485i
\(361\) 355.819 + 60.9394i 0.985649 + 0.168807i
\(362\) 95.8247 0.264709
\(363\) −424.081 + 244.843i −1.16827 + 0.674500i
\(364\) 0.0805640 0.0465136i 0.000221330 0.000127785i
\(365\) −294.482 + 510.058i −0.806801 + 1.39742i
\(366\) −97.9151 169.594i −0.267527 0.463371i
\(367\) 248.090 429.704i 0.675994 1.17086i −0.300183 0.953882i \(-0.597048\pi\)
0.976177 0.216975i \(-0.0696189\pi\)
\(368\) −89.0714 −0.242042
\(369\) 104.245i 0.282506i
\(370\) 282.858 489.924i 0.764480 1.32412i
\(371\) −109.560 63.2545i −0.295310 0.170497i
\(372\) 7.78877 0.0209375
\(373\) 449.613i 1.20540i 0.797969 + 0.602698i \(0.205908\pi\)
−0.797969 + 0.602698i \(0.794092\pi\)
\(374\) 884.755 + 510.814i 2.36566 + 1.36581i
\(375\) 85.1381 49.1545i 0.227035 0.131079i
\(376\) 196.162 + 113.254i 0.521707 + 0.301208i
\(377\) 2.84104 + 4.92083i 0.00753592 + 0.0130526i
\(378\) 12.1380 + 21.0237i 0.0321112 + 0.0556182i
\(379\) 471.336i 1.24363i −0.783163 0.621816i \(-0.786395\pi\)
0.783163 0.621816i \(-0.213605\pi\)
\(380\) 31.9177 + 2.71344i 0.0839940 + 0.00714064i
\(381\) 51.3095 0.134670
\(382\) 65.6611 37.9094i 0.171888 0.0992393i
\(383\) −23.4258 + 13.5249i −0.0611641 + 0.0353131i −0.530270 0.847829i \(-0.677910\pi\)
0.469106 + 0.883142i \(0.344576\pi\)
\(384\) −120.504 + 208.719i −0.313813 + 0.543540i
\(385\) −145.833 252.590i −0.378787 0.656078i
\(386\) 206.784 358.160i 0.535709 0.927875i
\(387\) 75.3319 0.194656
\(388\) 21.2528i 0.0547752i
\(389\) 177.144 306.822i 0.455382 0.788745i −0.543328 0.839520i \(-0.682836\pi\)
0.998710 + 0.0507758i \(0.0161694\pi\)
\(390\) 3.10779 + 1.79428i 0.00796870 + 0.00460073i
\(391\) −129.166 −0.330348
\(392\) 338.576i 0.863715i
\(393\) 85.9579 + 49.6278i 0.218722 + 0.126279i
\(394\) 306.672 177.057i 0.778354 0.449383i
\(395\) 340.829 + 196.777i 0.862857 + 0.498171i
\(396\) 7.92095 + 13.7195i 0.0200024 + 0.0346452i
\(397\) −79.5105 137.716i −0.200278 0.346892i 0.748340 0.663316i \(-0.230851\pi\)
−0.948618 + 0.316423i \(0.897518\pi\)
\(398\) 180.657i 0.453913i
\(399\) −67.4123 + 31.6367i −0.168953 + 0.0792901i
\(400\) −274.299 −0.685748
\(401\) −277.534 + 160.234i −0.692105 + 0.399587i −0.804400 0.594088i \(-0.797513\pi\)
0.112295 + 0.993675i \(0.464180\pi\)
\(402\) 236.272 136.412i 0.587741 0.339332i
\(403\) −1.33829 + 2.31798i −0.00332081 + 0.00575181i
\(404\) 20.1517 + 34.9037i 0.0498803 + 0.0863953i
\(405\) −28.8675 + 50.0000i −0.0712777 + 0.123457i
\(406\) −169.702 −0.417986
\(407\) 858.211i 2.10863i
\(408\) −164.561 + 285.028i −0.403336 + 0.698599i
\(409\) −251.776 145.363i −0.615590 0.355411i 0.159560 0.987188i \(-0.448992\pi\)
−0.775150 + 0.631777i \(0.782326\pi\)
\(410\) 460.232 1.12252
\(411\) 164.371i 0.399930i
\(412\) −38.4529 22.2008i −0.0933323 0.0538854i
\(413\) 67.7189 39.0975i 0.163968 0.0946671i
\(414\) −28.1349 16.2437i −0.0679586 0.0392359i
\(415\) 477.253 + 826.626i 1.15001 + 1.99187i
\(416\) 0.328370 + 0.568753i 0.000789350 + 0.00136719i
\(417\) 316.185i 0.758237i
\(418\) −713.541 + 334.866i −1.70704 + 0.801115i
\(419\) −141.846 −0.338535 −0.169267 0.985570i \(-0.554140\pi\)
−0.169267 + 0.985570i \(0.554140\pi\)
\(420\) −5.72245 + 3.30386i −0.0136249 + 0.00786632i
\(421\) 98.6666 56.9652i 0.234362 0.135309i −0.378220 0.925716i \(-0.623464\pi\)
0.612583 + 0.790406i \(0.290131\pi\)
\(422\) −19.5433 + 33.8501i −0.0463112 + 0.0802134i
\(423\) 44.0334 + 76.2681i 0.104098 + 0.180303i
\(424\) 215.693 373.591i 0.508710 0.881111i
\(425\) −397.773 −0.935936
\(426\) 262.657i 0.616567i
\(427\) −61.9568 + 107.312i −0.145098 + 0.251317i
\(428\) −31.6504 18.2734i −0.0739496 0.0426948i
\(429\) −5.44399 −0.0126900
\(430\) 332.585i 0.773453i
\(431\) 229.263 + 132.365i 0.531932 + 0.307111i 0.741803 0.670618i \(-0.233971\pi\)
−0.209871 + 0.977729i \(0.567304\pi\)
\(432\) −76.4198 + 44.1210i −0.176898 + 0.102132i
\(433\) −631.333 364.500i −1.45804 0.841802i −0.459129 0.888369i \(-0.651839\pi\)
−0.998915 + 0.0465669i \(0.985172\pi\)
\(434\) −39.9695 69.2293i −0.0920957 0.159514i
\(435\) −201.799 349.526i −0.463905 0.803507i
\(436\) 2.77944i 0.00637486i
\(437\) 56.9589 81.7726i 0.130341 0.187123i
\(438\) −328.323 −0.749596
\(439\) 319.591 184.516i 0.727998 0.420310i −0.0896911 0.995970i \(-0.528588\pi\)
0.817689 + 0.575660i \(0.195255\pi\)
\(440\) 861.312 497.279i 1.95753 1.13018i
\(441\) −65.8195 + 114.003i −0.149251 + 0.258510i
\(442\) 3.97684 + 6.88809i 0.00899738 + 0.0155839i
\(443\) −291.547 + 504.975i −0.658120 + 1.13990i 0.322982 + 0.946405i \(0.395315\pi\)
−0.981102 + 0.193492i \(0.938019\pi\)
\(444\) 19.4428 0.0437902
\(445\) 465.058i 1.04507i
\(446\) 267.208 462.818i 0.599121 1.03771i
\(447\) 16.5132 + 9.53389i 0.0369422 + 0.0213286i
\(448\) 134.096 0.299321
\(449\) 314.423i 0.700273i −0.936699 0.350137i \(-0.886135\pi\)
0.936699 0.350137i \(-0.113865\pi\)
\(450\) −86.6426 50.0231i −0.192539 0.111162i
\(451\) −604.649 + 349.094i −1.34068 + 0.774045i
\(452\) 15.7405 + 9.08779i 0.0348242 + 0.0201057i
\(453\) −206.847 358.270i −0.456616 0.790882i
\(454\) 133.227 + 230.755i 0.293451 + 0.508272i
\(455\) 2.27071i 0.00499057i
\(456\) −107.879 229.871i −0.236576 0.504103i
\(457\) 505.253 1.10559 0.552793 0.833319i \(-0.313562\pi\)
0.552793 + 0.833319i \(0.313562\pi\)
\(458\) 176.828 102.092i 0.386088 0.222908i
\(459\) −110.820 + 63.9817i −0.241437 + 0.139394i
\(460\) 4.42137 7.65803i 0.00961167 0.0166479i
\(461\) 136.902 + 237.122i 0.296968 + 0.514364i 0.975441 0.220262i \(-0.0706912\pi\)
−0.678473 + 0.734626i \(0.737358\pi\)
\(462\) 81.2957 140.808i 0.175965 0.304780i
\(463\) 319.780 0.690669 0.345334 0.938480i \(-0.387765\pi\)
0.345334 + 0.938480i \(0.387765\pi\)
\(464\) 616.857i 1.32943i
\(465\) 95.0582 164.646i 0.204426 0.354077i
\(466\) −624.855 360.760i −1.34089 0.774164i
\(467\) −295.510 −0.632785 −0.316392 0.948628i \(-0.602472\pi\)
−0.316392 + 0.948628i \(0.602472\pi\)
\(468\) 0.123334i 0.000263534i
\(469\) −149.504 86.3159i −0.318771 0.184042i
\(470\) −336.718 + 194.404i −0.716421 + 0.413626i
\(471\) −68.4375 39.5124i −0.145303 0.0838905i
\(472\) 133.319 + 230.916i 0.282457 + 0.489229i
\(473\) −252.271 436.947i −0.533344 0.923778i
\(474\) 219.390i 0.462849i
\(475\) 175.408 251.822i 0.369279 0.530153i
\(476\) −14.6453 −0.0307674
\(477\) 145.253 83.8618i 0.304513 0.175811i
\(478\) −538.364 + 310.825i −1.12629 + 0.650261i
\(479\) 204.559 354.306i 0.427054 0.739679i −0.569556 0.821953i \(-0.692885\pi\)
0.996610 + 0.0822735i \(0.0262181\pi\)
\(480\) −23.3240 40.3984i −0.0485917 0.0841634i
\(481\) −3.34072 + 5.78629i −0.00694536 + 0.0120297i
\(482\) −262.825 −0.545280
\(483\) 20.5567i 0.0425605i
\(484\) 37.1512 64.3478i 0.0767588 0.132950i
\(485\) 449.259 + 259.380i 0.926308 + 0.534804i
\(486\) −32.1848 −0.0662239
\(487\) 638.208i 1.31049i −0.755417 0.655244i \(-0.772566\pi\)
0.755417 0.655244i \(-0.227434\pi\)
\(488\) −365.927 211.268i −0.749850 0.432926i
\(489\) −8.83738 + 5.10227i −0.0180724 + 0.0104341i
\(490\) −503.314 290.588i −1.02717 0.593037i
\(491\) −173.278 300.126i −0.352908 0.611255i 0.633850 0.773456i \(-0.281474\pi\)
−0.986758 + 0.162202i \(0.948141\pi\)
\(492\) 7.90876 + 13.6984i 0.0160747 + 0.0278422i
\(493\) 894.530i 1.81446i
\(494\) −6.11440 0.519808i −0.0123773 0.00105224i
\(495\) 386.686 0.781184
\(496\) 251.644 145.287i 0.507347 0.292917i
\(497\) −143.933 + 83.0997i −0.289603 + 0.167203i
\(498\) −266.048 + 460.809i −0.534234 + 0.925320i
\(499\) −40.3510 69.8900i −0.0808638 0.140060i 0.822757 0.568393i \(-0.192435\pi\)
−0.903621 + 0.428333i \(0.859101\pi\)
\(500\) −7.45844 + 12.9184i −0.0149169 + 0.0258368i
\(501\) −284.280 −0.567425
\(502\) 730.984i 1.45614i
\(503\) −247.050 + 427.903i −0.491153 + 0.850701i −0.999948 0.0101862i \(-0.996758\pi\)
0.508796 + 0.860887i \(0.330091\pi\)
\(504\) 45.3621 + 26.1898i 0.0900042 + 0.0519640i
\(505\) 983.766 1.94805
\(506\) 217.587i 0.430014i
\(507\) 253.463 + 146.337i 0.499928 + 0.288633i
\(508\) −6.74237 + 3.89271i −0.0132724 + 0.00766282i
\(509\) 63.9084 + 36.8975i 0.125557 + 0.0724902i 0.561463 0.827502i \(-0.310239\pi\)
−0.435906 + 0.899992i \(0.643572\pi\)
\(510\) −282.474 489.260i −0.553871 0.959333i
\(511\) 103.875 + 179.917i 0.203278 + 0.352088i
\(512\) 452.842i 0.884457i
\(513\) 8.36297 98.3721i 0.0163021 0.191758i
\(514\) 564.232 1.09773
\(515\) −938.599 + 541.900i −1.82252 + 1.05223i
\(516\) −9.89907 + 5.71523i −0.0191842 + 0.0110760i
\(517\) 294.918 510.814i 0.570442 0.988034i
\(518\) −99.7746 172.815i −0.192615 0.333619i
\(519\) −234.355 + 405.914i −0.451551 + 0.782109i
\(520\) 7.74294 0.0148903
\(521\) 357.582i 0.686337i −0.939274 0.343169i \(-0.888500\pi\)
0.939274 0.343169i \(-0.111500\pi\)
\(522\) 112.494 194.846i 0.215506 0.373268i
\(523\) 382.935 + 221.088i 0.732190 + 0.422730i 0.819223 0.573475i \(-0.194405\pi\)
−0.0870328 + 0.996205i \(0.527739\pi\)
\(524\) −15.0605 −0.0287415
\(525\) 63.3053i 0.120582i
\(526\) 270.225 + 156.014i 0.513735 + 0.296605i
\(527\) 364.919 210.686i 0.692447 0.399784i
\(528\) 511.829 + 295.505i 0.969374 + 0.559668i
\(529\) 250.745 + 434.303i 0.473998 + 0.820989i
\(530\) 370.243 + 641.281i 0.698573 + 1.20996i
\(531\) 103.670i 0.195235i
\(532\) 6.45819 9.27165i 0.0121395 0.0174279i
\(533\) −5.43561 −0.0101981
\(534\) −224.518 + 129.625i −0.420445 + 0.242744i
\(535\) −772.557 + 446.036i −1.44403 + 0.833712i
\(536\) 294.331 509.796i 0.549124 0.951111i
\(537\) 161.461 + 279.658i 0.300672 + 0.520779i
\(538\) −70.2539 + 121.683i −0.130584 + 0.226177i
\(539\) 881.666 1.63574
\(540\) 8.76040i 0.0162230i
\(541\) −487.737 + 844.785i −0.901547 + 1.56152i −0.0760596 + 0.997103i \(0.524234\pi\)
−0.825487 + 0.564421i \(0.809099\pi\)
\(542\) −203.476 117.477i −0.375418 0.216747i
\(543\) 80.3877 0.148044
\(544\) 103.390i 0.190056i
\(545\) 58.7542 + 33.9217i 0.107806 + 0.0622417i
\(546\) 1.09624 0.632912i 0.00200776 0.00115918i
\(547\) 350.050 + 202.102i 0.639945 + 0.369473i 0.784594 0.620010i \(-0.212872\pi\)
−0.144648 + 0.989483i \(0.546205\pi\)
\(548\) −12.4704 21.5994i −0.0227562 0.0394149i
\(549\) −82.1414 142.273i −0.149620 0.259149i
\(550\) 670.070i 1.21831i
\(551\) 566.310 + 394.465i 1.02779 + 0.715907i
\(552\) −70.0968 −0.126987
\(553\) 120.223 69.4109i 0.217402 0.125517i
\(554\) −788.368 + 455.164i −1.42305 + 0.821596i
\(555\) 237.291 410.999i 0.427551 0.740539i
\(556\) 23.9881 + 41.5486i 0.0431441 + 0.0747277i
\(557\) −29.9352 + 51.8492i −0.0537435 + 0.0930866i −0.891646 0.452734i \(-0.850449\pi\)
0.837902 + 0.545821i \(0.183782\pi\)
\(558\) 105.982 0.189932
\(559\) 3.92802i 0.00702687i
\(560\) −123.256 + 213.486i −0.220100 + 0.381225i
\(561\) 742.225 + 428.524i 1.32304 + 0.763857i
\(562\) −186.178 −0.331278
\(563\) 247.579i 0.439749i 0.975528 + 0.219874i \(0.0705648\pi\)
−0.975528 + 0.219874i \(0.929435\pi\)
\(564\) −11.5725 6.68140i −0.0205187 0.0118464i
\(565\) 384.211 221.824i 0.680020 0.392610i
\(566\) −123.494 71.2990i −0.218186 0.125970i
\(567\) 10.1827 + 17.6369i 0.0179588 + 0.0311056i
\(568\) −283.363 490.800i −0.498879 0.864084i
\(569\) 76.4991i 0.134445i −0.997738 0.0672224i \(-0.978586\pi\)
0.997738 0.0672224i \(-0.0214137\pi\)
\(570\) 434.305 + 36.9219i 0.761939 + 0.0647752i
\(571\) −624.523 −1.09373 −0.546867 0.837219i \(-0.684180\pi\)
−0.546867 + 0.837219i \(0.684180\pi\)
\(572\) 0.715374 0.413021i 0.00125065 0.000722065i
\(573\) 55.0834 31.8024i 0.0961315 0.0555016i
\(574\) 81.1706 140.592i 0.141412 0.244933i
\(575\) −42.3590 73.3680i −0.0736679 0.127597i
\(576\) −88.8909 + 153.964i −0.154324 + 0.267298i
\(577\) 185.550 0.321577 0.160789 0.986989i \(-0.448596\pi\)
0.160789 + 0.986989i \(0.448596\pi\)
\(578\) 655.462i 1.13402i
\(579\) 173.472 300.462i 0.299606 0.518932i
\(580\) 53.0352 + 30.6199i 0.0914399 + 0.0527929i
\(581\) 336.690 0.579501
\(582\) 289.187i 0.496885i
\(583\) −972.846 561.673i −1.66869 0.963418i
\(584\) −613.503 + 354.206i −1.05052 + 0.606517i
\(585\) 2.60714 + 1.50523i 0.00445665 + 0.00257305i
\(586\) −423.501 733.525i −0.722698 1.25175i
\(587\) −130.891 226.710i −0.222983 0.386218i 0.732729 0.680520i \(-0.238246\pi\)
−0.955712 + 0.294302i \(0.904913\pi\)
\(588\) 19.9742i 0.0339697i
\(589\) −27.5386 + 323.931i −0.0467548 + 0.549968i
\(590\) −457.694 −0.775752
\(591\) 257.268 148.534i 0.435310 0.251326i
\(592\) 628.170 362.674i 1.06110 0.612626i
\(593\) −124.254 + 215.215i −0.209535 + 0.362925i −0.951568 0.307438i \(-0.900528\pi\)
0.742033 + 0.670363i \(0.233862\pi\)
\(594\) 107.781 + 186.681i 0.181449 + 0.314279i
\(595\) −178.739 + 309.585i −0.300401 + 0.520310i
\(596\) −2.89324 −0.00485443
\(597\) 151.554i 0.253860i
\(598\) −0.846992 + 1.46703i −0.00141637 + 0.00245323i
\(599\) −167.646 96.7905i −0.279877 0.161587i 0.353491 0.935438i \(-0.384995\pi\)
−0.633368 + 0.773851i \(0.718328\pi\)
\(600\) −215.866 −0.359777
\(601\) 675.975i 1.12475i −0.826882 0.562375i \(-0.809888\pi\)
0.826882 0.562375i \(-0.190112\pi\)
\(602\) 101.598 + 58.6576i 0.168767 + 0.0974378i
\(603\) 198.209 114.436i 0.328706 0.189778i
\(604\) 54.3619 + 31.3859i 0.0900032 + 0.0519634i
\(605\) −906.827 1570.67i −1.49889 2.59615i
\(606\) 274.204 + 474.935i 0.452482 + 0.783722i
\(607\) 383.052i 0.631057i 0.948916 + 0.315528i \(0.102182\pi\)
−0.948916 + 0.315528i \(0.897818\pi\)
\(608\) 65.4546 + 45.5925i 0.107656 + 0.0749877i
\(609\) −142.364 −0.233767
\(610\) 628.125 362.648i 1.02971 0.594505i
\(611\) 3.97684 2.29603i 0.00650874 0.00375782i
\(612\) 9.70824 16.8152i 0.0158631 0.0274758i
\(613\) −27.5410 47.7025i −0.0449283 0.0778180i 0.842687 0.538404i \(-0.180973\pi\)
−0.887615 + 0.460586i \(0.847639\pi\)
\(614\) 240.649 416.817i 0.391937 0.678854i
\(615\) 386.091 0.627789
\(616\) 350.818i 0.569510i
\(617\) −51.7851 + 89.6944i −0.0839305 + 0.145372i −0.904935 0.425550i \(-0.860081\pi\)
0.821004 + 0.570922i \(0.193414\pi\)
\(618\) −523.230 302.087i −0.846650 0.488814i
\(619\) −263.102 −0.425043 −0.212521 0.977156i \(-0.568168\pi\)
−0.212521 + 0.977156i \(0.568168\pi\)
\(620\) 28.8473i 0.0465278i
\(621\) −23.6025 13.6269i −0.0380072 0.0219435i
\(622\) 789.030 455.547i 1.26854 0.732390i
\(623\) 142.066 + 82.0218i 0.228035 + 0.131656i
\(624\) 2.30060 + 3.98475i 0.00368685 + 0.00638581i
\(625\) 383.956 + 665.031i 0.614329 + 1.06405i
\(626\) 250.377i 0.399963i
\(627\) −598.593 + 280.921i −0.954693 + 0.448039i
\(628\) 11.9908 0.0190936
\(629\) 910.936 525.929i 1.44823 0.836135i
\(630\) −77.8655 + 44.9557i −0.123596 + 0.0713582i
\(631\) 72.5474 125.656i 0.114972 0.199137i −0.802797 0.596253i \(-0.796655\pi\)
0.917769 + 0.397116i \(0.129989\pi\)
\(632\) 236.686 + 409.952i 0.374503 + 0.648658i
\(633\) −16.3950 + 28.3970i −0.0259005 + 0.0448609i
\(634\) −682.817 −1.07700
\(635\) 190.035i 0.299267i
\(636\) −12.7247 + 22.0399i −0.0200075 + 0.0346539i
\(637\) 5.94443 + 3.43202i 0.00933192 + 0.00538779i
\(638\) −1506.88 −2.36189
\(639\) 220.344i 0.344827i
\(640\) −773.034 446.311i −1.20787 0.697361i
\(641\) −583.796 + 337.055i −0.910758 + 0.525826i −0.880675 0.473721i \(-0.842911\pi\)
−0.0300832 + 0.999547i \(0.509577\pi\)
\(642\) −430.668 248.646i −0.670823 0.387300i
\(643\) 0.719856 + 1.24683i 0.00111953 + 0.00193908i 0.866585 0.499030i \(-0.166310\pi\)
−0.865465 + 0.500969i \(0.832977\pi\)
\(644\) −1.55958 2.70128i −0.00242171 0.00419453i
\(645\) 279.007i 0.432569i
\(646\) 792.711 + 552.165i 1.22711 + 0.854745i
\(647\) −614.044 −0.949063 −0.474532 0.880239i \(-0.657383\pi\)
−0.474532 + 0.880239i \(0.657383\pi\)
\(648\) −60.1404 + 34.7221i −0.0928092 + 0.0535834i
\(649\) 601.315 347.169i 0.926525 0.534929i
\(650\) −2.60835 + 4.51779i −0.00401284 + 0.00695045i
\(651\) −33.5306 58.0768i −0.0515064 0.0892116i
\(652\) 0.774191 1.34094i 0.00118741 0.00205665i
\(653\) 822.374 1.25938 0.629689 0.776847i \(-0.283182\pi\)
0.629689 + 0.776847i \(0.283182\pi\)
\(654\) 37.8199i 0.0578286i
\(655\) −183.807 + 318.362i −0.280621 + 0.486049i
\(656\) 511.041 + 295.050i 0.779027 + 0.449771i
\(657\) −275.432 −0.419227
\(658\) 137.147i 0.208431i
\(659\) −549.386 317.188i −0.833666 0.481317i 0.0214404 0.999770i \(-0.493175\pi\)
−0.855106 + 0.518453i \(0.826508\pi\)
\(660\) −50.8129 + 29.3368i −0.0769892 + 0.0444497i
\(661\) −818.470 472.544i −1.23823 0.714893i −0.269498 0.963001i \(-0.586858\pi\)
−0.968732 + 0.248108i \(0.920191\pi\)
\(662\) 450.413 + 780.138i 0.680382 + 1.17846i
\(663\) 3.33619 + 5.77845i 0.00503196 + 0.00871561i
\(664\) 1148.09i 1.72905i
\(665\) −117.173 249.675i −0.176200 0.375451i
\(666\) 264.559 0.397236
\(667\) 164.993 95.2590i 0.247366 0.142817i
\(668\) 37.3561 21.5676i 0.0559223 0.0322868i
\(669\) 224.162 388.260i 0.335070 0.580358i
\(670\) 505.228 + 875.080i 0.754071 + 1.30609i
\(671\) −550.150 + 952.888i −0.819896 + 1.42010i
\(672\) −16.4545 −0.0244859
\(673\) 570.803i 0.848147i −0.905628 0.424074i \(-0.860600\pi\)
0.905628 0.424074i \(-0.139400\pi\)
\(674\) 258.703 448.086i 0.383832 0.664817i
\(675\) −72.6848 41.9646i −0.107681 0.0621698i
\(676\) −44.4088 −0.0656935
\(677\) 275.976i 0.407646i −0.979008 0.203823i \(-0.934663\pi\)
0.979008 0.203823i \(-0.0653367\pi\)
\(678\) 214.182 + 123.658i 0.315902 + 0.182386i
\(679\) 158.471 91.4931i 0.233388 0.134747i
\(680\) −1055.66 609.485i −1.55244 0.896302i
\(681\) 111.764 + 193.582i 0.164118 + 0.284261i
\(682\) −354.913 614.727i −0.520400 0.901359i
\(683\) 106.224i 0.155525i 0.996972 + 0.0777627i \(0.0247776\pi\)
−0.996972 + 0.0777627i \(0.975222\pi\)
\(684\) 6.36428 + 13.5612i 0.00930450 + 0.0198263i
\(685\) −608.781 −0.888732
\(686\) −375.792 + 216.964i −0.547802 + 0.316274i
\(687\) 148.342 85.6453i 0.215927 0.124666i
\(688\) −213.217 + 369.302i −0.309908 + 0.536776i
\(689\) −4.37279 7.57390i −0.00634658 0.0109926i
\(690\) 60.1617 104.203i 0.0871908 0.151019i
\(691\) 244.177 0.353367 0.176684 0.984268i \(-0.443463\pi\)
0.176684 + 0.984268i \(0.443463\pi\)
\(692\) 71.1195i 0.102774i
\(693\) 68.1994 118.125i 0.0984118 0.170454i
\(694\) 299.201 + 172.744i 0.431125 + 0.248910i
\(695\) 1171.05 1.68497
\(696\) 485.450i 0.697486i
\(697\) 741.082 + 427.864i 1.06325 + 0.613865i
\(698\) 870.378 502.513i 1.24696 0.719932i
\(699\) −524.194 302.644i −0.749920 0.432966i
\(700\) −4.80281 8.31871i −0.00686115 0.0118839i
\(701\) 143.276 + 248.161i 0.204388 + 0.354010i 0.949938 0.312440i \(-0.101146\pi\)
−0.745550 + 0.666450i \(0.767813\pi\)
\(702\) 1.67821i 0.00239061i
\(703\) −68.7436 + 808.618i −0.0977860 + 1.15024i
\(704\) 1190.71 1.69135
\(705\) −282.474 + 163.087i −0.400673 + 0.231329i
\(706\) −53.9108 + 31.1254i −0.0763610 + 0.0440870i
\(707\) 173.506 300.521i 0.245411 0.425065i
\(708\) −7.86514 13.6228i −0.0111090 0.0192413i
\(709\) −5.70585 + 9.88282i −0.00804774 + 0.0139391i −0.870021 0.493014i \(-0.835895\pi\)
0.861973 + 0.506953i \(0.169228\pi\)
\(710\) 972.804 1.37015
\(711\) 184.048i 0.258857i
\(712\) −279.688 + 484.434i −0.392820 + 0.680385i
\(713\) 77.7209 + 44.8722i 0.109006 + 0.0629344i
\(714\) −199.279 −0.279102
\(715\) 20.1629i 0.0281999i
\(716\) −42.4339 24.4992i −0.0592652 0.0342168i
\(717\) −451.636 + 260.752i −0.629897 + 0.363671i
\(718\) 268.238 + 154.867i 0.373591 + 0.215693i
\(719\) 438.491 + 759.488i 0.609862 + 1.05631i 0.991263 + 0.131902i \(0.0421084\pi\)
−0.381401 + 0.924410i \(0.624558\pi\)
\(720\) −163.411 283.036i −0.226960 0.393106i
\(721\) 382.298i 0.530232i
\(722\) −699.131 + 258.360i −0.968325 + 0.357839i
\(723\) −220.485 −0.304958
\(724\) −10.5634 + 6.09880i −0.0145904 + 0.00842376i
\(725\) 508.105 293.354i 0.700834 0.404627i
\(726\) 505.518 875.583i 0.696306 1.20604i
\(727\) −360.167 623.827i −0.495415 0.858084i 0.504571 0.863370i \(-0.331651\pi\)
−0.999986 + 0.00528653i \(0.998317\pi\)
\(728\) 1.36561 2.36531i 0.00187584 0.00324905i
\(729\) −27.0000 −0.0370370
\(730\) 1216.01i 1.66577i
\(731\) −309.194 + 535.540i −0.422974 + 0.732613i
\(732\) 21.5878 + 12.4637i 0.0294915 + 0.0170269i
\(733\) −170.651 −0.232812 −0.116406 0.993202i \(-0.537137\pi\)
−0.116406 + 0.993202i \(0.537137\pi\)
\(734\) 1024.44i 1.39570i
\(735\) −422.232 243.776i −0.574465 0.331668i
\(736\) 19.0701 11.0101i 0.0259104 0.0149594i
\(737\) −1327.53 766.449i −1.80126 1.03996i
\(738\) 107.615 + 186.394i 0.145819 + 0.252566i
\(739\) 530.334 + 918.566i 0.717637 + 1.24298i 0.961933 + 0.273284i \(0.0881098\pi\)
−0.244296 + 0.969701i \(0.578557\pi\)
\(740\) 72.0104i 0.0973114i
\(741\) −5.12940 0.436069i −0.00692227 0.000588487i
\(742\) 261.198 0.352019
\(743\) 290.537 167.742i 0.391033 0.225763i −0.291575 0.956548i \(-0.594179\pi\)
0.682607 + 0.730785i \(0.260846\pi\)
\(744\) 198.037 114.337i 0.266179 0.153679i
\(745\) −35.3107 + 61.1599i −0.0473969 + 0.0820938i
\(746\) −464.148 803.928i −0.622182 1.07765i
\(747\) −223.189 + 386.575i −0.298781 + 0.517503i
\(748\) −130.044 −0.173855
\(749\) 314.668i 0.420117i
\(750\) −101.487 + 175.781i −0.135316 + 0.234375i
\(751\) −1128.41 651.490i −1.50255 0.867497i −0.999996 0.00295120i \(-0.999061\pi\)
−0.502554 0.864546i \(-0.667606\pi\)
\(752\) −498.522 −0.662929
\(753\) 613.226i 0.814377i
\(754\) −10.1598 5.86578i −0.0134746 0.00777955i
\(755\) 1326.92 766.100i 1.75751 1.01470i
\(756\) −2.67613 1.54506i −0.00353985 0.00204373i
\(757\) −60.1511 104.185i −0.0794598 0.137628i 0.823557 0.567233i \(-0.191986\pi\)
−0.903017 + 0.429605i \(0.858653\pi\)
\(758\) 486.574 + 842.771i 0.641919 + 1.11184i
\(759\) 182.535i 0.240494i
\(760\) 851.373 399.551i 1.12023 0.525725i
\(761\) 1346.45 1.76932 0.884658 0.466240i \(-0.154392\pi\)
0.884658 + 0.466240i \(0.154392\pi\)
\(762\) −91.7437 + 52.9682i −0.120399 + 0.0695121i
\(763\) 20.7248 11.9655i 0.0271623 0.0156822i
\(764\) −4.82553 + 8.35805i −0.00631613 + 0.0109399i
\(765\) −236.969 410.442i −0.309763 0.536526i
\(766\) 27.9243 48.3663i 0.0364547 0.0631414i
\(767\) 5.40564 0.00704777
\(768\) 87.0301i 0.113320i
\(769\) 109.016 188.821i 0.141763 0.245541i −0.786398 0.617721i \(-0.788056\pi\)
0.928161 + 0.372180i \(0.121390\pi\)
\(770\) 521.512 + 301.095i 0.677288 + 0.391033i
\(771\) 473.337 0.6139