Properties

Label 105.3.t.b.86.1
Level 105
Weight 3
Character 105.86
Analytic conductor 2.861
Analytic rank 0
Dimension 36
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 86.1
Character \(\chi\) \(=\) 105.86
Dual form 105.3.t.b.11.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.31814 - 1.91573i) q^{2} +(1.84164 - 2.36819i) q^{3} +(5.34002 + 9.24919i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-10.6476 + 4.32991i) q^{6} +(-5.86414 - 3.82255i) q^{7} -25.5943i q^{8} +(-2.21669 - 8.72274i) q^{9} +O(q^{10})\) \(q+(-3.31814 - 1.91573i) q^{2} +(1.84164 - 2.36819i) q^{3} +(5.34002 + 9.24919i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-10.6476 + 4.32991i) q^{6} +(-5.86414 - 3.82255i) q^{7} -25.5943i q^{8} +(-2.21669 - 8.72274i) q^{9} +(4.28370 + 7.41958i) q^{10} +(-9.48205 + 5.47446i) q^{11} +(31.7383 + 4.38750i) q^{12} -3.75260 q^{13} +(12.1351 + 23.9178i) q^{14} +(-6.21405 + 2.52697i) q^{15} +(-27.6716 + 47.9286i) q^{16} +(-12.6515 + 7.30435i) q^{17} +(-9.35510 + 33.1898i) q^{18} +(5.54612 - 9.60616i) q^{19} -23.8813i q^{20} +(-19.8522 + 6.84766i) q^{21} +41.9503 q^{22} +(8.53608 + 4.92831i) q^{23} +(-60.6123 - 47.1356i) q^{24} +(2.50000 + 4.33013i) q^{25} +(12.4516 + 7.18896i) q^{26} +(-24.7395 - 10.8146i) q^{27} +(4.04080 - 74.6510i) q^{28} +10.0771i q^{29} +(25.4601 + 3.51960i) q^{30} +(-12.0674 - 20.9013i) q^{31} +(94.9750 - 54.8338i) q^{32} +(-4.49796 + 32.5374i) q^{33} +55.9726 q^{34} +(7.08212 + 13.9586i) q^{35} +(68.8411 - 67.0823i) q^{36} +(19.1895 - 33.2372i) q^{37} +(-36.8056 + 21.2497i) q^{38} +(-6.91096 + 8.88689i) q^{39} +(-28.6153 + 49.5631i) q^{40} -67.5044i q^{41} +(78.9905 + 15.3099i) q^{42} -77.4222 q^{43} +(-101.269 - 58.4675i) q^{44} +(-5.45971 + 19.3699i) q^{45} +(-18.8826 - 32.7056i) q^{46} +(-4.91770 - 2.83924i) q^{47} +(62.5430 + 153.799i) q^{48} +(19.7763 + 44.8319i) q^{49} -19.1573i q^{50} +(-6.00145 + 43.4133i) q^{51} +(-20.0390 - 34.7085i) q^{52} +(59.9505 - 34.6124i) q^{53} +(61.3712 + 83.2786i) q^{54} +24.4825 q^{55} +(-97.8353 + 150.088i) q^{56} +(-12.5353 - 30.8254i) q^{57} +(19.3049 - 33.4371i) q^{58} +(45.4375 - 26.2334i) q^{59} +(-56.5556 - 43.9809i) q^{60} +(6.77556 - 11.7356i) q^{61} +92.4712i q^{62} +(-20.3441 + 59.6248i) q^{63} -198.814 q^{64} +(7.26688 + 4.19554i) q^{65} +(77.2576 - 99.3465i) q^{66} +(-10.6264 - 18.4054i) q^{67} +(-135.119 - 78.0108i) q^{68} +(27.3916 - 11.1389i) q^{69} +(3.24148 - 59.8841i) q^{70} +25.6835i q^{71} +(-223.252 + 56.7347i) q^{72} +(12.4056 + 21.4871i) q^{73} +(-127.347 + 73.5238i) q^{74} +(14.8587 + 2.05407i) q^{75} +118.466 q^{76} +(76.5305 + 4.14254i) q^{77} +(39.9564 - 16.2484i) q^{78} +(55.3563 - 95.8799i) q^{79} +(107.172 - 61.8755i) q^{80} +(-71.1725 + 38.6713i) q^{81} +(-129.320 + 223.989i) q^{82} -102.155i q^{83} +(-169.346 - 147.050i) q^{84} +32.6661 q^{85} +(256.898 + 148.320i) q^{86} +(23.8645 + 18.5584i) q^{87} +(140.115 + 242.686i) q^{88} +(62.5361 + 36.1052i) q^{89} +(55.2234 - 53.8125i) q^{90} +(22.0058 + 14.3445i) q^{91} +105.269i q^{92} +(-71.7222 - 9.91487i) q^{93} +(10.8784 + 18.8420i) q^{94} +(-21.4800 + 12.4015i) q^{95} +(45.0529 - 325.904i) q^{96} -6.23399 q^{97} +(20.2652 - 186.644i) q^{98} +(68.7712 + 70.5743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + O(q^{10}) \) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + 20q^{10} - 42q^{12} - 100q^{13} + 20q^{15} - 12q^{16} - 14q^{18} + 50q^{19} - 12q^{21} + 256q^{22} - 140q^{24} + 90q^{25} + 4q^{27} - 48q^{28} + 60q^{30} - 82q^{31} - 76q^{33} - 64q^{34} + 296q^{36} - 26q^{37} - 130q^{39} - 60q^{40} - 98q^{42} - 204q^{43} + 40q^{45} + 28q^{46} + 532q^{48} - 382q^{49} + 208q^{51} + 200q^{52} - 44q^{54} - 160q^{55} + 252q^{57} + 264q^{58} - 130q^{60} - 324q^{61} - 258q^{63} - 24q^{64} - 164q^{66} - 142q^{67} - 112q^{69} + 200q^{70} - 322q^{72} + 386q^{73} - 20q^{75} - 424q^{76} - 440q^{78} + 334q^{79} + 186q^{81} - 68q^{82} + 80q^{84} - 200q^{85} + 342q^{87} + 180q^{88} + 100q^{90} + 46q^{91} - 2q^{93} + 324q^{94} + 732q^{96} + 1616q^{97} + 384q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.31814 1.91573i −1.65907 0.957864i −0.973146 0.230189i \(-0.926066\pi\)
−0.685923 0.727675i \(-0.740601\pi\)
\(3\) 1.84164 2.36819i 0.613881 0.789398i
\(4\) 5.34002 + 9.24919i 1.33501 + 2.31230i
\(5\) −1.93649 1.11803i −0.387298 0.223607i
\(6\) −10.6476 + 4.32991i −1.77461 + 0.721651i
\(7\) −5.86414 3.82255i −0.837734 0.546078i
\(8\) 25.5943i 3.19929i
\(9\) −2.21669 8.72274i −0.246299 0.969194i
\(10\) 4.28370 + 7.41958i 0.428370 + 0.741958i
\(11\) −9.48205 + 5.47446i −0.862004 + 0.497679i −0.864683 0.502318i \(-0.832481\pi\)
0.00267854 + 0.999996i \(0.499147\pi\)
\(12\) 31.7383 + 4.38750i 2.64486 + 0.365625i
\(13\) −3.75260 −0.288662 −0.144331 0.989529i \(-0.546103\pi\)
−0.144331 + 0.989529i \(0.546103\pi\)
\(14\) 12.1351 + 23.9178i 0.866791 + 1.70842i
\(15\) −6.21405 + 2.52697i −0.414270 + 0.168465i
\(16\) −27.6716 + 47.9286i −1.72947 + 2.99554i
\(17\) −12.6515 + 7.30435i −0.744206 + 0.429668i −0.823597 0.567176i \(-0.808036\pi\)
0.0793904 + 0.996844i \(0.474703\pi\)
\(18\) −9.35510 + 33.1898i −0.519728 + 1.84388i
\(19\) 5.54612 9.60616i 0.291901 0.505587i −0.682358 0.731018i \(-0.739046\pi\)
0.974259 + 0.225431i \(0.0723789\pi\)
\(20\) 23.8813i 1.19407i
\(21\) −19.8522 + 6.84766i −0.945342 + 0.326079i
\(22\) 41.9503 1.90683
\(23\) 8.53608 + 4.92831i 0.371134 + 0.214274i 0.673954 0.738774i \(-0.264595\pi\)
−0.302820 + 0.953048i \(0.597928\pi\)
\(24\) −60.6123 47.1356i −2.52551 1.96398i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) 12.4516 + 7.18896i 0.478909 + 0.276499i
\(27\) −24.7395 10.8146i −0.916279 0.400542i
\(28\) 4.04080 74.6510i 0.144314 2.66611i
\(29\) 10.0771i 0.347485i 0.984791 + 0.173743i \(0.0555861\pi\)
−0.984791 + 0.173743i \(0.944414\pi\)
\(30\) 25.4601 + 3.51960i 0.848669 + 0.117320i
\(31\) −12.0674 20.9013i −0.389270 0.674236i 0.603081 0.797680i \(-0.293939\pi\)
−0.992352 + 0.123444i \(0.960606\pi\)
\(32\) 94.9750 54.8338i 2.96797 1.71356i
\(33\) −4.49796 + 32.5374i −0.136302 + 0.985980i
\(34\) 55.9726 1.64625
\(35\) 7.08212 + 13.9586i 0.202346 + 0.398818i
\(36\) 68.8411 67.0823i 1.91225 1.86340i
\(37\) 19.1895 33.2372i 0.518636 0.898303i −0.481130 0.876649i \(-0.659773\pi\)
0.999766 0.0216538i \(-0.00689317\pi\)
\(38\) −36.8056 + 21.2497i −0.968568 + 0.559203i
\(39\) −6.91096 + 8.88689i −0.177204 + 0.227869i
\(40\) −28.6153 + 49.5631i −0.715382 + 1.23908i
\(41\) 67.5044i 1.64645i −0.567716 0.823224i \(-0.692173\pi\)
0.567716 0.823224i \(-0.307827\pi\)
\(42\) 78.9905 + 15.3099i 1.88073 + 0.364522i
\(43\) −77.4222 −1.80052 −0.900258 0.435356i \(-0.856623\pi\)
−0.900258 + 0.435356i \(0.856623\pi\)
\(44\) −101.269 58.4675i −2.30156 1.32881i
\(45\) −5.45971 + 19.3699i −0.121327 + 0.430441i
\(46\) −18.8826 32.7056i −0.410491 0.710991i
\(47\) −4.91770 2.83924i −0.104632 0.0604093i 0.446771 0.894648i \(-0.352574\pi\)
−0.551403 + 0.834239i \(0.685907\pi\)
\(48\) 62.5430 + 153.799i 1.30298 + 3.20415i
\(49\) 19.7763 + 44.8319i 0.403598 + 0.914936i
\(50\) 19.1573i 0.383145i
\(51\) −6.00145 + 43.4133i −0.117675 + 0.851240i
\(52\) −20.0390 34.7085i −0.385365 0.667472i
\(53\) 59.9505 34.6124i 1.13114 0.653065i 0.186920 0.982375i \(-0.440150\pi\)
0.944222 + 0.329310i \(0.106816\pi\)
\(54\) 61.3712 + 83.2786i 1.13650 + 1.54220i
\(55\) 24.4825 0.445137
\(56\) −97.8353 + 150.088i −1.74706 + 2.68015i
\(57\) −12.5353 30.8254i −0.219917 0.540797i
\(58\) 19.3049 33.4371i 0.332844 0.576502i
\(59\) 45.4375 26.2334i 0.770128 0.444634i −0.0627923 0.998027i \(-0.520001\pi\)
0.832920 + 0.553393i \(0.186667\pi\)
\(60\) −56.5556 43.9809i −0.942593 0.733014i
\(61\) 6.77556 11.7356i 0.111075 0.192387i −0.805129 0.593100i \(-0.797904\pi\)
0.916204 + 0.400712i \(0.131237\pi\)
\(62\) 92.4712i 1.49147i
\(63\) −20.3441 + 59.6248i −0.322922 + 0.946426i
\(64\) −198.814 −3.10647
\(65\) 7.26688 + 4.19554i 0.111798 + 0.0645467i
\(66\) 77.2576 99.3465i 1.17057 1.50525i
\(67\) −10.6264 18.4054i −0.158603 0.274708i 0.775762 0.631025i \(-0.217366\pi\)
−0.934365 + 0.356317i \(0.884032\pi\)
\(68\) −135.119 78.0108i −1.98704 1.14722i
\(69\) 27.3916 11.1389i 0.396980 0.161433i
\(70\) 3.24148 59.8841i 0.0463069 0.855487i
\(71\) 25.6835i 0.361740i 0.983507 + 0.180870i \(0.0578913\pi\)
−0.983507 + 0.180870i \(0.942109\pi\)
\(72\) −223.252 + 56.7347i −3.10073 + 0.787982i
\(73\) 12.4056 + 21.4871i 0.169939 + 0.294344i 0.938398 0.345555i \(-0.112309\pi\)
−0.768459 + 0.639899i \(0.778976\pi\)
\(74\) −127.347 + 73.5238i −1.72090 + 0.993564i
\(75\) 14.8587 + 2.05407i 0.198116 + 0.0273875i
\(76\) 118.466 1.55876
\(77\) 76.5305 + 4.14254i 0.993902 + 0.0537992i
\(78\) 39.9564 16.2484i 0.512261 0.208313i
\(79\) 55.3563 95.8799i 0.700713 1.21367i −0.267504 0.963557i \(-0.586199\pi\)
0.968217 0.250113i \(-0.0804679\pi\)
\(80\) 107.172 61.8755i 1.33964 0.773444i
\(81\) −71.1725 + 38.6713i −0.878673 + 0.477424i
\(82\) −129.320 + 223.989i −1.57707 + 2.73157i
\(83\) 102.155i 1.23078i −0.788222 0.615392i \(-0.788998\pi\)
0.788222 0.615392i \(-0.211002\pi\)
\(84\) −169.346 147.050i −2.01603 1.75060i
\(85\) 32.6661 0.384307
\(86\) 256.898 + 148.320i 2.98718 + 1.72465i
\(87\) 23.8645 + 18.5584i 0.274304 + 0.213315i
\(88\) 140.115 + 242.686i 1.59222 + 2.75780i
\(89\) 62.5361 + 36.1052i 0.702652 + 0.405677i 0.808335 0.588723i \(-0.200369\pi\)
−0.105682 + 0.994400i \(0.533703\pi\)
\(90\) 55.2234 53.8125i 0.613594 0.597917i
\(91\) 22.0058 + 14.3445i 0.241822 + 0.157632i
\(92\) 105.269i 1.14423i
\(93\) −71.7222 9.91487i −0.771207 0.106612i
\(94\) 10.8784 + 18.8420i 0.115728 + 0.200446i
\(95\) −21.4800 + 12.4015i −0.226106 + 0.130542i
\(96\) 45.0529 325.904i 0.469301 3.39483i
\(97\) −6.23399 −0.0642680 −0.0321340 0.999484i \(-0.510230\pi\)
−0.0321340 + 0.999484i \(0.510230\pi\)
\(98\) 20.2652 186.644i 0.206788 1.90453i
\(99\) 68.7712 + 70.5743i 0.694658 + 0.712871i
\(100\) −26.7001 + 46.2459i −0.267001 + 0.462459i
\(101\) −44.7681 + 25.8469i −0.443249 + 0.255910i −0.704975 0.709232i \(-0.749042\pi\)
0.261726 + 0.965142i \(0.415708\pi\)
\(102\) 103.082 132.554i 1.01060 1.29955i
\(103\) 58.1765 100.765i 0.564821 0.978298i −0.432246 0.901756i \(-0.642279\pi\)
0.997066 0.0765423i \(-0.0243880\pi\)
\(104\) 96.0451i 0.923511i
\(105\) 46.0995 + 8.93499i 0.439043 + 0.0850951i
\(106\) −265.232 −2.50219
\(107\) −123.457 71.2779i −1.15380 0.666148i −0.203992 0.978973i \(-0.565392\pi\)
−0.949811 + 0.312824i \(0.898725\pi\)
\(108\) −32.0831 286.571i −0.297066 2.65343i
\(109\) 40.3534 + 69.8941i 0.370214 + 0.641230i 0.989598 0.143858i \(-0.0459509\pi\)
−0.619384 + 0.785088i \(0.712618\pi\)
\(110\) −81.2364 46.9019i −0.738513 0.426381i
\(111\) −43.3720 106.656i −0.390738 0.960862i
\(112\) 345.479 175.284i 3.08464 1.56504i
\(113\) 78.3508i 0.693370i 0.937982 + 0.346685i \(0.112693\pi\)
−0.937982 + 0.346685i \(0.887307\pi\)
\(114\) −17.4593 + 126.297i −0.153152 + 1.10787i
\(115\) −11.0200 19.0872i −0.0958263 0.165976i
\(116\) −93.2048 + 53.8118i −0.803490 + 0.463895i
\(117\) 8.31837 + 32.7330i 0.0710972 + 0.279769i
\(118\) −201.024 −1.70359
\(119\) 102.111 + 5.52722i 0.858079 + 0.0464472i
\(120\) 64.6760 + 159.044i 0.538966 + 1.32537i
\(121\) −0.560494 + 0.970804i −0.00463218 + 0.00802317i
\(122\) −44.9645 + 25.9603i −0.368561 + 0.212789i
\(123\) −159.864 124.319i −1.29970 1.01072i
\(124\) 128.880 223.227i 1.03936 1.80022i
\(125\) 11.1803i 0.0894427i
\(126\) 181.729 158.870i 1.44230 1.26087i
\(127\) −68.5186 −0.539517 −0.269758 0.962928i \(-0.586944\pi\)
−0.269758 + 0.962928i \(0.586944\pi\)
\(128\) 279.792 + 161.538i 2.18588 + 1.26202i
\(129\) −142.584 + 183.351i −1.10530 + 1.42133i
\(130\) −16.0750 27.8427i −0.123654 0.214175i
\(131\) 16.0698 + 9.27792i 0.122671 + 0.0708239i 0.560080 0.828439i \(-0.310771\pi\)
−0.437409 + 0.899263i \(0.644104\pi\)
\(132\) −324.963 + 132.148i −2.46184 + 1.00112i
\(133\) −69.2432 + 35.1316i −0.520626 + 0.264147i
\(134\) 81.4290i 0.607679i
\(135\) 35.8168 + 48.6021i 0.265309 + 0.360015i
\(136\) 186.950 + 323.806i 1.37463 + 2.38093i
\(137\) −116.043 + 66.9972i −0.847027 + 0.489031i −0.859646 0.510889i \(-0.829316\pi\)
0.0126199 + 0.999920i \(0.495983\pi\)
\(138\) −112.228 15.5144i −0.813248 0.112423i
\(139\) 89.7025 0.645342 0.322671 0.946511i \(-0.395419\pi\)
0.322671 + 0.946511i \(0.395419\pi\)
\(140\) −91.2874 + 140.043i −0.652053 + 1.00031i
\(141\) −15.7805 + 6.41721i −0.111919 + 0.0455122i
\(142\) 49.2026 85.2214i 0.346497 0.600151i
\(143\) 35.5824 20.5435i 0.248828 0.143661i
\(144\) 479.408 + 135.129i 3.32922 + 0.938396i
\(145\) 11.2665 19.5142i 0.0777001 0.134581i
\(146\) 95.0628i 0.651115i
\(147\) 142.592 + 35.7303i 0.970011 + 0.243063i
\(148\) 409.890 2.76953
\(149\) −100.678 58.1267i −0.675693 0.390112i 0.122537 0.992464i \(-0.460897\pi\)
−0.798230 + 0.602352i \(0.794230\pi\)
\(150\) −45.3682 35.2809i −0.302454 0.235206i
\(151\) −8.06785 13.9739i −0.0534295 0.0925425i 0.838074 0.545557i \(-0.183682\pi\)
−0.891503 + 0.453015i \(0.850349\pi\)
\(152\) −245.863 141.949i −1.61752 0.933875i
\(153\) 91.7585 + 94.1643i 0.599729 + 0.615453i
\(154\) −246.003 160.357i −1.59742 1.04128i
\(155\) 53.9670i 0.348174i
\(156\) −119.101 16.4645i −0.763469 0.105542i
\(157\) 96.1224 + 166.489i 0.612245 + 1.06044i 0.990861 + 0.134885i \(0.0430666\pi\)
−0.378617 + 0.925554i \(0.623600\pi\)
\(158\) −367.360 + 212.095i −2.32506 + 1.34237i
\(159\) 28.4385 205.718i 0.178858 1.29383i
\(160\) −245.224 −1.53265
\(161\) −31.2181 61.5298i −0.193901 0.382173i
\(162\) 310.244 + 8.03041i 1.91509 + 0.0495705i
\(163\) −138.563 + 239.999i −0.850081 + 1.47238i 0.0310533 + 0.999518i \(0.490114\pi\)
−0.881134 + 0.472866i \(0.843219\pi\)
\(164\) 624.361 360.475i 3.80708 2.19802i
\(165\) 45.0881 57.9794i 0.273261 0.351391i
\(166\) −195.701 + 338.964i −1.17892 + 2.04195i
\(167\) 34.5337i 0.206789i −0.994640 0.103394i \(-0.967030\pi\)
0.994640 0.103394i \(-0.0329704\pi\)
\(168\) 175.261 + 508.103i 1.04322 + 3.02442i
\(169\) −154.918 −0.916674
\(170\) −108.390 62.5792i −0.637591 0.368113i
\(171\) −96.0861 27.0835i −0.561907 0.158383i
\(172\) −413.436 716.093i −2.40370 4.16333i
\(173\) 280.241 + 161.797i 1.61989 + 0.935244i 0.986947 + 0.161046i \(0.0514867\pi\)
0.632943 + 0.774198i \(0.281847\pi\)
\(174\) −43.6328 107.297i −0.250763 0.616650i
\(175\) 1.89175 34.9488i 0.0108100 0.199708i
\(176\) 605.948i 3.44289i
\(177\) 21.5540 155.918i 0.121774 0.880890i
\(178\) −138.335 239.604i −0.777166 1.34609i
\(179\) 5.71552 3.29986i 0.0319303 0.0184350i −0.483950 0.875096i \(-0.660798\pi\)
0.515880 + 0.856661i \(0.327465\pi\)
\(180\) −208.311 + 52.9376i −1.15728 + 0.294098i
\(181\) 225.761 1.24730 0.623649 0.781704i \(-0.285649\pi\)
0.623649 + 0.781704i \(0.285649\pi\)
\(182\) −45.5381 89.7541i −0.250209 0.493154i
\(183\) −15.3141 37.6587i −0.0836834 0.205785i
\(184\) 126.136 218.475i 0.685524 1.18736i
\(185\) −74.3207 + 42.9091i −0.401733 + 0.231941i
\(186\) 218.990 + 170.299i 1.17737 + 0.915587i
\(187\) 79.9748 138.520i 0.427673 0.740751i
\(188\) 60.6463i 0.322587i
\(189\) 103.737 + 157.986i 0.548871 + 0.835907i
\(190\) 95.0316 0.500166
\(191\) −54.2635 31.3290i −0.284102 0.164026i 0.351177 0.936309i \(-0.385782\pi\)
−0.635279 + 0.772283i \(0.719115\pi\)
\(192\) −366.145 + 470.830i −1.90700 + 2.45224i
\(193\) 4.92768 + 8.53500i 0.0255320 + 0.0442228i 0.878509 0.477726i \(-0.158539\pi\)
−0.852977 + 0.521948i \(0.825205\pi\)
\(194\) 20.6852 + 11.9426i 0.106625 + 0.0615600i
\(195\) 23.3189 9.48271i 0.119584 0.0486293i
\(196\) −309.053 + 422.318i −1.57680 + 2.15468i
\(197\) 89.3102i 0.453351i 0.973970 + 0.226676i \(0.0727858\pi\)
−0.973970 + 0.226676i \(0.927214\pi\)
\(198\) −92.9910 365.922i −0.469652 1.84809i
\(199\) −51.3259 88.8991i −0.257919 0.446729i 0.707765 0.706448i \(-0.249704\pi\)
−0.965684 + 0.259719i \(0.916370\pi\)
\(200\) 110.827 63.9857i 0.554133 0.319929i
\(201\) −63.1577 8.73092i −0.314217 0.0434374i
\(202\) 198.062 0.980507
\(203\) 38.5201 59.0934i 0.189754 0.291101i
\(204\) −433.585 + 176.319i −2.12542 + 0.864310i
\(205\) −75.4722 + 130.722i −0.368157 + 0.637667i
\(206\) −386.075 + 222.901i −1.87415 + 1.08204i
\(207\) 24.0665 85.3826i 0.116263 0.412476i
\(208\) 103.840 179.857i 0.499233 0.864696i
\(209\) 121.448i 0.581091i
\(210\) −135.848 117.962i −0.646893 0.561722i
\(211\) −236.900 −1.12275 −0.561374 0.827562i \(-0.689727\pi\)
−0.561374 + 0.827562i \(0.689727\pi\)
\(212\) 640.274 + 369.662i 3.02016 + 1.74369i
\(213\) 60.8236 + 47.2999i 0.285557 + 0.222065i
\(214\) 273.098 + 473.019i 1.27616 + 2.21037i
\(215\) 149.928 + 86.5607i 0.697337 + 0.402608i
\(216\) −276.793 + 633.190i −1.28145 + 2.93144i
\(217\) −9.13141 + 168.696i −0.0420802 + 0.777403i
\(218\) 309.224i 1.41846i
\(219\) 73.7323 + 10.1927i 0.336677 + 0.0465422i
\(220\) 130.737 + 226.444i 0.594261 + 1.02929i
\(221\) 47.4761 27.4103i 0.214824 0.124029i
\(222\) −60.4090 + 436.987i −0.272113 + 1.96841i
\(223\) 198.043 0.888084 0.444042 0.896006i \(-0.353544\pi\)
0.444042 + 0.896006i \(0.353544\pi\)
\(224\) −766.551 41.4929i −3.42210 0.185236i
\(225\) 32.2289 31.4054i 0.143239 0.139580i
\(226\) 150.099 259.979i 0.664154 1.15035i
\(227\) −20.9608 + 12.1017i −0.0923382 + 0.0533115i −0.545458 0.838138i \(-0.683644\pi\)
0.453120 + 0.891450i \(0.350311\pi\)
\(228\) 218.171 280.550i 0.956892 1.23048i
\(229\) −92.0744 + 159.477i −0.402071 + 0.696408i −0.993976 0.109600i \(-0.965043\pi\)
0.591904 + 0.806008i \(0.298376\pi\)
\(230\) 84.4455i 0.367154i
\(231\) 150.752 173.610i 0.652607 0.751558i
\(232\) 257.916 1.11171
\(233\) 116.135 + 67.0507i 0.498434 + 0.287771i 0.728067 0.685506i \(-0.240419\pi\)
−0.229633 + 0.973277i \(0.573752\pi\)
\(234\) 35.1060 124.548i 0.150026 0.532257i
\(235\) 6.34873 + 10.9963i 0.0270159 + 0.0467928i
\(236\) 485.275 + 280.174i 2.05625 + 1.18718i
\(237\) −125.116 307.671i −0.527915 1.29819i
\(238\) −328.231 213.958i −1.37912 0.898982i
\(239\) 442.916i 1.85321i −0.376041 0.926603i \(-0.622715\pi\)
0.376041 0.926603i \(-0.377285\pi\)
\(240\) 50.8385 367.756i 0.211827 1.53232i
\(241\) −189.467 328.166i −0.786168 1.36168i −0.928299 0.371836i \(-0.878729\pi\)
0.142130 0.989848i \(-0.454605\pi\)
\(242\) 3.71959 2.14751i 0.0153702 0.00887399i
\(243\) −39.4932 + 239.769i −0.162524 + 0.986705i
\(244\) 144.727 0.593142
\(245\) 11.8269 108.927i 0.0482732 0.444601i
\(246\) 292.288 + 718.763i 1.18816 + 2.92180i
\(247\) −20.8124 + 36.0481i −0.0842606 + 0.145944i
\(248\) −534.954 + 308.856i −2.15707 + 1.24539i
\(249\) −241.923 188.133i −0.971578 0.755555i
\(250\) −21.4185 + 37.0979i −0.0856739 + 0.148392i
\(251\) 272.894i 1.08723i −0.839336 0.543614i \(-0.817056\pi\)
0.839336 0.543614i \(-0.182944\pi\)
\(252\) −660.119 + 130.232i −2.61952 + 0.516792i
\(253\) −107.919 −0.426559
\(254\) 227.354 + 131.263i 0.895095 + 0.516783i
\(255\) 60.1592 77.3596i 0.235919 0.303371i
\(256\) −221.298 383.299i −0.864445 1.49726i
\(257\) −152.437 88.0093i −0.593138 0.342448i 0.173199 0.984887i \(-0.444590\pi\)
−0.766337 + 0.642438i \(0.777923\pi\)
\(258\) 824.364 335.231i 3.19521 1.29935i
\(259\) −239.581 + 121.555i −0.925022 + 0.469324i
\(260\) 89.6170i 0.344681i
\(261\) 87.8998 22.3378i 0.336781 0.0855855i
\(262\) −35.5479 61.5709i −0.135679 0.235003i
\(263\) 185.007 106.814i 0.703450 0.406137i −0.105181 0.994453i \(-0.533542\pi\)
0.808631 + 0.588316i \(0.200209\pi\)
\(264\) 832.770 + 115.122i 3.15443 + 0.436069i
\(265\) −154.792 −0.584119
\(266\) 297.061 + 16.0797i 1.11677 + 0.0604500i
\(267\) 200.673 81.6046i 0.751586 0.305635i
\(268\) 113.490 196.571i 0.423471 0.733474i
\(269\) 121.886 70.3711i 0.453109 0.261602i −0.256034 0.966668i \(-0.582416\pi\)
0.709142 + 0.705065i \(0.249082\pi\)
\(270\) −25.7366 229.883i −0.0953209 0.851420i
\(271\) 59.6978 103.400i 0.220287 0.381548i −0.734608 0.678492i \(-0.762634\pi\)
0.954895 + 0.296943i \(0.0959673\pi\)
\(272\) 808.492i 2.97240i
\(273\) 74.4974 25.6965i 0.272884 0.0941265i
\(274\) 513.394 1.87370
\(275\) −47.4102 27.3723i −0.172401 0.0995357i
\(276\) 249.298 + 193.868i 0.903252 + 0.702421i
\(277\) 68.8872 + 119.316i 0.248690 + 0.430744i 0.963163 0.268920i \(-0.0866666\pi\)
−0.714472 + 0.699664i \(0.753333\pi\)
\(278\) −297.645 171.846i −1.07067 0.618150i
\(279\) −155.567 + 151.593i −0.557588 + 0.543342i
\(280\) 357.261 181.262i 1.27593 0.647364i
\(281\) 131.474i 0.467880i −0.972251 0.233940i \(-0.924838\pi\)
0.972251 0.233940i \(-0.0751619\pi\)
\(282\) 64.6556 + 8.93798i 0.229275 + 0.0316950i
\(283\) 259.772 + 449.938i 0.917922 + 1.58989i 0.802566 + 0.596563i \(0.203467\pi\)
0.115355 + 0.993324i \(0.463199\pi\)
\(284\) −237.552 + 137.151i −0.836450 + 0.482925i
\(285\) −10.1894 + 73.7080i −0.0357523 + 0.258625i
\(286\) −157.423 −0.550429
\(287\) −258.039 + 395.855i −0.899089 + 1.37929i
\(288\) −688.832 706.893i −2.39178 2.45449i
\(289\) −37.7929 + 65.4592i −0.130771 + 0.226503i
\(290\) −74.7677 + 43.1671i −0.257820 + 0.148852i
\(291\) −11.4808 + 14.7633i −0.0394529 + 0.0507330i
\(292\) −132.492 + 229.483i −0.453740 + 0.785901i
\(293\) 351.830i 1.20078i 0.799706 + 0.600392i \(0.204989\pi\)
−0.799706 + 0.600392i \(0.795011\pi\)
\(294\) −404.689 391.724i −1.37649 1.33240i
\(295\) −117.319 −0.397692
\(296\) −850.683 491.142i −2.87393 1.65926i
\(297\) 293.786 32.8908i 0.989177 0.110743i
\(298\) 222.710 + 385.744i 0.747348 + 1.29444i
\(299\) −32.0325 18.4940i −0.107132 0.0618527i
\(300\) 60.3473 + 148.400i 0.201158 + 0.494665i
\(301\) 454.015 + 295.950i 1.50835 + 0.983223i
\(302\) 61.8232i 0.204713i
\(303\) −21.2365 + 153.620i −0.0700874 + 0.506998i
\(304\) 306.940 + 531.635i 1.00967 + 1.74880i
\(305\) −26.2416 + 15.1506i −0.0860381 + 0.0496741i
\(306\) −124.074 488.234i −0.405471 1.59554i
\(307\) −390.275 −1.27126 −0.635628 0.771996i \(-0.719259\pi\)
−0.635628 + 0.771996i \(0.719259\pi\)
\(308\) 370.359 + 729.966i 1.20246 + 2.37002i
\(309\) −131.490 323.346i −0.425534 1.04643i
\(310\) 103.386 179.070i 0.333503 0.577644i
\(311\) −62.8518 + 36.2875i −0.202096 + 0.116680i −0.597633 0.801770i \(-0.703892\pi\)
0.395537 + 0.918450i \(0.370559\pi\)
\(312\) 227.454 + 176.881i 0.729018 + 0.566926i
\(313\) 247.662 428.963i 0.791253 1.37049i −0.133939 0.990990i \(-0.542763\pi\)
0.925192 0.379500i \(-0.123904\pi\)
\(314\) 736.577i 2.34579i
\(315\) 106.059 92.7176i 0.336694 0.294342i
\(316\) 1182.42 3.74182
\(317\) −310.675 179.369i −0.980048 0.565831i −0.0777637 0.996972i \(-0.524778\pi\)
−0.902285 + 0.431141i \(0.858111\pi\)
\(318\) −488.463 + 628.121i −1.53605 + 1.97522i
\(319\) −55.1666 95.5513i −0.172936 0.299534i
\(320\) 385.002 + 222.281i 1.20313 + 0.694628i
\(321\) −396.163 + 161.102i −1.23415 + 0.501874i
\(322\) −14.2885 + 263.970i −0.0443742 + 0.819782i
\(323\) 162.043i 0.501682i
\(324\) −737.741 451.782i −2.27698 1.39439i
\(325\) −9.38150 16.2492i −0.0288662 0.0499977i
\(326\) 919.543 530.899i 2.82069 1.62852i
\(327\) 239.839 + 33.1554i 0.733454 + 0.101393i
\(328\) −1727.73 −5.26746
\(329\) 17.9850 + 35.4478i 0.0546656 + 0.107744i
\(330\) −260.681 + 106.007i −0.789944 + 0.321234i
\(331\) 157.641 273.042i 0.476256 0.824899i −0.523374 0.852103i \(-0.675327\pi\)
0.999630 + 0.0272038i \(0.00866031\pi\)
\(332\) 944.851 545.510i 2.84594 1.64310i
\(333\) −332.457 93.7085i −0.998369 0.281407i
\(334\) −66.1572 + 114.588i −0.198076 + 0.343077i
\(335\) 47.5227i 0.141859i
\(336\) 221.143 1140.97i 0.658163 3.39575i
\(337\) 104.826 0.311058 0.155529 0.987831i \(-0.450292\pi\)
0.155529 + 0.987831i \(0.450292\pi\)
\(338\) 514.039 + 296.781i 1.52083 + 0.878049i
\(339\) 185.550 + 144.294i 0.547345 + 0.425647i
\(340\) 174.437 + 302.135i 0.513051 + 0.888631i
\(341\) 228.847 + 132.125i 0.671106 + 0.387463i
\(342\) 266.942 + 273.941i 0.780533 + 0.800998i
\(343\) 55.4009 338.496i 0.161519 0.986870i
\(344\) 1981.57i 5.76037i
\(345\) −65.4973 9.05434i −0.189847 0.0262445i
\(346\) −619.919 1073.73i −1.79167 3.10327i
\(347\) −377.205 + 217.779i −1.08705 + 0.627606i −0.932788 0.360424i \(-0.882632\pi\)
−0.154258 + 0.988031i \(0.549299\pi\)
\(348\) −44.2132 + 319.829i −0.127049 + 0.919050i
\(349\) −372.478 −1.06727 −0.533636 0.845715i \(-0.679175\pi\)
−0.533636 + 0.845715i \(0.679175\pi\)
\(350\) −73.2295 + 112.341i −0.209227 + 0.320974i
\(351\) 92.8376 + 40.5830i 0.264494 + 0.115621i
\(352\) −600.372 + 1039.87i −1.70560 + 2.95419i
\(353\) 44.5982 25.7488i 0.126341 0.0729428i −0.435498 0.900190i \(-0.643428\pi\)
0.561838 + 0.827247i \(0.310094\pi\)
\(354\) −370.215 + 476.064i −1.04580 + 1.34481i
\(355\) 28.7151 49.7359i 0.0808875 0.140101i
\(356\) 771.211i 2.16632i
\(357\) 201.142 231.641i 0.563424 0.648853i
\(358\) −25.2865 −0.0706327
\(359\) 321.578 + 185.663i 0.895759 + 0.517167i 0.875822 0.482634i \(-0.160320\pi\)
0.0199374 + 0.999801i \(0.493653\pi\)
\(360\) 495.758 + 139.737i 1.37710 + 0.388160i
\(361\) 118.981 + 206.081i 0.329588 + 0.570862i
\(362\) −749.106 432.497i −2.06935 1.19474i
\(363\) 1.26682 + 3.11523i 0.00348987 + 0.00858191i
\(364\) −15.1635 + 280.136i −0.0416580 + 0.769603i
\(365\) 55.4794i 0.151998i
\(366\) −21.3296 + 154.294i −0.0582777 + 0.421569i
\(367\) −166.498 288.383i −0.453672 0.785784i 0.544938 0.838476i \(-0.316553\pi\)
−0.998611 + 0.0526924i \(0.983220\pi\)
\(368\) −472.413 + 272.748i −1.28373 + 0.741163i
\(369\) −588.823 + 149.637i −1.59573 + 0.405519i
\(370\) 328.808 0.888671
\(371\) −483.866 26.1913i −1.30422 0.0705965i
\(372\) −291.294 716.318i −0.783047 1.92559i
\(373\) 21.0920 36.5325i 0.0565470 0.0979423i −0.836366 0.548171i \(-0.815324\pi\)
0.892913 + 0.450229i \(0.148658\pi\)
\(374\) −530.735 + 306.420i −1.41908 + 0.819304i
\(375\) −26.4772 20.5902i −0.0706059 0.0549072i
\(376\) −72.6682 + 125.865i −0.193267 + 0.334748i
\(377\) 37.8153i 0.100306i
\(378\) −41.5535 722.952i −0.109930 1.91257i
\(379\) −404.220 −1.06654 −0.533272 0.845944i \(-0.679038\pi\)
−0.533272 + 0.845944i \(0.679038\pi\)
\(380\) −229.408 132.449i −0.603704 0.348549i
\(381\) −126.187 + 162.265i −0.331199 + 0.425894i
\(382\) 120.036 + 207.908i 0.314230 + 0.544262i
\(383\) −338.568 195.472i −0.883989 0.510371i −0.0120171 0.999928i \(-0.503825\pi\)
−0.871971 + 0.489557i \(0.837159\pi\)
\(384\) 897.831 365.107i 2.33810 0.950799i
\(385\) −143.569 93.5856i −0.372907 0.243080i
\(386\) 37.7604i 0.0978249i
\(387\) 171.621 + 675.334i 0.443466 + 1.74505i
\(388\) −33.2897 57.6594i −0.0857981 0.148607i
\(389\) 327.986 189.363i 0.843152 0.486794i −0.0151826 0.999885i \(-0.504833\pi\)
0.858334 + 0.513091i \(0.171500\pi\)
\(390\) −95.5414 13.2076i −0.244978 0.0338658i
\(391\) −143.992 −0.368267
\(392\) 1147.44 506.160i 2.92714 1.29122i
\(393\) 51.5669 20.9699i 0.131213 0.0533585i
\(394\) 171.094 296.344i 0.434249 0.752141i
\(395\) −214.394 + 123.780i −0.542770 + 0.313368i
\(396\) −285.515 + 1012.95i −0.720998 + 2.55794i
\(397\) 127.529 220.886i 0.321231 0.556388i −0.659511 0.751695i \(-0.729237\pi\)
0.980742 + 0.195306i \(0.0625701\pi\)
\(398\) 393.306i 0.988206i
\(399\) −44.3229 + 228.681i −0.111085 + 0.573136i
\(400\) −276.716 −0.691789
\(401\) 185.343 + 107.008i 0.462203 + 0.266853i 0.712970 0.701194i \(-0.247349\pi\)
−0.250767 + 0.968047i \(0.580683\pi\)
\(402\) 192.840 + 149.963i 0.479701 + 0.373043i
\(403\) 45.2841 + 78.4343i 0.112367 + 0.194626i
\(404\) −478.126 276.046i −1.18348 0.683282i
\(405\) 181.061 + 4.68661i 0.447064 + 0.0115719i
\(406\) −241.022 + 122.286i −0.593650 + 0.301197i
\(407\) 420.209i 1.03246i
\(408\) 1111.13 + 153.603i 2.72336 + 0.376477i
\(409\) −170.178 294.757i −0.416083 0.720678i 0.579458 0.815002i \(-0.303264\pi\)
−0.995542 + 0.0943244i \(0.969931\pi\)
\(410\) 500.854 289.168i 1.22160 0.705288i
\(411\) −55.0467 + 398.197i −0.133934 + 0.968848i
\(412\) 1242.66 3.01616
\(413\) −366.730 19.8508i −0.887967 0.0480650i
\(414\) −243.426 + 237.206i −0.587984 + 0.572962i
\(415\) −114.213 + 197.822i −0.275211 + 0.476680i
\(416\) −356.403 + 205.770i −0.856739 + 0.494638i
\(417\) 165.200 212.433i 0.396163 0.509432i
\(418\) 232.661 402.981i 0.556606 0.964071i
\(419\) 586.646i 1.40011i −0.714088 0.700055i \(-0.753159\pi\)
0.714088 0.700055i \(-0.246841\pi\)
\(420\) 163.531 + 474.096i 0.389360 + 1.12880i
\(421\) −216.123 −0.513357 −0.256678 0.966497i \(-0.582628\pi\)
−0.256678 + 0.966497i \(0.582628\pi\)
\(422\) 786.066 + 453.835i 1.86271 + 1.07544i
\(423\) −13.8649 + 49.1896i −0.0327775 + 0.116287i
\(424\) −885.881 1534.39i −2.08934 3.61884i
\(425\) −63.2575 36.5218i −0.148841 0.0859335i
\(426\) −111.207 273.469i −0.261050 0.641946i
\(427\) −84.5928 + 42.9194i −0.198110 + 0.100514i
\(428\) 1522.50i 3.55725i
\(429\) 16.8791 122.100i 0.0393451 0.284615i
\(430\) −331.653 574.440i −0.771287 1.33591i
\(431\) −286.275 + 165.281i −0.664211 + 0.383483i −0.793880 0.608075i \(-0.791942\pi\)
0.129668 + 0.991557i \(0.458609\pi\)
\(432\) 1202.91 886.472i 2.78452 2.05202i
\(433\) 825.106 1.90556 0.952778 0.303668i \(-0.0982112\pi\)
0.952778 + 0.303668i \(0.0982112\pi\)
\(434\) 353.475 542.264i 0.814460 1.24946i
\(435\) −25.4645 62.6195i −0.0585390 0.143953i
\(436\) −430.976 + 746.472i −0.988477 + 1.71209i
\(437\) 94.6842 54.6659i 0.216669 0.125094i
\(438\) −225.127 175.072i −0.513989 0.399707i
\(439\) 363.096 628.901i 0.827099 1.43258i −0.0732063 0.997317i \(-0.523323\pi\)
0.900305 0.435260i \(-0.143344\pi\)
\(440\) 626.613i 1.42412i
\(441\) 347.219 271.882i 0.787345 0.616513i
\(442\) −210.043 −0.475210
\(443\) −620.467 358.227i −1.40060 0.808638i −0.406148 0.913807i \(-0.633128\pi\)
−0.994454 + 0.105169i \(0.966462\pi\)
\(444\) 754.871 970.699i 1.70016 2.18626i
\(445\) −80.7337 139.835i −0.181424 0.314236i
\(446\) −657.133 379.396i −1.47339 0.850664i
\(447\) −323.069 + 131.377i −0.722749 + 0.293909i
\(448\) 1165.87 + 759.976i 2.60240 + 1.69637i
\(449\) 564.847i 1.25801i 0.777401 + 0.629006i \(0.216538\pi\)
−0.777401 + 0.629006i \(0.783462\pi\)
\(450\) −167.104 + 42.4658i −0.371342 + 0.0943685i
\(451\) 369.550 + 640.080i 0.819402 + 1.41925i
\(452\) −724.681 + 418.395i −1.60328 + 0.925653i
\(453\) −47.9511 6.62875i −0.105852 0.0146330i
\(454\) 92.7343 0.204261
\(455\) −26.5764 52.3812i −0.0584096 0.115124i
\(456\) −788.955 + 320.832i −1.73016 + 0.703578i
\(457\) 426.738 739.133i 0.933782 1.61736i 0.156990 0.987600i \(-0.449821\pi\)
0.776792 0.629758i \(-0.216846\pi\)
\(458\) 611.031 352.779i 1.33413 0.770259i
\(459\) 391.986 43.8849i 0.854000 0.0956097i
\(460\) 117.694 203.853i 0.255857 0.443158i
\(461\) 891.718i 1.93431i 0.254185 + 0.967156i \(0.418193\pi\)
−0.254185 + 0.967156i \(0.581807\pi\)
\(462\) −832.806 + 287.262i −1.80261 + 0.621778i
\(463\) 750.155 1.62021 0.810103 0.586287i \(-0.199411\pi\)
0.810103 + 0.586287i \(0.199411\pi\)
\(464\) −482.980 278.849i −1.04091 0.600967i
\(465\) 127.804 + 99.3879i 0.274848 + 0.213737i
\(466\) −256.902 444.967i −0.551291 0.954864i
\(467\) −84.6817 48.8910i −0.181331 0.104692i 0.406587 0.913612i \(-0.366719\pi\)
−0.587918 + 0.808921i \(0.700052\pi\)
\(468\) −258.333 + 251.733i −0.551994 + 0.537891i
\(469\) −8.04101 + 148.552i −0.0171450 + 0.316742i
\(470\) 48.6497i 0.103510i
\(471\) 571.301 + 78.9767i 1.21295 + 0.167679i
\(472\) −671.425 1162.94i −1.42251 2.46386i
\(473\) 734.121 423.845i 1.55205 0.896079i
\(474\) −174.263 + 1260.58i −0.367643 + 2.65946i
\(475\) 55.4612 0.116760
\(476\) 494.155 + 973.963i 1.03814 + 2.04614i
\(477\) −434.807 446.208i −0.911546 0.935446i
\(478\) −848.507 + 1469.66i −1.77512 + 3.07460i
\(479\) −0.948693 + 0.547728i −0.00198057 + 0.00114348i −0.500990 0.865453i \(-0.667031\pi\)
0.499009 + 0.866597i \(0.333697\pi\)
\(480\) −451.616 + 580.739i −0.940867 + 1.20987i
\(481\) −72.0106 + 124.726i −0.149710 + 0.259306i
\(482\) 1451.87i 3.01217i
\(483\) −203.207 39.3855i −0.420719 0.0815435i
\(484\) −11.9722 −0.0247359
\(485\) 12.0721 + 6.96982i 0.0248909 + 0.0143708i
\(486\) 590.376 719.929i 1.21477 1.48134i
\(487\) 393.745 + 681.987i 0.808512 + 1.40038i 0.913895 + 0.405952i \(0.133060\pi\)
−0.105383 + 0.994432i \(0.533607\pi\)
\(488\) −300.365 173.416i −0.615501 0.355360i
\(489\) 313.179 + 770.137i 0.640448 + 1.57492i
\(490\) −247.918 + 338.778i −0.505955 + 0.691384i
\(491\) 294.128i 0.599039i −0.954090 0.299520i \(-0.903174\pi\)
0.954090 0.299520i \(-0.0968264\pi\)
\(492\) 296.176 2142.47i 0.601983 4.35462i
\(493\) −73.6065 127.490i −0.149303 0.258601i
\(494\) 138.117 79.7417i 0.279588 0.161420i
\(495\) −54.2703 213.555i −0.109637 0.431424i
\(496\) 1335.69 2.69293
\(497\) 98.1764 150.612i 0.197538 0.303042i
\(498\) 442.322 + 1087.71i 0.888196 + 2.18416i
\(499\) −248.981 + 431.248i −0.498960 + 0.864225i −0.999999 0.00119993i \(-0.999618\pi\)
0.501039 + 0.865425i \(0.332951\pi\)
\(500\) 103.409 59.7033i 0.206818 0.119407i
\(501\) −81.7826 63.5989i −0.163239 0.126944i
\(502\) −522.791 + 905.500i −1.04142 + 1.80378i
\(503\) 524.122i 1.04199i 0.853559 + 0.520996i \(0.174439\pi\)
−0.853559 + 0.520996i \(0.825561\pi\)
\(504\) 1526.05 + 520.692i 3.02789 + 1.03312i
\(505\) 115.591 0.228893
\(506\) 358.091 + 206.744i 0.707690 + 0.408585i
\(507\) −285.304 + 366.876i −0.562729 + 0.723621i
\(508\) −365.891 633.742i −0.720258 1.24752i
\(509\) −19.3736 11.1854i −0.0380621 0.0219752i 0.480848 0.876804i \(-0.340329\pi\)
−0.518910 + 0.854829i \(0.673662\pi\)
\(510\) −347.816 + 141.441i −0.681993 + 0.277335i
\(511\) 9.38732 173.424i 0.0183705 0.339382i
\(512\) 403.481i 0.788049i
\(513\) −241.095 + 177.673i −0.469971 + 0.346340i
\(514\) 337.203 + 584.054i 0.656038 + 1.13629i
\(515\) −225.317 + 130.087i −0.437508 + 0.252596i
\(516\) −2457.25 339.690i −4.76211 0.658314i
\(517\) 62.1732 0.120258
\(518\) 1027.83 + 55.6356i 1.98422 + 0.107405i
\(519\) 899.272 365.692i 1.73270 0.704610i
\(520\) 107.382 185.991i 0.206503 0.357674i
\(521\) 692.733 399.950i 1.32962 0.767658i 0.344382 0.938830i \(-0.388089\pi\)
0.985241 + 0.171172i \(0.0547553\pi\)
\(522\) −334.457 94.2721i −0.640721 0.180598i
\(523\) 205.763 356.392i 0.393429 0.681439i −0.599470 0.800397i \(-0.704622\pi\)
0.992899 + 0.118958i \(0.0379554\pi\)
\(524\) 198.177i 0.378201i
\(525\) −79.2817 68.8434i −0.151013 0.131130i
\(526\) −818.506 −1.55610
\(527\) 305.341 + 176.289i 0.579395 + 0.334514i
\(528\) −1435.00 1115.94i −2.71781 2.11352i
\(529\) −215.924 373.991i −0.408173 0.706977i
\(530\) 513.619 + 296.538i 0.969093 + 0.559506i
\(531\) −329.548 338.189i −0.620618 0.636890i
\(532\) −694.699 452.840i −1.30583 0.851203i
\(533\) 253.317i 0.475267i
\(534\) −822.194 113.660i −1.53969 0.212847i
\(535\) 159.382 + 276.058i 0.297911 + 0.515996i
\(536\) −471.074 + 271.975i −0.878870 + 0.507416i
\(537\) 2.71125 19.6126i 0.00504888 0.0365226i
\(538\) −539.247 −1.00232
\(539\) −432.950 316.834i −0.803247 0.587817i
\(540\) −258.267 + 590.812i −0.478273 + 1.09410i
\(541\) 325.969 564.595i 0.602530 1.04361i −0.389906 0.920855i \(-0.627493\pi\)
0.992437 0.122759i \(-0.0391741\pi\)
\(542\) −396.171 + 228.729i −0.730943 + 0.422010i
\(543\) 415.772 534.646i 0.765694 0.984616i
\(544\) −801.051 + 1387.46i −1.47252 + 2.55048i
\(545\) 180.466i 0.331130i
\(546\) −296.420 57.4520i −0.542894 0.105223i
\(547\) −85.9480 −0.157126 −0.0785631 0.996909i \(-0.525033\pi\)
−0.0785631 + 0.996909i \(0.525033\pi\)
\(548\) −1239.34 715.534i −2.26157 1.30572i
\(549\) −117.386 33.0872i −0.213818 0.0602681i
\(550\) 104.876 + 181.650i 0.190683 + 0.330273i
\(551\) 96.8020 + 55.8887i 0.175684 + 0.101431i
\(552\) −285.092 701.068i −0.516472 1.27005i
\(553\) −691.123 + 350.651i −1.24977 + 0.634090i
\(554\) 527.876i 0.952845i
\(555\) −35.2552 + 255.029i −0.0635229 + 0.459512i
\(556\) 479.013 + 829.676i 0.861535 + 1.49222i
\(557\) 858.157 495.457i 1.54068 0.889510i 0.541880 0.840456i \(-0.317713\pi\)
0.998796 0.0490540i \(-0.0156207\pi\)
\(558\) 806.603 204.981i 1.44552 0.367349i
\(559\) 290.535 0.519740
\(560\) −864.991 46.8213i −1.54463 0.0836095i
\(561\) −180.758 444.501i −0.322207 0.792337i
\(562\) −251.869 + 436.249i −0.448165 + 0.776245i
\(563\) 208.613 120.443i 0.370539 0.213931i −0.303155 0.952941i \(-0.598040\pi\)
0.673694 + 0.739011i \(0.264707\pi\)
\(564\) −143.622 111.689i −0.254650 0.198030i
\(565\) 87.5989 151.726i 0.155042 0.268541i
\(566\) 1990.61i 3.51698i
\(567\) 565.189 + 45.2861i 0.996805 + 0.0798697i
\(568\) 657.351 1.15731
\(569\) 100.616 + 58.0909i 0.176830 + 0.102093i 0.585803 0.810454i \(-0.300779\pi\)
−0.408972 + 0.912547i \(0.634113\pi\)
\(570\) 175.014 225.053i 0.307043 0.394830i
\(571\) 519.274 + 899.409i 0.909412 + 1.57515i 0.814883 + 0.579626i \(0.196801\pi\)
0.0945293 + 0.995522i \(0.469865\pi\)
\(572\) 380.021 + 219.405i 0.664373 + 0.383576i
\(573\) −174.127 + 70.8096i −0.303887 + 0.123577i
\(574\) 1614.56 819.170i 2.81282 1.42713i
\(575\) 49.2831i 0.0857097i
\(576\) 440.710 + 1734.20i 0.765122 + 3.01077i
\(577\) 37.6724 + 65.2504i 0.0652901 + 0.113086i 0.896823 0.442390i \(-0.145869\pi\)
−0.831533 + 0.555476i \(0.812536\pi\)
\(578\) 250.804 144.802i 0.433917 0.250522i
\(579\) 29.2876 + 4.04871i 0.0505830 + 0.00699260i
\(580\) 240.654 0.414920
\(581\) −390.492 + 599.051i −0.672103 + 1.03107i
\(582\) 66.3773 26.9926i 0.114050 0.0463791i
\(583\) −378.969 + 656.394i −0.650033 + 1.12589i
\(584\) 549.947 317.512i 0.941689 0.543685i
\(585\) 20.4881 72.6874i 0.0350224 0.124252i
\(586\) 674.009 1167.42i 1.15019 1.99218i
\(587\) 34.4849i 0.0587477i −0.999568 0.0293739i \(-0.990649\pi\)
0.999568 0.0293739i \(-0.00935134\pi\)
\(588\) 430.966 + 1509.66i 0.732935 + 2.56744i
\(589\) −267.709 −0.454514
\(590\) 389.281 + 224.752i 0.659799 + 0.380935i
\(591\) 211.504 + 164.478i 0.357875 + 0.278304i
\(592\) 1062.01 + 1839.45i 1.79393 + 3.10718i
\(593\) −179.738 103.772i −0.303099 0.174994i 0.340735 0.940159i \(-0.389324\pi\)
−0.643834 + 0.765165i \(0.722657\pi\)
\(594\) −1037.83 453.677i −1.74719 0.763766i
\(595\) −191.558 124.867i −0.321947 0.209861i
\(596\) 1241.59i 2.08321i
\(597\) −305.055 42.1707i −0.510979 0.0706377i
\(598\) 70.8588 + 122.731i 0.118493 + 0.205236i
\(599\) −99.0015 + 57.1586i −0.165278 + 0.0954233i −0.580357 0.814362i \(-0.697087\pi\)
0.415079 + 0.909785i \(0.363754\pi\)
\(600\) 52.5723 380.298i 0.0876205 0.633829i
\(601\) −705.812 −1.17440 −0.587198 0.809444i \(-0.699769\pi\)
−0.587198 + 0.809444i \(0.699769\pi\)
\(602\) −939.524 1851.77i −1.56067 3.07603i
\(603\) −136.991 + 133.491i −0.227182 + 0.221377i
\(604\) 86.1650 149.242i 0.142657 0.247090i
\(605\) 2.17078 1.25330i 0.00358807 0.00207157i
\(606\) 364.761 469.051i 0.601915 0.774011i
\(607\) 301.545 522.291i 0.496779 0.860446i −0.503214 0.864162i \(-0.667849\pi\)
0.999993 + 0.00371550i \(0.00118268\pi\)
\(608\) 1216.46i 2.00076i
\(609\) −69.0044 200.052i −0.113308 0.328493i
\(610\) 116.098 0.190324
\(611\) 18.4542 + 10.6545i 0.0302032 + 0.0174378i
\(612\) −380.951 + 1351.53i −0.622470 + 2.20838i
\(613\) −286.342 495.959i −0.467116 0.809069i 0.532178 0.846632i \(-0.321374\pi\)
−0.999294 + 0.0375638i \(0.988040\pi\)
\(614\) 1294.99 + 747.661i 2.10910 + 1.21769i
\(615\) 170.581 + 419.476i 0.277368 + 0.682074i
\(616\) 106.025 1958.74i 0.172119 3.17978i
\(617\) 30.2182i 0.0489759i 0.999700 + 0.0244880i \(0.00779554\pi\)
−0.999700 + 0.0244880i \(0.992204\pi\)
\(618\) −183.141 + 1324.81i −0.296345 + 2.14370i
\(619\) 92.6047 + 160.396i 0.149604 + 0.259121i 0.931081 0.364812i \(-0.118867\pi\)
−0.781477 + 0.623934i \(0.785534\pi\)
\(620\) −499.151 + 288.185i −0.805082 + 0.464814i
\(621\) −157.881 214.238i −0.254236 0.344989i
\(622\) 278.068 0.447054
\(623\) −228.706 450.773i −0.367105 0.723552i
\(624\) −234.699 577.147i −0.376120 0.924915i
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) −1643.55 + 948.906i −2.62548 + 1.51582i
\(627\) 287.613 + 223.664i 0.458713 + 0.356721i
\(628\) −1026.59 + 1778.11i −1.63470 + 2.83138i
\(629\) 560.668i 0.891364i
\(630\) −529.539 + 104.470i −0.840538 + 0.165826i
\(631\) 451.153 0.714981 0.357491 0.933917i \(-0.383632\pi\)
0.357491 + 0.933917i \(0.383632\pi\)
\(632\) −2453.98 1416.81i −3.88288 2.24178i
\(633\) −436.285 + 561.025i −0.689234 + 0.886295i
\(634\) 687.242 + 1190.34i 1.08398 + 1.87751i
\(635\) 132.686 + 76.6061i 0.208954 + 0.120640i
\(636\) 2054.59 835.507i 3.23049 1.31369i
\(637\) −74.2126 168.236i −0.116503 0.264107i
\(638\) 422.737i 0.662597i
\(639\) 224.031 56.9325i 0.350596 0.0890963i
\(640\) −361.210 625.634i −0.564391 0.977554i
\(641\) −240.850 + 139.055i −0.375741 + 0.216934i −0.675964 0.736935i \(-0.736272\pi\)
0.300223 + 0.953869i \(0.402939\pi\)
\(642\) 1623.15 + 224.384i 2.52827 + 0.349508i
\(643\) 231.489 0.360014 0.180007 0.983665i \(-0.442388\pi\)
0.180007 + 0.983665i \(0.442388\pi\)
\(644\) 402.396 617.313i 0.624838 0.958560i
\(645\) 481.106 195.644i 0.745900 0.303323i
\(646\) 310.431 537.682i 0.480543 0.832324i
\(647\) −397.213 + 229.331i −0.613930 + 0.354452i −0.774502 0.632572i \(-0.781999\pi\)
0.160572 + 0.987024i \(0.448666\pi\)
\(648\) 989.765 + 1821.61i 1.52741 + 2.81113i
\(649\) −287.227 + 497.492i −0.442569 + 0.766552i
\(650\) 71.8896i 0.110599i
\(651\) 382.689 + 332.304i 0.587848 + 0.510451i
\(652\) −2959.72 −4.53945
\(653\) 5.08630 + 2.93658i 0.00778913 + 0.00449706i 0.503890 0.863768i \(-0.331902\pi\)
−0.496100 + 0.868265i \(0.665235\pi\)
\(654\) −732.303 569.481i −1.11973 0.870766i
\(655\) −20.7461 35.9332i −0.0316734 0.0548599i
\(656\) 3235.39 + 1867.95i 4.93200 + 2.84749i
\(657\) 159.927 155.841i 0.243420 0.237201i
\(658\) 8.23171 152.075i 0.0125102 0.231117i
\(659\) 425.682i 0.645952i 0.946407 + 0.322976i \(0.104683\pi\)
−0.946407 + 0.322976i \(0.895317\pi\)
\(660\) 777.034 + 107.417i 1.17732 + 0.162753i
\(661\) −516.635 894.838i −0.781596 1.35376i −0.931012 0.364990i \(-0.881072\pi\)
0.149415 0.988775i \(-0.452261\pi\)
\(662\) −1046.15 + 603.993i −1.58028 + 0.912376i
\(663\) 22.5210 162.913i 0.0339684 0.245720i
\(664\) −2614.58 −3.93763
\(665\) 173.367 + 9.38424i 0.260703 + 0.0141116i
\(666\) 923.618 + 947.835i 1.38681 + 1.42317i
\(667\) −49.6629 + 86.0187i −0.0744572 + 0.128964i
\(668\) 319.409 184.411i 0.478157 0.276064i
\(669\) 364.724 469.004i 0.545178 0.701052i
\(670\) 91.0404 157.687i 0.135881 0.235353i
\(671\) 148.370i 0.221118i
\(672\) −1509.98 + 1738.93i −2.24699 + 2.58769i
\(673\) −726.867 −1.08004 −0.540020 0.841652i \(-0.681583\pi\)
−0.540020 + 0.841652i \(0.681583\pi\)
\(674\) −347.829 200.819i −0.516066 0.297951i
\(675\) −15.0201 134.162i −0.0222520 0.198758i
\(676\) −827.265 1432.87i −1.22377 2.11962i
\(677\) −139.975 80.8146i −0.206758 0.119372i 0.393046 0.919519i \(-0.371421\pi\)
−0.599804 + 0.800147i \(0.704755\pi\)
\(678\) −339.252 834.251i −0.500371 1.23046i
\(679\) 36.5570 + 23.8297i 0.0538395 + 0.0350953i
\(680\) 836.064i 1.22951i
\(681\) −9.94308 + 71.9263i −0.0146007 + 0.105619i
\(682\) −506.230 876.817i −0.742273 1.28566i
\(683\) −245.110 + 141.515i −0.358873 + 0.207195i −0.668586 0.743635i \(-0.733100\pi\)
0.309713 + 0.950830i \(0.399767\pi\)
\(684\) −262.602 1033.35i −0.383921 1.51074i
\(685\) 299.621 0.437403
\(686\) −832.294 + 1017.04i −1.21326 + 1.48257i
\(687\) 208.106 + 511.751i 0.302919 + 0.744906i
\(688\) 2142.40 3710.74i 3.11395 5.39351i
\(689\) −224.970 + 129.887i −0.326517 + 0.188515i
\(690\) 199.983 + 155.518i 0.289831 + 0.225389i
\(691\) −380.317 + 658.729i −0.550387 + 0.953298i 0.447860 + 0.894104i \(0.352186\pi\)
−0.998246 + 0.0591940i \(0.981147\pi\)
\(692\) 3456.00i 4.99422i
\(693\) −133.510 676.738i −0.192656 0.976534i
\(694\) 1668.82 2.40465
\(695\) −173.708 100.290i −0.249940 0.144303i
\(696\) 474.989 610.794i 0.682455 0.877578i
\(697\) 493.076 + 854.032i 0.707426 + 1.22530i
\(698\) 1235.93 + 713.565i 1.77068 + 1.02230i
\(699\) 372.669 151.547i 0.533145 0.216806i
\(700\) 333.350 169.130i 0.476215 0.241615i
\(701\) 193.212i 0.275624i −0.990458 0.137812i \(-0.955993\pi\)
0.990458 0.137812i \(-0.0440070\pi\)
\(702\) −230.302 312.511i −0.328065 0.445173i
\(703\) −212.855 368.675i −0.302780 0.524431i
\(704\) 1885.16 1088.40i 2.67779 1.54602i
\(705\) 37.7335 + 5.21628i 0.0535227 + 0.00739898i
\(706\) −197.311 −0.279477
\(707\) 361.328 + 19.5584i 0.511072 + 0.0276639i
\(708\) 1557.21 633.246i 2.19945 0.894415i
\(709\) 163.509 283.205i 0.230618 0.399443i −0.727372 0.686244i \(-0.759258\pi\)
0.957990 + 0.286801i \(0.0925917\pi\)
\(710\) −190.561 + 110.020i −0.268396 + 0.154958i
\(711\) −959.044 270.322i −1.34887 0.380200i
\(712\) 924.087 1600.57i 1.29788 2.24799i
\(713\) 237.887i 0.333642i
\(714\) −1111.18 + 383.281i −1.55627 + 0.536808i
\(715\) −91.8732 −0.128494
\(716\) 61.0420 + 35.2426i 0.0852542 + 0.0492216i
\(717\) −1048.91 815.694i −1.46292 1.13765i
\(718\) −711.359 1232.11i −0.990751 1.71603i
\(719\) −535.646 309.256i −0.744988 0.430119i 0.0788921 0.996883i \(-0.474862\pi\)
−0.823880 + 0.566764i \(0.808195\pi\)
\(720\) −777.291 797.671i −1.07957 1.10788i
\(721\) −726.333 + 368.516i −1.00740 + 0.511118i
\(722\) 911.741i 1.26280i
\(723\) −1126.09 155.671i −1.55752 0.215312i
\(724\) 1205.57 + 2088.11i 1.66515 + 2.88413i
\(725\) −43.6350 + 25.1927i −0.0601862 + 0.0347485i
\(726\) 1.76445 12.7637i 0.00243037 0.0175808i
\(727\) −944.743 −1.29951 −0.649755 0.760144i \(-0.725128\pi\)
−0.649755 + 0.760144i \(0.725128\pi\)
\(728\) 367.137 563.222i 0.504309 0.773657i
\(729\) 495.088 + 535.097i 0.679133 + 0.734015i
\(730\) −106.283 + 184.088i −0.145594 + 0.252176i
\(731\) 979.508 565.519i 1.33996 0.773624i
\(732\) 266.535 342.741i 0.364119 0.468225i
\(733\) −398.388 + 690.029i −0.543504 + 0.941377i 0.455195 + 0.890392i \(0.349569\pi\)
−0.998699 + 0.0509850i \(0.983764\pi\)
\(734\) 1275.86i 1.73823i
\(735\) −236.180 228.614i −0.321333 0.311039i
\(736\) 1080.95 1.46868
\(737\) 201.520 + 116.348i 0.273433 + 0.157866i
\(738\) 2240.46 + 631.510i 3.03585 + 0.855705i
\(739\) 526.190 + 911.387i 0.712029 + 1.23327i 0.964094 + 0.265561i \(0.0855571\pi\)
−0.252065 + 0.967710i \(0.581110\pi\)
\(740\) −793.748 458.271i −1.07263 0.619285i
\(741\) 47.0399 + 115.676i 0.0634817 + 0.156107i
\(742\) 1555.36 + 1013.86i 2.09617 + 1.36639i
\(743\) 923.243i 1.24259i −0.783577 0.621294i \(-0.786607\pi\)
0.783577 0.621294i \(-0.213393\pi\)
\(744\) −253.764 + 1835.68i −0.341081 + 2.46731i
\(745\) 129.975 + 225.124i 0.174463 + 0.302179i
\(746\) −139.972 + 80.8131i −0.187631 + 0.108329i
\(747\) −891.072 + 226.446i −1.19287 + 0.303141i
\(748\) 1708.27 2.28378
\(749\) 451.506 + 889.903i 0.602811 + 1.18812i
\(750\) 48.4098 + 119.044i 0.0645465 + 0.158726i
\(751\) 256.554 444.364i 0.341616 0.591697i −0.643117 0.765768i \(-0.722359\pi\)
0.984733 + 0.174071i \(0.0556924\pi\)
\(752\) 272.161 157.132i 0.361916 0.208953i
\(753\) −646.266 502.574i −0.858256 0.667429i
\(754\) −72.4437 + 125.476i −0.0960792 + 0.166414i
\(755\) 36.0805i 0.0477888i
\(756\) −907.290 + 1803.13i −1.20012 + 2.38509i
\(757\) −702.065 −0.927430 −0.463715 0.885984i \(-0.653484\pi\)
−0.463715 + 0.885984i \(0.653484\pi\)
\(758\) 1341.26 + 774.375i 1.76947 + 1.02160i
\(759\) −198.749 + 255.574i −0.261856 + 0.336725i
\(760\) 317.408 + 549.766i 0.417641 + 0.723376i
\(761\) −129.267 74.6326i −0.169865 0.0980717i 0.412657 0.910886i \(-0.364601\pi\)
−0.582522 + 0.812815i \(0.697934\pi\)
\(762\) 729.562 296.679i 0.957430 0.389343i
\(763\) 30.5355 564.121i 0.0400203 0.739347i
\(764\) 669.191i 0.875905i
\(765\) −72.4107 284.938i −0.0946545