Properties

Label 108.3.f.c.19.8
Level 108
Weight 3
Character 108.19
Analytic conductor 2.943
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.8
Root \(1.93353 - 0.511345i\) of \(x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + 1552 x^{8} - 3648 x^{7} + 6784 x^{6} - 9216 x^{5} + 19456 x^{4} - 30720 x^{3} + 28672 x^{2} - 49152 x + 65536\)
Character \(\chi\) \(=\) 108.19
Dual form 108.3.f.c.91.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.93353 - 0.511345i) q^{2} +(3.47705 - 1.97740i) q^{4} +(4.03104 + 6.98197i) q^{5} +(-3.90254 - 2.25313i) q^{7} +(5.71184 - 5.60133i) q^{8} +O(q^{10})\) \(q+(1.93353 - 0.511345i) q^{2} +(3.47705 - 1.97740i) q^{4} +(4.03104 + 6.98197i) q^{5} +(-3.90254 - 2.25313i) q^{7} +(5.71184 - 5.60133i) q^{8} +(11.3643 + 11.4386i) q^{10} +(-3.25842 - 1.88125i) q^{11} +(-3.52605 - 6.10730i) q^{13} +(-8.69780 - 2.36095i) q^{14} +(8.17979 - 13.7510i) q^{16} -0.517890 q^{17} -16.4164i q^{19} +(27.8223 + 16.3057i) q^{20} +(-7.26222 - 1.97127i) q^{22} +(-27.7049 + 15.9954i) q^{23} +(-19.9986 + 34.6387i) q^{25} +(-9.94065 - 10.0056i) q^{26} +(-18.0247 - 0.117384i) q^{28} +(-9.48394 + 16.4267i) q^{29} +(-13.1355 + 7.58377i) q^{31} +(8.78432 - 30.7707i) q^{32} +(-1.00135 + 0.264820i) q^{34} -36.3299i q^{35} +0.592061 q^{37} +(-8.39446 - 31.7416i) q^{38} +(62.1330 + 17.3007i) q^{40} +(-12.3766 - 21.4369i) q^{41} +(27.8686 + 16.0900i) q^{43} +(-15.0497 - 0.0980099i) q^{44} +(-45.3890 + 45.0944i) q^{46} +(52.4682 + 30.2925i) q^{47} +(-14.3468 - 24.8493i) q^{49} +(-20.9556 + 77.2010i) q^{50} +(-24.3368 - 14.2630i) q^{52} +0.664765 q^{53} -30.3336i q^{55} +(-34.9113 + 8.98987i) q^{56} +(-9.93776 + 36.6110i) q^{58} +(30.5921 - 17.6623i) q^{59} +(33.7750 - 58.5000i) q^{61} +(-21.5199 + 21.3802i) q^{62} +(1.25029 - 63.9878i) q^{64} +(28.4273 - 49.2376i) q^{65} +(-74.4692 + 42.9948i) q^{67} +(-1.80073 + 1.02407i) q^{68} +(-18.5771 - 70.2449i) q^{70} +56.4434i q^{71} +131.921 q^{73} +(1.14477 - 0.302748i) q^{74} +(-32.4618 - 57.0808i) q^{76} +(8.47743 + 14.6833i) q^{77} +(126.869 + 73.2481i) q^{79} +(128.982 + 1.68005i) q^{80} +(-34.8921 - 35.1201i) q^{82} +(-87.1029 - 50.2889i) q^{83} +(-2.08764 - 3.61589i) q^{85} +(62.1122 + 16.8599i) q^{86} +(-29.1491 + 7.50608i) q^{88} +25.8362 q^{89} +31.7786i q^{91} +(-64.7021 + 110.401i) q^{92} +(116.939 + 31.7420i) q^{94} +(114.619 - 66.1754i) q^{95} +(-48.2534 + 83.5773i) q^{97} +(-40.4465 - 40.7107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + O(q^{10}) \) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + 20q^{10} - 46q^{13} + 12q^{14} - 17q^{16} - 12q^{17} - 36q^{20} + 33q^{22} - 30q^{25} - 72q^{26} + 12q^{28} - 42q^{29} - 87q^{32} + 11q^{34} + 56q^{37} + 99q^{38} + 68q^{40} - 84q^{41} + 222q^{44} - 264q^{46} + 58q^{49} + 219q^{50} + 110q^{52} + 72q^{53} - 270q^{56} - 16q^{58} - 34q^{61} - 516q^{62} - 254q^{64} + 30q^{65} - 375q^{68} + 150q^{70} + 116q^{73} + 372q^{74} - 15q^{76} + 330q^{77} + 720q^{80} + 254q^{82} - 140q^{85} + 273q^{86} + 75q^{88} + 384q^{89} - 258q^{92} + 36q^{94} - 148q^{97} - 1170q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.93353 0.511345i 0.966763 0.255672i
\(3\) 0 0
\(4\) 3.47705 1.97740i 0.869263 0.494350i
\(5\) 4.03104 + 6.98197i 0.806209 + 1.39639i 0.915472 + 0.402382i \(0.131818\pi\)
−0.109263 + 0.994013i \(0.534849\pi\)
\(6\) 0 0
\(7\) −3.90254 2.25313i −0.557506 0.321876i 0.194638 0.980875i \(-0.437647\pi\)
−0.752144 + 0.658999i \(0.770980\pi\)
\(8\) 5.71184 5.60133i 0.713980 0.700166i
\(9\) 0 0
\(10\) 11.3643 + 11.4386i 1.13643 + 1.14386i
\(11\) −3.25842 1.88125i −0.296220 0.171023i 0.344523 0.938778i \(-0.388041\pi\)
−0.640744 + 0.767755i \(0.721374\pi\)
\(12\) 0 0
\(13\) −3.52605 6.10730i −0.271235 0.469792i 0.697944 0.716153i \(-0.254099\pi\)
−0.969178 + 0.246361i \(0.920765\pi\)
\(14\) −8.69780 2.36095i −0.621271 0.168639i
\(15\) 0 0
\(16\) 8.17979 13.7510i 0.511237 0.859440i
\(17\) −0.517890 −0.0304641 −0.0152321 0.999884i \(-0.504849\pi\)
−0.0152321 + 0.999884i \(0.504849\pi\)
\(18\) 0 0
\(19\) 16.4164i 0.864023i −0.901868 0.432012i \(-0.857804\pi\)
0.901868 0.432012i \(-0.142196\pi\)
\(20\) 27.8223 + 16.3057i 1.39111 + 0.815286i
\(21\) 0 0
\(22\) −7.26222 1.97127i −0.330101 0.0896033i
\(23\) −27.7049 + 15.9954i −1.20456 + 0.695454i −0.961566 0.274573i \(-0.911463\pi\)
−0.242996 + 0.970027i \(0.578130\pi\)
\(24\) 0 0
\(25\) −19.9986 + 34.6387i −0.799946 + 1.38555i
\(26\) −9.94065 10.0056i −0.382333 0.384831i
\(27\) 0 0
\(28\) −18.0247 0.117384i −0.643739 0.00419230i
\(29\) −9.48394 + 16.4267i −0.327032 + 0.566437i −0.981922 0.189288i \(-0.939382\pi\)
0.654889 + 0.755725i \(0.272715\pi\)
\(30\) 0 0
\(31\) −13.1355 + 7.58377i −0.423725 + 0.244638i −0.696670 0.717392i \(-0.745336\pi\)
0.272945 + 0.962030i \(0.412002\pi\)
\(32\) 8.78432 30.7707i 0.274510 0.961584i
\(33\) 0 0
\(34\) −1.00135 + 0.264820i −0.0294516 + 0.00778884i
\(35\) 36.3299i 1.03800i
\(36\) 0 0
\(37\) 0.592061 0.0160017 0.00800083 0.999968i \(-0.497453\pi\)
0.00800083 + 0.999968i \(0.497453\pi\)
\(38\) −8.39446 31.7416i −0.220907 0.835306i
\(39\) 0 0
\(40\) 62.1330 + 17.3007i 1.55333 + 0.432518i
\(41\) −12.3766 21.4369i −0.301868 0.522850i 0.674691 0.738100i \(-0.264277\pi\)
−0.976559 + 0.215250i \(0.930943\pi\)
\(42\) 0 0
\(43\) 27.8686 + 16.0900i 0.648107 + 0.374185i 0.787731 0.616020i \(-0.211256\pi\)
−0.139623 + 0.990205i \(0.544589\pi\)
\(44\) −15.0497 0.0980099i −0.342039 0.00222750i
\(45\) 0 0
\(46\) −45.3890 + 45.0944i −0.986718 + 0.980313i
\(47\) 52.4682 + 30.2925i 1.11634 + 0.644521i 0.940465 0.339890i \(-0.110390\pi\)
0.175879 + 0.984412i \(0.443723\pi\)
\(48\) 0 0
\(49\) −14.3468 24.8493i −0.292791 0.507129i
\(50\) −20.9556 + 77.2010i −0.419112 + 1.54402i
\(51\) 0 0
\(52\) −24.3368 14.2630i −0.468016 0.274288i
\(53\) 0.664765 0.0125427 0.00627137 0.999980i \(-0.498004\pi\)
0.00627137 + 0.999980i \(0.498004\pi\)
\(54\) 0 0
\(55\) 30.3336i 0.551521i
\(56\) −34.9113 + 8.98987i −0.623415 + 0.160533i
\(57\) 0 0
\(58\) −9.93776 + 36.6110i −0.171341 + 0.631224i
\(59\) 30.5921 17.6623i 0.518510 0.299362i −0.217815 0.975990i \(-0.569893\pi\)
0.736325 + 0.676628i \(0.236560\pi\)
\(60\) 0 0
\(61\) 33.7750 58.5000i 0.553688 0.959016i −0.444316 0.895870i \(-0.646553\pi\)
0.998004 0.0631460i \(-0.0201134\pi\)
\(62\) −21.5199 + 21.3802i −0.347095 + 0.344842i
\(63\) 0 0
\(64\) 1.25029 63.9878i 0.0195357 0.999809i
\(65\) 28.4273 49.2376i 0.437343 0.757501i
\(66\) 0 0
\(67\) −74.4692 + 42.9948i −1.11148 + 0.641714i −0.939213 0.343336i \(-0.888443\pi\)
−0.172269 + 0.985050i \(0.555110\pi\)
\(68\) −1.80073 + 1.02407i −0.0264813 + 0.0150599i
\(69\) 0 0
\(70\) −18.5771 70.2449i −0.265388 1.00350i
\(71\) 56.4434i 0.794977i 0.917607 + 0.397489i \(0.130118\pi\)
−0.917607 + 0.397489i \(0.869882\pi\)
\(72\) 0 0
\(73\) 131.921 1.80713 0.903567 0.428447i \(-0.140939\pi\)
0.903567 + 0.428447i \(0.140939\pi\)
\(74\) 1.14477 0.302748i 0.0154698 0.00409118i
\(75\) 0 0
\(76\) −32.4618 57.0808i −0.427129 0.751063i
\(77\) 8.47743 + 14.6833i 0.110096 + 0.190693i
\(78\) 0 0
\(79\) 126.869 + 73.2481i 1.60594 + 0.927191i 0.990265 + 0.139192i \(0.0444505\pi\)
0.615677 + 0.787999i \(0.288883\pi\)
\(80\) 128.982 + 1.68005i 1.61228 + 0.0210006i
\(81\) 0 0
\(82\) −34.8921 35.1201i −0.425513 0.428293i
\(83\) −87.1029 50.2889i −1.04943 0.605890i −0.126942 0.991910i \(-0.540516\pi\)
−0.922491 + 0.386020i \(0.873850\pi\)
\(84\) 0 0
\(85\) −2.08764 3.61589i −0.0245604 0.0425399i
\(86\) 62.1122 + 16.8599i 0.722235 + 0.196045i
\(87\) 0 0
\(88\) −29.1491 + 7.50608i −0.331240 + 0.0852964i
\(89\) 25.8362 0.290295 0.145147 0.989410i \(-0.453634\pi\)
0.145147 + 0.989410i \(0.453634\pi\)
\(90\) 0 0
\(91\) 31.7786i 0.349216i
\(92\) −64.7021 + 110.401i −0.703284 + 1.20001i
\(93\) 0 0
\(94\) 116.939 + 31.7420i 1.24403 + 0.337681i
\(95\) 114.619 66.1754i 1.20652 0.696583i
\(96\) 0 0
\(97\) −48.2534 + 83.5773i −0.497457 + 0.861621i −0.999996 0.00293363i \(-0.999066\pi\)
0.502538 + 0.864555i \(0.332400\pi\)
\(98\) −40.4465 40.7107i −0.412719 0.415415i
\(99\) 0 0
\(100\) −1.04189 + 159.986i −0.0104189 + 1.59986i
\(101\) 21.6600 37.5163i 0.214456 0.371448i −0.738648 0.674091i \(-0.764536\pi\)
0.953104 + 0.302643i \(0.0978689\pi\)
\(102\) 0 0
\(103\) 125.439 72.4223i 1.21786 0.703129i 0.253397 0.967362i \(-0.418452\pi\)
0.964459 + 0.264233i \(0.0851189\pi\)
\(104\) −54.3492 15.1334i −0.522588 0.145513i
\(105\) 0 0
\(106\) 1.28534 0.339924i 0.0121259 0.00320683i
\(107\) 54.9861i 0.513889i 0.966426 + 0.256944i \(0.0827158\pi\)
−0.966426 + 0.256944i \(0.917284\pi\)
\(108\) 0 0
\(109\) −63.9235 −0.586454 −0.293227 0.956043i \(-0.594729\pi\)
−0.293227 + 0.956043i \(0.594729\pi\)
\(110\) −15.5110 58.6509i −0.141009 0.533190i
\(111\) 0 0
\(112\) −62.9049 + 35.2338i −0.561651 + 0.314588i
\(113\) −17.8239 30.8720i −0.157734 0.273203i 0.776317 0.630342i \(-0.217086\pi\)
−0.934051 + 0.357139i \(0.883752\pi\)
\(114\) 0 0
\(115\) −223.360 128.957i −1.94226 1.12136i
\(116\) −0.494097 + 75.8699i −0.00425945 + 0.654051i
\(117\) 0 0
\(118\) 50.1190 49.7937i 0.424738 0.421981i
\(119\) 2.02109 + 1.16688i 0.0169839 + 0.00980568i
\(120\) 0 0
\(121\) −53.4218 92.5292i −0.441502 0.764704i
\(122\) 35.3912 130.382i 0.290091 1.06870i
\(123\) 0 0
\(124\) −30.6766 + 52.3432i −0.247392 + 0.422123i
\(125\) −120.909 −0.967276
\(126\) 0 0
\(127\) 9.81219i 0.0772613i 0.999254 + 0.0386307i \(0.0122996\pi\)
−0.999254 + 0.0386307i \(0.987700\pi\)
\(128\) −30.3024 124.361i −0.236737 0.971574i
\(129\) 0 0
\(130\) 29.7876 109.738i 0.229135 0.844141i
\(131\) −101.561 + 58.6365i −0.775278 + 0.447607i −0.834754 0.550623i \(-0.814390\pi\)
0.0594761 + 0.998230i \(0.481057\pi\)
\(132\) 0 0
\(133\) −36.9884 + 64.0659i −0.278109 + 0.481698i
\(134\) −122.003 + 121.211i −0.910471 + 0.904561i
\(135\) 0 0
\(136\) −2.95811 + 2.90087i −0.0217508 + 0.0213299i
\(137\) −125.606 + 217.556i −0.916831 + 1.58800i −0.112634 + 0.993637i \(0.535929\pi\)
−0.804198 + 0.594362i \(0.797405\pi\)
\(138\) 0 0
\(139\) −133.073 + 76.8298i −0.957361 + 0.552732i −0.895360 0.445344i \(-0.853081\pi\)
−0.0620009 + 0.998076i \(0.519748\pi\)
\(140\) −71.8388 126.321i −0.513134 0.902294i
\(141\) 0 0
\(142\) 28.8620 + 109.135i 0.203254 + 0.768555i
\(143\) 26.5335i 0.185549i
\(144\) 0 0
\(145\) −152.921 −1.05463
\(146\) 255.072 67.4570i 1.74707 0.462034i
\(147\) 0 0
\(148\) 2.05863 1.17074i 0.0139097 0.00791041i
\(149\) 45.8643 + 79.4393i 0.307814 + 0.533150i 0.977884 0.209148i \(-0.0670691\pi\)
−0.670070 + 0.742298i \(0.733736\pi\)
\(150\) 0 0
\(151\) 36.0215 + 20.7970i 0.238553 + 0.137729i 0.614512 0.788908i \(-0.289353\pi\)
−0.375958 + 0.926637i \(0.622686\pi\)
\(152\) −91.9538 93.7681i −0.604959 0.616895i
\(153\) 0 0
\(154\) 23.8996 + 24.0557i 0.155192 + 0.156206i
\(155\) −105.899 61.1410i −0.683222 0.394458i
\(156\) 0 0
\(157\) 112.909 + 195.565i 0.719167 + 1.24563i 0.961330 + 0.275399i \(0.0888099\pi\)
−0.242163 + 0.970236i \(0.577857\pi\)
\(158\) 282.760 + 76.7531i 1.78962 + 0.485779i
\(159\) 0 0
\(160\) 250.250 62.7061i 1.56406 0.391913i
\(161\) 144.160 0.895401
\(162\) 0 0
\(163\) 125.175i 0.767945i −0.923344 0.383973i \(-0.874556\pi\)
0.923344 0.383973i \(-0.125444\pi\)
\(164\) −85.4233 50.0637i −0.520874 0.305266i
\(165\) 0 0
\(166\) −194.131 52.6953i −1.16946 0.317442i
\(167\) −154.373 + 89.1274i −0.924390 + 0.533697i −0.885033 0.465528i \(-0.845864\pi\)
−0.0393573 + 0.999225i \(0.512531\pi\)
\(168\) 0 0
\(169\) 59.6340 103.289i 0.352864 0.611178i
\(170\) −5.88547 5.92393i −0.0346204 0.0348466i
\(171\) 0 0
\(172\) 128.717 + 0.838258i 0.748354 + 0.00487359i
\(173\) 75.5904 130.926i 0.436939 0.756800i −0.560513 0.828146i \(-0.689396\pi\)
0.997452 + 0.0713455i \(0.0227293\pi\)
\(174\) 0 0
\(175\) 156.091 90.1193i 0.891949 0.514967i
\(176\) −52.5224 + 29.4185i −0.298423 + 0.167150i
\(177\) 0 0
\(178\) 49.9551 13.2112i 0.280646 0.0742204i
\(179\) 276.827i 1.54652i −0.634088 0.773261i \(-0.718624\pi\)
0.634088 0.773261i \(-0.281376\pi\)
\(180\) 0 0
\(181\) −104.729 −0.578612 −0.289306 0.957237i \(-0.593425\pi\)
−0.289306 + 0.957237i \(0.593425\pi\)
\(182\) 16.2499 + 61.4449i 0.0892849 + 0.337609i
\(183\) 0 0
\(184\) −68.6504 + 246.548i −0.373100 + 1.33993i
\(185\) 2.38663 + 4.13376i 0.0129007 + 0.0223446i
\(186\) 0 0
\(187\) 1.68751 + 0.974282i 0.00902409 + 0.00521006i
\(188\) 242.335 + 1.57819i 1.28902 + 0.00839461i
\(189\) 0 0
\(190\) 187.781 186.562i 0.988320 0.981904i
\(191\) 192.972 + 111.413i 1.01033 + 0.583312i 0.911287 0.411772i \(-0.135090\pi\)
0.0990389 + 0.995084i \(0.468423\pi\)
\(192\) 0 0
\(193\) 56.6790 + 98.1709i 0.293674 + 0.508657i 0.974675 0.223624i \(-0.0717888\pi\)
−0.681002 + 0.732282i \(0.738455\pi\)
\(194\) −50.5623 + 186.273i −0.260631 + 0.960170i
\(195\) 0 0
\(196\) −99.0215 58.0332i −0.505212 0.296088i
\(197\) 120.998 0.614201 0.307100 0.951677i \(-0.400641\pi\)
0.307100 + 0.951677i \(0.400641\pi\)
\(198\) 0 0
\(199\) 82.2364i 0.413248i 0.978420 + 0.206624i \(0.0662477\pi\)
−0.978420 + 0.206624i \(0.933752\pi\)
\(200\) 79.7934 + 309.870i 0.398967 + 1.54935i
\(201\) 0 0
\(202\) 22.6965 83.6145i 0.112359 0.413933i
\(203\) 74.0230 42.7372i 0.364645 0.210528i
\(204\) 0 0
\(205\) 99.7811 172.826i 0.486737 0.843053i
\(206\) 205.507 204.173i 0.997607 0.991132i
\(207\) 0 0
\(208\) −112.824 1.46958i −0.542423 0.00706527i
\(209\) −30.8835 + 53.4917i −0.147768 + 0.255941i
\(210\) 0 0
\(211\) 93.5819 54.0295i 0.443516 0.256064i −0.261572 0.965184i \(-0.584241\pi\)
0.705088 + 0.709120i \(0.250907\pi\)
\(212\) 2.31142 1.31451i 0.0109029 0.00620050i
\(213\) 0 0
\(214\) 28.1169 + 106.317i 0.131387 + 0.496809i
\(215\) 259.437i 1.20668i
\(216\) 0 0
\(217\) 68.3490 0.314972
\(218\) −123.598 + 32.6870i −0.566962 + 0.149940i
\(219\) 0 0
\(220\) −59.9817 105.472i −0.272644 0.479417i
\(221\) 1.82611 + 3.16291i 0.00826292 + 0.0143118i
\(222\) 0 0
\(223\) −141.400 81.6371i −0.634079 0.366086i 0.148251 0.988950i \(-0.452636\pi\)
−0.782330 + 0.622864i \(0.785969\pi\)
\(224\) −103.612 + 100.292i −0.462552 + 0.447731i
\(225\) 0 0
\(226\) −50.2493 50.5776i −0.222342 0.223795i
\(227\) −9.56722 5.52364i −0.0421463 0.0243332i 0.478779 0.877936i \(-0.341080\pi\)
−0.520925 + 0.853602i \(0.674413\pi\)
\(228\) 0 0
\(229\) −16.1725 28.0116i −0.0706222 0.122321i 0.828552 0.559912i \(-0.189165\pi\)
−0.899174 + 0.437591i \(0.855832\pi\)
\(230\) −497.813 135.127i −2.16440 0.587511i
\(231\) 0 0
\(232\) 37.8404 + 146.949i 0.163105 + 0.633402i
\(233\) −181.049 −0.777036 −0.388518 0.921441i \(-0.627013\pi\)
−0.388518 + 0.921441i \(0.627013\pi\)
\(234\) 0 0
\(235\) 488.442i 2.07848i
\(236\) 71.4448 121.906i 0.302732 0.516549i
\(237\) 0 0
\(238\) 4.50450 + 1.22271i 0.0189265 + 0.00513745i
\(239\) 39.6432 22.8880i 0.165871 0.0957658i −0.414766 0.909928i \(-0.636137\pi\)
0.580638 + 0.814162i \(0.302803\pi\)
\(240\) 0 0
\(241\) 169.216 293.090i 0.702140 1.21614i −0.265573 0.964091i \(-0.585561\pi\)
0.967714 0.252052i \(-0.0811054\pi\)
\(242\) −150.607 151.591i −0.622342 0.626408i
\(243\) 0 0
\(244\) 1.75962 270.194i 0.00721154 1.10735i
\(245\) 115.665 200.338i 0.472102 0.817704i
\(246\) 0 0
\(247\) −100.260 + 57.8852i −0.405911 + 0.234353i
\(248\) −32.5486 + 116.893i −0.131244 + 0.471344i
\(249\) 0 0
\(250\) −233.782 + 61.8264i −0.935127 + 0.247306i
\(251\) 282.587i 1.12585i −0.826510 0.562923i \(-0.809677\pi\)
0.826510 0.562923i \(-0.190323\pi\)
\(252\) 0 0
\(253\) 120.366 0.475754
\(254\) 5.01741 + 18.9721i 0.0197536 + 0.0746934i
\(255\) 0 0
\(256\) −122.182 224.961i −0.477274 0.878755i
\(257\) −38.8897 67.3589i −0.151322 0.262097i 0.780392 0.625291i \(-0.215020\pi\)
−0.931714 + 0.363194i \(0.881686\pi\)
\(258\) 0 0
\(259\) −2.31055 1.33399i −0.00892102 0.00515056i
\(260\) 1.48101 227.414i 0.00569620 0.874668i
\(261\) 0 0
\(262\) −166.388 + 165.308i −0.635070 + 0.630947i
\(263\) 195.201 + 112.700i 0.742211 + 0.428516i 0.822873 0.568226i \(-0.192370\pi\)
−0.0806619 + 0.996742i \(0.525703\pi\)
\(264\) 0 0
\(265\) 2.67970 + 4.64138i 0.0101121 + 0.0175146i
\(266\) −38.7584 + 142.787i −0.145708 + 0.536793i
\(267\) 0 0
\(268\) −173.916 + 296.751i −0.648939 + 1.10728i
\(269\) −425.808 −1.58293 −0.791465 0.611214i \(-0.790681\pi\)
−0.791465 + 0.611214i \(0.790681\pi\)
\(270\) 0 0
\(271\) 56.3665i 0.207995i −0.994578 0.103997i \(-0.966837\pi\)
0.994578 0.103997i \(-0.0331633\pi\)
\(272\) −4.23623 + 7.12152i −0.0155744 + 0.0261821i
\(273\) 0 0
\(274\) −131.616 + 484.878i −0.480352 + 1.76963i
\(275\) 130.328 75.2450i 0.473920 0.273618i
\(276\) 0 0
\(277\) −209.641 + 363.109i −0.756828 + 1.31086i 0.187633 + 0.982239i \(0.439918\pi\)
−0.944461 + 0.328625i \(0.893415\pi\)
\(278\) −218.014 + 216.599i −0.784223 + 0.779132i
\(279\) 0 0
\(280\) −203.496 207.511i −0.726771 0.741110i
\(281\) 73.9638 128.109i 0.263216 0.455904i −0.703878 0.710320i \(-0.748550\pi\)
0.967095 + 0.254416i \(0.0818833\pi\)
\(282\) 0 0
\(283\) 229.852 132.705i 0.812198 0.468923i −0.0355207 0.999369i \(-0.511309\pi\)
0.847719 + 0.530446i \(0.177976\pi\)
\(284\) 111.611 + 196.257i 0.392997 + 0.691045i
\(285\) 0 0
\(286\) 13.5678 + 51.3033i 0.0474398 + 0.179382i
\(287\) 111.544i 0.388656i
\(288\) 0 0
\(289\) −288.732 −0.999072
\(290\) −295.676 + 78.1953i −1.01957 + 0.269639i
\(291\) 0 0
\(292\) 458.695 260.860i 1.57087 0.893356i
\(293\) −124.844 216.236i −0.426088 0.738006i 0.570433 0.821344i \(-0.306775\pi\)
−0.996521 + 0.0833379i \(0.973442\pi\)
\(294\) 0 0
\(295\) 246.636 + 142.395i 0.836054 + 0.482696i
\(296\) 3.38176 3.31633i 0.0114249 0.0112038i
\(297\) 0 0
\(298\) 129.301 + 130.146i 0.433895 + 0.436730i
\(299\) 195.378 + 112.801i 0.653438 + 0.377262i
\(300\) 0 0
\(301\) −72.5056 125.583i −0.240883 0.417221i
\(302\) 80.2830 + 21.7922i 0.265838 + 0.0721596i
\(303\) 0 0
\(304\) −225.743 134.283i −0.742576 0.441721i
\(305\) 544.594 1.78555
\(306\) 0 0
\(307\) 259.968i 0.846801i −0.905943 0.423401i \(-0.860836\pi\)
0.905943 0.423401i \(-0.139164\pi\)
\(308\) 58.5113 + 34.2915i 0.189972 + 0.111336i
\(309\) 0 0
\(310\) −236.023 64.0667i −0.761366 0.206667i
\(311\) 16.5959 9.58164i 0.0533630 0.0308091i −0.473081 0.881019i \(-0.656858\pi\)
0.526444 + 0.850210i \(0.323525\pi\)
\(312\) 0 0
\(313\) −21.9358 + 37.9939i −0.0700823 + 0.121386i −0.898937 0.438078i \(-0.855660\pi\)
0.828855 + 0.559464i \(0.188993\pi\)
\(314\) 318.314 + 320.394i 1.01374 + 1.02036i
\(315\) 0 0
\(316\) 585.972 + 3.81610i 1.85434 + 0.0120763i
\(317\) −68.9690 + 119.458i −0.217568 + 0.376838i −0.954064 0.299603i \(-0.903146\pi\)
0.736496 + 0.676442i \(0.236479\pi\)
\(318\) 0 0
\(319\) 61.8054 35.6834i 0.193747 0.111860i
\(320\) 451.801 249.208i 1.41188 0.778775i
\(321\) 0 0
\(322\) 278.736 73.7152i 0.865641 0.228929i
\(323\) 8.50191i 0.0263217i
\(324\) 0 0
\(325\) 282.065 0.867892
\(326\) −64.0076 242.029i −0.196342 0.742421i
\(327\) 0 0
\(328\) −190.768 53.1187i −0.581610 0.161947i
\(329\) −136.506 236.436i −0.414912 0.718649i
\(330\) 0 0
\(331\) −51.7490 29.8773i −0.156341 0.0902638i 0.419788 0.907622i \(-0.362104\pi\)
−0.576130 + 0.817358i \(0.695438\pi\)
\(332\) −402.303 2.61996i −1.21176 0.00789145i
\(333\) 0 0
\(334\) −252.910 + 251.268i −0.757215 + 0.752300i
\(335\) −600.378 346.628i −1.79217 1.03471i
\(336\) 0 0
\(337\) 224.356 + 388.595i 0.665743 + 1.15310i 0.979083 + 0.203460i \(0.0652188\pi\)
−0.313340 + 0.949641i \(0.601448\pi\)
\(338\) 62.4875 230.206i 0.184874 0.681082i
\(339\) 0 0
\(340\) −14.4089 8.44457i −0.0423791 0.0248370i
\(341\) 57.0679 0.167355
\(342\) 0 0
\(343\) 350.108i 1.02072i
\(344\) 249.306 64.1979i 0.724727 0.186622i
\(345\) 0 0
\(346\) 79.2075 291.803i 0.228924 0.843360i
\(347\) −500.441 + 288.930i −1.44219 + 0.832651i −0.997996 0.0632779i \(-0.979845\pi\)
−0.444198 + 0.895929i \(0.646511\pi\)
\(348\) 0 0
\(349\) 66.1311 114.542i 0.189487 0.328202i −0.755592 0.655042i \(-0.772651\pi\)
0.945079 + 0.326841i \(0.105984\pi\)
\(350\) 255.724 254.064i 0.730641 0.725898i
\(351\) 0 0
\(352\) −86.5105 + 83.7384i −0.245768 + 0.237893i
\(353\) −270.562 + 468.628i −0.766465 + 1.32756i 0.173003 + 0.984921i \(0.444653\pi\)
−0.939468 + 0.342636i \(0.888680\pi\)
\(354\) 0 0
\(355\) −394.086 + 227.526i −1.11010 + 0.640918i
\(356\) 89.8339 51.0885i 0.252343 0.143507i
\(357\) 0 0
\(358\) −141.554 535.253i −0.395403 1.49512i
\(359\) 292.754i 0.815470i −0.913100 0.407735i \(-0.866319\pi\)
0.913100 0.407735i \(-0.133681\pi\)
\(360\) 0 0
\(361\) 91.5006 0.253464
\(362\) −202.496 + 53.5525i −0.559381 + 0.147935i
\(363\) 0 0
\(364\) 62.8390 + 110.496i 0.172635 + 0.303561i
\(365\) 531.779 + 921.067i 1.45693 + 2.52347i
\(366\) 0 0
\(367\) −378.870 218.741i −1.03234 0.596024i −0.114689 0.993401i \(-0.536587\pi\)
−0.917655 + 0.397377i \(0.869920\pi\)
\(368\) −6.66653 + 511.811i −0.0181156 + 1.39079i
\(369\) 0 0
\(370\) 6.72838 + 6.77234i 0.0181848 + 0.0183036i
\(371\) −2.59428 1.49781i −0.00699266 0.00403721i
\(372\) 0 0
\(373\) −352.979 611.377i −0.946323 1.63908i −0.753080 0.657929i \(-0.771433\pi\)
−0.193243 0.981151i \(-0.561901\pi\)
\(374\) 3.76103 + 1.02090i 0.0100562 + 0.00272969i
\(375\) 0 0
\(376\) 469.368 120.865i 1.24832 0.321450i
\(377\) 133.763 0.354810
\(378\) 0 0
\(379\) 541.432i 1.42858i −0.699850 0.714290i \(-0.746750\pi\)
0.699850 0.714290i \(-0.253250\pi\)
\(380\) 267.682 456.743i 0.704426 1.20196i
\(381\) 0 0
\(382\) 430.087 + 116.744i 1.12588 + 0.305612i
\(383\) 311.941 180.099i 0.814467 0.470233i −0.0340377 0.999421i \(-0.510837\pi\)
0.848505 + 0.529188i \(0.177503\pi\)
\(384\) 0 0
\(385\) −68.3458 + 118.378i −0.177521 + 0.307476i
\(386\) 159.790 + 160.834i 0.413963 + 0.416667i
\(387\) 0 0
\(388\) −2.51391 + 386.019i −0.00647916 + 0.994893i
\(389\) 43.9057 76.0468i 0.112868 0.195493i −0.804057 0.594552i \(-0.797330\pi\)
0.916926 + 0.399058i \(0.130663\pi\)
\(390\) 0 0
\(391\) 14.3481 8.28388i 0.0366959 0.0211864i
\(392\) −221.136 61.5745i −0.564122 0.157078i
\(393\) 0 0
\(394\) 233.952 61.8715i 0.593787 0.157034i
\(395\) 1181.07i 2.99004i
\(396\) 0 0
\(397\) −48.4128 −0.121947 −0.0609733 0.998139i \(-0.519420\pi\)
−0.0609733 + 0.998139i \(0.519420\pi\)
\(398\) 42.0512 + 159.006i 0.105656 + 0.399513i
\(399\) 0 0
\(400\) 312.733 + 558.339i 0.781832 + 1.39585i
\(401\) −217.859 377.343i −0.543290 0.941005i −0.998712 0.0507299i \(-0.983845\pi\)
0.455423 0.890275i \(-0.349488\pi\)
\(402\) 0 0
\(403\) 92.6326 + 53.4815i 0.229858 + 0.132708i
\(404\) 1.12845 173.277i 0.00279319 0.428902i
\(405\) 0 0
\(406\) 121.272 120.485i 0.298699 0.296761i
\(407\) −1.92919 1.11382i −0.00474002 0.00273665i
\(408\) 0 0
\(409\) −27.1145 46.9636i −0.0662945 0.114825i 0.830973 0.556313i \(-0.187784\pi\)
−0.897267 + 0.441487i \(0.854451\pi\)
\(410\) 104.556 385.186i 0.255014 0.939479i
\(411\) 0 0
\(412\) 292.951 499.859i 0.711045 1.21325i
\(413\) −159.182 −0.385430
\(414\) 0 0
\(415\) 810.867i 1.95390i
\(416\) −218.900 + 54.8505i −0.526201 + 0.131852i
\(417\) 0 0
\(418\) −32.3613 + 119.220i −0.0774193 + 0.285215i
\(419\) 552.029 318.714i 1.31749 0.760655i 0.334168 0.942514i \(-0.391545\pi\)
0.983325 + 0.181859i \(0.0582114\pi\)
\(420\) 0 0
\(421\) −95.7757 + 165.888i −0.227496 + 0.394034i −0.957065 0.289873i \(-0.906387\pi\)
0.729570 + 0.683907i \(0.239720\pi\)
\(422\) 153.315 152.320i 0.363307 0.360948i
\(423\) 0 0
\(424\) 3.79704 3.72357i 0.00895527 0.00878200i
\(425\) 10.3571 17.9390i 0.0243696 0.0422095i
\(426\) 0 0
\(427\) −263.617 + 152.199i −0.617369 + 0.356438i
\(428\) 108.729 + 191.190i 0.254041 + 0.446705i
\(429\) 0 0
\(430\) 132.662 + 501.629i 0.308516 + 1.16658i
\(431\) 481.190i 1.11645i −0.829689 0.558225i \(-0.811482\pi\)
0.829689 0.558225i \(-0.188518\pi\)
\(432\) 0 0
\(433\) −360.347 −0.832209 −0.416105 0.909317i \(-0.636605\pi\)
−0.416105 + 0.909317i \(0.636605\pi\)
\(434\) 132.155 34.9499i 0.304504 0.0805297i
\(435\) 0 0
\(436\) −222.265 + 126.402i −0.509783 + 0.289913i
\(437\) 262.588 + 454.816i 0.600888 + 1.04077i
\(438\) 0 0
\(439\) 488.267 + 281.901i 1.11223 + 0.642144i 0.939405 0.342809i \(-0.111378\pi\)
0.172821 + 0.984953i \(0.444712\pi\)
\(440\) −169.909 173.261i −0.386156 0.393775i
\(441\) 0 0
\(442\) 5.14816 + 5.18180i 0.0116474 + 0.0117235i
\(443\) −569.917 329.042i −1.28649 0.742757i −0.308467 0.951235i \(-0.599816\pi\)
−0.978027 + 0.208478i \(0.933149\pi\)
\(444\) 0 0
\(445\) 104.147 + 180.388i 0.234038 + 0.405366i
\(446\) −315.145 85.5436i −0.706603 0.191802i
\(447\) 0 0
\(448\) −149.052 + 246.898i −0.332706 + 0.551112i
\(449\) −227.569 −0.506836 −0.253418 0.967357i \(-0.581555\pi\)
−0.253418 + 0.967357i \(0.581555\pi\)
\(450\) 0 0
\(451\) 93.1339i 0.206505i
\(452\) −123.021 72.0984i −0.272170 0.159510i
\(453\) 0 0
\(454\) −21.3230 5.78795i −0.0469669 0.0127488i
\(455\) −221.878 + 128.101i −0.487643 + 0.281541i
\(456\) 0 0
\(457\) −358.879 + 621.596i −0.785292 + 1.36017i 0.143532 + 0.989646i \(0.454154\pi\)
−0.928824 + 0.370520i \(0.879179\pi\)
\(458\) −45.5935 45.8914i −0.0995492 0.100200i
\(459\) 0 0
\(460\) −1031.63 6.71842i −2.24268 0.0146053i
\(461\) 200.873 347.922i 0.435733 0.754712i −0.561622 0.827394i \(-0.689822\pi\)
0.997355 + 0.0726819i \(0.0231558\pi\)
\(462\) 0 0
\(463\) −396.754 + 229.066i −0.856920 + 0.494743i −0.862980 0.505239i \(-0.831405\pi\)
0.00605956 + 0.999982i \(0.498071\pi\)
\(464\) 148.307 + 264.781i 0.319627 + 0.570648i
\(465\) 0 0
\(466\) −350.064 + 92.5787i −0.751210 + 0.198667i
\(467\) 204.395i 0.437677i −0.975761 0.218838i \(-0.929773\pi\)
0.975761 0.218838i \(-0.0702267\pi\)
\(468\) 0 0
\(469\) 387.493 0.826210
\(470\) 249.762 + 944.415i 0.531409 + 2.00939i
\(471\) 0 0
\(472\) 75.8045 272.241i 0.160603 0.576781i
\(473\) −60.5385 104.856i −0.127988 0.221682i
\(474\) 0 0
\(475\) 568.643 + 328.306i 1.19714 + 0.691172i
\(476\) 9.33481 + 0.0607922i 0.0196109 + 0.000127715i
\(477\) 0 0
\(478\) 64.9475 64.5259i 0.135874 0.134992i
\(479\) −78.4548 45.2959i −0.163789 0.0945634i 0.415865 0.909426i \(-0.363479\pi\)
−0.579654 + 0.814863i \(0.696812\pi\)
\(480\) 0 0
\(481\) −2.08764 3.61589i −0.00434020 0.00751745i
\(482\) 177.313 653.226i 0.367869 1.35524i
\(483\) 0 0
\(484\) −368.718 216.093i −0.761813 0.446473i
\(485\) −778.046 −1.60422
\(486\) 0 0
\(487\) 301.289i 0.618663i 0.950954 + 0.309332i \(0.100105\pi\)
−0.950954 + 0.309332i \(0.899895\pi\)
\(488\) −134.760 523.327i −0.276148 1.07239i
\(489\) 0 0
\(490\) 121.200 446.503i 0.247346 0.911230i
\(491\) −389.556 + 224.911i −0.793394 + 0.458066i −0.841156 0.540792i \(-0.818124\pi\)
0.0477620 + 0.998859i \(0.484791\pi\)
\(492\) 0 0
\(493\) 4.91164 8.50721i 0.00996276 0.0172560i
\(494\) −164.256 + 163.190i −0.332502 + 0.330344i
\(495\) 0 0
\(496\) −3.16074 + 242.660i −0.00637246 + 0.489234i
\(497\) 127.175 220.273i 0.255884 0.443205i
\(498\) 0 0
\(499\) 552.630 319.061i 1.10748 0.639401i 0.169301 0.985564i \(-0.445849\pi\)
0.938174 + 0.346163i \(0.112516\pi\)
\(500\) −420.409 + 239.086i −0.840817 + 0.478172i
\(501\) 0 0
\(502\) −144.500 546.390i −0.287848 1.08843i
\(503\) 182.179i 0.362185i 0.983466 + 0.181093i \(0.0579634\pi\)
−0.983466 + 0.181093i \(0.942037\pi\)
\(504\) 0 0
\(505\) 349.250 0.691585
\(506\) 232.731 61.5485i 0.459942 0.121637i
\(507\) 0 0
\(508\) 19.4026 + 34.1175i 0.0381941 + 0.0671604i
\(509\) −471.123 816.009i −0.925585 1.60316i −0.790617 0.612311i \(-0.790240\pi\)
−0.134968 0.990850i \(-0.543093\pi\)
\(510\) 0 0
\(511\) −514.827 297.235i −1.00749 0.581674i
\(512\) −351.275 372.491i −0.686084 0.727522i
\(513\) 0 0
\(514\) −109.638 110.354i −0.213303 0.214697i
\(515\) 1011.30 + 583.875i 1.96369 + 1.13374i
\(516\) 0 0
\(517\) −113.976 197.412i −0.220456 0.381841i
\(518\) −5.14963 1.39783i −0.00994138 0.00269851i
\(519\) 0 0
\(520\) −113.423 440.468i −0.218122 0.847054i
\(521\) 634.330 1.21752 0.608762 0.793353i \(-0.291666\pi\)
0.608762 + 0.793353i \(0.291666\pi\)
\(522\) 0 0
\(523\) 534.777i 1.02252i 0.859426 + 0.511259i \(0.170821\pi\)
−0.859426 + 0.511259i \(0.829179\pi\)
\(524\) −237.187 + 404.710i −0.452646 + 0.772347i
\(525\) 0 0
\(526\) 435.056 + 118.092i 0.827102 + 0.224510i
\(527\) 6.80273 3.92756i 0.0129084 0.00745267i
\(528\) 0 0
\(529\) 247.208 428.178i 0.467313 0.809409i
\(530\) 7.55461 + 7.60397i 0.0142540 + 0.0143471i
\(531\) 0 0
\(532\) −1.92703 + 295.901i −0.00362224 + 0.556205i
\(533\) −87.2809 + 151.175i −0.163754 + 0.283630i
\(534\) 0 0
\(535\) −383.912 + 221.652i −0.717592 + 0.414302i
\(536\) −184.528 + 662.706i −0.344270 + 1.23639i
\(537\) 0 0
\(538\) −823.312 + 217.735i −1.53032 + 0.404712i
\(539\) 107.960i 0.200296i
\(540\) 0 0
\(541\) −61.0097 −0.112772 −0.0563860 0.998409i \(-0.517958\pi\)
−0.0563860 + 0.998409i \(0.517958\pi\)
\(542\) −28.8227 108.986i −0.0531785 0.201082i
\(543\) 0 0
\(544\) −4.54931 + 15.9358i −0.00836271 + 0.0292938i
\(545\) −257.678 446.312i −0.472805 0.818921i
\(546\) 0 0
\(547\) 104.430 + 60.2925i 0.190914 + 0.110224i 0.592410 0.805637i \(-0.298177\pi\)
−0.401497 + 0.915861i \(0.631510\pi\)
\(548\) −6.54385 + 1004.83i −0.0119413 + 1.83362i
\(549\) 0 0
\(550\) 213.517 212.131i 0.388212 0.385692i
\(551\) 269.667 + 155.693i 0.489415 + 0.282564i
\(552\) 0 0
\(553\) −330.076 571.708i −0.596882 1.03383i
\(554\) −219.673 + 809.281i −0.396521 + 1.46080i
\(555\) 0 0
\(556\) −310.779 + 530.280i −0.558955 + 0.953741i
\(557\) 527.461 0.946968 0.473484 0.880802i \(-0.342996\pi\)
0.473484 + 0.880802i \(0.342996\pi\)
\(558\) 0 0
\(559\) 226.936i 0.405967i
\(560\) −499.574 297.171i −0.892097 0.530663i
\(561\) 0 0
\(562\) 77.5031 285.523i 0.137906 0.508049i
\(563\) 595.478 343.800i 1.05769 0.610656i 0.132896 0.991130i \(-0.457572\pi\)
0.924792 + 0.380474i \(0.124239\pi\)
\(564\) 0 0
\(565\) 143.698 248.893i 0.254333 0.440518i
\(566\) 376.567 374.123i 0.665313 0.660994i
\(567\) 0 0
\(568\) 316.158 + 322.396i 0.556616 + 0.567598i
\(569\) −293.677 + 508.664i −0.516128 + 0.893961i 0.483696 + 0.875236i \(0.339294\pi\)
−0.999825 + 0.0187248i \(0.994039\pi\)
\(570\) 0 0
\(571\) 742.245 428.535i 1.29990 0.750500i 0.319517 0.947581i \(-0.396479\pi\)
0.980387 + 0.197081i \(0.0631461\pi\)
\(572\) 52.4674 + 92.2585i 0.0917262 + 0.161291i
\(573\) 0 0
\(574\) 57.0377 + 215.674i 0.0993688 + 0.375739i
\(575\) 1279.55i 2.22530i
\(576\) 0 0
\(577\) 871.732 1.51080 0.755401 0.655263i \(-0.227442\pi\)
0.755401 + 0.655263i \(0.227442\pi\)
\(578\) −558.271 + 147.642i −0.965866 + 0.255435i
\(579\) 0 0
\(580\) −531.714 + 302.385i −0.916748 + 0.521354i
\(581\) 226.615 + 392.509i 0.390044 + 0.675575i
\(582\) 0 0
\(583\) −2.16609 1.25059i −0.00371542 0.00214510i
\(584\) 753.511 738.931i 1.29026 1.26529i
\(585\) 0 0
\(586\) −351.960 354.259i −0.600614 0.604538i
\(587\) 700.071 + 404.186i 1.19263 + 0.688563i 0.958901 0.283740i \(-0.0915753\pi\)
0.233725 + 0.972303i \(0.424909\pi\)
\(588\) 0 0
\(589\) 124.498 + 215.638i 0.211373 + 0.366108i
\(590\) 549.690 + 149.209i 0.931679 + 0.252897i
\(591\) 0 0
\(592\) 4.84294 8.14146i 0.00818064 0.0137525i
\(593\) 445.123 0.750628 0.375314 0.926898i \(-0.377535\pi\)
0.375314 + 0.926898i \(0.377535\pi\)
\(594\) 0 0
\(595\) 18.8149i 0.0316217i
\(596\) 316.556 + 185.523i 0.531134 + 0.311280i
\(597\) 0 0
\(598\) 435.449 + 118.199i 0.728175 + 0.197657i
\(599\) −684.932 + 395.445i −1.14346 + 0.660176i −0.947285 0.320393i \(-0.896185\pi\)
−0.196174 + 0.980569i \(0.562852\pi\)
\(600\) 0 0
\(601\) 193.532 335.208i 0.322017 0.557750i −0.658887 0.752242i \(-0.728972\pi\)
0.980904 + 0.194492i \(0.0623057\pi\)
\(602\) −204.408 205.744i −0.339548 0.341767i
\(603\) 0 0
\(604\) 166.373 + 1.08349i 0.275451 + 0.00179385i
\(605\) 430.691 745.979i 0.711886 1.23302i
\(606\) 0 0
\(607\) −902.512 + 521.066i −1.48684 + 0.858428i −0.999887 0.0150003i \(-0.995225\pi\)
−0.486953 + 0.873428i \(0.661892\pi\)
\(608\) −505.145 144.207i −0.830831 0.237183i
\(609\) 0 0
\(610\) 1052.99 278.475i 1.72621 0.456517i
\(611\) 427.251i 0.699266i
\(612\) 0 0
\(613\) 256.336 0.418166 0.209083 0.977898i \(-0.432952\pi\)
0.209083 + 0.977898i \(0.432952\pi\)
\(614\) −132.933 502.655i −0.216504 0.818657i
\(615\) 0 0
\(616\) 130.668 + 36.3841i 0.212123 + 0.0590650i
\(617\) 253.519 + 439.108i 0.410890 + 0.711683i 0.994987 0.100001i \(-0.0318846\pi\)
−0.584097 + 0.811684i \(0.698551\pi\)
\(618\) 0 0
\(619\) 662.787 + 382.660i 1.07074 + 0.618191i 0.928383 0.371624i \(-0.121199\pi\)
0.142355 + 0.989816i \(0.454532\pi\)
\(620\) −489.118 3.18534i −0.788900 0.00513764i
\(621\) 0 0
\(622\) 27.1891 27.0126i 0.0437123 0.0434286i
\(623\) −100.827 58.2125i −0.161841 0.0934390i
\(624\) 0 0
\(625\) 12.5746 + 21.7799i 0.0201194 + 0.0348479i
\(626\) −22.9854 + 84.6789i −0.0367179 + 0.135270i
\(627\) 0 0
\(628\) 779.301 + 456.722i 1.24092 + 0.727264i
\(629\) −0.306623 −0.000487477
\(630\) 0 0
\(631\) 719.756i 1.14066i 0.821416 + 0.570330i \(0.193185\pi\)
−0.821416 + 0.570330i \(0.806815\pi\)
\(632\) 1134.94 292.255i 1.79580 0.462429i
\(633\) 0 0
\(634\) −72.2692 + 266.242i −0.113989 + 0.419940i
\(635\) −68.5084 + 39.5534i −0.107887 + 0.0622888i
\(636\) 0 0
\(637\) −101.175 + 175.240i −0.158830 + 0.275102i
\(638\) 101.256 100.599i 0.158708 0.157678i
\(639\) 0 0
\(640\) 746.138 712.877i 1.16584 1.11387i
\(641\) −351.516 + 608.844i −0.548388 + 0.949835i 0.449998 + 0.893030i \(0.351425\pi\)
−0.998385 + 0.0568054i \(0.981909\pi\)
\(642\) 0 0
\(643\) 507.224 292.846i 0.788841 0.455437i −0.0507136 0.998713i \(-0.516150\pi\)
0.839554 + 0.543276i \(0.182816\pi\)
\(644\) 501.250 285.061i 0.778339 0.442641i
\(645\) 0 0
\(646\) 4.34741 + 16.4387i 0.00672973 + 0.0254469i
\(647\) 791.553i 1.22342i 0.791082 + 0.611710i \(0.209518\pi\)
−0.791082 + 0.611710i \(0.790482\pi\)
\(648\) 0 0
\(649\) −132.909 −0.204791
\(650\) 545.380 144.232i 0.839046 0.221896i
\(651\) 0 0
\(652\) −247.521 435.240i −0.379633 0.667547i
\(653\) 196.385 + 340.148i 0.300742 + 0.520901i 0.976304 0.216402i \(-0.0694323\pi\)
−0.675562 + 0.737303i \(0.736099\pi\)
\(654\) 0 0
\(655\) −818.797 472.733i −1.25007 0.721730i
\(656\) −396.017 5.15827i −0.603685 0.00786322i
\(657\) 0 0
\(658\) −384.838 387.353i −0.584861 0.588682i
\(659\) −372.557 215.096i −0.565337 0.326398i 0.189948 0.981794i \(-0.439168\pi\)
−0.755285 + 0.655397i \(0.772501\pi\)
\(660\) 0 0
\(661\) 453.865 + 786.117i 0.686633 + 1.18928i 0.972920 + 0.231140i \(0.0742456\pi\)
−0.286287 + 0.958144i \(0.592421\pi\)
\(662\) −115.336 31.3070i −0.174223 0.0472915i
\(663\) 0 0
\(664\) −779.203 + 200.650i −1.17350 + 0.302183i
\(665\) −596.408 −0.896854
\(666\) 0 0
\(667\) 606.799i 0.909744i
\(668\) −360.523 + 615.158i −0.539706 + 0.920895i
\(669\) 0 0
\(670\) −1338.09 363.215i −1.99715 0.542112i
\(671\) −220.106 + 127.078i −0.328027 + 0.189387i
\(672\) 0 0
\(673\) −34.8528 + 60.3668i −0.0517872 + 0.0896980i −0.890757 0.454480i \(-0.849825\pi\)
0.838970 + 0.544178i \(0.183158\pi\)
\(674\) 632.504 + 636.636i 0.938433 + 0.944564i
\(675\) 0 0
\(676\) 3.10682 477.062i 0.00459589 0.705712i
\(677\) 144.502 250.285i 0.213444 0.369697i −0.739346 0.673326i \(-0.764865\pi\)
0.952790 + 0.303629i \(0.0981984\pi\)
\(678\) 0 0
\(679\) 376.622 217.443i 0.554671 0.320239i
\(680\) −32.1781 8.95988i −0.0473207 0.0131763i
\(681\) 0 0
\(682\) 110.342 29.1814i 0.161792 0.0427880i
\(683\) 522.729i 0.765343i 0.923884 + 0.382672i \(0.124996\pi\)
−0.923884 + 0.382672i \(0.875004\pi\)
\(684\) 0 0
\(685\) −2025.29 −2.95663
\(686\) 179.026 + 676.943i 0.260971 + 0.986798i
\(687\) 0 0
\(688\) 449.213 251.610i 0.652926 0.365712i
\(689\) −2.34400 4.05992i −0.00340203 0.00589248i
\(690\) 0 0
\(691\) −485.917 280.544i −0.703208 0.405997i 0.105333 0.994437i \(-0.466409\pi\)
−0.808541 + 0.588440i \(0.799742\pi\)
\(692\) 3.93813 604.711i 0.00569093 0.873859i
\(693\) 0 0
\(694\) −819.874 + 814.552i −1.18137 + 1.17371i
\(695\) −1072.85 619.409i −1.54367 0.891236i
\(696\) 0 0
\(697\) 6.40971 + 11.1019i 0.00919614 + 0.0159282i
\(698\) 69.2956 255.287i 0.0992773 0.365740i
\(699\) 0 0
\(700\) 364.535 622.004i 0.520765 0.888577i
\(701\) −1203.11 −1.71627 −0.858137 0.513421i \(-0.828378\pi\)
−0.858137 + 0.513421i \(0.828378\pi\)
\(702\) 0 0
\(703\) 9.71954i 0.0138258i
\(704\) −124.451 + 206.147i −0.176777 + 0.292823i
\(705\) 0 0
\(706\) −283.509 + 1044.45i −0.401571 + 1.47940i
\(707\) −169.058 + 97.6059i −0.239121 + 0.138056i
\(708\) 0 0
\(709\) 89.2724 154.624i 0.125913 0.218088i −0.796176 0.605065i \(-0.793147\pi\)
0.922090 + 0.386977i \(0.126481\pi\)
\(710\) −645.632 + 641.441i −0.909341 + 0.903439i
\(711\) 0 0
\(712\) 147.572 144.717i 0.207265 0.203254i
\(713\) 242.611 420.215i 0.340269 0.589362i
\(714\) 0 0
\(715\) −185.257 + 106.958i −0.259100 + 0.149591i
\(716\) −547.398 962.543i −0.764522 1.34433i
\(717\) 0 0
\(718\) −149.698 566.048i −0.208493 0.788367i
\(719\) 53.0278i 0.0737521i −0.999320 0.0368760i \(-0.988259\pi\)
0.999320 0.0368760i \(-0.0117407\pi\)
\(720\) 0 0
\(721\) −652.709 −0.905282
\(722\) 176.919 46.7884i 0.245040 0.0648038i
\(723\) 0 0
\(724\) −364.148 + 207.091i −0.502966 + 0.286037i
\(725\) −379.332 657.022i −0.523216 0.906238i
\(726\) 0 0
\(727\) −436.956 252.277i −0.601041 0.347011i 0.168410 0.985717i \(-0.446137\pi\)
−0.769451 + 0.638706i \(0.779470\pi\)
\(728\) 178.003 + 181.515i 0.244509 + 0.249333i
\(729\) 0 0
\(730\) 1499.19 + 1508.99i 2.05369 + 2.06710i
\(731\) −14.4329 8.33283i −0.0197440 0.0113992i
\(732\) 0 0
\(733\) 410.964 + 711.811i 0.560660 + 0.971092i 0.997439 + 0.0715233i \(0.0227860\pi\)
−0.436779 + 0.899569i \(0.643881\pi\)
\(734\) −844.408 229.208i −1.15042 0.312272i
\(735\) 0 0
\(736\) 248.822 + 993.009i 0.338073 + 1.34920i
\(737\) 323.536 0.438991
\(738\) 0 0
\(739\) 190.298i 0.257507i −0.991677 0.128754i \(-0.958902\pi\)
0.991677 0.128754i \(-0.0410977\pi\)
\(740\) 16.4725 + 9.65398i 0.0222602 + 0.0130459i
\(741\) 0 0
\(742\) −5.78200 1.56948i −0.00779245 0.00211520i
\(743\) 664.128 383.435i 0.893847 0.516063i 0.0186481 0.999826i \(-0.494064\pi\)
0.875199 + 0.483763i \(0.160730\pi\)
\(744\) 0 0
\(745\) −369.762 + 640.447i −0.496325 + 0.859660i
\(746\) −995.118 1001.62i −1.33394 1.34265i
\(747\) 0 0
\(748\) 7.79409 + 0.0507583i 0.0104199 + 6.78587e-5i
\(749\) 123.891 214.586i 0.165409 0.286496i
\(750\) 0 0
\(751\) 519.601 299.992i 0.691879 0.399456i −0.112437 0.993659i \(-0.535866\pi\)
0.804315 + 0.594202i \(0.202532\pi\)
\(752\) 845.732 473.705i 1.12464 0.629927i
\(753\) 0 0
\(754\) 258.635 68.3992i 0.343017 0.0907152i
\(755\) 335.335i 0.444152i
\(756\) 0 0
\(757\) −343.082 −0.453213 −0.226606 0.973986i \(-0.572763\pi\)
−0.226606 + 0.973986i \(0.572763\pi\)
\(758\) −276.858 1046.87i −0.365249 1.38110i
\(759\) 0 0
\(760\) 284.017 1020.00i 0.373706 1.34211i
\(761\) 149.365 + 258.708i 0.196275 + 0.339958i 0.947318 0.320295i \(-0.103782\pi\)
−0.751043 + 0.660253i \(0.770449\pi\)
\(762\) 0 0
\(763\) 249.464 + 144.028i 0.326952 + 0.188766i
\(764\) 891.282 + 5.80440i 1.16660 + 0.00759738i
\(765\) 0 0
\(766\) 511.053 507.736i 0.667171 0.662841i
\(767\) −215.738 124.557i −0.281275 0.162394i
\(768\) 0 0
\(769\) −466.241 807.553i −0.606295 1.05013i −0.991845 0.127447i \(-0.959322\pi\)
0.385550 0.922687i \(-0.374012\pi\)
\(770\) −71.6162 + 263.836i −0.0930081 + 0.342644i
\(771\) 0 0
\(772\) 391.199 + 229.268i 0.506734 + 0.296980i
\(773\) 173.239 0.224113 0.112056 0.993702i \(-0.464256\pi\)
0.112056 + 0.993702i \(0.464256\pi\)
\(774\) 0 0
\(775\) 606.660i 0.782787i
\(776\) 192.528 + 747.663i 0.248103 + 0.963483i
\(777\) 0 0
\(778\) 46.0066 169.490i 0.0591345 0.217853i
\(779\) −351.917 + 203.179i −0.451755 + 0.260821i
\(780\) 0 0
\(781\) 106.184 183.916i 0.135959 0.235488i
\(782\) 23.5065 23.3539i