Properties

Label 108.3.f.c.19.4
Level 108
Weight 3
Character 108.19
Analytic conductor 2.943
Analytic rank 0
Dimension 16
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 19.4
Root \(-0.523926 - 1.93016i\) 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.91.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.523926 - 1.93016i) q^{2} +(-3.45100 + 2.02252i) q^{4} +(4.03104 + 6.98197i) q^{5} +(3.90254 + 2.25313i) q^{7} +(5.71184 + 5.60133i) q^{8} +O(q^{10})\) \(q+(-0.523926 - 1.93016i) q^{2} +(-3.45100 + 2.02252i) q^{4} +(4.03104 + 6.98197i) q^{5} +(3.90254 + 2.25313i) q^{7} +(5.71184 + 5.60133i) q^{8} +(11.3643 - 11.4386i) q^{10} +(3.25842 + 1.88125i) q^{11} +(-3.52605 - 6.10730i) q^{13} +(2.30426 - 8.71299i) q^{14} +(7.81885 - 13.9594i) q^{16} -0.517890 q^{17} +16.4164i q^{19} +(-28.0323 - 15.9420i) q^{20} +(1.92394 - 7.27490i) q^{22} +(27.7049 - 15.9954i) q^{23} +(-19.9986 + 34.6387i) q^{25} +(-9.94065 + 10.0056i) q^{26} +(-18.0247 + 0.117384i) q^{28} +(-9.48394 + 16.4267i) q^{29} +(13.1355 - 7.58377i) q^{31} +(-31.0404 - 7.77790i) q^{32} +(0.271336 + 0.999608i) q^{34} +36.3299i q^{35} +0.592061 q^{37} +(31.6863 - 8.60099i) q^{38} +(-16.0836 + 62.4591i) q^{40} +(-12.3766 - 21.4369i) q^{41} +(-27.8686 - 16.0900i) q^{43} +(-15.0497 + 0.0980099i) q^{44} +(-45.3890 - 45.0944i) q^{46} +(-52.4682 - 30.2925i) q^{47} +(-14.3468 - 24.8493i) q^{49} +(77.3358 + 20.4524i) q^{50} +(24.5205 + 13.9448i) q^{52} +0.664765 q^{53} +30.3336i q^{55} +(9.67017 + 34.7290i) q^{56} +(36.6749 + 9.69913i) q^{58} +(-30.5921 + 17.6623i) q^{59} +(33.7750 - 58.5000i) q^{61} +(-21.5199 - 21.3802i) q^{62} +(1.25029 + 63.9878i) q^{64} +(28.4273 - 49.2376i) q^{65} +(74.4692 - 42.9948i) q^{67} +(1.78724 - 1.04744i) q^{68} +(70.1224 - 19.0342i) q^{70} -56.4434i q^{71} +131.921 q^{73} +(-0.310196 - 1.14277i) q^{74} +(-33.2025 - 56.6532i) q^{76} +(8.47743 + 14.6833i) q^{77} +(-126.869 - 73.2481i) q^{79} +(128.982 - 1.68005i) q^{80} +(-34.8921 + 35.1201i) q^{82} +(87.1029 + 50.2889i) q^{83} +(-2.08764 - 3.61589i) q^{85} +(-16.4550 + 62.2207i) q^{86} +(8.07410 + 28.9969i) q^{88} +25.8362 q^{89} -31.7786i q^{91} +(-63.2587 + 111.234i) q^{92} +(-30.9798 + 117.143i) q^{94} +(-114.619 + 66.1754i) q^{95} +(-48.2534 + 83.5773i) q^{97} +(-40.4465 + 40.7107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + O(q^{10}) \) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + 20q^{10} - 46q^{13} + 12q^{14} - 17q^{16} - 12q^{17} - 36q^{20} + 33q^{22} - 30q^{25} - 72q^{26} + 12q^{28} - 42q^{29} - 87q^{32} + 11q^{34} + 56q^{37} + 99q^{38} + 68q^{40} - 84q^{41} + 222q^{44} - 264q^{46} + 58q^{49} + 219q^{50} + 110q^{52} + 72q^{53} - 270q^{56} - 16q^{58} - 34q^{61} - 516q^{62} - 254q^{64} + 30q^{65} - 375q^{68} + 150q^{70} + 116q^{73} + 372q^{74} - 15q^{76} + 330q^{77} + 720q^{80} + 254q^{82} - 140q^{85} + 273q^{86} + 75q^{88} + 384q^{89} - 258q^{92} + 36q^{94} - 148q^{97} - 1170q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.523926 1.93016i −0.261963 0.965078i
\(3\) 0 0
\(4\) −3.45100 + 2.02252i −0.862751 + 0.505629i
\(5\) 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 0.752144 0.658999i \(-0.229020\pi\)
−0.194638 + 0.980875i \(0.562353\pi\)
\(8\) 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 0.640744 0.767755i \(-0.278626\pi\)
−0.344523 + 0.938778i \(0.611959\pi\)
\(12\) 0 0
\(13\) −3.52605 6.10730i −0.271235 0.469792i 0.697944 0.716153i \(-0.254099\pi\)
−0.969178 + 0.246361i \(0.920765\pi\)
\(14\) 2.30426 8.71299i 0.164590 0.622357i
\(15\) 0 0
\(16\) 7.81885 13.9594i 0.488678 0.872464i
\(17\) −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 \(0.142196\pi\)
−0.901868 + 0.432012i \(0.857804\pi\)
\(20\) −28.0323 15.9420i −1.40162 0.797098i
\(21\) 0 0
\(22\) 1.92394 7.27490i 0.0874517 0.330677i
\(23\) 27.7049 15.9954i 1.20456 0.695454i 0.242996 0.970027i \(-0.421870\pi\)
0.961566 + 0.274573i \(0.0885366\pi\)
\(24\) 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 −0.272945 0.962030i \(-0.587998\pi\)
0.696670 + 0.717392i \(0.254664\pi\)
\(32\) −31.0404 7.77790i −0.970011 0.243059i
\(33\) 0 0
\(34\) 0.271336 + 0.999608i 0.00798047 + 0.0294002i
\(35\) 36.3299i 1.03800i
\(36\) 0 0
\(37\) 0.592061 0.0160017 0.00800083 0.999968i \(-0.497453\pi\)
0.00800083 + 0.999968i \(0.497453\pi\)
\(38\) 31.6863 8.60099i 0.833850 0.226342i
\(39\) 0 0
\(40\) −16.0836 + 62.4591i −0.402091 + 1.56148i
\(41\) −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 0.139623 0.990205i \(-0.455411\pi\)
−0.787731 + 0.616020i \(0.788744\pi\)
\(44\) −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 −0.175879 0.984412i \(-0.556277\pi\)
−0.940465 + 0.339890i \(0.889610\pi\)
\(48\) 0 0
\(49\) −14.3468 24.8493i −0.292791 0.507129i
\(50\) 77.3358 + 20.4524i 1.54672 + 0.409048i
\(51\) 0 0
\(52\) 24.5205 + 13.9448i 0.471548 + 0.268169i
\(53\) 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
\(56\) 9.67017 + 34.7290i 0.172682 + 0.620160i
\(57\) 0 0
\(58\) 36.6749 + 9.69913i 0.632326 + 0.167226i
\(59\) −30.5921 + 17.6623i −0.518510 + 0.299362i −0.736325 0.676628i \(-0.763440\pi\)
0.217815 + 0.975990i \(0.430107\pi\)
\(60\) 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 0.172269 0.985050i \(-0.444890\pi\)
0.939213 + 0.343336i \(0.111557\pi\)
\(68\) 1.78724 1.04744i 0.0262829 0.0154035i
\(69\) 0 0
\(70\) 70.1224 19.0342i 1.00175 0.271917i
\(71\) 56.4434i 0.794977i −0.917607 0.397489i \(-0.869882\pi\)
0.917607 0.397489i \(-0.130118\pi\)
\(72\) 0 0
\(73\) 131.921 1.80713 0.903567 0.428447i \(-0.140939\pi\)
0.903567 + 0.428447i \(0.140939\pi\)
\(74\) −0.310196 1.14277i −0.00419184 0.0154429i
\(75\) 0 0
\(76\) −33.2025 56.6532i −0.436875 0.745437i
\(77\) 8.47743 + 14.6833i 0.110096 + 0.190693i
\(78\) 0 0
\(79\) −126.869 73.2481i −1.60594 0.927191i −0.990265 0.139192i \(-0.955549\pi\)
−0.615677 0.787999i \(1.28888\pi\)
\(80\) 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 0.922491 0.386020i \(-0.126150\pi\)
0.126942 + 0.991910i \(0.459484\pi\)
\(84\) 0 0
\(85\) −2.08764 3.61589i −0.0245604 0.0425399i
\(86\) −16.4550 + 62.2207i −0.191338 + 0.723497i
\(87\) 0 0
\(88\) 8.07410 + 28.9969i 0.0917511 + 0.329510i
\(89\) 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
\(92\) −63.2587 + 111.234i −0.687595 + 1.20907i
\(93\) 0 0
\(94\) −30.9798 + 117.143i −0.329573 + 1.24620i
\(95\) −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 −0.964459 0.264233i \(-0.914881\pi\)
−0.253397 + 0.967362i \(0.581548\pi\)
\(104\) 14.0687 54.6345i 0.135276 0.525331i
\(105\) 0 0
\(106\) −0.348288 1.28310i −0.00328573 0.0121047i
\(107\) 54.9861i 0.513889i −0.966426 0.256944i \(-0.917284\pi\)
0.966426 0.256944i \(-0.0827158\pi\)
\(108\) 0 0
\(109\) −63.9235 −0.586454 −0.293227 0.956043i \(-0.594729\pi\)
−0.293227 + 0.956043i \(0.594729\pi\)
\(110\) 58.5487 15.8926i 0.532261 0.144478i
\(111\) 0 0
\(112\) 61.9659 36.8603i 0.553267 0.329110i
\(113\) −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
\(122\) −130.610 34.5413i −1.07057 0.283126i
\(123\) 0 0
\(124\) −29.9923 + 52.7383i −0.241873 + 0.425309i
\(125\) −120.909 −0.967276
\(126\) 0 0
\(127\) 9.81219i 0.0772613i −0.999254 0.0386307i \(-0.987700\pi\)
0.999254 0.0386307i \(-0.0122996\pi\)
\(128\) 122.851 35.9381i 0.959776 0.280766i
\(129\) 0 0
\(130\) −109.930 29.0723i −0.845615 0.223633i
\(131\) 101.561 58.6365i 0.775278 0.447607i −0.0594761 0.998230i \(-0.518943\pi\)
0.834754 + 0.550623i \(0.185610\pi\)
\(132\) 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 0.0620009 0.998076i \(-0.480252\pi\)
0.895360 + 0.445344i \(0.146919\pi\)
\(140\) −73.4779 125.375i −0.524842 0.895534i
\(141\) 0 0
\(142\) −108.945 + 29.5721i −0.767215 + 0.208255i
\(143\) 26.5335i 0.185549i
\(144\) 0 0
\(145\) −152.921 −1.05463
\(146\) −69.1167 254.628i −0.473402 1.74403i
\(147\) 0 0
\(148\) −2.04321 + 1.19745i −0.0138054 + 0.00809091i
\(149\) 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 0.375958 0.926637i \(-0.377314\pi\)
−0.614512 + 0.788908i \(0.710647\pi\)
\(152\) −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 \(0.577857\pi\)
\(158\) −74.9101 + 283.254i −0.474114 + 1.79275i
\(159\) 0 0
\(160\) −70.8200 248.076i −0.442625 1.55048i
\(161\) 144.160 0.895401
\(162\) 0 0
\(163\) 125.175i 0.767945i 0.923344 + 0.383973i \(0.125444\pi\)
−0.923344 + 0.383973i \(0.874556\pi\)
\(164\) 86.0681 + 48.9469i 0.524805 + 0.298457i
\(165\) 0 0
\(166\) 51.4299 194.470i 0.309819 1.17151i
\(167\) 154.373 89.1274i 0.924390 0.533697i 0.0393573 0.999225i \(-0.487469\pi\)
0.885033 + 0.465528i \(0.154136\pi\)
\(168\) 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
\(176\) 51.7383 30.7765i 0.293968 0.174866i
\(177\) 0 0
\(178\) −13.5363 49.8680i −0.0760465 0.280157i
\(179\) 276.827i 1.54652i 0.634088 + 0.773261i \(0.281376\pi\)
−0.634088 + 0.773261i \(0.718624\pi\)
\(180\) 0 0
\(181\) −104.729 −0.578612 −0.289306 0.957237i \(-0.593425\pi\)
−0.289306 + 0.957237i \(0.593425\pi\)
\(182\) −61.3377 + 16.6497i −0.337021 + 0.0914816i
\(183\) 0 0
\(184\) 247.842 + 63.8209i 1.34697 + 0.346852i
\(185\) 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 −0.0990389 0.995084i \(-0.531577\pi\)
−0.911287 + 0.411772i \(0.864910\pi\)
\(192\) 0 0
\(193\) 56.6790 + 98.1709i 0.293674 + 0.508657i 0.974675 0.223624i \(-0.0717888\pi\)
−0.681002 + 0.732282i \(0.738455\pi\)
\(194\) 186.598 + 49.3482i 0.961847 + 0.254372i
\(195\) 0 0
\(196\) 99.7690 + 56.7386i 0.509025 + 0.289482i
\(197\) 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 \(-0.933752\pi\)
0.978420 0.206624i \(-0.0662477\pi\)
\(200\) −308.252 + 85.8317i −1.54126 + 0.429158i
\(201\) 0 0
\(202\) −83.7605 22.1515i −0.414656 0.109661i
\(203\) −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 −0.705088 0.709120i \(-0.749093\pi\)
0.261572 + 0.965184i \(0.415759\pi\)
\(212\) −2.29411 + 1.34450i −0.0108213 + 0.00634198i
\(213\) 0 0
\(214\) −106.132 + 28.8086i −0.495943 + 0.134620i
\(215\) 259.437i 1.20668i
\(216\) 0 0
\(217\) 68.3490 0.314972
\(218\) 33.4912 + 123.382i 0.153629 + 0.565974i
\(219\) 0 0
\(220\) −61.3503 104.682i −0.278865 0.475825i
\(221\) 1.82611 + 3.16291i 0.00826292 + 0.0143118i
\(222\) 0 0
\(223\) 141.400 + 81.6371i 0.634079 + 0.366086i 0.782330 0.622864i \(-0.214031\pi\)
−0.148251 + 0.988950i \(0.547364\pi\)
\(224\) −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 0.520925 0.853602i \(-0.325587\pi\)
−0.478779 + 0.877936i \(0.658920\pi\)
\(228\) 0 0
\(229\) −16.1725 28.0116i −0.0706222 0.122321i 0.828552 0.559912i \(-0.189165\pi\)
−0.899174 + 0.437591i \(0.855832\pi\)
\(230\) 131.883 498.683i 0.573403 2.16818i
\(231\) 0 0
\(232\) −146.182 + 40.7039i −0.630094 + 0.175448i
\(233\) −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
\(236\) 69.8510 122.826i 0.295979 0.520448i
\(237\) 0 0
\(238\) −1.19335 + 4.51237i −0.00501408 + 0.0189595i
\(239\) −39.6432 + 22.8880i −0.165871 + 0.0957658i −0.580638 0.814162i \(-0.697197\pi\)
0.414766 + 0.909928i \(0.363863\pi\)
\(240\) 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
\(248\) 117.507 + 30.2588i 0.473818 + 0.122011i
\(249\) 0 0
\(250\) 63.3476 + 233.374i 0.253390 + 0.933496i
\(251\) 282.587i 1.12585i 0.826510 + 0.562923i \(0.190323\pi\)
−0.826510 + 0.562923i \(0.809677\pi\)
\(252\) 0 0
\(253\) 120.366 0.475754
\(254\) −18.9391 + 5.14086i −0.0745632 + 0.0202396i
\(255\) 0 0
\(256\) −133.731 218.293i −0.522387 0.852708i
\(257\) −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 0.0806619 0.996742i \(-0.474297\pi\)
−0.822873 + 0.568226i \(0.807630\pi\)
\(264\) 0 0
\(265\) 2.67970 + 4.64138i 0.0101121 + 0.0175146i
\(266\) 143.036 + 37.8277i 0.537730 + 0.142209i
\(267\) 0 0
\(268\) −170.036 + 298.991i −0.634462 + 1.11564i
\(269\) −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 \(0.0331633\pi\)
−0.994578 + 0.103997i \(0.966837\pi\)
\(272\) −4.04931 + 7.22945i −0.0148872 + 0.0265788i
\(273\) 0 0
\(274\) 485.725 + 128.456i 1.77272 + 0.468817i
\(275\) −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 −0.847719 0.530446i \(-0.822024\pi\)
0.0355207 + 0.999369i \(0.488691\pi\)
\(284\) 114.158 + 194.786i 0.401964 + 0.685867i
\(285\) 0 0
\(286\) −51.2139 + 13.9016i −0.179070 + 0.0486070i
\(287\) 111.544i 0.388656i
\(288\) 0 0
\(289\) −288.732 −0.999072
\(290\) 80.1191 + 295.161i 0.276273 + 1.01780i
\(291\) 0 0
\(292\) −455.259 + 266.812i −1.55911 + 0.913740i
\(293\) −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
\(302\) −21.2689 + 80.4232i −0.0704269 + 0.266302i
\(303\) 0 0
\(304\) 229.164 + 128.358i 0.753829 + 0.422229i
\(305\) 544.594 1.78555
\(306\) 0 0
\(307\) 259.968i 0.846801i 0.905943 + 0.423401i \(0.139164\pi\)
−0.905943 + 0.423401i \(0.860836\pi\)
\(308\) −58.9529 33.5265i −0.191406 0.108852i
\(309\) 0 0
\(310\) 62.5283 236.436i 0.201704 0.762695i
\(311\) −16.5959 + 9.58164i −0.0533630 + 0.0308091i −0.526444 0.850210i \(-0.676475\pi\)
0.473081 + 0.881019i \(0.343142\pi\)
\(312\) 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
\(320\) −441.721 + 266.667i −1.38038 + 0.833335i
\(321\) 0 0
\(322\) −75.5289 278.250i −0.234562 0.864132i
\(323\) 8.50191i 0.0263217i
\(324\) 0 0
\(325\) 282.065 0.867892
\(326\) 241.607 65.5824i 0.741127 0.201173i
\(327\) 0 0
\(328\) 49.3818 191.769i 0.150554 0.584662i
\(329\) −136.506 236.436i −0.414912 0.718649i
\(330\) 0 0
\(331\) 51.7490 + 29.8773i 0.156341 + 0.0902638i 0.576130 0.817358i \(-0.304562\pi\)
−0.419788 + 0.907622i \(0.637896\pi\)
\(332\) −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 \(0.601448\pi\)
\(338\) −230.608 60.9870i −0.682271 0.180435i
\(339\) 0 0
\(340\) 14.5177 + 8.25618i 0.0426990 + 0.0242829i
\(341\) 57.0679 0.167355
\(342\) 0 0
\(343\) 350.108i 1.02072i
\(344\) −69.0561 248.004i −0.200744 0.720943i
\(345\) 0 0
\(346\) −292.312 77.3056i −0.844833 0.223426i
\(347\) 500.441 288.930i 1.44219 0.832651i 0.444198 0.895929i \(-0.353489\pi\)
0.997996 + 0.0632779i \(0.0201555\pi\)
\(348\) 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
\(356\) −89.1609 + 52.2542i −0.250452 + 0.146782i
\(357\) 0 0
\(358\) 534.320 145.037i 1.49251 0.405131i
\(359\) 292.754i 0.815470i 0.913100 + 0.407735i \(0.133681\pi\)
−0.913100 + 0.407735i \(0.866319\pi\)
\(360\) 0 0
\(361\) 91.5006 0.253464
\(362\) 54.8701 + 202.143i 0.151575 + 0.558406i
\(363\) 0 0
\(364\) 64.2728 + 109.668i 0.176574 + 0.301286i
\(365\) 531.779 + 921.067i 1.45693 + 2.52347i
\(366\) 0 0
\(367\) 378.870 + 218.741i 1.03234 + 0.596024i 0.917655 0.397377i \(-0.130080\pi\)
0.114689 + 0.993401i \(0.463413\pi\)
\(368\) −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 \(-0.561901\pi\)
\(374\) −0.996388 + 3.76760i −0.00266414 + 0.0100738i
\(375\) 0 0
\(376\) −130.012 466.917i −0.345776 1.24180i
\(377\) 133.763 0.354810
\(378\) 0 0
\(379\) 541.432i 1.42858i 0.699850 + 0.714290i \(0.253250\pi\)
−0.699850 + 0.714290i \(0.746750\pi\)
\(380\) 261.710 460.191i 0.688711 1.21103i
\(381\) 0 0
\(382\) −113.941 + 430.838i −0.298274 + 1.12785i
\(383\) −311.941 + 180.099i −0.814467 + 0.470233i −0.848505 0.529188i \(-0.822497\pi\)
0.0340377 + 0.999421i \(0.489163\pi\)
\(384\) 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
\(392\) 57.2428 222.296i 0.146027 0.567083i
\(393\) 0 0
\(394\) −63.3937 233.544i −0.160898 0.592751i
\(395\) 1181.07i 2.99004i
\(396\) 0 0
\(397\) −48.4128 −0.121947 −0.0609733 0.998139i \(-0.519420\pi\)
−0.0609733 + 0.998139i \(0.519420\pi\)
\(398\) −158.729 + 43.0858i −0.398817 + 0.108256i
\(399\) 0 0
\(400\) 327.169 + 550.004i 0.817924 + 1.37501i
\(401\) −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 \(0.854451\pi\)
\(410\) −385.859 102.045i −0.941119 0.248891i
\(411\) 0 0
\(412\) 286.415 503.632i 0.695183 1.22241i
\(413\) −159.182 −0.385430
\(414\) 0 0
\(415\) 810.867i 1.95390i
\(416\) 61.9479 + 216.998i 0.148913 + 0.521630i
\(417\) 0 0
\(418\) 119.428 + 31.5842i 0.285713 + 0.0755603i
\(419\) −552.029 + 318.714i −1.31749 + 0.760655i −0.983325 0.181859i \(-0.941789\pi\)
−0.334168 + 0.942514i \(0.608455\pi\)
\(420\) 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
\(428\) 111.210 + 189.757i 0.259837 + 0.443358i
\(429\) 0 0
\(430\) −500.754 + 135.926i −1.16454 + 0.316107i
\(431\) 481.190i 1.11645i 0.829689 + 0.558225i \(0.188518\pi\)
−0.829689 + 0.558225i \(0.811482\pi\)
\(432\) 0 0
\(433\) −360.347 −0.832209 −0.416105 0.909317i \(-0.636605\pi\)
−0.416105 + 0.909317i \(0.636605\pi\)
\(434\) −35.8098 131.924i −0.0825110 0.303973i
\(435\) 0 0
\(436\) 220.600 129.286i 0.505964 0.296528i
\(437\) 262.588 + 454.816i 0.600888 + 1.04077i
\(438\) 0 0
\(439\) −488.267 281.901i −1.11223 0.642144i −0.172821 0.984953i \(-0.555288\pi\)
−0.939405 + 0.342809i \(0.888622\pi\)
\(440\) −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 0.978027 0.208478i \(-0.0668509\pi\)
0.308467 + 0.951235i \(0.400184\pi\)
\(444\) 0 0
\(445\) 104.147 + 180.388i 0.234038 + 0.405366i
\(446\) 83.4895 315.695i 0.187196 0.707837i
\(447\) 0 0
\(448\) −139.294 + 252.532i −0.310924 + 0.563688i
\(449\) −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
\(452\) 123.950 + 70.4901i 0.274225 + 0.155951i
\(453\) 0 0
\(454\) 5.64897 21.3602i 0.0124427 0.0470489i
\(455\) 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 −0.00605956 0.999982i \(-0.501929\pi\)
0.862980 + 0.505239i \(0.168595\pi\)
\(464\) 155.153 + 260.828i 0.334382 + 0.562129i
\(465\) 0 0
\(466\) 94.8565 + 349.454i 0.203555 + 0.749900i
\(467\) 204.395i 0.437677i 0.975761 + 0.218838i \(0.0702267\pi\)
−0.975761 + 0.218838i \(0.929773\pi\)
\(468\) 0 0
\(469\) 387.493 0.826210
\(470\) −942.769 + 255.907i −2.00589 + 0.544483i
\(471\) 0 0
\(472\) −273.670 70.4717i −0.579808 0.149304i
\(473\) −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 0.579654 0.814863i \(-0.303188\pi\)
−0.415865 + 0.909426i \(0.636521\pi\)
\(480\) 0 0
\(481\) −2.08764 3.61589i −0.00434020 0.00751745i
\(482\) −654.367 173.055i −1.35761 0.359036i
\(483\) 0 0
\(484\) 371.501 + 211.272i 0.767563 + 0.436513i
\(485\) −778.046 −1.60422
\(486\) 0 0
\(487\) 301.289i 0.618663i −0.950954 0.309332i \(-0.899895\pi\)
0.950954 0.309332i \(-0.100105\pi\)
\(488\) 520.595 144.958i 1.06679 0.297045i
\(489\) 0 0
\(490\) −447.283 118.289i −0.912822 0.241407i
\(491\) 389.556 224.911i 0.793394 0.458066i −0.0477620 0.998859i \(-0.515209\pi\)
0.841156 + 0.540792i \(0.181876\pi\)
\(492\) 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 −0.938174 0.346163i \(-0.887484\pi\)
−0.169301 + 0.985564i \(0.554151\pi\)
\(500\) 417.259 244.541i 0.834518 0.489083i
\(501\) 0 0
\(502\) 545.437 148.055i 1.08653 0.294930i
\(503\) 182.179i 0.362185i −0.983466 0.181093i \(-0.942037\pi\)
0.983466 0.181093i \(-0.0579634\pi\)
\(504\) 0 0
\(505\) 349.250 0.691585
\(506\) −63.0628 232.325i −0.124630 0.459140i
\(507\) 0 0
\(508\) 19.8453 + 33.8619i 0.0390656 + 0.0666573i
\(509\) −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
\(518\) 1.36426 5.15863i 0.00263371 0.00995874i
\(519\) 0 0
\(520\) 438.168 122.007i 0.842631 0.234628i
\(521\) 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 \(-0.829179\pi\)
0.859426 0.511259i \(-0.170821\pi\)
\(524\) −231.896 + 407.765i −0.442549 + 0.778177i
\(525\) 0 0
\(526\) −115.257 + 435.815i −0.219119 + 0.828546i
\(527\) −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
\(536\) 666.185 + 171.547i 1.24288 + 0.320050i
\(537\) 0 0
\(538\) 223.092 + 821.876i 0.414669 + 1.52765i
\(539\) 107.960i 0.200296i
\(540\) 0 0
\(541\) −61.0097 −0.112772 −0.0563860 0.998409i \(-0.517958\pi\)
−0.0563860 + 0.998409i \(0.517958\pi\)
\(542\) 108.796 29.5319i 0.200731 0.0544869i
\(543\) 0 0
\(544\) 16.0755 + 4.02810i 0.0295505 + 0.00740459i
\(545\) −257.678 446.312i −0.472805 0.818921i
\(546\) 0 0
\(547\) −104.430 60.2925i −0.190914 0.110224i 0.401497 0.915861i \(-0.368490\pi\)
−0.592410 + 0.805637i \(0.701823\pi\)
\(548\) −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
\(554\) 810.694 + 214.398i 1.46335 + 0.387000i
\(555\) 0 0
\(556\) −303.846 + 534.283i −0.546486 + 0.960940i
\(557\) 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
\(560\) 507.145 + 284.058i 0.905616 + 0.507247i
\(561\) 0 0
\(562\) −286.022 75.6420i −0.508936 0.134594i
\(563\) −595.478 + 343.800i −1.05769 + 0.610656i −0.924792 0.380474i \(-0.875761\pi\)
−0.132896 + 0.991130i \(0.542428\pi\)
\(564\) 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 −0.980387 0.197081i \(-0.936854\pi\)
−0.319517 + 0.947581i \(0.603521\pi\)
\(572\) 53.6645 + 91.5674i 0.0938191 + 0.160083i
\(573\) 0 0
\(574\) −215.298 + 58.4410i −0.375084 + 0.101814i
\(575\) 1279.55i 2.22530i
\(576\) 0 0
\(577\) 871.732 1.51080 0.755401 0.655263i \(-0.227442\pi\)
0.755401 + 0.655263i \(0.227442\pi\)
\(578\) 151.274 + 557.297i 0.261720 + 0.964182i
\(579\) 0 0
\(580\) 527.730 309.285i 0.909880 0.533250i
\(581\) 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 −0.233725 0.972303i \(-0.575091\pi\)
−0.958901 + 0.283740i \(0.908425\pi\)
\(588\) 0 0
\(589\) 124.498 + 215.638i 0.211373 + 0.366108i
\(590\) −145.626 + 550.651i −0.246824 + 0.933306i
\(591\) 0 0
\(592\) 4.62924 8.26484i 0.00781966 0.0139609i
\(593\) 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
\(596\) −318.945 181.384i −0.535143 0.304336i
\(597\) 0 0
\(598\) −115.361 + 436.209i −0.192911 + 0.729447i
\(599\) 684.932 395.445i 1.14346 0.660176i 0.196174 0.980569i \(-0.437148\pi\)
0.947285 + 0.320393i \(0.103815\pi\)
\(600\) 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 0.486953 0.873428i \(-0.338108\pi\)
0.999887 + 0.0150003i \(0.00477491\pi\)
\(608\) 127.685 509.572i 0.210009 0.838112i
\(609\) 0 0
\(610\) −285.327 1051.15i −0.467749 1.72320i
\(611\) 427.251i 0.699266i
\(612\) 0 0
\(613\) 256.336 0.418166 0.209083 0.977898i \(-0.432952\pi\)
0.209083 + 0.977898i \(0.432952\pi\)
\(614\) 501.779 136.204i 0.817229 0.221831i
\(615\) 0 0
\(616\) −33.8244 + 131.354i −0.0549098 + 0.213237i
\(617\) 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 −0.142355 0.989816i \(-0.545468\pi\)
−0.928383 + 0.371624i \(0.878801\pi\)
\(620\) −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
\(626\) 84.8268 + 22.4335i 0.135506 + 0.0358362i
\(627\) 0 0
\(628\) −785.183 446.533i −1.25029 0.711040i
\(629\) −0.306623 −0.000487477
\(630\) 0 0
\(631\) 719.756i 1.14066i −0.821416 0.570330i \(-0.806815\pi\)
0.821416 0.570330i \(-0.193185\pi\)
\(632\) −314.372 1129.02i −0.497423 1.78642i
\(633\) 0 0
\(634\) 266.707 + 70.5338i 0.420673 + 0.111252i
\(635\) 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 −0.839554 0.543276i \(-0.817184\pi\)
0.0507136 + 0.998713i \(0.483850\pi\)
\(644\) −497.495 + 291.565i −0.772508 + 0.452741i
\(645\) 0 0
\(646\) −16.4100 + 4.45437i −0.0254025 + 0.00689531i
\(647\) 791.553i 1.22342i −0.791082 0.611710i \(-0.790482\pi\)
0.791082 0.611710i \(-0.209518\pi\)
\(648\) 0 0
\(649\) −132.909 −0.204791
\(650\) −147.781 544.429i −0.227355 0.837583i
\(651\) 0 0
\(652\) −253.169 431.980i −0.388296 0.662545i
\(653\) 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 0.755285 0.655397i \(-0.227499\pi\)
−0.189948 + 0.981794i \(0.560832\pi\)
\(660\) 0 0
\(661\) 453.865 + 786.117i 0.686633 + 1.18928i 0.972920 + 0.231140i \(0.0742456\pi\)
−0.286287 + 0.958144i \(0.592421\pi\)
\(662\) 30.5552 115.537i 0.0461559 0.174527i
\(663\) 0 0
\(664\) 215.834 + 775.134i 0.325051 + 1.16737i
\(665\) −596.408 −0.896854
\(666\) 0 0
\(667\) 606.799i 0.909744i
\(668\) −352.481 + 619.801i −0.527666 + 0.927846i
\(669\) 0 0
\(670\) 354.493 1340.43i 0.529094 2.00064i
\(671\) 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
\(680\) 8.32955 32.3470i 0.0122493 0.0475691i
\(681\) 0 0
\(682\) −29.8993 110.150i −0.0438407 0.161510i
\(683\) 522.729i 0.765343i −0.923884 0.382672i \(-0.875004\pi\)
0.923884 0.382672i \(-0.124996\pi\)
\(684\) 0 0
\(685\) −2025.29 −2.95663
\(686\) −675.763 + 183.431i −0.985077 + 0.267392i
\(687\) 0 0
\(688\) −442.507 + 263.225i −0.643179 + 0.382594i
\(689\) −2.34400 4.05992i −0.00340203 0.00589248i
\(690\) 0 0
\(691\) 485.917 + 280.544i 0.703208 + 0.405997i 0.808541 0.588440i \(-0.200258\pi\)
−0.105333 + 0.994437i \(0.533591\pi\)
\(692\) 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
\(698\) −255.733 67.6316i −0.366379 0.0968934i
\(699\) 0 0
\(700\) 356.403 626.699i 0.509148 0.895284i
\(701\) −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
\(704\) −116.303 + 210.851i −0.165203 + 0.299505i
\(705\) 0 0
\(706\) 1046.28 + 276.701i 1.48198 + 0.391928i
\(707\) 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
\(716\) −559.888 955.332i −0.781966 1.33426i
\(717\) 0 0
\(718\) 565.061 153.381i 0.786993 0.213623i
\(719\) 53.0278i 0.0737521i 0.999320 + 0.0368760i \(0.0117407\pi\)
−0.999320 + 0.0368760i \(0.988259\pi\)
\(720\) 0 0
\(721\) −652.709 −0.905282
\(722\) −47.9395 176.610i −0.0663982 0.244613i
\(723\) 0 0
\(724\) 361.419 211.816i 0.499198 0.292563i
\(725\) −379.332 657.022i −0.523216 0.906238i
\(726\) 0 0
\(727\) 436.956 + 252.277i 0.601041 + 0.347011i 0.769451 0.638706i \(-0.220530\pi\)
−0.168410 + 0.985717i \(0.553863\pi\)
\(728\) 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 \(0.643881\pi\)
\(734\) 223.704 845.883i 0.304774 1.15243i
\(735\) 0 0
\(736\) −984.382 + 281.018i −1.33748 + 0.381818i
\(737\) 323.536 0.438991
\(738\) 0 0
\(739\) 190.298i 0.257507i 0.991677 + 0.128754i \(0.0410977\pi\)
−0.991677 + 0.128754i \(0.958902\pi\)
\(740\) −16.5969 9.43862i −0.0224282 0.0127549i
\(741\) 0 0
\(742\) 1.53179 5.79210i 0.00206441 0.00780606i
\(743\) −664.128 + 383.435i −0.893847 + 0.516063i −0.875199 0.483763i \(-0.839270\pi\)
−0.0186481 + 0.999826i \(0.505936\pi\)
\(744\) 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 −0.804315 0.594202i \(-0.797468\pi\)
0.112437 + 0.993659i \(0.464134\pi\)
\(752\) −833.107 + 495.573i −1.10785 + 0.659006i
\(753\) 0 0
\(754\) −70.0821 258.184i −0.0929471 0.342419i
\(755\) 335.335i 0.444152i
\(756\) 0 0
\(757\) −343.082 −0.453213 −0.226606 0.973986i \(-0.572763\pi\)
−0.226606 + 0.973986i \(0.572763\pi\)
\(758\) 1045.05 283.670i 1.37869 0.374235i
\(759\) 0 0
\(760\) −1025.36 264.036i −1.34915 0.347416i
\(761\) 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 \(-0.374012\pi\)
\(770\) 264.297 + 69.8965i 0.343243 + 0.0907747i
\(771\) 0 0
\(772\) −394.152 224.154i −0.510559 0.290355i
\(773\) 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
\(776\) −743.759 + 207.097i −0.958452 + 0.266878i
\(777\) 0 0
\(778\) −169.786 44.9019i −0.218233 0.0577145i
\(779\) 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 0.0300595 + 0.0298644i