Properties

Label 441.2.bg.a.278.4
Level $441$
Weight $2$
Character 441.278
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 278.4
Character \(\chi\) \(=\) 441.278
Dual form 441.2.bg.a.395.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.72508 + 0.677046i) q^{2} +(1.05142 - 0.975576i) q^{4} +(-0.820216 + 0.559214i) q^{5} +(0.202012 - 2.63803i) q^{7} +(0.454856 - 0.944519i) q^{8} +O(q^{10})\) \(q+(-1.72508 + 0.677046i) q^{2} +(1.05142 - 0.975576i) q^{4} +(-0.820216 + 0.559214i) q^{5} +(0.202012 - 2.63803i) q^{7} +(0.454856 - 0.944519i) q^{8} +(1.03633 - 1.52001i) q^{10} +(-0.669436 + 4.44142i) q^{11} +(0.491128 + 0.391661i) q^{13} +(1.43758 + 4.68759i) q^{14} +(-0.359555 + 4.79792i) q^{16} +(-7.67525 + 2.36750i) q^{17} +(0.358138 + 0.206771i) q^{19} +(-0.316837 + 1.38815i) q^{20} +(-1.85221 - 8.11506i) q^{22} +(2.22443 - 7.21144i) q^{23} +(-1.46667 + 3.73702i) q^{25} +(-1.11241 - 0.343133i) q^{26} +(-2.36120 - 2.97076i) q^{28} +(0.523301 + 0.119440i) q^{29} +(-7.47171 + 4.31379i) q^{31} +(-2.01015 - 6.51673i) q^{32} +(11.6376 - 9.28064i) q^{34} +(1.30953 + 2.27672i) q^{35} +(-5.17164 - 4.79859i) q^{37} +(-0.757811 - 0.114222i) q^{38} +(0.155108 + 1.02907i) q^{40} +(-4.20951 - 2.02719i) q^{41} +(-6.50862 + 3.13439i) q^{43} +(3.62908 + 5.32289i) q^{44} +(1.04514 + 13.9464i) q^{46} +(2.32547 + 5.92521i) q^{47} +(-6.91838 - 1.06583i) q^{49} -7.43967i q^{50} +(0.898477 - 0.0673315i) q^{52} +(-1.40866 - 1.51817i) q^{53} +(-1.93462 - 4.01728i) q^{55} +(-2.39978 - 1.39073i) q^{56} +(-0.983605 + 0.148255i) q^{58} +(-10.2496 - 6.98805i) q^{59} +(3.28105 - 3.53613i) q^{61} +(9.96870 - 12.5003i) q^{62} +(1.88011 + 2.35758i) q^{64} +(-0.621853 - 0.0466015i) q^{65} +(1.75271 + 3.03578i) q^{67} +(-5.76024 + 9.97704i) q^{68} +(-3.80049 - 3.04093i) q^{70} +(2.14164 - 0.488815i) q^{71} +(2.40700 + 0.944676i) q^{73} +(12.1704 + 4.77652i) q^{74} +(0.578274 - 0.131987i) q^{76} +(11.5814 + 2.66321i) q^{77} +(-6.85221 + 11.8684i) q^{79} +(-2.38815 - 4.13640i) q^{80} +(8.63426 + 0.647049i) q^{82} +(6.36642 + 7.98324i) q^{83} +(4.97143 - 6.23397i) q^{85} +(9.10580 - 9.81371i) q^{86} +(3.89051 + 2.65250i) q^{88} +(-6.09136 + 0.918124i) q^{89} +(1.13243 - 1.21649i) q^{91} +(-4.69649 - 9.75236i) q^{92} +(-8.02328 - 8.64704i) q^{94} +(-0.409380 + 0.0306788i) q^{95} +12.9594i q^{97} +(12.6564 - 2.84542i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q - 16q^{4} + 2q^{7} + O(q^{10}) \) \( 216q - 16q^{4} + 2q^{7} + 12q^{10} + 12q^{16} - 6q^{19} + 44q^{22} + 26q^{25} + 84q^{28} - 6q^{31} - 112q^{34} + 60q^{37} - 304q^{40} + 20q^{43} - 20q^{46} - 86q^{49} - 168q^{52} - 84q^{55} - 120q^{58} - 2q^{61} + 32q^{64} + 22q^{67} - 136q^{70} - 6q^{73} + 84q^{76} + 2q^{79} - 104q^{82} + 96q^{85} - 12q^{88} + 58q^{91} + 52q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{41}{42}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.72508 + 0.677046i −1.21982 + 0.478744i −0.885908 0.463861i \(-0.846464\pi\)
−0.333911 + 0.942605i \(0.608368\pi\)
\(3\) 0 0
\(4\) 1.05142 0.975576i 0.525710 0.487788i
\(5\) −0.820216 + 0.559214i −0.366812 + 0.250088i −0.732672 0.680582i \(-0.761727\pi\)
0.365860 + 0.930670i \(0.380775\pi\)
\(6\) 0 0
\(7\) 0.202012 2.63803i 0.0763535 0.997081i
\(8\) 0.454856 0.944519i 0.160816 0.333938i
\(9\) 0 0
\(10\) 1.03633 1.52001i 0.327716 0.480671i
\(11\) −0.669436 + 4.44142i −0.201843 + 1.33914i 0.626721 + 0.779244i \(0.284397\pi\)
−0.828564 + 0.559895i \(0.810842\pi\)
\(12\) 0 0
\(13\) 0.491128 + 0.391661i 0.136214 + 0.108627i 0.689227 0.724546i \(-0.257950\pi\)
−0.553012 + 0.833173i \(0.686522\pi\)
\(14\) 1.43758 + 4.68759i 0.384209 + 1.25281i
\(15\) 0 0
\(16\) −0.359555 + 4.79792i −0.0898887 + 1.19948i
\(17\) −7.67525 + 2.36750i −1.86152 + 0.574204i −0.864029 + 0.503441i \(0.832067\pi\)
−0.997493 + 0.0707625i \(0.977457\pi\)
\(18\) 0 0
\(19\) 0.358138 + 0.206771i 0.0821624 + 0.0474365i 0.540518 0.841332i \(-0.318228\pi\)
−0.458356 + 0.888769i \(0.651561\pi\)
\(20\) −0.316837 + 1.38815i −0.0708468 + 0.310400i
\(21\) 0 0
\(22\) −1.85221 8.11506i −0.394892 1.73014i
\(23\) 2.22443 7.21144i 0.463827 1.50369i −0.357874 0.933770i \(-0.616498\pi\)
0.821701 0.569919i \(-0.193025\pi\)
\(24\) 0 0
\(25\) −1.46667 + 3.73702i −0.293334 + 0.747403i
\(26\) −1.11241 0.343133i −0.218161 0.0672939i
\(27\) 0 0
\(28\) −2.36120 2.97076i −0.446224 0.561420i
\(29\) 0.523301 + 0.119440i 0.0971746 + 0.0221795i 0.270832 0.962627i \(-0.412701\pi\)
−0.173657 + 0.984806i \(0.555558\pi\)
\(30\) 0 0
\(31\) −7.47171 + 4.31379i −1.34196 + 0.774780i −0.987095 0.160137i \(-0.948806\pi\)
−0.354864 + 0.934918i \(0.615473\pi\)
\(32\) −2.01015 6.51673i −0.355347 1.15201i
\(33\) 0 0
\(34\) 11.6376 9.28064i 1.99582 1.59162i
\(35\) 1.30953 + 2.27672i 0.221351 + 0.384836i
\(36\) 0 0
\(37\) −5.17164 4.79859i −0.850213 0.788883i 0.129015 0.991643i \(-0.458818\pi\)
−0.979228 + 0.202760i \(0.935009\pi\)
\(38\) −0.757811 0.114222i −0.122933 0.0185292i
\(39\) 0 0
\(40\) 0.155108 + 1.02907i 0.0245247 + 0.162711i
\(41\) −4.20951 2.02719i −0.657415 0.316594i 0.0752690 0.997163i \(-0.476018\pi\)
−0.732684 + 0.680569i \(0.761733\pi\)
\(42\) 0 0
\(43\) −6.50862 + 3.13439i −0.992555 + 0.477989i −0.858406 0.512972i \(-0.828545\pi\)
−0.134150 + 0.990961i \(0.542830\pi\)
\(44\) 3.62908 + 5.32289i 0.547105 + 0.802455i
\(45\) 0 0
\(46\) 1.04514 + 13.9464i 0.154097 + 2.05628i
\(47\) 2.32547 + 5.92521i 0.339205 + 0.864281i 0.994091 + 0.108553i \(0.0346216\pi\)
−0.654885 + 0.755728i \(0.727283\pi\)
\(48\) 0 0
\(49\) −6.91838 1.06583i −0.988340 0.152261i
\(50\) 7.43967i 1.05213i
\(51\) 0 0
\(52\) 0.898477 0.0673315i 0.124596 0.00933720i
\(53\) −1.40866 1.51817i −0.193494 0.208537i 0.628851 0.777525i \(-0.283525\pi\)
−0.822346 + 0.568988i \(0.807335\pi\)
\(54\) 0 0
\(55\) −1.93462 4.01728i −0.260864 0.541690i
\(56\) −2.39978 1.39073i −0.320684 0.185844i
\(57\) 0 0
\(58\) −0.983605 + 0.148255i −0.129154 + 0.0194668i
\(59\) −10.2496 6.98805i −1.33438 0.909767i −0.334911 0.942250i \(-0.608706\pi\)
−0.999472 + 0.0324825i \(0.989659\pi\)
\(60\) 0 0
\(61\) 3.28105 3.53613i 0.420096 0.452756i −0.487174 0.873305i \(-0.661972\pi\)
0.907270 + 0.420549i \(0.138163\pi\)
\(62\) 9.96870 12.5003i 1.26603 1.58755i
\(63\) 0 0
\(64\) 1.88011 + 2.35758i 0.235013 + 0.294697i
\(65\) −0.621853 0.0466015i −0.0771314 0.00578020i
\(66\) 0 0
\(67\) 1.75271 + 3.03578i 0.214127 + 0.370879i 0.953002 0.302963i \(-0.0979759\pi\)
−0.738875 + 0.673843i \(0.764643\pi\)
\(68\) −5.76024 + 9.97704i −0.698532 + 1.20989i
\(69\) 0 0
\(70\) −3.80049 3.04093i −0.454245 0.363460i
\(71\) 2.14164 0.488815i 0.254166 0.0580117i −0.0935395 0.995616i \(-0.529818\pi\)
0.347705 + 0.937604i \(0.386961\pi\)
\(72\) 0 0
\(73\) 2.40700 + 0.944676i 0.281718 + 0.110566i 0.501993 0.864872i \(-0.332600\pi\)
−0.220275 + 0.975438i \(0.570696\pi\)
\(74\) 12.1704 + 4.77652i 1.41478 + 0.555260i
\(75\) 0 0
\(76\) 0.578274 0.131987i 0.0663326 0.0151400i
\(77\) 11.5814 + 2.66321i 1.31982 + 0.303501i
\(78\) 0 0
\(79\) −6.85221 + 11.8684i −0.770934 + 1.33530i 0.166118 + 0.986106i \(0.446877\pi\)
−0.937052 + 0.349191i \(0.886457\pi\)
\(80\) −2.38815 4.13640i −0.267004 0.462464i
\(81\) 0 0
\(82\) 8.63426 + 0.647049i 0.953495 + 0.0714546i
\(83\) 6.36642 + 7.98324i 0.698806 + 0.876275i 0.996934 0.0782513i \(-0.0249336\pi\)
−0.298128 + 0.954526i \(0.596362\pi\)
\(84\) 0 0
\(85\) 4.97143 6.23397i 0.539227 0.676169i
\(86\) 9.10580 9.81371i 0.981903 1.05824i
\(87\) 0 0
\(88\) 3.89051 + 2.65250i 0.414730 + 0.282758i
\(89\) −6.09136 + 0.918124i −0.645683 + 0.0973210i −0.463716 0.885984i \(-0.653484\pi\)
−0.181966 + 0.983305i \(0.558246\pi\)
\(90\) 0 0
\(91\) 1.13243 1.21649i 0.118711 0.127523i
\(92\) −4.69649 9.75236i −0.489643 1.01675i
\(93\) 0 0
\(94\) −8.02328 8.64704i −0.827538 0.891874i
\(95\) −0.409380 + 0.0306788i −0.0420015 + 0.00314757i
\(96\) 0 0
\(97\) 12.9594i 1.31582i 0.753095 + 0.657912i \(0.228560\pi\)
−0.753095 + 0.657912i \(0.771440\pi\)
\(98\) 12.6564 2.84542i 1.27849 0.287430i
\(99\) 0 0
\(100\) 2.10365 + 5.36003i 0.210365 + 0.536003i
\(101\) 0.00754295 + 0.100654i 0.000750552 + 0.0100154i 0.997566 0.0697214i \(-0.0222110\pi\)
−0.996816 + 0.0797369i \(0.974592\pi\)
\(102\) 0 0
\(103\) 0.269415 + 0.395159i 0.0265462 + 0.0389362i 0.839283 0.543696i \(-0.182975\pi\)
−0.812736 + 0.582632i \(0.802023\pi\)
\(104\) 0.593324 0.285730i 0.0581802 0.0280181i
\(105\) 0 0
\(106\) 3.45793 + 1.66525i 0.335863 + 0.161743i
\(107\) −0.0362310 0.240377i −0.00350259 0.0232381i 0.987011 0.160651i \(-0.0513594\pi\)
−0.990514 + 0.137413i \(0.956121\pi\)
\(108\) 0 0
\(109\) 12.8218 + 1.93257i 1.22810 + 0.185107i 0.730875 0.682512i \(-0.239112\pi\)
0.497230 + 0.867619i \(0.334351\pi\)
\(110\) 6.05727 + 5.62032i 0.577538 + 0.535877i
\(111\) 0 0
\(112\) 12.5844 + 1.91776i 1.18912 + 0.181211i
\(113\) 0.781027 0.622848i 0.0734728 0.0585926i −0.586065 0.810264i \(-0.699324\pi\)
0.659538 + 0.751672i \(0.270752\pi\)
\(114\) 0 0
\(115\) 2.20822 + 7.15887i 0.205918 + 0.667568i
\(116\) 0.666733 0.384938i 0.0619046 0.0357406i
\(117\) 0 0
\(118\) 22.4126 + 5.11554i 2.06325 + 0.470924i
\(119\) 4.69504 + 20.7258i 0.430394 + 1.89993i
\(120\) 0 0
\(121\) −8.76676 2.70419i −0.796978 0.245835i
\(122\) −3.26597 + 8.32155i −0.295687 + 0.753398i
\(123\) 0 0
\(124\) −3.64748 + 11.8248i −0.327553 + 1.06190i
\(125\) −1.99130 8.72445i −0.178107 0.780339i
\(126\) 0 0
\(127\) 3.34854 14.6709i 0.297135 1.30183i −0.577237 0.816577i \(-0.695869\pi\)
0.874372 0.485256i \(-0.161274\pi\)
\(128\) 6.97256 + 4.02561i 0.616293 + 0.355817i
\(129\) 0 0
\(130\) 1.10430 0.340632i 0.0968535 0.0298754i
\(131\) −1.56593 + 20.8959i −0.136816 + 1.82568i 0.333007 + 0.942924i \(0.391937\pi\)
−0.469823 + 0.882760i \(0.655682\pi\)
\(132\) 0 0
\(133\) 0.617816 0.903007i 0.0535714 0.0783006i
\(134\) −5.07893 4.05031i −0.438753 0.349893i
\(135\) 0 0
\(136\) −1.25499 + 8.32630i −0.107614 + 0.713974i
\(137\) 1.62029 2.37653i 0.138431 0.203040i −0.750763 0.660572i \(-0.770314\pi\)
0.889193 + 0.457531i \(0.151266\pi\)
\(138\) 0 0
\(139\) 7.02750 14.5927i 0.596064 1.23774i −0.356754 0.934198i \(-0.616116\pi\)
0.952818 0.303542i \(-0.0981693\pi\)
\(140\) 3.59798 + 1.11625i 0.304085 + 0.0943402i
\(141\) 0 0
\(142\) −3.36356 + 2.29323i −0.282263 + 0.192444i
\(143\) −2.06831 + 1.91911i −0.172961 + 0.160484i
\(144\) 0 0
\(145\) −0.496013 + 0.194671i −0.0411916 + 0.0161665i
\(146\) −4.79186 −0.396577
\(147\) 0 0
\(148\) −10.1190 −0.831773
\(149\) 10.5563 4.14306i 0.864809 0.339412i 0.108871 0.994056i \(-0.465276\pi\)
0.755938 + 0.654643i \(0.227181\pi\)
\(150\) 0 0
\(151\) 5.26545 4.88563i 0.428497 0.397587i −0.436225 0.899837i \(-0.643685\pi\)
0.864722 + 0.502251i \(0.167495\pi\)
\(152\) 0.358200 0.244217i 0.0290539 0.0198086i
\(153\) 0 0
\(154\) −21.7819 + 3.24684i −1.75524 + 0.261638i
\(155\) 3.71608 7.71653i 0.298483 0.619807i
\(156\) 0 0
\(157\) 8.37154 12.2788i 0.668121 0.979954i −0.331216 0.943555i \(-0.607459\pi\)
0.999337 0.0363992i \(-0.0115888\pi\)
\(158\) 3.78521 25.1132i 0.301135 1.99790i
\(159\) 0 0
\(160\) 5.29300 + 4.22103i 0.418449 + 0.333702i
\(161\) −18.5746 7.32492i −1.46388 0.577285i
\(162\) 0 0
\(163\) −0.909893 + 12.1417i −0.0712684 + 0.951010i 0.840899 + 0.541192i \(0.182027\pi\)
−0.912167 + 0.409818i \(0.865592\pi\)
\(164\) −6.40365 + 1.97526i −0.500041 + 0.154242i
\(165\) 0 0
\(166\) −16.3876 9.46141i −1.27193 0.734347i
\(167\) −0.136107 + 0.596325i −0.0105323 + 0.0461450i −0.979921 0.199386i \(-0.936105\pi\)
0.969389 + 0.245531i \(0.0789624\pi\)
\(168\) 0 0
\(169\) −2.80496 12.2894i −0.215766 0.945335i
\(170\) −4.35545 + 14.1200i −0.334048 + 1.08296i
\(171\) 0 0
\(172\) −3.78547 + 9.64521i −0.288639 + 0.735441i
\(173\) −13.2392 4.08374i −1.00655 0.310481i −0.252716 0.967541i \(-0.581324\pi\)
−0.753839 + 0.657060i \(0.771800\pi\)
\(174\) 0 0
\(175\) 9.56207 + 4.62404i 0.722824 + 0.349545i
\(176\) −21.0689 4.80884i −1.58813 0.362480i
\(177\) 0 0
\(178\) 9.88649 5.70797i 0.741024 0.427830i
\(179\) 1.47460 + 4.78053i 0.110217 + 0.357313i 0.993831 0.110901i \(-0.0353737\pi\)
−0.883615 + 0.468214i \(0.844897\pi\)
\(180\) 0 0
\(181\) −14.6220 + 11.6606i −1.08684 + 0.866727i −0.991679 0.128735i \(-0.958908\pi\)
−0.0951625 + 0.995462i \(0.530337\pi\)
\(182\) −1.12991 + 2.86525i −0.0837548 + 0.212386i
\(183\) 0 0
\(184\) −5.79954 5.38119i −0.427548 0.396707i
\(185\) 6.92530 + 1.04382i 0.509158 + 0.0767433i
\(186\) 0 0
\(187\) −5.37698 35.6739i −0.393204 2.60874i
\(188\) 8.22555 + 3.96121i 0.599910 + 0.288901i
\(189\) 0 0
\(190\) 0.685443 0.330092i 0.0497273 0.0239474i
\(191\) 5.70823 + 8.37244i 0.413033 + 0.605809i 0.975230 0.221195i \(-0.0709958\pi\)
−0.562196 + 0.827004i \(0.690043\pi\)
\(192\) 0 0
\(193\) −0.696044 9.28806i −0.0501023 0.668569i −0.964556 0.263878i \(-0.914998\pi\)
0.914454 0.404691i \(-0.132621\pi\)
\(194\) −8.77408 22.3560i −0.629942 1.60507i
\(195\) 0 0
\(196\) −8.31393 + 5.62877i −0.593852 + 0.402055i
\(197\) 8.73158i 0.622099i −0.950394 0.311050i \(-0.899319\pi\)
0.950394 0.311050i \(-0.100681\pi\)
\(198\) 0 0
\(199\) −11.0033 + 0.824586i −0.780006 + 0.0584533i −0.458781 0.888550i \(-0.651714\pi\)
−0.321225 + 0.947003i \(0.604095\pi\)
\(200\) 2.86256 + 3.08510i 0.202413 + 0.218150i
\(201\) 0 0
\(202\) −0.0811594 0.168529i −0.00571036 0.0118577i
\(203\) 0.420800 1.35635i 0.0295343 0.0951974i
\(204\) 0 0
\(205\) 4.58634 0.691280i 0.320324 0.0482811i
\(206\) −0.732304 0.499276i −0.0510220 0.0347862i
\(207\) 0 0
\(208\) −2.05575 + 2.21557i −0.142540 + 0.153622i
\(209\) −1.15811 + 1.45222i −0.0801079 + 0.100452i
\(210\) 0 0
\(211\) 1.58614 + 1.98896i 0.109195 + 0.136926i 0.833426 0.552632i \(-0.186376\pi\)
−0.724231 + 0.689558i \(0.757805\pi\)
\(212\) −2.96219 0.221985i −0.203444 0.0152460i
\(213\) 0 0
\(214\) 0.225248 + 0.390141i 0.0153976 + 0.0266695i
\(215\) 3.58568 6.21059i 0.244542 0.423558i
\(216\) 0 0
\(217\) 9.87053 + 20.5820i 0.670055 + 1.39720i
\(218\) −23.4271 + 5.34708i −1.58668 + 0.362150i
\(219\) 0 0
\(220\) −5.95327 2.33648i −0.401369 0.157526i
\(221\) −4.69679 1.84335i −0.315940 0.123997i
\(222\) 0 0
\(223\) −20.1361 + 4.59593i −1.34841 + 0.307766i −0.834940 0.550341i \(-0.814498\pi\)
−0.513471 + 0.858107i \(0.671640\pi\)
\(224\) −17.5974 + 3.98636i −1.17578 + 0.266350i
\(225\) 0 0
\(226\) −0.925640 + 1.60326i −0.0615727 + 0.106647i
\(227\) −2.55915 4.43258i −0.169857 0.294201i 0.768512 0.639835i \(-0.220997\pi\)
−0.938369 + 0.345634i \(0.887664\pi\)
\(228\) 0 0
\(229\) −17.1475 1.28503i −1.13314 0.0849172i −0.505074 0.863076i \(-0.668535\pi\)
−0.628068 + 0.778159i \(0.716154\pi\)
\(230\) −8.65625 10.8546i −0.570776 0.715731i
\(231\) 0 0
\(232\) 0.350840 0.439940i 0.0230338 0.0288835i
\(233\) 2.12482 2.29001i 0.139202 0.150024i −0.659603 0.751614i \(-0.729276\pi\)
0.798805 + 0.601591i \(0.205466\pi\)
\(234\) 0 0
\(235\) −5.22085 3.55952i −0.340571 0.232197i
\(236\) −17.5940 + 2.65187i −1.14527 + 0.172622i
\(237\) 0 0
\(238\) −22.1317 32.5750i −1.43458 2.11152i
\(239\) 10.2085 + 21.1981i 0.660332 + 1.37119i 0.914719 + 0.404091i \(0.132412\pi\)
−0.254387 + 0.967103i \(0.581874\pi\)
\(240\) 0 0
\(241\) 3.01254 + 3.24675i 0.194055 + 0.209142i 0.822582 0.568646i \(-0.192533\pi\)
−0.628527 + 0.777787i \(0.716342\pi\)
\(242\) 16.9543 1.27055i 1.08986 0.0816738i
\(243\) 0 0
\(244\) 6.91888i 0.442936i
\(245\) 6.27060 2.99465i 0.400614 0.191321i
\(246\) 0 0
\(247\) 0.0949072 + 0.241820i 0.00603880 + 0.0153866i
\(248\) 0.675905 + 9.01933i 0.0429200 + 0.572728i
\(249\) 0 0
\(250\) 9.34201 + 13.7022i 0.590841 + 0.866604i
\(251\) 12.7904 6.15955i 0.807325 0.388787i 0.0157627 0.999876i \(-0.494982\pi\)
0.791562 + 0.611089i \(0.209268\pi\)
\(252\) 0 0
\(253\) 30.5399 + 14.7072i 1.92003 + 0.924637i
\(254\) 4.15636 + 27.5757i 0.260793 + 1.73025i
\(255\) 0 0
\(256\) −20.7173 3.12263i −1.29483 0.195165i
\(257\) 21.1023 + 19.5801i 1.31633 + 1.22137i 0.957658 + 0.287908i \(0.0929598\pi\)
0.358669 + 0.933465i \(0.383231\pi\)
\(258\) 0 0
\(259\) −13.7035 + 12.6736i −0.851496 + 0.787497i
\(260\) −0.699293 + 0.557667i −0.0433683 + 0.0345851i
\(261\) 0 0
\(262\) −11.4461 37.1074i −0.707144 2.29250i
\(263\) −9.22658 + 5.32697i −0.568935 + 0.328475i −0.756724 0.653734i \(-0.773201\pi\)
0.187789 + 0.982209i \(0.439868\pi\)
\(264\) 0 0
\(265\) 2.00439 + 0.457488i 0.123129 + 0.0281033i
\(266\) −0.454407 + 1.97605i −0.0278615 + 0.121160i
\(267\) 0 0
\(268\) 4.80447 + 1.48198i 0.293479 + 0.0905264i
\(269\) 6.03987 15.3893i 0.368257 0.938304i −0.619875 0.784700i \(-0.712817\pi\)
0.988132 0.153604i \(-0.0490880\pi\)
\(270\) 0 0
\(271\) −5.23438 + 16.9695i −0.317966 + 1.03082i 0.645673 + 0.763614i \(0.276577\pi\)
−0.963639 + 0.267207i \(0.913899\pi\)
\(272\) −8.59942 37.6765i −0.521417 2.28448i
\(273\) 0 0
\(274\) −1.18612 + 5.19672i −0.0716559 + 0.313945i
\(275\) −15.6158 9.01579i −0.941669 0.543673i
\(276\) 0 0
\(277\) 30.7732 9.49229i 1.84899 0.570336i 0.849929 0.526897i \(-0.176645\pi\)
0.999056 0.0434394i \(-0.0138316\pi\)
\(278\) −2.24307 + 29.9316i −0.134530 + 1.79518i
\(279\) 0 0
\(280\) 2.74605 0.201293i 0.164108 0.0120296i
\(281\) 5.50516 + 4.39022i 0.328410 + 0.261899i 0.773789 0.633444i \(-0.218359\pi\)
−0.445378 + 0.895343i \(0.646931\pi\)
\(282\) 0 0
\(283\) 1.92498 12.7714i 0.114428 0.759180i −0.855856 0.517213i \(-0.826969\pi\)
0.970285 0.241967i \(-0.0777925\pi\)
\(284\) 1.77489 2.60328i 0.105320 0.154476i
\(285\) 0 0
\(286\) 2.26868 4.71097i 0.134150 0.278565i
\(287\) −6.19817 + 10.6953i −0.365866 + 0.631323i
\(288\) 0 0
\(289\) 39.2584 26.7659i 2.30932 1.57447i
\(290\) 0.723863 0.671646i 0.0425067 0.0394404i
\(291\) 0 0
\(292\) 3.45237 1.35496i 0.202035 0.0792928i
\(293\) −12.8563 −0.751072 −0.375536 0.926808i \(-0.622541\pi\)
−0.375536 + 0.926808i \(0.622541\pi\)
\(294\) 0 0
\(295\) 12.3147 0.716990
\(296\) −6.88471 + 2.70205i −0.400166 + 0.157053i
\(297\) 0 0
\(298\) −15.4055 + 14.2942i −0.892418 + 0.828043i
\(299\) 3.91692 2.67051i 0.226521 0.154440i
\(300\) 0 0
\(301\) 6.95378 + 17.8031i 0.400809 + 1.02615i
\(302\) −5.77556 + 11.9931i −0.332346 + 0.690124i
\(303\) 0 0
\(304\) −1.12084 + 1.64397i −0.0642847 + 0.0942883i
\(305\) −0.713717 + 4.73520i −0.0408673 + 0.271137i
\(306\) 0 0
\(307\) −3.22712 2.57354i −0.184182 0.146880i 0.527059 0.849829i \(-0.323295\pi\)
−0.711240 + 0.702949i \(0.751866\pi\)
\(308\) 14.7750 8.49833i 0.841886 0.484237i
\(309\) 0 0
\(310\) −1.18612 + 15.8276i −0.0673669 + 0.898948i
\(311\) −22.1482 + 6.83180i −1.25591 + 0.387396i −0.850128 0.526576i \(-0.823476\pi\)
−0.405778 + 0.913972i \(0.633000\pi\)
\(312\) 0 0
\(313\) −21.1197 12.1935i −1.19375 0.689215i −0.234599 0.972092i \(-0.575378\pi\)
−0.959156 + 0.282878i \(0.908711\pi\)
\(314\) −6.12831 + 26.8499i −0.345840 + 1.51523i
\(315\) 0 0
\(316\) 4.37395 + 19.1635i 0.246054 + 1.07803i
\(317\) 5.67594 18.4010i 0.318793 1.03350i −0.644400 0.764689i \(-0.722893\pi\)
0.963193 0.268812i \(-0.0866310\pi\)
\(318\) 0 0
\(319\) −0.880800 + 2.24424i −0.0493153 + 0.125653i
\(320\) −2.86049 0.882343i −0.159906 0.0493245i
\(321\) 0 0
\(322\) 37.0021 + 0.0602417i 2.06205 + 0.00335714i
\(323\) −3.23833 0.739128i −0.180185 0.0411262i
\(324\) 0 0
\(325\) −2.18397 + 1.26091i −0.121145 + 0.0699429i
\(326\) −6.65083 21.5615i −0.368356 1.19418i
\(327\) 0 0
\(328\) −3.82945 + 3.05388i −0.211446 + 0.168622i
\(329\) 16.1006 4.93770i 0.887657 0.272224i
\(330\) 0 0
\(331\) −6.09235 5.65287i −0.334866 0.310710i 0.494760 0.869030i \(-0.335256\pi\)
−0.829626 + 0.558319i \(0.811446\pi\)
\(332\) 14.4820 + 2.18282i 0.794806 + 0.119798i
\(333\) 0 0
\(334\) −0.168943 1.12086i −0.00924414 0.0613309i
\(335\) −3.13525 1.50986i −0.171297 0.0824922i
\(336\) 0 0
\(337\) 25.4191 12.2412i 1.38467 0.666820i 0.414676 0.909969i \(-0.363895\pi\)
0.969989 + 0.243149i \(0.0781806\pi\)
\(338\) 13.1593 + 19.3011i 0.715769 + 1.04984i
\(339\) 0 0
\(340\) −0.854652 11.4045i −0.0463500 0.618498i
\(341\) −14.1575 36.0728i −0.766674 1.95345i
\(342\) 0 0
\(343\) −4.20928 + 18.0356i −0.227280 + 0.973829i
\(344\) 7.57321i 0.408320i
\(345\) 0 0
\(346\) 25.6035 1.91872i 1.37645 0.103151i
\(347\) 1.79422 + 1.93371i 0.0963188 + 0.103807i 0.779371 0.626562i \(-0.215539\pi\)
−0.683053 + 0.730369i \(0.739348\pi\)
\(348\) 0 0
\(349\) −8.44042 17.5267i −0.451805 0.938184i −0.995122 0.0986556i \(-0.968546\pi\)
0.543316 0.839528i \(-0.317168\pi\)
\(350\) −19.6261 1.50291i −1.04906 0.0803337i
\(351\) 0 0
\(352\) 30.2892 4.56536i 1.61442 0.243335i
\(353\) −14.3780 9.80275i −0.765263 0.521748i 0.116642 0.993174i \(-0.462787\pi\)
−0.881905 + 0.471426i \(0.843739\pi\)
\(354\) 0 0
\(355\) −1.48325 + 1.59857i −0.0787230 + 0.0848432i
\(356\) −5.50888 + 6.90792i −0.291970 + 0.366119i
\(357\) 0 0
\(358\) −5.78044 7.24844i −0.305506 0.383092i
\(359\) 6.62300 + 0.496326i 0.349549 + 0.0261951i 0.248348 0.968671i \(-0.420112\pi\)
0.101201 + 0.994866i \(0.467731\pi\)
\(360\) 0 0
\(361\) −9.41449 16.3064i −0.495500 0.858230i
\(362\) 17.3293 30.0153i 0.910810 1.57757i
\(363\) 0 0
\(364\) 0.00388099 2.38381i 0.000203419 0.124946i
\(365\) −2.50253 + 0.571187i −0.130989 + 0.0298973i
\(366\) 0 0
\(367\) 20.6789 + 8.11586i 1.07943 + 0.423645i 0.837381 0.546620i \(-0.184086\pi\)
0.242048 + 0.970264i \(0.422181\pi\)
\(368\) 33.8001 + 13.2656i 1.76195 + 0.691516i
\(369\) 0 0
\(370\) −12.6534 + 2.88807i −0.657821 + 0.150143i
\(371\) −4.28955 + 3.40939i −0.222702 + 0.177007i
\(372\) 0 0
\(373\) 2.15951 3.74039i 0.111815 0.193670i −0.804687 0.593699i \(-0.797667\pi\)
0.916502 + 0.400030i \(0.131000\pi\)
\(374\) 33.4286 + 57.9001i 1.72855 + 2.99394i
\(375\) 0 0
\(376\) 6.65423 + 0.498666i 0.343166 + 0.0257167i
\(377\) 0.210228 + 0.263617i 0.0108273 + 0.0135770i
\(378\) 0 0
\(379\) −17.9466 + 22.5043i −0.921853 + 1.15597i 0.0655670 + 0.997848i \(0.479114\pi\)
−0.987420 + 0.158119i \(0.949457\pi\)
\(380\) −0.400501 + 0.431637i −0.0205453 + 0.0221425i
\(381\) 0 0
\(382\) −15.5157 10.5784i −0.793853 0.541240i
\(383\) 27.5261 4.14889i 1.40652 0.211998i 0.598483 0.801135i \(-0.295770\pi\)
0.808033 + 0.589137i \(0.200532\pi\)
\(384\) 0 0
\(385\) −10.9885 + 4.29204i −0.560027 + 0.218743i
\(386\) 7.48917 + 15.5514i 0.381189 + 0.791547i
\(387\) 0 0
\(388\) 12.6428 + 13.6257i 0.641843 + 0.691743i
\(389\) 25.2049 1.88884i 1.27794 0.0957681i 0.581595 0.813478i \(-0.302429\pi\)
0.696342 + 0.717710i \(0.254810\pi\)
\(390\) 0 0
\(391\) 60.6160i 3.06548i
\(392\) −4.15357 + 6.04974i −0.209787 + 0.305558i
\(393\) 0 0
\(394\) 5.91168 + 15.0627i 0.297826 + 0.758849i
\(395\) −1.01667 13.5665i −0.0511541 0.682604i
\(396\) 0 0
\(397\) −2.72275 3.99355i −0.136651 0.200430i 0.751813 0.659376i \(-0.229180\pi\)
−0.888464 + 0.458946i \(0.848227\pi\)
\(398\) 18.4234 8.87224i 0.923481 0.444725i
\(399\) 0 0
\(400\) −17.4026 8.38064i −0.870129 0.419032i
\(401\) 0.602095 + 3.99464i 0.0300672 + 0.199483i 0.998821 0.0485407i \(-0.0154571\pi\)
−0.968754 + 0.248024i \(0.920219\pi\)
\(402\) 0 0
\(403\) −5.35911 0.807756i −0.266956 0.0402372i
\(404\) 0.106126 + 0.0984707i 0.00527997 + 0.00489910i
\(405\) 0 0
\(406\) 0.192399 + 2.62473i 0.00954862 + 0.130263i
\(407\) 24.7746 19.7571i 1.22803 0.979323i
\(408\) 0 0
\(409\) 2.49502 + 8.08867i 0.123371 + 0.399959i 0.996098 0.0882487i \(-0.0281270\pi\)
−0.872727 + 0.488208i \(0.837651\pi\)
\(410\) −7.44380 + 4.29768i −0.367623 + 0.212247i
\(411\) 0 0
\(412\) 0.668776 + 0.152644i 0.0329482 + 0.00752022i
\(413\) −20.5052 + 25.6270i −1.00900 + 1.26102i
\(414\) 0 0
\(415\) −9.68618 2.98779i −0.475476 0.146665i
\(416\) 1.56511 3.98784i 0.0767360 0.195520i
\(417\) 0 0
\(418\) 1.01461 3.28929i 0.0496263 0.160885i
\(419\) −6.41958 28.1260i −0.313617 1.37405i −0.848534 0.529141i \(-0.822514\pi\)
0.534917 0.844904i \(-0.320343\pi\)
\(420\) 0 0
\(421\) −7.12201 + 31.2035i −0.347105 + 1.52077i 0.436612 + 0.899650i \(0.356178\pi\)
−0.783717 + 0.621118i \(0.786679\pi\)
\(422\) −4.08285 2.35724i −0.198750 0.114748i
\(423\) 0 0
\(424\) −2.07468 + 0.639954i −0.100755 + 0.0310789i
\(425\) 2.40968 32.1549i 0.116886 1.55974i
\(426\) 0 0
\(427\) −8.66561 9.36985i −0.419358 0.453439i
\(428\) −0.272600 0.217392i −0.0131766 0.0105080i
\(429\) 0 0
\(430\) −1.98076 + 13.1415i −0.0955205 + 0.633737i
\(431\) −14.8179 + 21.7338i −0.713751 + 1.04688i 0.282406 + 0.959295i \(0.408868\pi\)
−0.996157 + 0.0875856i \(0.972085\pi\)
\(432\) 0 0
\(433\) 6.84177 14.2071i 0.328794 0.682748i −0.669394 0.742907i \(-0.733446\pi\)
0.998189 + 0.0601587i \(0.0191607\pi\)
\(434\) −30.9625 28.8229i −1.48625 1.38354i
\(435\) 0 0
\(436\) 15.3665 10.4767i 0.735920 0.501742i
\(437\) 2.28777 2.12274i 0.109439 0.101544i
\(438\) 0 0
\(439\) −10.8305 + 4.25068i −0.516914 + 0.202874i −0.609434 0.792837i \(-0.708603\pi\)
0.0925199 + 0.995711i \(0.470508\pi\)
\(440\) −4.67437 −0.222842
\(441\) 0 0
\(442\) 9.35039 0.444753
\(443\) 1.42415 0.558937i 0.0676633 0.0265559i −0.331268 0.943537i \(-0.607476\pi\)
0.398931 + 0.916981i \(0.369381\pi\)
\(444\) 0 0
\(445\) 4.48280 4.15943i 0.212505 0.197176i
\(446\) 31.6248 21.5614i 1.49748 1.02096i
\(447\) 0 0
\(448\) 6.59917 4.48351i 0.311781 0.211826i
\(449\) 8.49715 17.6445i 0.401005 0.832696i −0.598496 0.801126i \(-0.704235\pi\)
0.999502 0.0315705i \(-0.0100509\pi\)
\(450\) 0 0
\(451\) 11.8216 17.3391i 0.556658 0.816468i
\(452\) 0.213552 1.41683i 0.0100446 0.0666419i
\(453\) 0 0
\(454\) 7.41582 + 5.91392i 0.348042 + 0.277554i
\(455\) −0.248558 + 1.63105i −0.0116526 + 0.0764649i
\(456\) 0 0
\(457\) −2.42706 + 32.3868i −0.113533 + 1.51499i 0.591782 + 0.806098i \(0.298425\pi\)
−0.705315 + 0.708894i \(0.749194\pi\)
\(458\) 30.4510 9.39289i 1.42288 0.438901i
\(459\) 0 0
\(460\) 9.30579 + 5.37270i 0.433885 + 0.250504i
\(461\) −2.97254 + 13.0235i −0.138445 + 0.606567i 0.857332 + 0.514763i \(0.172120\pi\)
−0.995777 + 0.0918033i \(0.970737\pi\)
\(462\) 0 0
\(463\) 2.86102 + 12.5350i 0.132963 + 0.582549i 0.996881 + 0.0789168i \(0.0251461\pi\)
−0.863918 + 0.503632i \(0.831997\pi\)
\(464\) −0.761220 + 2.46781i −0.0353387 + 0.114565i
\(465\) 0 0
\(466\) −2.11505 + 5.38906i −0.0979778 + 0.249643i
\(467\) −4.18418 1.29065i −0.193621 0.0597241i 0.196428 0.980518i \(-0.437066\pi\)
−0.390049 + 0.920794i \(0.627542\pi\)
\(468\) 0 0
\(469\) 8.36254 4.01043i 0.386146 0.185184i
\(470\) 11.4164 + 2.60571i 0.526598 + 0.120192i
\(471\) 0 0
\(472\) −11.2624 + 6.50238i −0.518396 + 0.299296i
\(473\) −9.56402 31.0058i −0.439754 1.42565i
\(474\) 0 0
\(475\) −1.29798 + 1.03510i −0.0595552 + 0.0474937i
\(476\) 25.1561 + 17.2112i 1.15303 + 0.788873i
\(477\) 0 0
\(478\) −31.9626 29.6570i −1.46194 1.35648i
\(479\) 20.9513 + 3.15790i 0.957290 + 0.144288i 0.609063 0.793122i \(-0.291546\pi\)
0.348227 + 0.937410i \(0.386784\pi\)
\(480\) 0 0
\(481\) −0.660518 4.38225i −0.0301170 0.199813i
\(482\) −7.39509 3.56129i −0.336837 0.162212i
\(483\) 0 0
\(484\) −11.8557 + 5.70940i −0.538895 + 0.259518i
\(485\) −7.24706 10.6295i −0.329072 0.482660i
\(486\) 0 0
\(487\) 0.730807 + 9.75194i 0.0331160 + 0.441902i 0.988976 + 0.148079i \(0.0473089\pi\)
−0.955860 + 0.293824i \(0.905072\pi\)
\(488\) −1.84754 4.70745i −0.0836341 0.213096i
\(489\) 0 0
\(490\) −8.78979 + 9.41150i −0.397082 + 0.425168i
\(491\) 23.7594i 1.07224i 0.844140 + 0.536122i \(0.180111\pi\)
−0.844140 + 0.536122i \(0.819889\pi\)
\(492\) 0 0
\(493\) −4.29924 + 0.322184i −0.193628 + 0.0145104i
\(494\) −0.327446 0.352903i −0.0147325 0.0158778i
\(495\) 0 0
\(496\) −18.0108 37.3998i −0.808708 1.67930i
\(497\) −0.856870 5.74845i −0.0384359 0.257853i
\(498\) 0 0
\(499\) 21.3120 3.21226i 0.954055 0.143801i 0.346475 0.938059i \(-0.387379\pi\)
0.607580 + 0.794259i \(0.292141\pi\)
\(500\) −10.6051 7.23041i −0.474273 0.323354i
\(501\) 0 0
\(502\) −17.8943 + 19.2854i −0.798661 + 0.860751i
\(503\) −10.7609 + 13.4938i −0.479807 + 0.601659i −0.961542 0.274658i \(-0.911435\pi\)
0.481735 + 0.876317i \(0.340007\pi\)
\(504\) 0 0
\(505\) −0.0624738 0.0783397i −0.00278005 0.00348607i
\(506\) −62.6414 4.69432i −2.78475 0.208688i
\(507\) 0 0
\(508\) −10.7919 18.6921i −0.478812 0.829326i
\(509\) −16.3177 + 28.2630i −0.723268 + 1.25274i 0.236415 + 0.971652i \(0.424028\pi\)
−0.959683 + 0.281085i \(0.909306\pi\)
\(510\) 0 0
\(511\) 2.97833 6.15889i 0.131753 0.272453i
\(512\) 22.1546 5.05664i 0.979104 0.223474i
\(513\) 0 0
\(514\) −49.6599 19.4901i −2.19040 0.859671i
\(515\) −0.441957 0.173455i −0.0194749 0.00764335i
\(516\) 0 0
\(517\) −27.8731 + 6.36185i −1.22586 + 0.279794i
\(518\) 15.0592 31.1409i 0.661662 1.36825i
\(519\) 0 0
\(520\) −0.326870 + 0.566155i −0.0143342 + 0.0248275i
\(521\) −7.83292 13.5670i −0.343166 0.594382i 0.641852 0.766828i \(-0.278166\pi\)
−0.985019 + 0.172446i \(0.944833\pi\)
\(522\) 0 0
\(523\) 25.4385 + 1.90635i 1.11235 + 0.0833589i 0.618201 0.786020i \(-0.287862\pi\)
0.494146 + 0.869379i \(0.335481\pi\)
\(524\) 18.7391 + 23.4981i 0.818621 + 1.02652i
\(525\) 0 0
\(526\) 12.3100 15.4363i 0.536743 0.673054i
\(527\) 47.1344 50.7988i 2.05321 2.21283i
\(528\) 0 0
\(529\) −28.0533 19.1264i −1.21971 0.831582i
\(530\) −3.76748 + 0.567856i −0.163649 + 0.0246661i
\(531\) 0 0
\(532\) −0.231368 1.55217i −0.0100311 0.0672950i
\(533\) −1.27343 2.64431i −0.0551585 0.114538i
\(534\) 0 0
\(535\) 0.164140 + 0.176900i 0.00709637 + 0.00764807i
\(536\) 3.66458 0.274622i 0.158286 0.0118619i
\(537\) 0 0
\(538\) 30.6372i 1.32086i
\(539\) 9.36521 30.0139i 0.403388 1.29279i
\(540\) 0 0
\(541\) −1.49182 3.80109i −0.0641383 0.163422i 0.895211 0.445642i \(-0.147024\pi\)
−0.959350 + 0.282220i \(0.908929\pi\)
\(542\) −2.45934 32.8176i −0.105638 1.40964i
\(543\) 0 0
\(544\) 30.8568 + 45.2586i 1.32297 + 1.94044i
\(545\) −11.5974 + 5.58499i −0.496776 + 0.239235i
\(546\) 0 0
\(547\) −19.6664 9.47084i −0.840875 0.404944i −0.0366923 0.999327i \(-0.511682\pi\)
−0.804182 + 0.594383i \(0.797396\pi\)
\(548\) −0.614877 4.07944i −0.0262662 0.174265i
\(549\) 0 0
\(550\) 33.0427 + 4.98039i 1.40895 + 0.212364i
\(551\) 0.162717 + 0.150979i 0.00693198 + 0.00643194i
\(552\) 0 0
\(553\) 29.9249 + 20.4739i 1.27253 + 0.870638i
\(554\) −46.6597 + 37.2099i −1.98238 + 1.58090i
\(555\) 0 0
\(556\) −6.84748 22.1990i −0.290398 0.941446i
\(557\) −16.2512 + 9.38264i −0.688586 + 0.397555i −0.803082 0.595868i \(-0.796808\pi\)
0.114496 + 0.993424i \(0.463475\pi\)
\(558\) 0 0
\(559\) −4.42418 1.00979i −0.187123 0.0427096i
\(560\) −11.3944 + 5.46441i −0.481501 + 0.230914i
\(561\) 0 0
\(562\) −12.4692 3.84625i −0.525984 0.162244i
\(563\) −14.0988 + 35.9232i −0.594194 + 1.51398i 0.244651 + 0.969611i \(0.421326\pi\)
−0.838845 + 0.544370i \(0.816769\pi\)
\(564\) 0 0
\(565\) −0.292305 + 0.947631i −0.0122974 + 0.0398671i
\(566\) 5.32607 + 23.3350i 0.223871 + 0.980844i
\(567\) 0 0
\(568\) 0.512443 2.24516i 0.0215016 0.0942048i
\(569\) −5.55960 3.20984i −0.233071 0.134563i 0.378917 0.925431i \(-0.376297\pi\)
−0.611988 + 0.790867i \(0.709630\pi\)
\(570\) 0 0
\(571\) 6.14518 1.89554i 0.257168 0.0793258i −0.163491 0.986545i \(-0.552275\pi\)
0.420658 + 0.907219i \(0.361799\pi\)
\(572\) −0.302425 + 4.03559i −0.0126450 + 0.168736i
\(573\) 0 0
\(574\) 3.45116 22.6467i 0.144049 0.945256i
\(575\) 23.6868 + 18.8896i 0.987806 + 0.787749i
\(576\) 0 0
\(577\) −6.23729 + 41.3817i −0.259662 + 1.72274i 0.355787 + 0.934567i \(0.384213\pi\)
−0.615449 + 0.788177i \(0.711025\pi\)
\(578\) −49.6023 + 72.7532i −2.06318 + 3.02613i
\(579\) 0 0
\(580\) −0.331602 + 0.688579i −0.0137690 + 0.0285917i
\(581\) 22.3461 15.1821i 0.927073 0.629859i
\(582\) 0 0
\(583\) 7.68585 5.24012i 0.318315 0.217024i
\(584\) 1.98710 1.84376i 0.0822269 0.0762954i
\(585\) 0 0
\(586\) 22.1782 8.70429i 0.916172 0.359571i
\(587\) −21.8194 −0.900582 −0.450291 0.892882i \(-0.648680\pi\)
−0.450291 + 0.892882i \(0.648680\pi\)
\(588\) 0 0
\(589\) −3.56787 −0.147011
\(590\) −21.2439 + 8.33761i −0.874597 + 0.343254i
\(591\) 0 0
\(592\) 24.8827 23.0878i 1.02267 0.948903i
\(593\) −6.97370 + 4.75459i −0.286375 + 0.195247i −0.697984 0.716113i \(-0.745919\pi\)
0.411609 + 0.911361i \(0.364967\pi\)
\(594\) 0 0
\(595\) −15.4411 14.3741i −0.633024 0.589281i
\(596\) 7.05729 14.6546i 0.289078 0.600276i
\(597\) 0 0
\(598\) −4.94896 + 7.25879i −0.202378 + 0.296834i
\(599\) −0.490638 + 3.25517i −0.0200469 + 0.133003i −0.996616 0.0822034i \(-0.973804\pi\)
0.976569 + 0.215206i \(0.0690424\pi\)
\(600\) 0 0
\(601\) −7.11733 5.67588i −0.290322 0.231524i 0.467488 0.883999i \(-0.345159\pi\)
−0.757810 + 0.652475i \(0.773731\pi\)
\(602\) −24.0494 26.0038i −0.980179 1.05984i
\(603\) 0 0
\(604\) 0.769908 10.2737i 0.0313271 0.418031i
\(605\) 8.70286 2.68448i 0.353822 0.109140i
\(606\) 0 0
\(607\) −21.0241 12.1383i −0.853343 0.492678i 0.00843430 0.999964i \(-0.497315\pi\)
−0.861777 + 0.507287i \(0.830649\pi\)
\(608\) 0.627562 2.74953i 0.0254510 0.111508i
\(609\) 0 0
\(610\) −1.97473 8.65185i −0.0799544 0.350303i
\(611\) −1.17857 + 3.82083i −0.0476799 + 0.154574i
\(612\) 0 0
\(613\) −6.08264 + 15.4983i −0.245675 + 0.625971i −0.999517 0.0310857i \(-0.990104\pi\)
0.753841 + 0.657057i \(0.228199\pi\)
\(614\) 7.30947 + 2.25467i 0.294986 + 0.0909911i
\(615\) 0 0
\(616\) 7.78331 9.72743i 0.313598 0.391929i
\(617\) −12.8385 2.93030i −0.516857 0.117969i −0.0438676 0.999037i \(-0.513968\pi\)
−0.472989 + 0.881068i \(0.656825\pi\)
\(618\) 0 0
\(619\) 17.8653 10.3145i 0.718066 0.414575i −0.0959747 0.995384i \(-0.530597\pi\)
0.814040 + 0.580808i \(0.197263\pi\)
\(620\) −3.62089 11.7386i −0.145419 0.471435i
\(621\) 0 0
\(622\) 33.5820 26.7807i 1.34652 1.07381i
\(623\) 1.19151 + 16.2546i 0.0477368 + 0.651229i
\(624\) 0 0
\(625\) −8.20215 7.61048i −0.328086 0.304419i
\(626\) 44.6887 + 6.73574i 1.78612 + 0.269214i
\(627\) 0 0
\(628\) −3.17688 21.0772i −0.126771 0.841074i
\(629\) 51.0544 + 24.5865i 2.03567 + 0.980327i
\(630\) 0 0
\(631\) −9.60985 + 4.62786i −0.382562 + 0.184232i −0.615274 0.788314i \(-0.710954\pi\)
0.232712 + 0.972546i \(0.425240\pi\)
\(632\) 8.09313 + 11.8704i 0.321928 + 0.472181i
\(633\) 0 0
\(634\) 2.66681 + 35.5861i 0.105912 + 1.41330i
\(635\) 5.45765 + 13.9059i 0.216580 + 0.551838i
\(636\) 0 0
\(637\) −2.98036 3.23312i −0.118086 0.128101i
\(638\) 4.46785i 0.176884i
\(639\) 0 0
\(640\) −7.97018 + 0.597283i −0.315049 + 0.0236097i
\(641\) −16.3629 17.6350i −0.646295 0.696540i 0.321890 0.946777i \(-0.395682\pi\)
−0.968185 + 0.250237i \(0.919492\pi\)
\(642\) 0 0
\(643\) −14.0765 29.2301i −0.555122 1.15272i −0.970058 0.242872i \(-0.921911\pi\)
0.414937 0.909850i \(-0.363804\pi\)
\(644\) −26.6758 + 10.4194i −1.05117 + 0.410581i
\(645\) 0 0
\(646\) 6.08681 0.917440i 0.239482 0.0360962i
\(647\) −5.94010 4.04989i −0.233529 0.159218i 0.440902 0.897555i \(-0.354659\pi\)
−0.674431 + 0.738338i \(0.735611\pi\)
\(648\) 0 0
\(649\) 37.8983 40.8447i 1.48764 1.60329i
\(650\) 2.91383 3.65383i 0.114290 0.143315i
\(651\) 0 0
\(652\) 10.8885 + 13.6537i 0.426425 + 0.534720i
\(653\) −43.3656 3.24980i −1.69703 0.127174i −0.809254 0.587459i \(-0.800128\pi\)
−0.887772 + 0.460284i \(0.847747\pi\)
\(654\) 0 0
\(655\) −10.4009 18.0149i −0.406396 0.703899i
\(656\) 11.2399 19.4680i 0.438843 0.760099i
\(657\) 0 0
\(658\) −24.4319 + 19.4188i −0.952456 + 0.757024i
\(659\) −2.19881 + 0.501864i −0.0856535 + 0.0195498i −0.265133 0.964212i \(-0.585416\pi\)
0.179479 + 0.983762i \(0.442559\pi\)
\(660\) 0 0
\(661\) 12.9098 + 5.06672i 0.502133 + 0.197073i 0.602868 0.797841i \(-0.294024\pi\)
−0.100736 + 0.994913i \(0.532120\pi\)
\(662\) 14.3371 + 5.62688i 0.557226 + 0.218695i
\(663\) 0 0
\(664\) 10.4361 2.38198i 0.405000 0.0924387i
\(665\) −0.00176832 + 1.08615i −6.85727e−5 + 0.0421192i
\(666\) 0 0
\(667\) 2.02538 3.50807i 0.0784232 0.135833i
\(668\) 0.438655 + 0.759772i 0.0169721 + 0.0293965i
\(669\) 0 0
\(670\) 6.43081 + 0.481922i 0.248444 + 0.0186183i
\(671\) 13.5090 + 16.9397i 0.521509 + 0.653952i
\(672\) 0 0
\(673\) −4.69254 + 5.88425i −0.180884 + 0.226821i −0.864004 0.503485i \(-0.832051\pi\)
0.683120 + 0.730306i \(0.260622\pi\)
\(674\) −35.5622 + 38.3269i −1.36980 + 1.47630i
\(675\) 0 0
\(676\) −14.9384 10.1848i −0.574554 0.391724i
\(677\) −42.8122 + 6.45290i −1.64541 + 0.248005i −0.905389 0.424584i \(-0.860421\pi\)
−0.740017 + 0.672588i \(0.765182\pi\)
\(678\) 0 0
\(679\) 34.1872 + 2.61795i 1.31198 + 0.100468i
\(680\) −3.62682 7.53117i −0.139082 0.288807i
\(681\) 0 0
\(682\) 48.8459 + 52.6433i 1.87041 + 2.01582i
\(683\) −42.8746 + 3.21301i −1.64055 + 0.122942i −0.862771 0.505595i \(-0.831273\pi\)
−0.777780 + 0.628537i \(0.783654\pi\)
\(684\) 0 0
\(685\) 2.85535i 0.109097i
\(686\) −4.94954 33.9628i −0.188974 1.29670i
\(687\) 0 0
\(688\) −12.6983 32.3549i −0.484120 1.23352i
\(689\) −0.0972217 1.29733i −0.00370385 0.0494245i
\(690\) 0 0
\(691\) 26.8099 + 39.3229i 1.01990 + 1.49591i 0.860991 + 0.508621i \(0.169845\pi\)
0.158907 + 0.987294i \(0.449203\pi\)
\(692\) −17.9039 + 8.62208i −0.680605 + 0.327762i
\(693\) 0 0
\(694\) −4.40439 2.12104i −0.167188 0.0805137i
\(695\) 2.39640 + 15.8991i 0.0909007 + 0.603086i
\(696\) 0 0
\(697\) 37.1085 + 5.59320i 1.40558 + 0.211858i
\(698\) 26.4268 + 24.5205i 1.00027 + 0.928115i
\(699\) 0 0
\(700\) 14.5649 4.46671i 0.550500 0.168826i
\(701\) 23.0987 18.4206i 0.872425 0.695736i −0.0812112 0.996697i \(-0.525879\pi\)
0.953636 + 0.300961i \(0.0973074\pi\)
\(702\) 0 0
\(703\) −0.859953 2.78790i −0.0324338 0.105148i
\(704\) −11.7296 + 6.77210i −0.442076 + 0.255233i
\(705\) 0 0
\(706\) 31.4402 + 7.17601i 1.18327 + 0.270073i
\(707\) 0.267051 0.000434776i 0.0100435 1.63514e-5i
\(708\) 0 0
\(709\) −44.0766 13.5958i −1.65533 0.510602i −0.680350 0.732887i \(-0.738172\pi\)
−0.974982 + 0.222285i \(0.928648\pi\)
\(710\) 1.47644 3.76190i 0.0554096 0.141181i
\(711\) 0 0
\(712\) −1.90351 + 6.17102i −0.0713369 + 0.231269i
\(713\) 14.4883 + 63.4775i 0.542592 + 2.37725i
\(714\) 0 0
\(715\) 0.623268 2.73071i 0.0233089 0.102123i
\(716\) 6.21419 + 3.58776i 0.232235 + 0.134081i
\(717\) 0 0
\(718\) −11.7613 + 3.62787i −0.438927 + 0.135391i
\(719\) −2.85860 + 38.1454i −0.106608 + 1.42258i 0.645610 + 0.763667i \(0.276603\pi\)
−0.752218 + 0.658914i \(0.771016\pi\)
\(720\) 0 0
\(721\) 1.09687 0.630897i 0.0408494 0.0234958i
\(722\) 27.2810 + 21.7558i 1.01529 + 0.809668i
\(723\) 0 0
\(724\) −3.99801 + 26.5251i −0.148585 + 0.985796i
\(725\) −1.21386 + 1.78041i −0.0450816 + 0.0661226i
\(726\) 0 0
\(727\) −2.68945 + 5.58469i −0.0997460 + 0.207125i −0.944870 0.327446i \(-0.893812\pi\)
0.845124 + 0.534570i \(0.179526\pi\)
\(728\) −0.633904 1.62293i −0.0234941 0.0601496i
\(729\) 0 0
\(730\) 3.93036 2.67968i 0.145469 0.0991792i
\(731\) 42.5347 39.4664i 1.57320 1.45972i
\(732\) 0 0
\(733\) 14.3982 5.65086i 0.531808 0.208719i −0.0842147 0.996448i \(-0.526838\pi\)
0.616023 + 0.787728i \(0.288743\pi\)
\(734\) −41.1676 −1.51952
\(735\) 0 0
\(736\) −51.4665 −1.89708
\(737\) −14.6565 + 5.75225i −0.539879 + 0.211887i
\(738\) 0 0
\(739\) −19.7284 + 18.3053i −0.725720 + 0.673370i −0.953858 0.300259i \(-0.902927\pi\)
0.228138 + 0.973629i \(0.426736\pi\)
\(740\) 8.29973 5.65866i 0.305104 0.208017i
\(741\) 0 0
\(742\) 5.09152 8.78570i 0.186916 0.322533i
\(743\) −2.69592 + 5.59814i −0.0989037 + 0.205376i −0.944550 0.328369i \(-0.893501\pi\)
0.845646 + 0.533744i \(0.179216\pi\)
\(744\) 0 0
\(745\) −6.34162 + 9.30145i −0.232339 + 0.340779i
\(746\) −1.19293 + 7.91457i −0.0436762 + 0.289773i
\(747\) 0 0
\(748\) −40.4561 32.2627i −1.47922 1.17964i
\(749\) −0.641441 + 0.0470193i −0.0234377 + 0.00171805i
\(750\) 0 0
\(751\) 0.320811 4.28092i 0.0117065 0.156213i −0.988287 0.152607i \(-0.951233\pi\)
0.999993 0.00360597i \(-0.00114782\pi\)
\(752\) −29.2649 + 9.02701i −1.06718 + 0.329181i
\(753\) 0 0
\(754\) −0.541141 0.312428i −0.0197072 0.0113780i
\(755\) −1.58670 + 6.95179i −0.0577459 + 0.253001i
\(756\) 0 0
\(757\) −3.16549 13.8689i −0.115052 0.504074i −0.999312 0.0370804i \(-0.988194\pi\)
0.884261 0.466994i \(-0.154663\pi\)
\(758\) 15.7229 50.9724i 0.571082 1.85140i
\(759\) 0 0
\(760\) −0.157232 + 0.400621i −0.00570341 + 0.0145321i
\(761\) 21.2922 + 6.56776i 0.771840 + 0.238081i 0.655568 0.755136i \(-0.272429\pi\)
0.116272 + 0.993217i \(0.462905\pi\)
\(762\) 0 0
\(763\) 7.68834 33.4338i 0.278337 1.21039i
\(764\) 14.1697 + 3.23414i 0.512642 + 0.117007i
\(765\) 0 0
\(766\) −44.6758 + 25.7936i −1.61420 + 0.931960i
\(767\) −2.29691 7.44639i −0.0829366 0.268874i
\(768\) 0 0
\(769\) 15.8299 12.6239i 0.570841 0.455230i −0.295037 0.955486i \(-0.595332\pi\)
0.865878 + 0.500255i \(0.166761\pi\)
\(770\) 16.0502 14.8439i 0.578410 0.534936i
\(771\) 0 0
\(772\) −9.79304 9.08662i −0.352459 0.327034i
\(773\) −34.2387 5.16066i −1.23148 0.185616i −0.499120 0.866533i \(-0.666343\pi\)
−0.732361 + 0.680917i \(0.761582\pi\)
\(774\) 0 0
\(775\) −5.16218 34.2488i −0.185431 1.23025i
\(776\) 12.2404 + 5.89465i 0.439404 + 0.211606i
\(777\) 0 0
\(778\) −42.2017 + 20.3233i −1.51300 + 0.728624i
\(779\) −1.08842 1.59642i −0.0389967 0.0571976i
\(780\) 0 0
\(781\) 0.737342 + 9.83915i 0.0263842 + 0.352072i
\(782\) −41.0398 104.568i −1.46758 3.73933i
\(783\) 0 0
\(784\) 7.60130 32.8107i 0.271475 1.17181i
\(785\) 14.7527i 0.526548i
\(786\) 0 0
\(787\) 20.7770 1.55702i 0.740621 0.0555019i 0.300924 0.953648i \(-0.402705\pi\)
0.439697 + 0.898146i \(0.355086\pi\)