Properties

Label 16.5.f.a.11.4
Level $16$
Weight $5$
Character 16.11
Analytic conductor $1.654$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.65391940934\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} - 1048576 x + 2097152\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{21} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.4
Root \(-2.15805 + 1.82834i\) of defining polynomial
Character \(\chi\) \(=\) 16.11
Dual form 16.5.f.a.3.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.329715 + 3.98639i) q^{2} +(3.91498 + 3.91498i) q^{3} +(-15.7826 + 2.62875i) q^{4} +(4.72348 + 4.72348i) q^{5} +(-14.3158 + 16.8975i) q^{6} +45.3712 q^{7} +(-15.6830 - 62.0487i) q^{8} -50.3458i q^{9} +O(q^{10})\) \(q+(0.329715 + 3.98639i) q^{2} +(3.91498 + 3.91498i) q^{3} +(-15.7826 + 2.62875i) q^{4} +(4.72348 + 4.72348i) q^{5} +(-14.3158 + 16.8975i) q^{6} +45.3712 q^{7} +(-15.6830 - 62.0487i) q^{8} -50.3458i q^{9} +(-17.2722 + 20.3870i) q^{10} +(110.228 - 110.228i) q^{11} +(-72.0800 - 51.4970i) q^{12} +(-157.128 + 157.128i) q^{13} +(14.9596 + 180.867i) q^{14} +36.9847i q^{15} +(242.179 - 82.9768i) q^{16} -378.592 q^{17} +(200.698 - 16.5998i) q^{18} +(203.127 + 203.127i) q^{19} +(-86.9656 - 62.1319i) q^{20} +(177.627 + 177.627i) q^{21} +(475.755 + 403.067i) q^{22} -740.444 q^{23} +(181.521 - 304.318i) q^{24} -580.377i q^{25} +(-678.183 - 574.567i) q^{26} +(514.217 - 514.217i) q^{27} +(-716.074 + 119.269i) q^{28} +(82.6244 - 82.6244i) q^{29} +(-147.435 + 12.1944i) q^{30} +286.217i q^{31} +(410.628 + 938.062i) q^{32} +863.080 q^{33} +(-124.828 - 1509.21i) q^{34} +(214.310 + 214.310i) q^{35} +(132.346 + 794.587i) q^{36} +(1470.39 + 1470.39i) q^{37} +(-742.770 + 876.719i) q^{38} -1230.31 q^{39} +(219.008 - 367.164i) q^{40} -1301.21i q^{41} +(-649.525 + 766.658i) q^{42} +(-366.979 + 366.979i) q^{43} +(-1449.92 + 2029.44i) q^{44} +(237.808 - 237.808i) q^{45} +(-244.136 - 2951.70i) q^{46} +751.307i q^{47} +(1272.98 + 623.275i) q^{48} -342.455 q^{49} +(2313.61 - 191.359i) q^{50} +(-1482.18 - 1482.18i) q^{51} +(2066.84 - 2892.94i) q^{52} +(-1929.33 - 1929.33i) q^{53} +(2219.41 + 1880.32i) q^{54} +1041.32 q^{55} +(-711.555 - 2815.22i) q^{56} +1590.48i q^{57} +(356.616 + 302.130i) q^{58} +(-1357.57 + 1357.57i) q^{59} +(-97.2234 - 583.714i) q^{60} +(-1835.78 + 1835.78i) q^{61} +(-1140.97 + 94.3702i) q^{62} -2284.25i q^{63} +(-3604.09 + 1946.22i) q^{64} -1484.39 q^{65} +(284.571 + 3440.57i) q^{66} +(2205.02 + 2205.02i) q^{67} +(5975.15 - 995.222i) q^{68} +(-2898.83 - 2898.83i) q^{69} +(-783.662 + 924.984i) q^{70} +8970.40 q^{71} +(-3123.90 + 789.572i) q^{72} +9350.46i q^{73} +(-5376.75 + 6346.37i) q^{74} +(2272.17 - 2272.17i) q^{75} +(-3739.84 - 2671.90i) q^{76} +(5001.17 - 5001.17i) q^{77} +(-405.652 - 4904.49i) q^{78} -2860.08i q^{79} +(1535.87 + 751.991i) q^{80} -51.7173 q^{81} +(5187.13 - 429.029i) q^{82} +(-1036.63 - 1036.63i) q^{83} +(-3270.35 - 2336.48i) q^{84} +(-1788.27 - 1788.27i) q^{85} +(-1583.92 - 1341.92i) q^{86} +646.946 q^{87} +(-8568.19 - 5110.80i) q^{88} -5171.06i q^{89} +(1026.40 + 869.585i) q^{90} +(-7129.10 + 7129.10i) q^{91} +(11686.1 - 1946.44i) q^{92} +(-1120.54 + 1120.54i) q^{93} +(-2995.00 + 247.717i) q^{94} +1918.94i q^{95} +(-2064.90 + 5280.10i) q^{96} +8539.92 q^{97} +(-112.913 - 1365.16i) q^{98} +(-5549.51 - 5549.51i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 64q^{6} - 4q^{7} - 92q^{8} + O(q^{10}) \) \( 14q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 64q^{6} - 4q^{7} - 92q^{8} - 100q^{10} + 94q^{11} - 332q^{12} - 2q^{13} + 44q^{14} - 168q^{16} - 4q^{17} + 1390q^{18} - 706q^{19} + 1900q^{20} - 164q^{21} + 900q^{22} + 1148q^{23} - 1872q^{24} - 3416q^{26} - 1664q^{27} - 3784q^{28} + 862q^{29} - 3740q^{30} + 3208q^{32} - 4q^{33} + 7508q^{34} + 1340q^{35} + 11468q^{36} - 1826q^{37} + 3568q^{38} + 2684q^{39} - 5144q^{40} - 17064q^{42} + 1694q^{43} - 14636q^{44} + 1410q^{45} - 5316q^{46} + 6888q^{48} + 682q^{49} + 20070q^{50} - 3012q^{51} + 20452q^{52} - 482q^{53} + 10784q^{54} - 11780q^{55} - 6952q^{56} - 20456q^{58} - 2786q^{59} - 29920q^{60} - 3778q^{61} - 11472q^{62} + 15808q^{64} - 2020q^{65} + 30148q^{66} + 7998q^{67} + 18032q^{68} + 9628q^{69} + 15296q^{70} + 19964q^{71} - 17708q^{72} - 23780q^{74} + 17570q^{75} - 23996q^{76} - 9508q^{77} - 8052q^{78} + 1384q^{80} + 1454q^{81} + 16016q^{82} - 17282q^{83} + 19624q^{84} + 9948q^{85} - 4796q^{86} - 49284q^{87} + 7288q^{88} - 5416q^{90} - 28036q^{91} - 14632q^{92} + 8896q^{93} + 432q^{94} + 6064q^{96} - 4q^{97} - 12246q^{98} + 49214q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.329715 + 3.98639i 0.0824289 + 0.996597i
\(3\) 3.91498 + 3.91498i 0.434998 + 0.434998i 0.890324 0.455327i \(-0.150477\pi\)
−0.455327 + 0.890324i \(0.650477\pi\)
\(4\) −15.7826 + 2.62875i −0.986411 + 0.164297i
\(5\) 4.72348 + 4.72348i 0.188939 + 0.188939i 0.795237 0.606298i \(-0.207346\pi\)
−0.606298 + 0.795237i \(0.707346\pi\)
\(6\) −14.3158 + 16.8975i −0.397661 + 0.469374i
\(7\) 45.3712 0.925943 0.462971 0.886373i \(-0.346783\pi\)
0.462971 + 0.886373i \(0.346783\pi\)
\(8\) −15.6830 62.0487i −0.245046 0.969511i
\(9\) 50.3458i 0.621554i
\(10\) −17.2722 + 20.3870i −0.172722 + 0.203870i
\(11\) 110.228 110.228i 0.910974 0.910974i −0.0853752 0.996349i \(-0.527209\pi\)
0.996349 + 0.0853752i \(0.0272089\pi\)
\(12\) −72.0800 51.4970i −0.500555 0.357618i
\(13\) −157.128 + 157.128i −0.929754 + 0.929754i −0.997690 0.0679357i \(-0.978359\pi\)
0.0679357 + 0.997690i \(0.478359\pi\)
\(14\) 14.9596 + 180.867i 0.0763244 + 0.922792i
\(15\) 36.9847i 0.164376i
\(16\) 242.179 82.9768i 0.946013 0.324128i
\(17\) −378.592 −1.31001 −0.655003 0.755626i \(-0.727333\pi\)
−0.655003 + 0.755626i \(0.727333\pi\)
\(18\) 200.698 16.5998i 0.619438 0.0512340i
\(19\) 203.127 + 203.127i 0.562680 + 0.562680i 0.930068 0.367388i \(-0.119748\pi\)
−0.367388 + 0.930068i \(0.619748\pi\)
\(20\) −86.9656 62.1319i −0.217414 0.155330i
\(21\) 177.627 + 177.627i 0.402783 + 0.402783i
\(22\) 475.755 + 403.067i 0.982964 + 0.832783i
\(23\) −740.444 −1.39971 −0.699853 0.714287i \(-0.746751\pi\)
−0.699853 + 0.714287i \(0.746751\pi\)
\(24\) 181.521 304.318i 0.315141 0.528330i
\(25\) 580.377i 0.928604i
\(26\) −678.183 574.567i −1.00323 0.849951i
\(27\) 514.217 514.217i 0.705372 0.705372i
\(28\) −716.074 + 119.269i −0.913360 + 0.152129i
\(29\) 82.6244 82.6244i 0.0982455 0.0982455i −0.656276 0.754521i \(-0.727869\pi\)
0.754521 + 0.656276i \(0.227869\pi\)
\(30\) −147.435 + 12.1944i −0.163817 + 0.0135494i
\(31\) 286.217i 0.297833i 0.988850 + 0.148916i \(0.0475785\pi\)
−0.988850 + 0.148916i \(0.952421\pi\)
\(32\) 410.628 + 938.062i 0.401004 + 0.916076i
\(33\) 863.080 0.792543
\(34\) −124.828 1509.21i −0.107982 1.30555i
\(35\) 214.310 + 214.310i 0.174947 + 0.174947i
\(36\) 132.346 + 794.587i 0.102119 + 0.613107i
\(37\) 1470.39 + 1470.39i 1.07406 + 1.07406i 0.997028 + 0.0770352i \(0.0245454\pi\)
0.0770352 + 0.997028i \(0.475455\pi\)
\(38\) −742.770 + 876.719i −0.514384 + 0.607146i
\(39\) −1230.31 −0.808882
\(40\) 219.008 367.164i 0.136880 0.229478i
\(41\) 1301.21i 0.774070i −0.922065 0.387035i \(-0.873499\pi\)
0.922065 0.387035i \(-0.126501\pi\)
\(42\) −649.525 + 766.658i −0.368212 + 0.434613i
\(43\) −366.979 + 366.979i −0.198474 + 0.198474i −0.799346 0.600871i \(-0.794820\pi\)
0.600871 + 0.799346i \(0.294820\pi\)
\(44\) −1449.92 + 2029.44i −0.748924 + 1.04826i
\(45\) 237.808 237.808i 0.117436 0.117436i
\(46\) −244.136 2951.70i −0.115376 1.39494i
\(47\) 751.307i 0.340112i 0.985434 + 0.170056i \(0.0543948\pi\)
−0.985434 + 0.170056i \(0.945605\pi\)
\(48\) 1272.98 + 623.275i 0.552509 + 0.270519i
\(49\) −342.455 −0.142630
\(50\) 2313.61 191.359i 0.925444 0.0765437i
\(51\) −1482.18 1482.18i −0.569850 0.569850i
\(52\) 2066.84 2892.94i 0.764364 1.06988i
\(53\) −1929.33 1929.33i −0.686838 0.686838i 0.274693 0.961532i \(-0.411424\pi\)
−0.961532 + 0.274693i \(0.911424\pi\)
\(54\) 2219.41 + 1880.32i 0.761115 + 0.644829i
\(55\) 1041.32 0.344238
\(56\) −711.555 2815.22i −0.226899 0.897712i
\(57\) 1590.48i 0.489529i
\(58\) 356.616 + 302.130i 0.106009 + 0.0898129i
\(59\) −1357.57 + 1357.57i −0.389994 + 0.389994i −0.874685 0.484691i \(-0.838932\pi\)
0.484691 + 0.874685i \(0.338932\pi\)
\(60\) −97.2234 583.714i −0.0270065 0.162143i
\(61\) −1835.78 + 1835.78i −0.493356 + 0.493356i −0.909362 0.416006i \(-0.863430\pi\)
0.416006 + 0.909362i \(0.363430\pi\)
\(62\) −1140.97 + 94.3702i −0.296819 + 0.0245500i
\(63\) 2284.25i 0.575523i
\(64\) −3604.09 + 1946.22i −0.879905 + 0.475150i
\(65\) −1484.39 −0.351334
\(66\) 284.571 + 3440.57i 0.0653284 + 0.789846i
\(67\) 2205.02 + 2205.02i 0.491204 + 0.491204i 0.908686 0.417481i \(-0.137087\pi\)
−0.417481 + 0.908686i \(0.637087\pi\)
\(68\) 5975.15 995.222i 1.29220 0.215230i
\(69\) −2898.83 2898.83i −0.608869 0.608869i
\(70\) −783.662 + 924.984i −0.159931 + 0.188772i
\(71\) 8970.40 1.77949 0.889744 0.456460i \(-0.150883\pi\)
0.889744 + 0.456460i \(0.150883\pi\)
\(72\) −3123.90 + 789.572i −0.602603 + 0.152309i
\(73\) 9350.46i 1.75464i 0.479909 + 0.877318i \(0.340670\pi\)
−0.479909 + 0.877318i \(0.659330\pi\)
\(74\) −5376.75 + 6346.37i −0.981875 + 1.15894i
\(75\) 2272.17 2272.17i 0.403941 0.403941i
\(76\) −3739.84 2671.90i −0.647480 0.462587i
\(77\) 5001.17 5001.17i 0.843509 0.843509i
\(78\) −405.652 4904.49i −0.0666752 0.806129i
\(79\) 2860.08i 0.458273i −0.973394 0.229137i \(-0.926410\pi\)
0.973394 0.229137i \(-0.0735903\pi\)
\(80\) 1535.87 + 751.991i 0.239980 + 0.117499i
\(81\) −51.7173 −0.00788253
\(82\) 5187.13 429.029i 0.771436 0.0638057i
\(83\) −1036.63 1036.63i −0.150477 0.150477i 0.627854 0.778331i \(-0.283933\pi\)
−0.778331 + 0.627854i \(0.783933\pi\)
\(84\) −3270.35 2336.48i −0.463486 0.331134i
\(85\) −1788.27 1788.27i −0.247512 0.247512i
\(86\) −1583.92 1341.92i −0.214159 0.181439i
\(87\) 646.946 0.0854731
\(88\) −8568.19 5110.80i −1.10643 0.659969i
\(89\) 5171.06i 0.652830i −0.945227 0.326415i \(-0.894159\pi\)
0.945227 0.326415i \(-0.105841\pi\)
\(90\) 1026.40 + 869.585i 0.126716 + 0.107356i
\(91\) −7129.10 + 7129.10i −0.860899 + 0.860899i
\(92\) 11686.1 1946.44i 1.38068 0.229967i
\(93\) −1120.54 + 1120.54i −0.129557 + 0.129557i
\(94\) −2995.00 + 247.717i −0.338954 + 0.0280350i
\(95\) 1918.94i 0.212625i
\(96\) −2064.90 + 5280.10i −0.224055 + 0.572927i
\(97\) 8539.92 0.907633 0.453817 0.891095i \(-0.350062\pi\)
0.453817 + 0.891095i \(0.350062\pi\)
\(98\) −112.913 1365.16i −0.0117568 0.142145i
\(99\) −5549.51 5549.51i −0.566219 0.566219i
\(100\) 1525.67 + 9159.85i 0.152567 + 0.915985i
\(101\) 537.642 + 537.642i 0.0527049 + 0.0527049i 0.732968 0.680263i \(-0.238134\pi\)
−0.680263 + 0.732968i \(0.738134\pi\)
\(102\) 5419.85 6397.24i 0.520939 0.614883i
\(103\) −5543.86 −0.522562 −0.261281 0.965263i \(-0.584145\pi\)
−0.261281 + 0.965263i \(0.584145\pi\)
\(104\) 12213.9 + 7285.38i 1.12924 + 0.673574i
\(105\) 1678.04i 0.152203i
\(106\) 7054.92 8327.18i 0.627886 0.741116i
\(107\) −2989.60 + 2989.60i −0.261123 + 0.261123i −0.825510 0.564387i \(-0.809113\pi\)
0.564387 + 0.825510i \(0.309113\pi\)
\(108\) −6763.92 + 9467.41i −0.579897 + 0.811677i
\(109\) −3353.83 + 3353.83i −0.282285 + 0.282285i −0.834020 0.551734i \(-0.813966\pi\)
0.551734 + 0.834020i \(0.313966\pi\)
\(110\) 343.339 + 4151.10i 0.0283751 + 0.343066i
\(111\) 11513.1i 0.934431i
\(112\) 10988.0 3764.76i 0.875954 0.300124i
\(113\) −3193.81 −0.250122 −0.125061 0.992149i \(-0.539913\pi\)
−0.125061 + 0.992149i \(0.539913\pi\)
\(114\) −6340.27 + 524.406i −0.487863 + 0.0403513i
\(115\) −3497.48 3497.48i −0.264459 0.264459i
\(116\) −1086.83 + 1521.22i −0.0807690 + 0.113052i
\(117\) 7910.76 + 7910.76i 0.577892 + 0.577892i
\(118\) −5859.41 4964.18i −0.420813 0.356520i
\(119\) −17177.2 −1.21299
\(120\) 2294.85 580.030i 0.159365 0.0402798i
\(121\) 9659.34i 0.659746i
\(122\) −7923.41 6712.84i −0.532344 0.451010i
\(123\) 5094.22 5094.22i 0.336719 0.336719i
\(124\) −752.393 4517.24i −0.0489329 0.293785i
\(125\) 5693.58 5693.58i 0.364389 0.364389i
\(126\) 9105.91 753.153i 0.573565 0.0474397i
\(127\) 22900.5i 1.41983i −0.704287 0.709915i \(-0.748733\pi\)
0.704287 0.709915i \(-0.251267\pi\)
\(128\) −8946.69 13725.6i −0.546063 0.837744i
\(129\) −2873.43 −0.172672
\(130\) −489.425 5917.34i −0.0289601 0.350139i
\(131\) 19255.9 + 19255.9i 1.12207 + 1.12207i 0.991429 + 0.130644i \(0.0417045\pi\)
0.130644 + 0.991429i \(0.458296\pi\)
\(132\) −13621.6 + 2268.82i −0.781773 + 0.130212i
\(133\) 9216.13 + 9216.13i 0.521009 + 0.521009i
\(134\) −8063.02 + 9517.08i −0.449043 + 0.530022i
\(135\) 4857.79 0.266545
\(136\) 5937.44 + 23491.1i 0.321012 + 1.27007i
\(137\) 19938.2i 1.06229i −0.847280 0.531147i \(-0.821761\pi\)
0.847280 0.531147i \(-0.178239\pi\)
\(138\) 10600.1 12511.6i 0.556609 0.656985i
\(139\) 25175.4 25175.4i 1.30301 1.30301i 0.376649 0.926356i \(-0.377076\pi\)
0.926356 0.376649i \(-0.122924\pi\)
\(140\) −3945.73 2819.00i −0.201313 0.143826i
\(141\) −2941.35 + 2941.35i −0.147948 + 0.147948i
\(142\) 2957.68 + 35759.5i 0.146681 + 1.77343i
\(143\) 34639.8i 1.69396i
\(144\) −4177.54 12192.7i −0.201463 0.587998i
\(145\) 780.550 0.0371249
\(146\) −37274.5 + 3082.99i −1.74867 + 0.144633i
\(147\) −1340.70 1340.70i −0.0620438 0.0620438i
\(148\) −27071.9 19341.3i −1.23593 0.883003i
\(149\) −3216.99 3216.99i −0.144903 0.144903i 0.630934 0.775837i \(-0.282672\pi\)
−0.775837 + 0.630934i \(0.782672\pi\)
\(150\) 9806.91 + 8308.57i 0.435862 + 0.369270i
\(151\) −14770.5 −0.647802 −0.323901 0.946091i \(-0.604994\pi\)
−0.323901 + 0.946091i \(0.604994\pi\)
\(152\) 9418.15 15789.4i 0.407642 0.683407i
\(153\) 19060.5i 0.814239i
\(154\) 21585.6 + 18287.6i 0.910168 + 0.771109i
\(155\) −1351.94 + 1351.94i −0.0562723 + 0.0562723i
\(156\) 19417.5 3234.17i 0.797890 0.132897i
\(157\) −18014.6 + 18014.6i −0.730845 + 0.730845i −0.970787 0.239942i \(-0.922872\pi\)
0.239942 + 0.970787i \(0.422872\pi\)
\(158\) 11401.4 943.014i 0.456714 0.0377749i
\(159\) 15106.6i 0.597547i
\(160\) −2491.33 + 6370.52i −0.0973175 + 0.248848i
\(161\) −33594.8 −1.29605
\(162\) −17.0520 206.165i −0.000649748 0.00785571i
\(163\) 15083.2 + 15083.2i 0.567700 + 0.567700i 0.931483 0.363784i \(-0.118515\pi\)
−0.363784 + 0.931483i \(0.618515\pi\)
\(164\) 3420.55 + 20536.5i 0.127177 + 0.763551i
\(165\) 4076.74 + 4076.74i 0.149743 + 0.149743i
\(166\) 3790.63 4474.22i 0.137561 0.162368i
\(167\) 23733.6 0.851001 0.425501 0.904958i \(-0.360098\pi\)
0.425501 + 0.904958i \(0.360098\pi\)
\(168\) 8235.83 13807.3i 0.291802 0.489203i
\(169\) 20817.7i 0.728885i
\(170\) 6539.13 7718.37i 0.226267 0.267072i
\(171\) 10226.6 10226.6i 0.349736 0.349736i
\(172\) 4827.18 6756.57i 0.163169 0.228386i
\(173\) −12072.3 + 12072.3i −0.403363 + 0.403363i −0.879416 0.476053i \(-0.842067\pi\)
0.476053 + 0.879416i \(0.342067\pi\)
\(174\) 213.308 + 2578.98i 0.00704545 + 0.0851823i
\(175\) 26332.4i 0.859834i
\(176\) 17548.6 35841.3i 0.566521 1.15707i
\(177\) −10629.7 −0.339293
\(178\) 20613.9 1704.98i 0.650608 0.0538120i
\(179\) −28111.5 28111.5i −0.877361 0.877361i 0.115900 0.993261i \(-0.463025\pi\)
−0.993261 + 0.115900i \(0.963025\pi\)
\(180\) −3128.08 + 4378.36i −0.0965458 + 0.135134i
\(181\) −15906.7 15906.7i −0.485539 0.485539i 0.421356 0.906895i \(-0.361554\pi\)
−0.906895 + 0.421356i \(0.861554\pi\)
\(182\) −30770.0 26068.8i −0.928932 0.787006i
\(183\) −14374.1 −0.429218
\(184\) 11612.4 + 45943.6i 0.342993 + 1.35703i
\(185\) 13890.8i 0.405866i
\(186\) −4836.34 4097.43i −0.139795 0.118437i
\(187\) −41731.4 + 41731.4i −1.19338 + 1.19338i
\(188\) −1975.00 11857.6i −0.0558792 0.335490i
\(189\) 23330.6 23330.6i 0.653134 0.653134i
\(190\) −7649.63 + 632.703i −0.211901 + 0.0175264i
\(191\) 28038.6i 0.768581i 0.923212 + 0.384290i \(0.125554\pi\)
−0.923212 + 0.384290i \(0.874446\pi\)
\(192\) −21729.3 6490.54i −0.589446 0.176067i
\(193\) 56713.1 1.52254 0.761270 0.648436i \(-0.224576\pi\)
0.761270 + 0.648436i \(0.224576\pi\)
\(194\) 2815.74 + 34043.4i 0.0748152 + 0.904544i
\(195\) −5811.35 5811.35i −0.152830 0.152830i
\(196\) 5404.82 900.227i 0.140692 0.0234337i
\(197\) −10179.3 10179.3i −0.262292 0.262292i 0.563692 0.825985i \(-0.309380\pi\)
−0.825985 + 0.563692i \(0.809380\pi\)
\(198\) 20292.7 23952.3i 0.517619 0.610965i
\(199\) 31787.3 0.802689 0.401344 0.915927i \(-0.368543\pi\)
0.401344 + 0.915927i \(0.368543\pi\)
\(200\) −36011.7 + 9102.04i −0.900292 + 0.227551i
\(201\) 17265.2i 0.427346i
\(202\) −1965.98 + 2320.52i −0.0481811 + 0.0568699i
\(203\) 3748.77 3748.77i 0.0909697 0.0909697i
\(204\) 27288.9 + 19496.3i 0.655731 + 0.468482i
\(205\) 6146.25 6146.25i 0.146252 0.146252i
\(206\) −1827.89 22100.0i −0.0430742 0.520783i
\(207\) 37278.3i 0.869992i
\(208\) −25015.3 + 51091.3i −0.578200 + 1.18092i
\(209\) 44780.6 1.02517
\(210\) −6689.32 + 553.276i −0.151685 + 0.0125459i
\(211\) −10699.8 10699.8i −0.240332 0.240332i 0.576655 0.816988i \(-0.304358\pi\)
−0.816988 + 0.576655i \(0.804358\pi\)
\(212\) 35521.5 + 25378.1i 0.790350 + 0.564660i
\(213\) 35118.9 + 35118.9i 0.774073 + 0.774073i
\(214\) −12903.4 10932.0i −0.281759 0.238711i
\(215\) −3466.84 −0.0749992
\(216\) −39970.9 23842.0i −0.856716 0.511018i
\(217\) 12986.0i 0.275776i
\(218\) −14475.5 12263.9i −0.304593 0.258056i
\(219\) −36606.9 + 36606.9i −0.763263 + 0.763263i
\(220\) −16434.7 + 2737.36i −0.339560 + 0.0565571i
\(221\) 59487.5 59487.5i 1.21798 1.21798i
\(222\) −45895.8 + 3796.05i −0.931251 + 0.0770241i
\(223\) 91700.4i 1.84400i −0.387187 0.922001i \(-0.626553\pi\)
0.387187 0.922001i \(-0.373447\pi\)
\(224\) 18630.7 + 42561.0i 0.371307 + 0.848234i
\(225\) −29219.6 −0.577177
\(226\) −1053.05 12731.8i −0.0206173 0.249271i
\(227\) 17499.5 + 17499.5i 0.339605 + 0.339605i 0.856218 0.516614i \(-0.172808\pi\)
−0.516614 + 0.856218i \(0.672808\pi\)
\(228\) −4180.97 25101.9i −0.0804280 0.482877i
\(229\) −63859.8 63859.8i −1.21775 1.21775i −0.968420 0.249326i \(-0.919791\pi\)
−0.249326 0.968420i \(-0.580209\pi\)
\(230\) 12789.1 15095.5i 0.241760 0.285359i
\(231\) 39159.0 0.733850
\(232\) −6422.54 3830.94i −0.119325 0.0711754i
\(233\) 63891.7i 1.17688i 0.808540 + 0.588441i \(0.200258\pi\)
−0.808540 + 0.588441i \(0.799742\pi\)
\(234\) −28927.1 + 34143.7i −0.528290 + 0.623560i
\(235\) −3548.79 + 3548.79i −0.0642605 + 0.0642605i
\(236\) 17857.2 24994.6i 0.320620 0.448769i
\(237\) 11197.2 11197.2i 0.199348 0.199348i
\(238\) −5663.58 68474.8i −0.0999855 1.20886i
\(239\) 12096.4i 0.211768i 0.994378 + 0.105884i \(0.0337672\pi\)
−0.994378 + 0.105884i \(0.966233\pi\)
\(240\) 3068.87 + 8956.93i 0.0532790 + 0.155502i
\(241\) 27978.6 0.481717 0.240859 0.970560i \(-0.422571\pi\)
0.240859 + 0.970560i \(0.422571\pi\)
\(242\) 38505.9 3184.83i 0.657501 0.0543821i
\(243\) −41854.0 41854.0i −0.708801 0.708801i
\(244\) 24147.5 33799.1i 0.405595 0.567709i
\(245\) −1617.58 1617.58i −0.0269484 0.0269484i
\(246\) 21987.2 + 18627.9i 0.363328 + 0.307818i
\(247\) −63834.2 −1.04631
\(248\) 17759.4 4488.73i 0.288752 0.0729828i
\(249\) 8116.80i 0.130914i
\(250\) 24574.1 + 20819.6i 0.393185 + 0.333113i
\(251\) 1996.06 1996.06i 0.0316830 0.0316830i −0.691088 0.722771i \(-0.742868\pi\)
0.722771 + 0.691088i \(0.242868\pi\)
\(252\) 6004.72 + 36051.4i 0.0945565 + 0.567702i
\(253\) −81617.5 + 81617.5i −1.27509 + 1.27509i
\(254\) 91290.1 7550.63i 1.41500 0.117035i
\(255\) 14002.1i 0.215334i
\(256\) 51765.7 40190.5i 0.789882 0.613259i
\(257\) −73510.4 −1.11297 −0.556484 0.830859i \(-0.687850\pi\)
−0.556484 + 0.830859i \(0.687850\pi\)
\(258\) −947.415 11454.6i −0.0142331 0.172084i
\(259\) 66713.5 + 66713.5i 0.994521 + 0.994521i
\(260\) 23427.5 3902.08i 0.346560 0.0577231i
\(261\) −4159.80 4159.80i −0.0610648 0.0610648i
\(262\) −70412.5 + 83110.5i −1.02576 + 1.21075i
\(263\) 68109.3 0.984680 0.492340 0.870403i \(-0.336142\pi\)
0.492340 + 0.870403i \(0.336142\pi\)
\(264\) −13535.6 53553.0i −0.194210 0.768380i
\(265\) 18226.3i 0.259542i
\(266\) −33700.4 + 39777.8i −0.476290 + 0.562182i
\(267\) 20244.6 20244.6i 0.283980 0.283980i
\(268\) −40597.3 29004.4i −0.565232 0.403826i
\(269\) −15056.1 + 15056.1i −0.208069 + 0.208069i −0.803446 0.595377i \(-0.797003\pi\)
0.595377 + 0.803446i \(0.297003\pi\)
\(270\) 1601.69 + 19365.0i 0.0219710 + 0.265638i
\(271\) 104320.i 1.42046i 0.703968 + 0.710232i \(0.251410\pi\)
−0.703968 + 0.710232i \(0.748590\pi\)
\(272\) −91687.1 + 31414.3i −1.23928 + 0.424610i
\(273\) −55820.6 −0.748979
\(274\) 79481.4 6573.93i 1.05868 0.0875637i
\(275\) −63973.7 63973.7i −0.845934 0.845934i
\(276\) 53371.2 + 38130.6i 0.700630 + 0.500560i
\(277\) 2136.36 + 2136.36i 0.0278430 + 0.0278430i 0.720891 0.693048i \(-0.243733\pi\)
−0.693048 + 0.720891i \(0.743733\pi\)
\(278\) 108659. + 92058.1i 1.40598 + 1.19117i
\(279\) 14409.8 0.185119
\(280\) 9936.65 16658.7i 0.126743 0.212483i
\(281\) 36783.7i 0.465846i −0.972495 0.232923i \(-0.925171\pi\)
0.972495 0.232923i \(-0.0748290\pi\)
\(282\) −12695.2 10755.6i −0.159640 0.135249i
\(283\) 14172.0 14172.0i 0.176953 0.176953i −0.613073 0.790026i \(-0.710067\pi\)
0.790026 + 0.613073i \(0.210067\pi\)
\(284\) −141576. + 23580.9i −1.75531 + 0.292364i
\(285\) −7512.60 + 7512.60i −0.0924913 + 0.0924913i
\(286\) −138088. + 11421.3i −1.68820 + 0.139631i
\(287\) 59037.5i 0.716744i
\(288\) 47227.5 20673.4i 0.569391 0.249245i
\(289\) 59810.8 0.716117
\(290\) 257.359 + 3111.58i 0.00306016 + 0.0369985i
\(291\) 33433.6 + 33433.6i 0.394819 + 0.394819i
\(292\) −24580.0 147574.i −0.288281 1.73079i
\(293\) 80721.8 + 80721.8i 0.940276 + 0.940276i 0.998314 0.0580384i \(-0.0184846\pi\)
−0.0580384 + 0.998314i \(0.518485\pi\)
\(294\) 4902.52 5786.62i 0.0567185 0.0669469i
\(295\) −12824.9 −0.147370
\(296\) 68175.9 114296.i 0.778122 1.30451i
\(297\) 113362.i 1.28515i
\(298\) 11763.5 13884.9i 0.132466 0.156354i
\(299\) 116345. 116345.i 1.30138 1.30138i
\(300\) −29887.7 + 41833.6i −0.332085 + 0.464818i
\(301\) −16650.3 + 16650.3i −0.183776 + 0.183776i
\(302\) −4870.07 58881.1i −0.0533976 0.645598i
\(303\) 4209.72i 0.0458530i
\(304\) 66048.1 + 32338.4i 0.714683 + 0.349922i
\(305\) −17342.5 −0.186429
\(306\) −75982.7 + 6284.55i −0.811468 + 0.0671168i
\(307\) 113714. + 113714.i 1.20653 + 1.20653i 0.972143 + 0.234389i \(0.0753090\pi\)
0.234389 + 0.972143i \(0.424691\pi\)
\(308\) −65784.5 + 92078.1i −0.693461 + 0.970633i
\(309\) −21704.1 21704.1i −0.227313 0.227313i
\(310\) −5835.12 4943.61i −0.0607193 0.0514424i
\(311\) −93801.8 −0.969819 −0.484909 0.874564i \(-0.661147\pi\)
−0.484909 + 0.874564i \(0.661147\pi\)
\(312\) 19294.9 + 76339.2i 0.198214 + 0.784220i
\(313\) 9229.52i 0.0942086i −0.998890 0.0471043i \(-0.985001\pi\)
0.998890 0.0471043i \(-0.0149993\pi\)
\(314\) −77752.9 65873.5i −0.788601 0.668115i
\(315\) 10789.6 10789.6i 0.108739 0.108739i
\(316\) 7518.44 + 45139.5i 0.0752928 + 0.452046i
\(317\) −8447.44 + 8447.44i −0.0840634 + 0.0840634i −0.747888 0.663825i \(-0.768932\pi\)
0.663825 + 0.747888i \(0.268932\pi\)
\(318\) 60220.7 4980.87i 0.595513 0.0492551i
\(319\) 18215.0i 0.178998i
\(320\) −26216.8 7830.94i −0.256023 0.0764740i
\(321\) −23408.5 −0.227176
\(322\) −11076.7 133922.i −0.106832 1.29164i
\(323\) −76902.4 76902.4i −0.737114 0.737114i
\(324\) 816.232 135.952i 0.00777542 0.00129507i
\(325\) 91193.8 + 91193.8i 0.863373 + 0.863373i
\(326\) −55154.4 + 65100.7i −0.518973 + 0.612562i
\(327\) −26260.4 −0.245587
\(328\) −80738.5 + 20406.8i −0.750469 + 0.189683i
\(329\) 34087.7i 0.314924i
\(330\) −14907.3 + 17595.6i −0.136890 + 0.161576i
\(331\) −46092.1 + 46092.1i −0.420698 + 0.420698i −0.885444 0.464746i \(-0.846146\pi\)
0.464746 + 0.885444i \(0.346146\pi\)
\(332\) 19085.8 + 13635.7i 0.173155 + 0.123709i
\(333\) 74028.2 74028.2i 0.667588 0.667588i
\(334\) 7825.33 + 94611.2i 0.0701471 + 0.848105i
\(335\) 20830.7i 0.185616i
\(336\) 57756.6 + 28278.7i 0.511592 + 0.250485i
\(337\) 39317.8 0.346201 0.173101 0.984904i \(-0.444621\pi\)
0.173101 + 0.984904i \(0.444621\pi\)
\(338\) 82987.4 6863.91i 0.726405 0.0600812i
\(339\) −12503.7 12503.7i −0.108803 0.108803i
\(340\) 32924.5 + 23522.6i 0.284814 + 0.203483i
\(341\) 31549.1 + 31549.1i 0.271318 + 0.271318i
\(342\) 44139.1 + 37395.4i 0.377374 + 0.319717i
\(343\) −124474. −1.05801
\(344\) 28525.9 + 17015.3i 0.241059 + 0.143788i
\(345\) 27385.1i 0.230079i
\(346\) −52105.1 44144.3i −0.435239 0.368742i
\(347\) −67694.0 + 67694.0i −0.562201 + 0.562201i −0.929932 0.367731i \(-0.880135\pi\)
0.367731 + 0.929932i \(0.380135\pi\)
\(348\) −10210.5 + 1700.66i −0.0843116 + 0.0140430i
\(349\) −7662.83 + 7662.83i −0.0629127 + 0.0629127i −0.737863 0.674950i \(-0.764165\pi\)
0.674950 + 0.737863i \(0.264165\pi\)
\(350\) 104971. 8682.20i 0.856908 0.0708751i
\(351\) 161596.i 1.31165i
\(352\) 148663. + 58137.9i 1.19983 + 0.469217i
\(353\) 70618.0 0.566716 0.283358 0.959014i \(-0.408551\pi\)
0.283358 + 0.959014i \(0.408551\pi\)
\(354\) −3504.78 42374.2i −0.0279675 0.338138i
\(355\) 42371.5 + 42371.5i 0.336215 + 0.336215i
\(356\) 13593.4 + 81612.7i 0.107258 + 0.643958i
\(357\) −67248.3 67248.3i −0.527649 0.527649i
\(358\) 102795. 121332.i 0.802055 0.946695i
\(359\) −168144. −1.30465 −0.652323 0.757941i \(-0.726206\pi\)
−0.652323 + 0.757941i \(0.726206\pi\)
\(360\) −18485.2 11026.1i −0.142633 0.0850782i
\(361\) 47799.6i 0.366783i
\(362\) 58165.8 68655.2i 0.443864 0.523909i
\(363\) 37816.1 37816.1i 0.286988 0.286988i
\(364\) 93775.0 131256.i 0.707757 0.990643i
\(365\) −44166.7 + 44166.7i −0.331520 + 0.331520i
\(366\) −4739.35 57300.6i −0.0353799 0.427757i
\(367\) 82596.4i 0.613238i −0.951832 0.306619i \(-0.900802\pi\)
0.951832 0.306619i \(-0.0991977\pi\)
\(368\) −179320. + 61439.7i −1.32414 + 0.453684i
\(369\) −65510.6 −0.481126
\(370\) −55373.9 + 4580.00i −0.404485 + 0.0334550i
\(371\) −87536.0 87536.0i −0.635973 0.635973i
\(372\) 14739.3 20630.5i 0.106510 0.149082i
\(373\) −76631.0 76631.0i −0.550791 0.550791i 0.375878 0.926669i \(-0.377341\pi\)
−0.926669 + 0.375878i \(0.877341\pi\)
\(374\) −180117. 152598.i −1.28769 1.09095i
\(375\) 44580.5 0.317017
\(376\) 46617.6 11782.7i 0.329742 0.0833431i
\(377\) 25965.3i 0.182688i
\(378\) 100697. + 85312.4i 0.704749 + 0.597075i
\(379\) −95935.8 + 95935.8i −0.667886 + 0.667886i −0.957226 0.289340i \(-0.906564\pi\)
0.289340 + 0.957226i \(0.406564\pi\)
\(380\) −5044.40 30285.8i −0.0349335 0.209735i
\(381\) 89654.8 89654.8i 0.617623 0.617623i
\(382\) −111773. + 9244.76i −0.765965 + 0.0633532i
\(383\) 168708.i 1.15011i −0.818116 0.575054i \(-0.804981\pi\)
0.818116 0.575054i \(-0.195019\pi\)
\(384\) 18709.3 88761.6i 0.126881 0.601953i
\(385\) 47245.9 0.318744
\(386\) 18699.2 + 226080.i 0.125501 + 1.51736i
\(387\) 18475.9 + 18475.9i 0.123362 + 0.123362i
\(388\) −134782. + 22449.3i −0.895299 + 0.149121i
\(389\) 66490.0 + 66490.0i 0.439397 + 0.439397i 0.891809 0.452412i \(-0.149436\pi\)
−0.452412 + 0.891809i \(0.649436\pi\)
\(390\) 21250.2 25082.4i 0.139712 0.164907i
\(391\) 280326. 1.83362
\(392\) 5370.71 + 21248.9i 0.0349510 + 0.138282i
\(393\) 150773.i 0.976199i
\(394\) 37222.4 43934.9i 0.239779 0.283020i
\(395\) 13509.6 13509.6i 0.0865859 0.0865859i
\(396\) 102174. + 72997.3i 0.651552 + 0.465497i
\(397\) 18578.8 18578.8i 0.117879 0.117879i −0.645706 0.763586i \(-0.723437\pi\)
0.763586 + 0.645706i \(0.223437\pi\)
\(398\) 10480.8 + 126716.i 0.0661647 + 0.799957i
\(399\) 72162.0i 0.453276i
\(400\) −48157.9 140555.i −0.300987 0.878471i
\(401\) −129108. −0.802908 −0.401454 0.915879i \(-0.631495\pi\)
−0.401454 + 0.915879i \(0.631495\pi\)
\(402\) −68825.7 + 5692.60i −0.425891 + 0.0352256i
\(403\) −44972.9 44972.9i −0.276911 0.276911i
\(404\) −9898.70 7072.05i −0.0606479 0.0433294i
\(405\) −244.286 244.286i −0.00148932 0.00148932i
\(406\) 16180.1 + 13708.0i 0.0981586 + 0.0831616i
\(407\) 324156. 1.95689
\(408\) −68722.4 + 115212.i −0.412836 + 0.692116i
\(409\) 17952.4i 0.107319i −0.998559 0.0536594i \(-0.982911\pi\)
0.998559 0.0536594i \(-0.0170885\pi\)
\(410\) 26527.8 + 22474.8i 0.157810 + 0.133699i
\(411\) 78057.7 78057.7i 0.462096 0.462096i
\(412\) 87496.3 14573.4i 0.515461 0.0858551i
\(413\) −61594.5 + 61594.5i −0.361112 + 0.361112i
\(414\) −148606. + 12291.2i −0.867031 + 0.0717124i
\(415\) 9793.04i 0.0568619i
\(416\) −211918. 82874.9i −1.22456 0.478891i
\(417\) 197122. 1.13361
\(418\) 14764.8 + 178513.i 0.0845038 + 1.02168i
\(419\) 56887.3 + 56887.3i 0.324031 + 0.324031i 0.850311 0.526280i \(-0.176414\pi\)
−0.526280 + 0.850311i \(0.676414\pi\)
\(420\) −4411.14 26483.8i −0.0250065 0.150135i
\(421\) −144162. 144162.i −0.813365 0.813365i 0.171772 0.985137i \(-0.445051\pi\)
−0.985137 + 0.171772i \(0.945051\pi\)
\(422\) 39125.8 46181.6i 0.219704 0.259325i
\(423\) 37825.2 0.211398
\(424\) −89454.8 + 149970.i −0.497590 + 0.834205i
\(425\) 219726.i 1.21648i
\(426\) −128418. + 151577.i −0.707633 + 0.835245i
\(427\) −83291.4 + 83291.4i −0.456819 + 0.456819i
\(428\) 39324.7 55042.5i 0.214673 0.300477i
\(429\) −135614. + 135614.i −0.736870 + 0.736870i
\(430\) −1143.07 13820.2i −0.00618210 0.0747440i
\(431\) 18641.5i 0.100352i 0.998740 + 0.0501760i \(0.0159782\pi\)
−0.998740 + 0.0501760i \(0.984022\pi\)
\(432\) 81864.6 167201.i 0.438661 0.895923i
\(433\) 2193.97 0.0117019 0.00585094 0.999983i \(-0.498138\pi\)
0.00585094 + 0.999983i \(0.498138\pi\)
\(434\) −51767.3 + 4281.69i −0.274838 + 0.0227319i
\(435\) 3055.84 + 3055.84i 0.0161492 + 0.0161492i
\(436\) 44115.7 61748.5i 0.232071 0.324828i
\(437\) −150404. 150404.i −0.787586 0.787586i
\(438\) −157999. 133859.i −0.823581 0.697751i
\(439\) 118115. 0.612880 0.306440 0.951890i \(-0.400862\pi\)
0.306440 + 0.951890i \(0.400862\pi\)
\(440\) −16331.0 64612.5i −0.0843541 0.333742i
\(441\) 17241.2i 0.0886523i
\(442\) 256754. + 217526.i 1.31424 + 1.11344i
\(443\) 37885.8 37885.8i 0.193050 0.193050i −0.603963 0.797013i \(-0.706412\pi\)
0.797013 + 0.603963i \(0.206412\pi\)
\(444\) −30265.1 181707.i −0.153524 0.921733i
\(445\) 24425.4 24425.4i 0.123345 0.123345i
\(446\) 365553. 30235.0i 1.83773 0.151999i
\(447\) 25188.9i 0.126065i
\(448\) −163522. + 88302.1i −0.814741 + 0.439962i
\(449\) −85186.6 −0.422550 −0.211275 0.977427i \(-0.567762\pi\)
−0.211275 + 0.977427i \(0.567762\pi\)
\(450\) −9634.15 116481.i −0.0475760 0.575213i
\(451\) −143430. 143430.i −0.705157 0.705157i
\(452\) 50406.5 8395.71i 0.246723 0.0410942i
\(453\) −57826.4 57826.4i −0.281793 0.281793i
\(454\) −63989.9 + 75529.6i −0.310456 + 0.366442i
\(455\) −67348.4 −0.325315
\(456\) 98687.2 24943.4i 0.474604 0.119957i
\(457\) 96935.7i 0.464142i −0.972699 0.232071i \(-0.925450\pi\)
0.972699 0.232071i \(-0.0745502\pi\)
\(458\) 233514. 275625.i 1.11322 1.31398i
\(459\) −194678. + 194678.i −0.924042 + 0.924042i
\(460\) 64393.2 + 46005.2i 0.304315 + 0.217416i
\(461\) 295014. 295014.i 1.38816 1.38816i 0.558988 0.829176i \(-0.311190\pi\)
0.829176 0.558988i \(-0.188810\pi\)
\(462\) 12911.3 + 156103.i 0.0604904 + 0.731352i
\(463\) 224348.i 1.04655i −0.852164 0.523275i \(-0.824710\pi\)
0.852164 0.523275i \(-0.175290\pi\)
\(464\) 13154.0 26865.8i 0.0610974 0.124786i
\(465\) −10585.7 −0.0489567
\(466\) −254697. + 21066.1i −1.17288 + 0.0970090i
\(467\) 189556. + 189556.i 0.869168 + 0.869168i 0.992380 0.123212i \(-0.0393196\pi\)
−0.123212 + 0.992380i \(0.539320\pi\)
\(468\) −145648. 104057.i −0.664985 0.475093i
\(469\) 100044. + 100044.i 0.454827 + 0.454827i
\(470\) −15316.9 12976.7i −0.0693387 0.0587449i
\(471\) −141054. −0.635832
\(472\) 105526. + 62944.7i 0.473670 + 0.282537i
\(473\) 80902.6i 0.361610i
\(474\) 48328.2 + 40944.4i 0.215102 + 0.182238i
\(475\) 117891. 117891.i 0.522506 0.522506i
\(476\) 271100. 45154.4i 1.19651 0.199290i
\(477\) −97133.7 + 97133.7i −0.426907 + 0.426907i
\(478\) −48221.0 + 3988.37i −0.211047 + 0.0174558i
\(479\) 132796.i 0.578781i 0.957211 + 0.289390i \(0.0934526\pi\)
−0.957211 + 0.289390i \(0.906547\pi\)
\(480\) −34693.9 + 15187.0i −0.150581 + 0.0659156i
\(481\) −462081. −1.99723
\(482\) 9224.98 + 111534.i 0.0397074 + 0.480078i
\(483\) −131523. 131523.i −0.563778 0.563778i
\(484\) 25392.0 + 152449.i 0.108394 + 0.650781i
\(485\) 40338.2 + 40338.2i 0.171488 + 0.171488i
\(486\) 153046. 180646.i 0.647964 0.764815i
\(487\) −283936. −1.19719 −0.598595 0.801052i \(-0.704274\pi\)
−0.598595 + 0.801052i \(0.704274\pi\)
\(488\) 142698. + 85117.3i 0.599209 + 0.357419i
\(489\) 118101.i 0.493896i
\(490\) 5914.96 6981.64i 0.0246354 0.0290781i
\(491\) −111725. + 111725.i −0.463435 + 0.463435i −0.899780 0.436345i \(-0.856273\pi\)
0.436345 + 0.899780i \(0.356273\pi\)
\(492\) −67008.5 + 93791.3i −0.276821 + 0.387465i
\(493\) −31280.9 + 31280.9i −0.128702 + 0.128702i
\(494\) −21047.1 254468.i −0.0862459 1.04275i
\(495\) 52426.1i 0.213962i
\(496\) 23749.4 + 69315.9i 0.0965359 + 0.281754i
\(497\) 406998. 1.64770
\(498\) 32356.7 2676.23i 0.130468 0.0107911i
\(499\) 61595.1 + 61595.1i 0.247369 + 0.247369i 0.819890 0.572521i \(-0.194035\pi\)
−0.572521 + 0.819890i \(0.694035\pi\)
\(500\) −74892.4 + 104826.i −0.299570 + 0.419305i
\(501\) 92916.5 + 92916.5i 0.370184 + 0.370184i
\(502\) 8615.21 + 7298.95i 0.0341868 + 0.0289636i
\(503\) −70874.1 −0.280125 −0.140062 0.990143i \(-0.544730\pi\)
−0.140062 + 0.990143i \(0.544730\pi\)
\(504\) −141735. + 35823.8i −0.557976 + 0.141030i
\(505\) 5079.09i 0.0199160i
\(506\) −352270. 298449.i −1.37586 1.16565i
\(507\) 81500.9 81500.9i 0.317064 0.317064i
\(508\) 60199.5 + 361428.i 0.233274 + 1.40054i
\(509\) −128181. + 128181.i −0.494754 + 0.494754i −0.909800 0.415046i \(-0.863765\pi\)
0.415046 + 0.909800i \(0.363765\pi\)
\(510\) 55817.8 4616.71i 0.214601 0.0177498i
\(511\) 424241.i 1.62469i
\(512\) 177283. + 193107.i 0.676281 + 0.736644i
\(513\) 208903. 0.793797
\(514\) −24237.5 293041.i −0.0917406 1.10918i
\(515\) −26186.3 26186.3i −0.0987324 0.0987324i
\(516\) 45350.2 7553.53i 0.170325 0.0283694i
\(517\) 82814.9 + 82814.9i 0.309833 + 0.309833i
\(518\) −243949. + 287942.i −0.909160 + 1.07311i
\(519\) −94525.3 −0.350924
\(520\) 23279.6 + 92104.3i 0.0860932 + 0.340623i
\(521\) 494250.i 1.82084i −0.413688 0.910419i \(-0.635759\pi\)
0.413688 0.910419i \(-0.364241\pi\)
\(522\) 15211.0 17954.1i 0.0558235 0.0658905i
\(523\) 179670. 179670.i 0.656859 0.656859i −0.297776 0.954636i \(-0.596245\pi\)
0.954636 + 0.297776i \(0.0962450\pi\)
\(524\) −354527. 253289.i −1.29118 0.922473i
\(525\) 103091. 103091.i 0.374026 0.374026i
\(526\) 22456.7 + 271510.i 0.0811660 + 0.981329i
\(527\) 108360.i 0.390163i
\(528\) 209020. 71615.6i 0.749756 0.256886i
\(529\) 268417. 0.959175
\(530\) 72657.1 6009.50i 0.258658 0.0213937i
\(531\) 68347.9 + 68347.9i 0.242402 + 0.242402i
\(532\) −169681. 121227.i −0.599529 0.428329i
\(533\) 204457. + 204457.i 0.719694 + 0.719694i
\(534\) 87377.9 + 74027.9i 0.306421 + 0.259605i
\(535\) −28242.7 −0.0986729
\(536\) 102237. 171400.i 0.355860 0.596596i
\(537\) 220112.i 0.763300i
\(538\) −64983.7 55055.2i −0.224512 0.190210i
\(539\) −37748.1 + 37748.1i −0.129932 + 0.129932i
\(540\) −76668.4 + 12769.9i −0.262923 + 0.0437925i
\(541\) 300961. 300961.i 1.02829 1.02829i 0.0287034 0.999588i \(-0.490862\pi\)
0.999588 0.0287034i \(-0.00913784\pi\)
\(542\) −415861. + 34396.0i −1.41563 + 0.117087i
\(543\) 124549.i 0.422417i
\(544\) −155460. 355143.i −0.525318 1.20007i
\(545\) −31683.6 −0.106670
\(546\) −18404.9 222523.i −0.0617374 0.746430i
\(547\) −159057. 159057.i −0.531591 0.531591i 0.389455 0.921046i \(-0.372663\pi\)
−0.921046 + 0.389455i \(0.872663\pi\)
\(548\) 52412.5 + 314676.i 0.174531 + 1.04786i
\(549\) 92423.8 + 92423.8i 0.306647 + 0.306647i
\(550\) 233931. 276117.i 0.773326 0.912784i
\(551\) 33566.6 0.110561
\(552\) −134406. + 225331.i −0.441104 + 0.739506i
\(553\) 129765.i 0.424335i
\(554\) −7811.98 + 9220.76i −0.0254532 + 0.0300433i
\(555\) −54382.0 + 54382.0i −0.176551 + 0.176551i
\(556\) −331152. + 463512.i −1.07122 + 1.49938i
\(557\) −394524. + 394524.i −1.27164 + 1.27164i −0.326409 + 0.945229i \(0.605839\pi\)
−0.945229 + 0.326409i \(0.894161\pi\)
\(558\) 4751.15 + 57443.2i 0.0152591 + 0.184489i
\(559\) 115326.i 0.369065i
\(560\) 69684.2 + 34118.7i 0.222207 + 0.108797i
\(561\) −326755. −1.03824
\(562\) 146634. 12128.1i 0.464261 0.0383992i
\(563\) 169317. + 169317.i 0.534177 + 0.534177i 0.921813 0.387636i \(-0.126708\pi\)
−0.387636 + 0.921813i \(0.626708\pi\)
\(564\) 38690.0 54154.2i 0.121630 0.170245i
\(565\) −15085.9 15085.9i −0.0472579 0.0472579i
\(566\) 61167.9 + 51822.4i 0.190937 + 0.161765i
\(567\) −2346.48 −0.00729877
\(568\) −140682. 556602.i −0.436057 1.72523i
\(569\) 165645.i 0.511626i −0.966726 0.255813i \(-0.917657\pi\)
0.966726 0.255813i \(-0.0823432\pi\)
\(570\) −32425.2 27471.1i −0.0998005 0.0845526i
\(571\) 335641. 335641.i 1.02945 1.02945i 0.0298925 0.999553i \(-0.490483\pi\)
0.999553 0.0298925i \(-0.00951651\pi\)
\(572\) −91059.4 546706.i −0.278312 1.67094i
\(573\) −109771. + 109771.i −0.334331 + 0.334331i
\(574\) 235346. 19465.6i 0.714305 0.0590804i
\(575\) 429737.i 1.29977i
\(576\) 97983.9 + 181451.i 0.295331 + 0.546908i
\(577\) −99615.9 −0.299211 −0.149605 0.988746i \(-0.547800\pi\)
−0.149605 + 0.988746i \(0.547800\pi\)
\(578\) 19720.5 + 238429.i 0.0590287 + 0.713680i
\(579\) 222031. + 222031.i 0.662301 + 0.662301i
\(580\) −12319.1 + 2051.87i −0.0366204 + 0.00609949i
\(581\) −47033.3 47033.3i −0.139333 0.139333i
\(582\) −122256. + 144303.i −0.360930 + 0.426019i
\(583\) −425331. −1.25138
\(584\) 580184. 146643.i 1.70114 0.429967i
\(585\) 74732.7i 0.218373i
\(586\) −295173. + 348403.i −0.859570 + 1.01458i
\(587\) −45023.9 + 45023.9i −0.130667 + 0.130667i −0.769416 0.638748i \(-0.779452\pi\)
0.638748 + 0.769416i \(0.279452\pi\)
\(588\) 24684.1 + 17635.4i 0.0713943 + 0.0510071i
\(589\) −58138.5 + 58138.5i −0.167584 + 0.167584i
\(590\) −4228.57 51125.1i −0.0121476 0.146869i
\(591\) 79703.6i 0.228193i
\(592\) 478107. + 234090.i 1.36421 + 0.667944i
\(593\) −385101. −1.09513 −0.547564 0.836764i \(-0.684445\pi\)
−0.547564 + 0.836764i \(0.684445\pi\)
\(594\) 451905. 37377.2i 1.28078 0.105934i
\(595\) −81136.1 81136.1i −0.229182 0.229182i
\(596\) 59229.0 + 42315.7i 0.166741 + 0.119127i
\(597\) 124447. + 124447.i 0.349168 + 0.349168i
\(598\) 502156. + 425435.i 1.40422 + 1.18968i
\(599\) 209331. 0.583417 0.291709 0.956507i \(-0.405776\pi\)
0.291709 + 0.956507i \(0.405776\pi\)
\(600\) −176619. 105351.i −0.490609 0.292641i
\(601\) 515555.i 1.42734i 0.700484 + 0.713668i \(0.252967\pi\)
−0.700484 + 0.713668i \(0.747033\pi\)
\(602\) −71864.3 60884.6i −0.198299 0.168002i
\(603\) 111013. 111013.i 0.305310 0.305310i
\(604\) 233117. 38828.0i 0.638999 0.106432i
\(605\) 45625.7 45625.7i 0.124652 0.124652i
\(606\) −16781.6 + 1388.01i −0.0456970 + 0.00377961i
\(607\) 30292.7i 0.0822167i 0.999155 + 0.0411084i \(0.0130889\pi\)
−0.999155 + 0.0411084i \(0.986911\pi\)
\(608\) −107136. + 273956.i −0.289821 + 0.741094i
\(609\) 29352.7 0.0791432
\(610\) −5718.10 69134.1i −0.0153671 0.185794i
\(611\) −118052. 118052.i −0.316220 0.316220i
\(612\) −50105.3 300824.i −0.133777 0.803175i
\(613\) −99803.4 99803.4i −0.265598 0.265598i 0.561726 0.827324i \(-0.310138\pi\)
−0.827324 + 0.561726i \(0.810138\pi\)
\(614\) −415816. + 490803.i −1.10297 + 1.30188i
\(615\) 48124.9 0.127239
\(616\) −388749. 231883.i −1.02449 0.611093i
\(617\) 102196.i 0.268451i −0.990951 0.134226i \(-0.957145\pi\)
0.990951 0.134226i \(-0.0428547\pi\)
\(618\) 79364.8 93677.1i 0.207802 0.245277i
\(619\) −105904. + 105904.i −0.276395 + 0.276395i −0.831668 0.555273i \(-0.812614\pi\)
0.555273 + 0.831668i \(0.312614\pi\)
\(620\) 17783.2 24891.0i 0.0462623 0.0647530i
\(621\) −380749. + 380749.i −0.987314 + 0.987314i
\(622\) −30927.9 373930.i −0.0799410 0.966518i
\(623\) 234617.i 0.604483i
\(624\) −297956. + 102087.i −0.765213 + 0.262181i
\(625\) −308949. −0.790909
\(626\) 36792.5 3043.12i 0.0938880 0.00776551i
\(627\) 175315. + 175315.i 0.445948 + 0.445948i
\(628\) 236961. 331673.i 0.600838 0.840989i
\(629\) −556679. 556679.i −1.40703 1.40703i
\(630\) 46569.1 + 39454.1i 0.117332 + 0.0994057i
\(631\) 692480. 1.73920 0.869598 0.493760i \(-0.164378\pi\)
0.869598 + 0.493760i \(0.164378\pi\)
\(632\) −177465. + 44854.6i −0.444301 + 0.112298i
\(633\) 83779.3i 0.209088i
\(634\) −36460.0 30889.5i −0.0907065 0.0768481i
\(635\) 108170. 108170.i 0.268262 0.268262i
\(636\) 39711.4 + 238421.i 0.0981749 + 0.589427i
\(637\) 53809.4 53809.4i 0.132611 0.132611i
\(638\) 72612.1 6005.77i 0.178389 0.0147546i
\(639\) 451622.i 1.10605i
\(640\) 22573.1 107092.i 0.0551101 0.261456i
\(641\) 49519.0 0.120519 0.0602595 0.998183i \(-0.480807\pi\)
0.0602595 + 0.998183i \(0.480807\pi\)
\(642\) −7718.13 93315.2i −0.0187259 0.226403i
\(643\) −165494. 165494.i −0.400276 0.400276i 0.478054 0.878330i \(-0.341342\pi\)
−0.878330 + 0.478054i \(0.841342\pi\)
\(644\) 530213. 88312.3i 1.27844 0.212936i
\(645\) −13572.6 13572.6i −0.0326245 0.0326245i
\(646\) 281207. 331919.i 0.673846 0.795365i
\(647\) −666565. −1.59233 −0.796166 0.605078i \(-0.793142\pi\)
−0.796166 + 0.605078i \(0.793142\pi\)
\(648\) 811.080 + 3208.99i 0.00193159 + 0.00764221i
\(649\) 299284.i 0.710548i
\(650\) −333466. + 393602.i −0.789268 + 0.931602i
\(651\) −50840.0 + 50840.0i −0.119962 + 0.119962i
\(652\) −277702. 198402.i −0.653256 0.466714i
\(653\) 461118. 461118.i 1.08140 1.08140i 0.0850198 0.996379i \(-0.472905\pi\)
0.996379 0.0850198i \(-0.0270954\pi\)
\(654\) −8658.45 104684.i −0.0202435 0.244751i
\(655\) 181910.i 0.424008i
\(656\) −107970. 315127.i −0.250898 0.732280i
\(657\) 470757. 1.09060
\(658\) −135887. + 11239.2i −0.313852 + 0.0259588i
\(659\) 326883. + 326883.i 0.752698 + 0.752698i 0.974982 0.222284i \(-0.0713511\pi\)
−0.222284 + 0.974982i \(0.571351\pi\)
\(660\) −75058.2 53624.8i −0.172310 0.123106i
\(661\) 549615. + 549615.i 1.25793 + 1.25793i 0.952080 + 0.305848i \(0.0989401\pi\)
0.305848 + 0.952080i \(0.401060\pi\)
\(662\) −198938. 168544.i −0.453944 0.384589i
\(663\) 465785. 1.05964
\(664\) −48064.3 + 80579.2i −0.109015 + 0.182762i
\(665\) 87064.5i 0.196878i
\(666\) 319513. + 270697.i 0.720345 + 0.610288i
\(667\) −61178.8 + 61178.8i −0.137515 + 0.137515i
\(668\) −374577. + 62389.6i −0.839437 + 0.139817i
\(669\) 359005. 359005.i 0.802137 0.802137i
\(670\) −83039.3 + 6868.21i −0.184984 + 0.0153001i
\(671\) 404708.i 0.898869i
\(672\) −93686.8 + 239564.i −0.207463 + 0.530498i
\(673\) 191664. 0.423166 0.211583 0.977360i \(-0.432138\pi\)
0.211583 + 0.977360i \(0.432138\pi\)
\(674\) 12963.7 + 156736.i 0.0285370 + 0.345023i
\(675\) −298440. 298440.i −0.655012 0.655012i
\(676\) 54724.4 + 328557.i 0.119753 + 0.718980i
\(677\) −544201. 544201.i −1.18736 1.18736i −0.977795 0.209564i \(-0.932796\pi\)
−0.209564 0.977795i \(-0.567204\pi\)
\(678\) 45721.9 53967.3i 0.0994638 0.117401i
\(679\) 387466. 0.840416
\(680\) −82914.6 + 139005.i −0.179314 + 0.300617i
\(681\) 137020.i 0.295455i
\(682\) −115365. + 136169.i −0.248030 + 0.292759i
\(683\) −570769. + 570769.i −1.22354 + 1.22354i −0.257179 + 0.966364i \(0.582793\pi\)
−0.966364 + 0.257179i \(0.917207\pi\)
\(684\) −134519. + 188286.i −0.287523 + 0.402443i
\(685\) 94177.8 94177.8i 0.200709 0.200709i
\(686\) −41040.9 496201.i −0.0872106 1.05441i
\(687\) 500020.i 1.05943i
\(688\) −58424.0 + 119325.i −0.123428 + 0.252090i
\(689\) 606305. 1.27718
\(690\) 109168. 9029.29i 0.229296 0.0189651i
\(691\) −333477. 333477.i −0.698409 0.698409i 0.265658 0.964067i \(-0.414411\pi\)
−0.964067 + 0.265658i \(0.914411\pi\)
\(692\) 158796. 222266.i 0.331611 0.464153i
\(693\) −251788. 251788.i −0.524286 0.524286i
\(694\) −292174. 247535.i −0.606629 0.513946i
\(695\) 237831. 0.492378
\(696\) −10146.0 40142.2i −0.0209449 0.0828672i
\(697\) 492628.i 1.01404i
\(698\) −33073.6 28020.5i −0.0678845 0.0575128i
\(699\) −250135. + 250135.i −0.511941 + 0.511941i
\(700\) 69221.3 + 415593.i 0.141268 + 0.848150i
\(701\) 31503.2 31503.2i 0.0641089 0.0641089i −0.674325 0.738434i \(-0.735565\pi\)
0.738434 + 0.674325i \(0.235565\pi\)
\(702\) −644185. + 53280.7i −1.30718 + 0.108117i
\(703\) 597354.i 1.20871i
\(704\) −182744. + 611798.i −0.368720 + 1.23442i
\(705\) −27786.9 −0.0559064
\(706\) 23283.8 + 281511.i 0.0467138 + 0.564788i
\(707\) 24393.5 + 24393.5i 0.0488017 + 0.0488017i
\(708\) 167764. 27942.8i 0.334682 0.0557447i
\(709\) 609708. + 609708.i 1.21291 + 1.21291i 0.970064 + 0.242847i \(0.0780815\pi\)
0.242847 + 0.970064i \(0.421919\pi\)
\(710\) −154939. + 182880.i −0.307357 + 0.362785i
\(711\) −143993. −0.284841
\(712\) −320858. + 81097.6i −0.632926 + 0.159973i
\(713\) 211928.i 0.416878i
\(714\) 245905. 290251.i 0.482359 0.569346i
\(715\) −163621. + 163621.i −0.320056 + 0.320056i
\(716\) 517570. + 369774.i 1.00959 + 0.721291i
\(717\) −47357.2 + 47357.2i −0.0921187 + 0.0921187i
\(718\) −55439.7 670288.i −0.107541 1.30021i
\(719\) 720908.i 1.39451i −0.716823 0.697256i \(-0.754404\pi\)
0.716823 0.697256i \(-0.245596\pi\)
\(720\) 37859.6 77324.7i 0.0730317 0.149160i
\(721\) −251531. −0.483862
\(722\) 190548. 15760.3i 0.365535 0.0302335i
\(723\) 109536. + 109536.i 0.209546 + 0.209546i
\(724\) 292864. + 209235.i 0.558714 + 0.399169i
\(725\) −47953.4 47953.4i −0.0912311 0.0912311i
\(726\) 163218. + 138281.i 0.309668 + 0.262355i
\(727\) −279904. −0.529591 −0.264796 0.964305i \(-0.585304\pi\)
−0.264796 + 0.964305i \(0.585304\pi\)
\(728\) 554157. + 330546.i 1.04561 + 0.623691i
\(729\) 323526.i 0.608772i
\(730\) −190628. 161503.i −0.357718 0.303065i
\(731\) 138935. 138935.i 0.260003 0.260003i
\(732\) 226860. 37785.8i 0.423385 0.0705191i
\(733\) −266306. + 266306.i −0.495648 + 0.495648i −0.910080 0.414432i \(-0.863980\pi\)
0.414432 + 0.910080i \(0.363980\pi\)
\(734\) 329261. 27233.3i 0.611151 0.0505485i
\(735\) 12665.6i 0.0234450i
\(736\) −304047. 694583.i −0.561287 1.28224i
\(737\) 486108. 0.894948
\(738\) −21599.8 261151.i −0.0396587 0.479489i
\(739\) −594958. 594958.i −1.08943 1.08943i −0.995587 0.0938378i \(-0.970086\pi\)
−0.0938378 0.995587i \(-0.529914\pi\)
\(740\) −36515.3 219232.i −0.0666824 0.400350i
\(741\) −249910. 249910.i −0.455142 0.455142i
\(742\) 320090. 377814.i 0.581386 0.686231i
\(743\) 289367. 0.524170 0.262085 0.965045i \(-0.415590\pi\)
0.262085 + 0.965045i \(0.415590\pi\)
\(744\) 87101.1 + 51954.5i 0.157354 + 0.0938592i
\(745\) 30390.8i 0.0547557i
\(746\) 280214. 330747.i 0.503515 0.594317i
\(747\) −52190.2 + 52190.2i −0.0935293 + 0.0935293i
\(748\) 548927. 768329.i 0.981096 1.37323i
\(749\) −135642. + 135642.i −0.241785 + 0.241785i
\(750\) 14698.9 + 177715.i 0.0261314 + 0.315938i
\(751\) 935795.i 1.65921i 0.558352 + 0.829604i \(0.311434\pi\)
−0.558352 + 0.829604i \(0.688566\pi\)
\(752\) 62341.0 + 181951.i 0.110240 + 0.321750i
\(753\) 15629.1 0.0275641
\(754\) −103508. + 8561.16i −0.182067 + 0.0150588i
\(755\) −69768.4 69768.4i −0.122395 0.122395i
\(756\) −306887. + 429547.i −0.536951 + 0.751567i
\(757\) −626956. 626956.i −1.09407 1.09407i −0.995089 0.0989818i \(-0.968441\pi\)
−0.0989818 0.995089i \(-0.531559\pi\)
\(758\) −414069. 350806.i −0.720666 0.610560i
\(759\) −639062. −1.10933
\(760\) 119068. 30094.6i 0.206142 0.0521029i
\(761\) 253505.i 0.437741i 0.975754 + 0.218871i \(0.0702372\pi\)
−0.975754 + 0.218871i \(0.929763\pi\)
\(762\) 386960. + 327838.i 0.666432 + 0.564612i
\(763\) −152167. + 152167.i −0.261380 + 0.261380i
\(764\) −73706.4 442521.i −0.126275 0.758137i
\(765\) −90032.1 + 90032.1i −0.153842 + 0.153842i
\(766\) 672536. 55625.7i 1.14619 0.0948021i
\(767\) 426625.i 0.725197i
\(768\) 360007. + 45316.6i 0.610363 + 0.0768306i
\(769\) −740462. −1.25213 −0.626066 0.779770i \(-0.715336\pi\)
−0.626066 + 0.779770i \(0.715336\pi\)
\(770\) 15577.7 + 188340.i 0.0262737 + 0.317660i