Properties

Label 105.3.t.b.11.4
Level 105
Weight 3
Character 105.11
Analytic conductor 2.861
Analytic rank 0
Dimension 36
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 11.4
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.46897 + 1.42546i) q^{2} +(-2.92531 - 0.665249i) q^{3} +(2.06389 - 3.57476i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(8.17081 - 2.52744i) q^{6} +(-5.93505 - 3.71149i) q^{7} +0.364297i q^{8} +(8.11489 + 3.89212i) q^{9} +O(q^{10})\) \(q+(-2.46897 + 1.42546i) q^{2} +(-2.92531 - 0.665249i) q^{3} +(2.06389 - 3.57476i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(8.17081 - 2.52744i) q^{6} +(-5.93505 - 3.71149i) q^{7} +0.364297i q^{8} +(8.11489 + 3.89212i) q^{9} +(3.18743 - 5.52080i) q^{10} +(8.97923 + 5.18416i) q^{11} +(-8.41563 + 9.08430i) q^{12} +11.1104 q^{13} +(19.9441 + 0.703368i) q^{14} +(6.40861 - 1.98235i) q^{15} +(7.73627 + 13.3996i) q^{16} +(11.2821 + 6.51372i) q^{17} +(-25.5835 + 1.95793i) q^{18} +(-8.07471 - 13.9858i) q^{19} +9.23000i q^{20} +(14.8928 + 14.8055i) q^{21} -29.5593 q^{22} +(19.0766 - 11.0139i) q^{23} +(0.242348 - 1.06568i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-27.4312 + 15.8374i) q^{26} +(-21.1493 - 16.7841i) q^{27} +(-25.5170 + 13.5563i) q^{28} -20.2647i q^{29} +(-12.9969 + 14.0296i) q^{30} +(19.5875 - 33.9265i) q^{31} +(-39.4633 - 22.7841i) q^{32} +(-22.8183 - 21.1387i) q^{33} -37.1403 q^{34} +(15.6428 + 0.551673i) q^{35} +(30.6617 - 20.9759i) q^{36} +(16.1127 + 27.9081i) q^{37} +(39.8725 + 23.0204i) q^{38} +(-32.5012 - 7.39115i) q^{39} +(-0.407296 - 0.705457i) q^{40} -49.3431i q^{41} +(-57.8747 - 15.3253i) q^{42} +35.3127 q^{43} +(37.0643 - 21.3991i) q^{44} +(-20.0659 + 1.53566i) q^{45} +(-31.3998 + 54.3861i) q^{46} +(-72.6572 + 41.9486i) q^{47} +(-13.7169 - 44.3446i) q^{48} +(21.4497 + 44.0558i) q^{49} +14.2546i q^{50} +(-28.6704 - 26.5601i) q^{51} +(22.9306 - 39.7169i) q^{52} +(78.3583 + 45.2402i) q^{53} +(76.1423 + 11.2919i) q^{54} -23.1843 q^{55} +(1.35208 - 2.16212i) q^{56} +(14.3170 + 46.2846i) q^{57} +(28.8865 + 50.0330i) q^{58} +(30.9922 + 17.8933i) q^{59} +(6.14025 - 27.0006i) q^{60} +(-3.02027 - 5.23126i) q^{61} +111.685i q^{62} +(-33.7167 - 53.2182i) q^{63} +68.0216 q^{64} +(-21.5151 + 12.4218i) q^{65} +(86.4702 + 19.6643i) q^{66} +(57.4710 - 99.5427i) q^{67} +(46.5700 - 26.8872i) q^{68} +(-63.1321 + 19.5284i) q^{69} +(-39.4079 + 20.9361i) q^{70} -45.9746i q^{71} +(-1.41789 + 2.95623i) q^{72} +(16.2758 - 28.1905i) q^{73} +(-79.5639 - 45.9363i) q^{74} +(-10.1939 + 11.0038i) q^{75} -66.6613 q^{76} +(-34.0513 - 64.0946i) q^{77} +(90.7806 - 28.0808i) q^{78} +(41.0891 + 71.1683i) q^{79} +(-29.9625 - 17.2988i) q^{80} +(50.7028 + 63.1682i) q^{81} +(70.3368 + 121.827i) q^{82} +0.951632i q^{83} +(83.6635 - 22.6813i) q^{84} -29.1302 q^{85} +(-87.1862 + 50.3370i) q^{86} +(-13.4811 + 59.2805i) q^{87} +(-1.88857 + 3.27110i) q^{88} +(-14.2959 + 8.25374i) q^{89} +(47.3533 - 32.3948i) q^{90} +(-65.9406 - 41.2359i) q^{91} -90.9260i q^{92} +(-79.8689 + 86.2149i) q^{93} +(119.592 - 207.140i) q^{94} +(31.2732 + 18.0556i) q^{95} +(100.285 + 92.9036i) q^{96} +143.204 q^{97} +(-115.759 - 78.1967i) q^{98} +(52.6881 + 77.0171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + O(q^{10}) \) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + 20q^{10} - 42q^{12} - 100q^{13} + 20q^{15} - 12q^{16} - 14q^{18} + 50q^{19} - 12q^{21} + 256q^{22} - 140q^{24} + 90q^{25} + 4q^{27} - 48q^{28} + 60q^{30} - 82q^{31} - 76q^{33} - 64q^{34} + 296q^{36} - 26q^{37} - 130q^{39} - 60q^{40} - 98q^{42} - 204q^{43} + 40q^{45} + 28q^{46} + 532q^{48} - 382q^{49} + 208q^{51} + 200q^{52} - 44q^{54} - 160q^{55} + 252q^{57} + 264q^{58} - 130q^{60} - 324q^{61} - 258q^{63} - 24q^{64} - 164q^{66} - 142q^{67} - 112q^{69} + 200q^{70} - 322q^{72} + 386q^{73} - 20q^{75} - 424q^{76} - 440q^{78} + 334q^{79} + 186q^{81} - 68q^{82} + 80q^{84} - 200q^{85} + 342q^{87} + 180q^{88} + 100q^{90} + 46q^{91} - 2q^{93} + 324q^{94} + 732q^{96} + 1616q^{97} + 384q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46897 + 1.42546i −1.23449 + 0.712732i −0.967962 0.251096i \(-0.919209\pi\)
−0.266525 + 0.963828i \(0.585876\pi\)
\(3\) −2.92531 0.665249i −0.975104 0.221750i
\(4\) 2.06389 3.57476i 0.515973 0.893691i
\(5\) −1.93649 + 1.11803i −0.387298 + 0.223607i
\(6\) 8.17081 2.52744i 1.36180 0.421240i
\(7\) −5.93505 3.71149i −0.847865 0.530212i
\(8\) 0.364297i 0.0455371i
\(9\) 8.11489 + 3.89212i 0.901654 + 0.432458i
\(10\) 3.18743 5.52080i 0.318743 0.552080i
\(11\) 8.97923 + 5.18416i 0.816294 + 0.471287i 0.849137 0.528173i \(-0.177123\pi\)
−0.0328429 + 0.999461i \(0.510456\pi\)
\(12\) −8.41563 + 9.08430i −0.701303 + 0.757025i
\(13\) 11.1104 0.854643 0.427321 0.904100i \(-0.359457\pi\)
0.427321 + 0.904100i \(0.359457\pi\)
\(14\) 19.9441 + 0.703368i 1.42458 + 0.0502405i
\(15\) 6.40861 1.98235i 0.427241 0.132157i
\(16\) 7.73627 + 13.3996i 0.483517 + 0.837476i
\(17\) 11.2821 + 6.51372i 0.663653 + 0.383160i 0.793667 0.608352i \(-0.208169\pi\)
−0.130015 + 0.991512i \(0.541502\pi\)
\(18\) −25.5835 + 1.95793i −1.42131 + 0.108774i
\(19\) −8.07471 13.9858i −0.424985 0.736096i 0.571434 0.820648i \(-0.306387\pi\)
−0.996419 + 0.0845524i \(0.973054\pi\)
\(20\) 9.23000i 0.461500i
\(21\) 14.8928 + 14.8055i 0.709182 + 0.705026i
\(22\) −29.5593 −1.34361
\(23\) 19.0766 11.0139i 0.829419 0.478865i −0.0242347 0.999706i \(-0.507715\pi\)
0.853654 + 0.520841i \(0.174382\pi\)
\(24\) 0.242348 1.06568i 0.0100978 0.0444034i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) −27.4312 + 15.8374i −1.05505 + 0.609131i
\(27\) −21.1493 16.7841i −0.783309 0.621633i
\(28\) −25.5170 + 13.5563i −0.911321 + 0.484154i
\(29\) 20.2647i 0.698782i −0.936977 0.349391i \(-0.886389\pi\)
0.936977 0.349391i \(-0.113611\pi\)
\(30\) −12.9969 + 14.0296i −0.433231 + 0.467654i
\(31\) 19.5875 33.9265i 0.631853 1.09440i −0.355319 0.934745i \(-0.615628\pi\)
0.987173 0.159657i \(-0.0510389\pi\)
\(32\) −39.4633 22.7841i −1.23323 0.712004i
\(33\) −22.8183 21.1387i −0.691463 0.640567i
\(34\) −37.1403 −1.09236
\(35\) 15.6428 + 0.551673i 0.446936 + 0.0157621i
\(36\) 30.6617 20.9759i 0.851713 0.582664i
\(37\) 16.1127 + 27.9081i 0.435480 + 0.754273i 0.997335 0.0729628i \(-0.0232454\pi\)
−0.561855 + 0.827236i \(0.689912\pi\)
\(38\) 39.8725 + 23.0204i 1.04928 + 0.605800i
\(39\) −32.5012 7.39115i −0.833365 0.189517i
\(40\) −0.407296 0.705457i −0.0101824 0.0176364i
\(41\) 49.3431i 1.20349i −0.798688 0.601745i \(-0.794472\pi\)
0.798688 0.601745i \(-0.205528\pi\)
\(42\) −57.8747 15.3253i −1.37797 0.364889i
\(43\) 35.3127 0.821226 0.410613 0.911810i \(-0.365315\pi\)
0.410613 + 0.911810i \(0.365315\pi\)
\(44\) 37.0643 21.3991i 0.842371 0.486343i
\(45\) −20.0659 + 1.53566i −0.445910 + 0.0341259i
\(46\) −31.3998 + 54.3861i −0.682605 + 1.18231i
\(47\) −72.6572 + 41.9486i −1.54590 + 0.892524i −0.547449 + 0.836839i \(0.684401\pi\)
−0.998448 + 0.0556851i \(0.982266\pi\)
\(48\) −13.7169 44.3446i −0.285769 0.923846i
\(49\) 21.4497 + 44.0558i 0.437749 + 0.899097i
\(50\) 14.2546i 0.285093i
\(51\) −28.6704 26.5601i −0.562164 0.520785i
\(52\) 22.9306 39.7169i 0.440972 0.763787i
\(53\) 78.3583 + 45.2402i 1.47846 + 0.853589i 0.999703 0.0243596i \(-0.00775467\pi\)
0.478756 + 0.877948i \(0.341088\pi\)
\(54\) 76.1423 + 11.2919i 1.41004 + 0.209108i
\(55\) −23.1843 −0.421532
\(56\) 1.35208 2.16212i 0.0241443 0.0386093i
\(57\) 14.3170 + 46.2846i 0.251176 + 0.812010i
\(58\) 28.8865 + 50.0330i 0.498044 + 0.862637i
\(59\) 30.9922 + 17.8933i 0.525291 + 0.303277i 0.739097 0.673599i \(-0.235253\pi\)
−0.213806 + 0.976876i \(0.568586\pi\)
\(60\) 6.14025 27.0006i 0.102337 0.450010i
\(61\) −3.02027 5.23126i −0.0495126 0.0857583i 0.840207 0.542266i \(-0.182433\pi\)
−0.889720 + 0.456508i \(0.849100\pi\)
\(62\) 111.685i 1.80137i
\(63\) −33.7167 53.2182i −0.535186 0.844734i
\(64\) 68.0216 1.06284
\(65\) −21.5151 + 12.4218i −0.331002 + 0.191104i
\(66\) 86.4702 + 19.6643i 1.31015 + 0.297944i
\(67\) 57.4710 99.5427i 0.857776 1.48571i −0.0162686 0.999868i \(-0.505179\pi\)
0.874045 0.485845i \(-0.161488\pi\)
\(68\) 46.5700 26.8872i 0.684853 0.395400i
\(69\) −63.1321 + 19.5284i −0.914958 + 0.283020i
\(70\) −39.4079 + 20.9361i −0.562971 + 0.299087i
\(71\) 45.9746i 0.647530i −0.946138 0.323765i \(-0.895051\pi\)
0.946138 0.323765i \(-0.104949\pi\)
\(72\) −1.41789 + 2.95623i −0.0196929 + 0.0410587i
\(73\) 16.2758 28.1905i 0.222956 0.386171i −0.732748 0.680500i \(-0.761763\pi\)
0.955704 + 0.294329i \(0.0950960\pi\)
\(74\) −79.5639 45.9363i −1.07519 0.620760i
\(75\) −10.1939 + 11.0038i −0.135919 + 0.146718i
\(76\) −66.6613 −0.877123
\(77\) −34.0513 64.0946i −0.442224 0.832397i
\(78\) 90.7806 28.0808i 1.16385 0.360010i
\(79\) 41.0891 + 71.1683i 0.520115 + 0.900865i 0.999727 + 0.0233842i \(0.00744411\pi\)
−0.479612 + 0.877481i \(0.659223\pi\)
\(80\) −29.9625 17.2988i −0.374531 0.216235i
\(81\) 50.7028 + 63.1682i 0.625961 + 0.779855i
\(82\) 70.3368 + 121.827i 0.857766 + 1.48569i
\(83\) 0.951632i 0.0114654i 0.999984 + 0.00573272i \(0.00182479\pi\)
−0.999984 + 0.00573272i \(0.998175\pi\)
\(84\) 83.6635 22.6813i 0.995994 0.270015i
\(85\) −29.1302 −0.342709
\(86\) −87.1862 + 50.3370i −1.01379 + 0.585314i
\(87\) −13.4811 + 59.2805i −0.154955 + 0.681385i
\(88\) −1.88857 + 3.27110i −0.0214611 + 0.0371716i
\(89\) −14.2959 + 8.25374i −0.160628 + 0.0927386i −0.578159 0.815924i \(-0.696229\pi\)
0.417531 + 0.908663i \(0.362895\pi\)
\(90\) 47.3533 32.3948i 0.526147 0.359942i
\(91\) −65.9406 41.2359i −0.724622 0.453142i
\(92\) 90.9260i 0.988326i
\(93\) −79.8689 + 86.2149i −0.858806 + 0.927042i
\(94\) 119.592 207.140i 1.27226 2.20362i
\(95\) 31.2732 + 18.0556i 0.329192 + 0.190059i
\(96\) 100.285 + 92.9036i 1.04464 + 0.967746i
\(97\) 143.204 1.47633 0.738164 0.674622i \(-0.235693\pi\)
0.738164 + 0.674622i \(0.235693\pi\)
\(98\) −115.759 78.1967i −1.18121 0.797926i
\(99\) 52.6881 + 77.0171i 0.532203 + 0.777951i
\(100\) −10.3195 17.8738i −0.103195 0.178738i
\(101\) −83.0925 47.9735i −0.822698 0.474985i 0.0286482 0.999590i \(-0.490880\pi\)
−0.851346 + 0.524605i \(0.824213\pi\)
\(102\) 108.647 + 24.7075i 1.06517 + 0.242231i
\(103\) −75.5216 130.807i −0.733220 1.26997i −0.955500 0.294991i \(-0.904683\pi\)
0.222280 0.974983i \(-0.428650\pi\)
\(104\) 4.04747i 0.0389179i
\(105\) −45.3929 12.0201i −0.432313 0.114477i
\(106\) −257.953 −2.43352
\(107\) 41.0753 23.7148i 0.383881 0.221634i −0.295624 0.955304i \(-0.595528\pi\)
0.679506 + 0.733670i \(0.262194\pi\)
\(108\) −103.649 + 40.9634i −0.959713 + 0.379291i
\(109\) −97.7409 + 169.292i −0.896706 + 1.55314i −0.0650270 + 0.997884i \(0.520713\pi\)
−0.831679 + 0.555257i \(0.812620\pi\)
\(110\) 57.2414 33.0483i 0.520376 0.300439i
\(111\) −28.5690 92.3589i −0.257378 0.832062i
\(112\) 3.81732 108.241i 0.0340832 0.966433i
\(113\) 100.129i 0.886097i 0.896498 + 0.443049i \(0.146103\pi\)
−0.896498 + 0.443049i \(0.853897\pi\)
\(114\) −101.325 93.8670i −0.888818 0.823395i
\(115\) −24.6278 + 42.6567i −0.214155 + 0.370927i
\(116\) −72.4414 41.8241i −0.624495 0.360552i
\(117\) 90.1593 + 43.2428i 0.770592 + 0.369597i
\(118\) −102.025 −0.864620
\(119\) −42.7842 80.5326i −0.359531 0.676745i
\(120\) 0.722163 + 2.33464i 0.00601802 + 0.0194553i
\(121\) −6.74893 11.6895i −0.0557763 0.0966073i
\(122\) 14.9139 + 8.61056i 0.122245 + 0.0705784i
\(123\) −32.8254 + 144.344i −0.266874 + 1.17353i
\(124\) −80.8527 140.041i −0.652038 1.12936i
\(125\) 11.1803i 0.0894427i
\(126\) 159.106 + 83.3325i 1.26275 + 0.661369i
\(127\) −153.104 −1.20554 −0.602771 0.797914i \(-0.705937\pi\)
−0.602771 + 0.797914i \(0.705937\pi\)
\(128\) −10.0905 + 5.82577i −0.0788323 + 0.0455138i
\(129\) −103.301 23.4917i −0.800780 0.182107i
\(130\) 35.4135 61.3380i 0.272412 0.471831i
\(131\) 123.570 71.3430i 0.943281 0.544603i 0.0522935 0.998632i \(-0.483347\pi\)
0.890987 + 0.454028i \(0.150014\pi\)
\(132\) −122.660 + 37.9420i −0.929245 + 0.287439i
\(133\) −3.98431 + 112.976i −0.0299572 + 0.849442i
\(134\) 327.691i 2.44546i
\(135\) 59.7207 + 8.85654i 0.442376 + 0.0656040i
\(136\) −2.37293 + 4.11003i −0.0174480 + 0.0302208i
\(137\) −1.15617 0.667514i −0.00843918 0.00487236i 0.495774 0.868451i \(-0.334884\pi\)
−0.504214 + 0.863579i \(0.668218\pi\)
\(138\) 128.035 138.208i 0.927787 1.00150i
\(139\) 42.8276 0.308113 0.154056 0.988062i \(-0.450766\pi\)
0.154056 + 0.988062i \(0.450766\pi\)
\(140\) 34.2570 54.7805i 0.244693 0.391290i
\(141\) 240.451 74.3777i 1.70533 0.527502i
\(142\) 65.5351 + 113.510i 0.461515 + 0.799367i
\(143\) 99.7625 + 57.5979i 0.697640 + 0.402782i
\(144\) 10.6261 + 138.847i 0.0737922 + 0.964214i
\(145\) 22.6566 + 39.2424i 0.156252 + 0.270637i
\(146\) 92.8022i 0.635632i
\(147\) −33.4391 143.146i −0.227477 0.973784i
\(148\) 133.020 0.898783
\(149\) 164.476 94.9604i 1.10387 0.637318i 0.166633 0.986019i \(-0.446710\pi\)
0.937234 + 0.348701i \(0.113377\pi\)
\(150\) 9.48288 41.6992i 0.0632192 0.277995i
\(151\) −46.5602 + 80.6446i −0.308346 + 0.534070i −0.978001 0.208602i \(-0.933109\pi\)
0.669655 + 0.742672i \(0.266442\pi\)
\(152\) 5.09499 2.94159i 0.0335196 0.0193526i
\(153\) 66.2008 + 96.7694i 0.432685 + 0.632479i
\(154\) 175.436 + 109.709i 1.13920 + 0.712397i
\(155\) 87.5978i 0.565147i
\(156\) −93.5007 + 100.930i −0.599363 + 0.646986i
\(157\) −33.4000 + 57.8506i −0.212739 + 0.368475i −0.952571 0.304317i \(-0.901572\pi\)
0.739832 + 0.672792i \(0.234905\pi\)
\(158\) −202.896 117.142i −1.28415 0.741404i
\(159\) −199.126 184.469i −1.25237 1.16019i
\(160\) 101.894 0.636836
\(161\) −154.099 5.43460i −0.957136 0.0337553i
\(162\) −215.228 83.6857i −1.32857 0.516579i
\(163\) −29.0660 50.3438i −0.178319 0.308857i 0.762986 0.646415i \(-0.223733\pi\)
−0.941305 + 0.337558i \(0.890399\pi\)
\(164\) −176.390 101.839i −1.07555 0.620968i
\(165\) 67.8212 + 15.4233i 0.411038 + 0.0934746i
\(166\) −1.35652 2.34956i −0.00817179 0.0141539i
\(167\) 102.831i 0.615755i −0.951426 0.307877i \(-0.900381\pi\)
0.951426 0.307877i \(-0.0996187\pi\)
\(168\) −5.39361 + 5.42540i −0.0321048 + 0.0322941i
\(169\) −45.5600 −0.269586
\(170\) 71.9218 41.5241i 0.423070 0.244259i
\(171\) −11.0909 144.921i −0.0648593 0.847492i
\(172\) 72.8816 126.235i 0.423730 0.733922i
\(173\) 95.7931 55.3062i 0.553718 0.319689i −0.196903 0.980423i \(-0.563088\pi\)
0.750620 + 0.660734i \(0.229755\pi\)
\(174\) −51.2178 165.579i −0.294355 0.951602i
\(175\) −30.9088 + 16.4208i −0.176622 + 0.0938332i
\(176\) 160.424i 0.911502i
\(177\) −78.7582 72.9610i −0.444961 0.412209i
\(178\) 23.5308 40.7565i 0.132196 0.228969i
\(179\) −61.4074 35.4536i −0.343058 0.198065i 0.318566 0.947901i \(-0.396799\pi\)
−0.661623 + 0.749836i \(0.730132\pi\)
\(180\) −35.9243 + 74.9004i −0.199579 + 0.416113i
\(181\) 199.219 1.10066 0.550329 0.834948i \(-0.314502\pi\)
0.550329 + 0.834948i \(0.314502\pi\)
\(182\) 221.586 + 7.81467i 1.21751 + 0.0429377i
\(183\) 5.35513 + 17.3123i 0.0292630 + 0.0946026i
\(184\) 4.01233 + 6.94955i 0.0218061 + 0.0377693i
\(185\) −62.4044 36.0292i −0.337321 0.194752i
\(186\) 74.2982 326.713i 0.399453 1.75652i
\(187\) 67.5364 + 116.976i 0.361157 + 0.625542i
\(188\) 346.310i 1.84207i
\(189\) 63.2286 + 178.110i 0.334543 + 0.942381i
\(190\) −102.950 −0.541844
\(191\) 170.185 98.2561i 0.891018 0.514430i 0.0167430 0.999860i \(-0.494670\pi\)
0.874275 + 0.485430i \(0.161337\pi\)
\(192\) −198.984 45.2513i −1.03638 0.235684i
\(193\) 121.341 210.169i 0.628711 1.08896i −0.359100 0.933299i \(-0.616916\pi\)
0.987811 0.155660i \(-0.0497505\pi\)
\(194\) −353.566 + 204.132i −1.82251 + 1.05223i
\(195\) 71.2020 22.0246i 0.365138 0.112947i
\(196\) 201.759 + 14.2486i 1.02938 + 0.0726968i
\(197\) 133.478i 0.677553i −0.940867 0.338777i \(-0.889987\pi\)
0.940867 0.338777i \(-0.110013\pi\)
\(198\) −239.871 115.048i −1.21147 0.581053i
\(199\) −47.2126 + 81.7747i −0.237249 + 0.410928i −0.959924 0.280260i \(-0.909579\pi\)
0.722675 + 0.691188i \(0.242913\pi\)
\(200\) 1.57745 + 0.910741i 0.00788725 + 0.00455371i
\(201\) −234.341 + 252.961i −1.16588 + 1.25851i
\(202\) 273.538 1.35415
\(203\) −75.2121 + 120.272i −0.370503 + 0.592473i
\(204\) −154.118 + 47.6728i −0.755483 + 0.233690i
\(205\) 55.1673 + 95.5525i 0.269109 + 0.466110i
\(206\) 372.922 + 215.307i 1.81030 + 1.04518i
\(207\) 197.672 15.1280i 0.954938 0.0730823i
\(208\) 85.9527 + 148.875i 0.413234 + 0.715743i
\(209\) 167.443i 0.801160i
\(210\) 129.208 35.0285i 0.615277 0.166802i
\(211\) 78.2298 0.370758 0.185379 0.982667i \(-0.440649\pi\)
0.185379 + 0.982667i \(0.440649\pi\)
\(212\) 323.446 186.742i 1.52569 0.880857i
\(213\) −30.5846 + 134.490i −0.143589 + 0.631409i
\(214\) −67.6092 + 117.103i −0.315931 + 0.547209i
\(215\) −68.3828 + 39.4808i −0.318059 + 0.183632i
\(216\) 6.11438 7.70463i 0.0283073 0.0356696i
\(217\) −242.170 + 128.657i −1.11599 + 0.592889i
\(218\) 557.305i 2.55644i
\(219\) −66.3655 + 71.6386i −0.303039 + 0.327117i
\(220\) −47.8498 + 82.8783i −0.217499 + 0.376720i
\(221\) 125.348 + 72.3697i 0.567186 + 0.327465i
\(222\) 202.190 + 187.308i 0.910767 + 0.843728i
\(223\) −302.053 −1.35450 −0.677249 0.735754i \(-0.736828\pi\)
−0.677249 + 0.735754i \(0.736828\pi\)
\(224\) 149.654 + 281.693i 0.668097 + 1.25756i
\(225\) 37.1406 25.4082i 0.165069 0.112925i
\(226\) −142.730 247.216i −0.631550 1.09388i
\(227\) 278.504 + 160.795i 1.22689 + 0.708346i 0.966378 0.257124i \(-0.0827748\pi\)
0.260514 + 0.965470i \(0.416108\pi\)
\(228\) 195.005 + 44.3464i 0.855286 + 0.194502i
\(229\) −103.283 178.891i −0.451016 0.781183i 0.547433 0.836849i \(-0.315605\pi\)
−0.998449 + 0.0556665i \(0.982272\pi\)
\(230\) 140.424i 0.610540i
\(231\) 56.9717 + 210.149i 0.246631 + 0.909737i
\(232\) 7.38235 0.0318205
\(233\) −198.117 + 114.383i −0.850289 + 0.490914i −0.860748 0.509031i \(-0.830004\pi\)
0.0104596 + 0.999945i \(0.496671\pi\)
\(234\) −284.242 + 21.7533i −1.21471 + 0.0929629i
\(235\) 93.8000 162.466i 0.399149 0.691346i
\(236\) 127.929 73.8598i 0.542071 0.312965i
\(237\) −72.8536 235.524i −0.307399 0.993772i
\(238\) 220.430 + 137.846i 0.926174 + 0.579183i
\(239\) 164.805i 0.689562i 0.938683 + 0.344781i \(0.112047\pi\)
−0.938683 + 0.344781i \(0.887953\pi\)
\(240\) 76.1415 + 70.5369i 0.317256 + 0.293904i
\(241\) −118.758 + 205.695i −0.492772 + 0.853507i −0.999965 0.00832573i \(-0.997350\pi\)
0.507193 + 0.861833i \(0.330683\pi\)
\(242\) 33.3259 + 19.2407i 0.137710 + 0.0795070i
\(243\) −106.299 218.517i −0.437444 0.899246i
\(244\) −24.9340 −0.102189
\(245\) −90.7930 61.3321i −0.370584 0.250335i
\(246\) −124.712 403.173i −0.506958 1.63891i
\(247\) −89.7130 155.387i −0.363210 0.629099i
\(248\) 12.3593 + 7.13564i 0.0498359 + 0.0287728i
\(249\) 0.633072 2.78382i 0.00254246 0.0111800i
\(250\) −15.9372 27.6040i −0.0637487 0.110416i
\(251\) 468.137i 1.86509i 0.361056 + 0.932544i \(0.382416\pi\)
−0.361056 + 0.932544i \(0.617584\pi\)
\(252\) −259.830 + 10.6928i −1.03107 + 0.0424316i
\(253\) 228.391 0.902733
\(254\) 378.010 218.244i 1.48823 0.859228i
\(255\) 85.2150 + 19.3789i 0.334176 + 0.0759955i
\(256\) −119.434 + 206.866i −0.466541 + 0.808072i
\(257\) −225.231 + 130.037i −0.876384 + 0.505981i −0.869465 0.493995i \(-0.835536\pi\)
−0.00691968 + 0.999976i \(0.502203\pi\)
\(258\) 288.533 89.2508i 1.11835 0.345933i
\(259\) 7.95053 225.438i 0.0306970 0.870418i
\(260\) 102.549i 0.394418i
\(261\) 78.8725 164.446i 0.302194 0.630060i
\(262\) −203.394 + 352.288i −0.776312 + 1.34461i
\(263\) −192.735 111.276i −0.732834 0.423102i 0.0866239 0.996241i \(-0.472392\pi\)
−0.819458 + 0.573139i \(0.805725\pi\)
\(264\) 7.70076 8.31262i 0.0291695 0.0314872i
\(265\) −202.320 −0.763473
\(266\) −151.206 284.614i −0.568442 1.06998i
\(267\) 47.3107 14.6344i 0.177194 0.0548106i
\(268\) −237.228 410.891i −0.885179 1.53317i
\(269\) 71.2791 + 41.1530i 0.264978 + 0.152985i 0.626603 0.779338i \(-0.284445\pi\)
−0.361625 + 0.932324i \(0.617778\pi\)
\(270\) −160.074 + 63.2631i −0.592865 + 0.234308i
\(271\) −158.301 274.186i −0.584138 1.01176i −0.994982 0.100051i \(-0.968099\pi\)
0.410844 0.911706i \(-0.365234\pi\)
\(272\) 201.568i 0.741057i
\(273\) 165.464 + 164.495i 0.606097 + 0.602545i
\(274\) 3.80606 0.0138907
\(275\) 44.8962 25.9208i 0.163259 0.0942575i
\(276\) −60.4884 + 265.987i −0.219161 + 0.963720i
\(277\) 240.836 417.139i 0.869442 1.50592i 0.00687507 0.999976i \(-0.497812\pi\)
0.862567 0.505942i \(-0.168855\pi\)
\(278\) −105.740 + 61.0492i −0.380361 + 0.219602i
\(279\) 290.996 199.073i 1.04300 0.713523i
\(280\) −0.200972 + 5.69860i −0.000717759 + 0.0203521i
\(281\) 219.532i 0.781254i −0.920549 0.390627i \(-0.872258\pi\)
0.920549 0.390627i \(-0.127742\pi\)
\(282\) −487.645 + 526.391i −1.72924 + 1.86663i
\(283\) −188.686 + 326.814i −0.666735 + 1.15482i 0.312076 + 0.950057i \(0.398976\pi\)
−0.978812 + 0.204762i \(0.934358\pi\)
\(284\) −164.348 94.8866i −0.578692 0.334108i
\(285\) −79.4725 73.6228i −0.278851 0.258325i
\(286\) −328.415 −1.14830
\(287\) −183.136 + 292.854i −0.638106 + 1.02040i
\(288\) −231.562 338.487i −0.804033 1.17530i
\(289\) −59.6429 103.305i −0.206377 0.357455i
\(290\) −111.877 64.5923i −0.385783 0.222732i
\(291\) −418.916 95.2661i −1.43957 0.327375i
\(292\) −67.1830 116.364i −0.230079 0.398508i
\(293\) 101.422i 0.346149i −0.984909 0.173074i \(-0.944630\pi\)
0.984909 0.173074i \(-0.0553701\pi\)
\(294\) 286.610 + 305.758i 0.974863 + 1.03999i
\(295\) −80.0214 −0.271259
\(296\) −10.1668 + 5.86982i −0.0343474 + 0.0198305i
\(297\) −102.893 260.350i −0.346443 0.876598i
\(298\) −270.725 + 468.910i −0.908473 + 1.57352i
\(299\) 211.948 122.368i 0.708857 0.409259i
\(300\) 18.2971 + 59.1515i 0.0609903 + 0.197172i
\(301\) −209.583 131.063i −0.696289 0.435424i
\(302\) 265.479i 0.879071i
\(303\) 211.157 + 195.614i 0.696888 + 0.645592i
\(304\) 124.936 216.396i 0.410975 0.711829i
\(305\) 11.6974 + 6.75352i 0.0383523 + 0.0221427i
\(306\) −301.389 144.554i −0.984932 0.472400i
\(307\) 418.952 1.36467 0.682333 0.731042i \(-0.260966\pi\)
0.682333 + 0.731042i \(0.260966\pi\)
\(308\) −299.401 10.5590i −0.972082 0.0342824i
\(309\) 133.905 + 432.893i 0.433349 + 1.40095i
\(310\) −124.867 216.277i −0.402798 0.697667i
\(311\) −220.311 127.197i −0.708396 0.408993i 0.102071 0.994777i \(-0.467453\pi\)
−0.810467 + 0.585784i \(0.800787\pi\)
\(312\) 2.69257 11.8401i 0.00863004 0.0379490i
\(313\) 130.448 + 225.942i 0.416765 + 0.721859i 0.995612 0.0935778i \(-0.0298304\pi\)
−0.578847 + 0.815436i \(0.696497\pi\)
\(314\) 190.442i 0.606503i
\(315\) 124.792 + 65.3602i 0.396165 + 0.207493i
\(316\) 339.213 1.07346
\(317\) −348.433 + 201.168i −1.09916 + 0.634599i −0.936000 0.352001i \(-0.885501\pi\)
−0.163158 + 0.986600i \(0.552168\pi\)
\(318\) 754.593 + 171.603i 2.37293 + 0.539632i
\(319\) 105.055 181.961i 0.329327 0.570411i
\(320\) −131.723 + 76.0505i −0.411635 + 0.237658i
\(321\) −135.934 + 42.0480i −0.423471 + 0.130991i
\(322\) 388.213 206.244i 1.20563 0.640510i
\(323\) 210.386i 0.651349i
\(324\) 330.457 50.8783i 1.01993 0.157032i
\(325\) 27.7759 48.1093i 0.0854643 0.148028i
\(326\) 143.526 + 82.8650i 0.440265 + 0.254187i
\(327\) 398.544 430.211i 1.21879 1.31563i
\(328\) 17.9755 0.0548034
\(329\) 586.916 + 20.6988i 1.78394 + 0.0629142i
\(330\) −189.434 + 58.5969i −0.574043 + 0.177566i
\(331\) 179.035 + 310.098i 0.540891 + 0.936851i 0.998853 + 0.0478793i \(0.0152463\pi\)
−0.457962 + 0.888972i \(0.651420\pi\)
\(332\) 3.40186 + 1.96406i 0.0102466 + 0.00591586i
\(333\) 22.1315 + 289.184i 0.0664610 + 0.868420i
\(334\) 146.582 + 253.887i 0.438868 + 0.760142i
\(335\) 257.018i 0.767219i
\(336\) −83.1737 + 314.098i −0.247541 + 0.934815i
\(337\) 84.7770 0.251564 0.125782 0.992058i \(-0.459856\pi\)
0.125782 + 0.992058i \(0.459856\pi\)
\(338\) 112.486 64.9441i 0.332800 0.192142i
\(339\) 66.6107 292.908i 0.196492 0.864037i
\(340\) −60.1216 + 104.134i −0.176828 + 0.306276i
\(341\) 351.761 203.089i 1.03156 0.595569i
\(342\) 233.963 + 341.997i 0.684102 + 0.999991i
\(343\) 36.2071 341.084i 0.105560 0.994413i
\(344\) 12.8643i 0.0373962i
\(345\) 100.421 108.400i 0.291076 0.314204i
\(346\) −157.674 + 273.099i −0.455705 + 0.789304i
\(347\) −92.7077 53.5248i −0.267169 0.154250i 0.360431 0.932786i \(-0.382630\pi\)
−0.627601 + 0.778536i \(0.715963\pi\)
\(348\) 184.090 + 170.540i 0.528995 + 0.490057i
\(349\) 158.877 0.455234 0.227617 0.973751i \(-0.426907\pi\)
0.227617 + 0.973751i \(0.426907\pi\)
\(350\) 52.9059 84.6020i 0.151160 0.241720i
\(351\) −234.977 186.477i −0.669449 0.531274i
\(352\) −236.233 409.168i −0.671117 1.16241i
\(353\) 259.886 + 150.045i 0.736222 + 0.425058i 0.820694 0.571368i \(-0.193587\pi\)
−0.0844720 + 0.996426i \(0.526920\pi\)
\(354\) 298.455 + 67.8721i 0.843094 + 0.191729i
\(355\) 51.4012 + 89.0295i 0.144792 + 0.250787i
\(356\) 68.1393i 0.191402i
\(357\) 71.5830 + 264.045i 0.200513 + 0.739622i
\(358\) 202.151 0.564668
\(359\) −120.127 + 69.3556i −0.334617 + 0.193191i −0.657889 0.753115i \(-0.728550\pi\)
0.323272 + 0.946306i \(0.395217\pi\)
\(360\) −0.559437 7.30995i −0.00155399 0.0203054i
\(361\) 50.0980 86.7722i 0.138776 0.240366i
\(362\) −491.867 + 283.980i −1.35875 + 0.784474i
\(363\) 11.9663 + 38.6851i 0.0329650 + 0.106571i
\(364\) −283.503 + 150.615i −0.778854 + 0.413779i
\(365\) 72.7876i 0.199418i
\(366\) −37.8997 35.1100i −0.103551 0.0959291i
\(367\) −243.334 + 421.468i −0.663036 + 1.14841i 0.316777 + 0.948500i \(0.397399\pi\)
−0.979814 + 0.199913i \(0.935934\pi\)
\(368\) 295.164 + 170.413i 0.802076 + 0.463079i
\(369\) 192.049 400.414i 0.520459 1.08513i
\(370\) 205.433 0.555225
\(371\) −297.152 559.329i −0.800950 1.50763i
\(372\) 143.357 + 463.451i 0.385369 + 1.24584i
\(373\) 164.757 + 285.367i 0.441707 + 0.765060i 0.997816 0.0660498i \(-0.0210396\pi\)
−0.556109 + 0.831109i \(0.687706\pi\)
\(374\) −333.491 192.541i −0.891687 0.514816i
\(375\) 7.43771 32.7060i 0.0198339 0.0872159i
\(376\) −15.2817 26.4688i −0.0406429 0.0703956i
\(377\) 225.148i 0.597209i
\(378\) −409.999 349.619i −1.08465 0.924918i
\(379\) 165.444 0.436528 0.218264 0.975890i \(-0.429961\pi\)
0.218264 + 0.975890i \(0.429961\pi\)
\(380\) 129.089 74.5296i 0.339708 0.196131i
\(381\) 447.877 + 101.852i 1.17553 + 0.267329i
\(382\) −280.121 + 485.184i −0.733301 + 1.27011i
\(383\) −39.4178 + 22.7579i −0.102918 + 0.0594200i −0.550576 0.834785i \(-0.685592\pi\)
0.447657 + 0.894205i \(0.352258\pi\)
\(384\) 33.3935 10.3295i 0.0869623 0.0268997i
\(385\) 137.600 + 86.0482i 0.357402 + 0.223502i
\(386\) 691.870i 1.79241i
\(387\) 286.559 + 137.441i 0.740462 + 0.355145i
\(388\) 295.557 511.920i 0.761745 1.31938i
\(389\) −221.480 127.871i −0.569356 0.328718i 0.187536 0.982258i \(-0.439950\pi\)
−0.756892 + 0.653540i \(0.773283\pi\)
\(390\) −144.401 + 155.874i −0.370258 + 0.399677i
\(391\) 286.966 0.733928
\(392\) −16.0494 + 7.81406i −0.0409422 + 0.0199338i
\(393\) −408.941 + 126.496i −1.04056 + 0.321873i
\(394\) 190.268 + 329.554i 0.482914 + 0.836431i
\(395\) −159.137 91.8779i −0.402879 0.232602i
\(396\) 384.061 29.3925i 0.969850 0.0742235i
\(397\) 29.5642 + 51.2068i 0.0744691 + 0.128984i 0.900855 0.434120i \(-0.142940\pi\)
−0.826386 + 0.563104i \(0.809607\pi\)
\(398\) 269.200i 0.676381i
\(399\) 86.8124 327.839i 0.217575 0.821651i
\(400\) 77.3627 0.193407
\(401\) −155.996 + 90.0643i −0.389017 + 0.224599i −0.681734 0.731600i \(-0.738774\pi\)
0.292717 + 0.956199i \(0.405441\pi\)
\(402\) 217.996 958.599i 0.542279 2.38457i
\(403\) 217.624 376.935i 0.540009 0.935323i
\(404\) −342.988 + 198.024i −0.848979 + 0.490158i
\(405\) −168.810 65.6373i −0.416814 0.162067i
\(406\) 14.2535 404.160i 0.0351072 0.995469i
\(407\) 334.124i 0.820944i
\(408\) 9.67574 10.4445i 0.0237150 0.0255993i
\(409\) −72.3928 + 125.388i −0.177000 + 0.306572i −0.940851 0.338819i \(-0.889972\pi\)
0.763852 + 0.645392i \(0.223306\pi\)
\(410\) −272.413 157.278i −0.664422 0.383604i
\(411\) 2.93809 + 2.72182i 0.00714863 + 0.00662244i
\(412\) −623.474 −1.51329
\(413\) −117.529 221.225i −0.284574 0.535653i
\(414\) −466.483 + 319.125i −1.12677 + 0.770834i
\(415\) −1.06396 1.84283i −0.00256375 0.00444055i
\(416\) −438.451 253.140i −1.05397 0.608509i
\(417\) −125.284 28.4910i −0.300442 0.0683238i
\(418\) 238.683 + 413.411i 0.571012 + 0.989022i
\(419\) 534.928i 1.27668i 0.769756 + 0.638339i \(0.220378\pi\)
−0.769756 + 0.638339i \(0.779622\pi\)
\(420\) −136.655 + 137.461i −0.325369 + 0.327287i
\(421\) 314.435 0.746876 0.373438 0.927655i \(-0.378179\pi\)
0.373438 + 0.927655i \(0.378179\pi\)
\(422\) −193.148 + 111.514i −0.457696 + 0.264251i
\(423\) −752.874 + 57.6181i −1.77984 + 0.136213i
\(424\) −16.4808 + 28.5457i −0.0388699 + 0.0673247i
\(425\) 56.4105 32.5686i 0.132731 0.0766320i
\(426\) −116.198 375.650i −0.272766 0.881807i
\(427\) −1.49029 + 42.2575i −0.00349015 + 0.0989636i
\(428\) 195.779i 0.457428i
\(429\) −253.519 234.859i −0.590954 0.547456i
\(430\) 112.557 194.954i 0.261760 0.453382i
\(431\) 144.893 + 83.6543i 0.336180 + 0.194093i 0.658581 0.752510i \(-0.271157\pi\)
−0.322402 + 0.946603i \(0.604490\pi\)
\(432\) 61.2831 413.239i 0.141859 0.956572i
\(433\) −307.177 −0.709415 −0.354707 0.934977i \(-0.615420\pi\)
−0.354707 + 0.934977i \(0.615420\pi\)
\(434\) 414.517 662.855i 0.955108 1.52732i
\(435\) −40.1716 129.868i −0.0923486 0.298548i
\(436\) 403.453 + 698.802i 0.925352 + 1.60276i
\(437\) −308.077 177.868i −0.704981 0.407021i
\(438\) 61.7366 271.475i 0.140951 0.619807i
\(439\) 281.613 + 487.769i 0.641488 + 1.11109i 0.985101 + 0.171979i \(0.0550160\pi\)
−0.343612 + 0.939112i \(0.611651\pi\)
\(440\) 8.44595i 0.0191953i
\(441\) 2.59187 + 440.992i 0.00587726 + 0.999983i
\(442\) −412.642 −0.933578
\(443\) −275.103 + 158.831i −0.621000 + 0.358535i −0.777258 0.629182i \(-0.783390\pi\)
0.156258 + 0.987716i \(0.450057\pi\)
\(444\) −389.124 88.4913i −0.876406 0.199305i
\(445\) 18.4559 31.9666i 0.0414740 0.0718350i
\(446\) 745.762 430.566i 1.67211 0.965394i
\(447\) −544.316 + 168.371i −1.21771 + 0.376669i
\(448\) −403.712 252.461i −0.901143 0.563530i
\(449\) 343.801i 0.765705i −0.923810 0.382852i \(-0.874942\pi\)
0.923810 0.382852i \(-0.125058\pi\)
\(450\) −55.4807 + 115.675i −0.123291 + 0.257055i
\(451\) 255.803 443.063i 0.567190 0.982402i
\(452\) 357.938 + 206.655i 0.791897 + 0.457202i
\(453\) 189.852 204.936i 0.419099 0.452398i
\(454\) −916.827 −2.01944
\(455\) 173.797 + 6.12928i 0.381970 + 0.0134709i
\(456\) −16.8613 + 5.21564i −0.0369765 + 0.0114378i
\(457\) −238.079 412.365i −0.520960 0.902330i −0.999703 0.0243743i \(-0.992241\pi\)
0.478743 0.877955i \(-0.341093\pi\)
\(458\) 510.005 + 294.451i 1.11355 + 0.642907i
\(459\) −129.282 327.120i −0.281660 0.712681i
\(460\) 101.658 + 176.077i 0.220996 + 0.382777i
\(461\) 137.889i 0.299109i 0.988754 + 0.149554i \(0.0477839\pi\)
−0.988754 + 0.149554i \(0.952216\pi\)
\(462\) −440.222 437.642i −0.952861 0.947277i
\(463\) −436.221 −0.942163 −0.471081 0.882090i \(-0.656136\pi\)
−0.471081 + 0.882090i \(0.656136\pi\)
\(464\) 271.539 156.773i 0.585213 0.337873i
\(465\) 58.2743 256.251i 0.125321 0.551077i
\(466\) 326.098 564.818i 0.699780 1.21206i
\(467\) 66.6417 38.4756i 0.142702 0.0823889i −0.426949 0.904276i \(-0.640412\pi\)
0.569651 + 0.821887i \(0.307078\pi\)
\(468\) 340.662 233.050i 0.727910 0.497970i
\(469\) −710.545 + 377.488i −1.51502 + 0.804880i
\(470\) 534.834i 1.13794i
\(471\) 136.191 147.012i 0.289152 0.312126i
\(472\) −6.51848 + 11.2903i −0.0138103 + 0.0239202i
\(473\) 317.081 + 183.067i 0.670362 + 0.387034i
\(474\) 515.604 + 477.652i 1.08777 + 1.00771i
\(475\) −80.7471 −0.169994
\(476\) −376.187 13.2670i −0.790309 0.0278718i
\(477\) 459.789 + 672.099i 0.963918 + 1.40901i
\(478\) −234.924 406.900i −0.491473 0.851256i
\(479\) −372.658 215.154i −0.777992 0.449174i 0.0577262 0.998332i \(-0.481615\pi\)
−0.835718 + 0.549159i \(0.814948\pi\)
\(480\) −298.071 67.7847i −0.620981 0.141218i
\(481\) 179.018 + 310.069i 0.372180 + 0.644634i
\(482\) 677.141i 1.40486i
\(483\) 447.172 + 118.412i 0.925821 + 0.245159i
\(484\) −55.7162 −0.115116
\(485\) −277.313 + 160.107i −0.571779 + 0.330117i
\(486\) 573.937 + 387.987i 1.18094 + 0.798327i
\(487\) −457.072 + 791.671i −0.938546 + 1.62561i −0.170360 + 0.985382i \(0.554493\pi\)
−0.768186 + 0.640227i \(0.778840\pi\)
\(488\) 1.90573 1.10027i 0.00390518 0.00225466i
\(489\) 51.5359 + 166.607i 0.105390 + 0.340710i
\(490\) 311.592 + 22.0052i 0.635903 + 0.0449086i
\(491\) 668.798i 1.36211i 0.732230 + 0.681057i \(0.238480\pi\)
−0.732230 + 0.681057i \(0.761520\pi\)
\(492\) 448.247 + 415.253i 0.911072 + 0.844011i
\(493\) 131.998 228.628i 0.267745 0.463748i
\(494\) 442.998 + 255.765i 0.896757 + 0.517743i
\(495\) −188.138 90.2360i −0.380076 0.182295i
\(496\) 606.136 1.22205
\(497\) −170.634 + 272.862i −0.343328 + 0.549018i
\(498\) 2.40519 + 7.77560i 0.00482971 + 0.0156137i
\(499\) 215.322 + 372.948i 0.431506 + 0.747391i 0.997003 0.0773597i \(-0.0246490\pi\)
−0.565497 + 0.824750i \(0.691316\pi\)
\(500\) 39.9671 + 23.0750i 0.0799342 + 0.0461500i
\(501\) −68.4082 + 300.813i −0.136543 + 0.600425i
\(502\) −667.312 1155.82i −1.32931 2.30243i
\(503\) 188.768i 0.375285i 0.982237 + 0.187643i \(0.0600846\pi\)
−0.982237 + 0.187643i \(0.939915\pi\)
\(504\) 19.3872 12.2829i 0.0384667 0.0243708i
\(505\) 214.544 0.424839
\(506\) −563.893 + 325.564i −1.11441 + 0.643406i
\(507\) 133.277 + 30.3087i 0.262874 + 0.0597805i
\(508\) −315.990 + 547.310i −0.622027 + 1.07738i
\(509\) 51.9288 29.9811i 0.102021 0.0589019i −0.448121 0.893973i \(-0.647907\pi\)
0.550142 + 0.835071i \(0.314573\pi\)
\(510\) −238.018 + 73.6250i −0.466701 + 0.144363i
\(511\) −201.226 + 106.905i −0.393790 + 0.209207i
\(512\) 727.604i 1.42110i
\(513\) −63.9641 + 431.317i −0.124686 + 0.840775i
\(514\) 370.726 642.116i 0.721257 1.24925i
\(515\) 292.494 + 168.872i 0.567950 + 0.327906i
\(516\) −297.179 + 320.791i −0.575928 + 0.621688i
\(517\) −869.874 −1.68254
\(518\) 301.724 + 567.935i 0.582480 + 1.09640i
\(519\) −317.017 + 98.0615i −0.610823 + 0.188943i
\(520\) −4.52520 7.83788i −0.00870231 0.0150729i
\(521\) −162.262 93.6823i −0.311444 0.179812i 0.336128 0.941816i \(-0.390882\pi\)
−0.647573 + 0.762004i \(0.724216\pi\)
\(522\) 39.6768 + 518.442i 0.0760093 + 0.993184i
\(523\) −37.8206 65.5072i −0.0723147 0.125253i 0.827601 0.561317i \(-0.189705\pi\)
−0.899915 + 0.436065i \(0.856372\pi\)
\(524\) 588.977i 1.12400i
\(525\) 101.342 27.4739i 0.193032 0.0523313i
\(526\) 634.478 1.20623
\(527\) 441.975 255.174i 0.838662 0.484202i
\(528\) 106.722 469.291i 0.202125 0.888809i
\(529\) −21.8879 + 37.9110i −0.0413760 + 0.0716653i
\(530\) 499.524 288.400i 0.942498 0.544151i
\(531\) 181.855 + 265.828i 0.342476 + 0.500617i
\(532\) 395.639 + 247.413i 0.743681 + 0.465061i
\(533\) 548.220i 1.02855i
\(534\) −95.9482 + 103.572i −0.179678 + 0.193955i
\(535\) −53.0280 + 91.8471i −0.0991177 + 0.171677i
\(536\) 36.2631 + 20.9365i 0.0676550 + 0.0390606i
\(537\) 156.050 + 144.564i 0.290596 + 0.269206i
\(538\) −234.648 −0.436149
\(539\) −35.7901 + 506.786i −0.0664010 + 0.940233i
\(540\) 154.917 195.208i 0.286883 0.361497i
\(541\) −514.257 890.720i −0.950568 1.64643i −0.744199 0.667958i \(-0.767169\pi\)
−0.206369 0.978474i \(-0.566165\pi\)
\(542\) 781.684 + 451.306i 1.44222 + 0.832667i
\(543\) −582.778 132.530i −1.07326 0.244071i
\(544\) −296.819 514.106i −0.545623 0.945047i
\(545\) 437.111i 0.802038i
\(546\) −643.009 170.270i −1.17767 0.311850i
\(547\) 886.579 1.62080 0.810401 0.585875i \(-0.199249\pi\)
0.810401 + 0.585875i \(0.199249\pi\)
\(548\) −4.77241 + 2.75535i −0.00870877 + 0.00502801i
\(549\) −4.14846 54.2063i −0.00755639 0.0987364i
\(550\) −73.8983 + 127.996i −0.134361 + 0.232719i
\(551\) −283.418 + 163.631i −0.514370 + 0.296972i
\(552\) −7.11412 22.9988i −0.0128879 0.0416645i
\(553\) 20.2746 574.889i 0.0366629 1.03958i
\(554\) 1373.21i 2.47872i
\(555\) 158.584 + 146.911i 0.285737 + 0.264705i
\(556\) 88.3916 153.099i 0.158978 0.275357i
\(557\) −938.357 541.760i −1.68466 0.972640i −0.958490 0.285126i \(-0.907964\pi\)
−0.726172 0.687513i \(-0.758702\pi\)
\(558\) −434.691 + 906.310i −0.779015 + 1.62421i
\(559\) 392.337 0.701855
\(560\) 113.624 + 213.875i 0.202901 + 0.381919i
\(561\) −119.746 387.121i −0.213452 0.690055i
\(562\) 312.935 + 542.020i 0.556824 + 0.964448i
\(563\) 522.999 + 301.954i 0.928951 + 0.536330i 0.886480 0.462768i \(-0.153144\pi\)
0.0424714 + 0.999098i \(0.486477\pi\)
\(564\) 230.382 1013.06i 0.408479 1.79621i
\(565\) −111.948 193.899i −0.198137 0.343184i
\(566\) 1075.86i 1.90081i
\(567\) −66.4759 563.090i −0.117241 0.993103i
\(568\) 16.7484 0.0294866
\(569\) −26.9827 + 15.5785i −0.0474213 + 0.0273787i −0.523523 0.852011i \(-0.675383\pi\)
0.476102 + 0.879390i \(0.342049\pi\)
\(570\) 301.162 + 68.4877i 0.528354 + 0.120154i
\(571\) −118.832 + 205.822i −0.208111 + 0.360460i −0.951120 0.308823i \(-0.900065\pi\)
0.743008 + 0.669282i \(0.233398\pi\)
\(572\) 411.798 237.752i 0.719926 0.415650i
\(573\) −563.207 + 174.215i −0.982910 + 0.304039i
\(574\) 34.7063 984.103i 0.0604640 1.71447i
\(575\) 110.139i 0.191546i
\(576\) 551.988 + 264.748i 0.958312 + 0.459632i
\(577\) 423.514 733.547i 0.733993 1.27131i −0.221171 0.975235i \(-0.570988\pi\)
0.955164 0.296078i \(-0.0956787\pi\)
\(578\) 294.514 + 170.038i 0.509539 + 0.294183i
\(579\) −494.776 + 534.088i −0.854535 + 0.922432i
\(580\) 187.043 0.322488
\(581\) 3.53197 5.64799i 0.00607912 0.00972115i
\(582\) 1170.09 361.939i 2.01046 0.621888i
\(583\) 469.065 + 812.444i 0.804571 + 1.39356i
\(584\) 10.2697 + 5.92922i 0.0175851 + 0.0101528i
\(585\) −222.940 + 17.0618i −0.381093 + 0.0291654i
\(586\) 144.573 + 250.407i 0.246711 + 0.427316i
\(587\) 741.750i 1.26363i 0.775120 + 0.631814i \(0.217689\pi\)
−0.775120 + 0.631814i \(0.782311\pi\)
\(588\) −580.728 175.901i −0.987633 0.299152i
\(589\) −632.653 −1.07411
\(590\) 197.571 114.068i 0.334866 0.193335i
\(591\) −88.7961 + 390.465i −0.150247 + 0.660685i
\(592\) −249.305 + 431.809i −0.421124 + 0.729408i
\(593\) 228.049 131.664i 0.384568 0.222031i −0.295236 0.955424i \(-0.595398\pi\)
0.679804 + 0.733394i \(0.262065\pi\)
\(594\) 625.160 + 496.126i 1.05246 + 0.835229i
\(595\) 172.890 + 108.117i 0.290571 + 0.181708i
\(596\) 783.951i 1.31535i
\(597\) 192.512 207.808i 0.322466 0.348088i
\(598\) −348.863 + 604.249i −0.583383 + 1.01045i
\(599\) −539.808 311.658i −0.901182 0.520298i −0.0235986 0.999722i \(-0.507512\pi\)
−0.877584 + 0.479424i \(0.840846\pi\)
\(600\) −4.00866 3.71360i −0.00668111 0.00618933i
\(601\) 120.748 0.200911 0.100455 0.994942i \(-0.467970\pi\)
0.100455 + 0.994942i \(0.467970\pi\)
\(602\) 704.280 + 24.8378i 1.16990 + 0.0412588i
\(603\) 853.803 584.094i 1.41593 0.968647i
\(604\) 192.190 + 332.883i 0.318196 + 0.551131i
\(605\) 26.1385 + 15.0911i 0.0432041 + 0.0249439i
\(606\) −800.183 181.971i −1.32043 0.300281i
\(607\) 61.3136 + 106.198i 0.101011 + 0.174956i 0.912101 0.409965i \(-0.134459\pi\)
−0.811090 + 0.584921i \(0.801126\pi\)
\(608\) 735.902i 1.21036i
\(609\) 300.029 301.798i 0.492659 0.495563i
\(610\) −38.5076 −0.0631272
\(611\) −807.247 + 466.064i −1.32119 + 0.762789i
\(612\) 482.559 36.9307i 0.788495 0.0603442i
\(613\) 397.390 688.299i 0.648271 1.12284i −0.335265 0.942124i \(-0.608826\pi\)
0.983536 0.180714i \(-0.0578408\pi\)
\(614\) −1034.38 + 597.201i −1.68466 + 0.972640i
\(615\) −97.8152 316.221i −0.159049 0.514180i
\(616\) 23.3494 12.4048i 0.0379049 0.0201376i
\(617\) 505.078i 0.818603i −0.912399 0.409301i \(-0.865772\pi\)
0.912399 0.409301i \(-0.134228\pi\)
\(618\) −947.680 877.925i −1.53346 1.42059i
\(619\) −184.318 + 319.249i −0.297768 + 0.515749i −0.975625 0.219445i \(-0.929575\pi\)
0.677857 + 0.735194i \(0.262909\pi\)
\(620\) 313.141 + 180.792i 0.505067 + 0.291600i
\(621\) −588.317 87.2470i −0.947370 0.140494i
\(622\) 725.257 1.16601
\(623\) 115.481 + 4.07265i 0.185362 + 0.00653716i
\(624\) −152.400 492.684i −0.244231 0.789558i
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) −644.143 371.896i −1.02898 0.594084i
\(627\) −111.391 + 489.821i −0.177657 + 0.781214i
\(628\) 137.868 + 238.794i 0.219535 + 0.380246i
\(629\) 419.816i 0.667434i
\(630\) −401.277 + 16.5137i −0.636947 + 0.0262122i
\(631\) −332.061 −0.526245 −0.263123 0.964762i \(-0.584752\pi\)
−0.263123 + 0.964762i \(0.584752\pi\)
\(632\) −25.9264 + 14.9686i −0.0410228 + 0.0236845i
\(633\) −228.847 52.0423i −0.361527 0.0822153i
\(634\) 573.515 993.357i 0.904598 1.56681i
\(635\) 296.484 171.175i 0.466905 0.269568i
\(636\) −1070.41 + 331.105i −1.68303 + 0.520606i
\(637\) 238.314 + 489.475i 0.374119 + 0.768407i
\(638\) 599.010i 0.938887i
\(639\) 178.939 373.079i 0.280029 0.583848i
\(640\) 13.0268 22.5631i 0.0203544 0.0352549i
\(641\) 877.294 + 506.506i 1.36863 + 0.790181i 0.990754 0.135673i \(-0.0433197\pi\)
0.377880 + 0.925854i \(0.376653\pi\)
\(642\) 275.680 297.585i 0.429409 0.463527i
\(643\) 779.296 1.21197 0.605984 0.795477i \(-0.292779\pi\)
0.605984 + 0.795477i \(0.292779\pi\)
\(644\) −337.471 + 539.651i −0.524023 + 0.837967i
\(645\) 226.305 70.0021i 0.350861 0.108530i
\(646\) 299.897 + 519.437i 0.464237 + 0.804082i
\(647\) 1057.92 + 610.788i 1.63511 + 0.944031i 0.982483 + 0.186351i \(0.0596662\pi\)
0.652626 + 0.757680i \(0.273667\pi\)
\(648\) −23.0120 + 18.4709i −0.0355123 + 0.0285044i
\(649\) 185.524 + 321.337i 0.285861 + 0.495126i
\(650\) 158.374i 0.243652i
\(651\) 794.012 215.258i 1.21968 0.330657i
\(652\) −239.956 −0.368031
\(653\) 91.8529 53.0313i 0.140663 0.0812118i −0.428017 0.903771i \(-0.640788\pi\)
0.568680 + 0.822559i \(0.307454\pi\)
\(654\) −370.746 + 1630.29i −0.566890 + 2.49280i
\(655\) −159.528 + 276.310i −0.243554 + 0.421848i
\(656\) 661.179 381.732i 1.00789 0.581908i
\(657\) 241.797 165.416i 0.368032 0.251774i
\(658\) −1478.59 + 785.523i −2.24709 + 1.19380i
\(659\) 1145.05i 1.73756i −0.495202 0.868778i \(-0.664906\pi\)
0.495202 0.868778i \(-0.335094\pi\)
\(660\) 195.110 210.613i 0.295622 0.319110i
\(661\) 32.4640 56.2292i 0.0491134 0.0850669i −0.840424 0.541930i \(-0.817694\pi\)
0.889537 + 0.456863i \(0.151027\pi\)
\(662\) −884.066 510.416i −1.33545 0.771021i
\(663\) −318.538 295.092i −0.480450 0.445085i
\(664\) −0.346676 −0.000522103
\(665\) −118.595 223.231i −0.178339 0.335686i
\(666\) −466.863 682.440i −0.700996 1.02468i
\(667\) −223.193 386.582i −0.334622 0.579583i
\(668\) −367.597 212.232i −0.550294 0.317713i
\(669\) 883.599 + 200.941i 1.32078 + 0.300359i
\(670\) −366.370 634.572i −0.546821 0.947122i
\(671\) 62.6302i 0.0933386i
\(672\) −250.388 923.595i −0.372601 1.37440i
\(673\) −414.755 −0.616278 −0.308139 0.951341i \(-0.599706\pi\)
−0.308139 + 0.951341i \(0.599706\pi\)
\(674\) −209.312 + 120.846i −0.310552 + 0.179297i
\(675\) −125.551 + 49.6191i −0.186001 + 0.0735098i
\(676\) −94.0308 + 162.866i −0.139099 + 0.240926i
\(677\) −254.799 + 147.109i −0.376366 + 0.217295i −0.676236 0.736685i \(-0.736390\pi\)
0.299870 + 0.953980i \(0.403057\pi\)
\(678\) 253.070 + 818.135i 0.373260 + 1.20669i
\(679\) −849.922 531.499i −1.25173 0.782767i
\(680\) 10.6120i 0.0156060i
\(681\) −707.744 655.649i −1.03927 0.962774i
\(682\) −578.992 + 1002.84i −0.848962 + 1.47045i
\(683\) −363.270 209.734i −0.531874 0.307078i 0.209905 0.977722i \(-0.432684\pi\)
−0.741779 + 0.670644i \(0.766018\pi\)
\(684\) −540.949 259.454i −0.790861 0.379318i
\(685\) 2.98521 0.00435797
\(686\) 396.808 + 893.739i 0.578437 + 1.30283i
\(687\) 183.127 + 592.020i 0.266560 + 0.861747i
\(688\) 273.189 + 473.177i 0.397077 + 0.687757i
\(689\) 870.589 + 502.635i 1.26355 + 0.729513i
\(690\) −93.4171 + 410.785i −0.135387 + 0.595340i
\(691\) −65.4780 113.411i −0.0947583 0.164126i 0.814749 0.579813i \(-0.196874\pi\)
−0.909508 + 0.415687i \(0.863541\pi\)
\(692\) 456.584i 0.659803i
\(693\) −26.8585 652.652i −0.0387569 0.941778i
\(694\) 305.191 0.439756
\(695\) −82.9354 + 47.8828i −0.119331 + 0.0688961i
\(696\) −21.5957 4.91110i −0.0310283 0.00705618i
\(697\) 321.407 556.694i 0.461129 0.798699i
\(698\) −392.262 + 226.473i −0.561980 + 0.324459i
\(699\) 655.648 202.809i 0.937980 0.290141i
\(700\) −5.09194 + 144.383i −0.00727420 + 0.206261i
\(701\) 585.441i 0.835152i −0.908642 0.417576i \(-0.862880\pi\)
0.908642 0.417576i \(-0.137120\pi\)
\(702\) 845.968 + 125.457i 1.20508 + 0.178713i
\(703\) 260.212 450.700i 0.370145 0.641109i
\(704\) 610.782 + 352.635i 0.867588 + 0.500902i
\(705\) −382.475 + 412.864i −0.542517 + 0.585623i
\(706\) −855.537 −1.21181
\(707\) 315.105 + 593.122i 0.445694 + 0.838927i
\(708\) −423.367 + 130.958i −0.597976 + 0.184969i
\(709\) 458.739 + 794.560i 0.647023 + 1.12068i 0.983830 + 0.179103i \(0.0573196\pi\)
−0.336807 + 0.941574i \(0.609347\pi\)
\(710\) −253.816 146.541i −0.357488 0.206396i
\(711\) 56.4375 + 737.447i 0.0793776 + 1.03720i
\(712\) −3.00681 5.20795i −0.00422305 0.00731453i
\(713\) 862.937i 1.21029i
\(714\) −553.123 549.882i −0.774682 0.770143i
\(715\) −257.586 −0.360260
\(716\) −253.476 + 146.345i −0.354017 + 0.204392i
\(717\) 109.637 482.107i 0.152910 0.672395i
\(718\) 197.728 342.474i 0.275387 0.476984i
\(719\) −115.945 + 66.9409i −0.161259 + 0.0931028i −0.578458 0.815712i \(-0.696345\pi\)
0.417199 + 0.908815i \(0.363012\pi\)
\(720\) −175.813 256.996i −0.244185 0.356938i
\(721\) −37.2647 + 1056.65i −0.0516848 + 1.46553i
\(722\) 285.651i 0.395639i
\(723\) 484.243 522.719i 0.669769 0.722986i
\(724\) 411.167 712.161i 0.567910 0.983648i
\(725\) −87.7486 50.6617i −0.121033 0.0698782i
\(726\) −84.6887 78.4550i −0.116651 0.108065i
\(727\) −71.4890 −0.0983343 −0.0491672 0.998791i \(-0.515657\pi\)
−0.0491672 + 0.998791i \(0.515657\pi\)
\(728\) 15.0221 24.0219i 0.0206348 0.0329971i
\(729\) 165.589 + 709.944i 0.227146 + 0.973861i
\(730\) −103.756 179.711i −0.142132 0.246179i
\(731\) 398.401 + 230.017i 0.545009 + 0.314661i
\(732\) 72.9397 + 16.5873i 0.0996444 + 0.0226603i
\(733\) −12.2559 21.2278i −0.0167201 0.0289601i 0.857544 0.514410i \(-0.171989\pi\)
−0.874264 + 0.485450i \(0.838656\pi\)
\(734\) 1387.46i 1.89027i
\(735\) 224.797 + 239.815i 0.305846 + 0.326279i
\(736\) −1003.77 −1.36382
\(737\) 1032.09 595.878i 1.40040 0.808519i
\(738\) 96.6104 + 1262.37i 0.130908 + 1.71053i
\(739\) −492.233 + 852.573i −0.666080 + 1.15368i 0.312911 + 0.949782i \(0.398696\pi\)
−0.978991 + 0.203902i \(0.934638\pi\)
\(740\) −257.592 + 148.721i −0.348097 + 0.200974i
\(741\) 159.067 + 514.238i 0.214665 + 0.693978i
\(742\) 1530.96 + 957.389i 2.06329 + 1.29028i
\(743\) 409.859i 0.551627i −0.961211 0.275813i \(-0.911053\pi\)
0.961211 0.275813i \(-0.0889472\pi\)
\(744\) −31.4078 29.0960i −0.0422148 0.0391075i
\(745\) −212.338 + 367.780i −0.285017 + 0.493664i
\(746\) −813.561 469.710i −1.09056 0.629638i
\(747\) −3.70387 + 7.72239i −0.00495832 + 0.0103379i
\(748\) 557.551 0.745389
\(749\) −331.801 11.7016i −0.442992 0.0156230i
\(750\) 28.2576 + 91.3524i 0.0376769 + 0.121803i
\(751\) −272.435 471.871i −0.362762 0.628323i 0.625652 0.780102i \(-0.284833\pi\)
−0.988414 + 0.151779i \(0.951500\pi\)
\(752\) −1124.19 649.052i −1.49494 0.863101i
\(753\) 311.428 1369.45i 0.413583 1.81865i
\(754\) 320.940 + 555.884i 0.425650 + 0.737247i
\(755\) 208.223i 0.275793i
\(756\) 767.198 + 141.572i 1.01481 + 0.187265i
\(757\) −878.475 −1.16047 −0.580234 0.814450i \(-0.697039\pi\)
−0.580234 + 0.814450i \(0.697039\pi\)
\(758\) −408.477 + 235.834i −0.538888 + 0.311127i
\(759\) −668.116 151.937i −0.880258 0.200181i
\(760\) −6.57760 + 11.3927i −0.00865473 + 0.0149904i
\(761\) −153.563 + 88.6596i −0.201791 + 0.116504i −0.597491 0.801876i \(-0.703835\pi\)
0.395700 + 0.918380i \(0.370502\pi\)
\(762\) −1250.98 + 386.961i −1.64171 + 0.507823i
\(763\) 1208.42 641.995i 1.58378 0.841408i
\(764\) 811.159i 1.06173i
\(765\) −236.389 113.378i −0.309005