Properties

Label 324.5.d.f.163.2
Level 324
Weight 5
Character 324.163
Analytic conductor 33.492
Analytic rank 0
Dimension 22
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.4918680392\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 163.2
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.f.163.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.92469 + 0.772521i) q^{2} +(14.8064 - 6.06382i) q^{4} +21.1512 q^{5} -44.6184i q^{7} +(-53.4262 + 35.2369i) q^{8} +O(q^{10})\) \(q+(-3.92469 + 0.772521i) q^{2} +(14.8064 - 6.06382i) q^{4} +21.1512 q^{5} -44.6184i q^{7} +(-53.4262 + 35.2369i) q^{8} +(-83.0119 + 16.3397i) q^{10} +67.7698i q^{11} -29.1038 q^{13} +(34.4687 + 175.114i) q^{14} +(182.460 - 179.567i) q^{16} +402.841 q^{17} +644.741i q^{19} +(313.173 - 128.257i) q^{20} +(-52.3536 - 265.976i) q^{22} +387.433i q^{23} -177.628 q^{25} +(114.223 - 22.4833i) q^{26} +(-270.558 - 660.639i) q^{28} +724.420 q^{29} -1259.67i q^{31} +(-577.381 + 845.699i) q^{32} +(-1581.03 + 311.203i) q^{34} -943.733i q^{35} -1402.04 q^{37} +(-498.076 - 2530.41i) q^{38} +(-1130.03 + 745.302i) q^{40} +1548.33 q^{41} -1871.75i q^{43} +(410.944 + 1003.43i) q^{44} +(-299.300 - 1520.56i) q^{46} +4169.19i q^{47} +410.195 q^{49} +(697.134 - 137.221i) q^{50} +(-430.923 + 176.480i) q^{52} +906.566 q^{53} +1433.41i q^{55} +(1572.21 + 2383.79i) q^{56} +(-2843.13 + 559.630i) q^{58} -4522.33i q^{59} +2628.44 q^{61} +(973.119 + 4943.80i) q^{62} +(1612.72 - 3765.15i) q^{64} -615.579 q^{65} -67.7999i q^{67} +(5964.64 - 2442.76i) q^{68} +(729.053 + 3703.86i) q^{70} +1315.04i q^{71} +9470.72 q^{73} +(5502.56 - 1083.10i) q^{74} +(3909.59 + 9546.31i) q^{76} +3023.78 q^{77} +4369.33i q^{79} +(3859.25 - 3798.05i) q^{80} +(-6076.73 + 1196.12i) q^{82} +762.015i q^{83} +8520.57 q^{85} +(1445.97 + 7346.04i) q^{86} +(-2388.00 - 3620.69i) q^{88} +8083.40 q^{89} +1298.56i q^{91} +(2349.32 + 5736.50i) q^{92} +(-3220.79 - 16362.8i) q^{94} +13637.0i q^{95} +6665.42 q^{97} +(-1609.89 + 316.884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + O(q^{10}) \) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + 14q^{10} + 2q^{13} - 252q^{14} + q^{16} - 28q^{17} + 140q^{20} + 33q^{22} + 1752q^{25} + 548q^{26} - 258q^{28} - 526q^{29} + 121q^{32} - 385q^{34} - 4q^{37} - 1395q^{38} + 2276q^{40} + 2762q^{41} + 3357q^{44} + 1788q^{46} - 3428q^{49} - 6375q^{50} - 1438q^{52} - 5044q^{53} + 7506q^{56} + 4064q^{58} + 2q^{61} - 9162q^{62} + 4513q^{64} + 2014q^{65} + 11405q^{68} - 3666q^{70} - 1708q^{73} - 14620q^{74} - 1581q^{76} + 3942q^{77} + 22760q^{80} - 4243q^{82} + 1252q^{85} - 22113q^{86} - 1995q^{88} + 6524q^{89} + 30294q^{92} - 7524q^{94} - 5638q^{97} - 46469q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.92469 + 0.772521i −0.981173 + 0.193130i
\(3\) 0 0
\(4\) 14.8064 6.06382i 0.925401 0.378988i
\(5\) 21.1512 0.846047 0.423024 0.906119i \(-0.360969\pi\)
0.423024 + 0.906119i \(0.360969\pi\)
\(6\) 0 0
\(7\) 44.6184i 0.910580i −0.890343 0.455290i \(-0.849536\pi\)
0.890343 0.455290i \(-0.150464\pi\)
\(8\) −53.4262 + 35.2369i −0.834785 + 0.550576i
\(9\) 0 0
\(10\) −83.0119 + 16.3397i −0.830119 + 0.163397i
\(11\) 67.7698i 0.560081i 0.959988 + 0.280041i \(0.0903480\pi\)
−0.959988 + 0.280041i \(0.909652\pi\)
\(12\) 0 0
\(13\) −29.1038 −0.172212 −0.0861058 0.996286i \(-0.527442\pi\)
−0.0861058 + 0.996286i \(0.527442\pi\)
\(14\) 34.4687 + 175.114i 0.175861 + 0.893437i
\(15\) 0 0
\(16\) 182.460 179.567i 0.712735 0.701433i
\(17\) 402.841 1.39391 0.696957 0.717113i \(-0.254537\pi\)
0.696957 + 0.717113i \(0.254537\pi\)
\(18\) 0 0
\(19\) 644.741i 1.78599i 0.450070 + 0.892993i \(0.351399\pi\)
−0.450070 + 0.892993i \(0.648601\pi\)
\(20\) 313.173 128.257i 0.782933 0.320642i
\(21\) 0 0
\(22\) −52.3536 265.976i −0.108169 0.549537i
\(23\) 387.433i 0.732388i 0.930539 + 0.366194i \(0.119339\pi\)
−0.930539 + 0.366194i \(0.880661\pi\)
\(24\) 0 0
\(25\) −177.628 −0.284204
\(26\) 114.223 22.4833i 0.168969 0.0332593i
\(27\) 0 0
\(28\) −270.558 660.639i −0.345099 0.842652i
\(29\) 724.420 0.861380 0.430690 0.902500i \(-0.358270\pi\)
0.430690 + 0.902500i \(0.358270\pi\)
\(30\) 0 0
\(31\) 1259.67i 1.31079i −0.755288 0.655393i \(-0.772503\pi\)
0.755288 0.655393i \(-0.227497\pi\)
\(32\) −577.381 + 845.699i −0.563849 + 0.825878i
\(33\) 0 0
\(34\) −1581.03 + 311.203i −1.36767 + 0.269207i
\(35\) 943.733i 0.770394i
\(36\) 0 0
\(37\) −1402.04 −1.02413 −0.512066 0.858946i \(-0.671120\pi\)
−0.512066 + 0.858946i \(0.671120\pi\)
\(38\) −498.076 2530.41i −0.344928 1.75236i
\(39\) 0 0
\(40\) −1130.03 + 745.302i −0.706267 + 0.465814i
\(41\) 1548.33 0.921078 0.460539 0.887640i \(-0.347656\pi\)
0.460539 + 0.887640i \(0.347656\pi\)
\(42\) 0 0
\(43\) 1871.75i 1.01230i −0.862444 0.506152i \(-0.831068\pi\)
0.862444 0.506152i \(-0.168932\pi\)
\(44\) 410.944 + 1003.43i 0.212264 + 0.518300i
\(45\) 0 0
\(46\) −299.300 1520.56i −0.141446 0.718599i
\(47\) 4169.19i 1.88737i 0.330851 + 0.943683i \(0.392664\pi\)
−0.330851 + 0.943683i \(0.607336\pi\)
\(48\) 0 0
\(49\) 410.195 0.170843
\(50\) 697.134 137.221i 0.278854 0.0548884i
\(51\) 0 0
\(52\) −430.923 + 176.480i −0.159365 + 0.0652662i
\(53\) 906.566 0.322736 0.161368 0.986894i \(-0.448409\pi\)
0.161368 + 0.986894i \(0.448409\pi\)
\(54\) 0 0
\(55\) 1433.41i 0.473855i
\(56\) 1572.21 + 2383.79i 0.501344 + 0.760139i
\(57\) 0 0
\(58\) −2843.13 + 559.630i −0.845162 + 0.166358i
\(59\) 4522.33i 1.29915i −0.760299 0.649573i \(-0.774948\pi\)
0.760299 0.649573i \(-0.225052\pi\)
\(60\) 0 0
\(61\) 2628.44 0.706380 0.353190 0.935552i \(-0.385097\pi\)
0.353190 + 0.935552i \(0.385097\pi\)
\(62\) 973.119 + 4943.80i 0.253153 + 1.28611i
\(63\) 0 0
\(64\) 1612.72 3765.15i 0.393731 0.919226i
\(65\) −615.579 −0.145699
\(66\) 0 0
\(67\) 67.7999i 0.0151036i −0.999971 0.00755179i \(-0.997596\pi\)
0.999971 0.00755179i \(-0.00240383\pi\)
\(68\) 5964.64 2442.76i 1.28993 0.528277i
\(69\) 0 0
\(70\) 729.053 + 3703.86i 0.148786 + 0.755890i
\(71\) 1315.04i 0.260869i 0.991457 + 0.130434i \(0.0416372\pi\)
−0.991457 + 0.130434i \(0.958363\pi\)
\(72\) 0 0
\(73\) 9470.72 1.77720 0.888602 0.458680i \(-0.151678\pi\)
0.888602 + 0.458680i \(0.151678\pi\)
\(74\) 5502.56 1083.10i 1.00485 0.197791i
\(75\) 0 0
\(76\) 3909.59 + 9546.31i 0.676868 + 1.65275i
\(77\) 3023.78 0.509999
\(78\) 0 0
\(79\) 4369.33i 0.700101i 0.936731 + 0.350050i \(0.113836\pi\)
−0.936731 + 0.350050i \(0.886164\pi\)
\(80\) 3859.25 3798.05i 0.603008 0.593445i
\(81\) 0 0
\(82\) −6076.73 + 1196.12i −0.903737 + 0.177888i
\(83\) 762.015i 0.110613i 0.998469 + 0.0553067i \(0.0176136\pi\)
−0.998469 + 0.0553067i \(0.982386\pi\)
\(84\) 0 0
\(85\) 8520.57 1.17932
\(86\) 1445.97 + 7346.04i 0.195507 + 0.993245i
\(87\) 0 0
\(88\) −2388.00 3620.69i −0.308368 0.467547i
\(89\) 8083.40 1.02050 0.510251 0.860025i \(-0.329552\pi\)
0.510251 + 0.860025i \(0.329552\pi\)
\(90\) 0 0
\(91\) 1298.56i 0.156813i
\(92\) 2349.32 + 5736.50i 0.277567 + 0.677753i
\(93\) 0 0
\(94\) −3220.79 16362.8i −0.364508 1.85183i
\(95\) 13637.0i 1.51103i
\(96\) 0 0
\(97\) 6665.42 0.708408 0.354204 0.935168i \(-0.384752\pi\)
0.354204 + 0.935168i \(0.384752\pi\)
\(98\) −1609.89 + 316.884i −0.167627 + 0.0329950i
\(99\) 0 0
\(100\) −2630.03 + 1077.10i −0.263003 + 0.107710i
\(101\) 9286.07 0.910310 0.455155 0.890412i \(-0.349584\pi\)
0.455155 + 0.890412i \(0.349584\pi\)
\(102\) 0 0
\(103\) 11307.4i 1.06583i 0.846169 + 0.532915i \(0.178903\pi\)
−0.846169 + 0.532915i \(0.821097\pi\)
\(104\) 1554.90 1025.53i 0.143760 0.0948156i
\(105\) 0 0
\(106\) −3557.99 + 700.341i −0.316660 + 0.0623301i
\(107\) 6261.61i 0.546913i 0.961884 + 0.273456i \(0.0881669\pi\)
−0.961884 + 0.273456i \(0.911833\pi\)
\(108\) 0 0
\(109\) 3452.85 0.290620 0.145310 0.989386i \(-0.453582\pi\)
0.145310 + 0.989386i \(0.453582\pi\)
\(110\) −1107.34 5625.70i −0.0915158 0.464934i
\(111\) 0 0
\(112\) −8011.99 8141.09i −0.638711 0.649003i
\(113\) −2545.11 −0.199319 −0.0996597 0.995022i \(-0.531775\pi\)
−0.0996597 + 0.995022i \(0.531775\pi\)
\(114\) 0 0
\(115\) 8194.67i 0.619635i
\(116\) 10726.1 4392.75i 0.797122 0.326453i
\(117\) 0 0
\(118\) 3493.59 + 17748.7i 0.250904 + 1.27469i
\(119\) 17974.1i 1.26927i
\(120\) 0 0
\(121\) 10048.2 0.686309
\(122\) −10315.8 + 2030.52i −0.693081 + 0.136423i
\(123\) 0 0
\(124\) −7638.38 18651.1i −0.496773 1.21300i
\(125\) −16976.5 −1.08650
\(126\) 0 0
\(127\) 530.060i 0.0328638i −0.999865 0.0164319i \(-0.994769\pi\)
0.999865 0.0164319i \(-0.00523067\pi\)
\(128\) −3420.79 + 16022.9i −0.208788 + 0.977961i
\(129\) 0 0
\(130\) 2415.96 475.548i 0.142956 0.0281389i
\(131\) 926.298i 0.0539769i 0.999636 + 0.0269885i \(0.00859174\pi\)
−0.999636 + 0.0269885i \(0.991408\pi\)
\(132\) 0 0
\(133\) 28767.3 1.62628
\(134\) 52.3769 + 266.094i 0.00291696 + 0.0148192i
\(135\) 0 0
\(136\) −21522.3 + 14194.9i −1.16362 + 0.767456i
\(137\) 1668.23 0.0888820 0.0444410 0.999012i \(-0.485849\pi\)
0.0444410 + 0.999012i \(0.485849\pi\)
\(138\) 0 0
\(139\) 828.805i 0.0428966i −0.999770 0.0214483i \(-0.993172\pi\)
0.999770 0.0214483i \(-0.00682773\pi\)
\(140\) −5722.62 13973.3i −0.291970 0.712924i
\(141\) 0 0
\(142\) −1015.90 5161.13i −0.0503817 0.255958i
\(143\) 1972.36i 0.0964525i
\(144\) 0 0
\(145\) 15322.3 0.728768
\(146\) −37169.6 + 7316.33i −1.74374 + 0.343232i
\(147\) 0 0
\(148\) −20759.1 + 8501.69i −0.947732 + 0.388134i
\(149\) 3122.76 0.140658 0.0703292 0.997524i \(-0.477595\pi\)
0.0703292 + 0.997524i \(0.477595\pi\)
\(150\) 0 0
\(151\) 9159.51i 0.401715i −0.979620 0.200858i \(-0.935627\pi\)
0.979620 0.200858i \(-0.0643729\pi\)
\(152\) −22718.7 34446.1i −0.983322 1.49091i
\(153\) 0 0
\(154\) −11867.4 + 2335.94i −0.500397 + 0.0984963i
\(155\) 26643.4i 1.10899i
\(156\) 0 0
\(157\) 21103.7 0.856168 0.428084 0.903739i \(-0.359189\pi\)
0.428084 + 0.903739i \(0.359189\pi\)
\(158\) −3375.40 17148.3i −0.135211 0.686920i
\(159\) 0 0
\(160\) −12212.3 + 17887.5i −0.477043 + 0.698732i
\(161\) 17286.7 0.666898
\(162\) 0 0
\(163\) 42771.0i 1.60981i −0.593405 0.804904i \(-0.702217\pi\)
0.593405 0.804904i \(-0.297783\pi\)
\(164\) 22925.3 9388.80i 0.852367 0.349078i
\(165\) 0 0
\(166\) −588.673 2990.68i −0.0213628 0.108531i
\(167\) 11048.3i 0.396153i −0.980187 0.198077i \(-0.936531\pi\)
0.980187 0.198077i \(-0.0634695\pi\)
\(168\) 0 0
\(169\) −27714.0 −0.970343
\(170\) −33440.6 + 6582.32i −1.15711 + 0.227762i
\(171\) 0 0
\(172\) −11349.9 27713.9i −0.383651 0.936787i
\(173\) −21935.6 −0.732922 −0.366461 0.930433i \(-0.619431\pi\)
−0.366461 + 0.930433i \(0.619431\pi\)
\(174\) 0 0
\(175\) 7925.47i 0.258791i
\(176\) 12169.2 + 12365.3i 0.392860 + 0.399190i
\(177\) 0 0
\(178\) −31724.9 + 6244.60i −1.00129 + 0.197090i
\(179\) 11479.2i 0.358265i 0.983825 + 0.179133i \(0.0573291\pi\)
−0.983825 + 0.179133i \(0.942671\pi\)
\(180\) 0 0
\(181\) 45472.2 1.38800 0.693999 0.719976i \(-0.255847\pi\)
0.693999 + 0.719976i \(0.255847\pi\)
\(182\) −1003.17 5096.47i −0.0302852 0.153860i
\(183\) 0 0
\(184\) −13651.9 20699.1i −0.403235 0.611386i
\(185\) −29654.7 −0.866463
\(186\) 0 0
\(187\) 27300.5i 0.780705i
\(188\) 25281.2 + 61730.8i 0.715290 + 1.74657i
\(189\) 0 0
\(190\) −10534.9 53521.2i −0.291825 1.48258i
\(191\) 70040.6i 1.91992i 0.280135 + 0.959961i \(0.409621\pi\)
−0.280135 + 0.959961i \(0.590379\pi\)
\(192\) 0 0
\(193\) −34852.9 −0.935672 −0.467836 0.883815i \(-0.654966\pi\)
−0.467836 + 0.883815i \(0.654966\pi\)
\(194\) −26159.7 + 5149.17i −0.695071 + 0.136815i
\(195\) 0 0
\(196\) 6073.52 2487.35i 0.158099 0.0647477i
\(197\) −30858.0 −0.795124 −0.397562 0.917575i \(-0.630144\pi\)
−0.397562 + 0.917575i \(0.630144\pi\)
\(198\) 0 0
\(199\) 34262.5i 0.865192i 0.901588 + 0.432596i \(0.142402\pi\)
−0.901588 + 0.432596i \(0.857598\pi\)
\(200\) 9489.97 6259.04i 0.237249 0.156476i
\(201\) 0 0
\(202\) −36445.0 + 7173.69i −0.893172 + 0.175808i
\(203\) 32322.5i 0.784355i
\(204\) 0 0
\(205\) 32749.0 0.779275
\(206\) −8735.19 44378.0i −0.205844 1.04576i
\(207\) 0 0
\(208\) −5310.28 + 5226.07i −0.122741 + 0.120795i
\(209\) −43694.0 −1.00030
\(210\) 0 0
\(211\) 17308.5i 0.388772i −0.980925 0.194386i \(-0.937728\pi\)
0.980925 0.194386i \(-0.0622715\pi\)
\(212\) 13423.0 5497.25i 0.298661 0.122313i
\(213\) 0 0
\(214\) −4837.22 24574.9i −0.105625 0.536616i
\(215\) 39589.7i 0.856457i
\(216\) 0 0
\(217\) −56204.3 −1.19358
\(218\) −13551.4 + 2667.40i −0.285148 + 0.0561274i
\(219\) 0 0
\(220\) 8691.95 + 21223.7i 0.179586 + 0.438506i
\(221\) −11724.2 −0.240048
\(222\) 0 0
\(223\) 64068.3i 1.28835i −0.764879 0.644174i \(-0.777201\pi\)
0.764879 0.644174i \(-0.222799\pi\)
\(224\) 37733.8 + 25761.9i 0.752028 + 0.513430i
\(225\) 0 0
\(226\) 9988.77 1966.15i 0.195567 0.0384946i
\(227\) 13692.2i 0.265719i −0.991135 0.132859i \(-0.957584\pi\)
0.991135 0.132859i \(-0.0424159\pi\)
\(228\) 0 0
\(229\) 65992.3 1.25841 0.629205 0.777239i \(-0.283380\pi\)
0.629205 + 0.777239i \(0.283380\pi\)
\(230\) −6330.55 32161.6i −0.119670 0.607969i
\(231\) 0 0
\(232\) −38703.0 + 25526.3i −0.719067 + 0.474255i
\(233\) −63342.4 −1.16676 −0.583381 0.812198i \(-0.698271\pi\)
−0.583381 + 0.812198i \(0.698271\pi\)
\(234\) 0 0
\(235\) 88183.3i 1.59680i
\(236\) −27422.6 66959.5i −0.492361 1.20223i
\(237\) 0 0
\(238\) 13885.4 + 70543.0i 0.245135 + 1.24537i
\(239\) 317.551i 0.00555928i 0.999996 + 0.00277964i \(0.000884788\pi\)
−0.999996 + 0.00277964i \(0.999115\pi\)
\(240\) 0 0
\(241\) 25505.3 0.439133 0.219566 0.975598i \(-0.429536\pi\)
0.219566 + 0.975598i \(0.429536\pi\)
\(242\) −39436.3 + 7762.48i −0.673388 + 0.132547i
\(243\) 0 0
\(244\) 38917.8 15938.4i 0.653685 0.267710i
\(245\) 8676.11 0.144542
\(246\) 0 0
\(247\) 18764.4i 0.307568i
\(248\) 44386.7 + 67299.2i 0.721688 + 1.09423i
\(249\) 0 0
\(250\) 66627.6 13114.7i 1.06604 0.209836i
\(251\) 40987.7i 0.650588i −0.945613 0.325294i \(-0.894537\pi\)
0.945613 0.325294i \(-0.105463\pi\)
\(252\) 0 0
\(253\) −26256.3 −0.410197
\(254\) 409.483 + 2080.32i 0.00634700 + 0.0322451i
\(255\) 0 0
\(256\) 1047.51 65527.6i 0.0159837 0.999872i
\(257\) 30958.1 0.468715 0.234357 0.972151i \(-0.424701\pi\)
0.234357 + 0.972151i \(0.424701\pi\)
\(258\) 0 0
\(259\) 62556.6i 0.932554i
\(260\) −9114.52 + 3732.76i −0.134830 + 0.0552183i
\(261\) 0 0
\(262\) −715.585 3635.44i −0.0104246 0.0529607i
\(263\) 15371.1i 0.222225i 0.993808 + 0.111113i \(0.0354414\pi\)
−0.993808 + 0.111113i \(0.964559\pi\)
\(264\) 0 0
\(265\) 19174.9 0.273050
\(266\) −112903. + 22223.4i −1.59567 + 0.314085i
\(267\) 0 0
\(268\) −411.126 1003.87i −0.00572408 0.0139769i
\(269\) 76105.5 1.05175 0.525873 0.850563i \(-0.323739\pi\)
0.525873 + 0.850563i \(0.323739\pi\)
\(270\) 0 0
\(271\) 78076.4i 1.06312i 0.847021 + 0.531559i \(0.178394\pi\)
−0.847021 + 0.531559i \(0.821606\pi\)
\(272\) 73502.5 72336.9i 0.993492 0.977737i
\(273\) 0 0
\(274\) −6547.28 + 1288.74i −0.0872087 + 0.0171658i
\(275\) 12037.8i 0.159177i
\(276\) 0 0
\(277\) 4739.93 0.0617750 0.0308875 0.999523i \(-0.490167\pi\)
0.0308875 + 0.999523i \(0.490167\pi\)
\(278\) 640.269 + 3252.80i 0.00828463 + 0.0420890i
\(279\) 0 0
\(280\) 33254.2 + 50420.1i 0.424161 + 0.643113i
\(281\) 43209.3 0.547223 0.273612 0.961840i \(-0.411782\pi\)
0.273612 + 0.961840i \(0.411782\pi\)
\(282\) 0 0
\(283\) 36115.6i 0.450944i −0.974250 0.225472i \(-0.927608\pi\)
0.974250 0.225472i \(-0.0723924\pi\)
\(284\) 7974.16 + 19471.0i 0.0988663 + 0.241408i
\(285\) 0 0
\(286\) 1523.69 + 7740.90i 0.0186279 + 0.0946366i
\(287\) 69084.1i 0.838715i
\(288\) 0 0
\(289\) 78760.1 0.942997
\(290\) −60135.5 + 11836.8i −0.715047 + 0.140747i
\(291\) 0 0
\(292\) 140227. 57428.7i 1.64463 0.673540i
\(293\) −96093.3 −1.11933 −0.559665 0.828719i \(-0.689070\pi\)
−0.559665 + 0.828719i \(0.689070\pi\)
\(294\) 0 0
\(295\) 95652.6i 1.09914i
\(296\) 74905.5 49403.4i 0.854929 0.563862i
\(297\) 0 0
\(298\) −12255.9 + 2412.40i −0.138010 + 0.0271654i
\(299\) 11275.8i 0.126126i
\(300\) 0 0
\(301\) −83514.6 −0.921784
\(302\) 7075.92 + 35948.3i 0.0775834 + 0.394152i
\(303\) 0 0
\(304\) 115774. + 117640.i 1.25275 + 1.27294i
\(305\) 55594.6 0.597631
\(306\) 0 0
\(307\) 140641.i 1.49223i −0.665817 0.746115i \(-0.731917\pi\)
0.665817 0.746115i \(-0.268083\pi\)
\(308\) 44771.4 18335.7i 0.471954 0.193284i
\(309\) 0 0
\(310\) 20582.6 + 104567.i 0.214179 + 1.08811i
\(311\) 163464.i 1.69005i 0.534724 + 0.845027i \(0.320416\pi\)
−0.534724 + 0.845027i \(0.679584\pi\)
\(312\) 0 0
\(313\) −51290.3 −0.523536 −0.261768 0.965131i \(-0.584306\pi\)
−0.261768 + 0.965131i \(0.584306\pi\)
\(314\) −82825.4 + 16303.0i −0.840049 + 0.165352i
\(315\) 0 0
\(316\) 26494.8 + 64694.1i 0.265330 + 0.647874i
\(317\) −28050.0 −0.279135 −0.139568 0.990213i \(-0.544571\pi\)
−0.139568 + 0.990213i \(0.544571\pi\)
\(318\) 0 0
\(319\) 49093.8i 0.482443i
\(320\) 34111.0 79637.3i 0.333115 0.777708i
\(321\) 0 0
\(322\) −67844.8 + 13354.3i −0.654342 + 0.128798i
\(323\) 259728.i 2.48951i
\(324\) 0 0
\(325\) 5169.63 0.0489433
\(326\) 33041.5 + 167863.i 0.310903 + 1.57950i
\(327\) 0 0
\(328\) −82721.5 + 54558.4i −0.768902 + 0.507124i
\(329\) 186023. 1.71860
\(330\) 0 0
\(331\) 112789.i 1.02946i 0.857352 + 0.514731i \(0.172108\pi\)
−0.857352 + 0.514731i \(0.827892\pi\)
\(332\) 4620.72 + 11282.7i 0.0419212 + 0.102362i
\(333\) 0 0
\(334\) 8535.06 + 43361.2i 0.0765092 + 0.388695i
\(335\) 1434.05i 0.0127783i
\(336\) 0 0
\(337\) −20819.6 −0.183321 −0.0916606 0.995790i \(-0.529217\pi\)
−0.0916606 + 0.995790i \(0.529217\pi\)
\(338\) 108769. 21409.6i 0.952075 0.187403i
\(339\) 0 0
\(340\) 126159. 51667.2i 1.09134 0.446948i
\(341\) 85367.4 0.734147
\(342\) 0 0
\(343\) 125431.i 1.06615i
\(344\) 65954.6 + 100001.i 0.557351 + 0.845056i
\(345\) 0 0
\(346\) 86090.5 16945.7i 0.719123 0.141549i
\(347\) 161213.i 1.33888i −0.742866 0.669440i \(-0.766534\pi\)
0.742866 0.669440i \(-0.233466\pi\)
\(348\) 0 0
\(349\) −221484. −1.81841 −0.909205 0.416349i \(-0.863310\pi\)
−0.909205 + 0.416349i \(0.863310\pi\)
\(350\) −6122.59 31105.0i −0.0499803 0.253919i
\(351\) 0 0
\(352\) −57312.9 39129.0i −0.462559 0.315801i
\(353\) 218790. 1.75581 0.877904 0.478836i \(-0.158941\pi\)
0.877904 + 0.478836i \(0.158941\pi\)
\(354\) 0 0
\(355\) 27814.6i 0.220707i
\(356\) 119686. 49016.2i 0.944374 0.386759i
\(357\) 0 0
\(358\) −8867.91 45052.2i −0.0691919 0.351520i
\(359\) 924.606i 0.00717411i 0.999994 + 0.00358705i \(0.00114180\pi\)
−0.999994 + 0.00358705i \(0.998858\pi\)
\(360\) 0 0
\(361\) −285370. −2.18975
\(362\) −178464. + 35128.2i −1.36187 + 0.268064i
\(363\) 0 0
\(364\) 7874.25 + 19227.1i 0.0594301 + 0.145115i
\(365\) 200317. 1.50360
\(366\) 0 0
\(367\) 40797.9i 0.302904i −0.988465 0.151452i \(-0.951605\pi\)
0.988465 0.151452i \(-0.0483950\pi\)
\(368\) 69570.1 + 70691.2i 0.513721 + 0.521999i
\(369\) 0 0
\(370\) 116386. 22908.9i 0.850150 0.167340i
\(371\) 40449.6i 0.293877i
\(372\) 0 0
\(373\) −234530. −1.68570 −0.842851 0.538146i \(-0.819125\pi\)
−0.842851 + 0.538146i \(0.819125\pi\)
\(374\) −21090.2 107146.i −0.150778 0.766007i
\(375\) 0 0
\(376\) −146909. 222744.i −1.03914 1.57554i
\(377\) −21083.4 −0.148340
\(378\) 0 0
\(379\) 185553.i 1.29178i −0.763428 0.645892i \(-0.776485\pi\)
0.763428 0.645892i \(-0.223515\pi\)
\(380\) 82692.4 + 201916.i 0.572662 + 1.39831i
\(381\) 0 0
\(382\) −54107.9 274888.i −0.370795 1.88378i
\(383\) 60264.1i 0.410829i 0.978675 + 0.205415i \(0.0658543\pi\)
−0.978675 + 0.205415i \(0.934146\pi\)
\(384\) 0 0
\(385\) 63956.6 0.431483
\(386\) 136787. 26924.6i 0.918056 0.180707i
\(387\) 0 0
\(388\) 98691.0 40417.8i 0.655562 0.268479i
\(389\) −12009.3 −0.0793633 −0.0396816 0.999212i \(-0.512634\pi\)
−0.0396816 + 0.999212i \(0.512634\pi\)
\(390\) 0 0
\(391\) 156074.i 1.02089i
\(392\) −21915.2 + 14454.0i −0.142617 + 0.0940623i
\(393\) 0 0
\(394\) 121108. 23838.4i 0.780154 0.153562i
\(395\) 92416.5i 0.592318i
\(396\) 0 0
\(397\) 32276.3 0.204787 0.102394 0.994744i \(-0.467350\pi\)
0.102394 + 0.994744i \(0.467350\pi\)
\(398\) −26468.5 134470.i −0.167095 0.848903i
\(399\) 0 0
\(400\) −32410.0 + 31896.0i −0.202562 + 0.199350i
\(401\) −187726. −1.16744 −0.583722 0.811953i \(-0.698404\pi\)
−0.583722 + 0.811953i \(0.698404\pi\)
\(402\) 0 0
\(403\) 36661.0i 0.225733i
\(404\) 137494. 56309.0i 0.842402 0.344997i
\(405\) 0 0
\(406\) 24969.8 + 126856.i 0.151483 + 0.769588i
\(407\) 95015.7i 0.573597i
\(408\) 0 0
\(409\) −134544. −0.804299 −0.402149 0.915574i \(-0.631737\pi\)
−0.402149 + 0.915574i \(0.631737\pi\)
\(410\) −128530. + 25299.3i −0.764604 + 0.150502i
\(411\) 0 0
\(412\) 68565.9 + 167422.i 0.403937 + 0.986320i
\(413\) −201779. −1.18298
\(414\) 0 0
\(415\) 16117.5i 0.0935841i
\(416\) 16804.0 24613.0i 0.0971013 0.142226i
\(417\) 0 0
\(418\) 171486. 33754.5i 0.981465 0.193188i
\(419\) 84663.5i 0.482245i 0.970495 + 0.241123i \(0.0775156\pi\)
−0.970495 + 0.241123i \(0.922484\pi\)
\(420\) 0 0
\(421\) −115700. −0.652782 −0.326391 0.945235i \(-0.605833\pi\)
−0.326391 + 0.945235i \(0.605833\pi\)
\(422\) 13371.2 + 67930.7i 0.0750837 + 0.381453i
\(423\) 0 0
\(424\) −48434.4 + 31944.6i −0.269415 + 0.177691i
\(425\) −71555.7 −0.396156
\(426\) 0 0
\(427\) 117277.i 0.643216i
\(428\) 37969.2 + 92712.0i 0.207274 + 0.506114i
\(429\) 0 0
\(430\) 30583.9 + 155377.i 0.165408 + 0.840332i
\(431\) 294896.i 1.58750i −0.608241 0.793752i \(-0.708125\pi\)
0.608241 0.793752i \(-0.291875\pi\)
\(432\) 0 0
\(433\) −151284. −0.806895 −0.403447 0.915003i \(-0.632188\pi\)
−0.403447 + 0.915003i \(0.632188\pi\)
\(434\) 220585. 43419.0i 1.17111 0.230516i
\(435\) 0 0
\(436\) 51124.4 20937.5i 0.268940 0.110141i
\(437\) −249794. −1.30803
\(438\) 0 0
\(439\) 20014.1i 0.103850i 0.998651 + 0.0519251i \(0.0165357\pi\)
−0.998651 + 0.0519251i \(0.983464\pi\)
\(440\) −50509.0 76581.8i −0.260893 0.395567i
\(441\) 0 0
\(442\) 46013.9 9057.19i 0.235529 0.0463606i
\(443\) 38644.0i 0.196913i −0.995141 0.0984567i \(-0.968609\pi\)
0.995141 0.0984567i \(-0.0313906\pi\)
\(444\) 0 0
\(445\) 170973. 0.863393
\(446\) 49494.1 + 251448.i 0.248819 + 1.26409i
\(447\) 0 0
\(448\) −167995. 71957.2i −0.837029 0.358524i
\(449\) 79457.9 0.394135 0.197067 0.980390i \(-0.436858\pi\)
0.197067 + 0.980390i \(0.436858\pi\)
\(450\) 0 0
\(451\) 104930.i 0.515878i
\(452\) −37684.0 + 15433.1i −0.184450 + 0.0755398i
\(453\) 0 0
\(454\) 10577.5 + 53737.8i 0.0513183 + 0.260716i
\(455\) 27466.2i 0.132671i
\(456\) 0 0
\(457\) −263552. −1.26193 −0.630963 0.775813i \(-0.717340\pi\)
−0.630963 + 0.775813i \(0.717340\pi\)
\(458\) −259000. + 50980.5i −1.23472 + 0.243037i
\(459\) 0 0
\(460\) 49691.0 + 121334.i 0.234834 + 0.573411i
\(461\) −200610. −0.943952 −0.471976 0.881611i \(-0.656459\pi\)
−0.471976 + 0.881611i \(0.656459\pi\)
\(462\) 0 0
\(463\) 237056.i 1.10583i −0.833237 0.552916i \(-0.813515\pi\)
0.833237 0.552916i \(-0.186485\pi\)
\(464\) 132178. 130082.i 0.613936 0.604200i
\(465\) 0 0
\(466\) 248599. 48933.3i 1.14480 0.225337i
\(467\) 230464.i 1.05674i 0.849014 + 0.528371i \(0.177197\pi\)
−0.849014 + 0.528371i \(0.822803\pi\)
\(468\) 0 0
\(469\) −3025.13 −0.0137530
\(470\) −68123.5 346092.i −0.308391 1.56674i
\(471\) 0 0
\(472\) 159353. + 241611.i 0.715279 + 1.08451i
\(473\) 126848. 0.566973
\(474\) 0 0
\(475\) 114524.i 0.507585i
\(476\) −108992. 266133.i −0.481039 1.17459i
\(477\) 0 0
\(478\) −245.315 1246.29i −0.00107366 0.00545461i
\(479\) 2401.48i 0.0104666i −0.999986 0.00523332i \(-0.998334\pi\)
0.999986 0.00523332i \(-0.00166583\pi\)
\(480\) 0 0
\(481\) 40804.5 0.176367
\(482\) −100100. + 19703.4i −0.430865 + 0.0848098i
\(483\) 0 0
\(484\) 148779. 60930.7i 0.635111 0.260103i
\(485\) 140981. 0.599347
\(486\) 0 0
\(487\) 405227.i 1.70860i 0.519781 + 0.854300i \(0.326014\pi\)
−0.519781 + 0.854300i \(0.673986\pi\)
\(488\) −140428. + 92618.0i −0.589675 + 0.388916i
\(489\) 0 0
\(490\) −34051.1 + 6702.48i −0.141820 + 0.0279154i
\(491\) 128547.i 0.533210i 0.963806 + 0.266605i \(0.0859019\pi\)
−0.963806 + 0.266605i \(0.914098\pi\)
\(492\) 0 0
\(493\) 291826. 1.20069
\(494\) 14495.9 + 73644.5i 0.0594006 + 0.301777i
\(495\) 0 0
\(496\) −226194. 229839.i −0.919429 0.934244i
\(497\) 58675.0 0.237542
\(498\) 0 0
\(499\) 128607.i 0.516493i −0.966079 0.258246i \(-0.916855\pi\)
0.966079 0.258246i \(-0.0831446\pi\)
\(500\) −251362. + 102942.i −1.00545 + 0.411770i
\(501\) 0 0
\(502\) 31663.8 + 160864.i 0.125648 + 0.638339i
\(503\) 368128.i 1.45500i −0.686109 0.727499i \(-0.740683\pi\)
0.686109 0.727499i \(-0.259317\pi\)
\(504\) 0 0
\(505\) 196411. 0.770165
\(506\) 103048. 20283.5i 0.402474 0.0792214i
\(507\) 0 0
\(508\) −3214.19 7848.30i −0.0124550 0.0304122i
\(509\) −81396.7 −0.314175 −0.157087 0.987585i \(-0.550210\pi\)
−0.157087 + 0.987585i \(0.550210\pi\)
\(510\) 0 0
\(511\) 422569.i 1.61829i
\(512\) 46510.3 + 257985.i 0.177423 + 0.984135i
\(513\) 0 0
\(514\) −121501. + 23915.8i −0.459890 + 0.0905230i
\(515\) 239164.i 0.901742i
\(516\) 0 0
\(517\) −282545. −1.05708
\(518\) −48326.3 245516.i −0.180104 0.914997i
\(519\) 0 0
\(520\) 32888.1 21691.1i 0.121627 0.0802185i
\(521\) −17832.5 −0.0656956 −0.0328478 0.999460i \(-0.510458\pi\)
−0.0328478 + 0.999460i \(0.510458\pi\)
\(522\) 0 0
\(523\) 51996.2i 0.190094i 0.995473 + 0.0950470i \(0.0303001\pi\)
−0.995473 + 0.0950470i \(0.969700\pi\)
\(524\) 5616.90 + 13715.2i 0.0204566 + 0.0499503i
\(525\) 0 0
\(526\) −11874.5 60326.8i −0.0429184 0.218041i
\(527\) 507446.i 1.82712i
\(528\) 0 0
\(529\) 129737. 0.463608
\(530\) −75255.7 + 14813.0i −0.267909 + 0.0527342i
\(531\) 0 0
\(532\) 425941. 174440.i 1.50497 0.616343i
\(533\) −45062.3 −0.158620
\(534\) 0 0
\(535\) 132440.i 0.462714i
\(536\) 2389.06 + 3622.30i 0.00831567 + 0.0126082i
\(537\) 0 0
\(538\) −298691. + 58793.1i −1.03195 + 0.203124i
\(539\) 27798.8i 0.0956862i
\(540\) 0 0
\(541\) −329819. −1.12689 −0.563444 0.826154i \(-0.690524\pi\)
−0.563444 + 0.826154i \(0.690524\pi\)
\(542\) −60315.7 306426.i −0.205320 1.04310i
\(543\) 0 0
\(544\) −232593. + 340682.i −0.785957 + 1.15120i
\(545\) 73031.9 0.245878
\(546\) 0 0
\(547\) 353376.i 1.18103i 0.807025 + 0.590517i \(0.201076\pi\)
−0.807025 + 0.590517i \(0.798924\pi\)
\(548\) 24700.5 10115.8i 0.0822516 0.0336853i
\(549\) 0 0
\(550\) 9299.45 + 47244.6i 0.0307420 + 0.156181i
\(551\) 467063.i 1.53841i
\(552\) 0 0
\(553\) 194953. 0.637498
\(554\) −18602.8 + 3661.70i −0.0606120 + 0.0119306i
\(555\) 0 0
\(556\) −5025.72 12271.6i −0.0162573 0.0396966i
\(557\) −381405. −1.22935 −0.614676 0.788780i \(-0.710713\pi\)
−0.614676 + 0.788780i \(0.710713\pi\)
\(558\) 0 0
\(559\) 54475.0i 0.174330i
\(560\) −169463. 172194.i −0.540380 0.549087i
\(561\) 0 0
\(562\) −169583. + 33380.1i −0.536921 + 0.105685i
\(563\) 235336.i 0.742459i −0.928541 0.371229i \(-0.878936\pi\)
0.928541 0.371229i \(-0.121064\pi\)
\(564\) 0 0
\(565\) −53832.1 −0.168634
\(566\) 27900.1 + 141743.i 0.0870909 + 0.442454i
\(567\) 0 0
\(568\) −46337.9 70257.6i −0.143628 0.217769i
\(569\) −221943. −0.685515 −0.342757 0.939424i \(-0.611361\pi\)
−0.342757 + 0.939424i \(0.611361\pi\)
\(570\) 0 0
\(571\) 39939.1i 0.122497i −0.998123 0.0612486i \(-0.980492\pi\)
0.998123 0.0612486i \(-0.0195082\pi\)
\(572\) −11960.0 29203.6i −0.0365544 0.0892573i
\(573\) 0 0
\(574\) 53369.0 + 271134.i 0.161981 + 0.822925i
\(575\) 68818.8i 0.208148i
\(576\) 0 0
\(577\) 511135. 1.53527 0.767634 0.640889i \(-0.221434\pi\)
0.767634 + 0.640889i \(0.221434\pi\)
\(578\) −309109. + 60843.8i −0.925244 + 0.182121i
\(579\) 0 0
\(580\) 226869. 92911.9i 0.674403 0.276195i
\(581\) 33999.9 0.100722
\(582\) 0 0
\(583\) 61437.8i 0.180759i
\(584\) −505985. + 333719.i −1.48358 + 0.978486i
\(585\) 0 0
\(586\) 377137. 74234.1i 1.09826 0.216176i
\(587\) 69870.4i 0.202776i −0.994847 0.101388i \(-0.967672\pi\)
0.994847 0.101388i \(-0.0323284\pi\)
\(588\) 0 0
\(589\) 812158. 2.34105
\(590\) 73893.6 + 375407.i 0.212277 + 1.07845i
\(591\) 0 0
\(592\) −255816. + 251759.i −0.729935 + 0.718359i
\(593\) 206980. 0.588599 0.294299 0.955713i \(-0.404914\pi\)
0.294299 + 0.955713i \(0.404914\pi\)
\(594\) 0 0
\(595\) 380174.i 1.07386i
\(596\) 46236.9 18935.8i 0.130165 0.0533079i
\(597\) 0 0
\(598\) 8710.76 + 44253.9i 0.0243587 + 0.123751i
\(599\) 278466.i 0.776101i 0.921638 + 0.388051i \(0.126851\pi\)
−0.921638 + 0.388051i \(0.873149\pi\)
\(600\) 0 0
\(601\) 427472. 1.18347 0.591737 0.806131i \(-0.298443\pi\)
0.591737 + 0.806131i \(0.298443\pi\)
\(602\) 327769. 64516.8i 0.904430 0.178024i
\(603\) 0 0
\(604\) −55541.6 135620.i −0.152246 0.371748i
\(605\) 212532. 0.580650
\(606\) 0 0
\(607\) 417400.i 1.13286i 0.824111 + 0.566428i \(0.191675\pi\)
−0.824111 + 0.566428i \(0.808325\pi\)
\(608\) −545257. 372261.i −1.47501 1.00703i
\(609\) 0 0
\(610\) −218192. + 42948.0i −0.586379 + 0.115421i
\(611\) 121339.i 0.325026i
\(612\) 0 0
\(613\) −23327.6 −0.0620796 −0.0310398 0.999518i \(-0.509882\pi\)
−0.0310398 + 0.999518i \(0.509882\pi\)
\(614\) 108648. + 551973.i 0.288195 + 1.46414i
\(615\) 0 0
\(616\) −161549. + 106549.i −0.425740 + 0.280793i
\(617\) 78771.3 0.206918 0.103459 0.994634i \(-0.467009\pi\)
0.103459 + 0.994634i \(0.467009\pi\)
\(618\) 0 0
\(619\) 441852.i 1.15317i 0.817036 + 0.576587i \(0.195616\pi\)
−0.817036 + 0.576587i \(0.804384\pi\)
\(620\) −161561. 394494.i −0.420293 1.02626i
\(621\) 0 0
\(622\) −126279. 641545.i −0.326401 1.65824i
\(623\) 360669.i 0.929249i
\(624\) 0 0
\(625\) −248056. −0.635024
\(626\) 201299. 39622.8i 0.513679 0.101111i
\(627\) 0 0
\(628\) 312470. 127969.i 0.792299 0.324478i
\(629\) −564798. −1.42755
\(630\) 0 0
\(631\) 211599.i 0.531440i 0.964050 + 0.265720i \(0.0856097\pi\)
−0.964050 + 0.265720i \(0.914390\pi\)
\(632\) −153962. 233437.i −0.385459 0.584434i
\(633\) 0 0
\(634\) 110088. 21669.2i 0.273880 0.0539094i
\(635\) 11211.4i 0.0278043i
\(636\) 0 0
\(637\) −11938.2 −0.0294212
\(638\) −37926.0 192678.i −0.0931743 0.473360i
\(639\) 0 0
\(640\) −72353.7 + 338903.i −0.176645 + 0.827401i
\(641\) −5105.48 −0.0124257 −0.00621284 0.999981i \(-0.501978\pi\)
−0.00621284 + 0.999981i \(0.501978\pi\)
\(642\) 0 0
\(643\) 79821.9i 0.193064i 0.995330 + 0.0965318i \(0.0307749\pi\)
−0.995330 + 0.0965318i \(0.969225\pi\)
\(644\) 255954. 104823.i 0.617148 0.252747i
\(645\) 0 0
\(646\) −200646. 1.01935e6i −0.480800 2.44264i
\(647\) 531516.i 1.26972i 0.772628 + 0.634859i \(0.218942\pi\)
−0.772628 + 0.634859i \(0.781058\pi\)
\(648\) 0 0
\(649\) 306477. 0.727627
\(650\) −20289.2 + 3993.65i −0.0480218 + 0.00945243i
\(651\) 0 0
\(652\) −259355. 633285.i −0.610099 1.48972i
\(653\) −471230. −1.10511 −0.552556 0.833476i \(-0.686347\pi\)
−0.552556 + 0.833476i \(0.686347\pi\)
\(654\) 0 0
\(655\) 19592.3i 0.0456670i
\(656\) 282509. 278029.i 0.656485 0.646074i
\(657\) 0 0
\(658\) −730082. + 143707.i −1.68624 + 0.331913i
\(659\) 357344.i 0.822841i −0.911446 0.411420i \(-0.865033\pi\)
0.911446 0.411420i \(-0.134967\pi\)
\(660\) 0 0
\(661\) −565583. −1.29447 −0.647237 0.762289i \(-0.724076\pi\)
−0.647237 + 0.762289i \(0.724076\pi\)
\(662\) −87131.7 442661.i −0.198820 1.01008i
\(663\) 0 0
\(664\) −26851.0 40711.6i −0.0609011 0.0923383i
\(665\) 608463. 1.37591
\(666\) 0 0
\(667\) 280664.i 0.630864i
\(668\) −66995.0 163586.i −0.150138 0.366601i
\(669\) 0 0
\(670\) 1107.83 + 5628.20i 0.00246788 + 0.0125378i
\(671\) 178129.i 0.395630i
\(672\) 0 0
\(673\) −316237. −0.698205 −0.349103 0.937085i \(-0.613514\pi\)
−0.349103 + 0.937085i \(0.613514\pi\)
\(674\) 81710.5 16083.6i 0.179870 0.0354049i
\(675\) 0 0
\(676\) −410345. + 168052.i −0.897957 + 0.367749i
\(677\) −601827. −1.31309 −0.656545 0.754287i \(-0.727983\pi\)
−0.656545 + 0.754287i \(0.727983\pi\)
\(678\) 0 0
\(679\) 297400.i 0.645063i
\(680\) −455222. + 300238.i −0.984476 + 0.649304i
\(681\) 0 0
\(682\) −335041. + 65948.1i −0.720326 + 0.141786i
\(683\) 385277.i 0.825909i −0.910752 0.412955i \(-0.864497\pi\)
0.910752 0.412955i \(-0.135503\pi\)
\(684\) 0 0
\(685\) 35285.0 0.0751984
\(686\) 96898.2 + 492279.i 0.205905 + 1.04607i
\(687\) 0 0
\(688\) −336104. 341520.i −0.710063 0.721505i
\(689\) −26384.5 −0.0555789
\(690\) 0 0
\(691\) 459302.i 0.961927i −0.876741 0.480963i \(-0.840287\pi\)
0.876741 0.480963i \(-0.159713\pi\)
\(692\) −324788. + 133014.i −0.678247 + 0.277769i
\(693\) 0 0
\(694\) 124541. + 632712.i 0.258578 + 1.31367i
\(695\) 17530.2i 0.0362925i
\(696\) 0 0
\(697\) 623732. 1.28390
\(698\) 869257. 171101.i 1.78418 0.351190i
\(699\) 0 0
\(700\) 48058.6 + 117348.i 0.0980787 + 0.239485i
\(701\) −127011. −0.258467 −0.129234 0.991614i \(-0.541252\pi\)
−0.129234 + 0.991614i \(0.541252\pi\)
\(702\) 0 0
\(703\) 903950.i 1.82908i
\(704\) 255163. + 109294.i 0.514841 + 0.220522i
\(705\) 0 0
\(706\) −858682. + 169020.i −1.72275 + 0.339100i
\(707\) 414330.i 0.828910i
\(708\) 0 0
\(709\) 494816. 0.984353 0.492177 0.870495i \(-0.336201\pi\)
0.492177 + 0.870495i \(0.336201\pi\)
\(710\) −21487.4 109164.i −0.0426253 0.216552i
\(711\) 0 0
\(712\) −431865. + 284834.i −0.851900 + 0.561864i
\(713\) 488036. 0.960004
\(714\) 0 0
\(715\) 41717.7i 0.0816034i
\(716\) 69607.6 + 169966.i 0.135778 + 0.331539i
\(717\) 0 0
\(718\) −714.278 3628.80i −0.00138554 0.00703904i
\(719\) 614613.i 1.18890i 0.804134 + 0.594448i \(0.202629\pi\)
−0.804134 + 0.594448i \(0.797371\pi\)
\(720\) 0 0
\(721\) 504518. 0.970523
\(722\) 1.11999e6 220454.i 2.14852 0.422906i
\(723\) 0 0
\(724\) 673280. 275735.i 1.28445 0.526035i
\(725\) −128677. −0.244808
\(726\) 0 0
\(727\) 331397.i 0.627018i −0.949585 0.313509i \(-0.898495\pi\)
0.949585 0.313509i \(-0.101505\pi\)
\(728\) −45757.4 69377.4i −0.0863373 0.130905i
\(729\) 0 0
\(730\) −786182. + 154749.i −1.47529 + 0.290390i
\(731\) 754018.i 1.41106i
\(732\) 0 0
\(733\) −51616.8 −0.0960690 −0.0480345 0.998846i \(-0.515296\pi\)
−0.0480345 + 0.998846i \(0.515296\pi\)
\(734\) 31517.2 + 160119.i 0.0585000 + 0.297202i
\(735\) 0 0
\(736\) −327652. 223697.i −0.604863 0.412956i
\(737\) 4594.79 0.00845923
\(738\) 0 0
\(739\) 228968.i 0.419263i −0.977780 0.209631i \(-0.932774\pi\)
0.977780 0.209631i \(-0.0672264\pi\)
\(740\) −439080. + 179821.i −0.801826 + 0.328380i
\(741\) 0 0
\(742\) 31248.1 + 158752.i 0.0567566 + 0.288344i
\(743\) 1.05079e6i 1.90343i 0.306980 + 0.951716i \(0.400681\pi\)
−0.306980 + 0.951716i \(0.599319\pi\)
\(744\) 0 0
\(745\) 66050.0 0.119004
\(746\) 920459. 181179.i 1.65397 0.325560i
\(747\) 0 0
\(748\) 165545. + 404223.i 0.295878 + 0.722466i
\(749\) 279383. 0.498008
\(750\) 0 0
\(751\) 269386.i 0.477634i 0.971065 + 0.238817i \(0.0767596\pi\)
−0.971065 + 0.238817i \(0.923240\pi\)
\(752\) 748649. + 760712.i 1.32386 + 1.34519i
\(753\) 0 0
\(754\) 82745.7 16287.3i 0.145547 0.0286489i
\(755\) 193735.i 0.339870i
\(756\) 0 0
\(757\) −476176. −0.830952 −0.415476 0.909604i \(-0.636385\pi\)
−0.415476 + 0.909604i \(0.636385\pi\)
\(758\) 143344. + 728239.i 0.249483 + 1.26746i
\(759\) 0 0
\(760\) −480527. 728575.i −0.831937 1.26138i
\(761\) 484394. 0.836430 0.418215 0.908348i \(-0.362656\pi\)
0.418215 + 0.908348i \(0.362656\pi\)
\(762\) 0 0
\(763\) 154061.i 0.264632i
\(764\) 424714. + 1.03705e6i 0.727628 + 1.77670i
\(765\) 0 0
\(766\) −46555.3 236518.i −0.0793436 0.403095i
\(767\) 131617.i 0.223728i
\(768\) 0 0
\(769\) 502123. 0.849097 0.424549 0.905405i \(-0.360433\pi\)
0.424549 + 0.905405i \(0.360433\pi\)
\(770\) −251010. + 49407.8i −0.423360 + 0.0833325i
\(771\) 0 0
\(772\) −516046. + 211341.i −0.865872 + 0.354609i
\(773\) 435529. 0.728884 0.364442 0.931226i \(-0.381260\pi\)
0.364442 + 0.931226i \(0.381260\pi\)
\(774\) 0 0
\(775\) 223752.i 0.372531i
\(776\) −356108. + 234868.i −0.591369 + 0.390033i
\(777\) 0 0
\(778\) 47132.9 9277.46i 0.0778691 0.0153275i
\(779\) 998273.i 1.64503i
\(780\) 0 0
\(781\) −89120.1 −0.146108
\(782\) −120571. 612543.i −0.197164 1.00167i
\(783\) 0 0
\(784\) 74844.3 73657.4i 0.121766 0.119835i
\(785\) 446368. 0.724358
\(786\) 0 0
\(787\) </