Properties

Label 33.6.d.b.32.11
Level $33$
Weight $6$
Character 33.32
Analytic conductor $5.293$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 33.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.29266605383\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{15} - 195 x^{14} - 642 x^{13} + 89670 x^{12} + 53946 x^{11} + 91115757 x^{10} - 2121785838 x^{9} + 37710373995 x^{8} - 835758339660 x^{7} + 12972600642204 x^{6} - 129499271268696 x^{5} + 2168293345395660 x^{4} - 17336133272224368 x^{3} + 169639595563975056 x^{2} - 1075523563426213440 x + 9241272870780234240\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{11}\cdot 3^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 32.11
Root \(15.7319 + 6.27606i\) of defining polynomial
Character \(\chi\) \(=\) 33.32
Dual form 33.6.d.b.32.12

$q$-expansion

\(f(q)\) \(=\) \(q+4.46270 q^{2} +(-14.2692 - 6.27606i) q^{3} -12.0843 q^{4} +59.8956i q^{5} +(-63.6794 - 28.0082i) q^{6} +169.425i q^{7} -196.735 q^{8} +(164.222 + 179.109i) q^{9} +O(q^{10})\) \(q+4.46270 q^{2} +(-14.2692 - 6.27606i) q^{3} -12.0843 q^{4} +59.8956i q^{5} +(-63.6794 - 28.0082i) q^{6} +169.425i q^{7} -196.735 q^{8} +(164.222 + 179.109i) q^{9} +267.296i q^{10} +(-358.129 - 181.093i) q^{11} +(172.433 + 75.8416i) q^{12} -838.100i q^{13} +756.094i q^{14} +(375.908 - 854.664i) q^{15} -491.273 q^{16} -512.592 q^{17} +(732.875 + 799.311i) q^{18} +1878.22i q^{19} -723.795i q^{20} +(1063.32 - 2417.57i) q^{21} +(-1598.22 - 808.163i) q^{22} +3339.01i q^{23} +(2807.26 + 1234.72i) q^{24} -462.483 q^{25} -3740.19i q^{26} +(-1219.22 - 3586.42i) q^{27} -2047.38i q^{28} -1329.42 q^{29} +(1677.57 - 3814.11i) q^{30} +6737.49 q^{31} +4103.11 q^{32} +(3973.68 + 4831.69i) q^{33} -2287.55 q^{34} -10147.8 q^{35} +(-1984.51 - 2164.40i) q^{36} +4959.19 q^{37} +8381.92i q^{38} +(-5259.96 + 11959.0i) q^{39} -11783.6i q^{40} -17769.0 q^{41} +(4745.29 - 10788.9i) q^{42} +7851.09i q^{43} +(4327.73 + 2188.37i) q^{44} +(-10727.8 + 9836.18i) q^{45} +14901.0i q^{46} +20190.6i q^{47} +(7010.10 + 3083.26i) q^{48} -11897.8 q^{49} -2063.92 q^{50} +(7314.30 + 3217.06i) q^{51} +10127.8i q^{52} -18738.7i q^{53} +(-5441.04 - 16005.1i) q^{54} +(10846.7 - 21450.4i) q^{55} -33331.8i q^{56} +(11787.8 - 26800.7i) q^{57} -5932.81 q^{58} +5842.82i q^{59} +(-4542.58 + 10328.0i) q^{60} -1703.10i q^{61} +30067.4 q^{62} +(-30345.6 + 27823.3i) q^{63} +34031.7 q^{64} +50198.5 q^{65} +(17733.4 + 21562.4i) q^{66} -29337.8 q^{67} +6194.30 q^{68} +(20955.8 - 47645.1i) q^{69} -45286.7 q^{70} +17330.8i q^{71} +(-32308.3 - 35237.0i) q^{72} +16626.5i q^{73} +22131.4 q^{74} +(6599.28 + 2902.57i) q^{75} -22696.9i q^{76} +(30681.6 - 60676.0i) q^{77} +(-23473.7 + 53369.7i) q^{78} -2586.42i q^{79} -29425.1i q^{80} +(-5111.17 + 58827.4i) q^{81} -79297.6 q^{82} -31993.8 q^{83} +(-12849.5 + 29214.5i) q^{84} -30702.0i q^{85} +35037.1i q^{86} +(18969.8 + 8343.52i) q^{87} +(70456.6 + 35627.3i) q^{88} +63768.5i q^{89} +(-47875.2 + 43896.0i) q^{90} +141995. q^{91} -40349.5i q^{92} +(-96138.9 - 42284.9i) q^{93} +90104.9i q^{94} -112497. q^{95} +(-58548.3 - 25751.4i) q^{96} +103785. q^{97} -53096.5 q^{98} +(-26377.4 - 93883.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 54q^{3} + 316q^{4} - 222q^{9} + O(q^{10}) \) \( 16q - 54q^{3} + 316q^{4} - 222q^{9} - 552q^{12} - 1674q^{15} + 1684q^{16} + 7932q^{22} - 1356q^{25} - 3240q^{27} - 11980q^{31} - 5106q^{33} - 34032q^{34} + 14016q^{36} + 9356q^{37} + 45912q^{42} + 77430q^{45} - 78012q^{48} - 1136q^{49} + 117308q^{55} + 31848q^{58} - 220548q^{60} + 5860q^{64} - 164796q^{66} - 364132q^{67} + 113790q^{69} + 231144q^{70} + 320364q^{75} + 296088q^{78} - 251334q^{81} + 4824q^{82} + 586836q^{88} - 209184q^{91} - 521046q^{93} + 119852q^{97} - 243894q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.46270 0.788902 0.394451 0.918917i \(-0.370935\pi\)
0.394451 + 0.918917i \(0.370935\pi\)
\(3\) −14.2692 6.27606i −0.915372 0.402609i
\(4\) −12.0843 −0.377634
\(5\) 59.8956i 1.07145i 0.844394 + 0.535723i \(0.179961\pi\)
−0.844394 + 0.535723i \(0.820039\pi\)
\(6\) −63.6794 28.0082i −0.722139 0.317619i
\(7\) 169.425i 1.30687i 0.756983 + 0.653435i \(0.226673\pi\)
−0.756983 + 0.653435i \(0.773327\pi\)
\(8\) −196.735 −1.08682
\(9\) 164.222 + 179.109i 0.675811 + 0.737075i
\(10\) 267.296i 0.845265i
\(11\) −358.129 181.093i −0.892397 0.451252i
\(12\) 172.433 + 75.8416i 0.345675 + 0.152039i
\(13\) 838.100i 1.37543i −0.725983 0.687713i \(-0.758615\pi\)
0.725983 0.687713i \(-0.241385\pi\)
\(14\) 756.094i 1.03099i
\(15\) 375.908 854.664i 0.431374 0.980771i
\(16\) −491.273 −0.479759
\(17\) −512.592 −0.430179 −0.215090 0.976594i \(-0.569004\pi\)
−0.215090 + 0.976594i \(0.569004\pi\)
\(18\) 732.875 + 799.311i 0.533149 + 0.581480i
\(19\) 1878.22i 1.19361i 0.802387 + 0.596804i \(0.203563\pi\)
−0.802387 + 0.596804i \(0.796437\pi\)
\(20\) 723.795i 0.404614i
\(21\) 1063.32 2417.57i 0.526158 1.19627i
\(22\) −1598.22 808.163i −0.704013 0.355994i
\(23\) 3339.01i 1.31613i 0.752963 + 0.658063i \(0.228624\pi\)
−0.752963 + 0.658063i \(0.771376\pi\)
\(24\) 2807.26 + 1234.72i 0.994843 + 0.437563i
\(25\) −462.483 −0.147995
\(26\) 3740.19i 1.08508i
\(27\) −1219.22 3586.42i −0.321865 0.946785i
\(28\) 2047.38i 0.493518i
\(29\) −1329.42 −0.293540 −0.146770 0.989171i \(-0.546888\pi\)
−0.146770 + 0.989171i \(0.546888\pi\)
\(30\) 1677.57 3814.11i 0.340312 0.773732i
\(31\) 6737.49 1.25920 0.629599 0.776920i \(-0.283219\pi\)
0.629599 + 0.776920i \(0.283219\pi\)
\(32\) 4103.11 0.708335
\(33\) 3973.68 + 4831.69i 0.635197 + 0.772351i
\(34\) −2287.55 −0.339369
\(35\) −10147.8 −1.40024
\(36\) −1984.51 2164.40i −0.255209 0.278344i
\(37\) 4959.19 0.595534 0.297767 0.954639i \(-0.403758\pi\)
0.297767 + 0.954639i \(0.403758\pi\)
\(38\) 8381.92i 0.941639i
\(39\) −5259.96 + 11959.0i −0.553759 + 1.25903i
\(40\) 11783.6i 1.16447i
\(41\) −17769.0 −1.65083 −0.825415 0.564527i \(-0.809059\pi\)
−0.825415 + 0.564527i \(0.809059\pi\)
\(42\) 4745.29 10788.9i 0.415087 0.943741i
\(43\) 7851.09i 0.647528i 0.946138 + 0.323764i \(0.104948\pi\)
−0.946138 + 0.323764i \(0.895052\pi\)
\(44\) 4327.73 + 2188.37i 0.336999 + 0.170408i
\(45\) −10727.8 + 9836.18i −0.789735 + 0.724095i
\(46\) 14901.0i 1.03829i
\(47\) 20190.6i 1.33323i 0.745402 + 0.666616i \(0.232258\pi\)
−0.745402 + 0.666616i \(0.767742\pi\)
\(48\) 7010.10 + 3083.26i 0.439158 + 0.193156i
\(49\) −11897.8 −0.707909
\(50\) −2063.92 −0.116753
\(51\) 7314.30 + 3217.06i 0.393774 + 0.173194i
\(52\) 10127.8i 0.519407i
\(53\) 18738.7i 0.916325i −0.888868 0.458163i \(-0.848508\pi\)
0.888868 0.458163i \(-0.151492\pi\)
\(54\) −5441.04 16005.1i −0.253920 0.746921i
\(55\) 10846.7 21450.4i 0.483492 0.956154i
\(56\) 33331.8i 1.42033i
\(57\) 11787.8 26800.7i 0.480557 1.09259i
\(58\) −5932.81 −0.231574
\(59\) 5842.82i 0.218520i 0.994013 + 0.109260i \(0.0348482\pi\)
−0.994013 + 0.109260i \(0.965152\pi\)
\(60\) −4542.58 + 10328.0i −0.162901 + 0.370372i
\(61\) 1703.10i 0.0586026i −0.999571 0.0293013i \(-0.990672\pi\)
0.999571 0.0293013i \(-0.00932822\pi\)
\(62\) 30067.4 0.993384
\(63\) −30345.6 + 27823.3i −0.963261 + 0.883198i
\(64\) 34031.7 1.03857
\(65\) 50198.5 1.47369
\(66\) 17733.4 + 21562.4i 0.501108 + 0.609309i
\(67\) −29337.8 −0.798437 −0.399218 0.916856i \(-0.630718\pi\)
−0.399218 + 0.916856i \(0.630718\pi\)
\(68\) 6194.30 0.162450
\(69\) 20955.8 47645.1i 0.529885 1.20475i
\(70\) −45286.7 −1.10465
\(71\) 17330.8i 0.408011i 0.978970 + 0.204006i \(0.0653961\pi\)
−0.978970 + 0.204006i \(0.934604\pi\)
\(72\) −32308.3 35237.0i −0.734484 0.801066i
\(73\) 16626.5i 0.365168i 0.983190 + 0.182584i \(0.0584462\pi\)
−0.983190 + 0.182584i \(0.941554\pi\)
\(74\) 22131.4 0.469818
\(75\) 6599.28 + 2902.57i 0.135470 + 0.0595840i
\(76\) 22696.9i 0.450746i
\(77\) 30681.6 60676.0i 0.589728 1.16625i
\(78\) −23473.7 + 53369.7i −0.436862 + 0.993248i
\(79\) 2586.42i 0.0466263i −0.999728 0.0233132i \(-0.992579\pi\)
0.999728 0.0233132i \(-0.00742148\pi\)
\(80\) 29425.1i 0.514036i
\(81\) −5111.17 + 58827.4i −0.0865581 + 0.996247i
\(82\) −79297.6 −1.30234
\(83\) −31993.8 −0.509766 −0.254883 0.966972i \(-0.582037\pi\)
−0.254883 + 0.966972i \(0.582037\pi\)
\(84\) −12849.5 + 29214.5i −0.198695 + 0.451753i
\(85\) 30702.0i 0.460913i
\(86\) 35037.1i 0.510836i
\(87\) 18969.8 + 8343.52i 0.268698 + 0.118182i
\(88\) 70456.6 + 35627.3i 0.969873 + 0.490429i
\(89\) 63768.5i 0.853357i 0.904403 + 0.426679i \(0.140316\pi\)
−0.904403 + 0.426679i \(0.859684\pi\)
\(90\) −47875.2 + 43896.0i −0.623024 + 0.571240i
\(91\) 141995. 1.79750
\(92\) 40349.5i 0.497014i
\(93\) −96138.9 42284.9i −1.15263 0.506965i
\(94\) 90104.9i 1.05179i
\(95\) −112497. −1.27888
\(96\) −58548.3 25751.4i −0.648390 0.285182i
\(97\) 103785. 1.11997 0.559984 0.828503i \(-0.310807\pi\)
0.559984 + 0.828503i \(0.310807\pi\)
\(98\) −53096.5 −0.558471
\(99\) −26377.4 93883.6i −0.270485 0.962724i
\(100\) 5588.77 0.0558877
\(101\) −24287.2 −0.236905 −0.118453 0.992960i \(-0.537793\pi\)
−0.118453 + 0.992960i \(0.537793\pi\)
\(102\) 32641.5 + 14356.8i 0.310649 + 0.136633i
\(103\) −108341. −1.00624 −0.503119 0.864217i \(-0.667814\pi\)
−0.503119 + 0.864217i \(0.667814\pi\)
\(104\) 164884.i 1.49484i
\(105\) 144802. + 63688.3i 1.28174 + 0.563750i
\(106\) 83625.2i 0.722891i
\(107\) 115625. 0.976317 0.488158 0.872755i \(-0.337669\pi\)
0.488158 + 0.872755i \(0.337669\pi\)
\(108\) 14733.4 + 43339.3i 0.121547 + 0.357538i
\(109\) 33180.5i 0.267496i −0.991015 0.133748i \(-0.957299\pi\)
0.991015 0.133748i \(-0.0427012\pi\)
\(110\) 48405.4 95726.6i 0.381427 0.754312i
\(111\) −70763.8 31124.2i −0.545135 0.239767i
\(112\) 83234.0i 0.626983i
\(113\) 75910.6i 0.559250i −0.960109 0.279625i \(-0.909790\pi\)
0.960109 0.279625i \(-0.0902102\pi\)
\(114\) 52605.4 119604.i 0.379113 0.861950i
\(115\) −199992. −1.41016
\(116\) 16065.1 0.110851
\(117\) 150111. 137635.i 1.01379 0.929529i
\(118\) 26074.8i 0.172391i
\(119\) 86845.9i 0.562188i
\(120\) −73954.4 + 168142.i −0.468825 + 1.06592i
\(121\) 95461.9 + 129709.i 0.592743 + 0.805391i
\(122\) 7600.45i 0.0462317i
\(123\) 253549. + 111519.i 1.51112 + 0.664640i
\(124\) −81417.7 −0.475515
\(125\) 159473.i 0.912877i
\(126\) −135423. + 124167.i −0.759918 + 0.696756i
\(127\) 258255.i 1.42082i −0.703787 0.710411i \(-0.748509\pi\)
0.703787 0.710411i \(-0.251491\pi\)
\(128\) 20573.9 0.110992
\(129\) 49273.9 112029.i 0.260701 0.592729i
\(130\) 224021. 1.16260
\(131\) −185955. −0.946736 −0.473368 0.880865i \(-0.656962\pi\)
−0.473368 + 0.880865i \(0.656962\pi\)
\(132\) −48019.1 58387.5i −0.239872 0.291666i
\(133\) −318217. −1.55989
\(134\) −130926. −0.629888
\(135\) 214811. 73026.2i 1.01443 0.344861i
\(136\) 100845. 0.467527
\(137\) 79544.3i 0.362083i −0.983475 0.181041i \(-0.942053\pi\)
0.983475 0.181041i \(-0.0579468\pi\)
\(138\) 93519.5 212626.i 0.418027 0.950426i
\(139\) 419383.i 1.84109i 0.390642 + 0.920543i \(0.372253\pi\)
−0.390642 + 0.920543i \(0.627747\pi\)
\(140\) 122629. 0.528777
\(141\) 126718. 288105.i 0.536772 1.22040i
\(142\) 77342.1i 0.321881i
\(143\) −151774. + 300148.i −0.620664 + 1.22743i
\(144\) −80678.0 87991.6i −0.324227 0.353618i
\(145\) 79626.5i 0.314512i
\(146\) 74199.1i 0.288082i
\(147\) 169773. + 74671.5i 0.648000 + 0.285011i
\(148\) −59928.2 −0.224894
\(149\) −61974.2 −0.228689 −0.114344 0.993441i \(-0.536477\pi\)
−0.114344 + 0.993441i \(0.536477\pi\)
\(150\) 29450.6 + 12953.3i 0.106873 + 0.0470059i
\(151\) 36038.3i 0.128624i 0.997930 + 0.0643121i \(0.0204853\pi\)
−0.997930 + 0.0643121i \(0.979515\pi\)
\(152\) 369511.i 1.29723i
\(153\) −84179.0 91809.9i −0.290720 0.317074i
\(154\) 136923. 270779.i 0.465237 0.920054i
\(155\) 403546.i 1.34916i
\(156\) 63562.8 144516.i 0.209118 0.475451i
\(157\) −65185.9 −0.211059 −0.105530 0.994416i \(-0.533654\pi\)
−0.105530 + 0.994416i \(0.533654\pi\)
\(158\) 11542.4i 0.0367836i
\(159\) −117605. + 267387.i −0.368921 + 0.838778i
\(160\) 245758.i 0.758942i
\(161\) −565711. −1.72001
\(162\) −22809.6 + 262529.i −0.0682859 + 0.785941i
\(163\) 304117. 0.896543 0.448272 0.893897i \(-0.352040\pi\)
0.448272 + 0.893897i \(0.352040\pi\)
\(164\) 214725. 0.623409
\(165\) −289397. + 238006.i −0.827531 + 0.680578i
\(166\) −142779. −0.402155
\(167\) −452837. −1.25647 −0.628233 0.778025i \(-0.716222\pi\)
−0.628233 + 0.778025i \(0.716222\pi\)
\(168\) −209193. + 475620.i −0.571838 + 1.30013i
\(169\) −331118. −0.891797
\(170\) 137014.i 0.363616i
\(171\) −336406. + 308445.i −0.879778 + 0.806653i
\(172\) 94874.7i 0.244528i
\(173\) 573310. 1.45638 0.728189 0.685376i \(-0.240362\pi\)
0.728189 + 0.685376i \(0.240362\pi\)
\(174\) 84656.7 + 37234.7i 0.211977 + 0.0932340i
\(175\) 78356.2i 0.193410i
\(176\) 175939. + 88966.0i 0.428136 + 0.216492i
\(177\) 36669.9 83372.5i 0.0879784 0.200028i
\(178\) 284580.i 0.673215i
\(179\) 331246.i 0.772713i −0.922349 0.386357i \(-0.873733\pi\)
0.922349 0.386357i \(-0.126267\pi\)
\(180\) 129638. 118863.i 0.298230 0.273443i
\(181\) 593309. 1.34612 0.673061 0.739587i \(-0.264979\pi\)
0.673061 + 0.739587i \(0.264979\pi\)
\(182\) 633682. 1.41805
\(183\) −10688.8 + 24302.0i −0.0235939 + 0.0536431i
\(184\) 656900.i 1.43039i
\(185\) 297034.i 0.638082i
\(186\) −429039. 188705.i −0.909316 0.399946i
\(187\) 183574. + 92826.6i 0.383891 + 0.194119i
\(188\) 243989.i 0.503473i
\(189\) 607629. 206567.i 1.23733 0.420636i
\(190\) −502040. −1.00891
\(191\) 434454.i 0.861709i −0.902421 0.430855i \(-0.858212\pi\)
0.902421 0.430855i \(-0.141788\pi\)
\(192\) −485607. 213585.i −0.950674 0.418136i
\(193\) 71460.4i 0.138093i −0.997613 0.0690466i \(-0.978004\pi\)
0.997613 0.0690466i \(-0.0219957\pi\)
\(194\) 463162. 0.883545
\(195\) −716294. 315049.i −1.34898 0.593323i
\(196\) 143777. 0.267330
\(197\) 909746. 1.67015 0.835073 0.550139i \(-0.185425\pi\)
0.835073 + 0.550139i \(0.185425\pi\)
\(198\) −117714. 418975.i −0.213387 0.759495i
\(199\) 177806. 0.318283 0.159142 0.987256i \(-0.449127\pi\)
0.159142 + 0.987256i \(0.449127\pi\)
\(200\) 90986.6 0.160843
\(201\) 418628. + 184126.i 0.730866 + 0.321458i
\(202\) −108387. −0.186895
\(203\) 225237.i 0.383619i
\(204\) −88388.0 38875.8i −0.148702 0.0654040i
\(205\) 1.06428e6i 1.76877i
\(206\) −483495. −0.793823
\(207\) −598047. + 548339.i −0.970084 + 0.889453i
\(208\) 411736.i 0.659873i
\(209\) 340131. 672644.i 0.538617 1.06517i
\(210\) 646206. + 284222.i 1.01117 + 0.444743i
\(211\) 323638.i 0.500442i 0.968189 + 0.250221i \(0.0805032\pi\)
−0.968189 + 0.250221i \(0.919497\pi\)
\(212\) 226444.i 0.346035i
\(213\) 108769. 247297.i 0.164269 0.373482i
\(214\) 515998. 0.770218
\(215\) −470246. −0.693791
\(216\) 239864. + 705574.i 0.349809 + 1.02898i
\(217\) 1.14150e6i 1.64561i
\(218\) 148075.i 0.211028i
\(219\) 104349. 237247.i 0.147020 0.334265i
\(220\) −131074. + 259212.i −0.182583 + 0.361076i
\(221\) 429603.i 0.591680i
\(222\) −315798. 138898.i −0.430058 0.189153i
\(223\) 13271.8 0.0178718 0.00893588 0.999960i \(-0.497156\pi\)
0.00893588 + 0.999960i \(0.497156\pi\)
\(224\) 695170.i 0.925702i
\(225\) −75949.9 82834.9i −0.100016 0.109083i
\(226\) 338766.i 0.441194i
\(227\) 281859. 0.363051 0.181525 0.983386i \(-0.441897\pi\)
0.181525 + 0.983386i \(0.441897\pi\)
\(228\) −142447. + 323867.i −0.181475 + 0.412600i
\(229\) −1.35791e6 −1.71113 −0.855566 0.517693i \(-0.826791\pi\)
−0.855566 + 0.517693i \(0.826791\pi\)
\(230\) −892504. −1.11248
\(231\) −818610. + 673241.i −1.00936 + 0.830119i
\(232\) 261544. 0.319025
\(233\) −66995.0 −0.0808449 −0.0404224 0.999183i \(-0.512870\pi\)
−0.0404224 + 0.999183i \(0.512870\pi\)
\(234\) 669902. 614222.i 0.799782 0.733307i
\(235\) −1.20933e6 −1.42848
\(236\) 70606.2i 0.0825207i
\(237\) −16232.5 + 36906.2i −0.0187722 + 0.0426804i
\(238\) 387567.i 0.443512i
\(239\) −383601. −0.434395 −0.217198 0.976128i \(-0.569692\pi\)
−0.217198 + 0.976128i \(0.569692\pi\)
\(240\) −184674. + 419874.i −0.206956 + 0.470534i
\(241\) 23367.5i 0.0259161i 0.999916 + 0.0129581i \(0.00412480\pi\)
−0.999916 + 0.0129581i \(0.995875\pi\)
\(242\) 426018. + 578853.i 0.467617 + 0.635375i
\(243\) 442137. 807344.i 0.480331 0.877087i
\(244\) 20580.8i 0.0221303i
\(245\) 712628.i 0.758486i
\(246\) 1.13152e6 + 497676.i 1.19213 + 0.524336i
\(247\) 1.57413e6 1.64172
\(248\) −1.32550e6 −1.36852
\(249\) 456527. + 200795.i 0.466626 + 0.205237i
\(250\) 711681.i 0.720171i
\(251\) 1.73283e6i 1.73608i 0.496491 + 0.868042i \(0.334622\pi\)
−0.496491 + 0.868042i \(0.665378\pi\)
\(252\) 366704. 336225.i 0.363760 0.333525i
\(253\) 604669. 1.19580e6i 0.593905 1.17451i
\(254\) 1.15252e6i 1.12089i
\(255\) −192688. + 438094.i −0.185568 + 0.421907i
\(256\) −997200. −0.951004
\(257\) 83741.8i 0.0790878i −0.999218 0.0395439i \(-0.987410\pi\)
0.999218 0.0395439i \(-0.0125905\pi\)
\(258\) 219895. 499952.i 0.205668 0.467605i
\(259\) 840210.i 0.778285i
\(260\) −606612. −0.556516
\(261\) −218320. 238111.i −0.198378 0.216361i
\(262\) −829860. −0.746882
\(263\) 1.45210e6 1.29451 0.647256 0.762272i \(-0.275916\pi\)
0.647256 + 0.762272i \(0.275916\pi\)
\(264\) −781762. 950563.i −0.690343 0.839404i
\(265\) 1.12237e6 0.981792
\(266\) −1.42011e6 −1.23060
\(267\) 400215. 909927.i 0.343570 0.781139i
\(268\) 354526. 0.301517
\(269\) 335334.i 0.282551i 0.989970 + 0.141275i \(0.0451203\pi\)
−0.989970 + 0.141275i \(0.954880\pi\)
\(270\) 958636. 325894.i 0.800285 0.272062i
\(271\) 2.35862e6i 1.95090i 0.220227 + 0.975449i \(0.429320\pi\)
−0.220227 + 0.975449i \(0.570680\pi\)
\(272\) 251823. 0.206382
\(273\) −2.02616e6 891169.i −1.64538 0.723692i
\(274\) 354983.i 0.285648i
\(275\) 165629. + 83752.2i 0.132070 + 0.0667828i
\(276\) −253236. + 575756.i −0.200102 + 0.454952i
\(277\) 1.98229e6i 1.55227i −0.630564 0.776137i \(-0.717176\pi\)
0.630564 0.776137i \(-0.282824\pi\)
\(278\) 1.87158e6i 1.45244i
\(279\) 1.10645e6 + 1.20675e6i 0.850980 + 0.928123i
\(280\) 1.99643e6 1.52181
\(281\) −119166. −0.0900299 −0.0450150 0.998986i \(-0.514334\pi\)
−0.0450150 + 0.998986i \(0.514334\pi\)
\(282\) 565504. 1.28573e6i 0.423460 0.962778i
\(283\) 2.04647e6i 1.51894i −0.650544 0.759468i \(-0.725459\pi\)
0.650544 0.759468i \(-0.274541\pi\)
\(284\) 209430.i 0.154079i
\(285\) 1.60524e6 + 706037.i 1.17065 + 0.514891i
\(286\) −677321. + 1.33947e6i −0.489643 + 0.968319i
\(287\) 3.01051e6i 2.15742i
\(288\) 673822. + 734905.i 0.478701 + 0.522096i
\(289\) −1.15711e6 −0.814946
\(290\) 355349.i 0.248119i
\(291\) −1.48093e6 651362.i −1.02519 0.450910i
\(292\) 200919.i 0.137900i
\(293\) −874404. −0.595036 −0.297518 0.954716i \(-0.596159\pi\)
−0.297518 + 0.954716i \(0.596159\pi\)
\(294\) 757646. + 333237.i 0.511209 + 0.224846i
\(295\) −349959. −0.234133
\(296\) −975646. −0.647237
\(297\) −212834. + 1.50519e6i −0.140007 + 0.990151i
\(298\) −276572. −0.180413
\(299\) 2.79842e6 1.81023
\(300\) −79747.5 35075.5i −0.0511580 0.0225009i
\(301\) −1.33017e6 −0.846235
\(302\) 160828.i 0.101472i
\(303\) 346560. + 152428.i 0.216856 + 0.0953803i
\(304\) 922717.i 0.572644i
\(305\) 102008. 0.0627894
\(306\) −375666. 409720.i −0.229350 0.250141i
\(307\) 2.22344e6i 1.34642i −0.739452 0.673209i \(-0.764915\pi\)
0.739452 0.673209i \(-0.235085\pi\)
\(308\) −370765. + 733226.i −0.222701 + 0.440414i
\(309\) 1.54595e6 + 679956.i 0.921082 + 0.405121i
\(310\) 1.80091e6i 1.06436i
\(311\) 2.04294e6i 1.19772i 0.800854 + 0.598860i \(0.204379\pi\)
−0.800854 + 0.598860i \(0.795621\pi\)
\(312\) 1.03482e6 2.35276e6i 0.601836 1.36833i
\(313\) 2.46189e6 1.42039 0.710195 0.704005i \(-0.248607\pi\)
0.710195 + 0.704005i \(0.248607\pi\)
\(314\) −290905. −0.166505
\(315\) −1.66650e6 1.81757e6i −0.946298 1.03208i
\(316\) 31255.0i 0.0176077i
\(317\) 59333.5i 0.0331628i −0.999863 0.0165814i \(-0.994722\pi\)
0.999863 0.0165814i \(-0.00527827\pi\)
\(318\) −524837. + 1.19327e6i −0.291043 + 0.661714i
\(319\) 476104. + 240748.i 0.261954 + 0.132461i
\(320\) 2.03835e6i 1.11277i
\(321\) −1.64987e6 725667.i −0.893693 0.393074i
\(322\) −2.52460e6 −1.35692
\(323\) 962758.i 0.513465i
\(324\) 61764.8 710886.i 0.0326872 0.376216i
\(325\) 387607.i 0.203556i
\(326\) 1.35718e6 0.707285
\(327\) −208243. + 473461.i −0.107696 + 0.244858i
\(328\) 3.49578e6 1.79415
\(329\) −3.42080e6 −1.74236
\(330\) −1.29149e6 + 1.06215e6i −0.652841 + 0.536909i
\(331\) 1.38194e6 0.693297 0.346648 0.937995i \(-0.387320\pi\)
0.346648 + 0.937995i \(0.387320\pi\)
\(332\) 386622. 0.192505
\(333\) 814409. + 888236.i 0.402468 + 0.438953i
\(334\) −2.02088e6 −0.991229
\(335\) 1.75720e6i 0.855481i
\(336\) −522382. + 1.18769e6i −0.252429 + 0.573923i
\(337\) 1.39179e6i 0.667572i 0.942649 + 0.333786i \(0.108326\pi\)
−0.942649 + 0.333786i \(0.891674\pi\)
\(338\) −1.47768e6 −0.703540
\(339\) −476419. + 1.08319e6i −0.225159 + 0.511922i
\(340\) 371011.i 0.174056i
\(341\) −2.41289e6 1.22011e6i −1.12370 0.568215i
\(342\) −1.50128e6 + 1.37650e6i −0.694058 + 0.636370i
\(343\) 831736.i 0.381725i
\(344\) 1.54458e6i 0.703745i
\(345\) 2.85373e6 + 1.25516e6i 1.29082 + 0.567743i
\(346\) 2.55851e6 1.14894
\(347\) 4.18029e6 1.86373 0.931865 0.362806i \(-0.118181\pi\)
0.931865 + 0.362806i \(0.118181\pi\)
\(348\) −229237. 100825.i −0.101470 0.0446295i
\(349\) 1.74185e6i 0.765506i 0.923851 + 0.382753i \(0.125024\pi\)
−0.923851 + 0.382753i \(0.874976\pi\)
\(350\) 349680.i 0.152581i
\(351\) −3.00578e6 + 1.02183e6i −1.30223 + 0.442702i
\(352\) −1.46944e6 743044.i −0.632116 0.319637i
\(353\) 2.80701e6i 1.19897i 0.800387 + 0.599483i \(0.204627\pi\)
−0.800387 + 0.599483i \(0.795373\pi\)
\(354\) 163647. 372067.i 0.0694063 0.157802i
\(355\) −1.03804e6 −0.437162
\(356\) 770596.i 0.322256i
\(357\) −545050. + 1.23922e6i −0.226342 + 0.514611i
\(358\) 1.47825e6i 0.609595i
\(359\) 596226. 0.244160 0.122080 0.992520i \(-0.461044\pi\)
0.122080 + 0.992520i \(0.461044\pi\)
\(360\) 2.11054e6 1.93512e6i 0.858298 0.786959i
\(361\) −1.05159e6 −0.424698
\(362\) 2.64776e6 1.06196
\(363\) −548107. 2.44997e6i −0.218323 0.975877i
\(364\) −1.71591e6 −0.678798
\(365\) −995853. −0.391258
\(366\) −47700.9 + 108453.i −0.0186133 + 0.0423192i
\(367\) −3.46674e6 −1.34356 −0.671779 0.740752i \(-0.734470\pi\)
−0.671779 + 0.740752i \(0.734470\pi\)
\(368\) 1.64037e6i 0.631424i
\(369\) −2.91806e6 3.18258e6i −1.11565 1.21678i
\(370\) 1.32557e6i 0.503384i
\(371\) 3.17480e6 1.19752
\(372\) 1.16177e6 + 510982.i 0.435273 + 0.191447i
\(373\) 4.41525e6i 1.64317i 0.570085 + 0.821586i \(0.306910\pi\)
−0.570085 + 0.821586i \(0.693090\pi\)
\(374\) 819237. + 414258.i 0.302852 + 0.153141i
\(375\) 1.00086e6 2.27556e6i 0.367533 0.835622i
\(376\) 3.97221e6i 1.44898i
\(377\) 1.11419e6i 0.403743i
\(378\) 2.71167e6 921848.i 0.976129 0.331841i
\(379\) −2.65164e6 −0.948236 −0.474118 0.880461i \(-0.657233\pi\)
−0.474118 + 0.880461i \(0.657233\pi\)
\(380\) 1.35944e6 0.482950
\(381\) −1.62083e6 + 3.68510e6i −0.572036 + 1.30058i
\(382\) 1.93884e6i 0.679804i
\(383\) 1.60664e6i 0.559656i −0.960050 0.279828i \(-0.909723\pi\)
0.960050 0.279828i \(-0.0902774\pi\)
\(384\) −293574. 129123.i −0.101599 0.0446864i
\(385\) 3.63423e6 + 1.83769e6i 1.24957 + 0.631861i
\(386\) 318907.i 0.108942i
\(387\) −1.40620e6 + 1.28932e6i −0.477277 + 0.437607i
\(388\) −1.25417e6 −0.422938
\(389\) 243726.i 0.0816634i −0.999166 0.0408317i \(-0.986999\pi\)
0.999166 0.0408317i \(-0.0130008\pi\)
\(390\) −3.19661e6 1.40597e6i −1.06421 0.468074i
\(391\) 1.71155e6i 0.566170i
\(392\) 2.34072e6 0.769368
\(393\) 2.65343e6 + 1.16706e6i 0.866615 + 0.381165i
\(394\) 4.05993e6 1.31758
\(395\) 154915. 0.0499576
\(396\) 318752. + 1.13452e6i 0.102144 + 0.363557i
\(397\) 181651. 0.0578445 0.0289223 0.999582i \(-0.490792\pi\)
0.0289223 + 0.999582i \(0.490792\pi\)
\(398\) 793496. 0.251094
\(399\) 4.54071e6 + 1.99715e6i 1.42788 + 0.628026i
\(400\) 227206. 0.0710017
\(401\) 3.23285e6i 1.00398i 0.864874 + 0.501989i \(0.167398\pi\)
−0.864874 + 0.501989i \(0.832602\pi\)
\(402\) 1.86821e6 + 821699.i 0.576582 + 0.253599i
\(403\) 5.64669e6i 1.73193i
\(404\) 293494. 0.0894634
\(405\) −3.52350e6 306137.i −1.06742 0.0927423i
\(406\) 1.00517e6i 0.302638i
\(407\) −1.77603e6 898072.i −0.531452 0.268736i
\(408\) −1.43898e6 632908.i −0.427961 0.188231i
\(409\) 2.73058e6i 0.807135i 0.914950 + 0.403567i \(0.132230\pi\)
−0.914950 + 0.403567i \(0.867770\pi\)
\(410\) 4.74958e6i 1.39539i
\(411\) −499225. + 1.13504e6i −0.145778 + 0.331440i
\(412\) 1.30923e6 0.379989
\(413\) −989919. −0.285578
\(414\) −2.66890e6 + 2.44707e6i −0.765301 + 0.701691i
\(415\) 1.91629e6i 0.546186i
\(416\) 3.43882e6i 0.974262i
\(417\) 2.63207e6 5.98428e6i 0.741238 1.68528i
\(418\) 1.51790e6 3.00181e6i 0.424916 0.840316i
\(419\) 2.32728e6i 0.647611i −0.946124 0.323805i \(-0.895038\pi\)
0.946124 0.323805i \(-0.104962\pi\)
\(420\) −1.74982e6 769627.i −0.484028 0.212891i
\(421\) 2.07600e6 0.570851 0.285425 0.958401i \(-0.407865\pi\)
0.285425 + 0.958401i \(0.407865\pi\)
\(422\) 1.44430e6i 0.394799i
\(423\) −3.61633e6 + 3.31575e6i −0.982691 + 0.901013i
\(424\) 3.68656e6i 0.995879i
\(425\) 237065. 0.0636642
\(426\) 485404. 1.10361e6i 0.129592 0.294641i
\(427\) 288548. 0.0765859
\(428\) −1.39724e6 −0.368690
\(429\) 4.04944e6 3.33034e6i 1.06231 0.873666i
\(430\) −2.09857e6 −0.547333
\(431\) 4.32285e6 1.12092 0.560462 0.828180i \(-0.310623\pi\)
0.560462 + 0.828180i \(0.310623\pi\)
\(432\) 598973. + 1.76191e6i 0.154418 + 0.454229i
\(433\) −2.24130e6 −0.574488 −0.287244 0.957857i \(-0.592739\pi\)
−0.287244 + 0.957857i \(0.592739\pi\)
\(434\) 5.09417e6i 1.29822i
\(435\) −499740. + 1.13621e6i −0.126626 + 0.287896i
\(436\) 400963.i 0.101015i
\(437\) −6.27137e6 −1.57094
\(438\) 465678. 1.05876e6i 0.115985 0.263702i
\(439\) 771175.i 0.190982i 0.995430 + 0.0954908i \(0.0304421\pi\)
−0.995430 + 0.0954908i \(0.969558\pi\)
\(440\) −2.13392e6 + 4.22004e6i −0.525467 + 1.03917i
\(441\) −1.95389e6 2.13101e6i −0.478413 0.521782i
\(442\) 1.91719e6i 0.466777i
\(443\) 4.38448e6i 1.06147i −0.847537 0.530737i \(-0.821915\pi\)
0.847537 0.530737i \(-0.178085\pi\)
\(444\) 855130. + 376113.i 0.205861 + 0.0905442i
\(445\) −3.81945e6 −0.914325
\(446\) 59228.0 0.0140991
\(447\) 884324. + 388954.i 0.209335 + 0.0920723i
\(448\) 5.76583e6i 1.35727i
\(449\) 6.62600e6i 1.55108i 0.631295 + 0.775542i \(0.282524\pi\)
−0.631295 + 0.775542i \(0.717476\pi\)
\(450\) −338942. 369668.i −0.0789031 0.0860558i
\(451\) 6.36358e6 + 3.21783e6i 1.47319 + 0.744940i
\(452\) 917324.i 0.211192i
\(453\) 226179. 514240.i 0.0517853 0.117739i
\(454\) 1.25785e6 0.286412
\(455\) 8.50488e6i 1.92593i
\(456\) −2.31907e6 + 5.27264e6i −0.522278 + 1.18745i
\(457\) 1.04547e6i 0.234164i 0.993122 + 0.117082i \(0.0373540\pi\)
−0.993122 + 0.117082i \(0.962646\pi\)
\(458\) −6.05997e6 −1.34992
\(459\) 624965. + 1.83837e6i 0.138460 + 0.407287i
\(460\) 2.41676e6 0.532523
\(461\) −4.96719e6 −1.08857 −0.544287 0.838899i \(-0.683200\pi\)
−0.544287 + 0.838899i \(0.683200\pi\)
\(462\) −3.65321e6 + 3.00447e6i −0.796288 + 0.654883i
\(463\) −3.13080e6 −0.678739 −0.339370 0.940653i \(-0.610214\pi\)
−0.339370 + 0.940653i \(0.610214\pi\)
\(464\) 653109. 0.140829
\(465\) 2.53268e6 5.75829e6i 0.543185 1.23498i
\(466\) −298979. −0.0637787
\(467\) 6.97533e6i 1.48004i −0.672587 0.740018i \(-0.734817\pi\)
0.672587 0.740018i \(-0.265183\pi\)
\(468\) −1.81399e6 + 1.66321e6i −0.382842 + 0.351021i
\(469\) 4.97056e6i 1.04345i
\(470\) −5.39688e6 −1.12693
\(471\) 930153. + 409110.i 0.193198 + 0.0849744i
\(472\) 1.14949e6i 0.237492i
\(473\) 1.42177e6 2.81170e6i 0.292198 0.577852i
\(474\) −72440.9 + 164702.i −0.0148094 + 0.0336707i
\(475\) 868643.i 0.176647i
\(476\) 1.04947e6i 0.212301i
\(477\) 3.35627e6 3.07731e6i 0.675400 0.619263i
\(478\) −1.71190e6 −0.342695
\(479\) −5.09382e6 −1.01439 −0.507194 0.861832i \(-0.669317\pi\)
−0.507194 + 0.861832i \(0.669317\pi\)
\(480\) 1.54239e6 3.50679e6i 0.305557 0.694714i
\(481\) 4.15629e6i 0.819112i
\(482\) 104282.i 0.0204453i
\(483\) 8.07226e6 + 3.55044e6i 1.57445 + 0.692491i
\(484\) −1.15359e6 1.56744e6i −0.223840 0.304143i
\(485\) 6.21627e6i 1.19998i
\(486\) 1.97312e6 3.60294e6i 0.378934 0.691936i
\(487\) 7.86781e6 1.50325 0.751625 0.659590i \(-0.229270\pi\)
0.751625 + 0.659590i \(0.229270\pi\)
\(488\) 335060.i 0.0636903i
\(489\) −4.33951e6 1.90865e6i −0.820670 0.360957i
\(490\) 3.18025e6i 0.598371i
\(491\) 8.05135e6 1.50718 0.753590 0.657345i \(-0.228320\pi\)
0.753590 + 0.657345i \(0.228320\pi\)
\(492\) −3.06396e6 1.34763e6i −0.570651 0.250990i
\(493\) 681450. 0.126275
\(494\) 7.02488e6 1.29515
\(495\) 5.62322e6 1.57989e6i 1.03151 0.289810i
\(496\) −3.30995e6 −0.604112
\(497\) −2.93627e6 −0.533218
\(498\) 2.03735e6 + 896089.i 0.368122 + 0.161912i
\(499\) −9.10103e6 −1.63621 −0.818106 0.575068i \(-0.804976\pi\)
−0.818106 + 0.575068i \(0.804976\pi\)
\(500\) 1.92712e6i 0.344733i
\(501\) 6.46164e6 + 2.84203e6i 1.15013 + 0.505865i
\(502\) 7.73309e6i 1.36960i
\(503\) −1.00620e6 −0.177323 −0.0886615 0.996062i \(-0.528259\pi\)
−0.0886615 + 0.996062i \(0.528259\pi\)
\(504\) 5.97004e6 5.47383e6i 1.04689 0.959875i
\(505\) 1.45470e6i 0.253831i
\(506\) 2.69846e6 5.33648e6i 0.468533 0.926571i
\(507\) 4.72480e6 + 2.07812e6i 0.816326 + 0.359046i
\(508\) 3.12083e6i 0.536550i
\(509\) 2.93973e6i 0.502936i −0.967866 0.251468i \(-0.919087\pi\)
0.967866 0.251468i \(-0.0809134\pi\)
\(510\) −859908. + 1.95508e6i −0.146395 + 0.332843i
\(511\) −2.81694e6 −0.477228
\(512\) −5.10857e6 −0.861241
\(513\) 6.73607e6 2.28997e6i 1.13009 0.384181i
\(514\) 373715.i 0.0623925i
\(515\) 6.48916e6i 1.07813i
\(516\) −595439. + 1.35379e6i −0.0984495 + 0.223834i
\(517\) 3.65638e6 7.23086e6i 0.601623 1.18977i
\(518\) 3.74961e6i 0.613991i
\(519\) −8.18069e6 3.59813e6i −1.33313 0.586352i
\(520\) −9.87580e6 −1.60164
\(521\) 9.05577e6i 1.46161i −0.682587 0.730804i \(-0.739145\pi\)
0.682587 0.730804i \(-0.260855\pi\)
\(522\) −974299. 1.06262e6i −0.156501 0.170688i
\(523\) 912191.i 0.145825i −0.997338 0.0729124i \(-0.976771\pi\)
0.997338 0.0729124i \(-0.0232294\pi\)
\(524\) 2.24713e6 0.357519
\(525\) −491768. + 1.11808e6i −0.0778685 + 0.177042i
\(526\) 6.48028e6 1.02124
\(527\) −3.45358e6 −0.541681
\(528\) −1.95216e6 2.37368e6i −0.304741 0.370542i
\(529\) −4.71262e6 −0.732189
\(530\) 5.00878e6 0.774538
\(531\) −1.04650e6 + 959520.i −0.161066 + 0.147679i
\(532\) 3.84542e6 0.589067
\(533\) 1.48922e7i 2.27059i
\(534\) 1.78604e6 4.06074e6i 0.271043 0.616242i
\(535\) 6.92540e6i 1.04607i
\(536\) 5.77177e6 0.867755
\(537\) −2.07892e6 + 4.72663e6i −0.311102 + 0.707320i
\(538\) 1.49649e6i 0.222905i
\(539\) 4.26096e6 + 2.15461e6i 0.631736 + 0.319445i
\(540\) −2.59583e6 + 882469.i −0.383082 + 0.130231i
\(541\) 2.77036e6i 0.406952i 0.979080 + 0.203476i \(0.0652238\pi\)
−0.979080 + 0.203476i \(0.934776\pi\)
\(542\) 1.05258e7i 1.53907i
\(543\) −8.46606e6 3.72364e6i −1.23220 0.541961i
\(544\) −2.10322e6 −0.304711
\(545\) 1.98737e6 0.286607
\(546\) −9.04215e6 3.97702e6i −1.29805 0.570922i
\(547\) 9.31603e6i 1.33126i 0.746282 + 0.665630i \(0.231837\pi\)
−0.746282 + 0.665630i \(0.768163\pi\)
\(548\) 961236.i 0.136735i
\(549\) 305041. 279687.i 0.0431945 0.0396043i
\(550\) 739151. + 373761.i 0.104190 + 0.0526851i
\(551\) 2.49694e6i 0.350372i
\(552\) −4.12274e6 + 9.37345e6i −0.575888 + 1.30934i
\(553\) 438204. 0.0609346
\(554\) 8.84639e6i 1.22459i
\(555\) 1.86420e6 4.23844e6i 0.256898 0.584082i
\(556\) 5.06794e6i 0.695256i
\(557\) −109865. −0.0150045 −0.00750225 0.999972i \(-0.502388\pi\)
−0.00750225 + 0.999972i \(0.502388\pi\)
\(558\) 4.93774e6 + 5.38535e6i 0.671340 + 0.732198i
\(559\) 6.57999e6 0.890627
\(560\) 4.98535e6 0.671778
\(561\) −2.03688e6 2.47669e6i −0.273248 0.332249i
\(562\) −531803. −0.0710248
\(563\) −4.75207e6 −0.631847 −0.315924 0.948785i \(-0.602314\pi\)
−0.315924 + 0.948785i \(0.602314\pi\)
\(564\) −1.53129e6 + 3.48154e6i −0.202703 + 0.460865i
\(565\) 4.54671e6 0.599206
\(566\) 9.13279e6i 1.19829i
\(567\) −9.96683e6 865960.i −1.30197 0.113120i
\(568\) 3.40957e6i 0.443434i
\(569\) −76851.0 −0.00995105 −0.00497552 0.999988i \(-0.501584\pi\)
−0.00497552 + 0.999988i \(0.501584\pi\)
\(570\) 7.16373e6 + 3.15083e6i 0.923532 + 0.406199i
\(571\) 9.51570e6i 1.22138i −0.791870 0.610689i \(-0.790892\pi\)
0.791870 0.610689i \(-0.209108\pi\)
\(572\) 1.83407e6 3.62707e6i 0.234383 0.463517i
\(573\) −2.72666e6 + 6.19933e6i −0.346932 + 0.788784i
\(574\) 1.34350e7i 1.70199i
\(575\) 1.54423e6i 0.194780i
\(576\) 5.58876e6 + 6.09539e6i 0.701875 + 0.765501i
\(577\) 3.79444e6 0.474470 0.237235 0.971452i \(-0.423759\pi\)
0.237235 + 0.971452i \(0.423759\pi\)
\(578\) −5.16382e6 −0.642912
\(579\) −448490. + 1.01969e6i −0.0555976 + 0.126407i
\(580\) 962228.i 0.118770i
\(581\) 5.42055e6i 0.666198i
\(582\) −6.60897e6 2.90683e6i −0.808772 0.355724i
\(583\) −3.39344e6 + 6.71087e6i −0.413493 + 0.817726i
\(584\) 3.27101e6i 0.396872i
\(585\) 8.24370e6 + 8.99101e6i 0.995939 + 1.08622i
\(586\) −3.90221e6 −0.469425
\(587\) 1.06797e7i 1.27927i 0.768679 + 0.639635i \(0.220915\pi\)
−0.768679 + 0.639635i \(0.779085\pi\)
\(588\) −2.05158e6 902351.i −0.244707 0.107630i
\(589\) 1.26545e7i 1.50299i
\(590\) −1.56176e6 −0.184708
\(591\) −1.29814e7 5.70962e6i −1.52880 0.672417i
\(592\) −2.43632e6 −0.285713
\(593\) −1.56261e6 −0.182480 −0.0912400 0.995829i \(-0.529083\pi\)
−0.0912400 + 0.995829i \(0.529083\pi\)
\(594\) −949815. + 6.71723e6i −0.110452 + 0.781132i
\(595\) 5.20169e6 0.602354
\(596\) 748913. 0.0863606
\(597\) −2.53716e6 1.11592e6i −0.291348 0.128144i
\(598\) 1.24885e7 1.42810
\(599\) 8.24346e6i 0.938734i 0.883003 + 0.469367i \(0.155518\pi\)
−0.883003 + 0.469367i \(0.844482\pi\)
\(600\) −1.29831e6 571037.i −0.147231 0.0647569i
\(601\) 3.24701e6i 0.366689i −0.983049 0.183344i \(-0.941308\pi\)
0.983049 0.183344i \(-0.0586923\pi\)
\(602\) −5.93616e6 −0.667597
\(603\) −4.81792e6 5.25467e6i −0.539593 0.588507i
\(604\) 435497.i 0.0485728i
\(605\) −7.76900e6 + 5.71775e6i −0.862933 + 0.635092i
\(606\) 1.54660e6 + 680242.i 0.171078 + 0.0752457i
\(607\) 4.58595e6i 0.505194i −0.967572 0.252597i \(-0.918715\pi\)
0.967572 0.252597i \(-0.0812846\pi\)
\(608\) 7.70653e6i 0.845474i
\(609\) −1.41360e6 + 3.21396e6i −0.154449 + 0.351154i
\(610\) 455233. 0.0495347
\(611\) 1.69218e7 1.83376
\(612\) 1.01724e6 + 1.10946e6i 0.109786 + 0.119738i
\(613\) 1.50334e7i 1.61587i −0.589274 0.807933i \(-0.700586\pi\)
0.589274 0.807933i \(-0.299414\pi\)
\(614\) 9.92257e6i 1.06219i
\(615\) −6.67950e6 + 1.51865e7i −0.712125 + 1.61909i
\(616\) −6.03615e6 + 1.19371e7i −0.640926 + 1.26750i
\(617\) 1.03976e7i 1.09956i −0.835308 0.549782i \(-0.814711\pi\)
0.835308 0.549782i \(-0.185289\pi\)
\(618\) 6.89910e6 + 3.03444e6i 0.726643 + 0.319601i
\(619\) 7.96319e6 0.835335 0.417667 0.908600i \(-0.362848\pi\)
0.417667 + 0.908600i \(0.362848\pi\)
\(620\) 4.87656e6i 0.509489i
\(621\) 1.19751e7 4.07100e6i 1.24609 0.423616i
\(622\) 9.11704e6i 0.944883i
\(623\) −1.08040e7 −1.11523
\(624\) 2.58408e6 5.87516e6i 0.265671 0.604030i
\(625\) −1.09970e7 −1.12609
\(626\) 1.09867e7 1.12055
\(627\) −9.07496e6 + 7.46343e6i −0.921883 + 0.758175i
\(628\) 787724. 0.0797031
\(629\) −2.54204e6 −0.256186
\(630\) −7.43708e6 8.11126e6i −0.746536 0.814211i
\(631\) −3.40838e6 −0.340780 −0.170390 0.985377i \(-0.554503\pi\)
−0.170390 + 0.985377i \(0.554503\pi\)
\(632\) 508839.i 0.0506743i
\(633\) 2.03117e6 4.61807e6i 0.201483 0.458090i
\(634\) 264788.i 0.0261622i
\(635\) 1.54684e7 1.52233
\(636\) 1.42117e6 3.23118e6i 0.139317 0.316751i
\(637\) 9.97156e6i 0.973677i
\(638\) 2.12471e6 + 1.07439e6i 0.206656 + 0.104498i
\(639\) −3.10410e6 + 2.84610e6i −0.300735 + 0.275739i
\(640\) 1.23229e6i 0.118922i
\(641\) 3.31964e6i 0.319114i −0.987189 0.159557i \(-0.948993\pi\)
0.987189 0.159557i \(-0.0510066\pi\)
\(642\) −7.36290e6 3.23844e6i −0.705036 0.310097i
\(643\) 1.41646e6 0.135107 0.0675534 0.997716i \(-0.478481\pi\)
0.0675534 + 0.997716i \(0.478481\pi\)
\(644\) 6.83621e6 0.649532
\(645\) 6.71005e6 + 2.95129e6i 0.635077 + 0.279327i
\(646\) 4.29650e6i 0.405074i
\(647\) 1.40678e7i 1.32119i 0.750742 + 0.660596i \(0.229696\pi\)
−0.750742 + 0.660596i \(0.770304\pi\)
\(648\) 1.00555e6 1.15734e7i 0.0940729 1.08274i
\(649\) 1.05809e6 2.09248e6i 0.0986078 0.195007i
\(650\) 1.72977e6i 0.160585i
\(651\) 7.16412e6 1.62883e7i 0.662537 1.50634i
\(652\) −3.67503e6 −0.338565
\(653\) 1.38283e6i 0.126907i −0.997985 0.0634535i \(-0.979789\pi\)
0.997985 0.0634535i \(-0.0202114\pi\)
\(654\) −929326. + 2.11291e6i −0.0849618 + 0.193169i
\(655\) 1.11379e7i 1.01438i
\(656\) 8.72942e6 0.792001
\(657\) −2.97795e6 + 2.73044e6i −0.269156 + 0.246785i
\(658\) −1.52660e7 −1.37455
\(659\) −9.61639e6 −0.862578 −0.431289 0.902214i \(-0.641941\pi\)
−0.431289 + 0.902214i \(0.641941\pi\)
\(660\) 3.49715e6 2.87613e6i 0.312504 0.257009i
\(661\) −3.17414e6 −0.282568 −0.141284 0.989969i \(-0.545123\pi\)
−0.141284 + 0.989969i \(0.545123\pi\)
\(662\) 6.16719e6 0.546943
\(663\) 2.69621e6 6.13011e6i 0.238216 0.541607i
\(664\) 6.29431e6 0.554023
\(665\) 1.90598e7i 1.67134i
\(666\) 3.63446e6 + 3.96393e6i 0.317508 + 0.346291i
\(667\) 4.43894e6i 0.386336i
\(668\) 5.47221e6 0.474484
\(669\) −189378. 83294.5i −0.0163593 0.00719534i
\(670\) 7.84188e6i 0.674891i
\(671\) −308420. + 609931.i −0.0264445 + 0.0522967i
\(672\) 4.36293e6 9.91955e6i 0.372696 0.847361i
\(673\) 6.37989e6i 0.542969i 0.962443 + 0.271485i \(0.0875146\pi\)
−0.962443 + 0.271485i \(0.912485\pi\)
\(674\) 6.21113e6i 0.526649i
\(675\) 563871. + 1.65866e6i 0.0476343 + 0.140119i
\(676\) 4.00132e6 0.336772
\(677\) −2.33822e6 −0.196071 −0.0980356 0.995183i \(-0.531256\pi\)
−0.0980356 + 0.995183i \(0.531256\pi\)
\(678\) −2.12612e6 + 4.83394e6i −0.177629 + 0.403856i
\(679\) 1.75838e7i 1.46365i
\(680\) 6.04016e6i 0.500929i
\(681\) −4.02191e6 1.76896e6i −0.332327 0.146168i
\(682\) −1.07680e7 5.44499e6i −0.886492 0.448266i
\(683\) 1.64219e7i 1.34701i −0.739183 0.673505i \(-0.764788\pi\)
0.739183 0.673505i \(-0.235212\pi\)
\(684\) 4.06522e6 3.72733e6i 0.332234 0.304619i
\(685\) 4.76435e6 0.387952
\(686\) 3.71179e6i 0.301143i
\(687\) 1.93764e7 + 8.52235e6i 1.56632 + 0.688918i
\(688\) 3.85703e6i 0.310658i
\(689\) −1.57049e7 −1.26034
\(690\) 1.27354e7 + 5.60141e6i 1.01833 + 0.447893i
\(691\) −8.80612e6 −0.701600 −0.350800 0.936450i \(-0.614090\pi\)
−0.350800 + 0.936450i \(0.614090\pi\)
\(692\) −6.92803e6 −0.549977
\(693\) 1.59062e7 4.46899e6i 1.25816 0.353489i
\(694\) 1.86554e7 1.47030
\(695\) −2.51192e7 −1.97262
\(696\) −3.73203e6 1.64146e6i −0.292026 0.128442i
\(697\) 9.10823e6 0.710153
\(698\) 7.77338e6i 0.603909i
\(699\) 955967. + 420464.i 0.0740031 + 0.0325489i
\(700\) 946877.i 0.0730380i
\(701\) 1.86560e7 1.43392 0.716958 0.697117i \(-0.245534\pi\)
0.716958 + 0.697117i \(0.245534\pi\)
\(702\) −1.34139e7 + 4.56013e6i −1.02733 + 0.349249i
\(703\) 9.31442e6i 0.710833i
\(704\) −1.21878e7 6.16290e6i −0.926813 0.468655i
\(705\) 1.72562e7 + 7.58983e6i 1.30759 + 0.575121i
\(706\) 1.25268e7i 0.945867i
\(707\) 4.11486e6i 0.309604i
\(708\) −443129. + 1.00750e6i −0.0332236 + 0.0755371i
\(709\) −1.00665e7 −0.752076 −0.376038 0.926604i \(-0.622714\pi\)
−0.376038 + 0.926604i \(0.622714\pi\)
\(710\) −4.63245e6 −0.344878
\(711\) 463251. 424747.i 0.0343671 0.0315106i
\(712\) 1.25455e7i 0.927444i
\(713\) 2.24965e7i 1.65726i
\(714\) −2.43240e6 + 5.53029e6i −0.178562 + 0.405978i
\(715\) −1.79775e7 9.09057e6i −1.31512 0.665007i
\(716\) 4.00287e6i 0.291803i
\(717\) 5.47369e6 + 2.40750e6i 0.397633 + 0.174892i
\(718\) 2.66078e6 0.192618
\(719\) 8.33326e6i 0.601164i 0.953756 + 0.300582i \(0.0971809\pi\)
−0.953756 + 0.300582i \(0.902819\pi\)
\(720\) 5.27031e6 4.83226e6i 0.378883 0.347391i
\(721\) 1.83557e7i 1.31502i
\(722\) −4.69296e6 −0.335045
\(723\) 146656. 333437.i 0.0104341 0.0237229i
\(724\) −7.16971e6 −0.508341
\(725\) 614834. 0.0434423
\(726\) −2.44604e6 1.09335e7i −0.172235 0.769871i
\(727\) 1.38279e7 0.970333 0.485167 0.874422i \(-0.338759\pi\)
0.485167 + 0.874422i \(0.338759\pi\)
\(728\) −2.79354e7 −1.95356
\(729\) −1.13759e7 + 8.74530e6i −0.792805 + 0.609475i
\(730\) −4.44420e6 −0.308664
\(731\) 4.02440e6i 0.278553i
\(732\) 129166. 293672.i 0.00890987 0.0202574i
\(733\) 1.35485e7i 0.931390i 0.884945 + 0.465695i \(0.154196\pi\)
−0.884945 + 0.465695i \(0.845804\pi\)
\(734\) −1.54710e7 −1.05994
\(735\) −4.47249e6 + 1.01687e7i −0.305373 + 0.694296i
\(736\) 1.37003e7i 0.932258i
\(737\) 1.05067e7 + 5.31286e6i 0.712522 + 0.360296i
\(738\) −1.30224e7 1.42029e7i −0.880138 0.959924i
\(739\) 1.17902e7i 0.794164i 0.917783 + 0.397082i \(0.129977\pi\)
−0.917783 + 0.397082i \(0.870023\pi\)
\(740\) 3.58944e6i 0.240961i
\(741\) −2.24617e7 9.87934e6i −1.50278 0.660971i
\(742\) 1.41682e7 0.944724
\(743\) −1.50901e6 −0.100281 −0.0501407 0.998742i \(-0.515967\pi\)
−0.0501407 + 0.998742i \(0.515967\pi\)
\(744\) 1.89139e7 + 8.31892e6i 1.25270 + 0.550979i
\(745\) 3.71198e6i 0.245028i
\(746\) 1.97039e7i 1.29630i
\(747\) −5.25409e6 5.73039e6i −0.344506 0.375736i
\(748\) −2.21836e6 1.12174e6i −0.144970 0.0733059i
\(749\) 1.95897e7i 1.27592i
\(750\) 4.46655e6 1.01551e7i 0.289947 0.659224i
\(751\) 1.29385e7 0.837112 0.418556 0.908191i \(-0.362536\pi\)
0.418556 + 0.908191i \(0.362536\pi\)
\(752\) 9.91913e6i 0.639630i
\(753\) 1.08753e7 2.47261e7i 0.698964 1.58916i
\(754\) 4.97229e6i 0.318513i
\(755\) −2.15854e6 −0.137814
\(756\) −7.34276e6 + 2.49621e6i −0.467256 + 0.158846i
\(757\) −2.29160e7 −1.45345 −0.726724 0.686929i \(-0.758958\pi\)
−0.726724 + 0.686929i \(0.758958\pi\)
\(758\) −1.18335e7 −0.748065
\(759\) −1.61331e7 + 1.32681e7i −1.01651 + 0.835999i
\(760\) 2.21321e7 1.38991
\(761\) 2.50919e7 1.57062 0.785311 0.619101i \(-0.212503\pi\)
0.785311 + 0.619101i \(0.212503\pi\)
\(762\) −7.23326e6 + 1.64455e7i −0.451281 + 1.02603i
\(763\) 5.62161e6 0.349582
\(764\) 5.25007e6i 0.325410i
\(765\) 5.49901e6 5.04195e6i 0.339728 0.311491i
\(766\) 7.16995e6i 0.441513i
\(767\) 4.89686e6 0.300559
\(768\) 1.42293e7 + 6.25849e6i 0.870523 + 0.382883i
\(769\) 4.73793e6i 0.288917i −0.989511 0.144458i \(-0.953856\pi\)
0.989511 0.144458i \(-0.0461440\pi\)
\(770\) 1.62185e7 + 8.20108e6i 0.985787 + 0.498476i
\(771\) −525568. + 1.19493e6i −0.0318415 + 0.0723947i
\(772\) 863548.i 0.0521487i
\(773\) 2.64966e6i 0.159493i 0.996815 + 0.0797466i \(0.0254111\pi\)
−0.996815 + 0.0797466i \(0.974589\pi\)
\(774\) −6.27546e6 + 5.75386e6i −0.376525 + 0.345229i
\(775\) −3.11597e6 −0.186354