Properties

Label 6.17.b.a.5.4
Level 6
Weight 17
Character 6.5
Analytic conductor 9.739
Analytic rank 0
Dimension 6
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 6.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(9.7394726314\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{27}\cdot 3^{13} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.4
Root \(-12.8250i\)
Character \(\chi\) = 6.5
Dual form 6.17.b.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+181.019i q^{2} +(-4654.10 - 4624.51i) q^{3} -32768.0 q^{4} -1539.79i q^{5} +(837125. - 842482. i) q^{6} +5.92137e6 q^{7} -5.93164e6i q^{8} +(274580. + 4.30458e7i) q^{9} +O(q^{10})\) \(q+181.019i q^{2} +(-4654.10 - 4624.51i) q^{3} -32768.0 q^{4} -1539.79i q^{5} +(837125. - 842482. i) q^{6} +5.92137e6 q^{7} -5.93164e6i q^{8} +(274580. + 4.30458e7i) q^{9} +278731. q^{10} +2.30420e8i q^{11} +(1.52506e8 + 1.51536e8i) q^{12} +1.44595e9 q^{13} +1.07188e9i q^{14} +(-7.12076e6 + 7.16633e6i) q^{15} +1.07374e9 q^{16} -1.68474e8i q^{17} +(-7.79213e9 + 4.97043e7i) q^{18} +4.32262e9 q^{19} +5.04558e7i q^{20} +(-2.75587e10 - 2.73834e10i) q^{21} -4.17105e10 q^{22} -9.99787e10i q^{23} +(-2.74309e10 + 2.76065e10i) q^{24} +1.52586e11 q^{25} +2.61744e11i q^{26} +(1.97788e11 - 2.01609e11i) q^{27} -1.94032e11 q^{28} +7.44960e11i q^{29} +(-1.29724e9 - 1.28900e9i) q^{30} +1.99388e11 q^{31} +1.94368e11i q^{32} +(1.06558e12 - 1.07240e12i) q^{33} +3.04970e10 q^{34} -9.11766e9i q^{35} +(-8.99744e9 - 1.41053e12i) q^{36} -3.98927e12 q^{37} +7.82478e11i q^{38} +(-6.72958e12 - 6.68679e12i) q^{39} -9.13347e9 q^{40} +1.34623e13i q^{41} +(4.95693e12 - 4.98865e12i) q^{42} +9.66403e12 q^{43} -7.55040e12i q^{44} +(6.62815e10 - 4.22795e8i) q^{45} +1.80981e13 q^{46} +2.89266e13i q^{47} +(-4.99730e12 - 4.96553e12i) q^{48} +1.82973e12 q^{49} +2.76209e13i q^{50} +(-7.79109e11 + 7.84094e11i) q^{51} -4.73808e13 q^{52} -8.03602e13i q^{53} +(3.64952e13 + 3.58034e13i) q^{54} +3.54798e11 q^{55} -3.51235e13i q^{56} +(-2.01179e13 - 1.99900e13i) q^{57} -1.34852e14 q^{58} -1.63088e14i q^{59} +(2.33333e11 - 2.34826e11i) q^{60} +8.55778e13 q^{61} +3.60931e13i q^{62} +(1.62589e12 + 2.54891e14i) q^{63} -3.51844e13 q^{64} -2.22645e12i q^{65} +(1.94125e14 + 1.92890e14i) q^{66} +5.13528e14 q^{67} +5.52055e12i q^{68} +(-4.62352e14 + 4.65311e14i) q^{69} +1.65047e12 q^{70} -3.19873e14i q^{71} +(2.55333e14 - 1.62871e12i) q^{72} +2.79061e13 q^{73} -7.22134e14i q^{74} +(-7.10148e14 - 7.05633e14i) q^{75} -1.41644e14 q^{76} +1.36440e15i q^{77} +(1.21044e15 - 1.21818e15i) q^{78} -4.23333e14 q^{79} -1.65333e12i q^{80} +(-1.85287e15 + 2.36391e13i) q^{81} -2.43693e15 q^{82} -6.58853e14i q^{83} +(9.03042e14 + 8.97300e14i) q^{84} -2.59414e11 q^{85} +1.74938e15i q^{86} +(3.44507e15 - 3.46712e15i) q^{87} +1.36677e15 q^{88} +4.19706e15i q^{89} +(7.65340e10 + 1.19982e13i) q^{90} +8.56199e15 q^{91} +3.27610e15i q^{92} +(-9.27971e14 - 9.22071e14i) q^{93} -5.23628e15 q^{94} -6.65591e12i q^{95} +(8.98856e14 - 9.04608e14i) q^{96} -3.81842e15 q^{97} +3.31216e14i q^{98} +(-9.91863e15 + 6.32687e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6006q^{3} - 196608q^{4} + 159744q^{6} - 167892q^{7} - 10215738q^{9} + O(q^{10}) \) \( 6q + 6006q^{3} - 196608q^{4} + 159744q^{6} - 167892q^{7} - 10215738q^{9} + 39297024q^{10} - 196804608q^{12} + 1763152140q^{13} - 8080218432q^{15} + 6442450944q^{16} - 12549169152q^{18} + 60306979692q^{19} - 155770661748q^{21} + 94233305088q^{22} - 5234491392q^{24} - 75722441466q^{25} + 330190979958q^{27} + 5501485056q^{28} + 987679531008q^{30} - 2846203650132q^{31} + 3282289396416q^{33} - 1812957659136q^{34} + 334749302784q^{36} + 2483836081932q^{37} - 8759076866580q^{39} - 1287684882432q^{40} - 3652917731328q^{42} + 46155081190764q^{43} - 46496752783488q^{45} - 17111605395456q^{46} + 6448893394944q^{48} + 42155513811090q^{49} - 3055668993792q^{51} - 57774969323520q^{52} + 240022278328320q^{54} - 155561818958208q^{55} + 27052692784332q^{57} - 366644114104320q^{58} + 264772597579776q^{60} + 306036501898764q^{61} - 801652315914324q^{63} - 211106232532992q^{64} + 1157574327017472q^{66} + 1979846570008812q^{67} - 2345782552693632q^{69} - 2197723307360256q^{70} + 411211174772736q^{72} + 3864207384753420q^{73} - 3376263465802122q^{75} - 1976139110547456q^{76} + 5837442492456960q^{78} + 1835806484101548q^{79} - 703356001465338q^{81} - 9913023387353088q^{82} + 5104293044158464q^{84} + 2872972366990848q^{85} - 3000080900606400q^{87} - 3087836941123584q^{88} + 12789804912058368q^{90} - 1824281133603240q^{91} - 11156835457641972q^{93} - 4579876939530240q^{94} + 171523813933056q^{96} + 31097493125645196q^{97} - 28794216850745472q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 181.019i 0.707107i
\(3\) −4654.10 4624.51i −0.709358 0.704848i
\(4\) −32768.0 −0.500000
\(5\) 1539.79i 0.00394186i −0.999998 0.00197093i \(-0.999373\pi\)
0.999998 0.00197093i \(-0.000627366\pi\)
\(6\) 837125. 842482.i 0.498403 0.501592i
\(7\) 5.92137e6 1.02716 0.513580 0.858042i \(-0.328319\pi\)
0.513580 + 0.858042i \(0.328319\pi\)
\(8\) 5.93164e6i 0.353553i
\(9\) 274580. + 4.30458e7i 0.00637865 + 0.999980i
\(10\) 278731. 0.00278731
\(11\) 2.30420e8i 1.07493i 0.843287 + 0.537463i \(0.180617\pi\)
−0.843287 + 0.537463i \(0.819383\pi\)
\(12\) 1.52506e8 + 1.51536e8i 0.354679 + 0.352424i
\(13\) 1.44595e9 1.77258 0.886290 0.463131i \(-0.153274\pi\)
0.886290 + 0.463131i \(0.153274\pi\)
\(14\) 1.07188e9i 0.726312i
\(15\) −7.12076e6 + 7.16633e6i −0.00277841 + 0.00279619i
\(16\) 1.07374e9 0.250000
\(17\) 1.68474e8i 0.0241513i −0.999927 0.0120757i \(-0.996156\pi\)
0.999927 0.0120757i \(-0.00384390\pi\)
\(18\) −7.79213e9 + 4.97043e7i −0.707092 + 0.00451039i
\(19\) 4.32262e9 0.254518 0.127259 0.991870i \(-0.459382\pi\)
0.127259 + 0.991870i \(0.459382\pi\)
\(20\) 5.04558e7i 0.00197093i
\(21\) −2.75587e10 2.73834e10i −0.728625 0.723992i
\(22\) −4.17105e10 −0.760088
\(23\) 9.99787e10i 1.27669i −0.769751 0.638344i \(-0.779620\pi\)
0.769751 0.638344i \(-0.220380\pi\)
\(24\) −2.74309e10 + 2.76065e10i −0.249201 + 0.250796i
\(25\) 1.52586e11 0.999984
\(26\) 2.61744e11i 1.25340i
\(27\) 1.97788e11 2.01609e11i 0.700309 0.713840i
\(28\) −1.94032e11 −0.513580
\(29\) 7.44960e11i 1.48919i 0.667519 + 0.744593i \(0.267356\pi\)
−0.667519 + 0.744593i \(0.732644\pi\)
\(30\) −1.29724e9 1.28900e9i −0.00197720 0.00196463i
\(31\) 1.99388e11 0.233779 0.116889 0.993145i \(-0.462708\pi\)
0.116889 + 0.993145i \(0.462708\pi\)
\(32\) 1.94368e11i 0.176777i
\(33\) 1.06558e12 1.07240e12i 0.757660 0.762508i
\(34\) 3.04970e10 0.0170776
\(35\) 9.11766e9i 0.00404892i
\(36\) −8.99744e9 1.41053e12i −0.00318933 0.499990i
\(37\) −3.98927e12 −1.13574 −0.567871 0.823118i \(-0.692233\pi\)
−0.567871 + 0.823118i \(0.692233\pi\)
\(38\) 7.82478e11i 0.179971i
\(39\) −6.72958e12 6.68679e12i −1.25739 1.24940i
\(40\) −9.13347e9 −0.00139366
\(41\) 1.34623e13i 1.68596i 0.537943 + 0.842981i \(0.319202\pi\)
−0.537943 + 0.842981i \(0.680798\pi\)
\(42\) 4.95693e12 4.98865e12i 0.511939 0.515215i
\(43\) 9.66403e12 0.826819 0.413410 0.910545i \(-0.364338\pi\)
0.413410 + 0.910545i \(0.364338\pi\)
\(44\) 7.55040e12i 0.537463i
\(45\) 6.62815e10 4.22795e8i 0.00394178 2.51437e-5i
\(46\) 1.80981e13 0.902755
\(47\) 2.89266e13i 1.21483i 0.794385 + 0.607415i \(0.207793\pi\)
−0.794385 + 0.607415i \(0.792207\pi\)
\(48\) −4.99730e12 4.96553e12i −0.177340 0.176212i
\(49\) 1.82973e12 0.0550576
\(50\) 2.76209e13i 0.707096i
\(51\) −7.79109e11 + 7.84094e11i −0.0170230 + 0.0171320i
\(52\) −4.73808e13 −0.886290
\(53\) 8.03602e13i 1.29073i −0.763876 0.645363i \(-0.776706\pi\)
0.763876 0.645363i \(-0.223294\pi\)
\(54\) 3.64952e13 + 3.58034e13i 0.504761 + 0.495193i
\(55\) 3.54798e11 0.00423721
\(56\) 3.51235e13i 0.363156i
\(57\) −2.01179e13 1.99900e13i −0.180544 0.179396i
\(58\) −1.34852e14 −1.05301
\(59\) 1.63088e14i 1.11072i −0.831610 0.555360i \(-0.812580\pi\)
0.831610 0.555360i \(-0.187420\pi\)
\(60\) 2.33333e11 2.34826e11i 0.00138920 0.00139809i
\(61\) 8.55778e13 0.446398 0.223199 0.974773i \(-0.428350\pi\)
0.223199 + 0.974773i \(0.428350\pi\)
\(62\) 3.60931e13i 0.165307i
\(63\) 1.62589e12 + 2.54891e14i 0.00655189 + 1.02714i
\(64\) −3.51844e13 −0.125000
\(65\) 2.22645e12i 0.00698725i
\(66\) 1.94125e14 + 1.92890e14i 0.539175 + 0.535746i
\(67\) 5.13528e14 1.26464 0.632319 0.774709i \(-0.282103\pi\)
0.632319 + 0.774709i \(0.282103\pi\)
\(68\) 5.52055e12i 0.0120757i
\(69\) −4.62352e14 + 4.65311e14i −0.899871 + 0.905630i
\(70\) 1.65047e12 0.00286302
\(71\) 3.19873e14i 0.495349i −0.968843 0.247675i \(-0.920334\pi\)
0.968843 0.247675i \(-0.0796664\pi\)
\(72\) 2.55333e14 1.62871e12i 0.353546 0.00225519i
\(73\) 2.79061e13 0.0346032 0.0173016 0.999850i \(-0.494492\pi\)
0.0173016 + 0.999850i \(0.494492\pi\)
\(74\) 7.22134e14i 0.803090i
\(75\) −7.10148e14 7.05633e14i −0.709347 0.704837i
\(76\) −1.41644e14 −0.127259
\(77\) 1.36440e15i 1.10412i
\(78\) 1.21044e15 1.21818e15i 0.883458 0.889112i
\(79\) −4.23333e14 −0.279040 −0.139520 0.990219i \(-0.544556\pi\)
−0.139520 + 0.990219i \(0.544556\pi\)
\(80\) 1.65333e12i 0.000985464i
\(81\) −1.85287e15 + 2.36391e13i −0.999919 + 0.0127570i
\(82\) −2.43693e15 −1.19216
\(83\) 6.58853e14i 0.292525i −0.989246 0.146263i \(-0.953276\pi\)
0.989246 0.146263i \(-0.0467245\pi\)
\(84\) 9.03042e14 + 8.97300e14i 0.364312 + 0.361996i
\(85\) −2.59414e11 −9.52011e−5
\(86\) 1.74938e15i 0.584650i
\(87\) 3.44507e15 3.46712e15i 1.04965 1.05637i
\(88\) 1.36677e15 0.380044
\(89\) 4.19706e15i 1.06617i 0.846062 + 0.533084i \(0.178967\pi\)
−0.846062 + 0.533084i \(0.821033\pi\)
\(90\) 7.65340e10 + 1.19982e13i 1.77793e−5 + 0.00278726i
\(91\) 8.56199e15 1.82072
\(92\) 3.27610e15i 0.638344i
\(93\) −9.27971e14 9.22071e14i −0.165833 0.164779i
\(94\) −5.23628e15 −0.859014
\(95\) 6.65591e12i 0.00100327i
\(96\) 8.98856e14 9.04608e14i 0.124601 0.125398i
\(97\) −3.81842e15 −0.487202 −0.243601 0.969875i \(-0.578329\pi\)
−0.243601 + 0.969875i \(0.578329\pi\)
\(98\) 3.31216e14i 0.0389316i
\(99\) −9.91863e15 + 6.32687e13i −1.07490 + 0.00685658i
\(100\) −4.99992e15 −0.499992
\(101\) 3.95394e15i 0.365140i −0.983193 0.182570i \(-0.941558\pi\)
0.983193 0.182570i \(-0.0584415\pi\)
\(102\) −1.41936e14 1.41034e14i −0.0121141 0.0120371i
\(103\) 9.78409e15 0.772365 0.386182 0.922422i \(-0.373794\pi\)
0.386182 + 0.922422i \(0.373794\pi\)
\(104\) 8.57684e15i 0.626701i
\(105\) −4.21647e13 + 4.24345e13i −0.00285387 + 0.00287213i
\(106\) 1.45468e16 0.912681
\(107\) 2.46522e16i 1.43478i −0.696671 0.717390i \(-0.745336\pi\)
0.696671 0.717390i \(-0.254664\pi\)
\(108\) −6.48111e15 + 6.60634e15i −0.350154 + 0.356920i
\(109\) −3.20807e16 −1.61002 −0.805012 0.593258i \(-0.797841\pi\)
−0.805012 + 0.593258i \(0.797841\pi\)
\(110\) 6.42253e13i 0.00299616i
\(111\) 1.85664e16 + 1.84484e16i 0.805647 + 0.800525i
\(112\) 6.35803e15 0.256790
\(113\) 2.62806e16i 0.988572i 0.869299 + 0.494286i \(0.164570\pi\)
−0.869299 + 0.494286i \(0.835430\pi\)
\(114\) 3.61857e15 3.64173e15i 0.126852 0.127664i
\(115\) −1.53946e14 −0.00503252
\(116\) 2.44108e16i 0.744593i
\(117\) 3.97028e14 + 6.22420e16i 0.0113067 + 1.77254i
\(118\) 2.95220e16 0.785398
\(119\) 9.97597e14i 0.0248073i
\(120\) 4.25081e13 + 4.22378e13i 0.000988602 + 0.000982316i
\(121\) −7.14366e15 −0.155467
\(122\) 1.54912e16i 0.315651i
\(123\) 6.22564e16 6.26548e16i 1.18835 1.19595i
\(124\) −6.53354e15 −0.116889
\(125\) 4.69902e14i 0.00788365i
\(126\) −4.61401e16 + 2.94318e14i −0.726297 + 0.00463289i
\(127\) −5.11153e16 −0.755303 −0.377652 0.925948i \(-0.623268\pi\)
−0.377652 + 0.925948i \(0.623268\pi\)
\(128\) 6.36905e15i 0.0883883i
\(129\) −4.49774e16 4.46914e16i −0.586511 0.582782i
\(130\) 4.03031e14 0.00494073
\(131\) 1.07461e17i 1.23903i −0.784985 0.619515i \(-0.787329\pi\)
0.784985 0.619515i \(-0.212671\pi\)
\(132\) −3.49169e16 + 3.51403e16i −0.378830 + 0.381254i
\(133\) 2.55958e16 0.261430
\(134\) 9.29585e16i 0.894233i
\(135\) −3.10436e14 3.04551e14i −0.00281385 0.00276052i
\(136\) −9.99327e14 −0.00853879
\(137\) 5.88231e16i 0.474006i 0.971509 + 0.237003i \(0.0761651\pi\)
−0.971509 + 0.237003i \(0.923835\pi\)
\(138\) −8.42303e16 8.36947e16i −0.640377 0.636305i
\(139\) 3.28378e16 0.235643 0.117822 0.993035i \(-0.462409\pi\)
0.117822 + 0.993035i \(0.462409\pi\)
\(140\) 2.98767e14i 0.00202446i
\(141\) 1.33771e17 1.34628e17i 0.856270 0.861749i
\(142\) 5.79033e16 0.350265
\(143\) 3.33175e17i 1.90539i
\(144\) 2.94828e14 + 4.62201e16i 0.00159466 + 0.249995i
\(145\) 1.14708e15 0.00587016
\(146\) 5.05155e15i 0.0244682i
\(147\) −8.51573e15 8.46158e15i −0.0390556 0.0388073i
\(148\) 1.30720e17 0.567871
\(149\) 1.74764e16i 0.0719384i −0.999353 0.0359692i \(-0.988548\pi\)
0.999353 0.0359692i \(-0.0114518\pi\)
\(150\) 1.27733e17 1.28551e17i 0.498395 0.501584i
\(151\) 3.48492e16 0.128937 0.0644685 0.997920i \(-0.479465\pi\)
0.0644685 + 0.997920i \(0.479465\pi\)
\(152\) 2.56402e16i 0.0899856i
\(153\) 7.25210e15 4.62596e13i 0.0241508 0.000154053i
\(154\) −2.46983e17 −0.780732
\(155\) 3.07015e14i 0.000921523i
\(156\) 2.20515e17 + 2.19113e17i 0.628697 + 0.624699i
\(157\) −1.85733e17 −0.503144 −0.251572 0.967839i \(-0.580948\pi\)
−0.251572 + 0.967839i \(0.580948\pi\)
\(158\) 7.66315e16i 0.197311i
\(159\) −3.71626e17 + 3.74005e17i −0.909766 + 0.915588i
\(160\) 2.99285e14 0.000696828
\(161\) 5.92011e17i 1.31136i
\(162\) −4.27913e15 3.35405e17i −0.00902059 0.707049i
\(163\) −8.14420e17 −1.63436 −0.817180 0.576383i \(-0.804464\pi\)
−0.817180 + 0.576383i \(0.804464\pi\)
\(164\) 4.41132e17i 0.842981i
\(165\) −1.65126e15 1.64077e15i −0.00300570 0.00298659i
\(166\) 1.19265e17 0.206847
\(167\) 1.51746e17i 0.250834i 0.992104 + 0.125417i \(0.0400268\pi\)
−0.992104 + 0.125417i \(0.959973\pi\)
\(168\) −1.62429e17 + 1.63468e17i −0.255970 + 0.257608i
\(169\) 1.42535e18 2.14204
\(170\) 4.69589e13i 6.73173e-5i
\(171\) 1.18690e15 + 1.86071e17i 0.00162348 + 0.254513i
\(172\) −3.16671e17 −0.413410
\(173\) 4.17219e17i 0.519990i −0.965610 0.259995i \(-0.916279\pi\)
0.965610 0.259995i \(-0.0837210\pi\)
\(174\) 6.27615e17 + 6.23625e17i 0.746964 + 0.742214i
\(175\) 9.03516e17 1.02714
\(176\) 2.47412e17i 0.268732i
\(177\) −7.54199e17 + 7.59026e17i −0.782889 + 0.787899i
\(178\) −7.59750e17 −0.753895
\(179\) 1.38626e17i 0.131529i −0.997835 0.0657645i \(-0.979051\pi\)
0.997835 0.0657645i \(-0.0209486\pi\)
\(180\) −2.17191e15 + 1.38541e13i −0.00197089 + 1.25719e-5i
\(181\) 6.47300e17 0.561923 0.280961 0.959719i \(-0.409347\pi\)
0.280961 + 0.959719i \(0.409347\pi\)
\(182\) 1.54989e18i 1.28745i
\(183\) −3.98288e17 3.95755e17i −0.316656 0.314643i
\(184\) −5.93038e17 −0.451377
\(185\) 6.14262e15i 0.00447693i
\(186\) 1.66913e17 1.67981e17i 0.116516 0.117262i
\(187\) 3.88198e16 0.0259609
\(188\) 9.47868e17i 0.607415i
\(189\) 1.17118e18 1.19380e18i 0.719329 0.733228i
\(190\) 1.20485e15 0.000709421
\(191\) 7.46429e17i 0.421426i −0.977548 0.210713i \(-0.932421\pi\)
0.977548 0.210713i \(-0.0675786\pi\)
\(192\) 1.63752e17 + 1.62710e17i 0.0886698 + 0.0881060i
\(193\) −2.21274e17 −0.114940 −0.0574700 0.998347i \(-0.518303\pi\)
−0.0574700 + 0.998347i \(0.518303\pi\)
\(194\) 6.91207e17i 0.344504i
\(195\) −1.02962e16 + 1.03621e16i −0.00492495 + 0.00495647i
\(196\) −5.99565e16 −0.0275288
\(197\) 1.21371e18i 0.535041i 0.963552 + 0.267520i \(0.0862043\pi\)
−0.963552 + 0.267520i \(0.913796\pi\)
\(198\) −1.14529e16 1.79546e18i −0.00484833 0.760072i
\(199\) −4.59820e18 −1.86966 −0.934832 0.355090i \(-0.884450\pi\)
−0.934832 + 0.355090i \(0.884450\pi\)
\(200\) 9.05083e17i 0.353548i
\(201\) −2.39001e18 2.37482e18i −0.897081 0.891377i
\(202\) 7.15739e17 0.258193
\(203\) 4.41119e18i 1.52963i
\(204\) 2.55298e16 2.56932e16i 0.00851151 0.00856598i
\(205\) 2.07291e16 0.00664582
\(206\) 1.77111e18i 0.546144i
\(207\) 4.30367e18 2.74522e16i 1.27666 0.00814355i
\(208\) 1.55257e18 0.443145
\(209\) 9.96018e17i 0.273588i
\(210\) −7.68146e15 7.63262e15i −0.00203090 0.00201799i
\(211\) 3.18692e18 0.811169 0.405585 0.914057i \(-0.367068\pi\)
0.405585 + 0.914057i \(0.367068\pi\)
\(212\) 2.63324e18i 0.645363i
\(213\) −1.47926e18 + 1.48872e18i −0.349146 + 0.351380i
\(214\) 4.46253e18 1.01454
\(215\) 1.48806e16i 0.00325920i
\(216\) −1.19588e18 1.17321e18i −0.252381 0.247597i
\(217\) 1.18065e18 0.240128
\(218\) 5.80723e18i 1.13846i
\(219\) −1.29878e17 1.29052e17i −0.0245461 0.0243900i
\(220\) −1.16260e16 −0.00211860
\(221\) 2.43604e17i 0.0428102i
\(222\) −3.33952e18 + 3.36089e18i −0.566056 + 0.569679i
\(223\) −7.13227e17 −0.116624 −0.0583121 0.998298i \(-0.518572\pi\)
−0.0583121 + 0.998298i \(0.518572\pi\)
\(224\) 1.15093e18i 0.181578i
\(225\) 4.18969e16 + 6.56817e18i 0.00637855 + 0.999964i
\(226\) −4.75730e18 −0.699026
\(227\) 9.97663e18i 1.41507i −0.706680 0.707534i \(-0.749808\pi\)
0.706680 0.707534i \(-0.250192\pi\)
\(228\) 6.59223e17 + 6.55032e17i 0.0902722 + 0.0896982i
\(229\) −7.93251e18 −1.04888 −0.524441 0.851447i \(-0.675726\pi\)
−0.524441 + 0.851447i \(0.675726\pi\)
\(230\) 2.78672e16i 0.00355853i
\(231\) 6.30969e18 6.35007e18i 0.778238 0.783218i
\(232\) 4.41884e18 0.526507
\(233\) 8.97259e16i 0.0103293i −0.999987 0.00516465i \(-0.998356\pi\)
0.999987 0.00516465i \(-0.00164397\pi\)
\(234\) −1.12670e19 + 7.18698e16i −1.25338 + 0.00799502i
\(235\) 4.45409e16 0.00478868
\(236\) 5.34405e18i 0.555360i
\(237\) 1.97024e18 + 1.95771e18i 0.197939 + 0.196680i
\(238\) 1.80584e17 0.0175414
\(239\) 1.76298e19i 1.65602i −0.560716 0.828008i \(-0.689474\pi\)
0.560716 0.828008i \(-0.310526\pi\)
\(240\) −7.64586e15 + 7.69478e15i −0.000694602 + 0.000699047i
\(241\) −7.62250e18 −0.669825 −0.334912 0.942249i \(-0.608707\pi\)
−0.334912 + 0.942249i \(0.608707\pi\)
\(242\) 1.29314e18i 0.109932i
\(243\) 8.73276e18 + 8.45859e18i 0.718292 + 0.695741i
\(244\) −2.80421e18 −0.223199
\(245\) 2.81739e15i 0.000217029i
\(246\) 1.13417e19 + 1.12696e19i 0.845666 + 0.840288i
\(247\) 6.25028e18 0.451153
\(248\) 1.18270e18i 0.0826533i
\(249\) −3.04687e18 + 3.06637e18i −0.206186 + 0.207505i
\(250\) 8.50614e16 0.00557458
\(251\) 1.50703e19i 0.956606i 0.878195 + 0.478303i \(0.158748\pi\)
−0.878195 + 0.478303i \(0.841252\pi\)
\(252\) −5.32772e16 8.35225e18i −0.00327595 0.513570i
\(253\) 2.30371e19 1.37235
\(254\) 9.25286e18i 0.534080i
\(255\) 1.20734e15 + 1.19966e15i 6.75317e−5 + 6.71023e-5i
\(256\) 1.15292e18 0.0625000
\(257\) 3.63998e19i 1.91265i 0.292313 + 0.956323i \(0.405575\pi\)
−0.292313 + 0.956323i \(0.594425\pi\)
\(258\) 8.09000e18 8.14177e18i 0.412089 0.414726i
\(259\) −2.36219e19 −1.16659
\(260\) 7.29564e16i 0.00349363i
\(261\) −3.20674e19 + 2.04551e17i −1.48916 + 0.00949900i
\(262\) 1.94526e19 0.876126
\(263\) 6.06063e18i 0.264772i −0.991198 0.132386i \(-0.957736\pi\)
0.991198 0.132386i \(-0.0422638\pi\)
\(264\) −6.36108e18 6.32063e18i −0.269587 0.267873i
\(265\) −1.23738e17 −0.00508786
\(266\) 4.63334e18i 0.184859i
\(267\) 1.94094e19 1.95336e19i 0.751486 0.756295i
\(268\) −1.68273e19 −0.632319
\(269\) 2.59397e19i 0.946122i −0.881030 0.473061i \(-0.843149\pi\)
0.881030 0.473061i \(-0.156851\pi\)
\(270\) 5.51297e16 5.61949e16i 0.00195198 0.00198970i
\(271\) −1.40860e19 −0.484208 −0.242104 0.970250i \(-0.577838\pi\)
−0.242104 + 0.970250i \(0.577838\pi\)
\(272\) 1.80897e17i 0.00603783i
\(273\) −3.98484e19 3.95950e19i −1.29154 1.28333i
\(274\) −1.06481e19 −0.335173
\(275\) 3.51588e19i 1.07491i
\(276\) 1.51504e19 1.52473e19i 0.449936 0.452815i
\(277\) 6.17005e19 1.78013 0.890063 0.455838i \(-0.150660\pi\)
0.890063 + 0.455838i \(0.150660\pi\)
\(278\) 5.94427e18i 0.166625i
\(279\) 5.47479e16 + 8.58282e18i 0.00149119 + 0.233774i
\(280\) −5.40827e16 −0.00143151
\(281\) 3.85570e19i 0.991866i −0.868361 0.495933i \(-0.834826\pi\)
0.868361 0.495933i \(-0.165174\pi\)
\(282\) 2.43702e19 + 2.42152e19i 0.609349 + 0.605474i
\(283\) −3.08609e19 −0.750096 −0.375048 0.927005i \(-0.622374\pi\)
−0.375048 + 0.927005i \(0.622374\pi\)
\(284\) 1.04816e19i 0.247675i
\(285\) −3.07803e16 + 3.09773e16i −0.000707155 + 0.000711680i
\(286\) −6.03112e19 −1.34732
\(287\) 7.97152e19i 1.73175i
\(288\) −8.36674e18 + 5.33696e16i −0.176773 + 0.00112760i
\(289\) 4.86328e19 0.999417
\(290\) 2.07644e17i 0.00415083i
\(291\) 1.77713e19 + 1.76583e19i 0.345601 + 0.343404i
\(292\) −9.14428e17 −0.0173016
\(293\) 9.45764e18i 0.174117i −0.996203 0.0870586i \(-0.972253\pi\)
0.996203 0.0870586i \(-0.0277468\pi\)
\(294\) 1.53171e18 1.54151e18i 0.0274409 0.0276165i
\(295\) −2.51120e17 −0.00437830
\(296\) 2.36629e19i 0.401545i
\(297\) 4.64549e19 + 4.55743e19i 0.767325 + 0.752781i
\(298\) 3.16356e18 0.0508681
\(299\) 1.44564e20i 2.26303i
\(300\) 2.32701e19 + 2.31222e19i 0.354674 + 0.352419i
\(301\) 5.72243e19 0.849276
\(302\) 6.30838e18i 0.0911722i
\(303\) −1.82850e19 + 1.84020e19i −0.257368 + 0.259015i
\(304\) 4.64138e18 0.0636294
\(305\) 1.31772e17i 0.00175964i
\(306\) 8.37387e15 + 1.31277e18i 0.000108932 + 0.0170772i
\(307\) −3.19426e19 −0.404821 −0.202411 0.979301i \(-0.564878\pi\)
−0.202411 + 0.979301i \(0.564878\pi\)
\(308\) 4.47088e19i 0.552061i
\(309\) −4.55361e19 4.52466e19i −0.547883 0.544400i
\(310\) 5.55757e16 0.000651615
\(311\) 5.04871e19i 0.576895i 0.957496 + 0.288448i \(0.0931391\pi\)
−0.957496 + 0.288448i \(0.906861\pi\)
\(312\) −3.96637e19 + 3.99175e19i −0.441729 + 0.444556i
\(313\) −9.61081e19 −1.04329 −0.521645 0.853163i \(-0.674681\pi\)
−0.521645 + 0.853163i \(0.674681\pi\)
\(314\) 3.36213e19i 0.355777i
\(315\) 3.92477e17 2.50353e15i 0.00404883 2.58266e-5i
\(316\) 1.38718e19 0.139520
\(317\) 1.08055e20i 1.05967i −0.848101 0.529834i \(-0.822254\pi\)
0.848101 0.529834i \(-0.177746\pi\)
\(318\) −6.77021e19 6.72716e19i −0.647418 0.643302i
\(319\) −1.71654e20 −1.60077
\(320\) 5.41765e16i 0.000492732i
\(321\) −1.14004e20 + 1.14734e20i −1.01130 + 1.01777i
\(322\) 1.07165e20 0.927274
\(323\) 7.28248e17i 0.00614694i
\(324\) 6.07148e19 7.74605e17i 0.499959 0.00637852i
\(325\) 2.20631e20 1.77255
\(326\) 1.47426e20i 1.15567i
\(327\) 1.49307e20 + 1.48358e20i 1.14208 + 1.13482i
\(328\) 7.98535e19 0.596078
\(329\) 1.71285e20i 1.24782i
\(330\) 2.97010e17 2.98911e17i 0.00211183 0.00212535i
\(331\) −5.10944e19 −0.354608 −0.177304 0.984156i \(-0.556738\pi\)
−0.177304 + 0.984156i \(0.556738\pi\)
\(332\) 2.15893e19i 0.146263i
\(333\) −1.09537e18 1.71721e20i −0.00724449 1.13572i
\(334\) −2.74690e19 −0.177366
\(335\) 7.90724e17i 0.00498502i
\(336\) −2.95909e19 2.94027e19i −0.182156 0.180998i
\(337\) 5.25258e19 0.315743 0.157871 0.987460i \(-0.449537\pi\)
0.157871 + 0.987460i \(0.449537\pi\)
\(338\) 2.58015e20i 1.51465i
\(339\) 1.21535e20 1.22313e20i 0.696793 0.701252i
\(340\) 8.50048e15 4.76005e−5
\(341\) 4.59430e19i 0.251295i
\(342\) −3.36824e19 + 2.14853e17i −0.179968 + 0.00114797i
\(343\) −1.85950e20 −0.970607
\(344\) 5.73236e19i 0.292325i
\(345\) 7.16480e17 + 7.11924e17i 0.00356986 + 0.00354716i
\(346\) 7.55247e19 0.367689
\(347\) 3.17727e20i 1.51154i 0.654839 + 0.755768i \(0.272736\pi\)
−0.654839 + 0.755768i \(0.727264\pi\)
\(348\) −1.12888e20 + 1.13611e20i −0.524825 + 0.528183i
\(349\) −7.84605e19 −0.356490 −0.178245 0.983986i \(-0.557042\pi\)
−0.178245 + 0.983986i \(0.557042\pi\)
\(350\) 1.63554e20i 0.726301i
\(351\) 2.85991e20 2.91517e20i 1.24135 1.26534i
\(352\) −4.47863e19 −0.190022
\(353\) 2.44715e20i 1.01499i −0.861653 0.507497i \(-0.830571\pi\)
0.861653 0.507497i \(-0.169429\pi\)
\(354\) −1.37398e20 1.36525e20i −0.557128 0.553586i
\(355\) −4.92537e17 −0.00195260
\(356\) 1.37529e20i 0.533084i
\(357\) −4.61339e18 + 4.64292e18i −0.0174854 + 0.0175973i
\(358\) 2.50941e19 0.0930051
\(359\) 1.77162e20i 0.642119i −0.947059 0.321060i \(-0.895961\pi\)
0.947059 0.321060i \(-0.104039\pi\)
\(360\) −2.50787e15 3.93158e17i −8.88965e−6 0.00139363i
\(361\) −2.69756e20 −0.935221
\(362\) 1.17174e20i 0.397340i
\(363\) 3.32473e19 + 3.30359e19i 0.110282 + 0.109581i
\(364\) −2.80559e20 −0.910361
\(365\) 4.29695e16i 0.000136401i
\(366\) 7.16393e19 7.20977e19i 0.222486 0.223910i
\(367\) 3.41194e20 1.03675 0.518373 0.855154i \(-0.326538\pi\)
0.518373 + 0.855154i \(0.326538\pi\)
\(368\) 1.07351e20i 0.319172i
\(369\) −5.79495e20 + 3.69647e18i −1.68593 + 0.0107542i
\(370\) −1.11193e18 −0.00316567
\(371\) 4.75843e20i 1.32578i
\(372\) 3.04078e19 + 3.02144e19i 0.0829165 + 0.0823893i
\(373\) 4.31198e20 1.15082 0.575409 0.817866i \(-0.304843\pi\)
0.575409 + 0.817866i \(0.304843\pi\)
\(374\) 7.02713e18i 0.0183571i
\(375\) −2.17307e18 + 2.18697e18i −0.00555678 + 0.00559233i
\(376\) 1.71583e20 0.429507
\(377\) 1.07717e21i 2.63970i
\(378\) 2.16102e20 + 2.12006e20i 0.518470 + 0.508643i
\(379\) −9.46277e19 −0.222282 −0.111141 0.993805i \(-0.535451\pi\)
−0.111141 + 0.993805i \(0.535451\pi\)
\(380\) 2.18101e17i 0.000501636i
\(381\) 2.37896e20 + 2.36383e20i 0.535781 + 0.532374i
\(382\) 1.35118e20 0.297993
\(383\) 1.63118e20i 0.352300i −0.984363 0.176150i \(-0.943636\pi\)
0.984363 0.176150i \(-0.0563643\pi\)
\(384\) −2.94537e19 + 2.96422e19i −0.0623003 + 0.0626990i
\(385\) 2.10089e18 0.00435229
\(386\) 4.00548e19i 0.0812749i
\(387\) 2.65355e18 + 4.15996e20i 0.00527399 + 0.826803i
\(388\) 1.25122e20 0.243601
\(389\) 7.07561e20i 1.34948i −0.738055 0.674741i \(-0.764255\pi\)
0.738055 0.674741i \(-0.235745\pi\)
\(390\) −1.87575e18 1.86382e18i −0.00350475 0.00348247i
\(391\) −1.68438e19 −0.0308337
\(392\) 1.08533e19i 0.0194658i
\(393\) −4.96955e20 + 5.00135e20i −0.873327 + 0.878916i
\(394\) −2.19706e20 −0.378331
\(395\) 6.51843e17i 0.00109993i
\(396\) 3.25014e20 2.07319e18i 0.537452 0.00342829i
\(397\) −7.54229e19 −0.122230 −0.0611152 0.998131i \(-0.519466\pi\)
−0.0611152 + 0.998131i \(0.519466\pi\)
\(398\) 8.32364e20i 1.32205i
\(399\) −1.19126e20 1.18368e20i −0.185448 0.184269i
\(400\) 1.63837e20 0.249996
\(401\) 5.73495e20i 0.857777i 0.903357 + 0.428889i \(0.141095\pi\)
−0.903357 + 0.428889i \(0.858905\pi\)
\(402\) 4.29887e20 4.32638e20i 0.630299 0.634332i
\(403\) 2.88304e20 0.414392
\(404\) 1.29563e20i 0.182570i
\(405\) 3.63991e16 + 2.85303e18i 5.02864e−5 + 0.00394154i
\(406\) −7.98510e20 −1.08161
\(407\) 9.19207e20i 1.22084i
\(408\) 4.65097e18 + 4.62139e18i 0.00605706 + 0.00601855i
\(409\) −8.16315e20 −1.04249 −0.521244 0.853407i \(-0.674532\pi\)
−0.521244 + 0.853407i \(0.674532\pi\)
\(410\) 3.75236e18i 0.00469931i
\(411\) 2.72028e20 2.73769e20i 0.334102 0.336240i
\(412\) −3.20605e20 −0.386182
\(413\) 9.65702e20i 1.14089i
\(414\) 4.96937e18 + 7.79047e20i 0.00575836 + 0.902737i
\(415\) −1.01449e18 −0.00115309
\(416\) 2.81046e20i 0.313351i
\(417\) −1.52830e20 1.51858e20i −0.167156 0.166093i
\(418\) −1.80299e20 −0.193456
\(419\) 9.99098e20i 1.05171i 0.850574 + 0.525855i \(0.176254\pi\)
−0.850574 + 0.525855i \(0.823746\pi\)
\(420\) 1.38165e18 1.39049e18i 0.00142694 0.00143607i
\(421\) 8.93599e20 0.905494 0.452747 0.891639i \(-0.350444\pi\)
0.452747 + 0.891639i \(0.350444\pi\)
\(422\) 5.76894e20i 0.573583i
\(423\) −1.24517e21 + 7.94268e18i −1.21480 + 0.00774897i
\(424\) −4.76668e20 −0.456341
\(425\) 2.57067e19i 0.0241510i
\(426\) −2.69488e20 2.67774e20i −0.248463 0.246883i
\(427\) 5.06738e20 0.458522
\(428\) 8.07803e20i 0.717390i
\(429\) 1.54077e21 1.55063e21i 1.34301 1.35161i
\(430\) 2.69367e18 0.00230460
\(431\) 1.38442e21i 1.16265i 0.813670 + 0.581327i \(0.197466\pi\)
−0.813670 + 0.581327i \(0.802534\pi\)
\(432\) 2.12373e20 2.16477e20i 0.175077 0.178460i
\(433\) 1.26892e21 1.02690 0.513452 0.858118i \(-0.328366\pi\)
0.513452 + 0.858118i \(0.328366\pi\)
\(434\) 2.13721e20i 0.169796i
\(435\) −5.33863e18 5.30468e18i −0.00416404 0.00413757i
\(436\) 1.05122e21 0.805012
\(437\) 4.32170e20i 0.324940i
\(438\) 2.33609e19 2.35104e19i 0.0172463 0.0173567i
\(439\) 7.85494e20 0.569412 0.284706 0.958615i \(-0.408104\pi\)
0.284706 + 0.958615i \(0.408104\pi\)
\(440\) 2.10453e18i 0.00149808i
\(441\) 5.02406e17 + 7.87621e19i 0.000351193 + 0.0550565i
\(442\) 4.40971e19 0.0302714
\(443\) 1.76848e21i 1.19225i 0.802890 + 0.596127i \(0.203295\pi\)
−0.802890 + 0.596127i \(0.796705\pi\)
\(444\) −6.08385e20 6.04517e20i −0.402824 0.400262i
\(445\) 6.46259e18 0.00420268
\(446\) 1.29108e20i 0.0824657i
\(447\) −8.08195e19 + 8.13367e19i −0.0507056 + 0.0510301i
\(448\) −2.08340e20 −0.128395
\(449\) 1.12071e20i 0.0678456i 0.999424 + 0.0339228i \(0.0108000\pi\)
−0.999424 + 0.0339228i \(0.989200\pi\)
\(450\) −1.18897e21 + 7.58415e18i −0.707081 + 0.00451032i
\(451\) −3.10198e21 −1.81229
\(452\) 8.61164e20i 0.494286i
\(453\) −1.62192e20 1.61160e20i −0.0914625 0.0908810i
\(454\) 1.80596e21 1.00060
\(455\) 1.31837e19i 0.00717703i
\(456\) −1.18573e20 + 1.19332e20i −0.0634262 + 0.0638321i
\(457\) −2.74111e21 −1.44078 −0.720389 0.693571i \(-0.756037\pi\)
−0.720389 + 0.693571i \(0.756037\pi\)
\(458\) 1.43594e21i 0.741672i
\(459\) −3.39659e19 3.33221e19i −0.0172402 0.0169134i
\(460\) 5.04450e18 0.00251626
\(461\) 1.29478e21i 0.634728i −0.948304 0.317364i \(-0.897202\pi\)
0.948304 0.317364i \(-0.102798\pi\)
\(462\) 1.14949e21 + 1.14218e21i 0.553819 + 0.550297i
\(463\) −1.59724e21 −0.756351 −0.378176 0.925734i \(-0.623448\pi\)
−0.378176 + 0.925734i \(0.623448\pi\)
\(464\) 7.99895e20i 0.372296i
\(465\) −1.41979e18 + 1.42888e18i −0.000649533 + 0.000653690i
\(466\) 1.62421e19 0.00730391
\(467\) 3.21129e21i 1.41953i −0.704439 0.709765i \(-0.748801\pi\)
0.704439 0.709765i \(-0.251199\pi\)
\(468\) −1.30098e19 2.03955e21i −0.00565333 0.886272i
\(469\) 3.04079e21 1.29898
\(470\) 8.06276e18i 0.00338611i
\(471\) 8.64421e20 + 8.58925e20i 0.356909 + 0.354640i
\(472\) −9.67377e20 −0.392699
\(473\) 2.22679e21i 0.888770i
\(474\) −3.54383e20 + 3.56651e20i −0.139074 + 0.139964i
\(475\) 6.59569e20 0.254514
\(476\) 3.26892e19i 0.0124036i
\(477\) 3.45917e21 2.20653e19i 1.29070 0.00823309i
\(478\) 3.19134e21 1.17098
\(479\) 9.37816e20i 0.338403i 0.985582 + 0.169201i \(0.0541188\pi\)
−0.985582 + 0.169201i \(0.945881\pi\)
\(480\) −1.39290e18 1.38405e18i −0.000494301 0.000491158i
\(481\) −5.76827e21 −2.01319
\(482\) 1.37982e21i 0.473638i
\(483\) −2.73776e21 + 2.75528e21i −0.924312 + 0.930226i
\(484\) 2.34084e20 0.0777334
\(485\) 5.87955e18i 0.00192048i
\(486\) −1.53117e21 + 1.58080e21i −0.491963 + 0.507909i
\(487\) 2.10022e21 0.663793 0.331896 0.943316i \(-0.392312\pi\)
0.331896 + 0.943316i \(0.392312\pi\)
\(488\) 5.07617e20i 0.157826i
\(489\) 3.79039e21 + 3.76629e21i 1.15935 + 1.15197i
\(490\) 5.10002e17 0.000153463
\(491\) 1.84865e21i 0.547271i −0.961833 0.273636i \(-0.911774\pi\)
0.961833 0.273636i \(-0.0882262\pi\)
\(492\) −2.04002e21 + 2.05307e21i −0.594174 + 0.597976i
\(493\) 1.25506e20 0.0359658
\(494\) 1.13142e21i 0.319013i
\(495\) 9.74204e16 + 1.52726e19i 2.70277e−5 + 0.00423712i
\(496\) 2.14091e20 0.0584447
\(497\) 1.89409e21i 0.508803i
\(498\) −5.55072e20 5.51542e20i −0.146728 0.145795i
\(499\) 7.18549e21 1.86918 0.934591 0.355723i \(-0.115765\pi\)
0.934591 + 0.355723i \(0.115765\pi\)
\(500\) 1.53978e19i 0.00394183i
\(501\) 7.01751e20 7.06242e20i 0.176800 0.177931i
\(502\) −2.72802e21 −0.676423
\(503\) 1.44507e21i 0.352652i 0.984332 + 0.176326i \(0.0564212\pi\)
−0.984332 + 0.176326i \(0.943579\pi\)
\(504\) 1.51192e21 9.64420e18i 0.363149 0.00231644i
\(505\) −6.08822e18 −0.00143933
\(506\) 4.17016e21i 0.970395i
\(507\) −6.63371e21 6.59153e21i −1.51947 1.50981i
\(508\) 1.67495e21 0.377652
\(509\) 7.91565e21i 1.75689i −0.477845 0.878444i \(-0.658582\pi\)
0.477845 0.878444i \(-0.341418\pi\)
\(510\) −2.17162e17 + 2.18552e17i −4.74485e−5 + 4.77521e-5i
\(511\) 1.65243e20 0.0355430
\(512\) 2.08701e20i 0.0441942i
\(513\) 8.54962e20 8.71481e20i 0.178241 0.181685i
\(514\) −6.58907e21 −1.35244
\(515\) 1.50654e19i 0.00304455i
\(516\) 1.47382e21 + 1.46445e21i 0.293256 + 0.291391i
\(517\) −6.66528e21 −1.30585
\(518\) 4.27603e21i 0.824902i
\(519\) −1.92943e21 + 1.94178e21i −0.366514 + 0.368859i
\(520\) −1.32065e19 −0.00247037
\(521\) 4.02768e21i 0.741914i 0.928650 + 0.370957i \(0.120970\pi\)
−0.928650 + 0.370957i \(0.879030\pi\)
\(522\) −3.70277e19 5.80482e21i −0.00671680 1.05299i
\(523\) 7.03477e21 1.25671 0.628357 0.777925i \(-0.283728\pi\)
0.628357 + 0.777925i \(0.283728\pi\)
\(524\) 3.52129e21i 0.619515i
\(525\) −4.20505e21 4.17832e21i −0.728613 0.723980i
\(526\) 1.09709e21 0.187222
\(527\) 3.35917e19i 0.00564607i
\(528\) 1.14416e21 1.15148e21i 0.189415 0.190627i
\(529\) −3.86313e21 −0.629933
\(530\) 2.23989e19i 0.00359766i
\(531\) 7.02024e21 4.47806e19i 1.11070 0.00708489i
\(532\) −8.38724e20 −0.130715
\(533\) 1.94658e22i 2.98850i
\(534\) 3.53595e21 + 3.51347e21i 0.534781 + 0.531381i
\(535\) −3.79592e19 −0.00565570
\(536\) 3.04607e21i 0.447117i
\(537\) −6.41079e20 + 6.45181e20i −0.0927080 + 0.0933012i
\(538\) 4.69559e21 0.669009
\(539\) 4.21606e20i 0.0591829i
\(540\) 1.01724e19 + 9.97954e18i 0.00140693 + 0.00138026i
\(541\) 4.29480e21 0.585281 0.292641 0.956222i \(-0.405466\pi\)
0.292641 + 0.956222i \(0.405466\pi\)
\(542\) 2.54983e21i 0.342387i
\(543\) −3.01260e21 2.99344e21i −0.398605 0.396070i
\(544\) 3.27459e19 0.00426939
\(545\) 4.93975e19i 0.00634648i
\(546\) 7.16746e21 7.21333e21i 0.907453 0.913260i
\(547\) −3.57218e21 −0.445692 −0.222846 0.974854i \(-0.571535\pi\)
−0.222846 + 0.974854i \(0.571535\pi\)
\(548\) 1.92752e21i 0.237003i
\(549\) 2.34979e19 + 3.68377e21i 0.00284742 + 0.446389i
\(550\) −6.36442e21 −0.760076
\(551\) 3.22018e21i 0.379024i
\(552\) 2.76006e21 + 2.74251e21i 0.320188 + 0.318153i
\(553\) −2.50671e21 −0.286618
\(554\) 1.11690e22i 1.25874i
\(555\) 2.84066e19 2.85884e19i 0.00315555 0.00317575i
\(556\) −1.07603e21 −0.117822
\(557\) 9.60998e21i 1.03724i −0.855004 0.518622i \(-0.826445\pi\)
0.855004 0.518622i \(-0.173555\pi\)
\(558\) −1.55366e21 + 9.91043e18i −0.165303 + 0.00105443i
\(559\) 1.39737e22 1.46560
\(560\) 9.79001e18i 0.00101223i
\(561\) −1.80671e20 1.79522e20i −0.0184156 0.0182985i
\(562\) 6.97957e21 0.701355
\(563\) 1.05802e22i 1.04816i −0.851669 0.524079i \(-0.824410\pi\)
0.851669 0.524079i \(-0.175590\pi\)
\(564\) −4.38342e21 + 4.41147e21i −0.428135 + 0.430875i
\(565\) 4.04666e19 0.00389681
\(566\) 5.58641e21i 0.530398i
\(567\) −1.09715e22 + 1.39976e20i −1.02708 + 0.0131035i
\(568\) −1.89737e21 −0.175132
\(569\) 9.33207e21i 0.849336i 0.905349 + 0.424668i \(0.139609\pi\)
−0.905349 + 0.424668i \(0.860391\pi\)
\(570\) −5.60749e18 5.57183e18i −0.000503234 0.000500034i
\(571\) −9.20209e21 −0.814324 −0.407162 0.913356i \(-0.633482\pi\)
−0.407162 + 0.913356i \(0.633482\pi\)
\(572\) 1.09175e22i 0.952696i
\(573\) −3.45186e21 + 3.47395e21i −0.297041 + 0.298942i
\(574\) −1.44300e22 −1.22453
\(575\) 1.52553e22i 1.27667i
\(576\) −9.66092e18 1.51454e21i −0.000797331 0.124997i
\(577\) −7.92579e21 −0.645113 −0.322557 0.946550i \(-0.604542\pi\)
−0.322557 + 0.946550i \(0.604542\pi\)
\(578\) 8.80348e21i 0.706694i
\(579\) 1.02983e21 + 1.02328e21i 0.0815337 + 0.0810153i
\(580\) −3.75875e19 −0.00293508
\(581\) 3.90131e21i 0.300470i
\(582\) −3.19649e21 + 3.21695e21i −0.242823 + 0.244377i
\(583\) 1.85166e22 1.38744
\(584\) 1.65529e20i 0.0122341i
\(585\) 9.58395e19 6.11339e17i 0.00698711 4.45692e-5i
\(586\) 1.71202e21 0.123120
\(587\) 8.82724e21i 0.626210i 0.949719 + 0.313105i \(0.101369\pi\)
−0.949719 + 0.313105i \(0.898631\pi\)
\(588\) 2.79043e20 + 2.77269e20i 0.0195278 + 0.0194036i
\(589\) 8.61878e20 0.0595009
\(590\) 4.54576e19i 0.00309592i
\(591\) 5.61283e21 5.64875e21i 0.377122 0.379536i
\(592\) −4.28344e21 −0.283935
\(593\) 2.25118e22i 1.47222i −0.676863 0.736109i \(-0.736661\pi\)
0.676863 0.736109i \(-0.263339\pi\)
\(594\) −8.24983e21 + 8.40923e21i −0.532296 + 0.542581i
\(595\) −1.53609e18 −9.77868e−5
\(596\) 5.72665e20i 0.0359692i
\(597\) 2.14005e22 + 2.12644e22i 1.32626 + 1.31783i
\(598\) 2.61689e22 1.60020
\(599\) 1.26203e22i 0.761472i −0.924684 0.380736i \(-0.875671\pi\)
0.924684 0.380736i \(-0.124329\pi\)
\(600\) −4.18556e21 + 4.21235e21i −0.249198 + 0.250792i
\(601\) 2.45052e22 1.43967 0.719834 0.694146i \(-0.244218\pi\)
0.719834 + 0.694146i \(0.244218\pi\)
\(602\) 1.03587e22i 0.600529i
\(603\) 1.41005e20 + 2.21053e22i 0.00806668 + 1.26461i
\(604\) −1.14194e21 −0.0644685
\(605\) 1.09997e19i 0.000612828i
\(606\) −3.33112e21 3.30994e21i −0.183151 0.181987i
\(607\) −3.45572e22 −1.87512 −0.937561 0.347820i \(-0.886922\pi\)
−0.937561 + 0.347820i \(0.886922\pi\)
\(608\) 8.40179e20i 0.0449928i
\(609\) 2.03996e22 2.05301e22i 1.07816 1.08506i
\(610\) 2.38532e19 0.00124425
\(611\) 4.18264e22i 2.15338i
\(612\) −2.37637e20 + 1.51583e18i −0.0120754 + 7.70265e-5i
\(613\) −3.57279e22 −1.79194 −0.895971 0.444113i \(-0.853519\pi\)
−0.895971 + 0.444113i \(0.853519\pi\)
\(614\) 5.78223e21i 0.286252i
\(615\) −9.64751e19 9.58617e19i −0.00471427 0.00468429i
\(616\) 8.09315e21 0.390366
\(617\) 6.54663e21i 0.311700i −0.987781 0.155850i \(-0.950188\pi\)
0.987781 0.155850i \(-0.0498116\pi\)
\(618\) 8.19051e21 8.24292e21i 0.384949 0.387412i
\(619\) −6.20428e21 −0.287850 −0.143925 0.989589i \(-0.545972\pi\)
−0.143925 + 0.989589i \(0.545972\pi\)
\(620\) 1.00603e19i 0.000460761i
\(621\) −2.01567e22 1.97746e22i −0.911351 0.894076i
\(622\) −9.13914e21 −0.407927
\(623\) 2.48524e22i 1.09513i
\(624\) −7.22584e21 7.17989e21i −0.314349 0.312350i
\(625\) 2.32820e22 0.999953
\(626\) 1.73974e22i 0.737718i
\(627\) 4.60609e21 4.63557e21i 0.192838 0.194072i
\(628\) 6.08611e21 0.251572
\(629\) 6.72087e20i 0.0274297i
\(630\) 4.53187e17 + 7.10460e19i 1.82622e−5 + 0.00286296i
\(631\) −1.70005e22 −0.676436 −0.338218 0.941068i \(-0.609824\pi\)
−0.338218 + 0.941068i \(0.609824\pi\)
\(632\) 2.51106e21i 0.0986554i
\(633\) −1.48322e22 1.47379e22i −0.575410 0.571751i
\(634\) 1.95600e22 0.749299
\(635\) 7.87067e19i 0.00297730i
\(636\) 1.21775e22 1.22554e22i 0.454883 0.457794i
\(637\) 2.64569e21 0.0975940
\(638\) 3.10726e22i 1.13191i
\(639\) 1.37692e22 8.78309e19i 0.495339 0.00315966i
\(640\) −9.80699e18 −0.000348414
\(641\) 7.96286e21i 0.279386i −0.990195 0.139693i \(-0.955388\pi\)
0.990195 0.139693i \(-0.0446116\pi\)
\(642\) −2.07690e22 2.06370e22i −0.719675 0.715099i
\(643\) −4.33342e22 −1.48301 −0.741503 0.670950i \(-0.765887\pi\)
−0.741503 + 0.670950i \(0.765887\pi\)
\(644\) 1.93990e22i 0.655682i
\(645\) −6.88152e19 + 6.92556e19i −0.00229724 + 0.00231194i
\(646\) 1.31827e20 0.00434655
\(647\) 9.44823e21i 0.307692i −0.988095 0.153846i \(-0.950834\pi\)
0.988095 0.153846i \(-0.0491660\pi\)
\(648\) 1.40218e20 + 1.09906e22i 0.00451030 + 0.353525i
\(649\) 3.75786e22 1.19394
\(650\) 3.99384e22i 1.25338i
\(651\) −5.49486e21 5.45993e21i −0.170337 0.169254i
\(652\) 2.66869e22 0.817180
\(653\) 3.94924e22i 1.19456i 0.802032 + 0.597281i \(0.203752\pi\)
−0.802032 + 0.597281i \(0.796248\pi\)
\(654\) −2.68556e22 + 2.70275e22i −0.802441 + 0.807575i
\(655\) −1.65467e20 −0.00488407
\(656\) 1.44550e22i 0.421491i
\(657\) 7.66246e18 + 1.20124e21i 0.000220722 + 0.0346025i
\(658\) −3.10060e22 −0.882345
\(659\) 1.45144e22i 0.408054i −0.978965 0.204027i \(-0.934597\pi\)
0.978965 0.204027i \(-0.0654030\pi\)
\(660\) 5.41086e19 + 5.37646e19i 0.00150285 + 0.00149329i
\(661\) −2.68605e21 −0.0737061 −0.0368530 0.999321i \(-0.511733\pi\)
−0.0368530 + 0.999321i \(0.511733\pi\)
\(662\) 9.24907e21i 0.250746i
\(663\) −1.12655e21 + 1.13376e21i −0.0301747 + 0.0303677i
\(664\) −3.90808e21 −0.103423
\(665\) 3.94121e19i 0.00103052i
\(666\) 3.10849e22 1.98284e20i 0.803074 0.00512263i
\(667\) 7.44801e22 1.90123
\(668\) 4.97242e21i 0.125417i
\(669\) 3.31943e21 + 3.29832e21i 0.0827283 + 0.0822023i
\(670\) 1.43136e20 0.00352494
\(671\) 1.97188e22i 0.479845i
\(672\) 5.32246e21 5.35652e21i 0.127985 0.128804i
\(673\) 4.46588e22 1.06117 0.530587 0.847630i \(-0.321971\pi\)
0.530587 + 0.847630i \(0.321971\pi\)
\(674\) 9.50819e21i 0.223264i
\(675\) 3.01796e22 3.07627e22i 0.700298 0.713829i
\(676\) −4.67058e22 −1.07102
\(677\) 1.65298e22i 0.374592i 0.982304 + 0.187296i \(0.0599723\pi\)
−0.982304 + 0.187296i \(0.940028\pi\)
\(678\) 2.21410e22 + 2.20002e22i 0.495860 + 0.492707i
\(679\) −2.26103e22 −0.500435
\(680\) 1.53875e18i 3.36587e-5i
\(681\) −4.61370e22 + 4.64323e22i −0.997407 + 1.00379i
\(682\) −8.31657e21 −0.177692
\(683\) 6.32799e22i 1.33629i −0.744032 0.668144i \(-0.767089\pi\)
0.744032 0.668144i \(-0.232911\pi\)
\(684\) −3.88925e19 6.09717e21i −0.000811740 0.127256i
\(685\) 9.05751e19 0.00186846
\(686\) 3.36606e22i 0.686323i
\(687\) 3.69187e22 + 3.66840e22i 0.744034 + 0.739303i
\(688\) 1.03767e22 0.206705
\(689\) 1.16197e23i 2.28792i
\(690\) −1.28872e20 + 1.29697e20i −0.00250822 + 0.00252427i
\(691\) −6.70574e22 −1.29010 −0.645049 0.764141i \(-0.723163\pi\)
−0.645049 + 0.764141i \(0.723163\pi\)
\(692\) 1.36714e22i 0.259995i
\(693\) −5.87319e22 + 3.74638e20i −1.10410 + 0.00704280i
\(694\) −5.75148e22 −1.06882
\(695\) 5.05632e19i 0.000928872i
\(696\) −2.05657e22 2.04349e22i −0.373482 0.371107i
\(697\) 2.26804e21 0.0407183
\(698\) 1.42029e22i 0.252077i
\(699\) −4.14938e20 + 4.17593e20i −0.00728058 + 0.00732717i
\(700\) −2.96064e22 −0.513572
\(701\) 5.60289e22i 0.960877i 0.877028 + 0.480439i \(0.159522\pi\)
−0.877028 + 0.480439i \(0.840478\pi\)
\(702\) 5.27702e22 + 5.17699e22i 0.894729 + 0.877769i
\(703\) −1.72441e22 −0.289066
\(704\) 8.10718e21i 0.134366i
\(705\) −2.07298e20 2.05980e20i −0.00339689 0.00337529i
\(706\) 4.42982e22 0.717709
\(707\) 2.34127e22i 0.375057i
\(708\) 2.47136e22 2.48718e22i 0.391444 0.393949i
\(709\) 6.28170e21 0.0983801 0.0491900 0.998789i \(-0.484336\pi\)
0.0491900 + 0.998789i \(0.484336\pi\)
\(710\) 8.91588e19i 0.00138069i
\(711\) −1.16239e20 1.82227e22i −0.00177990 0.279034i
\(712\) 2.48955e22 0.376947
\(713\) 1.99345e22i 0.298463i
\(714\) −8.40457e20 8.35113e20i −0.0124431 0.0123640i
\(715\) 5.13019e20 0.00751078
\(716\) 4.54251e21i 0.0657645i
\(717\) −8.15292e22 + 8.20510e22i −1.16724 + 1.17471i
\(718\) 3.20698e22 0.454047
\(719\) 7.38151e21i 0.103351i −0.998664 0.0516755i \(-0.983544\pi\)
0.998664 0.0516755i \(-0.0164561\pi\)
\(720\) 7.11692e19 4.53972e17i 0.000985444 6.28593e-6i
\(721\) 5.79352e22 0.793342
\(722\) 4.88311e22i 0.661301i
\(723\) 3.54759e22 + 3.52503e22i 0.475146 + 0.472125i
\(724\) −2.12107e22 −0.280961
\(725\) 1.13670e23i 1.48916i
\(726\) −5.98014e21 + 6.01841e21i −0.0774851 + 0.0779810i
\(727\) 1.20780e23 1.54782 0.773909 0.633296i \(-0.218299\pi\)
0.773909 + 0.633296i \(0.218299\pi\)
\(728\) 5.07867e22i 0.643723i
\(729\) −1.52632e21 7.97518e22i −0.0191349 0.999817i
\(730\) 7.77831e18 9.64500e−5
\(731\) 1.62814e21i 0.0199688i
\(732\) 1.30511e22 + 1.29681e22i 0.158328 + 0.157321i
\(733\) −1.21835e23 −1.46198 −0.730989 0.682389i \(-0.760941\pi\)
−0.730989 + 0.682389i \(0.760941\pi\)
\(734\) 6.17627e22i 0.733091i
\(735\) −1.30290e19 + 1.31124e19i −0.000152973 + 0.000153952i
\(736\) 1.94327e22 0.225689
\(737\) 1.18327e23i 1.35939i
\(738\) −6.69133e20 1.04900e23i −0.00760434 1.19213i
\(739\) 4.92047e22 0.553161 0.276580 0.960991i \(-0.410799\pi\)
0.276580 + 0.960991i \(0.410799\pi\)
\(740\) 2.01281e20i 0.00223846i
\(741\) −2.90894e22 2.89045e22i −0.320029 0.317994i
\(742\) 8.61368e22 0.937470
\(743\) 1.09751e23i 1.18168i 0.806790 + 0.590838i \(0.201203\pi\)
−0.806790 + 0.590838i \(0.798797\pi\)
\(744\) −5.46939e21 + 5.50439e21i −0.0582580 + 0.0586308i
\(745\) −2.69099e19 −0.000283571
\(746\) 7.80552e22i 0.813751i
\(747\) 2.83609e22 1.80908e20i 0.292519 0.00186592i
\(748\) −1.27205e21 −0.0129805
\(749\) 1.45975e23i 1.47375i
\(750\) −3.95884e20 3.93367e20i −0.00395438 0.00392923i
\(751\) −1.90969e22 −0.188731 −0.0943656 0.995538i \(-0.530082\pi\)
−0.0943656 + 0.995538i \(0.530082\pi\)
\(752\) 3.10598e22i 0.303707i
\(753\) 6.96929e22 7.01389e22i 0.674262 0.678577i
\(754\) −1.94989e23 −1.86655
\(755\) 5.36604e19i 0.000508251i
\(756\) −3.83771e22 + 3.91186e22i −0.359665 + 0.366614i
\(757\) 8.80933e22 0.816913 0.408456 0.912778i \(-0.366067\pi\)
0.408456 + 0.912778i \(0.366067\pi\)
\(758\) 1.71294e22i 0.157177i
\(759\) −1.07217e23 1.06535e23i −0.973485 0.967295i
\(760\) −3.94805e19 −0.000354710
\(761\) 3.94699e22i 0.350904i 0.984488 + 0.175452i \(0.0561387\pi\)
−0.984488 + 0.175452i \(0.943861\pi\)
\(762\) −4.27899e22 + 4.30638e22i −0.376445 + 0.378854i
\(763\) −1.89962e23 −1.65375
\(764\) 2.44590e22i 0.210713i
\(765\) −7.12299e16 1.11667e19i −6.07255e−7 9.51992e-5i
\(766\) 2.95275e22 0.249113
\(767\) 2.35816e23i 1.96884i
\(768\) −5.36581e21 5.33169e21i −0.0443349 0.0440530i
\(769\) −1.37597e23 −1.12512 −0.562561 0.826756i \(-0.690184\pi\)
−0.562561 + 0.826756i \(0.690184\pi\)
\(770\) 3.80302e20i 0.00307753i
\(771\) 1.68331e23 1.69408e23i 1.34812 1.35675i
\(772\) 7.25070e21 0.0574700
\(773\)