Properties

Label 6.7.b.a.5.1
Level $6$
Weight $7$
Character 6.5
Analytic conductor $1.380$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.38032450172\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
Defining polynomial: \(x^{2} + 2\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.1
Root \(-1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.7.b.a.5.2

$q$-expansion

\(f(q)\) \(=\) \(q-5.65685i q^{2} +(21.0000 - 16.9706i) q^{3} -32.0000 q^{4} +169.706i q^{5} +(-96.0000 - 118.794i) q^{6} +2.00000 q^{7} +181.019i q^{8} +(153.000 - 712.764i) q^{9} +O(q^{10})\) \(q-5.65685i q^{2} +(21.0000 - 16.9706i) q^{3} -32.0000 q^{4} +169.706i q^{5} +(-96.0000 - 118.794i) q^{6} +2.00000 q^{7} +181.019i q^{8} +(153.000 - 712.764i) q^{9} +960.000 q^{10} +33.9411i q^{11} +(-672.000 + 543.058i) q^{12} -2950.00 q^{13} -11.3137i q^{14} +(2880.00 + 3563.82i) q^{15} +1024.00 q^{16} -4480.23i q^{17} +(-4032.00 - 865.499i) q^{18} +5258.00 q^{19} -5430.58i q^{20} +(42.0000 - 33.9411i) q^{21} +192.000 q^{22} +10250.2i q^{23} +(3072.00 + 3801.41i) q^{24} -13175.0 q^{25} +16687.7i q^{26} +(-8883.00 - 17564.5i) q^{27} -64.0000 q^{28} -2206.17i q^{29} +(20160.0 - 16291.7i) q^{30} +22898.0 q^{31} -5792.62i q^{32} +(576.000 + 712.764i) q^{33} -25344.0 q^{34} +339.411i q^{35} +(-4896.00 + 22808.4i) q^{36} +34058.0 q^{37} -29743.7i q^{38} +(-61950.0 + 50063.2i) q^{39} -30720.0 q^{40} +16766.9i q^{41} +(-192.000 - 237.588i) q^{42} -6406.00 q^{43} -1086.12i q^{44} +(120960. + 25965.0i) q^{45} +57984.0 q^{46} -179888. i q^{47} +(21504.0 - 17377.9i) q^{48} -117645. q^{49} +74529.1i q^{50} +(-76032.0 - 94084.8i) q^{51} +94400.0 q^{52} +192548. i q^{53} +(-99360.0 + 50249.8i) q^{54} -5760.00 q^{55} +362.039i q^{56} +(110418. - 89231.2i) q^{57} -12480.0 q^{58} +326819. i q^{59} +(-92160.0 - 114042. i) q^{60} -62566.0 q^{61} -129531. i q^{62} +(306.000 - 1425.53i) q^{63} -32768.0 q^{64} -500632. i q^{65} +(4032.00 - 3258.35i) q^{66} +438698. q^{67} +143367. i q^{68} +(173952. + 215255. i) q^{69} +1920.00 q^{70} +68221.7i q^{71} +(129024. + 27696.0i) q^{72} -730510. q^{73} -192661. i q^{74} +(-276675. + 223587. i) q^{75} -168256. q^{76} +67.8823i q^{77} +(283200. + 350442. i) q^{78} +340562. q^{79} +173779. i q^{80} +(-484623. - 218106. i) q^{81} +94848.0 q^{82} -496253. i q^{83} +(-1344.00 + 1086.12i) q^{84} +760320. q^{85} +36237.8i q^{86} +(-37440.0 - 46329.6i) q^{87} -6144.00 q^{88} +386725. i q^{89} +(146880. - 684253. i) q^{90} -5900.00 q^{91} -328007. i q^{92} +(480858. - 388592. i) q^{93} -1.01760e6 q^{94} +892312. i q^{95} +(-98304.0 - 121645. i) q^{96} -281086. q^{97} +665501. i q^{98} +(24192.0 + 5192.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9} + O(q^{10}) \) \( 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9} + 1920 q^{10} - 1344 q^{12} - 5900 q^{13} + 5760 q^{15} + 2048 q^{16} - 8064 q^{18} + 10516 q^{19} + 84 q^{21} + 384 q^{22} + 6144 q^{24} - 26350 q^{25} - 17766 q^{27} - 128 q^{28} + 40320 q^{30} + 45796 q^{31} + 1152 q^{33} - 50688 q^{34} - 9792 q^{36} + 68116 q^{37} - 123900 q^{39} - 61440 q^{40} - 384 q^{42} - 12812 q^{43} + 241920 q^{45} + 115968 q^{46} + 43008 q^{48} - 235290 q^{49} - 152064 q^{51} + 188800 q^{52} - 198720 q^{54} - 11520 q^{55} + 220836 q^{57} - 24960 q^{58} - 184320 q^{60} - 125132 q^{61} + 612 q^{63} - 65536 q^{64} + 8064 q^{66} + 877396 q^{67} + 347904 q^{69} + 3840 q^{70} + 258048 q^{72} - 1461020 q^{73} - 553350 q^{75} - 336512 q^{76} + 566400 q^{78} + 681124 q^{79} - 969246 q^{81} + 189696 q^{82} - 2688 q^{84} + 1520640 q^{85} - 74880 q^{87} - 12288 q^{88} + 293760 q^{90} - 11800 q^{91} + 961716 q^{93} - 2035200 q^{94} - 196608 q^{96} - 562172 q^{97} + 48384 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.65685i 0.707107i
\(3\) 21.0000 16.9706i 0.777778 0.628539i
\(4\) −32.0000 −0.500000
\(5\) 169.706i 1.35765i 0.734302 + 0.678823i \(0.237509\pi\)
−0.734302 + 0.678823i \(0.762491\pi\)
\(6\) −96.0000 118.794i −0.444444 0.549972i
\(7\) 2.00000 0.00583090 0.00291545 0.999996i \(-0.499072\pi\)
0.00291545 + 0.999996i \(0.499072\pi\)
\(8\) 181.019i 0.353553i
\(9\) 153.000 712.764i 0.209877 0.977728i
\(10\) 960.000 0.960000
\(11\) 33.9411i 0.0255005i 0.999919 + 0.0127502i \(0.00405864\pi\)
−0.999919 + 0.0127502i \(0.995941\pi\)
\(12\) −672.000 + 543.058i −0.388889 + 0.314270i
\(13\) −2950.00 −1.34274 −0.671370 0.741122i \(-0.734294\pi\)
−0.671370 + 0.741122i \(0.734294\pi\)
\(14\) 11.3137i 0.00412307i
\(15\) 2880.00 + 3563.82i 0.853333 + 1.05595i
\(16\) 1024.00 0.250000
\(17\) 4480.23i 0.911913i −0.890002 0.455956i \(-0.849297\pi\)
0.890002 0.455956i \(-0.150703\pi\)
\(18\) −4032.00 865.499i −0.691358 0.148405i
\(19\) 5258.00 0.766584 0.383292 0.923627i \(-0.374790\pi\)
0.383292 + 0.923627i \(0.374790\pi\)
\(20\) 5430.58i 0.678823i
\(21\) 42.0000 33.9411i 0.00453515 0.00366495i
\(22\) 192.000 0.0180316
\(23\) 10250.2i 0.842461i 0.906954 + 0.421230i \(0.138402\pi\)
−0.906954 + 0.421230i \(0.861598\pi\)
\(24\) 3072.00 + 3801.41i 0.222222 + 0.274986i
\(25\) −13175.0 −0.843200
\(26\) 16687.7i 0.949461i
\(27\) −8883.00 17564.5i −0.451303 0.892371i
\(28\) −64.0000 −0.00291545
\(29\) 2206.17i 0.0904577i −0.998977 0.0452289i \(-0.985598\pi\)
0.998977 0.0452289i \(-0.0144017\pi\)
\(30\) 20160.0 16291.7i 0.746667 0.603398i
\(31\) 22898.0 0.768621 0.384311 0.923204i \(-0.374439\pi\)
0.384311 + 0.923204i \(0.374439\pi\)
\(32\) 5792.62i 0.176777i
\(33\) 576.000 + 712.764i 0.0160280 + 0.0198337i
\(34\) −25344.0 −0.644820
\(35\) 339.411i 0.00791630i
\(36\) −4896.00 + 22808.4i −0.104938 + 0.488864i
\(37\) 34058.0 0.672379 0.336189 0.941794i \(-0.390862\pi\)
0.336189 + 0.941794i \(0.390862\pi\)
\(38\) 29743.7i 0.542057i
\(39\) −61950.0 + 50063.2i −1.04435 + 0.843965i
\(40\) −30720.0 −0.480000
\(41\) 16766.9i 0.243277i 0.992574 + 0.121639i \(0.0388149\pi\)
−0.992574 + 0.121639i \(0.961185\pi\)
\(42\) −192.000 237.588i −0.00259151 0.00320683i
\(43\) −6406.00 −0.0805715 −0.0402858 0.999188i \(-0.512827\pi\)
−0.0402858 + 0.999188i \(0.512827\pi\)
\(44\) 1086.12i 0.0127502i
\(45\) 120960. + 25965.0i 1.32741 + 0.284938i
\(46\) 57984.0 0.595710
\(47\) 179888.i 1.73264i −0.499489 0.866320i \(-0.666479\pi\)
0.499489 0.866320i \(-0.333521\pi\)
\(48\) 21504.0 17377.9i 0.194444 0.157135i
\(49\) −117645. −0.999966
\(50\) 74529.1i 0.596232i
\(51\) −76032.0 94084.8i −0.573173 0.709266i
\(52\) 94400.0 0.671370
\(53\) 192548.i 1.29334i 0.762772 + 0.646668i \(0.223838\pi\)
−0.762772 + 0.646668i \(0.776162\pi\)
\(54\) −99360.0 + 50249.8i −0.631001 + 0.319120i
\(55\) −5760.00 −0.0346206
\(56\) 362.039i 0.00206154i
\(57\) 110418. 89231.2i 0.596232 0.481828i
\(58\) −12480.0 −0.0639633
\(59\) 326819.i 1.59130i 0.605758 + 0.795649i \(0.292870\pi\)
−0.605758 + 0.795649i \(0.707130\pi\)
\(60\) −92160.0 114042.i −0.426667 0.527973i
\(61\) −62566.0 −0.275644 −0.137822 0.990457i \(-0.544010\pi\)
−0.137822 + 0.990457i \(0.544010\pi\)
\(62\) 129531.i 0.543497i
\(63\) 306.000 1425.53i 0.00122377 0.00570104i
\(64\) −32768.0 −0.125000
\(65\) 500632.i 1.82296i
\(66\) 4032.00 3258.35i 0.0140245 0.0113335i
\(67\) 438698. 1.45862 0.729308 0.684185i \(-0.239842\pi\)
0.729308 + 0.684185i \(0.239842\pi\)
\(68\) 143367.i 0.455956i
\(69\) 173952. + 215255.i 0.529520 + 0.655247i
\(70\) 1920.00 0.00559767
\(71\) 68221.7i 0.190611i 0.995448 + 0.0953053i \(0.0303827\pi\)
−0.995448 + 0.0953053i \(0.969617\pi\)
\(72\) 129024. + 27696.0i 0.345679 + 0.0742026i
\(73\) −730510. −1.87784 −0.938918 0.344141i \(-0.888170\pi\)
−0.938918 + 0.344141i \(0.888170\pi\)
\(74\) 192661.i 0.475444i
\(75\) −276675. + 223587.i −0.655822 + 0.529984i
\(76\) −168256. −0.383292
\(77\) 67.8823i 0.000148691i
\(78\) 283200. + 350442.i 0.596773 + 0.738469i
\(79\) 340562. 0.690740 0.345370 0.938467i \(-0.387753\pi\)
0.345370 + 0.938467i \(0.387753\pi\)
\(80\) 173779.i 0.339411i
\(81\) −484623. 218106.i −0.911904 0.410404i
\(82\) 94848.0 0.172023
\(83\) 496253.i 0.867899i −0.900937 0.433949i \(-0.857120\pi\)
0.900937 0.433949i \(-0.142880\pi\)
\(84\) −1344.00 + 1086.12i −0.00226757 + 0.00183248i
\(85\) 760320. 1.23805
\(86\) 36237.8i 0.0569727i
\(87\) −37440.0 46329.6i −0.0568562 0.0703560i
\(88\) −6144.00 −0.00901578
\(89\) 386725.i 0.548570i 0.961648 + 0.274285i \(0.0884412\pi\)
−0.961648 + 0.274285i \(0.911559\pi\)
\(90\) 146880. 684253.i 0.201481 0.938619i
\(91\) −5900.00 −0.00782939
\(92\) 328007.i 0.421230i
\(93\) 480858. 388592.i 0.597817 0.483109i
\(94\) −1.01760e6 −1.22516
\(95\) 892312.i 1.04075i
\(96\) −98304.0 121645.i −0.111111 0.137493i
\(97\) −281086. −0.307981 −0.153991 0.988072i \(-0.549213\pi\)
−0.153991 + 0.988072i \(0.549213\pi\)
\(98\) 665501.i 0.707083i
\(99\) 24192.0 + 5192.99i 0.0249325 + 0.00535195i
\(100\) 421600. 0.421600
\(101\) 945362.i 0.917559i 0.888550 + 0.458780i \(0.151713\pi\)
−0.888550 + 0.458780i \(0.848287\pi\)
\(102\) −532224. + 430102.i −0.501527 + 0.405295i
\(103\) −865726. −0.792262 −0.396131 0.918194i \(-0.629647\pi\)
−0.396131 + 0.918194i \(0.629647\pi\)
\(104\) 534007.i 0.474730i
\(105\) 5760.00 + 7127.64i 0.00497570 + 0.00615712i
\(106\) 1.08922e6 0.914527
\(107\) 1.47410e6i 1.20330i −0.798759 0.601651i \(-0.794510\pi\)
0.798759 0.601651i \(-0.205490\pi\)
\(108\) 284256. + 562065.i 0.225652 + 0.446185i
\(109\) 650810. 0.502545 0.251272 0.967916i \(-0.419151\pi\)
0.251272 + 0.967916i \(0.419151\pi\)
\(110\) 32583.5i 0.0244805i
\(111\) 715218. 577983.i 0.522961 0.422616i
\(112\) 2048.00 0.00145773
\(113\) 1.74417e6i 1.20879i −0.796683 0.604397i \(-0.793414\pi\)
0.796683 0.604397i \(-0.206586\pi\)
\(114\) −504768. 624619.i −0.340704 0.421600i
\(115\) −1.73952e6 −1.14376
\(116\) 70597.5i 0.0452289i
\(117\) −451350. + 2.10265e6i −0.281810 + 1.31283i
\(118\) 1.84877e6 1.12522
\(119\) 8960.46i 0.00531728i
\(120\) −645120. + 521336.i −0.373333 + 0.301699i
\(121\) 1.77041e6 0.999350
\(122\) 353927.i 0.194910i
\(123\) 284544. + 352105.i 0.152909 + 0.189216i
\(124\) −732736. −0.384311
\(125\) 415779.i 0.212879i
\(126\) −8064.00 1731.00i −0.00403124 0.000865336i
\(127\) −2.28053e6 −1.11333 −0.556665 0.830737i \(-0.687919\pi\)
−0.556665 + 0.830737i \(0.687919\pi\)
\(128\) 185364.i 0.0883883i
\(129\) −134526. + 108713.i −0.0626667 + 0.0506424i
\(130\) −2.83200e6 −1.28903
\(131\) 1.07196e6i 0.476832i 0.971163 + 0.238416i \(0.0766282\pi\)
−0.971163 + 0.238416i \(0.923372\pi\)
\(132\) −18432.0 22808.4i −0.00801402 0.00991685i
\(133\) 10516.0 0.00446988
\(134\) 2.48165e6i 1.03140i
\(135\) 2.98080e6 1.50750e6i 1.21152 0.612709i
\(136\) 811008. 0.322410
\(137\) 2.78338e6i 1.08246i 0.840876 + 0.541228i \(0.182040\pi\)
−0.840876 + 0.541228i \(0.817960\pi\)
\(138\) 1.21766e6 984021.i 0.463330 0.374427i
\(139\) 4.57395e6 1.70313 0.851563 0.524253i \(-0.175655\pi\)
0.851563 + 0.524253i \(0.175655\pi\)
\(140\) 10861.2i 0.00395815i
\(141\) −3.05280e6 3.77765e6i −1.08903 1.34761i
\(142\) 385920. 0.134782
\(143\) 100126.i 0.0342405i
\(144\) 156672. 729870.i 0.0524691 0.244432i
\(145\) 374400. 0.122809
\(146\) 4.13239e6i 1.32783i
\(147\) −2.47054e6 + 1.99650e6i −0.777751 + 0.628518i
\(148\) −1.08986e6 −0.336189
\(149\) 4.46010e6i 1.34830i −0.738595 0.674149i \(-0.764511\pi\)
0.738595 0.674149i \(-0.235489\pi\)
\(150\) 1.26480e6 + 1.56511e6i 0.374756 + 0.463736i
\(151\) −2.20809e6 −0.641338 −0.320669 0.947191i \(-0.603908\pi\)
−0.320669 + 0.947191i \(0.603908\pi\)
\(152\) 951800.i 0.271028i
\(153\) −3.19334e6 685475.i −0.891603 0.191389i
\(154\) 384.000 0.000105140
\(155\) 3.88592e6i 1.04352i
\(156\) 1.98240e6 1.60202e6i 0.522177 0.421983i
\(157\) −1.28887e6 −0.333051 −0.166525 0.986037i \(-0.553255\pi\)
−0.166525 + 0.986037i \(0.553255\pi\)
\(158\) 1.92651e6i 0.488427i
\(159\) 3.26765e6 + 4.04351e6i 0.812913 + 1.00593i
\(160\) 983040. 0.240000
\(161\) 20500.4i 0.00491231i
\(162\) −1.23379e6 + 2.74144e6i −0.290200 + 0.644813i
\(163\) 879914. 0.203178 0.101589 0.994826i \(-0.467607\pi\)
0.101589 + 0.994826i \(0.467607\pi\)
\(164\) 536541.i 0.121639i
\(165\) −120960. + 97750.4i −0.0269271 + 0.0217604i
\(166\) −2.80723e6 −0.613697
\(167\) 5.96760e6i 1.28130i −0.767834 0.640649i \(-0.778665\pi\)
0.767834 0.640649i \(-0.221335\pi\)
\(168\) 6144.00 + 7602.81i 0.00129576 + 0.00160342i
\(169\) 3.87569e6 0.802951
\(170\) 4.30102e6i 0.875436i
\(171\) 804474. 3.74771e6i 0.160888 0.749511i
\(172\) 204992. 0.0402858
\(173\) 418867.i 0.0808981i −0.999182 0.0404490i \(-0.987121\pi\)
0.999182 0.0404490i \(-0.0128788\pi\)
\(174\) −262080. + 211793.i −0.0497492 + 0.0402034i
\(175\) −26350.0 −0.00491662
\(176\) 34755.7i 0.00637512i
\(177\) 5.54630e6 + 6.86320e6i 1.00019 + 1.23768i
\(178\) 2.18765e6 0.387898
\(179\) 302110.i 0.0526752i −0.999653 0.0263376i \(-0.991616\pi\)
0.999653 0.0263376i \(-0.00838448\pi\)
\(180\) −3.87072e6 830879.i −0.663704 0.142469i
\(181\) −6.47618e6 −1.09215 −0.546076 0.837735i \(-0.683879\pi\)
−0.546076 + 0.837735i \(0.683879\pi\)
\(182\) 33375.4i 0.00553621i
\(183\) −1.31389e6 + 1.06178e6i −0.214390 + 0.173253i
\(184\) −1.85549e6 −0.297855
\(185\) 5.77983e6i 0.912852i
\(186\) −2.19821e6 2.72014e6i −0.341610 0.422720i
\(187\) 152064. 0.0232542
\(188\) 5.75641e6i 0.866320i
\(189\) −17766.0 35129.1i −0.00263151 0.00520333i
\(190\) 5.04768e6 0.735921
\(191\) 5.02166e6i 0.720687i 0.932820 + 0.360344i \(0.117341\pi\)
−0.932820 + 0.360344i \(0.882659\pi\)
\(192\) −688128. + 556091.i −0.0972222 + 0.0785674i
\(193\) 3.50093e6 0.486980 0.243490 0.969903i \(-0.421708\pi\)
0.243490 + 0.969903i \(0.421708\pi\)
\(194\) 1.59006e6i 0.217775i
\(195\) −8.49600e6 1.05133e7i −1.14580 1.41786i
\(196\) 3.76464e6 0.499983
\(197\) 4.85423e6i 0.634923i −0.948271 0.317462i \(-0.897170\pi\)
0.948271 0.317462i \(-0.102830\pi\)
\(198\) 29376.0 136851.i 0.00378440 0.0176300i
\(199\) −9.50976e6 −1.20673 −0.603365 0.797465i \(-0.706174\pi\)
−0.603365 + 0.797465i \(0.706174\pi\)
\(200\) 2.38493e6i 0.298116i
\(201\) 9.21266e6 7.44495e6i 1.13448 0.916798i
\(202\) 5.34778e6 0.648812
\(203\) 4412.35i 0.000527450i
\(204\) 2.43302e6 + 3.01071e6i 0.286587 + 0.354633i
\(205\) −2.84544e6 −0.330284
\(206\) 4.89729e6i 0.560214i
\(207\) 7.30598e6 + 1.56828e6i 0.823697 + 0.176813i
\(208\) −3.02080e6 −0.335685
\(209\) 178462.i 0.0195483i
\(210\) 40320.0 32583.5i 0.00435374 0.00351835i
\(211\) 7.06414e6 0.751990 0.375995 0.926622i \(-0.377301\pi\)
0.375995 + 0.926622i \(0.377301\pi\)
\(212\) 6.16154e6i 0.646668i
\(213\) 1.15776e6 + 1.43265e6i 0.119806 + 0.148253i
\(214\) −8.33875e6 −0.850863
\(215\) 1.08713e6i 0.109388i
\(216\) 3.17952e6 1.60799e6i 0.315501 0.159560i
\(217\) 45796.0 0.00448176
\(218\) 3.68154e6i 0.355353i
\(219\) −1.53407e7 + 1.23972e7i −1.46054 + 1.18029i
\(220\) 184320. 0.0173103
\(221\) 1.32167e7i 1.22446i
\(222\) −3.26957e6 4.04588e6i −0.298835 0.369789i
\(223\) 4.66891e6 0.421019 0.210509 0.977592i \(-0.432488\pi\)
0.210509 + 0.977592i \(0.432488\pi\)
\(224\) 11585.2i 0.00103077i
\(225\) −2.01578e6 + 9.39066e6i −0.176968 + 0.824420i
\(226\) −9.86650e6 −0.854747
\(227\) 1.96525e7i 1.68012i −0.542494 0.840059i \(-0.682520\pi\)
0.542494 0.840059i \(-0.317480\pi\)
\(228\) −3.53338e6 + 2.85540e6i −0.298116 + 0.240914i
\(229\) −4.48178e6 −0.373202 −0.186601 0.982436i \(-0.559747\pi\)
−0.186601 + 0.982436i \(0.559747\pi\)
\(230\) 9.84021e6i 0.808762i
\(231\) 1152.00 + 1425.53i 9.34580e−5 + 0.000115648i
\(232\) 399360. 0.0319816
\(233\) 2.29286e6i 0.181263i −0.995884 0.0906316i \(-0.971111\pi\)
0.995884 0.0906316i \(-0.0288886\pi\)
\(234\) 1.18944e7 + 2.55322e6i 0.928314 + 0.199270i
\(235\) 3.05280e7 2.35231
\(236\) 1.04582e7i 0.795649i
\(237\) 7.15180e6 5.77953e6i 0.537243 0.434158i
\(238\) −50688.0 −0.00375988
\(239\) 2.64564e6i 0.193793i 0.995294 + 0.0968964i \(0.0308915\pi\)
−0.995294 + 0.0968964i \(0.969108\pi\)
\(240\) 2.94912e6 + 3.64935e6i 0.213333 + 0.263987i
\(241\) −6.99581e6 −0.499789 −0.249894 0.968273i \(-0.580396\pi\)
−0.249894 + 0.968273i \(0.580396\pi\)
\(242\) 1.00149e7i 0.706647i
\(243\) −1.38785e7 + 3.64411e6i −0.967214 + 0.253964i
\(244\) 2.00211e6 0.137822
\(245\) 1.99650e7i 1.35760i
\(246\) 1.99181e6 1.60962e6i 0.133796 0.108123i
\(247\) −1.55111e7 −1.02932
\(248\) 4.14498e6i 0.271749i
\(249\) −8.42170e6 1.04213e7i −0.545508 0.675032i
\(250\) 2.35200e6 0.150528
\(251\) 2.84990e7i 1.80223i 0.433585 + 0.901113i \(0.357248\pi\)
−0.433585 + 0.901113i \(0.642752\pi\)
\(252\) −9792.00 + 45616.9i −0.000611885 + 0.00285052i
\(253\) −347904. −0.0214831
\(254\) 1.29006e7i 0.787243i
\(255\) 1.59667e7 1.29031e7i 0.962931 0.778166i
\(256\) 1.04858e6 0.0625000
\(257\) 186812.i 0.0110054i 0.999985 + 0.00550269i \(0.00175157\pi\)
−0.999985 + 0.00550269i \(0.998248\pi\)
\(258\) 614976. + 760994.i 0.0358096 + 0.0443121i
\(259\) 68116.0 0.00392058
\(260\) 1.60202e7i 0.911482i
\(261\) −1.57248e6 337544.i −0.0884430 0.0189850i
\(262\) 6.06394e6 0.337171
\(263\) 8.61541e6i 0.473597i 0.971559 + 0.236798i \(0.0760981\pi\)
−0.971559 + 0.236798i \(0.923902\pi\)
\(264\) −129024. + 104267.i −0.00701227 + 0.00566677i
\(265\) −3.26765e7 −1.75589
\(266\) 59487.5i 0.00316068i
\(267\) 6.56294e6 + 8.12123e6i 0.344798 + 0.426666i
\(268\) −1.40383e7 −0.729308
\(269\) 7.55132e6i 0.387941i 0.981007 + 0.193971i \(0.0621367\pi\)
−0.981007 + 0.193971i \(0.937863\pi\)
\(270\) −8.52768e6 1.68620e7i −0.433251 0.856676i
\(271\) 1.39445e7 0.700642 0.350321 0.936630i \(-0.386073\pi\)
0.350321 + 0.936630i \(0.386073\pi\)
\(272\) 4.58775e6i 0.227978i
\(273\) −123900. + 100126.i −0.00608952 + 0.00492108i
\(274\) 1.57452e7 0.765412
\(275\) 447174.i 0.0215020i
\(276\) −5.56646e6 6.88815e6i −0.264760 0.327624i
\(277\) 2.81293e7 1.32349 0.661744 0.749730i \(-0.269817\pi\)
0.661744 + 0.749730i \(0.269817\pi\)
\(278\) 2.58741e7i 1.20429i
\(279\) 3.50339e6 1.63209e7i 0.161316 0.751503i
\(280\) −61440.0 −0.00279883
\(281\) 2.23430e7i 1.00698i −0.864000 0.503491i \(-0.832049\pi\)
0.864000 0.503491i \(-0.167951\pi\)
\(282\) −2.13696e7 + 1.72692e7i −0.952904 + 0.770063i
\(283\) 1.01418e7 0.447464 0.223732 0.974651i \(-0.428176\pi\)
0.223732 + 0.974651i \(0.428176\pi\)
\(284\) 2.18309e6i 0.0953053i
\(285\) 1.51430e7 + 1.87386e7i 0.654152 + 0.809471i
\(286\) −566400. −0.0242117
\(287\) 33533.8i 0.00141853i
\(288\) −4.12877e6 886271.i −0.172840 0.0371013i
\(289\) 4.06512e6 0.168415
\(290\) 2.11793e6i 0.0868394i
\(291\) −5.90281e6 + 4.77019e6i −0.239541 + 0.193578i
\(292\) 2.33763e7 0.938918
\(293\) 2.78468e7i 1.10706i 0.832828 + 0.553532i \(0.186720\pi\)
−0.832828 + 0.553532i \(0.813280\pi\)
\(294\) 1.12939e7 + 1.39755e7i 0.444429 + 0.549953i
\(295\) −5.54630e7 −2.16042
\(296\) 6.16516e6i 0.237722i
\(297\) 596160. 301499.i 0.0227559 0.0115084i
\(298\) −2.52301e7 −0.953391
\(299\) 3.02381e7i 1.13121i
\(300\) 8.85360e6 7.15479e6i 0.327911 0.264992i
\(301\) −12812.0 −0.000469805
\(302\) 1.24909e7i 0.453494i
\(303\) 1.60433e7 + 1.98526e7i 0.576722 + 0.713657i
\(304\) 5.38419e6 0.191646
\(305\) 1.06178e7i 0.374227i
\(306\) −3.87763e6 + 1.80643e7i −0.135333 + 0.630458i
\(307\) −3.63254e7 −1.25544 −0.627718 0.778440i \(-0.716011\pi\)
−0.627718 + 0.778440i \(0.716011\pi\)
\(308\) 2172.23i 7.43454e-5i
\(309\) −1.81802e7 + 1.46919e7i −0.616204 + 0.497968i
\(310\) 2.19821e7 0.737877
\(311\) 3.59921e7i 1.19654i −0.801296 0.598268i \(-0.795856\pi\)
0.801296 0.598268i \(-0.204144\pi\)
\(312\) −9.06240e6 1.12141e7i −0.298387 0.369235i
\(313\) 4.01099e7 1.30803 0.654016 0.756480i \(-0.273083\pi\)
0.654016 + 0.756480i \(0.273083\pi\)
\(314\) 7.29095e6i 0.235502i
\(315\) 241920. + 51929.9i 0.00773998 + 0.00166145i
\(316\) −1.08980e7 −0.345370
\(317\) 3.94377e7i 1.23804i 0.785377 + 0.619018i \(0.212469\pi\)
−0.785377 + 0.619018i \(0.787531\pi\)
\(318\) 2.28735e7 1.84846e7i 0.711299 0.574816i
\(319\) 74880.0 0.00230671
\(320\) 5.56091e6i 0.169706i
\(321\) −2.50163e7 3.09560e7i −0.756323 0.935902i
\(322\) 115968. 0.00347353
\(323\) 2.35570e7i 0.699058i
\(324\) 1.55079e7 + 6.97938e6i 0.455952 + 0.205202i
\(325\) 3.88662e7 1.13220
\(326\) 4.97755e6i 0.143669i
\(327\) 1.36670e7 1.10446e7i 0.390868 0.315869i
\(328\) −3.03514e6 −0.0860115
\(329\) 359776.i 0.0101029i
\(330\) 552960. + 684253.i 0.0153869 + 0.0190404i
\(331\) 2.78363e7 0.767586 0.383793 0.923419i \(-0.374618\pi\)
0.383793 + 0.923419i \(0.374618\pi\)
\(332\) 1.58801e7i 0.433949i
\(333\) 5.21087e6 2.42753e7i 0.141117 0.657403i
\(334\) −3.37578e7 −0.906014
\(335\) 7.44495e7i 1.98028i
\(336\) 43008.0 34755.7i 0.00113379 0.000916238i
\(337\) −2.37897e7 −0.621582 −0.310791 0.950478i \(-0.600594\pi\)
−0.310791 + 0.950478i \(0.600594\pi\)
\(338\) 2.19242e7i 0.567772i
\(339\) −2.95995e7 3.66275e7i −0.759775 0.940174i
\(340\) −2.43302e7 −0.619027
\(341\) 777184.i 0.0196002i
\(342\) −2.12003e7 4.55079e6i −0.529984 0.113765i
\(343\) −470588. −0.0116616
\(344\) 1.15961e6i 0.0284863i
\(345\) −3.65299e7 + 2.95206e7i −0.889593 + 0.718900i
\(346\) −2.36947e6 −0.0572036
\(347\) 5.34078e7i 1.27825i 0.769103 + 0.639125i \(0.220703\pi\)
−0.769103 + 0.639125i \(0.779297\pi\)
\(348\) 1.19808e6 + 1.48255e6i 0.0284281 + 0.0351780i
\(349\) 4.71677e7 1.10961 0.554803 0.831982i \(-0.312794\pi\)
0.554803 + 0.831982i \(0.312794\pi\)
\(350\) 149058.i 0.00347657i
\(351\) 2.62048e7 + 5.18154e7i 0.605983 + 1.19822i
\(352\) 196608. 0.00450789
\(353\) 1.75443e7i 0.398852i 0.979913 + 0.199426i \(0.0639078\pi\)
−0.979913 + 0.199426i \(0.936092\pi\)
\(354\) 3.88241e7 3.13746e7i 0.875169 0.707243i
\(355\) −1.15776e7 −0.258782
\(356\) 1.23752e7i 0.274285i
\(357\) −152064. 188170.i −0.00334212 0.00413566i
\(358\) −1.70899e6 −0.0372470
\(359\) 6.18249e7i 1.33623i −0.744059 0.668113i \(-0.767102\pi\)
0.744059 0.668113i \(-0.232898\pi\)
\(360\) −4.70016e6 + 2.18961e7i −0.100741 + 0.469309i
\(361\) −1.93993e7 −0.412349
\(362\) 3.66348e7i 0.772269i
\(363\) 3.71786e7 3.00448e7i 0.777272 0.628131i
\(364\) 188800. 0.00391469
\(365\) 1.23972e8i 2.54943i
\(366\) 6.00634e6 + 7.43246e6i 0.122509 + 0.151597i
\(367\) −3.40461e7 −0.688761 −0.344381 0.938830i \(-0.611911\pi\)
−0.344381 + 0.938830i \(0.611911\pi\)
\(368\) 1.04962e7i 0.210615i
\(369\) 1.19508e7 + 2.56534e6i 0.237859 + 0.0510582i
\(370\) 3.26957e7 0.645484
\(371\) 385096.i 0.00754132i
\(372\) −1.53875e7 + 1.24349e7i −0.298908 + 0.241554i
\(373\) −5.15781e7 −0.993892 −0.496946 0.867782i \(-0.665545\pi\)
−0.496946 + 0.867782i \(0.665545\pi\)
\(374\) 860204.i 0.0164432i
\(375\) 7.05600e6 + 8.73135e6i 0.133803 + 0.165572i
\(376\) 3.25632e7 0.612581
\(377\) 6.50821e6i 0.121461i
\(378\) −198720. + 100500.i −0.00367931 + 0.00186076i
\(379\) 4.28828e7 0.787709 0.393855 0.919173i \(-0.371141\pi\)
0.393855 + 0.919173i \(0.371141\pi\)
\(380\) 2.85540e7i 0.520375i
\(381\) −4.78910e7 + 3.87018e7i −0.865923 + 0.699772i
\(382\) 2.84068e7 0.509603
\(383\) 1.51307e7i 0.269316i −0.990892 0.134658i \(-0.957006\pi\)
0.990892 0.134658i \(-0.0429936\pi\)
\(384\) 3.14573e6 + 3.89264e6i 0.0555556 + 0.0687465i
\(385\) −11520.0 −0.000201869
\(386\) 1.98043e7i 0.344347i
\(387\) −980118. + 4.56596e6i −0.0169101 + 0.0787770i
\(388\) 8.99475e6 0.153991
\(389\) 6.15319e7i 1.04533i 0.852540 + 0.522663i \(0.175061\pi\)
−0.852540 + 0.522663i \(0.824939\pi\)
\(390\) −5.94720e7 + 4.80606e7i −1.00258 + 0.810206i
\(391\) 4.59233e7 0.768251
\(392\) 2.12960e7i 0.353541i
\(393\) 1.81918e7 + 2.25112e7i 0.299708 + 0.370870i
\(394\) −2.74596e7 −0.448959
\(395\) 5.77953e7i 0.937780i
\(396\) −774144. 166176.i −0.0124663 0.00267598i
\(397\) −8.55816e7 −1.36776 −0.683878 0.729596i \(-0.739708\pi\)
−0.683878 + 0.729596i \(0.739708\pi\)
\(398\) 5.37953e7i 0.853287i
\(399\) 220836. 178462.i 0.00347657 0.00280949i
\(400\) −1.34912e7 −0.210800
\(401\) 4.09739e7i 0.635439i −0.948185 0.317719i \(-0.897083\pi\)
0.948185 0.317719i \(-0.102917\pi\)
\(402\) −4.21150e7 5.21147e7i −0.648274 0.802198i
\(403\) −6.75491e7 −1.03206
\(404\) 3.02516e7i 0.458780i
\(405\) 3.70138e7 8.22433e7i 0.557183 1.23804i
\(406\) −24960.0 −0.000372964
\(407\) 1.15597e6i 0.0171460i
\(408\) 1.70312e7 1.37633e7i 0.250763 0.202647i
\(409\) 6.10556e7 0.892391 0.446196 0.894935i \(-0.352779\pi\)
0.446196 + 0.894935i \(0.352779\pi\)
\(410\) 1.60962e7i 0.233546i
\(411\) 4.72355e7 + 5.84509e7i 0.680366 + 0.841910i
\(412\) 2.77032e7 0.396131
\(413\) 653638.i 0.00927870i
\(414\) 8.87155e6 4.13289e7i 0.125025 0.582442i
\(415\) 8.42170e7 1.17830
\(416\) 1.70882e7i 0.237365i
\(417\) 9.60529e7 7.76224e7i 1.32465 1.07048i
\(418\) 1.00954e6 0.0138227
\(419\) 3.38860e7i 0.460657i 0.973113 + 0.230329i \(0.0739801\pi\)
−0.973113 + 0.230329i \(0.926020\pi\)
\(420\) −184320. 228084.i −0.00248785 0.00307856i
\(421\) −1.96156e7 −0.262879 −0.131439 0.991324i \(-0.541960\pi\)
−0.131439 + 0.991324i \(0.541960\pi\)
\(422\) 3.99608e7i 0.531737i
\(423\) −1.28218e8 2.75229e7i −1.69405 0.363641i
\(424\) −3.48549e7 −0.457263
\(425\) 5.90270e7i 0.768925i
\(426\) 8.10432e6 6.54928e6i 0.104831 0.0847159i
\(427\) −125132. −0.00160725
\(428\) 4.71711e7i 0.601651i
\(429\) −1.69920e6 2.10265e6i −0.0215215 0.0266315i
\(430\) −6.14976e6 −0.0773487
\(431\) 4.01587e7i 0.501589i −0.968040 0.250795i \(-0.919308\pi\)
0.968040 0.250795i \(-0.0806919\pi\)
\(432\) −9.09619e6 1.79861e7i −0.112826 0.223093i
\(433\) −845854. −0.0104191 −0.00520957 0.999986i \(-0.501658\pi\)
−0.00520957 + 0.999986i \(0.501658\pi\)
\(434\) 259061.i 0.00316908i
\(435\) 7.86240e6 6.35378e6i 0.0955185 0.0771906i
\(436\) −2.08259e7 −0.251272
\(437\) 5.38957e7i 0.645817i
\(438\) 7.01290e7 + 8.67802e7i 0.834594 + 1.03276i
\(439\) −7.48204e7 −0.884354 −0.442177 0.896928i \(-0.645794\pi\)
−0.442177 + 0.896928i \(0.645794\pi\)
\(440\) 1.04267e6i 0.0122402i
\(441\) −1.79997e7 + 8.38531e7i −0.209869 + 0.977695i
\(442\) 7.47648e7 0.865825
\(443\) 1.25246e8i 1.44063i −0.693649 0.720313i \(-0.743998\pi\)
0.693649 0.720313i \(-0.256002\pi\)
\(444\) −2.28870e7 + 1.84955e7i −0.261481 + 0.211308i
\(445\) −6.56294e7 −0.744764
\(446\) 2.64114e7i 0.297705i
\(447\) −7.56904e7 9.36621e7i −0.847458 1.04868i
\(448\) −65536.0 −0.000728863
\(449\) 1.12812e8i 1.24628i 0.782109 + 0.623142i \(0.214144\pi\)
−0.782109 + 0.623142i \(0.785856\pi\)
\(450\) 5.31216e7 + 1.14029e7i 0.582953 + 0.125135i
\(451\) −569088. −0.00620369
\(452\) 5.58133e7i 0.604397i
\(453\) −4.63700e7 + 3.74726e7i −0.498818 + 0.403106i
\(454\) −1.11171e8 −1.18802
\(455\) 1.00126e6i 0.0106295i
\(456\) 1.61526e7 + 1.99878e7i 0.170352 + 0.210800i
\(457\) 1.57358e8 1.64870 0.824350 0.566081i \(-0.191541\pi\)
0.824350 + 0.566081i \(0.191541\pi\)
\(458\) 2.53528e7i 0.263894i
\(459\) −7.86931e7 + 3.97979e7i −0.813764 + 0.411549i
\(460\) 5.56646e7 0.571881
\(461\) 1.83107e8i 1.86897i −0.356002 0.934485i \(-0.615860\pi\)
0.356002 0.934485i \(-0.384140\pi\)
\(462\) 8064.00 6516.70i 8.17758e−5 6.60848e-5i
\(463\) 1.77978e8 1.79318 0.896588 0.442866i \(-0.146038\pi\)
0.896588 + 0.442866i \(0.146038\pi\)
\(464\) 2.25912e6i 0.0226144i
\(465\) 6.59462e7 + 8.16043e7i 0.655890 + 0.811623i
\(466\) −1.29704e7 −0.128172
\(467\) 9.35797e7i 0.918821i −0.888224 0.459410i \(-0.848061\pi\)
0.888224 0.459410i \(-0.151939\pi\)
\(468\) 1.44432e7 6.72849e7i 0.140905 0.656417i
\(469\) 877396. 0.00850505
\(470\) 1.72692e8i 1.66334i
\(471\) −2.70663e7 + 2.18728e7i −0.259039 + 0.209335i
\(472\) −5.91606e7 −0.562609
\(473\) 217427.i 0.00205461i
\(474\) −3.26940e7 4.04567e7i −0.306996 0.379888i
\(475\) −6.92742e7 −0.646384
\(476\) 286735.i 0.00265864i
\(477\) 1.37241e8 + 2.94598e7i 1.26453 + 0.271441i
\(478\) 1.49660e7 0.137032
\(479\) 1.07662e8i 0.979617i 0.871830 + 0.489808i \(0.162933\pi\)
−0.871830 + 0.489808i \(0.837067\pi\)
\(480\) 2.06438e7 1.66827e7i 0.186667 0.150849i
\(481\) −1.00471e8 −0.902830
\(482\) 3.95743e7i 0.353404i
\(483\) 347904. + 430509.i 0.00308758 + 0.00382068i
\(484\) −5.66531e7 −0.499675
\(485\) 4.77019e7i 0.418129i
\(486\) 2.06142e7 + 7.85084e7i 0.179580 + 0.683923i
\(487\) −4.14432e6 −0.0358811 −0.0179406 0.999839i \(-0.505711\pi\)
−0.0179406 + 0.999839i \(0.505711\pi\)
\(488\) 1.13257e7i 0.0974549i
\(489\) 1.84782e7 1.49326e7i 0.158028 0.127706i
\(490\) −1.12939e8 −0.959967
\(491\) 1.19347e8i 1.00824i 0.863633 + 0.504122i \(0.168184\pi\)
−0.863633 + 0.504122i \(0.831816\pi\)
\(492\) −9.10541e6 1.12674e7i −0.0764547 0.0946078i
\(493\) −9.88416e6 −0.0824896
\(494\) 8.77440e7i 0.727841i
\(495\) −881280. + 4.10552e6i −0.00726605 + 0.0338495i
\(496\) 2.34476e7 0.192155
\(497\) 136443.i 0.00111143i
\(498\) −5.89519e7 + 4.76403e7i −0.477320 + 0.385733i
\(499\) 1.17436e8 0.945144 0.472572 0.881292i \(-0.343326\pi\)
0.472572 + 0.881292i \(0.343326\pi\)
\(500\) 1.33049e7i 0.106439i
\(501\) −1.01273e8 1.25320e8i −0.805346 0.996565i
\(502\) 1.61215e8 1.27437
\(503\) 1.99753e8i 1.56960i 0.619747 + 0.784802i \(0.287235\pi\)
−0.619747 + 0.784802i \(0.712765\pi\)
\(504\) 258048. + 55391.9i 0.00201562 + 0.000432668i
\(505\) −1.60433e8 −1.24572
\(506\) 1.96804e6i 0.0151909i
\(507\) 8.13895e7 6.57727e7i 0.624517 0.504686i
\(508\) 7.29768e7 0.556665
\(509\) 1.12725e8i 0.854804i 0.904062 + 0.427402i \(0.140571\pi\)
−0.904062 + 0.427402i \(0.859429\pi\)
\(510\) −7.29907e7 9.03214e7i −0.550246 0.680895i
\(511\) −1.46102e6 −0.0109495
\(512\) 5.93164e6i 0.0441942i
\(513\) −4.67068e7 9.23543e7i −0.345962 0.684077i
\(514\) 1.05677e6 0.00778198
\(515\) 1.46919e8i 1.07561i
\(516\) 4.30483e6 3.47883e6i 0.0313334 0.0253212i
\(517\) 6.10560e6 0.0441832
\(518\) 385322.i 0.00277227i
\(519\) −7.10842e6 8.79622e6i −0.0508476 0.0629207i
\(520\) 9.06240e7 0.644515
\(521\) 1.14581e8i 0.810215i −0.914269 0.405108i \(-0.867234\pi\)
0.914269 0.405108i \(-0.132766\pi\)
\(522\) −1.90944e6 + 8.89529e6i −0.0134244 + 0.0625387i
\(523\) −1.49806e8 −1.04719 −0.523594 0.851968i \(-0.675409\pi\)
−0.523594 + 0.851968i \(0.675409\pi\)
\(524\) 3.43028e7i 0.238416i
\(525\) −553350. + 447174.i −0.00382404 + 0.00309029i
\(526\) 4.87361e7 0.334884
\(527\) 1.02588e8i 0.700916i
\(528\) 589824. + 729870.i 0.00400701 + 0.00495842i
\(529\) 4.29689e7 0.290260
\(530\) 1.84846e8i 1.24160i
\(531\) 2.32945e8 + 5.00033e7i 1.55586 + 0.333976i
\(532\) −336512. −0.00223494
\(533\) 4.94624e7i 0.326658i
\(534\) 4.59406e7 3.71256e7i 0.301698 0.243809i
\(535\) 2.50163e8 1.63366
\(536\) 7.94128e7i 0.515699i
\(537\) −5.12698e6 6.34431e6i −0.0331084 0.0409696i
\(538\) 4.27167e7 0.274316
\(539\) 3.99300e6i 0.0254996i
\(540\) −9.53856e7 + 4.82398e7i −0.605761 + 0.306355i
\(541\) −1.57017e8 −0.991644 −0.495822 0.868424i \(-0.665133\pi\)
−0.495822 + 0.868424i \(0.665133\pi\)
\(542\) 7.88822e7i 0.495429i
\(543\) −1.36000e8 + 1.09904e8i −0.849452 + 0.686461i
\(544\) −2.59523e7 −0.161205
\(545\) 1.10446e8i 0.682277i
\(546\) 566400. + 700884.i 0.00347973 + 0.00430594i
\(547\) −2.79469e8 −1.70754 −0.853770 0.520650i \(-0.825690\pi\)
−0.853770 + 0.520650i \(0.825690\pi\)
\(548\) 8.90680e7i 0.541228i
\(549\) −9.57260e6 + 4.45948e7i −0.0578513 + 0.269505i
\(550\) −2.52960e6 −0.0152042
\(551\) 1.16001e7i 0.0693434i
\(552\) −3.89652e7 + 3.14887e7i −0.231665 + 0.187213i
\(553\) 681124. 0.00402764
\(554\) 1.59123e8i 0.935847i
\(555\) 9.80870e7 + 1.21377e8i 0.573763 + 0.709996i
\(556\) −1.46366e8 −0.851563
\(557\) 1.50294e8i 0.869712i 0.900500 + 0.434856i \(0.143201\pi\)
−0.900500 + 0.434856i \(0.856799\pi\)
\(558\) −9.23247e7 1.98182e7i −0.531393 0.114067i
\(559\) 1.88977e7 0.108187
\(560\) 347557.i 0.00197907i
\(561\) 3.19334e6 2.58061e6i 0.0180866 0.0146162i
\(562\) −1.26391e8 −0.712044
\(563\) 8.27836e7i 0.463894i 0.972728 + 0.231947i \(0.0745097\pi\)
−0.972728 + 0.231947i \(0.925490\pi\)
\(564\) 9.76896e7 + 1.20885e8i 0.544516 + 0.673805i
\(565\) 2.95995e8 1.64111
\(566\) 5.73710e7i 0.316405i
\(567\) −969246. 436211.i −0.00531722 0.00239303i
\(568\) −1.23494e7 −0.0673911
\(569\) 2.57230e8i 1.39632i −0.715942 0.698160i \(-0.754003\pi\)
0.715942 0.698160i \(-0.245997\pi\)
\(570\) 1.06001e8 8.56620e7i 0.572383 0.462555i
\(571\) 2.84039e7 0.152570 0.0762852 0.997086i \(-0.475694\pi\)
0.0762852 + 0.997086i \(0.475694\pi\)
\(572\) 3.20404e6i 0.0171203i
\(573\) 8.52204e7 + 1.05455e8i 0.452980 + 0.560535i
\(574\) 189696. 0.00100305
\(575\) 1.35047e8i 0.710363i
\(576\) −5.01350e6 + 2.33558e7i −0.0262346 + 0.122216i
\(577\) 6.52476e7 0.339654 0.169827 0.985474i \(-0.445679\pi\)
0.169827 + 0.985474i \(0.445679\pi\)
\(578\) 2.29958e7i 0.119087i
\(579\) 7.35195e7 5.94128e7i 0.378763 0.306086i
\(580\) −1.19808e7 −0.0614047
\(581\) 992506.i 0.00506063i
\(582\) 2.69843e7 + 3.33913e7i 0.136880 + 0.169381i
\(583\) −6.53530e6 −0.0329807
\(584\) 1.32236e8i 0.663915i
\(585\) −3.56832e8 7.65966e7i −1.78236 0.382597i
\(586\) 1.57525e8 0.782813
\(587\) 6.66740e7i 0.329642i 0.986324 + 0.164821i \(0.0527046\pi\)
−0.986324 + 0.164821i \(0.947295\pi\)
\(588\) 7.90574e7 6.38881e7i 0.388876 0.314259i
\(589\) 1.20398e8 0.589213
\(590\) 3.13746e8i 1.52765i
\(591\) −8.23789e7 1.01939e8i −0.399074 0.493829i
\(592\) 3.48754e7 0.168095
\(593\) 1.53324e8i 0.735271i −0.929970 0.367635i \(-0.880167\pi\)
0.929970 0.367635i \(-0.119833\pi\)
\(594\) −1.70554e6 3.37239e6i −0.00813770 0.0160908i
\(595\) 1.52064e6 0.00721897
\(596\) 1.42723e8i 0.674149i
\(597\) −1.99705e8 + 1.61386e8i −0.938568 + 0.758478i
\(598\) −1.71053e8 −0.799883
\(599\) 2.18294e8i 1.01569i −0.861448 0.507846i \(-0.830442\pi\)
0.861448 0.507846i \(-0.169558\pi\)
\(600\) −4.04736e7 5.00835e7i −0.187378 0.231868i
\(601\) 1.08478e8 0.499709 0.249854 0.968283i \(-0.419617\pi\)
0.249854 + 0.968283i \(0.419617\pi\)
\(602\) 72475.6i 0.000332202i
\(603\) 6.71208e7 3.12688e8i 0.306129 1.42613i
\(604\) 7.06590e7 0.320669
\(605\) 3.00448e8i 1.35676i
\(606\) 1.12303e8 9.07548e7i 0.504632 0.407804i
\(607\) −3.43321e8 −1.53509 −0.767547 0.640993i \(-0.778523\pi\)
−0.767547 + 0.640993i \(0.778523\pi\)
\(608\) 3.04576e7i 0.135514i
\(609\) −74880.0 92659.3i −0.000331523 0.000410239i
\(610\) −6.00634e7 −0.264618
\(611\) 5.30669e8i 2.32649i
\(612\) 1.02187e8 + 2.19352e7i 0.445801 + 0.0956946i
\(613\) 2.96325e8 1.28643 0.643216 0.765685i \(-0.277600\pi\)
0.643216 + 0.765685i \(0.277600\pi\)
\(614\) 2.05487e8i 0.887728i
\(615\) −5.97542e7 + 4.82887e7i −0.256888 + 0.207597i
\(616\) −12288.0 −5.25701e−5
\(617\) 1.32676e8i 0.564853i 0.959289 + 0.282426i \(0.0911393\pi\)
−0.959289 + 0.282426i \(0.908861\pi\)
\(618\) 8.31097e7 + 1.02843e8i 0.352116 + 0.435722i
\(619\) −4.14773e8 −1.74879 −0.874397 0.485211i \(-0.838743\pi\)
−0.874397 + 0.485211i \(0.838743\pi\)
\(620\) 1.24349e8i 0.521758i
\(621\) 1.80040e8 9.10527e7i 0.751787 0.380205i
\(622\) −2.03602e8 −0.846078
\(623\) 773450.i 0.00319866i
\(624\) −6.34368e7 + 5.12647e7i −0.261088 + 0.210991i
\(625\) −2.76419e8 −1.13221
\(626\) 2.26896e8i 0.924919i
\(627\) 3.02861e6 + 3.74771e6i 0.0122868 + 0.0152042i
\(628\) 4.12438e7 0.166525
\(629\) 1.52588e8i 0.613151i
\(630\) 293760. 1.36851e6i 0.00117482 0.00547300i
\(631\) 3.03858e8 1.20944 0.604718 0.796440i \(-0.293286\pi\)
0.604718 + 0.796440i \(0.293286\pi\)
\(632\) 6.16483e7i 0.244214i
\(633\) 1.48347e8 1.19882e8i 0.584881 0.472655i
\(634\) 2.23093e8 0.875424
\(635\) 3.87018e8i 1.51151i
\(636\) −1.04565e8 1.29392e8i −0.406456 0.502964i
\(637\) 3.47053e8 1.34269
\(638\) 423585.i 0.00163109i
\(639\) 4.86259e7 + 1.04379e7i 0.186365 + 0.0400047i
\(640\) −3.14573e7 −0.120000
\(641\) 1.81629e8i 0.689622i 0.938672 + 0.344811i \(0.112057\pi\)
−0.938672 + 0.344811i \(0.887943\pi\)
\(642\) −1.75114e8 + 1.41513e8i −0.661782 + 0.534801i
\(643\) 1.73811e8 0.653798 0.326899 0.945059i \(-0.393996\pi\)
0.326899 + 0.945059i \(0.393996\pi\)
\(644\) 656014.i 0.00245615i
\(645\) −1.84493e7 2.28298e7i −0.0687544 0.0850792i
\(646\) −1.33259e8 −0.494309
\(647\) 2.43137e8i 0.897713i −0.893604 0.448856i \(-0.851832\pi\)
0.893604 0.448856i \(-0.148168\pi\)
\(648\) 3.94813e7 8.77261e7i 0.145100 0.322407i
\(649\) −1.10926e7 −0.0405788
\(650\) 2.19861e8i 0.800585i
\(651\) 961716. 777184.i 0.00348581 0.00281696i
\(652\) −2.81572e7 −0.101589
\(653\) 4.47562e7i 0.160736i 0.996765 + 0.0803681i \(0.0256096\pi\)
−0.996765 + 0.0803681i \(0.974390\pi\)
\(654\) −6.24778e7 7.73123e7i −0.223353 0.276386i
\(655\) −1.81918e8 −0.647369
\(656\) 1.71693e7i 0.0608193i
\(657\) −1.11768e8 + 5.20681e8i −0.394114 + 1.83601i
\(658\) −2.03520e6 −0.00714380
\(659\) 1.13574e8i 0.396845i 0.980117 + 0.198423i \(0.0635819\pi\)
−0.980117 + 0.198423i \(0.936418\pi\)
\(660\) 3.87072e6 3.12801e6i 0.0134636 0.0108802i
\(661\) −9.93464e7 −0.343992 −0.171996 0.985098i \(-0.555022\pi\)
−0.171996 + 0.985098i \(0.555022\pi\)
\(662\) 1.57466e8i 0.542766i
\(663\) 2.24294e8 + 2.77550e8i 0.769623 + 0.952359i
\(664\) 8.98314e7 0.306849
\(665\) 1.78462e6i 0.00606851i
\(666\) −1.37322e8 2.94772e7i −0.464854 0.0997845i
\(667\) 2.26138e7 0.0762071
\(668\) 1.90963e8i 0.640649i
\(669\) 9.80472e7 7.92341e7i 0.327459 0.264627i
\(670\) 4.21150e8 1.40027
\(671\) 2.12356e6i 0.00702906i
\(672\) −196608. 243290.i −0.000647878 0.000801708i
\(673\) −2.79412e8 −0.916642 −0.458321 0.888787i \(-0.651549\pi\)
−0.458321 + 0.888787i \(0.651549\pi\)
\(674\) 1.34575e8i 0.439525i
\(675\) 1.17034e8 + 2.31413e8i 0.380539 + 0.752447i
\(676\) −1.24022e8 −0.401475
\(677\) 4.09293e7i 0.131907i −0.997823 0.0659536i \(-0.978991\pi\)
0.997823 0.0659536i \(-0.0210089\pi\)
\(678\) −2.07196e8 + 1.67440e8i −0.664803 + 0.537242i
\(679\) −562172. −0.00179581
\(680\) 1.37633e8i 0.437718i
\(681\) −3.33514e8 4.12702e8i −1.05602 1.30676i
\(682\) 4.39642e6 0.0138594
\(683\) 3.74260e8i 1.17466i −0.809348 0.587329i \(-0.800180\pi\)
0.809348 0.587329i \(-0.199820\pi\)
\(684\) −2.57432e7 + 1.19927e8i −0.0804440 + 0.374755i
\(685\) −4.72355e8 −1.46959
\(686\) 2.66205e6i 0.00824600i
\(687\) −9.41174e7 + 7.60584e7i −0.290268 + 0.234572i
\(688\) −6.55974e6 −0.0201429
\(689\) 5.68017e8i 1.73661i
\(690\) 1.66994e8 + 2.06644e8i 0.508339 + 0.629037i
\(691\) 1.15164e8 0.349047 0.174524 0.984653i \(-0.444161\pi\)
0.174524 + 0.984653i \(0.444161\pi\)
\(692\) 1.34038e7i 0.0404490i
\(693\) 48384.0 + 10386.0i 0.000145379 + 3.12067e-5i
\(694\) 3.02120e8 0.903859
\(695\) 7.76224e8i 2.31224i
\(696\) 8.38656e6 6.77736e6i 0.0248746 0.0201017i
\(697\) 7.51196e7 0.221848
\(698\) 2.66821e8i 0.784609i
\(699\) −3.89111e7 4.81500e7i −0.113931 0.140982i
\(700\) 843200. 0.00245831
\(701\) 5.65717e7i 0.164227i −0.996623 0.0821137i \(-0.973833\pi\)
0.996623 0.0821137i \(-0.0261671\pi\)
\(702\) 2.93112e8 1.48237e8i 0.847271 0.428495i
\(703\) 1.79077e8 0.515435
\(704\) 1.11218e6i 0.00318756i
\(705\) 6.41088e8 5.18077e8i 1.82958 1.47852i
\(706\) 9.92456e7 0.282031
\(707\) 1.89072e6i 0.00535020i
\(708\) −1.77482e8 2.19622e8i −0.500097 0.618838i
\(709\) −1.28652e8 −0.360975 −0.180488 0.983577i \(-0.557768\pi\)
−0.180488 + 0.983577i \(0.557768\pi\)
\(710\) 6.54928e7i 0.182986i
\(711\) 5.21060e7 2.42740e8i 0.144970 0.675356i
\(712\) −7.00047e7 −0.193949
\(713\) 2.34710e8i 0.647533i
\(714\) −1.06445e6 + 860204.i −0.00292435 + 0.00236323i
\(715\) 1.69920e7 0.0464864
\(716\) 9.66752e6i 0.0263376i
\(717\) 4.48980e7 + 5.55585e7i 0.121806 + 0.150728i
\(718\) −3.49735e8 −0.944855
\(719\) 2.01053e8i 0.540908i 0.962733 + 0.270454i \(0.0871738\pi\)
−0.962733 + 0.270454i \(0.912826\pi\)
\(720\) 1.23863e8 + 2.65881e7i 0.331852 + 0.0712345i
\(721\) −1.73145e6 −0.00461960
\(722\) 1.09739e8i 0.291575i
\(723\) −1.46912e8 + 1.18723e8i −0.388725 + 0.314137i
\(724\) 2.07238e8 0.546076
\(725\) 2.90663e7i 0.0762739i
\(726\) −1.69959e8 2.10314e8i −0.444155 0.549614i
\(727\) 5.23208e8 1.36167 0.680833 0.732438i \(-0.261618\pi\)
0.680833 + 0.732438i \(0.261618\pi\)
\(728\) 1.06801e6i 0.00276811i
\(729\) −2.29605e8 + 3.12051e8i −0.592651 + 0.805459i
\(730\) −7.01290e8 −1.80272
\(731\) 2.87003e7i 0.0734742i
\(732\) 4.20444e7 3.39770e7i 0.107195 0.0866266i
\(733\) −6.57372e8 −1.66917 −0.834583 0.550882i \(-0.814291\pi\)
−0.834583 + 0.550882i \(0.814291\pi\)
\(734\) 1.92594e8i 0.487028i
\(735\) −3.38818e8 4.19265e8i −0.853304 1.05591i
\(736\) 5.93756e7 0.148927
\(737\) 1.48899e7i 0.0371954i
\(738\) 1.45117e7 6.76042e7i 0.0361036 0.168192i
\(739\) 3.50495e8 0.868458 0.434229 0.900803i \(-0.357021\pi\)
0.434229 + 0.900803i \(0.357021\pi\)
\(740\) 1.84955e8i 0.456426i
\(741\) −3.25733e8 + 2.63232e8i −0.800585 + 0.646970i
\(742\) 2.17843e6 0.00533252
\(743\) 4.66667e8i 1.13773i 0.822429 + 0.568867i \(0.192618\pi\)
−0.822429 + 0.568867i \(0.807382\pi\)
\(744\) 7.03427e7 + 8.70446e7i 0.170805 + 0.211360i
\(745\) 7.56904e8 1.83051
\(746\) 2.91770e8i 0.702788i
\(747\) −3.53711e8 7.59267e7i −0.848569 0.182152i
\(748\) −4.86605e6 −0.0116271
\(749\) 2.94819e6i 0.00701634i
\(750\) 4.93920e7 3.99148e7i 0.117077 0.0946128i
\(751\) −3.36993e7 −0.0795612 −0.0397806 0.999208i \(-0.512666\pi\)
−0.0397806 + 0.999208i \(0.512666\pi\)
\(752\) 1.84205e8i 0.433160i
\(753\) 4.83645e8 + 5.98480e8i 1.13277 + 1.40173i
\(754\) 3.68160e7 0.0858860
\(755\) 3.74726e8i 0.870709i
\(756\) 568512. + 1.12413e6i 0.00131575 + 0.00260166i
\(757\) 2.98552e8 0.688227 0.344113 0.938928i \(-0.388180\pi\)
0.344113 + 0.938928i \(0.388180\pi\)
\(758\) 2.42582e8i 0.556995i
\(759\) −7.30598e6 + 5.90413e6i −0.0167091 + 0.0135030i
\(760\) −1.61526e8 −0.367960
\(761\) 3.98702e8i 0.904679i 0.891846 + 0.452340i \(0.149410\pi\)
−0.891846 + 0.452340i \(0.850590\pi\)
\(762\) 2.18930e8 + 2.70913e8i 0.494813 + 0.612300i
\(763\) 1.30162e6 0.00293029
\(764\) 1.60693e8i 0.360344i
\(765\) 1.16329e8 5.41928e8i 0.259839 1.21048i
\(766\) −8.55921e7 −0.190435
\(767\) 9.64116e8i 2.13670i
\(768\) 2.20201e7 1.77949e7i 0.0486111 0.0392837i
\(769\) −5.17372e8 −1.13769 −0.568845 0.822444i \(-0.692610\pi\)
−0.568845 + 0.822444i \(0.692610\pi\)
\(770\) 65167.0i 0.000142743i
\(771\) 3.17030e6 + 3.92305e6i 0.00691732 + 0.00855974i
\(772\) −1.12030e8 −0.243490
\(773\) 1.83241e8i 0.396719i −0.980129 0.198360i \(-0.936439\pi\)
0.980129 0.198360i \(-0.0635614\pi\)
\(774\) 2.58290e7 + 5.54438e6i 0.0557038 + 0.0