Properties

Label 38.6.e.b.23.1
Level $38$
Weight $6$
Character 38.23
Analytic conductor $6.095$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.09458515289\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 23.1
Character \(\chi\) \(=\) 38.23
Dual form 38.6.e.b.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.75877 - 1.36808i) q^{2} +(-5.14875 - 29.2000i) q^{3} +(12.2567 + 10.2846i) q^{4} +(68.5412 - 57.5129i) q^{5} +(-20.5950 + 116.800i) q^{6} +(68.7063 - 119.003i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(-597.784 + 217.576i) q^{9} +O(q^{10})\) \(q+(-3.75877 - 1.36808i) q^{2} +(-5.14875 - 29.2000i) q^{3} +(12.2567 + 10.2846i) q^{4} +(68.5412 - 57.5129i) q^{5} +(-20.5950 + 116.800i) q^{6} +(68.7063 - 119.003i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(-597.784 + 217.576i) q^{9} +(-336.313 + 122.408i) q^{10} +(152.529 + 264.188i) q^{11} +(237.204 - 410.849i) q^{12} +(15.9575 - 90.4993i) q^{13} +(-421.056 + 353.308i) q^{14} +(-2032.28 - 1705.28i) q^{15} +(44.4539 + 252.111i) q^{16} +(54.3140 + 19.7687i) q^{17} +2544.60 q^{18} +(920.562 + 1276.19i) q^{19} +1431.59 q^{20} +(-3828.63 - 1393.51i) q^{21} +(-211.891 - 1201.70i) q^{22} +(2223.62 + 1865.84i) q^{23} +(-1453.67 + 1219.77i) q^{24} +(847.513 - 4806.48i) q^{25} +(-183.791 + 318.335i) q^{26} +(5828.52 + 10095.3i) q^{27} +(2066.01 - 751.966i) q^{28} +(-5079.71 + 1848.86i) q^{29} +(5305.90 + 9190.09i) q^{30} +(2969.66 - 5143.60i) q^{31} +(177.816 - 1008.44i) q^{32} +(6928.96 - 5814.09i) q^{33} +(-177.109 - 148.612i) q^{34} +(-2134.98 - 12108.1i) q^{35} +(-9564.55 - 3481.21i) q^{36} -287.050 q^{37} +(-1714.25 - 6056.31i) q^{38} -2724.74 q^{39} +(-5381.01 - 1958.53i) q^{40} +(-240.363 - 1363.17i) q^{41} +(12484.5 + 10475.8i) q^{42} +(6184.72 - 5189.60i) q^{43} +(-847.565 + 4806.78i) q^{44} +(-28459.5 + 49293.2i) q^{45} +(-5805.47 - 10055.4i) q^{46} +(-1477.74 + 537.854i) q^{47} +(7132.75 - 2596.11i) q^{48} +(-1037.61 - 1797.18i) q^{49} +(-9761.26 + 16907.0i) q^{50} +(297.596 - 1687.75i) q^{51} +(1126.34 - 945.107i) q^{52} +(-29674.8 - 24900.1i) q^{53} +(-8096.90 - 45919.8i) q^{54} +(25648.8 + 9335.39i) q^{55} -8794.40 q^{56} +(32525.0 - 33451.2i) q^{57} +21622.8 q^{58} +(-1902.67 - 692.517i) q^{59} +(-7370.88 - 41802.3i) q^{60} +(16685.4 + 14000.7i) q^{61} +(-18199.1 + 15270.9i) q^{62} +(-15179.4 + 86086.8i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-4111.13 - 7120.69i) q^{65} +(-33998.5 + 12374.5i) q^{66} +(59312.6 - 21588.0i) q^{67} +(462.398 + 800.897i) q^{68} +(43033.7 - 74536.5i) q^{69} +(-8539.93 + 48432.4i) q^{70} +(-19296.9 + 16192.0i) q^{71} +(31188.4 + 26170.2i) q^{72} +(5900.50 + 33463.4i) q^{73} +(1078.96 + 392.708i) q^{74} -144713. q^{75} +(-1842.06 + 25109.5i) q^{76} +41918.9 q^{77} +(10241.7 + 3727.66i) q^{78} +(-2420.67 - 13728.3i) q^{79} +(17546.5 + 14723.3i) q^{80} +(146355. - 122806. i) q^{81} +(-961.451 + 5452.66i) q^{82} +(-40109.9 + 69472.5i) q^{83} +(-32594.7 - 56455.8i) q^{84} +(4859.70 - 1768.79i) q^{85} +(-30346.7 + 11045.3i) q^{86} +(80140.9 + 138808. i) q^{87} +(9761.87 - 16908.1i) q^{88} +(-8648.18 + 49046.2i) q^{89} +(174410. - 146347. i) q^{90} +(-9673.29 - 8116.85i) q^{91} +(8064.87 + 45738.1i) q^{92} +(-165483. - 60231.0i) q^{93} +6290.32 q^{94} +(136494. + 34527.5i) q^{95} -30362.1 q^{96} +(-38298.0 - 13939.3i) q^{97} +(1441.43 + 8174.73i) q^{98} +(-148661. - 124741. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 15q^{3} + 60q^{6} - 84q^{7} - 960q^{8} - 345q^{9} + O(q^{10}) \) \( 30q + 15q^{3} + 60q^{6} - 84q^{7} - 960q^{8} - 345q^{9} - 126q^{11} - 2610q^{13} - 864q^{14} - 5160q^{15} + 1902q^{17} + 17016q^{18} - 2400q^{19} + 3456q^{20} - 6426q^{21} + 216q^{22} - 3306q^{23} + 960q^{24} - 18060q^{25} + 456q^{26} + 13017q^{27} + 6048q^{28} + 5988q^{29} - 6840q^{31} + 51867q^{33} - 10752q^{34} + 24408q^{35} - 5520q^{36} - 8556q^{37} + 2772q^{38} + 9912q^{39} - 40527q^{41} + 27432q^{42} + 3678q^{43} + 864q^{44} - 31770q^{45} - 15744q^{46} - 133740q^{47} - 7680q^{48} - 63777q^{49} - 107580q^{50} + 45657q^{51} + 5760q^{52} - 64626q^{53} + 1476q^{54} + 142056q^{55} + 10752q^{56} + 232824q^{57} + 117264q^{58} + 169041q^{59} - 56640q^{60} + 61698q^{61} - 101616q^{62} - 188064q^{63} - 61440q^{64} - 80646q^{65} - 173772q^{66} - 72129q^{67} - 65904q^{68} - 124224q^{69} + 97632q^{70} + 417828q^{71} + 44160q^{72} + 239082q^{73} - 116112q^{74} - 174960q^{75} + 6912q^{76} + 242436q^{77} + 336624q^{78} - 145740q^{79} + 14781q^{81} - 162108q^{82} - 201630q^{83} - 54528q^{84} - 46512q^{85} - 75720q^{86} - 376512q^{87} - 8064q^{88} + 416928q^{89} + 560640q^{90} - 380316q^{91} + 269376q^{92} - 205146q^{93} + 5616q^{94} + 708168q^{95} + 858363q^{97} + 308328q^{98} - 1068531q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.75877 1.36808i −0.664463 0.241845i
\(3\) −5.14875 29.2000i −0.330292 1.87318i −0.469523 0.882920i \(-0.655574\pi\)
0.139231 0.990260i \(-0.455537\pi\)
\(4\) 12.2567 + 10.2846i 0.383022 + 0.321394i
\(5\) 68.5412 57.5129i 1.22610 1.02882i 0.227620 0.973750i \(-0.426906\pi\)
0.998482 0.0550720i \(-0.0175388\pi\)
\(6\) −20.5950 + 116.800i −0.233552 + 1.32454i
\(7\) 68.7063 119.003i 0.529970 0.917935i −0.469419 0.882976i \(-0.655536\pi\)
0.999389 0.0349593i \(-0.0111302\pi\)
\(8\) −32.0000 55.4256i −0.176777 0.306186i
\(9\) −597.784 + 217.576i −2.46002 + 0.895373i
\(10\) −336.313 + 122.408i −1.06351 + 0.387088i
\(11\) 152.529 + 264.188i 0.380077 + 0.658312i 0.991073 0.133321i \(-0.0425642\pi\)
−0.610996 + 0.791634i \(0.709231\pi\)
\(12\) 237.204 410.849i 0.475519 0.823623i
\(13\) 15.9575 90.4993i 0.0261882 0.148521i −0.968910 0.247414i \(-0.920419\pi\)
0.995098 + 0.0988935i \(0.0315303\pi\)
\(14\) −421.056 + 353.308i −0.574143 + 0.481763i
\(15\) −2032.28 1705.28i −2.33214 1.95690i
\(16\) 44.4539 + 252.111i 0.0434120 + 0.246202i
\(17\) 54.3140 + 19.7687i 0.0455816 + 0.0165903i 0.364710 0.931121i \(-0.381168\pi\)
−0.319129 + 0.947711i \(0.603390\pi\)
\(18\) 2544.60 1.85113
\(19\) 920.562 + 1276.19i 0.585018 + 0.811021i
\(20\) 1431.59 0.800281
\(21\) −3828.63 1393.51i −1.89450 0.689543i
\(22\) −211.891 1201.70i −0.0933376 0.529344i
\(23\) 2223.62 + 1865.84i 0.876479 + 0.735453i 0.965452 0.260581i \(-0.0839141\pi\)
−0.0889731 + 0.996034i \(0.528359\pi\)
\(24\) −1453.67 + 1219.77i −0.515154 + 0.432266i
\(25\) 847.513 4806.48i 0.271204 1.53807i
\(26\) −183.791 + 318.335i −0.0533200 + 0.0923530i
\(27\) 5828.52 + 10095.3i 1.53868 + 2.66508i
\(28\) 2066.01 751.966i 0.498009 0.181260i
\(29\) −5079.71 + 1848.86i −1.12161 + 0.408234i −0.835241 0.549884i \(-0.814672\pi\)
−0.286374 + 0.958118i \(0.592450\pi\)
\(30\) 5305.90 + 9190.09i 1.07636 + 1.86430i
\(31\) 2969.66 5143.60i 0.555012 0.961310i −0.442890 0.896576i \(-0.646047\pi\)
0.997903 0.0647339i \(-0.0206199\pi\)
\(32\) 177.816 1008.44i 0.0306970 0.174091i
\(33\) 6928.96 5814.09i 1.10760 0.929388i
\(34\) −177.109 148.612i −0.0262750 0.0220473i
\(35\) −2134.98 12108.1i −0.294594 1.67073i
\(36\) −9564.55 3481.21i −1.23001 0.447687i
\(37\) −287.050 −0.0344710 −0.0172355 0.999851i \(-0.505486\pi\)
−0.0172355 + 0.999851i \(0.505486\pi\)
\(38\) −1714.25 6056.31i −0.192581 0.680377i
\(39\) −2724.74 −0.286856
\(40\) −5381.01 1958.53i −0.531757 0.193544i
\(41\) −240.363 1363.17i −0.0223310 0.126645i 0.971604 0.236611i \(-0.0760368\pi\)
−0.993935 + 0.109966i \(0.964926\pi\)
\(42\) 12484.5 + 10475.8i 1.09206 + 0.916351i
\(43\) 6184.72 5189.60i 0.510093 0.428018i −0.351069 0.936350i \(-0.614182\pi\)
0.861162 + 0.508331i \(0.169737\pi\)
\(44\) −847.565 + 4806.78i −0.0659996 + 0.374303i
\(45\) −28459.5 + 49293.2i −2.09505 + 3.62874i
\(46\) −5805.47 10055.4i −0.404522 0.700653i
\(47\) −1477.74 + 537.854i −0.0975784 + 0.0355156i −0.390348 0.920667i \(-0.627645\pi\)
0.292770 + 0.956183i \(0.405423\pi\)
\(48\) 7132.75 2596.11i 0.446842 0.162637i
\(49\) −1037.61 1797.18i −0.0617365 0.106931i
\(50\) −9761.26 + 16907.0i −0.552180 + 0.956404i
\(51\) 297.596 1687.75i 0.0160214 0.0908622i
\(52\) 1126.34 945.107i 0.0577643 0.0484700i
\(53\) −29674.8 24900.1i −1.45110 1.21762i −0.931772 0.363045i \(-0.881737\pi\)
−0.519330 0.854574i \(-0.673818\pi\)
\(54\) −8096.90 45919.8i −0.377863 2.14297i
\(55\) 25648.8 + 9335.39i 1.14330 + 0.416127i
\(56\) −8794.40 −0.374745
\(57\) 32525.0 33451.2i 1.32596 1.36372i
\(58\) 21622.8 0.844001
\(59\) −1902.67 692.517i −0.0711597 0.0259000i 0.306195 0.951969i \(-0.400944\pi\)
−0.377355 + 0.926069i \(0.623166\pi\)
\(60\) −7370.88 41802.3i −0.264327 1.49907i
\(61\) 16685.4 + 14000.7i 0.574131 + 0.481753i 0.883014 0.469347i \(-0.155511\pi\)
−0.308883 + 0.951100i \(0.599955\pi\)
\(62\) −18199.1 + 15270.9i −0.601273 + 0.504528i
\(63\) −15179.4 + 86086.8i −0.481841 + 2.73266i
\(64\) −2048.00 + 3547.24i −0.0625000 + 0.108253i
\(65\) −4111.13 7120.69i −0.120692 0.209044i
\(66\) −33998.5 + 12374.5i −0.960728 + 0.349676i
\(67\) 59312.6 21588.0i 1.61421 0.587525i 0.631944 0.775014i \(-0.282257\pi\)
0.982267 + 0.187490i \(0.0600351\pi\)
\(68\) 462.398 + 800.897i 0.0121267 + 0.0210041i
\(69\) 43033.7 74536.5i 1.08814 1.88472i
\(70\) −8539.93 + 48432.4i −0.208310 + 1.18138i
\(71\) −19296.9 + 16192.0i −0.454299 + 0.381202i −0.841028 0.540991i \(-0.818049\pi\)
0.386730 + 0.922193i \(0.373605\pi\)
\(72\) 31188.4 + 26170.2i 0.709025 + 0.594943i
\(73\) 5900.50 + 33463.4i 0.129593 + 0.734958i 0.978473 + 0.206373i \(0.0661661\pi\)
−0.848880 + 0.528585i \(0.822723\pi\)
\(74\) 1078.96 + 392.708i 0.0229047 + 0.00833663i
\(75\) −144713. −2.97067
\(76\) −1842.06 + 25109.5i −0.0365823 + 0.498660i
\(77\) 41918.9 0.805717
\(78\) 10241.7 + 3727.66i 0.190605 + 0.0693745i
\(79\) −2420.67 13728.3i −0.0436382 0.247485i 0.955184 0.296014i \(-0.0956576\pi\)
−0.998822 + 0.0485295i \(0.984547\pi\)
\(80\) 17546.5 + 14723.3i 0.306526 + 0.257206i
\(81\) 146355. 122806.i 2.47853 2.07973i
\(82\) −961.451 + 5452.66i −0.0157904 + 0.0895517i
\(83\) −40109.9 + 69472.5i −0.639082 + 1.10692i 0.346552 + 0.938031i \(0.387352\pi\)
−0.985634 + 0.168892i \(0.945981\pi\)
\(84\) −32594.7 56455.8i −0.504022 0.872992i
\(85\) 4859.70 1768.79i 0.0729562 0.0265539i
\(86\) −30346.7 + 11045.3i −0.442452 + 0.161039i
\(87\) 80140.9 + 138808.i 1.13516 + 1.96615i
\(88\) 9761.87 16908.1i 0.134377 0.232749i
\(89\) −8648.18 + 49046.2i −0.115731 + 0.656343i 0.870655 + 0.491895i \(0.163695\pi\)
−0.986386 + 0.164448i \(0.947416\pi\)
\(90\) 174410. 146347.i 2.26968 1.90449i
\(91\) −9673.29 8116.85i −0.122453 0.102751i
\(92\) 8064.87 + 45738.1i 0.0993408 + 0.563390i
\(93\) −165483. 60231.0i −1.98402 0.722125i
\(94\) 6290.32 0.0734265
\(95\) 136494. + 34527.5i 1.55169 + 0.392515i
\(96\) −30362.1 −0.336243
\(97\) −38298.0 13939.3i −0.413282 0.150423i 0.127007 0.991902i \(-0.459463\pi\)
−0.540289 + 0.841479i \(0.681685\pi\)
\(98\) 1441.43 + 8174.73i 0.0151610 + 0.0859822i
\(99\) −148661. 124741.i −1.52443 1.27915i
\(100\) 59820.5 50195.3i 0.598205 0.501953i
\(101\) 22627.5 128327.i 0.220716 1.25174i −0.649992 0.759941i \(-0.725228\pi\)
0.870708 0.491800i \(-0.163661\pi\)
\(102\) −3427.58 + 5936.73i −0.0326202 + 0.0564998i
\(103\) −85564.0 148201.i −0.794691 1.37644i −0.923035 0.384715i \(-0.874300\pi\)
0.128345 0.991730i \(-0.459034\pi\)
\(104\) −5526.62 + 2011.52i −0.0501044 + 0.0182365i
\(105\) −342564. + 124683.i −3.03227 + 1.10366i
\(106\) 77475.3 + 134191.i 0.669729 + 1.16000i
\(107\) −74229.7 + 128570.i −0.626784 + 1.08562i 0.361409 + 0.932408i \(0.382296\pi\)
−0.988193 + 0.153215i \(0.951037\pi\)
\(108\) −32387.6 + 183679.i −0.267189 + 1.51531i
\(109\) −16788.0 + 14086.8i −0.135342 + 0.113566i −0.707946 0.706267i \(-0.750378\pi\)
0.572603 + 0.819832i \(0.305933\pi\)
\(110\) −83636.3 70179.2i −0.659042 0.553002i
\(111\) 1477.95 + 8381.87i 0.0113855 + 0.0645704i
\(112\) 33056.1 + 12031.5i 0.249004 + 0.0906302i
\(113\) 96750.2 0.712780 0.356390 0.934337i \(-0.384007\pi\)
0.356390 + 0.934337i \(0.384007\pi\)
\(114\) −168018. + 81238.4i −1.21086 + 0.585463i
\(115\) 259720. 1.83130
\(116\) −81275.3 29581.8i −0.560807 0.204117i
\(117\) 10151.3 + 57571.0i 0.0685580 + 0.388812i
\(118\) 6204.29 + 5206.02i 0.0410192 + 0.0344192i
\(119\) 6084.24 5105.28i 0.0393857 0.0330485i
\(120\) −29483.5 + 167209.i −0.186907 + 1.06000i
\(121\) 33995.2 58881.4i 0.211083 0.365607i
\(122\) −43562.4 75452.3i −0.264980 0.458958i
\(123\) −38566.8 + 14037.2i −0.229854 + 0.0836599i
\(124\) 89298.2 32501.9i 0.521541 0.189825i
\(125\) −78541.8 136038.i −0.449600 0.778729i
\(126\) 174830. 302814.i 0.981045 1.69922i
\(127\) 28613.4 162275.i 0.157420 0.892774i −0.799120 0.601172i \(-0.794701\pi\)
0.956540 0.291602i \(-0.0941883\pi\)
\(128\) 12550.9 10531.4i 0.0677094 0.0568149i
\(129\) −183380. 153874.i −0.970235 0.814124i
\(130\) 5711.13 + 32389.4i 0.0296390 + 0.168091i
\(131\) −120080. 43705.6i −0.611354 0.222515i 0.0177417 0.999843i \(-0.494352\pi\)
−0.629096 + 0.777328i \(0.716575\pi\)
\(132\) 144722. 0.722935
\(133\) 215119. 21867.0i 1.05451 0.107191i
\(134\) −252477. −1.21467
\(135\) 980103. + 356728.i 4.62847 + 1.68463i
\(136\) −642.356 3642.98i −0.00297803 0.0168892i
\(137\) −10307.4 8648.94i −0.0469189 0.0393696i 0.619027 0.785370i \(-0.287527\pi\)
−0.665946 + 0.746000i \(0.731972\pi\)
\(138\) −263726. + 221292.i −1.17884 + 0.989163i
\(139\) −19213.9 + 108968.i −0.0843488 + 0.478366i 0.913146 + 0.407632i \(0.133645\pi\)
−0.997495 + 0.0707342i \(0.977466\pi\)
\(140\) 98359.0 170363.i 0.424125 0.734606i
\(141\) 23313.8 + 40380.8i 0.0987566 + 0.171051i
\(142\) 94684.5 34462.3i 0.394056 0.143425i
\(143\) 26342.8 9588.01i 0.107726 0.0392092i
\(144\) −81427.1 141036.i −0.327237 0.566791i
\(145\) −241836. + 418872.i −0.955214 + 1.65448i
\(146\) 23602.0 133854.i 0.0916361 0.519694i
\(147\) −47135.4 + 39551.3i −0.179909 + 0.150962i
\(148\) −3518.29 2952.20i −0.0132032 0.0110788i
\(149\) 44149.2 + 250383.i 0.162914 + 0.923930i 0.951189 + 0.308607i \(0.0998629\pi\)
−0.788276 + 0.615322i \(0.789026\pi\)
\(150\) 543942. + 197979.i 1.97390 + 0.718440i
\(151\) 312599. 1.11569 0.557847 0.829944i \(-0.311627\pi\)
0.557847 + 0.829944i \(0.311627\pi\)
\(152\) 41275.7 91860.8i 0.144906 0.322494i
\(153\) −36769.2 −0.126986
\(154\) −157563. 57348.4i −0.535369 0.194858i
\(155\) −92279.4 523343.i −0.308515 1.74967i
\(156\) −33396.3 28022.9i −0.109872 0.0921936i
\(157\) −189761. + 159228.i −0.614409 + 0.515550i −0.896041 0.443972i \(-0.853569\pi\)
0.281632 + 0.959523i \(0.409124\pi\)
\(158\) −9682.67 + 54913.1i −0.0308569 + 0.174998i
\(159\) −574295. + 994708.i −1.80153 + 3.12034i
\(160\) −45810.8 79346.6i −0.141471 0.245035i
\(161\) 374817. 136422.i 1.13961 0.414783i
\(162\) −718122. + 261375.i −2.14986 + 0.782486i
\(163\) −187055. 323988.i −0.551441 0.955124i −0.998171 0.0604553i \(-0.980745\pi\)
0.446730 0.894669i \(-0.352589\pi\)
\(164\) 11073.6 19180.0i 0.0321497 0.0556850i
\(165\) 140534. 797009.i 0.401858 2.27905i
\(166\) 245808. 206257.i 0.692350 0.580951i
\(167\) 475581. + 399060.i 1.31957 + 1.10725i 0.986395 + 0.164390i \(0.0525656\pi\)
0.333179 + 0.942864i \(0.391879\pi\)
\(168\) 45280.1 + 256796.i 0.123775 + 0.701966i
\(169\) 340966. + 124101.i 0.918320 + 0.334241i
\(170\) −20686.3 −0.0548986
\(171\) −827966. 562596.i −2.16532 1.47132i
\(172\) 129177. 0.332939
\(173\) −209477. 76243.5i −0.532135 0.193681i 0.0619566 0.998079i \(-0.480266\pi\)
−0.594091 + 0.804398i \(0.702488\pi\)
\(174\) −111331. 631387.i −0.278767 1.58097i
\(175\) −513755. 431092.i −1.26812 1.06408i
\(176\) −59824.2 + 50198.5i −0.145578 + 0.122154i
\(177\) −10425.1 + 59123.6i −0.0250119 + 0.141850i
\(178\) 99605.7 172522.i 0.235632 0.408127i
\(179\) 214754. + 371965.i 0.500967 + 0.867700i 0.999999 + 0.00111653i \(0.000355401\pi\)
−0.499033 + 0.866583i \(0.666311\pi\)
\(180\) −855780. + 311479.i −1.96871 + 0.716551i
\(181\) −421285. + 153335.i −0.955828 + 0.347893i −0.772397 0.635140i \(-0.780943\pi\)
−0.183431 + 0.983033i \(0.558720\pi\)
\(182\) 25255.2 + 43743.2i 0.0565160 + 0.0978886i
\(183\) 322911. 559299.i 0.712780 1.23457i
\(184\) 32259.5 182953.i 0.0702446 0.398377i
\(185\) −19674.8 + 16509.1i −0.0422650 + 0.0354645i
\(186\) 539613. + 452789.i 1.14367 + 0.959651i
\(187\) 3061.82 + 17364.4i 0.00640288 + 0.0363125i
\(188\) −23643.9 8605.66i −0.0487892 0.0177578i
\(189\) 1.60182e6 3.26182
\(190\) −465813. 316516.i −0.936111 0.636079i
\(191\) −154108. −0.305663 −0.152832 0.988252i \(-0.548839\pi\)
−0.152832 + 0.988252i \(0.548839\pi\)
\(192\) 114124. + 41537.7i 0.223421 + 0.0813186i
\(193\) 162839. + 923503.i 0.314676 + 1.78462i 0.574029 + 0.818835i \(0.305380\pi\)
−0.259353 + 0.965783i \(0.583509\pi\)
\(194\) 124883. + 104790.i 0.238232 + 0.199900i
\(195\) −186757. + 156708.i −0.351714 + 0.295123i
\(196\) 5765.70 32698.9i 0.0107204 0.0607986i
\(197\) −3836.98 + 6645.84i −0.00704407 + 0.0122007i −0.869526 0.493887i \(-0.835576\pi\)
0.862482 + 0.506088i \(0.168909\pi\)
\(198\) 388125. + 672253.i 0.703573 + 1.21862i
\(199\) −211297. + 76906.0i −0.378235 + 0.137666i −0.524139 0.851632i \(-0.675613\pi\)
0.145905 + 0.989299i \(0.453391\pi\)
\(200\) −293523. + 106834.i −0.518880 + 0.188857i
\(201\) −935756. 1.62078e6i −1.63370 2.82965i
\(202\) −260613. + 451395.i −0.449385 + 0.778357i
\(203\) −128988. + 731528.i −0.219690 + 1.24592i
\(204\) 21005.4 17625.6i 0.0353391 0.0296530i
\(205\) −94874.4 79609.0i −0.157675 0.132305i
\(206\) 118864. + 674113.i 0.195157 + 1.10679i
\(207\) −1.73521e6 631564.i −2.81466 1.02445i
\(208\) 23525.2 0.0377029
\(209\) −196742. + 437858.i −0.311553 + 0.693374i
\(210\) 1.45819e6 2.28175
\(211\) 113006. + 41130.8i 0.174741 + 0.0636005i 0.427909 0.903822i \(-0.359250\pi\)
−0.253168 + 0.967422i \(0.581473\pi\)
\(212\) −107628. 610387.i −0.164469 0.932750i
\(213\) 572161. + 480100.i 0.864111 + 0.725075i
\(214\) 454906. 381711.i 0.679027 0.569771i
\(215\) 125439. 711403.i 0.185071 1.04959i
\(216\) 373025. 646099.i 0.544006 0.942247i
\(217\) −408069. 706796.i −0.588280 1.01893i
\(218\) 82374.3 29981.8i 0.117395 0.0427284i
\(219\) 946750. 344589.i 1.33391 0.485502i
\(220\) 218359. + 378209.i 0.304168 + 0.526835i
\(221\) 2655.76 4599.92i 0.00365771 0.00633533i
\(222\) 5911.80 33527.5i 0.00805076 0.0456581i
\(223\) 16886.0 14169.0i 0.0227386 0.0190800i −0.631347 0.775500i \(-0.717498\pi\)
0.654086 + 0.756420i \(0.273053\pi\)
\(224\) −107790. 90446.9i −0.143536 0.120441i
\(225\) 539144. + 3.05764e6i 0.709984 + 4.02652i
\(226\) −363662. 132362.i −0.473616 0.172382i
\(227\) 1.27626e6 1.64390 0.821949 0.569561i \(-0.192887\pi\)
0.821949 + 0.569561i \(0.192887\pi\)
\(228\) 742682. 75494.3i 0.946163 0.0961783i
\(229\) 77951.9 0.0982286 0.0491143 0.998793i \(-0.484360\pi\)
0.0491143 + 0.998793i \(0.484360\pi\)
\(230\) −976227. 355317.i −1.21683 0.442891i
\(231\) −215830. 1.22403e6i −0.266122 1.50925i
\(232\) 265025. + 222382.i 0.323271 + 0.271257i
\(233\) 186016. 156086.i 0.224472 0.188354i −0.523615 0.851955i \(-0.675417\pi\)
0.748087 + 0.663601i \(0.230973\pi\)
\(234\) 40605.3 230284.i 0.0484778 0.274931i
\(235\) −70352.6 + 121854.i −0.0831018 + 0.143937i
\(236\) −16198.3 28056.2i −0.0189316 0.0327906i
\(237\) −388402. + 141367.i −0.449170 + 0.163485i
\(238\) −29853.7 + 10865.9i −0.0341630 + 0.0124343i
\(239\) 69523.4 + 120418.i 0.0787293 + 0.136363i 0.902702 0.430266i \(-0.141580\pi\)
−0.823973 + 0.566630i \(0.808247\pi\)
\(240\) 339578. 588166.i 0.380549 0.659131i
\(241\) −107689. + 610732.i −0.119434 + 0.677342i 0.865025 + 0.501728i \(0.167302\pi\)
−0.984459 + 0.175614i \(0.943809\pi\)
\(242\) −208335. + 174813.i −0.228677 + 0.191883i
\(243\) −2.16953e6 1.82045e6i −2.35695 1.97772i
\(244\) 60516.3 + 343205.i 0.0650725 + 0.369045i
\(245\) −174480. 63505.5i −0.185708 0.0675922i
\(246\) 164168. 0.172962
\(247\) 130184. 62945.4i 0.135774 0.0656480i
\(248\) −380117. −0.392453
\(249\) 2.23511e6 + 813514.i 2.28455 + 0.831508i
\(250\) 109109. + 618789.i 0.110411 + 0.626170i
\(251\) 676721. + 567837.i 0.677993 + 0.568904i 0.915419 0.402502i \(-0.131859\pi\)
−0.237426 + 0.971406i \(0.576304\pi\)
\(252\) −1.07142e6 + 899027.i −1.06282 + 0.891808i
\(253\) −153766. + 872050.i −0.151029 + 0.856525i
\(254\) −329556. + 570808.i −0.320513 + 0.555144i
\(255\) −76669.9 132796.i −0.0738371 0.127890i
\(256\) −61583.7 + 22414.6i −0.0587308 + 0.0213763i
\(257\) −1.52060e6 + 553453.i −1.43609 + 0.522695i −0.938671 0.344815i \(-0.887942\pi\)
−0.497421 + 0.867509i \(0.665720\pi\)
\(258\) 478771. + 829255.i 0.447794 + 0.775602i
\(259\) −19722.2 + 34159.8i −0.0182686 + 0.0316421i
\(260\) 22844.5 129558.i 0.0209579 0.118858i
\(261\) 2.63430e6 2.21044e6i 2.39367 2.00853i
\(262\) 391561. + 328558.i 0.352408 + 0.295705i
\(263\) −89497.2 507564.i −0.0797848 0.452482i −0.998361 0.0572373i \(-0.981771\pi\)
0.918576 0.395245i \(-0.129340\pi\)
\(264\) −543976. 197991.i −0.480364 0.174838i
\(265\) −3.46602e6 −3.03191
\(266\) −838498. 212107.i −0.726604 0.183802i
\(267\) 1.47668e6 1.26767
\(268\) 949002. + 345409.i 0.807105 + 0.293762i
\(269\) 107698. + 610787.i 0.0907461 + 0.514647i 0.995968 + 0.0897078i \(0.0285933\pi\)
−0.905222 + 0.424939i \(0.860296\pi\)
\(270\) −3.19595e6 2.68172e6i −2.66803 2.23874i
\(271\) 860317. 721892.i 0.711599 0.597103i −0.213448 0.976954i \(-0.568469\pi\)
0.925047 + 0.379852i \(0.124025\pi\)
\(272\) −2569.43 + 14571.9i −0.00210578 + 0.0119425i
\(273\) −187207. + 324251.i −0.152025 + 0.263315i
\(274\) 26910.7 + 46610.7i 0.0216545 + 0.0375067i
\(275\) 1.39909e6 509226.i 1.11561 0.406049i
\(276\) 1.29403e6 470988.i 1.02252 0.372166i
\(277\) −966368. 1.67380e6i −0.756734 1.31070i −0.944508 0.328489i \(-0.893460\pi\)
0.187774 0.982212i \(-0.439873\pi\)
\(278\) 221297. 383298.i 0.171737 0.297457i
\(279\) −656094. + 3.72089e6i −0.504610 + 2.86178i
\(280\) −602779. + 505792.i −0.459476 + 0.385546i
\(281\) 718458. + 602858.i 0.542795 + 0.455459i 0.872492 0.488628i \(-0.162502\pi\)
−0.329698 + 0.944087i \(0.606947\pi\)
\(282\) −32387.2 183677.i −0.0242522 0.137541i
\(283\) 442657. + 161114.i 0.328550 + 0.119582i 0.501028 0.865431i \(-0.332955\pi\)
−0.172478 + 0.985013i \(0.555178\pi\)
\(284\) −403045. −0.296522
\(285\) 305431. 4.16339e6i 0.222742 3.03623i
\(286\) −112134. −0.0810628
\(287\) −178735. 65054.2i −0.128087 0.0466198i
\(288\) 113117. + 641520.i 0.0803615 + 0.455752i
\(289\) −1.08511e6 910519.i −0.764242 0.641275i
\(290\) 1.48206e6 1.24359e6i 1.03483 0.868327i
\(291\) −209842. + 1.19007e6i −0.145265 + 0.823836i
\(292\) −271837. + 470835.i −0.186574 + 0.323156i
\(293\) 225114. + 389910.i 0.153191 + 0.265335i 0.932399 0.361431i \(-0.117712\pi\)
−0.779208 + 0.626766i \(0.784378\pi\)
\(294\) 231281. 84179.2i 0.156053 0.0567985i
\(295\) −170240. + 61962.4i −0.113896 + 0.0414546i
\(296\) 9185.61 + 15909.9i 0.00609367 + 0.0105545i
\(297\) −1.77804e6 + 3.07965e6i −1.16963 + 2.02587i
\(298\) 176597. 1.00153e6i 0.115197 0.653317i
\(299\) 204341. 171462.i 0.132183 0.110915i
\(300\) −1.77370e6 1.48831e6i −1.13783 0.954754i
\(301\) −192647. 1.09256e6i −0.122559 0.695069i
\(302\) −1.17499e6 427661.i −0.741338 0.269825i
\(303\) −3.86365e6 −2.41764
\(304\) −280819. + 288815.i −0.174278 + 0.179241i
\(305\) 1.94886e6 1.19958
\(306\) 138207. + 50303.3i 0.0843775 + 0.0307109i
\(307\) −35345.3 200453.i −0.0214035 0.121385i 0.972234 0.234011i \(-0.0751851\pi\)
−0.993638 + 0.112625i \(0.964074\pi\)
\(308\) 513787. + 431119.i 0.308608 + 0.258953i
\(309\) −3.88693e6 + 3.26152e6i −2.31585 + 1.94323i
\(310\) −369118. + 2.09337e6i −0.218153 + 1.23721i
\(311\) 1.17180e6 2.02961e6i 0.686991 1.18990i −0.285816 0.958284i \(-0.592265\pi\)
0.972807 0.231618i \(-0.0744020\pi\)
\(312\) 87191.6 + 151020.i 0.0507094 + 0.0878312i
\(313\) 2.00887e6 731169.i 1.15902 0.421849i 0.310274 0.950647i \(-0.399579\pi\)
0.848748 + 0.528798i \(0.177357\pi\)
\(314\) 931105. 338894.i 0.532935 0.193973i
\(315\) 3.91069e6 + 6.77351e6i 2.22063 + 3.84625i
\(316\) 111521. 193159.i 0.0628257 0.108817i
\(317\) −120470. + 683220.i −0.0673335 + 0.381867i 0.932455 + 0.361287i \(0.117662\pi\)
−0.999788 + 0.0205802i \(0.993449\pi\)
\(318\) 3.51948e6 2.95320e6i 1.95169 1.63766i
\(319\) −1.26325e6 1.05999e6i −0.695045 0.583212i
\(320\) 63639.7 + 360919.i 0.0347419 + 0.197031i
\(321\) 4.13642e6 + 1.50553e6i 2.24059 + 0.815507i
\(322\) −1.59549e6 −0.857539
\(323\) 24770.8 + 87513.3i 0.0132109 + 0.0466732i
\(324\) 3.05684e6 1.61774
\(325\) −421459. 153399.i −0.221333 0.0805588i
\(326\) 259853. + 1.47370e6i 0.135421 + 0.768008i
\(327\) 497773. + 417681.i 0.257432 + 0.216011i
\(328\) −67862.7 + 56943.6i −0.0348294 + 0.0292254i
\(329\) −37524.0 + 212809.i −0.0191126 + 0.108393i
\(330\) −1.61861e6 + 2.80351e6i −0.818196 + 1.41716i
\(331\) −724122. 1.25422e6i −0.363280 0.629219i 0.625219 0.780450i \(-0.285010\pi\)
−0.988499 + 0.151230i \(0.951677\pi\)
\(332\) −1.20611e6 + 438989.i −0.600541 + 0.218579i
\(333\) 171594. 62455.2i 0.0847993 0.0308644i
\(334\) −1.24166e6 2.15061e6i −0.609025 1.05486i
\(335\) 2.82377e6 4.89091e6i 1.37473 2.38110i
\(336\) 181121. 1.02719e6i 0.0875225 0.496365i
\(337\) −1.02994e6 + 864226.i −0.494014 + 0.414527i −0.855462 0.517865i \(-0.826727\pi\)
0.361448 + 0.932392i \(0.382282\pi\)
\(338\) −1.11183e6 932937.i −0.529355 0.444182i
\(339\) −498142. 2.82510e6i −0.235426 1.33517i
\(340\) 77755.2 + 28300.6i 0.0364781 + 0.0132769i
\(341\) 1.81184e6 0.843789
\(342\) 2.34246e6 + 3.24739e6i 1.08295 + 1.50131i
\(343\) 2.02433e6 0.929066
\(344\) −485548. 176725.i −0.221226 0.0805196i
\(345\) −1.33723e6 7.58381e6i −0.604865 3.43036i
\(346\) 683070. + 573163.i 0.306743 + 0.257388i
\(347\) 2.33731e6 1.96124e6i 1.04206 0.874394i 0.0498251 0.998758i \(-0.484134\pi\)
0.992237 + 0.124364i \(0.0396892\pi\)
\(348\) −445322. + 2.52555e6i −0.197118 + 1.11791i
\(349\) 60414.7 104641.i 0.0265509 0.0459875i −0.852445 0.522817i \(-0.824881\pi\)
0.878996 + 0.476830i \(0.158214\pi\)
\(350\) 1.34132e6 + 2.32323e6i 0.585278 + 1.01373i
\(351\) 1.00663e6 366382.i 0.436114 0.158733i
\(352\) 293541. 106840.i 0.126273 0.0459598i
\(353\) −827804. 1.43380e6i −0.353582 0.612423i 0.633292 0.773913i \(-0.281703\pi\)
−0.986874 + 0.161490i \(0.948370\pi\)
\(354\) 120071. 207970.i 0.0509251 0.0882048i
\(355\) −391382. + 2.21964e6i −0.164828 + 0.934785i
\(356\) −610419. + 512203.i −0.255272 + 0.214199i
\(357\) −180400. 151374.i −0.0749147 0.0628609i
\(358\) −298333. 1.69193e6i −0.123025 0.697710i
\(359\) −4.38925e6 1.59756e6i −1.79744 0.654214i −0.998613 0.0526518i \(-0.983233\pi\)
−0.798826 0.601562i \(-0.794545\pi\)
\(360\) 3.64281e6 1.48143
\(361\) −781231. + 2.34963e6i −0.315509 + 0.948923i
\(362\) 1.79329e6 0.719249
\(363\) −1.89437e6 689494.i −0.754567 0.274640i
\(364\) −35084.1 198972.i −0.0138790 0.0787115i
\(365\) 2.32900e6 + 1.95427e6i 0.915036 + 0.767806i
\(366\) −1.97891e6 + 1.66051e6i −0.772190 + 0.647945i
\(367\) −696706. + 3.95122e6i −0.270013 + 1.53132i 0.484358 + 0.874870i \(0.339053\pi\)
−0.754371 + 0.656449i \(0.772058\pi\)
\(368\) −371550. + 643543.i −0.143020 + 0.247718i
\(369\) 440277. + 762582.i 0.168329 + 0.291555i
\(370\) 96538.7 35137.2i 0.0366604 0.0133433i
\(371\) −5.00202e6 + 1.82059e6i −1.88674 + 0.686716i
\(372\) −1.40883e6 2.44016e6i −0.527838 0.914243i
\(373\) 586251. 1.01542e6i 0.218178 0.377896i −0.736073 0.676902i \(-0.763322\pi\)
0.954251 + 0.299006i \(0.0966552\pi\)
\(374\) 12247.3 69457.7i 0.00452752 0.0256768i
\(375\) −3.56793e6 + 2.99385e6i −1.31020 + 1.09939i
\(376\) 77098.6 + 64693.4i 0.0281240 + 0.0235988i
\(377\) 86261.5 + 489213.i 0.0312582 + 0.177274i
\(378\) −6.02089e6 2.19142e6i −2.16736 0.788855i
\(379\) 1.22032e6 0.436391 0.218196 0.975905i \(-0.429983\pi\)
0.218196 + 0.975905i \(0.429983\pi\)
\(380\) 1.31786e6 + 1.82698e6i 0.468179 + 0.649045i
\(381\) −4.88574e6 −1.72432
\(382\) 579258. + 210833.i 0.203102 + 0.0739230i
\(383\) 436551. + 2.47580e6i 0.152068 + 0.862421i 0.961417 + 0.275094i \(0.0887089\pi\)
−0.809349 + 0.587328i \(0.800180\pi\)
\(384\) −372139. 312262.i −0.128788 0.108066i
\(385\) 2.87317e6 2.41088e6i 0.987892 0.828940i
\(386\) 651354. 3.69401e6i 0.222510 1.26192i
\(387\) −2.56800e6 + 4.44791e6i −0.871601 + 1.50966i
\(388\) −326047. 564730.i −0.109952 0.190442i
\(389\) −2.82772e6 + 1.02921e6i −0.947464 + 0.344849i −0.769109 0.639117i \(-0.779300\pi\)
−0.178355 + 0.983966i \(0.557078\pi\)
\(390\) 916365. 333530.i 0.305075 0.111038i
\(391\) 83888.6 + 145299.i 0.0277499 + 0.0480642i
\(392\) −66406.7 + 115020.i −0.0218271 + 0.0378057i
\(393\) −657940. + 3.73137e6i −0.214885 + 1.21867i
\(394\) 23514.4 19730.9i 0.00763120 0.00640334i
\(395\) −955469. 801734.i −0.308123 0.258546i
\(396\) −539178. 3.05783e6i −0.172780 0.979885i
\(397\) 3.11142e6 + 1.13246e6i 0.990791 + 0.360618i 0.786026 0.618193i \(-0.212135\pi\)
0.204764 + 0.978811i \(0.434357\pi\)
\(398\) 899432. 0.284617
\(399\) −1.74611e6 6.16888e6i −0.549084 1.93988i
\(400\) 1.24944e6 0.390450
\(401\) −4.45114e6 1.62008e6i −1.38232 0.503125i −0.459442 0.888208i \(-0.651951\pi\)
−0.922882 + 0.385083i \(0.874173\pi\)
\(402\) 1.29994e6 + 7.37232e6i 0.401197 + 2.27530i
\(403\) −418104. 350831.i −0.128240 0.107606i
\(404\) 1.59713e6 1.34015e6i 0.486841 0.408508i
\(405\) 2.96839e6 1.68345e7i 0.899255 5.09993i
\(406\) 1.48563e6 2.57318e6i 0.447295 0.774738i
\(407\) −43783.6 75835.3i −0.0131016 0.0226927i
\(408\) −103068. + 37513.6i −0.0306530 + 0.0111568i
\(409\) 1.70521e6 620644.i 0.504044 0.183457i −0.0774680 0.996995i \(-0.524684\pi\)
0.581512 + 0.813538i \(0.302461\pi\)
\(410\) 247699. + 429028.i 0.0727722 + 0.126045i
\(411\) −199479. + 345507.i −0.0582494 + 0.100891i
\(412\) 475457. 2.69645e6i 0.137997 0.782618i
\(413\) −213137. + 178843.i −0.0614871 + 0.0515938i
\(414\) 5.65822e6 + 4.74781e6i 1.62248 + 1.36142i
\(415\) 1.24638e6 + 7.06857e6i 0.355247 + 2.01470i
\(416\) −88425.9 32184.4i −0.0250522 0.00911826i
\(417\) 3.28078e6 0.923925
\(418\) 1.33853e6 1.37665e6i 0.374705 0.385374i
\(419\) −4.58004e6 −1.27448 −0.637242 0.770664i \(-0.719925\pi\)
−0.637242 + 0.770664i \(0.719925\pi\)
\(420\) −5.48102e6 1.99493e6i −1.51614 0.551828i
\(421\) −568605. 3.22472e6i −0.156353 0.886720i −0.957539 0.288305i \(-0.906908\pi\)
0.801186 0.598415i \(-0.204203\pi\)
\(422\) −368493. 309202.i −0.100727 0.0845204i
\(423\) 766347. 643041.i 0.208245 0.174738i
\(424\) −430511. + 2.44155e6i −0.116297 + 0.659554i
\(425\) 141050. 244305.i 0.0378791 0.0656085i
\(426\) −1.49381e6 2.58735e6i −0.398814 0.690766i
\(427\) 2.81251e6 1.02367e6i 0.746491 0.271700i
\(428\) −2.23210e6 + 812417.i −0.588985 + 0.214373i
\(429\) −415602. 719844.i −0.109027 0.188841i
\(430\) −1.44475e6 + 2.50239e6i −0.376810 + 0.652655i
\(431\) −582299. + 3.30238e6i −0.150992 + 0.856315i 0.811368 + 0.584536i \(0.198723\pi\)
−0.962359 + 0.271780i \(0.912388\pi\)
\(432\) −2.28603e6 + 1.91821e6i −0.589349 + 0.494523i
\(433\) 5.11023e6 + 4.28799e6i 1.30985 + 1.09909i 0.988353 + 0.152180i \(0.0486295\pi\)
0.321494 + 0.946912i \(0.395815\pi\)
\(434\) 566883. + 3.21495e6i 0.144467 + 0.819314i
\(435\) 1.34762e7 + 4.90494e6i 3.41464 + 1.24283i
\(436\) −350644. −0.0883384
\(437\) −334189. + 4.55539e6i −0.0837121 + 1.14110i
\(438\) −4.03004e6 −1.00375
\(439\) 2.94187e6 + 1.07075e6i 0.728555 + 0.265172i 0.679553 0.733627i \(-0.262174\pi\)
0.0490017 + 0.998799i \(0.484396\pi\)
\(440\) −303341. 1.72033e6i −0.0746963 0.423624i
\(441\) 1.01129e6 + 848571.i 0.247616 + 0.207774i
\(442\) −16275.5 + 13656.7i −0.00396258 + 0.00332500i
\(443\) −291485. + 1.65310e6i −0.0705679 + 0.400211i 0.928980 + 0.370131i \(0.120687\pi\)
−0.999548 + 0.0300797i \(0.990424\pi\)
\(444\) −68089.4 + 117934.i −0.0163916 + 0.0283911i
\(445\) 2.22804e6 + 3.85907e6i 0.533362 + 0.923810i
\(446\) −82855.0 + 30156.7i −0.0197234 + 0.00717872i
\(447\) 7.08386e6 2.57832e6i 1.67688 0.610333i
\(448\) 281421. + 487435.i 0.0662463 + 0.114742i
\(449\) −1.31514e6 + 2.27789e6i −0.307862 + 0.533233i −0.977895 0.209099i \(-0.932947\pi\)
0.670032 + 0.742332i \(0.266280\pi\)
\(450\) 2.15658e6 1.22306e7i 0.502035 2.84718i
\(451\) 323470. 271424.i 0.0748846 0.0628357i
\(452\) 1.18584e6 + 995037.i 0.273011 + 0.229083i
\(453\) −1.60949e6 9.12789e6i −0.368505 2.08990i
\(454\) −4.79717e6 1.74603e6i −1.09231 0.397568i
\(455\) −1.12984e6 −0.255852
\(456\) −2.89485e6 732283.i −0.651950 0.164918i
\(457\) −8.76096e6 −1.96228 −0.981141 0.193296i \(-0.938082\pi\)
−0.981141 + 0.193296i \(0.938082\pi\)
\(458\) −293003. 106644.i −0.0652693 0.0237561i
\(459\) 117000. + 663538.i 0.0259211 + 0.147006i
\(460\) 3.18331e6 + 2.67111e6i 0.701430 + 0.588569i
\(461\) −2.37088e6 + 1.98941e6i −0.519587 + 0.435985i −0.864488 0.502654i \(-0.832357\pi\)
0.344901 + 0.938639i \(0.387912\pi\)
\(462\) −863318. + 4.89612e6i −0.188177 + 1.06720i
\(463\) 652858. 1.13078e6i 0.141536 0.245147i −0.786539 0.617540i \(-0.788129\pi\)
0.928075 + 0.372393i \(0.121463\pi\)
\(464\) −691931. 1.19846e6i −0.149200 0.258421i
\(465\) −1.48065e7 + 5.38912e6i −3.17555 + 1.15581i
\(466\) −912732. + 332207.i −0.194706 + 0.0708670i
\(467\) −2.08329e6 3.60836e6i −0.442036 0.765629i 0.555805 0.831313i \(-0.312410\pi\)
−0.997840 + 0.0656843i \(0.979077\pi\)
\(468\) −467673. + 810034.i −0.0987024 + 0.170958i
\(469\) 1.50611e6 8.54160e6i 0.316174 1.79311i
\(470\) 431146. 361774.i 0.0900284 0.0755428i
\(471\) 5.62650e6 + 4.72119e6i 1.16865 + 0.980617i
\(472\) 22502.4 + 127617.i 0.00464915 + 0.0263666i
\(473\) 2.31438e6 + 842366.i 0.475644 + 0.173120i
\(474\) 1.65332e6 0.337995
\(475\) 6.91418e6 3.34308e6i 1.40607 0.679849i
\(476\) 127079. 0.0257072
\(477\) 2.31568e7 + 8.42838e6i 4.65996 + 1.69609i
\(478\) −96580.9 547738.i −0.0193340 0.109649i
\(479\) 3.87663e6 + 3.25288e6i 0.771997 + 0.647783i 0.941220 0.337795i \(-0.109681\pi\)
−0.169222 + 0.985578i \(0.554126\pi\)
\(480\) −2.08105e6 + 1.74621e6i −0.412268 + 0.345934i
\(481\) −4580.60 + 25977.8i −0.000902733 + 0.00511965i
\(482\) 1.24031e6 2.14828e6i 0.243171 0.421184i
\(483\) −5.91337e6 1.02422e7i −1.15337 1.99769i
\(484\) 1.02224e6 372065.i 0.198353 0.0721947i
\(485\) −3.42668e6 + 1.24721e6i −0.661485 + 0.240761i
\(486\) 5.66425e6 + 9.81077e6i 1.08781 + 1.88414i
\(487\) 1.44573e6 2.50408e6i 0.276226 0.478438i −0.694218 0.719765i \(-0.744249\pi\)
0.970444 + 0.241328i \(0.0775828\pi\)
\(488\) 242065. 1.37282e6i 0.0460132 0.260954i
\(489\) −8.49735e6 + 7.13012e6i −1.60698 + 1.34842i
\(490\) 568950. + 477405.i 0.107049 + 0.0898250i
\(491\) 759487. + 4.30726e6i 0.142173 + 0.806302i 0.969594 + 0.244720i \(0.0786960\pi\)
−0.827421 + 0.561582i \(0.810193\pi\)
\(492\) −617070. 224595.i −0.114927 0.0418299i
\(493\) −312449. −0.0578977
\(494\) −575447. + 58494.7i −0.106093 + 0.0107845i
\(495\) −1.73636e7 −3.18513
\(496\) 1.42877e6 + 520030.i 0.260771 + 0.0949127i
\(497\) 601077. + 3.40888e6i 0.109154 + 0.619042i
\(498\) −7.28832e6 6.11562e6i −1.31690 1.10501i
\(499\) −6.77754e6 + 5.68703e6i −1.21849 + 1.02243i −0.219583 + 0.975594i \(0.570470\pi\)
−0.998903 + 0.0468372i \(0.985086\pi\)
\(500\) 436437. 2.47516e6i 0.0780722 0.442769i
\(501\) 9.20391e6 1.59416e7i 1.63824 2.83752i
\(502\) −1.76679e6 3.06018e6i −0.312915 0.541985i
\(503\) 9.49612e6 3.45631e6i 1.67350 0.609105i 0.681105 0.732185i \(-0.261500\pi\)
0.992397 + 0.123081i \(0.0392773\pi\)
\(504\) 5.25716e6 1.91345e6i 0.921881 0.335537i
\(505\) −5.82954e6 1.00971e7i −1.01720 1.76184i
\(506\) 1.77101e6 3.06747e6i 0.307499 0.532604i
\(507\) 1.86821e6 1.05952e7i 0.322780 1.83058i
\(508\) 2.01964e6 1.69468e6i 0.347227 0.291358i
\(509\) −4.66555e6 3.91486e6i −0.798194 0.669765i 0.149565 0.988752i \(-0.452213\pi\)
−0.947759 + 0.318987i \(0.896657\pi\)
\(510\) 106509. + 604041.i 0.0181326 + 0.102835i
\(511\) 4.38764e6 + 1.59697e6i 0.743325 + 0.270548i
\(512\) 262144. 0.0441942
\(513\) −7.51802e6 + 1.67317e7i −1.26128 + 2.80702i
\(514\) 6.47276e6 1.08064
\(515\) −1.43881e7 5.23686e6i −2.39049 0.870067i
\(516\) −665101. 3.77198e6i −0.109967 0.623655i
\(517\) −367493. 308364.i −0.0604677 0.0507384i
\(518\) 120864. 101417.i 0.0197913 0.0166069i
\(519\) −1.14776e6 + 6.50929e6i −0.187040 + 1.06076i
\(520\) −263112. + 455724.i −0.0426710 + 0.0739084i
\(521\) −2.16135e6 3.74356e6i −0.348843 0.604214i 0.637201 0.770698i \(-0.280092\pi\)
−0.986044 + 0.166484i \(0.946759\pi\)
\(522\) −1.29258e7 + 4.70461e6i −2.07626 + 0.755696i
\(523\) 5.13671e6 1.86961e6i 0.821166 0.298880i 0.102938 0.994688i \(-0.467176\pi\)
0.718228 + 0.695808i \(0.244954\pi\)
\(524\) −1.02229e6 1.77066e6i −0.162647 0.281713i
\(525\) −9.94268e6 + 1.72212e7i −1.57436 + 2.72688i
\(526\) −357989. + 2.03026e6i −0.0564164 + 0.319953i
\(527\) 262976. 220663.i 0.0412468 0.0346102i
\(528\) 1.77381e6 + 1.48841e6i 0.276900 + 0.232347i
\(529\) 345476. + 1.95929e6i 0.0536758 + 0.304410i
\(530\) 1.30280e7 + 4.74180e6i 2.01459 + 0.733252i
\(531\) 1.28806e6 0.198244
\(532\) 2.86154e6 + 1.94439e6i 0.438350 + 0.297855i
\(533\) −127201. −0.0193942
\(534\) −5.55049e6 2.02021e6i −0.842322 0.306580i
\(535\) 2.30662e6 + 1.30815e7i 0.348410 + 1.97593i
\(536\) −3.09453e6 2.59662e6i −0.465247 0.390388i
\(537\) 9.75566e6 8.18597e6i 1.45989 1.22500i
\(538\) 430793. 2.44315e6i 0.0641672 0.363910i
\(539\) 316530. 548246.i 0.0469292 0.0812838i
\(540\) 8.34403e6 + 1.44523e7i 1.23138 + 2.13281i
\(541\) 5.55355e6 2.02133e6i 0.815789 0.296923i 0.0997758 0.995010i \(-0.468187\pi\)
0.716013 + 0.698087i \(0.245965\pi\)
\(542\) −4.22134e6 + 1.53644e6i −0.617237 + 0.224656i
\(543\) 6.64648e6 + 1.15120e7i 0.967369 + 1.67553i
\(544\) 29593.5 51257.4i 0.00428744 0.00742607i
\(545\) −340497. + 1.93106e6i −0.0491047 + 0.278486i
\(546\) 1.14727e6 962673.i 0.164696 0.138197i
\(547\) −7.89559e6 6.62518e6i −1.12828 0.946738i −0.129285 0.991607i \(-0.541268\pi\)
−0.998993 + 0.0448700i \(0.985713\pi\)
\(548\) −37384.0 212015.i −0.00531782 0.0301589i
\(549\) −1.30205e7 4.73906e6i −1.84372 0.671060i
\(550\) −5.95551e6 −0.839484
\(551\) −7.03569e6 4.78069e6i −0.987251 0.670828i
\(552\) −5.50831e6 −0.769433
\(553\) −1.80002e6 655153.i −0.250302 0.0911025i
\(554\) 1.34246e6 + 7.61350e6i 0.185835 + 1.05393i
\(555\) 583366. + 489502.i 0.0803912 + 0.0674562i
\(556\) −1.35619e6 + 1.13798e6i −0.186051 + 0.156116i
\(557\) 1.94188e6 1.10129e7i 0.265206 1.50406i −0.503240 0.864146i \(-0.667859\pi\)
0.768447 0.639914i \(-0.221030\pi\)
\(558\) 7.55659e6 1.30884e7i 1.02740 1.77951i
\(559\) −370962. 642526.i −0.0502112 0.0869683i
\(560\) 2.95767e6 1.07650e6i 0.398547 0.145059i
\(561\) 491276. 178810.i 0.0659051 0.0239875i
\(562\) −1.87576e6 3.24891e6i −0.250517 0.433908i
\(563\) −2.12649e6 + 3.68319e6i −0.282744 + 0.489726i −0.972060 0.234735i \(-0.924578\pi\)
0.689316 + 0.724461i \(0.257911\pi\)
\(564\) −129549. + 734709.i −0.0171489 + 0.0972562i
\(565\) 6.63137e6 5.56438e6i 0.873941 0.733324i
\(566\) −1.44343e6 1.21118e6i −0.189389 0.158916i
\(567\) −4.55878e6 2.58541e7i −0.595513 3.37732i
\(568\) 1.51495e6 + 551398.i 0.197028 + 0.0717124i
\(569\) 2.55215e6 0.330465 0.165233 0.986255i \(-0.447163\pi\)
0.165233 + 0.986255i \(0.447163\pi\)
\(570\) −6.84390e6 + 1.52314e7i −0.882301 + 1.96360i
\(571\) −5.71384e6 −0.733395 −0.366698 0.930340i \(-0.619512\pi\)
−0.366698 + 0.930340i \(0.619512\pi\)
\(572\) 421485. + 153408.i 0.0538632 + 0.0196046i
\(573\) 793465. + 4.49996e6i 0.100958 + 0.572562i
\(574\) 582824. + 489047.i 0.0738342 + 0.0619543i
\(575\) 1.08527e7 9.10648e6i 1.36889 1.14863i
\(576\) 452469. 2.56608e6i 0.0568241 0.322266i
\(577\) −7.76723e6 + 1.34532e7i −0.971240 + 1.68224i −0.279415 + 0.960170i \(0.590141\pi\)
−0.691824 + 0.722066i \(0.743193\pi\)
\(578\) 2.83303e6 + 4.90696e6i 0.352722 + 0.610932i
\(579\) 2.61279e7 9.50977e6i 3.23898 1.17889i
\(580\) −7.27204e6 + 2.64681e6i −0.897608 + 0.326702i
\(581\) 5.51161e6 + 9.54639e6i 0.677389 + 1.17327i
\(582\) 2.41686e6 4.18613e6i 0.295763 0.512277i
\(583\) 2.05204e6 1.16377e7i 0.250043 1.41807i
\(584\) 1.66591e6 1.39787e6i 0.202125 0.169603i
\(585\) 4.00686e6 + 3.36216e6i 0.484077 + 0.406189i
\(586\) −312726. 1.77356e6i −0.0376201 0.213354i
\(587\) −1.51226e7 5.50419e6i −1.81147 0.659322i −0.996848 0.0793349i \(-0.974720\pi\)
−0.814625 0.579987i \(-0.803057\pi\)
\(588\) −984495. −0.117428
\(589\) 9.29798e6 945148.i 1.10433 0.112257i
\(590\) 724663. 0.0857050
\(591\) 213814. + 77822.0i 0.0251807 + 0.00916502i
\(592\) −12760.5 72368.5i −0.00149646 0.00848682i
\(593\) 8.40984e6 + 7.05669e6i 0.982089 + 0.824071i 0.984403 0.175926i \(-0.0562921\pi\)
−0.00231383 + 0.999997i \(0.500737\pi\)
\(594\) 1.08965e7 9.14321e6i 1.26712 1.06324i
\(595\) 123401. 699844.i 0.0142899 0.0810418i
\(596\) −2.03396e6 + 3.52293e6i −0.234546 + 0.406245i
\(597\) 3.33357e6 + 5.77391e6i 0.382802 + 0.663032i
\(598\) −1.00264e6 + 364932.i −0.114655 + 0.0417311i
\(599\) −1.35227e7 + 4.92188e6i −1.53992 + 0.560485i −0.966026 0.258445i \(-0.916790\pi\)
−0.573893 + 0.818930i \(0.694568\pi\)
\(600\) 4.63081e6 + 8.02080e6i 0.525145 + 0.909577i
\(601\) −830649. + 1.43873e6i −0.0938062 + 0.162477i −0.909110 0.416557i \(-0.863237\pi\)
0.815304 + 0.579034i \(0.196570\pi\)
\(602\) −770589. + 4.37023e6i −0.0866626 + 0.491488i
\(603\) −3.07591e7 + 2.58100e7i −3.44493 + 2.89064i
\(604\) 3.83144e6 + 3.21496e6i 0.427336 + 0.358577i
\(605\) −1.05637e6 5.99096e6i −0.117335 0.665439i
\(606\) 1.45226e7 + 5.28578e6i 1.60643 + 0.584693i
\(607\) −2.67042e6 −0.294177 −0.147088 0.989123i \(-0.546990\pi\)
−0.147088 + 0.989123i \(0.546990\pi\)
\(608\) 1.45066e6 701407.i 0.159150 0.0769505i
\(609\) 2.20247e7 2.40640
\(610\) −7.32530e6 2.66619e6i −0.797078 0.290113i
\(611\) 25094.4 + 142317.i 0.00271940 + 0.0154225i
\(612\) −450670. 378157.i −0.0486385 0.0408125i
\(613\) 672954. 564676.i 0.0723326 0.0606943i −0.605905 0.795537i \(-0.707189\pi\)
0.678237 + 0.734843i \(0.262744\pi\)
\(614\) −141381. + 801812.i −0.0151346 + 0.0858325i
\(615\) −1.83610e6 + 3.18022e6i −0.195753 + 0.339054i
\(616\) −1.34140e6 2.32338e6i −0.142432 0.246700i
\(617\) 1.29954e7 4.72996e6i 1.37429 0.500201i 0.453848 0.891079i \(-0.350051\pi\)
0.920442 + 0.390879i \(0.127829\pi\)
\(618\) 1.90721e7 6.94167e6i 2.00876 0.731127i
\(619\) −3.33999e6 5.78502e6i −0.350363 0.606846i 0.635950 0.771730i \(-0.280608\pi\)
−0.986313 + 0.164884i \(0.947275\pi\)
\(620\) 4.25133e6 7.36352e6i 0.444166 0.769318i
\(621\) −5.87578e6 + 3.33232e7i −0.611416 + 3.46751i
\(622\) −7.18118e6 + 6.02572e6i −0.744251 + 0.624501i
\(623\) 5.24246e6 + 4.39894e6i 0.541146 + 0.454076i
\(624\) −121125. 686936.i −0.0124530 0.0706244i
\(625\) 1.12485e6 + 409412.i 0.115185 + 0.0419237i
\(626\) −8.55119e6 −0.872149
\(627\) 1.37984e7 + 3.49046e6i 1.40172 + 0.354579i
\(628\) −3.96344e6 −0.401027
\(629\) −15590.8 5674.60i −0.00157124 0.000571885i
\(630\) −5.43267e6 3.08102e7i −0.545333 3.09274i
\(631\) 8.82660e6 + 7.40640e6i 0.882511 + 0.740515i 0.966694 0.255936i \(-0.0823836\pi\)
−0.0841830 + 0.996450i \(0.526828\pi\)
\(632\) −683437. + 573472.i −0.0680622 + 0.0571110i
\(633\) 619179. 3.51154e6i 0.0614196 0.348328i
\(634\) 1.38752e6 2.40325e6i 0.137093 0.237452i
\(635\) −7.37169e6 1.27681e7i −0.725492 1.25659i
\(636\) −1.72691e7 + 6.28545e6i −1.69289 + 0.616160i
\(637\) −179201. + 65224.0i −0.0174982 + 0.00636882i
\(638\) 3.29812e6 + 5.71250e6i 0.320785 + 0.555616i
\(639\) 8.01239e6 1.38779e7i 0.776265 1.34453i
\(640\) 254559. 1.44367e6i 0.0245662 0.139322i
\(641\) 1.18820e7 9.97017e6i 1.14220 0.958423i 0.142696 0.989767i \(-0.454423\pi\)
0.999509 + 0.0313431i \(0.00997845\pi\)
\(642\) −1.34882e7 1.13179e7i −1.29156 1.08375i
\(643\) 1.90688e6 + 1.08145e7i 0.181885 + 1.03152i 0.929893 + 0.367831i \(0.119899\pi\)
−0.748008 + 0.663690i \(0.768989\pi\)
\(644\) 5.99707e6 + 2.18276e6i 0.569803 + 0.207391i
\(645\) −2.14188e7 −2.02720
\(646\) 26617.7 362831.i 0.00250951 0.0342076i
\(647\) 670576. 0.0629778 0.0314889 0.999504i \(-0.489975\pi\)
0.0314889 + 0.999504i \(0.489975\pi\)
\(648\) −1.14899e7 4.18200e6i −1.07493 0.391243i
\(649\) −107259. 608293.i −0.00999586 0.0566893i
\(650\) 1.37431e6 + 1.15318e6i 0.127585 + 0.107057i
\(651\) −1.85374e7 + 1.55547e7i −1.71434 + 1.43850i
\(652\) 1.03941e6 5.89481e6i 0.0957568 0.543064i
\(653\) 972476. 1.68438e6i 0.0892475 0.154581i −0.817946 0.575295i \(-0.804887\pi\)
0.907193 + 0.420714i \(0.138220\pi\)
\(654\) −1.29959e6 2.25096e6i −0.118813 0.205790i
\(655\) −1.07441e7 + 3.91052e6i −0.978510 + 0.356149i
\(656\) 332984. 121196.i 0.0302109 0.0109959i
\(657\) −1.08080e7 1.87201e7i −0.976863 1.69198i
\(658\) 432184. 748565.i 0.0389139 0.0674008i
\(659\) −498145. + 2.82512e6i −0.0446830 + 0.253410i −0.998964 0.0455001i \(-0.985512\pi\)
0.954281 + 0.298910i \(0.0966230\pi\)
\(660\) 9.91941e6 8.32338e6i 0.886393 0.743772i
\(661\) −4.39101e6 3.68450e6i −0.390896 0.328001i 0.426066 0.904692i \(-0.359899\pi\)
−0.816962 + 0.576691i \(0.804344\pi\)
\(662\) 1.00594e6 + 5.70496e6i 0.0892127 + 0.505950i
\(663\) −147991. 53864.5i −0.0130753 0.00475903i
\(664\) 5.13407e6 0.451899
\(665\) 1.34869e7 1.38709e7i 1.18265 1.21633i
\(666\) −730427. −0.0638104
\(667\) −1.47450e7 5.36675e6i −1.28331 0.467086i
\(668\) 1.72489e6 + 9.78233e6i 0.149562 + 0.848206i
\(669\) −500677. 420118.i −0.0432506 0.0362916i
\(670\) −1.73051e7 + 1.45207e7i −1.48931 + 1.24968i
\(671\) −1.15381e6 + 6.54359e6i −0.0989302 + 0.561061i
\(672\) −2.08606e6 + 3.61317e6i −0.178199 + 0.308649i
\(673\) 7.14930e6 + 1.23830e7i 0.608452 + 1.05387i 0.991496 + 0.130139i \(0.0415423\pi\)
−0.383044 + 0.923730i \(0.625124\pi\)
\(674\) 5.05366e6 1.83938e6i 0.428505 0.155963i
\(675\) 5.34626e7 1.94588e7i 4.51638 1.64383i
\(676\) 2.90279e6 + 5.02777e6i 0.244314 + 0.423164i
\(677\) −8.02151e6 + 1.38937e7i −0.672643 + 1.16505i 0.304509 + 0.952509i \(0.401508\pi\)
−0.977152 + 0.212542i \(0.931826\pi\)
\(678\) −1.99257e6 + 1.13004e7i −0.166471 + 0.944105i
\(679\) −4.29013e6 + 3.59985e6i −0.357105 + 0.299647i
\(680\) −253546. 212751.i −0.0210274 0.0176441i
\(681\) −6.57114e6 3.72668e7i −0.542967 3.07932i
\(682\) −6.81029e6 2.47874e6i −0.560667 0.204066i
\(683\) −2.01746e6 −0.165483 −0.0827416 0.996571i \(-0.526368\pi\)
−0.0827416 + 0.996571i \(0.526368\pi\)
\(684\) −4.36207e6 1.54109e7i −0.356494 1.25947i
\(685\) −1.20391e6 −0.0980317
\(686\) −7.60900e6 2.76945e6i −0.617330 0.224690i
\(687\) −401354. 2.27619e6i −0.0324441 0.184000i
\(688\) 1.58329e6 + 1.32854e6i 0.127523 + 0.107005i
\(689\) −2.72698e6 + 2.28820e6i −0.218843 + 0.183631i
\(690\) −5.34892e6 + 3.03352e7i −0.427704 + 2.42563i
\(691\) −1.72264e6 + 2.98370e6i −0.137246 + 0.237717i −0.926453 0.376410i \(-0.877158\pi\)
0.789207 + 0.614127i \(0.210492\pi\)
\(692\) −1.78337e6 3.08888e6i −0.141571 0.245209i
\(693\) −2.50584e7 + 9.12053e6i −1.98208 + 0.721418i
\(694\) −1.14686e7 + 4.17422e6i −0.903879 + 0.328985i
\(695\) 4.95010e6 + 8.57382e6i 0.388733 + 0.673306i
\(696\) 5.12902e6 8.88372e6i 0.401339 0.695139i
\(697\) 13892.9 78790.6i 0.00108321 0.00614317i
\(698\) −370243. + 310670.i −0.0287639 + 0.0241358i
\(699\) −5.51547e6 4.62803e6i −0.426962 0.358264i
\(700\) −1.86334e6 1.05675e7i −0.143730 0.815133i
\(701\) 9.34576e6 + 3.40158e6i 0.718323 + 0.261448i 0.675214 0.737622i \(-0.264051\pi\)
0.0431092 + 0.999070i \(0.486274\pi\)
\(702\) −4.28491e6 −0.328170
\(703\) −264248. 366331.i −0.0201661 0.0279567i
\(704\) −1.24952e6 −0.0950192
\(705\) 3.92037e6 + 1.42690e6i 0.297067 + 0.108124i
\(706\) 1.14997e6 + 6.52182e6i 0.0868312 + 0.492444i
\(707\) −1.37166e7 1.15096e7i −1.03204 0.865988i
\(708\) −735840. + 617443.i −0.0551697 + 0.0462929i
\(709\) −3.57390e6 + 2.02686e7i −0.267010 + 1.51429i 0.496240 + 0.868185i \(0.334714\pi\)
−0.763250 + 0.646103i \(0.776398\pi\)
\(710\) 4.50776e6 7.80767e6i 0.335595 0.581267i
\(711\) 4.43398e6 + 7.67988e6i 0.328942 + 0.569745i
\(712\) 2.99516e6 1.09015e6i 0.221422 0.0805909i
\(713\) 1.62006e7 5.89652e6i 1.19345 0.434382i
\(714\) 470992. + 815782.i 0.0345755 + 0.0598864i
\(715\) 1.25414e6 2.17223e6i 0.0917444 0.158906i
\(716\) −1.19333e6 + 6.76773e6i −0.0869919 + 0.493356i
\(717\) 3.15825e6 2.65008e6i 0.229429 0.192514i
\(718\) 1.43126e7 + 1.20097e7i 1.03611 + 0.869402i
\(719\) 608105. + 3.44874e6i 0.0438689 + 0.248793i 0.998854 0.0478609i \(-0.0152404\pi\)
−0.954985 + 0.296654i \(0.904129\pi\)
\(720\) −1.36925e7 4.98366e6i −0.984354 0.358275i
\(721\) −2.35151e7 −1.68465
\(722\) 6.15095e6 7.76292e6i 0.439136 0.554220i
\(723\) 1.83878e7 1.30823
\(724\) −6.74056e6 2.45336e6i −0.477914 0.173946i
\(725\) 4.58141e6 + 2.59825e7i 0.323708 + 1.83584i
\(726\) 6.17721e6 + 5.18330e6i 0.434962 + 0.364976i
\(727\) 1.62731e7 1.36548e7i 1.14192 0.958183i 0.142418 0.989807i \(-0.454512\pi\)
0.999500 + 0.0316233i \(0.0100677\pi\)
\(728\) −140336. + 795887.i −0.00981390 + 0.0556574i
\(729\) −1.87740e7 + 3.25176e7i −1.30839 + 2.26620i
\(730\) −6.08060e6 1.05319e7i −0.422318 0.731475i
\(731\) 438508. 159604.i 0.0303518 0.0110471i
\(732\) 9.70999e6 3.53415e6i 0.669794 0.243785i
\(733\) −1.23297e7 2.13557e7i −0.847603 1.46809i −0.883342 0.468730i \(-0.844712\pi\)
0.0357389 0.999361i \(-0.488622\pi\)
\(734\) 8.02434e6 1.38986e7i 0.549755 0.952204i
\(735\) −956008. + 5.42179e6i −0.0652744 + 0.370190i
\(736\) 2.27699e6 1.91062e6i 0.154941 0.130011i
\(737\) 1.47502e7 + 1.23769e7i 1.00030 + 0.839350i
\(738\) −611626. 3.46871e6i −0.0413376 0.234437i
\(739\) −9.29858e6 3.38441e6i −0.626333 0.227967i 0.00930138 0.999957i \(-0.497039\pi\)
−0.635635 + 0.771990i \(0.719261\pi\)
\(740\) −410937. −0.0275865
\(741\) −2.50829e6 3.47729e6i −0.167816 0.232646i
\(742\) 2.12922e7 1.41974
\(743\) 1.24700e7 + 4.53872e6i 0.828696 + 0.301621i 0.721324 0.692598i \(-0.243534\pi\)
0.107372 + 0.994219i \(0.465756\pi\)
\(744\) 1.95712e6 + 1.10994e7i 0.129624 + 0.735135i
\(745\) 1.74263e7 + 1.46224e7i 1.15031 + 0.965223i
\(746\) −3.59276e6 + 3.01468e6i −0.236364 + 0.198333i
\(747\) 8.86158e6 5.02565e7i 0.581045 3.29527i
\(748\) −141058. + 244320.i −0.00921817 + 0.0159663i
\(749\) 1.02001e7 + 1.76671e7i 0.664354 + 1.15069i
\(750\) 1.75068e7 6.37197e6i 1.13646 0.413638i
\(751\) −1.82592e7 + 6.64582e6i −1.18136 + 0.429981i −0.856683 0.515844i \(-0.827479\pi\)
−0.324679 + 0.945824i \(0.605256\pi\)
\(752\) −201290. 348645.i −0.0129801 0.0224822i
\(753\) 1.30966e7 2.26839e7i 0.841724 1.45791i
\(754\) 345046. 1.95685e6i 0.0221029 0.125352i
\(755\) 2.14259e7 1.79785e7i 1.36796 1.14785i
\(756\) 1.96331e7 + 1.64741e7i 1.24935 + 1.04833i
\(757\) −3.11786e6 1.76823e7i −0.197750 1.12150i −0.908447 0.417999i \(-0.862732\pi\)
0.710697 0.703498i \(-0.248380\pi\)
\(758\) −4.58691e6 1.66950e6i −0.289966 0.105539i
\(759\) 2.62556e7 1.65431
\(760\) −2.45409e6 8.67014e6i −0.154119 0.544493i
\(761\) −3.11076e7 −1.94717 −0.973587 0.228315i \(-0.926678\pi\)
−0.973587 + 0.228315i \(0.926678\pi\)
\(762\) 1.83644e7 + 6.68409e6i 1.14575 + 0.417018i
\(763\) 522929. + 2.96568e6i 0.0325186 + 0.184422i
\(764\) −1.88886e6 1.58494e6i −0.117076 0.0982382i
\(765\) −2.52021e6 + 2.11471e6i −0.155698 + 0.130646i
\(766\) 1.74620e6 9.90322e6i 0.107528 0.609824i
\(767\) −93034.1 + 161140.i −0.00571023 + 0.00989041i
\(768\)