Properties

Label 13.7.f.a.7.3
Level 13
Weight 7
Character 13.7
Analytic conductor 2.991
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 13.f (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.99070308706\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 7.3
Character \(\chi\) = 13.7
Dual form 13.7.f.a.2.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.77368 + 1.27910i) q^{2} +(4.54257 - 7.86796i) q^{3} +(-34.2737 + 19.7879i) q^{4} +(-109.630 - 109.630i) q^{5} +(-11.6208 + 43.3696i) q^{6} +(-504.391 - 135.151i) q^{7} +(361.954 - 361.954i) q^{8} +(323.230 + 559.851i) q^{9} +O(q^{10})\) \(q+(-4.77368 + 1.27910i) q^{2} +(4.54257 - 7.86796i) q^{3} +(-34.2737 + 19.7879i) q^{4} +(-109.630 - 109.630i) q^{5} +(-11.6208 + 43.3696i) q^{6} +(-504.391 - 135.151i) q^{7} +(361.954 - 361.954i) q^{8} +(323.230 + 559.851i) q^{9} +(663.567 + 383.110i) q^{10} +(246.492 + 919.919i) q^{11} +359.552i q^{12} +(300.508 - 2176.35i) q^{13} +2580.68 q^{14} +(-1360.56 + 364.562i) q^{15} +(1.54938 - 2.68361i) q^{16} +(-5348.10 + 3087.73i) q^{17} +(-2259.11 - 2259.11i) q^{18} +(1060.35 - 3957.28i) q^{19} +(5926.77 + 1588.07i) q^{20} +(-3354.60 + 3354.60i) q^{21} +(-2353.35 - 4076.12i) q^{22} +(-9993.12 - 5769.53i) q^{23} +(-1203.64 - 4492.04i) q^{24} +8412.42i q^{25} +(1349.25 + 10773.6i) q^{26} +12496.2 q^{27} +(19961.7 - 5348.72i) q^{28} +(-186.040 + 322.231i) q^{29} +(6028.59 - 3480.61i) q^{30} +(-10895.2 - 10895.2i) q^{31} +(-8482.96 + 31658.8i) q^{32} +(8357.59 + 2239.41i) q^{33} +(21580.6 - 21580.6i) q^{34} +(40479.7 + 70113.0i) q^{35} +(-22156.6 - 12792.1i) q^{36} +(-22349.7 - 83410.4i) q^{37} +20247.1i q^{38} +(-15758.4 - 12250.6i) q^{39} -79361.9 q^{40} +(1614.20 - 432.523i) q^{41} +(11722.9 - 20304.7i) q^{42} +(-88370.0 + 51020.4i) q^{43} +(-26651.5 - 26651.5i) q^{44} +(25940.7 - 96812.1i) q^{45} +(55083.8 + 14759.7i) q^{46} +(-27686.6 + 27686.6i) q^{47} +(-14.0764 - 24.3810i) q^{48} +(134258. + 77513.7i) q^{49} +(-10760.4 - 40158.3i) q^{50} +56104.9i q^{51} +(32765.9 + 80538.0i) q^{52} +239411. q^{53} +(-59653.1 + 15984.0i) q^{54} +(73827.8 - 127874. i) q^{55} +(-231485. + 133648. i) q^{56} +(-26319.0 - 26319.0i) q^{57} +(475.930 - 1776.20i) q^{58} +(120217. + 32212.1i) q^{59} +(39417.6 - 39417.6i) q^{60} +(38209.4 + 66180.6i) q^{61} +(65946.4 + 38074.2i) q^{62} +(-87369.9 - 326069. i) q^{63} -161782. i q^{64} +(-271538. + 205648. i) q^{65} -42761.0 q^{66} +(-354858. + 95083.9i) q^{67} +(122199. - 211656. i) q^{68} +(-90788.9 + 52417.0i) q^{69} +(-282919. - 282919. i) q^{70} +(-111837. + 417380. i) q^{71} +(319635. + 85645.9i) q^{72} +(343212. - 343212. i) q^{73} +(213381. + 369587. i) q^{74} +(66188.6 + 38214.0i) q^{75} +(41964.2 + 156613. i) q^{76} -497313. i q^{77} +(90895.3 + 38323.9i) q^{78} -559268. q^{79} +(-464.063 + 124.345i) q^{80} +(-178870. + 309811. i) q^{81} +(-7152.43 + 4129.46i) q^{82} +(-55181.9 - 55181.9i) q^{83} +(48593.9 - 181355. i) q^{84} +(924819. + 247805. i) q^{85} +(356590. - 356590. i) q^{86} +(1690.20 + 2927.52i) q^{87} +(422187. + 243750. i) q^{88} +(-189901. - 708722. i) q^{89} +495331. i q^{90} +(-445710. + 1.05712e6i) q^{91} +456668. q^{92} +(-135215. + 36230.8i) q^{93} +(96753.1 - 167581. i) q^{94} +(-550082. + 317590. i) q^{95} +(210556. + 210556. i) q^{96} +(328784. - 1.22704e6i) q^{97} +(-740052. - 198296. i) q^{98} +(-435344. + 435344. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{2} - 2q^{3} - 6q^{4} - 114q^{5} + 634q^{6} + 316q^{7} - 1398q^{8} - 1946q^{9} + O(q^{10}) \) \( 24q - 12q^{2} - 2q^{3} - 6q^{4} - 114q^{5} + 634q^{6} + 316q^{7} - 1398q^{8} - 1946q^{9} + 4674q^{10} + 228q^{11} - 1552q^{13} - 14616q^{14} + 7486q^{15} - 2138q^{16} + 20898q^{17} - 5630q^{18} - 14036q^{19} - 14634q^{20} - 314q^{21} + 37852q^{22} + 29634q^{23} + 47154q^{24} + 510q^{26} - 107060q^{27} - 40572q^{28} + 1026q^{29} - 247734q^{30} - 118116q^{31} + 180876q^{32} + 306046q^{33} + 101898q^{34} + 104862q^{35} + 105066q^{36} - 31470q^{37} + 28510q^{39} - 275328q^{40} - 357216q^{41} - 25636q^{42} - 480486q^{43} - 797712q^{44} + 464248q^{45} + 1012050q^{46} + 140028q^{47} + 676102q^{48} + 854562q^{49} + 756714q^{50} - 771704q^{52} - 1397076q^{53} - 1271048q^{54} - 205490q^{55} - 1461108q^{56} - 1483394q^{57} + 1133806q^{58} + 1568052q^{59} + 886808q^{60} + 768676q^{61} + 3741966q^{62} + 1336264q^{63} - 946968q^{65} - 5076928q^{66} - 1489892q^{67} - 569052q^{68} - 1475766q^{69} - 2626556q^{70} + 2136948q^{71} + 4787052q^{72} + 326326q^{73} + 2159718q^{74} + 3466008q^{75} + 1522158q^{76} - 1573544q^{78} - 1734344q^{79} - 5214300q^{80} - 773072q^{81} - 3540426q^{82} - 3642132q^{83} + 2952364q^{84} + 3509916q^{85} - 132324q^{86} + 531698q^{87} + 4478052q^{88} + 632754q^{89} - 2946788q^{91} - 1656060q^{92} - 295514q^{93} + 1552210q^{94} - 2753718q^{95} - 3979208q^{96} + 2258214q^{97} + 4984308q^{98} + 4336480q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.77368 + 1.27910i −0.596711 + 0.159888i −0.544518 0.838749i \(-0.683288\pi\)
−0.0521922 + 0.998637i \(0.516621\pi\)
\(3\) 4.54257 7.86796i 0.168243 0.291406i −0.769559 0.638576i \(-0.779524\pi\)
0.937802 + 0.347170i \(0.112857\pi\)
\(4\) −34.2737 + 19.7879i −0.535526 + 0.309186i
\(5\) −109.630 109.630i −0.877039 0.877039i 0.116188 0.993227i \(-0.462932\pi\)
−0.993227 + 0.116188i \(0.962932\pi\)
\(6\) −11.6208 + 43.3696i −0.0538002 + 0.200785i
\(7\) −504.391 135.151i −1.47053 0.394027i −0.567416 0.823431i \(-0.692057\pi\)
−0.903112 + 0.429404i \(0.858724\pi\)
\(8\) 361.954 361.954i 0.706941 0.706941i
\(9\) 323.230 + 559.851i 0.443388 + 0.767971i
\(10\) 663.567 + 383.110i 0.663567 + 0.383110i
\(11\) 246.492 + 919.919i 0.185193 + 0.691149i 0.994589 + 0.103886i \(0.0331278\pi\)
−0.809396 + 0.587263i \(0.800206\pi\)
\(12\) 359.552i 0.208074i
\(13\) 300.508 2176.35i 0.136781 0.990601i
\(14\) 2580.68 0.940480
\(15\) −1360.56 + 364.562i −0.403130 + 0.108018i
\(16\) 1.54938 2.68361i 0.000378267 0.000655178i
\(17\) −5348.10 + 3087.73i −1.08856 + 0.628481i −0.933193 0.359375i \(-0.882990\pi\)
−0.155368 + 0.987857i \(0.549656\pi\)
\(18\) −2259.11 2259.11i −0.387364 0.387364i
\(19\) 1060.35 3957.28i 0.154592 0.576947i −0.844547 0.535481i \(-0.820130\pi\)
0.999140 0.0414662i \(-0.0132029\pi\)
\(20\) 5926.77 + 1588.07i 0.740846 + 0.198509i
\(21\) −3354.60 + 3354.60i −0.362228 + 0.362228i
\(22\) −2353.35 4076.12i −0.221013 0.382806i
\(23\) −9993.12 5769.53i −0.821330 0.474195i 0.0295450 0.999563i \(-0.490594\pi\)
−0.850875 + 0.525368i \(0.823927\pi\)
\(24\) −1203.64 4492.04i −0.0870687 0.324945i
\(25\) 8412.42i 0.538395i
\(26\) 1349.25 + 10773.6i 0.0767666 + 0.612972i
\(27\) 12496.2 0.634875
\(28\) 19961.7 5348.72i 0.909334 0.243655i
\(29\) −186.040 + 322.231i −0.00762804 + 0.0132122i −0.869814 0.493379i \(-0.835761\pi\)
0.862186 + 0.506592i \(0.169095\pi\)
\(30\) 6028.59 3480.61i 0.223281 0.128911i
\(31\) −10895.2 10895.2i −0.365722 0.365722i 0.500193 0.865914i \(-0.333263\pi\)
−0.865914 + 0.500193i \(0.833263\pi\)
\(32\) −8482.96 + 31658.8i −0.258879 + 0.966151i
\(33\) 8357.59 + 2239.41i 0.232562 + 0.0623149i
\(34\) 21580.6 21580.6i 0.549069 0.549069i
\(35\) 40479.7 + 70113.0i 0.944134 + 1.63529i
\(36\) −22156.6 12792.1i −0.474892 0.274179i
\(37\) −22349.7 83410.4i −0.441232 1.64670i −0.725696 0.688015i \(-0.758482\pi\)
0.284464 0.958687i \(-0.408184\pi\)
\(38\) 20247.1i 0.368988i
\(39\) −15758.4 12250.6i −0.265655 0.206521i
\(40\) −79361.9 −1.24003
\(41\) 1614.20 432.523i 0.0234210 0.00627563i −0.247090 0.968993i \(-0.579474\pi\)
0.270511 + 0.962717i \(0.412808\pi\)
\(42\) 11722.9 20304.7i 0.158229 0.274061i
\(43\) −88370.0 + 51020.4i −1.11147 + 0.641710i −0.939211 0.343341i \(-0.888441\pi\)
−0.172264 + 0.985051i \(0.555108\pi\)
\(44\) −26651.5 26651.5i −0.312869 0.312869i
\(45\) 25940.7 96812.1i 0.284672 1.06241i
\(46\) 55083.8 + 14759.7i 0.565914 + 0.151636i
\(47\) −27686.6 + 27686.6i −0.266671 + 0.266671i −0.827758 0.561086i \(-0.810384\pi\)
0.561086 + 0.827758i \(0.310384\pi\)
\(48\) −14.0764 24.3810i −0.000127282 0.000220459i
\(49\) 134258. + 77513.7i 1.14117 + 0.658856i
\(50\) −10760.4 40158.3i −0.0860830 0.321266i
\(51\) 56104.9i 0.422951i
\(52\) 32765.9 + 80538.0i 0.233030 + 0.572784i
\(53\) 239411. 1.60811 0.804056 0.594554i \(-0.202671\pi\)
0.804056 + 0.594554i \(0.202671\pi\)
\(54\) −59653.1 + 15984.0i −0.378837 + 0.101509i
\(55\) 73827.8 127874.i 0.443743 0.768586i
\(56\) −231485. + 133648.i −1.31813 + 0.761024i
\(57\) −26319.0 26319.0i −0.142117 0.142117i
\(58\) 475.930 1776.20i 0.00243927 0.00910347i
\(59\) 120217. + 32212.1i 0.585344 + 0.156842i 0.539324 0.842098i \(-0.318680\pi\)
0.0460194 + 0.998941i \(0.485346\pi\)
\(60\) 39417.6 39417.6i 0.182489 0.182489i
\(61\) 38209.4 + 66180.6i 0.168337 + 0.291569i 0.937835 0.347080i \(-0.112827\pi\)
−0.769498 + 0.638649i \(0.779494\pi\)
\(62\) 65946.4 + 38074.2i 0.276704 + 0.159755i
\(63\) −87369.9 326069.i −0.349414 1.30403i
\(64\) 161782.i 0.617148i
\(65\) −271538. + 205648.i −0.988758 + 0.748834i
\(66\) −42761.0 −0.148736
\(67\) −354858. + 95083.9i −1.17986 + 0.316142i −0.794870 0.606779i \(-0.792461\pi\)
−0.384988 + 0.922921i \(0.625795\pi\)
\(68\) 122199. 211656.i 0.388635 0.673136i
\(69\) −90788.9 + 52417.0i −0.276366 + 0.159560i
\(70\) −282919. 282919.i −0.824838 0.824838i
\(71\) −111837. + 417380.i −0.312470 + 1.16616i 0.613851 + 0.789422i \(0.289619\pi\)
−0.926322 + 0.376734i \(0.877047\pi\)
\(72\) 319635. + 85645.9i 0.856360 + 0.229461i
\(73\) 343212. 343212.i 0.882256 0.882256i −0.111508 0.993764i \(-0.535568\pi\)
0.993764 + 0.111508i \(0.0355681\pi\)
\(74\) 213381. + 369587.i 0.526576 + 0.912057i
\(75\) 66188.6 + 38214.0i 0.156892 + 0.0905814i
\(76\) 41964.2 + 156613.i 0.0955957 + 0.356768i
\(77\) 497313.i 1.08933i
\(78\) 90895.3 + 38323.9i 0.191539 + 0.0807582i
\(79\) −559268. −1.13433 −0.567164 0.823605i \(-0.691959\pi\)
−0.567164 + 0.823605i \(0.691959\pi\)
\(80\) −464.063 + 124.345i −0.000906372 + 0.000242862i
\(81\) −178870. + 309811.i −0.336575 + 0.582965i
\(82\) −7152.43 + 4129.46i −0.0129721 + 0.00748947i
\(83\) −55181.9 55181.9i −0.0965078 0.0965078i 0.657205 0.753712i \(-0.271739\pi\)
−0.753712 + 0.657205i \(0.771739\pi\)
\(84\) 48593.9 181355.i 0.0819867 0.305979i
\(85\) 924819. + 247805.i 1.50591 + 0.403508i
\(86\) 356590. 356590.i 0.560627 0.560627i
\(87\) 1690.20 + 2927.52i 0.00256673 + 0.00444571i
\(88\) 422187. + 243750.i 0.619522 + 0.357681i
\(89\) −189901. 708722.i −0.269376 1.00532i −0.959517 0.281649i \(-0.909119\pi\)
0.690142 0.723674i \(-0.257548\pi\)
\(90\) 495331.i 0.679467i
\(91\) −445710. + 1.05712e6i −0.591464 + 1.40281i
\(92\) 456668. 0.586458
\(93\) −135215. + 36230.8i −0.168104 + 0.0450432i
\(94\) 96753.1 167581.i 0.116488 0.201763i
\(95\) −550082. + 317590.i −0.641589 + 0.370421i
\(96\) 210556. + 210556.i 0.237987 + 0.237987i
\(97\) 328784. 1.22704e6i 0.360243 1.34444i −0.513514 0.858081i \(-0.671657\pi\)
0.873757 0.486363i \(-0.161677\pi\)
\(98\) −740052. 198296.i −0.786293 0.210686i
\(99\) −435344. + 435344.i −0.448670 + 0.448670i
\(100\) −166464. 288325.i −0.166464 0.288325i
\(101\) −304548. 175831.i −0.295591 0.170660i 0.344869 0.938651i \(-0.387923\pi\)
−0.640461 + 0.767991i \(0.721257\pi\)
\(102\) −71764.0 267827.i −0.0676248 0.252379i
\(103\) 272950.i 0.249788i 0.992170 + 0.124894i \(0.0398591\pi\)
−0.992170 + 0.124894i \(0.960141\pi\)
\(104\) −678969. 896509.i −0.603601 0.796993i
\(105\) 735528. 0.635377
\(106\) −1.14287e6 + 306232.i −0.959577 + 0.257118i
\(107\) 635277. 1.10033e6i 0.518575 0.898199i −0.481192 0.876615i \(-0.659796\pi\)
0.999767 0.0215836i \(-0.00687080\pi\)
\(108\) −428292. + 247275.i −0.339992 + 0.196295i
\(109\) 201347. + 201347.i 0.155477 + 0.155477i 0.780559 0.625082i \(-0.214935\pi\)
−0.625082 + 0.780559i \(0.714935\pi\)
\(110\) −188867. + 704861.i −0.141899 + 0.529573i
\(111\) −757795. 203050.i −0.554093 0.148469i
\(112\) −1144.19 + 1144.19i −0.000814411 + 0.000814411i
\(113\) 186229. + 322559.i 0.129066 + 0.223549i 0.923315 0.384043i \(-0.125469\pi\)
−0.794249 + 0.607593i \(0.792135\pi\)
\(114\) 159303. + 91973.8i 0.107525 + 0.0620797i
\(115\) 463032. + 1.72806e6i 0.304451 + 1.13623i
\(116\) 14725.4i 0.00943394i
\(117\) 1.31557e6 535222.i 0.821401 0.334177i
\(118\) −615082. −0.374358
\(119\) 3.11485e6 834621.i 1.84840 0.495277i
\(120\) −360507. + 624417.i −0.208627 + 0.361352i
\(121\) 748723. 432276.i 0.422635 0.244008i
\(122\) −267052. 267052.i −0.147067 0.147067i
\(123\) 3929.53 14665.2i 0.00211167 0.00788084i
\(124\) 589012. + 157825.i 0.308930 + 0.0827774i
\(125\) −790714. + 790714.i −0.404846 + 0.404846i
\(126\) 834153. + 1.44480e6i 0.416998 + 0.722262i
\(127\) 281444. + 162492.i 0.137398 + 0.0793270i 0.567123 0.823633i \(-0.308056\pi\)
−0.429725 + 0.902960i \(0.641390\pi\)
\(128\) −335974. 1.25387e6i −0.160205 0.597893i
\(129\) 927055.i 0.431854i
\(130\) 1.03319e6 1.32903e6i 0.470273 0.604928i
\(131\) −855957. −0.380748 −0.190374 0.981712i \(-0.560970\pi\)
−0.190374 + 0.981712i \(0.560970\pi\)
\(132\) −330759. + 88626.5i −0.143810 + 0.0385338i
\(133\) −1.06966e6 + 1.85271e6i −0.454665 + 0.787503i
\(134\) 1.57236e6 907801.i 0.653487 0.377291i
\(135\) −1.36996e6 1.36996e6i −0.556810 0.556810i
\(136\) −818151. + 3.05338e6i −0.325250 + 1.21385i
\(137\) −1.84280e6 493778.i −0.716667 0.192030i −0.117983 0.993016i \(-0.537643\pi\)
−0.598684 + 0.800985i \(0.704309\pi\)
\(138\) 366351. 366351.i 0.139399 0.139399i
\(139\) −2.06373e6 3.57448e6i −0.768437 1.33097i −0.938410 0.345523i \(-0.887702\pi\)
0.169973 0.985449i \(-0.445632\pi\)
\(140\) −2.77478e6 1.60202e6i −1.01122 0.583826i
\(141\) 92068.9 + 343606.i 0.0328440 + 0.122575i
\(142\) 2.13549e6i 0.745818i
\(143\) 2.07614e6 260009.i 0.709984 0.0889161i
\(144\) 2003.23 0.000670877
\(145\) 55721.8 14930.6i 0.0182777 0.00489749i
\(146\) −1.19938e6 + 2.07739e6i −0.385389 + 0.667513i
\(147\) 1.21975e6 704223.i 0.383989 0.221696i
\(148\) 2.41653e6 + 2.41653e6i 0.745429 + 0.745429i
\(149\) 176765. 659697.i 0.0534366 0.199428i −0.934047 0.357150i \(-0.883748\pi\)
0.987484 + 0.157722i \(0.0504151\pi\)
\(150\) −364843. 97759.5i −0.108102 0.0289658i
\(151\) −3.13486e6 + 3.13486e6i −0.910515 + 0.910515i −0.996313 0.0857972i \(-0.972656\pi\)
0.0857972 + 0.996313i \(0.472656\pi\)
\(152\) −1.04856e6 1.81615e6i −0.298580 0.517155i
\(153\) −3.45734e6 1.99609e6i −0.965311 0.557323i
\(154\) 636116. + 2.37402e6i 0.174170 + 0.650012i
\(155\) 2.38888e6i 0.641504i
\(156\) 782511. + 108048.i 0.206118 + 0.0284606i
\(157\) 3.83603e6 0.991250 0.495625 0.868537i \(-0.334939\pi\)
0.495625 + 0.868537i \(0.334939\pi\)
\(158\) 2.66977e6 715362.i 0.676865 0.181366i
\(159\) 1.08754e6 1.88367e6i 0.270554 0.468613i
\(160\) 4.40074e6 2.54077e6i 1.07440 0.620305i
\(161\) 4.26068e6 + 4.26068e6i 1.02094 + 1.02094i
\(162\) 457586. 1.70774e6i 0.107629 0.401676i
\(163\) −4.52726e6 1.21308e6i −1.04538 0.280108i −0.305036 0.952341i \(-0.598669\pi\)
−0.740340 + 0.672233i \(0.765335\pi\)
\(164\) −46765.7 + 46765.7i −0.0106022 + 0.0106022i
\(165\) −670736. 1.16175e6i −0.149314 0.258619i
\(166\) 334004. + 192837.i 0.0730176 + 0.0421568i
\(167\) 1.65611e6 + 6.18070e6i 0.355582 + 1.32705i 0.879750 + 0.475437i \(0.157710\pi\)
−0.524167 + 0.851615i \(0.675623\pi\)
\(168\) 2.42842e6i 0.512148i
\(169\) −4.64620e6 1.30802e6i −0.962582 0.270991i
\(170\) −4.73176e6 −0.963111
\(171\) 2.55822e6 685474.i 0.511623 0.137089i
\(172\) 2.01918e6 3.49732e6i 0.396816 0.687305i
\(173\) −1.88157e6 + 1.08632e6i −0.363397 + 0.209807i −0.670570 0.741846i \(-0.733950\pi\)
0.307173 + 0.951654i \(0.400617\pi\)
\(174\) −11813.1 11813.1i −0.00224241 0.00224241i
\(175\) 1.13695e6 4.24315e6i 0.212142 0.791725i
\(176\) 2850.62 + 763.820i 0.000522878 + 0.000140105i
\(177\) 799539. 799539.i 0.144185 0.144185i
\(178\) 1.81306e6 + 3.14031e6i 0.321479 + 0.556817i
\(179\) 7.13572e6 + 4.11981e6i 1.24417 + 0.718320i 0.969940 0.243345i \(-0.0782447\pi\)
0.274227 + 0.961665i \(0.411578\pi\)
\(180\) 1.02663e6 + 3.83142e6i 0.176033 + 0.656965i
\(181\) 6.89585e6i 1.16293i −0.813573 0.581463i \(-0.802481\pi\)
0.813573 0.581463i \(-0.197519\pi\)
\(182\) 775515. 5.61646e6i 0.128640 0.931641i
\(183\) 694275. 0.113287
\(184\) −5.70535e6 + 1.52875e6i −0.915860 + 0.245404i
\(185\) −6.69407e6 + 1.15945e7i −1.05724 + 1.83120i
\(186\) 599132. 345909.i 0.0931073 0.0537555i
\(187\) −4.15872e6 4.15872e6i −0.635968 0.635968i
\(188\) 401062. 1.49678e6i 0.0603584 0.225261i
\(189\) −6.30300e6 1.68888e6i −0.933602 0.250158i
\(190\) 2.21969e6 2.21969e6i 0.323617 0.323617i
\(191\) −3.49255e6 6.04927e6i −0.501236 0.868166i −0.999999 0.00142767i \(-0.999546\pi\)
0.498763 0.866738i \(-0.333788\pi\)
\(192\) −1.27289e6 734904.i −0.179841 0.103831i
\(193\) −170632. 636806.i −0.0237349 0.0885799i 0.953042 0.302837i \(-0.0979337\pi\)
−0.976777 + 0.214257i \(0.931267\pi\)
\(194\) 6.27804e6i 0.859842i
\(195\) 384554. + 3.07062e6i 0.0518626 + 0.414116i
\(196\) −6.13534e6 −0.814836
\(197\) −3.13085e6 + 838909.i −0.409509 + 0.109728i −0.457692 0.889111i \(-0.651324\pi\)
0.0481825 + 0.998839i \(0.484657\pi\)
\(198\) 1.52135e6 2.63505e6i 0.195989 0.339463i
\(199\) 1.17491e7 6.78336e6i 1.49089 0.860767i 0.490947 0.871190i \(-0.336651\pi\)
0.999946 + 0.0104224i \(0.00331760\pi\)
\(200\) 3.04491e6 + 3.04491e6i 0.380614 + 0.380614i
\(201\) −863850. + 3.22393e6i −0.106378 + 0.397007i
\(202\) 1.67872e6 + 449813.i 0.203669 + 0.0545730i
\(203\) 137387. 137387.i 0.0164232 0.0164232i
\(204\) −1.11020e6 1.92292e6i −0.130771 0.226501i
\(205\) −224382. 129547.i −0.0260451 0.0150371i
\(206\) −349132. 1.30298e6i −0.0399381 0.149051i
\(207\) 7.45954e6i 0.841010i
\(208\) −5374.88 4178.45i −0.000597281 0.000464328i
\(209\) 3.90175e6 0.427386
\(210\) −3.51118e6 + 940818.i −0.379136 + 0.101589i
\(211\) −167666. + 290406.i −0.0178483 + 0.0309142i −0.874812 0.484463i \(-0.839015\pi\)
0.856963 + 0.515377i \(0.172348\pi\)
\(212\) −8.20549e6 + 4.73744e6i −0.861186 + 0.497206i
\(213\) 2.77590e6 + 2.77590e6i 0.287253 + 0.287253i
\(214\) −1.62517e6 + 6.06523e6i −0.165828 + 0.618879i
\(215\) 1.52814e7 + 4.09463e6i 1.53761 + 0.412002i
\(216\) 4.52307e6 4.52307e6i 0.448819 0.448819i
\(217\) 4.02295e6 + 6.96795e6i 0.393700 + 0.681908i
\(218\) −1.21871e6 703624.i −0.117634 0.0679158i
\(219\) −1.14132e6 4.25945e6i −0.108661 0.405528i
\(220\) 5.84359e6i 0.548797i
\(221\) 5.11283e6 + 1.25672e7i 0.473680 + 1.16429i
\(222\) 3.87720e6 0.354372
\(223\) 7.94252e6 2.12819e6i 0.716215 0.191909i 0.117733 0.993045i \(-0.462437\pi\)
0.598482 + 0.801136i \(0.295771\pi\)
\(224\) 8.55747e6 1.48220e7i 0.761379 1.31875i
\(225\) −4.70970e6 + 2.71915e6i −0.413472 + 0.238718i
\(226\) −1.30159e6 1.30159e6i −0.112758 0.112758i
\(227\) −1.76030e6 + 6.56953e6i −0.150490 + 0.561638i 0.848959 + 0.528459i \(0.177230\pi\)
−0.999449 + 0.0331793i \(0.989437\pi\)
\(228\) 1.42285e6 + 381251.i 0.120048 + 0.0321667i
\(229\) −7.40252e6 + 7.40252e6i −0.616415 + 0.616415i −0.944610 0.328195i \(-0.893560\pi\)
0.328195 + 0.944610i \(0.393560\pi\)
\(230\) −4.42073e6 7.65694e6i −0.363338 0.629320i
\(231\) −3.91284e6 2.25908e6i −0.317436 0.183272i
\(232\) 49294.9 + 183971.i 0.00394764 + 0.0147328i
\(233\) 2.35159e7i 1.85906i −0.368745 0.929531i \(-0.620212\pi\)
0.368745 0.929531i \(-0.379788\pi\)
\(234\) −5.59549e6 + 4.23773e6i −0.436707 + 0.330739i
\(235\) 6.07057e6 0.467763
\(236\) −4.75770e6 + 1.27482e6i −0.361960 + 0.0969870i
\(237\) −2.54051e6 + 4.40030e6i −0.190843 + 0.330550i
\(238\) −1.38017e7 + 7.96843e6i −1.02377 + 0.591074i
\(239\) −1.42176e7 1.42176e7i −1.04144 1.04144i −0.999103 0.0423355i \(-0.986520\pi\)
−0.0423355 0.999103i \(-0.513480\pi\)
\(240\) −1129.69 + 4216.07i −8.17197e−5 + 0.000304982i
\(241\) 3.44530e6 + 923165.i 0.246136 + 0.0659520i 0.379778 0.925078i \(-0.376000\pi\)
−0.133642 + 0.991030i \(0.542667\pi\)
\(242\) −3.02124e6 + 3.02124e6i −0.213177 + 0.213177i
\(243\) 6.17994e6 + 1.07040e7i 0.430690 + 0.745978i
\(244\) −2.61915e6 1.51217e6i −0.180298 0.104095i
\(245\) −6.22084e6 2.32165e7i −0.423010 1.57869i
\(246\) 75033.3i 0.00504021i
\(247\) −8.29378e6 3.49689e6i −0.550379 0.232055i
\(248\) −7.88713e6 −0.517087
\(249\) −684836. + 183501.i −0.0443597 + 0.0118861i
\(250\) 2.76321e6 4.78602e6i 0.176846 0.306306i
\(251\) −6.54138e6 + 3.77667e6i −0.413665 + 0.238829i −0.692363 0.721549i \(-0.743430\pi\)
0.278699 + 0.960379i \(0.410097\pi\)
\(252\) 9.44671e6 + 9.44671e6i 0.590309 + 0.590309i
\(253\) 2.84428e6 1.06150e7i 0.175635 0.655479i
\(254\) −1.55137e6 415689.i −0.0946705 0.0253669i
\(255\) 6.15077e6 6.15077e6i 0.370945 0.370945i
\(256\) 8.38468e6 + 1.45227e7i 0.499766 + 0.865620i
\(257\) 2.36040e7 + 1.36278e7i 1.39055 + 0.802834i 0.993376 0.114910i \(-0.0366580\pi\)
0.397173 + 0.917744i \(0.369991\pi\)
\(258\) −1.18580e6 4.42547e6i −0.0690483 0.257692i
\(259\) 4.50921e7i 2.59538i
\(260\) 5.23724e6 1.24215e7i 0.297977 0.706730i
\(261\) −240535. −0.0135287
\(262\) 4.08607e6 1.09486e6i 0.227197 0.0608771i
\(263\) −1.21155e6 + 2.09846e6i −0.0665998 + 0.115354i −0.897403 0.441213i \(-0.854548\pi\)
0.830803 + 0.556567i \(0.187882\pi\)
\(264\) 3.83563e6 2.21450e6i 0.208461 0.120355i
\(265\) −2.62466e7 2.62466e7i −1.41038 1.41038i
\(266\) 2.73642e6 1.02125e7i 0.145391 0.542607i
\(267\) −6.43884e6 1.72528e6i −0.338278 0.0906413i
\(268\) 1.02808e7 1.02808e7i 0.534098 0.534098i
\(269\) 1.25867e7 + 2.18008e7i 0.646628 + 1.11999i 0.983923 + 0.178594i \(0.0571548\pi\)
−0.337295 + 0.941399i \(0.609512\pi\)
\(270\) 8.29209e6 + 4.78744e6i 0.421282 + 0.243227i
\(271\) −3.19870e6 1.19377e7i −0.160719 0.599810i −0.998548 0.0538771i \(-0.982842\pi\)
0.837829 0.545933i \(-0.183825\pi\)
\(272\) 19136.3i 0.000950936i
\(273\) 6.29270e6 + 8.30886e6i 0.309278 + 0.408370i
\(274\) 9.42855e6 0.458346
\(275\) −7.73875e6 + 2.07359e6i −0.372111 + 0.0997069i
\(276\) 2.07444e6 3.59304e6i 0.0986676 0.170897i
\(277\) −3.22905e7 + 1.86429e7i −1.51927 + 0.877153i −0.519530 + 0.854452i \(0.673893\pi\)
−0.999742 + 0.0227006i \(0.992774\pi\)
\(278\) 1.44237e7 + 1.44237e7i 0.671341 + 0.671341i
\(279\) 2.57803e6 9.62136e6i 0.118707 0.443020i
\(280\) 4.00295e7 + 1.07259e7i 1.82350 + 0.488605i
\(281\) 1.19883e7 1.19883e7i 0.540304 0.540304i −0.383314 0.923618i \(-0.625217\pi\)
0.923618 + 0.383314i \(0.125217\pi\)
\(282\) −879016. 1.52250e6i −0.0391967 0.0678906i
\(283\) 1.22628e6 + 707994.i 0.0541042 + 0.0312371i 0.526808 0.849984i \(-0.323389\pi\)
−0.472704 + 0.881221i \(0.656722\pi\)
\(284\) −4.42603e6 1.65182e7i −0.193223 0.721118i
\(285\) 5.77070e6i 0.249284i
\(286\) −9.57826e6 + 3.89680e6i −0.409438 + 0.166575i
\(287\) −872643. −0.0369140
\(288\) −2.04662e7 + 5.48390e6i −0.856761 + 0.229568i
\(289\) 6.99935e6 1.21232e7i 0.289977 0.502256i
\(290\) −246900. + 142548.i −0.0101234 + 0.00584476i
\(291\) −8.16076e6 8.16076e6i −0.331170 0.331170i
\(292\) −4.97169e6 + 1.85546e7i −0.199690 + 0.745252i
\(293\) −2.35256e7 6.30367e6i −0.935273 0.250606i −0.241171 0.970483i \(-0.577531\pi\)
−0.694102 + 0.719877i \(0.744198\pi\)
\(294\) −4.92193e6 + 4.92193e6i −0.193684 + 0.193684i
\(295\) −9.64800e6 1.67108e7i −0.375812 0.650926i
\(296\) −3.82803e7 2.21011e7i −1.47605 0.852196i
\(297\) 3.08022e6 + 1.14955e7i 0.117574 + 0.438793i
\(298\) 3.37529e6i 0.127545i
\(299\) −1.55595e7 + 2.00147e7i −0.582081 + 0.748749i
\(300\) −3.02470e6 −0.112026
\(301\) 5.14685e7 1.37910e7i 1.88731 0.505702i
\(302\) 1.09550e7 1.89746e7i 0.397734 0.688895i
\(303\) −2.76686e6 + 1.59745e6i −0.0994626 + 0.0574247i
\(304\) −8976.91 8976.91i −0.000319526 0.000319526i
\(305\) 3.06648e6 1.14443e7i 0.108079 0.403356i
\(306\) 1.90574e7 + 5.10643e6i 0.665121 + 0.178219i
\(307\) −1.63598e7 + 1.63598e7i −0.565410 + 0.565410i −0.930839 0.365429i \(-0.880922\pi\)
0.365429 + 0.930839i \(0.380922\pi\)
\(308\) 9.84079e6 + 1.70447e7i 0.336804 + 0.583362i
\(309\) 2.14756e6 + 1.23989e6i 0.0727897 + 0.0420251i
\(310\) −3.05563e6 1.14038e7i −0.102569 0.382792i
\(311\) 5.07520e7i 1.68722i −0.536957 0.843610i \(-0.680426\pi\)
0.536957 0.843610i \(-0.319574\pi\)
\(312\) −1.01380e7 + 1.26964e6i −0.333800 + 0.0418041i
\(313\) −2.28509e6 −0.0745197 −0.0372599 0.999306i \(-0.511863\pi\)
−0.0372599 + 0.999306i \(0.511863\pi\)
\(314\) −1.83120e7 + 4.90669e6i −0.591489 + 0.158489i
\(315\) −2.61686e7 + 4.53253e7i −0.837236 + 1.45014i
\(316\) 1.91682e7 1.10667e7i 0.607462 0.350718i
\(317\) 7.52499e6 + 7.52499e6i 0.236226 + 0.236226i 0.815285 0.579059i \(-0.196580\pi\)
−0.579059 + 0.815285i \(0.696580\pi\)
\(318\) −2.78216e6 + 1.03831e7i −0.0865167 + 0.322885i
\(319\) −342284. 91714.8i −0.0105442 0.00282532i
\(320\) −1.77361e7 + 1.77361e7i −0.541263 + 0.541263i
\(321\) −5.77158e6 9.99667e6i −0.174494 0.302232i
\(322\) −2.57890e7 1.48893e7i −0.772444 0.445971i
\(323\) 6.54814e6 + 2.44380e7i 0.194317 + 0.725201i
\(324\) 1.41578e7i 0.416257i
\(325\) 1.83084e7 + 2.52800e6i 0.533335 + 0.0736423i
\(326\) 2.31634e7 0.668573
\(327\) 2.49882e6 669558.i 0.0714649 0.0191489i
\(328\) 427712. 740819.i 0.0121208 0.0209938i
\(329\) 1.77068e7 1.02230e7i 0.497224 0.287072i
\(330\) 4.68788e6 + 4.68788e6i 0.130447 + 0.130447i
\(331\) −2.71683e6 + 1.01394e7i −0.0749168 + 0.279593i −0.993214 0.116297i \(-0.962897\pi\)
0.918298 + 0.395891i \(0.129564\pi\)
\(332\) 2.98322e6 + 799351.i 0.0815213 + 0.0218436i
\(333\) 3.94733e7 3.94733e7i 1.06898 1.06898i
\(334\) −1.58115e7 2.73863e7i −0.424360 0.735012i
\(335\) 4.93271e7 + 2.84790e7i 1.31205 + 0.757513i
\(336\) 3804.87 + 14200.0i 0.000100305 + 0.000374343i
\(337\) 6.33481e6i 0.165518i 0.996570 + 0.0827588i \(0.0263731\pi\)
−0.996570 + 0.0827588i \(0.973627\pi\)
\(338\) 2.38526e7 + 301113.i 0.617711 + 0.00779794i
\(339\) 3.38384e6 0.0868581
\(340\) −3.66005e7 + 9.80707e6i −0.931215 + 0.249518i
\(341\) 7.33714e6 1.27083e7i 0.185039 0.320497i
\(342\) −1.13354e7 + 6.54447e6i −0.283372 + 0.163605i
\(343\) −1.38016e7 1.38016e7i −0.342017 0.342017i
\(344\) −1.35188e7 + 5.04529e7i −0.332096 + 1.23940i
\(345\) 1.56996e7 + 4.20671e6i 0.382325 + 0.102444i
\(346\) 7.59248e6 7.59248e6i 0.183297 0.183297i
\(347\) 1.00637e7 + 1.74308e7i 0.240862 + 0.417186i 0.960960 0.276687i \(-0.0892365\pi\)
−0.720098 + 0.693872i \(0.755903\pi\)
\(348\) −115859. 66891.1i −0.00274911 0.00158720i
\(349\) 1.03111e7 + 3.84816e7i 0.242566 + 0.905268i 0.974591 + 0.223991i \(0.0719086\pi\)
−0.732025 + 0.681277i \(0.761425\pi\)
\(350\) 2.17098e7i 0.506350i
\(351\) 3.75522e6 2.71962e7i 0.0868389 0.628908i
\(352\) −3.12146e7 −0.715697
\(353\) −1.26671e7 + 3.39413e6i −0.287973 + 0.0771622i −0.399914 0.916553i \(-0.630960\pi\)
0.111941 + 0.993715i \(0.464293\pi\)
\(354\) −2.79405e6 + 4.83944e6i −0.0629832 + 0.109090i
\(355\) 5.80179e7 3.34967e7i 1.29681 0.748715i
\(356\) 2.05327e7 + 2.05327e7i 0.455090 + 0.455090i
\(357\) 7.58264e6 2.82988e7i 0.166654 0.621961i
\(358\) −3.93333e7 1.05393e7i −0.857258 0.229702i
\(359\) −1.46920e7 + 1.46920e7i −0.317538 + 0.317538i −0.847821 0.530283i \(-0.822086\pi\)
0.530283 + 0.847821i \(0.322086\pi\)
\(360\) −2.56522e7 4.44309e7i −0.549815 0.952308i
\(361\) 2.62072e7 + 1.51307e7i 0.557056 + 0.321617i
\(362\) 8.82052e6 + 3.29186e7i 0.185938 + 0.693930i
\(363\) 7.85457e6i 0.164211i
\(364\) −5.64204e6 4.50510e7i −0.116986 0.934115i
\(365\) −7.52527e7 −1.54755
\(366\) −3.31425e6 + 888051.i −0.0675993 + 0.0181132i
\(367\) −1.81304e7 + 3.14028e7i −0.366784 + 0.635288i −0.989061 0.147509i \(-0.952874\pi\)
0.622277 + 0.782797i \(0.286208\pi\)
\(368\) −30966.3 + 17878.4i −0.000621365 + 0.000358745i
\(369\) 763906. + 763906.i 0.0152041 + 0.0152041i
\(370\) 1.71248e7 6.39108e7i 0.338081 1.26174i
\(371\) −1.20757e8 3.23567e7i −2.36477 0.633639i
\(372\) 3.91739e6 3.91739e6i 0.0760971 0.0760971i
\(373\) −2.08755e7 3.61574e7i −0.402263 0.696740i 0.591735 0.806132i \(-0.298443\pi\)
−0.993999 + 0.109392i \(0.965110\pi\)
\(374\) 2.51719e7 + 1.45330e7i 0.481173 + 0.277805i
\(375\) 2.62943e6 + 9.81318e6i 0.0498618 + 0.186087i
\(376\) 2.00426e7i 0.377042i
\(377\) 645382. + 501722.i 0.0120446 + 0.00936352i
\(378\) 3.22488e7 0.597087
\(379\) −4.40128e6 + 1.17932e6i −0.0808466 + 0.0216628i −0.299016 0.954248i \(-0.596658\pi\)
0.218169 + 0.975911i \(0.429992\pi\)
\(380\) 1.25689e7 2.17700e7i 0.229058 0.396741i
\(381\) 2.55696e6 1.47626e6i 0.0462327 0.0266925i
\(382\) 2.44100e7 + 2.44100e7i 0.437902 + 0.437902i
\(383\) −2.73848e6 + 1.02201e7i −0.0487431 + 0.181912i −0.986005 0.166713i \(-0.946685\pi\)
0.937262 + 0.348625i \(0.113351\pi\)
\(384\) −1.13916e7 3.05237e6i −0.201183 0.0539068i
\(385\) −5.45204e7 + 5.45204e7i −0.955381 + 0.955381i
\(386\) 1.62908e6 + 2.82165e6i 0.0283257 + 0.0490616i
\(387\) −5.71277e7 3.29827e7i −0.985630 0.569054i
\(388\) 1.30119e7 + 4.85610e7i 0.222764 + 0.831367i
\(389\) 3.79607e7i 0.644889i −0.946588 0.322445i \(-0.895495\pi\)
0.946588 0.322445i \(-0.104505\pi\)
\(390\) −5.76339e6 1.41663e7i −0.0971592 0.238815i
\(391\) 7.12590e7 1.19209
\(392\) 7.66515e7 2.05387e7i 1.27251 0.340969i
\(393\) −3.88824e6 + 6.73463e6i −0.0640583 + 0.110952i
\(394\) 1.38726e7 8.00938e6i 0.226814 0.130951i
\(395\) 6.13125e7 + 6.13125e7i 0.994850 + 0.994850i
\(396\) 6.30629e6 2.35354e7i 0.101552 0.378997i
\(397\) 4.47978e7 + 1.20035e7i 0.715954 + 0.191839i 0.598366 0.801223i \(-0.295817\pi\)
0.117588 + 0.993062i \(0.462484\pi\)
\(398\) −4.74100e7 + 4.74100e7i −0.752005 + 0.752005i
\(399\) 9.71803e6 + 1.68321e7i 0.152989 + 0.264984i
\(400\) 22575.7 + 13034.1i 0.000352745 + 0.000203657i
\(401\) −1.78451e6 6.65990e6i −0.0276750 0.103284i 0.950707 0.310091i \(-0.100360\pi\)
−0.978382 + 0.206807i \(0.933693\pi\)
\(402\) 1.64950e7i 0.253907i
\(403\) −2.69859e7 + 2.04377e7i −0.412308 + 0.312260i
\(404\) 1.39173e7 0.211063
\(405\) 5.35741e7 1.43551e7i 0.806472 0.216094i
\(406\) −480110. + 831575.i −0.00717402 + 0.0124258i
\(407\) 7.12218e7 4.11199e7i 1.05640 0.609915i
\(408\) 2.03074e7 + 2.03074e7i 0.299002 + 0.299002i
\(409\) −1.04813e7 + 3.91166e7i −0.153195 + 0.571730i 0.846058 + 0.533090i \(0.178969\pi\)
−0.999253 + 0.0386403i \(0.987697\pi\)
\(410\) 1.23683e6 + 331408.i 0.0179456 + 0.00480852i
\(411\) −1.22561e7 + 1.22561e7i −0.176533 + 0.176533i
\(412\) −5.40111e6 9.35500e6i −0.0772309 0.133768i
\(413\) −5.62830e7 3.24950e7i −0.798964 0.461282i
\(414\) 9.54154e6 + 3.56095e7i 0.134468 + 0.501840i
\(415\) 1.20992e7i 0.169282i
\(416\) 6.63516e7 + 2.79756e7i 0.921661 + 0.388598i
\(417\) −3.74985e7 −0.517137
\(418\) −1.86257e7 + 4.99074e6i −0.255026 + 0.0683339i
\(419\) −1.96125e7 + 3.39698e7i −0.266619 + 0.461797i −0.967986 0.251002i \(-0.919240\pi\)
0.701368 + 0.712800i \(0.252573\pi\)
\(420\) −2.52092e7 + 1.45546e7i −0.340261 + 0.196450i
\(421\) −2.96788e7 2.96788e7i −0.397740 0.397740i 0.479695 0.877435i \(-0.340747\pi\)
−0.877435 + 0.479695i \(0.840747\pi\)
\(422\) 428925. 1.60077e6i 0.00570747 0.0213006i
\(423\) −2.44495e7 6.55124e6i −0.323035 0.0865570i
\(424\) 8.66557e7 8.66557e7i 1.13684 1.13684i
\(425\) −2.59753e7 4.49905e7i −0.338371 0.586076i
\(426\) −1.68019e7 9.70061e6i −0.217336 0.125479i
\(427\) −1.03281e7 3.85450e7i −0.132659 0.495090i
\(428\) 5.02832e7i 0.641345i
\(429\) 7.38527e6 1.75161e7i 0.0935394 0.221853i
\(430\) −7.81858e7 −0.983383
\(431\) 4.23018e6 1.13347e6i 0.0528357 0.0141573i −0.232304 0.972643i \(-0.574627\pi\)
0.285140 + 0.958486i \(0.407960\pi\)
\(432\) 19361.5 33535.0i 0.000240152 0.000415956i
\(433\) 7.46948e7 4.31251e7i 0.920082 0.531210i 0.0364211 0.999337i \(-0.488404\pi\)
0.883661 + 0.468127i \(0.155071\pi\)
\(434\) −2.81170e7 2.81170e7i −0.343954 0.343954i
\(435\) 135647. 506240.i 0.00164794 0.00615019i
\(436\) −1.08851e7 2.91667e6i −0.131333 0.0351906i
\(437\) −3.34278e7 + 3.34278e7i −0.400557 + 0.400557i
\(438\) 1.08966e7 + 1.88734e7i 0.129678 + 0.224609i
\(439\) −8.03083e7 4.63660e7i −0.949220 0.548032i −0.0563814 0.998409i \(-0.517956\pi\)
−0.892839 + 0.450377i \(0.851290\pi\)
\(440\) −1.95621e7 7.30066e7i −0.229645 0.857046i
\(441\) 1.00219e8i 1.16852i
\(442\) −4.04819e7 5.34522e7i −0.468807 0.619011i
\(443\) −5.32456e6 −0.0612453 −0.0306226 0.999531i \(-0.509749\pi\)
−0.0306226 + 0.999531i \(0.509749\pi\)
\(444\) 2.99903e7 8.03589e6i 0.342636 0.0918090i
\(445\) −5.68782e7 + 9.85160e7i −0.645455 + 1.11796i
\(446\) −3.51929e7 + 2.03186e7i −0.396689 + 0.229029i
\(447\) −4.38750e6 4.38750e6i −0.0491241 0.0491241i
\(448\) −2.18650e7 + 8.16012e7i −0.243173 + 0.907534i
\(449\) 1.37952e7 + 3.69642e6i 0.152402 + 0.0408360i 0.334213 0.942497i \(-0.391529\pi\)
−0.181811 + 0.983333i \(0.558196\pi\)
\(450\) 1.90046e7 1.90046e7i 0.208555 0.208555i
\(451\) 795772. + 1.37832e6i 0.00867479 + 0.0150252i
\(452\) −1.27655e7 7.37018e6i −0.138237 0.0798110i
\(453\) 1.04246e7 + 3.89053e7i 0.112141 + 0.418518i
\(454\) 3.36125e7i 0.359197i
\(455\) 1.64755e8 6.70286e7i 1.74906 0.711584i
\(456\) −1.90525e7 −0.200936
\(457\) −2.19469e7 + 5.88065e6i −0.229945 + 0.0616137i −0.371952 0.928252i \(-0.621311\pi\)
0.142006 + 0.989866i \(0.454645\pi\)
\(458\) 2.58687e7 4.48059e7i 0.269264 0.466379i
\(459\) −6.68312e7 + 3.85850e7i −0.691100 + 0.399007i
\(460\) −5.00644e7 5.00644e7i −0.514347 0.514347i
\(461\) −6.59036e6 + 2.45955e7i −0.0672676 + 0.251046i −0.991369 0.131101i \(-0.958149\pi\)
0.924101 + 0.382147i \(0.124815\pi\)
\(462\) 2.15683e7 + 5.77920e6i 0.218720 + 0.0586059i
\(463\) 6.94735e7 6.94735e7i 0.699965 0.699965i −0.264438 0.964403i \(-0.585186\pi\)
0.964403 + 0.264438i \(0.0851864\pi\)
\(464\) 576.495 + 998.519i 5.77088e−6 + 9.99546e-6i
\(465\) 1.87956e7 + 1.08517e7i 0.186938 + 0.107929i
\(466\) 3.00793e7 + 1.12257e8i 0.297242 + 1.10932i
\(467\) 3.86547e7i 0.379534i −0.981829 0.189767i \(-0.939227\pi\)
0.981829 0.189767i \(-0.0607733\pi\)
\(468\) −3.44983e7 + 4.43763e7i −0.336558 + 0.432926i
\(469\) 1.91838e8 1.85958
\(470\) −2.89790e7 + 7.76489e6i −0.279119 + 0.0747897i
\(471\) 1.74254e7 3.01817e7i 0.166771 0.288856i
\(472\) 5.51724e7 3.18538e7i 0.524682 0.302925i
\(473\) −6.87172e7 6.87172e7i −0.649354 0.649354i
\(474\) 6.49916e6 2.42552e7i 0.0610271 0.227756i
\(475\) 3.32903e7 + 8.92011e6i 0.310625 + 0.0832318i
\(476\) −9.02418e7 + 9.02418e7i −0.836733 + 0.836733i
\(477\) 7.73848e7 + 1.34034e8i 0.713018 + 1.23498i
\(478\) 8.60564e7 + 4.96847e7i 0.787951 + 0.454924i
\(479\) −4.41084e7 1.64615e8i −0.401342 1.49783i −0.810704 0.585457i \(-0.800915\pi\)
0.409361 0.912372i \(-0.365752\pi\)
\(480\) 4.61665e7i 0.417449i
\(481\) −1.88247e8 + 2.35754e7i −1.69158 + 0.211848i
\(482\) −1.76276e7 −0.157417
\(483\) 5.28773e7 1.41684e7i 0.469276 0.125742i
\(484\) −1.71077e7 + 2.96313e7i −0.150888 + 0.261346i
\(485\) −1.70564e8 + 9.84755e7i −1.49508 + 0.863183i
\(486\) −4.31926e7 4.31926e7i −0.376271 0.376271i
\(487\) 2.56860e7 9.58613e7i 0.222387 0.829959i −0.761048 0.648696i \(-0.775315\pi\)
0.983435 0.181263i \(-0.0580185\pi\)
\(488\) 3.77844e7 + 1.01243e7i 0.325127 + 0.0871175i
\(489\) −3.01098e7 + 3.01098e7i −0.257502 + 0.257502i
\(490\) 5.93926e7 + 1.02871e8i 0.504829 + 0.874390i
\(491\) 1.91410e8 + 1.10511e8i 1.61704 + 0.933599i 0.987680 + 0.156486i \(0.0500165\pi\)
0.629361 + 0.777113i \(0.283317\pi\)
\(492\) 155514. + 580388.i 0.00130580 + 0.00487330i
\(493\) 2.29777e6i 0.0191763i
\(494\) 4.40648e7 + 6.08442e6i 0.365520 + 0.0504706i
\(495\) 9.54535e7 0.787003
\(496\) −46119.4 + 12357.6i −0.000377953 + 0.000101272i
\(497\) 1.12819e8 1.95408e8i 0.918993 1.59174i
\(498\) 3.03447e6 1.75195e6i 0.0245695 0.0141852i
\(499\) 1.58111e8 + 1.58111e8i 1.27251 + 1.27251i 0.944768 + 0.327739i \(0.106287\pi\)
0.327739 + 0.944768i \(0.393713\pi\)
\(500\) 1.14541e7 4.27472e7i 0.0916327 0.341978i
\(501\) 5.61525e7 + 1.50460e7i 0.446535 + 0.119649i
\(502\) 2.63957e7 2.63957e7i 0.208652 0.208652i
\(503\) −8.01396e7 1.38806e8i −0.629713 1.09070i −0.987609 0.156934i \(-0.949839\pi\)
0.357896 0.933762i \(-0.383494\pi\)
\(504\) −1.49646e8 8.63981e7i −1.16889 0.674858i
\(505\) 1.41113e7 + 5.26639e7i 0.109570 + 0.408921i
\(506\) 5.43108e7i 0.419213i
\(507\) −3.13971e7 + 3.06143e7i −0.240916 + 0.234910i
\(508\) −1.28615e7 −0.0981072
\(509\) −1.30303e8 + 3.49146e7i −0.988100 + 0.264760i −0.716452 0.697636i \(-0.754235\pi\)
−0.271648 + 0.962397i \(0.587568\pi\)
\(510\) −2.14944e7 + 3.72293e7i −0.162037 + 0.280656i
\(511\) −2.19499e8 + 1.26728e8i −1.64501 + 0.949750i
\(512\) 143600. + 143600.i 0.00106990 + 0.00106990i
\(513\) 1.32504e7 4.94511e7i 0.0981469 0.366289i
\(514\) −1.30109e8 3.48627e7i −0.958119 0.256727i
\(515\) 2.99235e7 2.99235e7i 0.219074 0.219074i
\(516\) −1.83445e7 3.17736e7i −0.133523 0.231269i
\(517\) −3.22940e7 1.86449e7i −0.233695 0.134924i
\(518\) −5.76775e7 2.15255e8i −0.414970 1.54869i
\(519\) 1.97388e7i 0.141195i
\(520\) −2.38489e7 + 1.72719e8i −0.169613 + 1.22838i
\(521\) −1.31409e8 −0.929203 −0.464602 0.885520i \(-0.653802\pi\)
−0.464602 + 0.885520i \(0.653802\pi\)
\(522\) 1.14824e6 307670.i 0.00807274 0.00216309i
\(523\) 1.29159e8 2.23710e8i 0.902857 1.56379i 0.0790898 0.996867i \(-0.474799\pi\)
0.823768 0.566927i \(-0.191868\pi\)
\(524\) 2.93368e7 1.69376e7i 0.203901 0.117722i
\(525\) −2.82203e7 2.82203e7i −0.195022 0.195022i
\(526\) 3.09939e6 1.15671e7i 0.0212970 0.0794816i
\(527\) 9.19102e7 + 2.46273e7i 0.627960 + 0.168261i
\(528\) 18958.8 18958.8i 0.000128798 0.000128798i
\(529\) −7.44298e6 1.28916e7i −0.0502782 0.0870844i
\(530\) 1.58865e8 + 9.17208e7i 1.06709 + 0.616084i
\(531\) 2.08239e7 + 7.77157e7i 0.139084 + 0.519069i
\(532\) 8.46655e7i 0.562305i
\(533\) −456242. 3.64304e6i −0.00301310 0.0240592i
\(534\) 3.29438e7 0.216346
\(535\) −1.90275e8 + 5.09839e7i −1.24257 + 0.332945i
\(536\) −9.40262e7 + 1.62858e8i −0.610597 + 1.05758i
\(537\) 6.48290e7 3.74290e7i 0.418645 0.241705i
\(538\) −8.79704e7 8.79704e7i −0.564924 0.564924i
\(539\) −3.82130e7 + 1.42613e8i −0.244031 + 0.910735i
\(540\) 7.40623e7 + 1.98449e7i 0.470344 + 0.126028i
\(541\) 5.85677e7 5.85677e7i 0.369885 0.369885i −0.497550 0.867435i \(-0.665767\pi\)
0.867435 + 0.497550i \(0.165767\pi\)
\(542\) 3.05392e7 + 5.28954e7i 0.191805 + 0.332216i
\(543\) −5.42563e7 3.13249e7i −0.338883 0.195654i
\(544\) −5.23862e7 1.95508e8i −0.325402 1.21442i
\(545\) 4.41473e7i 0.272719i
\(546\) −4.06673e7 3.16149e7i −0.249843 0.194229i
\(547\) −2.34576e8 −1.43325 −0.716623 0.697461i \(-0.754313\pi\)
−0.716623 + 0.697461i \(0.754313\pi\)
\(548\) 7.29304e7 1.95417e7i 0.443167 0.118746i
\(549\) −2.47009e7 + 4.27831e7i −0.149278 + 0.258557i
\(550\) 3.42900e7 1.97974e7i 0.206101 0.118992i
\(551\) 1.07789e6 + 1.07789e6i 0.00644348 + 0.00644348i
\(552\) −1.38889e7 + 5.18339e7i −0.0825751 + 0.308175i
\(553\) 2.82090e8 + 7.55858e7i 1.66806 + 0.446956i
\(554\) 1.30298e8 1.30298e8i 0.766320 0.766320i
\(555\) 6.08165e7 + 1.05337e8i 0.355748 + 0.616174i
\(556\) 1.41463e8 + 8.16738e7i 0.823036 + 0.475180i
\(557\) −4.49513e7 1.67761e8i −0.260122 0.970788i −0.965169 0.261627i \(-0.915741\pi\)
0.705047 0.709160i \(-0.250926\pi\)
\(558\) 4.92269e7i 0.283335i
\(559\) 8.44825e7 + 2.07656e8i 0.483650 + 1.18880i
\(560\) 250875. 0.00142854
\(561\) −5.16120e7 + 1.38294e7i −0.292322 + 0.0783275i
\(562\) −4.18941e7 + 7.25626e7i −0.236017 + 0.408794i
\(563\) 9.12800e6 5.27005e6i 0.0511505 0.0295318i −0.474207 0.880414i \(-0.657265\pi\)
0.525357 + 0.850882i \(0.323932\pi\)
\(564\) −9.95478e6 9.95478e6i −0.0554874 0.0554874i
\(565\) 1.49458e7 5.57784e7i 0.0828653 0.309258i
\(566\) −6.75948e6 1.81120e6i −0.0372790 0.00998888i
\(567\) 1.32092e8 1.32092e8i 0.724647 0.724647i
\(568\) 1.10593e8 + 1.91552e8i 0.603505 + 1.04530i
\(569\) 1.67525e8 + 9.67207e7i 0.909376 + 0.525028i 0.880230 0.474547i \(-0.157388\pi\)
0.0291456 + 0.999575i \(0.490721\pi\)
\(570\) −7.38133e6 2.75475e7i −0.0398575 0.148750i
\(571\) 2.47411e6i 0.0132896i −0.999978 0.00664479i \(-0.997885\pi\)
0.999978 0.00664479i \(-0.00211512\pi\)
\(572\) −6.60119e7 + 4.99939e7i −0.352723 + 0.267134i
\(573\) −6.34605e7 −0.337318
\(574\) 4.16572e6 1.11620e6i 0.0220270 0.00590211i
\(575\) 4.85357e7 8.40664e7i 0.255304 0.442200i
\(576\) 9.05736e7 5.22927e7i 0.473952 0.273636i
\(577\) −2.77747e7 2.77747e7i −0.144584 0.144584i 0.631109 0.775694i \(-0.282600\pi\)
−0.775694 + 0.631109i \(0.782600\pi\)
\(578\) −1.79058e7 + 6.68254e7i −0.0927279 + 0.346065i
\(579\) −5.78547e6 1.55021e6i −0.0298059 0.00798648i
\(580\) −1.61434e6 + 1.61434e6i −0.00827393 + 0.00827393i
\(581\) 2.03754e7 + 3.52912e7i 0.103891 + 0.179944i
\(582\) 4.93953e7 + 2.85184e7i 0.250563 + 0.144663i
\(583\) 5.90128e7 + 2.20239e8i 0.297811 + 1.11144i
\(584\) 2.48454e8i 1.24741i
\(585\) −2.02902e8 8.55489e7i −1.01349 0.427314i
\(586\) 1.20367e8 0.598156
\(587\) 2.88532e6 773119.i 0.0142653 0.00382236i −0.251679 0.967811i \(-0.580983\pi\)
0.265945 + 0.963988i \(0.414316\pi\)
\(588\) −2.78702e7 + 4.82726e7i −0.137091 + 0.237448i
\(589\) −5.46681e7 + 3.15627e7i −0.267540 + 0.154464i
\(590\) 6.74314e7 + 6.74314e7i 0.328327 + 0.328327i
\(591\) −7.62161e6 + 2.84442e7i −0.0369219 + 0.137794i
\(592\) −258469. 69256.6i −0.00124579 0.000333808i
\(593\) −2.70643e8 + 2.70643e8i −1.29787 + 1.29787i −0.368079 + 0.929795i \(0.619984\pi\)
−0.929795 + 0.368079i \(0.880016\pi\)
\(594\) −2.94080e7 5.09361e7i −0.140316 0.243034i
\(595\) −4.32980e8 2.49981e8i −2.05550 1.18674i
\(596\) 6.99564e6 + 2.61081e7i 0.0330437 + 0.123321i
\(597\) 1.23256e8i 0.579273i
\(598\) 4.86754e7 1.15446e8i 0.227618 0.539854i
\(599\) 1.05246e6 0.00489697 0.00244848 0.999997i \(-0.499221\pi\)
0.00244848 + 0.999997i \(0.499221\pi\)
\(600\) 3.77889e7 1.01255e7i 0.174949 0.0468774i
\(601\) 6.30053e7 1.09128e8i 0.290238 0.502706i −0.683628 0.729831i \(-0.739599\pi\)
0.973866 + 0.227124i \(0.0729323\pi\)
\(602\) −2.28054e8 + 1.31667e8i −1.04532 + 0.603516i
\(603\) −1.67934e8 1.67934e8i −0.765924 0.765924i
\(604\) 4.54108e7 1.69476e8i 0.206086 0.769124i
\(605\) −1.29473e8 3.46921e7i −0.584672 0.156662i
\(606\) 1.11648e7 1.11648e7i 0.0501688 0.0501688i
\(607\) −1.44340e8 2.50004e8i −0.645387 1.11784i −0.984212 0.176994i \(-0.943363\pi\)
0.338825 0.940850i \(-0.389971\pi\)
\(608\) 1.16288e8 + 6.71389e7i 0.517397 + 0.298719i
\(609\) −456866. 1.70505e6i −0.00202272 0.00754891i
\(610\) 5.85537e7i 0.257967i
\(611\) 5.19358e7 + 6.85759e7i 0.227689 + 0.300641i
\(612\) 1.57994e8 0.689266
\(613\) 3.95247e7 1.05906e7i 0.171588 0.0459769i −0.172002 0.985097i \(-0.555024\pi\)
0.343590 + 0.939120i \(0.388357\pi\)
\(614\) 5.71707e7 9.90226e7i 0.246984 0.427789i
\(615\) −2.03854e6 + 1.17695e6i −0.00876382 + 0.00505979i
\(616\) −1.80004e8 1.80004e8i −0.770089 0.770089i
\(617\) −8.63032e7 + 3.22088e8i −0.367427 + 1.37126i 0.496673 + 0.867938i \(0.334555\pi\)
−0.864100 + 0.503319i \(0.832112\pi\)
\(618\) −1.18377e7 3.17191e6i −0.0501537 0.0134386i
\(619\) 1.42624e8 1.42624e8i 0.601341 0.601341i −0.339327 0.940668i \(-0.610199\pi\)
0.940668 + 0.339327i \(0.110199\pi\)
\(620\) −4.72710e7 8.18757e7i −0.198344 0.343542i
\(621\) −1.24876e8 7.20975e7i −0.521442 0.301055i
\(622\) 6.49171e7 + 2.42274e8i 0.269766 + 1.00678i
\(623\) 3.83139e8i 1.58450i
\(624\) −57291.6 + 23308.4i −0.000235796 + 9.59310e-5i
\(625\) 3.04816e8 1.24853
\(626\) 1.09083e7 2.92288e6i 0.0444667 0.0119148i
\(627\) 1.77239e7 3.06988e7i 0.0719048 0.124543i
\(628\) −1.31475e8 + 7.59071e7i −0.530840 + 0.306481i
\(629\) 3.77077e8 + 3.77077e8i 1.51523 + 1.51523i
\(630\) 6.69446e7 2.49841e8i 0.267728 0.999175i
\(631\) −2.27876e7 6.10592e6i −0.0907006 0.0243032i 0.213183 0.977012i \(-0.431617\pi\)
−0.303884 + 0.952709i \(0.598284\pi\)
\(632\) −2.02429e8 + 2.02429e8i −0.801903 + 0.801903i
\(633\) 1.52327e6 + 2.63838e6i 0.00600572 + 0.0104022i
\(634\) −4.55472e7 2.62967e7i −0.178729 0.103189i
\(635\) −1.30407e7 4.86687e7i −0.0509309 0.190077i
\(636\) 8.60806e7i 0.334606i
\(637\) 2.09043e8 2.68898e8i 0.808754 1.04033i
\(638\) 1.75127e6 0.00674359
\(639\) −2.69819e8 + 7.22979e7i −1.03412 + 0.277091i
\(640\) −1.00629e8 + 1.74295e8i −0.383869 + 0.664881i
\(641\) 1.99071e8 1.14934e8i 0.755849 0.436389i −0.0719545 0.997408i \(-0.522924\pi\)
0.827803 + 0.561018i \(0.189590\pi\)
\(642\) 4.03385e7 + 4.03385e7i 0.152445 + 0.152445i
\(643\) 7.17624e7 2.67821e8i 0.269938 1.00742i −0.689220 0.724552i \(-0.742047\pi\)
0.959158 0.282871i \(-0.0912867\pi\)
\(644\) −2.30339e8 6.17192e7i −0.862403 0.231080i
\(645\) 1.01633e8 1.01633e8i 0.378752 0.378752i
\(646\) −6.25175e7 1.08284e8i −0.231902 0.401666i
\(647\) 1.76730e8 + 1.02035e8i 0.652524 + 0.376735i 0.789422 0.613850i \(-0.210380\pi\)
−0.136899 + 0.990585i \(0.543714\pi\)
\(648\) 4.73949e7 + 1.76880e8i 0.174183 + 0.650061i
\(649\) 1.18530e8i 0.433606i
\(650\) −9.06320e7 + 1.13505e7i −0.330021 + 0.0413308i
\(651\) 7.30981e7 0.264949
\(652\) 1.79170e8 4.80085e7i 0.646431 0.173211i
\(653\) 8.95105e7 1.55037e8i 0.321465 0.556795i −0.659325 0.751858i \(-0.729158\pi\)
0.980791 + 0.195063i \(0.0624913\pi\)
\(654\) −1.10722e7 + 6.39252e6i −0.0395821 + 0.0228528i
\(655\) 9.38385e7 + 9.38385e7i 0.333931 + 0.333931i
\(656\) 1340.29 5002.02i 4.74773e−6 1.77188e-5i
\(657\) 3.03084e8 + 8.12112e7i 1.06873 + 0.286365i
\(658\) −7.14503e7 + 7.14503e7i −0.250799 + 0.250799i
\(659\) 1.25284e8 + 2.16998e8i 0.437763 + 0.758227i 0.997517 0.0704316i \(-0.0224376\pi\)
−0.559754 + 0.828659i \(0.689104\pi\)
\(660\) 4.59771e7 + 2.65449e7i 0.159923 + 0.0923314i
\(661\) −4.96236e7 1.85198e8i −0.171824 0.641256i −0.997071 0.0764838i \(-0.975631\pi\)
0.825247 0.564772i \(-0.191036\pi\)
\(662\) 5.18772e7i 0.178815i
\(663\) 1.22104e8 + 1.68600e7i 0.418976 + 0.0578517i
\(664\) −3.99466e7 −0.136451
\(665\) 3.20379e8 8.58454e7i 1.08943 0.291912i
\(666\) −1.37943e8 + 2.38923e8i −0.466955 + 0.808791i
\(667\) 3.71825e6 2.14673e6i 0.0125303 0.00723436i
\(668\) −1.79064e8 1.79064e8i −0.600730 0.600730i
\(669\) 1.93349e7 7.21589e7i 0.0645749 0.240997i
\(670\) −2.71899e8 7.28552e7i −0.904032 0.242235i
\(671\) −5.14625e7 + 5.14625e7i −0.170343 + 0.170343i
\(672\) −7.77457e7 1.34660e8i −0.256194 0.443741i
\(673\) −3.11179e8 1.79659e8i −1.02086 0.589392i −0.106505 0.994312i \(-0.533966\pi\)
−0.914352 + 0.404920i \(0.867299\pi\)
\(674\) −8.10289e6 3.02404e7i −0.0264643 0.0987661i
\(675\) 1.05124e8i 0.341814i
\(676\) 1.85125e8 4.71078e7i 0.599274 0.152494i
\(677\) −3.39447e8 −1.09397 −0.546985 0.837142i \(-0.684225\pi\)
−0.546985 + 0.837142i \(0.684225\pi\)
\(678\) −1.61534e7 + 4.32828e6i −0.0518291 + 0.0138876i
\(679\) −3.31671e8 + 5.74471e8i −1.05949 + 1.83510i
\(680\) 4.24436e8 2.45048e8i 1.34985 0.779336i
\(681\) 4.36925e7 + 4.36925e7i 0.138346 + 0.138346i
\(682\) −1.87699e7 + 7.00504e7i −0.0591711 + 0.220830i
\(683\) −4.37240e8 1.17158e8i −1.37233 0.367714i −0.503999 0.863704i \(-0.668139\pi\)
−0.868328 + 0.495990i \(0.834805\pi\)
\(684\) −7.41156e7 + 7.41156e7i −0.231602 + 0.231602i
\(685\) 1.47893e8 + 2.56159e8i 0.460127 + 0.796963i
\(686\) 8.35384e7 + 4.82309e7i 0.258770 + 0.149401i
\(687\) 2.46163e7 + 9.18692e7i 0.0759193 + 0.283335i
\(688\) 316201.i 0.000970952i
\(689\) 7.19449e7 5.21042e8i 0.219959 1.59300i
\(690\) −8.03259e7 −0.244517
\(691\) 4.02652e8 1.07890e8i 1.22038 0.327000i 0.409554 0.912286i \(-0.365684\pi\)
0.810827 + 0.585286i \(0.199018\pi\)
\(692\) 4.29921e7 7.44645e7i 0.129739 0.224715i
\(693\) 2.78421e8 1.60747e8i 0.836571 0.482994i
\(694\) −7.03367e7 7.03367e7i −0.210428 0.210428i
\(695\) −1.65624e8 + 6.18116e8i −0.493365 + 1.84126i
\(696\) 1.67140e6 + 447851.i 0.00495739 + 0.00132833i
\(697\) −7.29738e6 + 7.29738e6i −0.0215511 + 0.0215511i
\(698\) −9.84441e7 1.70510e8i −0.289483 0.501400i
\(699\) −1.85022e8 1.06823e8i −0.541741 0.312775i
\(700\) 4.49957e7 + 1.67926e8i 0.131183 + 0.489581i
\(701\) 5.12960e8i 1.48912i −0.667556 0.744560i \(-0.732659\pi\)
0.667556 0.744560i \(-0.267341\pi\)
\(702\) 1.68606e7 + 1.34629e8i 0.0487372 + 0.389161i
\(703\) −3.53777e8 −1.01827
\(704\) 1.48826e8 3.98778e7i 0.426541 0.114291i
\(705\) 2.75760e7 4.77630e7i 0.0786979 0.136309i
\(706\) 5.61271e7 3.24050e7i 0.159499 0.0920870i
\(707\) 1.29848e8 + 1.29848e8i 0.367431 + 0.367431i
\(708\) −1.15819e7 + 4.32243e7i −0.0326348 + 0.121795i
\(709\) −5.53793e6 1.48388e6i −0.0155385 0.00416353i 0.251041 0.967976i \(-0.419227\pi\)
−0.266580 + 0.963813i \(0.585894\pi\)
\(710\) −2.34114e8 + 2.34114e8i −0.654111 + 0.654111i
\(711\) −1.80772e8 3.13107e8i −0.502948 0.871131i
\(712\) −3.25260e8 1.87789e8i −0.901138 0.520272i
\(713\) 4.60169e7 + 1.71737e8i 0.126955 + 0.473801i
\(714\) 1.44789e8i 0.397777i
\(715\) −2.56112e8 1.99102e8i −0.700667 0.544701i
\(716\) −3.26090e8 −0.888378
\(717\) −1.76448e8 + 4.72792e7i −0.478697 + 0.128266i
\(718\) 5.13422e7 8.89273e7i 0.138708 0.240249i
\(719\) 2.99105e8 1.72689e8i 0.804707 0.464598i −0.0404077 0.999183i \(-0.512866\pi\)
0.845114 + 0.534586i \(0.179532\pi\)
\(720\) −219614. 219614.i −0.000588386 0.000588386i
\(721\) 3.68895e7 1.37674e8i 0.0984232 0.367320i
\(722\) −1.44459e8 3.87076e7i −0.383824 0.102845i
\(723\) 2.29139e7 2.29139e7i 0.0606296 0.0606296i
\(724\) 1.36454e8 + 2.36346e8i 0.359561 + 0.622777i
\(725\) −2.71075e6 1.56505e6i −0.00711336 0.00410690i
\(726\) 1.00468e7 + 3.74952e7i 0.0262554 + 0.0979865i
\(727\) 5.82836e8i 1.51685i 0.651759 + 0.758426i \(0.274031\pi\)
−0.651759 + 0.758426i \(0.725969\pi\)
\(728\) 2.21302e8 + 5.43955e8i 0.573575 + 1.40984i
\(729\) −1.48501e8 −0.383307
\(730\) 3.59233e8 9.62561e7i 0.923437 0.247434i
\(731\) 3.15075e8 5.45725e8i 0.806605 1.39708i
\(732\) −2.37954e7 + 1.37383e7i −0.0606679 + 0.0350266i
\(733\) 5.00617e8 + 5.00617e8i 1.27114 + 1.27114i 0.945491 + 0.325649i \(0.105583\pi\)
0.325649 + 0.945491i \(0.394417\pi\)
\(734\) 4.63815e7 1.73098e8i 0.117289 0.437727i
\(735\) −2.10925e8 5.65172e7i −0.531210 0.142337i
\(736\) 2.67428e8 2.67428e8i 0.670770 0.670770i
\(737\) −1.74939e8 3.03003e8i −0.437003 0.756911i
\(738\) −4.62376e6 2.66953e6i −0.0115034 0.00664149i
\(739\) −3.66647e7 1.36834e8i −0.0908478 0.339049i 0.905509 0.424326i \(-0.139489\pi\)
−0.996357 + 0.0852775i \(0.972822\pi\)
\(740\) 5.29847e8i 1.30754i
\(741\) −6.51885e7 + 4.93703e7i −0.160220 + 0.121342i
\(742\) 6.17842e8 1.51240
\(743\) −4.36580e8 + 1.16981e8i −1.06438 + 0.285200i −0.748182 0.663493i \(-0.769073\pi\)
−0.316198 + 0.948693i \(0.602407\pi\)
\(744\) −3.58278e7 + 6.20556e7i −0.0869965 + 0.150682i
\(745\) −9.17013e7 + 5.29438e7i −0.221772 + 0.128040i
\(746\) 1.45902e8 + 1.45902e8i 0.351435 + 0.351435i
\(747\) 1.30572e7 4.87301e7i 0.0313248 0.116906i
\(748\) 2.24827e8 + 6.02423e7i 0.537210 + 0.143945i
\(749\) −4.69140e8 + 4.69140e8i −1.11649 + 1.11649i
\(750\) −2.51042e7 4.34817e7i −0.0595062 0.103068i
\(751\) 1.58016e8 + 9.12306e7i 0.373062 + 0.215388i 0.674795 0.738005i \(-0.264232\pi\)
−0.301733 + 0.953392i \(0.597565\pi\)
\(752\) 31402.9 + 117197.i 7.38442e−5 + 0.000275590i
\(753\) 6.86231e7i 0.160726i
\(754\) −3.72260e6 1.56955e6i −0.00868426 0.00366152i
\(755\) 6.87349e8 1.59712
\(756\) 2.49446e8 6.68389e7i 0.577314 0.154691i
\(757\) −3.53297e8 + 6.11929e8i −0.814428 + 1.41063i 0.0953102 + 0.995448i \(0.469616\pi\)
−0.909738 + 0.415183i \(0.863718\pi\)
\(758\) 1.95019e7 1.12594e7i 0.0447784 0.0258528i
\(759\) −7.05981e7 7.05981e7i −0.161461 0.161461i
\(760\) −8.41514e7 + 3.14057e8i −0.191699 + 0.715432i
\(761\) −2.31789e7 6.21078e6i −0.0525944 0.0140926i 0.232426 0.972614i \(-0.425334\pi\)
−0.285020 + 0.958521i \(0.592000\pi\)
\(762\) −1.03178e7 + 1.03178e7i −0.0233197 + 0.0233197i
\(763\) −7.43454e7 1.28770e8i