Properties

Label 13.7.f.a.2.3
Level 13
Weight 7
Character 13.2
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 2.3
Character \(\chi\) = 13.2
Dual form 13.7.f.a.7.3

$q$-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 \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\)

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 −0.0521922 0.998637i \(-0.516621\pi\)
−0.544518 + 0.838749i \(0.683288\pi\)
\(3\) 4.54257 + 7.86796i 0.168243 + 0.291406i 0.937802 0.347170i \(-0.112857\pi\)
−0.769559 + 0.638576i \(0.779524\pi\)
\(4\) −34.2737 19.7879i −0.535526 0.309186i
\(5\) −109.630 + 109.630i −0.877039 + 0.877039i −0.993227 0.116188i \(-0.962932\pi\)
0.116188 + 0.993227i \(0.462932\pi\)
\(6\) −11.6208 43.3696i −0.0538002 0.200785i
\(7\) −504.391 + 135.151i −1.47053 + 0.394027i −0.903112 0.429404i \(-0.858724\pi\)
−0.567416 + 0.823431i \(0.692057\pi\)
\(8\) 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 −0.809396 0.587263i \(-0.800206\pi\)
0.994589 0.103886i \(-0.0331278\pi\)
\(12\) 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 −0.155368 0.987857i \(-0.549656\pi\)
−0.933193 + 0.359375i \(0.882990\pi\)
\(18\) −2259.11 + 2259.11i −0.387364 + 0.387364i
\(19\) 1060.35 + 3957.28i 0.154592 + 0.576947i 0.999140 + 0.0414662i \(0.0132029\pi\)
−0.844547 + 0.535481i \(0.820130\pi\)
\(20\) 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 −0.850875 0.525368i \(-0.823927\pi\)
0.0295450 + 0.999563i \(0.490594\pi\)
\(24\) −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 0.862186 0.506592i \(-0.169095\pi\)
−0.869814 + 0.493379i \(0.835761\pi\)
\(30\) 6028.59 + 3480.61i 0.223281 + 0.128911i
\(31\) −10895.2 + 10895.2i −0.365722 + 0.365722i −0.865914 0.500193i \(-0.833263\pi\)
0.500193 + 0.865914i \(0.333263\pi\)
\(32\) −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 0.284464 + 0.958687i \(0.408184\pi\)
−0.725696 + 0.688015i \(0.758482\pi\)
\(38\) 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 0.270511 0.962717i \(-0.412808\pi\)
−0.247090 + 0.968993i \(0.579474\pi\)
\(42\) 11722.9 + 20304.7i 0.158229 + 0.274061i
\(43\) −88370.0 51020.4i −1.11147 0.641710i −0.172264 0.985051i \(-0.555108\pi\)
−0.939211 + 0.343341i \(0.888441\pi\)
\(44\) −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 0.561086 0.827758i \(-0.310384\pi\)
−0.827758 + 0.561086i \(0.810384\pi\)
\(48\) −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 0.0460194 0.998941i \(-0.485346\pi\)
0.539324 + 0.842098i \(0.318680\pi\)
\(60\) 39417.6 + 39417.6i 0.182489 + 0.182489i
\(61\) 38209.4 66180.6i 0.168337 0.291569i −0.769498 0.638649i \(-0.779494\pi\)
0.937835 + 0.347080i \(0.112827\pi\)
\(62\) 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 −0.384988 0.922921i \(-0.625795\pi\)
−0.794870 + 0.606779i \(0.792461\pi\)
\(68\) 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 −0.926322 0.376734i \(-0.877047\pi\)
0.613851 0.789422i \(-0.289619\pi\)
\(72\) 319635. 85645.9i 0.856360 0.229461i
\(73\) 343212. + 343212.i 0.882256 + 0.882256i 0.993764 0.111508i \(-0.0355681\pi\)
−0.111508 + 0.993764i \(0.535568\pi\)
\(74\) 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 −0.753712 0.657205i \(-0.771739\pi\)
0.657205 + 0.753712i \(0.271739\pi\)
\(84\) 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 0.690142 + 0.723674i \(0.257548\pi\)
−0.959517 + 0.281649i \(0.909119\pi\)
\(90\) 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 0.873757 + 0.486363i \(0.161677\pi\)
−0.513514 + 0.858081i \(0.671657\pi\)
\(98\) −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 −0.640461 0.767991i \(-0.721257\pi\)
0.344869 + 0.938651i \(0.387923\pi\)
\(102\) −71764.0 + 267827.i −0.0676248 + 0.252379i
\(103\) 272950.i 0.249788i −0.992170 0.124894i \(-0.960141\pi\)
0.992170 0.124894i \(-0.0398591\pi\)
\(104\) −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 0.999767 + 0.0215836i \(0.00687080\pi\)
−0.481192 + 0.876615i \(0.659796\pi\)
\(108\) −428292. 247275.i −0.339992 0.196295i
\(109\) 201347. 201347.i 0.155477 0.155477i −0.625082 0.780559i \(-0.714935\pi\)
0.780559 + 0.625082i \(0.214935\pi\)
\(110\) −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 −0.794249 0.607593i \(-0.792135\pi\)
0.923315 + 0.384043i \(0.125469\pi\)
\(114\) 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 −0.429725 0.902960i \(-0.641390\pi\)
0.567123 + 0.823633i \(0.308056\pi\)
\(128\) −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 −0.598684 0.800985i \(-0.704309\pi\)
−0.117983 + 0.993016i \(0.537643\pi\)
\(138\) 366351. + 366351.i 0.139399 + 0.139399i
\(139\) −2.06373e6 + 3.57448e6i −0.768437 + 1.33097i 0.169973 + 0.985449i \(0.445632\pi\)
−0.938410 + 0.345523i \(0.887702\pi\)
\(140\) −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 0.987484 0.157722i \(-0.0504151\pi\)
−0.934047 + 0.357150i \(0.883748\pi\)
\(150\) −364843. + 97759.5i −0.108102 + 0.0289658i
\(151\) −3.13486e6 3.13486e6i −0.910515 0.910515i 0.0857972 0.996313i \(-0.472656\pi\)
−0.996313 + 0.0857972i \(0.972656\pi\)
\(152\) −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 −0.740340 0.672233i \(-0.765335\pi\)
−0.305036 + 0.952341i \(0.598669\pi\)
\(164\) −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 −0.524167 0.851615i \(-0.675623\pi\)
0.879750 0.475437i \(-0.157710\pi\)
\(168\) 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 0.307173 0.951654i \(-0.400617\pi\)
−0.670570 + 0.741846i \(0.733950\pi\)
\(174\) −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 0.274227 0.961665i \(-0.411578\pi\)
0.969940 + 0.243345i \(0.0782447\pi\)
\(180\) 1.02663e6 3.83142e6i 0.176033 0.656965i
\(181\) 6.89585e6i 1.16293i 0.813573 + 0.581463i \(0.197519\pi\)
−0.813573 + 0.581463i \(0.802481\pi\)
\(182\) 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 0.498763 + 0.866738i \(0.333788\pi\)
−0.999999 + 0.00142767i \(0.999546\pi\)
\(192\) −1.27289e6 + 734904.i −0.179841 + 0.103831i
\(193\) −170632. + 636806.i −0.0237349 + 0.0885799i −0.976777 0.214257i \(-0.931267\pi\)
0.953042 + 0.302837i \(0.0979337\pi\)
\(194\) 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 0.0481825 0.998839i \(-0.484657\pi\)
−0.457692 + 0.889111i \(0.651324\pi\)
\(198\) 1.52135e6 + 2.63505e6i 0.195989 + 0.339463i
\(199\) 1.17491e7 + 6.78336e6i 1.49089 + 0.860767i 0.999946 0.0104224i \(-0.00331760\pi\)
0.490947 + 0.871190i \(0.336651\pi\)
\(200\) 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 0.856963 0.515377i \(-0.172348\pi\)
−0.874812 + 0.484463i \(0.839015\pi\)
\(212\) −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 0.598482 0.801136i \(-0.295771\pi\)
0.117733 + 0.993045i \(0.462437\pi\)
\(224\) 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 −0.999449 0.0331793i \(-0.989437\pi\)
0.848959 0.528459i \(-0.177230\pi\)
\(228\) 1.42285e6 381251.i 0.120048 0.0321667i
\(229\) −7.40252e6 7.40252e6i −0.616415 0.616415i 0.328195 0.944610i \(-0.393560\pi\)
−0.944610 + 0.328195i \(0.893560\pi\)
\(230\) −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 \(0.379788\pi\)
−0.368745 + 0.929531i \(0.620212\pi\)
\(234\) −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 −0.0423355 + 0.999103i \(0.513480\pi\)
−0.999103 + 0.0423355i \(0.986520\pi\)
\(240\) −1129.69 4216.07i −8.17197e−5 0.000304982i
\(241\) 3.44530e6 923165.i 0.246136 0.0659520i −0.133642 0.991030i \(-0.542667\pi\)
0.379778 + 0.925078i \(0.376000\pi\)
\(242\) −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 0.278699 0.960379i \(-0.410097\pi\)
−0.692363 + 0.721549i \(0.743430\pi\)
\(252\) 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 0.397173 0.917744i \(-0.369991\pi\)
0.993376 + 0.114910i \(0.0366580\pi\)
\(258\) −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 0.830803 0.556567i \(-0.187882\pi\)
−0.897403 + 0.441213i \(0.854548\pi\)
\(264\) 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 −0.337295 0.941399i \(-0.609512\pi\)
0.983923 0.178594i \(-0.0571548\pi\)
\(270\) 8.29209e6 4.78744e6i 0.421282 0.243227i
\(271\) −3.19870e6 + 1.19377e7i −0.160719 + 0.599810i 0.837829 + 0.545933i \(0.183825\pi\)
−0.998548 + 0.0538771i \(0.982842\pi\)
\(272\) 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 −0.999742 0.0227006i \(-0.992774\pi\)
−0.519530 0.854452i \(-0.673893\pi\)
\(278\) 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 0.923618 0.383314i \(-0.125217\pi\)
−0.383314 + 0.923618i \(0.625217\pi\)
\(282\) −879016. + 1.52250e6i −0.0391967 + 0.0678906i
\(283\) 1.22628e6 707994.i 0.0541042 0.0312371i −0.472704 0.881221i \(-0.656722\pi\)
0.526808 + 0.849984i \(0.323389\pi\)
\(284\) −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 −0.694102 0.719877i \(-0.744198\pi\)
−0.241171 + 0.970483i \(0.577531\pi\)
\(294\) −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 0.365429 0.930839i \(-0.380922\pi\)
−0.930839 + 0.365429i \(0.880922\pi\)
\(308\) 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 \(0.319574\pi\)
−0.536957 + 0.843610i \(0.680426\pi\)
\(312\) −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 −0.579059 0.815285i \(-0.696580\pi\)
0.815285 + 0.579059i \(0.196580\pi\)
\(318\) −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 0.918298 0.395891i \(-0.129564\pi\)
−0.993214 + 0.116297i \(0.962897\pi\)
\(332\) 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 \(-0.973627\pi\)
0.996570 0.0827588i \(-0.0263731\pi\)
\(338\) 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 −0.720098 0.693872i \(-0.755903\pi\)
0.960960 + 0.276687i \(0.0892365\pi\)
\(348\) −115859. + 66891.1i −0.00274911 + 0.00158720i
\(349\) 1.03111e7 3.84816e7i 0.242566 0.905268i −0.732025 0.681277i \(-0.761425\pi\)
0.974591 0.223991i \(-0.0719086\pi\)
\(350\) 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 0.111941 0.993715i \(-0.464293\pi\)
−0.399914 + 0.916553i \(0.630960\pi\)
\(354\) −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 0.530283 0.847821i \(-0.322086\pi\)
−0.847821 + 0.530283i \(0.822086\pi\)
\(360\) −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 0.622277 0.782797i \(-0.286208\pi\)
−0.989061 + 0.147509i \(0.952874\pi\)
\(368\) −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 −0.993999 0.109392i \(-0.965110\pi\)
0.591735 + 0.806132i \(0.298443\pi\)
\(374\) 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 0.218169 0.975911i \(-0.429992\pi\)
−0.299016 + 0.954248i \(0.596658\pi\)
\(380\) 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 0.937262 0.348625i \(-0.113351\pi\)
−0.986005 + 0.166713i \(0.946685\pi\)
\(384\) −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 \(0.104505\pi\)
−0.946588 + 0.322445i \(0.895495\pi\)
\(390\) −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 0.117588 0.993062i \(-0.462484\pi\)
0.598366 + 0.801223i \(0.295817\pi\)
\(398\) −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 −0.978382 0.206807i \(-0.933693\pi\)
0.950707 + 0.310091i \(0.100360\pi\)
\(402\) 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 −0.999253 0.0386403i \(-0.987697\pi\)
0.846058 0.533090i \(-0.178969\pi\)
\(410\) 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 0.701368 0.712800i \(-0.252573\pi\)
−0.967986 + 0.251002i \(0.919240\pi\)
\(420\) −2.52092e7 1.45546e7i −0.340261 0.196450i
\(421\) −2.96788e7 + 2.96788e7i −0.397740 + 0.397740i −0.877435 0.479695i \(-0.840747\pi\)
0.479695 + 0.877435i \(0.340747\pi\)
\(422\) 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 0.285140 0.958486i \(-0.407960\pi\)
−0.232304 + 0.972643i \(0.574627\pi\)
\(432\) 19361.5 + 33535.0i 0.000240152 + 0.000415956i
\(433\) 7.46948e7 + 4.31251e7i 0.920082 + 0.531210i 0.883661 0.468127i \(-0.155071\pi\)
0.0364211 + 0.999337i \(0.488404\pi\)
\(434\) −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 −0.892839 0.450377i \(-0.851290\pi\)
−0.0563814 + 0.998409i \(0.517956\pi\)
\(440\) −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 −0.181811 0.983333i \(-0.558196\pi\)
0.334213 + 0.942497i \(0.391529\pi\)
\(450\) 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 0.142006 0.989866i \(-0.454645\pi\)
−0.371952 + 0.928252i \(0.621311\pi\)
\(458\) 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 0.924101 0.382147i \(-0.124815\pi\)
−0.991369 + 0.131101i \(0.958149\pi\)
\(462\) 2.15683e7 5.77920e6i 0.218720 0.0586059i
\(463\) 6.94735e7 + 6.94735e7i 0.699965 + 0.699965i 0.964403 0.264438i \(-0.0851864\pi\)
−0.264438 + 0.964403i \(0.585186\pi\)
\(464\) 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 \(0.0607733\pi\)
−0.981829 + 0.189767i \(0.939227\pi\)
\(468\) −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 0.409361 + 0.912372i \(0.365752\pi\)
−0.810704 + 0.585457i \(0.800915\pi\)
\(480\) 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 0.983435 + 0.181263i \(0.0580185\pi\)
−0.761048 + 0.648696i \(0.775315\pi\)
\(488\) 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 0.629361 0.777113i \(-0.283317\pi\)
0.987680 0.156486i \(-0.0500165\pi\)
\(492\) 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 0.327739 0.944768i \(-0.393713\pi\)
0.944768 0.327739i \(-0.106287\pi\)
\(500\) 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 0.357896 + 0.933762i \(0.383494\pi\)
−0.987609 + 0.156934i \(0.949839\pi\)
\(504\) −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 −0.271648 0.962397i \(-0.587568\pi\)
−0.716452 + 0.697636i \(0.754235\pi\)
\(510\) −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 0.823768 + 0.566927i \(0.191868\pi\)
0.0790898 + 0.996867i \(0.474799\pi\)
\(524\) 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 0.867435 0.497550i \(-0.165767\pi\)
−0.497550 + 0.867435i \(0.665767\pi\)
\(542\) 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 0.705047 + 0.709160i \(0.250926\pi\)
−0.965169 + 0.261627i \(0.915741\pi\)
\(558\) 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 0.525357 0.850882i \(-0.323932\pi\)
−0.474207 + 0.880414i \(0.657265\pi\)
\(564\) −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 0.0291456 0.999575i \(-0.490721\pi\)
0.880230 + 0.474547i \(0.157388\pi\)
\(570\) −7.38133e6 + 2.75475e7i −0.0398575 + 0.148750i
\(571\) 2.47411e6i 0.0132896i 0.999978 + 0.00664479i \(0.00211512\pi\)
−0.999978 + 0.00664479i \(0.997885\pi\)
\(572\) −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 −0.775694 0.631109i \(-0.782600\pi\)
0.631109 + 0.775694i \(0.282600\pi\)
\(578\) −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 0.265945 0.963988i \(-0.414316\pi\)
−0.251679 + 0.967811i \(0.580983\pi\)
\(588\) −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 −0.929795 0.368079i \(-0.880016\pi\)
−0.368079 0.929795i \(-0.619984\pi\)
\(594\) −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 0.973866 0.227124i \(-0.0729323\pi\)
−0.683628 + 0.729831i \(0.739599\pi\)
\(602\) −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 0.338825 + 0.940850i \(0.389971\pi\)
−0.984212 + 0.176994i \(0.943363\pi\)
\(608\) 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 0.343590 0.939120i \(-0.388357\pi\)
−0.172002 + 0.985097i \(0.555024\pi\)
\(614\) 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 −0.864100 0.503319i \(-0.832112\pi\)
0.496673 0.867938i \(-0.334555\pi\)
\(618\) −1.18377e7 + 3.17191e6i −0.0501537 + 0.0134386i
\(619\) 1.42624e8 + 1.42624e8i 0.601341 + 0.601341i 0.940668 0.339327i \(-0.110199\pi\)
−0.339327 + 0.940668i \(0.610199\pi\)
\(620\) −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 −0.303884 0.952709i \(-0.598284\pi\)
0.213183 + 0.977012i \(0.431617\pi\)
\(632\) −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 0.827803 0.561018i \(-0.189590\pi\)
−0.0719545 + 0.997408i \(0.522924\pi\)
\(642\) 4.03385e7 4.03385e7i 0.152445 0.152445i
\(643\) 7.17624e7 + 2.67821e8i 0.269938 + 1.00742i 0.959158 + 0.282871i \(0.0912867\pi\)
−0.689220 + 0.724552i \(0.742047\pi\)
\(644\) −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 −0.136899 0.990585i \(-0.543714\pi\)
0.789422 + 0.613850i \(0.210380\pi\)
\(648\) 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 0.980791 0.195063i \(-0.0624913\pi\)
−0.659325 + 0.751858i \(0.729158\pi\)
\(654\) −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 −0.559754 0.828659i \(-0.689104\pi\)
0.997517 + 0.0704316i \(0.0224376\pi\)
\(660\) 4.59771e7 2.65449e7i 0.159923 0.0923314i
\(661\) −4.96236e7 + 1.85198e8i −0.171824 + 0.641256i 0.825247 + 0.564772i \(0.191036\pi\)
−0.997071 + 0.0764838i \(0.975631\pi\)
\(662\) 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 −0.914352 0.404920i \(-0.867299\pi\)
−0.106505 + 0.994312i \(0.533966\pi\)
\(674\) −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 −0.868328 0.495990i \(-0.834805\pi\)
−0.503999 + 0.863704i \(0.668139\pi\)
\(684\) −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 0.810827 0.585286i \(-0.199018\pi\)
0.409554 + 0.912286i \(0.365684\pi\)
\(692\) 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 \(0.267341\pi\)
−0.667556 + 0.744560i \(0.732659\pi\)
\(702\) 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 −0.266580 0.963813i \(-0.585894\pi\)
0.251041 + 0.967976i \(0.419227\pi\)
\(710\) −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 0.845114 0.534586i \(-0.179532\pi\)
−0.0404077 + 0.999183i \(0.512866\pi\)
\(720\) −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 \(-0.725969\pi\)
0.651759 0.758426i \(-0.274031\pi\)
\(728\) 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 0.325649 0.945491i \(-0.394417\pi\)
0.945491 0.325649i \(-0.105583\pi\)
\(734\) 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 −0.996357 0.0852775i \(-0.972822\pi\)
0.905509 + 0.424326i \(0.139489\pi\)
\(740\) 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 −0.316198 0.948693i \(-0.602407\pi\)
−0.748182 + 0.663493i \(0.769073\pi\)
\(744\) −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 −0.301733 0.953392i \(-0.597565\pi\)
0.674795 + 0.738005i \(0.264232\pi\)
\(752\) 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 −0.909738 0.415183i \(-0.863718\pi\)
0.0953102 0.995448i \(-0.469616\pi\)
\(758\) 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 −0.285020 0.958521i \(-0.592000\pi\)
0.232426 + 0.972614i \(0.425334\pi\)
\(762\) −1.03178e7 1.03178e7i −0.0233197 0.0233197i
\(763\) −7.43454e7 + 1.28770e8i −0.167371 +