Properties

Label 13.7.f.a.7.4
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 7.4
Character \(\chi\) = 13.7
Dual form 13.7.f.a.2.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.48669 - 0.666306i) q^{2} +(-16.9072 + 29.2841i) q^{3} +(-49.6860 + 28.6862i) q^{4} +(34.0715 + 34.0715i) q^{5} +(-22.5307 + 84.0857i) q^{6} +(190.342 + 51.0019i) q^{7} +(-220.944 + 220.944i) q^{8} +(-207.205 - 358.889i) q^{9} +O(q^{10})\) \(q+(2.48669 - 0.666306i) q^{2} +(-16.9072 + 29.2841i) q^{3} +(-49.6860 + 28.6862i) q^{4} +(34.0715 + 34.0715i) q^{5} +(-22.5307 + 84.0857i) q^{6} +(190.342 + 51.0019i) q^{7} +(-220.944 + 220.944i) q^{8} +(-207.205 - 358.889i) q^{9} +(107.427 + 62.0232i) q^{10} +(-120.972 - 451.473i) q^{11} -1940.01i q^{12} +(2156.00 + 422.473i) q^{13} +507.303 q^{14} +(-1573.81 + 421.700i) q^{15} +(1433.71 - 2483.27i) q^{16} +(-1343.96 + 775.937i) q^{17} +(-754.384 - 754.384i) q^{18} +(-3123.25 + 11656.1i) q^{19} +(-2670.26 - 715.494i) q^{20} +(-4711.68 + 4711.68i) q^{21} +(-601.639 - 1042.07i) q^{22} +(17806.4 + 10280.5i) q^{23} +(-2734.61 - 10205.7i) q^{24} -13303.3i q^{25} +(5642.79 - 385.995i) q^{26} -10637.7 q^{27} +(-10920.4 + 2926.10i) q^{28} +(11154.3 - 19319.8i) q^{29} +(-3632.59 + 2097.27i) q^{30} +(1680.77 + 1680.77i) q^{31} +(7086.34 - 26446.6i) q^{32} +(15266.3 + 4090.58i) q^{33} +(-2825.00 + 2825.00i) q^{34} +(4747.52 + 8222.94i) q^{35} +(20590.3 + 11887.8i) q^{36} +(-7659.24 - 28584.7i) q^{37} +31066.2i q^{38} +(-48823.6 + 55993.6i) q^{39} -15055.8 q^{40} +(-19684.5 + 5274.43i) q^{41} +(-8577.06 + 14855.9i) q^{42} +(-60100.8 + 34699.2i) q^{43} +(18961.7 + 18961.7i) q^{44} +(5168.12 - 19287.7i) q^{45} +(51129.0 + 13700.0i) q^{46} +(133594. - 133594. i) q^{47} +(48480.1 + 83970.0i) q^{48} +(-68258.3 - 39409.0i) q^{49} +(-8864.04 - 33081.1i) q^{50} -52475.6i q^{51} +(-119242. + 40856.4i) q^{52} +106247. q^{53} +(-26452.6 + 7087.94i) q^{54} +(11260.7 - 19504.1i) q^{55} +(-53323.4 + 30786.3i) q^{56} +(-288533. - 288533. i) q^{57} +(14864.4 - 55474.6i) q^{58} +(365659. + 97978.2i) q^{59} +(66099.1 - 66099.1i) q^{60} +(100762. + 174526. i) q^{61} +(5299.47 + 3059.65i) q^{62} +(-21135.7 - 78879.4i) q^{63} +113029. i q^{64} +(59063.8 + 87852.5i) q^{65} +40688.0 q^{66} +(-225048. + 60301.4i) q^{67} +(44517.4 - 77106.3i) q^{68} +(-602112. + 347630. i) q^{69} +(17284.6 + 17284.6i) q^{70} +(-84973.0 + 317124. i) q^{71} +(125075. + 33513.8i) q^{72} +(-40750.8 + 40750.8i) q^{73} +(-38092.3 - 65977.7i) q^{74} +(389574. + 224921. i) q^{75} +(-179188. - 668740. i) q^{76} -92103.9i q^{77} +(-84100.1 + 171770. i) q^{78} +435228. q^{79} +(133458. - 35759.8i) q^{80} +(330905. - 573145. i) q^{81} +(-45434.7 + 26231.7i) q^{82} +(-256625. - 256625. i) q^{83} +(98944.1 - 369265. i) q^{84} +(-72228.2 - 19353.5i) q^{85} +(-126332. + 126332. i) q^{86} +(377176. + 653287. i) q^{87} +(126478. + 73022.3i) q^{88} +(-242124. - 903619. i) q^{89} -51406.1i q^{90} +(388829. + 190374. i) q^{91} -1.17964e6 q^{92} +(-77637.0 + 20802.8i) q^{93} +(243192. - 421220. i) q^{94} +(-503556. + 290728. i) q^{95} +(654654. + 654654. i) q^{96} +(-90722.7 + 338582. i) q^{97} +(-195996. - 52516.9i) q^{98} +(-136963. + 136963. 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.48669 0.666306i 0.310836 0.0832883i −0.100029 0.994985i \(-0.531893\pi\)
0.410865 + 0.911696i \(0.365227\pi\)
\(3\) −16.9072 + 29.2841i −0.626192 + 1.08460i 0.362118 + 0.932132i \(0.382054\pi\)
−0.988309 + 0.152463i \(0.951279\pi\)
\(4\) −49.6860 + 28.6862i −0.776343 + 0.448222i
\(5\) 34.0715 + 34.0715i 0.272572 + 0.272572i 0.830135 0.557563i \(-0.188263\pi\)
−0.557563 + 0.830135i \(0.688263\pi\)
\(6\) −22.5307 + 84.0857i −0.104309 + 0.389286i
\(7\) 190.342 + 51.0019i 0.554932 + 0.148693i 0.525377 0.850870i \(-0.323924\pi\)
0.0295548 + 0.999563i \(0.490591\pi\)
\(8\) −220.944 + 220.944i −0.431532 + 0.431532i
\(9\) −207.205 358.889i −0.284232 0.492304i
\(10\) 107.427 + 62.0232i 0.107427 + 0.0620232i
\(11\) −120.972 451.473i −0.0908880 0.339198i 0.905476 0.424397i \(-0.139514\pi\)
−0.996364 + 0.0851990i \(0.972847\pi\)
\(12\) 1940.01i 1.12269i
\(13\) 2156.00 + 422.473i 0.981337 + 0.192296i
\(14\) 507.303 0.184877
\(15\) −1573.81 + 421.700i −0.466313 + 0.124948i
\(16\) 1433.71 2483.27i 0.350028 0.606266i
\(17\) −1343.96 + 775.937i −0.273552 + 0.157935i −0.630501 0.776189i \(-0.717150\pi\)
0.356949 + 0.934124i \(0.383817\pi\)
\(18\) −754.384 754.384i −0.129353 0.129353i
\(19\) −3123.25 + 11656.1i −0.455350 + 1.69939i 0.231706 + 0.972786i \(0.425569\pi\)
−0.687056 + 0.726604i \(0.741097\pi\)
\(20\) −2670.26 715.494i −0.333783 0.0894368i
\(21\) −4711.68 + 4711.68i −0.508766 + 0.508766i
\(22\) −601.639 1042.07i −0.0565025 0.0978652i
\(23\) 17806.4 + 10280.5i 1.46350 + 0.844953i 0.999171 0.0407095i \(-0.0129618\pi\)
0.464330 + 0.885662i \(0.346295\pi\)
\(24\) −2734.61 10205.7i −0.197816 0.738259i
\(25\) 13303.3i 0.851409i
\(26\) 5642.79 385.995i 0.321051 0.0219615i
\(27\) −10637.7 −0.540449
\(28\) −10920.4 + 2926.10i −0.497465 + 0.133295i
\(29\) 11154.3 19319.8i 0.457350 0.792154i −0.541470 0.840720i \(-0.682132\pi\)
0.998820 + 0.0485666i \(0.0154653\pi\)
\(30\) −3632.59 + 2097.27i −0.134540 + 0.0776768i
\(31\) 1680.77 + 1680.77i 0.0564188 + 0.0564188i 0.734753 0.678334i \(-0.237298\pi\)
−0.678334 + 0.734753i \(0.737298\pi\)
\(32\) 7086.34 26446.6i 0.216258 0.807086i
\(33\) 15266.3 + 4090.58i 0.424806 + 0.113827i
\(34\) −2825.00 + 2825.00i −0.0718757 + 0.0718757i
\(35\) 4747.52 + 8222.94i 0.110729 + 0.191789i
\(36\) 20590.3 + 11887.8i 0.441323 + 0.254798i
\(37\) −7659.24 28584.7i −0.151210 0.564323i −0.999400 0.0346313i \(-0.988974\pi\)
0.848190 0.529692i \(-0.177692\pi\)
\(38\) 31066.2i 0.566157i
\(39\) −48823.6 + 55993.6i −0.823068 + 0.943940i
\(40\) −15055.8 −0.235247
\(41\) −19684.5 + 5274.43i −0.285609 + 0.0765287i −0.398779 0.917047i \(-0.630566\pi\)
0.113170 + 0.993576i \(0.463899\pi\)
\(42\) −8577.06 + 14855.9i −0.115769 + 0.200517i
\(43\) −60100.8 + 34699.2i −0.755918 + 0.436429i −0.827828 0.560982i \(-0.810424\pi\)
0.0719102 + 0.997411i \(0.477090\pi\)
\(44\) 18961.7 + 18961.7i 0.222596 + 0.222596i
\(45\) 5168.12 19287.7i 0.0567147 0.211662i
\(46\) 51129.0 + 13700.0i 0.525284 + 0.140749i
\(47\) 133594. 133594.i 1.28675 1.28675i 0.349993 0.936752i \(-0.386184\pi\)
0.936752 0.349993i \(-0.113816\pi\)
\(48\) 48480.1 + 83970.0i 0.438369 + 0.759277i
\(49\) −68258.3 39409.0i −0.580186 0.334971i
\(50\) −8864.04 33081.1i −0.0709124 0.264649i
\(51\) 52475.6i 0.395591i
\(52\) −119242. + 40856.4i −0.848046 + 0.290569i
\(53\) 106247. 0.713654 0.356827 0.934170i \(-0.383859\pi\)
0.356827 + 0.934170i \(0.383859\pi\)
\(54\) −26452.6 + 7087.94i −0.167991 + 0.0450131i
\(55\) 11260.7 19504.1i 0.0676826 0.117230i
\(56\) −53323.4 + 30786.3i −0.303636 + 0.175305i
\(57\) −288533. 288533.i −1.55801 1.55801i
\(58\) 14864.4 55474.6i 0.0761838 0.284322i
\(59\) 365659. + 97978.2i 1.78041 + 0.477060i 0.990659 0.136363i \(-0.0435415\pi\)
0.789754 + 0.613424i \(0.210208\pi\)
\(60\) 66099.1 66099.1i 0.306015 0.306015i
\(61\) 100762. + 174526.i 0.443924 + 0.768899i 0.997977 0.0635826i \(-0.0202526\pi\)
−0.554052 + 0.832482i \(0.686919\pi\)
\(62\) 5299.47 + 3059.65i 0.0222360 + 0.0128380i
\(63\) −21135.7 78879.4i −0.0845268 0.315458i
\(64\) 113029.i 0.431173i
\(65\) 59063.8 + 87852.5i 0.215071 + 0.319900i
\(66\) 40688.0 0.141526
\(67\) −225048. + 60301.4i −0.748257 + 0.200495i −0.612745 0.790281i \(-0.709935\pi\)
−0.135512 + 0.990776i \(0.543268\pi\)
\(68\) 44517.4 77106.3i 0.141580 0.245224i
\(69\) −602112. + 347630.i −1.83286 + 1.05820i
\(70\) 17284.6 + 17284.6i 0.0503924 + 0.0503924i
\(71\) −84973.0 + 317124.i −0.237414 + 0.886041i 0.739632 + 0.673012i \(0.235000\pi\)
−0.977046 + 0.213029i \(0.931667\pi\)
\(72\) 125075. + 33513.8i 0.335100 + 0.0897896i
\(73\) −40750.8 + 40750.8i −0.104753 + 0.104753i −0.757541 0.652788i \(-0.773599\pi\)
0.652788 + 0.757541i \(0.273599\pi\)
\(74\) −38092.3 65977.7i −0.0940030 0.162818i
\(75\) 389574. + 224921.i 0.923434 + 0.533145i
\(76\) −179188. 668740.i −0.408196 1.52341i
\(77\) 92103.9i 0.201746i
\(78\) −84100.1 + 171770.i −0.177220 + 0.361962i
\(79\) 435228. 0.882745 0.441373 0.897324i \(-0.354492\pi\)
0.441373 + 0.897324i \(0.354492\pi\)
\(80\) 133458. 35759.8i 0.260659 0.0698434i
\(81\) 330905. 573145.i 0.622656 1.07847i
\(82\) −45434.7 + 26231.7i −0.0824036 + 0.0475757i
\(83\) −256625. 256625.i −0.448813 0.448813i 0.446147 0.894960i \(-0.352796\pi\)
−0.894960 + 0.446147i \(0.852796\pi\)
\(84\) 98944.1 369265.i 0.166937 0.623017i
\(85\) −72228.2 19353.5i −0.117612 0.0315139i
\(86\) −126332. + 126332.i −0.198617 + 0.198617i
\(87\) 377176. + 653287.i 0.572777 + 0.992080i
\(88\) 126478. + 73022.3i 0.185596 + 0.107154i
\(89\) −242124. 903619.i −0.343453 1.28178i −0.894409 0.447250i \(-0.852403\pi\)
0.550956 0.834535i \(-0.314263\pi\)
\(90\) 51406.1i 0.0705158i
\(91\) 388829. + 190374.i 0.515982 + 0.252629i
\(92\) −1.17964e6 −1.51491
\(93\) −77637.0 + 20802.8i −0.0965206 + 0.0258626i
\(94\) 243192. 421220.i 0.292796 0.507138i
\(95\) −503556. + 290728.i −0.587323 + 0.339091i
\(96\) 654654. + 654654.i 0.739943 + 0.739943i
\(97\) −90722.7 + 338582.i −0.0994033 + 0.370978i −0.997650 0.0685131i \(-0.978175\pi\)
0.898247 + 0.439491i \(0.144841\pi\)
\(98\) −195996. 52516.9i −0.208242 0.0557982i
\(99\) −136963. + 136963.i −0.141155 + 0.141155i
\(100\) 381620. + 660985.i 0.381620 + 0.660985i
\(101\) 701692. + 405122.i 0.681056 + 0.393208i 0.800253 0.599663i \(-0.204699\pi\)
−0.119197 + 0.992871i \(0.538032\pi\)
\(102\) −34964.8 130490.i −0.0329481 0.122964i
\(103\) 87516.3i 0.0800898i −0.999198 0.0400449i \(-0.987250\pi\)
0.999198 0.0400449i \(-0.0127501\pi\)
\(104\) −569698. + 383012.i −0.506460 + 0.340496i
\(105\) −321068. −0.277351
\(106\) 264202. 70792.8i 0.221829 0.0594390i
\(107\) −617565. + 1.06965e6i −0.504117 + 0.873156i 0.495872 + 0.868396i \(0.334849\pi\)
−0.999989 + 0.00476029i \(0.998485\pi\)
\(108\) 528543. 305154.i 0.419574 0.242241i
\(109\) −711838. 711838.i −0.549670 0.549670i 0.376676 0.926345i \(-0.377067\pi\)
−0.926345 + 0.376676i \(0.877067\pi\)
\(110\) 15006.1 56003.6i 0.0112743 0.0420764i
\(111\) 966571. + 258992.i 0.706749 + 0.189373i
\(112\) 399547. 399547.i 0.284389 0.284389i
\(113\) −1.00864e6 1.74702e6i −0.699041 1.21077i −0.968799 0.247846i \(-0.920277\pi\)
0.269759 0.962928i \(-0.413056\pi\)
\(114\) −909744. 525241.i −0.614051 0.354523i
\(115\) 256418. + 956966.i 0.168599 + 0.629221i
\(116\) 1.27990e6i 0.819977i
\(117\) −295112. 861303.i −0.184259 0.537772i
\(118\) 974565. 0.593150
\(119\) −295386. + 79148.4i −0.175287 + 0.0469679i
\(120\) 254551. 440896.i 0.147310 0.255148i
\(121\) 1.34502e6 776549.i 0.759230 0.438342i
\(122\) 366852. + 366852.i 0.202028 + 0.202028i
\(123\) 178351. 665617.i 0.0958432 0.357692i
\(124\) −131726. 35295.8i −0.0690885 0.0185122i
\(125\) 985630. 985630.i 0.504643 0.504643i
\(126\) −105116. 182066.i −0.0525479 0.0910157i
\(127\) −1.74129e6 1.00533e6i −0.850080 0.490794i 0.0105981 0.999944i \(-0.496626\pi\)
−0.860678 + 0.509150i \(0.829960\pi\)
\(128\) 528838. + 1.97365e6i 0.252170 + 0.941110i
\(129\) 2.34666e6i 1.09315i
\(130\) 205410. + 179107.i 0.0934957 + 0.0815235i
\(131\) 2.68360e6 1.19372 0.596862 0.802344i \(-0.296414\pi\)
0.596862 + 0.802344i \(0.296414\pi\)
\(132\) −875863. + 234687.i −0.380815 + 0.102039i
\(133\) −1.18897e6 + 2.05935e6i −0.505377 + 0.875338i
\(134\) −519445. + 299902.i −0.215886 + 0.124642i
\(135\) −362442. 362442.i −0.147312 0.147312i
\(136\) 125502. 468379.i 0.0498923 0.186200i
\(137\) −2.58680e6 693130.i −1.00601 0.269559i −0.282046 0.959401i \(-0.591013\pi\)
−0.723960 + 0.689842i \(0.757680\pi\)
\(138\) −1.26564e6 + 1.26564e6i −0.481584 + 0.481584i
\(139\) −188967. 327300.i −0.0703625 0.121871i 0.828698 0.559696i \(-0.189082\pi\)
−0.899060 + 0.437825i \(0.855749\pi\)
\(140\) −471770. 272377.i −0.171928 0.0992626i
\(141\) 1.65348e6 + 6.17086e6i 0.589849 + 2.20135i
\(142\) 845206.i 0.295187i
\(143\) −70079.6 1.02448e6i −0.0239653 0.350345i
\(144\) −1.18829e6 −0.397956
\(145\) 1.03830e6 278212.i 0.340580 0.0912582i
\(146\) −74181.9 + 128487.i −0.0238363 + 0.0412858i
\(147\) 2.30811e6 1.33259e6i 0.726615 0.419511i
\(148\) 1.20054e6 + 1.20054e6i 0.370333 + 0.370333i
\(149\) −592234. + 2.21025e6i −0.179033 + 0.668162i 0.816796 + 0.576927i \(0.195748\pi\)
−0.995829 + 0.0912352i \(0.970918\pi\)
\(150\) 1.11861e6 + 299732.i 0.331441 + 0.0888094i
\(151\) −10900.0 + 10900.0i −0.00316587 + 0.00316587i −0.708688 0.705522i \(-0.750713\pi\)
0.705522 + 0.708688i \(0.250713\pi\)
\(152\) −1.88529e6 3.26541e6i −0.536843 0.929839i
\(153\) 556951. + 321556.i 0.155504 + 0.0897805i
\(154\) −61369.4 229034.i −0.0168031 0.0627101i
\(155\) 114533.i 0.0307564i
\(156\) 819603. 4.18266e6i 0.215889 1.10174i
\(157\) −3.15946e6 −0.816420 −0.408210 0.912888i \(-0.633847\pi\)
−0.408210 + 0.912888i \(0.633847\pi\)
\(158\) 1.08228e6 289995.i 0.274389 0.0735223i
\(159\) −1.79633e6 + 3.11134e6i −0.446884 + 0.774026i
\(160\) 1.14252e6 659633.i 0.278935 0.161043i
\(161\) 2.86497e6 + 2.86497e6i 0.686504 + 0.686504i
\(162\) 440968. 1.64572e6i 0.103720 0.387088i
\(163\) −6.90788e6 1.85096e6i −1.59508 0.427400i −0.651526 0.758626i \(-0.725871\pi\)
−0.943551 + 0.331226i \(0.892538\pi\)
\(164\) 826738. 826738.i 0.187429 0.187429i
\(165\) 380773. + 659518.i 0.0847645 + 0.146816i
\(166\) −809138. 467156.i −0.176888 0.102126i
\(167\) −1.36920e6 5.10994e6i −0.293981 1.09715i −0.942023 0.335547i \(-0.891079\pi\)
0.648043 0.761604i \(-0.275588\pi\)
\(168\) 2.08204e6i 0.439097i
\(169\) 4.46984e6 + 1.82170e6i 0.926045 + 0.377414i
\(170\) −192504. −0.0391826
\(171\) 4.83041e6 1.29430e6i 0.966041 0.258850i
\(172\) 1.99078e6 3.44813e6i 0.391235 0.677638i
\(173\) 7.51531e6 4.33897e6i 1.45147 0.838008i 0.452907 0.891558i \(-0.350387\pi\)
0.998565 + 0.0535501i \(0.0170537\pi\)
\(174\) 1.37321e6 + 1.37321e6i 0.260668 + 0.260668i
\(175\) 678491. 2.53216e6i 0.126599 0.472474i
\(176\) −1.29457e6 346878.i −0.237458 0.0636267i
\(177\) −9.05147e6 + 9.05147e6i −1.63230 + 1.63230i
\(178\) −1.20417e6 2.08569e6i −0.213515 0.369819i
\(179\) 3.85702e6 + 2.22685e6i 0.672500 + 0.388268i 0.797023 0.603949i \(-0.206407\pi\)
−0.124523 + 0.992217i \(0.539740\pi\)
\(180\) 296508. + 1.10658e6i 0.0508415 + 0.189743i
\(181\) 5.91755e6i 0.997943i 0.866618 + 0.498972i \(0.166289\pi\)
−0.866618 + 0.498972i \(0.833711\pi\)
\(182\) 1.09374e6 + 214322.i 0.181427 + 0.0355511i
\(183\) −6.81442e6 −1.11193
\(184\) −6.20565e6 + 1.66280e6i −0.996171 + 0.266923i
\(185\) 712961. 1.23489e6i 0.112603 0.195034i
\(186\) −179198. + 103460.i −0.0278480 + 0.0160781i
\(187\) 512896. + 512896.i 0.0784340 + 0.0784340i
\(188\) −2.80544e6 + 1.04700e7i −0.422209 + 1.57570i
\(189\) −2.02479e6 542541.i −0.299912 0.0803613i
\(190\) −1.05847e6 + 1.05847e6i −0.154319 + 0.154319i
\(191\) −368146. 637647.i −0.0528348 0.0915125i 0.838398 0.545058i \(-0.183492\pi\)
−0.891233 + 0.453545i \(0.850159\pi\)
\(192\) −3.30996e6 1.91101e6i −0.467648 0.269997i
\(193\) 301583. + 1.12552e6i 0.0419502 + 0.156560i 0.983724 0.179688i \(-0.0575087\pi\)
−0.941774 + 0.336248i \(0.890842\pi\)
\(194\) 902396.i 0.123592i
\(195\) −3.57128e6 + 244293.i −0.481637 + 0.0329464i
\(196\) 4.52197e6 0.600565
\(197\) 1.08614e7 2.91029e6i 1.42064 0.380660i 0.534932 0.844895i \(-0.320337\pi\)
0.885712 + 0.464235i \(0.153671\pi\)
\(198\) −249325. + 431843.i −0.0321196 + 0.0556328i
\(199\) −3.79899e6 + 2.19335e6i −0.482069 + 0.278322i −0.721278 0.692646i \(-0.756445\pi\)
0.239210 + 0.970968i \(0.423112\pi\)
\(200\) 2.93928e6 + 2.93928e6i 0.367410 + 0.367410i
\(201\) 2.03905e6 7.60985e6i 0.251096 0.937104i
\(202\) 2.01483e6 + 539871.i 0.244446 + 0.0654992i
\(203\) 3.10848e6 3.10848e6i 0.371586 0.371586i
\(204\) 1.50533e6 + 2.60730e6i 0.177313 + 0.307115i
\(205\) −850388. 490971.i −0.0987087 0.0569895i
\(206\) −58312.7 217626.i −0.00667054 0.0248948i
\(207\) 8.52071e6i 0.960649i
\(208\) 4.14020e6 4.74821e6i 0.460078 0.527643i
\(209\) 5.64025e6 0.617816
\(210\) −798397. + 213930.i −0.0862107 + 0.0231001i
\(211\) −1.42125e6 + 2.46167e6i −0.151294 + 0.262049i −0.931703 0.363220i \(-0.881677\pi\)
0.780409 + 0.625269i \(0.215011\pi\)
\(212\) −5.27897e6 + 3.04782e6i −0.554041 + 0.319876i
\(213\) −7.85002e6 7.85002e6i −0.812329 0.812329i
\(214\) −822974. + 3.07138e6i −0.0839740 + 0.313395i
\(215\) −3.22998e6 865471.i −0.325001 0.0870837i
\(216\) 2.35033e6 2.35033e6i 0.233221 0.233221i
\(217\) 234198. + 405644.i 0.0229195 + 0.0396977i
\(218\) −2.24442e6 1.29582e6i −0.216638 0.125076i
\(219\) −504368. 1.88233e6i −0.0480193 0.179210i
\(220\) 1.29211e6i 0.121347i
\(221\) −3.22539e6 + 1.10513e6i −0.298817 + 0.102385i
\(222\) 2.57613e6 0.235455
\(223\) −7.01335e6 + 1.87922e6i −0.632428 + 0.169459i −0.560771 0.827971i \(-0.689495\pi\)
−0.0716567 + 0.997429i \(0.522829\pi\)
\(224\) 2.69765e6 4.67247e6i 0.240017 0.415721i
\(225\) −4.77440e6 + 2.75650e6i −0.419152 + 0.241997i
\(226\) −3.67223e6 3.67223e6i −0.318130 0.318130i
\(227\) 1.86595e6 6.96381e6i 0.159522 0.595346i −0.839153 0.543895i \(-0.816949\pi\)
0.998676 0.0514505i \(-0.0163844\pi\)
\(228\) 2.26130e7 + 6.05913e6i 1.90789 + 0.511218i
\(229\) 1.17933e7 1.17933e7i 0.982037 0.982037i −0.0178049 0.999841i \(-0.505668\pi\)
0.999841 + 0.0178049i \(0.00566779\pi\)
\(230\) 1.27526e6 + 2.20882e6i 0.104813 + 0.181542i
\(231\) 2.69718e6 + 1.55722e6i 0.218813 + 0.126332i
\(232\) 1.80412e6 + 6.73309e6i 0.144478 + 0.539200i
\(233\) 9.60469e6i 0.759304i 0.925129 + 0.379652i \(0.123956\pi\)
−0.925129 + 0.379652i \(0.876044\pi\)
\(234\) −1.30774e6 1.94516e6i −0.102065 0.151812i
\(235\) 9.10349e6 0.701462
\(236\) −2.09788e7 + 5.62124e6i −1.59604 + 0.427658i
\(237\) −7.35847e6 + 1.27452e7i −0.552768 + 0.957422i
\(238\) −681796. + 393635.i −0.0505735 + 0.0291986i
\(239\) −1.02477e7 1.02477e7i −0.750644 0.750644i 0.223955 0.974599i \(-0.428103\pi\)
−0.974599 + 0.223955i \(0.928103\pi\)
\(240\) −1.20920e6 + 4.51278e6i −0.0874707 + 0.326445i
\(241\) 1.89066e6 + 506602.i 0.135071 + 0.0361922i 0.325721 0.945466i \(-0.394393\pi\)
−0.190650 + 0.981658i \(0.561060\pi\)
\(242\) 2.82723e6 2.82723e6i 0.199487 0.199487i
\(243\) 7.31191e6 + 1.26646e7i 0.509580 + 0.882618i
\(244\) −1.00130e7 5.78098e6i −0.689275 0.397953i
\(245\) −982942. 3.66839e6i −0.0668389 0.249446i
\(246\) 1.77402e6i 0.119166i
\(247\) −1.16581e7 + 2.38111e7i −0.773637 + 1.58011i
\(248\) −742714. −0.0486930
\(249\) 1.18538e7 3.17623e6i 0.767823 0.205738i
\(250\) 1.79422e6 3.10769e6i 0.114830 0.198892i
\(251\) −1.37625e7 + 7.94579e6i −0.870315 + 0.502476i −0.867453 0.497519i \(-0.834244\pi\)
−0.00286188 + 0.999996i \(0.500911\pi\)
\(252\) 3.31290e6 + 3.31290e6i 0.207017 + 0.207017i
\(253\) 2.48731e6 9.28278e6i 0.153592 0.573213i
\(254\) −4.99990e6 1.33972e6i −0.305113 0.0817547i
\(255\) 1.78792e6 1.78792e6i 0.107827 0.107827i
\(256\) −986829. 1.70924e6i −0.0588196 0.101879i
\(257\) 1.36068e7 + 7.85587e6i 0.801596 + 0.462802i 0.844029 0.536297i \(-0.180177\pi\)
−0.0424327 + 0.999099i \(0.513511\pi\)
\(258\) −1.56359e6 5.83541e6i −0.0910469 0.339792i
\(259\) 5.83148e6i 0.335645i
\(260\) −5.45480e6 2.67072e6i −0.310355 0.151953i
\(261\) −9.24491e6 −0.519973
\(262\) 6.67328e6 1.78810e6i 0.371053 0.0994232i
\(263\) 6.89603e6 1.19443e7i 0.379081 0.656587i −0.611848 0.790975i \(-0.709574\pi\)
0.990929 + 0.134388i \(0.0429070\pi\)
\(264\) −4.27678e6 + 2.46920e6i −0.232437 + 0.134198i
\(265\) 3.61999e6 + 3.61999e6i 0.194522 + 0.194522i
\(266\) −1.58443e6 + 5.91318e6i −0.0841839 + 0.314178i
\(267\) 3.05553e7 + 8.18726e6i 1.60529 + 0.430135i
\(268\) 9.45191e6 9.45191e6i 0.491038 0.491038i
\(269\) −2.59768e6 4.49932e6i −0.133453 0.231148i 0.791552 0.611102i \(-0.209273\pi\)
−0.925006 + 0.379954i \(0.875940\pi\)
\(270\) −1.14278e6 659782.i −0.0580590 0.0335204i
\(271\) −8.57768e6 3.20123e7i −0.430985 1.60846i −0.750496 0.660875i \(-0.770185\pi\)
0.319511 0.947583i \(-0.396481\pi\)
\(272\) 4.44989e6i 0.221127i
\(273\) −1.21489e7 + 8.16781e6i −0.597104 + 0.401437i
\(274\) −6.89440e6 −0.335154
\(275\) −6.00607e6 + 1.60932e6i −0.288797 + 0.0773828i
\(276\) 1.99444e7 3.45446e7i 0.948621 1.64306i
\(277\) 5.55508e6 3.20723e6i 0.261367 0.150900i −0.363591 0.931559i \(-0.618449\pi\)
0.624958 + 0.780658i \(0.285116\pi\)
\(278\) −687983. 687983.i −0.0320216 0.0320216i
\(279\) 254947. 951476.i 0.0117392 0.0438112i
\(280\) −2.86575e6 767875.i −0.130546 0.0349797i
\(281\) −2.21347e7 + 2.21347e7i −0.997598 + 0.997598i −0.999997 0.00239922i \(-0.999236\pi\)
0.00239922 + 0.999997i \(0.499236\pi\)
\(282\) 8.22337e6 + 1.42433e7i 0.366693 + 0.635131i
\(283\) 2.71144e7 + 1.56545e7i 1.19630 + 0.690684i 0.959728 0.280930i \(-0.0906430\pi\)
0.236571 + 0.971614i \(0.423976\pi\)
\(284\) −4.87511e6 1.81942e7i −0.212828 0.794286i
\(285\) 1.96616e7i 0.849343i
\(286\) −856885. 2.50087e6i −0.0366290 0.106904i
\(287\) −4.01577e6 −0.169873
\(288\) −1.09597e7 + 2.93665e6i −0.458799 + 0.122935i
\(289\) −1.08646e7 + 1.88181e7i −0.450113 + 0.779618i
\(290\) 2.39656e6 1.38365e6i 0.0982638 0.0567327i
\(291\) −8.38119e6 8.38119e6i −0.340116 0.340116i
\(292\) 855756. 3.19373e6i 0.0343717 0.128277i
\(293\) −1.82967e7 4.90260e6i −0.727396 0.194905i −0.123927 0.992291i \(-0.539549\pi\)
−0.603469 + 0.797386i \(0.706215\pi\)
\(294\) 4.85164e6 4.85164e6i 0.190918 0.190918i
\(295\) 9.12031e6 + 1.57968e7i 0.355258 + 0.615325i
\(296\) 8.00788e6 + 4.62335e6i 0.308775 + 0.178271i
\(297\) 1.28686e6 + 4.80262e6i 0.0491203 + 0.183320i
\(298\) 5.89080e6i 0.222600i
\(299\) 3.40473e7 + 2.96876e7i 1.27371 + 1.11061i
\(300\) −2.58085e7 −0.955869
\(301\) −1.32094e7 + 3.53945e6i −0.484377 + 0.129788i
\(302\) −19842.1 + 34367.5i −0.000720388 + 0.00124775i
\(303\) −2.37273e7 + 1.36989e7i −0.852943 + 0.492447i
\(304\) 2.44674e7 + 2.44674e7i 0.870898 + 0.870898i
\(305\) −2.51322e6 + 9.37948e6i −0.0885792 + 0.330582i
\(306\) 1.59922e6 + 428509.i 0.0558140 + 0.0149553i
\(307\) 2.71510e6 2.71510e6i 0.0938363 0.0938363i −0.658630 0.752467i \(-0.728864\pi\)
0.752467 + 0.658630i \(0.228864\pi\)
\(308\) 2.64211e6 + 4.57627e6i 0.0904272 + 0.156624i
\(309\) 2.56283e6 + 1.47965e6i 0.0868651 + 0.0501516i
\(310\) 76314.1 + 284808.i 0.00256165 + 0.00956020i
\(311\) 5.23932e6i 0.174178i −0.996201 0.0870891i \(-0.972244\pi\)
0.996201 0.0870891i \(-0.0277565\pi\)
\(312\) −1.58417e6 2.31587e7i −0.0521601 0.762520i
\(313\) 3.09546e7 1.00947 0.504734 0.863275i \(-0.331590\pi\)
0.504734 + 0.863275i \(0.331590\pi\)
\(314\) −7.85659e6 + 2.10517e6i −0.253773 + 0.0679982i
\(315\) 1.96742e6 3.40767e6i 0.0629455 0.109025i
\(316\) −2.16247e7 + 1.24850e7i −0.685314 + 0.395666i
\(317\) −2.16477e7 2.16477e7i −0.679571 0.679571i 0.280332 0.959903i \(-0.409555\pi\)
−0.959903 + 0.280332i \(0.909555\pi\)
\(318\) −2.39381e6 + 8.93383e6i −0.0744404 + 0.277815i
\(319\) −1.00717e7 2.69872e6i −0.310265 0.0831352i
\(320\) −3.85108e6 + 3.85108e6i −0.117526 + 0.117526i
\(321\) −2.08825e7 3.61696e7i −0.631347 1.09353i
\(322\) 9.03325e6 + 5.21535e6i 0.270568 + 0.156212i
\(323\) −4.84688e6 1.80888e7i −0.143832 0.536788i
\(324\) 3.79697e7i 1.11635i
\(325\) 5.62027e6 2.86818e7i 0.163722 0.835519i
\(326\) −1.84110e7 −0.531405
\(327\) 3.28807e7 8.81036e6i 0.940368 0.251971i
\(328\) 3.18381e6 5.51452e6i 0.0902247 0.156274i
\(329\) 3.22420e7 1.86149e7i 0.905386 0.522725i
\(330\) 1.38630e6 + 1.38630e6i 0.0385759 + 0.0385759i
\(331\) −5.23754e6 + 1.95468e7i −0.144425 + 0.539002i 0.855355 + 0.518042i \(0.173339\pi\)
−0.999780 + 0.0209602i \(0.993328\pi\)
\(332\) 2.01123e7 + 5.38907e6i 0.549601 + 0.147265i
\(333\) −8.67170e6 + 8.67170e6i −0.234840 + 0.234840i
\(334\) −6.80957e6 1.17945e7i −0.182760 0.316549i
\(335\) −9.72229e6 5.61317e6i −0.258603 0.149305i
\(336\) 4.94515e6 + 1.84556e7i 0.130365 + 0.486530i
\(337\) 5.57292e7i 1.45611i −0.685521 0.728053i \(-0.740426\pi\)
0.685521 0.728053i \(-0.259574\pi\)
\(338\) 1.23289e7 + 1.55173e6i 0.319282 + 0.0401851i
\(339\) 6.82132e7 1.75093
\(340\) 4.14391e6 1.11036e6i 0.105432 0.0282505i
\(341\) 555498. 962150.i 0.0140094 0.0242650i
\(342\) 1.11493e7 6.43706e6i 0.278721 0.160920i
\(343\) −2.73756e7 2.73756e7i −0.678394 0.678394i
\(344\) 5.61233e6 2.09455e7i 0.137869 0.514536i
\(345\) −3.23592e7 8.67061e6i −0.788025 0.211151i
\(346\) 1.57972e7 1.57972e7i 0.381374 0.381374i
\(347\) 6.81417e6 + 1.18025e7i 0.163089 + 0.282478i 0.935975 0.352066i \(-0.114521\pi\)
−0.772886 + 0.634545i \(0.781188\pi\)
\(348\) −3.74807e7 2.16395e7i −0.889344 0.513463i
\(349\) 2.02019e7 + 7.53945e7i 0.475243 + 1.77363i 0.620468 + 0.784232i \(0.286943\pi\)
−0.145225 + 0.989399i \(0.546391\pi\)
\(350\) 6.74878e6i 0.157406i
\(351\) −2.29348e7 4.49413e6i −0.530363 0.103926i
\(352\) −1.27972e7 −0.293418
\(353\) 1.63820e7 4.38955e6i 0.372429 0.0997920i −0.0677495 0.997702i \(-0.521582\pi\)
0.440178 + 0.897910i \(0.354915\pi\)
\(354\) −1.64771e7 + 2.85392e7i −0.371426 + 0.643328i
\(355\) −1.37001e7 + 7.90973e6i −0.306223 + 0.176798i
\(356\) 3.79516e7 + 3.79516e7i 0.841162 + 0.841162i
\(357\) 2.67635e6 9.98828e6i 0.0588218 0.219526i
\(358\) 1.10750e7 + 2.96753e6i 0.241375 + 0.0646763i
\(359\) −2.34840e7 + 2.34840e7i −0.507561 + 0.507561i −0.913777 0.406216i \(-0.866848\pi\)
0.406216 + 0.913777i \(0.366848\pi\)
\(360\) 3.11964e6 + 5.40337e6i 0.0668647 + 0.115813i
\(361\) −8.53675e7 4.92869e7i −1.81456 1.04764i
\(362\) 3.94290e6 + 1.47151e7i 0.0831170 + 0.310197i
\(363\) 5.25170e7i 1.09794i
\(364\) −2.47805e7 + 1.69510e6i −0.513813 + 0.0351473i
\(365\) −2.77688e6 −0.0571056
\(366\) −1.69454e7 + 4.54049e6i −0.345627 + 0.0926104i
\(367\) −3.18205e7 + 5.51148e7i −0.643738 + 1.11499i 0.340853 + 0.940116i \(0.389284\pi\)
−0.984591 + 0.174870i \(0.944049\pi\)
\(368\) 5.10586e7 2.94787e7i 1.02453 0.591514i
\(369\) 5.97165e6 + 5.97165e6i 0.118854 + 0.118854i
\(370\) 950101. 3.54582e6i 0.0187571 0.0700023i
\(371\) 2.02232e7 + 5.41878e6i 0.396029 + 0.106116i
\(372\) 3.26072e6 3.26072e6i 0.0633409 0.0633409i
\(373\) −1.27798e7 2.21353e7i −0.246263 0.426539i 0.716223 0.697871i \(-0.245869\pi\)
−0.962486 + 0.271332i \(0.912536\pi\)
\(374\) 1.61716e6 + 933667.i 0.0309128 + 0.0178475i
\(375\) 1.21991e7 + 4.55275e7i 0.231330 + 0.863336i
\(376\) 5.90335e7i 1.11054i
\(377\) 3.22108e7 3.69411e7i 0.601142 0.689423i
\(378\) −5.39652e6 −0.0999167
\(379\) 3.62432e7 9.71133e6i 0.665746 0.178386i 0.0899082 0.995950i \(-0.471343\pi\)
0.575838 + 0.817564i \(0.304676\pi\)
\(380\) 1.66798e7 2.88902e7i 0.303976 0.526502i
\(381\) 5.88805e7 3.39947e7i 1.06463 0.614662i
\(382\) −1.34033e6 1.34033e6i −0.0240449 0.0240449i
\(383\) 3.87209e6 1.44508e7i 0.0689206 0.257215i −0.922866 0.385122i \(-0.874159\pi\)
0.991786 + 0.127907i \(0.0408259\pi\)
\(384\) −6.67377e7 1.78823e7i −1.17863 0.315813i
\(385\) 3.13812e6 3.13812e6i 0.0549905 0.0549905i
\(386\) 1.49988e6 + 2.59788e6i 0.0260793 + 0.0451707i
\(387\) 2.49063e7 + 1.43797e7i 0.429712 + 0.248094i
\(388\) −5.20498e6 1.94252e7i −0.0891095 0.332561i
\(389\) 3.23998e6i 0.0550420i −0.999621 0.0275210i \(-0.991239\pi\)
0.999621 0.0275210i \(-0.00876130\pi\)
\(390\) −8.71789e6 + 2.98705e6i −0.146966 + 0.0503557i
\(391\) −3.19082e7 −0.533792
\(392\) 2.37885e7 6.37410e6i 0.394919 0.105818i
\(393\) −4.53721e7 + 7.85868e7i −0.747500 + 1.29471i
\(394\) 2.50697e7 1.44740e7i 0.409883 0.236646i
\(395\) 1.48289e7 + 1.48289e7i 0.240612 + 0.240612i
\(396\) 2.87619e6 1.07341e7i 0.0463161 0.172854i
\(397\) −4.20284e7 1.12615e7i −0.671693 0.179980i −0.0931757 0.995650i \(-0.529702\pi\)
−0.578517 + 0.815670i \(0.696369\pi\)
\(398\) −7.98546e6 + 7.98546e6i −0.126663 + 0.126663i
\(399\) −4.02042e7 6.96356e7i −0.632925 1.09626i
\(400\) −3.30355e7 1.90731e7i −0.516180 0.298017i
\(401\) 6.35234e6 + 2.37072e7i 0.0985146 + 0.367661i 0.997529 0.0702579i \(-0.0223822\pi\)
−0.899014 + 0.437919i \(0.855716\pi\)
\(402\) 2.02820e7i 0.312199i
\(403\) 2.91366e6 + 4.33383e6i 0.0445168 + 0.0662150i
\(404\) −4.64857e7 −0.704977
\(405\) 3.08024e7 8.25347e6i 0.463681 0.124243i
\(406\) 5.65861e6 9.80101e6i 0.0845536 0.146451i
\(407\) −1.19787e7 + 6.91588e6i −0.177674 + 0.102580i
\(408\) 1.15942e7 + 1.15942e7i 0.170710 + 0.170710i
\(409\) 6.97679e6 2.60377e7i 0.101973 0.380569i −0.896011 0.444032i \(-0.853548\pi\)
0.997984 + 0.0634628i \(0.0202144\pi\)
\(410\) −2.44179e6 654275.i −0.0354288 0.00949311i
\(411\) 6.40331e7 6.40331e7i 0.922315 0.922315i
\(412\) 2.51051e6 + 4.34833e6i 0.0358980 + 0.0621772i
\(413\) 6.46031e7 + 3.72986e7i 0.917072 + 0.529472i
\(414\) −5.67740e6 2.11884e7i −0.0800108 0.298604i
\(415\) 1.74872e7i 0.244668i
\(416\) 2.64511e7 5.40250e7i 0.367421 0.750438i
\(417\) 1.27796e7 0.176241
\(418\) 1.40255e7 3.75813e6i 0.192040 0.0514569i
\(419\) 3.40584e7 5.89909e7i 0.463002 0.801943i −0.536107 0.844150i \(-0.680106\pi\)
0.999109 + 0.0422074i \(0.0134390\pi\)
\(420\) 1.59526e7 9.21023e6i 0.215320 0.124315i
\(421\) 8.72935e7 + 8.72935e7i 1.16986 + 1.16986i 0.982241 + 0.187624i \(0.0600786\pi\)
0.187624 + 0.982241i \(0.439921\pi\)
\(422\) −1.89397e6 + 7.06839e6i −0.0252020 + 0.0940553i
\(423\) −7.56267e7 2.02641e7i −0.999203 0.267736i
\(424\) −2.34746e7 + 2.34746e7i −0.307964 + 0.307964i
\(425\) 1.03225e7 + 1.78791e7i 0.134468 + 0.232905i
\(426\) −2.47511e7 1.42900e7i −0.320159 0.184844i
\(427\) 1.02781e7 + 3.83585e7i 0.132017 + 0.492695i
\(428\) 7.08624e7i 0.903825i
\(429\) 3.11859e7 + 1.52689e7i 0.394990 + 0.193391i
\(430\) −8.60862e6 −0.108275
\(431\) −9.75385e7 + 2.61354e7i −1.21827 + 0.326435i −0.810003 0.586426i \(-0.800534\pi\)
−0.408270 + 0.912861i \(0.633868\pi\)
\(432\) −1.52514e7 + 2.64162e7i −0.189172 + 0.327656i
\(433\) 1.67973e7 9.69793e6i 0.206907 0.119458i −0.392966 0.919553i \(-0.628551\pi\)
0.599873 + 0.800095i \(0.295218\pi\)
\(434\) 852661. + 852661.i 0.0104306 + 0.0104306i
\(435\) −9.40755e6 + 3.51095e7i −0.114290 + 0.426537i
\(436\) 5.57883e7 + 1.49484e7i 0.673107 + 0.180358i
\(437\) −1.75445e8 + 1.75445e8i −2.10231 + 2.10231i
\(438\) −2.50841e6 4.34470e6i −0.0298522 0.0517056i
\(439\) 3.41904e7 + 1.97399e7i 0.404121 + 0.233319i 0.688260 0.725464i \(-0.258375\pi\)
−0.284140 + 0.958783i \(0.591708\pi\)
\(440\) 1.82133e6 + 6.79730e6i 0.0213811 + 0.0797955i
\(441\) 3.26629e7i 0.380837i
\(442\) −7.28419e6 + 4.89721e6i −0.0843557 + 0.0567129i
\(443\) −4.31028e7 −0.495786 −0.247893 0.968787i \(-0.579738\pi\)
−0.247893 + 0.968787i \(0.579738\pi\)
\(444\) −5.54545e7 + 1.48590e7i −0.633561 + 0.169762i
\(445\) 2.25381e7 3.90372e7i 0.255763 0.442995i
\(446\) −1.61879e7 + 9.34608e6i −0.182467 + 0.105348i
\(447\) −5.47120e7 5.47120e7i −0.612576 0.612576i
\(448\) −5.76471e6 + 2.15142e7i −0.0641126 + 0.239271i
\(449\) −6.71882e7 1.80030e7i −0.742256 0.198887i −0.132176 0.991226i \(-0.542196\pi\)
−0.610081 + 0.792339i \(0.708863\pi\)
\(450\) −1.00358e7 + 1.00358e7i −0.110132 + 0.110132i
\(451\) 4.76253e6 + 8.24894e6i 0.0519168 + 0.0899226i
\(452\) 1.00231e8 + 5.78683e7i 1.08539 + 0.626651i
\(453\) −134908. 503482.i −0.00145125 0.00541614i
\(454\) 1.85601e7i 0.198341i
\(455\) 6.76166e6 + 1.97343e7i 0.0717826 + 0.209502i
\(456\) 1.27500e8 1.34467
\(457\) 8.40017e7 2.25082e7i 0.880115 0.235826i 0.209658 0.977775i \(-0.432765\pi\)
0.670457 + 0.741949i \(0.266098\pi\)
\(458\) 2.14683e7 3.71841e7i 0.223460 0.387044i
\(459\) 1.42966e7 8.25415e6i 0.147841 0.0853561i
\(460\) −4.01921e7 4.01921e7i −0.412921 0.412921i
\(461\) −3.27309e7 + 1.22153e8i −0.334083 + 1.24682i 0.570776 + 0.821106i \(0.306642\pi\)
−0.904859 + 0.425711i \(0.860024\pi\)
\(462\) 7.74462e6 + 2.07517e6i 0.0785370 + 0.0210439i
\(463\) 4.92350e7 4.92350e7i 0.496056 0.496056i −0.414152 0.910208i \(-0.635922\pi\)
0.910208 + 0.414152i \(0.135922\pi\)
\(464\) −3.19842e7 5.53983e7i −0.320171 0.554552i
\(465\) −3.35400e6 1.93643e6i −0.0333583 0.0192594i
\(466\) 6.39967e6 + 2.38839e7i 0.0632411 + 0.236019i
\(467\) 1.23464e8i 1.21224i −0.795372 0.606121i \(-0.792725\pi\)
0.795372 0.606121i \(-0.207275\pi\)
\(468\) 3.93704e7 + 3.43290e7i 0.384090 + 0.334907i
\(469\) −4.59115e7 −0.445044
\(470\) 2.26375e7 6.06571e6i 0.218040 0.0584236i
\(471\) 5.34175e7 9.25218e7i 0.511235 0.885486i
\(472\) −1.02438e8 + 5.91426e7i −0.974171 + 0.562438i
\(473\) 2.29363e7 + 2.29363e7i 0.216740 + 0.216740i
\(474\) −9.80599e6 + 3.65965e7i −0.0920781 + 0.343640i
\(475\) 1.55064e8 + 4.15494e7i 1.44688 + 0.387689i
\(476\) 1.24061e7 1.24061e7i 0.115031 0.115031i
\(477\) −2.20148e7 3.81308e7i −0.202843 0.351335i
\(478\) −3.23110e7 1.86548e7i −0.295847 0.170807i
\(479\) −5.58880e7 2.08577e8i −0.508525 1.89784i −0.434714 0.900569i \(-0.643150\pi\)
−0.0738112 0.997272i \(-0.523516\pi\)
\(480\) 4.46101e7i 0.403376i
\(481\) −4.43703e6 6.48643e7i −0.0398710 0.582868i
\(482\) 5.03904e6 0.0449994
\(483\) −1.32337e8 + 3.54595e7i −1.17446 + 0.314696i
\(484\) −4.45525e7 + 7.71672e7i −0.392949 + 0.680608i
\(485\) −1.46271e7 + 8.44494e6i −0.128213 + 0.0740238i
\(486\) 2.66209e7 + 2.66209e7i 0.231907 + 0.231907i
\(487\) 4.00706e7 1.49546e8i 0.346928 1.29475i −0.543416 0.839464i \(-0.682869\pi\)
0.890344 0.455289i \(-0.150464\pi\)
\(488\) −6.08233e7 1.62975e7i −0.523372 0.140237i
\(489\) 1.70996e8 1.70996e8i 1.46238 1.46238i
\(490\) −4.88854e6 8.46720e6i −0.0415519 0.0719700i
\(491\) −4.67388e6 2.69846e6i −0.0394851 0.0227967i 0.480128 0.877199i \(-0.340590\pi\)
−0.519613 + 0.854402i \(0.673924\pi\)
\(492\) 1.02325e7 + 3.81880e7i 0.0859181 + 0.320651i
\(493\) 3.46202e7i 0.288927i
\(494\) −1.31246e7 + 6.69786e7i −0.108870 + 0.555591i
\(495\) −9.33308e6 −0.0769501
\(496\) 6.58356e6 1.76406e6i 0.0539530 0.0144567i
\(497\) −3.23478e7 + 5.60280e7i −0.263497 + 0.456390i
\(498\) 2.73605e7 1.57966e7i 0.221532 0.127901i
\(499\) −1.25075e8 1.25075e8i −1.00663 1.00663i −0.999978 0.00665368i \(-0.997882\pi\)
−0.00665368 0.999978i \(-0.502118\pi\)
\(500\) −2.06980e7 + 7.72460e7i −0.165584 + 0.617968i
\(501\) 1.72789e8 + 4.62987e7i 1.37405 + 0.368176i
\(502\) −2.89287e7 + 2.89287e7i −0.228675 + 0.228675i
\(503\) 7.06862e7 + 1.22432e8i 0.555432 + 0.962036i 0.997870 + 0.0652367i \(0.0207803\pi\)
−0.442438 + 0.896799i \(0.645886\pi\)
\(504\) 2.20977e7 + 1.27581e7i 0.172606 + 0.0996542i
\(505\) 1.01046e7 + 3.77109e7i 0.0784594 + 0.292814i
\(506\) 2.47407e7i 0.190968i
\(507\) −1.28919e8 + 1.00095e8i −0.989222 + 0.768051i
\(508\) 1.15357e8 0.879938
\(509\) 3.61400e7 9.68369e6i 0.274053 0.0734324i −0.119175 0.992873i \(-0.538025\pi\)
0.393228 + 0.919441i \(0.371358\pi\)
\(510\) 3.25470e6 5.63731e6i 0.0245358 0.0424973i
\(511\) −9.83493e6 + 5.67820e6i −0.0737069 + 0.0425547i
\(512\) −9.60608e7 9.60608e7i −0.715709 0.715709i
\(513\) 3.32241e7 1.23994e8i 0.246094 0.918434i
\(514\) 3.90702e7 + 1.04688e7i 0.287711 + 0.0770919i
\(515\) 2.98182e6 2.98182e6i 0.0218303 0.0218303i
\(516\) 6.73168e7 + 1.16596e8i 0.489976 + 0.848663i
\(517\) −7.64751e7 4.41529e7i −0.553412 0.319512i
\(518\) −3.88555e6 1.45011e7i −0.0279553 0.104330i
\(519\) 2.93439e8i 2.09901i
\(520\) −3.24603e7 6.36068e6i −0.230857 0.0452370i
\(521\) −2.05966e8 −1.45640 −0.728202 0.685363i \(-0.759644\pi\)
−0.728202 + 0.685363i \(0.759644\pi\)
\(522\) −2.29892e7 + 6.15994e6i −0.161626 + 0.0433077i
\(523\) −2.36020e7 + 4.08798e7i −0.164985 + 0.285762i −0.936650 0.350267i \(-0.886091\pi\)
0.771665 + 0.636029i \(0.219424\pi\)
\(524\) −1.33337e8 + 7.69823e7i −0.926740 + 0.535054i
\(525\) 6.26807e7 + 6.26807e7i 0.433168 + 0.433168i
\(526\) 9.18973e6 3.42965e7i 0.0631459 0.235664i
\(527\) −3.56307e6 954721.i −0.0243440 0.00652296i
\(528\) 3.20455e7 3.20455e7i 0.217703 0.217703i
\(529\) 1.37361e8 + 2.37916e8i 0.927890 + 1.60715i
\(530\) 1.14138e7 + 6.58976e6i 0.0766660 + 0.0442631i
\(531\) −4.06031e7 1.51533e8i −0.271191 1.01210i
\(532\) 1.36428e8i 0.906083i
\(533\) −4.46679e7 + 3.05551e6i −0.294995 + 0.0201791i
\(534\) 8.14367e7 0.534806
\(535\) −5.74861e7 + 1.54034e7i −0.375406 + 0.100590i
\(536\) 3.63998e7 6.30463e7i 0.236377 0.409416i
\(537\) −1.30422e8 + 7.52994e7i −0.842228 + 0.486260i
\(538\) −9.45756e6 9.45756e6i −0.0607340 0.0607340i
\(539\) −9.53475e6 + 3.55842e7i −0.0608896 + 0.227243i
\(540\) 2.84053e7 + 7.61119e6i 0.180393 + 0.0483360i
\(541\) 8.56938e7 8.56938e7i 0.541200 0.541200i −0.382681 0.923881i \(-0.624999\pi\)
0.923881 + 0.382681i \(0.124999\pi\)
\(542\) −4.26600e7 7.38894e7i −0.267931 0.464071i
\(543\) −1.73290e8 1.00049e8i −1.08236 0.624904i
\(544\) 1.09971e7 + 4.10417e7i 0.0683096 + 0.254935i
\(545\) 4.85069e7i 0.299650i
\(546\) −2.47683e7 + 2.84057e7i −0.152166 + 0.174513i
\(547\) 1.03787e8 0.634132 0.317066 0.948404i \(-0.397302\pi\)
0.317066 + 0.948404i \(0.397302\pi\)
\(548\) 1.48411e8 3.97666e7i 0.901828 0.241644i
\(549\) 4.17569e7 7.23251e7i 0.252355 0.437091i
\(550\) −1.38629e7 + 8.00376e6i −0.0833233 + 0.0481067i
\(551\) 1.90357e8 + 1.90357e8i 1.13792 + 1.13792i
\(552\) 5.62265e7 2.09840e8i 0.334290 1.24759i
\(553\) 8.28420e7 + 2.21974e7i 0.489863 + 0.131258i
\(554\) 1.16768e7 1.16768e7i 0.0686741 0.0686741i
\(555\) 2.41083e7 + 4.17568e7i 0.141022 + 0.244258i
\(556\) 1.87780e7 + 1.08415e7i 0.109251 + 0.0630760i
\(557\) −3.35268e7 1.25124e8i −0.194011 0.724058i −0.992521 0.122076i \(-0.961045\pi\)
0.798510 0.601982i \(-0.205622\pi\)
\(558\) 2.53590e6i 0.0145958i
\(559\) −1.44237e8 + 4.94204e7i −0.825734 + 0.282925i
\(560\) 2.72263e7 0.155033
\(561\) −2.36913e7 + 6.34807e6i −0.134184 + 0.0359545i
\(562\) −4.02937e7 + 6.97907e7i −0.227001 + 0.393178i
\(563\) −8.47000e7 + 4.89016e7i −0.474633 + 0.274030i −0.718177 0.695860i \(-0.755023\pi\)
0.243544 + 0.969890i \(0.421690\pi\)
\(564\) −2.59173e8 2.59173e8i −1.44462 1.44462i
\(565\) 2.51577e7 9.38898e7i 0.139484 0.520563i
\(566\) 7.78556e7 + 2.08614e7i 0.429379 + 0.115052i
\(567\) 9.22164e7 9.22164e7i 0.505894 0.505894i
\(568\) −5.12923e7 8.88409e7i −0.279903 0.484806i
\(569\) 2.49325e8 + 1.43948e8i 1.35341 + 0.781392i 0.988726 0.149739i \(-0.0478435\pi\)
0.364685 + 0.931131i \(0.381177\pi\)
\(570\) −1.31006e7 4.88922e7i −0.0707403 0.264007i
\(571\) 2.36093e8i 1.26816i 0.773267 + 0.634080i \(0.218621\pi\)
−0.773267 + 0.634080i \(0.781379\pi\)
\(572\) 3.28705e7 + 4.88921e7i 0.175638 + 0.261246i
\(573\) 2.48972e7 0.132339
\(574\) −9.98598e6 + 2.67574e6i −0.0528026 + 0.0141484i
\(575\) 1.36765e8 2.36883e8i 0.719400 1.24604i
\(576\) 4.05650e7 2.34202e7i 0.212268 0.122553i
\(577\) −9.29466e7 9.29466e7i −0.483845 0.483845i 0.422512 0.906357i \(-0.361148\pi\)
−0.906357 + 0.422512i \(0.861148\pi\)
\(578\) −1.44783e7 + 5.40339e7i −0.0749782 + 0.279823i
\(579\) −3.80588e7 1.01978e7i −0.196074 0.0525378i
\(580\) −4.36081e7 + 4.36081e7i −0.223503 + 0.223503i
\(581\) −3.57581e7 6.19348e7i −0.182325 0.315796i
\(582\) −2.64258e7 1.52570e7i −0.134048 0.0773925i
\(583\) −1.28529e7 4.79675e7i −0.0648626 0.242070i
\(584\) 1.80073e7i 0.0904086i
\(585\) 1.92910e7 3.94008e7i 0.0963579 0.196806i
\(586\) −4.87649e7 −0.242334
\(587\) 8.08230e7 2.16565e7i 0.399596 0.107071i −0.0534238 0.998572i \(-0.517013\pi\)
0.453020 + 0.891501i \(0.350347\pi\)
\(588\) −7.64538e7 + 1.32422e8i −0.376069 + 0.651370i
\(589\) −2.48408e7 + 1.43418e7i −0.121568 + 0.0701873i
\(590\) 3.32049e7 + 3.32049e7i 0.161676 + 0.161676i
\(591\) −9.84096e7 + 3.67270e8i −0.476733 + 1.77919i
\(592\) −8.19645e7 2.19623e7i −0.395058 0.105855i
\(593\) −2.03498e8 + 2.03498e8i −0.975879 + 0.975879i −0.999716 0.0238368i \(-0.992412\pi\)
0.0238368 + 0.999716i \(0.492412\pi\)
\(594\) 6.40003e6 + 1.10852e7i 0.0305367 + 0.0528912i
\(595\) −1.27610e7 7.36754e6i −0.0605804 0.0349761i
\(596\) −3.39779e7 1.26807e8i −0.160493 0.598970i
\(597\) 1.48333e8i 0.697133i
\(598\) 1.04446e8 + 5.11378e7i 0.488415 + 0.239132i
\(599\) 3.68580e7 0.171495 0.0857474 0.996317i \(-0.472672\pi\)
0.0857474 + 0.996317i \(0.472672\pi\)
\(600\) −1.35769e8 + 3.63792e7i −0.628560 + 0.168422i
\(601\) 7.48450e7 1.29635e8i 0.344778 0.597173i −0.640536 0.767929i \(-0.721288\pi\)
0.985313 + 0.170756i \(0.0546209\pi\)
\(602\) −3.04893e7 + 1.76030e7i −0.139752 + 0.0806858i
\(603\) 6.82726e7 + 6.82726e7i 0.311383 + 0.311383i
\(604\) 228896. 854253.i 0.00103879 0.00387682i
\(605\) 7.22852e7 + 1.93688e7i 0.326425 + 0.0874653i
\(606\) −4.98746e7 + 4.98746e7i −0.224110 + 0.224110i
\(607\) 6.21691e7 + 1.07680e8i 0.277977 + 0.481470i 0.970882 0.239559i \(-0.0770028\pi\)
−0.692905 + 0.721029i \(0.743669\pi\)
\(608\) 2.86132e8 + 1.65198e8i 1.27308 + 0.735013i
\(609\) 3.84733e7 + 1.43584e8i 0.170337 + 0.635705i
\(610\) 2.49984e7i 0.110134i
\(611\) 3.44468e8 2.31588e8i 1.51017 1.01530i
\(612\) −3.68968e7 −0.160966
\(613\) −3.52229e8 + 9.43795e7i −1.52913 + 0.409728i −0.922734 0.385436i \(-0.874051\pi\)
−0.606393 + 0.795165i \(0.707384\pi\)
\(614\) 4.94252e6 8.56070e6i 0.0213522 0.0369832i
\(615\) 2.87553e7 1.66019e7i 0.123621 0.0713727i
\(616\) 2.03498e7 + 2.03498e7i 0.0870600 + 0.0870600i
\(617\) −4.02260e7 + 1.50125e8i −0.171258 + 0.639144i 0.825901 + 0.563816i \(0.190667\pi\)
−0.997159 + 0.0753284i \(0.975999\pi\)
\(618\) 7.35887e6 + 1.97180e6i 0.0311778 + 0.00835407i
\(619\) −3.74477e7 + 3.74477e7i −0.157889 + 0.157889i −0.781631 0.623741i \(-0.785612\pi\)
0.623741 + 0.781631i \(0.285612\pi\)
\(620\) −3.28552e6 5.69069e6i −0.0137857 0.0238775i
\(621\) −1.89419e8 1.09361e8i −0.790948 0.456654i
\(622\) −3.49099e6 1.30286e7i −0.0145070 0.0541409i
\(623\) 1.84345e8i 0.762372i
\(624\) 6.90479e7 + 2.01521e8i 0.284182 + 0.829404i
\(625\) −1.40700e8 −0.576305
\(626\) 7.69745e7 2.06253e7i 0.313779 0.0840769i
\(627\) −9.53607e7 + 1.65170e8i −0.386871 + 0.670081i
\(628\) 1.56981e8 9.06329e7i 0.633822 0.365938i
\(629\) 3.24736e7 + 3.24736e7i 0.130490 + 0.130490i
\(630\) 2.62180e6 9.78471e6i 0.0104852 0.0391315i
\(631\) −8.23230e7 2.20584e7i −0.327667 0.0877981i 0.0912354 0.995829i \(-0.470918\pi\)
−0.418903 + 0.908031i \(0.637585\pi\)
\(632\) −9.61611e7 + 9.61611e7i −0.380933 + 0.380933i
\(633\) −4.80585e7 8.32397e7i −0.189478 0.328186i
\(634\) −6.82552e7 3.94071e7i −0.267835 0.154635i
\(635\) −2.50751e7 9.35816e7i −0.0979314 0.365485i
\(636\) 2.06120e8i 0.801213i
\(637\) −1.30516e8 1.13803e8i −0.504945 0.440286i
\(638\) −2.68435e7 −0.103366
\(639\) 1.31419e8 3.52136e7i 0.503682 0.134961i
\(640\) −4.92270e7 + 8.52636e7i −0.187786 + 0.325255i
\(641\) −6.50975e7 + 3.75841e7i −0.247167 + 0.142702i −0.618466 0.785811i \(-0.712246\pi\)
0.371299 + 0.928513i \(0.378912\pi\)
\(642\) −7.60284e7 7.60284e7i −0.287323 0.287323i
\(643\) −2.11559e7 + 7.89549e7i −0.0795791 + 0.296993i −0.994233 0.107246i \(-0.965797\pi\)
0.914653 + 0.404239i \(0.132464\pi\)
\(644\) −2.24534e8 6.01638e7i −0.840669 0.225257i
\(645\) 7.99543e7 7.99543e7i 0.297963 0.297963i
\(646\) −2.41054e7 4.17517e7i −0.0894162 0.154873i
\(647\) 3.30237e8 + 1.90663e8i 1.21931 + 0.703968i 0.964770 0.263095i \(-0.0847433\pi\)
0.254538 + 0.967063i \(0.418077\pi\)
\(648\) 5.35214e7 + 1.99745e8i 0.196699 + 0.734091i
\(649\) 1.76938e8i 0.647272i
\(650\) −5.13499e6 7.50675e7i −0.0186982 0.273346i
\(651\) −1.58385e7 −0.0574079
\(652\) 3.96322e8 1.06194e8i 1.42990 0.383140i
\(653\) 1.68195e8 2.91323e8i 0.604053 1.04625i −0.388148 0.921597i \(-0.626885\pi\)
0.992200 0.124653i \(-0.0397817\pi\)
\(654\) 7.58937e7 4.38172e7i 0.271314 0.156643i
\(655\) 9.14344e7 + 9.14344e7i 0.325376 + 0.325376i
\(656\) −1.51241e7 + 5.64438e7i −0.0535743 + 0.199942i
\(657\) 2.30688e7 + 6.18126e6i 0.0813445 + 0.0217962i
\(658\) 6.77725e7 6.77725e7i 0.237890 0.237890i
\(659\) −2.61457e8 4.52857e8i −0.913575 1.58236i −0.808974 0.587844i \(-0.799977\pi\)
−0.104601 0.994514i \(-0.533356\pi\)
\(660\) −3.78381e7 2.18459e7i −0.131613 0.0759866i
\(661\) 6.57527e7 + 2.45392e8i 0.227672 + 0.849683i 0.981316 + 0.192401i \(0.0616273\pi\)
−0.753645 + 0.657282i \(0.771706\pi\)
\(662\) 5.20965e7i 0.179570i
\(663\) 2.21695e7 1.13137e8i 0.0760704 0.388208i
\(664\) 1.13400e8 0.387354
\(665\) −1.10675e8 + 2.96553e7i −0.376344 + 0.100841i
\(666\) −1.57858e7 + 2.73418e7i −0.0534372 + 0.0925560i
\(667\) 3.97237e8 2.29345e8i 1.33866 0.772878i
\(668\) 2.14615e8 + 2.14615e8i 0.719997 + 0.719997i
\(669\) 6.35446e7 2.37152e8i 0.212227 0.792042i
\(670\) −2.79164e7 7.48018e6i −0.0928186 0.0248707i
\(671\) 6.66042e7 6.66042e7i 0.220462 0.220462i
\(672\) 9.12193e7 + 1.57996e8i 0.300593 + 0.520642i
\(673\) −3.64176e8 2.10257e8i −1.19472 0.689772i −0.235346 0.971912i \(-0.575622\pi\)
−0.959373 + 0.282140i \(0.908956\pi\)
\(674\) −3.71327e7 1.38581e8i −0.121277 0.452610i
\(675\) 1.41516e8i 0.460143i
\(676\) −2.74346e8 + 3.77097e7i −0.888094 + 0.122071i
\(677\) −1.62659e8 −0.524218 −0.262109 0.965038i \(-0.584418\pi\)
−0.262109 + 0.965038i \(0.584418\pi\)
\(678\) 1.69625e8 4.54509e7i 0.544253 0.145832i
\(679\) −3.45366e7 + 5.98191e7i −0.110324 + 0.191087i
\(680\) 2.02344e7 1.16824e7i 0.0643524 0.0371538i
\(681\) 1.72381e8 + 1.72381e8i 0.545818 + 0.545818i
\(682\) 740263. 2.76270e6i 0.00233364 0.00870925i
\(683\) −3.66101e8 9.80965e7i −1.14905 0.307887i −0.366466 0.930431i \(-0.619432\pi\)
−0.782585 + 0.622544i \(0.786099\pi\)
\(684\) −2.02875e8 + 2.02875e8i −0.633957 + 0.633957i
\(685\) −6.45201e7 1.11752e8i −0.200735 0.347684i
\(686\) −8.63152e7 4.98341e7i −0.267371 0.154367i
\(687\) 1.45964e8 + 5.44746e8i 0.450169 + 1.68006i
\(688\) 1.98995e8i 0.611050i
\(689\) 2.29068e8 + 4.48864e7i 0.700335 + 0.137233i
\(690\) −8.62445e7 −0.262533
\(691\) −4.82179e8 + 1.29199e8i −1.46142 + 0.391585i −0.899979 0.435934i \(-0.856418\pi\)
−0.561437 + 0.827519i \(0.689751\pi\)
\(692\) −2.48937e8 + 4.31172e8i −0.751227 + 1.30116i
\(693\) −3.30551e7 + 1.90844e7i −0.0993205 + 0.0573427i
\(694\) 2.48088e7 + 2.48088e7i 0.0742211 + 0.0742211i
\(695\) 4.71323e6 1.75900e7i 0.0140399 0.0523976i
\(696\) −2.27675e8 6.10053e7i −0.675285 0.180942i
\(697\) 2.23625e7 2.23625e7i 0.0660423 0.0660423i
\(698\) 1.00472e8 + 1.74022e8i 0.295445 + 0.511726i
\(699\) −2.81265e8 1.62388e8i −0.823538 0.475470i
\(700\) 3.89267e7 + 1.45276e8i 0.113489 + 0.423546i
\(701\) 2.54219e8i 0.737996i 0.929430 + 0.368998i \(0.120299\pi\)
−0.929430 + 0.368998i \(0.879701\pi\)
\(702\) −6.00261e7 + 4.10608e6i −0.173512 + 0.0118691i
\(703\) 3.57108e8 1.02786
\(704\) 5.10297e7 1.36734e7i 0.146253 0.0391884i
\(705\) −1.53914e8 + 2.66587e8i −0.439250 + 0.760803i
\(706\) 3.78122e7 2.18309e7i 0.107453 0.0620379i
\(707\) 1.12899e8 + 1.12899e8i 0.319472 + 0.319472i
\(708\) 1.90079e8 7.09383e8i 0.535591 1.99885i
\(709\) 3.25675e8 + 8.72644e7i 0.913789 + 0.244849i 0.684929 0.728610i \(-0.259833\pi\)
0.228860 + 0.973459i \(0.426500\pi\)
\(710\) −2.87975e7 + 2.87975e7i −0.0804598 + 0.0804598i
\(711\) −9.01813e7 1.56199e8i −0.250904 0.434579i
\(712\) 2.53145e8 + 1.46153e8i 0.701342 + 0.404920i
\(713\) 1.26493e7 + 4.72078e7i 0.0348978 + 0.130240i
\(714\) 2.66210e7i 0.0731358i
\(715\) 3.25180e7 3.72934e7i 0.0889622 0.102027i
\(716\) −2.55519e8 −0.696121
\(717\) 4.73356e8 1.26835e8i 1.28419 0.344098i
\(718\) −4.27498e7 + 7.40448e7i −0.115494 + 0.200042i
\(719\) 4.40096e8 2.54090e8i 1.18403 0.683598i 0.227083 0.973875i \(-0.427081\pi\)
0.956942 + 0.290278i \(0.0937476\pi\)
\(720\) −4.04869e7 4.04869e7i −0.108472 0.108472i
\(721\) 4.46349e6 1.66580e7i 0.0119088 0.0444444i
\(722\) −2.45123e8 6.56804e7i −0.651286 0.174512i
\(723\) −4.68011e7 + 4.68011e7i −0.123834 + 0.123834i
\(724\) −1.69752e8 2.94019e8i −0.447300 0.774747i
\(725\) −2.57017e8 1.48389e8i −0.674446 0.389392i
\(726\) 3.49924e7 + 1.30593e8i 0.0914458 + 0.341281i
\(727\) 3.97223e8i 1.03379i 0.856050 + 0.516893i \(0.172912\pi\)
−0.856050 + 0.516893i \(0.827088\pi\)
\(728\) −1.27972e8 + 4.38474e7i −0.331680 + 0.113645i
\(729\) −1.20352e7 −0.0310650
\(730\) −6.90524e6 + 1.85025e6i −0.0177505 + 0.00475623i
\(731\) 5.38487e7 9.32688e7i 0.137855 0.238772i
\(732\) 3.38581e8 1.95480e8i 0.863236 0.498390i
\(733\) −2.50473e8 2.50473e8i −0.635989 0.635989i 0.313575 0.949563i \(-0.398473\pi\)
−0.949563 + 0.313575i \(0.898473\pi\)
\(734\) −4.24044e7 + 1.58255e8i −0.107232 + 0.400194i
\(735\) 1.24044e8 + 3.32375e7i 0.312402 + 0.0837080i
\(736\) 3.98068e8 3.98068e8i 0.998443 0.998443i
\(737\) 5.44489e7 + 9.43083e7i 0.136015 + 0.235585i
\(738\) 1.88286e7 + 1.08707e7i 0.0468434 + 0.0270451i
\(739\) 1.84240e8 + 6.87591e8i 0.456509 + 1.70372i 0.683612 + 0.729845i \(0.260408\pi\)
−0.227103 + 0.973871i \(0.572925\pi\)
\(740\) 8.18086e7i 0.201885i
\(741\) −5.00180e8 7.43975e8i −1.22934 1.82854i
\(742\) 5.38993e7 0.131938
\(743\) −2.69928e8 + 7.23271e7i −0.658085 + 0.176333i −0.572382 0.819987i \(-0.693980\pi\)
−0.0857035 + 0.996321i \(0.527314\pi\)
\(744\) 1.25572e7 2.17497e7i 0.0304912 0.0528122i
\(745\) −9.54848e7 + 5.51282e7i −0.230922 + 0.133323i
\(746\) −4.65283e7 4.65283e7i −0.112073 0.112073i
\(747\) −3.89261e7 + 1.45274e8i −0.0933854 + 0.348519i
\(748\) −4.01968e7 1.07707e7i −0.0960476 0.0257359i
\(749\) −1.72103e8 + 1.72103e8i −0.409583 + 0.409583i
\(750\) 6.06705e7 + 1.05084e8i 0.143812 + 0.249089i
\(751\) −3.26160e8 1.88309e8i −0.770037 0.444581i 0.0628509 0.998023i \(-0.479981\pi\)
−0.832888 + 0.553442i \(0.813314\pi\)
\(752\) −1.40214e8 5.23284e8i −0.329713 1.23051i
\(753\) 5.37363e8i 1.25859i
\(754\) 5.54841e7 1.13323e8i 0.129436 0.264366i
\(755\) −742756. −0.00172586
\(756\) 1.16167e8 3.11269e7i 0.268855 0.0720394i
\(757\) −2.35032e7 + 4.07087e7i −0.0541800 + 0.0938425i −0.891843 0.452344i \(-0.850588\pi\)
0.837663 + 0.546187i \(0.183921\pi\)
\(758\) 8.36548e7 4.82981e7i 0.192080 0.110898i
\(759\) 2.29784e8 + 2.29784e8i 0.525527 + 0.525527i
\(760\) 4.70230e7 1.75492e8i 0.107120 0.399777i
\(761\) 1.73881e8 + 4.65914e7i 0.394548 + 0.105719i 0.450638 0.892707i \(-0.351197\pi\)
−0.0560900 + 0.998426i \(0.517863\pi\)
\(762\) 1.23767e8 1.23767e8i 0.279730 0.279730i
\(763\) −9.91873e7 1.71797e8i −0.223297