Properties

Label 13.7.f.a.6.2
Level 13
Weight 7
Character 13.6
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 6.2
Character \(\chi\) = 13.6
Dual form 13.7.f.a.11.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.74273 - 10.2360i) q^{2} +(-22.3986 + 38.7956i) q^{3} +(-41.8275 + 24.1491i) q^{4} +(-35.0169 + 35.0169i) q^{5} +(458.545 + 122.867i) q^{6} +(-112.597 + 420.218i) q^{7} +(-117.658 - 117.658i) q^{8} +(-638.899 - 1106.61i) q^{9} +O(q^{10})\) \(q+(-2.74273 - 10.2360i) q^{2} +(-22.3986 + 38.7956i) q^{3} +(-41.8275 + 24.1491i) q^{4} +(-35.0169 + 35.0169i) q^{5} +(458.545 + 122.867i) q^{6} +(-112.597 + 420.218i) q^{7} +(-117.658 - 117.658i) q^{8} +(-638.899 - 1106.61i) q^{9} +(454.475 + 262.391i) q^{10} +(-1837.55 + 492.370i) q^{11} -2163.63i q^{12} +(2158.38 - 410.139i) q^{13} +4610.17 q^{14} +(-574.171 - 2142.84i) q^{15} +(-2427.18 + 4204.01i) q^{16} +(2973.01 - 1716.47i) q^{17} +(-9574.89 + 9574.89i) q^{18} +(1319.54 + 353.570i) q^{19} +(619.043 - 2310.30i) q^{20} +(-13780.6 - 13780.6i) q^{21} +(10079.8 + 17458.7i) q^{22} +(4730.68 + 2731.26i) q^{23} +(7199.97 - 1929.23i) q^{24} +13172.6i q^{25} +(-10118.0 - 20968.3i) q^{26} +24584.7 q^{27} +(-5438.24 - 20295.8i) q^{28} +(6245.69 - 10817.9i) q^{29} +(-20359.3 + 11754.4i) q^{30} +(-39371.6 + 39371.6i) q^{31} +(39403.0 + 10558.0i) q^{32} +(22056.9 - 82317.3i) q^{33} +(-25723.9 - 25723.9i) q^{34} +(-10771.9 - 18657.5i) q^{35} +(53447.1 + 30857.7i) q^{36} +(-41656.4 + 11161.8i) q^{37} -14476.6i q^{38} +(-32433.2 + 92922.1i) q^{39} +8240.02 q^{40} +(9281.22 + 34638.0i) q^{41} +(-103262. + 178854. i) q^{42} +(80790.5 - 46644.4i) q^{43} +(64969.8 - 64969.8i) q^{44} +(61122.2 + 16377.6i) q^{45} +(14982.2 - 55914.4i) q^{46} +(31648.7 + 31648.7i) q^{47} +(-108731. - 188328. i) q^{48} +(-62018.0 - 35806.1i) q^{49} +(134835. - 36128.9i) q^{50} +153786. i q^{51} +(-80375.0 + 69278.0i) q^{52} -162774. q^{53} +(-67429.0 - 251649. i) q^{54} +(47104.1 - 81586.7i) q^{55} +(62689.7 - 36193.9i) q^{56} +(-43272.9 + 43272.9i) q^{57} +(-127862. - 34260.5i) q^{58} +(15131.0 - 56469.6i) q^{59} +(75763.7 + 75763.7i) q^{60} +(98176.5 + 170047. i) q^{61} +(510994. + 295022. i) q^{62} +(536954. - 143876. i) q^{63} -121607. i q^{64} +(-61218.0 + 89941.6i) q^{65} -903096. q^{66} +(-31145.1 - 116235. i) q^{67} +(-82902.4 + 143591. i) q^{68} +(-211922. + 122353. i) q^{69} +(-161434. + 161434. i) q^{70} +(47294.5 + 12672.5i) q^{71} +(-55029.2 + 205372. i) q^{72} +(18999.6 + 18999.6i) q^{73} +(228504. + 395781. i) q^{74} +(-511040. - 295049. i) q^{75} +(-63731.5 + 17076.8i) q^{76} -827611. i q^{77} +(1.04011e6 + 77125.7i) q^{78} -91032.3 q^{79} +(-62218.9 - 232204. i) q^{80} +(-84905.9 + 147061. i) q^{81} +(329099. - 190005. i) q^{82} +(240687. - 240687. i) q^{83} +(909196. + 243618. i) q^{84} +(-44000.3 + 164211. i) q^{85} +(-699039. - 699039. i) q^{86} +(279790. + 484611. i) q^{87} +(274133. + 158271. i) q^{88} +(-1.15977e6 + 310760. i) q^{89} -670566. i q^{90} +(-70679.2 + 953169. i) q^{91} -263830. q^{92} +(-645575. - 2.40932e6i) q^{93} +(237152. - 410760. i) q^{94} +(-58587.2 + 33825.4i) q^{95} +(-1.29218e6 + 1.29218e6i) q^{96} +(469423. + 125781. i) q^{97} +(-196413. + 733022. i) q^{98} +(1.71887e6 + 1.71887e6i) 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 \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74273 10.2360i −0.342841 1.27950i −0.895114 0.445837i \(-0.852906\pi\)
0.552273 0.833663i \(-0.313760\pi\)
\(3\) −22.3986 + 38.7956i −0.829580 + 1.43687i 0.0687888 + 0.997631i \(0.478087\pi\)
−0.898368 + 0.439243i \(0.855247\pi\)
\(4\) −41.8275 + 24.1491i −0.653555 + 0.377330i
\(5\) −35.0169 + 35.0169i −0.280136 + 0.280136i −0.833163 0.553027i \(-0.813472\pi\)
0.553027 + 0.833163i \(0.313472\pi\)
\(6\) 458.545 + 122.867i 2.12289 + 0.568828i
\(7\) −112.597 + 420.218i −0.328271 + 1.22513i 0.582711 + 0.812679i \(0.301992\pi\)
−0.910982 + 0.412446i \(0.864675\pi\)
\(8\) −117.658 117.658i −0.229800 0.229800i
\(9\) −638.899 1106.61i −0.876405 1.51798i
\(10\) 454.475 + 262.391i 0.454475 + 0.262391i
\(11\) −1837.55 + 492.370i −1.38058 + 0.369925i −0.871331 0.490695i \(-0.836743\pi\)
−0.509248 + 0.860620i \(0.670076\pi\)
\(12\) 2163.63i 1.25210i
\(13\) 2158.38 410.139i 0.982421 0.186681i
\(14\) 4610.17 1.68009
\(15\) −574.171 2142.84i −0.170125 0.634914i
\(16\) −2427.18 + 4204.01i −0.592574 + 1.02637i
\(17\) 2973.01 1716.47i 0.605132 0.349373i −0.165926 0.986138i \(-0.553061\pi\)
0.771058 + 0.636765i \(0.219728\pi\)
\(18\) −9574.89 + 9574.89i −1.64178 + 1.64178i
\(19\) 1319.54 + 353.570i 0.192381 + 0.0515483i 0.353723 0.935350i \(-0.384916\pi\)
−0.161342 + 0.986899i \(0.551582\pi\)
\(20\) 619.043 2310.30i 0.0773803 0.288787i
\(21\) −13780.6 13780.6i −1.48802 1.48802i
\(22\) 10079.8 + 17458.7i 0.946638 + 1.63963i
\(23\) 4730.68 + 2731.26i 0.388812 + 0.224481i 0.681645 0.731683i \(-0.261265\pi\)
−0.292833 + 0.956164i \(0.594598\pi\)
\(24\) 7199.97 1929.23i 0.520831 0.139556i
\(25\) 13172.6i 0.843048i
\(26\) −10118.0 20968.3i −0.575673 1.19300i
\(27\) 24584.7 1.24903
\(28\) −5438.24 20295.8i −0.247733 0.924553i
\(29\) 6245.69 10817.9i 0.256086 0.443555i −0.709104 0.705104i \(-0.750900\pi\)
0.965190 + 0.261550i \(0.0842335\pi\)
\(30\) −20359.3 + 11754.4i −0.754047 + 0.435349i
\(31\) −39371.6 + 39371.6i −1.32160 + 1.32160i −0.409111 + 0.912485i \(0.634161\pi\)
−0.912485 + 0.409111i \(0.865839\pi\)
\(32\) 39403.0 + 10558.0i 1.20248 + 0.322205i
\(33\) 22056.9 82317.3i 0.613764 2.29060i
\(34\) −25723.9 25723.9i −0.654487 0.654487i
\(35\) −10771.9 18657.5i −0.251241 0.435161i
\(36\) 53447.1 + 30857.7i 1.14556 + 0.661387i
\(37\) −41656.4 + 11161.8i −0.822388 + 0.220358i −0.645390 0.763853i \(-0.723305\pi\)
−0.176998 + 0.984211i \(0.556638\pi\)
\(38\) 14476.6i 0.263824i
\(39\) −32433.2 + 92922.1i −0.546758 + 1.56648i
\(40\) 8240.02 0.128750
\(41\) 9281.22 + 34638.0i 0.134665 + 0.502575i 0.999999 + 0.00138043i \(0.000439406\pi\)
−0.865334 + 0.501195i \(0.832894\pi\)
\(42\) −103262. + 178854.i −1.39377 + 2.41408i
\(43\) 80790.5 46644.4i 1.01614 0.586671i 0.103159 0.994665i \(-0.467105\pi\)
0.912985 + 0.407994i \(0.133772\pi\)
\(44\) 64969.8 64969.8i 0.762700 0.762700i
\(45\) 61122.2 + 16377.6i 0.670751 + 0.179727i
\(46\) 14982.2 55914.4i 0.153923 0.574447i
\(47\) 31648.7 + 31648.7i 0.304833 + 0.304833i 0.842901 0.538068i \(-0.180846\pi\)
−0.538068 + 0.842901i \(0.680846\pi\)
\(48\) −108731. 188328.i −0.983175 1.70291i
\(49\) −62018.0 35806.1i −0.527144 0.304347i
\(50\) 134835. 36128.9i 1.07868 0.289031i
\(51\) 153786.i 1.15933i
\(52\) −80375.0 + 69278.0i −0.571625 + 0.492703i
\(53\) −162774. −1.09334 −0.546672 0.837347i \(-0.684106\pi\)
−0.546672 + 0.837347i \(0.684106\pi\)
\(54\) −67429.0 251649.i −0.428219 1.59813i
\(55\) 47104.1 81586.7i 0.283120 0.490378i
\(56\) 62689.7 36193.9i 0.356970 0.206097i
\(57\) −43272.9 + 43272.9i −0.233664 + 0.233664i
\(58\) −127862. 34260.5i −0.655325 0.175594i
\(59\) 15131.0 56469.6i 0.0736735 0.274953i −0.919256 0.393661i \(-0.871208\pi\)
0.992929 + 0.118708i \(0.0378751\pi\)
\(60\) 75763.7 + 75763.7i 0.350758 + 0.350758i
\(61\) 98176.5 + 170047.i 0.432532 + 0.749167i 0.997091 0.0762257i \(-0.0242869\pi\)
−0.564559 + 0.825393i \(0.690954\pi\)
\(62\) 510994. + 295022.i 2.14408 + 1.23788i
\(63\) 536954. 143876.i 2.14741 0.575397i
\(64\) 121607.i 0.463896i
\(65\) −61218.0 + 89941.6i −0.222915 + 0.327507i
\(66\) −903096. −3.14125
\(67\) −31145.1 116235.i −0.103554 0.386468i 0.894623 0.446821i \(-0.147444\pi\)
−0.998177 + 0.0603532i \(0.980777\pi\)
\(68\) −82902.4 + 143591.i −0.263658 + 0.456669i
\(69\) −211922. + 122353.i −0.645102 + 0.372450i
\(70\) −161434. + 161434.i −0.470653 + 0.470653i
\(71\) 47294.5 + 12672.5i 0.132140 + 0.0354069i 0.324283 0.945960i \(-0.394877\pi\)
−0.192143 + 0.981367i \(0.561544\pi\)
\(72\) −55029.2 + 205372.i −0.147433 + 0.550229i
\(73\) 18999.6 + 18999.6i 0.0488400 + 0.0488400i 0.731105 0.682265i \(-0.239005\pi\)
−0.682265 + 0.731105i \(0.739005\pi\)
\(74\) 228504. + 395781.i 0.563896 + 0.976697i
\(75\) −511040. 295049.i −1.21135 0.699376i
\(76\) −63731.5 + 17076.8i −0.145182 + 0.0389015i
\(77\) 827611.i 1.81282i
\(78\) 1.04011e6 + 77125.7i 2.19176 + 0.162523i
\(79\) −91032.3 −0.184635 −0.0923175 0.995730i \(-0.529427\pi\)
−0.0923175 + 0.995730i \(0.529427\pi\)
\(80\) −62218.9 232204.i −0.121521 0.453523i
\(81\) −84905.9 + 147061.i −0.159765 + 0.276722i
\(82\) 329099. 190005.i 0.596877 0.344607i
\(83\) 240687. 240687.i 0.420939 0.420939i −0.464588 0.885527i \(-0.653798\pi\)
0.885527 + 0.464588i \(0.153798\pi\)
\(84\) 909196. + 243618.i 1.53398 + 0.411029i
\(85\) −44000.3 + 164211.i −0.0716471 + 0.267391i
\(86\) −699039. 699039.i −1.09902 1.09902i
\(87\) 279790. + 484611.i 0.424888 + 0.735928i
\(88\) 274133. + 158271.i 0.402266 + 0.232248i
\(89\) −1.15977e6 + 310760.i −1.64514 + 0.440813i −0.958246 0.285946i \(-0.907692\pi\)
−0.686892 + 0.726760i \(0.741025\pi\)
\(90\) 670566.i 0.919844i
\(91\) −70679.2 + 953169.i −0.0937924 + 1.26487i
\(92\) −263830. −0.338814
\(93\) −645575. 2.40932e6i −0.802598 2.99533i
\(94\) 237152. 410760.i 0.285525 0.494544i
\(95\) −58587.2 + 33825.4i −0.0683333 + 0.0394522i
\(96\) −1.29218e6 + 1.29218e6i −1.46052 + 1.46052i
\(97\) 469423. + 125781.i 0.514338 + 0.137817i 0.506646 0.862154i \(-0.330885\pi\)
0.00769174 + 0.999970i \(0.497552\pi\)
\(98\) −196413. + 733022.i −0.208685 + 0.778823i
\(99\) 1.71887e6 + 1.71887e6i 1.77148 + 1.77148i
\(100\) −318107. 550978.i −0.318107 0.550978i
\(101\) −783713. 452477.i −0.760664 0.439170i 0.0688700 0.997626i \(-0.478061\pi\)
−0.829534 + 0.558456i \(0.811394\pi\)
\(102\) 1.57416e6 421794.i 1.48336 0.397466i
\(103\) 765882.i 0.700890i 0.936583 + 0.350445i \(0.113970\pi\)
−0.936583 + 0.350445i \(0.886030\pi\)
\(104\) −302206. 205694.i −0.268660 0.182861i
\(105\) 965108. 0.833696
\(106\) 446444. + 1.66615e6i 0.374843 + 1.39893i
\(107\) −281545. + 487651.i −0.229825 + 0.398068i −0.957756 0.287582i \(-0.907149\pi\)
0.727931 + 0.685650i \(0.240482\pi\)
\(108\) −1.02831e6 + 593698.i −0.816310 + 0.471297i
\(109\) 744338. 744338.i 0.574766 0.574766i −0.358691 0.933456i \(-0.616777\pi\)
0.933456 + 0.358691i \(0.116777\pi\)
\(110\) −964315. 258387.i −0.724504 0.194130i
\(111\) 500018. 1.86609e6i 0.365609 1.36447i
\(112\) −1.49330e6 1.49330e6i −1.06290 1.06290i
\(113\) 1.27719e6 + 2.21215e6i 0.885154 + 1.53313i 0.845537 + 0.533917i \(0.179281\pi\)
0.0396172 + 0.999215i \(0.487386\pi\)
\(114\) 561627. + 324256.i 0.379082 + 0.218863i
\(115\) −261294. + 70013.6i −0.171805 + 0.0460351i
\(116\) 603312.i 0.386516i
\(117\) −1.83285e6 2.12644e6i −1.14438 1.32768i
\(118\) −619523. −0.377061
\(119\) 386539. + 1.44258e6i 0.229378 + 0.856051i
\(120\) −184565. + 319676.i −0.106809 + 0.184998i
\(121\) 1.59995e6 923730.i 0.903128 0.521421i
\(122\) 1.47133e6 1.47133e6i 0.810270 0.810270i
\(123\) −1.55169e6 415774.i −0.833853 0.223430i
\(124\) 696027. 2.59761e6i 0.365057 1.36241i
\(125\) −1.00840e6 1.00840e6i −0.516303 0.516303i
\(126\) −2.94543e6 5.10164e6i −1.47244 2.55034i
\(127\) 1.97165e6 + 1.13833e6i 0.962541 + 0.555724i 0.896954 0.442123i \(-0.145775\pi\)
0.0655872 + 0.997847i \(0.479108\pi\)
\(128\) 1.27702e6 342176.i 0.608930 0.163162i
\(129\) 4.17909e6i 1.94676i
\(130\) 1.08855e6 + 379942.i 0.495469 + 0.172937i
\(131\) 480340. 0.213666 0.106833 0.994277i \(-0.465929\pi\)
0.106833 + 0.994277i \(0.465929\pi\)
\(132\) 1.06531e6 + 3.97578e6i 0.463183 + 1.72862i
\(133\) −297153. + 514684.i −0.126306 + 0.218769i
\(134\) −1.10436e6 + 637603.i −0.458983 + 0.264994i
\(135\) −860880. + 860880.i −0.349898 + 0.349898i
\(136\) −551753. 147842.i −0.219345 0.0587734i
\(137\) −284731. + 1.06263e6i −0.110732 + 0.413258i −0.998932 0.0461990i \(-0.985289\pi\)
0.888200 + 0.459457i \(0.151956\pi\)
\(138\) 1.83365e6 + 1.83365e6i 0.697717 + 0.697717i
\(139\) −1.74244e6 3.01799e6i −0.648803 1.12376i −0.983409 0.181401i \(-0.941937\pi\)
0.334607 0.942358i \(-0.391397\pi\)
\(140\) 901127. + 520266.i 0.328399 + 0.189601i
\(141\) −1.93672e6 + 518942.i −0.690891 + 0.185124i
\(142\) 518864.i 0.181213i
\(143\) −3.76419e6 + 1.81637e6i −1.28725 + 0.621150i
\(144\) 6.20290e6 2.07734
\(145\) 160103. + 597513.i 0.0525165 + 0.195994i
\(146\) 142369. 246590.i 0.0457464 0.0792351i
\(147\) 2.77824e6 1.60402e6i 0.874616 0.504960i
\(148\) 1.47284e6 1.47284e6i 0.454328 0.454328i
\(149\) 177890. + 47665.4i 0.0537764 + 0.0144093i 0.285607 0.958347i \(-0.407805\pi\)
−0.231831 + 0.972756i \(0.574471\pi\)
\(150\) −1.61848e6 + 6.04024e6i −0.479549 + 1.78970i
\(151\) −506362. 506362.i −0.147072 0.147072i 0.629737 0.776809i \(-0.283163\pi\)
−0.776809 + 0.629737i \(0.783163\pi\)
\(152\) −113654. 196854.i −0.0323633 0.0560550i
\(153\) −3.79891e6 2.19330e6i −1.06068 0.612384i
\(154\) −8.47143e6 + 2.26991e6i −2.31950 + 0.621508i
\(155\) 2.75735e6i 0.740452i
\(156\) −887389. 4.66993e6i −0.233744 1.23009i
\(157\) 4.96205e6 1.28222 0.641109 0.767450i \(-0.278475\pi\)
0.641109 + 0.767450i \(0.278475\pi\)
\(158\) 249677. + 931806.i 0.0633004 + 0.236240i
\(159\) 3.64592e6 6.31491e6i 0.907016 1.57100i
\(160\) −1.74948e6 + 1.01006e6i −0.427120 + 0.246598i
\(161\) −1.68039e6 + 1.68039e6i −0.402653 + 0.402653i
\(162\) 1.73819e6 + 465747.i 0.408840 + 0.109548i
\(163\) −319624. + 1.19285e6i −0.0738035 + 0.275438i −0.992959 0.118456i \(-0.962206\pi\)
0.919156 + 0.393894i \(0.128872\pi\)
\(164\) −1.22469e6 1.22469e6i −0.277648 0.277648i
\(165\) 2.11014e6 + 3.65486e6i 0.469741 + 0.813616i
\(166\) −3.12381e6 1.80353e6i −0.682906 0.394276i
\(167\) 5.05372e6 1.35414e6i 1.08508 0.290746i 0.328405 0.944537i \(-0.393489\pi\)
0.756675 + 0.653791i \(0.226822\pi\)
\(168\) 3.24278e6i 0.683895i
\(169\) 4.49038e6 1.77047e6i 0.930300 0.366799i
\(170\) 1.80155e6 0.366690
\(171\) −451791. 1.68611e6i −0.0903544 0.337207i
\(172\) −2.25284e6 + 3.90204e6i −0.442737 + 0.766843i
\(173\) 3.33895e6 1.92775e6i 0.644870 0.372316i −0.141618 0.989921i \(-0.545231\pi\)
0.786488 + 0.617606i \(0.211897\pi\)
\(174\) 4.19309e6 4.19309e6i 0.795951 0.795951i
\(175\) −5.53537e6 1.48320e6i −1.03284 0.276748i
\(176\) 2.39015e6 8.92015e6i 0.438416 1.63619i
\(177\) 1.85186e6 + 1.85186e6i 0.333955 + 0.333955i
\(178\) 6.36187e6 + 1.10191e7i 1.12804 + 1.95382i
\(179\) −6.89365e6 3.98005e6i −1.20196 0.693952i −0.240969 0.970533i \(-0.577465\pi\)
−0.960991 + 0.276581i \(0.910799\pi\)
\(180\) −2.95210e6 + 791012.i −0.506189 + 0.135633i
\(181\) 3.85125e6i 0.649480i −0.945803 0.324740i \(-0.894723\pi\)
0.945803 0.324740i \(-0.105277\pi\)
\(182\) 9.95050e6 1.89081e6i 1.65056 0.313642i
\(183\) −8.79609e6 −1.43528
\(184\) −235247. 877954.i −0.0377634 0.140935i
\(185\) 1.06783e6 1.84953e6i 0.168650 0.292110i
\(186\) −2.28911e7 + 1.32162e7i −3.55737 + 2.05385i
\(187\) −4.61792e6 + 4.61792e6i −0.706190 + 0.706190i
\(188\) −2.08808e6 559498.i −0.314248 0.0842025i
\(189\) −2.76816e6 + 1.03309e7i −0.410021 + 1.53022i
\(190\) 506925. + 506925.i 0.0739066 + 0.0739066i
\(191\) 3.72332e6 + 6.44898e6i 0.534355 + 0.925531i 0.999194 + 0.0401354i \(0.0127789\pi\)
−0.464839 + 0.885395i \(0.653888\pi\)
\(192\) 4.71783e6 + 2.72384e6i 0.666559 + 0.384838i
\(193\) −2.45144e6 + 656860.i −0.340996 + 0.0913695i −0.425253 0.905075i \(-0.639815\pi\)
0.0842574 + 0.996444i \(0.473148\pi\)
\(194\) 5.14999e6i 0.705345i
\(195\) −2.11814e6 4.38956e6i −0.285661 0.591994i
\(196\) 3.45874e6 0.459357
\(197\) 3.17394e6 + 1.18453e7i 0.415145 + 1.54934i 0.784545 + 0.620072i \(0.212896\pi\)
−0.369400 + 0.929270i \(0.620437\pi\)
\(198\) 1.28799e7 2.23087e7i 1.65928 2.87395i
\(199\) 9.99408e6 5.77009e6i 1.26819 0.732189i 0.293543 0.955946i \(-0.405166\pi\)
0.974645 + 0.223757i \(0.0718322\pi\)
\(200\) 1.54986e6 1.54986e6i 0.193732 0.193732i
\(201\) 5.20702e6 + 1.39522e6i 0.641212 + 0.171812i
\(202\) −2.48204e6 + 9.26311e6i −0.301131 + 1.12383i
\(203\) 3.84261e6 + 3.84261e6i 0.459344 + 0.459344i
\(204\) −3.71381e6 6.43250e6i −0.437450 0.757686i
\(205\) −1.53792e6 887917.i −0.178514 0.103065i
\(206\) 7.83956e6 2.10060e6i 0.896789 0.240294i
\(207\) 6.98000e6i 0.786945i
\(208\) −3.51455e6 + 1.00693e7i −0.390553 + 1.11895i
\(209\) −2.59881e6 −0.284666
\(210\) −2.64703e6 9.87884e6i −0.285825 1.06671i
\(211\) −9.00955e6 + 1.56050e7i −0.959082 + 1.66118i −0.234345 + 0.972153i \(0.575295\pi\)
−0.724737 + 0.689026i \(0.758039\pi\)
\(212\) 6.80842e6 3.93085e6i 0.714561 0.412552i
\(213\) −1.55097e6 + 1.55097e6i −0.160496 + 0.160496i
\(214\) 5.76379e6 + 1.54440e6i 0.588121 + 0.157587i
\(215\) −1.19569e6 + 4.46238e6i −0.120311 + 0.449005i
\(216\) −2.89257e6 2.89257e6i −0.287027 0.287027i
\(217\) −1.21115e7 2.09778e7i −1.18528 2.05296i
\(218\) −9.66056e6 5.57753e6i −0.932466 0.538359i
\(219\) −1.16267e6 + 311535.i −0.110694 + 0.0296603i
\(220\) 4.55009e6i 0.427319i
\(221\) 5.71289e6 4.92414e6i 0.529272 0.456198i
\(222\) −2.04728e7 −1.87119
\(223\) −3.89432e6 1.45338e7i −0.351170 1.31058i −0.885237 0.465141i \(-0.846004\pi\)
0.534067 0.845442i \(-0.320663\pi\)
\(224\) −8.87333e6 + 1.53691e7i −0.789482 + 1.36742i
\(225\) 1.45769e7 8.41598e6i 1.27973 0.738851i
\(226\) 1.91406e7 1.91406e7i 1.65818 1.65818i
\(227\) −1.59344e7 4.26961e6i −1.36225 0.365015i −0.497610 0.867401i \(-0.665789\pi\)
−0.864643 + 0.502386i \(0.832455\pi\)
\(228\) 764995. 2.85500e6i 0.0645437 0.240880i
\(229\) 1.18424e7 + 1.18424e7i 0.986129 + 0.986129i 0.999905 0.0137758i \(-0.00438511\pi\)
−0.0137758 + 0.999905i \(0.504385\pi\)
\(230\) 1.43332e6 + 2.48258e6i 0.117804 + 0.204042i
\(231\) 3.21077e7 + 1.85374e7i 2.60479 + 1.50388i
\(232\) −2.00766e6 + 537950.i −0.160778 + 0.0430802i
\(233\) 7.43970e6i 0.588149i 0.955782 + 0.294075i \(0.0950114\pi\)
−0.955782 + 0.294075i \(0.904989\pi\)
\(234\) −1.67392e7 + 2.45933e7i −1.30643 + 1.91941i
\(235\) −2.21648e6 −0.170789
\(236\) 730800. + 2.72738e6i 0.0555984 + 0.207496i
\(237\) 2.03900e6 3.53165e6i 0.153169 0.265297i
\(238\) 1.37061e7 7.91322e6i 1.01668 0.586979i
\(239\) −6.12730e6 + 6.12730e6i −0.448823 + 0.448823i −0.894963 0.446140i \(-0.852798\pi\)
0.446140 + 0.894963i \(0.352798\pi\)
\(240\) 1.04021e7 + 2.78724e6i 0.752467 + 0.201623i
\(241\) 2.04649e6 7.63762e6i 0.146204 0.545641i −0.853495 0.521101i \(-0.825521\pi\)
0.999699 0.0245395i \(-0.00781195\pi\)
\(242\) −1.38435e7 1.38435e7i −0.976788 0.976788i
\(243\) 5.15756e6 + 8.93315e6i 0.359439 + 0.622566i
\(244\) −8.21296e6 4.74175e6i −0.565366 0.326414i
\(245\) 3.42550e6 917860.i 0.232930 0.0624134i
\(246\) 1.70234e7i 1.14352i
\(247\) 2.99308e6 + 221942.i 0.198622 + 0.0147282i
\(248\) 9.26475e6 0.607405
\(249\) 3.94654e6 + 1.47287e7i 0.255634 + 0.954038i
\(250\) −7.55625e6 + 1.30878e7i −0.483600 + 0.837620i
\(251\) −2.56187e7 + 1.47909e7i −1.62008 + 0.935351i −0.633178 + 0.774006i \(0.718250\pi\)
−0.986898 + 0.161345i \(0.948417\pi\)
\(252\) −1.89849e7 + 1.89849e7i −1.18634 + 1.18634i
\(253\) −1.00377e7 2.68958e6i −0.619827 0.166082i
\(254\) 6.24428e6 2.33040e7i 0.381050 1.42210i
\(255\) −5.38513e6 5.38513e6i −0.324770 0.324770i
\(256\) −1.08965e7 1.88732e7i −0.649480 1.12493i
\(257\) 9.33621e6 + 5.39026e6i 0.550011 + 0.317549i 0.749126 0.662427i \(-0.230474\pi\)
−0.199116 + 0.979976i \(0.563807\pi\)
\(258\) 4.27772e7 1.14621e7i 2.49088 0.667429i
\(259\) 1.87616e7i 1.07986i
\(260\) 388584. 5.24039e6i 0.0221088 0.298156i
\(261\) −1.59615e7 −0.897741
\(262\) −1.31744e6 4.91676e6i −0.0732533 0.273385i
\(263\) −6.80533e6 + 1.17872e7i −0.374095 + 0.647952i −0.990191 0.139719i \(-0.955380\pi\)
0.616096 + 0.787671i \(0.288713\pi\)
\(264\) −1.22804e7 + 7.09010e6i −0.667423 + 0.385337i
\(265\) 5.69984e6 5.69984e6i 0.306285 0.306285i
\(266\) 6.08331e6 + 1.63002e6i 0.323218 + 0.0866060i
\(267\) 1.39212e7 5.19546e7i 0.731379 2.72954i
\(268\) 4.10970e6 + 4.10970e6i 0.213504 + 0.213504i
\(269\) 4.72355e6 + 8.18142e6i 0.242667 + 0.420312i 0.961473 0.274899i \(-0.0886443\pi\)
−0.718806 + 0.695211i \(0.755311\pi\)
\(270\) 1.11731e7 + 6.45080e6i 0.567653 + 0.327735i
\(271\) −4.86135e6 + 1.30259e6i −0.244258 + 0.0654487i −0.378871 0.925450i \(-0.623688\pi\)
0.134613 + 0.990898i \(0.457021\pi\)
\(272\) 1.66647e7i 0.828118i
\(273\) −3.53957e7 2.40917e7i −1.73965 1.18408i
\(274\) 1.16580e7 0.566726
\(275\) −6.48581e6 2.42054e7i −0.311865 1.16389i
\(276\) 5.90944e6 1.02354e7i 0.281073 0.486832i
\(277\) −470330. + 271545.i −0.0221291 + 0.0127762i −0.511024 0.859567i \(-0.670734\pi\)
0.488895 + 0.872343i \(0.337400\pi\)
\(278\) −2.61131e7 + 2.61131e7i −1.21541 + 1.21541i
\(279\) 6.87234e7 + 1.84144e7i 3.16440 + 0.847900i
\(280\) −927802. + 3.46260e6i −0.0422650 + 0.157735i
\(281\) −5.98773e6 5.98773e6i −0.269863 0.269863i 0.559182 0.829045i \(-0.311115\pi\)
−0.829045 + 0.559182i \(0.811115\pi\)
\(282\) 1.06238e7 + 1.84009e7i 0.473731 + 0.820527i
\(283\) −4.18888e6 2.41845e6i −0.184816 0.106703i 0.404738 0.914433i \(-0.367363\pi\)
−0.589553 + 0.807730i \(0.700696\pi\)
\(284\) −2.28424e6 + 612061.i −0.0997211 + 0.0267202i
\(285\) 3.03057e6i 0.130915i
\(286\) 2.89165e7 + 3.35484e7i 1.23608 + 1.43408i
\(287\) −1.56005e7 −0.659924
\(288\) −1.34910e7 5.03491e7i −0.564763 2.10773i
\(289\) −6.17625e6 + 1.06976e7i −0.255877 + 0.443192i
\(290\) 5.67703e6 3.27763e6i 0.232770 0.134390i
\(291\) −1.53942e7 + 1.53942e7i −0.624709 + 0.624709i
\(292\) −1.25353e6 335882.i −0.0503484 0.0134908i
\(293\) 87568.3 326809.i 0.00348132 0.0129925i −0.964163 0.265309i \(-0.914526\pi\)
0.967645 + 0.252317i \(0.0811926\pi\)
\(294\) −2.40387e7 2.40387e7i −0.945950 0.945950i
\(295\) 1.44755e6 + 2.50723e6i 0.0563856 + 0.0976627i
\(296\) 6.21446e6 + 3.58792e6i 0.239623 + 0.138346i
\(297\) −4.51756e7 + 1.21048e7i −1.72438 + 0.462048i
\(298\) 1.95161e6i 0.0737470i
\(299\) 1.13308e7 + 3.95485e6i 0.423884 + 0.147951i
\(300\) 2.85007e7 1.05558
\(301\) 1.05041e7 + 3.92017e7i 0.385174 + 1.43749i
\(302\) −3.79431e6 + 6.57193e6i −0.137756 + 0.238601i
\(303\) 3.51082e7 2.02697e7i 1.26206 0.728652i
\(304\) −4.68918e6 + 4.68918e6i −0.166908 + 0.166908i
\(305\) −9.39236e6 2.51667e6i −0.331036 0.0887008i
\(306\) −1.20313e7 + 4.49013e7i −0.419901 + 1.56709i
\(307\) −3.39944e6 3.39944e6i −0.117488 0.117488i 0.645919 0.763406i \(-0.276475\pi\)
−0.763406 + 0.645919i \(0.776475\pi\)
\(308\) 1.99861e7 + 3.46169e7i 0.684030 + 1.18478i
\(309\) −2.97128e7 1.71547e7i −1.00709 0.581444i
\(310\) −2.82242e7 + 7.56266e6i −0.947408 + 0.253857i
\(311\) 3.40131e7i 1.13075i −0.824836 0.565373i \(-0.808732\pi\)
0.824836 0.565373i \(-0.191268\pi\)
\(312\) 1.47490e7 7.11699e6i 0.485623 0.234332i
\(313\) 4.48299e7 1.46196 0.730979 0.682400i \(-0.239064\pi\)
0.730979 + 0.682400i \(0.239064\pi\)
\(314\) −1.36095e7 5.07915e7i −0.439597 1.64060i
\(315\) −1.37644e7 + 2.38406e7i −0.440377 + 0.762755i
\(316\) 3.80765e6 2.19835e6i 0.120669 0.0696683i
\(317\) 9.35503e6 9.35503e6i 0.293675 0.293675i −0.544855 0.838530i \(-0.683415\pi\)
0.838530 + 0.544855i \(0.183415\pi\)
\(318\) −7.46392e7 1.99995e7i −2.32105 0.621925i
\(319\) −6.15039e6 + 2.29536e7i −0.189466 + 0.707095i
\(320\) 4.25832e6 + 4.25832e6i 0.129954 + 0.129954i
\(321\) −1.26125e7 2.18454e7i −0.381316 0.660458i
\(322\) 2.18093e7 + 1.25916e7i 0.653241 + 0.377149i
\(323\) 4.52990e6 1.21378e6i 0.134425 0.0360192i
\(324\) 8.20161e6i 0.241137i
\(325\) 5.40261e6 + 2.84315e7i 0.157381 + 0.828228i
\(326\) 1.30867e7 0.377726
\(327\) 1.22049e7 + 4.55492e7i 0.349052 + 1.30268i
\(328\) 2.98342e6 5.16743e6i 0.0845459 0.146438i
\(329\) −1.68629e7 + 9.73581e6i −0.473527 + 0.273391i
\(330\) 3.16236e7 3.16236e7i 0.879975 0.879975i
\(331\) 6.54407e7 + 1.75348e7i 1.80453 + 0.483522i 0.994671 0.103102i \(-0.0328767\pi\)
0.809859 + 0.586624i \(0.199543\pi\)
\(332\) −4.25496e6 + 1.58797e7i −0.116274 + 0.433939i
\(333\) 3.89659e7 + 3.89659e7i 1.05524 + 1.05524i
\(334\) −2.77220e7 4.80158e7i −0.744020 1.28868i
\(335\) 5.16081e6 + 2.97959e6i 0.137272 + 0.0792543i
\(336\) 9.13817e7 2.44856e7i 2.40902 0.645496i
\(337\) 5.67785e7i 1.48352i −0.670663 0.741762i \(-0.733990\pi\)
0.670663 0.741762i \(-0.266010\pi\)
\(338\) −3.04384e7 4.11076e7i −0.788265 1.06457i
\(339\) −1.14429e8 −2.93722
\(340\) −2.12514e6 7.93112e6i −0.0540692 0.201789i
\(341\) 5.29620e7 9.17328e7i 1.33568 2.31346i
\(342\) −1.60199e7 + 9.24907e6i −0.400479 + 0.231217i
\(343\) −1.41619e7 + 1.41619e7i −0.350945 + 0.350945i
\(344\) −1.49937e7 4.01755e6i −0.368327 0.0986929i
\(345\) 3.13642e6 1.17053e7i 0.0763795 0.285052i
\(346\) −2.88902e7 2.88902e7i −0.697466 0.697466i
\(347\) 2.88325e7 + 4.99393e7i 0.690071 + 1.19524i 0.971814 + 0.235748i \(0.0757539\pi\)
−0.281744 + 0.959490i \(0.590913\pi\)
\(348\) −2.34058e7 1.35134e7i −0.555375 0.320646i
\(349\) −1.91080e7 + 5.11998e6i −0.449510 + 0.120446i −0.476470 0.879191i \(-0.658084\pi\)
0.0269602 + 0.999637i \(0.491417\pi\)
\(350\) 6.07281e7i 1.41640i
\(351\) 5.30630e7 1.00831e7i 1.22707 0.233171i
\(352\) −7.76035e7 −1.77932
\(353\) 1.34885e7 + 5.03397e7i 0.306647 + 1.14442i 0.931518 + 0.363694i \(0.118485\pi\)
−0.624872 + 0.780728i \(0.714849\pi\)
\(354\) 1.38765e7 2.40348e7i 0.312802 0.541789i
\(355\) −2.09986e6 + 1.21236e6i −0.0469360 + 0.0270985i
\(356\) 4.10057e7 4.10057e7i 0.908855 0.908855i
\(357\) −6.46238e7 1.73159e7i −1.42033 0.380575i
\(358\) −2.18324e7 + 8.14796e7i −0.475830 + 1.77582i
\(359\) 3.32982e7 + 3.32982e7i 0.719677 + 0.719677i 0.968539 0.248862i \(-0.0800566\pi\)
−0.248862 + 0.968539i \(0.580057\pi\)
\(360\) −5.26454e6 9.11845e6i −0.112837 0.195440i
\(361\) −3.91268e7 2.25898e7i −0.831672 0.480166i
\(362\) −3.94214e7 + 1.05629e7i −0.831009 + 0.222668i
\(363\) 8.27612e7i 1.73024i
\(364\) −2.00619e7 4.15755e7i −0.415975 0.862052i
\(365\) −1.33061e6 −0.0273636
\(366\) 2.41253e7 + 9.00367e7i 0.492072 + 1.83644i
\(367\) −7.64573e6 + 1.32428e7i −0.154675 + 0.267905i −0.932941 0.360030i \(-0.882766\pi\)
0.778266 + 0.627935i \(0.216100\pi\)
\(368\) −2.29645e7 + 1.32585e7i −0.460800 + 0.266043i
\(369\) 3.24008e7 3.24008e7i 0.644877 0.644877i
\(370\) −2.18606e7 5.85752e6i −0.431575 0.115640i
\(371\) 1.83279e7 6.84005e7i 0.358914 1.33948i
\(372\) 8.51857e7 + 8.51857e7i 1.65477 + 1.65477i
\(373\) −2.38613e7 4.13291e7i −0.459799 0.796396i 0.539151 0.842209i \(-0.318745\pi\)
−0.998950 + 0.0458134i \(0.985412\pi\)
\(374\) 5.99347e7 + 3.46033e7i 1.14568 + 0.661459i
\(375\) 6.17086e7 1.65348e7i 1.17018 0.313548i
\(376\) 7.44742e6i 0.140101i
\(377\) 9.04374e6 2.59106e7i 0.168781 0.483564i
\(378\) 1.13340e8 2.09849
\(379\) −1.63755e6 6.11142e6i −0.0300800 0.112260i 0.949254 0.314512i \(-0.101841\pi\)
−0.979334 + 0.202252i \(0.935174\pi\)
\(380\) 1.63371e6 2.82966e6i 0.0297730 0.0515684i
\(381\) −8.83248e7 + 5.09943e7i −1.59701 + 0.922034i
\(382\) 5.57997e7 5.57997e7i 1.00102 1.00102i
\(383\) −2.14519e7 5.74801e6i −0.381829 0.102311i 0.0627990 0.998026i \(-0.479997\pi\)
−0.444628 + 0.895716i \(0.646664\pi\)
\(384\) −1.53286e7 + 5.72070e7i −0.270712 + 1.01031i
\(385\) 2.89804e7 + 2.89804e7i 0.507835 + 0.507835i
\(386\) 1.34472e7 + 2.32913e7i 0.233815 + 0.404979i
\(387\) −1.03234e8 5.96022e7i −1.78111 1.02832i
\(388\) −2.26723e7 + 6.07502e6i −0.388150 + 0.104005i
\(389\) 1.23645e7i 0.210052i −0.994469 0.105026i \(-0.966507\pi\)
0.994469 0.105026i \(-0.0334926\pi\)
\(390\) −3.91220e7 + 3.37206e7i −0.659520 + 0.568462i
\(391\) 1.87525e7 0.313710
\(392\) 3.08403e6 + 1.15097e7i 0.0511988 + 0.191077i
\(393\) −1.07590e7 + 1.86351e7i −0.177253 + 0.307011i
\(394\) 1.12543e8 6.49769e7i 1.84005 1.06236i
\(395\) 3.18767e6 3.18767e6i 0.0517228 0.0517228i
\(396\) −1.13405e8 3.03868e7i −1.82620 0.489327i
\(397\) 4.15671e6 1.55130e7i 0.0664321 0.247928i −0.924722 0.380643i \(-0.875703\pi\)
0.991154 + 0.132715i \(0.0423694\pi\)
\(398\) −8.64736e7 8.64736e7i −1.37162 1.37162i
\(399\) −1.33116e7 2.30565e7i −0.209562 0.362973i
\(400\) −5.53778e7 3.19724e7i −0.865278 0.499569i
\(401\) −7.96929e7 + 2.13537e7i −1.23591 + 0.331161i −0.816878 0.576811i \(-0.804297\pi\)
−0.419032 + 0.907972i \(0.637630\pi\)
\(402\) 5.71258e7i 0.879335i
\(403\) −6.88310e7 + 1.01127e8i −1.05165 + 1.54508i
\(404\) 4.37077e7 0.662847
\(405\) −2.17649e6 8.12278e6i −0.0327636 0.122276i
\(406\) 2.87937e7 4.98722e7i 0.430249 0.745213i
\(407\) 7.10500e7 4.10207e7i 1.05386 0.608444i
\(408\) 1.80941e7 1.80941e7i 0.266414 0.266414i
\(409\) 6.40200e7 + 1.71541e7i 0.935720 + 0.250725i 0.694292 0.719694i \(-0.255718\pi\)
0.241428 + 0.970419i \(0.422384\pi\)
\(410\) −4.87063e6 + 1.81774e7i −0.0706697 + 0.263743i
\(411\) −3.48478e7 3.48478e7i −0.501938 0.501938i
\(412\) −1.84954e7 3.20349e7i −0.264467 0.458070i
\(413\) 2.20258e7 + 1.27166e7i 0.312667 + 0.180518i
\(414\) −7.14472e7 + 1.91442e7i −1.00690 + 0.269797i
\(415\) 1.68563e7i 0.235840i
\(416\) 8.93768e7 + 6.62745e6i 1.24150 + 0.0920591i
\(417\) 1.56113e8 2.15293
\(418\) 7.12783e6 + 2.66014e7i 0.0975952 + 0.364230i
\(419\) 5.81531e6 1.00724e7i 0.0790553 0.136928i −0.823787 0.566899i \(-0.808143\pi\)
0.902843 + 0.429971i \(0.141476\pi\)
\(420\) −4.03680e7 + 2.33065e7i −0.544866 + 0.314579i
\(421\) −2.21342e7 + 2.21342e7i −0.296631 + 0.296631i −0.839693 0.543062i \(-0.817265\pi\)
0.543062 + 0.839693i \(0.317265\pi\)
\(422\) 1.84444e8 + 4.94215e7i 2.45429 + 0.657625i
\(423\) 1.48023e7 5.52430e7i 0.195573 0.729888i
\(424\) 1.91516e7 + 1.91516e7i 0.251251 + 0.251251i
\(425\) 2.26104e7 + 3.91624e7i 0.294538 + 0.510155i
\(426\) 2.01296e7 + 1.16219e7i 0.260380 + 0.150330i
\(427\) −8.25111e7 + 2.21088e7i −1.05981 + 0.283976i
\(428\) 2.71963e7i 0.346879i
\(429\) 1.38455e7 1.86718e8i 0.175362 2.36491i
\(430\) 4.89564e7 0.615750
\(431\) −2.81478e7 1.05049e8i −0.351571 1.31208i −0.884745 0.466076i \(-0.845667\pi\)
0.533174 0.846006i \(-0.320999\pi\)
\(432\) −5.96715e7 + 1.03354e8i −0.740143 + 1.28197i
\(433\) −1.07623e7 + 6.21361e6i −0.132569 + 0.0765385i −0.564818 0.825216i \(-0.691053\pi\)
0.432249 + 0.901754i \(0.357720\pi\)
\(434\) −1.81510e8 + 1.81510e8i −2.22040 + 2.22040i
\(435\) −2.67670e7 7.17219e6i −0.325186 0.0871333i
\(436\) −1.31587e7 + 4.91089e7i −0.158764 + 0.592517i
\(437\) 5.27664e6 + 5.27664e6i 0.0632285 + 0.0632285i
\(438\) 6.37775e6 + 1.10466e7i 0.0759006 + 0.131464i
\(439\) 1.21251e8 + 7.00045e7i 1.43315 + 0.827432i 0.997360 0.0726141i \(-0.0231342\pi\)
0.435794 + 0.900046i \(0.356467\pi\)
\(440\) −1.51414e7 + 4.05714e6i −0.177750 + 0.0476279i
\(441\) 9.15059e7i 1.06692i
\(442\) −6.60724e7 4.49716e7i −0.765162 0.520801i
\(443\) −5.57799e6 −0.0641603 −0.0320802 0.999485i \(-0.510213\pi\)
−0.0320802 + 0.999485i \(0.510213\pi\)
\(444\) 2.41500e7 + 9.01291e7i 0.275911 + 1.02971i
\(445\) 2.97298e7 5.14935e7i 0.337374 0.584349i
\(446\) −1.38087e8 + 7.97245e7i −1.55649 + 0.898643i
\(447\) −5.83369e6 + 5.83369e6i −0.0653162 + 0.0653162i
\(448\) 5.11016e7 + 1.36926e7i 0.568330 + 0.152284i
\(449\) −2.77229e7 + 1.03463e8i −0.306267 + 1.14300i 0.625583 + 0.780158i \(0.284861\pi\)
−0.931849 + 0.362845i \(0.881805\pi\)
\(450\) −1.26126e8 1.26126e8i −1.38410 1.38410i
\(451\) −3.41094e7 5.90793e7i −0.371830 0.644029i
\(452\) −1.06843e8 6.16858e7i −1.15699 0.667990i
\(453\) 3.09864e7 8.30279e6i 0.333332 0.0893160i
\(454\) 1.74815e8i 1.86814i
\(455\) −3.09021e7 3.58520e7i −0.328060 0.380610i
\(456\) 1.01828e7 0.107392
\(457\) 2.34105e7 + 8.73693e7i 0.245280 + 0.915399i 0.973242 + 0.229781i \(0.0738011\pi\)
−0.727962 + 0.685618i \(0.759532\pi\)
\(458\) 8.87384e7 1.53699e8i 0.923667 1.59984i
\(459\) 7.30905e7 4.21988e7i 0.755828 0.436377i
\(460\) 9.23852e6 9.23852e6i 0.0949137 0.0949137i
\(461\) −4.74836e7 1.27232e7i −0.484664 0.129865i 0.00820964 0.999966i \(-0.497387\pi\)
−0.492873 + 0.870101i \(0.664053\pi\)
\(462\) 1.01686e8 3.79497e8i 1.03118 3.84842i
\(463\) −3.72735e7 3.72735e7i −0.375541 0.375541i 0.493950 0.869490i \(-0.335553\pi\)
−0.869490 + 0.493950i \(0.835553\pi\)
\(464\) 3.03189e7 + 5.25139e7i 0.303500 + 0.525678i
\(465\) 1.06973e8 + 6.17609e7i 1.06394 + 0.614264i
\(466\) 7.61527e7 2.04051e7i 0.752537 0.201642i
\(467\) 1.88934e8i 1.85507i −0.373735 0.927535i \(-0.621923\pi\)
0.373735 0.927535i \(-0.378077\pi\)
\(468\) 1.28015e8 + 4.46818e7i 1.24889 + 0.435906i
\(469\) 5.23510e7 0.507465
\(470\) 6.07921e6 + 2.26879e7i 0.0585536 + 0.218525i
\(471\) −1.11143e8 + 1.92506e8i −1.06370 + 1.84239i
\(472\) −8.42436e6 + 4.86380e6i −0.0801144 + 0.0462541i
\(473\) −1.25490e8 + 1.25490e8i −1.18584 + 1.18584i
\(474\) −4.17424e7 1.11848e7i −0.391961 0.105026i
\(475\) −4.65745e6 + 1.73818e7i −0.0434577 + 0.162186i
\(476\) −5.10050e7 5.10050e7i −0.472925 0.472925i
\(477\) 1.03996e8 + 1.80126e8i 0.958212 + 1.65967i
\(478\) 7.95245e7 + 4.59135e7i 0.728144 + 0.420394i
\(479\) 1.61769e8 4.33459e7i 1.47194 0.394404i 0.568341 0.822793i \(-0.307585\pi\)
0.903594 + 0.428389i \(0.140919\pi\)
\(480\) 9.04963e7i 0.818289i
\(481\) −8.53324e7 + 4.11763e7i −0.766794 + 0.370009i
\(482\) −8.37916e7 −0.748272
\(483\) −2.75532e7 1.02830e8i −0.244529 0.912595i
\(484\) −4.46145e7 + 7.72746e7i −0.393496 + 0.681555i
\(485\) −2.08422e7 + 1.20333e7i −0.182692 + 0.105477i
\(486\) 7.72939e7 7.72939e7i 0.673343 0.673343i
\(487\) −1.33546e8 3.57835e7i −1.15623 0.309810i −0.370770 0.928725i \(-0.620906\pi\)
−0.785459 + 0.618914i \(0.787573\pi\)
\(488\) 8.45608e6 3.15585e7i 0.0727628 0.271554i
\(489\) −3.91183e7 3.91183e7i −0.334544 0.334544i
\(490\) −1.87904e7 3.25460e7i −0.159716 0.276636i
\(491\) 3.54372e7 + 2.04597e7i 0.299375 + 0.172844i 0.642162 0.766569i \(-0.278038\pi\)
−0.342787 + 0.939413i \(0.611371\pi\)
\(492\) 7.49438e7 2.00811e7i 0.629275 0.168614i
\(493\) 4.28822e7i 0.357879i
\(494\) −5.93741e6 3.12459e7i −0.0492511 0.259186i
\(495\) −1.20379e8 −0.992511
\(496\) −6.99564e7 2.61081e8i −0.573301 2.13959i
\(497\) −1.06504e7 + 1.84471e7i −0.0867558 + 0.150266i
\(498\) 1.39938e8 8.07935e7i 1.13305 0.654167i
\(499\) 1.11022e8 1.11022e8i 0.893529 0.893529i −0.101324 0.994853i \(-0.532308\pi\)
0.994853 + 0.101324i \(0.0323080\pi\)
\(500\) 6.65311e7 + 1.78270e7i 0.532249 + 0.142616i
\(501\) −6.06618e7 + 2.26393e8i −0.482394 + 1.80032i
\(502\) 2.21665e8 + 2.21665e8i 1.75221 + 1.75221i
\(503\) −5.26695e7 9.12262e7i −0.413861 0.716829i 0.581447 0.813584i \(-0.302487\pi\)
−0.995308 + 0.0967555i \(0.969154\pi\)
\(504\) −8.01048e7 4.62485e7i −0.625701 0.361249i
\(505\) 4.32876e7 1.15989e7i 0.336116 0.0900620i
\(506\) 1.10122e8i 0.850009i
\(507\) −3.18920e7 + 2.13863e8i −0.244714 + 1.64101i
\(508\) −1.09959e8 −0.838765
\(509\) −2.05536e7 7.67073e7i −0.155860 0.581679i −0.999030 0.0440313i \(-0.985980\pi\)
0.843170 0.537647i \(-0.180687\pi\)
\(510\) −4.03522e7 + 6.98921e7i −0.304198 + 0.526887i
\(511\) −1.01233e7 + 5.84467e6i −0.0758679 + 0.0438023i
\(512\) −1.03470e8 + 1.03470e8i −0.770915 + 0.770915i
\(513\) 3.24405e7 + 8.69240e6i 0.240290 + 0.0643854i
\(514\) 2.95680e7 1.10349e8i 0.217737 0.812607i
\(515\) −2.68188e7 2.68188e7i −0.196344 0.196344i
\(516\) −1.00921e8 1.74801e8i −0.734571 1.27231i
\(517\) −7.37390e7 4.25732e7i −0.533612 0.308081i
\(518\) −1.92043e8 + 5.14578e7i −1.38169 + 0.370222i
\(519\) 1.72716e8i 1.23546i
\(520\) 1.77851e7 3.37955e6i 0.126487 0.0240353i
\(521\) 1.34838e8 0.953451 0.476726 0.879052i \(-0.341823\pi\)
0.476726 + 0.879052i \(0.341823\pi\)
\(522\) 4.37780e7 + 1.63382e8i 0.307783 + 1.14866i
\(523\) 9.18849e6 1.59149e7i 0.0642302 0.111250i −0.832122 0.554593i \(-0.812874\pi\)
0.896352 + 0.443343i \(0.146207\pi\)
\(524\) −2.00914e7 + 1.15998e7i −0.139642 + 0.0806225i
\(525\) 1.81526e8 1.81526e8i 1.25448 1.25448i
\(526\) 1.39319e8 + 3.73303e7i 0.957309 + 0.256510i
\(527\) −4.94722e7 + 1.84633e8i −0.338010 + 1.26147i
\(528\) 2.92526e8 + 2.92526e8i 1.98730 + 1.98730i
\(529\) −5.90984e7 1.02361e8i −0.399217 0.691463i
\(530\) −7.39767e7 4.27105e7i −0.496898 0.286884i
\(531\) −7.21568e7 + 1.93343e7i −0.481941 + 0.129136i
\(532\) 2.87039e7i 0.190637i
\(533\) 3.42388e7 + 7.09553e7i 0.226119 + 0.468601i
\(534\) −5.69989e8 −3.74320
\(535\) −7.21718e6 2.69349e7i −0.0471309 0.175895i
\(536\) −1.00115e7 + 1.73404e7i −0.0650137 + 0.112607i
\(537\) 3.08817e8 1.78295e8i 1.99424 1.15138i
\(538\) 7.07896e7 7.07896e7i 0.454593 0.454593i
\(539\) 1.31591e8 + 3.52597e7i 0.840349 + 0.225171i
\(540\) 1.52190e7 5.67979e7i 0.0966504 0.360704i
\(541\) −9.24441e7 9.24441e7i −0.583831 0.583831i 0.352123 0.935954i \(-0.385460\pi\)
−0.935954 + 0.352123i \(0.885460\pi\)
\(542\) 2.66667e7 + 4.61881e7i 0.167483 + 0.290089i
\(543\) 1.49411e8 + 8.62627e7i 0.933221 + 0.538795i
\(544\) 1.35268e8 3.62450e7i 0.840231 0.225139i
\(545\) 5.21289e7i 0.322025i
\(546\) −1.49522e8 + 4.28387e8i −0.918604 + 2.63183i
\(547\) −1.87443e8 −1.14527 −0.572634 0.819811i \(-0.694078\pi\)
−0.572634 + 0.819811i \(0.694078\pi\)
\(548\) −1.37520e7 5.13232e7i −0.0835650 0.311869i
\(549\) 1.25450e8 2.17285e8i 0.758146 1.31315i
\(550\) −2.29977e8 + 1.32777e8i −1.38228 + 0.798061i
\(551\) 1.20663e7 1.20663e7i 0.0721307 0.0721307i
\(552\) 3.93300e7 + 1.05384e7i 0.233833 + 0.0626555i
\(553\) 1.02500e7 3.82534e7i 0.0606104 0.226201i
\(554\) 4.06952e6 + 4.06952e6i 0.0239339 + 0.0239339i
\(555\) 4.78358e7 + 8.28540e7i 0.279817 + 0.484657i
\(556\) 1.45764e8 + 8.41566e7i 0.848056 + 0.489625i
\(557\) 2.35465e8 6.30928e7i 1.36258 0.365102i 0.497816 0.867283i \(-0.334135\pi\)
0.864763 + 0.502181i \(0.167469\pi\)
\(558\) 7.53958e8i 4.33955i
\(559\) 1.55246e8 1.33812e8i 0.888760 0.766053i
\(560\) 1.04582e8 0.595515
\(561\) −7.57198e7 2.82590e8i −0.428865 1.60055i
\(562\) −4.48677e7 + 7.77132e7i −0.252770 + 0.437810i
\(563\) −1.62504e8 + 9.38219e7i −0.910625 + 0.525750i −0.880632 0.473801i \(-0.842882\pi\)
−0.0299928 + 0.999550i \(0.509548\pi\)
\(564\) 6.84761e7 6.84761e7i 0.381682 0.381682i
\(565\) −1.22186e8 3.27396e7i −0.677448 0.181522i
\(566\) −1.32663e7 + 4.95105e7i −0.0731645 + 0.273054i
\(567\) −5.22376e7 5.22376e7i −0.286572 0.286572i
\(568\) −4.07354e6 7.05558e6i −0.0222294 0.0385024i
\(569\) −2.84383e8 1.64188e8i −1.54371 0.891262i −0.998600 0.0528992i \(-0.983154\pi\)
−0.545112 0.838363i \(-0.683513\pi\)
\(570\) −3.10209e7 + 8.31203e6i −0.167506 + 0.0448830i
\(571\) 7.79925e7i 0.418933i 0.977816 + 0.209466i \(0.0671727\pi\)
−0.977816 + 0.209466i \(0.932827\pi\)
\(572\) 1.13583e8 1.66876e8i 0.606910 0.891674i
\(573\) −3.33589e8 −1.77316
\(574\) 4.27881e7 + 1.59687e8i 0.226249 + 0.844373i
\(575\) −3.59779e7 + 6.23155e7i −0.189248 + 0.327788i
\(576\) −1.34571e8 + 7.76949e7i −0.704183 + 0.406560i
\(577\) −2.05841e8 + 2.05841e8i −1.07153 + 1.07153i −0.0742941 + 0.997236i \(0.523670\pi\)
−0.997236 + 0.0742941i \(0.976330\pi\)
\(578\) 1.26440e8 + 3.38795e7i 0.654789 + 0.175450i
\(579\) 2.94256e7 1.09818e8i 0.151597 0.565766i
\(580\) −2.11261e7 2.11261e7i −0.108277 0.108277i
\(581\) 7.40404e7 + 1.28242e8i 0.377520 + 0.653885i
\(582\) 1.99797e8 + 1.15353e8i 1.01349 + 0.585140i
\(583\) 2.99105e8 8.01450e7i 1.50945 0.404456i
\(584\) 4.47089e6i 0.0224469i
\(585\) 1.38642e8 + 1.02805e7i 0.692512 + 0.0513510i
\(586\) −3.58540e6 −0.0178174
\(587\) −1.33945e7 4.99891e7i −0.0662237 0.247150i 0.924877 0.380267i \(-0.124168\pi\)
−0.991100 + 0.133117i \(0.957501\pi\)
\(588\) −7.74711e7 + 1.34184e8i −0.381073 + 0.660037i
\(589\) −6.58732e7 + 3.80319e7i −0.322376 + 0.186124i
\(590\) 2.16938e7 2.16938e7i 0.105628 0.105628i
\(591\) −5.30637e8 1.42184e8i −2.57061 0.688792i
\(592\) 5.41835e7 2.02215e8i 0.261157 0.974651i
\(593\) 1.03640e7 + 1.03640e7i 0.0497006 + 0.0497006i 0.731520 0.681820i \(-0.238811\pi\)
−0.681820 + 0.731520i \(0.738811\pi\)
\(594\) 2.47809e8 + 4.29217e8i 1.18238 + 2.04794i
\(595\) −6.40502e7 3.69794e7i −0.304067 0.175553i
\(596\) −8.59175e6 + 2.30215e6i −0.0405829 + 0.0108742i
\(597\) 5.16968e8i 2.42964i
\(598\) 9.40460e6 1.26829e8i 0.0439782 0.593083i
\(599\) 2.97465e8 1.38406 0.692030 0.721869i \(-0.256717\pi\)
0.692030 + 0.721869i \(0.256717\pi\)
\(600\) 2.54130e7 + 9.48425e7i 0.117653 + 0.439086i
\(601\) 1.20393e8 2.08527e8i 0.554597 0.960590i −0.443338 0.896355i \(-0.646206\pi\)
0.997935 0.0642355i \(-0.0204609\pi\)
\(602\) 3.72458e8 2.15039e8i 1.70722 0.985661i
\(603\) −1.08728e8 + 1.08728e8i −0.495894 + 0.495894i
\(604\) 3.34080e7 + 8.95166e6i 0.151614 + 0.0406249i
\(605\) −2.36791e7 + 8.83714e7i −0.106930 + 0.399067i
\(606\) −3.03773e8 3.03773e8i −1.36500 1.36500i
\(607\) 9.79862e7 + 1.69717e8i 0.438126 + 0.758856i 0.997545 0.0700287i \(-0.0223091\pi\)
−0.559419 + 0.828885i \(0.688976\pi\)
\(608\) 4.82609e7 + 2.78635e7i 0.214726 + 0.123972i
\(609\) −2.35146e8 + 6.30071e7i −1.04108 + 0.278957i
\(610\) 1.03043e8i 0.453971i
\(611\) 8.12903e7 + 5.53295e7i 0.356381 + 0.242568i
\(612\) 2.11865e8 0.924284
\(613\) 3.45751e7 + 1.29036e8i 0.150101 + 0.560183i 0.999475 + 0.0323928i \(0.0103127\pi\)
−0.849375 + 0.527791i \(0.823021\pi\)
\(614\) −2.54730e7 + 4.41205e7i −0.110046 + 0.190605i
\(615\) 6.88945e7 3.97763e7i 0.296182 0.171001i
\(616\) −9.73747e7 + 9.73747e7i −0.416585 + 0.416585i
\(617\) 2.69658e8 + 7.22546e7i 1.14804 + 0.307617i 0.782180 0.623053i \(-0.214108\pi\)
0.365861 + 0.930669i \(0.380774\pi\)
\(618\) −9.41014e7 + 3.51191e8i −0.398686 + 1.48792i
\(619\) 1.11666e8 + 1.11666e8i 0.470812 + 0.470812i 0.902177 0.431365i \(-0.141968\pi\)
−0.431365 + 0.902177i \(0.641968\pi\)
\(620\) 6.65876e7 + 1.15333e8i 0.279395 + 0.483926i
\(621\) 1.16302e8 + 6.71471e7i 0.485639 + 0.280384i
\(622\) −3.48158e8 + 9.32886e7i −1.44679 + 0.387666i
\(623\) 5.22347e8i 2.16021i
\(624\) −3.11924e8 3.61888e8i −1.28379 1.48943i
\(625\) −1.35200e8 −0.553778
\(626\) −1.22956e8 4.58879e8i −0.501219 1.87057i
\(627\) 5.82099e7 1.00822e8i 0.236153 0.409029i
\(628\) −2.07550e8 + 1.19829e8i −0.838000 + 0.483819i
\(629\) −1.04686e8 + 1.04686e8i −0.420666 + 0.420666i
\(630\) 2.81784e8 + 7.55038e7i 1.12692 + 0.301958i
\(631\) −2.77506e7 + 1.03566e8i −0.110455 + 0.412222i −0.998907 0.0467472i \(-0.985114\pi\)
0.888452 + 0.458969i \(0.151781\pi\)
\(632\) 1.07106e7 + 1.07106e7i 0.0424291 + 0.0424291i
\(633\) −4.03604e8 6.99062e8i −1.59127 2.75616i
\(634\) −1.21416e8 7.00998e7i −0.476442 0.275074i
\(635\) −1.08902e8 + 2.91803e7i −0.425320 + 0.113964i
\(636\) 3.52183e8i 1.36898i
\(637\) −1.48544e8 5.18471e7i −0.574693 0.200588i
\(638\) 2.51821e8 0.969685
\(639\) −1.61929e7 6.04328e7i −0.0620616 0.231617i
\(640\) −3.27353e7 + 5.66993e7i −0.124875 + 0.216291i
\(641\) −1.66234e8 + 9.59755e7i −0.631171 + 0.364407i −0.781205 0.624274i \(-0.785395\pi\)
0.150035 + 0.988681i \(0.452062\pi\)
\(642\) −1.89017e8 + 1.89017e8i −0.714326 + 0.714326i
\(643\) 2.50967e7 + 6.72465e6i 0.0944027 + 0.0252951i 0.305711 0.952124i \(-0.401106\pi\)
−0.211309 + 0.977419i \(0.567772\pi\)
\(644\) 2.97065e7 1.10866e8i 0.111223 0.415089i
\(645\) −1.46339e8 1.46339e8i −0.545357 0.545357i
\(646\) −2.48486e7 4.30390e7i −0.0921731 0.159649i
\(647\) −3.77670e7 2.18048e7i −0.139444 0.0805080i 0.428655 0.903468i \(-0.358988\pi\)
−0.568099 + 0.822960i \(0.692321\pi\)
\(648\) 2.72927e7 7.31306e6i 0.100305 0.0268766i
\(649\) 1.11216e8i 0.406848i
\(650\) 2.76207e8 1.33281e8i 1.00576 0.485320i
\(651\) 1.08513e9 3.93313
\(652\) −1.54373e7 5.76128e7i −0.0556966 0.207862i
\(653\) −2.45478e8 + 4.25180e8i −0.881602 + 1.52698i −0.0320418 + 0.999487i \(0.510201\pi\)
−0.849560 + 0.527492i \(0.823132\pi\)
\(654\) 4.32767e8 2.49858e8i 1.54711 0.893224i
\(655\) −1.68200e7 + 1.68200e7i −0.0598553 + 0.0598553i
\(656\) −1.68146e8 4.50545e7i −0.595626 0.159598i
\(657\) 8.88623e6 3.31639e7i 0.0313344 0.116942i
\(658\) 1.45906e8 + 1.45906e8i 0.512148 + 0.512148i
\(659\) 9.41451e7 + 1.63064e8i 0.328959 + 0.569773i 0.982306 0.187286i \(-0.0599690\pi\)
−0.653347 + 0.757059i \(0.726636\pi\)
\(660\) −1.76523e8 1.01916e8i −0.614003 0.354495i
\(661\) 4.77650e8 1.27986e8i 1.65389 0.443157i 0.693188 0.720756i \(-0.256205\pi\)
0.960697 + 0.277599i \(0.0895387\pi\)
\(662\) 7.17944e8i 2.47467i
\(663\) 6.30738e7 + 3.31929e8i 0.216425 + 1.13895i
\(664\) −5.66374e7 −0.193463
\(665\) −7.61727e6 2.84280e7i −0.0259021 0.0966678i
\(666\) 2.91982e8 5.05728e8i 0.988403 1.71196i
\(667\) 5.90928e7 3.41172e7i 0.199139 0.114973i
\(668\) −1.78683e8 + 1.78683e8i −0.599452 + 0.599452i
\(669\) 6.51075e8 + 1.74455e8i 2.17447 + 0.582646i
\(670\) 1.63444e7 6.09983e7i 0.0543432 0.202812i
\(671\) −2.64130e8 2.64130e8i −0.874280 0.874280i
\(672\) −3.97501e8 6.88492e8i −1.30988 2.26877i
\(673\) 7.91210e7 + 4.56806e7i 0.259565 + 0.149860i 0.624136 0.781315i \(-0.285451\pi\)
−0.364571 + 0.931176i \(0.618784\pi\)
\(674\) −5.81185e8 + 1.55728e8i −1.89817 + 0.508613i
\(675\) 3.23845e8i 1.05299i
\(676\) −1.45066e8 + 1.82493e8i −0.469598 + 0.590753i
\(677\) 1.89023e8 0.609185 0.304592 0.952483i \(-0.401480\pi\)
0.304592 + 0.952483i \(0.401480\pi\)
\(678\) 3.13848e8 + 1.17129e9i 1.00700 + 3.75818i
\(679\) −1.05711e8 + 1.83097e8i −0.337685 + 0.584887i
\(680\) 2.44977e7 1.41437e7i 0.0779109 0.0449819i
\(681\) 5.22551e8 5.22551e8i 1.65458 1.65458i
\(682\) −1.08424e9 2.90521e8i −3.41799 0.915849i
\(683\) 1.03234e8 3.85274e8i 0.324011 1.20923i −0.591291 0.806458i \(-0.701382\pi\)
0.915302 0.402767i \(-0.131952\pi\)
\(684\) 5.96153e7 + 5.96153e7i 0.186290 + 0.186290i
\(685\) −2.72397e7 4.71805e7i −0.0847481 0.146788i
\(686\) 1.83803e8 + 1.06119e8i 0.569352 + 0.328716i
\(687\) −7.24688e8 + 1.94179e8i −2.23502 + 0.598871i
\(688\) 4.52859e8i 1.39058i
\(689\) −3.51328e8 + 6.67599e7i −1.07412 + 0.204107i
\(690\) −1.28418e8 −0.390910
\(691\) 1.53209e8 + 5.71784e8i 0.464355 + 1.73300i 0.659018 + 0.752128i \(0.270972\pi\)
−0.194662 + 0.980870i \(0.562361\pi\)
\(692\) −9.31067e7 + 1.61266e8i −0.280972 + 0.486657i
\(693\) −9.15839e8 + 5.28760e8i −2.75182 + 1.58876i
\(694\) 4.32099e8 4.32099e8i 1.29272 1.29272i
\(695\) 1.66696e8 + 4.46659e7i 0.496557 + 0.133052i
\(696\) 2.40987e7 8.99376e7i 0.0714769 0.266756i
\(697\) 8.70483e7 + 8.70483e7i 0.257076 + 0.257076i
\(698\) 1.04816e8 + 1.81547e8i 0.308221 + 0.533854i
\(699\) −2.88628e8 1.66639e8i −0.845096 0.487917i
\(700\) 2.67349e8 7.16359e7i 0.779443 0.208851i
\(701\) 2.63303e8i 0.764368i 0.924086 + 0.382184i \(0.124828\pi\)
−0.924086 + 0.382184i \(0.875172\pi\)
\(702\) −2.48748e8 5.15497e8i −0.719033 1.49010i
\(703\) −5.89138e7 −0.169571
\(704\) 5.98759e7 + 2.23460e8i 0.171607 + 0.640444i
\(705\) 4.96462e7 8.59898e7i 0.141683 0.245403i
\(706\) 4.78281e8 2.76136e8i 1.35916 0.784709i
\(707\) 2.78383e8 2.78383e8i 0.787742 0.787742i
\(708\) −1.22179e8 3.27379e7i −0.344269 0.0922466i
\(709\) 1.15331e8 4.30422e8i 0.323600 1.20769i −0.592113 0.805855i \(-0.701706\pi\)
0.915712 0.401835i \(-0.131627\pi\)
\(710\) 1.81690e7 + 1.81690e7i 0.0507641 + 0.0507641i
\(711\) 5.81604e7 + 1.00737e8i 0.161815 + 0.280272i
\(712\) 1.73019e8 + 9.98926e7i 0.479351 + 0.276754i
\(713\) −2.93789e8 + 7.87205e7i −0.810526 + 0.217180i
\(714\) 7.08982e8i 1.94778i
\(715\) 6.82066e7 1.95414e8i 0.186598 0.534611i
\(716\) 3.84459e8 1.04740
\(717\) −1.00469e8 3.74955e8i −0.272568 1.01724i
\(718\) 2.49512e8 4.32168e8i 0.674092 1.16756i
\(719\) −2.17714e8 + 1.25697e8i −0.585733 + 0.338173i −0.763408 0.645916i \(-0.776476\pi\)
0.177676 + 0.984089i \(0.443142\pi\)
\(720\) −2.17207e8 + 2.17207e8i −0.581936 + 0.581936i
\(721\) −3.21837e8 8.62360e7i −0.858678 0.230082i
\(722\) −1.23916e8 + 4.62459e8i −0.329241 + 1.22875i
\(723\) 2.50467e8 + 2.50467e8i 0.662729 + 0.662729i
\(724\) 9.30042e7 + 1.61088e8i 0.245068 + 0.424471i
\(725\) 1.42500e8 + 8.22722e7i 0.373938 + 0.215893i
\(726\) 8.47144e8 2.26991e8i 2.21384 0.593198i
\(727\) 1.12064e8i 0.291651i 0.989310 + 0.145826i \(0.0465838\pi\)
−0.989310 + 0.145826i \(0.953416\pi\)
\(728\) 1.20464e8 1.03832e8i 0.312221 0.269114i
\(729\) −5.85882e8 −1.51226
\(730\) 3.64951e6 + 1.36202e7i 0.00938138 + 0.0350118i
\(731\) 1.60128e8 2.77349e8i 0.409934 0.710026i
\(732\) 3.67918e8 2.12418e8i 0.938033 0.541574i
\(733\) 2.55879e8 2.55879e8i 0.649715 0.649715i −0.303209 0.952924i \(-0.598058\pi\)
0.952924 + 0.303209i \(0.0980581\pi\)
\(734\) 1.56523e8 + 4.19403e7i 0.395814 + 0.106058i
\(735\) −4.11176e7 + 1.53453e8i −0.103554 + 0.386468i
\(736\) 1.57566e8 + 1.57566e8i 0.395212 + 0.395212i
\(737\) 1.14462e8 + 1.98253e8i 0.285928 + 0.495242i
\(738\) −4.20522e8 2.42788e8i −1.04621 0.604030i
\(739\) 5.22885e8 1.40107e8i 1.29561 0.347157i 0.455819 0.890072i \(-0.349346\pi\)
0.839787 + 0.542916i \(0.182680\pi\)
\(740\) 1.03148e8i 0.254547i
\(741\) −7.56514e7 + 1.11147e8i −0.185935 + 0.273177i
\(742\) −7.50416e8 −1.83692
\(743\) 9.53453e7 + 3.55833e8i 0.232452 + 0.867521i 0.979281 + 0.202506i \(0.0649085\pi\)
−0.746829 + 0.665016i \(0.768425\pi\)
\(744\) −2.07518e8 + 3.59431e8i −0.503891 + 0.872765i
\(745\) −7.89824e6 + 4.56005e6i −0.0191012 + 0.0110281i
\(746\) −3.57599e8 + 3.57599e8i −0.861350 + 0.861350i
\(747\) −4.20121e8 1.12571e8i −1.00789 0.270063i
\(748\) 8.16374e7 3.04675e8i 0.195067 0.728001i
\(749\) −1.73218e8 1.73218e8i −0.412238 0.412238i
\(750\) −3.38500e8 5.86299e8i −0.802369 1.38974i
\(751\) −3.28271e8 1.89527e8i −0.775019 0.447458i 0.0596430 0.998220i \(-0.481004\pi\)
−0.834662 + 0.550762i \(0.814337\pi\)
\(752\) −2.09869e8 + 5.62341e7i −0.493508 + 0.132235i
\(753\) 1.32519e9i 3.10379i
\(754\) −2.90026e8 2.15059e7i −0.676585 0.0501700i
\(755\) 3.54625e7 0.0824002
\(756\) −1.33697e8 4.98965e8i −0.309426 1.15479i
\(757\) 2.80059e8 4.85076e8i 0.645597 1.11821i −0.338566 0.940943i \(-0.609942\pi\)
0.984163 0.177264i \(-0.0567248\pi\)
\(758\) −5.80652e7 + 3.35239e7i −0.133324 + 0.0769746i
\(759\) 3.29174e8 3.29174e8i 0.752836 0.752836i
\(760\) 1.08730e7 + 2.91342e6i 0.0247691 + 0.00663686i
\(761\) −1.22377e8 + 4.56717e8i −0.277680 + 1.03632i 0.676343 + 0.736586i \(0.263564\pi\)
−0.954024 + 0.299731i \(0.903103\pi\)
\(762\) 7.64229e8 + 7.64229e8i 1.72726 + 1.72726i
\(763\) 2.28974e8 + 3.96594e8i 0.515481 + 0.892839i