Properties

Label 69.7.f.a.7.5
Level $69$
Weight $7$
Character 69.7
Analytic conductor $15.874$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 69.f (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.8737317698\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(24\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 7.5
Character \(\chi\) \(=\) 69.7
Dual form 69.7.f.a.10.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.37873 + 8.51551i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(-8.96008 - 62.3187i) q^{4} +(186.661 - 85.2451i) q^{5} +(24.9969 - 173.857i) q^{6} +(65.3761 + 222.650i) q^{7} +(-9.86246 - 6.33822i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})\) \(q+(-7.37873 + 8.51551i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(-8.96008 - 62.3187i) q^{4} +(186.661 - 85.2451i) q^{5} +(24.9969 - 173.857i) q^{6} +(65.3761 + 222.650i) q^{7} +(-9.86246 - 6.33822i) q^{8} +(100.946 - 221.041i) q^{9} +(-651.414 + 2218.51i) q^{10} +(-1470.73 + 1274.40i) q^{11} +(642.708 + 741.724i) q^{12} +(-1703.94 - 500.321i) q^{13} +(-2378.37 - 1086.17i) q^{14} +(-1729.41 + 2691.02i) q^{15} +(3992.94 - 1172.43i) q^{16} +(-235.748 - 33.8954i) q^{17} +(1137.42 + 2490.60i) q^{18} +(-3800.51 + 546.430i) q^{19} +(-6984.86 - 10868.7i) q^{20} +(-2733.78 - 2368.83i) q^{21} -21927.5i q^{22} +(-5306.25 + 10949.0i) q^{23} +182.752 q^{24} +(17343.3 - 20015.2i) q^{25} +(16833.4 - 10818.2i) q^{26} +(539.088 + 3749.44i) q^{27} +(13289.5 - 6069.12i) q^{28} +(496.323 - 3452.00i) q^{29} +(-10154.5 - 34583.2i) q^{30} +(-27080.9 - 17403.9i) q^{31} +(-19167.3 + 41970.4i) q^{32} +(8546.66 - 29107.2i) q^{33} +(2028.16 - 1757.41i) q^{34} +(31183.0 + 35987.1i) q^{35} +(-14679.4 - 4310.27i) q^{36} +(-59518.2 - 27181.1i) q^{37} +(23389.8 - 36395.2i) q^{38} +(26561.7 - 7799.23i) q^{39} +(-2381.24 - 342.370i) q^{40} +(585.616 + 1282.32i) q^{41} +(40343.6 - 5800.53i) q^{42} +(-53958.4 - 83960.9i) q^{43} +(92596.7 + 80235.5i) q^{44} -49864.7i q^{45} +(-54082.6 - 125975. i) q^{46} -131918. q^{47} +(-42481.8 + 49026.6i) q^{48} +(53673.4 - 34493.8i) q^{49} +(42468.4 + 295374. i) q^{50} +(3377.22 - 1542.33i) q^{51} +(-15911.9 + 110670. i) q^{52} +(26247.8 + 89391.8i) q^{53} +(-35906.2 - 23075.5i) q^{54} +(-165892. + 363253. i) q^{55} +(766.439 - 2610.25i) q^{56} +(45234.1 - 39195.6i) q^{57} +(25733.3 + 29697.8i) q^{58} +(80114.4 + 23523.7i) q^{59} +(183197. + 83663.1i) q^{60} +(30952.6 - 48163.1i) q^{61} +(348026. - 102190. i) q^{62} +(55814.2 + 8024.88i) q^{63} +(-105329. - 230639. i) q^{64} +(-360708. + 51862.0i) q^{65} +(184800. + 287554. i) q^{66} +(329120. + 285184. i) q^{67} +14995.2i q^{68} +(-22689.8 - 188303. i) q^{69} -536540. q^{70} +(-447235. + 516137. i) q^{71} +(-2396.58 + 1540.19i) q^{72} +(-58498.6 - 406866. i) q^{73} +(670629. - 306266. i) q^{74} +(-58753.8 + 408642. i) q^{75} +(68105.7 + 231947. i) q^{76} +(-379896. - 244144. i) q^{77} +(-129577. + 283735. i) q^{78} +(219982. - 749190. i) q^{79} +(645380. - 559225. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(-15240.7 - 4475.08i) q^{82} +(-652242. - 297869. i) q^{83} +(-123128. + 191590. i) q^{84} +(-46894.2 + 13769.4i) q^{85} +(1.11311e6 + 160042. i) q^{86} +(22583.9 + 49451.9i) q^{87} +(22582.5 - 3246.87i) q^{88} +(-84710.6 - 131812. i) q^{89} +(424624. + 367938. i) q^{90} -412091. i q^{91} +(729869. + 232575. i) q^{92} +501811. q^{93} +(973386. - 1.12335e6i) q^{94} +(-662825. + 425972. i) q^{95} +(-102360. - 711931. i) q^{96} +(-995439. + 454602. i) q^{97} +(-102309. + 711577. i) q^{98} +(133229. + 453737. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240q + 20q^{2} - 816q^{4} + 324q^{6} + 940q^{8} - 5832q^{9} + O(q^{10}) \) \( 240q + 20q^{2} - 816q^{4} + 324q^{6} + 940q^{8} - 5832q^{9} - 384q^{13} + 33816q^{16} + 22880q^{17} + 4860q^{18} - 31680q^{19} - 157696q^{20} + 36488q^{23} + 39204q^{24} + 200664q^{25} + 99032q^{26} - 202752q^{28} - 181712q^{29} - 128496q^{31} + 439300q^{32} - 400026q^{34} + 368744q^{35} + 42282q^{36} + 446688q^{37} + 550550q^{38} - 52488q^{39} - 156750q^{40} - 606080q^{41} - 1274130q^{42} - 429000q^{43} - 867482q^{44} + 309288q^{46} + 1111152q^{47} + 837864q^{48} + 722136q^{49} + 1786926q^{50} + 463320q^{51} - 812550q^{52} - 367840q^{53} - 354294q^{54} - 398088q^{55} - 3696550q^{56} - 1240272q^{57} + 1903134q^{58} + 545800q^{59} + 2450250q^{60} - 495264q^{61} + 488776q^{62} - 2699808q^{64} - 290400q^{67} + 23328q^{69} - 392616q^{70} + 255392q^{71} + 228420q^{72} + 1346880q^{73} - 5387470q^{74} + 365472q^{75} + 2123022q^{76} + 6134240q^{77} + 171072q^{78} + 4025472q^{79} + 10626462q^{80} - 1417176q^{81} + 2025492q^{82} - 2474560q^{83} - 8866152q^{85} - 15634300q^{86} - 611712q^{87} - 10636560q^{88} - 5901720q^{89} + 6566394q^{92} - 2484432q^{93} + 13931490q^{94} + 8183072q^{95} - 4682124q^{96} + 12319560q^{97} + 14139580q^{98} + 2993760q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{19}{22}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.37873 + 8.51551i −0.922341 + 1.06444i 0.0753926 + 0.997154i \(0.475979\pi\)
−0.997734 + 0.0672846i \(0.978566\pi\)
\(3\) −13.1138 + 8.42776i −0.485698 + 0.312139i
\(4\) −8.96008 62.3187i −0.140001 0.973730i
\(5\) 186.661 85.2451i 1.49329 0.681961i 0.509362 0.860552i \(-0.329881\pi\)
0.983923 + 0.178591i \(0.0571540\pi\)
\(6\) 24.9969 173.857i 0.115726 0.804894i
\(7\) 65.3761 + 222.650i 0.190601 + 0.649127i 0.998232 + 0.0594388i \(0.0189311\pi\)
−0.807631 + 0.589688i \(0.799251\pi\)
\(8\) −9.86246 6.33822i −0.0192626 0.0123793i
\(9\) 100.946 221.041i 0.138472 0.303211i
\(10\) −651.414 + 2218.51i −0.651414 + 2.21851i
\(11\) −1470.73 + 1274.40i −1.10498 + 0.957474i −0.999318 0.0369274i \(-0.988243\pi\)
−0.105666 + 0.994402i \(0.533698\pi\)
\(12\) 642.708 + 741.724i 0.371937 + 0.429239i
\(13\) −1703.94 500.321i −0.775574 0.227729i −0.130089 0.991502i \(-0.541526\pi\)
−0.645485 + 0.763773i \(0.723345\pi\)
\(14\) −2378.37 1086.17i −0.866755 0.395834i
\(15\) −1729.41 + 2691.02i −0.512419 + 0.797340i
\(16\) 3992.94 1172.43i 0.974838 0.286238i
\(17\) −235.748 33.8954i −0.0479845 0.00689912i 0.118281 0.992980i \(-0.462262\pi\)
−0.166265 + 0.986081i \(0.553171\pi\)
\(18\) 1137.42 + 2490.60i 0.195031 + 0.427058i
\(19\) −3800.51 + 546.430i −0.554091 + 0.0796662i −0.413672 0.910426i \(-0.635754\pi\)
−0.140419 + 0.990092i \(0.544845\pi\)
\(20\) −6984.86 10868.7i −0.873107 1.35858i
\(21\) −2733.78 2368.83i −0.295192 0.255786i
\(22\) 21927.5i 2.05931i
\(23\) −5306.25 + 10949.0i −0.436118 + 0.899890i
\(24\) 182.752 0.0132199
\(25\) 17343.3 20015.2i 1.10997 1.28097i
\(26\) 16833.4 10818.2i 0.957748 0.615507i
\(27\) 539.088 + 3749.44i 0.0273885 + 0.190491i
\(28\) 13289.5 6069.12i 0.605390 0.276472i
\(29\) 496.323 3452.00i 0.0203503 0.141539i −0.977113 0.212720i \(-0.931768\pi\)
0.997463 + 0.0711810i \(0.0226768\pi\)
\(30\) −10154.5 34583.2i −0.376094 1.28086i
\(31\) −27080.9 17403.9i −0.909031 0.584199i 0.000424692 1.00000i \(-0.499865\pi\)
−0.909455 + 0.415801i \(0.863501\pi\)
\(32\) −19167.3 + 41970.4i −0.584938 + 1.28084i
\(33\) 8546.66 29107.2i 0.237823 0.809952i
\(34\) 2028.16 1757.41i 0.0516017 0.0447132i
\(35\) 31183.0 + 35987.1i 0.727300 + 0.839349i
\(36\) −14679.4 4310.27i −0.314631 0.0923841i
\(37\) −59518.2 27181.1i −1.17502 0.536613i −0.270364 0.962758i \(-0.587144\pi\)
−0.904655 + 0.426145i \(0.859871\pi\)
\(38\) 23389.8 36395.2i 0.426261 0.663275i
\(39\) 26561.7 7799.23i 0.447778 0.131479i
\(40\) −2381.24 342.370i −0.0372068 0.00534953i
\(41\) 585.616 + 1282.32i 0.00849691 + 0.0186056i 0.913833 0.406090i \(-0.133108\pi\)
−0.905336 + 0.424696i \(0.860381\pi\)
\(42\) 40343.6 5800.53i 0.544536 0.0782925i
\(43\) −53958.4 83960.9i −0.678662 1.05602i −0.994246 0.107121i \(-0.965837\pi\)
0.315584 0.948898i \(-0.397800\pi\)
\(44\) 92596.7 + 80235.5i 1.08702 + 0.941908i
\(45\) 49864.7i 0.547212i
\(46\) −54082.6 125975.i −0.555628 1.29423i
\(47\) −131918. −1.27060 −0.635302 0.772264i \(-0.719124\pi\)
−0.635302 + 0.772264i \(0.719124\pi\)
\(48\) −42481.8 + 49026.6i −0.384131 + 0.443310i
\(49\) 53673.4 34493.8i 0.456217 0.293193i
\(50\) 42468.4 + 295374.i 0.339747 + 2.36299i
\(51\) 3377.22 1542.33i 0.0254594 0.0116269i
\(52\) −15911.9 + 110670.i −0.113165 + 0.787082i
\(53\) 26247.8 + 89391.8i 0.176305 + 0.600441i 0.999467 + 0.0326342i \(0.0103896\pi\)
−0.823162 + 0.567807i \(0.807792\pi\)
\(54\) −35906.2 23075.5i −0.228028 0.146545i
\(55\) −165892. + 363253.i −0.997097 + 2.18334i
\(56\) 766.439 2610.25i 0.00436429 0.0148634i
\(57\) 45234.1 39195.6i 0.244254 0.211647i
\(58\) 25733.3 + 29697.8i 0.131890 + 0.152209i
\(59\) 80114.4 + 23523.7i 0.390081 + 0.114538i 0.470891 0.882191i \(-0.343933\pi\)
−0.0808101 + 0.996730i \(0.525751\pi\)
\(60\) 183197. + 83663.1i 0.848133 + 0.387329i
\(61\) 30952.6 48163.1i 0.136366 0.212190i −0.766353 0.642419i \(-0.777931\pi\)
0.902720 + 0.430229i \(0.141567\pi\)
\(62\) 348026. 102190.i 1.46028 0.428777i
\(63\) 55814.2 + 8024.88i 0.223215 + 0.0320935i
\(64\) −105329. 230639.i −0.401800 0.879819i
\(65\) −360708. + 51862.0i −1.31346 + 0.188846i
\(66\) 184800. + 287554.i 0.642790 + 1.00020i
\(67\) 329120. + 285184.i 1.09428 + 0.948202i 0.998884 0.0472369i \(-0.0150416\pi\)
0.0953999 + 0.995439i \(0.469587\pi\)
\(68\) 14995.2i 0.0476898i
\(69\) −22689.8 188303.i −0.0690692 0.573204i
\(70\) −536540. −1.56426
\(71\) −447235. + 516137.i −1.24957 + 1.44208i −0.398385 + 0.917218i \(0.630429\pi\)
−0.851186 + 0.524864i \(0.824116\pi\)
\(72\) −2396.58 + 1540.19i −0.00642087 + 0.00412644i
\(73\) −58498.6 406866.i −0.150375 1.04588i −0.915591 0.402110i \(-0.868277\pi\)
0.765216 0.643774i \(-0.222632\pi\)
\(74\) 670629. 306266.i 1.65496 0.755795i
\(75\) −58753.8 + 408642.i −0.139268 + 0.968632i
\(76\) 68105.7 + 231947.i 0.155147 + 0.528381i
\(77\) −379896. 244144.i −0.832133 0.534779i
\(78\) −129577. + 283735.i −0.273052 + 0.597901i
\(79\) 219982. 749190.i 0.446176 1.51953i −0.362899 0.931829i \(-0.618213\pi\)
0.809074 0.587706i \(-0.199969\pi\)
\(80\) 645380. 559225.i 1.26051 1.09224i
\(81\) −38668.9 44626.3i −0.0727623 0.0839722i
\(82\) −15240.7 4475.08i −0.0276416 0.00811631i
\(83\) −652242. 297869.i −1.14071 0.520944i −0.246744 0.969081i \(-0.579361\pi\)
−0.893965 + 0.448136i \(0.852088\pi\)
\(84\) −123128. + 191590.i −0.207739 + 0.323248i
\(85\) −46894.2 + 13769.4i −0.0763595 + 0.0224212i
\(86\) 1.11311e6 + 160042.i 1.75003 + 0.251616i
\(87\) 22583.9 + 49451.9i 0.0342958 + 0.0750974i
\(88\) 22582.5 3246.87i 0.0331378 0.00476449i
\(89\) −84710.6 131812.i −0.120162 0.186976i 0.775962 0.630780i \(-0.217265\pi\)
−0.896124 + 0.443804i \(0.853629\pi\)
\(90\) 424624. + 367938.i 0.582474 + 0.504717i
\(91\) 412091.i 0.546851i
\(92\) 729869. + 232575.i 0.937306 + 0.298675i
\(93\) 501811. 0.623866
\(94\) 973386. 1.12335e6i 1.17193 1.35248i
\(95\) −662825. + 425972.i −0.773086 + 0.496832i
\(96\) −102360. 711931.i −0.115696 0.804682i
\(97\) −995439. + 454602.i −1.09068 + 0.498099i −0.877824 0.478983i \(-0.841005\pi\)
−0.212861 + 0.977083i \(0.568278\pi\)
\(98\) −102309. + 711577.i −0.108702 + 0.756038i
\(99\) 133229. + 453737.i 0.137307 + 0.467626i
\(100\) −1.40272e6 901474.i −1.40272 0.901474i
\(101\) 107051. 234409.i 0.103903 0.227515i −0.850539 0.525911i \(-0.823724\pi\)
0.954442 + 0.298396i \(0.0964517\pi\)
\(102\) −11785.9 + 40139.2i −0.0111061 + 0.0378240i
\(103\) −899051. + 779032.i −0.822759 + 0.712925i −0.960722 0.277512i \(-0.910490\pi\)
0.137963 + 0.990437i \(0.455945\pi\)
\(104\) 13633.9 + 15734.3i 0.0121205 + 0.0139877i
\(105\) −712220. 209127.i −0.615242 0.180651i
\(106\) −954892. 436085.i −0.801746 0.366145i
\(107\) 355327. 552899.i 0.290052 0.451330i −0.665395 0.746491i \(-0.731737\pi\)
0.955448 + 0.295161i \(0.0953733\pi\)
\(108\) 228830. 67190.5i 0.181653 0.0533380i
\(109\) −1.85533e6 266756.i −1.43266 0.205985i −0.618113 0.786089i \(-0.712103\pi\)
−0.814542 + 0.580104i \(0.803012\pi\)
\(110\) −1.86921e6 4.09300e6i −1.40437 3.07513i
\(111\) 1.00959e6 145157.i 0.738202 0.106137i
\(112\) 522085. + 812380.i 0.371610 + 0.578236i
\(113\) 1.38209e6 + 1.19759e6i 0.957858 + 0.829989i 0.985508 0.169629i \(-0.0542568\pi\)
−0.0276496 + 0.999618i \(0.508802\pi\)
\(114\) 674405.i 0.455204i
\(115\) −57122.9 + 2.49607e6i −0.0375592 + 1.64121i
\(116\) −219571. −0.140670
\(117\) −282596. + 326134.i −0.176445 + 0.203628i
\(118\) −791459. + 508640.i −0.481706 + 0.309574i
\(119\) −7865.43 54705.3i −0.00466747 0.0324630i
\(120\) 34112.6 15578.7i 0.0197411 0.00901545i
\(121\) 286848. 1.99507e6i 0.161918 1.12617i
\(122\) 181743. + 618960.i 0.100087 + 0.340865i
\(123\) −18486.8 11880.7i −0.00993448 0.00638451i
\(124\) −841939. + 1.84359e6i −0.441586 + 0.966939i
\(125\) 627786. 2.13804e6i 0.321427 1.09468i
\(126\) −480174. + 416073.i −0.240042 + 0.207998i
\(127\) 2.43726e6 + 2.81275e6i 1.18985 + 1.37316i 0.910784 + 0.412882i \(0.135478\pi\)
0.279062 + 0.960273i \(0.409977\pi\)
\(128\) −92136.7 27053.8i −0.0439342 0.0129002i
\(129\) 1.41520e6 + 646302.i 0.659250 + 0.301069i
\(130\) 2.21993e6 3.45429e6i 1.01044 1.57227i
\(131\) −786338. + 230890.i −0.349780 + 0.102705i −0.451903 0.892067i \(-0.649255\pi\)
0.102123 + 0.994772i \(0.467437\pi\)
\(132\) −1.89050e6 271814.i −0.821970 0.118181i
\(133\) −370125. 810461.i −0.157324 0.344491i
\(134\) −4.85698e6 + 698328.i −2.01861 + 0.290232i
\(135\) 420248. + 653918.i 0.170806 + 0.265780i
\(136\) 2110.22 + 1828.51i 0.000838900 + 0.000726911i
\(137\) 4.26794e6i 1.65980i 0.557910 + 0.829901i \(0.311603\pi\)
−0.557910 + 0.829901i \(0.688397\pi\)
\(138\) 1.77092e6 + 1.19622e6i 0.673846 + 0.455170i
\(139\) 4.46179e6 1.66136 0.830682 0.556747i \(-0.187951\pi\)
0.830682 + 0.556747i \(0.187951\pi\)
\(140\) 1.96327e6 2.26573e6i 0.715477 0.825704i
\(141\) 1.72995e6 1.11177e6i 0.617130 0.396605i
\(142\) −1.09514e6 7.61687e6i −0.382477 2.66018i
\(143\) 3.14364e6 1.43565e6i 1.07504 0.490955i
\(144\) 143915. 1.00095e6i 0.0481970 0.335217i
\(145\) −201622. 686662.i −0.0661354 0.225237i
\(146\) 3.89632e6 + 2.50401e6i 1.25198 + 0.804596i
\(147\) −413159. + 904693.i −0.130067 + 0.284806i
\(148\) −1.16060e6 + 3.95264e6i −0.358012 + 1.21928i
\(149\) 1.42467e6 1.23448e6i 0.430681 0.373187i −0.412374 0.911015i \(-0.635300\pi\)
0.843055 + 0.537828i \(0.180755\pi\)
\(150\) −3.04626e6 3.51558e6i −0.902597 1.04165i
\(151\) −3.91386e6 1.14921e6i −1.13677 0.333787i −0.341408 0.939915i \(-0.610904\pi\)
−0.795367 + 0.606128i \(0.792722\pi\)
\(152\) 40945.8 + 18699.3i 0.0116595 + 0.00532469i
\(153\) −31290.0 + 48688.2i −0.00873638 + 0.0135941i
\(154\) 4.88217e6 1.43353e6i 1.33675 0.392505i
\(155\) −6.53854e6 940100.i −1.75584 0.252452i
\(156\) −724033. 1.58541e6i −0.190715 0.417607i
\(157\) −1.31116e6 + 188517.i −0.338811 + 0.0487137i −0.309621 0.950860i \(-0.600202\pi\)
−0.0291905 + 0.999574i \(0.509293\pi\)
\(158\) 4.75654e6 + 7.40133e6i 1.20593 + 1.87646i
\(159\) −1.09758e6 951060.i −0.273052 0.236601i
\(160\) 9.46815e6i 2.31156i
\(161\) −2.78469e6 465638.i −0.667267 0.111576i
\(162\) 665342. 0.156495
\(163\) −905428. + 1.04492e6i −0.209070 + 0.241279i −0.850593 0.525824i \(-0.823757\pi\)
0.641524 + 0.767103i \(0.278303\pi\)
\(164\) 74665.3 47984.5i 0.0169273 0.0108785i
\(165\) −885925. 6.16174e6i −0.197217 1.37168i
\(166\) 7.34923e6 3.35628e6i 1.60664 0.733726i
\(167\) −1.14097e6 + 7.93559e6i −0.244976 + 1.70384i 0.381472 + 0.924380i \(0.375417\pi\)
−0.626448 + 0.779464i \(0.715492\pi\)
\(168\) 11947.6 + 40689.8i 0.00251972 + 0.00858139i
\(169\) −1.40749e6 904541.i −0.291599 0.187399i
\(170\) 228767. 500929.i 0.0465635 0.101960i
\(171\) −262862. + 895226.i −0.0525702 + 0.179038i
\(172\) −4.74886e6 + 4.11491e6i −0.933263 + 0.808677i
\(173\) 4.55385e6 + 5.25542e6i 0.879509 + 1.01501i 0.999752 + 0.0222634i \(0.00708724\pi\)
−0.120243 + 0.992745i \(0.538367\pi\)
\(174\) −587748. 172579.i −0.111569 0.0327596i
\(175\) 5.59024e6 + 2.55298e6i 1.04308 + 0.476357i
\(176\) −4.37840e6 + 6.81293e6i −0.803115 + 1.24967i
\(177\) −1.24886e6 + 366698.i −0.225213 + 0.0661286i
\(178\) 1.74750e6 + 251253.i 0.309855 + 0.0445504i
\(179\) −1.08657e6 2.37926e6i −0.189452 0.414841i 0.790942 0.611891i \(-0.209591\pi\)
−0.980393 + 0.197050i \(0.936864\pi\)
\(180\) −3.10751e6 + 446792.i −0.532837 + 0.0766104i
\(181\) 4.23003e6 + 6.58206e6i 0.713359 + 1.11001i 0.988880 + 0.148713i \(0.0475131\pi\)
−0.275522 + 0.961295i \(0.588851\pi\)
\(182\) 3.50917e6 + 3.04071e6i 0.582090 + 0.504383i
\(183\) 892465.i 0.145626i
\(184\) 121730. 74351.5i 0.0195408 0.0119354i
\(185\) −1.34268e7 −2.12059
\(186\) −3.70273e6 + 4.27317e6i −0.575417 + 0.664067i
\(187\) 389918. 250585.i 0.0596278 0.0383205i
\(188\) 1.18199e6 + 8.22095e6i 0.177886 + 1.23722i
\(189\) −799571. + 365152.i −0.118433 + 0.0540864i
\(190\) 1.26344e6 8.78742e6i 0.184202 1.28115i
\(191\) −811561. 2.76392e6i −0.116472 0.396667i 0.880535 0.473981i \(-0.157184\pi\)
−0.997007 + 0.0773146i \(0.975365\pi\)
\(192\) 3.32505e6 + 2.13688e6i 0.469779 + 0.301909i
\(193\) −1.95404e6 + 4.27876e6i −0.271808 + 0.595177i −0.995480 0.0949670i \(-0.969725\pi\)
0.723672 + 0.690144i \(0.242453\pi\)
\(194\) 3.47391e6 1.18310e7i 0.475788 1.62038i
\(195\) 4.29319e6 3.72007e6i 0.578996 0.501703i
\(196\) −2.63053e6 3.03579e6i −0.349361 0.403184i
\(197\) −3.47467e6 1.02025e6i −0.454480 0.133447i 0.0464774 0.998919i \(-0.485200\pi\)
−0.500957 + 0.865472i \(0.667019\pi\)
\(198\) −4.84686e6 2.21349e6i −0.624403 0.285156i
\(199\) 5.24302e6 8.15830e6i 0.665307 1.03524i −0.330504 0.943805i \(-0.607219\pi\)
0.995811 0.0914339i \(-0.0291450\pi\)
\(200\) −297909. + 87473.8i −0.0372386 + 0.0109342i
\(201\) −6.71949e6 966117.i −0.827462 0.118971i
\(202\) 1.20621e6 + 2.64124e6i 0.146342 + 0.320445i
\(203\) 801037. 115172.i 0.0957557 0.0137676i
\(204\) −126376. 196645.i −0.0148858 0.0231628i
\(205\) 218623. + 189438.i 0.0253766 + 0.0219890i
\(206\) 1.34041e7i 1.53334i
\(207\) 1.88452e6 + 2.27815e6i 0.212466 + 0.256845i
\(208\) −7.39030e6 −0.821244
\(209\) 4.89317e6 5.64701e6i 0.535983 0.618557i
\(210\) 7.03610e6 4.52182e6i 0.759756 0.488265i
\(211\) 104394. + 726076.i 0.0111129 + 0.0772920i 0.994623 0.103560i \(-0.0330235\pi\)
−0.983510 + 0.180852i \(0.942114\pi\)
\(212\) 5.33560e6 2.43669e6i 0.559984 0.255736i
\(213\) 1.51510e6 1.05377e7i 0.156784 1.09046i
\(214\) 2.08636e6 + 7.10548e6i 0.212886 + 0.725024i
\(215\) −1.72292e7 1.10725e7i −1.73360 1.11412i
\(216\) 18448.0 40395.6i 0.00183058 0.00400841i
\(217\) 2.10453e6 7.16738e6i 0.205957 0.701425i
\(218\) 1.59615e7 1.38308e7i 1.54066 1.33499i
\(219\) 4.19611e6 + 4.84257e6i 0.399498 + 0.461045i
\(220\) 2.41239e7 + 7.08340e6i 2.26558 + 0.665233i
\(221\) 384740. + 175705.i 0.0356444 + 0.0162782i
\(222\) −6.21339e6 + 9.66823e6i −0.567897 + 0.883666i
\(223\) 4.97232e6 1.46000e6i 0.448378 0.131656i −0.0497451 0.998762i \(-0.515841\pi\)
0.498123 + 0.867106i \(0.334023\pi\)
\(224\) −1.05978e7 1.52374e6i −0.942915 0.135571i
\(225\) −2.67344e6 5.85403e6i −0.234706 0.513934i
\(226\) −2.03962e7 + 2.93252e6i −1.76694 + 0.254048i
\(227\) −9.72692e6 1.51354e7i −0.831568 1.29395i −0.953496 0.301406i \(-0.902544\pi\)
0.121928 0.992539i \(-0.461092\pi\)
\(228\) −2.84792e6 2.46773e6i −0.240283 0.208206i
\(229\) 1.86165e7i 1.55021i 0.631831 + 0.775106i \(0.282304\pi\)
−0.631831 + 0.775106i \(0.717696\pi\)
\(230\) −2.08338e7 1.89043e7i −1.71232 1.55373i
\(231\) 7.03949e6 0.571091
\(232\) −26774.5 + 30899.4i −0.00214416 + 0.00247449i
\(233\) 1.38298e7 8.88785e6i 1.09332 0.702634i 0.135723 0.990747i \(-0.456664\pi\)
0.957596 + 0.288113i \(0.0930279\pi\)
\(234\) −691991. 4.81291e6i −0.0540074 0.375630i
\(235\) −2.46239e7 + 1.12454e7i −1.89737 + 0.866502i
\(236\) 748136. 5.20340e6i 0.0569173 0.395869i
\(237\) 3.42918e6 + 1.16787e7i 0.257600 + 0.877304i
\(238\) 523880. + 336677.i 0.0388599 + 0.0249737i
\(239\) 5.60696e6 1.22775e7i 0.410709 0.899327i −0.585362 0.810772i \(-0.699048\pi\)
0.996071 0.0885553i \(-0.0282250\pi\)
\(240\) −3.75040e6 + 1.27727e7i −0.271297 + 0.923951i
\(241\) 2.38491e6 2.06654e6i 0.170381 0.147636i −0.565497 0.824751i \(-0.691315\pi\)
0.735877 + 0.677115i \(0.236770\pi\)
\(242\) 1.48725e7 + 1.71638e7i 1.04939 + 1.21106i
\(243\) 883197. + 259330.i 0.0615515 + 0.0180732i
\(244\) −3.27880e6 1.49738e6i −0.225707 0.103077i
\(245\) 7.07829e6 1.10140e7i 0.481316 0.748942i
\(246\) 237579. 69759.5i 0.0159589 0.00468596i
\(247\) 6.74921e6 + 970390.i 0.447881 + 0.0643955i
\(248\) 156775. + 343290.i 0.0102783 + 0.0225064i
\(249\) 1.10638e7 1.59073e6i 0.716647 0.103038i
\(250\) 1.35743e7 + 2.11220e7i 0.868753 + 1.35181i
\(251\) 1.30887e7 + 1.13414e7i 0.827705 + 0.717210i 0.961799 0.273758i \(-0.0882668\pi\)
−0.134094 + 0.990969i \(0.542812\pi\)
\(252\) 3.55017e6i 0.221844i
\(253\) −6.14925e6 2.28653e7i −0.379718 1.41194i
\(254\) −4.19359e7 −2.55908
\(255\) 498919. 575783.i 0.0300891 0.0347247i
\(256\) 1.45615e7 9.35814e6i 0.867936 0.557788i
\(257\) 3.67029e6 + 2.55274e7i 0.216223 + 1.50386i 0.751809 + 0.659381i \(0.229182\pi\)
−0.535586 + 0.844481i \(0.679909\pi\)
\(258\) −1.59460e7 + 7.28229e6i −0.928523 + 0.424042i
\(259\) 2.16081e6 1.50288e7i 0.124370 0.865015i
\(260\) 6.46394e6 + 2.20142e7i 0.367771 + 1.25251i
\(261\) −712930. 458172.i −0.0400983 0.0257696i
\(262\) 3.83603e6 8.39974e6i 0.213294 0.467049i
\(263\) 5.11883e6 1.74331e7i 0.281387 0.958315i −0.690592 0.723245i \(-0.742650\pi\)
0.971978 0.235070i \(-0.0755319\pi\)
\(264\) −268779. + 232899.i −0.0146078 + 0.0126577i
\(265\) 1.25196e7 + 1.44484e7i 0.672751 + 0.776396i
\(266\) 9.63255e6 + 2.82837e6i 0.511795 + 0.150277i
\(267\) 2.22176e6 + 1.01465e6i 0.116725 + 0.0533065i
\(268\) 1.48234e7 2.30656e7i 0.770092 1.19829i
\(269\) 9.59407e6 2.81707e6i 0.492885 0.144724i −0.0258384 0.999666i \(-0.508226\pi\)
0.518724 + 0.854942i \(0.326407\pi\)
\(270\) −8.66934e6 1.24646e6i −0.440448 0.0633269i
\(271\) 7.44509e6 + 1.63025e7i 0.374078 + 0.819116i 0.999253 + 0.0386323i \(0.0123001\pi\)
−0.625176 + 0.780484i \(0.714973\pi\)
\(272\) −981066. + 141056.i −0.0487519 + 0.00700946i
\(273\) 3.47300e6 + 5.40410e6i 0.170694 + 0.265605i
\(274\) −3.63437e7 3.14920e7i −1.76676 1.53090i
\(275\) 5.15393e7i 2.47823i
\(276\) −1.15315e7 + 3.10121e6i −0.548476 + 0.147504i
\(277\) −2.27641e7 −1.07105 −0.535527 0.844518i \(-0.679887\pi\)
−0.535527 + 0.844518i \(0.679887\pi\)
\(278\) −3.29224e7 + 3.79944e7i −1.53235 + 1.76842i
\(279\) −6.58067e6 + 4.22914e6i −0.303010 + 0.194733i
\(280\) −79447.0 552566.i −0.00361912 0.0251716i
\(281\) −2.49007e7 + 1.13717e7i −1.12226 + 0.512517i −0.888085 0.459679i \(-0.847965\pi\)
−0.234170 + 0.972196i \(0.575237\pi\)
\(282\) −3.29754e6 + 2.29349e7i −0.147042 + 1.02270i
\(283\) 5.98753e6 + 2.03917e7i 0.264173 + 0.899691i 0.979592 + 0.200996i \(0.0644177\pi\)
−0.715419 + 0.698696i \(0.753764\pi\)
\(284\) 3.61723e7 + 2.32465e7i 1.57914 + 1.01485i
\(285\) 5.10220e6 1.11723e7i 0.220406 0.482621i
\(286\) −1.09708e7 + 3.73630e7i −0.468964 + 1.59714i
\(287\) −247224. + 214221.i −0.0104579 + 0.00906183i
\(288\) 7.34232e6 + 8.47348e6i 0.307366 + 0.354719i
\(289\) −2.31054e7 6.78436e6i −0.957238 0.281070i
\(290\) 7.33499e6 + 3.34978e6i 0.300750 + 0.137348i
\(291\) 9.22276e6 1.43509e7i 0.374267 0.582371i
\(292\) −2.48312e7 + 7.29111e6i −0.997355 + 0.292850i
\(293\) 3.32659e6 + 478291.i 0.132250 + 0.0190147i 0.208122 0.978103i \(-0.433265\pi\)
−0.0758719 + 0.997118i \(0.524174\pi\)
\(294\) −4.65533e6 1.01937e7i −0.183193 0.401136i
\(295\) 1.69595e7 2.43841e6i 0.660613 0.0949817i
\(296\) 414717. + 645312.i 0.0159910 + 0.0248825i
\(297\) −5.57113e6 4.82741e6i −0.212654 0.184266i
\(298\) 2.12407e7i 0.802639i
\(299\) 1.45195e7 1.60015e7i 0.543173 0.598614i
\(300\) 2.59925e7 0.962684
\(301\) 1.51663e7 1.75029e7i 0.556137 0.641816i
\(302\) 3.86655e7 2.48488e7i 1.40379 0.902161i
\(303\) 571692. + 3.97620e6i 0.0205511 + 0.142936i
\(304\) −1.45345e7 + 6.63770e6i −0.517345 + 0.236264i
\(305\) 1.67196e6 1.16287e7i 0.0589285 0.409857i
\(306\) −183724. 625707.i −0.00641213 0.0218377i
\(307\) −1.23726e7 7.95137e6i −0.427607 0.274807i 0.309085 0.951034i \(-0.399977\pi\)
−0.736693 + 0.676228i \(0.763614\pi\)
\(308\) −1.18109e7 + 2.58622e7i −0.404231 + 0.885143i
\(309\) 5.22452e6 1.77931e7i 0.177081 0.603082i
\(310\) 5.62516e7 4.87423e7i 1.88821 1.63614i
\(311\) 2.19522e6 + 2.53342e6i 0.0729789 + 0.0842221i 0.791065 0.611732i \(-0.209527\pi\)
−0.718086 + 0.695954i \(0.754982\pi\)
\(312\) −311397. 91434.5i −0.0102530 0.00301055i
\(313\) 2.18339e7 + 9.97120e6i 0.712029 + 0.325173i 0.738291 0.674482i \(-0.235633\pi\)
−0.0262619 + 0.999655i \(0.508360\pi\)
\(314\) 8.06940e6 1.25562e7i 0.260647 0.405574i
\(315\) 1.11024e7 3.25996e6i 0.355210 0.104299i
\(316\) −4.86596e7 6.99619e6i −1.54208 0.221718i
\(317\) −7.12528e6 1.56022e7i −0.223678 0.489787i 0.764207 0.644971i \(-0.223130\pi\)
−0.987886 + 0.155183i \(0.950403\pi\)
\(318\) 1.61975e7 2.32885e6i 0.503695 0.0724203i
\(319\) 3.66926e6 + 5.70949e6i 0.113033 + 0.175883i
\(320\) −3.93217e7 3.40725e7i −1.20000 1.03981i
\(321\) 1.02452e7i 0.309747i
\(322\) 2.45126e7 2.02772e7i 0.734214 0.607353i
\(323\) 914482. 0.0271374
\(324\) −2.43457e6 + 2.80965e6i −0.0715794 + 0.0826070i
\(325\) −3.95659e7 + 2.54275e7i −1.15258 + 0.740718i
\(326\) −2.21711e6 1.54204e7i −0.0639934 0.445084i
\(327\) 2.65787e7 1.21381e7i 0.760134 0.347141i
\(328\) 2352.01 16358.6i 6.66527e−5 0.000463580i
\(329\) −8.62427e6 2.93716e7i −0.242178 0.824783i
\(330\) 5.90074e7 + 3.79217e7i 1.64197 + 1.05523i
\(331\) 9.99532e6 2.18867e7i 0.275621 0.603526i −0.720309 0.693653i \(-0.756000\pi\)
0.995930 + 0.0901269i \(0.0287273\pi\)
\(332\) −1.27187e7 + 4.33158e7i −0.347558 + 1.18367i
\(333\) −1.20162e7 + 1.04121e7i −0.325414 + 0.281972i
\(334\) −5.91567e7 6.82705e7i −1.58769 1.83229i
\(335\) 8.57443e7 + 2.51768e7i 2.28071 + 0.669678i
\(336\) −1.36931e7 6.25342e6i −0.360980 0.164854i
\(337\) 2.22855e7 3.46769e7i 0.582281 0.906047i −0.417716 0.908578i \(-0.637169\pi\)
0.999997 + 0.00253052i \(0.000805492\pi\)
\(338\) 1.80881e7 5.31115e6i 0.468429 0.137543i
\(339\) −2.82175e7 4.05707e6i −0.724302 0.104139i
\(340\) 1.27827e6 + 2.79901e6i 0.0325226 + 0.0712145i
\(341\) 6.20083e7 8.91545e6i 1.56382 0.224843i
\(342\) −5.68372e6 8.84404e6i −0.142087 0.221092i
\(343\) 3.18213e7 + 2.75733e7i 0.788563 + 0.683293i
\(344\) 1.17006e6i 0.0287431i
\(345\) −2.02872e7 3.32145e7i −0.494043 0.808855i
\(346\) −7.83542e7 −1.89162
\(347\) −4.34651e7 + 5.01613e7i −1.04028 + 1.20055i −0.0609833 + 0.998139i \(0.519424\pi\)
−0.979300 + 0.202413i \(0.935122\pi\)
\(348\) 2.87942e6 1.85049e6i 0.0683231 0.0439086i
\(349\) −9.24022e6 6.42672e7i −0.217373 1.51186i −0.747680 0.664059i \(-0.768832\pi\)
0.530307 0.847806i \(-0.322077\pi\)
\(350\) −6.29887e7 + 2.87660e7i −1.46913 + 0.670927i
\(351\) 957351. 6.65852e6i 0.0221386 0.153977i
\(352\) −2.52971e7 8.61541e7i −0.580020 1.97537i
\(353\) 6.22076e7 + 3.99784e7i 1.41423 + 0.908869i 0.999999 0.00130420i \(-0.000415139\pi\)
0.414228 + 0.910173i \(0.364052\pi\)
\(354\) 6.09238e6 1.33404e7i 0.137334 0.300719i
\(355\) −3.94831e7 + 1.34467e8i −0.882523 + 3.00560i
\(356\) −7.45535e6 + 6.46010e6i −0.165241 + 0.143182i
\(357\) 564189. + 651109.i 0.0123999 + 0.0143103i
\(358\) 2.82781e7 + 8.30319e6i 0.616312 + 0.180966i
\(359\) 3.39707e7 + 1.55139e7i 0.734212 + 0.335304i 0.747188 0.664612i \(-0.231403\pi\)
−0.0129760 + 0.999916i \(0.504131\pi\)
\(360\) −316054. + 491789.i −0.00677413 + 0.0105407i
\(361\) −3.09949e7 + 9.10093e6i −0.658823 + 0.193448i
\(362\) −8.72619e7 1.25464e7i −1.83950 0.264480i
\(363\) 1.30523e7 + 2.85806e7i 0.272877 + 0.597518i
\(364\) −2.56810e7 + 3.69237e6i −0.532485 + 0.0765598i
\(365\) −4.56028e7 7.09593e7i −0.937805 1.45925i
\(366\) −7.59979e6 6.58525e6i −0.155009 0.134316i
\(367\) 1.70815e7i 0.345564i 0.984960 + 0.172782i \(0.0552757\pi\)
−0.984960 + 0.172782i \(0.944724\pi\)
\(368\) −8.35060e6 + 4.99397e7i −0.167561 + 1.00208i
\(369\) 342560. 0.00681801
\(370\) 9.90725e7 1.14336e8i 1.95591 2.25723i
\(371\) −1.81872e7 + 1.16882e7i −0.356158 + 0.228889i
\(372\) −4.49626e6 3.12722e7i −0.0873419 0.607477i
\(373\) −4.04664e7 + 1.84804e7i −0.779773 + 0.356110i −0.765208 0.643784i \(-0.777364\pi\)
−0.0145652 + 0.999894i \(0.504636\pi\)
\(374\) −743241. + 5.16935e6i −0.0142074 + 0.0988147i
\(375\) 9.78622e6 + 3.33288e7i 0.185576 + 0.632013i
\(376\) 1.30104e6 + 836125.i 0.0244752 + 0.0157292i
\(377\) −2.57281e6 + 5.63367e6i −0.0480157 + 0.105140i
\(378\) 2.79036e6 9.50311e6i 0.0516637 0.175950i
\(379\) −3.85178e6 + 3.33759e6i −0.0707529 + 0.0613077i −0.689519 0.724267i \(-0.742178\pi\)
0.618766 + 0.785575i \(0.287633\pi\)
\(380\) 3.24850e7 + 3.74896e7i 0.592013 + 0.683220i
\(381\) −5.56670e7 1.63453e7i −1.00652 0.295541i
\(382\) 2.95245e7 + 1.34834e7i 0.529654 + 0.241885i
\(383\) 2.52306e7 3.92596e7i 0.449088 0.698794i −0.540720 0.841202i \(-0.681848\pi\)
0.989808 + 0.142408i \(0.0454846\pi\)
\(384\) 1.43627e6 421727.i 0.0253654 0.00744796i
\(385\) −9.17238e7 1.31879e7i −1.60731 0.231096i
\(386\) −2.20174e7 4.82115e7i −0.382829 0.838279i
\(387\) −2.40056e7 + 3.45149e6i −0.414172 + 0.0595489i
\(388\) 3.72494e7 + 5.79612e7i 0.637711 + 0.992298i
\(389\) −1.35164e7 1.17121e7i −0.229622 0.198969i 0.532449 0.846462i \(-0.321272\pi\)
−0.762071 + 0.647494i \(0.775817\pi\)
\(390\) 6.40080e7i 1.07905i
\(391\) 1.62205e6 2.40133e6i 0.0271353 0.0401719i
\(392\) −747981. −0.0124175
\(393\) 8.36603e6 9.65492e6i 0.137829 0.159064i
\(394\) 3.43266e7 2.20604e7i 0.561232 0.360682i
\(395\) −2.28028e7 1.58597e8i −0.369995 2.57337i
\(396\) 2.70826e7 1.23682e7i 0.436118 0.199169i
\(397\) −187878. + 1.30672e6i −0.00300264 + 0.0208838i −0.991268 0.131865i \(-0.957903\pi\)
0.988265 + 0.152749i \(0.0488126\pi\)
\(398\) 3.07852e7 + 1.04845e8i 0.488307 + 1.66302i
\(399\) 1.16841e7 + 7.50894e6i 0.183941 + 0.118212i
\(400\) 4.57842e7 1.00253e8i 0.715378 1.56646i
\(401\) 2.09783e6 7.14454e6i 0.0325339 0.110800i −0.941625 0.336663i \(-0.890702\pi\)
0.974159 + 0.225862i \(0.0725200\pi\)
\(402\) 5.78083e7 5.00912e7i 0.889840 0.771051i
\(403\) 3.74367e7 + 4.32042e7i 0.571982 + 0.660102i
\(404\) −1.55673e7 4.57096e6i −0.236085 0.0693207i
\(405\) −1.10221e7 5.03364e6i −0.165921 0.0757734i
\(406\) −4.92989e6 + 7.67106e6i −0.0736647 + 0.114624i
\(407\) 1.22175e8 3.58738e7i 1.81217 0.532101i
\(408\) −43083.3 6194.44i −0.000634349 9.12057e-5i
\(409\) −5.25971e6 1.15172e7i −0.0768762 0.168335i 0.867292 0.497801i \(-0.165859\pi\)
−0.944168 + 0.329465i \(0.893132\pi\)
\(410\) −3.22632e6 + 463875.i −0.0468118 + 0.00673053i
\(411\) −3.59691e7 5.59691e7i −0.518089 0.806163i
\(412\) 5.66039e7 + 4.90475e7i 0.809384 + 0.701335i
\(413\) 1.93754e7i 0.275043i
\(414\) −3.33049e7 762187.i −0.469362 0.0107414i
\(415\) −1.47140e8 −2.05867
\(416\) 5.36585e7 6.19252e7i 0.745347 0.860176i
\(417\) −5.85113e7 + 3.76029e7i −0.806921 + 0.518577i
\(418\) 1.19818e7 + 8.33356e7i 0.164057 + 1.14104i
\(419\) −7.52073e7 + 3.43460e7i −1.02239 + 0.466912i −0.854807 0.518946i \(-0.826325\pi\)
−0.167587 + 0.985857i \(0.553597\pi\)
\(420\) −6.65095e6 + 4.62584e7i −0.0897710 + 0.624371i
\(421\) 2.99294e7 + 1.01930e8i 0.401099 + 1.36602i 0.874438 + 0.485137i \(0.161230\pi\)
−0.473339 + 0.880880i \(0.656951\pi\)
\(422\) −6.95320e6 4.46855e6i −0.0925225 0.0594606i
\(423\) −1.33166e7 + 2.91592e7i −0.175943 + 0.385261i
\(424\) 307717. 1.04799e6i 0.00403695 0.0137486i
\(425\) −4.76707e6 + 4.13069e6i −0.0620990 + 0.0538091i
\(426\) 7.85546e7 + 9.06569e7i 1.01612 + 1.17266i
\(427\) 1.27471e7 + 3.74289e6i 0.163730 + 0.0480754i
\(428\) −3.76397e7 1.71895e7i −0.480082 0.219246i
\(429\) −2.91259e7 + 4.53208e7i −0.368899 + 0.574019i
\(430\) 2.21417e8 6.50140e7i 2.78488 0.817714i
\(431\) −5.52300e7 7.94087e6i −0.689832 0.0991828i −0.211521 0.977373i \(-0.567842\pi\)
−0.478311 + 0.878191i \(0.658751\pi\)
\(432\) 6.54851e6 + 1.43392e7i 0.0812252 + 0.177858i
\(433\) −8.77449e7 + 1.26158e7i −1.08083 + 0.155400i −0.659648 0.751575i \(-0.729294\pi\)
−0.421184 + 0.906975i \(0.638385\pi\)
\(434\) 4.55051e7 + 7.08073e7i 0.556661 + 0.866182i
\(435\) 8.43106e6 + 7.30555e6i 0.102427 + 0.0887535i
\(436\) 1.18012e8i 1.42386i
\(437\) 1.41836e7 4.45111e7i 0.169958 0.533364i
\(438\) −7.21989e7 −0.859228
\(439\) 2.85888e7 3.29932e7i 0.337911 0.389970i −0.561208 0.827675i \(-0.689663\pi\)
0.899119 + 0.437705i \(0.144209\pi\)
\(440\) 3.93848e6 2.53111e6i 0.0462350 0.0297134i
\(441\) −2.20642e6 1.53460e7i −0.0257260 0.178929i
\(442\) −4.33511e6 + 1.97978e6i −0.0502035 + 0.0229272i
\(443\) −1.78636e7 + 1.24244e8i −0.205475 + 1.42911i 0.582214 + 0.813036i \(0.302187\pi\)
−0.787689 + 0.616074i \(0.788722\pi\)
\(444\) −1.80920e7 6.16156e7i −0.206698 0.703950i
\(445\) −2.70485e7 1.73830e7i −0.306947 0.197263i
\(446\) −2.42567e7 + 5.31148e7i −0.273418 + 0.598702i
\(447\) −8.27897e6 + 2.81956e7i −0.0926945 + 0.315688i
\(448\) 4.44659e7 3.85300e7i 0.494531 0.428513i
\(449\) −5.35915e7 6.18479e7i −0.592048 0.683260i 0.378102 0.925764i \(-0.376577\pi\)
−0.970150 + 0.242504i \(0.922031\pi\)
\(450\) 6.95766e7 + 2.04295e7i 0.763530 + 0.224193i
\(451\) −2.49547e6 1.13964e6i −0.0272034 0.0124234i
\(452\) 6.22485e7 9.68606e7i 0.674084 1.04889i
\(453\) 6.10110e7 1.79145e7i 0.656317 0.192712i
\(454\) 2.00658e8 + 2.88502e7i 2.14431 + 0.308306i
\(455\) −3.51288e7 7.69212e7i −0.372931 0.816605i
\(456\) −694549. + 99861.1i −0.00732502 + 0.00105318i
\(457\) −4.91103e7 7.64172e7i −0.514546 0.800649i 0.482624 0.875828i \(-0.339684\pi\)
−0.997170 + 0.0751784i \(0.976047\pi\)
\(458\) −1.58529e8 1.37366e8i −1.65011 1.42982i
\(459\) 902194.i 0.00932958i
\(460\) 1.56064e8 1.88052e7i 1.60335 0.193198i
\(461\) −6.03203e7 −0.615688 −0.307844 0.951437i \(-0.599607\pi\)
−0.307844 + 0.951437i \(0.599607\pi\)
\(462\) −5.19425e7 + 5.99448e7i −0.526741 + 0.607891i
\(463\) −6.83343e7 + 4.39158e7i −0.688487 + 0.442464i −0.837548 0.546364i \(-0.816011\pi\)
0.149061 + 0.988828i \(0.452375\pi\)
\(464\) −2.06545e6 1.43655e7i −0.0206757 0.143803i
\(465\) 9.36683e7 4.27769e7i 0.931610 0.425452i
\(466\) −2.63615e7 + 1.83349e8i −0.260503 + 1.81184i
\(467\) −2.59497e7 8.83765e7i −0.254790 0.867733i −0.983191 0.182582i \(-0.941554\pi\)
0.728401 0.685151i \(-0.240264\pi\)
\(468\) 2.28563e7 + 1.46889e7i 0.222981 + 0.143301i
\(469\) −4.19798e7 + 9.19230e7i −0.406932 + 0.891057i
\(470\) 8.59331e7 2.92661e8i 0.827689 2.81885i
\(471\) 1.56056e7 1.35223e7i 0.149354 0.129416i
\(472\) −641027. 739784.i −0.00609607 0.00703524i
\(473\) 1.86358e8 + 5.47197e7i 1.76102 + 0.517083i
\(474\) −1.24753e8 5.69729e7i −1.17143 0.534974i
\(475\) −5.49764e7 + 8.55449e7i −0.512974 + 0.798203i
\(476\) −3.33869e6 + 980327.i −0.0309567 + 0.00908971i
\(477\) 2.24088e7 + 3.22190e6i 0.206473 + 0.0296864i
\(478\) 6.31772e7 + 1.38339e8i 0.578465 + 1.26666i
\(479\) 2.06067e8 2.96279e7i 1.87500 0.269585i 0.891844 0.452343i \(-0.149412\pi\)
0.983158 + 0.182759i \(0.0585028\pi\)
\(480\) −7.97952e7 1.24164e8i −0.721528 1.12272i
\(481\) 8.78160e7 + 7.60930e7i 0.789111 + 0.683769i
\(482\) 3.55571e7i 0.317531i
\(483\) 4.04423e7 1.73624e7i 0.358917 0.154088i
\(484\) −1.26901e8 −1.11925
\(485\) −1.47057e8 + 1.69713e8i −1.28902 + 1.48761i
\(486\) −8.72520e6 + 5.60734e6i −0.0760092 + 0.0488482i
\(487\) 1.13982e7 + 7.92763e7i 0.0986847 + 0.686367i 0.977767 + 0.209696i \(0.0672476\pi\)
−0.879082 + 0.476671i \(0.841843\pi\)
\(488\) −610537. + 278823.i −0.00525355 + 0.00239921i
\(489\) 3.06731e6 2.13336e7i 0.0262320 0.182448i
\(490\) 4.15613e7 + 1.41545e8i 0.353265 + 1.20311i
\(491\) −7.32270e7 4.70602e7i −0.618624 0.397566i 0.193458 0.981109i \(-0.438030\pi\)
−0.812082 + 0.583543i \(0.801666\pi\)
\(492\) −574748. + 1.25852e6i −0.00482594 + 0.0105673i
\(493\) −234014. + 796978.i −0.00195299 + 0.00665128i
\(494\) −5.80640e7 + 5.03127e7i −0.481644 + 0.417347i
\(495\) 6.35475e7 + 7.33378e7i 0.523942 + 0.604661i
\(496\) −1.28537e8 3.77420e7i −1.05338 0.309300i
\(497\) −1.44157e8 6.58341e7i −1.17426 0.536268i
\(498\) −6.80907e7 + 1.05951e8i −0.551315 + 0.857863i
\(499\) 9.31153e7 2.73411e7i 0.749410 0.220047i 0.115344 0.993326i \(-0.463203\pi\)
0.634066 + 0.773279i \(0.281385\pi\)
\(500\) −1.38865e8 1.99658e7i −1.11092 0.159726i
\(501\) −5.19168e7 1.13682e8i −0.412852 0.904020i
\(502\) −1.93156e8 + 2.77716e7i −1.52685 + 0.219528i
\(503\) 8.60982e7 + 1.33971e8i 0.676535 + 1.05271i 0.994513 + 0.104611i \(0.0333598\pi\)
−0.317978 + 0.948098i \(0.603004\pi\)
\(504\) −499602. 432908.i −0.00390241 0.00338146i
\(505\) 5.28805e7i 0.410603i
\(506\) 2.40083e8 + 1.16353e8i 1.85315 + 0.898100i
\(507\) 2.60809e7 0.200124
\(508\) 1.53449e8 1.77089e8i 1.17050 1.35083i
\(509\) 6.43364e7 4.13465e7i 0.487869 0.313535i −0.273479 0.961878i \(-0.588174\pi\)
0.761348 + 0.648343i \(0.224538\pi\)
\(510\) 1.22170e6 + 8.49709e6i 0.00920986 + 0.0640560i
\(511\) 8.67646e7 3.96241e7i 0.650249 0.296959i
\(512\) −2.68818e7 + 1.86967e8i −0.200285 + 1.39301i
\(513\) −4.09762e6 1.39552e7i −0.0303514 0.103367i
\(514\) −2.44461e8 1.57106e8i −1.80020 1.15692i
\(515\) −1.01409e8 + 2.22054e8i −0.742428 + 1.62569i
\(516\) 2.75964e7 9.39846e7i 0.200864 0.684081i
\(517\) 1.94016e8 1.68116e8i 1.40400 1.21657i
\(518\) 1.12033e8 + 1.29293e8i 0.806043 + 0.930223i
\(519\) −1.04010e8 3.05401e7i −0.744000 0.218458i
\(520\) 3.88618e6 + 1.77476e6i 0.0276384 + 0.0126220i
\(521\) −1.06236e7 + 1.65307e7i −0.0751206 + 0.116890i −0.876781 0.480890i \(-0.840314\pi\)
0.801661 + 0.597780i \(0.203950\pi\)
\(522\) 9.16209e6 2.69023e6i 0.0644144 0.0189138i
\(523\) 1.63449e7 + 2.35004e6i 0.114255 + 0.0164274i 0.199205 0.979958i \(-0.436164\pi\)
−0.0849500 + 0.996385i \(0.527073\pi\)
\(524\) 2.14344e7 + 4.69348e7i 0.148976 + 0.326213i
\(525\) −9.48254e7 + 1.36338e7i −0.655310 + 0.0942193i
\(526\) 1.10682e8 + 1.72224e8i 0.760533 + 1.18341i
\(527\) 5.79436e6 + 5.02084e6i 0.0395889 + 0.0343040i
\(528\) 1.26244e8i 0.857646i
\(529\) −9.17234e7 1.16196e8i −0.619602 0.784916i
\(530\) −2.15415e8 −1.44693
\(531\) 1.32869e7 1.53339e7i 0.0887443 0.102416i
\(532\) −4.71905e7 + 3.03275e7i −0.313415 + 0.201420i
\(533\) −356281. 2.47799e6i −0.00235294 0.0163651i
\(534\) −2.50340e7 + 1.14326e7i −0.164402 + 0.0750798i
\(535\) 1.91936e7 1.33494e8i 0.125342 0.871770i
\(536\) −1.43837e6 4.89865e6i −0.00934066 0.0318114i
\(537\) 3.43009e7 + 2.20438e7i 0.221505 + 0.142352i
\(538\) −4.68032e7 + 1.02485e8i −0.300558 + 0.658131i
\(539\) −3.49805e7 + 1.19133e8i −0.223388 + 0.760789i
\(540\) 3.69859e7 3.20485e7i 0.234885 0.203529i
\(541\) −5.06728e7 5.84795e7i −0.320024 0.369328i 0.572829 0.819675i \(-0.305846\pi\)
−0.892854 + 0.450347i \(0.851300\pi\)
\(542\) −1.93759e8 5.68928e7i −1.21693 0.357322i
\(543\) −1.10944e8 5.06664e7i −0.692954 0.316461i
\(544\) 5.94124e6 9.24475e6i 0.0369046 0.0574247i
\(545\) −3.69057e8 + 1.08365e8i −2.27984 + 0.669421i
\(546\) −7.16450e7 1.03010e7i −0.440158 0.0632851i
\(547\) 1.23420e7 + 2.70252e7i 0.0754091 + 0.165123i 0.943582 0.331139i \(-0.107433\pi\)
−0.868173 + 0.496262i \(0.834706\pi\)
\(548\) 2.65972e8 3.82411e7i 1.61620 0.232374i
\(549\) −7.52147e6 1.17036e7i −0.0454554 0.0707301i
\(550\) −4.38884e8 3.80295e8i −2.63792 2.28577i
\(551\) 1.33906e7i 0.0800468i
\(552\) −969726. + 2.00094e6i −0.00576543 + 0.0118964i
\(553\) 1.81189e8 1.07141
\(554\) 1.67970e8 1.93848e8i 0.987877 1.14007i
\(555\) 1.76076e8 1.13157e8i 1.02996 0.661918i
\(556\) −3.99780e7 2.78053e8i −0.232593 1.61772i
\(557\) 2.57512e8 1.17602e8i 1.49016 0.680531i 0.506774 0.862079i \(-0.330838\pi\)
0.983382 + 0.181548i \(0.0581106\pi\)
\(558\) 1.25437e7 8.72434e7i 0.0721977 0.502146i
\(559\) 4.99343e7 + 1.70061e8i 0.285867 + 0.973572i
\(560\) 1.66704e8 + 1.07134e8i 0.949254 + 0.610049i
\(561\) −3.00146e6 + 6.57227e6i −0.0169998 + 0.0372243i
\(562\) 8.68990e7 2.95951e8i 0.489560 1.66729i
\(563\) 1.21378e8 1.05174e8i 0.680163 0.589365i −0.244730 0.969591i \(-0.578699\pi\)
0.924893 + 0.380227i \(0.124154\pi\)
\(564\) −8.47847e7 9.78467e7i −0.472585 0.545392i
\(565\) 3.60071e8 + 1.05726e8i 1.99638 + 0.586189i
\(566\) −2.17826e8 9.94777e7i −1.20132 0.548626i
\(567\) 7.40804e6 1.15271e7i 0.0406400 0.0632371i
\(568\) 7.68223e6 2.25571e6i 0.0419220 0.0123094i
\(569\) −1.09384e8 1.57271e7i −0.593770 0.0853713i −0.161123 0.986934i \(-0.551511\pi\)
−0.432648 + 0.901563i \(0.642421\pi\)
\(570\) 5.74897e7 + 1.25885e8i 0.310431 + 0.679749i
\(571\) 1.05483e8 1.51662e7i 0.566598 0.0814645i 0.146938 0.989146i \(-0.453058\pi\)
0.419660 + 0.907681i \(0.362149\pi\)
\(572\) −1.17635e8 1.83044e8i −0.628565 0.978066i
\(573\) 3.39363e7 + 2.94060e7i 0.180385 + 0.156305i
\(574\) 3.68591e6i 0.0194899i
\(575\) 1.27118e8 + 2.96097e8i 0.668658 + 1.55751i
\(576\) −6.16132e7 −0.322409
\(577\) 1.80182e8 2.07941e8i 0.937959 1.08246i −0.0584918 0.998288i \(-0.518629\pi\)
0.996451 0.0841748i \(-0.0268254\pi\)
\(578\) 2.28261e8 1.46694e8i 1.18208 0.759678i
\(579\) −1.04353e7 7.25792e7i −0.0537613 0.373918i
\(580\) −4.09853e7 + 1.87174e7i −0.210060 + 0.0959314i
\(581\) 2.36797e7 1.64696e8i 0.120739 0.839757i
\(582\) 5.41529e7 + 1.84428e8i 0.274696 + 0.935529i
\(583\) −1.52524e8 9.80214e7i −0.769721 0.494670i
\(584\) −2.00187e6 + 4.38348e6i −0.0100507 + 0.0220080i
\(585\) −2.49484e7 + 8.49663e7i −0.124616 + 0.424404i
\(586\) −2.86189e7 + 2.47984e7i −0.142220 + 0.123234i
\(587\) −5.24661e7 6.05491e7i −0.259397 0.299360i 0.611081 0.791568i \(-0.290735\pi\)
−0.870477 + 0.492209i \(0.836190\pi\)
\(588\) 6.00812e7 + 1.76414e7i 0.295534 + 0.0867765i
\(589\) 1.12431e8 + 5.13457e7i 0.550226 + 0.251280i
\(590\) −1.04375e8 + 1.62411e8i −0.508208 + 0.790787i
\(591\) 5.41647e7 1.59042e7i 0.262394 0.0770459i
\(592\) −2.69520e8 3.87512e7i −1.29905 0.186775i
\(593\) −1.32343e7 2.89791e7i −0.0634655 0.138970i 0.875241 0.483686i \(-0.160702\pi\)
−0.938707 + 0.344716i \(0.887975\pi\)
\(594\) 8.22158e7 1.18208e7i 0.392280 0.0564013i
\(595\) −6.13152e6 9.54084e6i −0.0291083 0.0452935i
\(596\) −8.96965e7 7.77225e7i −0.423679 0.367120i
\(597\) 1.51174e8i 0.710482i
\(598\) 2.91255e7 + 2.41712e8i 0.136197 + 1.13030i
\(599\) 3.33888e7 0.155353 0.0776767 0.996979i \(-0.475250\pi\)
0.0776767 + 0.996979i \(0.475250\pi\)
\(600\) 3.16952e6 3.65782e6i 0.0146737 0.0169343i
\(601\) −1.82832e8 + 1.17499e8i −0.842226 + 0.541266i −0.889141 0.457633i \(-0.848697\pi\)
0.0469152 + 0.998899i \(0.485061\pi\)
\(602\) 3.71377e7 + 2.58298e8i 0.170226 + 1.18395i
\(603\) 9.62606e7 4.39607e7i 0.439032 0.200499i
\(604\) −3.65490e7 + 2.54204e8i −0.165869 + 1.15364i
\(605\) −1.16527e8 3.96854e8i −0.526211 1.79211i
\(606\) −3.80778e7 2.44711e7i −0.171101 0.109960i
\(607\) −1.40254e8 + 3.07113e8i −0.627118 + 1.37320i 0.283110 + 0.959087i \(0.408634\pi\)
−0.910228 + 0.414108i \(0.864093\pi\)
\(608\) 4.99114e7 1.69983e8i 0.222069 0.756299i
\(609\) −9.53404e6 + 8.26129e6i −0.0422109 + 0.0365760i
\(610\) 8.66875e7 + 1.00043e8i 0.381915 + 0.440754i
\(611\) 2.24780e8 + 6.60013e7i 0.985447 + 0.289353i
\(612\) 3.31455e6 + 1.51370e6i 0.0144601 + 0.00660368i
\(613\) 9.03812e7 1.40636e8i 0.392371 0.610541i −0.587726 0.809060i \(-0.699977\pi\)
0.980097 + 0.198519i \(0.0636132\pi\)
\(614\) 1.59004e8 4.66878e7i 0.686914 0.201696i
\(615\) −4.46352e6 641758.i −0.0191890 0.00275896i
\(616\) 2.19927e6 + 4.81573e6i 0.00940885 + 0.0206025i
\(617\) −3.17018e8 + 4.55803e7i −1.34967 + 0.194053i −0.778948 0.627089i \(-0.784246\pi\)
−0.570724 + 0.821142i \(0.693337\pi\)
\(618\) 1.12967e8 + 1.75780e8i 0.478614 + 0.744739i
\(619\) −1.95481e8 1.69385e8i −0.824201 0.714174i 0.136836 0.990594i \(-0.456307\pi\)
−0.961037 + 0.276419i \(0.910852\pi\)
\(620\) 4.15897e8i 1.74506i
\(621\) −4.39130e7 1.39930e7i −0.183366 0.0584300i
\(622\) −3.77713e7 −0.156961
\(623\) 2.38100e7 2.74782e7i 0.0984681 0.113638i
\(624\) 9.69153e7 6.22837e7i 0.398876 0.256342i
\(625\) −6.18317e6 4.30049e7i −0.0253263 0.176148i
\(626\) −2.46016e8 + 1.12352e8i −1.00286 + 0.457991i
\(627\) −1.65766e7 + 1.15292e8i −0.0672499 + 0.467733i
\(628\) 2.34962e7 + 8.00208e7i 0.0948679 + 0.323090i
\(629\) 1.31100e7 + 8.42526e6i 0.0526805 + 0.0338557i
\(630\) −5.41614e7 + 1.18597e8i −0.216605 + 0.474299i
\(631\) 1.74293e7 5.93586e7i 0.0693730 0.236263i −0.917507 0.397721i \(-0.869801\pi\)
0.986880 + 0.161458i \(0.0516195\pi\)
\(632\) −6.91809e6 + 5.99456e6i −0.0274053 + 0.0237469i
\(633\) −7.48819e6 8.64184e6i −0.0295234 0.0340718i
\(634\) 1.85436e8 + 5.44489e7i 0.727656 + 0.213659i
\(635\) 6.94714e8 + 3.17265e8i 2.71322 + 1.23909i
\(636\) −4.94344e7 + 7.69215e7i −0.192158 + 0.299003i
\(637\) −1.08714e8 + 3.19213e7i −0.420598 + 0.123499i
\(638\) −7.56937e7 1.08831e7i −0.291472 0.0419074i
\(639\) 6.89407e7 + 1.50959e8i 0.264224 + 0.578571i
\(640\) −1.95045e7 + 2.80433e6i −0.0744038 + 0.0106977i
\(641\) −1.28385e8 1.99770e8i −0.487459 0.758502i 0.507187 0.861836i \(-0.330685\pi\)
−0.994647 + 0.103334i \(0.967049\pi\)
\(642\) −8.72434e7 7.55969e7i −0.329707 0.285692i
\(643\) 4.24391e8i 1.59637i −0.602412 0.798185i \(-0.705794\pi\)
0.602412 0.798185i \(-0.294206\pi\)
\(644\) −4.06693e6 + 1.77711e8i −0.0152268 + 0.665358i
\(645\) 3.19257e8 1.18977
\(646\) −6.74772e6 + 7.78728e6i −0.0250299 + 0.0288861i
\(647\) −3.85687e8 + 2.47866e8i −1.42404 + 0.915176i −0.424087 + 0.905621i \(0.639405\pi\)
−0.999954 + 0.00955461i \(0.996959\pi\)
\(648\) 98519.3 + 685217.i 0.000362073 + 0.00251827i
\(649\) −1.47806e8 + 6.75005e7i −0.540700 + 0.246930i
\(650\) 7.54184e7 5.24546e8i 0.274623 1.91005i
\(651\) 3.28064e7 + 1.11728e8i 0.118909 + 0.404968i
\(652\) 7.32307e7 + 4.70625e7i 0.264211 + 0.169798i
\(653\) −8.51007e7 + 1.86344e8i −0.305628 + 0.669232i −0.998664 0.0516707i \(-0.983545\pi\)
0.693036 + 0.720903i \(0.256273\pi\)
\(654\) −9.27550e7 + 3.15894e8i −0.331592 + 1.12930i
\(655\) −1.27096e8 + 1.10129e8i −0.452281 + 0.391904i
\(656\) 3.84176e6 + 4.43363e6i 0.0136088 + 0.0157054i
\(657\) −9.58392e7 2.81409e7i −0.337946 0.0992298i
\(658\) 3.13750e8 + 1.43285e8i 1.10130 + 0.502948i
\(659\) −1.03392e8 + 1.60881e8i −0.361268 + 0.562144i −0.973544 0.228500i \(-0.926618\pi\)
0.612276 + 0.790644i \(0.290254\pi\)
\(660\) −3.76054e8 + 1.10419e8i −1.30803 + 0.384073i
\(661\) −2.75222e8 3.95709e7i −0.952967 0.137016i −0.351743 0.936097i \(-0.614411\pi\)
−0.601224 + 0.799080i \(0.705320\pi\)
\(662\) 1.12624e8 + 2.46611e8i 0.388200 + 0.850039i
\(663\) −6.52623e6 + 938330.i −0.0223935 + 0.00321970i
\(664\) 4.54476e6 + 7.07178e6i 0.0155241 + 0.0241560i
\(665\) −1.38176e8 1.19730e8i −0.469858 0.407134i
\(666\) 1.79153e8i 0.606458i
\(667\) 3.51622e7 + 2.37514e7i 0.118495 + 0.0800408i
\(668\) 5.04759e8 1.69338
\(669\) −5.29017e7 + 6.10518e7i −0.176681 + 0.203901i
\(670\) −8.47077e8 + 5.44384e8i −2.81643 + 1.81001i
\(671\) 1.58560e7 + 1.10281e8i 0.0524840 + 0.365034i
\(672\) 1.51820e8 6.93338e7i 0.500289 0.228474i
\(673\) 1.04790e7 7.28830e7i 0.0343775 0.239101i −0.965387 0.260823i \(-0.916006\pi\)
0.999764 + 0.0217226i \(0.00691506\pi\)
\(674\) 1.30853e8 + 4.45644e8i 0.427370 + 1.45549i
\(675\) 8.43954e7 + 5.42377e7i 0.274415 + 0.176356i
\(676\) −4.37586e7 + 9.58179e7i −0.141652 + 0.310175i
\(677\) 1.11934e8 3.81211e8i 0.360740 1.22857i −0.556707 0.830709i \(-0.687935\pi\)
0.917447 0.397858i \(-0.130246\pi\)
\(678\) 2.42757e8 2.10350e8i 0.778903 0.674923i
\(679\) −1.66295e8 1.91915e8i −0.531215 0.613055i
\(680\) 549766. + 161426.i 0.00174844 + 0.000513389i
\(681\) 2.55115e8 + 1.16507e8i 0.807782 + 0.368902i
\(682\) −3.81623e8 + 5.93817e8i −1.20304 + 1.87197i
\(683\) −4.07859e8 + 1.19758e8i −1.28011 + 0.375875i −0.849944 0.526874i \(-0.823364\pi\)
−0.430169 + 0.902748i \(0.641546\pi\)
\(684\) 5.81446e7 + 8.35993e6i 0.181694 + 0.0261237i
\(685\) 3.63821e8 + 7.96656e8i 1.13192 + 2.47856i
\(686\) −4.69602e8 + 6.75186e7i −1.45465 + 0.209147i
\(687\) −1.56895e8 2.44134e8i −0.483882 0.752935i
\(688\) −3.13891e8 2.71988e8i −0.963859 0.835188i
\(689\) 1.65450e8i 0.505836i
\(690\) 4.32532e8 + 7.23252e7i 1.31665 + 0.220162i
\(691\) 5.37861e8 1.63018 0.815091 0.579333i \(-0.196687\pi\)
0.815091 + 0.579333i \(0.196687\pi\)
\(692\) 2.86708e8 3.30879e8i 0.865211 0.998507i
\(693\) −9.23148e7 + 5.93271e7i −0.277378 + 0.178260i
\(694\) −1.06432e8 7.40254e8i −0.318417 2.21464i
\(695\) 8.32841e8 3.80346e8i 2.48089 1.13299i
\(696\) 90703.8 630859.i 0.000269028 0.00187113i
\(697\) −94592.8 322154.i −0.000279357 0.000951403i
\(698\) 6.15449e8 + 3.95525e8i 1.80978 + 1.16307i
\(699\) −1.06457e8 + 2.33108e8i −0.311704 + 0.682535i
\(700\) 1.09009e8 3.71251e8i 0.317811 1.08237i
\(701\) 3.03913e8 2.63343e8i 0.882259 0.764481i −0.0905986 0.995887i \(-0.528878\pi\)
0.972857 + 0.231406i \(0.0743326\pi\)
\(702\) 4.96367e7 + 5.72838e7i 0.143480 + 0.165585i
\(703\) 2.41052e8 + 7.07792e7i 0.693817 + 0.203723i
\(704\) 4.48838e8 + 2.04977e8i 1.28639 + 0.587473i
\(705\) 2.28141e8 3.54994e8i 0.651082 1.01310i
\(706\) −7.99449e8 + 2.34740e8i −2.27184 + 0.667071i
\(707\) 5.91899e7 + 8.51022e6i 0.167490 + 0.0240814i
\(708\) 3.40420e7 + 7.45417e7i 0.0959215 + 0.210039i
\(709\) 2.33352e8 3.35510e7i 0.654747 0.0941385i 0.193068 0.981185i \(-0.438156\pi\)
0.461679 + 0.887047i \(0.347247\pi\)
\(710\) −8.53721e8 1.32842e9i −2.38529 3.71158i
\(711\) −1.43395e8 1.24253e8i −0.398956 0.345698i
\(712\) 1.83691e6i 0.00508917i
\(713\) 3.34252e8 2.04159e8i 0.922159 0.563248i
\(714\) −9.70752e6 −0.0266694
\(715\) 4.64412e8 5.35961e8i 1.27053 1.46627i
\(716\) −1.38536e8 + 8.90319e7i −0.377420 + 0.242553i
\(717\) 2.99433e7 + 2.08260e8i 0.0812347 + 0.565000i
\(718\) −3.82770e8 + 1.74805e8i −1.03410 + 0.472260i
\(719\) −4.71800e7 + 3.28144e8i −0.126932 + 0.882832i 0.822479 + 0.568796i \(0.192590\pi\)
−0.949411 + 0.314036i \(0.898319\pi\)
\(720\) −5.84630e7 1.99107e8i −0.156633 0.533443i
\(721\) −2.32228e8 1.49244e8i −0.619597 0.398191i
\(722\) 1.51204e8 3.31091e8i 0.401746 0.879702i
\(723\) −1.38591e7 + 4.71997e7i −0.0366707 + 0.124889i
\(724\) 3.72284e8 3.22586e8i 0.980977 0.850021i
\(725\) −6.04847e7 6.98031e7i −0.158720 0.183173i
\(726\) −3.39687e8 9.97412e7i −0.887707 0.260654i
\(727\) −4.69212e8 2.14282e8i −1.22114 0.557676i −0.302643 0.953104i \(-0.597869\pi\)
−0.918497 + 0.395428i \(0.870596\pi\)
\(728\) −2.61192e6 + 4.06423e6i −0.00676965 + 0.0105338i
\(729\) −1.37677e7 + 4.04255e6i −0.0355368 + 0.0104345i
\(730\) 9.40745e8 + 1.35259e8i 2.41826 + 0.347693i
\(731\) 9.87468e6 + 2.16225e7i 0.0252796 + 0.0553547i
\(732\) 5.56172e7 7.99655e6i 0.141800 0.0203878i
\(733\) −6.38266e7 9.93162e7i −0.162065 0.252179i 0.750718 0.660623i \(-0.229708\pi\)
−0.912783 + 0.408444i \(0.866071\pi\)
\(734\) −1.45458e8 1.26040e8i −0.367832 0.318728i
\(735\) 2.04090e8i 0.513997i
\(736\) −3.57826e8 4.32567e8i −0.897509 1.08498i
\(737\) −8.47486e8 −2.11705
\(738\) −2.52766e6 + 2.91707e6i −0.00628853 + 0.00725736i
\(739\) 4.74662e8 3.05046e8i 1.17612 0.755845i 0.201449 0.979499i \(-0.435435\pi\)
0.974669 + 0.223654i \(0.0717986\pi\)
\(740\) 1.20305e8 + 8.36738e8i 0.296885 + 2.06488i
\(741\) −9.66863e7 + 4.41552e7i −0.237635 + 0.108524i
\(742\) 3.46674e7 2.41117e8i 0.0848612 0.590222i
\(743\) −1.02806e8 3.50124e8i −0.250640 0.853602i −0.984661 0.174476i \(-0.944177\pi\)
0.734021 0.679126i \(-0.237641\pi\)
\(744\) −4.94909e6 3.18059e6i −0.0120173 0.00772304i
\(745\) 1.60696e8 3.51876e8i 0.388630 0.850982i
\(746\) 1.41221e8 4.80954e8i 0.340159 1.15848i
\(747\) −1.31682e8 + 1.14103e8i −0.315912 + 0.273739i
\(748\) −1.91099e7 2.20539e7i −0.0456617 0.0526965i
\(749\) 1.46333e8 + 4.29673e7i 0.348255 + 0.102257i
\(750\) −3.56022e8 1.62590e8i −0.843903 0.385398i
\(751\) −8.47727e7 + 1.31909e8i −0.200141 + 0.311426i −0.926788 0.375586i \(-0.877441\pi\)
0.726646 + 0.687012i \(0.241078\pi\)
\(752\) −5.26740e8 + 1.54665e8i −1.23863 + 0.363695i
\(753\) −2.67226e8 3.84213e7i −0.625884 0.0899885i
\(754\) −2.89895e7 6.34781e7i −0.0676279 0.148085i
\(755\) −8.28529e8 + 1.19124e8i −1.92516 + 0.276796i
\(756\) 2.99200e7 + 4.65564e7i 0.0692463 + 0.107749i
\(757\) 4.08608e8 + 3.54061e8i 0.941931 + 0.816188i 0.983120 0.182964i \(-0.0585690\pi\)
−0.0411887 + 0.999151i \(0.513114\pi\)
\(758\) 5.74270e7i 0.131859i
\(759\) 2.73343e8 + 2.48027e8i 0.625148 + 0.567249i
\(760\) 9.23699e6 0.0210421
\(761\) −3.95173e8 + 4.56054e8i −0.896672 + 1.03481i 0.102525 + 0.994730i \(0.467308\pi\)
−0.999196 + 0.0400839i \(0.987237\pi\)
\(762\) 5.49940e8 3.53425e8i 1.24294 0.798790i
\(763\) −6.19008e7 4.30530e8i −0.139355 0.969236i
\(764\) −1.64972e8 + 7.53404e7i −0.369940 + 0.168946i
\(765\) −1.69018e6 + 1.17555e7i