Properties

Label 69.7.f.a.7.2
Level $69$
Weight $7$
Character 69.7
Analytic conductor $15.874$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 7.2
Character \(\chi\) \(=\) 69.7
Dual form 69.7.f.a.10.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.70976 + 11.2057i) q^{2} +(13.1138 - 8.42776i) q^{3} +(-22.1792 - 154.260i) q^{4} +(28.9455 - 13.2190i) q^{5} +(-32.8937 + 228.781i) q^{6} +(60.2734 + 205.272i) q^{7} +(1145.64 + 736.258i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})\) \(q+(-9.70976 + 11.2057i) q^{2} +(13.1138 - 8.42776i) q^{3} +(-22.1792 - 154.260i) q^{4} +(28.9455 - 13.2190i) q^{5} +(-32.8937 + 228.781i) q^{6} +(60.2734 + 205.272i) q^{7} +(1145.64 + 736.258i) q^{8} +(100.946 - 221.041i) q^{9} +(-132.927 + 452.706i) q^{10} +(-69.4560 + 60.1840i) q^{11} +(-1590.92 - 1836.02i) q^{12} +(-3136.24 - 920.882i) q^{13} +(-2885.45 - 1317.74i) q^{14} +(268.181 - 417.297i) q^{15} +(-9804.00 + 2878.71i) q^{16} +(891.372 + 128.160i) q^{17} +(1496.75 + 3277.42i) q^{18} +(-5500.63 + 790.871i) q^{19} +(-2681.15 - 4171.94i) q^{20} +(2520.40 + 2183.94i) q^{21} -1362.67i q^{22} +(-506.963 - 12156.4i) q^{23} +21228.7 q^{24} +(-9569.10 + 11043.3i) q^{25} +(40771.2 - 26202.1i) q^{26} +(-539.088 - 3749.44i) q^{27} +(30328.5 - 13850.6i) q^{28} +(3482.95 - 24224.5i) q^{29} +(2072.12 + 7056.99i) q^{30} +(3404.85 + 2188.17i) q^{31} +(26730.4 - 58531.3i) q^{32} +(-403.619 + 1374.60i) q^{33} +(-10091.1 + 8744.01i) q^{34} +(4458.13 + 5144.96i) q^{35} +(-36336.6 - 10669.4i) q^{36} +(-7702.24 - 3517.50i) q^{37} +(44547.5 - 69317.3i) q^{38} +(-48889.1 + 14355.1i) q^{39} +(42893.7 + 6167.18i) q^{40} +(-3482.20 - 7624.94i) q^{41} +(-48945.0 + 7037.23i) q^{42} +(-76974.2 - 119774. i) q^{43} +(10824.5 + 9379.45i) q^{44} -7732.53i q^{45} +(141143. + 112355. i) q^{46} -119592. q^{47} +(-104307. + 120377. i) q^{48} +(60468.7 - 38860.9i) q^{49} +(-30834.1 - 214456. i) q^{50} +(12769.4 - 5831.59i) q^{51} +(-72495.9 + 504220. i) q^{52} +(-1797.38 - 6121.30i) q^{53} +(47249.4 + 30365.3i) q^{54} +(-1214.87 + 2660.19i) q^{55} +(-82081.8 + 279545. i) q^{56} +(-65469.1 + 56729.3i) q^{57} +(237632. + 274242. i) q^{58} +(-117702. - 34560.4i) q^{59} +(-70320.3 - 32114.2i) q^{60} +(-43756.1 + 68085.8i) q^{61} +(-57580.2 + 16907.1i) q^{62} +(51457.9 + 7398.53i) q^{63} +(124678. + 273007. i) q^{64} +(-102953. + 14802.4i) q^{65} +(-11484.3 - 17869.9i) q^{66} +(-414164. - 358875. i) q^{67} -140345. i q^{68} +(-109100. - 155145. i) q^{69} -100940. q^{70} +(214254. - 247263. i) q^{71} +(278390. - 178911. i) q^{72} +(-88796.7 - 617594. i) q^{73} +(114203. - 52154.7i) q^{74} +(-32417.2 + 225467. i) q^{75} +(243999. + 830985. i) q^{76} +(-16540.5 - 10629.9i) q^{77} +(313843. - 687220. i) q^{78} +(-215813. + 734992. i) q^{79} +(-245728. + 212924. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(119254. + 35016.1i) q^{82} +(809609. + 369736. i) q^{83} +(280994. - 437235. i) q^{84} +(27495.3 - 8073.36i) q^{85} +(2.08955e6 + 300432. i) q^{86} +(-158483. - 347029. i) q^{87} +(-123882. + 17811.6i) q^{88} +(-261310. - 406607. i) q^{89} +(86648.1 + 75081.0i) q^{90} -699288. i q^{91} +(-1.86401e6 + 347824. i) q^{92} +63092.0 q^{93} +(1.16121e6 - 1.34011e6i) q^{94} +(-148764. + 95604.7i) q^{95} +(-142750. - 992848. i) q^{96} +(-1.25587e6 + 573535. i) q^{97} +(-151675. + 1.05492e6i) q^{98} +(6291.81 + 21427.9i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.70976 + 11.2057i −1.21372 + 1.40071i −0.322849 + 0.946450i \(0.604641\pi\)
−0.890871 + 0.454257i \(0.849905\pi\)
\(3\) 13.1138 8.42776i 0.485698 0.312139i
\(4\) −22.1792 154.260i −0.346551 2.41031i
\(5\) 28.9455 13.2190i 0.231564 0.105752i −0.296254 0.955109i \(-0.595738\pi\)
0.527818 + 0.849357i \(0.323010\pi\)
\(6\) −32.8937 + 228.781i −0.152286 + 1.05917i
\(7\) 60.2734 + 205.272i 0.175724 + 0.598462i 0.999502 + 0.0315493i \(0.0100441\pi\)
−0.823778 + 0.566913i \(0.808138\pi\)
\(8\) 1145.64 + 736.258i 2.23758 + 1.43800i
\(9\) 100.946 221.041i 0.138472 0.303211i
\(10\) −132.927 + 452.706i −0.132927 + 0.452706i
\(11\) −69.4560 + 60.1840i −0.0521833 + 0.0452171i −0.680562 0.732690i \(-0.738264\pi\)
0.628379 + 0.777908i \(0.283719\pi\)
\(12\) −1590.92 1836.02i −0.920672 1.06251i
\(13\) −3136.24 920.882i −1.42751 0.419154i −0.525471 0.850811i \(-0.676111\pi\)
−0.902038 + 0.431657i \(0.857929\pi\)
\(14\) −2885.45 1317.74i −1.05155 0.480227i
\(15\) 268.181 417.297i 0.0794609 0.123644i
\(16\) −9804.00 + 2878.71i −2.39355 + 0.702811i
\(17\) 891.372 + 128.160i 0.181431 + 0.0260859i 0.232432 0.972613i \(-0.425332\pi\)
−0.0510003 + 0.998699i \(0.516241\pi\)
\(18\) 1496.75 + 3277.42i 0.256644 + 0.561971i
\(19\) −5500.63 + 790.871i −0.801957 + 0.115304i −0.531093 0.847313i \(-0.678219\pi\)
−0.270864 + 0.962618i \(0.587309\pi\)
\(20\) −2681.15 4171.94i −0.335143 0.521493i
\(21\) 2520.40 + 2183.94i 0.272152 + 0.235821i
\(22\) 1362.67i 0.127974i
\(23\) −506.963 12156.4i −0.0416671 0.999132i
\(24\) 21228.7 1.53564
\(25\) −9569.10 + 11043.3i −0.612422 + 0.706773i
\(26\) 40771.2 26202.1i 2.31971 1.49079i
\(27\) −539.088 3749.44i −0.0273885 0.190491i
\(28\) 30328.5 13850.6i 1.38158 0.630948i
\(29\) 3482.95 24224.5i 0.142808 0.993253i −0.784813 0.619732i \(-0.787241\pi\)
0.927622 0.373521i \(-0.121850\pi\)
\(30\) 2072.12 + 7056.99i 0.0767452 + 0.261370i
\(31\) 3404.85 + 2188.17i 0.114291 + 0.0734506i 0.596538 0.802585i \(-0.296543\pi\)
−0.482246 + 0.876036i \(0.660179\pi\)
\(32\) 26730.4 58531.3i 0.815746 1.78623i
\(33\) −403.619 + 1374.60i −0.0112313 + 0.0382503i
\(34\) −10091.1 + 8744.01i −0.256745 + 0.222471i
\(35\) 4458.13 + 5144.96i 0.103980 + 0.119999i
\(36\) −36336.6 10669.4i −0.778820 0.228682i
\(37\) −7702.24 3517.50i −0.152059 0.0694430i 0.337932 0.941171i \(-0.390273\pi\)
−0.489991 + 0.871728i \(0.663000\pi\)
\(38\) 44547.5 69317.3i 0.811844 1.26325i
\(39\) −48889.1 + 14355.1i −0.824173 + 0.241999i
\(40\) 42893.7 + 6167.18i 0.670213 + 0.0963621i
\(41\) −3482.20 7624.94i −0.0505244 0.110633i 0.882686 0.469963i \(-0.155733\pi\)
−0.933211 + 0.359330i \(0.883005\pi\)
\(42\) −48945.0 + 7037.23i −0.660633 + 0.0949847i
\(43\) −76974.2 119774.i −0.968143 1.50646i −0.858707 0.512466i \(-0.828732\pi\)
−0.109436 0.993994i \(-0.534904\pi\)
\(44\) 10824.5 + 9379.45i 0.127072 + 0.110108i
\(45\) 7732.53i 0.0848563i
\(46\) 141143. + 112355.i 1.45006 + 1.15430i
\(47\) −119592. −1.15189 −0.575943 0.817490i \(-0.695365\pi\)
−0.575943 + 0.817490i \(0.695365\pi\)
\(48\) −104307. + 120377.i −0.943170 + 1.08848i
\(49\) 60468.7 38860.9i 0.513976 0.330312i
\(50\) −30834.1 214456.i −0.246673 1.71565i
\(51\) 12769.4 5831.59i 0.0962632 0.0439619i
\(52\) −72495.9 + 504220.i −0.515589 + 3.58600i
\(53\) −1797.38 6121.30i −0.0120729 0.0411165i 0.953236 0.302226i \(-0.0977298\pi\)
−0.965309 + 0.261110i \(0.915912\pi\)
\(54\) 47249.4 + 30365.3i 0.300064 + 0.192840i
\(55\) −1214.87 + 2660.19i −0.00730199 + 0.0159891i
\(56\) −82081.8 + 279545.i −0.467394 + 1.59180i
\(57\) −65469.1 + 56729.3i −0.353518 + 0.306325i
\(58\) 237632. + 274242.i 1.21793 + 1.40556i
\(59\) −117702. 34560.4i −0.573097 0.168276i −0.0176730 0.999844i \(-0.505626\pi\)
−0.555424 + 0.831567i \(0.687444\pi\)
\(60\) −70320.3 32114.2i −0.325557 0.148677i
\(61\) −43756.1 + 68085.8i −0.192774 + 0.299963i −0.924163 0.381998i \(-0.875236\pi\)
0.731389 + 0.681961i \(0.238872\pi\)
\(62\) −57580.2 + 16907.1i −0.241600 + 0.0709403i
\(63\) 51457.9 + 7398.53i 0.205793 + 0.0295886i
\(64\) 124678. + 273007.i 0.475609 + 1.04144i
\(65\) −102953. + 14802.4i −0.374886 + 0.0539005i
\(66\) −11484.3 17869.9i −0.0399458 0.0621570i
\(67\) −414164. 358875.i −1.37704 1.19322i −0.958525 0.285008i \(-0.908004\pi\)
−0.418519 0.908208i \(-0.637451\pi\)
\(68\) 140345.i 0.446346i
\(69\) −109100. 155145.i −0.332106 0.472270i
\(70\) −100940. −0.294286
\(71\) 214254. 247263.i 0.598625 0.690850i −0.372877 0.927881i \(-0.621629\pi\)
0.971502 + 0.237031i \(0.0761742\pi\)
\(72\) 278390. 178911.i 0.745859 0.479334i
\(73\) −88796.7 617594.i −0.228259 1.58758i −0.705439 0.708771i \(-0.749250\pi\)
0.477180 0.878806i \(-0.341659\pi\)
\(74\) 114203. 52154.7i 0.281826 0.128706i
\(75\) −32417.2 + 225467.i −0.0768407 + 0.534439i
\(76\) 243999. + 830985.i 0.555838 + 1.89301i
\(77\) −16540.5 10629.9i −0.0362306 0.0232840i
\(78\) 313843. 687220.i 0.661345 1.44814i
\(79\) −215813. + 734992.i −0.437720 + 1.49074i 0.385335 + 0.922777i \(0.374086\pi\)
−0.823055 + 0.567962i \(0.807732\pi\)
\(80\) −245728. + 212924.i −0.479937 + 0.415868i
\(81\) −38668.9 44626.3i −0.0727623 0.0839722i
\(82\) 119254. + 35016.1i 0.216287 + 0.0635076i
\(83\) 809609. + 369736.i 1.41593 + 0.646633i 0.968801 0.247838i \(-0.0797201\pi\)
0.447126 + 0.894471i \(0.352447\pi\)
\(84\) 280994. 437235.i 0.474088 0.737696i
\(85\) 27495.3 8073.36i 0.0447716 0.0131461i
\(86\) 2.08955e6 + 300432.i 3.28516 + 0.472335i
\(87\) −158483. 347029.i −0.240672 0.526997i
\(88\) −123882. + 17811.6i −0.181787 + 0.0261370i
\(89\) −261310. 406607.i −0.370669 0.576772i 0.604944 0.796268i \(-0.293195\pi\)
−0.975614 + 0.219495i \(0.929559\pi\)
\(90\) 86648.1 + 75081.0i 0.118859 + 0.102992i
\(91\) 699288.i 0.927966i
\(92\) −1.86401e6 + 347824.i −2.39378 + 0.446680i
\(93\) 63092.0 0.0784379
\(94\) 1.16121e6 1.34011e6i 1.39807 1.61345i
\(95\) −148764. + 95604.7i −0.173511 + 0.111509i
\(96\) −142750. 992848.i −0.161347 1.12220i
\(97\) −1.25587e6 + 573535.i −1.37603 + 0.628412i −0.959758 0.280827i \(-0.909391\pi\)
−0.416273 + 0.909240i \(0.636664\pi\)
\(98\) −151675. + 1.05492e6i −0.161152 + 1.12084i
\(99\) 6291.81 + 21427.9i 0.00648440 + 0.0220838i
\(100\) 1.91578e6 + 1.23120e6i 1.91578 + 1.23120i
\(101\) −229593. + 502739.i −0.222841 + 0.487954i −0.987723 0.156217i \(-0.950070\pi\)
0.764882 + 0.644171i \(0.222797\pi\)
\(102\) −58641.0 + 199713.i −0.0552588 + 0.188194i
\(103\) −704320. + 610297.i −0.644553 + 0.558508i −0.914611 0.404336i \(-0.867503\pi\)
0.270058 + 0.962844i \(0.412957\pi\)
\(104\) −2.91499e6 3.36408e6i −2.59142 2.99065i
\(105\) 101824. + 29898.2i 0.0879592 + 0.0258271i
\(106\) 86045.3 + 39295.6i 0.0722453 + 0.0329933i
\(107\) −758015. + 1.17949e6i −0.618766 + 0.962818i 0.380510 + 0.924777i \(0.375748\pi\)
−0.999276 + 0.0380416i \(0.987888\pi\)
\(108\) −566432. + 166319.i −0.449652 + 0.132030i
\(109\) 2.34459e6 + 337101.i 1.81045 + 0.260304i 0.962794 0.270238i \(-0.0871023\pi\)
0.847659 + 0.530542i \(0.178011\pi\)
\(110\) −18013.1 39443.2i −0.0135335 0.0296343i
\(111\) −130651. + 18784.7i −0.0955306 + 0.0137352i
\(112\) −1.18184e6 1.83898e6i −0.841211 1.30895i
\(113\) 472090. + 409068.i 0.327182 + 0.283505i 0.802926 0.596079i \(-0.203276\pi\)
−0.475744 + 0.879584i \(0.657821\pi\)
\(114\) 1.28445e6i 0.866969i
\(115\) −175370. 345172.i −0.115308 0.226957i
\(116\) −3.81411e6 −2.44354
\(117\) −520143. + 600276.i −0.324762 + 0.374795i
\(118\) 1.53013e6 983356.i 0.931285 0.598501i
\(119\) 27418.3 + 190699.i 0.0162705 + 0.113164i
\(120\) 614476. 280622.i 0.355600 0.162397i
\(121\) −250917. + 1.74517e6i −0.141636 + 0.985102i
\(122\) −338085. 1.15141e6i −0.186186 0.634091i
\(123\) −109926. 70645.2i −0.0590725 0.0379636i
\(124\) 262029. 573764.i 0.137431 0.300932i
\(125\) −271080. + 923213.i −0.138793 + 0.472685i
\(126\) −582549. + 504782.i −0.291220 + 0.252343i
\(127\) −555249. 640792.i −0.271067 0.312828i 0.603853 0.797096i \(-0.293632\pi\)
−0.874920 + 0.484268i \(0.839086\pi\)
\(128\) −318477. 93513.3i −0.151862 0.0445906i
\(129\) −2.01885e6 921980.i −0.940450 0.429489i
\(130\) 833779. 1.29738e6i 0.379508 0.590526i
\(131\) 3.19161e6 937141.i 1.41970 0.416861i 0.520297 0.853986i \(-0.325821\pi\)
0.899401 + 0.437125i \(0.144003\pi\)
\(132\) 220998. + 31774.7i 0.0960874 + 0.0138153i
\(133\) −493886. 1.08146e6i −0.209929 0.459679i
\(134\) 8.04287e6 1.15639e6i 3.34269 0.480607i
\(135\) −65167.9 101403.i −0.0264870 0.0412145i
\(136\) 926832. + 803104.i 0.368455 + 0.319268i
\(137\) 2.77007e6i 1.07728i 0.842535 + 0.538641i \(0.181062\pi\)
−0.842535 + 0.538641i \(0.818938\pi\)
\(138\) 2.79783e6 + 283887.i 1.06460 + 0.108021i
\(139\) 1.94468e6 0.724108 0.362054 0.932157i \(-0.382076\pi\)
0.362054 + 0.932157i \(0.382076\pi\)
\(140\) 694784. 801823.i 0.253201 0.292210i
\(141\) −1.56831e6 + 1.00789e6i −0.559468 + 0.359549i
\(142\) 690384. + 4.80173e6i 0.241116 + 1.67700i
\(143\) 273253. 124790.i 0.0934451 0.0426750i
\(144\) −353360. + 2.45768e6i −0.118340 + 0.823070i
\(145\) −219407. 747230.i −0.0719690 0.245104i
\(146\) 7.78275e6 + 5.00167e6i 2.50077 + 1.60715i
\(147\) 465467. 1.01923e6i 0.146534 0.320864i
\(148\) −371779. + 1.26616e6i −0.114683 + 0.390575i
\(149\) 755222. 654403.i 0.228305 0.197828i −0.533195 0.845992i \(-0.679009\pi\)
0.761500 + 0.648165i \(0.224463\pi\)
\(150\) −2.21174e6 2.55248e6i −0.655330 0.756291i
\(151\) −3.23601e6 950179.i −0.939895 0.275978i −0.224321 0.974515i \(-0.572016\pi\)
−0.715574 + 0.698537i \(0.753835\pi\)
\(152\) −6.88402e6 3.14383e6i −1.96025 0.895216i
\(153\) 118309. 184092.i 0.0330326 0.0513997i
\(154\) 279719. 82132.9i 0.0765879 0.0224882i
\(155\) 127480. + 18328.9i 0.0342333 + 0.00492200i
\(156\) 3.29875e6 + 7.22324e6i 0.868910 + 1.90265i
\(157\) −4.27224e6 + 614255.i −1.10397 + 0.158727i −0.670115 0.742257i \(-0.733755\pi\)
−0.433852 + 0.900984i \(0.642846\pi\)
\(158\) −6.14058e6 9.55493e6i −1.55682 2.42246i
\(159\) −75159.4 65126.0i −0.0186979 0.0162018i
\(160\) 2.04757e6i 0.499894i
\(161\) 2.46482e6 836776.i 0.590620 0.200508i
\(162\) 875532. 0.205934
\(163\) 1.54227e6 1.77987e6i 0.356120 0.410985i −0.549216 0.835681i \(-0.685073\pi\)
0.905336 + 0.424696i \(0.139619\pi\)
\(164\) −1.09899e6 + 706279.i −0.249151 + 0.160120i
\(165\) 6487.85 + 45124.0i 0.00144427 + 0.0100451i
\(166\) −1.20042e7 + 5.48216e6i −2.62428 + 1.19847i
\(167\) 294554. 2.04867e6i 0.0632434 0.439868i −0.933456 0.358691i \(-0.883223\pi\)
0.996700 0.0811766i \(-0.0258678\pi\)
\(168\) 1.27953e6 + 4.35767e6i 0.269850 + 0.919024i
\(169\) 4.92739e6 + 3.16664e6i 1.02084 + 0.656053i
\(170\) −176506. + 386494.i −0.0359263 + 0.0786676i
\(171\) −380451. + 1.29570e6i −0.0760870 + 0.259128i
\(172\) −1.67691e7 + 1.45305e7i −3.29553 + 2.85559i
\(173\) −5.58379e6 6.44404e6i −1.07843 1.24457i −0.968070 0.250679i \(-0.919346\pi\)
−0.110357 0.993892i \(-0.535199\pi\)
\(174\) 5.42752e6 + 1.59366e6i 1.03028 + 0.302517i
\(175\) −2.84365e6 1.29865e6i −0.530594 0.242314i
\(176\) 507694. 789988.i 0.0931245 0.144905i
\(177\) −1.83479e6 + 538744.i −0.330878 + 0.0971544i
\(178\) 7.09356e6 + 1.01990e6i 1.25778 + 0.180841i
\(179\) 2.84632e6 + 6.23256e6i 0.496277 + 1.08669i 0.977662 + 0.210185i \(0.0674068\pi\)
−0.481385 + 0.876510i \(0.659866\pi\)
\(180\) −1.19282e6 + 171502.i −0.204530 + 0.0294070i
\(181\) −3.06832e6 4.77440e6i −0.517446 0.805162i 0.479949 0.877297i \(-0.340655\pi\)
−0.997395 + 0.0721344i \(0.977019\pi\)
\(182\) 7.83598e6 + 6.78992e6i 1.29981 + 1.12629i
\(183\) 1.26163e6i 0.205864i
\(184\) 8.36947e6 1.43001e7i 1.34352 2.29555i
\(185\) −269443. −0.0425551
\(186\) −612609. + 706988.i −0.0952016 + 0.109869i
\(187\) −69624.3 + 44744.8i −0.0106472 + 0.00684255i
\(188\) 2.65246e6 + 1.84483e7i 0.399187 + 2.77640i
\(189\) 737164. 336651.i 0.109189 0.0498649i
\(190\) 373147. 2.59530e6i 0.0544026 0.378378i
\(191\) 1.52719e6 + 5.20115e6i 0.219177 + 0.746447i 0.993518 + 0.113678i \(0.0362634\pi\)
−0.774341 + 0.632769i \(0.781918\pi\)
\(192\) 3.93584e6 + 2.52941e6i 0.556076 + 0.357368i
\(193\) 981646. 2.14951e6i 0.136547 0.298997i −0.828989 0.559265i \(-0.811084\pi\)
0.965536 + 0.260268i \(0.0838108\pi\)
\(194\) 5.76732e6 1.96417e7i 0.789895 2.69013i
\(195\) −1.22536e6 + 1.06178e6i −0.165257 + 0.143196i
\(196\) −7.33583e6 8.46600e6i −0.974274 1.12437i
\(197\) 1.20821e7 + 3.54764e6i 1.58032 + 0.464024i 0.949984 0.312298i \(-0.101099\pi\)
0.630336 + 0.776322i \(0.282917\pi\)
\(198\) −301206. 137556.i −0.0388032 0.0177208i
\(199\) −4.97523e6 + 7.74161e6i −0.631327 + 0.982363i 0.367307 + 0.930100i \(0.380280\pi\)
−0.998633 + 0.0522635i \(0.983356\pi\)
\(200\) −1.90935e7 + 5.60635e6i −2.38668 + 0.700794i
\(201\) −8.45580e6 1.21576e6i −1.04128 0.149713i
\(202\) −3.40423e6 7.45422e6i −0.413014 0.904374i
\(203\) 5.18254e6 745137.i 0.619519 0.0890734i
\(204\) −1.18280e6 1.84047e6i −0.139322 0.216789i
\(205\) −201588. 174677.i −0.0233993 0.0202756i
\(206\) 1.38182e7i 1.58070i
\(207\) −2.73824e6 1.11508e6i −0.308717 0.125718i
\(208\) 3.33986e7 3.71141
\(209\) 334454. 385980.i 0.0366351 0.0422792i
\(210\) −1.32371e6 + 850699.i −0.142934 + 0.0918582i
\(211\) −617634. 4.29574e6i −0.0657482 0.457288i −0.995926 0.0901783i \(-0.971256\pi\)
0.930177 0.367110i \(-0.119653\pi\)
\(212\) −904408. + 413029.i −0.0949197 + 0.0433484i
\(213\) 725829. 5.04825e6i 0.0751096 0.522399i
\(214\) −5.85687e6 1.99467e7i −0.597618 2.03530i
\(215\) −3.81135e6 2.44940e6i −0.383498 0.246459i
\(216\) 2.14295e6 4.69241e6i 0.212643 0.465623i
\(217\) −243948. + 830811.i −0.0238736 + 0.0813061i
\(218\) −2.65428e7 + 2.29995e7i −2.56199 + 2.21998i
\(219\) −6.36940e6 7.35068e6i −0.606410 0.699834i
\(220\) 437306. + 128405.i 0.0410693 + 0.0120590i
\(221\) −2.67753e6 1.22279e6i −0.248061 0.113286i
\(222\) 1.05809e6 1.64642e6i 0.0967083 0.150481i
\(223\) 1.35488e7 3.97827e6i 1.22176 0.358740i 0.393624 0.919272i \(-0.371221\pi\)
0.828133 + 0.560532i \(0.189403\pi\)
\(224\) 1.36260e7 + 1.95912e6i 1.21234 + 0.174308i
\(225\) 1.47506e6 + 3.22994e6i 0.129498 + 0.283561i
\(226\) −9.16776e6 + 1.31812e6i −0.794214 + 0.114191i
\(227\) 710221. + 1.10512e6i 0.0607177 + 0.0944787i 0.870285 0.492548i \(-0.163935\pi\)
−0.809567 + 0.587027i \(0.800298\pi\)
\(228\) 1.02031e7 + 8.84105e6i 0.860851 + 0.745932i
\(229\) 1.55349e7i 1.29361i −0.762657 0.646803i \(-0.776106\pi\)
0.762657 0.646803i \(-0.223894\pi\)
\(230\) 5.57068e6 + 1.38641e6i 0.457852 + 0.113948i
\(231\) −306495. −0.0248650
\(232\) 2.18256e7 2.51881e7i 1.74785 2.01712i
\(233\) −6.65908e6 + 4.27953e6i −0.526437 + 0.338321i −0.776714 0.629854i \(-0.783115\pi\)
0.250277 + 0.968174i \(0.419478\pi\)
\(234\) −1.67604e6 1.16571e7i −0.130808 0.909792i
\(235\) −3.46166e6 + 1.58089e6i −0.266735 + 0.121814i
\(236\) −2.72075e6 + 1.89232e7i −0.206992 + 1.43966i
\(237\) 3.36419e6 + 1.14574e7i 0.252718 + 0.860678i
\(238\) −2.40313e6 1.54440e6i −0.178257 0.114559i
\(239\) 5.37885e6 1.17780e7i 0.393999 0.862738i −0.603844 0.797102i \(-0.706365\pi\)
0.997844 0.0656360i \(-0.0209076\pi\)
\(240\) −1.42796e6 + 4.86319e6i −0.103296 + 0.351794i
\(241\) 1.00532e7 8.71115e6i 0.718213 0.622335i −0.217103 0.976149i \(-0.569661\pi\)
0.935316 + 0.353814i \(0.115115\pi\)
\(242\) −1.71194e7 1.97569e7i −1.20793 1.39403i
\(243\) −883197. 259330.i −0.0615515 0.0180732i
\(244\) 1.14734e7 + 5.23972e6i 0.789809 + 0.360694i
\(245\) 1.23660e6 1.92418e6i 0.0840872 0.130842i
\(246\) 1.85898e6 545847.i 0.124873 0.0366662i
\(247\) 1.79796e7 + 2.58507e6i 1.19313 + 0.171546i
\(248\) 2.28968e6 + 5.01370e6i 0.150113 + 0.328703i
\(249\) 1.37331e7 1.97453e6i 0.889553 0.127898i
\(250\) −7.71309e6 1.20018e7i −0.493638 0.768115i
\(251\) −3.17052e6 2.74727e6i −0.200498 0.173732i 0.548825 0.835937i \(-0.315075\pi\)
−0.749323 + 0.662205i \(0.769621\pi\)
\(252\) 8.10199e6i 0.506279i
\(253\) 766834. + 813826.i 0.0473522 + 0.0502539i
\(254\) 1.25718e7 0.767180
\(255\) 292529. 337597.i 0.0176420 0.0203600i
\(256\) −1.20188e7 + 7.72401e6i −0.716376 + 0.460387i
\(257\) 1.84288e6 + 1.28175e7i 0.108567 + 0.755098i 0.969271 + 0.245994i \(0.0791143\pi\)
−0.860705 + 0.509105i \(0.829977\pi\)
\(258\) 2.99340e7 1.36704e7i 1.74303 0.796016i
\(259\) 257804. 1.79307e6i 0.0148385 0.103204i
\(260\) 4.56684e6 + 1.55532e7i 0.259834 + 0.884913i
\(261\) −5.00300e6 3.21523e6i −0.281390 0.180838i
\(262\) −2.04885e7 + 4.48635e7i −1.13922 + 2.49453i
\(263\) −3.05089e6 + 1.03904e7i −0.167710 + 0.571169i 0.832152 + 0.554548i \(0.187109\pi\)
−0.999862 + 0.0166204i \(0.994709\pi\)
\(264\) −1.47446e6 + 1.27763e6i −0.0801350 + 0.0694374i
\(265\) −132943. 153425.i −0.00714379 0.00824437i
\(266\) 1.69140e7 + 4.96639e6i 0.898671 + 0.263874i
\(267\) −6.85356e6 3.12992e6i −0.360066 0.164437i
\(268\) −4.61742e7 + 7.18485e7i −2.39881 + 3.73262i
\(269\) −2.03846e7 + 5.98545e6i −1.04724 + 0.307496i −0.759700 0.650274i \(-0.774654\pi\)
−0.287536 + 0.957770i \(0.592836\pi\)
\(270\) 1.76905e6 + 254352.i 0.0898773 + 0.0129224i
\(271\) 4.91500e6 + 1.07623e7i 0.246954 + 0.540753i 0.991997 0.126263i \(-0.0402984\pi\)
−0.745043 + 0.667016i \(0.767571\pi\)
\(272\) −9.10794e6 + 1.30952e6i −0.452599 + 0.0650739i
\(273\) −5.89343e6 9.17035e6i −0.289654 0.450711i
\(274\) −3.10405e7 2.68968e7i −1.50896 1.30752i
\(275\) 1.34293e6i 0.0645737i
\(276\) −2.15129e7 + 2.02707e7i −1.02323 + 0.964144i
\(277\) 1.96931e6 0.0926564 0.0463282 0.998926i \(-0.485248\pi\)
0.0463282 + 0.998926i \(0.485248\pi\)
\(278\) −1.88824e7 + 2.17914e7i −0.878864 + 1.01426i
\(279\) 827379. 531724.i 0.0380971 0.0244835i
\(280\) 1.31940e6 + 9.17660e6i 0.0601037 + 0.418030i
\(281\) 3.79770e7 1.73435e7i 1.71160 0.781660i 0.715010 0.699114i \(-0.246422\pi\)
0.996587 0.0825457i \(-0.0263050\pi\)
\(282\) 3.93383e6 2.73604e7i 0.175416 1.22004i
\(283\) −905002. 3.08215e6i −0.0399292 0.135986i 0.937116 0.349017i \(-0.113485\pi\)
−0.977045 + 0.213031i \(0.931666\pi\)
\(284\) −4.28948e7 2.75668e7i −1.87262 1.20346i
\(285\) −1.14513e6 + 2.50749e6i −0.0494677 + 0.108319i
\(286\) −1.25486e6 + 4.27366e6i −0.0536411 + 0.182685i
\(287\) 1.35531e6 1.17438e6i 0.0573313 0.0496779i
\(288\) −1.02395e7 1.18170e7i −0.428648 0.494686i
\(289\) −2.23817e7 6.57186e6i −0.927256 0.272267i
\(290\) 1.05036e7 + 4.79683e6i 0.430669 + 0.196680i
\(291\) −1.16356e7 + 1.81054e7i −0.472183 + 0.734732i
\(292\) −9.33006e7 + 2.73955e7i −3.74745 + 1.10035i
\(293\) 1.35412e7 + 1.94693e6i 0.538336 + 0.0774010i 0.406120 0.913820i \(-0.366882\pi\)
0.132216 + 0.991221i \(0.457791\pi\)
\(294\) 6.90159e6 + 1.51124e7i 0.271586 + 0.594690i
\(295\) −3.86380e6 + 555530.i −0.150504 + 0.0216392i
\(296\) −6.23421e6 9.70061e6i −0.240384 0.374045i
\(297\) 263099. + 227977.i 0.0100427 + 0.00870204i
\(298\) 1.48169e7i 0.559896i
\(299\) −9.60469e6 + 3.85923e7i −0.359310 + 1.44373i
\(300\) 3.54994e7 1.31479
\(301\) 1.99468e7 2.30199e7i 0.731433 0.844118i
\(302\) 4.20683e7 2.70356e7i 1.52733 0.981558i
\(303\) 1.22611e6 + 8.52780e6i 0.0440760 + 0.306555i
\(304\) 5.16514e7 2.35884e7i 1.83849 0.839611i
\(305\) −366518. + 2.54919e6i −0.0129180 + 0.0898467i
\(306\) 914123. + 3.11322e6i 0.0319037 + 0.108654i
\(307\) 3.42474e7 + 2.20095e7i 1.18362 + 0.760667i 0.976049 0.217553i \(-0.0698075\pi\)
0.207572 + 0.978220i \(0.433444\pi\)
\(308\) −1.27291e6 + 2.78729e6i −0.0435660 + 0.0953961i
\(309\) −4.09291e6 + 1.39392e7i −0.138726 + 0.472456i
\(310\) −1.44319e6 + 1.25053e6i −0.0484439 + 0.0419769i
\(311\) 1.31722e7 + 1.52015e7i 0.437902 + 0.505365i 0.931207 0.364491i \(-0.118757\pi\)
−0.493305 + 0.869856i \(0.664211\pi\)
\(312\) −6.65783e7 1.95492e7i −2.19214 0.643672i
\(313\) 3.85127e7 + 1.75881e7i 1.25594 + 0.573571i 0.928511 0.371304i \(-0.121089\pi\)
0.327433 + 0.944874i \(0.393816\pi\)
\(314\) 3.45992e7 5.38375e7i 1.11758 1.73898i
\(315\) 1.58728e6 466066.i 0.0507833 0.0149113i
\(316\) 1.18166e8 + 1.69898e7i 3.74484 + 0.538426i
\(317\) −1.52907e7 3.34819e7i −0.480008 1.05107i −0.982461 0.186466i \(-0.940296\pi\)
0.502453 0.864604i \(-0.332431\pi\)
\(318\) 1.45956e6 209853.i 0.0453879 0.00652580i
\(319\) 1.21601e6 + 1.89215e6i 0.0374598 + 0.0582886i
\(320\) 7.21774e6 + 6.25421e6i 0.220268 + 0.190863i
\(321\) 2.18561e7i 0.660780i
\(322\) −1.45562e7 + 3.57449e7i −0.435995 + 1.07065i
\(323\) −5.00446e6 −0.148508
\(324\) −6.02640e6 + 6.95483e6i −0.177183 + 0.204480i
\(325\) 4.01806e7 2.58225e7i 1.17049 0.752225i
\(326\) 4.96959e6 + 3.45642e7i 0.143439 + 0.997641i
\(327\) 3.35876e7 1.53389e7i 0.960584 0.438684i
\(328\) 1.62458e6 1.12992e7i 0.0460384 0.320204i
\(329\) −7.20823e6 2.45490e7i −0.202414 0.689360i
\(330\) −568639. 365442.i −0.0158232 0.0101690i
\(331\) −2.60535e7 + 5.70493e7i −0.718427 + 1.57313i 0.0976696 + 0.995219i \(0.468861\pi\)
−0.816096 + 0.577916i \(0.803866\pi\)
\(332\) 3.90790e7 1.33091e8i 1.06790 3.63692i
\(333\) −1.55502e6 + 1.34743e6i −0.0421117 + 0.0364900i
\(334\) 2.00966e7 + 2.31927e7i 0.539366 + 0.622462i
\(335\) −1.67321e7 4.91300e6i −0.445059 0.130681i
\(336\) −3.09970e7 1.41558e7i −0.817149 0.373179i
\(337\) 6.41077e6 9.97536e6i 0.167502 0.260639i −0.747347 0.664434i \(-0.768673\pi\)
0.914849 + 0.403795i \(0.132309\pi\)
\(338\) −8.33281e7 + 2.44673e7i −2.15795 + 0.633631i
\(339\) 9.63844e6 + 1.38580e6i 0.247404 + 0.0355714i
\(340\) −1.85522e6 4.06237e6i −0.0472019 0.103358i
\(341\) −368180. + 52936.3i −0.00928533 + 0.00133503i
\(342\) −1.08250e7 1.68441e7i −0.270615 0.421085i
\(343\) 3.06437e7 + 2.65529e7i 0.759379 + 0.658006i
\(344\) 1.93891e8i 4.76301i
\(345\) −5.20880e6 3.04856e6i −0.126847 0.0742400i
\(346\) 1.26427e8 3.05219
\(347\) −2.86009e7 + 3.30072e7i −0.684529 + 0.789988i −0.986576 0.163305i \(-0.947785\pi\)
0.302047 + 0.953293i \(0.402330\pi\)
\(348\) −5.00177e7 + 3.21444e7i −1.18682 + 0.762725i
\(349\) −5.54798e6 3.85870e7i −0.130514 0.907748i −0.944885 0.327403i \(-0.893827\pi\)
0.814371 0.580345i \(-0.197082\pi\)
\(350\) 4.21635e7 1.92554e7i 0.983404 0.449106i
\(351\) −1.76208e6 + 1.22556e7i −0.0407479 + 0.283408i
\(352\) 1.66606e6 + 5.67409e6i 0.0382000 + 0.130097i
\(353\) −6.16668e7 3.96309e7i −1.40193 0.900968i −0.402041 0.915621i \(-0.631699\pi\)
−0.999893 + 0.0146532i \(0.995336\pi\)
\(354\) 1.17784e7 2.57911e7i 0.265508 0.581381i
\(355\) 2.93314e6 9.98937e6i 0.0655614 0.223282i
\(356\) −5.69275e7 + 4.93279e7i −1.26175 + 1.09331i
\(357\) 1.96672e6 + 2.26972e6i 0.0432253 + 0.0498847i
\(358\) −9.74770e7 2.86218e7i −2.12448 0.623805i
\(359\) 3.48493e7 + 1.59151e7i 0.753200 + 0.343975i 0.754740 0.656024i \(-0.227763\pi\)
−0.00154022 + 0.999999i \(0.500490\pi\)
\(360\) 5.69313e6 8.85869e6i 0.122024 0.189872i
\(361\) −1.55088e7 + 4.55379e6i −0.329652 + 0.0967946i
\(362\) 8.32930e7 + 1.19757e7i 1.75583 + 0.252451i
\(363\) 1.14174e7 + 2.50005e7i 0.238696 + 0.522672i
\(364\) −1.07872e8 + 1.55097e7i −2.23669 + 0.321587i
\(365\) −1.07342e7 1.67028e7i −0.220746 0.343487i
\(366\) −1.41374e7 1.22501e7i −0.288355 0.249861i
\(367\) 2.64547e7i 0.535186i −0.963532 0.267593i \(-0.913772\pi\)
0.963532 0.267593i \(-0.0862283\pi\)
\(368\) 3.99652e7 + 1.17722e8i 0.801933 + 2.36219i
\(369\) −2.03694e6 −0.0405413
\(370\) 2.61623e6 3.01928e6i 0.0516500 0.0596072i
\(371\) 1.14820e6 737904.i 0.0224852 0.0144503i
\(372\) −1.39933e6 9.73258e6i −0.0271827 0.189060i
\(373\) −2.40472e7 + 1.09820e7i −0.463380 + 0.211619i −0.633404 0.773821i \(-0.718343\pi\)
0.170024 + 0.985440i \(0.445616\pi\)
\(374\) 174640. 1.21465e6i 0.00333833 0.0232186i
\(375\) 4.22571e6 + 1.43915e7i 0.0801321 + 0.272905i
\(376\) −1.37010e8 8.80507e7i −2.57743 1.65642i
\(377\) −3.32312e7 + 7.27663e7i −0.620187 + 1.35802i
\(378\) −3.38528e6 + 1.15292e7i −0.0626786 + 0.213464i
\(379\) 4.89644e7 4.24279e7i 0.899420 0.779352i −0.0765934 0.997062i \(-0.524404\pi\)
0.976013 + 0.217711i \(0.0698589\pi\)
\(380\) 1.80475e7 + 2.08279e7i 0.328901 + 0.379572i
\(381\) −1.26819e7 3.72374e6i −0.229303 0.0673293i
\(382\) −7.31110e7 3.33887e7i −1.31157 0.598975i
\(383\) −4.91645e7 + 7.65014e7i −0.875094 + 1.36167i 0.0565874 + 0.998398i \(0.481978\pi\)
−0.931682 + 0.363276i \(0.881658\pi\)
\(384\) −4.96457e6 + 1.45773e6i −0.0876774 + 0.0257444i
\(385\) −619288. 89040.2i −0.0108520 0.00156029i
\(386\) 1.45551e7 + 3.18712e7i 0.253077 + 0.554161i
\(387\) −3.42452e7 + 4.92371e6i −0.590835 + 0.0849493i
\(388\) 1.16328e8 + 1.81009e8i 1.99153 + 3.09889i
\(389\) −4.11124e7 3.56241e7i −0.698432 0.605195i 0.231540 0.972825i \(-0.425624\pi\)
−0.929972 + 0.367631i \(0.880169\pi\)
\(390\) 2.40406e7i 0.405276i
\(391\) 1.10607e6 1.09009e7i 0.0185035 0.182361i
\(392\) 9.78870e7 1.62505
\(393\) 3.39563e7 3.91876e7i 0.559426 0.645612i
\(394\) −1.57068e8 + 1.00942e8i −2.56803 + 1.65037i
\(395\) 3.46902e6 + 2.41275e7i 0.0562879 + 0.391491i
\(396\) 3.16592e6 1.44583e6i 0.0509818 0.0232826i
\(397\) 5.52115e6 3.84005e7i 0.0882385 0.613713i −0.896936 0.442160i \(-0.854212\pi\)
0.985175 0.171553i \(-0.0548784\pi\)
\(398\) −3.84416e7 1.30920e8i −0.609750 2.07662i
\(399\) −1.55910e7 1.00197e7i −0.245446 0.157738i
\(400\) 6.20248e7 1.35815e8i 0.969138 2.12212i
\(401\) 3.55766e7 1.21163e8i 0.551736 1.87904i 0.0811155 0.996705i \(-0.474152\pi\)
0.470621 0.882336i \(-0.344030\pi\)
\(402\) 9.57271e7 8.29480e7i 1.47352 1.27681i
\(403\) −8.66338e6 9.99808e6i −0.132365 0.152757i
\(404\) 8.26447e7 + 2.42667e7i 1.25335 + 0.368016i
\(405\) −1.70920e6 780567.i −0.0257293 0.0117502i
\(406\) −4.19715e7 + 6.53089e7i −0.627157 + 0.975875i
\(407\) 746664. 219240.i 0.0110750 0.00325190i
\(408\) 1.89227e7 + 2.72067e6i 0.278614 + 0.0400586i
\(409\) 1.24419e7 + 2.72439e7i 0.181851 + 0.398198i 0.978501 0.206243i \(-0.0661237\pi\)
−0.796650 + 0.604441i \(0.793396\pi\)
\(410\) 3.91474e6 562854.i 0.0568004 0.00816666i
\(411\) 2.33455e7 + 3.63263e7i 0.336262 + 0.523234i
\(412\) 1.09766e8 + 9.51125e7i 1.56955 + 1.36002i
\(413\) 2.62441e7i 0.372547i
\(414\) 3.90829e7 1.98566e7i 0.550790 0.279836i
\(415\) 2.83221e7 0.396260
\(416\) −1.37733e8 + 1.58953e8i −1.91319 + 2.20794i
\(417\) 2.55022e7 1.63893e7i 0.351698 0.226022i
\(418\) 1.07770e6 + 7.49555e6i 0.0147560 + 0.102630i
\(419\) −9.80070e7 + 4.47583e7i −1.33234 + 0.608460i −0.949038 0.315163i \(-0.897941\pi\)
−0.383303 + 0.923623i \(0.625213\pi\)
\(420\) 2.35371e6 1.63704e7i 0.0317692 0.220959i
\(421\) −8.02198e6 2.73203e7i −0.107507 0.366134i 0.888114 0.459624i \(-0.152016\pi\)
−0.995620 + 0.0934901i \(0.970198\pi\)
\(422\) 5.41336e7 + 3.47896e7i 0.720327 + 0.462926i
\(423\) −1.20723e7 + 2.64347e7i −0.159504 + 0.349264i
\(424\) 2.44771e6 8.33614e6i 0.0321116 0.109362i
\(425\) −9.94493e6 + 8.61733e6i −0.129549 + 0.112255i
\(426\) 4.95214e7 + 5.71507e7i 0.640566 + 0.739252i
\(427\) −1.66135e7 4.87816e6i −0.213391 0.0626574i
\(428\) 1.98761e8 + 9.07710e7i 2.53513 + 1.15775i
\(429\) 2.53169e6 3.93939e6i 0.0320656 0.0498950i
\(430\) 6.44544e7 1.89255e7i 0.810676 0.238036i
\(431\) −1.38427e8 1.99028e7i −1.72898 0.248589i −0.795175 0.606380i \(-0.792621\pi\)
−0.933802 + 0.357790i \(0.883530\pi\)
\(432\) 1.60788e7 + 3.52076e7i 0.199435 + 0.436702i
\(433\) 1.08926e7 1.56612e6i 0.134174 0.0192913i −0.0749006 0.997191i \(-0.523864\pi\)
0.209075 + 0.977900i \(0.432955\pi\)
\(434\) −6.94111e6 1.08006e7i −0.0849101 0.132123i
\(435\) −9.17474e6 7.94995e6i −0.111462 0.0965821i
\(436\) 3.69153e8i 4.45396i
\(437\) 1.24028e7 + 6.64671e7i 0.148619 + 0.796457i
\(438\) 1.44215e8 1.71627
\(439\) 4.74391e6 5.47477e6i 0.0560716 0.0647101i −0.727021 0.686615i \(-0.759096\pi\)
0.783092 + 0.621905i \(0.213641\pi\)
\(440\) −3.35039e6 + 2.15316e6i −0.0393312 + 0.0252766i
\(441\) −2.48577e6 1.72889e7i −0.0289831 0.201582i
\(442\) 3.97004e7 1.81305e7i 0.459756 0.209964i
\(443\) 1.48162e6 1.03049e7i 0.0170422 0.118531i −0.979525 0.201325i \(-0.935475\pi\)
0.996567 + 0.0827941i \(0.0263844\pi\)
\(444\) 5.79546e6 + 1.97375e7i 0.0662123 + 0.225499i
\(445\) −1.29387e7 8.31518e6i −0.146828 0.0943608i
\(446\) −8.69760e7 + 1.90451e8i −0.980381 + 2.14673i
\(447\) 4.38871e6 1.49466e7i 0.0491376 0.167347i
\(448\) −4.85260e7 + 4.20480e7i −0.539685 + 0.467640i
\(449\) −8.22713e7 9.49461e7i −0.908886 1.04891i −0.998598 0.0529421i \(-0.983140\pi\)
0.0897120 0.995968i \(-0.471405\pi\)
\(450\) −5.05161e7 1.48329e7i −0.554360 0.162775i
\(451\) 700759. + 320026.i 0.00763904 + 0.00348863i
\(452\) 5.26322e7 8.18974e7i 0.569950 0.886859i
\(453\) −5.04444e7 + 1.48118e7i −0.542649 + 0.159336i
\(454\) −1.92797e7 2.77201e6i −0.206031 0.0296228i
\(455\) −9.24386e6 2.02412e7i −0.0981340 0.214883i
\(456\) −1.16771e8 + 1.67892e7i −1.23152 + 0.177066i
\(457\) −5.85782e6 9.11495e6i −0.0613745 0.0955005i 0.809210 0.587519i \(-0.199895\pi\)
−0.870584 + 0.492019i \(0.836259\pi\)
\(458\) 1.74079e8 + 1.50840e8i 1.81196 + 1.57008i
\(459\) 3.41123e6i 0.0352755i
\(460\) −4.93567e7 + 3.47082e7i −0.507076 + 0.356581i
\(461\) −1.77980e8 −1.81664 −0.908320 0.418276i \(-0.862634\pi\)
−0.908320 + 0.418276i \(0.862634\pi\)
\(462\) 2.97600e6 3.43448e6i 0.0301791 0.0348286i
\(463\) −1.26307e8 + 8.11726e7i −1.27258 + 0.817836i −0.989953 0.141394i \(-0.954842\pi\)
−0.282625 + 0.959230i \(0.591205\pi\)
\(464\) 3.55884e7 + 2.47523e8i 0.356250 + 2.47777i
\(465\) 1.82623e6 834012.i 0.0181634 0.00829494i
\(466\) 1.67031e7 1.16173e8i 0.165059 1.14801i
\(467\) −4.34132e7 1.47852e8i −0.426257 1.45170i −0.840640 0.541595i \(-0.817821\pi\)
0.414383 0.910103i \(-0.363997\pi\)
\(468\) 1.04135e8 + 6.69235e7i 1.01592 + 0.652892i
\(469\) 4.87041e7 1.06647e8i 0.472114 1.03379i
\(470\) 1.58970e7 5.41402e7i 0.153116 0.521466i
\(471\) −5.08486e7 + 4.40606e7i −0.486650 + 0.421685i
\(472\) −1.09399e8 1.26253e8i −1.04037 1.20065i
\(473\) 1.25548e7 + 3.68642e6i 0.118639 + 0.0348355i
\(474\) −1.61053e8 7.35505e7i −1.51229 0.690638i
\(475\) 4.39022e7 6.83131e7i 0.409643 0.637417i
\(476\) 2.88091e7 8.45910e6i 0.267121 0.0784338i
\(477\) −1.53449e6 220627.i −0.0141387 0.00203284i
\(478\) 7.97533e7 + 1.74635e8i 0.730239 + 1.59900i
\(479\) 1.30443e8 1.87549e7i 1.18690 0.170651i 0.479552 0.877513i \(-0.340799\pi\)
0.707351 + 0.706862i \(0.249890\pi\)
\(480\) −1.72564e7 2.68515e7i −0.156036 0.242798i
\(481\) 2.09169e7 + 1.81246e7i 0.187958 + 0.162867i
\(482\) 1.97236e8i 1.76135i
\(483\) 2.52712e7 3.17463e7i 0.224277 0.281742i
\(484\) 2.74775e8 2.42349
\(485\) −2.87701e7 + 3.32025e7i −0.252184 + 0.291035i
\(486\) 1.14816e7 7.37877e6i 0.100021 0.0642799i
\(487\) 2.16935e7 + 1.50882e8i 0.187820 + 1.30632i 0.837636 + 0.546228i \(0.183937\pi\)
−0.649816 + 0.760092i \(0.725154\pi\)
\(488\) −1.00257e8 + 4.57860e7i −0.862694 + 0.393979i
\(489\) 5.22473e6 3.63388e7i 0.0446825 0.310774i
\(490\) 9.55467e6 + 3.25402e7i 0.0812134 + 0.276587i
\(491\) 8.30705e7 + 5.33862e7i 0.701782 + 0.451008i 0.842257 0.539076i \(-0.181227\pi\)
−0.140475 + 0.990084i \(0.544863\pi\)
\(492\) −8.45965e6 + 1.85241e7i −0.0710325 + 0.155540i
\(493\) 6.20921e6 2.11466e7i 0.0518198 0.176482i
\(494\) −2.03545e8 + 1.76372e8i −1.68841 + 1.46302i
\(495\) 465374. + 537071.i 0.00383696 + 0.00442808i
\(496\) −3.96803e7 1.16512e7i −0.325184 0.0954827i
\(497\) 6.36701e7 + 2.90772e7i 0.518640 + 0.236855i
\(498\) −1.11220e8 + 1.73061e8i −0.900520 + 1.40124i
\(499\) −1.94712e7 + 5.71727e6i −0.156708 + 0.0460137i −0.359146 0.933282i \(-0.616932\pi\)
0.202438 + 0.979295i \(0.435114\pi\)
\(500\) 1.48427e8 + 2.13406e7i 1.18742 + 0.170725i
\(501\) −1.34029e7 2.93483e7i −0.106583 0.233384i
\(502\) 6.15699e7 8.85242e6i 0.486696 0.0699763i
\(503\) −1.55780e7 2.42398e7i −0.122407 0.190469i 0.774642 0.632400i \(-0.217930\pi\)
−0.897049 + 0.441931i \(0.854294\pi\)
\(504\) 5.35050e7 + 4.63623e7i 0.417929 + 0.362137i
\(505\) 1.75870e7i 0.136558i
\(506\) −1.65652e7 + 690825.i −0.127863 + 0.00533232i
\(507\) 9.13047e7 0.700599
\(508\) −8.65335e7 + 9.98650e7i −0.660075 + 0.761767i
\(509\) 6.09965e7 3.92001e7i 0.462543 0.297258i −0.288538 0.957468i \(-0.593169\pi\)
0.751081 + 0.660210i \(0.229533\pi\)
\(510\) 942606. + 6.55597e6i 0.00710591 + 0.0494227i
\(511\) 1.21423e8 5.54520e7i 0.909994 0.415580i
\(512\) 3.31702e7 2.30704e8i 0.247137 1.71888i
\(513\) 5.93064e6 + 2.01979e7i 0.0439288 + 0.149608i
\(514\) −1.61522e8 1.03804e8i −1.18944 0.764408i
\(515\) −1.23194e7 + 2.69757e7i −0.0901920 + 0.197493i
\(516\) −9.74479e7 + 3.31877e8i −0.709289 + 2.41562i
\(517\) 8.30640e6 7.19754e6i 0.0601092 0.0520849i
\(518\) 1.75893e7 + 2.02991e7i 0.126549 + 0.146046i
\(519\) −1.27534e8 3.74473e7i −0.912269 0.267866i
\(520\) −1.28845e8 5.88417e7i −0.916345 0.418481i
\(521\) 1.15440e7 1.79628e7i 0.0816286 0.127017i −0.798039 0.602606i \(-0.794129\pi\)
0.879667 + 0.475590i \(0.157765\pi\)
\(522\) 8.46067e7 2.48428e7i 0.594831 0.174658i
\(523\) −9.13467e7 1.31337e7i −0.638539 0.0918081i −0.184561 0.982821i \(-0.559086\pi\)
−0.453978 + 0.891013i \(0.649996\pi\)
\(524\) −2.15351e8 4.71553e8i −1.49676 3.27745i
\(525\) −4.82360e7 + 6.93528e6i −0.333344 + 0.0479277i
\(526\) −8.68077e7 1.35075e8i −0.596487 0.928152i
\(527\) 2.75455e6 + 2.38684e6i 0.0188200 + 0.0163076i
\(528\) 1.46385e7i 0.0994477i
\(529\) −1.47522e8 + 1.23257e7i −0.996528 + 0.0832617i
\(530\) 3.01007e6 0.0202185
\(531\) −1.95208e7 + 2.25282e7i −0.130381 + 0.150468i
\(532\) −1.55872e8 + 1.00173e8i −1.03522 + 0.665295i
\(533\) 3.89931e6 + 2.71203e7i 0.0257517 + 0.179107i
\(534\) 1.01619e8 4.64080e7i 0.667348 0.304767i
\(535\) −6.34942e6 + 4.41612e7i −0.0414642 + 0.288390i
\(536\) −2.10258e8 7.16073e8i −1.36539 4.65011i
\(537\) 8.98527e7 + 5.77448e7i 0.580241 + 0.372898i
\(538\) 1.30858e8 2.86540e8i 0.840339 1.84009i
\(539\) −1.86111e6 + 6.33837e6i −0.0118852 + 0.0404773i
\(540\) −1.41971e7 + 1.23018e7i −0.0901608 + 0.0781248i
\(541\) −1.32783e8 1.53240e8i −0.838594 0.967789i 0.161223 0.986918i \(-0.448456\pi\)
−0.999817 + 0.0191290i \(0.993911\pi\)
\(542\) −1.68323e8 4.94240e7i −1.05717 0.310413i
\(543\) −8.04750e7 3.67517e7i −0.502645 0.229550i
\(544\) 3.13281e7 4.87474e7i 0.194597 0.302799i
\(545\) 7.23214e7 2.12355e7i 0.446763 0.131182i
\(546\) 1.59984e8 + 2.30022e7i 0.982873 + 0.141316i
\(547\) 6.29557e7 + 1.37854e8i 0.384656 + 0.842280i 0.998598 + 0.0529289i \(0.0168557\pi\)
−0.613942 + 0.789351i \(0.710417\pi\)
\(548\) 4.27312e8 6.14381e7i 2.59659 0.373333i
\(549\) 1.06327e7 + 1.65449e7i 0.0642581 + 0.0999875i
\(550\) 1.50484e7 + 1.30395e7i 0.0904489 + 0.0783744i
\(551\) 1.36004e8i 0.813013i
\(552\) −1.07622e7 2.58066e8i −0.0639857 1.53431i
\(553\) −1.63881e8 −0.969068
\(554\) −1.91216e7 + 2.20675e7i −0.112459 + 0.129785i
\(555\) −3.53343e6 + 2.27080e6i −0.0206689 + 0.0132831i
\(556\) −4.31315e7 2.99986e8i −0.250940 1.74533i
\(557\) 8.13539e7 3.71531e7i 0.470774 0.214995i −0.165878 0.986146i \(-0.553046\pi\)
0.636652 + 0.771151i \(0.280319\pi\)
\(558\) −2.07533e6 + 1.44342e7i −0.0119450 + 0.0830791i
\(559\) 1.31111e8 + 4.46524e8i 0.750594 + 2.55629i
\(560\) −5.85184e7 3.76075e7i −0.333218 0.214146i
\(561\) −535944. + 1.17355e6i −0.00303550 + 0.00664682i
\(562\) −1.74402e8 + 5.93958e8i −0.982522 + 3.34616i
\(563\) 9.78275e6 8.47680e6i 0.0548196 0.0475015i −0.627020 0.779003i \(-0.715726\pi\)
0.681840 + 0.731502i \(0.261180\pi\)
\(564\) 1.90262e8 + 2.19574e8i 1.06051 + 1.22389i
\(565\) 1.90723e7 + 5.60014e6i 0.105745 + 0.0310494i
\(566\) 4.33249e7 + 1.97858e7i 0.238940 + 0.109120i
\(567\) 6.82984e6 1.06274e7i 0.0374681 0.0583014i
\(568\) 4.27507e8 1.25528e8i 2.33291 0.685005i
\(569\) 3.53284e8 + 5.07946e7i 1.91773 + 0.275728i 0.994178 0.107748i \(-0.0343641\pi\)
0.923551 + 0.383476i \(0.125273\pi\)
\(570\) −1.69791e7 3.71791e7i −0.0916834 0.200759i
\(571\) 3.18663e8 4.58168e7i 1.71168 0.246103i 0.784343 0.620327i \(-0.213000\pi\)
0.927338 + 0.374225i \(0.122091\pi\)
\(572\) −2.53107e7 3.93842e7i −0.135243 0.210443i
\(573\) 6.38614e7 + 5.53362e7i 0.339449 + 0.294134i
\(574\) 2.65901e7i 0.140599i
\(575\) 1.39099e8 + 1.10728e8i 0.731677 + 0.582441i
\(576\) 7.29313e7 0.381634
\(577\) 8.64110e7 9.97236e7i 0.449823 0.519123i −0.484867 0.874588i \(-0.661132\pi\)
0.934690 + 0.355465i \(0.115677\pi\)
\(578\) 2.90963e8 1.86991e8i 1.50680 0.968359i
\(579\) −5.24235e6 3.64614e7i −0.0270079 0.187844i
\(580\) −1.10401e8 + 5.04186e7i −0.565836 + 0.258409i
\(581\) −2.70987e7 + 1.88476e8i −0.138172 + 0.961008i
\(582\) −8.99037e7 3.06184e8i −0.456046 1.55315i
\(583\) 493243. + 316988.i 0.00248917 + 0.00159970i
\(584\) 3.52980e8 7.72917e8i 1.77219 3.88056i
\(585\) −7.12075e6 + 2.42510e7i −0.0355679 + 0.121133i
\(586\) −1.53298e8 + 1.32833e8i −0.761805 + 0.660108i
\(587\) 4.58065e7 + 5.28636e7i 0.226471 + 0.261362i 0.857601 0.514315i \(-0.171954\pi\)
−0.631130 + 0.775677i \(0.717408\pi\)
\(588\) −1.67550e8 4.91972e7i −0.824163 0.241996i
\(589\) −2.04594e7 9.34349e6i −0.100126 0.0457260i
\(590\) 3.12915e7 4.86905e7i 0.152360 0.237076i
\(591\) 1.88342e8 5.53022e7i 0.912398 0.267904i
\(592\) 8.56386e7 + 1.23130e7i 0.412766 + 0.0593469i
\(593\) −9.64616e6 2.11221e7i −0.0462584 0.101292i 0.885092 0.465416i \(-0.154095\pi\)
−0.931350 + 0.364125i \(0.881368\pi\)
\(594\) −5.10926e6 + 734600.i −0.0243780 + 0.00350503i
\(595\) 3.31448e6 + 5.15743e6i 0.0157349 + 0.0244840i
\(596\) −1.17698e8 1.01986e8i −0.555945 0.481729i
\(597\) 1.43452e8i 0.674194i
\(598\) −3.39193e8 4.82349e8i −1.58615 2.25558i
\(599\) −1.40347e8 −0.653016 −0.326508 0.945194i \(-0.605872\pi\)
−0.326508 + 0.945194i \(0.605872\pi\)
\(600\) −2.03140e8 + 2.34436e8i −0.940462 + 1.08535i
\(601\) 1.77822e7 1.14279e7i 0.0819146 0.0526433i −0.499042 0.866578i \(-0.666315\pi\)
0.580957 + 0.813934i \(0.302678\pi\)
\(602\) 6.42739e7 + 4.47035e8i 0.294608 + 2.04905i
\(603\) −1.21134e8 + 5.53201e7i −0.552477 + 0.252308i
\(604\) −7.48023e7 + 5.20261e8i −0.339472 + 2.36108i
\(605\) 1.58064e7 + 5.38316e7i 0.0713784 + 0.243092i
\(606\) −1.07465e8 6.90635e7i −0.482890 0.310335i
\(607\) 6.44601e7 1.41148e8i 0.288221 0.631115i −0.709033 0.705175i \(-0.750868\pi\)
0.997254 + 0.0740602i \(0.0235957\pi\)
\(608\) −1.00743e8 + 3.43099e8i −0.448233 + 1.52654i
\(609\) 6.16832e7 5.34488e7i 0.273096 0.236639i
\(610\) −2.50065e7 2.88591e7i −0.110170 0.127143i
\(611\) 3.75070e8 + 1.10130e8i 1.64433 + 0.482818i
\(612\) −3.10220e7 1.41673e7i −0.135337 0.0618063i
\(613\) −5.53950e7 + 8.61964e7i −0.240486 + 0.374203i −0.940426 0.339998i \(-0.889574\pi\)
0.699940 + 0.714201i \(0.253210\pi\)
\(614\) −5.79165e8 + 1.70058e8i −2.50206 + 0.734670i
\(615\) −4.11572e6 591752.i −0.0176938 0.00254398i
\(616\) −1.11231e7 2.43561e7i −0.0475863 0.104199i
\(617\) 2.48960e8 3.57951e7i 1.05992 0.152394i 0.409764 0.912192i \(-0.365611\pi\)
0.650159 + 0.759798i \(0.274702\pi\)
\(618\) −1.16456e8 1.81210e8i −0.493399 0.767744i
\(619\) −1.06018e8 9.18653e7i −0.447001 0.387329i 0.402069 0.915610i \(-0.368291\pi\)
−0.849070 + 0.528281i \(0.822837\pi\)
\(620\) 2.00717e7i 0.0842186i
\(621\) −4.53065e7 + 8.45421e6i −0.189185 + 0.0353019i
\(622\) −2.98242e8 −1.23936
\(623\) 6.77151e7 7.81474e7i 0.280041 0.323184i
\(624\) 4.37984e8 2.81475e8i 1.80262 1.15848i
\(625\) −2.81358e7 1.95689e8i −0.115244 0.801541i
\(626\) −5.71035e8 + 2.60783e8i −2.32777 + 1.06306i
\(627\) 1.13303e6 7.88038e6i 0.00459661 0.0319701i
\(628\) 1.89510e8 + 6.45411e8i 0.765161 + 2.60590i
\(629\) −6.41476e6 4.12251e6i −0.0257768 0.0165657i
\(630\) −1.01895e7 + 2.23119e7i −0.0407503 + 0.0892307i
\(631\) 3.18808e7 1.08576e8i 0.126894 0.432162i −0.871398 0.490576i \(-0.836786\pi\)
0.998292 + 0.0584145i \(0.0186045\pi\)
\(632\) −7.88388e8 + 6.83142e8i −3.12312 + 2.70620i
\(633\) −4.43030e7 5.11284e7i −0.174671 0.201582i
\(634\) 5.23655e8 + 1.53759e8i 2.05484 + 0.603355i
\(635\) −2.45426e7 1.12082e7i −0.0958515 0.0437739i
\(636\) −8.37935e6 + 1.30385e7i −0.0325716 + 0.0506824i
\(637\) −2.25431e8 + 6.61924e7i −0.872157 + 0.256088i
\(638\) −3.30100e7 4.74612e6i −0.127111 0.0182758i
\(639\) −3.30270e7 7.23191e7i −0.126581 0.277173i
\(640\) −1.04546e7 + 1.50315e6i −0.0398812 + 0.00573406i
\(641\) 3.66423e7 + 5.70165e7i 0.139126 + 0.216484i 0.903824 0.427905i \(-0.140748\pi\)
−0.764698 + 0.644389i \(0.777112\pi\)
\(642\) −2.44912e8 2.12217e8i −0.925559 0.802002i
\(643\) 4.10061e8i 1.54247i 0.636553 + 0.771233i \(0.280360\pi\)
−0.636553 + 0.771233i \(0.719640\pi\)
\(644\) −1.83749e8 3.61665e8i −0.687966 1.35409i
\(645\) −7.06244e7 −0.263194
\(646\) 4.85921e7 5.60783e7i 0.180247 0.208016i
\(647\) −1.75398e8 + 1.12721e8i −0.647607 + 0.416192i −0.822791 0.568344i \(-0.807584\pi\)
0.175184 + 0.984536i \(0.443948\pi\)
\(648\) −1.14442e7 7.95958e7i −0.0420590 0.292527i
\(649\) 1.02551e7 4.68335e6i 0.0375151 0.0171326i
\(650\) −1.00786e8 + 7.00980e8i −0.366994 + 2.55250i
\(651\) 3.80277e6 + 1.29511e7i 0.0137834 + 0.0469421i
\(652\) −3.08769e8 1.98434e8i −1.11402 0.715934i
\(653\) 1.16443e8 2.54975e8i 0.418192 0.915712i −0.576906 0.816811i \(-0.695740\pi\)
0.995097 0.0989011i \(-0.0315328\pi\)
\(654\) −1.54244e8 + 5.25308e8i −0.551412 + 1.87794i
\(655\) 7.99947e7 6.93158e7i 0.284667 0.246665i
\(656\) 5.60895e7 + 6.47307e7i 0.198687 + 0.229297i
\(657\) −1.45477e8 4.27159e7i −0.512978 0.150624i
\(658\) 3.45078e8 + 1.57592e8i 1.21127 + 0.553166i
\(659\) 1.20446e8 1.87418e8i 0.420860 0.654870i −0.564485 0.825443i \(-0.690925\pi\)
0.985345 + 0.170573i \(0.0545617\pi\)
\(660\) 6.81693e6 2.00163e6i 0.0237114 0.00696229i
\(661\) 5.91682e7 + 8.50710e6i 0.204873 + 0.0294562i 0.243987 0.969779i \(-0.421545\pi\)
−0.0391144 + 0.999235i \(0.512454\pi\)
\(662\) −3.86301e8 8.45881e8i −1.33153 2.91565i
\(663\) −4.54181e7 + 6.53014e6i −0.155843 + 0.0224069i
\(664\) 6.55299e8 + 1.01967e9i 2.23839 + 3.48300i
\(665\) −2.85915e7 2.47747e7i −0.0972238 0.0842449i
\(666\) 3.05082e7i 0.103275i
\(667\) −2.96249e8 3.00594e7i −0.998341 0.101298i
\(668\) −3.22560e8 −1.08214
\(669\) 1.44148e8 1.66356e8i 0.481428 0.555597i
\(670\) 2.17518e8 1.39791e8i 0.723222 0.464787i
\(671\) −1.05855e6 7.36239e6i −0.00350384 0.0243697i
\(672\) 1.95200e8 8.91450e7i 0.643239 0.293758i
\(673\) 3.28120e7 2.28212e8i 0.107643 0.748676i −0.862485 0.506083i \(-0.831093\pi\)
0.970128 0.242593i \(-0.0779979\pi\)
\(674\) 4.95334e7 + 1.68695e8i 0.161778 + 0.550964i
\(675\) 4.65649e7 + 2.99254e7i 0.151407 + 0.0973036i
\(676\) 3.79200e8 8.30333e8i 1.22752 2.68789i
\(677\) −8.46431e7 + 2.88268e8i −0.272788 + 0.929031i 0.703161 + 0.711031i \(0.251771\pi\)
−0.975949 + 0.218000i \(0.930047\pi\)
\(678\) −1.09116e8 + 9.45493e7i −0.350105 + 0.303368i
\(679\) −1.93426e8 2.23226e8i −0.617883 0.713075i
\(680\) 3.74438e7 + 1.09945e7i 0.119084 + 0.0349662i
\(681\) 1.86274e7 + 8.50687e6i 0.0589810 + 0.0269357i
\(682\) 2.98175e6 4.63970e6i 0.00939980 0.0146264i
\(683\) 3.92156e8 1.15147e8i 1.23083 0.361403i 0.399265 0.916836i \(-0.369265\pi\)
0.831562 + 0.555433i \(0.187447\pi\)
\(684\) 2.08312e8 + 2.99508e7i 0.650948 + 0.0935922i
\(685\) 3.66175e7 + 8.01812e7i 0.113925 + 0.249460i
\(686\) −5.95086e8 + 8.55604e7i −1.84335 + 0.265033i
\(687\) −1.30924e8 2.03722e8i −0.403785 0.628302i
\(688\) 1.09945e9 + 9.52679e8i 3.37606 + 2.92537i
\(689\) 2.08530e7i 0.0637546i
\(690\) 8.47374e7 2.87672e7i 0.257945 0.0875691i
\(691\) 5.60224e7 0.169796 0.0848980 0.996390i \(-0.472944\pi\)
0.0848980 + 0.996390i \(0.472944\pi\)
\(692\) −8.70213e8 + 1.00428e9i −2.62608 + 3.03065i
\(693\) −4.01933e6 + 2.58307e6i −0.0120769 + 0.00776133i
\(694\) −9.21597e7 6.40985e8i −0.275716 1.91765i
\(695\) 5.62897e7 2.57066e7i 0.167677 0.0765757i
\(696\) 7.39386e7 5.14255e8i 0.219303 1.52528i
\(697\) −2.12672e6 7.24294e6i −0.00628075 0.0213903i
\(698\) 4.86263e8 + 3.12502e8i 1.42990 + 0.918939i
\(699\) −5.12593e7 + 1.12242e8i −0.150086 + 0.328643i
\(700\) −1.37260e8 + 4.67465e8i −0.400175 + 1.36287i
\(701\) 1.19513e8 1.03559e8i 0.346946 0.300630i −0.463903 0.885886i \(-0.653551\pi\)
0.810849 + 0.585256i \(0.199006\pi\)
\(702\) −1.20222e8 1.38744e8i −0.347515 0.401054i
\(703\) 4.51490e7 + 1.32569e7i 0.129952 + 0.0381573i
\(704\) −2.50903e7 1.14583e7i −0.0719097 0.0328401i
\(705\) −3.20723e7 + 4.99055e7i −0.0915299 + 0.142423i
\(706\) 1.04286e9 3.06211e8i 2.96355 0.870176i
\(707\) −1.17037e8 1.68274e7i −0.331180 0.0476165i
\(708\) 1.23801e8 + 2.71086e8i 0.348838 + 0.763849i
\(709\) −5.52066e7 + 7.93751e6i −0.154900 + 0.0222713i −0.219329 0.975651i \(-0.570387\pi\)
0.0644283 + 0.997922i \(0.479478\pi\)
\(710\) 8.34574e7 + 1.29862e8i 0.233179 + 0.362834i
\(711\) 1.40678e8 + 1.21898e8i 0.391396 + 0.339147i
\(712\) 6.58216e8i 1.82360i
\(713\) 2.48742e7 4.25002e7i 0.0686246 0.117253i
\(714\) −4.45301e7 −0.122337
\(715\) 6.25984e6 7.22424e6i 0.0171256 0.0197640i
\(716\) 8.98306e8 5.77306e8i 2.44729 1.57278i
\(717\) −2.87250e7 1.99787e8i −0.0779297 0.542013i
\(718\) −5.16717e8 + 2.35977e8i −1.39598 + 0.637524i
\(719\) −3.02343e6 + 2.10284e7i −0.00813417 + 0.0565744i −0.993484 0.113970i \(-0.963643\pi\)
0.985350 + 0.170544i \(0.0545525\pi\)
\(720\) 2.22597e7 + 7.58097e7i 0.0596379 + 0.203108i
\(721\) −1.67729e8 1.07793e8i −0.447509 0.287597i
\(722\) 9.95583e7 2.18002e8i 0.264525 0.579228i
\(723\) 5.84207e7 1.98963e8i 0.154579 0.526449i
\(724\) −6.68446e8 + 5.79212e8i −1.76137 + 1.52624i
\(725\) 2.34190e8 + 2.70270e8i 0.614546 + 0.709224i
\(726\) −3.91007e8 1.14810e8i −1.02182 0.300034i
\(727\) −3.19275e8 1.45808e8i −0.830924 0.379470i −0.0459080 0.998946i \(-0.514618\pi\)
−0.785016 + 0.619475i \(0.787345\pi\)
\(728\) 5.14856e8 8.01132e8i 1.33442 2.07639i
\(729\) −1.37677e7 + 4.04255e6i −0.0355368 + 0.0104345i
\(730\) 2.91392e8 + 4.18959e7i 0.749048 + 0.107697i
\(731\) −5.32623e7 1.16628e8i −0.136354 0.298574i
\(732\) 1.94619e8 2.79820e7i 0.496196 0.0713421i
\(733\) −8.52217e7 1.32608e8i −0.216391 0.336710i 0.716040 0.698059i \(-0.245953\pi\)
−0.932431 + 0.361349i \(0.882316\pi\)
\(734\) 2.96443e8 + 2.56869e8i 0.749639 + 0.649566i
\(735\) 3.56552e7i 0.0897967i
\(736\) −7.25083e8 2.95273e8i −1.81867 0.740610i
\(737\) 5.03647e7 0.125813
\(738\) 1.97782e7 2.28252e7i 0.0492058 0.0567866i
\(739\) −6.99587e7 + 4.49597e7i −0.173344 + 0.111401i −0.624436 0.781076i \(-0.714671\pi\)
0.451092 + 0.892477i \(0.351035\pi\)
\(740\) 5.97604e6 + 4.15642e7i 0.0147475 + 0.102571i
\(741\) 2.57568e8 1.17627e8i 0.633048 0.289103i
\(742\) −2.88005e6 + 2.00312e7i −0.00705000 + 0.0490338i
\(743\) −1.42771e8 4.86234e8i −0.348076 1.18544i −0.928565 0.371169i \(-0.878957\pi\)
0.580490 0.814268i \(-0.302861\pi\)
\(744\) 7.22807e7 + 4.64520e7i 0.175511 + 0.112794i
\(745\) 1.32097e7 2.89253e7i 0.0319466 0.0699534i
\(746\) 1.10432e8 3.76097e8i 0.265998 0.905905i
\(747\) 1.63453e8 1.41633e8i 0.392132 0.339784i
\(748\) 8.44655e6 + 9.74784e6i 0.0201825 + 0.0232918i
\(749\) −2.87806e8 8.45074e7i −0.684942 0.201117i
\(750\) −2.02297e8 9.23857e7i −0.479518 0.218988i
\(751\) −2.30440e8 + 3.58571e8i −0.544049 + 0.846556i −0.999034 0.0439425i \(-0.986008\pi\)
0.454985 + 0.890499i \(0.349645\pi\)
\(752\) 1.17248e9 3.44272e8i 2.75710 0.809558i
\(753\) −6.47310e7 9.30691e6i −0.151610 0.0217982i
\(754\) −4.92727e8 1.07892e9i −1.14946 2.51696i
\(755\) −1.06228e8 + 1.52733e7i −0.246831 + 0.0354889i
\(756\) −6.82816e7 1.06248e8i −0.158029 0.245899i
\(757\) −3.22115e8 2.79114e8i −0.742547 0.643420i 0.199117 0.979976i \(-0.436193\pi\)
−0.941664 + 0.336555i \(0.890738\pi\)
\(758\) 9.60642e8i 2.20574i
\(759\) 1.69149e7 + 4.20970e6i 0.0386851 + 0.00962778i
\(760\) −2.40819e8 −0.548594
\(761\) −2.35107e7 + 2.71328e7i −0.0533473 + 0.0615660i −0.781796 0.623534i \(-0.785696\pi\)
0.728449 + 0.685100i \(0.240242\pi\)
\(762\) 1.64865e8 1.05952e8i 0.372618 0.239467i
\(763\) 7.21189e7 + 5.01598e8i 0.162359 + 1.12923i
\(764\) 7.68457e8 3.50942e8i 1.72321 0.786966i
\(765\) 991000.