Properties

Label 177.6.d.b.176.17
Level $177$
Weight $6$
Character 177.176
Analytic conductor $28.388$
Analytic rank $0$
Dimension $92$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.3879361069\)
Analytic rank: \(0\)
Dimension: \(92\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.17
Character \(\chi\) \(=\) 177.176
Dual form 177.6.d.b.176.18

$q$-expansion

\(f(q)\) \(=\) \(q-7.56324 q^{2} +(11.2364 + 10.8048i) q^{3} +25.2027 q^{4} -51.3528i q^{5} +(-84.9838 - 81.7190i) q^{6} +90.7178 q^{7} +51.4099 q^{8} +(9.51431 + 242.814i) q^{9} +O(q^{10})\) \(q-7.56324 q^{2} +(11.2364 + 10.8048i) q^{3} +25.2027 q^{4} -51.3528i q^{5} +(-84.9838 - 81.7190i) q^{6} +90.7178 q^{7} +51.4099 q^{8} +(9.51431 + 242.814i) q^{9} +388.394i q^{10} -682.512 q^{11} +(283.188 + 272.309i) q^{12} +90.5395i q^{13} -686.121 q^{14} +(554.855 - 577.022i) q^{15} -1195.31 q^{16} +771.900i q^{17} +(-71.9590 - 1836.46i) q^{18} +2480.56 q^{19} -1294.23i q^{20} +(1019.34 + 980.185i) q^{21} +5162.01 q^{22} -440.319 q^{23} +(577.663 + 555.472i) q^{24} +487.887 q^{25} -684.772i q^{26} +(-2516.64 + 2831.16i) q^{27} +2286.33 q^{28} -6844.72i q^{29} +(-4196.50 + 4364.16i) q^{30} -1052.51i q^{31} +7395.31 q^{32} +(-7668.99 - 7374.38i) q^{33} -5838.07i q^{34} -4658.62i q^{35} +(239.786 + 6119.55i) q^{36} +10492.0i q^{37} -18761.1 q^{38} +(-978.258 + 1017.34i) q^{39} -2640.04i q^{40} +16643.5i q^{41} +(-7709.55 - 7413.38i) q^{42} -6372.48i q^{43} -17201.1 q^{44} +(12469.2 - 488.587i) q^{45} +3330.24 q^{46} +27748.5 q^{47} +(-13431.0 - 12915.0i) q^{48} -8577.27 q^{49} -3690.01 q^{50} +(-8340.20 + 8673.40i) q^{51} +2281.84i q^{52} +26135.8i q^{53} +(19033.9 - 21412.7i) q^{54} +35048.9i q^{55} +4663.80 q^{56} +(27872.6 + 26801.9i) q^{57} +51768.3i q^{58} +(13187.9 + 23259.5i) q^{59} +(13983.8 - 14542.5i) q^{60} -9403.19i q^{61} +7960.42i q^{62} +(863.118 + 22027.5i) q^{63} -17682.6 q^{64} +4649.46 q^{65} +(58002.5 + 55774.2i) q^{66} +73133.4i q^{67} +19453.9i q^{68} +(-4947.61 - 4757.54i) q^{69} +35234.3i q^{70} -43754.6i q^{71} +(489.130 + 12483.0i) q^{72} +37991.9i q^{73} -79353.6i q^{74} +(5482.10 + 5271.50i) q^{75} +62516.8 q^{76} -61916.0 q^{77} +(7398.80 - 7694.39i) q^{78} -18676.1 q^{79} +61382.6i q^{80} +(-58868.0 + 4620.41i) q^{81} -125879. i q^{82} +108851. q^{83} +(25690.2 + 24703.3i) q^{84} +39639.3 q^{85} +48196.6i q^{86} +(73955.5 - 76910.1i) q^{87} -35087.9 q^{88} -51749.3 q^{89} +(-94307.4 + 3695.30i) q^{90} +8213.55i q^{91} -11097.2 q^{92} +(11372.2 - 11826.5i) q^{93} -209869. q^{94} -127384. i q^{95} +(83096.8 + 79904.6i) q^{96} +90907.7i q^{97} +64872.0 q^{98} +(-6493.63 - 165723. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} + O(q^{10}) \) \( 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} - 1244q^{12} + 1116q^{15} + 14724q^{16} + 1784q^{19} + 6388q^{21} - 8140q^{22} - 48208q^{25} - 6458q^{27} - 19092q^{28} - 20832q^{36} - 134984q^{45} + 51180q^{46} + 61720q^{48} + 174556q^{49} + 8332q^{51} + 236784q^{57} + 375208q^{60} - 429890q^{63} + 561472q^{64} - 11596q^{66} + 169948q^{75} + 111488q^{76} + 356264q^{78} + 180260q^{79} + 79554q^{81} + 269308q^{84} + 111028q^{85} - 318764q^{87} - 1242976q^{88} - 513608q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.56324 −1.33701 −0.668503 0.743710i \(-0.733064\pi\)
−0.668503 + 0.743710i \(0.733064\pi\)
\(3\) 11.2364 + 10.8048i 0.720817 + 0.693126i
\(4\) 25.2027 0.787583
\(5\) 51.3528i 0.918627i −0.888274 0.459314i \(-0.848095\pi\)
0.888274 0.459314i \(-0.151905\pi\)
\(6\) −84.9838 81.7190i −0.963736 0.926713i
\(7\) 90.7178 0.699758 0.349879 0.936795i \(-0.386223\pi\)
0.349879 + 0.936795i \(0.386223\pi\)
\(8\) 51.4099 0.284002
\(9\) 9.51431 + 242.814i 0.0391535 + 0.999233i
\(10\) 388.394i 1.22821i
\(11\) −682.512 −1.70070 −0.850352 0.526214i \(-0.823611\pi\)
−0.850352 + 0.526214i \(0.823611\pi\)
\(12\) 283.188 + 272.309i 0.567703 + 0.545894i
\(13\) 90.5395i 0.148587i 0.997236 + 0.0742933i \(0.0236701\pi\)
−0.997236 + 0.0742933i \(0.976330\pi\)
\(14\) −686.121 −0.935580
\(15\) 554.855 577.022i 0.636724 0.662162i
\(16\) −1195.31 −1.16730
\(17\) 771.900i 0.647797i 0.946092 + 0.323899i \(0.104994\pi\)
−0.946092 + 0.323899i \(0.895006\pi\)
\(18\) −71.9590 1836.46i −0.0523485 1.33598i
\(19\) 2480.56 1.57640 0.788199 0.615420i \(-0.211014\pi\)
0.788199 + 0.615420i \(0.211014\pi\)
\(20\) 1294.23i 0.723496i
\(21\) 1019.34 + 980.185i 0.504397 + 0.485020i
\(22\) 5162.01 2.27385
\(23\) −440.319 −0.173559 −0.0867796 0.996228i \(-0.527658\pi\)
−0.0867796 + 0.996228i \(0.527658\pi\)
\(24\) 577.663 + 555.472i 0.204714 + 0.196849i
\(25\) 487.887 0.156124
\(26\) 684.772i 0.198661i
\(27\) −2516.64 + 2831.16i −0.664372 + 0.747402i
\(28\) 2286.33 0.551117
\(29\) 6844.72i 1.51133i −0.654956 0.755667i \(-0.727313\pi\)
0.654956 0.755667i \(-0.272687\pi\)
\(30\) −4196.50 + 4364.16i −0.851304 + 0.885314i
\(31\) 1052.51i 0.196709i −0.995151 0.0983544i \(-0.968642\pi\)
0.995151 0.0983544i \(-0.0313579\pi\)
\(32\) 7395.31 1.27668
\(33\) −7668.99 7374.38i −1.22590 1.17880i
\(34\) 5838.07i 0.866108i
\(35\) 4658.62i 0.642816i
\(36\) 239.786 + 6119.55i 0.0308367 + 0.786979i
\(37\) 10492.0i 1.25995i 0.776614 + 0.629976i \(0.216935\pi\)
−0.776614 + 0.629976i \(0.783065\pi\)
\(38\) −18761.1 −2.10765
\(39\) −978.258 + 1017.34i −0.102989 + 0.107104i
\(40\) 2640.04i 0.260892i
\(41\) 16643.5i 1.54627i 0.634242 + 0.773134i \(0.281312\pi\)
−0.634242 + 0.773134i \(0.718688\pi\)
\(42\) −7709.55 7413.38i −0.674381 0.648474i
\(43\) 6372.48i 0.525578i −0.964853 0.262789i \(-0.915358\pi\)
0.964853 0.262789i \(-0.0846423\pi\)
\(44\) −17201.1 −1.33945
\(45\) 12469.2 488.587i 0.917923 0.0359675i
\(46\) 3330.24 0.232049
\(47\) 27748.5 1.83229 0.916146 0.400845i \(-0.131284\pi\)
0.916146 + 0.400845i \(0.131284\pi\)
\(48\) −13431.0 12915.0i −0.841406 0.809083i
\(49\) −8577.27 −0.510339
\(50\) −3690.01 −0.208738
\(51\) −8340.20 + 8673.40i −0.449005 + 0.466943i
\(52\) 2281.84i 0.117024i
\(53\) 26135.8i 1.27805i 0.769187 + 0.639023i \(0.220661\pi\)
−0.769187 + 0.639023i \(0.779339\pi\)
\(54\) 19033.9 21412.7i 0.888269 0.999281i
\(55\) 35048.9i 1.56231i
\(56\) 4663.80 0.198733
\(57\) 27872.6 + 26801.9i 1.13629 + 1.09264i
\(58\) 51768.3i 2.02066i
\(59\) 13187.9 + 23259.5i 0.493225 + 0.869902i
\(60\) 13983.8 14542.5i 0.501473 0.521508i
\(61\) 9403.19i 0.323557i −0.986827 0.161778i \(-0.948277\pi\)
0.986827 0.161778i \(-0.0517230\pi\)
\(62\) 7960.42i 0.263001i
\(63\) 863.118 + 22027.5i 0.0273980 + 0.699221i
\(64\) −17682.6 −0.539630
\(65\) 4649.46 0.136496
\(66\) 58002.5 + 55774.2i 1.63903 + 1.57606i
\(67\) 73133.4i 1.99035i 0.0981376 + 0.995173i \(0.468711\pi\)
−0.0981376 + 0.995173i \(0.531289\pi\)
\(68\) 19453.9i 0.510194i
\(69\) −4947.61 4757.54i −0.125104 0.120298i
\(70\) 35234.3i 0.859449i
\(71\) 43754.6i 1.03010i −0.857161 0.515048i \(-0.827774\pi\)
0.857161 0.515048i \(-0.172226\pi\)
\(72\) 489.130 + 12483.0i 0.0111197 + 0.283785i
\(73\) 37991.9i 0.834419i 0.908810 + 0.417210i \(0.136992\pi\)
−0.908810 + 0.417210i \(0.863008\pi\)
\(74\) 79353.6i 1.68456i
\(75\) 5482.10 + 5271.50i 0.112537 + 0.108213i
\(76\) 62516.8 1.24155
\(77\) −61916.0 −1.19008
\(78\) 7398.80 7694.39i 0.137697 0.143198i
\(79\) −18676.1 −0.336681 −0.168340 0.985729i \(-0.553841\pi\)
−0.168340 + 0.985729i \(0.553841\pi\)
\(80\) 61382.6i 1.07231i
\(81\) −58868.0 + 4620.41i −0.996934 + 0.0782470i
\(82\) 125879.i 2.06737i
\(83\) 108851. 1.73436 0.867179 0.497996i \(-0.165931\pi\)
0.867179 + 0.497996i \(0.165931\pi\)
\(84\) 25690.2 + 24703.3i 0.397255 + 0.381994i
\(85\) 39639.3 0.595084
\(86\) 48196.6i 0.702700i
\(87\) 73955.5 76910.1i 1.04754 1.08939i
\(88\) −35087.9 −0.483004
\(89\) −51749.3 −0.692516 −0.346258 0.938139i \(-0.612548\pi\)
−0.346258 + 0.938139i \(0.612548\pi\)
\(90\) −94307.4 + 3695.30i −1.22727 + 0.0480887i
\(91\) 8213.55i 0.103975i
\(92\) −11097.2 −0.136692
\(93\) 11372.2 11826.5i 0.136344 0.141791i
\(94\) −209869. −2.44978
\(95\) 127384.i 1.44812i
\(96\) 83096.8 + 79904.6i 0.920251 + 0.884899i
\(97\) 90907.7i 0.981005i 0.871440 + 0.490503i \(0.163187\pi\)
−0.871440 + 0.490503i \(0.836813\pi\)
\(98\) 64872.0 0.682326
\(99\) −6493.63 165723.i −0.0665886 1.69940i
\(100\) 12296.0 0.122960
\(101\) −73494.3 −0.716886 −0.358443 0.933552i \(-0.616692\pi\)
−0.358443 + 0.933552i \(0.616692\pi\)
\(102\) 63079.0 65599.0i 0.600322 0.624305i
\(103\) 105537.i 0.980193i 0.871668 + 0.490096i \(0.163038\pi\)
−0.871668 + 0.490096i \(0.836962\pi\)
\(104\) 4654.63i 0.0421989i
\(105\) 50335.3 52346.2i 0.445553 0.463353i
\(106\) 197672.i 1.70875i
\(107\) 205373.i 1.73414i 0.498186 + 0.867070i \(0.334000\pi\)
−0.498186 + 0.867070i \(0.666000\pi\)
\(108\) −63426.0 + 71352.7i −0.523248 + 0.588642i
\(109\) 15975.9i 0.128795i −0.997924 0.0643976i \(-0.979487\pi\)
0.997924 0.0643976i \(-0.0205126\pi\)
\(110\) 265084.i 2.08882i
\(111\) −113364. + 117893.i −0.873305 + 0.908195i
\(112\) −108436. −0.816824
\(113\) 187107. 1.37846 0.689229 0.724544i \(-0.257950\pi\)
0.689229 + 0.724544i \(0.257950\pi\)
\(114\) −210808. 202709.i −1.51923 1.46087i
\(115\) 22611.6i 0.159436i
\(116\) 172505.i 1.19030i
\(117\) −21984.2 + 861.421i −0.148473 + 0.00581769i
\(118\) −99743.2 175917.i −0.659444 1.16306i
\(119\) 70025.1i 0.453301i
\(120\) 28525.0 29664.6i 0.180831 0.188056i
\(121\) 304772. 1.89239
\(122\) 71118.6i 0.432597i
\(123\) −179829. + 187013.i −1.07176 + 1.11458i
\(124\) 26526.2i 0.154925i
\(125\) 185532.i 1.06205i
\(126\) −6527.97 166600.i −0.0366312 0.934862i
\(127\) −160262. −0.881703 −0.440851 0.897580i \(-0.645323\pi\)
−0.440851 + 0.897580i \(0.645323\pi\)
\(128\) −102912. −0.555190
\(129\) 68853.1 71603.8i 0.364291 0.378845i
\(130\) −35165.0 −0.182496
\(131\) 16913.4 0.0861098 0.0430549 0.999073i \(-0.486291\pi\)
0.0430549 + 0.999073i \(0.486291\pi\)
\(132\) −193279. 185854.i −0.965495 0.928404i
\(133\) 225031. 1.10310
\(134\) 553125.i 2.66110i
\(135\) 145388. + 129236.i 0.686584 + 0.610310i
\(136\) 39683.3i 0.183976i
\(137\) 125031.i 0.569135i 0.958656 + 0.284568i \(0.0918500\pi\)
−0.958656 + 0.284568i \(0.908150\pi\)
\(138\) 37419.9 + 35982.4i 0.167265 + 0.160839i
\(139\) −85153.3 −0.373822 −0.186911 0.982377i \(-0.559848\pi\)
−0.186911 + 0.982377i \(0.559848\pi\)
\(140\) 117410.i 0.506272i
\(141\) 311794. + 299816.i 1.32075 + 1.27001i
\(142\) 330927.i 1.37724i
\(143\) 61794.3i 0.252702i
\(144\) −11372.6 290238.i −0.0457038 1.16640i
\(145\) −351496. −1.38835
\(146\) 287342.i 1.11562i
\(147\) −96377.8 92675.4i −0.367861 0.353729i
\(148\) 264426.i 0.992318i
\(149\) 160185. 0.591092 0.295546 0.955329i \(-0.404498\pi\)
0.295546 + 0.955329i \(0.404498\pi\)
\(150\) −41462.5 39869.6i −0.150462 0.144682i
\(151\) 271823.i 0.970160i −0.874470 0.485080i \(-0.838790\pi\)
0.874470 0.485080i \(-0.161210\pi\)
\(152\) 127525. 0.447701
\(153\) −187428. + 7344.10i −0.647300 + 0.0253635i
\(154\) 468286. 1.59114
\(155\) −54049.6 −0.180702
\(156\) −24654.7 + 25639.7i −0.0811126 + 0.0843531i
\(157\) 116338.i 0.376681i −0.982104 0.188340i \(-0.939689\pi\)
0.982104 0.188340i \(-0.0603108\pi\)
\(158\) 141252. 0.450144
\(159\) −282391. + 293673.i −0.885847 + 0.921237i
\(160\) 379770.i 1.17279i
\(161\) −39944.8 −0.121449
\(162\) 445233. 34945.3i 1.33291 0.104617i
\(163\) −157521. −0.464377 −0.232188 0.972671i \(-0.574589\pi\)
−0.232188 + 0.972671i \(0.574589\pi\)
\(164\) 419461.i 1.21782i
\(165\) −378695. + 393825.i −1.08288 + 1.12614i
\(166\) −823270. −2.31885
\(167\) 284864.i 0.790399i −0.918595 0.395199i \(-0.870676\pi\)
0.918595 0.395199i \(-0.129324\pi\)
\(168\) 52404.4 + 50391.2i 0.143250 + 0.137747i
\(169\) 363096. 0.977922
\(170\) −299802. −0.795631
\(171\) 23600.8 + 602314.i 0.0617216 + 1.57519i
\(172\) 160603.i 0.413936i
\(173\) 331355. 0.841740 0.420870 0.907121i \(-0.361725\pi\)
0.420870 + 0.907121i \(0.361725\pi\)
\(174\) −559344. + 581690.i −1.40057 + 1.45653i
\(175\) 44260.0 0.109249
\(176\) 815814. 1.98522
\(177\) −103129. + 403845.i −0.247426 + 0.968907i
\(178\) 391393. 0.925897
\(179\) −284128. −0.662799 −0.331399 0.943491i \(-0.607521\pi\)
−0.331399 + 0.943491i \(0.607521\pi\)
\(180\) 314256. 12313.7i 0.722941 0.0283274i
\(181\) 353188. 0.801327 0.400663 0.916225i \(-0.368780\pi\)
0.400663 + 0.916225i \(0.368780\pi\)
\(182\) 62121.1i 0.139015i
\(183\) 101599. 105658.i 0.224266 0.233225i
\(184\) −22636.7 −0.0492912
\(185\) 538794. 1.15743
\(186\) −86010.4 + 89446.6i −0.182293 + 0.189575i
\(187\) 526831.i 1.10171i
\(188\) 699336. 1.44308
\(189\) −228304. + 256836.i −0.464899 + 0.523000i
\(190\) 963435.i 1.93615i
\(191\) 409474. 0.812162 0.406081 0.913837i \(-0.366895\pi\)
0.406081 + 0.913837i \(0.366895\pi\)
\(192\) −198689. 191056.i −0.388974 0.374032i
\(193\) −77555.3 −0.149871 −0.0749356 0.997188i \(-0.523875\pi\)
−0.0749356 + 0.997188i \(0.523875\pi\)
\(194\) 687557.i 1.31161i
\(195\) 52243.3 + 50236.3i 0.0983884 + 0.0946087i
\(196\) −216170. −0.401935
\(197\) 666250.i 1.22313i 0.791195 + 0.611564i \(0.209459\pi\)
−0.791195 + 0.611564i \(0.790541\pi\)
\(198\) 49112.9 + 1.25341e6i 0.0890293 + 2.27211i
\(199\) −151342. −0.270911 −0.135456 0.990783i \(-0.543250\pi\)
−0.135456 + 0.990783i \(0.543250\pi\)
\(200\) 25082.2 0.0443395
\(201\) −790188. + 821757.i −1.37956 + 1.43467i
\(202\) 555855. 0.958480
\(203\) 620938.i 1.05757i
\(204\) −210195. + 218593.i −0.353629 + 0.367756i
\(205\) 854691. 1.42044
\(206\) 798202.i 1.31052i
\(207\) −4189.33 106915.i −0.00679545 0.173426i
\(208\) 108223.i 0.173445i
\(209\) −1.69301e6 −2.68099
\(210\) −380698. + 395907.i −0.595706 + 0.619505i
\(211\) 252243.i 0.390043i 0.980799 + 0.195021i \(0.0624776\pi\)
−0.980799 + 0.195021i \(0.937522\pi\)
\(212\) 658693.i 1.00657i
\(213\) 472758. 491645.i 0.713986 0.742511i
\(214\) 1.55329e6i 2.31856i
\(215\) −327245. −0.482810
\(216\) −129380. + 145549.i −0.188683 + 0.212264i
\(217\) 95481.8i 0.137648i
\(218\) 120830.i 0.172200i
\(219\) −410494. + 426893.i −0.578357 + 0.601463i
\(220\) 883327.i 1.23045i
\(221\) −69887.5 −0.0962540
\(222\) 857397. 891650.i 1.16761 1.21426i
\(223\) 278083. 0.374466 0.187233 0.982315i \(-0.440048\pi\)
0.187233 + 0.982315i \(0.440048\pi\)
\(224\) 670887. 0.893366
\(225\) 4641.91 + 118466.i 0.00611280 + 0.156004i
\(226\) −1.41513e6 −1.84300
\(227\) −1.13709e6 −1.46463 −0.732317 0.680964i \(-0.761561\pi\)
−0.732317 + 0.680964i \(0.761561\pi\)
\(228\) 702465. + 675479.i 0.894927 + 0.860547i
\(229\) 556703.i 0.701511i −0.936467 0.350756i \(-0.885925\pi\)
0.936467 0.350756i \(-0.114075\pi\)
\(230\) 171017.i 0.213167i
\(231\) −695715. 668988.i −0.857830 0.824875i
\(232\) 351886.i 0.429222i
\(233\) 1.01799e6 1.22844 0.614218 0.789137i \(-0.289472\pi\)
0.614218 + 0.789137i \(0.289472\pi\)
\(234\) 166272. 6515.14i 0.198509 0.00777828i
\(235\) 1.42496e6i 1.68319i
\(236\) 332370. + 586201.i 0.388456 + 0.685120i
\(237\) −209852. 201791.i −0.242685 0.233362i
\(238\) 529617.i 0.606066i
\(239\) 141346.i 0.160062i −0.996792 0.0800311i \(-0.974498\pi\)
0.996792 0.0800311i \(-0.0255020\pi\)
\(240\) −663224. + 689721.i −0.743246 + 0.772939i
\(241\) 405397. 0.449612 0.224806 0.974403i \(-0.427825\pi\)
0.224806 + 0.974403i \(0.427825\pi\)
\(242\) −2.30506e6 −2.53014
\(243\) −711388. 584137.i −0.772842 0.634599i
\(244\) 236985.i 0.254828i
\(245\) 440467.i 0.468812i
\(246\) 1.36009e6 1.41443e6i 1.43295 1.49019i
\(247\) 224589.i 0.234232i
\(248\) 54109.6i 0.0558657i
\(249\) 1.22310e6 + 1.17611e6i 1.25015 + 1.20213i
\(250\) 1.40322e6i 1.41996i
\(251\) 1.09091e6i 1.09296i 0.837471 + 0.546482i \(0.184033\pi\)
−0.837471 + 0.546482i \(0.815967\pi\)
\(252\) 21752.9 + 555153.i 0.0215782 + 0.550695i
\(253\) 300523. 0.295173
\(254\) 1.21210e6 1.17884
\(255\) 445404. + 428293.i 0.428947 + 0.412468i
\(256\) 1.34419e6 1.28192
\(257\) 4748.15i 0.00448427i 0.999997 + 0.00224213i \(0.000713694\pi\)
−0.999997 + 0.00224213i \(0.999286\pi\)
\(258\) −520753. + 541557.i −0.487060 + 0.506518i
\(259\) 951812.i 0.881661i
\(260\) 117179. 0.107502
\(261\) 1.66199e6 65122.7i 1.51018 0.0591741i
\(262\) −127920. −0.115129
\(263\) 500879.i 0.446522i 0.974759 + 0.223261i \(0.0716703\pi\)
−0.974759 + 0.223261i \(0.928330\pi\)
\(264\) −394262. 379116.i −0.348157 0.334782i
\(265\) 1.34215e6 1.17405
\(266\) −1.70197e6 −1.47485
\(267\) −581477. 559139.i −0.499177 0.480000i
\(268\) 1.84316e6i 1.56756i
\(269\) −1.84500e6 −1.55459 −0.777293 0.629139i \(-0.783408\pi\)
−0.777293 + 0.629139i \(0.783408\pi\)
\(270\) −1.09960e6 977447.i −0.917967 0.815988i
\(271\) 417363. 0.345216 0.172608 0.984991i \(-0.444781\pi\)
0.172608 + 0.984991i \(0.444781\pi\)
\(272\) 922661.i 0.756171i
\(273\) −88745.4 + 92290.9i −0.0720675 + 0.0749467i
\(274\) 945638.i 0.760937i
\(275\) −332989. −0.265520
\(276\) −124693. 119903.i −0.0985301 0.0947449i
\(277\) 50456.3 0.0395108 0.0197554 0.999805i \(-0.493711\pi\)
0.0197554 + 0.999805i \(0.493711\pi\)
\(278\) 644035. 0.499802
\(279\) 255565. 10013.9i 0.196558 0.00770184i
\(280\) 239499.i 0.182561i
\(281\) 289552.i 0.218756i 0.994000 + 0.109378i \(0.0348859\pi\)
−0.994000 + 0.109378i \(0.965114\pi\)
\(282\) −2.35817e6 2.26758e6i −1.76584 1.69801i
\(283\) 1.82269e6i 1.35284i −0.736514 0.676422i \(-0.763530\pi\)
0.736514 0.676422i \(-0.236470\pi\)
\(284\) 1.10273e6i 0.811287i
\(285\) 1.37635e6 1.43134e6i 1.00373 1.04383i
\(286\) 467366.i 0.337864i
\(287\) 1.50986e6i 1.08201i
\(288\) 70361.3 + 1.79568e6i 0.0499865 + 1.27570i
\(289\) 824027. 0.580359
\(290\) 2.65845e6 1.85624
\(291\) −982236. + 1.02148e6i −0.679960 + 0.707125i
\(292\) 957498.i 0.657175i
\(293\) 2.68342e6i 1.82608i −0.407872 0.913039i \(-0.633729\pi\)
0.407872 0.913039i \(-0.366271\pi\)
\(294\) 728929. + 700926.i 0.491832 + 0.472938i
\(295\) 1.19444e6 677235.i 0.799116 0.453090i
\(296\) 539393.i 0.357829i
\(297\) 1.71764e6 1.93230e6i 1.12990 1.27111i
\(298\) −1.21151e6 −0.790293
\(299\) 39866.2i 0.0257886i
\(300\) 138164. + 132856.i 0.0886320 + 0.0852271i
\(301\) 578097.i 0.367777i
\(302\) 2.05586e6i 1.29711i
\(303\) −825813. 794088.i −0.516743 0.496892i
\(304\) −2.96504e6 −1.84012
\(305\) −482880. −0.297228
\(306\) 1.41756e6 55545.2i 0.865444 0.0339112i
\(307\) 509116. 0.308298 0.154149 0.988048i \(-0.450736\pi\)
0.154149 + 0.988048i \(0.450736\pi\)
\(308\) −1.56045e6 −0.937288
\(309\) −1.14030e6 + 1.18586e6i −0.679397 + 0.706539i
\(310\) 408790. 0.241600
\(311\) 1.38212e6i 0.810297i 0.914251 + 0.405148i \(0.132780\pi\)
−0.914251 + 0.405148i \(0.867220\pi\)
\(312\) −50292.1 + 52301.4i −0.0292492 + 0.0304177i
\(313\) 1.90212e6i 1.09743i 0.836009 + 0.548716i \(0.184883\pi\)
−0.836009 + 0.548716i \(0.815117\pi\)
\(314\) 879895.i 0.503624i
\(315\) 1.13118e6 44323.5i 0.642324 0.0251685i
\(316\) −470687. −0.265164
\(317\) 3.01161e6i 1.68326i −0.540055 0.841630i \(-0.681597\pi\)
0.540055 0.841630i \(-0.318403\pi\)
\(318\) 2.13579e6 2.22112e6i 1.18438 1.23170i
\(319\) 4.67160e6i 2.57033i
\(320\) 908052.i 0.495719i
\(321\) −2.21901e6 + 2.30766e6i −1.20198 + 1.25000i
\(322\) 302112. 0.162378
\(323\) 1.91475e6i 1.02119i
\(324\) −1.48363e6 + 116447.i −0.785169 + 0.0616260i
\(325\) 44173.0i 0.0231979i
\(326\) 1.19137e6 0.620874
\(327\) 172616. 179512.i 0.0892712 0.0928377i
\(328\) 855641.i 0.439144i
\(329\) 2.51728e6 1.28216
\(330\) 2.86417e6 2.97859e6i 1.44782 1.50566i
\(331\) −2.25633e6 −1.13196 −0.565981 0.824418i \(-0.691503\pi\)
−0.565981 + 0.824418i \(0.691503\pi\)
\(332\) 2.74335e6 1.36595
\(333\) −2.54760e6 + 99824.2i −1.25899 + 0.0493316i
\(334\) 2.15449e6i 1.05677i
\(335\) 3.75560e6 1.82839
\(336\) −1.21843e6 1.17163e6i −0.588781 0.566162i
\(337\) 893788.i 0.428706i −0.976756 0.214353i \(-0.931236\pi\)
0.976756 0.214353i \(-0.0687643\pi\)
\(338\) −2.74618e6 −1.30749
\(339\) 2.10241e6 + 2.02164e6i 0.993615 + 0.955444i
\(340\) 999015. 0.468678
\(341\) 718354.i 0.334543i
\(342\) −178499. 4.55545e6i −0.0825221 2.10604i
\(343\) −2.30281e6 −1.05687
\(344\) 327608.i 0.149265i
\(345\) −244313. + 254074.i −0.110509 + 0.114924i
\(346\) −2.50612e6 −1.12541
\(347\) 208504. 0.0929589 0.0464794 0.998919i \(-0.485200\pi\)
0.0464794 + 0.998919i \(0.485200\pi\)
\(348\) 1.86388e6 1.93834e6i 0.825029 0.857989i
\(349\) 3.61848e6i 1.59024i −0.606454 0.795119i \(-0.707408\pi\)
0.606454 0.795119i \(-0.292592\pi\)
\(350\) −334750. −0.146066
\(351\) −256332. 227855.i −0.111054 0.0987168i
\(352\) −5.04739e6 −2.17125
\(353\) −920606. −0.393221 −0.196611 0.980482i \(-0.562993\pi\)
−0.196611 + 0.980482i \(0.562993\pi\)
\(354\) 779987. 3.05438e6i 0.330811 1.29543i
\(355\) −2.24692e6 −0.946275
\(356\) −1.30422e6 −0.545414
\(357\) −756605. + 786832.i −0.314195 + 0.326747i
\(358\) 2.14893e6 0.886166
\(359\) 3.37657e6i 1.38274i −0.722503 0.691368i \(-0.757008\pi\)
0.722503 0.691368i \(-0.242992\pi\)
\(360\) 641039. 25118.2i 0.260692 0.0102149i
\(361\) 3.67709e6 1.48503
\(362\) −2.67125e6 −1.07138
\(363\) 3.42455e6 + 3.29299e6i 1.36407 + 1.31167i
\(364\) 207003.i 0.0818887i
\(365\) 1.95099e6 0.766520
\(366\) −768420. + 799119.i −0.299844 + 0.311823i
\(367\) 752319.i 0.291566i 0.989317 + 0.145783i \(0.0465701\pi\)
−0.989317 + 0.145783i \(0.953430\pi\)
\(368\) 526318. 0.202595
\(369\) −4.04127e6 + 158351.i −1.54508 + 0.0605419i
\(370\) −4.07503e6 −1.54749
\(371\) 2.37099e6i 0.894323i
\(372\) 286609. 298059.i 0.107382 0.111672i
\(373\) −3.35113e6 −1.24715 −0.623576 0.781763i \(-0.714321\pi\)
−0.623576 + 0.781763i \(0.714321\pi\)
\(374\) 3.98456e6i 1.47299i
\(375\) 2.00463e6 2.08472e6i 0.736132 0.765541i
\(376\) 1.42655e6 0.520375
\(377\) 619717. 0.224564
\(378\) 1.72672e6 1.94252e6i 0.621573 0.699254i
\(379\) −1.39388e6 −0.498456 −0.249228 0.968445i \(-0.580177\pi\)
−0.249228 + 0.968445i \(0.580177\pi\)
\(380\) 3.21041e6i 1.14052i
\(381\) −1.80078e6 1.73160e6i −0.635546 0.611131i
\(382\) −3.09695e6 −1.08587
\(383\) 5.08435e6i 1.77108i −0.464560 0.885541i \(-0.653788\pi\)
0.464560 0.885541i \(-0.346212\pi\)
\(384\) −1.15636e6 1.11194e6i −0.400190 0.384817i
\(385\) 3.17956e6i 1.09324i
\(386\) 586569. 0.200379
\(387\) 1.54732e6 60629.7i 0.525175 0.0205782i
\(388\) 2.29112e6i 0.772623i
\(389\) 133568.i 0.0447536i −0.999750 0.0223768i \(-0.992877\pi\)
0.999750 0.0223768i \(-0.00712335\pi\)
\(390\) −395129. 379949.i −0.131546 0.126492i
\(391\) 339882.i 0.112431i
\(392\) −440957. −0.144938
\(393\) 190046. + 182745.i 0.0620694 + 0.0596849i
\(394\) 5.03901e6i 1.63533i
\(395\) 959070.i 0.309284i
\(396\) −163657. 4.17667e6i −0.0524440 1.33842i
\(397\) 4.15269e6i 1.32237i −0.750223 0.661185i \(-0.770054\pi\)
0.750223 0.661185i \(-0.229946\pi\)
\(398\) 1.14464e6 0.362210
\(399\) 2.52855e6 + 2.43141e6i 0.795131 + 0.764585i
\(400\) −583177. −0.182243
\(401\) −2.86291e6 −0.889092 −0.444546 0.895756i \(-0.646635\pi\)
−0.444546 + 0.895756i \(0.646635\pi\)
\(402\) 5.97639e6 6.21515e6i 1.84448 1.91817i
\(403\) 95294.1 0.0292283
\(404\) −1.85225e6 −0.564607
\(405\) 237271. + 3.02304e6i 0.0718798 + 0.915811i
\(406\) 4.69631e6i 1.41397i
\(407\) 7.16092e6i 2.14281i
\(408\) −428769. + 445899.i −0.127518 + 0.132613i
\(409\) 1.11852e6i 0.330625i 0.986241 + 0.165313i \(0.0528633\pi\)
−0.986241 + 0.165313i \(0.947137\pi\)
\(410\) −6.46423e6 −1.89914
\(411\) −1.35093e6 + 1.40490e6i −0.394482 + 0.410242i
\(412\) 2.65981e6i 0.771983i
\(413\) 1.19638e6 + 2.11005e6i 0.345138 + 0.608720i
\(414\) 31684.9 + 808627.i 0.00908556 + 0.231872i
\(415\) 5.58983e6i 1.59323i
\(416\) 669568.i 0.189697i
\(417\) −956818. 920061.i −0.269457 0.259105i
\(418\) 1.28047e7 3.58449
\(419\) 2.23799e6 0.622764 0.311382 0.950285i \(-0.399208\pi\)
0.311382 + 0.950285i \(0.399208\pi\)
\(420\) 1.26858e6 1.31926e6i 0.350910 0.364929i
\(421\) 5.55658e6i 1.52793i −0.645260 0.763963i \(-0.723251\pi\)
0.645260 0.763963i \(-0.276749\pi\)
\(422\) 1.90777e6i 0.521489i
\(423\) 264008. + 6.73771e6i 0.0717407 + 1.83089i
\(424\) 1.34364e6i 0.362968i
\(425\) 376600.i 0.101137i
\(426\) −3.57559e6 + 3.71843e6i −0.954604 + 0.992741i
\(427\) 853037.i 0.226411i
\(428\) 5.17595e6i 1.36578i
\(429\) 667673. 694347.i 0.175154 0.182152i
\(430\) 2.47503e6 0.645520
\(431\) −4.62303e6 −1.19876 −0.599381 0.800464i \(-0.704587\pi\)
−0.599381 + 0.800464i \(0.704587\pi\)
\(432\) 3.00816e6 3.38411e6i 0.775518 0.872440i
\(433\) 1.20291e6 0.308328 0.154164 0.988045i \(-0.450732\pi\)
0.154164 + 0.988045i \(0.450732\pi\)
\(434\) 722152.i 0.184037i
\(435\) −3.94955e6 3.79783e6i −1.00075 0.962303i
\(436\) 402636.i 0.101437i
\(437\) −1.09224e6 −0.273598
\(438\) 3.10466e6 3.22870e6i 0.773267 0.804160i
\(439\) 1.81269e6 0.448912 0.224456 0.974484i \(-0.427939\pi\)
0.224456 + 0.974484i \(0.427939\pi\)
\(440\) 1.80186e6i 0.443700i
\(441\) −81606.8 2.08268e6i −0.0199816 0.509948i
\(442\) 528576. 0.128692
\(443\) −4.60126e6 −1.11395 −0.556977 0.830528i \(-0.688039\pi\)
−0.556977 + 0.830528i \(0.688039\pi\)
\(444\) −2.85706e6 + 2.97121e6i −0.687801 + 0.715279i
\(445\) 2.65747e6i 0.636164i
\(446\) −2.10321e6 −0.500664
\(447\) 1.79990e6 + 1.73076e6i 0.426069 + 0.409701i
\(448\) −1.60413e6 −0.377610
\(449\) 3.94651e6i 0.923840i 0.886921 + 0.461920i \(0.152839\pi\)
−0.886921 + 0.461920i \(0.847161\pi\)
\(450\) −35107.9 895984.i −0.00817284 0.208578i
\(451\) 1.13594e7i 2.62975i
\(452\) 4.71559e6 1.08565
\(453\) 2.93698e6 3.05432e6i 0.672443 0.699308i
\(454\) 8.60007e6 1.95822
\(455\) 421789. 0.0955139
\(456\) 1.43293e6 + 1.37788e6i 0.322710 + 0.310313i
\(457\) 1.48061e6i 0.331626i 0.986157 + 0.165813i \(0.0530248\pi\)
−0.986157 + 0.165813i \(0.946975\pi\)
\(458\) 4.21048e6i 0.937924i
\(459\) −2.18537e6 1.94259e6i −0.484165 0.430378i
\(460\) 569873.i 0.125569i
\(461\) 1.08421e6i 0.237608i −0.992918 0.118804i \(-0.962094\pi\)
0.992918 0.118804i \(-0.0379060\pi\)
\(462\) 5.26186e6 + 5.05972e6i 1.14692 + 1.10286i
\(463\) 5.94024e6i 1.28781i 0.765106 + 0.643904i \(0.222687\pi\)
−0.765106 + 0.643904i \(0.777313\pi\)
\(464\) 8.18157e6i 1.76417i
\(465\) −607324. 583993.i −0.130253 0.125249i
\(466\) −7.69928e6 −1.64242
\(467\) −4.27370e6 −0.906800 −0.453400 0.891307i \(-0.649789\pi\)
−0.453400 + 0.891307i \(0.649789\pi\)
\(468\) −554061. + 21710.1i −0.116935 + 0.00458192i
\(469\) 6.63450e6i 1.39276i
\(470\) 1.07773e7i 2.25044i
\(471\) 1.25701e6 1.30723e6i 0.261087 0.271518i
\(472\) 677988. + 1.19577e6i 0.140077 + 0.247054i
\(473\) 4.34929e6i 0.893852i
\(474\) 1.58716e6 + 1.52619e6i 0.324471 + 0.312006i
\(475\) 1.21023e6 0.246113
\(476\) 1.76482e6i 0.357012i
\(477\) −6.34614e6 + 248664.i −1.27707 + 0.0500400i
\(478\) 1.06903e6i 0.214004i
\(479\) 8.56691e6i 1.70602i 0.521891 + 0.853012i \(0.325227\pi\)
−0.521891 + 0.853012i \(0.674773\pi\)
\(480\) 4.10333e6 4.26726e6i 0.812892 0.845368i
\(481\) −949941. −0.187212
\(482\) −3.06612e6 −0.601134
\(483\) −448836. 431594.i −0.0875427 0.0841796i
\(484\) 7.68106e6 1.49042
\(485\) 4.66837e6 0.901178
\(486\) 5.38040e6 + 4.41797e6i 1.03329 + 0.848462i
\(487\) 6.39670e6 1.22217 0.611087 0.791563i \(-0.290732\pi\)
0.611087 + 0.791563i \(0.290732\pi\)
\(488\) 483417.i 0.0918909i
\(489\) −1.76998e6 1.70198e6i −0.334731 0.321872i
\(490\) 3.33136e6i 0.626804i
\(491\) 355606.i 0.0665681i −0.999446 0.0332840i \(-0.989403\pi\)
0.999446 0.0332840i \(-0.0105966\pi\)
\(492\) −4.53217e6 + 4.71323e6i −0.844099 + 0.877822i
\(493\) 5.28344e6 0.979038
\(494\) 1.69862e6i 0.313169i
\(495\) −8.51036e6 + 333466.i −1.56112 + 0.0611701i
\(496\) 1.25808e6i 0.229617i
\(497\) 3.96932e6i 0.720818i
\(498\) −9.25061e6 8.89523e6i −1.67146 1.60725i
\(499\) −6.30405e6 −1.13336 −0.566681 0.823937i \(-0.691773\pi\)
−0.566681 + 0.823937i \(0.691773\pi\)
\(500\) 4.67590e6i 0.836450i
\(501\) 3.07789e6 3.20085e6i 0.547846 0.569733i
\(502\) 8.25085e6i 1.46130i
\(503\) 8.08256e6 1.42439 0.712195 0.701982i \(-0.247701\pi\)
0.712195 + 0.701982i \(0.247701\pi\)
\(504\) 44372.8 + 1.13243e6i 0.00778109 + 0.198580i
\(505\) 3.77414e6i 0.658551i
\(506\) −2.27293e6 −0.394647
\(507\) 4.07989e6 + 3.92316e6i 0.704903 + 0.677823i
\(508\) −4.03904e6 −0.694414
\(509\) 1.08452e6 0.185542 0.0927709 0.995687i \(-0.470428\pi\)
0.0927709 + 0.995687i \(0.470428\pi\)
\(510\) −3.36870e6 3.23928e6i −0.573504 0.551472i
\(511\) 3.44655e6i 0.583891i
\(512\) −6.87327e6 −1.15875
\(513\) −6.24267e6 + 7.02286e6i −1.04731 + 1.17820i
\(514\) 35911.4i 0.00599549i
\(515\) 5.41962e6 0.900432
\(516\) 1.73528e6 1.80461e6i 0.286910 0.298372i
\(517\) −1.89387e7 −3.11619
\(518\) 7.19879e6i 1.17879i
\(519\) 3.72324e6 + 3.58021e6i 0.606740 + 0.583432i
\(520\) 239028. 0.0387651
\(521\) 2.94176e6i 0.474802i −0.971412 0.237401i \(-0.923704\pi\)
0.971412 0.237401i \(-0.0762956\pi\)
\(522\) −1.25700e7 + 492539.i −2.01911 + 0.0791160i
\(523\) −7.68801e6 −1.22902 −0.614511 0.788908i \(-0.710647\pi\)
−0.614511 + 0.788908i \(0.710647\pi\)
\(524\) 426263. 0.0678186
\(525\) 497325. + 478219.i 0.0787484 + 0.0757232i
\(526\) 3.78827e6i 0.597003i
\(527\) 812436. 0.127427
\(528\) 9.16683e6 + 8.81468e6i 1.43098 + 1.37601i
\(529\) −6.24246e6 −0.969877
\(530\) −1.01510e7 −1.56971
\(531\) −5.52225e6 + 3.42350e6i −0.849923 + 0.526906i
\(532\) 5.67139e6 0.868781
\(533\) −1.50689e6 −0.229755
\(534\) 4.39785e6 + 4.22890e6i 0.667402 + 0.641763i
\(535\) 1.05465e7 1.59303
\(536\) 3.75978e6i 0.565263i
\(537\) −3.19258e6 3.06994e6i −0.477757 0.459403i
\(538\) 1.39542e7 2.07849
\(539\) 5.85409e6 0.867936
\(540\) 3.66416e6 + 3.25710e6i 0.540742 + 0.480670i
\(541\) 5.59453e6i 0.821809i 0.911678 + 0.410904i \(0.134787\pi\)
−0.911678 + 0.410904i \(0.865213\pi\)
\(542\) −3.15662e6 −0.461556
\(543\) 3.96857e6 + 3.81611e6i 0.577610 + 0.555420i
\(544\) 5.70844e6i 0.827029i
\(545\) −820409. −0.118315
\(546\) 671203. 698019.i 0.0963546 0.100204i
\(547\) 8.95135e6 1.27915 0.639573 0.768730i \(-0.279111\pi\)
0.639573 + 0.768730i \(0.279111\pi\)
\(548\) 3.15111e6i 0.448241i
\(549\) 2.28322e6 89464.9i 0.323309 0.0126684i
\(550\) 2.51848e6 0.355002
\(551\) 1.69787e7i 2.38247i
\(552\) −254356. 244585.i −0.0355299 0.0341650i
\(553\) −1.69425e6 −0.235595
\(554\) −381613. −0.0528261
\(555\) 6.05412e6 + 5.82154e6i 0.834293 + 0.802242i
\(556\) −2.14609e6 −0.294416
\(557\) 3.54159e6i 0.483683i −0.970316 0.241841i \(-0.922249\pi\)
0.970316 0.241841i \(-0.0777513\pi\)
\(558\) −1.93290e6 + 75737.9i −0.262799 + 0.0102974i
\(559\) 576961. 0.0780938
\(560\) 5.56850e6i 0.750357i
\(561\) 5.69229e6 5.91970e6i 0.763624 0.794132i
\(562\) 2.18995e6i 0.292478i
\(563\) 5.89504e6 0.783818 0.391909 0.920004i \(-0.371815\pi\)
0.391909 + 0.920004i \(0.371815\pi\)
\(564\) 7.85803e6 + 7.55615e6i 1.04020 + 1.00024i
\(565\) 9.60846e6i 1.26629i
\(566\) 1.37855e7i 1.80876i
\(567\) −5.34037e6 + 419153.i −0.697612 + 0.0547539i
\(568\) 2.24942e6i 0.292550i
\(569\) 1.23342e7 1.59710 0.798548 0.601931i \(-0.205602\pi\)
0.798548 + 0.601931i \(0.205602\pi\)
\(570\) −1.04097e7 + 1.08256e7i −1.34199 + 1.39561i
\(571\) 1.24034e7i 1.59203i 0.605276 + 0.796015i \(0.293063\pi\)
−0.605276 + 0.796015i \(0.706937\pi\)
\(572\) 1.55738e6i 0.199024i
\(573\) 4.60102e6 + 4.42427e6i 0.585420 + 0.562930i
\(574\) 1.14195e7i 1.44666i
\(575\) −214826. −0.0270967
\(576\) −168238. 4.29358e6i −0.0211284 0.539216i
\(577\) 9.28511e6 1.16104 0.580520 0.814246i \(-0.302849\pi\)
0.580520 + 0.814246i \(0.302849\pi\)
\(578\) −6.23231e6 −0.775943
\(579\) −871444. 837966.i −0.108030 0.103880i
\(580\) −8.85863e6 −1.09344
\(581\) 9.87476e6 1.21363
\(582\) 7.42889e6 7.72568e6i 0.909110 0.945430i
\(583\) 1.78380e7i 2.17358i
\(584\) 1.95316e6i 0.236977i
\(585\) 44236.4 + 1.12895e6i 0.00534429 + 0.136391i
\(586\) 2.02954e7i 2.44148i
\(587\) −2.94212e6 −0.352423 −0.176212 0.984352i \(-0.556384\pi\)
−0.176212 + 0.984352i \(0.556384\pi\)
\(588\) −2.42898e6 2.33567e6i −0.289721 0.278591i
\(589\) 2.61083e6i 0.310091i
\(590\) −9.03385e6 + 5.12209e6i −1.06842 + 0.605784i
\(591\) −7.19868e6 + 7.48627e6i −0.847781 + 0.881651i
\(592\) 1.25412e7i 1.47074i
\(593\) 185695.i 0.0216852i −0.999941 0.0108426i \(-0.996549\pi\)
0.999941 0.0108426i \(-0.00345137\pi\)
\(594\) −1.29909e7 + 1.46144e7i −1.51068 + 1.69948i
\(595\) 3.59599e6 0.416415
\(596\) 4.03708e6 0.465534
\(597\) −1.70054e6 1.63521e6i −0.195277 0.187775i
\(598\) 301518.i 0.0344795i
\(599\) 7.69736e6i 0.876547i −0.898842 0.438273i \(-0.855590\pi\)
0.898842 0.438273i \(-0.144410\pi\)
\(600\) 281834. + 271007.i 0.0319607 + 0.0307329i
\(601\) 4.64907e6i 0.525025i −0.964929 0.262513i \(-0.915449\pi\)
0.964929 0.262513i \(-0.0845511\pi\)
\(602\) 4.37229e6i 0.491720i
\(603\) −1.77578e7 + 695813.i −1.98882 + 0.0779291i
\(604\) 6.85066e6i 0.764082i
\(605\) 1.56509e7i 1.73840i
\(606\) 6.24582e6 + 6.00588e6i 0.690889 + 0.664347i
\(607\) 4.50819e6 0.496628 0.248314 0.968680i \(-0.420124\pi\)
0.248314 + 0.968680i \(0.420124\pi\)
\(608\) 1.83445e7 2.01255
\(609\) 6.70909e6 6.97712e6i 0.733027 0.762312i
\(610\) 3.65214e6 0.397396
\(611\) 2.51233e6i 0.272254i
\(612\) −4.72368e6 + 185091.i −0.509803 + 0.0199759i
\(613\) 1.23655e7i 1.32911i 0.747240 + 0.664554i \(0.231379\pi\)
−0.747240 + 0.664554i \(0.768621\pi\)
\(614\) −3.85057e6 −0.412196
\(615\) 9.60366e6 + 9.23473e6i 1.02388 + 0.984547i
\(616\) −3.18310e6 −0.337986
\(617\) 8.93156e6i 0.944527i 0.881457 + 0.472264i \(0.156563\pi\)
−0.881457 + 0.472264i \(0.843437\pi\)
\(618\) 8.62438e6 8.96893e6i 0.908357 0.944647i
\(619\) 9.58850e6 1.00583 0.502914 0.864336i \(-0.332261\pi\)
0.502914 + 0.864336i \(0.332261\pi\)
\(620\) −1.36219e6 −0.142318
\(621\) 1.10812e6 1.24661e6i 0.115308 0.129719i
\(622\) 1.04533e7i 1.08337i
\(623\) −4.69459e6 −0.484593
\(624\) 1.16932e6 1.21604e6i 0.120219 0.125022i
\(625\) −8.00294e6 −0.819502
\(626\) 1.43862e7i 1.46727i
\(627\) −1.90234e7 1.82926e7i −1.93250 1.85826i
\(628\) 2.93203e6i 0.296668i
\(629\) −8.09878e6 −0.816194
\(630\) −8.55536e6 + 335230.i −0.858790 + 0.0336505i
\(631\) −1.05488e7 −1.05470 −0.527350 0.849648i \(-0.676814\pi\)
−0.527350 + 0.849648i \(0.676814\pi\)
\(632\) −960135. −0.0956180
\(633\) −2.72542e6 + 2.83430e6i −0.270349 + 0.281149i
\(634\) 2.27776e7i 2.25053i
\(635\) 8.22993e6i 0.809956i
\(636\) −7.11701e6 + 7.40135e6i −0.697678 + 0.725551i
\(637\) 776582.i 0.0758296i
\(638\) 3.53325e7i 3.43655i
\(639\) 1.06242e7 416295.i 1.02931 0.0403319i
\(640\) 5.28483e6i 0.510013i
\(641\) 1.11258e7i 1.06952i −0.845005 0.534758i \(-0.820403\pi\)
0.845005 0.534758i \(-0.179597\pi\)
\(642\) 1.67829e7 1.74534e7i 1.60705 1.67125i
\(643\) −909665. −0.0867669 −0.0433834 0.999058i \(-0.513814\pi\)
−0.0433834 + 0.999058i \(0.513814\pi\)
\(644\) −1.00671e6 −0.0956515
\(645\) −3.67706e6 3.53580e6i −0.348018 0.334648i
\(646\) 1.44817e7i 1.36533i
\(647\) 557807.i 0.0523869i 0.999657 + 0.0261935i \(0.00833859\pi\)
−0.999657 + 0.0261935i \(0.991661\pi\)
\(648\) −3.02640e6 + 237535.i −0.283132 + 0.0222223i
\(649\) −9.00089e6 1.58749e7i −0.838830 1.47945i
\(650\) 334091.i 0.0310157i
\(651\) 1.03166e6 1.07287e6i 0.0954077 0.0992193i
\(652\) −3.96996e6 −0.365736
\(653\) 5.96299e6i 0.547244i −0.961837 0.273622i \(-0.911778\pi\)
0.961837 0.273622i \(-0.0882217\pi\)
\(654\) −1.30554e6 + 1.35769e6i −0.119356 + 0.124125i
\(655\) 868551.i 0.0791028i
\(656\) 1.98942e7i 1.80495i
\(657\) −9.22496e6 + 361467.i −0.833779 + 0.0326705i
\(658\) −1.90388e7 −1.71425
\(659\) −92952.4 −0.00833772 −0.00416886 0.999991i \(-0.501327\pi\)
−0.00416886 + 0.999991i \(0.501327\pi\)
\(660\) −9.54413e6 + 9.92543e6i −0.852858 + 0.886930i
\(661\) 934288. 0.0831720 0.0415860 0.999135i \(-0.486759\pi\)
0.0415860 + 0.999135i \(0.486759\pi\)
\(662\) 1.70652e7 1.51344
\(663\) −785285. 755118.i −0.0693815 0.0667161i
\(664\) 5.59604e6 0.492562
\(665\) 1.15560e7i 1.01334i
\(666\) 1.92681e7 754995.i 1.68327 0.0659566i
\(667\) 3.01386e6i 0.262306i
\(668\) 7.17933e6i 0.622505i
\(669\) 3.12466e6 + 3.00462e6i 0.269922 + 0.259552i
\(670\) −2.84046e7 −2.44456
\(671\) 6.41779e6i 0.550275i
\(672\) 7.53837e6 + 7.24877e6i 0.643953 + 0.619215i
\(673\) 8.53811e6i 0.726648i −0.931663 0.363324i \(-0.881642\pi\)
0.931663 0.363324i \(-0.118358\pi\)
\(674\) 6.75994e6i 0.573183i
\(675\) −1.22783e6 + 1.38128e6i −0.103724 + 0.116687i
\(676\) 9.15098e6 0.770195
\(677\) 1.23950e7i 1.03938i −0.854356 0.519689i \(-0.826048\pi\)
0.854356 0.519689i \(-0.173952\pi\)
\(678\) −1.59010e7 1.52902e7i −1.32847 1.27743i
\(679\) 8.24695e6i 0.686466i
\(680\) 2.03785e6 0.169005
\(681\) −1.27768e7 1.22860e7i −1.05573 1.01518i
\(682\) 5.43308e6i 0.447286i
\(683\) −2.08318e7 −1.70874 −0.854369 0.519667i \(-0.826056\pi\)
−0.854369 + 0.519667i \(0.826056\pi\)
\(684\) 594804. + 1.51799e7i 0.0486109 + 1.24059i
\(685\) 6.42068e6 0.522823
\(686\) 1.74167e7 1.41304
\(687\) 6.01504e6 6.25535e6i 0.486235 0.505661i
\(688\) 7.61709e6i 0.613505i
\(689\) −2.36633e6 −0.189901
\(690\) 1.84780e6 1.92162e6i 0.147752 0.153654i
\(691\) 2.11131e7i 1.68212i −0.540945 0.841058i \(-0.681933\pi\)
0.540945 0.841058i \(-0.318067\pi\)
\(692\) 8.35102e6 0.662940
\(693\) −589088. 1.50341e7i −0.0465959 1.18917i
\(694\) −1.57697e6 −0.124287
\(695\) 4.37286e6i 0.343403i
\(696\) 3.80205e6 3.95394e6i 0.297505 0.309391i
\(697\) −1.28471e7 −1.00167
\(698\) 2.73674e7i 2.12616i
\(699\) 1.14385e7 + 1.09991e7i 0.885477 + 0.851460i
\(700\) 1.11547e6 0.0860425
\(701\) 4.36551e6 0.335537 0.167768 0.985826i \(-0.446344\pi\)
0.167768 + 0.985826i \(0.446344\pi\)
\(702\) 1.93870e6 + 1.72332e6i 0.148480 + 0.131985i
\(703\) 2.60261e7i 1.98619i
\(704\) 1.20686e7 0.917751
\(705\) 1.53964e7 1.60115e7i 1.16666 1.21327i
\(706\) 6.96277e6 0.525739
\(707\) −6.66724e6 −0.501646
\(708\) −2.59912e6 + 1.01780e7i −0.194869 + 0.763095i
\(709\) −1.32319e7 −0.988567 −0.494284 0.869301i \(-0.664570\pi\)
−0.494284 + 0.869301i \(0.664570\pi\)
\(710\) 1.69940e7 1.26517
\(711\) −177690. 4.53481e6i −0.0131822 0.336422i
\(712\) −2.66043e6 −0.196676
\(713\) 463442.i 0.0341406i
\(714\) 5.72239e6 5.95100e6i 0.420080 0.436862i
\(715\) −3.17331e6 −0.232139
\(716\) −7.16079e6 −0.522009
\(717\) 1.52721e6 1.58822e6i 0.110943 0.115376i
\(718\) 2.55378e7i 1.84872i
\(719\) 9.06635e6 0.654049 0.327024 0.945016i \(-0.393954\pi\)
0.327024 + 0.945016i \(0.393954\pi\)
\(720\) −1.49045e7 + 584013.i −1.07149 + 0.0419847i
\(721\) 9.57408e6i 0.685897i
\(722\) −2.78107e7 −1.98550
\(723\) 4.55522e6 + 4.38022e6i 0.324088 + 0.311638i
\(724\) 8.90128e6 0.631112
\(725\) 3.33945e6i 0.235955i
\(726\) −2.59007e7 2.49057e7i −1.82377 1.75371i
\(727\) −8.46504e6 −0.594009 −0.297004 0.954876i \(-0.595988\pi\)
−0.297004 + 0.954876i \(0.595988\pi\)
\(728\) 422258.i 0.0295290i
\(729\) −1.68199e6 1.42500e7i −0.117221 0.993106i
\(730\) −1.47558e7 −1.02484
\(731\) 4.91892e6 0.340468
\(732\) 2.56057e6 2.66287e6i 0.176628 0.183684i
\(733\) 1.86428e7 1.28159 0.640797 0.767710i \(-0.278604\pi\)
0.640797 + 0.767710i \(0.278604\pi\)
\(734\) 5.68997e6i 0.389825i
\(735\) −4.75914e6 + 4.94927e6i −0.324945 + 0.337927i
\(736\) −3.25629e6 −0.221579
\(737\) 4.99144e7i 3.38499i
\(738\) 3.05651e7 1.19765e6i 2.06578 0.0809448i
\(739\) 1.79550e7i 1.20941i 0.796449 + 0.604705i \(0.206709\pi\)
−0.796449 + 0.604705i \(0.793291\pi\)
\(740\) 1.35790e7 0.911570
\(741\) −2.42663e6 + 2.52358e6i −0.162352 + 0.168838i
\(742\) 1.79323e7i 1.19571i
\(743\) 6.34797e6i 0.421854i 0.977502 + 0.210927i \(0.0676483\pi\)
−0.977502 + 0.210927i \(0.932352\pi\)
\(744\) 584642. 607999.i 0.0387220 0.0402690i
\(745\) 8.22593e6i 0.542993i
\(746\) 2.53454e7 1.66745
\(747\) 1.03565e6 + 2.64306e7i 0.0679062 + 1.73303i
\(748\) 1.32776e7i 0.867689i
\(749\) 1.86310e7i 1.21348i
\(750\) −1.51615e7 + 1.57672e7i −0.984212 + 1.02353i
\(751\) 1.02347e7i 0.662177i −0.943600 0.331089i \(-0.892584\pi\)
0.943600 0.331089i \(-0.107416\pi\)
\(752\) −3.31681e7 −2.13883
\(753\) −1.17871e7 + 1.22580e7i −0.757562 + 0.787827i
\(754\) −4.68707e6 −0.300243
\(755\) −1.39589e7 −0.891216
\(756\) −5.75387e6 + 6.47296e6i −0.366147 + 0.411906i
\(757\) 6.04589e6 0.383460 0.191730 0.981448i \(-0.438590\pi\)
0.191730 + 0.981448i \(0.438590\pi\)
\(758\) 1.05423e7 0.666439
\(759\) 3.37680e6 + 3.24708e6i 0.212765 + 0.204592i
\(760\) 6.54879e6i 0.411270i
\(761\) 3.64475e6i 0.228142i −0.993473 0.114071i \(-0.963611\pi\)
0.993473 0.114071i \(-0.0363892\pi\)
\(762\) 1.36197e7 + 1.30965e7i 0.849729 + 0.817085i
\(763\) 1.44930e6i 0.0901254i
\(764\) 1.03198e7 0.639645
\(765\) 377140. + 9.62496e6i 0.0232996 + 0.594628i
\(766\) 3.84542e7i 2.36795i
\(767\) −2.10590e6 + 1.19402e6i −0.129256 + 0.0732866i
\(768\) 1.51039e7 + 1.45237e7i 0.924031 + 0.888533i
\(769\) 1.02131e7i 0.622790i 0.950281 + 0.311395i \(0.100796\pi\)
−0.950281 + 0.311395i \(0.899204\pi\)
\(770\) 2.40478e7i 1.46167i
\(771\) −51302.6 + 53352.2i −0.00310816 + 0.00323234i
\(772\) −1.95460e6 −0.118036
\(773\) 1.74197e7 1.04856 0.524278 0.851547i \(-0.324335\pi\)
0.524278 + 0.851547i \(0.324335\pi\)
\(774\) −1.17028e7 + 458557.i −0.702162 + 0.0275132i
\(775\) 513508.i 0.0307109i
\(776\) 4.67356e6i 0.278608i
\(777\) −1.02841e7 + 1.06950e7i −0.611102 + 0.635516i
\(778\) 1.01021e6i 0.0598358i
\(779\) 4.12852e7i 2.43754i