Properties

Label 8.7.d.b.3.2
Level 8
Weight 7
Character 8.3
Analytic conductor 1.840
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 8.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.84043266896\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.3803625.2
Defining polynomial: \(x^{4} - x^{3} + 6 x^{2} - 16 x + 256\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.2
Root \(-2.31174 + 3.26433i\) of defining polynomial
Character \(\chi\) \(=\) 8.3
Dual form 8.7.d.b.3.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.62348 + 6.52867i) q^{2} -32.4939 q^{3} +(-21.2470 - 60.3702i) q^{4} +199.084i q^{5} +(150.235 - 212.142i) q^{6} -19.6656i q^{7} +(492.372 + 140.406i) q^{8} +326.854 q^{9} +O(q^{10})\) \(q+(-4.62348 + 6.52867i) q^{2} -32.4939 q^{3} +(-21.2470 - 60.3702i) q^{4} +199.084i q^{5} +(150.235 - 212.142i) q^{6} -19.6656i q^{7} +(492.372 + 140.406i) q^{8} +326.854 q^{9} +(-1299.76 - 920.462i) q^{10} -924.152 q^{11} +(690.396 + 1961.66i) q^{12} +1550.92i q^{13} +(128.390 + 90.9235i) q^{14} -6469.03i q^{15} +(-3193.13 + 2565.37i) q^{16} +5140.78 q^{17} +(-1511.20 + 2133.92i) q^{18} -1696.10 q^{19} +(12018.8 - 4229.94i) q^{20} +639.013i q^{21} +(4272.80 - 6033.48i) q^{22} +19210.4i q^{23} +(-15999.1 - 4562.34i) q^{24} -24009.6 q^{25} +(-10125.4 - 7170.62i) q^{26} +13067.3 q^{27} +(-1187.22 + 417.835i) q^{28} -16588.1i q^{29} +(42234.1 + 29909.4i) q^{30} +7550.64i q^{31} +(-1985.05 - 32707.8i) q^{32} +30029.3 q^{33} +(-23768.3 + 33562.4i) q^{34} +3915.12 q^{35} +(-6944.64 - 19732.2i) q^{36} -28960.5i q^{37} +(7841.89 - 11073.3i) q^{38} -50395.3i q^{39} +(-27952.7 + 98023.6i) q^{40} -52111.3 q^{41} +(-4171.90 - 2954.46i) q^{42} +5896.43 q^{43} +(19635.4 + 55791.3i) q^{44} +65071.5i q^{45} +(-125419. - 88819.0i) q^{46} +64453.4i q^{47} +(103757. - 83358.8i) q^{48} +117262. q^{49} +(111008. - 156751. i) q^{50} -167044. q^{51} +(93629.2 - 32952.2i) q^{52} +197386. i q^{53} +(-60416.4 + 85312.1i) q^{54} -183984. i q^{55} +(2761.17 - 9682.80i) q^{56} +55113.0 q^{57} +(108298. + 76694.7i) q^{58} +142210. q^{59} +(-390537. + 137447. i) q^{60} -96476.4i q^{61} +(-49295.6 - 34910.2i) q^{62} -6427.78i q^{63} +(222716. + 138264. i) q^{64} -308763. q^{65} +(-138840. + 196051. i) q^{66} -75260.9 q^{67} +(-109226. - 310350. i) q^{68} -624222. i q^{69} +(-18101.5 + 25560.5i) q^{70} +556121. i q^{71} +(160934. + 45892.3i) q^{72} +285914. q^{73} +(189073. + 133898. i) q^{74} +780167. q^{75} +(36037.0 + 102394. i) q^{76} +18174.0i q^{77} +(329014. + 233002. i) q^{78} -342014. i q^{79} +(-510725. - 635703. i) q^{80} -662884. q^{81} +(240935. - 340217. i) q^{82} -929558. q^{83} +(38577.4 - 13577.1i) q^{84} +1.02345e6i q^{85} +(-27262.0 + 38495.9i) q^{86} +539012. i q^{87} +(-455027. - 129757. i) q^{88} +434757. q^{89} +(-424830. - 300856. i) q^{90} +30499.7 q^{91} +(1.15974e6 - 408163. i) q^{92} -245350. i q^{93} +(-420795. - 297999. i) q^{94} -337668. i q^{95} +(64502.0 + 1.06280e6i) q^{96} +643314. q^{97} +(-542159. + 765566. i) q^{98} -302063. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 48q^{3} - 44q^{4} + 396q^{6} + 248q^{8} - 660q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 48q^{3} - 44q^{4} + 396q^{6} + 248q^{8} - 660q^{9} - 1920q^{10} + 976q^{11} + 1368q^{12} + 5760q^{14} - 14576q^{16} + 4168q^{17} - 10410q^{18} - 1456q^{19} + 31680q^{20} + 24428q^{22} - 38256q^{24} - 23900q^{25} - 59520q^{26} + 2592q^{27} + 59520q^{28} + 90240q^{30} - 48928q^{32} + 84048q^{33} - 81916q^{34} - 49920q^{35} - 12900q^{36} + 26572q^{38} - 13440q^{40} - 117944q^{41} + 38400q^{42} + 197456q^{43} + 37144q^{44} - 213120q^{46} + 137952q^{48} + 2116q^{49} + 357650q^{50} - 386016q^{51} - 254400q^{52} - 253224q^{54} + 349440q^{56} + 126672q^{57} + 516480q^{58} + 542032q^{59} - 716160q^{60} - 407040q^{62} + 463936q^{64} - 205440q^{65} - 142776q^{66} - 790192q^{67} - 213848q^{68} - 360960q^{70} + 805800q^{72} + 443912q^{73} - 32640q^{74} + 1765200q^{75} + 70616q^{76} + 324480q^{78} - 1032960q^{80} - 568044q^{81} + 404708q^{82} - 3465008q^{83} + 602880q^{84} + 989548q^{86} - 1950448q^{88} + 761224q^{89} - 1296000q^{90} + 3398400q^{91} + 2743680q^{92} + 971520q^{94} - 252864q^{96} - 926776q^{97} - 2391262q^{98} - 2459280q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.62348 + 6.52867i −0.577934 + 0.816083i
\(3\) −32.4939 −1.20348 −0.601739 0.798693i \(-0.705525\pi\)
−0.601739 + 0.798693i \(0.705525\pi\)
\(4\) −21.2470 60.3702i −0.331984 0.943285i
\(5\) 199.084i 1.59268i 0.604852 + 0.796338i \(0.293232\pi\)
−0.604852 + 0.796338i \(0.706768\pi\)
\(6\) 150.235 212.142i 0.695531 0.982138i
\(7\) 19.6656i 0.0573342i −0.999589 0.0286671i \(-0.990874\pi\)
0.999589 0.0286671i \(-0.00912627\pi\)
\(8\) 492.372 + 140.406i 0.961664 + 0.274231i
\(9\) 326.854 0.448359
\(10\) −1299.76 920.462i −1.29976 0.920462i
\(11\) −924.152 −0.694329 −0.347165 0.937804i \(-0.612856\pi\)
−0.347165 + 0.937804i \(0.612856\pi\)
\(12\) 690.396 + 1961.66i 0.399535 + 1.13522i
\(13\) 1550.92i 0.705925i 0.935638 + 0.352962i \(0.114826\pi\)
−0.935638 + 0.352962i \(0.885174\pi\)
\(14\) 128.390 + 90.9235i 0.0467895 + 0.0331354i
\(15\) 6469.03i 1.91675i
\(16\) −3193.13 + 2565.37i −0.779574 + 0.626310i
\(17\) 5140.78 1.04636 0.523181 0.852221i \(-0.324745\pi\)
0.523181 + 0.852221i \(0.324745\pi\)
\(18\) −1511.20 + 2133.92i −0.259122 + 0.365898i
\(19\) −1696.10 −0.247281 −0.123641 0.992327i \(-0.539457\pi\)
−0.123641 + 0.992327i \(0.539457\pi\)
\(20\) 12018.8 4229.94i 1.50235 0.528742i
\(21\) 639.013i 0.0690004i
\(22\) 4272.80 6033.48i 0.401277 0.566631i
\(23\) 19210.4i 1.57890i 0.613817 + 0.789448i \(0.289633\pi\)
−0.613817 + 0.789448i \(0.710367\pi\)
\(24\) −15999.1 4562.34i −1.15734 0.330031i
\(25\) −24009.6 −1.53662
\(26\) −10125.4 7170.62i −0.576093 0.407978i
\(27\) 13067.3 0.663888
\(28\) −1187.22 + 417.835i −0.0540825 + 0.0190340i
\(29\) 16588.1i 0.680147i −0.940399 0.340074i \(-0.889548\pi\)
0.940399 0.340074i \(-0.110452\pi\)
\(30\) 42234.1 + 29909.4i 1.56423 + 1.10776i
\(31\) 7550.64i 0.253454i 0.991938 + 0.126727i \(0.0404472\pi\)
−0.991938 + 0.126727i \(0.959553\pi\)
\(32\) −1985.05 32707.8i −0.0605789 0.998163i
\(33\) 30029.3 0.835610
\(34\) −23768.3 + 33562.4i −0.604729 + 0.853919i
\(35\) 3915.12 0.0913148
\(36\) −6944.64 19732.2i −0.148848 0.422930i
\(37\) 28960.5i 0.571743i −0.958268 0.285871i \(-0.907717\pi\)
0.958268 0.285871i \(-0.0922830\pi\)
\(38\) 7841.89 11073.3i 0.142912 0.201802i
\(39\) 50395.3i 0.849565i
\(40\) −27952.7 + 98023.6i −0.436761 + 1.53162i
\(41\) −52111.3 −0.756101 −0.378051 0.925785i \(-0.623406\pi\)
−0.378051 + 0.925785i \(0.623406\pi\)
\(42\) −4171.90 2954.46i −0.0563101 0.0398777i
\(43\) 5896.43 0.0741625 0.0370812 0.999312i \(-0.488194\pi\)
0.0370812 + 0.999312i \(0.488194\pi\)
\(44\) 19635.4 + 55791.3i 0.230506 + 0.654951i
\(45\) 65071.5i 0.714090i
\(46\) −125419. 88819.0i −1.28851 0.912499i
\(47\) 64453.4i 0.620801i 0.950606 + 0.310400i \(0.100463\pi\)
−0.950606 + 0.310400i \(0.899537\pi\)
\(48\) 103757. 83358.8i 0.938200 0.753751i
\(49\) 117262. 0.996713
\(50\) 111008. 156751.i 0.888064 1.25401i
\(51\) −167044. −1.25927
\(52\) 93629.2 32952.2i 0.665888 0.234355i
\(53\) 197386.i 1.32583i 0.748694 + 0.662916i \(0.230681\pi\)
−0.748694 + 0.662916i \(0.769319\pi\)
\(54\) −60416.4 + 85312.1i −0.383684 + 0.541788i
\(55\) 183984.i 1.10584i
\(56\) 2761.17 9682.80i 0.0157228 0.0551362i
\(57\) 55113.0 0.297598
\(58\) 108298. + 76694.7i 0.555057 + 0.393080i
\(59\) 142210. 0.692425 0.346212 0.938156i \(-0.387468\pi\)
0.346212 + 0.938156i \(0.387468\pi\)
\(60\) −390537. + 137447.i −1.80804 + 0.636330i
\(61\) 96476.4i 0.425042i −0.977157 0.212521i \(-0.931833\pi\)
0.977157 0.212521i \(-0.0681673\pi\)
\(62\) −49295.6 34910.2i −0.206839 0.146480i
\(63\) 6427.78i 0.0257063i
\(64\) 222716. + 138264.i 0.849595 + 0.527436i
\(65\) −308763. −1.12431
\(66\) −138840. + 196051.i −0.482928 + 0.681927i
\(67\) −75260.9 −0.250233 −0.125117 0.992142i \(-0.539930\pi\)
−0.125117 + 0.992142i \(0.539930\pi\)
\(68\) −109226. 310350.i −0.347375 0.987018i
\(69\) 624222.i 1.90017i
\(70\) −18101.5 + 25560.5i −0.0527740 + 0.0745205i
\(71\) 556121.i 1.55380i 0.629625 + 0.776899i \(0.283208\pi\)
−0.629625 + 0.776899i \(0.716792\pi\)
\(72\) 160934. + 45892.3i 0.431171 + 0.122954i
\(73\) 285914. 0.734965 0.367483 0.930030i \(-0.380220\pi\)
0.367483 + 0.930030i \(0.380220\pi\)
\(74\) 189073. + 133898.i 0.466590 + 0.330430i
\(75\) 780167. 1.84928
\(76\) 36037.0 + 102394.i 0.0820934 + 0.233257i
\(77\) 18174.0i 0.0398088i
\(78\) 329014. + 233002.i 0.693315 + 0.490993i
\(79\) 342014.i 0.693686i −0.937923 0.346843i \(-0.887254\pi\)
0.937923 0.346843i \(-0.112746\pi\)
\(80\) −510725. 635703.i −0.997510 1.24161i
\(81\) −662884. −1.24733
\(82\) 240935. 340217.i 0.436977 0.617042i
\(83\) −929558. −1.62571 −0.812853 0.582469i \(-0.802087\pi\)
−0.812853 + 0.582469i \(0.802087\pi\)
\(84\) 38577.4 13577.1i 0.0650871 0.0229070i
\(85\) 1.02345e6i 1.66652i
\(86\) −27262.0 + 38495.9i −0.0428610 + 0.0605227i
\(87\) 539012.i 0.818542i
\(88\) −455027. 129757.i −0.667712 0.190406i
\(89\) 434757. 0.616704 0.308352 0.951272i \(-0.400223\pi\)
0.308352 + 0.951272i \(0.400223\pi\)
\(90\) −424830. 300856.i −0.582757 0.412697i
\(91\) 30499.7 0.0404736
\(92\) 1.15974e6 408163.i 1.48935 0.524168i
\(93\) 245350.i 0.305026i
\(94\) −420795. 297999.i −0.506625 0.358782i
\(95\) 337668.i 0.393839i
\(96\) 64502.0 + 1.06280e6i 0.0729054 + 1.20127i
\(97\) 643314. 0.704868 0.352434 0.935837i \(-0.385354\pi\)
0.352434 + 0.935837i \(0.385354\pi\)
\(98\) −542159. + 765566.i −0.576035 + 0.813401i
\(99\) −302063. −0.311309
\(100\) 510131. + 1.44947e6i 0.510131 + 1.44947i
\(101\) 858368.i 0.833123i −0.909107 0.416562i \(-0.863235\pi\)
0.909107 0.416562i \(-0.136765\pi\)
\(102\) 772324. 1.09057e6i 0.727778 1.02767i
\(103\) 2.13382e6i 1.95275i −0.216089 0.976374i \(-0.569330\pi\)
0.216089 0.976374i \(-0.430670\pi\)
\(104\) −217758. + 763628.i −0.193586 + 0.678862i
\(105\) −127218. −0.109895
\(106\) −1.28867e6 912609.i −1.08199 0.766244i
\(107\) 1.81311e6 1.48004 0.740019 0.672585i \(-0.234816\pi\)
0.740019 + 0.672585i \(0.234816\pi\)
\(108\) −277640. 788876.i −0.220400 0.626236i
\(109\) 1.43023e6i 1.10440i 0.833711 + 0.552201i \(0.186212\pi\)
−0.833711 + 0.552201i \(0.813788\pi\)
\(110\) 1.20117e6 + 850647.i 0.902459 + 0.639104i
\(111\) 941039.i 0.688080i
\(112\) 50449.6 + 62795.0i 0.0359090 + 0.0446962i
\(113\) 628373. 0.435494 0.217747 0.976005i \(-0.430129\pi\)
0.217747 + 0.976005i \(0.430129\pi\)
\(114\) −254814. + 359815.i −0.171992 + 0.242865i
\(115\) −3.82450e6 −2.51467
\(116\) −1.00143e6 + 352447.i −0.641573 + 0.225798i
\(117\) 506923.i 0.316508i
\(118\) −657502. + 928438.i −0.400176 + 0.565076i
\(119\) 101097.i 0.0599924i
\(120\) 908292. 3.18517e6i 0.525632 1.84327i
\(121\) −917503. −0.517907
\(122\) 629862. + 446056.i 0.346869 + 0.245646i
\(123\) 1.69330e6 0.909951
\(124\) 455834. 160428.i 0.239079 0.0841425i
\(125\) 1.66925e6i 0.854656i
\(126\) 41964.8 + 29718.7i 0.0209785 + 0.0148566i
\(127\) 2.43195e6i 1.18725i 0.804741 + 0.593626i \(0.202304\pi\)
−0.804741 + 0.593626i \(0.797696\pi\)
\(128\) −1.93240e6 + 814779.i −0.921442 + 0.388517i
\(129\) −191598. −0.0892529
\(130\) 1.42756e6 2.01581e6i 0.649777 0.917530i
\(131\) 2.66985e6 1.18761 0.593804 0.804610i \(-0.297626\pi\)
0.593804 + 0.804610i \(0.297626\pi\)
\(132\) −638031. 1.81288e6i −0.277409 0.788219i
\(133\) 33354.9i 0.0141777i
\(134\) 347967. 491353.i 0.144618 0.204211i
\(135\) 2.60150e6i 1.05736i
\(136\) 2.53118e6 + 721797.i 1.00625 + 0.286945i
\(137\) −4.00205e6 −1.55640 −0.778199 0.628018i \(-0.783867\pi\)
−0.778199 + 0.628018i \(0.783867\pi\)
\(138\) 4.07534e6 + 2.88608e6i 1.55069 + 1.09817i
\(139\) 1.89422e6 0.705319 0.352660 0.935752i \(-0.385277\pi\)
0.352660 + 0.935752i \(0.385277\pi\)
\(140\) −83184.4 236357.i −0.0303150 0.0861359i
\(141\) 2.09434e6i 0.747120i
\(142\) −3.63073e6 2.57121e6i −1.26803 0.897993i
\(143\) 1.43328e6i 0.490144i
\(144\) −1.04369e6 + 838500.i −0.349529 + 0.280812i
\(145\) 3.30243e6 1.08325
\(146\) −1.32192e6 + 1.86664e6i −0.424762 + 0.599793i
\(147\) −3.81031e6 −1.19952
\(148\) −1.74835e6 + 615322.i −0.539316 + 0.189809i
\(149\) 3.06394e6i 0.926235i −0.886297 0.463118i \(-0.846731\pi\)
0.886297 0.463118i \(-0.153269\pi\)
\(150\) −3.60708e6 + 5.09345e6i −1.06876 + 1.50917i
\(151\) 2.24437e6i 0.651873i −0.945392 0.325936i \(-0.894320\pi\)
0.945392 0.325936i \(-0.105680\pi\)
\(152\) −835114. 238143.i −0.237802 0.0678122i
\(153\) 1.68028e6 0.469146
\(154\) −118652. 84027.2i −0.0324873 0.0230069i
\(155\) −1.50322e6 −0.403670
\(156\) −3.04238e6 + 1.07075e6i −0.801382 + 0.282042i
\(157\) 4.89064e6i 1.26377i 0.775064 + 0.631883i \(0.217718\pi\)
−0.775064 + 0.631883i \(0.782282\pi\)
\(158\) 2.23290e6 + 1.58129e6i 0.566105 + 0.400905i
\(159\) 6.41384e6i 1.59561i
\(160\) 6.51162e6 395193.i 1.58975 0.0964825i
\(161\) 377785. 0.0905248
\(162\) 3.06483e6 4.32775e6i 0.720877 1.01793i
\(163\) 1.82987e6 0.422529 0.211265 0.977429i \(-0.432242\pi\)
0.211265 + 0.977429i \(0.432242\pi\)
\(164\) 1.10721e6 + 3.14597e6i 0.251013 + 0.713219i
\(165\) 5.97837e6i 1.33086i
\(166\) 4.29779e6 6.06877e6i 0.939552 1.32671i
\(167\) 3.94279e6i 0.846554i 0.906000 + 0.423277i \(0.139120\pi\)
−0.906000 + 0.423277i \(0.860880\pi\)
\(168\) −89721.3 + 314632.i −0.0189220 + 0.0663552i
\(169\) 2.42147e6 0.501670
\(170\) −6.68176e6 4.73189e6i −1.36002 0.963137i
\(171\) −554378. −0.110871
\(172\) −125281. 355969.i −0.0246207 0.0699563i
\(173\) 205167.i 0.0396249i −0.999804 0.0198125i \(-0.993693\pi\)
0.999804 0.0198125i \(-0.00630692\pi\)
\(174\) −3.51903e6 2.49211e6i −0.667998 0.473064i
\(175\) 472164.i 0.0881007i
\(176\) 2.95094e6 2.37079e6i 0.541281 0.434866i
\(177\) −4.62094e6 −0.833318
\(178\) −2.01009e6 + 2.83838e6i −0.356415 + 0.503282i
\(179\) −3.36007e6 −0.585853 −0.292927 0.956135i \(-0.594629\pi\)
−0.292927 + 0.956135i \(0.594629\pi\)
\(180\) 3.92838e6 1.38257e6i 0.673591 0.237066i
\(181\) 2.39145e6i 0.403298i −0.979458 0.201649i \(-0.935370\pi\)
0.979458 0.201649i \(-0.0646300\pi\)
\(182\) −141015. + 199123.i −0.0233911 + 0.0330298i
\(183\) 3.13489e6i 0.511528i
\(184\) −2.69726e6 + 9.45868e6i −0.432982 + 1.51837i
\(185\) 5.76558e6 0.910601
\(186\) 1.60181e6 + 1.13437e6i 0.248927 + 0.176285i
\(187\) −4.75086e6 −0.726520
\(188\) 3.89107e6 1.36944e6i 0.585592 0.206096i
\(189\) 256977.i 0.0380635i
\(190\) 2.20452e6 + 1.56120e6i 0.321406 + 0.227613i
\(191\) 2.02441e6i 0.290535i 0.989392 + 0.145268i \(0.0464043\pi\)
−0.989392 + 0.145268i \(0.953596\pi\)
\(192\) −7.23692e6 4.49274e6i −1.02247 0.634757i
\(193\) −7.92510e6 −1.10238 −0.551192 0.834378i \(-0.685827\pi\)
−0.551192 + 0.834378i \(0.685827\pi\)
\(194\) −2.97434e6 + 4.19998e6i −0.407367 + 0.575231i
\(195\) 1.00329e7 1.35308
\(196\) −2.49147e6 7.07915e6i −0.330892 0.940184i
\(197\) 4.12787e6i 0.539917i 0.962872 + 0.269959i \(0.0870100\pi\)
−0.962872 + 0.269959i \(0.912990\pi\)
\(198\) 1.39658e6 1.97207e6i 0.179916 0.254054i
\(199\) 1.18196e7i 1.49983i −0.661532 0.749917i \(-0.730093\pi\)
0.661532 0.749917i \(-0.269907\pi\)
\(200\) −1.18217e7 3.37110e6i −1.47771 0.421387i
\(201\) 2.44552e6 0.301150
\(202\) 5.60400e6 + 3.96864e6i 0.679898 + 0.481491i
\(203\) −326215. −0.0389957
\(204\) 3.54918e6 + 1.00845e7i 0.418058 + 1.18785i
\(205\) 1.03745e7i 1.20422i
\(206\) 1.39310e7 + 9.86566e6i 1.59360 + 1.12856i
\(207\) 6.27900e6i 0.707912i
\(208\) −3.97867e6 4.95228e6i −0.442128 0.550320i
\(209\) 1.56746e6 0.171695
\(210\) 588187. 830561.i 0.0635123 0.0896837i
\(211\) 1.19422e7 1.27127 0.635635 0.771989i \(-0.280738\pi\)
0.635635 + 0.771989i \(0.280738\pi\)
\(212\) 1.19162e7 4.19385e6i 1.25064 0.440155i
\(213\) 1.80706e7i 1.86996i
\(214\) −8.38288e6 + 1.18372e7i −0.855365 + 1.20783i
\(215\) 1.17389e6i 0.118117i
\(216\) 6.43397e6 + 1.83473e6i 0.638437 + 0.182058i
\(217\) 148488. 0.0145316
\(218\) −9.33752e6 6.61265e6i −0.901284 0.638272i
\(219\) −9.29046e6 −0.884514
\(220\) −1.11072e7 + 3.90911e6i −1.04312 + 0.367121i
\(221\) 7.97292e6i 0.738653i
\(222\) −6.14373e6 4.35087e6i −0.561530 0.397665i
\(223\) 2.10926e7i 1.90202i 0.309153 + 0.951012i \(0.399955\pi\)
−0.309153 + 0.951012i \(0.600045\pi\)
\(224\) −643220. + 39037.2i −0.0572289 + 0.00347324i
\(225\) −7.84764e6 −0.688956
\(226\) −2.90526e6 + 4.10243e6i −0.251687 + 0.355399i
\(227\) 2.73658e6 0.233954 0.116977 0.993135i \(-0.462680\pi\)
0.116977 + 0.993135i \(0.462680\pi\)
\(228\) −1.17098e6 3.32719e6i −0.0987976 0.280720i
\(229\) 7.23777e6i 0.602696i 0.953514 + 0.301348i \(0.0974366\pi\)
−0.953514 + 0.301348i \(0.902563\pi\)
\(230\) 1.76825e7 2.49689e7i 1.45331 2.05218i
\(231\) 590545.i 0.0479090i
\(232\) 2.32907e6 8.16752e6i 0.186517 0.654073i
\(233\) −1.63958e7 −1.29618 −0.648088 0.761565i \(-0.724431\pi\)
−0.648088 + 0.761565i \(0.724431\pi\)
\(234\) −3.30953e6 2.34374e6i −0.258297 0.182921i
\(235\) −1.28317e7 −0.988734
\(236\) −3.02152e6 8.58522e6i −0.229874 0.653154i
\(237\) 1.11134e7i 0.834835i
\(238\) 660026. + 467418.i 0.0489588 + 0.0346717i
\(239\) 1.73985e7i 1.27443i −0.770685 0.637217i \(-0.780086\pi\)
0.770685 0.637217i \(-0.219914\pi\)
\(240\) 1.65954e7 + 2.06565e7i 1.20048 + 1.49425i
\(241\) 1.34047e7 0.957645 0.478822 0.877912i \(-0.341064\pi\)
0.478822 + 0.877912i \(0.341064\pi\)
\(242\) 4.24205e6 5.99007e6i 0.299316 0.422655i
\(243\) 1.20136e7 0.837250
\(244\) −5.82430e6 + 2.04983e6i −0.400935 + 0.141107i
\(245\) 2.33451e7i 1.58744i
\(246\) −7.82892e6 + 1.10550e7i −0.525892 + 0.742596i
\(247\) 2.63051e6i 0.174562i
\(248\) −1.06016e6 + 3.71772e6i −0.0695048 + 0.243737i
\(249\) 3.02050e7 1.95650
\(250\) 1.08980e7 + 7.71774e6i 0.697471 + 0.493935i
\(251\) −1.70047e7 −1.07534 −0.537672 0.843154i \(-0.680696\pi\)
−0.537672 + 0.843154i \(0.680696\pi\)
\(252\) −388047. + 136571.i −0.0242484 + 0.00853407i
\(253\) 1.77534e7i 1.09627i
\(254\) −1.58774e7 1.12440e7i −0.968896 0.686154i
\(255\) 3.32559e7i 2.00562i
\(256\) 3.61500e6 1.63831e7i 0.215471 0.976510i
\(257\) 1.94325e7 1.14480 0.572400 0.819974i \(-0.306012\pi\)
0.572400 + 0.819974i \(0.306012\pi\)
\(258\) 885849. 1.25088e6i 0.0515823 0.0728378i
\(259\) −569526. −0.0327804
\(260\) 6.56028e6 + 1.86401e7i 0.373252 + 1.06054i
\(261\) 5.42188e6i 0.304950i
\(262\) −1.23440e7 + 1.74305e7i −0.686359 + 0.969186i
\(263\) 1.33303e7i 0.732778i 0.930462 + 0.366389i \(0.119406\pi\)
−0.930462 + 0.366389i \(0.880594\pi\)
\(264\) 1.47856e7 + 4.21630e6i 0.803576 + 0.229150i
\(265\) −3.92965e7 −2.11162
\(266\) −217763. 154216.i −0.0115702 0.00819377i
\(267\) −1.41270e7 −0.742190
\(268\) 1.59906e6 + 4.54352e6i 0.0830733 + 0.236041i
\(269\) 7.13509e6i 0.366558i 0.983061 + 0.183279i \(0.0586712\pi\)
−0.983061 + 0.183279i \(0.941329\pi\)
\(270\) −1.69843e7 1.20280e7i −0.862892 0.611084i
\(271\) 6.93561e6i 0.348479i 0.984703 + 0.174240i \(0.0557467\pi\)
−0.984703 + 0.174240i \(0.944253\pi\)
\(272\) −1.64152e7 + 1.31880e7i −0.815717 + 0.655348i
\(273\) −991056. −0.0487091
\(274\) 1.85034e7 2.61280e7i 0.899496 1.27015i
\(275\) 2.21886e7 1.06692
\(276\) −3.76844e7 + 1.32628e7i −1.79240 + 0.630824i
\(277\) 1.79332e7i 0.843757i −0.906652 0.421879i \(-0.861371\pi\)
0.906652 0.421879i \(-0.138629\pi\)
\(278\) −8.75787e6 + 1.23667e7i −0.407628 + 0.575599i
\(279\) 2.46795e6i 0.113638i
\(280\) 1.92770e6 + 549707.i 0.0878141 + 0.0250413i
\(281\) −4.29329e6 −0.193496 −0.0967479 0.995309i \(-0.530844\pi\)
−0.0967479 + 0.995309i \(0.530844\pi\)
\(282\) 1.36733e7 + 9.68314e6i 0.609712 + 0.431786i
\(283\) 3.39377e7 1.49735 0.748674 0.662938i \(-0.230691\pi\)
0.748674 + 0.662938i \(0.230691\pi\)
\(284\) 3.35732e7 1.18159e7i 1.46567 0.515835i
\(285\) 1.09721e7i 0.473977i
\(286\) 9.35743e6 + 6.62675e6i 0.399998 + 0.283271i
\(287\) 1.02480e6i 0.0433505i
\(288\) −648821. 1.06907e7i −0.0271611 0.447535i
\(289\) 2.29005e6 0.0948751
\(290\) −1.52687e7 + 2.15605e7i −0.626050 + 0.884025i
\(291\) −2.09038e7 −0.848293
\(292\) −6.07480e6 1.72607e7i −0.243996 0.693282i
\(293\) 3.15178e7i 1.25301i −0.779419 0.626504i \(-0.784485\pi\)
0.779419 0.626504i \(-0.215515\pi\)
\(294\) 1.76169e7 2.48762e7i 0.693245 0.978910i
\(295\) 2.83117e7i 1.10281i
\(296\) 4.06623e6 1.42593e7i 0.156789 0.549824i
\(297\) −1.20762e7 −0.460957
\(298\) 2.00034e7 + 1.41660e7i 0.755885 + 0.535303i
\(299\) −2.97938e7 −1.11458
\(300\) −1.65762e7 4.70989e7i −0.613932 1.74440i
\(301\) 115957.i 0.00425204i
\(302\) 1.46527e7 + 1.03768e7i 0.531983 + 0.376740i
\(303\) 2.78917e7i 1.00265i
\(304\) 5.41589e6 4.35113e6i 0.192774 0.154875i
\(305\) 1.92069e7 0.676953
\(306\) −7.76875e6 + 1.09700e7i −0.271136 + 0.382862i
\(307\) 3.45268e7 1.19328 0.596638 0.802510i \(-0.296503\pi\)
0.596638 + 0.802510i \(0.296503\pi\)
\(308\) 1.09717e6 386143.i 0.0375511 0.0132159i
\(309\) 6.93361e7i 2.35009i
\(310\) 6.95008e6 9.81399e6i 0.233295 0.329428i
\(311\) 1.55896e7i 0.518268i −0.965841 0.259134i \(-0.916563\pi\)
0.965841 0.259134i \(-0.0834371\pi\)
\(312\) 7.07581e6 2.48132e7i 0.232977 0.816996i
\(313\) 2.13473e6 0.0696160 0.0348080 0.999394i \(-0.488918\pi\)
0.0348080 + 0.999394i \(0.488918\pi\)
\(314\) −3.19293e7 2.26117e7i −1.03134 0.730374i
\(315\) 1.27967e6 0.0409418
\(316\) −2.06475e7 + 7.26676e6i −0.654343 + 0.230292i
\(317\) 4.15440e7i 1.30416i −0.758151 0.652079i \(-0.773897\pi\)
0.758151 0.652079i \(-0.226103\pi\)
\(318\) 4.18738e7 + 2.96542e7i 1.30215 + 0.922158i
\(319\) 1.53299e7i 0.472246i
\(320\) −2.75262e7 + 4.43393e7i −0.840034 + 1.35313i
\(321\) −5.89151e7 −1.78119
\(322\) −1.74668e6 + 2.46643e6i −0.0523174 + 0.0738757i
\(323\) −8.71930e6 −0.258746
\(324\) 1.40843e7 + 4.00185e7i 0.414094 + 1.17659i
\(325\) 3.72369e7i 1.08474i
\(326\) −8.46034e6 + 1.19466e7i −0.244194 + 0.344819i
\(327\) 4.64739e7i 1.32912i
\(328\) −2.56581e7 7.31674e6i −0.727115 0.207346i
\(329\) 1.26752e6 0.0355931
\(330\) −3.90308e7 2.76409e7i −1.08609 0.769147i
\(331\) 1.78997e7 0.493585 0.246793 0.969068i \(-0.420623\pi\)
0.246793 + 0.969068i \(0.420623\pi\)
\(332\) 1.97503e7 + 5.61176e7i 0.539708 + 1.53350i
\(333\) 9.46584e6i 0.256346i
\(334\) −2.57412e7 1.82294e7i −0.690858 0.489253i
\(335\) 1.49833e7i 0.398540i
\(336\) −1.63930e6 2.04045e6i −0.0432157 0.0537909i
\(337\) 1.86244e7 0.486624 0.243312 0.969948i \(-0.421766\pi\)
0.243312 + 0.969948i \(0.421766\pi\)
\(338\) −1.11956e7 + 1.58089e7i −0.289933 + 0.409405i
\(339\) −2.04183e7 −0.524107
\(340\) 6.17859e7 2.17452e7i 1.57200 0.553256i
\(341\) 6.97794e6i 0.175980i
\(342\) 2.56315e6 3.61935e6i 0.0640761 0.0904798i
\(343\) 4.61968e6i 0.114480i
\(344\) 2.90324e6 + 827896.i 0.0713194 + 0.0203376i
\(345\) 1.24273e8 3.02635
\(346\) 1.33946e6 + 948583.i 0.0323372 + 0.0229006i
\(347\) 3.96438e7 0.948827 0.474414 0.880302i \(-0.342660\pi\)
0.474414 + 0.880302i \(0.342660\pi\)
\(348\) 3.25403e7 1.14524e7i 0.772118 0.271742i
\(349\) 6.84414e7i 1.61006i 0.593232 + 0.805031i \(0.297852\pi\)
−0.593232 + 0.805031i \(0.702148\pi\)
\(350\) −3.08260e6 2.18304e6i −0.0718975 0.0509164i
\(351\) 2.02663e7i 0.468655i
\(352\) 1.83449e6 + 3.02270e7i 0.0420617 + 0.693054i
\(353\) −3.01604e7 −0.685666 −0.342833 0.939396i \(-0.611387\pi\)
−0.342833 + 0.939396i \(0.611387\pi\)
\(354\) 2.13648e7 3.01686e7i 0.481603 0.680057i
\(355\) −1.10715e8 −2.47470
\(356\) −9.23727e6 2.62464e7i −0.204736 0.581728i
\(357\) 3.28503e6i 0.0721995i
\(358\) 1.55352e7 2.19368e7i 0.338585 0.478105i
\(359\) 6.13950e7i 1.32694i −0.748205 0.663468i \(-0.769084\pi\)
0.748205 0.663468i \(-0.230916\pi\)
\(360\) −9.13644e6 + 3.20394e7i −0.195826 + 0.686715i
\(361\) −4.41691e7 −0.938852
\(362\) 1.56130e7 + 1.10568e7i 0.329125 + 0.233080i
\(363\) 2.98133e7 0.623289
\(364\) −648027. 1.84128e6i −0.0134366 0.0381782i
\(365\) 5.69210e7i 1.17056i
\(366\) −2.04667e7 1.44941e7i −0.417449 0.295630i
\(367\) 4.17679e7i 0.844976i −0.906368 0.422488i \(-0.861157\pi\)
0.906368 0.422488i \(-0.138843\pi\)
\(368\) −4.92818e7 6.13415e7i −0.988880 1.23087i
\(369\) −1.70328e7 −0.339005
\(370\) −2.66570e7 + 3.76416e7i −0.526268 + 0.743126i
\(371\) 3.88172e6 0.0760155
\(372\) −1.48118e7 + 5.21293e6i −0.287726 + 0.101264i
\(373\) 5.61502e7i 1.08199i 0.841025 + 0.540997i \(0.181953\pi\)
−0.841025 + 0.540997i \(0.818047\pi\)
\(374\) 2.19655e7 3.10168e7i 0.419881 0.592901i
\(375\) 5.42405e7i 1.02856i
\(376\) −9.04965e6 + 3.17350e7i −0.170243 + 0.597001i
\(377\) 2.57268e7 0.480133
\(378\) 1.67772e6 + 1.18813e6i 0.0310630 + 0.0219982i
\(379\) −1.96484e7 −0.360919 −0.180460 0.983582i \(-0.557758\pi\)
−0.180460 + 0.983582i \(0.557758\pi\)
\(380\) −2.03851e7 + 7.17441e6i −0.371503 + 0.130748i
\(381\) 7.90234e7i 1.42883i
\(382\) −1.32167e7 9.35982e6i −0.237101 0.167910i
\(383\) 3.86630e7i 0.688176i 0.938937 + 0.344088i \(0.111812\pi\)
−0.938937 + 0.344088i \(0.888188\pi\)
\(384\) 6.27913e7 2.64754e7i 1.10893 0.467572i
\(385\) −3.61817e6 −0.0634025
\(386\) 3.66415e7 5.17403e7i 0.637106 0.899637i
\(387\) 1.92727e6 0.0332514
\(388\) −1.36685e7 3.88370e7i −0.234004 0.664891i
\(389\) 2.94915e6i 0.0501012i 0.999686 + 0.0250506i \(0.00797470\pi\)
−0.999686 + 0.0250506i \(0.992025\pi\)
\(390\) −4.63870e7 + 6.55016e7i −0.781992 + 1.10423i
\(391\) 9.87566e7i 1.65210i
\(392\) 5.77366e7 + 1.64643e7i 0.958503 + 0.273329i
\(393\) −8.67538e7 −1.42926
\(394\) −2.69495e7 1.90851e7i −0.440617 0.312037i
\(395\) 6.80897e7 1.10482
\(396\) 6.41791e6 + 1.82356e7i 0.103349 + 0.293653i
\(397\) 6.88167e7i 1.09982i −0.835223 0.549911i \(-0.814662\pi\)
0.835223 0.549911i \(-0.185338\pi\)
\(398\) 7.71662e7 + 5.46476e7i 1.22399 + 0.866806i
\(399\) 1.08383e6i 0.0170625i
\(400\) 7.66660e7 6.15935e7i 1.19791 0.962399i
\(401\) 3.42281e7 0.530823 0.265412 0.964135i \(-0.414492\pi\)
0.265412 + 0.964135i \(0.414492\pi\)
\(402\) −1.13068e7 + 1.59660e7i −0.174045 + 0.245764i
\(403\) −1.17104e7 −0.178919
\(404\) −5.18199e7 + 1.82377e7i −0.785873 + 0.276583i
\(405\) 1.31970e8i 1.98660i
\(406\) 1.50825e6 2.12975e6i 0.0225369 0.0318237i
\(407\) 2.67639e7i 0.396978i
\(408\) −8.22478e7 2.34540e7i −1.21100 0.345332i
\(409\) 7.43891e7 1.08728 0.543638 0.839320i \(-0.317047\pi\)
0.543638 + 0.839320i \(0.317047\pi\)
\(410\) 6.77319e7 + 4.79665e7i 0.982747 + 0.695963i
\(411\) 1.30042e8 1.87309
\(412\) −1.28819e8 + 4.53372e7i −1.84200 + 0.648280i
\(413\) 2.79664e6i 0.0396996i
\(414\) −4.09935e7 2.90308e7i −0.577715 0.409127i
\(415\) 1.85061e8i 2.58922i
\(416\) 5.07271e7 3.07865e6i 0.704628 0.0427641i
\(417\) −6.15505e7 −0.848836
\(418\) −7.24710e6 + 1.02334e7i −0.0992283 + 0.140117i
\(419\) −3.78200e7 −0.514138 −0.257069 0.966393i \(-0.582757\pi\)
−0.257069 + 0.966393i \(0.582757\pi\)
\(420\) 2.70299e6 + 7.68016e6i 0.0364834 + 0.103663i
\(421\) 6.21731e7i 0.833213i 0.909087 + 0.416607i \(0.136781\pi\)
−0.909087 + 0.416607i \(0.863219\pi\)
\(422\) −5.52146e7 + 7.79668e7i −0.734711 + 1.03746i
\(423\) 2.10668e7i 0.278341i
\(424\) −2.77142e7 + 9.71873e7i −0.363584 + 1.27501i
\(425\) −1.23428e8 −1.60786
\(426\) 1.17977e8 + 8.35488e7i 1.52604 + 1.08072i
\(427\) −1.89727e6 −0.0243694
\(428\) −3.85231e7 1.09458e8i −0.491349 1.39610i
\(429\) 4.65730e7i 0.589878i
\(430\) −7.66393e6 5.42745e6i −0.0963931 0.0682637i
\(431\) 1.00561e8i 1.25603i 0.778202 + 0.628014i \(0.216132\pi\)
−0.778202 + 0.628014i \(0.783868\pi\)
\(432\) −4.17257e7 + 3.35224e7i −0.517550 + 0.415800i
\(433\) 1.07677e8 1.32636 0.663179 0.748461i \(-0.269207\pi\)
0.663179 + 0.748461i \(0.269207\pi\)
\(434\) −686531. + 969429.i −0.00839829 + 0.0118590i
\(435\) −1.07309e8 −1.30367
\(436\) 8.63436e7 3.03881e7i 1.04177 0.366644i
\(437\) 3.25829e7i 0.390432i
\(438\) 4.29542e7 6.06543e7i 0.511191 0.721837i
\(439\) 6.85796e7i 0.810590i −0.914186 0.405295i \(-0.867169\pi\)
0.914186 0.405295i \(-0.132831\pi\)
\(440\) 2.58325e7 9.05888e7i 0.303256 1.06345i
\(441\) 3.83276e7 0.446885
\(442\) −5.20525e7 3.68626e7i −0.602803 0.426893i
\(443\) −8.84819e7 −1.01776 −0.508878 0.860839i \(-0.669939\pi\)
−0.508878 + 0.860839i \(0.669939\pi\)
\(444\) 5.68108e7 1.99942e7i 0.649055 0.228431i
\(445\) 8.65534e7i 0.982210i
\(446\) −1.37707e8 9.75213e7i −1.55221 1.09925i
\(447\) 9.95593e7i 1.11470i
\(448\) 2.71905e6 4.37985e6i 0.0302401 0.0487108i
\(449\) 4.28752e7 0.473661 0.236830 0.971551i \(-0.423891\pi\)
0.236830 + 0.971551i \(0.423891\pi\)
\(450\) 3.62834e7 5.12346e7i 0.398171 0.562245i
\(451\) 4.81588e7 0.524983
\(452\) −1.33510e7 3.79350e7i −0.144577 0.410795i
\(453\) 7.29282e7i 0.784515i
\(454\) −1.26525e7 + 1.78662e7i −0.135210 + 0.190926i
\(455\) 6.07203e6i 0.0644614i
\(456\) 2.71361e7 + 7.73821e6i 0.286189 + 0.0816104i
\(457\) −7.01681e7 −0.735176 −0.367588 0.929989i \(-0.619816\pi\)
−0.367588 + 0.929989i \(0.619816\pi\)
\(458\) −4.72530e7 3.34637e7i −0.491850 0.348319i
\(459\) 6.71761e7 0.694668
\(460\) 8.12590e7 + 2.30886e8i 0.834830 + 2.37205i
\(461\) 5.37805e7i 0.548937i −0.961596 0.274468i \(-0.911498\pi\)
0.961596 0.274468i \(-0.0885018\pi\)
\(462\) 3.85547e6 + 2.73037e6i 0.0390977 + 0.0276883i
\(463\) 4.36059e7i 0.439342i −0.975574 0.219671i \(-0.929502\pi\)
0.975574 0.219671i \(-0.0704984\pi\)
\(464\) 4.25546e7 + 5.29680e7i 0.425983 + 0.530225i
\(465\) 4.88453e7 0.485808
\(466\) 7.58055e7 1.07043e8i 0.749105 1.05779i
\(467\) −3.09469e7 −0.303855 −0.151928 0.988392i \(-0.548548\pi\)
−0.151928 + 0.988392i \(0.548548\pi\)
\(468\) 3.06030e7 1.07706e7i 0.298557 0.105075i
\(469\) 1.48005e6i 0.0143469i
\(470\) 5.93269e7 8.37737e7i 0.571423 0.806889i
\(471\) 1.58916e8i 1.52091i
\(472\) 7.00200e7 + 1.99671e7i 0.665880 + 0.189884i
\(473\) −5.44920e6 −0.0514932
\(474\) −7.25555e7 5.13824e7i −0.681295 0.482480i
\(475\) 4.07228e7 0.379977
\(476\) −6.10323e6 + 2.14800e6i −0.0565899 + 0.0199165i
\(477\) 6.45163e7i 0.594449i
\(478\) 1.13589e8 + 8.04414e7i 1.04004 + 0.736539i
\(479\) 9.72219e7i 0.884622i 0.896862 + 0.442311i \(0.145841\pi\)
−0.896862 + 0.442311i \(0.854159\pi\)
\(480\) −2.11588e8 + 1.28413e7i −1.91323 + 0.116115i
\(481\) 4.49153e7 0.403607
\(482\) −6.19761e7 + 8.75145e7i −0.553456 + 0.781518i
\(483\) −1.22757e7 −0.108945
\(484\) 1.94941e7 + 5.53899e7i 0.171937 + 0.488534i
\(485\) 1.28074e8i 1.12263i
\(486\) −5.55447e7 + 7.84329e7i −0.483876 + 0.683266i
\(487\) 9.02434e7i 0.781320i −0.920535 0.390660i \(-0.872247\pi\)
0.920535 0.390660i \(-0.127753\pi\)
\(488\) 1.35459e7 4.75022e7i 0.116559 0.408747i
\(489\) −5.94595e7 −0.508504
\(490\) −1.52412e8 1.07935e8i −1.29548 0.917436i
\(491\) −1.00966e8 −0.852962 −0.426481 0.904497i \(-0.640247\pi\)
−0.426481 + 0.904497i \(0.640247\pi\)
\(492\) −3.59774e7 1.02225e8i −0.302089 0.858344i
\(493\) 8.52758e7i 0.711681i
\(494\) 1.71738e7 + 1.21621e7i 0.142457 + 0.100885i
\(495\) 6.01360e7i 0.495814i
\(496\) −1.93702e7 2.41102e7i −0.158741 0.197586i
\(497\) 1.09365e7 0.0890857
\(498\) −1.39652e8 + 1.97198e8i −1.13073 + 1.59667i
\(499\) −1.47819e8 −1.18968 −0.594839 0.803845i \(-0.702784\pi\)
−0.594839 + 0.803845i \(0.702784\pi\)
\(500\) −1.00773e8 + 3.54665e7i −0.806185 + 0.283732i
\(501\) 1.28117e8i 1.01881i
\(502\) 7.86207e7 1.11018e8i 0.621478 0.877570i
\(503\) 3.38774e7i 0.266199i 0.991103 + 0.133099i \(0.0424929\pi\)
−0.991103 + 0.133099i \(0.957507\pi\)
\(504\) 902500. 3.16486e6i 0.00704946 0.0247208i
\(505\) 1.70888e8 1.32690
\(506\) 1.15906e8 + 8.20823e7i 0.894651 + 0.633575i
\(507\) −7.86829e7 −0.603749
\(508\) 1.46817e8 5.16714e7i 1.11992 0.394148i
\(509\) 5.16056e7i 0.391331i −0.980671 0.195665i \(-0.937313\pi\)
0.980671 0.195665i \(-0.0626866\pi\)
\(510\) 2.17116e8 + 1.53758e8i 1.63675 + 1.15911i
\(511\) 5.62268e6i 0.0421386i
\(512\) 9.02461e7 + 9.93481e7i 0.672386 + 0.740201i
\(513\) −2.21635e7 −0.164167
\(514\) −8.98458e7 + 1.26868e8i −0.661620 + 0.934253i
\(515\) 4.24810e8 3.11009
\(516\) 4.07088e6 + 1.15668e7i 0.0296305 + 0.0841909i
\(517\) 5.95647e7i 0.431040i
\(518\) 2.63319e6 3.71825e6i 0.0189449 0.0267515i
\(519\) 6.66667e6i 0.0476877i
\(520\) −1.52026e8 4.33523e7i −1.08121 0.308320i
\(521\) −1.06575e8 −0.753602 −0.376801 0.926294i \(-0.622976\pi\)
−0.376801 + 0.926294i \(0.622976\pi\)
\(522\) 3.53977e7 + 2.50679e7i 0.248865 + 0.176241i
\(523\) 1.10885e8 0.775117 0.387558 0.921845i \(-0.373319\pi\)
0.387558 + 0.921845i \(0.373319\pi\)
\(524\) −5.67261e7 1.61179e8i −0.394266 1.12025i
\(525\) 1.53425e7i 0.106027i
\(526\) −8.70290e7 6.16323e7i −0.598008 0.423498i
\(527\) 3.88162e7i 0.265205i
\(528\) −9.58876e7 + 7.70362e7i −0.651420 + 0.523351i
\(529\) −2.21005e8 −1.49292
\(530\) 1.81686e8 2.56554e8i 1.22038 1.72326i
\(531\) 4.64817e7 0.310455
\(532\) 2.01365e6 708691.i 0.0133736 0.00470676i
\(533\) 8.08202e7i 0.533751i
\(534\) 6.53156e7 9.22302e7i 0.428937 0.605689i
\(535\) 3.60962e8i 2.35722i
\(536\) −3.70563e7 1.05671e7i −0.240640 0.0686216i
\(537\) 1.09182e8 0.705062
\(538\) −4.65826e7 3.29889e7i −0.299142 0.211846i
\(539\) −1.08368e8 −0.692047
\(540\) 1.57053e8 5.52739e7i 0.997390 0.351026i
\(541\) 8.74191e7i 0.552096i 0.961144 + 0.276048i \(0.0890248\pi\)
−0.961144 + 0.276048i \(0.910975\pi\)
\(542\) −4.52803e7 3.20666e7i −0.284388 0.201398i
\(543\) 7.77076e7i 0.485360i
\(544\) −1.02047e7 1.68144e8i −0.0633875 1.04444i
\(545\) −2.84737e8 −1.75896
\(546\) 4.58212e6 6.47027e6i 0.0281507 0.0397507i
\(547\) −1.11073e7 −0.0678653 −0.0339326 0.999424i \(-0.510803\pi\)
−0.0339326 + 0.999424i \(0.510803\pi\)
\(548\) 8.50313e7 + 2.41605e8i 0.516699 + 1.46813i
\(549\) 3.15336e7i 0.190571i
\(550\) −1.02588e8 + 1.44862e8i −0.616609 + 0.870694i
\(551\) 2.81351e7i 0.168188i
\(552\) 8.76446e7 3.07349e8i 0.521084 1.82732i
\(553\) −6.72592e6 −0.0397719
\(554\) 1.17080e8 + 8.29135e7i 0.688576 + 0.487636i
\(555\) −1.87346e8 −1.09589
\(556\) −4.02464e7 1.14354e8i −0.234154 0.665317i
\(557\) 4.54249e7i 0.262862i 0.991325 + 0.131431i \(0.0419573\pi\)
−0.991325 + 0.131431i \(0.958043\pi\)
\(558\) −1.61125e7 1.14105e7i −0.0927383 0.0656755i
\(559\) 9.14488e6i 0.0523531i
\(560\) −1.25015e7 + 1.00437e7i −0.0711866 + 0.0571914i
\(561\) 1.54374e8 0.874351
\(562\) 1.98499e7 2.80295e7i 0.111828 0.157909i
\(563\) 5.57201e7 0.312239 0.156119 0.987738i \(-0.450102\pi\)
0.156119 + 0.987738i \(0.450102\pi\)
\(564\) −1.26436e8 + 4.44984e7i −0.704747 + 0.248031i
\(565\) 1.25099e8i 0.693600i
\(566\) −1.56910e8 + 2.21568e8i −0.865369 + 1.22196i
\(567\) 1.30360e7i 0.0715148i
\(568\) −7.80828e7 + 2.73819e8i −0.426099 + 1.49423i
\(569\) 3.43539e8 1.86483 0.932416 0.361387i \(-0.117697\pi\)
0.932416 + 0.361387i \(0.117697\pi\)
\(570\) −7.16335e7 5.07295e7i −0.386805 0.273928i
\(571\) −2.25486e8 −1.21119 −0.605593 0.795775i \(-0.707064\pi\)
−0.605593 + 0.795775i \(0.707064\pi\)
\(572\) −8.65277e7 + 3.04529e7i −0.462346 + 0.162720i
\(573\) 6.57811e7i 0.349653i
\(574\) −6.69058e6 4.73814e6i −0.0353776 0.0250537i
\(575\) 4.61236e8i 2.42616i
\(576\) 7.27956e7 + 4.51921e7i 0.380923 + 0.236480i
\(577\) −8.79050e7 −0.457600 −0.228800 0.973473i \(-0.573480\pi\)
−0.228800 + 0.973473i \(0.573480\pi\)
\(578\) −1.05880e7 + 1.49510e7i −0.0548316 + 0.0774259i
\(579\) 2.57518e8 1.32669
\(580\) −7.01667e7 1.99369e8i −0.359622 1.02182i
\(581\) 1.82803e7i 0.0932085i
\(582\) 9.66481e7 1.36474e8i 0.490257 0.692277i
\(583\) 1.82415e8i 0.920564i
\(584\) 1.40776e8 + 4.01441e7i 0.706789 + 0.201550i
\(585\) −1.00920e8 −0.504094
\(586\) 2.05769e8 + 1.45722e8i 1.02256 + 0.724156i
\(587\) −3.94523e7 −0.195056 −0.0975278 0.995233i \(-0.531093\pi\)
−0.0975278 + 0.995233i \(0.531093\pi\)
\(588\) 8.09574e7 + 2.30029e8i 0.398222 + 1.13149i
\(589\) 1.28067e7i 0.0626744i
\(590\) −1.84838e8 1.30898e8i −0.899983 0.637351i
\(591\) 1.34131e8i 0.649778i
\(592\) 7.42943e7 + 9.24747e7i 0.358088 + 0.445716i
\(593\) 2.30474e8 1.10524 0.552622 0.833432i \(-0.313627\pi\)
0.552622 + 0.833432i \(0.313627\pi\)
\(594\) 5.58339e7 7.88413e7i 0.266403 0.376179i
\(595\) 2.01268e7 0.0955484
\(596\) −1.84971e8 + 6.50994e7i −0.873704 + 0.307495i
\(597\) 3.84065e8i 1.80502i
\(598\) 1.37751e8 1.94514e8i 0.644155 0.909592i
\(599\) 1.85523e8i 0.863212i −0.902062 0.431606i \(-0.857947\pi\)
0.902062 0.431606i \(-0.142053\pi\)
\(600\) 3.84132e8 + 1.09540e8i 1.77839 + 0.507130i
\(601\) −4.38545e7 −0.202018 −0.101009 0.994885i \(-0.532207\pi\)
−0.101009 + 0.994885i \(0.532207\pi\)
\(602\) 757045. + 536125.i 0.00347002 + 0.00245740i
\(603\) −2.45993e7 −0.112194
\(604\) −1.35493e8 + 4.76859e7i −0.614902 + 0.216411i
\(605\) 1.82661e8i 0.824858i
\(606\) −1.82096e8 1.28957e8i −0.818242 0.579463i
\(607\) 2.43622e8i 1.08931i 0.838661 + 0.544654i \(0.183339\pi\)
−0.838661 + 0.544654i \(0.816661\pi\)
\(608\) 3.36685e6 + 5.54758e7i 0.0149800 + 0.246827i
\(609\) 1.06000e7 0.0469304
\(610\) −8.88028e7 + 1.25396e8i −0.391235 + 0.552450i
\(611\) −9.99618e7 −0.438238
\(612\) −3.57009e7 1.01439e8i −0.155749 0.442539i
\(613\) 3.31194e8i 1.43781i −0.695109 0.718905i \(-0.744644\pi\)
0.695109 0.718905i \(-0.255356\pi\)
\(614\) −1.59634e8 + 2.25414e8i −0.689635 + 0.973813i
\(615\) 3.37109e8i 1.44926i
\(616\) −2.55175e6 + 8.94839e6i −0.0109168 + 0.0382827i
\(617\) 1.49869e8 0.638054 0.319027 0.947746i \(-0.396644\pi\)
0.319027 + 0.947746i \(0.396644\pi\)
\(618\) −4.52672e8 3.20574e8i −1.91787 1.35820i
\(619\) 8.10701e7 0.341813 0.170907 0.985287i \(-0.445330\pi\)
0.170907 + 0.985287i \(0.445330\pi\)
\(620\) 3.19387e7 + 9.07495e7i 0.134012 + 0.380776i
\(621\) 2.51029e8i 1.04821i
\(622\) 1.01779e8 + 7.20782e7i 0.422949 + 0.299525i
\(623\) 8.54977e6i 0.0353582i
\(624\) 1.29283e8 + 1.60919e8i 0.532091 + 0.662298i
\(625\) −4.28287e7 −0.175426
\(626\) −9.86985e6 + 1.39369e7i −0.0402335 + 0.0568125i
\(627\) −5.09328e7 −0.206631
\(628\) 2.95249e8 1.03911e8i 1.19209 0.419550i
\(629\) 1.48879e8i 0.598250i
\(630\) −5.91653e6 + 8.35455e6i −0.0236617 + 0.0334119i
\(631\) 2.70423e8i 1.07635i −0.842832 0.538177i \(-0.819113\pi\)
0.842832 0.538177i \(-0.180887\pi\)
\(632\) 4.80209e7 1.68398e8i 0.190230 0.667092i
\(633\) −3.88050e8 −1.52995
\(634\) 2.71227e8 + 1.92078e8i 1.06430 + 0.753718i
\(635\) −4.84163e8 −1.89091
\(636\) −3.87205e8 + 1.36275e8i −1.50512 + 0.529716i
\(637\) 1.81864e8i 0.703604i
\(638\) −1.00084e8 7.08776e7i −0.385392 0.272927i
\(639\) 1.81770e8i 0.696659i
\(640\) −1.62210e8 3.84711e8i −0.618782 1.46756i
\(641\) 7.98693e7 0.303254 0.151627 0.988438i \(-0.451549\pi\)
0.151627 + 0.988438i \(0.451549\pi\)
\(642\) 2.72392e8 3.84637e8i 1.02941 1.45360i
\(643\) 3.07378e8 1.15622 0.578110 0.815959i \(-0.303791\pi\)
0.578110 + 0.815959i \(0.303791\pi\)
\(644\) −8.02679e6 2.28070e7i −0.0300527 0.0853907i
\(645\) 3.81442e7i 0.142151i
\(646\) 4.03135e7 5.69254e7i 0.149538 0.211158i
\(647\) 3.33867e7i 0.123271i −0.998099 0.0616354i \(-0.980368\pi\)
0.998099 0.0616354i \(-0.0196316\pi\)
\(648\) −3.26385e8 9.30730e7i −1.19952 0.342057i
\(649\) −1.31423e8 −0.480771
\(650\) 2.43107e8 + 1.72164e8i 0.885234 + 0.626906i
\(651\) −4.82496e6 −0.0174884
\(652\) −3.88791e7 1.10469e8i −0.140273 0.398565i
\(653\) 3.92550e8i 1.40979i 0.709309 + 0.704897i \(0.249007\pi\)
−0.709309 + 0.704897i \(0.750993\pi\)
\(654\) 3.03412e8 + 2.14871e8i 1.08468 + 0.768147i
\(655\) 5.31525e8i 1.89147i
\(656\) 1.66398e8 1.33685e8i 0.589437 0.473554i
\(657\) 9.34520e7 0.329528
\(658\) −5.86033e6 + 8.27519e6i −0.0205705 + 0.0290469i
\(659\) 4.88173e8 1.70576 0.852879 0.522109i \(-0.174855\pi\)
0.852879 + 0.522109i \(0.174855\pi\)
\(660\) 3.60916e8 1.27022e8i 1.25538 0.441822i
\(661\) 2.56127e8i 0.886853i 0.896311 + 0.443427i \(0.146237\pi\)
−0.896311 + 0.443427i \(0.853763\pi\)
\(662\) −8.27589e7 + 1.16861e8i −0.285260 + 0.402807i
\(663\) 2.59071e8i 0.888953i
\(664\) −4.57688e8 1.30516e8i −1.56338 0.445819i
\(665\) −6.64045e6 −0.0225805
\(666\) 6.17993e7 + 4.37651e7i 0.209200 + 0.148151i
\(667\) 3.18665e8 1.07388
\(668\) 2.38027e8 8.37723e7i 0.798542 0.281042i
\(669\) 6.85382e8i 2.28904i
\(670\) 9.78208e7 + 6.92748e7i 0.325242 + 0.230330i
\(671\) 8.91589e7i 0.295119i
\(672\) 2.09007e7 1.26847e6i 0.0688737 0.00417997i
\(673\) 2.16653e8 0.710754 0.355377 0.934723i \(-0.384352\pi\)
0.355377 + 0.934723i \(0.384352\pi\)
\(674\) −8.61096e7 + 1.21593e8i −0.281237 + 0.397126i
\(675\) −3.13741e8 −1.02014
\(676\) −5.14488e7 1.46185e8i −0.166546 0.473218i
\(677\) 1.50931e8i 0.486420i −0.969974 0.243210i \(-0.921800\pi\)
0.969974 0.243210i \(-0.0782005\pi\)
\(678\) 9.44034e7 1.33304e8i 0.302899 0.427715i
\(679\) 1.26512e7i 0.0404130i
\(680\) −1.43699e8 + 5.03918e8i −0.457010 + 1.60263i
\(681\) −8.89223e7 −0.281559
\(682\) 4.55567e7 + 3.22623e7i 0.143615 + 0.101705i
\(683\) −3.69947e8 −1.16112 −0.580561 0.814217i \(-0.697167\pi\)
−0.580561 + 0.814217i \(0.697167\pi\)
\(684\) 1.17788e7 + 3.34679e7i 0.0368073 + 0.104583i
\(685\) 7.96746e8i 2.47884i
\(686\) 3.01603e7 + 2.13590e7i 0.0934251 + 0.0661619i
\(687\) 2.35183e8i 0.725332i
\(688\) −1.88281e7 + 1.51265e7i −0.0578151 + 0.0464487i
\(689\) −3.06129e8 −0.935938
\(690\) −5.74573e8 + 8.11336e8i −1.74903 + 2.46975i
\(691\) −2.15167e7 −0.0652141 −0.0326070 0.999468i \(-0.510381\pi\)
−0.0326070 + 0.999468i \(0.510381\pi\)
\(692\) −1.23860e7 + 4.35917e6i −0.0373776 + 0.0131548i
\(693\) 5.94025e6i 0.0178486i
\(694\) −1.83292e8 + 2.58821e8i −0.548360 + 0.774322i
\(695\) 3.77109e8i 1.12334i
\(696\) −7.56806e7 + 2.65395e8i −0.224469 + 0.787162i
\(697\) −2.67893e8 −0.791156
\(698\) −4.46831e8 3.16437e8i −1.31394 0.930511i
\(699\) 5.32763e8 1.55992
\(700\) 2.85047e7 1.00321e7i 0.0831040 0.0292480i
\(701\) 2.95578e8i 0.858060i 0.903290 + 0.429030i \(0.141145\pi\)
−0.903290 + 0.429030i \(0.858855\pi\)
\(702\) −1.32312e8 9.37007e7i −0.382461 0.270852i
\(703\) 4.91200e7i 0.141381i
\(704\) −2.05824e8 1.27777e8i −0.589899 0.366214i
\(705\) 4.16951e8 1.18992
\(706\) 1.39446e8 1.96907e8i 0.396270 0.559561i
\(707\) −1.68803e7 −0.0477665
\(708\) 9.81809e7 + 2.78967e8i 0.276648 + 0.786056i
\(709\) 3.43066e8i 0.962584i −0.876560 0.481292i \(-0.840168\pi\)
0.876560 0.481292i \(-0.159832\pi\)
\(710\) 5.11889e8 7.22822e8i 1.43021 2.01956i
\(711\) 1.11789e8i 0.311020i
\(712\) 2.14062e8 + 6.10426e7i 0.593062 + 0.169119i
\(713\) −1.45051e8 −0.400177
\(714\) −2.14468e7 1.51882e7i −0.0589208 0.0417266i
\(715\) 2.85344e8 0.780641
\(716\) 7.13912e7 + 2.02848e8i 0.194494 + 0.552627i
\(717\) 5.65344e8i 1.53375i
\(718\) 4.00828e8 + 2.83858e8i 1.08289 + 0.766882i
\(719\) 2.69203e8i 0.724257i −0.932128 0.362129i \(-0.882050\pi\)
0.932128 0.362129i \(-0.117950\pi\)
\(720\) −1.66932e8 2.07782e8i −0.447242 0.556686i
\(721\) −4.19629e7 −0.111959
\(722\) 2.04215e8 2.88365e8i 0.542595 0.766181i
\(723\) −4.35569e8 −1.15250
\(724\) −1.44373e8 + 5.08111e7i −0.380425 + 0.133888i
\(725\) 3.98274e8i 1.04513i
\(726\) −1.37841e8 + 1.94641e8i −0.360220 + 0.508656i
\(727\) 1.90694e8i 0.496287i 0.968723 + 0.248144i \(0.0798205\pi\)
−0.968723 + 0.248144i \(0.920180\pi\)
\(728\) 1.50172e7 + 4.28235e6i 0.0389220 + 0.0110991i
\(729\) 9.28730e7 0.239721
\(730\) −3.71618e8 2.63173e8i −0.955275 0.676508i
\(731\) 3.03123e7 0.0776008
\(732\) 1.89254e8 6.66069e7i 0.482517 0.169819i
\(733\) 4.68798e8i 1.19035i 0.803597 + 0.595174i \(0.202917\pi\)
−0.803597 + 0.595174i \(0.797083\pi\)
\(734\) 2.72689e8 + 1.93113e8i 0.689571 + 0.488341i
\(735\) 7.58573e8i 1.91045i
\(736\) 6.28332e8 3.81337e7i 1.57600 0.0956478i
\(737\) 6.95525e7 0.173744
\(738\) 7.87505e7 1.11201e8i 0.195923 0.276656i
\(739\) −6.73855e8 −1.66968 −0.834840 0.550493i \(-0.814440\pi\)
−0.834840 + 0.550493i \(0.814440\pi\)
\(740\) −1.22501e8 3.48070e8i −0.302305 0.858956i
\(741\) 8.54757e7i 0.210082i
\(742\) −1.79470e7 + 2.53424e7i −0.0439320 + 0.0620350i
\(743\) 7.42053e7i 0.180913i −0.995900 0.0904563i \(-0.971167\pi\)
0.995900 0.0904563i \(-0.0288325\pi\)
\(744\) 3.44486e7 1.20803e8i 0.0836475 0.293332i
\(745\) 6.09983e8 1.47519
\(746\) −3.66586e8 2.59609e8i −0.882997 0.625321i
\(747\) −3.03829e8 −0.728900
\(748\) 1.00941e8 + 2.86811e8i 0.241193 + 0.685316i
\(749\) 3.56560e7i 0.0848568i
\(750\) −3.54118e8 2.50779e8i −0.839390 0.594440i
\(751\) 9.05182e7i 0.213706i −0.994275 0.106853i \(-0.965923\pi\)
0.994275 0.106853i \(-0.0340774\pi\)
\(752\) −1.65347e8 2.05808e8i −0.388814 0.483960i
\(753\) 5.52548e8 1.29415
\(754\) −1.18947e8 + 1.67961e8i −0.277485 + 0.391828i
\(755\) 4.46819e8 1.03822
\(756\) −1.55137e7 + 5.45997e6i −0.0359047 + 0.0126364i
\(757\) 2.19809e8i 0.506709i −0.967374 0.253354i \(-0.918466\pi\)
0.967374 0.253354i \(-0.0815339\pi\)
\(758\) 9.08439e7 1.28278e8i 0.208588 0.294540i
\(759\) 5.76876e8i 1.31934i
\(760\) 4.74106e7 1.66258e8i 0.108003 0.378741i
\(761\) 8.05220e7 0.182709 0.0913547 0.995818i \(-0.470880\pi\)
0.0913547 + 0.995818i \(0.470880\pi\)
\(762\) 5.15918e8 + 3.65363e8i 1.16605 + 0.825771i
\(763\) 2.81264e7 0.0633200
\(764\) 1.22214e8 4.30126e7i 0.274058 0.0964530i
\(765\) 3.34518e8i 0.747198i
\(766\) −2.52418e8 1.78758e8i −0.561609 0.397721i
\(767\) 2.20555e8i 0.488800i
\(768\) −1.17465e8 + 5.32352e8i −0.259314 + 1.17521i
\(769\) −8.94416e8 −1.96680 −0.983400 0.181449i \(-0.941921\pi\)
−0.983400 + 0.181449i \(0.941921\pi\)
\(770\) 1.67285e7 2.36218e7i 0.0366425 0.0517417i
\(771\) −6.31439e8 −1.37774
\(772\) 1.68384e8 + 4.78440e8i 0.365973 + 1.03986i
\(773\) 7.83108e8i 1.69544i 0.530442 + 0.847721i \(0.322026\pi\)
−0.530442 + 0.847721i \(0.677974\pi\)
\(774\) −8.91069e6 + 1.25825e7i −0.0192171 + 0.0271359i
\(775\) 1.81288e8i 0.389461i
\(776\) 3.16750e8 + 9.03252e7i 0.677846 + 0.193296i
\(777\) 1.85061e7 0.0394505
\(778\) −1.92540e7 1.36353e7i −0.0408868 0.0289552i
\(779\) 8.83861e7 0.186970
\(780\) −2.13169e8 6.05690e8i −0.449201 1.27634i
\(781\) 5.13941e8i 1.07885i
\(782\) −6.44749e8