Properties

Label 165.6.c.b.34.4
Level $165$
Weight $6$
Character 165.34
Analytic conductor $26.463$
Analytic rank $0$
Dimension $26$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 165.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.4633302691\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.4
Character \(\chi\) \(=\) 165.34
Dual form 165.6.c.b.34.23

$q$-expansion

\(f(q)\) \(=\) \(q-8.57523i q^{2} +9.00000i q^{3} -41.5346 q^{4} +(-51.2624 - 22.2971i) q^{5} +77.1771 q^{6} -178.462i q^{7} +81.7612i q^{8} -81.0000 q^{9} +O(q^{10})\) \(q-8.57523i q^{2} +9.00000i q^{3} -41.5346 q^{4} +(-51.2624 - 22.2971i) q^{5} +77.1771 q^{6} -178.462i q^{7} +81.7612i q^{8} -81.0000 q^{9} +(-191.203 + 439.587i) q^{10} +121.000 q^{11} -373.811i q^{12} -361.980i q^{13} -1530.36 q^{14} +(200.674 - 461.362i) q^{15} -627.985 q^{16} -934.004i q^{17} +694.594i q^{18} -753.929 q^{19} +(2129.16 + 926.102i) q^{20} +1606.16 q^{21} -1037.60i q^{22} +3231.01i q^{23} -735.851 q^{24} +(2130.68 + 2286.01i) q^{25} -3104.06 q^{26} -729.000i q^{27} +7412.36i q^{28} -2606.34 q^{29} +(-3956.29 - 1720.83i) q^{30} +662.215 q^{31} +8001.48i q^{32} +1089.00i q^{33} -8009.30 q^{34} +(-3979.20 + 9148.42i) q^{35} +3364.30 q^{36} +12924.2i q^{37} +6465.11i q^{38} +3257.82 q^{39} +(1823.04 - 4191.28i) q^{40} -2538.56 q^{41} -13773.2i q^{42} +22022.8i q^{43} -5025.68 q^{44} +(4152.26 + 1806.07i) q^{45} +27706.7 q^{46} -20835.4i q^{47} -5651.87i q^{48} -15041.8 q^{49} +(19603.1 - 18271.0i) q^{50} +8406.03 q^{51} +15034.7i q^{52} -27450.5i q^{53} -6251.34 q^{54} +(-6202.76 - 2697.95i) q^{55} +14591.3 q^{56} -6785.36i q^{57} +22350.0i q^{58} -7759.71 q^{59} +(-8334.92 + 19162.5i) q^{60} +38469.2 q^{61} -5678.65i q^{62} +14455.5i q^{63} +48519.0 q^{64} +(-8071.11 + 18556.0i) q^{65} +9338.43 q^{66} -35521.3i q^{67} +38793.4i q^{68} -29079.1 q^{69} +(78449.8 + 34122.5i) q^{70} -62677.1 q^{71} -6622.66i q^{72} +68950.2i q^{73} +110828. q^{74} +(-20574.1 + 19176.1i) q^{75} +31314.1 q^{76} -21594.0i q^{77} -27936.5i q^{78} +17313.8 q^{79} +(32192.1 + 14002.3i) q^{80} +6561.00 q^{81} +21768.7i q^{82} -89017.9i q^{83} -66711.2 q^{84} +(-20825.6 + 47879.3i) q^{85} +188850. q^{86} -23457.1i q^{87} +9893.11i q^{88} -129627. q^{89} +(15487.4 - 35606.6i) q^{90} -64599.8 q^{91} -134199. i q^{92} +5959.94i q^{93} -178668. q^{94} +(38648.2 + 16810.4i) q^{95} -72013.3 q^{96} +136732. i q^{97} +128987. i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.57523i 1.51590i −0.652312 0.757950i \(-0.726201\pi\)
0.652312 0.757950i \(-0.273799\pi\)
\(3\) 9.00000i 0.577350i
\(4\) −41.5346 −1.29796
\(5\) −51.2624 22.2971i −0.917010 0.398863i
\(6\) 77.1771 0.875206
\(7\) 178.462i 1.37658i −0.725435 0.688290i \(-0.758362\pi\)
0.725435 0.688290i \(-0.241638\pi\)
\(8\) 81.7612i 0.451671i
\(9\) −81.0000 −0.333333
\(10\) −191.203 + 439.587i −0.604637 + 1.39010i
\(11\) 121.000 0.301511
\(12\) 373.811i 0.749375i
\(13\) 361.980i 0.594054i −0.954869 0.297027i \(-0.904005\pi\)
0.954869 0.297027i \(-0.0959951\pi\)
\(14\) −1530.36 −2.08676
\(15\) 200.674 461.362i 0.230284 0.529436i
\(16\) −627.985 −0.613267
\(17\) 934.004i 0.783838i −0.920000 0.391919i \(-0.871811\pi\)
0.920000 0.391919i \(-0.128189\pi\)
\(18\) 694.594i 0.505300i
\(19\) −753.929 −0.479122 −0.239561 0.970881i \(-0.577004\pi\)
−0.239561 + 0.970881i \(0.577004\pi\)
\(20\) 2129.16 + 926.102i 1.19024 + 0.517707i
\(21\) 1606.16 0.794769
\(22\) 1037.60i 0.457061i
\(23\) 3231.01i 1.27356i 0.771046 + 0.636780i \(0.219734\pi\)
−0.771046 + 0.636780i \(0.780266\pi\)
\(24\) −735.851 −0.260773
\(25\) 2130.68 + 2286.01i 0.681816 + 0.731523i
\(26\) −3104.06 −0.900527
\(27\) 729.000i 0.192450i
\(28\) 7412.36i 1.78674i
\(29\) −2606.34 −0.575488 −0.287744 0.957707i \(-0.592905\pi\)
−0.287744 + 0.957707i \(0.592905\pi\)
\(30\) −3956.29 1720.83i −0.802573 0.349087i
\(31\) 662.215 0.123764 0.0618821 0.998083i \(-0.480290\pi\)
0.0618821 + 0.998083i \(0.480290\pi\)
\(32\) 8001.48i 1.38132i
\(33\) 1089.00i 0.174078i
\(34\) −8009.30 −1.18822
\(35\) −3979.20 + 9148.42i −0.549067 + 1.26234i
\(36\) 3364.30 0.432652
\(37\) 12924.2i 1.55203i 0.630717 + 0.776013i \(0.282761\pi\)
−0.630717 + 0.776013i \(0.717239\pi\)
\(38\) 6465.11i 0.726302i
\(39\) 3257.82 0.342977
\(40\) 1823.04 4191.28i 0.180155 0.414187i
\(41\) −2538.56 −0.235846 −0.117923 0.993023i \(-0.537624\pi\)
−0.117923 + 0.993023i \(0.537624\pi\)
\(42\) 13773.2i 1.20479i
\(43\) 22022.8i 1.81636i 0.418583 + 0.908178i \(0.362527\pi\)
−0.418583 + 0.908178i \(0.637473\pi\)
\(44\) −5025.68 −0.391348
\(45\) 4152.26 + 1806.07i 0.305670 + 0.132954i
\(46\) 27706.7 1.93059
\(47\) 20835.4i 1.37581i −0.725802 0.687903i \(-0.758531\pi\)
0.725802 0.687903i \(-0.241469\pi\)
\(48\) 5651.87i 0.354070i
\(49\) −15041.8 −0.894974
\(50\) 19603.1 18271.0i 1.10892 1.03357i
\(51\) 8406.03 0.452549
\(52\) 15034.7i 0.771056i
\(53\) 27450.5i 1.34233i −0.741307 0.671166i \(-0.765794\pi\)
0.741307 0.671166i \(-0.234206\pi\)
\(54\) −6251.34 −0.291735
\(55\) −6202.76 2697.95i −0.276489 0.120262i
\(56\) 14591.3 0.621762
\(57\) 6785.36i 0.276621i
\(58\) 22350.0i 0.872383i
\(59\) −7759.71 −0.290212 −0.145106 0.989416i \(-0.546352\pi\)
−0.145106 + 0.989416i \(0.546352\pi\)
\(60\) −8334.92 + 19162.5i −0.298898 + 0.687185i
\(61\) 38469.2 1.32370 0.661849 0.749638i \(-0.269772\pi\)
0.661849 + 0.749638i \(0.269772\pi\)
\(62\) 5678.65i 0.187614i
\(63\) 14455.5i 0.458860i
\(64\) 48519.0 1.48068
\(65\) −8071.11 + 18556.0i −0.236946 + 0.544754i
\(66\) 9338.43 0.263884
\(67\) 35521.3i 0.966723i −0.875421 0.483362i \(-0.839416\pi\)
0.875421 0.483362i \(-0.160584\pi\)
\(68\) 38793.4i 1.01739i
\(69\) −29079.1 −0.735290
\(70\) 78449.8 + 34122.5i 1.91358 + 0.832332i
\(71\) −62677.1 −1.47558 −0.737790 0.675030i \(-0.764131\pi\)
−0.737790 + 0.675030i \(0.764131\pi\)
\(72\) 6622.66i 0.150557i
\(73\) 68950.2i 1.51436i 0.653208 + 0.757179i \(0.273423\pi\)
−0.653208 + 0.757179i \(0.726577\pi\)
\(74\) 110828. 2.35272
\(75\) −20574.1 + 19176.1i −0.422345 + 0.393647i
\(76\) 31314.1 0.621879
\(77\) 21594.0i 0.415055i
\(78\) 27936.5i 0.519919i
\(79\) 17313.8 0.312123 0.156061 0.987747i \(-0.450120\pi\)
0.156061 + 0.987747i \(0.450120\pi\)
\(80\) 32192.1 + 14002.3i 0.562372 + 0.244610i
\(81\) 6561.00 0.111111
\(82\) 21768.7i 0.357518i
\(83\) 89017.9i 1.41835i −0.705035 0.709173i \(-0.749069\pi\)
0.705035 0.709173i \(-0.250931\pi\)
\(84\) −66711.2 −1.03158
\(85\) −20825.6 + 47879.3i −0.312644 + 0.718787i
\(86\) 188850. 2.75342
\(87\) 23457.1i 0.332258i
\(88\) 9893.11i 0.136184i
\(89\) −129627. −1.73468 −0.867341 0.497714i \(-0.834173\pi\)
−0.867341 + 0.497714i \(0.834173\pi\)
\(90\) 15487.4 35606.6i 0.201546 0.463366i
\(91\) −64599.8 −0.817763
\(92\) 134199.i 1.65302i
\(93\) 5959.94i 0.0714553i
\(94\) −178668. −2.08559
\(95\) 38648.2 + 16810.4i 0.439360 + 0.191104i
\(96\) −72013.3 −0.797507
\(97\) 136732.i 1.47551i 0.675069 + 0.737755i \(0.264114\pi\)
−0.675069 + 0.737755i \(0.735886\pi\)
\(98\) 128987.i 1.35669i
\(99\) −9801.00 −0.100504
\(100\) −88496.7 94948.5i −0.884967 0.949485i
\(101\) 51376.9 0.501146 0.250573 0.968098i \(-0.419381\pi\)
0.250573 + 0.968098i \(0.419381\pi\)
\(102\) 72083.7i 0.686019i
\(103\) 94899.7i 0.881398i −0.897655 0.440699i \(-0.854731\pi\)
0.897655 0.440699i \(-0.145269\pi\)
\(104\) 29595.9 0.268317
\(105\) −82335.8 35812.8i −0.728812 0.317004i
\(106\) −235394. −2.03484
\(107\) 52232.6i 0.441045i 0.975382 + 0.220522i \(0.0707762\pi\)
−0.975382 + 0.220522i \(0.929224\pi\)
\(108\) 30278.7i 0.249792i
\(109\) −138553. −1.11699 −0.558496 0.829507i \(-0.688622\pi\)
−0.558496 + 0.829507i \(0.688622\pi\)
\(110\) −23135.6 + 53190.1i −0.182305 + 0.419130i
\(111\) −116318. −0.896063
\(112\) 112072.i 0.844211i
\(113\) 136642.i 1.00667i −0.864091 0.503336i \(-0.832106\pi\)
0.864091 0.503336i \(-0.167894\pi\)
\(114\) −58186.0 −0.419330
\(115\) 72042.3 165630.i 0.507976 1.16787i
\(116\) 108253. 0.746958
\(117\) 29320.4i 0.198018i
\(118\) 66541.3i 0.439933i
\(119\) −166685. −1.07902
\(120\) 37721.5 + 16407.4i 0.239131 + 0.104013i
\(121\) 14641.0 0.0909091
\(122\) 329882.i 2.00659i
\(123\) 22847.0i 0.136165i
\(124\) −27504.8 −0.160640
\(125\) −58252.2 164694.i −0.333455 0.942766i
\(126\) 123959. 0.695587
\(127\) 23888.8i 0.131427i −0.997839 0.0657136i \(-0.979068\pi\)
0.997839 0.0657136i \(-0.0209324\pi\)
\(128\) 160014.i 0.863244i
\(129\) −198205. −1.04867
\(130\) 159122. + 69211.6i 0.825793 + 0.359187i
\(131\) 67597.5 0.344154 0.172077 0.985084i \(-0.444952\pi\)
0.172077 + 0.985084i \(0.444952\pi\)
\(132\) 45231.2i 0.225945i
\(133\) 134548.i 0.659550i
\(134\) −304604. −1.46546
\(135\) −16254.6 + 37370.3i −0.0767613 + 0.176479i
\(136\) 76365.3 0.354037
\(137\) 205843.i 0.936991i 0.883466 + 0.468496i \(0.155204\pi\)
−0.883466 + 0.468496i \(0.844796\pi\)
\(138\) 249360.i 1.11463i
\(139\) −43495.6 −0.190945 −0.0954724 0.995432i \(-0.530436\pi\)
−0.0954724 + 0.995432i \(0.530436\pi\)
\(140\) 165274. 379976.i 0.712665 1.63846i
\(141\) 187519. 0.794323
\(142\) 537470.i 2.23683i
\(143\) 43799.6i 0.179114i
\(144\) 50866.8 0.204422
\(145\) 133607. + 58113.9i 0.527728 + 0.229541i
\(146\) 591264. 2.29562
\(147\) 135376.i 0.516713i
\(148\) 536801.i 2.01446i
\(149\) −219355. −0.809436 −0.404718 0.914442i \(-0.632630\pi\)
−0.404718 + 0.914442i \(0.632630\pi\)
\(150\) 164439. + 176428.i 0.596730 + 0.640234i
\(151\) −32928.1 −0.117523 −0.0587616 0.998272i \(-0.518715\pi\)
−0.0587616 + 0.998272i \(0.518715\pi\)
\(152\) 61642.1i 0.216406i
\(153\) 75654.3i 0.261279i
\(154\) −185173. −0.629182
\(155\) −33946.8 14765.5i −0.113493 0.0493650i
\(156\) −135312. −0.445169
\(157\) 457292.i 1.48062i −0.672265 0.740311i \(-0.734678\pi\)
0.672265 0.740311i \(-0.265322\pi\)
\(158\) 148470.i 0.473147i
\(159\) 247054. 0.774996
\(160\) 178410. 410175.i 0.550959 1.26669i
\(161\) 576614. 1.75316
\(162\) 56262.1i 0.168433i
\(163\) 52822.0i 0.155721i −0.996964 0.0778603i \(-0.975191\pi\)
0.996964 0.0778603i \(-0.0248088\pi\)
\(164\) 105438. 0.306117
\(165\) 24281.6 55824.8i 0.0694332 0.159631i
\(166\) −763349. −2.15007
\(167\) 327606.i 0.908993i 0.890748 + 0.454497i \(0.150181\pi\)
−0.890748 + 0.454497i \(0.849819\pi\)
\(168\) 131322.i 0.358974i
\(169\) 240264. 0.647100
\(170\) 410576. + 178584.i 1.08961 + 0.473937i
\(171\) 61068.2 0.159707
\(172\) 914707.i 2.35755i
\(173\) 246387.i 0.625897i 0.949770 + 0.312949i \(0.101317\pi\)
−0.949770 + 0.312949i \(0.898683\pi\)
\(174\) −201150. −0.503670
\(175\) 407967. 380246.i 1.00700 0.938575i
\(176\) −75986.2 −0.184907
\(177\) 69837.4i 0.167554i
\(178\) 1.11158e6i 2.62961i
\(179\) −302341. −0.705285 −0.352643 0.935758i \(-0.614717\pi\)
−0.352643 + 0.935758i \(0.614717\pi\)
\(180\) −172462. 75014.3i −0.396746 0.172569i
\(181\) −465374. −1.05586 −0.527929 0.849288i \(-0.677031\pi\)
−0.527929 + 0.849288i \(0.677031\pi\)
\(182\) 553958.i 1.23965i
\(183\) 346223.i 0.764237i
\(184\) −264172. −0.575230
\(185\) 288172. 662526.i 0.619046 1.42322i
\(186\) 51107.8 0.108319
\(187\) 113014.i 0.236336i
\(188\) 865390.i 1.78574i
\(189\) −130099. −0.264923
\(190\) 144153. 331417.i 0.289695 0.666026i
\(191\) 294182. 0.583489 0.291745 0.956496i \(-0.405764\pi\)
0.291745 + 0.956496i \(0.405764\pi\)
\(192\) 436671.i 0.854872i
\(193\) 280529.i 0.542106i −0.962564 0.271053i \(-0.912628\pi\)
0.962564 0.271053i \(-0.0873718\pi\)
\(194\) 1.17251e6 2.23673
\(195\) −167004. 72640.0i −0.314514 0.136801i
\(196\) 624756. 1.16164
\(197\) 241625.i 0.443585i 0.975094 + 0.221792i \(0.0711907\pi\)
−0.975094 + 0.221792i \(0.928809\pi\)
\(198\) 84045.8i 0.152354i
\(199\) −621763. −1.11299 −0.556496 0.830850i \(-0.687855\pi\)
−0.556496 + 0.830850i \(0.687855\pi\)
\(200\) −186907. + 174207.i −0.330408 + 0.307957i
\(201\) 319692. 0.558138
\(202\) 440569.i 0.759688i
\(203\) 465134.i 0.792205i
\(204\) −349141. −0.587389
\(205\) 130133. + 56602.6i 0.216273 + 0.0940701i
\(206\) −813787. −1.33611
\(207\) 261712.i 0.424520i
\(208\) 227318.i 0.364314i
\(209\) −91225.4 −0.144461
\(210\) −307103. + 706048.i −0.480547 + 1.10481i
\(211\) −446582. −0.690550 −0.345275 0.938502i \(-0.612214\pi\)
−0.345275 + 0.938502i \(0.612214\pi\)
\(212\) 1.14014e6i 1.74229i
\(213\) 564094.i 0.851927i
\(214\) 447907. 0.668580
\(215\) 491045. 1.12894e6i 0.724478 1.66562i
\(216\) 59603.9 0.0869242
\(217\) 118181.i 0.170371i
\(218\) 1.18813e6i 1.69325i
\(219\) −620552. −0.874314
\(220\) 257629. + 112058.i 0.358871 + 0.156094i
\(221\) −338090. −0.465642
\(222\) 997451.i 1.35834i
\(223\) 29867.7i 0.0402198i 0.999798 + 0.0201099i \(0.00640161\pi\)
−0.999798 + 0.0201099i \(0.993598\pi\)
\(224\) 1.42796e6 1.90150
\(225\) −172585. 185167.i −0.227272 0.243841i
\(226\) −1.17174e6 −1.52602
\(227\) 425464.i 0.548022i −0.961726 0.274011i \(-0.911649\pi\)
0.961726 0.274011i \(-0.0883505\pi\)
\(228\) 281827.i 0.359042i
\(229\) 1.31835e6 1.66127 0.830637 0.556814i \(-0.187977\pi\)
0.830637 + 0.556814i \(0.187977\pi\)
\(230\) −1.42031e6 617780.i −1.77037 0.770041i
\(231\) 194346. 0.239632
\(232\) 213098.i 0.259931i
\(233\) 320062.i 0.386228i −0.981176 0.193114i \(-0.938141\pi\)
0.981176 0.193114i \(-0.0618588\pi\)
\(234\) 251429. 0.300176
\(235\) −464570. + 1.06807e6i −0.548759 + 1.26163i
\(236\) 322296. 0.376683
\(237\) 155825.i 0.180204i
\(238\) 1.42936e6i 1.63568i
\(239\) −1.25534e6 −1.42156 −0.710781 0.703414i \(-0.751658\pi\)
−0.710781 + 0.703414i \(0.751658\pi\)
\(240\) −126020. + 289728.i −0.141225 + 0.324686i
\(241\) −1.07813e6 −1.19572 −0.597859 0.801601i \(-0.703982\pi\)
−0.597859 + 0.801601i \(0.703982\pi\)
\(242\) 125550.i 0.137809i
\(243\) 59049.0i 0.0641500i
\(244\) −1.59780e6 −1.71810
\(245\) 771081. + 335390.i 0.820700 + 0.356972i
\(246\) −195919. −0.206413
\(247\) 272907.i 0.284624i
\(248\) 54143.5i 0.0559007i
\(249\) 801161. 0.818882
\(250\) −1.41229e6 + 499526.i −1.42914 + 0.505485i
\(251\) −918775. −0.920502 −0.460251 0.887789i \(-0.652241\pi\)
−0.460251 + 0.887789i \(0.652241\pi\)
\(252\) 600401.i 0.595580i
\(253\) 390953.i 0.383993i
\(254\) −204852. −0.199231
\(255\) −430914. 187430.i −0.414992 0.180505i
\(256\) 180449. 0.172089
\(257\) 797355.i 0.753041i −0.926408 0.376521i \(-0.877120\pi\)
0.926408 0.376521i \(-0.122880\pi\)
\(258\) 1.69965e6i 1.58969i
\(259\) 2.30648e6 2.13649
\(260\) 335230. 770714.i 0.307546 0.707066i
\(261\) 211114. 0.191829
\(262\) 579664.i 0.521703i
\(263\) 980563.i 0.874150i −0.899425 0.437075i \(-0.856014\pi\)
0.899425 0.437075i \(-0.143986\pi\)
\(264\) −89038.0 −0.0786259
\(265\) −612067. + 1.40718e6i −0.535407 + 1.23093i
\(266\) 1.15378e6 0.999813
\(267\) 1.16664e6i 1.00152i
\(268\) 1.47536e6i 1.25476i
\(269\) 1.32137e6 1.11338 0.556691 0.830719i \(-0.312071\pi\)
0.556691 + 0.830719i \(0.312071\pi\)
\(270\) 320459. + 139387.i 0.267524 + 0.116362i
\(271\) −62864.5 −0.0519975 −0.0259987 0.999662i \(-0.508277\pi\)
−0.0259987 + 0.999662i \(0.508277\pi\)
\(272\) 586540.i 0.480702i
\(273\) 581398.i 0.472136i
\(274\) 1.76515e6 1.42039
\(275\) 257812. + 276607.i 0.205575 + 0.220563i
\(276\) 1.20779e6 0.954374
\(277\) 1.44313e6i 1.13007i −0.825066 0.565037i \(-0.808862\pi\)
0.825066 0.565037i \(-0.191138\pi\)
\(278\) 372984.i 0.289453i
\(279\) −53639.4 −0.0412547
\(280\) −747986. 325344.i −0.570162 0.247998i
\(281\) −143939. −0.108746 −0.0543731 0.998521i \(-0.517316\pi\)
−0.0543731 + 0.998521i \(0.517316\pi\)
\(282\) 1.60802e6i 1.20411i
\(283\) 9060.12i 0.00672462i −0.999994 0.00336231i \(-0.998930\pi\)
0.999994 0.00336231i \(-0.00107026\pi\)
\(284\) 2.60327e6 1.91524
\(285\) −151294. + 347834.i −0.110334 + 0.253665i
\(286\) −375591. −0.271519
\(287\) 453037.i 0.324660i
\(288\) 648120.i 0.460441i
\(289\) 547494. 0.385598
\(290\) 498340. 1.14571e6i 0.347961 0.799984i
\(291\) −1.23059e6 −0.851886
\(292\) 2.86382e6i 1.96557i
\(293\) 1.85674e6i 1.26352i −0.775165 0.631759i \(-0.782333\pi\)
0.775165 0.631759i \(-0.217667\pi\)
\(294\) −1.16088e6 −0.783286
\(295\) 397782. + 173019.i 0.266128 + 0.115755i
\(296\) −1.05670e6 −0.701006
\(297\) 88209.0i 0.0580259i
\(298\) 1.88102e6i 1.22703i
\(299\) 1.16956e6 0.756563
\(300\) 854536. 796471.i 0.548185 0.510936i
\(301\) 3.93024e6 2.50036
\(302\) 282366.i 0.178154i
\(303\) 462392.i 0.289337i
\(304\) 473456. 0.293830
\(305\) −1.97203e6 857753.i −1.21384 0.527974i
\(306\) 648753. 0.396074
\(307\) 504688.i 0.305617i 0.988256 + 0.152808i \(0.0488318\pi\)
−0.988256 + 0.152808i \(0.951168\pi\)
\(308\) 896896.i 0.538723i
\(309\) 854097. 0.508875
\(310\) −126618. + 291101.i −0.0748324 + 0.172044i
\(311\) −448511. −0.262950 −0.131475 0.991320i \(-0.541971\pi\)
−0.131475 + 0.991320i \(0.541971\pi\)
\(312\) 266363.i 0.154913i
\(313\) 825146.i 0.476069i 0.971257 + 0.238035i \(0.0765031\pi\)
−0.971257 + 0.238035i \(0.923497\pi\)
\(314\) −3.92138e6 −2.24448
\(315\) 322315. 741022.i 0.183022 0.420780i
\(316\) −719123. −0.405122
\(317\) 3.26266e6i 1.82358i −0.410659 0.911789i \(-0.634701\pi\)
0.410659 0.911789i \(-0.365299\pi\)
\(318\) 2.11855e6i 1.17482i
\(319\) −315367. −0.173516
\(320\) −2.48720e6 1.08183e6i −1.35780 0.590589i
\(321\) −470094. −0.254637
\(322\) 4.94460e6i 2.65761i
\(323\) 704172.i 0.375554i
\(324\) −272508. −0.144217
\(325\) 827490. 771262.i 0.434564 0.405036i
\(326\) −452961. −0.236057
\(327\) 1.24698e6i 0.644896i
\(328\) 207556.i 0.106525i
\(329\) −3.71834e6 −1.89391
\(330\) −478711. 208220.i −0.241985 0.105254i
\(331\) −3.48175e6 −1.74674 −0.873369 0.487059i \(-0.838070\pi\)
−0.873369 + 0.487059i \(0.838070\pi\)
\(332\) 3.69732e6i 1.84095i
\(333\) 1.04686e6i 0.517342i
\(334\) 2.80930e6 1.37794
\(335\) −792024. + 1.82091e6i −0.385590 + 0.886495i
\(336\) −1.00865e6 −0.487406
\(337\) 1.52759e6i 0.732710i 0.930475 + 0.366355i \(0.119394\pi\)
−0.930475 + 0.366355i \(0.880606\pi\)
\(338\) 2.06032e6i 0.980939i
\(339\) 1.22978e6 0.581203
\(340\) 864982. 1.98865e6i 0.405798 0.932954i
\(341\) 80128.0 0.0373163
\(342\) 523674.i 0.242101i
\(343\) 315017.i 0.144577i
\(344\) −1.80061e6 −0.820396
\(345\) 1.49067e6 + 648381.i 0.674268 + 0.293280i
\(346\) 2.11283e6 0.948798
\(347\) 4.01479e6i 1.78994i 0.446122 + 0.894972i \(0.352805\pi\)
−0.446122 + 0.894972i \(0.647195\pi\)
\(348\) 974279.i 0.431256i
\(349\) 511478. 0.224783 0.112391 0.993664i \(-0.464149\pi\)
0.112391 + 0.993664i \(0.464149\pi\)
\(350\) −3.26069e6 3.49841e6i −1.42279 1.52651i
\(351\) −263883. −0.114326
\(352\) 968179.i 0.416485i
\(353\) 722636.i 0.308662i −0.988019 0.154331i \(-0.950678\pi\)
0.988019 0.154331i \(-0.0493221\pi\)
\(354\) −598872. −0.253995
\(355\) 3.21298e6 + 1.39752e6i 1.35312 + 0.588555i
\(356\) 5.38400e6 2.25154
\(357\) 1.50016e6i 0.622970i
\(358\) 2.59264e6i 1.06914i
\(359\) −393345. −0.161078 −0.0805392 0.996751i \(-0.525664\pi\)
−0.0805392 + 0.996751i \(0.525664\pi\)
\(360\) −147666. + 339494.i −0.0600517 + 0.138062i
\(361\) −1.90769e6 −0.770442
\(362\) 3.99069e6i 1.60058i
\(363\) 131769.i 0.0524864i
\(364\) 2.68312e6 1.06142
\(365\) 1.53739e6 3.53455e6i 0.604021 1.38868i
\(366\) 2.96894e6 1.15851
\(367\) 2.87578e6i 1.11453i 0.830336 + 0.557264i \(0.188149\pi\)
−0.830336 + 0.557264i \(0.811851\pi\)
\(368\) 2.02903e6i 0.781032i
\(369\) 205623. 0.0786152
\(370\) −5.68131e6 2.47114e6i −2.15747 0.938413i
\(371\) −4.89888e6 −1.84783
\(372\) 247543.i 0.0927458i
\(373\) 3.86030e6i 1.43665i 0.695710 + 0.718323i \(0.255090\pi\)
−0.695710 + 0.718323i \(0.744910\pi\)
\(374\) −969125. −0.358262
\(375\) 1.48225e6 524270.i 0.544306 0.192520i
\(376\) 1.70353e6 0.621412
\(377\) 943443.i 0.341871i
\(378\) 1.11563e6i 0.401597i
\(379\) 1.63355e6 0.584162 0.292081 0.956394i \(-0.405652\pi\)
0.292081 + 0.956394i \(0.405652\pi\)
\(380\) −1.60524e6 698215.i −0.570270 0.248045i
\(381\) 214999. 0.0758795
\(382\) 2.52268e6i 0.884512i
\(383\) 3.86858e6i 1.34758i 0.738923 + 0.673790i \(0.235335\pi\)
−0.738923 + 0.673790i \(0.764665\pi\)
\(384\) 1.44013e6 0.498394
\(385\) −481483. + 1.10696e6i −0.165550 + 0.380609i
\(386\) −2.40560e6 −0.821779
\(387\) 1.78385e6i 0.605452i
\(388\) 5.67912e6i 1.91515i
\(389\) 10040.7 0.00336428 0.00168214 0.999999i \(-0.499465\pi\)
0.00168214 + 0.999999i \(0.499465\pi\)
\(390\) −622905. + 1.43210e6i −0.207377 + 0.476772i
\(391\) 3.01778e6 0.998264
\(392\) 1.22984e6i 0.404234i
\(393\) 608378.i 0.198697i
\(394\) 2.07199e6 0.672431
\(395\) −887550. 386049.i −0.286220 0.124494i
\(396\) 407080. 0.130449
\(397\) 3.77944e6i 1.20352i 0.798679 + 0.601758i \(0.205533\pi\)
−0.798679 + 0.601758i \(0.794467\pi\)
\(398\) 5.33176e6i 1.68719i
\(399\) −1.21093e6 −0.380791
\(400\) −1.33803e6 1.43558e6i −0.418135 0.448619i
\(401\) −5.77840e6 −1.79451 −0.897256 0.441510i \(-0.854443\pi\)
−0.897256 + 0.441510i \(0.854443\pi\)
\(402\) 2.74143e6i 0.846082i
\(403\) 239708.i 0.0735226i
\(404\) −2.13392e6 −0.650465
\(405\) −336333. 146291.i −0.101890 0.0443181i
\(406\) 3.98863e6 1.20090
\(407\) 1.56383e6i 0.467954i
\(408\) 687287.i 0.204403i
\(409\) −4.93158e6 −1.45773 −0.728866 0.684656i \(-0.759952\pi\)
−0.728866 + 0.684656i \(0.759952\pi\)
\(410\) 485380. 1.11592e6i 0.142601 0.327848i
\(411\) −1.85259e6 −0.540972
\(412\) 3.94162e6i 1.14401i
\(413\) 1.38482e6i 0.399501i
\(414\) −2.24424e6 −0.643530
\(415\) −1.98484e6 + 4.56327e6i −0.565726 + 1.30064i
\(416\) 2.89637e6 0.820580
\(417\) 391460.i 0.110242i
\(418\) 782278.i 0.218988i
\(419\) 4.38879e6 1.22126 0.610632 0.791914i \(-0.290915\pi\)
0.610632 + 0.791914i \(0.290915\pi\)
\(420\) 3.41978e6 + 1.48747e6i 0.945965 + 0.411457i
\(421\) −6.32905e6 −1.74034 −0.870169 0.492754i \(-0.835990\pi\)
−0.870169 + 0.492754i \(0.835990\pi\)
\(422\) 3.82954e6i 1.04681i
\(423\) 1.68767e6i 0.458602i
\(424\) 2.24438e6 0.606293
\(425\) 2.13514e6 1.99006e6i 0.573396 0.534433i
\(426\) −4.83723e6 −1.29144
\(427\) 6.86531e6i 1.82218i
\(428\) 2.16946e6i 0.572456i
\(429\) 394196. 0.103412
\(430\) −9.68094e6 4.21082e6i −2.52491 1.09824i
\(431\) −4.39779e6 −1.14036 −0.570179 0.821520i \(-0.693126\pi\)
−0.570179 + 0.821520i \(0.693126\pi\)
\(432\) 457801.i 0.118023i
\(433\) 1.57360e6i 0.403344i −0.979453 0.201672i \(-0.935362\pi\)
0.979453 0.201672i \(-0.0646375\pi\)
\(434\) −1.01343e6 −0.258266
\(435\) −523025. + 1.20247e6i −0.132526 + 0.304684i
\(436\) 5.75475e6 1.44981
\(437\) 2.43595e6i 0.610190i
\(438\) 5.32137e6i 1.32537i
\(439\) 7.89299e6 1.95470 0.977351 0.211626i \(-0.0678759\pi\)
0.977351 + 0.211626i \(0.0678759\pi\)
\(440\) 220588. 507145.i 0.0543188 0.124882i
\(441\) 1.21839e6 0.298325
\(442\) 2.89920e6i 0.705867i
\(443\) 557226.i 0.134903i −0.997723 0.0674516i \(-0.978513\pi\)
0.997723 0.0674516i \(-0.0214868\pi\)
\(444\) 4.83121e6 1.16305
\(445\) 6.64499e6 + 2.89031e6i 1.59072 + 0.691901i
\(446\) 256123. 0.0609693
\(447\) 1.97420e6i 0.467328i
\(448\) 8.65881e6i 2.03828i
\(449\) −2.27558e6 −0.532691 −0.266346 0.963878i \(-0.585816\pi\)
−0.266346 + 0.963878i \(0.585816\pi\)
\(450\) −1.58785e6 + 1.47995e6i −0.369639 + 0.344522i
\(451\) −307166. −0.0711101
\(452\) 5.67537e6i 1.30662i
\(453\) 296352.i 0.0678521i
\(454\) −3.64845e6 −0.830748
\(455\) 3.31154e6 + 1.44039e6i 0.749897 + 0.326176i
\(456\) 554779. 0.124942
\(457\) 7.50427e6i 1.68081i −0.541961 0.840404i \(-0.682318\pi\)
0.541961 0.840404i \(-0.317682\pi\)
\(458\) 1.13051e7i 2.51833i
\(459\) −680889. −0.150850
\(460\) −2.99225e6 + 6.87936e6i −0.659330 + 1.51584i
\(461\) 436978. 0.0957652 0.0478826 0.998853i \(-0.484753\pi\)
0.0478826 + 0.998853i \(0.484753\pi\)
\(462\) 1.66656e6i 0.363258i
\(463\) 3.11651e6i 0.675642i −0.941210 0.337821i \(-0.890310\pi\)
0.941210 0.337821i \(-0.109690\pi\)
\(464\) 1.63674e6 0.352928
\(465\) 132889. 305521.i 0.0285009 0.0655252i
\(466\) −2.74460e6 −0.585484
\(467\) 1.89749e6i 0.402613i 0.979528 + 0.201307i \(0.0645187\pi\)
−0.979528 + 0.201307i \(0.935481\pi\)
\(468\) 1.21781e6i 0.257019i
\(469\) −6.33922e6 −1.33077
\(470\) 9.15898e6 + 3.98379e6i 1.91251 + 0.831864i
\(471\) 4.11562e6 0.854837
\(472\) 634444.i 0.131081i
\(473\) 2.66476e6i 0.547652i
\(474\) 1.33623e6 0.273172
\(475\) −1.60638e6 1.72349e6i −0.326673 0.350489i
\(476\) 6.92317e6 1.40051
\(477\) 2.22349e6i 0.447444i
\(478\) 1.07648e7i 2.15495i
\(479\) 6.10287e6 1.21533 0.607666 0.794193i \(-0.292106\pi\)
0.607666 + 0.794193i \(0.292106\pi\)
\(480\) 3.69158e6 + 1.60569e6i 0.731322 + 0.318096i
\(481\) 4.67830e6 0.921987
\(482\) 9.24522e6i 1.81259i
\(483\) 5.18953e6i 1.01219i
\(484\) −608108. −0.117996
\(485\) 3.04874e6 7.00924e6i 0.588527 1.35306i
\(486\) 506359. 0.0972451
\(487\) 7.30170e6i 1.39509i 0.716542 + 0.697544i \(0.245724\pi\)
−0.716542 + 0.697544i \(0.754276\pi\)
\(488\) 3.14529e6i 0.597876i
\(489\) 475398. 0.0899053
\(490\) 2.87604e6 6.61220e6i 0.541134 1.24410i
\(491\) 4.40884e6 0.825317 0.412658 0.910886i \(-0.364600\pi\)
0.412658 + 0.910886i \(0.364600\pi\)
\(492\) 948942.i 0.176737i
\(493\) 2.43433e6i 0.451089i
\(494\) 2.34024e6 0.431462
\(495\) 502423. + 218534.i 0.0921630 + 0.0400873i
\(496\) −415861. −0.0759004
\(497\) 1.11855e7i 2.03125i
\(498\) 6.87014e6i 1.24134i
\(499\) −3.45620e6 −0.621367 −0.310683 0.950513i \(-0.600558\pi\)
−0.310683 + 0.950513i \(0.600558\pi\)
\(500\) 2.41948e6 + 6.84051e6i 0.432810 + 1.22367i
\(501\) −2.94845e6 −0.524808
\(502\) 7.87871e6i 1.39539i
\(503\) 5.07651e6i 0.894634i 0.894375 + 0.447317i \(0.147620\pi\)
−0.894375 + 0.447317i \(0.852380\pi\)
\(504\) −1.18190e6 −0.207254
\(505\) −2.63370e6 1.14556e6i −0.459556 0.199889i
\(506\) 3.35251e6 0.582095
\(507\) 2.16237e6i 0.373603i
\(508\) 992212.i 0.170587i
\(509\) −7.63894e6 −1.30689 −0.653445 0.756974i \(-0.726677\pi\)
−0.653445 + 0.756974i \(0.726677\pi\)
\(510\) −1.60726e6 + 3.69518e6i −0.273628 + 0.629087i
\(511\) 1.23050e7 2.08463
\(512\) 6.66784e6i 1.12411i
\(513\) 549614.i 0.0922071i
\(514\) −6.83750e6 −1.14154
\(515\) −2.11599e6 + 4.86479e6i −0.351557 + 0.808251i
\(516\) 8.23237e6 1.36113
\(517\) 2.52109e6i 0.414821i
\(518\) 1.97786e7i 3.23871i
\(519\) −2.21748e6 −0.361362
\(520\) −1.51716e6 659904.i −0.246050 0.107022i
\(521\) −9.46786e6 −1.52812 −0.764060 0.645145i \(-0.776797\pi\)
−0.764060 + 0.645145i \(0.776797\pi\)
\(522\) 1.81035e6i 0.290794i
\(523\) 1.12533e6i 0.179898i −0.995946 0.0899490i \(-0.971330\pi\)
0.995946 0.0899490i \(-0.0286704\pi\)
\(524\) −2.80764e6 −0.446696
\(525\) 3.42221e6 + 3.67170e6i 0.541887 + 0.581392i
\(526\) −8.40855e6 −1.32512
\(527\) 618511.i 0.0970110i
\(528\) 683876.i 0.106756i
\(529\) −4.00311e6 −0.621953
\(530\) 1.20669e7 + 5.24861e6i 1.86597 + 0.811624i
\(531\) 628537. 0.0967374
\(532\) 5.58839e6i 0.856067i
\(533\) 918907.i 0.140105i
\(534\) −1.00042e7 −1.51820
\(535\) 1.16464e6 2.67757e6i 0.175916 0.404442i
\(536\) 2.90427e6 0.436641
\(537\) 2.72107e6i 0.407196i
\(538\) 1.13311e7i 1.68778i
\(539\) −1.82006e6 −0.269845
\(540\) 675128. 1.55216e6i 0.0996327 0.229062i
\(541\) 1.05433e7 1.54876 0.774379 0.632722i \(-0.218062\pi\)
0.774379 + 0.632722i \(0.218062\pi\)
\(542\) 539078.i 0.0788230i
\(543\) 4.18837e6i 0.609600i
\(544\) 7.47341e6 1.08273
\(545\) 7.10258e6 + 3.08934e6i 1.02429 + 0.445527i
\(546\) −4.98562e6 −0.715711
\(547\) 9.65329e6i 1.37945i −0.724070 0.689727i \(-0.757731\pi\)
0.724070 0.689727i \(-0.242269\pi\)
\(548\) 8.54962e6i 1.21617i
\(549\) −3.11601e6 −0.441232
\(550\) 2.37197e6 2.21080e6i 0.334351 0.311632i
\(551\) 1.96499e6 0.275729
\(552\) 2.37754e6i 0.332109i
\(553\) 3.08987e6i 0.429662i
\(554\) −1.23752e7 −1.71308
\(555\) 5.96273e6 + 2.59355e6i 0.821699 + 0.357406i
\(556\) 1.80657e6 0.247838
\(557\) 4.21289e6i 0.575363i −0.957726 0.287682i \(-0.907115\pi\)
0.957726 0.287682i \(-0.0928845\pi\)
\(558\) 459970.i 0.0625381i
\(559\) 7.97180e6 1.07901
\(560\) 2.49888e6 5.74507e6i 0.336725 0.774150i
\(561\) 1.01713e6 0.136449
\(562\) 1.23431e6i 0.164848i
\(563\) 9.59902e6i 1.27631i 0.769908 + 0.638155i \(0.220302\pi\)
−0.769908 + 0.638155i \(0.779698\pi\)
\(564\) −7.78851e6 −1.03100
\(565\) −3.04673e6 + 7.00461e6i −0.401525 + 0.923129i
\(566\) −77692.6 −0.0101939
\(567\) 1.17089e6i 0.152953i
\(568\) 5.12455e6i 0.666477i
\(569\) −4.20682e6 −0.544720 −0.272360 0.962195i \(-0.587804\pi\)
−0.272360 + 0.962195i \(0.587804\pi\)
\(570\) 2.98276e6 + 1.29738e6i 0.384530 + 0.167255i
\(571\) −1.22447e7 −1.57165 −0.785826 0.618447i \(-0.787762\pi\)
−0.785826 + 0.618447i \(0.787762\pi\)
\(572\) 1.81920e6i 0.232482i
\(573\) 2.64764e6i 0.336878i
\(574\) 3.88490e6 0.492153
\(575\) −7.38613e6 + 6.88424e6i −0.931638 + 0.868334i
\(576\) −3.93004e6 −0.493561
\(577\) 5.32012e6i 0.665245i −0.943060 0.332623i \(-0.892066\pi\)
0.943060 0.332623i \(-0.107934\pi\)
\(578\) 4.69489e6i 0.584529i
\(579\) 2.52476e6 0.312985
\(580\) −5.54933e6 2.41374e6i −0.684968 0.297934i
\(581\) −1.58863e7 −1.95247
\(582\) 1.05526e7i 1.29137i
\(583\) 3.32151e6i 0.404728i
\(584\) −5.63745e6 −0.683992
\(585\) 653760. 1.50303e6i 0.0789821 0.181585i
\(586\) −1.59220e7 −1.91537
\(587\) 5.70534e6i 0.683418i 0.939806 + 0.341709i \(0.111006\pi\)
−0.939806 + 0.341709i \(0.888994\pi\)
\(588\) 5.62280e6i 0.670671i
\(589\) −499263. −0.0592981
\(590\) 1.48368e6 3.41107e6i 0.175473 0.403423i
\(591\) −2.17463e6 −0.256104
\(592\) 8.11620e6i 0.951806i
\(593\) 2.15575e6i 0.251746i 0.992046 + 0.125873i \(0.0401731\pi\)
−0.992046 + 0.125873i \(0.959827\pi\)
\(594\) −756413. −0.0879615
\(595\) 8.54466e6 + 3.71659e6i 0.989469 + 0.430380i
\(596\) 9.11083e6 1.05061
\(597\) 5.59587e6i 0.642587i
\(598\) 1.00293e7i 1.14687i
\(599\) −5.13968e6 −0.585287 −0.292643 0.956222i \(-0.594535\pi\)
−0.292643 + 0.956222i \(0.594535\pi\)
\(600\) −1.56786e6 1.68216e6i −0.177799 0.190761i
\(601\) −7.48666e6 −0.845478 −0.422739 0.906252i \(-0.638931\pi\)
−0.422739 + 0.906252i \(0.638931\pi\)
\(602\) 3.37027e7i 3.79030i
\(603\) 2.87723e6i 0.322241i
\(604\) 1.36765e6 0.152540
\(605\) −750533. 326452.i −0.0833646 0.0362603i
\(606\) 3.96512e6 0.438606
\(607\) 8.62794e6i 0.950464i 0.879861 + 0.475232i \(0.157636\pi\)
−0.879861 + 0.475232i \(0.842364\pi\)
\(608\) 6.03254e6i 0.661822i
\(609\) −4.18620e6 −0.457380
\(610\) −7.35543e6 + 1.69106e7i −0.800356 + 1.84007i
\(611\) −7.54200e6 −0.817304
\(612\) 3.14227e6i 0.339129i
\(613\) 1.44646e7i 1.55473i −0.629047 0.777367i \(-0.716555\pi\)
0.629047 0.777367i \(-0.283445\pi\)
\(614\) 4.32782e6 0.463285
\(615\) −509423. + 1.17119e6i −0.0543114 + 0.124865i
\(616\) 1.76555e6 0.187468
\(617\) 5.82746e6i 0.616264i −0.951344 0.308132i \(-0.900296\pi\)
0.951344 0.308132i \(-0.0997038\pi\)
\(618\) 7.32408e6i 0.771404i
\(619\) 2.32647e6 0.244045 0.122023 0.992527i \(-0.461062\pi\)
0.122023 + 0.992527i \(0.461062\pi\)
\(620\) 1.40996e6 + 613279.i 0.147309 + 0.0640735i
\(621\) 2.35541e6 0.245097
\(622\) 3.84609e6i 0.398605i
\(623\) 2.31335e7i 2.38793i
\(624\) −2.04586e6 −0.210337
\(625\) −686064. + 9.74150e6i −0.0702529 + 0.997529i
\(626\) 7.07582e6 0.721674
\(627\) 821028.i 0.0834044i
\(628\) 1.89934e7i 1.92178i
\(629\) 1.20712e7 1.21654
\(630\) −6.35443e6 2.76393e6i −0.637860 0.277444i
\(631\) −398154. −0.0398087 −0.0199043 0.999802i \(-0.506336\pi\)
−0.0199043 + 0.999802i \(0.506336\pi\)
\(632\) 1.41560e6i 0.140977i
\(633\) 4.01924e6i 0.398689i
\(634\) −2.79781e7 −2.76436
\(635\) −532652. + 1.22460e6i −0.0524215 + 0.120520i
\(636\) −1.02613e7 −1.00591
\(637\) 5.44484e6i 0.531663i
\(638\) 2.70435e6i 0.263033i
\(639\) 5.07684e6 0.491860
\(640\) −3.56786e6 + 8.20272e6i −0.344316 + 0.791604i
\(641\) 1.81586e7 1.74557 0.872784 0.488107i \(-0.162312\pi\)
0.872784 + 0.488107i \(0.162312\pi\)
\(642\) 4.03116e6i 0.386005i
\(643\) 4.48264e6i 0.427569i −0.976881 0.213784i \(-0.931421\pi\)
0.976881 0.213784i \(-0.0685790\pi\)
\(644\) −2.39494e7 −2.27552
\(645\) 1.01605e7 + 4.41940e6i 0.961645 + 0.418277i
\(646\) 6.03844e6 0.569303
\(647\) 1.75122e7i 1.64467i −0.569003 0.822336i \(-0.692671\pi\)
0.569003 0.822336i \(-0.307329\pi\)
\(648\) 536435.i 0.0501857i
\(649\) −938925. −0.0875023
\(650\) −6.61375e6 7.09591e6i −0.613994 0.658757i
\(651\) 1.06362e6 0.0983639
\(652\) 2.19394e6i 0.202118i
\(653\) 1.89639e7i 1.74039i −0.492711 0.870193i \(-0.663994\pi\)
0.492711 0.870193i \(-0.336006\pi\)
\(654\) −1.06931e7 −0.977599
\(655\) −3.46521e6 1.50723e6i −0.315593 0.137270i
\(656\) 1.59418e6 0.144636
\(657\) 5.58496e6i 0.504786i
\(658\) 3.18856e7i 2.87098i
\(659\) −23732.7 −0.00212879 −0.00106440 0.999999i \(-0.500339\pi\)
−0.00106440 + 0.999999i \(0.500339\pi\)
\(660\) −1.00852e6 + 2.31866e6i −0.0901212 + 0.207194i
\(661\) 1.09938e7 0.978686 0.489343 0.872091i \(-0.337237\pi\)
0.489343 + 0.872091i \(0.337237\pi\)
\(662\) 2.98568e7i 2.64788i
\(663\) 3.04281e6i 0.268839i
\(664\) 7.27821e6 0.640626
\(665\) 3.00003e6 6.89725e6i 0.263070 0.604814i
\(666\) −8.97706e6 −0.784239
\(667\) 8.42112e6i 0.732918i
\(668\) 1.36070e7i 1.17983i
\(669\) −268810. −0.0232209
\(670\) 1.56147e7 + 6.79179e6i 1.34384 + 0.584517i
\(671\) 4.65477e6 0.399110
\(672\) 1.28517e7i 1.09783i
\(673\) 1.19040e6i 0.101310i 0.998716 + 0.0506552i \(0.0161310\pi\)
−0.998716 + 0.0506552i \(0.983869\pi\)
\(674\) 1.30994e7 1.11072
\(675\) 1.66650e6 1.55326e6i 0.140782 0.131216i
\(676\) −9.97925e6 −0.839907
\(677\) 2.03890e7i 1.70972i 0.518859 + 0.854860i \(0.326357\pi\)
−0.518859 + 0.854860i \(0.673643\pi\)
\(678\) 1.05456e7i 0.881046i
\(679\) 2.44016e7 2.03116
\(680\) −3.91467e6 1.70273e6i −0.324656 0.141212i
\(681\) 3.82918e6 0.316401
\(682\) 687116.i 0.0565678i
\(683\) 2.37020e7i 1.94416i −0.234640 0.972082i \(-0.575391\pi\)
0.234640 0.972082i \(-0.424609\pi\)
\(684\) −2.53644e6 −0.207293
\(685\) 4.58972e6 1.05520e7i 0.373731 0.859231i
\(686\) −2.70134e6 −0.219164
\(687\) 1.18651e7i 0.959137i
\(688\) 1.38300e7i 1.11391i
\(689\) −9.93651e6 −0.797418
\(690\) 5.56002e6 1.27828e7i 0.444583 1.02212i
\(691\) −1.32012e7 −1.05176 −0.525881 0.850558i \(-0.676264\pi\)
−0.525881 + 0.850558i \(0.676264\pi\)
\(692\) 1.02336e7i 0.812387i
\(693\) 1.74911e6i 0.138352i
\(694\) 3.44278e7 2.71338
\(695\) 2.22969e6 + 969826.i 0.175098 + 0.0761608i
\(696\) 1.91788e6 0.150071
\(697\) 2.37102e6i 0.184865i
\(698\) 4.38604e6i 0.340749i
\(699\) 2.88056e6 0.222989
\(700\) −1.69447e7 + 1.57933e7i −1.30704 + 1.21823i
\(701\) 9.76550e6 0.750584 0.375292 0.926907i \(-0.377542\pi\)
0.375292 + 0.926907i \(0.377542\pi\)
\(702\) 2.26286e6i 0.173306i
\(703\) 9.74392e6i 0.743610i
\(704\) 5.87080e6 0.446442
\(705\) −9.61267e6 4.18113e6i −0.728402 0.316826i
\(706\) −6.19677e6 −0.467900
\(707\) 9.16884e6i 0.689868i
\(708\) 2.90067e6i 0.217478i
\(709\) 6.77780e6 0.506376 0.253188 0.967417i \(-0.418521\pi\)
0.253188 + 0.967417i \(0.418521\pi\)
\(710\) 1.19840e7 2.75520e7i 0.892190 2.05120i
\(711\) −1.40242e6 −0.104041
\(712\) 1.05985e7i 0.783506i
\(713\) 2.13963e6i 0.157621i
\(714\) −1.28642e7 −0.944361
\(715\) −976604. + 2.24527e6i −0.0714420 + 0.164249i
\(716\) 1.25576e7 0.915429
\(717\) 1.12980e7i 0.820739i
\(718\) 3.37302e6i 0.244179i
\(719\) 9.77686e6 0.705305 0.352653 0.935754i \(-0.385280\pi\)
0.352653 + 0.935754i \(0.385280\pi\)
\(720\) −2.60756e6 1.13418e6i −0.187457 0.0815365i
\(721\) −1.69360e7 −1.21331
\(722\) 1.63589e7i 1.16791i
\(723\) 9.70317e6i 0.690348i
\(724\) 1.93291e7 1.37046
\(725\) −5.55327e6 5.95812e6i −0.392377 0.420983i
\(726\) 1.12995e6 0.0795642
\(727\) 1.13969e7i 0.799745i 0.916571 + 0.399873i \(0.130946\pi\)
−0.916571 + 0.399873i \(0.869054\pi\)
\(728\) 5.28176e6i 0.369360i
\(729\) −531441. −0.0370370
\(730\) −3.03096e7 1.31835e7i −2.10510 0.915636i
\(731\) 2.05694e7 1.42373
\(732\) 1.43802e7i 0.991946i
\(733\) 6.58492e6i 0.452679i −0.974048 0.226340i \(-0.927324\pi\)
0.974048 0.226340i \(-0.0726759\pi\)
\(734\) 2.46605e7 1.68951
\(735\) −3.01851e6 + 6.93973e6i −0.206098 + 0.473832i
\(736\) −2.58529e7 −1.75920
\(737\) 4.29808e6i 0.291478i
\(738\) 1.76327e6i 0.119173i
\(739\) 1.51924e7 1.02333 0.511664 0.859186i \(-0.329029\pi\)
0.511664 + 0.859186i \(0.329029\pi\)
\(740\) −1.19691e7 + 2.75177e7i −0.803494 + 1.84728i
\(741\) −2.45616e6 −0.164328
\(742\) 4.20090e7i 2.80112i
\(743\) 6.92543e6i 0.460230i −0.973163 0.230115i \(-0.926090\pi\)
0.973163 0.230115i \(-0.0739102\pi\)
\(744\) −487292. −0.0322743
\(745\) 1.12447e7 + 4.89100e6i 0.742261 + 0.322854i
\(746\) 3.31030e7 2.17781
\(747\) 7.21045e6i 0.472782i
\(748\) 4.69401e6i 0.306754i
\(749\) 9.32156e6 0.607133
\(750\) −4.49573e6 1.27106e7i −0.291842 0.825114i
\(751\) −1.53073e7 −0.990370 −0.495185 0.868788i \(-0.664900\pi\)
−0.495185 + 0.868788i \(0.664900\pi\)
\(752\) 1.30843e7i 0.843737i
\(753\) 8.26898e6i 0.531452i
\(754\) 8.09024e6 0.518242
\(755\) 1.68797e6 + 734201.i 0.107770 + 0.0468757i
\(756\) 5.40361e6 0.343858
\(757\) 9.00842e6i 0.571359i −0.958325 0.285679i \(-0.907781\pi\)
0.958325 0.285679i \(-0.0922193\pi\)
\(758\) 1.40080e7i 0.885531i
\(759\) −3.51857e6 −0.221698
\(760\) −1.37444e6 + 3.15993e6i −0.0863162 + 0.198446i
\(761\) 1.62103e7 1.01468 0.507339 0.861746i \(-0.330629\pi\)
0.507339 + 0.861746i \(0.330629\pi\)
\(762\) 1.84367e6i 0.115026i
\(763\) 2.47265e7i 1.53763i
\(764\) −1.22187e7 −0.757343
\(765\) 1.68687e6 3.87822e6i 0.104215 0.239596i
\(766\) 3.31740e7 2.04280
\(767\) 2.80886e6i 0.172402i
\(768\) 1.62404e6i 0.0993558i
\(769\) −1.67909e7 −1.02390 −0.511950 0.859015i \(-0.671077\pi\)
−0.511950 + 0.859015i \(0.671077\pi\)
\(770\) 9.49243e6 + 4.12883e6i 0.576966 + 0.250957i
\(771\) 7.17619e6 0.434768
\(772\) 1.16516e7i 0.703629i
\(773\) 1.62605e7i 0.978780i 0.872065 + 0.489390i \(0.162781\pi\)
−0.872065 + 0.489390i \(0.837219\pi\)
\(774\) −1.52969e7 −0.917806
\(775\) 1.41097e6 + 1.51383e6i 0.0843844 + 0.0905364i
\(776\) −1.11794e7 −0.666445
\(777\) 2.07583e7i 1.23350i
\(778\) 86101.7i 0.00509991i
\(779\) 1.91389e6 0.112999
\(780\) 6.93643e6 +