Properties

Label 177.6.d.b.176.1
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 176.1
Character \(\chi\) \(=\) 177.176
Dual form 177.6.d.b.176.2

$q$-expansion

\(f(q)\) \(=\) \(q-10.9379 q^{2} +(4.58836 + 14.8979i) q^{3} +87.6366 q^{4} -82.7497i q^{5} +(-50.1868 - 162.951i) q^{6} +211.698 q^{7} -608.545 q^{8} +(-200.894 + 136.714i) q^{9} +O(q^{10})\) \(q-10.9379 q^{2} +(4.58836 + 14.8979i) q^{3} +87.6366 q^{4} -82.7497i q^{5} +(-50.1868 - 162.951i) q^{6} +211.698 q^{7} -608.545 q^{8} +(-200.894 + 136.714i) q^{9} +905.104i q^{10} +575.171 q^{11} +(402.108 + 1305.60i) q^{12} +586.318i q^{13} -2315.52 q^{14} +(1232.80 - 379.685i) q^{15} +3851.81 q^{16} +230.745i q^{17} +(2197.35 - 1495.35i) q^{18} +39.4470 q^{19} -7251.91i q^{20} +(971.346 + 3153.85i) q^{21} -6291.14 q^{22} +1717.40 q^{23} +(-2792.22 - 9066.04i) q^{24} -3722.52 q^{25} -6413.06i q^{26} +(-2958.52 - 2365.60i) q^{27} +18552.5 q^{28} +7866.89i q^{29} +(-13484.1 + 4152.94i) q^{30} -1806.70i q^{31} -22657.1 q^{32} +(2639.09 + 8568.84i) q^{33} -2523.86i q^{34} -17517.9i q^{35} +(-17605.7 + 11981.1i) q^{36} -13241.2i q^{37} -431.465 q^{38} +(-8734.90 + 2690.24i) q^{39} +50357.0i q^{40} +282.328i q^{41} +(-10624.4 - 34496.4i) q^{42} -7615.16i q^{43} +50406.1 q^{44} +(11313.0 + 16623.9i) q^{45} -18784.7 q^{46} +12556.7 q^{47} +(17673.5 + 57383.8i) q^{48} +28009.0 q^{49} +40716.3 q^{50} +(-3437.62 + 1058.74i) q^{51} +51382.9i q^{52} -9284.33i q^{53} +(32359.8 + 25874.6i) q^{54} -47595.3i q^{55} -128828. q^{56} +(180.997 + 587.676i) q^{57} -86046.9i q^{58} +(5254.69 + 26216.6i) q^{59} +(108038. - 33274.3i) q^{60} +17311.7i q^{61} +19761.4i q^{62} +(-42528.8 + 28942.0i) q^{63} +124562. q^{64} +48517.6 q^{65} +(-28866.0 - 93724.7i) q^{66} +9818.20i q^{67} +20221.7i q^{68} +(7880.06 + 25585.7i) q^{69} +191609. i q^{70} -12464.1i q^{71} +(122253. - 83196.4i) q^{72} +59580.4i q^{73} +144830. i q^{74} +(-17080.2 - 55457.6i) q^{75} +3457.00 q^{76} +121763. q^{77} +(95541.0 - 29425.4i) q^{78} +4419.42 q^{79} -318736. i q^{80} +(21667.8 - 54929.9i) q^{81} -3088.07i q^{82} +39420.5 q^{83} +(85125.5 + 276393. i) q^{84} +19094.1 q^{85} +83293.5i q^{86} +(-117200. + 36096.1i) q^{87} -350018. q^{88} -57202.6 q^{89} +(-123740. - 181830. i) q^{90} +124122. i q^{91} +150508. q^{92} +(26916.0 - 8289.78i) q^{93} -137344. q^{94} -3264.22i q^{95} +(-103959. - 337542. i) q^{96} +40889.7i q^{97} -306359. q^{98} +(-115548. + 78633.8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.9379 −1.93356 −0.966779 0.255615i \(-0.917722\pi\)
−0.966779 + 0.255615i \(0.917722\pi\)
\(3\) 4.58836 + 14.8979i 0.294343 + 0.955700i
\(4\) 87.6366 2.73864
\(5\) 82.7497i 1.48027i −0.672457 0.740136i \(-0.734761\pi\)
0.672457 0.740136i \(-0.265239\pi\)
\(6\) −50.1868 162.951i −0.569130 1.84790i
\(7\) 211.698 1.63295 0.816473 0.577384i \(-0.195926\pi\)
0.816473 + 0.577384i \(0.195926\pi\)
\(8\) −608.545 −3.36177
\(9\) −200.894 + 136.714i −0.826724 + 0.562607i
\(10\) 905.104i 2.86219i
\(11\) 575.171 1.43323 0.716614 0.697470i \(-0.245691\pi\)
0.716614 + 0.697470i \(0.245691\pi\)
\(12\) 402.108 + 1305.60i 0.806102 + 2.61732i
\(13\) 586.318i 0.962221i 0.876660 + 0.481111i \(0.159766\pi\)
−0.876660 + 0.481111i \(0.840234\pi\)
\(14\) −2315.52 −3.15739
\(15\) 1232.80 379.685i 1.41470 0.435708i
\(16\) 3851.81 3.76153
\(17\) 230.745i 0.193647i 0.995302 + 0.0968235i \(0.0308682\pi\)
−0.995302 + 0.0968235i \(0.969132\pi\)
\(18\) 2197.35 1495.35i 1.59852 1.08783i
\(19\) 39.4470 0.0250686 0.0125343 0.999921i \(-0.496010\pi\)
0.0125343 + 0.999921i \(0.496010\pi\)
\(20\) 7251.91i 4.05394i
\(21\) 971.346 + 3153.85i 0.480646 + 1.56061i
\(22\) −6291.14 −2.77123
\(23\) 1717.40 0.676944 0.338472 0.940976i \(-0.390090\pi\)
0.338472 + 0.940976i \(0.390090\pi\)
\(24\) −2792.22 9066.04i −0.989514 3.21284i
\(25\) −3722.52 −1.19120
\(26\) 6413.06i 1.86051i
\(27\) −2958.52 2365.60i −0.781024 0.624500i
\(28\) 18552.5 4.47206
\(29\) 7866.89i 1.73703i 0.495661 + 0.868516i \(0.334926\pi\)
−0.495661 + 0.868516i \(0.665074\pi\)
\(30\) −13484.1 + 4152.94i −2.73540 + 0.842466i
\(31\) 1806.70i 0.337662i −0.985645 0.168831i \(-0.946001\pi\)
0.985645 0.168831i \(-0.0539992\pi\)
\(32\) −22657.1 −3.91137
\(33\) 2639.09 + 8568.84i 0.421861 + 1.36974i
\(34\) 2523.86i 0.374428i
\(35\) 17517.9i 2.41720i
\(36\) −17605.7 + 11981.1i −2.26410 + 1.54078i
\(37\) 13241.2i 1.59010i −0.606546 0.795048i \(-0.707446\pi\)
0.606546 0.795048i \(-0.292554\pi\)
\(38\) −431.465 −0.0484715
\(39\) −8734.90 + 2690.24i −0.919594 + 0.283223i
\(40\) 50357.0i 4.97633i
\(41\) 282.328i 0.0262298i 0.999914 + 0.0131149i \(0.00417472\pi\)
−0.999914 + 0.0131149i \(0.995825\pi\)
\(42\) −10624.4 34496.4i −0.929357 3.01752i
\(43\) 7615.16i 0.628070i −0.949411 0.314035i \(-0.898319\pi\)
0.949411 0.314035i \(-0.101681\pi\)
\(44\) 50406.1 3.92510
\(45\) 11313.0 + 16623.9i 0.832812 + 1.22378i
\(46\) −18784.7 −1.30891
\(47\) 12556.7 0.829148 0.414574 0.910016i \(-0.363931\pi\)
0.414574 + 0.910016i \(0.363931\pi\)
\(48\) 17673.5 + 57383.8i 1.10718 + 3.59489i
\(49\) 28009.0 1.66651
\(50\) 40716.3 2.30326
\(51\) −3437.62 + 1058.74i −0.185068 + 0.0569987i
\(52\) 51382.9i 2.63518i
\(53\) 9284.33i 0.454005i −0.973894 0.227003i \(-0.927107\pi\)
0.973894 0.227003i \(-0.0728926\pi\)
\(54\) 32359.8 + 25874.6i 1.51016 + 1.20751i
\(55\) 47595.3i 2.12157i
\(56\) −128828. −5.48959
\(57\) 180.997 + 587.676i 0.00737876 + 0.0239580i
\(58\) 86046.9i 3.35865i
\(59\) 5254.69 + 26216.6i 0.196525 + 0.980499i
\(60\) 108038. 33274.3i 3.87435 1.19325i
\(61\) 17311.7i 0.595683i 0.954615 + 0.297842i \(0.0962668\pi\)
−0.954615 + 0.297842i \(0.903733\pi\)
\(62\) 19761.4i 0.652888i
\(63\) −42528.8 + 28942.0i −1.35000 + 0.918707i
\(64\) 124562. 3.80132
\(65\) 48517.6 1.42435
\(66\) −28866.0 93724.7i −0.815693 2.64846i
\(67\) 9818.20i 0.267205i 0.991035 + 0.133603i \(0.0426546\pi\)
−0.991035 + 0.133603i \(0.957345\pi\)
\(68\) 20221.7i 0.530330i
\(69\) 7880.06 + 25585.7i 0.199254 + 0.646955i
\(70\) 191609.i 4.67380i
\(71\) 12464.1i 0.293437i −0.989178 0.146718i \(-0.953129\pi\)
0.989178 0.146718i \(-0.0468711\pi\)
\(72\) 122253. 83196.4i 2.77926 1.89136i
\(73\) 59580.4i 1.30857i 0.756249 + 0.654284i \(0.227030\pi\)
−0.756249 + 0.654284i \(0.772970\pi\)
\(74\) 144830.i 3.07454i
\(75\) −17080.2 55457.6i −0.350623 1.13843i
\(76\) 3457.00 0.0686539
\(77\) 121763. 2.34038
\(78\) 95541.0 29425.4i 1.77809 0.547628i
\(79\) 4419.42 0.0796706 0.0398353 0.999206i \(-0.487317\pi\)
0.0398353 + 0.999206i \(0.487317\pi\)
\(80\) 318736.i 5.56809i
\(81\) 21667.8 54929.9i 0.366946 0.930242i
\(82\) 3088.07i 0.0507168i
\(83\) 39420.5 0.628097 0.314048 0.949407i \(-0.398315\pi\)
0.314048 + 0.949407i \(0.398315\pi\)
\(84\) 85125.5 + 276393.i 1.31632 + 4.27394i
\(85\) 19094.1 0.286650
\(86\) 83293.5i 1.21441i
\(87\) −117200. + 36096.1i −1.66008 + 0.511284i
\(88\) −350018. −4.81819
\(89\) −57202.6 −0.765493 −0.382746 0.923853i \(-0.625022\pi\)
−0.382746 + 0.923853i \(0.625022\pi\)
\(90\) −123740. 181830.i −1.61029 2.36624i
\(91\) 124122.i 1.57125i
\(92\) 150508. 1.85391
\(93\) 26916.0 8289.78i 0.322703 0.0993884i
\(94\) −137344. −1.60321
\(95\) 3264.22i 0.0371083i
\(96\) −103959. 337542.i −1.15128 3.73809i
\(97\) 40889.7i 0.441250i 0.975359 + 0.220625i \(0.0708097\pi\)
−0.975359 + 0.220625i \(0.929190\pi\)
\(98\) −306359. −3.22229
\(99\) −115548. + 78633.8i −1.18488 + 0.806345i
\(100\) −326229. −3.26229
\(101\) −112074. −1.09320 −0.546601 0.837393i \(-0.684078\pi\)
−0.546601 + 0.837393i \(0.684078\pi\)
\(102\) 37600.2 11580.4i 0.357840 0.110210i
\(103\) 3686.87i 0.0342424i −0.999853 0.0171212i \(-0.994550\pi\)
0.999853 0.0171212i \(-0.00545012\pi\)
\(104\) 356801.i 3.23477i
\(105\) 260980. 80378.6i 2.31012 0.711487i
\(106\) 101551.i 0.877846i
\(107\) 187067.i 1.57957i −0.613387 0.789783i \(-0.710193\pi\)
0.613387 0.789783i \(-0.289807\pi\)
\(108\) −259274. 207314.i −2.13895 1.71028i
\(109\) 208962.i 1.68462i 0.538994 + 0.842309i \(0.318804\pi\)
−0.538994 + 0.842309i \(0.681196\pi\)
\(110\) 520590.i 4.10217i
\(111\) 197266. 60755.4i 1.51965 0.468034i
\(112\) 815420. 6.14237
\(113\) 171171. 1.26105 0.630527 0.776167i \(-0.282839\pi\)
0.630527 + 0.776167i \(0.282839\pi\)
\(114\) −1979.72 6427.92i −0.0142673 0.0463242i
\(115\) 142115.i 1.00206i
\(116\) 689428.i 4.75711i
\(117\) −80157.7 117788.i −0.541353 0.795491i
\(118\) −57475.0 286754.i −0.379992 1.89585i
\(119\) 48848.3i 0.316215i
\(120\) −750212. + 231056.i −4.75588 + 1.46475i
\(121\) 169771. 1.05414
\(122\) 189353.i 1.15179i
\(123\) −4206.10 + 1295.42i −0.0250678 + 0.00772056i
\(124\) 158333.i 0.924735i
\(125\) 49444.2i 0.283035i
\(126\) 465174. 316563.i 2.61029 1.77637i
\(127\) −9967.86 −0.0548394 −0.0274197 0.999624i \(-0.508729\pi\)
−0.0274197 + 0.999624i \(0.508729\pi\)
\(128\) −637412. −3.43871
\(129\) 113450. 34941.1i 0.600246 0.184868i
\(130\) −530679. −2.75406
\(131\) 181309. 0.923086 0.461543 0.887118i \(-0.347296\pi\)
0.461543 + 0.887118i \(0.347296\pi\)
\(132\) 231281. + 750944.i 1.15533 + 3.75122i
\(133\) 8350.84 0.0409356
\(134\) 107390.i 0.516656i
\(135\) −195753. + 244816.i −0.924430 + 1.15613i
\(136\) 140419.i 0.650997i
\(137\) 24010.2i 0.109294i −0.998506 0.0546468i \(-0.982597\pi\)
0.998506 0.0546468i \(-0.0174033\pi\)
\(138\) −86191.0 279852.i −0.385269 1.25093i
\(139\) 223534. 0.981310 0.490655 0.871354i \(-0.336758\pi\)
0.490655 + 0.871354i \(0.336758\pi\)
\(140\) 1.53521e6i 6.61986i
\(141\) 57614.8 + 187069.i 0.244054 + 0.792417i
\(142\) 136330.i 0.567377i
\(143\) 337233.i 1.37908i
\(144\) −773805. + 526595.i −3.10975 + 2.11627i
\(145\) 650983. 2.57128
\(146\) 651681.i 2.53019i
\(147\) 128515. + 417275.i 0.490526 + 1.59268i
\(148\) 1.16042e6i 4.35471i
\(149\) 342010. 1.26204 0.631021 0.775766i \(-0.282636\pi\)
0.631021 + 0.775766i \(0.282636\pi\)
\(150\) 186821. + 606587.i 0.677950 + 2.20123i
\(151\) 110011.i 0.392638i −0.980540 0.196319i \(-0.937101\pi\)
0.980540 0.196319i \(-0.0628987\pi\)
\(152\) −24005.3 −0.0842747
\(153\) −31546.0 46355.4i −0.108947 0.160093i
\(154\) −1.33182e6 −4.52527
\(155\) −149504. −0.499831
\(156\) −765497. + 235763.i −2.51844 + 0.775648i
\(157\) 339957.i 1.10071i −0.834930 0.550357i \(-0.814492\pi\)
0.834930 0.550357i \(-0.185508\pi\)
\(158\) −48339.0 −0.154048
\(159\) 138317. 42599.8i 0.433893 0.133633i
\(160\) 1.87486e6i 5.78989i
\(161\) 363571. 1.10541
\(162\) −236999. + 600815.i −0.709511 + 1.79868i
\(163\) 160683. 0.473696 0.236848 0.971547i \(-0.423886\pi\)
0.236848 + 0.971547i \(0.423886\pi\)
\(164\) 24742.3i 0.0718341i
\(165\) 709069. 218384.i 2.02758 0.624469i
\(166\) −431175. −1.21446
\(167\) 311168.i 0.863383i 0.902021 + 0.431692i \(0.142083\pi\)
−0.902021 + 0.431692i \(0.857917\pi\)
\(168\) −591108. 1.91926e6i −1.61582 5.24640i
\(169\) 27524.2 0.0741307
\(170\) −208849. −0.554255
\(171\) −7924.66 + 5392.94i −0.0207248 + 0.0141038i
\(172\) 667367.i 1.72006i
\(173\) −756531. −1.92181 −0.960907 0.276870i \(-0.910703\pi\)
−0.960907 + 0.276870i \(0.910703\pi\)
\(174\) 1.28192e6 394814.i 3.20986 0.988596i
\(175\) −788049. −1.94517
\(176\) 2.21545e6 5.39113
\(177\) −366462. + 198575.i −0.879217 + 0.476422i
\(178\) 625674. 1.48012
\(179\) 473943. 1.10559 0.552794 0.833318i \(-0.313562\pi\)
0.552794 + 0.833318i \(0.313562\pi\)
\(180\) 991434. + 1.45686e6i 2.28078 + 3.35149i
\(181\) 209709. 0.475795 0.237897 0.971290i \(-0.423542\pi\)
0.237897 + 0.971290i \(0.423542\pi\)
\(182\) 1.35763e6i 3.03811i
\(183\) −257908. + 79432.3i −0.569295 + 0.175335i
\(184\) −1.04512e6 −2.27573
\(185\) −1.09571e6 −2.35377
\(186\) −294403. + 90672.4i −0.623965 + 0.192173i
\(187\) 132718.i 0.277540i
\(188\) 1.10043e6 2.27074
\(189\) −626312. 500794.i −1.27537 1.01977i
\(190\) 35703.6i 0.0717510i
\(191\) −194882. −0.386534 −0.193267 0.981146i \(-0.561908\pi\)
−0.193267 + 0.981146i \(0.561908\pi\)
\(192\) 571533. + 1.85571e6i 1.11889 + 3.63292i
\(193\) 509476. 0.984534 0.492267 0.870444i \(-0.336168\pi\)
0.492267 + 0.870444i \(0.336168\pi\)
\(194\) 447246.i 0.853182i
\(195\) 222616. + 722810.i 0.419247 + 1.36125i
\(196\) 2.45462e6 4.56398
\(197\) 327612.i 0.601443i −0.953712 0.300721i \(-0.902773\pi\)
0.953712 0.300721i \(-0.0972274\pi\)
\(198\) 1.26385e6 860084.i 2.29104 1.55911i
\(199\) −521051. −0.932712 −0.466356 0.884597i \(-0.654433\pi\)
−0.466356 + 0.884597i \(0.654433\pi\)
\(200\) 2.26532e6 4.00456
\(201\) −146270. + 45049.4i −0.255368 + 0.0786500i
\(202\) 1.22585e6 2.11377
\(203\) 1.66540e6i 2.83648i
\(204\) −301261. + 92784.6i −0.506836 + 0.156099i
\(205\) 23362.6 0.0388272
\(206\) 40326.4i 0.0662097i
\(207\) −345016. + 234793.i −0.559646 + 0.380854i
\(208\) 2.25838e6i 3.61942i
\(209\) 22688.8 0.0359290
\(210\) −2.85457e6 + 879169.i −4.46675 + 1.37570i
\(211\) 557715.i 0.862395i −0.902258 0.431197i \(-0.858091\pi\)
0.902258 0.431197i \(-0.141909\pi\)
\(212\) 813648.i 1.24336i
\(213\) 185688. 57189.6i 0.280437 0.0863711i
\(214\) 2.04611e6i 3.05418i
\(215\) −630152. −0.929714
\(216\) 1.80039e6 + 1.43958e6i 2.62562 + 2.09943i
\(217\) 382475.i 0.551383i
\(218\) 2.28560e6i 3.25731i
\(219\) −887621. + 273376.i −1.25060 + 0.385168i
\(220\) 4.17109e6i 5.81022i
\(221\) −135290. −0.186331
\(222\) −2.15767e6 + 664534.i −2.93834 + 0.904971i
\(223\) 123192. 0.165890 0.0829450 0.996554i \(-0.473567\pi\)
0.0829450 + 0.996554i \(0.473567\pi\)
\(224\) −4.79645e6 −6.38705
\(225\) 747831. 508919.i 0.984798 0.670181i
\(226\) −1.87224e6 −2.43832
\(227\) 668195. 0.860673 0.430337 0.902668i \(-0.358395\pi\)
0.430337 + 0.902668i \(0.358395\pi\)
\(228\) 15861.9 + 51502.0i 0.0202078 + 0.0656125i
\(229\) 547272.i 0.689627i 0.938671 + 0.344813i \(0.112058\pi\)
−0.938671 + 0.344813i \(0.887942\pi\)
\(230\) 1.55443e6i 1.93754i
\(231\) 558690. + 1.81401e6i 0.688876 + 2.23670i
\(232\) 4.78736e6i 5.83950i
\(233\) −978602. −1.18091 −0.590454 0.807071i \(-0.701051\pi\)
−0.590454 + 0.807071i \(0.701051\pi\)
\(234\) 876753. + 1.28835e6i 1.04674 + 1.53813i
\(235\) 1.03907e6i 1.22736i
\(236\) 460503. + 2.29754e6i 0.538211 + 2.68524i
\(237\) 20277.9 + 65840.1i 0.0234505 + 0.0761411i
\(238\) 534296.i 0.611420i
\(239\) 441167.i 0.499584i 0.968300 + 0.249792i \(0.0803622\pi\)
−0.968300 + 0.249792i \(0.919638\pi\)
\(240\) 4.74849e6 1.46247e6i 5.32142 1.63893i
\(241\) 457362. 0.507244 0.253622 0.967303i \(-0.418378\pi\)
0.253622 + 0.967303i \(0.418378\pi\)
\(242\) −1.85693e6 −2.03825
\(243\) 917759. + 70766.1i 0.997040 + 0.0768794i
\(244\) 1.51714e6i 1.63137i
\(245\) 2.31774e6i 2.46689i
\(246\) 46005.7 14169.2i 0.0484701 0.0149282i
\(247\) 23128.5i 0.0241215i
\(248\) 1.09946e6i 1.13514i
\(249\) 180875. + 587282.i 0.184876 + 0.600272i
\(250\) 540814.i 0.547265i
\(251\) 928891.i 0.930637i 0.885143 + 0.465319i \(0.154060\pi\)
−0.885143 + 0.465319i \(0.845940\pi\)
\(252\) −3.72709e6 + 2.53638e6i −3.69716 + 2.51601i
\(253\) 987801. 0.970216
\(254\) 109027. 0.106035
\(255\) 87610.6 + 284462.i 0.0843735 + 0.273951i
\(256\) 2.98594e6 2.84762
\(257\) 641285.i 0.605645i 0.953047 + 0.302823i \(0.0979289\pi\)
−0.953047 + 0.302823i \(0.902071\pi\)
\(258\) −1.24090e6 + 382180.i −1.16061 + 0.357453i
\(259\) 2.80314e6i 2.59654i
\(260\) 4.25192e6 3.90079
\(261\) −1.07551e6 1.58041e6i −0.977267 1.43605i
\(262\) −1.98314e6 −1.78484
\(263\) 1.41692e6i 1.26316i −0.775312 0.631578i \(-0.782407\pi\)
0.775312 0.631578i \(-0.217593\pi\)
\(264\) −1.60601e6 5.21453e6i −1.41820 4.60474i
\(265\) −768276. −0.672052
\(266\) −91340.3 −0.0791513
\(267\) −262466. 852198.i −0.225318 0.731581i
\(268\) 860434.i 0.731780i
\(269\) 1.07898e6 0.909146 0.454573 0.890709i \(-0.349792\pi\)
0.454573 + 0.890709i \(0.349792\pi\)
\(270\) 2.14112e6 2.67777e6i 1.78744 2.23544i
\(271\) 1.58918e6 1.31447 0.657235 0.753685i \(-0.271726\pi\)
0.657235 + 0.753685i \(0.271726\pi\)
\(272\) 888787.i 0.728409i
\(273\) −1.84916e6 + 569518.i −1.50165 + 0.462488i
\(274\) 262620.i 0.211326i
\(275\) −2.14108e6 −1.70727
\(276\) 690582. + 2.24224e6i 0.545686 + 1.77178i
\(277\) −1.02921e6 −0.805942 −0.402971 0.915213i \(-0.632022\pi\)
−0.402971 + 0.915213i \(0.632022\pi\)
\(278\) −2.44498e6 −1.89742
\(279\) 247000. + 362955.i 0.189971 + 0.279153i
\(280\) 1.06605e7i 8.12608i
\(281\) 677260.i 0.511670i 0.966721 + 0.255835i \(0.0823503\pi\)
−0.966721 + 0.255835i \(0.917650\pi\)
\(282\) −630182. 2.04613e6i −0.471893 1.53218i
\(283\) 445884.i 0.330945i −0.986214 0.165472i \(-0.947085\pi\)
0.986214 0.165472i \(-0.0529149\pi\)
\(284\) 1.09231e6i 0.803619i
\(285\) 48630.0 14977.4i 0.0354644 0.0109226i
\(286\) 3.68861e6i 2.66654i
\(287\) 59768.4i 0.0428318i
\(288\) 4.55167e6 3.09753e6i 3.23362 2.20056i
\(289\) 1.36661e6 0.962501
\(290\) −7.12035e6 −4.97172
\(291\) −609170. + 187617.i −0.421703 + 0.129879i
\(292\) 5.22142e6i 3.58370i
\(293\) 968607.i 0.659141i −0.944131 0.329571i \(-0.893096\pi\)
0.944131 0.329571i \(-0.106904\pi\)
\(294\) −1.40568e6 4.56410e6i −0.948460 3.07955i
\(295\) 2.16942e6 434824.i 1.45140 0.290910i
\(296\) 8.05788e6i 5.34554i
\(297\) −1.70165e6 1.36063e6i −1.11939 0.895052i
\(298\) −3.74086e6 −2.44023
\(299\) 1.00694e6i 0.651370i
\(300\) −1.49685e6 4.86012e6i −0.960232 3.11777i
\(301\) 1.61211e6i 1.02560i
\(302\) 1.20328e6i 0.759187i
\(303\) −514234. 1.66966e6i −0.321776 1.04477i
\(304\) 151942. 0.0942962
\(305\) 1.43254e6 0.881773
\(306\) 345046. + 507028.i 0.210656 + 0.309548i
\(307\) −942100. −0.570494 −0.285247 0.958454i \(-0.592076\pi\)
−0.285247 + 0.958454i \(0.592076\pi\)
\(308\) 1.06709e7 6.40948
\(309\) 54926.5 16916.7i 0.0327255 0.0100790i
\(310\) 1.63525e6 0.966452
\(311\) 2.24070e6i 1.31366i −0.754039 0.656830i \(-0.771897\pi\)
0.754039 0.656830i \(-0.228103\pi\)
\(312\) 5.31558e6 1.63713e6i 3.09146 0.952131i
\(313\) 1.70178e6i 0.981843i 0.871204 + 0.490922i \(0.163340\pi\)
−0.871204 + 0.490922i \(0.836660\pi\)
\(314\) 3.71840e6i 2.12829i
\(315\) 2.39494e6 + 3.51925e6i 1.35994 + 1.99836i
\(316\) 387303. 0.218189
\(317\) 645139.i 0.360583i −0.983613 0.180291i \(-0.942296\pi\)
0.983613 0.180291i \(-0.0577041\pi\)
\(318\) −1.51289e6 + 465951.i −0.838957 + 0.258388i
\(319\) 4.52481e6i 2.48956i
\(320\) 1.03074e7i 5.62699i
\(321\) 2.78690e6 858330.i 1.50959 0.464934i
\(322\) −3.97669e6 −2.13738
\(323\) 9102.20i 0.00485445i
\(324\) 1.89889e6 4.81387e6i 1.00493 2.54760i
\(325\) 2.18258e6i 1.14620i
\(326\) −1.75752e6 −0.915919
\(327\) −3.11310e6 + 958793.i −1.60999 + 0.495856i
\(328\) 171810.i 0.0881786i
\(329\) 2.65824e6 1.35395
\(330\) −7.75569e6 + 2.38865e6i −3.92045 + 1.20745i
\(331\) 964683. 0.483966 0.241983 0.970281i \(-0.422202\pi\)
0.241983 + 0.970281i \(0.422202\pi\)
\(332\) 3.45468e6 1.72013
\(333\) 1.81025e6 + 2.66008e6i 0.894600 + 1.31457i
\(334\) 3.40351e6i 1.66940i
\(335\) 812453. 0.395536
\(336\) 3.74144e6 + 1.21480e7i 1.80797 + 5.87027i
\(337\) 596925.i 0.286316i 0.989700 + 0.143158i \(0.0457256\pi\)
−0.989700 + 0.143158i \(0.954274\pi\)
\(338\) −301056. −0.143336
\(339\) 785393. + 2.55008e6i 0.371183 + 1.20519i
\(340\) 1.67334e6 0.785033
\(341\) 1.03916e6i 0.483946i
\(342\) 86678.7 58987.1i 0.0400726 0.0272704i
\(343\) 2.37145e6 1.08837
\(344\) 4.63417e6i 2.11143i
\(345\) 2.11721e6 652073.i 0.957670 0.294950i
\(346\) 8.27483e6 3.71594
\(347\) −560552. −0.249915 −0.124958 0.992162i \(-0.539879\pi\)
−0.124958 + 0.992162i \(0.539879\pi\)
\(348\) −1.02710e7 + 3.16334e6i −4.54637 + 1.40022i
\(349\) 3.18569e6i 1.40004i 0.714124 + 0.700019i \(0.246825\pi\)
−0.714124 + 0.700019i \(0.753175\pi\)
\(350\) 8.61956e6 3.76110
\(351\) 1.38700e6 1.73463e6i 0.600907 0.751518i
\(352\) −1.30317e7 −5.60588
\(353\) −3.12050e6 −1.33287 −0.666435 0.745563i \(-0.732181\pi\)
−0.666435 + 0.745563i \(0.732181\pi\)
\(354\) 4.00831e6 2.17198e6i 1.70002 0.921189i
\(355\) −1.03140e6 −0.434366
\(356\) −5.01305e6 −2.09641
\(357\) −727737. + 224134.i −0.302206 + 0.0930757i
\(358\) −5.18391e6 −2.13772
\(359\) 1.15889e6i 0.474576i −0.971439 0.237288i \(-0.923741\pi\)
0.971439 0.237288i \(-0.0762586\pi\)
\(360\) −6.88448e6 1.01164e7i −2.79972 4.11406i
\(361\) −2.47454e6 −0.999372
\(362\) −2.29376e6 −0.919977
\(363\) 778970. + 2.52923e6i 0.310280 + 1.00745i
\(364\) 1.08777e7i 4.30311i
\(365\) 4.93026e6 1.93704
\(366\) 2.82096e6 868819.i 1.10076 0.339021i
\(367\) 4.65500e6i 1.80408i −0.431657 0.902038i \(-0.642071\pi\)
0.431657 0.902038i \(-0.357929\pi\)
\(368\) 6.61511e6 2.54635
\(369\) −38598.1 56718.1i −0.0147571 0.0216848i
\(370\) 1.19847e7 4.55116
\(371\) 1.96547e6i 0.741366i
\(372\) 2.35883e6 726489.i 0.883769 0.272190i
\(373\) −4.30976e6 −1.60391 −0.801956 0.597383i \(-0.796207\pi\)
−0.801956 + 0.597383i \(0.796207\pi\)
\(374\) 1.45165e6i 0.536640i
\(375\) −736614. + 226868.i −0.270497 + 0.0833095i
\(376\) −7.64134e6 −2.78741
\(377\) −4.61250e6 −1.67141
\(378\) 6.85051e6 + 5.47761e6i 2.46600 + 1.97179i
\(379\) −4.75138e6 −1.69911 −0.849556 0.527499i \(-0.823130\pi\)
−0.849556 + 0.527499i \(0.823130\pi\)
\(380\) 286066.i 0.101626i
\(381\) −45736.1 148500.i −0.0161416 0.0524100i
\(382\) 2.13159e6 0.747385
\(383\) 681890.i 0.237529i −0.992922 0.118765i \(-0.962107\pi\)
0.992922 0.118765i \(-0.0378934\pi\)
\(384\) −2.92467e6 9.49609e6i −1.01216 3.28637i
\(385\) 1.00758e7i 3.46440i
\(386\) −5.57257e6 −1.90365
\(387\) 1.04110e6 + 1.52984e6i 0.353357 + 0.519241i
\(388\) 3.58344e6i 1.20843i
\(389\) 4.06334e6i 1.36147i 0.732529 + 0.680736i \(0.238340\pi\)
−0.732529 + 0.680736i \(0.761660\pi\)
\(390\) −2.43494e6 7.90599e6i −0.810639 2.63205i
\(391\) 396283.i 0.131088i
\(392\) −1.70448e7 −5.60242
\(393\) 831912. + 2.70113e6i 0.271704 + 0.882193i
\(394\) 3.58337e6i 1.16292i
\(395\) 365706.i 0.117934i
\(396\) −1.01263e7 + 6.89120e6i −3.24498 + 2.20829i
\(397\) 3.10911e6i 0.990058i −0.868877 0.495029i \(-0.835157\pi\)
0.868877 0.495029i \(-0.164843\pi\)
\(398\) 5.69918e6 1.80345
\(399\) 38316.6 + 124410.i 0.0120491 + 0.0391221i
\(400\) −1.43384e7 −4.48075
\(401\) −1.83192e6 −0.568913 −0.284456 0.958689i \(-0.591813\pi\)
−0.284456 + 0.958689i \(0.591813\pi\)
\(402\) 1.59988e6 492744.i 0.493768 0.152074i
\(403\) 1.05930e6 0.324905
\(404\) −9.82176e6 −2.99389
\(405\) −4.54543e6 1.79300e6i −1.37701 0.543179i
\(406\) 1.82159e7i 5.48450i
\(407\) 7.61597e6i 2.27897i
\(408\) 2.09195e6 644293.i 0.622157 0.191616i
\(409\) 3.65587e6i 1.08064i 0.841458 + 0.540322i \(0.181698\pi\)
−0.841458 + 0.540322i \(0.818302\pi\)
\(410\) −255537. −0.0750747
\(411\) 357702. 110168.i 0.104452 0.0321699i
\(412\) 323105.i 0.0937778i
\(413\) 1.11241e6 + 5.55001e6i 0.320914 + 1.60110i
\(414\) 3.77374e6 2.56813e6i 1.08211 0.736403i
\(415\) 3.26203e6i 0.929754i
\(416\) 1.32842e7i 3.76360i
\(417\) 1.02565e6 + 3.33018e6i 0.288842 + 0.937837i
\(418\) −248166. −0.0694708
\(419\) 5.27692e6 1.46840 0.734202 0.678931i \(-0.237556\pi\)
0.734202 + 0.678931i \(0.237556\pi\)
\(420\) 2.28714e7 7.04411e6i 6.32660 1.94851i
\(421\) 1.31301e6i 0.361046i 0.983571 + 0.180523i \(0.0577790\pi\)
−0.983571 + 0.180523i \(0.942221\pi\)
\(422\) 6.10020e6i 1.66749i
\(423\) −2.52257e6 + 1.71668e6i −0.685477 + 0.466485i
\(424\) 5.64994e6i 1.52626i
\(425\) 858953.i 0.230673i
\(426\) −2.03103e6 + 625532.i −0.542242 + 0.167003i
\(427\) 3.66486e6i 0.972718i
\(428\) 1.63939e7i 4.32587i
\(429\) −5.02406e6 + 1.54735e6i −1.31799 + 0.405924i
\(430\) 6.89251e6 1.79766
\(431\) −2.94982e6 −0.764896 −0.382448 0.923977i \(-0.624919\pi\)
−0.382448 + 0.923977i \(0.624919\pi\)
\(432\) −1.13956e7 9.11185e6i −2.93785 2.34908i
\(433\) 4.16711e6 1.06811 0.534054 0.845450i \(-0.320668\pi\)
0.534054 + 0.845450i \(0.320668\pi\)
\(434\) 4.18345e6i 1.06613i
\(435\) 2.98694e6 + 9.69827e6i 0.756839 + 2.45737i
\(436\) 1.83127e7i 4.61357i
\(437\) 67746.4 0.0169700
\(438\) 9.70867e6 2.99015e6i 2.41810 0.744744i
\(439\) 1.65701e6 0.410359 0.205180 0.978724i \(-0.434222\pi\)
0.205180 + 0.978724i \(0.434222\pi\)
\(440\) 2.89639e7i 7.13222i
\(441\) −5.62685e6 + 3.82922e6i −1.37774 + 0.937591i
\(442\) 1.47978e6 0.360282
\(443\) −4.88064e6 −1.18159 −0.590796 0.806821i \(-0.701186\pi\)
−0.590796 + 0.806821i \(0.701186\pi\)
\(444\) 1.72877e7 5.32440e6i 4.16179 1.28178i
\(445\) 4.73350e6i 1.13314i
\(446\) −1.34746e6 −0.320758
\(447\) 1.56927e6 + 5.09523e6i 0.371473 + 1.20613i
\(448\) 2.63695e7 6.20735
\(449\) 4.26247e6i 0.997803i −0.866659 0.498902i \(-0.833737\pi\)
0.866659 0.498902i \(-0.166263\pi\)
\(450\) −8.17966e6 + 5.56648e6i −1.90416 + 1.29583i
\(451\) 162387.i 0.0375933i
\(452\) 1.50008e7 3.45358
\(453\) 1.63892e6 504767.i 0.375244 0.115570i
\(454\) −7.30861e6 −1.66416
\(455\) 1.02711e7 2.32588
\(456\) −110145. 357628.i −0.0248057 0.0805414i
\(457\) 3.75535e6i 0.841123i −0.907264 0.420561i \(-0.861833\pi\)
0.907264 0.420561i \(-0.138167\pi\)
\(458\) 5.98598e6i 1.33343i
\(459\) 545852. 682664.i 0.120933 0.151243i
\(460\) 1.24545e7i 2.74429i
\(461\) 4.23096e6i 0.927229i 0.886037 + 0.463614i \(0.153448\pi\)
−0.886037 + 0.463614i \(0.846552\pi\)
\(462\) −6.11087e6 1.98413e7i −1.33198 4.32480i
\(463\) 8.02997e6i 1.74085i −0.492301 0.870425i \(-0.663844\pi\)
0.492301 0.870425i \(-0.336156\pi\)
\(464\) 3.03017e7i 6.53390i
\(465\) −685977. 2.22729e6i −0.147122 0.477688i
\(466\) 1.07038e7 2.28335
\(467\) −6.56680e6 −1.39336 −0.696678 0.717384i \(-0.745339\pi\)
−0.696678 + 0.717384i \(0.745339\pi\)
\(468\) −7.02475e6 1.03225e7i −1.48257 2.17857i
\(469\) 2.07849e6i 0.436331i
\(470\) 1.13652e7i 2.37318i
\(471\) 5.06463e6 1.55984e6i 1.05195 0.323988i
\(472\) −3.19772e6 1.59540e7i −0.660670 3.29621i
\(473\) 4.38002e6i 0.900168i
\(474\) −221797. 720149.i −0.0453429 0.147223i
\(475\) −146842. −0.0298618
\(476\) 4.28090e6i 0.866000i
\(477\) 1.26929e6 + 1.86517e6i 0.255427 + 0.375337i
\(478\) 4.82542e6i 0.965974i
\(479\) 8.13362e6i 1.61974i −0.586610 0.809870i \(-0.699538\pi\)
0.586610 0.809870i \(-0.300462\pi\)
\(480\) −2.79315e7 + 8.60255e6i −5.53339 + 1.70421i
\(481\) 7.76356e6 1.53002
\(482\) −5.00255e6 −0.980786
\(483\) 1.66819e6 + 5.41644e6i 0.325371 + 1.05644i
\(484\) 1.48782e7 2.88693
\(485\) 3.38361e6 0.653170
\(486\) −1.00383e7 774030.i −1.92784 0.148651i
\(487\) −5.76281e6 −1.10106 −0.550532 0.834814i \(-0.685575\pi\)
−0.550532 + 0.834814i \(0.685575\pi\)
\(488\) 1.05350e7i 2.00255i
\(489\) 737269. + 2.39383e6i 0.139429 + 0.452711i
\(490\) 2.53511e7i 4.76987i
\(491\) 29783.7i 0.00557538i −0.999996 0.00278769i \(-0.999113\pi\)
0.999996 0.00278769i \(-0.000887351\pi\)
\(492\) −368608. + 113527.i −0.0686518 + 0.0211439i
\(493\) −1.81525e6 −0.336371
\(494\) 252976.i 0.0466403i
\(495\) 6.50692e6 + 9.56160e6i 1.19361 + 1.75395i
\(496\) 6.95906e6i 1.27012i
\(497\) 2.63862e6i 0.479166i
\(498\) −1.97839e6 6.42360e6i −0.357468 1.16066i
\(499\) −6.44186e6 −1.15814 −0.579068 0.815279i \(-0.696584\pi\)
−0.579068 + 0.815279i \(0.696584\pi\)
\(500\) 4.33313e6i 0.775133i
\(501\) −4.63574e6 + 1.42775e6i −0.825135 + 0.254131i
\(502\) 1.01601e7i 1.79944i
\(503\) 8.29145e6 1.46120 0.730601 0.682805i \(-0.239240\pi\)
0.730601 + 0.682805i \(0.239240\pi\)
\(504\) 2.58807e7 1.76125e7i 4.53837 3.08848i
\(505\) 9.27406e6i 1.61823i
\(506\) −1.08044e7 −1.87597
\(507\) 126291. + 410052.i 0.0218199 + 0.0708467i
\(508\) −873550. −0.150186
\(509\) −8.34624e6 −1.42789 −0.713947 0.700199i \(-0.753094\pi\)
−0.713947 + 0.700199i \(0.753094\pi\)
\(510\) −958272. 3.11140e6i −0.163141 0.529701i
\(511\) 1.26130e7i 2.13682i
\(512\) −1.22626e7 −2.06732
\(513\) −116704. 93315.9i −0.0195792 0.0156553i
\(514\) 7.01428e6i 1.17105i
\(515\) −305087. −0.0506881
\(516\) 9.94236e6 3.06212e6i 1.64386 0.506288i
\(517\) 7.22228e6 1.18836
\(518\) 3.06603e7i 5.02056i
\(519\) −3.47123e6 1.12707e7i −0.565673 1.83668i
\(520\) −2.95252e7 −4.78833
\(521\) 9.84429e6i 1.58888i 0.607345 + 0.794438i \(0.292235\pi\)
−0.607345 + 0.794438i \(0.707765\pi\)
\(522\) 1.17638e7 + 1.72863e7i 1.88960 + 2.77668i
\(523\) −5.24419e6 −0.838348 −0.419174 0.907906i \(-0.637680\pi\)
−0.419174 + 0.907906i \(0.637680\pi\)
\(524\) 1.58893e7 2.52800
\(525\) −3.61585e6 1.17403e7i −0.572548 1.85900i
\(526\) 1.54981e7i 2.44239i
\(527\) 416888. 0.0653872
\(528\) 1.01653e7 + 3.30055e7i 1.58684 + 5.15231i
\(529\) −3.48687e6 −0.541747
\(530\) 8.40329e6 1.29945
\(531\) −4.63981e6 4.54838e6i −0.714108 0.700036i
\(532\) 731840. 0.112108
\(533\) −165534. −0.0252389
\(534\) 2.87082e6 + 9.32122e6i 0.435664 + 1.41455i
\(535\) −1.54797e7 −2.33819
\(536\) 5.97482e6i 0.898282i
\(537\) 2.17462e6 + 7.06074e6i 0.325422 + 1.05661i
\(538\) −1.18017e7 −1.75789
\(539\) 1.61100e7 2.38849
\(540\) −1.71551e7 + 2.14549e7i −2.53169 + 3.16623i
\(541\) 1.21868e7i 1.79018i −0.445881 0.895092i \(-0.647110\pi\)
0.445881 0.895092i \(-0.352890\pi\)
\(542\) −1.73823e7 −2.54161
\(543\) 962218. + 3.12421e6i 0.140047 + 0.454717i
\(544\) 5.22801e6i 0.757424i
\(545\) 1.72916e7 2.49369
\(546\) 2.02258e7 6.22930e6i 2.90352 0.894247i
\(547\) 750385. 0.107230 0.0536149 0.998562i \(-0.482926\pi\)
0.0536149 + 0.998562i \(0.482926\pi\)
\(548\) 2.10418e6i 0.299317i
\(549\) −2.36675e6 3.47782e6i −0.335136 0.492466i
\(550\) 2.34189e7 3.30110
\(551\) 310325.i 0.0435449i
\(552\) −4.79537e6 1.55701e7i −0.669846 2.17492i
\(553\) 935583. 0.130098
\(554\) 1.12573e7 1.55833
\(555\) −5.02749e6 1.63237e7i −0.692818 2.24950i
\(556\) 1.95897e7 2.68746
\(557\) 984038.i 0.134392i 0.997740 + 0.0671961i \(0.0214053\pi\)
−0.997740 + 0.0671961i \(0.978595\pi\)
\(558\) −2.70165e6 3.96995e6i −0.367320 0.539758i
\(559\) 4.46491e6 0.604342
\(560\) 6.74758e7i 9.09238i
\(561\) −1.97722e6 + 608958.i −0.265245 + 0.0816921i
\(562\) 7.40777e6i 0.989343i
\(563\) 1.88523e6 0.250664 0.125332 0.992115i \(-0.460000\pi\)
0.125332 + 0.992115i \(0.460000\pi\)
\(564\) 5.04917e6 + 1.63941e7i 0.668378 + 2.17015i
\(565\) 1.41643e7i 1.86670i
\(566\) 4.87701e6i 0.639901i
\(567\) 4.58702e6 1.16285e7i 0.599202 1.51903i
\(568\) 7.58496e6i 0.986466i
\(569\) −9.06285e6 −1.17350 −0.586751 0.809767i \(-0.699593\pi\)
−0.586751 + 0.809767i \(0.699593\pi\)
\(570\) −531908. + 163821.i −0.0685724 + 0.0211194i
\(571\) 2.73395e6i 0.350914i 0.984487 + 0.175457i \(0.0561403\pi\)
−0.984487 + 0.175457i \(0.943860\pi\)
\(572\) 2.95540e7i 3.77682i
\(573\) −894186. 2.90332e6i −0.113774 0.369410i
\(574\) 653738.i 0.0828178i
\(575\) −6.39306e6 −0.806379
\(576\) −2.50237e7 + 1.70293e7i −3.14264 + 2.13865i
\(577\) −1.88079e6 −0.235181 −0.117590 0.993062i \(-0.537517\pi\)
−0.117590 + 0.993062i \(0.537517\pi\)
\(578\) −1.49478e7 −1.86105
\(579\) 2.33766e6 + 7.59012e6i 0.289791 + 0.940918i
\(580\) 5.70499e7 7.04182
\(581\) 8.34523e6 1.02565
\(582\) 6.66301e6 2.05212e6i 0.815386 0.251128i
\(583\) 5.34008e6i 0.650694i
\(584\) 3.62574e7i 4.39910i
\(585\) −9.74690e6 + 6.63302e6i −1.17754 + 0.801349i
\(586\) 1.05945e7i 1.27449i
\(587\) −9.02658e6 −1.08125 −0.540627 0.841262i \(-0.681813\pi\)
−0.540627 + 0.841262i \(0.681813\pi\)
\(588\) 1.12627e7 + 3.65686e7i 1.34338 + 4.36179i
\(589\) 71268.8i 0.00846469i
\(590\) −2.37288e7 + 4.75604e6i −2.80638 + 0.562491i
\(591\) 4.88073e6 1.50320e6i 0.574799 0.177031i
\(592\) 5.10026e7i 5.98120i
\(593\) 3.53803e6i 0.413166i 0.978429 + 0.206583i \(0.0662343\pi\)
−0.978429 + 0.206583i \(0.933766\pi\)
\(594\) 1.86124e7 + 1.48823e7i 2.16440 + 1.73063i
\(595\) 4.04219e6 0.468084
\(596\) 2.99726e7 3.45628
\(597\) −2.39077e6 7.76256e6i −0.274537 0.891393i
\(598\) 1.10138e7i 1.25946i
\(599\) 1.42114e7i 1.61834i −0.587574 0.809170i \(-0.699917\pi\)
0.587574 0.809170i \(-0.300083\pi\)
\(600\) 1.03941e7 + 3.37485e7i 1.17871 + 3.82715i
\(601\) 1.35365e7i 1.52869i −0.644806 0.764346i \(-0.723062\pi\)
0.644806 0.764346i \(-0.276938\pi\)
\(602\) 1.76331e7i 1.98306i
\(603\) −1.34228e6 1.97242e6i −0.150332 0.220905i
\(604\) 9.64095e6i 1.07529i
\(605\) 1.40485e7i 1.56042i
\(606\) 5.62461e6 + 1.82625e7i 0.622173 + 2.02013i
\(607\) −5004.17 −0.000551265 −0.000275633 1.00000i \(-0.500088\pi\)
−0.000275633 1.00000i \(0.500088\pi\)
\(608\) −893752. −0.0980523
\(609\) −2.48110e7 + 7.64147e6i −2.71082 + 0.834898i
\(610\) −1.56689e7 −1.70496
\(611\) 7.36224e6i 0.797824i
\(612\) −2.76459e6 4.06243e6i −0.298368 0.438437i
\(613\) 9.45865e6i 1.01667i 0.861161 + 0.508333i \(0.169738\pi\)
−0.861161 + 0.508333i \(0.830262\pi\)
\(614\) 1.03045e7 1.10308
\(615\) 107196. + 348053.i 0.0114285 + 0.0371072i
\(616\) −7.40981e7 −7.86783
\(617\) 1.35592e7i 1.43391i −0.697120 0.716954i \(-0.745536\pi\)
0.697120 0.716954i \(-0.254464\pi\)
\(618\) −600778. + 185032.i −0.0632766 + 0.0194884i
\(619\) 6.13962e6 0.644043 0.322022 0.946732i \(-0.395638\pi\)
0.322022 + 0.946732i \(0.395638\pi\)
\(620\) −1.31020e7 −1.36886
\(621\) −5.08097e6 4.06270e6i −0.528710 0.422752i
\(622\) 2.45085e7i 2.54004i
\(623\) −1.21097e7 −1.25001
\(624\) −3.36451e7 + 1.03623e7i −3.45908 + 1.06535i
\(625\) −7.54136e6 −0.772236
\(626\) 1.86138e7i 1.89845i
\(627\) 104104. + 338015.i 0.0105755 + 0.0343373i
\(628\) 2.97927e7i 3.01446i
\(629\) 3.05535e6 0.307917
\(630\) −2.61955e7 3.84930e7i −2.62952 3.86394i
\(631\) 1.01365e7 1.01348 0.506739 0.862099i \(-0.330851\pi\)
0.506739 + 0.862099i \(0.330851\pi\)
\(632\) −2.68942e6 −0.267834
\(633\) 8.30877e6 2.55900e6i 0.824191 0.253840i
\(634\) 7.05644e6i 0.697208i
\(635\) 824837.i 0.0811772i
\(636\) 1.21216e7 3.73331e6i 1.18828 0.365974i
\(637\) 1.64222e7i 1.60355i
\(638\) 4.94917e7i 4.81372i
\(639\) 1.70401e6 + 2.50396e6i 0.165090 + 0.242591i
\(640\) 5.27456e7i 5.09022i
\(641\) 1.31805e7i 1.26703i 0.773731 + 0.633514i \(0.218388\pi\)
−0.773731 + 0.633514i \(0.781612\pi\)
\(642\) −3.04827e7 + 9.38828e6i −2.91888 + 0.898977i
\(643\) 1.28000e7 1.22091 0.610453 0.792053i \(-0.290988\pi\)
0.610453 + 0.792053i \(0.290988\pi\)
\(644\) 3.18621e7 3.02733
\(645\) −2.89136e6 9.38794e6i −0.273655 0.888528i
\(646\) 99558.6i 0.00938636i
\(647\) 1.22343e7i 1.14900i 0.818506 + 0.574498i \(0.194803\pi\)
−0.818506 + 0.574498i \(0.805197\pi\)
\(648\) −1.31858e7 + 3.34273e7i −1.23359 + 3.12726i
\(649\) 3.02235e6 + 1.50791e7i 0.281665 + 1.40528i
\(650\) 2.38727e7i 2.21625i
\(651\) 5.69806e6 1.75493e6i 0.526957 0.162296i
\(652\) 1.40817e7 1.29729
\(653\) 6.66464e6i 0.611637i −0.952090 0.305818i \(-0.901070\pi\)
0.952090 0.305818i \(-0.0989300\pi\)
\(654\) 3.40506e7 1.04871e7i 3.11301 0.958766i
\(655\) 1.50033e7i 1.36642i
\(656\) 1.08747e6i 0.0986642i
\(657\) −8.14545e6 1.19693e7i −0.736210 1.08182i
\(658\) −2.90754e7 −2.61795
\(659\) 7.72743e6 0.693141 0.346570 0.938024i \(-0.387346\pi\)
0.346570 + 0.938024i \(0.387346\pi\)
\(660\) 6.21404e7 1.91384e7i 5.55283 1.71020i
\(661\) −1.82927e7 −1.62845 −0.814227 0.580547i \(-0.802839\pi\)
−0.814227 + 0.580547i \(0.802839\pi\)
\(662\) −1.05516e7 −0.935775
\(663\) −620759. 2.01554e6i −0.0548453 0.178077i
\(664\) −2.39891e7 −2.11152
\(665\) 691030.i 0.0605958i
\(666\) −1.98003e7 2.90956e7i −1.72976 2.54180i
\(667\) 1.35106e7i 1.17587i
\(668\) 2.72697e7i 2.36450i
\(669\) 565249. + 1.83530e6i 0.0488286 + 0.158541i
\(670\) −8.88649e6 −0.764792
\(671\) 9.95720e6i 0.853751i
\(672\) −2.20078e7 7.14570e7i −1.87998 6.10410i
\(673\) 5.36267e6i 0.456398i 0.973615 + 0.228199i \(0.0732836\pi\)
−0.973615 + 0.228199i \(0.926716\pi\)
\(674\) 6.52908e6i 0.553608i
\(675\) 1.10131e7 + 8.80600e6i 0.930360 + 0.743908i
\(676\) 2.41213e6 0.203018
\(677\) 7.82835e6i 0.656445i 0.944600 + 0.328222i \(0.106450\pi\)
−0.944600 + 0.328222i \(0.893550\pi\)
\(678\) −8.59051e6 2.78924e7i −0.717703 2.33030i
\(679\) 8.65627e6i 0.720537i
\(680\) −1.16196e7 −0.963652
\(681\) 3.06591e6 + 9.95469e6i 0.253333 + 0.822545i
\(682\) 1.13662e7i 0.935738i
\(683\) 1.11818e6 0.0917191 0.0458596 0.998948i \(-0.485397\pi\)
0.0458596 + 0.998948i \(0.485397\pi\)
\(684\) −694490. + 472619.i −0.0567578 + 0.0386252i
\(685\) −1.98684e6 −0.161784
\(686\) −2.59386e7 −2.10444
\(687\) −8.15319e6 + 2.51108e6i −0.659076 + 0.202987i
\(688\) 2.93321e7i 2.36250i
\(689\) 5.44357e6 0.436854
\(690\) −2.31577e7 + 7.13228e6i −1.85171 + 0.570303i
\(691\) 2.04795e6i 0.163164i 0.996667 + 0.0815818i \(0.0259972\pi\)
−0.996667 + 0.0815818i \(0.974003\pi\)
\(692\) −6.62998e7 −5.26317
\(693\) −2.44614e7 + 1.66466e7i −1.93485 + 1.31672i
\(694\) 6.13124e6 0.483225
\(695\) 1.84974e7i 1.45261i
\(696\) 7.13215e7 2.19661e7i 5.58081 1.71882i
\(697\) −65146.0 −0.00507932
\(698\) 3.48446e7i 2.70706i
\(699\) −4.49017e6 1.45791e7i −0.347592 1.12859i
\(700\) −6.90620e7 −5.32714
\(701\) −8.72479e6 −0.670594 −0.335297 0.942112i \(-0.608837\pi\)
−0.335297 + 0.942112i \(0.608837\pi\)
\(702\) −1.51708e7 + 1.89731e7i −1.16189 + 1.45310i
\(703\) 522326.i 0.0398614i
\(704\) 7.16443e7 5.44816
\(705\) 1.54799e7 4.76761e6i 1.17299 0.361267i
\(706\) 3.41316e7 2.57718
\(707\) −2.37258e7 −1.78514
\(708\) −3.21155e7 + 1.74024e7i −2.40786 + 1.30475i
\(709\) −2.37271e7 −1.77268 −0.886338 0.463038i \(-0.846759\pi\)
−0.886338 + 0.463038i \(0.846759\pi\)
\(710\) 1.12813e7 0.839872
\(711\) −887835. + 604195.i −0.0658656 + 0.0448233i
\(712\) 3.48104e7 2.57341
\(713\) 3.10283e6i 0.228578i
\(714\) 7.95988e6 2.45154e6i 0.584334 0.179967i
\(715\) 2.79060e7 2.04142
\(716\) 4.15347e7 3.02781
\(717\) −6.57245e6 + 2.02423e6i −0.477452 + 0.147049i
\(718\) 1.26758e7i 0.917621i
\(719\) −1.98910e7 −1.43495 −0.717473 0.696586i \(-0.754701\pi\)
−0.717473 + 0.696586i \(0.754701\pi\)
\(720\) 4.35755e7 + 6.40321e7i 3.13265 + 4.60327i
\(721\) 780502.i 0.0559160i
\(722\) 2.70662e7 1.93234
\(723\) 2.09854e6 + 6.81372e6i 0.149304 + 0.484773i
\(724\) 1.83782e7 1.30303
\(725\) 2.92846e7i 2.06916i
\(726\) −8.52026e6 2.76643e7i −0.599945 1.94795i
\(727\) 1.36021e7 0.954489 0.477244 0.878771i \(-0.341636\pi\)
0.477244 + 0.878771i \(0.341636\pi\)
\(728\) 7.55341e7i 5.28220i
\(729\) 3.15674e6 + 1.39974e7i 0.219998 + 0.975500i
\(730\) −5.39264e7 −3.74537
\(731\) 1.75716e6 0.121624
\(732\) −2.26022e7 + 6.96118e6i −1.55910 + 0.480181i
\(733\) 1.37934e7 0.948224 0.474112 0.880465i \(-0.342769\pi\)
0.474112 + 0.880465i \(0.342769\pi\)
\(734\) 5.09157e7i 3.48828i
\(735\) 3.45294e7 1.06346e7i 2.35760 0.726112i
\(736\) −3.89113e7 −2.64778
\(737\) 5.64714e6i 0.382966i
\(738\) 422181. + 620374.i 0.0285337 + 0.0419288i
\(739\) 8.43574e6i 0.568214i 0.958793 + 0.284107i \(0.0916971\pi\)
−0.958793 + 0.284107i \(0.908303\pi\)
\(740\) −9.60240e7 −6.44615
\(741\) −344565. + 106122.i −0.0230529 + 0.00710000i
\(742\) 2.14981e7i 1.43347i
\(743\) 2.88582e7i 1.91777i 0.283794 + 0.958885i \(0.408407\pi\)
−0.283794 + 0.958885i \(0.591593\pi\)
\(744\) −1.63796e7 + 5.04471e6i −1.08485 + 0.334121i
\(745\) 2.83013e7i 1.86816i
\(746\) 4.71395e7 3.10126
\(747\) −7.91933e6 + 5.38931e6i −0.519263 + 0.353372i
\(748\) 1.16310e7i 0.760085i
\(749\) 3.96017e7i 2.57934i
\(750\) 8.05698e6 2.48145e6i 0.523021 0.161084i
\(751\) 1.56331e7i 1.01145i 0.862694 + 0.505726i \(0.168775\pi\)
−0.862694 + 0.505726i \(0.831225\pi\)
\(752\) 4.83661e7 3.11887
\(753\) −1.38385e7 + 4.26208e6i −0.889410 + 0.273927i
\(754\) 5.04508e7 3.23177
\(755\) −9.10334e6 −0.581210
\(756\) −5.48879e7 4.38879e7i −3.49279 2.79280i
\(757\) −2.27834e7 −1.44504 −0.722518 0.691352i \(-0.757015\pi\)
−0.722518 + 0.691352i \(0.757015\pi\)
\(758\) 5.19699e7 3.28533
\(759\) 4.53239e6 + 1.47162e7i 0.285576 + 0.927235i
\(760\) 1.98643e6i 0.124750i
\(761\) 1.72608e7i 1.08044i −0.841524 0.540220i \(-0.818341\pi\)
0.841524 0.540220i \(-0.181659\pi\)
\(762\) 500255. + 1.62427e6i 0.0312107 + 0.101338i
\(763\) 4.42369e7i 2.75089i
\(764\) −1.70788e7 −1.05858
\(765\) −3.83589e6 + 2.61043e6i −0.236981 + 0.161272i
\(766\) 7.45841e6i 0.459277i
\(767\) −1.53713e7 + 3.08092e6i −0.943457 + 0.189100i
\(768\) 1.37006e7 + 4.44842e7i 0.838177 + 2.72147i
\(769\) 5.09443e6i 0.310656i 0.987863 + 0.155328i \(0.0496434\pi\)
−0.987863 + 0.155328i \(0.950357\pi\)
\(770\) 1.10208e8i 6.69863i
\(771\) −9.55379e6 + 2.94244e6i −0.578815 + 0.178267i
\(772\) 4.46488e7 2.69629
\(773\) −2.45291e7 −1.47650 −0.738250 0.674527i \(-0.764348\pi\)
−0.738250 + 0.674527i \(0.764348\pi\)
\(774\) −1.13874e7 1.67332e7i −0.683236 1.00398i
\(775\) 6.72547e6i 0.402224i
\(776\) 2.48832e7i 1.48338i
\(777\) 4.17608e7 1.28618e7i 2.48151 0.764274i
\(778\) 4.44442e7i 2.63248i
\(779\) 11137.0i 0.000657543i
\(780\) 1.95093e7 + 6.33447e7i