Properties

Label 177.6.d.b.176.12
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 176.12
Character \(\chi\) \(=\) 177.176
Dual form 177.6.d.b.176.11

$q$-expansion

\(f(q)\) \(=\) \(q-9.16184 q^{2} +(-4.65820 - 14.8762i) q^{3} +51.9393 q^{4} +80.4460i q^{5} +(42.6777 + 136.293i) q^{6} -176.825 q^{7} -182.680 q^{8} +(-199.602 + 138.593i) q^{9} +O(q^{10})\) \(q-9.16184 q^{2} +(-4.65820 - 14.8762i) q^{3} +51.9393 q^{4} +80.4460i q^{5} +(42.6777 + 136.293i) q^{6} -176.825 q^{7} -182.680 q^{8} +(-199.602 + 138.593i) q^{9} -737.033i q^{10} -681.939 q^{11} +(-241.943 - 772.659i) q^{12} -634.160i q^{13} +1620.04 q^{14} +(1196.73 - 374.733i) q^{15} +11.6301 q^{16} +1790.65i q^{17} +(1828.72 - 1269.76i) q^{18} -2481.42 q^{19} +4178.30i q^{20} +(823.686 + 2630.48i) q^{21} +6247.82 q^{22} -3057.87 q^{23} +(850.961 + 2717.59i) q^{24} -3346.56 q^{25} +5810.07i q^{26} +(2991.52 + 2323.73i) q^{27} -9184.16 q^{28} -546.719i q^{29} +(-10964.2 + 3433.25i) q^{30} +555.314i q^{31} +5739.21 q^{32} +(3176.61 + 10144.7i) q^{33} -16405.6i q^{34} -14224.9i q^{35} +(-10367.2 + 7198.39i) q^{36} -4130.23i q^{37} +22734.3 q^{38} +(-9433.89 + 2954.05i) q^{39} -14695.9i q^{40} +14697.6i q^{41} +(-7546.48 - 24100.1i) q^{42} +19748.6i q^{43} -35419.4 q^{44} +(-11149.2 - 16057.2i) q^{45} +28015.7 q^{46} -10422.4 q^{47} +(-54.1755 - 173.012i) q^{48} +14460.1 q^{49} +30660.6 q^{50} +(26638.1 - 8341.20i) q^{51} -32937.8i q^{52} -8205.73i q^{53} +(-27407.8 - 21289.7i) q^{54} -54859.3i q^{55} +32302.4 q^{56} +(11558.9 + 36914.0i) q^{57} +5008.95i q^{58} +(24643.1 - 10375.2i) q^{59} +(62157.3 - 19463.4i) q^{60} -24796.7i q^{61} -5087.70i q^{62} +(35294.7 - 24506.6i) q^{63} -52953.9 q^{64} +51015.7 q^{65} +(-29103.6 - 92943.8i) q^{66} +1477.02i q^{67} +93005.0i q^{68} +(14244.2 + 45489.4i) q^{69} +130326. i q^{70} -45951.7i q^{71} +(36463.4 - 25318.1i) q^{72} -34710.8i q^{73} +37840.5i q^{74} +(15588.9 + 49784.0i) q^{75} -128883. q^{76} +120584. q^{77} +(86431.8 - 27064.5i) q^{78} -15432.4 q^{79} +935.598i q^{80} +(20633.2 - 55326.8i) q^{81} -134657. i q^{82} -29051.1 q^{83} +(42781.6 + 136625. i) q^{84} -144051. q^{85} -180933. i q^{86} +(-8133.10 + 2546.73i) q^{87} +124577. q^{88} -114778. q^{89} +(102147. + 147114. i) q^{90} +112135. i q^{91} -158823. q^{92} +(8260.96 - 2586.76i) q^{93} +95488.3 q^{94} -199620. i q^{95} +(-26734.4 - 85377.7i) q^{96} +56580.8i q^{97} -132481. q^{98} +(136117. - 94511.7i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.16184 −1.61960 −0.809800 0.586707i \(-0.800424\pi\)
−0.809800 + 0.586707i \(0.800424\pi\)
\(3\) −4.65820 14.8762i −0.298824 0.954308i
\(4\) 51.9393 1.62310
\(5\) 80.4460i 1.43906i 0.694461 + 0.719531i \(0.255643\pi\)
−0.694461 + 0.719531i \(0.744357\pi\)
\(6\) 42.6777 + 136.293i 0.483974 + 1.54560i
\(7\) −176.825 −1.36395 −0.681975 0.731375i \(-0.738879\pi\)
−0.681975 + 0.731375i \(0.738879\pi\)
\(8\) −182.680 −1.00918
\(9\) −199.602 + 138.593i −0.821409 + 0.570340i
\(10\) 737.033i 2.33070i
\(11\) −681.939 −1.69928 −0.849638 0.527366i \(-0.823180\pi\)
−0.849638 + 0.527366i \(0.823180\pi\)
\(12\) −241.943 772.659i −0.485021 1.54894i
\(13\) 634.160i 1.04074i −0.853942 0.520368i \(-0.825795\pi\)
0.853942 0.520368i \(-0.174205\pi\)
\(14\) 1620.04 2.20905
\(15\) 1196.73 374.733i 1.37331 0.430026i
\(16\) 11.6301 0.0113576
\(17\) 1790.65i 1.50276i 0.659872 + 0.751378i \(0.270610\pi\)
−0.659872 + 0.751378i \(0.729390\pi\)
\(18\) 1828.72 1269.76i 1.33035 0.923722i
\(19\) −2481.42 −1.57694 −0.788471 0.615072i \(-0.789127\pi\)
−0.788471 + 0.615072i \(0.789127\pi\)
\(20\) 4178.30i 2.33574i
\(21\) 823.686 + 2630.48i 0.407581 + 1.30163i
\(22\) 6247.82 2.75215
\(23\) −3057.87 −1.20531 −0.602655 0.798002i \(-0.705891\pi\)
−0.602655 + 0.798002i \(0.705891\pi\)
\(24\) 850.961 + 2717.59i 0.301565 + 0.963064i
\(25\) −3346.56 −1.07090
\(26\) 5810.07i 1.68558i
\(27\) 2991.52 + 2323.73i 0.789736 + 0.613446i
\(28\) −9184.16 −2.21383
\(29\) 546.719i 0.120717i −0.998177 0.0603586i \(-0.980776\pi\)
0.998177 0.0603586i \(-0.0192244\pi\)
\(30\) −10964.2 + 3433.25i −2.22421 + 0.696469i
\(31\) 555.314i 0.103785i 0.998653 + 0.0518925i \(0.0165253\pi\)
−0.998653 + 0.0518925i \(0.983475\pi\)
\(32\) 5739.21 0.990780
\(33\) 3176.61 + 10144.7i 0.507784 + 1.62163i
\(34\) 16405.6i 2.43386i
\(35\) 14224.9i 1.96281i
\(36\) −10367.2 + 7198.39i −1.33323 + 0.925719i
\(37\) 4130.23i 0.495987i −0.968762 0.247993i \(-0.920229\pi\)
0.968762 0.247993i \(-0.0797711\pi\)
\(38\) 22734.3 2.55401
\(39\) −9433.89 + 2954.05i −0.993183 + 0.310997i
\(40\) 14695.9i 1.45227i
\(41\) 14697.6i 1.36548i 0.730661 + 0.682740i \(0.239212\pi\)
−0.730661 + 0.682740i \(0.760788\pi\)
\(42\) −7546.48 24100.1i −0.660117 2.10812i
\(43\) 19748.6i 1.62879i 0.580312 + 0.814394i \(0.302931\pi\)
−0.580312 + 0.814394i \(0.697069\pi\)
\(44\) −35419.4 −2.75810
\(45\) −11149.2 16057.2i −0.820754 1.18206i
\(46\) 28015.7 1.95212
\(47\) −10422.4 −0.688213 −0.344107 0.938931i \(-0.611818\pi\)
−0.344107 + 0.938931i \(0.611818\pi\)
\(48\) −54.1755 173.012i −0.00339391 0.0108386i
\(49\) 14460.1 0.860360
\(50\) 30660.6 1.73443
\(51\) 26638.1 8341.20i 1.43409 0.449059i
\(52\) 32937.8i 1.68922i
\(53\) 8205.73i 0.401262i −0.979667 0.200631i \(-0.935701\pi\)
0.979667 0.200631i \(-0.0642991\pi\)
\(54\) −27407.8 21289.7i −1.27906 0.993537i
\(55\) 54859.3i 2.44536i
\(56\) 32302.4 1.37646
\(57\) 11558.9 + 36914.0i 0.471227 + 1.50489i
\(58\) 5008.95i 0.195514i
\(59\) 24643.1 10375.2i 0.921647 0.388030i
\(60\) 62157.3 19463.4i 2.22902 0.697975i
\(61\) 24796.7i 0.853238i −0.904432 0.426619i \(-0.859705\pi\)
0.904432 0.426619i \(-0.140295\pi\)
\(62\) 5087.70i 0.168090i
\(63\) 35294.7 24506.6i 1.12036 0.777915i
\(64\) −52953.9 −1.61602
\(65\) 51015.7 1.49768
\(66\) −29103.6 92943.8i −0.822407 2.62640i
\(67\) 1477.02i 0.0401974i 0.999798 + 0.0200987i \(0.00639805\pi\)
−0.999798 + 0.0200987i \(0.993602\pi\)
\(68\) 93005.0i 2.43913i
\(69\) 14244.2 + 45489.4i 0.360175 + 1.15024i
\(70\) 130326.i 3.17896i
\(71\) 45951.7i 1.08182i −0.841080 0.540911i \(-0.818079\pi\)
0.841080 0.540911i \(-0.181921\pi\)
\(72\) 36463.4 25318.1i 0.828945 0.575573i
\(73\) 34710.8i 0.762354i −0.924502 0.381177i \(-0.875519\pi\)
0.924502 0.381177i \(-0.124481\pi\)
\(74\) 37840.5i 0.803299i
\(75\) 15588.9 + 49784.0i 0.320010 + 1.02197i
\(76\) −128883. −2.55954
\(77\) 120584. 2.31773
\(78\) 86431.8 27064.5i 1.60856 0.503690i
\(79\) −15432.4 −0.278205 −0.139102 0.990278i \(-0.544422\pi\)
−0.139102 + 0.990278i \(0.544422\pi\)
\(80\) 935.598i 0.0163442i
\(81\) 20633.2 55326.8i 0.349425 0.936964i
\(82\) 134657.i 2.21153i
\(83\) −29051.1 −0.462878 −0.231439 0.972849i \(-0.574343\pi\)
−0.231439 + 0.972849i \(0.574343\pi\)
\(84\) 42781.6 + 136625.i 0.661545 + 2.11268i
\(85\) −144051. −2.16256
\(86\) 180933.i 2.63798i
\(87\) −8133.10 + 2546.73i −0.115201 + 0.0360732i
\(88\) 124577. 1.71487
\(89\) −114778. −1.53597 −0.767984 0.640469i \(-0.778740\pi\)
−0.767984 + 0.640469i \(0.778740\pi\)
\(90\) 102147. + 147114.i 1.32929 + 1.91446i
\(91\) 112135.i 1.41951i
\(92\) −158823. −1.95634
\(93\) 8260.96 2586.76i 0.0990429 0.0310134i
\(94\) 95488.3 1.11463
\(95\) 199620.i 2.26932i
\(96\) −26734.4 85377.7i −0.296069 0.945510i
\(97\) 56580.8i 0.610576i 0.952260 + 0.305288i \(0.0987528\pi\)
−0.952260 + 0.305288i \(0.901247\pi\)
\(98\) −132481. −1.39344
\(99\) 136117. 94511.7i 1.39580 0.969165i
\(100\) −173818. −1.73818
\(101\) 119797. 1.16854 0.584268 0.811561i \(-0.301382\pi\)
0.584268 + 0.811561i \(0.301382\pi\)
\(102\) −244054. + 76420.7i −2.32265 + 0.727295i
\(103\) 52970.9i 0.491976i 0.969273 + 0.245988i \(0.0791124\pi\)
−0.969273 + 0.245988i \(0.920888\pi\)
\(104\) 115849.i 1.05029i
\(105\) −211612. + 66262.2i −1.87312 + 0.586533i
\(106\) 75179.6i 0.649883i
\(107\) 104552.i 0.882824i 0.897304 + 0.441412i \(0.145522\pi\)
−0.897304 + 0.441412i \(0.854478\pi\)
\(108\) 155377. + 120693.i 1.28182 + 0.995686i
\(109\) 71125.1i 0.573399i −0.958021 0.286699i \(-0.907442\pi\)
0.958021 0.286699i \(-0.0925581\pi\)
\(110\) 502612.i 3.96051i
\(111\) −61442.1 + 19239.4i −0.473324 + 0.148212i
\(112\) −2056.50 −0.0154911
\(113\) −104847. −0.772430 −0.386215 0.922409i \(-0.626218\pi\)
−0.386215 + 0.922409i \(0.626218\pi\)
\(114\) −105901. 338200.i −0.763199 2.43732i
\(115\) 245993.i 1.73452i
\(116\) 28396.2i 0.195936i
\(117\) 87889.9 + 126580.i 0.593573 + 0.854870i
\(118\) −225776. + 95055.6i −1.49270 + 0.628453i
\(119\) 316632.i 2.04968i
\(120\) −218619. + 68456.4i −1.38591 + 0.433971i
\(121\) 303990. 1.88754
\(122\) 227184.i 1.38190i
\(123\) 218644. 68464.1i 1.30309 0.408038i
\(124\) 28842.6i 0.168454i
\(125\) 17823.3i 0.102026i
\(126\) −323364. + 224526.i −1.81454 + 1.25991i
\(127\) −202124. −1.11201 −0.556005 0.831179i \(-0.687667\pi\)
−0.556005 + 0.831179i \(0.687667\pi\)
\(128\) 301500. 1.62653
\(129\) 293784. 91992.8i 1.55437 0.486720i
\(130\) −467397. −2.42565
\(131\) −53541.7 −0.272593 −0.136296 0.990668i \(-0.543520\pi\)
−0.136296 + 0.990668i \(0.543520\pi\)
\(132\) 164991. + 526906.i 0.824185 + 2.63208i
\(133\) 438776. 2.15087
\(134\) 13532.2i 0.0651037i
\(135\) −186935. + 240656.i −0.882787 + 1.13648i
\(136\) 327116.i 1.51654i
\(137\) 158725.i 0.722510i 0.932467 + 0.361255i \(0.117652\pi\)
−0.932467 + 0.361255i \(0.882348\pi\)
\(138\) −130503. 416767.i −0.583340 1.86292i
\(139\) 328342. 1.44142 0.720709 0.693238i \(-0.243816\pi\)
0.720709 + 0.693238i \(0.243816\pi\)
\(140\) 738829.i 3.18584i
\(141\) 48549.6 + 155046.i 0.205654 + 0.656768i
\(142\) 421002.i 1.75212i
\(143\) 432459.i 1.76850i
\(144\) −2321.40 + 1611.85i −0.00932920 + 0.00647767i
\(145\) 43981.4 0.173719
\(146\) 318014.i 1.23471i
\(147\) −67357.9 215111.i −0.257096 0.821049i
\(148\) 214521.i 0.805037i
\(149\) −195395. −0.721019 −0.360509 0.932756i \(-0.617397\pi\)
−0.360509 + 0.932756i \(0.617397\pi\)
\(150\) −142823. 456113.i −0.518287 1.65518i
\(151\) 347241.i 1.23933i −0.784865 0.619667i \(-0.787268\pi\)
0.784865 0.619667i \(-0.212732\pi\)
\(152\) 453306. 1.59141
\(153\) −248171. 357418.i −0.857081 1.23438i
\(154\) −1.10477e6 −3.75379
\(155\) −44672.8 −0.149353
\(156\) −489989. + 153431.i −1.61204 + 0.504779i
\(157\) 477438.i 1.54585i 0.634497 + 0.772925i \(0.281207\pi\)
−0.634497 + 0.772925i \(0.718793\pi\)
\(158\) 141389. 0.450581
\(159\) −122070. + 38223.9i −0.382927 + 0.119906i
\(160\) 461697.i 1.42579i
\(161\) 540707. 1.64398
\(162\) −189038. + 506895.i −0.565929 + 1.51751i
\(163\) 37008.3 0.109101 0.0545507 0.998511i \(-0.482627\pi\)
0.0545507 + 0.998511i \(0.482627\pi\)
\(164\) 763380.i 2.21631i
\(165\) −816097. + 255545.i −2.33363 + 0.730732i
\(166\) 266161. 0.749677
\(167\) 345255.i 0.957963i −0.877825 0.478981i \(-0.841006\pi\)
0.877825 0.478981i \(-0.158994\pi\)
\(168\) −150471. 480537.i −0.411320 1.31357i
\(169\) −30866.4 −0.0831322
\(170\) 1.31977e6 3.50248
\(171\) 495296. 343906.i 1.29531 0.899392i
\(172\) 1.02573e6i 2.64369i
\(173\) 193763. 0.492215 0.246107 0.969243i \(-0.420848\pi\)
0.246107 + 0.969243i \(0.420848\pi\)
\(174\) 74514.1 23332.7i 0.186580 0.0584241i
\(175\) 591755. 1.46065
\(176\) −7931.05 −0.0192996
\(177\) −269135. 318265.i −0.645710 0.763583i
\(178\) 1.05157e6 2.48765
\(179\) −558627. −1.30313 −0.651567 0.758591i \(-0.725888\pi\)
−0.651567 + 0.758591i \(0.725888\pi\)
\(180\) −579082. 833999.i −1.33217 1.91860i
\(181\) 569227. 1.29148 0.645742 0.763556i \(-0.276548\pi\)
0.645742 + 0.763556i \(0.276548\pi\)
\(182\) 1.02737e6i 2.29904i
\(183\) −368881. + 115508.i −0.814252 + 0.254968i
\(184\) 558612. 1.21637
\(185\) 332260. 0.713755
\(186\) −75685.6 + 23699.5i −0.160410 + 0.0502293i
\(187\) 1.22111e6i 2.55360i
\(188\) −541332. −1.11704
\(189\) −528975. 410894.i −1.07716 0.836710i
\(190\) 1.82888e6i 3.67538i
\(191\) 148572. 0.294681 0.147341 0.989086i \(-0.452929\pi\)
0.147341 + 0.989086i \(0.452929\pi\)
\(192\) 246670. + 787753.i 0.482906 + 1.54219i
\(193\) 312887. 0.604637 0.302318 0.953207i \(-0.402239\pi\)
0.302318 + 0.953207i \(0.402239\pi\)
\(194\) 518384.i 0.988889i
\(195\) −237641. 758919.i −0.447543 1.42925i
\(196\) 751045. 1.39645
\(197\) 501783.i 0.921193i 0.887610 + 0.460596i \(0.152364\pi\)
−0.887610 + 0.460596i \(0.847636\pi\)
\(198\) −1.24708e6 + 865901.i −2.26064 + 1.56966i
\(199\) −219905. −0.393642 −0.196821 0.980439i \(-0.563062\pi\)
−0.196821 + 0.980439i \(0.563062\pi\)
\(200\) 611350. 1.08072
\(201\) 21972.4 6880.24i 0.0383607 0.0120119i
\(202\) −1.09756e6 −1.89256
\(203\) 96673.6i 0.164652i
\(204\) 1.38356e6 433236.i 2.32768 0.728868i
\(205\) −1.18236e6 −1.96501
\(206\) 485311.i 0.796804i
\(207\) 610358. 423798.i 0.990053 0.687437i
\(208\) 7375.38i 0.0118202i
\(209\) 1.69218e6 2.67966
\(210\) 1.93875e6 607084.i 3.03371 0.949949i
\(211\) 1.04563e6i 1.61685i −0.588597 0.808426i \(-0.700320\pi\)
0.588597 0.808426i \(-0.299680\pi\)
\(212\) 426199.i 0.651288i
\(213\) −683587. + 214052.i −1.03239 + 0.323274i
\(214\) 957892.i 1.42982i
\(215\) −1.58869e6 −2.34393
\(216\) −546491. 424500.i −0.796982 0.619075i
\(217\) 98193.4i 0.141558i
\(218\) 651637.i 0.928676i
\(219\) −516364. + 161690.i −0.727521 + 0.227810i
\(220\) 2.84935e6i 3.96907i
\(221\) 1.13556e6 1.56397
\(222\) 562922. 176269.i 0.766595 0.240045i
\(223\) 193752. 0.260906 0.130453 0.991455i \(-0.458357\pi\)
0.130453 + 0.991455i \(0.458357\pi\)
\(224\) −1.01484e6 −1.35138
\(225\) 667980. 463808.i 0.879645 0.610776i
\(226\) 960589. 1.25103
\(227\) −890277. −1.14673 −0.573364 0.819301i \(-0.694362\pi\)
−0.573364 + 0.819301i \(0.694362\pi\)
\(228\) 600362. + 1.91729e6i 0.764850 + 2.44259i
\(229\) 354344.i 0.446516i 0.974759 + 0.223258i \(0.0716692\pi\)
−0.974759 + 0.223258i \(0.928331\pi\)
\(230\) 2.25375e6i 2.80922i
\(231\) −561704. 1.79383e6i −0.692592 2.21183i
\(232\) 99874.8i 0.121825i
\(233\) −214265. −0.258560 −0.129280 0.991608i \(-0.541267\pi\)
−0.129280 + 0.991608i \(0.541267\pi\)
\(234\) −805233. 1.15970e6i −0.961351 1.38455i
\(235\) 838440.i 0.990381i
\(236\) 1.27994e6 538879.i 1.49593 0.629812i
\(237\) 71887.0 + 229575.i 0.0831342 + 0.265493i
\(238\) 2.90093e6i 3.31967i
\(239\) 660462.i 0.747916i −0.927446 0.373958i \(-0.878000\pi\)
0.927446 0.373958i \(-0.122000\pi\)
\(240\) 13918.1 4358.20i 0.0155974 0.00488404i
\(241\) 170229. 0.188795 0.0943974 0.995535i \(-0.469908\pi\)
0.0943974 + 0.995535i \(0.469908\pi\)
\(242\) −2.78511e6 −3.05706
\(243\) −919166. 49220.3i −0.998569 0.0534723i
\(244\) 1.28792e6i 1.38489i
\(245\) 1.16325e6i 1.23811i
\(246\) −2.00318e6 + 627257.i −2.11048 + 0.660858i
\(247\) 1.57362e6i 1.64118i
\(248\) 101445.i 0.104737i
\(249\) 135326. + 432169.i 0.138319 + 0.441728i
\(250\) 163294.i 0.165242i
\(251\) 1.67146e6i 1.67460i 0.546744 + 0.837300i \(0.315867\pi\)
−0.546744 + 0.837300i \(0.684133\pi\)
\(252\) 1.83318e6 1.27286e6i 1.81846 1.26264i
\(253\) 2.08528e6 2.04816
\(254\) 1.85183e6 1.80101
\(255\) 671016. + 2.14292e6i 0.646223 + 2.06375i
\(256\) −1.06777e6 −1.01831
\(257\) 774034.i 0.731016i 0.930808 + 0.365508i \(0.119105\pi\)
−0.930808 + 0.365508i \(0.880895\pi\)
\(258\) −2.69160e6 + 842823.i −2.51745 + 0.788292i
\(259\) 730328.i 0.676501i
\(260\) 2.64972e6 2.43089
\(261\) 75771.2 + 109126.i 0.0688498 + 0.0991582i
\(262\) 490541. 0.441491
\(263\) 235538.i 0.209977i −0.994473 0.104988i \(-0.966519\pi\)
0.994473 0.104988i \(-0.0334806\pi\)
\(264\) −580304. 1.85323e6i −0.512443 1.63651i
\(265\) 660118. 0.577440
\(266\) −4.02000e6 −3.48355
\(267\) 534657. + 1.70745e6i 0.458983 + 1.46579i
\(268\) 76715.1i 0.0652445i
\(269\) −1.99154e6 −1.67806 −0.839031 0.544084i \(-0.816877\pi\)
−0.839031 + 0.544084i \(0.816877\pi\)
\(270\) 1.71267e6 2.20485e6i 1.42976 1.84064i
\(271\) −1.86535e6 −1.54290 −0.771448 0.636292i \(-0.780467\pi\)
−0.771448 + 0.636292i \(0.780467\pi\)
\(272\) 20825.5i 0.0170676i
\(273\) 1.66815e6 522349.i 1.35465 0.424184i
\(274\) 1.45421e6i 1.17018i
\(275\) 2.28215e6 1.81975
\(276\) 739831. + 2.36269e6i 0.584601 + 1.86695i
\(277\) 218807. 0.171341 0.0856704 0.996324i \(-0.472697\pi\)
0.0856704 + 0.996324i \(0.472697\pi\)
\(278\) −3.00822e6 −2.33452
\(279\) −76962.4 110842.i −0.0591927 0.0852499i
\(280\) 2.59860e6i 1.98082i
\(281\) 497486.i 0.375851i 0.982183 + 0.187925i \(0.0601763\pi\)
−0.982183 + 0.187925i \(0.939824\pi\)
\(282\) −444804. 1.42050e6i −0.333078 1.06370i
\(283\) 1.69218e6i 1.25597i 0.778224 + 0.627987i \(0.216121\pi\)
−0.778224 + 0.627987i \(0.783879\pi\)
\(284\) 2.38670e6i 1.75591i
\(285\) −2.96958e6 + 929869.i −2.16563 + 0.678125i
\(286\) 3.96212e6i 2.86426i
\(287\) 2.59890e6i 1.86245i
\(288\) −1.14556e6 + 795412.i −0.813836 + 0.565081i
\(289\) −1.78657e6 −1.25827
\(290\) −402950. −0.281356
\(291\) 841707. 263565.i 0.582678 0.182455i
\(292\) 1.80285e6i 1.23738i
\(293\) 536830.i 0.365315i −0.983177 0.182657i \(-0.941530\pi\)
0.983177 0.182657i \(-0.0584699\pi\)
\(294\) 617122. + 1.97081e6i 0.416392 + 1.32977i
\(295\) 834641. + 1.98243e6i 0.558399 + 1.32631i
\(296\) 754511.i 0.500537i
\(297\) −2.04003e6 1.58464e6i −1.34198 1.04242i
\(298\) 1.79017e6 1.16776
\(299\) 1.93918e6i 1.25441i
\(300\) 809677. + 2.58574e6i 0.519408 + 1.65876i
\(301\) 3.49204e6i 2.22159i
\(302\) 3.18136e6i 2.00722i
\(303\) −558038. 1.78212e6i −0.349186 1.11514i
\(304\) −28859.2 −0.0179102
\(305\) 1.99480e6 1.22786
\(306\) 2.27370e6 + 3.27460e6i 1.38813 + 1.99920i
\(307\) 823530. 0.498693 0.249347 0.968414i \(-0.419784\pi\)
0.249347 + 0.968414i \(0.419784\pi\)
\(308\) 6.26304e6 3.76191
\(309\) 788005. 246749.i 0.469497 0.147014i
\(310\) 409285. 0.241892
\(311\) 1.22316e6i 0.717106i 0.933509 + 0.358553i \(0.116730\pi\)
−0.933509 + 0.358553i \(0.883270\pi\)
\(312\) 1.72339e6 539646.i 1.00230 0.313850i
\(313\) 447349.i 0.258099i −0.991638 0.129049i \(-0.958807\pi\)
0.991638 0.129049i \(-0.0411925\pi\)
\(314\) 4.37420e6i 2.50366i
\(315\) 1.97146e6 + 2.83932e6i 1.11947 + 1.61227i
\(316\) −801546. −0.451555
\(317\) 2.24078e6i 1.25242i 0.779654 + 0.626210i \(0.215395\pi\)
−0.779654 + 0.626210i \(0.784605\pi\)
\(318\) 1.11839e6 350201.i 0.620189 0.194200i
\(319\) 372829.i 0.205132i
\(320\) 4.25993e6i 2.32556i
\(321\) 1.55534e6 487026.i 0.842487 0.263809i
\(322\) −4.95387e6 −2.66260
\(323\) 4.44335e6i 2.36976i
\(324\) 1.07167e6 2.87363e6i 0.567153 1.52079i
\(325\) 2.12225e6i 1.11452i
\(326\) −339064. −0.176700
\(327\) −1.05807e6 + 331315.i −0.547199 + 0.171345i
\(328\) 2.68495e6i 1.37801i
\(329\) 1.84294e6 0.938689
\(330\) 7.47695e6 2.34127e6i 3.77955 1.18349i
\(331\) −341059. −0.171104 −0.0855519 0.996334i \(-0.527265\pi\)
−0.0855519 + 0.996334i \(0.527265\pi\)
\(332\) −1.50889e6 −0.751298
\(333\) 572419. + 824404.i 0.282881 + 0.407408i
\(334\) 3.16317e6i 1.55152i
\(335\) −118820. −0.0578466
\(336\) 9579.59 + 30592.9i 0.00462912 + 0.0147833i
\(337\) 359249.i 0.172314i −0.996282 0.0861569i \(-0.972541\pi\)
0.996282 0.0861569i \(-0.0274586\pi\)
\(338\) 282793. 0.134641
\(339\) 488397. + 1.55972e6i 0.230820 + 0.737136i
\(340\) −7.48188e6 −3.51005
\(341\) 378691.i 0.176359i
\(342\) −4.53782e6 + 3.15081e6i −2.09789 + 1.45665i
\(343\) 414995. 0.190462
\(344\) 3.60767e6i 1.64373i
\(345\) −3.65944e6 + 1.14589e6i −1.65526 + 0.518314i
\(346\) −1.77522e6 −0.797191
\(347\) 842913. 0.375802 0.187901 0.982188i \(-0.439832\pi\)
0.187901 + 0.982188i \(0.439832\pi\)
\(348\) −422427. + 132275.i −0.186984 + 0.0585504i
\(349\) 3.55229e6i 1.56115i −0.625060 0.780576i \(-0.714926\pi\)
0.625060 0.780576i \(-0.285074\pi\)
\(350\) −5.42156e6 −2.36567
\(351\) 1.47362e6 1.89710e6i 0.638436 0.821907i
\(352\) −3.91380e6 −1.68361
\(353\) −1.35698e6 −0.579611 −0.289805 0.957086i \(-0.593591\pi\)
−0.289805 + 0.957086i \(0.593591\pi\)
\(354\) 2.46577e6 + 2.91589e6i 1.04579 + 1.23670i
\(355\) 3.69663e6 1.55681
\(356\) −5.96146e6 −2.49303
\(357\) −4.71027e6 + 1.47493e6i −1.95603 + 0.612494i
\(358\) 5.11805e6 2.11056
\(359\) 2.31729e6i 0.948952i −0.880268 0.474476i \(-0.842638\pi\)
0.880268 0.474476i \(-0.157362\pi\)
\(360\) 2.03674e6 + 2.93333e6i 0.828284 + 1.19290i
\(361\) 3.68132e6 1.48674
\(362\) −5.21516e6 −2.09169
\(363\) −1.41605e6 4.52222e6i −0.564042 1.80130i
\(364\) 5.82423e6i 2.30401i
\(365\) 2.79234e6 1.09707
\(366\) 3.37963e6 1.05827e6i 1.31876 0.412945i
\(367\) 155574.i 0.0602935i 0.999545 + 0.0301468i \(0.00959747\pi\)
−0.999545 + 0.0301468i \(0.990403\pi\)
\(368\) −35563.4 −0.0136894
\(369\) −2.03697e6 2.93367e6i −0.778788 1.12162i
\(370\) −3.04412e6 −1.15600
\(371\) 1.45098e6i 0.547301i
\(372\) 429068. 134355.i 0.160757 0.0503379i
\(373\) −763121. −0.284002 −0.142001 0.989867i \(-0.545354\pi\)
−0.142001 + 0.989867i \(0.545354\pi\)
\(374\) 1.11877e7i 4.13580i
\(375\) −265142. + 83024.3i −0.0973646 + 0.0304879i
\(376\) 1.90397e6 0.694528
\(377\) −346708. −0.125635
\(378\) 4.84638e6 + 3.76454e6i 1.74457 + 1.35514i
\(379\) −2.81095e6 −1.00521 −0.502603 0.864518i \(-0.667624\pi\)
−0.502603 + 0.864518i \(0.667624\pi\)
\(380\) 1.03681e7i 3.68333i
\(381\) 941534. + 3.00684e6i 0.332295 + 1.06120i
\(382\) −1.36119e6 −0.477266
\(383\) 3.65382e6i 1.27277i 0.771372 + 0.636385i \(0.219571\pi\)
−0.771372 + 0.636385i \(0.780429\pi\)
\(384\) −1.40445e6 4.48518e6i −0.486046 1.55221i
\(385\) 9.70049e6i 3.33535i
\(386\) −2.86662e6 −0.979269
\(387\) −2.73701e6 3.94186e6i −0.928963 1.33790i
\(388\) 2.93877e6i 0.991027i
\(389\) 2.80517e6i 0.939908i 0.882691 + 0.469954i \(0.155730\pi\)
−0.882691 + 0.469954i \(0.844270\pi\)
\(390\) 2.17723e6 + 6.95309e6i 0.724841 + 2.31482i
\(391\) 5.47557e6i 1.81129i
\(392\) −2.64157e6 −0.868254
\(393\) 249408. + 796497.i 0.0814571 + 0.260137i
\(394\) 4.59725e6i 1.49196i
\(395\) 1.24147e6i 0.400354i
\(396\) 7.06980e6 4.90887e6i 2.26553 1.57305i
\(397\) 2.58042e6i 0.821700i 0.911703 + 0.410850i \(0.134768\pi\)
−0.911703 + 0.410850i \(0.865232\pi\)
\(398\) 2.01473e6 0.637543
\(399\) −2.04391e6 6.52732e6i −0.642730 2.05259i
\(400\) −38920.9 −0.0121628
\(401\) −4.89083e6 −1.51887 −0.759437 0.650581i \(-0.774525\pi\)
−0.759437 + 0.650581i \(0.774525\pi\)
\(402\) −201307. + 63035.6i −0.0621290 + 0.0194545i
\(403\) 352158. 0.108013
\(404\) 6.22217e6 1.89665
\(405\) 4.45082e6 + 1.65986e6i 1.34835 + 0.502844i
\(406\) 885708.i 0.266671i
\(407\) 2.81657e6i 0.842818i
\(408\) −4.86625e6 + 1.52377e6i −1.44725 + 0.453179i
\(409\) 4.39663e6i 1.29961i 0.760103 + 0.649803i \(0.225149\pi\)
−0.760103 + 0.649803i \(0.774851\pi\)
\(410\) 1.08326e7 3.18253
\(411\) 2.36122e6 739373.i 0.689497 0.215903i
\(412\) 2.75127e6i 0.798528i
\(413\) −4.35751e6 + 1.83459e6i −1.25708 + 0.529254i
\(414\) −5.59200e6 + 3.88277e6i −1.60349 + 1.11337i
\(415\) 2.33704e6i 0.666110i
\(416\) 3.63958e6i 1.03114i
\(417\) −1.52948e6 4.88448e6i −0.430730 1.37556i
\(418\) −1.55034e7 −4.33997
\(419\) −5.69297e6 −1.58418 −0.792089 0.610405i \(-0.791007\pi\)
−0.792089 + 0.610405i \(0.791007\pi\)
\(420\) −1.09910e7 + 3.44161e6i −3.04027 + 0.952003i
\(421\) 3.23499e6i 0.889545i 0.895644 + 0.444773i \(0.146716\pi\)
−0.895644 + 0.444773i \(0.853284\pi\)
\(422\) 9.57986e6i 2.61865i
\(423\) 2.08034e6 1.44447e6i 0.565305 0.392515i
\(424\) 1.49902e6i 0.404943i
\(425\) 5.99251e6i 1.60930i
\(426\) 6.26291e6 1.96111e6i 1.67206 0.523574i
\(427\) 4.38468e6i 1.16377i
\(428\) 5.43037e6i 1.43291i
\(429\) 6.43334e6 2.01448e6i 1.68769 0.528469i
\(430\) 1.45554e7 3.79622
\(431\) 3.56169e6 0.923555 0.461778 0.886996i \(-0.347212\pi\)
0.461778 + 0.886996i \(0.347212\pi\)
\(432\) 34791.8 + 27025.3i 0.00896948 + 0.00696726i
\(433\) −3.31805e6 −0.850478 −0.425239 0.905081i \(-0.639810\pi\)
−0.425239 + 0.905081i \(0.639810\pi\)
\(434\) 899632.i 0.229267i
\(435\) −204874. 654275.i −0.0519115 0.165782i
\(436\) 3.69419e6i 0.930685i
\(437\) 7.58784e6 1.90070
\(438\) 4.73084e6 1.48137e6i 1.17829 0.368960i
\(439\) 739530. 0.183145 0.0915724 0.995798i \(-0.470811\pi\)
0.0915724 + 0.995798i \(0.470811\pi\)
\(440\) 1.00217e7i 2.46780i
\(441\) −2.88626e6 + 2.00406e6i −0.706707 + 0.490698i
\(442\) −1.04038e7 −2.53301
\(443\) 4.52167e6 1.09469 0.547343 0.836908i \(-0.315639\pi\)
0.547343 + 0.836908i \(0.315639\pi\)
\(444\) −3.19126e6 + 999282.i −0.768253 + 0.240564i
\(445\) 9.23339e6i 2.21035i
\(446\) −1.77512e6 −0.422563
\(447\) 910187. + 2.90673e6i 0.215457 + 0.688074i
\(448\) 9.36357e6 2.20418
\(449\) 998571.i 0.233756i −0.993146 0.116878i \(-0.962711\pi\)
0.993146 0.116878i \(-0.0372887\pi\)
\(450\) −6.11993e6 + 4.24933e6i −1.42467 + 0.989212i
\(451\) 1.00228e7i 2.32033i
\(452\) −5.44566e6 −1.25373
\(453\) −5.16562e6 + 1.61752e6i −1.18271 + 0.370342i
\(454\) 8.15658e6 1.85724
\(455\) −9.02084e6 −2.04277
\(456\) −2.11159e6 6.74346e6i −0.475551 1.51870i
\(457\) 2.58310e6i 0.578564i −0.957244 0.289282i \(-0.906583\pi\)
0.957244 0.289282i \(-0.0934166\pi\)
\(458\) 3.24644e6i 0.723176i
\(459\) −4.16099e6 + 5.35676e6i −0.921860 + 1.18678i
\(460\) 1.27767e7i 2.81530i
\(461\) 5.67517e6i 1.24373i −0.783124 0.621866i \(-0.786375\pi\)
0.783124 0.621866i \(-0.213625\pi\)
\(462\) 5.14624e6 + 1.64348e7i 1.12172 + 3.58227i
\(463\) 7.42680e6i 1.61009i 0.593216 + 0.805043i \(0.297858\pi\)
−0.593216 + 0.805043i \(0.702142\pi\)
\(464\) 6358.42i 0.00137105i
\(465\) 208095. + 664561.i 0.0446302 + 0.142529i
\(466\) 1.96306e6 0.418764
\(467\) 2.95086e6 0.626118 0.313059 0.949734i \(-0.398646\pi\)
0.313059 + 0.949734i \(0.398646\pi\)
\(468\) 4.56494e6 + 6.57447e6i 0.963430 + 1.38754i
\(469\) 261173.i 0.0548273i
\(470\) 7.68165e6i 1.60402i
\(471\) 7.10245e6 2.22400e6i 1.47522 0.461937i
\(472\) −4.50180e6 + 1.89534e6i −0.930103 + 0.391590i
\(473\) 1.34673e7i 2.76776i
\(474\) −658617. 2.10333e6i −0.134644 0.429993i
\(475\) 8.30420e6 1.68874
\(476\) 1.64456e7i 3.32685i
\(477\) 1.13725e6 + 1.63788e6i 0.228855 + 0.329600i
\(478\) 6.05104e6i 1.21132i
\(479\) 3.16680e6i 0.630640i 0.948985 + 0.315320i \(0.102112\pi\)
−0.948985 + 0.315320i \(0.897888\pi\)
\(480\) 6.86829e6 2.15067e6i 1.36065 0.426061i
\(481\) −2.61923e6 −0.516191
\(482\) −1.55961e6 −0.305772
\(483\) −2.51872e6 8.04367e6i −0.491261 1.56887i
\(484\) 1.57890e7 3.06367
\(485\) −4.55170e6 −0.878657
\(486\) 8.42125e6 + 450949.i 1.61728 + 0.0866037i
\(487\) −4.91557e6 −0.939185 −0.469593 0.882883i \(-0.655599\pi\)
−0.469593 + 0.882883i \(0.655599\pi\)
\(488\) 4.52987e6i 0.861066i
\(489\) −172392. 550543.i −0.0326021 0.104116i
\(490\) 1.06576e7i 2.00524i
\(491\) 1.47985e6i 0.277022i −0.990361 0.138511i \(-0.955768\pi\)
0.990361 0.138511i \(-0.0442316\pi\)
\(492\) 1.13562e7 3.55598e6i 2.11505 0.662287i
\(493\) 978982. 0.181408
\(494\) 1.44172e7i 2.65805i
\(495\) 7.60309e6 + 1.09500e7i 1.39469 + 2.00864i
\(496\) 6458.38i 0.00117874i
\(497\) 8.12541e6i 1.47555i
\(498\) −1.23983e6 3.95946e6i −0.224021 0.715423i
\(499\) 394162. 0.0708637 0.0354318 0.999372i \(-0.488719\pi\)
0.0354318 + 0.999372i \(0.488719\pi\)
\(500\) 925728.i 0.165599i
\(501\) −5.13608e6 + 1.60827e6i −0.914192 + 0.286262i
\(502\) 1.53136e7i 2.71218i
\(503\) 5.69031e6 1.00280 0.501402 0.865214i \(-0.332818\pi\)
0.501402 + 0.865214i \(0.332818\pi\)
\(504\) −6.44764e6 + 4.47688e6i −1.13064 + 0.785052i
\(505\) 9.63718e6i 1.68160i
\(506\) −1.91050e7 −3.31719
\(507\) 143782. + 459174.i 0.0248419 + 0.0793337i
\(508\) −1.04982e7 −1.80491
\(509\) 1.16724e6 0.199695 0.0998475 0.995003i \(-0.468165\pi\)
0.0998475 + 0.995003i \(0.468165\pi\)
\(510\) −6.14774e6 1.96331e7i −1.04662 3.34244i
\(511\) 6.13773e6i 1.03981i
\(512\) 134735. 0.0227146
\(513\) −7.42320e6 5.76614e6i −1.24537 0.967369i
\(514\) 7.09157e6i 1.18395i
\(515\) −4.26129e6 −0.707984
\(516\) 1.52589e7 4.77804e6i 2.52290 0.789997i
\(517\) 7.10745e6 1.16946
\(518\) 6.69114e6i 1.09566i
\(519\) −902585. 2.88245e6i −0.147085 0.469725i
\(520\) −9.31955e6 −1.51143
\(521\) 2.30794e6i 0.372503i 0.982502 + 0.186251i \(0.0596339\pi\)
−0.982502 + 0.186251i \(0.940366\pi\)
\(522\) −694203. 999798.i −0.111509 0.160597i
\(523\) −952520. −0.152272 −0.0761359 0.997097i \(-0.524258\pi\)
−0.0761359 + 0.997097i \(0.524258\pi\)
\(524\) −2.78092e6 −0.442446
\(525\) −2.75651e6 8.80306e6i −0.436477 1.39391i
\(526\) 2.15796e6i 0.340078i
\(527\) −994373. −0.155964
\(528\) 36944.4 + 117984.i 0.00576719 + 0.0184178i
\(529\) 2.91421e6 0.452774
\(530\) −6.04789e6 −0.935221
\(531\) −3.48089e6 + 5.48625e6i −0.535740 + 0.844383i
\(532\) 2.27897e7 3.49108
\(533\) 9.32061e6 1.42111
\(534\) −4.89844e6 1.56434e7i −0.743369 2.37399i
\(535\) −8.41082e6 −1.27044
\(536\) 269822.i 0.0405662i
\(537\) 2.60220e6 + 8.31024e6i 0.389407 + 1.24359i
\(538\) 1.82461e7 2.71779
\(539\) −9.86089e6 −1.46199
\(540\) −9.70926e6 + 1.24995e7i −1.43285 + 1.84462i
\(541\) 86095.6i 0.0126470i −0.999980 0.00632350i \(-0.997987\pi\)
0.999980 0.00632350i \(-0.00201285\pi\)
\(542\) 1.70900e7 2.49887
\(543\) −2.65157e6 8.46793e6i −0.385926 1.23247i
\(544\) 1.02769e7i 1.48890i
\(545\) 5.72173e6 0.825156
\(546\) −1.52833e7 + 4.78568e6i −2.19399 + 0.687008i
\(547\) −4.91272e6 −0.702027 −0.351014 0.936370i \(-0.614163\pi\)
−0.351014 + 0.936370i \(0.614163\pi\)
\(548\) 8.24406e6i 1.17271i
\(549\) 3.43664e6 + 4.94949e6i 0.486635 + 0.700857i
\(550\) −2.09087e7 −2.94727
\(551\) 1.35664e6i 0.190364i
\(552\) −2.60213e6 8.31002e6i −0.363480 1.16079i
\(553\) 2.72883e6 0.379458
\(554\) −2.00467e6 −0.277504
\(555\) −1.54773e6 4.94277e6i −0.213287 0.681142i
\(556\) 1.70539e7 2.33957
\(557\) 1.40167e7i 1.91430i −0.289601 0.957148i \(-0.593522\pi\)
0.289601 0.957148i \(-0.406478\pi\)
\(558\) 705117. + 1.01552e6i 0.0958685 + 0.138071i
\(559\) 1.25238e7 1.69514
\(560\) 165437.i 0.0222927i
\(561\) −1.81655e7 + 5.68820e6i −2.43692 + 0.763075i
\(562\) 4.55789e6i 0.608728i
\(563\) 1.49572e7 1.98875 0.994374 0.105929i \(-0.0337817\pi\)
0.994374 + 0.105929i \(0.0337817\pi\)
\(564\) 2.52163e6 + 8.05296e6i 0.333798 + 1.06600i
\(565\) 8.43450e6i 1.11157i
\(566\) 1.55035e7i 2.03417i
\(567\) −3.64847e6 + 9.78316e6i −0.476599 + 1.27797i
\(568\) 8.39447e6i 1.09175i
\(569\) −8.86429e6 −1.14779 −0.573896 0.818928i \(-0.694569\pi\)
−0.573896 + 0.818928i \(0.694569\pi\)
\(570\) 2.72068e7 8.51931e6i 3.50745 1.09829i
\(571\) 5.05196e6i 0.648440i 0.945982 + 0.324220i \(0.105102\pi\)
−0.945982 + 0.324220i \(0.894898\pi\)
\(572\) 2.24616e7i 2.87045i
\(573\) −692076. 2.21018e6i −0.0880577 0.281217i
\(574\) 2.38107e7i 3.01642i
\(575\) 1.02333e7 1.29076
\(576\) 1.05697e7 7.33902e6i 1.32742 0.921683i
\(577\) 3.42759e6 0.428598 0.214299 0.976768i \(-0.431253\pi\)
0.214299 + 0.976768i \(0.431253\pi\)
\(578\) 1.63683e7 2.03790
\(579\) −1.45749e6 4.65457e6i −0.180680 0.577010i
\(580\) 2.28436e6 0.281964
\(581\) 5.13695e6 0.631343
\(582\) −7.71159e6 + 2.41474e6i −0.943705 + 0.295503i
\(583\) 5.59581e6i 0.681854i
\(584\) 6.34097e6i 0.769349i
\(585\) −1.01828e7 + 7.07039e6i −1.23021 + 0.854188i
\(586\) 4.91835e6i 0.591664i
\(587\) −4.69796e6 −0.562749 −0.281374 0.959598i \(-0.590790\pi\)
−0.281374 + 0.959598i \(0.590790\pi\)
\(588\) −3.49852e6 1.11727e7i −0.417293 1.33265i
\(589\) 1.37797e6i 0.163663i
\(590\) −7.64684e6 1.81627e7i −0.904383 2.14808i
\(591\) 7.46462e6 2.33741e6i 0.879102 0.275274i
\(592\) 48035.2i 0.00563320i
\(593\) 1.44386e7i 1.68612i 0.537816 + 0.843062i \(0.319250\pi\)
−0.537816 + 0.843062i \(0.680750\pi\)
\(594\) 1.86905e7 + 1.45183e7i 2.17347 + 1.68829i
\(595\) 2.54717e7 2.94962
\(596\) −1.01486e7 −1.17029
\(597\) 1.02436e6 + 3.27134e6i 0.117630 + 0.375656i
\(598\) 1.77664e7i 2.03164i
\(599\) 6.19040e6i 0.704939i −0.935823 0.352470i \(-0.885342\pi\)
0.935823 0.352470i \(-0.114658\pi\)
\(600\) −2.84779e6 9.09455e6i −0.322946 1.03134i
\(601\) 8.66635e6i 0.978701i 0.872087 + 0.489351i \(0.162766\pi\)
−0.872087 + 0.489351i \(0.837234\pi\)
\(602\) 3.19935e7i 3.59808i
\(603\) −204703. 294816.i −0.0229262 0.0330185i
\(604\) 1.80354e7i 2.01157i
\(605\) 2.44548e7i 2.71629i
\(606\) 5.11265e6 + 1.63275e7i 0.565542 + 1.80609i
\(607\) −1.58133e6 −0.174201 −0.0871006 0.996200i \(-0.527760\pi\)
−0.0871006 + 0.996200i \(0.527760\pi\)
\(608\) −1.42414e7 −1.56240
\(609\) 1.43814e6 450325.i 0.157129 0.0492020i
\(610\) −1.82760e7 −1.98864
\(611\) 6.60947e6i 0.716249i
\(612\) −1.28898e7 1.85640e7i −1.39113 2.00352i
\(613\) 6.50036e6i 0.698693i −0.936994 0.349346i \(-0.886404\pi\)
0.936994 0.349346i \(-0.113596\pi\)
\(614\) −7.54505e6 −0.807684
\(615\) 5.50767e6 + 1.75890e7i 0.587191 + 1.87523i
\(616\) −2.20283e7 −2.33899
\(617\) 1.47931e7i 1.56439i −0.623033 0.782195i \(-0.714100\pi\)
0.623033 0.782195i \(-0.285900\pi\)
\(618\) −7.21958e6 + 2.26067e6i −0.760397 + 0.238104i
\(619\) −1.53234e7 −1.60741 −0.803706 0.595026i \(-0.797142\pi\)
−0.803706 + 0.595026i \(0.797142\pi\)
\(620\) −2.32027e6 −0.242415
\(621\) −9.14766e6 7.10566e6i −0.951878 0.739394i
\(622\) 1.12064e7i 1.16142i
\(623\) 2.02955e7 2.09498
\(624\) −109718. + 34356.0i −0.0112801 + 0.00353216i
\(625\) −9.02418e6 −0.924076
\(626\) 4.09854e6i 0.418016i
\(627\) −7.88249e6 2.51731e7i −0.800745 2.55722i
\(628\) 2.47977e7i 2.50907i
\(629\) 7.39579e6 0.745347
\(630\) −1.80622e7 2.60133e7i −1.81309 2.61123i
\(631\) 2.15806e6 0.215770 0.107885 0.994163i \(-0.465592\pi\)
0.107885 + 0.994163i \(0.465592\pi\)
\(632\) 2.81919e6 0.280758
\(633\) −1.55549e7 + 4.87074e6i −1.54298 + 0.483154i
\(634\) 2.05296e7i 2.02842i
\(635\) 1.62601e7i 1.60025i
\(636\) −6.34023e6 + 1.98532e6i −0.621530 + 0.194620i
\(637\) 9.17001e6i 0.895408i
\(638\) 3.41580e6i 0.332232i
\(639\) 6.36857e6 + 9.17207e6i 0.617006 + 0.888619i
\(640\) 2.42545e7i 2.34068i
\(641\) 4.56382e6i 0.438716i −0.975644 0.219358i \(-0.929604\pi\)
0.975644 0.219358i \(-0.0703962\pi\)
\(642\) −1.42498e7 + 4.46205e6i −1.36449 + 0.427264i
\(643\) 41456.8 0.00395429 0.00197715 0.999998i \(-0.499371\pi\)
0.00197715 + 0.999998i \(0.499371\pi\)
\(644\) 2.80839e7 2.66835
\(645\) 7.40045e6 + 2.36337e7i 0.700421 + 2.23683i
\(646\) 4.07092e7i 3.83806i
\(647\) 2.88969e6i 0.271388i 0.990751 + 0.135694i \(0.0433264\pi\)
−0.990751 + 0.135694i \(0.956674\pi\)
\(648\) −3.76928e6 + 1.01071e7i −0.352631 + 0.945561i
\(649\) −1.68051e7 + 7.07524e6i −1.56613 + 0.659370i
\(650\) 1.94437e7i 1.80508i
\(651\) −1.46074e6 + 457405.i −0.135090 + 0.0423007i
\(652\) 1.92218e6 0.177083
\(653\) 1.31921e7i 1.21068i −0.795966 0.605342i \(-0.793036\pi\)
0.795966 0.605342i \(-0.206964\pi\)
\(654\) 9.69388e6 3.03545e6i 0.886244 0.277510i
\(655\) 4.30722e6i 0.392278i
\(656\) 170935.i 0.0155085i
\(657\) 4.81065e6 + 6.92835e6i 0.434801 + 0.626205i
\(658\) −1.68847e7 −1.52030
\(659\) 9.13543e6 0.819437 0.409718 0.912212i \(-0.365627\pi\)
0.409718 + 0.912212i \(0.365627\pi\)
\(660\) −4.23875e7 + 1.32728e7i −3.78772 + 1.18605i
\(661\) −7.05245e6 −0.627822 −0.313911 0.949452i \(-0.601639\pi\)
−0.313911 + 0.949452i \(0.601639\pi\)
\(662\) 3.12473e6 0.277120
\(663\) −5.28966e6 1.68928e7i −0.467352 1.49251i
\(664\) 5.30705e6 0.467125
\(665\) 3.52978e7i 3.09523i
\(666\) −5.24441e6 7.55305e6i −0.458154 0.659837i
\(667\) 1.67179e6i 0.145502i
\(668\) 1.79323e7i 1.55487i
\(669\) −902534. 2.88229e6i −0.0779648 0.248985i
\(670\) 1.08861e6 0.0936883
\(671\) 1.69099e7i 1.44989i
\(672\) 4.72731e6 + 1.50969e7i 0.403823 + 1.28963i
\(673\) 5.02410e6i 0.427583i 0.976879 + 0.213791i \(0.0685813\pi\)
−0.976879 + 0.213791i \(0.931419\pi\)
\(674\) 3.29138e6i 0.279079i
\(675\) −1.00113e7 7.77650e6i −0.845727 0.656938i
\(676\) −1.60318e6 −0.134932
\(677\) 2.88568e6i 0.241978i −0.992654 0.120989i \(-0.961393\pi\)
0.992654 0.120989i \(-0.0386066\pi\)
\(678\) −4.47462e6 1.42899e7i −0.373836 1.19387i
\(679\) 1.00049e7i 0.832796i
\(680\) 2.63152e7 2.18240
\(681\) 4.14709e6 + 1.32439e7i 0.342670 + 1.09433i
\(682\) 3.46950e6i 0.285632i
\(683\) 2.90899e6 0.238611 0.119306 0.992858i \(-0.461933\pi\)
0.119306 + 0.992858i \(0.461933\pi\)
\(684\) 2.57253e7 1.78622e7i 2.10243 1.45981i
\(685\) −1.27688e7 −1.03974
\(686\) −3.80212e6 −0.308472
\(687\) 5.27129e6 1.65061e6i 0.426114 0.133429i
\(688\) 229679.i 0.0184991i
\(689\) −5.20375e6 −0.417607
\(690\) 3.35272e7 1.04984e7i 2.68086 0.839462i
\(691\) 5.13481e6i 0.409100i −0.978856 0.204550i \(-0.934427\pi\)
0.978856 0.204550i \(-0.0655731\pi\)
\(692\) 1.00639e7 0.798915
\(693\) −2.40688e7 + 1.67120e7i −1.90380 + 1.32189i
\(694\) −7.72263e6 −0.608648
\(695\) 2.64138e7i 2.07429i
\(696\) 1.48576e6 465236.i 0.116258 0.0364041i
\(697\) −2.63182e7 −2.05198
\(698\) 3.25455e7i 2.52844i
\(699\) 998089. + 3.18745e6i 0.0772638 + 0.246746i
\(700\) 3.07353e7 2.37079
\(701\) −1.35238e7 −1.03945 −0.519724 0.854334i \(-0.673965\pi\)
−0.519724 + 0.854334i \(0.673965\pi\)
\(702\) −1.35011e7 + 1.73809e7i −1.03401 + 1.33116i
\(703\) 1.02488e7i 0.782142i
\(704\) 3.61114e7 2.74607
\(705\) −1.24728e7 + 3.90562e6i −0.945129 + 0.295949i
\(706\) 1.24324e7 0.938737
\(707\) −2.11831e7 −1.59383
\(708\) −1.39787e7 1.65305e7i −1.04805 1.23937i
\(709\) 2.23574e6 0.167034 0.0835171 0.996506i \(-0.473385\pi\)
0.0835171 + 0.996506i \(0.473385\pi\)
\(710\) −3.38679e7 −2.52141
\(711\) 3.08034e6 2.13881e6i 0.228520 0.158671i
\(712\) 2.09676e7 1.55006
\(713\) 1.69808e6i 0.125093i
\(714\) 4.31548e7 1.35131e7i 3.16799 0.991995i
\(715\) −3.47896e7 −2.54498
\(716\) −2.90147e7 −2.11512
\(717\) −9.82515e6 + 3.07656e6i −0.713742 + 0.223495i
\(718\) 2.12306e7i 1.53692i
\(719\) 1.93988e7 1.39943 0.699716 0.714421i \(-0.253310\pi\)
0.699716 + 0.714421i \(0.253310\pi\)
\(720\) −129667. 186748.i −0.00932176 0.0134253i
\(721\) 9.36658e6i 0.671031i
\(722\) −3.37277e7 −2.40793
\(723\) −792959. 2.53236e6i −0.0564164 0.180169i
\(724\) 2.95652e7 2.09621
\(725\) 1.82963e6i 0.129276i
\(726\) 1.29736e7 + 4.14318e7i 0.913522 + 2.91738i
\(727\) 1.24094e7 0.870790 0.435395 0.900239i \(-0.356609\pi\)
0.435395 + 0.900239i \(0.356609\pi\)
\(728\) 2.04849e7i 1.43254i
\(729\) 3.54945e6 + 1.39030e7i 0.247367 + 0.968922i
\(730\) −2.55830e7 −1.77682
\(731\) −3.53628e7 −2.44767
\(732\) −1.91594e7 + 5.99941e6i −1.32161 + 0.413838i
\(733\) −1.46720e7 −1.00862 −0.504312 0.863521i \(-0.668254\pi\)
−0.504312 + 0.863521i \(0.668254\pi\)
\(734\) 1.42534e6i 0.0976513i
\(735\) 1.73048e7 5.41867e6i 1.18154 0.369977i
\(736\) −1.75498e7 −1.19420
\(737\) 1.00724e6i 0.0683066i
\(738\) 1.86624e7 + 2.68778e7i 1.26132 + 1.81657i
\(739\) 2.12296e7i 1.42998i −0.699135 0.714990i \(-0.746431\pi\)
0.699135 0.714990i \(-0.253569\pi\)
\(740\) 1.72574e7 1.15850
\(741\) 2.34094e7 7.33021e6i 1.56619 0.490423i
\(742\) 1.32936e7i 0.886408i
\(743\) 9.72699e6i 0.646408i 0.946329 + 0.323204i \(0.104760\pi\)
−0.946329 + 0.323204i \(0.895240\pi\)
\(744\) −1.50911e6 + 472551.i −0.0999516 + 0.0312980i
\(745\) 1.57187e7i 1.03759i
\(746\) 6.99159e6 0.459969
\(747\) 5.79866e6 4.02626e6i 0.380212 0.263998i
\(748\) 6.34238e7i 4.14475i
\(749\) 1.84875e7i 1.20413i
\(750\) 2.42919e6 760656.i 0.157692 0.0493782i
\(751\) 1.37883e7i 0.892093i 0.895010 + 0.446047i \(0.147168\pi\)
−0.895010 + 0.446047i \(0.852832\pi\)
\(752\) −121214. −0.00781643
\(753\) 2.48649e7 7.78598e6i 1.59808 0.500410i
\(754\) 3.17648e6 0.203478
\(755\) 2.79341e7 1.78348
\(756\) −2.74746e7 2.13415e7i −1.74834 1.35807i
\(757\) 1.54228e7 0.978191 0.489096 0.872230i \(-0.337327\pi\)
0.489096 + 0.872230i \(0.337327\pi\)
\(758\) 2.57534e7 1.62803
\(759\) −9.71365e6 3.10210e7i −0.612038 1.95457i
\(760\) 3.64666e7i 2.29014i
\(761\) 1.29251e7i 0.809045i 0.914528 + 0.404522i \(0.132562\pi\)
−0.914528 + 0.404522i \(0.867438\pi\)
\(762\) −8.62618e6 2.75482e7i −0.538185 1.71872i
\(763\) 1.25767e7i 0.782088i
\(764\) 7.71670e6 0.478298
\(765\) 2.87528e7 1.99643e7i 1.77634 1.23339i
\(766\) 3.34757e7i 2.06138i
\(767\) −6.57952e6 1.56276e7i −0.403837 0.959191i
\(768\) 4.97389e6 + 1.58844e7i 0.304294 + 0.971777i
\(769\) 1.01524e7i 0.619089i −0.950885 0.309545i \(-0.899823\pi\)
0.950885 0.309545i \(-0.100177\pi\)
\(770\) 8.88743e7i 5.40194i
\(771\) 1.15147e7 3.60560e6i 0.697615 0.218445i
\(772\) 1.62511e7 0.981387
\(773\) 2.62986e7 1.58301 0.791504 0.611163i \(-0.209298\pi\)
0.791504 + 0.611163i \(0.209298\pi\)
\(774\) 2.50760e7 + 3.61147e7i 1.50455 + 2.16686i
\(775\) 1.85839e6i 0.111143i
\(776\) 1.03362e7i 0.616178i
\(777\) 1.08645e7 3.40201e6i 0.645590 0.202154i
\(778\) 2.57005e7i 1.52227i
\(779\) 3.64707e7i 2.15328i