Properties

Label 177.6.d.b.176.3
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 176.3
Character \(\chi\) \(=\) 177.176
Dual form 177.6.d.b.176.4

$q$-expansion

\(f(q)\) \(=\) \(q-10.7490 q^{2} +(9.69295 + 12.2085i) q^{3} +83.5412 q^{4} +33.1454i q^{5} +(-104.190 - 131.229i) q^{6} -174.539 q^{7} -554.017 q^{8} +(-55.0934 + 236.672i) q^{9} +O(q^{10})\) \(q-10.7490 q^{2} +(9.69295 + 12.2085i) q^{3} +83.5412 q^{4} +33.1454i q^{5} +(-104.190 - 131.229i) q^{6} -174.539 q^{7} -554.017 q^{8} +(-55.0934 + 236.672i) q^{9} -356.281i q^{10} -67.7482 q^{11} +(809.761 + 1019.91i) q^{12} -762.395i q^{13} +1876.13 q^{14} +(-404.655 + 321.277i) q^{15} +3281.82 q^{16} -1054.79i q^{17} +(592.199 - 2543.99i) q^{18} +1517.46 q^{19} +2769.01i q^{20} +(-1691.80 - 2130.86i) q^{21} +728.226 q^{22} -1504.53 q^{23} +(-5370.06 - 6763.70i) q^{24} +2026.38 q^{25} +8194.99i q^{26} +(-3423.42 + 1621.45i) q^{27} -14581.2 q^{28} -4785.21i q^{29} +(4349.64 - 3453.41i) q^{30} +4004.32i q^{31} -17547.8 q^{32} +(-656.680 - 827.102i) q^{33} +11337.9i q^{34} -5785.18i q^{35} +(-4602.57 + 19771.9i) q^{36} -6219.64i q^{37} -16311.1 q^{38} +(9307.68 - 7389.86i) q^{39} -18363.2i q^{40} -14687.7i q^{41} +(18185.2 + 22904.6i) q^{42} +19978.1i q^{43} -5659.77 q^{44} +(-7844.60 - 1826.09i) q^{45} +16172.2 q^{46} +17461.3 q^{47} +(31810.5 + 40066.0i) q^{48} +13657.0 q^{49} -21781.6 q^{50} +(12877.4 - 10224.0i) q^{51} -63691.4i q^{52} +3262.05i q^{53} +(36798.4 - 17428.9i) q^{54} -2245.54i q^{55} +96697.9 q^{56} +(14708.6 + 18525.8i) q^{57} +51436.2i q^{58} +(-16303.5 + 21192.4i) q^{59} +(-33805.4 + 26839.9i) q^{60} -21833.5i q^{61} -43042.5i q^{62} +(9615.97 - 41308.6i) q^{63} +83602.8 q^{64} +25269.9 q^{65} +(7058.66 + 8890.53i) q^{66} -20335.2i q^{67} -88118.3i q^{68} +(-14583.3 - 18368.0i) q^{69} +62185.0i q^{70} +26490.5i q^{71} +(30522.7 - 131121. i) q^{72} +78490.3i q^{73} +66854.9i q^{74} +(19641.6 + 24739.0i) q^{75} +126770. q^{76} +11824.7 q^{77} +(-100048. + 79433.7i) q^{78} +78139.6 q^{79} +108777. i q^{80} +(-52978.4 - 26078.1i) q^{81} +157878. i q^{82} -36801.4 q^{83} +(-141335. - 178015. i) q^{84} +34961.4 q^{85} -214745. i q^{86} +(58420.0 - 46382.8i) q^{87} +37533.7 q^{88} +93253.5 q^{89} +(84321.7 + 19628.7i) q^{90} +133068. i q^{91} -125690. q^{92} +(-48886.7 + 38813.7i) q^{93} -187691. q^{94} +50296.7i q^{95} +(-170090. - 214231. i) q^{96} -42572.4i q^{97} -146799. q^{98} +(3732.48 - 16034.1i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.7490 −1.90017 −0.950087 0.311984i \(-0.899006\pi\)
−0.950087 + 0.311984i \(0.899006\pi\)
\(3\) 9.69295 + 12.2085i 0.621803 + 0.783174i
\(4\) 83.5412 2.61066
\(5\) 33.1454i 0.592924i 0.955045 + 0.296462i \(0.0958068\pi\)
−0.955045 + 0.296462i \(0.904193\pi\)
\(6\) −104.190 131.229i −1.18153 1.48817i
\(7\) −174.539 −1.34632 −0.673160 0.739497i \(-0.735063\pi\)
−0.673160 + 0.739497i \(0.735063\pi\)
\(8\) −554.017 −3.06054
\(9\) −55.0934 + 236.672i −0.226722 + 0.973960i
\(10\) 356.281i 1.12666i
\(11\) −67.7482 −0.168817 −0.0844085 0.996431i \(-0.526900\pi\)
−0.0844085 + 0.996431i \(0.526900\pi\)
\(12\) 809.761 + 1019.91i 1.62332 + 2.04460i
\(13\) 762.395i 1.25119i −0.780150 0.625593i \(-0.784857\pi\)
0.780150 0.625593i \(-0.215143\pi\)
\(14\) 1876.13 2.55824
\(15\) −404.655 + 321.277i −0.464362 + 0.368682i
\(16\) 3281.82 3.20490
\(17\) 1054.79i 0.885203i −0.896718 0.442602i \(-0.854056\pi\)
0.896718 0.442602i \(-0.145944\pi\)
\(18\) 592.199 2543.99i 0.430811 1.85069i
\(19\) 1517.46 0.964344 0.482172 0.876077i \(-0.339848\pi\)
0.482172 + 0.876077i \(0.339848\pi\)
\(20\) 2769.01i 1.54792i
\(21\) −1691.80 2130.86i −0.837146 1.05440i
\(22\) 728.226 0.320782
\(23\) −1504.53 −0.593036 −0.296518 0.955027i \(-0.595826\pi\)
−0.296518 + 0.955027i \(0.595826\pi\)
\(24\) −5370.06 6763.70i −1.90306 2.39694i
\(25\) 2026.38 0.648442
\(26\) 8194.99i 2.37747i
\(27\) −3423.42 + 1621.45i −0.903756 + 0.428049i
\(28\) −14581.2 −3.51479
\(29\) 4785.21i 1.05659i −0.849061 0.528294i \(-0.822832\pi\)
0.849061 0.528294i \(-0.177168\pi\)
\(30\) 4349.64 3453.41i 0.882369 0.700560i
\(31\) 4004.32i 0.748385i 0.927351 + 0.374192i \(0.122080\pi\)
−0.927351 + 0.374192i \(0.877920\pi\)
\(32\) −17547.8 −3.02933
\(33\) −656.680 827.102i −0.104971 0.132213i
\(34\) 11337.9i 1.68204i
\(35\) 5785.18i 0.798265i
\(36\) −4602.57 + 19771.9i −0.591894 + 2.54268i
\(37\) 6219.64i 0.746897i −0.927651 0.373449i \(-0.878175\pi\)
0.927651 0.373449i \(-0.121825\pi\)
\(38\) −16311.1 −1.83242
\(39\) 9307.68 7389.86i 0.979895 0.777991i
\(40\) 18363.2i 1.81467i
\(41\) 14687.7i 1.36457i −0.731088 0.682283i \(-0.760987\pi\)
0.731088 0.682283i \(-0.239013\pi\)
\(42\) 18185.2 + 22904.6i 1.59072 + 2.00355i
\(43\) 19978.1i 1.64772i 0.566795 + 0.823859i \(0.308183\pi\)
−0.566795 + 0.823859i \(0.691817\pi\)
\(44\) −5659.77 −0.440724
\(45\) −7844.60 1826.09i −0.577484 0.134429i
\(46\) 16172.2 1.12687
\(47\) 17461.3 1.15300 0.576502 0.817096i \(-0.304417\pi\)
0.576502 + 0.817096i \(0.304417\pi\)
\(48\) 31810.5 + 40066.0i 1.99282 + 2.50999i
\(49\) 13657.0 0.812578
\(50\) −21781.6 −1.23215
\(51\) 12877.4 10224.0i 0.693268 0.550422i
\(52\) 63691.4i 3.26642i
\(53\) 3262.05i 0.159515i 0.996814 + 0.0797574i \(0.0254146\pi\)
−0.996814 + 0.0797574i \(0.974585\pi\)
\(54\) 36798.4 17428.9i 1.71729 0.813367i
\(55\) 2245.54i 0.100096i
\(56\) 96697.9 4.12047
\(57\) 14708.6 + 18525.8i 0.599632 + 0.755248i
\(58\) 51436.2i 2.00770i
\(59\) −16303.5 + 21192.4i −0.609749 + 0.792594i
\(60\) −33805.4 + 26839.9i −1.21229 + 0.962504i
\(61\) 21833.5i 0.751276i −0.926766 0.375638i \(-0.877424\pi\)
0.926766 0.375638i \(-0.122576\pi\)
\(62\) 43042.5i 1.42206i
\(63\) 9615.97 41308.6i 0.305240 1.31126i
\(64\) 83602.8 2.55136
\(65\) 25269.9 0.741857
\(66\) 7058.66 + 8890.53i 0.199463 + 0.251228i
\(67\) 20335.2i 0.553427i −0.960952 0.276714i \(-0.910755\pi\)
0.960952 0.276714i \(-0.0892454\pi\)
\(68\) 88118.3i 2.31097i
\(69\) −14583.3 18368.0i −0.368752 0.464450i
\(70\) 62185.0i 1.51684i
\(71\) 26490.5i 0.623655i 0.950139 + 0.311827i \(0.100941\pi\)
−0.950139 + 0.311827i \(0.899059\pi\)
\(72\) 30522.7 131121.i 0.693892 2.98085i
\(73\) 78490.3i 1.72389i 0.507003 + 0.861944i \(0.330753\pi\)
−0.507003 + 0.861944i \(0.669247\pi\)
\(74\) 66854.9i 1.41923i
\(75\) 19641.6 + 24739.0i 0.403203 + 0.507842i
\(76\) 126770. 2.51758
\(77\) 11824.7 0.227282
\(78\) −100048. + 79433.7i −1.86197 + 1.47832i
\(79\) 78139.6 1.40865 0.704326 0.709877i \(-0.251249\pi\)
0.704326 + 0.709877i \(0.251249\pi\)
\(80\) 108777.i 1.90026i
\(81\) −52978.4 26078.1i −0.897194 0.441636i
\(82\) 157878.i 2.59291i
\(83\) −36801.4 −0.586366 −0.293183 0.956056i \(-0.594715\pi\)
−0.293183 + 0.956056i \(0.594715\pi\)
\(84\) −141335. 178015.i −2.18551 2.75269i
\(85\) 34961.4 0.524858
\(86\) 214745.i 3.13095i
\(87\) 58420.0 46382.8i 0.827492 0.656990i
\(88\) 37533.7 0.516671
\(89\) 93253.5 1.24793 0.623965 0.781453i \(-0.285521\pi\)
0.623965 + 0.781453i \(0.285521\pi\)
\(90\) 84321.7 + 19628.7i 1.09732 + 0.255438i
\(91\) 133068.i 1.68450i
\(92\) −125690. −1.54822
\(93\) −48886.7 + 38813.7i −0.586115 + 0.465348i
\(94\) −187691. −2.19091
\(95\) 50296.7i 0.571782i
\(96\) −170090. 214231.i −1.88365 2.37249i
\(97\) 42572.4i 0.459408i −0.973261 0.229704i \(-0.926224\pi\)
0.973261 0.229704i \(-0.0737759\pi\)
\(98\) −146799. −1.54404
\(99\) 3732.48 16034.1i 0.0382745 0.164421i
\(100\) 169286. 1.69286
\(101\) 130012. 1.26817 0.634086 0.773262i \(-0.281376\pi\)
0.634086 + 0.773262i \(0.281376\pi\)
\(102\) −138419. + 109898.i −1.31733 + 1.04590i
\(103\) 183784.i 1.70693i −0.521150 0.853465i \(-0.674497\pi\)
0.521150 0.853465i \(-0.325503\pi\)
\(104\) 422380.i 3.82931i
\(105\) 70628.2 56075.5i 0.625180 0.496364i
\(106\) 35063.8i 0.303106i
\(107\) 142238.i 1.20104i −0.799610 0.600519i \(-0.794961\pi\)
0.799610 0.600519i \(-0.205039\pi\)
\(108\) −285997. + 135458.i −2.35940 + 1.11749i
\(109\) 29378.8i 0.236847i 0.992963 + 0.118424i \(0.0377841\pi\)
−0.992963 + 0.118424i \(0.962216\pi\)
\(110\) 24137.4i 0.190199i
\(111\) 75932.2 60286.6i 0.584950 0.464423i
\(112\) −572807. −4.31482
\(113\) −56037.4 −0.412840 −0.206420 0.978464i \(-0.566181\pi\)
−0.206420 + 0.978464i \(0.566181\pi\)
\(114\) −158103. 199134.i −1.13941 1.43510i
\(115\) 49868.3i 0.351625i
\(116\) 399762.i 2.75840i
\(117\) 180438. + 42002.9i 1.21860 + 0.283671i
\(118\) 175247. 227798.i 1.15863 1.50607i
\(119\) 184102.i 1.19177i
\(120\) 224186. 177993.i 1.42120 1.12837i
\(121\) −156461. −0.971501
\(122\) 234689.i 1.42756i
\(123\) 179314. 142367.i 1.06869 0.848491i
\(124\) 334526.i 1.95378i
\(125\) 170745.i 0.977400i
\(126\) −103362. + 444027.i −0.580009 + 2.49163i
\(127\) 339103. 1.86562 0.932808 0.360374i \(-0.117351\pi\)
0.932808 + 0.360374i \(0.117351\pi\)
\(128\) −337120. −1.81869
\(129\) −243902. + 193647.i −1.29045 + 1.02456i
\(130\) −271627. −1.40966
\(131\) 349637. 1.78008 0.890039 0.455884i \(-0.150677\pi\)
0.890039 + 0.455884i \(0.150677\pi\)
\(132\) −54859.9 69097.1i −0.274044 0.345164i
\(133\) −264856. −1.29832
\(134\) 218583.i 1.05161i
\(135\) −53743.5 113471.i −0.253800 0.535858i
\(136\) 584371.i 2.70920i
\(137\) 120090.i 0.546643i −0.961923 0.273322i \(-0.911878\pi\)
0.961923 0.273322i \(-0.0881223\pi\)
\(138\) 156756. + 197438.i 0.700693 + 0.882537i
\(139\) 20574.2 0.0903204 0.0451602 0.998980i \(-0.485620\pi\)
0.0451602 + 0.998980i \(0.485620\pi\)
\(140\) 483301.i 2.08400i
\(141\) 169251. + 213175.i 0.716942 + 0.903003i
\(142\) 284747.i 1.18505i
\(143\) 51650.9i 0.211221i
\(144\) −180807. + 776715.i −0.726621 + 3.12145i
\(145\) 158608. 0.626476
\(146\) 843694.i 3.27569i
\(147\) 132377. + 166731.i 0.505263 + 0.636389i
\(148\) 519596.i 1.94990i
\(149\) −172905. −0.638031 −0.319015 0.947750i \(-0.603352\pi\)
−0.319015 + 0.947750i \(0.603352\pi\)
\(150\) −211128. 265920.i −0.766156 0.964989i
\(151\) 115365.i 0.411747i 0.978579 + 0.205873i \(0.0660035\pi\)
−0.978579 + 0.205873i \(0.933996\pi\)
\(152\) −840697. −2.95142
\(153\) 249639. + 58111.9i 0.862152 + 0.200695i
\(154\) −127104. −0.431875
\(155\) −132725. −0.443735
\(156\) 777575. 617358.i 2.55818 2.03107i
\(157\) 66650.4i 0.215801i −0.994162 0.107901i \(-0.965587\pi\)
0.994162 0.107901i \(-0.0344128\pi\)
\(158\) −839924. −2.67668
\(159\) −39824.7 + 31618.9i −0.124928 + 0.0991868i
\(160\) 581628.i 1.79616i
\(161\) 262600. 0.798417
\(162\) 569466. + 280314.i 1.70483 + 0.839185i
\(163\) −416761. −1.22862 −0.614311 0.789064i \(-0.710566\pi\)
−0.614311 + 0.789064i \(0.710566\pi\)
\(164\) 1.22703e6i 3.56242i
\(165\) 27414.6 21765.9i 0.0783922 0.0622397i
\(166\) 395578. 1.11420
\(167\) 650842.i 1.80586i −0.429785 0.902931i \(-0.641411\pi\)
0.429785 0.902931i \(-0.358589\pi\)
\(168\) 937288. + 1.18053e6i 2.56212 + 3.22704i
\(169\) −209953. −0.565465
\(170\) −375801. −0.997322
\(171\) −83601.7 + 359139.i −0.218638 + 0.939232i
\(172\) 1.66899e6i 4.30164i
\(173\) 203386. 0.516660 0.258330 0.966057i \(-0.416828\pi\)
0.258330 + 0.966057i \(0.416828\pi\)
\(174\) −627958. + 498569.i −1.57238 + 1.24840i
\(175\) −353683. −0.873010
\(176\) −222337. −0.541042
\(177\) −416756. + 6376.39i −0.999883 + 0.0152983i
\(178\) −1.00238e6 −2.37128
\(179\) 465710. 1.08638 0.543192 0.839609i \(-0.317216\pi\)
0.543192 + 0.839609i \(0.317216\pi\)
\(180\) −655348. 152554.i −1.50762 0.350948i
\(181\) 863836. 1.95990 0.979952 0.199234i \(-0.0638455\pi\)
0.979952 + 0.199234i \(0.0638455\pi\)
\(182\) 1.43035e6i 3.20084i
\(183\) 266554. 211631.i 0.588380 0.467146i
\(184\) 833536. 1.81501
\(185\) 206153. 0.442853
\(186\) 525483. 417209.i 1.11372 0.884243i
\(187\) 71460.0i 0.149437i
\(188\) 1.45874e6 3.01011
\(189\) 597522. 283006.i 1.21674 0.576290i
\(190\) 540640.i 1.08649i
\(191\) 560153. 1.11102 0.555512 0.831509i \(-0.312522\pi\)
0.555512 + 0.831509i \(0.312522\pi\)
\(192\) 810358. + 1.02066e6i 1.58644 + 1.99816i
\(193\) 27809.8 0.0537408 0.0268704 0.999639i \(-0.491446\pi\)
0.0268704 + 0.999639i \(0.491446\pi\)
\(194\) 457611.i 0.872956i
\(195\) 244940. + 308507.i 0.461289 + 0.581003i
\(196\) 1.14092e6 2.12137
\(197\) 151601.i 0.278316i −0.990270 0.139158i \(-0.955560\pi\)
0.990270 0.139158i \(-0.0444395\pi\)
\(198\) −40120.4 + 172351.i −0.0727282 + 0.312428i
\(199\) 72452.3 0.129694 0.0648469 0.997895i \(-0.479344\pi\)
0.0648469 + 0.997895i \(0.479344\pi\)
\(200\) −1.12265e6 −1.98458
\(201\) 248261. 197108.i 0.433430 0.344123i
\(202\) −1.39750e6 −2.40975
\(203\) 835207.i 1.42251i
\(204\) 1.07579e6 854127.i 1.80989 1.43697i
\(205\) 486831. 0.809083
\(206\) 1.97550e6i 3.24346i
\(207\) 82889.7 356080.i 0.134454 0.577594i
\(208\) 2.50204e6i 4.00993i
\(209\) −102805. −0.162798
\(210\) −759184. + 602756.i −1.18795 + 0.943178i
\(211\) 923790.i 1.42846i −0.699913 0.714228i \(-0.746778\pi\)
0.699913 0.714228i \(-0.253222\pi\)
\(212\) 272516.i 0.416440i
\(213\) −323408. + 256771.i −0.488430 + 0.387790i
\(214\) 1.52892e6i 2.28218i
\(215\) −662182. −0.976971
\(216\) 1.89664e6 898309.i 2.76598 1.31006i
\(217\) 698912.i 1.00757i
\(218\) 315793.i 0.450051i
\(219\) −958247. + 760803.i −1.35010 + 1.07192i
\(220\) 187596.i 0.261316i
\(221\) −804166. −1.10755
\(222\) −816197. + 648022.i −1.11151 + 0.882485i
\(223\) −290482. −0.391162 −0.195581 0.980688i \(-0.562659\pi\)
−0.195581 + 0.980688i \(0.562659\pi\)
\(224\) 3.06278e6 4.07845
\(225\) −111640. + 479588.i −0.147016 + 0.631556i
\(226\) 602346. 0.784468
\(227\) −1.29140e6 −1.66340 −0.831700 0.555225i \(-0.812632\pi\)
−0.831700 + 0.555225i \(0.812632\pi\)
\(228\) 1.22878e6 + 1.54767e6i 1.56544 + 1.97170i
\(229\) 1.12370e6i 1.41600i −0.706214 0.707998i \(-0.749599\pi\)
0.706214 0.707998i \(-0.250401\pi\)
\(230\) 536035.i 0.668150i
\(231\) 114617. + 144362.i 0.141324 + 0.178001i
\(232\) 2.65109e6i 3.23373i
\(233\) −606409. −0.731772 −0.365886 0.930660i \(-0.619234\pi\)
−0.365886 + 0.930660i \(0.619234\pi\)
\(234\) −1.93953e6 451490.i −2.31556 0.539024i
\(235\) 578761.i 0.683644i
\(236\) −1.36202e6 + 1.77044e6i −1.59185 + 2.06920i
\(237\) 757404. + 953965.i 0.875904 + 1.10322i
\(238\) 1.97892e6i 2.26457i
\(239\) 819859.i 0.928420i 0.885725 + 0.464210i \(0.153662\pi\)
−0.885725 + 0.464210i \(0.846338\pi\)
\(240\) −1.32800e6 + 1.05437e6i −1.48824 + 1.18159i
\(241\) −1.16362e6 −1.29053 −0.645266 0.763958i \(-0.723253\pi\)
−0.645266 + 0.763958i \(0.723253\pi\)
\(242\) 1.68180e6 1.84602
\(243\) −195143. 899560.i −0.212001 0.977269i
\(244\) 1.82400e6i 1.96133i
\(245\) 452667.i 0.481797i
\(246\) −1.92745e6 + 1.53031e6i −2.03070 + 1.61228i
\(247\) 1.15690e6i 1.20657i
\(248\) 2.21847e6i 2.29046i
\(249\) −356714. 449288.i −0.364604 0.459226i
\(250\) 1.83534e6i 1.85723i
\(251\) 1.79587e6i 1.79925i 0.436663 + 0.899625i \(0.356160\pi\)
−0.436663 + 0.899625i \(0.643840\pi\)
\(252\) 803330. 3.45097e6i 0.796879 3.42326i
\(253\) 101929. 0.100115
\(254\) −3.64502e6 −3.54500
\(255\) 338879. + 426825.i 0.326358 + 0.411055i
\(256\) 948411. 0.904476
\(257\) 1.48356e6i 1.40111i −0.713599 0.700554i \(-0.752936\pi\)
0.713599 0.700554i \(-0.247064\pi\)
\(258\) 2.62170e6 2.08151e6i 2.45208 1.94684i
\(259\) 1.08557e6i 1.00556i
\(260\) 2.11108e6 1.93674
\(261\) 1.13253e6 + 263633.i 1.02907 + 0.239552i
\(262\) −3.75825e6 −3.38246
\(263\) 485145.i 0.432496i −0.976338 0.216248i \(-0.930618\pi\)
0.976338 0.216248i \(-0.0693820\pi\)
\(264\) 363812. + 458229.i 0.321268 + 0.404643i
\(265\) −108122. −0.0945801
\(266\) 2.84694e6 2.46703
\(267\) 903901. + 1.13848e6i 0.775966 + 0.977345i
\(268\) 1.69882e6i 1.44481i
\(269\) 324626. 0.273528 0.136764 0.990604i \(-0.456330\pi\)
0.136764 + 0.990604i \(0.456330\pi\)
\(270\) 577690. + 1.21970e6i 0.482265 + 1.01822i
\(271\) −1.01698e6 −0.841179 −0.420589 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(272\) 3.46163e6i 2.83699i
\(273\) −1.62456e6 + 1.28982e6i −1.31925 + 1.04742i
\(274\) 1.29084e6i 1.03872i
\(275\) −137284. −0.109468
\(276\) −1.21831e6 1.53449e6i −0.962687 1.21252i
\(277\) −49056.0 −0.0384143 −0.0192072 0.999816i \(-0.506114\pi\)
−0.0192072 + 0.999816i \(0.506114\pi\)
\(278\) −221152. −0.171624
\(279\) −947712. 220612.i −0.728897 0.169675i
\(280\) 3.20509e6i 2.44312i
\(281\) 720981.i 0.544701i −0.962198 0.272350i \(-0.912199\pi\)
0.962198 0.272350i \(-0.0878010\pi\)
\(282\) −1.81928e6 2.29142e6i −1.36231 1.71586i
\(283\) 1.88644e6i 1.40016i −0.714066 0.700079i \(-0.753148\pi\)
0.714066 0.700079i \(-0.246852\pi\)
\(284\) 2.21305e6i 1.62815i
\(285\) −614046. + 487524.i −0.447805 + 0.355536i
\(286\) 555196.i 0.401357i
\(287\) 2.56358e6i 1.83714i
\(288\) 966766. 4.15307e6i 0.686815 2.95045i
\(289\) 307278. 0.216415
\(290\) −1.70488e6 −1.19041
\(291\) 519744. 412652.i 0.359796 0.285661i
\(292\) 6.55718e6i 4.50049i
\(293\) 645578.i 0.439319i 0.975577 + 0.219659i \(0.0704946\pi\)
−0.975577 + 0.219659i \(0.929505\pi\)
\(294\) −1.42292e6 1.79219e6i −0.960089 1.20925i
\(295\) −702433. 540387.i −0.469948 0.361535i
\(296\) 3.44579e6i 2.28591i
\(297\) 231931. 109850.i 0.152569 0.0722619i
\(298\) 1.85856e6 1.21237
\(299\) 1.14705e6i 0.741999i
\(300\) 1.64088e6 + 2.06673e6i 1.05263 + 1.32581i
\(301\) 3.48696e6i 2.21836i
\(302\) 1.24006e6i 0.782391i
\(303\) 1.26020e6 + 1.58724e6i 0.788554 + 0.993199i
\(304\) 4.98001e6 3.09063
\(305\) 723682. 0.445449
\(306\) −2.68337e6 624645.i −1.63824 0.381355i
\(307\) −820548. −0.496888 −0.248444 0.968646i \(-0.579919\pi\)
−0.248444 + 0.968646i \(0.579919\pi\)
\(308\) 987852. 0.593356
\(309\) 2.24373e6 1.78141e6i 1.33682 1.06137i
\(310\) 1.42666e6 0.843174
\(311\) 1.29992e6i 0.762107i −0.924553 0.381053i \(-0.875561\pi\)
0.924553 0.381053i \(-0.124439\pi\)
\(312\) −5.15661e6 + 4.09411e6i −2.99901 + 2.38107i
\(313\) 769798.i 0.444136i 0.975031 + 0.222068i \(0.0712807\pi\)
−0.975031 + 0.222068i \(0.928719\pi\)
\(314\) 716426.i 0.410060i
\(315\) 1.36919e6 + 318725.i 0.777478 + 0.180984i
\(316\) 6.52788e6 3.67752
\(317\) 1.00921e6i 0.564068i −0.959404 0.282034i \(-0.908991\pi\)
0.959404 0.282034i \(-0.0910092\pi\)
\(318\) 428076. 339872.i 0.237385 0.188472i
\(319\) 324189.i 0.178370i
\(320\) 2.77105e6i 1.51276i
\(321\) 1.73651e6 1.37871e6i 0.940622 0.746810i
\(322\) −2.82269e6 −1.51713
\(323\) 1.60059e6i 0.853640i
\(324\) −4.42588e6 2.17860e6i −2.34227 1.15296i
\(325\) 1.54490e6i 0.811321i
\(326\) 4.47977e6 2.33460
\(327\) −358670. + 284767.i −0.185492 + 0.147272i
\(328\) 8.13725e6i 4.17631i
\(329\) −3.04768e6 −1.55231
\(330\) −294680. + 233962.i −0.148959 + 0.118266i
\(331\) 1.87477e6 0.940539 0.470270 0.882523i \(-0.344157\pi\)
0.470270 + 0.882523i \(0.344157\pi\)
\(332\) −3.07443e6 −1.53080
\(333\) 1.47202e6 + 342661.i 0.727447 + 0.169338i
\(334\) 6.99591e6i 3.43145i
\(335\) 674018. 0.328140
\(336\) −5.55219e6 6.99309e6i −2.68297 3.37926i
\(337\) 1.12324e6i 0.538763i 0.963034 + 0.269381i \(0.0868192\pi\)
−0.963034 + 0.269381i \(0.913181\pi\)
\(338\) 2.25679e6 1.07448
\(339\) −543167. 684130.i −0.256705 0.323325i
\(340\) 2.92072e6 1.37023
\(341\) 271286.i 0.126340i
\(342\) 898636. 3.86039e6i 0.415450 1.78470i
\(343\) 549800. 0.252330
\(344\) 1.10682e7i 5.04291i
\(345\) 608816. 483371.i 0.275384 0.218642i
\(346\) −2.18620e6 −0.981745
\(347\) 827946. 0.369129 0.184565 0.982820i \(-0.440913\pi\)
0.184565 + 0.982820i \(0.440913\pi\)
\(348\) 4.88048e6 3.87487e6i 2.16030 1.71518i
\(349\) 2.51515e6i 1.10535i −0.833396 0.552676i \(-0.813607\pi\)
0.833396 0.552676i \(-0.186393\pi\)
\(350\) 3.80174e6 1.65887
\(351\) 1.23618e6 + 2.61000e6i 0.535568 + 1.13077i
\(352\) 1.18883e6 0.511402
\(353\) 3.47327e6 1.48355 0.741775 0.670649i \(-0.233984\pi\)
0.741775 + 0.670649i \(0.233984\pi\)
\(354\) 4.47972e6 68539.9i 1.89995 0.0290694i
\(355\) −878039. −0.369780
\(356\) 7.79051e6 3.25792
\(357\) −2.24760e6 + 1.78449e6i −0.933360 + 0.741044i
\(358\) −5.00592e6 −2.06432
\(359\) 1.49142e6i 0.610751i −0.952232 0.305376i \(-0.901218\pi\)
0.952232 0.305376i \(-0.0987820\pi\)
\(360\) 4.34605e6 + 1.01169e6i 1.76741 + 0.411425i
\(361\) −173429. −0.0700413
\(362\) −9.28538e6 −3.72416
\(363\) −1.51657e6 1.91015e6i −0.604082 0.760854i
\(364\) 1.11167e7i 4.39765i
\(365\) −2.60160e6 −1.02213
\(366\) −2.86519e6 + 2.27483e6i −1.11802 + 0.887659i
\(367\) 3.83867e6i 1.48770i −0.668346 0.743850i \(-0.732997\pi\)
0.668346 0.743850i \(-0.267003\pi\)
\(368\) −4.93760e6 −1.90062
\(369\) 3.47617e6 + 809196.i 1.32903 + 0.309377i
\(370\) −2.21594e6 −0.841498
\(371\) 569356.i 0.214758i
\(372\) −4.08405e6 + 3.24255e6i −1.53015 + 1.21487i
\(373\) 2.13313e6 0.793862 0.396931 0.917848i \(-0.370075\pi\)
0.396931 + 0.917848i \(0.370075\pi\)
\(374\) 768125.i 0.283957i
\(375\) −2.08453e6 + 1.65502e6i −0.765474 + 0.607750i
\(376\) −9.67384e6 −3.52882
\(377\) −3.64822e6 −1.32199
\(378\) −6.42277e6 + 3.04204e6i −2.31203 + 1.09505i
\(379\) −341863. −0.122252 −0.0611258 0.998130i \(-0.519469\pi\)
−0.0611258 + 0.998130i \(0.519469\pi\)
\(380\) 4.20185e6i 1.49273i
\(381\) 3.28691e6 + 4.13993e6i 1.16005 + 1.46110i
\(382\) −6.02109e6 −2.11114
\(383\) 2.17138e6i 0.756378i −0.925728 0.378189i \(-0.876547\pi\)
0.925728 0.378189i \(-0.123453\pi\)
\(384\) −3.26768e6 4.11571e6i −1.13087 1.42435i
\(385\) 391936.i 0.134761i
\(386\) −298928. −0.102117
\(387\) −4.72826e6 1.10066e6i −1.60481 0.373573i
\(388\) 3.55655e6i 1.19936i
\(389\) 1.49102e6i 0.499586i 0.968299 + 0.249793i \(0.0803625\pi\)
−0.968299 + 0.249793i \(0.919638\pi\)
\(390\) −2.63286e6 3.31615e6i −0.876530 1.10401i
\(391\) 1.58696e6i 0.524958i
\(392\) −7.56621e6 −2.48693
\(393\) 3.38902e6 + 4.26853e6i 1.10686 + 1.39411i
\(394\) 1.62957e6i 0.528848i
\(395\) 2.58997e6i 0.835223i
\(396\) 311816. 1.33951e6i 0.0999218 0.429248i
\(397\) 89427.3i 0.0284770i 0.999899 + 0.0142385i \(0.00453240\pi\)
−0.999899 + 0.0142385i \(0.995468\pi\)
\(398\) −778790. −0.246441
\(399\) −2.56723e6 3.23348e6i −0.807296 1.01681i
\(400\) 6.65021e6 2.07819
\(401\) −1.56878e6 −0.487194 −0.243597 0.969877i \(-0.578327\pi\)
−0.243597 + 0.969877i \(0.578327\pi\)
\(402\) −2.66856e6 + 2.11871e6i −0.823592 + 0.653894i
\(403\) 3.05288e6 0.936368
\(404\) 1.08613e7 3.31077
\(405\) 864372. 1.75599e6i 0.261856 0.531968i
\(406\) 8.97765e6i 2.70301i
\(407\) 421369.i 0.126089i
\(408\) −7.13428e6 + 5.66428e6i −2.12178 + 1.68459i
\(409\) 5.10075e6i 1.50774i −0.657025 0.753869i \(-0.728185\pi\)
0.657025 0.753869i \(-0.271815\pi\)
\(410\) −5.23295e6 −1.53740
\(411\) 1.46611e6 1.16402e6i 0.428117 0.339904i
\(412\) 1.53536e7i 4.45622i
\(413\) 2.84561e6 3.69892e6i 0.820918 1.06709i
\(414\) −890982. + 3.82751e6i −0.255487 + 1.09753i
\(415\) 1.21980e6i 0.347670i
\(416\) 1.33783e7i 3.79026i
\(417\) 199425. + 251179.i 0.0561615 + 0.0707365i
\(418\) 1.10505e6 0.309344
\(419\) 1.49547e6 0.416143 0.208071 0.978114i \(-0.433281\pi\)
0.208071 + 0.978114i \(0.433281\pi\)
\(420\) 5.90037e6 4.68462e6i 1.63214 1.29584i
\(421\) 4.23420e6i 1.16430i 0.813080 + 0.582151i \(0.197789\pi\)
−0.813080 + 0.582151i \(0.802211\pi\)
\(422\) 9.92983e6i 2.71432i
\(423\) −962000. + 4.13259e6i −0.261411 + 1.12298i
\(424\) 1.80723e6i 0.488202i
\(425\) 2.13740e6i 0.574003i
\(426\) 3.47632e6 2.76003e6i 0.928102 0.736870i
\(427\) 3.81081e6i 1.01146i
\(428\) 1.18828e7i 3.13551i
\(429\) −630578. + 500650.i −0.165423 + 0.131338i
\(430\) 7.11781e6 1.85641
\(431\) 2.91462e6 0.755769 0.377885 0.925853i \(-0.376652\pi\)
0.377885 + 0.925853i \(0.376652\pi\)
\(432\) −1.12351e7 + 5.32129e6i −2.89645 + 1.37185i
\(433\) −2.84121e6 −0.728256 −0.364128 0.931349i \(-0.618633\pi\)
−0.364128 + 0.931349i \(0.618633\pi\)
\(434\) 7.51262e6i 1.91455i
\(435\) 1.53738e6 + 1.93636e6i 0.389545 + 0.490640i
\(436\) 2.45434e6i 0.618328i
\(437\) −2.28306e6 −0.571891
\(438\) 1.03002e7 8.17788e6i 2.56543 2.03683i
\(439\) −6.42656e6 −1.59154 −0.795769 0.605600i \(-0.792933\pi\)
−0.795769 + 0.605600i \(0.792933\pi\)
\(440\) 1.24407e6i 0.306347i
\(441\) −752410. + 3.23223e6i −0.184229 + 0.791418i
\(442\) 8.64398e6 2.10455
\(443\) 5.11084e6 1.23732 0.618662 0.785657i \(-0.287675\pi\)
0.618662 + 0.785657i \(0.287675\pi\)
\(444\) 6.34347e6 5.03642e6i 1.52711 1.21245i
\(445\) 3.09093e6i 0.739927i
\(446\) 3.12239e6 0.743277
\(447\) −1.67596e6 2.11090e6i −0.396729 0.499689i
\(448\) −1.45920e7 −3.43494
\(449\) 3.61586e6i 0.846438i −0.906027 0.423219i \(-0.860900\pi\)
0.906027 0.423219i \(-0.139100\pi\)
\(450\) 1.20002e6 5.15509e6i 0.279356 1.20007i
\(451\) 995066.i 0.230362i
\(452\) −4.68143e6 −1.07779
\(453\) −1.40843e6 + 1.11822e6i −0.322469 + 0.256026i
\(454\) 1.38813e7 3.16075
\(455\) −4.41060e6 −0.998778
\(456\) −8.14883e6 1.02636e7i −1.83520 2.31147i
\(457\) 7.99940e6i 1.79171i 0.444350 + 0.895853i \(0.353435\pi\)
−0.444350 + 0.895853i \(0.646565\pi\)
\(458\) 1.20787e7i 2.69064i
\(459\) 1.71028e6 + 3.61099e6i 0.378910 + 0.800008i
\(460\) 4.16606e6i 0.917976i
\(461\) 2.33966e6i 0.512743i −0.966578 0.256372i \(-0.917473\pi\)
0.966578 0.256372i \(-0.0825271\pi\)
\(462\) −1.23201e6 1.55175e6i −0.268541 0.338233i
\(463\) 6.12417e6i 1.32768i 0.747873 + 0.663842i \(0.231075\pi\)
−0.747873 + 0.663842i \(0.768925\pi\)
\(464\) 1.57042e7i 3.38626i
\(465\) −1.28650e6 1.62037e6i −0.275916 0.347522i
\(466\) 6.51829e6 1.39049
\(467\) 2.76756e6 0.587225 0.293612 0.955925i \(-0.405142\pi\)
0.293612 + 0.955925i \(0.405142\pi\)
\(468\) 1.50740e7 + 3.50898e6i 3.18137 + 0.740570i
\(469\) 3.54929e6i 0.745090i
\(470\) 6.22111e6i 1.29904i
\(471\) 813700. 646040.i 0.169010 0.134186i
\(472\) 9.03243e6 1.17410e7i 1.86616 2.42577i
\(473\) 1.35348e6i 0.278163i
\(474\) −8.14134e6 1.02542e7i −1.66437 2.09631i
\(475\) 3.07494e6 0.625320
\(476\) 1.53801e7i 3.11130i
\(477\) −772037. 179717.i −0.155361 0.0361655i
\(478\) 8.81268e6i 1.76416i
\(479\) 3.22713e6i 0.642656i −0.946968 0.321328i \(-0.895871\pi\)
0.946968 0.321328i \(-0.104129\pi\)
\(480\) 7.10079e6 5.63769e6i 1.40671 1.11686i
\(481\) −4.74182e6 −0.934507
\(482\) 1.25078e7 2.45223
\(483\) 2.54537e6 + 3.20594e6i 0.496458 + 0.625299i
\(484\) −1.30710e7 −2.53626
\(485\) 1.41108e6 0.272394
\(486\) 2.09760e6 + 9.66938e6i 0.402839 + 1.85698i
\(487\) 1.97410e6 0.377178 0.188589 0.982056i \(-0.439609\pi\)
0.188589 + 0.982056i \(0.439609\pi\)
\(488\) 1.20962e7i 2.29931i
\(489\) −4.03965e6 5.08802e6i −0.763961 0.962225i
\(490\) 4.86572e6i 0.915498i
\(491\) 8.54422e6i 1.59944i 0.600371 + 0.799722i \(0.295020\pi\)
−0.600371 + 0.799722i \(0.704980\pi\)
\(492\) 1.49801e7 1.18935e7i 2.78999 2.21513i
\(493\) −5.04738e6 −0.935295
\(494\) 1.24355e7i 2.29270i
\(495\) 531458. + 123715.i 0.0974890 + 0.0226938i
\(496\) 1.31415e7i 2.39850i
\(497\) 4.62363e6i 0.839639i
\(498\) 3.83432e6 + 4.82941e6i 0.692812 + 0.872610i
\(499\) −5.53151e6 −0.994472 −0.497236 0.867615i \(-0.665652\pi\)
−0.497236 + 0.867615i \(0.665652\pi\)
\(500\) 1.42642e7i 2.55166i
\(501\) 7.94579e6 6.30858e6i 1.41430 1.12289i
\(502\) 1.93039e7i 3.41889i
\(503\) 2.37831e6 0.419130 0.209565 0.977795i \(-0.432795\pi\)
0.209565 + 0.977795i \(0.432795\pi\)
\(504\) −5.32741e6 + 2.28857e7i −0.934200 + 4.01317i
\(505\) 4.30929e6i 0.751930i
\(506\) −1.09564e6 −0.190235
\(507\) −2.03507e6 2.56321e6i −0.351608 0.442857i
\(508\) 2.83291e7 4.87050
\(509\) −9.30835e6 −1.59250 −0.796248 0.604971i \(-0.793185\pi\)
−0.796248 + 0.604971i \(0.793185\pi\)
\(510\) −3.64262e6 4.58795e6i −0.620138 0.781076i
\(511\) 1.36997e7i 2.32090i
\(512\) 593343. 0.100030
\(513\) −5.19489e6 + 2.46047e6i −0.871531 + 0.412786i
\(514\) 1.59468e7i 2.66235i
\(515\) 6.09162e6 1.01208
\(516\) −2.03759e7 + 1.61775e7i −3.36893 + 2.67477i
\(517\) −1.18297e6 −0.194647
\(518\) 1.16688e7i 1.91074i
\(519\) 1.97141e6 + 2.48303e6i 0.321261 + 0.404635i
\(520\) −1.40000e7 −2.27049
\(521\) 7.87657e6i 1.27129i −0.771983 0.635643i \(-0.780735\pi\)
0.771983 0.635643i \(-0.219265\pi\)
\(522\) −1.21735e7 2.83380e6i −1.95542 0.455190i
\(523\) −715534. −0.114387 −0.0571934 0.998363i \(-0.518215\pi\)
−0.0571934 + 0.998363i \(0.518215\pi\)
\(524\) 2.92091e7 4.64719
\(525\) −3.42823e6 4.31793e6i −0.542840 0.683718i
\(526\) 5.21483e6i 0.821818i
\(527\) 4.22372e6 0.662473
\(528\) −2.15511e6 2.71440e6i −0.336421 0.423730i
\(529\) −4.17273e6 −0.648308
\(530\) 1.16221e6 0.179719
\(531\) −4.11745e6 5.02615e6i −0.633712 0.773569i
\(532\) −2.21264e7 −3.38946
\(533\) −1.11978e7 −1.70732
\(534\) −9.71605e6 1.22376e7i −1.47447 1.85713i
\(535\) 4.71455e6 0.712124
\(536\) 1.12660e7i 1.69379i
\(537\) 4.51411e6 + 5.68561e6i 0.675517 + 0.850827i
\(538\) −3.48941e6 −0.519752
\(539\) −925237. −0.137177
\(540\) −4.48980e6 9.47949e6i −0.662587 1.39895i
\(541\) 5.55517e6i 0.816027i 0.912976 + 0.408013i \(0.133778\pi\)
−0.912976 + 0.408013i \(0.866222\pi\)
\(542\) 1.09315e7 1.59839
\(543\) 8.37312e6 + 1.05461e7i 1.21867 + 1.53494i
\(544\) 1.85092e7i 2.68157i
\(545\) −973774. −0.140432
\(546\) 1.74624e7 1.38643e7i 2.50681 1.99029i
\(547\) −2.56306e6 −0.366261 −0.183131 0.983089i \(-0.558623\pi\)
−0.183131 + 0.983089i \(0.558623\pi\)
\(548\) 1.00324e7i 1.42710i
\(549\) 5.16739e6 + 1.20288e6i 0.731712 + 0.170331i
\(550\) 1.47566e6 0.208008
\(551\) 7.26134e6i 1.01891i
\(552\) 8.07942e6 + 1.01762e7i 1.12858 + 1.42147i
\(553\) −1.36384e7 −1.89650
\(554\) 527304. 0.0729939
\(555\) 1.99823e6 + 2.51681e6i 0.275367 + 0.346831i
\(556\) 1.71879e6 0.235796
\(557\) 7.81111e6i 1.06678i −0.845870 0.533390i \(-0.820918\pi\)
0.845870 0.533390i \(-0.179082\pi\)
\(558\) 1.01870e7 + 2.37136e6i 1.38503 + 0.322412i
\(559\) 1.52312e7 2.06160
\(560\) 1.89859e7i 2.55836i
\(561\) −872417. + 692658.i −0.117035 + 0.0929206i
\(562\) 7.74984e6i 1.03503i
\(563\) 2.06962e6 0.275182 0.137591 0.990489i \(-0.456064\pi\)
0.137591 + 0.990489i \(0.456064\pi\)
\(564\) 1.41395e7 + 1.78089e7i 1.87169 + 2.35744i
\(565\) 1.85738e6i 0.244782i
\(566\) 2.02774e7i 2.66054i
\(567\) 9.24682e6 + 4.55166e6i 1.20791 + 0.594583i
\(568\) 1.46762e7i 1.90872i
\(569\) −4.95942e6 −0.642170 −0.321085 0.947050i \(-0.604047\pi\)
−0.321085 + 0.947050i \(0.604047\pi\)
\(570\) 6.60039e6 5.24040e6i 0.850907 0.675580i
\(571\) 1.32636e7i 1.70244i −0.524809 0.851220i \(-0.675863\pi\)
0.524809 0.851220i \(-0.324137\pi\)
\(572\) 4.31498e6i 0.551428i
\(573\) 5.42954e6 + 6.83861e6i 0.690838 + 0.870124i
\(574\) 2.75560e7i 3.49089i
\(575\) −3.04875e6 −0.384549
\(576\) −4.60596e6 + 1.97865e7i −0.578448 + 2.48492i
\(577\) −5.63487e6 −0.704603 −0.352302 0.935887i \(-0.614601\pi\)
−0.352302 + 0.935887i \(0.614601\pi\)
\(578\) −3.30294e6 −0.411226
\(579\) 269559. + 339515.i 0.0334162 + 0.0420884i
\(580\) 1.32503e7 1.63552
\(581\) 6.42329e6 0.789436
\(582\) −5.58673e6 + 4.43560e6i −0.683676 + 0.542807i
\(583\) 220998.i 0.0269288i
\(584\) 4.34850e7i 5.27603i
\(585\) −1.39221e6 + 5.98069e6i −0.168195 + 0.722539i
\(586\) 6.93933e6i 0.834783i
\(587\) −2.95346e6 −0.353782 −0.176891 0.984230i \(-0.556604\pi\)
−0.176891 + 0.984230i \(0.556604\pi\)
\(588\) 1.10589e7 + 1.39289e7i 1.31907 + 1.66140i
\(589\) 6.07638e6i 0.721700i
\(590\) 7.55046e6 + 5.80863e6i 0.892983 + 0.686979i
\(591\) 1.85082e6 1.46947e6i 0.217970 0.173058i
\(592\) 2.04117e7i 2.39373i
\(593\) 2.61462e6i 0.305331i 0.988278 + 0.152666i \(0.0487858\pi\)
−0.988278 + 0.152666i \(0.951214\pi\)
\(594\) −2.49303e6 + 1.18078e6i −0.289908 + 0.137310i
\(595\) −6.10215e6 −0.706627
\(596\) −1.44447e7 −1.66568
\(597\) 702276. + 884531.i 0.0806440 + 0.101573i
\(598\) 1.23296e7i 1.40993i
\(599\) 5.62418e6i 0.640460i −0.947340 0.320230i \(-0.896240\pi\)
0.947340 0.320230i \(-0.103760\pi\)
\(600\) −1.08818e7 1.37058e7i −1.23402 1.55427i
\(601\) 9.21924e6i 1.04114i 0.853819 + 0.520570i \(0.174280\pi\)
−0.853819 + 0.520570i \(0.825720\pi\)
\(602\) 3.74814e7i 4.21526i
\(603\) 4.81277e6 + 1.12033e6i 0.539016 + 0.125474i
\(604\) 9.63771e6i 1.07493i
\(605\) 5.18597e6i 0.576026i
\(606\) −1.35459e7 1.70613e7i −1.49839 1.88725i
\(607\) 6.39908e6 0.704930 0.352465 0.935825i \(-0.385344\pi\)
0.352465 + 0.935825i \(0.385344\pi\)
\(608\) −2.66279e7 −2.92132
\(609\) −1.01966e7 + 8.09562e6i −1.11407 + 0.884518i
\(610\) −7.77887e6 −0.846432
\(611\) 1.33124e7i 1.44262i
\(612\) 2.08552e7 + 4.85474e6i 2.25079 + 0.523947i
\(613\) 1.13754e7i 1.22269i −0.791366 0.611343i \(-0.790630\pi\)
0.791366 0.611343i \(-0.209370\pi\)
\(614\) 8.82008e6 0.944173
\(615\) 4.71882e6 + 5.94346e6i 0.503090 + 0.633653i
\(616\) −6.55111e6 −0.695605
\(617\) 4.96198e6i 0.524737i 0.964968 + 0.262369i \(0.0845036\pi\)
−0.964968 + 0.262369i \(0.915496\pi\)
\(618\) −2.41178e7 + 1.91484e7i −2.54020 + 2.01680i
\(619\) 7.34946e6 0.770955 0.385477 0.922717i \(-0.374037\pi\)
0.385477 + 0.922717i \(0.374037\pi\)
\(620\) −1.10880e7 −1.15844
\(621\) 5.15064e6 2.43951e6i 0.535960 0.253848i
\(622\) 1.39729e7i 1.44814i
\(623\) −1.62764e7 −1.68011
\(624\) 3.05461e7 2.42522e7i 3.14047 2.49339i
\(625\) 673027. 0.0689180
\(626\) 8.27457e6i 0.843936i
\(627\) −996482. 1.25509e6i −0.101228 0.127499i
\(628\) 5.56806e6i 0.563384i
\(629\) −6.56040e6 −0.661156
\(630\) −1.47175e7 3.42598e6i −1.47734 0.343901i
\(631\) −5.08043e6 −0.507957 −0.253979 0.967210i \(-0.581739\pi\)
−0.253979 + 0.967210i \(0.581739\pi\)
\(632\) −4.32907e7 −4.31124
\(633\) 1.12781e7 8.95425e6i 1.11873 0.888219i
\(634\) 1.08480e7i 1.07183i
\(635\) 1.12397e7i 1.10617i
\(636\) −3.32700e6 + 2.64148e6i −0.326145 + 0.258944i
\(637\) 1.04120e7i 1.01669i
\(638\) 3.48471e6i 0.338934i
\(639\) −6.26956e6 1.45945e6i −0.607414 0.141396i
\(640\) 1.11740e7i 1.07835i
\(641\) 398727.i 0.0383292i −0.999816 0.0191646i \(-0.993899\pi\)
0.999816 0.0191646i \(-0.00610066\pi\)
\(642\) −1.86658e7 + 1.48198e7i −1.78735 + 1.41907i
\(643\) 1.90598e7 1.81799 0.908994 0.416810i \(-0.136852\pi\)
0.908994 + 0.416810i \(0.136852\pi\)
\(644\) 2.19379e7 2.08440
\(645\) −6.41850e6 8.08423e6i −0.607483 0.765138i
\(646\) 1.72048e7i 1.62207i
\(647\) 1.69729e7i 1.59403i 0.603963 + 0.797013i \(0.293588\pi\)
−0.603963 + 0.797013i \(0.706412\pi\)
\(648\) 2.93510e7 + 1.44477e7i 2.74590 + 1.35164i
\(649\) 1.10453e6 1.43575e6i 0.102936 0.133803i
\(650\) 1.66062e7i 1.54165i
\(651\) 8.53265e6 6.77452e6i 0.789099 0.626507i
\(652\) −3.48168e7 −3.20752
\(653\) 5.01672e6i 0.460402i 0.973143 + 0.230201i \(0.0739384\pi\)
−0.973143 + 0.230201i \(0.926062\pi\)
\(654\) 3.85535e6 3.06097e6i 0.352468 0.279843i
\(655\) 1.15889e7i 1.05545i
\(656\) 4.82024e7i 4.37330i
\(657\) −1.85765e7 4.32430e6i −1.67900 0.390843i
\(658\) 3.27595e7 2.94967
\(659\) 1.03472e6 0.0928127 0.0464063 0.998923i \(-0.485223\pi\)
0.0464063 + 0.998923i \(0.485223\pi\)
\(660\) 2.29025e6 1.81835e6i 0.204656 0.162487i
\(661\) 2.39787e6 0.213463 0.106731 0.994288i \(-0.465961\pi\)
0.106731 + 0.994288i \(0.465961\pi\)
\(662\) −2.01519e7 −1.78719
\(663\) −7.79474e6 9.81763e6i −0.688680 0.867407i
\(664\) 2.03886e7 1.79460
\(665\) 8.77876e6i 0.769802i
\(666\) −1.58227e7 3.68327e6i −1.38228 0.321771i
\(667\) 7.19949e6i 0.626595i
\(668\) 5.43722e7i 4.71450i
\(669\) −2.81563e6 3.54634e6i −0.243226 0.306348i
\(670\) −7.24503e6 −0.623524
\(671\) 1.47918e6i 0.126828i
\(672\) 2.96873e7 + 3.73918e7i 2.53599 + 3.19413i
\(673\) 4.67594e6i 0.397952i 0.980004 + 0.198976i \(0.0637617\pi\)
−0.980004 + 0.198976i \(0.936238\pi\)
\(674\) 1.20737e7i 1.02374i
\(675\) −6.93715e6 + 3.28567e6i −0.586033 + 0.277564i
\(676\) −1.75398e7 −1.47624
\(677\) 5.07682e6i 0.425716i 0.977083 + 0.212858i \(0.0682772\pi\)
−0.977083 + 0.212858i \(0.931723\pi\)
\(678\) 5.83851e6 + 7.35372e6i 0.487785 + 0.614374i
\(679\) 7.43056e6i 0.618511i
\(680\) −1.93692e7 −1.60635
\(681\) −1.25175e7 1.57660e7i −1.03431 1.30273i
\(682\) 2.91605e6i 0.240068i
\(683\) −2.30885e7 −1.89384 −0.946921 0.321467i \(-0.895824\pi\)
−0.946921 + 0.321467i \(0.895824\pi\)
\(684\) −6.98419e6 + 3.00030e7i −0.570790 + 2.45202i
\(685\) 3.98042e6 0.324118
\(686\) −5.90981e6 −0.479472
\(687\) 1.37187e7 1.08920e7i 1.10897 0.880471i
\(688\) 6.55645e7i 5.28077i
\(689\) 2.48697e6 0.199583
\(690\) −6.54417e6 + 5.19576e6i −0.523277 + 0.415457i
\(691\) 1.33115e7i 1.06055i −0.847825 0.530277i \(-0.822088\pi\)
0.847825 0.530277i \(-0.177912\pi\)
\(692\) 1.69911e7 1.34883
\(693\) −651464. + 2.79858e6i −0.0515297 + 0.221363i
\(694\) −8.89960e6 −0.701410
\(695\) 681940.i 0.0535531i
\(696\) −3.23657e7 + 2.56969e7i −2.53257 + 2.01075i
\(697\) −1.54924e7 −1.20792
\(698\) 2.70354e7i 2.10036i
\(699\) −5.87789e6 7.40332e6i −0.455018 0.573104i
\(700\) −2.95471e7 −2.27914
\(701\) −9.60518e6 −0.738262 −0.369131 0.929377i \(-0.620345\pi\)
−0.369131 + 0.929377i \(0.620345\pi\)
\(702\) −1.32877e7 2.80549e7i −1.01767 2.14865i
\(703\) 9.43802e6i 0.720265i
\(704\) −5.66394e6 −0.430712
\(705\) −7.06579e6 + 5.60990e6i −0.535412 + 0.425092i
\(706\) −3.73342e7 −2.81900
\(707\) −2.26921e7 −1.70737
\(708\) −3.48164e7 + 532692.i −2.61036 + 0.0399386i
\(709\) 576086. 0.0430400 0.0215200 0.999768i \(-0.493149\pi\)
0.0215200 + 0.999768i \(0.493149\pi\)
\(710\) 9.43805e6 0.702646
\(711\) −4.30498e6 + 1.84935e7i −0.319372 + 1.37197i
\(712\) −5.16640e7 −3.81934
\(713\) 6.02463e6i 0.443820i
\(714\) 2.41595e7 1.91815e7i 1.77355 1.40811i
\(715\) −1.71199e6 −0.125238
\(716\) 3.89060e7 2.83618
\(717\) −1.00092e7 + 7.94686e6i −0.727114 + 0.577295i
\(718\) 1.60313e7i 1.16053i
\(719\) −4.40017e6 −0.317430 −0.158715 0.987324i \(-0.550735\pi\)
−0.158715 + 0.987324i \(0.550735\pi\)
\(720\) −2.57446e7 5.99291e6i −1.85078 0.430831i
\(721\) 3.20776e7i 2.29807i
\(722\) 1.86419e6 0.133091
\(723\) −1.12789e7 1.42060e7i −0.802456 1.01071i
\(724\) 7.21659e7 5.11665
\(725\) 9.69665e6i 0.685136i
\(726\) 1.63016e7 + 2.05322e7i 1.14786 + 1.44576i
\(727\) 8.07553e6 0.566677 0.283338 0.959020i \(-0.408558\pi\)
0.283338 + 0.959020i \(0.408558\pi\)
\(728\) 7.37220e7i 5.15547i
\(729\) 9.09073e6 1.11018e7i 0.633549 0.773703i
\(730\) 2.79646e7 1.94223
\(731\) 2.10727e7 1.45857
\(732\) 2.22683e7 1.76800e7i 1.53606 1.21956i
\(733\) −1.12591e7 −0.774005 −0.387002 0.922079i \(-0.626489\pi\)
−0.387002 + 0.922079i \(0.626489\pi\)
\(734\) 4.12619e7i 2.82689i
\(735\) −5.52637e6 + 4.38768e6i −0.377330 + 0.299583i
\(736\) 2.64011e7 1.79650
\(737\) 1.37767e6i 0.0934279i
\(738\) −3.73654e7 8.69805e6i −2.52539 0.587870i
\(739\) 5.14515e6i 0.346567i 0.984872 + 0.173283i \(0.0554377\pi\)
−0.984872 + 0.173283i \(0.944562\pi\)
\(740\) 1.72222e7 1.15614
\(741\) 1.41240e7 1.12138e7i 0.944956 0.750251i
\(742\) 6.12002e6i 0.408078i
\(743\) 4.93562e6i 0.327997i −0.986461 0.163998i \(-0.947561\pi\)
0.986461 0.163998i \(-0.0524392\pi\)
\(744\) 2.70841e7 2.15035e7i 1.79383 1.42422i
\(745\) 5.73101e6i 0.378303i
\(746\) −2.29290e7 −1.50848
\(747\) 2.02751e6 8.70986e6i 0.132942 0.571097i
\(748\) 5.96986e6i 0.390131i
\(749\) 2.48262e7i 1.61698i
\(750\) 2.24067e7 1.77898e7i 1.45453 1.15483i
\(751\) 8.39631e6i 0.543236i −0.962405 0.271618i \(-0.912441\pi\)
0.962405 0.271618i \(-0.0875588\pi\)
\(752\) 5.73047e7 3.69527
\(753\) −2.19249e7 + 1.74073e7i −1.40913 + 1.11878i
\(754\) 3.92147e7 2.51201
\(755\) −3.82381e6 −0.244134
\(756\) 4.99177e7 2.36427e7i 3.17651 1.50450i
\(757\) 2.42372e7 1.53725 0.768623 0.639703i \(-0.220942\pi\)
0.768623 + 0.639703i \(0.220942\pi\)
\(758\) 3.67469e6 0.232299
\(759\) 987995. + 1.24440e6i 0.0622516 + 0.0784071i
\(760\) 2.78653e7i 1.74996i
\(761\) 6.17608e6i 0.386591i 0.981141 + 0.193295i \(0.0619175\pi\)
−0.981141 + 0.193295i \(0.938082\pi\)
\(762\) −3.53310e7 4.45001e7i −2.20429 2.77635i
\(763\) 5.12776e6i 0.318872i
\(764\) 4.67959e7 2.90051
\(765\) −1.92614e6 + 8.27440e6i −0.118997 + 0.511190i
\(766\) 2.33402e7i 1.43725i
\(767\) 1.61570e7 + 1.24297e7i 0.991683 + 0.762909i
\(768\) 9.19291e6 + 1.15787e7i 0.562406 + 0.708361i
\(769\) 1.75329e7i 1.06915i 0.845121 + 0.534575i \(0.179528\pi\)
−0.845121 + 0.534575i \(0.820472\pi\)
\(770\) 4.21292e6i 0.256069i
\(771\) 1.81120e7 1.43801e7i 1.09731 0.871213i
\(772\) 2.32326e6 0.140299
\(773\) −1.85958e7 −1.11935 −0.559674 0.828713i \(-0.689074\pi\)
−0.559674 + 0.828713i \(0.689074\pi\)
\(774\) 5.08241e7 + 1.18310e7i 3.04942 + 0.709855i
\(775\) 8.11428e6i 0.485284i
\(776\) 2.35859e7i 1.40604i
\(777\) −1.32532e7 + 1.05224e7i −0.787530 + 0.625262i
\(778\) 1.60270e7i 0.949300i
\(779\) 2.22879e7i 1.31591i