Properties

Label 177.5.b.a.119.74
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [177,5,Mod(119,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.119");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.74
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+7.37175i q^{2} +(8.47141 + 3.03895i) q^{3} -38.3427 q^{4} +40.5786i q^{5} +(-22.4024 + 62.4491i) q^{6} +39.1148 q^{7} -164.705i q^{8} +(62.5296 + 51.4883i) q^{9} +O(q^{10})\) \(q+7.37175i q^{2} +(8.47141 + 3.03895i) q^{3} -38.3427 q^{4} +40.5786i q^{5} +(-22.4024 + 62.4491i) q^{6} +39.1148 q^{7} -164.705i q^{8} +(62.5296 + 51.4883i) q^{9} -299.136 q^{10} +101.974i q^{11} +(-324.817 - 116.522i) q^{12} -227.096 q^{13} +288.344i q^{14} +(-123.316 + 343.758i) q^{15} +600.682 q^{16} -150.341i q^{17} +(-379.559 + 460.953i) q^{18} +458.086 q^{19} -1555.90i q^{20} +(331.357 + 118.868i) q^{21} -751.730 q^{22} +193.289i q^{23} +(500.530 - 1395.28i) q^{24} -1021.62 q^{25} -1674.10i q^{26} +(373.243 + 626.203i) q^{27} -1499.77 q^{28} -1038.06i q^{29} +(-2534.10 - 909.057i) q^{30} +1462.33 q^{31} +1792.79i q^{32} +(-309.895 + 863.867i) q^{33} +1108.28 q^{34} +1587.22i q^{35} +(-2397.56 - 1974.20i) q^{36} -693.059 q^{37} +3376.90i q^{38} +(-1923.82 - 690.133i) q^{39} +6683.51 q^{40} +119.484i q^{41} +(-876.263 + 2442.68i) q^{42} +1666.91 q^{43} -3909.98i q^{44} +(-2089.33 + 2537.36i) q^{45} -1424.88 q^{46} -2047.53i q^{47} +(5088.62 + 1825.44i) q^{48} -871.036 q^{49} -7531.16i q^{50} +(456.880 - 1273.60i) q^{51} +8707.48 q^{52} -0.219985i q^{53} +(-4616.21 + 2751.46i) q^{54} -4137.98 q^{55} -6442.40i q^{56} +(3880.63 + 1392.10i) q^{57} +7652.31 q^{58} +453.188i q^{59} +(4728.28 - 13180.6i) q^{60} +7367.02 q^{61} +10779.9i q^{62} +(2445.83 + 2013.95i) q^{63} -3605.13 q^{64} -9215.24i q^{65} +(-6368.21 - 2284.47i) q^{66} -2787.93 q^{67} +5764.50i q^{68} +(-587.394 + 1637.43i) q^{69} -11700.6 q^{70} +8947.65i q^{71} +(8480.39 - 10298.9i) q^{72} -8302.29 q^{73} -5109.06i q^{74} +(-8654.60 - 3104.66i) q^{75} -17564.3 q^{76} +3988.70i q^{77} +(5087.49 - 14181.9i) q^{78} -1825.77 q^{79} +24374.8i q^{80} +(1258.90 + 6439.09i) q^{81} -880.804 q^{82} +10928.3i q^{83} +(-12705.1 - 4557.71i) q^{84} +6100.64 q^{85} +12288.1i q^{86} +(3154.60 - 8793.81i) q^{87} +16795.7 q^{88} -7604.36i q^{89} +(-18704.8 - 15402.0i) q^{90} -8882.80 q^{91} -7411.21i q^{92} +(12388.0 + 4443.95i) q^{93} +15093.9 q^{94} +18588.5i q^{95} +(-5448.21 + 15187.5i) q^{96} -10747.3 q^{97} -6421.06i q^{98} +(-5250.49 + 6376.42i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.37175i 1.84294i 0.388452 + 0.921469i \(0.373010\pi\)
−0.388452 + 0.921469i \(0.626990\pi\)
\(3\) 8.47141 + 3.03895i 0.941268 + 0.337661i
\(4\) −38.3427 −2.39642
\(5\) 40.5786i 1.62314i 0.584252 + 0.811572i \(0.301388\pi\)
−0.584252 + 0.811572i \(0.698612\pi\)
\(6\) −22.4024 + 62.4491i −0.622288 + 1.73470i
\(7\) 39.1148 0.798260 0.399130 0.916894i \(-0.369312\pi\)
0.399130 + 0.916894i \(0.369312\pi\)
\(8\) 164.705i 2.57352i
\(9\) 62.5296 + 51.4883i 0.771970 + 0.635659i
\(10\) −299.136 −2.99136
\(11\) 101.974i 0.842764i 0.906883 + 0.421382i \(0.138455\pi\)
−0.906883 + 0.421382i \(0.861545\pi\)
\(12\) −324.817 116.522i −2.25567 0.809178i
\(13\) −227.096 −1.34376 −0.671882 0.740659i \(-0.734514\pi\)
−0.671882 + 0.740659i \(0.734514\pi\)
\(14\) 288.344i 1.47114i
\(15\) −123.316 + 343.758i −0.548072 + 1.52781i
\(16\) 600.682 2.34641
\(17\) 150.341i 0.520212i −0.965580 0.260106i \(-0.916242\pi\)
0.965580 0.260106i \(-0.0837576\pi\)
\(18\) −379.559 + 460.953i −1.17148 + 1.42269i
\(19\) 458.086 1.26894 0.634468 0.772949i \(-0.281219\pi\)
0.634468 + 0.772949i \(0.281219\pi\)
\(20\) 1555.90i 3.88974i
\(21\) 331.357 + 118.868i 0.751377 + 0.269541i
\(22\) −751.730 −1.55316
\(23\) 193.289i 0.365385i 0.983170 + 0.182692i \(0.0584812\pi\)
−0.983170 + 0.182692i \(0.941519\pi\)
\(24\) 500.530 1395.28i 0.868976 2.42237i
\(25\) −1021.62 −1.63460
\(26\) 1674.10i 2.47647i
\(27\) 373.243 + 626.203i 0.511994 + 0.858989i
\(28\) −1499.77 −1.91297
\(29\) 1038.06i 1.23431i −0.786840 0.617157i \(-0.788284\pi\)
0.786840 0.617157i \(-0.211716\pi\)
\(30\) −2534.10 909.057i −2.81567 1.01006i
\(31\) 1462.33 1.52168 0.760838 0.648942i \(-0.224788\pi\)
0.760838 + 0.648942i \(0.224788\pi\)
\(32\) 1792.79i 1.75078i
\(33\) −309.895 + 863.867i −0.284568 + 0.793266i
\(34\) 1108.28 0.958719
\(35\) 1587.22i 1.29569i
\(36\) −2397.56 1974.20i −1.84997 1.52331i
\(37\) −693.059 −0.506252 −0.253126 0.967433i \(-0.581459\pi\)
−0.253126 + 0.967433i \(0.581459\pi\)
\(38\) 3376.90i 2.33857i
\(39\) −1923.82 690.133i −1.26484 0.453736i
\(40\) 6683.51 4.17719
\(41\) 119.484i 0.0710789i 0.999368 + 0.0355395i \(0.0113149\pi\)
−0.999368 + 0.0355395i \(0.988685\pi\)
\(42\) −876.263 + 2442.68i −0.496748 + 1.38474i
\(43\) 1666.91 0.901520 0.450760 0.892645i \(-0.351153\pi\)
0.450760 + 0.892645i \(0.351153\pi\)
\(44\) 3909.98i 2.01962i
\(45\) −2089.33 + 2537.36i −1.03177 + 1.25302i
\(46\) −1424.88 −0.673382
\(47\) 2047.53i 0.926905i −0.886122 0.463452i \(-0.846611\pi\)
0.886122 0.463452i \(-0.153389\pi\)
\(48\) 5088.62 + 1825.44i 2.20860 + 0.792292i
\(49\) −871.036 −0.362780
\(50\) 7531.16i 3.01246i
\(51\) 456.880 1273.60i 0.175655 0.489659i
\(52\) 8707.48 3.22022
\(53\) 0.219985i 7.83144e-5i −1.00000 3.91572e-5i \(-0.999988\pi\)
1.00000 3.91572e-5i \(-1.24641e-5\pi\)
\(54\) −4616.21 + 2751.46i −1.58306 + 0.943573i
\(55\) −4137.98 −1.36793
\(56\) 6442.40i 2.05434i
\(57\) 3880.63 + 1392.10i 1.19441 + 0.428470i
\(58\) 7652.31 2.27476
\(59\) 453.188i 0.130189i
\(60\) 4728.28 13180.6i 1.31341 3.66129i
\(61\) 7367.02 1.97985 0.989925 0.141594i \(-0.0452229\pi\)
0.989925 + 0.141594i \(0.0452229\pi\)
\(62\) 10779.9i 2.80435i
\(63\) 2445.83 + 2013.95i 0.616233 + 0.507421i
\(64\) −3605.13 −0.880158
\(65\) 9215.24i 2.18112i
\(66\) −6368.21 2284.47i −1.46194 0.524442i
\(67\) −2787.93 −0.621059 −0.310530 0.950564i \(-0.600506\pi\)
−0.310530 + 0.950564i \(0.600506\pi\)
\(68\) 5764.50i 1.24665i
\(69\) −587.394 + 1637.43i −0.123376 + 0.343925i
\(70\) −11700.6 −2.38788
\(71\) 8947.65i 1.77498i 0.460831 + 0.887488i \(0.347551\pi\)
−0.460831 + 0.887488i \(0.652449\pi\)
\(72\) 8480.39 10298.9i 1.63588 1.98668i
\(73\) −8302.29 −1.55794 −0.778972 0.627058i \(-0.784259\pi\)
−0.778972 + 0.627058i \(0.784259\pi\)
\(74\) 5109.06i 0.932991i
\(75\) −8654.60 3104.66i −1.53860 0.551940i
\(76\) −17564.3 −3.04090
\(77\) 3988.70i 0.672745i
\(78\) 5087.49 14181.9i 0.836208 2.33102i
\(79\) −1825.77 −0.292544 −0.146272 0.989244i \(-0.546728\pi\)
−0.146272 + 0.989244i \(0.546728\pi\)
\(80\) 24374.8i 3.80857i
\(81\) 1258.90 + 6439.09i 0.191876 + 0.981419i
\(82\) −880.804 −0.130994
\(83\) 10928.3i 1.58634i 0.608998 + 0.793172i \(0.291572\pi\)
−0.608998 + 0.793172i \(0.708428\pi\)
\(84\) −12705.1 4557.71i −1.80061 0.645934i
\(85\) 6100.64 0.844380
\(86\) 12288.1i 1.66145i
\(87\) 3154.60 8793.81i 0.416779 1.16182i
\(88\) 16795.7 2.16887
\(89\) 7604.36i 0.960025i −0.877262 0.480013i \(-0.840632\pi\)
0.877262 0.480013i \(-0.159368\pi\)
\(90\) −18704.8 15402.0i −2.30924 1.90148i
\(91\) −8882.80 −1.07267
\(92\) 7411.21i 0.875616i
\(93\) 12388.0 + 4443.95i 1.43230 + 0.513810i
\(94\) 15093.9 1.70823
\(95\) 18588.5i 2.05967i
\(96\) −5448.21 + 15187.5i −0.591168 + 1.64795i
\(97\) −10747.3 −1.14224 −0.571119 0.820867i \(-0.693490\pi\)
−0.571119 + 0.820867i \(0.693490\pi\)
\(98\) 6421.06i 0.668582i
\(99\) −5250.49 + 6376.42i −0.535710 + 0.650589i
\(100\) 39171.9 3.91719
\(101\) 9016.80i 0.883913i 0.897037 + 0.441956i \(0.145715\pi\)
−0.897037 + 0.441956i \(0.854285\pi\)
\(102\) 9388.69 + 3368.00i 0.902412 + 0.323722i
\(103\) 11441.8 1.07850 0.539250 0.842146i \(-0.318708\pi\)
0.539250 + 0.842146i \(0.318708\pi\)
\(104\) 37403.9i 3.45820i
\(105\) −4823.49 + 13446.0i −0.437504 + 1.21959i
\(106\) 1.62168 0.000144329
\(107\) 5080.56i 0.443755i 0.975074 + 0.221878i \(0.0712186\pi\)
−0.975074 + 0.221878i \(0.928781\pi\)
\(108\) −14311.2 24010.3i −1.22695 2.05850i
\(109\) −18603.1 −1.56579 −0.782893 0.622157i \(-0.786257\pi\)
−0.782893 + 0.622157i \(0.786257\pi\)
\(110\) 30504.2i 2.52101i
\(111\) −5871.19 2106.17i −0.476519 0.170942i
\(112\) 23495.5 1.87305
\(113\) 20964.8i 1.64185i −0.571038 0.820924i \(-0.693459\pi\)
0.571038 0.820924i \(-0.306541\pi\)
\(114\) −10262.2 + 28607.1i −0.789644 + 2.20122i
\(115\) −7843.38 −0.593072
\(116\) 39802.0i 2.95794i
\(117\) −14200.2 11692.8i −1.03735 0.854175i
\(118\) −3340.79 −0.239930
\(119\) 5880.57i 0.415265i
\(120\) 56618.7 + 20310.8i 3.93186 + 1.41047i
\(121\) 4242.22 0.289749
\(122\) 54307.8i 3.64874i
\(123\) −363.105 + 1012.20i −0.0240006 + 0.0669043i
\(124\) −56069.8 −3.64658
\(125\) 16094.5i 1.03005i
\(126\) −14846.4 + 18030.1i −0.935146 + 1.13568i
\(127\) −29996.7 −1.85980 −0.929900 0.367812i \(-0.880107\pi\)
−0.929900 + 0.367812i \(0.880107\pi\)
\(128\) 2108.59i 0.128698i
\(129\) 14121.1 + 5065.66i 0.848572 + 0.304408i
\(130\) 67932.5 4.01967
\(131\) 10098.3i 0.588445i −0.955737 0.294223i \(-0.904939\pi\)
0.955737 0.294223i \(-0.0950607\pi\)
\(132\) 11882.2 33123.0i 0.681945 1.90100i
\(133\) 17917.9 1.01294
\(134\) 20552.0i 1.14457i
\(135\) −25410.5 + 15145.7i −1.39426 + 0.831040i
\(136\) −24762.0 −1.33878
\(137\) 4692.61i 0.250019i 0.992156 + 0.125010i \(0.0398961\pi\)
−0.992156 + 0.125010i \(0.960104\pi\)
\(138\) −12070.7 4330.12i −0.633832 0.227375i
\(139\) 11174.9 0.578382 0.289191 0.957271i \(-0.406614\pi\)
0.289191 + 0.957271i \(0.406614\pi\)
\(140\) 60858.5i 3.10502i
\(141\) 6222.35 17345.5i 0.312979 0.872466i
\(142\) −65959.9 −3.27117
\(143\) 23158.0i 1.13247i
\(144\) 37560.4 + 30928.1i 1.81136 + 1.49152i
\(145\) 42123.0 2.00347
\(146\) 61202.4i 2.87120i
\(147\) −7378.90 2647.03i −0.341474 0.122497i
\(148\) 26573.8 1.21319
\(149\) 13264.6i 0.597476i 0.954335 + 0.298738i \(0.0965657\pi\)
−0.954335 + 0.298738i \(0.903434\pi\)
\(150\) 22886.8 63799.5i 1.01719 2.83554i
\(151\) 24846.5 1.08971 0.544856 0.838529i \(-0.316584\pi\)
0.544856 + 0.838529i \(0.316584\pi\)
\(152\) 75449.1i 3.26563i
\(153\) 7740.83 9400.78i 0.330677 0.401588i
\(154\) −29403.7 −1.23983
\(155\) 59339.4i 2.46990i
\(156\) 73764.6 + 26461.6i 3.03109 + 1.08734i
\(157\) 16104.2 0.653342 0.326671 0.945138i \(-0.394073\pi\)
0.326671 + 0.945138i \(0.394073\pi\)
\(158\) 13459.1i 0.539141i
\(159\) 0.668524 1.86359i 2.64437e−5 7.37149e-5i
\(160\) −72749.1 −2.84176
\(161\) 7560.44i 0.291672i
\(162\) −47467.4 + 9280.30i −1.80869 + 0.353616i
\(163\) 16936.7 0.637462 0.318731 0.947845i \(-0.396743\pi\)
0.318731 + 0.947845i \(0.396743\pi\)
\(164\) 4581.33i 0.170335i
\(165\) −35054.5 12575.1i −1.28759 0.461896i
\(166\) −80560.9 −2.92353
\(167\) 38560.4i 1.38264i 0.722549 + 0.691320i \(0.242970\pi\)
−0.722549 + 0.691320i \(0.757030\pi\)
\(168\) 19578.1 54576.2i 0.693669 1.93368i
\(169\) 23011.6 0.805700
\(170\) 44972.4i 1.55614i
\(171\) 28643.9 + 23586.1i 0.979581 + 0.806610i
\(172\) −63913.9 −2.16042
\(173\) 10278.6i 0.343431i 0.985147 + 0.171716i \(0.0549310\pi\)
−0.985147 + 0.171716i \(0.945069\pi\)
\(174\) 64825.8 + 23255.0i 2.14116 + 0.768099i
\(175\) −39960.6 −1.30484
\(176\) 61254.1i 1.97747i
\(177\) −1377.21 + 3839.14i −0.0439597 + 0.122543i
\(178\) 56057.5 1.76927
\(179\) 26311.2i 0.821173i −0.911822 0.410587i \(-0.865324\pi\)
0.911822 0.410587i \(-0.134676\pi\)
\(180\) 80110.5 97289.5i 2.47255 3.00276i
\(181\) 7323.15 0.223533 0.111766 0.993735i \(-0.464349\pi\)
0.111766 + 0.993735i \(0.464349\pi\)
\(182\) 65481.8i 1.97687i
\(183\) 62409.1 + 22388.0i 1.86357 + 0.668518i
\(184\) 31835.6 0.940324
\(185\) 28123.4i 0.821720i
\(186\) −32759.7 + 91321.3i −0.946921 + 2.63965i
\(187\) 15331.0 0.438416
\(188\) 78508.0i 2.22125i
\(189\) 14599.3 + 24493.8i 0.408704 + 0.685697i
\(190\) −137030. −3.79584
\(191\) 22139.5i 0.606878i −0.952851 0.303439i \(-0.901865\pi\)
0.952851 0.303439i \(-0.0981349\pi\)
\(192\) −30540.5 10955.8i −0.828465 0.297195i
\(193\) 20014.2 0.537307 0.268654 0.963237i \(-0.413421\pi\)
0.268654 + 0.963237i \(0.413421\pi\)
\(194\) 79226.5i 2.10507i
\(195\) 28004.6 78066.1i 0.736480 2.05302i
\(196\) 33397.9 0.869375
\(197\) 5398.39i 0.139102i 0.997578 + 0.0695508i \(0.0221566\pi\)
−0.997578 + 0.0695508i \(0.977843\pi\)
\(198\) −47005.4 38705.3i −1.19899 0.987280i
\(199\) 31903.3 0.805619 0.402810 0.915284i \(-0.368034\pi\)
0.402810 + 0.915284i \(0.368034\pi\)
\(200\) 168267.i 4.20667i
\(201\) −23617.7 8472.39i −0.584583 0.209707i
\(202\) −66469.6 −1.62900
\(203\) 40603.4i 0.985304i
\(204\) −17518.0 + 48833.4i −0.420944 + 1.17343i
\(205\) −4848.48 −0.115371
\(206\) 84346.1i 1.98761i
\(207\) −9952.11 + 12086.3i −0.232260 + 0.282066i
\(208\) −136412. −3.15302
\(209\) 46713.0i 1.06941i
\(210\) −99120.7 35557.6i −2.24763 0.806294i
\(211\) 58686.4 1.31817 0.659087 0.752067i \(-0.270943\pi\)
0.659087 + 0.752067i \(0.270943\pi\)
\(212\) 8.43484i 0.000187674i
\(213\) −27191.5 + 75799.2i −0.599340 + 1.67073i
\(214\) −37452.6 −0.817814
\(215\) 67641.0i 1.46330i
\(216\) 103139. 61475.1i 2.21062 1.31762i
\(217\) 57198.7 1.21469
\(218\) 137137.i 2.88564i
\(219\) −70332.1 25230.2i −1.46644 0.526057i
\(220\) 158661. 3.27813
\(221\) 34141.9i 0.699042i
\(222\) 15526.2 43280.9i 0.315035 0.878195i
\(223\) 59945.6 1.20545 0.602723 0.797950i \(-0.294082\pi\)
0.602723 + 0.797950i \(0.294082\pi\)
\(224\) 70124.7i 1.39757i
\(225\) −63881.7 52601.7i −1.26186 1.03905i
\(226\) 154547. 3.02582
\(227\) 57698.6i 1.11973i −0.828584 0.559865i \(-0.810853\pi\)
0.828584 0.559865i \(-0.189147\pi\)
\(228\) −148794. 53376.9i −2.86231 1.02679i
\(229\) −38112.5 −0.726770 −0.363385 0.931639i \(-0.618379\pi\)
−0.363385 + 0.931639i \(0.618379\pi\)
\(230\) 57819.5i 1.09300i
\(231\) −12121.5 + 33789.9i −0.227160 + 0.633233i
\(232\) −170973. −3.17653
\(233\) 101881.i 1.87665i −0.345755 0.938325i \(-0.612377\pi\)
0.345755 0.938325i \(-0.387623\pi\)
\(234\) 86196.4 104680.i 1.57419 1.91176i
\(235\) 83086.0 1.50450
\(236\) 17376.5i 0.311987i
\(237\) −15466.8 5548.42i −0.275363 0.0987808i
\(238\) 43350.1 0.765307
\(239\) 31516.2i 0.551745i 0.961194 + 0.275873i \(0.0889668\pi\)
−0.961194 + 0.275873i \(0.911033\pi\)
\(240\) −74073.8 + 206489.i −1.28600 + 3.58488i
\(241\) −3021.93 −0.0520295 −0.0260148 0.999662i \(-0.508282\pi\)
−0.0260148 + 0.999662i \(0.508282\pi\)
\(242\) 31272.6i 0.533990i
\(243\) −8903.41 + 58373.9i −0.150780 + 0.988567i
\(244\) −282472. −4.74455
\(245\) 35345.4i 0.588845i
\(246\) −7461.65 2676.72i −0.123301 0.0442316i
\(247\) −104029. −1.70515
\(248\) 240853.i 3.91606i
\(249\) −33210.6 + 92578.3i −0.535646 + 1.49317i
\(250\) 118644. 1.89831
\(251\) 3350.92i 0.0531883i −0.999646 0.0265941i \(-0.991534\pi\)
0.999646 0.0265941i \(-0.00846618\pi\)
\(252\) −93779.8 77220.5i −1.47675 1.21599i
\(253\) −19710.5 −0.307933
\(254\) 221128.i 3.42750i
\(255\) 51681.1 + 18539.5i 0.794788 + 0.285114i
\(256\) −73226.1 −1.11734
\(257\) 96436.2i 1.46007i −0.683409 0.730035i \(-0.739504\pi\)
0.683409 0.730035i \(-0.260496\pi\)
\(258\) −37342.8 + 104097.i −0.561005 + 1.56387i
\(259\) −27108.8 −0.404121
\(260\) 353338.i 5.22689i
\(261\) 53447.9 64909.3i 0.784602 0.952854i
\(262\) 74442.2 1.08447
\(263\) 113800.i 1.64524i 0.568591 + 0.822620i \(0.307489\pi\)
−0.568591 + 0.822620i \(0.692511\pi\)
\(264\) 142283. + 51041.3i 2.04148 + 0.732342i
\(265\) 8.92670 0.000127116
\(266\) 132086.i 1.86679i
\(267\) 23109.3 64419.7i 0.324163 0.903641i
\(268\) 106897. 1.48832
\(269\) 35924.4i 0.496460i −0.968701 0.248230i \(-0.920151\pi\)
0.968701 0.248230i \(-0.0798489\pi\)
\(270\) −111650. 187320.i −1.53156 2.56954i
\(271\) 57390.3 0.781448 0.390724 0.920508i \(-0.372225\pi\)
0.390724 + 0.920508i \(0.372225\pi\)
\(272\) 90307.3i 1.22063i
\(273\) −75249.9 26994.4i −1.00967 0.362200i
\(274\) −34592.7 −0.460770
\(275\) 104180.i 1.37758i
\(276\) 22522.3 62783.4i 0.295661 0.824189i
\(277\) 9503.14 0.123853 0.0619266 0.998081i \(-0.480276\pi\)
0.0619266 + 0.998081i \(0.480276\pi\)
\(278\) 82378.7i 1.06592i
\(279\) 91438.9 + 75293.0i 1.17469 + 0.967267i
\(280\) 261424. 3.33449
\(281\) 123020.i 1.55798i 0.627037 + 0.778989i \(0.284267\pi\)
−0.627037 + 0.778989i \(0.715733\pi\)
\(282\) 127867. + 45869.6i 1.60790 + 0.576802i
\(283\) 76953.7 0.960852 0.480426 0.877035i \(-0.340482\pi\)
0.480426 + 0.877035i \(0.340482\pi\)
\(284\) 343078.i 4.25359i
\(285\) −56489.4 + 157471.i −0.695469 + 1.93870i
\(286\) 170715. 2.08708
\(287\) 4673.58i 0.0567395i
\(288\) −92308.0 + 112103.i −1.11290 + 1.35155i
\(289\) 60918.5 0.729379
\(290\) 310520.i 3.69227i
\(291\) −91044.9 32660.5i −1.07515 0.385689i
\(292\) 318332. 3.73349
\(293\) 14637.7i 0.170505i −0.996359 0.0852525i \(-0.972830\pi\)
0.996359 0.0852525i \(-0.0271697\pi\)
\(294\) 19513.3 54395.4i 0.225754 0.629315i
\(295\) −18389.7 −0.211315
\(296\) 114150.i 1.30285i
\(297\) −63856.7 + 38061.3i −0.723925 + 0.431490i
\(298\) −97783.1 −1.10111
\(299\) 43895.1i 0.490991i
\(300\) 331841. + 119041.i 3.68712 + 1.32268i
\(301\) 65200.8 0.719648
\(302\) 183163.i 2.00827i
\(303\) −27401.6 + 76385.0i −0.298463 + 0.831999i
\(304\) 275164. 2.97745
\(305\) 298943.i 3.21358i
\(306\) 69300.3 + 57063.5i 0.740103 + 0.609418i
\(307\) 59016.0 0.626171 0.313086 0.949725i \(-0.398637\pi\)
0.313086 + 0.949725i \(0.398637\pi\)
\(308\) 152938.i 1.61218i
\(309\) 96928.2 + 34771.0i 1.01516 + 0.364167i
\(310\) −437435. −4.55187
\(311\) 105910.i 1.09501i −0.836803 0.547505i \(-0.815578\pi\)
0.836803 0.547505i \(-0.184422\pi\)
\(312\) −113668. + 316864.i −1.16770 + 3.25509i
\(313\) −150512. −1.53632 −0.768161 0.640257i \(-0.778828\pi\)
−0.768161 + 0.640257i \(0.778828\pi\)
\(314\) 118716.i 1.20407i
\(315\) −81723.5 + 99248.4i −0.823618 + 1.00024i
\(316\) 70005.0 0.701059
\(317\) 140514.i 1.39830i −0.714974 0.699151i \(-0.753561\pi\)
0.714974 0.699151i \(-0.246439\pi\)
\(318\) 13.7379 + 4.92819i 0.000135852 + 4.87341e-5i
\(319\) 105855. 1.04023
\(320\) 146291.i 1.42862i
\(321\) −15439.5 + 43039.5i −0.149839 + 0.417693i
\(322\) −55733.7 −0.537534
\(323\) 68869.3i 0.660116i
\(324\) −48269.7 246892.i −0.459816 2.35189i
\(325\) 232007. 2.19651
\(326\) 124853.i 1.17480i
\(327\) −157594. 56533.8i −1.47382 0.528704i
\(328\) 19679.6 0.182923
\(329\) 80088.7i 0.739911i
\(330\) 92700.6 258413.i 0.851245 2.37294i
\(331\) 39780.2 0.363087 0.181544 0.983383i \(-0.441891\pi\)
0.181544 + 0.983383i \(0.441891\pi\)
\(332\) 419022.i 3.80155i
\(333\) −43336.7 35684.5i −0.390812 0.321803i
\(334\) −284258. −2.54812
\(335\) 113131.i 1.00807i
\(336\) 199040. + 71401.6i 1.76304 + 0.632455i
\(337\) 56088.1 0.493868 0.246934 0.969032i \(-0.420577\pi\)
0.246934 + 0.969032i \(0.420577\pi\)
\(338\) 169636.i 1.48485i
\(339\) 63710.8 177601.i 0.554388 1.54542i
\(340\) −233915. −2.02349
\(341\) 149120.i 1.28241i
\(342\) −173871. + 211156.i −1.48653 + 1.80531i
\(343\) −127985. −1.08785
\(344\) 274549.i 2.32008i
\(345\) −66444.5 23835.6i −0.558240 0.200257i
\(346\) −75771.0 −0.632923
\(347\) 163511.i 1.35797i −0.734154 0.678983i \(-0.762421\pi\)
0.734154 0.678983i \(-0.237579\pi\)
\(348\) −120956. + 337179.i −0.998779 + 2.78421i
\(349\) −42912.4 −0.352316 −0.176158 0.984362i \(-0.556367\pi\)
−0.176158 + 0.984362i \(0.556367\pi\)
\(350\) 294579.i 2.40473i
\(351\) −84762.1 142208.i −0.687998 1.15428i
\(352\) −182819. −1.47549
\(353\) 14104.9i 0.113193i −0.998397 0.0565967i \(-0.981975\pi\)
0.998397 0.0565967i \(-0.0180249\pi\)
\(354\) −28301.2 10152.5i −0.225838 0.0810150i
\(355\) −363083. −2.88104
\(356\) 291572.i 2.30062i
\(357\) 17870.7 49816.7i 0.140219 0.390875i
\(358\) 193960. 1.51337
\(359\) 133490.i 1.03576i 0.855452 + 0.517882i \(0.173279\pi\)
−0.855452 + 0.517882i \(0.826721\pi\)
\(360\) 417917. + 344123.i 3.22467 + 2.65527i
\(361\) 79521.6 0.610198
\(362\) 53984.5i 0.411957i
\(363\) 35937.6 + 12891.9i 0.272732 + 0.0978370i
\(364\) 340591. 2.57058
\(365\) 336895.i 2.52877i
\(366\) −165039. + 460064.i −1.23204 + 3.43444i
\(367\) 106223. 0.788652 0.394326 0.918971i \(-0.370978\pi\)
0.394326 + 0.918971i \(0.370978\pi\)
\(368\) 116105.i 0.857343i
\(369\) −6152.02 + 7471.27i −0.0451819 + 0.0548708i
\(370\) 207319. 1.51438
\(371\) 8.60467i 6.25153e-5i
\(372\) −474990. 170393.i −3.43241 1.23131i
\(373\) 37218.8 0.267513 0.133756 0.991014i \(-0.457296\pi\)
0.133756 + 0.991014i \(0.457296\pi\)
\(374\) 113016.i 0.807974i
\(375\) 48910.2 136343.i 0.347806 0.969548i
\(376\) −337239. −2.38541
\(377\) 235739.i 1.65863i
\(378\) −180562. + 107623.i −1.26370 + 0.753217i
\(379\) 7019.81 0.0488705 0.0244353 0.999701i \(-0.492221\pi\)
0.0244353 + 0.999701i \(0.492221\pi\)
\(380\) 712733.i 4.93583i
\(381\) −254114. 91158.5i −1.75057 0.627982i
\(382\) 163207. 1.11844
\(383\) 27986.2i 0.190786i −0.995440 0.0953928i \(-0.969589\pi\)
0.995440 0.0953928i \(-0.0304107\pi\)
\(384\) −6407.90 + 17862.7i −0.0434563 + 0.121139i
\(385\) −161856. −1.09196
\(386\) 147539.i 0.990224i
\(387\) 104231. + 85826.5i 0.695947 + 0.573059i
\(388\) 412081. 2.73728
\(389\) 71584.3i 0.473062i 0.971624 + 0.236531i \(0.0760105\pi\)
−0.971624 + 0.236531i \(0.923989\pi\)
\(390\) 575484. + 206443.i 3.78359 + 1.35729i
\(391\) 29059.3 0.190078
\(392\) 143464.i 0.933622i
\(393\) 30688.2 85546.9i 0.198695 0.553885i
\(394\) −39795.6 −0.256356
\(395\) 74087.2i 0.474842i
\(396\) 201318. 244489.i 1.28379 1.55908i
\(397\) −84214.2 −0.534324 −0.267162 0.963652i \(-0.586086\pi\)
−0.267162 + 0.963652i \(0.586086\pi\)
\(398\) 235183.i 1.48471i
\(399\) 151790. + 54451.6i 0.953449 + 0.342031i
\(400\) −613671. −3.83544
\(401\) 72922.3i 0.453494i 0.973954 + 0.226747i \(0.0728091\pi\)
−0.973954 + 0.226747i \(0.927191\pi\)
\(402\) 62456.3 174104.i 0.386478 1.07735i
\(403\) −332089. −2.04477
\(404\) 345729.i 2.11823i
\(405\) −261289. + 51084.4i −1.59299 + 0.311443i
\(406\) 299318. 1.81585
\(407\) 70674.3i 0.426651i
\(408\) −209769. 75250.4i −1.26015 0.452052i
\(409\) −172315. −1.03009 −0.515046 0.857163i \(-0.672225\pi\)
−0.515046 + 0.857163i \(0.672225\pi\)
\(410\) 35741.8i 0.212622i
\(411\) −14260.6 + 39753.0i −0.0844217 + 0.235335i
\(412\) −438710. −2.58454
\(413\) 17726.3i 0.103925i
\(414\) −89096.9 73364.5i −0.519831 0.428041i
\(415\) −443456. −2.57487
\(416\) 407136.i 2.35263i
\(417\) 94667.2 + 33960.0i 0.544412 + 0.195297i
\(418\) −344357. −1.97086
\(419\) 19352.7i 0.110233i −0.998480 0.0551166i \(-0.982447\pi\)
0.998480 0.0551166i \(-0.0175531\pi\)
\(420\) 184946. 515557.i 1.04844 2.92266i
\(421\) −34510.7 −0.194710 −0.0973552 0.995250i \(-0.531038\pi\)
−0.0973552 + 0.995250i \(0.531038\pi\)
\(422\) 432622.i 2.42931i
\(423\) 105424. 128031.i 0.589195 0.715543i
\(424\) −36.2327 −0.000201544
\(425\) 153592.i 0.850338i
\(426\) −558773. 200449.i −3.07905 1.10455i
\(427\) 288159. 1.58044
\(428\) 194802.i 1.06342i
\(429\) 70375.9 196181.i 0.382392 1.06596i
\(430\) −498632. −2.69677
\(431\) 27612.2i 0.148644i −0.997234 0.0743219i \(-0.976321\pi\)
0.997234 0.0743219i \(-0.0236792\pi\)
\(432\) 224200. + 376149.i 1.20135 + 2.01554i
\(433\) 245311. 1.30840 0.654200 0.756322i \(-0.273005\pi\)
0.654200 + 0.756322i \(0.273005\pi\)
\(434\) 421655.i 2.23861i
\(435\) 356841. + 128009.i 1.88580 + 0.676493i
\(436\) 713293. 3.75228
\(437\) 88542.8i 0.463650i
\(438\) 185991. 518471.i 0.969491 2.70256i
\(439\) 69211.8 0.359130 0.179565 0.983746i \(-0.442531\pi\)
0.179565 + 0.983746i \(0.442531\pi\)
\(440\) 681546.i 3.52038i
\(441\) −54465.5 44848.2i −0.280056 0.230605i
\(442\) −251686. −1.28829
\(443\) 76359.2i 0.389094i −0.980893 0.194547i \(-0.937676\pi\)
0.980893 0.194547i \(-0.0623236\pi\)
\(444\) 225117. + 80756.3i 1.14194 + 0.409648i
\(445\) 308574. 1.55826
\(446\) 441904.i 2.22156i
\(447\) −40310.3 + 112370.i −0.201744 + 0.562385i
\(448\) −141014. −0.702595
\(449\) 327103.i 1.62253i −0.584681 0.811263i \(-0.698780\pi\)
0.584681 0.811263i \(-0.301220\pi\)
\(450\) 387767. 470920.i 1.91490 2.32553i
\(451\) −12184.3 −0.0599027
\(452\) 803846.i 3.93456i
\(453\) 210485. + 75507.3i 1.02571 + 0.367953i
\(454\) 425340. 2.06359
\(455\) 360452.i 1.74110i
\(456\) 229286. 639160.i 1.10267 3.07383i
\(457\) −304096. −1.45606 −0.728029 0.685546i \(-0.759564\pi\)
−0.728029 + 0.685546i \(0.759564\pi\)
\(458\) 280956.i 1.33939i
\(459\) 94144.2 56113.9i 0.446857 0.266345i
\(460\) 300737. 1.42125
\(461\) 130871.i 0.615802i 0.951418 + 0.307901i \(0.0996265\pi\)
−0.951418 + 0.307901i \(0.900373\pi\)
\(462\) −249091. 89356.4i −1.16701 0.418641i
\(463\) −362078. −1.68904 −0.844520 0.535524i \(-0.820114\pi\)
−0.844520 + 0.535524i \(0.820114\pi\)
\(464\) 623542.i 2.89621i
\(465\) −180329. + 502688.i −0.833989 + 2.32484i
\(466\) 751045. 3.45855
\(467\) 935.101i 0.00428771i −0.999998 0.00214385i \(-0.999318\pi\)
0.999998 0.00214385i \(-0.000682410\pi\)
\(468\) 544475. + 448334.i 2.48592 + 2.04696i
\(469\) −109049. −0.495767
\(470\) 612490.i 2.77270i
\(471\) 136426. + 48939.9i 0.614970 + 0.220608i
\(472\) 74642.3 0.335043
\(473\) 169982.i 0.759769i
\(474\) 40901.6 114018.i 0.182047 0.507476i
\(475\) −467991. −2.07420
\(476\) 225477.i 0.995149i
\(477\) 11.3267 13.7556i 4.97813e−5 6.04564e-5i
\(478\) −232330. −1.01683
\(479\) 3931.82i 0.0171365i −0.999963 0.00856825i \(-0.997273\pi\)
0.999963 0.00856825i \(-0.00272739\pi\)
\(480\) −616287. 221081.i −2.67486 0.959552i
\(481\) 157391. 0.680283
\(482\) 22276.9i 0.0958872i
\(483\) −22975.8 + 64047.6i −0.0984863 + 0.274542i
\(484\) −162658. −0.694361
\(485\) 436111.i 1.85402i
\(486\) −430318. 65633.7i −1.82187 0.277878i
\(487\) −74782.1 −0.315312 −0.157656 0.987494i \(-0.550394\pi\)
−0.157656 + 0.987494i \(0.550394\pi\)
\(488\) 1.21339e6i 5.09518i
\(489\) 143478. + 51469.8i 0.600023 + 0.215246i
\(490\) 260558. 1.08521
\(491\) 274270.i 1.13767i −0.822453 0.568833i \(-0.807395\pi\)
0.822453 0.568833i \(-0.192605\pi\)
\(492\) 13922.4 38810.3i 0.0575155 0.160331i
\(493\) −156063. −0.642105
\(494\) 766879.i 3.14248i
\(495\) −258746. 213058.i −1.05600 0.869535i
\(496\) 878395. 3.57048
\(497\) 349985.i 1.41689i
\(498\) −682464. 244820.i −2.75183 0.987163i
\(499\) −15103.7 −0.0606573 −0.0303287 0.999540i \(-0.509655\pi\)
−0.0303287 + 0.999540i \(0.509655\pi\)
\(500\) 617105.i 2.46842i
\(501\) −117183. + 326661.i −0.466863 + 1.30143i
\(502\) 24702.1 0.0980227
\(503\) 100739.i 0.398164i −0.979983 0.199082i \(-0.936204\pi\)
0.979983 0.199082i \(-0.0637961\pi\)
\(504\) 331709. 402841.i 1.30586 1.58589i
\(505\) −365889. −1.43472
\(506\) 145301.i 0.567502i
\(507\) 194941. + 69931.0i 0.758379 + 0.272053i
\(508\) 1.15016e6 4.45686
\(509\) 239942.i 0.926125i 0.886326 + 0.463063i \(0.153250\pi\)
−0.886326 + 0.463063i \(0.846750\pi\)
\(510\) −136669. + 380980.i −0.525448 + 1.46474i
\(511\) −324742. −1.24365
\(512\) 506067.i 1.93049i
\(513\) 170978. + 286855.i 0.649687 + 1.09000i
\(514\) 710904. 2.69082
\(515\) 464293.i 1.75056i
\(516\) −541441. 194231.i −2.03354 0.729490i
\(517\) 208796. 0.781162
\(518\) 199840.i 0.744770i
\(519\) −31236.0 + 87073.9i −0.115963 + 0.323261i
\(520\) −1.51780e6 −5.61316
\(521\) 194196.i 0.715425i −0.933832 0.357712i \(-0.883557\pi\)
0.933832 0.357712i \(-0.116443\pi\)
\(522\) 478496. + 394005.i 1.75605 + 1.44597i
\(523\) 407345. 1.48922 0.744610 0.667499i \(-0.232635\pi\)
0.744610 + 0.667499i \(0.232635\pi\)
\(524\) 387197.i 1.41016i
\(525\) −338522. 121438.i −1.22820 0.440592i
\(526\) −838903. −3.03208
\(527\) 219849.i 0.791595i
\(528\) −186148. + 518909.i −0.667715 + 1.86133i
\(529\) 242481. 0.866494
\(530\) 65.8054i 0.000234266i
\(531\) −23333.9 + 28337.6i −0.0827557 + 0.100502i
\(532\) −687022. −2.42743
\(533\) 27134.3i 0.0955133i
\(534\) 474886. + 170356.i 1.66535 + 0.597412i
\(535\) −206162. −0.720279
\(536\) 459187.i 1.59831i
\(537\) 79958.4 222893.i 0.277278 0.772944i
\(538\) 264826. 0.914946
\(539\) 88823.4i 0.305738i
\(540\) 974306. 580728.i 3.34124 1.99152i
\(541\) −197440. −0.674591 −0.337296 0.941399i \(-0.609512\pi\)
−0.337296 + 0.941399i \(0.609512\pi\)
\(542\) 423067.i 1.44016i
\(543\) 62037.4 + 22254.7i 0.210404 + 0.0754782i
\(544\) 269531. 0.910775
\(545\) 754888.i 2.54150i
\(546\) 198996. 554723.i 0.667512 1.86076i
\(547\) 162871. 0.544337 0.272169 0.962250i \(-0.412259\pi\)
0.272169 + 0.962250i \(0.412259\pi\)
\(548\) 179927.i 0.599151i
\(549\) 460657. + 379316.i 1.52838 + 1.25851i
\(550\) 767986. 2.53880
\(551\) 475520.i 1.56626i
\(552\) 269693. + 96746.8i 0.885097 + 0.317511i
\(553\) −71414.5 −0.233527
\(554\) 70054.8i 0.228254i
\(555\) 85465.5 238245.i 0.277463 0.773459i
\(556\) −428477. −1.38605
\(557\) 162633.i 0.524201i 0.965041 + 0.262100i \(0.0844151\pi\)
−0.965041 + 0.262100i \(0.915585\pi\)
\(558\) −555041. + 674065.i −1.78261 + 2.16488i
\(559\) −378549. −1.21143
\(560\) 953415.i 3.04023i
\(561\) 129875. + 46590.0i 0.412667 + 0.148036i
\(562\) −906870. −2.87126
\(563\) 361668.i 1.14102i 0.821291 + 0.570510i \(0.193255\pi\)
−0.821291 + 0.570510i \(0.806745\pi\)
\(564\) −238582. + 665074.i −0.750031 + 2.09079i
\(565\) 850721. 2.66496
\(566\) 567283.i 1.77079i
\(567\) 49241.6 + 251863.i 0.153167 + 0.783428i
\(568\) 1.47372e6 4.56793
\(569\) 136555.i 0.421776i −0.977510 0.210888i \(-0.932364\pi\)
0.977510 0.210888i \(-0.0676356\pi\)
\(570\) −1.16084e6 416426.i −3.57290 1.28171i
\(571\) 17778.1 0.0545272 0.0272636 0.999628i \(-0.491321\pi\)
0.0272636 + 0.999628i \(0.491321\pi\)
\(572\) 887940.i 2.71389i
\(573\) 67280.8 187553.i 0.204919 0.571235i
\(574\) −34452.4 −0.104567
\(575\) 197468.i 0.597258i
\(576\) −225427. 185622.i −0.679456 0.559480i
\(577\) −108734. −0.326597 −0.163298 0.986577i \(-0.552213\pi\)
−0.163298 + 0.986577i \(0.552213\pi\)
\(578\) 449076.i 1.34420i
\(579\) 169548. + 60822.0i 0.505750 + 0.181428i
\(580\) −1.61511e6 −4.80116
\(581\) 427459.i 1.26632i
\(582\) 240765. 671161.i 0.710801 1.98144i
\(583\) 22.4329 6.60006e−5
\(584\) 1.36743e6i 4.00940i
\(585\) 474478. 576225.i 1.38645 1.68376i
\(586\) 107905. 0.314230
\(587\) 586908.i 1.70331i −0.524102 0.851655i \(-0.675599\pi\)
0.524102 0.851655i \(-0.324401\pi\)
\(588\) 282927. + 101494.i 0.818314 + 0.293554i
\(589\) 669873. 1.93091
\(590\) 135565.i 0.389441i
\(591\) −16405.4 + 45732.0i −0.0469691 + 0.130932i
\(592\) −416308. −1.18788
\(593\) 137926.i 0.392227i −0.980581 0.196113i \(-0.937168\pi\)
0.980581 0.196113i \(-0.0628321\pi\)
\(594\) −280578. 470736.i −0.795209 1.33415i
\(595\) 238625. 0.674035
\(596\) 508600.i 1.43180i
\(597\) 270266. + 96952.6i 0.758304 + 0.272026i
\(598\) 323584. 0.904865
\(599\) 37284.7i 0.103915i −0.998649 0.0519574i \(-0.983454\pi\)
0.998649 0.0519574i \(-0.0165460\pi\)
\(600\) −511354. + 1.42546e6i −1.42043 + 3.95960i
\(601\) 152155. 0.421248 0.210624 0.977567i \(-0.432450\pi\)
0.210624 + 0.977567i \(0.432450\pi\)
\(602\) 480644.i 1.32627i
\(603\) −174328. 143546.i −0.479439 0.394782i
\(604\) −952684. −2.61141
\(605\) 172143.i 0.470305i
\(606\) −563091. 201998.i −1.53332 0.550048i
\(607\) 97390.8 0.264326 0.132163 0.991228i \(-0.457808\pi\)
0.132163 + 0.991228i \(0.457808\pi\)
\(608\) 821253.i 2.22162i
\(609\) 123392. 343968.i 0.332699 0.927435i
\(610\) −2.20374e6 −5.92243
\(611\) 464986.i 1.24554i
\(612\) −296805. + 360452.i −0.792442 + 0.962375i
\(613\) 177806. 0.473180 0.236590 0.971610i \(-0.423970\pi\)
0.236590 + 0.971610i \(0.423970\pi\)
\(614\) 435051.i 1.15399i
\(615\) −41073.5 14734.3i −0.108595 0.0389564i
\(616\) 656960. 1.73132
\(617\) 16269.5i 0.0427370i 0.999772 + 0.0213685i \(0.00680232\pi\)
−0.999772 + 0.0213685i \(0.993198\pi\)
\(618\) −256324. + 714531.i −0.671138 + 1.87087i
\(619\) −34352.4 −0.0896552 −0.0448276 0.998995i \(-0.514274\pi\)
−0.0448276 + 0.998995i \(0.514274\pi\)
\(620\) 2.27523e6i 5.91892i
\(621\) −121038. + 72143.7i −0.313862 + 0.187075i
\(622\) 780745. 2.01803
\(623\) 297443.i 0.766350i
\(624\) −1.15561e6 414550.i −2.96784 1.06465i
\(625\) 14575.7 0.0373138
\(626\) 1.10954e6i 2.83135i
\(627\) −141958. + 395725.i −0.361099 + 1.00660i
\(628\) −617480. −1.56568
\(629\) 104195.i 0.263359i
\(630\) −731635. 602445.i −1.84337 1.51788i
\(631\) −726363. −1.82429 −0.912147 0.409864i \(-0.865576\pi\)
−0.912147 + 0.409864i \(0.865576\pi\)
\(632\) 300714.i 0.752868i
\(633\) 497157. + 178345.i 1.24075 + 0.445096i
\(634\) 1.03583e6 2.57698
\(635\) 1.21723e6i 3.01872i
\(636\) −25.6330 + 71.4550i −6.33703e−5 + 0.000176652i
\(637\) 197809. 0.487491
\(638\) 780339.i 1.91709i
\(639\) −460700. + 559493.i −1.12828 + 1.37023i
\(640\) −85563.7 −0.208896
\(641\) 368854.i 0.897714i 0.893604 + 0.448857i \(0.148169\pi\)
−0.893604 + 0.448857i \(0.851831\pi\)
\(642\) −317276. 113817.i −0.769782 0.276144i
\(643\) 248032. 0.599910 0.299955 0.953953i \(-0.403028\pi\)
0.299955 + 0.953953i \(0.403028\pi\)
\(644\) 289888.i 0.698969i
\(645\) −205557. + 573014.i −0.494098 + 1.37736i
\(646\) 507687. 1.21655
\(647\) 491048.i 1.17305i −0.809932 0.586524i \(-0.800496\pi\)
0.809932 0.586524i \(-0.199504\pi\)
\(648\) 1.06055e6 207347.i 2.52570 0.493797i
\(649\) −46213.5 −0.109718
\(650\) 1.71030e6i 4.04804i
\(651\) 484554. + 173824.i 1.14335 + 0.410155i
\(652\) −649401. −1.52763
\(653\) 699337.i 1.64006i 0.572319 + 0.820031i \(0.306044\pi\)
−0.572319 + 0.820031i \(0.693956\pi\)
\(654\) 416753. 1.16175e6i 0.974369 2.71616i
\(655\) 409775. 0.955132
\(656\) 71771.7i 0.166780i
\(657\) −519139. 427471.i −1.20269 0.990321i
\(658\) 590394. 1.36361
\(659\) 321977.i 0.741403i −0.928752 0.370702i \(-0.879117\pi\)
0.928752 0.370702i \(-0.120883\pi\)
\(660\) 1.34409e6 + 482164.i 3.08560 + 1.10690i
\(661\) 197653. 0.452376 0.226188 0.974084i \(-0.427374\pi\)
0.226188 + 0.974084i \(0.427374\pi\)
\(662\) 293250.i 0.669147i
\(663\) −103756. + 289230.i −0.236039 + 0.657986i
\(664\) 1.79995e6 4.08248
\(665\) 727084.i 1.64415i
\(666\) 263057. 319467.i 0.593064 0.720241i
\(667\) 200645. 0.451000
\(668\) 1.47851e6i 3.31339i
\(669\) 507824. + 182172.i 1.13465 + 0.407032i
\(670\) 833970. 1.85781
\(671\) 751248.i 1.66855i
\(672\) −213105. + 594055.i −0.471906 + 1.31549i
\(673\) 430587. 0.950673 0.475337 0.879804i \(-0.342326\pi\)
0.475337 + 0.879804i \(0.342326\pi\)
\(674\) 413468.i 0.910168i
\(675\) −381314. 639744.i −0.836904 1.40410i
\(676\) −882327. −1.93080
\(677\) 74792.4i 0.163185i 0.996666 + 0.0815925i \(0.0260006\pi\)
−0.996666 + 0.0815925i \(0.973999\pi\)
\(678\) 1.30923e6 + 469660.i 2.84811 + 1.02170i
\(679\) −420379. −0.911803
\(680\) 1.00481e6i 2.17303i
\(681\) 175343. 488789.i 0.378089 1.05397i
\(682\) −1.09928e6 −2.36341
\(683\) 424167.i 0.909275i −0.890677 0.454637i \(-0.849769\pi\)
0.890677 0.454637i \(-0.150231\pi\)
\(684\) −1.09829e6 904355.i −2.34749 1.93298i
\(685\) −190420. −0.405817
\(686\) 943473.i 2.00485i
\(687\) −322867. 115822.i −0.684085 0.245402i
\(688\) 1.00128e6 2.11534
\(689\) 49.9578i 0.000105236i
\(690\) 175710. 489813.i 0.369062 1.02880i
\(691\) 450906. 0.944344 0.472172 0.881506i \(-0.343470\pi\)
0.472172 + 0.881506i \(0.343470\pi\)
\(692\) 394108.i 0.823006i
\(693\) −205372. + 249412.i −0.427636 + 0.519339i
\(694\) 1.20537e6 2.50265
\(695\) 453462.i 0.938797i
\(696\) −1.44839e6 519579.i −2.98996 1.07259i
\(697\) 17963.3 0.0369761
\(698\) 316340.i 0.649296i
\(699\) 309612. 863079.i 0.633671 1.76643i
\(700\) 1.53220e6 3.12693
\(701\) 183180.i 0.372770i −0.982477 0.186385i \(-0.940323\pi\)
0.982477 0.186385i \(-0.0596772\pi\)
\(702\) 1.04832e6 624845.i 2.12726 1.26794i
\(703\) −317481. −0.642401
\(704\) 367631.i 0.741765i
\(705\) 703856. + 252494.i 1.41614 + 0.508011i
\(706\) 103978. 0.208609
\(707\) 352690.i 0.705593i
\(708\) 52806.1 147203.i 0.105346 0.293664i
\(709\) −419548. −0.834622 −0.417311 0.908764i \(-0.637027\pi\)
−0.417311 + 0.908764i \(0.637027\pi\)
\(710\) 2.67656e6i 5.30958i
\(711\) −114165. 94005.9i −0.225836 0.185958i
\(712\) −1.25248e6 −2.47064
\(713\) 282652.i 0.555997i
\(714\) 367236. + 131739.i 0.720359 + 0.258414i
\(715\) 939719. 1.83817
\(716\) 1.00884e6i 1.96788i
\(717\) −95776.2 + 266987.i −0.186303 + 0.519340i
\(718\) −984057. −1.90885
\(719\) 388924.i 0.752327i −0.926553 0.376164i \(-0.877243\pi\)
0.926553 0.376164i \(-0.122757\pi\)
\(720\) −1.25502e6 + 1.52415e6i −2.42095 + 2.94010i
\(721\) 447543. 0.860924
\(722\) 586214.i 1.12456i
\(723\) −25600.0 9183.47i −0.0489737 0.0175683i
\(724\) −280790. −0.535678
\(725\) 1.06050e6i 2.01761i
\(726\) −95035.8 + 264923.i −0.180308 + 0.502628i
\(727\) 142364. 0.269358 0.134679 0.990889i \(-0.457000\pi\)
0.134679 + 0.990889i \(0.457000\pi\)
\(728\) 1.46304e6i 2.76054i
\(729\) −252820. + 467452.i −0.475725 + 0.879594i
\(730\) 2.48351e6 4.66037
\(731\) 250606.i 0.468982i
\(732\) −2.39293e6 858417.i −4.46589 1.60205i
\(733\) 576062. 1.07216 0.536082 0.844166i \(-0.319904\pi\)
0.536082 + 0.844166i \(0.319904\pi\)
\(734\) 783048.i 1.45344i
\(735\) 107413. 299426.i 0.198830 0.554261i
\(736\) −346527. −0.639707
\(737\) 284298.i 0.523406i
\(738\) −55076.3 45351.2i −0.101124 0.0832675i
\(739\) −341810. −0.625887 −0.312944 0.949772i \(-0.601315\pi\)
−0.312944 + 0.949772i \(0.601315\pi\)
\(740\) 1.07833e6i 1.96919i
\(741\) −881276. 316140.i −1.60500 0.575762i
\(742\) 63.4315 0.000115212
\(743\) 197408.i 0.357591i 0.983886 + 0.178795i \(0.0572200\pi\)
−0.983886 + 0.178795i \(0.942780\pi\)
\(744\) 731941. 2.04037e6i 1.32230 3.68606i
\(745\) −538258. −0.969790
\(746\) 274368.i 0.493009i
\(747\) −562681. + 683344.i −1.00837 + 1.22461i
\(748\) −587831. −1.05063
\(749\) 198725.i 0.354232i
\(750\) 1.00508e6 + 360554.i 1.78682 + 0.640985i
\(751\) −297608. −0.527673 −0.263836 0.964567i \(-0.584988\pi\)
−0.263836 + 0.964567i \(0.584988\pi\)
\(752\) 1.22992e6i 2.17490i
\(753\) 10183.3 28387.0i 0.0179596 0.0500644i
\(754\) −1.73781e6 −3.05674
\(755\) 1.00824e6i 1.76876i
\(756\) −559778. 939159.i −0.979427 1.64322i
\(757\) 507520. 0.885649 0.442824 0.896608i \(-0.353977\pi\)
0.442824 + 0.896608i \(0.353977\pi\)
\(758\) 51748.3i 0.0900654i
\(759\) −166976. 59899.1i −0.289847 0.103977i
\(760\) 3.06162e6 5.30059
\(761\) 291086.i 0.502635i 0.967905 + 0.251317i \(0.0808637\pi\)
−0.967905 + 0.251317i \(0.919136\pi\)
\(762\) 671998. 1.87327e6i 1.15733 3.22619i
\(763\) −727655. −1.24990
\(764\) 848890.i 1.45433i
\(765\) 381471. + 314112.i 0.651836 + 0.536737i
\(766\) 206307. 0.351606
\(767\) 102917.i 0.174943i
\(768\) −620328. 222530.i −1.05172 0.377282i
\(769\) 173980. 0.294203 0.147102 0.989121i \(-0.453006\pi\)
0.147102 + 0.989121i \(0.453006\pi\)
\(770\) 1.19316e6i 2.01242i
\(771\) 293065. 816951.i 0.493009 1.37432i
\(772\) −767398. −1.28761
\(773\) 98287.5i 0.164490i −0.996612 0.0822450i \(-0.973791\pi\)
0.996612 0.0822450i \(-0.0262090\pi\)
\(774\) −632692. + 768367.i −1.05611 + 1.28259i
\(775\) −1.49395e6 −2.48733
\(776\) 1.77014e6i 2.93957i
\(777\) −229650. 82382.3i −0.380386 0.136456i
\(778\) −527702. −0.871825
\(779\) 54733.8i 0.0901946i
\(780\) −1.07377e6 + 2.99327e6i −1.76492 + 4.91990i
\(781\) −912432. −1.49589
\(782\) 214218.i 0.350301i
\(783\) 650035. 387448.i 1.06026 0.631961i
\(784\) −523215. −0.851233
\(785\) 653487.i 1.06047i
\(786\) 630631. + 226226.i 1.02077 + 0.366182i
\(787\) 900591. 1.45405 0.727023 0.686613i \(-0.240903\pi\)
0.727023 + 0.686613i \(0.240903\pi\)
\(788\) 206989.i 0.333346i
\(789\) −345831. + 964043.i −0.555533 + 1.54861i
\(790\) 546152. 0.875104
\(791\) 820031.i 1.31062i
\(792\) 1.05023e6 + 864783.i 1.67430 + 1.37866i
\(793\) −1.67302e6 −2.66045
\(794\) 620806.i 0.984726i
\(795\) 75.6217 + 27.1278i 0.000119650 + 4.29220e-5i
\(796\) −1.22326e6 −1.93060
\(797\) 31498.7i 0.0495880i 0.999693 + 0.0247940i \(0.00789298\pi\)
−0.999693 + 0.0247940i \(0.992107\pi\)
\(798\) −401404. + 1.11896e6i −0.630341 + 1.75715i
\(799\) −307829. −0.482187
\(800\) 1.83156e6i 2.86181i
\(801\) 391536. 475498.i 0.610248 0.741111i
\(802\) −537565. −0.835762
\(803\) 846621.i 1.31298i
\(804\) 905569. + 324855.i 1.40091 + 0.502547i
\(805\) −306792. −0.473426
\(806\) 2.44808e6i 3.76839i
\(807\) 109172. 304330.i 0.167635 0.467302i
\(808\) 1.48511e6 2.27477
\(809\) 769946.i 1.17642i −0.808707 0.588211i \(-0.799832\pi\)
0.808707 0.588211i \(-0.200168\pi\)
\(810\) −376582. 1.92616e6i −0.573970 2.93577i
\(811\) −964850. −1.46696 −0.733480 0.679711i \(-0.762105\pi\)
−0.733480 + 0.679711i \(0.762105\pi\)
\(812\) 1.55684e6i 2.36120i
\(813\) 486177. + 174406.i 0.735552 + 0.263864i
\(814\) 520993. 0.786291
\(815\) 687269.i 1.03469i
\(816\) 274439. 765030.i 0.412160 1.14894i
\(817\) 763588. 1.14397
\(818\) 1.27026e6i 1.89840i
\(819\) −555438. 457361.i −0.828072 0.681854i
\(820\) 185904. 0.276478
\(821\) 101347.i 0.150358i −0.997170 0.0751788i \(-0.976047\pi\)
0.997170 0.0751788i \(-0.0239528\pi\)
\(822\) −293049. 105126.i −0.433708 0.155584i
\(823\) 15672.4 0.0231385 0.0115693 0.999933i \(-0.496317\pi\)
0.0115693 + 0.999933i \(0.496317\pi\)
\(824\) 1.88452e6i 2.77554i
\(825\) 316596. 882547.i 0.465155 1.29667i
\(826\) −130674. −0.191527
\(827\) 133176.i 0.194722i −0.995249 0.0973610i \(-0.968960\pi\)
0.995249 0.0973610i \(-0.0310401\pi\)
\(828\) 381591. 463420.i 0.556593 0.675949i
\(829\) 408389. 0.594245 0.297122 0.954839i \(-0.403973\pi\)
0.297122 + 0.954839i \(0.403973\pi\)
\(830\) 3.26905e6i 4.74532i
\(831\) 80505.0 + 28879.5i 0.116579 + 0.0418204i
\(832\) 818710. 1.18272
\(833\) 130953.i 0.188723i
\(834\) −250344. + 697864.i −0.359920 + 1.00332i
\(835\) −1.56473e6 −2.24422
\(836\) 1.79111e6i 2.56276i
\(837\) 545805. + 915716.i 0.779089 + 1.30710i
\(838\) 142663. 0.203153
\(839\) 1.07239e6i 1.52345i 0.647902 + 0.761723i \(0.275646\pi\)
−0.647902 + 0.761723i \(0.724354\pi\)
\(840\) 2.21463e6 + 794453.i 3.13864 + 1.12593i
\(841\) −370283. −0.523531
\(842\) 254404.i 0.358839i
\(843\) −373850. + 1.04215e6i −0.526068 + 1.46648i
\(844\) −2.25020e6 −3.15890
\(845\) 933778.i 1.30777i
\(846\) 943816. + 777160.i 1.31870 + 1.08585i
\(847\) 165933. 0.231295
\(848\) 132.141i 0.000183758i
\(849\) 651906. + 233858.i 0.904419 + 0.324442i
\(850\) −1.13224e6 −1.56712
\(851\) 133960.i 0.184977i
\(852\) 1.04259e6 2.90635e6i 1.43627 4.00377i
\(853\) −1.05056e6 −1.44385 −0.721926 0.691970i \(-0.756743\pi\)
−0.721926 + 0.691970i \(0.756743\pi\)
\(854\) 2.12424e6i 2.91264i
\(855\) −957091. + 1.16233e6i −1.30924 + 1.59000i
\(856\) 836794. 1.14201
\(857\) 339342.i 0.462036i 0.972950 + 0.231018i \(0.0742056\pi\)
−0.972950 + 0.231018i \(0.925794\pi\)
\(858\) 1.44620e6 + 518794.i 1.96450 + 0.704726i
\(859\) 1.01922e6 1.38128 0.690639 0.723200i \(-0.257329\pi\)
0.690639 + 0.723200i \(0.257329\pi\)
\(860\) 2.59354e6i 3.50668i
\(861\) −14202.8 + 39591.8i −0.0191587 + 0.0534071i
\(862\) 203551. 0.273941
\(863\) 100127.i 0.134440i −0.997738 0.0672201i \(-0.978587\pi\)
0.997738 0.0672201i \(-0.0214130\pi\)
\(864\) −1.12265e6 + 669149.i −1.50390 + 0.896386i
\(865\) −417090. −0.557439
\(866\) 1.80837e6i 2.41130i
\(867\) 516065. + 185128.i 0.686541 + 0.246283i
\(868\) −2.19315e6 −2.91092
\(869\) 186182.i 0.246546i
\(870\) −943654. + 2.63054e6i −1.24674 + 3.47542i
\(871\) 633129. 0.834556
\(872\) 3.06402e6i 4.02957i
\(873\) −672025. 553362.i −0.881774 0.726073i
\(874\) −652715. −0.854478
\(875\) 629531.i 0.822244i
\(876\) 2.69672e6 + 967396.i 3.51422 + 1.26065i
\(877\) −384649. −0.500109 −0.250055 0.968232i \(-0.580449\pi\)
−0.250055 + 0.968232i \(0.580449\pi\)
\(878\) 510212.i 0.661854i
\(879\) 44483.2 124002.i 0.0575729 0.160491i
\(880\) −2.48561e6 −3.20972
\(881\) 649770.i 0.837158i 0.908180 + 0.418579i \(0.137472\pi\)
−0.908180 + 0.418579i \(0.862528\pi\)
\(882\) 330610. 401506.i 0.424990 0.516125i
\(883\) −509794. −0.653843 −0.326922 0.945051i \(-0.606011\pi\)
−0.326922 + 0.945051i \(0.606011\pi\)
\(884\) 1.30909e6i 1.67520i
\(885\) −155787. 55885.4i −0.198904 0.0713530i
\(886\) 562901. 0.717076
\(887\) 345280.i 0.438858i −0.975628 0.219429i \(-0.929581\pi\)
0.975628 0.219429i \(-0.0704194\pi\)
\(888\) −346897. + 967015.i −0.439921 + 1.22633i
\(889\) −1.17331e6 −1.48460
\(890\) 2.27473e6i 2.87178i
\(891\) −656622. + 128376.i −0.827104 + 0.161706i
\(892\) −2.29848e6 −2.88876
\(893\) 937946.i 1.17618i
\(894\) −828361. 297158.i −1.03644 0.371802i
\(895\) 1.06767e6 1.33288
\(896\) 82477.0i 0.102735i
\(897\) 133395. 371853.i 0.165788 0.462154i
\(898\) 2.41132e6 2.99022
\(899\) 1.51798e6i 1.87823i
\(900\) 2.44940e6 + 2.01689e6i 3.02395 + 2.48999i
\(901\) −33.0729 −4.07401e−5
\(902\) 89819.5i 0.110397i
\(903\) 552343. + 198142.i 0.677382 + 0.242997i
\(904\) −3.45300e6 −4.22532
\(905\) 297163.i 0.362826i
\(906\) −556621. + 1.55165e6i −0.678115 + 1.89032i
\(907\) 1.14955e6 1.39738 0.698691 0.715424i \(-0.253766\pi\)
0.698691 + 0.715424i \(0.253766\pi\)
\(908\) 2.21232e6i 2.68335i
\(909\) −464260. + 563817.i −0.561867 + 0.682354i
\(910\) 2.65716e6 3.20875
\(911\) 263358.i 0.317329i −0.987333 0.158665i \(-0.949281\pi\)
0.987333 0.158665i \(-0.0507188\pi\)
\(912\) 2.33102e6 + 836208.i 2.80257 + 1.00537i
\(913\) −1.11441e6 −1.33691
\(914\) 2.24172e6i 2.68343i
\(915\) −908474. + 2.53247e6i −1.08510 + 3.02484i
\(916\) 1.46134e6 1.74165
\(917\) 394993.i 0.469732i
\(918\) 413658. + 694008.i 0.490858 + 0.823529i
\(919\) 1.68157e6 1.99106 0.995529 0.0944589i \(-0.0301121\pi\)
0.995529 + 0.0944589i \(0.0301121\pi\)
\(920\) 1.29185e6i 1.52628i
\(921\) 499949. + 179347.i 0.589395 + 0.211434i
\(922\) −964747. −1.13488
\(923\) 2.03198e6i 2.38515i
\(924\) 464770. 1.29560e6i 0.544370 1.51749i
\(925\) 708046. 0.827519
\(926\) 2.66915e6i 3.11280i
\(927\) 715451. + 589120.i 0.832570 + 0.685558i
\(928\) 1.86102e6 2.16101
\(929\) 119186.i 0.138100i −0.997613 0.0690500i \(-0.978003\pi\)
0.997613 0.0690500i \(-0.0219968\pi\)
\(930\) −3.70569e6 1.32934e6i −4.28453 1.53699i
\(931\) −399009. −0.460345
\(932\) 3.90641e6i 4.49724i
\(933\) 321856. 897210.i 0.369742 1.03070i
\(934\) 6893.34 0.00790198
\(935\) 622110.i 0.711613i
\(936\) −1.92586e6 + 2.33885e6i −2.19823 + 2.66963i
\(937\) −1.53037e6 −1.74308 −0.871538 0.490328i \(-0.836877\pi\)
−0.871538 + 0.490328i \(0.836877\pi\)
\(938\) 803885.i 0.913668i
\(939\) −1.27505e6 457398.i −1.44609 0.518756i
\(940\) −3.18575e6 −3.60542
\(941\) 340341.i 0.384357i 0.981360 + 0.192179i \(0.0615553\pi\)
−0.981360 + 0.192179i \(0.938445\pi\)
\(942\) −360773. + 1.00570e6i −0.406567 + 1.13335i
\(943\) −23094.8 −0.0259712
\(944\) 272221.i 0.305477i
\(945\) −993924. + 592420.i −1.11299 + 0.663386i
\(946\) −1.25307e6 −1.40021
\(947\) 383908.i 0.428082i 0.976825 + 0.214041i \(0.0686626\pi\)
−0.976825 + 0.214041i \(0.931337\pi\)
\(948\) 593041. + 212742.i 0.659885 + 0.236720i
\(949\) 1.88542e6 2.09351
\(950\) 3.44992e6i 3.82262i
\(951\) 427015. 1.19035e6i 0.472152 1.31618i
\(952\) −968559. −1.06869
\(953\) 126216.i 0.138972i 0.997583 + 0.0694862i \(0.0221360\pi\)
−0.997583 + 0.0694862i \(0.977864\pi\)
\(954\) 101.403 + 83.4975i 0.000111417 + 9.17438e-5i
\(955\) 898391. 0.985051
\(956\) 1.20842e6i 1.32221i
\(957\) 896744. + 321689.i 0.979140 + 0.351247i
\(958\) 28984.4 0.0315815
\(959\) 183550.i 0.199580i
\(960\) 444571. 1.23929e6i 0.482390 1.34472i
\(961\) 1.21489e6 1.31550
\(962\) 1.16025e6i 1.25372i
\(963\) −261589. + 317685.i −0.282077 + 0.342566i
\(964\) 115869. 0.124685
\(965\) 812147.i 0.872127i
\(966\) −472143. 169372.i −0.505963 0.181504i
\(967\) 923991. 0.988131 0.494066 0.869425i \(-0.335510\pi\)
0.494066 + 0.869425i \(0.335510\pi\)
\(968\) 698715.i 0.745675i
\(969\) 209290. 583420.i 0.222895 0.621346i
\(970\) 3.21490e6 3.41684
\(971\) 336724.i 0.357137i 0.983927 + 0.178569i \(0.0571466\pi\)
−0.983927 + 0.178569i \(0.942853\pi\)
\(972\) 341381. 2.23822e6i 0.361332 2.36902i
\(973\) 437104. 0.461699
\(974\) 551275.i 0.581100i
\(975\) 1.96542e6 + 705056.i 2.06751 + 0.741677i
\(976\) 4.42523e6 4.64554
\(977\) 916422.i 0.960077i 0.877247 + 0.480039i \(0.159377\pi\)
−0.877247 + 0.480039i \(0.840623\pi\)
\(978\) −379423. + 1.05768e6i −0.396685 + 1.10580i
\(979\) 775450. 0.809074
\(980\) 1.35524e6i 1.41112i
\(981\) −1.16324e6 957842.i −1.20874 0.995305i
\(982\) 2.02185e6 2.09665
\(983\) 1.44522e6i 1.49564i 0.663904 + 0.747818i \(0.268898\pi\)
−0.663904 + 0.747818i \(0.731102\pi\)
\(984\) 166714. + 59805.2i 0.172179 + 0.0617659i
\(985\) −219059. −0.225782
\(986\) 1.15046e6i 1.18336i
\(987\) 243386. 678465.i 0.249839 0.696455i
\(988\) 3.98877e6 4.08626
\(989\) 322195.i 0.329402i
\(990\) 1.57061e6 1.90741e6i 1.60250 1.94614i
\(991\) 570072. 0.580474 0.290237 0.956955i \(-0.406266\pi\)
0.290237 + 0.956955i \(0.406266\pi\)
\(992\) 2.62166e6i 2.66411i
\(993\) 336994. + 120890.i 0.341762 + 0.122600i
\(994\) −2.58000e6 −2.61125
\(995\) 1.29459e6i 1.30764i
\(996\) 1.27339e6 3.54971e6i 1.28363 3.57827i
\(997\) 115417. 0.116112 0.0580562 0.998313i \(-0.481510\pi\)
0.0580562 + 0.998313i \(0.481510\pi\)
\(998\) 111341.i 0.111788i
\(999\) −258680. 433996.i −0.259198 0.434865i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.5.b.a.119.74 yes 78
3.2 odd 2 inner 177.5.b.a.119.5 78
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.5.b.a.119.5 78 3.2 odd 2 inner
177.5.b.a.119.74 yes 78 1.1 even 1 trivial