Properties

Label 230.6.b.a.139.8
Level $230$
Weight $6$
Character 230.139
Analytic conductor $36.888$
Analytic rank $0$
Dimension $26$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [230,6,Mod(139,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("230.139");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 230.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: \(36.8882785570\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.8
Character \(\chi\) \(=\) 230.139
Dual form 230.6.b.a.139.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000i q^{2} +5.15388i q^{3} -16.0000 q^{4} +(33.2902 - 44.9084i) q^{5} +20.6155 q^{6} +47.7267i q^{7} +64.0000i q^{8} +216.438 q^{9} +O(q^{10})\) \(q-4.00000i q^{2} +5.15388i q^{3} -16.0000 q^{4} +(33.2902 - 44.9084i) q^{5} +20.6155 q^{6} +47.7267i q^{7} +64.0000i q^{8} +216.438 q^{9} +(-179.633 - 133.161i) q^{10} -454.115 q^{11} -82.4620i q^{12} +981.506i q^{13} +190.907 q^{14} +(231.452 + 171.574i) q^{15} +256.000 q^{16} +62.6745i q^{17} -865.750i q^{18} -779.572 q^{19} +(-532.644 + 718.534i) q^{20} -245.978 q^{21} +1816.46i q^{22} -529.000i q^{23} -329.848 q^{24} +(-908.521 - 2990.02i) q^{25} +3926.03 q^{26} +2367.88i q^{27} -763.627i q^{28} -6540.49 q^{29} +(686.295 - 925.809i) q^{30} -393.393 q^{31} -1024.00i q^{32} -2340.45i q^{33} +250.698 q^{34} +(2143.33 + 1588.83i) q^{35} -3463.00 q^{36} +13388.5i q^{37} +3118.29i q^{38} -5058.56 q^{39} +(2874.13 + 2130.57i) q^{40} +18185.9 q^{41} +983.910i q^{42} +10967.2i q^{43} +7265.84 q^{44} +(7205.26 - 9719.85i) q^{45} -2116.00 q^{46} +22561.4i q^{47} +1319.39i q^{48} +14529.2 q^{49} +(-11960.1 + 3634.08i) q^{50} -323.016 q^{51} -15704.1i q^{52} -1560.04i q^{53} +9471.54 q^{54} +(-15117.6 + 20393.6i) q^{55} -3054.51 q^{56} -4017.82i q^{57} +26162.0i q^{58} -16812.1 q^{59} +(-3703.23 - 2745.18i) q^{60} -25646.1 q^{61} +1573.57i q^{62} +10329.8i q^{63} -4096.00 q^{64} +(44077.8 + 32674.6i) q^{65} -9361.82 q^{66} +46004.1i q^{67} -1002.79i q^{68} +2726.40 q^{69} +(6355.33 - 8573.31i) q^{70} -20838.0 q^{71} +13852.0i q^{72} +47021.0i q^{73} +53554.1 q^{74} +(15410.2 - 4682.41i) q^{75} +12473.2 q^{76} -21673.4i q^{77} +20234.3i q^{78} +86675.9 q^{79} +(8522.30 - 11496.5i) q^{80} +40390.5 q^{81} -72743.7i q^{82} -48624.8i q^{83} +3935.64 q^{84} +(2814.61 + 2086.45i) q^{85} +43868.7 q^{86} -33708.9i q^{87} -29063.4i q^{88} +97581.8 q^{89} +(-38879.4 - 28821.0i) q^{90} -46844.1 q^{91} +8464.00i q^{92} -2027.50i q^{93} +90245.6 q^{94} +(-25952.1 + 35009.3i) q^{95} +5277.57 q^{96} +169813. i q^{97} -58116.7i q^{98} -98287.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000i 0.707107i
\(3\) 5.15388i 0.330621i 0.986242 + 0.165311i \(0.0528627\pi\)
−0.986242 + 0.165311i \(0.947137\pi\)
\(4\) −16.0000 −0.500000
\(5\) 33.2902 44.9084i 0.595514 0.803345i
\(6\) 20.6155 0.233785
\(7\) 47.7267i 0.368143i 0.982913 + 0.184071i \(0.0589278\pi\)
−0.982913 + 0.184071i \(0.941072\pi\)
\(8\) 64.0000i 0.353553i
\(9\) 216.438 0.890689
\(10\) −179.633 133.161i −0.568051 0.421092i
\(11\) −454.115 −1.13158 −0.565789 0.824550i \(-0.691428\pi\)
−0.565789 + 0.824550i \(0.691428\pi\)
\(12\) 82.4620i 0.165311i
\(13\) 981.506i 1.61077i 0.592749 + 0.805387i \(0.298043\pi\)
−0.592749 + 0.805387i \(0.701957\pi\)
\(14\) 190.907 0.260316
\(15\) 231.452 + 171.574i 0.265603 + 0.196890i
\(16\) 256.000 0.250000
\(17\) 62.6745i 0.0525979i 0.999654 + 0.0262989i \(0.00837218\pi\)
−0.999654 + 0.0262989i \(0.991628\pi\)
\(18\) 865.750i 0.629813i
\(19\) −779.572 −0.495419 −0.247709 0.968834i \(-0.579678\pi\)
−0.247709 + 0.968834i \(0.579678\pi\)
\(20\) −532.644 + 718.534i −0.297757 + 0.401673i
\(21\) −245.978 −0.121716
\(22\) 1816.46i 0.800146i
\(23\) 529.000i 0.208514i
\(24\) −329.848 −0.116892
\(25\) −908.521 2990.02i −0.290727 0.956806i
\(26\) 3926.03 1.13899
\(27\) 2367.88i 0.625102i
\(28\) 763.627i 0.184071i
\(29\) −6540.49 −1.44416 −0.722081 0.691809i \(-0.756814\pi\)
−0.722081 + 0.691809i \(0.756814\pi\)
\(30\) 686.295 925.809i 0.139222 0.187810i
\(31\) −393.393 −0.0735229 −0.0367614 0.999324i \(-0.511704\pi\)
−0.0367614 + 0.999324i \(0.511704\pi\)
\(32\) 1024.00i 0.176777i
\(33\) 2340.45i 0.374124i
\(34\) 250.698 0.0371923
\(35\) 2143.33 + 1588.83i 0.295746 + 0.219234i
\(36\) −3463.00 −0.445345
\(37\) 13388.5i 1.60779i 0.594773 + 0.803894i \(0.297242\pi\)
−0.594773 + 0.803894i \(0.702758\pi\)
\(38\) 3118.29i 0.350314i
\(39\) −5058.56 −0.532557
\(40\) 2874.13 + 2130.57i 0.284025 + 0.210546i
\(41\) 18185.9 1.68957 0.844784 0.535107i \(-0.179729\pi\)
0.844784 + 0.535107i \(0.179729\pi\)
\(42\) 983.910i 0.0860661i
\(43\) 10967.2i 0.904531i 0.891883 + 0.452266i \(0.149384\pi\)
−0.891883 + 0.452266i \(0.850616\pi\)
\(44\) 7265.84 0.565789
\(45\) 7205.26 9719.85i 0.530418 0.715531i
\(46\) −2116.00 −0.147442
\(47\) 22561.4i 1.48978i 0.667189 + 0.744888i \(0.267497\pi\)
−0.667189 + 0.744888i \(0.732503\pi\)
\(48\) 1319.39i 0.0826554i
\(49\) 14529.2 0.864471
\(50\) −11960.1 + 3634.08i −0.676564 + 0.205575i
\(51\) −323.016 −0.0173900
\(52\) 15704.1i 0.805387i
\(53\) 1560.04i 0.0762863i −0.999272 0.0381432i \(-0.987856\pi\)
0.999272 0.0381432i \(-0.0121443\pi\)
\(54\) 9471.54 0.442014
\(55\) −15117.6 + 20393.6i −0.673870 + 0.909047i
\(56\) −3054.51 −0.130158
\(57\) 4017.82i 0.163796i
\(58\) 26162.0i 1.02118i
\(59\) −16812.1 −0.628768 −0.314384 0.949296i \(-0.601798\pi\)
−0.314384 + 0.949296i \(0.601798\pi\)
\(60\) −3703.23 2745.18i −0.132802 0.0984448i
\(61\) −25646.1 −0.882464 −0.441232 0.897393i \(-0.645458\pi\)
−0.441232 + 0.897393i \(0.645458\pi\)
\(62\) 1573.57i 0.0519885i
\(63\) 10329.8i 0.327901i
\(64\) −4096.00 −0.125000
\(65\) 44077.8 + 32674.6i 1.29401 + 0.959238i
\(66\) −9361.82 −0.264545
\(67\) 46004.1i 1.25202i 0.779817 + 0.626008i \(0.215312\pi\)
−0.779817 + 0.626008i \(0.784688\pi\)
\(68\) 1002.79i 0.0262989i
\(69\) 2726.40 0.0689393
\(70\) 6355.33 8573.31i 0.155022 0.209124i
\(71\) −20838.0 −0.490580 −0.245290 0.969450i \(-0.578883\pi\)
−0.245290 + 0.969450i \(0.578883\pi\)
\(72\) 13852.0i 0.314906i
\(73\) 47021.0i 1.03273i 0.856370 + 0.516363i \(0.172714\pi\)
−0.856370 + 0.516363i \(0.827286\pi\)
\(74\) 53554.1 1.13688
\(75\) 15410.2 4682.41i 0.316341 0.0961205i
\(76\) 12473.2 0.247709
\(77\) 21673.4i 0.416582i
\(78\) 20234.3i 0.376574i
\(79\) 86675.9 1.56254 0.781269 0.624194i \(-0.214573\pi\)
0.781269 + 0.624194i \(0.214573\pi\)
\(80\) 8522.30 11496.5i 0.148878 0.200836i
\(81\) 40390.5 0.684017
\(82\) 72743.7i 1.19471i
\(83\) 48624.8i 0.774751i −0.921922 0.387376i \(-0.873382\pi\)
0.921922 0.387376i \(-0.126618\pi\)
\(84\) 3935.64 0.0608579
\(85\) 2814.61 + 2086.45i 0.0422543 + 0.0313228i
\(86\) 43868.7 0.639600
\(87\) 33708.9i 0.477471i
\(88\) 29063.4i 0.400073i
\(89\) 97581.8 1.30585 0.652926 0.757422i \(-0.273541\pi\)
0.652926 + 0.757422i \(0.273541\pi\)
\(90\) −38879.4 28821.0i −0.505957 0.375062i
\(91\) −46844.1 −0.592995
\(92\) 8464.00i 0.104257i
\(93\) 2027.50i 0.0243082i
\(94\) 90245.6 1.05343
\(95\) −25952.1 + 35009.3i −0.295029 + 0.397992i
\(96\) 5277.57 0.0584462
\(97\) 169813.i 1.83249i 0.400620 + 0.916244i \(0.368795\pi\)
−0.400620 + 0.916244i \(0.631205\pi\)
\(98\) 58116.7i 0.611273i
\(99\) −98287.6 −1.00788
\(100\) 14536.3 + 47840.3i 0.145363 + 0.478403i
\(101\) −17646.0 −0.172125 −0.0860625 0.996290i \(-0.527428\pi\)
−0.0860625 + 0.996290i \(0.527428\pi\)
\(102\) 1292.07i 0.0122966i
\(103\) 171436.i 1.59224i −0.605140 0.796119i \(-0.706883\pi\)
0.605140 0.796119i \(-0.293117\pi\)
\(104\) −62816.4 −0.569495
\(105\) −8188.65 + 11046.4i −0.0724835 + 0.0977798i
\(106\) −6240.17 −0.0539426
\(107\) 59037.9i 0.498507i −0.968438 0.249254i \(-0.919815\pi\)
0.968438 0.249254i \(-0.0801853\pi\)
\(108\) 37886.2i 0.312551i
\(109\) 185647. 1.49665 0.748326 0.663331i \(-0.230858\pi\)
0.748326 + 0.663331i \(0.230858\pi\)
\(110\) 81574.3 + 60470.4i 0.642794 + 0.476498i
\(111\) −69002.9 −0.531569
\(112\) 12218.0i 0.0920357i
\(113\) 18178.3i 0.133923i 0.997756 + 0.0669617i \(0.0213305\pi\)
−0.997756 + 0.0669617i \(0.978669\pi\)
\(114\) −16071.3 −0.115821
\(115\) −23756.5 17610.5i −0.167509 0.124173i
\(116\) 104648. 0.722081
\(117\) 212435.i 1.43470i
\(118\) 67248.2i 0.444606i
\(119\) −2991.24 −0.0193635
\(120\) −10980.7 + 14812.9i −0.0696110 + 0.0939049i
\(121\) 45169.6 0.280468
\(122\) 102584.i 0.623996i
\(123\) 93728.1i 0.558608i
\(124\) 6294.29 0.0367614
\(125\) −164522. 58738.2i −0.941777 0.336237i
\(126\) 41319.4 0.231861
\(127\) 271569.i 1.49407i 0.664786 + 0.747034i \(0.268523\pi\)
−0.664786 + 0.747034i \(0.731477\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) −56523.5 −0.299057
\(130\) 130698. 176311.i 0.678284 0.915002i
\(131\) −302459. −1.53989 −0.769943 0.638113i \(-0.779715\pi\)
−0.769943 + 0.638113i \(0.779715\pi\)
\(132\) 37447.3i 0.187062i
\(133\) 37206.4i 0.182385i
\(134\) 184016. 0.885308
\(135\) 106338. + 78827.4i 0.502173 + 0.372257i
\(136\) −4011.17 −0.0185962
\(137\) 290889.i 1.32412i −0.749453 0.662058i \(-0.769683\pi\)
0.749453 0.662058i \(-0.230317\pi\)
\(138\) 10905.6i 0.0487475i
\(139\) −315327. −1.38428 −0.692140 0.721763i \(-0.743332\pi\)
−0.692140 + 0.721763i \(0.743332\pi\)
\(140\) −34293.2 25421.3i −0.147873 0.109617i
\(141\) −116279. −0.492552
\(142\) 83351.9i 0.346892i
\(143\) 445717.i 1.82272i
\(144\) 55408.0 0.222672
\(145\) −217735. + 293723.i −0.860018 + 1.16016i
\(146\) 188084. 0.730247
\(147\) 74881.5i 0.285813i
\(148\) 214217.i 0.803894i
\(149\) −425427. −1.56986 −0.784928 0.619587i \(-0.787300\pi\)
−0.784928 + 0.619587i \(0.787300\pi\)
\(150\) −18729.6 61640.8i −0.0679674 0.223687i
\(151\) −187722. −0.669998 −0.334999 0.942219i \(-0.608736\pi\)
−0.334999 + 0.942219i \(0.608736\pi\)
\(152\) 49892.6i 0.175157i
\(153\) 13565.1i 0.0468484i
\(154\) −86693.7 −0.294568
\(155\) −13096.1 + 17666.6i −0.0437839 + 0.0590642i
\(156\) 80937.0 0.266278
\(157\) 46448.3i 0.150391i −0.997169 0.0751953i \(-0.976042\pi\)
0.997169 0.0751953i \(-0.0239580\pi\)
\(158\) 346704.i 1.10488i
\(159\) 8040.27 0.0252219
\(160\) −45986.2 34089.2i −0.142013 0.105273i
\(161\) 25247.4 0.0767631
\(162\) 161562.i 0.483673i
\(163\) 382470.i 1.12753i 0.825935 + 0.563765i \(0.190648\pi\)
−0.825935 + 0.563765i \(0.809352\pi\)
\(164\) −290975. −0.844784
\(165\) −105106. 77914.3i −0.300551 0.222796i
\(166\) −194499. −0.547832
\(167\) 586145.i 1.62635i −0.582021 0.813174i \(-0.697738\pi\)
0.582021 0.813174i \(-0.302262\pi\)
\(168\) 15742.6i 0.0430331i
\(169\) −592062. −1.59460
\(170\) 8345.79 11258.4i 0.0221485 0.0298783i
\(171\) −168729. −0.441264
\(172\) 175475.i 0.452266i
\(173\) 43802.8i 0.111272i 0.998451 + 0.0556362i \(0.0177187\pi\)
−0.998451 + 0.0556362i \(0.982281\pi\)
\(174\) −134836. −0.337623
\(175\) 142704. 43360.7i 0.352241 0.107029i
\(176\) −116253. −0.282894
\(177\) 86647.3i 0.207884i
\(178\) 390327.i 0.923377i
\(179\) 766442. 1.78791 0.893957 0.448153i \(-0.147918\pi\)
0.893957 + 0.448153i \(0.147918\pi\)
\(180\) −115284. + 155518.i −0.265209 + 0.357766i
\(181\) 342316. 0.776660 0.388330 0.921520i \(-0.373052\pi\)
0.388330 + 0.921520i \(0.373052\pi\)
\(182\) 187376.i 0.419311i
\(183\) 132177.i 0.291762i
\(184\) 33856.0 0.0737210
\(185\) 601257. + 445707.i 1.29161 + 0.957460i
\(186\) −8110.00 −0.0171885
\(187\) 28461.4i 0.0595186i
\(188\) 360982.i 0.744888i
\(189\) −113011. −0.230127
\(190\) 140037. + 103809.i 0.281423 + 0.208617i
\(191\) −561074. −1.11285 −0.556425 0.830898i \(-0.687827\pi\)
−0.556425 + 0.830898i \(0.687827\pi\)
\(192\) 21110.3i 0.0413277i
\(193\) 329086.i 0.635940i −0.948101 0.317970i \(-0.896999\pi\)
0.948101 0.317970i \(-0.103001\pi\)
\(194\) 679251. 1.29576
\(195\) −168401. + 227172.i −0.317145 + 0.427827i
\(196\) −232467. −0.432235
\(197\) 264621.i 0.485801i 0.970051 + 0.242900i \(0.0780988\pi\)
−0.970051 + 0.242900i \(0.921901\pi\)
\(198\) 393150.i 0.712682i
\(199\) −49430.4 −0.0884832 −0.0442416 0.999021i \(-0.514087\pi\)
−0.0442416 + 0.999021i \(0.514087\pi\)
\(200\) 191361. 58145.3i 0.338282 0.102787i
\(201\) −237100. −0.413943
\(202\) 70584.1i 0.121711i
\(203\) 312156.i 0.531657i
\(204\) 5168.26 0.00869499
\(205\) 605414. 816700.i 1.00616 1.35731i
\(206\) −685742. −1.12588
\(207\) 114495.i 0.185722i
\(208\) 251266.i 0.402694i
\(209\) 354016. 0.560604
\(210\) 44185.8 + 32754.6i 0.0691408 + 0.0512536i
\(211\) −891923. −1.37918 −0.689591 0.724199i \(-0.742210\pi\)
−0.689591 + 0.724199i \(0.742210\pi\)
\(212\) 24960.7i 0.0381432i
\(213\) 107396.i 0.162196i
\(214\) −236152. −0.352498
\(215\) 492518. + 365100.i 0.726651 + 0.538661i
\(216\) −151545. −0.221007
\(217\) 18775.3i 0.0270669i
\(218\) 742587.i 1.05829i
\(219\) −242340. −0.341441
\(220\) 241882. 326297.i 0.336935 0.454524i
\(221\) −61515.4 −0.0847233
\(222\) 276012.i 0.375876i
\(223\) 597814.i 0.805015i 0.915417 + 0.402507i \(0.131861\pi\)
−0.915417 + 0.402507i \(0.868139\pi\)
\(224\) 48872.1 0.0650791
\(225\) −196638. 647152.i −0.258947 0.852217i
\(226\) 72713.1 0.0946981
\(227\) 230418.i 0.296791i 0.988928 + 0.148396i \(0.0474109\pi\)
−0.988928 + 0.148396i \(0.952589\pi\)
\(228\) 64285.1i 0.0818980i
\(229\) −728543. −0.918050 −0.459025 0.888423i \(-0.651801\pi\)
−0.459025 + 0.888423i \(0.651801\pi\)
\(230\) −70442.1 + 95026.1i −0.0878037 + 0.118447i
\(231\) 111702. 0.137731
\(232\) 418592.i 0.510588i
\(233\) 895475.i 1.08060i −0.841473 0.540299i \(-0.818311\pi\)
0.841473 0.540299i \(-0.181689\pi\)
\(234\) 849739. 1.01449
\(235\) 1.01319e6 + 751074.i 1.19680 + 0.887183i
\(236\) 268993. 0.314384
\(237\) 446717.i 0.516609i
\(238\) 11965.0i 0.0136921i
\(239\) −271856. −0.307854 −0.153927 0.988082i \(-0.549192\pi\)
−0.153927 + 0.988082i \(0.549192\pi\)
\(240\) 59251.8 + 43922.9i 0.0664008 + 0.0492224i
\(241\) 901747. 1.00010 0.500049 0.865997i \(-0.333315\pi\)
0.500049 + 0.865997i \(0.333315\pi\)
\(242\) 180679.i 0.198321i
\(243\) 783564.i 0.851253i
\(244\) 410338. 0.441232
\(245\) 483679. 652481.i 0.514804 0.694469i
\(246\) 374912. 0.394995
\(247\) 765155.i 0.798008i
\(248\) 25177.2i 0.0259943i
\(249\) 250606. 0.256149
\(250\) −234953. + 658087.i −0.237756 + 0.665937i
\(251\) −464035. −0.464907 −0.232454 0.972608i \(-0.574675\pi\)
−0.232454 + 0.972608i \(0.574675\pi\)
\(252\) 165278.i 0.163950i
\(253\) 240227.i 0.235950i
\(254\) 1.08627e6 1.05647
\(255\) −10753.3 + 14506.1i −0.0103560 + 0.0139702i
\(256\) 65536.0 0.0625000
\(257\) 722423.i 0.682274i 0.940014 + 0.341137i \(0.110812\pi\)
−0.940014 + 0.341137i \(0.889188\pi\)
\(258\) 226094.i 0.211466i
\(259\) −638991. −0.591895
\(260\) −705245. 522793.i −0.647004 0.479619i
\(261\) −1.41561e6 −1.28630
\(262\) 1.20984e6i 1.08886i
\(263\) 348644.i 0.310808i −0.987851 0.155404i \(-0.950332\pi\)
0.987851 0.155404i \(-0.0496680\pi\)
\(264\) 149789. 0.132273
\(265\) −70058.9 51934.2i −0.0612843 0.0454296i
\(266\) −148826. −0.128965
\(267\) 502925.i 0.431743i
\(268\) 736066.i 0.626008i
\(269\) 1.51710e6 1.27830 0.639152 0.769080i \(-0.279285\pi\)
0.639152 + 0.769080i \(0.279285\pi\)
\(270\) 315310. 425351.i 0.263226 0.355090i
\(271\) 733012. 0.606300 0.303150 0.952943i \(-0.401962\pi\)
0.303150 + 0.952943i \(0.401962\pi\)
\(272\) 16044.7i 0.0131495i
\(273\) 241429.i 0.196057i
\(274\) −1.16356e6 −0.936291
\(275\) 412573. + 1.35781e6i 0.328980 + 1.08270i
\(276\) −43622.4 −0.0344697
\(277\) 115106.i 0.0901364i −0.998984 0.0450682i \(-0.985649\pi\)
0.998984 0.0450682i \(-0.0143505\pi\)
\(278\) 1.26131e6i 0.978834i
\(279\) −85145.0 −0.0654860
\(280\) −101685. + 137173.i −0.0775109 + 0.104562i
\(281\) 1.10282e6 0.833178 0.416589 0.909095i \(-0.363225\pi\)
0.416589 + 0.909095i \(0.363225\pi\)
\(282\) 465115.i 0.348287i
\(283\) 2.18776e6i 1.62381i −0.583793 0.811903i \(-0.698432\pi\)
0.583793 0.811903i \(-0.301568\pi\)
\(284\) 333408. 0.245290
\(285\) −180434. 133754.i −0.131585 0.0975428i
\(286\) −1.78287e6 −1.28886
\(287\) 867954.i 0.622002i
\(288\) 221632.i 0.157453i
\(289\) 1.41593e6 0.997233
\(290\) 1.17489e6 + 870938.i 0.820357 + 0.608124i
\(291\) −875195. −0.605860
\(292\) 752336.i 0.516363i
\(293\) 1.30722e6i 0.889569i 0.895638 + 0.444785i \(0.146720\pi\)
−0.895638 + 0.444785i \(0.853280\pi\)
\(294\) 299526. 0.202100
\(295\) −559677. + 755002.i −0.374440 + 0.505118i
\(296\) −856866. −0.568439
\(297\) 1.07529e6i 0.707352i
\(298\) 1.70171e6i 1.11006i
\(299\) 519217. 0.335870
\(300\) −246563. + 74918.5i −0.158170 + 0.0480602i
\(301\) −523427. −0.332997
\(302\) 750889.i 0.473760i
\(303\) 90945.5i 0.0569082i
\(304\) −199570. −0.123855
\(305\) −853765. + 1.15172e6i −0.525519 + 0.708923i
\(306\) 54260.4 0.0331268
\(307\) 3.16021e6i 1.91368i −0.290607 0.956842i \(-0.593857\pi\)
0.290607 0.956842i \(-0.406143\pi\)
\(308\) 346775.i 0.208291i
\(309\) 883558. 0.526428
\(310\) 70666.5 + 52384.6i 0.0417647 + 0.0309599i
\(311\) −2.82259e6 −1.65481 −0.827403 0.561608i \(-0.810183\pi\)
−0.827403 + 0.561608i \(0.810183\pi\)
\(312\) 323748.i 0.188287i
\(313\) 1.35221e6i 0.780157i 0.920782 + 0.390079i \(0.127552\pi\)
−0.920782 + 0.390079i \(0.872448\pi\)
\(314\) −185793. −0.106342
\(315\) 463896. + 343883.i 0.263418 + 0.195269i
\(316\) −1.38681e6 −0.781269
\(317\) 27641.1i 0.0154492i 0.999970 + 0.00772461i \(0.00245884\pi\)
−0.999970 + 0.00772461i \(0.997541\pi\)
\(318\) 32161.1i 0.0178346i
\(319\) 2.97014e6 1.63418
\(320\) −136357. + 183945.i −0.0744392 + 0.100418i
\(321\) 304274. 0.164817
\(322\) 100990.i 0.0542797i
\(323\) 48859.3i 0.0260580i
\(324\) −646249. −0.342009
\(325\) 2.93472e6 891719.i 1.54120 0.468295i
\(326\) 1.52988e6 0.797284
\(327\) 956800.i 0.494825i
\(328\) 1.16390e6i 0.597353i
\(329\) −1.07678e6 −0.548450
\(330\) −311657. + 420424.i −0.157540 + 0.212521i
\(331\) 2.58398e6 1.29634 0.648171 0.761495i \(-0.275534\pi\)
0.648171 + 0.761495i \(0.275534\pi\)
\(332\) 777996.i 0.387376i
\(333\) 2.89778e6i 1.43204i
\(334\) −2.34458e6 −1.15000
\(335\) 2.06597e6 + 1.53149e6i 1.00580 + 0.745592i
\(336\) −62970.2 −0.0304290
\(337\) 19157.4i 0.00918884i −0.999989 0.00459442i \(-0.998538\pi\)
0.999989 0.00459442i \(-0.00146246\pi\)
\(338\) 2.36825e6i 1.12755i
\(339\) −93688.5 −0.0442779
\(340\) −45033.7 33383.2i −0.0211271 0.0156614i
\(341\) 178646. 0.0831968
\(342\) 674915.i 0.312021i
\(343\) 1.49557e6i 0.686391i
\(344\) −701899. −0.319800
\(345\) 90762.5 122438.i 0.0410543 0.0553821i
\(346\) 175211. 0.0786814
\(347\) 2.85865e6i 1.27449i 0.770660 + 0.637247i \(0.219927\pi\)
−0.770660 + 0.637247i \(0.780073\pi\)
\(348\) 539343.i 0.238735i
\(349\) −1.89625e6 −0.833361 −0.416680 0.909053i \(-0.636807\pi\)
−0.416680 + 0.909053i \(0.636807\pi\)
\(350\) −173443. 570815.i −0.0756809 0.249072i
\(351\) −2.32409e6 −1.00690
\(352\) 465014.i 0.200037i
\(353\) 867325.i 0.370463i −0.982695 0.185232i \(-0.940696\pi\)
0.982695 0.185232i \(-0.0593035\pi\)
\(354\) −346589. −0.146996
\(355\) −693701. + 935799.i −0.292147 + 0.394105i
\(356\) −1.56131e6 −0.652926
\(357\) 15416.5i 0.00640200i
\(358\) 3.06577e6i 1.26425i
\(359\) 2.49173e6 1.02039 0.510194 0.860059i \(-0.329573\pi\)
0.510194 + 0.860059i \(0.329573\pi\)
\(360\) 622071. + 461136.i 0.252978 + 0.187531i
\(361\) −1.86837e6 −0.754560
\(362\) 1.36926e6i 0.549182i
\(363\) 232799.i 0.0927287i
\(364\) 749505. 0.296497
\(365\) 2.11164e6 + 1.56534e6i 0.829635 + 0.615002i
\(366\) −528708. −0.206307
\(367\) 384354.i 0.148959i −0.997223 0.0744794i \(-0.976270\pi\)
0.997223 0.0744794i \(-0.0237295\pi\)
\(368\) 135424.i 0.0521286i
\(369\) 3.93612e6 1.50488
\(370\) 1.78283e6 2.40503e6i 0.677026 0.913305i
\(371\) 74455.7 0.0280843
\(372\) 32440.0i 0.0121541i
\(373\) 43070.0i 0.0160289i −0.999968 0.00801443i \(-0.997449\pi\)
0.999968 0.00801443i \(-0.00255110\pi\)
\(374\) −113846. −0.0420860
\(375\) 302730. 847925.i 0.111167 0.311372i
\(376\) −1.44393e6 −0.526716
\(377\) 6.41954e6i 2.32622i
\(378\) 452045.i 0.162724i
\(379\) −2.63305e6 −0.941587 −0.470794 0.882243i \(-0.656032\pi\)
−0.470794 + 0.882243i \(0.656032\pi\)
\(380\) 415234. 560149.i 0.147514 0.198996i
\(381\) −1.39963e6 −0.493971
\(382\) 2.24429e6i 0.786903i
\(383\) 1.25106e6i 0.435795i −0.975972 0.217897i \(-0.930080\pi\)
0.975972 0.217897i \(-0.0699198\pi\)
\(384\) −84441.1 −0.0292231
\(385\) −973317. 721513.i −0.334659 0.248080i
\(386\) −1.31634e6 −0.449678
\(387\) 2.37371e6i 0.805657i
\(388\) 2.71701e6i 0.916244i
\(389\) 5.02700e6 1.68436 0.842180 0.539196i \(-0.181272\pi\)
0.842180 + 0.539196i \(0.181272\pi\)
\(390\) 908687. + 673603.i 0.302519 + 0.224255i
\(391\) 33154.8 0.0109674
\(392\) 929866.i 0.305637i
\(393\) 1.55884e6i 0.509119i
\(394\) 1.05848e6 0.343513
\(395\) 2.88546e6 3.89247e6i 0.930513 1.25526i
\(396\) 1.57260e6 0.503942
\(397\) 1.43004e6i 0.455379i −0.973734 0.227690i \(-0.926883\pi\)
0.973734 0.227690i \(-0.0731171\pi\)
\(398\) 197721.i 0.0625671i
\(399\) 191757. 0.0603003
\(400\) −232581. 765445.i −0.0726817 0.239202i
\(401\) −3.20563e6 −0.995525 −0.497762 0.867313i \(-0.665845\pi\)
−0.497762 + 0.867313i \(0.665845\pi\)
\(402\) 948398.i 0.292702i
\(403\) 386118.i 0.118429i
\(404\) 282337. 0.0860625
\(405\) 1.34461e6 1.81387e6i 0.407342 0.549502i
\(406\) −1.24862e6 −0.375939
\(407\) 6.07994e6i 1.81934i
\(408\) 20673.1i 0.00614829i
\(409\) −3.66769e6 −1.08414 −0.542068 0.840334i \(-0.682359\pi\)
−0.542068 + 0.840334i \(0.682359\pi\)
\(410\) −3.26680e6 2.42166e6i −0.959761 0.711464i
\(411\) 1.49921e6 0.437781
\(412\) 2.74297e6i 0.796119i
\(413\) 802384.i 0.231477i
\(414\) −457982. −0.131325
\(415\) −2.18366e6 1.61873e6i −0.622393 0.461375i
\(416\) 1.00506e6 0.284747
\(417\) 1.62516e6i 0.457673i
\(418\) 1.41606e6i 0.396407i
\(419\) 1.91459e6 0.532772 0.266386 0.963866i \(-0.414170\pi\)
0.266386 + 0.963866i \(0.414170\pi\)
\(420\) 131018. 176743.i 0.0362417 0.0488899i
\(421\) −3.44059e6 −0.946080 −0.473040 0.881041i \(-0.656843\pi\)
−0.473040 + 0.881041i \(0.656843\pi\)
\(422\) 3.56769e6i 0.975229i
\(423\) 4.88313e6i 1.32693i
\(424\) 99842.7 0.0269713
\(425\) 187398. 56941.1i 0.0503260 0.0152916i
\(426\) −429586. −0.114690
\(427\) 1.22400e6i 0.324873i
\(428\) 944607.i 0.249254i
\(429\) 2.29717e6 0.602629
\(430\) 1.46040e6 1.97007e6i 0.380891 0.513820i
\(431\) −5.26168e6 −1.36437 −0.682184 0.731181i \(-0.738970\pi\)
−0.682184 + 0.731181i \(0.738970\pi\)
\(432\) 606179.i 0.156276i
\(433\) 3.67109e6i 0.940968i −0.882408 0.470484i \(-0.844079\pi\)
0.882408 0.470484i \(-0.155921\pi\)
\(434\) −75101.4 −0.0191392
\(435\) −1.51381e6 1.12218e6i −0.383574 0.284340i
\(436\) −2.97035e6 −0.748326
\(437\) 412394.i 0.103302i
\(438\) 969362.i 0.241435i
\(439\) −1.05642e6 −0.261623 −0.130812 0.991407i \(-0.541758\pi\)
−0.130812 + 0.991407i \(0.541758\pi\)
\(440\) −1.30519e6 967526.i −0.321397 0.238249i
\(441\) 3.14466e6 0.769975
\(442\) 246062.i 0.0599084i
\(443\) 4.92747e6i 1.19293i 0.802639 + 0.596464i \(0.203428\pi\)
−0.802639 + 0.596464i \(0.796572\pi\)
\(444\) 1.10405e6 0.265785
\(445\) 3.24852e6 4.38224e6i 0.777653 1.04905i
\(446\) 2.39126e6 0.569231
\(447\) 2.19260e6i 0.519028i
\(448\) 195489.i 0.0460178i
\(449\) 4.10998e6 0.962109 0.481054 0.876691i \(-0.340254\pi\)
0.481054 + 0.876691i \(0.340254\pi\)
\(450\) −2.58861e6 + 786552.i −0.602609 + 0.183103i
\(451\) −8.25851e6 −1.91188
\(452\) 290852.i 0.0669617i
\(453\) 967497.i 0.221516i
\(454\) 921671. 0.209863
\(455\) −1.55945e6 + 2.10369e6i −0.353137 + 0.476380i
\(456\) 257140. 0.0579106
\(457\) 137840.i 0.0308733i −0.999881 0.0154367i \(-0.995086\pi\)
0.999881 0.0154367i \(-0.00491384\pi\)
\(458\) 2.91417e6i 0.649160i
\(459\) −148406. −0.0328791
\(460\) 380104. + 281769.i 0.0837545 + 0.0620866i
\(461\) 8.88101e6 1.94630 0.973150 0.230171i \(-0.0739285\pi\)
0.973150 + 0.230171i \(0.0739285\pi\)
\(462\) 446809.i 0.0973905i
\(463\) 332466.i 0.0720768i 0.999350 + 0.0360384i \(0.0114739\pi\)
−0.999350 + 0.0360384i \(0.988526\pi\)
\(464\) −1.67437e6 −0.361040
\(465\) −91051.7 67495.9i −0.0195279 0.0144759i
\(466\) −3.58190e6 −0.764098
\(467\) 2.48842e6i 0.527997i −0.964523 0.263999i \(-0.914959\pi\)
0.964523 0.263999i \(-0.0850415\pi\)
\(468\) 3.39896e6i 0.717350i
\(469\) −2.19562e6 −0.460920
\(470\) 3.00430e6 4.05278e6i 0.627333 0.846269i
\(471\) 239389. 0.0497223
\(472\) 1.07597e6i 0.222303i
\(473\) 4.98036e6i 1.02355i
\(474\) 1.78687e6 0.365297
\(475\) 708258. + 2.33094e6i 0.144031 + 0.474019i
\(476\) 47859.9 0.00968176
\(477\) 337652.i 0.0679474i
\(478\) 1.08742e6i 0.217685i
\(479\) −4.38795e6 −0.873821 −0.436911 0.899505i \(-0.643927\pi\)
−0.436911 + 0.899505i \(0.643927\pi\)
\(480\) 175692. 237007.i 0.0348055 0.0469524i
\(481\) −1.31409e7 −2.58978
\(482\) 3.60699e6i 0.707176i
\(483\) 130122.i 0.0253795i
\(484\) −722714. −0.140234
\(485\) 7.62602e6 + 5.65311e6i 1.47212 + 1.09127i
\(486\) 3.13426e6 0.601927
\(487\) 7.34951e6i 1.40422i 0.712067 + 0.702112i \(0.247759\pi\)
−0.712067 + 0.702112i \(0.752241\pi\)
\(488\) 1.64135e6i 0.311998i
\(489\) −1.97120e6 −0.372786
\(490\) −2.60992e6 1.93472e6i −0.491063 0.364022i
\(491\) −2.27547e6 −0.425958 −0.212979 0.977057i \(-0.568317\pi\)
−0.212979 + 0.977057i \(0.568317\pi\)
\(492\) 1.49965e6i 0.279304i
\(493\) 409922.i 0.0759598i
\(494\) −3.06062e6 −0.564277
\(495\) −3.27202e6 + 4.41393e6i −0.600209 + 0.809679i
\(496\) −100709. −0.0183807
\(497\) 994528.i 0.180603i
\(498\) 1.00242e6i 0.181125i
\(499\) 1.78996e6 0.321804 0.160902 0.986970i \(-0.448560\pi\)
0.160902 + 0.986970i \(0.448560\pi\)
\(500\) 2.63235e6 + 939812.i 0.470889 + 0.168119i
\(501\) 3.02092e6 0.537706
\(502\) 1.85614e6i 0.328739i
\(503\) 5.19307e6i 0.915176i 0.889164 + 0.457588i \(0.151286\pi\)
−0.889164 + 0.457588i \(0.848714\pi\)
\(504\) −661110. −0.115930
\(505\) −587441. + 792454.i −0.102503 + 0.138276i
\(506\) 960908. 0.166842
\(507\) 3.05141e6i 0.527207i
\(508\) 4.34510e6i 0.747034i
\(509\) 2.76160e6 0.472462 0.236231 0.971697i \(-0.424088\pi\)
0.236231 + 0.971697i \(0.424088\pi\)
\(510\) 58024.6 + 43013.2i 0.00987840 + 0.00732278i
\(511\) −2.24416e6 −0.380190
\(512\) 262144.i 0.0441942i
\(513\) 1.84594e6i 0.309687i
\(514\) 2.88969e6 0.482440
\(515\) −7.69889e6 5.70713e6i −1.27912 0.948199i
\(516\) 904376. 0.149529
\(517\) 1.02455e7i 1.68580i
\(518\) 2.55596e6i 0.418533i
\(519\) −225755. −0.0367890
\(520\) −2.09117e6 + 2.82098e6i −0.339142 + 0.457501i
\(521\) 87258.4 0.0140836 0.00704178 0.999975i \(-0.497759\pi\)
0.00704178 + 0.999975i \(0.497759\pi\)
\(522\) 5.66243e6i 0.909551i
\(523\) 4.39249e6i 0.702194i 0.936339 + 0.351097i \(0.114191\pi\)
−0.936339 + 0.351097i \(0.885809\pi\)
\(524\) 4.83934e6 0.769943
\(525\) 223476. + 735478.i 0.0353861 + 0.116458i
\(526\) −1.39458e6 −0.219775
\(527\) 24655.7i 0.00386715i
\(528\) 599156.i 0.0935309i
\(529\) −279841. −0.0434783
\(530\) −207737. + 280236.i −0.0321236 + 0.0433345i
\(531\) −3.63876e6 −0.560037
\(532\) 595302.i 0.0911924i
\(533\) 1.78496e7i 2.72151i
\(534\) 2.01170e6 0.305288
\(535\) −2.65130e6 1.96539e6i −0.400474 0.296868i
\(536\) −2.94426e6 −0.442654
\(537\) 3.95015e6i 0.591123i
\(538\) 6.06841e6i 0.903898i
\(539\) −6.59791e6 −0.978216
\(540\) −1.70141e6 1.26124e6i −0.251086 0.186129i
\(541\) 5.93941e6 0.872469 0.436234 0.899833i \(-0.356312\pi\)
0.436234 + 0.899833i \(0.356312\pi\)
\(542\) 2.93205e6i 0.428719i
\(543\) 1.76426e6i 0.256780i
\(544\) 64178.6 0.00929808
\(545\) 6.18022e6 8.33709e6i 0.891277 1.20233i
\(546\) −965714. −0.138633
\(547\) 7.11819e6i 1.01719i −0.861007 0.508594i \(-0.830166\pi\)
0.861007 0.508594i \(-0.169834\pi\)
\(548\) 4.65422e6i 0.662058i
\(549\) −5.55078e6 −0.786001
\(550\) 5.43125e6 1.65029e6i 0.765585 0.232624i
\(551\) 5.09879e6 0.715464
\(552\) 174490.i 0.0243737i
\(553\) 4.13675e6i 0.575237i
\(554\) −460426. −0.0637361
\(555\) −2.29712e6 + 3.09881e6i −0.316557 + 0.427034i
\(556\) 5.04523e6 0.692140
\(557\) 4.09500e6i 0.559262i −0.960108 0.279631i \(-0.909788\pi\)
0.960108 0.279631i \(-0.0902122\pi\)
\(558\) 340580.i 0.0463056i
\(559\) −1.07644e7 −1.45700
\(560\) 548692. + 406741.i 0.0739364 + 0.0548085i
\(561\) 146687. 0.0196781
\(562\) 4.41127e6i 0.589146i
\(563\) 6.45950e6i 0.858871i −0.903097 0.429436i \(-0.858712\pi\)
0.903097 0.429436i \(-0.141288\pi\)
\(564\) 1.86046e6 0.246276
\(565\) 816356. + 605159.i 0.107587 + 0.0797532i
\(566\) −8.75105e6 −1.14820
\(567\) 1.92771e6i 0.251816i
\(568\) 1.33363e6i 0.173446i
\(569\) 5.79214e6 0.749995 0.374997 0.927026i \(-0.377644\pi\)
0.374997 + 0.927026i \(0.377644\pi\)
\(570\) −535016. + 721735.i −0.0689731 + 0.0930444i
\(571\) 9.17311e6 1.17741 0.588703 0.808350i \(-0.299639\pi\)
0.588703 + 0.808350i \(0.299639\pi\)
\(572\) 7.13147e6i 0.911358i
\(573\) 2.89170e6i 0.367932i
\(574\) 3.47182e6 0.439822
\(575\) −1.58172e6 + 480608.i −0.199508 + 0.0606207i
\(576\) −886528. −0.111336
\(577\) 3.11516e6i 0.389529i −0.980850 0.194765i \(-0.937606\pi\)
0.980850 0.194765i \(-0.0623943\pi\)
\(578\) 5.66372e6i 0.705151i
\(579\) 1.69607e6 0.210255
\(580\) 3.48375e6 4.69957e6i 0.430009 0.580080i
\(581\) 2.32070e6 0.285219
\(582\) 3.50078e6i 0.428408i
\(583\) 708439.i 0.0863239i
\(584\) −3.00934e6 −0.365123
\(585\) 9.54010e6 + 7.07201e6i 1.15256 + 0.854384i
\(586\) 5.22888e6 0.629020
\(587\) 1.29305e7i 1.54889i 0.632640 + 0.774446i \(0.281971\pi\)
−0.632640 + 0.774446i \(0.718029\pi\)
\(588\) 1.19810e6i 0.142906i
\(589\) 306678. 0.0364246
\(590\) 3.02001e6 + 2.23871e6i 0.357172 + 0.264769i
\(591\) −1.36382e6 −0.160616
\(592\) 3.42747e6i 0.401947i
\(593\) 532524.i 0.0621874i 0.999516 + 0.0310937i \(0.00989903\pi\)
−0.999516 + 0.0310937i \(0.990101\pi\)
\(594\) −4.30117e6 −0.500173
\(595\) −99579.2 + 134332.i −0.0115312 + 0.0155556i
\(596\) 6.80684e6 0.784928
\(597\) 254758.i 0.0292545i
\(598\) 2.07687e6i 0.237496i
\(599\) −1.08520e6 −0.123578 −0.0617892 0.998089i \(-0.519681\pi\)
−0.0617892 + 0.998089i \(0.519681\pi\)
\(600\) 299674. + 986252.i 0.0339837 + 0.111843i
\(601\) −1.02764e7 −1.16053 −0.580264 0.814429i \(-0.697051\pi\)
−0.580264 + 0.814429i \(0.697051\pi\)
\(602\) 2.09371e6i 0.235464i
\(603\) 9.95702e6i 1.11516i
\(604\) 3.00356e6 0.334999
\(605\) 1.50371e6 2.02849e6i 0.167022 0.225312i
\(606\) −363782. −0.0402402
\(607\) 8.62437e6i 0.950070i −0.879967 0.475035i \(-0.842435\pi\)
0.879967 0.475035i \(-0.157565\pi\)
\(608\) 798282.i 0.0875784i
\(609\) 1.60881e6 0.175777
\(610\) 4.60690e6 + 3.41506e6i 0.501284 + 0.371598i
\(611\) −2.21441e7 −2.39969
\(612\) 217042.i 0.0234242i
\(613\) 1.62760e7i 1.74943i −0.484639 0.874714i \(-0.661049\pi\)
0.484639 0.874714i \(-0.338951\pi\)
\(614\) −1.26409e7 −1.35318
\(615\) 4.20917e6 + 3.12023e6i 0.448755 + 0.332658i
\(616\) 1.38710e6 0.147284
\(617\) 5.40371e6i 0.571451i 0.958312 + 0.285725i \(0.0922345\pi\)
−0.958312 + 0.285725i \(0.907765\pi\)
\(618\) 3.53423e6i 0.372241i
\(619\) 3.18243e6 0.333835 0.166917 0.985971i \(-0.446619\pi\)
0.166917 + 0.985971i \(0.446619\pi\)
\(620\) 209538. 282666.i 0.0218919 0.0295321i
\(621\) 1.25261e6 0.130343
\(622\) 1.12904e7i 1.17013i
\(623\) 4.65726e6i 0.480740i
\(624\) −1.29499e6 −0.133139
\(625\) −8.11480e6 + 5.43299e6i −0.830956 + 0.556338i
\(626\) 5.40882e6 0.551654
\(627\) 1.82455e6i 0.185348i
\(628\) 743172.i 0.0751953i
\(629\) −839119. −0.0845663
\(630\) 1.37553e6 1.85559e6i 0.138076 0.186264i
\(631\) 1.02411e7 1.02393 0.511966 0.859006i \(-0.328917\pi\)
0.511966 + 0.859006i \(0.328917\pi\)
\(632\) 5.54726e6i 0.552441i
\(633\) 4.59686e6i 0.455987i
\(634\) 110564. 0.0109242
\(635\) 1.21957e7 + 9.04058e6i 1.20025 + 0.889738i
\(636\) −128644. −0.0126109
\(637\) 1.42605e7i 1.39247i
\(638\) 1.18806e7i 1.15554i
\(639\) −4.51012e6 −0.436954
\(640\) 735779. + 545427.i 0.0710063 + 0.0526365i
\(641\) −2.49786e6 −0.240117 −0.120059 0.992767i \(-0.538308\pi\)
−0.120059 + 0.992767i \(0.538308\pi\)
\(642\) 1.21710e6i 0.116543i
\(643\) 7.82876e6i 0.746733i 0.927684 + 0.373367i \(0.121797\pi\)
−0.927684 + 0.373367i \(0.878203\pi\)
\(644\) −403959. −0.0383815
\(645\) −1.88168e6 + 2.53838e6i −0.178093 + 0.240246i
\(646\) −195437. −0.0184258
\(647\) 1.44592e7i 1.35795i 0.734160 + 0.678977i \(0.237576\pi\)
−0.734160 + 0.678977i \(0.762424\pi\)
\(648\) 2.58499e6i 0.241837i
\(649\) 7.63461e6 0.711500
\(650\) −3.56688e6 1.17389e7i −0.331135 1.08979i
\(651\) 96765.8 0.00894890
\(652\) 6.11952e6i 0.563765i
\(653\) 4.86495e6i 0.446473i 0.974764 + 0.223236i \(0.0716622\pi\)
−0.974764 + 0.223236i \(0.928338\pi\)
\(654\) 3.82720e6 0.349894
\(655\) −1.00689e7 + 1.35829e7i −0.917023 + 1.23706i
\(656\) 4.65560e6 0.422392
\(657\) 1.01771e7i 0.919837i
\(658\) 4.30712e6i 0.387813i
\(659\) 8.41470e6 0.754788 0.377394 0.926053i \(-0.376820\pi\)
0.377394 + 0.926053i \(0.376820\pi\)
\(660\) 1.68170e6 + 1.24663e6i 0.150275 + 0.111398i
\(661\) −7.10332e6 −0.632351 −0.316175 0.948701i \(-0.602399\pi\)
−0.316175 + 0.948701i \(0.602399\pi\)
\(662\) 1.03359e7i 0.916652i
\(663\) 317043.i 0.0280113i
\(664\) 3.11198e6 0.273916
\(665\) −1.67088e6 1.23861e6i −0.146518 0.108613i
\(666\) 1.15911e7 1.01261
\(667\) 3.45992e6i 0.301128i
\(668\) 9.37831e6i 0.813174i
\(669\) −3.08106e6 −0.266155
\(670\) 6.12595e6 8.26388e6i 0.527213 0.711208i
\(671\) 1.16463e7 0.998577
\(672\) 251881.i 0.0215165i
\(673\) 2.28964e6i 0.194863i −0.995242 0.0974315i \(-0.968937\pi\)
0.995242 0.0974315i \(-0.0310627\pi\)
\(674\) −76629.4 −0.00649749
\(675\) 7.08002e6 2.15127e6i 0.598102 0.181734i
\(676\) 9.47299e6 0.797298
\(677\) 1.52700e7i 1.28046i −0.768183 0.640230i \(-0.778839\pi\)
0.768183 0.640230i \(-0.221161\pi\)
\(678\) 374754.i 0.0313092i
\(679\) −8.10460e6 −0.674617
\(680\) −133533. + 180135.i −0.0110743 + 0.0149391i
\(681\) −1.18755e6 −0.0981256
\(682\) 714583.i 0.0588290i
\(683\) 1.11283e6i 0.0912803i −0.998958 0.0456402i \(-0.985467\pi\)
0.998958 0.0456402i \(-0.0145328\pi\)
\(684\) 2.69966e6 0.220632
\(685\) −1.30633e7 9.68376e6i −1.06372 0.788529i
\(686\) 5.98229e6 0.485352
\(687\) 3.75482e6i 0.303527i
\(688\) 2.80760e6i 0.226133i
\(689\) 1.53119e6 0.122880
\(690\) −489753. 363050.i −0.0391610 0.0290298i
\(691\) 1.47185e7 1.17265 0.586324 0.810077i \(-0.300575\pi\)
0.586324 + 0.810077i \(0.300575\pi\)
\(692\) 700846.i 0.0556362i
\(693\) 4.69094e6i 0.371045i
\(694\) 1.14346e7 0.901203
\(695\) −1.04973e7 + 1.41608e7i −0.824358 + 1.11205i
\(696\) 2.15737e6 0.168811
\(697\) 1.13979e6i 0.0888677i
\(698\) 7.58502e6i 0.589275i
\(699\) 4.61517e6 0.357269
\(700\) −2.28326e6 + 693771.i −0.176121 + 0.0535145i
\(701\) 1.61884e7 1.24426 0.622128 0.782916i \(-0.286268\pi\)
0.622128 + 0.782916i \(0.286268\pi\)
\(702\) 9.29638e6i 0.711985i
\(703\) 1.04373e7i 0.796528i
\(704\) 1.86006e6 0.141447
\(705\) −3.87094e6 + 5.22188e6i −0.293322 + 0.395689i
\(706\) −3.46930e6 −0.261957
\(707\) 842187.i 0.0633665i
\(708\) 1.38636e6i 0.103942i
\(709\) 1.12554e7 0.840905 0.420453 0.907314i \(-0.361871\pi\)
0.420453 + 0.907314i \(0.361871\pi\)
\(710\) 3.74320e6 + 2.77480e6i 0.278674 + 0.206579i
\(711\) 1.87599e7 1.39174
\(712\) 6.24524e6i 0.461688i
\(713\) 208105.i 0.0153306i
\(714\) −61666.0 −0.00452690
\(715\) −2.00164e7 1.48380e7i −1.46427 1.08545i
\(716\) −1.22631e7 −0.893957
\(717\) 1.40111e6i 0.101783i
\(718\) 9.96694e6i 0.721524i
\(719\) 4.29127e6 0.309574 0.154787 0.987948i \(-0.450531\pi\)
0.154787 + 0.987948i \(0.450531\pi\)
\(720\) 1.84455e6 2.48828e6i 0.132604 0.178883i
\(721\) 8.18205e6 0.586171
\(722\) 7.47347e6i 0.533555i
\(723\) 4.64750e6i 0.330654i
\(724\) −5.47706e6 −0.388330
\(725\) 5.94218e6 + 1.95562e7i 0.419856 + 1.38178i
\(726\) 931195. 0.0655691
\(727\) 8.16127e6i 0.572693i −0.958126 0.286346i \(-0.907559\pi\)
0.958126 0.286346i \(-0.0924408\pi\)
\(728\) 2.99802e6i 0.209655i
\(729\) 5.77651e6 0.402575
\(730\) 6.26136e6 8.44654e6i 0.434872 0.586640i
\(731\) −687362. −0.0475764
\(732\) 2.11483e6i 0.145881i
\(733\) 1.67910e7i 1.15429i −0.816641 0.577146i \(-0.804166\pi\)
0.816641 0.577146i \(-0.195834\pi\)
\(734\) −1.53742e6 −0.105330
\(735\) 3.36281e6 + 2.49282e6i 0.229606 + 0.170205i
\(736\) −541696. −0.0368605
\(737\) 2.08912e7i 1.41675i
\(738\) 1.57445e7i 1.06411i
\(739\) −2.61646e7 −1.76239 −0.881196 0.472751i \(-0.843261\pi\)
−0.881196 + 0.472751i \(0.843261\pi\)
\(740\) −9.62012e6 7.13132e6i −0.645804 0.478730i
\(741\) 3.94352e6 0.263838
\(742\) 297823.i 0.0198586i
\(743\) 5.75330e6i 0.382336i 0.981557 + 0.191168i \(0.0612275\pi\)
−0.981557 + 0.191168i \(0.938773\pi\)
\(744\) 129760. 0.00859426
\(745\) −1.41626e7 + 1.91052e7i −0.934871 + 1.26114i
\(746\) −172280. −0.0113341
\(747\) 1.05242e7i 0.690063i
\(748\) 455383.i 0.0297593i
\(749\) 2.81769e6 0.183522
\(750\) −3.39170e6 1.21092e6i −0.220173 0.0786071i
\(751\) 2.82333e6 0.182668 0.0913339 0.995820i \(-0.470887\pi\)
0.0913339 + 0.995820i \(0.470887\pi\)
\(752\) 5.77572e6i 0.372444i
\(753\) 2.39158e6i 0.153708i
\(754\) −2.56782e7 −1.64488
\(755\) −6.24932e6 + 8.43030e6i −0.398993 + 0.538239i
\(756\) 1.80818e6 0.115063
\(757\) 2.09725e6i 0.133018i −0.997786 0.0665089i \(-0.978814\pi\)
0.997786 0.0665089i \(-0.0211861\pi\)
\(758\) 1.05322e7i 0.665803i
\(759\) −1.23810e6 −0.0780102
\(760\) −2.24060e6 1.66094e6i −0.140711 0.104308i
\(761\) −8.97561e6 −0.561827 −0.280913 0.959733i \(-0.590637\pi\)
−0.280913 + 0.959733i \(0.590637\pi\)
\(762\) 5.59853e6i 0.349290i
\(763\) 8.86030e6i 0.550982i
\(764\) 8.97718e6 0.556425
\(765\) 609187. + 451585.i 0.0376354 + 0.0278989i
\(766\) −5.00425e6 −0.308154
\(767\) 1.65011e7i 1.01280i
\(768\) 337765.i 0.0206638i
\(769\) 2.44757e7 1.49252 0.746259 0.665655i \(-0.231848\pi\)
0.746259 + 0.665655i \(0.231848\pi\)
\(770\) −2.88605e6 + 3.89327e6i −0.175419 + 0.236640i
\(771\) −3.72328e6 −0.225574
\(772\) 5.26538e6i 0.317970i
\(773\) 3.21038e7i 1.93245i 0.257701 + 0.966225i \(0.417035\pi\)
−0.257701 + 0.966225i \(0.582965\pi\)
\(774\) 9.49483e6 0.569685
\(775\) 357406. + 1.17625e6i 0.0213751 + 0.0703471i
\(776\) −1.08680e7 −0.647882
\(777\) 3.29328e6i 0.195693i
\(778\) 2.01080e7i 1.19102i
\(779\) −1.41772e7 −0.837044
\(780\) 2.69441e6 3.63475e6i 0.158572 0.213913i
\(781\) 9.46284e6 0.555129
\(782\) 132619.i 0.00775513i
\(783\) 1.54871e7i 0.902749i
\(784\) 3.71947e6 0.216118
\(785\) −2.08592e6 1.54627e6i −0.120815 0.0895596i
\(786\) −6.23535e6 −0.360001
\(787\) 1.17100e7i 0.673940i −0.941515 0.336970i \(-0.890598\pi\)
0.941515 0.336970i \(-0.109402\pi\)
\(788\) 4.23393e6i 0.242900i
\(789\) 1.79687e6 0.102760
\(790\) −1.55699e7 1.15418e7i −0.887601 0.657972i
\(791\) −867588. −0.0493029
\(792\) 6.29041e6i 0.356341i
\(793\) 2.51718e7i 1.42145i
\(794\) −5.72018e6 −0.322002
\(795\) 267662. 361075.i 0.0150200 0.0202619i
\(796\) 790886. 0.0442416
\(797\) 3.52707e7i 1.96684i −0.181347 0.983419i \(-0.558046\pi\)
0.181347 0.983419i \(-0.441954\pi\)
\(798\) 767029.i 0.0426387i
\(799\) −1.41402e6 −0.0783591
\(800\) −3.06178e6 + 930326.i −0.169141 + 0.0513937i
\(801\) 2.11204e7 1.16311
\(802\) 1.28225e7i 0.703942i
\(803\) 2.13530e7i 1.16861i
\(804\) 3.79359e6 0.206972
\(805\) 840492. 1.13382e6i 0.0457135 0.0616672i
\(806\) −1.54447e6 −0.0837418
\(807\) 7.81896e6i 0.422635i
\(808\) 1.12935e6i 0.0608553i
\(809\) −19341.9 −0.00103903 −0.000519515 1.00000i \(-0.500165\pi\)
−0.000519515 1.00000i \(0.500165\pi\)
\(810\) −7.25549e6 5.37844e6i −0.388557 0.288034i
\(811\) 1.59463e7 0.851347 0.425674 0.904877i \(-0.360037\pi\)
0.425674 + 0.904877i \(0.360037\pi\)
\(812\) 4.99450e6i 0.265829i
\(813\) 3.77785e6i 0.200456i
\(814\) −2.43198e7 −1.28647
\(815\) 1.71761e7 + 1.27325e7i 0.905796 + 0.671460i
\(816\) −82692.2 −0.00434750
\(817\) 8.54970e6i 0.448122i
\(818\) 1.46707e7i 0.766600i
\(819\) −1.01388e7 −0.528174
\(820\) −9.68662e6 + 1.30672e7i −0.503081 + 0.678653i
\(821\) −1.92344e7 −0.995914 −0.497957 0.867202i \(-0.665916\pi\)
−0.497957 + 0.867202i \(0.665916\pi\)
\(822\) 5.99682e6i 0.309558i
\(823\) 3.02552e7i 1.55704i 0.627617 + 0.778522i \(0.284030\pi\)
−0.627617 + 0.778522i \(0.715970\pi\)
\(824\) 1.09719e7 0.562941
\(825\) −6.99800e6 + 2.12635e6i −0.357964 + 0.108768i
\(826\) −3.20953e6 −0.163679
\(827\) 1.75000e7i 0.889763i 0.895589 + 0.444882i \(0.146754\pi\)
−0.895589 + 0.444882i \(0.853246\pi\)
\(828\) 1.83193e6i 0.0928608i
\(829\) −3.01168e7 −1.52203 −0.761013 0.648737i \(-0.775298\pi\)
−0.761013 + 0.648737i \(0.775298\pi\)
\(830\) −6.47492e6 + 8.73463e6i −0.326241 + 0.440098i
\(831\) 593245. 0.0298010
\(832\) 4.02025e6i 0.201347i
\(833\) 910607.i 0.0454693i
\(834\) −6.50063e6 −0.323624
\(835\) −2.63228e7 1.95129e7i −1.30652 0.968513i
\(836\) −5.66425e6 −0.280302
\(837\) 931509.i 0.0459593i
\(838\) 7.65837e6i 0.376726i
\(839\) 2.73092e6 0.133938 0.0669690 0.997755i \(-0.478667\pi\)
0.0669690 + 0.997755i \(0.478667\pi\)
\(840\) −706973. 524074.i −0.0345704 0.0256268i
\(841\) 2.22669e7 1.08560
\(842\) 1.37624e7i 0.668980i
\(843\) 5.68379e6i 0.275466i
\(844\) 1.42708e7 0.689591
\(845\) −1.97099e7 + 2.65885e7i −0.949603 + 1.28101i
\(846\) 1.95325e7 0.938280
\(847\) 2.15580e6i 0.103252i
\(848\) 399371.i 0.0190716i
\(849\) 1.12755e7 0.536865
\(850\) −227764. 749591.i −0.0108128 0.0355858i
\(851\) 7.08254e6 0.335247
\(852\) 1.71834e6i 0.0810981i
\(853\) 8.15836e6i 0.383911i −0.981404 0.191955i \(-0.938517\pi\)
0.981404 0.191955i \(-0.0614829\pi\)
\(854\) −4.89602e6 −0.229720
\(855\) −5.61702e6 + 7.57733e6i −0.262779 + 0.354487i
\(856\) 3.77843e6 0.176249
\(857\) 1.09824e7i 0.510792i −0.966837 0.255396i \(-0.917794\pi\)
0.966837 0.255396i \(-0.0822058\pi\)
\(858\) 9.18868e6i 0.426123i
\(859\) 6.02173e6 0.278444 0.139222 0.990261i \(-0.455540\pi\)
0.139222 + 0.990261i \(0.455540\pi\)
\(860\) −7.88028e6 5.84160e6i −0.363325 0.269330i
\(861\) −4.47333e6 −0.205647
\(862\) 2.10467e7i 0.964754i
\(863\) 2.07350e7i 0.947716i −0.880601 0.473858i \(-0.842861\pi\)
0.880601 0.473858i \(-0.157139\pi\)
\(864\) 2.42471e6 0.110504
\(865\) 1.96711e6 + 1.45821e6i 0.0893901 + 0.0662642i
\(866\) −1.46843e7 −0.665365
\(867\) 7.29752e6i 0.329707i
\(868\) 300406.i 0.0135335i
\(869\) −3.93608e7 −1.76813
\(870\) −4.48871e6 + 6.05525e6i −0.201059 + 0.271228i
\(871\) −4.51533e7 −2.01671
\(872\) 1.18814e7i 0.529147i
\(873\) 3.67539e7i 1.63218i
\(874\) 1.64957e6 0.0730455
\(875\) 2.80338e6 7.85208e6i 0.123783 0.346708i
\(876\) 3.87745e6 0.170721
\(877\) 1.22456e7i 0.537628i −0.963192 0.268814i \(-0.913368\pi\)
0.963192 0.268814i \(-0.0866317\pi\)
\(878\) 4.22569e6i 0.184995i
\(879\) −6.73725e6 −0.294111
\(880\) −3.87011e6 + 5.22075e6i −0.168468 + 0.227262i
\(881\) 3.35119e7 1.45465 0.727326 0.686292i \(-0.240763\pi\)
0.727326 + 0.686292i \(0.240763\pi\)
\(882\) 1.25786e7i 0.544455i
\(883\) 3.06726e7i 1.32388i −0.749556 0.661941i \(-0.769733\pi\)
0.749556 0.661941i \(-0.230267\pi\)
\(884\) 984246. 0.0423617
\(885\) −3.89119e6 2.88451e6i −0.167003 0.123798i
\(886\) 1.97099e7 0.843528
\(887\) 1.24883e7i 0.532958i 0.963841 + 0.266479i \(0.0858603\pi\)
−0.963841 + 0.266479i \(0.914140\pi\)
\(888\) 4.41618e6i 0.187938i
\(889\) −1.29611e7 −0.550030
\(890\) −1.75290e7 1.29941e7i −0.741790 0.549883i
\(891\) −1.83420e7 −0.774019
\(892\) 9.56502e6i 0.402507i
\(893\) 1.75882e7i 0.738063i
\(894\) −8.77040e6 −0.367008
\(895\) 2.55150e7 3.44196e7i 1.06473 1.43631i
\(896\) −781954. −0.0325395
\(897\) 2.67598e6i 0.111046i
\(898\) 1.64399e7i 0.680314i
\(899\) 2.57299e6 0.106179
\(900\) 3.14621e6 + 1.03544e7i 0.129474 + 0.426109i
\(901\) 97774.8 0.00401250
\(902\) 3.30340e7i 1.35190i
\(903\) 2.69768e6i 0.110096i
\(904\) −1.16341e6 −0.0473491
\(905\) 1.13958e7 1.53729e7i 0.462512 0.623926i
\(906\) −3.86999e6 −0.156635
\(907\) 3.27276e7i 1.32098i −0.750835 0.660490i \(-0.770349\pi\)
0.750835 0.660490i \(-0.229651\pi\)
\(908\) 3.68668e6i 0.148396i
\(909\) −3.81926e6 −0.153310
\(910\) 8.41476e6 + 6.23780e6i 0.336851 + 0.249705i
\(911\) −6.74533e6 −0.269282 −0.134641 0.990894i \(-0.542988\pi\)
−0.134641 + 0.990894i \(0.542988\pi\)
\(912\) 1.02856e6i 0.0409490i
\(913\) 2.20812e7i 0.876691i
\(914\) −551358. −0.0218307
\(915\) −5.93585e6 4.40020e6i −0.234385 0.173748i
\(916\) 1.16567e7 0.459025
\(917\) 1.44354e7i 0.566897i
\(918\) 593624.i 0.0232490i
\(919\) 4.62049e7 1.80467 0.902337 0.431031i \(-0.141850\pi\)
0.902337 + 0.431031i \(0.141850\pi\)
\(920\) 1.12707e6 1.52042e6i 0.0439019 0.0592234i
\(921\) 1.62874e7 0.632705
\(922\) 3.55240e7i 1.37624i
\(923\) 2.04526e7i 0.790214i
\(924\) −1.78723e6 −0.0688655
\(925\) 4.00320e7 1.21638e7i 1.53834 0.467427i
\(926\) 1.32987e6 0.0509660
\(927\) 3.71051e7i 1.41819i
\(928\) 6.69747e6i 0.255294i
\(929\) 5.73732e6 0.218107 0.109054 0.994036i \(-0.465218\pi\)
0.109054 + 0.994036i \(0.465218\pi\)
\(930\) −269984. + 364207.i −0.0102360 + 0.0138083i
\(931\) −1.13265e7 −0.428275
\(932\) 1.43276e7i 0.540299i
\(933\) 1.45473e7i 0.547115i
\(934\) −9.95369e6 −0.373351
\(935\) −1.27816e6 947487.i −0.0478140 0.0354441i
\(936\) −1.35958e7 −0.507243
\(937\) 3.04441e7i 1.13280i −0.824130 0.566401i \(-0.808335\pi\)
0.824130 0.566401i \(-0.191665\pi\)
\(938\) 8.78250e6i 0.325920i
\(939\) −6.96910e6 −0.257937
\(940\) −1.62111e7 1.20172e7i −0.598402 0.443591i
\(941\) 3.08461e7 1.13560 0.567802 0.823165i \(-0.307794\pi\)
0.567802 + 0.823165i \(0.307794\pi\)
\(942\) 957555.i 0.0351590i
\(943\) 9.62036e6i 0.352299i
\(944\) −4.30389e6 −0.157192
\(945\) −3.76217e6 + 5.07515e6i −0.137044 + 0.184871i
\(946\) −1.99214e7 −0.723757
\(947\) 4.85787e7i 1.76024i 0.474754 + 0.880119i \(0.342537\pi\)
−0.474754 + 0.880119i \(0.657463\pi\)
\(948\) 7.14747e6i 0.258304i
\(949\) −4.61514e7 −1.66349
\(950\) 9.32374e6 2.83303e6i 0.335182 0.101846i
\(951\) −142459. −0.00510784
\(952\) 191440.i 0.00684604i
\(953\) 1.42581e6i 0.0508545i 0.999677 + 0.0254273i \(0.00809462\pi\)
−0.999677 + 0.0254273i \(0.991905\pi\)
\(954\) −1.35061e6 −0.0480461
\(955\) −1.86783e7 + 2.51969e7i −0.662717 + 0.894002i
\(956\) 4.34970e6 0.153927
\(957\) 1.53077e7i 0.540295i
\(958\) 1.75518e7i 0.617885i
\(959\) 1.38832e7 0.487463
\(960\) −948028. 702766.i −0.0332004 0.0246112i
\(961\) −2.84744e7 −0.994594
\(962\) 5.25637e7i 1.83125i
\(963\) 1.27780e7i 0.444015i
\(964\) −1.44280e7 −0.500049
\(965\) −1.47787e7 1.09554e7i −0.510879 0.378711i
\(966\) 520488. 0.0179460
\(967\) 422721.i 0.0145374i 0.999974 + 0.00726872i \(0.00231373\pi\)
−0.999974 + 0.00726872i \(0.997686\pi\)
\(968\) 2.89086e6i 0.0991604i
\(969\) 251815. 0.00861532
\(970\) 2.26124e7 3.05041e7i 0.771646 1.04095i
\(971\) 5.33281e7 1.81513 0.907565 0.419912i \(-0.137939\pi\)
0.907565 + 0.419912i \(0.137939\pi\)
\(972\) 1.25370e7i 0.425627i
\(973\) 1.50495e7i 0.509613i
\(974\) 2.93981e7 0.992936
\(975\) 4.59581e6 + 1.51252e7i 0.154828 + 0.509553i
\(976\) −6.56541e6 −0.220616
\(977\) 3.30224e6i 0.110681i 0.998468 + 0.0553404i \(0.0176244\pi\)
−0.998468 + 0.0553404i \(0.982376\pi\)
\(978\) 7.88481e6i 0.263599i
\(979\) −4.43134e7 −1.47767
\(980\) −7.73887e6 + 1.04397e7i −0.257402 + 0.347234i
\(981\) 4.01809e7 1.33305
\(982\) 9.10187e6i 0.301198i
\(983\) 1.73555e7i 0.572867i 0.958100 + 0.286433i \(0.0924697\pi\)
−0.958100 + 0.286433i \(0.907530\pi\)
\(984\) −5.99860e6 −0.197498
\(985\) 1.18837e7 + 8.80928e6i 0.390265 + 0.289301i
\(986\) −1.63969e6 −0.0537117
\(987\) 5.54959e6i 0.181329i
\(988\) 1.22425e7i 0.399004i
\(989\) 5.80164e6 0.188608
\(990\) 1.76557e7 + 1.30881e7i 0.572529 + 0.424412i
\(991\) 2.92913e7 0.947446 0.473723 0.880674i \(-0.342910\pi\)
0.473723 + 0.880674i \(0.342910\pi\)
\(992\) 402834.i 0.0129971i
\(993\) 1.33175e7i 0.428598i
\(994\) −3.97811e6 −0.127706
\(995\) −1.64555e6 + 2.21984e6i −0.0526930 + 0.0710826i
\(996\) −4.00970e6 −0.128075
\(997\) 4.65977e6i 0.148466i −0.997241 0.0742329i \(-0.976349\pi\)
0.997241 0.0742329i \(-0.0236508\pi\)
\(998\) 7.15983e6i 0.227550i
\(999\) −3.17025e7 −1.00503
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 230.6.b.a.139.8 26
5.4 even 2 inner 230.6.b.a.139.19 yes 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.6.b.a.139.8 26 1.1 even 1 trivial
230.6.b.a.139.19 yes 26 5.4 even 2 inner