Properties

Label 300.5.c.d.151.12
Level $300$
Weight $5$
Character 300.151
Analytic conductor $31.011$
Analytic rank $0$
Dimension $16$
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] = [300,5,Mod(151,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.151");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 300.c (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: \(31.0109889252\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + 25296 x^{8} - 6656 x^{7} - 110848 x^{6} - 227328 x^{5} + 1077248 x^{4} + \cdots + 16777216 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{36}\cdot 3^{4}\cdot 5^{4} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.12
Root \(1.85226 - 2.13755i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.5.c.d.151.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.34902 + 2.18726i) q^{2} -5.19615i q^{3} +(6.43181 + 14.6503i) q^{4} +(11.3653 - 17.4020i) q^{6} +1.39605i q^{7} +(-10.5038 + 63.1322i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(3.34902 + 2.18726i) q^{2} -5.19615i q^{3} +(6.43181 + 14.6503i) q^{4} +(11.3653 - 17.4020i) q^{6} +1.39605i q^{7} +(-10.5038 + 63.1322i) q^{8} -27.0000 q^{9} -164.588i q^{11} +(76.1253 - 33.4207i) q^{12} +158.663 q^{13} +(-3.05352 + 4.67540i) q^{14} +(-173.264 + 188.456i) q^{16} +548.214 q^{17} +(-90.4234 - 59.0560i) q^{18} -25.6686i q^{19} +7.25409 q^{21} +(359.996 - 551.208i) q^{22} +730.150i q^{23} +(328.044 + 54.5793i) q^{24} +(531.364 + 347.036i) q^{26} +140.296i q^{27} +(-20.4526 + 8.97913i) q^{28} +773.909 q^{29} -194.974i q^{31} +(-992.465 + 252.170i) q^{32} -855.224 q^{33} +(1835.98 + 1199.09i) q^{34} +(-173.659 - 395.559i) q^{36} +1373.19 q^{37} +(56.1439 - 85.9646i) q^{38} -824.435i q^{39} -647.851 q^{41} +(24.2941 + 15.8666i) q^{42} -1502.44i q^{43} +(2411.27 - 1058.60i) q^{44} +(-1597.03 + 2445.28i) q^{46} -647.613i q^{47} +(979.247 + 900.305i) q^{48} +2399.05 q^{49} -2848.61i q^{51} +(1020.49 + 2324.46i) q^{52} +4407.11 q^{53} +(-306.864 + 469.854i) q^{54} +(-88.1357 - 14.6638i) q^{56} -133.378 q^{57} +(2591.83 + 1692.74i) q^{58} +5978.96i q^{59} -560.288 q^{61} +(426.459 - 652.971i) q^{62} -37.6934i q^{63} +(-3875.34 - 1326.26i) q^{64} +(-2864.16 - 1870.60i) q^{66} +2986.47i q^{67} +(3526.01 + 8031.52i) q^{68} +3793.97 q^{69} -2673.19i q^{71} +(283.603 - 1704.57i) q^{72} -2649.09 q^{73} +(4598.82 + 3003.51i) q^{74} +(376.053 - 165.096i) q^{76} +229.773 q^{77} +(1803.25 - 2761.05i) q^{78} -3158.78i q^{79} +729.000 q^{81} +(-2169.66 - 1417.02i) q^{82} -13095.0i q^{83} +(46.6569 + 106.275i) q^{84} +(3286.22 - 5031.69i) q^{86} -4021.35i q^{87} +(10390.8 + 1728.80i) q^{88} -7112.37 q^{89} +221.501i q^{91} +(-10696.9 + 4696.19i) q^{92} -1013.12 q^{93} +(1416.50 - 2168.87i) q^{94} +(1310.31 + 5157.00i) q^{96} -5310.91 q^{97} +(8034.46 + 5247.34i) q^{98} +4443.88i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} + 352 q^{13} - 804 q^{14} - 190 q^{16} - 324 q^{18} + 288 q^{21} - 436 q^{22} - 1998 q^{24} - 852 q^{26} + 1156 q^{28} - 3456 q^{29} - 7668 q^{32} + 4772 q^{34} - 702 q^{36} - 9376 q^{37} + 1320 q^{38} + 1248 q^{41} + 324 q^{42} - 6420 q^{44} - 1112 q^{46} + 4176 q^{48} - 3952 q^{49} - 12704 q^{52} + 5184 q^{53} - 486 q^{54} - 2604 q^{56} + 11232 q^{57} - 12708 q^{58} - 3808 q^{61} + 16152 q^{62} - 11902 q^{64} - 2916 q^{66} + 12312 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} + 30516 q^{74} - 5160 q^{76} + 27456 q^{77} + 3600 q^{78} + 11664 q^{81} + 54040 q^{82} - 2052 q^{84} + 39768 q^{86} + 7220 q^{88} + 7584 q^{89} - 28848 q^{92} - 19872 q^{93} + 49776 q^{94} + 18882 q^{96} + 14496 q^{97} - 23940 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.34902 + 2.18726i 0.837254 + 0.546814i
\(3\) 5.19615i 0.577350i
\(4\) 6.43181 + 14.6503i 0.401988 + 0.915645i
\(5\) 0 0
\(6\) 11.3653 17.4020i 0.315703 0.483389i
\(7\) 1.39605i 0.0284908i 0.999899 + 0.0142454i \(0.00453461\pi\)
−0.999899 + 0.0142454i \(0.995465\pi\)
\(8\) −10.5038 + 63.1322i −0.164122 + 0.986440i
\(9\) −27.0000 −0.333333
\(10\) 0 0
\(11\) 164.588i 1.36023i −0.733105 0.680116i \(-0.761930\pi\)
0.733105 0.680116i \(-0.238070\pi\)
\(12\) 76.1253 33.4207i 0.528648 0.232088i
\(13\) 158.663 0.938832 0.469416 0.882977i \(-0.344464\pi\)
0.469416 + 0.882977i \(0.344464\pi\)
\(14\) −3.05352 + 4.67540i −0.0155792 + 0.0238541i
\(15\) 0 0
\(16\) −173.264 + 188.456i −0.676811 + 0.736157i
\(17\) 548.214 1.89694 0.948468 0.316873i \(-0.102633\pi\)
0.948468 + 0.316873i \(0.102633\pi\)
\(18\) −90.4234 59.0560i −0.279085 0.182271i
\(19\) 25.6686i 0.0711042i −0.999368 0.0355521i \(-0.988681\pi\)
0.999368 0.0355521i \(-0.0113190\pi\)
\(20\) 0 0
\(21\) 7.25409 0.0164492
\(22\) 359.996 551.208i 0.743794 1.13886i
\(23\) 730.150i 1.38025i 0.723692 + 0.690123i \(0.242444\pi\)
−0.723692 + 0.690123i \(0.757556\pi\)
\(24\) 328.044 + 54.5793i 0.569521 + 0.0947558i
\(25\) 0 0
\(26\) 531.364 + 347.036i 0.786041 + 0.513367i
\(27\) 140.296i 0.192450i
\(28\) −20.4526 + 8.97913i −0.0260875 + 0.0114530i
\(29\) 773.909 0.920225 0.460112 0.887861i \(-0.347809\pi\)
0.460112 + 0.887861i \(0.347809\pi\)
\(30\) 0 0
\(31\) 194.974i 0.202887i −0.994841 0.101443i \(-0.967654\pi\)
0.994841 0.101443i \(-0.0323461\pi\)
\(32\) −992.465 + 252.170i −0.969204 + 0.246260i
\(33\) −855.224 −0.785330
\(34\) 1835.98 + 1199.09i 1.58822 + 1.03727i
\(35\) 0 0
\(36\) −173.659 395.559i −0.133996 0.305215i
\(37\) 1373.19 1.00306 0.501529 0.865141i \(-0.332771\pi\)
0.501529 + 0.865141i \(0.332771\pi\)
\(38\) 56.1439 85.9646i 0.0388808 0.0595323i
\(39\) 824.435i 0.542035i
\(40\) 0 0
\(41\) −647.851 −0.385396 −0.192698 0.981258i \(-0.561724\pi\)
−0.192698 + 0.981258i \(0.561724\pi\)
\(42\) 24.2941 + 15.8666i 0.0137721 + 0.00899465i
\(43\) 1502.44i 0.812568i −0.913747 0.406284i \(-0.866824\pi\)
0.913747 0.406284i \(-0.133176\pi\)
\(44\) 2411.27 1058.60i 1.24549 0.546797i
\(45\) 0 0
\(46\) −1597.03 + 2445.28i −0.754738 + 1.15562i
\(47\) 647.613i 0.293170i −0.989198 0.146585i \(-0.953172\pi\)
0.989198 0.146585i \(-0.0468282\pi\)
\(48\) 979.247 + 900.305i 0.425020 + 0.390757i
\(49\) 2399.05 0.999188
\(50\) 0 0
\(51\) 2848.61i 1.09520i
\(52\) 1020.49 + 2324.46i 0.377399 + 0.859637i
\(53\) 4407.11 1.56892 0.784462 0.620177i \(-0.212939\pi\)
0.784462 + 0.620177i \(0.212939\pi\)
\(54\) −306.864 + 469.854i −0.105234 + 0.161130i
\(55\) 0 0
\(56\) −88.1357 14.6638i −0.0281045 0.00467597i
\(57\) −133.378 −0.0410520
\(58\) 2591.83 + 1692.74i 0.770462 + 0.503192i
\(59\) 5978.96i 1.71760i 0.512311 + 0.858800i \(0.328789\pi\)
−0.512311 + 0.858800i \(0.671211\pi\)
\(60\) 0 0
\(61\) −560.288 −0.150575 −0.0752873 0.997162i \(-0.523987\pi\)
−0.0752873 + 0.997162i \(0.523987\pi\)
\(62\) 426.459 652.971i 0.110941 0.169868i
\(63\) 37.6934i 0.00949694i
\(64\) −3875.34 1326.26i −0.946128 0.323793i
\(65\) 0 0
\(66\) −2864.16 1870.60i −0.657521 0.429430i
\(67\) 2986.47i 0.665286i 0.943053 + 0.332643i \(0.107940\pi\)
−0.943053 + 0.332643i \(0.892060\pi\)
\(68\) 3526.01 + 8031.52i 0.762545 + 1.73692i
\(69\) 3793.97 0.796885
\(70\) 0 0
\(71\) 2673.19i 0.530290i −0.964209 0.265145i \(-0.914580\pi\)
0.964209 0.265145i \(-0.0854198\pi\)
\(72\) 283.603 1704.57i 0.0547073 0.328813i
\(73\) −2649.09 −0.497108 −0.248554 0.968618i \(-0.579955\pi\)
−0.248554 + 0.968618i \(0.579955\pi\)
\(74\) 4598.82 + 3003.51i 0.839815 + 0.548487i
\(75\) 0 0
\(76\) 376.053 165.096i 0.0651062 0.0285830i
\(77\) 229.773 0.0387541
\(78\) 1803.25 2761.05i 0.296393 0.453821i
\(79\) 3158.78i 0.506134i −0.967449 0.253067i \(-0.918561\pi\)
0.967449 0.253067i \(-0.0814393\pi\)
\(80\) 0 0
\(81\) 729.000 0.111111
\(82\) −2169.66 1417.02i −0.322675 0.210740i
\(83\) 13095.0i 1.90085i −0.310952 0.950426i \(-0.600648\pi\)
0.310952 0.950426i \(-0.399352\pi\)
\(84\) 46.6569 + 106.275i 0.00661238 + 0.0150616i
\(85\) 0 0
\(86\) 3286.22 5031.69i 0.444324 0.680325i
\(87\) 4021.35i 0.531292i
\(88\) 10390.8 + 1728.80i 1.34179 + 0.223244i
\(89\) −7112.37 −0.897913 −0.448956 0.893554i \(-0.648204\pi\)
−0.448956 + 0.893554i \(0.648204\pi\)
\(90\) 0 0
\(91\) 221.501i 0.0267481i
\(92\) −10696.9 + 4696.19i −1.26382 + 0.554842i
\(93\) −1013.12 −0.117137
\(94\) 1416.50 2168.87i 0.160310 0.245458i
\(95\) 0 0
\(96\) 1310.31 + 5157.00i 0.142178 + 0.559570i
\(97\) −5310.91 −0.564450 −0.282225 0.959348i \(-0.591073\pi\)
−0.282225 + 0.959348i \(0.591073\pi\)
\(98\) 8034.46 + 5247.34i 0.836574 + 0.546371i
\(99\) 4443.88i 0.453410i
\(100\) 0 0
\(101\) −17042.8 −1.67070 −0.835348 0.549721i \(-0.814734\pi\)
−0.835348 + 0.549721i \(0.814734\pi\)
\(102\) 6230.64 9540.03i 0.598869 0.916957i
\(103\) 3359.31i 0.316647i 0.987387 + 0.158323i \(0.0506089\pi\)
−0.987387 + 0.158323i \(0.949391\pi\)
\(104\) −1666.56 + 10016.7i −0.154083 + 0.926102i
\(105\) 0 0
\(106\) 14759.5 + 9639.48i 1.31359 + 0.857910i
\(107\) 6655.05i 0.581278i 0.956833 + 0.290639i \(0.0938678\pi\)
−0.956833 + 0.290639i \(0.906132\pi\)
\(108\) −2055.38 + 902.358i −0.176216 + 0.0773626i
\(109\) 10400.1 0.875355 0.437677 0.899132i \(-0.355801\pi\)
0.437677 + 0.899132i \(0.355801\pi\)
\(110\) 0 0
\(111\) 7135.29i 0.579116i
\(112\) −263.094 241.885i −0.0209737 0.0192829i
\(113\) −11224.7 −0.879056 −0.439528 0.898229i \(-0.644854\pi\)
−0.439528 + 0.898229i \(0.644854\pi\)
\(114\) −446.685 291.732i −0.0343710 0.0224478i
\(115\) 0 0
\(116\) 4977.63 + 11338.0i 0.369919 + 0.842599i
\(117\) −4283.89 −0.312944
\(118\) −13077.5 + 20023.6i −0.939208 + 1.43807i
\(119\) 765.335i 0.0540453i
\(120\) 0 0
\(121\) −12448.2 −0.850229
\(122\) −1876.41 1225.50i −0.126069 0.0823364i
\(123\) 3366.33i 0.222509i
\(124\) 2856.43 1254.04i 0.185772 0.0815580i
\(125\) 0 0
\(126\) 82.4451 126.236i 0.00519307 0.00795135i
\(127\) 25607.7i 1.58768i 0.608128 + 0.793839i \(0.291921\pi\)
−0.608128 + 0.793839i \(0.708079\pi\)
\(128\) −10077.7 12918.0i −0.615095 0.788453i
\(129\) −7806.89 −0.469136
\(130\) 0 0
\(131\) 16564.8i 0.965256i −0.875825 0.482628i \(-0.839682\pi\)
0.875825 0.482628i \(-0.160318\pi\)
\(132\) −5500.64 12529.3i −0.315693 0.719083i
\(133\) 35.8347 0.00202582
\(134\) −6532.18 + 10001.7i −0.363788 + 0.557013i
\(135\) 0 0
\(136\) −5758.33 + 34610.0i −0.311329 + 1.87121i
\(137\) 5619.61 0.299409 0.149705 0.988731i \(-0.452168\pi\)
0.149705 + 0.988731i \(0.452168\pi\)
\(138\) 12706.1 + 8298.39i 0.667195 + 0.435748i
\(139\) 33597.0i 1.73888i −0.494036 0.869442i \(-0.664479\pi\)
0.494036 0.869442i \(-0.335521\pi\)
\(140\) 0 0
\(141\) −3365.10 −0.169262
\(142\) 5846.96 8952.55i 0.289970 0.443987i
\(143\) 26114.0i 1.27703i
\(144\) 4678.12 5088.31i 0.225604 0.245386i
\(145\) 0 0
\(146\) −8871.84 5794.24i −0.416206 0.271826i
\(147\) 12465.8i 0.576882i
\(148\) 8832.08 + 20117.6i 0.403217 + 0.918445i
\(149\) −19602.3 −0.882946 −0.441473 0.897275i \(-0.645544\pi\)
−0.441473 + 0.897275i \(0.645544\pi\)
\(150\) 0 0
\(151\) 9340.31i 0.409645i −0.978799 0.204822i \(-0.934338\pi\)
0.978799 0.204822i \(-0.0656617\pi\)
\(152\) 1620.52 + 269.618i 0.0701400 + 0.0116698i
\(153\) −14801.8 −0.632312
\(154\) 769.514 + 502.573i 0.0324470 + 0.0211913i
\(155\) 0 0
\(156\) 12078.2 5302.61i 0.496312 0.217892i
\(157\) 34913.2 1.41642 0.708208 0.706004i \(-0.249504\pi\)
0.708208 + 0.706004i \(0.249504\pi\)
\(158\) 6909.07 10578.8i 0.276761 0.423763i
\(159\) 22900.0i 0.905818i
\(160\) 0 0
\(161\) −1019.33 −0.0393244
\(162\) 2441.43 + 1594.51i 0.0930282 + 0.0607572i
\(163\) 49700.0i 1.87060i −0.353853 0.935301i \(-0.615129\pi\)
0.353853 0.935301i \(-0.384871\pi\)
\(164\) −4166.85 9491.23i −0.154925 0.352886i
\(165\) 0 0
\(166\) 28642.1 43855.2i 1.03941 1.59149i
\(167\) 51638.7i 1.85158i 0.378038 + 0.925790i \(0.376599\pi\)
−0.378038 + 0.925790i \(0.623401\pi\)
\(168\) −76.1955 + 457.967i −0.00269967 + 0.0162261i
\(169\) −3387.16 −0.118594
\(170\) 0 0
\(171\) 693.053i 0.0237014i
\(172\) 22011.2 9663.39i 0.744023 0.326642i
\(173\) −48824.2 −1.63133 −0.815667 0.578522i \(-0.803630\pi\)
−0.815667 + 0.578522i \(0.803630\pi\)
\(174\) 8795.73 13467.6i 0.290518 0.444826i
\(175\) 0 0
\(176\) 31017.6 + 28517.1i 1.00134 + 0.920620i
\(177\) 31067.6 0.991657
\(178\) −23819.4 15556.6i −0.751781 0.490992i
\(179\) 51061.1i 1.59362i 0.604233 + 0.796808i \(0.293480\pi\)
−0.604233 + 0.796808i \(0.706520\pi\)
\(180\) 0 0
\(181\) 16788.0 0.512438 0.256219 0.966619i \(-0.417523\pi\)
0.256219 + 0.966619i \(0.417523\pi\)
\(182\) −484.480 + 741.811i −0.0146263 + 0.0223950i
\(183\) 2911.34i 0.0869343i
\(184\) −46096.0 7669.35i −1.36153 0.226529i
\(185\) 0 0
\(186\) −3392.94 2215.94i −0.0980732 0.0640520i
\(187\) 90229.5i 2.58027i
\(188\) 9487.74 4165.32i 0.268440 0.117851i
\(189\) −195.861 −0.00548306
\(190\) 0 0
\(191\) 34310.5i 0.940504i −0.882532 0.470252i \(-0.844163\pi\)
0.882532 0.470252i \(-0.155837\pi\)
\(192\) −6891.42 + 20136.9i −0.186942 + 0.546247i
\(193\) −33325.8 −0.894675 −0.447338 0.894365i \(-0.647628\pi\)
−0.447338 + 0.894365i \(0.647628\pi\)
\(194\) −17786.3 11616.3i −0.472588 0.308650i
\(195\) 0 0
\(196\) 15430.2 + 35146.9i 0.401662 + 0.914902i
\(197\) −53779.0 −1.38573 −0.692867 0.721065i \(-0.743653\pi\)
−0.692867 + 0.721065i \(0.743653\pi\)
\(198\) −9719.90 + 14882.6i −0.247931 + 0.379620i
\(199\) 7992.31i 0.201821i −0.994896 0.100910i \(-0.967824\pi\)
0.994896 0.100910i \(-0.0321755\pi\)
\(200\) 0 0
\(201\) 15518.2 0.384103
\(202\) −57076.5 37276.9i −1.39880 0.913561i
\(203\) 1080.42i 0.0262180i
\(204\) 41733.0 18321.7i 1.00281 0.440256i
\(205\) 0 0
\(206\) −7347.67 + 11250.4i −0.173147 + 0.265114i
\(207\) 19714.1i 0.460082i
\(208\) −27490.5 + 29900.9i −0.635412 + 0.691128i
\(209\) −4224.75 −0.0967182
\(210\) 0 0
\(211\) 23096.8i 0.518785i 0.965772 + 0.259393i \(0.0835224\pi\)
−0.965772 + 0.259393i \(0.916478\pi\)
\(212\) 28345.7 + 64565.5i 0.630688 + 1.43658i
\(213\) −13890.3 −0.306163
\(214\) −14556.3 + 22287.9i −0.317851 + 0.486677i
\(215\) 0 0
\(216\) −8857.20 1473.64i −0.189840 0.0315853i
\(217\) 272.194 0.00578041
\(218\) 34830.1 + 22747.7i 0.732894 + 0.478657i
\(219\) 13765.1i 0.287006i
\(220\) 0 0
\(221\) 86981.2 1.78090
\(222\) 15606.7 23896.2i 0.316669 0.484867i
\(223\) 46059.3i 0.926206i −0.886305 0.463103i \(-0.846736\pi\)
0.886305 0.463103i \(-0.153264\pi\)
\(224\) −352.042 1385.53i −0.00701615 0.0276134i
\(225\) 0 0
\(226\) −37591.6 24551.2i −0.735993 0.480681i
\(227\) 49636.5i 0.963274i 0.876371 + 0.481637i \(0.159958\pi\)
−0.876371 + 0.481637i \(0.840042\pi\)
\(228\) −857.862 1954.03i −0.0165024 0.0375891i
\(229\) −8900.38 −0.169722 −0.0848609 0.996393i \(-0.527045\pi\)
−0.0848609 + 0.996393i \(0.527045\pi\)
\(230\) 0 0
\(231\) 1193.94i 0.0223747i
\(232\) −8128.98 + 48858.5i −0.151029 + 0.907747i
\(233\) 13357.8 0.246050 0.123025 0.992404i \(-0.460740\pi\)
0.123025 + 0.992404i \(0.460740\pi\)
\(234\) −14346.8 9369.98i −0.262014 0.171122i
\(235\) 0 0
\(236\) −87593.7 + 38455.5i −1.57271 + 0.690454i
\(237\) −16413.5 −0.292217
\(238\) −1673.99 + 2563.12i −0.0295527 + 0.0452496i
\(239\) 40201.8i 0.703801i −0.936037 0.351900i \(-0.885536\pi\)
0.936037 0.351900i \(-0.114464\pi\)
\(240\) 0 0
\(241\) −91284.7 −1.57168 −0.785840 0.618430i \(-0.787769\pi\)
−0.785840 + 0.618430i \(0.787769\pi\)
\(242\) −41689.2 27227.4i −0.711858 0.464918i
\(243\) 3788.00i 0.0641500i
\(244\) −3603.67 8208.40i −0.0605292 0.137873i
\(245\) 0 0
\(246\) −7363.04 + 11273.9i −0.121671 + 0.186296i
\(247\) 4072.65i 0.0667549i
\(248\) 12309.1 + 2047.97i 0.200136 + 0.0332981i
\(249\) −68043.4 −1.09746
\(250\) 0 0
\(251\) 85298.2i 1.35392i 0.736021 + 0.676959i \(0.236703\pi\)
−0.736021 + 0.676959i \(0.763297\pi\)
\(252\) 552.220 242.437i 0.00869583 0.00381766i
\(253\) 120174. 1.87745
\(254\) −56010.6 + 85760.5i −0.868166 + 1.32929i
\(255\) 0 0
\(256\) −5495.39 65305.2i −0.0838529 0.996478i
\(257\) −23409.7 −0.354429 −0.177214 0.984172i \(-0.556709\pi\)
−0.177214 + 0.984172i \(0.556709\pi\)
\(258\) −26145.4 17075.7i −0.392786 0.256530i
\(259\) 1917.04i 0.0285780i
\(260\) 0 0
\(261\) −20895.5 −0.306742
\(262\) 36231.4 55475.6i 0.527816 0.808164i
\(263\) 88925.7i 1.28563i 0.766021 + 0.642815i \(0.222234\pi\)
−0.766021 + 0.642815i \(0.777766\pi\)
\(264\) 8983.10 53992.2i 0.128890 0.774681i
\(265\) 0 0
\(266\) 120.011 + 78.3797i 0.00169612 + 0.00110775i
\(267\) 36956.9i 0.518410i
\(268\) −43752.7 + 19208.4i −0.609166 + 0.267437i
\(269\) −78384.1 −1.08324 −0.541619 0.840624i \(-0.682188\pi\)
−0.541619 + 0.840624i \(0.682188\pi\)
\(270\) 0 0
\(271\) 79821.4i 1.08688i −0.839449 0.543439i \(-0.817122\pi\)
0.839449 0.543439i \(-0.182878\pi\)
\(272\) −94985.7 + 103314.i −1.28387 + 1.39644i
\(273\) 1150.95 0.0154430
\(274\) 18820.2 + 12291.5i 0.250682 + 0.163721i
\(275\) 0 0
\(276\) 24402.1 + 55582.9i 0.320338 + 0.729664i
\(277\) 13987.6 0.182299 0.0911494 0.995837i \(-0.470946\pi\)
0.0911494 + 0.995837i \(0.470946\pi\)
\(278\) 73485.2 112517.i 0.950847 1.45589i
\(279\) 5264.30i 0.0676289i
\(280\) 0 0
\(281\) −14451.9 −0.183026 −0.0915132 0.995804i \(-0.529170\pi\)
−0.0915132 + 0.995804i \(0.529170\pi\)
\(282\) −11269.8 7360.33i −0.141715 0.0925549i
\(283\) 117174.i 1.46305i 0.681817 + 0.731523i \(0.261190\pi\)
−0.681817 + 0.731523i \(0.738810\pi\)
\(284\) 39163.1 17193.4i 0.485557 0.213170i
\(285\) 0 0
\(286\) 57118.0 87456.1i 0.698298 1.06920i
\(287\) 904.433i 0.0109803i
\(288\) 26796.5 6808.59i 0.323068 0.0820866i
\(289\) 217018. 2.59837
\(290\) 0 0
\(291\) 27596.3i 0.325885i
\(292\) −17038.4 38810.0i −0.199832 0.455175i
\(293\) 29064.0 0.338548 0.169274 0.985569i \(-0.445858\pi\)
0.169274 + 0.985569i \(0.445858\pi\)
\(294\) 27266.0 41748.3i 0.315447 0.482996i
\(295\) 0 0
\(296\) −14423.7 + 86692.3i −0.164624 + 0.989457i
\(297\) 23091.1 0.261777
\(298\) −65648.3 42875.2i −0.739250 0.482808i
\(299\) 115848.i 1.29582i
\(300\) 0 0
\(301\) 2097.48 0.0231507
\(302\) 20429.7 31280.8i 0.224000 0.342977i
\(303\) 88556.8i 0.964577i
\(304\) 4837.41 + 4447.44i 0.0523438 + 0.0481241i
\(305\) 0 0
\(306\) −49571.4 32375.3i −0.529406 0.345757i
\(307\) 35059.6i 0.371989i −0.982551 0.185995i \(-0.940449\pi\)
0.982551 0.185995i \(-0.0595507\pi\)
\(308\) 1477.86 + 3366.25i 0.0155787 + 0.0354850i
\(309\) 17455.5 0.182816
\(310\) 0 0
\(311\) 52153.5i 0.539216i 0.962970 + 0.269608i \(0.0868942\pi\)
−0.962970 + 0.269608i \(0.913106\pi\)
\(312\) 52048.4 + 8659.70i 0.534685 + 0.0889598i
\(313\) 120087. 1.22577 0.612885 0.790172i \(-0.290009\pi\)
0.612885 + 0.790172i \(0.290009\pi\)
\(314\) 116925. + 76364.2i 1.18590 + 0.774516i
\(315\) 0 0
\(316\) 46277.2 20316.7i 0.463439 0.203460i
\(317\) −16118.8 −0.160404 −0.0802018 0.996779i \(-0.525556\pi\)
−0.0802018 + 0.996779i \(0.525556\pi\)
\(318\) 50088.2 76692.4i 0.495314 0.758400i
\(319\) 127376.i 1.25172i
\(320\) 0 0
\(321\) 34580.6 0.335601
\(322\) −3413.74 2229.53i −0.0329245 0.0215031i
\(323\) 14071.9i 0.134880i
\(324\) 4688.79 + 10680.1i 0.0446653 + 0.101738i
\(325\) 0 0
\(326\) 108707. 166446.i 1.02287 1.56617i
\(327\) 54040.4i 0.505386i
\(328\) 6804.90 40900.3i 0.0632520 0.380170i
\(329\) 904.101 0.00835267
\(330\) 0 0
\(331\) 7678.94i 0.0700882i −0.999386 0.0350441i \(-0.988843\pi\)
0.999386 0.0350441i \(-0.0111572\pi\)
\(332\) 191845. 84224.3i 1.74050 0.764119i
\(333\) −37076.1 −0.334353
\(334\) −112947. + 172939.i −1.01247 + 1.55024i
\(335\) 0 0
\(336\) −1256.87 + 1367.08i −0.0111330 + 0.0121092i
\(337\) −68133.9 −0.599934 −0.299967 0.953950i \(-0.596976\pi\)
−0.299967 + 0.953950i \(0.596976\pi\)
\(338\) −11343.7 7408.59i −0.0992932 0.0648489i
\(339\) 58325.1i 0.507523i
\(340\) 0 0
\(341\) −32090.4 −0.275973
\(342\) −1515.88 + 2321.04i −0.0129603 + 0.0198441i
\(343\) 6701.12i 0.0569585i
\(344\) 94852.1 + 15781.3i 0.801549 + 0.133360i
\(345\) 0 0
\(346\) −163513. 106791.i −1.36584 0.892037i
\(347\) 33524.6i 0.278423i 0.990263 + 0.139212i \(0.0444568\pi\)
−0.990263 + 0.139212i \(0.955543\pi\)
\(348\) 58914.0 25864.5i 0.486475 0.213573i
\(349\) 178271. 1.46362 0.731811 0.681508i \(-0.238676\pi\)
0.731811 + 0.681508i \(0.238676\pi\)
\(350\) 0 0
\(351\) 22259.8i 0.180678i
\(352\) 41504.1 + 163348.i 0.334970 + 1.31834i
\(353\) 80952.7 0.649654 0.324827 0.945773i \(-0.394694\pi\)
0.324827 + 0.945773i \(0.394694\pi\)
\(354\) 104046. + 67952.9i 0.830268 + 0.542252i
\(355\) 0 0
\(356\) −45745.4 104198.i −0.360950 0.822169i
\(357\) 3976.80 0.0312031
\(358\) −111684. + 171004.i −0.871412 + 1.33426i
\(359\) 95946.6i 0.744459i 0.928141 + 0.372229i \(0.121407\pi\)
−0.928141 + 0.372229i \(0.878593\pi\)
\(360\) 0 0
\(361\) 129662. 0.994944
\(362\) 56223.2 + 36719.7i 0.429041 + 0.280209i
\(363\) 64682.8i 0.490880i
\(364\) −3245.06 + 1424.65i −0.0244918 + 0.0107524i
\(365\) 0 0
\(366\) −6367.86 + 9750.14i −0.0475369 + 0.0727861i
\(367\) 36711.3i 0.272564i −0.990670 0.136282i \(-0.956485\pi\)
0.990670 0.136282i \(-0.0435153\pi\)
\(368\) −137601. 126509.i −1.01608 0.934166i
\(369\) 17492.0 0.128465
\(370\) 0 0
\(371\) 6152.54i 0.0446999i
\(372\) −6516.16 14842.5i −0.0470876 0.107256i
\(373\) 234487. 1.68539 0.842696 0.538390i \(-0.180967\pi\)
0.842696 + 0.538390i \(0.180967\pi\)
\(374\) 197355. 302180.i 1.41093 2.16034i
\(375\) 0 0
\(376\) 40885.2 + 6802.40i 0.289195 + 0.0481157i
\(377\) 122790. 0.863937
\(378\) −655.940 428.397i −0.00459072 0.00299822i
\(379\) 25997.1i 0.180987i −0.995897 0.0904933i \(-0.971156\pi\)
0.995897 0.0904933i \(-0.0288444\pi\)
\(380\) 0 0
\(381\) 133061. 0.916647
\(382\) 75046.0 114906.i 0.514281 0.787441i
\(383\) 135973.i 0.926948i 0.886110 + 0.463474i \(0.153397\pi\)
−0.886110 + 0.463474i \(0.846603\pi\)
\(384\) −67124.0 + 52365.3i −0.455214 + 0.355125i
\(385\) 0 0
\(386\) −111609. 72892.0i −0.749070 0.489221i
\(387\) 40565.8i 0.270856i
\(388\) −34158.8 77806.6i −0.226902 0.516836i
\(389\) 104895. 0.693196 0.346598 0.938014i \(-0.387337\pi\)
0.346598 + 0.938014i \(0.387337\pi\)
\(390\) 0 0
\(391\) 400279.i 2.61824i
\(392\) −25199.1 + 151457.i −0.163989 + 0.985639i
\(393\) −86073.0 −0.557291
\(394\) −180107. 117628.i −1.16021 0.757740i
\(395\) 0 0
\(396\) −65104.2 + 28582.2i −0.415163 + 0.182266i
\(397\) −4591.59 −0.0291328 −0.0145664 0.999894i \(-0.504637\pi\)
−0.0145664 + 0.999894i \(0.504637\pi\)
\(398\) 17481.2 26766.4i 0.110359 0.168975i
\(399\) 186.203i 0.00116961i
\(400\) 0 0
\(401\) −108079. −0.672128 −0.336064 0.941839i \(-0.609096\pi\)
−0.336064 + 0.941839i \(0.609096\pi\)
\(402\) 51970.5 + 33942.2i 0.321592 + 0.210033i
\(403\) 30935.1i 0.190477i
\(404\) −109616. 249682.i −0.671600 1.52976i
\(405\) 0 0
\(406\) −2363.15 + 3618.33i −0.0143364 + 0.0219511i
\(407\) 226010.i 1.36439i
\(408\) 179839. + 29921.2i 1.08035 + 0.179746i
\(409\) 94485.1 0.564829 0.282414 0.959293i \(-0.408865\pi\)
0.282414 + 0.959293i \(0.408865\pi\)
\(410\) 0 0
\(411\) 29200.4i 0.172864i
\(412\) −49214.9 + 21606.4i −0.289936 + 0.127288i
\(413\) −8346.94 −0.0489358
\(414\) 43119.7 66022.7i 0.251579 0.385205i
\(415\) 0 0
\(416\) −157467. + 40010.0i −0.909920 + 0.231197i
\(417\) −174575. −1.00394
\(418\) −14148.7 9240.61i −0.0809777 0.0528869i
\(419\) 33591.5i 0.191338i 0.995413 + 0.0956691i \(0.0304991\pi\)
−0.995413 + 0.0956691i \(0.969501\pi\)
\(420\) 0 0
\(421\) −187912. −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(422\) −50518.7 + 77351.7i −0.283679 + 0.434355i
\(423\) 17485.6i 0.0977234i
\(424\) −46291.3 + 278230.i −0.257495 + 1.54765i
\(425\) 0 0
\(426\) −46518.8 30381.7i −0.256336 0.167414i
\(427\) 782.191i 0.00429000i
\(428\) −97498.6 + 42804.0i −0.532244 + 0.233667i
\(429\) −135692. −0.737293
\(430\) 0 0
\(431\) 59456.6i 0.320070i 0.987111 + 0.160035i \(0.0511608\pi\)
−0.987111 + 0.160035i \(0.948839\pi\)
\(432\) −26439.7 24308.2i −0.141673 0.130252i
\(433\) −199941. −1.06641 −0.533206 0.845985i \(-0.679013\pi\)
−0.533206 + 0.845985i \(0.679013\pi\)
\(434\) 911.581 + 595.358i 0.00483967 + 0.00316081i
\(435\) 0 0
\(436\) 66891.4 + 152365.i 0.351882 + 0.801514i
\(437\) 18741.9 0.0981413
\(438\) −30107.8 + 46099.4i −0.156939 + 0.240297i
\(439\) 12289.2i 0.0637670i −0.999492 0.0318835i \(-0.989849\pi\)
0.999492 0.0318835i \(-0.0101505\pi\)
\(440\) 0 0
\(441\) −64774.4 −0.333063
\(442\) 291301. + 190250.i 1.49107 + 0.973824i
\(443\) 294620.i 1.50125i 0.660726 + 0.750627i \(0.270249\pi\)
−0.660726 + 0.750627i \(0.729751\pi\)
\(444\) 104534. 45892.8i 0.530265 0.232798i
\(445\) 0 0
\(446\) 100744. 154253.i 0.506463 0.775469i
\(447\) 101856.i 0.509769i
\(448\) 1851.52 5410.17i 0.00922512 0.0269560i
\(449\) −301030. −1.49320 −0.746599 0.665274i \(-0.768315\pi\)
−0.746599 + 0.665274i \(0.768315\pi\)
\(450\) 0 0
\(451\) 106629.i 0.524228i
\(452\) −72194.9 164445.i −0.353370 0.804903i
\(453\) −48533.7 −0.236508
\(454\) −108568. + 166234.i −0.526732 + 0.806505i
\(455\) 0 0
\(456\) 1400.98 8420.44i 0.00673753 0.0404954i
\(457\) 65670.5 0.314440 0.157220 0.987564i \(-0.449747\pi\)
0.157220 + 0.987564i \(0.449747\pi\)
\(458\) −29807.5 19467.4i −0.142100 0.0928063i
\(459\) 76912.4i 0.365065i
\(460\) 0 0
\(461\) 330337. 1.55437 0.777187 0.629270i \(-0.216646\pi\)
0.777187 + 0.629270i \(0.216646\pi\)
\(462\) 2611.45 3998.51i 0.0122348 0.0187333i
\(463\) 212356.i 0.990609i −0.868719 0.495304i \(-0.835057\pi\)
0.868719 0.495304i \(-0.164943\pi\)
\(464\) −134090. + 145848.i −0.622818 + 0.677429i
\(465\) 0 0
\(466\) 44735.6 + 29217.0i 0.206007 + 0.134544i
\(467\) 275863.i 1.26491i −0.774596 0.632456i \(-0.782047\pi\)
0.774596 0.632456i \(-0.217953\pi\)
\(468\) −27553.2 62760.4i −0.125800 0.286546i
\(469\) −4169.26 −0.0189546
\(470\) 0 0
\(471\) 181414.i 0.817768i
\(472\) −377465. 62801.8i −1.69431 0.281896i
\(473\) −247283. −1.10528
\(474\) −54969.1 35900.6i −0.244660 0.159788i
\(475\) 0 0
\(476\) −11212.4 + 4922.49i −0.0494863 + 0.0217256i
\(477\) −118992. −0.522974
\(478\) 87931.7 134636.i 0.384848 0.589260i
\(479\) 129251.i 0.563329i −0.959513 0.281664i \(-0.909114\pi\)
0.959513 0.281664i \(-0.0908865\pi\)
\(480\) 0 0
\(481\) 217874. 0.941704
\(482\) −305714. 199663.i −1.31589 0.859417i
\(483\) 5296.58i 0.0227039i
\(484\) −80064.5 182370.i −0.341782 0.778508i
\(485\) 0 0
\(486\) 8285.32 12686.1i 0.0350782 0.0537099i
\(487\) 296541.i 1.25034i 0.780490 + 0.625168i \(0.214969\pi\)
−0.780490 + 0.625168i \(0.785031\pi\)
\(488\) 5885.16 35372.2i 0.0247126 0.148533i
\(489\) −258249. −1.07999
\(490\) 0 0
\(491\) 340038.i 1.41047i −0.708972 0.705236i \(-0.750841\pi\)
0.708972 0.705236i \(-0.249159\pi\)
\(492\) −49317.9 + 21651.6i −0.203739 + 0.0894458i
\(493\) 424268. 1.74561
\(494\) 8907.94 13639.4i 0.0365026 0.0558908i
\(495\) 0 0
\(496\) 36744.1 + 33781.9i 0.149356 + 0.137316i
\(497\) 3731.91 0.0151084
\(498\) −227878. 148828.i −0.918850 0.600105i
\(499\) 146808.i 0.589587i −0.955561 0.294794i \(-0.904749\pi\)
0.955561 0.294794i \(-0.0952509\pi\)
\(500\) 0 0
\(501\) 268323. 1.06901
\(502\) −186569. + 285665.i −0.740342 + 1.13357i
\(503\) 410402.i 1.62208i −0.584989 0.811041i \(-0.698901\pi\)
0.584989 0.811041i \(-0.301099\pi\)
\(504\) 2379.66 + 395.924i 0.00936817 + 0.00155866i
\(505\) 0 0
\(506\) 402464. + 262851.i 1.57191 + 1.02662i
\(507\) 17600.2i 0.0684702i
\(508\) −375161. + 164704.i −1.45375 + 0.638228i
\(509\) −170171. −0.656825 −0.328413 0.944534i \(-0.606514\pi\)
−0.328413 + 0.944534i \(0.606514\pi\)
\(510\) 0 0
\(511\) 3698.26i 0.0141630i
\(512\) 124435. 230728.i 0.474682 0.880157i
\(513\) 3601.21 0.0136840
\(514\) −78399.3 51202.9i −0.296747 0.193807i
\(515\) 0 0
\(516\) −50212.4 114373.i −0.188587 0.429562i
\(517\) −106589. −0.398779
\(518\) −4193.06 + 6420.19i −0.0156268 + 0.0239270i
\(519\) 253698.i 0.941851i
\(520\) 0 0
\(521\) 64423.8 0.237340 0.118670 0.992934i \(-0.462137\pi\)
0.118670 + 0.992934i \(0.462137\pi\)
\(522\) −69979.5 45703.9i −0.256821 0.167731i
\(523\) 108085.i 0.395150i 0.980288 + 0.197575i \(0.0633066\pi\)
−0.980288 + 0.197575i \(0.936693\pi\)
\(524\) 242679. 106541.i 0.883832 0.388021i
\(525\) 0 0
\(526\) −194504. + 297814.i −0.703001 + 1.07640i
\(527\) 106888.i 0.384863i
\(528\) 148179. 161172.i 0.531520 0.578126i
\(529\) −253278. −0.905079
\(530\) 0 0
\(531\) 161432.i 0.572533i
\(532\) 230.482 + 524.990i 0.000814354 + 0.00185493i
\(533\) −102790. −0.361823
\(534\) −80834.4 + 123769.i −0.283474 + 0.434041i
\(535\) 0 0
\(536\) −188542. 31369.3i −0.656265 0.109188i
\(537\) 265321. 0.920075
\(538\) −262510. 171446.i −0.906945 0.592330i
\(539\) 394855.i 1.35913i
\(540\) 0 0
\(541\) −343195. −1.17259 −0.586295 0.810098i \(-0.699414\pi\)
−0.586295 + 0.810098i \(0.699414\pi\)
\(542\) 174590. 267323.i 0.594321 0.909993i
\(543\) 87233.0i 0.295856i
\(544\) −544084. + 138243.i −1.83852 + 0.467139i
\(545\) 0 0
\(546\) 3854.56 + 2517.43i 0.0129297 + 0.00844447i
\(547\) 310047.i 1.03622i 0.855313 + 0.518111i \(0.173365\pi\)
−0.855313 + 0.518111i \(0.826635\pi\)
\(548\) 36144.3 + 82329.1i 0.120359 + 0.274153i
\(549\) 15127.8 0.0501916
\(550\) 0 0
\(551\) 19865.2i 0.0654318i
\(552\) −39851.1 + 239522.i −0.130786 + 0.786080i
\(553\) 4409.82 0.0144202
\(554\) 46844.7 + 30594.5i 0.152630 + 0.0996836i
\(555\) 0 0
\(556\) 492206. 216089.i 1.59220 0.699010i
\(557\) −1815.28 −0.00585104 −0.00292552 0.999996i \(-0.500931\pi\)
−0.00292552 + 0.999996i \(0.500931\pi\)
\(558\) −11514.4 + 17630.2i −0.0369805 + 0.0566226i
\(559\) 238381.i 0.762865i
\(560\) 0 0
\(561\) −468846. −1.48972
\(562\) −48399.8 31610.1i −0.153240 0.100081i
\(563\) 240858.i 0.759878i 0.925012 + 0.379939i \(0.124055\pi\)
−0.925012 + 0.379939i \(0.875945\pi\)
\(564\) −21643.7 49299.7i −0.0680413 0.154984i
\(565\) 0 0
\(566\) −256289. + 392417.i −0.800014 + 1.22494i
\(567\) 1017.72i 0.00316565i
\(568\) 168764. + 28078.6i 0.523099 + 0.0870321i
\(569\) −240114. −0.741639 −0.370820 0.928705i \(-0.620923\pi\)
−0.370820 + 0.928705i \(0.620923\pi\)
\(570\) 0 0
\(571\) 301943.i 0.926090i −0.886335 0.463045i \(-0.846757\pi\)
0.886335 0.463045i \(-0.153243\pi\)
\(572\) 382578. 167960.i 1.16931 0.513350i
\(573\) −178283. −0.543000
\(574\) 1978.23 3028.96i 0.00600417 0.00919327i
\(575\) 0 0
\(576\) 104634. + 35808.9i 0.315376 + 0.107931i
\(577\) 67660.1 0.203227 0.101613 0.994824i \(-0.467600\pi\)
0.101613 + 0.994824i \(0.467600\pi\)
\(578\) 726797. + 474675.i 2.17549 + 1.42082i
\(579\) 173166.i 0.516541i
\(580\) 0 0
\(581\) 18281.2 0.0541568
\(582\) −60360.2 + 92420.5i −0.178199 + 0.272849i
\(583\) 725357.i 2.13410i
\(584\) 27825.5 167243.i 0.0815863 0.490367i
\(585\) 0 0
\(586\) 97335.7 + 63570.4i 0.283450 + 0.185123i
\(587\) 204755.i 0.594235i 0.954841 + 0.297117i \(0.0960253\pi\)
−0.954841 + 0.297117i \(0.903975\pi\)
\(588\) 182628. 80177.9i 0.528219 0.231899i
\(589\) −5004.72 −0.0144261
\(590\) 0 0
\(591\) 279444.i 0.800054i
\(592\) −237923. + 258785.i −0.678881 + 0.738408i
\(593\) −361586. −1.02826 −0.514129 0.857713i \(-0.671885\pi\)
−0.514129 + 0.857713i \(0.671885\pi\)
\(594\) 77332.3 + 50506.1i 0.219174 + 0.143143i
\(595\) 0 0
\(596\) −126078. 287180.i −0.354934 0.808465i
\(597\) −41529.2 −0.116521
\(598\) −253388. + 387975.i −0.708573 + 1.08493i
\(599\) 314411.i 0.876284i −0.898906 0.438142i \(-0.855637\pi\)
0.898906 0.438142i \(-0.144363\pi\)
\(600\) 0 0
\(601\) 4980.63 0.0137891 0.00689454 0.999976i \(-0.497805\pi\)
0.00689454 + 0.999976i \(0.497805\pi\)
\(602\) 7024.49 + 4587.73i 0.0193830 + 0.0126592i
\(603\) 80634.7i 0.221762i
\(604\) 136838. 60075.1i 0.375089 0.164672i
\(605\) 0 0
\(606\) −193697. + 296578.i −0.527445 + 0.807596i
\(607\) 224016.i 0.607998i −0.952672 0.303999i \(-0.901678\pi\)
0.952672 0.303999i \(-0.0983219\pi\)
\(608\) 6472.85 + 25475.2i 0.0175101 + 0.0689145i
\(609\) 5614.01 0.0151370
\(610\) 0 0
\(611\) 102752.i 0.275238i
\(612\) −95202.3 216851.i −0.254182 0.578973i
\(613\) −606099. −1.61296 −0.806478 0.591264i \(-0.798629\pi\)
−0.806478 + 0.591264i \(0.798629\pi\)
\(614\) 76684.4 117415.i 0.203409 0.311449i
\(615\) 0 0
\(616\) −2413.49 + 14506.1i −0.00636040 + 0.0382286i
\(617\) −223682. −0.587571 −0.293786 0.955871i \(-0.594915\pi\)
−0.293786 + 0.955871i \(0.594915\pi\)
\(618\) 58458.6 + 38179.6i 0.153064 + 0.0999665i
\(619\) 218632.i 0.570602i 0.958438 + 0.285301i \(0.0920936\pi\)
−0.958438 + 0.285301i \(0.907906\pi\)
\(620\) 0 0
\(621\) −102437. −0.265628
\(622\) −114073. + 174663.i −0.294851 + 0.451461i
\(623\) 9929.23i 0.0255823i
\(624\) 155370. + 142845.i 0.399023 + 0.366855i
\(625\) 0 0
\(626\) 402175. + 262662.i 1.02628 + 0.670269i
\(627\) 21952.4i 0.0558403i
\(628\) 224555. + 511490.i 0.569382 + 1.29693i
\(629\) 752801. 1.90274
\(630\) 0 0
\(631\) 57752.6i 0.145048i 0.997367 + 0.0725242i \(0.0231054\pi\)
−0.997367 + 0.0725242i \(0.976895\pi\)
\(632\) 199421. + 33179.2i 0.499271 + 0.0830677i
\(633\) 120015. 0.299521
\(634\) −53982.1 35255.9i −0.134298 0.0877110i
\(635\) 0 0
\(636\) 335492. 147288.i 0.829408 0.364128i
\(637\) 380640. 0.938070
\(638\) 278604. 426585.i 0.684458 1.04801i
\(639\) 72176.1i 0.176763i
\(640\) 0 0
\(641\) −239533. −0.582974 −0.291487 0.956575i \(-0.594150\pi\)
−0.291487 + 0.956575i \(0.594150\pi\)
\(642\) 115811. + 75636.8i 0.280983 + 0.183511i
\(643\) 131015.i 0.316884i −0.987368 0.158442i \(-0.949353\pi\)
0.987368 0.158442i \(-0.0506471\pi\)
\(644\) −6556.11 14933.5i −0.0158079 0.0360071i
\(645\) 0 0
\(646\) 30778.9 47127.0i 0.0737544 0.112929i
\(647\) 227917.i 0.544464i −0.962232 0.272232i \(-0.912238\pi\)
0.962232 0.272232i \(-0.0877618\pi\)
\(648\) −7657.27 + 46023.3i −0.0182358 + 0.109604i
\(649\) 984066. 2.33633
\(650\) 0 0
\(651\) 1414.36i 0.00333732i
\(652\) 728121. 319661.i 1.71281 0.751960i
\(653\) −334292. −0.783970 −0.391985 0.919972i \(-0.628211\pi\)
−0.391985 + 0.919972i \(0.628211\pi\)
\(654\) 118200. 180982.i 0.276352 0.423137i
\(655\) 0 0
\(656\) 112249. 122092.i 0.260841 0.283712i
\(657\) 71525.4 0.165703
\(658\) 3027.85 + 1977.50i 0.00699330 + 0.00456736i
\(659\) 820031.i 1.88825i 0.329588 + 0.944125i \(0.393090\pi\)
−0.329588 + 0.944125i \(0.606910\pi\)
\(660\) 0 0
\(661\) −368205. −0.842727 −0.421363 0.906892i \(-0.638448\pi\)
−0.421363 + 0.906892i \(0.638448\pi\)
\(662\) 16795.8 25716.9i 0.0383253 0.0586816i
\(663\) 451967.i 1.02821i
\(664\) 826713. + 137547.i 1.87508 + 0.311971i
\(665\) 0 0
\(666\) −124168. 81094.9i −0.279938 0.182829i
\(667\) 565070.i 1.27014i
\(668\) −756524. + 332130.i −1.69539 + 0.744313i
\(669\) −239331. −0.534745
\(670\) 0 0
\(671\) 92216.7i 0.204816i
\(672\) −7199.43 + 1829.26i −0.0159426 + 0.00405077i
\(673\) 272051. 0.600649 0.300325 0.953837i \(-0.402905\pi\)
0.300325 + 0.953837i \(0.402905\pi\)
\(674\) −228181. 149026.i −0.502297 0.328053i
\(675\) 0 0
\(676\) −21785.6 49623.0i −0.0476733 0.108590i
\(677\) 348582. 0.760549 0.380275 0.924874i \(-0.375829\pi\)
0.380275 + 0.924874i \(0.375829\pi\)
\(678\) −127572. + 195332.i −0.277521 + 0.424926i
\(679\) 7414.30i 0.0160817i
\(680\) 0 0
\(681\) 257919. 0.556147
\(682\) −107471. 70190.0i −0.231059 0.150906i
\(683\) 146496.i 0.314040i 0.987595 + 0.157020i \(0.0501887\pi\)
−0.987595 + 0.157020i \(0.949811\pi\)
\(684\) −10153.4 + 4457.58i −0.0217021 + 0.00952768i
\(685\) 0 0
\(686\) −14657.1 + 22442.1i −0.0311458 + 0.0476888i
\(687\) 46247.7i 0.0979889i
\(688\) 283143. + 260318.i 0.598177 + 0.549955i
\(689\) 699243. 1.47296
\(690\) 0 0
\(691\) 79772.8i 0.167070i −0.996505 0.0835350i \(-0.973379\pi\)
0.996505 0.0835350i \(-0.0266211\pi\)
\(692\) −314028. 715290.i −0.655776 1.49372i
\(693\) −6203.88 −0.0129180
\(694\) −73327.0 + 112275.i −0.152246 + 0.233111i
\(695\) 0 0
\(696\) 253876. + 42239.4i 0.524088 + 0.0871966i
\(697\) −355161. −0.731072
\(698\) 597031. + 389924.i 1.22542 + 0.800329i
\(699\) 69409.3i 0.142057i
\(700\) 0 0
\(701\) −1418.50 −0.00288665 −0.00144332 0.999999i \(-0.500459\pi\)
−0.00144332 + 0.999999i \(0.500459\pi\)
\(702\) −48687.8 + 74548.3i −0.0987975 + 0.151274i
\(703\) 35247.8i 0.0713217i
\(704\) −218286. + 637835.i −0.440433 + 1.28695i
\(705\) 0 0
\(706\) 271112. + 177064.i 0.543925 + 0.355240i
\(707\) 23792.6i 0.0475995i
\(708\) 199821. + 455150.i 0.398634 + 0.908005i
\(709\) −794794. −1.58111 −0.790555 0.612391i \(-0.790208\pi\)
−0.790555 + 0.612391i \(0.790208\pi\)
\(710\) 0 0
\(711\) 85287.1i 0.168711i
\(712\) 74706.9 449019.i 0.147367 0.885737i
\(713\) 142360. 0.280034
\(714\) 13318.4 + 8698.28i 0.0261249 + 0.0170623i
\(715\) 0 0
\(716\) −748061. + 328415.i −1.45919 + 0.640615i
\(717\) −208895. −0.406339
\(718\) −209860. + 321327.i −0.407081 + 0.623301i
\(719\) 713193.i 1.37959i −0.724006 0.689794i \(-0.757701\pi\)
0.724006 0.689794i \(-0.242299\pi\)
\(720\) 0 0
\(721\) −4689.76 −0.00902153
\(722\) 434240. + 283604.i 0.833021 + 0.544050i
\(723\) 474329.i 0.907410i
\(724\) 107977. + 245949.i 0.205994 + 0.469212i
\(725\) 0 0
\(726\) −141478. + 216624.i −0.268420 + 0.410991i
\(727\) 886306.i 1.67693i −0.544955 0.838465i \(-0.683453\pi\)
0.544955 0.838465i \(-0.316547\pi\)
\(728\) −13983.8 2326.60i −0.0263854 0.00438995i
\(729\) −19683.0 −0.0370370
\(730\) 0 0
\(731\) 823658.i 1.54139i
\(732\) −42652.1 + 18725.2i −0.0796010 + 0.0349466i
\(733\) 267035. 0.497005 0.248502 0.968631i \(-0.420062\pi\)
0.248502 + 0.968631i \(0.420062\pi\)
\(734\) 80297.2 122947.i 0.149042 0.228205i
\(735\) 0 0
\(736\) −184122. 724648.i −0.339899 1.33774i
\(737\) 491537. 0.904943
\(738\) 58580.9 + 38259.5i 0.107558 + 0.0702468i
\(739\) 706999.i 1.29458i 0.762242 + 0.647292i \(0.224099\pi\)
−0.762242 + 0.647292i \(0.775901\pi\)
\(740\) 0 0
\(741\) −21162.1 −0.0385410
\(742\) −13457.2 + 20605.0i −0.0244426 + 0.0374252i
\(743\) 990710.i 1.79461i −0.441416 0.897303i \(-0.645524\pi\)
0.441416 0.897303i \(-0.354476\pi\)
\(744\) 10641.6 63960.2i 0.0192247 0.115548i
\(745\) 0 0
\(746\) 785300. + 512883.i 1.41110 + 0.921596i
\(747\) 353564.i 0.633617i
\(748\) 1.32189e6 580339.i 2.36261 1.03724i
\(749\) −9290.78 −0.0165611
\(750\) 0 0
\(751\) 629696.i 1.11648i −0.829679 0.558240i \(-0.811477\pi\)
0.829679 0.558240i \(-0.188523\pi\)
\(752\) 122047. + 112208.i 0.215819 + 0.198421i
\(753\) 443222. 0.781685
\(754\) 411227. + 268574.i 0.723334 + 0.472413i
\(755\) 0 0
\(756\) −1259.74 2869.42i −0.00220413 0.00502054i
\(757\) 14822.4 0.0258658 0.0129329 0.999916i \(-0.495883\pi\)
0.0129329 + 0.999916i \(0.495883\pi\)
\(758\) 56862.4 87064.7i 0.0989661 0.151532i
\(759\) 624442.i 1.08395i
\(760\) 0 0
\(761\) −458988. −0.792559 −0.396280 0.918130i \(-0.629699\pi\)
−0.396280 + 0.918130i \(0.629699\pi\)
\(762\) 445625. + 291039.i 0.767466 + 0.501236i
\(763\) 14519.1i 0.0249396i
\(764\) 502660. 220679.i 0.861168 0.378071i
\(765\) 0 0
\(766\) −297408. + 455376.i −0.506869 + 0.776091i
\(767\) 948638.i 1.61254i
\(768\) −339336. + 28554.9i −0.575317 + 0.0484125i
\(769\) 179362. 0.303304 0.151652 0.988434i \(-0.451541\pi\)
0.151652 + 0.988434i \(0.451541\pi\)
\(770\) 0 0
\(771\) 121640.i 0.204629i
\(772\) −214345. 488233.i −0.359649 0.819205i
\(773\) 129744. 0.217134 0.108567 0.994089i \(-0.465374\pi\)
0.108567 + 0.994089i \(0.465374\pi\)
\(774\) −88727.9 + 135856.i −0.148108 + 0.226775i
\(775\) 0 0
\(776\) 55784.8 335289.i 0.0926386 0.556796i
\(777\) 9961.23 0.0164995
\(778\) 351295. + 229433.i 0.580381 + 0.379050i
\(779\) 16629.4i 0.0274033i
\(780\) 0 0
\(781\) −439975. −0.721317
\(782\) −875513. + 1.34054e6i −1.43169 + 2.19213i
\(783\) 108576.i 0.177097i
\(784\) −415668. + 452116.i −0.676262 + 0.735559i
\(785\) 0 0
\(786\) −288260. 188264.i −0.466594 0.304735i
\(787\) 293979.i 0.474643i −0.971431 0.237322i \(-0.923730\pi\)
0.971431 0.237322i \(-0.0762695\pi\)
\(788\) −345896. 787879.i −0.557049 1.26884i
\(789\) 462072. 0.742259
\(790\) 0 0
\(791\) 15670.2i 0.0250450i
\(792\) −280552. 46677.6i −0.447262 0.0744146i
\(793\) −88896.9 −0.141364
\(794\) −15377.3 10043.0i −0.0243915 0.0159302i
\(795\) 0 0
\(796\) 117090. 51405.0i 0.184796 0.0811295i
\(797\) −281322. −0.442881 −0.221441 0.975174i \(-0.571076\pi\)
−0.221441 + 0.975174i \(0.571076\pi\)
\(798\) 407.273 623.595i 0.000639558 0.000979258i
\(799\) 355031.i 0.556125i
\(800\) 0 0
\(801\) 192034. 0.299304
\(802\) −361958. 236396.i −0.562742 0.367529i
\(803\) 436008.i 0.676182i
\(804\) 99809.8 + 227346.i 0.154405 + 0.351702i
\(805\) 0 0
\(806\) 67663.1 103602.i 0.104155 0.159477i
\(807\) 407296.i 0.625407i
\(808\) 179014. 1.07595e6i 0.274198 1.64804i
\(809\) −1.00560e6 −1.53648 −0.768239 0.640163i \(-0.778867\pi\)
−0.768239 + 0.640163i \(0.778867\pi\)
\(810\) 0 0
\(811\) 669583.i 1.01804i −0.860756 0.509018i \(-0.830009\pi\)
0.860756 0.509018i \(-0.169991\pi\)
\(812\) −15828.4 + 6949.03i −0.0240064 + 0.0105393i
\(813\) −414764. −0.627509
\(814\) 494342. 756911.i 0.746069 1.14234i
\(815\) 0 0
\(816\) 536837. + 493560.i 0.806236 + 0.741241i
\(817\) −38565.5 −0.0577770
\(818\) 316432. + 206663.i 0.472905 + 0.308856i
\(819\) 5980.53i 0.00891604i
\(820\) 0 0
\(821\) −706530. −1.04820 −0.524100 0.851657i \(-0.675598\pi\)
−0.524100 + 0.851657i \(0.675598\pi\)
\(822\) 63868.7 97792.5i 0.0945246 0.144731i
\(823\) 925866.i 1.36694i 0.729980 + 0.683468i \(0.239529\pi\)
−0.729980 + 0.683468i \(0.760471\pi\)
\(824\) −212080. 35285.5i −0.312353 0.0519687i
\(825\) 0 0
\(826\) −27954.0 18256.9i −0.0409717 0.0267588i
\(827\) 639584.i 0.935162i 0.883950 + 0.467581i \(0.154874\pi\)
−0.883950 + 0.467581i \(0.845126\pi\)
\(828\) 288817. 126797.i 0.421272 0.184947i
\(829\) −458584. −0.667283 −0.333642 0.942700i \(-0.608278\pi\)
−0.333642 + 0.942700i \(0.608278\pi\)
\(830\) 0 0
\(831\) 72681.7i 0.105250i
\(832\) −614872. 210427.i −0.888256 0.303987i
\(833\) 1.31519e6 1.89540
\(834\) −584654. 381840.i −0.840557 0.548971i
\(835\) 0 0
\(836\) −27172.8 61893.9i −0.0388795 0.0885595i
\(837\) 27354.1 0.0390456
\(838\) −73473.3 + 112499.i −0.104626 + 0.160199i
\(839\) 734005.i 1.04274i 0.853331 + 0.521369i \(0.174579\pi\)
−0.853331 + 0.521369i \(0.825421\pi\)
\(840\) 0 0
\(841\) −108346. −0.153186
\(842\) −629321. 411013.i −0.887663 0.579737i
\(843\) 75094.5i 0.105670i
\(844\) −338376. + 148554.i −0.475023 + 0.208545i
\(845\) 0 0
\(846\) −38245.4 + 58559.4i −0.0534366 + 0.0818193i
\(847\) 17378.3i 0.0242237i
\(848\) −763591. + 830546.i −1.06186 + 1.15497i
\(849\) 608853. 0.844690
\(850\) 0 0
\(851\) 1.00263e6i 1.38447i
\(852\) −89339.8 203497.i −0.123074 0.280336i
\(853\) 144945. 0.199208 0.0996039 0.995027i \(-0.468242\pi\)
0.0996039 + 0.995027i \(0.468242\pi\)
\(854\) 1710.85 2619.57i 0.00234583 0.00359182i
\(855\) 0 0
\(856\) −420148. 69903.3i −0.573396 0.0954004i
\(857\) −749831. −1.02094 −0.510472 0.859894i \(-0.670529\pi\)
−0.510472 + 0.859894i \(0.670529\pi\)
\(858\) −454435. 296794.i −0.617302 0.403163i
\(859\) 991769.i 1.34408i 0.740516 + 0.672038i \(0.234581\pi\)
−0.740516 + 0.672038i \(0.765419\pi\)
\(860\) 0 0
\(861\) −4699.57 −0.00633946
\(862\) −130047. + 199121.i −0.175019 + 0.267980i
\(863\) 254191.i 0.341301i −0.985332 0.170651i \(-0.945413\pi\)
0.985332 0.170651i \(-0.0545870\pi\)
\(864\) −35378.5 139239.i −0.0473927 0.186523i
\(865\) 0 0
\(866\) −669604. 437322.i −0.892858 0.583130i
\(867\) 1.12766e6i 1.50017i
\(868\) 1750.70 + 3987.73i 0.00232366 + 0.00529280i
\(869\) −519898. −0.688460
\(870\) 0 0
\(871\) 473841.i 0.624592i
\(872\) −109240. + 656580.i −0.143665 + 0.863485i
\(873\) 143395. 0.188150
\(874\) 62767.1 + 40993.5i 0.0821692 + 0.0536651i
\(875\) 0 0
\(876\) −201663. + 88534.3i −0.262795 + 0.115373i
\(877\) 378981. 0.492740 0.246370 0.969176i \(-0.420762\pi\)
0.246370 + 0.969176i \(0.420762\pi\)
\(878\) 26879.7 41156.8i 0.0348687 0.0533891i
\(879\) 151021.i 0.195461i
\(880\) 0 0
\(881\) 1.18545e6 1.52733 0.763665 0.645613i \(-0.223398\pi\)
0.763665 + 0.645613i \(0.223398\pi\)
\(882\) −216930. 141678.i −0.278858 0.182124i
\(883\) 161617.i 0.207284i 0.994615 + 0.103642i \(0.0330496\pi\)
−0.994615 + 0.103642i \(0.966950\pi\)
\(884\) 559446. + 1.27430e6i 0.715902 + 1.63068i
\(885\) 0 0
\(886\) −644409. + 986686.i −0.820908 + 1.25693i
\(887\) 185284.i 0.235499i −0.993043 0.117750i \(-0.962432\pi\)
0.993043 0.117750i \(-0.0375680\pi\)
\(888\) 450466. + 74947.6i 0.571263 + 0.0950456i
\(889\) −35749.6 −0.0452343
\(890\) 0 0
\(891\) 119985.i 0.151137i
\(892\) 674783. 296244.i 0.848076 0.372324i
\(893\) −16623.3 −0.0208456
\(894\) −222786. + 341119.i −0.278749 + 0.426806i
\(895\) 0 0
\(896\) 18034.2 14069.0i 0.0224637 0.0175246i
\(897\) 601962. 0.748142
\(898\) −1.00816e6 658431.i −1.25019 0.816502i
\(899\) 150892.i 0.186701i
\(900\) 0 0
\(901\) 2.41604e6 2.97615
\(902\) −233224. + 357101.i −0.286656 + 0.438912i
\(903\) 10898.8i 0.0133661i
\(904\) 117902. 708638.i 0.144272 0.867136i
\(905\) 0 0
\(906\) −162540. 106156.i −0.198018 0.129326i
\(907\) 81044.4i 0.0985163i 0.998786 + 0.0492582i \(0.0156857\pi\)
−0.998786 + 0.0492582i \(0.984314\pi\)
\(908\) −727191. + 319253.i −0.882017 + 0.387225i
\(909\) 460155. 0.556899
\(910\) 0 0
\(911\) 990859.i 1.19392i 0.802271 + 0.596960i \(0.203625\pi\)
−0.802271 + 0.596960i \(0.796375\pi\)
\(912\) 23109.6 25135.9i 0.0277845 0.0302207i
\(913\) −2.15527e6 −2.58560
\(914\) 219932. + 143638.i 0.263266 + 0.171940i
\(915\) 0 0
\(916\) −57245.5 130393.i −0.0682261 0.155405i
\(917\) 23125.2 0.0275009
\(918\) −168227. + 257581.i −0.199623 + 0.305652i
\(919\) 1.33459e6i 1.58021i −0.612969 0.790107i \(-0.710025\pi\)
0.612969 0.790107i \(-0.289975\pi\)
\(920\) 0 0
\(921\) −182175. −0.214768
\(922\) 1.10630e6 + 722532.i 1.30141 + 0.849954i
\(923\) 424135.i 0.497853i
\(924\) 17491.6 7679.17i 0.0204873 0.00899436i
\(925\) 0 0
\(926\) 464477. 711183.i 0.541679 0.829391i
\(927\) 90701.3i 0.105549i
\(928\) −768077. + 195157.i −0.891885 + 0.226614i
\(929\) −264841. −0.306870 −0.153435 0.988159i \(-0.549034\pi\)
−0.153435 + 0.988159i \(0.549034\pi\)
\(930\) 0 0
\(931\) 61580.3i 0.0710465i
\(932\) 85915.0 + 195696.i 0.0989093 + 0.225295i
\(933\) 270998. 0.311317
\(934\) 603384. 923871.i 0.691672 1.05905i
\(935\) 0 0
\(936\) 44997.1 270451.i 0.0513610 0.308701i
\(937\) −1.27942e6 −1.45724 −0.728622 0.684916i \(-0.759839\pi\)
−0.728622 + 0.684916i \(0.759839\pi\)
\(938\) −13962.9 9119.25i −0.0158698 0.0103646i
\(939\) 623993.i 0.707698i
\(940\) 0 0
\(941\) −117710. −0.132934 −0.0664668 0.997789i \(-0.521173\pi\)
−0.0664668 + 0.997789i \(0.521173\pi\)
\(942\) 396800. 607560.i 0.447167 0.684679i
\(943\) 473029.i 0.531942i
\(944\) −1.12677e6 1.03594e6i −1.26442 1.16249i
\(945\) 0 0
\(946\) −828155. 540872.i −0.925400 0.604383i
\(947\) 1.42125e6i 1.58479i −0.610011 0.792393i \(-0.708835\pi\)
0.610011 0.792393i \(-0.291165\pi\)
\(948\) −105569. 240463.i −0.117468 0.267567i
\(949\) −420312. −0.466701
\(950\) 0 0
\(951\) 83755.7i 0.0926090i
\(952\) −48317.3 8038.93i −0.0533124 0.00887001i
\(953\) 544751. 0.599808 0.299904 0.953969i \(-0.403045\pi\)
0.299904 + 0.953969i \(0.403045\pi\)
\(954\) −398506. 260266.i −0.437862 0.285970i
\(955\) 0 0
\(956\) 588969. 258570.i 0.644431 0.282919i
\(957\) −661866. −0.722680
\(958\) 282705. 432863.i 0.308036 0.471649i
\(959\) 7845.27i 0.00853042i
\(960\) 0 0
\(961\) 885506. 0.958837
\(962\) 729662. + 476546.i 0.788445 + 0.514937i
\(963\) 179686.i 0.193759i
\(964\) −587126. 1.33735e6i −0.631796 1.43910i
\(965\) 0 0
\(966\) −11585.0 + 17738.3i −0.0124148 + 0.0190090i
\(967\) 369389.i 0.395031i −0.980300 0.197516i \(-0.936713\pi\)
0.980300 0.197516i \(-0.0632873\pi\)
\(968\) 130753. 785882.i 0.139541 0.838700i
\(969\) −73119.8 −0.0778731
\(970\) 0 0
\(971\) 750410.i 0.795903i 0.917406 + 0.397952i \(0.130279\pi\)
−0.917406 + 0.397952i \(0.869721\pi\)
\(972\) 55495.3 24363.7i 0.0587386 0.0257875i
\(973\) 46903.1 0.0495422
\(974\) −648611. + 993120.i −0.683702 + 1.04685i
\(975\) 0 0
\(976\) 97077.6 105590.i 0.101911 0.110847i
\(977\) 1.18852e6 1.24513 0.622566 0.782567i \(-0.286090\pi\)
0.622566 + 0.782567i \(0.286090\pi\)
\(978\) −864880. 564857.i −0.904228 0.590556i
\(979\) 1.17061e6i 1.22137i
\(980\) 0 0
\(981\) −280802. −0.291785
\(982\) 743751. 1.13879e6i 0.771267 1.18092i
\(983\) 144516.i 0.149558i 0.997200 + 0.0747789i \(0.0238251\pi\)
−0.997200 + 0.0747789i \(0.976175\pi\)
\(984\) −212524. 35359.3i −0.219491 0.0365185i
\(985\) 0 0
\(986\) 1.42088e6 + 927984.i 1.46152 + 0.954523i
\(987\) 4697.85i 0.00482241i
\(988\) 59665.6 26194.5i 0.0611238 0.0268347i
\(989\) 1.09700e6 1.12154
\(990\) 0 0
\(991\) 382181.i 0.389154i −0.980887 0.194577i \(-0.937667\pi\)
0.980887 0.194577i \(-0.0623334\pi\)
\(992\) 49166.6 + 193505.i 0.0499628 + 0.196639i
\(993\) −39900.9 −0.0404655
\(994\) 12498.2 + 8162.65i 0.0126496 + 0.00826149i
\(995\) 0 0
\(996\) −437642. 996858.i −0.441164 1.00488i
\(997\) 1.03299e6 1.03921 0.519607 0.854406i \(-0.326079\pi\)
0.519607 + 0.854406i \(0.326079\pi\)
\(998\) 321106. 491662.i 0.322395 0.493634i
\(999\) 192653.i 0.193039i
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 300.5.c.d.151.12 16
4.3 odd 2 inner 300.5.c.d.151.11 16
5.2 odd 4 300.5.f.b.199.10 32
5.3 odd 4 300.5.f.b.199.23 32
5.4 even 2 60.5.c.a.31.5 16
15.14 odd 2 180.5.c.c.91.12 16
20.3 even 4 300.5.f.b.199.9 32
20.7 even 4 300.5.f.b.199.24 32
20.19 odd 2 60.5.c.a.31.6 yes 16
40.19 odd 2 960.5.e.f.511.15 16
40.29 even 2 960.5.e.f.511.6 16
60.59 even 2 180.5.c.c.91.11 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.5.c.a.31.5 16 5.4 even 2
60.5.c.a.31.6 yes 16 20.19 odd 2
180.5.c.c.91.11 16 60.59 even 2
180.5.c.c.91.12 16 15.14 odd 2
300.5.c.d.151.11 16 4.3 odd 2 inner
300.5.c.d.151.12 16 1.1 even 1 trivial
300.5.f.b.199.9 32 20.3 even 4
300.5.f.b.199.10 32 5.2 odd 4
300.5.f.b.199.23 32 5.3 odd 4
300.5.f.b.199.24 32 20.7 even 4
960.5.e.f.511.6 16 40.29 even 2
960.5.e.f.511.15 16 40.19 odd 2