Properties

Label 147.6.c.c.146.13
Level $147$
Weight $6$
Character 147.146
Analytic conductor $23.576$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [147,6,Mod(146,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("147.146");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.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: \(23.5764215125\)
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: \( x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + 7244325760 x^{4} - 29387167488 x^{2} + 90230547456 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{8}\cdot 7^{4} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.13
Root \(-5.89199 - 3.40174i\) of defining polynomial
Character \(\chi\) \(=\) 147.146
Dual form 147.6.c.c.146.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+6.80349i q^{2} +(-12.4320 - 9.40448i) q^{3} -14.2874 q^{4} -14.9141 q^{5} +(63.9832 - 84.5813i) q^{6} +120.507i q^{8} +(66.1117 + 233.834i) q^{9} +O(q^{10})\) \(q+6.80349i q^{2} +(-12.4320 - 9.40448i) q^{3} -14.2874 q^{4} -14.9141 q^{5} +(63.9832 - 84.5813i) q^{6} +120.507i q^{8} +(66.1117 + 233.834i) q^{9} -101.468i q^{10} +96.0737i q^{11} +(177.622 + 134.366i) q^{12} +416.854i q^{13} +(185.413 + 140.259i) q^{15} -1277.07 q^{16} -208.498 q^{17} +(-1590.89 + 449.790i) q^{18} -2651.38i q^{19} +213.085 q^{20} -653.636 q^{22} +2617.73i q^{23} +(1133.31 - 1498.15i) q^{24} -2902.57 q^{25} -2836.06 q^{26} +(1377.18 - 3528.78i) q^{27} -7220.50i q^{29} +(-954.253 + 1261.45i) q^{30} -4297.41i q^{31} -4832.28i q^{32} +(903.523 - 1194.39i) q^{33} -1418.52i q^{34} +(-944.567 - 3340.89i) q^{36} +3679.00 q^{37} +18038.6 q^{38} +(3920.29 - 5182.35i) q^{39} -1797.26i q^{40} -15452.3 q^{41} -6011.11 q^{43} -1372.65i q^{44} +(-985.997 - 3487.42i) q^{45} -17809.7 q^{46} +3907.44 q^{47} +(15876.6 + 12010.1i) q^{48} -19747.6i q^{50} +(2592.06 + 1960.82i) q^{51} -5955.77i q^{52} -36297.2i q^{53} +(24008.0 + 9369.63i) q^{54} -1432.85i q^{55} +(-24934.8 + 32962.1i) q^{57} +49124.6 q^{58} +7827.45 q^{59} +(-2649.08 - 2003.95i) q^{60} +20193.7i q^{61} +29237.3 q^{62} -7989.78 q^{64} -6217.00i q^{65} +(8126.04 + 6147.10i) q^{66} +43937.9 q^{67} +2978.91 q^{68} +(24618.3 - 32543.7i) q^{69} -26028.0i q^{71} +(-28178.6 + 7966.93i) q^{72} -50911.3i q^{73} +25030.0i q^{74} +(36084.9 + 27297.1i) q^{75} +37881.4i q^{76} +(35258.0 + 26671.6i) q^{78} -50114.3 q^{79} +19046.3 q^{80} +(-50307.5 + 30918.3i) q^{81} -105129. i q^{82} -107835. q^{83} +3109.57 q^{85} -40896.5i q^{86} +(-67905.0 + 89765.6i) q^{87} -11577.6 q^{88} -136779. q^{89} +(23726.6 - 6708.22i) q^{90} -37400.6i q^{92} +(-40414.8 + 53425.6i) q^{93} +26584.2i q^{94} +39543.0i q^{95} +(-45445.1 + 60075.2i) q^{96} -25183.4i q^{97} +(-22465.3 + 6351.59i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.80349i 1.20270i 0.798986 + 0.601349i \(0.205370\pi\)
−0.798986 + 0.601349i \(0.794630\pi\)
\(3\) −12.4320 9.40448i −0.797516 0.603297i
\(4\) −14.2874 −0.446483
\(5\) −14.9141 −0.266792 −0.133396 0.991063i \(-0.542588\pi\)
−0.133396 + 0.991063i \(0.542588\pi\)
\(6\) 63.9832 84.5813i 0.725585 0.959171i
\(7\) 0 0
\(8\) 120.507i 0.665714i
\(9\) 66.1117 + 233.834i 0.272065 + 0.962279i
\(10\) 101.468i 0.320870i
\(11\) 96.0737i 0.239399i 0.992810 + 0.119700i \(0.0381931\pi\)
−0.992810 + 0.119700i \(0.961807\pi\)
\(12\) 177.622 + 134.366i 0.356077 + 0.269362i
\(13\) 416.854i 0.684109i 0.939680 + 0.342055i \(0.111123\pi\)
−0.939680 + 0.342055i \(0.888877\pi\)
\(14\) 0 0
\(15\) 185.413 + 140.259i 0.212771 + 0.160955i
\(16\) −1277.07 −1.24714
\(17\) −208.498 −0.174977 −0.0874884 0.996166i \(-0.527884\pi\)
−0.0874884 + 0.996166i \(0.527884\pi\)
\(18\) −1590.89 + 449.790i −1.15733 + 0.327211i
\(19\) 2651.38i 1.68495i −0.538733 0.842476i \(-0.681097\pi\)
0.538733 0.842476i \(-0.318903\pi\)
\(20\) 213.085 0.119118
\(21\) 0 0
\(22\) −653.636 −0.287925
\(23\) 2617.73i 1.03182i 0.856642 + 0.515911i \(0.172546\pi\)
−0.856642 + 0.515911i \(0.827454\pi\)
\(24\) 1133.31 1498.15i 0.401624 0.530918i
\(25\) −2902.57 −0.928822
\(26\) −2836.06 −0.822777
\(27\) 1377.18 3528.78i 0.363564 0.931569i
\(28\) 0 0
\(29\) 7220.50i 1.59431i −0.603776 0.797154i \(-0.706338\pi\)
0.603776 0.797154i \(-0.293662\pi\)
\(30\) −954.253 + 1261.45i −0.193580 + 0.255899i
\(31\) 4297.41i 0.803160i −0.915824 0.401580i \(-0.868461\pi\)
0.915824 0.401580i \(-0.131539\pi\)
\(32\) 4832.28i 0.834214i
\(33\) 903.523 1194.39i 0.144429 0.190925i
\(34\) 1418.52i 0.210444i
\(35\) 0 0
\(36\) −944.567 3340.89i −0.121472 0.429641i
\(37\) 3679.00 0.441799 0.220900 0.975297i \(-0.429101\pi\)
0.220900 + 0.975297i \(0.429101\pi\)
\(38\) 18038.6 2.02649
\(39\) 3920.29 5182.35i 0.412721 0.545588i
\(40\) 1797.26i 0.177607i
\(41\) −15452.3 −1.43560 −0.717798 0.696251i \(-0.754850\pi\)
−0.717798 + 0.696251i \(0.754850\pi\)
\(42\) 0 0
\(43\) −6011.11 −0.495774 −0.247887 0.968789i \(-0.579736\pi\)
−0.247887 + 0.968789i \(0.579736\pi\)
\(44\) 1372.65i 0.106888i
\(45\) −985.997 3487.42i −0.0725846 0.256728i
\(46\) −17809.7 −1.24097
\(47\) 3907.44 0.258016 0.129008 0.991644i \(-0.458821\pi\)
0.129008 + 0.991644i \(0.458821\pi\)
\(48\) 15876.6 + 12010.1i 0.994611 + 0.752394i
\(49\) 0 0
\(50\) 19747.6i 1.11709i
\(51\) 2592.06 + 1960.82i 0.139547 + 0.105563i
\(52\) 5955.77i 0.305443i
\(53\) 36297.2i 1.77494i −0.460868 0.887469i \(-0.652462\pi\)
0.460868 0.887469i \(-0.347538\pi\)
\(54\) 24008.0 + 9369.63i 1.12040 + 0.437258i
\(55\) 1432.85i 0.0638697i
\(56\) 0 0
\(57\) −24934.8 + 32962.1i −1.01653 + 1.34378i
\(58\) 49124.6 1.91747
\(59\) 7827.45 0.292746 0.146373 0.989230i \(-0.453240\pi\)
0.146373 + 0.989230i \(0.453240\pi\)
\(60\) −2649.08 2003.95i −0.0949984 0.0718635i
\(61\) 20193.7i 0.694850i 0.937708 + 0.347425i \(0.112944\pi\)
−0.937708 + 0.347425i \(0.887056\pi\)
\(62\) 29237.3 0.965959
\(63\) 0 0
\(64\) −7989.78 −0.243829
\(65\) 6217.00i 0.182515i
\(66\) 8126.04 + 6147.10i 0.229625 + 0.173704i
\(67\) 43937.9 1.19578 0.597892 0.801577i \(-0.296005\pi\)
0.597892 + 0.801577i \(0.296005\pi\)
\(68\) 2978.91 0.0781241
\(69\) 24618.3 32543.7i 0.622495 0.822894i
\(70\) 0 0
\(71\) 26028.0i 0.612765i −0.951908 0.306383i \(-0.900881\pi\)
0.951908 0.306383i \(-0.0991187\pi\)
\(72\) −28178.6 + 7966.93i −0.640603 + 0.181117i
\(73\) 50911.3i 1.11817i −0.829111 0.559084i \(-0.811153\pi\)
0.829111 0.559084i \(-0.188847\pi\)
\(74\) 25030.0i 0.531351i
\(75\) 36084.9 + 27297.1i 0.740751 + 0.560356i
\(76\) 37881.4i 0.752302i
\(77\) 0 0
\(78\) 35258.0 + 26671.6i 0.656178 + 0.496379i
\(79\) −50114.3 −0.903429 −0.451715 0.892163i \(-0.649187\pi\)
−0.451715 + 0.892163i \(0.649187\pi\)
\(80\) 19046.3 0.332726
\(81\) −50307.5 + 30918.3i −0.851962 + 0.523604i
\(82\) 105129.i 1.72659i
\(83\) −107835. −1.71817 −0.859086 0.511832i \(-0.828967\pi\)
−0.859086 + 0.511832i \(0.828967\pi\)
\(84\) 0 0
\(85\) 3109.57 0.0466824
\(86\) 40896.5i 0.596266i
\(87\) −67905.0 + 89765.6i −0.961842 + 1.27149i
\(88\) −11577.6 −0.159371
\(89\) −136779. −1.83039 −0.915194 0.403013i \(-0.867963\pi\)
−0.915194 + 0.403013i \(0.867963\pi\)
\(90\) 23726.6 6708.22i 0.308766 0.0872973i
\(91\) 0 0
\(92\) 37400.6i 0.460690i
\(93\) −40414.8 + 53425.6i −0.484544 + 0.640533i
\(94\) 26584.2i 0.310316i
\(95\) 39543.0i 0.449531i
\(96\) −45445.1 + 60075.2i −0.503279 + 0.665299i
\(97\) 25183.4i 0.271759i −0.990725 0.135880i \(-0.956614\pi\)
0.990725 0.135880i \(-0.0433861\pi\)
\(98\) 0 0
\(99\) −22465.3 + 6351.59i −0.230369 + 0.0651320i
\(100\) 41470.3 0.414703
\(101\) −78062.7 −0.761448 −0.380724 0.924689i \(-0.624325\pi\)
−0.380724 + 0.924689i \(0.624325\pi\)
\(102\) −13340.4 + 17635.1i −0.126960 + 0.167833i
\(103\) 97991.9i 0.910117i −0.890462 0.455059i \(-0.849618\pi\)
0.890462 0.455059i \(-0.150382\pi\)
\(104\) −50233.9 −0.455421
\(105\) 0 0
\(106\) 246947. 2.13471
\(107\) 135095.i 1.14072i 0.821395 + 0.570360i \(0.193196\pi\)
−0.821395 + 0.570360i \(0.806804\pi\)
\(108\) −19676.4 + 50417.2i −0.162325 + 0.415929i
\(109\) 75132.0 0.605702 0.302851 0.953038i \(-0.402062\pi\)
0.302851 + 0.953038i \(0.402062\pi\)
\(110\) 9748.40 0.0768160
\(111\) −45737.5 34599.0i −0.352342 0.266536i
\(112\) 0 0
\(113\) 88078.7i 0.648895i 0.945904 + 0.324448i \(0.105178\pi\)
−0.945904 + 0.324448i \(0.894822\pi\)
\(114\) −224257. 169644.i −1.61616 1.22258i
\(115\) 39041.0i 0.275281i
\(116\) 103163.i 0.711831i
\(117\) −97474.5 + 27558.9i −0.658304 + 0.186122i
\(118\) 53254.0i 0.352085i
\(119\) 0 0
\(120\) −16902.3 + 22343.6i −0.107150 + 0.141645i
\(121\) 151821. 0.942688
\(122\) −137388. −0.835695
\(123\) 192103. + 145320.i 1.14491 + 0.866091i
\(124\) 61398.9i 0.358597i
\(125\) 89895.8 0.514594
\(126\) 0 0
\(127\) −141581. −0.778923 −0.389462 0.921043i \(-0.627339\pi\)
−0.389462 + 0.921043i \(0.627339\pi\)
\(128\) 208991.i 1.12747i
\(129\) 74730.4 + 56531.3i 0.395388 + 0.299099i
\(130\) 42297.3 0.219510
\(131\) 153197. 0.779959 0.389979 0.920824i \(-0.372482\pi\)
0.389979 + 0.920824i \(0.372482\pi\)
\(132\) −12909.0 + 17064.8i −0.0644850 + 0.0852446i
\(133\) 0 0
\(134\) 298931.i 1.43817i
\(135\) −20539.4 + 52628.6i −0.0969960 + 0.248535i
\(136\) 25125.6i 0.116485i
\(137\) 90239.8i 0.410768i 0.978681 + 0.205384i \(0.0658444\pi\)
−0.978681 + 0.205384i \(0.934156\pi\)
\(138\) 221411. + 167491.i 0.989694 + 0.748674i
\(139\) 133215.i 0.584814i 0.956294 + 0.292407i \(0.0944562\pi\)
−0.956294 + 0.292407i \(0.905544\pi\)
\(140\) 0 0
\(141\) −48577.5 36747.4i −0.205772 0.155661i
\(142\) 177081. 0.736972
\(143\) −40048.7 −0.163775
\(144\) −84429.1 298621.i −0.339301 1.20009i
\(145\) 107687.i 0.425348i
\(146\) 346374. 1.34482
\(147\) 0 0
\(148\) −52563.5 −0.197256
\(149\) 28153.3i 0.103888i −0.998650 0.0519439i \(-0.983458\pi\)
0.998650 0.0519439i \(-0.0165417\pi\)
\(150\) −185716. + 245503.i −0.673939 + 0.890900i
\(151\) −6546.74 −0.0233659 −0.0116830 0.999932i \(-0.503719\pi\)
−0.0116830 + 0.999932i \(0.503719\pi\)
\(152\) 319510. 1.12170
\(153\) −13784.2 48754.0i −0.0476050 0.168377i
\(154\) 0 0
\(155\) 64092.0i 0.214276i
\(156\) −56010.9 + 74042.5i −0.184273 + 0.243596i
\(157\) 68166.3i 0.220709i 0.993892 + 0.110355i \(0.0351986\pi\)
−0.993892 + 0.110355i \(0.964801\pi\)
\(158\) 340952.i 1.08655i
\(159\) −341356. + 451248.i −1.07081 + 1.41554i
\(160\) 72069.2i 0.222561i
\(161\) 0 0
\(162\) −210352. 342266.i −0.629738 1.02465i
\(163\) 423816. 1.24942 0.624709 0.780857i \(-0.285217\pi\)
0.624709 + 0.780857i \(0.285217\pi\)
\(164\) 220773. 0.640969
\(165\) −13475.2 + 17813.3i −0.0385324 + 0.0509371i
\(166\) 733657.i 2.06644i
\(167\) 30916.2 0.0857818 0.0428909 0.999080i \(-0.486343\pi\)
0.0428909 + 0.999080i \(0.486343\pi\)
\(168\) 0 0
\(169\) 197526. 0.531995
\(170\) 21155.9i 0.0561448i
\(171\) 619982. 175287.i 1.62139 0.458416i
\(172\) 85883.4 0.221354
\(173\) −179220. −0.455272 −0.227636 0.973746i \(-0.573100\pi\)
−0.227636 + 0.973746i \(0.573100\pi\)
\(174\) −610719. 461991.i −1.52921 1.15681i
\(175\) 0 0
\(176\) 122693.i 0.298563i
\(177\) −97311.3 73613.1i −0.233469 0.176613i
\(178\) 930572.i 2.20140i
\(179\) 142179.i 0.331667i 0.986154 + 0.165834i \(0.0530315\pi\)
−0.986154 + 0.165834i \(0.946969\pi\)
\(180\) 14087.4 + 49826.4i 0.0324077 + 0.114625i
\(181\) 321437.i 0.729288i 0.931147 + 0.364644i \(0.118809\pi\)
−0.931147 + 0.364644i \(0.881191\pi\)
\(182\) 0 0
\(183\) 189911. 251049.i 0.419201 0.554154i
\(184\) −315455. −0.686898
\(185\) −54869.0 −0.117868
\(186\) −363480. 274962.i −0.770368 0.582761i
\(187\) 20031.2i 0.0418893i
\(188\) −55827.3 −0.115200
\(189\) 0 0
\(190\) −269030. −0.540651
\(191\) 528819.i 1.04887i 0.851449 + 0.524437i \(0.175724\pi\)
−0.851449 + 0.524437i \(0.824276\pi\)
\(192\) 99329.4 + 75139.7i 0.194457 + 0.147101i
\(193\) −95232.1 −0.184031 −0.0920153 0.995758i \(-0.529331\pi\)
−0.0920153 + 0.995758i \(0.529331\pi\)
\(194\) 171335. 0.326844
\(195\) −58467.6 + 77290.1i −0.110111 + 0.145558i
\(196\) 0 0
\(197\) 705756.i 1.29565i −0.761787 0.647827i \(-0.775678\pi\)
0.761787 0.647827i \(-0.224322\pi\)
\(198\) −43213.0 152842.i −0.0783342 0.277064i
\(199\) 87307.3i 0.156285i 0.996942 + 0.0781426i \(0.0248990\pi\)
−0.996942 + 0.0781426i \(0.975101\pi\)
\(200\) 349780.i 0.618330i
\(201\) −546239. 413213.i −0.953657 0.721413i
\(202\) 531099.i 0.915792i
\(203\) 0 0
\(204\) −37034.0 28015.1i −0.0623053 0.0471321i
\(205\) 230457. 0.383005
\(206\) 666687. 1.09460
\(207\) −612113. + 173062.i −0.992900 + 0.280722i
\(208\) 532350.i 0.853177i
\(209\) 254728. 0.403376
\(210\) 0 0
\(211\) −330657. −0.511294 −0.255647 0.966770i \(-0.582289\pi\)
−0.255647 + 0.966770i \(0.582289\pi\)
\(212\) 518594.i 0.792479i
\(213\) −244779. + 323581.i −0.369680 + 0.488690i
\(214\) −919115. −1.37194
\(215\) 89650.4 0.132268
\(216\) 425243. + 165960.i 0.620159 + 0.242030i
\(217\) 0 0
\(218\) 511160.i 0.728476i
\(219\) −478794. + 632931.i −0.674587 + 0.891757i
\(220\) 20471.8i 0.0285167i
\(221\) 86913.4i 0.119703i
\(222\) 235394. 311174.i 0.320563 0.423761i
\(223\) 232532.i 0.313128i −0.987668 0.156564i \(-0.949958\pi\)
0.987668 0.156564i \(-0.0500417\pi\)
\(224\) 0 0
\(225\) −191894. 678719.i −0.252700 0.893786i
\(226\) −599242. −0.780425
\(227\) −448252. −0.577375 −0.288687 0.957423i \(-0.593219\pi\)
−0.288687 + 0.957423i \(0.593219\pi\)
\(228\) 356255. 470944.i 0.453862 0.599973i
\(229\) 576156.i 0.726025i 0.931784 + 0.363012i \(0.118252\pi\)
−0.931784 + 0.363012i \(0.881748\pi\)
\(230\) 265615. 0.331080
\(231\) 0 0
\(232\) 870122. 1.06135
\(233\) 406966.i 0.491098i −0.969384 0.245549i \(-0.921032\pi\)
0.969384 0.245549i \(-0.0789682\pi\)
\(234\) −187497. 663167.i −0.223848 0.791741i
\(235\) −58276.0 −0.0688367
\(236\) −111834. −0.130706
\(237\) 623024. + 471299.i 0.720499 + 0.545036i
\(238\) 0 0
\(239\) 266151.i 0.301393i 0.988580 + 0.150696i \(0.0481516\pi\)
−0.988580 + 0.150696i \(0.951848\pi\)
\(240\) −236785. 179121.i −0.265354 0.200732i
\(241\) 388486.i 0.430857i −0.976520 0.215428i \(-0.930885\pi\)
0.976520 0.215428i \(-0.0691148\pi\)
\(242\) 1.03291e6i 1.13377i
\(243\) 916196. + 88737.8i 0.995342 + 0.0964036i
\(244\) 288516.i 0.310238i
\(245\) 0 0
\(246\) −988685. + 1.30697e6i −1.04165 + 1.37698i
\(247\) 1.10524e6 1.15269
\(248\) 517868. 0.534675
\(249\) 1.34062e6 + 1.01414e6i 1.37027 + 1.03657i
\(250\) 611605.i 0.618901i
\(251\) −1.09673e6 −1.09879 −0.549397 0.835561i \(-0.685143\pi\)
−0.549397 + 0.835561i \(0.685143\pi\)
\(252\) 0 0
\(253\) −251495. −0.247017
\(254\) 963242.i 0.936810i
\(255\) −38658.3 29243.9i −0.0372300 0.0281634i
\(256\) 1.16620e6 1.11217
\(257\) −100324. −0.0947482 −0.0473741 0.998877i \(-0.515085\pi\)
−0.0473741 + 0.998877i \(0.515085\pi\)
\(258\) −384610. + 508427.i −0.359726 + 0.475532i
\(259\) 0 0
\(260\) 88825.1i 0.0814896i
\(261\) 1.68840e6 477359.i 1.53417 0.433755i
\(262\) 1.04227e6i 0.938055i
\(263\) 1.30495e6i 1.16333i −0.813427 0.581667i \(-0.802401\pi\)
0.813427 0.581667i \(-0.197599\pi\)
\(264\) 143933. + 108881.i 0.127101 + 0.0961484i
\(265\) 541340.i 0.473539i
\(266\) 0 0
\(267\) 1.70044e6 + 1.28633e6i 1.45976 + 1.10427i
\(268\) −627761. −0.533897
\(269\) −1.26072e6 −1.06228 −0.531139 0.847285i \(-0.678236\pi\)
−0.531139 + 0.847285i \(0.678236\pi\)
\(270\) −358058. 139740.i −0.298912 0.116657i
\(271\) 1.24738e6i 1.03176i 0.856662 + 0.515878i \(0.172534\pi\)
−0.856662 + 0.515878i \(0.827466\pi\)
\(272\) 266267. 0.218220
\(273\) 0 0
\(274\) −613945. −0.494030
\(275\) 278861.i 0.222359i
\(276\) −351733. + 464966.i −0.277933 + 0.367408i
\(277\) 658899. 0.515964 0.257982 0.966150i \(-0.416942\pi\)
0.257982 + 0.966150i \(0.416942\pi\)
\(278\) −906330. −0.703354
\(279\) 1.00488e6 284109.i 0.772864 0.218511i
\(280\) 0 0
\(281\) 1.28896e6i 0.973809i −0.873455 0.486904i \(-0.838126\pi\)
0.873455 0.486904i \(-0.161874\pi\)
\(282\) 250011. 330496.i 0.187213 0.247482i
\(283\) 1.00909e6i 0.748966i 0.927234 + 0.374483i \(0.122180\pi\)
−0.927234 + 0.374483i \(0.877820\pi\)
\(284\) 371873.i 0.273589i
\(285\) 371881. 491600.i 0.271201 0.358509i
\(286\) 272471.i 0.196972i
\(287\) 0 0
\(288\) 1.12995e6 319470.i 0.802746 0.226960i
\(289\) −1.37639e6 −0.969383
\(290\) −732650. −0.511566
\(291\) −236836. + 313081.i −0.163952 + 0.216733i
\(292\) 727392.i 0.499242i
\(293\) −1.94711e6 −1.32502 −0.662508 0.749055i \(-0.730508\pi\)
−0.662508 + 0.749055i \(0.730508\pi\)
\(294\) 0 0
\(295\) −116739. −0.0781021
\(296\) 443345.i 0.294112i
\(297\) 339023. + 132311.i 0.223017 + 0.0870371i
\(298\) 191541. 0.124946
\(299\) −1.09121e6 −0.705878
\(300\) −515561. 390006.i −0.330732 0.250189i
\(301\) 0 0
\(302\) 44540.7i 0.0281022i
\(303\) 970480. + 734139.i 0.607267 + 0.459380i
\(304\) 3.38599e6i 2.10137i
\(305\) 301171.i 0.185380i
\(306\) 331697. 93780.5i 0.202506 0.0572544i
\(307\) 1.97804e6i 1.19782i 0.800818 + 0.598908i \(0.204398\pi\)
−0.800818 + 0.598908i \(0.795602\pi\)
\(308\) 0 0
\(309\) −921563. + 1.21824e6i −0.549071 + 0.725833i
\(310\) −436049. −0.257710
\(311\) 1.07146e6 0.628169 0.314084 0.949395i \(-0.398303\pi\)
0.314084 + 0.949395i \(0.398303\pi\)
\(312\) 624510. + 472423.i 0.363206 + 0.274754i
\(313\) 416279.i 0.240173i −0.992763 0.120086i \(-0.961683\pi\)
0.992763 0.120086i \(-0.0383172\pi\)
\(314\) −463768. −0.265446
\(315\) 0 0
\(316\) 716005. 0.403365
\(317\) 2.89214e6i 1.61648i −0.588851 0.808242i \(-0.700420\pi\)
0.588851 0.808242i \(-0.299580\pi\)
\(318\) −3.07006e6 2.32241e6i −1.70247 1.28787i
\(319\) 693700. 0.381676
\(320\) 119160. 0.0650515
\(321\) 1.27049e6 1.67950e6i 0.688193 0.909743i
\(322\) 0 0
\(323\) 552808.i 0.294828i
\(324\) 718765. 441743.i 0.380386 0.233780i
\(325\) 1.20995e6i 0.635416i
\(326\) 2.88342e6i 1.50267i
\(327\) −934045. 706577.i −0.483057 0.365418i
\(328\) 1.86211e6i 0.955697i
\(329\) 0 0
\(330\) −121193. 91678.6i −0.0612620 0.0463429i
\(331\) −3.47755e6 −1.74463 −0.872315 0.488944i \(-0.837382\pi\)
−0.872315 + 0.488944i \(0.837382\pi\)
\(332\) 1.54069e6 0.767134
\(333\) 243225. + 860274.i 0.120198 + 0.425134i
\(334\) 210338.i 0.103170i
\(335\) −655295. −0.319025
\(336\) 0 0
\(337\) 916887. 0.439786 0.219893 0.975524i \(-0.429429\pi\)
0.219893 + 0.975524i \(0.429429\pi\)
\(338\) 1.34387e6i 0.639829i
\(339\) 828334. 1.09500e6i 0.391477 0.517504i
\(340\) −44427.8 −0.0208429
\(341\) 412868. 0.192276
\(342\) 1.19256e6 + 4.21804e6i 0.551336 + 1.95005i
\(343\) 0 0
\(344\) 724382.i 0.330044i
\(345\) −367161. + 485360.i −0.166077 + 0.219541i
\(346\) 1.21932e6i 0.547555i
\(347\) 1.23792e6i 0.551912i 0.961170 + 0.275956i \(0.0889945\pi\)
−0.961170 + 0.275956i \(0.911006\pi\)
\(348\) 970189. 1.28252e6i 0.429446 0.567697i
\(349\) 2.19902e6i 0.966419i −0.875505 0.483210i \(-0.839471\pi\)
0.875505 0.483210i \(-0.160529\pi\)
\(350\) 0 0
\(351\) 1.47098e6 + 574083.i 0.637295 + 0.248718i
\(352\) 464255. 0.199710
\(353\) −2.66911e6 −1.14006 −0.570032 0.821622i \(-0.693069\pi\)
−0.570032 + 0.821622i \(0.693069\pi\)
\(354\) 500826. 662056.i 0.212412 0.280793i
\(355\) 388184.i 0.163481i
\(356\) 1.95422e6 0.817237
\(357\) 0 0
\(358\) −967312. −0.398896
\(359\) 4.54793e6i 1.86242i 0.364484 + 0.931210i \(0.381245\pi\)
−0.364484 + 0.931210i \(0.618755\pi\)
\(360\) 420259. 118820.i 0.170908 0.0483206i
\(361\) −4.55371e6 −1.83907
\(362\) −2.18689e6 −0.877113
\(363\) −1.88744e6 1.42780e6i −0.751809 0.568721i
\(364\) 0 0
\(365\) 759296.i 0.298318i
\(366\) 1.70801e6 + 1.29206e6i 0.666480 + 0.504173i
\(367\) 2.13509e6i 0.827469i 0.910398 + 0.413735i \(0.135776\pi\)
−0.910398 + 0.413735i \(0.864224\pi\)
\(368\) 3.34301e6i 1.28682i
\(369\) −1.02157e6 3.61326e6i −0.390575 1.38144i
\(370\) 373300.i 0.141760i
\(371\) 0 0
\(372\) 577425. 763315.i 0.216341 0.285987i
\(373\) −3.25854e6 −1.21269 −0.606346 0.795201i \(-0.707365\pi\)
−0.606346 + 0.795201i \(0.707365\pi\)
\(374\) 136282. 0.0503802
\(375\) −1.11759e6 845423.i −0.410397 0.310453i
\(376\) 470874.i 0.171765i
\(377\) 3.00989e6 1.09068
\(378\) 0 0
\(379\) −3.32017e6 −1.18730 −0.593652 0.804722i \(-0.702314\pi\)
−0.593652 + 0.804722i \(0.702314\pi\)
\(380\) 564968.i 0.200708i
\(381\) 1.76014e6 + 1.33149e6i 0.621204 + 0.469922i
\(382\) −3.59781e6 −1.26148
\(383\) 3.46201e6 1.20596 0.602978 0.797758i \(-0.293981\pi\)
0.602978 + 0.797758i \(0.293981\pi\)
\(384\) −1.96545e6 + 2.59819e6i −0.680197 + 0.899173i
\(385\) 0 0
\(386\) 647910.i 0.221333i
\(387\) −397405. 1.40560e6i −0.134882 0.477073i
\(388\) 359806.i 0.121336i
\(389\) 2.49213e6i 0.835018i −0.908673 0.417509i \(-0.862903\pi\)
0.908673 0.417509i \(-0.137097\pi\)
\(390\) −525842. 397784.i −0.175063 0.132430i
\(391\) 545792.i 0.180545i
\(392\) 0 0
\(393\) −1.90455e6 1.44074e6i −0.622030 0.470547i
\(394\) 4.80161e6 1.55828
\(395\) 747410. 0.241027
\(396\) 320971. 90748.0i 0.102856 0.0290803i
\(397\) 3.04840e6i 0.970722i 0.874314 + 0.485361i \(0.161312\pi\)
−0.874314 + 0.485361i \(0.838688\pi\)
\(398\) −593994. −0.187964
\(399\) 0 0
\(400\) 3.70678e6 1.15837
\(401\) 51572.9i 0.0160162i −0.999968 0.00800812i \(-0.997451\pi\)
0.999968 0.00800812i \(-0.00254909\pi\)
\(402\) 2.81129e6 3.71633e6i 0.867642 1.14696i
\(403\) 1.79139e6 0.549449
\(404\) 1.11532e6 0.339973
\(405\) 750291. 461119.i 0.227296 0.139693i
\(406\) 0 0
\(407\) 353455.i 0.105766i
\(408\) −236293. + 312362.i −0.0702748 + 0.0928983i
\(409\) 4.53920e6i 1.34175i −0.741571 0.670875i \(-0.765919\pi\)
0.741571 0.670875i \(-0.234081\pi\)
\(410\) 1.56791e6i 0.460639i
\(411\) 848658. 1.12187e6i 0.247815 0.327594i
\(412\) 1.40005e6i 0.406351i
\(413\) 0 0
\(414\) −1.17743e6 4.16450e6i −0.337624 1.19416i
\(415\) 1.60827e6 0.458394
\(416\) 2.01435e6 0.570693
\(417\) 1.25282e6 1.65614e6i 0.352817 0.466399i
\(418\) 1.73304e6i 0.485140i
\(419\) −1.89078e6 −0.526145 −0.263072 0.964776i \(-0.584736\pi\)
−0.263072 + 0.964776i \(0.584736\pi\)
\(420\) 0 0
\(421\) −5.04901e6 −1.38836 −0.694178 0.719803i \(-0.744232\pi\)
−0.694178 + 0.719803i \(0.744232\pi\)
\(422\) 2.24962e6i 0.614933i
\(423\) 258327. + 913691.i 0.0701971 + 0.248284i
\(424\) 4.37407e6 1.18160
\(425\) 605181. 0.162522
\(426\) −2.20148e6 1.66535e6i −0.587747 0.444613i
\(427\) 0 0
\(428\) 1.93016e6i 0.509312i
\(429\) 497887. + 376637.i 0.130613 + 0.0988051i
\(430\) 609935.i 0.159079i
\(431\) 3.26850e6i 0.847530i −0.905772 0.423765i \(-0.860708\pi\)
0.905772 0.423765i \(-0.139292\pi\)
\(432\) −1.75875e6 + 4.50649e6i −0.453414 + 1.16179i
\(433\) 1.69788e6i 0.435198i −0.976038 0.217599i \(-0.930177\pi\)
0.976038 0.217599i \(-0.0698226\pi\)
\(434\) 0 0
\(435\) 1.01274e6 1.33877e6i 0.256612 0.339222i
\(436\) −1.07344e6 −0.270435
\(437\) 6.94058e6 1.73857
\(438\) −4.30614e6 3.25747e6i −1.07251 0.811325i
\(439\) 4.42320e6i 1.09541i −0.836673 0.547703i \(-0.815502\pi\)
0.836673 0.547703i \(-0.184498\pi\)
\(440\) 172669. 0.0425190
\(441\) 0 0
\(442\) 591314. 0.143967
\(443\) 5.22017e6i 1.26379i −0.775054 0.631895i \(-0.782277\pi\)
0.775054 0.631895i \(-0.217723\pi\)
\(444\) 653471. + 494332.i 0.157315 + 0.119004i
\(445\) 2.03993e6 0.488332
\(446\) 1.58203e6 0.376598
\(447\) −264767. + 350004.i −0.0626752 + 0.0828522i
\(448\) 0 0
\(449\) 3.80274e6i 0.890186i 0.895484 + 0.445093i \(0.146829\pi\)
−0.895484 + 0.445093i \(0.853171\pi\)
\(450\) 4.61765e6 1.30555e6i 1.07495 0.303921i
\(451\) 1.48456e6i 0.343681i
\(452\) 1.25842e6i 0.289720i
\(453\) 81389.4 + 61568.7i 0.0186347 + 0.0140966i
\(454\) 3.04968e6i 0.694407i
\(455\) 0 0
\(456\) −3.97217e6 3.00482e6i −0.894572 0.676717i
\(457\) 1.83749e6 0.411561 0.205781 0.978598i \(-0.434027\pi\)
0.205781 + 0.978598i \(0.434027\pi\)
\(458\) −3.91987e6 −0.873188
\(459\) −287140. + 735745.i −0.0636154 + 0.163003i
\(460\) 557797.i 0.122908i
\(461\) 7.79775e6 1.70890 0.854450 0.519533i \(-0.173894\pi\)
0.854450 + 0.519533i \(0.173894\pi\)
\(462\) 0 0
\(463\) 254809. 0.0552410 0.0276205 0.999618i \(-0.491207\pi\)
0.0276205 + 0.999618i \(0.491207\pi\)
\(464\) 9.22106e6i 1.98832i
\(465\) 602751. 796795.i 0.129272 0.170889i
\(466\) 2.76878e6 0.590642
\(467\) 4.98525e6 1.05778 0.528889 0.848691i \(-0.322609\pi\)
0.528889 + 0.848691i \(0.322609\pi\)
\(468\) 1.39266e6 393746.i 0.293921 0.0831002i
\(469\) 0 0
\(470\) 396480.i 0.0827897i
\(471\) 641068. 847446.i 0.133153 0.176019i
\(472\) 943264.i 0.194885i
\(473\) 577509.i 0.118688i
\(474\) −3.20648e6 + 4.23873e6i −0.655514 + 0.866543i
\(475\) 7.69581e6i 1.56502i
\(476\) 0 0
\(477\) 8.48750e6 2.39967e6i 1.70798 0.482897i
\(478\) −1.81075e6 −0.362485
\(479\) −7.71216e6 −1.53581 −0.767904 0.640564i \(-0.778700\pi\)
−0.767904 + 0.640564i \(0.778700\pi\)
\(480\) 677773. 895968.i 0.134271 0.177496i
\(481\) 1.53360e6i 0.302239i
\(482\) 2.64306e6 0.518191
\(483\) 0 0
\(484\) −2.16913e6 −0.420894
\(485\) 375588.i 0.0725031i
\(486\) −603727. + 6.23332e6i −0.115944 + 1.19710i
\(487\) −8.12051e6 −1.55153 −0.775767 0.631020i \(-0.782637\pi\)
−0.775767 + 0.631020i \(0.782637\pi\)
\(488\) −2.43348e6 −0.462572
\(489\) −5.26890e6 3.98576e6i −0.996432 0.753771i
\(490\) 0 0
\(491\) 7.72726e6i 1.44651i 0.690581 + 0.723255i \(0.257355\pi\)
−0.690581 + 0.723255i \(0.742645\pi\)
\(492\) −2.74466e6 2.07626e6i −0.511183 0.386695i
\(493\) 1.50546e6i 0.278967i
\(494\) 7.51947e6i 1.38634i
\(495\) 335050. 94728.4i 0.0614605 0.0173767i
\(496\) 5.48808e6i 1.00165i
\(497\) 0 0
\(498\) −6.89966e6 + 9.12086e6i −1.24668 + 1.64802i
\(499\) 2.33074e6 0.419028 0.209514 0.977806i \(-0.432812\pi\)
0.209514 + 0.977806i \(0.432812\pi\)
\(500\) −1.28438e6 −0.229757
\(501\) −384352. 290751.i −0.0684124 0.0517519i
\(502\) 7.46161e6i 1.32152i
\(503\) −3.86914e6 −0.681859 −0.340930 0.940089i \(-0.610742\pi\)
−0.340930 + 0.940089i \(0.610742\pi\)
\(504\) 0 0
\(505\) 1.16424e6 0.203148
\(506\) 1.71104e6i 0.297087i
\(507\) −2.45565e6 1.85763e6i −0.424275 0.320951i
\(508\) 2.02283e6 0.347776
\(509\) 4.29903e6 0.735489 0.367744 0.929927i \(-0.380130\pi\)
0.367744 + 0.929927i \(0.380130\pi\)
\(510\) 198960. 263011.i 0.0338720 0.0447764i
\(511\) 0 0
\(512\) 1.24648e6i 0.210142i
\(513\) −9.35613e6 3.65143e6i −1.56965 0.612589i
\(514\) 682552.i 0.113953i
\(515\) 1.46146e6i 0.242812i
\(516\) −1.06771e6 807688.i −0.176534 0.133543i
\(517\) 375402.i 0.0617689i
\(518\) 0 0
\(519\) 2.22807e6 + 1.68547e6i 0.363087 + 0.274664i
\(520\) 749193. 0.121503
\(521\) 4.57032e6 0.737653 0.368827 0.929498i \(-0.379760\pi\)
0.368827 + 0.929498i \(0.379760\pi\)
\(522\) 3.24771e6 + 1.14870e7i 0.521676 + 1.84514i
\(523\) 2.15375e6i 0.344304i −0.985070 0.172152i \(-0.944928\pi\)
0.985070 0.172152i \(-0.0550720\pi\)
\(524\) −2.18879e6 −0.348238
\(525\) 0 0
\(526\) 8.87821e6 1.39914
\(527\) 896002.i 0.140534i
\(528\) −1.15386e6 + 1.52532e6i −0.180122 + 0.238109i
\(529\) −416145. −0.0646555
\(530\) −3.68300e6 −0.569524
\(531\) 517486. + 1.83032e6i 0.0796457 + 0.281703i
\(532\) 0 0
\(533\) 6.44133e6i 0.982104i
\(534\) −8.75154e6 + 1.15689e7i −1.32810 + 1.75566i
\(535\) 2.01482e6i 0.304335i
\(536\) 5.29484e6i 0.796051i
\(537\) 1.33712e6 1.76757e6i 0.200094 0.264510i
\(538\) 8.57730e6i 1.27760i
\(539\) 0 0
\(540\) 293456. 751928.i 0.0433070 0.110967i
\(541\) −5.46624e6 −0.802963 −0.401481 0.915867i \(-0.631505\pi\)
−0.401481 + 0.915867i \(0.631505\pi\)
\(542\) −8.48656e6 −1.24089
\(543\) 3.02294e6 3.99612e6i 0.439978 0.581619i
\(544\) 1.00752e6i 0.145968i
\(545\) −1.12053e6 −0.161596
\(546\) 0 0
\(547\) 7.32611e6 1.04690 0.523450 0.852056i \(-0.324645\pi\)
0.523450 + 0.852056i \(0.324645\pi\)
\(548\) 1.28930e6i 0.183401i
\(549\) −4.72197e6 + 1.33504e6i −0.668640 + 0.189044i
\(550\) 1.89722e6 0.267431
\(551\) −1.91443e7 −2.68633
\(552\) 3.92175e6 + 2.96669e6i 0.547813 + 0.414404i
\(553\) 0 0
\(554\) 4.48281e6i 0.620549i
\(555\) 682134. + 516014.i 0.0940020 + 0.0711097i
\(556\) 1.90331e6i 0.261109i
\(557\) 7.63525e6i 1.04276i 0.853324 + 0.521381i \(0.174583\pi\)
−0.853324 + 0.521381i \(0.825417\pi\)
\(558\) 1.93293e6 + 6.83668e6i 0.262803 + 0.929522i
\(559\) 2.50575e6i 0.339163i
\(560\) 0 0
\(561\) −188383. + 249029.i −0.0252717 + 0.0334074i
\(562\) 8.76942e6 1.17120
\(563\) −2.17576e6 −0.289295 −0.144648 0.989483i \(-0.546205\pi\)
−0.144648 + 0.989483i \(0.546205\pi\)
\(564\) 694048. + 525026.i 0.0918738 + 0.0694998i
\(565\) 1.31361e6i 0.173120i
\(566\) −6.86531e6 −0.900780
\(567\) 0 0
\(568\) 3.13656e6 0.407927
\(569\) 8.38705e6i 1.08600i −0.839734 0.542998i \(-0.817289\pi\)
0.839734 0.542998i \(-0.182711\pi\)
\(570\) 3.34459e6 + 2.53009e6i 0.431178 + 0.326173i
\(571\) 2.54473e6 0.326626 0.163313 0.986574i \(-0.447782\pi\)
0.163313 + 0.986574i \(0.447782\pi\)
\(572\) 572193. 0.0731228
\(573\) 4.97326e6 6.57430e6i 0.632783 0.836494i
\(574\) 0 0
\(575\) 7.59813e6i 0.958379i
\(576\) −528218. 1.86828e6i −0.0663372 0.234631i
\(577\) 1.02039e7i 1.27592i 0.770068 + 0.637962i \(0.220222\pi\)
−0.770068 + 0.637962i \(0.779778\pi\)
\(578\) 9.36422e6i 1.16588i
\(579\) 1.18393e6 + 895608.i 0.146767 + 0.111025i
\(580\) 1.53858e6i 0.189911i
\(581\) 0 0
\(582\) −2.13004e6 1.61131e6i −0.260664 0.197184i
\(583\) 3.48720e6 0.424919
\(584\) 6.13517e6 0.744380
\(585\) 1.45375e6 411017.i 0.175630 0.0496558i
\(586\) 1.32471e7i 1.59359i
\(587\) 1.90974e6 0.228760 0.114380 0.993437i \(-0.463512\pi\)
0.114380 + 0.993437i \(0.463512\pi\)
\(588\) 0 0
\(589\) −1.13940e7 −1.35329
\(590\) 794235.i 0.0939332i
\(591\) −6.63727e6 + 8.77400e6i −0.781665 + 1.03331i
\(592\) −4.69833e6 −0.550984
\(593\) 9.68502e6 1.13100 0.565502 0.824747i \(-0.308683\pi\)
0.565502 + 0.824747i \(0.308683\pi\)
\(594\) −900175. + 2.30654e6i −0.104679 + 0.268222i
\(595\) 0 0
\(596\) 402239.i 0.0463841i
\(597\) 821080. 1.08541e6i 0.0942865 0.124640i
\(598\) 7.42403e6i 0.848959i
\(599\) 4.03346e6i 0.459315i −0.973271 0.229658i \(-0.926239\pi\)
0.973271 0.229658i \(-0.0737606\pi\)
\(600\) −3.28950e6 + 4.34849e6i −0.373037 + 0.493128i
\(601\) 1.16260e7i 1.31293i 0.754356 + 0.656466i \(0.227949\pi\)
−0.754356 + 0.656466i \(0.772051\pi\)
\(602\) 0 0
\(603\) 2.90481e6 + 1.02742e7i 0.325330 + 1.15068i
\(604\) 93536.2 0.0104325
\(605\) −2.26427e6 −0.251501
\(606\) −4.99471e6 + 6.60265e6i −0.552495 + 0.730359i
\(607\) 7.51421e6i 0.827774i 0.910328 + 0.413887i \(0.135829\pi\)
−0.910328 + 0.413887i \(0.864171\pi\)
\(608\) −1.28122e7 −1.40561
\(609\) 0 0
\(610\) 2.04901e6 0.222956
\(611\) 1.62883e6i 0.176511i
\(612\) 196941. + 696570.i 0.0212548 + 0.0751772i
\(613\) 3.74103e6 0.402105 0.201053 0.979580i \(-0.435564\pi\)
0.201053 + 0.979580i \(0.435564\pi\)
\(614\) −1.34576e7 −1.44061
\(615\) −2.86505e6 2.16732e6i −0.305453 0.231066i
\(616\) 0 0
\(617\) 1.48513e7i 1.57055i −0.619146 0.785276i \(-0.712521\pi\)
0.619146 0.785276i \(-0.287479\pi\)
\(618\) −8.28828e6 6.26984e6i −0.872958 0.660367i
\(619\) 8.36596e6i 0.877585i −0.898588 0.438793i \(-0.855406\pi\)
0.898588 0.438793i \(-0.144594\pi\)
\(620\) 915711.i 0.0956707i
\(621\) 9.23738e6 + 3.60508e6i 0.961213 + 0.375134i
\(622\) 7.28969e6i 0.755497i
\(623\) 0 0
\(624\) −5.00647e6 + 6.61820e6i −0.514719 + 0.680423i
\(625\) 7.72981e6 0.791533
\(626\) 2.83215e6 0.288855
\(627\) −3.16679e6 2.39558e6i −0.321699 0.243356i
\(628\) 973922.i 0.0985428i
\(629\) −767065. −0.0773047
\(630\) 0 0
\(631\) 8.21939e6 0.821800 0.410900 0.911680i \(-0.365215\pi\)
0.410900 + 0.911680i \(0.365215\pi\)
\(632\) 6.03913e6i 0.601426i
\(633\) 4.11074e6 + 3.10965e6i 0.407766 + 0.308463i
\(634\) 1.96766e7 1.94414
\(635\) 2.11155e6 0.207810
\(636\) 4.87710e6 6.44718e6i 0.478100 0.632015i
\(637\) 0 0
\(638\) 4.71958e6i 0.459041i
\(639\) 6.08622e6 1.72075e6i 0.589651 0.166712i
\(640\) 3.11692e6i 0.300799i
\(641\) 4.93371e6i 0.474273i 0.971476 + 0.237137i \(0.0762089\pi\)
−0.971476 + 0.237137i \(0.923791\pi\)
\(642\) 1.14265e7 + 8.64380e6i 1.09415 + 0.827689i
\(643\) 1.06965e7i 1.02027i 0.860094 + 0.510135i \(0.170405\pi\)
−0.860094 + 0.510135i \(0.829595\pi\)
\(644\) 0 0
\(645\) −1.11454e6 843115.i −0.105486 0.0797971i
\(646\) −3.76102e6 −0.354589
\(647\) 8.71767e6 0.818728 0.409364 0.912371i \(-0.365751\pi\)
0.409364 + 0.912371i \(0.365751\pi\)
\(648\) −3.72588e6 6.06241e6i −0.348571 0.567163i
\(649\) 752012.i 0.0700831i
\(650\) 8.23186e6 0.764213
\(651\) 0 0
\(652\) −6.05524e6 −0.557844
\(653\) 9.86209e6i 0.905078i 0.891745 + 0.452539i \(0.149482\pi\)
−0.891745 + 0.452539i \(0.850518\pi\)
\(654\) 4.80719e6 6.35476e6i 0.439488 0.580972i
\(655\) −2.28479e6 −0.208087
\(656\) 1.97336e7 1.79038
\(657\) 1.19048e7 3.36583e6i 1.07599 0.304214i
\(658\) 0 0
\(659\) 7.63431e6i 0.684788i 0.939556 + 0.342394i \(0.111238\pi\)
−0.939556 + 0.342394i \(0.888762\pi\)
\(660\) 192527. 254507.i 0.0172041 0.0227426i
\(661\) 1.40247e7i 1.24850i −0.781223 0.624252i \(-0.785404\pi\)
0.781223 0.624252i \(-0.214596\pi\)
\(662\) 2.36595e7i 2.09826i
\(663\) −817375. + 1.08051e6i −0.0722166 + 0.0954653i
\(664\) 1.29949e7i 1.14381i
\(665\) 0 0
\(666\) −5.85286e6 + 1.65478e6i −0.511308 + 0.144562i
\(667\) 1.89013e7 1.64504
\(668\) −441714. −0.0383001
\(669\) −2.18684e6 + 2.89085e6i −0.188909 + 0.249724i
\(670\) 4.45829e6i 0.383691i
\(671\) −1.94008e6 −0.166347
\(672\) 0 0
\(673\) −1.03156e7 −0.877920 −0.438960 0.898507i \(-0.644653\pi\)
−0.438960 + 0.898507i \(0.644653\pi\)
\(674\) 6.23803e6i 0.528930i
\(675\) −3.99736e6 + 1.02425e7i −0.337687 + 0.865262i
\(676\) −2.82214e6 −0.237526
\(677\) −4.53726e6 −0.380472 −0.190236 0.981738i \(-0.560925\pi\)
−0.190236 + 0.981738i \(0.560925\pi\)
\(678\) 7.44981e6 + 5.63556e6i 0.622402 + 0.470828i
\(679\) 0 0
\(680\) 374725.i 0.0310771i
\(681\) 5.57269e6 + 4.21558e6i 0.460466 + 0.348329i
\(682\) 2.80894e6i 0.231250i
\(683\) 901559.i 0.0739507i −0.999316 0.0369754i \(-0.988228\pi\)
0.999316 0.0369754i \(-0.0117723\pi\)
\(684\) −8.85796e6 + 2.50440e6i −0.723925 + 0.204675i
\(685\) 1.34585e6i 0.109590i
\(686\) 0 0
\(687\) 5.41844e6 7.16280e6i 0.438009 0.579016i
\(688\) 7.67659e6 0.618297
\(689\) 1.51306e7 1.21425
\(690\) −3.30214e6 2.49797e6i −0.264042 0.199740i
\(691\) 1.71097e7i 1.36316i 0.731742 + 0.681582i \(0.238708\pi\)
−0.731742 + 0.681582i \(0.761292\pi\)
\(692\) 2.56059e6 0.203271
\(693\) 0 0
\(694\) −8.42220e6 −0.663784
\(695\) 1.98679e6i 0.156023i
\(696\) −1.08174e7 8.18304e6i −0.846447 0.640312i
\(697\) 3.22177e6 0.251196
\(698\) 1.49610e7 1.16231
\(699\) −3.82730e6 + 5.05942e6i −0.296278 + 0.391658i
\(700\) 0 0
\(701\) 2.02857e6i 0.155917i 0.996957 + 0.0779587i \(0.0248402\pi\)
−0.996957 + 0.0779587i \(0.975160\pi\)
\(702\) −3.90577e6 + 1.00078e7i −0.299132 + 0.766473i
\(703\) 9.75441e6i 0.744411i
\(704\) 767608.i 0.0583724i
\(705\) 724490. + 548055.i 0.0548984 + 0.0415290i
\(706\) 1.81592e7i 1.37115i
\(707\) 0 0
\(708\) 1.39033e6 + 1.05174e6i 0.104240 + 0.0788545i
\(709\) −1.67894e7 −1.25435 −0.627176 0.778878i \(-0.715789\pi\)
−0.627176 + 0.778878i \(0.715789\pi\)
\(710\) −2.64100e6 −0.196618
\(711\) −3.31314e6 1.17184e7i −0.245791 0.869351i
\(712\) 1.64828e7i 1.21852i
\(713\) 1.12494e7 0.828718
\(714\) 0 0
\(715\) 597290. 0.0436939
\(716\) 2.03137e6i 0.148084i
\(717\) 2.50301e6 3.30880e6i 0.181829 0.240366i
\(718\) −3.09418e7 −2.23993
\(719\) −2.63704e7 −1.90237 −0.951183 0.308627i \(-0.900130\pi\)
−0.951183 + 0.308627i \(0.900130\pi\)
\(720\) 1.25918e6 + 4.45367e6i 0.0905228 + 0.320175i
\(721\) 0 0
\(722\) 3.09811e7i 2.21184i
\(723\) −3.65351e6 + 4.82968e6i −0.259935 + 0.343615i
\(724\) 4.59251e6i 0.325614i
\(725\) 2.09580e7i 1.48083i
\(726\) 9.71399e6 1.28412e7i 0.684000 0.904199i
\(727\) 1.63660e7i 1.14844i 0.818702 + 0.574218i \(0.194694\pi\)
−0.818702 + 0.574218i \(0.805306\pi\)
\(728\) 0 0
\(729\) −1.05557e7 9.71953e6i −0.735642 0.677371i
\(730\) −5.16586e6 −0.358786
\(731\) 1.25331e6 0.0867489
\(732\) −2.71334e6 + 3.58685e6i −0.187166 + 0.247420i
\(733\) 2.65023e7i 1.82189i −0.412525 0.910946i \(-0.635353\pi\)
0.412525 0.910946i \(-0.364647\pi\)
\(734\) −1.45261e7 −0.995196
\(735\) 0 0
\(736\) 1.26496e7 0.860759
\(737\) 4.22128e6i 0.286270i
\(738\) 2.45828e7 6.95027e6i 1.66146 0.469743i
\(739\) −1.36791e7 −0.921397 −0.460698 0.887557i \(-0.652401\pi\)
−0.460698 + 0.887557i \(0.652401\pi\)
\(740\) 783937. 0.0526262
\(741\) −1.37404e7 1.03942e7i −0.919290 0.695416i
\(742\) 0 0
\(743\) 9.39766e6i 0.624522i 0.949996 + 0.312261i \(0.101086\pi\)
−0.949996 + 0.312261i \(0.898914\pi\)
\(744\) −6.43816e6 4.87028e6i −0.426412 0.322568i
\(745\) 419882.i 0.0277164i
\(746\) 2.21694e7i 1.45850i
\(747\) −7.12918e6 2.52156e7i −0.467453 1.65336i
\(748\) 286195.i 0.0187029i
\(749\) 0 0
\(750\) 5.75183e6 7.60351e6i 0.373381 0.493584i
\(751\) −1.35043e7 −0.873723 −0.436862 0.899529i \(-0.643910\pi\)
−0.436862 + 0.899529i \(0.643910\pi\)
\(752\) −4.99006e6 −0.321782
\(753\) 1.36346e7 + 1.03142e7i 0.876307 + 0.662900i
\(754\) 2.04778e7i 1.31176i
\(755\) 97638.9 0.00623383
\(756\) 0 0
\(757\) −7.36283e6 −0.466987 −0.233494 0.972358i \(-0.575016\pi\)
−0.233494 + 0.972358i \(0.575016\pi\)
\(758\) 2.25887e7i 1.42797i
\(759\) 3.12659e6 + 2.36517e6i 0.197000 + 0.149025i
\(760\) −4.76521e6 −0.299259
\(761\) −2.48311e6 −0.155430 −0.0777150 0.996976i \(-0.524762\pi\)
−0.0777150 + 0.996976i \(0.524762\pi\)
\(762\) −9.05879e6 + 1.19751e7i −0.565175 + 0.747121i
\(763\) 0 0
\(764\) 7.55547e6i 0.468304i
\(765\) 205579. + 727122.i 0.0127006 + 0.0449215i
\(766\) 2.35538e7i 1.45040i
\(767\) 3.26290e6i 0.200270i
\(768\) −1.44982e7 1.09675e7i −0.886976 0.670971i
\(769\) 2.15050e7i 1.31136i −0.755038 0.655681i \(-0.772382\pi\)
0.755038 0.655681i \(-0.227618\pi\)
\(770\) 0 0
\(771\) 1.24723e6 + 943492.i 0.0755632 + 0.0571614i
\(772\) 1.36062e6 0.0821664
\(773\) 9.92550e6 0.597453 0.298726 0.954339i \(-0.403438\pi\)
0.298726 + 0.954339i \(0.403438\pi\)
\(774\) 9.56299e6 2.70374e6i 0.573774 0.162223i
\(775\) 1.24735e7i 0.745993i
\(776\) 3.03478e6 0.180914
\(777\) 0 0
\(778\) 1.69551e7 1.00427
\(779\) 4.09698e7i 2.41891i
\(780\) 835353. 1.10428e6i 0.0491625 0.0649893i
\(781\) 2.50060e6 0.146696
\(782\) 3.71329e6 0.217141
\(783\) −2.54796e7 9.94393e6i −1.48521 0.579634i
\(784\) 0 0
\(785\) 1.01664e6i 0.0588834i
\(786\) 9.80203e6 1.29576e7i 0.565926 0.748114i
\(787\) 1.03681e6i 0.0596708i 0.999555 + 0.0298354i \(0.00949831\pi\)
−0.999555 + 0.0298354i \(0.990502\pi\)
\(788\) 1.00835e7i 0.578487i
\(789\) −1.22724e7 + 1.62232e7i −0.701836 + 0.927778i
\(790\) 5.08500e6i 0.289883i
\(791\) 0 0
\(792\) −765412. 2.70723e6i −0.0433593 0.153360i
\(793\) −8.41782e6 −0.475353
\(794\) −2.07397e7 −1.16749
\(795\) 5.09102e6 6.72996e6i 0.285685 0.377655i
\(796\) 1.24740e6i 0.0697786i
\(797\) 1.52399e7 0.849838 0.424919 0.905231i \(-0.360303\pi\)
0.424919 + 0.905231i \(0.360303\pi\)
\(798\) 0 0
\(799\) −814695. −0.0451469
\(800\) 1.40260e7i 0.774836i
\(801\) −9.04267e6 3.19835e7i −0.497984 1.76134i
\(802\) 350875. 0.0192627
\(803\) 4.89123e6 0.267688
\(804\) 7.80435e6 + 5.90376e6i 0.425791 + 0.322099i
\(805\) 0 0
\(806\) 1.21877e7i 0.660821i
\(807\) 1.56733e7 + 1.18564e7i 0.847184 + 0.640869i
\(808\) 9.40712e6i 0.506907i
\(809\) 5.45336e6i 0.292949i 0.989214 + 0.146475i \(0.0467927\pi\)
−0.989214 + 0.146475i \(0.953207\pi\)
\(810\) 3.13722e6 + 5.10460e6i 0.168009 + 0.273369i
\(811\) 9.69507e6i 0.517605i −0.965930 0.258803i \(-0.916672\pi\)
0.965930 0.258803i \(-0.0833279\pi\)
\(812\) 0 0
\(813\) 1.17310e7 1.55075e7i 0.622456 0.822842i
\(814\) −2.40473e6 −0.127205
\(815\) −6.32083e6 −0.333335
\(816\) −3.31024e6 2.50410e6i −0.174034 0.131651i
\(817\) 1.59377e7i 0.835355i
\(818\) 3.08824e7 1.61372
\(819\) 0 0
\(820\) −3.29264e6 −0.171005
\(821\) 1.63719e7i 0.847699i −0.905733 0.423849i \(-0.860679\pi\)
0.905733 0.423849i \(-0.139321\pi\)
\(822\) 7.63260e6 + 5.77384e6i 0.393997 + 0.298047i
\(823\) 2.37540e7 1.22247 0.611233 0.791451i \(-0.290674\pi\)
0.611233 + 0.791451i \(0.290674\pi\)
\(824\) 1.18087e7 0.605878
\(825\) −2.62254e6 + 3.46681e6i −0.134149 + 0.177335i
\(826\) 0 0
\(827\) 2.87632e7i 1.46242i 0.682151 + 0.731211i \(0.261045\pi\)
−0.682151 + 0.731211i \(0.738955\pi\)
\(828\) 8.74553e6 2.47262e6i 0.443313 0.125338i
\(829\) 3.69015e7i 1.86491i 0.361286 + 0.932455i \(0.382338\pi\)
−0.361286 + 0.932455i \(0.617662\pi\)
\(830\) 1.09418e7i 0.551309i
\(831\) −8.19146e6 6.19660e6i −0.411490 0.311280i
\(832\) 3.33057e6i 0.166805i
\(833\) 0 0
\(834\) 1.12675e7 + 8.52356e6i 0.560937 + 0.424332i
\(835\) −461088. −0.0228859
\(836\) −3.63941e6 −0.180101
\(837\) −1.51646e7 5.91830e6i −0.748199 0.292000i
\(838\) 1.28639e7i 0.632793i
\(839\) −2.41096e7 −1.18246 −0.591229 0.806504i \(-0.701357\pi\)
−0.591229 + 0.806504i \(0.701357\pi\)
\(840\) 0 0
\(841\) −3.16245e7 −1.54182
\(842\) 3.43509e7i 1.66977i
\(843\) −1.21220e7 + 1.60244e7i −0.587496 + 0.776628i
\(844\) 4.72424e6 0.228284
\(845\) −2.94592e6 −0.141932
\(846\) −6.21629e6 + 1.75753e6i −0.298611 + 0.0844260i
\(847\) 0 0
\(848\) 4.63539e7i 2.21359i
\(849\) 9.48993e6 1.25450e7i 0.451849 0.597313i
\(850\) 4.11734e6i 0.195465i
\(851\) 9.63060e6i 0.455858i
\(852\) 3.49727e6 4.62314e6i 0.165056 0.218192i
\(853\) 1.08498e7i 0.510561i 0.966867 + 0.255281i \(0.0821678\pi\)
−0.966867 + 0.255281i \(0.917832\pi\)
\(854\) 0 0
\(855\) −9.24648e6 + 2.61425e6i −0.432575 + 0.122302i
\(856\) −1.62799e7 −0.759393
\(857\) −2.90805e7 −1.35254 −0.676270 0.736654i \(-0.736405\pi\)
−0.676270 + 0.736654i \(0.736405\pi\)
\(858\) −2.56244e6 + 3.38737e6i −0.118833 + 0.157088i
\(859\) 3.67954e7i 1.70142i 0.525636 + 0.850709i \(0.323827\pi\)
−0.525636 + 0.850709i \(0.676173\pi\)
\(860\) −1.28087e6 −0.0590555
\(861\) 0 0
\(862\) 2.22372e7 1.01932
\(863\) 2.85606e6i 0.130539i −0.997868 0.0652695i \(-0.979209\pi\)
0.997868 0.0652695i \(-0.0207907\pi\)
\(864\) −1.70521e7 6.65492e6i −0.777128 0.303290i
\(865\) 2.67290e6 0.121463
\(866\) 1.15515e7 0.523412
\(867\) 1.71113e7 + 1.29442e7i 0.773099 + 0.584826i
\(868\) 0 0
\(869\) 4.81467e6i 0.216280i
\(870\) 9.10834e6 + 6.89018e6i 0.407982 + 0.308626i
\(871\) 1.83157e7i 0.818047i
\(872\) 9.05395e6i 0.403224i
\(873\) 5.88872e6 1.66491e6i 0.261508 0.0739361i
\(874\) 4.72202e7i 2.09098i
\(875\) 0 0
\(876\) 6.84074e6 9.04297e6i 0.301192 0.398154i
\(877\) −5.35187e6 −0.234967 −0.117483 0.993075i \(-0.537483\pi\)
−0.117483 + 0.993075i \(0.537483\pi\)
\(878\) 3.00932e7 1.31744
\(879\) 2.42065e7 + 1.83115e7i 1.05672 + 0.799378i
\(880\) 1.82985e6i 0.0796542i
\(881\) 2.78347e6 0.120822 0.0604111 0.998174i \(-0.480759\pi\)
0.0604111 + 0.998174i \(0.480759\pi\)
\(882\) 0 0
\(883\) −626626. −0.0270462 −0.0135231 0.999909i \(-0.504305\pi\)
−0.0135231 + 0.999909i \(0.504305\pi\)
\(884\) 1.24177e6i 0.0534454i
\(885\) 1.45131e6 + 1.09787e6i 0.0622877 + 0.0471188i
\(886\) 3.55153e7 1.51996
\(887\) 4.27454e7 1.82423 0.912117 0.409930i \(-0.134447\pi\)
0.912117 + 0.409930i \(0.134447\pi\)
\(888\) 4.16943e6 5.51169e6i 0.177437 0.234559i
\(889\) 0 0
\(890\) 1.38786e7i 0.587316i
\(891\) −2.97043e6 4.83323e6i −0.125350 0.203959i
\(892\) 3.32229e6i 0.139806i
\(893\) 1.03601e7i 0.434746i
\(894\) −2.38125e6 1.80134e6i −0.0996461 0.0753793i
\(895\) 2.12047e6i 0.0884861i
\(896\) 0 0
\(897\) 1.35660e7 + 1.02622e7i 0.562950 + 0.425855i
\(898\) −2.58719e7 −1.07062
\(899\) −3.10294e7 −1.28048
\(900\) 2.74167e6 + 9.69716e6i 0.112826 + 0.399060i
\(901\) 7.56790e6i 0.310573i
\(902\) 1.01002e7 0.413344
\(903\) 0 0
\(904\) −1.06141e7 −0.431979
\(905\) 4.79394e6i 0.194568i
\(906\) −418882. + 553732.i −0.0169540 + 0.0224119i
\(907\) 7.04109e6 0.284198 0.142099 0.989852i \(-0.454615\pi\)
0.142099 + 0.989852i \(0.454615\pi\)
\(908\) 6.40438e6 0.257788
\(909\) −5.16086e6 1.82537e7i −0.207163 0.732726i
\(910\) 0 0
\(911\) 1.05335e6i 0.0420509i −0.999779 0.0210255i \(-0.993307\pi\)
0.999779 0.0210255i \(-0.00669310\pi\)
\(912\) 3.18434e7 4.20948e7i 1.26775 1.67587i
\(913\) 1.03602e7i 0.411329i
\(914\) 1.25013e7i 0.494984i
\(915\) −2.83235e6 + 3.74417e6i −0.111839 + 0.147844i
\(916\) 8.23180e6i 0.324157i
\(917\) 0 0
\(918\) −5.00563e6 1.95355e6i −0.196043 0.0765101i
\(919\) 1.81997e7 0.710844 0.355422 0.934706i \(-0.384337\pi\)
0.355422 + 0.934706i \(0.384337\pi\)
\(920\) 4.70473e6 0.183259
\(921\) 1.86025e7 2.45911e7i 0.722639 0.955278i
\(922\) 5.30519e7i 2.05529i
\(923\) 1.08499e7 0.419198
\(924\) 0 0
\(925\) −1.06785e7 −0.410353
\(926\) 1.73359e6i 0.0664383i
\(927\) 2.29138e7 6.47841e6i 0.875787 0.247611i
\(928\) −3.48915e7 −1.32999
\(929\) −3.36714e7 −1.28004 −0.640018 0.768360i \(-0.721073\pi\)
−0.640018 + 0.768360i \(0.721073\pi\)
\(930\) 5.42098e6 + 4.10081e6i 0.205528 + 0.155476i
\(931\) 0 0
\(932\) 5.81450e6i 0.219267i
\(933\) −1.33205e7 1.00765e7i −0.500975 0.378973i
\(934\) 3.39171e7i 1.27219i
\(935\) 298748.i 0.0111757i
\(936\) −3.32105e6 1.17464e7i −0.123904 0.438242i
\(937\) 3.25239e7i 1.21019i −0.796153 0.605095i \(-0.793135\pi\)
0.796153 0.605095i \(-0.206865\pi\)
\(938\) 0 0
\(939\) −3.91489e6 + 5.17520e6i −0.144896 + 0.191542i
\(940\) 832615. 0.0307344
\(941\) −1.62948e7 −0.599895 −0.299947 0.953956i \(-0.596969\pi\)
−0.299947 + 0.953956i \(0.596969\pi\)
\(942\) 5.76559e6 + 4.36150e6i 0.211698 + 0.160143i
\(943\) 4.04498e7i 1.48128i
\(944\) −9.99618e6 −0.365093
\(945\) 0 0
\(946\) 3.92908e6 0.142746
\(947\) 1.21518e7i 0.440317i 0.975464 + 0.220158i \(0.0706574\pi\)
−0.975464 + 0.220158i \(0.929343\pi\)
\(948\) −8.90142e6 6.73366e6i −0.321690 0.243349i
\(949\) 2.12226e7 0.764948
\(950\) −5.23583e7 −1.88225
\(951\) −2.71991e7 + 3.59552e7i −0.975220 + 1.28917i
\(952\) 0 0
\(953\) 2.91378e7i 1.03926i −0.854391 0.519630i \(-0.826070\pi\)
0.854391 0.519630i \(-0.173930\pi\)
\(954\) 1.63261e7 + 5.77446e7i 0.580780 + 2.05419i
\(955\) 7.88686e6i 0.279831i
\(956\) 3.80261e6i 0.134567i
\(957\) −8.62411e6 6.52389e6i −0.304393 0.230264i
\(958\) 5.24696e7i 1.84711i
\(959\) 0 0
\(960\) −1.48141e6 1.12064e6i −0.0518796 0.0392454i
\(961\) 1.01615e7 0.354934
\(962\) −1.04339e7 −0.363502
\(963\) −3.15897e7 + 8.93134e6i −1.09769 + 0.310349i
\(964\) 5.55047e6i 0.192370i
\(965\) 1.42030e6 0.0490978
\(966\) 0 0
\(967\) 4.05970e7 1.39614 0.698068 0.716032i \(-0.254043\pi\)
0.698068 + 0.716032i \(0.254043\pi\)
\(968\) 1.82955e7i 0.627561i
\(969\) 5.19887e6 6.87254e6i 0.177869 0.235130i
\(970\) −2.55531e6 −0.0871994
\(971\) 1.12136e7 0.381677 0.190838 0.981621i \(-0.438879\pi\)
0.190838 + 0.981621i \(0.438879\pi\)
\(972\) −1.30901e7 1.26784e6i −0.444403 0.0430425i
\(973\) 0 0
\(974\) 5.52478e7i 1.86603i
\(975\) −1.13789e7 + 1.50421e7i −0.383345 + 0.506754i
\(976\) 2.57887e7i 0.866572i
\(977\) 2.82925e7i 0.948276i −0.880451 0.474138i \(-0.842760\pi\)
0.880451 0.474138i \(-0.157240\pi\)
\(978\) 2.71171e7 3.58469e7i 0.906559 1.19841i
\(979\) 1.31408e7i 0.438194i
\(980\) 0 0
\(981\) 4.96710e6 + 1.75684e7i 0.164790 + 0.582854i
\(982\) −5.25723e7 −1.73972
\(983\) 3.44078e7 1.13573 0.567863 0.823123i \(-0.307770\pi\)
0.567863 + 0.823123i \(0.307770\pi\)
\(984\) −1.75121e7 + 2.31498e7i −0.576569 + 0.762184i
\(985\) 1.05257e7i 0.345670i
\(986\) −1.02424e7 −0.335513
\(987\) 0 0
\(988\) −1.57910e7 −0.514657
\(989\) 1.57354e7i 0.511550i
\(990\) 644483. + 2.27951e6i 0.0208989 + 0.0739184i
\(991\) −4.97942e7 −1.61063 −0.805313 0.592850i \(-0.798003\pi\)
−0.805313 + 0.592850i \(0.798003\pi\)
\(992\) −2.07663e7 −0.670007
\(993\) 4.32331e7 + 3.27045e7i 1.39137 + 1.05253i
\(994\) 0 0
\(995\) 1.30211e6i 0.0416956i
\(996\) −1.91540e7 1.44894e7i −0.611802 0.462810i
\(997\) 1.01229e7i 0.322529i −0.986911 0.161265i \(-0.948443\pi\)
0.986911 0.161265i \(-0.0515572\pi\)
\(998\) 1.58572e7i 0.503964i
\(999\) 5.06664e6 1.29824e7i 0.160623 0.411567i
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 147.6.c.c.146.13 16
3.2 odd 2 inner 147.6.c.c.146.4 16
7.2 even 3 21.6.g.c.17.7 yes 16
7.3 odd 6 21.6.g.c.5.2 16
7.6 odd 2 inner 147.6.c.c.146.14 16
21.2 odd 6 21.6.g.c.17.2 yes 16
21.17 even 6 21.6.g.c.5.7 yes 16
21.20 even 2 inner 147.6.c.c.146.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.g.c.5.2 16 7.3 odd 6
21.6.g.c.5.7 yes 16 21.17 even 6
21.6.g.c.17.2 yes 16 21.2 odd 6
21.6.g.c.17.7 yes 16 7.2 even 3
147.6.c.c.146.3 16 21.20 even 2 inner
147.6.c.c.146.4 16 3.2 odd 2 inner
147.6.c.c.146.13 16 1.1 even 1 trivial
147.6.c.c.146.14 16 7.6 odd 2 inner