Properties

Label 108.6.h.a.71.7
Level $108$
Weight $6$
Character 108.71
Analytic conductor $17.321$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [108,6,Mod(35,108)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(108, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("108.35");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not 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: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.7
Character \(\chi\) \(=\) 108.71
Dual form 108.6.h.a.35.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.95514 + 4.04436i) q^{2} +(-0.713689 - 31.9920i) q^{4} +(77.8058 + 44.9212i) q^{5} +(124.034 - 71.6112i) q^{7} +(132.210 + 123.647i) q^{8} +O(q^{10})\) \(q+(-3.95514 + 4.04436i) q^{2} +(-0.713689 - 31.9920i) q^{4} +(77.8058 + 44.9212i) q^{5} +(124.034 - 71.6112i) q^{7} +(132.210 + 123.647i) q^{8} +(-489.410 + 137.005i) q^{10} +(-278.231 - 481.910i) q^{11} +(179.796 - 311.416i) q^{13} +(-200.952 + 784.871i) q^{14} +(-1022.98 + 45.6648i) q^{16} -1076.42i q^{17} -348.135i q^{19} +(1381.59 - 2521.23i) q^{20} +(3049.46 + 780.757i) q^{22} +(1469.06 - 2544.48i) q^{23} +(2473.33 + 4283.93i) q^{25} +(548.358 + 1958.85i) q^{26} +(-2379.51 - 3917.00i) q^{28} +(-3331.19 + 1923.26i) q^{29} +(2346.41 + 1354.70i) q^{31} +(3861.35 - 4317.91i) q^{32} +(4353.43 + 4257.39i) q^{34} +12867.4 q^{35} -1992.90 q^{37} +(1407.98 + 1376.92i) q^{38} +(4732.35 + 15559.5i) q^{40} +(13432.0 + 7754.99i) q^{41} +(12474.1 - 7201.91i) q^{43} +(-15218.7 + 9245.10i) q^{44} +(4480.46 + 16005.2i) q^{46} +(-1232.97 - 2135.56i) q^{47} +(1852.82 - 3209.17i) q^{49} +(-27108.1 - 6940.52i) q^{50} +(-10091.1 - 5529.78i) q^{52} +13364.2i q^{53} -49993.8i q^{55} +(25253.0 + 5868.70i) q^{56} +(5396.96 - 21079.3i) q^{58} +(19878.8 - 34431.1i) q^{59} +(-211.489 - 366.310i) q^{61} +(-14759.3 + 4131.70i) q^{62} +(2191.00 + 32694.7i) q^{64} +(27978.3 - 16153.3i) q^{65} +(-14018.6 - 8093.63i) q^{67} +(-34436.8 + 768.229i) q^{68} +(-50892.5 + 52040.5i) q^{70} -6902.73 q^{71} -11089.5 q^{73} +(7882.20 - 8060.00i) q^{74} +(-11137.6 + 248.460i) q^{76} +(-69020.2 - 39848.8i) q^{77} +(-64310.3 + 37129.6i) q^{79} +(-81645.2 - 42400.5i) q^{80} +(-84489.6 + 23651.9i) q^{82} +(48564.9 + 84116.9i) q^{83} +(48354.0 - 83751.6i) q^{85} +(-20209.6 + 78934.2i) q^{86} +(22801.6 - 98115.6i) q^{88} +74459.8i q^{89} -51501.6i q^{91} +(-82451.5 - 45182.1i) q^{92} +(13513.5 + 3459.88i) q^{94} +(15638.6 - 27086.9i) q^{95} +(47958.5 + 83066.5i) q^{97} +(5650.89 + 20186.2i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.95514 + 4.04436i −0.699177 + 0.714949i
\(3\) 0 0
\(4\) −0.713689 31.9920i −0.0223028 0.999751i
\(5\) 77.8058 + 44.9212i 1.39183 + 0.803575i 0.993518 0.113675i \(-0.0362621\pi\)
0.398314 + 0.917249i \(0.369595\pi\)
\(6\) 0 0
\(7\) 124.034 71.6112i 0.956745 0.552377i 0.0615753 0.998102i \(-0.480388\pi\)
0.895170 + 0.445725i \(0.147054\pi\)
\(8\) 132.210 + 123.647i 0.730364 + 0.683058i
\(9\) 0 0
\(10\) −489.410 + 137.005i −1.54765 + 0.433247i
\(11\) −278.231 481.910i −0.693303 1.20084i −0.970749 0.240095i \(-0.922821\pi\)
0.277446 0.960741i \(-0.410512\pi\)
\(12\) 0 0
\(13\) 179.796 311.416i 0.295068 0.511072i −0.679933 0.733274i \(-0.737991\pi\)
0.975001 + 0.222202i \(0.0713245\pi\)
\(14\) −200.952 + 784.871i −0.274013 + 1.07023i
\(15\) 0 0
\(16\) −1022.98 + 45.6648i −0.999005 + 0.0445945i
\(17\) 1076.42i 0.903356i −0.892181 0.451678i \(-0.850826\pi\)
0.892181 0.451678i \(-0.149174\pi\)
\(18\) 0 0
\(19\) 348.135i 0.221240i −0.993863 0.110620i \(-0.964716\pi\)
0.993863 0.110620i \(-0.0352837\pi\)
\(20\) 1381.59 2521.23i 0.772333 1.40941i
\(21\) 0 0
\(22\) 3049.46 + 780.757i 1.34328 + 0.343921i
\(23\) 1469.06 2544.48i 0.579054 1.00295i −0.416535 0.909120i \(-0.636756\pi\)
0.995588 0.0938304i \(-0.0299111\pi\)
\(24\) 0 0
\(25\) 2473.33 + 4283.93i 0.791464 + 1.37086i
\(26\) 548.358 + 1958.85i 0.159086 + 0.568288i
\(27\) 0 0
\(28\) −2379.51 3917.00i −0.573578 0.944188i
\(29\) −3331.19 + 1923.26i −0.735536 + 0.424662i −0.820444 0.571727i \(-0.806274\pi\)
0.0849079 + 0.996389i \(0.472940\pi\)
\(30\) 0 0
\(31\) 2346.41 + 1354.70i 0.438531 + 0.253186i 0.702974 0.711215i \(-0.251855\pi\)
−0.264443 + 0.964401i \(0.585188\pi\)
\(32\) 3861.35 4317.91i 0.666599 0.745417i
\(33\) 0 0
\(34\) 4353.43 + 4257.39i 0.645853 + 0.631606i
\(35\) 12867.4 1.77550
\(36\) 0 0
\(37\) −1992.90 −0.239321 −0.119661 0.992815i \(-0.538181\pi\)
−0.119661 + 0.992815i \(0.538181\pi\)
\(38\) 1407.98 + 1376.92i 0.158175 + 0.154686i
\(39\) 0 0
\(40\) 4732.35 + 15559.5i 0.467657 + 1.53760i
\(41\) 13432.0 + 7754.99i 1.24791 + 0.720479i 0.970692 0.240329i \(-0.0772552\pi\)
0.277215 + 0.960808i \(0.410589\pi\)
\(42\) 0 0
\(43\) 12474.1 7201.91i 1.02882 0.593987i 0.112170 0.993689i \(-0.464220\pi\)
0.916645 + 0.399702i \(0.130887\pi\)
\(44\) −15218.7 + 9245.10i −1.18508 + 0.719913i
\(45\) 0 0
\(46\) 4480.46 + 16005.2i 0.312197 + 1.11523i
\(47\) −1232.97 2135.56i −0.0814153 0.141015i 0.822443 0.568848i \(-0.192611\pi\)
−0.903858 + 0.427832i \(0.859277\pi\)
\(48\) 0 0
\(49\) 1852.82 3209.17i 0.110241 0.190943i
\(50\) −27108.1 6940.52i −1.53347 0.392615i
\(51\) 0 0
\(52\) −10091.1 5529.78i −0.517526 0.283596i
\(53\) 13364.2i 0.653514i 0.945108 + 0.326757i \(0.105956\pi\)
−0.945108 + 0.326757i \(0.894044\pi\)
\(54\) 0 0
\(55\) 49993.8i 2.22848i
\(56\) 25253.0 + 5868.70i 1.07608 + 0.250076i
\(57\) 0 0
\(58\) 5396.96 21079.3i 0.210659 0.822785i
\(59\) 19878.8 34431.1i 0.743464 1.28772i −0.207445 0.978247i \(-0.566515\pi\)
0.950909 0.309470i \(-0.100152\pi\)
\(60\) 0 0
\(61\) −211.489 366.310i −0.00727718 0.0126044i 0.862364 0.506289i \(-0.168983\pi\)
−0.869641 + 0.493685i \(0.835650\pi\)
\(62\) −14759.3 + 4131.70i −0.487626 + 0.136505i
\(63\) 0 0
\(64\) 2191.00 + 32694.7i 0.0668640 + 0.997762i
\(65\) 27978.3 16153.3i 0.821369 0.474218i
\(66\) 0 0
\(67\) −14018.6 8093.63i −0.381520 0.220271i 0.296960 0.954890i \(-0.404027\pi\)
−0.678479 + 0.734620i \(0.737361\pi\)
\(68\) −34436.8 + 768.229i −0.903132 + 0.0201474i
\(69\) 0 0
\(70\) −50892.5 + 52040.5i −1.24139 + 1.26939i
\(71\) −6902.73 −0.162508 −0.0812541 0.996693i \(-0.525893\pi\)
−0.0812541 + 0.996693i \(0.525893\pi\)
\(72\) 0 0
\(73\) −11089.5 −0.243558 −0.121779 0.992557i \(-0.538860\pi\)
−0.121779 + 0.992557i \(0.538860\pi\)
\(74\) 7882.20 8060.00i 0.167328 0.171102i
\(75\) 0 0
\(76\) −11137.6 + 248.460i −0.221185 + 0.00493427i
\(77\) −69020.2 39848.8i −1.32663 0.765930i
\(78\) 0 0
\(79\) −64310.3 + 37129.6i −1.15935 + 0.669349i −0.951147 0.308738i \(-0.900093\pi\)
−0.208199 + 0.978086i \(0.566760\pi\)
\(80\) −81645.2 42400.5i −1.42628 0.740707i
\(81\) 0 0
\(82\) −84489.6 + 23651.9i −1.38761 + 0.388446i
\(83\) 48564.9 + 84116.9i 0.773798 + 1.34026i 0.935468 + 0.353412i \(0.114979\pi\)
−0.161670 + 0.986845i \(0.551688\pi\)
\(84\) 0 0
\(85\) 48354.0 83751.6i 0.725914 1.25732i
\(86\) −20209.6 + 78934.2i −0.294654 + 1.15085i
\(87\) 0 0
\(88\) 22801.6 98115.6i 0.313877 1.35061i
\(89\) 74459.8i 0.996430i 0.867054 + 0.498215i \(0.166011\pi\)
−0.867054 + 0.498215i \(0.833989\pi\)
\(90\) 0 0
\(91\) 51501.6i 0.651954i
\(92\) −82451.5 45182.1i −1.01562 0.556541i
\(93\) 0 0
\(94\) 13513.5 + 3459.88i 0.157743 + 0.0403870i
\(95\) 15638.6 27086.9i 0.177783 0.307929i
\(96\) 0 0
\(97\) 47958.5 + 83066.5i 0.517530 + 0.896389i 0.999793 + 0.0203622i \(0.00648193\pi\)
−0.482262 + 0.876027i \(0.660185\pi\)
\(98\) 5650.89 + 20186.2i 0.0594363 + 0.212319i
\(99\) 0 0
\(100\) 135286. 82184.1i 1.35286 0.821841i
\(101\) 34890.0 20143.7i 0.340328 0.196488i −0.320089 0.947387i \(-0.603713\pi\)
0.660417 + 0.750899i \(0.270380\pi\)
\(102\) 0 0
\(103\) −42984.3 24817.0i −0.399225 0.230492i 0.286925 0.957953i \(-0.407367\pi\)
−0.686149 + 0.727461i \(0.740700\pi\)
\(104\) 62276.3 18941.1i 0.564599 0.171721i
\(105\) 0 0
\(106\) −54049.8 52857.5i −0.467229 0.456922i
\(107\) 14176.4 0.119703 0.0598517 0.998207i \(-0.480937\pi\)
0.0598517 + 0.998207i \(0.480937\pi\)
\(108\) 0 0
\(109\) 21788.2 0.175653 0.0878264 0.996136i \(-0.472008\pi\)
0.0878264 + 0.996136i \(0.472008\pi\)
\(110\) 202193. + 197733.i 1.59325 + 1.55810i
\(111\) 0 0
\(112\) −123615. + 78920.9i −0.931160 + 0.594493i
\(113\) −129459. 74743.4i −0.953756 0.550651i −0.0595101 0.998228i \(-0.518954\pi\)
−0.894246 + 0.447577i \(0.852287\pi\)
\(114\) 0 0
\(115\) 228602. 131983.i 1.61189 0.930625i
\(116\) 63906.5 + 105199.i 0.440961 + 0.725882i
\(117\) 0 0
\(118\) 60628.2 + 216577.i 0.400839 + 1.43188i
\(119\) −77083.6 133513.i −0.498993 0.864282i
\(120\) 0 0
\(121\) −74299.1 + 128690.i −0.461339 + 0.799062i
\(122\) 2317.96 + 593.470i 0.0140996 + 0.00360993i
\(123\) 0 0
\(124\) 41665.1 76033.4i 0.243343 0.444069i
\(125\) 163661.i 0.936853i
\(126\) 0 0
\(127\) 257349.i 1.41584i 0.706293 + 0.707919i \(0.250366\pi\)
−0.706293 + 0.707919i \(0.749634\pi\)
\(128\) −140895. 120451.i −0.760098 0.649808i
\(129\) 0 0
\(130\) −45328.5 + 177043.i −0.235241 + 0.918799i
\(131\) 3161.94 5476.65i 0.0160982 0.0278828i −0.857864 0.513877i \(-0.828209\pi\)
0.873962 + 0.485994i \(0.161542\pi\)
\(132\) 0 0
\(133\) −24930.4 43180.7i −0.122208 0.211670i
\(134\) 88179.0 24684.7i 0.424232 0.118759i
\(135\) 0 0
\(136\) 133096. 142313.i 0.617045 0.659779i
\(137\) 250464. 144606.i 1.14010 0.658239i 0.193647 0.981071i \(-0.437968\pi\)
0.946456 + 0.322832i \(0.104635\pi\)
\(138\) 0 0
\(139\) 86135.1 + 49730.1i 0.378132 + 0.218315i 0.677005 0.735978i \(-0.263277\pi\)
−0.298873 + 0.954293i \(0.596611\pi\)
\(140\) −9183.35 411655.i −0.0395987 1.77506i
\(141\) 0 0
\(142\) 27301.3 27917.1i 0.113622 0.116185i
\(143\) −200099. −0.818285
\(144\) 0 0
\(145\) −345581. −1.36499
\(146\) 43860.4 44849.7i 0.170290 0.174132i
\(147\) 0 0
\(148\) 1422.31 + 63756.9i 0.00533753 + 0.239262i
\(149\) 323359. + 186691.i 1.19322 + 0.688904i 0.959035 0.283289i \(-0.0914255\pi\)
0.234182 + 0.972193i \(0.424759\pi\)
\(150\) 0 0
\(151\) −320356. + 184958.i −1.14338 + 0.660131i −0.947266 0.320450i \(-0.896166\pi\)
−0.196115 + 0.980581i \(0.562833\pi\)
\(152\) 43045.8 46027.0i 0.151120 0.161586i
\(153\) 0 0
\(154\) 434148. 121535.i 1.47515 0.412951i
\(155\) 121710. + 210807.i 0.406908 + 0.704785i
\(156\) 0 0
\(157\) 196653. 340613.i 0.636724 1.10284i −0.349423 0.936965i \(-0.613622\pi\)
0.986147 0.165873i \(-0.0530442\pi\)
\(158\) 104191. 406947.i 0.332038 1.29687i
\(159\) 0 0
\(160\) 494401. 162502.i 1.52679 0.501833i
\(161\) 420803.i 1.27942i
\(162\) 0 0
\(163\) 154747.i 0.456198i 0.973638 + 0.228099i \(0.0732509\pi\)
−0.973638 + 0.228099i \(0.926749\pi\)
\(164\) 238512. 435253.i 0.692468 1.26367i
\(165\) 0 0
\(166\) −532280. 136280.i −1.49924 0.383852i
\(167\) −98410.6 + 170452.i −0.273055 + 0.472946i −0.969643 0.244526i \(-0.921368\pi\)
0.696587 + 0.717472i \(0.254701\pi\)
\(168\) 0 0
\(169\) 120993. + 209567.i 0.325870 + 0.564424i
\(170\) 147475. + 526811.i 0.391377 + 1.39808i
\(171\) 0 0
\(172\) −239306. 393931.i −0.616784 1.01531i
\(173\) −583484. + 336874.i −1.48222 + 0.855762i −0.999796 0.0201751i \(-0.993578\pi\)
−0.482426 + 0.875937i \(0.660244\pi\)
\(174\) 0 0
\(175\) 613554. + 354235.i 1.51446 + 0.874373i
\(176\) 306631. + 480279.i 0.746164 + 1.16872i
\(177\) 0 0
\(178\) −301142. 294499.i −0.712396 0.696681i
\(179\) −583842. −1.36196 −0.680978 0.732304i \(-0.738445\pi\)
−0.680978 + 0.732304i \(0.738445\pi\)
\(180\) 0 0
\(181\) −623067. −1.41364 −0.706819 0.707395i \(-0.749870\pi\)
−0.706819 + 0.707395i \(0.749870\pi\)
\(182\) 208291. + 203696.i 0.466114 + 0.455831i
\(183\) 0 0
\(184\) 508840. 154762.i 1.10799 0.336992i
\(185\) −155059. 89523.4i −0.333095 0.192312i
\(186\) 0 0
\(187\) −518737. + 299493.i −1.08478 + 0.626300i
\(188\) −67440.9 + 40969.2i −0.139165 + 0.0845401i
\(189\) 0 0
\(190\) 47696.2 + 170381.i 0.0958517 + 0.342403i
\(191\) −92566.8 160330.i −0.183600 0.318004i 0.759504 0.650502i \(-0.225442\pi\)
−0.943104 + 0.332499i \(0.892108\pi\)
\(192\) 0 0
\(193\) 145169. 251439.i 0.280530 0.485892i −0.690985 0.722869i \(-0.742823\pi\)
0.971515 + 0.236977i \(0.0761565\pi\)
\(194\) −525633. 134579.i −1.00272 0.256727i
\(195\) 0 0
\(196\) −103990. 56985.0i −0.193354 0.105955i
\(197\) 232595.i 0.427007i −0.976942 0.213504i \(-0.931512\pi\)
0.976942 0.213504i \(-0.0684875\pi\)
\(198\) 0 0
\(199\) 524007.i 0.938004i −0.883197 0.469002i \(-0.844614\pi\)
0.883197 0.469002i \(-0.155386\pi\)
\(200\) −202695. + 872197.i −0.358317 + 1.54184i
\(201\) 0 0
\(202\) −56526.3 + 220779.i −0.0974703 + 0.380697i
\(203\) −275454. + 477100.i −0.469147 + 0.812587i
\(204\) 0 0
\(205\) 696727. + 1.20677e6i 1.15792 + 2.00557i
\(206\) 270378. 75689.3i 0.443919 0.124270i
\(207\) 0 0
\(208\) −169707. + 326783.i −0.271983 + 0.523722i
\(209\) −167770. + 96861.9i −0.265673 + 0.153386i
\(210\) 0 0
\(211\) −389705. 224996.i −0.602601 0.347912i 0.167463 0.985878i \(-0.446442\pi\)
−0.770064 + 0.637967i \(0.779776\pi\)
\(212\) 427549. 9537.92i 0.653351 0.0145752i
\(213\) 0 0
\(214\) −56069.7 + 57334.5i −0.0836939 + 0.0855818i
\(215\) 1.29407e6 1.90925
\(216\) 0 0
\(217\) 388047. 0.559416
\(218\) −86175.4 + 88119.3i −0.122812 + 0.125583i
\(219\) 0 0
\(220\) −1.59940e6 + 35680.0i −2.22793 + 0.0497014i
\(221\) −335214. 193536.i −0.461680 0.266551i
\(222\) 0 0
\(223\) 33442.0 19307.7i 0.0450329 0.0259998i −0.477315 0.878733i \(-0.658390\pi\)
0.522347 + 0.852733i \(0.325056\pi\)
\(224\) 169729. 812085.i 0.226014 1.08139i
\(225\) 0 0
\(226\) 814319. 227959.i 1.06053 0.296884i
\(227\) −447303. 774752.i −0.576152 0.997925i −0.995915 0.0902911i \(-0.971220\pi\)
0.419763 0.907634i \(-0.362113\pi\)
\(228\) 0 0
\(229\) 714088. 1.23684e6i 0.899836 1.55856i 0.0721321 0.997395i \(-0.477020\pi\)
0.827703 0.561166i \(-0.189647\pi\)
\(230\) −370365. + 1.44656e6i −0.461648 + 1.80309i
\(231\) 0 0
\(232\) −678221. 157616.i −0.827278 0.192256i
\(233\) 379913.i 0.458453i −0.973373 0.229226i \(-0.926380\pi\)
0.973373 0.229226i \(-0.0736196\pi\)
\(234\) 0 0
\(235\) 221545.i 0.261693i
\(236\) −1.11571e6 611390.i −1.30398 0.714559i
\(237\) 0 0
\(238\) 844850. + 216308.i 0.966802 + 0.247531i
\(239\) −379157. + 656720.i −0.429363 + 0.743679i −0.996817 0.0797266i \(-0.974595\pi\)
0.567454 + 0.823405i \(0.307929\pi\)
\(240\) 0 0
\(241\) −595565. 1.03155e6i −0.660520 1.14405i −0.980479 0.196623i \(-0.937002\pi\)
0.319959 0.947432i \(-0.396331\pi\)
\(242\) −226604. 809479.i −0.248731 0.888520i
\(243\) 0 0
\(244\) −11568.1 + 7027.40i −0.0124390 + 0.00755649i
\(245\) 288320. 166461.i 0.306873 0.177173i
\(246\) 0 0
\(247\) −108415. 62593.3i −0.113070 0.0652808i
\(248\) 142715. + 469231.i 0.147347 + 0.484460i
\(249\) 0 0
\(250\) −661906. 647305.i −0.669802 0.655026i
\(251\) −705353. −0.706679 −0.353340 0.935495i \(-0.614954\pi\)
−0.353340 + 0.935495i \(0.614954\pi\)
\(252\) 0 0
\(253\) −1.63495e6 −1.60584
\(254\) −1.04081e6 1.01785e6i −1.01225 0.989922i
\(255\) 0 0
\(256\) 1.04441e6 93428.4i 0.996023 0.0891003i
\(257\) 1.11396e6 + 643145.i 1.05205 + 0.607402i 0.923223 0.384265i \(-0.125545\pi\)
0.128828 + 0.991667i \(0.458878\pi\)
\(258\) 0 0
\(259\) −247188. + 142714.i −0.228969 + 0.132196i
\(260\) −536745. 883555.i −0.492418 0.810588i
\(261\) 0 0
\(262\) 9643.59 + 34449.0i 0.00867932 + 0.0310044i
\(263\) 812371. + 1.40707e6i 0.724211 + 1.25437i 0.959298 + 0.282396i \(0.0911292\pi\)
−0.235087 + 0.971974i \(0.575537\pi\)
\(264\) 0 0
\(265\) −600338. + 1.03982e6i −0.525147 + 0.909581i
\(266\) 273241. + 69958.3i 0.236778 + 0.0606227i
\(267\) 0 0
\(268\) −248927. + 454259.i −0.211707 + 0.386337i
\(269\) 1.30693e6i 1.10121i 0.834766 + 0.550605i \(0.185603\pi\)
−0.834766 + 0.550605i \(0.814397\pi\)
\(270\) 0 0
\(271\) 109448.i 0.0905280i −0.998975 0.0452640i \(-0.985587\pi\)
0.998975 0.0452640i \(-0.0144129\pi\)
\(272\) 49154.4 + 1.10116e6i 0.0402847 + 0.902458i
\(273\) 0 0
\(274\) −405785. + 1.58490e6i −0.326527 + 1.27534i
\(275\) 1.37631e6 2.38384e6i 1.09745 1.90084i
\(276\) 0 0
\(277\) 377853. + 654461.i 0.295885 + 0.512488i 0.975190 0.221368i \(-0.0710520\pi\)
−0.679305 + 0.733856i \(0.737719\pi\)
\(278\) −541803. + 151672.i −0.420465 + 0.117704i
\(279\) 0 0
\(280\) 1.70120e6 + 1.59102e6i 1.29677 + 1.21277i
\(281\) 133655. 77165.9i 0.100977 0.0582988i −0.448661 0.893702i \(-0.648099\pi\)
0.549638 + 0.835403i \(0.314766\pi\)
\(282\) 0 0
\(283\) −921332. 531931.i −0.683833 0.394811i 0.117465 0.993077i \(-0.462523\pi\)
−0.801298 + 0.598266i \(0.795857\pi\)
\(284\) 4926.41 + 220833.i 0.00362439 + 0.162468i
\(285\) 0 0
\(286\) 791420. 809272.i 0.572126 0.585032i
\(287\) 2.22137e6 1.59190
\(288\) 0 0
\(289\) 261179. 0.183947
\(290\) 1.36682e6 1.39765e6i 0.954370 0.975898i
\(291\) 0 0
\(292\) 7914.43 + 354774.i 0.00543203 + 0.243498i
\(293\) 519996. + 300220.i 0.353860 + 0.204301i 0.666384 0.745609i \(-0.267841\pi\)
−0.312524 + 0.949910i \(0.601175\pi\)
\(294\) 0 0
\(295\) 3.09337e6 1.78596e6i 2.06955 1.19486i
\(296\) −263481. 246415.i −0.174792 0.163470i
\(297\) 0 0
\(298\) −2.03398e6 + 569389.i −1.32680 + 0.371423i
\(299\) −528261. 914974.i −0.341720 0.591876i
\(300\) 0 0
\(301\) 1.03147e6 1.78657e6i 0.656209 1.13659i
\(302\) 519019. 2.02717e6i 0.327466 1.27901i
\(303\) 0 0
\(304\) 15897.5 + 356136.i 0.00986609 + 0.221020i
\(305\) 38001.3i 0.0233910i
\(306\) 0 0
\(307\) 2.78186e6i 1.68457i −0.539031 0.842286i \(-0.681209\pi\)
0.539031 0.842286i \(-0.318791\pi\)
\(308\) −1.22559e6 + 2.23654e6i −0.736152 + 1.34338i
\(309\) 0 0
\(310\) −1.33396e6 341535.i −0.788385 0.201851i
\(311\) 1.14667e6 1.98609e6i 0.672262 1.16439i −0.304999 0.952353i \(-0.598656\pi\)
0.977261 0.212039i \(-0.0680104\pi\)
\(312\) 0 0
\(313\) 1.41302e6 + 2.44742e6i 0.815244 + 1.41204i 0.909153 + 0.416463i \(0.136730\pi\)
−0.0939092 + 0.995581i \(0.529936\pi\)
\(314\) 599770. + 2.14251e6i 0.343290 + 1.22630i
\(315\) 0 0
\(316\) 1.23375e6 + 2.03092e6i 0.695039 + 1.14413i
\(317\) 185665. 107194.i 0.103773 0.0599132i −0.447215 0.894426i \(-0.647584\pi\)
0.550988 + 0.834513i \(0.314251\pi\)
\(318\) 0 0
\(319\) 1.85368e6 + 1.07022e6i 1.01990 + 0.588839i
\(320\) −1.29821e6 + 2.64226e6i −0.708713 + 1.44245i
\(321\) 0 0
\(322\) 1.70188e6 + 1.66434e6i 0.914722 + 0.894544i
\(323\) −374739. −0.199859
\(324\) 0 0
\(325\) 1.77878e6 0.934142
\(326\) −625852. 612046.i −0.326158 0.318963i
\(327\) 0 0
\(328\) 816971. + 2.68611e6i 0.419298 + 1.37860i
\(329\) −305860. 176588.i −0.155787 0.0899439i
\(330\) 0 0
\(331\) −352745. + 203658.i −0.176967 + 0.102172i −0.585867 0.810407i \(-0.699246\pi\)
0.408900 + 0.912579i \(0.365912\pi\)
\(332\) 2.65641e6 1.61372e6i 1.32267 0.803497i
\(333\) 0 0
\(334\) −300142. 1.07217e6i −0.147218 0.525893i
\(335\) −727151. 1.25946e6i −0.354008 0.613159i
\(336\) 0 0
\(337\) −1.44822e6 + 2.50838e6i −0.694638 + 1.20315i 0.275664 + 0.961254i \(0.411102\pi\)
−0.970302 + 0.241895i \(0.922231\pi\)
\(338\) −1.32611e6 339525.i −0.631375 0.161652i
\(339\) 0 0
\(340\) −2.71390e6 1.48717e6i −1.27320 0.697692i
\(341\) 1.50768e6i 0.702139i
\(342\) 0 0
\(343\) 1.87641e6i 0.861176i
\(344\) 2.53969e6 + 590213.i 1.15714 + 0.268914i
\(345\) 0 0
\(346\) 945320. 3.69220e6i 0.424511 1.65804i
\(347\) −1.79724e6 + 3.11291e6i −0.801275 + 1.38785i 0.117502 + 0.993073i \(0.462512\pi\)
−0.918777 + 0.394777i \(0.870822\pi\)
\(348\) 0 0
\(349\) −956981. 1.65754e6i −0.420571 0.728451i 0.575424 0.817855i \(-0.304837\pi\)
−0.995995 + 0.0894044i \(0.971504\pi\)
\(350\) −3.85935e6 + 1.08038e6i −1.68401 + 0.471418i
\(351\) 0 0
\(352\) −3.15519e6 659447.i −1.35728 0.283676i
\(353\) −2.21063e6 + 1.27631e6i −0.944232 + 0.545152i −0.891284 0.453445i \(-0.850195\pi\)
−0.0529474 + 0.998597i \(0.516862\pi\)
\(354\) 0 0
\(355\) −537073. 310079.i −0.226184 0.130587i
\(356\) 2.38212e6 53141.1i 0.996182 0.0222232i
\(357\) 0 0
\(358\) 2.30918e6 2.36127e6i 0.952248 0.973728i
\(359\) 2.70497e6 1.10771 0.553856 0.832612i \(-0.313156\pi\)
0.553856 + 0.832612i \(0.313156\pi\)
\(360\) 0 0
\(361\) 2.35490e6 0.951053
\(362\) 2.46432e6 2.51991e6i 0.988383 1.01068i
\(363\) 0 0
\(364\) −1.64764e6 + 36756.1i −0.651792 + 0.0145404i
\(365\) −862824. 498151.i −0.338992 0.195717i
\(366\) 0 0
\(367\) −3.78493e6 + 2.18523e6i −1.46687 + 0.846900i −0.999313 0.0370602i \(-0.988201\pi\)
−0.467561 + 0.883961i \(0.654867\pi\)
\(368\) −1.38662e6 + 2.67004e6i −0.533751 + 1.02778i
\(369\) 0 0
\(370\) 975346. 273037.i 0.370386 0.103685i
\(371\) 957029. + 1.65762e6i 0.360986 + 0.625246i
\(372\) 0 0
\(373\) −1.08643e6 + 1.88176e6i −0.404325 + 0.700312i −0.994243 0.107152i \(-0.965827\pi\)
0.589917 + 0.807464i \(0.299160\pi\)
\(374\) 840421. 3.28249e6i 0.310683 1.21346i
\(375\) 0 0
\(376\) 101044. 434794.i 0.0368589 0.158604i
\(377\) 1.38318e6i 0.501216i
\(378\) 0 0
\(379\) 872712.i 0.312085i 0.987750 + 0.156043i \(0.0498737\pi\)
−0.987750 + 0.156043i \(0.950126\pi\)
\(380\) −877727. 480980.i −0.311818 0.170871i
\(381\) 0 0
\(382\) 1.01455e6 + 259756.i 0.355725 + 0.0910767i
\(383\) −817267. + 1.41555e6i −0.284687 + 0.493092i −0.972533 0.232764i \(-0.925223\pi\)
0.687846 + 0.725856i \(0.258556\pi\)
\(384\) 0 0
\(385\) −3.58011e6 6.20094e6i −1.23096 2.13209i
\(386\) 442748. + 1.58159e6i 0.151248 + 0.540289i
\(387\) 0 0
\(388\) 2.62324e6 1.59357e6i 0.884624 0.537394i
\(389\) 89924.7 51918.0i 0.0301304 0.0173958i −0.484859 0.874592i \(-0.661129\pi\)
0.514990 + 0.857196i \(0.327796\pi\)
\(390\) 0 0
\(391\) −2.73893e6 1.58132e6i −0.906021 0.523092i
\(392\) 641764. 195190.i 0.210941 0.0641568i
\(393\) 0 0
\(394\) 940699. + 919948.i 0.305288 + 0.298554i
\(395\) −6.67162e6 −2.15149
\(396\) 0 0
\(397\) −3.33523e6 −1.06206 −0.531031 0.847352i \(-0.678195\pi\)
−0.531031 + 0.847352i \(0.678195\pi\)
\(398\) 2.11927e6 + 2.07252e6i 0.670625 + 0.655831i
\(399\) 0 0
\(400\) −2.72579e6 4.26943e6i −0.851810 1.33420i
\(401\) −144161. 83231.6i −0.0447701 0.0258480i 0.477448 0.878660i \(-0.341562\pi\)
−0.522218 + 0.852812i \(0.674895\pi\)
\(402\) 0 0
\(403\) 843751. 487140.i 0.258793 0.149414i
\(404\) −669340. 1.10183e6i −0.204030 0.335861i
\(405\) 0 0
\(406\) −840105. 3.00104e6i −0.252941 0.903558i
\(407\) 554486. + 960398.i 0.165922 + 0.287386i
\(408\) 0 0
\(409\) 2.56963e6 4.45073e6i 0.759560 1.31560i −0.183515 0.983017i \(-0.558748\pi\)
0.943075 0.332580i \(-0.107919\pi\)
\(410\) −7.63625e6 1.95512e6i −2.24347 0.574399i
\(411\) 0 0
\(412\) −763270. + 1.39287e6i −0.221531 + 0.404266i
\(413\) 5.69417e6i 1.64269i
\(414\) 0 0
\(415\) 8.72638e6i 2.48722i
\(416\) −650411. 1.97883e6i −0.184270 0.560628i
\(417\) 0 0
\(418\) 271809. 1.06162e6i 0.0760892 0.297187i
\(419\) −1.65720e6 + 2.87035e6i −0.461146 + 0.798729i −0.999018 0.0442975i \(-0.985895\pi\)
0.537872 + 0.843027i \(0.319228\pi\)
\(420\) 0 0
\(421\) 1.80550e6 + 3.12721e6i 0.496468 + 0.859908i 0.999992 0.00407351i \(-0.00129664\pi\)
−0.503524 + 0.863981i \(0.667963\pi\)
\(422\) 2.45130e6 686214.i 0.670064 0.187577i
\(423\) 0 0
\(424\) −1.65244e6 + 1.76689e6i −0.446388 + 0.477303i
\(425\) 4.61130e6 2.66234e6i 1.23837 0.714974i
\(426\) 0 0
\(427\) −52463.7 30289.9i −0.0139248 0.00803950i
\(428\) −10117.5 453532.i −0.00266972 0.119674i
\(429\) 0 0
\(430\) −5.11825e6 + 5.23370e6i −1.33490 + 1.36502i
\(431\) −7.53077e6 −1.95275 −0.976374 0.216090i \(-0.930670\pi\)
−0.976374 + 0.216090i \(0.930670\pi\)
\(432\) 0 0
\(433\) 2.24585e6 0.575653 0.287827 0.957683i \(-0.407067\pi\)
0.287827 + 0.957683i \(0.407067\pi\)
\(434\) −1.53478e6 + 1.56940e6i −0.391131 + 0.399954i
\(435\) 0 0
\(436\) −15550.0 697049.i −0.00391755 0.175609i
\(437\) −885823. 511430.i −0.221893 0.128110i
\(438\) 0 0
\(439\) −925006. + 534052.i −0.229078 + 0.132258i −0.610147 0.792289i \(-0.708889\pi\)
0.381069 + 0.924547i \(0.375556\pi\)
\(440\) 6.18157e6 6.60968e6i 1.52218 1.62760i
\(441\) 0 0
\(442\) 2.10855e6 590263.i 0.513367 0.143711i
\(443\) −149436. 258831.i −0.0361781 0.0626623i 0.847369 0.531004i \(-0.178185\pi\)
−0.883548 + 0.468342i \(0.844852\pi\)
\(444\) 0 0
\(445\) −3.34482e6 + 5.79340e6i −0.800705 + 1.38686i
\(446\) −54180.4 + 211616.i −0.0128975 + 0.0503747i
\(447\) 0 0
\(448\) 2.61306e6 + 3.89836e6i 0.615113 + 0.917670i
\(449\) 8.39456e6i 1.96509i 0.186028 + 0.982544i \(0.440439\pi\)
−0.186028 + 0.982544i \(0.559561\pi\)
\(450\) 0 0
\(451\) 8.63070e6i 1.99804i
\(452\) −2.29880e6 + 4.19501e6i −0.529243 + 0.965800i
\(453\) 0 0
\(454\) 4.90252e6 + 1.25520e6i 1.11630 + 0.285807i
\(455\) 2.31351e6 4.00712e6i 0.523894 0.907411i
\(456\) 0 0
\(457\) −1.98648e6 3.44069e6i −0.444933 0.770646i 0.553115 0.833105i \(-0.313439\pi\)
−0.998048 + 0.0624588i \(0.980106\pi\)
\(458\) 2.17789e6 + 7.77990e6i 0.485146 + 1.73305i
\(459\) 0 0
\(460\) −4.38557e6 7.21925e6i −0.966344 1.59073i
\(461\) 2.12064e6 1.22435e6i 0.464744 0.268320i −0.249293 0.968428i \(-0.580198\pi\)
0.714037 + 0.700108i \(0.246865\pi\)
\(462\) 0 0
\(463\) 5.77486e6 + 3.33412e6i 1.25196 + 0.722817i 0.971498 0.237049i \(-0.0761801\pi\)
0.280459 + 0.959866i \(0.409513\pi\)
\(464\) 3.31992e6 2.11958e6i 0.715867 0.457040i
\(465\) 0 0
\(466\) 1.53651e6 + 1.50261e6i 0.327770 + 0.320540i
\(467\) 3.34371e6 0.709474 0.354737 0.934966i \(-0.384570\pi\)
0.354737 + 0.934966i \(0.384570\pi\)
\(468\) 0 0
\(469\) −2.31838e6 −0.486689
\(470\) 896008. + 876242.i 0.187097 + 0.182970i
\(471\) 0 0
\(472\) 6.88546e6 2.09419e6i 1.42258 0.432674i
\(473\) −6.94134e6 4.00759e6i −1.42656 0.823626i
\(474\) 0 0
\(475\) 1.49139e6 861052.i 0.303288 0.175104i
\(476\) −4.21633e6 + 2.56135e6i −0.852938 + 0.518145i
\(477\) 0 0
\(478\) −1.15639e6 4.13087e6i −0.231491 0.826936i
\(479\) 2.32045e6 + 4.01914e6i 0.462097 + 0.800376i 0.999065 0.0432268i \(-0.0137638\pi\)
−0.536968 + 0.843603i \(0.680430\pi\)
\(480\) 0 0
\(481\) −358315. + 620620.i −0.0706159 + 0.122310i
\(482\) 6.52749e6 + 1.67124e6i 1.27976 + 0.327659i
\(483\) 0 0
\(484\) 4.17008e6 + 2.28513e6i 0.809153 + 0.443403i
\(485\) 8.61740e6i 1.66350i
\(486\) 0 0
\(487\) 4.91616e6i 0.939299i 0.882853 + 0.469650i \(0.155620\pi\)
−0.882853 + 0.469650i \(0.844380\pi\)
\(488\) 17332.0 74579.7i 0.00329457 0.0141766i
\(489\) 0 0
\(490\) −467115. + 1.82445e6i −0.0878889 + 0.343274i
\(491\) −346602. + 600332.i −0.0648824 + 0.112380i −0.896642 0.442757i \(-0.854001\pi\)
0.831759 + 0.555136i \(0.187334\pi\)
\(492\) 0 0
\(493\) 2.07024e6 + 3.58575e6i 0.383621 + 0.664451i
\(494\) 681946. 190903.i 0.125728 0.0351961i
\(495\) 0 0
\(496\) −2.46220e6 1.27869e6i −0.449385 0.233378i
\(497\) −856175. + 494313.i −0.155479 + 0.0897658i
\(498\) 0 0
\(499\) −400079. 230986.i −0.0719274 0.0415273i 0.463605 0.886042i \(-0.346556\pi\)
−0.535532 + 0.844515i \(0.679889\pi\)
\(500\) 5.23587e6 116803.i 0.936620 0.0208944i
\(501\) 0 0
\(502\) 2.78977e6 2.85270e6i 0.494094 0.505239i
\(503\) 3.22518e6 0.568373 0.284187 0.958769i \(-0.408276\pi\)
0.284187 + 0.958769i \(0.408276\pi\)
\(504\) 0 0
\(505\) 3.61952e6 0.631572
\(506\) 6.46644e6 6.61231e6i 1.12277 1.14809i
\(507\) 0 0
\(508\) 8.23313e6 183667.i 1.41549 0.0315772i
\(509\) 213328. + 123165.i 0.0364967 + 0.0210714i 0.518137 0.855297i \(-0.326626\pi\)
−0.481641 + 0.876369i \(0.659959\pi\)
\(510\) 0 0
\(511\) −1.37547e6 + 794129.i −0.233023 + 0.134536i
\(512\) −3.75291e6 + 4.59347e6i −0.632694 + 0.774402i
\(513\) 0 0
\(514\) −7.00698e6 + 1.96152e6i −1.16983 + 0.327481i
\(515\) −2.22962e6 3.86181e6i −0.370436 0.641613i
\(516\) 0 0
\(517\) −686097. + 1.18836e6i −0.112891 + 0.195533i
\(518\) 400476. 1.56417e6i 0.0655771 0.256129i
\(519\) 0 0
\(520\) 5.69632e6 + 1.32380e6i 0.923817 + 0.214691i
\(521\) 5.09612e6i 0.822519i −0.911518 0.411259i \(-0.865089\pi\)
0.911518 0.411259i \(-0.134911\pi\)
\(522\) 0 0
\(523\) 5.13482e6i 0.820863i 0.911891 + 0.410432i \(0.134622\pi\)
−0.911891 + 0.410432i \(0.865378\pi\)
\(524\) −177466. 97248.4i −0.0282349 0.0154723i
\(525\) 0 0
\(526\) −8.90373e6 2.27963e6i −1.40316 0.359253i
\(527\) 1.45823e6 2.52572e6i 0.228717 0.396150i
\(528\) 0 0
\(529\) −1.09808e6 1.90193e6i −0.170606 0.295498i
\(530\) −1.83097e6 6.54060e6i −0.283133 1.01141i
\(531\) 0 0
\(532\) −1.36364e6 + 828391.i −0.208892 + 0.126898i
\(533\) 4.83005e6 2.78863e6i 0.736434 0.425180i
\(534\) 0 0
\(535\) 1.10301e6 + 636821.i 0.166607 + 0.0961906i
\(536\) −852647. 2.80341e6i −0.128191 0.421478i
\(537\) 0 0
\(538\) −5.28568e6 5.16908e6i −0.787309 0.769941i
\(539\) −2.06204e6 −0.305721
\(540\) 0 0
\(541\) 1.10092e7 1.61720 0.808601 0.588357i \(-0.200225\pi\)
0.808601 + 0.588357i \(0.200225\pi\)
\(542\) 442645. + 432881.i 0.0647229 + 0.0632951i
\(543\) 0 0
\(544\) −4.64789e6 4.15643e6i −0.673377 0.602176i
\(545\) 1.69525e6 + 978751.i 0.244479 + 0.141150i
\(546\) 0 0
\(547\) 3.43955e6 1.98583e6i 0.491511 0.283774i −0.233690 0.972311i \(-0.575080\pi\)
0.725201 + 0.688537i \(0.241747\pi\)
\(548\) −4.80498e6 7.90966e6i −0.683503 1.12514i
\(549\) 0 0
\(550\) 4.19760e6 + 1.49947e7i 0.591690 + 2.11364i
\(551\) 669555. + 1.15970e6i 0.0939523 + 0.162730i
\(552\) 0 0
\(553\) −5.31779e6 + 9.21068e6i −0.739466 + 1.28079i
\(554\) −4.14134e6 1.06031e6i −0.573279 0.146777i
\(555\) 0 0
\(556\) 1.52949e6 2.79113e6i 0.209827 0.382907i
\(557\) 9.38422e6i 1.28162i −0.767698 0.640812i \(-0.778598\pi\)
0.767698 0.640812i \(-0.221402\pi\)
\(558\) 0 0
\(559\) 5.17950e6i 0.701065i
\(560\) −1.31631e7 + 587588.i −1.77374 + 0.0791777i
\(561\) 0 0
\(562\) −216539. + 845753.i −0.0289198 + 0.112954i
\(563\) 2.54261e6 4.40393e6i 0.338072 0.585558i −0.645998 0.763339i \(-0.723559\pi\)
0.984070 + 0.177781i \(0.0568919\pi\)
\(564\) 0 0
\(565\) −6.71512e6 1.16309e7i −0.884978 1.53283i
\(566\) 5.79532e6 1.62233e6i 0.760390 0.212863i
\(567\) 0 0
\(568\) −912611. 853500.i −0.118690 0.111002i
\(569\) −7.59213e6 + 4.38332e6i −0.983067 + 0.567574i −0.903195 0.429231i \(-0.858785\pi\)
−0.0798721 + 0.996805i \(0.525451\pi\)
\(570\) 0 0
\(571\) −1.07595e7 6.21203e6i −1.38103 0.797339i −0.388750 0.921343i \(-0.627093\pi\)
−0.992282 + 0.124004i \(0.960426\pi\)
\(572\) 142809. + 6.40157e6i 0.0182500 + 0.818082i
\(573\) 0 0
\(574\) −8.78585e6 + 8.98404e6i −1.11302 + 1.13813i
\(575\) 1.45338e7 1.83320
\(576\) 0 0
\(577\) 9.43597e6 1.17990 0.589952 0.807438i \(-0.299146\pi\)
0.589952 + 0.807438i \(0.299146\pi\)
\(578\) −1.03300e6 + 1.05630e6i −0.128612 + 0.131513i
\(579\) 0 0
\(580\) 246637. + 1.10558e7i 0.0304431 + 1.36465i
\(581\) 1.20474e7 + 6.95558e6i 1.48065 + 0.854856i
\(582\) 0 0
\(583\) 6.44036e6 3.71834e6i 0.784763 0.453083i
\(584\) −1.46614e6 1.37117e6i −0.177886 0.166364i
\(585\) 0 0
\(586\) −3.27086e6 + 915639.i −0.393475 + 0.110149i
\(587\) −6.76932e6 1.17248e7i −0.810868 1.40446i −0.912258 0.409617i \(-0.865662\pi\)
0.101390 0.994847i \(-0.467671\pi\)
\(588\) 0 0
\(589\) 471619. 816869.i 0.0560149 0.0970206i
\(590\) −5.01166e6 + 1.95744e7i −0.592723 + 2.31504i
\(591\) 0 0
\(592\) 2.03870e6 91005.3i 0.239083 0.0106724i
\(593\) 1.76321e6i 0.205905i −0.994686 0.102952i \(-0.967171\pi\)
0.994686 0.102952i \(-0.0328289\pi\)
\(594\) 0 0
\(595\) 1.38508e7i 1.60391i
\(596\) 5.74186e6 1.04782e7i 0.662120 1.20828i
\(597\) 0 0
\(598\) 5.78983e6 + 1.48238e6i 0.662084 + 0.169514i
\(599\) 3.59905e6 6.23374e6i 0.409846 0.709875i −0.585026 0.811015i \(-0.698916\pi\)
0.994872 + 0.101140i \(0.0322489\pi\)
\(600\) 0 0
\(601\) 1.35517e6 + 2.34722e6i 0.153041 + 0.265075i 0.932344 0.361573i \(-0.117760\pi\)
−0.779303 + 0.626647i \(0.784427\pi\)
\(602\) 3.14589e6 + 1.12378e7i 0.353795 + 1.26383i
\(603\) 0 0
\(604\) 6.14581e6 + 1.01168e7i 0.685467 + 1.12837i
\(605\) −1.15618e7 + 6.67521e6i −1.28421 + 0.741440i
\(606\) 0 0
\(607\) 1.91340e6 + 1.10470e6i 0.210782 + 0.121695i 0.601675 0.798741i \(-0.294500\pi\)
−0.390893 + 0.920436i \(0.627834\pi\)
\(608\) −1.50322e6 1.34427e6i −0.164916 0.147478i
\(609\) 0 0
\(610\) 153691. + 150301.i 0.0167234 + 0.0163545i
\(611\) −886728. −0.0960921
\(612\) 0 0
\(613\) −4.95842e6 −0.532957 −0.266478 0.963841i \(-0.585860\pi\)
−0.266478 + 0.963841i \(0.585860\pi\)
\(614\) 1.12508e7 + 1.10027e7i 1.20438 + 1.17781i
\(615\) 0 0
\(616\) −4.19799e6 1.38025e7i −0.445748 1.46557i
\(617\) 6.51356e6 + 3.76060e6i 0.688819 + 0.397690i 0.803170 0.595750i \(-0.203145\pi\)
−0.114350 + 0.993440i \(0.536479\pi\)
\(618\) 0 0
\(619\) 3.79004e6 2.18818e6i 0.397573 0.229539i −0.287863 0.957671i \(-0.592945\pi\)
0.685436 + 0.728133i \(0.259612\pi\)
\(620\) 6.65729e6 4.04419e6i 0.695534 0.422525i
\(621\) 0 0
\(622\) 3.49723e6 + 1.24928e7i 0.362450 + 1.29475i
\(623\) 5.33215e6 + 9.23555e6i 0.550405 + 0.953329i
\(624\) 0 0
\(625\) 377275. 653459.i 0.0386329 0.0669142i
\(626\) −1.54870e7 3.96514e6i −1.57954 0.404411i
\(627\) 0 0
\(628\) −1.10372e7 6.04824e6i −1.11676 0.611969i
\(629\) 2.14520e6i 0.216192i
\(630\) 0 0
\(631\) 2.79597e6i 0.279549i −0.990183 0.139775i \(-0.955362\pi\)
0.990183 0.139775i \(-0.0446378\pi\)
\(632\) −1.30934e7 3.04285e6i −1.30395 0.303032i
\(633\) 0 0
\(634\) −300802. + 1.17487e6i −0.0297206 + 0.116082i
\(635\) −1.15604e7 + 2.00233e7i −1.13773 + 1.97061i
\(636\) 0 0
\(637\) −666257. 1.15399e6i −0.0650569 0.112682i
\(638\) −1.16599e7 + 3.26406e6i −1.13408 + 0.317473i
\(639\) 0 0
\(640\) −5.55163e6 1.57009e7i −0.535760 1.51522i
\(641\) 4.59173e6 2.65104e6i 0.441399 0.254842i −0.262792 0.964853i \(-0.584643\pi\)
0.704191 + 0.710011i \(0.251310\pi\)
\(642\) 0 0
\(643\) −1.45248e7 8.38588e6i −1.38542 0.799873i −0.392626 0.919698i \(-0.628433\pi\)
−0.992795 + 0.119825i \(0.961767\pi\)
\(644\) −1.34624e7 + 300323.i −1.27911 + 0.0285347i
\(645\) 0 0
\(646\) 1.48215e6 1.51558e6i 0.139737 0.142889i
\(647\) 8.06422e6 0.757359 0.378679 0.925528i \(-0.376378\pi\)
0.378679 + 0.925528i \(0.376378\pi\)
\(648\) 0 0
\(649\) −2.21235e7 −2.06178
\(650\) −7.03531e6 + 7.19401e6i −0.653130 + 0.667863i
\(651\) 0 0
\(652\) 4.95067e6 110441.i 0.456084 0.0101745i
\(653\) 620058. + 357991.i 0.0569049 + 0.0328540i 0.528183 0.849131i \(-0.322874\pi\)
−0.471278 + 0.881985i \(0.656207\pi\)
\(654\) 0 0
\(655\) 492035. 284077.i 0.0448118 0.0258721i
\(656\) −1.40948e7 7.31984e6i −1.27879 0.664113i
\(657\) 0 0
\(658\) 1.92390e6 538575.i 0.173228 0.0484933i
\(659\) 15687.4 + 27171.4i 0.00140714 + 0.00243724i 0.866728 0.498781i \(-0.166219\pi\)
−0.865321 + 0.501218i \(0.832885\pi\)
\(660\) 0 0
\(661\) 4.41600e6 7.64875e6i 0.393121 0.680905i −0.599739 0.800196i \(-0.704729\pi\)
0.992859 + 0.119291i \(0.0380621\pi\)
\(662\) 571493. 2.23212e6i 0.0506834 0.197958i
\(663\) 0 0
\(664\) −3.98001e6 + 1.71260e7i −0.350319 + 1.50742i
\(665\) 4.47961e6i 0.392813i
\(666\) 0 0
\(667\) 1.13015e7i 0.983608i
\(668\) 5.52335e6 + 3.02671e6i 0.478918 + 0.262439i
\(669\) 0 0
\(670\) 7.96970e6 + 2.04049e6i 0.685891 + 0.175610i
\(671\) −117685. + 203837.i −0.0100906 + 0.0174774i
\(672\) 0 0
\(673\) 3.33892e6 + 5.78318e6i 0.284163 + 0.492186i 0.972406 0.233295i \(-0.0749508\pi\)
−0.688242 + 0.725481i \(0.741617\pi\)
\(674\) −4.41691e6 1.57781e7i −0.374514 1.33784i
\(675\) 0 0
\(676\) 6.61811e6 4.02039e6i 0.557016 0.338377i
\(677\) −1.26099e7 + 7.28033e6i −1.05740 + 0.610491i −0.924712 0.380667i \(-0.875694\pi\)
−0.132689 + 0.991158i \(0.542361\pi\)
\(678\) 0 0
\(679\) 1.18970e7 + 6.86872e6i 0.990289 + 0.571744i
\(680\) 1.67485e7 5.09399e6i 1.38900 0.422460i
\(681\) 0 0
\(682\) 6.09760e6 + 5.96308e6i 0.501993 + 0.490919i
\(683\) −5.63380e6 −0.462114 −0.231057 0.972940i \(-0.574218\pi\)
−0.231057 + 0.972940i \(0.574218\pi\)
\(684\) 0 0
\(685\) 2.59834e7 2.11578
\(686\) −7.58887e6 7.42146e6i −0.615697 0.602115i
\(687\) 0 0
\(688\) −1.24319e7 + 7.93705e6i −1.00130 + 0.639275i
\(689\) 4.16183e6 + 2.40284e6i 0.333993 + 0.192831i
\(690\) 0 0
\(691\) −9.00873e6 + 5.20119e6i −0.717742 + 0.414389i −0.813921 0.580975i \(-0.802671\pi\)
0.0961788 + 0.995364i \(0.469338\pi\)
\(692\) 1.11937e7 + 1.84264e7i 0.888606 + 1.46277i
\(693\) 0 0
\(694\) −5.48138e6 1.95807e7i −0.432008 1.54322i
\(695\) 4.46787e6 + 7.73858e6i 0.350864 + 0.607714i
\(696\) 0 0
\(697\) 8.34762e6 1.44585e7i 0.650850 1.12730i
\(698\) 1.04887e7 + 2.68543e6i 0.814859 + 0.208629i
\(699\) 0 0
\(700\) 1.08948e7 1.98817e7i 0.840379 1.53358i
\(701\) 1.19679e7i 0.919862i −0.887955 0.459931i \(-0.847874\pi\)
0.887955 0.459931i \(-0.152126\pi\)
\(702\) 0 0
\(703\) 693798.i 0.0529474i
\(704\) 1.51463e7 1.01525e7i 1.15179 0.772044i
\(705\) 0 0
\(706\) 3.58150e6 1.39885e7i 0.270429 1.05624i
\(707\) 2.88503e6 4.99702e6i 0.217071 0.375978i
\(708\) 0 0
\(709\) −3.72698e6 6.45531e6i −0.278446 0.482283i 0.692553 0.721367i \(-0.256486\pi\)
−0.970999 + 0.239084i \(0.923153\pi\)
\(710\) 3.37827e6 945708.i 0.251506 0.0704062i
\(711\) 0 0
\(712\) −9.20670e6 + 9.84433e6i −0.680619 + 0.727757i
\(713\) 6.89402e6 3.98027e6i 0.507866 0.293216i
\(714\) 0 0
\(715\) −1.55689e7 8.98868e6i −1.13892 0.657553i
\(716\) 416682. + 1.86783e7i 0.0303754 + 1.36162i
\(717\) 0 0
\(718\) −1.06986e7 + 1.09399e7i −0.774487 + 0.791957i
\(719\) 1.53936e7 1.11050 0.555248 0.831685i \(-0.312623\pi\)
0.555248 + 0.831685i \(0.312623\pi\)
\(720\) 0 0
\(721\) −7.10870e6 −0.509275
\(722\) −9.31397e6 + 9.52407e6i −0.664954 + 0.679954i
\(723\) 0 0
\(724\) 444676. + 1.99332e7i 0.0315281 + 1.41329i
\(725\) −1.64782e7 9.51371e6i −1.16430 0.672210i
\(726\) 0 0
\(727\) −7.42385e6 + 4.28616e6i −0.520946 + 0.300768i −0.737322 0.675542i \(-0.763910\pi\)
0.216375 + 0.976310i \(0.430576\pi\)
\(728\) 6.36800e6 6.80903e6i 0.445322 0.476164i
\(729\) 0 0
\(730\) 5.42729e6 1.51931e6i 0.376943 0.105521i
\(731\) −7.75228e6 1.34273e7i −0.536582 0.929387i
\(732\) 0 0
\(733\) −8.79172e6 + 1.52277e7i −0.604386 + 1.04683i 0.387763 + 0.921759i \(0.373248\pi\)
−0.992148 + 0.125067i \(0.960085\pi\)
\(734\) 6.13209e6 2.39505e7i 0.420115 1.64087i
\(735\) 0 0
\(736\) −5.31430e6 1.61684e7i −0.361619 1.10020i
\(737\) 9.00758e6i 0.610857i
\(738\) 0 0
\(739\) 186950.i 0.0125926i −0.999980 0.00629629i \(-0.997996\pi\)
0.999980 0.00629629i \(-0.00200418\pi\)
\(740\) −2.75337e6 + 5.02455e6i −0.184836 + 0.337301i
\(741\) 0 0
\(742\) −1.04892e7 2.68557e6i −0.699412 0.179071i
\(743\) 3.19316e6 5.53072e6i 0.212202 0.367544i −0.740202 0.672385i \(-0.765270\pi\)
0.952403 + 0.304841i \(0.0986033\pi\)
\(744\) 0 0
\(745\) 1.67728e7 + 2.90513e7i 1.10717 + 1.91768i
\(746\) −3.31351e6 1.18365e7i −0.217992 0.778714i
\(747\) 0 0
\(748\) 9.95160e6 + 1.63817e7i 0.650338 + 1.07055i
\(749\) 1.75836e6 1.01519e6i 0.114526 0.0661214i
\(750\) 0 0
\(751\) 2.55553e7 + 1.47544e7i 1.65341 + 0.954598i 0.975655 + 0.219312i \(0.0703814\pi\)
0.677757 + 0.735286i \(0.262952\pi\)
\(752\) 1.35882e6 + 2.12833e6i 0.0876228 + 0.137245i
\(753\) 0 0
\(754\) −5.59407e6 5.47067e6i −0.358344 0.350439i
\(755\) −3.32341e7 −2.12186
\(756\) 0 0
\(757\) −2.98899e7 −1.89576 −0.947882 0.318621i \(-0.896780\pi\)
−0.947882 + 0.318621i \(0.896780\pi\)
\(758\) −3.52956e6 3.45170e6i −0.223125 0.218203i
\(759\) 0 0
\(760\) 5.41679e6 1.64750e6i 0.340180 0.103464i
\(761\) −1.12672e7 6.50513e6i −0.705269 0.407187i 0.104038 0.994573i \(-0.466824\pi\)
−0.809307 + 0.587386i \(0.800157\pi\)
\(762\) 0 0
\(763\) 2.70248e6 1.56028e6i 0.168055 0.0970265i
\(764\) −5.06323e6 + 3.07583e6i −0.313830 + 0.190646i
\(765\) 0 0
\(766\) −2.49258e6 8.90402e6i −0.153489 0.548295i
\(767\) −7.14825e6 1.23811e7i −0.438744 0.759927i
\(768\) 0 0
\(769\) −1.45635e6 + 2.52248e6i −0.0888077 + 0.153819i −0.907007 0.421115i \(-0.861639\pi\)
0.818200 + 0.574934i \(0.194972\pi\)
\(770\) 3.92387e7 + 1.00463e7i 2.38500 + 0.610634i
\(771\) 0 0
\(772\) −8.14766e6 4.46479e6i −0.492028 0.269623i
\(773\) 6.84734e6i 0.412167i 0.978534 + 0.206084i \(0.0660719\pi\)
−0.978534 + 0.206084i \(0.933928\pi\)
\(774\) 0 0
\(775\) 1.34025e7i 0.801551i
\(776\) −3.93030e6 + 1.69121e7i −0.234300 + 1.00819i
\(777\) 0 0
\(778\) −145690. + 569031.i −0.00862939 + 0.0337044i
\(779\) 2.69978e6 4.67616e6i 0.159399 0.276087i
\(780\) 0 0
\(781\) 1.92055e6 + 3.32649e6i 0.112667 + 0.195146i
\(782\) 1.72283e7 4.82286e6i 1.00745 0.282025i
\(783\) 0 0
\(784\) −1.74885e6 + 3.36753e6i −0.101616 + 0.195669i
\(785\) 3.06015e7 1.76678e7i 1.77243 1.02331i
\(786\) 0 0
\(787\) 2.80432e7 + 1.61907e7i 1.61395 + 0.931814i 0.988443 + 0.151596i \(0.0484413\pi\)
0.625507 + 0.780218i \(0.284892\pi\)
\(788\) −7.44120e6 + 166001.i −0.426901 + 0.00952346i
\(789\) 0 0
\(790\) 2.63872e7 2.69824e7i 1.50427 1.53820i
\(791\) −2.14098e7 −1.21667
\(792\) 0 0
\(793\) −152099. −0.00858904
\(794\) 1.31913e7 1.34889e7i 0.742570 0.759320i
\(795\) 0 0
\(796\) −1.67641e7 + 373979.i −0.937771 + 0.0209201i
\(797\) 4.17052e6 + 2.40785e6i 0.232565 + 0.134271i 0.611755 0.791047i \(-0.290464\pi\)
−0.379190 + 0.925319i \(0.623797\pi\)
\(798\) 0 0
\(799\) −2.29876e6 + 1.32719e6i −0.127387 + 0.0735471i
\(800\) 2.80480e7 + 5.86214e6i 1.54945 + 0.323840i
\(801\) 0 0
\(802\) 906797. 253847.i 0.0497822 0.0139360i
\(803\) 3.08543e6 + 5.34411e6i 0.168860 + 0.292474i
\(804\) 0 0
\(805\) 1.89030e7 3.27409e7i 1.02811 1.78074i
\(806\) −1.36699e6 + 5.33914e6i −0.0741185 + 0.289490i
\(807\) 0 0
\(808\) 7.10351e6 + 1.65083e6i 0.382776 + 0.0889555i
\(809\) 7.74333e6i 0.415965i 0.978133 + 0.207982i \(0.0666897\pi\)
−0.978133 + 0.207982i \(0.933310\pi\)
\(810\) 0 0
\(811\) 2.68630e7i 1.43417i −0.696984 0.717087i \(-0.745475\pi\)
0.696984 0.717087i \(-0.254525\pi\)
\(812\) 1.54600e7 + 8.47183e6i 0.822848 + 0.450907i
\(813\) 0 0
\(814\) −6.07726e6 1.55597e6i −0.321475 0.0823076i
\(815\) −6.95142e6 + 1.20402e7i −0.366589 + 0.634951i
\(816\) 0 0
\(817\) −2.50724e6 4.34267e6i −0.131414 0.227615i
\(818\) 7.83709e6 + 2.79958e7i 0.409517 + 1.46288i
\(819\) 0 0
\(820\) 3.81097e7 2.31510e7i 1.97925 1.20236i
\(821\) −1.13361e7 + 6.54492e6i −0.586958 + 0.338881i −0.763894 0.645342i \(-0.776715\pi\)
0.176936 + 0.984222i \(0.443382\pi\)
\(822\) 0 0
\(823\) −5.45404e6 3.14889e6i −0.280684 0.162053i 0.353049 0.935605i \(-0.385145\pi\)
−0.633733 + 0.773552i \(0.718478\pi\)
\(824\) −2.61442e6 8.59593e6i −0.134140 0.441037i
\(825\) 0 0
\(826\) 2.30293e7 + 2.25213e7i 1.17444 + 1.14853i
\(827\) 1.03982e7 0.528680 0.264340 0.964430i \(-0.414846\pi\)
0.264340 + 0.964430i \(0.414846\pi\)
\(828\) 0 0
\(829\) 7.24354e6 0.366070 0.183035 0.983106i \(-0.441408\pi\)
0.183035 + 0.983106i \(0.441408\pi\)
\(830\) −3.52926e7 3.45141e7i −1.77823 1.73901i
\(831\) 0 0
\(832\) 1.05756e7 + 5.19606e6i 0.529658 + 0.260235i
\(833\) −3.45441e6 1.99441e6i −0.172489 0.0995867i
\(834\) 0 0
\(835\) −1.53138e7 + 8.84144e6i −0.760094 + 0.438841i
\(836\) 3.21854e6 + 5.29816e6i 0.159274 + 0.262186i
\(837\) 0 0
\(838\) −5.05427e6 1.80549e7i −0.248627 0.888149i
\(839\) 1.22662e7 + 2.12456e7i 0.601595 + 1.04199i 0.992580 + 0.121596i \(0.0388011\pi\)
−0.390985 + 0.920397i \(0.627866\pi\)
\(840\) 0 0
\(841\) −2.85770e6 + 4.94968e6i −0.139324 + 0.241317i
\(842\) −1.97886e7 5.06649e6i −0.961909 0.246279i
\(843\) 0 0
\(844\) −6.91996e6 + 1.26280e7i −0.334385 + 0.610210i
\(845\) 2.17407e7i 1.04744i
\(846\) 0 0
\(847\) 2.12826e7i 1.01933i
\(848\) −610275. 1.36714e7i −0.0291431 0.652864i
\(849\) 0 0
\(850\) −7.47091e6 + 2.91797e7i −0.354671 + 1.38527i
\(851\) −2.92768e6 + 5.07089e6i −0.138580 + 0.240027i
\(852\) 0 0
\(853\) −2.26783e6 3.92799e6i −0.106718 0.184841i 0.807721 0.589565i \(-0.200701\pi\)
−0.914439 + 0.404724i \(0.867368\pi\)
\(854\) 330005. 92381.1i 0.0154837 0.00433449i
\(855\) 0 0
\(856\) 1.87426e6 + 1.75287e6i 0.0874271 + 0.0817644i
\(857\) −4.32468e6 + 2.49686e6i −0.201142 + 0.116129i −0.597188 0.802101i \(-0.703715\pi\)
0.396046 + 0.918231i \(0.370382\pi\)
\(858\) 0 0
\(859\) 2.79301e7 + 1.61254e7i 1.29149 + 0.745640i 0.978918 0.204256i \(-0.0654774\pi\)
0.312568 + 0.949895i \(0.398811\pi\)
\(860\) −923567. 4.14001e7i −0.0425816 1.90878i
\(861\) 0 0
\(862\) 2.97853e7 3.04571e7i 1.36532 1.39611i
\(863\) 2.09873e7 0.959247 0.479624 0.877474i \(-0.340773\pi\)
0.479624 + 0.877474i \(0.340773\pi\)
\(864\) 0 0
\(865\) −6.05312e7 −2.75067
\(866\) −8.88266e6 + 9.08302e6i −0.402483 + 0.411562i
\(867\) 0 0
\(868\) −276945. 1.24144e7i −0.0124766 0.559277i
\(869\) 3.57862e7 + 2.06612e7i 1.60756 + 0.928123i
\(870\) 0 0
\(871\) −5.04097e6 + 2.91040e6i −0.225148 + 0.129989i
\(872\) 2.88062e6 + 2.69404e6i 0.128290 + 0.119981i
\(873\) 0 0
\(874\) 5.57196e6 1.55981e6i 0.246734 0.0690705i
\(875\) 1.17200e7 + 2.02996e7i 0.517496 + 0.896330i
\(876\) 0 0
\(877\) −1.12204e7 + 1.94343e7i −0.492616 + 0.853236i −0.999964 0.00850516i \(-0.997293\pi\)
0.507348 + 0.861742i \(0.330626\pi\)
\(878\) 1.49863e6 5.85331e6i 0.0656082 0.256251i
\(879\) 0 0
\(880\) 2.28296e6 + 5.11427e7i 0.0993781 + 2.22627i
\(881\) 2.46288e7i 1.06906i −0.845149 0.534531i \(-0.820488\pi\)
0.845149 0.534531i \(-0.179512\pi\)
\(882\) 0 0
\(883\) 1.33073e7i 0.574365i 0.957876 + 0.287183i \(0.0927187\pi\)
−0.957876 + 0.287183i \(0.907281\pi\)
\(884\) −5.95237e6 + 1.08623e7i −0.256188 + 0.467510i
\(885\) 0 0
\(886\) 1.63784e6 + 419339.i 0.0700952 + 0.0179466i
\(887\) −1.14459e7 + 1.98249e7i −0.488474 + 0.846062i −0.999912 0.0132580i \(-0.995780\pi\)
0.511438 + 0.859320i \(0.329113\pi\)
\(888\) 0 0
\(889\) 1.84291e7 + 3.19201e7i 0.782077 + 1.35460i
\(890\) −1.02013e7 3.64414e7i −0.431700 1.54213i
\(891\) 0 0
\(892\) −641561. 1.05610e6i −0.0269977 0.0444418i
\(893\) −743463. + 429239.i −0.0311983 + 0.0180123i
\(894\) 0 0
\(895\) −4.54263e7 2.62269e7i −1.89561 1.09443i
\(896\) −2.61014e7 4.85039e6i −1.08616 0.201840i
\(897\) 0 0
\(898\) −3.39506e7 3.32017e7i −1.40494 1.37395i
\(899\) −1.04218e7 −0.430074
\(900\) 0 0
\(901\) 1.43855e7 0.590356
\(902\) 3.49057e7 + 3.41357e7i 1.42850 + 1.39699i
\(903\) 0 0
\(904\) −7.87405e6 2.58890e7i −0.320463 1.05365i
\(905\) −4.84782e7 2.79889e7i −1.96755 1.13596i
\(906\) 0 0
\(907\) −2.40173e7 + 1.38664e7i −0.969407 + 0.559688i −0.899055 0.437835i \(-0.855746\pi\)
−0.0703518 + 0.997522i \(0.522412\pi\)
\(908\) −2.44666e7 + 1.48631e7i −0.984827 + 0.598265i
\(909\) 0 0
\(910\) 7.05596e6 + 2.52054e7i 0.282457 + 1.00900i
\(911\) −1.93415e7 3.35005e7i −0.772138 1.33738i −0.936389 0.350964i \(-0.885854\pi\)
0.164250 0.986419i \(-0.447479\pi\)
\(912\) 0 0
\(913\) 2.70245e7 4.68078e7i 1.07295 1.85841i
\(914\) 2.17722e7 + 5.57437e6i 0.862059 + 0.220714i
\(915\) 0 0
\(916\) −4.00786e7 2.19624e7i −1.57824 0.864851i
\(917\) 905722.i 0.0355690i
\(918\) 0 0
\(919\) 1.70205e6i 0.0664790i −0.999447 0.0332395i \(-0.989418\pi\)
0.999447 0.0332395i \(-0.0105824\pi\)
\(920\) 4.65428e7 + 1.08163e7i 1.81294 + 0.421319i
\(921\) 0 0
\(922\) −3.43571e6 + 1.34191e7i −0.133103 + 0.519871i
\(923\) −1.24108e6 + 2.14962e6i −0.0479509 + 0.0830534i
\(924\) 0 0
\(925\) −4.92909e6 8.53743e6i −0.189414 0.328075i
\(926\) −3.63248e7 + 1.01687e7i −1.39212 + 0.389707i
\(927\) 0 0
\(928\) −4.55841e6 + 2.18102e7i −0.173757 + 0.831360i
\(929\) −2.05945e6 + 1.18902e6i −0.0782908 + 0.0452012i −0.538634 0.842540i \(-0.681060\pi\)
0.460344 + 0.887741i \(0.347726\pi\)
\(930\) 0 0
\(931\) −1.11723e6 645030.i −0.0422441 0.0243897i
\(932\) −1.21542e7 + 271140.i −0.458339 + 0.0102248i
\(933\) 0 0
\(934\) −1.32249e7 + 1.35232e7i −0.496048 + 0.507237i
\(935\) −5.38143e7 −2.01311
\(936\) 0 0
\(937\) −1.36658e6 −0.0508495 −0.0254248 0.999677i \(-0.508094\pi\)
−0.0254248 + 0.999677i \(0.508094\pi\)
\(938\) 9.16951e6 9.37635e6i 0.340282 0.347958i
\(939\) 0 0
\(940\) −7.08768e6 + 158114.i −0.261628 + 0.00583649i
\(941\) −1.57768e7 9.10873e6i −0.580824 0.335339i 0.180637 0.983550i \(-0.442184\pi\)
−0.761461 + 0.648211i \(0.775517\pi\)
\(942\) 0 0
\(943\) 3.94648e7 2.27850e7i 1.44521 0.834392i
\(944\) −1.87633e7 + 3.61301e7i −0.685299 + 1.31959i
\(945\) 0 0
\(946\) 4.36621e7 1.22227e7i 1.58627 0.444058i
\(947\) 1.49933e6 + 2.59692e6i 0.0543279 + 0.0940987i 0.891910 0.452212i \(-0.149365\pi\)
−0.837582 + 0.546311i \(0.816032\pi\)
\(948\) 0 0
\(949\) −1.99384e6 + 3.45343e6i −0.0718662 + 0.124476i
\(950\) −2.41624e6 + 9.43728e6i −0.0868622 + 0.339264i
\(951\) 0 0
\(952\) 6.31718e6 2.71829e7i 0.225908 0.972082i
\(953\) 5.86700e6i 0.209259i 0.994511 + 0.104629i \(0.0333656\pi\)
−0.994511 + 0.104629i \(0.966634\pi\)
\(954\) 0 0
\(955\) 1.66328e7i 0.590144i
\(956\) 2.12804e7 + 1.16613e7i 0.753070 + 0.412670i
\(957\) 0 0
\(958\) −2.54325e7 6.51153e6i −0.895315 0.229229i
\(959\) 2.07107e7 3.58721e7i 0.727192 1.25953i
\(960\) 0 0
\(961\) −1.06441e7 1.84362e7i −0.371794 0.643966i
\(962\) −1.09282e6 3.90380e6i −0.0380726 0.136003i
\(963\) 0 0
\(964\) −3.25763e7 + 1.97895e7i −1.12904 + 0.685872i
\(965\) 2.25899e7 1.30423e7i 0.780901 0.450853i
\(966\) 0 0
\(967\) −2.39133e7 1.38063e7i −0.822381 0.474802i 0.0288561 0.999584i \(-0.490814\pi\)
−0.851237 + 0.524782i \(0.824147\pi\)
\(968\) −2.57351e7 + 7.82725e6i −0.882751 + 0.268485i
\(969\) 0 0
\(970\) −3.48519e7 3.40831e7i −1.18932 1.16308i
\(971\) 3.42357e7 1.16528 0.582642 0.812729i \(-0.302019\pi\)
0.582642 + 0.812729i \(0.302019\pi\)
\(972\) 0 0
\(973\) 1.42449e7 0.482368
\(974\) −1.98827e7 1.94441e7i −0.671551 0.656737i
\(975\) 0 0
\(976\) 233077. + 365070.i 0.00783203 + 0.0122674i
\(977\) 2.71573e7 + 1.56793e7i 0.910229 + 0.525521i 0.880505 0.474037i \(-0.157204\pi\)
0.0297244 + 0.999558i \(0.490537\pi\)
\(978\) 0 0
\(979\) 3.58829e7 2.07170e7i 1.19655 0.690828i
\(980\) −5.53121e6 9.10513e6i −0.183973 0.302845i
\(981\) 0 0
\(982\) −1.05710e6 3.77618e6i −0.0349814 0.124961i
\(983\) −3.01652e6 5.22477e6i −0.0995686 0.172458i 0.811938 0.583744i \(-0.198413\pi\)
−0.911506 + 0.411286i \(0.865080\pi\)
\(984\) 0 0
\(985\) 1.04485e7 1.80973e7i 0.343132 0.594322i
\(986\) −2.26902e7 5.80939e6i −0.743268 0.190300i
\(987\) 0 0
\(988\) −1.92511e6 + 3.51308e6i −0.0627428 + 0.114497i
\(989\) 4.23200e7i 1.37580i
\(990\) 0 0
\(991\) 3.95516e7i 1.27932i −0.768657 0.639661i \(-0.779075\pi\)
0.768657 0.639661i \(-0.220925\pi\)
\(992\) 1.49098e7 4.90063e6i 0.481053 0.158115i
\(993\) 0 0
\(994\) 1.38712e6 5.41776e6i 0.0445294 0.173922i
\(995\) 2.35390e7 4.07708e7i 0.753756 1.30554i
\(996\) 0 0
\(997\) 8.17737e6 + 1.41636e7i 0.260541 + 0.451270i 0.966386 0.257096i \(-0.0827658\pi\)
−0.705845 + 0.708366i \(0.749432\pi\)
\(998\) 2.51656e6 704482.i 0.0799799 0.0223894i
\(999\) 0 0
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 108.6.h.a.71.7 56
3.2 odd 2 36.6.h.a.23.22 yes 56
4.3 odd 2 inner 108.6.h.a.71.3 56
9.2 odd 6 inner 108.6.h.a.35.3 56
9.7 even 3 36.6.h.a.11.26 yes 56
12.11 even 2 36.6.h.a.23.26 yes 56
36.7 odd 6 36.6.h.a.11.22 56
36.11 even 6 inner 108.6.h.a.35.7 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.6.h.a.11.22 56 36.7 odd 6
36.6.h.a.11.26 yes 56 9.7 even 3
36.6.h.a.23.22 yes 56 3.2 odd 2
36.6.h.a.23.26 yes 56 12.11 even 2
108.6.h.a.35.3 56 9.2 odd 6 inner
108.6.h.a.35.7 56 36.11 even 6 inner
108.6.h.a.71.3 56 4.3 odd 2 inner
108.6.h.a.71.7 56 1.1 even 1 trivial