Properties

Label 117.4.q.f.82.1
Level $117$
Weight $4$
Character 117.82
Analytic conductor $6.903$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [117,4,Mod(10,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.10");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.q (of order \(6\), degree \(2\), 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: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 32x^{10} + 823x^{8} - 5964x^{6} + 32913x^{4} - 47034x^{2} + 54756 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 82.1
Root \(-4.24667 + 2.45182i\) of defining polynomial
Character \(\chi\) \(=\) 117.82
Dual form 117.4.q.f.10.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.24667 - 2.45182i) q^{2} +(8.02279 + 13.8959i) q^{4} -5.61325i q^{5} +(2.78293 - 1.60672i) q^{7} -39.4526i q^{8} +O(q^{10})\) \(q+(-4.24667 - 2.45182i) q^{2} +(8.02279 + 13.8959i) q^{4} -5.61325i q^{5} +(2.78293 - 1.60672i) q^{7} -39.4526i q^{8} +(-13.7627 + 23.8376i) q^{10} +(-37.7991 - 21.8233i) q^{11} +(-46.8108 + 2.39816i) q^{13} -15.7576 q^{14} +(-32.5481 + 56.3750i) q^{16} +(32.9378 + 57.0500i) q^{17} +(-2.65374 + 1.53214i) q^{19} +(78.0011 - 45.0340i) q^{20} +(107.013 + 185.353i) q^{22} +(-81.8821 + 141.824i) q^{23} +93.4914 q^{25} +(204.670 + 104.587i) q^{26} +(44.6537 + 25.7808i) q^{28} +(-77.7243 + 134.622i) q^{29} +240.463i q^{31} +(3.10650 - 1.79354i) q^{32} -323.030i q^{34} +(-9.01895 - 15.6213i) q^{35} +(-275.104 - 158.831i) q^{37} +15.0261 q^{38} -221.457 q^{40} +(110.773 + 63.9551i) q^{41} +(-189.501 - 328.225i) q^{43} -700.336i q^{44} +(695.452 - 401.519i) q^{46} +79.4626i q^{47} +(-166.337 + 288.104i) q^{49} +(-397.027 - 229.224i) q^{50} +(-408.878 - 631.237i) q^{52} -571.746 q^{53} +(-122.500 + 212.176i) q^{55} +(-63.3895 - 109.794i) q^{56} +(660.139 - 381.131i) q^{58} +(-91.3986 + 52.7690i) q^{59} +(362.319 + 627.555i) q^{61} +(589.571 - 1021.17i) q^{62} +503.180 q^{64} +(13.4615 + 262.761i) q^{65} +(-261.732 - 151.111i) q^{67} +(-528.507 + 915.401i) q^{68} +88.4512i q^{70} +(868.960 - 501.694i) q^{71} -277.988i q^{73} +(778.849 + 1349.01i) q^{74} +(-42.5808 - 24.5840i) q^{76} -140.256 q^{77} -959.137 q^{79} +(316.447 + 182.701i) q^{80} +(-313.612 - 543.192i) q^{82} -410.957i q^{83} +(320.236 - 184.888i) q^{85} +1858.48i q^{86} +(-860.986 + 1491.27i) q^{88} +(195.894 + 113.100i) q^{89} +(-126.418 + 81.8860i) q^{91} -2627.69 q^{92} +(194.828 - 337.451i) q^{94} +(8.60027 + 14.8961i) q^{95} +(-769.427 + 444.229i) q^{97} +(1412.76 - 815.655i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 16 q^{4} - 18 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 16 q^{4} - 18 q^{7} - 56 q^{10} - 154 q^{13} - 92 q^{16} - 48 q^{19} + 292 q^{22} - 92 q^{25} + 552 q^{28} - 360 q^{37} - 448 q^{40} - 810 q^{43} + 996 q^{46} - 1068 q^{49} - 700 q^{52} + 460 q^{55} + 3048 q^{58} + 1294 q^{61} - 184 q^{64} + 2658 q^{67} + 1188 q^{76} - 6380 q^{79} - 1268 q^{82} - 3768 q^{85} - 5140 q^{88} + 342 q^{91} + 1660 q^{94} + 1686 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.24667 2.45182i −1.50142 0.866848i −0.999999 0.00164665i \(-0.999476\pi\)
−0.501425 0.865201i \(-0.667191\pi\)
\(3\) 0 0
\(4\) 8.02279 + 13.8959i 1.00285 + 1.73699i
\(5\) 5.61325i 0.502065i −0.967979 0.251032i \(-0.919230\pi\)
0.967979 0.251032i \(-0.0807701\pi\)
\(6\) 0 0
\(7\) 2.78293 1.60672i 0.150264 0.0867550i −0.422983 0.906138i \(-0.639017\pi\)
0.573247 + 0.819383i \(0.305684\pi\)
\(8\) 39.4526i 1.74357i
\(9\) 0 0
\(10\) −13.7627 + 23.8376i −0.435214 + 0.753812i
\(11\) −37.7991 21.8233i −1.03608 0.598179i −0.117357 0.993090i \(-0.537442\pi\)
−0.918720 + 0.394910i \(0.870776\pi\)
\(12\) 0 0
\(13\) −46.8108 + 2.39816i −0.998690 + 0.0511639i
\(14\) −15.7576 −0.300813
\(15\) 0 0
\(16\) −32.5481 + 56.3750i −0.508564 + 0.880859i
\(17\) 32.9378 + 57.0500i 0.469918 + 0.813921i 0.999408 0.0343944i \(-0.0109502\pi\)
−0.529491 + 0.848316i \(0.677617\pi\)
\(18\) 0 0
\(19\) −2.65374 + 1.53214i −0.0320426 + 0.0184998i −0.515936 0.856627i \(-0.672556\pi\)
0.483893 + 0.875127i \(0.339222\pi\)
\(20\) 78.0011 45.0340i 0.872079 0.503495i
\(21\) 0 0
\(22\) 107.013 + 185.353i 1.03706 + 1.79624i
\(23\) −81.8821 + 141.824i −0.742330 + 1.28575i 0.209102 + 0.977894i \(0.432946\pi\)
−0.951432 + 0.307859i \(0.900387\pi\)
\(24\) 0 0
\(25\) 93.4914 0.747931
\(26\) 204.670 + 104.587i 1.54381 + 0.788894i
\(27\) 0 0
\(28\) 44.6537 + 25.7808i 0.301384 + 0.174004i
\(29\) −77.7243 + 134.622i −0.497691 + 0.862027i −0.999996 0.00266388i \(-0.999152\pi\)
0.502305 + 0.864690i \(0.332485\pi\)
\(30\) 0 0
\(31\) 240.463i 1.39318i 0.717471 + 0.696588i \(0.245299\pi\)
−0.717471 + 0.696588i \(0.754701\pi\)
\(32\) 3.10650 1.79354i 0.0171611 0.00990799i
\(33\) 0 0
\(34\) 323.030i 1.62939i
\(35\) −9.01895 15.6213i −0.0435566 0.0754423i
\(36\) 0 0
\(37\) −275.104 158.831i −1.22234 0.705721i −0.256927 0.966431i \(-0.582710\pi\)
−0.965417 + 0.260710i \(0.916043\pi\)
\(38\) 15.0261 0.0641460
\(39\) 0 0
\(40\) −221.457 −0.875387
\(41\) 110.773 + 63.9551i 0.421949 + 0.243612i 0.695911 0.718128i \(-0.255001\pi\)
−0.273962 + 0.961741i \(0.588334\pi\)
\(42\) 0 0
\(43\) −189.501 328.225i −0.672060 1.16404i −0.977319 0.211773i \(-0.932076\pi\)
0.305259 0.952269i \(-0.401257\pi\)
\(44\) 700.336i 2.39954i
\(45\) 0 0
\(46\) 695.452 401.519i 2.22910 1.28697i
\(47\) 79.4626i 0.246613i 0.992369 + 0.123306i \(0.0393498\pi\)
−0.992369 + 0.123306i \(0.960650\pi\)
\(48\) 0 0
\(49\) −166.337 + 288.104i −0.484947 + 0.839953i
\(50\) −397.027 229.224i −1.12296 0.648342i
\(51\) 0 0
\(52\) −408.878 631.237i −1.09041 1.68340i
\(53\) −571.746 −1.48180 −0.740899 0.671616i \(-0.765600\pi\)
−0.740899 + 0.671616i \(0.765600\pi\)
\(54\) 0 0
\(55\) −122.500 + 212.176i −0.300325 + 0.520178i
\(56\) −63.3895 109.794i −0.151264 0.261997i
\(57\) 0 0
\(58\) 660.139 381.131i 1.49449 0.862845i
\(59\) −91.3986 + 52.7690i −0.201679 + 0.116440i −0.597439 0.801915i \(-0.703815\pi\)
0.395759 + 0.918354i \(0.370482\pi\)
\(60\) 0 0
\(61\) 362.319 + 627.555i 0.760495 + 1.31722i 0.942596 + 0.333936i \(0.108377\pi\)
−0.182101 + 0.983280i \(0.558290\pi\)
\(62\) 589.571 1021.17i 1.20767 2.09175i
\(63\) 0 0
\(64\) 503.180 0.982774
\(65\) 13.4615 + 262.761i 0.0256876 + 0.501407i
\(66\) 0 0
\(67\) −261.732 151.111i −0.477248 0.275539i 0.242021 0.970271i \(-0.422190\pi\)
−0.719269 + 0.694732i \(0.755523\pi\)
\(68\) −528.507 + 915.401i −0.942513 + 1.63248i
\(69\) 0 0
\(70\) 88.4512i 0.151028i
\(71\) 868.960 501.694i 1.45249 0.838594i 0.453865 0.891071i \(-0.350045\pi\)
0.998622 + 0.0524770i \(0.0167116\pi\)
\(72\) 0 0
\(73\) 277.988i 0.445699i −0.974853 0.222850i \(-0.928464\pi\)
0.974853 0.222850i \(-0.0715359\pi\)
\(74\) 778.849 + 1349.01i 1.22350 + 2.11917i
\(75\) 0 0
\(76\) −42.5808 24.5840i −0.0642678 0.0371050i
\(77\) −140.256 −0.207580
\(78\) 0 0
\(79\) −959.137 −1.36597 −0.682983 0.730434i \(-0.739318\pi\)
−0.682983 + 0.730434i \(0.739318\pi\)
\(80\) 316.447 + 182.701i 0.442248 + 0.255332i
\(81\) 0 0
\(82\) −313.612 543.192i −0.422349 0.731531i
\(83\) 410.957i 0.543475i −0.962371 0.271737i \(-0.912402\pi\)
0.962371 0.271737i \(-0.0875982\pi\)
\(84\) 0 0
\(85\) 320.236 184.888i 0.408641 0.235929i
\(86\) 1858.48i 2.33029i
\(87\) 0 0
\(88\) −860.986 + 1491.27i −1.04297 + 1.80648i
\(89\) 195.894 + 113.100i 0.233312 + 0.134703i 0.612099 0.790781i \(-0.290325\pi\)
−0.378787 + 0.925484i \(0.623659\pi\)
\(90\) 0 0
\(91\) −126.418 + 81.8860i −0.145629 + 0.0943295i
\(92\) −2627.69 −2.97778
\(93\) 0 0
\(94\) 194.828 337.451i 0.213776 0.370271i
\(95\) 8.60027 + 14.8961i 0.00928810 + 0.0160875i
\(96\) 0 0
\(97\) −769.427 + 444.229i −0.805397 + 0.464996i −0.845355 0.534205i \(-0.820611\pi\)
0.0399579 + 0.999201i \(0.487278\pi\)
\(98\) 1412.76 815.655i 1.45622 0.840750i
\(99\) 0 0
\(100\) 750.062 + 1299.15i 0.750062 + 1.29915i
\(101\) 930.180 1611.12i 0.916400 1.58725i 0.111561 0.993758i \(-0.464415\pi\)
0.804839 0.593494i \(-0.202252\pi\)
\(102\) 0 0
\(103\) −328.512 −0.314265 −0.157132 0.987578i \(-0.550225\pi\)
−0.157132 + 0.987578i \(0.550225\pi\)
\(104\) 94.6137 + 1846.81i 0.0892081 + 1.74129i
\(105\) 0 0
\(106\) 2428.01 + 1401.81i 2.22481 + 1.28449i
\(107\) 164.387 284.727i 0.148522 0.257248i −0.782159 0.623079i \(-0.785882\pi\)
0.930682 + 0.365830i \(0.119215\pi\)
\(108\) 0 0
\(109\) 201.673i 0.177218i 0.996066 + 0.0886092i \(0.0282422\pi\)
−0.996066 + 0.0886092i \(0.971758\pi\)
\(110\) 1040.43 600.693i 0.901830 0.520672i
\(111\) 0 0
\(112\) 209.183i 0.176482i
\(113\) 144.992 + 251.134i 0.120705 + 0.209068i 0.920046 0.391810i \(-0.128151\pi\)
−0.799341 + 0.600878i \(0.794818\pi\)
\(114\) 0 0
\(115\) 796.094 + 459.625i 0.645531 + 0.372698i
\(116\) −2494.27 −1.99644
\(117\) 0 0
\(118\) 517.520 0.403742
\(119\) 183.327 + 105.844i 0.141223 + 0.0815354i
\(120\) 0 0
\(121\) 287.013 + 497.121i 0.215637 + 0.373494i
\(122\) 3553.36i 2.63693i
\(123\) 0 0
\(124\) −3341.45 + 1929.19i −2.41993 + 1.39715i
\(125\) 1226.45i 0.877574i
\(126\) 0 0
\(127\) 376.283 651.742i 0.262911 0.455376i −0.704103 0.710098i \(-0.748651\pi\)
0.967014 + 0.254722i \(0.0819840\pi\)
\(128\) −2161.69 1248.05i −1.49272 0.861823i
\(129\) 0 0
\(130\) 587.074 1148.86i 0.396076 0.775092i
\(131\) −2200.41 −1.46756 −0.733782 0.679385i \(-0.762247\pi\)
−0.733782 + 0.679385i \(0.762247\pi\)
\(132\) 0 0
\(133\) −4.92345 + 8.52766i −0.00320990 + 0.00555971i
\(134\) 740.992 + 1283.44i 0.477701 + 0.827402i
\(135\) 0 0
\(136\) 2250.77 1299.48i 1.41913 0.819337i
\(137\) 315.299 182.038i 0.196626 0.113522i −0.398455 0.917188i \(-0.630453\pi\)
0.595081 + 0.803666i \(0.297120\pi\)
\(138\) 0 0
\(139\) −1226.79 2124.87i −0.748600 1.29661i −0.948494 0.316795i \(-0.897393\pi\)
0.199894 0.979817i \(-0.435940\pi\)
\(140\) 144.714 250.653i 0.0873614 0.151314i
\(141\) 0 0
\(142\) −4920.25 −2.90773
\(143\) 1821.74 + 930.917i 1.06533 + 0.544386i
\(144\) 0 0
\(145\) 755.670 + 436.286i 0.432793 + 0.249873i
\(146\) −681.575 + 1180.52i −0.386353 + 0.669183i
\(147\) 0 0
\(148\) 5097.08i 2.83093i
\(149\) 56.4171 32.5724i 0.0310192 0.0179090i −0.484410 0.874841i \(-0.660966\pi\)
0.515429 + 0.856932i \(0.327632\pi\)
\(150\) 0 0
\(151\) 250.204i 0.134843i 0.997725 + 0.0674216i \(0.0214773\pi\)
−0.997725 + 0.0674216i \(0.978523\pi\)
\(152\) 60.4468 + 104.697i 0.0322558 + 0.0558687i
\(153\) 0 0
\(154\) 595.621 + 343.882i 0.311666 + 0.179940i
\(155\) 1349.78 0.699464
\(156\) 0 0
\(157\) 1768.99 0.899242 0.449621 0.893219i \(-0.351559\pi\)
0.449621 + 0.893219i \(0.351559\pi\)
\(158\) 4073.13 + 2351.63i 2.05089 + 1.18408i
\(159\) 0 0
\(160\) −10.0676 17.4376i −0.00497445 0.00861600i
\(161\) 526.248i 0.257603i
\(162\) 0 0
\(163\) −2344.60 + 1353.66i −1.12665 + 0.650470i −0.943090 0.332538i \(-0.892095\pi\)
−0.183558 + 0.983009i \(0.558762\pi\)
\(164\) 2052.39i 0.977226i
\(165\) 0 0
\(166\) −1007.59 + 1745.20i −0.471110 + 0.815986i
\(167\) −3024.42 1746.15i −1.40142 0.809107i −0.406877 0.913483i \(-0.633382\pi\)
−0.994538 + 0.104375i \(0.966716\pi\)
\(168\) 0 0
\(169\) 2185.50 224.520i 0.994765 0.102194i
\(170\) −1813.25 −0.818058
\(171\) 0 0
\(172\) 3040.65 5266.56i 1.34795 2.33472i
\(173\) 1990.98 + 3448.48i 0.874979 + 1.51551i 0.856785 + 0.515674i \(0.172458\pi\)
0.0181944 + 0.999834i \(0.494208\pi\)
\(174\) 0 0
\(175\) 260.180 150.215i 0.112387 0.0648868i
\(176\) 2460.58 1420.61i 1.05382 0.608425i
\(177\) 0 0
\(178\) −554.598 960.593i −0.233533 0.404491i
\(179\) −1127.53 + 1952.93i −0.470812 + 0.815470i −0.999443 0.0333818i \(-0.989372\pi\)
0.528631 + 0.848852i \(0.322706\pi\)
\(180\) 0 0
\(181\) 890.108 0.365532 0.182766 0.983156i \(-0.441495\pi\)
0.182766 + 0.983156i \(0.441495\pi\)
\(182\) 737.624 37.7892i 0.300419 0.0153908i
\(183\) 0 0
\(184\) 5595.32 + 3230.46i 2.24181 + 1.29431i
\(185\) −891.559 + 1544.23i −0.354318 + 0.613696i
\(186\) 0 0
\(187\) 2875.25i 1.12438i
\(188\) −1104.20 + 637.512i −0.428363 + 0.247316i
\(189\) 0 0
\(190\) 84.3451i 0.0322055i
\(191\) 399.887 + 692.624i 0.151491 + 0.262390i 0.931776 0.363034i \(-0.118259\pi\)
−0.780285 + 0.625424i \(0.784926\pi\)
\(192\) 0 0
\(193\) 2332.56 + 1346.70i 0.869954 + 0.502268i 0.867333 0.497729i \(-0.165832\pi\)
0.00262073 + 0.999997i \(0.499166\pi\)
\(194\) 4356.67 1.61232
\(195\) 0 0
\(196\) −5337.95 −1.94532
\(197\) −2369.19 1367.85i −0.856842 0.494698i 0.00611178 0.999981i \(-0.498055\pi\)
−0.862953 + 0.505284i \(0.831388\pi\)
\(198\) 0 0
\(199\) −588.218 1018.82i −0.209536 0.362927i 0.742033 0.670364i \(-0.233862\pi\)
−0.951568 + 0.307437i \(0.900529\pi\)
\(200\) 3688.48i 1.30407i
\(201\) 0 0
\(202\) −7900.33 + 4561.26i −2.75181 + 1.58876i
\(203\) 499.526i 0.172709i
\(204\) 0 0
\(205\) 358.996 621.799i 0.122309 0.211846i
\(206\) 1395.08 + 805.451i 0.471845 + 0.272420i
\(207\) 0 0
\(208\) 1388.41 2717.01i 0.462830 0.905726i
\(209\) 133.745 0.0442648
\(210\) 0 0
\(211\) 1457.33 2524.16i 0.475481 0.823556i −0.524125 0.851641i \(-0.675608\pi\)
0.999606 + 0.0280849i \(0.00894088\pi\)
\(212\) −4587.00 7944.91i −1.48602 2.57386i
\(213\) 0 0
\(214\) −1396.19 + 806.093i −0.445990 + 0.257492i
\(215\) −1842.41 + 1063.72i −0.584425 + 0.337418i
\(216\) 0 0
\(217\) 386.358 + 669.192i 0.120865 + 0.209344i
\(218\) 494.466 856.440i 0.153621 0.266080i
\(219\) 0 0
\(220\) −3931.16 −1.20472
\(221\) −1678.66 2591.57i −0.510946 0.788813i
\(222\) 0 0
\(223\) −1282.92 740.694i −0.385250 0.222424i 0.294850 0.955543i \(-0.404730\pi\)
−0.680100 + 0.733120i \(0.738064\pi\)
\(224\) 5.76344 9.98258i 0.00171914 0.00297763i
\(225\) 0 0
\(226\) 1421.98i 0.418533i
\(227\) 3.79613 2.19169i 0.00110995 0.000640828i −0.499445 0.866346i \(-0.666463\pi\)
0.500555 + 0.865705i \(0.333129\pi\)
\(228\) 0 0
\(229\) 4689.58i 1.35326i 0.736324 + 0.676629i \(0.236560\pi\)
−0.736324 + 0.676629i \(0.763440\pi\)
\(230\) −2253.83 3903.75i −0.646144 1.11915i
\(231\) 0 0
\(232\) 5311.21 + 3066.43i 1.50301 + 0.867762i
\(233\) −4124.52 −1.15968 −0.579842 0.814729i \(-0.696886\pi\)
−0.579842 + 0.814729i \(0.696886\pi\)
\(234\) 0 0
\(235\) 446.044 0.123816
\(236\) −1466.54 846.710i −0.404508 0.233543i
\(237\) 0 0
\(238\) −519.020 898.970i −0.141358 0.244838i
\(239\) 3455.41i 0.935196i 0.883941 + 0.467598i \(0.154880\pi\)
−0.883941 + 0.467598i \(0.845120\pi\)
\(240\) 0 0
\(241\) 3559.08 2054.83i 0.951288 0.549226i 0.0578069 0.998328i \(-0.481589\pi\)
0.893481 + 0.449102i \(0.148256\pi\)
\(242\) 2814.81i 0.747698i
\(243\) 0 0
\(244\) −5813.62 + 10069.5i −1.52532 + 2.64194i
\(245\) 1617.20 + 933.691i 0.421711 + 0.243475i
\(246\) 0 0
\(247\) 120.549 78.0846i 0.0310541 0.0201150i
\(248\) 9486.89 2.42911
\(249\) 0 0
\(250\) −3007.02 + 5208.32i −0.760723 + 1.31761i
\(251\) 2516.11 + 4358.03i 0.632730 + 1.09592i 0.986991 + 0.160774i \(0.0513991\pi\)
−0.354261 + 0.935147i \(0.615268\pi\)
\(252\) 0 0
\(253\) 6190.13 3573.87i 1.53822 0.888093i
\(254\) −3195.90 + 1845.15i −0.789483 + 0.455808i
\(255\) 0 0
\(256\) 4107.27 + 7114.00i 1.00275 + 1.73682i
\(257\) 2816.99 4879.16i 0.683731 1.18426i −0.290103 0.956995i \(-0.593690\pi\)
0.973834 0.227261i \(-0.0729770\pi\)
\(258\) 0 0
\(259\) −1020.79 −0.244899
\(260\) −3543.30 + 2295.14i −0.845176 + 0.547455i
\(261\) 0 0
\(262\) 9344.42 + 5395.00i 2.20344 + 1.27215i
\(263\) 2556.31 4427.66i 0.599350 1.03810i −0.393568 0.919296i \(-0.628759\pi\)
0.992917 0.118808i \(-0.0379074\pi\)
\(264\) 0 0
\(265\) 3209.35i 0.743959i
\(266\) 41.8165 24.1428i 0.00963884 0.00556499i
\(267\) 0 0
\(268\) 4849.32i 1.10530i
\(269\) 3281.24 + 5683.28i 0.743721 + 1.28816i 0.950790 + 0.309836i \(0.100274\pi\)
−0.207069 + 0.978326i \(0.566392\pi\)
\(270\) 0 0
\(271\) −7067.90 4080.66i −1.58430 0.914694i −0.994222 0.107346i \(-0.965765\pi\)
−0.590075 0.807348i \(-0.700902\pi\)
\(272\) −4288.26 −0.955934
\(273\) 0 0
\(274\) −1785.29 −0.393626
\(275\) −3533.89 2040.29i −0.774914 0.447397i
\(276\) 0 0
\(277\) 1363.28 + 2361.28i 0.295710 + 0.512185i 0.975150 0.221546i \(-0.0711104\pi\)
−0.679440 + 0.733731i \(0.737777\pi\)
\(278\) 12031.5i 2.59569i
\(279\) 0 0
\(280\) −616.300 + 355.821i −0.131539 + 0.0759442i
\(281\) 1216.67i 0.258294i −0.991625 0.129147i \(-0.958776\pi\)
0.991625 0.129147i \(-0.0412238\pi\)
\(282\) 0 0
\(283\) −1624.16 + 2813.13i −0.341153 + 0.590895i −0.984647 0.174557i \(-0.944151\pi\)
0.643494 + 0.765451i \(0.277484\pi\)
\(284\) 13943.0 + 8049.98i 2.91325 + 1.68197i
\(285\) 0 0
\(286\) −5453.89 8419.87i −1.12761 1.74083i
\(287\) 411.033 0.0845383
\(288\) 0 0
\(289\) 286.696 496.573i 0.0583547 0.101073i
\(290\) −2139.39 3705.53i −0.433204 0.750331i
\(291\) 0 0
\(292\) 3862.89 2230.24i 0.774173 0.446969i
\(293\) −7986.99 + 4611.29i −1.59251 + 0.919435i −0.599634 + 0.800274i \(0.704687\pi\)
−0.992875 + 0.119161i \(0.961980\pi\)
\(294\) 0 0
\(295\) 296.206 + 513.044i 0.0584602 + 0.101256i
\(296\) −6266.30 + 10853.5i −1.23048 + 2.13125i
\(297\) 0 0
\(298\) −319.446 −0.0620974
\(299\) 3492.85 6835.25i 0.675574 1.32205i
\(300\) 0 0
\(301\) −1054.73 608.951i −0.201973 0.116609i
\(302\) 613.455 1062.53i 0.116889 0.202457i
\(303\) 0 0
\(304\) 199.473i 0.0376334i
\(305\) 3522.62 2033.79i 0.661327 0.381818i
\(306\) 0 0
\(307\) 2993.33i 0.556477i −0.960512 0.278238i \(-0.910249\pi\)
0.960512 0.278238i \(-0.0897505\pi\)
\(308\) −1125.25 1948.98i −0.208172 0.360564i
\(309\) 0 0
\(310\) −5732.07 3309.41i −1.05019 0.606329i
\(311\) 7261.04 1.32391 0.661955 0.749544i \(-0.269727\pi\)
0.661955 + 0.749544i \(0.269727\pi\)
\(312\) 0 0
\(313\) −3903.02 −0.704829 −0.352415 0.935844i \(-0.614639\pi\)
−0.352415 + 0.935844i \(0.614639\pi\)
\(314\) −7512.33 4337.25i −1.35014 0.779506i
\(315\) 0 0
\(316\) −7694.96 13328.1i −1.36986 2.37266i
\(317\) 4592.24i 0.813646i 0.913507 + 0.406823i \(0.133363\pi\)
−0.913507 + 0.406823i \(0.866637\pi\)
\(318\) 0 0
\(319\) 5875.81 3392.40i 1.03129 0.595417i
\(320\) 2824.48i 0.493416i
\(321\) 0 0
\(322\) 1290.26 2234.80i 0.223303 0.386772i
\(323\) −174.817 100.931i −0.0301148 0.0173868i
\(324\) 0 0
\(325\) −4376.40 + 224.208i −0.746951 + 0.0382671i
\(326\) 13275.7 2.25543
\(327\) 0 0
\(328\) 2523.19 4370.30i 0.424756 0.735699i
\(329\) 127.674 + 221.139i 0.0213949 + 0.0370571i
\(330\) 0 0
\(331\) −4430.30 + 2557.84i −0.735684 + 0.424747i −0.820498 0.571649i \(-0.806304\pi\)
0.0848138 + 0.996397i \(0.472970\pi\)
\(332\) 5710.62 3297.03i 0.944008 0.545023i
\(333\) 0 0
\(334\) 8562.46 + 14830.6i 1.40275 + 2.42963i
\(335\) −848.223 + 1469.17i −0.138339 + 0.239609i
\(336\) 0 0
\(337\) 6808.37 1.10052 0.550260 0.834993i \(-0.314529\pi\)
0.550260 + 0.834993i \(0.314529\pi\)
\(338\) −9831.56 4404.98i −1.58215 0.708873i
\(339\) 0 0
\(340\) 5138.38 + 2966.64i 0.819611 + 0.473203i
\(341\) 5247.70 9089.28i 0.833369 1.44344i
\(342\) 0 0
\(343\) 2171.24i 0.341796i
\(344\) −12949.3 + 7476.30i −2.02960 + 1.17179i
\(345\) 0 0
\(346\) 19526.1i 3.03389i
\(347\) −5459.09 9455.42i −0.844551 1.46281i −0.886010 0.463665i \(-0.846534\pi\)
0.0414594 0.999140i \(-0.486799\pi\)
\(348\) 0 0
\(349\) 8867.43 + 5119.62i 1.36007 + 0.785234i 0.989632 0.143625i \(-0.0458759\pi\)
0.370433 + 0.928859i \(0.379209\pi\)
\(350\) −1473.20 −0.224988
\(351\) 0 0
\(352\) −156.564 −0.0237070
\(353\) −748.273 432.015i −0.112823 0.0651384i 0.442527 0.896755i \(-0.354082\pi\)
−0.555350 + 0.831617i \(0.687416\pi\)
\(354\) 0 0
\(355\) −2816.14 4877.69i −0.421028 0.729242i
\(356\) 3629.50i 0.540346i
\(357\) 0 0
\(358\) 9576.47 5528.98i 1.41378 0.816244i
\(359\) 11430.0i 1.68036i −0.542305 0.840182i \(-0.682448\pi\)
0.542305 0.840182i \(-0.317552\pi\)
\(360\) 0 0
\(361\) −3424.81 + 5931.94i −0.499316 + 0.864840i
\(362\) −3779.99 2182.38i −0.548818 0.316860i
\(363\) 0 0
\(364\) −2152.10 1099.73i −0.309892 0.158356i
\(365\) −1560.42 −0.223770
\(366\) 0 0
\(367\) −4606.01 + 7977.85i −0.655128 + 1.13471i 0.326734 + 0.945116i \(0.394052\pi\)
−0.981862 + 0.189598i \(0.939281\pi\)
\(368\) −5330.21 9232.20i −0.755045 1.30778i
\(369\) 0 0
\(370\) 7572.31 4371.88i 1.06396 0.614279i
\(371\) −1591.13 + 918.638i −0.222661 + 0.128553i
\(372\) 0 0
\(373\) 559.064 + 968.327i 0.0776065 + 0.134418i 0.902217 0.431283i \(-0.141939\pi\)
−0.824610 + 0.565701i \(0.808606\pi\)
\(374\) −7049.58 + 12210.2i −0.974666 + 1.68817i
\(375\) 0 0
\(376\) 3135.00 0.429988
\(377\) 3315.49 6488.18i 0.452935 0.886361i
\(378\) 0 0
\(379\) −6987.09 4034.00i −0.946973 0.546735i −0.0548334 0.998496i \(-0.517463\pi\)
−0.892139 + 0.451761i \(0.850796\pi\)
\(380\) −137.996 + 239.017i −0.0186291 + 0.0322666i
\(381\) 0 0
\(382\) 3921.79i 0.525279i
\(383\) −1752.61 + 1011.87i −0.233822 + 0.134997i −0.612334 0.790599i \(-0.709769\pi\)
0.378512 + 0.925596i \(0.376436\pi\)
\(384\) 0 0
\(385\) 787.293i 0.104219i
\(386\) −6603.73 11438.0i −0.870779 1.50823i
\(387\) 0 0
\(388\) −12345.9 7127.92i −1.61538 0.932642i
\(389\) 9697.21 1.26393 0.631964 0.774998i \(-0.282249\pi\)
0.631964 + 0.774998i \(0.282249\pi\)
\(390\) 0 0
\(391\) −10788.1 −1.39534
\(392\) 11366.4 + 6562.42i 1.46452 + 0.845542i
\(393\) 0 0
\(394\) 6707.44 + 11617.6i 0.857655 + 1.48550i
\(395\) 5383.88i 0.685803i
\(396\) 0 0
\(397\) −2941.24 + 1698.13i −0.371830 + 0.214676i −0.674258 0.738496i \(-0.735536\pi\)
0.302427 + 0.953172i \(0.402203\pi\)
\(398\) 5768.80i 0.726543i
\(399\) 0 0
\(400\) −3042.97 + 5270.58i −0.380371 + 0.658822i
\(401\) −5758.99 3324.95i −0.717183 0.414066i 0.0965322 0.995330i \(-0.469225\pi\)
−0.813715 + 0.581264i \(0.802558\pi\)
\(402\) 0 0
\(403\) −576.670 11256.3i −0.0712803 1.39135i
\(404\) 29850.6 3.67604
\(405\) 0 0
\(406\) 1224.75 2121.32i 0.149712 0.259309i
\(407\) 6932.44 + 12007.3i 0.844295 + 1.46236i
\(408\) 0 0
\(409\) −2178.44 + 1257.72i −0.263366 + 0.152055i −0.625869 0.779928i \(-0.715256\pi\)
0.362503 + 0.931983i \(0.381922\pi\)
\(410\) −3049.07 + 1760.38i −0.367276 + 0.212047i
\(411\) 0 0
\(412\) −2635.59 4564.97i −0.315160 0.545873i
\(413\) −169.571 + 293.705i −0.0202034 + 0.0349934i
\(414\) 0 0
\(415\) −2306.81 −0.272860
\(416\) −141.116 + 91.4068i −0.0166317 + 0.0107730i
\(417\) 0 0
\(418\) −567.971 327.918i −0.0664602 0.0383708i
\(419\) −5953.72 + 10312.2i −0.694173 + 1.20234i 0.276286 + 0.961076i \(0.410896\pi\)
−0.970459 + 0.241267i \(0.922437\pi\)
\(420\) 0 0
\(421\) 2382.88i 0.275854i 0.990442 + 0.137927i \(0.0440440\pi\)
−0.990442 + 0.137927i \(0.955956\pi\)
\(422\) −12377.6 + 7146.18i −1.42780 + 0.824338i
\(423\) 0 0
\(424\) 22556.9i 2.58363i
\(425\) 3079.40 + 5333.69i 0.351466 + 0.608757i
\(426\) 0 0
\(427\) 2016.62 + 1164.29i 0.228550 + 0.131953i
\(428\) 5275.37 0.595782
\(429\) 0 0
\(430\) 10432.1 1.16996
\(431\) 248.155 + 143.273i 0.0277337 + 0.0160121i 0.513803 0.857908i \(-0.328236\pi\)
−0.486069 + 0.873920i \(0.661570\pi\)
\(432\) 0 0
\(433\) −424.177 734.696i −0.0470777 0.0815410i 0.841526 0.540216i \(-0.181658\pi\)
−0.888604 + 0.458675i \(0.848324\pi\)
\(434\) 3789.11i 0.419086i
\(435\) 0 0
\(436\) −2802.43 + 1617.98i −0.307826 + 0.177723i
\(437\) 501.818i 0.0549318i
\(438\) 0 0
\(439\) 34.8466 60.3561i 0.00378847 0.00656182i −0.864125 0.503277i \(-0.832127\pi\)
0.867913 + 0.496716i \(0.165461\pi\)
\(440\) 8370.88 + 4832.93i 0.906969 + 0.523639i
\(441\) 0 0
\(442\) 774.678 + 15121.3i 0.0833658 + 1.62725i
\(443\) −7331.02 −0.786247 −0.393123 0.919486i \(-0.628605\pi\)
−0.393123 + 0.919486i \(0.628605\pi\)
\(444\) 0 0
\(445\) 634.856 1099.60i 0.0676294 0.117138i
\(446\) 3632.09 + 6290.96i 0.385615 + 0.667905i
\(447\) 0 0
\(448\) 1400.31 808.472i 0.147676 0.0852605i
\(449\) −12309.0 + 7106.59i −1.29376 + 0.746950i −0.979318 0.202328i \(-0.935149\pi\)
−0.314438 + 0.949278i \(0.601816\pi\)
\(450\) 0 0
\(451\) −2791.42 4834.88i −0.291448 0.504802i
\(452\) −2326.48 + 4029.59i −0.242099 + 0.419327i
\(453\) 0 0
\(454\) −21.4945 −0.00222200
\(455\) 459.647 + 709.616i 0.0473595 + 0.0731149i
\(456\) 0 0
\(457\) 5112.33 + 2951.60i 0.523292 + 0.302123i 0.738281 0.674494i \(-0.235638\pi\)
−0.214988 + 0.976617i \(0.568971\pi\)
\(458\) 11498.0 19915.1i 1.17307 2.03181i
\(459\) 0 0
\(460\) 14749.9i 1.49504i
\(461\) −488.270 + 281.903i −0.0493297 + 0.0284805i −0.524462 0.851434i \(-0.675734\pi\)
0.475132 + 0.879914i \(0.342400\pi\)
\(462\) 0 0
\(463\) 17543.8i 1.76097i 0.474070 + 0.880487i \(0.342784\pi\)
−0.474070 + 0.880487i \(0.657216\pi\)
\(464\) −5059.56 8763.42i −0.506216 0.876792i
\(465\) 0 0
\(466\) 17515.5 + 10112.6i 1.74118 + 1.00527i
\(467\) 9125.81 0.904266 0.452133 0.891951i \(-0.350663\pi\)
0.452133 + 0.891951i \(0.350663\pi\)
\(468\) 0 0
\(469\) −971.174 −0.0956176
\(470\) −1894.20 1093.62i −0.185900 0.107329i
\(471\) 0 0
\(472\) 2081.87 + 3605.91i 0.203021 + 0.351643i
\(473\) 16542.1i 1.60805i
\(474\) 0 0
\(475\) −248.102 + 143.242i −0.0239657 + 0.0138366i
\(476\) 3396.66i 0.327071i
\(477\) 0 0
\(478\) 8472.02 14674.0i 0.810672 1.40413i
\(479\) −4304.28 2485.08i −0.410579 0.237048i 0.280459 0.959866i \(-0.409513\pi\)
−0.691039 + 0.722818i \(0.742847\pi\)
\(480\) 0 0
\(481\) 13258.7 + 6775.26i 1.25685 + 0.642257i
\(482\) −20152.3 −1.90438
\(483\) 0 0
\(484\) −4605.29 + 7976.60i −0.432503 + 0.749117i
\(485\) 2493.57 + 4318.99i 0.233458 + 0.404361i
\(486\) 0 0
\(487\) −4950.89 + 2858.40i −0.460670 + 0.265968i −0.712326 0.701849i \(-0.752358\pi\)
0.251656 + 0.967817i \(0.419025\pi\)
\(488\) 24758.7 14294.4i 2.29666 1.32598i
\(489\) 0 0
\(490\) −4578.48 7930.15i −0.422111 0.731118i
\(491\) 3022.11 5234.44i 0.277771 0.481114i −0.693059 0.720881i \(-0.743738\pi\)
0.970831 + 0.239767i \(0.0770709\pi\)
\(492\) 0 0
\(493\) −10240.3 −0.935496
\(494\) −703.382 + 36.0349i −0.0640620 + 0.00328196i
\(495\) 0 0
\(496\) −13556.1 7826.62i −1.22719 0.708520i
\(497\) 1612.17 2792.36i 0.145504 0.252021i
\(498\) 0 0
\(499\) 1101.16i 0.0987870i 0.998779 + 0.0493935i \(0.0157288\pi\)
−0.998779 + 0.0493935i \(0.984271\pi\)
\(500\) 17042.6 9839.54i 1.52433 0.880075i
\(501\) 0 0
\(502\) 24676.1i 2.19392i
\(503\) −670.986 1162.18i −0.0594787 0.103020i 0.834753 0.550625i \(-0.185611\pi\)
−0.894232 + 0.447605i \(0.852277\pi\)
\(504\) 0 0
\(505\) −9043.62 5221.34i −0.796903 0.460092i
\(506\) −35049.9 −3.07937
\(507\) 0 0
\(508\) 12075.4 1.05464
\(509\) −11668.5 6736.80i −1.01610 0.586647i −0.103130 0.994668i \(-0.532886\pi\)
−0.912973 + 0.408021i \(0.866219\pi\)
\(510\) 0 0
\(511\) −446.650 773.621i −0.0386666 0.0669725i
\(512\) 20312.2i 1.75328i
\(513\) 0 0
\(514\) −23925.6 + 13813.5i −2.05314 + 1.18538i
\(515\) 1844.02i 0.157781i
\(516\) 0 0
\(517\) 1734.14 3003.61i 0.147519 0.255510i
\(518\) 4334.96 + 2502.79i 0.367698 + 0.212290i
\(519\) 0 0
\(520\) 10366.6 531.091i 0.874241 0.0447882i
\(521\) −10374.9 −0.872423 −0.436211 0.899844i \(-0.643680\pi\)
−0.436211 + 0.899844i \(0.643680\pi\)
\(522\) 0 0
\(523\) 11147.7 19308.4i 0.932037 1.61433i 0.152202 0.988349i \(-0.451364\pi\)
0.779835 0.625985i \(-0.215303\pi\)
\(524\) −17653.4 30576.7i −1.47175 2.54914i
\(525\) 0 0
\(526\) −21711.6 + 12535.2i −1.79976 + 1.03909i
\(527\) −13718.4 + 7920.34i −1.13394 + 0.654678i
\(528\) 0 0
\(529\) −7325.85 12688.7i −0.602108 1.04288i
\(530\) 7868.74 13629.1i 0.644899 1.11700i
\(531\) 0 0
\(532\) −157.999 −0.0128762
\(533\) −5338.76 2728.13i −0.433860 0.221705i
\(534\) 0 0
\(535\) −1598.24 922.746i −0.129155 0.0745678i
\(536\) −5961.71 + 10326.0i −0.480423 + 0.832117i
\(537\) 0 0
\(538\) 32180.0i 2.57877i
\(539\) 12574.8 7260.04i 1.00489 0.580171i
\(540\) 0 0
\(541\) 10201.9i 0.810747i 0.914151 + 0.405373i \(0.132859\pi\)
−0.914151 + 0.405373i \(0.867141\pi\)
\(542\) 20010.0 + 34658.4i 1.58580 + 2.74669i
\(543\) 0 0
\(544\) 204.643 + 118.151i 0.0161287 + 0.00931188i
\(545\) 1132.04 0.0889751
\(546\) 0 0
\(547\) −9312.12 −0.727893 −0.363947 0.931420i \(-0.618571\pi\)
−0.363947 + 0.931420i \(0.618571\pi\)
\(548\) 5059.15 + 2920.90i 0.394373 + 0.227691i
\(549\) 0 0
\(550\) 10004.8 + 17328.9i 0.775650 + 1.34346i
\(551\) 476.337i 0.0368288i
\(552\) 0 0
\(553\) −2669.21 + 1541.07i −0.205256 + 0.118504i
\(554\) 13370.1i 1.02534i
\(555\) 0 0
\(556\) 19684.6 34094.8i 1.50147 2.60061i
\(557\) 124.988 + 72.1618i 0.00950791 + 0.00548940i 0.504746 0.863268i \(-0.331586\pi\)
−0.495239 + 0.868757i \(0.664919\pi\)
\(558\) 0 0
\(559\) 9657.81 + 14910.0i 0.730737 + 1.12813i
\(560\) 1174.20 0.0886054
\(561\) 0 0
\(562\) −2983.05 + 5166.80i −0.223901 + 0.387808i
\(563\) 7333.48 + 12702.0i 0.548968 + 0.950841i 0.998346 + 0.0574990i \(0.0183126\pi\)
−0.449377 + 0.893342i \(0.648354\pi\)
\(564\) 0 0
\(565\) 1409.68 813.877i 0.104966 0.0606019i
\(566\) 13794.5 7964.28i 1.02443 0.591456i
\(567\) 0 0
\(568\) −19793.1 34282.7i −1.46215 2.53252i
\(569\) 9377.03 16241.5i 0.690871 1.19662i −0.280682 0.959801i \(-0.590561\pi\)
0.971553 0.236822i \(-0.0761059\pi\)
\(570\) 0 0
\(571\) 13886.4 1.01773 0.508867 0.860845i \(-0.330065\pi\)
0.508867 + 0.860845i \(0.330065\pi\)
\(572\) 1679.52 + 32783.2i 0.122770 + 2.39639i
\(573\) 0 0
\(574\) −1745.52 1007.78i −0.126928 0.0732818i
\(575\) −7655.27 + 13259.3i −0.555212 + 0.961655i
\(576\) 0 0
\(577\) 9338.81i 0.673795i −0.941541 0.336898i \(-0.890622\pi\)
0.941541 0.336898i \(-0.109378\pi\)
\(578\) −2435.01 + 1405.85i −0.175230 + 0.101169i
\(579\) 0 0
\(580\) 14000.9i 1.00234i
\(581\) −660.295 1143.66i −0.0471492 0.0816647i
\(582\) 0 0
\(583\) 21611.5 + 12477.4i 1.53526 + 0.886381i
\(584\) −10967.3 −0.777110
\(585\) 0 0
\(586\) 45224.1 3.18804
\(587\) 3225.20 + 1862.07i 0.226777 + 0.130930i 0.609084 0.793105i \(-0.291537\pi\)
−0.382307 + 0.924035i \(0.624870\pi\)
\(588\) 0 0
\(589\) −368.422 638.126i −0.0257735 0.0446410i
\(590\) 2904.97i 0.202704i
\(591\) 0 0
\(592\) 17908.2 10339.3i 1.24328 0.717809i
\(593\) 19910.2i 1.37877i 0.724393 + 0.689387i \(0.242120\pi\)
−0.724393 + 0.689387i \(0.757880\pi\)
\(594\) 0 0
\(595\) 594.130 1029.06i 0.0409361 0.0709033i
\(596\) 905.245 + 522.644i 0.0622153 + 0.0359200i
\(597\) 0 0
\(598\) −31591.7 + 20463.2i −2.16034 + 1.39934i
\(599\) −14756.0 −1.00653 −0.503265 0.864132i \(-0.667868\pi\)
−0.503265 + 0.864132i \(0.667868\pi\)
\(600\) 0 0
\(601\) 3969.53 6875.42i 0.269418 0.466646i −0.699293 0.714835i \(-0.746502\pi\)
0.968712 + 0.248189i \(0.0798352\pi\)
\(602\) 2986.07 + 5172.03i 0.202165 + 0.350160i
\(603\) 0 0
\(604\) −3476.81 + 2007.34i −0.234221 + 0.135227i
\(605\) 2790.47 1611.08i 0.187518 0.108264i
\(606\) 0 0
\(607\) 1281.94 + 2220.39i 0.0857205 + 0.148472i 0.905698 0.423923i \(-0.139347\pi\)
−0.819977 + 0.572396i \(0.806014\pi\)
\(608\) −5.49589 + 9.51916i −0.000366592 + 0.000634956i
\(609\) 0 0
\(610\) −19945.9 −1.32391
\(611\) −190.564 3719.70i −0.0126177 0.246290i
\(612\) 0 0
\(613\) −15236.4 8796.72i −1.00390 0.579602i −0.0945004 0.995525i \(-0.530125\pi\)
−0.909400 + 0.415923i \(0.863459\pi\)
\(614\) −7339.09 + 12711.7i −0.482381 + 0.835508i
\(615\) 0 0
\(616\) 5533.47i 0.361932i
\(617\) 21200.0 12239.8i 1.38328 0.798635i 0.390730 0.920506i \(-0.372223\pi\)
0.992546 + 0.121871i \(0.0388894\pi\)
\(618\) 0 0
\(619\) 2927.43i 0.190086i −0.995473 0.0950431i \(-0.969701\pi\)
0.995473 0.0950431i \(-0.0302989\pi\)
\(620\) 10829.0 + 18756.4i 0.701457 + 1.21496i
\(621\) 0 0
\(622\) −30835.2 17802.7i −1.98775 1.14763i
\(623\) 726.879 0.0467445
\(624\) 0 0
\(625\) 4802.06 0.307332
\(626\) 16574.8 + 9569.47i 1.05825 + 0.610979i
\(627\) 0 0
\(628\) 14192.3 + 24581.7i 0.901805 + 1.56197i
\(629\) 20926.2i 1.32652i
\(630\) 0 0
\(631\) −8818.74 + 5091.50i −0.556369 + 0.321220i −0.751687 0.659520i \(-0.770759\pi\)
0.195318 + 0.980740i \(0.437426\pi\)
\(632\) 37840.4i 2.38166i
\(633\) 0 0
\(634\) 11259.3 19501.7i 0.705307 1.22163i
\(635\) −3658.39 2112.17i −0.228628 0.131999i
\(636\) 0 0
\(637\) 7095.44 13885.3i 0.441337 0.863665i
\(638\) −33270.2 −2.06454
\(639\) 0 0
\(640\) −7005.64 + 12134.1i −0.432691 + 0.749443i
\(641\) 8551.71 + 14812.0i 0.526946 + 0.912697i 0.999507 + 0.0313988i \(0.00999620\pi\)
−0.472561 + 0.881298i \(0.656670\pi\)
\(642\) 0 0
\(643\) 18822.1 10866.9i 1.15439 0.666485i 0.204434 0.978880i \(-0.434465\pi\)
0.949952 + 0.312395i \(0.101131\pi\)
\(644\) −7312.68 + 4221.98i −0.447453 + 0.258337i
\(645\) 0 0
\(646\) 494.926 + 857.237i 0.0301434 + 0.0522098i
\(647\) 11151.1 19314.3i 0.677584 1.17361i −0.298123 0.954528i \(-0.596360\pi\)
0.975706 0.219082i \(-0.0703062\pi\)
\(648\) 0 0
\(649\) 4606.38 0.278607
\(650\) 19134.9 + 9778.00i 1.15466 + 0.590038i
\(651\) 0 0
\(652\) −37620.6 21720.2i −2.25972 1.30465i
\(653\) 3488.57 6042.39i 0.209063 0.362109i −0.742356 0.670005i \(-0.766292\pi\)
0.951420 + 0.307897i \(0.0996251\pi\)
\(654\) 0 0
\(655\) 12351.5i 0.736812i
\(656\) −7210.93 + 4163.23i −0.429176 + 0.247785i
\(657\) 0 0
\(658\) 1252.14i 0.0741845i
\(659\) 5013.09 + 8682.92i 0.296331 + 0.513260i 0.975294 0.220913i \(-0.0709035\pi\)
−0.678963 + 0.734173i \(0.737570\pi\)
\(660\) 0 0
\(661\) 4079.54 + 2355.32i 0.240054 + 0.138595i 0.615202 0.788370i \(-0.289075\pi\)
−0.375148 + 0.926965i \(0.622408\pi\)
\(662\) 25085.4 1.47277
\(663\) 0 0
\(664\) −16213.3 −0.947589
\(665\) 47.8679 + 27.6365i 0.00279133 + 0.00161158i
\(666\) 0 0
\(667\) −12728.5 22046.3i −0.738902 1.27982i
\(668\) 56035.9i 3.24565i
\(669\) 0 0
\(670\) 7204.25 4159.37i 0.415409 0.239837i
\(671\) 31628.0i 1.81965i
\(672\) 0 0
\(673\) −7363.59 + 12754.1i −0.421762 + 0.730512i −0.996112 0.0880972i \(-0.971921\pi\)
0.574350 + 0.818610i \(0.305255\pi\)
\(674\) −28912.9 16692.9i −1.65235 0.953983i
\(675\) 0 0
\(676\) 20653.7 + 28568.2i 1.17511 + 1.62541i
\(677\) −2118.31 −0.120256 −0.0601279 0.998191i \(-0.519151\pi\)
−0.0601279 + 0.998191i \(0.519151\pi\)
\(678\) 0 0
\(679\) −1427.51 + 2472.52i −0.0806815 + 0.139744i
\(680\) −7294.33 12634.2i −0.411360 0.712497i
\(681\) 0 0
\(682\) −44570.5 + 25732.8i −2.50248 + 1.44481i
\(683\) −6123.42 + 3535.36i −0.343054 + 0.198063i −0.661622 0.749838i \(-0.730132\pi\)
0.318568 + 0.947900i \(0.396798\pi\)
\(684\) 0 0
\(685\) −1021.82 1769.85i −0.0569955 0.0987191i
\(686\) 5323.49 9220.55i 0.296285 0.513181i
\(687\) 0 0
\(688\) 24671.6 1.36714
\(689\) 26763.9 1371.14i 1.47986 0.0758146i
\(690\) 0 0
\(691\) 13496.1 + 7791.98i 0.743004 + 0.428974i 0.823160 0.567809i \(-0.192209\pi\)
−0.0801566 + 0.996782i \(0.525542\pi\)
\(692\) −31946.4 + 55332.9i −1.75494 + 3.03965i
\(693\) 0 0
\(694\) 53538.7i 2.92839i
\(695\) −11927.4 + 6886.31i −0.650983 + 0.375845i
\(696\) 0 0
\(697\) 8426.17i 0.457911i
\(698\) −25104.7 43482.6i −1.36136 2.35794i
\(699\) 0 0
\(700\) 4174.74 + 2410.29i 0.225415 + 0.130143i
\(701\) 13190.6 0.710703 0.355352 0.934733i \(-0.384361\pi\)
0.355352 + 0.934733i \(0.384361\pi\)
\(702\) 0 0
\(703\) 973.404 0.0522228
\(704\) −19019.7 10981.1i −1.01823 0.587875i
\(705\) 0 0
\(706\) 2118.44 + 3669.25i 0.112930 + 0.195601i
\(707\) 5978.17i 0.318009i
\(708\) 0 0
\(709\) 27336.9 15783.0i 1.44804 0.836025i 0.449673 0.893193i \(-0.351541\pi\)
0.998365 + 0.0571687i \(0.0182073\pi\)
\(710\) 27618.6i 1.45987i
\(711\) 0 0
\(712\) 4462.07 7728.53i 0.234864 0.406796i
\(713\) −34103.4 19689.6i −1.79128 1.03420i
\(714\) 0 0
\(715\) 5225.48 10225.9i 0.273317 0.534862i
\(716\) −36183.7 −1.88861
\(717\) 0 0
\(718\) −28024.2 + 48539.3i −1.45662 + 2.52294i
\(719\) −7767.67 13454.0i −0.402900 0.697844i 0.591174 0.806544i \(-0.298665\pi\)
−0.994075 + 0.108700i \(0.965331\pi\)
\(720\) 0 0
\(721\) −914.226 + 527.829i −0.0472227 + 0.0272640i
\(722\) 29088.0 16794.0i 1.49937 0.865661i
\(723\) 0 0
\(724\) 7141.16 + 12368.8i 0.366573 + 0.634923i
\(725\) −7266.56 + 12586.0i −0.372239 + 0.644736i
\(726\) 0 0
\(727\) 27639.6 1.41004 0.705018 0.709189i \(-0.250939\pi\)
0.705018 + 0.709189i \(0.250939\pi\)
\(728\) 3230.61 + 4987.51i 0.164470 + 0.253914i
\(729\) 0 0
\(730\) 6626.57 + 3825.85i 0.335973 + 0.193974i
\(731\) 12483.5 21622.0i 0.631626 1.09401i
\(732\) 0 0
\(733\) 1318.97i 0.0664629i 0.999448 + 0.0332314i \(0.0105798\pi\)
−0.999448 + 0.0332314i \(0.989420\pi\)
\(734\) 39120.4 22586.2i 1.96725 1.13579i
\(735\) 0 0
\(736\) 587.434i 0.0294200i
\(737\) 6595.47 + 11423.7i 0.329644 + 0.570960i
\(738\) 0 0
\(739\) 2572.74 + 1485.37i 0.128065 + 0.0739382i 0.562664 0.826686i \(-0.309777\pi\)
−0.434599 + 0.900624i \(0.643110\pi\)
\(740\) −28611.2 −1.42131
\(741\) 0 0
\(742\) 9009.32 0.445745
\(743\) 24935.1 + 14396.3i 1.23120 + 0.710833i 0.967280 0.253712i \(-0.0816515\pi\)
0.263919 + 0.964545i \(0.414985\pi\)
\(744\) 0 0
\(745\) −182.837 316.683i −0.00899146 0.0155737i
\(746\) 5482.88i 0.269092i
\(747\) 0 0
\(748\) 39954.2 23067.5i 1.95303 1.12758i
\(749\) 1056.50i 0.0515402i
\(750\) 0 0
\(751\) −3919.72 + 6789.16i −0.190456 + 0.329880i −0.945402 0.325908i \(-0.894330\pi\)
0.754945 + 0.655788i \(0.227663\pi\)
\(752\) −4479.70 2586.36i −0.217231 0.125419i
\(753\) 0 0
\(754\) −29987.6 + 19424.2i −1.44839 + 0.938179i
\(755\) 1404.46 0.0677000
\(756\) 0 0
\(757\) 1596.21 2764.71i 0.0766383 0.132741i −0.825159 0.564900i \(-0.808915\pi\)
0.901798 + 0.432159i \(0.142248\pi\)
\(758\) 19781.2 + 34262.1i 0.947872 + 1.64176i
\(759\) 0 0
\(760\) 587.690 339.303i 0.0280497 0.0161945i
\(761\) 22016.0 12710.9i 1.04872 0.605481i 0.126432 0.991975i \(-0.459648\pi\)
0.922292 + 0.386495i \(0.126314\pi\)
\(762\) 0 0
\(763\) 324.034 + 561.243i 0.0153746 + 0.0266296i
\(764\) −6416.42 + 11113.6i −0.303845 + 0.526276i
\(765\) 0 0
\(766\) 9923.64 0.468089
\(767\) 4151.89 2689.35i 0.195458 0.126606i
\(768\) 0 0
\(769\) −29384.8 16965.3i −1.37795 0.795559i −0.386036 0.922484i \(-0.626156\pi\)
−0.991912 + 0.126925i \(0.959489\pi\)
\(770\) 1930.30 3343.37i 0.0903417 0.156476i
\(771\) 0 0
\(772\) 43217.2i 2.01480i
\(773\) −35158.0 + 20298.5i −1.63589 + 0.944483i −0.653666 + 0.756783i \(0.726770\pi\)
−0.982226 + 0.187700i \(0.939897\pi\)
\(774\) 0 0
\(775\) 22481.2i 1.04200i
\(776\) 17526.0 + 30355.9i 0.810756 + 1.40427i
\(777\) 0 0
\(778\) −41180.8 23775.8i −1.89769 1.09563i
\(779\) −391.952 −0.0180271
\(780\) 0 0
\(781\) −43794.5 −2.00652
\(782\) 45813.4 + 26450.4i 2.09499 + 1.20954i
\(783\) 0 0
\(784\) −10827.9 18754.5i −0.493254 0.854340i
\(785\) 9929.81i 0.451478i
\(786\) 0 0
\(787\) 33815.0 19523.1i 1.53161 0.884274i 0.532319 0.846544i \(-0.321321\pi\)
0.999288 0.0377296i \(-0.0120126\pi\)
\(788\) 43896.0i 1.98443i
\(789\) 0 0
\(790\) 13200.3 22863.5i 0.594487 1.02968i
\(791\) 807.005 + 465.925i 0.0362754 + 0.0209436i
\(792\) 0 0
\(793\) −18465.4 28507.4i −0.826893 1.27658i
\(794\) 16654.0 0.744367
\(795\) 0 0
\(796\) 9438.30 16347.6i 0.420266 0.727922i
\(797\) 4037.40 + 6992.98i 0.179438 + 0.310795i 0.941688 0.336487i \(-0.109239\pi\)
−0.762250 + 0.647282i \(0.775905\pi\)
\(798\) 0 0
\(799\) −4533.34 + 2617.33i −0.200724 + 0.115888i
\(800\) 290.431 167.680i 0.0128354 0.00741049i
\(801\) 0 0
\(802\) 16304.3 + 28240.0i 0.717863 + 1.24338i
\(803\) −6066.62 + 10507.7i −0.266608 + 0.461779i
\(804\) 0 0
\(805\) 2953.96 0.129334
\(806\) −25149.4 + 49215.5i −1.09907 + 2.15080i
\(807\) 0 0
\(808\) −63562.8 36698.0i −2.76749 1.59781i
\(809\) −15064.0 + 26091.6i −0.654663 + 1.13391i 0.327316 + 0.944915i \(0.393856\pi\)
−0.981978 + 0.188994i \(0.939477\pi\)
\(810\) 0 0
\(811\) 707.812i 0.0306469i 0.999883 + 0.0153235i \(0.00487780\pi\)
−0.999883 + 0.0153235i \(0.995122\pi\)
\(812\) −6941.36 + 4007.60i −0.299993 + 0.173201i
\(813\) 0 0
\(814\) 67988.2i 2.92750i
\(815\) 7598.43 + 13160.9i 0.326578 + 0.565650i
\(816\) 0 0
\(817\) 1005.77 + 580.682i 0.0430691 + 0.0248660i
\(818\) 12334.8 0.527233
\(819\) 0 0
\(820\) 11520.6 0.490630
\(821\) −13527.5 7810.13i −0.575048 0.332004i 0.184115 0.982905i \(-0.441058\pi\)
−0.759163 + 0.650900i \(0.774392\pi\)
\(822\) 0 0
\(823\) 16355.0 + 28327.7i 0.692710 + 1.19981i 0.970947 + 0.239296i \(0.0769168\pi\)
−0.278236 + 0.960513i \(0.589750\pi\)
\(824\) 12960.7i 0.547944i
\(825\) 0 0
\(826\) 1440.22 831.511i 0.0606679 0.0350266i
\(827\) 28246.1i 1.18768i 0.804582 + 0.593842i \(0.202389\pi\)
−0.804582 + 0.593842i \(0.797611\pi\)
\(828\) 0 0
\(829\) −7049.60 + 12210.3i −0.295347 + 0.511556i −0.975066 0.221917i \(-0.928769\pi\)
0.679719 + 0.733473i \(0.262102\pi\)
\(830\) 9796.24 + 5655.86i 0.409678 + 0.236528i
\(831\) 0 0
\(832\) −23554.3 + 1206.71i −0.981487 + 0.0502825i
\(833\) −21915.1 −0.911541
\(834\) 0 0
\(835\) −9801.57 + 16976.8i −0.406224 + 0.703601i
\(836\) 1073.01 + 1858.51i 0.0443909 + 0.0768874i
\(837\) 0 0
\(838\) 50567.0 29194.9i 2.08450 1.20348i
\(839\) −9946.53 + 5742.63i −0.409288 + 0.236302i −0.690484 0.723348i \(-0.742602\pi\)
0.281196 + 0.959650i \(0.409269\pi\)
\(840\) 0 0
\(841\) 112.357 + 194.608i 0.00460687 + 0.00797933i
\(842\) 5842.39 10119.3i 0.239123 0.414174i
\(843\) 0 0
\(844\) 46767.3 1.90734
\(845\) −1260.29 12267.8i −0.0513079 0.499436i
\(846\) 0 0
\(847\) 1597.47 + 922.302i 0.0648050 + 0.0374152i
\(848\) 18609.2 32232.2i 0.753590 1.30526i
\(849\) 0 0
\(850\) 30200.5i 1.21867i
\(851\) 45052.1 26010.8i 1.81477 1.04776i
\(852\) 0 0
\(853\) 11836.8i 0.475128i 0.971372 + 0.237564i \(0.0763489\pi\)
−0.971372 + 0.237564i \(0.923651\pi\)
\(854\) −5709.26 9888.74i −0.228767 0.396236i
\(855\) 0 0
\(856\) −11233.2 6485.49i −0.448532 0.258960i
\(857\) −31156.2 −1.24186 −0.620931 0.783865i \(-0.713245\pi\)
−0.620931 + 0.783865i \(0.713245\pi\)
\(858\) 0 0
\(859\) −1584.88 −0.0629515 −0.0314758 0.999505i \(-0.510021\pi\)
−0.0314758 + 0.999505i \(0.510021\pi\)
\(860\) −29562.5 17067.9i −1.17218 0.676758i
\(861\) 0 0
\(862\) −702.556 1216.86i −0.0277600 0.0480818i
\(863\) 19884.8i 0.784340i 0.919893 + 0.392170i \(0.128276\pi\)
−0.919893 + 0.392170i \(0.871724\pi\)
\(864\) 0 0
\(865\) 19357.2 11175.9i 0.760883 0.439296i
\(866\) 4160.02i 0.163237i
\(867\) 0 0
\(868\) −6199.34 + 10737.6i −0.242419 + 0.419881i
\(869\) 36254.5 + 20931.5i 1.41525 + 0.817093i
\(870\) 0 0
\(871\) 12614.2 + 6445.94i 0.490720 + 0.250760i
\(872\) 7956.54 0.308994
\(873\) 0 0
\(874\) −1230.37 + 2131.06i −0.0476175 + 0.0824760i
\(875\) −1970.56 3413.12i −0.0761340 0.131868i
\(876\) 0 0
\(877\) 4748.79 2741.72i 0.182845 0.105566i −0.405784 0.913969i \(-0.633001\pi\)
0.588629 + 0.808403i \(0.299668\pi\)
\(878\) −295.964 + 170.875i −0.0113762 + 0.00656805i
\(879\) 0 0
\(880\) −7974.27 13811.8i −0.305469 0.529088i
\(881\) 3290.56 5699.41i 0.125836 0.217955i −0.796223 0.605003i \(-0.793172\pi\)
0.922060 + 0.387048i \(0.126505\pi\)
\(882\) 0 0
\(883\) −6942.60 −0.264595 −0.132297 0.991210i \(-0.542235\pi\)
−0.132297 + 0.991210i \(0.542235\pi\)
\(884\) 22544.6 44118.1i 0.857755 1.67857i
\(885\) 0 0
\(886\) 31132.4 + 17974.3i 1.18049 + 0.681556i
\(887\) 3281.34 5683.45i 0.124213 0.215143i −0.797212 0.603699i \(-0.793693\pi\)
0.921425 + 0.388557i \(0.127026\pi\)
\(888\) 0 0
\(889\) 2418.34i 0.0912355i
\(890\) −5392.05 + 3113.10i −0.203081 + 0.117249i
\(891\) 0 0
\(892\) 23769.7i 0.892231i
\(893\) −121.748 210.873i −0.00456229 0.00790212i
\(894\) 0 0
\(895\) 10962.3 + 6329.09i 0.409419 + 0.236378i
\(896\) −8021.11 −0.299070
\(897\) 0 0
\(898\) 69696.2 2.58997
\(899\) −32371.7 18689.8i −1.20095 0.693371i
\(900\) 0 0
\(901\) −18832.1 32618.1i −0.696323 1.20607i
\(902\) 27376.2i 1.01056i
\(903\) 0 0
\(904\) 9907.88 5720.31i 0.364526 0.210459i
\(905\) 4996.40i 0.183521i
\(906\) 0 0
\(907\) −826.163 + 1430.96i −0.0302451 + 0.0523860i −0.880752 0.473578i \(-0.842962\pi\)
0.850507 + 0.525964i \(0.176295\pi\)
\(908\) 60.9111 + 35.1670i 0.00222622 + 0.00128531i
\(909\) 0 0
\(910\) −212.120 4140.47i −0.00772717 0.150830i
\(911\) 506.240 0.0184110 0.00920552 0.999958i \(-0.497070\pi\)
0.00920552 + 0.999958i \(0.497070\pi\)
\(912\) 0 0
\(913\) −8968.44 + 15533.8i −0.325095 + 0.563082i
\(914\) −14473.6 25069.0i −0.523789 0.907229i
\(915\) 0 0
\(916\) −65165.9 + 37623.5i −2.35059 + 1.35711i
\(917\) −6123.59 + 3535.46i −0.220522 + 0.127318i
\(918\) 0 0
\(919\) 1234.64 + 2138.47i 0.0443168 + 0.0767590i 0.887333 0.461129i \(-0.152556\pi\)
−0.843016 + 0.537888i \(0.819222\pi\)
\(920\) 18133.4 31408.0i 0.649826 1.12553i
\(921\) 0 0
\(922\) 2764.69 0.0987531
\(923\) −39473.5 + 25568.6i −1.40768 + 0.911810i
\(924\) 0 0
\(925\) −25719.8 14849.3i −0.914229 0.527831i
\(926\) 43014.2 74502.8i 1.52650 2.64397i
\(927\) 0 0
\(928\) 557.606i 0.0197245i
\(929\) −36066.2 + 20822.9i −1.27373 + 0.735388i −0.975688 0.219164i \(-0.929667\pi\)
−0.298042 + 0.954553i \(0.596334\pi\)
\(930\) 0 0
\(931\) 1019.40i 0.0358857i
\(932\) −33090.2 57313.8i −1.16299 2.01435i
\(933\) 0 0
\(934\) −38754.3 22374.8i −1.35769 0.783860i
\(935\) −16139.5 −0.564512
\(936\) 0 0
\(937\) −33891.2 −1.18162 −0.590810 0.806811i \(-0.701192\pi\)
−0.590810 + 0.806811i \(0.701192\pi\)
\(938\) 4124.25 + 2381.14i 0.143563 + 0.0828859i
\(939\) 0 0
\(940\) 3578.52 + 6198.17i 0.124168 + 0.215066i
\(941\) 28351.3i 0.982173i 0.871111 + 0.491087i \(0.163400\pi\)
−0.871111 + 0.491087i \(0.836600\pi\)
\(942\) 0 0
\(943\) −18140.7 + 10473.5i −0.626451 + 0.361681i
\(944\) 6870.13i 0.236868i
\(945\) 0 0
\(946\) 40558.2 70248.9i 1.39393 2.41437i
\(947\) 3232.62 + 1866.36i 0.110925 + 0.0640427i 0.554436 0.832226i \(-0.312934\pi\)
−0.443511 + 0.896269i \(0.646267\pi\)
\(948\) 0 0
\(949\) 666.660 + 13012.8i 0.0228037 + 0.445115i
\(950\) 1404.81 0.0479768
\(951\) 0 0
\(952\) 4175.83 7232.74i 0.142163 0.246234i
\(953\) −4826.05 8358.96i −0.164041 0.284127i 0.772273 0.635290i \(-0.219120\pi\)
−0.936314 + 0.351163i \(0.885786\pi\)
\(954\) 0 0
\(955\) 3887.88 2244.67i 0.131737 0.0760583i
\(956\) −48016.0 + 27722.0i −1.62442 + 0.937860i
\(957\) 0 0
\(958\) 12185.9 + 21106.6i 0.410969 + 0.711819i
\(959\) 584.969 1013.20i 0.0196972 0.0341166i
\(960\) 0 0
\(961\) −28031.5 −0.940939
\(962\) −39693.7 61280.2i −1.33033 2.05380i
\(963\) 0 0
\(964\) 57107.5 + 32971.0i 1.90800 + 1.10158i
\(965\) 7559.38 13093.2i 0.252171 0.436773i
\(966\) 0 0
\(967\) 36196.6i 1.20373i 0.798598 + 0.601864i \(0.205575\pi\)
−0.798598 + 0.601864i \(0.794425\pi\)
\(968\) 19612.7 11323.4i 0.651216 0.375979i
\(969\) 0 0
\(970\) 24455.1i 0.809490i
\(971\) −2625.49 4547.48i −0.0867723 0.150294i 0.819373 0.573261i \(-0.194322\pi\)
−0.906145 + 0.422967i \(0.860989\pi\)
\(972\) 0 0
\(973\) −6828.16 3942.24i −0.224975 0.129890i
\(974\) 28033.1 0.922215
\(975\) 0 0
\(976\) −47171.2 −1.54704
\(977\) 20069.9 + 11587.4i 0.657210 + 0.379440i 0.791213 0.611541i \(-0.209450\pi\)
−0.134003 + 0.990981i \(0.542783\pi\)
\(978\) 0 0
\(979\) −4936.41 8550.12i −0.161153 0.279124i
\(980\) 29963.2i 0.976674i
\(981\) 0 0
\(982\) −25667.8 + 14819.3i −0.834105 + 0.481571i
\(983\) 33285.5i 1.08000i 0.841664 + 0.540001i \(0.181576\pi\)
−0.841664 + 0.540001i \(0.818424\pi\)
\(984\) 0 0
\(985\) −7678.10 + 13298.9i −0.248370 + 0.430190i
\(986\) 43487.1 + 25107.3i 1.40458 + 0.810932i
\(987\) 0 0
\(988\) 2052.20 + 1048.68i 0.0660821 + 0.0337682i
\(989\) 62066.8 1.99556
\(990\) 0 0
\(991\) 7767.68 13454.0i 0.248990 0.431262i −0.714256 0.699884i \(-0.753235\pi\)
0.963246 + 0.268622i \(0.0865682\pi\)
\(992\) 431.280 + 746.998i 0.0138036 + 0.0239085i
\(993\) 0 0
\(994\) −13692.7 + 7905.48i −0.436927 + 0.252260i
\(995\) −5718.91 + 3301.81i −0.182213 + 0.105201i
\(996\) 0 0
\(997\) −13151.2 22778.5i −0.417756 0.723574i 0.577958 0.816067i \(-0.303850\pi\)
−0.995713 + 0.0924929i \(0.970516\pi\)
\(998\) 2699.84 4676.27i 0.0856333 0.148321i
\(999\) 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 117.4.q.f.82.1 yes 12
3.2 odd 2 inner 117.4.q.f.82.6 yes 12
13.6 odd 12 1521.4.a.bl.1.11 12
13.7 odd 12 1521.4.a.bl.1.2 12
13.10 even 6 inner 117.4.q.f.10.1 12
39.20 even 12 1521.4.a.bl.1.12 12
39.23 odd 6 inner 117.4.q.f.10.6 yes 12
39.32 even 12 1521.4.a.bl.1.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.q.f.10.1 12 13.10 even 6 inner
117.4.q.f.10.6 yes 12 39.23 odd 6 inner
117.4.q.f.82.1 yes 12 1.1 even 1 trivial
117.4.q.f.82.6 yes 12 3.2 odd 2 inner
1521.4.a.bl.1.1 12 39.32 even 12
1521.4.a.bl.1.2 12 13.7 odd 12
1521.4.a.bl.1.11 12 13.6 odd 12
1521.4.a.bl.1.12 12 39.20 even 12