# Properties

 Label 1008.6.a.d.1.1 Level $1008$ Weight $6$ Character 1008.1 Self dual yes Analytic conductor $161.667$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,6,Mod(1,1008)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1008.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 1008.a (trivial)

## 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: yes Analytic conductor: $$161.666890371$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 42) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1008.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-76.0000 q^{5} +49.0000 q^{7} +O(q^{10})$$ $$q-76.0000 q^{5} +49.0000 q^{7} +650.000 q^{11} +762.000 q^{13} +556.000 q^{17} +2452.00 q^{19} -2950.00 q^{23} +2651.00 q^{25} +674.000 q^{29} +3024.00 q^{31} -3724.00 q^{35} +7730.00 q^{37} +17016.0 q^{41} -21836.0 q^{43} -23940.0 q^{47} +2401.00 q^{49} -15594.0 q^{53} -49400.0 q^{55} +5608.00 q^{59} +150.000 q^{61} -57912.0 q^{65} +43784.0 q^{67} -39178.0 q^{71} -23570.0 q^{73} +31850.0 q^{77} +17892.0 q^{79} +38972.0 q^{83} -42256.0 q^{85} -6024.00 q^{89} +37338.0 q^{91} -186352. q^{95} +108430. q^{97} +O(q^{100})$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −76.0000 −1.35953 −0.679765 0.733430i $$-0.737918\pi$$
−0.679765 + 0.733430i $$0.737918\pi$$
$$6$$ 0 0
$$7$$ 49.0000 0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 650.000 1.61969 0.809845 0.586645i $$-0.199551\pi$$
0.809845 + 0.586645i $$0.199551\pi$$
$$12$$ 0 0
$$13$$ 762.000 1.25054 0.625269 0.780410i $$-0.284989\pi$$
0.625269 + 0.780410i $$0.284989\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 556.000 0.466608 0.233304 0.972404i $$-0.425046\pi$$
0.233304 + 0.972404i $$0.425046\pi$$
$$18$$ 0 0
$$19$$ 2452.00 1.55825 0.779124 0.626870i $$-0.215664\pi$$
0.779124 + 0.626870i $$0.215664\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −2950.00 −1.16279 −0.581397 0.813620i $$-0.697493\pi$$
−0.581397 + 0.813620i $$0.697493\pi$$
$$24$$ 0 0
$$25$$ 2651.00 0.848320
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 674.000 0.148821 0.0744106 0.997228i $$-0.476292\pi$$
0.0744106 + 0.997228i $$0.476292\pi$$
$$30$$ 0 0
$$31$$ 3024.00 0.565168 0.282584 0.959243i $$-0.408808\pi$$
0.282584 + 0.959243i $$0.408808\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −3724.00 −0.513854
$$36$$ 0 0
$$37$$ 7730.00 0.928272 0.464136 0.885764i $$-0.346365\pi$$
0.464136 + 0.885764i $$0.346365\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 17016.0 1.58088 0.790438 0.612542i $$-0.209853\pi$$
0.790438 + 0.612542i $$0.209853\pi$$
$$42$$ 0 0
$$43$$ −21836.0 −1.80095 −0.900476 0.434907i $$-0.856781\pi$$
−0.900476 + 0.434907i $$0.856781\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −23940.0 −1.58081 −0.790405 0.612585i $$-0.790130\pi$$
−0.790405 + 0.612585i $$0.790130\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −15594.0 −0.762549 −0.381275 0.924462i $$-0.624515\pi$$
−0.381275 + 0.924462i $$0.624515\pi$$
$$54$$ 0 0
$$55$$ −49400.0 −2.20201
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 5608.00 0.209738 0.104869 0.994486i $$-0.466558\pi$$
0.104869 + 0.994486i $$0.466558\pi$$
$$60$$ 0 0
$$61$$ 150.000 0.00516139 0.00258069 0.999997i $$-0.499179\pi$$
0.00258069 + 0.999997i $$0.499179\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −57912.0 −1.70014
$$66$$ 0 0
$$67$$ 43784.0 1.19159 0.595797 0.803135i $$-0.296836\pi$$
0.595797 + 0.803135i $$0.296836\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −39178.0 −0.922351 −0.461176 0.887309i $$-0.652572\pi$$
−0.461176 + 0.887309i $$0.652572\pi$$
$$72$$ 0 0
$$73$$ −23570.0 −0.517669 −0.258835 0.965922i $$-0.583338\pi$$
−0.258835 + 0.965922i $$0.583338\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 31850.0 0.612185
$$78$$ 0 0
$$79$$ 17892.0 0.322546 0.161273 0.986910i $$-0.448440\pi$$
0.161273 + 0.986910i $$0.448440\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 38972.0 0.620951 0.310476 0.950581i $$-0.399512\pi$$
0.310476 + 0.950581i $$0.399512\pi$$
$$84$$ 0 0
$$85$$ −42256.0 −0.634368
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −6024.00 −0.0806139 −0.0403070 0.999187i $$-0.512834\pi$$
−0.0403070 + 0.999187i $$0.512834\pi$$
$$90$$ 0 0
$$91$$ 37338.0 0.472659
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −186352. −2.11848
$$96$$ 0 0
$$97$$ 108430. 1.17009 0.585046 0.811000i $$-0.301076\pi$$
0.585046 + 0.811000i $$0.301076\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 70424.0 0.686938 0.343469 0.939164i $$-0.388398\pi$$
0.343469 + 0.939164i $$0.388398\pi$$
$$102$$ 0 0
$$103$$ 31552.0 0.293045 0.146522 0.989207i $$-0.453192\pi$$
0.146522 + 0.989207i $$0.453192\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 108282. 0.914317 0.457159 0.889385i $$-0.348867\pi$$
0.457159 + 0.889385i $$0.348867\pi$$
$$108$$ 0 0
$$109$$ −72146.0 −0.581629 −0.290814 0.956779i $$-0.593926\pi$$
−0.290814 + 0.956779i $$0.593926\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −220906. −1.62746 −0.813732 0.581240i $$-0.802568\pi$$
−0.813732 + 0.581240i $$0.802568\pi$$
$$114$$ 0 0
$$115$$ 224200. 1.58085
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 27244.0 0.176361
$$120$$ 0 0
$$121$$ 261449. 1.62339
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 36024.0 0.206213
$$126$$ 0 0
$$127$$ 239652. 1.31847 0.659237 0.751935i $$-0.270879\pi$$
0.659237 + 0.751935i $$0.270879\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −274172. −1.39587 −0.697935 0.716161i $$-0.745897\pi$$
−0.697935 + 0.716161i $$0.745897\pi$$
$$132$$ 0 0
$$133$$ 120148. 0.588962
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 391154. 1.78052 0.890259 0.455455i $$-0.150523\pi$$
0.890259 + 0.455455i $$0.150523\pi$$
$$138$$ 0 0
$$139$$ −339364. −1.48980 −0.744901 0.667175i $$-0.767503\pi$$
−0.744901 + 0.667175i $$0.767503\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 495300. 2.02548
$$144$$ 0 0
$$145$$ −51224.0 −0.202327
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 29334.0 0.108244 0.0541222 0.998534i $$-0.482764\pi$$
0.0541222 + 0.998534i $$0.482764\pi$$
$$150$$ 0 0
$$151$$ −71608.0 −0.255575 −0.127788 0.991802i $$-0.540788\pi$$
−0.127788 + 0.991802i $$0.540788\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −229824. −0.768362
$$156$$ 0 0
$$157$$ 296318. 0.959420 0.479710 0.877427i $$-0.340742\pi$$
0.479710 + 0.877427i $$0.340742\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −144550. −0.439494
$$162$$ 0 0
$$163$$ 480400. 1.41623 0.708115 0.706097i $$-0.249546\pi$$
0.708115 + 0.706097i $$0.249546\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 160180. 0.444444 0.222222 0.974996i $$-0.428669\pi$$
0.222222 + 0.974996i $$0.428669\pi$$
$$168$$ 0 0
$$169$$ 209351. 0.563843
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 8984.00 0.0228220 0.0114110 0.999935i $$-0.496368\pi$$
0.0114110 + 0.999935i $$0.496368\pi$$
$$174$$ 0 0
$$175$$ 129899. 0.320635
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 182886. 0.426627 0.213313 0.976984i $$-0.431575\pi$$
0.213313 + 0.976984i $$0.431575\pi$$
$$180$$ 0 0
$$181$$ 138330. 0.313848 0.156924 0.987611i $$-0.449842\pi$$
0.156924 + 0.987611i $$0.449842\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −587480. −1.26201
$$186$$ 0 0
$$187$$ 361400. 0.755760
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 327222. 0.649021 0.324511 0.945882i $$-0.394800\pi$$
0.324511 + 0.945882i $$0.394800\pi$$
$$192$$ 0 0
$$193$$ 786902. 1.52064 0.760322 0.649547i $$-0.225041\pi$$
0.760322 + 0.649547i $$0.225041\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −423098. −0.776740 −0.388370 0.921504i $$-0.626962\pi$$
−0.388370 + 0.921504i $$0.626962\pi$$
$$198$$ 0 0
$$199$$ −1.02392e6 −1.83288 −0.916439 0.400175i $$-0.868949\pi$$
−0.916439 + 0.400175i $$0.868949\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 33026.0 0.0562491
$$204$$ 0 0
$$205$$ −1.29322e6 −2.14925
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 1.59380e6 2.52388
$$210$$ 0 0
$$211$$ −461516. −0.713642 −0.356821 0.934173i $$-0.616139\pi$$
−0.356821 + 0.934173i $$0.616139\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1.65954e6 2.44845
$$216$$ 0 0
$$217$$ 148176. 0.213613
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 423672. 0.583511
$$222$$ 0 0
$$223$$ −995048. −1.33993 −0.669965 0.742393i $$-0.733691\pi$$
−0.669965 + 0.742393i $$0.733691\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −95568.0 −0.123097 −0.0615486 0.998104i $$-0.519604\pi$$
−0.0615486 + 0.998104i $$0.519604\pi$$
$$228$$ 0 0
$$229$$ −1.04409e6 −1.31567 −0.657836 0.753161i $$-0.728528\pi$$
−0.657836 + 0.753161i $$0.728528\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.16941e6 1.41116 0.705581 0.708629i $$-0.250686\pi$$
0.705581 + 0.708629i $$0.250686\pi$$
$$234$$ 0 0
$$235$$ 1.81944e6 2.14916
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −27342.0 −0.0309625 −0.0154812 0.999880i $$-0.504928\pi$$
−0.0154812 + 0.999880i $$0.504928\pi$$
$$240$$ 0 0
$$241$$ −907714. −1.00671 −0.503357 0.864078i $$-0.667902\pi$$
−0.503357 + 0.864078i $$0.667902\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −182476. −0.194218
$$246$$ 0 0
$$247$$ 1.86842e6 1.94865
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 44088.0 0.0441709 0.0220854 0.999756i $$-0.492969\pi$$
0.0220854 + 0.999756i $$0.492969\pi$$
$$252$$ 0 0
$$253$$ −1.91750e6 −1.88336
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 829200. 0.783117 0.391558 0.920153i $$-0.371936\pi$$
0.391558 + 0.920153i $$0.371936\pi$$
$$258$$ 0 0
$$259$$ 378770. 0.350854
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.31947e6 1.17627 0.588137 0.808761i $$-0.299861\pi$$
0.588137 + 0.808761i $$0.299861\pi$$
$$264$$ 0 0
$$265$$ 1.18514e6 1.03671
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 783788. 0.660416 0.330208 0.943908i $$-0.392881\pi$$
0.330208 + 0.943908i $$0.392881\pi$$
$$270$$ 0 0
$$271$$ −955080. −0.789981 −0.394990 0.918685i $$-0.629252\pi$$
−0.394990 + 0.918685i $$0.629252\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.72315e6 1.37401
$$276$$ 0 0
$$277$$ 1.91273e6 1.49780 0.748901 0.662682i $$-0.230582\pi$$
0.748901 + 0.662682i $$0.230582\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.02620e6 0.775295 0.387648 0.921808i $$-0.373288\pi$$
0.387648 + 0.921808i $$0.373288\pi$$
$$282$$ 0 0
$$283$$ −1.74668e6 −1.29642 −0.648211 0.761461i $$-0.724482\pi$$
−0.648211 + 0.761461i $$0.724482\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 833784. 0.597515
$$288$$ 0 0
$$289$$ −1.11072e6 −0.782277
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −2.23212e6 −1.51897 −0.759484 0.650526i $$-0.774548\pi$$
−0.759484 + 0.650526i $$0.774548\pi$$
$$294$$ 0 0
$$295$$ −426208. −0.285146
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −2.24790e6 −1.45412
$$300$$ 0 0
$$301$$ −1.06996e6 −0.680696
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −11400.0 −0.00701706
$$306$$ 0 0
$$307$$ −1.85324e6 −1.12224 −0.561119 0.827735i $$-0.689629\pi$$
−0.561119 + 0.827735i $$0.689629\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −450956. −0.264383 −0.132191 0.991224i $$-0.542201\pi$$
−0.132191 + 0.991224i $$0.542201\pi$$
$$312$$ 0 0
$$313$$ 1.60263e6 0.924642 0.462321 0.886713i $$-0.347017\pi$$
0.462321 + 0.886713i $$0.347017\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 20862.0 0.0116602 0.00583012 0.999983i $$-0.498144\pi$$
0.00583012 + 0.999983i $$0.498144\pi$$
$$318$$ 0 0
$$319$$ 438100. 0.241044
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 1.36331e6 0.727091
$$324$$ 0 0
$$325$$ 2.02006e6 1.06086
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −1.17306e6 −0.597490
$$330$$ 0 0
$$331$$ −2.07621e6 −1.04160 −0.520801 0.853678i $$-0.674367\pi$$
−0.520801 + 0.853678i $$0.674367\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −3.32758e6 −1.62001
$$336$$ 0 0
$$337$$ 1.20508e6 0.578019 0.289009 0.957326i $$-0.406674\pi$$
0.289009 + 0.957326i $$0.406674\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.96560e6 0.915396
$$342$$ 0 0
$$343$$ 117649. 0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −876642. −0.390840 −0.195420 0.980720i $$-0.562607\pi$$
−0.195420 + 0.980720i $$0.562607\pi$$
$$348$$ 0 0
$$349$$ −1.29593e6 −0.569532 −0.284766 0.958597i $$-0.591916\pi$$
−0.284766 + 0.958597i $$0.591916\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 3.99040e6 1.70443 0.852215 0.523192i $$-0.175259\pi$$
0.852215 + 0.523192i $$0.175259\pi$$
$$354$$ 0 0
$$355$$ 2.97753e6 1.25396
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 4.06452e6 1.66446 0.832229 0.554432i $$-0.187064\pi$$
0.832229 + 0.554432i $$0.187064\pi$$
$$360$$ 0 0
$$361$$ 3.53620e6 1.42814
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 1.79132e6 0.703787
$$366$$ 0 0
$$367$$ 1.67243e6 0.648162 0.324081 0.946029i $$-0.394945\pi$$
0.324081 + 0.946029i $$0.394945\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −764106. −0.288216
$$372$$ 0 0
$$373$$ 3.16769e6 1.17888 0.589441 0.807812i $$-0.299348\pi$$
0.589441 + 0.807812i $$0.299348\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 513588. 0.186106
$$378$$ 0 0
$$379$$ 4.20388e6 1.50332 0.751662 0.659548i $$-0.229252\pi$$
0.751662 + 0.659548i $$0.229252\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −342616. −0.119347 −0.0596734 0.998218i $$-0.519006\pi$$
−0.0596734 + 0.998218i $$0.519006\pi$$
$$384$$ 0 0
$$385$$ −2.42060e6 −0.832283
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 3.83959e6 1.28650 0.643252 0.765654i $$-0.277585\pi$$
0.643252 + 0.765654i $$0.277585\pi$$
$$390$$ 0 0
$$391$$ −1.64020e6 −0.542569
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −1.35979e6 −0.438510
$$396$$ 0 0
$$397$$ 3.43894e6 1.09509 0.547543 0.836777i $$-0.315563\pi$$
0.547543 + 0.836777i $$0.315563\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 3.89421e6 1.20937 0.604684 0.796466i $$-0.293299\pi$$
0.604684 + 0.796466i $$0.293299\pi$$
$$402$$ 0 0
$$403$$ 2.30429e6 0.706764
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 5.02450e6 1.50351
$$408$$ 0 0
$$409$$ −1.64679e6 −0.486778 −0.243389 0.969929i $$-0.578259\pi$$
−0.243389 + 0.969929i $$0.578259\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 274792. 0.0792737
$$414$$ 0 0
$$415$$ −2.96187e6 −0.844201
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −1.67659e6 −0.466544 −0.233272 0.972412i $$-0.574943\pi$$
−0.233272 + 0.972412i $$0.574943\pi$$
$$420$$ 0 0
$$421$$ −566742. −0.155840 −0.0779202 0.996960i $$-0.524828\pi$$
−0.0779202 + 0.996960i $$0.524828\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.47396e6 0.395833
$$426$$ 0 0
$$427$$ 7350.00 0.00195082
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 6.68468e6 1.73335 0.866677 0.498870i $$-0.166251\pi$$
0.866677 + 0.498870i $$0.166251\pi$$
$$432$$ 0 0
$$433$$ 6.91337e6 1.77203 0.886013 0.463661i $$-0.153464\pi$$
0.886013 + 0.463661i $$0.153464\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −7.23340e6 −1.81192
$$438$$ 0 0
$$439$$ 4.56281e6 1.12998 0.564990 0.825098i $$-0.308880\pi$$
0.564990 + 0.825098i $$0.308880\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 4.59760e6 1.11307 0.556534 0.830825i $$-0.312131\pi$$
0.556534 + 0.830825i $$0.312131\pi$$
$$444$$ 0 0
$$445$$ 457824. 0.109597
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −1.70658e6 −0.399494 −0.199747 0.979848i $$-0.564012\pi$$
−0.199747 + 0.979848i $$0.564012\pi$$
$$450$$ 0 0
$$451$$ 1.10604e7 2.56053
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −2.83769e6 −0.642593
$$456$$ 0 0
$$457$$ −6.93916e6 −1.55423 −0.777117 0.629356i $$-0.783319\pi$$
−0.777117 + 0.629356i $$0.783319\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 2.61805e6 0.573753 0.286877 0.957968i $$-0.407383\pi$$
0.286877 + 0.957968i $$0.407383\pi$$
$$462$$ 0 0
$$463$$ −7.13602e6 −1.54705 −0.773524 0.633767i $$-0.781508\pi$$
−0.773524 + 0.633767i $$0.781508\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −2.17398e6 −0.461278 −0.230639 0.973039i $$-0.574082\pi$$
−0.230639 + 0.973039i $$0.574082\pi$$
$$468$$ 0 0
$$469$$ 2.14542e6 0.450380
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −1.41934e7 −2.91698
$$474$$ 0 0
$$475$$ 6.50025e6 1.32189
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −4.63294e6 −0.922609 −0.461305 0.887242i $$-0.652619\pi$$
−0.461305 + 0.887242i $$0.652619\pi$$
$$480$$ 0 0
$$481$$ 5.89026e6 1.16084
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −8.24068e6 −1.59077
$$486$$ 0 0
$$487$$ 4.56645e6 0.872481 0.436241 0.899830i $$-0.356310\pi$$
0.436241 + 0.899830i $$0.356310\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −5.31429e6 −0.994813 −0.497407 0.867518i $$-0.665714\pi$$
−0.497407 + 0.867518i $$0.665714\pi$$
$$492$$ 0 0
$$493$$ 374744. 0.0694412
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −1.91972e6 −0.348616
$$498$$ 0 0
$$499$$ 2.46314e6 0.442831 0.221415 0.975180i $$-0.428932\pi$$
0.221415 + 0.975180i $$0.428932\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 2.79924e6 0.493310 0.246655 0.969103i $$-0.420669\pi$$
0.246655 + 0.969103i $$0.420669\pi$$
$$504$$ 0 0
$$505$$ −5.35222e6 −0.933912
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −1.99914e6 −0.342018 −0.171009 0.985269i $$-0.554703\pi$$
−0.171009 + 0.985269i $$0.554703\pi$$
$$510$$ 0 0
$$511$$ −1.15493e6 −0.195661
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −2.39795e6 −0.398403
$$516$$ 0 0
$$517$$ −1.55610e7 −2.56042
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −3.52160e6 −0.568390 −0.284195 0.958767i $$-0.591726\pi$$
−0.284195 + 0.958767i $$0.591726\pi$$
$$522$$ 0 0
$$523$$ −2.60685e6 −0.416737 −0.208369 0.978050i $$-0.566815\pi$$
−0.208369 + 0.978050i $$0.566815\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 1.68134e6 0.263712
$$528$$ 0 0
$$529$$ 2.26616e6 0.352088
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 1.29662e7 1.97694
$$534$$ 0 0
$$535$$ −8.22943e6 −1.24304
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 1.56065e6 0.231384
$$540$$ 0 0
$$541$$ −1.37441e6 −0.201894 −0.100947 0.994892i $$-0.532187\pi$$
−0.100947 + 0.994892i $$0.532187\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 5.48310e6 0.790742
$$546$$ 0 0
$$547$$ 8.78398e6 1.25523 0.627614 0.778524i $$-0.284032\pi$$
0.627614 + 0.778524i $$0.284032\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 1.65265e6 0.231900
$$552$$ 0 0
$$553$$ 876708. 0.121911
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −6.29262e6 −0.859396 −0.429698 0.902973i $$-0.641380\pi$$
−0.429698 + 0.902973i $$0.641380\pi$$
$$558$$ 0 0
$$559$$ −1.66390e7 −2.25216
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 4.86582e6 0.646971 0.323485 0.946233i $$-0.395145\pi$$
0.323485 + 0.946233i $$0.395145\pi$$
$$564$$ 0 0
$$565$$ 1.67889e7 2.21259
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 4.46383e6 0.577998 0.288999 0.957329i $$-0.406678\pi$$
0.288999 + 0.957329i $$0.406678\pi$$
$$570$$ 0 0
$$571$$ −8.17054e6 −1.04872 −0.524361 0.851496i $$-0.675696\pi$$
−0.524361 + 0.851496i $$0.675696\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −7.82045e6 −0.986421
$$576$$ 0 0
$$577$$ −5.50343e6 −0.688167 −0.344084 0.938939i $$-0.611810\pi$$
−0.344084 + 0.938939i $$0.611810\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 1.90963e6 0.234697
$$582$$ 0 0
$$583$$ −1.01361e7 −1.23509
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 8.14251e6 0.975356 0.487678 0.873024i $$-0.337844\pi$$
0.487678 + 0.873024i $$0.337844\pi$$
$$588$$ 0 0
$$589$$ 7.41485e6 0.880672
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 2.73136e6 0.318964 0.159482 0.987201i $$-0.449018\pi$$
0.159482 + 0.987201i $$0.449018\pi$$
$$594$$ 0 0
$$595$$ −2.07054e6 −0.239768
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 1.23733e6 0.140902 0.0704510 0.997515i $$-0.477556\pi$$
0.0704510 + 0.997515i $$0.477556\pi$$
$$600$$ 0 0
$$601$$ −1.59756e7 −1.80414 −0.902071 0.431587i $$-0.857954\pi$$
−0.902071 + 0.431587i $$0.857954\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −1.98701e7 −2.20705
$$606$$ 0 0
$$607$$ 1.88275e6 0.207406 0.103703 0.994608i $$-0.466931\pi$$
0.103703 + 0.994608i $$0.466931\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −1.82423e7 −1.97686
$$612$$ 0 0
$$613$$ −9.82804e6 −1.05637 −0.528185 0.849130i $$-0.677127\pi$$
−0.528185 + 0.849130i $$0.677127\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 8.21262e6 0.868498 0.434249 0.900793i $$-0.357014\pi$$
0.434249 + 0.900793i $$0.357014\pi$$
$$618$$ 0 0
$$619$$ −6.98465e6 −0.732686 −0.366343 0.930480i $$-0.619390\pi$$
−0.366343 + 0.930480i $$0.619390\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −295176. −0.0304692
$$624$$ 0 0
$$625$$ −1.10222e7 −1.12867
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 4.29788e6 0.433139
$$630$$ 0 0
$$631$$ −1.26789e7 −1.26767 −0.633837 0.773467i $$-0.718521\pi$$
−0.633837 + 0.773467i $$0.718521\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −1.82136e7 −1.79250
$$636$$ 0 0
$$637$$ 1.82956e6 0.178648
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 1.40324e7 1.34892 0.674460 0.738311i $$-0.264376\pi$$
0.674460 + 0.738311i $$0.264376\pi$$
$$642$$ 0 0
$$643$$ −1.30368e6 −0.124349 −0.0621745 0.998065i $$-0.519804\pi$$
−0.0621745 + 0.998065i $$0.519804\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.57110e6 0.147551 0.0737757 0.997275i $$-0.476495\pi$$
0.0737757 + 0.997275i $$0.476495\pi$$
$$648$$ 0 0
$$649$$ 3.64520e6 0.339711
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 8.34115e6 0.765496 0.382748 0.923853i $$-0.374978\pi$$
0.382748 + 0.923853i $$0.374978\pi$$
$$654$$ 0 0
$$655$$ 2.08371e7 1.89773
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 6.18334e6 0.554638 0.277319 0.960778i $$-0.410554\pi$$
0.277319 + 0.960778i $$0.410554\pi$$
$$660$$ 0 0
$$661$$ 928966. 0.0826982 0.0413491 0.999145i $$-0.486834\pi$$
0.0413491 + 0.999145i $$0.486834\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −9.13125e6 −0.800711
$$666$$ 0 0
$$667$$ −1.98830e6 −0.173048
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 97500.0 0.00835985
$$672$$ 0 0
$$673$$ 1.79131e7 1.52452 0.762259 0.647272i $$-0.224090\pi$$
0.762259 + 0.647272i $$0.224090\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 4.96397e6 0.416253 0.208126 0.978102i $$-0.433263\pi$$
0.208126 + 0.978102i $$0.433263\pi$$
$$678$$ 0 0
$$679$$ 5.31307e6 0.442253
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 89526.0 0.00734340 0.00367170 0.999993i $$-0.498831\pi$$
0.00367170 + 0.999993i $$0.498831\pi$$
$$684$$ 0 0
$$685$$ −2.97277e7 −2.42067
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −1.18826e7 −0.953596
$$690$$ 0 0
$$691$$ 142396. 0.0113450 0.00567248 0.999984i $$-0.498194\pi$$
0.00567248 + 0.999984i $$0.498194\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 2.57917e7 2.02543
$$696$$ 0 0
$$697$$ 9.46090e6 0.737650
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −1.03935e7 −0.798852 −0.399426 0.916765i $$-0.630791\pi$$
−0.399426 + 0.916765i $$0.630791\pi$$
$$702$$ 0 0
$$703$$ 1.89540e7 1.44648
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 3.45078e6 0.259638
$$708$$ 0 0
$$709$$ 4.65503e6 0.347782 0.173891 0.984765i $$-0.444366\pi$$
0.173891 + 0.984765i $$0.444366\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −8.92080e6 −0.657173
$$714$$ 0 0
$$715$$ −3.76428e7 −2.75370
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −6.72134e6 −0.484880 −0.242440 0.970166i $$-0.577948\pi$$
−0.242440 + 0.970166i $$0.577948\pi$$
$$720$$ 0 0
$$721$$ 1.54605e6 0.110760
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 1.78677e6 0.126248
$$726$$ 0 0
$$727$$ 1.24076e7 0.870670 0.435335 0.900269i $$-0.356630\pi$$
0.435335 + 0.900269i $$0.356630\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −1.21408e7 −0.840339
$$732$$ 0 0
$$733$$ 1.35958e7 0.934641 0.467321 0.884088i $$-0.345219\pi$$
0.467321 + 0.884088i $$0.345219\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 2.84596e7 1.93001
$$738$$ 0 0
$$739$$ −2.56819e6 −0.172988 −0.0864941 0.996252i $$-0.527566\pi$$
−0.0864941 + 0.996252i $$0.527566\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −2.02133e7 −1.34327 −0.671637 0.740880i $$-0.734409\pi$$
−0.671637 + 0.740880i $$0.734409\pi$$
$$744$$ 0 0
$$745$$ −2.22938e6 −0.147161
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 5.30582e6 0.345579
$$750$$ 0 0
$$751$$ −7.04813e6 −0.456010 −0.228005 0.973660i $$-0.573220\pi$$
−0.228005 + 0.973660i $$0.573220\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 5.44221e6 0.347462
$$756$$ 0 0
$$757$$ −2.04120e7 −1.29463 −0.647315 0.762223i $$-0.724108\pi$$
−0.647315 + 0.762223i $$0.724108\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 5.07974e6 0.317965 0.158983 0.987281i $$-0.449179\pi$$
0.158983 + 0.987281i $$0.449179\pi$$
$$762$$ 0 0
$$763$$ −3.53515e6 −0.219835
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 4.27330e6 0.262286
$$768$$ 0 0
$$769$$ 2.33898e7 1.42630 0.713149 0.701012i $$-0.247268\pi$$
0.713149 + 0.701012i $$0.247268\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1.11253e6 0.0669672 0.0334836 0.999439i $$-0.489340\pi$$
0.0334836 + 0.999439i $$0.489340\pi$$
$$774$$ 0 0
$$775$$ 8.01662e6 0.479443
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 4.17232e7 2.46340
$$780$$ 0 0
$$781$$ −2.54657e7 −1.49392
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −2.25202e7 −1.30436
$$786$$ 0 0
$$787$$ −2.00812e6 −0.115572 −0.0577859 0.998329i $$-0.518404\pi$$
−0.0577859 + 0.998329i $$0.518404\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −1.08244e7 −0.615124
$$792$$ 0 0
$$793$$ 114300. 0.00645451
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −3.00897e7 −1.67792 −0.838961 0.544191i $$-0.816837\pi$$
−0.838961 + 0.544191i $$0.816837\pi$$
$$798$$ 0 0
$$799$$ −1.33106e7 −0.737619
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −1.53205e7 −0.838463
$$804$$ 0 0
$$805$$ 1.09858e7 0.597506
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 1.88207e6 0.101103 0.0505515 0.998721i $$-0.483902\pi$$
0.0505515 + 0.998721i $$0.483902\pi$$
$$810$$ 0 0
$$811$$ −4.88220e6 −0.260654 −0.130327 0.991471i $$-0.541603\pi$$
−0.130327 + 0.991471i $$0.541603\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −3.65104e7 −1.92541
$$816$$ 0 0
$$817$$ −5.35419e7 −2.80633
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −8.37096e6 −0.433429 −0.216714 0.976235i $$-0.569534\pi$$
−0.216714 + 0.976235i $$0.569534\pi$$
$$822$$ 0 0
$$823$$ 2.02090e7 1.04003 0.520015 0.854157i $$-0.325926\pi$$
0.520015 + 0.854157i $$0.325926\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −1.31059e7 −0.666352 −0.333176 0.942865i $$-0.608120\pi$$
−0.333176 + 0.942865i $$0.608120\pi$$
$$828$$ 0 0
$$829$$ 3.18667e7 1.61046 0.805232 0.592960i $$-0.202041\pi$$
0.805232 + 0.592960i $$0.202041\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 1.33496e6 0.0666583
$$834$$ 0 0
$$835$$ −1.21737e7 −0.604235
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 9.94742e6 0.487872 0.243936 0.969791i $$-0.421561\pi$$
0.243936 + 0.969791i $$0.421561\pi$$
$$840$$ 0 0
$$841$$ −2.00569e7 −0.977852
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −1.59107e7 −0.766561
$$846$$ 0 0
$$847$$ 1.28110e7 0.613585
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −2.28035e7 −1.07939
$$852$$ 0 0
$$853$$ −6.52611e6 −0.307102 −0.153551 0.988141i $$-0.549071\pi$$
−0.153551 + 0.988141i $$0.549071\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 8.76238e6 0.407540 0.203770 0.979019i $$-0.434681\pi$$
0.203770 + 0.979019i $$0.434681\pi$$
$$858$$ 0 0
$$859$$ −6.47942e6 −0.299608 −0.149804 0.988716i $$-0.547864\pi$$
−0.149804 + 0.988716i $$0.547864\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −1.83417e7 −0.838323 −0.419162 0.907912i $$-0.637676\pi$$
−0.419162 + 0.907912i $$0.637676\pi$$
$$864$$ 0 0
$$865$$ −682784. −0.0310272
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 1.16298e7 0.522424
$$870$$ 0 0
$$871$$ 3.33634e7 1.49013
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 1.76518e6 0.0779413
$$876$$ 0 0
$$877$$ 2.69065e7 1.18129 0.590647 0.806930i $$-0.298873\pi$$
0.590647 + 0.806930i $$0.298873\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 1.52174e7 0.660542 0.330271 0.943886i $$-0.392860\pi$$
0.330271 + 0.943886i $$0.392860\pi$$
$$882$$ 0 0
$$883$$ 2.61520e7 1.12877 0.564383 0.825513i $$-0.309114\pi$$
0.564383 + 0.825513i $$0.309114\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −1.08021e7 −0.460997 −0.230499 0.973073i $$-0.574036\pi$$
−0.230499 + 0.973073i $$0.574036\pi$$
$$888$$ 0 0
$$889$$ 1.17429e7 0.498337
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −5.87009e7 −2.46329
$$894$$ 0 0
$$895$$ −1.38993e7 −0.580011
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 2.03818e6 0.0841090
$$900$$ 0 0
$$901$$ −8.67026e6 −0.355812
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −1.05131e7 −0.426686
$$906$$ 0 0
$$907$$ 9.84167e6 0.397238 0.198619 0.980077i $$-0.436354\pi$$
0.198619 + 0.980077i $$0.436354\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 2.72509e7 1.08789 0.543945 0.839121i $$-0.316930\pi$$
0.543945 + 0.839121i $$0.316930\pi$$
$$912$$ 0 0
$$913$$ 2.53318e7 1.00575
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −1.34344e7 −0.527589
$$918$$ 0 0
$$919$$ −2.86432e7 −1.11875 −0.559374 0.828916i $$-0.688958\pi$$
−0.559374 + 0.828916i $$0.688958\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −2.98536e7 −1.15343
$$924$$ 0 0
$$925$$ 2.04922e7 0.787472
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −6.78492e6 −0.257932 −0.128966 0.991649i $$-0.541166\pi$$
−0.128966 + 0.991649i $$0.541166\pi$$
$$930$$ 0 0
$$931$$ 5.88725e6 0.222607
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −2.74664e7 −1.02748
$$936$$ 0 0
$$937$$ 3.00308e7 1.11742 0.558712 0.829362i $$-0.311296\pi$$
0.558712 + 0.829362i $$0.311296\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −2.30725e7 −0.849415 −0.424707 0.905331i $$-0.639623\pi$$
−0.424707 + 0.905331i $$0.639623\pi$$
$$942$$ 0 0
$$943$$ −5.01972e7 −1.83823
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 2.71433e7 0.983531 0.491765 0.870728i $$-0.336352\pi$$
0.491765 + 0.870728i $$0.336352\pi$$
$$948$$ 0 0
$$949$$ −1.79603e7 −0.647365
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 1.61552e7 0.576209 0.288104 0.957599i $$-0.406975\pi$$
0.288104 + 0.957599i $$0.406975\pi$$
$$954$$ 0 0
$$955$$ −2.48689e7 −0.882364
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 1.91665e7 0.672973
$$960$$ 0 0
$$961$$ −1.94846e7 −0.680585
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −5.98046e7 −2.06736
$$966$$ 0 0
$$967$$ 3.80323e7 1.30793 0.653967 0.756523i $$-0.273103\pi$$
0.653967 + 0.756523i $$0.273103\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −2.23104e7 −0.759379 −0.379689 0.925114i $$-0.623969\pi$$
−0.379689 + 0.925114i $$0.623969\pi$$
$$972$$ 0 0
$$973$$ −1.66288e7 −0.563093
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −3.06930e7 −1.02873 −0.514367 0.857570i $$-0.671973\pi$$
−0.514367 + 0.857570i $$0.671973\pi$$
$$978$$ 0 0
$$979$$ −3.91560e6 −0.130569
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −1.52706e7 −0.504048 −0.252024 0.967721i $$-0.581096\pi$$
−0.252024 + 0.967721i $$0.581096\pi$$
$$984$$ 0 0
$$985$$ 3.21554e7 1.05600
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 6.44162e7 2.09413
$$990$$ 0 0
$$991$$ −3.16279e7 −1.02303 −0.511513 0.859276i $$-0.670915\pi$$
−0.511513 + 0.859276i $$0.670915\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 7.78179e7 2.49185
$$996$$ 0 0
$$997$$ −3.55842e7 −1.13376 −0.566878 0.823802i $$-0.691849\pi$$
−0.566878 + 0.823802i $$0.691849\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1008.6.a.d.1.1 1
3.2 odd 2 336.6.a.q.1.1 1
4.3 odd 2 126.6.a.a.1.1 1
12.11 even 2 42.6.a.e.1.1 1
28.27 even 2 882.6.a.j.1.1 1
60.23 odd 4 1050.6.g.h.799.1 2
60.47 odd 4 1050.6.g.h.799.2 2
60.59 even 2 1050.6.a.f.1.1 1
84.11 even 6 294.6.e.d.79.1 2
84.23 even 6 294.6.e.d.67.1 2
84.47 odd 6 294.6.e.c.67.1 2
84.59 odd 6 294.6.e.c.79.1 2
84.83 odd 2 294.6.a.k.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.a.e.1.1 1 12.11 even 2
126.6.a.a.1.1 1 4.3 odd 2
294.6.a.k.1.1 1 84.83 odd 2
294.6.e.c.67.1 2 84.47 odd 6
294.6.e.c.79.1 2 84.59 odd 6
294.6.e.d.67.1 2 84.23 even 6
294.6.e.d.79.1 2 84.11 even 6
336.6.a.q.1.1 1 3.2 odd 2
882.6.a.j.1.1 1 28.27 even 2
1008.6.a.d.1.1 1 1.1 even 1 trivial
1050.6.a.f.1.1 1 60.59 even 2
1050.6.g.h.799.1 2 60.23 odd 4
1050.6.g.h.799.2 2 60.47 odd 4