# Properties

 Label 1584.4.a.l.1.1 Level $1584$ Weight $4$ Character 1584.1 Self dual yes Analytic conductor $93.459$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1584,4,Mod(1,1584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1584, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1584.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1584 = 2^{4} \cdot 3^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1584.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: $$93.4590254491$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 33) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1584.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+4.00000 q^{5} +26.0000 q^{7} +O(q^{10})$$ $$q+4.00000 q^{5} +26.0000 q^{7} +11.0000 q^{11} -32.0000 q^{13} -74.0000 q^{17} +60.0000 q^{19} -182.000 q^{23} -109.000 q^{25} +90.0000 q^{29} +8.00000 q^{31} +104.000 q^{35} -66.0000 q^{37} -422.000 q^{41} -408.000 q^{43} -506.000 q^{47} +333.000 q^{49} -348.000 q^{53} +44.0000 q^{55} -200.000 q^{59} +132.000 q^{61} -128.000 q^{65} +1036.00 q^{67} +762.000 q^{71} -542.000 q^{73} +286.000 q^{77} +550.000 q^{79} -132.000 q^{83} -296.000 q^{85} -570.000 q^{89} -832.000 q^{91} +240.000 q^{95} +14.0000 q^{97} +O(q^{100})$$

## 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
$$5$$ 4.00000 0.357771 0.178885 0.983870i $$-0.442751\pi$$
0.178885 + 0.983870i $$0.442751\pi$$
$$6$$ 0 0
$$7$$ 26.0000 1.40387 0.701934 0.712242i $$-0.252320\pi$$
0.701934 + 0.712242i $$0.252320\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 11.0000 0.301511
$$12$$ 0 0
$$13$$ −32.0000 −0.682708 −0.341354 0.939935i $$-0.610885\pi$$
−0.341354 + 0.939935i $$0.610885\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −74.0000 −1.05574 −0.527872 0.849324i $$-0.677010\pi$$
−0.527872 + 0.849324i $$0.677010\pi$$
$$18$$ 0 0
$$19$$ 60.0000 0.724471 0.362235 0.932087i $$-0.382014\pi$$
0.362235 + 0.932087i $$0.382014\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −182.000 −1.64998 −0.824992 0.565145i $$-0.808820\pi$$
−0.824992 + 0.565145i $$0.808820\pi$$
$$24$$ 0 0
$$25$$ −109.000 −0.872000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 90.0000 0.576296 0.288148 0.957586i $$-0.406961\pi$$
0.288148 + 0.957586i $$0.406961\pi$$
$$30$$ 0 0
$$31$$ 8.00000 0.0463498 0.0231749 0.999731i $$-0.492623\pi$$
0.0231749 + 0.999731i $$0.492623\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 104.000 0.502263
$$36$$ 0 0
$$37$$ −66.0000 −0.293252 −0.146626 0.989192i $$-0.546841\pi$$
−0.146626 + 0.989192i $$0.546841\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −422.000 −1.60745 −0.803724 0.595003i $$-0.797151\pi$$
−0.803724 + 0.595003i $$0.797151\pi$$
$$42$$ 0 0
$$43$$ −408.000 −1.44696 −0.723482 0.690344i $$-0.757459\pi$$
−0.723482 + 0.690344i $$0.757459\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −506.000 −1.57038 −0.785188 0.619257i $$-0.787434\pi$$
−0.785188 + 0.619257i $$0.787434\pi$$
$$48$$ 0 0
$$49$$ 333.000 0.970845
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −348.000 −0.901915 −0.450957 0.892546i $$-0.648917\pi$$
−0.450957 + 0.892546i $$0.648917\pi$$
$$54$$ 0 0
$$55$$ 44.0000 0.107872
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −200.000 −0.441318 −0.220659 0.975351i $$-0.570821\pi$$
−0.220659 + 0.975351i $$0.570821\pi$$
$$60$$ 0 0
$$61$$ 132.000 0.277063 0.138532 0.990358i $$-0.455762\pi$$
0.138532 + 0.990358i $$0.455762\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −128.000 −0.244253
$$66$$ 0 0
$$67$$ 1036.00 1.88907 0.944534 0.328414i $$-0.106514\pi$$
0.944534 + 0.328414i $$0.106514\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 762.000 1.27370 0.636850 0.770987i $$-0.280237\pi$$
0.636850 + 0.770987i $$0.280237\pi$$
$$72$$ 0 0
$$73$$ −542.000 −0.868990 −0.434495 0.900674i $$-0.643073\pi$$
−0.434495 + 0.900674i $$0.643073\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 286.000 0.423282
$$78$$ 0 0
$$79$$ 550.000 0.783289 0.391645 0.920117i $$-0.371906\pi$$
0.391645 + 0.920117i $$0.371906\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −132.000 −0.174565 −0.0872824 0.996184i $$-0.527818\pi$$
−0.0872824 + 0.996184i $$0.527818\pi$$
$$84$$ 0 0
$$85$$ −296.000 −0.377714
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −570.000 −0.678875 −0.339438 0.940629i $$-0.610237\pi$$
−0.339438 + 0.940629i $$0.610237\pi$$
$$90$$ 0 0
$$91$$ −832.000 −0.958432
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 240.000 0.259195
$$96$$ 0 0
$$97$$ 14.0000 0.0146545 0.00732724 0.999973i $$-0.497668\pi$$
0.00732724 + 0.999973i $$0.497668\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −1702.00 −1.67679 −0.838393 0.545067i $$-0.816504\pi$$
−0.838393 + 0.545067i $$0.816504\pi$$
$$102$$ 0 0
$$103$$ 1132.00 1.08291 0.541453 0.840731i $$-0.317874\pi$$
0.541453 + 0.840731i $$0.317874\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 564.000 0.509570 0.254785 0.966998i $$-0.417995\pi$$
0.254785 + 0.966998i $$0.417995\pi$$
$$108$$ 0 0
$$109$$ −320.000 −0.281197 −0.140598 0.990067i $$-0.544903\pi$$
−0.140598 + 0.990067i $$0.544903\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2142.00 1.78321 0.891604 0.452817i $$-0.149581\pi$$
0.891604 + 0.452817i $$0.149581\pi$$
$$114$$ 0 0
$$115$$ −728.000 −0.590316
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −1924.00 −1.48212
$$120$$ 0 0
$$121$$ 121.000 0.0909091
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −936.000 −0.669747
$$126$$ 0 0
$$127$$ 1606.00 1.12212 0.561061 0.827775i $$-0.310393\pi$$
0.561061 + 0.827775i $$0.310393\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1908.00 −1.27254 −0.636270 0.771466i $$-0.719524\pi$$
−0.636270 + 0.771466i $$0.719524\pi$$
$$132$$ 0 0
$$133$$ 1560.00 1.01706
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2186.00 1.36323 0.681615 0.731711i $$-0.261278\pi$$
0.681615 + 0.731711i $$0.261278\pi$$
$$138$$ 0 0
$$139$$ −2740.00 −1.67197 −0.835985 0.548753i $$-0.815103\pi$$
−0.835985 + 0.548753i $$0.815103\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −352.000 −0.205844
$$144$$ 0 0
$$145$$ 360.000 0.206182
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 1310.00 0.720264 0.360132 0.932901i $$-0.382732\pi$$
0.360132 + 0.932901i $$0.382732\pi$$
$$150$$ 0 0
$$151$$ 1198.00 0.645641 0.322821 0.946460i $$-0.395369\pi$$
0.322821 + 0.946460i $$0.395369\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 32.0000 0.0165826
$$156$$ 0 0
$$157$$ 2114.00 1.07462 0.537311 0.843384i $$-0.319440\pi$$
0.537311 + 0.843384i $$0.319440\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −4732.00 −2.31636
$$162$$ 0 0
$$163$$ −3868.00 −1.85868 −0.929341 0.369223i $$-0.879624\pi$$
−0.929341 + 0.369223i $$0.879624\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2004.00 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ 0 0
$$169$$ −1173.00 −0.533910
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −678.000 −0.297962 −0.148981 0.988840i $$-0.547599\pi$$
−0.148981 + 0.988840i $$0.547599\pi$$
$$174$$ 0 0
$$175$$ −2834.00 −1.22417
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −1680.00 −0.701503 −0.350752 0.936469i $$-0.614074\pi$$
−0.350752 + 0.936469i $$0.614074\pi$$
$$180$$ 0 0
$$181$$ −4358.00 −1.78966 −0.894828 0.446412i $$-0.852702\pi$$
−0.894828 + 0.446412i $$0.852702\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −264.000 −0.104917
$$186$$ 0 0
$$187$$ −814.000 −0.318319
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1778.00 −0.673568 −0.336784 0.941582i $$-0.609339\pi$$
−0.336784 + 0.941582i $$0.609339\pi$$
$$192$$ 0 0
$$193$$ −3962.00 −1.47767 −0.738837 0.673884i $$-0.764625\pi$$
−0.738837 + 0.673884i $$0.764625\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −374.000 −0.135261 −0.0676304 0.997710i $$-0.521544\pi$$
−0.0676304 + 0.997710i $$0.521544\pi$$
$$198$$ 0 0
$$199$$ −2100.00 −0.748066 −0.374033 0.927415i $$-0.622025\pi$$
−0.374033 + 0.927415i $$0.622025\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 2340.00 0.809043
$$204$$ 0 0
$$205$$ −1688.00 −0.575098
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 660.000 0.218436
$$210$$ 0 0
$$211$$ −2232.00 −0.728233 −0.364117 0.931353i $$-0.618629\pi$$
−0.364117 + 0.931353i $$0.618629\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −1632.00 −0.517681
$$216$$ 0 0
$$217$$ 208.000 0.0650689
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 2368.00 0.720764
$$222$$ 0 0
$$223$$ −2128.00 −0.639020 −0.319510 0.947583i $$-0.603518\pi$$
−0.319510 + 0.947583i $$0.603518\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 2964.00 0.866641 0.433321 0.901240i $$-0.357342\pi$$
0.433321 + 0.901240i $$0.357342\pi$$
$$228$$ 0 0
$$229$$ −2550.00 −0.735846 −0.367923 0.929856i $$-0.619931\pi$$
−0.367923 + 0.929856i $$0.619931\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 3042.00 0.855314 0.427657 0.903941i $$-0.359339\pi$$
0.427657 + 0.903941i $$0.359339\pi$$
$$234$$ 0 0
$$235$$ −2024.00 −0.561835
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 2700.00 0.730747 0.365373 0.930861i $$-0.380941\pi$$
0.365373 + 0.930861i $$0.380941\pi$$
$$240$$ 0 0
$$241$$ −578.000 −0.154491 −0.0772453 0.997012i $$-0.524612\pi$$
−0.0772453 + 0.997012i $$0.524612\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 1332.00 0.347340
$$246$$ 0 0
$$247$$ −1920.00 −0.494602
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 3752.00 0.943522 0.471761 0.881726i $$-0.343618\pi$$
0.471761 + 0.881726i $$0.343618\pi$$
$$252$$ 0 0
$$253$$ −2002.00 −0.497489
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −674.000 −0.163591 −0.0817957 0.996649i $$-0.526065\pi$$
−0.0817957 + 0.996649i $$0.526065\pi$$
$$258$$ 0 0
$$259$$ −1716.00 −0.411687
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −4352.00 −1.02036 −0.510182 0.860066i $$-0.670422\pi$$
−0.510182 + 0.860066i $$0.670422\pi$$
$$264$$ 0 0
$$265$$ −1392.00 −0.322679
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −500.000 −0.113329 −0.0566646 0.998393i $$-0.518047\pi$$
−0.0566646 + 0.998393i $$0.518047\pi$$
$$270$$ 0 0
$$271$$ 6538.00 1.46552 0.732759 0.680489i $$-0.238232\pi$$
0.732759 + 0.680489i $$0.238232\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1199.00 −0.262918
$$276$$ 0 0
$$277$$ 124.000 0.0268969 0.0134484 0.999910i $$-0.495719\pi$$
0.0134484 + 0.999910i $$0.495719\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −3642.00 −0.773180 −0.386590 0.922252i $$-0.626347\pi$$
−0.386590 + 0.922252i $$0.626347\pi$$
$$282$$ 0 0
$$283$$ −4648.00 −0.976307 −0.488154 0.872758i $$-0.662329\pi$$
−0.488154 + 0.872758i $$0.662329\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −10972.0 −2.25664
$$288$$ 0 0
$$289$$ 563.000 0.114594
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 3102.00 0.618501 0.309250 0.950981i $$-0.399922\pi$$
0.309250 + 0.950981i $$0.399922\pi$$
$$294$$ 0 0
$$295$$ −800.000 −0.157891
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 5824.00 1.12646
$$300$$ 0 0
$$301$$ −10608.0 −2.03135
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 528.000 0.0991252
$$306$$ 0 0
$$307$$ −1244.00 −0.231267 −0.115633 0.993292i $$-0.536890\pi$$
−0.115633 + 0.993292i $$0.536890\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 2082.00 0.379612 0.189806 0.981822i $$-0.439214\pi$$
0.189806 + 0.981822i $$0.439214\pi$$
$$312$$ 0 0
$$313$$ 2378.00 0.429433 0.214716 0.976676i $$-0.431117\pi$$
0.214716 + 0.976676i $$0.431117\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 496.000 0.0878806 0.0439403 0.999034i $$-0.486009\pi$$
0.0439403 + 0.999034i $$0.486009\pi$$
$$318$$ 0 0
$$319$$ 990.000 0.173760
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −4440.00 −0.764855
$$324$$ 0 0
$$325$$ 3488.00 0.595321
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −13156.0 −2.20460
$$330$$ 0 0
$$331$$ 2708.00 0.449683 0.224842 0.974395i $$-0.427814\pi$$
0.224842 + 0.974395i $$0.427814\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 4144.00 0.675853
$$336$$ 0 0
$$337$$ 4034.00 0.652065 0.326033 0.945359i $$-0.394288\pi$$
0.326033 + 0.945359i $$0.394288\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 88.0000 0.0139750
$$342$$ 0 0
$$343$$ −260.000 −0.0409291
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 11084.0 1.71476 0.857378 0.514687i $$-0.172092\pi$$
0.857378 + 0.514687i $$0.172092\pi$$
$$348$$ 0 0
$$349$$ −3120.00 −0.478538 −0.239269 0.970953i $$-0.576908\pi$$
−0.239269 + 0.970953i $$0.576908\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 5622.00 0.847674 0.423837 0.905739i $$-0.360683\pi$$
0.423837 + 0.905739i $$0.360683\pi$$
$$354$$ 0 0
$$355$$ 3048.00 0.455693
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −8500.00 −1.24962 −0.624809 0.780778i $$-0.714823\pi$$
−0.624809 + 0.780778i $$0.714823\pi$$
$$360$$ 0 0
$$361$$ −3259.00 −0.475142
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −2168.00 −0.310899
$$366$$ 0 0
$$367$$ −7144.00 −1.01611 −0.508057 0.861324i $$-0.669636\pi$$
−0.508057 + 0.861324i $$0.669636\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −9048.00 −1.26617
$$372$$ 0 0
$$373$$ −632.000 −0.0877312 −0.0438656 0.999037i $$-0.513967\pi$$
−0.0438656 + 0.999037i $$0.513967\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −2880.00 −0.393442
$$378$$ 0 0
$$379$$ 4220.00 0.571944 0.285972 0.958238i $$-0.407684\pi$$
0.285972 + 0.958238i $$0.407684\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 8458.00 1.12842 0.564208 0.825632i $$-0.309181\pi$$
0.564208 + 0.825632i $$0.309181\pi$$
$$384$$ 0 0
$$385$$ 1144.00 0.151438
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −1740.00 −0.226790 −0.113395 0.993550i $$-0.536173\pi$$
−0.113395 + 0.993550i $$0.536173\pi$$
$$390$$ 0 0
$$391$$ 13468.0 1.74196
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 2200.00 0.280238
$$396$$ 0 0
$$397$$ −5126.00 −0.648027 −0.324013 0.946053i $$-0.605032\pi$$
−0.324013 + 0.946053i $$0.605032\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 3098.00 0.385802 0.192901 0.981218i $$-0.438210\pi$$
0.192901 + 0.981218i $$0.438210\pi$$
$$402$$ 0 0
$$403$$ −256.000 −0.0316433
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −726.000 −0.0884189
$$408$$ 0 0
$$409$$ 6390.00 0.772531 0.386265 0.922388i $$-0.373765\pi$$
0.386265 + 0.922388i $$0.373765\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −5200.00 −0.619553
$$414$$ 0 0
$$415$$ −528.000 −0.0624542
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 9760.00 1.13796 0.568982 0.822350i $$-0.307337\pi$$
0.568982 + 0.822350i $$0.307337\pi$$
$$420$$ 0 0
$$421$$ −5138.00 −0.594800 −0.297400 0.954753i $$-0.596119\pi$$
−0.297400 + 0.954753i $$0.596119\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 8066.00 0.920608
$$426$$ 0 0
$$427$$ 3432.00 0.388960
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −7008.00 −0.783210 −0.391605 0.920133i $$-0.628080\pi$$
−0.391605 + 0.920133i $$0.628080\pi$$
$$432$$ 0 0
$$433$$ 5578.00 0.619080 0.309540 0.950886i $$-0.399825\pi$$
0.309540 + 0.950886i $$0.399825\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −10920.0 −1.19536
$$438$$ 0 0
$$439$$ 10430.0 1.13393 0.566967 0.823741i $$-0.308117\pi$$
0.566967 + 0.823741i $$0.308117\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −4432.00 −0.475329 −0.237664 0.971347i $$-0.576382\pi$$
−0.237664 + 0.971347i $$0.576382\pi$$
$$444$$ 0 0
$$445$$ −2280.00 −0.242882
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 6290.00 0.661121 0.330561 0.943785i $$-0.392762\pi$$
0.330561 + 0.943785i $$0.392762\pi$$
$$450$$ 0 0
$$451$$ −4642.00 −0.484664
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −3328.00 −0.342899
$$456$$ 0 0
$$457$$ 3054.00 0.312604 0.156302 0.987709i $$-0.450043\pi$$
0.156302 + 0.987709i $$0.450043\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −12882.0 −1.30146 −0.650732 0.759308i $$-0.725538\pi$$
−0.650732 + 0.759308i $$0.725538\pi$$
$$462$$ 0 0
$$463$$ −6148.00 −0.617110 −0.308555 0.951207i $$-0.599845\pi$$
−0.308555 + 0.951207i $$0.599845\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 5124.00 0.507731 0.253866 0.967240i $$-0.418298\pi$$
0.253866 + 0.967240i $$0.418298\pi$$
$$468$$ 0 0
$$469$$ 26936.0 2.65200
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −4488.00 −0.436276
$$474$$ 0 0
$$475$$ −6540.00 −0.631738
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −16520.0 −1.57582 −0.787910 0.615790i $$-0.788837\pi$$
−0.787910 + 0.615790i $$0.788837\pi$$
$$480$$ 0 0
$$481$$ 2112.00 0.200206
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 56.0000 0.00524295
$$486$$ 0 0
$$487$$ −524.000 −0.0487571 −0.0243785 0.999703i $$-0.507761\pi$$
−0.0243785 + 0.999703i $$0.507761\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −15028.0 −1.38127 −0.690636 0.723203i $$-0.742669\pi$$
−0.690636 + 0.723203i $$0.742669\pi$$
$$492$$ 0 0
$$493$$ −6660.00 −0.608421
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 19812.0 1.78811
$$498$$ 0 0
$$499$$ −9020.00 −0.809200 −0.404600 0.914494i $$-0.632589\pi$$
−0.404600 + 0.914494i $$0.632589\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −14812.0 −1.31299 −0.656495 0.754330i $$-0.727962\pi$$
−0.656495 + 0.754330i $$0.727962\pi$$
$$504$$ 0 0
$$505$$ −6808.00 −0.599905
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −12660.0 −1.10245 −0.551223 0.834358i $$-0.685839\pi$$
−0.551223 + 0.834358i $$0.685839\pi$$
$$510$$ 0 0
$$511$$ −14092.0 −1.21995
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 4528.00 0.387432
$$516$$ 0 0
$$517$$ −5566.00 −0.473486
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 3738.00 0.314328 0.157164 0.987573i $$-0.449765\pi$$
0.157164 + 0.987573i $$0.449765\pi$$
$$522$$ 0 0
$$523$$ 6352.00 0.531078 0.265539 0.964100i $$-0.414450\pi$$
0.265539 + 0.964100i $$0.414450\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −592.000 −0.0489334
$$528$$ 0 0
$$529$$ 20957.0 1.72245
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 13504.0 1.09742
$$534$$ 0 0
$$535$$ 2256.00 0.182309
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 3663.00 0.292721
$$540$$ 0 0
$$541$$ −24728.0 −1.96514 −0.982569 0.185898i $$-0.940481\pi$$
−0.982569 + 0.185898i $$0.940481\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −1280.00 −0.100604
$$546$$ 0 0
$$547$$ 22756.0 1.77875 0.889375 0.457178i $$-0.151140\pi$$
0.889375 + 0.457178i $$0.151140\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 5400.00 0.417509
$$552$$ 0 0
$$553$$ 14300.0 1.09963
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 9526.00 0.724649 0.362325 0.932052i $$-0.381983\pi$$
0.362325 + 0.932052i $$0.381983\pi$$
$$558$$ 0 0
$$559$$ 13056.0 0.987853
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 12068.0 0.903385 0.451692 0.892174i $$-0.350820\pi$$
0.451692 + 0.892174i $$0.350820\pi$$
$$564$$ 0 0
$$565$$ 8568.00 0.637980
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −15090.0 −1.11179 −0.555893 0.831254i $$-0.687623\pi$$
−0.555893 + 0.831254i $$0.687623\pi$$
$$570$$ 0 0
$$571$$ −4412.00 −0.323356 −0.161678 0.986844i $$-0.551691\pi$$
−0.161678 + 0.986844i $$0.551691\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 19838.0 1.43879
$$576$$ 0 0
$$577$$ −3906.00 −0.281818 −0.140909 0.990023i $$-0.545002\pi$$
−0.140909 + 0.990023i $$0.545002\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −3432.00 −0.245066
$$582$$ 0 0
$$583$$ −3828.00 −0.271937
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −12016.0 −0.844895 −0.422448 0.906387i $$-0.638829\pi$$
−0.422448 + 0.906387i $$0.638829\pi$$
$$588$$ 0 0
$$589$$ 480.000 0.0335790
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 11342.0 0.785430 0.392715 0.919660i $$-0.371536\pi$$
0.392715 + 0.919660i $$0.371536\pi$$
$$594$$ 0 0
$$595$$ −7696.00 −0.530261
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 20690.0 1.41130 0.705651 0.708559i $$-0.250654\pi$$
0.705651 + 0.708559i $$0.250654\pi$$
$$600$$ 0 0
$$601$$ −598.000 −0.0405872 −0.0202936 0.999794i $$-0.506460\pi$$
−0.0202936 + 0.999794i $$0.506460\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 484.000 0.0325246
$$606$$ 0 0
$$607$$ 166.000 0.0111001 0.00555003 0.999985i $$-0.498233\pi$$
0.00555003 + 0.999985i $$0.498233\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 16192.0 1.07211
$$612$$ 0 0
$$613$$ 20108.0 1.32488 0.662442 0.749113i $$-0.269520\pi$$
0.662442 + 0.749113i $$0.269520\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 2286.00 0.149159 0.0745793 0.997215i $$-0.476239\pi$$
0.0745793 + 0.997215i $$0.476239\pi$$
$$618$$ 0 0
$$619$$ 25660.0 1.66618 0.833088 0.553141i $$-0.186571\pi$$
0.833088 + 0.553141i $$0.186571\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −14820.0 −0.953051
$$624$$ 0 0
$$625$$ 9881.00 0.632384
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 4884.00 0.309599
$$630$$ 0 0
$$631$$ 11408.0 0.719723 0.359862 0.933006i $$-0.382824\pi$$
0.359862 + 0.933006i $$0.382824\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 6424.00 0.401462
$$636$$ 0 0
$$637$$ −10656.0 −0.662804
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 3378.00 0.208148 0.104074 0.994570i $$-0.466812\pi$$
0.104074 + 0.994570i $$0.466812\pi$$
$$642$$ 0 0
$$643$$ 11212.0 0.687649 0.343824 0.939034i $$-0.388278\pi$$
0.343824 + 0.939034i $$0.388278\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −86.0000 −0.00522567 −0.00261284 0.999997i $$-0.500832\pi$$
−0.00261284 + 0.999997i $$0.500832\pi$$
$$648$$ 0 0
$$649$$ −2200.00 −0.133062
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 4432.00 0.265601 0.132801 0.991143i $$-0.457603\pi$$
0.132801 + 0.991143i $$0.457603\pi$$
$$654$$ 0 0
$$655$$ −7632.00 −0.455278
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 4580.00 0.270731 0.135365 0.990796i $$-0.456779\pi$$
0.135365 + 0.990796i $$0.456779\pi$$
$$660$$ 0 0
$$661$$ 4282.00 0.251967 0.125984 0.992032i $$-0.459791\pi$$
0.125984 + 0.992032i $$0.459791\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 6240.00 0.363875
$$666$$ 0 0
$$667$$ −16380.0 −0.950879
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 1452.00 0.0835378
$$672$$ 0 0
$$673$$ 8438.00 0.483300 0.241650 0.970363i $$-0.422311\pi$$
0.241650 + 0.970363i $$0.422311\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −34494.0 −1.95822 −0.979108 0.203341i $$-0.934820\pi$$
−0.979108 + 0.203341i $$0.934820\pi$$
$$678$$ 0 0
$$679$$ 364.000 0.0205730
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −13712.0 −0.768192 −0.384096 0.923293i $$-0.625487\pi$$
−0.384096 + 0.923293i $$0.625487\pi$$
$$684$$ 0 0
$$685$$ 8744.00 0.487724
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 11136.0 0.615744
$$690$$ 0 0
$$691$$ −11372.0 −0.626066 −0.313033 0.949742i $$-0.601345\pi$$
−0.313033 + 0.949742i $$0.601345\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −10960.0 −0.598182
$$696$$ 0 0
$$697$$ 31228.0 1.69705
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 6398.00 0.344721 0.172360 0.985034i $$-0.444861\pi$$
0.172360 + 0.985034i $$0.444861\pi$$
$$702$$ 0 0
$$703$$ −3960.00 −0.212453
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −44252.0 −2.35399
$$708$$ 0 0
$$709$$ −5830.00 −0.308816 −0.154408 0.988007i $$-0.549347\pi$$
−0.154408 + 0.988007i $$0.549347\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −1456.00 −0.0764763
$$714$$ 0 0
$$715$$ −1408.00 −0.0736451
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 34530.0 1.79103 0.895516 0.445030i $$-0.146807\pi$$
0.895516 + 0.445030i $$0.146807\pi$$
$$720$$ 0 0
$$721$$ 29432.0 1.52026
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −9810.00 −0.502530
$$726$$ 0 0
$$727$$ 17316.0 0.883377 0.441688 0.897169i $$-0.354380\pi$$
0.441688 + 0.897169i $$0.354380\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 30192.0 1.52762
$$732$$ 0 0
$$733$$ −27072.0 −1.36416 −0.682079 0.731279i $$-0.738924\pi$$
−0.682079 + 0.731279i $$0.738924\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 11396.0 0.569575
$$738$$ 0 0
$$739$$ 17320.0 0.862147 0.431073 0.902317i $$-0.358135\pi$$
0.431073 + 0.902317i $$0.358135\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 14588.0 0.720299 0.360149 0.932895i $$-0.382726\pi$$
0.360149 + 0.932895i $$0.382726\pi$$
$$744$$ 0 0
$$745$$ 5240.00 0.257690
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 14664.0 0.715368
$$750$$ 0 0
$$751$$ −26152.0 −1.27071 −0.635353 0.772222i $$-0.719145\pi$$
−0.635353 + 0.772222i $$0.719145\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 4792.00 0.230992
$$756$$ 0 0
$$757$$ −1066.00 −0.0511815 −0.0255908 0.999673i $$-0.508147\pi$$
−0.0255908 + 0.999673i $$0.508147\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 37518.0 1.78716 0.893578 0.448907i $$-0.148187\pi$$
0.893578 + 0.448907i $$0.148187\pi$$
$$762$$ 0 0
$$763$$ −8320.00 −0.394763
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 6400.00 0.301292
$$768$$ 0 0
$$769$$ −17290.0 −0.810785 −0.405392 0.914143i $$-0.632865\pi$$
−0.405392 + 0.914143i $$0.632865\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 17172.0 0.799009 0.399504 0.916731i $$-0.369182\pi$$
0.399504 + 0.916731i $$0.369182\pi$$
$$774$$ 0 0
$$775$$ −872.000 −0.0404170
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −25320.0 −1.16455
$$780$$ 0 0
$$781$$ 8382.00 0.384035
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 8456.00 0.384468
$$786$$ 0 0
$$787$$ 9536.00 0.431921 0.215960 0.976402i $$-0.430712\pi$$
0.215960 + 0.976402i $$0.430712\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 55692.0 2.50339
$$792$$ 0 0
$$793$$ −4224.00 −0.189153
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 20516.0 0.911812 0.455906 0.890028i $$-0.349315\pi$$
0.455906 + 0.890028i $$0.349315\pi$$
$$798$$ 0 0
$$799$$ 37444.0 1.65791
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −5962.00 −0.262010
$$804$$ 0 0
$$805$$ −18928.0 −0.828726
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −22470.0 −0.976518 −0.488259 0.872699i $$-0.662368\pi$$
−0.488259 + 0.872699i $$0.662368\pi$$
$$810$$ 0 0
$$811$$ 3368.00 0.145828 0.0729140 0.997338i $$-0.476770\pi$$
0.0729140 + 0.997338i $$0.476770\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −15472.0 −0.664982
$$816$$ 0 0
$$817$$ −24480.0 −1.04828
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 10738.0 0.456466 0.228233 0.973607i $$-0.426705\pi$$
0.228233 + 0.973607i $$0.426705\pi$$
$$822$$ 0 0
$$823$$ 15912.0 0.673946 0.336973 0.941514i $$-0.390597\pi$$
0.336973 + 0.941514i $$0.390597\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 22924.0 0.963900 0.481950 0.876199i $$-0.339929\pi$$
0.481950 + 0.876199i $$0.339929\pi$$
$$828$$ 0 0
$$829$$ −41690.0 −1.74663 −0.873313 0.487159i $$-0.838033\pi$$
−0.873313 + 0.487159i $$0.838033\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −24642.0 −1.02496
$$834$$ 0 0
$$835$$ 8016.00 0.332222
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −16450.0 −0.676898 −0.338449 0.940985i $$-0.609902\pi$$
−0.338449 + 0.940985i $$0.609902\pi$$
$$840$$ 0 0
$$841$$ −16289.0 −0.667883
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −4692.00 −0.191017
$$846$$ 0 0
$$847$$ 3146.00 0.127624
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 12012.0 0.483861
$$852$$ 0 0
$$853$$ −30892.0 −1.24000 −0.620001 0.784601i $$-0.712868\pi$$
−0.620001 + 0.784601i $$0.712868\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 38906.0 1.55076 0.775381 0.631493i $$-0.217558\pi$$
0.775381 + 0.631493i $$0.217558\pi$$
$$858$$ 0 0
$$859$$ 1020.00 0.0405145 0.0202572 0.999795i $$-0.493551\pi$$
0.0202572 + 0.999795i $$0.493551\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 15078.0 0.594741 0.297370 0.954762i $$-0.403890\pi$$
0.297370 + 0.954762i $$0.403890\pi$$
$$864$$ 0 0
$$865$$ −2712.00 −0.106602
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 6050.00 0.236171
$$870$$ 0 0
$$871$$ −33152.0 −1.28968
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −24336.0 −0.940237
$$876$$ 0 0
$$877$$ 22704.0 0.874184 0.437092 0.899417i $$-0.356008\pi$$
0.437092 + 0.899417i $$0.356008\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 19358.0 0.740281 0.370141 0.928976i $$-0.379310\pi$$
0.370141 + 0.928976i $$0.379310\pi$$
$$882$$ 0 0
$$883$$ 11252.0 0.428833 0.214417 0.976742i $$-0.431215\pi$$
0.214417 + 0.976742i $$0.431215\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 43684.0 1.65362 0.826812 0.562478i $$-0.190152\pi$$
0.826812 + 0.562478i $$0.190152\pi$$
$$888$$ 0 0
$$889$$ 41756.0 1.57531
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −30360.0 −1.13769
$$894$$ 0 0
$$895$$ −6720.00 −0.250977
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 720.000 0.0267112
$$900$$ 0 0
$$901$$ 25752.0 0.952190
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −17432.0 −0.640287
$$906$$ 0 0
$$907$$ −45804.0 −1.67684 −0.838422 0.545022i $$-0.816521\pi$$
−0.838422 + 0.545022i $$0.816521\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −15318.0 −0.557089 −0.278544 0.960423i $$-0.589852\pi$$
−0.278544 + 0.960423i $$0.589852\pi$$
$$912$$ 0 0
$$913$$ −1452.00 −0.0526333
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −49608.0 −1.78648
$$918$$ 0 0
$$919$$ −11350.0 −0.407401 −0.203701 0.979033i $$-0.565297\pi$$
−0.203701 + 0.979033i $$0.565297\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −24384.0 −0.869566
$$924$$ 0 0
$$925$$ 7194.00 0.255716
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −33030.0 −1.16650 −0.583250 0.812292i $$-0.698219\pi$$
−0.583250 + 0.812292i $$0.698219\pi$$
$$930$$ 0 0
$$931$$ 19980.0 0.703349
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −3256.00 −0.113885
$$936$$ 0 0
$$937$$ −10006.0 −0.348860 −0.174430 0.984670i $$-0.555808\pi$$
−0.174430 + 0.984670i $$0.555808\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −2622.00 −0.0908340 −0.0454170 0.998968i $$-0.514462\pi$$
−0.0454170 + 0.998968i $$0.514462\pi$$
$$942$$ 0 0
$$943$$ 76804.0 2.65226
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −39876.0 −1.36832 −0.684158 0.729334i $$-0.739830\pi$$
−0.684158 + 0.729334i $$0.739830\pi$$
$$948$$ 0 0
$$949$$ 17344.0 0.593267
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −38918.0 −1.32285 −0.661426 0.750011i $$-0.730048\pi$$
−0.661426 + 0.750011i $$0.730048\pi$$
$$954$$ 0 0
$$955$$ −7112.00 −0.240983
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 56836.0 1.91380
$$960$$ 0 0
$$961$$ −29727.0 −0.997852
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −15848.0 −0.528669
$$966$$ 0 0
$$967$$ −1114.00 −0.0370464 −0.0185232 0.999828i $$-0.505896\pi$$
−0.0185232 + 0.999828i $$0.505896\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −1688.00 −0.0557884 −0.0278942 0.999611i $$-0.508880\pi$$
−0.0278942 + 0.999611i $$0.508880\pi$$
$$972$$ 0 0
$$973$$ −71240.0 −2.34722
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 41826.0 1.36963 0.684817 0.728715i $$-0.259882\pi$$
0.684817 + 0.728715i $$0.259882\pi$$
$$978$$ 0 0
$$979$$ −6270.00 −0.204689
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 978.000 0.0317328 0.0158664 0.999874i $$-0.494949\pi$$
0.0158664 + 0.999874i $$0.494949\pi$$
$$984$$ 0 0
$$985$$ −1496.00 −0.0483924
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 74256.0 2.38747
$$990$$ 0 0
$$991$$ −47272.0 −1.51528 −0.757641 0.652671i $$-0.773648\pi$$
−0.757641 + 0.652671i $$0.773648\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −8400.00 −0.267636
$$996$$ 0 0
$$997$$ 51104.0 1.62335 0.811675 0.584109i $$-0.198556\pi$$
0.811675 + 0.584109i $$0.198556\pi$$
$$998$$ 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 1584.4.a.l.1.1 1
3.2 odd 2 528.4.a.h.1.1 1
4.3 odd 2 99.4.a.a.1.1 1
12.11 even 2 33.4.a.b.1.1 1
20.19 odd 2 2475.4.a.e.1.1 1
24.5 odd 2 2112.4.a.h.1.1 1
24.11 even 2 2112.4.a.u.1.1 1
44.43 even 2 1089.4.a.e.1.1 1
60.23 odd 4 825.4.c.f.199.2 2
60.47 odd 4 825.4.c.f.199.1 2
60.59 even 2 825.4.a.f.1.1 1
84.83 odd 2 1617.4.a.d.1.1 1
132.131 odd 2 363.4.a.d.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
33.4.a.b.1.1 1 12.11 even 2
99.4.a.a.1.1 1 4.3 odd 2
363.4.a.d.1.1 1 132.131 odd 2
528.4.a.h.1.1 1 3.2 odd 2
825.4.a.f.1.1 1 60.59 even 2
825.4.c.f.199.1 2 60.47 odd 4
825.4.c.f.199.2 2 60.23 odd 4
1089.4.a.e.1.1 1 44.43 even 2
1584.4.a.l.1.1 1 1.1 even 1 trivial
1617.4.a.d.1.1 1 84.83 odd 2
2112.4.a.h.1.1 1 24.5 odd 2
2112.4.a.u.1.1 1 24.11 even 2
2475.4.a.e.1.1 1 20.19 odd 2