# Properties

 Label 720.4.a.bc.1.1 Level $720$ Weight $4$ Character 720.1 Self dual yes Analytic conductor $42.481$ 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] = [720,4,Mod(1,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, 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("720.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 720.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: $$42.4813752041$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 45) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 720.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+5.00000 q^{5} +30.0000 q^{7} +O(q^{10})$$ $$q+5.00000 q^{5} +30.0000 q^{7} +50.0000 q^{11} -20.0000 q^{13} +10.0000 q^{17} +44.0000 q^{19} +120.000 q^{23} +25.0000 q^{25} +50.0000 q^{29} -108.000 q^{31} +150.000 q^{35} -40.0000 q^{37} -400.000 q^{41} -280.000 q^{43} -280.000 q^{47} +557.000 q^{49} +610.000 q^{53} +250.000 q^{55} +50.0000 q^{59} -518.000 q^{61} -100.000 q^{65} +180.000 q^{67} +700.000 q^{71} -410.000 q^{73} +1500.00 q^{77} +516.000 q^{79} +660.000 q^{83} +50.0000 q^{85} +1500.00 q^{89} -600.000 q^{91} +220.000 q^{95} -1630.00 q^{97} +O(q^{100})$$

## 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
$$5$$ 5.00000 0.447214
$$6$$ 0 0
$$7$$ 30.0000 1.61985 0.809924 0.586535i $$-0.199508\pi$$
0.809924 + 0.586535i $$0.199508\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 50.0000 1.37051 0.685253 0.728305i $$-0.259692\pi$$
0.685253 + 0.728305i $$0.259692\pi$$
$$12$$ 0 0
$$13$$ −20.0000 −0.426692 −0.213346 0.976977i $$-0.568436\pi$$
−0.213346 + 0.976977i $$0.568436\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 10.0000 0.142668 0.0713340 0.997452i $$-0.477274\pi$$
0.0713340 + 0.997452i $$0.477274\pi$$
$$18$$ 0 0
$$19$$ 44.0000 0.531279 0.265639 0.964072i $$-0.414417\pi$$
0.265639 + 0.964072i $$0.414417\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 120.000 1.08790 0.543951 0.839117i $$-0.316928\pi$$
0.543951 + 0.839117i $$0.316928\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 50.0000 0.320164 0.160082 0.987104i $$-0.448824\pi$$
0.160082 + 0.987104i $$0.448824\pi$$
$$30$$ 0 0
$$31$$ −108.000 −0.625722 −0.312861 0.949799i $$-0.601287\pi$$
−0.312861 + 0.949799i $$0.601287\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 150.000 0.724418
$$36$$ 0 0
$$37$$ −40.0000 −0.177729 −0.0888643 0.996044i $$-0.528324\pi$$
−0.0888643 + 0.996044i $$0.528324\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −400.000 −1.52365 −0.761823 0.647785i $$-0.775696\pi$$
−0.761823 + 0.647785i $$0.775696\pi$$
$$42$$ 0 0
$$43$$ −280.000 −0.993014 −0.496507 0.868033i $$-0.665384\pi$$
−0.496507 + 0.868033i $$0.665384\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −280.000 −0.868983 −0.434491 0.900676i $$-0.643072\pi$$
−0.434491 + 0.900676i $$0.643072\pi$$
$$48$$ 0 0
$$49$$ 557.000 1.62391
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 610.000 1.58094 0.790471 0.612499i $$-0.209836\pi$$
0.790471 + 0.612499i $$0.209836\pi$$
$$54$$ 0 0
$$55$$ 250.000 0.612909
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 50.0000 0.110330 0.0551648 0.998477i $$-0.482432\pi$$
0.0551648 + 0.998477i $$0.482432\pi$$
$$60$$ 0 0
$$61$$ −518.000 −1.08726 −0.543632 0.839324i $$-0.682951\pi$$
−0.543632 + 0.839324i $$0.682951\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −100.000 −0.190823
$$66$$ 0 0
$$67$$ 180.000 0.328216 0.164108 0.986442i $$-0.447525\pi$$
0.164108 + 0.986442i $$0.447525\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 700.000 1.17007 0.585033 0.811009i $$-0.301081\pi$$
0.585033 + 0.811009i $$0.301081\pi$$
$$72$$ 0 0
$$73$$ −410.000 −0.657354 −0.328677 0.944442i $$-0.606603\pi$$
−0.328677 + 0.944442i $$0.606603\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1500.00 2.22001
$$78$$ 0 0
$$79$$ 516.000 0.734868 0.367434 0.930050i $$-0.380236\pi$$
0.367434 + 0.930050i $$0.380236\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 660.000 0.872824 0.436412 0.899747i $$-0.356249\pi$$
0.436412 + 0.899747i $$0.356249\pi$$
$$84$$ 0 0
$$85$$ 50.0000 0.0638031
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1500.00 1.78651 0.893257 0.449547i $$-0.148415\pi$$
0.893257 + 0.449547i $$0.148415\pi$$
$$90$$ 0 0
$$91$$ −600.000 −0.691177
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 220.000 0.237595
$$96$$ 0 0
$$97$$ −1630.00 −1.70620 −0.853100 0.521747i $$-0.825280\pi$$
−0.853100 + 0.521747i $$0.825280\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 450.000 0.443333 0.221667 0.975122i $$-0.428850\pi$$
0.221667 + 0.975122i $$0.428850\pi$$
$$102$$ 0 0
$$103$$ −770.000 −0.736605 −0.368303 0.929706i $$-0.620061\pi$$
−0.368303 + 0.929706i $$0.620061\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 660.000 0.596305 0.298152 0.954518i $$-0.403630\pi$$
0.298152 + 0.954518i $$0.403630\pi$$
$$108$$ 0 0
$$109$$ 1754.00 1.54131 0.770655 0.637253i $$-0.219929\pi$$
0.770655 + 0.637253i $$0.219929\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 310.000 0.258074 0.129037 0.991640i $$-0.458811\pi$$
0.129037 + 0.991640i $$0.458811\pi$$
$$114$$ 0 0
$$115$$ 600.000 0.486524
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 300.000 0.231100
$$120$$ 0 0
$$121$$ 1169.00 0.878287
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ 1070.00 0.747615 0.373808 0.927506i $$-0.378052\pi$$
0.373808 + 0.927506i $$0.378052\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1950.00 1.30055 0.650276 0.759698i $$-0.274653\pi$$
0.650276 + 0.759698i $$0.274653\pi$$
$$132$$ 0 0
$$133$$ 1320.00 0.860590
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1050.00 −0.654800 −0.327400 0.944886i $$-0.606172\pi$$
−0.327400 + 0.944886i $$0.606172\pi$$
$$138$$ 0 0
$$139$$ −1676.00 −1.02271 −0.511354 0.859370i $$-0.670856\pi$$
−0.511354 + 0.859370i $$0.670856\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −1000.00 −0.584785
$$144$$ 0 0
$$145$$ 250.000 0.143182
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2050.00 −1.12713 −0.563566 0.826071i $$-0.690571\pi$$
−0.563566 + 0.826071i $$0.690571\pi$$
$$150$$ 0 0
$$151$$ −448.000 −0.241442 −0.120721 0.992686i $$-0.538521\pi$$
−0.120721 + 0.992686i $$0.538521\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −540.000 −0.279831
$$156$$ 0 0
$$157$$ −100.000 −0.0508336 −0.0254168 0.999677i $$-0.508091\pi$$
−0.0254168 + 0.999677i $$0.508091\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 3600.00 1.76223
$$162$$ 0 0
$$163$$ 1900.00 0.913003 0.456501 0.889723i $$-0.349102\pi$$
0.456501 + 0.889723i $$0.349102\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1920.00 0.889665 0.444833 0.895614i $$-0.353263\pi$$
0.444833 + 0.895614i $$0.353263\pi$$
$$168$$ 0 0
$$169$$ −1797.00 −0.817934
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −2550.00 −1.12065 −0.560326 0.828272i $$-0.689324\pi$$
−0.560326 + 0.828272i $$0.689324\pi$$
$$174$$ 0 0
$$175$$ 750.000 0.323970
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 3650.00 1.52410 0.762050 0.647518i $$-0.224193\pi$$
0.762050 + 0.647518i $$0.224193\pi$$
$$180$$ 0 0
$$181$$ −4342.00 −1.78308 −0.891542 0.452937i $$-0.850376\pi$$
−0.891542 + 0.452937i $$0.850376\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −200.000 −0.0794827
$$186$$ 0 0
$$187$$ 500.000 0.195527
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3500.00 −1.32592 −0.662961 0.748654i $$-0.730701\pi$$
−0.662961 + 0.748654i $$0.730701\pi$$
$$192$$ 0 0
$$193$$ 3350.00 1.24942 0.624711 0.780856i $$-0.285217\pi$$
0.624711 + 0.780856i $$0.285217\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −90.0000 −0.0325494 −0.0162747 0.999868i $$-0.505181\pi$$
−0.0162747 + 0.999868i $$0.505181\pi$$
$$198$$ 0 0
$$199$$ −3664.00 −1.30520 −0.652598 0.757704i $$-0.726321\pi$$
−0.652598 + 0.757704i $$0.726321\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 1500.00 0.518618
$$204$$ 0 0
$$205$$ −2000.00 −0.681395
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 2200.00 0.728120
$$210$$ 0 0
$$211$$ 268.000 0.0874402 0.0437201 0.999044i $$-0.486079\pi$$
0.0437201 + 0.999044i $$0.486079\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −1400.00 −0.444089
$$216$$ 0 0
$$217$$ −3240.00 −1.01357
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −200.000 −0.0608754
$$222$$ 0 0
$$223$$ 3670.00 1.10207 0.551034 0.834482i $$-0.314233\pi$$
0.551034 + 0.834482i $$0.314233\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 3760.00 1.09938 0.549692 0.835368i $$-0.314745\pi$$
0.549692 + 0.835368i $$0.314745\pi$$
$$228$$ 0 0
$$229$$ −1434.00 −0.413805 −0.206903 0.978362i $$-0.566338\pi$$
−0.206903 + 0.978362i $$0.566338\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 3450.00 0.970030 0.485015 0.874506i $$-0.338814\pi$$
0.485015 + 0.874506i $$0.338814\pi$$
$$234$$ 0 0
$$235$$ −1400.00 −0.388621
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −4900.00 −1.32617 −0.663085 0.748544i $$-0.730753\pi$$
−0.663085 + 0.748544i $$0.730753\pi$$
$$240$$ 0 0
$$241$$ 4822.00 1.28885 0.644424 0.764668i $$-0.277097\pi$$
0.644424 + 0.764668i $$0.277097\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 2785.00 0.726233
$$246$$ 0 0
$$247$$ −880.000 −0.226693
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −4650.00 −1.16934 −0.584672 0.811270i $$-0.698777\pi$$
−0.584672 + 0.811270i $$0.698777\pi$$
$$252$$ 0 0
$$253$$ 6000.00 1.49098
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −5130.00 −1.24514 −0.622569 0.782565i $$-0.713911\pi$$
−0.622569 + 0.782565i $$0.713911\pi$$
$$258$$ 0 0
$$259$$ −1200.00 −0.287893
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −1280.00 −0.300107 −0.150054 0.988678i $$-0.547945\pi$$
−0.150054 + 0.988678i $$0.547945\pi$$
$$264$$ 0 0
$$265$$ 3050.00 0.707019
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −3350.00 −0.759305 −0.379653 0.925129i $$-0.623956\pi$$
−0.379653 + 0.925129i $$0.623956\pi$$
$$270$$ 0 0
$$271$$ −5512.00 −1.23554 −0.617768 0.786361i $$-0.711963\pi$$
−0.617768 + 0.786361i $$0.711963\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1250.00 0.274101
$$276$$ 0 0
$$277$$ 4920.00 1.06720 0.533600 0.845737i $$-0.320839\pi$$
0.533600 + 0.845737i $$0.320839\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −4500.00 −0.955329 −0.477665 0.878542i $$-0.658517\pi$$
−0.477665 + 0.878542i $$0.658517\pi$$
$$282$$ 0 0
$$283$$ 6900.00 1.44934 0.724669 0.689098i $$-0.241993\pi$$
0.724669 + 0.689098i $$0.241993\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −12000.0 −2.46808
$$288$$ 0 0
$$289$$ −4813.00 −0.979646
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1530.00 −0.305063 −0.152532 0.988299i $$-0.548743\pi$$
−0.152532 + 0.988299i $$0.548743\pi$$
$$294$$ 0 0
$$295$$ 250.000 0.0493409
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −2400.00 −0.464199
$$300$$ 0 0
$$301$$ −8400.00 −1.60853
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −2590.00 −0.486239
$$306$$ 0 0
$$307$$ −3040.00 −0.565153 −0.282576 0.959245i $$-0.591189\pi$$
−0.282576 + 0.959245i $$0.591189\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −5700.00 −1.03928 −0.519642 0.854384i $$-0.673935\pi$$
−0.519642 + 0.854384i $$0.673935\pi$$
$$312$$ 0 0
$$313$$ 3110.00 0.561622 0.280811 0.959763i $$-0.409397\pi$$
0.280811 + 0.959763i $$0.409397\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 950.000 0.168320 0.0841598 0.996452i $$-0.473179\pi$$
0.0841598 + 0.996452i $$0.473179\pi$$
$$318$$ 0 0
$$319$$ 2500.00 0.438787
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 440.000 0.0757965
$$324$$ 0 0
$$325$$ −500.000 −0.0853385
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −8400.00 −1.40762
$$330$$ 0 0
$$331$$ −2292.00 −0.380603 −0.190302 0.981726i $$-0.560947\pi$$
−0.190302 + 0.981726i $$0.560947\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 900.000 0.146783
$$336$$ 0 0
$$337$$ −7730.00 −1.24950 −0.624748 0.780827i $$-0.714798\pi$$
−0.624748 + 0.780827i $$0.714798\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −5400.00 −0.857555
$$342$$ 0 0
$$343$$ 6420.00 1.01063
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1120.00 −0.173270 −0.0866351 0.996240i $$-0.527611\pi$$
−0.0866351 + 0.996240i $$0.527611\pi$$
$$348$$ 0 0
$$349$$ 1186.00 0.181906 0.0909529 0.995855i $$-0.471009\pi$$
0.0909529 + 0.995855i $$0.471009\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −3630.00 −0.547324 −0.273662 0.961826i $$-0.588235\pi$$
−0.273662 + 0.961826i $$0.588235\pi$$
$$354$$ 0 0
$$355$$ 3500.00 0.523270
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −1800.00 −0.264625 −0.132312 0.991208i $$-0.542240\pi$$
−0.132312 + 0.991208i $$0.542240\pi$$
$$360$$ 0 0
$$361$$ −4923.00 −0.717743
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −2050.00 −0.293978
$$366$$ 0 0
$$367$$ −8490.00 −1.20756 −0.603780 0.797151i $$-0.706339\pi$$
−0.603780 + 0.797151i $$0.706339\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 18300.0 2.56089
$$372$$ 0 0
$$373$$ 100.000 0.0138815 0.00694076 0.999976i $$-0.497791\pi$$
0.00694076 + 0.999976i $$0.497791\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −1000.00 −0.136612
$$378$$ 0 0
$$379$$ 8084.00 1.09564 0.547820 0.836597i $$-0.315458\pi$$
0.547820 + 0.836597i $$0.315458\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −9480.00 −1.26477 −0.632383 0.774656i $$-0.717923\pi$$
−0.632383 + 0.774656i $$0.717923\pi$$
$$384$$ 0 0
$$385$$ 7500.00 0.992819
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 10950.0 1.42722 0.713608 0.700545i $$-0.247060\pi$$
0.713608 + 0.700545i $$0.247060\pi$$
$$390$$ 0 0
$$391$$ 1200.00 0.155209
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 2580.00 0.328643
$$396$$ 0 0
$$397$$ 13840.0 1.74965 0.874823 0.484442i $$-0.160977\pi$$
0.874823 + 0.484442i $$0.160977\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −9300.00 −1.15815 −0.579077 0.815273i $$-0.696587\pi$$
−0.579077 + 0.815273i $$0.696587\pi$$
$$402$$ 0 0
$$403$$ 2160.00 0.266991
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −2000.00 −0.243578
$$408$$ 0 0
$$409$$ −2854.00 −0.345040 −0.172520 0.985006i $$-0.555191\pi$$
−0.172520 + 0.985006i $$0.555191\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 1500.00 0.178717
$$414$$ 0 0
$$415$$ 3300.00 0.390339
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 1150.00 0.134084 0.0670420 0.997750i $$-0.478644\pi$$
0.0670420 + 0.997750i $$0.478644\pi$$
$$420$$ 0 0
$$421$$ −11162.0 −1.29217 −0.646084 0.763266i $$-0.723594\pi$$
−0.646084 + 0.763266i $$0.723594\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 250.000 0.0285336
$$426$$ 0 0
$$427$$ −15540.0 −1.76120
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1200.00 −0.134111 −0.0670556 0.997749i $$-0.521361\pi$$
−0.0670556 + 0.997749i $$0.521361\pi$$
$$432$$ 0 0
$$433$$ 1510.00 0.167589 0.0837944 0.996483i $$-0.473296\pi$$
0.0837944 + 0.996483i $$0.473296\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 5280.00 0.577979
$$438$$ 0 0
$$439$$ −424.000 −0.0460966 −0.0230483 0.999734i $$-0.507337\pi$$
−0.0230483 + 0.999734i $$0.507337\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 12360.0 1.32560 0.662801 0.748796i $$-0.269368\pi$$
0.662801 + 0.748796i $$0.269368\pi$$
$$444$$ 0 0
$$445$$ 7500.00 0.798953
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 1300.00 0.136639 0.0683194 0.997664i $$-0.478236\pi$$
0.0683194 + 0.997664i $$0.478236\pi$$
$$450$$ 0 0
$$451$$ −20000.0 −2.08817
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −3000.00 −0.309104
$$456$$ 0 0
$$457$$ −7190.00 −0.735961 −0.367980 0.929834i $$-0.619951\pi$$
−0.367980 + 0.929834i $$0.619951\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 150.000 0.0151544 0.00757722 0.999971i $$-0.497588\pi$$
0.00757722 + 0.999971i $$0.497588\pi$$
$$462$$ 0 0
$$463$$ −2670.00 −0.268003 −0.134002 0.990981i $$-0.542783\pi$$
−0.134002 + 0.990981i $$0.542783\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 1180.00 0.116925 0.0584624 0.998290i $$-0.481380\pi$$
0.0584624 + 0.998290i $$0.481380\pi$$
$$468$$ 0 0
$$469$$ 5400.00 0.531661
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −14000.0 −1.36093
$$474$$ 0 0
$$475$$ 1100.00 0.106256
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −14100.0 −1.34498 −0.672490 0.740106i $$-0.734775\pi$$
−0.672490 + 0.740106i $$0.734775\pi$$
$$480$$ 0 0
$$481$$ 800.000 0.0758355
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −8150.00 −0.763036
$$486$$ 0 0
$$487$$ 9850.00 0.916522 0.458261 0.888818i $$-0.348473\pi$$
0.458261 + 0.888818i $$0.348473\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −2450.00 −0.225187 −0.112594 0.993641i $$-0.535916\pi$$
−0.112594 + 0.993641i $$0.535916\pi$$
$$492$$ 0 0
$$493$$ 500.000 0.0456772
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 21000.0 1.89533
$$498$$ 0 0
$$499$$ 17036.0 1.52833 0.764164 0.645021i $$-0.223152\pi$$
0.764164 + 0.645021i $$0.223152\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −20600.0 −1.82606 −0.913030 0.407891i $$-0.866264\pi$$
−0.913030 + 0.407891i $$0.866264\pi$$
$$504$$ 0 0
$$505$$ 2250.00 0.198265
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −5750.00 −0.500716 −0.250358 0.968153i $$-0.580548\pi$$
−0.250358 + 0.968153i $$0.580548\pi$$
$$510$$ 0 0
$$511$$ −12300.0 −1.06481
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −3850.00 −0.329420
$$516$$ 0 0
$$517$$ −14000.0 −1.19095
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 15500.0 1.30339 0.651696 0.758480i $$-0.274058\pi$$
0.651696 + 0.758480i $$0.274058\pi$$
$$522$$ 0 0
$$523$$ 13940.0 1.16549 0.582747 0.812653i $$-0.301978\pi$$
0.582747 + 0.812653i $$0.301978\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −1080.00 −0.0892705
$$528$$ 0 0
$$529$$ 2233.00 0.183529
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 8000.00 0.650128
$$534$$ 0 0
$$535$$ 3300.00 0.266676
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 27850.0 2.22557
$$540$$ 0 0
$$541$$ −20478.0 −1.62739 −0.813695 0.581292i $$-0.802547\pi$$
−0.813695 + 0.581292i $$0.802547\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 8770.00 0.689295
$$546$$ 0 0
$$547$$ −12040.0 −0.941121 −0.470561 0.882368i $$-0.655948\pi$$
−0.470561 + 0.882368i $$0.655948\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 2200.00 0.170096
$$552$$ 0 0
$$553$$ 15480.0 1.19037
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −23550.0 −1.79146 −0.895732 0.444594i $$-0.853348\pi$$
−0.895732 + 0.444594i $$0.853348\pi$$
$$558$$ 0 0
$$559$$ 5600.00 0.423712
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −6120.00 −0.458130 −0.229065 0.973411i $$-0.573567\pi$$
−0.229065 + 0.973411i $$0.573567\pi$$
$$564$$ 0 0
$$565$$ 1550.00 0.115414
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 11700.0 0.862020 0.431010 0.902347i $$-0.358157\pi$$
0.431010 + 0.902347i $$0.358157\pi$$
$$570$$ 0 0
$$571$$ 8188.00 0.600100 0.300050 0.953923i $$-0.402997\pi$$
0.300050 + 0.953923i $$0.402997\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 3000.00 0.217580
$$576$$ 0 0
$$577$$ 11690.0 0.843433 0.421717 0.906728i $$-0.361428\pi$$
0.421717 + 0.906728i $$0.361428\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 19800.0 1.41384
$$582$$ 0 0
$$583$$ 30500.0 2.16669
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 21060.0 1.48082 0.740408 0.672157i $$-0.234632\pi$$
0.740408 + 0.672157i $$0.234632\pi$$
$$588$$ 0 0
$$589$$ −4752.00 −0.332433
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 22910.0 1.58651 0.793255 0.608889i $$-0.208385\pi$$
0.793255 + 0.608889i $$0.208385\pi$$
$$594$$ 0 0
$$595$$ 1500.00 0.103351
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −1400.00 −0.0954966 −0.0477483 0.998859i $$-0.515205\pi$$
−0.0477483 + 0.998859i $$0.515205\pi$$
$$600$$ 0 0
$$601$$ −11002.0 −0.746724 −0.373362 0.927686i $$-0.621795\pi$$
−0.373362 + 0.927686i $$0.621795\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 5845.00 0.392782
$$606$$ 0 0
$$607$$ −4630.00 −0.309598 −0.154799 0.987946i $$-0.549473\pi$$
−0.154799 + 0.987946i $$0.549473\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 5600.00 0.370788
$$612$$ 0 0
$$613$$ 24040.0 1.58396 0.791979 0.610548i $$-0.209051\pi$$
0.791979 + 0.610548i $$0.209051\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1890.00 0.123320 0.0616601 0.998097i $$-0.480361\pi$$
0.0616601 + 0.998097i $$0.480361\pi$$
$$618$$ 0 0
$$619$$ −19244.0 −1.24957 −0.624783 0.780798i $$-0.714813\pi$$
−0.624783 + 0.780798i $$0.714813\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 45000.0 2.89388
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −400.000 −0.0253562
$$630$$ 0 0
$$631$$ −15892.0 −1.00262 −0.501308 0.865269i $$-0.667148\pi$$
−0.501308 + 0.865269i $$0.667148\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 5350.00 0.334344
$$636$$ 0 0
$$637$$ −11140.0 −0.692909
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 12600.0 0.776396 0.388198 0.921576i $$-0.373098\pi$$
0.388198 + 0.921576i $$0.373098\pi$$
$$642$$ 0 0
$$643$$ −7260.00 −0.445267 −0.222633 0.974902i $$-0.571465\pi$$
−0.222633 + 0.974902i $$0.571465\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 7400.00 0.449651 0.224825 0.974399i $$-0.427819\pi$$
0.224825 + 0.974399i $$0.427819\pi$$
$$648$$ 0 0
$$649$$ 2500.00 0.151207
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 4790.00 0.287055 0.143528 0.989646i $$-0.454155\pi$$
0.143528 + 0.989646i $$0.454155\pi$$
$$654$$ 0 0
$$655$$ 9750.00 0.581624
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −1450.00 −0.0857117 −0.0428558 0.999081i $$-0.513646\pi$$
−0.0428558 + 0.999081i $$0.513646\pi$$
$$660$$ 0 0
$$661$$ 11818.0 0.695411 0.347706 0.937604i $$-0.386961\pi$$
0.347706 + 0.937604i $$0.386961\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 6600.00 0.384868
$$666$$ 0 0
$$667$$ 6000.00 0.348307
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −25900.0 −1.49010
$$672$$ 0 0
$$673$$ 5550.00 0.317885 0.158943 0.987288i $$-0.449192\pi$$
0.158943 + 0.987288i $$0.449192\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −12930.0 −0.734033 −0.367016 0.930214i $$-0.619621\pi$$
−0.367016 + 0.930214i $$0.619621\pi$$
$$678$$ 0 0
$$679$$ −48900.0 −2.76378
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 32580.0 1.82524 0.912620 0.408809i $$-0.134056\pi$$
0.912620 + 0.408809i $$0.134056\pi$$
$$684$$ 0 0
$$685$$ −5250.00 −0.292835
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −12200.0 −0.674576
$$690$$ 0 0
$$691$$ −10228.0 −0.563085 −0.281542 0.959549i $$-0.590846\pi$$
−0.281542 + 0.959549i $$0.590846\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −8380.00 −0.457369
$$696$$ 0 0
$$697$$ −4000.00 −0.217376
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −8350.00 −0.449893 −0.224947 0.974371i $$-0.572221\pi$$
−0.224947 + 0.974371i $$0.572221\pi$$
$$702$$ 0 0
$$703$$ −1760.00 −0.0944234
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 13500.0 0.718133
$$708$$ 0 0
$$709$$ −14954.0 −0.792115 −0.396057 0.918226i $$-0.629622\pi$$
−0.396057 + 0.918226i $$0.629622\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −12960.0 −0.680723
$$714$$ 0 0
$$715$$ −5000.00 −0.261524
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 29400.0 1.52494 0.762472 0.647021i $$-0.223985\pi$$
0.762472 + 0.647021i $$0.223985\pi$$
$$720$$ 0 0
$$721$$ −23100.0 −1.19319
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 1250.00 0.0640329
$$726$$ 0 0
$$727$$ 16330.0 0.833076 0.416538 0.909118i $$-0.363243\pi$$
0.416538 + 0.909118i $$0.363243\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −2800.00 −0.141671
$$732$$ 0 0
$$733$$ 30800.0 1.55201 0.776005 0.630726i $$-0.217243\pi$$
0.776005 + 0.630726i $$0.217243\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 9000.00 0.449823
$$738$$ 0 0
$$739$$ 9524.00 0.474081 0.237041 0.971500i $$-0.423823\pi$$
0.237041 + 0.971500i $$0.423823\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −28600.0 −1.41216 −0.706078 0.708134i $$-0.749537\pi$$
−0.706078 + 0.708134i $$0.749537\pi$$
$$744$$ 0 0
$$745$$ −10250.0 −0.504068
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 19800.0 0.965923
$$750$$ 0 0
$$751$$ 8252.00 0.400958 0.200479 0.979698i $$-0.435750\pi$$
0.200479 + 0.979698i $$0.435750\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −2240.00 −0.107976
$$756$$ 0 0
$$757$$ −24920.0 −1.19648 −0.598238 0.801318i $$-0.704132\pi$$
−0.598238 + 0.801318i $$0.704132\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −27900.0 −1.32901 −0.664503 0.747285i $$-0.731357\pi$$
−0.664503 + 0.747285i $$0.731357\pi$$
$$762$$ 0 0
$$763$$ 52620.0 2.49669
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −1000.00 −0.0470768
$$768$$ 0 0
$$769$$ −11506.0 −0.539554 −0.269777 0.962923i $$-0.586950\pi$$
−0.269777 + 0.962923i $$0.586950\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 12510.0 0.582087 0.291044 0.956710i $$-0.405998\pi$$
0.291044 + 0.956710i $$0.405998\pi$$
$$774$$ 0 0
$$775$$ −2700.00 −0.125144
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −17600.0 −0.809481
$$780$$ 0 0
$$781$$ 35000.0 1.60358
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −500.000 −0.0227335
$$786$$ 0 0
$$787$$ 1100.00 0.0498231 0.0249115 0.999690i $$-0.492070\pi$$
0.0249115 + 0.999690i $$0.492070\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 9300.00 0.418040
$$792$$ 0 0
$$793$$ 10360.0 0.463927
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 4490.00 0.199553 0.0997766 0.995010i $$-0.468187\pi$$
0.0997766 + 0.995010i $$0.468187\pi$$
$$798$$ 0 0
$$799$$ −2800.00 −0.123976
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −20500.0 −0.900908
$$804$$ 0 0
$$805$$ 18000.0 0.788095
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −28600.0 −1.24292 −0.621460 0.783446i $$-0.713460\pi$$
−0.621460 + 0.783446i $$0.713460\pi$$
$$810$$ 0 0
$$811$$ −10068.0 −0.435925 −0.217963 0.975957i $$-0.569941\pi$$
−0.217963 + 0.975957i $$0.569941\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 9500.00 0.408307
$$816$$ 0 0
$$817$$ −12320.0 −0.527567
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 14250.0 0.605759 0.302880 0.953029i $$-0.402052\pi$$
0.302880 + 0.953029i $$0.402052\pi$$
$$822$$ 0 0
$$823$$ −6830.00 −0.289282 −0.144641 0.989484i $$-0.546203\pi$$
−0.144641 + 0.989484i $$0.546203\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −8920.00 −0.375065 −0.187533 0.982258i $$-0.560049\pi$$
−0.187533 + 0.982258i $$0.560049\pi$$
$$828$$ 0 0
$$829$$ −3534.00 −0.148059 −0.0740295 0.997256i $$-0.523586\pi$$
−0.0740295 + 0.997256i $$0.523586\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 5570.00 0.231680
$$834$$ 0 0
$$835$$ 9600.00 0.397870
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −8000.00 −0.329190 −0.164595 0.986361i $$-0.552632\pi$$
−0.164595 + 0.986361i $$0.552632\pi$$
$$840$$ 0 0
$$841$$ −21889.0 −0.897495
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −8985.00 −0.365791
$$846$$ 0 0
$$847$$ 35070.0 1.42269
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −4800.00 −0.193351
$$852$$ 0 0
$$853$$ 5160.00 0.207122 0.103561 0.994623i $$-0.466976\pi$$
0.103561 + 0.994623i $$0.466976\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −7670.00 −0.305720 −0.152860 0.988248i $$-0.548848\pi$$
−0.152860 + 0.988248i $$0.548848\pi$$
$$858$$ 0 0
$$859$$ −25804.0 −1.02494 −0.512469 0.858706i $$-0.671269\pi$$
−0.512469 + 0.858706i $$0.671269\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 400.000 0.0157777 0.00788885 0.999969i $$-0.497489\pi$$
0.00788885 + 0.999969i $$0.497489\pi$$
$$864$$ 0 0
$$865$$ −12750.0 −0.501171
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 25800.0 1.00714
$$870$$ 0 0
$$871$$ −3600.00 −0.140047
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 3750.00 0.144884
$$876$$ 0 0
$$877$$ −35100.0 −1.35147 −0.675737 0.737143i $$-0.736175\pi$$
−0.675737 + 0.737143i $$0.736175\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 18700.0 0.715118 0.357559 0.933891i $$-0.383609\pi$$
0.357559 + 0.933891i $$0.383609\pi$$
$$882$$ 0 0
$$883$$ 2980.00 0.113573 0.0567865 0.998386i $$-0.481915\pi$$
0.0567865 + 0.998386i $$0.481915\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −35880.0 −1.35821 −0.679105 0.734041i $$-0.737632\pi$$
−0.679105 + 0.734041i $$0.737632\pi$$
$$888$$ 0 0
$$889$$ 32100.0 1.21102
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −12320.0 −0.461672
$$894$$ 0 0
$$895$$ 18250.0 0.681598
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −5400.00 −0.200334
$$900$$ 0 0
$$901$$ 6100.00 0.225550
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −21710.0 −0.797420
$$906$$ 0 0
$$907$$ −45240.0 −1.65620 −0.828098 0.560584i $$-0.810577\pi$$
−0.828098 + 0.560584i $$0.810577\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 33200.0 1.20743 0.603713 0.797202i $$-0.293687\pi$$
0.603713 + 0.797202i $$0.293687\pi$$
$$912$$ 0 0
$$913$$ 33000.0 1.19621
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 58500.0 2.10670
$$918$$ 0 0
$$919$$ −35356.0 −1.26908 −0.634541 0.772889i $$-0.718811\pi$$
−0.634541 + 0.772889i $$0.718811\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −14000.0 −0.499259
$$924$$ 0 0
$$925$$ −1000.00 −0.0355457
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 25700.0 0.907631 0.453816 0.891096i $$-0.350062\pi$$
0.453816 + 0.891096i $$0.350062\pi$$
$$930$$ 0 0
$$931$$ 24508.0 0.862747
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 2500.00 0.0874425
$$936$$ 0 0
$$937$$ 52890.0 1.84401 0.922007 0.387173i $$-0.126549\pi$$
0.922007 + 0.387173i $$0.126549\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −38050.0 −1.31817 −0.659083 0.752070i $$-0.729055\pi$$
−0.659083 + 0.752070i $$0.729055\pi$$
$$942$$ 0 0
$$943$$ −48000.0 −1.65758
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −29640.0 −1.01708 −0.508538 0.861040i $$-0.669814\pi$$
−0.508538 + 0.861040i $$0.669814\pi$$
$$948$$ 0 0
$$949$$ 8200.00 0.280488
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −15170.0 −0.515640 −0.257820 0.966193i $$-0.583004\pi$$
−0.257820 + 0.966193i $$0.583004\pi$$
$$954$$ 0 0
$$955$$ −17500.0 −0.592970
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −31500.0 −1.06068
$$960$$ 0 0
$$961$$ −18127.0 −0.608472
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 16750.0 0.558758
$$966$$ 0 0
$$967$$ 5470.00 0.181906 0.0909531 0.995855i $$-0.471009\pi$$
0.0909531 + 0.995855i $$0.471009\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 15150.0 0.500707 0.250354 0.968154i $$-0.419453\pi$$
0.250354 + 0.968154i $$0.419453\pi$$
$$972$$ 0 0
$$973$$ −50280.0 −1.65663
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −31190.0 −1.02135 −0.510674 0.859775i $$-0.670604\pi$$
−0.510674 + 0.859775i $$0.670604\pi$$
$$978$$ 0 0
$$979$$ 75000.0 2.44843
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −7560.00 −0.245297 −0.122648 0.992450i $$-0.539139\pi$$
−0.122648 + 0.992450i $$0.539139\pi$$
$$984$$ 0 0
$$985$$ −450.000 −0.0145565
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −33600.0 −1.08030
$$990$$ 0 0
$$991$$ −32672.0 −1.04729 −0.523643 0.851938i $$-0.675427\pi$$
−0.523643 + 0.851938i $$0.675427\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −18320.0 −0.583702
$$996$$ 0 0
$$997$$ −4740.00 −0.150569 −0.0752845 0.997162i $$-0.523986\pi$$
−0.0752845 + 0.997162i $$0.523986\pi$$
$$998$$ 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 720.4.a.bc.1.1 1
3.2 odd 2 720.4.a.o.1.1 1
4.3 odd 2 45.4.a.a.1.1 1
12.11 even 2 45.4.a.e.1.1 yes 1
20.3 even 4 225.4.b.a.199.2 2
20.7 even 4 225.4.b.a.199.1 2
20.19 odd 2 225.4.a.h.1.1 1
28.27 even 2 2205.4.a.a.1.1 1
36.7 odd 6 405.4.e.n.271.1 2
36.11 even 6 405.4.e.b.271.1 2
36.23 even 6 405.4.e.b.136.1 2
36.31 odd 6 405.4.e.n.136.1 2
60.23 odd 4 225.4.b.b.199.1 2
60.47 odd 4 225.4.b.b.199.2 2
60.59 even 2 225.4.a.a.1.1 1
84.83 odd 2 2205.4.a.t.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.a.a.1.1 1 4.3 odd 2
45.4.a.e.1.1 yes 1 12.11 even 2
225.4.a.a.1.1 1 60.59 even 2
225.4.a.h.1.1 1 20.19 odd 2
225.4.b.a.199.1 2 20.7 even 4
225.4.b.a.199.2 2 20.3 even 4
225.4.b.b.199.1 2 60.23 odd 4
225.4.b.b.199.2 2 60.47 odd 4
405.4.e.b.136.1 2 36.23 even 6
405.4.e.b.271.1 2 36.11 even 6
405.4.e.n.136.1 2 36.31 odd 6
405.4.e.n.271.1 2 36.7 odd 6
720.4.a.o.1.1 1 3.2 odd 2
720.4.a.bc.1.1 1 1.1 even 1 trivial
2205.4.a.a.1.1 1 28.27 even 2
2205.4.a.t.1.1 1 84.83 odd 2