# Properties

 Label 1872.4.a.f.1.1 Level $1872$ Weight $4$ Character 1872.1 Self dual yes Analytic conductor $110.452$ 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] = [1872,4,Mod(1,1872)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1872, 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("1872.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1872 = 2^{4} \cdot 3^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1872.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: $$110.451575531$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 78) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1872.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-4.00000 q^{5} -4.00000 q^{7} +O(q^{10})$$ $$q-4.00000 q^{5} -4.00000 q^{7} +2.00000 q^{11} -13.0000 q^{13} +6.00000 q^{17} +36.0000 q^{19} -20.0000 q^{23} -109.000 q^{25} +14.0000 q^{29} +152.000 q^{31} +16.0000 q^{35} -258.000 q^{37} -84.0000 q^{41} +188.000 q^{43} +254.000 q^{47} -327.000 q^{49} -366.000 q^{53} -8.00000 q^{55} +550.000 q^{59} -14.0000 q^{61} +52.0000 q^{65} -448.000 q^{67} +926.000 q^{71} +254.000 q^{73} -8.00000 q^{77} -1328.00 q^{79} +186.000 q^{83} -24.0000 q^{85} +336.000 q^{89} +52.0000 q^{91} -144.000 q^{95} +614.000 q^{97} +O(q^{100})$$

## 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 $$-0.557249\pi$$
−0.178885 + 0.983870i $$0.557249\pi$$
$$6$$ 0 0
$$7$$ −4.00000 −0.215980 −0.107990 0.994152i $$-0.534441\pi$$
−0.107990 + 0.994152i $$0.534441\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.00000 0.0548202 0.0274101 0.999624i $$-0.491274\pi$$
0.0274101 + 0.999624i $$0.491274\pi$$
$$12$$ 0 0
$$13$$ −13.0000 −0.277350
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 6.00000 0.0856008 0.0428004 0.999084i $$-0.486372\pi$$
0.0428004 + 0.999084i $$0.486372\pi$$
$$18$$ 0 0
$$19$$ 36.0000 0.434682 0.217341 0.976096i $$-0.430262\pi$$
0.217341 + 0.976096i $$0.430262\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −20.0000 −0.181317 −0.0906584 0.995882i $$-0.528897\pi$$
−0.0906584 + 0.995882i $$0.528897\pi$$
$$24$$ 0 0
$$25$$ −109.000 −0.872000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 14.0000 0.0896460 0.0448230 0.998995i $$-0.485728\pi$$
0.0448230 + 0.998995i $$0.485728\pi$$
$$30$$ 0 0
$$31$$ 152.000 0.880645 0.440323 0.897840i $$-0.354864\pi$$
0.440323 + 0.897840i $$0.354864\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 16.0000 0.0772712
$$36$$ 0 0
$$37$$ −258.000 −1.14635 −0.573175 0.819433i $$-0.694288\pi$$
−0.573175 + 0.819433i $$0.694288\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −84.0000 −0.319966 −0.159983 0.987120i $$-0.551144\pi$$
−0.159983 + 0.987120i $$0.551144\pi$$
$$42$$ 0 0
$$43$$ 188.000 0.666738 0.333369 0.942796i $$-0.391815\pi$$
0.333369 + 0.942796i $$0.391815\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 254.000 0.788292 0.394146 0.919048i $$-0.371040\pi$$
0.394146 + 0.919048i $$0.371040\pi$$
$$48$$ 0 0
$$49$$ −327.000 −0.953353
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −366.000 −0.948565 −0.474283 0.880373i $$-0.657293\pi$$
−0.474283 + 0.880373i $$0.657293\pi$$
$$54$$ 0 0
$$55$$ −8.00000 −0.0196131
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 550.000 1.21363 0.606813 0.794845i $$-0.292448\pi$$
0.606813 + 0.794845i $$0.292448\pi$$
$$60$$ 0 0
$$61$$ −14.0000 −0.0293855 −0.0146928 0.999892i $$-0.504677\pi$$
−0.0146928 + 0.999892i $$0.504677\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 52.0000 0.0992278
$$66$$ 0 0
$$67$$ −448.000 −0.816894 −0.408447 0.912782i $$-0.633930\pi$$
−0.408447 + 0.912782i $$0.633930\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 926.000 1.54783 0.773915 0.633289i $$-0.218296\pi$$
0.773915 + 0.633289i $$0.218296\pi$$
$$72$$ 0 0
$$73$$ 254.000 0.407239 0.203620 0.979050i $$-0.434729\pi$$
0.203620 + 0.979050i $$0.434729\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −8.00000 −0.0118401
$$78$$ 0 0
$$79$$ −1328.00 −1.89129 −0.945644 0.325205i $$-0.894567\pi$$
−0.945644 + 0.325205i $$0.894567\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 186.000 0.245978 0.122989 0.992408i $$-0.460752\pi$$
0.122989 + 0.992408i $$0.460752\pi$$
$$84$$ 0 0
$$85$$ −24.0000 −0.0306255
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 336.000 0.400179 0.200089 0.979778i $$-0.435877\pi$$
0.200089 + 0.979778i $$0.435877\pi$$
$$90$$ 0 0
$$91$$ 52.0000 0.0599020
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −144.000 −0.155517
$$96$$ 0 0
$$97$$ 614.000 0.642704 0.321352 0.946960i $$-0.395863\pi$$
0.321352 + 0.946960i $$0.395863\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1606.00 1.58221 0.791104 0.611682i $$-0.209507\pi$$
0.791104 + 0.611682i $$0.209507\pi$$
$$102$$ 0 0
$$103$$ −208.000 −0.198979 −0.0994896 0.995039i $$-0.531721\pi$$
−0.0994896 + 0.995039i $$0.531721\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −248.000 −0.224066 −0.112033 0.993704i $$-0.535736\pi$$
−0.112033 + 0.993704i $$0.535736\pi$$
$$108$$ 0 0
$$109$$ −542.000 −0.476277 −0.238138 0.971231i $$-0.576537\pi$$
−0.238138 + 0.971231i $$0.576537\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2042.00 1.69996 0.849979 0.526817i $$-0.176615\pi$$
0.849979 + 0.526817i $$0.176615\pi$$
$$114$$ 0 0
$$115$$ 80.0000 0.0648699
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −24.0000 −0.0184880
$$120$$ 0 0
$$121$$ −1327.00 −0.996995
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 936.000 0.669747
$$126$$ 0 0
$$127$$ 488.000 0.340968 0.170484 0.985360i $$-0.445467\pi$$
0.170484 + 0.985360i $$0.445467\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1744.00 1.16316 0.581580 0.813489i $$-0.302435\pi$$
0.581580 + 0.813489i $$0.302435\pi$$
$$132$$ 0 0
$$133$$ −144.000 −0.0938826
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 828.000 0.516356 0.258178 0.966097i $$-0.416878\pi$$
0.258178 + 0.966097i $$0.416878\pi$$
$$138$$ 0 0
$$139$$ 404.000 0.246524 0.123262 0.992374i $$-0.460664\pi$$
0.123262 + 0.992374i $$0.460664\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −26.0000 −0.0152044
$$144$$ 0 0
$$145$$ −56.0000 −0.0320727
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2928.00 −1.60987 −0.804937 0.593361i $$-0.797801\pi$$
−0.804937 + 0.593361i $$0.797801\pi$$
$$150$$ 0 0
$$151$$ −1944.00 −1.04769 −0.523843 0.851815i $$-0.675502\pi$$
−0.523843 + 0.851815i $$0.675502\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −608.000 −0.315069
$$156$$ 0 0
$$157$$ 3590.00 1.82492 0.912462 0.409161i $$-0.134178\pi$$
0.912462 + 0.409161i $$0.134178\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 80.0000 0.0391608
$$162$$ 0 0
$$163$$ 2284.00 1.09753 0.548763 0.835978i $$-0.315099\pi$$
0.548763 + 0.835978i $$0.315099\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 3174.00 1.47073 0.735364 0.677673i $$-0.237011\pi$$
0.735364 + 0.677673i $$0.237011\pi$$
$$168$$ 0 0
$$169$$ 169.000 0.0769231
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1358.00 0.596802 0.298401 0.954441i $$-0.403547\pi$$
0.298401 + 0.954441i $$0.403547\pi$$
$$174$$ 0 0
$$175$$ 436.000 0.188334
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 708.000 0.295634 0.147817 0.989015i $$-0.452775\pi$$
0.147817 + 0.989015i $$0.452775\pi$$
$$180$$ 0 0
$$181$$ −546.000 −0.224220 −0.112110 0.993696i $$-0.535761\pi$$
−0.112110 + 0.993696i $$0.535761\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1032.00 0.410131
$$186$$ 0 0
$$187$$ 12.0000 0.00469266
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3472.00 −1.31531 −0.657657 0.753317i $$-0.728453\pi$$
−0.657657 + 0.753317i $$0.728453\pi$$
$$192$$ 0 0
$$193$$ −310.000 −0.115618 −0.0578090 0.998328i $$-0.518411\pi$$
−0.0578090 + 0.998328i $$0.518411\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1020.00 −0.368893 −0.184447 0.982843i $$-0.559049\pi$$
−0.184447 + 0.982843i $$0.559049\pi$$
$$198$$ 0 0
$$199$$ 3256.00 1.15986 0.579929 0.814667i $$-0.303080\pi$$
0.579929 + 0.814667i $$0.303080\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −56.0000 −0.0193617
$$204$$ 0 0
$$205$$ 336.000 0.114474
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 72.0000 0.0238294
$$210$$ 0 0
$$211$$ 4564.00 1.48909 0.744547 0.667570i $$-0.232666\pi$$
0.744547 + 0.667570i $$0.232666\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −752.000 −0.238539
$$216$$ 0 0
$$217$$ −608.000 −0.190202
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −78.0000 −0.0237414
$$222$$ 0 0
$$223$$ 72.0000 0.0216210 0.0108105 0.999942i $$-0.496559\pi$$
0.0108105 + 0.999942i $$0.496559\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 2694.00 0.787696 0.393848 0.919176i $$-0.371144\pi$$
0.393848 + 0.919176i $$0.371144\pi$$
$$228$$ 0 0
$$229$$ 5922.00 1.70889 0.854447 0.519538i $$-0.173896\pi$$
0.854447 + 0.519538i $$0.173896\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 5122.00 1.44014 0.720072 0.693900i $$-0.244109\pi$$
0.720072 + 0.693900i $$0.244109\pi$$
$$234$$ 0 0
$$235$$ −1016.00 −0.282028
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 5022.00 1.35919 0.679595 0.733588i $$-0.262156\pi$$
0.679595 + 0.733588i $$0.262156\pi$$
$$240$$ 0 0
$$241$$ −1218.00 −0.325553 −0.162777 0.986663i $$-0.552045\pi$$
−0.162777 + 0.986663i $$0.552045\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 1308.00 0.341082
$$246$$ 0 0
$$247$$ −468.000 −0.120559
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −2112.00 −0.531109 −0.265554 0.964096i $$-0.585555\pi$$
−0.265554 + 0.964096i $$0.585555\pi$$
$$252$$ 0 0
$$253$$ −40.0000 −0.00993984
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −2814.00 −0.683006 −0.341503 0.939881i $$-0.610936\pi$$
−0.341503 + 0.939881i $$0.610936\pi$$
$$258$$ 0 0
$$259$$ 1032.00 0.247588
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −4044.00 −0.948151 −0.474076 0.880484i $$-0.657218\pi$$
−0.474076 + 0.880484i $$0.657218\pi$$
$$264$$ 0 0
$$265$$ 1464.00 0.339369
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1470.00 0.333188 0.166594 0.986026i $$-0.446723\pi$$
0.166594 + 0.986026i $$0.446723\pi$$
$$270$$ 0 0
$$271$$ 1844.00 0.413340 0.206670 0.978411i $$-0.433737\pi$$
0.206670 + 0.978411i $$0.433737\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −218.000 −0.0478033
$$276$$ 0 0
$$277$$ 5766.00 1.25071 0.625353 0.780342i $$-0.284955\pi$$
0.625353 + 0.780342i $$0.284955\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 7468.00 1.58542 0.792711 0.609598i $$-0.208669\pi$$
0.792711 + 0.609598i $$0.208669\pi$$
$$282$$ 0 0
$$283$$ −1228.00 −0.257940 −0.128970 0.991648i $$-0.541167\pi$$
−0.128970 + 0.991648i $$0.541167\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 336.000 0.0691061
$$288$$ 0 0
$$289$$ −4877.00 −0.992673
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −6608.00 −1.31755 −0.658777 0.752338i $$-0.728926\pi$$
−0.658777 + 0.752338i $$0.728926\pi$$
$$294$$ 0 0
$$295$$ −2200.00 −0.434200
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 260.000 0.0502883
$$300$$ 0 0
$$301$$ −752.000 −0.144002
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 56.0000 0.0105133
$$306$$ 0 0
$$307$$ −7664.00 −1.42478 −0.712390 0.701784i $$-0.752387\pi$$
−0.712390 + 0.701784i $$0.752387\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −2340.00 −0.426653 −0.213327 0.976981i $$-0.568430\pi$$
−0.213327 + 0.976981i $$0.568430\pi$$
$$312$$ 0 0
$$313$$ 6710.00 1.21173 0.605865 0.795567i $$-0.292827\pi$$
0.605865 + 0.795567i $$0.292827\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −4164.00 −0.737771 −0.368886 0.929475i $$-0.620261\pi$$
−0.368886 + 0.929475i $$0.620261\pi$$
$$318$$ 0 0
$$319$$ 28.0000 0.00491442
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 216.000 0.0372092
$$324$$ 0 0
$$325$$ 1417.00 0.241849
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −1016.00 −0.170255
$$330$$ 0 0
$$331$$ 10072.0 1.67253 0.836265 0.548326i $$-0.184735\pi$$
0.836265 + 0.548326i $$0.184735\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 1792.00 0.292261
$$336$$ 0 0
$$337$$ 2990.00 0.483311 0.241655 0.970362i $$-0.422310\pi$$
0.241655 + 0.970362i $$0.422310\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 304.000 0.0482772
$$342$$ 0 0
$$343$$ 2680.00 0.421885
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 6564.00 1.01549 0.507743 0.861508i $$-0.330480\pi$$
0.507743 + 0.861508i $$0.330480\pi$$
$$348$$ 0 0
$$349$$ −674.000 −0.103376 −0.0516882 0.998663i $$-0.516460\pi$$
−0.0516882 + 0.998663i $$0.516460\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 10732.0 1.61815 0.809075 0.587706i $$-0.199969\pi$$
0.809075 + 0.587706i $$0.199969\pi$$
$$354$$ 0 0
$$355$$ −3704.00 −0.553769
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −4842.00 −0.711841 −0.355921 0.934516i $$-0.615833\pi$$
−0.355921 + 0.934516i $$0.615833\pi$$
$$360$$ 0 0
$$361$$ −5563.00 −0.811051
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −1016.00 −0.145698
$$366$$ 0 0
$$367$$ 6280.00 0.893224 0.446612 0.894728i $$-0.352630\pi$$
0.446612 + 0.894728i $$0.352630\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 1464.00 0.204871
$$372$$ 0 0
$$373$$ 6434.00 0.893136 0.446568 0.894750i $$-0.352646\pi$$
0.446568 + 0.894750i $$0.352646\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −182.000 −0.0248633
$$378$$ 0 0
$$379$$ 9068.00 1.22900 0.614501 0.788916i $$-0.289357\pi$$
0.614501 + 0.788916i $$0.289357\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 3162.00 0.421855 0.210928 0.977502i $$-0.432352\pi$$
0.210928 + 0.977502i $$0.432352\pi$$
$$384$$ 0 0
$$385$$ 32.0000 0.00423603
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 3666.00 0.477824 0.238912 0.971041i $$-0.423209\pi$$
0.238912 + 0.971041i $$0.423209\pi$$
$$390$$ 0 0
$$391$$ −120.000 −0.0155209
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 5312.00 0.676647
$$396$$ 0 0
$$397$$ 11054.0 1.39744 0.698721 0.715394i $$-0.253753\pi$$
0.698721 + 0.715394i $$0.253753\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 5328.00 0.663510 0.331755 0.943366i $$-0.392359\pi$$
0.331755 + 0.943366i $$0.392359\pi$$
$$402$$ 0 0
$$403$$ −1976.00 −0.244247
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −516.000 −0.0628432
$$408$$ 0 0
$$409$$ −12074.0 −1.45971 −0.729854 0.683603i $$-0.760412\pi$$
−0.729854 + 0.683603i $$0.760412\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −2200.00 −0.262118
$$414$$ 0 0
$$415$$ −744.000 −0.0880037
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 13584.0 1.58382 0.791911 0.610636i $$-0.209086\pi$$
0.791911 + 0.610636i $$0.209086\pi$$
$$420$$ 0 0
$$421$$ −7406.00 −0.857355 −0.428677 0.903458i $$-0.641020\pi$$
−0.428677 + 0.903458i $$0.641020\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −654.000 −0.0746439
$$426$$ 0 0
$$427$$ 56.0000 0.00634667
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −10134.0 −1.13257 −0.566285 0.824210i $$-0.691620\pi$$
−0.566285 + 0.824210i $$0.691620\pi$$
$$432$$ 0 0
$$433$$ 9406.00 1.04393 0.521967 0.852966i $$-0.325198\pi$$
0.521967 + 0.852966i $$0.325198\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −720.000 −0.0788153
$$438$$ 0 0
$$439$$ −4088.00 −0.444441 −0.222220 0.974996i $$-0.571330\pi$$
−0.222220 + 0.974996i $$0.571330\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −5328.00 −0.571424 −0.285712 0.958315i $$-0.592230\pi$$
−0.285712 + 0.958315i $$0.592230\pi$$
$$444$$ 0 0
$$445$$ −1344.00 −0.143172
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −13160.0 −1.38320 −0.691602 0.722279i $$-0.743095\pi$$
−0.691602 + 0.722279i $$0.743095\pi$$
$$450$$ 0 0
$$451$$ −168.000 −0.0175406
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −208.000 −0.0214312
$$456$$ 0 0
$$457$$ −9146.00 −0.936175 −0.468087 0.883682i $$-0.655057\pi$$
−0.468087 + 0.883682i $$0.655057\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −5580.00 −0.563745 −0.281873 0.959452i $$-0.590956\pi$$
−0.281873 + 0.959452i $$0.590956\pi$$
$$462$$ 0 0
$$463$$ −14788.0 −1.48436 −0.742178 0.670203i $$-0.766207\pi$$
−0.742178 + 0.670203i $$0.766207\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 12376.0 1.22632 0.613162 0.789957i $$-0.289897\pi$$
0.613162 + 0.789957i $$0.289897\pi$$
$$468$$ 0 0
$$469$$ 1792.00 0.176433
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 376.000 0.0365507
$$474$$ 0 0
$$475$$ −3924.00 −0.379043
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 834.000 0.0795541 0.0397771 0.999209i $$-0.487335\pi$$
0.0397771 + 0.999209i $$0.487335\pi$$
$$480$$ 0 0
$$481$$ 3354.00 0.317940
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −2456.00 −0.229941
$$486$$ 0 0
$$487$$ 13192.0 1.22749 0.613744 0.789505i $$-0.289663\pi$$
0.613744 + 0.789505i $$0.289663\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 16568.0 1.52282 0.761409 0.648272i $$-0.224508\pi$$
0.761409 + 0.648272i $$0.224508\pi$$
$$492$$ 0 0
$$493$$ 84.0000 0.00767377
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −3704.00 −0.334300
$$498$$ 0 0
$$499$$ 10136.0 0.909318 0.454659 0.890666i $$-0.349761\pi$$
0.454659 + 0.890666i $$0.349761\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 10412.0 0.922959 0.461479 0.887151i $$-0.347319\pi$$
0.461479 + 0.887151i $$0.347319\pi$$
$$504$$ 0 0
$$505$$ −6424.00 −0.566068
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 4180.00 0.363999 0.181999 0.983299i $$-0.441743\pi$$
0.181999 + 0.983299i $$0.441743\pi$$
$$510$$ 0 0
$$511$$ −1016.00 −0.0879554
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 832.000 0.0711889
$$516$$ 0 0
$$517$$ 508.000 0.0432143
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 14610.0 1.22855 0.614276 0.789091i $$-0.289448\pi$$
0.614276 + 0.789091i $$0.289448\pi$$
$$522$$ 0 0
$$523$$ 2172.00 0.181596 0.0907982 0.995869i $$-0.471058\pi$$
0.0907982 + 0.995869i $$0.471058\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 912.000 0.0753840
$$528$$ 0 0
$$529$$ −11767.0 −0.967124
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 1092.00 0.0887425
$$534$$ 0 0
$$535$$ 992.000 0.0801643
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −654.000 −0.0522630
$$540$$ 0 0
$$541$$ −11758.0 −0.934410 −0.467205 0.884149i $$-0.654739\pi$$
−0.467205 + 0.884149i $$0.654739\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 2168.00 0.170398
$$546$$ 0 0
$$547$$ −340.000 −0.0265765 −0.0132883 0.999912i $$-0.504230\pi$$
−0.0132883 + 0.999912i $$0.504230\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 504.000 0.0389676
$$552$$ 0 0
$$553$$ 5312.00 0.408480
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 3768.00 0.286634 0.143317 0.989677i $$-0.454223\pi$$
0.143317 + 0.989677i $$0.454223\pi$$
$$558$$ 0 0
$$559$$ −2444.00 −0.184920
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −10172.0 −0.761454 −0.380727 0.924687i $$-0.624326\pi$$
−0.380727 + 0.924687i $$0.624326\pi$$
$$564$$ 0 0
$$565$$ −8168.00 −0.608195
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 5506.00 0.405665 0.202833 0.979213i $$-0.434985\pi$$
0.202833 + 0.979213i $$0.434985\pi$$
$$570$$ 0 0
$$571$$ −2340.00 −0.171499 −0.0857495 0.996317i $$-0.527328\pi$$
−0.0857495 + 0.996317i $$0.527328\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 2180.00 0.158108
$$576$$ 0 0
$$577$$ −20094.0 −1.44978 −0.724891 0.688864i $$-0.758110\pi$$
−0.724891 + 0.688864i $$0.758110\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −744.000 −0.0531262
$$582$$ 0 0
$$583$$ −732.000 −0.0520006
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −7118.00 −0.500496 −0.250248 0.968182i $$-0.580512\pi$$
−0.250248 + 0.968182i $$0.580512\pi$$
$$588$$ 0 0
$$589$$ 5472.00 0.382801
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 10328.0 0.715211 0.357606 0.933873i $$-0.383593\pi$$
0.357606 + 0.933873i $$0.383593\pi$$
$$594$$ 0 0
$$595$$ 96.0000 0.00661448
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −19732.0 −1.34596 −0.672978 0.739662i $$-0.734985\pi$$
−0.672978 + 0.739662i $$0.734985\pi$$
$$600$$ 0 0
$$601$$ −12026.0 −0.816224 −0.408112 0.912932i $$-0.633813\pi$$
−0.408112 + 0.912932i $$0.633813\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 5308.00 0.356696
$$606$$ 0 0
$$607$$ −17016.0 −1.13782 −0.568911 0.822399i $$-0.692635\pi$$
−0.568911 + 0.822399i $$0.692635\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −3302.00 −0.218633
$$612$$ 0 0
$$613$$ 11654.0 0.767864 0.383932 0.923361i $$-0.374570\pi$$
0.383932 + 0.923361i $$0.374570\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −11612.0 −0.757669 −0.378834 0.925465i $$-0.623675\pi$$
−0.378834 + 0.925465i $$0.623675\pi$$
$$618$$ 0 0
$$619$$ −4024.00 −0.261290 −0.130645 0.991429i $$-0.541705\pi$$
−0.130645 + 0.991429i $$0.541705\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −1344.00 −0.0864305
$$624$$ 0 0
$$625$$ 9881.00 0.632384
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −1548.00 −0.0981285
$$630$$ 0 0
$$631$$ 1088.00 0.0686412 0.0343206 0.999411i $$-0.489073\pi$$
0.0343206 + 0.999411i $$0.489073\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −1952.00 −0.121989
$$636$$ 0 0
$$637$$ 4251.00 0.264412
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 7078.00 0.436138 0.218069 0.975933i $$-0.430024\pi$$
0.218069 + 0.975933i $$0.430024\pi$$
$$642$$ 0 0
$$643$$ −8336.00 −0.511259 −0.255630 0.966775i $$-0.582283\pi$$
−0.255630 + 0.966775i $$0.582283\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 32.0000 0.00194444 0.000972218 1.00000i $$-0.499691\pi$$
0.000972218 1.00000i $$0.499691\pi$$
$$648$$ 0 0
$$649$$ 1100.00 0.0665312
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 15822.0 0.948182 0.474091 0.880476i $$-0.342777\pi$$
0.474091 + 0.880476i $$0.342777\pi$$
$$654$$ 0 0
$$655$$ −6976.00 −0.416145
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 21540.0 1.27326 0.636631 0.771169i $$-0.280328\pi$$
0.636631 + 0.771169i $$0.280328\pi$$
$$660$$ 0 0
$$661$$ 8270.00 0.486635 0.243317 0.969947i $$-0.421764\pi$$
0.243317 + 0.969947i $$0.421764\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 576.000 0.0335885
$$666$$ 0 0
$$667$$ −280.000 −0.0162543
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −28.0000 −0.00161092
$$672$$ 0 0
$$673$$ 8482.00 0.485820 0.242910 0.970049i $$-0.421898\pi$$
0.242910 + 0.970049i $$0.421898\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −2550.00 −0.144763 −0.0723814 0.997377i $$-0.523060\pi$$
−0.0723814 + 0.997377i $$0.523060\pi$$
$$678$$ 0 0
$$679$$ −2456.00 −0.138811
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −31534.0 −1.76664 −0.883320 0.468771i $$-0.844697\pi$$
−0.883320 + 0.468771i $$0.844697\pi$$
$$684$$ 0 0
$$685$$ −3312.00 −0.184737
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 4758.00 0.263085
$$690$$ 0 0
$$691$$ −33832.0 −1.86256 −0.931281 0.364302i $$-0.881307\pi$$
−0.931281 + 0.364302i $$0.881307\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −1616.00 −0.0881991
$$696$$ 0 0
$$697$$ −504.000 −0.0273893
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −19422.0 −1.04645 −0.523223 0.852196i $$-0.675271\pi$$
−0.523223 + 0.852196i $$0.675271\pi$$
$$702$$ 0 0
$$703$$ −9288.00 −0.498298
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −6424.00 −0.341725
$$708$$ 0 0
$$709$$ −1894.00 −0.100325 −0.0501627 0.998741i $$-0.515974\pi$$
−0.0501627 + 0.998741i $$0.515974\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −3040.00 −0.159676
$$714$$ 0 0
$$715$$ 104.000 0.00543969
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −20156.0 −1.04547 −0.522734 0.852496i $$-0.675088\pi$$
−0.522734 + 0.852496i $$0.675088\pi$$
$$720$$ 0 0
$$721$$ 832.000 0.0429754
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1526.00 −0.0781713
$$726$$ 0 0
$$727$$ −11128.0 −0.567696 −0.283848 0.958869i $$-0.591611\pi$$
−0.283848 + 0.958869i $$0.591611\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 1128.00 0.0570733
$$732$$ 0 0
$$733$$ 16202.0 0.816418 0.408209 0.912888i $$-0.366153\pi$$
0.408209 + 0.912888i $$0.366153\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −896.000 −0.0447823
$$738$$ 0 0
$$739$$ 5328.00 0.265215 0.132607 0.991169i $$-0.457665\pi$$
0.132607 + 0.991169i $$0.457665\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −20482.0 −1.01132 −0.505661 0.862732i $$-0.668751\pi$$
−0.505661 + 0.862732i $$0.668751\pi$$
$$744$$ 0 0
$$745$$ 11712.0 0.575966
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 992.000 0.0483937
$$750$$ 0 0
$$751$$ −8040.00 −0.390657 −0.195329 0.980738i $$-0.562577\pi$$
−0.195329 + 0.980738i $$0.562577\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 7776.00 0.374831
$$756$$ 0 0
$$757$$ −15822.0 −0.759657 −0.379829 0.925057i $$-0.624017\pi$$
−0.379829 + 0.925057i $$0.624017\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1452.00 0.0691655 0.0345828 0.999402i $$-0.488990\pi$$
0.0345828 + 0.999402i $$0.488990\pi$$
$$762$$ 0 0
$$763$$ 2168.00 0.102866
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −7150.00 −0.336599
$$768$$ 0 0
$$769$$ 32298.0 1.51456 0.757279 0.653091i $$-0.226528\pi$$
0.757279 + 0.653091i $$0.226528\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −18736.0 −0.871781 −0.435891 0.900000i $$-0.643567\pi$$
−0.435891 + 0.900000i $$0.643567\pi$$
$$774$$ 0 0
$$775$$ −16568.0 −0.767923
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −3024.00 −0.139083
$$780$$ 0 0
$$781$$ 1852.00 0.0848525
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −14360.0 −0.652905
$$786$$ 0 0
$$787$$ 40816.0 1.84871 0.924354 0.381536i $$-0.124605\pi$$
0.924354 + 0.381536i $$0.124605\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −8168.00 −0.367156
$$792$$ 0 0
$$793$$ 182.000 0.00815008
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −4518.00 −0.200798 −0.100399 0.994947i $$-0.532012\pi$$
−0.100399 + 0.994947i $$0.532012\pi$$
$$798$$ 0 0
$$799$$ 1524.00 0.0674784
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 508.000 0.0223249
$$804$$ 0 0
$$805$$ −320.000 −0.0140106
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 5058.00 0.219814 0.109907 0.993942i $$-0.464945\pi$$
0.109907 + 0.993942i $$0.464945\pi$$
$$810$$ 0 0
$$811$$ 22564.0 0.976978 0.488489 0.872570i $$-0.337548\pi$$
0.488489 + 0.872570i $$0.337548\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −9136.00 −0.392663
$$816$$ 0 0
$$817$$ 6768.00 0.289819
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −32584.0 −1.38513 −0.692564 0.721357i $$-0.743519\pi$$
−0.692564 + 0.721357i $$0.743519\pi$$
$$822$$ 0 0
$$823$$ 9288.00 0.393389 0.196695 0.980465i $$-0.436979\pi$$
0.196695 + 0.980465i $$0.436979\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 20586.0 0.865593 0.432796 0.901492i $$-0.357527\pi$$
0.432796 + 0.901492i $$0.357527\pi$$
$$828$$ 0 0
$$829$$ −46118.0 −1.93214 −0.966070 0.258280i $$-0.916844\pi$$
−0.966070 + 0.258280i $$0.916844\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −1962.00 −0.0816078
$$834$$ 0 0
$$835$$ −12696.0 −0.526183
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −39230.0 −1.61427 −0.807133 0.590369i $$-0.798982\pi$$
−0.807133 + 0.590369i $$0.798982\pi$$
$$840$$ 0 0
$$841$$ −24193.0 −0.991964
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −676.000 −0.0275208
$$846$$ 0 0
$$847$$ 5308.00 0.215331
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 5160.00 0.207853
$$852$$ 0 0
$$853$$ −18674.0 −0.749573 −0.374786 0.927111i $$-0.622284\pi$$
−0.374786 + 0.927111i $$0.622284\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −41678.0 −1.66125 −0.830626 0.556830i $$-0.812017\pi$$
−0.830626 + 0.556830i $$0.812017\pi$$
$$858$$ 0 0
$$859$$ 14740.0 0.585474 0.292737 0.956193i $$-0.405434\pi$$
0.292737 + 0.956193i $$0.405434\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −24982.0 −0.985396 −0.492698 0.870200i $$-0.663989\pi$$
−0.492698 + 0.870200i $$0.663989\pi$$
$$864$$ 0 0
$$865$$ −5432.00 −0.213519
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −2656.00 −0.103681
$$870$$ 0 0
$$871$$ 5824.00 0.226566
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −3744.00 −0.144652
$$876$$ 0 0
$$877$$ 1134.00 0.0436630 0.0218315 0.999762i $$-0.493050\pi$$
0.0218315 + 0.999762i $$0.493050\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −34950.0 −1.33654 −0.668272 0.743917i $$-0.732966\pi$$
−0.668272 + 0.743917i $$0.732966\pi$$
$$882$$ 0 0
$$883$$ 3068.00 0.116927 0.0584634 0.998290i $$-0.481380\pi$$
0.0584634 + 0.998290i $$0.481380\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −14080.0 −0.532988 −0.266494 0.963837i $$-0.585865\pi$$
−0.266494 + 0.963837i $$0.585865\pi$$
$$888$$ 0 0
$$889$$ −1952.00 −0.0736423
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 9144.00 0.342657
$$894$$ 0 0
$$895$$ −2832.00 −0.105769
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 2128.00 0.0789464
$$900$$ 0 0
$$901$$ −2196.00 −0.0811980
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 2184.00 0.0802195
$$906$$ 0 0
$$907$$ 24876.0 0.910688 0.455344 0.890316i $$-0.349516\pi$$
0.455344 + 0.890316i $$0.349516\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 51456.0 1.87136 0.935682 0.352843i $$-0.114785\pi$$
0.935682 + 0.352843i $$0.114785\pi$$
$$912$$ 0 0
$$913$$ 372.000 0.0134846
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −6976.00 −0.251219
$$918$$ 0 0
$$919$$ 31032.0 1.11388 0.556938 0.830554i $$-0.311976\pi$$
0.556938 + 0.830554i $$0.311976\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −12038.0 −0.429291
$$924$$ 0 0
$$925$$ 28122.0 0.999617
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −50820.0 −1.79478 −0.897390 0.441239i $$-0.854539\pi$$
−0.897390 + 0.441239i $$0.854539\pi$$
$$930$$ 0 0
$$931$$ −11772.0 −0.414406
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −48.0000 −0.00167890
$$936$$ 0 0
$$937$$ 5982.00 0.208563 0.104281 0.994548i $$-0.466746\pi$$
0.104281 + 0.994548i $$0.466746\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 20224.0 0.700620 0.350310 0.936634i $$-0.386076\pi$$
0.350310 + 0.936634i $$0.386076\pi$$
$$942$$ 0 0
$$943$$ 1680.00 0.0580152
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 8478.00 0.290917 0.145458 0.989364i $$-0.453534\pi$$
0.145458 + 0.989364i $$0.453534\pi$$
$$948$$ 0 0
$$949$$ −3302.00 −0.112948
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −40918.0 −1.39083 −0.695417 0.718607i $$-0.744780\pi$$
−0.695417 + 0.718607i $$0.744780\pi$$
$$954$$ 0 0
$$955$$ 13888.0 0.470581
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −3312.00 −0.111522
$$960$$ 0 0
$$961$$ −6687.00 −0.224464
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 1240.00 0.0413648
$$966$$ 0 0
$$967$$ 4624.00 0.153772 0.0768862 0.997040i $$-0.475502\pi$$
0.0768862 + 0.997040i $$0.475502\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 15300.0 0.505665 0.252832 0.967510i $$-0.418638\pi$$
0.252832 + 0.967510i $$0.418638\pi$$
$$972$$ 0 0
$$973$$ −1616.00 −0.0532442
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −19584.0 −0.641298 −0.320649 0.947198i $$-0.603901\pi$$
−0.320649 + 0.947198i $$0.603901\pi$$
$$978$$ 0 0
$$979$$ 672.000 0.0219379
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −17582.0 −0.570477 −0.285238 0.958457i $$-0.592073\pi$$
−0.285238 + 0.958457i $$0.592073\pi$$
$$984$$ 0 0
$$985$$ 4080.00 0.131979
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −3760.00 −0.120891
$$990$$ 0 0
$$991$$ −47904.0 −1.53554 −0.767770 0.640725i $$-0.778634\pi$$
−0.767770 + 0.640725i $$0.778634\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −13024.0 −0.414963
$$996$$ 0 0
$$997$$ −44578.0 −1.41605 −0.708024 0.706189i $$-0.750413\pi$$
−0.708024 + 0.706189i $$0.750413\pi$$
$$998$$ 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 1872.4.a.f.1.1 1
3.2 odd 2 624.4.a.c.1.1 1
4.3 odd 2 234.4.a.c.1.1 1
12.11 even 2 78.4.a.f.1.1 1
24.5 odd 2 2496.4.a.l.1.1 1
24.11 even 2 2496.4.a.c.1.1 1
60.59 even 2 1950.4.a.a.1.1 1
156.47 odd 4 1014.4.b.g.337.2 2
156.83 odd 4 1014.4.b.g.337.1 2
156.155 even 2 1014.4.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
78.4.a.f.1.1 1 12.11 even 2
234.4.a.c.1.1 1 4.3 odd 2
624.4.a.c.1.1 1 3.2 odd 2
1014.4.a.e.1.1 1 156.155 even 2
1014.4.b.g.337.1 2 156.83 odd 4
1014.4.b.g.337.2 2 156.47 odd 4
1872.4.a.f.1.1 1 1.1 even 1 trivial
1950.4.a.a.1.1 1 60.59 even 2
2496.4.a.c.1.1 1 24.11 even 2
2496.4.a.l.1.1 1 24.5 odd 2