Properties

 Label 1216.2.a.e.1.1 Level $1216$ Weight $2$ Character 1216.1 Self dual yes Analytic conductor $9.710$ Analytic rank $1$ 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] = [1216,2,Mod(1,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1216.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1216 = 2^{6} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1216.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: $$9.70980888579$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 38) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1216.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} +6.00000 q^{11} -5.00000 q^{13} +3.00000 q^{17} -1.00000 q^{19} +1.00000 q^{21} +3.00000 q^{23} -5.00000 q^{25} +5.00000 q^{27} -9.00000 q^{29} -4.00000 q^{31} -6.00000 q^{33} -2.00000 q^{37} +5.00000 q^{39} -8.00000 q^{43} -6.00000 q^{49} -3.00000 q^{51} +3.00000 q^{53} +1.00000 q^{57} -9.00000 q^{59} +10.0000 q^{61} +2.00000 q^{63} -5.00000 q^{67} -3.00000 q^{69} -6.00000 q^{71} -7.00000 q^{73} +5.00000 q^{75} -6.00000 q^{77} -10.0000 q^{79} +1.00000 q^{81} +6.00000 q^{83} +9.00000 q^{87} -12.0000 q^{89} +5.00000 q^{91} +4.00000 q^{93} -10.0000 q^{97} -12.0000 q^{99} +O(q^{100})$$

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
$$3$$ −1.00000 −0.577350 −0.288675 0.957427i $$-0.593215\pi$$
−0.288675 + 0.957427i $$0.593215\pi$$
$$4$$ 0 0
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ 0 0
$$9$$ −2.00000 −0.666667
$$10$$ 0 0
$$11$$ 6.00000 1.80907 0.904534 0.426401i $$-0.140219\pi$$
0.904534 + 0.426401i $$0.140219\pi$$
$$12$$ 0 0
$$13$$ −5.00000 −1.38675 −0.693375 0.720577i $$-0.743877\pi$$
−0.693375 + 0.720577i $$0.743877\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 0 0
$$19$$ −1.00000 −0.229416
$$20$$ 0 0
$$21$$ 1.00000 0.218218
$$22$$ 0 0
$$23$$ 3.00000 0.625543 0.312772 0.949828i $$-0.398743\pi$$
0.312772 + 0.949828i $$0.398743\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 0 0
$$27$$ 5.00000 0.962250
$$28$$ 0 0
$$29$$ −9.00000 −1.67126 −0.835629 0.549294i $$-0.814897\pi$$
−0.835629 + 0.549294i $$0.814897\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ −6.00000 −1.04447
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 0 0
$$39$$ 5.00000 0.800641
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ 0 0
$$53$$ 3.00000 0.412082 0.206041 0.978543i $$-0.433942\pi$$
0.206041 + 0.978543i $$0.433942\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.00000 0.132453
$$58$$ 0 0
$$59$$ −9.00000 −1.17170 −0.585850 0.810419i $$-0.699239\pi$$
−0.585850 + 0.810419i $$0.699239\pi$$
$$60$$ 0 0
$$61$$ 10.0000 1.28037 0.640184 0.768221i $$-0.278858\pi$$
0.640184 + 0.768221i $$0.278858\pi$$
$$62$$ 0 0
$$63$$ 2.00000 0.251976
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −5.00000 −0.610847 −0.305424 0.952217i $$-0.598798\pi$$
−0.305424 + 0.952217i $$0.598798\pi$$
$$68$$ 0 0
$$69$$ −3.00000 −0.361158
$$70$$ 0 0
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ 0 0
$$73$$ −7.00000 −0.819288 −0.409644 0.912245i $$-0.634347\pi$$
−0.409644 + 0.912245i $$0.634347\pi$$
$$74$$ 0 0
$$75$$ 5.00000 0.577350
$$76$$ 0 0
$$77$$ −6.00000 −0.683763
$$78$$ 0 0
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 9.00000 0.964901
$$88$$ 0 0
$$89$$ −12.0000 −1.27200 −0.635999 0.771690i $$-0.719412\pi$$
−0.635999 + 0.771690i $$0.719412\pi$$
$$90$$ 0 0
$$91$$ 5.00000 0.524142
$$92$$ 0 0
$$93$$ 4.00000 0.414781
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 0 0
$$99$$ −12.0000 −1.20605
$$100$$ 0 0
$$101$$ −18.0000 −1.79107 −0.895533 0.444994i $$-0.853206\pi$$
−0.895533 + 0.444994i $$0.853206\pi$$
$$102$$ 0 0
$$103$$ 14.0000 1.37946 0.689730 0.724066i $$-0.257729\pi$$
0.689730 + 0.724066i $$0.257729\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 9.00000 0.870063 0.435031 0.900415i $$-0.356737\pi$$
0.435031 + 0.900415i $$0.356737\pi$$
$$108$$ 0 0
$$109$$ −11.0000 −1.05361 −0.526804 0.849987i $$-0.676610\pi$$
−0.526804 + 0.849987i $$0.676610\pi$$
$$110$$ 0 0
$$111$$ 2.00000 0.189832
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 10.0000 0.924500
$$118$$ 0 0
$$119$$ −3.00000 −0.275010
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ 0 0
$$129$$ 8.00000 0.704361
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 1.00000 0.0867110
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −9.00000 −0.768922 −0.384461 0.923141i $$-0.625613\pi$$
−0.384461 + 0.923141i $$0.625613\pi$$
$$138$$ 0 0
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −30.0000 −2.50873
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 6.00000 0.494872
$$148$$ 0 0
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ −10.0000 −0.813788 −0.406894 0.913475i $$-0.633388\pi$$
−0.406894 + 0.913475i $$0.633388\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 22.0000 1.75579 0.877896 0.478852i $$-0.158947\pi$$
0.877896 + 0.478852i $$0.158947\pi$$
$$158$$ 0 0
$$159$$ −3.00000 −0.237915
$$160$$ 0 0
$$161$$ −3.00000 −0.236433
$$162$$ 0 0
$$163$$ −20.0000 −1.56652 −0.783260 0.621694i $$-0.786445\pi$$
−0.783260 + 0.621694i $$0.786445\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 12.0000 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ 2.00000 0.152944
$$172$$ 0 0
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 0 0
$$175$$ 5.00000 0.377964
$$176$$ 0 0
$$177$$ 9.00000 0.676481
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ −10.0000 −0.739221
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 18.0000 1.31629
$$188$$ 0 0
$$189$$ −5.00000 −0.363696
$$190$$ 0 0
$$191$$ 3.00000 0.217072 0.108536 0.994092i $$-0.465384\pi$$
0.108536 + 0.994092i $$0.465384\pi$$
$$192$$ 0 0
$$193$$ 14.0000 1.00774 0.503871 0.863779i $$-0.331909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 11.0000 0.779769 0.389885 0.920864i $$-0.372515\pi$$
0.389885 + 0.920864i $$0.372515\pi$$
$$200$$ 0 0
$$201$$ 5.00000 0.352673
$$202$$ 0 0
$$203$$ 9.00000 0.631676
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −6.00000 −0.417029
$$208$$ 0 0
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ −5.00000 −0.344214 −0.172107 0.985078i $$-0.555058\pi$$
−0.172107 + 0.985078i $$0.555058\pi$$
$$212$$ 0 0
$$213$$ 6.00000 0.411113
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 4.00000 0.271538
$$218$$ 0 0
$$219$$ 7.00000 0.473016
$$220$$ 0 0
$$221$$ −15.0000 −1.00901
$$222$$ 0 0
$$223$$ 26.0000 1.74109 0.870544 0.492090i $$-0.163767\pi$$
0.870544 + 0.492090i $$0.163767\pi$$
$$224$$ 0 0
$$225$$ 10.0000 0.666667
$$226$$ 0 0
$$227$$ 15.0000 0.995585 0.497792 0.867296i $$-0.334144\pi$$
0.497792 + 0.867296i $$0.334144\pi$$
$$228$$ 0 0
$$229$$ 22.0000 1.45380 0.726900 0.686743i $$-0.240960\pi$$
0.726900 + 0.686743i $$0.240960\pi$$
$$230$$ 0 0
$$231$$ 6.00000 0.394771
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 10.0000 0.649570
$$238$$ 0 0
$$239$$ −21.0000 −1.35838 −0.679189 0.733964i $$-0.737668\pi$$
−0.679189 + 0.733964i $$0.737668\pi$$
$$240$$ 0 0
$$241$$ 8.00000 0.515325 0.257663 0.966235i $$-0.417048\pi$$
0.257663 + 0.966235i $$0.417048\pi$$
$$242$$ 0 0
$$243$$ −16.0000 −1.02640
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 5.00000 0.318142
$$248$$ 0 0
$$249$$ −6.00000 −0.380235
$$250$$ 0 0
$$251$$ −6.00000 −0.378717 −0.189358 0.981908i $$-0.560641\pi$$
−0.189358 + 0.981908i $$0.560641\pi$$
$$252$$ 0 0
$$253$$ 18.0000 1.13165
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 12.0000 0.748539 0.374270 0.927320i $$-0.377893\pi$$
0.374270 + 0.927320i $$0.377893\pi$$
$$258$$ 0 0
$$259$$ 2.00000 0.124274
$$260$$ 0 0
$$261$$ 18.0000 1.11417
$$262$$ 0 0
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 12.0000 0.734388
$$268$$ 0 0
$$269$$ 6.00000 0.365826 0.182913 0.983129i $$-0.441447\pi$$
0.182913 + 0.983129i $$0.441447\pi$$
$$270$$ 0 0
$$271$$ 11.0000 0.668202 0.334101 0.942537i $$-0.391567\pi$$
0.334101 + 0.942537i $$0.391567\pi$$
$$272$$ 0 0
$$273$$ −5.00000 −0.302614
$$274$$ 0 0
$$275$$ −30.0000 −1.80907
$$276$$ 0 0
$$277$$ −8.00000 −0.480673 −0.240337 0.970690i $$-0.577258\pi$$
−0.240337 + 0.970690i $$0.577258\pi$$
$$278$$ 0 0
$$279$$ 8.00000 0.478947
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ 22.0000 1.30776 0.653882 0.756596i $$-0.273139\pi$$
0.653882 + 0.756596i $$0.273139\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 10.0000 0.586210
$$292$$ 0 0
$$293$$ 21.0000 1.22683 0.613417 0.789760i $$-0.289795\pi$$
0.613417 + 0.789760i $$0.289795\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 30.0000 1.74078
$$298$$ 0 0
$$299$$ −15.0000 −0.867472
$$300$$ 0 0
$$301$$ 8.00000 0.461112
$$302$$ 0 0
$$303$$ 18.0000 1.03407
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ −14.0000 −0.796432
$$310$$ 0 0
$$311$$ −21.0000 −1.19080 −0.595400 0.803429i $$-0.703007\pi$$
−0.595400 + 0.803429i $$0.703007\pi$$
$$312$$ 0 0
$$313$$ −19.0000 −1.07394 −0.536972 0.843600i $$-0.680432\pi$$
−0.536972 + 0.843600i $$0.680432\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 9.00000 0.505490 0.252745 0.967533i $$-0.418667\pi$$
0.252745 + 0.967533i $$0.418667\pi$$
$$318$$ 0 0
$$319$$ −54.0000 −3.02342
$$320$$ 0 0
$$321$$ −9.00000 −0.502331
$$322$$ 0 0
$$323$$ −3.00000 −0.166924
$$324$$ 0 0
$$325$$ 25.0000 1.38675
$$326$$ 0 0
$$327$$ 11.0000 0.608301
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 1.00000 0.0549650 0.0274825 0.999622i $$-0.491251\pi$$
0.0274825 + 0.999622i $$0.491251\pi$$
$$332$$ 0 0
$$333$$ 4.00000 0.219199
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −4.00000 −0.217894 −0.108947 0.994048i $$-0.534748\pi$$
−0.108947 + 0.994048i $$0.534748\pi$$
$$338$$ 0 0
$$339$$ −6.00000 −0.325875
$$340$$ 0 0
$$341$$ −24.0000 −1.29967
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −18.0000 −0.966291 −0.483145 0.875540i $$-0.660506\pi$$
−0.483145 + 0.875540i $$0.660506\pi$$
$$348$$ 0 0
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 0 0
$$351$$ −25.0000 −1.33440
$$352$$ 0 0
$$353$$ −15.0000 −0.798369 −0.399185 0.916871i $$-0.630707\pi$$
−0.399185 + 0.916871i $$0.630707\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 3.00000 0.158777
$$358$$ 0 0
$$359$$ 21.0000 1.10834 0.554169 0.832404i $$-0.313036\pi$$
0.554169 + 0.832404i $$0.313036\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ −25.0000 −1.31216
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −28.0000 −1.46159 −0.730794 0.682598i $$-0.760850\pi$$
−0.730794 + 0.682598i $$0.760850\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −3.00000 −0.155752
$$372$$ 0 0
$$373$$ −23.0000 −1.19089 −0.595447 0.803394i $$-0.703025\pi$$
−0.595447 + 0.803394i $$0.703025\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 45.0000 2.31762
$$378$$ 0 0
$$379$$ 7.00000 0.359566 0.179783 0.983706i $$-0.442460\pi$$
0.179783 + 0.983706i $$0.442460\pi$$
$$380$$ 0 0
$$381$$ −2.00000 −0.102463
$$382$$ 0 0
$$383$$ 18.0000 0.919757 0.459879 0.887982i $$-0.347893\pi$$
0.459879 + 0.887982i $$0.347893\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 16.0000 0.813326
$$388$$ 0 0
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 0 0
$$391$$ 9.00000 0.455150
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −20.0000 −1.00377 −0.501886 0.864934i $$-0.667360\pi$$
−0.501886 + 0.864934i $$0.667360\pi$$
$$398$$ 0 0
$$399$$ −1.00000 −0.0500626
$$400$$ 0 0
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 0 0
$$403$$ 20.0000 0.996271
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −12.0000 −0.594818
$$408$$ 0 0
$$409$$ 32.0000 1.58230 0.791149 0.611623i $$-0.209483\pi$$
0.791149 + 0.611623i $$0.209483\pi$$
$$410$$ 0 0
$$411$$ 9.00000 0.443937
$$412$$ 0 0
$$413$$ 9.00000 0.442861
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −4.00000 −0.195881
$$418$$ 0 0
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −17.0000 −0.828529 −0.414265 0.910156i $$-0.635961\pi$$
−0.414265 + 0.910156i $$0.635961\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −15.0000 −0.727607
$$426$$ 0 0
$$427$$ −10.0000 −0.483934
$$428$$ 0 0
$$429$$ 30.0000 1.44841
$$430$$ 0 0
$$431$$ 6.00000 0.289010 0.144505 0.989504i $$-0.453841\pi$$
0.144505 + 0.989504i $$0.453841\pi$$
$$432$$ 0 0
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −3.00000 −0.143509
$$438$$ 0 0
$$439$$ −28.0000 −1.33637 −0.668184 0.743996i $$-0.732928\pi$$
−0.668184 + 0.743996i $$0.732928\pi$$
$$440$$ 0 0
$$441$$ 12.0000 0.571429
$$442$$ 0 0
$$443$$ 18.0000 0.855206 0.427603 0.903967i $$-0.359358\pi$$
0.427603 + 0.903967i $$0.359358\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 10.0000 0.469841
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 17.0000 0.795226 0.397613 0.917553i $$-0.369839\pi$$
0.397613 + 0.917553i $$0.369839\pi$$
$$458$$ 0 0
$$459$$ 15.0000 0.700140
$$460$$ 0 0
$$461$$ 12.0000 0.558896 0.279448 0.960161i $$-0.409849\pi$$
0.279448 + 0.960161i $$0.409849\pi$$
$$462$$ 0 0
$$463$$ −4.00000 −0.185896 −0.0929479 0.995671i $$-0.529629\pi$$
−0.0929479 + 0.995671i $$0.529629\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −18.0000 −0.832941 −0.416470 0.909149i $$-0.636733\pi$$
−0.416470 + 0.909149i $$0.636733\pi$$
$$468$$ 0 0
$$469$$ 5.00000 0.230879
$$470$$ 0 0
$$471$$ −22.0000 −1.01371
$$472$$ 0 0
$$473$$ −48.0000 −2.20704
$$474$$ 0 0
$$475$$ 5.00000 0.229416
$$476$$ 0 0
$$477$$ −6.00000 −0.274721
$$478$$ 0 0
$$479$$ 36.0000 1.64488 0.822441 0.568850i $$-0.192612\pi$$
0.822441 + 0.568850i $$0.192612\pi$$
$$480$$ 0 0
$$481$$ 10.0000 0.455961
$$482$$ 0 0
$$483$$ 3.00000 0.136505
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 2.00000 0.0906287 0.0453143 0.998973i $$-0.485571\pi$$
0.0453143 + 0.998973i $$0.485571\pi$$
$$488$$ 0 0
$$489$$ 20.0000 0.904431
$$490$$ 0 0
$$491$$ 36.0000 1.62466 0.812329 0.583200i $$-0.198200\pi$$
0.812329 + 0.583200i $$0.198200\pi$$
$$492$$ 0 0
$$493$$ −27.0000 −1.21602
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 6.00000 0.269137
$$498$$ 0 0
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ 0 0
$$501$$ −12.0000 −0.536120
$$502$$ 0 0
$$503$$ −21.0000 −0.936344 −0.468172 0.883637i $$-0.655087\pi$$
−0.468172 + 0.883637i $$0.655087\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −12.0000 −0.532939
$$508$$ 0 0
$$509$$ −30.0000 −1.32973 −0.664863 0.746965i $$-0.731510\pi$$
−0.664863 + 0.746965i $$0.731510\pi$$
$$510$$ 0 0
$$511$$ 7.00000 0.309662
$$512$$ 0 0
$$513$$ −5.00000 −0.220755
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 6.00000 0.263371
$$520$$ 0 0
$$521$$ −36.0000 −1.57719 −0.788594 0.614914i $$-0.789191\pi$$
−0.788594 + 0.614914i $$0.789191\pi$$
$$522$$ 0 0
$$523$$ −11.0000 −0.480996 −0.240498 0.970650i $$-0.577311\pi$$
−0.240498 + 0.970650i $$0.577311\pi$$
$$524$$ 0 0
$$525$$ −5.00000 −0.218218
$$526$$ 0 0
$$527$$ −12.0000 −0.522728
$$528$$ 0 0
$$529$$ −14.0000 −0.608696
$$530$$ 0 0
$$531$$ 18.0000 0.781133
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −36.0000 −1.55063
$$540$$ 0 0
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 0 0
$$543$$ 2.00000 0.0858282
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −44.0000 −1.88130 −0.940652 0.339372i $$-0.889785\pi$$
−0.940652 + 0.339372i $$0.889785\pi$$
$$548$$ 0 0
$$549$$ −20.0000 −0.853579
$$550$$ 0 0
$$551$$ 9.00000 0.383413
$$552$$ 0 0
$$553$$ 10.0000 0.425243
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −24.0000 −1.01691 −0.508456 0.861088i $$-0.669784\pi$$
−0.508456 + 0.861088i $$0.669784\pi$$
$$558$$ 0 0
$$559$$ 40.0000 1.69182
$$560$$ 0 0
$$561$$ −18.0000 −0.759961
$$562$$ 0 0
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −1.00000 −0.0419961
$$568$$ 0 0
$$569$$ −24.0000 −1.00613 −0.503066 0.864248i $$-0.667795\pi$$
−0.503066 + 0.864248i $$0.667795\pi$$
$$570$$ 0 0
$$571$$ 4.00000 0.167395 0.0836974 0.996491i $$-0.473327\pi$$
0.0836974 + 0.996491i $$0.473327\pi$$
$$572$$ 0 0
$$573$$ −3.00000 −0.125327
$$574$$ 0 0
$$575$$ −15.0000 −0.625543
$$576$$ 0 0
$$577$$ 11.0000 0.457936 0.228968 0.973434i $$-0.426465\pi$$
0.228968 + 0.973434i $$0.426465\pi$$
$$578$$ 0 0
$$579$$ −14.0000 −0.581820
$$580$$ 0 0
$$581$$ −6.00000 −0.248922
$$582$$ 0 0
$$583$$ 18.0000 0.745484
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ 4.00000 0.164817
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −30.0000 −1.23195 −0.615976 0.787765i $$-0.711238\pi$$
−0.615976 + 0.787765i $$0.711238\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −11.0000 −0.450200
$$598$$ 0 0
$$599$$ −24.0000 −0.980613 −0.490307 0.871550i $$-0.663115\pi$$
−0.490307 + 0.871550i $$0.663115\pi$$
$$600$$ 0 0
$$601$$ −28.0000 −1.14214 −0.571072 0.820900i $$-0.693472\pi$$
−0.571072 + 0.820900i $$0.693472\pi$$
$$602$$ 0 0
$$603$$ 10.0000 0.407231
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −22.0000 −0.892952 −0.446476 0.894795i $$-0.647321\pi$$
−0.446476 + 0.894795i $$0.647321\pi$$
$$608$$ 0 0
$$609$$ −9.00000 −0.364698
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −2.00000 −0.0807792 −0.0403896 0.999184i $$-0.512860\pi$$
−0.0403896 + 0.999184i $$0.512860\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 0 0
$$619$$ 10.0000 0.401934 0.200967 0.979598i $$-0.435592\pi$$
0.200967 + 0.979598i $$0.435592\pi$$
$$620$$ 0 0
$$621$$ 15.0000 0.601929
$$622$$ 0 0
$$623$$ 12.0000 0.480770
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ 0 0
$$627$$ 6.00000 0.239617
$$628$$ 0 0
$$629$$ −6.00000 −0.239236
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 0 0
$$633$$ 5.00000 0.198732
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 30.0000 1.18864
$$638$$ 0 0
$$639$$ 12.0000 0.474713
$$640$$ 0 0
$$641$$ 6.00000 0.236986 0.118493 0.992955i $$-0.462194\pi$$
0.118493 + 0.992955i $$0.462194\pi$$
$$642$$ 0 0
$$643$$ 22.0000 0.867595 0.433798 0.901010i $$-0.357173\pi$$
0.433798 + 0.901010i $$0.357173\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 27.0000 1.06148 0.530740 0.847535i $$-0.321914\pi$$
0.530740 + 0.847535i $$0.321914\pi$$
$$648$$ 0 0
$$649$$ −54.0000 −2.11969
$$650$$ 0 0
$$651$$ −4.00000 −0.156772
$$652$$ 0 0
$$653$$ −24.0000 −0.939193 −0.469596 0.882881i $$-0.655601\pi$$
−0.469596 + 0.882881i $$0.655601\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 14.0000 0.546192
$$658$$ 0 0
$$659$$ 45.0000 1.75295 0.876476 0.481446i $$-0.159888\pi$$
0.876476 + 0.481446i $$0.159888\pi$$
$$660$$ 0 0
$$661$$ 13.0000 0.505641 0.252821 0.967513i $$-0.418642\pi$$
0.252821 + 0.967513i $$0.418642\pi$$
$$662$$ 0 0
$$663$$ 15.0000 0.582552
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −27.0000 −1.04544
$$668$$ 0 0
$$669$$ −26.0000 −1.00522
$$670$$ 0 0
$$671$$ 60.0000 2.31627
$$672$$ 0 0
$$673$$ 44.0000 1.69608 0.848038 0.529936i $$-0.177784\pi$$
0.848038 + 0.529936i $$0.177784\pi$$
$$674$$ 0 0
$$675$$ −25.0000 −0.962250
$$676$$ 0 0
$$677$$ 33.0000 1.26829 0.634147 0.773213i $$-0.281352\pi$$
0.634147 + 0.773213i $$0.281352\pi$$
$$678$$ 0 0
$$679$$ 10.0000 0.383765
$$680$$ 0 0
$$681$$ −15.0000 −0.574801
$$682$$ 0 0
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −22.0000 −0.839352
$$688$$ 0 0
$$689$$ −15.0000 −0.571454
$$690$$ 0 0
$$691$$ 10.0000 0.380418 0.190209 0.981744i $$-0.439083\pi$$
0.190209 + 0.981744i $$0.439083\pi$$
$$692$$ 0 0
$$693$$ 12.0000 0.455842
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 6.00000 0.226941
$$700$$ 0 0
$$701$$ −12.0000 −0.453234 −0.226617 0.973984i $$-0.572767\pi$$
−0.226617 + 0.973984i $$0.572767\pi$$
$$702$$ 0 0
$$703$$ 2.00000 0.0754314
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 18.0000 0.676960
$$708$$ 0 0
$$709$$ 10.0000 0.375558 0.187779 0.982211i $$-0.439871\pi$$
0.187779 + 0.982211i $$0.439871\pi$$
$$710$$ 0 0
$$711$$ 20.0000 0.750059
$$712$$ 0 0
$$713$$ −12.0000 −0.449404
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 21.0000 0.784259
$$718$$ 0 0
$$719$$ 39.0000 1.45445 0.727227 0.686397i $$-0.240809\pi$$
0.727227 + 0.686397i $$0.240809\pi$$
$$720$$ 0 0
$$721$$ −14.0000 −0.521387
$$722$$ 0 0
$$723$$ −8.00000 −0.297523
$$724$$ 0 0
$$725$$ 45.0000 1.67126
$$726$$ 0 0
$$727$$ −37.0000 −1.37225 −0.686127 0.727482i $$-0.740691\pi$$
−0.686127 + 0.727482i $$0.740691\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −24.0000 −0.887672
$$732$$ 0 0
$$733$$ −32.0000 −1.18195 −0.590973 0.806691i $$-0.701256\pi$$
−0.590973 + 0.806691i $$0.701256\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −30.0000 −1.10506
$$738$$ 0 0
$$739$$ 16.0000 0.588570 0.294285 0.955718i $$-0.404919\pi$$
0.294285 + 0.955718i $$0.404919\pi$$
$$740$$ 0 0
$$741$$ −5.00000 −0.183680
$$742$$ 0 0
$$743$$ −36.0000 −1.32071 −0.660356 0.750953i $$-0.729595\pi$$
−0.660356 + 0.750953i $$0.729595\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ −9.00000 −0.328853
$$750$$ 0 0
$$751$$ −40.0000 −1.45962 −0.729810 0.683650i $$-0.760392\pi$$
−0.729810 + 0.683650i $$0.760392\pi$$
$$752$$ 0 0
$$753$$ 6.00000 0.218652
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −2.00000 −0.0726912 −0.0363456 0.999339i $$-0.511572\pi$$
−0.0363456 + 0.999339i $$0.511572\pi$$
$$758$$ 0 0
$$759$$ −18.0000 −0.653359
$$760$$ 0 0
$$761$$ −21.0000 −0.761249 −0.380625 0.924730i $$-0.624291\pi$$
−0.380625 + 0.924730i $$0.624291\pi$$
$$762$$ 0 0
$$763$$ 11.0000 0.398227
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 45.0000 1.62486
$$768$$ 0 0
$$769$$ 5.00000 0.180305 0.0901523 0.995928i $$-0.471265\pi$$
0.0901523 + 0.995928i $$0.471265\pi$$
$$770$$ 0 0
$$771$$ −12.0000 −0.432169
$$772$$ 0 0
$$773$$ −51.0000 −1.83434 −0.917171 0.398493i $$-0.869533\pi$$
−0.917171 + 0.398493i $$0.869533\pi$$
$$774$$ 0 0
$$775$$ 20.0000 0.718421
$$776$$ 0 0
$$777$$ −2.00000 −0.0717496
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −36.0000 −1.28818
$$782$$ 0 0
$$783$$ −45.0000 −1.60817
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 31.0000 1.10503 0.552515 0.833503i $$-0.313668\pi$$
0.552515 + 0.833503i $$0.313668\pi$$
$$788$$ 0 0
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ −6.00000 −0.213335
$$792$$ 0 0
$$793$$ −50.0000 −1.77555
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 39.0000 1.38145 0.690725 0.723117i $$-0.257291\pi$$
0.690725 + 0.723117i $$0.257291\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 24.0000 0.847998
$$802$$ 0 0
$$803$$ −42.0000 −1.48215
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −6.00000 −0.211210
$$808$$ 0 0
$$809$$ 9.00000 0.316423 0.158212 0.987405i $$-0.449427\pi$$
0.158212 + 0.987405i $$0.449427\pi$$
$$810$$ 0 0
$$811$$ −11.0000 −0.386262 −0.193131 0.981173i $$-0.561864\pi$$
−0.193131 + 0.981173i $$0.561864\pi$$
$$812$$ 0 0
$$813$$ −11.0000 −0.385787
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 8.00000 0.279885
$$818$$ 0 0
$$819$$ −10.0000 −0.349428
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 0 0
$$823$$ 41.0000 1.42917 0.714585 0.699549i $$-0.246616\pi$$
0.714585 + 0.699549i $$0.246616\pi$$
$$824$$ 0 0
$$825$$ 30.0000 1.04447
$$826$$ 0 0
$$827$$ −33.0000 −1.14752 −0.573761 0.819023i $$-0.694516\pi$$
−0.573761 + 0.819023i $$0.694516\pi$$
$$828$$ 0 0
$$829$$ −11.0000 −0.382046 −0.191023 0.981586i $$-0.561180\pi$$
−0.191023 + 0.981586i $$0.561180\pi$$
$$830$$ 0 0
$$831$$ 8.00000 0.277517
$$832$$ 0 0
$$833$$ −18.0000 −0.623663
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −20.0000 −0.691301
$$838$$ 0 0
$$839$$ −48.0000 −1.65714 −0.828572 0.559883i $$-0.810846\pi$$
−0.828572 + 0.559883i $$0.810846\pi$$
$$840$$ 0 0
$$841$$ 52.0000 1.79310
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −25.0000 −0.859010
$$848$$ 0 0
$$849$$ −22.0000 −0.755038
$$850$$ 0 0
$$851$$ −6.00000 −0.205677
$$852$$ 0 0
$$853$$ 46.0000 1.57501 0.787505 0.616308i $$-0.211372\pi$$
0.787505 + 0.616308i $$0.211372\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −12.0000 −0.409912 −0.204956 0.978771i $$-0.565705\pi$$
−0.204956 + 0.978771i $$0.565705\pi$$
$$858$$ 0 0
$$859$$ −14.0000 −0.477674 −0.238837 0.971060i $$-0.576766\pi$$
−0.238837 + 0.971060i $$0.576766\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −18.0000 −0.612727 −0.306364 0.951915i $$-0.599112\pi$$
−0.306364 + 0.951915i $$0.599112\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 8.00000 0.271694
$$868$$ 0 0
$$869$$ −60.0000 −2.03536
$$870$$ 0 0
$$871$$ 25.0000 0.847093
$$872$$ 0 0
$$873$$ 20.0000 0.676897
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −23.0000 −0.776655 −0.388327 0.921521i $$-0.626947\pi$$
−0.388327 + 0.921521i $$0.626947\pi$$
$$878$$ 0 0
$$879$$ −21.0000 −0.708312
$$880$$ 0 0
$$881$$ −18.0000 −0.606435 −0.303218 0.952921i $$-0.598061\pi$$
−0.303218 + 0.952921i $$0.598061\pi$$
$$882$$ 0 0
$$883$$ 34.0000 1.14419 0.572096 0.820187i $$-0.306131\pi$$
0.572096 + 0.820187i $$0.306131\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −42.0000 −1.41022 −0.705111 0.709097i $$-0.749103\pi$$
−0.705111 + 0.709097i $$0.749103\pi$$
$$888$$ 0 0
$$889$$ −2.00000 −0.0670778
$$890$$ 0 0
$$891$$ 6.00000 0.201008
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 15.0000 0.500835
$$898$$ 0 0
$$899$$ 36.0000 1.20067
$$900$$ 0 0
$$901$$ 9.00000 0.299833
$$902$$ 0 0
$$903$$ −8.00000 −0.266223
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 37.0000 1.22856 0.614282 0.789086i $$-0.289446\pi$$
0.614282 + 0.789086i $$0.289446\pi$$
$$908$$ 0 0
$$909$$ 36.0000 1.19404
$$910$$ 0 0
$$911$$ 48.0000 1.59031 0.795155 0.606406i $$-0.207389\pi$$
0.795155 + 0.606406i $$0.207389\pi$$
$$912$$ 0 0
$$913$$ 36.0000 1.19143
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −7.00000 −0.230909 −0.115454 0.993313i $$-0.536832\pi$$
−0.115454 + 0.993313i $$0.536832\pi$$
$$920$$ 0 0
$$921$$ 20.0000 0.659022
$$922$$ 0 0
$$923$$ 30.0000 0.987462
$$924$$ 0 0
$$925$$ 10.0000 0.328798
$$926$$ 0 0
$$927$$ −28.0000 −0.919641
$$928$$ 0 0
$$929$$ 33.0000 1.08269 0.541347 0.840799i $$-0.317914\pi$$
0.541347 + 0.840799i $$0.317914\pi$$
$$930$$ 0 0
$$931$$ 6.00000 0.196642
$$932$$ 0 0
$$933$$ 21.0000 0.687509
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −7.00000 −0.228680 −0.114340 0.993442i $$-0.536475\pi$$
−0.114340 + 0.993442i $$0.536475\pi$$
$$938$$ 0 0
$$939$$ 19.0000 0.620042
$$940$$ 0 0
$$941$$ −21.0000 −0.684580 −0.342290 0.939594i $$-0.611203\pi$$
−0.342290 + 0.939594i $$0.611203\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 48.0000 1.55979 0.779895 0.625910i $$-0.215272\pi$$
0.779895 + 0.625910i $$0.215272\pi$$
$$948$$ 0 0
$$949$$ 35.0000 1.13615
$$950$$ 0 0
$$951$$ −9.00000 −0.291845
$$952$$ 0 0
$$953$$ 30.0000 0.971795 0.485898 0.874016i $$-0.338493\pi$$
0.485898 + 0.874016i $$0.338493\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 54.0000 1.74557
$$958$$ 0 0
$$959$$ 9.00000 0.290625
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ 0 0
$$963$$ −18.0000 −0.580042
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 32.0000 1.02905 0.514525 0.857475i $$-0.327968\pi$$
0.514525 + 0.857475i $$0.327968\pi$$
$$968$$ 0 0
$$969$$ 3.00000 0.0963739
$$970$$ 0 0
$$971$$ −12.0000 −0.385098 −0.192549 0.981287i $$-0.561675\pi$$
−0.192549 + 0.981287i $$0.561675\pi$$
$$972$$ 0 0
$$973$$ −4.00000 −0.128234
$$974$$ 0 0
$$975$$ −25.0000 −0.800641
$$976$$ 0 0
$$977$$ −12.0000 −0.383914 −0.191957 0.981403i $$-0.561483\pi$$
−0.191957 + 0.981403i $$0.561483\pi$$
$$978$$ 0 0
$$979$$ −72.0000 −2.30113
$$980$$ 0 0
$$981$$ 22.0000 0.702406
$$982$$ 0 0
$$983$$ −30.0000 −0.956851 −0.478426 0.878128i $$-0.658792\pi$$
−0.478426 + 0.878128i $$0.658792\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −24.0000 −0.763156
$$990$$ 0 0
$$991$$ 20.0000 0.635321 0.317660 0.948205i $$-0.397103\pi$$
0.317660 + 0.948205i $$0.397103\pi$$
$$992$$ 0 0
$$993$$ −1.00000 −0.0317340
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −8.00000 −0.253363 −0.126681 0.991943i $$-0.540433\pi$$
−0.126681 + 0.991943i $$0.540433\pi$$
$$998$$ 0 0
$$999$$ −10.0000 −0.316386
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 1216.2.a.e.1.1 1
4.3 odd 2 1216.2.a.m.1.1 1
8.3 odd 2 304.2.a.c.1.1 1
8.5 even 2 38.2.a.a.1.1 1
24.5 odd 2 342.2.a.e.1.1 1
24.11 even 2 2736.2.a.n.1.1 1
40.13 odd 4 950.2.b.b.799.2 2
40.19 odd 2 7600.2.a.n.1.1 1
40.29 even 2 950.2.a.d.1.1 1
40.37 odd 4 950.2.b.b.799.1 2
56.13 odd 2 1862.2.a.b.1.1 1
88.21 odd 2 4598.2.a.p.1.1 1
104.77 even 2 6422.2.a.h.1.1 1
120.29 odd 2 8550.2.a.m.1.1 1
152.5 even 18 722.2.e.f.595.1 6
152.13 odd 18 722.2.e.e.245.1 6
152.21 odd 18 722.2.e.e.99.1 6
152.29 odd 18 722.2.e.e.423.1 6
152.37 odd 2 722.2.a.e.1.1 1
152.45 even 6 722.2.c.e.429.1 2
152.53 odd 18 722.2.e.e.415.1 6
152.61 even 18 722.2.e.f.415.1 6
152.69 odd 6 722.2.c.c.429.1 2
152.75 even 2 5776.2.a.m.1.1 1
152.85 even 18 722.2.e.f.423.1 6
152.93 even 18 722.2.e.f.99.1 6
152.101 even 18 722.2.e.f.245.1 6
152.109 odd 18 722.2.e.e.595.1 6
152.117 odd 18 722.2.e.e.389.1 6
152.125 even 6 722.2.c.e.653.1 2
152.141 odd 6 722.2.c.c.653.1 2
152.149 even 18 722.2.e.f.389.1 6
456.341 even 2 6498.2.a.f.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.a.a.1.1 1 8.5 even 2
304.2.a.c.1.1 1 8.3 odd 2
342.2.a.e.1.1 1 24.5 odd 2
722.2.a.e.1.1 1 152.37 odd 2
722.2.c.c.429.1 2 152.69 odd 6
722.2.c.c.653.1 2 152.141 odd 6
722.2.c.e.429.1 2 152.45 even 6
722.2.c.e.653.1 2 152.125 even 6
722.2.e.e.99.1 6 152.21 odd 18
722.2.e.e.245.1 6 152.13 odd 18
722.2.e.e.389.1 6 152.117 odd 18
722.2.e.e.415.1 6 152.53 odd 18
722.2.e.e.423.1 6 152.29 odd 18
722.2.e.e.595.1 6 152.109 odd 18
722.2.e.f.99.1 6 152.93 even 18
722.2.e.f.245.1 6 152.101 even 18
722.2.e.f.389.1 6 152.149 even 18
722.2.e.f.415.1 6 152.61 even 18
722.2.e.f.423.1 6 152.85 even 18
722.2.e.f.595.1 6 152.5 even 18
950.2.a.d.1.1 1 40.29 even 2
950.2.b.b.799.1 2 40.37 odd 4
950.2.b.b.799.2 2 40.13 odd 4
1216.2.a.e.1.1 1 1.1 even 1 trivial
1216.2.a.m.1.1 1 4.3 odd 2
1862.2.a.b.1.1 1 56.13 odd 2
2736.2.a.n.1.1 1 24.11 even 2
4598.2.a.p.1.1 1 88.21 odd 2
5776.2.a.m.1.1 1 152.75 even 2
6422.2.a.h.1.1 1 104.77 even 2
6498.2.a.f.1.1 1 456.341 even 2
7600.2.a.n.1.1 1 40.19 odd 2
8550.2.a.m.1.1 1 120.29 odd 2