# Properties

 Label 2790.2.a.ba.1.1 Level $2790$ Weight $2$ Character 2790.1 Self dual yes Analytic conductor $22.278$ 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] = [2790,2,Mod(1,2790)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2790, 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("2790.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2790.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: $$22.2782621639$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 930) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2790.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{8} +1.00000 q^{10} +4.00000 q^{11} +6.00000 q^{13} +1.00000 q^{16} -2.00000 q^{17} -4.00000 q^{19} +1.00000 q^{20} +4.00000 q^{22} +4.00000 q^{23} +1.00000 q^{25} +6.00000 q^{26} -2.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} -2.00000 q^{34} -2.00000 q^{37} -4.00000 q^{38} +1.00000 q^{40} +6.00000 q^{41} -4.00000 q^{43} +4.00000 q^{44} +4.00000 q^{46} -7.00000 q^{49} +1.00000 q^{50} +6.00000 q^{52} -2.00000 q^{53} +4.00000 q^{55} -2.00000 q^{58} +4.00000 q^{59} -6.00000 q^{61} -1.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +16.0000 q^{67} -2.00000 q^{68} +12.0000 q^{71} -6.00000 q^{73} -2.00000 q^{74} -4.00000 q^{76} -16.0000 q^{79} +1.00000 q^{80} +6.00000 q^{82} +12.0000 q^{83} -2.00000 q^{85} -4.00000 q^{86} +4.00000 q^{88} +18.0000 q^{89} +4.00000 q^{92} -4.00000 q^{95} -14.0000 q^{97} -7.00000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 1.00000 0.316228
$$11$$ 4.00000 1.20605 0.603023 0.797724i $$-0.293963\pi$$
0.603023 + 0.797724i $$0.293963\pi$$
$$12$$ 0 0
$$13$$ 6.00000 1.66410 0.832050 0.554700i $$-0.187167\pi$$
0.832050 + 0.554700i $$0.187167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ −4.00000 −0.917663 −0.458831 0.888523i $$-0.651732\pi$$
−0.458831 + 0.888523i $$0.651732\pi$$
$$20$$ 1.00000 0.223607
$$21$$ 0 0
$$22$$ 4.00000 0.852803
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 6.00000 1.17670
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ −1.00000 −0.179605
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ −4.00000 −0.648886
$$39$$ 0 0
$$40$$ 1.00000 0.158114
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 4.00000 0.603023
$$45$$ 0 0
$$46$$ 4.00000 0.589768
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −7.00000 −1.00000
$$50$$ 1.00000 0.141421
$$51$$ 0 0
$$52$$ 6.00000 0.832050
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ 0 0
$$55$$ 4.00000 0.539360
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −2.00000 −0.262613
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −6.00000 −0.768221 −0.384111 0.923287i $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ −1.00000 −0.127000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 6.00000 0.744208
$$66$$ 0 0
$$67$$ 16.0000 1.95471 0.977356 0.211604i $$-0.0678686\pi$$
0.977356 + 0.211604i $$0.0678686\pi$$
$$68$$ −2.00000 −0.242536
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ −6.00000 −0.702247 −0.351123 0.936329i $$-0.614200\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ 0 0
$$76$$ −4.00000 −0.458831
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −16.0000 −1.80014 −0.900070 0.435745i $$-0.856485\pi$$
−0.900070 + 0.435745i $$0.856485\pi$$
$$80$$ 1.00000 0.111803
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ −2.00000 −0.216930
$$86$$ −4.00000 −0.431331
$$87$$ 0 0
$$88$$ 4.00000 0.426401
$$89$$ 18.0000 1.90800 0.953998 0.299813i $$-0.0969242\pi$$
0.953998 + 0.299813i $$0.0969242\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −4.00000 −0.410391
$$96$$ 0 0
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ −7.00000 −0.707107
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ −2.00000 −0.199007 −0.0995037 0.995037i $$-0.531726\pi$$
−0.0995037 + 0.995037i $$0.531726\pi$$
$$102$$ 0 0
$$103$$ 8.00000 0.788263 0.394132 0.919054i $$-0.371045\pi$$
0.394132 + 0.919054i $$0.371045\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 0 0
$$106$$ −2.00000 −0.194257
$$107$$ −4.00000 −0.386695 −0.193347 0.981130i $$-0.561934\pi$$
−0.193347 + 0.981130i $$0.561934\pi$$
$$108$$ 0 0
$$109$$ 6.00000 0.574696 0.287348 0.957826i $$-0.407226\pi$$
0.287348 + 0.957826i $$0.407226\pi$$
$$110$$ 4.00000 0.381385
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 10.0000 0.940721 0.470360 0.882474i $$-0.344124\pi$$
0.470360 + 0.882474i $$0.344124\pi$$
$$114$$ 0 0
$$115$$ 4.00000 0.373002
$$116$$ −2.00000 −0.185695
$$117$$ 0 0
$$118$$ 4.00000 0.368230
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ −6.00000 −0.543214
$$123$$ 0 0
$$124$$ −1.00000 −0.0898027
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 6.00000 0.526235
$$131$$ 4.00000 0.349482 0.174741 0.984614i $$-0.444091\pi$$
0.174741 + 0.984614i $$0.444091\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 16.0000 1.38219
$$135$$ 0 0
$$136$$ −2.00000 −0.171499
$$137$$ −18.0000 −1.53784 −0.768922 0.639343i $$-0.779207\pi$$
−0.768922 + 0.639343i $$0.779207\pi$$
$$138$$ 0 0
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 12.0000 1.00702
$$143$$ 24.0000 2.00698
$$144$$ 0 0
$$145$$ −2.00000 −0.166091
$$146$$ −6.00000 −0.496564
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ −10.0000 −0.819232 −0.409616 0.912258i $$-0.634337\pi$$
−0.409616 + 0.912258i $$0.634337\pi$$
$$150$$ 0 0
$$151$$ 16.0000 1.30206 0.651031 0.759051i $$-0.274337\pi$$
0.651031 + 0.759051i $$0.274337\pi$$
$$152$$ −4.00000 −0.324443
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1.00000 −0.0803219
$$156$$ 0 0
$$157$$ 18.0000 1.43656 0.718278 0.695756i $$-0.244931\pi$$
0.718278 + 0.695756i $$0.244931\pi$$
$$158$$ −16.0000 −1.27289
$$159$$ 0 0
$$160$$ 1.00000 0.0790569
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −24.0000 −1.87983 −0.939913 0.341415i $$-0.889094\pi$$
−0.939913 + 0.341415i $$0.889094\pi$$
$$164$$ 6.00000 0.468521
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ −2.00000 −0.153393
$$171$$ 0 0
$$172$$ −4.00000 −0.304997
$$173$$ 14.0000 1.06440 0.532200 0.846619i $$-0.321365\pi$$
0.532200 + 0.846619i $$0.321365\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 4.00000 0.301511
$$177$$ 0 0
$$178$$ 18.0000 1.34916
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ −6.00000 −0.445976 −0.222988 0.974821i $$-0.571581\pi$$
−0.222988 + 0.974821i $$0.571581\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 4.00000 0.294884
$$185$$ −2.00000 −0.147043
$$186$$ 0 0
$$187$$ −8.00000 −0.585018
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −4.00000 −0.290191
$$191$$ −4.00000 −0.289430 −0.144715 0.989473i $$-0.546227\pi$$
−0.144715 + 0.989473i $$0.546227\pi$$
$$192$$ 0 0
$$193$$ −22.0000 −1.58359 −0.791797 0.610784i $$-0.790854\pi$$
−0.791797 + 0.610784i $$0.790854\pi$$
$$194$$ −14.0000 −1.00514
$$195$$ 0 0
$$196$$ −7.00000 −0.500000
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ 16.0000 1.13421 0.567105 0.823646i $$-0.308063\pi$$
0.567105 + 0.823646i $$0.308063\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ 0 0
$$202$$ −2.00000 −0.140720
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 6.00000 0.419058
$$206$$ 8.00000 0.557386
$$207$$ 0 0
$$208$$ 6.00000 0.416025
$$209$$ −16.0000 −1.10674
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ −2.00000 −0.137361
$$213$$ 0 0
$$214$$ −4.00000 −0.273434
$$215$$ −4.00000 −0.272798
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 6.00000 0.406371
$$219$$ 0 0
$$220$$ 4.00000 0.269680
$$221$$ −12.0000 −0.807207
$$222$$ 0 0
$$223$$ −8.00000 −0.535720 −0.267860 0.963458i $$-0.586316\pi$$
−0.267860 + 0.963458i $$0.586316\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 10.0000 0.665190
$$227$$ −20.0000 −1.32745 −0.663723 0.747978i $$-0.731025\pi$$
−0.663723 + 0.747978i $$0.731025\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 4.00000 0.263752
$$231$$ 0 0
$$232$$ −2.00000 −0.131306
$$233$$ −22.0000 −1.44127 −0.720634 0.693316i $$-0.756149\pi$$
−0.720634 + 0.693316i $$0.756149\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 4.00000 0.260378
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −14.0000 −0.901819 −0.450910 0.892570i $$-0.648900\pi$$
−0.450910 + 0.892570i $$0.648900\pi$$
$$242$$ 5.00000 0.321412
$$243$$ 0 0
$$244$$ −6.00000 −0.384111
$$245$$ −7.00000 −0.447214
$$246$$ 0 0
$$247$$ −24.0000 −1.52708
$$248$$ −1.00000 −0.0635001
$$249$$ 0 0
$$250$$ 1.00000 0.0632456
$$251$$ −20.0000 −1.26239 −0.631194 0.775625i $$-0.717435\pi$$
−0.631194 + 0.775625i $$0.717435\pi$$
$$252$$ 0 0
$$253$$ 16.0000 1.00591
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −22.0000 −1.37232 −0.686161 0.727450i $$-0.740706\pi$$
−0.686161 + 0.727450i $$0.740706\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 6.00000 0.372104
$$261$$ 0 0
$$262$$ 4.00000 0.247121
$$263$$ 12.0000 0.739952 0.369976 0.929041i $$-0.379366\pi$$
0.369976 + 0.929041i $$0.379366\pi$$
$$264$$ 0 0
$$265$$ −2.00000 −0.122859
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 16.0000 0.977356
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ −18.0000 −1.08742
$$275$$ 4.00000 0.241209
$$276$$ 0 0
$$277$$ 6.00000 0.360505 0.180253 0.983620i $$-0.442309\pi$$
0.180253 + 0.983620i $$0.442309\pi$$
$$278$$ 8.00000 0.479808
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −10.0000 −0.596550 −0.298275 0.954480i $$-0.596411\pi$$
−0.298275 + 0.954480i $$0.596411\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 0 0
$$286$$ 24.0000 1.41915
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ −2.00000 −0.117444
$$291$$ 0 0
$$292$$ −6.00000 −0.351123
$$293$$ 6.00000 0.350524 0.175262 0.984522i $$-0.443923\pi$$
0.175262 + 0.984522i $$0.443923\pi$$
$$294$$ 0 0
$$295$$ 4.00000 0.232889
$$296$$ −2.00000 −0.116248
$$297$$ 0 0
$$298$$ −10.0000 −0.579284
$$299$$ 24.0000 1.38796
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 16.0000 0.920697
$$303$$ 0 0
$$304$$ −4.00000 −0.229416
$$305$$ −6.00000 −0.343559
$$306$$ 0 0
$$307$$ −16.0000 −0.913168 −0.456584 0.889680i $$-0.650927\pi$$
−0.456584 + 0.889680i $$0.650927\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −1.00000 −0.0567962
$$311$$ 28.0000 1.58773 0.793867 0.608091i $$-0.208065\pi$$
0.793867 + 0.608091i $$0.208065\pi$$
$$312$$ 0 0
$$313$$ 26.0000 1.46961 0.734803 0.678280i $$-0.237274\pi$$
0.734803 + 0.678280i $$0.237274\pi$$
$$314$$ 18.0000 1.01580
$$315$$ 0 0
$$316$$ −16.0000 −0.900070
$$317$$ −2.00000 −0.112331 −0.0561656 0.998421i $$-0.517887\pi$$
−0.0561656 + 0.998421i $$0.517887\pi$$
$$318$$ 0 0
$$319$$ −8.00000 −0.447914
$$320$$ 1.00000 0.0559017
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.00000 0.445132
$$324$$ 0 0
$$325$$ 6.00000 0.332820
$$326$$ −24.0000 −1.32924
$$327$$ 0 0
$$328$$ 6.00000 0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 24.0000 1.31916 0.659580 0.751635i $$-0.270734\pi$$
0.659580 + 0.751635i $$0.270734\pi$$
$$332$$ 12.0000 0.658586
$$333$$ 0 0
$$334$$ −12.0000 −0.656611
$$335$$ 16.0000 0.874173
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 23.0000 1.25104
$$339$$ 0 0
$$340$$ −2.00000 −0.108465
$$341$$ −4.00000 −0.216612
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −4.00000 −0.215666
$$345$$ 0 0
$$346$$ 14.0000 0.752645
$$347$$ 4.00000 0.214731 0.107366 0.994220i $$-0.465758\pi$$
0.107366 + 0.994220i $$0.465758\pi$$
$$348$$ 0 0
$$349$$ −2.00000 −0.107058 −0.0535288 0.998566i $$-0.517047\pi$$
−0.0535288 + 0.998566i $$0.517047\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 4.00000 0.213201
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ 12.0000 0.636894
$$356$$ 18.0000 0.953998
$$357$$ 0 0
$$358$$ 4.00000 0.211407
$$359$$ 20.0000 1.05556 0.527780 0.849381i $$-0.323025\pi$$
0.527780 + 0.849381i $$0.323025\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ −6.00000 −0.315353
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −6.00000 −0.314054
$$366$$ 0 0
$$367$$ 16.0000 0.835193 0.417597 0.908633i $$-0.362873\pi$$
0.417597 + 0.908633i $$0.362873\pi$$
$$368$$ 4.00000 0.208514
$$369$$ 0 0
$$370$$ −2.00000 −0.103975
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −38.0000 −1.96757 −0.983783 0.179364i $$-0.942596\pi$$
−0.983783 + 0.179364i $$0.942596\pi$$
$$374$$ −8.00000 −0.413670
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ −4.00000 −0.205196
$$381$$ 0 0
$$382$$ −4.00000 −0.204658
$$383$$ −4.00000 −0.204390 −0.102195 0.994764i $$-0.532587\pi$$
−0.102195 + 0.994764i $$0.532587\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −22.0000 −1.11977
$$387$$ 0 0
$$388$$ −14.0000 −0.710742
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ −8.00000 −0.404577
$$392$$ −7.00000 −0.353553
$$393$$ 0 0
$$394$$ −2.00000 −0.100759
$$395$$ −16.0000 −0.805047
$$396$$ 0 0
$$397$$ −14.0000 −0.702640 −0.351320 0.936255i $$-0.614267\pi$$
−0.351320 + 0.936255i $$0.614267\pi$$
$$398$$ 16.0000 0.802008
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ −14.0000 −0.699127 −0.349563 0.936913i $$-0.613670\pi$$
−0.349563 + 0.936913i $$0.613670\pi$$
$$402$$ 0 0
$$403$$ −6.00000 −0.298881
$$404$$ −2.00000 −0.0995037
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −8.00000 −0.396545
$$408$$ 0 0
$$409$$ −6.00000 −0.296681 −0.148340 0.988936i $$-0.547393\pi$$
−0.148340 + 0.988936i $$0.547393\pi$$
$$410$$ 6.00000 0.296319
$$411$$ 0 0
$$412$$ 8.00000 0.394132
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 12.0000 0.589057
$$416$$ 6.00000 0.294174
$$417$$ 0 0
$$418$$ −16.0000 −0.782586
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ 14.0000 0.682318 0.341159 0.940006i $$-0.389181\pi$$
0.341159 + 0.940006i $$0.389181\pi$$
$$422$$ −4.00000 −0.194717
$$423$$ 0 0
$$424$$ −2.00000 −0.0971286
$$425$$ −2.00000 −0.0970143
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −4.00000 −0.193347
$$429$$ 0 0
$$430$$ −4.00000 −0.192897
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 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
$$436$$ 6.00000 0.287348
$$437$$ −16.0000 −0.765384
$$438$$ 0 0
$$439$$ −32.0000 −1.52728 −0.763638 0.645644i $$-0.776589\pi$$
−0.763638 + 0.645644i $$0.776589\pi$$
$$440$$ 4.00000 0.190693
$$441$$ 0 0
$$442$$ −12.0000 −0.570782
$$443$$ 4.00000 0.190046 0.0950229 0.995475i $$-0.469708\pi$$
0.0950229 + 0.995475i $$0.469708\pi$$
$$444$$ 0 0
$$445$$ 18.0000 0.853282
$$446$$ −8.00000 −0.378811
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ 24.0000 1.13012
$$452$$ 10.0000 0.470360
$$453$$ 0 0
$$454$$ −20.0000 −0.938647
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −22.0000 −1.02912 −0.514558 0.857455i $$-0.672044\pi$$
−0.514558 + 0.857455i $$0.672044\pi$$
$$458$$ 10.0000 0.467269
$$459$$ 0 0
$$460$$ 4.00000 0.186501
$$461$$ 14.0000 0.652045 0.326023 0.945362i $$-0.394291\pi$$
0.326023 + 0.945362i $$0.394291\pi$$
$$462$$ 0 0
$$463$$ −24.0000 −1.11537 −0.557687 0.830051i $$-0.688311\pi$$
−0.557687 + 0.830051i $$0.688311\pi$$
$$464$$ −2.00000 −0.0928477
$$465$$ 0 0
$$466$$ −22.0000 −1.01913
$$467$$ 4.00000 0.185098 0.0925490 0.995708i $$-0.470499\pi$$
0.0925490 + 0.995708i $$0.470499\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 4.00000 0.184115
$$473$$ −16.0000 −0.735681
$$474$$ 0 0
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −36.0000 −1.64488 −0.822441 0.568850i $$-0.807388\pi$$
−0.822441 + 0.568850i $$0.807388\pi$$
$$480$$ 0 0
$$481$$ −12.0000 −0.547153
$$482$$ −14.0000 −0.637683
$$483$$ 0 0
$$484$$ 5.00000 0.227273
$$485$$ −14.0000 −0.635707
$$486$$ 0 0
$$487$$ −40.0000 −1.81257 −0.906287 0.422664i $$-0.861095\pi$$
−0.906287 + 0.422664i $$0.861095\pi$$
$$488$$ −6.00000 −0.271607
$$489$$ 0 0
$$490$$ −7.00000 −0.316228
$$491$$ −20.0000 −0.902587 −0.451294 0.892375i $$-0.649037\pi$$
−0.451294 + 0.892375i $$0.649037\pi$$
$$492$$ 0 0
$$493$$ 4.00000 0.180151
$$494$$ −24.0000 −1.07981
$$495$$ 0 0
$$496$$ −1.00000 −0.0449013
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 16.0000 0.716258 0.358129 0.933672i $$-0.383415\pi$$
0.358129 + 0.933672i $$0.383415\pi$$
$$500$$ 1.00000 0.0447214
$$501$$ 0 0
$$502$$ −20.0000 −0.892644
$$503$$ −32.0000 −1.42681 −0.713405 0.700752i $$-0.752848\pi$$
−0.713405 + 0.700752i $$0.752848\pi$$
$$504$$ 0 0
$$505$$ −2.00000 −0.0889988
$$506$$ 16.0000 0.711287
$$507$$ 0 0
$$508$$ −8.00000 −0.354943
$$509$$ −18.0000 −0.797836 −0.398918 0.916987i $$-0.630614\pi$$
−0.398918 + 0.916987i $$0.630614\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −22.0000 −0.970378
$$515$$ 8.00000 0.352522
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 6.00000 0.263117
$$521$$ 14.0000 0.613351 0.306676 0.951814i $$-0.400783\pi$$
0.306676 + 0.951814i $$0.400783\pi$$
$$522$$ 0 0
$$523$$ 20.0000 0.874539 0.437269 0.899331i $$-0.355946\pi$$
0.437269 + 0.899331i $$0.355946\pi$$
$$524$$ 4.00000 0.174741
$$525$$ 0 0
$$526$$ 12.0000 0.523225
$$527$$ 2.00000 0.0871214
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ −2.00000 −0.0868744
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 36.0000 1.55933
$$534$$ 0 0
$$535$$ −4.00000 −0.172935
$$536$$ 16.0000 0.691095
$$537$$ 0 0
$$538$$ −18.0000 −0.776035
$$539$$ −28.0000 −1.20605
$$540$$ 0 0
$$541$$ −10.0000 −0.429934 −0.214967 0.976621i $$-0.568964\pi$$
−0.214967 + 0.976621i $$0.568964\pi$$
$$542$$ −8.00000 −0.343629
$$543$$ 0 0
$$544$$ −2.00000 −0.0857493
$$545$$ 6.00000 0.257012
$$546$$ 0 0
$$547$$ 16.0000 0.684111 0.342055 0.939680i $$-0.388877\pi$$
0.342055 + 0.939680i $$0.388877\pi$$
$$548$$ −18.0000 −0.768922
$$549$$ 0 0
$$550$$ 4.00000 0.170561
$$551$$ 8.00000 0.340811
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 6.00000 0.254916
$$555$$ 0 0
$$556$$ 8.00000 0.339276
$$557$$ 30.0000 1.27114 0.635570 0.772043i $$-0.280765\pi$$
0.635570 + 0.772043i $$0.280765\pi$$
$$558$$ 0 0
$$559$$ −24.0000 −1.01509
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −10.0000 −0.421825
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 0 0
$$565$$ 10.0000 0.420703
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 12.0000 0.503509
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ 0 0
$$571$$ 40.0000 1.67395 0.836974 0.547243i $$-0.184323\pi$$
0.836974 + 0.547243i $$0.184323\pi$$
$$572$$ 24.0000 1.00349
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 4.00000 0.166812
$$576$$ 0 0
$$577$$ −30.0000 −1.24892 −0.624458 0.781058i $$-0.714680\pi$$
−0.624458 + 0.781058i $$0.714680\pi$$
$$578$$ −13.0000 −0.540729
$$579$$ 0 0
$$580$$ −2.00000 −0.0830455
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −8.00000 −0.331326
$$584$$ −6.00000 −0.248282
$$585$$ 0 0
$$586$$ 6.00000 0.247858
$$587$$ −4.00000 −0.165098 −0.0825488 0.996587i $$-0.526306\pi$$
−0.0825488 + 0.996587i $$0.526306\pi$$
$$588$$ 0 0
$$589$$ 4.00000 0.164817
$$590$$ 4.00000 0.164677
$$591$$ 0 0
$$592$$ −2.00000 −0.0821995
$$593$$ −14.0000 −0.574911 −0.287456 0.957794i $$-0.592809\pi$$
−0.287456 + 0.957794i $$0.592809\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −10.0000 −0.409616
$$597$$ 0 0
$$598$$ 24.0000 0.981433
$$599$$ 4.00000 0.163436 0.0817178 0.996656i $$-0.473959\pi$$
0.0817178 + 0.996656i $$0.473959\pi$$
$$600$$ 0 0
$$601$$ 10.0000 0.407909 0.203954 0.978980i $$-0.434621\pi$$
0.203954 + 0.978980i $$0.434621\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 16.0000 0.651031
$$605$$ 5.00000 0.203279
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ −4.00000 −0.162221
$$609$$ 0 0
$$610$$ −6.00000 −0.242933
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −26.0000 −1.05013 −0.525065 0.851062i $$-0.675959\pi$$
−0.525065 + 0.851062i $$0.675959\pi$$
$$614$$ −16.0000 −0.645707
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −46.0000 −1.85189 −0.925945 0.377658i $$-0.876729\pi$$
−0.925945 + 0.377658i $$0.876729\pi$$
$$618$$ 0 0
$$619$$ 32.0000 1.28619 0.643094 0.765787i $$-0.277650\pi$$
0.643094 + 0.765787i $$0.277650\pi$$
$$620$$ −1.00000 −0.0401610
$$621$$ 0 0
$$622$$ 28.0000 1.12270
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 26.0000 1.03917
$$627$$ 0 0
$$628$$ 18.0000 0.718278
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ −16.0000 −0.636446
$$633$$ 0 0
$$634$$ −2.00000 −0.0794301
$$635$$ −8.00000 −0.317470
$$636$$ 0 0
$$637$$ −42.0000 −1.66410
$$638$$ −8.00000 −0.316723
$$639$$ 0 0
$$640$$ 1.00000 0.0395285
$$641$$ −30.0000 −1.18493 −0.592464 0.805597i $$-0.701845\pi$$
−0.592464 + 0.805597i $$0.701845\pi$$
$$642$$ 0 0
$$643$$ −20.0000 −0.788723 −0.394362 0.918955i $$-0.629034\pi$$
−0.394362 + 0.918955i $$0.629034\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 8.00000 0.314756
$$647$$ 12.0000 0.471769 0.235884 0.971781i $$-0.424201\pi$$
0.235884 + 0.971781i $$0.424201\pi$$
$$648$$ 0 0
$$649$$ 16.0000 0.628055
$$650$$ 6.00000 0.235339
$$651$$ 0 0
$$652$$ −24.0000 −0.939913
$$653$$ −18.0000 −0.704394 −0.352197 0.935926i $$-0.614565\pi$$
−0.352197 + 0.935926i $$0.614565\pi$$
$$654$$ 0 0
$$655$$ 4.00000 0.156293
$$656$$ 6.00000 0.234261
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ −34.0000 −1.32245 −0.661223 0.750189i $$-0.729962\pi$$
−0.661223 + 0.750189i $$0.729962\pi$$
$$662$$ 24.0000 0.932786
$$663$$ 0 0
$$664$$ 12.0000 0.465690
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −8.00000 −0.309761
$$668$$ −12.0000 −0.464294
$$669$$ 0 0
$$670$$ 16.0000 0.618134
$$671$$ −24.0000 −0.926510
$$672$$ 0 0
$$673$$ 34.0000 1.31060 0.655302 0.755367i $$-0.272541\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ 2.00000 0.0770371
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ −42.0000 −1.61419 −0.807096 0.590421i $$-0.798962\pi$$
−0.807096 + 0.590421i $$0.798962\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −2.00000 −0.0766965
$$681$$ 0 0
$$682$$ −4.00000 −0.153168
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 0 0
$$685$$ −18.0000 −0.687745
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −4.00000 −0.152499
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ 28.0000 1.06517 0.532585 0.846376i $$-0.321221\pi$$
0.532585 + 0.846376i $$0.321221\pi$$
$$692$$ 14.0000 0.532200
$$693$$ 0 0
$$694$$ 4.00000 0.151838
$$695$$ 8.00000 0.303457
$$696$$ 0 0
$$697$$ −12.0000 −0.454532
$$698$$ −2.00000 −0.0757011
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 38.0000 1.43524 0.717620 0.696435i $$-0.245231\pi$$
0.717620 + 0.696435i $$0.245231\pi$$
$$702$$ 0 0
$$703$$ 8.00000 0.301726
$$704$$ 4.00000 0.150756
$$705$$ 0 0
$$706$$ 6.00000 0.225813
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −46.0000 −1.72757 −0.863783 0.503864i $$-0.831911\pi$$
−0.863783 + 0.503864i $$0.831911\pi$$
$$710$$ 12.0000 0.450352
$$711$$ 0 0
$$712$$ 18.0000 0.674579
$$713$$ −4.00000 −0.149801
$$714$$ 0 0
$$715$$ 24.0000 0.897549
$$716$$ 4.00000 0.149487
$$717$$ 0 0
$$718$$ 20.0000 0.746393
$$719$$ 24.0000 0.895049 0.447524 0.894272i $$-0.352306\pi$$
0.447524 + 0.894272i $$0.352306\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −3.00000 −0.111648
$$723$$ 0 0
$$724$$ −6.00000 −0.222988
$$725$$ −2.00000 −0.0742781
$$726$$ 0 0
$$727$$ 16.0000 0.593407 0.296704 0.954970i $$-0.404113\pi$$
0.296704 + 0.954970i $$0.404113\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −6.00000 −0.222070
$$731$$ 8.00000 0.295891
$$732$$ 0 0
$$733$$ 2.00000 0.0738717 0.0369358 0.999318i $$-0.488240\pi$$
0.0369358 + 0.999318i $$0.488240\pi$$
$$734$$ 16.0000 0.590571
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ 64.0000 2.35747
$$738$$ 0 0
$$739$$ −16.0000 −0.588570 −0.294285 0.955718i $$-0.595081\pi$$
−0.294285 + 0.955718i $$0.595081\pi$$
$$740$$ −2.00000 −0.0735215
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −12.0000 −0.440237 −0.220119 0.975473i $$-0.570644\pi$$
−0.220119 + 0.975473i $$0.570644\pi$$
$$744$$ 0 0
$$745$$ −10.0000 −0.366372
$$746$$ −38.0000 −1.39128
$$747$$ 0 0
$$748$$ −8.00000 −0.292509
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −24.0000 −0.875772 −0.437886 0.899030i $$-0.644273\pi$$
−0.437886 + 0.899030i $$0.644273\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ −12.0000 −0.437014
$$755$$ 16.0000 0.582300
$$756$$ 0 0
$$757$$ −18.0000 −0.654221 −0.327111 0.944986i $$-0.606075\pi$$
−0.327111 + 0.944986i $$0.606075\pi$$
$$758$$ −20.0000 −0.726433
$$759$$ 0 0
$$760$$ −4.00000 −0.145095
$$761$$ −22.0000 −0.797499 −0.398750 0.917060i $$-0.630556\pi$$
−0.398750 + 0.917060i $$0.630556\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −4.00000 −0.144715
$$765$$ 0 0
$$766$$ −4.00000 −0.144526
$$767$$ 24.0000 0.866590
$$768$$ 0 0
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −22.0000 −0.791797
$$773$$ −50.0000 −1.79838 −0.899188 0.437564i $$-0.855842\pi$$
−0.899188 + 0.437564i $$0.855842\pi$$
$$774$$ 0 0
$$775$$ −1.00000 −0.0359211
$$776$$ −14.0000 −0.502571
$$777$$ 0 0
$$778$$ 6.00000 0.215110
$$779$$ −24.0000 −0.859889
$$780$$ 0 0
$$781$$ 48.0000 1.71758
$$782$$ −8.00000 −0.286079
$$783$$ 0 0
$$784$$ −7.00000 −0.250000
$$785$$ 18.0000 0.642448
$$786$$ 0 0
$$787$$ 28.0000 0.998092 0.499046 0.866575i $$-0.333684\pi$$
0.499046 + 0.866575i $$0.333684\pi$$
$$788$$ −2.00000 −0.0712470
$$789$$ 0 0
$$790$$ −16.0000 −0.569254
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −36.0000 −1.27840
$$794$$ −14.0000 −0.496841
$$795$$ 0 0
$$796$$ 16.0000 0.567105
$$797$$ −18.0000 −0.637593 −0.318796 0.947823i $$-0.603279\pi$$
−0.318796 + 0.947823i $$0.603279\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 1.00000 0.0353553
$$801$$ 0 0
$$802$$ −14.0000 −0.494357
$$803$$ −24.0000 −0.846942
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −6.00000 −0.211341
$$807$$ 0 0
$$808$$ −2.00000 −0.0703598
$$809$$ 10.0000 0.351581 0.175791 0.984428i $$-0.443752\pi$$
0.175791 + 0.984428i $$0.443752\pi$$
$$810$$ 0 0
$$811$$ 12.0000 0.421377 0.210688 0.977553i $$-0.432429\pi$$
0.210688 + 0.977553i $$0.432429\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ −8.00000 −0.280400
$$815$$ −24.0000 −0.840683
$$816$$ 0 0
$$817$$ 16.0000 0.559769
$$818$$ −6.00000 −0.209785
$$819$$ 0 0
$$820$$ 6.00000 0.209529
$$821$$ 22.0000 0.767805 0.383903 0.923374i $$-0.374580\pi$$
0.383903 + 0.923374i $$0.374580\pi$$
$$822$$ 0 0
$$823$$ 40.0000 1.39431 0.697156 0.716919i $$-0.254448\pi$$
0.697156 + 0.716919i $$0.254448\pi$$
$$824$$ 8.00000 0.278693
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −52.0000 −1.80822 −0.904109 0.427303i $$-0.859464\pi$$
−0.904109 + 0.427303i $$0.859464\pi$$
$$828$$ 0 0
$$829$$ 50.0000 1.73657 0.868286 0.496064i $$-0.165222\pi$$
0.868286 + 0.496064i $$0.165222\pi$$
$$830$$ 12.0000 0.416526
$$831$$ 0 0
$$832$$ 6.00000 0.208013
$$833$$ 14.0000 0.485071
$$834$$ 0 0
$$835$$ −12.0000 −0.415277
$$836$$ −16.0000 −0.553372
$$837$$ 0 0
$$838$$ 12.0000 0.414533
$$839$$ −28.0000 −0.966667 −0.483334 0.875436i $$-0.660574\pi$$
−0.483334 + 0.875436i $$0.660574\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ 14.0000 0.482472
$$843$$ 0 0
$$844$$ −4.00000 −0.137686
$$845$$ 23.0000 0.791224
$$846$$ 0 0
$$847$$ 0 0
$$848$$ −2.00000 −0.0686803
$$849$$ 0 0
$$850$$ −2.00000 −0.0685994
$$851$$ −8.00000 −0.274236
$$852$$ 0 0
$$853$$ 58.0000 1.98588 0.992941 0.118609i $$-0.0378434\pi$$
0.992941 + 0.118609i $$0.0378434\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −4.00000 −0.136717
$$857$$ −54.0000 −1.84460 −0.922302 0.386469i $$-0.873695\pi$$
−0.922302 + 0.386469i $$0.873695\pi$$
$$858$$ 0 0
$$859$$ 48.0000 1.63774 0.818869 0.573980i $$-0.194601\pi$$
0.818869 + 0.573980i $$0.194601\pi$$
$$860$$ −4.00000 −0.136399
$$861$$ 0 0
$$862$$ 12.0000 0.408722
$$863$$ −36.0000 −1.22545 −0.612727 0.790295i $$-0.709928\pi$$
−0.612727 + 0.790295i $$0.709928\pi$$
$$864$$ 0 0
$$865$$ 14.0000 0.476014
$$866$$ 2.00000 0.0679628
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −64.0000 −2.17105
$$870$$ 0 0
$$871$$ 96.0000 3.25284
$$872$$ 6.00000 0.203186
$$873$$ 0 0
$$874$$ −16.0000 −0.541208
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −38.0000 −1.28317 −0.641584 0.767052i $$-0.721723\pi$$
−0.641584 + 0.767052i $$0.721723\pi$$
$$878$$ −32.0000 −1.07995
$$879$$ 0 0
$$880$$ 4.00000 0.134840
$$881$$ 42.0000 1.41502 0.707508 0.706705i $$-0.249819\pi$$
0.707508 + 0.706705i $$0.249819\pi$$
$$882$$ 0 0
$$883$$ 52.0000 1.74994 0.874970 0.484178i $$-0.160881\pi$$
0.874970 + 0.484178i $$0.160881\pi$$
$$884$$ −12.0000 −0.403604
$$885$$ 0 0
$$886$$ 4.00000 0.134383
$$887$$ 24.0000 0.805841 0.402921 0.915235i $$-0.367995\pi$$
0.402921 + 0.915235i $$0.367995\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 18.0000 0.603361
$$891$$ 0 0
$$892$$ −8.00000 −0.267860
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 4.00000 0.133705
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 18.0000 0.600668
$$899$$ 2.00000 0.0667037
$$900$$ 0 0
$$901$$ 4.00000 0.133259
$$902$$ 24.0000 0.799113
$$903$$ 0 0
$$904$$ 10.0000 0.332595
$$905$$ −6.00000 −0.199447
$$906$$ 0 0
$$907$$ −56.0000 −1.85945 −0.929725 0.368255i $$-0.879955\pi$$
−0.929725 + 0.368255i $$0.879955\pi$$
$$908$$ −20.0000 −0.663723
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 48.0000 1.59031 0.795155 0.606406i $$-0.207389\pi$$
0.795155 + 0.606406i $$0.207389\pi$$
$$912$$ 0 0
$$913$$ 48.0000 1.58857
$$914$$ −22.0000 −0.727695
$$915$$ 0 0
$$916$$ 10.0000 0.330409
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −32.0000 −1.05558 −0.527791 0.849374i $$-0.676980\pi$$
−0.527791 + 0.849374i $$0.676980\pi$$
$$920$$ 4.00000 0.131876
$$921$$ 0 0
$$922$$ 14.0000 0.461065
$$923$$ 72.0000 2.36991
$$924$$ 0 0
$$925$$ −2.00000 −0.0657596
$$926$$ −24.0000 −0.788689
$$927$$ 0 0
$$928$$ −2.00000 −0.0656532
$$929$$ 42.0000 1.37798 0.688988 0.724773i $$-0.258055\pi$$
0.688988 + 0.724773i $$0.258055\pi$$
$$930$$ 0 0
$$931$$ 28.0000 0.917663
$$932$$ −22.0000 −0.720634
$$933$$ 0 0
$$934$$ 4.00000 0.130884
$$935$$ −8.00000 −0.261628
$$936$$ 0 0
$$937$$ 10.0000 0.326686 0.163343 0.986569i $$-0.447772\pi$$
0.163343 + 0.986569i $$0.447772\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −18.0000 −0.586783 −0.293392 0.955992i $$-0.594784\pi$$
−0.293392 + 0.955992i $$0.594784\pi$$
$$942$$ 0 0
$$943$$ 24.0000 0.781548
$$944$$ 4.00000 0.130189
$$945$$ 0 0
$$946$$ −16.0000 −0.520205
$$947$$ 44.0000 1.42981 0.714904 0.699223i $$-0.246470\pi$$
0.714904 + 0.699223i $$0.246470\pi$$
$$948$$ 0 0
$$949$$ −36.0000 −1.16861
$$950$$ −4.00000 −0.129777
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 30.0000 0.971795 0.485898 0.874016i $$-0.338493\pi$$
0.485898 + 0.874016i $$0.338493\pi$$
$$954$$ 0 0
$$955$$ −4.00000 −0.129437
$$956$$ 0 0
$$957$$ 0 0
$$958$$ −36.0000 −1.16311
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 1.00000 0.0322581
$$962$$ −12.0000 −0.386896
$$963$$ 0 0
$$964$$ −14.0000 −0.450910
$$965$$ −22.0000 −0.708205
$$966$$ 0 0
$$967$$ −8.00000 −0.257263 −0.128631 0.991692i $$-0.541058\pi$$
−0.128631 + 0.991692i $$0.541058\pi$$
$$968$$ 5.00000 0.160706
$$969$$ 0 0
$$970$$ −14.0000 −0.449513
$$971$$ 12.0000 0.385098 0.192549 0.981287i $$-0.438325\pi$$
0.192549 + 0.981287i $$0.438325\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ −40.0000 −1.28168
$$975$$ 0 0
$$976$$ −6.00000 −0.192055
$$977$$ −22.0000 −0.703842 −0.351921 0.936030i $$-0.614471\pi$$
−0.351921 + 0.936030i $$0.614471\pi$$
$$978$$ 0 0
$$979$$ 72.0000 2.30113
$$980$$ −7.00000 −0.223607
$$981$$ 0 0
$$982$$ −20.0000 −0.638226
$$983$$ 4.00000 0.127580 0.0637901 0.997963i $$-0.479681\pi$$
0.0637901 + 0.997963i $$0.479681\pi$$
$$984$$ 0 0
$$985$$ −2.00000 −0.0637253
$$986$$ 4.00000 0.127386
$$987$$ 0 0
$$988$$ −24.0000 −0.763542
$$989$$ −16.0000 −0.508770
$$990$$ 0 0
$$991$$ −16.0000 −0.508257 −0.254128 0.967170i $$-0.581789\pi$$
−0.254128 + 0.967170i $$0.581789\pi$$
$$992$$ −1.00000 −0.0317500
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 16.0000 0.507234
$$996$$ 0 0
$$997$$ 26.0000 0.823428 0.411714 0.911313i $$-0.364930\pi$$
0.411714 + 0.911313i $$0.364930\pi$$
$$998$$ 16.0000 0.506471
$$999$$ 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 2790.2.a.ba.1.1 1
3.2 odd 2 930.2.a.b.1.1 1
12.11 even 2 7440.2.a.q.1.1 1
15.2 even 4 4650.2.d.o.3349.1 2
15.8 even 4 4650.2.d.o.3349.2 2
15.14 odd 2 4650.2.a.bp.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.a.b.1.1 1 3.2 odd 2
2790.2.a.ba.1.1 1 1.1 even 1 trivial
4650.2.a.bp.1.1 1 15.14 odd 2
4650.2.d.o.3349.1 2 15.2 even 4
4650.2.d.o.3349.2 2 15.8 even 4
7440.2.a.q.1.1 1 12.11 even 2