# Properties

 Label 7600.2.a.a.1.1 Level $7600$ Weight $2$ Character 7600.1 Self dual yes Analytic conductor $60.686$ 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] = [7600,2,Mod(1,7600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7600.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$7600 = 2^{4} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7600.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: $$60.6863055362$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7600.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-3.00000 q^{3} -5.00000 q^{7} +6.00000 q^{9} +O(q^{10})$$ $$q-3.00000 q^{3} -5.00000 q^{7} +6.00000 q^{9} +4.00000 q^{11} +1.00000 q^{13} +3.00000 q^{17} -1.00000 q^{19} +15.0000 q^{21} +7.00000 q^{23} -9.00000 q^{27} -3.00000 q^{29} +2.00000 q^{31} -12.0000 q^{33} +2.00000 q^{37} -3.00000 q^{39} -6.00000 q^{41} +6.00000 q^{43} +18.0000 q^{49} -9.00000 q^{51} +13.0000 q^{53} +3.00000 q^{57} +9.00000 q^{59} -12.0000 q^{61} -30.0000 q^{63} -3.00000 q^{67} -21.0000 q^{69} -11.0000 q^{73} -20.0000 q^{77} +2.00000 q^{79} +9.00000 q^{81} -10.0000 q^{83} +9.00000 q^{87} +2.00000 q^{89} -5.00000 q^{91} -6.00000 q^{93} +2.00000 q^{97} +24.0000 q^{99} +O(q^{100})$$

## 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
$$3$$ −3.00000 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −5.00000 −1.88982 −0.944911 0.327327i $$-0.893852\pi$$
−0.944911 + 0.327327i $$0.893852\pi$$
$$8$$ 0 0
$$9$$ 6.00000 2.00000
$$10$$ 0 0
$$11$$ 4.00000 1.20605 0.603023 0.797724i $$-0.293963\pi$$
0.603023 + 0.797724i $$0.293963\pi$$
$$12$$ 0 0
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 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
$$21$$ 15.0000 3.27327
$$22$$ 0 0
$$23$$ 7.00000 1.45960 0.729800 0.683660i $$-0.239613\pi$$
0.729800 + 0.683660i $$0.239613\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −9.00000 −1.73205
$$28$$ 0 0
$$29$$ −3.00000 −0.557086 −0.278543 0.960424i $$-0.589851\pi$$
−0.278543 + 0.960424i $$0.589851\pi$$
$$30$$ 0 0
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ 0 0
$$33$$ −12.0000 −2.08893
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 0 0
$$39$$ −3.00000 −0.480384
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 6.00000 0.914991 0.457496 0.889212i $$-0.348747\pi$$
0.457496 + 0.889212i $$0.348747\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 18.0000 2.57143
$$50$$ 0 0
$$51$$ −9.00000 −1.26025
$$52$$ 0 0
$$53$$ 13.0000 1.78569 0.892844 0.450367i $$-0.148707\pi$$
0.892844 + 0.450367i $$0.148707\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 3.00000 0.397360
$$58$$ 0 0
$$59$$ 9.00000 1.17170 0.585850 0.810419i $$-0.300761\pi$$
0.585850 + 0.810419i $$0.300761\pi$$
$$60$$ 0 0
$$61$$ −12.0000 −1.53644 −0.768221 0.640184i $$-0.778858\pi$$
−0.768221 + 0.640184i $$0.778858\pi$$
$$62$$ 0 0
$$63$$ −30.0000 −3.77964
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −3.00000 −0.366508 −0.183254 0.983066i $$-0.558663\pi$$
−0.183254 + 0.983066i $$0.558663\pi$$
$$68$$ 0 0
$$69$$ −21.0000 −2.52810
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −11.0000 −1.28745 −0.643726 0.765256i $$-0.722612\pi$$
−0.643726 + 0.765256i $$0.722612\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −20.0000 −2.27921
$$78$$ 0 0
$$79$$ 2.00000 0.225018 0.112509 0.993651i $$-0.464111\pi$$
0.112509 + 0.993651i $$0.464111\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ −10.0000 −1.09764 −0.548821 0.835940i $$-0.684923\pi$$
−0.548821 + 0.835940i $$0.684923\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 9.00000 0.964901
$$88$$ 0 0
$$89$$ 2.00000 0.212000 0.106000 0.994366i $$-0.466196\pi$$
0.106000 + 0.994366i $$0.466196\pi$$
$$90$$ 0 0
$$91$$ −5.00000 −0.524142
$$92$$ 0 0
$$93$$ −6.00000 −0.622171
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 2.00000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ 0 0
$$99$$ 24.0000 2.41209
$$100$$ 0 0
$$101$$ −8.00000 −0.796030 −0.398015 0.917379i $$-0.630301\pi$$
−0.398015 + 0.917379i $$0.630301\pi$$
$$102$$ 0 0
$$103$$ 4.00000 0.394132 0.197066 0.980390i $$-0.436859\pi$$
0.197066 + 0.980390i $$0.436859\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −13.0000 −1.25676 −0.628379 0.777908i $$-0.716281\pi$$
−0.628379 + 0.777908i $$0.716281\pi$$
$$108$$ 0 0
$$109$$ 19.0000 1.81987 0.909935 0.414751i $$-0.136131\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ 0 0
$$111$$ −6.00000 −0.569495
$$112$$ 0 0
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 6.00000 0.554700
$$118$$ 0 0
$$119$$ −15.0000 −1.37505
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 0 0
$$123$$ 18.0000 1.62301
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −6.00000 −0.532414 −0.266207 0.963916i $$-0.585770\pi$$
−0.266207 + 0.963916i $$0.585770\pi$$
$$128$$ 0 0
$$129$$ −18.0000 −1.58481
$$130$$ 0 0
$$131$$ −16.0000 −1.39793 −0.698963 0.715158i $$-0.746355\pi$$
−0.698963 + 0.715158i $$0.746355\pi$$
$$132$$ 0 0
$$133$$ 5.00000 0.433555
$$134$$ 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
$$139$$ −16.0000 −1.35710 −0.678551 0.734553i $$-0.737392\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 4.00000 0.334497
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −54.0000 −4.45384
$$148$$ 0 0
$$149$$ −4.00000 −0.327693 −0.163846 0.986486i $$-0.552390\pi$$
−0.163846 + 0.986486i $$0.552390\pi$$
$$150$$ 0 0
$$151$$ 10.0000 0.813788 0.406894 0.913475i $$-0.366612\pi$$
0.406894 + 0.913475i $$0.366612\pi$$
$$152$$ 0 0
$$153$$ 18.0000 1.45521
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −6.00000 −0.478852 −0.239426 0.970915i $$-0.576959\pi$$
−0.239426 + 0.970915i $$0.576959\pi$$
$$158$$ 0 0
$$159$$ −39.0000 −3.09290
$$160$$ 0 0
$$161$$ −35.0000 −2.75839
$$162$$ 0 0
$$163$$ 22.0000 1.72317 0.861586 0.507611i $$-0.169471\pi$$
0.861586 + 0.507611i $$0.169471\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2.00000 −0.154765 −0.0773823 0.997001i $$-0.524656\pi$$
−0.0773823 + 0.997001i $$0.524656\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ −6.00000 −0.458831
$$172$$ 0 0
$$173$$ 14.0000 1.06440 0.532200 0.846619i $$-0.321365\pi$$
0.532200 + 0.846619i $$0.321365\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −27.0000 −2.02944
$$178$$ 0 0
$$179$$ 8.00000 0.597948 0.298974 0.954261i $$-0.403356\pi$$
0.298974 + 0.954261i $$0.403356\pi$$
$$180$$ 0 0
$$181$$ 26.0000 1.93256 0.966282 0.257485i $$-0.0828937\pi$$
0.966282 + 0.257485i $$0.0828937\pi$$
$$182$$ 0 0
$$183$$ 36.0000 2.66120
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 12.0000 0.877527
$$188$$ 0 0
$$189$$ 45.0000 3.27327
$$190$$ 0 0
$$191$$ −9.00000 −0.651217 −0.325609 0.945505i $$-0.605569\pi$$
−0.325609 + 0.945505i $$0.605569\pi$$
$$192$$ 0 0
$$193$$ −10.0000 −0.719816 −0.359908 0.932988i $$-0.617192\pi$$
−0.359908 + 0.932988i $$0.617192\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 22.0000 1.56744 0.783718 0.621117i $$-0.213321\pi$$
0.783718 + 0.621117i $$0.213321\pi$$
$$198$$ 0 0
$$199$$ 15.0000 1.06332 0.531661 0.846957i $$-0.321568\pi$$
0.531661 + 0.846957i $$0.321568\pi$$
$$200$$ 0 0
$$201$$ 9.00000 0.634811
$$202$$ 0 0
$$203$$ 15.0000 1.05279
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 42.0000 2.91920
$$208$$ 0 0
$$209$$ −4.00000 −0.276686
$$210$$ 0 0
$$211$$ 5.00000 0.344214 0.172107 0.985078i $$-0.444942\pi$$
0.172107 + 0.985078i $$0.444942\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −10.0000 −0.678844
$$218$$ 0 0
$$219$$ 33.0000 2.22993
$$220$$ 0 0
$$221$$ 3.00000 0.201802
$$222$$ 0 0
$$223$$ −2.00000 −0.133930 −0.0669650 0.997755i $$-0.521332\pi$$
−0.0669650 + 0.997755i $$0.521332\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 5.00000 0.331862 0.165931 0.986137i $$-0.446937\pi$$
0.165931 + 0.986137i $$0.446937\pi$$
$$228$$ 0 0
$$229$$ −6.00000 −0.396491 −0.198246 0.980152i $$-0.563524\pi$$
−0.198246 + 0.980152i $$0.563524\pi$$
$$230$$ 0 0
$$231$$ 60.0000 3.94771
$$232$$ 0 0
$$233$$ −10.0000 −0.655122 −0.327561 0.944830i $$-0.606227\pi$$
−0.327561 + 0.944830i $$0.606227\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −6.00000 −0.389742
$$238$$ 0 0
$$239$$ 11.0000 0.711531 0.355765 0.934575i $$-0.384220\pi$$
0.355765 + 0.934575i $$0.384220\pi$$
$$240$$ 0 0
$$241$$ −12.0000 −0.772988 −0.386494 0.922292i $$-0.626314\pi$$
−0.386494 + 0.922292i $$0.626314\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −1.00000 −0.0636285
$$248$$ 0 0
$$249$$ 30.0000 1.90117
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 28.0000 1.76034
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −22.0000 −1.37232 −0.686161 0.727450i $$-0.740706\pi$$
−0.686161 + 0.727450i $$0.740706\pi$$
$$258$$ 0 0
$$259$$ −10.0000 −0.621370
$$260$$ 0 0
$$261$$ −18.0000 −1.11417
$$262$$ 0 0
$$263$$ 8.00000 0.493301 0.246651 0.969104i $$-0.420670\pi$$
0.246651 + 0.969104i $$0.420670\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −6.00000 −0.367194
$$268$$ 0 0
$$269$$ 2.00000 0.121942 0.0609711 0.998140i $$-0.480580\pi$$
0.0609711 + 0.998140i $$0.480580\pi$$
$$270$$ 0 0
$$271$$ 27.0000 1.64013 0.820067 0.572268i $$-0.193936\pi$$
0.820067 + 0.572268i $$0.193936\pi$$
$$272$$ 0 0
$$273$$ 15.0000 0.907841
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ 0 0
$$279$$ 12.0000 0.718421
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ −2.00000 −0.118888 −0.0594438 0.998232i $$-0.518933\pi$$
−0.0594438 + 0.998232i $$0.518933\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 30.0000 1.77084
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ −6.00000 −0.351726
$$292$$ 0 0
$$293$$ 27.0000 1.57736 0.788678 0.614806i $$-0.210766\pi$$
0.788678 + 0.614806i $$0.210766\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −36.0000 −2.08893
$$298$$ 0 0
$$299$$ 7.00000 0.404820
$$300$$ 0 0
$$301$$ −30.0000 −1.72917
$$302$$ 0 0
$$303$$ 24.0000 1.37876
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 4.00000 0.228292 0.114146 0.993464i $$-0.463587\pi$$
0.114146 + 0.993464i $$0.463587\pi$$
$$308$$ 0 0
$$309$$ −12.0000 −0.682656
$$310$$ 0 0
$$311$$ −25.0000 −1.41762 −0.708810 0.705399i $$-0.750768\pi$$
−0.708810 + 0.705399i $$0.750768\pi$$
$$312$$ 0 0
$$313$$ 1.00000 0.0565233 0.0282617 0.999601i $$-0.491003\pi$$
0.0282617 + 0.999601i $$0.491003\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −9.00000 −0.505490 −0.252745 0.967533i $$-0.581333\pi$$
−0.252745 + 0.967533i $$0.581333\pi$$
$$318$$ 0 0
$$319$$ −12.0000 −0.671871
$$320$$ 0 0
$$321$$ 39.0000 2.17677
$$322$$ 0 0
$$323$$ −3.00000 −0.166924
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −57.0000 −3.15211
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 7.00000 0.384755 0.192377 0.981321i $$-0.438380\pi$$
0.192377 + 0.981321i $$0.438380\pi$$
$$332$$ 0 0
$$333$$ 12.0000 0.657596
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −6.00000 −0.326841 −0.163420 0.986557i $$-0.552253\pi$$
−0.163420 + 0.986557i $$0.552253\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 8.00000 0.433224
$$342$$ 0 0
$$343$$ −55.0000 −2.96972
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −6.00000 −0.322097 −0.161048 0.986947i $$-0.551488\pi$$
−0.161048 + 0.986947i $$0.551488\pi$$
$$348$$ 0 0
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ −9.00000 −0.480384
$$352$$ 0 0
$$353$$ −7.00000 −0.372572 −0.186286 0.982496i $$-0.559645\pi$$
−0.186286 + 0.982496i $$0.559645\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 45.0000 2.38165
$$358$$ 0 0
$$359$$ 5.00000 0.263890 0.131945 0.991257i $$-0.457878\pi$$
0.131945 + 0.991257i $$0.457878\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ −15.0000 −0.787296
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ 0 0
$$369$$ −36.0000 −1.87409
$$370$$ 0 0
$$371$$ −65.0000 −3.37463
$$372$$ 0 0
$$373$$ 23.0000 1.19089 0.595447 0.803394i $$-0.296975\pi$$
0.595447 + 0.803394i $$0.296975\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −3.00000 −0.154508
$$378$$ 0 0
$$379$$ 33.0000 1.69510 0.847548 0.530719i $$-0.178078\pi$$
0.847548 + 0.530719i $$0.178078\pi$$
$$380$$ 0 0
$$381$$ 18.0000 0.922168
$$382$$ 0 0
$$383$$ −4.00000 −0.204390 −0.102195 0.994764i $$-0.532587\pi$$
−0.102195 + 0.994764i $$0.532587\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 36.0000 1.82998
$$388$$ 0 0
$$389$$ −4.00000 −0.202808 −0.101404 0.994845i $$-0.532333\pi$$
−0.101404 + 0.994845i $$0.532333\pi$$
$$390$$ 0 0
$$391$$ 21.0000 1.06202
$$392$$ 0 0
$$393$$ 48.0000 2.42128
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 16.0000 0.803017 0.401508 0.915855i $$-0.368486\pi$$
0.401508 + 0.915855i $$0.368486\pi$$
$$398$$ 0 0
$$399$$ −15.0000 −0.750939
$$400$$ 0 0
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ 0 0
$$403$$ 2.00000 0.0996271
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 8.00000 0.396545
$$408$$ 0 0
$$409$$ 22.0000 1.08783 0.543915 0.839140i $$-0.316941\pi$$
0.543915 + 0.839140i $$0.316941\pi$$
$$410$$ 0 0
$$411$$ 27.0000 1.33181
$$412$$ 0 0
$$413$$ −45.0000 −2.21431
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 48.0000 2.35057
$$418$$ 0 0
$$419$$ −14.0000 −0.683945 −0.341972 0.939710i $$-0.611095\pi$$
−0.341972 + 0.939710i $$0.611095\pi$$
$$420$$ 0 0
$$421$$ 1.00000 0.0487370 0.0243685 0.999703i $$-0.492242\pi$$
0.0243685 + 0.999703i $$0.492242\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 60.0000 2.90360
$$428$$ 0 0
$$429$$ −12.0000 −0.579365
$$430$$ 0 0
$$431$$ 36.0000 1.73406 0.867029 0.498257i $$-0.166026\pi$$
0.867029 + 0.498257i $$0.166026\pi$$
$$432$$ 0 0
$$433$$ 16.0000 0.768911 0.384455 0.923144i $$-0.374389\pi$$
0.384455 + 0.923144i $$0.374389\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −7.00000 −0.334855
$$438$$ 0 0
$$439$$ −26.0000 −1.24091 −0.620456 0.784241i $$-0.713053\pi$$
−0.620456 + 0.784241i $$0.713053\pi$$
$$440$$ 0 0
$$441$$ 108.000 5.14286
$$442$$ 0 0
$$443$$ 36.0000 1.71041 0.855206 0.518289i $$-0.173431\pi$$
0.855206 + 0.518289i $$0.173431\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 12.0000 0.567581
$$448$$ 0 0
$$449$$ −22.0000 −1.03824 −0.519122 0.854700i $$-0.673741\pi$$
−0.519122 + 0.854700i $$0.673741\pi$$
$$450$$ 0 0
$$451$$ −24.0000 −1.13012
$$452$$ 0 0
$$453$$ −30.0000 −1.40952
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 29.0000 1.35656 0.678281 0.734802i $$-0.262725\pi$$
0.678281 + 0.734802i $$0.262725\pi$$
$$458$$ 0 0
$$459$$ −27.0000 −1.26025
$$460$$ 0 0
$$461$$ 18.0000 0.838344 0.419172 0.907907i $$-0.362320\pi$$
0.419172 + 0.907907i $$0.362320\pi$$
$$462$$ 0 0
$$463$$ −8.00000 −0.371792 −0.185896 0.982569i $$-0.559519\pi$$
−0.185896 + 0.982569i $$0.559519\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −8.00000 −0.370196 −0.185098 0.982720i $$-0.559260\pi$$
−0.185098 + 0.982720i $$0.559260\pi$$
$$468$$ 0 0
$$469$$ 15.0000 0.692636
$$470$$ 0 0
$$471$$ 18.0000 0.829396
$$472$$ 0 0
$$473$$ 24.0000 1.10352
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 78.0000 3.57137
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 2.00000 0.0911922
$$482$$ 0 0
$$483$$ 105.000 4.77767
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −38.0000 −1.72194 −0.860972 0.508652i $$-0.830144\pi$$
−0.860972 + 0.508652i $$0.830144\pi$$
$$488$$ 0 0
$$489$$ −66.0000 −2.98462
$$490$$ 0 0
$$491$$ −18.0000 −0.812329 −0.406164 0.913800i $$-0.633134\pi$$
−0.406164 + 0.913800i $$0.633134\pi$$
$$492$$ 0 0
$$493$$ −9.00000 −0.405340
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −42.0000 −1.88018 −0.940089 0.340929i $$-0.889258\pi$$
−0.940089 + 0.340929i $$0.889258\pi$$
$$500$$ 0 0
$$501$$ 6.00000 0.268060
$$502$$ 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
$$507$$ 36.0000 1.59882
$$508$$ 0 0
$$509$$ 2.00000 0.0886484 0.0443242 0.999017i $$-0.485887\pi$$
0.0443242 + 0.999017i $$0.485887\pi$$
$$510$$ 0 0
$$511$$ 55.0000 2.43306
$$512$$ 0 0
$$513$$ 9.00000 0.397360
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −42.0000 −1.84360
$$520$$ 0 0
$$521$$ 24.0000 1.05146 0.525730 0.850652i $$-0.323792\pi$$
0.525730 + 0.850652i $$0.323792\pi$$
$$522$$ 0 0
$$523$$ −9.00000 −0.393543 −0.196771 0.980449i $$-0.563046\pi$$
−0.196771 + 0.980449i $$0.563046\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 6.00000 0.261364
$$528$$ 0 0
$$529$$ 26.0000 1.13043
$$530$$ 0 0
$$531$$ 54.0000 2.34340
$$532$$ 0 0
$$533$$ −6.00000 −0.259889
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −24.0000 −1.03568
$$538$$ 0 0
$$539$$ 72.0000 3.10126
$$540$$ 0 0
$$541$$ 16.0000 0.687894 0.343947 0.938989i $$-0.388236\pi$$
0.343947 + 0.938989i $$0.388236\pi$$
$$542$$ 0 0
$$543$$ −78.0000 −3.34730
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 20.0000 0.855138 0.427569 0.903983i $$-0.359370\pi$$
0.427569 + 0.903983i $$0.359370\pi$$
$$548$$ 0 0
$$549$$ −72.0000 −3.07289
$$550$$ 0 0
$$551$$ 3.00000 0.127804
$$552$$ 0 0
$$553$$ −10.0000 −0.425243
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −12.0000 −0.508456 −0.254228 0.967144i $$-0.581821\pi$$
−0.254228 + 0.967144i $$0.581821\pi$$
$$558$$ 0 0
$$559$$ 6.00000 0.253773
$$560$$ 0 0
$$561$$ −36.0000 −1.51992
$$562$$ 0 0
$$563$$ 20.0000 0.842900 0.421450 0.906852i $$-0.361521\pi$$
0.421450 + 0.906852i $$0.361521\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −45.0000 −1.88982
$$568$$ 0 0
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ −6.00000 −0.251092 −0.125546 0.992088i $$-0.540068\pi$$
−0.125546 + 0.992088i $$0.540068\pi$$
$$572$$ 0 0
$$573$$ 27.0000 1.12794
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 7.00000 0.291414 0.145707 0.989328i $$-0.453454\pi$$
0.145707 + 0.989328i $$0.453454\pi$$
$$578$$ 0 0
$$579$$ 30.0000 1.24676
$$580$$ 0 0
$$581$$ 50.0000 2.07435
$$582$$ 0 0
$$583$$ 52.0000 2.15362
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 18.0000 0.742940 0.371470 0.928445i $$-0.378854\pi$$
0.371470 + 0.928445i $$0.378854\pi$$
$$588$$ 0 0
$$589$$ −2.00000 −0.0824086
$$590$$ 0 0
$$591$$ −66.0000 −2.71488
$$592$$ 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
$$597$$ −45.0000 −1.84173
$$598$$ 0 0
$$599$$ 26.0000 1.06233 0.531166 0.847268i $$-0.321754\pi$$
0.531166 + 0.847268i $$0.321754\pi$$
$$600$$ 0 0
$$601$$ 42.0000 1.71322 0.856608 0.515968i $$-0.172568\pi$$
0.856608 + 0.515968i $$0.172568\pi$$
$$602$$ 0 0
$$603$$ −18.0000 −0.733017
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −26.0000 −1.05531 −0.527654 0.849460i $$-0.676928\pi$$
−0.527654 + 0.849460i $$0.676928\pi$$
$$608$$ 0 0
$$609$$ −45.0000 −1.82349
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 20.0000 0.807792 0.403896 0.914805i $$-0.367656\pi$$
0.403896 + 0.914805i $$0.367656\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −14.0000 −0.563619 −0.281809 0.959470i $$-0.590935\pi$$
−0.281809 + 0.959470i $$0.590935\pi$$
$$618$$ 0 0
$$619$$ 24.0000 0.964641 0.482321 0.875995i $$-0.339794\pi$$
0.482321 + 0.875995i $$0.339794\pi$$
$$620$$ 0 0
$$621$$ −63.0000 −2.52810
$$622$$ 0 0
$$623$$ −10.0000 −0.400642
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 12.0000 0.479234
$$628$$ 0 0
$$629$$ 6.00000 0.239236
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 0 0
$$633$$ −15.0000 −0.596196
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 18.0000 0.713186
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 8.00000 0.315981 0.157991 0.987441i $$-0.449498\pi$$
0.157991 + 0.987441i $$0.449498\pi$$
$$642$$ 0 0
$$643$$ 26.0000 1.02534 0.512670 0.858586i $$-0.328656\pi$$
0.512670 + 0.858586i $$0.328656\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −21.0000 −0.825595 −0.412798 0.910823i $$-0.635448\pi$$
−0.412798 + 0.910823i $$0.635448\pi$$
$$648$$ 0 0
$$649$$ 36.0000 1.41312
$$650$$ 0 0
$$651$$ 30.0000 1.17579
$$652$$ 0 0
$$653$$ 16.0000 0.626128 0.313064 0.949732i $$-0.398644\pi$$
0.313064 + 0.949732i $$0.398644\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −66.0000 −2.57491
$$658$$ 0 0
$$659$$ −33.0000 −1.28550 −0.642749 0.766077i $$-0.722206\pi$$
−0.642749 + 0.766077i $$0.722206\pi$$
$$660$$ 0 0
$$661$$ 15.0000 0.583432 0.291716 0.956505i $$-0.405774\pi$$
0.291716 + 0.956505i $$0.405774\pi$$
$$662$$ 0 0
$$663$$ −9.00000 −0.349531
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −21.0000 −0.813123
$$668$$ 0 0
$$669$$ 6.00000 0.231973
$$670$$ 0 0
$$671$$ −48.0000 −1.85302
$$672$$ 0 0
$$673$$ 44.0000 1.69608 0.848038 0.529936i $$-0.177784\pi$$
0.848038 + 0.529936i $$0.177784\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 39.0000 1.49889 0.749446 0.662066i $$-0.230320\pi$$
0.749446 + 0.662066i $$0.230320\pi$$
$$678$$ 0 0
$$679$$ −10.0000 −0.383765
$$680$$ 0 0
$$681$$ −15.0000 −0.574801
$$682$$ 0 0
$$683$$ −44.0000 −1.68361 −0.841807 0.539779i $$-0.818508\pi$$
−0.841807 + 0.539779i $$0.818508\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 18.0000 0.686743
$$688$$ 0 0
$$689$$ 13.0000 0.495261
$$690$$ 0 0
$$691$$ 42.0000 1.59776 0.798878 0.601494i $$-0.205427\pi$$
0.798878 + 0.601494i $$0.205427\pi$$
$$692$$ 0 0
$$693$$ −120.000 −4.55842
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −18.0000 −0.681799
$$698$$ 0 0
$$699$$ 30.0000 1.13470
$$700$$ 0 0
$$701$$ 24.0000 0.906467 0.453234 0.891392i $$-0.350270\pi$$
0.453234 + 0.891392i $$0.350270\pi$$
$$702$$ 0 0
$$703$$ −2.00000 −0.0754314
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 40.0000 1.50435
$$708$$ 0 0
$$709$$ 2.00000 0.0751116 0.0375558 0.999295i $$-0.488043\pi$$
0.0375558 + 0.999295i $$0.488043\pi$$
$$710$$ 0 0
$$711$$ 12.0000 0.450035
$$712$$ 0 0
$$713$$ 14.0000 0.524304
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −33.0000 −1.23241
$$718$$ 0 0
$$719$$ 27.0000 1.00693 0.503465 0.864016i $$-0.332058\pi$$
0.503465 + 0.864016i $$0.332058\pi$$
$$720$$ 0 0
$$721$$ −20.0000 −0.744839
$$722$$ 0 0
$$723$$ 36.0000 1.33885
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 23.0000 0.853023 0.426511 0.904482i $$-0.359742\pi$$
0.426511 + 0.904482i $$0.359742\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 18.0000 0.665754
$$732$$ 0 0
$$733$$ −36.0000 −1.32969 −0.664845 0.746981i $$-0.731502\pi$$
−0.664845 + 0.746981i $$0.731502\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −12.0000 −0.442026
$$738$$ 0 0
$$739$$ 10.0000 0.367856 0.183928 0.982940i $$-0.441119\pi$$
0.183928 + 0.982940i $$0.441119\pi$$
$$740$$ 0 0
$$741$$ 3.00000 0.110208
$$742$$ 0 0
$$743$$ −18.0000 −0.660356 −0.330178 0.943919i $$-0.607109\pi$$
−0.330178 + 0.943919i $$0.607109\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −60.0000 −2.19529
$$748$$ 0 0
$$749$$ 65.0000 2.37505
$$750$$ 0 0
$$751$$ 26.0000 0.948753 0.474377 0.880322i $$-0.342673\pi$$
0.474377 + 0.880322i $$0.342673\pi$$
$$752$$ 0 0
$$753$$ −36.0000 −1.31191
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 6.00000 0.218074 0.109037 0.994038i $$-0.465223\pi$$
0.109037 + 0.994038i $$0.465223\pi$$
$$758$$ 0 0
$$759$$ −84.0000 −3.04901
$$760$$ 0 0
$$761$$ 11.0000 0.398750 0.199375 0.979923i $$-0.436109\pi$$
0.199375 + 0.979923i $$0.436109\pi$$
$$762$$ 0 0
$$763$$ −95.0000 −3.43923
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 9.00000 0.324971
$$768$$ 0 0
$$769$$ −47.0000 −1.69486 −0.847432 0.530904i $$-0.821852\pi$$
−0.847432 + 0.530904i $$0.821852\pi$$
$$770$$ 0 0
$$771$$ 66.0000 2.37693
$$772$$ 0 0
$$773$$ 51.0000 1.83434 0.917171 0.398493i $$-0.130467\pi$$
0.917171 + 0.398493i $$0.130467\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 30.0000 1.07624
$$778$$ 0 0
$$779$$ 6.00000 0.214972
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 27.0000 0.964901
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −39.0000 −1.39020 −0.695100 0.718913i $$-0.744640\pi$$
−0.695100 + 0.718913i $$0.744640\pi$$
$$788$$ 0 0
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −12.0000 −0.426132
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −31.0000 −1.09808 −0.549038 0.835797i $$-0.685006\pi$$
−0.549038 + 0.835797i $$0.685006\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 12.0000 0.423999
$$802$$ 0 0
$$803$$ −44.0000 −1.55273
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −6.00000 −0.211210
$$808$$ 0 0
$$809$$ 25.0000 0.878953 0.439477 0.898254i $$-0.355164\pi$$
0.439477 + 0.898254i $$0.355164\pi$$
$$810$$ 0 0
$$811$$ −37.0000 −1.29925 −0.649623 0.760257i $$-0.725073\pi$$
−0.649623 + 0.760257i $$0.725073\pi$$
$$812$$ 0 0
$$813$$ −81.0000 −2.84079
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −6.00000 −0.209913
$$818$$ 0 0
$$819$$ −30.0000 −1.04828
$$820$$ 0 0
$$821$$ −52.0000 −1.81481 −0.907406 0.420255i $$-0.861941\pi$$
−0.907406 + 0.420255i $$0.861941\pi$$
$$822$$ 0 0
$$823$$ −43.0000 −1.49889 −0.749443 0.662069i $$-0.769679\pi$$
−0.749443 + 0.662069i $$0.769679\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −3.00000 −0.104320 −0.0521601 0.998639i $$-0.516611\pi$$
−0.0521601 + 0.998639i $$0.516611\pi$$
$$828$$ 0 0
$$829$$ 35.0000 1.21560 0.607800 0.794090i $$-0.292052\pi$$
0.607800 + 0.794090i $$0.292052\pi$$
$$830$$ 0 0
$$831$$ −24.0000 −0.832551
$$832$$ 0 0
$$833$$ 54.0000 1.87099
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −18.0000 −0.622171
$$838$$ 0 0
$$839$$ 4.00000 0.138095 0.0690477 0.997613i $$-0.478004\pi$$
0.0690477 + 0.997613i $$0.478004\pi$$
$$840$$ 0 0
$$841$$ −20.0000 −0.689655
$$842$$ 0 0
$$843$$ 54.0000 1.85986
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −25.0000 −0.859010
$$848$$ 0 0
$$849$$ 6.00000 0.205919
$$850$$ 0 0
$$851$$ 14.0000 0.479914
$$852$$ 0 0
$$853$$ −42.0000 −1.43805 −0.719026 0.694983i $$-0.755412\pi$$
−0.719026 + 0.694983i $$0.755412\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 40.0000 1.36637 0.683187 0.730243i $$-0.260593\pi$$
0.683187 + 0.730243i $$0.260593\pi$$
$$858$$ 0 0
$$859$$ 28.0000 0.955348 0.477674 0.878537i $$-0.341480\pi$$
0.477674 + 0.878537i $$0.341480\pi$$
$$860$$ 0 0
$$861$$ −90.0000 −3.06719
$$862$$ 0 0
$$863$$ 56.0000 1.90626 0.953131 0.302558i $$-0.0978405\pi$$
0.953131 + 0.302558i $$0.0978405\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 24.0000 0.815083
$$868$$ 0 0
$$869$$ 8.00000 0.271381
$$870$$ 0 0
$$871$$ −3.00000 −0.101651
$$872$$ 0 0
$$873$$ 12.0000 0.406138
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −33.0000 −1.11433 −0.557165 0.830402i $$-0.688111\pi$$
−0.557165 + 0.830402i $$0.688111\pi$$
$$878$$ 0 0
$$879$$ −81.0000 −2.73206
$$880$$ 0 0
$$881$$ 10.0000 0.336909 0.168454 0.985709i $$-0.446122\pi$$
0.168454 + 0.985709i $$0.446122\pi$$
$$882$$ 0 0
$$883$$ 30.0000 1.00958 0.504790 0.863242i $$-0.331570\pi$$
0.504790 + 0.863242i $$0.331570\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −28.0000 −0.940148 −0.470074 0.882627i $$-0.655773\pi$$
−0.470074 + 0.882627i $$0.655773\pi$$
$$888$$ 0 0
$$889$$ 30.0000 1.00617
$$890$$ 0 0
$$891$$ 36.0000 1.20605
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −21.0000 −0.701170
$$898$$ 0 0
$$899$$ −6.00000 −0.200111
$$900$$ 0 0
$$901$$ 39.0000 1.29928
$$902$$ 0 0
$$903$$ 90.0000 2.99501
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −1.00000 −0.0332045 −0.0166022 0.999862i $$-0.505285\pi$$
−0.0166022 + 0.999862i $$0.505285\pi$$
$$908$$ 0 0
$$909$$ −48.0000 −1.59206
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ 0 0
$$913$$ −40.0000 −1.32381
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 80.0000 2.64183
$$918$$ 0 0
$$919$$ 5.00000 0.164935 0.0824674 0.996594i $$-0.473720\pi$$
0.0824674 + 0.996594i $$0.473720\pi$$
$$920$$ 0 0
$$921$$ −12.0000 −0.395413
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 24.0000 0.788263
$$928$$ 0 0
$$929$$ −3.00000 −0.0984268 −0.0492134 0.998788i $$-0.515671\pi$$
−0.0492134 + 0.998788i $$0.515671\pi$$
$$930$$ 0 0
$$931$$ −18.0000 −0.589926
$$932$$ 0 0
$$933$$ 75.0000 2.45539
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −47.0000 −1.53542 −0.767712 0.640796i $$-0.778605\pi$$
−0.767712 + 0.640796i $$0.778605\pi$$
$$938$$ 0 0
$$939$$ −3.00000 −0.0979013
$$940$$ 0 0
$$941$$ −51.0000 −1.66255 −0.831276 0.555860i $$-0.812389\pi$$
−0.831276 + 0.555860i $$0.812389\pi$$
$$942$$ 0 0
$$943$$ −42.0000 −1.36771
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −24.0000 −0.779895 −0.389948 0.920837i $$-0.627507\pi$$
−0.389948 + 0.920837i $$0.627507\pi$$
$$948$$ 0 0
$$949$$ −11.0000 −0.357075
$$950$$ 0 0
$$951$$ 27.0000 0.875535
$$952$$ 0 0
$$953$$ 24.0000 0.777436 0.388718 0.921357i $$-0.372918\pi$$
0.388718 + 0.921357i $$0.372918\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 36.0000 1.16371
$$958$$ 0 0
$$959$$ 45.0000 1.45313
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 0 0
$$963$$ −78.0000 −2.51351
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −44.0000 −1.41494 −0.707472 0.706741i $$-0.750165\pi$$
−0.707472 + 0.706741i $$0.750165\pi$$
$$968$$ 0 0
$$969$$ 9.00000 0.289122
$$970$$ 0 0
$$971$$ −28.0000 −0.898563 −0.449281 0.893390i $$-0.648320\pi$$
−0.449281 + 0.893390i $$0.648320\pi$$
$$972$$ 0 0
$$973$$ 80.0000 2.56468
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 62.0000 1.98356 0.991778 0.127971i $$-0.0408466\pi$$
0.991778 + 0.127971i $$0.0408466\pi$$
$$978$$ 0 0
$$979$$ 8.00000 0.255681
$$980$$ 0 0
$$981$$ 114.000 3.63974
$$982$$ 0 0
$$983$$ −42.0000 −1.33959 −0.669796 0.742545i $$-0.733618\pi$$
−0.669796 + 0.742545i $$0.733618\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 42.0000 1.33552
$$990$$ 0 0
$$991$$ −30.0000 −0.952981 −0.476491 0.879180i $$-0.658091\pi$$
−0.476491 + 0.879180i $$0.658091\pi$$
$$992$$ 0 0
$$993$$ −21.0000 −0.666415
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 50.0000 1.58352 0.791758 0.610835i $$-0.209166\pi$$
0.791758 + 0.610835i $$0.209166\pi$$
$$998$$ 0 0
$$999$$ −18.0000 −0.569495
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 7600.2.a.a.1.1 1
4.3 odd 2 950.2.a.c.1.1 1
5.4 even 2 1520.2.a.j.1.1 1
12.11 even 2 8550.2.a.bm.1.1 1
20.3 even 4 950.2.b.a.799.2 2
20.7 even 4 950.2.b.a.799.1 2
20.19 odd 2 190.2.a.b.1.1 1
40.19 odd 2 6080.2.a.x.1.1 1
40.29 even 2 6080.2.a.b.1.1 1
60.59 even 2 1710.2.a.g.1.1 1
140.139 even 2 9310.2.a.u.1.1 1
380.379 even 2 3610.2.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.a.b.1.1 1 20.19 odd 2
950.2.a.c.1.1 1 4.3 odd 2
950.2.b.a.799.1 2 20.7 even 4
950.2.b.a.799.2 2 20.3 even 4
1520.2.a.j.1.1 1 5.4 even 2
1710.2.a.g.1.1 1 60.59 even 2
3610.2.a.e.1.1 1 380.379 even 2
6080.2.a.b.1.1 1 40.29 even 2
6080.2.a.x.1.1 1 40.19 odd 2
7600.2.a.a.1.1 1 1.1 even 1 trivial
8550.2.a.bm.1.1 1 12.11 even 2
9310.2.a.u.1.1 1 140.139 even 2