# Properties

 Label 6080.2.a.p.1.1 Level $6080$ Weight $2$ Character 6080.1 Self dual yes Analytic conductor $48.549$ 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] = [6080,2,Mod(1,6080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6080, 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("6080.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$6080 = 2^{6} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6080.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: $$48.5490444289$$ Analytic rank: $$1$$ 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 $$\chi$$ $$=$$ 6080.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{3} -1.00000 q^{5} +1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{3} -1.00000 q^{5} +1.00000 q^{7} -2.00000 q^{9} +1.00000 q^{13} -1.00000 q^{15} -3.00000 q^{17} +1.00000 q^{19} +1.00000 q^{21} -3.00000 q^{23} +1.00000 q^{25} -5.00000 q^{27} +3.00000 q^{29} -2.00000 q^{31} -1.00000 q^{35} +10.0000 q^{37} +1.00000 q^{39} +6.00000 q^{41} +2.00000 q^{43} +2.00000 q^{45} -6.00000 q^{49} -3.00000 q^{51} -3.00000 q^{53} +1.00000 q^{57} +3.00000 q^{59} -8.00000 q^{61} -2.00000 q^{63} -1.00000 q^{65} -7.00000 q^{67} -3.00000 q^{69} -12.0000 q^{71} -13.0000 q^{73} +1.00000 q^{75} -14.0000 q^{79} +1.00000 q^{81} +6.00000 q^{83} +3.00000 q^{85} +3.00000 q^{87} +6.00000 q^{89} +1.00000 q^{91} -2.00000 q^{93} -1.00000 q^{95} -10.0000 q^{97} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.00000 0.577350 0.288675 0.957427i $$-0.406785\pi$$
0.288675 + 0.957427i $$0.406785\pi$$
$$4$$ 0 0
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ 1.00000 0.377964 0.188982 0.981981i $$-0.439481\pi$$
0.188982 + 0.981981i $$0.439481\pi$$
$$8$$ 0 0
$$9$$ −2.00000 −0.666667
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 0 0
$$15$$ −1.00000 −0.258199
$$16$$ 0 0
$$17$$ −3.00000 −0.727607 −0.363803 0.931476i $$-0.618522\pi$$
−0.363803 + 0.931476i $$0.618522\pi$$
$$18$$ 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 $$-0.601257\pi$$
−0.312772 + 0.949828i $$0.601257\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ −5.00000 −0.962250
$$28$$ 0 0
$$29$$ 3.00000 0.557086 0.278543 0.960424i $$-0.410149\pi$$
0.278543 + 0.960424i $$0.410149\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −1.00000 −0.169031
$$36$$ 0 0
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 0 0
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 0 0
$$45$$ 2.00000 0.298142
$$46$$ 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 $$-0.566058\pi$$
−0.206041 + 0.978543i $$0.566058\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.00000 0.132453
$$58$$ 0 0
$$59$$ 3.00000 0.390567 0.195283 0.980747i $$-0.437437\pi$$
0.195283 + 0.980747i $$0.437437\pi$$
$$60$$ 0 0
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 0 0
$$63$$ −2.00000 −0.251976
$$64$$ 0 0
$$65$$ −1.00000 −0.124035
$$66$$ 0 0
$$67$$ −7.00000 −0.855186 −0.427593 0.903971i $$-0.640638\pi$$
−0.427593 + 0.903971i $$0.640638\pi$$
$$68$$ 0 0
$$69$$ −3.00000 −0.361158
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 0 0
$$73$$ −13.0000 −1.52153 −0.760767 0.649025i $$-0.775177\pi$$
−0.760767 + 0.649025i $$0.775177\pi$$
$$74$$ 0 0
$$75$$ 1.00000 0.115470
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −14.0000 −1.57512 −0.787562 0.616236i $$-0.788657\pi$$
−0.787562 + 0.616236i $$0.788657\pi$$
$$80$$ 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
$$85$$ 3.00000 0.325396
$$86$$ 0 0
$$87$$ 3.00000 0.321634
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 1.00000 0.104828
$$92$$ 0 0
$$93$$ −2.00000 −0.207390
$$94$$ 0 0
$$95$$ −1.00000 −0.102598
$$96$$ 0 0
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −12.0000 −1.19404 −0.597022 0.802225i $$-0.703650\pi$$
−0.597022 + 0.802225i $$0.703650\pi$$
$$102$$ 0 0
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ 0 0
$$105$$ −1.00000 −0.0975900
$$106$$ 0 0
$$107$$ 15.0000 1.45010 0.725052 0.688694i $$-0.241816\pi$$
0.725052 + 0.688694i $$0.241816\pi$$
$$108$$ 0 0
$$109$$ −11.0000 −1.05361 −0.526804 0.849987i $$-0.676610\pi$$
−0.526804 + 0.849987i $$0.676610\pi$$
$$110$$ 0 0
$$111$$ 10.0000 0.949158
$$112$$ 0 0
$$113$$ −12.0000 −1.12887 −0.564433 0.825479i $$-0.690905\pi$$
−0.564433 + 0.825479i $$0.690905\pi$$
$$114$$ 0 0
$$115$$ 3.00000 0.279751
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ −3.00000 −0.275010
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ 6.00000 0.541002
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −2.00000 −0.177471 −0.0887357 0.996055i $$-0.528283\pi$$
−0.0887357 + 0.996055i $$0.528283\pi$$
$$128$$ 0 0
$$129$$ 2.00000 0.176090
$$130$$ 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
$$135$$ 5.00000 0.430331
$$136$$ 0 0
$$137$$ 9.00000 0.768922 0.384461 0.923141i $$-0.374387\pi$$
0.384461 + 0.923141i $$0.374387\pi$$
$$138$$ 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
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −3.00000 −0.249136
$$146$$ 0 0
$$147$$ −6.00000 −0.494872
$$148$$ 0 0
$$149$$ 12.0000 0.983078 0.491539 0.870855i $$-0.336434\pi$$
0.491539 + 0.870855i $$0.336434\pi$$
$$150$$ 0 0
$$151$$ 10.0000 0.813788 0.406894 0.913475i $$-0.366612\pi$$
0.406894 + 0.913475i $$0.366612\pi$$
$$152$$ 0 0
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 2.00000 0.160644
$$156$$ 0 0
$$157$$ 10.0000 0.798087 0.399043 0.916932i $$-0.369342\pi$$
0.399043 + 0.916932i $$0.369342\pi$$
$$158$$ 0 0
$$159$$ −3.00000 −0.237915
$$160$$ 0 0
$$161$$ −3.00000 −0.236433
$$162$$ 0 0
$$163$$ −22.0000 −1.72317 −0.861586 0.507611i $$-0.830529\pi$$
−0.861586 + 0.507611i $$0.830529\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −18.0000 −1.39288 −0.696441 0.717614i $$-0.745234\pi$$
−0.696441 + 0.717614i $$0.745234\pi$$
$$168$$ 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 $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ 1.00000 0.0755929
$$176$$ 0 0
$$177$$ 3.00000 0.225494
$$178$$ 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
$$183$$ −8.00000 −0.591377
$$184$$ 0 0
$$185$$ −10.0000 −0.735215
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −5.00000 −0.363696
$$190$$ 0 0
$$191$$ 27.0000 1.95365 0.976826 0.214036i $$-0.0686611\pi$$
0.976826 + 0.214036i $$0.0686611\pi$$
$$192$$ 0 0
$$193$$ −22.0000 −1.58359 −0.791797 0.610784i $$-0.790854\pi$$
−0.791797 + 0.610784i $$0.790854\pi$$
$$194$$ 0 0
$$195$$ −1.00000 −0.0716115
$$196$$ 0 0
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0 0
$$199$$ 19.0000 1.34687 0.673437 0.739244i $$-0.264817\pi$$
0.673437 + 0.739244i $$0.264817\pi$$
$$200$$ 0 0
$$201$$ −7.00000 −0.493742
$$202$$ 0 0
$$203$$ 3.00000 0.210559
$$204$$ 0 0
$$205$$ −6.00000 −0.419058
$$206$$ 0 0
$$207$$ 6.00000 0.417029
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −25.0000 −1.72107 −0.860535 0.509390i $$-0.829871\pi$$
−0.860535 + 0.509390i $$0.829871\pi$$
$$212$$ 0 0
$$213$$ −12.0000 −0.822226
$$214$$ 0 0
$$215$$ −2.00000 −0.136399
$$216$$ 0 0
$$217$$ −2.00000 −0.135769
$$218$$ 0 0
$$219$$ −13.0000 −0.878459
$$220$$ 0 0
$$221$$ −3.00000 −0.201802
$$222$$ 0 0
$$223$$ −14.0000 −0.937509 −0.468755 0.883328i $$-0.655297\pi$$
−0.468755 + 0.883328i $$0.655297\pi$$
$$224$$ 0 0
$$225$$ −2.00000 −0.133333
$$226$$ 0 0
$$227$$ −15.0000 −0.995585 −0.497792 0.867296i $$-0.665856\pi$$
−0.497792 + 0.867296i $$0.665856\pi$$
$$228$$ 0 0
$$229$$ −26.0000 −1.71813 −0.859064 0.511868i $$-0.828954\pi$$
−0.859064 + 0.511868i $$0.828954\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 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
$$237$$ −14.0000 −0.909398
$$238$$ 0 0
$$239$$ 15.0000 0.970269 0.485135 0.874439i $$-0.338771\pi$$
0.485135 + 0.874439i $$0.338771\pi$$
$$240$$ 0 0
$$241$$ −4.00000 −0.257663 −0.128831 0.991667i $$-0.541123\pi$$
−0.128831 + 0.991667i $$0.541123\pi$$
$$242$$ 0 0
$$243$$ 16.0000 1.02640
$$244$$ 0 0
$$245$$ 6.00000 0.383326
$$246$$ 0 0
$$247$$ 1.00000 0.0636285
$$248$$ 0 0
$$249$$ 6.00000 0.380235
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 3.00000 0.187867
$$256$$ 0 0
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 0 0
$$259$$ 10.0000 0.621370
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 0 0
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 3.00000 0.184289
$$266$$ 0 0
$$267$$ 6.00000 0.367194
$$268$$ 0 0
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ 7.00000 0.425220 0.212610 0.977137i $$-0.431804\pi$$
0.212610 + 0.977137i $$0.431804\pi$$
$$272$$ 0 0
$$273$$ 1.00000 0.0605228
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −8.00000 −0.480673 −0.240337 0.970690i $$-0.577258\pi$$
−0.240337 + 0.970690i $$0.577258\pi$$
$$278$$ 0 0
$$279$$ 4.00000 0.239474
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ 14.0000 0.832214 0.416107 0.909316i $$-0.363394\pi$$
0.416107 + 0.909316i $$0.363394\pi$$
$$284$$ 0 0
$$285$$ −1.00000 −0.0592349
$$286$$ 0 0
$$287$$ 6.00000 0.354169
$$288$$ 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 $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ 0 0
$$295$$ −3.00000 −0.174667
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −3.00000 −0.173494
$$300$$ 0 0
$$301$$ 2.00000 0.115278
$$302$$ 0 0
$$303$$ −12.0000 −0.689382
$$304$$ 0 0
$$305$$ 8.00000 0.458079
$$306$$ 0 0
$$307$$ 20.0000 1.14146 0.570730 0.821138i $$-0.306660\pi$$
0.570730 + 0.821138i $$0.306660\pi$$
$$308$$ 0 0
$$309$$ −8.00000 −0.455104
$$310$$ 0 0
$$311$$ 3.00000 0.170114 0.0850572 0.996376i $$-0.472893\pi$$
0.0850572 + 0.996376i $$0.472893\pi$$
$$312$$ 0 0
$$313$$ −1.00000 −0.0565233 −0.0282617 0.999601i $$-0.508997\pi$$
−0.0282617 + 0.999601i $$0.508997\pi$$
$$314$$ 0 0
$$315$$ 2.00000 0.112687
$$316$$ 0 0
$$317$$ −9.00000 −0.505490 −0.252745 0.967533i $$-0.581333\pi$$
−0.252745 + 0.967533i $$0.581333\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 15.0000 0.837218
$$322$$ 0 0
$$323$$ −3.00000 −0.166924
$$324$$ 0 0
$$325$$ 1.00000 0.0554700
$$326$$ 0 0
$$327$$ −11.0000 −0.608301
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 5.00000 0.274825 0.137412 0.990514i $$-0.456121\pi$$
0.137412 + 0.990514i $$0.456121\pi$$
$$332$$ 0 0
$$333$$ −20.0000 −1.09599
$$334$$ 0 0
$$335$$ 7.00000 0.382451
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 0 0
$$339$$ −12.0000 −0.651751
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −13.0000 −0.701934
$$344$$ 0 0
$$345$$ 3.00000 0.161515
$$346$$ 0 0
$$347$$ −30.0000 −1.61048 −0.805242 0.592946i $$-0.797965\pi$$
−0.805242 + 0.592946i $$0.797965\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ −5.00000 −0.266880
$$352$$ 0 0
$$353$$ −33.0000 −1.75641 −0.878206 0.478282i $$-0.841260\pi$$
−0.878206 + 0.478282i $$0.841260\pi$$
$$354$$ 0 0
$$355$$ 12.0000 0.636894
$$356$$ 0 0
$$357$$ −3.00000 −0.158777
$$358$$ 0 0
$$359$$ 33.0000 1.74167 0.870837 0.491572i $$-0.163578\pi$$
0.870837 + 0.491572i $$0.163578\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ −11.0000 −0.577350
$$364$$ 0 0
$$365$$ 13.0000 0.680451
$$366$$ 0 0
$$367$$ 16.0000 0.835193 0.417597 0.908633i $$-0.362873\pi$$
0.417597 + 0.908633i $$0.362873\pi$$
$$368$$ 0 0
$$369$$ −12.0000 −0.624695
$$370$$ 0 0
$$371$$ −3.00000 −0.155752
$$372$$ 0 0
$$373$$ 31.0000 1.60512 0.802560 0.596572i $$-0.203471\pi$$
0.802560 + 0.596572i $$0.203471\pi$$
$$374$$ 0 0
$$375$$ −1.00000 −0.0516398
$$376$$ 0 0
$$377$$ 3.00000 0.154508
$$378$$ 0 0
$$379$$ 35.0000 1.79783 0.898915 0.438124i $$-0.144357\pi$$
0.898915 + 0.438124i $$0.144357\pi$$
$$380$$ 0 0
$$381$$ −2.00000 −0.102463
$$382$$ 0 0
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −4.00000 −0.203331
$$388$$ 0 0
$$389$$ 24.0000 1.21685 0.608424 0.793612i $$-0.291802\pi$$
0.608424 + 0.793612i $$0.291802\pi$$
$$390$$ 0 0
$$391$$ 9.00000 0.455150
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 14.0000 0.704416
$$396$$ 0 0
$$397$$ −8.00000 −0.401508 −0.200754 0.979642i $$-0.564339\pi$$
−0.200754 + 0.979642i $$0.564339\pi$$
$$398$$ 0 0
$$399$$ 1.00000 0.0500626
$$400$$ 0 0
$$401$$ 6.00000 0.299626 0.149813 0.988714i $$-0.452133\pi$$
0.149813 + 0.988714i $$0.452133\pi$$
$$402$$ 0 0
$$403$$ −2.00000 −0.0996271
$$404$$ 0 0
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −22.0000 −1.08783 −0.543915 0.839140i $$-0.683059\pi$$
−0.543915 + 0.839140i $$0.683059\pi$$
$$410$$ 0 0
$$411$$ 9.00000 0.443937
$$412$$ 0 0
$$413$$ 3.00000 0.147620
$$414$$ 0 0
$$415$$ −6.00000 −0.294528
$$416$$ 0 0
$$417$$ 8.00000 0.391762
$$418$$ 0 0
$$419$$ −30.0000 −1.46560 −0.732798 0.680446i $$-0.761786\pi$$
−0.732798 + 0.680446i $$0.761786\pi$$
$$420$$ 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
$$425$$ −3.00000 −0.145521
$$426$$ 0 0
$$427$$ −8.00000 −0.387147
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −24.0000 −1.15604 −0.578020 0.816023i $$-0.696174\pi$$
−0.578020 + 0.816023i $$0.696174\pi$$
$$432$$ 0 0
$$433$$ −4.00000 −0.192228 −0.0961139 0.995370i $$-0.530641\pi$$
−0.0961139 + 0.995370i $$0.530641\pi$$
$$434$$ 0 0
$$435$$ −3.00000 −0.143839
$$436$$ 0 0
$$437$$ −3.00000 −0.143509
$$438$$ 0 0
$$439$$ −38.0000 −1.81364 −0.906821 0.421517i $$-0.861498\pi$$
−0.906821 + 0.421517i $$0.861498\pi$$
$$440$$ 0 0
$$441$$ 12.0000 0.571429
$$442$$ 0 0
$$443$$ −24.0000 −1.14027 −0.570137 0.821549i $$-0.693110\pi$$
−0.570137 + 0.821549i $$0.693110\pi$$
$$444$$ 0 0
$$445$$ −6.00000 −0.284427
$$446$$ 0 0
$$447$$ 12.0000 0.567581
$$448$$ 0 0
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 10.0000 0.469841
$$454$$ 0 0
$$455$$ −1.00000 −0.0468807
$$456$$ 0 0
$$457$$ 35.0000 1.63723 0.818615 0.574342i $$-0.194742\pi$$
0.818615 + 0.574342i $$0.194742\pi$$
$$458$$ 0 0
$$459$$ 15.0000 0.700140
$$460$$ 0 0
$$461$$ −6.00000 −0.279448 −0.139724 0.990190i $$-0.544622\pi$$
−0.139724 + 0.990190i $$0.544622\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ 0 0
$$465$$ 2.00000 0.0927478
$$466$$ 0 0
$$467$$ 12.0000 0.555294 0.277647 0.960683i $$-0.410445\pi$$
0.277647 + 0.960683i $$0.410445\pi$$
$$468$$ 0 0
$$469$$ −7.00000 −0.323230
$$470$$ 0 0
$$471$$ 10.0000 0.460776
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 1.00000 0.0458831
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ 0 0
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 0 0
$$481$$ 10.0000 0.455961
$$482$$ 0 0
$$483$$ −3.00000 −0.136505
$$484$$ 0 0
$$485$$ 10.0000 0.454077
$$486$$ 0 0
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ 0 0
$$489$$ −22.0000 −0.994874
$$490$$ 0 0
$$491$$ 30.0000 1.35388 0.676941 0.736038i $$-0.263305\pi$$
0.676941 + 0.736038i $$0.263305\pi$$
$$492$$ 0 0
$$493$$ −9.00000 −0.405340
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −12.0000 −0.538274
$$498$$ 0 0
$$499$$ −10.0000 −0.447661 −0.223831 0.974628i $$-0.571856\pi$$
−0.223831 + 0.974628i $$0.571856\pi$$
$$500$$ 0 0
$$501$$ −18.0000 −0.804181
$$502$$ 0 0
$$503$$ −39.0000 −1.73892 −0.869462 0.494000i $$-0.835534\pi$$
−0.869462 + 0.494000i $$0.835534\pi$$
$$504$$ 0 0
$$505$$ 12.0000 0.533993
$$506$$ 0 0
$$507$$ −12.0000 −0.532939
$$508$$ 0 0
$$509$$ −18.0000 −0.797836 −0.398918 0.916987i $$-0.630614\pi$$
−0.398918 + 0.916987i $$0.630614\pi$$
$$510$$ 0 0
$$511$$ −13.0000 −0.575086
$$512$$ 0 0
$$513$$ −5.00000 −0.220755
$$514$$ 0 0
$$515$$ 8.00000 0.352522
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 6.00000 0.263371
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ 11.0000 0.480996 0.240498 0.970650i $$-0.422689\pi$$
0.240498 + 0.970650i $$0.422689\pi$$
$$524$$ 0 0
$$525$$ 1.00000 0.0436436
$$526$$ 0 0
$$527$$ 6.00000 0.261364
$$528$$ 0 0
$$529$$ −14.0000 −0.608696
$$530$$ 0 0
$$531$$ −6.00000 −0.260378
$$532$$ 0 0
$$533$$ 6.00000 0.259889
$$534$$ 0 0
$$535$$ −15.0000 −0.648507
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −20.0000 −0.859867 −0.429934 0.902861i $$-0.641463\pi$$
−0.429934 + 0.902861i $$0.641463\pi$$
$$542$$ 0 0
$$543$$ −2.00000 −0.0858282
$$544$$ 0 0
$$545$$ 11.0000 0.471188
$$546$$ 0 0
$$547$$ −4.00000 −0.171028 −0.0855138 0.996337i $$-0.527253\pi$$
−0.0855138 + 0.996337i $$0.527253\pi$$
$$548$$ 0 0
$$549$$ 16.0000 0.682863
$$550$$ 0 0
$$551$$ 3.00000 0.127804
$$552$$ 0 0
$$553$$ −14.0000 −0.595341
$$554$$ 0 0
$$555$$ −10.0000 −0.424476
$$556$$ 0 0
$$557$$ 12.0000 0.508456 0.254228 0.967144i $$-0.418179\pi$$
0.254228 + 0.967144i $$0.418179\pi$$
$$558$$ 0 0
$$559$$ 2.00000 0.0845910
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −12.0000 −0.505740 −0.252870 0.967500i $$-0.581374\pi$$
−0.252870 + 0.967500i $$0.581374\pi$$
$$564$$ 0 0
$$565$$ 12.0000 0.504844
$$566$$ 0 0
$$567$$ 1.00000 0.0419961
$$568$$ 0 0
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ −22.0000 −0.920671 −0.460336 0.887745i $$-0.652271\pi$$
−0.460336 + 0.887745i $$0.652271\pi$$
$$572$$ 0 0
$$573$$ 27.0000 1.12794
$$574$$ 0 0
$$575$$ −3.00000 −0.125109
$$576$$ 0 0
$$577$$ −7.00000 −0.291414 −0.145707 0.989328i $$-0.546546\pi$$
−0.145707 + 0.989328i $$0.546546\pi$$
$$578$$ 0 0
$$579$$ −22.0000 −0.914289
$$580$$ 0 0
$$581$$ 6.00000 0.248922
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 2.00000 0.0826898
$$586$$ 0 0
$$587$$ 30.0000 1.23823 0.619116 0.785299i $$-0.287491\pi$$
0.619116 + 0.785299i $$0.287491\pi$$
$$588$$ 0 0
$$589$$ −2.00000 −0.0824086
$$590$$ 0 0
$$591$$ −6.00000 −0.246807
$$592$$ 0 0
$$593$$ 30.0000 1.23195 0.615976 0.787765i $$-0.288762\pi$$
0.615976 + 0.787765i $$0.288762\pi$$
$$594$$ 0 0
$$595$$ 3.00000 0.122988
$$596$$ 0 0
$$597$$ 19.0000 0.777618
$$598$$ 0 0
$$599$$ 30.0000 1.22577 0.612883 0.790173i $$-0.290010\pi$$
0.612883 + 0.790173i $$0.290010\pi$$
$$600$$ 0 0
$$601$$ −34.0000 −1.38689 −0.693444 0.720510i $$-0.743908\pi$$
−0.693444 + 0.720510i $$0.743908\pi$$
$$602$$ 0 0
$$603$$ 14.0000 0.570124
$$604$$ 0 0
$$605$$ 11.0000 0.447214
$$606$$ 0 0
$$607$$ 10.0000 0.405887 0.202944 0.979190i $$-0.434949\pi$$
0.202944 + 0.979190i $$0.434949\pi$$
$$608$$ 0 0
$$609$$ 3.00000 0.121566
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 16.0000 0.646234 0.323117 0.946359i $$-0.395269\pi$$
0.323117 + 0.946359i $$0.395269\pi$$
$$614$$ 0 0
$$615$$ −6.00000 −0.241943
$$616$$ 0 0
$$617$$ 6.00000 0.241551 0.120775 0.992680i $$-0.461462\pi$$
0.120775 + 0.992680i $$0.461462\pi$$
$$618$$ 0 0
$$619$$ 44.0000 1.76851 0.884255 0.467005i $$-0.154667\pi$$
0.884255 + 0.467005i $$0.154667\pi$$
$$620$$ 0 0
$$621$$ 15.0000 0.601929
$$622$$ 0 0
$$623$$ 6.00000 0.240385
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −30.0000 −1.19618
$$630$$ 0 0
$$631$$ −32.0000 −1.27390 −0.636950 0.770905i $$-0.719804\pi$$
−0.636950 + 0.770905i $$0.719804\pi$$
$$632$$ 0 0
$$633$$ −25.0000 −0.993661
$$634$$ 0 0
$$635$$ 2.00000 0.0793676
$$636$$ 0 0
$$637$$ −6.00000 −0.237729
$$638$$ 0 0
$$639$$ 24.0000 0.949425
$$640$$ 0 0
$$641$$ −12.0000 −0.473972 −0.236986 0.971513i $$-0.576159\pi$$
−0.236986 + 0.971513i $$0.576159\pi$$
$$642$$ 0 0
$$643$$ 50.0000 1.97181 0.985904 0.167313i $$-0.0535092\pi$$
0.985904 + 0.167313i $$0.0535092\pi$$
$$644$$ 0 0
$$645$$ −2.00000 −0.0787499
$$646$$ 0 0
$$647$$ 33.0000 1.29736 0.648682 0.761060i $$-0.275321\pi$$
0.648682 + 0.761060i $$0.275321\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −2.00000 −0.0783862
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 26.0000 1.01436
$$658$$ 0 0
$$659$$ 21.0000 0.818044 0.409022 0.912525i $$-0.365870\pi$$
0.409022 + 0.912525i $$0.365870\pi$$
$$660$$ 0 0
$$661$$ 49.0000 1.90588 0.952940 0.303160i $$-0.0980418\pi$$
0.952940 + 0.303160i $$0.0980418\pi$$
$$662$$ 0 0
$$663$$ −3.00000 −0.116510
$$664$$ 0 0
$$665$$ −1.00000 −0.0387783
$$666$$ 0 0
$$667$$ −9.00000 −0.348481
$$668$$ 0 0
$$669$$ −14.0000 −0.541271
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 20.0000 0.770943 0.385472 0.922720i $$-0.374039\pi$$
0.385472 + 0.922720i $$0.374039\pi$$
$$674$$ 0 0
$$675$$ −5.00000 −0.192450
$$676$$ 0 0
$$677$$ 15.0000 0.576497 0.288248 0.957556i $$-0.406927\pi$$
0.288248 + 0.957556i $$0.406927\pi$$
$$678$$ 0 0
$$679$$ −10.0000 −0.383765
$$680$$ 0 0
$$681$$ −15.0000 −0.574801
$$682$$ 0 0
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ −9.00000 −0.343872
$$686$$ 0 0
$$687$$ −26.0000 −0.991962
$$688$$ 0 0
$$689$$ −3.00000 −0.114291
$$690$$ 0 0
$$691$$ −10.0000 −0.380418 −0.190209 0.981744i $$-0.560917\pi$$
−0.190209 + 0.981744i $$0.560917\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −8.00000 −0.303457
$$696$$ 0 0
$$697$$ −18.0000 −0.681799
$$698$$ 0 0
$$699$$ −6.00000 −0.226941
$$700$$ 0 0
$$701$$ −48.0000 −1.81293 −0.906467 0.422276i $$-0.861231\pi$$
−0.906467 + 0.422276i $$0.861231\pi$$
$$702$$ 0 0
$$703$$ 10.0000 0.377157
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −12.0000 −0.451306
$$708$$ 0 0
$$709$$ −26.0000 −0.976450 −0.488225 0.872718i $$-0.662356\pi$$
−0.488225 + 0.872718i $$0.662356\pi$$
$$710$$ 0 0
$$711$$ 28.0000 1.05008
$$712$$ 0 0
$$713$$ 6.00000 0.224702
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 15.0000 0.560185
$$718$$ 0 0
$$719$$ −33.0000 −1.23069 −0.615346 0.788257i $$-0.710984\pi$$
−0.615346 + 0.788257i $$0.710984\pi$$
$$720$$ 0 0
$$721$$ −8.00000 −0.297936
$$722$$ 0 0
$$723$$ −4.00000 −0.148762
$$724$$ 0 0
$$725$$ 3.00000 0.111417
$$726$$ 0 0
$$727$$ 13.0000 0.482143 0.241072 0.970507i $$-0.422501\pi$$
0.241072 + 0.970507i $$0.422501\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −6.00000 −0.221918
$$732$$ 0 0
$$733$$ 4.00000 0.147743 0.0738717 0.997268i $$-0.476464\pi$$
0.0738717 + 0.997268i $$0.476464\pi$$
$$734$$ 0 0
$$735$$ 6.00000 0.221313
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 2.00000 0.0735712 0.0367856 0.999323i $$-0.488288\pi$$
0.0367856 + 0.999323i $$0.488288\pi$$
$$740$$ 0 0
$$741$$ 1.00000 0.0367359
$$742$$ 0 0
$$743$$ −18.0000 −0.660356 −0.330178 0.943919i $$-0.607109\pi$$
−0.330178 + 0.943919i $$0.607109\pi$$
$$744$$ 0 0
$$745$$ −12.0000 −0.439646
$$746$$ 0 0
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ 15.0000 0.548088
$$750$$ 0 0
$$751$$ −2.00000 −0.0729810 −0.0364905 0.999334i $$-0.511618\pi$$
−0.0364905 + 0.999334i $$0.511618\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −10.0000 −0.363937
$$756$$ 0 0
$$757$$ −2.00000 −0.0726912 −0.0363456 0.999339i $$-0.511572\pi$$
−0.0363456 + 0.999339i $$0.511572\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 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
$$765$$ −6.00000 −0.216930
$$766$$ 0 0
$$767$$ 3.00000 0.108324
$$768$$ 0 0
$$769$$ −55.0000 −1.98335 −0.991675 0.128763i $$-0.958899\pi$$
−0.991675 + 0.128763i $$0.958899\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 0 0
$$773$$ −21.0000 −0.755318 −0.377659 0.925945i $$-0.623271\pi$$
−0.377659 + 0.925945i $$0.623271\pi$$
$$774$$ 0 0
$$775$$ −2.00000 −0.0718421
$$776$$ 0 0
$$777$$ 10.0000 0.358748
$$778$$ 0 0
$$779$$ 6.00000 0.214972
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −15.0000 −0.536056
$$784$$ 0 0
$$785$$ −10.0000 −0.356915
$$786$$ 0 0
$$787$$ 5.00000 0.178231 0.0891154 0.996021i $$-0.471596\pi$$
0.0891154 + 0.996021i $$0.471596\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −12.0000 −0.426671
$$792$$ 0 0
$$793$$ −8.00000 −0.284088
$$794$$ 0 0
$$795$$ 3.00000 0.106399
$$796$$ 0 0
$$797$$ 33.0000 1.16892 0.584460 0.811423i $$-0.301306\pi$$
0.584460 + 0.811423i $$0.301306\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −12.0000 −0.423999
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 3.00000 0.105736
$$806$$ 0 0
$$807$$ −18.0000 −0.633630
$$808$$ 0 0
$$809$$ 33.0000 1.16022 0.580109 0.814539i $$-0.303010\pi$$
0.580109 + 0.814539i $$0.303010\pi$$
$$810$$ 0 0
$$811$$ −7.00000 −0.245803 −0.122902 0.992419i $$-0.539220\pi$$
−0.122902 + 0.992419i $$0.539220\pi$$
$$812$$ 0 0
$$813$$ 7.00000 0.245501
$$814$$ 0 0
$$815$$ 22.0000 0.770626
$$816$$ 0 0
$$817$$ 2.00000 0.0699711
$$818$$ 0 0
$$819$$ −2.00000 −0.0698857
$$820$$ 0 0
$$821$$ 12.0000 0.418803 0.209401 0.977830i $$-0.432848\pi$$
0.209401 + 0.977830i $$0.432848\pi$$
$$822$$ 0 0
$$823$$ 31.0000 1.08059 0.540296 0.841475i $$-0.318312\pi$$
0.540296 + 0.841475i $$0.318312\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 33.0000 1.14752 0.573761 0.819023i $$-0.305484\pi$$
0.573761 + 0.819023i $$0.305484\pi$$
$$828$$ 0 0
$$829$$ 13.0000 0.451509 0.225754 0.974184i $$-0.427515\pi$$
0.225754 + 0.974184i $$0.427515\pi$$
$$830$$ 0 0
$$831$$ −8.00000 −0.277517
$$832$$ 0 0
$$833$$ 18.0000 0.623663
$$834$$ 0 0
$$835$$ 18.0000 0.622916
$$836$$ 0 0
$$837$$ 10.0000 0.345651
$$838$$ 0 0
$$839$$ −36.0000 −1.24286 −0.621429 0.783470i $$-0.713448\pi$$
−0.621429 + 0.783470i $$0.713448\pi$$
$$840$$ 0 0
$$841$$ −20.0000 −0.689655
$$842$$ 0 0
$$843$$ 18.0000 0.619953
$$844$$ 0 0
$$845$$ 12.0000 0.412813
$$846$$ 0 0
$$847$$ −11.0000 −0.377964
$$848$$ 0 0
$$849$$ 14.0000 0.480479
$$850$$ 0 0
$$851$$ −30.0000 −1.02839
$$852$$ 0 0
$$853$$ −50.0000 −1.71197 −0.855984 0.517003i $$-0.827048\pi$$
−0.855984 + 0.517003i $$0.827048\pi$$
$$854$$ 0 0
$$855$$ 2.00000 0.0683986
$$856$$ 0 0
$$857$$ 48.0000 1.63965 0.819824 0.572615i $$-0.194071\pi$$
0.819824 + 0.572615i $$0.194071\pi$$
$$858$$ 0 0
$$859$$ −16.0000 −0.545913 −0.272956 0.962026i $$-0.588002\pi$$
−0.272956 + 0.962026i $$0.588002\pi$$
$$860$$ 0 0
$$861$$ 6.00000 0.204479
$$862$$ 0 0
$$863$$ 12.0000 0.408485 0.204242 0.978920i $$-0.434527\pi$$
0.204242 + 0.978920i $$0.434527\pi$$
$$864$$ 0 0
$$865$$ −6.00000 −0.204006
$$866$$ 0 0
$$867$$ −8.00000 −0.271694
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −7.00000 −0.237186
$$872$$ 0 0
$$873$$ 20.0000 0.676897
$$874$$ 0 0
$$875$$ −1.00000 −0.0338062
$$876$$ 0 0
$$877$$ 31.0000 1.04680 0.523398 0.852088i $$-0.324664\pi$$
0.523398 + 0.852088i $$0.324664\pi$$
$$878$$ 0 0
$$879$$ −21.0000 −0.708312
$$880$$ 0 0
$$881$$ 42.0000 1.41502 0.707508 0.706705i $$-0.249819\pi$$
0.707508 + 0.706705i $$0.249819\pi$$
$$882$$ 0 0
$$883$$ 38.0000 1.27880 0.639401 0.768874i $$-0.279182\pi$$
0.639401 + 0.768874i $$0.279182\pi$$
$$884$$ 0 0
$$885$$ −3.00000 −0.100844
$$886$$ 0 0
$$887$$ −24.0000 −0.805841 −0.402921 0.915235i $$-0.632005\pi$$
−0.402921 + 0.915235i $$0.632005\pi$$
$$888$$ 0 0
$$889$$ −2.00000 −0.0670778
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −3.00000 −0.100167
$$898$$ 0 0
$$899$$ −6.00000 −0.200111
$$900$$ 0 0
$$901$$ 9.00000 0.299833
$$902$$ 0 0
$$903$$ 2.00000 0.0665558
$$904$$ 0 0
$$905$$ 2.00000 0.0664822
$$906$$ 0 0
$$907$$ 35.0000 1.16216 0.581078 0.813848i $$-0.302631\pi$$
0.581078 + 0.813848i $$0.302631\pi$$
$$908$$ 0 0
$$909$$ 24.0000 0.796030
$$910$$ 0 0
$$911$$ 36.0000 1.19273 0.596367 0.802712i $$-0.296610\pi$$
0.596367 + 0.802712i $$0.296610\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 8.00000 0.264472
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 1.00000 0.0329870 0.0164935 0.999864i $$-0.494750\pi$$
0.0164935 + 0.999864i $$0.494750\pi$$
$$920$$ 0 0
$$921$$ 20.0000 0.659022
$$922$$ 0 0
$$923$$ −12.0000 −0.394985
$$924$$ 0 0
$$925$$ 10.0000 0.328798
$$926$$ 0 0
$$927$$ 16.0000 0.525509
$$928$$ 0 0
$$929$$ 21.0000 0.688988 0.344494 0.938789i $$-0.388051\pi$$
0.344494 + 0.938789i $$0.388051\pi$$
$$930$$ 0 0
$$931$$ −6.00000 −0.196642
$$932$$ 0 0
$$933$$ 3.00000 0.0982156
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 47.0000 1.53542 0.767712 0.640796i $$-0.221395\pi$$
0.767712 + 0.640796i $$0.221395\pi$$
$$938$$ 0 0
$$939$$ −1.00000 −0.0326338
$$940$$ 0 0
$$941$$ −45.0000 −1.46696 −0.733479 0.679712i $$-0.762105\pi$$
−0.733479 + 0.679712i $$0.762105\pi$$
$$942$$ 0 0
$$943$$ −18.0000 −0.586161
$$944$$ 0 0
$$945$$ 5.00000 0.162650
$$946$$ 0 0
$$947$$ 24.0000 0.779895 0.389948 0.920837i $$-0.372493\pi$$
0.389948 + 0.920837i $$0.372493\pi$$
$$948$$ 0 0
$$949$$ −13.0000 −0.421998
$$950$$ 0 0
$$951$$ −9.00000 −0.291845
$$952$$ 0 0
$$953$$ −36.0000 −1.16615 −0.583077 0.812417i $$-0.698151\pi$$
−0.583077 + 0.812417i $$0.698151\pi$$
$$954$$ 0 0
$$955$$ −27.0000 −0.873699
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 9.00000 0.290625
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 0 0
$$963$$ −30.0000 −0.966736
$$964$$ 0 0
$$965$$ 22.0000 0.708205
$$966$$ 0 0
$$967$$ −44.0000 −1.41494 −0.707472 0.706741i $$-0.750165\pi$$
−0.707472 + 0.706741i $$0.750165\pi$$
$$968$$ 0 0
$$969$$ −3.00000 −0.0963739
$$970$$ 0 0
$$971$$ 12.0000 0.385098 0.192549 0.981287i $$-0.438325\pi$$
0.192549 + 0.981287i $$0.438325\pi$$
$$972$$ 0 0
$$973$$ 8.00000 0.256468
$$974$$ 0 0
$$975$$ 1.00000 0.0320256
$$976$$ 0 0
$$977$$ 6.00000 0.191957 0.0959785 0.995383i $$-0.469402\pi$$
0.0959785 + 0.995383i $$0.469402\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 22.0000 0.702406
$$982$$ 0 0
$$983$$ −54.0000 −1.72233 −0.861166 0.508323i $$-0.830265\pi$$
−0.861166 + 0.508323i $$0.830265\pi$$
$$984$$ 0 0
$$985$$ 6.00000 0.191176
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −6.00000 −0.190789
$$990$$ 0 0
$$991$$ −2.00000 −0.0635321 −0.0317660 0.999495i $$-0.510113\pi$$
−0.0317660 + 0.999495i $$0.510113\pi$$
$$992$$ 0 0
$$993$$ 5.00000 0.158670
$$994$$ 0 0
$$995$$ −19.0000 −0.602340
$$996$$ 0 0
$$997$$ 46.0000 1.45683 0.728417 0.685134i $$-0.240256\pi$$
0.728417 + 0.685134i $$0.240256\pi$$
$$998$$ 0 0
$$999$$ −50.0000 −1.58193
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 6080.2.a.p.1.1 1
4.3 odd 2 6080.2.a.h.1.1 1
8.3 odd 2 190.2.a.c.1.1 1
8.5 even 2 1520.2.a.d.1.1 1
24.11 even 2 1710.2.a.d.1.1 1
40.3 even 4 950.2.b.e.799.1 2
40.19 odd 2 950.2.a.a.1.1 1
40.27 even 4 950.2.b.e.799.2 2
40.29 even 2 7600.2.a.m.1.1 1
56.27 even 2 9310.2.a.o.1.1 1
120.59 even 2 8550.2.a.bd.1.1 1
152.75 even 2 3610.2.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.a.c.1.1 1 8.3 odd 2
950.2.a.a.1.1 1 40.19 odd 2
950.2.b.e.799.1 2 40.3 even 4
950.2.b.e.799.2 2 40.27 even 4
1520.2.a.d.1.1 1 8.5 even 2
1710.2.a.d.1.1 1 24.11 even 2
3610.2.a.b.1.1 1 152.75 even 2
6080.2.a.h.1.1 1 4.3 odd 2
6080.2.a.p.1.1 1 1.1 even 1 trivial
7600.2.a.m.1.1 1 40.29 even 2
8550.2.a.bd.1.1 1 120.59 even 2
9310.2.a.o.1.1 1 56.27 even 2