# Properties

 Label 1800.4.a.bf.1.1 Level $1800$ Weight $4$ Character 1800.1 Self dual yes Analytic conductor $106.203$ 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] = [1800,4,Mod(1,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1800.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1800 = 2^{3} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1800.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: $$106.203438010$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 600) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1800.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+19.0000 q^{7} +O(q^{10})$$ $$q+19.0000 q^{7} -22.0000 q^{11} -1.00000 q^{13} -58.0000 q^{17} -53.0000 q^{19} +58.0000 q^{23} -22.0000 q^{29} -35.0000 q^{31} +270.000 q^{37} +468.000 q^{41} +431.000 q^{43} -230.000 q^{47} +18.0000 q^{49} -446.000 q^{59} +127.000 q^{61} +811.000 q^{67} -36.0000 q^{71} -522.000 q^{73} -418.000 q^{77} +1368.00 q^{79} -1138.00 q^{83} -144.000 q^{89} -19.0000 q^{91} +1079.00 q^{97} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 19.0000 1.02590 0.512952 0.858417i $$-0.328552\pi$$
0.512952 + 0.858417i $$0.328552\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −22.0000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.0213346 −0.0106673 0.999943i $$-0.503396\pi$$
−0.0106673 + 0.999943i $$0.503396\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −58.0000 −0.827474 −0.413737 0.910396i $$-0.635777\pi$$
−0.413737 + 0.910396i $$0.635777\pi$$
$$18$$ 0 0
$$19$$ −53.0000 −0.639949 −0.319975 0.947426i $$-0.603674\pi$$
−0.319975 + 0.947426i $$0.603674\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 58.0000 0.525819 0.262909 0.964821i $$-0.415318\pi$$
0.262909 + 0.964821i $$0.415318\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −22.0000 −0.140872 −0.0704362 0.997516i $$-0.522439\pi$$
−0.0704362 + 0.997516i $$0.522439\pi$$
$$30$$ 0 0
$$31$$ −35.0000 −0.202780 −0.101390 0.994847i $$-0.532329\pi$$
−0.101390 + 0.994847i $$0.532329\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 270.000 1.19967 0.599834 0.800124i $$-0.295233\pi$$
0.599834 + 0.800124i $$0.295233\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 468.000 1.78267 0.891333 0.453349i $$-0.149771\pi$$
0.891333 + 0.453349i $$0.149771\pi$$
$$42$$ 0 0
$$43$$ 431.000 1.52853 0.764266 0.644901i $$-0.223101\pi$$
0.764266 + 0.644901i $$0.223101\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −230.000 −0.713807 −0.356904 0.934141i $$-0.616168\pi$$
−0.356904 + 0.934141i $$0.616168\pi$$
$$48$$ 0 0
$$49$$ 18.0000 0.0524781
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −446.000 −0.984140 −0.492070 0.870556i $$-0.663760\pi$$
−0.492070 + 0.870556i $$0.663760\pi$$
$$60$$ 0 0
$$61$$ 127.000 0.266569 0.133284 0.991078i $$-0.457448\pi$$
0.133284 + 0.991078i $$0.457448\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 811.000 1.47880 0.739399 0.673268i $$-0.235110\pi$$
0.739399 + 0.673268i $$0.235110\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −36.0000 −0.0601748 −0.0300874 0.999547i $$-0.509579\pi$$
−0.0300874 + 0.999547i $$0.509579\pi$$
$$72$$ 0 0
$$73$$ −522.000 −0.836924 −0.418462 0.908234i $$-0.637431\pi$$
−0.418462 + 0.908234i $$0.637431\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −418.000 −0.618643
$$78$$ 0 0
$$79$$ 1368.00 1.94825 0.974127 0.226002i $$-0.0725657\pi$$
0.974127 + 0.226002i $$0.0725657\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −1138.00 −1.50496 −0.752480 0.658615i $$-0.771143\pi$$
−0.752480 + 0.658615i $$0.771143\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −144.000 −0.171505 −0.0857526 0.996316i $$-0.527329\pi$$
−0.0857526 + 0.996316i $$0.527329\pi$$
$$90$$ 0 0
$$91$$ −19.0000 −0.0218873
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1079.00 1.12944 0.564721 0.825282i $$-0.308984\pi$$
0.564721 + 0.825282i $$0.308984\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1440.00 1.41867 0.709333 0.704873i $$-0.248996\pi$$
0.709333 + 0.704873i $$0.248996\pi$$
$$102$$ 0 0
$$103$$ −124.000 −0.118622 −0.0593111 0.998240i $$-0.518890\pi$$
−0.0593111 + 0.998240i $$0.518890\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −432.000 −0.390309 −0.195154 0.980773i $$-0.562521\pi$$
−0.195154 + 0.980773i $$0.562521\pi$$
$$108$$ 0 0
$$109$$ 701.000 0.615997 0.307998 0.951387i $$-0.400341\pi$$
0.307998 + 0.951387i $$0.400341\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1044.00 −0.869126 −0.434563 0.900641i $$-0.643097\pi$$
−0.434563 + 0.900641i $$0.643097\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −1102.00 −0.848909
$$120$$ 0 0
$$121$$ −847.000 −0.636364
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −504.000 −0.352148 −0.176074 0.984377i $$-0.556340\pi$$
−0.176074 + 0.984377i $$0.556340\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −72.0000 −0.0480204 −0.0240102 0.999712i $$-0.507643\pi$$
−0.0240102 + 0.999712i $$0.507643\pi$$
$$132$$ 0 0
$$133$$ −1007.00 −0.656526
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1850.00 −1.15369 −0.576847 0.816852i $$-0.695717\pi$$
−0.576847 + 0.816852i $$0.695717\pi$$
$$138$$ 0 0
$$139$$ 1836.00 1.12034 0.560171 0.828377i $$-0.310735\pi$$
0.560171 + 0.828377i $$0.310735\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 22.0000 0.0128653
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 2398.00 1.31847 0.659234 0.751938i $$-0.270881\pi$$
0.659234 + 0.751938i $$0.270881\pi$$
$$150$$ 0 0
$$151$$ 1871.00 1.00834 0.504172 0.863604i $$-0.331798\pi$$
0.504172 + 0.863604i $$0.331798\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 3293.00 1.67395 0.836975 0.547242i $$-0.184322\pi$$
0.836975 + 0.547242i $$0.184322\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1102.00 0.539440
$$162$$ 0 0
$$163$$ −883.000 −0.424306 −0.212153 0.977236i $$-0.568048\pi$$
−0.212153 + 0.977236i $$0.568048\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 4104.00 1.90166 0.950830 0.309715i $$-0.100234\pi$$
0.950830 + 0.309715i $$0.100234\pi$$
$$168$$ 0 0
$$169$$ −2196.00 −0.999545
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1706.00 0.749739 0.374869 0.927078i $$-0.377688\pi$$
0.374869 + 0.927078i $$0.377688\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −662.000 −0.276426 −0.138213 0.990403i $$-0.544136\pi$$
−0.138213 + 0.990403i $$0.544136\pi$$
$$180$$ 0 0
$$181$$ 4121.00 1.69233 0.846164 0.532922i $$-0.178906\pi$$
0.846164 + 0.532922i $$0.178906\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 1276.00 0.498986
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 958.000 0.362924 0.181462 0.983398i $$-0.441917\pi$$
0.181462 + 0.983398i $$0.441917\pi$$
$$192$$ 0 0
$$193$$ −3187.00 −1.18863 −0.594314 0.804233i $$-0.702576\pi$$
−0.594314 + 0.804233i $$0.702576\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2282.00 −0.825308 −0.412654 0.910888i $$-0.635398\pi$$
−0.412654 + 0.910888i $$0.635398\pi$$
$$198$$ 0 0
$$199$$ 1043.00 0.371539 0.185770 0.982593i $$-0.440522\pi$$
0.185770 + 0.982593i $$0.440522\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −418.000 −0.144521
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 1166.00 0.385904
$$210$$ 0 0
$$211$$ 4139.00 1.35043 0.675214 0.737621i $$-0.264051\pi$$
0.675214 + 0.737621i $$0.264051\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −665.000 −0.208033
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 58.0000 0.0176539
$$222$$ 0 0
$$223$$ −413.000 −0.124020 −0.0620101 0.998076i $$-0.519751\pi$$
−0.0620101 + 0.998076i $$0.519751\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 5652.00 1.65258 0.826292 0.563242i $$-0.190446\pi$$
0.826292 + 0.563242i $$0.190446\pi$$
$$228$$ 0 0
$$229$$ −4391.00 −1.26710 −0.633549 0.773703i $$-0.718403\pi$$
−0.633549 + 0.773703i $$0.718403\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −2052.00 −0.576957 −0.288479 0.957486i $$-0.593149\pi$$
−0.288479 + 0.957486i $$0.593149\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 4320.00 1.16919 0.584597 0.811324i $$-0.301252\pi$$
0.584597 + 0.811324i $$0.301252\pi$$
$$240$$ 0 0
$$241$$ 4265.00 1.13997 0.569985 0.821655i $$-0.306949\pi$$
0.569985 + 0.821655i $$0.306949\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 53.0000 0.0136531
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2412.00 0.606550 0.303275 0.952903i $$-0.401920\pi$$
0.303275 + 0.952903i $$0.401920\pi$$
$$252$$ 0 0
$$253$$ −1276.00 −0.317081
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 6948.00 1.68640 0.843199 0.537601i $$-0.180669\pi$$
0.843199 + 0.537601i $$0.180669\pi$$
$$258$$ 0 0
$$259$$ 5130.00 1.23074
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −3564.00 −0.835611 −0.417805 0.908537i $$-0.637201\pi$$
−0.417805 + 0.908537i $$0.637201\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1534.00 0.347694 0.173847 0.984773i $$-0.444380\pi$$
0.173847 + 0.984773i $$0.444380\pi$$
$$270$$ 0 0
$$271$$ 7704.00 1.72688 0.863440 0.504451i $$-0.168305\pi$$
0.863440 + 0.504451i $$0.168305\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −4877.00 −1.05787 −0.528936 0.848662i $$-0.677409\pi$$
−0.528936 + 0.848662i $$0.677409\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 3758.00 0.797806 0.398903 0.916993i $$-0.369391\pi$$
0.398903 + 0.916993i $$0.369391\pi$$
$$282$$ 0 0
$$283$$ −935.000 −0.196396 −0.0981978 0.995167i $$-0.531308\pi$$
−0.0981978 + 0.995167i $$0.531308\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 8892.00 1.82884
$$288$$ 0 0
$$289$$ −1549.00 −0.315286
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 6214.00 1.23900 0.619498 0.784998i $$-0.287336\pi$$
0.619498 + 0.784998i $$0.287336\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −58.0000 −0.0112181
$$300$$ 0 0
$$301$$ 8189.00 1.56813
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 3905.00 0.725961 0.362981 0.931797i $$-0.381759\pi$$
0.362981 + 0.931797i $$0.381759\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −9662.00 −1.76168 −0.880839 0.473416i $$-0.843021\pi$$
−0.880839 + 0.473416i $$0.843021\pi$$
$$312$$ 0 0
$$313$$ −5147.00 −0.929475 −0.464737 0.885449i $$-0.653851\pi$$
−0.464737 + 0.885449i $$0.653851\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −9216.00 −1.63288 −0.816439 0.577432i $$-0.804055\pi$$
−0.816439 + 0.577432i $$0.804055\pi$$
$$318$$ 0 0
$$319$$ 484.000 0.0849492
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 3074.00 0.529542
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −4370.00 −0.732298
$$330$$ 0 0
$$331$$ 2196.00 0.364662 0.182331 0.983237i $$-0.441636\pi$$
0.182331 + 0.983237i $$0.441636\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −2521.00 −0.407500 −0.203750 0.979023i $$-0.565313\pi$$
−0.203750 + 0.979023i $$0.565313\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 770.000 0.122281
$$342$$ 0 0
$$343$$ −6175.00 −0.972066
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 7034.00 1.08820 0.544099 0.839021i $$-0.316871\pi$$
0.544099 + 0.839021i $$0.316871\pi$$
$$348$$ 0 0
$$349$$ 7362.00 1.12917 0.564583 0.825376i $$-0.309037\pi$$
0.564583 + 0.825376i $$0.309037\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −9382.00 −1.41460 −0.707300 0.706914i $$-0.750087\pi$$
−0.707300 + 0.706914i $$0.750087\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 10116.0 1.48719 0.743596 0.668629i $$-0.233119\pi$$
0.743596 + 0.668629i $$0.233119\pi$$
$$360$$ 0 0
$$361$$ −4050.00 −0.590465
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 3277.00 0.466098 0.233049 0.972465i $$-0.425130\pi$$
0.233049 + 0.972465i $$0.425130\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −10891.0 −1.51184 −0.755918 0.654667i $$-0.772809\pi$$
−0.755918 + 0.654667i $$0.772809\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 22.0000 0.00300546
$$378$$ 0 0
$$379$$ −2591.00 −0.351163 −0.175581 0.984465i $$-0.556181\pi$$
−0.175581 + 0.984465i $$0.556181\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −612.000 −0.0816494 −0.0408247 0.999166i $$-0.512999\pi$$
−0.0408247 + 0.999166i $$0.512999\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −3708.00 −0.483298 −0.241649 0.970364i $$-0.577688\pi$$
−0.241649 + 0.970364i $$0.577688\pi$$
$$390$$ 0 0
$$391$$ −3364.00 −0.435102
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 3833.00 0.484566 0.242283 0.970206i $$-0.422104\pi$$
0.242283 + 0.970206i $$0.422104\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 9288.00 1.15666 0.578330 0.815803i $$-0.303705\pi$$
0.578330 + 0.815803i $$0.303705\pi$$
$$402$$ 0 0
$$403$$ 35.0000 0.00432624
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −5940.00 −0.723427
$$408$$ 0 0
$$409$$ −755.000 −0.0912771 −0.0456386 0.998958i $$-0.514532\pi$$
−0.0456386 + 0.998958i $$0.514532\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −8474.00 −1.00963
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 9576.00 1.11651 0.558256 0.829669i $$-0.311471\pi$$
0.558256 + 0.829669i $$0.311471\pi$$
$$420$$ 0 0
$$421$$ 9414.00 1.08981 0.544905 0.838498i $$-0.316566\pi$$
0.544905 + 0.838498i $$0.316566\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 2413.00 0.273474
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 2254.00 0.251906 0.125953 0.992036i $$-0.459801\pi$$
0.125953 + 0.992036i $$0.459801\pi$$
$$432$$ 0 0
$$433$$ 6301.00 0.699323 0.349661 0.936876i $$-0.386297\pi$$
0.349661 + 0.936876i $$0.386297\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −3074.00 −0.336497
$$438$$ 0 0
$$439$$ −3779.00 −0.410847 −0.205423 0.978673i $$-0.565857\pi$$
−0.205423 + 0.978673i $$0.565857\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 7632.00 0.818527 0.409263 0.912416i $$-0.365786\pi$$
0.409263 + 0.912416i $$0.365786\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −2988.00 −0.314059 −0.157029 0.987594i $$-0.550192\pi$$
−0.157029 + 0.987594i $$0.550192\pi$$
$$450$$ 0 0
$$451$$ −10296.0 −1.07499
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 1370.00 0.140232 0.0701159 0.997539i $$-0.477663\pi$$
0.0701159 + 0.997539i $$0.477663\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 7992.00 0.807429 0.403714 0.914885i $$-0.367719\pi$$
0.403714 + 0.914885i $$0.367719\pi$$
$$462$$ 0 0
$$463$$ 3096.00 0.310763 0.155382 0.987855i $$-0.450339\pi$$
0.155382 + 0.987855i $$0.450339\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −8338.00 −0.826203 −0.413101 0.910685i $$-0.635554\pi$$
−0.413101 + 0.910685i $$0.635554\pi$$
$$468$$ 0 0
$$469$$ 15409.0 1.51710
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −9482.00 −0.921740
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −4918.00 −0.469121 −0.234561 0.972101i $$-0.575365\pi$$
−0.234561 + 0.972101i $$0.575365\pi$$
$$480$$ 0 0
$$481$$ −270.000 −0.0255945
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 19637.0 1.82718 0.913591 0.406635i $$-0.133298\pi$$
0.913591 + 0.406635i $$0.133298\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −3096.00 −0.284563 −0.142282 0.989826i $$-0.545444\pi$$
−0.142282 + 0.989826i $$0.545444\pi$$
$$492$$ 0 0
$$493$$ 1276.00 0.116568
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −684.000 −0.0617336
$$498$$ 0 0
$$499$$ 6875.00 0.616768 0.308384 0.951262i $$-0.400212\pi$$
0.308384 + 0.951262i $$0.400212\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 11268.0 0.998838 0.499419 0.866361i $$-0.333547\pi$$
0.499419 + 0.866361i $$0.333547\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −16078.0 −1.40009 −0.700044 0.714100i $$-0.746836\pi$$
−0.700044 + 0.714100i $$0.746836\pi$$
$$510$$ 0 0
$$511$$ −9918.00 −0.858604
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 5060.00 0.430442
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 17366.0 1.46030 0.730152 0.683285i $$-0.239449\pi$$
0.730152 + 0.683285i $$0.239449\pi$$
$$522$$ 0 0
$$523$$ 4913.00 0.410766 0.205383 0.978682i $$-0.434156\pi$$
0.205383 + 0.978682i $$0.434156\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 2030.00 0.167795
$$528$$ 0 0
$$529$$ −8803.00 −0.723514
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −468.000 −0.0380325
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −396.000 −0.0316455
$$540$$ 0 0
$$541$$ 17605.0 1.39907 0.699536 0.714597i $$-0.253390\pi$$
0.699536 + 0.714597i $$0.253390\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 14560.0 1.13810 0.569050 0.822303i $$-0.307311\pi$$
0.569050 + 0.822303i $$0.307311\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 1166.00 0.0901511
$$552$$ 0 0
$$553$$ 25992.0 1.99872
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −20614.0 −1.56812 −0.784060 0.620685i $$-0.786855\pi$$
−0.784060 + 0.620685i $$0.786855\pi$$
$$558$$ 0 0
$$559$$ −431.000 −0.0326107
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 3442.00 0.257661 0.128830 0.991667i $$-0.458878\pi$$
0.128830 + 0.991667i $$0.458878\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −22082.0 −1.62693 −0.813467 0.581611i $$-0.802423\pi$$
−0.813467 + 0.581611i $$0.802423\pi$$
$$570$$ 0 0
$$571$$ 451.000 0.0330539 0.0165269 0.999863i $$-0.494739\pi$$
0.0165269 + 0.999863i $$0.494739\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −20987.0 −1.51421 −0.757106 0.653292i $$-0.773387\pi$$
−0.757106 + 0.653292i $$0.773387\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −21622.0 −1.54394
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 3888.00 0.273381 0.136691 0.990614i $$-0.456353\pi$$
0.136691 + 0.990614i $$0.456353\pi$$
$$588$$ 0 0
$$589$$ 1855.00 0.129769
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −11268.0 −0.780306 −0.390153 0.920750i $$-0.627578\pi$$
−0.390153 + 0.920750i $$0.627578\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 3996.00 0.272575 0.136287 0.990669i $$-0.456483\pi$$
0.136287 + 0.990669i $$0.456483\pi$$
$$600$$ 0 0
$$601$$ −24965.0 −1.69442 −0.847208 0.531262i $$-0.821718\pi$$
−0.847208 + 0.531262i $$0.821718\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −4176.00 −0.279240 −0.139620 0.990205i $$-0.544588\pi$$
−0.139620 + 0.990205i $$0.544588\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 230.000 0.0152288
$$612$$ 0 0
$$613$$ 9558.00 0.629762 0.314881 0.949131i $$-0.398035\pi$$
0.314881 + 0.949131i $$0.398035\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −9000.00 −0.587239 −0.293619 0.955922i $$-0.594860\pi$$
−0.293619 + 0.955922i $$0.594860\pi$$
$$618$$ 0 0
$$619$$ −15625.0 −1.01457 −0.507287 0.861777i $$-0.669352\pi$$
−0.507287 + 0.861777i $$0.669352\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −2736.00 −0.175948
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −15660.0 −0.992695
$$630$$ 0 0
$$631$$ −31175.0 −1.96681 −0.983405 0.181424i $$-0.941929\pi$$
−0.983405 + 0.181424i $$0.941929\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −18.0000 −0.00111960
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 6732.00 0.414817 0.207409 0.978254i $$-0.433497\pi$$
0.207409 + 0.978254i $$0.433497\pi$$
$$642$$ 0 0
$$643$$ 6228.00 0.381973 0.190986 0.981593i $$-0.438831\pi$$
0.190986 + 0.981593i $$0.438831\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −396.000 −0.0240624 −0.0120312 0.999928i $$-0.503830\pi$$
−0.0120312 + 0.999928i $$0.503830\pi$$
$$648$$ 0 0
$$649$$ 9812.00 0.593459
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −4702.00 −0.281782 −0.140891 0.990025i $$-0.544997\pi$$
−0.140891 + 0.990025i $$0.544997\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 22140.0 1.30873 0.654364 0.756180i $$-0.272936\pi$$
0.654364 + 0.756180i $$0.272936\pi$$
$$660$$ 0 0
$$661$$ −13518.0 −0.795445 −0.397723 0.917506i $$-0.630199\pi$$
−0.397723 + 0.917506i $$0.630199\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −1276.00 −0.0740733
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −2794.00 −0.160747
$$672$$ 0 0
$$673$$ 11250.0 0.644362 0.322181 0.946678i $$-0.395584\pi$$
0.322181 + 0.946678i $$0.395584\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −15170.0 −0.861197 −0.430599 0.902544i $$-0.641698\pi$$
−0.430599 + 0.902544i $$0.641698\pi$$
$$678$$ 0 0
$$679$$ 20501.0 1.15870
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 22680.0 1.27061 0.635305 0.772262i $$-0.280875\pi$$
0.635305 + 0.772262i $$0.280875\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 128.000 0.00704682 0.00352341 0.999994i $$-0.498878\pi$$
0.00352341 + 0.999994i $$0.498878\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −27144.0 −1.47511
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −25682.0 −1.38373 −0.691866 0.722026i $$-0.743211\pi$$
−0.691866 + 0.722026i $$0.743211\pi$$
$$702$$ 0 0
$$703$$ −14310.0 −0.767727
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 27360.0 1.45542
$$708$$ 0 0
$$709$$ −4951.00 −0.262255 −0.131127 0.991366i $$-0.541860\pi$$
−0.131127 + 0.991366i $$0.541860\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −2030.00 −0.106626
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 22190.0 1.15097 0.575485 0.817812i $$-0.304813\pi$$
0.575485 + 0.817812i $$0.304813\pi$$
$$720$$ 0 0
$$721$$ −2356.00 −0.121695
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −7685.00 −0.392051 −0.196025 0.980599i $$-0.562803\pi$$
−0.196025 + 0.980599i $$0.562803\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −24998.0 −1.26482
$$732$$ 0 0
$$733$$ −29574.0 −1.49023 −0.745116 0.666934i $$-0.767606\pi$$
−0.745116 + 0.666934i $$0.767606\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −17842.0 −0.891748
$$738$$ 0 0
$$739$$ −32580.0 −1.62175 −0.810876 0.585218i $$-0.801009\pi$$
−0.810876 + 0.585218i $$0.801009\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −3060.00 −0.151091 −0.0755454 0.997142i $$-0.524070\pi$$
−0.0755454 + 0.997142i $$0.524070\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −8208.00 −0.400419
$$750$$ 0 0
$$751$$ −7992.00 −0.388325 −0.194163 0.980969i $$-0.562199\pi$$
−0.194163 + 0.980969i $$0.562199\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −22841.0 −1.09666 −0.548329 0.836263i $$-0.684736\pi$$
−0.548329 + 0.836263i $$0.684736\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 17172.0 0.817982 0.408991 0.912538i $$-0.365881\pi$$
0.408991 + 0.912538i $$0.365881\pi$$
$$762$$ 0 0
$$763$$ 13319.0 0.631953
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 446.000 0.0209963
$$768$$ 0 0
$$769$$ −30869.0 −1.44755 −0.723774 0.690037i $$-0.757594\pi$$
−0.723774 + 0.690037i $$0.757594\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 34884.0 1.62314 0.811572 0.584252i $$-0.198612\pi$$
0.811572 + 0.584252i $$0.198612\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −24804.0 −1.14082
$$780$$ 0 0
$$781$$ 792.000 0.0362868
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −5039.00 −0.228235 −0.114118 0.993467i $$-0.536404\pi$$
−0.114118 + 0.993467i $$0.536404\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −19836.0 −0.891640
$$792$$ 0 0
$$793$$ −127.000 −0.00568714
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 540.000 0.0239997 0.0119999 0.999928i $$-0.496180\pi$$
0.0119999 + 0.999928i $$0.496180\pi$$
$$798$$ 0 0
$$799$$ 13340.0 0.590657
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 11484.0 0.504684
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 41328.0 1.79606 0.898032 0.439931i $$-0.144997\pi$$
0.898032 + 0.439931i $$0.144997\pi$$
$$810$$ 0 0
$$811$$ −12853.0 −0.556510 −0.278255 0.960507i $$-0.589756\pi$$
−0.278255 + 0.960507i $$0.589756\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −22843.0 −0.978183
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −29470.0 −1.25275 −0.626376 0.779521i $$-0.715463\pi$$
−0.626376 + 0.779521i $$0.715463\pi$$
$$822$$ 0 0
$$823$$ 24407.0 1.03375 0.516874 0.856062i $$-0.327096\pi$$
0.516874 + 0.856062i $$0.327096\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 15048.0 0.632733 0.316367 0.948637i $$-0.397537\pi$$
0.316367 + 0.948637i $$0.397537\pi$$
$$828$$ 0 0
$$829$$ −28406.0 −1.19009 −0.595043 0.803694i $$-0.702865\pi$$
−0.595043 + 0.803694i $$0.702865\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −1044.00 −0.0434243
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 26914.0 1.10748 0.553739 0.832690i $$-0.313200\pi$$
0.553739 + 0.832690i $$0.313200\pi$$
$$840$$ 0 0
$$841$$ −23905.0 −0.980155
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −16093.0 −0.652848
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 15660.0 0.630808
$$852$$ 0 0
$$853$$ −21275.0 −0.853977 −0.426988 0.904257i $$-0.640425\pi$$
−0.426988 + 0.904257i $$0.640425\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 39132.0 1.55977 0.779885 0.625922i $$-0.215277\pi$$
0.779885 + 0.625922i $$0.215277\pi$$
$$858$$ 0 0
$$859$$ −448.000 −0.0177946 −0.00889730 0.999960i $$-0.502832\pi$$
−0.00889730 + 0.999960i $$0.502832\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −26856.0 −1.05932 −0.529658 0.848212i $$-0.677680\pi$$
−0.529658 + 0.848212i $$0.677680\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −30096.0 −1.17484
$$870$$ 0 0
$$871$$ −811.000 −0.0315496
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 3653.00 0.140653 0.0703267 0.997524i $$-0.477596\pi$$
0.0703267 + 0.997524i $$0.477596\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 6552.00 0.250559 0.125280 0.992121i $$-0.460017\pi$$
0.125280 + 0.992121i $$0.460017\pi$$
$$882$$ 0 0
$$883$$ −4481.00 −0.170779 −0.0853894 0.996348i $$-0.527213\pi$$
−0.0853894 + 0.996348i $$0.527213\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −14666.0 −0.555170 −0.277585 0.960701i $$-0.589534\pi$$
−0.277585 + 0.960701i $$0.589534\pi$$
$$888$$ 0 0
$$889$$ −9576.00 −0.361270
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 12190.0 0.456800
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 770.000 0.0285661
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −51804.0 −1.89650 −0.948249 0.317528i $$-0.897147\pi$$
−0.948249 + 0.317528i $$0.897147\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −31198.0 −1.13462 −0.567308 0.823505i $$-0.692015\pi$$
−0.567308 + 0.823505i $$0.692015\pi$$
$$912$$ 0 0
$$913$$ 25036.0 0.907525
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −1368.00 −0.0492643
$$918$$ 0 0
$$919$$ −27001.0 −0.969185 −0.484592 0.874740i $$-0.661032\pi$$
−0.484592 + 0.874740i $$0.661032\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 36.0000 0.00128381
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 22694.0 0.801470 0.400735 0.916194i $$-0.368755\pi$$
0.400735 + 0.916194i $$0.368755\pi$$
$$930$$ 0 0
$$931$$ −954.000 −0.0335833
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −29503.0 −1.02862 −0.514312 0.857603i $$-0.671953\pi$$
−0.514312 + 0.857603i $$0.671953\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −14566.0 −0.504610 −0.252305 0.967648i $$-0.581189\pi$$
−0.252305 + 0.967648i $$0.581189\pi$$
$$942$$ 0 0
$$943$$ 27144.0 0.937360
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 42322.0 1.45225 0.726125 0.687563i $$-0.241319\pi$$
0.726125 + 0.687563i $$0.241319\pi$$
$$948$$ 0 0
$$949$$ 522.000 0.0178555
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 43416.0 1.47574 0.737871 0.674942i $$-0.235831\pi$$
0.737871 + 0.674942i $$0.235831\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −35150.0 −1.18358
$$960$$ 0 0
$$961$$ −28566.0 −0.958880
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −21528.0 −0.715919 −0.357960 0.933737i $$-0.616527\pi$$
−0.357960 + 0.933737i $$0.616527\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −27050.0 −0.894002 −0.447001 0.894533i $$-0.647508\pi$$
−0.447001 + 0.894533i $$0.647508\pi$$
$$972$$ 0 0
$$973$$ 34884.0 1.14936
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −24934.0 −0.816489 −0.408244 0.912873i $$-0.633859\pi$$
−0.408244 + 0.912873i $$0.633859\pi$$
$$978$$ 0 0
$$979$$ 3168.00 0.103422
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 8388.00 0.272162 0.136081 0.990698i $$-0.456549\pi$$
0.136081 + 0.990698i $$0.456549\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 24998.0 0.803731
$$990$$ 0 0
$$991$$ 29033.0 0.930639 0.465320 0.885143i $$-0.345939\pi$$
0.465320 + 0.885143i $$0.345939\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 25326.0 0.804496 0.402248 0.915531i $$-0.368229\pi$$
0.402248 + 0.915531i $$0.368229\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1800.4.a.bf.1.1 1
3.2 odd 2 600.4.a.g.1.1 1
5.2 odd 4 1800.4.f.g.649.2 2
5.3 odd 4 1800.4.f.g.649.1 2
5.4 even 2 1800.4.a.g.1.1 1
12.11 even 2 1200.4.a.x.1.1 1
15.2 even 4 600.4.f.h.49.2 2
15.8 even 4 600.4.f.h.49.1 2
15.14 odd 2 600.4.a.j.1.1 yes 1
60.23 odd 4 1200.4.f.f.49.2 2
60.47 odd 4 1200.4.f.f.49.1 2
60.59 even 2 1200.4.a.n.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
600.4.a.g.1.1 1 3.2 odd 2
600.4.a.j.1.1 yes 1 15.14 odd 2
600.4.f.h.49.1 2 15.8 even 4
600.4.f.h.49.2 2 15.2 even 4
1200.4.a.n.1.1 1 60.59 even 2
1200.4.a.x.1.1 1 12.11 even 2
1200.4.f.f.49.1 2 60.47 odd 4
1200.4.f.f.49.2 2 60.23 odd 4
1800.4.a.g.1.1 1 5.4 even 2
1800.4.a.bf.1.1 1 1.1 even 1 trivial
1800.4.f.g.649.1 2 5.3 odd 4
1800.4.f.g.649.2 2 5.2 odd 4