# Properties

 Label 1008.6.a.a.1.1 Level $1008$ Weight $6$ Character 1008.1 Self dual yes Analytic conductor $161.667$ 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] = [1008,6,Mod(1,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("1008.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 1008.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: $$161.666890371$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 21) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1008.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-94.0000 q^{5} +49.0000 q^{7} +O(q^{10})$$ $$q-94.0000 q^{5} +49.0000 q^{7} +52.0000 q^{11} -770.000 q^{13} +2022.00 q^{17} -1732.00 q^{19} -576.000 q^{23} +5711.00 q^{25} -5518.00 q^{29} -6336.00 q^{31} -4606.00 q^{35} -7338.00 q^{37} +3262.00 q^{41} -5420.00 q^{43} +864.000 q^{47} +2401.00 q^{49} -4182.00 q^{53} -4888.00 q^{55} -11220.0 q^{59} -45602.0 q^{61} +72380.0 q^{65} -1396.00 q^{67} +18720.0 q^{71} +46362.0 q^{73} +2548.00 q^{77} -97424.0 q^{79} -81228.0 q^{83} -190068. q^{85} +3182.00 q^{89} -37730.0 q^{91} +162808. q^{95} +4914.00 q^{97} +O(q^{100})$$

## 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
$$5$$ −94.0000 −1.68152 −0.840762 0.541406i $$-0.817892\pi$$
−0.840762 + 0.541406i $$0.817892\pi$$
$$6$$ 0 0
$$7$$ 49.0000 0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 52.0000 0.129575 0.0647876 0.997899i $$-0.479363\pi$$
0.0647876 + 0.997899i $$0.479363\pi$$
$$12$$ 0 0
$$13$$ −770.000 −1.26367 −0.631833 0.775104i $$-0.717697\pi$$
−0.631833 + 0.775104i $$0.717697\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2022.00 1.69691 0.848455 0.529267i $$-0.177533\pi$$
0.848455 + 0.529267i $$0.177533\pi$$
$$18$$ 0 0
$$19$$ −1732.00 −1.10069 −0.550344 0.834938i $$-0.685503\pi$$
−0.550344 + 0.834938i $$0.685503\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −576.000 −0.227040 −0.113520 0.993536i $$-0.536213\pi$$
−0.113520 + 0.993536i $$0.536213\pi$$
$$24$$ 0 0
$$25$$ 5711.00 1.82752
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −5518.00 −1.21839 −0.609196 0.793020i $$-0.708508\pi$$
−0.609196 + 0.793020i $$0.708508\pi$$
$$30$$ 0 0
$$31$$ −6336.00 −1.18416 −0.592081 0.805879i $$-0.701693\pi$$
−0.592081 + 0.805879i $$0.701693\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −4606.00 −0.635556
$$36$$ 0 0
$$37$$ −7338.00 −0.881198 −0.440599 0.897704i $$-0.645234\pi$$
−0.440599 + 0.897704i $$0.645234\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3262.00 0.303057 0.151528 0.988453i $$-0.451580\pi$$
0.151528 + 0.988453i $$0.451580\pi$$
$$42$$ 0 0
$$43$$ −5420.00 −0.447021 −0.223511 0.974701i $$-0.571752\pi$$
−0.223511 + 0.974701i $$0.571752\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 864.000 0.0570518 0.0285259 0.999593i $$-0.490919\pi$$
0.0285259 + 0.999593i $$0.490919\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −4182.00 −0.204500 −0.102250 0.994759i $$-0.532604\pi$$
−0.102250 + 0.994759i $$0.532604\pi$$
$$54$$ 0 0
$$55$$ −4888.00 −0.217884
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −11220.0 −0.419626 −0.209813 0.977741i $$-0.567286\pi$$
−0.209813 + 0.977741i $$0.567286\pi$$
$$60$$ 0 0
$$61$$ −45602.0 −1.56913 −0.784566 0.620046i $$-0.787114\pi$$
−0.784566 + 0.620046i $$0.787114\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 72380.0 2.12488
$$66$$ 0 0
$$67$$ −1396.00 −0.0379925 −0.0189963 0.999820i $$-0.506047\pi$$
−0.0189963 + 0.999820i $$0.506047\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 18720.0 0.440717 0.220359 0.975419i $$-0.429277\pi$$
0.220359 + 0.975419i $$0.429277\pi$$
$$72$$ 0 0
$$73$$ 46362.0 1.01825 0.509126 0.860692i $$-0.329969\pi$$
0.509126 + 0.860692i $$0.329969\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 2548.00 0.0489748
$$78$$ 0 0
$$79$$ −97424.0 −1.75630 −0.878149 0.478387i $$-0.841222\pi$$
−0.878149 + 0.478387i $$0.841222\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −81228.0 −1.29423 −0.647114 0.762394i $$-0.724024\pi$$
−0.647114 + 0.762394i $$0.724024\pi$$
$$84$$ 0 0
$$85$$ −190068. −2.85339
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 3182.00 0.0425819 0.0212910 0.999773i $$-0.493222\pi$$
0.0212910 + 0.999773i $$0.493222\pi$$
$$90$$ 0 0
$$91$$ −37730.0 −0.477621
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 162808. 1.85083
$$96$$ 0 0
$$97$$ 4914.00 0.0530281 0.0265140 0.999648i $$-0.491559\pi$$
0.0265140 + 0.999648i $$0.491559\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 166354. 1.62267 0.811334 0.584583i $$-0.198742\pi$$
0.811334 + 0.584583i $$0.198742\pi$$
$$102$$ 0 0
$$103$$ −157160. −1.45965 −0.729825 0.683634i $$-0.760399\pi$$
−0.729825 + 0.683634i $$0.760399\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −6764.00 −0.0571142 −0.0285571 0.999592i $$-0.509091\pi$$
−0.0285571 + 0.999592i $$0.509091\pi$$
$$108$$ 0 0
$$109$$ 178398. 1.43821 0.719107 0.694899i $$-0.244551\pi$$
0.719107 + 0.694899i $$0.244551\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 45134.0 0.332512 0.166256 0.986083i $$-0.446832\pi$$
0.166256 + 0.986083i $$0.446832\pi$$
$$114$$ 0 0
$$115$$ 54144.0 0.381773
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 99078.0 0.641372
$$120$$ 0 0
$$121$$ −158347. −0.983210
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −243084. −1.39149
$$126$$ 0 0
$$127$$ 205056. 1.12814 0.564070 0.825727i $$-0.309235\pi$$
0.564070 + 0.825727i $$0.309235\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 72964.0 0.371476 0.185738 0.982599i $$-0.440532\pi$$
0.185738 + 0.982599i $$0.440532\pi$$
$$132$$ 0 0
$$133$$ −84868.0 −0.416021
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 94182.0 0.428713 0.214356 0.976756i $$-0.431235\pi$$
0.214356 + 0.976756i $$0.431235\pi$$
$$138$$ 0 0
$$139$$ 47796.0 0.209824 0.104912 0.994482i $$-0.466544\pi$$
0.104912 + 0.994482i $$0.466544\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −40040.0 −0.163740
$$144$$ 0 0
$$145$$ 518692. 2.04875
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 124266. 0.458550 0.229275 0.973362i $$-0.426364\pi$$
0.229275 + 0.973362i $$0.426364\pi$$
$$150$$ 0 0
$$151$$ 446296. 1.59287 0.796436 0.604723i $$-0.206716\pi$$
0.796436 + 0.604723i $$0.206716\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 595584. 1.99119
$$156$$ 0 0
$$157$$ −159746. −0.517227 −0.258613 0.965981i $$-0.583266\pi$$
−0.258613 + 0.965981i $$0.583266\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −28224.0 −0.0858132
$$162$$ 0 0
$$163$$ −247252. −0.728905 −0.364452 0.931222i $$-0.618744\pi$$
−0.364452 + 0.931222i $$0.618744\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −684488. −1.89922 −0.949609 0.313438i $$-0.898519\pi$$
−0.949609 + 0.313438i $$0.898519\pi$$
$$168$$ 0 0
$$169$$ 221607. 0.596852
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 610474. 1.55079 0.775393 0.631479i $$-0.217552\pi$$
0.775393 + 0.631479i $$0.217552\pi$$
$$174$$ 0 0
$$175$$ 279839. 0.690738
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 662252. 1.54487 0.772433 0.635097i $$-0.219040\pi$$
0.772433 + 0.635097i $$0.219040\pi$$
$$180$$ 0 0
$$181$$ 154630. 0.350830 0.175415 0.984495i $$-0.443873\pi$$
0.175415 + 0.984495i $$0.443873\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 689772. 1.48175
$$186$$ 0 0
$$187$$ 105144. 0.219877
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 486904. 0.965739 0.482870 0.875692i $$-0.339594\pi$$
0.482870 + 0.875692i $$0.339594\pi$$
$$192$$ 0 0
$$193$$ 620546. 1.19917 0.599585 0.800311i $$-0.295332\pi$$
0.599585 + 0.800311i $$0.295332\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 236570. 0.434304 0.217152 0.976138i $$-0.430323\pi$$
0.217152 + 0.976138i $$0.430323\pi$$
$$198$$ 0 0
$$199$$ −82104.0 −0.146971 −0.0734855 0.997296i $$-0.523412\pi$$
−0.0734855 + 0.997296i $$0.523412\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −270382. −0.460509
$$204$$ 0 0
$$205$$ −306628. −0.509597
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −90064.0 −0.142622
$$210$$ 0 0
$$211$$ −99892.0 −0.154463 −0.0772315 0.997013i $$-0.524608\pi$$
−0.0772315 + 0.997013i $$0.524608\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 509480. 0.751677
$$216$$ 0 0
$$217$$ −310464. −0.447571
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.55694e6 −2.14433
$$222$$ 0 0
$$223$$ 186704. 0.251415 0.125708 0.992067i $$-0.459880\pi$$
0.125708 + 0.992067i $$0.459880\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 336372. 0.433267 0.216633 0.976253i $$-0.430492\pi$$
0.216633 + 0.976253i $$0.430492\pi$$
$$228$$ 0 0
$$229$$ −926314. −1.16727 −0.583633 0.812018i $$-0.698369\pi$$
−0.583633 + 0.812018i $$0.698369\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −1.25711e6 −1.51700 −0.758499 0.651675i $$-0.774067\pi$$
−0.758499 + 0.651675i $$0.774067\pi$$
$$234$$ 0 0
$$235$$ −81216.0 −0.0959339
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −347016. −0.392966 −0.196483 0.980507i $$-0.562952\pi$$
−0.196483 + 0.980507i $$0.562952\pi$$
$$240$$ 0 0
$$241$$ 99170.0 0.109986 0.0549930 0.998487i $$-0.482486\pi$$
0.0549930 + 0.998487i $$0.482486\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −225694. −0.240218
$$246$$ 0 0
$$247$$ 1.33364e6 1.39090
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 344428. 0.345076 0.172538 0.985003i $$-0.444803\pi$$
0.172538 + 0.985003i $$0.444803\pi$$
$$252$$ 0 0
$$253$$ −29952.0 −0.0294188
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −295130. −0.278728 −0.139364 0.990241i $$-0.544506\pi$$
−0.139364 + 0.990241i $$0.544506\pi$$
$$258$$ 0 0
$$259$$ −359562. −0.333061
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −1.27246e6 −1.13437 −0.567187 0.823589i $$-0.691968\pi$$
−0.567187 + 0.823589i $$0.691968\pi$$
$$264$$ 0 0
$$265$$ 393108. 0.343872
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −276774. −0.233209 −0.116604 0.993178i $$-0.537201\pi$$
−0.116604 + 0.993178i $$0.537201\pi$$
$$270$$ 0 0
$$271$$ 1.28994e6 1.06695 0.533476 0.845815i $$-0.320885\pi$$
0.533476 + 0.845815i $$0.320885\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 296972. 0.236801
$$276$$ 0 0
$$277$$ 1.71655e6 1.34418 0.672089 0.740470i $$-0.265397\pi$$
0.672089 + 0.740470i $$0.265397\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.47218e6 1.11223 0.556116 0.831104i $$-0.312291\pi$$
0.556116 + 0.831104i $$0.312291\pi$$
$$282$$ 0 0
$$283$$ −1.02881e6 −0.763607 −0.381804 0.924244i $$-0.624697\pi$$
−0.381804 + 0.924244i $$0.624697\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 159838. 0.114545
$$288$$ 0 0
$$289$$ 2.66863e6 1.87950
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 1.18607e6 0.807123 0.403562 0.914952i $$-0.367772\pi$$
0.403562 + 0.914952i $$0.367772\pi$$
$$294$$ 0 0
$$295$$ 1.05468e6 0.705612
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 443520. 0.286903
$$300$$ 0 0
$$301$$ −265580. −0.168958
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 4.28659e6 2.63853
$$306$$ 0 0
$$307$$ −1.51892e6 −0.919788 −0.459894 0.887974i $$-0.652113\pi$$
−0.459894 + 0.887974i $$0.652113\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 212808. 0.124763 0.0623817 0.998052i $$-0.480130\pi$$
0.0623817 + 0.998052i $$0.480130\pi$$
$$312$$ 0 0
$$313$$ −1894.00 −0.00109275 −0.000546373 1.00000i $$-0.500174\pi$$
−0.000546373 1.00000i $$0.500174\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.57898e6 0.882527 0.441263 0.897378i $$-0.354530\pi$$
0.441263 + 0.897378i $$0.354530\pi$$
$$318$$ 0 0
$$319$$ −286936. −0.157873
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −3.50210e6 −1.86777
$$324$$ 0 0
$$325$$ −4.39747e6 −2.30938
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 42336.0 0.0215635
$$330$$ 0 0
$$331$$ 3.39471e6 1.70307 0.851535 0.524298i $$-0.175672\pi$$
0.851535 + 0.524298i $$0.175672\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 131224. 0.0638853
$$336$$ 0 0
$$337$$ 2.02731e6 0.972403 0.486201 0.873847i $$-0.338382\pi$$
0.486201 + 0.873847i $$0.338382\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −329472. −0.153438
$$342$$ 0 0
$$343$$ 117649. 0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 3.48885e6 1.55546 0.777730 0.628598i $$-0.216371\pi$$
0.777730 + 0.628598i $$0.216371\pi$$
$$348$$ 0 0
$$349$$ 965566. 0.424344 0.212172 0.977232i $$-0.431946\pi$$
0.212172 + 0.977232i $$0.431946\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −1.15393e6 −0.492882 −0.246441 0.969158i $$-0.579261\pi$$
−0.246441 + 0.969158i $$0.579261\pi$$
$$354$$ 0 0
$$355$$ −1.75968e6 −0.741076
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 1.61110e6 0.659762 0.329881 0.944022i $$-0.392991\pi$$
0.329881 + 0.944022i $$0.392991\pi$$
$$360$$ 0 0
$$361$$ 523725. 0.211512
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −4.35803e6 −1.71221
$$366$$ 0 0
$$367$$ −3.67747e6 −1.42523 −0.712614 0.701557i $$-0.752489\pi$$
−0.712614 + 0.701557i $$0.752489\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −204918. −0.0772939
$$372$$ 0 0
$$373$$ 649766. 0.241816 0.120908 0.992664i $$-0.461419\pi$$
0.120908 + 0.992664i $$0.461419\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 4.24886e6 1.53964
$$378$$ 0 0
$$379$$ −320700. −0.114683 −0.0573417 0.998355i $$-0.518262\pi$$
−0.0573417 + 0.998355i $$0.518262\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −2.36189e6 −0.822740 −0.411370 0.911469i $$-0.634950\pi$$
−0.411370 + 0.911469i $$0.634950\pi$$
$$384$$ 0 0
$$385$$ −239512. −0.0823522
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 3.53390e6 1.18408 0.592039 0.805910i $$-0.298323\pi$$
0.592039 + 0.805910i $$0.298323\pi$$
$$390$$ 0 0
$$391$$ −1.16467e6 −0.385267
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 9.15786e6 2.95326
$$396$$ 0 0
$$397$$ 4.04811e6 1.28907 0.644534 0.764575i $$-0.277051\pi$$
0.644534 + 0.764575i $$0.277051\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −2.07645e6 −0.644853 −0.322426 0.946595i $$-0.604498\pi$$
−0.322426 + 0.946595i $$0.604498\pi$$
$$402$$ 0 0
$$403$$ 4.87872e6 1.49638
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −381576. −0.114181
$$408$$ 0 0
$$409$$ 2.57431e6 0.760945 0.380472 0.924792i $$-0.375761\pi$$
0.380472 + 0.924792i $$0.375761\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −549780. −0.158604
$$414$$ 0 0
$$415$$ 7.63543e6 2.17627
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 848148. 0.236013 0.118007 0.993013i $$-0.462350\pi$$
0.118007 + 0.993013i $$0.462350\pi$$
$$420$$ 0 0
$$421$$ 1.43682e6 0.395092 0.197546 0.980294i $$-0.436703\pi$$
0.197546 + 0.980294i $$0.436703\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.15476e7 3.10114
$$426$$ 0 0
$$427$$ −2.23450e6 −0.593076
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 2.35438e6 0.610496 0.305248 0.952273i $$-0.401261\pi$$
0.305248 + 0.952273i $$0.401261\pi$$
$$432$$ 0 0
$$433$$ −3.78808e6 −0.970955 −0.485478 0.874249i $$-0.661354\pi$$
−0.485478 + 0.874249i $$0.661354\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 997632. 0.249900
$$438$$ 0 0
$$439$$ 3.64322e6 0.902245 0.451123 0.892462i $$-0.351024\pi$$
0.451123 + 0.892462i $$0.351024\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 2.48389e6 0.601345 0.300672 0.953728i $$-0.402789\pi$$
0.300672 + 0.953728i $$0.402789\pi$$
$$444$$ 0 0
$$445$$ −299108. −0.0716025
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 2.63177e6 0.616074 0.308037 0.951374i $$-0.400328\pi$$
0.308037 + 0.951374i $$0.400328\pi$$
$$450$$ 0 0
$$451$$ 169624. 0.0392686
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 3.54662e6 0.803131
$$456$$ 0 0
$$457$$ −1.16130e6 −0.260109 −0.130054 0.991507i $$-0.541515\pi$$
−0.130054 + 0.991507i $$0.541515\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −2.81385e6 −0.616663 −0.308332 0.951279i $$-0.599771\pi$$
−0.308332 + 0.951279i $$0.599771\pi$$
$$462$$ 0 0
$$463$$ −6.84299e6 −1.48352 −0.741760 0.670665i $$-0.766009\pi$$
−0.741760 + 0.670665i $$0.766009\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 3.34314e6 0.709353 0.354676 0.934989i $$-0.384591\pi$$
0.354676 + 0.934989i $$0.384591\pi$$
$$468$$ 0 0
$$469$$ −68404.0 −0.0143598
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −281840. −0.0579228
$$474$$ 0 0
$$475$$ −9.89145e6 −2.01153
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −4.28248e6 −0.852818 −0.426409 0.904530i $$-0.640222\pi$$
−0.426409 + 0.904530i $$0.640222\pi$$
$$480$$ 0 0
$$481$$ 5.65026e6 1.11354
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −461916. −0.0891679
$$486$$ 0 0
$$487$$ 8.93175e6 1.70653 0.853266 0.521477i $$-0.174619\pi$$
0.853266 + 0.521477i $$0.174619\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 2.75306e6 0.515361 0.257681 0.966230i $$-0.417042\pi$$
0.257681 + 0.966230i $$0.417042\pi$$
$$492$$ 0 0
$$493$$ −1.11574e7 −2.06750
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 917280. 0.166575
$$498$$ 0 0
$$499$$ −4.80408e6 −0.863693 −0.431846 0.901947i $$-0.642138\pi$$
−0.431846 + 0.901947i $$0.642138\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −6.02465e6 −1.06172 −0.530862 0.847458i $$-0.678132\pi$$
−0.530862 + 0.847458i $$0.678132\pi$$
$$504$$ 0 0
$$505$$ −1.56373e7 −2.72855
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 8.42987e6 1.44220 0.721101 0.692830i $$-0.243636\pi$$
0.721101 + 0.692830i $$0.243636\pi$$
$$510$$ 0 0
$$511$$ 2.27174e6 0.384863
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 1.47730e7 2.45444
$$516$$ 0 0
$$517$$ 44928.0 0.00739249
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −9.25058e6 −1.49305 −0.746525 0.665357i $$-0.768279\pi$$
−0.746525 + 0.665357i $$0.768279\pi$$
$$522$$ 0 0
$$523$$ −5.84494e6 −0.934385 −0.467192 0.884156i $$-0.654734\pi$$
−0.467192 + 0.884156i $$0.654734\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −1.28114e7 −2.00942
$$528$$ 0 0
$$529$$ −6.10457e6 −0.948453
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −2.51174e6 −0.382963
$$534$$ 0 0
$$535$$ 635816. 0.0960389
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 124852. 0.0185107
$$540$$ 0 0
$$541$$ 9.22533e6 1.35515 0.677577 0.735452i $$-0.263030\pi$$
0.677577 + 0.735452i $$0.263030\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −1.67694e7 −2.41839
$$546$$ 0 0
$$547$$ 6.44337e6 0.920757 0.460378 0.887723i $$-0.347714\pi$$
0.460378 + 0.887723i $$0.347714\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 9.55718e6 1.34107
$$552$$ 0 0
$$553$$ −4.77378e6 −0.663818
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −3.74213e6 −0.511070 −0.255535 0.966800i $$-0.582252\pi$$
−0.255535 + 0.966800i $$0.582252\pi$$
$$558$$ 0 0
$$559$$ 4.17340e6 0.564886
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −1.46384e7 −1.94635 −0.973176 0.230060i $$-0.926108\pi$$
−0.973176 + 0.230060i $$0.926108\pi$$
$$564$$ 0 0
$$565$$ −4.24260e6 −0.559127
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1.41805e7 −1.83616 −0.918078 0.396400i $$-0.870259\pi$$
−0.918078 + 0.396400i $$0.870259\pi$$
$$570$$ 0 0
$$571$$ 1.25160e6 0.160648 0.0803242 0.996769i $$-0.474404\pi$$
0.0803242 + 0.996769i $$0.474404\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −3.28954e6 −0.414921
$$576$$ 0 0
$$577$$ 5.94378e6 0.743230 0.371615 0.928387i $$-0.378804\pi$$
0.371615 + 0.928387i $$0.378804\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −3.98017e6 −0.489172
$$582$$ 0 0
$$583$$ −217464. −0.0264982
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −6.46192e6 −0.774046 −0.387023 0.922070i $$-0.626497\pi$$
−0.387023 + 0.922070i $$0.626497\pi$$
$$588$$ 0 0
$$589$$ 1.09740e7 1.30339
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 2.34605e6 0.273969 0.136984 0.990573i $$-0.456259\pi$$
0.136984 + 0.990573i $$0.456259\pi$$
$$594$$ 0 0
$$595$$ −9.31333e6 −1.07848
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −1.34959e7 −1.53686 −0.768432 0.639931i $$-0.778963\pi$$
−0.768432 + 0.639931i $$0.778963\pi$$
$$600$$ 0 0
$$601$$ 3.87849e6 0.438002 0.219001 0.975725i $$-0.429720\pi$$
0.219001 + 0.975725i $$0.429720\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 1.48846e7 1.65329
$$606$$ 0 0
$$607$$ 533488. 0.0587696 0.0293848 0.999568i $$-0.490645\pi$$
0.0293848 + 0.999568i $$0.490645\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −665280. −0.0720944
$$612$$ 0 0
$$613$$ 5.14610e6 0.553130 0.276565 0.960995i $$-0.410804\pi$$
0.276565 + 0.960995i $$0.410804\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 2.37860e6 0.251541 0.125770 0.992059i $$-0.459860\pi$$
0.125770 + 0.992059i $$0.459860\pi$$
$$618$$ 0 0
$$619$$ −1.60023e7 −1.67863 −0.839317 0.543642i $$-0.817045\pi$$
−0.839317 + 0.543642i $$0.817045\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 155918. 0.0160944
$$624$$ 0 0
$$625$$ 5.00302e6 0.512309
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −1.48374e7 −1.49531
$$630$$ 0 0
$$631$$ −1.23459e7 −1.23439 −0.617193 0.786812i $$-0.711730\pi$$
−0.617193 + 0.786812i $$0.711730\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −1.92753e7 −1.89699
$$636$$ 0 0
$$637$$ −1.84877e6 −0.180524
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 3.43755e6 0.330449 0.165224 0.986256i $$-0.447165\pi$$
0.165224 + 0.986256i $$0.447165\pi$$
$$642$$ 0 0
$$643$$ 1.62191e7 1.54703 0.773515 0.633778i $$-0.218497\pi$$
0.773515 + 0.633778i $$0.218497\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.19929e7 1.12632 0.563160 0.826348i $$-0.309585\pi$$
0.563160 + 0.826348i $$0.309585\pi$$
$$648$$ 0 0
$$649$$ −583440. −0.0543731
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −1.58009e6 −0.145011 −0.0725053 0.997368i $$-0.523099\pi$$
−0.0725053 + 0.997368i $$0.523099\pi$$
$$654$$ 0 0
$$655$$ −6.85862e6 −0.624645
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 6.98358e6 0.626419 0.313209 0.949684i $$-0.398596\pi$$
0.313209 + 0.949684i $$0.398596\pi$$
$$660$$ 0 0
$$661$$ 3.69602e6 0.329027 0.164513 0.986375i $$-0.447395\pi$$
0.164513 + 0.986375i $$0.447395\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 7.97759e6 0.699548
$$666$$ 0 0
$$667$$ 3.17837e6 0.276624
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −2.37130e6 −0.203320
$$672$$ 0 0
$$673$$ 1.84688e6 0.157182 0.0785908 0.996907i $$-0.474958\pi$$
0.0785908 + 0.996907i $$0.474958\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 7.68501e6 0.644426 0.322213 0.946667i $$-0.395573\pi$$
0.322213 + 0.946667i $$0.395573\pi$$
$$678$$ 0 0
$$679$$ 240786. 0.0200427
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 7.12180e6 0.584168 0.292084 0.956393i $$-0.405651\pi$$
0.292084 + 0.956393i $$0.405651\pi$$
$$684$$ 0 0
$$685$$ −8.85311e6 −0.720891
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 3.22014e6 0.258420
$$690$$ 0 0
$$691$$ 3.23787e6 0.257967 0.128983 0.991647i $$-0.458829\pi$$
0.128983 + 0.991647i $$0.458829\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −4.49282e6 −0.352823
$$696$$ 0 0
$$697$$ 6.59576e6 0.514260
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 7.39163e6 0.568127 0.284063 0.958805i $$-0.408317\pi$$
0.284063 + 0.958805i $$0.408317\pi$$
$$702$$ 0 0
$$703$$ 1.27094e7 0.969923
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 8.15135e6 0.613311
$$708$$ 0 0
$$709$$ −5.33361e6 −0.398479 −0.199240 0.979951i $$-0.563847\pi$$
−0.199240 + 0.979951i $$0.563847\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 3.64954e6 0.268852
$$714$$ 0 0
$$715$$ 3.76376e6 0.275332
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −1.14564e7 −0.826468 −0.413234 0.910625i $$-0.635601\pi$$
−0.413234 + 0.910625i $$0.635601\pi$$
$$720$$ 0 0
$$721$$ −7.70084e6 −0.551696
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −3.15133e7 −2.22663
$$726$$ 0 0
$$727$$ 2.49540e7 1.75107 0.875536 0.483153i $$-0.160508\pi$$
0.875536 + 0.483153i $$0.160508\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −1.09592e7 −0.758555
$$732$$ 0 0
$$733$$ −1.43398e7 −0.985789 −0.492894 0.870089i $$-0.664061\pi$$
−0.492894 + 0.870089i $$0.664061\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −72592.0 −0.00492289
$$738$$ 0 0
$$739$$ −922932. −0.0621668 −0.0310834 0.999517i $$-0.509896\pi$$
−0.0310834 + 0.999517i $$0.509896\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −9.38995e6 −0.624010 −0.312005 0.950081i $$-0.601001\pi$$
−0.312005 + 0.950081i $$0.601001\pi$$
$$744$$ 0 0
$$745$$ −1.16810e7 −0.771062
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −331436. −0.0215871
$$750$$ 0 0
$$751$$ 408032. 0.0263994 0.0131997 0.999913i $$-0.495798\pi$$
0.0131997 + 0.999913i $$0.495798\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −4.19518e7 −2.67845
$$756$$ 0 0
$$757$$ 2.59605e7 1.64654 0.823271 0.567649i $$-0.192147\pi$$
0.823271 + 0.567649i $$0.192147\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.83554e7 −1.14895 −0.574477 0.818521i $$-0.694794\pi$$
−0.574477 + 0.818521i $$0.694794\pi$$
$$762$$ 0 0
$$763$$ 8.74150e6 0.543594
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 8.63940e6 0.530268
$$768$$ 0 0
$$769$$ −747166. −0.0455618 −0.0227809 0.999740i $$-0.507252\pi$$
−0.0227809 + 0.999740i $$0.507252\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −2.02692e7 −1.22008 −0.610038 0.792372i $$-0.708846\pi$$
−0.610038 + 0.792372i $$0.708846\pi$$
$$774$$ 0 0
$$775$$ −3.61849e7 −2.16408
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −5.64978e6 −0.333571
$$780$$ 0 0
$$781$$ 973440. 0.0571060
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 1.50161e7 0.869729
$$786$$ 0 0
$$787$$ 4.69982e6 0.270486 0.135243 0.990812i $$-0.456819\pi$$
0.135243 + 0.990812i $$0.456819\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 2.21157e6 0.125678
$$792$$ 0 0
$$793$$ 3.51135e7 1.98286
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −584710. −0.0326058 −0.0163029 0.999867i $$-0.505190\pi$$
−0.0163029 + 0.999867i $$0.505190\pi$$
$$798$$ 0 0
$$799$$ 1.74701e6 0.0968117
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 2.41082e6 0.131940
$$804$$ 0 0
$$805$$ 2.65306e6 0.144297
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 1.64013e7 0.881061 0.440531 0.897738i $$-0.354790\pi$$
0.440531 + 0.897738i $$0.354790\pi$$
$$810$$ 0 0
$$811$$ 304948. 0.0162807 0.00814036 0.999967i $$-0.497409\pi$$
0.00814036 + 0.999967i $$0.497409\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 2.32417e7 1.22567
$$816$$ 0 0
$$817$$ 9.38744e6 0.492031
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −3.43428e7 −1.77819 −0.889095 0.457722i $$-0.848665\pi$$
−0.889095 + 0.457722i $$0.848665\pi$$
$$822$$ 0 0
$$823$$ −1.56684e7 −0.806351 −0.403176 0.915123i $$-0.632094\pi$$
−0.403176 + 0.915123i $$0.632094\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −2.96886e7 −1.50948 −0.754738 0.656026i $$-0.772236\pi$$
−0.754738 + 0.656026i $$0.772236\pi$$
$$828$$ 0 0
$$829$$ −2.30708e7 −1.16594 −0.582970 0.812494i $$-0.698110\pi$$
−0.582970 + 0.812494i $$0.698110\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 4.85482e6 0.242416
$$834$$ 0 0
$$835$$ 6.43419e7 3.19358
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 2.32642e7 1.14100 0.570498 0.821299i $$-0.306750\pi$$
0.570498 + 0.821299i $$0.306750\pi$$
$$840$$ 0 0
$$841$$ 9.93718e6 0.484477
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −2.08311e7 −1.00362
$$846$$ 0 0
$$847$$ −7.75900e6 −0.371619
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 4.22669e6 0.200067
$$852$$ 0 0
$$853$$ 1.91515e7 0.901219 0.450610 0.892721i $$-0.351207\pi$$
0.450610 + 0.892721i $$0.351207\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 5.34683e6 0.248682 0.124341 0.992240i $$-0.460318\pi$$
0.124341 + 0.992240i $$0.460318\pi$$
$$858$$ 0 0
$$859$$ −3.95858e7 −1.83045 −0.915223 0.402948i $$-0.867986\pi$$
−0.915223 + 0.402948i $$0.867986\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −2.50284e7 −1.14395 −0.571973 0.820272i $$-0.693822\pi$$
−0.571973 + 0.820272i $$0.693822\pi$$
$$864$$ 0 0
$$865$$ −5.73846e7 −2.60768
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −5.06605e6 −0.227573
$$870$$ 0 0
$$871$$ 1.07492e6 0.0480099
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −1.19111e7 −0.525935
$$876$$ 0 0
$$877$$ −5.02589e6 −0.220655 −0.110328 0.993895i $$-0.535190\pi$$
−0.110328 + 0.993895i $$0.535190\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 2.60490e7 1.13071 0.565356 0.824847i $$-0.308739\pi$$
0.565356 + 0.824847i $$0.308739\pi$$
$$882$$ 0 0
$$883$$ 6.82462e6 0.294562 0.147281 0.989095i $$-0.452948\pi$$
0.147281 + 0.989095i $$0.452948\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 2.33835e7 0.997931 0.498965 0.866622i $$-0.333713\pi$$
0.498965 + 0.866622i $$0.333713\pi$$
$$888$$ 0 0
$$889$$ 1.00477e7 0.426397
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −1.49645e6 −0.0627961
$$894$$ 0 0
$$895$$ −6.22517e7 −2.59773
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 3.49620e7 1.44277
$$900$$ 0 0
$$901$$ −8.45600e6 −0.347019
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −1.45352e7 −0.589930
$$906$$ 0 0
$$907$$ −3.95959e7 −1.59820 −0.799102 0.601196i $$-0.794691\pi$$
−0.799102 + 0.601196i $$0.794691\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −4.67570e6 −0.186660 −0.0933300 0.995635i $$-0.529751\pi$$
−0.0933300 + 0.995635i $$0.529751\pi$$
$$912$$ 0 0
$$913$$ −4.22386e6 −0.167700
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 3.57524e6 0.140405
$$918$$ 0 0
$$919$$ 4.92594e6 0.192398 0.0961990 0.995362i $$-0.469331\pi$$
0.0961990 + 0.995362i $$0.469331\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −1.44144e7 −0.556919
$$924$$ 0 0
$$925$$ −4.19073e7 −1.61041
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 3.23688e7 1.23052 0.615258 0.788326i $$-0.289052\pi$$
0.615258 + 0.788326i $$0.289052\pi$$
$$930$$ 0 0
$$931$$ −4.15853e6 −0.157241
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −9.88354e6 −0.369729
$$936$$ 0 0
$$937$$ −3.32337e7 −1.23660 −0.618301 0.785941i $$-0.712179\pi$$
−0.618301 + 0.785941i $$0.712179\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 2.66426e7 0.980852 0.490426 0.871483i $$-0.336841\pi$$
0.490426 + 0.871483i $$0.336841\pi$$
$$942$$ 0 0
$$943$$ −1.87891e6 −0.0688061
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 3.14663e7 1.14017 0.570086 0.821585i $$-0.306910\pi$$
0.570086 + 0.821585i $$0.306910\pi$$
$$948$$ 0 0
$$949$$ −3.56987e7 −1.28673
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 1.34516e7 0.479779 0.239890 0.970800i $$-0.422889\pi$$
0.239890 + 0.970800i $$0.422889\pi$$
$$954$$ 0 0
$$955$$ −4.57690e7 −1.62391
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 4.61492e6 0.162038
$$960$$ 0 0
$$961$$ 1.15157e7 0.402238
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −5.83313e7 −2.01643
$$966$$ 0 0
$$967$$ 2.84963e7 0.979992 0.489996 0.871725i $$-0.336998\pi$$
0.489996 + 0.871725i $$0.336998\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 1.81858e7 0.618990 0.309495 0.950901i $$-0.399840\pi$$
0.309495 + 0.950901i $$0.399840\pi$$
$$972$$ 0 0
$$973$$ 2.34200e6 0.0793059
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −3.20941e7 −1.07569 −0.537847 0.843042i $$-0.680762\pi$$
−0.537847 + 0.843042i $$0.680762\pi$$
$$978$$ 0 0
$$979$$ 165464. 0.00551756
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 1.56154e7 0.515429 0.257715 0.966221i $$-0.417031\pi$$
0.257715 + 0.966221i $$0.417031\pi$$
$$984$$ 0 0
$$985$$ −2.22376e7 −0.730293
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 3.12192e6 0.101492
$$990$$ 0 0
$$991$$ −4.84499e7 −1.56714 −0.783572 0.621301i $$-0.786605\pi$$
−0.783572 + 0.621301i $$0.786605\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 7.71778e6 0.247135
$$996$$ 0 0
$$997$$ −4.54336e7 −1.44757 −0.723784 0.690027i $$-0.757599\pi$$
−0.723784 + 0.690027i $$0.757599\pi$$
$$998$$ 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 1008.6.a.a.1.1 1
3.2 odd 2 336.6.a.i.1.1 1
4.3 odd 2 63.6.a.b.1.1 1
12.11 even 2 21.6.a.c.1.1 1
28.27 even 2 441.6.a.c.1.1 1
60.23 odd 4 525.6.d.c.274.1 2
60.47 odd 4 525.6.d.c.274.2 2
60.59 even 2 525.6.a.b.1.1 1
84.11 even 6 147.6.e.c.79.1 2
84.23 even 6 147.6.e.c.67.1 2
84.47 odd 6 147.6.e.d.67.1 2
84.59 odd 6 147.6.e.d.79.1 2
84.83 odd 2 147.6.a.f.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.a.c.1.1 1 12.11 even 2
63.6.a.b.1.1 1 4.3 odd 2
147.6.a.f.1.1 1 84.83 odd 2
147.6.e.c.67.1 2 84.23 even 6
147.6.e.c.79.1 2 84.11 even 6
147.6.e.d.67.1 2 84.47 odd 6
147.6.e.d.79.1 2 84.59 odd 6
336.6.a.i.1.1 1 3.2 odd 2
441.6.a.c.1.1 1 28.27 even 2
525.6.a.b.1.1 1 60.59 even 2
525.6.d.c.274.1 2 60.23 odd 4
525.6.d.c.274.2 2 60.47 odd 4
1008.6.a.a.1.1 1 1.1 even 1 trivial