# Properties

 Label 1008.6.a.b.1.1 Level $1008$ Weight $6$ Character 1008.1 Self dual yes Analytic conductor $161.667$ 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] = [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: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 14) 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)

 $$f(q)$$ $$=$$ $$q-84.0000 q^{5} -49.0000 q^{7} +O(q^{10})$$ $$q-84.0000 q^{5} -49.0000 q^{7} -336.000 q^{11} +584.000 q^{13} +1458.00 q^{17} -470.000 q^{19} -4200.00 q^{23} +3931.00 q^{25} -4866.00 q^{29} +7372.00 q^{31} +4116.00 q^{35} +14330.0 q^{37} -6222.00 q^{41} -3704.00 q^{43} -1812.00 q^{47} +2401.00 q^{49} +37242.0 q^{53} +28224.0 q^{55} +34302.0 q^{59} +24476.0 q^{61} -49056.0 q^{65} +17452.0 q^{67} +28224.0 q^{71} +3602.00 q^{73} +16464.0 q^{77} -42872.0 q^{79} -35202.0 q^{83} -122472. q^{85} -26730.0 q^{89} -28616.0 q^{91} +39480.0 q^{95} -16978.0 q^{97} +O(q^{100})$$

## 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
$$5$$ −84.0000 −1.50264 −0.751319 0.659939i $$-0.770582\pi$$
−0.751319 + 0.659939i $$0.770582\pi$$
$$6$$ 0 0
$$7$$ −49.0000 −0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −336.000 −0.837255 −0.418627 0.908158i $$-0.637489\pi$$
−0.418627 + 0.908158i $$0.637489\pi$$
$$12$$ 0 0
$$13$$ 584.000 0.958417 0.479208 0.877701i $$-0.340924\pi$$
0.479208 + 0.877701i $$0.340924\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1458.00 1.22359 0.611794 0.791017i $$-0.290448\pi$$
0.611794 + 0.791017i $$0.290448\pi$$
$$18$$ 0 0
$$19$$ −470.000 −0.298685 −0.149343 0.988786i $$-0.547716\pi$$
−0.149343 + 0.988786i $$0.547716\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4200.00 −1.65550 −0.827751 0.561096i $$-0.810380\pi$$
−0.827751 + 0.561096i $$0.810380\pi$$
$$24$$ 0 0
$$25$$ 3931.00 1.25792
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −4866.00 −1.07443 −0.537214 0.843446i $$-0.680523\pi$$
−0.537214 + 0.843446i $$0.680523\pi$$
$$30$$ 0 0
$$31$$ 7372.00 1.37778 0.688892 0.724864i $$-0.258097\pi$$
0.688892 + 0.724864i $$0.258097\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 4116.00 0.567944
$$36$$ 0 0
$$37$$ 14330.0 1.72085 0.860423 0.509581i $$-0.170200\pi$$
0.860423 + 0.509581i $$0.170200\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −6222.00 −0.578057 −0.289028 0.957321i $$-0.593332\pi$$
−0.289028 + 0.957321i $$0.593332\pi$$
$$42$$ 0 0
$$43$$ −3704.00 −0.305492 −0.152746 0.988265i $$-0.548812\pi$$
−0.152746 + 0.988265i $$0.548812\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −1812.00 −0.119650 −0.0598251 0.998209i $$-0.519054\pi$$
−0.0598251 + 0.998209i $$0.519054\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 37242.0 1.82114 0.910570 0.413355i $$-0.135643\pi$$
0.910570 + 0.413355i $$0.135643\pi$$
$$54$$ 0 0
$$55$$ 28224.0 1.25809
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 34302.0 1.28289 0.641445 0.767169i $$-0.278335\pi$$
0.641445 + 0.767169i $$0.278335\pi$$
$$60$$ 0 0
$$61$$ 24476.0 0.842201 0.421101 0.907014i $$-0.361644\pi$$
0.421101 + 0.907014i $$0.361644\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −49056.0 −1.44015
$$66$$ 0 0
$$67$$ 17452.0 0.474961 0.237481 0.971392i $$-0.423678\pi$$
0.237481 + 0.971392i $$0.423678\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 28224.0 0.664466 0.332233 0.943197i $$-0.392198\pi$$
0.332233 + 0.943197i $$0.392198\pi$$
$$72$$ 0 0
$$73$$ 3602.00 0.0791109 0.0395555 0.999217i $$-0.487406\pi$$
0.0395555 + 0.999217i $$0.487406\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 16464.0 0.316453
$$78$$ 0 0
$$79$$ −42872.0 −0.772869 −0.386435 0.922317i $$-0.626294\pi$$
−0.386435 + 0.922317i $$0.626294\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −35202.0 −0.560883 −0.280441 0.959871i $$-0.590481\pi$$
−0.280441 + 0.959871i $$0.590481\pi$$
$$84$$ 0 0
$$85$$ −122472. −1.83861
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −26730.0 −0.357704 −0.178852 0.983876i $$-0.557238\pi$$
−0.178852 + 0.983876i $$0.557238\pi$$
$$90$$ 0 0
$$91$$ −28616.0 −0.362248
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 39480.0 0.448816
$$96$$ 0 0
$$97$$ −16978.0 −0.183213 −0.0916067 0.995795i $$-0.529200\pi$$
−0.0916067 + 0.995795i $$0.529200\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −99204.0 −0.967667 −0.483833 0.875160i $$-0.660756\pi$$
−0.483833 + 0.875160i $$0.660756\pi$$
$$102$$ 0 0
$$103$$ 131644. 1.22267 0.611333 0.791373i $$-0.290634\pi$$
0.611333 + 0.791373i $$0.290634\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 48852.0 0.412499 0.206250 0.978499i $$-0.433874\pi$$
0.206250 + 0.978499i $$0.433874\pi$$
$$108$$ 0 0
$$109$$ −56374.0 −0.454478 −0.227239 0.973839i $$-0.572970\pi$$
−0.227239 + 0.973839i $$0.572970\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −8742.00 −0.0644043 −0.0322021 0.999481i $$-0.510252\pi$$
−0.0322021 + 0.999481i $$0.510252\pi$$
$$114$$ 0 0
$$115$$ 352800. 2.48762
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −71442.0 −0.462473
$$120$$ 0 0
$$121$$ −48155.0 −0.299005
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −67704.0 −0.387560
$$126$$ 0 0
$$127$$ −315992. −1.73847 −0.869234 0.494401i $$-0.835388\pi$$
−0.869234 + 0.494401i $$0.835388\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −24666.0 −0.125580 −0.0627900 0.998027i $$-0.520000\pi$$
−0.0627900 + 0.998027i $$0.520000\pi$$
$$132$$ 0 0
$$133$$ 23030.0 0.112892
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −303234. −1.38031 −0.690155 0.723662i $$-0.742458\pi$$
−0.690155 + 0.723662i $$0.742458\pi$$
$$138$$ 0 0
$$139$$ −250586. −1.10007 −0.550034 0.835142i $$-0.685385\pi$$
−0.550034 + 0.835142i $$0.685385\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −196224. −0.802439
$$144$$ 0 0
$$145$$ 408744. 1.61448
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 60594.0 0.223596 0.111798 0.993731i $$-0.464339\pi$$
0.111798 + 0.993731i $$0.464339\pi$$
$$150$$ 0 0
$$151$$ −124448. −0.444166 −0.222083 0.975028i $$-0.571286\pi$$
−0.222083 + 0.975028i $$0.571286\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −619248. −2.07031
$$156$$ 0 0
$$157$$ 76040.0 0.246203 0.123101 0.992394i $$-0.460716\pi$$
0.123101 + 0.992394i $$0.460716\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 205800. 0.625721
$$162$$ 0 0
$$163$$ −124256. −0.366310 −0.183155 0.983084i $$-0.558631\pi$$
−0.183155 + 0.983084i $$0.558631\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −72420.0 −0.200940 −0.100470 0.994940i $$-0.532035\pi$$
−0.100470 + 0.994940i $$0.532035\pi$$
$$168$$ 0 0
$$169$$ −30237.0 −0.0814370
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 441552. 1.12167 0.560837 0.827926i $$-0.310479\pi$$
0.560837 + 0.827926i $$0.310479\pi$$
$$174$$ 0 0
$$175$$ −192619. −0.475449
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −10692.0 −0.0249417 −0.0124709 0.999922i $$-0.503970\pi$$
−0.0124709 + 0.999922i $$0.503970\pi$$
$$180$$ 0 0
$$181$$ −546064. −1.23893 −0.619465 0.785024i $$-0.712651\pi$$
−0.619465 + 0.785024i $$0.712651\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1.20372e6 −2.58581
$$186$$ 0 0
$$187$$ −489888. −1.02445
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −575976. −1.14241 −0.571204 0.820808i $$-0.693523\pi$$
−0.571204 + 0.820808i $$0.693523\pi$$
$$192$$ 0 0
$$193$$ −413938. −0.799912 −0.399956 0.916534i $$-0.630975\pi$$
−0.399956 + 0.916534i $$0.630975\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 494946. 0.908641 0.454320 0.890838i $$-0.349882\pi$$
0.454320 + 0.890838i $$0.349882\pi$$
$$198$$ 0 0
$$199$$ −520364. −0.931482 −0.465741 0.884921i $$-0.654212\pi$$
−0.465741 + 0.884921i $$0.654212\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 238434. 0.406095
$$204$$ 0 0
$$205$$ 522648. 0.868610
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 157920. 0.250076
$$210$$ 0 0
$$211$$ −183284. −0.283412 −0.141706 0.989909i $$-0.545259\pi$$
−0.141706 + 0.989909i $$0.545259\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 311136. 0.459044
$$216$$ 0 0
$$217$$ −361228. −0.520753
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 851472. 1.17271
$$222$$ 0 0
$$223$$ 1.27746e6 1.72023 0.860115 0.510100i $$-0.170392\pi$$
0.860115 + 0.510100i $$0.170392\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −1.28764e6 −1.65856 −0.829279 0.558835i $$-0.811248\pi$$
−0.829279 + 0.558835i $$0.811248\pi$$
$$228$$ 0 0
$$229$$ 350936. 0.442221 0.221110 0.975249i $$-0.429032\pi$$
0.221110 + 0.975249i $$0.429032\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −836154. −1.00901 −0.504506 0.863408i $$-0.668325\pi$$
−0.504506 + 0.863408i $$0.668325\pi$$
$$234$$ 0 0
$$235$$ 152208. 0.179791
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 774336. 0.876869 0.438434 0.898763i $$-0.355533\pi$$
0.438434 + 0.898763i $$0.355533\pi$$
$$240$$ 0 0
$$241$$ −1.15285e6 −1.27859 −0.639293 0.768963i $$-0.720773\pi$$
−0.639293 + 0.768963i $$0.720773\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −201684. −0.214663
$$246$$ 0 0
$$247$$ −274480. −0.286265
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 1.35801e6 1.36056 0.680282 0.732951i $$-0.261858\pi$$
0.680282 + 0.732951i $$0.261858\pi$$
$$252$$ 0 0
$$253$$ 1.41120e6 1.38608
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 317742. 0.300083 0.150042 0.988680i $$-0.452059\pi$$
0.150042 + 0.988680i $$0.452059\pi$$
$$258$$ 0 0
$$259$$ −702170. −0.650418
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.05101e6 0.936951 0.468475 0.883477i $$-0.344804\pi$$
0.468475 + 0.883477i $$0.344804\pi$$
$$264$$ 0 0
$$265$$ −3.12833e6 −2.73651
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1.18958e6 −1.00234 −0.501169 0.865349i $$-0.667097\pi$$
−0.501169 + 0.865349i $$0.667097\pi$$
$$270$$ 0 0
$$271$$ 1.43008e6 1.18287 0.591435 0.806353i $$-0.298562\pi$$
0.591435 + 0.806353i $$0.298562\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.32082e6 −1.05320
$$276$$ 0 0
$$277$$ 63302.0 0.0495699 0.0247849 0.999693i $$-0.492110\pi$$
0.0247849 + 0.999693i $$0.492110\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 496614. 0.375192 0.187596 0.982246i $$-0.439930\pi$$
0.187596 + 0.982246i $$0.439930\pi$$
$$282$$ 0 0
$$283$$ 1.15842e6 0.859803 0.429902 0.902876i $$-0.358548\pi$$
0.429902 + 0.902876i $$0.358548\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 304878. 0.218485
$$288$$ 0 0
$$289$$ 705907. 0.497168
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.43886e6 −0.979151 −0.489575 0.871961i $$-0.662848\pi$$
−0.489575 + 0.871961i $$0.662848\pi$$
$$294$$ 0 0
$$295$$ −2.88137e6 −1.92772
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −2.45280e6 −1.58666
$$300$$ 0 0
$$301$$ 181496. 0.115465
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −2.05598e6 −1.26552
$$306$$ 0 0
$$307$$ 989098. 0.598954 0.299477 0.954104i $$-0.403188\pi$$
0.299477 + 0.954104i $$0.403188\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −2.22050e6 −1.30182 −0.650909 0.759155i $$-0.725612\pi$$
−0.650909 + 0.759155i $$0.725612\pi$$
$$312$$ 0 0
$$313$$ 2.33008e6 1.34434 0.672171 0.740396i $$-0.265362\pi$$
0.672171 + 0.740396i $$0.265362\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −427542. −0.238963 −0.119481 0.992836i $$-0.538123\pi$$
−0.119481 + 0.992836i $$0.538123\pi$$
$$318$$ 0 0
$$319$$ 1.63498e6 0.899569
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −685260. −0.365468
$$324$$ 0 0
$$325$$ 2.29570e6 1.20561
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 88788.0 0.0452235
$$330$$ 0 0
$$331$$ 396616. 0.198976 0.0994879 0.995039i $$-0.468280\pi$$
0.0994879 + 0.995039i $$0.468280\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −1.46597e6 −0.713695
$$336$$ 0 0
$$337$$ −3.21819e6 −1.54361 −0.771805 0.635860i $$-0.780646\pi$$
−0.771805 + 0.635860i $$0.780646\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −2.47699e6 −1.15356
$$342$$ 0 0
$$343$$ −117649. −0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 2.78018e6 1.23951 0.619755 0.784796i $$-0.287232\pi$$
0.619755 + 0.784796i $$0.287232\pi$$
$$348$$ 0 0
$$349$$ −338800. −0.148895 −0.0744475 0.997225i $$-0.523719\pi$$
−0.0744475 + 0.997225i $$0.523719\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 362046. 0.154642 0.0773209 0.997006i $$-0.475363\pi$$
0.0773209 + 0.997006i $$0.475363\pi$$
$$354$$ 0 0
$$355$$ −2.37082e6 −0.998451
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 876528. 0.358946 0.179473 0.983763i $$-0.442561\pi$$
0.179473 + 0.983763i $$0.442561\pi$$
$$360$$ 0 0
$$361$$ −2.25520e6 −0.910787
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −302568. −0.118875
$$366$$ 0 0
$$367$$ −2.98062e6 −1.15516 −0.577578 0.816335i $$-0.696002\pi$$
−0.577578 + 0.816335i $$0.696002\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −1.82486e6 −0.688326
$$372$$ 0 0
$$373$$ 3.91441e6 1.45678 0.728391 0.685162i $$-0.240268\pi$$
0.728391 + 0.685162i $$0.240268\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −2.84174e6 −1.02975
$$378$$ 0 0
$$379$$ −3.60661e6 −1.28974 −0.644868 0.764294i $$-0.723088\pi$$
−0.644868 + 0.764294i $$0.723088\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −2.66644e6 −0.928826 −0.464413 0.885619i $$-0.653735\pi$$
−0.464413 + 0.885619i $$0.653735\pi$$
$$384$$ 0 0
$$385$$ −1.38298e6 −0.475513
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 213366. 0.0714910 0.0357455 0.999361i $$-0.488619\pi$$
0.0357455 + 0.999361i $$0.488619\pi$$
$$390$$ 0 0
$$391$$ −6.12360e6 −2.02565
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 3.60125e6 1.16134
$$396$$ 0 0
$$397$$ −4.09408e6 −1.30371 −0.651854 0.758345i $$-0.726008\pi$$
−0.651854 + 0.758345i $$0.726008\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −942366. −0.292657 −0.146328 0.989236i $$-0.546746\pi$$
−0.146328 + 0.989236i $$0.546746\pi$$
$$402$$ 0 0
$$403$$ 4.30525e6 1.32049
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −4.81488e6 −1.44079
$$408$$ 0 0
$$409$$ −4.84561e6 −1.43232 −0.716160 0.697936i $$-0.754102\pi$$
−0.716160 + 0.697936i $$0.754102\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −1.68080e6 −0.484887
$$414$$ 0 0
$$415$$ 2.95697e6 0.842804
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −1.73485e6 −0.482754 −0.241377 0.970431i $$-0.577599\pi$$
−0.241377 + 0.970431i $$0.577599\pi$$
$$420$$ 0 0
$$421$$ −1.65145e6 −0.454109 −0.227055 0.973882i $$-0.572910\pi$$
−0.227055 + 0.973882i $$0.572910\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 5.73140e6 1.53918
$$426$$ 0 0
$$427$$ −1.19932e6 −0.318322
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 4.14360e6 1.07445 0.537223 0.843440i $$-0.319473\pi$$
0.537223 + 0.843440i $$0.319473\pi$$
$$432$$ 0 0
$$433$$ −3.03966e6 −0.779121 −0.389561 0.921001i $$-0.627373\pi$$
−0.389561 + 0.921001i $$0.627373\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 1.97400e6 0.494474
$$438$$ 0 0
$$439$$ −2.54271e6 −0.629703 −0.314852 0.949141i $$-0.601955\pi$$
−0.314852 + 0.949141i $$0.601955\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −2.43210e6 −0.588806 −0.294403 0.955681i $$-0.595121\pi$$
−0.294403 + 0.955681i $$0.595121\pi$$
$$444$$ 0 0
$$445$$ 2.24532e6 0.537500
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −1.82853e6 −0.428042 −0.214021 0.976829i $$-0.568656\pi$$
−0.214021 + 0.976829i $$0.568656\pi$$
$$450$$ 0 0
$$451$$ 2.09059e6 0.483981
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 2.40374e6 0.544327
$$456$$ 0 0
$$457$$ 1.58063e6 0.354030 0.177015 0.984208i $$-0.443356\pi$$
0.177015 + 0.984208i $$0.443356\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −5.09604e6 −1.11681 −0.558407 0.829567i $$-0.688587\pi$$
−0.558407 + 0.829567i $$0.688587\pi$$
$$462$$ 0 0
$$463$$ 7.02338e6 1.52263 0.761313 0.648384i $$-0.224555\pi$$
0.761313 + 0.648384i $$0.224555\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −4.24845e6 −0.901443 −0.450722 0.892665i $$-0.648833\pi$$
−0.450722 + 0.892665i $$0.648833\pi$$
$$468$$ 0 0
$$469$$ −855148. −0.179518
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 1.24454e6 0.255775
$$474$$ 0 0
$$475$$ −1.84757e6 −0.375722
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 559284. 0.111377 0.0556883 0.998448i $$-0.482265\pi$$
0.0556883 + 0.998448i $$0.482265\pi$$
$$480$$ 0 0
$$481$$ 8.36872e6 1.64929
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 1.42615e6 0.275303
$$486$$ 0 0
$$487$$ 1.32057e6 0.252312 0.126156 0.992010i $$-0.459736\pi$$
0.126156 + 0.992010i $$0.459736\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 6.27193e6 1.17408 0.587040 0.809558i $$-0.300293\pi$$
0.587040 + 0.809558i $$0.300293\pi$$
$$492$$ 0 0
$$493$$ −7.09463e6 −1.31466
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −1.38298e6 −0.251144
$$498$$ 0 0
$$499$$ 3.93785e6 0.707959 0.353979 0.935253i $$-0.384828\pi$$
0.353979 + 0.935253i $$0.384828\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −7.59830e6 −1.33905 −0.669525 0.742790i $$-0.733502\pi$$
−0.669525 + 0.742790i $$0.733502\pi$$
$$504$$ 0 0
$$505$$ 8.33314e6 1.45405
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 7.82664e6 1.33900 0.669501 0.742812i $$-0.266508\pi$$
0.669501 + 0.742812i $$0.266508\pi$$
$$510$$ 0 0
$$511$$ −176498. −0.0299011
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −1.10581e7 −1.83722
$$516$$ 0 0
$$517$$ 608832. 0.100178
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −8.94454e6 −1.44366 −0.721828 0.692072i $$-0.756698\pi$$
−0.721828 + 0.692072i $$0.756698\pi$$
$$522$$ 0 0
$$523$$ −4.07481e6 −0.651407 −0.325704 0.945472i $$-0.605601\pi$$
−0.325704 + 0.945472i $$0.605601\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 1.07484e7 1.68584
$$528$$ 0 0
$$529$$ 1.12037e7 1.74069
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −3.63365e6 −0.554019
$$534$$ 0 0
$$535$$ −4.10357e6 −0.619837
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −806736. −0.119608
$$540$$ 0 0
$$541$$ −1.18676e7 −1.74329 −0.871644 0.490140i $$-0.836946\pi$$
−0.871644 + 0.490140i $$0.836946\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 4.73542e6 0.682915
$$546$$ 0 0
$$547$$ 5.37801e6 0.768516 0.384258 0.923226i $$-0.374457\pi$$
0.384258 + 0.923226i $$0.374457\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 2.28702e6 0.320916
$$552$$ 0 0
$$553$$ 2.10073e6 0.292117
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 5.64878e6 0.771466 0.385733 0.922611i $$-0.373949\pi$$
0.385733 + 0.922611i $$0.373949\pi$$
$$558$$ 0 0
$$559$$ −2.16314e6 −0.292789
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 4.56407e6 0.606850 0.303425 0.952855i $$-0.401870\pi$$
0.303425 + 0.952855i $$0.401870\pi$$
$$564$$ 0 0
$$565$$ 734328. 0.0967763
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −8.00165e6 −1.03609 −0.518047 0.855352i $$-0.673341\pi$$
−0.518047 + 0.855352i $$0.673341\pi$$
$$570$$ 0 0
$$571$$ 1.37164e7 1.76055 0.880275 0.474464i $$-0.157358\pi$$
0.880275 + 0.474464i $$0.157358\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.65102e7 −2.08249
$$576$$ 0 0
$$577$$ 6.09797e6 0.762510 0.381255 0.924470i $$-0.375492\pi$$
0.381255 + 0.924470i $$0.375492\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 1.72490e6 0.211994
$$582$$ 0 0
$$583$$ −1.25133e7 −1.52476
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −8.08462e6 −0.968422 −0.484211 0.874951i $$-0.660893\pi$$
−0.484211 + 0.874951i $$0.660893\pi$$
$$588$$ 0 0
$$589$$ −3.46484e6 −0.411524
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.41575e6 −0.165330 −0.0826649 0.996577i $$-0.526343\pi$$
−0.0826649 + 0.996577i $$0.526343\pi$$
$$594$$ 0 0
$$595$$ 6.00113e6 0.694929
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 8.75460e6 0.996941 0.498470 0.866907i $$-0.333895\pi$$
0.498470 + 0.866907i $$0.333895\pi$$
$$600$$ 0 0
$$601$$ 8.70276e6 0.982813 0.491407 0.870930i $$-0.336483\pi$$
0.491407 + 0.870930i $$0.336483\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 4.04502e6 0.449296
$$606$$ 0 0
$$607$$ 1.69578e7 1.86809 0.934045 0.357157i $$-0.116254\pi$$
0.934045 + 0.357157i $$0.116254\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −1.05821e6 −0.114675
$$612$$ 0 0
$$613$$ 1.76743e7 1.89973 0.949866 0.312658i $$-0.101220\pi$$
0.949866 + 0.312658i $$0.101220\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 9.70636e6 1.02646 0.513232 0.858250i $$-0.328448\pi$$
0.513232 + 0.858250i $$0.328448\pi$$
$$618$$ 0 0
$$619$$ −1.48739e7 −1.56027 −0.780133 0.625613i $$-0.784849\pi$$
−0.780133 + 0.625613i $$0.784849\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 1.30977e6 0.135199
$$624$$ 0 0
$$625$$ −6.59724e6 −0.675557
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 2.08931e7 2.10561
$$630$$ 0 0
$$631$$ −1.26353e7 −1.26331 −0.631656 0.775248i $$-0.717625\pi$$
−0.631656 + 0.775248i $$0.717625\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 2.65433e7 2.61229
$$636$$ 0 0
$$637$$ 1.40218e6 0.136917
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −6.23398e6 −0.599267 −0.299634 0.954054i $$-0.596864\pi$$
−0.299634 + 0.954054i $$0.596864\pi$$
$$642$$ 0 0
$$643$$ −1.06874e7 −1.01940 −0.509701 0.860352i $$-0.670244\pi$$
−0.509701 + 0.860352i $$0.670244\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.83258e7 1.72109 0.860544 0.509376i $$-0.170124\pi$$
0.860544 + 0.509376i $$0.170124\pi$$
$$648$$ 0 0
$$649$$ −1.15255e7 −1.07411
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 7.28857e6 0.668897 0.334448 0.942414i $$-0.391450\pi$$
0.334448 + 0.942414i $$0.391450\pi$$
$$654$$ 0 0
$$655$$ 2.07194e6 0.188701
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 4.54337e6 0.407534 0.203767 0.979019i $$-0.434681\pi$$
0.203767 + 0.979019i $$0.434681\pi$$
$$660$$ 0 0
$$661$$ −2.10021e7 −1.86964 −0.934821 0.355120i $$-0.884440\pi$$
−0.934821 + 0.355120i $$0.884440\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −1.93452e6 −0.169636
$$666$$ 0 0
$$667$$ 2.04372e7 1.77872
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −8.22394e6 −0.705137
$$672$$ 0 0
$$673$$ 3.46923e6 0.295253 0.147627 0.989043i $$-0.452837\pi$$
0.147627 + 0.989043i $$0.452837\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 1.80916e7 1.51707 0.758536 0.651631i $$-0.225915\pi$$
0.758536 + 0.651631i $$0.225915\pi$$
$$678$$ 0 0
$$679$$ 831922. 0.0692481
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 4.67752e6 0.383675 0.191838 0.981427i $$-0.438555\pi$$
0.191838 + 0.981427i $$0.438555\pi$$
$$684$$ 0 0
$$685$$ 2.54717e7 2.07411
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 2.17493e7 1.74541
$$690$$ 0 0
$$691$$ −1.68960e7 −1.34614 −0.673069 0.739579i $$-0.735024\pi$$
−0.673069 + 0.739579i $$0.735024\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 2.10492e7 1.65300
$$696$$ 0 0
$$697$$ −9.07168e6 −0.707303
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −2.40964e6 −0.185207 −0.0926035 0.995703i $$-0.529519\pi$$
−0.0926035 + 0.995703i $$0.529519\pi$$
$$702$$ 0 0
$$703$$ −6.73510e6 −0.513991
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 4.86100e6 0.365744
$$708$$ 0 0
$$709$$ −5.77010e6 −0.431090 −0.215545 0.976494i $$-0.569153\pi$$
−0.215545 + 0.976494i $$0.569153\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −3.09624e7 −2.28092
$$714$$ 0 0
$$715$$ 1.64828e7 1.20578
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −1.43716e7 −1.03677 −0.518385 0.855147i $$-0.673467\pi$$
−0.518385 + 0.855147i $$0.673467\pi$$
$$720$$ 0 0
$$721$$ −6.45056e6 −0.462124
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1.91282e7 −1.35154
$$726$$ 0 0
$$727$$ 1.40705e7 0.987353 0.493676 0.869646i $$-0.335653\pi$$
0.493676 + 0.869646i $$0.335653\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −5.40043e6 −0.373796
$$732$$ 0 0
$$733$$ −3.75000e6 −0.257793 −0.128897 0.991658i $$-0.541144\pi$$
−0.128897 + 0.991658i $$0.541144\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −5.86387e6 −0.397664
$$738$$ 0 0
$$739$$ −2.61318e7 −1.76019 −0.880093 0.474802i $$-0.842520\pi$$
−0.880093 + 0.474802i $$0.842520\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −159072. −0.0105711 −0.00528557 0.999986i $$-0.501682\pi$$
−0.00528557 + 0.999986i $$0.501682\pi$$
$$744$$ 0 0
$$745$$ −5.08990e6 −0.335984
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −2.39375e6 −0.155910
$$750$$ 0 0
$$751$$ 2.65311e7 1.71654 0.858272 0.513196i $$-0.171539\pi$$
0.858272 + 0.513196i $$0.171539\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 1.04536e7 0.667421
$$756$$ 0 0
$$757$$ −1.52032e7 −0.964260 −0.482130 0.876100i $$-0.660137\pi$$
−0.482130 + 0.876100i $$0.660137\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −4.71380e6 −0.295059 −0.147530 0.989058i $$-0.547132\pi$$
−0.147530 + 0.989058i $$0.547132\pi$$
$$762$$ 0 0
$$763$$ 2.76233e6 0.171776
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 2.00324e7 1.22954
$$768$$ 0 0
$$769$$ −1.58977e6 −0.0969434 −0.0484717 0.998825i $$-0.515435\pi$$
−0.0484717 + 0.998825i $$0.515435\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 9.69095e6 0.583334 0.291667 0.956520i $$-0.405790\pi$$
0.291667 + 0.956520i $$0.405790\pi$$
$$774$$ 0 0
$$775$$ 2.89793e7 1.73314
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 2.92434e6 0.172657
$$780$$ 0 0
$$781$$ −9.48326e6 −0.556327
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −6.38736e6 −0.369954
$$786$$ 0 0
$$787$$ 1.57170e6 0.0904549 0.0452275 0.998977i $$-0.485599\pi$$
0.0452275 + 0.998977i $$0.485599\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 428358. 0.0243425
$$792$$ 0 0
$$793$$ 1.42940e7 0.807180
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 2.25298e6 0.125635 0.0628175 0.998025i $$-0.479991\pi$$
0.0628175 + 0.998025i $$0.479991\pi$$
$$798$$ 0 0
$$799$$ −2.64190e6 −0.146403
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −1.21027e6 −0.0662360
$$804$$ 0 0
$$805$$ −1.72872e7 −0.940232
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 2.37938e7 1.27818 0.639090 0.769132i $$-0.279311\pi$$
0.639090 + 0.769132i $$0.279311\pi$$
$$810$$ 0 0
$$811$$ −5.32300e6 −0.284187 −0.142093 0.989853i $$-0.545383\pi$$
−0.142093 + 0.989853i $$0.545383\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 1.04375e7 0.550431
$$816$$ 0 0
$$817$$ 1.74088e6 0.0912460
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −1.48802e7 −0.770464 −0.385232 0.922820i $$-0.625879\pi$$
−0.385232 + 0.922820i $$0.625879\pi$$
$$822$$ 0 0
$$823$$ −2.00601e7 −1.03236 −0.516182 0.856479i $$-0.672647\pi$$
−0.516182 + 0.856479i $$0.672647\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 1.21539e7 0.617949 0.308975 0.951070i $$-0.400014\pi$$
0.308975 + 0.951070i $$0.400014\pi$$
$$828$$ 0 0
$$829$$ 3.21197e7 1.62325 0.811625 0.584179i $$-0.198583\pi$$
0.811625 + 0.584179i $$0.198583\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 3.50066e6 0.174798
$$834$$ 0 0
$$835$$ 6.08328e6 0.301941
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −1.01320e6 −0.0496922 −0.0248461 0.999691i $$-0.507910\pi$$
−0.0248461 + 0.999691i $$0.507910\pi$$
$$840$$ 0 0
$$841$$ 3.16681e6 0.154394
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 2.53991e6 0.122370
$$846$$ 0 0
$$847$$ 2.35960e6 0.113013
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −6.01860e7 −2.84886
$$852$$ 0 0
$$853$$ 234824. 0.0110502 0.00552510 0.999985i $$-0.498241\pi$$
0.00552510 + 0.999985i $$0.498241\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −2.83802e7 −1.31997 −0.659985 0.751279i $$-0.729437\pi$$
−0.659985 + 0.751279i $$0.729437\pi$$
$$858$$ 0 0
$$859$$ −4.00081e7 −1.84997 −0.924986 0.380001i $$-0.875924\pi$$
−0.924986 + 0.380001i $$0.875924\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −2.08030e7 −0.950823 −0.475411 0.879764i $$-0.657701\pi$$
−0.475411 + 0.879764i $$0.657701\pi$$
$$864$$ 0 0
$$865$$ −3.70904e7 −1.68547
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 1.44050e7 0.647088
$$870$$ 0 0
$$871$$ 1.01920e7 0.455211
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 3.31750e6 0.146484
$$876$$ 0 0
$$877$$ 3.03559e7 1.33273 0.666367 0.745624i $$-0.267848\pi$$
0.666367 + 0.745624i $$0.267848\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 2.58936e7 1.12396 0.561981 0.827150i $$-0.310039\pi$$
0.561981 + 0.827150i $$0.310039\pi$$
$$882$$ 0 0
$$883$$ 1.88813e7 0.814950 0.407475 0.913216i $$-0.366409\pi$$
0.407475 + 0.913216i $$0.366409\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −2.34431e7 −1.00048 −0.500238 0.865888i $$-0.666754\pi$$
−0.500238 + 0.865888i $$0.666754\pi$$
$$888$$ 0 0
$$889$$ 1.54836e7 0.657079
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 851640. 0.0357378
$$894$$ 0 0
$$895$$ 898128. 0.0374784
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −3.58722e7 −1.48033
$$900$$ 0 0
$$901$$ 5.42988e7 2.22833
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 4.58694e7 1.86166
$$906$$ 0 0
$$907$$ 5.60873e6 0.226384 0.113192 0.993573i $$-0.463892\pi$$
0.113192 + 0.993573i $$0.463892\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 2.16215e7 0.863156 0.431578 0.902076i $$-0.357957\pi$$
0.431578 + 0.902076i $$0.357957\pi$$
$$912$$ 0 0
$$913$$ 1.18279e7 0.469602
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 1.20863e6 0.0474648
$$918$$ 0 0
$$919$$ −4.51695e7 −1.76424 −0.882119 0.471028i $$-0.843883\pi$$
−0.882119 + 0.471028i $$0.843883\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 1.64828e7 0.636835
$$924$$ 0 0
$$925$$ 5.63312e7 2.16469
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 2.28729e7 0.869524 0.434762 0.900545i $$-0.356832\pi$$
0.434762 + 0.900545i $$0.356832\pi$$
$$930$$ 0 0
$$931$$ −1.12847e6 −0.0426693
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 4.11506e7 1.53938
$$936$$ 0 0
$$937$$ −1.79616e7 −0.668336 −0.334168 0.942514i $$-0.608455\pi$$
−0.334168 + 0.942514i $$0.608455\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 1.79697e7 0.661558 0.330779 0.943708i $$-0.392689\pi$$
0.330779 + 0.943708i $$0.392689\pi$$
$$942$$ 0 0
$$943$$ 2.61324e7 0.956974
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 4.32115e7 1.56576 0.782879 0.622174i $$-0.213750\pi$$
0.782879 + 0.622174i $$0.213750\pi$$
$$948$$ 0 0
$$949$$ 2.10357e6 0.0758213
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 7.50965e6 0.267848 0.133924 0.990992i $$-0.457242\pi$$
0.133924 + 0.990992i $$0.457242\pi$$
$$954$$ 0 0
$$955$$ 4.83820e7 1.71662
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 1.48585e7 0.521708
$$960$$ 0 0
$$961$$ 2.57172e7 0.898288
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 3.47708e7 1.20198
$$966$$ 0 0
$$967$$ 1.69305e7 0.582242 0.291121 0.956686i $$-0.405972\pi$$
0.291121 + 0.956686i $$0.405972\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 2.86144e7 0.973949 0.486974 0.873416i $$-0.338101\pi$$
0.486974 + 0.873416i $$0.338101\pi$$
$$972$$ 0 0
$$973$$ 1.22787e7 0.415787
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −3.69445e7 −1.23826 −0.619132 0.785287i $$-0.712515\pi$$
−0.619132 + 0.785287i $$0.712515\pi$$
$$978$$ 0 0
$$979$$ 8.98128e6 0.299489
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −3.88787e7 −1.28330 −0.641650 0.766998i $$-0.721750\pi$$
−0.641650 + 0.766998i $$0.721750\pi$$
$$984$$ 0 0
$$985$$ −4.15755e7 −1.36536
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 1.55568e7 0.505743
$$990$$ 0 0
$$991$$ −2.49212e7 −0.806092 −0.403046 0.915180i $$-0.632049\pi$$
−0.403046 + 0.915180i $$0.632049\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 4.37106e7 1.39968
$$996$$ 0 0
$$997$$ 1.01956e7 0.324845 0.162422 0.986721i $$-0.448069\pi$$
0.162422 + 0.986721i $$0.448069\pi$$
$$998$$ 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.b.1.1 1
3.2 odd 2 112.6.a.c.1.1 1
4.3 odd 2 126.6.a.f.1.1 1
12.11 even 2 14.6.a.a.1.1 1
21.20 even 2 784.6.a.i.1.1 1
24.5 odd 2 448.6.a.l.1.1 1
24.11 even 2 448.6.a.e.1.1 1
28.27 even 2 882.6.a.x.1.1 1
60.23 odd 4 350.6.c.d.99.2 2
60.47 odd 4 350.6.c.d.99.1 2
60.59 even 2 350.6.a.i.1.1 1
84.11 even 6 98.6.c.c.79.1 2
84.23 even 6 98.6.c.c.67.1 2
84.47 odd 6 98.6.c.d.67.1 2
84.59 odd 6 98.6.c.d.79.1 2
84.83 odd 2 98.6.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
14.6.a.a.1.1 1 12.11 even 2
98.6.a.a.1.1 1 84.83 odd 2
98.6.c.c.67.1 2 84.23 even 6
98.6.c.c.79.1 2 84.11 even 6
98.6.c.d.67.1 2 84.47 odd 6
98.6.c.d.79.1 2 84.59 odd 6
112.6.a.c.1.1 1 3.2 odd 2
126.6.a.f.1.1 1 4.3 odd 2
350.6.a.i.1.1 1 60.59 even 2
350.6.c.d.99.1 2 60.47 odd 4
350.6.c.d.99.2 2 60.23 odd 4
448.6.a.e.1.1 1 24.11 even 2
448.6.a.l.1.1 1 24.5 odd 2
784.6.a.i.1.1 1 21.20 even 2
882.6.a.x.1.1 1 28.27 even 2
1008.6.a.b.1.1 1 1.1 even 1 trivial