# Properties

 Label 1008.6.a.v.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 168) 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)

 $$f(q)$$ $$=$$ $$q+38.0000 q^{5} +49.0000 q^{7} +O(q^{10})$$ $$q+38.0000 q^{5} +49.0000 q^{7} +600.000 q^{11} -674.000 q^{13} -78.0000 q^{17} +916.000 q^{19} -4604.00 q^{23} -1681.00 q^{25} +6810.00 q^{29} -7912.00 q^{31} +1862.00 q^{35} -9274.00 q^{37} +242.000 q^{41} -1116.00 q^{43} -28312.0 q^{47} +2401.00 q^{49} -10230.0 q^{53} +22800.0 q^{55} -4108.00 q^{59} +15878.0 q^{61} -25612.0 q^{65} +67668.0 q^{67} -67492.0 q^{71} +1106.00 q^{73} +29400.0 q^{77} -84152.0 q^{79} -2908.00 q^{83} -2964.00 q^{85} +8322.00 q^{89} -33026.0 q^{91} +34808.0 q^{95} +130810. q^{97} +O(q^{100})$$

## 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
$$5$$ 38.0000 0.679765 0.339882 0.940468i $$-0.389613\pi$$
0.339882 + 0.940468i $$0.389613\pi$$
$$6$$ 0 0
$$7$$ 49.0000 0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 600.000 1.49510 0.747549 0.664207i $$-0.231231\pi$$
0.747549 + 0.664207i $$0.231231\pi$$
$$12$$ 0 0
$$13$$ −674.000 −1.10612 −0.553059 0.833142i $$-0.686540\pi$$
−0.553059 + 0.833142i $$0.686540\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −78.0000 −0.0654594 −0.0327297 0.999464i $$-0.510420\pi$$
−0.0327297 + 0.999464i $$0.510420\pi$$
$$18$$ 0 0
$$19$$ 916.000 0.582119 0.291059 0.956705i $$-0.405992\pi$$
0.291059 + 0.956705i $$0.405992\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4604.00 −1.81475 −0.907373 0.420327i $$-0.861915\pi$$
−0.907373 + 0.420327i $$0.861915\pi$$
$$24$$ 0 0
$$25$$ −1681.00 −0.537920
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 6810.00 1.50367 0.751834 0.659352i $$-0.229169\pi$$
0.751834 + 0.659352i $$0.229169\pi$$
$$30$$ 0 0
$$31$$ −7912.00 −1.47871 −0.739353 0.673318i $$-0.764869\pi$$
−0.739353 + 0.673318i $$0.764869\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 1862.00 0.256927
$$36$$ 0 0
$$37$$ −9274.00 −1.11369 −0.556843 0.830618i $$-0.687988\pi$$
−0.556843 + 0.830618i $$0.687988\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 242.000 0.0224831 0.0112415 0.999937i $$-0.496422\pi$$
0.0112415 + 0.999937i $$0.496422\pi$$
$$42$$ 0 0
$$43$$ −1116.00 −0.0920435 −0.0460217 0.998940i $$-0.514654\pi$$
−0.0460217 + 0.998940i $$0.514654\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −28312.0 −1.86950 −0.934751 0.355304i $$-0.884377\pi$$
−0.934751 + 0.355304i $$0.884377\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −10230.0 −0.500249 −0.250124 0.968214i $$-0.580472\pi$$
−0.250124 + 0.968214i $$0.580472\pi$$
$$54$$ 0 0
$$55$$ 22800.0 1.01631
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −4108.00 −0.153639 −0.0768193 0.997045i $$-0.524476\pi$$
−0.0768193 + 0.997045i $$0.524476\pi$$
$$60$$ 0 0
$$61$$ 15878.0 0.546350 0.273175 0.961964i $$-0.411926\pi$$
0.273175 + 0.961964i $$0.411926\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −25612.0 −0.751900
$$66$$ 0 0
$$67$$ 67668.0 1.84160 0.920802 0.390030i $$-0.127535\pi$$
0.920802 + 0.390030i $$0.127535\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −67492.0 −1.58894 −0.794468 0.607306i $$-0.792250\pi$$
−0.794468 + 0.607306i $$0.792250\pi$$
$$72$$ 0 0
$$73$$ 1106.00 0.0242911 0.0121456 0.999926i $$-0.496134\pi$$
0.0121456 + 0.999926i $$0.496134\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 29400.0 0.565094
$$78$$ 0 0
$$79$$ −84152.0 −1.51704 −0.758519 0.651650i $$-0.774077\pi$$
−0.758519 + 0.651650i $$0.774077\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −2908.00 −0.0463339 −0.0231670 0.999732i $$-0.507375\pi$$
−0.0231670 + 0.999732i $$0.507375\pi$$
$$84$$ 0 0
$$85$$ −2964.00 −0.0444970
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 8322.00 0.111366 0.0556830 0.998448i $$-0.482266\pi$$
0.0556830 + 0.998448i $$0.482266\pi$$
$$90$$ 0 0
$$91$$ −33026.0 −0.418073
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 34808.0 0.395704
$$96$$ 0 0
$$97$$ 130810. 1.41160 0.705800 0.708411i $$-0.250588\pi$$
0.705800 + 0.708411i $$0.250588\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −159794. −1.55868 −0.779340 0.626601i $$-0.784446\pi$$
−0.779340 + 0.626601i $$0.784446\pi$$
$$102$$ 0 0
$$103$$ 91440.0 0.849265 0.424632 0.905366i $$-0.360403\pi$$
0.424632 + 0.905366i $$0.360403\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −139480. −1.17775 −0.588874 0.808225i $$-0.700429\pi$$
−0.588874 + 0.808225i $$0.700429\pi$$
$$108$$ 0 0
$$109$$ 141758. 1.14283 0.571415 0.820662i $$-0.306395\pi$$
0.571415 + 0.820662i $$0.306395\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 81742.0 0.602212 0.301106 0.953591i $$-0.402644\pi$$
0.301106 + 0.953591i $$0.402644\pi$$
$$114$$ 0 0
$$115$$ −174952. −1.23360
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −3822.00 −0.0247413
$$120$$ 0 0
$$121$$ 198949. 1.23532
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −182628. −1.04542
$$126$$ 0 0
$$127$$ −90488.0 −0.497831 −0.248915 0.968525i $$-0.580074\pi$$
−0.248915 + 0.968525i $$0.580074\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 187476. 0.954481 0.477241 0.878773i $$-0.341637\pi$$
0.477241 + 0.878773i $$0.341637\pi$$
$$132$$ 0 0
$$133$$ 44884.0 0.220020
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −168482. −0.766924 −0.383462 0.923557i $$-0.625268\pi$$
−0.383462 + 0.923557i $$0.625268\pi$$
$$138$$ 0 0
$$139$$ −668.000 −0.00293251 −0.00146625 0.999999i $$-0.500467\pi$$
−0.00146625 + 0.999999i $$0.500467\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −404400. −1.65375
$$144$$ 0 0
$$145$$ 258780. 1.02214
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 300618. 1.10930 0.554650 0.832084i $$-0.312852\pi$$
0.554650 + 0.832084i $$0.312852\pi$$
$$150$$ 0 0
$$151$$ −359032. −1.28142 −0.640709 0.767784i $$-0.721359\pi$$
−0.640709 + 0.767784i $$0.721359\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −300656. −1.00517
$$156$$ 0 0
$$157$$ 110822. 0.358820 0.179410 0.983774i $$-0.442581\pi$$
0.179410 + 0.983774i $$0.442581\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −225596. −0.685909
$$162$$ 0 0
$$163$$ −372380. −1.09779 −0.548893 0.835893i $$-0.684950\pi$$
−0.548893 + 0.835893i $$0.684950\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −109600. −0.304102 −0.152051 0.988373i $$-0.548588\pi$$
−0.152051 + 0.988373i $$0.548588\pi$$
$$168$$ 0 0
$$169$$ 82983.0 0.223497
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 388598. 0.987155 0.493577 0.869702i $$-0.335689\pi$$
0.493577 + 0.869702i $$0.335689\pi$$
$$174$$ 0 0
$$175$$ −82369.0 −0.203315
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −241656. −0.563722 −0.281861 0.959455i $$-0.590952\pi$$
−0.281861 + 0.959455i $$0.590952\pi$$
$$180$$ 0 0
$$181$$ 190854. 0.433017 0.216508 0.976281i $$-0.430533\pi$$
0.216508 + 0.976281i $$0.430533\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −352412. −0.757044
$$186$$ 0 0
$$187$$ −46800.0 −0.0978683
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 253300. 0.502402 0.251201 0.967935i $$-0.419174\pi$$
0.251201 + 0.967935i $$0.419174\pi$$
$$192$$ 0 0
$$193$$ −712302. −1.37648 −0.688242 0.725482i $$-0.741617\pi$$
−0.688242 + 0.725482i $$0.741617\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 107194. 0.196791 0.0983954 0.995147i $$-0.468629\pi$$
0.0983954 + 0.995147i $$0.468629\pi$$
$$198$$ 0 0
$$199$$ 956952. 1.71300 0.856500 0.516147i $$-0.172634\pi$$
0.856500 + 0.516147i $$0.172634\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 333690. 0.568333
$$204$$ 0 0
$$205$$ 9196.00 0.0152832
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 549600. 0.870324
$$210$$ 0 0
$$211$$ 320700. 0.495899 0.247949 0.968773i $$-0.420243\pi$$
0.247949 + 0.968773i $$0.420243\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −42408.0 −0.0625679
$$216$$ 0 0
$$217$$ −387688. −0.558899
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 52572.0 0.0724059
$$222$$ 0 0
$$223$$ −1.06840e6 −1.43870 −0.719352 0.694645i $$-0.755561\pi$$
−0.719352 + 0.694645i $$0.755561\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −806820. −1.03923 −0.519615 0.854400i $$-0.673925\pi$$
−0.519615 + 0.854400i $$0.673925\pi$$
$$228$$ 0 0
$$229$$ 1.21661e6 1.53308 0.766539 0.642198i $$-0.221977\pi$$
0.766539 + 0.642198i $$0.221977\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −214722. −0.259112 −0.129556 0.991572i $$-0.541355\pi$$
−0.129556 + 0.991572i $$0.541355\pi$$
$$234$$ 0 0
$$235$$ −1.07586e6 −1.27082
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −615780. −0.697318 −0.348659 0.937250i $$-0.613363\pi$$
−0.348659 + 0.937250i $$0.613363\pi$$
$$240$$ 0 0
$$241$$ −995590. −1.10418 −0.552088 0.833786i $$-0.686169\pi$$
−0.552088 + 0.833786i $$0.686169\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 91238.0 0.0971092
$$246$$ 0 0
$$247$$ −617384. −0.643892
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −169340. −0.169658 −0.0848292 0.996396i $$-0.527034\pi$$
−0.0848292 + 0.996396i $$0.527034\pi$$
$$252$$ 0 0
$$253$$ −2.76240e6 −2.71322
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1.67825e6 −1.58498 −0.792488 0.609887i $$-0.791215\pi$$
−0.792488 + 0.609887i $$0.791215\pi$$
$$258$$ 0 0
$$259$$ −454426. −0.420934
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −1.77507e6 −1.58243 −0.791217 0.611535i $$-0.790552\pi$$
−0.791217 + 0.611535i $$0.790552\pi$$
$$264$$ 0 0
$$265$$ −388740. −0.340051
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 15646.0 0.0131833 0.00659163 0.999978i $$-0.497902\pi$$
0.00659163 + 0.999978i $$0.497902\pi$$
$$270$$ 0 0
$$271$$ 635672. 0.525787 0.262894 0.964825i $$-0.415323\pi$$
0.262894 + 0.964825i $$0.415323\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.00860e6 −0.804243
$$276$$ 0 0
$$277$$ −92218.0 −0.0722131 −0.0361066 0.999348i $$-0.511496\pi$$
−0.0361066 + 0.999348i $$0.511496\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.15678e6 0.873948 0.436974 0.899474i $$-0.356050\pi$$
0.436974 + 0.899474i $$0.356050\pi$$
$$282$$ 0 0
$$283$$ −1.97380e6 −1.46500 −0.732498 0.680770i $$-0.761645\pi$$
−0.732498 + 0.680770i $$0.761645\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 11858.0 0.00849780
$$288$$ 0 0
$$289$$ −1.41377e6 −0.995715
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 113966. 0.0775544 0.0387772 0.999248i $$-0.487654\pi$$
0.0387772 + 0.999248i $$0.487654\pi$$
$$294$$ 0 0
$$295$$ −156104. −0.104438
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 3.10310e6 2.00732
$$300$$ 0 0
$$301$$ −54684.0 −0.0347892
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 603364. 0.371390
$$306$$ 0 0
$$307$$ −2.18500e6 −1.32314 −0.661571 0.749883i $$-0.730110\pi$$
−0.661571 + 0.749883i $$0.730110\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −365520. −0.214294 −0.107147 0.994243i $$-0.534172\pi$$
−0.107147 + 0.994243i $$0.534172\pi$$
$$312$$ 0 0
$$313$$ 1.24550e6 0.718592 0.359296 0.933224i $$-0.383017\pi$$
0.359296 + 0.933224i $$0.383017\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −1.79646e6 −1.00408 −0.502042 0.864843i $$-0.667418\pi$$
−0.502042 + 0.864843i $$0.667418\pi$$
$$318$$ 0 0
$$319$$ 4.08600e6 2.24813
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −71448.0 −0.0381052
$$324$$ 0 0
$$325$$ 1.13299e6 0.595003
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −1.38729e6 −0.706605
$$330$$ 0 0
$$331$$ −1.55840e6 −0.781822 −0.390911 0.920428i $$-0.627840\pi$$
−0.390911 + 0.920428i $$0.627840\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 2.57138e6 1.25186
$$336$$ 0 0
$$337$$ −1.33472e6 −0.640199 −0.320099 0.947384i $$-0.603716\pi$$
−0.320099 + 0.947384i $$0.603716\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −4.74720e6 −2.21081
$$342$$ 0 0
$$343$$ 117649. 0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 3.56086e6 1.58757 0.793783 0.608201i $$-0.208109\pi$$
0.793783 + 0.608201i $$0.208109\pi$$
$$348$$ 0 0
$$349$$ −1.60451e6 −0.705144 −0.352572 0.935785i $$-0.614693\pi$$
−0.352572 + 0.935785i $$0.614693\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 384290. 0.164143 0.0820715 0.996626i $$-0.473846\pi$$
0.0820715 + 0.996626i $$0.473846\pi$$
$$354$$ 0 0
$$355$$ −2.56470e6 −1.08010
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −500532. −0.204973 −0.102486 0.994734i $$-0.532680\pi$$
−0.102486 + 0.994734i $$0.532680\pi$$
$$360$$ 0 0
$$361$$ −1.63704e6 −0.661138
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 42028.0 0.0165123
$$366$$ 0 0
$$367$$ 4.13210e6 1.60142 0.800710 0.599052i $$-0.204456\pi$$
0.800710 + 0.599052i $$0.204456\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −501270. −0.189076
$$372$$ 0 0
$$373$$ 3.41287e6 1.27013 0.635064 0.772459i $$-0.280974\pi$$
0.635064 + 0.772459i $$0.280974\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4.58994e6 −1.66324
$$378$$ 0 0
$$379$$ 3.16959e6 1.13346 0.566728 0.823905i $$-0.308209\pi$$
0.566728 + 0.823905i $$0.308209\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −5.07848e6 −1.76904 −0.884518 0.466506i $$-0.845513\pi$$
−0.884518 + 0.466506i $$0.845513\pi$$
$$384$$ 0 0
$$385$$ 1.11720e6 0.384131
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −1.57224e6 −0.526798 −0.263399 0.964687i $$-0.584844\pi$$
−0.263399 + 0.964687i $$0.584844\pi$$
$$390$$ 0 0
$$391$$ 359112. 0.118792
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −3.19778e6 −1.03123
$$396$$ 0 0
$$397$$ −3.00804e6 −0.957872 −0.478936 0.877850i $$-0.658977\pi$$
−0.478936 + 0.877850i $$0.658977\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 54406.0 0.0168961 0.00844804 0.999964i $$-0.497311\pi$$
0.00844804 + 0.999964i $$0.497311\pi$$
$$402$$ 0 0
$$403$$ 5.33269e6 1.63562
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −5.56440e6 −1.66507
$$408$$ 0 0
$$409$$ −2.07030e6 −0.611963 −0.305982 0.952037i $$-0.598985\pi$$
−0.305982 + 0.952037i $$0.598985\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −201292. −0.0580699
$$414$$ 0 0
$$415$$ −110504. −0.0314962
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 1.48062e6 0.412011 0.206005 0.978551i $$-0.433954\pi$$
0.206005 + 0.978551i $$0.433954\pi$$
$$420$$ 0 0
$$421$$ −2.22283e6 −0.611224 −0.305612 0.952156i $$-0.598861\pi$$
−0.305612 + 0.952156i $$0.598861\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 131118. 0.0352119
$$426$$ 0 0
$$427$$ 778022. 0.206501
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1.96259e6 −0.508904 −0.254452 0.967085i $$-0.581895\pi$$
−0.254452 + 0.967085i $$0.581895\pi$$
$$432$$ 0 0
$$433$$ 1.92503e6 0.493420 0.246710 0.969089i $$-0.420650\pi$$
0.246710 + 0.969089i $$0.420650\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −4.21726e6 −1.05640
$$438$$ 0 0
$$439$$ −1.68838e6 −0.418127 −0.209063 0.977902i $$-0.567041\pi$$
−0.209063 + 0.977902i $$0.567041\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 7.37277e6 1.78493 0.892465 0.451116i $$-0.148974\pi$$
0.892465 + 0.451116i $$0.148974\pi$$
$$444$$ 0 0
$$445$$ 316236. 0.0757027
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 4.61309e6 1.07988 0.539940 0.841703i $$-0.318447\pi$$
0.539940 + 0.841703i $$0.318447\pi$$
$$450$$ 0 0
$$451$$ 145200. 0.0336144
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −1.25499e6 −0.284191
$$456$$ 0 0
$$457$$ −5.75663e6 −1.28937 −0.644685 0.764448i $$-0.723012\pi$$
−0.644685 + 0.764448i $$0.723012\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −5.67782e6 −1.24431 −0.622156 0.782893i $$-0.713743\pi$$
−0.622156 + 0.782893i $$0.713743\pi$$
$$462$$ 0 0
$$463$$ 8.06452e6 1.74834 0.874170 0.485619i $$-0.161406\pi$$
0.874170 + 0.485619i $$0.161406\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −6.92248e6 −1.46882 −0.734412 0.678704i $$-0.762542\pi$$
−0.734412 + 0.678704i $$0.762542\pi$$
$$468$$ 0 0
$$469$$ 3.31573e6 0.696061
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −669600. −0.137614
$$474$$ 0 0
$$475$$ −1.53980e6 −0.313133
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −8.33297e6 −1.65944 −0.829719 0.558182i $$-0.811499\pi$$
−0.829719 + 0.558182i $$0.811499\pi$$
$$480$$ 0 0
$$481$$ 6.25068e6 1.23187
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 4.97078e6 0.959556
$$486$$ 0 0
$$487$$ −496792. −0.0949188 −0.0474594 0.998873i $$-0.515112\pi$$
−0.0474594 + 0.998873i $$0.515112\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −760704. −0.142401 −0.0712003 0.997462i $$-0.522683\pi$$
−0.0712003 + 0.997462i $$0.522683\pi$$
$$492$$ 0 0
$$493$$ −531180. −0.0984293
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −3.30711e6 −0.600561
$$498$$ 0 0
$$499$$ −2.19192e6 −0.394071 −0.197035 0.980396i $$-0.563131\pi$$
−0.197035 + 0.980396i $$0.563131\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −790680. −0.139342 −0.0696708 0.997570i $$-0.522195\pi$$
−0.0696708 + 0.997570i $$0.522195\pi$$
$$504$$ 0 0
$$505$$ −6.07217e6 −1.05954
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −2.75272e6 −0.470943 −0.235471 0.971881i $$-0.575663\pi$$
−0.235471 + 0.971881i $$0.575663\pi$$
$$510$$ 0 0
$$511$$ 54194.0 0.00918119
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 3.47472e6 0.577300
$$516$$ 0 0
$$517$$ −1.69872e7 −2.79509
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 6.27911e6 1.01345 0.506727 0.862107i $$-0.330855\pi$$
0.506727 + 0.862107i $$0.330855\pi$$
$$522$$ 0 0
$$523$$ 5.60610e6 0.896203 0.448102 0.893983i $$-0.352100\pi$$
0.448102 + 0.893983i $$0.352100\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 617136. 0.0967953
$$528$$ 0 0
$$529$$ 1.47605e7 2.29330
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −163108. −0.0248689
$$534$$ 0 0
$$535$$ −5.30024e6 −0.800592
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 1.44060e6 0.213585
$$540$$ 0 0
$$541$$ 3.31128e6 0.486410 0.243205 0.969975i $$-0.421801\pi$$
0.243205 + 0.969975i $$0.421801\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 5.38680e6 0.776855
$$546$$ 0 0
$$547$$ −5.66566e6 −0.809622 −0.404811 0.914400i $$-0.632663\pi$$
−0.404811 + 0.914400i $$0.632663\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 6.23796e6 0.875313
$$552$$ 0 0
$$553$$ −4.12345e6 −0.573387
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 6.36880e6 0.869801 0.434900 0.900479i $$-0.356784\pi$$
0.434900 + 0.900479i $$0.356784\pi$$
$$558$$ 0 0
$$559$$ 752184. 0.101811
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 181404. 0.0241199 0.0120600 0.999927i $$-0.496161\pi$$
0.0120600 + 0.999927i $$0.496161\pi$$
$$564$$ 0 0
$$565$$ 3.10620e6 0.409362
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 5.02851e6 0.651116 0.325558 0.945522i $$-0.394448\pi$$
0.325558 + 0.945522i $$0.394448\pi$$
$$570$$ 0 0
$$571$$ 7.57430e6 0.972192 0.486096 0.873905i $$-0.338420\pi$$
0.486096 + 0.873905i $$0.338420\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 7.73932e6 0.976188
$$576$$ 0 0
$$577$$ 1.52011e7 1.90080 0.950400 0.311029i $$-0.100674\pi$$
0.950400 + 0.311029i $$0.100674\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −142492. −0.0175126
$$582$$ 0 0
$$583$$ −6.13800e6 −0.747921
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 4.64015e6 0.555823 0.277912 0.960607i $$-0.410358\pi$$
0.277912 + 0.960607i $$0.410358\pi$$
$$588$$ 0 0
$$589$$ −7.24739e6 −0.860783
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 4.18658e6 0.488903 0.244451 0.969662i $$-0.421392\pi$$
0.244451 + 0.969662i $$0.421392\pi$$
$$594$$ 0 0
$$595$$ −145236. −0.0168183
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −1.02901e7 −1.17180 −0.585898 0.810385i $$-0.699258\pi$$
−0.585898 + 0.810385i $$0.699258\pi$$
$$600$$ 0 0
$$601$$ 1.43512e7 1.62070 0.810349 0.585947i $$-0.199277\pi$$
0.810349 + 0.585947i $$0.199277\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 7.56006e6 0.839725
$$606$$ 0 0
$$607$$ −1.09870e7 −1.21034 −0.605169 0.796097i $$-0.706894\pi$$
−0.605169 + 0.796097i $$0.706894\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 1.90823e7 2.06789
$$612$$ 0 0
$$613$$ 3.00637e6 0.323141 0.161570 0.986861i $$-0.448344\pi$$
0.161570 + 0.986861i $$0.448344\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.82040e7 −1.92510 −0.962550 0.271105i $$-0.912611\pi$$
−0.962550 + 0.271105i $$0.912611\pi$$
$$618$$ 0 0
$$619$$ −6.45803e6 −0.677444 −0.338722 0.940887i $$-0.609995\pi$$
−0.338722 + 0.940887i $$0.609995\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 407778. 0.0420924
$$624$$ 0 0
$$625$$ −1.68674e6 −0.172722
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 723372. 0.0729013
$$630$$ 0 0
$$631$$ −3.59598e6 −0.359538 −0.179769 0.983709i $$-0.557535\pi$$
−0.179769 + 0.983709i $$0.557535\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −3.43854e6 −0.338408
$$636$$ 0 0
$$637$$ −1.61827e6 −0.158017
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −6.54433e6 −0.629101 −0.314550 0.949241i $$-0.601854\pi$$
−0.314550 + 0.949241i $$0.601854\pi$$
$$642$$ 0 0
$$643$$ −1.48417e7 −1.41565 −0.707827 0.706386i $$-0.750324\pi$$
−0.707827 + 0.706386i $$0.750324\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 4.34043e6 0.407636 0.203818 0.979009i $$-0.434665\pi$$
0.203818 + 0.979009i $$0.434665\pi$$
$$648$$ 0 0
$$649$$ −2.46480e6 −0.229705
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −5.31207e6 −0.487507 −0.243753 0.969837i $$-0.578379\pi$$
−0.243753 + 0.969837i $$0.578379\pi$$
$$654$$ 0 0
$$655$$ 7.12409e6 0.648823
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −2.78371e6 −0.249696 −0.124848 0.992176i $$-0.539844\pi$$
−0.124848 + 0.992176i $$0.539844\pi$$
$$660$$ 0 0
$$661$$ 2.01522e7 1.79398 0.896992 0.442047i $$-0.145747\pi$$
0.896992 + 0.442047i $$0.145747\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 1.70559e6 0.149562
$$666$$ 0 0
$$667$$ −3.13532e7 −2.72878
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 9.52680e6 0.816847
$$672$$ 0 0
$$673$$ −1.26277e7 −1.07470 −0.537349 0.843360i $$-0.680574\pi$$
−0.537349 + 0.843360i $$0.680574\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 6.94541e6 0.582406 0.291203 0.956661i $$-0.405944\pi$$
0.291203 + 0.956661i $$0.405944\pi$$
$$678$$ 0 0
$$679$$ 6.40969e6 0.533535
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −278144. −0.0228149 −0.0114074 0.999935i $$-0.503631\pi$$
−0.0114074 + 0.999935i $$0.503631\pi$$
$$684$$ 0 0
$$685$$ −6.40232e6 −0.521328
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 6.89502e6 0.553334
$$690$$ 0 0
$$691$$ 6.38656e6 0.508829 0.254414 0.967095i $$-0.418117\pi$$
0.254414 + 0.967095i $$0.418117\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −25384.0 −0.00199342
$$696$$ 0 0
$$697$$ −18876.0 −0.00147173
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1.26602e7 0.973075 0.486537 0.873660i $$-0.338260\pi$$
0.486537 + 0.873660i $$0.338260\pi$$
$$702$$ 0 0
$$703$$ −8.49498e6 −0.648297
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −7.82991e6 −0.589126
$$708$$ 0 0
$$709$$ −1.29990e7 −0.971169 −0.485585 0.874190i $$-0.661393\pi$$
−0.485585 + 0.874190i $$0.661393\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 3.64268e7 2.68348
$$714$$ 0 0
$$715$$ −1.53672e7 −1.12416
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1.27912e6 0.0922761 0.0461380 0.998935i $$-0.485309\pi$$
0.0461380 + 0.998935i $$0.485309\pi$$
$$720$$ 0 0
$$721$$ 4.48056e6 0.320992
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1.14476e7 −0.808853
$$726$$ 0 0
$$727$$ 2.01247e7 1.41219 0.706097 0.708115i $$-0.250454\pi$$
0.706097 + 0.708115i $$0.250454\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 87048.0 0.00602512
$$732$$ 0 0
$$733$$ 2.59171e7 1.78167 0.890835 0.454328i $$-0.150121\pi$$
0.890835 + 0.454328i $$0.150121\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 4.06008e7 2.75338
$$738$$ 0 0
$$739$$ −2.57638e6 −0.173540 −0.0867698 0.996228i $$-0.527654\pi$$
−0.0867698 + 0.996228i $$0.527654\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 2.36046e7 1.56865 0.784323 0.620353i $$-0.213010\pi$$
0.784323 + 0.620353i $$0.213010\pi$$
$$744$$ 0 0
$$745$$ 1.14235e7 0.754063
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −6.83452e6 −0.445147
$$750$$ 0 0
$$751$$ 9.32237e6 0.603151 0.301576 0.953442i $$-0.402487\pi$$
0.301576 + 0.953442i $$0.402487\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −1.36432e7 −0.871063
$$756$$ 0 0
$$757$$ 1.90696e7 1.20949 0.604744 0.796420i $$-0.293276\pi$$
0.604744 + 0.796420i $$0.293276\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 6.87530e6 0.430358 0.215179 0.976575i $$-0.430967\pi$$
0.215179 + 0.976575i $$0.430967\pi$$
$$762$$ 0 0
$$763$$ 6.94614e6 0.431949
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 2.76879e6 0.169942
$$768$$ 0 0
$$769$$ 1.90337e7 1.16067 0.580334 0.814379i $$-0.302922\pi$$
0.580334 + 0.814379i $$0.302922\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −1.64278e7 −0.988851 −0.494426 0.869220i $$-0.664622\pi$$
−0.494426 + 0.869220i $$0.664622\pi$$
$$774$$ 0 0
$$775$$ 1.33001e7 0.795426
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 221672. 0.0130878
$$780$$ 0 0
$$781$$ −4.04952e7 −2.37561
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 4.21124e6 0.243913
$$786$$ 0 0
$$787$$ 4.19153e6 0.241233 0.120616 0.992699i $$-0.461513\pi$$
0.120616 + 0.992699i $$0.461513\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 4.00536e6 0.227615
$$792$$ 0 0
$$793$$ −1.07018e7 −0.604328
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1.28046e7 0.714035 0.357018 0.934098i $$-0.383794\pi$$
0.357018 + 0.934098i $$0.383794\pi$$
$$798$$ 0 0
$$799$$ 2.20834e6 0.122377
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 663600. 0.0363176
$$804$$ 0 0
$$805$$ −8.57265e6 −0.466257
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 1.33669e7 0.718057 0.359029 0.933327i $$-0.383108\pi$$
0.359029 + 0.933327i $$0.383108\pi$$
$$810$$ 0 0
$$811$$ 3.51226e7 1.87514 0.937571 0.347794i $$-0.113069\pi$$
0.937571 + 0.347794i $$0.113069\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −1.41504e7 −0.746236
$$816$$ 0 0
$$817$$ −1.02226e6 −0.0535802
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 2.66290e7 1.37878 0.689392 0.724389i $$-0.257878\pi$$
0.689392 + 0.724389i $$0.257878\pi$$
$$822$$ 0 0
$$823$$ 1.11835e7 0.575545 0.287773 0.957699i $$-0.407085\pi$$
0.287773 + 0.957699i $$0.407085\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −2.56108e6 −0.130215 −0.0651073 0.997878i $$-0.520739\pi$$
−0.0651073 + 0.997878i $$0.520739\pi$$
$$828$$ 0 0
$$829$$ 2.27188e7 1.14815 0.574076 0.818802i $$-0.305362\pi$$
0.574076 + 0.818802i $$0.305362\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −187278. −0.00935135
$$834$$ 0 0
$$835$$ −4.16480e6 −0.206718
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 3.94627e7 1.93545 0.967725 0.252007i $$-0.0810907\pi$$
0.967725 + 0.252007i $$0.0810907\pi$$
$$840$$ 0 0
$$841$$ 2.58650e7 1.26102
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 3.15335e6 0.151926
$$846$$ 0 0
$$847$$ 9.74850e6 0.466906
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 4.26975e7 2.02106
$$852$$ 0 0
$$853$$ −2.87657e7 −1.35364 −0.676818 0.736150i $$-0.736642\pi$$
−0.676818 + 0.736150i $$0.736642\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 1.40799e7 0.654860 0.327430 0.944875i $$-0.393817\pi$$
0.327430 + 0.944875i $$0.393817\pi$$
$$858$$ 0 0
$$859$$ 3.10876e7 1.43749 0.718744 0.695275i $$-0.244718\pi$$
0.718744 + 0.695275i $$0.244718\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −9.66226e6 −0.441623 −0.220812 0.975316i $$-0.570871\pi$$
−0.220812 + 0.975316i $$0.570871\pi$$
$$864$$ 0 0
$$865$$ 1.47667e7 0.671033
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −5.04912e7 −2.26812
$$870$$ 0 0
$$871$$ −4.56082e7 −2.03703
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −8.94877e6 −0.395133
$$876$$ 0 0
$$877$$ −1.98937e7 −0.873409 −0.436704 0.899605i $$-0.643854\pi$$
−0.436704 + 0.899605i $$0.643854\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 2.03248e6 0.0882240 0.0441120 0.999027i $$-0.485954\pi$$
0.0441120 + 0.999027i $$0.485954\pi$$
$$882$$ 0 0
$$883$$ 3.69655e7 1.59549 0.797747 0.602993i $$-0.206025\pi$$
0.797747 + 0.602993i $$0.206025\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −2.75837e7 −1.17718 −0.588591 0.808431i $$-0.700317\pi$$
−0.588591 + 0.808431i $$0.700317\pi$$
$$888$$ 0 0
$$889$$ −4.43391e6 −0.188162
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −2.59338e7 −1.08827
$$894$$ 0 0
$$895$$ −9.18293e6 −0.383198
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −5.38807e7 −2.22348
$$900$$ 0 0
$$901$$ 797940. 0.0327460
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 7.25245e6 0.294350
$$906$$ 0 0
$$907$$ 1.73426e7 0.699997 0.349998 0.936750i $$-0.386182\pi$$
0.349998 + 0.936750i $$0.386182\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 3.98913e7 1.59251 0.796255 0.604961i $$-0.206811\pi$$
0.796255 + 0.604961i $$0.206811\pi$$
$$912$$ 0 0
$$913$$ −1.74480e6 −0.0692738
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 9.18632e6 0.360760
$$918$$ 0 0
$$919$$ −4.01774e7 −1.56925 −0.784626 0.619970i $$-0.787145\pi$$
−0.784626 + 0.619970i $$0.787145\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 4.54896e7 1.75755
$$924$$ 0 0
$$925$$ 1.55896e7 0.599074
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −3.03389e7 −1.15335 −0.576675 0.816974i $$-0.695650\pi$$
−0.576675 + 0.816974i $$0.695650\pi$$
$$930$$ 0 0
$$931$$ 2.19932e6 0.0831598
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −1.77840e6 −0.0665274
$$936$$ 0 0
$$937$$ −4.32143e7 −1.60797 −0.803986 0.594648i $$-0.797291\pi$$
−0.803986 + 0.594648i $$0.797291\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −4.39045e7 −1.61635 −0.808174 0.588944i $$-0.799544\pi$$
−0.808174 + 0.588944i $$0.799544\pi$$
$$942$$ 0 0
$$943$$ −1.11417e6 −0.0408011
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −4.80030e7 −1.73937 −0.869687 0.493603i $$-0.835680\pi$$
−0.869687 + 0.493603i $$0.835680\pi$$
$$948$$ 0 0
$$949$$ −745444. −0.0268689
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 2.26010e6 0.0806113 0.0403056 0.999187i $$-0.487167\pi$$
0.0403056 + 0.999187i $$0.487167\pi$$
$$954$$ 0 0
$$955$$ 9.62540e6 0.341515
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −8.25562e6 −0.289870
$$960$$ 0 0
$$961$$ 3.39706e7 1.18657
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −2.70675e7 −0.935685
$$966$$ 0 0
$$967$$ −2.43715e6 −0.0838140 −0.0419070 0.999122i $$-0.513343\pi$$
−0.0419070 + 0.999122i $$0.513343\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −4.15303e7 −1.41357 −0.706784 0.707429i $$-0.749855\pi$$
−0.706784 + 0.707429i $$0.749855\pi$$
$$972$$ 0 0
$$973$$ −32732.0 −0.00110838
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −3.59151e6 −0.120376 −0.0601882 0.998187i $$-0.519170\pi$$
−0.0601882 + 0.998187i $$0.519170\pi$$
$$978$$ 0 0
$$979$$ 4.99320e6 0.166503
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 3.84268e7 1.26838 0.634191 0.773176i $$-0.281333\pi$$
0.634191 + 0.773176i $$0.281333\pi$$
$$984$$ 0 0
$$985$$ 4.07337e6 0.133771
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 5.13806e6 0.167035
$$990$$ 0 0
$$991$$ −7.96056e6 −0.257489 −0.128745 0.991678i $$-0.541095\pi$$
−0.128745 + 0.991678i $$0.541095\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 3.63642e7 1.16444
$$996$$ 0 0
$$997$$ 2.67858e7 0.853427 0.426713 0.904387i $$-0.359671\pi$$
0.426713 + 0.904387i $$0.359671\pi$$
$$998$$ 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.v.1.1 1
3.2 odd 2 336.6.a.d.1.1 1
4.3 odd 2 504.6.a.g.1.1 1
12.11 even 2 168.6.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
168.6.a.e.1.1 1 12.11 even 2
336.6.a.d.1.1 1 3.2 odd 2
504.6.a.g.1.1 1 4.3 odd 2
1008.6.a.v.1.1 1 1.1 even 1 trivial