# Properties

 Label 1008.6.a.e.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 $1$

# Learn more

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 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)

 $$f(q)$$ $$=$$ $$q-74.0000 q^{5} -49.0000 q^{7} +O(q^{10})$$ $$q-74.0000 q^{5} -49.0000 q^{7} +216.000 q^{11} -186.000 q^{13} -1078.00 q^{17} +908.000 q^{19} -2236.00 q^{23} +2351.00 q^{25} -5366.00 q^{29} +536.000 q^{31} +3626.00 q^{35} +3798.00 q^{37} -18598.0 q^{41} -15308.0 q^{43} +23480.0 q^{47} +2401.00 q^{49} -9062.00 q^{53} -15984.0 q^{55} -49284.0 q^{59} +17806.0 q^{61} +13764.0 q^{65} -24876.0 q^{67} +3468.00 q^{71} -32414.0 q^{73} -10584.0 q^{77} -25384.0 q^{79} -67284.0 q^{83} +79772.0 q^{85} +698.000 q^{89} +9114.00 q^{91} -67192.0 q^{95} +154906. q^{97} +O(q^{100})$$

## 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
$$5$$ −74.0000 −1.32375 −0.661876 0.749613i $$-0.730240\pi$$
−0.661876 + 0.749613i $$0.730240\pi$$
$$6$$ 0 0
$$7$$ −49.0000 −0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 216.000 0.538235 0.269118 0.963107i $$-0.413268\pi$$
0.269118 + 0.963107i $$0.413268\pi$$
$$12$$ 0 0
$$13$$ −186.000 −0.305249 −0.152625 0.988284i $$-0.548773\pi$$
−0.152625 + 0.988284i $$0.548773\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1078.00 −0.904683 −0.452342 0.891845i $$-0.649411\pi$$
−0.452342 + 0.891845i $$0.649411\pi$$
$$18$$ 0 0
$$19$$ 908.000 0.577035 0.288517 0.957475i $$-0.406838\pi$$
0.288517 + 0.957475i $$0.406838\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −2236.00 −0.881358 −0.440679 0.897665i $$-0.645262\pi$$
−0.440679 + 0.897665i $$0.645262\pi$$
$$24$$ 0 0
$$25$$ 2351.00 0.752320
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −5366.00 −1.18483 −0.592414 0.805633i $$-0.701825\pi$$
−0.592414 + 0.805633i $$0.701825\pi$$
$$30$$ 0 0
$$31$$ 536.000 0.100175 0.0500876 0.998745i $$-0.484050\pi$$
0.0500876 + 0.998745i $$0.484050\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 3626.00 0.500331
$$36$$ 0 0
$$37$$ 3798.00 0.456090 0.228045 0.973651i $$-0.426767\pi$$
0.228045 + 0.973651i $$0.426767\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −18598.0 −1.72785 −0.863926 0.503619i $$-0.832002\pi$$
−0.863926 + 0.503619i $$0.832002\pi$$
$$42$$ 0 0
$$43$$ −15308.0 −1.26255 −0.631273 0.775561i $$-0.717467\pi$$
−0.631273 + 0.775561i $$0.717467\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 23480.0 1.55043 0.775217 0.631695i $$-0.217640\pi$$
0.775217 + 0.631695i $$0.217640\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −9062.00 −0.443133 −0.221567 0.975145i $$-0.571117\pi$$
−0.221567 + 0.975145i $$0.571117\pi$$
$$54$$ 0 0
$$55$$ −15984.0 −0.712490
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −49284.0 −1.84321 −0.921607 0.388124i $$-0.873123\pi$$
−0.921607 + 0.388124i $$0.873123\pi$$
$$60$$ 0 0
$$61$$ 17806.0 0.612691 0.306346 0.951920i $$-0.400894\pi$$
0.306346 + 0.951920i $$0.400894\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 13764.0 0.404074
$$66$$ 0 0
$$67$$ −24876.0 −0.677008 −0.338504 0.940965i $$-0.609921\pi$$
−0.338504 + 0.940965i $$0.609921\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 3468.00 0.0816457 0.0408228 0.999166i $$-0.487002\pi$$
0.0408228 + 0.999166i $$0.487002\pi$$
$$72$$ 0 0
$$73$$ −32414.0 −0.711911 −0.355955 0.934503i $$-0.615844\pi$$
−0.355955 + 0.934503i $$0.615844\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −10584.0 −0.203434
$$78$$ 0 0
$$79$$ −25384.0 −0.457607 −0.228803 0.973473i $$-0.573481\pi$$
−0.228803 + 0.973473i $$0.573481\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −67284.0 −1.07205 −0.536027 0.844201i $$-0.680075\pi$$
−0.536027 + 0.844201i $$0.680075\pi$$
$$84$$ 0 0
$$85$$ 79772.0 1.19758
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 698.000 0.00934072 0.00467036 0.999989i $$-0.498513\pi$$
0.00467036 + 0.999989i $$0.498513\pi$$
$$90$$ 0 0
$$91$$ 9114.00 0.115373
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −67192.0 −0.763851
$$96$$ 0 0
$$97$$ 154906. 1.67163 0.835813 0.549015i $$-0.184997\pi$$
0.835813 + 0.549015i $$0.184997\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −23538.0 −0.229597 −0.114798 0.993389i $$-0.536622\pi$$
−0.114798 + 0.993389i $$0.536622\pi$$
$$102$$ 0 0
$$103$$ −16464.0 −0.152912 −0.0764561 0.997073i $$-0.524361\pi$$
−0.0764561 + 0.997073i $$0.524361\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −113640. −0.959559 −0.479780 0.877389i $$-0.659283\pi$$
−0.479780 + 0.877389i $$0.659283\pi$$
$$108$$ 0 0
$$109$$ 107374. 0.865631 0.432816 0.901482i $$-0.357520\pi$$
0.432816 + 0.901482i $$0.357520\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 86766.0 0.639225 0.319612 0.947548i $$-0.396447\pi$$
0.319612 + 0.947548i $$0.396447\pi$$
$$114$$ 0 0
$$115$$ 165464. 1.16670
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 52822.0 0.341938
$$120$$ 0 0
$$121$$ −114395. −0.710303
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 57276.0 0.327867
$$126$$ 0 0
$$127$$ 98056.0 0.539467 0.269733 0.962935i $$-0.413064\pi$$
0.269733 + 0.962935i $$0.413064\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 160604. 0.817670 0.408835 0.912608i $$-0.365935\pi$$
0.408835 + 0.912608i $$0.365935\pi$$
$$132$$ 0 0
$$133$$ −44492.0 −0.218099
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 99694.0 0.453803 0.226902 0.973918i $$-0.427140\pi$$
0.226902 + 0.973918i $$0.427140\pi$$
$$138$$ 0 0
$$139$$ 110508. 0.485128 0.242564 0.970135i $$-0.422011\pi$$
0.242564 + 0.970135i $$0.422011\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −40176.0 −0.164296
$$144$$ 0 0
$$145$$ 397084. 1.56842
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 277562. 1.02422 0.512111 0.858919i $$-0.328864\pi$$
0.512111 + 0.858919i $$0.328864\pi$$
$$150$$ 0 0
$$151$$ 372872. 1.33081 0.665407 0.746481i $$-0.268258\pi$$
0.665407 + 0.746481i $$0.268258\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −39664.0 −0.132607
$$156$$ 0 0
$$157$$ 532638. 1.72458 0.862289 0.506416i $$-0.169030\pi$$
0.862289 + 0.506416i $$0.169030\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 109564. 0.333122
$$162$$ 0 0
$$163$$ −545164. −1.60716 −0.803578 0.595199i $$-0.797073\pi$$
−0.803578 + 0.595199i $$0.797073\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −304176. −0.843983 −0.421992 0.906600i $$-0.638669\pi$$
−0.421992 + 0.906600i $$0.638669\pi$$
$$168$$ 0 0
$$169$$ −336697. −0.906823
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −108506. −0.275638 −0.137819 0.990457i $$-0.544009\pi$$
−0.137819 + 0.990457i $$0.544009\pi$$
$$174$$ 0 0
$$175$$ −115199. −0.284350
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 62072.0 0.144798 0.0723991 0.997376i $$-0.476934\pi$$
0.0723991 + 0.997376i $$0.476934\pi$$
$$180$$ 0 0
$$181$$ 762734. 1.73052 0.865260 0.501323i $$-0.167153\pi$$
0.865260 + 0.501323i $$0.167153\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −281052. −0.603750
$$186$$ 0 0
$$187$$ −232848. −0.486932
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −371036. −0.735923 −0.367962 0.929841i $$-0.619944\pi$$
−0.367962 + 0.929841i $$0.619944\pi$$
$$192$$ 0 0
$$193$$ −375534. −0.725698 −0.362849 0.931848i $$-0.618196\pi$$
−0.362849 + 0.931848i $$0.618196\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1.07803e6 1.97908 0.989541 0.144254i $$-0.0460782\pi$$
0.989541 + 0.144254i $$0.0460782\pi$$
$$198$$ 0 0
$$199$$ 60280.0 0.107905 0.0539524 0.998544i $$-0.482818\pi$$
0.0539524 + 0.998544i $$0.482818\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 262934. 0.447823
$$204$$ 0 0
$$205$$ 1.37625e6 2.28725
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 196128. 0.310580
$$210$$ 0 0
$$211$$ −766436. −1.18514 −0.592570 0.805519i $$-0.701887\pi$$
−0.592570 + 0.805519i $$0.701887\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1.13279e6 1.67130
$$216$$ 0 0
$$217$$ −26264.0 −0.0378627
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 200508. 0.276154
$$222$$ 0 0
$$223$$ −300768. −0.405013 −0.202507 0.979281i $$-0.564909\pi$$
−0.202507 + 0.979281i $$0.564909\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1.20016e6 1.54588 0.772940 0.634479i $$-0.218785\pi$$
0.772940 + 0.634479i $$0.218785\pi$$
$$228$$ 0 0
$$229$$ −217330. −0.273861 −0.136931 0.990581i $$-0.543724\pi$$
−0.136931 + 0.990581i $$0.543724\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 612526. 0.739154 0.369577 0.929200i $$-0.379503\pi$$
0.369577 + 0.929200i $$0.379503\pi$$
$$234$$ 0 0
$$235$$ −1.73752e6 −2.05239
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −668164. −0.756638 −0.378319 0.925675i $$-0.623498\pi$$
−0.378319 + 0.925675i $$0.623498\pi$$
$$240$$ 0 0
$$241$$ −972038. −1.07805 −0.539027 0.842288i $$-0.681208\pi$$
−0.539027 + 0.842288i $$0.681208\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −177674. −0.189107
$$246$$ 0 0
$$247$$ −168888. −0.176139
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 1.73264e6 1.73589 0.867947 0.496657i $$-0.165439\pi$$
0.867947 + 0.496657i $$0.165439\pi$$
$$252$$ 0 0
$$253$$ −482976. −0.474378
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −514542. −0.485946 −0.242973 0.970033i $$-0.578123\pi$$
−0.242973 + 0.970033i $$0.578123\pi$$
$$258$$ 0 0
$$259$$ −186102. −0.172386
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 682836. 0.608733 0.304367 0.952555i $$-0.401555\pi$$
0.304367 + 0.952555i $$0.401555\pi$$
$$264$$ 0 0
$$265$$ 670588. 0.586599
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.05574e6 0.889564 0.444782 0.895639i $$-0.353281\pi$$
0.444782 + 0.895639i $$0.353281\pi$$
$$270$$ 0 0
$$271$$ −241400. −0.199671 −0.0998353 0.995004i $$-0.531832\pi$$
−0.0998353 + 0.995004i $$0.531832\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 507816. 0.404925
$$276$$ 0 0
$$277$$ −2.27139e6 −1.77865 −0.889327 0.457272i $$-0.848827\pi$$
−0.889327 + 0.457272i $$0.848827\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.91293e6 1.44521 0.722607 0.691259i $$-0.242944\pi$$
0.722607 + 0.691259i $$0.242944\pi$$
$$282$$ 0 0
$$283$$ 2.28975e6 1.69950 0.849751 0.527185i $$-0.176752\pi$$
0.849751 + 0.527185i $$0.176752\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 911302. 0.653067
$$288$$ 0 0
$$289$$ −257773. −0.181549
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 1.11253e6 0.757079 0.378539 0.925585i $$-0.376426\pi$$
0.378539 + 0.925585i $$0.376426\pi$$
$$294$$ 0 0
$$295$$ 3.64702e6 2.43996
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 415896. 0.269034
$$300$$ 0 0
$$301$$ 750092. 0.477198
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −1.31764e6 −0.811052
$$306$$ 0 0
$$307$$ −615988. −0.373015 −0.186508 0.982454i $$-0.559717\pi$$
−0.186508 + 0.982454i $$0.559717\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −891408. −0.522607 −0.261304 0.965257i $$-0.584152\pi$$
−0.261304 + 0.965257i $$0.584152\pi$$
$$312$$ 0 0
$$313$$ −1.65852e6 −0.956884 −0.478442 0.878119i $$-0.658798\pi$$
−0.478442 + 0.878119i $$0.658798\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −816798. −0.456527 −0.228264 0.973599i $$-0.573305\pi$$
−0.228264 + 0.973599i $$0.573305\pi$$
$$318$$ 0 0
$$319$$ −1.15906e6 −0.637717
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −978824. −0.522033
$$324$$ 0 0
$$325$$ −437286. −0.229645
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −1.15052e6 −0.586009
$$330$$ 0 0
$$331$$ 1.78008e6 0.893039 0.446520 0.894774i $$-0.352663\pi$$
0.446520 + 0.894774i $$0.352663\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 1.84082e6 0.896190
$$336$$ 0 0
$$337$$ 1.30551e6 0.626187 0.313094 0.949722i $$-0.398635\pi$$
0.313094 + 0.949722i $$0.398635\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 115776. 0.0539179
$$342$$ 0 0
$$343$$ −117649. −0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.32307e6 0.589875 0.294937 0.955517i $$-0.404701\pi$$
0.294937 + 0.955517i $$0.404701\pi$$
$$348$$ 0 0
$$349$$ −139330. −0.0612324 −0.0306162 0.999531i $$-0.509747\pi$$
−0.0306162 + 0.999531i $$0.509747\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2.75783e6 1.17796 0.588981 0.808147i $$-0.299529\pi$$
0.588981 + 0.808147i $$0.299529\pi$$
$$354$$ 0 0
$$355$$ −256632. −0.108079
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −2.47218e6 −1.01238 −0.506190 0.862422i $$-0.668947\pi$$
−0.506190 + 0.862422i $$0.668947\pi$$
$$360$$ 0 0
$$361$$ −1.65163e6 −0.667031
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2.39864e6 0.942393
$$366$$ 0 0
$$367$$ 3.89637e6 1.51006 0.755031 0.655689i $$-0.227622\pi$$
0.755031 + 0.655689i $$0.227622\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 444038. 0.167489
$$372$$ 0 0
$$373$$ 2.54231e6 0.946142 0.473071 0.881024i $$-0.343145\pi$$
0.473071 + 0.881024i $$0.343145\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 998076. 0.361668
$$378$$ 0 0
$$379$$ 4.60420e6 1.64648 0.823239 0.567695i $$-0.192165\pi$$
0.823239 + 0.567695i $$0.192165\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −128640. −0.0448104 −0.0224052 0.999749i $$-0.507132\pi$$
−0.0224052 + 0.999749i $$0.507132\pi$$
$$384$$ 0 0
$$385$$ 783216. 0.269296
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 5.82077e6 1.95032 0.975161 0.221496i $$-0.0710940\pi$$
0.975161 + 0.221496i $$0.0710940\pi$$
$$390$$ 0 0
$$391$$ 2.41041e6 0.797349
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 1.87842e6 0.605758
$$396$$ 0 0
$$397$$ 2.10091e6 0.669008 0.334504 0.942394i $$-0.391431\pi$$
0.334504 + 0.942394i $$0.391431\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −5.58388e6 −1.73410 −0.867052 0.498217i $$-0.833988\pi$$
−0.867052 + 0.498217i $$0.833988\pi$$
$$402$$ 0 0
$$403$$ −99696.0 −0.0305784
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 820368. 0.245484
$$408$$ 0 0
$$409$$ −4.96822e6 −1.46856 −0.734282 0.678845i $$-0.762481\pi$$
−0.734282 + 0.678845i $$0.762481\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 2.41492e6 0.696670
$$414$$ 0 0
$$415$$ 4.97902e6 1.41913
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 4.41098e6 1.22744 0.613720 0.789524i $$-0.289673\pi$$
0.613720 + 0.789524i $$0.289673\pi$$
$$420$$ 0 0
$$421$$ −2.69671e6 −0.741532 −0.370766 0.928726i $$-0.620905\pi$$
−0.370766 + 0.928726i $$0.620905\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −2.53438e6 −0.680611
$$426$$ 0 0
$$427$$ −872494. −0.231576
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −5.11504e6 −1.32634 −0.663171 0.748468i $$-0.730790\pi$$
−0.663171 + 0.748468i $$0.730790\pi$$
$$432$$ 0 0
$$433$$ 6.40472e6 1.64165 0.820825 0.571180i $$-0.193514\pi$$
0.820825 + 0.571180i $$0.193514\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2.03029e6 −0.508574
$$438$$ 0 0
$$439$$ −3.67092e6 −0.909104 −0.454552 0.890720i $$-0.650201\pi$$
−0.454552 + 0.890720i $$0.650201\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 4.91509e6 1.18993 0.594966 0.803751i $$-0.297166\pi$$
0.594966 + 0.803751i $$0.297166\pi$$
$$444$$ 0 0
$$445$$ −51652.0 −0.0123648
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −2.10147e6 −0.491936 −0.245968 0.969278i $$-0.579106\pi$$
−0.245968 + 0.969278i $$0.579106\pi$$
$$450$$ 0 0
$$451$$ −4.01717e6 −0.929991
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −674436. −0.152726
$$456$$ 0 0
$$457$$ 3.00356e6 0.672738 0.336369 0.941730i $$-0.390801\pi$$
0.336369 + 0.941730i $$0.390801\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −3.49454e6 −0.765839 −0.382919 0.923782i $$-0.625081\pi$$
−0.382919 + 0.923782i $$0.625081\pi$$
$$462$$ 0 0
$$463$$ 6.61804e6 1.43475 0.717376 0.696686i $$-0.245343\pi$$
0.717376 + 0.696686i $$0.245343\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 7.86853e6 1.66956 0.834779 0.550585i $$-0.185595\pi$$
0.834779 + 0.550585i $$0.185595\pi$$
$$468$$ 0 0
$$469$$ 1.21892e6 0.255885
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −3.30653e6 −0.679547
$$474$$ 0 0
$$475$$ 2.13471e6 0.434115
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 5.70513e6 1.13613 0.568063 0.822985i $$-0.307693\pi$$
0.568063 + 0.822985i $$0.307693\pi$$
$$480$$ 0 0
$$481$$ −706428. −0.139221
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.14630e7 −2.21282
$$486$$ 0 0
$$487$$ 1.40170e6 0.267814 0.133907 0.990994i $$-0.457248\pi$$
0.133907 + 0.990994i $$0.457248\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −6.85330e6 −1.28291 −0.641454 0.767161i $$-0.721669\pi$$
−0.641454 + 0.767161i $$0.721669\pi$$
$$492$$ 0 0
$$493$$ 5.78455e6 1.07189
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −169932. −0.0308592
$$498$$ 0 0
$$499$$ 699596. 0.125775 0.0628877 0.998021i $$-0.479969\pi$$
0.0628877 + 0.998021i $$0.479969\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −6.28585e6 −1.10776 −0.553878 0.832598i $$-0.686853\pi$$
−0.553878 + 0.832598i $$0.686853\pi$$
$$504$$ 0 0
$$505$$ 1.74181e6 0.303929
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −4.58181e6 −0.783867 −0.391934 0.919993i $$-0.628194\pi$$
−0.391934 + 0.919993i $$0.628194\pi$$
$$510$$ 0 0
$$511$$ 1.58829e6 0.269077
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 1.21834e6 0.202418
$$516$$ 0 0
$$517$$ 5.07168e6 0.834498
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.12576e7 1.81699 0.908493 0.417900i $$-0.137234\pi$$
0.908493 + 0.417900i $$0.137234\pi$$
$$522$$ 0 0
$$523$$ −8.20312e6 −1.31137 −0.655685 0.755035i $$-0.727620\pi$$
−0.655685 + 0.755035i $$0.727620\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −577808. −0.0906269
$$528$$ 0 0
$$529$$ −1.43665e6 −0.223209
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 3.45923e6 0.527426
$$534$$ 0 0
$$535$$ 8.40936e6 1.27022
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 518616. 0.0768907
$$540$$ 0 0
$$541$$ −8.20335e6 −1.20503 −0.602515 0.798108i $$-0.705835\pi$$
−0.602515 + 0.798108i $$0.705835\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −7.94568e6 −1.14588
$$546$$ 0 0
$$547$$ −1.21740e7 −1.73967 −0.869833 0.493346i $$-0.835774\pi$$
−0.869833 + 0.493346i $$0.835774\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −4.87233e6 −0.683687
$$552$$ 0 0
$$553$$ 1.24382e6 0.172959
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 6.31330e6 0.862220 0.431110 0.902299i $$-0.358122\pi$$
0.431110 + 0.902299i $$0.358122\pi$$
$$558$$ 0 0
$$559$$ 2.84729e6 0.385391
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −692588. −0.0920882 −0.0460441 0.998939i $$-0.514661\pi$$
−0.0460441 + 0.998939i $$0.514661\pi$$
$$564$$ 0 0
$$565$$ −6.42068e6 −0.846175
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 2.25329e6 0.291768 0.145884 0.989302i $$-0.453397\pi$$
0.145884 + 0.989302i $$0.453397\pi$$
$$570$$ 0 0
$$571$$ −1.11830e7 −1.43538 −0.717690 0.696363i $$-0.754800\pi$$
−0.717690 + 0.696363i $$0.754800\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −5.25684e6 −0.663063
$$576$$ 0 0
$$577$$ −9.00373e6 −1.12586 −0.562928 0.826506i $$-0.690325\pi$$
−0.562928 + 0.826506i $$0.690325\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 3.29692e6 0.405198
$$582$$ 0 0
$$583$$ −1.95739e6 −0.238510
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −2.98821e6 −0.357945 −0.178972 0.983854i $$-0.557277\pi$$
−0.178972 + 0.983854i $$0.557277\pi$$
$$588$$ 0 0
$$589$$ 486688. 0.0578046
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 1.32321e7 1.54522 0.772611 0.634880i $$-0.218951\pi$$
0.772611 + 0.634880i $$0.218951\pi$$
$$594$$ 0 0
$$595$$ −3.90883e6 −0.452641
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −1.03034e7 −1.17331 −0.586657 0.809836i $$-0.699556\pi$$
−0.586657 + 0.809836i $$0.699556\pi$$
$$600$$ 0 0
$$601$$ 1.18785e7 1.34145 0.670725 0.741706i $$-0.265983\pi$$
0.670725 + 0.741706i $$0.265983\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 8.46523e6 0.940265
$$606$$ 0 0
$$607$$ −1.21813e7 −1.34190 −0.670951 0.741502i $$-0.734114\pi$$
−0.670951 + 0.741502i $$0.734114\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −4.36728e6 −0.473269
$$612$$ 0 0
$$613$$ −5.67204e6 −0.609661 −0.304830 0.952407i $$-0.598600\pi$$
−0.304830 + 0.952407i $$0.598600\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −7.31301e6 −0.773363 −0.386681 0.922213i $$-0.626379\pi$$
−0.386681 + 0.922213i $$0.626379\pi$$
$$618$$ 0 0
$$619$$ −2.30831e6 −0.242140 −0.121070 0.992644i $$-0.538633\pi$$
−0.121070 + 0.992644i $$0.538633\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −34202.0 −0.00353046
$$624$$ 0 0
$$625$$ −1.15853e7 −1.18633
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −4.09424e6 −0.412617
$$630$$ 0 0
$$631$$ −1.10468e7 −1.10449 −0.552244 0.833682i $$-0.686228\pi$$
−0.552244 + 0.833682i $$0.686228\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −7.25614e6 −0.714121
$$636$$ 0 0
$$637$$ −446586. −0.0436070
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 3.48945e6 0.335437 0.167719 0.985835i $$-0.446360\pi$$
0.167719 + 0.985835i $$0.446360\pi$$
$$642$$ 0 0
$$643$$ 5.66155e6 0.540017 0.270009 0.962858i $$-0.412973\pi$$
0.270009 + 0.962858i $$0.412973\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −2.18746e6 −0.205437 −0.102718 0.994710i $$-0.532754\pi$$
−0.102718 + 0.994710i $$0.532754\pi$$
$$648$$ 0 0
$$649$$ −1.06453e7 −0.992083
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −8.36706e6 −0.767874 −0.383937 0.923359i $$-0.625432\pi$$
−0.383937 + 0.923359i $$0.625432\pi$$
$$654$$ 0 0
$$655$$ −1.18847e7 −1.08239
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 662336. 0.0594107 0.0297054 0.999559i $$-0.490543\pi$$
0.0297054 + 0.999559i $$0.490543\pi$$
$$660$$ 0 0
$$661$$ −1.00537e7 −0.894995 −0.447497 0.894285i $$-0.647685\pi$$
−0.447497 + 0.894285i $$0.647685\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 3.29241e6 0.288708
$$666$$ 0 0
$$667$$ 1.19984e7 1.04426
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 3.84610e6 0.329772
$$672$$ 0 0
$$673$$ 1.73547e7 1.47699 0.738497 0.674257i $$-0.235536\pi$$
0.738497 + 0.674257i $$0.235536\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 1.18052e7 0.989923 0.494962 0.868915i $$-0.335182\pi$$
0.494962 + 0.868915i $$0.335182\pi$$
$$678$$ 0 0
$$679$$ −7.59039e6 −0.631815
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 2.03419e6 0.166855 0.0834277 0.996514i $$-0.473413\pi$$
0.0834277 + 0.996514i $$0.473413\pi$$
$$684$$ 0 0
$$685$$ −7.37736e6 −0.600723
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 1.68553e6 0.135266
$$690$$ 0 0
$$691$$ 6.80453e6 0.542130 0.271065 0.962561i $$-0.412624\pi$$
0.271065 + 0.962561i $$0.412624\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −8.17759e6 −0.642190
$$696$$ 0 0
$$697$$ 2.00486e7 1.56316
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1.05452e7 0.810512 0.405256 0.914203i $$-0.367182\pi$$
0.405256 + 0.914203i $$0.367182\pi$$
$$702$$ 0 0
$$703$$ 3.44858e6 0.263180
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1.15336e6 0.0867795
$$708$$ 0 0
$$709$$ 2.31218e7 1.72745 0.863725 0.503964i $$-0.168125\pi$$
0.863725 + 0.503964i $$0.168125\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −1.19850e6 −0.0882903
$$714$$ 0 0
$$715$$ 2.97302e6 0.217487
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1.12905e7 0.814497 0.407249 0.913317i $$-0.366488\pi$$
0.407249 + 0.913317i $$0.366488\pi$$
$$720$$ 0 0
$$721$$ 806736. 0.0577954
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1.26155e7 −0.891371
$$726$$ 0 0
$$727$$ −1.10545e7 −0.775719 −0.387859 0.921719i $$-0.626785\pi$$
−0.387859 + 0.921719i $$0.626785\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 1.65020e7 1.14220
$$732$$ 0 0
$$733$$ −9.39718e6 −0.646007 −0.323004 0.946398i $$-0.604693\pi$$
−0.323004 + 0.946398i $$0.604693\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −5.37322e6 −0.364389
$$738$$ 0 0
$$739$$ −1.69963e7 −1.14484 −0.572418 0.819962i $$-0.693995\pi$$
−0.572418 + 0.819962i $$0.693995\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 4.70520e6 0.312684 0.156342 0.987703i $$-0.450030\pi$$
0.156342 + 0.987703i $$0.450030\pi$$
$$744$$ 0 0
$$745$$ −2.05396e7 −1.35582
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 5.56836e6 0.362679
$$750$$ 0 0
$$751$$ 8.00214e6 0.517734 0.258867 0.965913i $$-0.416651\pi$$
0.258867 + 0.965913i $$0.416651\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −2.75925e7 −1.76167
$$756$$ 0 0
$$757$$ 2.00466e7 1.27146 0.635729 0.771912i $$-0.280700\pi$$
0.635729 + 0.771912i $$0.280700\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −9.39759e6 −0.588240 −0.294120 0.955768i $$-0.595027\pi$$
−0.294120 + 0.955768i $$0.595027\pi$$
$$762$$ 0 0
$$763$$ −5.26133e6 −0.327178
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 9.16682e6 0.562640
$$768$$ 0 0
$$769$$ 8.43805e6 0.514548 0.257274 0.966338i $$-0.417176\pi$$
0.257274 + 0.966338i $$0.417176\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −2.59390e7 −1.56137 −0.780684 0.624926i $$-0.785129\pi$$
−0.780684 + 0.624926i $$0.785129\pi$$
$$774$$ 0 0
$$775$$ 1.26014e6 0.0753639
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1.68870e7 −0.997031
$$780$$ 0 0
$$781$$ 749088. 0.0439446
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −3.94152e7 −2.28291
$$786$$ 0 0
$$787$$ −2.77502e7 −1.59709 −0.798544 0.601936i $$-0.794396\pi$$
−0.798544 + 0.601936i $$0.794396\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −4.25153e6 −0.241604
$$792$$ 0 0
$$793$$ −3.31192e6 −0.187024
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 2.66947e7 1.48860 0.744301 0.667844i $$-0.232783\pi$$
0.744301 + 0.667844i $$0.232783\pi$$
$$798$$ 0 0
$$799$$ −2.53114e7 −1.40265
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −7.00142e6 −0.383175
$$804$$ 0 0
$$805$$ −8.10774e6 −0.440971
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −2.62003e6 −0.140745 −0.0703727 0.997521i $$-0.522419\pi$$
−0.0703727 + 0.997521i $$0.522419\pi$$
$$810$$ 0 0
$$811$$ 1.86925e7 0.997965 0.498983 0.866612i $$-0.333707\pi$$
0.498983 + 0.866612i $$0.333707\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 4.03421e7 2.12748
$$816$$ 0 0
$$817$$ −1.38997e7 −0.728533
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −7.31881e6 −0.378950 −0.189475 0.981886i $$-0.560679\pi$$
−0.189475 + 0.981886i $$0.560679\pi$$
$$822$$ 0 0
$$823$$ −1.28122e7 −0.659362 −0.329681 0.944092i $$-0.606941\pi$$
−0.329681 + 0.944092i $$0.606941\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −8.71034e6 −0.442865 −0.221433 0.975176i $$-0.571073\pi$$
−0.221433 + 0.975176i $$0.571073\pi$$
$$828$$ 0 0
$$829$$ −2.02190e7 −1.02182 −0.510909 0.859635i $$-0.670691\pi$$
−0.510909 + 0.859635i $$0.670691\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −2.58828e6 −0.129240
$$834$$ 0 0
$$835$$ 2.25090e7 1.11722
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −8.72741e6 −0.428036 −0.214018 0.976830i $$-0.568655\pi$$
−0.214018 + 0.976830i $$0.568655\pi$$
$$840$$ 0 0
$$841$$ 8.28281e6 0.403820
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 2.49156e7 1.20041
$$846$$ 0 0
$$847$$ 5.60536e6 0.268469
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −8.49233e6 −0.401979
$$852$$ 0 0
$$853$$ 2.45049e7 1.15313 0.576567 0.817050i $$-0.304392\pi$$
0.576567 + 0.817050i $$0.304392\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −4.02514e7 −1.87210 −0.936050 0.351867i $$-0.885547\pi$$
−0.936050 + 0.351867i $$0.885547\pi$$
$$858$$ 0 0
$$859$$ 2.23124e7 1.03172 0.515862 0.856672i $$-0.327472\pi$$
0.515862 + 0.856672i $$0.327472\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −3.76747e7 −1.72196 −0.860980 0.508639i $$-0.830149\pi$$
−0.860980 + 0.508639i $$0.830149\pi$$
$$864$$ 0 0
$$865$$ 8.02944e6 0.364876
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −5.48294e6 −0.246300
$$870$$ 0 0
$$871$$ 4.62694e6 0.206656
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −2.80652e6 −0.123922
$$876$$ 0 0
$$877$$ 2.44552e7 1.07367 0.536837 0.843686i $$-0.319619\pi$$
0.536837 + 0.843686i $$0.319619\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 1.92174e7 0.834169 0.417084 0.908868i $$-0.363052\pi$$
0.417084 + 0.908868i $$0.363052\pi$$
$$882$$ 0 0
$$883$$ −8.50546e6 −0.367110 −0.183555 0.983009i $$-0.558761\pi$$
−0.183555 + 0.983009i $$0.558761\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1.50375e7 0.641753 0.320876 0.947121i $$-0.396023\pi$$
0.320876 + 0.947121i $$0.396023\pi$$
$$888$$ 0 0
$$889$$ −4.80474e6 −0.203899
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 2.13198e7 0.894654
$$894$$ 0 0
$$895$$ −4.59333e6 −0.191677
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −2.87618e6 −0.118691
$$900$$ 0 0
$$901$$ 9.76884e6 0.400895
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −5.64423e7 −2.29078
$$906$$ 0 0
$$907$$ 7.46525e6 0.301319 0.150659 0.988586i $$-0.451860\pi$$
0.150659 + 0.988586i $$0.451860\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −2.50368e7 −0.999500 −0.499750 0.866170i $$-0.666575\pi$$
−0.499750 + 0.866170i $$0.666575\pi$$
$$912$$ 0 0
$$913$$ −1.45333e7 −0.577017
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −7.86960e6 −0.309050
$$918$$ 0 0
$$919$$ −2.32108e6 −0.0906570 −0.0453285 0.998972i $$-0.514433\pi$$
−0.0453285 + 0.998972i $$0.514433\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −645048. −0.0249223
$$924$$ 0 0
$$925$$ 8.92910e6 0.343126
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −2.84131e7 −1.08014 −0.540069 0.841621i $$-0.681602\pi$$
−0.540069 + 0.841621i $$0.681602\pi$$
$$930$$ 0 0
$$931$$ 2.18011e6 0.0824335
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 1.72308e7 0.644578
$$936$$ 0 0
$$937$$ −1.92186e7 −0.715109 −0.357555 0.933892i $$-0.616389\pi$$
−0.357555 + 0.933892i $$0.616389\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −6.13365e6 −0.225811 −0.112905 0.993606i $$-0.536016\pi$$
−0.112905 + 0.993606i $$0.536016\pi$$
$$942$$ 0 0
$$943$$ 4.15851e7 1.52286
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −1.89945e7 −0.688260 −0.344130 0.938922i $$-0.611826\pi$$
−0.344130 + 0.938922i $$0.611826\pi$$
$$948$$ 0 0
$$949$$ 6.02900e6 0.217310
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 459686. 0.0163957 0.00819783 0.999966i $$-0.497391\pi$$
0.00819783 + 0.999966i $$0.497391\pi$$
$$954$$ 0 0
$$955$$ 2.74567e7 0.974180
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −4.88501e6 −0.171522
$$960$$ 0 0
$$961$$ −2.83419e7 −0.989965
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 2.77895e7 0.960644
$$966$$ 0 0
$$967$$ −3.31883e7 −1.14135 −0.570674 0.821177i $$-0.693318\pi$$
−0.570674 + 0.821177i $$0.693318\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −5.06987e7 −1.72564 −0.862818 0.505515i $$-0.831303\pi$$
−0.862818 + 0.505515i $$0.831303\pi$$
$$972$$ 0 0
$$973$$ −5.41489e6 −0.183361
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 5.67557e6 0.190228 0.0951138 0.995466i $$-0.469679\pi$$
0.0951138 + 0.995466i $$0.469679\pi$$
$$978$$ 0 0
$$979$$ 150768. 0.00502750
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 1.81000e7 0.597441 0.298720 0.954341i $$-0.403440\pi$$
0.298720 + 0.954341i $$0.403440\pi$$
$$984$$ 0 0
$$985$$ −7.97739e7 −2.61981
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 3.42287e7 1.11275
$$990$$ 0 0
$$991$$ 3.99088e7 1.29088 0.645439 0.763812i $$-0.276675\pi$$
0.645439 + 0.763812i $$0.276675\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −4.46072e6 −0.142839
$$996$$ 0 0
$$997$$ −3.19517e7 −1.01802 −0.509009 0.860761i $$-0.669988\pi$$
−0.509009 + 0.860761i $$0.669988\pi$$
$$998$$ 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.e.1.1 1
3.2 odd 2 336.6.a.p.1.1 1
4.3 odd 2 504.6.a.a.1.1 1
12.11 even 2 168.6.a.c.1.1 1

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