Properties

 Label 2200.4.a.f.1.1 Level $2200$ Weight $4$ Character 2200.1 Self dual yes Analytic conductor $129.804$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2200,4,Mod(1,2200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2200, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2200.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2200 = 2^{3} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 2200.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: $$129.804202013$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 88) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2200.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{3} +6.00000 q^{7} -26.0000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{3} +6.00000 q^{7} -26.0000 q^{9} -11.0000 q^{11} +40.0000 q^{13} +78.0000 q^{17} +36.0000 q^{19} +6.00000 q^{21} -7.00000 q^{23} -53.0000 q^{27} +8.00000 q^{29} +183.000 q^{31} -11.0000 q^{33} -227.000 q^{37} +40.0000 q^{39} -36.0000 q^{41} -322.000 q^{43} +184.000 q^{47} -307.000 q^{49} +78.0000 q^{51} +6.00000 q^{53} +36.0000 q^{57} -99.0000 q^{59} +164.000 q^{61} -156.000 q^{63} +695.000 q^{67} -7.00000 q^{69} -987.000 q^{71} +248.000 q^{73} -66.0000 q^{77} -242.000 q^{79} +649.000 q^{81} +1494.00 q^{83} +8.00000 q^{87} -905.000 q^{89} +240.000 q^{91} +183.000 q^{93} +1031.00 q^{97} +286.000 q^{99} +O(q^{100})$$

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
$$3$$ 1.00000 0.192450 0.0962250 0.995360i $$-0.469323\pi$$
0.0962250 + 0.995360i $$0.469323\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 6.00000 0.323970 0.161985 0.986793i $$-0.448210\pi$$
0.161985 + 0.986793i $$0.448210\pi$$
$$8$$ 0 0
$$9$$ −26.0000 −0.962963
$$10$$ 0 0
$$11$$ −11.0000 −0.301511
$$12$$ 0 0
$$13$$ 40.0000 0.853385 0.426692 0.904397i $$-0.359679\pi$$
0.426692 + 0.904397i $$0.359679\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 78.0000 1.11281 0.556405 0.830911i $$-0.312180\pi$$
0.556405 + 0.830911i $$0.312180\pi$$
$$18$$ 0 0
$$19$$ 36.0000 0.434682 0.217341 0.976096i $$-0.430262\pi$$
0.217341 + 0.976096i $$0.430262\pi$$
$$20$$ 0 0
$$21$$ 6.00000 0.0623480
$$22$$ 0 0
$$23$$ −7.00000 −0.0634609 −0.0317305 0.999496i $$-0.510102\pi$$
−0.0317305 + 0.999496i $$0.510102\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −53.0000 −0.377772
$$28$$ 0 0
$$29$$ 8.00000 0.0512263 0.0256132 0.999672i $$-0.491846\pi$$
0.0256132 + 0.999672i $$0.491846\pi$$
$$30$$ 0 0
$$31$$ 183.000 1.06025 0.530125 0.847919i $$-0.322145\pi$$
0.530125 + 0.847919i $$0.322145\pi$$
$$32$$ 0 0
$$33$$ −11.0000 −0.0580259
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −227.000 −1.00861 −0.504305 0.863526i $$-0.668251\pi$$
−0.504305 + 0.863526i $$0.668251\pi$$
$$38$$ 0 0
$$39$$ 40.0000 0.164234
$$40$$ 0 0
$$41$$ −36.0000 −0.137128 −0.0685641 0.997647i $$-0.521842\pi$$
−0.0685641 + 0.997647i $$0.521842\pi$$
$$42$$ 0 0
$$43$$ −322.000 −1.14197 −0.570983 0.820962i $$-0.693438\pi$$
−0.570983 + 0.820962i $$0.693438\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 184.000 0.571046 0.285523 0.958372i $$-0.407833\pi$$
0.285523 + 0.958372i $$0.407833\pi$$
$$48$$ 0 0
$$49$$ −307.000 −0.895044
$$50$$ 0 0
$$51$$ 78.0000 0.214160
$$52$$ 0 0
$$53$$ 6.00000 0.0155503 0.00777513 0.999970i $$-0.497525\pi$$
0.00777513 + 0.999970i $$0.497525\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 36.0000 0.0836547
$$58$$ 0 0
$$59$$ −99.0000 −0.218453 −0.109226 0.994017i $$-0.534837\pi$$
−0.109226 + 0.994017i $$0.534837\pi$$
$$60$$ 0 0
$$61$$ 164.000 0.344230 0.172115 0.985077i $$-0.444940\pi$$
0.172115 + 0.985077i $$0.444940\pi$$
$$62$$ 0 0
$$63$$ −156.000 −0.311971
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 695.000 1.26728 0.633640 0.773628i $$-0.281560\pi$$
0.633640 + 0.773628i $$0.281560\pi$$
$$68$$ 0 0
$$69$$ −7.00000 −0.0122131
$$70$$ 0 0
$$71$$ −987.000 −1.64979 −0.824897 0.565283i $$-0.808767\pi$$
−0.824897 + 0.565283i $$0.808767\pi$$
$$72$$ 0 0
$$73$$ 248.000 0.397619 0.198810 0.980038i $$-0.436292\pi$$
0.198810 + 0.980038i $$0.436292\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −66.0000 −0.0976805
$$78$$ 0 0
$$79$$ −242.000 −0.344647 −0.172324 0.985040i $$-0.555127\pi$$
−0.172324 + 0.985040i $$0.555127\pi$$
$$80$$ 0 0
$$81$$ 649.000 0.890261
$$82$$ 0 0
$$83$$ 1494.00 1.97576 0.987878 0.155230i $$-0.0496119\pi$$
0.987878 + 0.155230i $$0.0496119\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 8.00000 0.00985851
$$88$$ 0 0
$$89$$ −905.000 −1.07786 −0.538932 0.842350i $$-0.681172\pi$$
−0.538932 + 0.842350i $$0.681172\pi$$
$$90$$ 0 0
$$91$$ 240.000 0.276471
$$92$$ 0 0
$$93$$ 183.000 0.204045
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1031.00 1.07920 0.539599 0.841922i $$-0.318576\pi$$
0.539599 + 0.841922i $$0.318576\pi$$
$$98$$ 0 0
$$99$$ 286.000 0.290344
$$100$$ 0 0
$$101$$ 630.000 0.620667 0.310333 0.950628i $$-0.399559\pi$$
0.310333 + 0.950628i $$0.399559\pi$$
$$102$$ 0 0
$$103$$ −1328.00 −1.27041 −0.635203 0.772346i $$-0.719083\pi$$
−0.635203 + 0.772346i $$0.719083\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −526.000 −0.475237 −0.237618 0.971359i $$-0.576367\pi$$
−0.237618 + 0.971359i $$0.576367\pi$$
$$108$$ 0 0
$$109$$ 2234.00 1.96310 0.981552 0.191194i $$-0.0612360\pi$$
0.981552 + 0.191194i $$0.0612360\pi$$
$$110$$ 0 0
$$111$$ −227.000 −0.194107
$$112$$ 0 0
$$113$$ 1239.00 1.03146 0.515731 0.856750i $$-0.327520\pi$$
0.515731 + 0.856750i $$0.327520\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1040.00 −0.821778
$$118$$ 0 0
$$119$$ 468.000 0.360517
$$120$$ 0 0
$$121$$ 121.000 0.0909091
$$122$$ 0 0
$$123$$ −36.0000 −0.0263903
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −132.000 −0.0922292 −0.0461146 0.998936i $$-0.514684\pi$$
−0.0461146 + 0.998936i $$0.514684\pi$$
$$128$$ 0 0
$$129$$ −322.000 −0.219771
$$130$$ 0 0
$$131$$ 1218.00 0.812345 0.406172 0.913796i $$-0.366863\pi$$
0.406172 + 0.913796i $$0.366863\pi$$
$$132$$ 0 0
$$133$$ 216.000 0.140824
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2775.00 1.73054 0.865271 0.501304i $$-0.167146\pi$$
0.865271 + 0.501304i $$0.167146\pi$$
$$138$$ 0 0
$$139$$ 1222.00 0.745674 0.372837 0.927897i $$-0.378385\pi$$
0.372837 + 0.927897i $$0.378385\pi$$
$$140$$ 0 0
$$141$$ 184.000 0.109898
$$142$$ 0 0
$$143$$ −440.000 −0.257305
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −307.000 −0.172251
$$148$$ 0 0
$$149$$ −1038.00 −0.570713 −0.285357 0.958421i $$-0.592112\pi$$
−0.285357 + 0.958421i $$0.592112\pi$$
$$150$$ 0 0
$$151$$ 3042.00 1.63943 0.819717 0.572769i $$-0.194131\pi$$
0.819717 + 0.572769i $$0.194131\pi$$
$$152$$ 0 0
$$153$$ −2028.00 −1.07160
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 1943.00 0.987696 0.493848 0.869548i $$-0.335590\pi$$
0.493848 + 0.869548i $$0.335590\pi$$
$$158$$ 0 0
$$159$$ 6.00000 0.00299265
$$160$$ 0 0
$$161$$ −42.0000 −0.0205594
$$162$$ 0 0
$$163$$ −2292.00 −1.10137 −0.550685 0.834713i $$-0.685633\pi$$
−0.550685 + 0.834713i $$0.685633\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 3832.00 1.77562 0.887812 0.460207i $$-0.152225\pi$$
0.887812 + 0.460207i $$0.152225\pi$$
$$168$$ 0 0
$$169$$ −597.000 −0.271734
$$170$$ 0 0
$$171$$ −936.000 −0.418583
$$172$$ 0 0
$$173$$ 1734.00 0.762044 0.381022 0.924566i $$-0.375572\pi$$
0.381022 + 0.924566i $$0.375572\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −99.0000 −0.0420412
$$178$$ 0 0
$$179$$ −2295.00 −0.958304 −0.479152 0.877732i $$-0.659056\pi$$
−0.479152 + 0.877732i $$0.659056\pi$$
$$180$$ 0 0
$$181$$ −2865.00 −1.17654 −0.588270 0.808665i $$-0.700191\pi$$
−0.588270 + 0.808665i $$0.700191\pi$$
$$182$$ 0 0
$$183$$ 164.000 0.0662472
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −858.000 −0.335525
$$188$$ 0 0
$$189$$ −318.000 −0.122387
$$190$$ 0 0
$$191$$ 2441.00 0.924736 0.462368 0.886688i $$-0.347000\pi$$
0.462368 + 0.886688i $$0.347000\pi$$
$$192$$ 0 0
$$193$$ 1532.00 0.571377 0.285689 0.958323i $$-0.407778\pi$$
0.285689 + 0.958323i $$0.407778\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2958.00 −1.06979 −0.534895 0.844918i $$-0.679649\pi$$
−0.534895 + 0.844918i $$0.679649\pi$$
$$198$$ 0 0
$$199$$ −2968.00 −1.05727 −0.528633 0.848850i $$-0.677295\pi$$
−0.528633 + 0.848850i $$0.677295\pi$$
$$200$$ 0 0
$$201$$ 695.000 0.243888
$$202$$ 0 0
$$203$$ 48.0000 0.0165958
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 182.000 0.0611105
$$208$$ 0 0
$$209$$ −396.000 −0.131062
$$210$$ 0 0
$$211$$ 60.0000 0.0195762 0.00978808 0.999952i $$-0.496884\pi$$
0.00978808 + 0.999952i $$0.496884\pi$$
$$212$$ 0 0
$$213$$ −987.000 −0.317503
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 1098.00 0.343489
$$218$$ 0 0
$$219$$ 248.000 0.0765219
$$220$$ 0 0
$$221$$ 3120.00 0.949656
$$222$$ 0 0
$$223$$ −723.000 −0.217111 −0.108555 0.994090i $$-0.534622\pi$$
−0.108555 + 0.994090i $$0.534622\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 4466.00 1.30581 0.652905 0.757440i $$-0.273550\pi$$
0.652905 + 0.757440i $$0.273550\pi$$
$$228$$ 0 0
$$229$$ −4609.00 −1.33001 −0.665003 0.746841i $$-0.731570\pi$$
−0.665003 + 0.746841i $$0.731570\pi$$
$$230$$ 0 0
$$231$$ −66.0000 −0.0187986
$$232$$ 0 0
$$233$$ −4768.00 −1.34061 −0.670305 0.742086i $$-0.733837\pi$$
−0.670305 + 0.742086i $$0.733837\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −242.000 −0.0663274
$$238$$ 0 0
$$239$$ 4802.00 1.29965 0.649823 0.760085i $$-0.274843\pi$$
0.649823 + 0.760085i $$0.274843\pi$$
$$240$$ 0 0
$$241$$ 3920.00 1.04776 0.523878 0.851793i $$-0.324485\pi$$
0.523878 + 0.851793i $$0.324485\pi$$
$$242$$ 0 0
$$243$$ 2080.00 0.549103
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1440.00 0.370951
$$248$$ 0 0
$$249$$ 1494.00 0.380235
$$250$$ 0 0
$$251$$ 6057.00 1.52317 0.761583 0.648068i $$-0.224423\pi$$
0.761583 + 0.648068i $$0.224423\pi$$
$$252$$ 0 0
$$253$$ 77.0000 0.0191342
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −3270.00 −0.793685 −0.396842 0.917887i $$-0.629894\pi$$
−0.396842 + 0.917887i $$0.629894\pi$$
$$258$$ 0 0
$$259$$ −1362.00 −0.326759
$$260$$ 0 0
$$261$$ −208.000 −0.0493290
$$262$$ 0 0
$$263$$ 6102.00 1.43067 0.715334 0.698783i $$-0.246275\pi$$
0.715334 + 0.698783i $$0.246275\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −905.000 −0.207435
$$268$$ 0 0
$$269$$ −1166.00 −0.264284 −0.132142 0.991231i $$-0.542185\pi$$
−0.132142 + 0.991231i $$0.542185\pi$$
$$270$$ 0 0
$$271$$ 6680.00 1.49735 0.748674 0.662939i $$-0.230691\pi$$
0.748674 + 0.662939i $$0.230691\pi$$
$$272$$ 0 0
$$273$$ 240.000 0.0532068
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −1014.00 −0.219947 −0.109974 0.993935i $$-0.535077\pi$$
−0.109974 + 0.993935i $$0.535077\pi$$
$$278$$ 0 0
$$279$$ −4758.00 −1.02098
$$280$$ 0 0
$$281$$ 8326.00 1.76757 0.883786 0.467892i $$-0.154986\pi$$
0.883786 + 0.467892i $$0.154986\pi$$
$$282$$ 0 0
$$283$$ −1308.00 −0.274744 −0.137372 0.990520i $$-0.543866\pi$$
−0.137372 + 0.990520i $$0.543866\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −216.000 −0.0444254
$$288$$ 0 0
$$289$$ 1171.00 0.238347
$$290$$ 0 0
$$291$$ 1031.00 0.207692
$$292$$ 0 0
$$293$$ 3516.00 0.701047 0.350524 0.936554i $$-0.386004\pi$$
0.350524 + 0.936554i $$0.386004\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 583.000 0.113903
$$298$$ 0 0
$$299$$ −280.000 −0.0541566
$$300$$ 0 0
$$301$$ −1932.00 −0.369962
$$302$$ 0 0
$$303$$ 630.000 0.119447
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 9652.00 1.79436 0.897180 0.441664i $$-0.145612\pi$$
0.897180 + 0.441664i $$0.145612\pi$$
$$308$$ 0 0
$$309$$ −1328.00 −0.244490
$$310$$ 0 0
$$311$$ −852.000 −0.155346 −0.0776728 0.996979i $$-0.524749\pi$$
−0.0776728 + 0.996979i $$0.524749\pi$$
$$312$$ 0 0
$$313$$ 3313.00 0.598281 0.299140 0.954209i $$-0.403300\pi$$
0.299140 + 0.954209i $$0.403300\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 3035.00 0.537737 0.268868 0.963177i $$-0.413350\pi$$
0.268868 + 0.963177i $$0.413350\pi$$
$$318$$ 0 0
$$319$$ −88.0000 −0.0154453
$$320$$ 0 0
$$321$$ −526.000 −0.0914594
$$322$$ 0 0
$$323$$ 2808.00 0.483719
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 2234.00 0.377800
$$328$$ 0 0
$$329$$ 1104.00 0.185001
$$330$$ 0 0
$$331$$ 1655.00 0.274825 0.137412 0.990514i $$-0.456121\pi$$
0.137412 + 0.990514i $$0.456121\pi$$
$$332$$ 0 0
$$333$$ 5902.00 0.971254
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 6130.00 0.990868 0.495434 0.868646i $$-0.335009\pi$$
0.495434 + 0.868646i $$0.335009\pi$$
$$338$$ 0 0
$$339$$ 1239.00 0.198505
$$340$$ 0 0
$$341$$ −2013.00 −0.319678
$$342$$ 0 0
$$343$$ −3900.00 −0.613936
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 696.000 0.107675 0.0538375 0.998550i $$-0.482855\pi$$
0.0538375 + 0.998550i $$0.482855\pi$$
$$348$$ 0 0
$$349$$ −12526.0 −1.92121 −0.960604 0.277922i $$-0.910354\pi$$
−0.960604 + 0.277922i $$0.910354\pi$$
$$350$$ 0 0
$$351$$ −2120.00 −0.322385
$$352$$ 0 0
$$353$$ −7411.00 −1.11742 −0.558708 0.829365i $$-0.688703\pi$$
−0.558708 + 0.829365i $$0.688703\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 468.000 0.0693815
$$358$$ 0 0
$$359$$ 4096.00 0.602169 0.301084 0.953597i $$-0.402651\pi$$
0.301084 + 0.953597i $$0.402651\pi$$
$$360$$ 0 0
$$361$$ −5563.00 −0.811051
$$362$$ 0 0
$$363$$ 121.000 0.0174955
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 6721.00 0.955949 0.477975 0.878374i $$-0.341371\pi$$
0.477975 + 0.878374i $$0.341371\pi$$
$$368$$ 0 0
$$369$$ 936.000 0.132049
$$370$$ 0 0
$$371$$ 36.0000 0.00503781
$$372$$ 0 0
$$373$$ 6854.00 0.951439 0.475719 0.879597i $$-0.342188\pi$$
0.475719 + 0.879597i $$0.342188\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 320.000 0.0437158
$$378$$ 0 0
$$379$$ 12155.0 1.64739 0.823694 0.567034i $$-0.191909\pi$$
0.823694 + 0.567034i $$0.191909\pi$$
$$380$$ 0 0
$$381$$ −132.000 −0.0177495
$$382$$ 0 0
$$383$$ −10447.0 −1.39378 −0.696889 0.717179i $$-0.745433\pi$$
−0.696889 + 0.717179i $$0.745433\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 8372.00 1.09967
$$388$$ 0 0
$$389$$ −7863.00 −1.02486 −0.512429 0.858729i $$-0.671254\pi$$
−0.512429 + 0.858729i $$0.671254\pi$$
$$390$$ 0 0
$$391$$ −546.000 −0.0706200
$$392$$ 0 0
$$393$$ 1218.00 0.156336
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −6142.00 −0.776469 −0.388234 0.921561i $$-0.626915\pi$$
−0.388234 + 0.921561i $$0.626915\pi$$
$$398$$ 0 0
$$399$$ 216.000 0.0271016
$$400$$ 0 0
$$401$$ 12074.0 1.50361 0.751804 0.659387i $$-0.229184\pi$$
0.751804 + 0.659387i $$0.229184\pi$$
$$402$$ 0 0
$$403$$ 7320.00 0.904802
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 2497.00 0.304107
$$408$$ 0 0
$$409$$ −1454.00 −0.175784 −0.0878920 0.996130i $$-0.528013\pi$$
−0.0878920 + 0.996130i $$0.528013\pi$$
$$410$$ 0 0
$$411$$ 2775.00 0.333043
$$412$$ 0 0
$$413$$ −594.000 −0.0707720
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 1222.00 0.143505
$$418$$ 0 0
$$419$$ 5308.00 0.618885 0.309442 0.950918i $$-0.399858\pi$$
0.309442 + 0.950918i $$0.399858\pi$$
$$420$$ 0 0
$$421$$ 13030.0 1.50842 0.754208 0.656635i $$-0.228021\pi$$
0.754208 + 0.656635i $$0.228021\pi$$
$$422$$ 0 0
$$423$$ −4784.00 −0.549896
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 984.000 0.111520
$$428$$ 0 0
$$429$$ −440.000 −0.0495184
$$430$$ 0 0
$$431$$ 2194.00 0.245200 0.122600 0.992456i $$-0.460877\pi$$
0.122600 + 0.992456i $$0.460877\pi$$
$$432$$ 0 0
$$433$$ 5459.00 0.605873 0.302936 0.953011i $$-0.402033\pi$$
0.302936 + 0.953011i $$0.402033\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −252.000 −0.0275853
$$438$$ 0 0
$$439$$ −12208.0 −1.32723 −0.663617 0.748072i $$-0.730980\pi$$
−0.663617 + 0.748072i $$0.730980\pi$$
$$440$$ 0 0
$$441$$ 7982.00 0.861894
$$442$$ 0 0
$$443$$ −10997.0 −1.17942 −0.589710 0.807615i $$-0.700758\pi$$
−0.589710 + 0.807615i $$0.700758\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −1038.00 −0.109834
$$448$$ 0 0
$$449$$ 891.000 0.0936501 0.0468250 0.998903i $$-0.485090\pi$$
0.0468250 + 0.998903i $$0.485090\pi$$
$$450$$ 0 0
$$451$$ 396.000 0.0413457
$$452$$ 0 0
$$453$$ 3042.00 0.315509
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −10396.0 −1.06412 −0.532062 0.846706i $$-0.678583\pi$$
−0.532062 + 0.846706i $$0.678583\pi$$
$$458$$ 0 0
$$459$$ −4134.00 −0.420389
$$460$$ 0 0
$$461$$ −3708.00 −0.374618 −0.187309 0.982301i $$-0.559977\pi$$
−0.187309 + 0.982301i $$0.559977\pi$$
$$462$$ 0 0
$$463$$ 2651.00 0.266096 0.133048 0.991110i $$-0.457524\pi$$
0.133048 + 0.991110i $$0.457524\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −1061.00 −0.105133 −0.0525666 0.998617i $$-0.516740\pi$$
−0.0525666 + 0.998617i $$0.516740\pi$$
$$468$$ 0 0
$$469$$ 4170.00 0.410560
$$470$$ 0 0
$$471$$ 1943.00 0.190082
$$472$$ 0 0
$$473$$ 3542.00 0.344316
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −156.000 −0.0149743
$$478$$ 0 0
$$479$$ 6752.00 0.644064 0.322032 0.946729i $$-0.395634\pi$$
0.322032 + 0.946729i $$0.395634\pi$$
$$480$$ 0 0
$$481$$ −9080.00 −0.860733
$$482$$ 0 0
$$483$$ −42.0000 −0.00395666
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 13073.0 1.21642 0.608208 0.793778i $$-0.291889\pi$$
0.608208 + 0.793778i $$0.291889\pi$$
$$488$$ 0 0
$$489$$ −2292.00 −0.211959
$$490$$ 0 0
$$491$$ −4072.00 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$492$$ 0 0
$$493$$ 624.000 0.0570052
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −5922.00 −0.534483
$$498$$ 0 0
$$499$$ −16060.0 −1.44077 −0.720385 0.693574i $$-0.756035\pi$$
−0.720385 + 0.693574i $$0.756035\pi$$
$$500$$ 0 0
$$501$$ 3832.00 0.341719
$$502$$ 0 0
$$503$$ 7650.00 0.678125 0.339062 0.940764i $$-0.389890\pi$$
0.339062 + 0.940764i $$0.389890\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −597.000 −0.0522953
$$508$$ 0 0
$$509$$ −3777.00 −0.328905 −0.164452 0.986385i $$-0.552586\pi$$
−0.164452 + 0.986385i $$0.552586\pi$$
$$510$$ 0 0
$$511$$ 1488.00 0.128817
$$512$$ 0 0
$$513$$ −1908.00 −0.164211
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −2024.00 −0.172177
$$518$$ 0 0
$$519$$ 1734.00 0.146655
$$520$$ 0 0
$$521$$ −10883.0 −0.915149 −0.457575 0.889171i $$-0.651282\pi$$
−0.457575 + 0.889171i $$0.651282\pi$$
$$522$$ 0 0
$$523$$ −12748.0 −1.06583 −0.532917 0.846168i $$-0.678904\pi$$
−0.532917 + 0.846168i $$0.678904\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 14274.0 1.17986
$$528$$ 0 0
$$529$$ −12118.0 −0.995973
$$530$$ 0 0
$$531$$ 2574.00 0.210362
$$532$$ 0 0
$$533$$ −1440.00 −0.117023
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −2295.00 −0.184426
$$538$$ 0 0
$$539$$ 3377.00 0.269866
$$540$$ 0 0
$$541$$ 23012.0 1.82877 0.914384 0.404849i $$-0.132676\pi$$
0.914384 + 0.404849i $$0.132676\pi$$
$$542$$ 0 0
$$543$$ −2865.00 −0.226425
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 8400.00 0.656596 0.328298 0.944574i $$-0.393525\pi$$
0.328298 + 0.944574i $$0.393525\pi$$
$$548$$ 0 0
$$549$$ −4264.00 −0.331481
$$550$$ 0 0
$$551$$ 288.000 0.0222672
$$552$$ 0 0
$$553$$ −1452.00 −0.111655
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −2426.00 −0.184547 −0.0922737 0.995734i $$-0.529413\pi$$
−0.0922737 + 0.995734i $$0.529413\pi$$
$$558$$ 0 0
$$559$$ −12880.0 −0.974537
$$560$$ 0 0
$$561$$ −858.000 −0.0645718
$$562$$ 0 0
$$563$$ 14484.0 1.08424 0.542121 0.840301i $$-0.317622\pi$$
0.542121 + 0.840301i $$0.317622\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 3894.00 0.288417
$$568$$ 0 0
$$569$$ 1784.00 0.131440 0.0657198 0.997838i $$-0.479066\pi$$
0.0657198 + 0.997838i $$0.479066\pi$$
$$570$$ 0 0
$$571$$ −3564.00 −0.261206 −0.130603 0.991435i $$-0.541691\pi$$
−0.130603 + 0.991435i $$0.541691\pi$$
$$572$$ 0 0
$$573$$ 2441.00 0.177966
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −1081.00 −0.0779941 −0.0389971 0.999239i $$-0.512416\pi$$
−0.0389971 + 0.999239i $$0.512416\pi$$
$$578$$ 0 0
$$579$$ 1532.00 0.109962
$$580$$ 0 0
$$581$$ 8964.00 0.640085
$$582$$ 0 0
$$583$$ −66.0000 −0.00468858
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 9324.00 0.655609 0.327805 0.944746i $$-0.393691\pi$$
0.327805 + 0.944746i $$0.393691\pi$$
$$588$$ 0 0
$$589$$ 6588.00 0.460872
$$590$$ 0 0
$$591$$ −2958.00 −0.205881
$$592$$ 0 0
$$593$$ 8548.00 0.591947 0.295973 0.955196i $$-0.404356\pi$$
0.295973 + 0.955196i $$0.404356\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −2968.00 −0.203471
$$598$$ 0 0
$$599$$ 4512.00 0.307772 0.153886 0.988089i $$-0.450821\pi$$
0.153886 + 0.988089i $$0.450821\pi$$
$$600$$ 0 0
$$601$$ −14242.0 −0.966628 −0.483314 0.875447i $$-0.660567\pi$$
−0.483314 + 0.875447i $$0.660567\pi$$
$$602$$ 0 0
$$603$$ −18070.0 −1.22034
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −24386.0 −1.63064 −0.815319 0.579012i $$-0.803438\pi$$
−0.815319 + 0.579012i $$0.803438\pi$$
$$608$$ 0 0
$$609$$ 48.0000 0.00319386
$$610$$ 0 0
$$611$$ 7360.00 0.487322
$$612$$ 0 0
$$613$$ −26608.0 −1.75316 −0.876580 0.481256i $$-0.840181\pi$$
−0.876580 + 0.481256i $$0.840181\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 5246.00 0.342295 0.171147 0.985245i $$-0.445253\pi$$
0.171147 + 0.985245i $$0.445253\pi$$
$$618$$ 0 0
$$619$$ 20823.0 1.35210 0.676048 0.736858i $$-0.263691\pi$$
0.676048 + 0.736858i $$0.263691\pi$$
$$620$$ 0 0
$$621$$ 371.000 0.0239738
$$622$$ 0 0
$$623$$ −5430.00 −0.349195
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −396.000 −0.0252228
$$628$$ 0 0
$$629$$ −17706.0 −1.12239
$$630$$ 0 0
$$631$$ 29279.0 1.84719 0.923596 0.383366i $$-0.125235\pi$$
0.923596 + 0.383366i $$0.125235\pi$$
$$632$$ 0 0
$$633$$ 60.0000 0.00376743
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −12280.0 −0.763817
$$638$$ 0 0
$$639$$ 25662.0 1.58869
$$640$$ 0 0
$$641$$ −9209.00 −0.567447 −0.283724 0.958906i $$-0.591570\pi$$
−0.283724 + 0.958906i $$0.591570\pi$$
$$642$$ 0 0
$$643$$ 21331.0 1.30826 0.654131 0.756381i $$-0.273034\pi$$
0.654131 + 0.756381i $$0.273034\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 18135.0 1.10195 0.550974 0.834522i $$-0.314256\pi$$
0.550974 + 0.834522i $$0.314256\pi$$
$$648$$ 0 0
$$649$$ 1089.00 0.0658659
$$650$$ 0 0
$$651$$ 1098.00 0.0661045
$$652$$ 0 0
$$653$$ 3193.00 0.191350 0.0956751 0.995413i $$-0.469499\pi$$
0.0956751 + 0.995413i $$0.469499\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −6448.00 −0.382893
$$658$$ 0 0
$$659$$ 31778.0 1.87844 0.939222 0.343309i $$-0.111548\pi$$
0.939222 + 0.343309i $$0.111548\pi$$
$$660$$ 0 0
$$661$$ −14747.0 −0.867764 −0.433882 0.900970i $$-0.642856\pi$$
−0.433882 + 0.900970i $$0.642856\pi$$
$$662$$ 0 0
$$663$$ 3120.00 0.182761
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −56.0000 −0.00325087
$$668$$ 0 0
$$669$$ −723.000 −0.0417830
$$670$$ 0 0
$$671$$ −1804.00 −0.103789
$$672$$ 0 0
$$673$$ −62.0000 −0.00355115 −0.00177558 0.999998i $$-0.500565\pi$$
−0.00177558 + 0.999998i $$0.500565\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 12670.0 0.719273 0.359636 0.933093i $$-0.382901\pi$$
0.359636 + 0.933093i $$0.382901\pi$$
$$678$$ 0 0
$$679$$ 6186.00 0.349627
$$680$$ 0 0
$$681$$ 4466.00 0.251303
$$682$$ 0 0
$$683$$ −11816.0 −0.661972 −0.330986 0.943636i $$-0.607381\pi$$
−0.330986 + 0.943636i $$0.607381\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −4609.00 −0.255960
$$688$$ 0 0
$$689$$ 240.000 0.0132704
$$690$$ 0 0
$$691$$ 3441.00 0.189438 0.0947191 0.995504i $$-0.469805\pi$$
0.0947191 + 0.995504i $$0.469805\pi$$
$$692$$ 0 0
$$693$$ 1716.00 0.0940627
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −2808.00 −0.152598
$$698$$ 0 0
$$699$$ −4768.00 −0.258000
$$700$$ 0 0
$$701$$ −13690.0 −0.737609 −0.368805 0.929507i $$-0.620233\pi$$
−0.368805 + 0.929507i $$0.620233\pi$$
$$702$$ 0 0
$$703$$ −8172.00 −0.438425
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 3780.00 0.201077
$$708$$ 0 0
$$709$$ 71.0000 0.00376088 0.00188044 0.999998i $$-0.499401\pi$$
0.00188044 + 0.999998i $$0.499401\pi$$
$$710$$ 0 0
$$711$$ 6292.00 0.331882
$$712$$ 0 0
$$713$$ −1281.00 −0.0672845
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 4802.00 0.250117
$$718$$ 0 0
$$719$$ 26503.0 1.37468 0.687340 0.726336i $$-0.258778\pi$$
0.687340 + 0.726336i $$0.258778\pi$$
$$720$$ 0 0
$$721$$ −7968.00 −0.411573
$$722$$ 0 0
$$723$$ 3920.00 0.201641
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 18165.0 0.926689 0.463344 0.886178i $$-0.346649\pi$$
0.463344 + 0.886178i $$0.346649\pi$$
$$728$$ 0 0
$$729$$ −15443.0 −0.784586
$$730$$ 0 0
$$731$$ −25116.0 −1.27079
$$732$$ 0 0
$$733$$ 572.000 0.0288231 0.0144115 0.999896i $$-0.495413\pi$$
0.0144115 + 0.999896i $$0.495413\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −7645.00 −0.382099
$$738$$ 0 0
$$739$$ 17026.0 0.847512 0.423756 0.905776i $$-0.360711\pi$$
0.423756 + 0.905776i $$0.360711\pi$$
$$740$$ 0 0
$$741$$ 1440.00 0.0713896
$$742$$ 0 0
$$743$$ −1028.00 −0.0507586 −0.0253793 0.999678i $$-0.508079\pi$$
−0.0253793 + 0.999678i $$0.508079\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −38844.0 −1.90258
$$748$$ 0 0
$$749$$ −3156.00 −0.153962
$$750$$ 0 0
$$751$$ −37527.0 −1.82341 −0.911704 0.410847i $$-0.865233\pi$$
−0.911704 + 0.410847i $$0.865233\pi$$
$$752$$ 0 0
$$753$$ 6057.00 0.293133
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −29330.0 −1.40821 −0.704106 0.710095i $$-0.748652\pi$$
−0.704106 + 0.710095i $$0.748652\pi$$
$$758$$ 0 0
$$759$$ 77.0000 0.00368238
$$760$$ 0 0
$$761$$ −30520.0 −1.45381 −0.726905 0.686738i $$-0.759042\pi$$
−0.726905 + 0.686738i $$0.759042\pi$$
$$762$$ 0 0
$$763$$ 13404.0 0.635986
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −3960.00 −0.186424
$$768$$ 0 0
$$769$$ −25816.0 −1.21060 −0.605298 0.795999i $$-0.706946\pi$$
−0.605298 + 0.795999i $$0.706946\pi$$
$$770$$ 0 0
$$771$$ −3270.00 −0.152745
$$772$$ 0 0
$$773$$ 37182.0 1.73007 0.865035 0.501712i $$-0.167296\pi$$
0.865035 + 0.501712i $$0.167296\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −1362.00 −0.0628848
$$778$$ 0 0
$$779$$ −1296.00 −0.0596072
$$780$$ 0 0
$$781$$ 10857.0 0.497432
$$782$$ 0 0
$$783$$ −424.000 −0.0193519
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 7848.00 0.355465 0.177733 0.984079i $$-0.443124\pi$$
0.177733 + 0.984079i $$0.443124\pi$$
$$788$$ 0 0
$$789$$ 6102.00 0.275332
$$790$$ 0 0
$$791$$ 7434.00 0.334163
$$792$$ 0 0
$$793$$ 6560.00 0.293761
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 6267.00 0.278530 0.139265 0.990255i $$-0.455526\pi$$
0.139265 + 0.990255i $$0.455526\pi$$
$$798$$ 0 0
$$799$$ 14352.0 0.635466
$$800$$ 0 0
$$801$$ 23530.0 1.03794
$$802$$ 0 0
$$803$$ −2728.00 −0.119887
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −1166.00 −0.0508614
$$808$$ 0 0
$$809$$ −10332.0 −0.449016 −0.224508 0.974472i $$-0.572077\pi$$
−0.224508 + 0.974472i $$0.572077\pi$$
$$810$$ 0 0
$$811$$ −24926.0 −1.07925 −0.539624 0.841906i $$-0.681434\pi$$
−0.539624 + 0.841906i $$0.681434\pi$$
$$812$$ 0 0
$$813$$ 6680.00 0.288165
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −11592.0 −0.496393
$$818$$ 0 0
$$819$$ −6240.00 −0.266231
$$820$$ 0 0
$$821$$ 11366.0 0.483162 0.241581 0.970381i $$-0.422334\pi$$
0.241581 + 0.970381i $$0.422334\pi$$
$$822$$ 0 0
$$823$$ 35337.0 1.49668 0.748342 0.663313i $$-0.230850\pi$$
0.748342 + 0.663313i $$0.230850\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 13128.0 0.552002 0.276001 0.961157i $$-0.410991\pi$$
0.276001 + 0.961157i $$0.410991\pi$$
$$828$$ 0 0
$$829$$ 25185.0 1.05514 0.527570 0.849512i $$-0.323103\pi$$
0.527570 + 0.849512i $$0.323103\pi$$
$$830$$ 0 0
$$831$$ −1014.00 −0.0423288
$$832$$ 0 0
$$833$$ −23946.0 −0.996014
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −9699.00 −0.400533
$$838$$ 0 0
$$839$$ −37821.0 −1.55629 −0.778144 0.628086i $$-0.783839\pi$$
−0.778144 + 0.628086i $$0.783839\pi$$
$$840$$ 0 0
$$841$$ −24325.0 −0.997376
$$842$$ 0 0
$$843$$ 8326.00 0.340169
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 726.000 0.0294518
$$848$$ 0 0
$$849$$ −1308.00 −0.0528745
$$850$$ 0 0
$$851$$ 1589.00 0.0640073
$$852$$ 0 0
$$853$$ −6638.00 −0.266449 −0.133224 0.991086i $$-0.542533\pi$$
−0.133224 + 0.991086i $$0.542533\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −42408.0 −1.69035 −0.845175 0.534490i $$-0.820504\pi$$
−0.845175 + 0.534490i $$0.820504\pi$$
$$858$$ 0 0
$$859$$ −16591.0 −0.658996 −0.329498 0.944156i $$-0.606880\pi$$
−0.329498 + 0.944156i $$0.606880\pi$$
$$860$$ 0 0
$$861$$ −216.000 −0.00854966
$$862$$ 0 0
$$863$$ −8128.00 −0.320603 −0.160301 0.987068i $$-0.551247\pi$$
−0.160301 + 0.987068i $$0.551247\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 1171.00 0.0458699
$$868$$ 0 0
$$869$$ 2662.00 0.103915
$$870$$ 0 0
$$871$$ 27800.0 1.08148
$$872$$ 0 0
$$873$$ −26806.0 −1.03923
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −32128.0 −1.23704 −0.618521 0.785768i $$-0.712268\pi$$
−0.618521 + 0.785768i $$0.712268\pi$$
$$878$$ 0 0
$$879$$ 3516.00 0.134917
$$880$$ 0 0
$$881$$ −25619.0 −0.979712 −0.489856 0.871803i $$-0.662951\pi$$
−0.489856 + 0.871803i $$0.662951\pi$$
$$882$$ 0 0
$$883$$ −50044.0 −1.90726 −0.953632 0.300974i $$-0.902688\pi$$
−0.953632 + 0.300974i $$0.902688\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −39938.0 −1.51182 −0.755911 0.654674i $$-0.772806\pi$$
−0.755911 + 0.654674i $$0.772806\pi$$
$$888$$ 0 0
$$889$$ −792.000 −0.0298794
$$890$$ 0 0
$$891$$ −7139.00 −0.268424
$$892$$ 0 0
$$893$$ 6624.00 0.248224
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −280.000 −0.0104224
$$898$$ 0 0
$$899$$ 1464.00 0.0543127
$$900$$ 0 0
$$901$$ 468.000 0.0173045
$$902$$ 0 0
$$903$$ −1932.00 −0.0711993
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 49196.0 1.80102 0.900511 0.434834i $$-0.143193\pi$$
0.900511 + 0.434834i $$0.143193\pi$$
$$908$$ 0 0
$$909$$ −16380.0 −0.597679
$$910$$ 0 0
$$911$$ −32644.0 −1.18721 −0.593603 0.804758i $$-0.702295\pi$$
−0.593603 + 0.804758i $$0.702295\pi$$
$$912$$ 0 0
$$913$$ −16434.0 −0.595713
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 7308.00 0.263175
$$918$$ 0 0
$$919$$ 24370.0 0.874747 0.437373 0.899280i $$-0.355909\pi$$
0.437373 + 0.899280i $$0.355909\pi$$
$$920$$ 0 0
$$921$$ 9652.00 0.345325
$$922$$ 0 0
$$923$$ −39480.0 −1.40791
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 34528.0 1.22335
$$928$$ 0 0
$$929$$ 2202.00 0.0777667 0.0388834 0.999244i $$-0.487620\pi$$
0.0388834 + 0.999244i $$0.487620\pi$$
$$930$$ 0 0
$$931$$ −11052.0 −0.389060
$$932$$ 0 0
$$933$$ −852.000 −0.0298963
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −28092.0 −0.979430 −0.489715 0.871883i $$-0.662899\pi$$
−0.489715 + 0.871883i $$0.662899\pi$$
$$938$$ 0 0
$$939$$ 3313.00 0.115139
$$940$$ 0 0
$$941$$ −31070.0 −1.07636 −0.538179 0.842831i $$-0.680888\pi$$
−0.538179 + 0.842831i $$0.680888\pi$$
$$942$$ 0 0
$$943$$ 252.000 0.00870228
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −33461.0 −1.14819 −0.574095 0.818789i $$-0.694646\pi$$
−0.574095 + 0.818789i $$0.694646\pi$$
$$948$$ 0 0
$$949$$ 9920.00 0.339322
$$950$$ 0 0
$$951$$ 3035.00 0.103488
$$952$$ 0 0
$$953$$ −21702.0 −0.737667 −0.368834 0.929495i $$-0.620243\pi$$
−0.368834 + 0.929495i $$0.620243\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −88.0000 −0.00297245
$$958$$ 0 0
$$959$$ 16650.0 0.560643
$$960$$ 0 0
$$961$$ 3698.00 0.124131
$$962$$ 0 0
$$963$$ 13676.0 0.457635
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 8744.00 0.290784 0.145392 0.989374i $$-0.453556\pi$$
0.145392 + 0.989374i $$0.453556\pi$$
$$968$$ 0 0
$$969$$ 2808.00 0.0930918
$$970$$ 0 0
$$971$$ 18303.0 0.604914 0.302457 0.953163i $$-0.402193\pi$$
0.302457 + 0.953163i $$0.402193\pi$$
$$972$$ 0 0
$$973$$ 7332.00 0.241576
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −34917.0 −1.14339 −0.571696 0.820466i $$-0.693714\pi$$
−0.571696 + 0.820466i $$0.693714\pi$$
$$978$$ 0 0
$$979$$ 9955.00 0.324988
$$980$$ 0 0
$$981$$ −58084.0 −1.89040
$$982$$ 0 0
$$983$$ −31375.0 −1.01801 −0.509007 0.860763i $$-0.669987\pi$$
−0.509007 + 0.860763i $$0.669987\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 1104.00 0.0356036
$$988$$ 0 0
$$989$$ 2254.00 0.0724702
$$990$$ 0 0
$$991$$ −28064.0 −0.899579 −0.449789 0.893135i $$-0.648501\pi$$
−0.449789 + 0.893135i $$0.648501\pi$$
$$992$$ 0 0
$$993$$ 1655.00 0.0528901
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 25534.0 0.811103 0.405552 0.914072i $$-0.367079\pi$$
0.405552 + 0.914072i $$0.367079\pi$$
$$998$$ 0 0
$$999$$ 12031.0 0.381025
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 2200.4.a.f.1.1 1
5.4 even 2 88.4.a.a.1.1 1
15.14 odd 2 792.4.a.e.1.1 1
20.19 odd 2 176.4.a.d.1.1 1
40.19 odd 2 704.4.a.f.1.1 1
40.29 even 2 704.4.a.h.1.1 1
55.54 odd 2 968.4.a.d.1.1 1
60.59 even 2 1584.4.a.o.1.1 1
220.219 even 2 1936.4.a.i.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
88.4.a.a.1.1 1 5.4 even 2
176.4.a.d.1.1 1 20.19 odd 2
704.4.a.f.1.1 1 40.19 odd 2
704.4.a.h.1.1 1 40.29 even 2
792.4.a.e.1.1 1 15.14 odd 2
968.4.a.d.1.1 1 55.54 odd 2
1584.4.a.o.1.1 1 60.59 even 2
1936.4.a.i.1.1 1 220.219 even 2
2200.4.a.f.1.1 1 1.1 even 1 trivial