# Properties

 Label 99.4.a.a.1.1 Level $99$ Weight $4$ Character 99.1 Self dual yes Analytic conductor $5.841$ 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] = [99,4,Mod(1,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("99.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$99 = 3^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 99.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: $$5.84118909057$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 33) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 99.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -7.00000 q^{4} +4.00000 q^{5} -26.0000 q^{7} -15.0000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} -7.00000 q^{4} +4.00000 q^{5} -26.0000 q^{7} -15.0000 q^{8} +4.00000 q^{10} -11.0000 q^{11} -32.0000 q^{13} -26.0000 q^{14} +41.0000 q^{16} -74.0000 q^{17} -60.0000 q^{19} -28.0000 q^{20} -11.0000 q^{22} +182.000 q^{23} -109.000 q^{25} -32.0000 q^{26} +182.000 q^{28} +90.0000 q^{29} -8.00000 q^{31} +161.000 q^{32} -74.0000 q^{34} -104.000 q^{35} -66.0000 q^{37} -60.0000 q^{38} -60.0000 q^{40} -422.000 q^{41} +408.000 q^{43} +77.0000 q^{44} +182.000 q^{46} +506.000 q^{47} +333.000 q^{49} -109.000 q^{50} +224.000 q^{52} -348.000 q^{53} -44.0000 q^{55} +390.000 q^{56} +90.0000 q^{58} +200.000 q^{59} +132.000 q^{61} -8.00000 q^{62} -167.000 q^{64} -128.000 q^{65} -1036.00 q^{67} +518.000 q^{68} -104.000 q^{70} -762.000 q^{71} -542.000 q^{73} -66.0000 q^{74} +420.000 q^{76} +286.000 q^{77} -550.000 q^{79} +164.000 q^{80} -422.000 q^{82} +132.000 q^{83} -296.000 q^{85} +408.000 q^{86} +165.000 q^{88} -570.000 q^{89} +832.000 q^{91} -1274.00 q^{92} +506.000 q^{94} -240.000 q^{95} +14.0000 q^{97} +333.000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.353553 0.176777 0.984251i $$-0.443433\pi$$
0.176777 + 0.984251i $$0.443433\pi$$
$$3$$ 0 0
$$4$$ −7.00000 −0.875000
$$5$$ 4.00000 0.357771 0.178885 0.983870i $$-0.442751\pi$$
0.178885 + 0.983870i $$0.442751\pi$$
$$6$$ 0 0
$$7$$ −26.0000 −1.40387 −0.701934 0.712242i $$-0.747680\pi$$
−0.701934 + 0.712242i $$0.747680\pi$$
$$8$$ −15.0000 −0.662913
$$9$$ 0 0
$$10$$ 4.00000 0.126491
$$11$$ −11.0000 −0.301511
$$12$$ 0 0
$$13$$ −32.0000 −0.682708 −0.341354 0.939935i $$-0.610885\pi$$
−0.341354 + 0.939935i $$0.610885\pi$$
$$14$$ −26.0000 −0.496342
$$15$$ 0 0
$$16$$ 41.0000 0.640625
$$17$$ −74.0000 −1.05574 −0.527872 0.849324i $$-0.677010\pi$$
−0.527872 + 0.849324i $$0.677010\pi$$
$$18$$ 0 0
$$19$$ −60.0000 −0.724471 −0.362235 0.932087i $$-0.617986\pi$$
−0.362235 + 0.932087i $$0.617986\pi$$
$$20$$ −28.0000 −0.313050
$$21$$ 0 0
$$22$$ −11.0000 −0.106600
$$23$$ 182.000 1.64998 0.824992 0.565145i $$-0.191180\pi$$
0.824992 + 0.565145i $$0.191180\pi$$
$$24$$ 0 0
$$25$$ −109.000 −0.872000
$$26$$ −32.0000 −0.241374
$$27$$ 0 0
$$28$$ 182.000 1.22838
$$29$$ 90.0000 0.576296 0.288148 0.957586i $$-0.406961\pi$$
0.288148 + 0.957586i $$0.406961\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −0.0463498 −0.0231749 0.999731i $$-0.507377\pi$$
−0.0231749 + 0.999731i $$0.507377\pi$$
$$32$$ 161.000 0.889408
$$33$$ 0 0
$$34$$ −74.0000 −0.373262
$$35$$ −104.000 −0.502263
$$36$$ 0 0
$$37$$ −66.0000 −0.293252 −0.146626 0.989192i $$-0.546841\pi$$
−0.146626 + 0.989192i $$0.546841\pi$$
$$38$$ −60.0000 −0.256139
$$39$$ 0 0
$$40$$ −60.0000 −0.237171
$$41$$ −422.000 −1.60745 −0.803724 0.595003i $$-0.797151\pi$$
−0.803724 + 0.595003i $$0.797151\pi$$
$$42$$ 0 0
$$43$$ 408.000 1.44696 0.723482 0.690344i $$-0.242541\pi$$
0.723482 + 0.690344i $$0.242541\pi$$
$$44$$ 77.0000 0.263822
$$45$$ 0 0
$$46$$ 182.000 0.583357
$$47$$ 506.000 1.57038 0.785188 0.619257i $$-0.212566\pi$$
0.785188 + 0.619257i $$0.212566\pi$$
$$48$$ 0 0
$$49$$ 333.000 0.970845
$$50$$ −109.000 −0.308299
$$51$$ 0 0
$$52$$ 224.000 0.597369
$$53$$ −348.000 −0.901915 −0.450957 0.892546i $$-0.648917\pi$$
−0.450957 + 0.892546i $$0.648917\pi$$
$$54$$ 0 0
$$55$$ −44.0000 −0.107872
$$56$$ 390.000 0.930642
$$57$$ 0 0
$$58$$ 90.0000 0.203751
$$59$$ 200.000 0.441318 0.220659 0.975351i $$-0.429179\pi$$
0.220659 + 0.975351i $$0.429179\pi$$
$$60$$ 0 0
$$61$$ 132.000 0.277063 0.138532 0.990358i $$-0.455762\pi$$
0.138532 + 0.990358i $$0.455762\pi$$
$$62$$ −8.00000 −0.0163871
$$63$$ 0 0
$$64$$ −167.000 −0.326172
$$65$$ −128.000 −0.244253
$$66$$ 0 0
$$67$$ −1036.00 −1.88907 −0.944534 0.328414i $$-0.893486\pi$$
−0.944534 + 0.328414i $$0.893486\pi$$
$$68$$ 518.000 0.923775
$$69$$ 0 0
$$70$$ −104.000 −0.177577
$$71$$ −762.000 −1.27370 −0.636850 0.770987i $$-0.719763\pi$$
−0.636850 + 0.770987i $$0.719763\pi$$
$$72$$ 0 0
$$73$$ −542.000 −0.868990 −0.434495 0.900674i $$-0.643073\pi$$
−0.434495 + 0.900674i $$0.643073\pi$$
$$74$$ −66.0000 −0.103680
$$75$$ 0 0
$$76$$ 420.000 0.633912
$$77$$ 286.000 0.423282
$$78$$ 0 0
$$79$$ −550.000 −0.783289 −0.391645 0.920117i $$-0.628094\pi$$
−0.391645 + 0.920117i $$0.628094\pi$$
$$80$$ 164.000 0.229197
$$81$$ 0 0
$$82$$ −422.000 −0.568318
$$83$$ 132.000 0.174565 0.0872824 0.996184i $$-0.472182\pi$$
0.0872824 + 0.996184i $$0.472182\pi$$
$$84$$ 0 0
$$85$$ −296.000 −0.377714
$$86$$ 408.000 0.511579
$$87$$ 0 0
$$88$$ 165.000 0.199876
$$89$$ −570.000 −0.678875 −0.339438 0.940629i $$-0.610237\pi$$
−0.339438 + 0.940629i $$0.610237\pi$$
$$90$$ 0 0
$$91$$ 832.000 0.958432
$$92$$ −1274.00 −1.44374
$$93$$ 0 0
$$94$$ 506.000 0.555212
$$95$$ −240.000 −0.259195
$$96$$ 0 0
$$97$$ 14.0000 0.0146545 0.00732724 0.999973i $$-0.497668\pi$$
0.00732724 + 0.999973i $$0.497668\pi$$
$$98$$ 333.000 0.343246
$$99$$ 0 0
$$100$$ 763.000 0.763000
$$101$$ −1702.00 −1.67679 −0.838393 0.545067i $$-0.816504\pi$$
−0.838393 + 0.545067i $$0.816504\pi$$
$$102$$ 0 0
$$103$$ −1132.00 −1.08291 −0.541453 0.840731i $$-0.682126\pi$$
−0.541453 + 0.840731i $$0.682126\pi$$
$$104$$ 480.000 0.452576
$$105$$ 0 0
$$106$$ −348.000 −0.318875
$$107$$ −564.000 −0.509570 −0.254785 0.966998i $$-0.582005\pi$$
−0.254785 + 0.966998i $$0.582005\pi$$
$$108$$ 0 0
$$109$$ −320.000 −0.281197 −0.140598 0.990067i $$-0.544903\pi$$
−0.140598 + 0.990067i $$0.544903\pi$$
$$110$$ −44.0000 −0.0381385
$$111$$ 0 0
$$112$$ −1066.00 −0.899353
$$113$$ 2142.00 1.78321 0.891604 0.452817i $$-0.149581\pi$$
0.891604 + 0.452817i $$0.149581\pi$$
$$114$$ 0 0
$$115$$ 728.000 0.590316
$$116$$ −630.000 −0.504259
$$117$$ 0 0
$$118$$ 200.000 0.156030
$$119$$ 1924.00 1.48212
$$120$$ 0 0
$$121$$ 121.000 0.0909091
$$122$$ 132.000 0.0979567
$$123$$ 0 0
$$124$$ 56.0000 0.0405560
$$125$$ −936.000 −0.669747
$$126$$ 0 0
$$127$$ −1606.00 −1.12212 −0.561061 0.827775i $$-0.689607\pi$$
−0.561061 + 0.827775i $$0.689607\pi$$
$$128$$ −1455.00 −1.00473
$$129$$ 0 0
$$130$$ −128.000 −0.0863565
$$131$$ 1908.00 1.27254 0.636270 0.771466i $$-0.280476\pi$$
0.636270 + 0.771466i $$0.280476\pi$$
$$132$$ 0 0
$$133$$ 1560.00 1.01706
$$134$$ −1036.00 −0.667886
$$135$$ 0 0
$$136$$ 1110.00 0.699866
$$137$$ 2186.00 1.36323 0.681615 0.731711i $$-0.261278\pi$$
0.681615 + 0.731711i $$0.261278\pi$$
$$138$$ 0 0
$$139$$ 2740.00 1.67197 0.835985 0.548753i $$-0.184897\pi$$
0.835985 + 0.548753i $$0.184897\pi$$
$$140$$ 728.000 0.439480
$$141$$ 0 0
$$142$$ −762.000 −0.450321
$$143$$ 352.000 0.205844
$$144$$ 0 0
$$145$$ 360.000 0.206182
$$146$$ −542.000 −0.307235
$$147$$ 0 0
$$148$$ 462.000 0.256596
$$149$$ 1310.00 0.720264 0.360132 0.932901i $$-0.382732\pi$$
0.360132 + 0.932901i $$0.382732\pi$$
$$150$$ 0 0
$$151$$ −1198.00 −0.645641 −0.322821 0.946460i $$-0.604631\pi$$
−0.322821 + 0.946460i $$0.604631\pi$$
$$152$$ 900.000 0.480261
$$153$$ 0 0
$$154$$ 286.000 0.149653
$$155$$ −32.0000 −0.0165826
$$156$$ 0 0
$$157$$ 2114.00 1.07462 0.537311 0.843384i $$-0.319440\pi$$
0.537311 + 0.843384i $$0.319440\pi$$
$$158$$ −550.000 −0.276934
$$159$$ 0 0
$$160$$ 644.000 0.318204
$$161$$ −4732.00 −2.31636
$$162$$ 0 0
$$163$$ 3868.00 1.85868 0.929341 0.369223i $$-0.120376\pi$$
0.929341 + 0.369223i $$0.120376\pi$$
$$164$$ 2954.00 1.40652
$$165$$ 0 0
$$166$$ 132.000 0.0617180
$$167$$ −2004.00 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ −1173.00 −0.533910
$$170$$ −296.000 −0.133542
$$171$$ 0 0
$$172$$ −2856.00 −1.26609
$$173$$ −678.000 −0.297962 −0.148981 0.988840i $$-0.547599\pi$$
−0.148981 + 0.988840i $$0.547599\pi$$
$$174$$ 0 0
$$175$$ 2834.00 1.22417
$$176$$ −451.000 −0.193156
$$177$$ 0 0
$$178$$ −570.000 −0.240019
$$179$$ 1680.00 0.701503 0.350752 0.936469i $$-0.385926\pi$$
0.350752 + 0.936469i $$0.385926\pi$$
$$180$$ 0 0
$$181$$ −4358.00 −1.78966 −0.894828 0.446412i $$-0.852702\pi$$
−0.894828 + 0.446412i $$0.852702\pi$$
$$182$$ 832.000 0.338857
$$183$$ 0 0
$$184$$ −2730.00 −1.09379
$$185$$ −264.000 −0.104917
$$186$$ 0 0
$$187$$ 814.000 0.318319
$$188$$ −3542.00 −1.37408
$$189$$ 0 0
$$190$$ −240.000 −0.0916391
$$191$$ 1778.00 0.673568 0.336784 0.941582i $$-0.390661\pi$$
0.336784 + 0.941582i $$0.390661\pi$$
$$192$$ 0 0
$$193$$ −3962.00 −1.47767 −0.738837 0.673884i $$-0.764625\pi$$
−0.738837 + 0.673884i $$0.764625\pi$$
$$194$$ 14.0000 0.00518114
$$195$$ 0 0
$$196$$ −2331.00 −0.849490
$$197$$ −374.000 −0.135261 −0.0676304 0.997710i $$-0.521544\pi$$
−0.0676304 + 0.997710i $$0.521544\pi$$
$$198$$ 0 0
$$199$$ 2100.00 0.748066 0.374033 0.927415i $$-0.377975\pi$$
0.374033 + 0.927415i $$0.377975\pi$$
$$200$$ 1635.00 0.578060
$$201$$ 0 0
$$202$$ −1702.00 −0.592833
$$203$$ −2340.00 −0.809043
$$204$$ 0 0
$$205$$ −1688.00 −0.575098
$$206$$ −1132.00 −0.382865
$$207$$ 0 0
$$208$$ −1312.00 −0.437360
$$209$$ 660.000 0.218436
$$210$$ 0 0
$$211$$ 2232.00 0.728233 0.364117 0.931353i $$-0.381371\pi$$
0.364117 + 0.931353i $$0.381371\pi$$
$$212$$ 2436.00 0.789175
$$213$$ 0 0
$$214$$ −564.000 −0.180160
$$215$$ 1632.00 0.517681
$$216$$ 0 0
$$217$$ 208.000 0.0650689
$$218$$ −320.000 −0.0994180
$$219$$ 0 0
$$220$$ 308.000 0.0943880
$$221$$ 2368.00 0.720764
$$222$$ 0 0
$$223$$ 2128.00 0.639020 0.319510 0.947583i $$-0.396482\pi$$
0.319510 + 0.947583i $$0.396482\pi$$
$$224$$ −4186.00 −1.24861
$$225$$ 0 0
$$226$$ 2142.00 0.630459
$$227$$ −2964.00 −0.866641 −0.433321 0.901240i $$-0.642658\pi$$
−0.433321 + 0.901240i $$0.642658\pi$$
$$228$$ 0 0
$$229$$ −2550.00 −0.735846 −0.367923 0.929856i $$-0.619931\pi$$
−0.367923 + 0.929856i $$0.619931\pi$$
$$230$$ 728.000 0.208708
$$231$$ 0 0
$$232$$ −1350.00 −0.382034
$$233$$ 3042.00 0.855314 0.427657 0.903941i $$-0.359339\pi$$
0.427657 + 0.903941i $$0.359339\pi$$
$$234$$ 0 0
$$235$$ 2024.00 0.561835
$$236$$ −1400.00 −0.386154
$$237$$ 0 0
$$238$$ 1924.00 0.524010
$$239$$ −2700.00 −0.730747 −0.365373 0.930861i $$-0.619059\pi$$
−0.365373 + 0.930861i $$0.619059\pi$$
$$240$$ 0 0
$$241$$ −578.000 −0.154491 −0.0772453 0.997012i $$-0.524612\pi$$
−0.0772453 + 0.997012i $$0.524612\pi$$
$$242$$ 121.000 0.0321412
$$243$$ 0 0
$$244$$ −924.000 −0.242430
$$245$$ 1332.00 0.347340
$$246$$ 0 0
$$247$$ 1920.00 0.494602
$$248$$ 120.000 0.0307258
$$249$$ 0 0
$$250$$ −936.000 −0.236791
$$251$$ −3752.00 −0.943522 −0.471761 0.881726i $$-0.656382\pi$$
−0.471761 + 0.881726i $$0.656382\pi$$
$$252$$ 0 0
$$253$$ −2002.00 −0.497489
$$254$$ −1606.00 −0.396730
$$255$$ 0 0
$$256$$ −119.000 −0.0290527
$$257$$ −674.000 −0.163591 −0.0817957 0.996649i $$-0.526065\pi$$
−0.0817957 + 0.996649i $$0.526065\pi$$
$$258$$ 0 0
$$259$$ 1716.00 0.411687
$$260$$ 896.000 0.213721
$$261$$ 0 0
$$262$$ 1908.00 0.449911
$$263$$ 4352.00 1.02036 0.510182 0.860066i $$-0.329578\pi$$
0.510182 + 0.860066i $$0.329578\pi$$
$$264$$ 0 0
$$265$$ −1392.00 −0.322679
$$266$$ 1560.00 0.359585
$$267$$ 0 0
$$268$$ 7252.00 1.65293
$$269$$ −500.000 −0.113329 −0.0566646 0.998393i $$-0.518047\pi$$
−0.0566646 + 0.998393i $$0.518047\pi$$
$$270$$ 0 0
$$271$$ −6538.00 −1.46552 −0.732759 0.680489i $$-0.761768\pi$$
−0.732759 + 0.680489i $$0.761768\pi$$
$$272$$ −3034.00 −0.676336
$$273$$ 0 0
$$274$$ 2186.00 0.481975
$$275$$ 1199.00 0.262918
$$276$$ 0 0
$$277$$ 124.000 0.0268969 0.0134484 0.999910i $$-0.495719\pi$$
0.0134484 + 0.999910i $$0.495719\pi$$
$$278$$ 2740.00 0.591131
$$279$$ 0 0
$$280$$ 1560.00 0.332957
$$281$$ −3642.00 −0.773180 −0.386590 0.922252i $$-0.626347\pi$$
−0.386590 + 0.922252i $$0.626347\pi$$
$$282$$ 0 0
$$283$$ 4648.00 0.976307 0.488154 0.872758i $$-0.337671\pi$$
0.488154 + 0.872758i $$0.337671\pi$$
$$284$$ 5334.00 1.11449
$$285$$ 0 0
$$286$$ 352.000 0.0727769
$$287$$ 10972.0 2.25664
$$288$$ 0 0
$$289$$ 563.000 0.114594
$$290$$ 360.000 0.0728963
$$291$$ 0 0
$$292$$ 3794.00 0.760367
$$293$$ 3102.00 0.618501 0.309250 0.950981i $$-0.399922\pi$$
0.309250 + 0.950981i $$0.399922\pi$$
$$294$$ 0 0
$$295$$ 800.000 0.157891
$$296$$ 990.000 0.194401
$$297$$ 0 0
$$298$$ 1310.00 0.254652
$$299$$ −5824.00 −1.12646
$$300$$ 0 0
$$301$$ −10608.0 −2.03135
$$302$$ −1198.00 −0.228269
$$303$$ 0 0
$$304$$ −2460.00 −0.464114
$$305$$ 528.000 0.0991252
$$306$$ 0 0
$$307$$ 1244.00 0.231267 0.115633 0.993292i $$-0.463110\pi$$
0.115633 + 0.993292i $$0.463110\pi$$
$$308$$ −2002.00 −0.370372
$$309$$ 0 0
$$310$$ −32.0000 −0.00586283
$$311$$ −2082.00 −0.379612 −0.189806 0.981822i $$-0.560786\pi$$
−0.189806 + 0.981822i $$0.560786\pi$$
$$312$$ 0 0
$$313$$ 2378.00 0.429433 0.214716 0.976676i $$-0.431117\pi$$
0.214716 + 0.976676i $$0.431117\pi$$
$$314$$ 2114.00 0.379936
$$315$$ 0 0
$$316$$ 3850.00 0.685378
$$317$$ 496.000 0.0878806 0.0439403 0.999034i $$-0.486009\pi$$
0.0439403 + 0.999034i $$0.486009\pi$$
$$318$$ 0 0
$$319$$ −990.000 −0.173760
$$320$$ −668.000 −0.116695
$$321$$ 0 0
$$322$$ −4732.00 −0.818957
$$323$$ 4440.00 0.764855
$$324$$ 0 0
$$325$$ 3488.00 0.595321
$$326$$ 3868.00 0.657143
$$327$$ 0 0
$$328$$ 6330.00 1.06560
$$329$$ −13156.0 −2.20460
$$330$$ 0 0
$$331$$ −2708.00 −0.449683 −0.224842 0.974395i $$-0.572186\pi$$
−0.224842 + 0.974395i $$0.572186\pi$$
$$332$$ −924.000 −0.152744
$$333$$ 0 0
$$334$$ −2004.00 −0.328305
$$335$$ −4144.00 −0.675853
$$336$$ 0 0
$$337$$ 4034.00 0.652065 0.326033 0.945359i $$-0.394288\pi$$
0.326033 + 0.945359i $$0.394288\pi$$
$$338$$ −1173.00 −0.188766
$$339$$ 0 0
$$340$$ 2072.00 0.330500
$$341$$ 88.0000 0.0139750
$$342$$ 0 0
$$343$$ 260.000 0.0409291
$$344$$ −6120.00 −0.959210
$$345$$ 0 0
$$346$$ −678.000 −0.105345
$$347$$ −11084.0 −1.71476 −0.857378 0.514687i $$-0.827908\pi$$
−0.857378 + 0.514687i $$0.827908\pi$$
$$348$$ 0 0
$$349$$ −3120.00 −0.478538 −0.239269 0.970953i $$-0.576908\pi$$
−0.239269 + 0.970953i $$0.576908\pi$$
$$350$$ 2834.00 0.432810
$$351$$ 0 0
$$352$$ −1771.00 −0.268167
$$353$$ 5622.00 0.847674 0.423837 0.905739i $$-0.360683\pi$$
0.423837 + 0.905739i $$0.360683\pi$$
$$354$$ 0 0
$$355$$ −3048.00 −0.455693
$$356$$ 3990.00 0.594016
$$357$$ 0 0
$$358$$ 1680.00 0.248019
$$359$$ 8500.00 1.24962 0.624809 0.780778i $$-0.285177\pi$$
0.624809 + 0.780778i $$0.285177\pi$$
$$360$$ 0 0
$$361$$ −3259.00 −0.475142
$$362$$ −4358.00 −0.632739
$$363$$ 0 0
$$364$$ −5824.00 −0.838628
$$365$$ −2168.00 −0.310899
$$366$$ 0 0
$$367$$ 7144.00 1.01611 0.508057 0.861324i $$-0.330364\pi$$
0.508057 + 0.861324i $$0.330364\pi$$
$$368$$ 7462.00 1.05702
$$369$$ 0 0
$$370$$ −264.000 −0.0370938
$$371$$ 9048.00 1.26617
$$372$$ 0 0
$$373$$ −632.000 −0.0877312 −0.0438656 0.999037i $$-0.513967\pi$$
−0.0438656 + 0.999037i $$0.513967\pi$$
$$374$$ 814.000 0.112543
$$375$$ 0 0
$$376$$ −7590.00 −1.04102
$$377$$ −2880.00 −0.393442
$$378$$ 0 0
$$379$$ −4220.00 −0.571944 −0.285972 0.958238i $$-0.592316\pi$$
−0.285972 + 0.958238i $$0.592316\pi$$
$$380$$ 1680.00 0.226795
$$381$$ 0 0
$$382$$ 1778.00 0.238142
$$383$$ −8458.00 −1.12842 −0.564208 0.825632i $$-0.690819\pi$$
−0.564208 + 0.825632i $$0.690819\pi$$
$$384$$ 0 0
$$385$$ 1144.00 0.151438
$$386$$ −3962.00 −0.522437
$$387$$ 0 0
$$388$$ −98.0000 −0.0128227
$$389$$ −1740.00 −0.226790 −0.113395 0.993550i $$-0.536173\pi$$
−0.113395 + 0.993550i $$0.536173\pi$$
$$390$$ 0 0
$$391$$ −13468.0 −1.74196
$$392$$ −4995.00 −0.643586
$$393$$ 0 0
$$394$$ −374.000 −0.0478219
$$395$$ −2200.00 −0.280238
$$396$$ 0 0
$$397$$ −5126.00 −0.648027 −0.324013 0.946053i $$-0.605032\pi$$
−0.324013 + 0.946053i $$0.605032\pi$$
$$398$$ 2100.00 0.264481
$$399$$ 0 0
$$400$$ −4469.00 −0.558625
$$401$$ 3098.00 0.385802 0.192901 0.981218i $$-0.438210\pi$$
0.192901 + 0.981218i $$0.438210\pi$$
$$402$$ 0 0
$$403$$ 256.000 0.0316433
$$404$$ 11914.0 1.46719
$$405$$ 0 0
$$406$$ −2340.00 −0.286040
$$407$$ 726.000 0.0884189
$$408$$ 0 0
$$409$$ 6390.00 0.772531 0.386265 0.922388i $$-0.373765\pi$$
0.386265 + 0.922388i $$0.373765\pi$$
$$410$$ −1688.00 −0.203328
$$411$$ 0 0
$$412$$ 7924.00 0.947542
$$413$$ −5200.00 −0.619553
$$414$$ 0 0
$$415$$ 528.000 0.0624542
$$416$$ −5152.00 −0.607206
$$417$$ 0 0
$$418$$ 660.000 0.0772288
$$419$$ −9760.00 −1.13796 −0.568982 0.822350i $$-0.692663\pi$$
−0.568982 + 0.822350i $$0.692663\pi$$
$$420$$ 0 0
$$421$$ −5138.00 −0.594800 −0.297400 0.954753i $$-0.596119\pi$$
−0.297400 + 0.954753i $$0.596119\pi$$
$$422$$ 2232.00 0.257469
$$423$$ 0 0
$$424$$ 5220.00 0.597891
$$425$$ 8066.00 0.920608
$$426$$ 0 0
$$427$$ −3432.00 −0.388960
$$428$$ 3948.00 0.445873
$$429$$ 0 0
$$430$$ 1632.00 0.183028
$$431$$ 7008.00 0.783210 0.391605 0.920133i $$-0.371920\pi$$
0.391605 + 0.920133i $$0.371920\pi$$
$$432$$ 0 0
$$433$$ 5578.00 0.619080 0.309540 0.950886i $$-0.399825\pi$$
0.309540 + 0.950886i $$0.399825\pi$$
$$434$$ 208.000 0.0230053
$$435$$ 0 0
$$436$$ 2240.00 0.246047
$$437$$ −10920.0 −1.19536
$$438$$ 0 0
$$439$$ −10430.0 −1.13393 −0.566967 0.823741i $$-0.691883\pi$$
−0.566967 + 0.823741i $$0.691883\pi$$
$$440$$ 660.000 0.0715097
$$441$$ 0 0
$$442$$ 2368.00 0.254829
$$443$$ 4432.00 0.475329 0.237664 0.971347i $$-0.423618\pi$$
0.237664 + 0.971347i $$0.423618\pi$$
$$444$$ 0 0
$$445$$ −2280.00 −0.242882
$$446$$ 2128.00 0.225928
$$447$$ 0 0
$$448$$ 4342.00 0.457902
$$449$$ 6290.00 0.661121 0.330561 0.943785i $$-0.392762\pi$$
0.330561 + 0.943785i $$0.392762\pi$$
$$450$$ 0 0
$$451$$ 4642.00 0.484664
$$452$$ −14994.0 −1.56031
$$453$$ 0 0
$$454$$ −2964.00 −0.306404
$$455$$ 3328.00 0.342899
$$456$$ 0 0
$$457$$ 3054.00 0.312604 0.156302 0.987709i $$-0.450043\pi$$
0.156302 + 0.987709i $$0.450043\pi$$
$$458$$ −2550.00 −0.260161
$$459$$ 0 0
$$460$$ −5096.00 −0.516527
$$461$$ −12882.0 −1.30146 −0.650732 0.759308i $$-0.725538\pi$$
−0.650732 + 0.759308i $$0.725538\pi$$
$$462$$ 0 0
$$463$$ 6148.00 0.617110 0.308555 0.951207i $$-0.400155\pi$$
0.308555 + 0.951207i $$0.400155\pi$$
$$464$$ 3690.00 0.369190
$$465$$ 0 0
$$466$$ 3042.00 0.302399
$$467$$ −5124.00 −0.507731 −0.253866 0.967240i $$-0.581702\pi$$
−0.253866 + 0.967240i $$0.581702\pi$$
$$468$$ 0 0
$$469$$ 26936.0 2.65200
$$470$$ 2024.00 0.198639
$$471$$ 0 0
$$472$$ −3000.00 −0.292555
$$473$$ −4488.00 −0.436276
$$474$$ 0 0
$$475$$ 6540.00 0.631738
$$476$$ −13468.0 −1.29686
$$477$$ 0 0
$$478$$ −2700.00 −0.258358
$$479$$ 16520.0 1.57582 0.787910 0.615790i $$-0.211163\pi$$
0.787910 + 0.615790i $$0.211163\pi$$
$$480$$ 0 0
$$481$$ 2112.00 0.200206
$$482$$ −578.000 −0.0546207
$$483$$ 0 0
$$484$$ −847.000 −0.0795455
$$485$$ 56.0000 0.00524295
$$486$$ 0 0
$$487$$ 524.000 0.0487571 0.0243785 0.999703i $$-0.492239\pi$$
0.0243785 + 0.999703i $$0.492239\pi$$
$$488$$ −1980.00 −0.183669
$$489$$ 0 0
$$490$$ 1332.00 0.122803
$$491$$ 15028.0 1.38127 0.690636 0.723203i $$-0.257331\pi$$
0.690636 + 0.723203i $$0.257331\pi$$
$$492$$ 0 0
$$493$$ −6660.00 −0.608421
$$494$$ 1920.00 0.174868
$$495$$ 0 0
$$496$$ −328.000 −0.0296928
$$497$$ 19812.0 1.78811
$$498$$ 0 0
$$499$$ 9020.00 0.809200 0.404600 0.914494i $$-0.367411\pi$$
0.404600 + 0.914494i $$0.367411\pi$$
$$500$$ 6552.00 0.586029
$$501$$ 0 0
$$502$$ −3752.00 −0.333586
$$503$$ 14812.0 1.31299 0.656495 0.754330i $$-0.272038\pi$$
0.656495 + 0.754330i $$0.272038\pi$$
$$504$$ 0 0
$$505$$ −6808.00 −0.599905
$$506$$ −2002.00 −0.175889
$$507$$ 0 0
$$508$$ 11242.0 0.981856
$$509$$ −12660.0 −1.10245 −0.551223 0.834358i $$-0.685839\pi$$
−0.551223 + 0.834358i $$0.685839\pi$$
$$510$$ 0 0
$$511$$ 14092.0 1.21995
$$512$$ 11521.0 0.994455
$$513$$ 0 0
$$514$$ −674.000 −0.0578383
$$515$$ −4528.00 −0.387432
$$516$$ 0 0
$$517$$ −5566.00 −0.473486
$$518$$ 1716.00 0.145553
$$519$$ 0 0
$$520$$ 1920.00 0.161918
$$521$$ 3738.00 0.314328 0.157164 0.987573i $$-0.449765\pi$$
0.157164 + 0.987573i $$0.449765\pi$$
$$522$$ 0 0
$$523$$ −6352.00 −0.531078 −0.265539 0.964100i $$-0.585550\pi$$
−0.265539 + 0.964100i $$0.585550\pi$$
$$524$$ −13356.0 −1.11347
$$525$$ 0 0
$$526$$ 4352.00 0.360753
$$527$$ 592.000 0.0489334
$$528$$ 0 0
$$529$$ 20957.0 1.72245
$$530$$ −1392.00 −0.114084
$$531$$ 0 0
$$532$$ −10920.0 −0.889929
$$533$$ 13504.0 1.09742
$$534$$ 0 0
$$535$$ −2256.00 −0.182309
$$536$$ 15540.0 1.25229
$$537$$ 0 0
$$538$$ −500.000 −0.0400679
$$539$$ −3663.00 −0.292721
$$540$$ 0 0
$$541$$ −24728.0 −1.96514 −0.982569 0.185898i $$-0.940481\pi$$
−0.982569 + 0.185898i $$0.940481\pi$$
$$542$$ −6538.00 −0.518139
$$543$$ 0 0
$$544$$ −11914.0 −0.938986
$$545$$ −1280.00 −0.100604
$$546$$ 0 0
$$547$$ −22756.0 −1.77875 −0.889375 0.457178i $$-0.848860\pi$$
−0.889375 + 0.457178i $$0.848860\pi$$
$$548$$ −15302.0 −1.19283
$$549$$ 0 0
$$550$$ 1199.00 0.0929555
$$551$$ −5400.00 −0.417509
$$552$$ 0 0
$$553$$ 14300.0 1.09963
$$554$$ 124.000 0.00950949
$$555$$ 0 0
$$556$$ −19180.0 −1.46297
$$557$$ 9526.00 0.724649 0.362325 0.932052i $$-0.381983\pi$$
0.362325 + 0.932052i $$0.381983\pi$$
$$558$$ 0 0
$$559$$ −13056.0 −0.987853
$$560$$ −4264.00 −0.321762
$$561$$ 0 0
$$562$$ −3642.00 −0.273360
$$563$$ −12068.0 −0.903385 −0.451692 0.892174i $$-0.649180\pi$$
−0.451692 + 0.892174i $$0.649180\pi$$
$$564$$ 0 0
$$565$$ 8568.00 0.637980
$$566$$ 4648.00 0.345177
$$567$$ 0 0
$$568$$ 11430.0 0.844352
$$569$$ −15090.0 −1.11179 −0.555893 0.831254i $$-0.687623\pi$$
−0.555893 + 0.831254i $$0.687623\pi$$
$$570$$ 0 0
$$571$$ 4412.00 0.323356 0.161678 0.986844i $$-0.448309\pi$$
0.161678 + 0.986844i $$0.448309\pi$$
$$572$$ −2464.00 −0.180114
$$573$$ 0 0
$$574$$ 10972.0 0.797844
$$575$$ −19838.0 −1.43879
$$576$$ 0 0
$$577$$ −3906.00 −0.281818 −0.140909 0.990023i $$-0.545002\pi$$
−0.140909 + 0.990023i $$0.545002\pi$$
$$578$$ 563.000 0.0405151
$$579$$ 0 0
$$580$$ −2520.00 −0.180409
$$581$$ −3432.00 −0.245066
$$582$$ 0 0
$$583$$ 3828.00 0.271937
$$584$$ 8130.00 0.576065
$$585$$ 0 0
$$586$$ 3102.00 0.218673
$$587$$ 12016.0 0.844895 0.422448 0.906387i $$-0.361171\pi$$
0.422448 + 0.906387i $$0.361171\pi$$
$$588$$ 0 0
$$589$$ 480.000 0.0335790
$$590$$ 800.000 0.0558228
$$591$$ 0 0
$$592$$ −2706.00 −0.187865
$$593$$ 11342.0 0.785430 0.392715 0.919660i $$-0.371536\pi$$
0.392715 + 0.919660i $$0.371536\pi$$
$$594$$ 0 0
$$595$$ 7696.00 0.530261
$$596$$ −9170.00 −0.630231
$$597$$ 0 0
$$598$$ −5824.00 −0.398263
$$599$$ −20690.0 −1.41130 −0.705651 0.708559i $$-0.749346\pi$$
−0.705651 + 0.708559i $$0.749346\pi$$
$$600$$ 0 0
$$601$$ −598.000 −0.0405872 −0.0202936 0.999794i $$-0.506460\pi$$
−0.0202936 + 0.999794i $$0.506460\pi$$
$$602$$ −10608.0 −0.718189
$$603$$ 0 0
$$604$$ 8386.00 0.564936
$$605$$ 484.000 0.0325246
$$606$$ 0 0
$$607$$ −166.000 −0.0111001 −0.00555003 0.999985i $$-0.501767\pi$$
−0.00555003 + 0.999985i $$0.501767\pi$$
$$608$$ −9660.00 −0.644350
$$609$$ 0 0
$$610$$ 528.000 0.0350461
$$611$$ −16192.0 −1.07211
$$612$$ 0 0
$$613$$ 20108.0 1.32488 0.662442 0.749113i $$-0.269520\pi$$
0.662442 + 0.749113i $$0.269520\pi$$
$$614$$ 1244.00 0.0817651
$$615$$ 0 0
$$616$$ −4290.00 −0.280599
$$617$$ 2286.00 0.149159 0.0745793 0.997215i $$-0.476239\pi$$
0.0745793 + 0.997215i $$0.476239\pi$$
$$618$$ 0 0
$$619$$ −25660.0 −1.66618 −0.833088 0.553141i $$-0.813429\pi$$
−0.833088 + 0.553141i $$0.813429\pi$$
$$620$$ 224.000 0.0145098
$$621$$ 0 0
$$622$$ −2082.00 −0.134213
$$623$$ 14820.0 0.953051
$$624$$ 0 0
$$625$$ 9881.00 0.632384
$$626$$ 2378.00 0.151827
$$627$$ 0 0
$$628$$ −14798.0 −0.940294
$$629$$ 4884.00 0.309599
$$630$$ 0 0
$$631$$ −11408.0 −0.719723 −0.359862 0.933006i $$-0.617176\pi$$
−0.359862 + 0.933006i $$0.617176\pi$$
$$632$$ 8250.00 0.519252
$$633$$ 0 0
$$634$$ 496.000 0.0310705
$$635$$ −6424.00 −0.401462
$$636$$ 0 0
$$637$$ −10656.0 −0.662804
$$638$$ −990.000 −0.0614333
$$639$$ 0 0
$$640$$ −5820.00 −0.359462
$$641$$ 3378.00 0.208148 0.104074 0.994570i $$-0.466812\pi$$
0.104074 + 0.994570i $$0.466812\pi$$
$$642$$ 0 0
$$643$$ −11212.0 −0.687649 −0.343824 0.939034i $$-0.611722\pi$$
−0.343824 + 0.939034i $$0.611722\pi$$
$$644$$ 33124.0 2.02681
$$645$$ 0 0
$$646$$ 4440.00 0.270417
$$647$$ 86.0000 0.00522567 0.00261284 0.999997i $$-0.499168\pi$$
0.00261284 + 0.999997i $$0.499168\pi$$
$$648$$ 0 0
$$649$$ −2200.00 −0.133062
$$650$$ 3488.00 0.210478
$$651$$ 0 0
$$652$$ −27076.0 −1.62635
$$653$$ 4432.00 0.265601 0.132801 0.991143i $$-0.457603\pi$$
0.132801 + 0.991143i $$0.457603\pi$$
$$654$$ 0 0
$$655$$ 7632.00 0.455278
$$656$$ −17302.0 −1.02977
$$657$$ 0 0
$$658$$ −13156.0 −0.779444
$$659$$ −4580.00 −0.270731 −0.135365 0.990796i $$-0.543221\pi$$
−0.135365 + 0.990796i $$0.543221\pi$$
$$660$$ 0 0
$$661$$ 4282.00 0.251967 0.125984 0.992032i $$-0.459791\pi$$
0.125984 + 0.992032i $$0.459791\pi$$
$$662$$ −2708.00 −0.158987
$$663$$ 0 0
$$664$$ −1980.00 −0.115721
$$665$$ 6240.00 0.363875
$$666$$ 0 0
$$667$$ 16380.0 0.950879
$$668$$ 14028.0 0.812514
$$669$$ 0 0
$$670$$ −4144.00 −0.238950
$$671$$ −1452.00 −0.0835378
$$672$$ 0 0
$$673$$ 8438.00 0.483300 0.241650 0.970363i $$-0.422311\pi$$
0.241650 + 0.970363i $$0.422311\pi$$
$$674$$ 4034.00 0.230540
$$675$$ 0 0
$$676$$ 8211.00 0.467171
$$677$$ −34494.0 −1.95822 −0.979108 0.203341i $$-0.934820\pi$$
−0.979108 + 0.203341i $$0.934820\pi$$
$$678$$ 0 0
$$679$$ −364.000 −0.0205730
$$680$$ 4440.00 0.250392
$$681$$ 0 0
$$682$$ 88.0000 0.00494090
$$683$$ 13712.0 0.768192 0.384096 0.923293i $$-0.374513\pi$$
0.384096 + 0.923293i $$0.374513\pi$$
$$684$$ 0 0
$$685$$ 8744.00 0.487724
$$686$$ 260.000 0.0144706
$$687$$ 0 0
$$688$$ 16728.0 0.926961
$$689$$ 11136.0 0.615744
$$690$$ 0 0
$$691$$ 11372.0 0.626066 0.313033 0.949742i $$-0.398655\pi$$
0.313033 + 0.949742i $$0.398655\pi$$
$$692$$ 4746.00 0.260717
$$693$$ 0 0
$$694$$ −11084.0 −0.606258
$$695$$ 10960.0 0.598182
$$696$$ 0 0
$$697$$ 31228.0 1.69705
$$698$$ −3120.00 −0.169189
$$699$$ 0 0
$$700$$ −19838.0 −1.07115
$$701$$ 6398.00 0.344721 0.172360 0.985034i $$-0.444861\pi$$
0.172360 + 0.985034i $$0.444861\pi$$
$$702$$ 0 0
$$703$$ 3960.00 0.212453
$$704$$ 1837.00 0.0983445
$$705$$ 0 0
$$706$$ 5622.00 0.299698
$$707$$ 44252.0 2.35399
$$708$$ 0 0
$$709$$ −5830.00 −0.308816 −0.154408 0.988007i $$-0.549347\pi$$
−0.154408 + 0.988007i $$0.549347\pi$$
$$710$$ −3048.00 −0.161112
$$711$$ 0 0
$$712$$ 8550.00 0.450035
$$713$$ −1456.00 −0.0764763
$$714$$ 0 0
$$715$$ 1408.00 0.0736451
$$716$$ −11760.0 −0.613815
$$717$$ 0 0
$$718$$ 8500.00 0.441807
$$719$$ −34530.0 −1.79103 −0.895516 0.445030i $$-0.853193\pi$$
−0.895516 + 0.445030i $$0.853193\pi$$
$$720$$ 0 0
$$721$$ 29432.0 1.52026
$$722$$ −3259.00 −0.167988
$$723$$ 0 0
$$724$$ 30506.0 1.56595
$$725$$ −9810.00 −0.502530
$$726$$ 0 0
$$727$$ −17316.0 −0.883377 −0.441688 0.897169i $$-0.645620\pi$$
−0.441688 + 0.897169i $$0.645620\pi$$
$$728$$ −12480.0 −0.635357
$$729$$ 0 0
$$730$$ −2168.00 −0.109920
$$731$$ −30192.0 −1.52762
$$732$$ 0 0
$$733$$ −27072.0 −1.36416 −0.682079 0.731279i $$-0.738924\pi$$
−0.682079 + 0.731279i $$0.738924\pi$$
$$734$$ 7144.00 0.359250
$$735$$ 0 0
$$736$$ 29302.0 1.46751
$$737$$ 11396.0 0.569575
$$738$$ 0 0
$$739$$ −17320.0 −0.862147 −0.431073 0.902317i $$-0.641865\pi$$
−0.431073 + 0.902317i $$0.641865\pi$$
$$740$$ 1848.00 0.0918025
$$741$$ 0 0
$$742$$ 9048.00 0.447658
$$743$$ −14588.0 −0.720299 −0.360149 0.932895i $$-0.617274\pi$$
−0.360149 + 0.932895i $$0.617274\pi$$
$$744$$ 0 0
$$745$$ 5240.00 0.257690
$$746$$ −632.000 −0.0310176
$$747$$ 0 0
$$748$$ −5698.00 −0.278529
$$749$$ 14664.0 0.715368
$$750$$ 0 0
$$751$$ 26152.0 1.27071 0.635353 0.772222i $$-0.280855\pi$$
0.635353 + 0.772222i $$0.280855\pi$$
$$752$$ 20746.0 1.00602
$$753$$ 0 0
$$754$$ −2880.00 −0.139103
$$755$$ −4792.00 −0.230992
$$756$$ 0 0
$$757$$ −1066.00 −0.0511815 −0.0255908 0.999673i $$-0.508147\pi$$
−0.0255908 + 0.999673i $$0.508147\pi$$
$$758$$ −4220.00 −0.202213
$$759$$ 0 0
$$760$$ 3600.00 0.171823
$$761$$ 37518.0 1.78716 0.893578 0.448907i $$-0.148187\pi$$
0.893578 + 0.448907i $$0.148187\pi$$
$$762$$ 0 0
$$763$$ 8320.00 0.394763
$$764$$ −12446.0 −0.589372
$$765$$ 0 0
$$766$$ −8458.00 −0.398956
$$767$$ −6400.00 −0.301292
$$768$$ 0 0
$$769$$ −17290.0 −0.810785 −0.405392 0.914143i $$-0.632865\pi$$
−0.405392 + 0.914143i $$0.632865\pi$$
$$770$$ 1144.00 0.0535414
$$771$$ 0 0
$$772$$ 27734.0 1.29296
$$773$$ 17172.0 0.799009 0.399504 0.916731i $$-0.369182\pi$$
0.399504 + 0.916731i $$0.369182\pi$$
$$774$$ 0 0
$$775$$ 872.000 0.0404170
$$776$$ −210.000 −0.00971464
$$777$$ 0 0
$$778$$ −1740.00 −0.0801825
$$779$$ 25320.0 1.16455
$$780$$ 0 0
$$781$$ 8382.00 0.384035
$$782$$ −13468.0 −0.615876
$$783$$ 0 0
$$784$$ 13653.0 0.621948
$$785$$ 8456.00 0.384468
$$786$$ 0 0
$$787$$ −9536.00 −0.431921 −0.215960 0.976402i $$-0.569288\pi$$
−0.215960 + 0.976402i $$0.569288\pi$$
$$788$$ 2618.00 0.118353
$$789$$ 0 0
$$790$$ −2200.00 −0.0990791
$$791$$ −55692.0 −2.50339
$$792$$ 0 0
$$793$$ −4224.00 −0.189153
$$794$$ −5126.00 −0.229112
$$795$$ 0 0
$$796$$ −14700.0 −0.654557
$$797$$ 20516.0 0.911812 0.455906 0.890028i $$-0.349315\pi$$
0.455906 + 0.890028i $$0.349315\pi$$
$$798$$ 0 0
$$799$$ −37444.0 −1.65791
$$800$$ −17549.0 −0.775564
$$801$$ 0 0
$$802$$ 3098.00 0.136402
$$803$$ 5962.00 0.262010
$$804$$ 0 0
$$805$$ −18928.0 −0.828726
$$806$$ 256.000 0.0111876
$$807$$ 0 0
$$808$$ 25530.0 1.11156
$$809$$ −22470.0 −0.976518 −0.488259 0.872699i $$-0.662368\pi$$
−0.488259 + 0.872699i $$0.662368\pi$$
$$810$$ 0 0
$$811$$ −3368.00 −0.145828 −0.0729140 0.997338i $$-0.523230\pi$$
−0.0729140 + 0.997338i $$0.523230\pi$$
$$812$$ 16380.0 0.707913
$$813$$ 0 0
$$814$$ 726.000 0.0312608
$$815$$ 15472.0 0.664982
$$816$$ 0 0
$$817$$ −24480.0 −1.04828
$$818$$ 6390.00 0.273131
$$819$$ 0 0
$$820$$ 11816.0 0.503211
$$821$$ 10738.0 0.456466 0.228233 0.973607i $$-0.426705\pi$$
0.228233 + 0.973607i $$0.426705\pi$$
$$822$$ 0 0
$$823$$ −15912.0 −0.673946 −0.336973 0.941514i $$-0.609403\pi$$
−0.336973 + 0.941514i $$0.609403\pi$$
$$824$$ 16980.0 0.717872
$$825$$ 0 0
$$826$$ −5200.00 −0.219045
$$827$$ −22924.0 −0.963900 −0.481950 0.876199i $$-0.660071\pi$$
−0.481950 + 0.876199i $$0.660071\pi$$
$$828$$ 0 0
$$829$$ −41690.0 −1.74663 −0.873313 0.487159i $$-0.838033\pi$$
−0.873313 + 0.487159i $$0.838033\pi$$
$$830$$ 528.000 0.0220809
$$831$$ 0 0
$$832$$ 5344.00 0.222680
$$833$$ −24642.0 −1.02496
$$834$$ 0 0
$$835$$ −8016.00 −0.332222
$$836$$ −4620.00 −0.191132
$$837$$ 0 0
$$838$$ −9760.00 −0.402331
$$839$$ 16450.0 0.676898 0.338449 0.940985i $$-0.390098\pi$$
0.338449 + 0.940985i $$0.390098\pi$$
$$840$$ 0 0
$$841$$ −16289.0 −0.667883
$$842$$ −5138.00 −0.210294
$$843$$ 0 0
$$844$$ −15624.0 −0.637204
$$845$$ −4692.00 −0.191017
$$846$$ 0 0
$$847$$ −3146.00 −0.127624
$$848$$ −14268.0 −0.577789
$$849$$ 0 0
$$850$$ 8066.00 0.325484
$$851$$ −12012.0 −0.483861
$$852$$ 0 0
$$853$$ −30892.0 −1.24000 −0.620001 0.784601i $$-0.712868\pi$$
−0.620001 + 0.784601i $$0.712868\pi$$
$$854$$ −3432.00 −0.137518
$$855$$ 0 0
$$856$$ 8460.00 0.337800
$$857$$ 38906.0 1.55076 0.775381 0.631493i $$-0.217558\pi$$
0.775381 + 0.631493i $$0.217558\pi$$
$$858$$ 0 0
$$859$$ −1020.00 −0.0405145 −0.0202572 0.999795i $$-0.506449\pi$$
−0.0202572 + 0.999795i $$0.506449\pi$$
$$860$$ −11424.0 −0.452971
$$861$$ 0 0
$$862$$ 7008.00 0.276907
$$863$$ −15078.0 −0.594741 −0.297370 0.954762i $$-0.596110\pi$$
−0.297370 + 0.954762i $$0.596110\pi$$
$$864$$ 0 0
$$865$$ −2712.00 −0.106602
$$866$$ 5578.00 0.218878
$$867$$ 0 0
$$868$$ −1456.00 −0.0569353
$$869$$ 6050.00 0.236171
$$870$$ 0 0
$$871$$ 33152.0 1.28968
$$872$$ 4800.00 0.186409
$$873$$ 0 0
$$874$$ −10920.0 −0.422625
$$875$$ 24336.0 0.940237
$$876$$ 0 0
$$877$$ 22704.0 0.874184 0.437092 0.899417i $$-0.356008\pi$$
0.437092 + 0.899417i $$0.356008\pi$$
$$878$$ −10430.0 −0.400906
$$879$$ 0 0
$$880$$ −1804.00 −0.0691055
$$881$$ 19358.0 0.740281 0.370141 0.928976i $$-0.379310\pi$$
0.370141 + 0.928976i $$0.379310\pi$$
$$882$$ 0 0
$$883$$ −11252.0 −0.428833 −0.214417 0.976742i $$-0.568785\pi$$
−0.214417 + 0.976742i $$0.568785\pi$$
$$884$$ −16576.0 −0.630669
$$885$$ 0 0
$$886$$ 4432.00 0.168054
$$887$$ −43684.0 −1.65362 −0.826812 0.562478i $$-0.809848\pi$$
−0.826812 + 0.562478i $$0.809848\pi$$
$$888$$ 0 0
$$889$$ 41756.0 1.57531
$$890$$ −2280.00 −0.0858717
$$891$$ 0 0
$$892$$ −14896.0 −0.559142
$$893$$ −30360.0 −1.13769
$$894$$ 0 0
$$895$$ 6720.00 0.250977
$$896$$ 37830.0 1.41050
$$897$$ 0 0
$$898$$ 6290.00 0.233742
$$899$$ −720.000 −0.0267112
$$900$$ 0 0
$$901$$ 25752.0 0.952190
$$902$$ 4642.00 0.171354
$$903$$ 0 0
$$904$$ −32130.0 −1.18211
$$905$$ −17432.0 −0.640287
$$906$$ 0 0
$$907$$ 45804.0 1.67684 0.838422 0.545022i $$-0.183479\pi$$
0.838422 + 0.545022i $$0.183479\pi$$
$$908$$ 20748.0 0.758311
$$909$$ 0 0
$$910$$ 3328.00 0.121233
$$911$$ 15318.0 0.557089 0.278544 0.960423i $$-0.410148\pi$$
0.278544 + 0.960423i $$0.410148\pi$$
$$912$$ 0 0
$$913$$ −1452.00 −0.0526333
$$914$$ 3054.00 0.110522
$$915$$ 0 0
$$916$$ 17850.0 0.643865
$$917$$ −49608.0 −1.78648
$$918$$ 0 0
$$919$$ 11350.0 0.407401 0.203701 0.979033i $$-0.434703\pi$$
0.203701 + 0.979033i $$0.434703\pi$$
$$920$$ −10920.0 −0.391328
$$921$$ 0 0
$$922$$ −12882.0 −0.460137
$$923$$ 24384.0 0.869566
$$924$$ 0 0
$$925$$ 7194.00 0.255716
$$926$$ 6148.00 0.218181
$$927$$ 0 0
$$928$$ 14490.0 0.512562
$$929$$ −33030.0 −1.16650 −0.583250 0.812292i $$-0.698219\pi$$
−0.583250 + 0.812292i $$0.698219\pi$$
$$930$$ 0 0
$$931$$ −19980.0 −0.703349
$$932$$ −21294.0 −0.748399
$$933$$ 0 0
$$934$$ −5124.00 −0.179510
$$935$$ 3256.00 0.113885
$$936$$ 0 0
$$937$$ −10006.0 −0.348860 −0.174430 0.984670i $$-0.555808\pi$$
−0.174430 + 0.984670i $$0.555808\pi$$
$$938$$ 26936.0 0.937624
$$939$$ 0 0
$$940$$ −14168.0 −0.491606
$$941$$ −2622.00 −0.0908340 −0.0454170 0.998968i $$-0.514462\pi$$
−0.0454170 + 0.998968i $$0.514462\pi$$
$$942$$ 0 0
$$943$$ −76804.0 −2.65226
$$944$$ 8200.00 0.282720
$$945$$ 0 0
$$946$$ −4488.00 −0.154247
$$947$$ 39876.0 1.36832 0.684158 0.729334i $$-0.260170\pi$$
0.684158 + 0.729334i $$0.260170\pi$$
$$948$$ 0 0
$$949$$ 17344.0 0.593267
$$950$$ 6540.00 0.223353
$$951$$ 0 0
$$952$$ −28860.0 −0.982519
$$953$$ −38918.0 −1.32285 −0.661426 0.750011i $$-0.730048\pi$$
−0.661426 + 0.750011i $$0.730048\pi$$
$$954$$ 0 0
$$955$$ 7112.00 0.240983
$$956$$ 18900.0 0.639403
$$957$$ 0 0
$$958$$ 16520.0 0.557137
$$959$$ −56836.0 −1.91380
$$960$$ 0 0
$$961$$ −29727.0 −0.997852
$$962$$ 2112.00 0.0707834
$$963$$ 0 0
$$964$$ 4046.00 0.135179
$$965$$ −15848.0 −0.528669
$$966$$ 0 0
$$967$$ 1114.00 0.0370464 0.0185232 0.999828i $$-0.494104\pi$$
0.0185232 + 0.999828i $$0.494104\pi$$
$$968$$ −1815.00 −0.0602648
$$969$$ 0 0
$$970$$ 56.0000 0.00185366
$$971$$ 1688.00 0.0557884 0.0278942 0.999611i $$-0.491120\pi$$
0.0278942 + 0.999611i $$0.491120\pi$$
$$972$$ 0 0
$$973$$ −71240.0 −2.34722
$$974$$ 524.000 0.0172382
$$975$$ 0 0
$$976$$ 5412.00 0.177494
$$977$$ 41826.0 1.36963 0.684817 0.728715i $$-0.259882\pi$$
0.684817 + 0.728715i $$0.259882\pi$$
$$978$$ 0 0
$$979$$ 6270.00 0.204689
$$980$$ −9324.00 −0.303923
$$981$$ 0 0
$$982$$ 15028.0 0.488353
$$983$$ −978.000 −0.0317328 −0.0158664 0.999874i $$-0.505051\pi$$
−0.0158664 + 0.999874i $$0.505051\pi$$
$$984$$ 0 0
$$985$$ −1496.00 −0.0483924
$$986$$ −6660.00 −0.215109
$$987$$ 0 0
$$988$$ −13440.0 −0.432777
$$989$$ 74256.0 2.38747
$$990$$ 0 0
$$991$$ 47272.0 1.51528 0.757641 0.652671i $$-0.226352\pi$$
0.757641 + 0.652671i $$0.226352\pi$$
$$992$$ −1288.00 −0.0412238
$$993$$ 0 0
$$994$$ 19812.0 0.632192
$$995$$ 8400.00 0.267636
$$996$$ 0 0
$$997$$ 51104.0 1.62335 0.811675 0.584109i $$-0.198556\pi$$
0.811675 + 0.584109i $$0.198556\pi$$
$$998$$ 9020.00 0.286095
$$999$$ 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 99.4.a.a.1.1 1
3.2 odd 2 33.4.a.b.1.1 1
4.3 odd 2 1584.4.a.l.1.1 1
5.4 even 2 2475.4.a.e.1.1 1
11.10 odd 2 1089.4.a.e.1.1 1
12.11 even 2 528.4.a.h.1.1 1
15.2 even 4 825.4.c.f.199.1 2
15.8 even 4 825.4.c.f.199.2 2
15.14 odd 2 825.4.a.f.1.1 1
21.20 even 2 1617.4.a.d.1.1 1
24.5 odd 2 2112.4.a.u.1.1 1
24.11 even 2 2112.4.a.h.1.1 1
33.32 even 2 363.4.a.d.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
33.4.a.b.1.1 1 3.2 odd 2
99.4.a.a.1.1 1 1.1 even 1 trivial
363.4.a.d.1.1 1 33.32 even 2
528.4.a.h.1.1 1 12.11 even 2
825.4.a.f.1.1 1 15.14 odd 2
825.4.c.f.199.1 2 15.2 even 4
825.4.c.f.199.2 2 15.8 even 4
1089.4.a.e.1.1 1 11.10 odd 2
1584.4.a.l.1.1 1 4.3 odd 2
1617.4.a.d.1.1 1 21.20 even 2
2112.4.a.h.1.1 1 24.11 even 2
2112.4.a.u.1.1 1 24.5 odd 2
2475.4.a.e.1.1 1 5.4 even 2