# Properties

 Label 1584.4.a.bc.1.1 Level $1584$ Weight $4$ Character 1584.1 Self dual yes Analytic conductor $93.459$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1584,4,Mod(1,1584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1584, 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("1584.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1584 = 2^{4} \cdot 3^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1584.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: $$93.4590254491$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{12})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - 3$$ x^2 - 3 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 11) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-1.73205$$ of defining polynomial Character $$\chi$$ $$=$$ 1584.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-14.8564 q^{5} -3.07180 q^{7} +O(q^{10})$$ $$q-14.8564 q^{5} -3.07180 q^{7} -11.0000 q^{11} +5.35898 q^{13} +41.2154 q^{17} -139.923 q^{19} -111.354 q^{23} +95.7128 q^{25} +24.9948 q^{29} -31.4974 q^{31} +45.6359 q^{35} +13.1436 q^{37} -261.072 q^{41} +57.7128 q^{43} -343.846 q^{47} -333.564 q^{49} +342.995 q^{53} +163.420 q^{55} +88.3693 q^{59} +738.697 q^{61} -79.6152 q^{65} -342.359 q^{67} -207.364 q^{71} -1010.60 q^{73} +33.7898 q^{77} -1294.23 q^{79} +441.846 q^{83} -612.313 q^{85} +1489.11 q^{89} -16.4617 q^{91} +2078.75 q^{95} +1346.42 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{5} - 20 q^{7}+O(q^{10})$$ 2 * q - 2 * q^5 - 20 * q^7 $$2 q - 2 q^{5} - 20 q^{7} - 22 q^{11} + 80 q^{13} + 124 q^{17} - 72 q^{19} - 98 q^{23} + 136 q^{25} - 144 q^{29} + 34 q^{31} - 172 q^{35} + 54 q^{37} - 536 q^{41} + 60 q^{43} - 272 q^{47} - 390 q^{49} + 492 q^{53} + 22 q^{55} + 634 q^{59} + 840 q^{61} + 880 q^{65} - 754 q^{67} - 678 q^{71} - 400 q^{73} + 220 q^{77} - 316 q^{79} + 468 q^{83} + 452 q^{85} + 1842 q^{89} - 1280 q^{91} + 2952 q^{95} + 2194 q^{97}+O(q^{100})$$ 2 * q - 2 * q^5 - 20 * q^7 - 22 * q^11 + 80 * q^13 + 124 * q^17 - 72 * q^19 - 98 * q^23 + 136 * q^25 - 144 * q^29 + 34 * q^31 - 172 * q^35 + 54 * q^37 - 536 * q^41 + 60 * q^43 - 272 * q^47 - 390 * q^49 + 492 * q^53 + 22 * q^55 + 634 * q^59 + 840 * q^61 + 880 * q^65 - 754 * q^67 - 678 * q^71 - 400 * q^73 + 220 * q^77 - 316 * q^79 + 468 * q^83 + 452 * q^85 + 1842 * q^89 - 1280 * q^91 + 2952 * q^95 + 2194 * q^97

## 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
$$5$$ −14.8564 −1.32880 −0.664399 0.747378i $$-0.731312\pi$$
−0.664399 + 0.747378i $$0.731312\pi$$
$$6$$ 0 0
$$7$$ −3.07180 −0.165861 −0.0829307 0.996555i $$-0.526428\pi$$
−0.0829307 + 0.996555i $$0.526428\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −11.0000 −0.301511
$$12$$ 0 0
$$13$$ 5.35898 0.114332 0.0571659 0.998365i $$-0.481794\pi$$
0.0571659 + 0.998365i $$0.481794\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 41.2154 0.588012 0.294006 0.955804i $$-0.405011\pi$$
0.294006 + 0.955804i $$0.405011\pi$$
$$18$$ 0 0
$$19$$ −139.923 −1.68950 −0.844751 0.535159i $$-0.820252\pi$$
−0.844751 + 0.535159i $$0.820252\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −111.354 −1.00952 −0.504758 0.863261i $$-0.668418\pi$$
−0.504758 + 0.863261i $$0.668418\pi$$
$$24$$ 0 0
$$25$$ 95.7128 0.765703
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 24.9948 0.160049 0.0800246 0.996793i $$-0.474500\pi$$
0.0800246 + 0.996793i $$0.474500\pi$$
$$30$$ 0 0
$$31$$ −31.4974 −0.182487 −0.0912436 0.995829i $$-0.529084\pi$$
−0.0912436 + 0.995829i $$0.529084\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 45.6359 0.220396
$$36$$ 0 0
$$37$$ 13.1436 0.0583998 0.0291999 0.999574i $$-0.490704\pi$$
0.0291999 + 0.999574i $$0.490704\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −261.072 −0.994453 −0.497226 0.867621i $$-0.665648\pi$$
−0.497226 + 0.867621i $$0.665648\pi$$
$$42$$ 0 0
$$43$$ 57.7128 0.204677 0.102339 0.994750i $$-0.467367\pi$$
0.102339 + 0.994750i $$0.467367\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −343.846 −1.06713 −0.533565 0.845759i $$-0.679148\pi$$
−0.533565 + 0.845759i $$0.679148\pi$$
$$48$$ 0 0
$$49$$ −333.564 −0.972490
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 342.995 0.888943 0.444471 0.895793i $$-0.353392\pi$$
0.444471 + 0.895793i $$0.353392\pi$$
$$54$$ 0 0
$$55$$ 163.420 0.400647
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 88.3693 0.194995 0.0974975 0.995236i $$-0.468916\pi$$
0.0974975 + 0.995236i $$0.468916\pi$$
$$60$$ 0 0
$$61$$ 738.697 1.55050 0.775250 0.631654i $$-0.217624\pi$$
0.775250 + 0.631654i $$0.217624\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −79.6152 −0.151924
$$66$$ 0 0
$$67$$ −342.359 −0.624266 −0.312133 0.950038i $$-0.601043\pi$$
−0.312133 + 0.950038i $$0.601043\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −207.364 −0.346614 −0.173307 0.984868i $$-0.555445\pi$$
−0.173307 + 0.984868i $$0.555445\pi$$
$$72$$ 0 0
$$73$$ −1010.60 −1.62030 −0.810149 0.586224i $$-0.800614\pi$$
−0.810149 + 0.586224i $$0.800614\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 33.7898 0.0500091
$$78$$ 0 0
$$79$$ −1294.23 −1.84319 −0.921593 0.388157i $$-0.873112\pi$$
−0.921593 + 0.388157i $$0.873112\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 441.846 0.584324 0.292162 0.956369i $$-0.405625\pi$$
0.292162 + 0.956369i $$0.405625\pi$$
$$84$$ 0 0
$$85$$ −612.313 −0.781349
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1489.11 1.77355 0.886773 0.462205i $$-0.152942\pi$$
0.886773 + 0.462205i $$0.152942\pi$$
$$90$$ 0 0
$$91$$ −16.4617 −0.0189633
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 2078.75 2.24501
$$96$$ 0 0
$$97$$ 1346.42 1.40936 0.704679 0.709526i $$-0.251091\pi$$
0.704679 + 0.709526i $$0.251091\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 161.461 0.159069 0.0795347 0.996832i $$-0.474657\pi$$
0.0795347 + 0.996832i $$0.474657\pi$$
$$102$$ 0 0
$$103$$ 34.7592 0.0332517 0.0166259 0.999862i $$-0.494708\pi$$
0.0166259 + 0.999862i $$0.494708\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 832.179 0.751867 0.375934 0.926647i $$-0.377322\pi$$
0.375934 + 0.926647i $$0.377322\pi$$
$$108$$ 0 0
$$109$$ 1044.26 0.917629 0.458815 0.888532i $$-0.348274\pi$$
0.458815 + 0.888532i $$0.348274\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −295.082 −0.245654 −0.122827 0.992428i $$-0.539196\pi$$
−0.122827 + 0.992428i $$0.539196\pi$$
$$114$$ 0 0
$$115$$ 1654.32 1.34144
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −126.605 −0.0975285
$$120$$ 0 0
$$121$$ 121.000 0.0909091
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 435.102 0.311334
$$126$$ 0 0
$$127$$ 1317.60 0.920618 0.460309 0.887759i $$-0.347739\pi$$
0.460309 + 0.887759i $$0.347739\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1600.71 −1.06759 −0.533797 0.845612i $$-0.679235\pi$$
−0.533797 + 0.845612i $$0.679235\pi$$
$$132$$ 0 0
$$133$$ 429.815 0.280223
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1611.68 −1.00507 −0.502536 0.864556i $$-0.667600\pi$$
−0.502536 + 0.864556i $$0.667600\pi$$
$$138$$ 0 0
$$139$$ 31.8619 0.0194424 0.00972120 0.999953i $$-0.496906\pi$$
0.00972120 + 0.999953i $$0.496906\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −58.9488 −0.0344724
$$144$$ 0 0
$$145$$ −371.334 −0.212673
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 2428.34 1.33515 0.667576 0.744542i $$-0.267332\pi$$
0.667576 + 0.744542i $$0.267332\pi$$
$$150$$ 0 0
$$151$$ 2576.68 1.38866 0.694328 0.719659i $$-0.255702\pi$$
0.694328 + 0.719659i $$0.255702\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 467.939 0.242489
$$156$$ 0 0
$$157$$ 2475.94 1.25861 0.629305 0.777158i $$-0.283340\pi$$
0.629305 + 0.777158i $$0.283340\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 342.056 0.167440
$$162$$ 0 0
$$163$$ 2725.11 1.30949 0.654745 0.755850i $$-0.272776\pi$$
0.654745 + 0.755850i $$0.272776\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2737.30 1.26837 0.634187 0.773180i $$-0.281335\pi$$
0.634187 + 0.773180i $$0.281335\pi$$
$$168$$ 0 0
$$169$$ −2168.28 −0.986928
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −2307.42 −1.01404 −0.507022 0.861933i $$-0.669254\pi$$
−0.507022 + 0.861933i $$0.669254\pi$$
$$174$$ 0 0
$$175$$ −294.010 −0.127001
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −1312.15 −0.547905 −0.273953 0.961743i $$-0.588331\pi$$
−0.273953 + 0.961743i $$0.588331\pi$$
$$180$$ 0 0
$$181$$ −803.174 −0.329831 −0.164916 0.986308i $$-0.552735\pi$$
−0.164916 + 0.986308i $$0.552735\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −195.267 −0.0776015
$$186$$ 0 0
$$187$$ −453.369 −0.177292
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 1718.25 0.650932 0.325466 0.945554i $$-0.394479\pi$$
0.325466 + 0.945554i $$0.394479\pi$$
$$192$$ 0 0
$$193$$ 1340.18 0.499837 0.249919 0.968267i $$-0.419596\pi$$
0.249919 + 0.968267i $$0.419596\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 3518.33 1.27244 0.636220 0.771508i $$-0.280497\pi$$
0.636220 + 0.771508i $$0.280497\pi$$
$$198$$ 0 0
$$199$$ −823.692 −0.293417 −0.146709 0.989180i $$-0.546868\pi$$
−0.146709 + 0.989180i $$0.546868\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −76.7791 −0.0265460
$$204$$ 0 0
$$205$$ 3878.59 1.32143
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 1539.15 0.509404
$$210$$ 0 0
$$211$$ 107.343 0.0350228 0.0175114 0.999847i $$-0.494426\pi$$
0.0175114 + 0.999847i $$0.494426\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −857.405 −0.271975
$$216$$ 0 0
$$217$$ 96.7537 0.0302676
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 220.873 0.0672285
$$222$$ 0 0
$$223$$ 3933.68 1.18125 0.590625 0.806946i $$-0.298881\pi$$
0.590625 + 0.806946i $$0.298881\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −1771.90 −0.518085 −0.259042 0.965866i $$-0.583407\pi$$
−0.259042 + 0.965866i $$0.583407\pi$$
$$228$$ 0 0
$$229$$ 1915.37 0.552713 0.276356 0.961055i $$-0.410873\pi$$
0.276356 + 0.961055i $$0.410873\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −4396.32 −1.23610 −0.618052 0.786137i $$-0.712078\pi$$
−0.618052 + 0.786137i $$0.712078\pi$$
$$234$$ 0 0
$$235$$ 5108.32 1.41800
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −4084.49 −1.10546 −0.552728 0.833362i $$-0.686413\pi$$
−0.552728 + 0.833362i $$0.686413\pi$$
$$240$$ 0 0
$$241$$ 3908.58 1.04471 0.522353 0.852730i $$-0.325054\pi$$
0.522353 + 0.852730i $$0.325054\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 4955.56 1.29224
$$246$$ 0 0
$$247$$ −749.845 −0.193164
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 1094.89 0.275335 0.137667 0.990479i $$-0.456040\pi$$
0.137667 + 0.990479i $$0.456040\pi$$
$$252$$ 0 0
$$253$$ 1224.89 0.304381
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −783.179 −0.190091 −0.0950454 0.995473i $$-0.530300\pi$$
−0.0950454 + 0.995473i $$0.530300\pi$$
$$258$$ 0 0
$$259$$ −40.3744 −0.00968628
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6180.06 1.44897 0.724484 0.689292i $$-0.242078\pi$$
0.724484 + 0.689292i $$0.242078\pi$$
$$264$$ 0 0
$$265$$ −5095.67 −1.18122
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −986.965 −0.223704 −0.111852 0.993725i $$-0.535678\pi$$
−0.111852 + 0.993725i $$0.535678\pi$$
$$270$$ 0 0
$$271$$ −4576.99 −1.02595 −0.512975 0.858404i $$-0.671457\pi$$
−0.512975 + 0.858404i $$0.671457\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1052.84 −0.230868
$$276$$ 0 0
$$277$$ 567.836 0.123169 0.0615847 0.998102i $$-0.480385\pi$$
0.0615847 + 0.998102i $$0.480385\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −5311.01 −1.12750 −0.563752 0.825944i $$-0.690643\pi$$
−0.563752 + 0.825944i $$0.690643\pi$$
$$282$$ 0 0
$$283$$ 4728.44 0.993204 0.496602 0.867978i $$-0.334581\pi$$
0.496602 + 0.867978i $$0.334581\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 801.960 0.164941
$$288$$ 0 0
$$289$$ −3214.29 −0.654242
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −2328.92 −0.464358 −0.232179 0.972673i $$-0.574585\pi$$
−0.232179 + 0.972673i $$0.574585\pi$$
$$294$$ 0 0
$$295$$ −1312.85 −0.259109
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −596.743 −0.115420
$$300$$ 0 0
$$301$$ −177.282 −0.0339481
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −10974.4 −2.06030
$$306$$ 0 0
$$307$$ 1678.07 0.311962 0.155981 0.987760i $$-0.450146\pi$$
0.155981 + 0.987760i $$0.450146\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 3572.71 0.651413 0.325707 0.945471i $$-0.394398\pi$$
0.325707 + 0.945471i $$0.394398\pi$$
$$312$$ 0 0
$$313$$ 7184.36 1.29739 0.648697 0.761047i $$-0.275314\pi$$
0.648697 + 0.761047i $$0.275314\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 15.7077 0.00278306 0.00139153 0.999999i $$-0.499557\pi$$
0.00139153 + 0.999999i $$0.499557\pi$$
$$318$$ 0 0
$$319$$ −274.943 −0.0482566
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −5766.98 −0.993447
$$324$$ 0 0
$$325$$ 512.923 0.0875442
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 1056.23 0.176996
$$330$$ 0 0
$$331$$ 1318.95 0.219022 0.109511 0.993986i $$-0.465072\pi$$
0.109511 + 0.993986i $$0.465072\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 5086.22 0.829523
$$336$$ 0 0
$$337$$ −239.183 −0.0386621 −0.0193310 0.999813i $$-0.506154\pi$$
−0.0193310 + 0.999813i $$0.506154\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 346.472 0.0550220
$$342$$ 0 0
$$343$$ 2078.27 0.327160
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −5862.79 −0.907006 −0.453503 0.891255i $$-0.649826\pi$$
−0.453503 + 0.891255i $$0.649826\pi$$
$$348$$ 0 0
$$349$$ 3491.73 0.535553 0.267776 0.963481i $$-0.413711\pi$$
0.267776 + 0.963481i $$0.413711\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 10916.7 1.64600 0.822999 0.568043i $$-0.192299\pi$$
0.822999 + 0.568043i $$0.192299\pi$$
$$354$$ 0 0
$$355$$ 3080.69 0.460580
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −11500.7 −1.69077 −0.845384 0.534160i $$-0.820628\pi$$
−0.845384 + 0.534160i $$0.820628\pi$$
$$360$$ 0 0
$$361$$ 12719.5 1.85442
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 15013.9 2.15305
$$366$$ 0 0
$$367$$ −6767.01 −0.962493 −0.481246 0.876585i $$-0.659816\pi$$
−0.481246 + 0.876585i $$0.659816\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −1053.61 −0.147441
$$372$$ 0 0
$$373$$ −5310.22 −0.737139 −0.368569 0.929600i $$-0.620152\pi$$
−0.368569 + 0.929600i $$0.620152\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 133.947 0.0182987
$$378$$ 0 0
$$379$$ 838.267 0.113612 0.0568059 0.998385i $$-0.481908\pi$$
0.0568059 + 0.998385i $$0.481908\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −2832.16 −0.377851 −0.188925 0.981991i $$-0.560500\pi$$
−0.188925 + 0.981991i $$0.560500\pi$$
$$384$$ 0 0
$$385$$ −501.994 −0.0664520
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −3111.25 −0.405519 −0.202759 0.979229i $$-0.564991\pi$$
−0.202759 + 0.979229i $$0.564991\pi$$
$$390$$ 0 0
$$391$$ −4589.49 −0.593608
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 19227.5 2.44922
$$396$$ 0 0
$$397$$ 14208.7 1.79626 0.898131 0.439728i $$-0.144925\pi$$
0.898131 + 0.439728i $$0.144925\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 6261.68 0.779784 0.389892 0.920861i $$-0.372512\pi$$
0.389892 + 0.920861i $$0.372512\pi$$
$$402$$ 0 0
$$403$$ −168.794 −0.0208641
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −144.580 −0.0176082
$$408$$ 0 0
$$409$$ −4192.50 −0.506860 −0.253430 0.967354i $$-0.581559\pi$$
−0.253430 + 0.967354i $$0.581559\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −271.453 −0.0323421
$$414$$ 0 0
$$415$$ −6564.25 −0.776448
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −9287.15 −1.08283 −0.541416 0.840755i $$-0.682112\pi$$
−0.541416 + 0.840755i $$0.682112\pi$$
$$420$$ 0 0
$$421$$ 13146.0 1.52185 0.760923 0.648842i $$-0.224746\pi$$
0.760923 + 0.648842i $$0.224746\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 3944.84 0.450242
$$426$$ 0 0
$$427$$ −2269.13 −0.257168
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 4909.67 0.548701 0.274351 0.961630i $$-0.411537\pi$$
0.274351 + 0.961630i $$0.411537\pi$$
$$432$$ 0 0
$$433$$ −11743.3 −1.30334 −0.651671 0.758502i $$-0.725932\pi$$
−0.651671 + 0.758502i $$0.725932\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 15581.0 1.70558
$$438$$ 0 0
$$439$$ 11824.2 1.28551 0.642754 0.766073i $$-0.277792\pi$$
0.642754 + 0.766073i $$0.277792\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 10102.1 1.08344 0.541722 0.840558i $$-0.317772\pi$$
0.541722 + 0.840558i $$0.317772\pi$$
$$444$$ 0 0
$$445$$ −22122.9 −2.35668
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 345.254 0.0362885 0.0181443 0.999835i $$-0.494224\pi$$
0.0181443 + 0.999835i $$0.494224\pi$$
$$450$$ 0 0
$$451$$ 2871.79 0.299839
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 244.562 0.0251983
$$456$$ 0 0
$$457$$ −10567.1 −1.08164 −0.540821 0.841138i $$-0.681886\pi$$
−0.540821 + 0.841138i $$0.681886\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −4733.96 −0.478270 −0.239135 0.970986i $$-0.576864\pi$$
−0.239135 + 0.970986i $$0.576864\pi$$
$$462$$ 0 0
$$463$$ −3431.20 −0.344409 −0.172204 0.985061i $$-0.555089\pi$$
−0.172204 + 0.985061i $$0.555089\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 5116.96 0.507034 0.253517 0.967331i $$-0.418413\pi$$
0.253517 + 0.967331i $$0.418413\pi$$
$$468$$ 0 0
$$469$$ 1051.66 0.103542
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −634.841 −0.0617125
$$474$$ 0 0
$$475$$ −13392.4 −1.29366
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 11566.9 1.10335 0.551675 0.834059i $$-0.313989\pi$$
0.551675 + 0.834059i $$0.313989\pi$$
$$480$$ 0 0
$$481$$ 70.4363 0.00667696
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −20002.9 −1.87275
$$486$$ 0 0
$$487$$ 18326.5 1.70525 0.852623 0.522527i $$-0.175010\pi$$
0.852623 + 0.522527i $$0.175010\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −7617.58 −0.700156 −0.350078 0.936721i $$-0.613845\pi$$
−0.350078 + 0.936721i $$0.613845\pi$$
$$492$$ 0 0
$$493$$ 1030.17 0.0941108
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 636.980 0.0574899
$$498$$ 0 0
$$499$$ −12909.1 −1.15810 −0.579050 0.815292i $$-0.696576\pi$$
−0.579050 + 0.815292i $$0.696576\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 10165.7 0.901121 0.450561 0.892746i $$-0.351224\pi$$
0.450561 + 0.892746i $$0.351224\pi$$
$$504$$ 0 0
$$505$$ −2398.74 −0.211371
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −6449.93 −0.561666 −0.280833 0.959757i $$-0.590611\pi$$
−0.280833 + 0.959757i $$0.590611\pi$$
$$510$$ 0 0
$$511$$ 3104.36 0.268745
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −516.397 −0.0441848
$$516$$ 0 0
$$517$$ 3782.31 0.321752
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 19327.4 1.62524 0.812620 0.582794i $$-0.198041\pi$$
0.812620 + 0.582794i $$0.198041\pi$$
$$522$$ 0 0
$$523$$ −6259.09 −0.523310 −0.261655 0.965161i $$-0.584268\pi$$
−0.261655 + 0.965161i $$0.584268\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −1298.18 −0.107305
$$528$$ 0 0
$$529$$ 232.675 0.0191235
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −1399.08 −0.113698
$$534$$ 0 0
$$535$$ −12363.2 −0.999079
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 3669.20 0.293217
$$540$$ 0 0
$$541$$ −14008.2 −1.11323 −0.556616 0.830770i $$-0.687900\pi$$
−0.556616 + 0.830770i $$0.687900\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −15513.9 −1.21934
$$546$$ 0 0
$$547$$ 4949.45 0.386879 0.193440 0.981112i $$-0.438036\pi$$
0.193440 + 0.981112i $$0.438036\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −3497.35 −0.270404
$$552$$ 0 0
$$553$$ 3975.60 0.305714
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 3801.58 0.289188 0.144594 0.989491i $$-0.453812\pi$$
0.144594 + 0.989491i $$0.453812\pi$$
$$558$$ 0 0
$$559$$ 309.282 0.0234011
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −9900.11 −0.741101 −0.370551 0.928812i $$-0.620831\pi$$
−0.370551 + 0.928812i $$0.620831\pi$$
$$564$$ 0 0
$$565$$ 4383.85 0.326425
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −5329.16 −0.392636 −0.196318 0.980540i $$-0.562898\pi$$
−0.196318 + 0.980540i $$0.562898\pi$$
$$570$$ 0 0
$$571$$ 16962.6 1.24319 0.621597 0.783337i $$-0.286484\pi$$
0.621597 + 0.783337i $$0.286484\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −10658.0 −0.772989
$$576$$ 0 0
$$577$$ −15487.0 −1.11738 −0.558692 0.829375i $$-0.688697\pi$$
−0.558692 + 0.829375i $$0.688697\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −1357.26 −0.0969169
$$582$$ 0 0
$$583$$ −3772.94 −0.268026
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 11084.2 0.779373 0.389686 0.920948i $$-0.372583\pi$$
0.389686 + 0.920948i $$0.372583\pi$$
$$588$$ 0 0
$$589$$ 4407.22 0.308313
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −4349.68 −0.301214 −0.150607 0.988594i $$-0.548123\pi$$
−0.150607 + 0.988594i $$0.548123\pi$$
$$594$$ 0 0
$$595$$ 1880.90 0.129596
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 13183.9 0.899299 0.449650 0.893205i $$-0.351549\pi$$
0.449650 + 0.893205i $$0.351549\pi$$
$$600$$ 0 0
$$601$$ −18765.0 −1.27361 −0.636806 0.771024i $$-0.719745\pi$$
−0.636806 + 0.771024i $$0.719745\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −1797.63 −0.120800
$$606$$ 0 0
$$607$$ −21871.4 −1.46249 −0.731244 0.682116i $$-0.761060\pi$$
−0.731244 + 0.682116i $$0.761060\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −1842.67 −0.122007
$$612$$ 0 0
$$613$$ −3527.85 −0.232445 −0.116222 0.993223i $$-0.537079\pi$$
−0.116222 + 0.993223i $$0.537079\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 22728.1 1.48298 0.741490 0.670963i $$-0.234119\pi$$
0.741490 + 0.670963i $$0.234119\pi$$
$$618$$ 0 0
$$619$$ 21443.3 1.39237 0.696187 0.717861i $$-0.254879\pi$$
0.696187 + 0.717861i $$0.254879\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −4574.25 −0.294163
$$624$$ 0 0
$$625$$ −18428.2 −1.17940
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 541.718 0.0343398
$$630$$ 0 0
$$631$$ −21532.0 −1.35844 −0.679219 0.733936i $$-0.737681\pi$$
−0.679219 + 0.733936i $$0.737681\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −19574.9 −1.22332
$$636$$ 0 0
$$637$$ −1787.56 −0.111187
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −20148.3 −1.24151 −0.620756 0.784004i $$-0.713174\pi$$
−0.620756 + 0.784004i $$0.713174\pi$$
$$642$$ 0 0
$$643$$ −28869.7 −1.77062 −0.885310 0.465000i $$-0.846054\pi$$
−0.885310 + 0.465000i $$0.846054\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −1590.02 −0.0966155 −0.0483077 0.998833i $$-0.515383\pi$$
−0.0483077 + 0.998833i $$0.515383\pi$$
$$648$$ 0 0
$$649$$ −972.062 −0.0587932
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −20028.1 −1.20024 −0.600122 0.799909i $$-0.704881\pi$$
−0.600122 + 0.799909i $$0.704881\pi$$
$$654$$ 0 0
$$655$$ 23780.8 1.41862
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −10520.7 −0.621897 −0.310948 0.950427i $$-0.600647\pi$$
−0.310948 + 0.950427i $$0.600647\pi$$
$$660$$ 0 0
$$661$$ 3295.83 0.193938 0.0969690 0.995287i $$-0.469085\pi$$
0.0969690 + 0.995287i $$0.469085\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −6385.51 −0.372360
$$666$$ 0 0
$$667$$ −2783.27 −0.161572
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −8125.67 −0.467493
$$672$$ 0 0
$$673$$ −1187.64 −0.0680239 −0.0340119 0.999421i $$-0.510828\pi$$
−0.0340119 + 0.999421i $$0.510828\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −13221.4 −0.750574 −0.375287 0.926909i $$-0.622456\pi$$
−0.375287 + 0.926909i $$0.622456\pi$$
$$678$$ 0 0
$$679$$ −4135.91 −0.233758
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −13831.4 −0.774882 −0.387441 0.921894i $$-0.626641\pi$$
−0.387441 + 0.921894i $$0.626641\pi$$
$$684$$ 0 0
$$685$$ 23943.7 1.33554
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 1838.10 0.101635
$$690$$ 0 0
$$691$$ 9817.07 0.540462 0.270231 0.962796i $$-0.412900\pi$$
0.270231 + 0.962796i $$0.412900\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −473.354 −0.0258350
$$696$$ 0 0
$$697$$ −10760.2 −0.584750
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −29949.8 −1.61368 −0.806838 0.590773i $$-0.798823\pi$$
−0.806838 + 0.590773i $$0.798823\pi$$
$$702$$ 0 0
$$703$$ −1839.09 −0.0986667
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −495.976 −0.0263835
$$708$$ 0 0
$$709$$ 11307.5 0.598959 0.299479 0.954103i $$-0.403187\pi$$
0.299479 + 0.954103i $$0.403187\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 3507.36 0.184224
$$714$$ 0 0
$$715$$ 875.768 0.0458068
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −32623.4 −1.69214 −0.846070 0.533071i $$-0.821038\pi$$
−0.846070 + 0.533071i $$0.821038\pi$$
$$720$$ 0 0
$$721$$ −106.773 −0.00551518
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2392.33 0.122550
$$726$$ 0 0
$$727$$ 502.545 0.0256373 0.0128187 0.999918i $$-0.495920\pi$$
0.0128187 + 0.999918i $$0.495920\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 2378.66 0.120353
$$732$$ 0 0
$$733$$ 8631.37 0.434935 0.217467 0.976068i $$-0.430220\pi$$
0.217467 + 0.976068i $$0.430220\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 3765.95 0.188223
$$738$$ 0 0
$$739$$ 18357.5 0.913792 0.456896 0.889520i $$-0.348961\pi$$
0.456896 + 0.889520i $$0.348961\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 11182.6 0.552155 0.276078 0.961135i $$-0.410965\pi$$
0.276078 + 0.961135i $$0.410965\pi$$
$$744$$ 0 0
$$745$$ −36076.4 −1.77415
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −2556.29 −0.124706
$$750$$ 0 0
$$751$$ −16733.4 −0.813063 −0.406531 0.913637i $$-0.633262\pi$$
−0.406531 + 0.913637i $$0.633262\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −38280.2 −1.84524
$$756$$ 0 0
$$757$$ −24402.4 −1.17163 −0.585813 0.810446i $$-0.699225\pi$$
−0.585813 + 0.810446i $$0.699225\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −8469.33 −0.403434 −0.201717 0.979444i $$-0.564652\pi$$
−0.201717 + 0.979444i $$0.564652\pi$$
$$762$$ 0 0
$$763$$ −3207.74 −0.152199
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 473.570 0.0222941
$$768$$ 0 0
$$769$$ 32834.7 1.53973 0.769864 0.638208i $$-0.220324\pi$$
0.769864 + 0.638208i $$0.220324\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 35571.4 1.65513 0.827564 0.561371i $$-0.189726\pi$$
0.827564 + 0.561371i $$0.189726\pi$$
$$774$$ 0 0
$$775$$ −3014.71 −0.139731
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 36530.0 1.68013
$$780$$ 0 0
$$781$$ 2281.01 0.104508
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −36783.6 −1.67244
$$786$$ 0 0
$$787$$ −15729.6 −0.712452 −0.356226 0.934400i $$-0.615937\pi$$
−0.356226 + 0.934400i $$0.615937\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 906.431 0.0407446
$$792$$ 0 0
$$793$$ 3958.67 0.177272
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −7888.07 −0.350577 −0.175288 0.984517i $$-0.556086\pi$$
−0.175288 + 0.984517i $$0.556086\pi$$
$$798$$ 0 0
$$799$$ −14171.8 −0.627485
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 11116.6 0.488538
$$804$$ 0 0
$$805$$ −5081.73 −0.222494
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −5896.97 −0.256275 −0.128138 0.991756i $$-0.540900\pi$$
−0.128138 + 0.991756i $$0.540900\pi$$
$$810$$ 0 0
$$811$$ −14197.9 −0.614744 −0.307372 0.951589i $$-0.599450\pi$$
−0.307372 + 0.951589i $$0.599450\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −40485.3 −1.74005
$$816$$ 0 0
$$817$$ −8075.35 −0.345803
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 19841.7 0.843459 0.421729 0.906722i $$-0.361423\pi$$
0.421729 + 0.906722i $$0.361423\pi$$
$$822$$ 0 0
$$823$$ 28202.2 1.19449 0.597246 0.802058i $$-0.296262\pi$$
0.597246 + 0.802058i $$0.296262\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 34031.0 1.43092 0.715462 0.698651i $$-0.246216\pi$$
0.715462 + 0.698651i $$0.246216\pi$$
$$828$$ 0 0
$$829$$ 4931.55 0.206610 0.103305 0.994650i $$-0.467058\pi$$
0.103305 + 0.994650i $$0.467058\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −13748.0 −0.571836
$$834$$ 0 0
$$835$$ −40666.4 −1.68541
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −38189.8 −1.57146 −0.785731 0.618568i $$-0.787713\pi$$
−0.785731 + 0.618568i $$0.787713\pi$$
$$840$$ 0 0
$$841$$ −23764.3 −0.974384
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 32212.9 1.31143
$$846$$ 0 0
$$847$$ −371.687 −0.0150783
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −1463.59 −0.0589556
$$852$$ 0 0
$$853$$ 42966.8 1.72469 0.862343 0.506325i $$-0.168997\pi$$
0.862343 + 0.506325i $$0.168997\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 17281.5 0.688828 0.344414 0.938818i $$-0.388078\pi$$
0.344414 + 0.938818i $$0.388078\pi$$
$$858$$ 0 0
$$859$$ −9316.75 −0.370062 −0.185031 0.982733i $$-0.559239\pi$$
−0.185031 + 0.982733i $$0.559239\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −9647.65 −0.380544 −0.190272 0.981731i $$-0.560937\pi$$
−0.190272 + 0.981731i $$0.560937\pi$$
$$864$$ 0 0
$$865$$ 34279.9 1.34746
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 14236.5 0.555742
$$870$$ 0 0
$$871$$ −1834.70 −0.0713735
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −1336.55 −0.0516383
$$876$$ 0 0
$$877$$ 19728.7 0.759624 0.379812 0.925064i $$-0.375989\pi$$
0.379812 + 0.925064i $$0.375989\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −19473.9 −0.744712 −0.372356 0.928090i $$-0.621450\pi$$
−0.372356 + 0.928090i $$0.621450\pi$$
$$882$$ 0 0
$$883$$ −49092.4 −1.87100 −0.935499 0.353329i $$-0.885050\pi$$
−0.935499 + 0.353329i $$0.885050\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 9292.86 0.351774 0.175887 0.984410i $$-0.443721\pi$$
0.175887 + 0.984410i $$0.443721\pi$$
$$888$$ 0 0
$$889$$ −4047.41 −0.152695
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 48112.0 1.80292
$$894$$ 0 0
$$895$$ 19493.9 0.728055
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −787.273 −0.0292069
$$900$$ 0 0
$$901$$ 14136.7 0.522709
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 11932.3 0.438279
$$906$$ 0 0
$$907$$ −37688.7 −1.37975 −0.689875 0.723928i $$-0.742335\pi$$
−0.689875 + 0.723928i $$0.742335\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 33049.6 1.20196 0.600979 0.799265i $$-0.294778\pi$$
0.600979 + 0.799265i $$0.294778\pi$$
$$912$$ 0 0
$$913$$ −4860.31 −0.176180
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 4917.06 0.177073
$$918$$ 0 0
$$919$$ 23148.0 0.830883 0.415442 0.909620i $$-0.363627\pi$$
0.415442 + 0.909620i $$0.363627\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −1111.26 −0.0396290
$$924$$ 0 0
$$925$$ 1258.01 0.0447169
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 23177.9 0.818561 0.409280 0.912409i $$-0.365780\pi$$
0.409280 + 0.912409i $$0.365780\pi$$
$$930$$ 0 0
$$931$$ 46673.3 1.64302
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 6735.44 0.235585
$$936$$ 0 0
$$937$$ −34574.7 −1.20545 −0.602724 0.797950i $$-0.705918\pi$$
−0.602724 + 0.797950i $$0.705918\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −41831.2 −1.44916 −0.724578 0.689192i $$-0.757966\pi$$
−0.724578 + 0.689192i $$0.757966\pi$$
$$942$$ 0 0
$$943$$ 29071.3 1.00392
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 27231.2 0.934419 0.467209 0.884147i $$-0.345259\pi$$
0.467209 + 0.884147i $$0.345259\pi$$
$$948$$ 0 0
$$949$$ −5415.79 −0.185252
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −40939.4 −1.39156 −0.695781 0.718254i $$-0.744942\pi$$
−0.695781 + 0.718254i $$0.744942\pi$$
$$954$$ 0 0
$$955$$ −25527.0 −0.864956
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 4950.74 0.166703
$$960$$ 0 0
$$961$$ −28798.9 −0.966698
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −19910.3 −0.664182
$$966$$ 0 0
$$967$$ 46173.1 1.53550 0.767750 0.640750i $$-0.221376\pi$$
0.767750 + 0.640750i $$0.221376\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −5153.91 −0.170337 −0.0851683 0.996367i $$-0.527143\pi$$
−0.0851683 + 0.996367i $$0.527143\pi$$
$$972$$ 0 0
$$973$$ −97.8734 −0.00322474
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −9692.13 −0.317378 −0.158689 0.987329i $$-0.550727\pi$$
−0.158689 + 0.987329i $$0.550727\pi$$
$$978$$ 0 0
$$979$$ −16380.2 −0.534744
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 32915.7 1.06800 0.534002 0.845483i $$-0.320687\pi$$
0.534002 + 0.845483i $$0.320687\pi$$
$$984$$ 0 0
$$985$$ −52269.7 −1.69081
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −6426.54 −0.206625
$$990$$ 0 0
$$991$$ −29477.9 −0.944901 −0.472451 0.881357i $$-0.656630\pi$$
−0.472451 + 0.881357i $$0.656630\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 12237.1 0.389892
$$996$$ 0 0
$$997$$ −31944.4 −1.01473 −0.507366 0.861731i $$-0.669381\pi$$
−0.507366 + 0.861731i $$0.669381\pi$$
$$998$$ 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 1584.4.a.bc.1.1 2
3.2 odd 2 176.4.a.i.1.2 2
4.3 odd 2 99.4.a.c.1.1 2
12.11 even 2 11.4.a.a.1.2 2
20.19 odd 2 2475.4.a.q.1.2 2
24.5 odd 2 704.4.a.n.1.1 2
24.11 even 2 704.4.a.p.1.2 2
33.32 even 2 1936.4.a.w.1.2 2
44.43 even 2 1089.4.a.v.1.2 2
60.23 odd 4 275.4.b.c.199.1 4
60.47 odd 4 275.4.b.c.199.4 4
60.59 even 2 275.4.a.b.1.1 2
84.83 odd 2 539.4.a.e.1.2 2
132.35 odd 10 121.4.c.f.81.2 8
132.47 even 10 121.4.c.c.9.2 8
132.59 even 10 121.4.c.c.27.2 8
132.71 even 10 121.4.c.c.3.1 8
132.83 odd 10 121.4.c.f.3.2 8
132.95 odd 10 121.4.c.f.27.1 8
132.107 odd 10 121.4.c.f.9.1 8
132.119 even 10 121.4.c.c.81.1 8
132.131 odd 2 121.4.a.c.1.1 2
156.155 even 2 1859.4.a.a.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
11.4.a.a.1.2 2 12.11 even 2
99.4.a.c.1.1 2 4.3 odd 2
121.4.a.c.1.1 2 132.131 odd 2
121.4.c.c.3.1 8 132.71 even 10
121.4.c.c.9.2 8 132.47 even 10
121.4.c.c.27.2 8 132.59 even 10
121.4.c.c.81.1 8 132.119 even 10
121.4.c.f.3.2 8 132.83 odd 10
121.4.c.f.9.1 8 132.107 odd 10
121.4.c.f.27.1 8 132.95 odd 10
121.4.c.f.81.2 8 132.35 odd 10
176.4.a.i.1.2 2 3.2 odd 2
275.4.a.b.1.1 2 60.59 even 2
275.4.b.c.199.1 4 60.23 odd 4
275.4.b.c.199.4 4 60.47 odd 4
539.4.a.e.1.2 2 84.83 odd 2
704.4.a.n.1.1 2 24.5 odd 2
704.4.a.p.1.2 2 24.11 even 2
1089.4.a.v.1.2 2 44.43 even 2
1584.4.a.bc.1.1 2 1.1 even 1 trivial
1859.4.a.a.1.1 2 156.155 even 2
1936.4.a.w.1.2 2 33.32 even 2
2475.4.a.q.1.2 2 20.19 odd 2