# Properties

 Label 1008.6.a.j.1.1 Level $1008$ Weight $6$ Character 1008.1 Self dual yes Analytic conductor $161.667$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,6,Mod(1,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("1008.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 1008.a (trivial)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: yes Analytic conductor: $$161.666890371$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 42) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1008.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-26.0000 q^{5} +49.0000 q^{7} +O(q^{10})$$ $$q-26.0000 q^{5} +49.0000 q^{7} +664.000 q^{11} +318.000 q^{13} -1582.00 q^{17} -236.000 q^{19} +2212.00 q^{23} -2449.00 q^{25} +4954.00 q^{29} +7128.00 q^{31} -1274.00 q^{35} +4358.00 q^{37} -10542.0 q^{41} +8452.00 q^{43} +5352.00 q^{47} +2401.00 q^{49} +33354.0 q^{53} -17264.0 q^{55} -15436.0 q^{59} -36762.0 q^{61} -8268.00 q^{65} -40972.0 q^{67} -9092.00 q^{71} -73454.0 q^{73} +32536.0 q^{77} -89400.0 q^{79} -6428.00 q^{83} +41132.0 q^{85} +122658. q^{89} +15582.0 q^{91} +6136.00 q^{95} +21370.0 q^{97} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −26.0000 −0.465102 −0.232551 0.972584i $$-0.574707\pi$$
−0.232551 + 0.972584i $$0.574707\pi$$
$$6$$ 0 0
$$7$$ 49.0000 0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 664.000 1.65457 0.827287 0.561779i $$-0.189883\pi$$
0.827287 + 0.561779i $$0.189883\pi$$
$$12$$ 0 0
$$13$$ 318.000 0.521878 0.260939 0.965355i $$-0.415968\pi$$
0.260939 + 0.965355i $$0.415968\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1582.00 −1.32765 −0.663826 0.747887i $$-0.731068\pi$$
−0.663826 + 0.747887i $$0.731068\pi$$
$$18$$ 0 0
$$19$$ −236.000 −0.149978 −0.0749891 0.997184i $$-0.523892\pi$$
−0.0749891 + 0.997184i $$0.523892\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2212.00 0.871898 0.435949 0.899971i $$-0.356413\pi$$
0.435949 + 0.899971i $$0.356413\pi$$
$$24$$ 0 0
$$25$$ −2449.00 −0.783680
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 4954.00 1.09386 0.546929 0.837179i $$-0.315797\pi$$
0.546929 + 0.837179i $$0.315797\pi$$
$$30$$ 0 0
$$31$$ 7128.00 1.33218 0.666091 0.745871i $$-0.267966\pi$$
0.666091 + 0.745871i $$0.267966\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −1274.00 −0.175792
$$36$$ 0 0
$$37$$ 4358.00 0.523339 0.261669 0.965158i $$-0.415727\pi$$
0.261669 + 0.965158i $$0.415727\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −10542.0 −0.979407 −0.489704 0.871889i $$-0.662895\pi$$
−0.489704 + 0.871889i $$0.662895\pi$$
$$42$$ 0 0
$$43$$ 8452.00 0.697089 0.348545 0.937292i $$-0.386676\pi$$
0.348545 + 0.937292i $$0.386676\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 5352.00 0.353404 0.176702 0.984264i $$-0.443457\pi$$
0.176702 + 0.984264i $$0.443457\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 33354.0 1.63102 0.815508 0.578746i $$-0.196458\pi$$
0.815508 + 0.578746i $$0.196458\pi$$
$$54$$ 0 0
$$55$$ −17264.0 −0.769546
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −15436.0 −0.577304 −0.288652 0.957434i $$-0.593207\pi$$
−0.288652 + 0.957434i $$0.593207\pi$$
$$60$$ 0 0
$$61$$ −36762.0 −1.26495 −0.632477 0.774579i $$-0.717962\pi$$
−0.632477 + 0.774579i $$0.717962\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −8268.00 −0.242726
$$66$$ 0 0
$$67$$ −40972.0 −1.11506 −0.557532 0.830155i $$-0.688252\pi$$
−0.557532 + 0.830155i $$0.688252\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −9092.00 −0.214049 −0.107025 0.994256i $$-0.534132\pi$$
−0.107025 + 0.994256i $$0.534132\pi$$
$$72$$ 0 0
$$73$$ −73454.0 −1.61327 −0.806637 0.591047i $$-0.798715\pi$$
−0.806637 + 0.591047i $$0.798715\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 32536.0 0.625370
$$78$$ 0 0
$$79$$ −89400.0 −1.61165 −0.805823 0.592156i $$-0.798277\pi$$
−0.805823 + 0.592156i $$0.798277\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −6428.00 −0.102419 −0.0512095 0.998688i $$-0.516308\pi$$
−0.0512095 + 0.998688i $$0.516308\pi$$
$$84$$ 0 0
$$85$$ 41132.0 0.617494
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 122658. 1.64142 0.820712 0.571342i $$-0.193577\pi$$
0.820712 + 0.571342i $$0.193577\pi$$
$$90$$ 0 0
$$91$$ 15582.0 0.197251
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 6136.00 0.0697552
$$96$$ 0 0
$$97$$ 21370.0 0.230608 0.115304 0.993330i $$-0.463216\pi$$
0.115304 + 0.993330i $$0.463216\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 36814.0 0.359095 0.179548 0.983749i $$-0.442537\pi$$
0.179548 + 0.983749i $$0.442537\pi$$
$$102$$ 0 0
$$103$$ −104528. −0.970822 −0.485411 0.874286i $$-0.661330\pi$$
−0.485411 + 0.874286i $$0.661330\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 214440. 1.81070 0.905350 0.424667i $$-0.139609\pi$$
0.905350 + 0.424667i $$0.139609\pi$$
$$108$$ 0 0
$$109$$ 28798.0 0.232165 0.116082 0.993240i $$-0.462966\pi$$
0.116082 + 0.993240i $$0.462966\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 56014.0 0.412668 0.206334 0.978482i $$-0.433847\pi$$
0.206334 + 0.978482i $$0.433847\pi$$
$$114$$ 0 0
$$115$$ −57512.0 −0.405521
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −77518.0 −0.501805
$$120$$ 0 0
$$121$$ 279845. 1.73762
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 144924. 0.829593
$$126$$ 0 0
$$127$$ −185400. −1.02000 −0.510000 0.860174i $$-0.670355\pi$$
−0.510000 + 0.860174i $$0.670355\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 64532.0 0.328547 0.164273 0.986415i $$-0.447472\pi$$
0.164273 + 0.986415i $$0.447472\pi$$
$$132$$ 0 0
$$133$$ −11564.0 −0.0566864
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −152930. −0.696131 −0.348066 0.937470i $$-0.613161\pi$$
−0.348066 + 0.937470i $$0.613161\pi$$
$$138$$ 0 0
$$139$$ 343460. 1.50778 0.753892 0.656998i $$-0.228174\pi$$
0.753892 + 0.656998i $$0.228174\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 211152. 0.863486
$$144$$ 0 0
$$145$$ −128804. −0.508756
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 174858. 0.645238 0.322619 0.946529i $$-0.395437\pi$$
0.322619 + 0.946529i $$0.395437\pi$$
$$150$$ 0 0
$$151$$ 452552. 1.61520 0.807600 0.589731i $$-0.200766\pi$$
0.807600 + 0.589731i $$0.200766\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −185328. −0.619601
$$156$$ 0 0
$$157$$ −499066. −1.61588 −0.807940 0.589265i $$-0.799417\pi$$
−0.807940 + 0.589265i $$0.799417\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 108388. 0.329546
$$162$$ 0 0
$$163$$ 475588. 1.40204 0.701022 0.713139i $$-0.252727\pi$$
0.701022 + 0.713139i $$0.252727\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 120224. 0.333580 0.166790 0.985992i $$-0.446660\pi$$
0.166790 + 0.985992i $$0.446660\pi$$
$$168$$ 0 0
$$169$$ −270169. −0.727644
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −508874. −1.29269 −0.646346 0.763045i $$-0.723704\pi$$
−0.646346 + 0.763045i $$0.723704\pi$$
$$174$$ 0 0
$$175$$ −120001. −0.296203
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 487560. 1.13735 0.568677 0.822561i $$-0.307456\pi$$
0.568677 + 0.822561i $$0.307456\pi$$
$$180$$ 0 0
$$181$$ −544410. −1.23518 −0.617589 0.786501i $$-0.711891\pi$$
−0.617589 + 0.786501i $$0.711891\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −113308. −0.243406
$$186$$ 0 0
$$187$$ −1.05045e6 −2.19670
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 376404. 0.746570 0.373285 0.927717i $$-0.378231\pi$$
0.373285 + 0.927717i $$0.378231\pi$$
$$192$$ 0 0
$$193$$ 844946. 1.63281 0.816405 0.577480i $$-0.195964\pi$$
0.816405 + 0.577480i $$0.195964\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 492794. 0.904690 0.452345 0.891843i $$-0.350588\pi$$
0.452345 + 0.891843i $$0.350588\pi$$
$$198$$ 0 0
$$199$$ 914776. 1.63750 0.818751 0.574148i $$-0.194667\pi$$
0.818751 + 0.574148i $$0.194667\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 242746. 0.413440
$$204$$ 0 0
$$205$$ 274092. 0.455524
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −156704. −0.248150
$$210$$ 0 0
$$211$$ −311780. −0.482106 −0.241053 0.970512i $$-0.577493\pi$$
−0.241053 + 0.970512i $$0.577493\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −219752. −0.324218
$$216$$ 0 0
$$217$$ 349272. 0.503517
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −503076. −0.692872
$$222$$ 0 0
$$223$$ 1.28776e6 1.73409 0.867047 0.498226i $$-0.166015\pi$$
0.867047 + 0.498226i $$0.166015\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1.28905e6 1.66037 0.830187 0.557485i $$-0.188234\pi$$
0.830187 + 0.557485i $$0.188234\pi$$
$$228$$ 0 0
$$229$$ 678214. 0.854630 0.427315 0.904103i $$-0.359460\pi$$
0.427315 + 0.904103i $$0.359460\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.11731e6 1.34829 0.674146 0.738598i $$-0.264512\pi$$
0.674146 + 0.738598i $$0.264512\pi$$
$$234$$ 0 0
$$235$$ −139152. −0.164369
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −1.26196e6 −1.42906 −0.714528 0.699606i $$-0.753359\pi$$
−0.714528 + 0.699606i $$0.753359\pi$$
$$240$$ 0 0
$$241$$ 948218. 1.05164 0.525818 0.850597i $$-0.323759\pi$$
0.525818 + 0.850597i $$0.323759\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −62426.0 −0.0664432
$$246$$ 0 0
$$247$$ −75048.0 −0.0782703
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −486396. −0.487310 −0.243655 0.969862i $$-0.578347\pi$$
−0.243655 + 0.969862i $$0.578347\pi$$
$$252$$ 0 0
$$253$$ 1.46877e6 1.44262
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1.03910e6 0.981349 0.490675 0.871343i $$-0.336750\pi$$
0.490675 + 0.871343i $$0.336750\pi$$
$$258$$ 0 0
$$259$$ 213542. 0.197803
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.35104e6 1.20443 0.602213 0.798335i $$-0.294286\pi$$
0.602213 + 0.798335i $$0.294286\pi$$
$$264$$ 0 0
$$265$$ −867204. −0.758589
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.11811e6 0.942115 0.471057 0.882103i $$-0.343872\pi$$
0.471057 + 0.882103i $$0.343872\pi$$
$$270$$ 0 0
$$271$$ 190104. 0.157242 0.0786209 0.996905i $$-0.474948\pi$$
0.0786209 + 0.996905i $$0.474948\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.62614e6 −1.29666
$$276$$ 0 0
$$277$$ −200506. −0.157010 −0.0785051 0.996914i $$-0.525015\pi$$
−0.0785051 + 0.996914i $$0.525015\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1.09237e6 −0.825285 −0.412643 0.910893i $$-0.635394\pi$$
−0.412643 + 0.910893i $$0.635394\pi$$
$$282$$ 0 0
$$283$$ −1.81258e6 −1.34534 −0.672669 0.739944i $$-0.734852\pi$$
−0.672669 + 0.739944i $$0.734852\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −516558. −0.370181
$$288$$ 0 0
$$289$$ 1.08287e6 0.762659
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −2.10031e6 −1.42927 −0.714634 0.699499i $$-0.753407\pi$$
−0.714634 + 0.699499i $$0.753407\pi$$
$$294$$ 0 0
$$295$$ 401336. 0.268505
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 703416. 0.455024
$$300$$ 0 0
$$301$$ 414148. 0.263475
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 955812. 0.588333
$$306$$ 0 0
$$307$$ 1.64104e6 0.993743 0.496872 0.867824i $$-0.334482\pi$$
0.496872 + 0.867824i $$0.334482\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −945232. −0.554163 −0.277081 0.960846i $$-0.589367\pi$$
−0.277081 + 0.960846i $$0.589367\pi$$
$$312$$ 0 0
$$313$$ 415354. 0.239639 0.119820 0.992796i $$-0.461768\pi$$
0.119820 + 0.992796i $$0.461768\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −1.18481e6 −0.662220 −0.331110 0.943592i $$-0.607423\pi$$
−0.331110 + 0.943592i $$0.607423\pi$$
$$318$$ 0 0
$$319$$ 3.28946e6 1.80987
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 373352. 0.199119
$$324$$ 0 0
$$325$$ −778782. −0.408985
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 262248. 0.133574
$$330$$ 0 0
$$331$$ −1.37155e6 −0.688083 −0.344042 0.938954i $$-0.611796\pi$$
−0.344042 + 0.938954i $$0.611796\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 1.06527e6 0.518619
$$336$$ 0 0
$$337$$ 963522. 0.462154 0.231077 0.972935i $$-0.425775\pi$$
0.231077 + 0.972935i $$0.425775\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 4.73299e6 2.20419
$$342$$ 0 0
$$343$$ 117649. 0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 2.57731e6 1.14906 0.574531 0.818483i $$-0.305185\pi$$
0.574531 + 0.818483i $$0.305185\pi$$
$$348$$ 0 0
$$349$$ −3.06751e6 −1.34810 −0.674051 0.738684i $$-0.735447\pi$$
−0.674051 + 0.738684i $$0.735447\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 3.10144e6 1.32473 0.662364 0.749182i $$-0.269553\pi$$
0.662364 + 0.749182i $$0.269553\pi$$
$$354$$ 0 0
$$355$$ 236392. 0.0995547
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −327508. −0.134118 −0.0670588 0.997749i $$-0.521362\pi$$
−0.0670588 + 0.997749i $$0.521362\pi$$
$$360$$ 0 0
$$361$$ −2.42040e6 −0.977507
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 1.90980e6 0.750337
$$366$$ 0 0
$$367$$ 2.86739e6 1.11128 0.555638 0.831424i $$-0.312474\pi$$
0.555638 + 0.831424i $$0.312474\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 1.63435e6 0.616466
$$372$$ 0 0
$$373$$ 3.58029e6 1.33244 0.666218 0.745757i $$-0.267912\pi$$
0.666218 + 0.745757i $$0.267912\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 1.57537e6 0.570860
$$378$$ 0 0
$$379$$ −1.64235e6 −0.587310 −0.293655 0.955912i $$-0.594872\pi$$
−0.293655 + 0.955912i $$0.594872\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −2.05698e6 −0.716527 −0.358263 0.933621i $$-0.616631\pi$$
−0.358263 + 0.933621i $$0.616631\pi$$
$$384$$ 0 0
$$385$$ −845936. −0.290861
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −616142. −0.206446 −0.103223 0.994658i $$-0.532916\pi$$
−0.103223 + 0.994658i $$0.532916\pi$$
$$390$$ 0 0
$$391$$ −3.49938e6 −1.15758
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 2.32440e6 0.749580
$$396$$ 0 0
$$397$$ 2.19212e6 0.698052 0.349026 0.937113i $$-0.386513\pi$$
0.349026 + 0.937113i $$0.386513\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −3.28454e6 −1.02003 −0.510015 0.860165i $$-0.670360\pi$$
−0.510015 + 0.860165i $$0.670360\pi$$
$$402$$ 0 0
$$403$$ 2.26670e6 0.695236
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 2.89371e6 0.865903
$$408$$ 0 0
$$409$$ −3.61219e6 −1.06773 −0.533866 0.845569i $$-0.679261\pi$$
−0.533866 + 0.845569i $$0.679261\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −756364. −0.218200
$$414$$ 0 0
$$415$$ 167128. 0.0476353
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 5.41489e6 1.50680 0.753398 0.657564i $$-0.228413\pi$$
0.753398 + 0.657564i $$0.228413\pi$$
$$420$$ 0 0
$$421$$ 3.60629e6 0.991644 0.495822 0.868424i $$-0.334867\pi$$
0.495822 + 0.868424i $$0.334867\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 3.87432e6 1.04045
$$426$$ 0 0
$$427$$ −1.80134e6 −0.478107
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −2.78214e6 −0.721416 −0.360708 0.932679i $$-0.617465\pi$$
−0.360708 + 0.932679i $$0.617465\pi$$
$$432$$ 0 0
$$433$$ 6.27619e6 1.60871 0.804353 0.594152i $$-0.202512\pi$$
0.804353 + 0.594152i $$0.202512\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −522032. −0.130766
$$438$$ 0 0
$$439$$ −641592. −0.158890 −0.0794452 0.996839i $$-0.525315\pi$$
−0.0794452 + 0.996839i $$0.525315\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 6.05546e6 1.46601 0.733006 0.680222i $$-0.238117\pi$$
0.733006 + 0.680222i $$0.238117\pi$$
$$444$$ 0 0
$$445$$ −3.18911e6 −0.763430
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 5.16681e6 1.20950 0.604752 0.796414i $$-0.293272\pi$$
0.604752 + 0.796414i $$0.293272\pi$$
$$450$$ 0 0
$$451$$ −6.99989e6 −1.62050
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −405132. −0.0917420
$$456$$ 0 0
$$457$$ −227798. −0.0510222 −0.0255111 0.999675i $$-0.508121\pi$$
−0.0255111 + 0.999675i $$0.508121\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −585146. −0.128237 −0.0641183 0.997942i $$-0.520423\pi$$
−0.0641183 + 0.997942i $$0.520423\pi$$
$$462$$ 0 0
$$463$$ 3.41454e6 0.740251 0.370126 0.928982i $$-0.379315\pi$$
0.370126 + 0.928982i $$0.379315\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 716300. 0.151986 0.0759929 0.997108i $$-0.475787\pi$$
0.0759929 + 0.997108i $$0.475787\pi$$
$$468$$ 0 0
$$469$$ −2.00763e6 −0.421455
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 5.61213e6 1.15339
$$474$$ 0 0
$$475$$ 577964. 0.117535
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 5.24092e6 1.04368 0.521842 0.853042i $$-0.325245\pi$$
0.521842 + 0.853042i $$0.325245\pi$$
$$480$$ 0 0
$$481$$ 1.38584e6 0.273119
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −555620. −0.107256
$$486$$ 0 0
$$487$$ −1.11702e6 −0.213421 −0.106710 0.994290i $$-0.534032\pi$$
−0.106710 + 0.994290i $$0.534032\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 1.34458e6 0.251699 0.125850 0.992049i $$-0.459834\pi$$
0.125850 + 0.992049i $$0.459834\pi$$
$$492$$ 0 0
$$493$$ −7.83723e6 −1.45226
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −445508. −0.0809030
$$498$$ 0 0
$$499$$ 6.54648e6 1.17695 0.588473 0.808517i $$-0.299729\pi$$
0.588473 + 0.808517i $$0.299729\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −8.22050e6 −1.44870 −0.724350 0.689432i $$-0.757860\pi$$
−0.724350 + 0.689432i $$0.757860\pi$$
$$504$$ 0 0
$$505$$ −957164. −0.167016
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 5.11045e6 0.874308 0.437154 0.899387i $$-0.355987\pi$$
0.437154 + 0.899387i $$0.355987\pi$$
$$510$$ 0 0
$$511$$ −3.59925e6 −0.609760
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 2.71773e6 0.451531
$$516$$ 0 0
$$517$$ 3.55373e6 0.584733
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −9.69999e6 −1.56559 −0.782793 0.622282i $$-0.786206\pi$$
−0.782793 + 0.622282i $$0.786206\pi$$
$$522$$ 0 0
$$523$$ 3.17295e6 0.507234 0.253617 0.967305i $$-0.418380\pi$$
0.253617 + 0.967305i $$0.418380\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −1.12765e7 −1.76867
$$528$$ 0 0
$$529$$ −1.54340e6 −0.239794
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −3.35236e6 −0.511131
$$534$$ 0 0
$$535$$ −5.57544e6 −0.842160
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 1.59426e6 0.236368
$$540$$ 0 0
$$541$$ −6.62575e6 −0.973289 −0.486644 0.873600i $$-0.661779\pi$$
−0.486644 + 0.873600i $$0.661779\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −748748. −0.107980
$$546$$ 0 0
$$547$$ −3.84707e6 −0.549745 −0.274873 0.961481i $$-0.588636\pi$$
−0.274873 + 0.961481i $$0.588636\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −1.16914e6 −0.164055
$$552$$ 0 0
$$553$$ −4.38060e6 −0.609145
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −5.00176e6 −0.683101 −0.341550 0.939863i $$-0.610952\pi$$
−0.341550 + 0.939863i $$0.610952\pi$$
$$558$$ 0 0
$$559$$ 2.68774e6 0.363795
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 2.27772e6 0.302852 0.151426 0.988469i $$-0.451614\pi$$
0.151426 + 0.988469i $$0.451614\pi$$
$$564$$ 0 0
$$565$$ −1.45636e6 −0.191933
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −8.86979e6 −1.14850 −0.574252 0.818678i $$-0.694707\pi$$
−0.574252 + 0.818678i $$0.694707\pi$$
$$570$$ 0 0
$$571$$ −1.40102e7 −1.79826 −0.899132 0.437678i $$-0.855801\pi$$
−0.899132 + 0.437678i $$0.855801\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −5.41719e6 −0.683289
$$576$$ 0 0
$$577$$ 8.75327e6 1.09454 0.547269 0.836957i $$-0.315668\pi$$
0.547269 + 0.836957i $$0.315668\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −314972. −0.0387108
$$582$$ 0 0
$$583$$ 2.21471e7 2.69864
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −1.06117e7 −1.27113 −0.635564 0.772048i $$-0.719232\pi$$
−0.635564 + 0.772048i $$0.719232\pi$$
$$588$$ 0 0
$$589$$ −1.68221e6 −0.199798
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.88552e6 −0.220188 −0.110094 0.993921i $$-0.535115\pi$$
−0.110094 + 0.993921i $$0.535115\pi$$
$$594$$ 0 0
$$595$$ 2.01547e6 0.233391
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 1.27256e7 1.44915 0.724573 0.689198i $$-0.242037\pi$$
0.724573 + 0.689198i $$0.242037\pi$$
$$600$$ 0 0
$$601$$ 7.18846e6 0.811801 0.405900 0.913917i $$-0.366958\pi$$
0.405900 + 0.913917i $$0.366958\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −7.27597e6 −0.808170
$$606$$ 0 0
$$607$$ −1.08494e7 −1.19519 −0.597593 0.801800i $$-0.703876\pi$$
−0.597593 + 0.801800i $$0.703876\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 1.70194e6 0.184434
$$612$$ 0 0
$$613$$ −4.90511e6 −0.527227 −0.263614 0.964628i $$-0.584914\pi$$
−0.263614 + 0.964628i $$0.584914\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −2.58445e6 −0.273310 −0.136655 0.990619i $$-0.543635\pi$$
−0.136655 + 0.990619i $$0.543635\pi$$
$$618$$ 0 0
$$619$$ 4.99336e6 0.523801 0.261901 0.965095i $$-0.415651\pi$$
0.261901 + 0.965095i $$0.415651\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 6.01024e6 0.620400
$$624$$ 0 0
$$625$$ 3.88510e6 0.397834
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −6.89436e6 −0.694812
$$630$$ 0 0
$$631$$ 1.18219e7 1.18199 0.590997 0.806674i $$-0.298735\pi$$
0.590997 + 0.806674i $$0.298735\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 4.82040e6 0.474404
$$636$$ 0 0
$$637$$ 763518. 0.0745540
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 5.47007e6 0.525833 0.262916 0.964819i $$-0.415316\pi$$
0.262916 + 0.964819i $$0.415316\pi$$
$$642$$ 0 0
$$643$$ −9.64934e6 −0.920386 −0.460193 0.887819i $$-0.652220\pi$$
−0.460193 + 0.887819i $$0.652220\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 292368. 0.0274580 0.0137290 0.999906i $$-0.495630\pi$$
0.0137290 + 0.999906i $$0.495630\pi$$
$$648$$ 0 0
$$649$$ −1.02495e7 −0.955193
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −6.94081e6 −0.636982 −0.318491 0.947926i $$-0.603176\pi$$
−0.318491 + 0.947926i $$0.603176\pi$$
$$654$$ 0 0
$$655$$ −1.67783e6 −0.152808
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −1.32912e7 −1.19221 −0.596104 0.802908i $$-0.703285\pi$$
−0.596104 + 0.802908i $$0.703285\pi$$
$$660$$ 0 0
$$661$$ 2.05219e6 0.182690 0.0913448 0.995819i $$-0.470883\pi$$
0.0913448 + 0.995819i $$0.470883\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 300664. 0.0263650
$$666$$ 0 0
$$667$$ 1.09582e7 0.953732
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −2.44100e7 −2.09296
$$672$$ 0 0
$$673$$ −1.57039e7 −1.33650 −0.668252 0.743935i $$-0.732957\pi$$
−0.668252 + 0.743935i $$0.732957\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 969534. 0.0813002 0.0406501 0.999173i $$-0.487057\pi$$
0.0406501 + 0.999173i $$0.487057\pi$$
$$678$$ 0 0
$$679$$ 1.04713e6 0.0871618
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −1.49908e7 −1.22962 −0.614812 0.788673i $$-0.710768\pi$$
−0.614812 + 0.788673i $$0.710768\pi$$
$$684$$ 0 0
$$685$$ 3.97618e6 0.323772
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 1.06066e7 0.851191
$$690$$ 0 0
$$691$$ 7.16038e6 0.570481 0.285240 0.958456i $$-0.407927\pi$$
0.285240 + 0.958456i $$0.407927\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −8.92996e6 −0.701274
$$696$$ 0 0
$$697$$ 1.66774e7 1.30031
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 91834.0 0.00705844 0.00352922 0.999994i $$-0.498877\pi$$
0.00352922 + 0.999994i $$0.498877\pi$$
$$702$$ 0 0
$$703$$ −1.02849e6 −0.0784894
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1.80389e6 0.135725
$$708$$ 0 0
$$709$$ 2.20981e7 1.65097 0.825487 0.564422i $$-0.190901\pi$$
0.825487 + 0.564422i $$0.190901\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.57671e7 1.16153
$$714$$ 0 0
$$715$$ −5.48995e6 −0.401609
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1.58388e7 1.14262 0.571308 0.820736i $$-0.306436\pi$$
0.571308 + 0.820736i $$0.306436\pi$$
$$720$$ 0 0
$$721$$ −5.12187e6 −0.366936
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1.21323e7 −0.857235
$$726$$ 0 0
$$727$$ −6.31418e6 −0.443078 −0.221539 0.975151i $$-0.571108\pi$$
−0.221539 + 0.975151i $$0.571108\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −1.33711e7 −0.925492
$$732$$ 0 0
$$733$$ 6.93003e6 0.476404 0.238202 0.971216i $$-0.423442\pi$$
0.238202 + 0.971216i $$0.423442\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −2.72054e7 −1.84496
$$738$$ 0 0
$$739$$ −1.42331e7 −0.958714 −0.479357 0.877620i $$-0.659130\pi$$
−0.479357 + 0.877620i $$0.659130\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −5.94460e6 −0.395048 −0.197524 0.980298i $$-0.563290\pi$$
−0.197524 + 0.980298i $$0.563290\pi$$
$$744$$ 0 0
$$745$$ −4.54631e6 −0.300102
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 1.05076e7 0.684380
$$750$$ 0 0
$$751$$ 682752. 0.0441736 0.0220868 0.999756i $$-0.492969\pi$$
0.0220868 + 0.999756i $$0.492969\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −1.17664e7 −0.751233
$$756$$ 0 0
$$757$$ 1.46333e7 0.928116 0.464058 0.885805i $$-0.346393\pi$$
0.464058 + 0.885805i $$0.346393\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1.16367e7 0.728399 0.364200 0.931321i $$-0.381343\pi$$
0.364200 + 0.931321i $$0.381343\pi$$
$$762$$ 0 0
$$763$$ 1.41110e6 0.0877500
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −4.90865e6 −0.301282
$$768$$ 0 0
$$769$$ 1.91472e7 1.16759 0.583793 0.811902i $$-0.301568\pi$$
0.583793 + 0.811902i $$0.301568\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 5.39261e6 0.324601 0.162301 0.986741i $$-0.448109\pi$$
0.162301 + 0.986741i $$0.448109\pi$$
$$774$$ 0 0
$$775$$ −1.74565e7 −1.04400
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 2.48791e6 0.146890
$$780$$ 0 0
$$781$$ −6.03709e6 −0.354160
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 1.29757e7 0.751549
$$786$$ 0 0
$$787$$ −3.04348e6 −0.175159 −0.0875796 0.996158i $$-0.527913\pi$$
−0.0875796 + 0.996158i $$0.527913\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 2.74469e6 0.155974
$$792$$ 0 0
$$793$$ −1.16903e7 −0.660151
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −2.29652e7 −1.28063 −0.640316 0.768111i $$-0.721197\pi$$
−0.640316 + 0.768111i $$0.721197\pi$$
$$798$$ 0 0
$$799$$ −8.46686e6 −0.469197
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −4.87735e7 −2.66928
$$804$$ 0 0
$$805$$ −2.81809e6 −0.153273
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −1.90787e7 −1.02489 −0.512445 0.858720i $$-0.671260\pi$$
−0.512445 + 0.858720i $$0.671260\pi$$
$$810$$ 0 0
$$811$$ −1.09414e7 −0.584147 −0.292074 0.956396i $$-0.594345\pi$$
−0.292074 + 0.956396i $$0.594345\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −1.23653e7 −0.652094
$$816$$ 0 0
$$817$$ −1.99467e6 −0.104548
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −2.12594e7 −1.10076 −0.550380 0.834914i $$-0.685517\pi$$
−0.550380 + 0.834914i $$0.685517\pi$$
$$822$$ 0 0
$$823$$ 1.42256e7 0.732103 0.366052 0.930595i $$-0.380709\pi$$
0.366052 + 0.930595i $$0.380709\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 2.76103e6 0.140381 0.0701904 0.997534i $$-0.477639\pi$$
0.0701904 + 0.997534i $$0.477639\pi$$
$$828$$ 0 0
$$829$$ −3.82147e7 −1.93127 −0.965637 0.259895i $$-0.916312\pi$$
−0.965637 + 0.259895i $$0.916312\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −3.79838e6 −0.189665
$$834$$ 0 0
$$835$$ −3.12582e6 −0.155149
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 1.06044e7 0.520094 0.260047 0.965596i $$-0.416262\pi$$
0.260047 + 0.965596i $$0.416262\pi$$
$$840$$ 0 0
$$841$$ 4.03097e6 0.196526
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 7.02439e6 0.338429
$$846$$ 0 0
$$847$$ 1.37124e7 0.656758
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 9.63990e6 0.456298
$$852$$ 0 0
$$853$$ −4.07009e7 −1.91527 −0.957637 0.287977i $$-0.907017\pi$$
−0.957637 + 0.287977i $$0.907017\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 3.10120e7 1.44237 0.721187 0.692741i $$-0.243597\pi$$
0.721187 + 0.692741i $$0.243597\pi$$
$$858$$ 0 0
$$859$$ −1.09104e7 −0.504495 −0.252247 0.967663i $$-0.581170\pi$$
−0.252247 + 0.967663i $$0.581170\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 1.04089e7 0.475751 0.237875 0.971296i $$-0.423549\pi$$
0.237875 + 0.971296i $$0.423549\pi$$
$$864$$ 0 0
$$865$$ 1.32307e7 0.601234
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −5.93616e7 −2.66659
$$870$$ 0 0
$$871$$ −1.30291e7 −0.581928
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 7.10128e6 0.313557
$$876$$ 0 0
$$877$$ 1.64064e7 0.720299 0.360150 0.932895i $$-0.382726\pi$$
0.360150 + 0.932895i $$0.382726\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −1.48577e7 −0.644927 −0.322464 0.946582i $$-0.604511\pi$$
−0.322464 + 0.946582i $$0.604511\pi$$
$$882$$ 0 0
$$883$$ 2.72018e7 1.17407 0.587037 0.809560i $$-0.300294\pi$$
0.587037 + 0.809560i $$0.300294\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 2.71242e7 1.15757 0.578785 0.815480i $$-0.303527\pi$$
0.578785 + 0.815480i $$0.303527\pi$$
$$888$$ 0 0
$$889$$ −9.08460e6 −0.385524
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −1.26307e6 −0.0530029
$$894$$ 0 0
$$895$$ −1.26766e7 −0.528986
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 3.53121e7 1.45722
$$900$$ 0 0
$$901$$ −5.27660e7 −2.16542
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 1.41547e7 0.574484
$$906$$ 0 0
$$907$$ 8.42269e6 0.339964 0.169982 0.985447i $$-0.445629\pi$$
0.169982 + 0.985447i $$0.445629\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 3.08637e7 1.23212 0.616060 0.787700i $$-0.288728\pi$$
0.616060 + 0.787700i $$0.288728\pi$$
$$912$$ 0 0
$$913$$ −4.26819e6 −0.169460
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 3.16207e6 0.124179
$$918$$ 0 0
$$919$$ −4.93895e6 −0.192906 −0.0964531 0.995338i $$-0.530750\pi$$
−0.0964531 + 0.995338i $$0.530750\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −2.89126e6 −0.111707
$$924$$ 0 0
$$925$$ −1.06727e7 −0.410130
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −5.62575e6 −0.213866 −0.106933 0.994266i $$-0.534103\pi$$
−0.106933 + 0.994266i $$0.534103\pi$$
$$930$$ 0 0
$$931$$ −566636. −0.0214255
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 2.73116e7 1.02169
$$936$$ 0 0
$$937$$ 2.60073e7 0.967714 0.483857 0.875147i $$-0.339236\pi$$
0.483857 + 0.875147i $$0.339236\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −3.02160e6 −0.111241 −0.0556203 0.998452i $$-0.517714\pi$$
−0.0556203 + 0.998452i $$0.517714\pi$$
$$942$$ 0 0
$$943$$ −2.33189e7 −0.853943
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −3.48282e7 −1.26199 −0.630995 0.775787i $$-0.717353\pi$$
−0.630995 + 0.775787i $$0.717353\pi$$
$$948$$ 0 0
$$949$$ −2.33584e7 −0.841932
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 9.39009e6 0.334917 0.167459 0.985879i $$-0.446444\pi$$
0.167459 + 0.985879i $$0.446444\pi$$
$$954$$ 0 0
$$955$$ −9.78650e6 −0.347232
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −7.49357e6 −0.263113
$$960$$ 0 0
$$961$$ 2.21792e7 0.774708
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −2.19686e7 −0.759423
$$966$$ 0 0
$$967$$ −1.44768e7 −0.497860 −0.248930 0.968521i $$-0.580079\pi$$
−0.248930 + 0.968521i $$0.580079\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 9.24976e6 0.314834 0.157417 0.987532i $$-0.449683\pi$$
0.157417 + 0.987532i $$0.449683\pi$$
$$972$$ 0 0
$$973$$ 1.68295e7 0.569889
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 4.97780e7 1.66840 0.834202 0.551459i $$-0.185929\pi$$
0.834202 + 0.551459i $$0.185929\pi$$
$$978$$ 0 0
$$979$$ 8.14449e7 2.71586
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −8.95601e6 −0.295618 −0.147809 0.989016i $$-0.547222\pi$$
−0.147809 + 0.989016i $$0.547222\pi$$
$$984$$ 0 0
$$985$$ −1.28126e7 −0.420773
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 1.86958e7 0.607790
$$990$$ 0 0
$$991$$ −2.62400e7 −0.848751 −0.424376 0.905486i $$-0.639506\pi$$
−0.424376 + 0.905486i $$0.639506\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −2.37842e7 −0.761606
$$996$$ 0 0
$$997$$ 2.80506e7 0.893727 0.446863 0.894602i $$-0.352541\pi$$
0.446863 + 0.894602i $$0.352541\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1008.6.a.j.1.1 1
3.2 odd 2 336.6.a.h.1.1 1
4.3 odd 2 126.6.a.i.1.1 1
12.11 even 2 42.6.a.d.1.1 1
28.27 even 2 882.6.a.s.1.1 1
60.23 odd 4 1050.6.g.i.799.2 2
60.47 odd 4 1050.6.g.i.799.1 2
60.59 even 2 1050.6.a.k.1.1 1
84.11 even 6 294.6.e.i.79.1 2
84.23 even 6 294.6.e.i.67.1 2
84.47 odd 6 294.6.e.p.67.1 2
84.59 odd 6 294.6.e.p.79.1 2
84.83 odd 2 294.6.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.a.d.1.1 1 12.11 even 2
126.6.a.i.1.1 1 4.3 odd 2
294.6.a.b.1.1 1 84.83 odd 2
294.6.e.i.67.1 2 84.23 even 6
294.6.e.i.79.1 2 84.11 even 6
294.6.e.p.67.1 2 84.47 odd 6
294.6.e.p.79.1 2 84.59 odd 6
336.6.a.h.1.1 1 3.2 odd 2
882.6.a.s.1.1 1 28.27 even 2
1008.6.a.j.1.1 1 1.1 even 1 trivial
1050.6.a.k.1.1 1 60.59 even 2
1050.6.g.i.799.1 2 60.47 odd 4
1050.6.g.i.799.2 2 60.23 odd 4