# Properties

 Label 1008.6.a.h.1.1 Level $1008$ Weight $6$ Character 1008.1 Self dual yes Analytic conductor $161.667$ Analytic rank $2$ 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: $$2$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 56) 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)

 $$f(q)$$ $$=$$ $$q-32.0000 q^{5} -49.0000 q^{7} +O(q^{10})$$ $$q-32.0000 q^{5} -49.0000 q^{7} -624.000 q^{11} -708.000 q^{13} -934.000 q^{17} -1858.00 q^{19} -1120.00 q^{23} -2101.00 q^{25} +1174.00 q^{29} -2908.00 q^{31} +1568.00 q^{35} -12462.0 q^{37} -2662.00 q^{41} +7144.00 q^{43} -7468.00 q^{47} +2401.00 q^{49} +27274.0 q^{53} +19968.0 q^{55} +2490.00 q^{59} -11096.0 q^{61} +22656.0 q^{65} -39756.0 q^{67} -69888.0 q^{71} +16450.0 q^{73} +30576.0 q^{77} -78376.0 q^{79} +109818. q^{83} +29888.0 q^{85} +56966.0 q^{89} +34692.0 q^{91} +59456.0 q^{95} -115946. q^{97} +O(q^{100})$$

## 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
$$5$$ −32.0000 −0.572433 −0.286217 0.958165i $$-0.592398\pi$$
−0.286217 + 0.958165i $$0.592398\pi$$
$$6$$ 0 0
$$7$$ −49.0000 −0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −624.000 −1.55490 −0.777451 0.628944i $$-0.783488\pi$$
−0.777451 + 0.628944i $$0.783488\pi$$
$$12$$ 0 0
$$13$$ −708.000 −1.16192 −0.580958 0.813933i $$-0.697322\pi$$
−0.580958 + 0.813933i $$0.697322\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −934.000 −0.783835 −0.391917 0.920000i $$-0.628188\pi$$
−0.391917 + 0.920000i $$0.628188\pi$$
$$18$$ 0 0
$$19$$ −1858.00 −1.18076 −0.590380 0.807125i $$-0.701022\pi$$
−0.590380 + 0.807125i $$0.701022\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −1120.00 −0.441467 −0.220734 0.975334i $$-0.570845\pi$$
−0.220734 + 0.975334i $$0.570845\pi$$
$$24$$ 0 0
$$25$$ −2101.00 −0.672320
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 1174.00 0.259223 0.129611 0.991565i $$-0.458627\pi$$
0.129611 + 0.991565i $$0.458627\pi$$
$$30$$ 0 0
$$31$$ −2908.00 −0.543488 −0.271744 0.962370i $$-0.587600\pi$$
−0.271744 + 0.962370i $$0.587600\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 1568.00 0.216359
$$36$$ 0 0
$$37$$ −12462.0 −1.49652 −0.748262 0.663404i $$-0.769111\pi$$
−0.748262 + 0.663404i $$0.769111\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −2662.00 −0.247314 −0.123657 0.992325i $$-0.539462\pi$$
−0.123657 + 0.992325i $$0.539462\pi$$
$$42$$ 0 0
$$43$$ 7144.00 0.589210 0.294605 0.955619i $$-0.404812\pi$$
0.294605 + 0.955619i $$0.404812\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −7468.00 −0.493128 −0.246564 0.969127i $$-0.579302\pi$$
−0.246564 + 0.969127i $$0.579302\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 27274.0 1.33370 0.666852 0.745191i $$-0.267642\pi$$
0.666852 + 0.745191i $$0.267642\pi$$
$$54$$ 0 0
$$55$$ 19968.0 0.890078
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 2490.00 0.0931257 0.0465628 0.998915i $$-0.485173\pi$$
0.0465628 + 0.998915i $$0.485173\pi$$
$$60$$ 0 0
$$61$$ −11096.0 −0.381805 −0.190903 0.981609i $$-0.561141\pi$$
−0.190903 + 0.981609i $$0.561141\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 22656.0 0.665120
$$66$$ 0 0
$$67$$ −39756.0 −1.08197 −0.540986 0.841032i $$-0.681949\pi$$
−0.540986 + 0.841032i $$0.681949\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −69888.0 −1.64534 −0.822672 0.568516i $$-0.807518\pi$$
−0.822672 + 0.568516i $$0.807518\pi$$
$$72$$ 0 0
$$73$$ 16450.0 0.361292 0.180646 0.983548i $$-0.442181\pi$$
0.180646 + 0.983548i $$0.442181\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 30576.0 0.587698
$$78$$ 0 0
$$79$$ −78376.0 −1.41291 −0.706456 0.707757i $$-0.749707\pi$$
−0.706456 + 0.707757i $$0.749707\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 109818. 1.74976 0.874880 0.484340i $$-0.160940\pi$$
0.874880 + 0.484340i $$0.160940\pi$$
$$84$$ 0 0
$$85$$ 29888.0 0.448693
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 56966.0 0.762326 0.381163 0.924508i $$-0.375524\pi$$
0.381163 + 0.924508i $$0.375524\pi$$
$$90$$ 0 0
$$91$$ 34692.0 0.439163
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 59456.0 0.675907
$$96$$ 0 0
$$97$$ −115946. −1.25120 −0.625600 0.780144i $$-0.715146\pi$$
−0.625600 + 0.780144i $$0.715146\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −8352.00 −0.0814680 −0.0407340 0.999170i $$-0.512970\pi$$
−0.0407340 + 0.999170i $$0.512970\pi$$
$$102$$ 0 0
$$103$$ −179484. −1.66699 −0.833494 0.552528i $$-0.813663\pi$$
−0.833494 + 0.552528i $$0.813663\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −53892.0 −0.455056 −0.227528 0.973772i $$-0.573064\pi$$
−0.227528 + 0.973772i $$0.573064\pi$$
$$108$$ 0 0
$$109$$ 105970. 0.854312 0.427156 0.904178i $$-0.359515\pi$$
0.427156 + 0.904178i $$0.359515\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −2502.00 −0.0184328 −0.00921640 0.999958i $$-0.502934\pi$$
−0.00921640 + 0.999958i $$0.502934\pi$$
$$114$$ 0 0
$$115$$ 35840.0 0.252711
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 45766.0 0.296262
$$120$$ 0 0
$$121$$ 228325. 1.41772
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 167232. 0.957292
$$126$$ 0 0
$$127$$ −287792. −1.58332 −0.791661 0.610960i $$-0.790784\pi$$
−0.791661 + 0.610960i $$0.790784\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −47662.0 −0.242658 −0.121329 0.992612i $$-0.538716\pi$$
−0.121329 + 0.992612i $$0.538716\pi$$
$$132$$ 0 0
$$133$$ 91042.0 0.446285
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −223154. −1.01579 −0.507894 0.861419i $$-0.669576\pi$$
−0.507894 + 0.861419i $$0.669576\pi$$
$$138$$ 0 0
$$139$$ −250542. −1.09988 −0.549938 0.835206i $$-0.685349\pi$$
−0.549938 + 0.835206i $$0.685349\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 441792. 1.80667
$$144$$ 0 0
$$145$$ −37568.0 −0.148388
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 487394. 1.79852 0.899258 0.437418i $$-0.144107\pi$$
0.899258 + 0.437418i $$0.144107\pi$$
$$150$$ 0 0
$$151$$ 54680.0 0.195158 0.0975790 0.995228i $$-0.468890\pi$$
0.0975790 + 0.995228i $$0.468890\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 93056.0 0.311111
$$156$$ 0 0
$$157$$ 211068. 0.683397 0.341699 0.939810i $$-0.388998\pi$$
0.341699 + 0.939810i $$0.388998\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 54880.0 0.166859
$$162$$ 0 0
$$163$$ 20192.0 0.0595265 0.0297632 0.999557i $$-0.490525\pi$$
0.0297632 + 0.999557i $$0.490525\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −4524.00 −0.0125525 −0.00627627 0.999980i $$-0.501998\pi$$
−0.00627627 + 0.999980i $$0.501998\pi$$
$$168$$ 0 0
$$169$$ 129971. 0.350050
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 104332. 0.265034 0.132517 0.991181i $$-0.457694\pi$$
0.132517 + 0.991181i $$0.457694\pi$$
$$174$$ 0 0
$$175$$ 102949. 0.254113
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −201724. −0.470571 −0.235285 0.971926i $$-0.575602\pi$$
−0.235285 + 0.971926i $$0.575602\pi$$
$$180$$ 0 0
$$181$$ 655700. 1.48768 0.743839 0.668359i $$-0.233003\pi$$
0.743839 + 0.668359i $$0.233003\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 398784. 0.856660
$$186$$ 0 0
$$187$$ 582816. 1.21879
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −151496. −0.300482 −0.150241 0.988649i $$-0.548005\pi$$
−0.150241 + 0.988649i $$0.548005\pi$$
$$192$$ 0 0
$$193$$ 229326. 0.443159 0.221580 0.975142i $$-0.428879\pi$$
0.221580 + 0.975142i $$0.428879\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −421086. −0.773046 −0.386523 0.922280i $$-0.626324\pi$$
−0.386523 + 0.922280i $$0.626324\pi$$
$$198$$ 0 0
$$199$$ −197300. −0.353179 −0.176589 0.984285i $$-0.556506\pi$$
−0.176589 + 0.984285i $$0.556506\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −57526.0 −0.0979770
$$204$$ 0 0
$$205$$ 85184.0 0.141571
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 1.15939e6 1.83597
$$210$$ 0 0
$$211$$ −679052. −1.05002 −0.525009 0.851097i $$-0.675938\pi$$
−0.525009 + 0.851097i $$0.675938\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −228608. −0.337284
$$216$$ 0 0
$$217$$ 142492. 0.205419
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 661272. 0.910751
$$222$$ 0 0
$$223$$ 184440. 0.248366 0.124183 0.992259i $$-0.460369\pi$$
0.124183 + 0.992259i $$0.460369\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −868078. −1.11813 −0.559067 0.829122i $$-0.688841\pi$$
−0.559067 + 0.829122i $$0.688841\pi$$
$$228$$ 0 0
$$229$$ −593860. −0.748334 −0.374167 0.927361i $$-0.622071\pi$$
−0.374167 + 0.927361i $$0.622071\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −48218.0 −0.0581861 −0.0290931 0.999577i $$-0.509262\pi$$
−0.0290931 + 0.999577i $$0.509262\pi$$
$$234$$ 0 0
$$235$$ 238976. 0.282283
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 241688. 0.273691 0.136845 0.990592i $$-0.456304\pi$$
0.136845 + 0.990592i $$0.456304\pi$$
$$240$$ 0 0
$$241$$ 565270. 0.626922 0.313461 0.949601i $$-0.398512\pi$$
0.313461 + 0.949601i $$0.398512\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −76832.0 −0.0817762
$$246$$ 0 0
$$247$$ 1.31546e6 1.37194
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1.43775e6 −1.44045 −0.720224 0.693741i $$-0.755961\pi$$
−0.720224 + 0.693741i $$0.755961\pi$$
$$252$$ 0 0
$$253$$ 698880. 0.686438
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −494802. −0.467303 −0.233652 0.972320i $$-0.575067\pi$$
−0.233652 + 0.972320i $$0.575067\pi$$
$$258$$ 0 0
$$259$$ 610638. 0.565633
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.55654e6 1.38762 0.693812 0.720156i $$-0.255930\pi$$
0.693812 + 0.720156i $$0.255930\pi$$
$$264$$ 0 0
$$265$$ −872768. −0.763456
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1.36204e6 −1.14765 −0.573823 0.818979i $$-0.694540\pi$$
−0.573823 + 0.818979i $$0.694540\pi$$
$$270$$ 0 0
$$271$$ −558320. −0.461806 −0.230903 0.972977i $$-0.574168\pi$$
−0.230903 + 0.972977i $$0.574168\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.31102e6 1.04539
$$276$$ 0 0
$$277$$ 586342. 0.459147 0.229573 0.973291i $$-0.426267\pi$$
0.229573 + 0.973291i $$0.426267\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −606234. −0.458010 −0.229005 0.973425i $$-0.573547\pi$$
−0.229005 + 0.973425i $$0.573547\pi$$
$$282$$ 0 0
$$283$$ 865174. 0.642151 0.321076 0.947054i $$-0.395956\pi$$
0.321076 + 0.947054i $$0.395956\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 130438. 0.0934758
$$288$$ 0 0
$$289$$ −547501. −0.385603
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 353352. 0.240458 0.120229 0.992746i $$-0.461637\pi$$
0.120229 + 0.992746i $$0.461637\pi$$
$$294$$ 0 0
$$295$$ −79680.0 −0.0533082
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 792960. 0.512948
$$300$$ 0 0
$$301$$ −350056. −0.222701
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 355072. 0.218558
$$306$$ 0 0
$$307$$ 1.95904e6 1.18631 0.593153 0.805090i $$-0.297883\pi$$
0.593153 + 0.805090i $$0.297883\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 3.06257e6 1.79550 0.897749 0.440508i $$-0.145202\pi$$
0.897749 + 0.440508i $$0.145202\pi$$
$$312$$ 0 0
$$313$$ −582634. −0.336151 −0.168076 0.985774i $$-0.553755\pi$$
−0.168076 + 0.985774i $$0.553755\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 3.09585e6 1.73034 0.865171 0.501478i $$-0.167210\pi$$
0.865171 + 0.501478i $$0.167210\pi$$
$$318$$ 0 0
$$319$$ −732576. −0.403066
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 1.73537e6 0.925521
$$324$$ 0 0
$$325$$ 1.48751e6 0.781180
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 365932. 0.186385
$$330$$ 0 0
$$331$$ −625496. −0.313801 −0.156901 0.987614i $$-0.550150\pi$$
−0.156901 + 0.987614i $$0.550150\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 1.27219e6 0.619356
$$336$$ 0 0
$$337$$ 2.32494e6 1.11516 0.557580 0.830123i $$-0.311730\pi$$
0.557580 + 0.830123i $$0.311730\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.81459e6 0.845071
$$342$$ 0 0
$$343$$ −117649. −0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −781128. −0.348256 −0.174128 0.984723i $$-0.555711\pi$$
−0.174128 + 0.984723i $$0.555711\pi$$
$$348$$ 0 0
$$349$$ 1.48586e6 0.653002 0.326501 0.945197i $$-0.394130\pi$$
0.326501 + 0.945197i $$0.394130\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −1.44463e6 −0.617048 −0.308524 0.951217i $$-0.599835\pi$$
−0.308524 + 0.951217i $$0.599835\pi$$
$$354$$ 0 0
$$355$$ 2.23642e6 0.941850
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 404040. 0.165458 0.0827291 0.996572i $$-0.473636\pi$$
0.0827291 + 0.996572i $$0.473636\pi$$
$$360$$ 0 0
$$361$$ 976065. 0.394195
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −526400. −0.206816
$$366$$ 0 0
$$367$$ 2.71698e6 1.05298 0.526492 0.850180i $$-0.323507\pi$$
0.526492 + 0.850180i $$0.323507\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −1.33643e6 −0.504092
$$372$$ 0 0
$$373$$ −1.79399e6 −0.667647 −0.333824 0.942636i $$-0.608339\pi$$
−0.333824 + 0.942636i $$0.608339\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −831192. −0.301195
$$378$$ 0 0
$$379$$ 18624.0 0.00666001 0.00333001 0.999994i $$-0.498940\pi$$
0.00333001 + 0.999994i $$0.498940\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −1.33004e6 −0.463307 −0.231654 0.972798i $$-0.574414\pi$$
−0.231654 + 0.972798i $$0.574414\pi$$
$$384$$ 0 0
$$385$$ −978432. −0.336418
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −2.26506e6 −0.758936 −0.379468 0.925205i $$-0.623893\pi$$
−0.379468 + 0.925205i $$0.623893\pi$$
$$390$$ 0 0
$$391$$ 1.04608e6 0.346037
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 2.50803e6 0.808798
$$396$$ 0 0
$$397$$ −4.48900e6 −1.42947 −0.714733 0.699398i $$-0.753452\pi$$
−0.714733 + 0.699398i $$0.753452\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 95442.0 0.0296400 0.0148200 0.999890i $$-0.495282\pi$$
0.0148200 + 0.999890i $$0.495282\pi$$
$$402$$ 0 0
$$403$$ 2.05886e6 0.631488
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 7.77629e6 2.32695
$$408$$ 0 0
$$409$$ −2.99003e6 −0.883828 −0.441914 0.897057i $$-0.645700\pi$$
−0.441914 + 0.897057i $$0.645700\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −122010. −0.0351982
$$414$$ 0 0
$$415$$ −3.51418e6 −1.00162
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 3.39037e6 0.943436 0.471718 0.881749i $$-0.343634\pi$$
0.471718 + 0.881749i $$0.343634\pi$$
$$420$$ 0 0
$$421$$ 3.38397e6 0.930512 0.465256 0.885176i $$-0.345962\pi$$
0.465256 + 0.885176i $$0.345962\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.96233e6 0.526988
$$426$$ 0 0
$$427$$ 543704. 0.144309
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1.98353e6 −0.514334 −0.257167 0.966367i $$-0.582789\pi$$
−0.257167 + 0.966367i $$0.582789\pi$$
$$432$$ 0 0
$$433$$ −7.17581e6 −1.83929 −0.919647 0.392746i $$-0.871525\pi$$
−0.919647 + 0.392746i $$0.871525\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 2.08096e6 0.521267
$$438$$ 0 0
$$439$$ 2.44390e6 0.605231 0.302616 0.953113i $$-0.402140\pi$$
0.302616 + 0.953113i $$0.402140\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 231716. 0.0560979 0.0280490 0.999607i $$-0.491071\pi$$
0.0280490 + 0.999607i $$0.491071\pi$$
$$444$$ 0 0
$$445$$ −1.82291e6 −0.436381
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 4.73637e6 1.10874 0.554370 0.832271i $$-0.312959\pi$$
0.554370 + 0.832271i $$0.312959\pi$$
$$450$$ 0 0
$$451$$ 1.66109e6 0.384549
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −1.11014e6 −0.251392
$$456$$ 0 0
$$457$$ −7.87486e6 −1.76381 −0.881906 0.471426i $$-0.843740\pi$$
−0.881906 + 0.471426i $$0.843740\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 8.23218e6 1.80411 0.902054 0.431623i $$-0.142059\pi$$
0.902054 + 0.431623i $$0.142059\pi$$
$$462$$ 0 0
$$463$$ −2.36038e6 −0.511717 −0.255859 0.966714i $$-0.582358\pi$$
−0.255859 + 0.966714i $$0.582358\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −6.31700e6 −1.34035 −0.670175 0.742203i $$-0.733781\pi$$
−0.670175 + 0.742203i $$0.733781\pi$$
$$468$$ 0 0
$$469$$ 1.94804e6 0.408947
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −4.45786e6 −0.916164
$$474$$ 0 0
$$475$$ 3.90366e6 0.793849
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 1.45856e6 0.290459 0.145229 0.989398i $$-0.453608\pi$$
0.145229 + 0.989398i $$0.453608\pi$$
$$480$$ 0 0
$$481$$ 8.82310e6 1.73883
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 3.71027e6 0.716228
$$486$$ 0 0
$$487$$ −9.28782e6 −1.77456 −0.887282 0.461228i $$-0.847409\pi$$
−0.887282 + 0.461228i $$0.847409\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −234972. −0.0439858 −0.0219929 0.999758i $$-0.507001\pi$$
−0.0219929 + 0.999758i $$0.507001\pi$$
$$492$$ 0 0
$$493$$ −1.09652e6 −0.203188
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 3.42451e6 0.621882
$$498$$ 0 0
$$499$$ 7.00792e6 1.25991 0.629953 0.776633i $$-0.283074\pi$$
0.629953 + 0.776633i $$0.283074\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 4.94752e6 0.871902 0.435951 0.899970i $$-0.356412\pi$$
0.435951 + 0.899970i $$0.356412\pi$$
$$504$$ 0 0
$$505$$ 267264. 0.0466350
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −5.50640e6 −0.942049 −0.471025 0.882120i $$-0.656116\pi$$
−0.471025 + 0.882120i $$0.656116\pi$$
$$510$$ 0 0
$$511$$ −806050. −0.136556
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 5.74349e6 0.954240
$$516$$ 0 0
$$517$$ 4.66003e6 0.766765
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.63076e6 −0.263206 −0.131603 0.991303i $$-0.542012\pi$$
−0.131603 + 0.991303i $$0.542012\pi$$
$$522$$ 0 0
$$523$$ 1.00765e7 1.61086 0.805429 0.592692i $$-0.201935\pi$$
0.805429 + 0.592692i $$0.201935\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 2.71607e6 0.426005
$$528$$ 0 0
$$529$$ −5.18194e6 −0.805107
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 1.88470e6 0.287358
$$534$$ 0 0
$$535$$ 1.72454e6 0.260489
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −1.49822e6 −0.222129
$$540$$ 0 0
$$541$$ −1.25225e7 −1.83949 −0.919746 0.392513i $$-0.871606\pi$$
−0.919746 + 0.392513i $$0.871606\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −3.39104e6 −0.489037
$$546$$ 0 0
$$547$$ −6.67430e6 −0.953756 −0.476878 0.878970i $$-0.658232\pi$$
−0.476878 + 0.878970i $$0.658232\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −2.18129e6 −0.306080
$$552$$ 0 0
$$553$$ 3.84042e6 0.534031
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 4.61643e6 0.630475 0.315238 0.949013i $$-0.397916\pi$$
0.315238 + 0.949013i $$0.397916\pi$$
$$558$$ 0 0
$$559$$ −5.05795e6 −0.684613
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −8.84218e6 −1.17568 −0.587839 0.808978i $$-0.700021\pi$$
−0.587839 + 0.808978i $$0.700021\pi$$
$$564$$ 0 0
$$565$$ 80064.0 0.0105515
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1.15771e7 −1.49906 −0.749532 0.661968i $$-0.769721\pi$$
−0.749532 + 0.661968i $$0.769721\pi$$
$$570$$ 0 0
$$571$$ −4.48069e6 −0.575115 −0.287557 0.957763i $$-0.592843\pi$$
−0.287557 + 0.957763i $$0.592843\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 2.35312e6 0.296807
$$576$$ 0 0
$$577$$ 1.32788e7 1.66042 0.830212 0.557448i $$-0.188220\pi$$
0.830212 + 0.557448i $$0.188220\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −5.38108e6 −0.661347
$$582$$ 0 0
$$583$$ −1.70190e7 −2.07378
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −1.11188e7 −1.33187 −0.665936 0.746009i $$-0.731968\pi$$
−0.665936 + 0.746009i $$0.731968\pi$$
$$588$$ 0 0
$$589$$ 5.40306e6 0.641729
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 3.92737e6 0.458632 0.229316 0.973352i $$-0.426351\pi$$
0.229316 + 0.973352i $$0.426351\pi$$
$$594$$ 0 0
$$595$$ −1.46451e6 −0.169590
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −1.74099e7 −1.98258 −0.991289 0.131704i $$-0.957955\pi$$
−0.991289 + 0.131704i $$0.957955\pi$$
$$600$$ 0 0
$$601$$ 7.46243e6 0.842740 0.421370 0.906889i $$-0.361549\pi$$
0.421370 + 0.906889i $$0.361549\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −7.30640e6 −0.811549
$$606$$ 0 0
$$607$$ −701152. −0.0772397 −0.0386198 0.999254i $$-0.512296\pi$$
−0.0386198 + 0.999254i $$0.512296\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 5.28734e6 0.572974
$$612$$ 0 0
$$613$$ 1.09575e7 1.17777 0.588886 0.808216i $$-0.299567\pi$$
0.588886 + 0.808216i $$0.299567\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.90666e6 −0.201633 −0.100816 0.994905i $$-0.532145\pi$$
−0.100816 + 0.994905i $$0.532145\pi$$
$$618$$ 0 0
$$619$$ 2.22346e6 0.233240 0.116620 0.993177i $$-0.462794\pi$$
0.116620 + 0.993177i $$0.462794\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −2.79133e6 −0.288132
$$624$$ 0 0
$$625$$ 1.21420e6 0.124334
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 1.16395e7 1.17303
$$630$$ 0 0
$$631$$ −752624. −0.0752497 −0.0376248 0.999292i $$-0.511979\pi$$
−0.0376248 + 0.999292i $$0.511979\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 9.20934e6 0.906347
$$636$$ 0 0
$$637$$ −1.69991e6 −0.165988
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 2.45429e6 0.235929 0.117964 0.993018i $$-0.462363\pi$$
0.117964 + 0.993018i $$0.462363\pi$$
$$642$$ 0 0
$$643$$ −1.58237e7 −1.50932 −0.754660 0.656116i $$-0.772198\pi$$
−0.754660 + 0.656116i $$0.772198\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −2.65489e6 −0.249337 −0.124668 0.992198i $$-0.539787\pi$$
−0.124668 + 0.992198i $$0.539787\pi$$
$$648$$ 0 0
$$649$$ −1.55376e6 −0.144801
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −9.26899e6 −0.850648 −0.425324 0.905041i $$-0.639840\pi$$
−0.425324 + 0.905041i $$0.639840\pi$$
$$654$$ 0 0
$$655$$ 1.52518e6 0.138905
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −1.68242e7 −1.50911 −0.754556 0.656235i $$-0.772148\pi$$
−0.754556 + 0.656235i $$0.772148\pi$$
$$660$$ 0 0
$$661$$ −6.77217e6 −0.602871 −0.301435 0.953487i $$-0.597466\pi$$
−0.301435 + 0.953487i $$0.597466\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −2.91334e6 −0.255469
$$666$$ 0 0
$$667$$ −1.31488e6 −0.114438
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 6.92390e6 0.593669
$$672$$ 0 0
$$673$$ 7.61315e6 0.647928 0.323964 0.946069i $$-0.394984\pi$$
0.323964 + 0.946069i $$0.394984\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −6.11672e6 −0.512917 −0.256459 0.966555i $$-0.582556\pi$$
−0.256459 + 0.966555i $$0.582556\pi$$
$$678$$ 0 0
$$679$$ 5.68135e6 0.472909
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −1.12588e7 −0.923511 −0.461755 0.887007i $$-0.652780\pi$$
−0.461755 + 0.887007i $$0.652780\pi$$
$$684$$ 0 0
$$685$$ 7.14093e6 0.581471
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −1.93100e7 −1.54965
$$690$$ 0 0
$$691$$ −9.50952e6 −0.757641 −0.378821 0.925470i $$-0.623670\pi$$
−0.378821 + 0.925470i $$0.623670\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 8.01734e6 0.629605
$$696$$ 0 0
$$697$$ 2.48631e6 0.193853
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −1.53868e7 −1.18264 −0.591322 0.806436i $$-0.701394\pi$$
−0.591322 + 0.806436i $$0.701394\pi$$
$$702$$ 0 0
$$703$$ 2.31544e7 1.76703
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 409248. 0.0307920
$$708$$ 0 0
$$709$$ −1.21379e6 −0.0906834 −0.0453417 0.998972i $$-0.514438\pi$$
−0.0453417 + 0.998972i $$0.514438\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 3.25696e6 0.239932
$$714$$ 0 0
$$715$$ −1.41373e7 −1.03420
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −1.00002e7 −0.721418 −0.360709 0.932678i $$-0.617465\pi$$
−0.360709 + 0.932678i $$0.617465\pi$$
$$720$$ 0 0
$$721$$ 8.79472e6 0.630063
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −2.46657e6 −0.174281
$$726$$ 0 0
$$727$$ −1.33745e7 −0.938514 −0.469257 0.883062i $$-0.655478\pi$$
−0.469257 + 0.883062i $$0.655478\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −6.67250e6 −0.461844
$$732$$ 0 0
$$733$$ 1.61380e7 1.10940 0.554701 0.832050i $$-0.312833\pi$$
0.554701 + 0.832050i $$0.312833\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 2.48077e7 1.68236
$$738$$ 0 0
$$739$$ −8.61059e6 −0.579992 −0.289996 0.957028i $$-0.593654\pi$$
−0.289996 + 0.957028i $$0.593654\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −2.85027e7 −1.89415 −0.947075 0.321012i $$-0.895977\pi$$
−0.947075 + 0.321012i $$0.895977\pi$$
$$744$$ 0 0
$$745$$ −1.55966e7 −1.02953
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 2.64071e6 0.171995
$$750$$ 0 0
$$751$$ 7.28721e6 0.471478 0.235739 0.971816i $$-0.424249\pi$$
0.235739 + 0.971816i $$0.424249\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −1.74976e6 −0.111715
$$756$$ 0 0
$$757$$ −2.77165e7 −1.75792 −0.878958 0.476899i $$-0.841761\pi$$
−0.878958 + 0.476899i $$0.841761\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −3.07625e7 −1.92557 −0.962787 0.270262i $$-0.912890\pi$$
−0.962787 + 0.270262i $$0.912890\pi$$
$$762$$ 0 0
$$763$$ −5.19253e6 −0.322900
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −1.76292e6 −0.108204
$$768$$ 0 0
$$769$$ −1.83665e7 −1.11998 −0.559990 0.828499i $$-0.689195\pi$$
−0.559990 + 0.828499i $$0.689195\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1.01397e7 0.610348 0.305174 0.952297i $$-0.401285\pi$$
0.305174 + 0.952297i $$0.401285\pi$$
$$774$$ 0 0
$$775$$ 6.10971e6 0.365398
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 4.94600e6 0.292018
$$780$$ 0 0
$$781$$ 4.36101e7 2.55835
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −6.75418e6 −0.391199
$$786$$ 0 0
$$787$$ 1.89442e7 1.09028 0.545140 0.838345i $$-0.316476\pi$$
0.545140 + 0.838345i $$0.316476\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 122598. 0.00696694
$$792$$ 0 0
$$793$$ 7.85597e6 0.443626
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1.19835e7 0.668248 0.334124 0.942529i $$-0.391560\pi$$
0.334124 + 0.942529i $$0.391560\pi$$
$$798$$ 0 0
$$799$$ 6.97511e6 0.386531
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −1.02648e7 −0.561774
$$804$$ 0 0
$$805$$ −1.75616e6 −0.0955156
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 6.31823e6 0.339410 0.169705 0.985495i $$-0.445719\pi$$
0.169705 + 0.985495i $$0.445719\pi$$
$$810$$ 0 0
$$811$$ −1.47079e6 −0.0785231 −0.0392615 0.999229i $$-0.512501\pi$$
−0.0392615 + 0.999229i $$0.512501\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −646144. −0.0340750
$$816$$ 0 0
$$817$$ −1.32736e7 −0.695716
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 2.10138e7 1.08804 0.544022 0.839071i $$-0.316901\pi$$
0.544022 + 0.839071i $$0.316901\pi$$
$$822$$ 0 0
$$823$$ 1.35856e7 0.699163 0.349582 0.936906i $$-0.386324\pi$$
0.349582 + 0.936906i $$0.386324\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −2.62070e7 −1.33246 −0.666230 0.745747i $$-0.732093\pi$$
−0.666230 + 0.745747i $$0.732093\pi$$
$$828$$ 0 0
$$829$$ −1.17710e7 −0.594876 −0.297438 0.954741i $$-0.596132\pi$$
−0.297438 + 0.954741i $$0.596132\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −2.24253e6 −0.111976
$$834$$ 0 0
$$835$$ 144768. 0.00718549
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 1.44898e7 0.710651 0.355326 0.934743i $$-0.384370\pi$$
0.355326 + 0.934743i $$0.384370\pi$$
$$840$$ 0 0
$$841$$ −1.91329e7 −0.932804
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −4.15907e6 −0.200380
$$846$$ 0 0
$$847$$ −1.11879e7 −0.535847
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 1.39574e7 0.660666
$$852$$ 0 0
$$853$$ 1.77865e7 0.836984 0.418492 0.908220i $$-0.362559\pi$$
0.418492 + 0.908220i $$0.362559\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −3.79124e7 −1.76331 −0.881656 0.471893i $$-0.843571\pi$$
−0.881656 + 0.471893i $$0.843571\pi$$
$$858$$ 0 0
$$859$$ −3.32376e7 −1.53690 −0.768451 0.639909i $$-0.778972\pi$$
−0.768451 + 0.639909i $$0.778972\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 2.33166e6 0.106571 0.0532853 0.998579i $$-0.483031\pi$$
0.0532853 + 0.998579i $$0.483031\pi$$
$$864$$ 0 0
$$865$$ −3.33862e6 −0.151715
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 4.89066e7 2.19694
$$870$$ 0 0
$$871$$ 2.81472e7 1.25716
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −8.19437e6 −0.361822
$$876$$ 0 0
$$877$$ −3.38189e7 −1.48477 −0.742386 0.669972i $$-0.766306\pi$$
−0.742386 + 0.669972i $$0.766306\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −2.65707e7 −1.15336 −0.576678 0.816972i $$-0.695651\pi$$
−0.576678 + 0.816972i $$0.695651\pi$$
$$882$$ 0 0
$$883$$ −1.74913e7 −0.754954 −0.377477 0.926019i $$-0.623208\pi$$
−0.377477 + 0.926019i $$0.623208\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −1.77452e7 −0.757305 −0.378652 0.925539i $$-0.623612\pi$$
−0.378652 + 0.925539i $$0.623612\pi$$
$$888$$ 0 0
$$889$$ 1.41018e7 0.598440
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 1.38755e7 0.582266
$$894$$ 0 0
$$895$$ 6.45517e6 0.269370
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −3.41399e6 −0.140885
$$900$$ 0 0
$$901$$ −2.54739e7 −1.04540
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −2.09824e7 −0.851596
$$906$$ 0 0
$$907$$ 2.82335e7 1.13958 0.569792 0.821789i $$-0.307024\pi$$
0.569792 + 0.821789i $$0.307024\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 1.71757e7 0.685674 0.342837 0.939395i $$-0.388612\pi$$
0.342837 + 0.939395i $$0.388612\pi$$
$$912$$ 0 0
$$913$$ −6.85264e7 −2.72070
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 2.33544e6 0.0917160
$$918$$ 0 0
$$919$$ −2.42273e7 −0.946273 −0.473137 0.880989i $$-0.656878\pi$$
−0.473137 + 0.880989i $$0.656878\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 4.94807e7 1.91175
$$924$$ 0 0
$$925$$ 2.61827e7 1.00614
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −2.45919e7 −0.934874 −0.467437 0.884026i $$-0.654822\pi$$
−0.467437 + 0.884026i $$0.654822\pi$$
$$930$$ 0 0
$$931$$ −4.46106e6 −0.168680
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −1.86501e7 −0.697674
$$936$$ 0 0
$$937$$ −1.31199e7 −0.488181 −0.244090 0.969753i $$-0.578489\pi$$
−0.244090 + 0.969753i $$0.578489\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −640776. −0.0235902 −0.0117951 0.999930i $$-0.503755\pi$$
−0.0117951 + 0.999930i $$0.503755\pi$$
$$942$$ 0 0
$$943$$ 2.98144e6 0.109181
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 2.01502e7 0.730135 0.365068 0.930981i $$-0.381046\pi$$
0.365068 + 0.930981i $$0.381046\pi$$
$$948$$ 0 0
$$949$$ −1.16466e7 −0.419791
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 3.33217e7 1.18849 0.594244 0.804285i $$-0.297451\pi$$
0.594244 + 0.804285i $$0.297451\pi$$
$$954$$ 0 0
$$955$$ 4.84787e6 0.172006
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 1.09345e7 0.383932
$$960$$ 0 0
$$961$$ −2.01727e7 −0.704621
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −7.33843e6 −0.253679
$$966$$ 0 0
$$967$$ −4.51857e7 −1.55394 −0.776970 0.629537i $$-0.783245\pi$$
−0.776970 + 0.629537i $$0.783245\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 2.62935e7 0.894953 0.447477 0.894296i $$-0.352323\pi$$
0.447477 + 0.894296i $$0.352323\pi$$
$$972$$ 0 0
$$973$$ 1.22766e7 0.415714
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −2.02548e7 −0.678879 −0.339440 0.940628i $$-0.610237\pi$$
−0.339440 + 0.940628i $$0.610237\pi$$
$$978$$ 0 0
$$979$$ −3.55468e7 −1.18534
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 9.43782e6 0.311521 0.155761 0.987795i $$-0.450217\pi$$
0.155761 + 0.987795i $$0.450217\pi$$
$$984$$ 0 0
$$985$$ 1.34748e7 0.442517
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −8.00128e6 −0.260117
$$990$$ 0 0
$$991$$ −1.53265e7 −0.495747 −0.247874 0.968792i $$-0.579732\pi$$
−0.247874 + 0.968792i $$0.579732\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 6.31360e6 0.202171
$$996$$ 0 0
$$997$$ −2.16514e6 −0.0689841 −0.0344920 0.999405i $$-0.510981\pi$$
−0.0344920 + 0.999405i $$0.510981\pi$$
$$998$$ 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.h.1.1 1
3.2 odd 2 112.6.a.a.1.1 1
4.3 odd 2 504.6.a.b.1.1 1
12.11 even 2 56.6.a.b.1.1 1
21.20 even 2 784.6.a.n.1.1 1
24.5 odd 2 448.6.a.p.1.1 1
24.11 even 2 448.6.a.a.1.1 1
84.11 even 6 392.6.i.a.177.1 2
84.23 even 6 392.6.i.a.361.1 2
84.47 odd 6 392.6.i.f.361.1 2
84.59 odd 6 392.6.i.f.177.1 2
84.83 odd 2 392.6.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
56.6.a.b.1.1 1 12.11 even 2
112.6.a.a.1.1 1 3.2 odd 2
392.6.a.a.1.1 1 84.83 odd 2
392.6.i.a.177.1 2 84.11 even 6
392.6.i.a.361.1 2 84.23 even 6
392.6.i.f.177.1 2 84.59 odd 6
392.6.i.f.361.1 2 84.47 odd 6
448.6.a.a.1.1 1 24.11 even 2
448.6.a.p.1.1 1 24.5 odd 2
504.6.a.b.1.1 1 4.3 odd 2
784.6.a.n.1.1 1 21.20 even 2
1008.6.a.h.1.1 1 1.1 even 1 trivial