# Properties

 Label 1008.6.a.g.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)

 $$f(q)$$ $$=$$ $$q-44.0000 q^{5} +49.0000 q^{7} +O(q^{10})$$ $$q-44.0000 q^{5} +49.0000 q^{7} -470.000 q^{11} -1158.00 q^{13} -1204.00 q^{17} +2644.00 q^{19} -1190.00 q^{23} -1189.00 q^{25} -3614.00 q^{29} -5616.00 q^{31} -2156.00 q^{35} -6478.00 q^{37} -2856.00 q^{41} +13492.0 q^{43} -18372.0 q^{47} +2401.00 q^{49} +4374.00 q^{53} +20680.0 q^{55} +30248.0 q^{59} +19542.0 q^{61} +50952.0 q^{65} -54328.0 q^{67} -10730.0 q^{71} +35374.0 q^{73} -23030.0 q^{77} +49956.0 q^{79} -26948.0 q^{83} +52976.0 q^{85} -100776. q^{89} -56742.0 q^{91} -116336. q^{95} +77134.0 q^{97} +O(q^{100})$$

## 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
$$5$$ −44.0000 −0.787096 −0.393548 0.919304i $$-0.628752\pi$$
−0.393548 + 0.919304i $$0.628752\pi$$
$$6$$ 0 0
$$7$$ 49.0000 0.377964
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −470.000 −1.17116 −0.585580 0.810615i $$-0.699133\pi$$
−0.585580 + 0.810615i $$0.699133\pi$$
$$12$$ 0 0
$$13$$ −1158.00 −1.90042 −0.950211 0.311606i $$-0.899133\pi$$
−0.950211 + 0.311606i $$0.899133\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1204.00 −1.01043 −0.505213 0.862995i $$-0.668586\pi$$
−0.505213 + 0.862995i $$0.668586\pi$$
$$18$$ 0 0
$$19$$ 2644.00 1.68026 0.840132 0.542382i $$-0.182478\pi$$
0.840132 + 0.542382i $$0.182478\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −1190.00 −0.469059 −0.234529 0.972109i $$-0.575355\pi$$
−0.234529 + 0.972109i $$0.575355\pi$$
$$24$$ 0 0
$$25$$ −1189.00 −0.380480
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −3614.00 −0.797982 −0.398991 0.916955i $$-0.630640\pi$$
−0.398991 + 0.916955i $$0.630640\pi$$
$$30$$ 0 0
$$31$$ −5616.00 −1.04960 −0.524799 0.851226i $$-0.675859\pi$$
−0.524799 + 0.851226i $$0.675859\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −2156.00 −0.297494
$$36$$ 0 0
$$37$$ −6478.00 −0.777923 −0.388962 0.921254i $$-0.627166\pi$$
−0.388962 + 0.921254i $$0.627166\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −2856.00 −0.265337 −0.132669 0.991160i $$-0.542355\pi$$
−0.132669 + 0.991160i $$0.542355\pi$$
$$42$$ 0 0
$$43$$ 13492.0 1.11277 0.556385 0.830925i $$-0.312188\pi$$
0.556385 + 0.830925i $$0.312188\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −18372.0 −1.21314 −0.606571 0.795029i $$-0.707456\pi$$
−0.606571 + 0.795029i $$0.707456\pi$$
$$48$$ 0 0
$$49$$ 2401.00 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 4374.00 0.213889 0.106945 0.994265i $$-0.465893\pi$$
0.106945 + 0.994265i $$0.465893\pi$$
$$54$$ 0 0
$$55$$ 20680.0 0.921815
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 30248.0 1.13127 0.565635 0.824655i $$-0.308631\pi$$
0.565635 + 0.824655i $$0.308631\pi$$
$$60$$ 0 0
$$61$$ 19542.0 0.672426 0.336213 0.941786i $$-0.390854\pi$$
0.336213 + 0.941786i $$0.390854\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 50952.0 1.49581
$$66$$ 0 0
$$67$$ −54328.0 −1.47855 −0.739276 0.673402i $$-0.764832\pi$$
−0.739276 + 0.673402i $$0.764832\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −10730.0 −0.252612 −0.126306 0.991991i $$-0.540312\pi$$
−0.126306 + 0.991991i $$0.540312\pi$$
$$72$$ 0 0
$$73$$ 35374.0 0.776921 0.388461 0.921465i $$-0.373007\pi$$
0.388461 + 0.921465i $$0.373007\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −23030.0 −0.442657
$$78$$ 0 0
$$79$$ 49956.0 0.900575 0.450288 0.892884i $$-0.351321\pi$$
0.450288 + 0.892884i $$0.351321\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −26948.0 −0.429370 −0.214685 0.976683i $$-0.568872\pi$$
−0.214685 + 0.976683i $$0.568872\pi$$
$$84$$ 0 0
$$85$$ 52976.0 0.795302
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −100776. −1.34860 −0.674298 0.738459i $$-0.735554\pi$$
−0.674298 + 0.738459i $$0.735554\pi$$
$$90$$ 0 0
$$91$$ −56742.0 −0.718292
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −116336. −1.32253
$$96$$ 0 0
$$97$$ 77134.0 0.832370 0.416185 0.909280i $$-0.363367\pi$$
0.416185 + 0.909280i $$0.363367\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −99464.0 −0.970203 −0.485101 0.874458i $$-0.661217\pi$$
−0.485101 + 0.874458i $$0.661217\pi$$
$$102$$ 0 0
$$103$$ −66944.0 −0.621754 −0.310877 0.950450i $$-0.600623\pi$$
−0.310877 + 0.950450i $$0.600623\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −228198. −1.92687 −0.963435 0.267942i $$-0.913656\pi$$
−0.963435 + 0.267942i $$0.913656\pi$$
$$108$$ 0 0
$$109$$ −95186.0 −0.767374 −0.383687 0.923463i $$-0.625346\pi$$
−0.383687 + 0.923463i $$0.625346\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 261142. 1.92389 0.961946 0.273240i $$-0.0880954\pi$$
0.961946 + 0.273240i $$0.0880954\pi$$
$$114$$ 0 0
$$115$$ 52360.0 0.369194
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −58996.0 −0.381905
$$120$$ 0 0
$$121$$ 59849.0 0.371615
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 189816. 1.08657
$$126$$ 0 0
$$127$$ 167652. 0.922358 0.461179 0.887307i $$-0.347427\pi$$
0.461179 + 0.887307i $$0.347427\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −83068.0 −0.422917 −0.211459 0.977387i $$-0.567821\pi$$
−0.211459 + 0.977387i $$0.567821\pi$$
$$132$$ 0 0
$$133$$ 129556. 0.635080
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −162254. −0.738574 −0.369287 0.929315i $$-0.620398\pi$$
−0.369287 + 0.929315i $$0.620398\pi$$
$$138$$ 0 0
$$139$$ 58844.0 0.258324 0.129162 0.991623i $$-0.458771\pi$$
0.129162 + 0.991623i $$0.458771\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 544260. 2.22570
$$144$$ 0 0
$$145$$ 159016. 0.628088
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −430698. −1.58930 −0.794652 0.607065i $$-0.792347\pi$$
−0.794652 + 0.607065i $$0.792347\pi$$
$$150$$ 0 0
$$151$$ 500936. 1.78789 0.893943 0.448180i $$-0.147928\pi$$
0.893943 + 0.448180i $$0.147928\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 247104. 0.826134
$$156$$ 0 0
$$157$$ −280258. −0.907421 −0.453711 0.891149i $$-0.649900\pi$$
−0.453711 + 0.891149i $$0.649900\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −58310.0 −0.177288
$$162$$ 0 0
$$163$$ 120016. 0.353810 0.176905 0.984228i $$-0.443391\pi$$
0.176905 + 0.984228i $$0.443391\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 546932. 1.51755 0.758774 0.651355i $$-0.225799\pi$$
0.758774 + 0.651355i $$0.225799\pi$$
$$168$$ 0 0
$$169$$ 969671. 2.61161
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 367096. 0.932533 0.466267 0.884644i $$-0.345599\pi$$
0.466267 + 0.884644i $$0.345599\pi$$
$$174$$ 0 0
$$175$$ −58261.0 −0.143808
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −88890.0 −0.207358 −0.103679 0.994611i $$-0.533061\pi$$
−0.103679 + 0.994611i $$0.533061\pi$$
$$180$$ 0 0
$$181$$ −782118. −1.77450 −0.887250 0.461290i $$-0.847387\pi$$
−0.887250 + 0.461290i $$0.847387\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 285032. 0.612300
$$186$$ 0 0
$$187$$ 565880. 1.18337
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 763350. 1.51405 0.757025 0.653386i $$-0.226652\pi$$
0.757025 + 0.653386i $$0.226652\pi$$
$$192$$ 0 0
$$193$$ −377002. −0.728535 −0.364267 0.931294i $$-0.618681\pi$$
−0.364267 + 0.931294i $$0.618681\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 68678.0 0.126082 0.0630409 0.998011i $$-0.479920\pi$$
0.0630409 + 0.998011i $$0.479920\pi$$
$$198$$ 0 0
$$199$$ −182576. −0.326822 −0.163411 0.986558i $$-0.552250\pi$$
−0.163411 + 0.986558i $$0.552250\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −177086. −0.301609
$$204$$ 0 0
$$205$$ 125664. 0.208846
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −1.24268e6 −1.96786
$$210$$ 0 0
$$211$$ −232652. −0.359750 −0.179875 0.983689i $$-0.557569\pi$$
−0.179875 + 0.983689i $$0.557569\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −593648. −0.875856
$$216$$ 0 0
$$217$$ −275184. −0.396711
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 1.39423e6 1.92023
$$222$$ 0 0
$$223$$ −167144. −0.225076 −0.112538 0.993647i $$-0.535898\pi$$
−0.112538 + 0.993647i $$0.535898\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 415728. 0.535482 0.267741 0.963491i $$-0.413723\pi$$
0.267741 + 0.963491i $$0.413723\pi$$
$$228$$ 0 0
$$229$$ 473482. 0.596643 0.298322 0.954465i $$-0.403573\pi$$
0.298322 + 0.954465i $$0.403573\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.55655e6 1.87833 0.939166 0.343465i $$-0.111601\pi$$
0.939166 + 0.343465i $$0.111601\pi$$
$$234$$ 0 0
$$235$$ 808368. 0.954859
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 655890. 0.742739 0.371370 0.928485i $$-0.378888\pi$$
0.371370 + 0.928485i $$0.378888\pi$$
$$240$$ 0 0
$$241$$ −889474. −0.986485 −0.493243 0.869892i $$-0.664189\pi$$
−0.493243 + 0.869892i $$0.664189\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −105644. −0.112442
$$246$$ 0 0
$$247$$ −3.06175e6 −3.19321
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 131832. 0.132080 0.0660399 0.997817i $$-0.478964\pi$$
0.0660399 + 0.997817i $$0.478964\pi$$
$$252$$ 0 0
$$253$$ 559300. 0.549343
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1.46482e6 1.38341 0.691704 0.722181i $$-0.256860\pi$$
0.691704 + 0.722181i $$0.256860\pi$$
$$258$$ 0 0
$$259$$ −317422. −0.294027
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.47969e6 1.31911 0.659556 0.751656i $$-0.270745\pi$$
0.659556 + 0.751656i $$0.270745\pi$$
$$264$$ 0 0
$$265$$ −192456. −0.168351
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 187852. 0.158283 0.0791417 0.996863i $$-0.474782\pi$$
0.0791417 + 0.996863i $$0.474782\pi$$
$$270$$ 0 0
$$271$$ −193800. −0.160299 −0.0801495 0.996783i $$-0.525540\pi$$
−0.0801495 + 0.996783i $$0.525540\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 558830. 0.445603
$$276$$ 0 0
$$277$$ −617062. −0.483203 −0.241601 0.970376i $$-0.577673\pi$$
−0.241601 + 0.970376i $$0.577673\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.73129e6 1.30799 0.653994 0.756499i $$-0.273092\pi$$
0.653994 + 0.756499i $$0.273092\pi$$
$$282$$ 0 0
$$283$$ −356020. −0.264246 −0.132123 0.991233i $$-0.542179\pi$$
−0.132123 + 0.991233i $$0.542179\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −139944. −0.100288
$$288$$ 0 0
$$289$$ 29759.0 0.0209592
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −536664. −0.365202 −0.182601 0.983187i $$-0.558452\pi$$
−0.182601 + 0.983187i $$0.558452\pi$$
$$294$$ 0 0
$$295$$ −1.33091e6 −0.890419
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 1.37802e6 0.891410
$$300$$ 0 0
$$301$$ 661108. 0.420587
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −859848. −0.529264
$$306$$ 0 0
$$307$$ 2.88398e6 1.74641 0.873205 0.487353i $$-0.162037\pi$$
0.873205 + 0.487353i $$0.162037\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.02958e6 −0.603614 −0.301807 0.953369i $$-0.597590\pi$$
−0.301807 + 0.953369i $$0.597590\pi$$
$$312$$ 0 0
$$313$$ 1.39297e6 0.803676 0.401838 0.915711i $$-0.368372\pi$$
0.401838 + 0.915711i $$0.368372\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 780030. 0.435977 0.217988 0.975951i $$-0.430051\pi$$
0.217988 + 0.975951i $$0.430051\pi$$
$$318$$ 0 0
$$319$$ 1.69858e6 0.934565
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −3.18338e6 −1.69778
$$324$$ 0 0
$$325$$ 1.37686e6 0.723073
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −900228. −0.458525
$$330$$ 0 0
$$331$$ 1.41204e6 0.708399 0.354200 0.935170i $$-0.384753\pi$$
0.354200 + 0.935170i $$0.384753\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 2.39043e6 1.16376
$$336$$ 0 0
$$337$$ −634662. −0.304416 −0.152208 0.988348i $$-0.548638\pi$$
−0.152208 + 0.988348i $$0.548638\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 2.63952e6 1.22925
$$342$$ 0 0
$$343$$ 117649. 0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 3.07942e6 1.37292 0.686460 0.727167i $$-0.259163\pi$$
0.686460 + 0.727167i $$0.259163\pi$$
$$348$$ 0 0
$$349$$ −2.60671e6 −1.14559 −0.572796 0.819698i $$-0.694141\pi$$
−0.572796 + 0.819698i $$0.694141\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 63132.0 0.0269658 0.0134829 0.999909i $$-0.495708\pi$$
0.0134829 + 0.999909i $$0.495708\pi$$
$$354$$ 0 0
$$355$$ 472120. 0.198830
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 479270. 0.196266 0.0981328 0.995173i $$-0.468713\pi$$
0.0981328 + 0.995173i $$0.468713\pi$$
$$360$$ 0 0
$$361$$ 4.51464e6 1.82329
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −1.55646e6 −0.611512
$$366$$ 0 0
$$367$$ 1.33451e6 0.517199 0.258599 0.965985i $$-0.416739\pi$$
0.258599 + 0.965985i $$0.416739\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 214326. 0.0808426
$$372$$ 0 0
$$373$$ −1.69759e6 −0.631774 −0.315887 0.948797i $$-0.602302\pi$$
−0.315887 + 0.948797i $$0.602302\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 4.18501e6 1.51650
$$378$$ 0 0
$$379$$ −2.51074e6 −0.897850 −0.448925 0.893569i $$-0.648193\pi$$
−0.448925 + 0.893569i $$0.648193\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 559144. 0.194772 0.0973860 0.995247i $$-0.468952\pi$$
0.0973860 + 0.995247i $$0.468952\pi$$
$$384$$ 0 0
$$385$$ 1.01332e6 0.348413
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −4.51055e6 −1.51132 −0.755658 0.654966i $$-0.772683\pi$$
−0.755658 + 0.654966i $$0.772683\pi$$
$$390$$ 0 0
$$391$$ 1.43276e6 0.473949
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −2.19806e6 −0.708839
$$396$$ 0 0
$$397$$ 5.19862e6 1.65543 0.827717 0.561145i $$-0.189639\pi$$
0.827717 + 0.561145i $$0.189639\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 6.34816e6 1.97146 0.985728 0.168346i $$-0.0538426\pi$$
0.985728 + 0.168346i $$0.0538426\pi$$
$$402$$ 0 0
$$403$$ 6.50333e6 1.99468
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 3.04466e6 0.911072
$$408$$ 0 0
$$409$$ −181642. −0.0536918 −0.0268459 0.999640i $$-0.508546\pi$$
−0.0268459 + 0.999640i $$0.508546\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 1.48215e6 0.427580
$$414$$ 0 0
$$415$$ 1.18571e6 0.337955
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −5.62699e6 −1.56582 −0.782909 0.622136i $$-0.786265\pi$$
−0.782909 + 0.622136i $$0.786265\pi$$
$$420$$ 0 0
$$421$$ −4.42671e6 −1.21724 −0.608619 0.793462i $$-0.708276\pi$$
−0.608619 + 0.793462i $$0.708276\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.43156e6 0.384447
$$426$$ 0 0
$$427$$ 957558. 0.254153
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1.44163e6 −0.373817 −0.186909 0.982377i $$-0.559847\pi$$
−0.186909 + 0.982377i $$0.559847\pi$$
$$432$$ 0 0
$$433$$ −3.89661e6 −0.998775 −0.499387 0.866379i $$-0.666442\pi$$
−0.499387 + 0.866379i $$0.666442\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −3.14636e6 −0.788143
$$438$$ 0 0
$$439$$ −5.11207e6 −1.26601 −0.633003 0.774149i $$-0.718178\pi$$
−0.633003 + 0.774149i $$0.718178\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 5.44070e6 1.31718 0.658591 0.752501i $$-0.271153\pi$$
0.658591 + 0.752501i $$0.271153\pi$$
$$444$$ 0 0
$$445$$ 4.43414e6 1.06147
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 1.31525e6 0.307887 0.153943 0.988080i $$-0.450803\pi$$
0.153943 + 0.988080i $$0.450803\pi$$
$$450$$ 0 0
$$451$$ 1.34232e6 0.310753
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 2.49665e6 0.565365
$$456$$ 0 0
$$457$$ 2.77604e6 0.621778 0.310889 0.950446i $$-0.399373\pi$$
0.310889 + 0.950446i $$0.399373\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −138080. −0.0302607 −0.0151303 0.999886i $$-0.504816\pi$$
−0.0151303 + 0.999886i $$0.504816\pi$$
$$462$$ 0 0
$$463$$ 364076. 0.0789295 0.0394648 0.999221i $$-0.487435\pi$$
0.0394648 + 0.999221i $$0.487435\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −5.73897e6 −1.21770 −0.608852 0.793284i $$-0.708370\pi$$
−0.608852 + 0.793284i $$0.708370\pi$$
$$468$$ 0 0
$$469$$ −2.66207e6 −0.558840
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −6.34124e6 −1.30323
$$474$$ 0 0
$$475$$ −3.14372e6 −0.639307
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 5.51996e6 1.09925 0.549625 0.835411i $$-0.314770\pi$$
0.549625 + 0.835411i $$0.314770\pi$$
$$480$$ 0 0
$$481$$ 7.50152e6 1.47838
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −3.39390e6 −0.655155
$$486$$ 0 0
$$487$$ −4.23022e6 −0.808241 −0.404121 0.914706i $$-0.632422\pi$$
−0.404121 + 0.914706i $$0.632422\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −7.21423e6 −1.35047 −0.675237 0.737601i $$-0.735959\pi$$
−0.675237 + 0.737601i $$0.735959\pi$$
$$492$$ 0 0
$$493$$ 4.35126e6 0.806301
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −525770. −0.0954783
$$498$$ 0 0
$$499$$ 224804. 0.0404159 0.0202080 0.999796i $$-0.493567\pi$$
0.0202080 + 0.999796i $$0.493567\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 5.06983e6 0.893457 0.446728 0.894670i $$-0.352589\pi$$
0.446728 + 0.894670i $$0.352589\pi$$
$$504$$ 0 0
$$505$$ 4.37642e6 0.763643
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −5.48135e6 −0.937763 −0.468881 0.883261i $$-0.655343\pi$$
−0.468881 + 0.883261i $$0.655343\pi$$
$$510$$ 0 0
$$511$$ 1.73333e6 0.293649
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 2.94554e6 0.489380
$$516$$ 0 0
$$517$$ 8.63484e6 1.42078
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −7.88932e6 −1.27334 −0.636671 0.771136i $$-0.719689\pi$$
−0.636671 + 0.771136i $$0.719689\pi$$
$$522$$ 0 0
$$523$$ 9.74950e6 1.55858 0.779288 0.626666i $$-0.215581\pi$$
0.779288 + 0.626666i $$0.215581\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 6.76166e6 1.06054
$$528$$ 0 0
$$529$$ −5.02024e6 −0.779984
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 3.30725e6 0.504253
$$534$$ 0 0
$$535$$ 1.00407e7 1.51663
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −1.12847e6 −0.167309
$$540$$ 0 0
$$541$$ −4.17454e6 −0.613219 −0.306610 0.951835i $$-0.599195\pi$$
−0.306610 + 0.951835i $$0.599195\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 4.18818e6 0.603997
$$546$$ 0 0
$$547$$ 2.72887e6 0.389955 0.194978 0.980808i $$-0.437537\pi$$
0.194978 + 0.980808i $$0.437537\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −9.55542e6 −1.34082
$$552$$ 0 0
$$553$$ 2.44784e6 0.340385
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 7.35103e6 1.00395 0.501973 0.864883i $$-0.332608\pi$$
0.501973 + 0.864883i $$0.332608\pi$$
$$558$$ 0 0
$$559$$ −1.56237e7 −2.11473
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −1.37821e7 −1.83250 −0.916248 0.400612i $$-0.868798\pi$$
−0.916248 + 0.400612i $$0.868798\pi$$
$$564$$ 0 0
$$565$$ −1.14902e7 −1.51429
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −2.71217e6 −0.351186 −0.175593 0.984463i $$-0.556184\pi$$
−0.175593 + 0.984463i $$0.556184\pi$$
$$570$$ 0 0
$$571$$ −4.94398e6 −0.634580 −0.317290 0.948329i $$-0.602773\pi$$
−0.317290 + 0.948329i $$0.602773\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.41491e6 0.178468
$$576$$ 0 0
$$577$$ −1.32683e7 −1.65911 −0.829556 0.558424i $$-0.811406\pi$$
−0.829556 + 0.558424i $$0.811406\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −1.32045e6 −0.162286
$$582$$ 0 0
$$583$$ −2.05578e6 −0.250499
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 1.67205e6 0.200287 0.100144 0.994973i $$-0.468070\pi$$
0.100144 + 0.994973i $$0.468070\pi$$
$$588$$ 0 0
$$589$$ −1.48487e7 −1.76360
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −5.11693e6 −0.597548 −0.298774 0.954324i $$-0.596578\pi$$
−0.298774 + 0.954324i $$0.596578\pi$$
$$594$$ 0 0
$$595$$ 2.59582e6 0.300596
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −7.15931e6 −0.815275 −0.407638 0.913144i $$-0.633647\pi$$
−0.407638 + 0.913144i $$0.633647\pi$$
$$600$$ 0 0
$$601$$ −9.63384e6 −1.08796 −0.543980 0.839098i $$-0.683083\pi$$
−0.543980 + 0.839098i $$0.683083\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −2.63336e6 −0.292497
$$606$$ 0 0
$$607$$ −5.52115e6 −0.608216 −0.304108 0.952638i $$-0.598358\pi$$
−0.304108 + 0.952638i $$0.598358\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 2.12748e7 2.30548
$$612$$ 0 0
$$613$$ 4.79890e6 0.515811 0.257906 0.966170i $$-0.416968\pi$$
0.257906 + 0.966170i $$0.416968\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −2.71826e6 −0.287461 −0.143730 0.989617i $$-0.545910\pi$$
−0.143730 + 0.989617i $$0.545910\pi$$
$$618$$ 0 0
$$619$$ 4.34335e6 0.455615 0.227807 0.973706i $$-0.426844\pi$$
0.227807 + 0.973706i $$0.426844\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −4.93802e6 −0.509722
$$624$$ 0 0
$$625$$ −4.63628e6 −0.474755
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 7.79951e6 0.786033
$$630$$ 0 0
$$631$$ −1.11952e6 −0.111933 −0.0559667 0.998433i $$-0.517824\pi$$
−0.0559667 + 0.998433i $$0.517824\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −7.37669e6 −0.725984
$$636$$ 0 0
$$637$$ −2.78036e6 −0.271489
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 3.96588e6 0.381237 0.190618 0.981664i $$-0.438951\pi$$
0.190618 + 0.981664i $$0.438951\pi$$
$$642$$ 0 0
$$643$$ −1.92086e7 −1.83218 −0.916092 0.400968i $$-0.868674\pi$$
−0.916092 + 0.400968i $$0.868674\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 4.72739e6 0.443977 0.221989 0.975049i $$-0.428745\pi$$
0.221989 + 0.975049i $$0.428745\pi$$
$$648$$ 0 0
$$649$$ −1.42166e7 −1.32490
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −1.21159e7 −1.11192 −0.555958 0.831210i $$-0.687648\pi$$
−0.555958 + 0.831210i $$0.687648\pi$$
$$654$$ 0 0
$$655$$ 3.65499e6 0.332877
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 5.91457e6 0.530530 0.265265 0.964176i $$-0.414541\pi$$
0.265265 + 0.964176i $$0.414541\pi$$
$$660$$ 0 0
$$661$$ 1.41779e7 1.26214 0.631072 0.775724i $$-0.282615\pi$$
0.631072 + 0.775724i $$0.282615\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −5.70046e6 −0.499869
$$666$$ 0 0
$$667$$ 4.30066e6 0.374301
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −9.18474e6 −0.787518
$$672$$ 0 0
$$673$$ 1.34245e7 1.14251 0.571256 0.820772i $$-0.306456\pi$$
0.571256 + 0.820772i $$0.306456\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 8.67312e6 0.727283 0.363642 0.931539i $$-0.381533\pi$$
0.363642 + 0.931539i $$0.381533\pi$$
$$678$$ 0 0
$$679$$ 3.77957e6 0.314606
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1.49777e7 1.22855 0.614275 0.789092i $$-0.289448\pi$$
0.614275 + 0.789092i $$0.289448\pi$$
$$684$$ 0 0
$$685$$ 7.13918e6 0.581329
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −5.06509e6 −0.406480
$$690$$ 0 0
$$691$$ 8.76742e6 0.698517 0.349258 0.937026i $$-0.386434\pi$$
0.349258 + 0.937026i $$0.386434\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −2.58914e6 −0.203326
$$696$$ 0 0
$$697$$ 3.43862e6 0.268104
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1.99459e7 1.53306 0.766529 0.642209i $$-0.221982\pi$$
0.766529 + 0.642209i $$0.221982\pi$$
$$702$$ 0 0
$$703$$ −1.71278e7 −1.30712
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −4.87374e6 −0.366702
$$708$$ 0 0
$$709$$ −2.66387e7 −1.99020 −0.995100 0.0988699i $$-0.968477\pi$$
−0.995100 + 0.0988699i $$0.968477\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 6.68304e6 0.492323
$$714$$ 0 0
$$715$$ −2.39474e7 −1.75184
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −1.17408e6 −0.0846985 −0.0423492 0.999103i $$-0.513484\pi$$
−0.0423492 + 0.999103i $$0.513484\pi$$
$$720$$ 0 0
$$721$$ −3.28026e6 −0.235001
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 4.29705e6 0.303616
$$726$$ 0 0
$$727$$ −1.05734e7 −0.741957 −0.370979 0.928641i $$-0.620978\pi$$
−0.370979 + 0.928641i $$0.620978\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −1.62444e7 −1.12437
$$732$$ 0 0
$$733$$ 2.31670e7 1.59261 0.796306 0.604894i $$-0.206785\pi$$
0.796306 + 0.604894i $$0.206785\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 2.55342e7 1.73162
$$738$$ 0 0
$$739$$ 1.55334e7 1.04630 0.523148 0.852242i $$-0.324757\pi$$
0.523148 + 0.852242i $$0.324757\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 2.54630e7 1.69215 0.846074 0.533066i $$-0.178960\pi$$
0.846074 + 0.533066i $$0.178960\pi$$
$$744$$ 0 0
$$745$$ 1.89507e7 1.25094
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −1.11817e7 −0.728288
$$750$$ 0 0
$$751$$ −9.88512e6 −0.639561 −0.319781 0.947492i $$-0.603609\pi$$
−0.319781 + 0.947492i $$0.603609\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −2.20412e7 −1.40724
$$756$$ 0 0
$$757$$ −6.41980e6 −0.407176 −0.203588 0.979057i $$-0.565260\pi$$
−0.203588 + 0.979057i $$0.565260\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 5.05052e6 0.316136 0.158068 0.987428i $$-0.449473\pi$$
0.158068 + 0.987428i $$0.449473\pi$$
$$762$$ 0 0
$$763$$ −4.66411e6 −0.290040
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −3.50272e7 −2.14989
$$768$$ 0 0
$$769$$ 2.28169e6 0.139136 0.0695682 0.997577i $$-0.477838\pi$$
0.0695682 + 0.997577i $$0.477838\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −2.73777e7 −1.64797 −0.823984 0.566613i $$-0.808254\pi$$
−0.823984 + 0.566613i $$0.808254\pi$$
$$774$$ 0 0
$$775$$ 6.67742e6 0.399351
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −7.55126e6 −0.445837
$$780$$ 0 0
$$781$$ 5.04310e6 0.295849
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 1.23314e7 0.714227
$$786$$ 0 0
$$787$$ −2.04263e7 −1.17558 −0.587791 0.809013i $$-0.700002\pi$$
−0.587791 + 0.809013i $$0.700002\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 1.27960e7 0.727163
$$792$$ 0 0
$$793$$ −2.26296e7 −1.27789
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −2.31557e7 −1.29126 −0.645628 0.763652i $$-0.723404\pi$$
−0.645628 + 0.763652i $$0.723404\pi$$
$$798$$ 0 0
$$799$$ 2.21199e7 1.22579
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −1.66258e7 −0.909899
$$804$$ 0 0
$$805$$ 2.56564e6 0.139542
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −1.14894e7 −0.617203 −0.308601 0.951191i $$-0.599861\pi$$
−0.308601 + 0.951191i $$0.599861\pi$$
$$810$$ 0 0
$$811$$ −1.72443e7 −0.920648 −0.460324 0.887751i $$-0.652267\pi$$
−0.460324 + 0.887751i $$0.652267\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −5.28070e6 −0.278482
$$816$$ 0 0
$$817$$ 3.56728e7 1.86975
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −1.37077e6 −0.0709752 −0.0354876 0.999370i $$-0.511298\pi$$
−0.0354876 + 0.999370i $$0.511298\pi$$
$$822$$ 0 0
$$823$$ −8.56851e6 −0.440967 −0.220483 0.975391i $$-0.570763\pi$$
−0.220483 + 0.975391i $$0.570763\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −1.33258e6 −0.0677533 −0.0338766 0.999426i $$-0.510785\pi$$
−0.0338766 + 0.999426i $$0.510785\pi$$
$$828$$ 0 0
$$829$$ 6.25659e6 0.316193 0.158096 0.987424i $$-0.449464\pi$$
0.158096 + 0.987424i $$0.449464\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −2.89080e6 −0.144346
$$834$$ 0 0
$$835$$ −2.40650e7 −1.19446
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −1.61258e6 −0.0790891 −0.0395445 0.999218i $$-0.512591\pi$$
−0.0395445 + 0.999218i $$0.512591\pi$$
$$840$$ 0 0
$$841$$ −7.45015e6 −0.363225
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −4.26655e7 −2.05558
$$846$$ 0 0
$$847$$ 2.93260e6 0.140457
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 7.70882e6 0.364892
$$852$$ 0 0
$$853$$ −3.44919e7 −1.62310 −0.811548 0.584286i $$-0.801375\pi$$
−0.811548 + 0.584286i $$0.801375\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 1.85487e7 0.862704 0.431352 0.902184i $$-0.358037\pi$$
0.431352 + 0.902184i $$0.358037\pi$$
$$858$$ 0 0
$$859$$ 2.56435e7 1.18575 0.592877 0.805293i $$-0.297992\pi$$
0.592877 + 0.805293i $$0.297992\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −2.49899e7 −1.14219 −0.571093 0.820885i $$-0.693481\pi$$
−0.571093 + 0.820885i $$0.693481\pi$$
$$864$$ 0 0
$$865$$ −1.61522e7 −0.733993
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −2.34793e7 −1.05472
$$870$$ 0 0
$$871$$ 6.29118e7 2.80987
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 9.30098e6 0.410685
$$876$$ 0 0
$$877$$ −3.46337e7 −1.52055 −0.760274 0.649602i $$-0.774935\pi$$
−0.760274 + 0.649602i $$0.774935\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −2.92434e7 −1.26937 −0.634685 0.772771i $$-0.718870\pi$$
−0.634685 + 0.772771i $$0.718870\pi$$
$$882$$ 0 0
$$883$$ 3.76532e7 1.62518 0.812588 0.582839i $$-0.198058\pi$$
0.812588 + 0.582839i $$0.198058\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −2.08201e6 −0.0888534 −0.0444267 0.999013i $$-0.514146\pi$$
−0.0444267 + 0.999013i $$0.514146\pi$$
$$888$$ 0 0
$$889$$ 8.21495e6 0.348618
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −4.85756e7 −2.03840
$$894$$ 0 0
$$895$$ 3.91116e6 0.163210
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 2.02962e7 0.837560
$$900$$ 0 0
$$901$$ −5.26630e6 −0.216119
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 3.44132e7 1.39670
$$906$$ 0 0
$$907$$ −1.62350e7 −0.655291 −0.327645 0.944801i $$-0.606255\pi$$
−0.327645 + 0.944801i $$0.606255\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −2.58656e7 −1.03259 −0.516294 0.856412i $$-0.672689\pi$$
−0.516294 + 0.856412i $$0.672689\pi$$
$$912$$ 0 0
$$913$$ 1.26656e7 0.502860
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −4.07033e6 −0.159848
$$918$$ 0 0
$$919$$ 1.23266e7 0.481453 0.240726 0.970593i $$-0.422614\pi$$
0.240726 + 0.970593i $$0.422614\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 1.24253e7 0.480069
$$924$$ 0 0
$$925$$ 7.70234e6 0.295984
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 4.15128e7 1.57813 0.789064 0.614310i $$-0.210566\pi$$
0.789064 + 0.614310i $$0.210566\pi$$
$$930$$ 0 0
$$931$$ 6.34824e6 0.240038
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −2.48987e7 −0.931425
$$936$$ 0 0
$$937$$ 2.26895e7 0.844260 0.422130 0.906535i $$-0.361283\pi$$
0.422130 + 0.906535i $$0.361283\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −1.58213e7 −0.582464 −0.291232 0.956652i $$-0.594065\pi$$
−0.291232 + 0.956652i $$0.594065\pi$$
$$942$$ 0 0
$$943$$ 3.39864e6 0.124459
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 5.17579e7 1.87543 0.937716 0.347402i $$-0.112936\pi$$
0.937716 + 0.347402i $$0.112936\pi$$
$$948$$ 0 0
$$949$$ −4.09631e7 −1.47648
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −2.29818e7 −0.819695 −0.409848 0.912154i $$-0.634418\pi$$
−0.409848 + 0.912154i $$0.634418\pi$$
$$954$$ 0 0
$$955$$ −3.35874e7 −1.19170
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −7.95045e6 −0.279155
$$960$$ 0 0
$$961$$ 2.91030e6 0.101655
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 1.65881e7 0.573427
$$966$$ 0 0
$$967$$ −3.20783e7 −1.10318 −0.551588 0.834117i $$-0.685978\pi$$
−0.551588 + 0.834117i $$0.685978\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 7.31101e6 0.248845 0.124423 0.992229i $$-0.460292\pi$$
0.124423 + 0.992229i $$0.460292\pi$$
$$972$$ 0 0
$$973$$ 2.88336e6 0.0976374
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −7.58600e6 −0.254259 −0.127129 0.991886i $$-0.540576\pi$$
−0.127129 + 0.991886i $$0.540576\pi$$
$$978$$ 0 0
$$979$$ 4.73647e7 1.57942
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −2.47823e7 −0.818007 −0.409004 0.912533i $$-0.634124\pi$$
−0.409004 + 0.912533i $$0.634124\pi$$
$$984$$ 0 0
$$985$$ −3.02183e6 −0.0992384
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −1.60555e7 −0.521954
$$990$$ 0 0
$$991$$ 7.63530e6 0.246969 0.123484 0.992347i $$-0.460593\pi$$
0.123484 + 0.992347i $$0.460593\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 8.03334e6 0.257240
$$996$$ 0 0
$$997$$ −2.89785e7 −0.923289 −0.461644 0.887065i $$-0.652740\pi$$
−0.461644 + 0.887065i $$0.652740\pi$$
$$998$$ 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.g.1.1 1
3.2 odd 2 336.6.a.o.1.1 1
4.3 odd 2 126.6.a.h.1.1 1
12.11 even 2 42.6.a.b.1.1 1
28.27 even 2 882.6.a.v.1.1 1
60.23 odd 4 1050.6.g.l.799.2 2
60.47 odd 4 1050.6.g.l.799.1 2
60.59 even 2 1050.6.a.o.1.1 1
84.11 even 6 294.6.e.o.79.1 2
84.23 even 6 294.6.e.o.67.1 2
84.47 odd 6 294.6.e.k.67.1 2
84.59 odd 6 294.6.e.k.79.1 2
84.83 odd 2 294.6.a.f.1.1 1

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