# Properties

 Label 441.6.a.a.1.1 Level $441$ Weight $6$ Character 441.1 Self dual yes Analytic conductor $70.729$ Analytic rank $1$ Dimension $1$ CM discriminant -7 Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 441.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$70.7292645375$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 49) Fricke sign: $$1$$ Sato-Tate group: $N(\mathrm{U}(1))$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 441.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-11.0000 q^{2} +89.0000 q^{4} -627.000 q^{8} +O(q^{10})$$ $$q-11.0000 q^{2} +89.0000 q^{4} -627.000 q^{8} +76.0000 q^{11} +4049.00 q^{16} -836.000 q^{22} +4952.00 q^{23} -3125.00 q^{25} -7282.00 q^{29} -24475.0 q^{32} -8886.00 q^{37} +11748.0 q^{43} +6764.00 q^{44} -54472.0 q^{46} +34375.0 q^{50} -24550.0 q^{53} +80102.0 q^{58} +139657. q^{64} +69364.0 q^{67} +2224.00 q^{71} +97746.0 q^{74} +80168.0 q^{79} -129228. q^{86} -47652.0 q^{88} +440728. q^{92} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −11.0000 −1.94454 −0.972272 0.233854i $$-0.924866\pi$$
−0.972272 + 0.233854i $$0.924866\pi$$
$$3$$ 0 0
$$4$$ 89.0000 2.78125
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −627.000 −3.46372
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 76.0000 0.189379 0.0946895 0.995507i $$-0.469814\pi$$
0.0946895 + 0.995507i $$0.469814\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 4049.00 3.95410
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −836.000 −0.368256
$$23$$ 4952.00 1.95192 0.975958 0.217959i $$-0.0699401\pi$$
0.975958 + 0.217959i $$0.0699401\pi$$
$$24$$ 0 0
$$25$$ −3125.00 −1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −7282.00 −1.60789 −0.803944 0.594705i $$-0.797269\pi$$
−0.803944 + 0.594705i $$0.797269\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −24475.0 −4.22520
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −8886.00 −1.06709 −0.533546 0.845771i $$-0.679141\pi$$
−0.533546 + 0.845771i $$0.679141\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 11748.0 0.968931 0.484465 0.874810i $$-0.339014\pi$$
0.484465 + 0.874810i $$0.339014\pi$$
$$44$$ 6764.00 0.526710
$$45$$ 0 0
$$46$$ −54472.0 −3.79559
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 34375.0 1.94454
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −24550.0 −1.20050 −0.600250 0.799813i $$-0.704932\pi$$
−0.600250 + 0.799813i $$0.704932\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 80102.0 3.12661
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 139657. 4.26199
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 69364.0 1.88776 0.943881 0.330286i $$-0.107145\pi$$
0.943881 + 0.330286i $$0.107145\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 2224.00 0.0523587 0.0261794 0.999657i $$-0.491666\pi$$
0.0261794 + 0.999657i $$0.491666\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 97746.0 2.07501
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 80168.0 1.44522 0.722609 0.691257i $$-0.242943\pi$$
0.722609 + 0.691257i $$0.242943\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −129228. −1.88413
$$87$$ 0 0
$$88$$ −47652.0 −0.655956
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 440728. 5.42877
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −278125. −2.78125
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 270050. 2.33442
$$107$$ 64900.0 0.548006 0.274003 0.961729i $$-0.411652\pi$$
0.274003 + 0.961729i $$0.411652\pi$$
$$108$$ 0 0
$$109$$ −219582. −1.77023 −0.885117 0.465369i $$-0.845922\pi$$
−0.885117 + 0.465369i $$0.845922\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −123202. −0.907657 −0.453828 0.891089i $$-0.649942\pi$$
−0.453828 + 0.891089i $$0.649942\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −648098. −4.47194
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −155275. −0.964136
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −262064. −1.44178 −0.720888 0.693051i $$-0.756266\pi$$
−0.720888 + 0.693051i $$0.756266\pi$$
$$128$$ −753027. −4.06243
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −763004. −3.67083
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 353450. 1.60889 0.804445 0.594027i $$-0.202463\pi$$
0.804445 + 0.594027i $$0.202463\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −24464.0 −0.101814
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ −790854. −2.96785
$$149$$ 337018. 1.24362 0.621810 0.783168i $$-0.286398\pi$$
0.621810 + 0.783168i $$0.286398\pi$$
$$150$$ 0 0
$$151$$ −261624. −0.933760 −0.466880 0.884321i $$-0.654622\pi$$
−0.466880 + 0.884321i $$0.654622\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ −881848. −2.81029
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 663100. 1.95483 0.977417 0.211318i $$-0.0677757\pi$$
0.977417 + 0.211318i $$0.0677757\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −371293. −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 1.04557e6 2.69484
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 307724. 0.748824
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −584564. −1.36364 −0.681820 0.731520i $$-0.738811\pi$$
−0.681820 + 0.731520i $$0.738811\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −3.10490e6 −6.76089
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1.00305e6 −1.98947 −0.994737 0.102461i $$-0.967328\pi$$
−0.994737 + 0.102461i $$0.967328\pi$$
$$192$$ 0 0
$$193$$ −385902. −0.745734 −0.372867 0.927885i $$-0.621625\pi$$
−0.372867 + 0.927885i $$0.621625\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −385814. −0.708292 −0.354146 0.935190i $$-0.615228\pi$$
−0.354146 + 0.935190i $$0.615228\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 1.95938e6 3.46372
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −1.09705e6 −1.69637 −0.848186 0.529699i $$-0.822305\pi$$
−0.848186 + 0.529699i $$0.822305\pi$$
$$212$$ −2.18495e6 −3.33889
$$213$$ 0 0
$$214$$ −713900. −1.06562
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 2.41540e6 3.44230
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1.35522e6 1.76498
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 4.56581e6 5.56927
$$233$$ 1.27950e6 1.54401 0.772004 0.635617i $$-0.219254\pi$$
0.772004 + 0.635617i $$0.219254\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −723536. −0.819342 −0.409671 0.912233i $$-0.634357\pi$$
−0.409671 + 0.912233i $$0.634357\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ 1.70802e6 1.87480
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 376352. 0.369652
$$254$$ 2.88270e6 2.80360
$$255$$ 0 0
$$256$$ 3.81427e6 3.63757
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −1.53155e6 −1.36534 −0.682672 0.730725i $$-0.739182\pi$$
−0.682672 + 0.730725i $$0.739182\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 6.17340e6 5.25034
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ −3.88795e6 −3.12856
$$275$$ −237500. −0.189379
$$276$$ 0 0
$$277$$ −2.55145e6 −1.99796 −0.998982 0.0451116i $$-0.985636\pi$$
−0.998982 + 0.0451116i $$0.985636\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −2.54797e6 −1.92499 −0.962497 0.271294i $$-0.912548\pi$$
−0.962497 + 0.271294i $$0.912548\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 197936. 0.145623
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −1.41986e6 −1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 5.57152e6 3.69611
$$297$$ 0 0
$$298$$ −3.70720e6 −2.41827
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 2.87786e6 1.81574
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 7.13495e6 4.01951
$$317$$ 221714. 0.123921 0.0619605 0.998079i $$-0.480265\pi$$
0.0619605 + 0.998079i $$0.480265\pi$$
$$318$$ 0 0
$$319$$ −553432. −0.304500
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −7.29410e6 −3.80126
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 2.97148e6 1.49074 0.745371 0.666650i $$-0.232273\pi$$
0.745371 + 0.666650i $$0.232273\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −4.15965e6 −1.99518 −0.997590 0.0693859i $$-0.977896\pi$$
−0.997590 + 0.0693859i $$0.977896\pi$$
$$338$$ 4.08422e6 1.94454
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −7.36600e6 −3.35610
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −2.29816e6 −1.02461 −0.512304 0.858804i $$-0.671208\pi$$
−0.512304 + 0.858804i $$0.671208\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −1.86010e6 −0.800165
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 6.43020e6 2.65166
$$359$$ −4.26897e6 −1.74818 −0.874091 0.485762i $$-0.838542\pi$$
−0.874091 + 0.485762i $$0.838542\pi$$
$$360$$ 0 0
$$361$$ −2.47610e6 −1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 2.00506e7 7.71807
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 599302. 0.223035 0.111518 0.993762i $$-0.464429\pi$$
0.111518 + 0.993762i $$0.464429\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −5.59273e6 −1.99998 −0.999991 0.00429827i $$-0.998632\pi$$
−0.999991 + 0.00429827i $$0.998632\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 1.10335e7 3.86862
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 4.24492e6 1.45011
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 1.26012e6 0.422218 0.211109 0.977462i $$-0.432292\pi$$
0.211109 + 0.977462i $$0.432292\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 4.24395e6 1.37730
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −1.26531e7 −3.95410
$$401$$ −6.03293e6 −1.87356 −0.936779 0.349922i $$-0.886208\pi$$
−0.936779 + 0.349922i $$0.886208\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −675336. −0.202085
$$408$$ 0 0
$$409$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 2.07477e6 0.570513 0.285257 0.958451i $$-0.407921\pi$$
0.285257 + 0.958451i $$0.407921\pi$$
$$422$$ 1.20676e7 3.29867
$$423$$ 0 0
$$424$$ 1.53929e7 4.15819
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 5.77610e6 1.52414
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 7.33885e6 1.90298 0.951491 0.307676i $$-0.0995514\pi$$
0.951491 + 0.307676i $$0.0995514\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −1.95428e7 −4.92346
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 5.10490e6 1.23588 0.617942 0.786223i $$-0.287967\pi$$
0.617942 + 0.786223i $$0.287967\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −1.99808e6 −0.467732 −0.233866 0.972269i $$-0.575138\pi$$
−0.233866 + 0.972269i $$0.575138\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −1.09650e7 −2.52442
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5.77969e6 −1.29453 −0.647267 0.762263i $$-0.724088\pi$$
−0.647267 + 0.762263i $$0.724088\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ 2.88620e6 0.625711 0.312856 0.949801i $$-0.398714\pi$$
0.312856 + 0.949801i $$0.398714\pi$$
$$464$$ −2.94848e7 −6.35775
$$465$$ 0 0
$$466$$ −1.40745e7 −3.00239
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 892848. 0.183495
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 7.95890e6 1.59325
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −1.38195e7 −2.68150
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −2.76146e6 −0.527615 −0.263807 0.964575i $$-0.584978\pi$$
−0.263807 + 0.964575i $$0.584978\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −8.82732e6 −1.65244 −0.826219 0.563349i $$-0.809513\pi$$
−0.826219 + 0.563349i $$0.809513\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −1.11204e7 −1.99925 −0.999626 0.0273386i $$-0.991297\pi$$
−0.999626 + 0.0273386i $$0.991297\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −4.13987e6 −0.718804
$$507$$ 0 0
$$508$$ −2.33237e7 −4.00994
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.78601e7 −3.01099
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 1.68471e7 2.65497
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.80860e7 2.80997
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −4.34912e7 −6.53867
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 1.11261e7 1.63437 0.817186 0.576374i $$-0.195533\pi$$
0.817186 + 0.576374i $$0.195533\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2.23604e6 −0.319529 −0.159765 0.987155i $$-0.551074\pi$$
−0.159765 + 0.987155i $$0.551074\pi$$
$$548$$ 3.14570e7 4.47473
$$549$$ 0 0
$$550$$ 2.61250e6 0.368256
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 2.80660e7 3.88513
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −6.23949e6 −0.852140 −0.426070 0.904690i $$-0.640102\pi$$
−0.426070 + 0.904690i $$0.640102\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 2.80277e7 3.74323
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ −1.39445e6 −0.181356
$$569$$ −1.04738e7 −1.35620 −0.678099 0.734971i $$-0.737196\pi$$
−0.678099 + 0.734971i $$0.737196\pi$$
$$570$$ 0 0
$$571$$ 6.33912e6 0.813653 0.406826 0.913506i $$-0.366635\pi$$
0.406826 + 0.913506i $$0.366635\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.54750e7 −1.95192
$$576$$ 0 0
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ 1.56184e7 1.94454
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −1.86580e6 −0.227349
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −3.59794e7 −4.21939
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 2.99946e7 3.45882
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 7.17757e6 0.817354 0.408677 0.912679i $$-0.365990\pi$$
0.408677 + 0.912679i $$0.365990\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −2.32845e7 −2.59702
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 1.75514e7 1.88652 0.943258 0.332060i $$-0.107744\pi$$
0.943258 + 0.332060i $$0.107744\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 7.14899e6 0.756017 0.378008 0.925802i $$-0.376609\pi$$
0.378008 + 0.925802i $$0.376609\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 9.76562e6 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 1.99786e7 1.99752 0.998760 0.0497844i $$-0.0158534\pi$$
0.998760 + 0.0497844i $$0.0158534\pi$$
$$632$$ −5.02653e7 −5.00583
$$633$$ 0 0
$$634$$ −2.43885e6 −0.240970
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 6.08775e6 0.592114
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 1.14963e7 1.10513 0.552563 0.833471i $$-0.313650\pi$$
0.552563 + 0.833471i $$0.313650\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 5.90159e7 5.43688
$$653$$ −1.09772e7 −1.00742 −0.503710 0.863873i $$-0.668032\pi$$
−0.503710 + 0.863873i $$0.668032\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 2.02232e7 1.81400 0.907000 0.421131i $$-0.138367\pi$$
0.907000 + 0.421131i $$0.138367\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$662$$ −3.26862e7 −2.89881
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −3.60605e7 −3.13846
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1.38435e6 0.117817 0.0589085 0.998263i $$-0.481238\pi$$
0.0589085 + 0.998263i $$0.481238\pi$$
$$674$$ 4.57562e7 3.87971
$$675$$ 0 0
$$676$$ −3.30451e7 −2.78125
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 2.13149e7 1.74836 0.874179 0.485603i $$-0.161400\pi$$
0.874179 + 0.485603i $$0.161400\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 4.75677e7 3.83125
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 2.52798e7 1.99239
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −4.88600e6 −0.375542 −0.187771 0.982213i $$-0.560126\pi$$
−0.187771 + 0.982213i $$0.560126\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 1.06139e7 0.807132
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −1.43225e7 −1.07005 −0.535023 0.844837i $$-0.679697\pi$$
−0.535023 + 0.844837i $$0.679697\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −5.20262e7 −3.79262
$$717$$ 0 0
$$718$$ 4.69586e7 3.39942
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 2.72371e7 1.94454
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2.27562e7 1.60789
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ −1.21200e8 −8.24724
$$737$$ 5.27166e6 0.357502
$$738$$ 0 0
$$739$$ −2.64893e6 −0.178427 −0.0892133 0.996013i $$-0.528435\pi$$
−0.0892133 + 0.996013i $$0.528435\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −2.49502e7 −1.65807 −0.829033 0.559199i $$-0.811109\pi$$
−0.829033 + 0.559199i $$0.811109\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −6.59232e6 −0.433702
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 2.51088e7 1.62452 0.812260 0.583295i $$-0.198237\pi$$
0.812260 + 0.583295i $$0.198237\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −1.78870e7 −1.13448 −0.567242 0.823551i $$-0.691989\pi$$
−0.567242 + 0.823551i $$0.691989\pi$$
$$758$$ 6.15201e7 3.88905
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −8.92713e7 −5.53322
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −3.43453e7 −2.07407
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −1.38613e7 −0.821022
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 169024. 0.00991564
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ −3.43374e7 −1.96994
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 7.64844e7 4.22520
$$801$$ 0 0
$$802$$ 6.63622e7 3.64321
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −1.83707e7 −0.986856 −0.493428 0.869787i $$-0.664256\pi$$
−0.493428 + 0.869787i $$0.664256\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 7.42870e6 0.392963
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −3.55881e7 −1.84267 −0.921334 0.388773i $$-0.872899\pi$$
−0.921334 + 0.388773i $$0.872899\pi$$
$$822$$ 0 0
$$823$$ 7.08675e6 0.364710 0.182355 0.983233i $$-0.441628\pi$$
0.182355 + 0.983233i $$0.441628\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 3.68552e7 1.87385 0.936926 0.349527i $$-0.113658\pi$$
0.936926 + 0.349527i $$0.113658\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 3.25164e7 1.58530
$$842$$ −2.28225e7 −1.10939
$$843$$ 0 0
$$844$$ −9.76376e7 −4.71803
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ −9.94030e7 −4.74690
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −4.40035e7 −2.08287
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −4.06923e7 −1.89814
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −8.07273e7 −3.70043
$$863$$ −2.76142e7 −1.26214 −0.631068 0.775727i $$-0.717383\pi$$
−0.631068 + 0.775727i $$0.717383\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 6.09277e6 0.273694
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 1.37678e8 6.13159
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −4.33428e7 −1.90291 −0.951453 0.307793i $$-0.900410\pi$$
−0.951453 + 0.307793i $$0.900410\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ −3.94011e7 −1.70062 −0.850308 0.526286i $$-0.823584\pi$$
−0.850308 + 0.526286i $$0.823584\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ −5.61539e7 −2.40323
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 2.19789e7 0.909526
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 7.72477e7 3.14387
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 4.48347e7 1.80966 0.904828 0.425777i $$-0.139999\pi$$
0.904828 + 0.425777i $$0.139999\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −4.87850e7 −1.94756 −0.973778 0.227498i $$-0.926945\pi$$
−0.973778 + 0.227498i $$0.926945\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 6.35765e7 2.51728
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 5.06716e7 1.97914 0.989569 0.144059i $$-0.0460156\pi$$
0.989569 + 0.144059i $$0.0460156\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 2.77688e7 1.06709
$$926$$ −3.17482e7 −1.21672
$$927$$ 0 0
$$928$$ 1.78227e8 6.79365
$$929$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 1.13875e8 4.29427
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ −9.82133e6 −0.356814
$$947$$ 5.50009e7 1.99294 0.996471 0.0839326i $$-0.0267480\pi$$
0.996471 + 0.0839326i $$0.0267480\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 9.97130e6 0.355647 0.177824 0.984062i $$-0.443094\pi$$
0.177824 + 0.984062i $$0.443094\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −6.43947e7 −2.27880
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −2.86292e7 −1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 2.00222e7 0.688566 0.344283 0.938866i $$-0.388122\pi$$
0.344283 + 0.938866i $$0.388122\pi$$
$$968$$ 9.73574e7 3.33949
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 3.03761e7 1.02597
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 4.99817e7 1.67523 0.837616 0.546260i $$-0.183949\pi$$
0.837616 + 0.546260i $$0.183949\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 9.71006e7 3.21324
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 5.81761e7 1.89127
$$990$$ 0 0
$$991$$ −5.73144e7 −1.85387 −0.926936 0.375219i $$-0.877567\pi$$
−0.926936 + 0.375219i $$0.877567\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 1.22324e8 3.88763
$$999$$ 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 441.6.a.a.1.1 1
3.2 odd 2 49.6.a.b.1.1 1
7.6 odd 2 CM 441.6.a.a.1.1 1
12.11 even 2 784.6.a.g.1.1 1
21.2 odd 6 49.6.c.a.18.1 2
21.5 even 6 49.6.c.a.18.1 2
21.11 odd 6 49.6.c.a.30.1 2
21.17 even 6 49.6.c.a.30.1 2
21.20 even 2 49.6.a.b.1.1 1
84.83 odd 2 784.6.a.g.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
49.6.a.b.1.1 1 3.2 odd 2
49.6.a.b.1.1 1 21.20 even 2
49.6.c.a.18.1 2 21.2 odd 6
49.6.c.a.18.1 2 21.5 even 6
49.6.c.a.30.1 2 21.11 odd 6
49.6.c.a.30.1 2 21.17 even 6
441.6.a.a.1.1 1 1.1 even 1 trivial
441.6.a.a.1.1 1 7.6 odd 2 CM
784.6.a.g.1.1 1 12.11 even 2
784.6.a.g.1.1 1 84.83 odd 2