# Properties

 Label 1568.2.a.o.1.2 Level $1568$ Weight $2$ Character 1568.1 Self dual yes Analytic conductor $12.521$ Analytic rank $1$ Dimension $2$ CM discriminant -4 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1568 = 2^{5} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1568.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$12.5205430369$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{8})^+$$ Defining polynomial: $$x^{2} - 2$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $N(\mathrm{U}(1))$

## Embedding invariants

 Embedding label 1.2 Root $$1.41421$$ of defining polynomial Character $$\chi$$ $$=$$ 1568.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.41421 q^{5} -3.00000 q^{9} +O(q^{10})$$ $$q+1.41421 q^{5} -3.00000 q^{9} -1.41421 q^{13} -7.07107 q^{17} -3.00000 q^{25} -4.00000 q^{29} -12.0000 q^{37} +12.7279 q^{41} -4.24264 q^{45} -14.0000 q^{53} +15.5563 q^{61} -2.00000 q^{65} -15.5563 q^{73} +9.00000 q^{81} -10.0000 q^{85} +4.24264 q^{89} +7.07107 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 6 q^{9} + O(q^{10})$$ $$2 q - 6 q^{9} - 6 q^{25} - 8 q^{29} - 24 q^{37} - 28 q^{53} - 4 q^{65} + 18 q^{81} - 20 q^{85} + O(q^{100})$$

## 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$4$$ 0 0
$$5$$ 1.41421 0.632456 0.316228 0.948683i $$-0.397584\pi$$
0.316228 + 0.948683i $$0.397584\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ −3.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ −1.41421 −0.392232 −0.196116 0.980581i $$-0.562833\pi$$
−0.196116 + 0.980581i $$0.562833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −7.07107 −1.71499 −0.857493 0.514496i $$-0.827979\pi$$
−0.857493 + 0.514496i $$0.827979\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ −3.00000 −0.600000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −12.0000 −1.97279 −0.986394 0.164399i $$-0.947432\pi$$
−0.986394 + 0.164399i $$0.947432\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 12.7279 1.98777 0.993884 0.110432i $$-0.0352233\pi$$
0.993884 + 0.110432i $$0.0352233\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ −4.24264 −0.632456
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −14.0000 −1.92305 −0.961524 0.274721i $$-0.911414\pi$$
−0.961524 + 0.274721i $$0.911414\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 15.5563 1.99179 0.995893 0.0905357i $$-0.0288579\pi$$
0.995893 + 0.0905357i $$0.0288579\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −2.00000 −0.248069
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −15.5563 −1.82073 −0.910366 0.413803i $$-0.864200\pi$$
−0.910366 + 0.413803i $$0.864200\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ −10.0000 −1.08465
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 4.24264 0.449719 0.224860 0.974391i $$-0.427808\pi$$
0.224860 + 0.974391i $$0.427808\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 7.07107 0.717958 0.358979 0.933346i $$-0.383125\pi$$
0.358979 + 0.933346i $$0.383125\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −12.7279 −1.26648 −0.633238 0.773957i $$-0.718274\pi$$
−0.633238 + 0.773957i $$0.718274\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ −20.0000 −1.91565 −0.957826 0.287348i $$-0.907226\pi$$
−0.957826 + 0.287348i $$0.907226\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 4.24264 0.392232
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −11.3137 −1.01193
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 8.00000 0.683486 0.341743 0.939793i $$-0.388983\pi$$
0.341743 + 0.939793i $$0.388983\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −5.65685 −0.469776
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −14.0000 −1.14692 −0.573462 0.819232i $$-0.694400\pi$$
−0.573462 + 0.819232i $$0.694400\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ 21.2132 1.71499
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 24.0416 1.91873 0.959366 0.282166i $$-0.0910530\pi$$
0.959366 + 0.282166i $$0.0910530\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −11.0000 −0.846154
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −21.2132 −1.61281 −0.806405 0.591364i $$-0.798590\pi$$
−0.806405 + 0.591364i $$0.798590\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ −26.8701 −1.99724 −0.998618 0.0525588i $$-0.983262\pi$$
−0.998618 + 0.0525588i $$0.983262\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −16.9706 −1.24770
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 14.0000 1.00774 0.503871 0.863779i $$-0.331909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 18.0000 1.25717
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 10.0000 0.672673
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 9.00000 0.600000
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 18.3848 1.21490 0.607450 0.794358i $$-0.292192\pi$$
0.607450 + 0.794358i $$0.292192\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 16.0000 1.04819 0.524097 0.851658i $$-0.324403\pi$$
0.524097 + 0.851658i $$0.324403\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 26.8701 1.73085 0.865426 0.501036i $$-0.167048\pi$$
0.865426 + 0.501036i $$0.167048\pi$$
$$242$$ 0 0
$$243$$ 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
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −21.2132 −1.32324 −0.661622 0.749838i $$-0.730131\pi$$
−0.661622 + 0.749838i $$0.730131\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 12.0000 0.742781
$$262$$ 0 0
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ −19.7990 −1.21624
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 32.5269 1.98320 0.991600 0.129339i $$-0.0412856\pi$$
0.991600 + 0.129339i $$0.0412856\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −18.0000 −1.08152 −0.540758 0.841178i $$-0.681862\pi$$
−0.540758 + 0.841178i $$0.681862\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 32.0000 1.90896 0.954480 0.298275i $$-0.0964112\pi$$
0.954480 + 0.298275i $$0.0964112\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 33.0000 1.94118
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 21.2132 1.23929 0.619644 0.784883i $$-0.287277\pi$$
0.619644 + 0.784883i $$0.287277\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 22.0000 1.25972
$$306$$ 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
$$313$$ 1.41421 0.0799361 0.0399680 0.999201i $$-0.487274\pi$$
0.0399680 + 0.999201i $$0.487274\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 22.0000 1.23564 0.617822 0.786318i $$-0.288015\pi$$
0.617822 + 0.786318i $$0.288015\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 4.24264 0.235339
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ 36.0000 1.97279
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −32.0000 −1.74315 −0.871576 0.490261i $$-0.836901\pi$$
−0.871576 + 0.490261i $$0.836901\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ −32.5269 −1.74113 −0.870563 0.492057i $$-0.836245\pi$$
−0.870563 + 0.492057i $$0.836245\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 35.3553 1.88177 0.940887 0.338719i $$-0.109994\pi$$
0.940887 + 0.338719i $$0.109994\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −22.0000 −1.15153
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ −38.1838 −1.98777
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −14.0000 −0.724893 −0.362446 0.932005i $$-0.618058\pi$$
−0.362446 + 0.932005i $$0.618058\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 5.65685 0.291343
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 20.0000 1.01404 0.507020 0.861934i $$-0.330747\pi$$
0.507020 + 0.861934i $$0.330747\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −35.3553 −1.77443 −0.887217 0.461353i $$-0.847364\pi$$
−0.887217 + 0.461353i $$0.847364\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 40.0000 1.99750 0.998752 0.0499376i $$-0.0159023\pi$$
0.998752 + 0.0499376i $$0.0159023\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 12.7279 0.632456
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 24.0416 1.18878 0.594391 0.804176i $$-0.297393\pi$$
0.594391 + 0.804176i $$0.297393\pi$$
$$410$$ 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
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 21.2132 1.02899
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ −41.0122 −1.97092 −0.985460 0.169907i $$-0.945653\pi$$
−0.985460 + 0.169907i $$0.945653\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 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
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 6.00000 0.284427
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 14.0000 0.660701 0.330350 0.943858i $$-0.392833\pi$$
0.330350 + 0.943858i $$0.392833\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −42.0000 −1.96468 −0.982339 0.187112i $$-0.940087\pi$$
−0.982339 + 0.187112i $$0.940087\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 12.7279 0.592798 0.296399 0.955064i $$-0.404214\pi$$
0.296399 + 0.955064i $$0.404214\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 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
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 42.0000 1.92305
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 16.9706 0.773791
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 10.0000 0.454077
$$486$$ 0 0
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 28.2843 1.27386
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ −18.0000 −0.800989
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −24.0416 −1.06563 −0.532813 0.846233i $$-0.678865\pi$$
−0.532813 + 0.846233i $$0.678865\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −43.8406 −1.92069 −0.960346 0.278810i $$-0.910060\pi$$
−0.960346 + 0.278810i $$0.910060\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −18.0000 −0.779667
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 42.0000 1.80572 0.902861 0.429934i $$-0.141463\pi$$
0.902861 + 0.429934i $$0.141463\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −28.2843 −1.21157
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 0 0
$$549$$ −46.6690 −1.99179
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 38.0000 1.61011 0.805056 0.593199i $$-0.202135\pi$$
0.805056 + 0.593199i $$0.202135\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 19.7990 0.832950
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −40.0000 −1.67689 −0.838444 0.544988i $$-0.816534\pi$$
−0.838444 + 0.544988i $$0.816534\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 32.5269 1.35411 0.677057 0.735931i $$-0.263255\pi$$
0.677057 + 0.735931i $$0.263255\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 6.00000 0.248069
$$586$$ 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
$$592$$ 0 0
$$593$$ 43.8406 1.80032 0.900159 0.435561i $$-0.143450\pi$$
0.900159 + 0.435561i $$0.143450\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −26.8701 −1.09605 −0.548026 0.836461i $$-0.684621\pi$$
−0.548026 + 0.836461i $$0.684621\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −15.5563 −0.632456
$$606$$ 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
$$613$$ −36.0000 −1.45403 −0.727013 0.686624i $$-0.759092\pi$$
−0.727013 + 0.686624i $$0.759092\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −32.0000 −1.28827 −0.644136 0.764911i $$-0.722783\pi$$
−0.644136 + 0.764911i $$0.722783\pi$$
$$618$$ 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
$$625$$ −1.00000 −0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 84.8528 3.38330
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −8.00000 −0.315981 −0.157991 0.987441i $$-0.550502\pi$$
−0.157991 + 0.987441i $$0.550502\pi$$
$$642$$ 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
$$652$$ 0 0
$$653$$ −44.0000 −1.72185 −0.860927 0.508729i $$-0.830115\pi$$
−0.860927 + 0.508729i $$0.830115\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 46.6690 1.82073
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ −43.8406 −1.70520 −0.852601 0.522562i $$-0.824976\pi$$
−0.852601 + 0.522562i $$0.824976\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −24.0000 −0.925132 −0.462566 0.886585i $$-0.653071\pi$$
−0.462566 + 0.886585i $$0.653071\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −38.1838 −1.46752 −0.733761 0.679408i $$-0.762237\pi$$
−0.733761 + 0.679408i $$0.762237\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 11.3137 0.432275
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 19.7990 0.754281
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −90.0000 −3.40899
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 52.0000 1.96401 0.982006 0.188847i $$-0.0604752\pi$$
0.982006 + 0.188847i $$0.0604752\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −44.0000 −1.65245 −0.826227 0.563337i $$-0.809517\pi$$
−0.826227 + 0.563337i $$0.809517\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 12.0000 0.445669
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 41.0122 1.51482 0.757410 0.652940i $$-0.226464\pi$$
0.757410 + 0.652940i $$0.226464\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ −19.7990 −0.725379
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −52.0000 −1.88997 −0.944986 0.327111i $$-0.893925\pi$$
−0.944986 + 0.327111i $$0.893925\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 55.1543 1.99934 0.999671 0.0256326i $$-0.00816000\pi$$
0.999671 + 0.0256326i $$0.00816000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 30.0000 1.08465
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −18.3848 −0.662972 −0.331486 0.943460i $$-0.607550\pi$$
−0.331486 + 0.943460i $$0.607550\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −55.1543 −1.98376 −0.991882 0.127164i $$-0.959412\pi$$
−0.991882 + 0.127164i $$0.959412\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 34.0000 1.21351
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −22.0000 −0.781243
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 21.2132 0.751410 0.375705 0.926739i $$-0.377401\pi$$
0.375705 + 0.926739i $$0.377401\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −12.7279 −0.449719
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 10.0000 0.351581 0.175791 0.984428i $$-0.443752\pi$$
0.175791 + 0.984428i $$0.443752\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −50.0000 −1.74501 −0.872506 0.488603i $$-0.837507\pi$$
−0.872506 + 0.488603i $$0.837507\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ −52.3259 −1.81735 −0.908677 0.417500i $$-0.862906\pi$$
−0.908677 + 0.417500i $$0.862906\pi$$
$$830$$ 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
$$841$$ −13.0000 −0.448276
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −15.5563 −0.535155
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 7.07107 0.242109 0.121054 0.992646i $$-0.461372\pi$$
0.121054 + 0.992646i $$0.461372\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −46.6690 −1.59418 −0.797092 0.603858i $$-0.793630\pi$$
−0.797092 + 0.603858i $$0.793630\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 0 0
$$865$$ −30.0000 −1.02003
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ −21.2132 −0.717958
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −12.0000 −0.405211 −0.202606 0.979260i $$-0.564941\pi$$
−0.202606 + 0.979260i $$0.564941\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −57.9828 −1.95349 −0.976744 0.214407i $$-0.931218\pi$$
−0.976744 + 0.214407i $$0.931218\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 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
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 98.9949 3.29800
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −38.0000 −1.26316
$$906$$ 0 0
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 0 0
$$909$$ 38.1838 1.26648
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 36.0000 1.18367
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 4.24264 0.139197 0.0695983 0.997575i $$-0.477828\pi$$
0.0695983 + 0.997575i $$0.477828\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 7.07107 0.231002 0.115501 0.993307i $$-0.463153\pi$$
0.115501 + 0.993307i $$0.463153\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 26.8701 0.875939 0.437969 0.898990i $$-0.355698\pi$$
0.437969 + 0.898990i $$0.355698\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ 22.0000 0.714150
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 26.0000 0.842223 0.421111 0.907009i $$-0.361640\pi$$
0.421111 + 0.907009i $$0.361640\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 19.7990 0.637352
$$966$$ 0 0
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −8.00000 −0.255943 −0.127971 0.991778i $$-0.540847\pi$$
−0.127971 + 0.991778i $$0.540847\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 60.0000 1.91565
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ −2.82843 −0.0901212
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 35.3553 1.11971 0.559857 0.828589i $$-0.310856\pi$$
0.559857 + 0.828589i $$0.310856\pi$$
$$998$$ 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 1568.2.a.o.1.2 yes 2
4.3 odd 2 CM 1568.2.a.o.1.2 yes 2
7.2 even 3 1568.2.i.t.1537.1 4
7.3 odd 6 1568.2.i.t.961.2 4
7.4 even 3 1568.2.i.t.961.1 4
7.5 odd 6 1568.2.i.t.1537.2 4
7.6 odd 2 inner 1568.2.a.o.1.1 2
8.3 odd 2 3136.2.a.bi.1.1 2
8.5 even 2 3136.2.a.bi.1.1 2
28.3 even 6 1568.2.i.t.961.2 4
28.11 odd 6 1568.2.i.t.961.1 4
28.19 even 6 1568.2.i.t.1537.2 4
28.23 odd 6 1568.2.i.t.1537.1 4
28.27 even 2 inner 1568.2.a.o.1.1 2
56.13 odd 2 3136.2.a.bi.1.2 2
56.27 even 2 3136.2.a.bi.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
1568.2.a.o.1.1 2 7.6 odd 2 inner
1568.2.a.o.1.1 2 28.27 even 2 inner
1568.2.a.o.1.2 yes 2 1.1 even 1 trivial
1568.2.a.o.1.2 yes 2 4.3 odd 2 CM
1568.2.i.t.961.1 4 7.4 even 3
1568.2.i.t.961.1 4 28.11 odd 6
1568.2.i.t.961.2 4 7.3 odd 6
1568.2.i.t.961.2 4 28.3 even 6
1568.2.i.t.1537.1 4 7.2 even 3
1568.2.i.t.1537.1 4 28.23 odd 6
1568.2.i.t.1537.2 4 7.5 odd 6
1568.2.i.t.1537.2 4 28.19 even 6
3136.2.a.bi.1.1 2 8.3 odd 2
3136.2.a.bi.1.1 2 8.5 even 2
3136.2.a.bi.1.2 2 56.13 odd 2
3136.2.a.bi.1.2 2 56.27 even 2