# Properties

 Label 1200.2.o.g.1199.2 Level $1200$ Weight $2$ Character 1200.1199 Analytic conductor $9.582$ Analytic rank $0$ Dimension $4$ CM discriminant -3 Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1200.o (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.58204824255$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 1199.2 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1200.1199 Dual form 1200.2.o.g.1199.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.73205 q^{3} +5.19615 q^{7} +3.00000 q^{9} +O(q^{10})$$ $$q-1.73205 q^{3} +5.19615 q^{7} +3.00000 q^{9} +7.00000i q^{13} -5.19615i q^{19} -9.00000 q^{21} -5.19615 q^{27} -1.73205i q^{31} +10.0000i q^{37} -12.1244i q^{39} +1.73205 q^{43} +20.0000 q^{49} +9.00000i q^{57} -1.00000 q^{61} +15.5885 q^{63} +12.1244 q^{67} +10.0000i q^{73} +17.3205i q^{79} +9.00000 q^{81} +36.3731i q^{91} +3.00000i q^{93} -19.0000i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 12q^{9} + O(q^{10})$$ $$4q + 12q^{9} - 36q^{21} + 80q^{49} - 4q^{61} + 36q^{81} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$$.

 $$n$$ $$401$$ $$577$$ $$751$$ $$901$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$ $$1$$

## 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
$$3$$ −1.73205 −1.00000
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 5.19615 1.96396 0.981981 0.188982i $$-0.0605189\pi$$
0.981981 + 0.188982i $$0.0605189\pi$$
$$8$$ 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
$$13$$ 7.00000i 1.94145i 0.240192 + 0.970725i $$0.422790\pi$$
−0.240192 + 0.970725i $$0.577210\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ − 5.19615i − 1.19208i −0.802955 0.596040i $$-0.796740\pi$$
0.802955 0.596040i $$-0.203260\pi$$
$$20$$ 0 0
$$21$$ −9.00000 −1.96396
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −5.19615 −1.00000
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ − 1.73205i − 0.311086i −0.987829 0.155543i $$-0.950287\pi$$
0.987829 0.155543i $$-0.0497126\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 10.0000i 1.64399i 0.569495 + 0.821995i $$0.307139\pi$$
−0.569495 + 0.821995i $$0.692861\pi$$
$$38$$ 0 0
$$39$$ − 12.1244i − 1.94145i
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 1.73205 0.264135 0.132068 0.991241i $$-0.457838\pi$$
0.132068 + 0.991241i $$0.457838\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 20.0000 2.85714
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 9.00000i 1.19208i
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −1.00000 −0.128037 −0.0640184 0.997949i $$-0.520392\pi$$
−0.0640184 + 0.997949i $$0.520392\pi$$
$$62$$ 0 0
$$63$$ 15.5885 1.96396
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 12.1244 1.48123 0.740613 0.671932i $$-0.234535\pi$$
0.740613 + 0.671932i $$0.234535\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 10.0000i 1.17041i 0.810885 + 0.585206i $$0.198986\pi$$
−0.810885 + 0.585206i $$0.801014\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 17.3205i 1.94871i 0.225018 + 0.974355i $$0.427756\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 36.3731i 3.81293i
$$92$$ 0 0
$$93$$ 3.00000i 0.311086i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ − 19.0000i − 1.92916i −0.263795 0.964579i $$-0.584974\pi$$
0.263795 0.964579i $$-0.415026\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 3.46410 0.341328 0.170664 0.985329i $$-0.445409\pi$$
0.170664 + 0.985329i $$0.445409\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 17.0000 1.62830 0.814152 0.580651i $$-0.197202\pi$$
0.814152 + 0.580651i $$0.197202\pi$$
$$110$$ 0 0
$$111$$ − 17.3205i − 1.64399i
$$112$$ 0 0
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 21.0000i 1.94145i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 10.3923 0.922168 0.461084 0.887357i $$-0.347461\pi$$
0.461084 + 0.887357i $$0.347461\pi$$
$$128$$ 0 0
$$129$$ −3.00000 −0.264135
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ − 27.0000i − 2.34120i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 0 0
$$139$$ − 17.3205i − 1.46911i −0.678551 0.734553i $$-0.737392\pi$$
0.678551 0.734553i $$-0.262608\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −34.6410 −2.85714
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ − 15.5885i − 1.26857i −0.773099 0.634285i $$-0.781294\pi$$
0.773099 0.634285i $$-0.218706\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ − 11.0000i − 0.877896i −0.898513 0.438948i $$-0.855351\pi$$
0.898513 0.438948i $$-0.144649\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −19.0526 −1.49231 −0.746156 0.665771i $$-0.768103\pi$$
−0.746156 + 0.665771i $$0.768103\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ −36.0000 −2.76923
$$170$$ 0 0
$$171$$ − 15.5885i − 1.19208i
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 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
$$181$$ 19.0000 1.41226 0.706129 0.708083i $$-0.250440\pi$$
0.706129 + 0.708083i $$0.250440\pi$$
$$182$$ 0 0
$$183$$ 1.73205 0.128037
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −27.0000 −1.96396
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 23.0000i 1.65558i 0.561041 + 0.827788i $$0.310401\pi$$
−0.561041 + 0.827788i $$0.689599\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 22.5167i 1.59616i 0.602549 + 0.798082i $$0.294152\pi$$
−0.602549 + 0.798082i $$0.705848\pi$$
$$200$$ 0 0
$$201$$ −21.0000 −1.48123
$$202$$ 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
$$211$$ − 1.73205i − 0.119239i −0.998221 0.0596196i $$-0.981011\pi$$
0.998221 0.0596196i $$-0.0189888\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ − 9.00000i − 0.610960i
$$218$$ 0 0
$$219$$ − 17.3205i − 1.17041i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −19.0526 −1.27585 −0.637927 0.770097i $$-0.720208\pi$$
−0.637927 + 0.770097i $$0.720208\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ −7.00000 −0.462573 −0.231287 0.972886i $$-0.574293\pi$$
−0.231287 + 0.972886i $$0.574293\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ − 30.0000i − 1.94871i
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 31.0000 1.99689 0.998443 0.0557856i $$-0.0177663\pi$$
0.998443 + 0.0557856i $$0.0177663\pi$$
$$242$$ 0 0
$$243$$ −15.5885 −1.00000
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 36.3731 2.31436
$$248$$ 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
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 51.9615i 3.22873i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ − 17.3205i − 1.05215i −0.850439 0.526073i $$-0.823664\pi$$
0.850439 0.526073i $$-0.176336\pi$$
$$272$$ 0 0
$$273$$ − 63.0000i − 3.81293i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ − 31.0000i − 1.86261i −0.364241 0.931305i $$-0.618672\pi$$
0.364241 0.931305i $$-0.381328\pi$$
$$278$$ 0 0
$$279$$ − 5.19615i − 0.311086i
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ −32.9090 −1.95623 −0.978117 0.208053i $$-0.933287\pi$$
−0.978117 + 0.208053i $$0.933287\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ 32.9090i 1.92916i
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 9.00000 0.518751
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −29.4449 −1.68051 −0.840254 0.542194i $$-0.817594\pi$$
−0.840254 + 0.542194i $$0.817594\pi$$
$$308$$ 0 0
$$309$$ −6.00000 −0.341328
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ − 13.0000i − 0.734803i −0.930062 0.367402i $$-0.880247\pi$$
0.930062 0.367402i $$-0.119753\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −29.4449 −1.62830
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 17.3205i 0.952021i 0.879440 + 0.476011i $$0.157918\pi$$
−0.879440 + 0.476011i $$0.842082\pi$$
$$332$$ 0 0
$$333$$ 30.0000i 1.64399i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 29.0000i 1.57973i 0.613280 + 0.789865i $$0.289850\pi$$
−0.613280 + 0.789865i $$0.710150\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 67.5500 3.64736
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ − 36.3731i − 1.94145i
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −8.00000 −0.421053
$$362$$ 0 0
$$363$$ 19.0526 1.00000
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −22.5167 −1.17536 −0.587680 0.809093i $$-0.699959\pi$$
−0.587680 + 0.809093i $$0.699959\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ − 13.0000i − 0.673114i −0.941663 0.336557i $$-0.890737\pi$$
0.941663 0.336557i $$-0.109263\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ − 12.1244i − 0.622786i −0.950281 0.311393i $$-0.899204\pi$$
0.950281 0.311393i $$-0.100796\pi$$
$$380$$ 0 0
$$381$$ −18.0000 −0.922168
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 5.19615 0.264135
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1.00000i 0.0501886i 0.999685 + 0.0250943i $$0.00798860\pi$$
−0.999685 + 0.0250943i $$0.992011\pi$$
$$398$$ 0 0
$$399$$ 46.7654i 2.34120i
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 12.1244 0.603957
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −7.00000 −0.346128 −0.173064 0.984911i $$-0.555367\pi$$
−0.173064 + 0.984911i $$0.555367\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 30.0000i 1.46911i
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 22.0000 1.07221 0.536107 0.844150i $$-0.319894\pi$$
0.536107 + 0.844150i $$0.319894\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −5.19615 −0.251459
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ − 37.0000i − 1.77811i −0.457804 0.889053i $$-0.651364\pi$$
0.457804 0.889053i $$-0.348636\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ − 39.8372i − 1.90132i −0.310228 0.950662i $$-0.600405\pi$$
0.310228 0.950662i $$-0.399595\pi$$
$$440$$ 0 0
$$441$$ 60.0000 2.85714
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 27.0000i 1.26857i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ − 10.0000i − 0.467780i −0.972263 0.233890i $$-0.924854\pi$$
0.972263 0.233890i $$-0.0751456\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ −38.1051 −1.77090 −0.885448 0.464739i $$-0.846148\pi$$
−0.885448 + 0.464739i $$0.846148\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 63.0000 2.90907
$$470$$ 0 0
$$471$$ 19.0526i 0.877896i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ −70.0000 −3.19173
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 39.8372 1.80519 0.902597 0.430486i $$-0.141658\pi$$
0.902597 + 0.430486i $$0.141658\pi$$
$$488$$ 0 0
$$489$$ 33.0000 1.49231
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ − 12.1244i − 0.542761i −0.962472 0.271380i $$-0.912520\pi$$
0.962472 0.271380i $$-0.0874801\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 62.3538 2.76923
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 51.9615i 2.29864i
$$512$$ 0 0
$$513$$ 27.0000i 1.19208i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 15.5885 0.681636 0.340818 0.940129i $$-0.389296\pi$$
0.340818 + 0.940129i $$0.389296\pi$$
$$524$$ 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
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −29.0000 −1.24681 −0.623404 0.781900i $$-0.714251\pi$$
−0.623404 + 0.781900i $$0.714251\pi$$
$$542$$ 0 0
$$543$$ −32.9090 −1.41226
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −24.2487 −1.03680 −0.518400 0.855138i $$-0.673472\pi$$
−0.518400 + 0.855138i $$0.673472\pi$$
$$548$$ 0 0
$$549$$ −3.00000 −0.128037
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 90.0000i 3.82719i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 12.1244i 0.512806i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 46.7654 1.96396
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ − 36.3731i − 1.52217i −0.648655 0.761083i $$-0.724668\pi$$
0.648655 0.761083i $$-0.275332\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ − 11.0000i − 0.457936i −0.973434 0.228968i $$-0.926465\pi$$
0.973434 0.228968i $$-0.0735351\pi$$
$$578$$ 0 0
$$579$$ − 39.8372i − 1.65558i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ −9.00000 −0.370839
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ − 39.0000i − 1.59616i
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −49.0000 −1.99875 −0.999376 0.0353259i $$-0.988753\pi$$
−0.999376 + 0.0353259i $$0.988753\pi$$
$$602$$ 0 0
$$603$$ 36.3731 1.48123
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −45.0333 −1.82785 −0.913923 0.405887i $$-0.866962\pi$$
−0.913923 + 0.405887i $$0.866962\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ − 10.0000i − 0.403896i −0.979396 0.201948i $$-0.935273\pi$$
0.979396 0.201948i $$-0.0647272\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ − 46.7654i − 1.87966i −0.341644 0.939829i $$-0.610984\pi$$
0.341644 0.939829i $$-0.389016\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ − 50.2295i − 1.99960i −0.0199047 0.999802i $$-0.506336\pi$$
0.0199047 0.999802i $$-0.493664\pi$$
$$632$$ 0 0
$$633$$ 3.00000i 0.119239i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 140.000i 5.54700i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ −31.1769 −1.22950 −0.614749 0.788723i $$-0.710743\pi$$
−0.614749 + 0.788723i $$0.710743\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 15.5885i 0.610960i
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 30.0000i 1.17041i
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 38.0000 1.47803 0.739014 0.673690i $$-0.235292\pi$$
0.739014 + 0.673690i $$0.235292\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 33.0000 1.27585
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 50.0000i 1.92736i 0.267063 + 0.963679i $$0.413947\pi$$
−0.267063 + 0.963679i $$0.586053\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ − 98.7269i − 3.78879i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 12.1244 0.462573
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ − 51.9615i − 1.97671i −0.152167 0.988355i $$-0.548625\pi$$
0.152167 0.988355i $$-0.451375\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 51.9615 1.95977
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 53.0000 1.99046 0.995228 0.0975728i $$-0.0311079\pi$$
0.995228 + 0.0975728i $$0.0311079\pi$$
$$710$$ 0 0
$$711$$ 51.9615i 1.94871i
$$712$$ 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
$$721$$ 18.0000 0.670355
$$722$$ 0 0
$$723$$ −53.6936 −1.99689
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −22.5167 −0.835097 −0.417548 0.908655i $$-0.637111\pi$$
−0.417548 + 0.908655i $$0.637111\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ − 50.0000i − 1.84679i −0.383849 0.923396i $$-0.625402\pi$$
0.383849 0.923396i $$-0.374598\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 51.9615i 1.91144i 0.294285 + 0.955718i $$0.404919\pi$$
−0.294285 + 0.955718i $$0.595081\pi$$
$$740$$ 0 0
$$741$$ −63.0000 −2.31436
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ − 17.3205i − 0.632034i −0.948753 0.316017i $$-0.897654\pi$$
0.948753 0.316017i $$-0.102346\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 29.0000i 1.05402i 0.849858 + 0.527011i $$0.176688\pi$$
−0.849858 + 0.527011i $$0.823312\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 88.3346 3.19793
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −47.0000 −1.69486 −0.847432 0.530904i $$-0.821852\pi$$
−0.847432 + 0.530904i $$0.821852\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ − 90.0000i − 3.22873i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 46.7654 1.66701 0.833503 0.552515i $$-0.186332\pi$$
0.833503 + 0.552515i $$0.186332\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ − 7.00000i − 0.248577i
$$794$$ 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
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ 53.6936i 1.88544i 0.333590 + 0.942718i $$0.391740\pi$$
−0.333590 + 0.942718i $$0.608260\pi$$
$$812$$ 0 0
$$813$$ 30.0000i 1.05215i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ − 9.00000i − 0.314870i
$$818$$ 0 0
$$819$$ 109.119i 3.81293i
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ −32.9090 −1.14713 −0.573567 0.819159i $$-0.694441\pi$$
−0.573567 + 0.819159i $$0.694441\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ −46.0000 −1.59765 −0.798823 0.601566i $$-0.794544\pi$$
−0.798823 + 0.601566i $$0.794544\pi$$
$$830$$ 0 0
$$831$$ 53.6936i 1.86261i
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 9.00000i 0.311086i
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 29.0000 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −57.1577 −1.96396
$$848$$ 0 0
$$849$$ 57.0000 1.95623
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 23.0000i 0.787505i 0.919216 + 0.393753i $$0.128823\pi$$
−0.919216 + 0.393753i $$0.871177\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ − 17.3205i − 0.590968i −0.955348 0.295484i $$-0.904519\pi$$
0.955348 0.295484i $$-0.0954809\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 29.4449 1.00000
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 84.8705i 2.87573i
$$872$$ 0 0
$$873$$ − 57.0000i − 1.92916i
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ − 59.0000i − 1.99229i −0.0877308 0.996144i $$-0.527962\pi$$
0.0877308 0.996144i $$-0.472038\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ 36.3731 1.22405 0.612026 0.790838i $$-0.290355\pi$$
0.612026 + 0.790838i $$0.290355\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ 54.0000 1.81110
$$890$$ 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
$$901$$ 0 0
$$902$$ 0 0
$$903$$ −15.5885 −0.518751
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 45.0333 1.49531 0.747653 0.664089i $$-0.231180\pi$$
0.747653 + 0.664089i $$0.231180\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 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
$$919$$ 29.4449i 0.971296i 0.874154 + 0.485648i $$0.161416\pi$$
−0.874154 + 0.485648i $$0.838584\pi$$
$$920$$ 0 0
$$921$$ 51.0000 1.68051
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 10.3923 0.341328
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ − 103.923i − 3.40594i
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 61.0000i 1.99278i 0.0848755 + 0.996392i $$0.472951\pi$$
−0.0848755 + 0.996392i $$0.527049\pi$$
$$938$$ 0 0
$$939$$ 22.5167i 0.734803i
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ −70.0000 −2.27230
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 28.0000 0.903226
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −58.8897 −1.89377 −0.946883 0.321578i $$-0.895787\pi$$
−0.946883 + 0.321578i $$0.895787\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ − 90.0000i − 2.88527i
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 51.0000 1.62830
$$982$$ 0 0
$$983$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ − 15.5885i − 0.495184i −0.968864 0.247592i $$-0.920361\pi$$
0.968864 0.247592i $$-0.0796392\pi$$
$$992$$ 0 0
$$993$$ − 30.0000i − 0.952021i
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 10.0000i 0.316703i 0.987383 + 0.158352i $$0.0506179\pi$$
−0.987383 + 0.158352i $$0.949382\pi$$
$$998$$ 0 0
$$999$$ − 51.9615i − 1.64399i
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 1200.2.o.g.1199.2 4
3.2 odd 2 CM 1200.2.o.g.1199.2 4
4.3 odd 2 inner 1200.2.o.g.1199.4 4
5.2 odd 4 1200.2.h.g.1151.2 yes 2
5.3 odd 4 1200.2.h.c.1151.1 2
5.4 even 2 inner 1200.2.o.g.1199.3 4
12.11 even 2 inner 1200.2.o.g.1199.4 4
15.2 even 4 1200.2.h.g.1151.2 yes 2
15.8 even 4 1200.2.h.c.1151.1 2
15.14 odd 2 inner 1200.2.o.g.1199.3 4
20.3 even 4 1200.2.h.c.1151.2 yes 2
20.7 even 4 1200.2.h.g.1151.1 yes 2
20.19 odd 2 inner 1200.2.o.g.1199.1 4
60.23 odd 4 1200.2.h.c.1151.2 yes 2
60.47 odd 4 1200.2.h.g.1151.1 yes 2
60.59 even 2 inner 1200.2.o.g.1199.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
1200.2.h.c.1151.1 2 5.3 odd 4
1200.2.h.c.1151.1 2 15.8 even 4
1200.2.h.c.1151.2 yes 2 20.3 even 4
1200.2.h.c.1151.2 yes 2 60.23 odd 4
1200.2.h.g.1151.1 yes 2 20.7 even 4
1200.2.h.g.1151.1 yes 2 60.47 odd 4
1200.2.h.g.1151.2 yes 2 5.2 odd 4
1200.2.h.g.1151.2 yes 2 15.2 even 4
1200.2.o.g.1199.1 4 20.19 odd 2 inner
1200.2.o.g.1199.1 4 60.59 even 2 inner
1200.2.o.g.1199.2 4 1.1 even 1 trivial
1200.2.o.g.1199.2 4 3.2 odd 2 CM
1200.2.o.g.1199.3 4 5.4 even 2 inner
1200.2.o.g.1199.3 4 15.14 odd 2 inner
1200.2.o.g.1199.4 4 4.3 odd 2 inner
1200.2.o.g.1199.4 4 12.11 even 2 inner