# Properties

 Label 1200.3.l.l.401.1 Level $1200$ Weight $3$ Character 1200.401 Analytic conductor $32.698$ Analytic rank $0$ Dimension $2$ CM discriminant -15 Inner twists $4$

# Related objects

## Newspace parameters

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

## Newform invariants

 Self dual: no Analytic conductor: $$32.6976317232$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{17}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 15) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 401.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1200.401 Dual form 1200.3.l.l.401.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.00000i q^{3} -9.00000 q^{9} +O(q^{10})$$ $$q-3.00000i q^{3} -9.00000 q^{9} -14.0000i q^{17} -22.0000 q^{19} +34.0000i q^{23} +27.0000i q^{27} -2.00000 q^{31} +14.0000i q^{47} -49.0000 q^{49} -42.0000 q^{51} +86.0000i q^{53} +66.0000i q^{57} -118.000 q^{61} +102.000 q^{69} +98.0000 q^{79} +81.0000 q^{81} +154.000i q^{83} +6.00000i q^{93} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 18 q^{9}+O(q^{10})$$ 2 * q - 18 * q^9 $$2 q - 18 q^{9} - 44 q^{19} - 4 q^{31} - 98 q^{49} - 84 q^{51} - 236 q^{61} + 204 q^{69} + 196 q^{79} + 162 q^{81}+O(q^{100})$$ 2 * q - 18 * q^9 - 44 * q^19 - 4 * q^31 - 98 * q^49 - 84 * q^51 - 236 * q^61 + 204 * q^69 + 196 * q^79 + 162 * q^81

## 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
$$3$$ − 3.00000i − 1.00000i
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 0 0
$$9$$ −9.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ − 14.0000i − 0.823529i −0.911290 0.411765i $$-0.864913\pi$$
0.911290 0.411765i $$-0.135087\pi$$
$$18$$ 0 0
$$19$$ −22.0000 −1.15789 −0.578947 0.815365i $$-0.696536\pi$$
−0.578947 + 0.815365i $$0.696536\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 34.0000i 1.47826i 0.673562 + 0.739130i $$0.264763\pi$$
−0.673562 + 0.739130i $$0.735237\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 27.0000i 1.00000i
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.0645161 −0.0322581 0.999480i $$-0.510270\pi$$
−0.0322581 + 0.999480i $$0.510270\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 14.0000i 0.297872i 0.988847 + 0.148936i $$0.0475849\pi$$
−0.988847 + 0.148936i $$0.952415\pi$$
$$48$$ 0 0
$$49$$ −49.0000 −1.00000
$$50$$ 0 0
$$51$$ −42.0000 −0.823529
$$52$$ 0 0
$$53$$ 86.0000i 1.62264i 0.584601 + 0.811321i $$0.301251\pi$$
−0.584601 + 0.811321i $$0.698749\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 66.0000i 1.15789i
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ −118.000 −1.93443 −0.967213 0.253966i $$-0.918265\pi$$
−0.967213 + 0.253966i $$0.918265\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0 0
$$69$$ 102.000 1.47826
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 98.0000 1.24051 0.620253 0.784402i $$-0.287030\pi$$
0.620253 + 0.784402i $$0.287030\pi$$
$$80$$ 0 0
$$81$$ 81.0000 1.00000
$$82$$ 0 0
$$83$$ 154.000i 1.85542i 0.373300 + 0.927711i $$0.378226\pi$$
−0.373300 + 0.927711i $$0.621774\pi$$
$$84$$ 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
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 6.00000i 0.0645161i
$$94$$ 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
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ − 106.000i − 0.990654i −0.868707 0.495327i $$-0.835048\pi$$
0.868707 0.495327i $$-0.164952\pi$$
$$108$$ 0 0
$$109$$ 22.0000 0.201835 0.100917 0.994895i $$-0.467822\pi$$
0.100917 + 0.994895i $$0.467822\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 206.000i 1.82301i 0.411290 + 0.911504i $$0.365078\pi$$
−0.411290 + 0.911504i $$0.634922\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 121.000 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 226.000i 1.64964i 0.565399 + 0.824818i $$0.308722\pi$$
−0.565399 + 0.824818i $$0.691278\pi$$
$$138$$ 0 0
$$139$$ −262.000 −1.88489 −0.942446 0.334358i $$-0.891480\pi$$
−0.942446 + 0.334358i $$0.891480\pi$$
$$140$$ 0 0
$$141$$ 42.0000 0.297872
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 147.000i 1.00000i
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 238.000 1.57616 0.788079 0.615574i $$-0.211076\pi$$
0.788079 + 0.615574i $$0.211076\pi$$
$$152$$ 0 0
$$153$$ 126.000i 0.823529i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0 0
$$159$$ 258.000 1.62264
$$160$$ 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
$$167$$ 254.000i 1.52096i 0.649362 + 0.760479i $$0.275036\pi$$
−0.649362 + 0.760479i $$0.724964\pi$$
$$168$$ 0 0
$$169$$ −169.000 −1.00000
$$170$$ 0 0
$$171$$ 198.000 1.15789
$$172$$ 0 0
$$173$$ − 154.000i − 0.890173i −0.895487 0.445087i $$-0.853173\pi$$
0.895487 0.445087i $$-0.146827\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 122.000 0.674033 0.337017 0.941499i $$-0.390582\pi$$
0.337017 + 0.941499i $$0.390582\pi$$
$$182$$ 0 0
$$183$$ 354.000i 1.93443i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ − 374.000i − 1.89848i −0.314557 0.949239i $$-0.601856\pi$$
0.314557 0.949239i $$-0.398144\pi$$
$$198$$ 0 0
$$199$$ −142.000 −0.713568 −0.356784 0.934187i $$-0.616127\pi$$
−0.356784 + 0.934187i $$0.616127\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ − 306.000i − 1.47826i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −362.000 −1.71564 −0.857820 0.513950i $$-0.828182\pi$$
−0.857820 + 0.513950i $$0.828182\pi$$
$$212$$ 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
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 134.000i 0.590308i 0.955450 + 0.295154i $$0.0953710\pi$$
−0.955450 + 0.295154i $$0.904629\pi$$
$$228$$ 0 0
$$229$$ −218.000 −0.951965 −0.475983 0.879455i $$-0.657907\pi$$
−0.475983 + 0.879455i $$0.657907\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ − 34.0000i − 0.145923i −0.997335 0.0729614i $$-0.976755\pi$$
0.997335 0.0729614i $$-0.0232450\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ − 294.000i − 1.24051i
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −478.000 −1.98340 −0.991701 0.128564i $$-0.958963\pi$$
−0.991701 + 0.128564i $$0.958963\pi$$
$$242$$ 0 0
$$243$$ − 243.000i − 1.00000i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 462.000 1.85542
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 466.000i 1.81323i 0.421959 + 0.906615i $$0.361343\pi$$
−0.421959 + 0.906615i $$0.638657\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ − 446.000i − 1.69582i −0.530142 0.847909i $$-0.677861\pi$$
0.530142 0.847909i $$-0.322139\pi$$
$$264$$ 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
$$271$$ −482.000 −1.77860 −0.889299 0.457326i $$-0.848807\pi$$
−0.889299 + 0.457326i $$0.848807\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ 0 0
$$279$$ 18.0000 0.0645161
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 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
$$289$$ 93.0000 0.321799
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ − 394.000i − 1.34471i −0.740229 0.672355i $$-0.765283\pi$$
0.740229 0.672355i $$-0.234717\pi$$
$$294$$ 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
$$305$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ − 134.000i − 0.422713i −0.977409 0.211356i $$-0.932212\pi$$
0.977409 0.211356i $$-0.0677881\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −318.000 −0.990654
$$322$$ 0 0
$$323$$ 308.000i 0.953560i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ − 66.0000i − 0.201835i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −122.000 −0.368580 −0.184290 0.982872i $$-0.558999\pi$$
−0.184290 + 0.982872i $$0.558999\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ 0 0
$$339$$ 618.000 1.82301
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ − 586.000i − 1.68876i −0.535744 0.844380i $$-0.679969\pi$$
0.535744 0.844380i $$-0.320031\pi$$
$$348$$ 0 0
$$349$$ −458.000 −1.31232 −0.656160 0.754621i $$-0.727821\pi$$
−0.656160 + 0.754621i $$0.727821\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ − 274.000i − 0.776204i −0.921616 0.388102i $$-0.873131\pi$$
0.921616 0.388102i $$-0.126869\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 123.000 0.340720
$$362$$ 0 0
$$363$$ − 363.000i − 1.00000i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −742.000 −1.95778 −0.978892 0.204379i $$-0.934482\pi$$
−0.978892 + 0.204379i $$0.934482\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ − 686.000i − 1.79112i −0.444938 0.895561i $$-0.646774\pi$$
0.444938 0.895561i $$-0.353226\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 476.000 1.21739
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 142.000 0.347188 0.173594 0.984817i $$-0.444462\pi$$
0.173594 + 0.984817i $$0.444462\pi$$
$$410$$ 0 0
$$411$$ 678.000 1.64964
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 786.000i 1.88489i
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 602.000 1.42993 0.714964 0.699161i $$-0.246443\pi$$
0.714964 + 0.699161i $$0.246443\pi$$
$$422$$ 0 0
$$423$$ − 126.000i − 0.297872i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ − 748.000i − 1.71167i
$$438$$ 0 0
$$439$$ −622.000 −1.41686 −0.708428 0.705783i $$-0.750595\pi$$
−0.708428 + 0.705783i $$0.750595\pi$$
$$440$$ 0 0
$$441$$ 441.000 1.00000
$$442$$ 0 0
$$443$$ − 566.000i − 1.27765i −0.769351 0.638826i $$-0.779420\pi$$
0.769351 0.638826i $$-0.220580\pi$$
$$444$$ 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
$$453$$ − 714.000i − 1.57616i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ 0 0
$$459$$ 378.000 0.823529
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ − 346.000i − 0.740899i −0.928853 0.370450i $$-0.879204\pi$$
0.928853 0.370450i $$-0.120796\pi$$
$$468$$ 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
$$477$$ − 774.000i − 1.62264i
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 938.000 1.87976 0.939880 0.341506i $$-0.110937\pi$$
0.939880 + 0.341506i $$0.110937\pi$$
$$500$$ 0 0
$$501$$ 762.000 1.52096
$$502$$ 0 0
$$503$$ 994.000i 1.97614i 0.153995 + 0.988072i $$0.450786\pi$$
−0.153995 + 0.988072i $$0.549214\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 507.000i 1.00000i
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ − 594.000i − 1.15789i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −462.000 −0.890173
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 28.0000i 0.0531309i
$$528$$ 0 0
$$529$$ −627.000 −1.18526
$$530$$ 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
$$541$$ −1078.00 −1.99261 −0.996303 0.0859072i $$-0.972621\pi$$
−0.996303 + 0.0859072i $$0.972621\pi$$
$$542$$ 0 0
$$543$$ − 366.000i − 0.674033i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 0 0
$$549$$ 1062.00 1.93443
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ − 614.000i − 1.10233i −0.834395 0.551167i $$-0.814183\pi$$
0.834395 0.551167i $$-0.185817\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 154.000i 0.273535i 0.990603 + 0.136767i $$0.0436713\pi$$
−0.990603 + 0.136767i $$0.956329\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 358.000 0.626970 0.313485 0.949593i $$-0.398503\pi$$
0.313485 + 0.949593i $$0.398503\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 854.000i 1.45486i 0.686184 + 0.727428i $$0.259284\pi$$
−0.686184 + 0.727428i $$0.740716\pi$$
$$588$$ 0 0
$$589$$ 44.0000 0.0747029
$$590$$ 0 0
$$591$$ −1122.00 −1.89848
$$592$$ 0 0
$$593$$ 1166.00i 1.96627i 0.182873 + 0.983137i $$0.441460\pi$$
−0.182873 + 0.983137i $$0.558540\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 426.000i 0.713568i
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 242.000 0.402662 0.201331 0.979523i $$-0.435473\pi$$
0.201331 + 0.979523i $$0.435473\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 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
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1186.00i 1.92220i 0.276193 + 0.961102i $$0.410927\pi$$
−0.276193 + 0.961102i $$0.589073\pi$$
$$618$$ 0 0
$$619$$ 698.000 1.12763 0.563813 0.825903i $$-0.309334\pi$$
0.563813 + 0.825903i $$0.309334\pi$$
$$620$$ 0 0
$$621$$ −918.000 −1.47826
$$622$$ 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
$$631$$ 238.000 0.377179 0.188590 0.982056i $$-0.439608\pi$$
0.188590 + 0.982056i $$0.439608\pi$$
$$632$$ 0 0
$$633$$ 1086.00i 1.71564i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ − 706.000i − 1.09119i −0.838049 0.545595i $$-0.816304\pi$$
0.838049 0.545595i $$-0.183696\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ − 1114.00i − 1.70597i −0.521933 0.852986i $$-0.674789\pi$$
0.521933 0.852986i $$-0.325211\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ −838.000 −1.26778 −0.633888 0.773425i $$-0.718542\pi$$
−0.633888 + 0.773425i $$0.718542\pi$$
$$662$$ 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
$$673$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ − 374.000i − 0.552437i −0.961095 0.276219i $$-0.910919\pi$$
0.961095 0.276219i $$-0.0890814\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 402.000 0.590308
$$682$$ 0 0
$$683$$ − 86.0000i − 0.125915i −0.998016 0.0629575i $$-0.979947\pi$$
0.998016 0.0629575i $$-0.0200533\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 654.000i 0.951965i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −1322.00 −1.91317 −0.956585 0.291455i $$-0.905861\pi$$
−0.956585 + 0.291455i $$0.905861\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ −102.000 −0.145923
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 742.000 1.04654 0.523272 0.852166i $$-0.324711\pi$$
0.523272 + 0.852166i $$0.324711\pi$$
$$710$$ 0 0
$$711$$ −882.000 −1.24051
$$712$$ 0 0
$$713$$ − 68.0000i − 0.0953717i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 1434.00i 1.98340i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ −729.000 −1.00000
$$730$$ 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
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −1462.00 −1.97835 −0.989175 0.146744i $$-0.953121\pi$$
−0.989175 + 0.146744i $$0.953121\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 514.000i 0.691790i 0.938273 + 0.345895i $$0.112425\pi$$
−0.938273 + 0.345895i $$0.887575\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ − 1386.00i − 1.85542i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 1438.00 1.91478 0.957390 0.288798i $$-0.0932555\pi$$
0.957390 + 0.288798i $$0.0932555\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −578.000 −0.751625 −0.375813 0.926696i $$-0.622636\pi$$
−0.375813 + 0.926696i $$0.622636\pi$$
$$770$$ 0 0
$$771$$ 1398.00 1.81323
$$772$$ 0 0
$$773$$ 1526.00i 1.97413i 0.160330 + 0.987063i $$0.448744\pi$$
−0.160330 + 0.987063i $$0.551256\pi$$
$$774$$ 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
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 0 0
$$789$$ −1338.00 −1.69582
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 826.000i 1.03639i 0.855264 + 0.518193i $$0.173395\pi$$
−0.855264 + 0.518193i $$0.826605\pi$$
$$798$$ 0 0
$$799$$ 196.000 0.245307
$$800$$ 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
$$811$$ −1082.00 −1.33416 −0.667078 0.744988i $$-0.732455\pi$$
−0.667078 + 0.744988i $$0.732455\pi$$
$$812$$ 0 0
$$813$$ 1446.00i 1.77860i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 374.000i 0.452237i 0.974100 + 0.226119i $$0.0726037\pi$$
−0.974100 + 0.226119i $$0.927396\pi$$
$$828$$ 0 0
$$829$$ 502.000 0.605549 0.302774 0.953062i $$-0.402087\pi$$
0.302774 + 0.953062i $$0.402087\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 686.000i 0.823529i
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ − 54.0000i − 0.0645161i
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 841.000 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 1666.00i 1.94399i 0.235000 + 0.971995i $$0.424491\pi$$
−0.235000 + 0.971995i $$0.575509\pi$$
$$858$$ 0 0
$$859$$ 218.000 0.253783 0.126892 0.991917i $$-0.459500\pi$$
0.126892 + 0.991917i $$0.459500\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 274.000i 0.317497i 0.987319 + 0.158749i $$0.0507459\pi$$
−0.987319 + 0.158749i $$0.949254\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ − 279.000i − 0.321799i
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$878$$ 0 0
$$879$$ −1182.00 −1.34471
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1694.00i 1.90981i 0.296914 + 0.954904i $$0.404042\pi$$
−0.296914 + 0.954904i $$0.595958\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ − 308.000i − 0.344905i
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 1204.00 1.33629
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 1298.00 1.41240 0.706202 0.708010i $$-0.250407\pi$$
0.706202 + 0.708010i $$0.250407\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ 1078.00 1.15789
$$932$$ 0 0
$$933$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 1574.00i 1.66209i 0.556205 + 0.831045i $$0.312257\pi$$
−0.556205 + 0.831045i $$0.687743\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ −402.000 −0.422713
$$952$$ 0 0
$$953$$ − 1474.00i − 1.54669i −0.633983 0.773347i $$-0.718581\pi$$
0.633983 0.773347i $$-0.281419\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −957.000 −0.995838
$$962$$ 0 0
$$963$$ 954.000i 0.990654i
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ 0 0
$$969$$ 924.000 0.953560
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ − 1934.00i − 1.97953i −0.142710 0.989765i $$-0.545582\pi$$
0.142710 0.989765i $$-0.454418\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −198.000 −0.201835
$$982$$ 0 0
$$983$$ 1954.00i 1.98779i 0.110319 + 0.993896i $$0.464813\pi$$
−0.110319 + 0.993896i $$0.535187\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 958.000 0.966700 0.483350 0.875427i $$-0.339420\pi$$
0.483350 + 0.875427i $$0.339420\pi$$
$$992$$ 0 0
$$993$$ 366.000i 0.368580i
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 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 1200.3.l.l.401.1 2
3.2 odd 2 inner 1200.3.l.l.401.2 2
4.3 odd 2 75.3.c.d.26.2 2
5.2 odd 4 240.3.c.a.209.1 1
5.3 odd 4 240.3.c.b.209.1 1
5.4 even 2 inner 1200.3.l.l.401.2 2
12.11 even 2 75.3.c.d.26.1 2
15.2 even 4 240.3.c.b.209.1 1
15.8 even 4 240.3.c.a.209.1 1
15.14 odd 2 CM 1200.3.l.l.401.1 2
20.3 even 4 15.3.d.b.14.1 yes 1
20.7 even 4 15.3.d.a.14.1 1
20.19 odd 2 75.3.c.d.26.1 2
40.3 even 4 960.3.c.c.449.1 1
40.13 odd 4 960.3.c.a.449.1 1
40.27 even 4 960.3.c.b.449.1 1
40.37 odd 4 960.3.c.d.449.1 1
60.23 odd 4 15.3.d.a.14.1 1
60.47 odd 4 15.3.d.b.14.1 yes 1
60.59 even 2 75.3.c.d.26.2 2
120.53 even 4 960.3.c.d.449.1 1
120.77 even 4 960.3.c.a.449.1 1
120.83 odd 4 960.3.c.b.449.1 1
120.107 odd 4 960.3.c.c.449.1 1
180.7 even 12 405.3.h.b.134.1 2
180.23 odd 12 405.3.h.b.269.1 2
180.43 even 12 405.3.h.a.134.1 2
180.47 odd 12 405.3.h.a.134.1 2
180.67 even 12 405.3.h.b.269.1 2
180.83 odd 12 405.3.h.b.134.1 2
180.103 even 12 405.3.h.a.269.1 2
180.167 odd 12 405.3.h.a.269.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
15.3.d.a.14.1 1 20.7 even 4
15.3.d.a.14.1 1 60.23 odd 4
15.3.d.b.14.1 yes 1 20.3 even 4
15.3.d.b.14.1 yes 1 60.47 odd 4
75.3.c.d.26.1 2 12.11 even 2
75.3.c.d.26.1 2 20.19 odd 2
75.3.c.d.26.2 2 4.3 odd 2
75.3.c.d.26.2 2 60.59 even 2
240.3.c.a.209.1 1 5.2 odd 4
240.3.c.a.209.1 1 15.8 even 4
240.3.c.b.209.1 1 5.3 odd 4
240.3.c.b.209.1 1 15.2 even 4
405.3.h.a.134.1 2 180.43 even 12
405.3.h.a.134.1 2 180.47 odd 12
405.3.h.a.269.1 2 180.103 even 12
405.3.h.a.269.1 2 180.167 odd 12
405.3.h.b.134.1 2 180.7 even 12
405.3.h.b.134.1 2 180.83 odd 12
405.3.h.b.269.1 2 180.23 odd 12
405.3.h.b.269.1 2 180.67 even 12
960.3.c.a.449.1 1 40.13 odd 4
960.3.c.a.449.1 1 120.77 even 4
960.3.c.b.449.1 1 40.27 even 4
960.3.c.b.449.1 1 120.83 odd 4
960.3.c.c.449.1 1 40.3 even 4
960.3.c.c.449.1 1 120.107 odd 4
960.3.c.d.449.1 1 40.37 odd 4
960.3.c.d.449.1 1 120.53 even 4
1200.3.l.l.401.1 2 1.1 even 1 trivial
1200.3.l.l.401.1 2 15.14 odd 2 CM
1200.3.l.l.401.2 2 3.2 odd 2 inner
1200.3.l.l.401.2 2 5.4 even 2 inner