# Properties

 Label 475.3.d.a.474.2 Level $475$ Weight $3$ Character 475.474 Analytic conductor $12.943$ Analytic rank $0$ Dimension $2$ CM discriminant -19 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 475.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.9428125571$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$5$$ Twist minimal: no (minimal twist has level 19) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 474.2 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 475.474 Dual form 475.3.d.a.474.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-4.00000 q^{4} +5.00000i q^{7} -9.00000 q^{9} +O(q^{10})$$ $$q-4.00000 q^{4} +5.00000i q^{7} -9.00000 q^{9} +3.00000 q^{11} +16.0000 q^{16} -15.0000i q^{17} +19.0000 q^{19} -30.0000i q^{23} -20.0000i q^{28} +36.0000 q^{36} -85.0000i q^{43} -12.0000 q^{44} -75.0000i q^{47} +24.0000 q^{49} +103.000 q^{61} -45.0000i q^{63} -64.0000 q^{64} +60.0000i q^{68} -25.0000i q^{73} -76.0000 q^{76} +15.0000i q^{77} +81.0000 q^{81} +90.0000i q^{83} +120.000i q^{92} -27.0000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 8 q^{4} - 18 q^{9} + O(q^{10})$$ $$2 q - 8 q^{4} - 18 q^{9} + 6 q^{11} + 32 q^{16} + 38 q^{19} + 72 q^{36} - 24 q^{44} + 48 q^{49} + 206 q^{61} - 128 q^{64} - 152 q^{76} + 162 q^{81} - 54 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$3$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$4$$ −4.00000 −1.00000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 5.00000i 0.714286i 0.934050 + 0.357143i $$0.116249\pi$$
−0.934050 + 0.357143i $$0.883751\pi$$
$$8$$ 0 0
$$9$$ −9.00000 −1.00000
$$10$$ 0 0
$$11$$ 3.00000 0.272727 0.136364 0.990659i $$-0.456458\pi$$
0.136364 + 0.990659i $$0.456458\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 16.0000 1.00000
$$17$$ − 15.0000i − 0.882353i −0.897420 0.441176i $$-0.854561\pi$$
0.897420 0.441176i $$-0.145439\pi$$
$$18$$ 0 0
$$19$$ 19.0000 1.00000
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ − 30.0000i − 1.30435i −0.758069 0.652174i $$-0.773857\pi$$
0.758069 0.652174i $$-0.226143\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ − 20.0000i − 0.714286i
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 36.0000 1.00000
$$37$$ 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
$$43$$ − 85.0000i − 1.97674i −0.152055 0.988372i $$-0.548589\pi$$
0.152055 0.988372i $$-0.451411\pi$$
$$44$$ −12.0000 −0.272727
$$45$$ 0 0
$$46$$ 0 0
$$47$$ − 75.0000i − 1.59574i −0.602826 0.797872i $$-0.705959\pi$$
0.602826 0.797872i $$-0.294041\pi$$
$$48$$ 0 0
$$49$$ 24.0000 0.489796
$$50$$ 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
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 103.000 1.68852 0.844262 0.535930i $$-0.180039\pi$$
0.844262 + 0.535930i $$0.180039\pi$$
$$62$$ 0 0
$$63$$ − 45.0000i − 0.714286i
$$64$$ −64.0000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 60.0000i 0.882353i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ − 25.0000i − 0.342466i −0.985231 0.171233i $$-0.945225\pi$$
0.985231 0.171233i $$-0.0547750\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ −76.0000 −1.00000
$$77$$ 15.0000i 0.194805i
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ 81.0000 1.00000
$$82$$ 0 0
$$83$$ 90.0000i 1.08434i 0.840270 + 0.542169i $$0.182397\pi$$
−0.840270 + 0.542169i $$0.817603\pi$$
$$84$$ 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
$$92$$ 120.000i 1.30435i
$$93$$ 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
$$99$$ −27.0000 −0.272727
$$100$$ 0 0
$$101$$ −102.000 −1.00990 −0.504950 0.863148i $$-0.668489\pi$$
−0.504950 + 0.863148i $$0.668489\pi$$
$$102$$ 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
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 80.0000i 0.714286i
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 75.0000 0.630252
$$120$$ 0 0
$$121$$ −112.000 −0.925620
$$122$$ 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
$$131$$ −213.000 −1.62595 −0.812977 0.582296i $$-0.802155\pi$$
−0.812977 + 0.582296i $$0.802155\pi$$
$$132$$ 0 0
$$133$$ 95.0000i 0.714286i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ − 255.000i − 1.86131i −0.365893 0.930657i $$-0.619236\pi$$
0.365893 0.930657i $$-0.380764\pi$$
$$138$$ 0 0
$$139$$ 197.000 1.41727 0.708633 0.705577i $$-0.249312\pi$$
0.708633 + 0.705577i $$0.249312\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −144.000 −1.00000
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 177.000 1.18792 0.593960 0.804495i $$-0.297564\pi$$
0.593960 + 0.804495i $$0.297564\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 135.000i 0.882353i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ − 10.0000i − 0.0636943i −0.999493 0.0318471i $$-0.989861\pi$$
0.999493 0.0318471i $$-0.0101390\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 150.000 0.931677
$$162$$ 0 0
$$163$$ 250.000i 1.53374i 0.641801 + 0.766871i $$0.278187\pi$$
−0.641801 + 0.766871i $$0.721813\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −169.000 −1.00000
$$170$$ 0 0
$$171$$ −171.000 −1.00000
$$172$$ 340.000i 1.97674i
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 48.0000 0.272727
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ − 45.0000i − 0.240642i
$$188$$ 300.000i 1.59574i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −93.0000 −0.486911 −0.243455 0.969912i $$-0.578281\pi$$
−0.243455 + 0.969912i $$0.578281\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −96.0000 −0.489796
$$197$$ − 90.0000i − 0.456853i −0.973561 0.228426i $$-0.926642\pi$$
0.973561 0.228426i $$-0.0733580\pi$$
$$198$$ 0 0
$$199$$ −227.000 −1.14070 −0.570352 0.821401i $$-0.693193\pi$$
−0.570352 + 0.821401i $$0.693193\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 270.000i 1.30435i
$$208$$ 0 0
$$209$$ 57.0000 0.272727
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 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
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 17.0000 0.0742358 0.0371179 0.999311i $$-0.488182\pi$$
0.0371179 + 0.999311i $$0.488182\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ − 465.000i − 1.99571i −0.0654770 0.997854i $$-0.520857\pi$$
0.0654770 0.997854i $$-0.479143\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 453.000 1.89540 0.947699 0.319166i $$-0.103403\pi$$
0.947699 + 0.319166i $$0.103403\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ −412.000 −1.68852
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 27.0000 0.107570 0.0537849 0.998553i $$-0.482871\pi$$
0.0537849 + 0.998553i $$0.482871\pi$$
$$252$$ 180.000i 0.714286i
$$253$$ − 90.0000i − 0.355731i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 256.000 1.00000
$$257$$ 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
$$263$$ − 405.000i − 1.53992i −0.638090 0.769962i $$-0.720275\pi$$
0.638090 0.769962i $$-0.279725\pi$$
$$264$$ 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
$$271$$ −142.000 −0.523985 −0.261993 0.965070i $$-0.584380\pi$$
−0.261993 + 0.965070i $$0.584380\pi$$
$$272$$ − 240.000i − 0.882353i
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ − 535.000i − 1.93141i −0.259646 0.965704i $$-0.583606\pi$$
0.259646 0.965704i $$-0.416394\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 395.000i 1.39576i 0.716215 + 0.697880i $$0.245873\pi$$
−0.716215 + 0.697880i $$0.754127\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 64.0000 0.221453
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 100.000i 0.342466i
$$293$$ 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
$$301$$ 425.000 1.41196
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 304.000 1.00000
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ − 60.0000i − 0.194805i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 603.000 1.93891 0.969453 0.245276i $$-0.0788785\pi$$
0.969453 + 0.245276i $$0.0788785\pi$$
$$312$$ 0 0
$$313$$ − 590.000i − 1.88498i −0.334229 0.942492i $$-0.608476\pi$$
0.334229 0.942492i $$-0.391524\pi$$
$$314$$ 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
$$323$$ − 285.000i − 0.882353i
$$324$$ −324.000 −1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 375.000 1.13982
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ − 360.000i − 1.08434i
$$333$$ 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
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 365.000i 1.06414i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ − 675.000i − 1.94524i −0.232391 0.972622i $$-0.574655\pi$$
0.232391 0.972622i $$-0.425345\pi$$
$$348$$ 0 0
$$349$$ −527.000 −1.51003 −0.755014 0.655708i $$-0.772370\pi$$
−0.755014 + 0.655708i $$0.772370\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ − 510.000i − 1.44476i −0.691497 0.722380i $$-0.743048\pi$$
0.691497 0.722380i $$-0.256952\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −243.000 −0.676880 −0.338440 0.940988i $$-0.609899\pi$$
−0.338440 + 0.940988i $$0.609899\pi$$
$$360$$ 0 0
$$361$$ 361.000 1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ − 50.0000i − 0.136240i −0.997677 0.0681199i $$-0.978300\pi$$
0.997677 0.0681199i $$-0.0217000\pi$$
$$368$$ − 480.000i − 1.30435i
$$369$$ 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
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 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
$$387$$ 765.000i 1.97674i
$$388$$ 0 0
$$389$$ 153.000 0.393316 0.196658 0.980472i $$-0.436991\pi$$
0.196658 + 0.980472i $$0.436991\pi$$
$$390$$ 0 0
$$391$$ −450.000 −1.15090
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 108.000 0.272727
$$397$$ 745.000i 1.87657i 0.345857 + 0.938287i $$0.387588\pi$$
−0.345857 + 0.938287i $$0.612412\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 408.000 1.00990
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 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
$$419$$ −762.000 −1.81862 −0.909308 0.416124i $$-0.863388\pi$$
−0.909308 + 0.416124i $$0.863388\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 675.000i 1.59574i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 515.000i 1.20609i
$$428$$ 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
$$437$$ − 570.000i − 1.30435i
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ −216.000 −0.489796
$$442$$ 0 0
$$443$$ − 45.0000i − 0.101580i −0.998709 0.0507901i $$-0.983826\pi$$
0.998709 0.0507901i $$-0.0161739\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ − 320.000i − 0.714286i
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 625.000i 1.36761i 0.729663 + 0.683807i $$0.239677\pi$$
−0.729663 + 0.683807i $$0.760323\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 447.000 0.969631 0.484816 0.874616i $$-0.338887\pi$$
0.484816 + 0.874616i $$0.338887\pi$$
$$462$$ 0 0
$$463$$ 755.000i 1.63067i 0.578990 + 0.815335i $$0.303447\pi$$
−0.578990 + 0.815335i $$0.696553\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ − 915.000i − 1.95931i −0.200677 0.979657i $$-0.564314\pi$$
0.200677 0.979657i $$-0.435686\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ − 255.000i − 0.539112i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −300.000 −0.630252
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 942.000 1.96660 0.983299 0.182000i $$-0.0582571\pi$$
0.983299 + 0.182000i $$0.0582571\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 448.000 0.925620
$$485$$ 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
$$491$$ −918.000 −1.86965 −0.934827 0.355104i $$-0.884446\pi$$
−0.934827 + 0.355104i $$0.884446\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −523.000 −1.04810 −0.524048 0.851689i $$-0.675579\pi$$
−0.524048 + 0.851689i $$0.675579\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 930.000i 1.84891i 0.381295 + 0.924453i $$0.375478\pi$$
−0.381295 + 0.924453i $$0.624522\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 125.000 0.244618
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ − 225.000i − 0.435203i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 852.000 1.62595
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −371.000 −0.701323
$$530$$ 0 0
$$531$$ 0 0
$$532$$ − 380.000i − 0.714286i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 72.0000 0.133581
$$540$$ 0 0
$$541$$ −457.000 −0.844732 −0.422366 0.906425i $$-0.638800\pi$$
−0.422366 + 0.906425i $$0.638800\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 1020.00i 1.86131i
$$549$$ −927.000 −1.68852
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −788.000 −1.41727
$$557$$ − 1095.00i − 1.96589i −0.183903 0.982944i $$-0.558873\pi$$
0.183903 0.982944i $$-0.441127\pi$$
$$558$$ 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
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 405.000i 0.714286i
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 458.000 0.802102 0.401051 0.916056i $$-0.368645\pi$$
0.401051 + 0.916056i $$0.368645\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 576.000 1.00000
$$577$$ 1145.00i 1.98440i 0.124648 + 0.992201i $$0.460220\pi$$
−0.124648 + 0.992201i $$0.539780\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −450.000 −0.774527
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 1125.00i 1.91652i 0.285890 + 0.958262i $$0.407711\pi$$
−0.285890 + 0.958262i $$0.592289\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ − 30.0000i − 0.0505902i −0.999680 0.0252951i $$-0.991947\pi$$
0.999680 0.0252951i $$-0.00805254\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −708.000 −1.18792
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 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
$$612$$ − 540.000i − 0.882353i
$$613$$ 295.000i 0.481240i 0.970619 + 0.240620i $$0.0773507\pi$$
−0.970619 + 0.240620i $$0.922649\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1065.00i 1.72609i 0.505124 + 0.863047i $$0.331447\pi$$
−0.505124 + 0.863047i $$0.668553\pi$$
$$618$$ 0 0
$$619$$ 662.000 1.06947 0.534733 0.845021i $$-0.320412\pi$$
0.534733 + 0.845021i $$0.320412\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 40.0000i 0.0636943i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −1037.00 −1.64342 −0.821712 0.569904i $$-0.806981\pi$$
−0.821712 + 0.569904i $$0.806981\pi$$
$$632$$ 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
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 1115.00i 1.73406i 0.498257 + 0.867030i $$0.333974\pi$$
−0.498257 + 0.867030i $$0.666026\pi$$
$$644$$ −600.000 −0.931677
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1005.00i 1.55332i 0.629918 + 0.776662i $$0.283088\pi$$
−0.629918 + 0.776662i $$0.716912\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ − 1000.00i − 1.53374i
$$653$$ 375.000i 0.574273i 0.957890 + 0.287136i $$0.0927033\pi$$
−0.957890 + 0.287136i $$0.907297\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 225.000i 0.342466i
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 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
$$671$$ 309.000 0.460507
$$672$$ 0 0
$$673$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 676.000 1.00000
$$677$$ 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
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 684.000 1.00000
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ − 1360.00i − 1.97674i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −157.000 −0.227207 −0.113603 0.993526i $$-0.536239\pi$$
−0.113603 + 0.993526i $$0.536239\pi$$
$$692$$ 0 0
$$693$$ − 135.000i − 0.194805i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1098.00 1.56633 0.783167 0.621812i $$-0.213603\pi$$
0.783167 + 0.621812i $$0.213603\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −192.000 −0.272727
$$705$$ 0 0
$$706$$ 0 0
$$707$$ − 510.000i − 0.721358i
$$708$$ 0 0
$$709$$ 1318.00 1.85896 0.929478 0.368877i $$-0.120258\pi$$
0.929478 + 0.368877i $$0.120258\pi$$
$$710$$ 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
$$719$$ −963.000 −1.33936 −0.669680 0.742650i $$-0.733569\pi$$
−0.669680 + 0.742650i $$0.733569\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 85.0000i 0.116919i 0.998290 + 0.0584594i $$0.0186188\pi$$
−0.998290 + 0.0584594i $$0.981381\pi$$
$$728$$ 0 0
$$729$$ −729.000 −1.00000
$$730$$ 0 0
$$731$$ −1275.00 −1.74419
$$732$$ 0 0
$$733$$ − 1270.00i − 1.73261i −0.499519 0.866303i $$-0.666490\pi$$
0.499519 0.866303i $$-0.333510\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −547.000 −0.740189 −0.370095 0.928994i $$-0.620675\pi$$
−0.370095 + 0.928994i $$0.620675\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ − 810.000i − 1.08434i
$$748$$ 180.000i 0.240642i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ − 1200.00i − 1.59574i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 785.000i 1.03699i 0.855081 + 0.518494i $$0.173507\pi$$
−0.855081 + 0.518494i $$0.826493\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1503.00 1.97503 0.987516 0.157516i $$-0.0503486\pi$$
0.987516 + 0.157516i $$0.0503486\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 372.000 0.486911
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −1063.00 −1.38231 −0.691157 0.722704i $$-0.742899\pi$$
−0.691157 + 0.722704i $$0.742899\pi$$
$$770$$ 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
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 384.000 0.489796
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 360.000i 0.456853i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 908.000 1.14070
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ −1125.00 −1.40801
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ − 75.0000i − 0.0933998i
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 1593.00 1.96910 0.984549 0.175110i $$-0.0560282\pi$$
0.984549 + 0.175110i $$0.0560282\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ − 1615.00i − 1.97674i
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 1167.00 1.42144 0.710719 0.703476i $$-0.248370\pi$$
0.710719 + 0.703476i $$0.248370\pi$$
$$822$$ 0 0
$$823$$ − 1565.00i − 1.90158i −0.309837 0.950790i $$-0.600274\pi$$
0.309837 0.950790i $$-0.399726\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ − 1080.00i − 1.30435i
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ − 360.000i − 0.432173i
$$834$$ 0 0
$$835$$ 0 0
$$836$$ −228.000 −0.272727
$$837$$ 0 0
$$838$$ 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
$$847$$ − 560.000i − 0.661157i
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ − 1030.00i − 1.20750i −0.797173 0.603751i $$-0.793672\pi$$
0.797173 0.603751i $$-0.206328\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ 1493.00 1.73807 0.869034 0.494753i $$-0.164741\pi$$
0.869034 + 0.494753i $$0.164741\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 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
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −537.000 −0.609535 −0.304767 0.952427i $$-0.598579\pi$$
−0.304767 + 0.952427i $$0.598579\pi$$
$$882$$ 0 0
$$883$$ 835.000i 0.945640i 0.881159 + 0.472820i $$0.156764\pi$$
−0.881159 + 0.472820i $$0.843236\pi$$
$$884$$ 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
$$891$$ 243.000 0.272727
$$892$$ 0 0
$$893$$ − 1425.00i − 1.59574i
$$894$$ 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
$$903$$ 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
$$909$$ 918.000 1.00990
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 270.000i 0.295728i
$$914$$ 0 0
$$915$$ 0 0
$$916$$ −68.0000 −0.0742358
$$917$$ − 1065.00i − 1.16140i
$$918$$ 0 0
$$919$$ −1762.00 −1.91730 −0.958651 0.284585i $$-0.908144\pi$$
−0.958651 + 0.284585i $$0.908144\pi$$
$$920$$ 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
$$929$$ −642.000 −0.691066 −0.345533 0.938407i $$-0.612302\pi$$
−0.345533 + 0.938407i $$0.612302\pi$$
$$930$$ 0 0
$$931$$ 456.000 0.489796
$$932$$ 1860.00i 1.99571i
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ − 335.000i − 0.357524i −0.983892 0.178762i $$-0.942791\pi$$
0.983892 0.178762i $$-0.0572092\pi$$
$$938$$ 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
$$947$$ 1830.00i 1.93242i 0.257760 + 0.966209i $$0.417016\pi$$
−0.257760 + 0.966209i $$0.582984\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 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
$$956$$ −1812.00 −1.89540
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 1275.00 1.32951
$$960$$ 0 0
$$961$$ 961.000 1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 1790.00i 1.85109i 0.378643 + 0.925543i $$0.376391\pi$$
−0.378643 + 0.925543i $$0.623609\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 985.000i 1.01233i
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 1648.00 1.68852
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 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
$$989$$ −2550.00 −2.57836
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ − 1975.00i − 1.98094i −0.137718 0.990471i $$-0.543977\pi$$
0.137718 0.990471i $$-0.456023\pi$$
$$998$$ 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 475.3.d.a.474.2 2
5.2 odd 4 19.3.b.a.18.1 1
5.3 odd 4 475.3.c.a.151.1 1
5.4 even 2 inner 475.3.d.a.474.1 2
15.2 even 4 171.3.c.a.37.1 1
19.18 odd 2 CM 475.3.d.a.474.2 2
20.7 even 4 304.3.e.a.113.1 1
40.27 even 4 1216.3.e.b.1025.1 1
40.37 odd 4 1216.3.e.a.1025.1 1
60.47 odd 4 2736.3.o.a.721.1 1
95.2 even 36 361.3.f.a.262.1 6
95.7 odd 12 361.3.d.a.293.1 2
95.12 even 12 361.3.d.a.293.1 2
95.17 odd 36 361.3.f.a.262.1 6
95.18 even 4 475.3.c.a.151.1 1
95.22 even 36 361.3.f.a.333.1 6
95.27 even 12 361.3.d.a.69.1 2
95.32 even 36 361.3.f.a.116.1 6
95.37 even 4 19.3.b.a.18.1 1
95.42 odd 36 361.3.f.a.307.1 6
95.47 odd 36 361.3.f.a.299.1 6
95.52 even 36 361.3.f.a.127.1 6
95.62 odd 36 361.3.f.a.127.1 6
95.67 even 36 361.3.f.a.299.1 6
95.72 even 36 361.3.f.a.307.1 6
95.82 odd 36 361.3.f.a.116.1 6
95.87 odd 12 361.3.d.a.69.1 2
95.92 odd 36 361.3.f.a.333.1 6
95.94 odd 2 inner 475.3.d.a.474.1 2
285.227 odd 4 171.3.c.a.37.1 1
380.227 odd 4 304.3.e.a.113.1 1
760.37 even 4 1216.3.e.a.1025.1 1
760.227 odd 4 1216.3.e.b.1025.1 1
1140.227 even 4 2736.3.o.a.721.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
19.3.b.a.18.1 1 5.2 odd 4
19.3.b.a.18.1 1 95.37 even 4
171.3.c.a.37.1 1 15.2 even 4
171.3.c.a.37.1 1 285.227 odd 4
304.3.e.a.113.1 1 20.7 even 4
304.3.e.a.113.1 1 380.227 odd 4
361.3.d.a.69.1 2 95.27 even 12
361.3.d.a.69.1 2 95.87 odd 12
361.3.d.a.293.1 2 95.7 odd 12
361.3.d.a.293.1 2 95.12 even 12
361.3.f.a.116.1 6 95.32 even 36
361.3.f.a.116.1 6 95.82 odd 36
361.3.f.a.127.1 6 95.52 even 36
361.3.f.a.127.1 6 95.62 odd 36
361.3.f.a.262.1 6 95.2 even 36
361.3.f.a.262.1 6 95.17 odd 36
361.3.f.a.299.1 6 95.47 odd 36
361.3.f.a.299.1 6 95.67 even 36
361.3.f.a.307.1 6 95.42 odd 36
361.3.f.a.307.1 6 95.72 even 36
361.3.f.a.333.1 6 95.22 even 36
361.3.f.a.333.1 6 95.92 odd 36
475.3.c.a.151.1 1 5.3 odd 4
475.3.c.a.151.1 1 95.18 even 4
475.3.d.a.474.1 2 5.4 even 2 inner
475.3.d.a.474.1 2 95.94 odd 2 inner
475.3.d.a.474.2 2 1.1 even 1 trivial
475.3.d.a.474.2 2 19.18 odd 2 CM
1216.3.e.a.1025.1 1 40.37 odd 4
1216.3.e.a.1025.1 1 760.37 even 4
1216.3.e.b.1025.1 1 40.27 even 4
1216.3.e.b.1025.1 1 760.227 odd 4
2736.3.o.a.721.1 1 60.47 odd 4
2736.3.o.a.721.1 1 1140.227 even 4