Properties

 Label 441.4.a.p.1.2 Level $441$ Weight $4$ Character 441.1 Self dual yes Analytic conductor $26.020$ Analytic rank $1$ Dimension $2$ CM discriminant -7 Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 441.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$26.0198423125$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{7})$$ Defining polynomial: $$x^{2} - 7$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

 Embedding label 1.2 Root $$2.64575$$ of defining polynomial Character $$\chi$$ $$=$$ 441.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+2.64575 q^{2} -1.00000 q^{4} -23.8118 q^{8} +O(q^{10})$$ $$q+2.64575 q^{2} -1.00000 q^{4} -23.8118 q^{8} +26.4575 q^{11} -55.0000 q^{16} +70.0000 q^{22} -216.952 q^{23} -125.000 q^{25} -264.575 q^{29} +44.9778 q^{32} -450.000 q^{37} +180.000 q^{43} -26.4575 q^{44} -574.000 q^{46} -330.719 q^{50} +497.401 q^{53} -700.000 q^{58} +559.000 q^{64} -740.000 q^{67} +978.928 q^{71} -1190.59 q^{74} -1384.00 q^{79} +476.235 q^{86} -630.000 q^{88} +216.952 q^{92} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{4} + O(q^{10})$$ $$2q - 2q^{4} - 110q^{16} + 140q^{22} - 250q^{25} - 900q^{37} + 360q^{43} - 1148q^{46} - 1400q^{58} + 1118q^{64} - 1480q^{67} - 2768q^{79} - 1260q^{88} + O(q^{100})$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.64575 0.935414 0.467707 0.883883i $$-0.345080\pi$$
0.467707 + 0.883883i $$0.345080\pi$$
$$3$$ 0 0
$$4$$ −1.00000 −0.125000
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −23.8118 −1.05234
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 26.4575 0.725204 0.362602 0.931944i $$-0.381889\pi$$
0.362602 + 0.931944i $$0.381889\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −55.0000 −0.859375
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 70.0000 0.678366
$$23$$ −216.952 −1.96685 −0.983425 0.181317i $$-0.941964\pi$$
−0.983425 + 0.181317i $$0.941964\pi$$
$$24$$ 0 0
$$25$$ −125.000 −1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −264.575 −1.69415 −0.847075 0.531473i $$-0.821639\pi$$
−0.847075 + 0.531473i $$0.821639\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 44.9778 0.248469
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −450.000 −1.99945 −0.999724 0.0235113i $$-0.992515\pi$$
−0.999724 + 0.0235113i $$0.992515\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 180.000 0.638366 0.319183 0.947693i $$-0.396592\pi$$
0.319183 + 0.947693i $$0.396592\pi$$
$$44$$ −26.4575 −0.0906505
$$45$$ 0 0
$$46$$ −574.000 −1.83982
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −330.719 −0.935414
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 497.401 1.28912 0.644560 0.764554i $$-0.277041\pi$$
0.644560 + 0.764554i $$0.277041\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −700.000 −1.58473
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 559.000 1.09180
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −740.000 −1.34933 −0.674667 0.738122i $$-0.735713\pi$$
−0.674667 + 0.738122i $$0.735713\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 978.928 1.63630 0.818151 0.575004i $$-0.195000\pi$$
0.818151 + 0.575004i $$0.195000\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ −1190.59 −1.87031
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −1384.00 −1.97104 −0.985520 0.169559i $$-0.945766\pi$$
−0.985520 + 0.169559i $$0.945766\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 476.235 0.597137
$$87$$ 0 0
$$88$$ −630.000 −0.763162
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 216.952 0.245856
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 125.000 0.125000
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 1316.00 1.20586
$$107$$ 1550.41 1.40078 0.700392 0.713759i $$-0.253009\pi$$
0.700392 + 0.713759i $$0.253009\pi$$
$$108$$ 0 0
$$109$$ 54.0000 0.0474519 0.0237260 0.999718i $$-0.492447\pi$$
0.0237260 + 0.999718i $$0.492447\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2307.10 1.92065 0.960324 0.278886i $$-0.0899653\pi$$
0.960324 + 0.278886i $$0.0899653\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 264.575 0.211769
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −631.000 −0.474080
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −2000.00 −1.39741 −0.698706 0.715409i $$-0.746240\pi$$
−0.698706 + 0.715409i $$0.746240\pi$$
$$128$$ 1119.15 0.772813
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −1957.86 −1.26219
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 783.142 0.488382 0.244191 0.969727i $$-0.421478\pi$$
0.244191 + 0.969727i $$0.421478\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 2590.00 1.53062
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 450.000 0.249931
$$149$$ −3545.31 −1.94928 −0.974640 0.223777i $$-0.928161\pi$$
−0.974640 + 0.223777i $$0.928161\pi$$
$$150$$ 0 0
$$151$$ 2952.00 1.59093 0.795465 0.606000i $$-0.207227\pi$$
0.795465 + 0.606000i $$0.207227\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ −3661.72 −1.84374
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 1780.00 0.855340 0.427670 0.903935i $$-0.359335\pi$$
0.427670 + 0.903935i $$0.359335\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −2197.00 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −180.000 −0.0797958
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −1455.16 −0.623222
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 4312.57 1.80077 0.900383 0.435099i $$-0.143287\pi$$
0.900383 + 0.435099i $$0.143287\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 5166.00 2.06980
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3360.10 −1.27292 −0.636462 0.771308i $$-0.719603\pi$$
−0.636462 + 0.771308i $$0.719603\pi$$
$$192$$ 0 0
$$193$$ 4590.00 1.71189 0.855947 0.517064i $$-0.172975\pi$$
0.855947 + 0.517064i $$0.172975\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −5069.26 −1.83335 −0.916675 0.399634i $$-0.869137\pi$$
−0.916675 + 0.399634i $$0.869137\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 2976.47 1.05234
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −5868.00 −1.91455 −0.957274 0.289181i $$-0.906617\pi$$
−0.957274 + 0.289181i $$0.906617\pi$$
$$212$$ −497.401 −0.161140
$$213$$ 0 0
$$214$$ 4102.00 1.31031
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 142.871 0.0443872
$$219$$ 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
$$226$$ 6104.00 1.79660
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 6300.00 1.78282
$$233$$ 5312.67 1.49375 0.746877 0.664963i $$-0.231553\pi$$
0.746877 + 0.664963i $$0.231553\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −449.778 −0.121731 −0.0608655 0.998146i $$-0.519386\pi$$
−0.0608655 + 0.998146i $$0.519386\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ −1669.47 −0.443461
$$243$$ 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
$$253$$ −5740.00 −1.42637
$$254$$ −5291.50 −1.30716
$$255$$ 0 0
$$256$$ −1511.00 −0.368896
$$257$$ 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
$$263$$ −4026.83 −0.944126 −0.472063 0.881565i $$-0.656491\pi$$
−0.472063 + 0.881565i $$0.656491\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 740.000 0.168667
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 2072.00 0.456840
$$275$$ −3307.19 −0.725204
$$276$$ 0 0
$$277$$ 7310.00 1.58561 0.792807 0.609472i $$-0.208619\pi$$
0.792807 + 0.609472i $$0.208619\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 8360.57 1.77491 0.887456 0.460893i $$-0.152471\pi$$
0.887456 + 0.460893i $$0.152471\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ −978.928 −0.204538
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −4913.00 −1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 10715.3 2.10410
$$297$$ 0 0
$$298$$ −9380.00 −1.82339
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 7810.26 1.48818
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 1384.00 0.246380
$$317$$ 8879.14 1.57319 0.786597 0.617467i $$-0.211841\pi$$
0.786597 + 0.617467i $$0.211841\pi$$
$$318$$ 0 0
$$319$$ −7000.00 −1.22860
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 4709.44 0.800097
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −10908.0 −1.81135 −0.905677 0.423969i $$-0.860636\pi$$
−0.905677 + 0.423969i $$0.860636\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 3330.00 0.538269 0.269135 0.963103i $$-0.413262\pi$$
0.269135 + 0.963103i $$0.413262\pi$$
$$338$$ −5812.72 −0.935414
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −4286.12 −0.671779
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −12260.4 −1.89675 −0.948377 0.317146i $$-0.897275\pi$$
−0.948377 + 0.317146i $$0.897275\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1190.00 0.180191
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 11410.0 1.68446
$$359$$ 10927.0 1.60641 0.803207 0.595700i $$-0.203125\pi$$
0.803207 + 0.595700i $$0.203125\pi$$
$$360$$ 0 0
$$361$$ −6859.00 −1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 11932.3 1.69026
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −13970.0 −1.93925 −0.969624 0.244602i $$-0.921343\pi$$
−0.969624 + 0.244602i $$0.921343\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −11916.0 −1.61500 −0.807498 0.589870i $$-0.799179\pi$$
−0.807498 + 0.589870i $$0.799179\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −8890.00 −1.19071
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 12144.0 1.60133
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −11165.1 −1.45525 −0.727624 0.685976i $$-0.759375\pi$$
−0.727624 + 0.685976i $$0.759375\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −13412.0 −1.71494
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 6875.00 0.859375
$$401$$ −15980.3 −1.99007 −0.995037 0.0995016i $$-0.968275\pi$$
−0.995037 + 0.0995016i $$0.968275\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −11905.9 −1.45001
$$408$$ 0 0
$$409$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 15262.0 1.76680 0.883402 0.468616i $$-0.155247\pi$$
0.883402 + 0.468616i $$0.155247\pi$$
$$422$$ −15525.3 −1.79090
$$423$$ 0 0
$$424$$ −11844.0 −1.35659
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −1550.41 −0.175098
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 15689.3 1.75343 0.876714 0.481012i $$-0.159731\pi$$
0.876714 + 0.481012i $$0.159731\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −54.0000 −0.00593149
$$437$$ 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
$$443$$ −1592.74 −0.170820 −0.0854102 0.996346i $$-0.527220\pi$$
−0.0854102 + 0.996346i $$0.527220\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −18837.7 −1.97997 −0.989987 0.141158i $$-0.954917\pi$$
−0.989987 + 0.141158i $$0.954917\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −2307.10 −0.240081
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −8010.00 −0.819895 −0.409947 0.912109i $$-0.634453\pi$$
−0.409947 + 0.912109i $$0.634453\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ −8440.00 −0.847171 −0.423585 0.905856i $$-0.639229\pi$$
−0.423585 + 0.905856i $$0.639229\pi$$
$$464$$ 14551.6 1.45591
$$465$$ 0 0
$$466$$ 14056.0 1.39728
$$467$$ 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
$$473$$ 4762.35 0.462945
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −1190.00 −0.113869
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 631.000 0.0592600
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −21240.0 −1.97634 −0.988169 0.153371i $$-0.950987\pi$$
−0.988169 + 0.153371i $$0.950987\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −7646.22 −0.702788 −0.351394 0.936228i $$-0.614292\pi$$
−0.351394 + 0.936228i $$0.614292\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 7236.00 0.649154 0.324577 0.945859i $$-0.394778\pi$$
0.324577 + 0.945859i $$0.394778\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −15186.6 −1.33424
$$507$$ 0 0
$$508$$ 2000.00 0.174676
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −12951.0 −1.11788
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −10654.0 −0.883149
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 34901.0 2.86850
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 17620.7 1.41996
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 15878.0 1.26183 0.630914 0.775853i $$-0.282680\pi$$
0.630914 + 0.775853i $$0.282680\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 12980.0 1.01460 0.507299 0.861770i $$-0.330644\pi$$
0.507299 + 0.861770i $$0.330644\pi$$
$$548$$ −783.142 −0.0610478
$$549$$ 0 0
$$550$$ −8750.00 −0.678366
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 19340.4 1.48321
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −16498.9 −1.25508 −0.627541 0.778583i $$-0.715939\pi$$
−0.627541 + 0.778583i $$0.715939\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 22120.0 1.66028
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ −23310.0 −1.72195
$$569$$ 3598.22 0.265106 0.132553 0.991176i $$-0.457683\pi$$
0.132553 + 0.991176i $$0.457683\pi$$
$$570$$ 0 0
$$571$$ −6788.00 −0.497494 −0.248747 0.968569i $$-0.580019\pi$$
−0.248747 + 0.968569i $$0.580019\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 27119.0 1.96685
$$576$$ 0 0
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ −12998.6 −0.935414
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 13160.0 0.934874
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 24750.0 1.71827
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 3545.31 0.243660
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −15742.2 −1.07381 −0.536903 0.843644i $$-0.680406\pi$$
−0.536903 + 0.843644i $$0.680406\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −2952.00 −0.198866
$$605$$ 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
$$613$$ 15010.0 0.988986 0.494493 0.869182i $$-0.335354\pi$$
0.494493 + 0.869182i $$0.335354\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −2497.59 −0.162965 −0.0814823 0.996675i $$-0.525965\pi$$
−0.0814823 + 0.996675i $$0.525965\pi$$
$$618$$ 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
$$625$$ 15625.0 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −26192.0 −1.65244 −0.826218 0.563351i $$-0.809512\pi$$
−0.826218 + 0.563351i $$0.809512\pi$$
$$632$$ 32955.5 2.07421
$$633$$ 0 0
$$634$$ 23492.0 1.47159
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −18520.3 −1.14925
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 31219.9 1.92373 0.961865 0.273526i $$-0.0881899\pi$$
0.961865 + 0.273526i $$0.0881899\pi$$
$$642$$ 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
$$652$$ −1780.00 −0.106917
$$653$$ 19546.8 1.17140 0.585701 0.810527i $$-0.300819\pi$$
0.585701 + 0.810527i $$0.300819\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 33786.2 1.99716 0.998578 0.0533186i $$-0.0169799\pi$$
0.998578 + 0.0533186i $$0.0169799\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$662$$ −28859.9 −1.69437
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 57400.0 3.33214
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 33570.0 1.92278 0.961388 0.275196i $$-0.0887428\pi$$
0.961388 + 0.275196i $$0.0887428\pi$$
$$674$$ 8810.35 0.503505
$$675$$ 0 0
$$676$$ 2197.00 0.125000
$$677$$ 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
$$683$$ −10694.1 −0.599121 −0.299560 0.954077i $$-0.596840\pi$$
−0.299560 + 0.954077i $$0.596840\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −9900.00 −0.548596
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −32438.0 −1.77425
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 36881.8 1.98717 0.993584 0.113093i $$-0.0360758\pi$$
0.993584 + 0.113093i $$0.0360758\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 14789.7 0.791775
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −12546.0 −0.664563 −0.332281 0.943180i $$-0.607818\pi$$
−0.332281 + 0.943180i $$0.607818\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −4312.57 −0.225096
$$717$$ 0 0
$$718$$ 28910.0 1.50266
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −18147.2 −0.935414
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 33071.9 1.69415
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ −9758.00 −0.488702
$$737$$ −19578.6 −0.978542
$$738$$ 0 0
$$739$$ −25324.0 −1.26057 −0.630283 0.776365i $$-0.717061\pi$$
−0.630283 + 0.776365i $$0.717061\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −31743.7 −1.56738 −0.783691 0.621151i $$-0.786665\pi$$
−0.783691 + 0.621151i $$0.786665\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −36961.1 −1.81400
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 2448.00 0.118946 0.0594732 0.998230i $$-0.481058\pi$$
0.0594732 + 0.998230i $$0.481058\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 34830.0 1.67228 0.836141 0.548514i $$-0.184806\pi$$
0.836141 + 0.548514i $$0.184806\pi$$
$$758$$ −31526.8 −1.51069
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 3360.10 0.159116
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −4590.00 −0.213987
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −29540.0 −1.36126
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 25900.0 1.18665
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 5069.26 0.229169
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ −5622.22 −0.248469
$$801$$ 0 0
$$802$$ −42280.0 −1.86154
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −26880.8 −1.16821 −0.584104 0.811679i $$-0.698554\pi$$
−0.584104 + 0.811679i $$0.698554\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ −31500.0 −1.35636
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −17832.4 −0.758044 −0.379022 0.925388i $$-0.623739\pi$$
−0.379022 + 0.925388i $$0.623739\pi$$
$$822$$ 0 0
$$823$$ −46240.0 −1.95848 −0.979238 0.202716i $$-0.935023\pi$$
−0.979238 + 0.202716i $$0.935023\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −41077.9 −1.72723 −0.863615 0.504151i $$-0.831805\pi$$
−0.863615 + 0.504151i $$0.831805\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 45611.0 1.87015
$$842$$ 40379.5 1.65269
$$843$$ 0 0
$$844$$ 5868.00 0.239319
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ −27357.1 −1.10784
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 97628.2 3.93261
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −36918.0 −1.47410
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 41510.0 1.64018
$$863$$ −46507.0 −1.83443 −0.917217 0.398387i $$-0.869570\pi$$
−0.917217 + 0.398387i $$0.869570\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −36617.2 −1.42941
$$870$$ 0 0
$$871$$ 0 0
$$872$$ −1285.84 −0.0499356
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −6550.00 −0.252198 −0.126099 0.992018i $$-0.540246\pi$$
−0.126099 + 0.992018i $$0.540246\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ −30060.0 −1.14564 −0.572820 0.819681i $$-0.694150\pi$$
−0.572820 + 0.819681i $$0.694150\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ −4214.00 −0.159788
$$887$$ 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
$$898$$ −49840.0 −1.85210
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ −54936.0 −2.02118
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −52740.0 −1.93076 −0.965382 0.260840i $$-0.916000\pi$$
−0.965382 + 0.260840i $$0.916000\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 38125.3 1.38655 0.693275 0.720673i $$-0.256167\pi$$
0.693275 + 0.720673i $$0.256167\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ −21192.5 −0.766942
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −21744.0 −0.780488 −0.390244 0.920711i $$-0.627609\pi$$
−0.390244 + 0.920711i $$0.627609\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 56250.0 1.99945
$$926$$ −22330.1 −0.792456
$$927$$ 0 0
$$928$$ −11900.0 −0.420945
$$929$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −5312.67 −0.186719
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 12600.0 0.433046
$$947$$ 31839.0 1.09253 0.546266 0.837612i $$-0.316049\pi$$
0.546266 + 0.837612i $$0.316049\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 51031.3 1.73459 0.867295 0.497794i $$-0.165857\pi$$
0.867295 + 0.497794i $$0.165857\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 449.778 0.0152164
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −29791.0 −1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 52040.0 1.73060 0.865302 0.501251i $$-0.167127\pi$$
0.865302 + 0.501251i $$0.167127\pi$$
$$968$$ 15025.2 0.498894
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ −56195.8 −1.84869
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −48216.2 −1.57889 −0.789443 0.613824i $$-0.789631\pi$$
−0.789443 + 0.613824i $$0.789631\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −20230.0 −0.657398
$$983$$ 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
$$989$$ −39051.3 −1.25557
$$990$$ 0 0
$$991$$ −57528.0 −1.84403 −0.922017 0.387150i $$-0.873460\pi$$
−0.922017 + 0.387150i $$0.873460\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 19144.7 0.607228
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 441.4.a.p.1.2 yes 2
3.2 odd 2 inner 441.4.a.p.1.1 2
7.2 even 3 441.4.e.t.361.1 4
7.3 odd 6 441.4.e.t.226.1 4
7.4 even 3 441.4.e.t.226.1 4
7.5 odd 6 441.4.e.t.361.1 4
7.6 odd 2 CM 441.4.a.p.1.2 yes 2
21.2 odd 6 441.4.e.t.361.2 4
21.5 even 6 441.4.e.t.361.2 4
21.11 odd 6 441.4.e.t.226.2 4
21.17 even 6 441.4.e.t.226.2 4
21.20 even 2 inner 441.4.a.p.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
441.4.a.p.1.1 2 3.2 odd 2 inner
441.4.a.p.1.1 2 21.20 even 2 inner
441.4.a.p.1.2 yes 2 1.1 even 1 trivial
441.4.a.p.1.2 yes 2 7.6 odd 2 CM
441.4.e.t.226.1 4 7.3 odd 6
441.4.e.t.226.1 4 7.4 even 3
441.4.e.t.226.2 4 21.11 odd 6
441.4.e.t.226.2 4 21.17 even 6
441.4.e.t.361.1 4 7.2 even 3
441.4.e.t.361.1 4 7.5 odd 6
441.4.e.t.361.2 4 21.2 odd 6
441.4.e.t.361.2 4 21.5 even 6