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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.34.a.a \(2\) \(6.898\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-121680\) \(37919880\) \(-181061536500\) \(-6\!\cdots\!00\) \(+\) \(q+(-60840-\beta )q^{2}+(18959940+312\beta )q^{3}+\cdots\)
1.36.a.a \(3\) \(7.760\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(139656\) \(-104875308\) \(892652054010\) \(87\!\cdots\!56\) \(+\) \(q+(46552+\beta _{1})q^{2}+(-34958436+\cdots)q^{3}+\cdots\)
1.38.a.a \(2\) \(8.671\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-194400\) \(13991400\) \(55\!\cdots\!00\) \(-3\!\cdots\!00\) \(+\) \(q+(-97200-\beta )q^{2}+(6995700+72\beta )q^{3}+\cdots\)
1.40.a.a \(3\) \(9.634\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(548856\) \(1109442852\) \(17\!\cdots\!90\) \(-1\!\cdots\!44\) \(+\) \(q+(182952-\beta _{1})q^{2}+(369814284+\cdots)q^{3}+\cdots\)
1.42.a.a \(3\) \(10.647\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-344688\) \(-10820953044\) \(-2\!\cdots\!50\) \(57\!\cdots\!92\) \(+\) \(q+(-114896+\beta _{1})q^{2}+(-3606984348+\cdots)q^{3}+\cdots\)
1.44.a.a \(3\) \(11.711\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-2209944\) \(24401437812\) \(53\!\cdots\!70\) \(30\!\cdots\!56\) \(+\) \(q+(-736648-\beta _{1})q^{2}+(8133812604+\cdots)q^{3}+\cdots\)
1.46.a.a \(3\) \(12.826\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(3814272\) \(5359866876\) \(-9\!\cdots\!50\) \(-7\!\cdots\!08\) \(+\) \(q+(1271424+\beta _{1})q^{2}+(1786622292+\cdots)q^{3}+\cdots\)
2.34.a.a \(1\) \(13.797\) \(\Q\) None \(-65536\) \(-133005564\) \(538799132550\) \(-3\!\cdots\!68\) \(+\) \(q-2^{16}q^{2}-133005564q^{3}+2^{32}q^{4}+\cdots\)
2.34.a.b \(2\) \(13.797\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(131072\) \(8356488\) \(-5332476660\) \(13\!\cdots\!56\) \(-\) \(q+2^{16}q^{2}+(4178244-\beta )q^{3}+2^{32}q^{4}+\cdots\)
1.48.a.a \(4\) \(13.991\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(5785560\) \(38461494960\) \(-3\!\cdots\!00\) \(-3\!\cdots\!00\) \(+\) \(q+(1446390+\beta _{1})q^{2}+(9615373740+\cdots)q^{3}+\cdots\)
1.50.a.a \(3\) \(15.207\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-24225168\) \(-326954692404\) \(63\!\cdots\!50\) \(50\!\cdots\!92\) \(+\) \(q+(-8075056+\beta _{1})q^{2}+(-108984897468+\cdots)q^{3}+\cdots\)
2.36.a.a \(1\) \(15.519\) \(\Q\) None \(-131072\) \(36494748\) \(389070858750\) \(-1\!\cdots\!56\) \(+\) \(q-2^{17}q^{2}+36494748q^{3}+2^{34}q^{4}+\cdots\)
2.36.a.b \(1\) \(15.519\) \(\Q\) None \(131072\) \(159933852\) \(-2\!\cdots\!90\) \(-7\!\cdots\!44\) \(-\) \(q+2^{17}q^{2}+159933852q^{3}+2^{34}q^{4}+\cdots\)
1.52.a.a \(4\) \(16.473\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(32756040\) \(403863773040\) \(12\!\cdots\!80\) \(65\!\cdots\!00\) \(+\) \(q+(8189010+\beta _{1})q^{2}+(100965943260+\cdots)q^{3}+\cdots\)
2.38.a.a \(2\) \(17.343\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-524288\) \(423071208\) \(-1\!\cdots\!40\) \(31\!\cdots\!56\) \(+\) \(q-2^{18}q^{2}+(211535604-\beta )q^{3}+2^{36}q^{4}+\cdots\)
2.38.a.b \(2\) \(17.343\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(524288\) \(-501686808\) \(41\!\cdots\!00\) \(-3\!\cdots\!56\) \(-\) \(q+2^{18}q^{2}+(-250843404-\beta )q^{3}+\cdots\)
1.54.a.a \(4\) \(17.790\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-68476320\) \(-1\!\cdots\!80\) \(-4\!\cdots\!00\) \(-2\!\cdots\!00\) \(+\) \(q+(-17119080+\beta _{1})q^{2}+(-262102751820+\cdots)q^{3}+\cdots\)
1.56.a.a \(4\) \(19.158\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(208622520\) \(-6\!\cdots\!80\) \(14\!\cdots\!60\) \(-2\!\cdots\!00\) \(+\) \(q+(52155630+\beta _{1})q^{2}+(-1705367672820+\cdots)q^{3}+\cdots\)
2.40.a.a \(1\) \(19.268\) \(\Q\) None \(524288\) \(-735458292\) \(-1\!\cdots\!50\) \(16\!\cdots\!64\) \(-\) \(q+2^{19}q^{2}-735458292q^{3}+2^{38}q^{4}+\cdots\)
2.40.a.b \(2\) \(19.268\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-1048576\) \(287418264\) \(53\!\cdots\!20\) \(74\!\cdots\!12\) \(+\) \(q-2^{19}q^{2}+(143709132-\beta )q^{3}+2^{38}q^{4}+\cdots\)
3.33.b.a \(10\) \(19.460\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-21387150\) \(0\) \(-5\!\cdots\!40\) \(q+\beta _{1}q^{2}+(-2138715+35\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
1.58.a.a \(4\) \(20.577\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-217744560\) \(37\!\cdots\!60\) \(-1\!\cdots\!00\) \(95\!\cdots\!00\) \(+\) \(q+(-54436140+\beta _{1})q^{2}+(9368965543140+\cdots)q^{3}+\cdots\)
3.34.a.a \(3\) \(20.695\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(41202\) \(129140163\) \(51261823890\) \(76\!\cdots\!56\) \(-\) \(q+(13734-\beta _{1})q^{2}+3^{16}q^{3}+(-369155924+\cdots)q^{4}+\cdots\)
3.34.a.b \(3\) \(20.695\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(136620\) \(-129140163\) \(-260488036134\) \(10\!\cdots\!32\) \(+\) \(q+(45540-\beta _{1})q^{2}-3^{16}q^{3}+(4863185200+\cdots)q^{4}+\cdots\)
2.42.a.a \(1\) \(21.294\) \(\Q\) None \(-1048576\) \(5043516516\) \(-4\!\cdots\!50\) \(-1\!\cdots\!68\) \(+\) \(q-2^{20}q^{2}+5043516516q^{3}+2^{40}q^{4}+\cdots\)
2.42.a.b \(2\) \(21.294\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(2097152\) \(8863347528\) \(97\!\cdots\!80\) \(21\!\cdots\!56\) \(-\) \(q+2^{20}q^{2}+(4431673764-\beta )q^{3}+\cdots\)
3.35.b.a \(10\) \(21.968\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(119369106\) \(0\) \(-1\!\cdots\!72\) \(q+\beta _{1}q^{2}+(11936911+41\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
1.60.a.a \(5\) \(22.046\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-449691864\) \(84\!\cdots\!32\) \(17\!\cdots\!90\) \(14\!\cdots\!56\) \(+\) \(q+(-89938373-\beta _{1})q^{2}+(16803326335969+\cdots)q^{3}+\cdots\)
3.36.a.a \(2\) \(23.279\) \(\Q(\sqrt{2196841}) \) None \(-60912\) \(258280326\) \(-1\!\cdots\!40\) \(-1\!\cdots\!44\) \(-\) \(q+(-30456-\beta )q^{2}+3^{17}q^{3}+(28571469952+\cdots)q^{4}+\cdots\)
3.36.a.b \(3\) \(23.279\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-87330\) \(-387420489\) \(27\!\cdots\!10\) \(48\!\cdots\!64\) \(+\) \(q+(-29110+\beta _{1})q^{2}-3^{17}q^{3}+(10829584300+\cdots)q^{4}+\cdots\)
2.44.a.a \(2\) \(23.422\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-4194304\) \(-12981630984\) \(-3\!\cdots\!00\) \(11\!\cdots\!08\) \(+\) \(q-2^{21}q^{2}+(-6490815492-\beta )q^{3}+\cdots\)
2.44.a.b \(2\) \(23.422\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(4194304\) \(-22341634056\) \(-4\!\cdots\!20\) \(-2\!\cdots\!28\) \(-\) \(q+2^{21}q^{2}+(-11170817028-\beta )q^{3}+\cdots\)
1.62.a.a \(4\) \(23.566\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(1146312000\) \(-5\!\cdots\!00\) \(-5\!\cdots\!00\) \(-6\!\cdots\!00\) \(+\) \(q+(286578000-\beta _{1})q^{2}+(-143430899755500+\cdots)q^{3}+\cdots\)
3.37.b.a \(1\) \(24.627\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(387420489\) \(0\) \(27\!\cdots\!98\) \(q+3^{18}q^{3}+2^{36}q^{4}+2757049053441698q^{7}+\cdots\)
3.37.b.b \(10\) \(24.627\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-552156750\) \(0\) \(-1\!\cdots\!00\) \(q+\beta _{1}q^{2}+(-55215675-69\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
1.64.a.a \(5\) \(25.136\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(507315096\) \(95\!\cdots\!52\) \(-5\!\cdots\!30\) \(37\!\cdots\!56\) \(+\) \(q+(101463019-\beta _{1})q^{2}+(190649070219572+\cdots)q^{3}+\cdots\)
2.46.a.a \(2\) \(25.651\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-8388608\) \(-69766206552\) \(-4\!\cdots\!00\) \(-9\!\cdots\!44\) \(+\) \(q-2^{22}q^{2}+(-34883103276-\beta )q^{3}+\cdots\)
2.46.a.b \(2\) \(25.651\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(8388608\) \(59861217192\) \(43\!\cdots\!00\) \(79\!\cdots\!24\) \(-\) \(q+2^{22}q^{2}+(29930608596-\beta )q^{3}+\cdots\)
4.33.b.a \(1\) \(25.947\) \(\Q\) \(\Q(\sqrt{-1}) \) \(65536\) \(0\) \(-196496109694\) \(0\) \(q+2^{16}q^{2}+2^{32}q^{4}-196496109694q^{5}+\cdots\)
4.33.b.b \(14\) \(25.947\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-23780\) \(0\) \(138121491740\) \(0\) \(q+(-1699+\beta _{1})q^{2}+(9-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
3.38.a.a \(3\) \(26.014\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-310908\) \(-1162261467\) \(-9\!\cdots\!90\) \(-4\!\cdots\!44\) \(+\) \(q+(-103636-\beta _{1})q^{2}-3^{18}q^{3}+(112825533616+\cdots)q^{4}+\cdots\)
3.38.a.b \(4\) \(26.014\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(437562\) \(1549681956\) \(-4\!\cdots\!04\) \(66\!\cdots\!84\) \(-\) \(q+(109391-\beta _{1})q^{2}+3^{18}q^{3}+(86524834843+\cdots)q^{4}+\cdots\)
3.39.b.a \(12\) \(27.439\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-114742404\) \(0\) \(81\!\cdots\!48\) \(q+\beta _{1}q^{2}+(-9561867+97\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
4.34.a.a \(3\) \(27.593\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(92491788\) \(-53880683886\) \(45\!\cdots\!92\) \(-\) \(q+(30830596+\beta _{1})q^{3}+(-17960227962+\cdots)q^{5}+\cdots\)
2.48.a.a \(1\) \(27.982\) \(\Q\) None \(8388608\) \(-196634580372\) \(20\!\cdots\!50\) \(-5\!\cdots\!96\) \(-\) \(q+2^{23}q^{2}-196634580372q^{3}+2^{46}q^{4}+\cdots\)
2.48.a.b \(2\) \(27.982\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-16777216\) \(122289844824\) \(18\!\cdots\!40\) \(16\!\cdots\!32\) \(+\) \(q-2^{23}q^{2}+(61144922412-5\beta )q^{3}+\cdots\)
3.40.a.a \(3\) \(28.902\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-1107000\) \(3486784401\) \(93\!\cdots\!90\) \(13\!\cdots\!04\) \(-\) \(q+(-369000-\beta _{1})q^{2}+3^{19}q^{3}+(335300075200+\cdots)q^{4}+\cdots\)
3.40.a.b \(3\) \(28.902\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(533574\) \(-3486784401\) \(-5\!\cdots\!30\) \(-1\!\cdots\!28\) \(+\) \(q+(177858-\beta _{1})q^{2}-3^{19}q^{3}+(319147551244+\cdots)q^{4}+\cdots\)
4.35.b.a \(16\) \(29.290\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-27372\) \(0\) \(-21372255840\) \(0\) \(q+(-1711+\beta _{1})q^{2}+(19-76\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.41.b.a \(12\) \(30.403\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-372082572\) \(0\) \(-9\!\cdots\!84\) \(q+\beta _{1}q^{2}+(-31006881-471\beta _{1}+\cdots)q^{3}+\cdots\)
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