Properties

Level $21$
Weight $0$
Character 21.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 6.83466200161 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.455811596\) \(a_{3}=+0.577350269\) \(a_{4}=+1.119387403\) \(a_{5}=+1.182673723\)
\(a_{6}=+0.840513217\) \(a_{7}=+0.377964473\) \(a_{8}=+0.173805565\) \(a_{9}=+0.333333333\) \(a_{10}=+1.721750121\)
\(a_{11}=+0.516204032\) \(a_{12}=+0.646278618\) \(a_{13}=-0.776375922\) \(a_{14}=+0.550245063\) \(a_{15}=+0.682816993\)
\(a_{16}=-0.866359245\) \(a_{17}=+0.817377394\) \(a_{18}=+0.485270532\) \(a_{19}=+1.321760863\) \(a_{20}=+1.323870068\)
\(a_{21}=+0.218217890\) \(a_{22}=+0.751495815\) \(a_{23}=+0.449398839\) \(a_{24}=+0.100346690\) \(a_{25}=+0.398717136\)
\(a_{26}=-1.130257071\) \(a_{27}=+0.192450090\) \(a_{28}=+0.423088670\) \(a_{29}=-1.577541445\) \(a_{30}=+0.994052896\)
\(a_{31}=+1.084761277\) \(a_{32}=-1.435061401\) \(a_{33}=+0.298030537\) \(a_{34}=+1.189947488\) \(a_{35}=+0.447008651\)
\(a_{36}=+0.373129134\) \(a_{37}=-0.380820791\) \(a_{38}=+1.924234791\) \(a_{39}=-0.448240848\) \(a_{40}=+0.205555275\)
\(a_{41}=-1.760863938\) \(a_{42}=+0.317684135\) \(a_{43}=-0.696206710\) \(a_{44}=+0.577832290\) \(a_{45}=+0.394224574\)
\(a_{46}=+0.654240041\) \(a_{47}=-1.616301166\) \(a_{48}=-0.500192743\) \(a_{49}=+0.142857143\) \(a_{50}=+0.580457030\)
\(a_{51}=+0.471913058\) \(a_{52}=-0.869065427\) \(a_{53}=+1.342359414\) \(a_{54}=+0.280171072\) \(a_{55}=+0.610500944\)
\(a_{56}=+0.065692329\) \(a_{57}=+0.763118990\) \(a_{58}=-2.296603128\) \(a_{59}=-1.675168804\) \(a_{60}=+0.764336740\)
\(a_{61}=-1.002027981\) \(a_{62}=+1.579208046\) \(a_{63}=+0.125988158\) \(a_{64}=-1.222819783\) \(a_{65}=-0.918199403\)
\(a_{66}=+0.433876311\) \(a_{67}=+0.867136799\) \(a_{68}=+0.914961958\) \(a_{69}=+0.259460541\) \(a_{70}=+0.650760377\)
\(a_{71}=+1.000615143\) \(a_{72}=+0.057935188\) \(a_{73}=+0.193786444\) \(a_{74}=-0.554403323\) \(a_{75}=+0.230199446\)
\(a_{76}=+1.479562459\) \(a_{77}=+0.195106785\) \(a_{78}=-0.652554224\) \(a_{79}=-0.829233843\) \(a_{80}=-1.024620314\)
\(a_{81}=+0.111111111\) \(a_{82}=-2.563486140\) \(a_{83}=+0.036460521\) \(a_{84}=+0.244270357\) \(a_{85}=+0.966690765\)
\(a_{86}=-1.013545801\) \(a_{87}=-0.910793978\) \(a_{88}=+0.089719134\) \(a_{89}=+1.398311546\) \(a_{90}=+0.573916707\)
\(a_{91}=-0.293442516\) \(a_{92}=+0.503051399\) \(a_{93}=+0.626287215\) \(a_{94}=-2.353029980\) \(a_{95}=+1.563211841\)
\(a_{96}=-0.828533086\) \(a_{97}=-1.235729539\) \(a_{98}=+0.207973085\) \(a_{99}=+0.172068011\) \(a_{100}=+0.446318939\)

Showing 100 of 240 available coefficients

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