Properties

Level $823$
Weight $0$
Character 823.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 823 \)
Weight: \( 0 \)
Character: 823.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.08617381 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.015465941\) \(a_{3}=+1.068001422\) \(a_{4}=-0.999760867\) \(a_{5}=+1.468033139\)
\(a_{6}=-0.016517647\) \(a_{7}=+1.396958014\) \(a_{8}=+0.030928091\) \(a_{9}=+0.140626941\) \(a_{10}=-0.022704440\)
\(a_{11}=+1.039949607\) \(a_{12}=-1.067745982\) \(a_{13}=-0.599753049\) \(a_{14}=-0.021605254\) \(a_{15}=+1.567861380\)
\(a_{16}=+0.999282445\) \(a_{17}=-0.829801535\) \(a_{18}=-0.002174961\) \(a_{19}=-0.025455591\) \(a_{20}=-1.467682031\)
\(a_{21}=+1.491953127\) \(a_{22}=-0.016083781\) \(a_{23}=+0.408204036\) \(a_{24}=+0.033031258\) \(a_{25}=+1.155121079\)
\(a_{26}=+0.009275720\) \(a_{27}=-0.917811711\) \(a_{28}=-1.396623878\) \(a_{29}=-0.061663606\) \(a_{30}=-0.024248407\)
\(a_{31}=-0.708103773\) \(a_{32}=-0.046382956\) \(a_{33}=+1.110667696\) \(a_{34}=+0.012833644\) \(a_{35}=+2.050780598\)
\(a_{36}=-0.140593426\) \(a_{37}=+1.061938448\) \(a_{38}=+0.000393683\) \(a_{39}=-0.640537072\) \(a_{40}=+0.045403478\)
\(a_{41}=-1.828736957\) \(a_{42}=-0.023074413\) \(a_{43}=+0.389359115\) \(a_{44}=-1.039700964\) \(a_{45}=+0.206445041\)
\(a_{46}=-0.006313291\) \(a_{47}=-0.159229518\) \(a_{48}=+1.067235080\) \(a_{49}=+0.951491570\) \(a_{50}=-0.017865026\)
\(a_{51}=-0.886229253\) \(a_{52}=+0.599609586\) \(a_{53}=-0.241456641\) \(a_{54}=+0.014194898\) \(a_{55}=+1.526680417\)
\(a_{56}=+0.043205345\) \(a_{57}=-0.027186626\) \(a_{58}=+0.000953597\) \(a_{59}=+1.045593493\) \(a_{60}=-1.567486510\)
\(a_{61}=+0.948192807\) \(a_{62}=+0.010951382\) \(a_{63}=+0.196449909\) \(a_{64}=-0.998565088\) \(a_{65}=-0.880457355\)
\(a_{66}=-0.017177347\) \(a_{67}=+1.551667066\) \(a_{68}=+0.829603315\) \(a_{69}=+0.435962363\) \(a_{70}=-0.031717003\)
\(a_{71}=-0.371289429\) \(a_{72}=+0.004349226\) \(a_{73}=-1.119427033\) \(a_{74}=-0.016423950\) \(a_{75}=+1.233670978\)
\(a_{76}=+0.025449450\) \(a_{77}=+1.452766019\) \(a_{78}=+0.009906431\) \(a_{79}=+1.200342964\) \(a_{80}=+1.466979930\)
\(a_{81}=-1.120851171\) \(a_{82}=+0.028283101\) \(a_{83}=+0.723542496\) \(a_{84}=-1.491596129\) \(a_{85}=-1.218176345\)
\(a_{86}=-0.006021771\) \(a_{87}=-0.065856777\) \(a_{88}=+0.032163480\) \(a_{89}=-0.558536498\) \(a_{90}=-0.003192868\)
\(a_{91}=-0.837829807\) \(a_{92}=-0.408106470\) \(a_{93}=-0.756255743\) \(a_{94}=+0.002462461\) \(a_{95}=-0.037369724\)
\(a_{96}=-0.049536969\) \(a_{97}=-1.346333309\) \(a_{98}=-0.014715677\) \(a_{99}=+0.146245021\) \(a_{100}=-1.154844735\)

Showing 100 of 2160 available coefficients

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