Properties

Level $421$
Weight $0$
Character 421.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 421 \)
Weight: \( 0 \)
Character: 421.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.86609031637 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.322541285\) \(a_{3}=-0.407570153\) \(a_{4}=+0.749115451\) \(a_{5}=-0.576426937\)
\(a_{6}=-0.539028353\) \(a_{7}=-0.786054893\) \(a_{8}=-0.331805173\) \(a_{9}=-0.833886553\) \(a_{10}=-0.762348412\)
\(a_{11}=-0.145158325\) \(a_{12}=-0.305317113\) \(a_{13}=-0.358207356\) \(a_{14}=-1.039590036\) \(a_{15}=+0.234934404\)
\(a_{16}=-1.187941494\) \(a_{17}=+0.134165759\) \(a_{18}=-1.102849411\) \(a_{19}=+1.017213301\) \(a_{20}=-0.431810311\)
\(a_{21}=+0.320372510\) \(a_{22}=-0.191977886\) \(a_{23}=+0.102837640\) \(a_{24}=+0.135233868\) \(a_{25}=-0.667731997\)
\(a_{26}=-0.473744021\) \(a_{27}=+0.747437437\) \(a_{28}=-0.588845844\) \(a_{29}=+0.273544612\) \(a_{30}=+0.310710451\)
\(a_{31}=-0.528878381\) \(a_{32}=-1.239296491\) \(a_{33}=+0.059162204\) \(a_{34}=+0.177439753\) \(a_{35}=+0.453103201\)
\(a_{36}=-0.624677320\) \(a_{37}=+0.271117197\) \(a_{38}=+1.345306585\) \(a_{39}=+0.145994625\) \(a_{40}=+0.191261438\)
\(a_{41}=-0.074683948\) \(a_{42}=+0.423705884\) \(a_{43}=-0.558611396\) \(a_{44}=-0.108740367\) \(a_{45}=+0.480674671\)
\(a_{46}=+0.136007030\) \(a_{47}=+0.447731627\) \(a_{48}=+0.484169493\) \(a_{49}=-0.382117718\) \(a_{50}=-0.883103131\)
\(a_{51}=-0.054681956\) \(a_{52}=-0.268338665\) \(a_{53}=-1.271312799\) \(a_{54}=+0.988516875\) \(a_{55}=+0.083673182\)
\(a_{56}=+0.260817093\) \(a_{57}=-0.414585808\) \(a_{58}=+0.361774038\) \(a_{59}=+1.306588757\) \(a_{60}=+0.175993014\)
\(a_{61}=-1.352824298\) \(a_{62}=-0.699463507\) \(a_{63}=+0.655480602\) \(a_{64}=-0.451079284\) \(a_{65}=+0.206480366\)
\(a_{66}=+0.078244472\) \(a_{67}=+1.056001123\) \(a_{68}=+0.100505627\) \(a_{69}=-0.041913562\) \(a_{70}=+0.599247679\)
\(a_{71}=-0.339352725\) \(a_{72}=+0.276687878\) \(a_{73}=-0.422911307\) \(a_{74}=+0.358563683\) \(a_{75}=+0.272147655\)
\(a_{76}=+0.762010195\) \(a_{77}=+0.114102406\) \(a_{78}=+0.193083918\) \(a_{79}=-1.398328253\) \(a_{80}=+0.684761462\)
\(a_{81}=+0.529253355\) \(a_{82}=-0.098772639\) \(a_{83}=-0.060340655\) \(a_{84}=+0.239996020\) \(a_{85}=-0.077336754\)
\(a_{86}=-0.738786633\) \(a_{87}=-0.111488616\) \(a_{88}=+0.048164294\) \(a_{89}=+1.255677731\) \(a_{90}=+0.635712106\)
\(a_{91}=+0.281570634\) \(a_{92}=+0.077037270\) \(a_{93}=+0.215555063\) \(a_{94}=+0.592143542\) \(a_{95}=-0.586349117\)
\(a_{96}=+0.505100283\) \(a_{97}=+0.164106240\) \(a_{98}=-0.505366478\) \(a_{99}=+0.121045580\) \(a_{100}=-0.500208367\)

Showing 100 of 1422 available coefficients

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