Properties

Level $14$
Weight $0$
Character 14.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 9.61574104808 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.712327217\) \(a_{4}=+0.500000000\) \(a_{5}=+1.159745470\)
\(a_{6}=+1.210798187\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+1.932064497\) \(a_{10}=+0.820063886\)
\(a_{11}=+1.497335474\) \(a_{12}=+0.856163608\) \(a_{13}=-1.234437469\) \(a_{14}=-0.267261242\) \(a_{15}=+1.985863732\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.570208956\) \(a_{18}=+1.366175908\) \(a_{19}=-0.807818922\) \(a_{20}=+0.579872735\)
\(a_{21}=-0.647198854\) \(a_{22}=+1.058776068\) \(a_{23}=+0.780264497\) \(a_{24}=+0.605399093\) \(a_{25}=+0.345009555\)
\(a_{26}=-0.872879105\) \(a_{27}=+1.595999407\) \(a_{28}=-0.188982236\) \(a_{29}=-0.340003980\) \(a_{30}=+1.404217712\)
\(a_{31}=+0.321433146\) \(a_{32}=+0.176776695\) \(a_{33}=+2.563928286\) \(a_{34}=-1.110305401\) \(a_{35}=-0.438342585\)
\(a_{36}=+0.966032249\) \(a_{37}=+0.704792544\) \(a_{38}=-0.571214238\) \(a_{39}=-2.113760876\) \(a_{40}=+0.410031943\)
\(a_{41}=-0.469933062\) \(a_{42}=-0.457638698\) \(a_{43}=+0.949819985\) \(a_{44}=+0.748667737\) \(a_{45}=+2.240703048\)
\(a_{46}=+0.551730318\) \(a_{47}=-0.444316198\) \(a_{48}=+0.428081803\) \(a_{49}=+0.142857144\) \(a_{50}=+0.243958594\)
\(a_{51}=-2.688711529\) \(a_{52}=-0.617218736\) \(a_{53}=-0.328055400\) \(a_{54}=+1.128542000\) \(a_{55}=+1.736528032\)
\(a_{56}=-0.133630615\) \(a_{57}=-1.383250342\) \(a_{58}=-0.240419084\) \(a_{59}=-0.160739896\) \(a_{60}=+0.992931866\)
\(a_{61}=-0.756126249\) \(a_{62}=+0.227287557\) \(a_{63}=-0.730251739\) \(a_{64}=+0.125000000\) \(a_{65}=-1.431633263\)
\(a_{66}=+1.812971077\) \(a_{67}=+0.708187329\) \(a_{68}=-0.785104478\) \(a_{69}=+1.336068136\) \(a_{70}=-0.309955016\)
\(a_{71}=+0.656033859\) \(a_{72}=+0.683087953\) \(a_{73}=-0.654727839\) \(a_{74}=+0.498363589\) \(a_{75}=+0.590769249\)
\(a_{76}=-0.403909459\) \(a_{77}=-0.565939613\) \(a_{78}=-1.494654651\) \(a_{79}=-0.985027471\) \(a_{80}=+0.289936355\)
\(a_{81}=+0.800808728\) \(a_{82}=-0.332292854\) \(a_{83}=+0.954368368\) \(a_{84}=-0.323599436\) \(a_{85}=-1.821042722\)
\(a_{86}=+0.671624124\) \(a_{87}=-0.582198061\) \(a_{88}=+0.529388048\) \(a_{89}=-1.495588667\) \(a_{90}=+1.584416381\)
\(a_{91}=+0.466573506\) \(a_{92}=+0.390132249\) \(a_{93}=+0.550398725\) \(a_{94}=-0.314178995\) \(a_{95}=-0.936864336\)
\(a_{96}=+0.302699548\) \(a_{97}=+1.354496928\) \(a_{98}=+0.101015255\) \(a_{99}=+2.892948708\) \(a_{100}=+0.172504783\)

Showing 100 of 2000 available coefficients

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