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: \( 6.01533951853 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.903859168\) \(a_{4}=+0.500000000\) \(a_{5}=+0.056259157\)
\(a_{6}=+1.346231728\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+2.624679733\) \(a_{10}=+0.039781231\)
\(a_{11}=-1.034216332\) \(a_{12}=+0.951929584\) \(a_{13}=+0.287080290\) \(a_{14}=-0.267261242\) \(a_{15}=+0.107109512\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.201087246\) \(a_{18}=+1.855928838\) \(a_{19}=-0.897807973\) \(a_{20}=+0.028129578\)
\(a_{21}=-0.719591127\) \(a_{22}=-0.731301382\) \(a_{23}=-1.017767699\) \(a_{24}=+0.673115864\) \(a_{25}=-0.996834907\)
\(a_{26}=+0.202996420\) \(a_{27}=+3.093161406\) \(a_{28}=-0.188982237\) \(a_{29}=-0.926658972\) \(a_{30}=+0.075737862\)
\(a_{31}=+0.200540484\) \(a_{32}=+0.176776695\) \(a_{33}=-1.969002246\) \(a_{34}=+0.849296937\) \(a_{35}=-0.021263963\)
\(a_{36}=+1.312339867\) \(a_{37}=-0.190053825\) \(a_{38}=-0.634846106\) \(a_{39}=+0.546560442\) \(a_{40}=+0.019890616\)
\(a_{41}=+0.076078951\) \(a_{42}=-0.508827766\) \(a_{43}=+0.127591615\) \(a_{44}=-0.517108166\) \(a_{45}=+0.147662269\)
\(a_{46}=-0.719670442\) \(a_{47}=-1.732053823\) \(a_{48}=+0.475964792\) \(a_{49}=+0.142857143\) \(a_{50}=-0.704868723\)
\(a_{51}=+2.286700966\) \(a_{52}=+0.143540145\) \(a_{53}=+0.982822751\) \(a_{54}=+2.187195405\) \(a_{55}=-0.058184139\)
\(a_{56}=-0.133630621\) \(a_{57}=-1.709299942\) \(a_{58}=-0.655246843\) \(a_{59}=-0.588527684\) \(a_{60}=+0.053554756\)
\(a_{61}=+0.621447661\) \(a_{62}=+0.141803536\) \(a_{63}=-0.992035692\) \(a_{64}=+0.125000000\) \(a_{65}=+0.016150895\)
\(a_{66}=-1.392294840\) \(a_{67}=+1.233525722\) \(a_{68}=+0.600543623\) \(a_{69}=-1.937686366\) \(a_{70}=-0.015035892\)
\(a_{71}=+0.763622670\) \(a_{72}=+0.927964419\) \(a_{73}=+0.607058032\) \(a_{74}=-0.134388349\) \(a_{75}=-1.897833278\)
\(a_{76}=-0.448903987\) \(a_{77}=+0.390897031\) \(a_{78}=+0.386476595\) \(a_{79}=-0.488807965\) \(a_{80}=+0.014064789\)
\(a_{81}=+3.264263969\) \(a_{82}=+0.053795942\) \(a_{83}=+0.504051546\) \(a_{84}=-0.359795564\) \(a_{85}=+0.067572156\)
\(a_{86}=+0.090220896\) \(a_{87}=-1.764228180\) \(a_{88}=-0.365650691\) \(a_{89}=+1.465133415\) \(a_{90}=+0.104412992\)
\(a_{91}=-0.108506150\) \(a_{92}=-0.508883850\) \(a_{93}=+0.381800839\) \(a_{94}=-1.224747004\) \(a_{95}=-0.050509920\)
\(a_{96}=+0.336557932\) \(a_{97}=-0.611067058\) \(a_{98}=+0.101015254\) \(a_{99}=-2.714486646\) \(a_{100}=-0.498417454\)

Showing 100 of 190 available coefficients

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