Properties

Level $7$
Weight $0$
Character 7.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.71971646829 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.334450847\) \(a_{3}=+1.195985257\) \(a_{4}=+0.780759064\) \(a_{5}=-1.283421141\)
\(a_{6}=+1.595983540\) \(a_{7}=+0.377964473\) \(a_{8}=-0.292566253\) \(a_{9}=+0.430380736\) \(a_{10}=-1.712662429\)
\(a_{11}=-0.201797744\) \(a_{12}=+0.933776330\) \(a_{13}=+1.382097035\) \(a_{14}=+0.504375011\) \(a_{15}=-1.534952764\)
\(a_{16}=-1.171174348\) \(a_{17}=+0.974143145\) \(a_{18}=+0.574321937\) \(a_{19}=+0.044422949\) \(a_{20}=-1.002042689\)
\(a_{21}=+0.452039937\) \(a_{22}=-0.269289171\) \(a_{23}=-0.134028826\) \(a_{24}=-0.349904925\) \(a_{25}=+0.647169826\)
\(a_{26}=+1.844340559\) \(a_{27}=-0.681256242\) \(a_{28}=+0.295099188\) \(a_{29}=-0.269410943\) \(a_{30}=-2.048319016\)
\(a_{31}=+1.077382449\) \(a_{32}=-1.270308348\) \(a_{33}=-0.241347127\) \(a_{34}=+1.299946146\) \(a_{35}=-0.485087595\)
\(a_{36}=+0.336023660\) \(a_{37}=-0.000213219\) \(a_{38}=+0.059280241\) \(a_{39}=+1.652967678\) \(a_{40}=+0.375485714\)
\(a_{41}=-0.737793293\) \(a_{42}=+0.603225078\) \(a_{43}=-1.260993513\) \(a_{44}=-0.157555418\) \(a_{45}=-0.552359735\)
\(a_{46}=-0.178854881\) \(a_{47}=-0.215931148\) \(a_{48}=-1.400707254\) \(a_{49}=+0.142857143\) \(a_{50}=+0.863616322\)
\(a_{51}=+1.165060840\) \(a_{52}=+1.079084787\) \(a_{53}=+0.183258472\) \(a_{54}=-0.909102970\) \(a_{55}=+0.258991491\)
\(a_{56}=-0.110579650\) \(a_{57}=+0.053129192\) \(a_{58}=-0.359515661\) \(a_{59}=+0.033501980\) \(a_{60}=-1.198428283\)
\(a_{61}=+0.640577387\) \(a_{62}=+1.437713922\) \(a_{63}=+0.162668628\) \(a_{64}=-0.523989704\) \(a_{65}=-1.773812554\)
\(a_{66}=-0.322065878\) \(a_{67}=+1.299878623\) \(a_{68}=+0.760571090\) \(a_{69}=-0.160296500\) \(a_{70}=-0.647325553\)
\(a_{71}=-0.563052550\) \(a_{72}=-0.125914879\) \(a_{73}=-1.301766935\) \(a_{74}=-0.000284531\) \(a_{75}=+0.774005570\)
\(a_{76}=+0.034683620\) \(a_{77}=-0.076272378\) \(a_{78}=+2.205804118\) \(a_{79}=+1.962907767\) \(a_{80}=+1.503109918\)
\(a_{81}=-1.245153158\) \(a_{82}=-0.984548885\) \(a_{83}=-1.072787699\) \(a_{84}=+0.352934279\) \(a_{85}=-1.250235907\)
\(a_{86}=-1.682733861\) \(a_{87}=-0.322211516\) \(a_{88}=+0.059039210\) \(a_{89}=+0.873840604\) \(a_{90}=-0.737096916\)
\(a_{91}=+0.522383577\) \(a_{92}=-0.104644221\) \(a_{93}=+1.288533525\) \(a_{94}=-0.288149503\) \(a_{95}=-0.057013351\)
\(a_{96}=-1.519270057\) \(a_{97}=+1.580828104\) \(a_{98}=+0.190635835\) \(a_{99}=-0.086849862\) \(a_{100}=+0.505283707\)

Showing 100 of 1228 available coefficients

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