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: \( 7.05407006402 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.400054314\) \(a_{3}=+0.777545535\) \(a_{4}=+0.960152083\) \(a_{5}=+0.342152088\)
\(a_{6}=-1.088605981\) \(a_{7}=-0.377964473\) \(a_{8}=+0.055789248\) \(a_{9}=-0.395422941\) \(a_{10}=-0.479031508\)
\(a_{11}=-1.648431064\) \(a_{12}=+0.746561966\) \(a_{13}=+0.367654230\) \(a_{14}=+0.529170791\) \(a_{15}=+0.266038829\)
\(a_{16}=-1.038260060\) \(a_{17}=-0.305737748\) \(a_{18}=+0.553613594\) \(a_{19}=-1.462942329\) \(a_{20}=+0.328518040\)
\(a_{21}=-0.293884588\) \(a_{22}=+2.307893023\) \(a_{23}=+0.150514190\) \(a_{24}=+0.043378680\) \(a_{25}=-0.882931948\)
\(a_{26}=-0.514735891\) \(a_{27}=-1.085004877\) \(a_{28}=-0.362903376\) \(a_{29}=+1.801982457\) \(a_{30}=-0.372468810\)
\(a_{31}=-0.358750824\) \(a_{32}=+1.397831229\) \(a_{33}=-1.281730214\) \(a_{34}=+0.428049454\) \(a_{35}=-0.129321334\)
\(a_{36}=-0.379666160\) \(a_{37}=-0.707792629\) \(a_{38}=+2.048198720\) \(a_{39}=+0.285867905\) \(a_{40}=+0.019088408\)
\(a_{41}=-1.223475246\) \(a_{42}=+0.411454386\) \(a_{43}=+0.103383730\) \(a_{44}=-1.582744520\) \(a_{45}=-0.135294785\)
\(a_{46}=-0.210728041\) \(a_{47}=+1.038330784\) \(a_{48}=-0.807294474\) \(a_{49}=+0.142857143\) \(a_{50}=+1.236152684\)
\(a_{51}=-0.237725021\) \(a_{52}=+0.353003975\) \(a_{53}=+0.701599502\) \(a_{54}=+1.519065760\) \(a_{55}=-0.564014131\)
\(a_{56}=-0.021086354\) \(a_{57}=-1.137504276\) \(a_{58}=-2.522873313\) \(a_{59}=+0.565231087\) \(a_{60}=+0.255437736\)
\(a_{61}=-0.479448095\) \(a_{62}=+0.502270640\) \(a_{63}=+0.149455823\) \(a_{64}=-0.918779583\) \(a_{65}=+0.125793663\)
\(a_{66}=+1.794491915\) \(a_{67}=+0.199053517\) \(a_{68}=-0.293554736\) \(a_{69}=+0.117031636\) \(a_{70}=+0.181056891\)
\(a_{71}=+0.859673690\) \(a_{72}=-0.022060348\) \(a_{73}=-0.790284304\) \(a_{74}=+0.990948124\) \(a_{75}=-0.686519794\)
\(a_{76}=-1.404647126\) \(a_{77}=+0.623048378\) \(a_{78}=-0.400230594\) \(a_{79}=-0.155785859\) \(a_{80}=-0.355242848\)
\(a_{81}=-0.448217757\) \(a_{82}=+1.712931797\) \(a_{83}=-0.876301498\) \(a_{84}=-0.282173900\) \(a_{85}=-0.104608809\)
\(a_{86}=-0.144742838\) \(a_{87}=+1.401123414\) \(a_{88}=-0.091964729\) \(a_{89}=-0.184612669\) \(a_{90}=+0.189420047\)
\(a_{91}=-0.138960237\) \(a_{92}=+0.144516513\) \(a_{93}=-0.278945102\) \(a_{94}=-1.453719493\) \(a_{95}=-0.500548773\)
\(a_{96}=+1.086877431\) \(a_{97}=+1.936941387\) \(a_{98}=-0.200007759\) \(a_{99}=+0.651827459\) \(a_{100}=-0.847748950\)

Showing 100 of 1228 available coefficients

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