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: \( 7.71956232873 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.263994096\) \(a_{3}=-0.699651923\) \(a_{4}=+0.597681074\) \(a_{5}=-0.673438488\)
\(a_{6}=-0.884355900\) \(a_{7}=-0.377964473\) \(a_{8}=-0.508528747\) \(a_{9}=-0.510487187\) \(a_{10}=-0.851222273\)
\(a_{11}=-0.750087566\) \(a_{12}=-0.418168713\) \(a_{13}=+0.616923173\) \(a_{14}=-0.477744862\) \(a_{15}=+0.471172533\)
\(a_{16}=-1.240458408\) \(a_{17}=+1.342191393\) \(a_{18}=-0.645252790\) \(a_{19}=-0.120991947\) \(a_{20}=-0.402501439\)
\(a_{21}=+0.264443570\) \(a_{22}=-0.948106255\) \(a_{23}=+0.919460169\) \(a_{24}=+0.355793115\) \(a_{25}=-0.546480603\)
\(a_{26}=+0.779787248\) \(a_{27}=+1.056815265\) \(a_{28}=-0.225902212\) \(a_{29}=-1.662946197\) \(a_{30}=+0.595559300\)
\(a_{31}=-1.340800111\) \(a_{32}=-1.059403357\) \(a_{33}=+0.524800208\) \(a_{34}=+1.696521996\) \(a_{35}=+0.254535823\)
\(a_{36}=-0.305108530\) \(a_{37}=+1.503288048\) \(a_{38}=-0.152933107\) \(a_{39}=-0.431631484\) \(a_{40}=+0.342462830\)
\(a_{41}=-1.563814145\) \(a_{42}=+0.334255112\) \(a_{43}=-1.255234391\) \(a_{44}=-0.448313142\) \(a_{45}=+0.343781719\)
\(a_{46}=+1.162192225\) \(a_{47}=-0.020062902\) \(a_{48}=+0.867889110\) \(a_{49}=+0.142857143\) \(a_{50}=-0.690748256\)
\(a_{51}=-0.939066789\) \(a_{52}=+0.368723305\) \(a_{53}=-0.352404240\) \(a_{54}=+1.335808255\) \(a_{55}=+0.505137836\)
\(a_{56}=+0.192205800\) \(a_{57}=+0.084652249\) \(a_{58}=-2.101954175\) \(a_{59}=+0.609868888\) \(a_{60}=+0.281610906\)
\(a_{61}=+0.889291906\) \(a_{62}=-1.694763425\) \(a_{63}=+0.192946021\) \(a_{64}=-0.098621181\) \(a_{65}=-0.415459809\)
\(a_{66}=+0.663344364\) \(a_{67}=-0.582350136\) \(a_{68}=+0.802202394\) \(a_{69}=-0.643302075\) \(a_{70}=+0.321731778\)
\(a_{71}=-0.226751061\) \(a_{72}=+0.259597409\) \(a_{73}=-0.188547957\) \(a_{74}=+1.900147217\) \(a_{75}=+0.382346205\)
\(a_{76}=-0.072314597\) \(a_{77}=+0.283506452\) \(a_{78}=-0.545579648\) \(a_{79}=-1.038788003\) \(a_{80}=+0.835372434\)
\(a_{81}=-0.228915645\) \(a_{82}=-1.976651847\) \(a_{83}=+0.196424265\) \(a_{84}=+0.158052917\) \(a_{85}=-0.903883342\)
\(a_{86}=-1.586608859\) \(a_{87}=+1.163483504\) \(a_{88}=+0.381441090\) \(a_{89}=+1.063230421\) \(a_{90}=+0.434538063\)
\(a_{91}=-0.233175042\) \(a_{92}=+0.549543942\) \(a_{93}=+0.938093376\) \(a_{94}=-0.025359390\) \(a_{95}=+0.081480634\)
\(a_{96}=+0.741213596\) \(a_{97}=-0.685072102\) \(a_{98}=+0.180570585\) \(a_{99}=+0.382910091\) \(a_{100}=-0.326621114\)

Showing 100 of 1228 available coefficients

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