Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 11.0009604498 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.863089481\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.317403206\) \(a_{7}=-0.752339590\) \(a_{8}=+0.353553391\) \(a_{9}=+2.471102415\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.229867700\) \(a_{12}=+0.931544741\) \(a_{13}=+1.147711167\) \(a_{14}=-0.531984426\) \(a_{15}=-0.833198946\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.424722457\) \(a_{18}=+1.747333274\) \(a_{19}=-0.014152799\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.401675977\) \(a_{22}=+0.869647791\) \(a_{23}=+0.937103462\) \(a_{24}=+0.658701603\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.811554349\) \(a_{27}=+2.740795435\) \(a_{28}=-0.376169795\) \(a_{29}=-0.432680618\) \(a_{30}=-0.589160625\)
\(a_{31}=-0.910979749\) \(a_{32}=+0.176776695\) \(a_{33}=+2.291353575\) \(a_{34}=-0.300324129\) \(a_{35}=+0.336456493\)
\(a_{36}=+1.235551207\) \(a_{37}=-1.773247845\) \(a_{38}=-0.010007540\) \(a_{39}=+2.138288602\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.233521758\) \(a_{42}=-0.991134588\) \(a_{43}=+0.947700521\) \(a_{44}=+0.614933850\) \(a_{45}=-1.105110596\)
\(a_{46}=+0.662632212\) \(a_{47}=-1.558931365\) \(a_{48}=+0.465772370\) \(a_{49}=-0.433985141\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.791295941\) \(a_{52}=+0.573855583\) \(a_{53}=+1.054451400\) \(a_{54}=+1.938035038\) \(a_{55}=-0.550013556\)
\(a_{56}=-0.265992213\) \(a_{57}=-0.026367930\) \(a_{58}=-0.305951399\) \(a_{59}=+0.034008333\) \(a_{60}=-0.416599473\)
\(a_{61}=+0.828426571\) \(a_{62}=-0.644159958\) \(a_{63}=-1.859108179\) \(a_{64}=+0.125000000\) \(a_{65}=-0.513272037\)
\(a_{66}=+1.620231651\) \(a_{67}=-0.801626940\) \(a_{68}=-0.212361228\) \(a_{69}=+1.745907602\) \(a_{70}=+0.237910668\)
\(a_{71}=-0.613527256\) \(a_{72}=+0.873666637\) \(a_{73}=-0.511441835\) \(a_{74}=-1.253875576\) \(a_{75}=+0.372617896\)
\(a_{76}=-0.007076399\) \(a_{77}=-0.925278162\) \(a_{78}=+1.511998371\) \(a_{79}=-0.652834903\) \(a_{80}=-0.111803399\)
\(a_{81}=+2.635244730\) \(a_{82}=-0.165124819\) \(a_{83}=-1.149353731\) \(a_{84}=-0.700837989\) \(a_{85}=+0.189941657\)
\(a_{86}=+0.670125465\) \(a_{87}=-0.806122707\) \(a_{88}=+0.434823895\) \(a_{89}=+0.485763238\) \(a_{90}=-0.781431196\)
\(a_{91}=-0.863468526\) \(a_{92}=+0.468551731\) \(a_{93}=-1.697236806\) \(a_{94}=-1.102330940\) \(a_{95}=+0.006329324\)
\(a_{96}=+0.329350802\) \(a_{97}=+0.888106013\) \(a_{98}=-0.306873836\) \(a_{99}=+3.039129030\) \(a_{100}=+0.099975586\)

Showing 100 of 162 available coefficients

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