Properties

Level $30$
Weight $0$
Character 30.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( 0 \)
Character: 30.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.94690379979 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.408248290\) \(a_{7}=-0.847794342\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.979171513\) \(a_{12}=-0.288675135\) \(a_{13}=+0.144154322\) \(a_{14}=-0.599481128\) \(a_{15}=+0.258198890\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.386512760\) \(a_{18}=+0.235702260\) \(a_{19}=+1.084858400\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.489474292\) \(a_{22}=+0.692378817\) \(a_{23}=-0.807497935\) \(a_{24}=-0.204124145\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.101932499\) \(a_{27}=-0.192450090\) \(a_{28}=-0.423897171\) \(a_{29}=-1.285124311\) \(a_{30}=+0.182574186\)
\(a_{31}=-1.578995869\) \(a_{32}=+0.176776695\) \(a_{33}=-0.565324937\) \(a_{34}=-0.273305794\) \(a_{35}=+0.379145156\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.332462223\) \(a_{38}=+0.767110731\) \(a_{39}=-0.083227537\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.397451079\) \(a_{42}=+0.346110591\) \(a_{43}=+0.165925265\) \(a_{44}=+0.489585756\) \(a_{45}=-0.149071198\)
\(a_{46}=-0.570987266\) \(a_{47}=+1.154059689\) \(a_{48}=-0.144337567\) \(a_{49}=-0.281244754\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.223153246\) \(a_{52}=+0.072077161\) \(a_{53}=+0.757028685\) \(a_{54}=-0.136082763\) \(a_{55}=-0.437898813\)
\(a_{56}=-0.299740564\) \(a_{57}=-0.626343289\) \(a_{58}=-0.908720115\) \(a_{59}=-0.458479303\) \(a_{60}=+0.129099445\)
\(a_{61}=+1.593535454\) \(a_{62}=-1.116518686\) \(a_{63}=-0.282598114\) \(a_{64}=+0.125000000\) \(a_{65}=-0.064467773\)
\(a_{66}=-0.399745096\) \(a_{67}=-1.508236664\) \(a_{68}=-0.193256380\) \(a_{69}=+0.466209150\) \(a_{70}=+0.268096111\)
\(a_{71}=-0.656530895\) \(a_{72}=+0.117851130\) \(a_{73}=+0.635607808\) \(a_{74}=+0.942193074\) \(a_{75}=-0.115470054\)
\(a_{76}=+0.542429200\) \(a_{77}=-0.830136069\) \(a_{78}=-0.058850756\) \(a_{79}=+0.360364514\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.281040353\) \(a_{83}=+0.092549726\) \(a_{84}=+0.244737146\) \(a_{85}=+0.172853761\)
\(a_{86}=+0.117326880\) \(a_{87}=+0.741966867\) \(a_{88}=+0.346189408\) \(a_{89}=-0.181792167\) \(a_{90}=-0.105409255\)
\(a_{91}=-0.122213219\) \(a_{92}=-0.403748968\) \(a_{93}=+0.911633690\) \(a_{94}=+0.816043432\) \(a_{95}=-0.485163426\)
\(a_{96}=-0.102062073\) \(a_{97}=-1.638737574\) \(a_{98}=-0.198870072\) \(a_{99}=+0.326390504\) \(a_{100}=+0.099975586\)

Showing 100 of 460 available coefficients

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