Properties

Level $14$
Weight $0$
Character 14.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 11.9684600064 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.200849261\) \(a_{4}=+0.500000000\) \(a_{5}=+0.644934809\)
\(a_{6}=+0.849128656\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+0.442038947\) \(a_{10}=+0.456037777\)
\(a_{11}=+0.951638864\) \(a_{12}=+0.600424630\) \(a_{13}=-0.602826101\) \(a_{14}=+0.267261242\) \(a_{15}=+0.774469488\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.025273317\) \(a_{18}=+0.312568737\) \(a_{19}=+0.611725628\) \(a_{20}=+0.322467404\)
\(a_{21}=+0.453878358\) \(a_{22}=+0.672910294\) \(a_{23}=+0.927111498\) \(a_{24}=+0.424564328\) \(a_{25}=-0.584059093\)
\(a_{26}=-0.426262424\) \(a_{27}=-0.670027118\) \(a_{28}=+0.188982237\) \(a_{29}=-1.754171237\) \(a_{30}=+0.547632627\)
\(a_{31}=+0.507682108\) \(a_{32}=+0.176776695\) \(a_{33}=+1.142774827\) \(a_{34}=+0.724977715\) \(a_{35}=+0.243762445\)
\(a_{36}=+0.221019474\) \(a_{37}=-0.352891027\) \(a_{38}=+0.432555340\) \(a_{39}=-0.723903278\) \(a_{40}=+0.228018888\)
\(a_{41}=-0.129633305\) \(a_{42}=+0.320940465\) \(a_{43}=+1.785340720\) \(a_{44}=+0.475819432\) \(a_{45}=+0.285086304\)
\(a_{46}=+0.655566827\) \(a_{47}=+0.479248021\) \(a_{48}=+0.300212315\) \(a_{49}=+0.142857143\) \(a_{50}=-0.412992145\)
\(a_{51}=+1.231198705\) \(a_{52}=-0.301413050\) \(a_{53}=+1.272315740\) \(a_{54}=-0.473780719\) \(a_{55}=+0.613745029\)
\(a_{56}=+0.133630621\) \(a_{57}=+0.734590269\) \(a_{58}=-1.240386377\) \(a_{59}=-0.673967902\) \(a_{60}=+0.387234744\)
\(a_{61}=-0.814694783\) \(a_{62}=+0.358985461\) \(a_{63}=+0.167075018\) \(a_{64}=+0.125000000\) \(a_{65}=-0.388783536\)
\(a_{66}=+0.808063829\) \(a_{67}=+1.050061884\) \(a_{68}=+0.512636658\) \(a_{69}=+1.113321157\) \(a_{70}=+0.172366078\)
\(a_{71}=-1.522221685\) \(a_{72}=+0.156284369\) \(a_{73}=+0.558808793\) \(a_{74}=-0.249531639\) \(a_{75}=-0.701366930\)
\(a_{76}=+0.305862814\) \(a_{77}=+0.359685682\) \(a_{78}=-0.511876917\) \(a_{79}=+0.534915593\) \(a_{80}=+0.161233702\)
\(a_{81}=-1.246640516\) \(a_{82}=-0.091664589\) \(a_{83}=-1.040352221\) \(a_{84}=+0.226939179\) \(a_{85}=+0.661234450\)
\(a_{86}=+1.262426530\) \(a_{87}=-2.106495233\) \(a_{88}=+0.336455147\) \(a_{89}=+0.860252549\) \(a_{90}=+0.201586459\)
\(a_{91}=-0.227846850\) \(a_{92}=+0.463555749\) \(a_{93}=+0.609649684\) \(a_{94}=+0.338879525\) \(a_{95}=+0.394523151\)
\(a_{96}=+0.212282164\) \(a_{97}=-1.738937431\) \(a_{98}=+0.101015254\) \(a_{99}=+0.420661442\) \(a_{100}=-0.292029546\)

Showing 100 of 210 available coefficients

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