Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 18.3266193296 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.478805993\) \(a_{3}=+0.577350269\) \(a_{4}=-0.770744821\) \(a_{5}=+0.379966435\)
\(a_{6}=+0.276438769\) \(a_{7}=+0.204632958\) \(a_{8}=-0.847843233\) \(a_{9}=+0.333333333\) \(a_{10}=+0.181930206\)
\(a_{11}=-0.955797366\) \(a_{12}=-0.444989730\) \(a_{13}=-0.674632593\) \(a_{14}=+0.097979487\) \(a_{15}=+0.219373724\)
\(a_{16}=+0.364792400\) \(a_{17}=+1.075127167\) \(a_{18}=+0.159601998\) \(a_{19}=-1.645001780\) \(a_{20}=-0.292857162\)
\(a_{21}=+0.118144893\) \(a_{22}=-0.457641507\) \(a_{23}=-1.600726076\) \(a_{24}=-0.489502519\) \(a_{25}=-0.855625508\)
\(a_{26}=-0.323018129\) \(a_{27}=+0.192450090\) \(a_{28}=-0.157719793\) \(a_{29}=-0.448657143\) \(a_{30}=+0.105037454\)
\(a_{31}=-1.503181995\) \(a_{32}=+1.022508020\) \(a_{33}=-0.551829867\) \(a_{34}=+0.514777331\) \(a_{35}=+0.077753656\)
\(a_{36}=-0.256914940\) \(a_{37}=+0.643725478\) \(a_{38}=-0.787636711\) \(a_{39}=-0.389499309\) \(a_{40}=-0.322151971\)
\(a_{41}=+0.727869150\) \(a_{42}=+0.056568483\) \(a_{43}=-0.170941339\) \(a_{44}=+0.736675870\) \(a_{45}=+0.126655478\)
\(a_{46}=-0.766437239\) \(a_{47}=+0.065952529\) \(a_{48}=+0.210612990\) \(a_{49}=-0.958125352\) \(a_{50}=-0.409678621\)
\(a_{51}=+0.620724959\) \(a_{52}=+0.519969577\) \(a_{53}=+0.902009892\) \(a_{54}=+0.092146256\) \(a_{55}=-0.363170918\)
\(a_{56}=-0.173496669\) \(a_{57}=-0.949742220\) \(a_{58}=-0.214819729\) \(a_{59}=-0.207064003\) \(a_{60}=-0.169081161\)
\(a_{61}=+1.883897108\) \(a_{62}=-0.719732548\) \(a_{63}=+0.068210986\) \(a_{64}=+0.124790569\) \(a_{65}=-0.256337741\)
\(a_{66}=-0.264219447\) \(a_{67}=+1.614522529\) \(a_{68}=-0.828648696\) \(a_{69}=-0.924179631\) \(a_{70}=+0.037228916\)
\(a_{71}=-0.338183608\) \(a_{72}=-0.282614411\) \(a_{73}=+0.632179549\) \(a_{74}=+0.308219617\) \(a_{75}=-0.493995617\)
\(a_{76}=+1.267876602\) \(a_{77}=-0.195587642\) \(a_{78}=-0.186494604\) \(a_{79}=-0.059243982\) \(a_{80}=+0.138608868\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.348508112\) \(a_{83}=-1.855502841\) \(a_{84}=-0.091059565\) \(a_{85}=+0.408512237\)
\(a_{86}=-0.081847738\) \(a_{87}=-0.259032322\) \(a_{88}=+0.810366329\) \(a_{89}=+0.500125608\) \(a_{90}=+0.060643402\)
\(a_{91}=-0.138052063\) \(a_{92}=+1.233751332\) \(a_{93}=-0.867862530\) \(a_{94}=+0.031578466\) \(a_{95}=-0.625045462\)
\(a_{96}=+0.590345281\) \(a_{97}=-1.111385382\) \(a_{98}=-0.458756161\) \(a_{99}=-0.318599122\) \(a_{100}=+0.659468929\)

Showing 100 of 1228 available coefficients

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