Properties

Level $13$
Weight $0$
Character 13.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.07311267591 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.089280643\) \(a_{3}=-1.454249753\) \(a_{4}=+0.186532319\) \(a_{5}=-1.101636326\)
\(a_{6}=+1.584086106\) \(a_{7}=-0.780322043\) \(a_{8}=+0.886094598\) \(a_{9}=+1.114842345\) \(a_{10}=+1.199991126\)
\(a_{11}=-1.717368169\) \(a_{12}=-0.271264579\) \(a_{13}=-0.277350098\) \(a_{14}=+0.849989696\) \(a_{15}=+1.602054355\)
\(a_{16}=-1.151738013\) \(a_{17}=+0.002807969\) \(a_{18}=-1.214376186\) \(a_{19}=+0.560591478\) \(a_{20}=-0.205490779\)
\(a_{21}=+1.134783138\) \(a_{22}=+1.870695903\) \(a_{23}=-0.910684314\) \(a_{24}=-1.288602851\) \(a_{25}=+0.213602595\)
\(a_{26}=+0.302112093\) \(a_{27}=-0.167009451\) \(a_{28}=-0.145555280\) \(a_{29}=-0.401578379\) \(a_{30}=-1.745086798\)
\(a_{31}=-0.958550385\) \(a_{32}=+0.368471325\) \(a_{33}=+2.497482236\) \(a_{34}=-0.003058666\) \(a_{35}=+0.859631108\)
\(a_{36}=+0.207954128\) \(a_{37}=+1.605027585\) \(a_{38}=-0.610641446\) \(a_{39}=+0.403336312\) \(a_{40}=-0.976153998\)
\(a_{41}=-1.223368978\) \(a_{42}=-1.236097306\) \(a_{43}=+0.932520410\) \(a_{44}=-0.320344668\) \(a_{45}=-1.228150825\)
\(a_{46}=+0.991990795\) \(a_{47}=-0.980493950\) \(a_{48}=+1.674914721\) \(a_{49}=-0.391097510\) \(a_{50}=-0.232673172\)
\(a_{51}=-0.004083488\) \(a_{52}=-0.051734757\) \(a_{53}=-0.004497425\) \(a_{54}=+0.181920163\) \(a_{55}=+1.891915160\)
\(a_{56}=-0.691439147\) \(a_{57}=-0.815240019\) \(a_{58}=+0.437431555\) \(a_{59}=-1.316962634\) \(a_{60}=+0.298834914\)
\(a_{61}=+1.557433759\) \(a_{62}=+1.044130380\) \(a_{63}=-0.869936055\) \(a_{64}=+0.750369331\) \(a_{65}=+0.305538943\)
\(a_{66}=-2.720459056\) \(a_{67}=+0.194380593\) \(a_{68}=+0.000523777\) \(a_{69}=+1.324362439\) \(a_{70}=-0.936379526\)
\(a_{71}=-0.636454795\) \(a_{72}=+0.987855780\) \(a_{73}=+0.079586524\) \(a_{74}=-1.748325480\) \(a_{75}=-0.310631521\)
\(a_{76}=+0.104568429\) \(a_{77}=+1.340100237\) \(a_{78}=-0.439346437\) \(a_{79}=-0.844810958\) \(a_{80}=+1.268796433\)
\(a_{81}=-0.871968891\) \(a_{82}=+1.332592147\) \(a_{83}=+0.092146789\) \(a_{84}=+0.211673730\) \(a_{85}=-0.003093360\)
\(a_{86}=-1.015776431\) \(a_{87}=+0.583995259\) \(a_{88}=-1.521750658\) \(a_{89}=+0.219842078\) \(a_{90}=+1.337800920\)
\(a_{91}=+0.216422395\) \(a_{92}=-0.169872057\) \(a_{93}=+1.393971661\) \(a_{94}=+1.068033080\) \(a_{95}=-0.617567936\)
\(a_{96}=-0.535849334\) \(a_{97}=-0.286614769\) \(a_{98}=+0.426014947\) \(a_{99}=-1.914594756\) \(a_{100}=+0.039843787\)

Showing 100 of 546 available coefficients

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