Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 31.5662754118 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.530998146\) \(a_{3}=-0.847994540\) \(a_{4}=-0.718040969\) \(a_{5}=-1.392498603\)
\(a_{6}=-0.450283529\) \(a_{7}=-0.541730327\) \(a_{8}=-0.912276569\) \(a_{9}=-0.280905260\) \(a_{10}=-0.739414177\)
\(a_{11}=+1.087881852\) \(a_{12}=+0.608894821\) \(a_{13}=-0.206561899\) \(a_{14}=-0.287657799\) \(a_{15}=+1.180831213\)
\(a_{16}=+0.233623802\) \(a_{17}=-0.627143858\) \(a_{18}=-0.149160172\) \(a_{19}=-1.625510172\) \(a_{20}=+0.999871046\)
\(a_{21}=+0.459384359\) \(a_{22}=+0.577663247\) \(a_{23}=+1.582425686\) \(a_{24}=+0.773605550\) \(a_{25}=+0.939052360\)
\(a_{26}=-0.109683985\) \(a_{27}=+1.086200667\) \(a_{28}=+0.388984569\) \(a_{29}=-0.644209156\) \(a_{30}=+0.627019185\)
\(a_{31}=-0.313618918\) \(a_{32}=+1.036330375\) \(a_{33}=-0.922517871\) \(a_{34}=-0.333012220\) \(a_{35}=+0.754358724\)
\(a_{36}=+0.201701485\) \(a_{37}=-0.109417945\) \(a_{38}=-0.863142888\) \(a_{39}=+0.175163362\) \(a_{40}=+1.270343849\)
\(a_{41}=-1.071875342\) \(a_{42}=+0.243932243\) \(a_{43}=+0.182280960\) \(a_{44}=-0.781143739\) \(a_{45}=+0.391160182\)
\(a_{46}=+0.840265105\) \(a_{47}=-0.444671688\) \(a_{48}=-0.198111708\) \(a_{49}=-0.706528253\) \(a_{50}=+0.498635062\)
\(a_{51}=+0.531814559\) \(a_{52}=+0.148319906\) \(a_{53}=-0.588928661\) \(a_{54}=+0.576770540\) \(a_{55}=-1.514873960\)
\(a_{56}=+0.494207884\) \(a_{57}=+1.378423751\) \(a_{58}=-0.342073868\) \(a_{59}=-0.261415055\) \(a_{60}=-0.847885187\)
\(a_{61}=+0.548830791\) \(a_{62}=-0.166531064\) \(a_{63}=+0.152174906\) \(a_{64}=+0.316665686\) \(a_{65}=+0.287637182\)
\(a_{66}=-0.489855279\) \(a_{67}=-0.177620523\) \(a_{68}=+0.450314976\) \(a_{69}=-1.341888342\) \(a_{70}=+0.400563084\)
\(a_{71}=+1.500316958\) \(a_{72}=+0.256263287\) \(a_{73}=-1.211054235\) \(a_{74}=-0.058100726\) \(a_{75}=-0.796311275\)
\(a_{76}=+1.167182899\) \(a_{77}=-0.589338591\) \(a_{78}=+0.093011421\) \(a_{79}=+1.261816851\) \(a_{80}=-0.325320818\)
\(a_{81}=-0.640186975\) \(a_{82}=-0.569163819\) \(a_{83}=+0.187128961\) \(a_{84}=-0.329856791\) \(a_{85}=+0.873296932\)
\(a_{86}=+0.096790852\) \(a_{87}=+0.546285847\) \(a_{88}=-0.992449124\) \(a_{89}=+0.132261939\) \(a_{90}=+0.207705331\)
\(a_{91}=+0.111900845\) \(a_{92}=-1.136246473\) \(a_{93}=+0.265947131\) \(a_{94}=-0.236119842\) \(a_{95}=+2.263520644\)
\(a_{96}=-0.878802500\) \(a_{97}=-0.096648046\) \(a_{98}=-0.375165192\) \(a_{99}=-0.305591735\) \(a_{100}=-0.674278067\)

Showing 100 of 5000 available coefficients

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