Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.10381155304 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.894738809\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.632675879\) \(a_{7}=+1.025104013\) \(a_{8}=+0.353553391\) \(a_{9}=-0.199442464\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.474671260\) \(a_{12}=+0.447369404\) \(a_{13}=+0.384530187\) \(a_{14}=+0.724857999\) \(a_{15}=+0.400139360\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.041797264\) \(a_{18}=-0.141027119\) \(a_{19}=-1.828150475\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.917200343\) \(a_{22}=-1.042750048\) \(a_{23}=+0.772404692\) \(a_{24}=+0.316337939\) \(a_{25}=+0.200000000\)
\(a_{26}=+0.271903903\) \(a_{27}=-1.073187721\) \(a_{28}=+0.512552006\) \(a_{29}=-0.290758145\) \(a_{30}=+0.282941255\)
\(a_{31}=+1.315929422\) \(a_{32}=+0.176776694\) \(a_{33}=-1.319445606\) \(a_{34}=-0.029555125\) \(a_{35}=+0.458440444\)
\(a_{36}=-0.099721231\) \(a_{37}=-1.091530611\) \(a_{38}=-1.292697572\) \(a_{39}=+0.344054081\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.169996089\) \(a_{42}=+0.648558582\) \(a_{43}=+1.877998262\) \(a_{44}=-0.737335630\) \(a_{45}=-0.089193382\)
\(a_{46}=+0.546172596\) \(a_{47}=-0.623799875\) \(a_{48}=+0.223684702\) \(a_{49}=+0.050838237\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.037397634\) \(a_{52}=+0.192265093\) \(a_{53}=+0.031384973\) \(a_{54}=-0.758858315\) \(a_{55}=-0.659493036\)
\(a_{56}=+0.362428999\) \(a_{57}=-1.635717178\) \(a_{58}=-0.205597056\) \(a_{59}=-0.062524821\) \(a_{60}=+0.200069680\)
\(a_{61}=+0.969705534\) \(a_{62}=+0.930502617\) \(a_{63}=-0.204449271\) \(a_{64}=+0.125000001\) \(a_{65}=+0.171967127\)
\(a_{66}=-0.932988934\) \(a_{67}=+1.298033277\) \(a_{68}=-0.020898629\) \(a_{69}=+0.691100453\) \(a_{70}=+0.324166355\)
\(a_{71}=+0.274781628\) \(a_{72}=-0.070513558\) \(a_{73}=-0.510994547\) \(a_{74}=-0.771828708\) \(a_{75}=+0.178947757\)
\(a_{76}=-0.914075286\) \(a_{77}=-1.511691326\) \(a_{78}=+0.243282984\) \(a_{79}=+1.406992288\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.760780239\) \(a_{82}=+0.120205387\) \(a_{83}=-0.579852471\) \(a_{84}=+0.458600172\) \(a_{85}=-0.018692305\)
\(a_{86}=+1.327945306\) \(a_{87}=-0.260152596\) \(a_{88}=-0.521375024\) \(a_{89}=-0.796776414\) \(a_{90}=-0.063069245\)
\(a_{91}=+0.394183438\) \(a_{92}=+0.386202346\) \(a_{93}=+1.177413122\) \(a_{94}=-0.441093122\) \(a_{95}=-0.817573747\)
\(a_{96}=+0.158168969\) \(a_{97}=+0.444893046\) \(a_{98}=+0.035948063\) \(a_{99}=+0.294112058\) \(a_{100}=+0.099999999\)

Showing 100 of 2000 available coefficients

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