Properties

Level $30$
Weight $0$
Character 30.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( 0 \)
Character: 30.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.5367120263 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213596\)
\(a_{6}=+0.408248290\) \(a_{7}=+1.351431877\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.305235378\) \(a_{12}=+0.288675135\) \(a_{13}=-1.385074731\) \(a_{14}=+0.955606644\) \(a_{15}=+0.258198890\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.460645594\) \(a_{18}=+0.235702260\) \(a_{19}=-0.143439833\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.780249558\) \(a_{22}=+0.215834006\) \(a_{23}=+0.751297742\) \(a_{24}=+0.204124145\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.979395735\) \(a_{27}=+0.192450090\) \(a_{28}=+0.675715938\) \(a_{29}=+1.090793067\) \(a_{30}=+0.182574186\)
\(a_{31}=-1.745950480\) \(a_{32}=+0.176776695\) \(a_{33}=+0.176227728\) \(a_{34}=-1.032832404\) \(a_{35}=+0.604378709\)
\(a_{36}=+0.166666667\) \(a_{37}=-1.039212573\) \(a_{38}=-0.101427279\) \(a_{39}=-0.799673269\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.083350925\) \(a_{42}=+0.551719753\) \(a_{43}=-0.278187422\) \(a_{44}=+0.152617689\) \(a_{45}=+0.149071198\)
\(a_{46}=+0.531247728\) \(a_{47}=+1.137310708\) \(a_{48}=+0.144337567\) \(a_{49}=+0.826368117\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.843304127\) \(a_{52}=-0.692537365\) \(a_{53}=+1.489427676\) \(a_{54}=+0.136082763\) \(a_{55}=+0.136505411\)
\(a_{56}=+0.477803322\) \(a_{57}=-0.082815026\) \(a_{58}=+0.771307174\) \(a_{59}=-0.600329916\) \(a_{60}=+0.129099445\)
\(a_{61}=+0.129028456\) \(a_{62}=-1.234573424\) \(a_{63}=+0.450477292\) \(a_{64}=+0.125000000\) \(a_{65}=-0.619424250\)
\(a_{66}=+0.124611821\) \(a_{67}=-1.750293897\) \(a_{68}=-0.730322797\) \(a_{69}=+0.433761953\) \(a_{70}=+0.427360283\)
\(a_{71}=-0.554313320\) \(a_{72}=+0.117851130\) \(a_{73}=+0.591646321\) \(a_{74}=-0.734834258\) \(a_{75}=+0.115470054\)
\(a_{76}=-0.071719916\) \(a_{77}=+0.412504820\) \(a_{78}=-0.565454391\) \(a_{79}=+0.942612853\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.766044785\) \(a_{83}=+1.202825798\) \(a_{84}=+0.390124779\) \(a_{85}=-0.653220568\)
\(a_{86}=-0.196708213\) \(a_{87}=+0.629769671\) \(a_{88}=+0.107917003\) \(a_{89}=-0.251721148\) \(a_{90}=+0.105409255\)
\(a_{91}=-1.871834143\) \(a_{92}=+0.375648871\) \(a_{93}=-1.008024980\) \(a_{94}=+0.804200114\) \(a_{95}=-0.064148243\)
\(a_{96}=+0.102062073\) \(a_{97}=+1.667303122\) \(a_{98}=+0.584330499\) \(a_{99}=+0.101745126\) \(a_{100}=+0.099975586\)

Showing 100 of 640 available coefficients

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