Properties

Level $51$
Weight $0$
Character 51.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.56727259021 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.970128634\) \(a_{3}=+0.577350269\) \(a_{4}=+2.881406833\) \(a_{5}=+0.406989856\)
\(a_{6}=-1.137454297\) \(a_{7}=+1.085877413\) \(a_{8}=-3.706613473\) \(a_{9}=+0.333333333\) \(a_{10}=-0.801822368\)
\(a_{11}=+0.581023022\) \(a_{12}=+1.663581011\) \(a_{13}=+0.862176703\) \(a_{14}=-2.139318185\) \(a_{15}=+0.234975703\)
\(a_{16}=+4.421098503\) \(a_{17}=+0.242535625\) \(a_{18}=-0.656709545\) \(a_{19}=-0.302249608\) \(a_{20}=+1.172703351\)
\(a_{21}=+0.626931617\) \(a_{22}=-1.144690092\) \(a_{23}=-0.134193032\) \(a_{24}=-2.140014286\) \(a_{25}=-0.834359258\)
\(a_{26}=-1.698599009\) \(a_{27}=+0.192450090\) \(a_{28}=+3.128854599\) \(a_{29}=+1.897125468\) \(a_{30}=-0.462932360\)
\(a_{31}=+0.610364650\) \(a_{32}=-5.003519280\) \(a_{33}=+0.335453798\) \(a_{34}=-0.477826380\) \(a_{35}=+0.441941092\)
\(a_{36}=+0.960468944\) \(a_{37}=-0.552318565\) \(a_{38}=+0.595470607\) \(a_{39}=+0.497777951\) \(a_{40}=-1.508554082\)
\(a_{41}=+1.240038660\) \(a_{42}=-1.235135930\) \(a_{43}=-0.778600376\) \(a_{44}=+1.674163705\) \(a_{45}=+0.135663285\)
\(a_{46}=+0.264377534\) \(a_{47}=-0.572961236\) \(a_{48}=+2.552522411\) \(a_{49}=+0.179129757\) \(a_{50}=+1.643795064\)
\(a_{51}=+0.140028008\) \(a_{52}=+2.484281842\) \(a_{53}=-0.587835407\) \(a_{54}=-0.379151432\) \(a_{55}=+0.236470476\)
\(a_{56}=-4.024927850\) \(a_{57}=-0.174503892\) \(a_{58}=-3.737581207\) \(a_{59}=-0.468464316\) \(a_{60}=+0.677060595\)
\(a_{61}=+0.104297964\) \(a_{62}=-1.202496874\) \(a_{63}=+0.361959138\) \(a_{64}=+5.436478099\) \(a_{65}=+0.350897172\)
\(a_{66}=-0.660887133\) \(a_{67}=-0.967569427\) \(a_{68}=+0.698843807\) \(a_{69}=-0.077476383\) \(a_{70}=-0.870680799\)
\(a_{71}=+0.570315854\) \(a_{72}=-1.235537824\) \(a_{73}=-0.342312352\) \(a_{74}=+1.088138619\) \(a_{75}=-0.481717542\)
\(a_{76}=-0.870904085\) \(a_{77}=+0.630919776\) \(a_{78}=-0.980686595\) \(a_{79}=+1.292844661\) \(a_{80}=+1.799342241\)
\(a_{81}=+0.111111111\) \(a_{82}=-2.443035670\) \(a_{83}=-0.004720898\) \(a_{84}=+1.806445045\) \(a_{85}=+0.098709539\)
\(a_{86}=+1.533942896\) \(a_{87}=+1.095305900\) \(a_{88}=-2.153627760\) \(a_{89}=-0.662036027\) \(a_{90}=-0.267274123\)
\(a_{91}=+0.936218208\) \(a_{92}=-0.386664718\) \(a_{93}=+0.352394195\) \(a_{94}=+1.128807337\) \(a_{95}=-0.123012524\)
\(a_{96}=-2.888783203\) \(a_{97}=-0.624769667\) \(a_{98}=-0.352908663\) \(a_{99}=+0.193674341\) \(a_{100}=-2.404128466\)

Showing 100 of 522 available coefficients

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