The Maass form of level 31 with the smallest eigenvalue. This Maass form is even, and for all smaller prime levels the Maass form with the smallest eigenvalue is odd.
Maass form invariants
| Level: | \( 31 \) |
| Weight: | \( 0 \) |
| Character: | 31.1 |
| Symmetry: | even |
| Fricke sign: | $+1$ |
| Spectral parameter: | \( 0.78935617774 \) |
Maass form coefficients
| \(a_{1}=+1.000000000\) | \(a_{2}=-1.374310443\) | \(a_{3}=-0.902704087\) | \(a_{4}=+0.888729194\) | \(a_{5}=-0.730042232\) |
| \(a_{6}=+1.240595654\) | \(a_{7}=+1.126296789\) | \(a_{8}=+0.152920630\) | \(a_{9}=-0.185125331\) | \(a_{10}=+1.003304663\) |
| \(a_{11}=-0.214467911\) | \(a_{12}=-0.802259476\) | \(a_{13}=-0.757205689\) | \(a_{14}=-1.547881439\) | \(a_{15}=+0.659012107\) |
| \(a_{16}=-1.098889613\) | \(a_{17}=+0.294474423\) | \(a_{18}=+0.254419676\) | \(a_{19}=+1.669683823\) | \(a_{20}=-0.648809845\) |
| \(a_{21}=-1.016712715\) | \(a_{22}=+0.294745490\) | \(a_{23}=-0.186602717\) | \(a_{24}=-0.138042078\) | \(a_{25}=-0.467038340\) |
| \(a_{26}=+1.040635685\) | \(a_{27}=+1.069817480\) | \(a_{28}=+1.000972838\) | \(a_{29}=+0.623885373\) | \(a_{30}=-0.905687220\) |
| \(a_{31}=-0.179605302\) | \(a_{32}=+1.357294842\) | \(a_{33}=+0.193601060\) | \(a_{34}=-0.404699275\) | \(a_{35}=-0.822244221\) |
| \(a_{36}=-0.164526286\) | \(a_{37}=-0.550425157\) | \(a_{38}=-2.294663915\) | \(a_{39}=+0.683532670\) | \(a_{40}=-0.111638518\) |
| \(a_{41}=+0.282161696\) | \(a_{42}=+1.397278901\) | \(a_{43}=-1.754380818\) | \(a_{44}=-0.190603894\) | \(a_{45}=+0.135149310\) |
| \(a_{46}=+0.256450063\) | \(a_{47}=+0.913504460\) | \(a_{48}=+0.991972145\) | \(a_{49}=+0.268544456\) | \(a_{50}=+0.641855668\) |
| \(a_{51}=-0.265823266\) | \(a_{52}=-0.672950802\) | \(a_{53}=-0.054369845\) | \(a_{54}=-1.470261335\) | \(a_{55}=+0.156570633\) |
| \(a_{56}=+0.172234015\) | \(a_{57}=-1.507230411\) | \(a_{58}=-0.857412183\) | \(a_{59}=+0.112243164\) | \(a_{60}=+0.585683299\) |
| \(a_{61}=+0.985441455\) | \(a_{62}=+0.246833442\) | \(a_{63}=-0.208506066\) | \(a_{64}=-0.766454862\) | \(a_{65}=+0.552792131\) |
| \(a_{66}=-0.266067959\) | \(a_{67}=+0.974063600\) | \(a_{68}=+0.261708017\) | \(a_{69}=+0.168447035\) | \(a_{70}=+1.130018820\) |
| \(a_{71}=-0.225908180\) | \(a_{72}=-0.028309482\) | \(a_{73}=-0.274541918\) | \(a_{74}=+0.756455042\) | \(a_{75}=+0.421597418\) |
| \(a_{76}=+1.483896759\) | \(a_{77}=-0.241554520\) | \(a_{78}=-0.939386087\) | \(a_{79}=+0.679788869\) | \(a_{80}=+0.802235826\) |
| \(a_{81}=-0.780603281\) | \(a_{82}=-0.387777765\) | \(a_{83}=-0.761608790\) | \(a_{84}=-0.903582272\) | \(a_{85}=-0.214978765\) |
| \(a_{86}=+2.411063880\) | \(a_{87}=-0.563183876\) | \(a_{88}=-0.032796568\) | \(a_{89}=-1.549844985\) | \(a_{90}=-0.185737108\) |
| \(a_{91}=-0.852838335\) | \(a_{92}=-0.165839282\) | \(a_{93}=+0.162130440\) | \(a_{94}=-1.255438719\) | \(a_{95}=-1.218939705\) |
| \(a_{96}=-1.225235601\) | \(a_{97}=+0.987747906\) | \(a_{98}=-0.369063451\) | \(a_{99}=+0.039703443\) | \(a_{100}=-0.415070607\) |
Showing 100 of 546 available coefficients