Basic properties
| Modulus: | \(69696\) | |
| Conductor: | \(7744\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(176\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{7744}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 69696.iy
\(\chi_{69696}(109,\cdot)\) \(\chi_{69696}(901,\cdot)\) \(\chi_{69696}(2485,\cdot)\) \(\chi_{69696}(3277,\cdot)\) \(\chi_{69696}(4069,\cdot)\) \(\chi_{69696}(4861,\cdot)\) \(\chi_{69696}(5653,\cdot)\) \(\chi_{69696}(6445,\cdot)\) \(\chi_{69696}(7237,\cdot)\) \(\chi_{69696}(8029,\cdot)\) \(\chi_{69696}(8821,\cdot)\) \(\chi_{69696}(9613,\cdot)\) \(\chi_{69696}(11197,\cdot)\) \(\chi_{69696}(11989,\cdot)\) \(\chi_{69696}(12781,\cdot)\) \(\chi_{69696}(13573,\cdot)\) \(\chi_{69696}(14365,\cdot)\) \(\chi_{69696}(15157,\cdot)\) \(\chi_{69696}(15949,\cdot)\) \(\chi_{69696}(16741,\cdot)\) \(\chi_{69696}(17533,\cdot)\) \(\chi_{69696}(18325,\cdot)\) \(\chi_{69696}(19909,\cdot)\) \(\chi_{69696}(20701,\cdot)\) \(\chi_{69696}(21493,\cdot)\) \(\chi_{69696}(22285,\cdot)\) \(\chi_{69696}(23077,\cdot)\) \(\chi_{69696}(23869,\cdot)\) \(\chi_{69696}(24661,\cdot)\) \(\chi_{69696}(25453,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{176})$ |
| Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((67519,4357,54209,14401)\) → \((1,e\left(\frac{7}{16}\right),1,e\left(\frac{7}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 69696 }(109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{173}{176}\right)\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{123}{176}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{83}{176}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{85}{88}\right)\) | \(e\left(\frac{39}{176}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{103}{176}\right)\) |