Basic properties
Modulus: | \(7942\) | |
Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{209}(127,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7942.ba
\(\chi_{7942}(127,\cdot)\) \(\chi_{7942}(299,\cdot)\) \(\chi_{7942}(623,\cdot)\) \(\chi_{7942}(849,\cdot)\) \(\chi_{7942}(1029,\cdot)\) \(\chi_{7942}(1751,\cdot)\) \(\chi_{7942}(1777,\cdot)\) \(\chi_{7942}(1921,\cdot)\) \(\chi_{7942}(2499,\cdot)\) \(\chi_{7942}(2789,\cdot)\) \(\chi_{7942}(3187,\cdot)\) \(\chi_{7942}(3511,\cdot)\) \(\chi_{7942}(3737,\cdot)\) \(\chi_{7942}(4087,\cdot)\) \(\chi_{7942}(4639,\cdot)\) \(\chi_{7942}(4809,\cdot)\) \(\chi_{7942}(5353,\cdot)\) \(\chi_{7942}(5387,\cdot)\) \(\chi_{7942}(5903,\cdot)\) \(\chi_{7942}(6399,\cdot)\) \(\chi_{7942}(6805,\cdot)\) \(\chi_{7942}(7519,\cdot)\) \(\chi_{7942}(7553,\cdot)\) \(\chi_{7942}(7697,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((5777,6139)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 7942 }(127, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{4}{45}\right)\) |