Basic properties
Modulus: | \(9464\) | |
Conductor: | \(4732\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4732}(375,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.jc
\(\chi_{9464}(375,\cdot)\) \(\chi_{9464}(431,\cdot)\) \(\chi_{9464}(527,\cdot)\) \(\chi_{9464}(1159,\cdot)\) \(\chi_{9464}(1255,\cdot)\) \(\chi_{9464}(1423,\cdot)\) \(\chi_{9464}(1831,\cdot)\) \(\chi_{9464}(1887,\cdot)\) \(\chi_{9464}(1983,\cdot)\) \(\chi_{9464}(2151,\cdot)\) \(\chi_{9464}(2559,\cdot)\) \(\chi_{9464}(2711,\cdot)\) \(\chi_{9464}(2879,\cdot)\) \(\chi_{9464}(3287,\cdot)\) \(\chi_{9464}(3343,\cdot)\) \(\chi_{9464}(3439,\cdot)\) \(\chi_{9464}(3607,\cdot)\) \(\chi_{9464}(4015,\cdot)\) \(\chi_{9464}(4071,\cdot)\) \(\chi_{9464}(4167,\cdot)\) \(\chi_{9464}(4335,\cdot)\) \(\chi_{9464}(4743,\cdot)\) \(\chi_{9464}(4799,\cdot)\) \(\chi_{9464}(4895,\cdot)\) \(\chi_{9464}(5063,\cdot)\) \(\chi_{9464}(5471,\cdot)\) \(\chi_{9464}(5527,\cdot)\) \(\chi_{9464}(5623,\cdot)\) \(\chi_{9464}(5791,\cdot)\) \(\chi_{9464}(6199,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,1,e\left(\frac{2}{3}\right),e\left(\frac{151}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 9464 }(375, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) |