Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(56,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.hp
\(\chi_{9464}(225,\cdot)\) \(\chi_{9464}(673,\cdot)\) \(\chi_{9464}(953,\cdot)\) \(\chi_{9464}(1401,\cdot)\) \(\chi_{9464}(1681,\cdot)\) \(\chi_{9464}(2129,\cdot)\) \(\chi_{9464}(2409,\cdot)\) \(\chi_{9464}(2857,\cdot)\) \(\chi_{9464}(3137,\cdot)\) \(\chi_{9464}(3585,\cdot)\) \(\chi_{9464}(4313,\cdot)\) \(\chi_{9464}(4593,\cdot)\) \(\chi_{9464}(5041,\cdot)\) \(\chi_{9464}(5321,\cdot)\) \(\chi_{9464}(6049,\cdot)\) \(\chi_{9464}(6497,\cdot)\) \(\chi_{9464}(6777,\cdot)\) \(\chi_{9464}(7225,\cdot)\) \(\chi_{9464}(7505,\cdot)\) \(\chi_{9464}(7953,\cdot)\) \(\chi_{9464}(8233,\cdot)\) \(\chi_{9464}(8681,\cdot)\) \(\chi_{9464}(8961,\cdot)\) \(\chi_{9464}(9409,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((1,1,1,e\left(\frac{55}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(225, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) |