Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(1352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1352}(603,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.fn
\(\chi_{9464}(603,\cdot)\) \(\chi_{9464}(827,\cdot)\) \(\chi_{9464}(1331,\cdot)\) \(\chi_{9464}(1555,\cdot)\) \(\chi_{9464}(2059,\cdot)\) \(\chi_{9464}(2283,\cdot)\) \(\chi_{9464}(2787,\cdot)\) \(\chi_{9464}(3011,\cdot)\) \(\chi_{9464}(3515,\cdot)\) \(\chi_{9464}(3739,\cdot)\) \(\chi_{9464}(4243,\cdot)\) \(\chi_{9464}(4467,\cdot)\) \(\chi_{9464}(5195,\cdot)\) \(\chi_{9464}(5699,\cdot)\) \(\chi_{9464}(5923,\cdot)\) \(\chi_{9464}(6427,\cdot)\) \(\chi_{9464}(6651,\cdot)\) \(\chi_{9464}(7155,\cdot)\) \(\chi_{9464}(7379,\cdot)\) \(\chi_{9464}(7883,\cdot)\) \(\chi_{9464}(8107,\cdot)\) \(\chi_{9464}(8611,\cdot)\) \(\chi_{9464}(8835,\cdot)\) \(\chi_{9464}(9339,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,-1,1,e\left(\frac{43}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(603, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) |