Basic properties
| Modulus: | \(8100\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(664,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8100.ct
\(\chi_{8100}(289,\cdot)\) \(\chi_{8100}(469,\cdot)\) \(\chi_{8100}(829,\cdot)\) \(\chi_{8100}(1009,\cdot)\) \(\chi_{8100}(1369,\cdot)\) \(\chi_{8100}(1909,\cdot)\) \(\chi_{8100}(2089,\cdot)\) \(\chi_{8100}(2629,\cdot)\) \(\chi_{8100}(2989,\cdot)\) \(\chi_{8100}(3169,\cdot)\) \(\chi_{8100}(3529,\cdot)\) \(\chi_{8100}(3709,\cdot)\) \(\chi_{8100}(4069,\cdot)\) \(\chi_{8100}(4609,\cdot)\) \(\chi_{8100}(4789,\cdot)\) \(\chi_{8100}(5329,\cdot)\) \(\chi_{8100}(5689,\cdot)\) \(\chi_{8100}(5869,\cdot)\) \(\chi_{8100}(6229,\cdot)\) \(\chi_{8100}(6409,\cdot)\) \(\chi_{8100}(6769,\cdot)\) \(\chi_{8100}(7309,\cdot)\) \(\chi_{8100}(7489,\cdot)\) \(\chi_{8100}(8029,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4051,6401,7777)\) → \((1,e\left(\frac{2}{9}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8100 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{44}{45}\right)\) |