Basic properties
| Modulus: | \(8100\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(617,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8100.dd
\(\chi_{8100}(17,\cdot)\) \(\chi_{8100}(197,\cdot)\) \(\chi_{8100}(233,\cdot)\) \(\chi_{8100}(413,\cdot)\) \(\chi_{8100}(737,\cdot)\) \(\chi_{8100}(773,\cdot)\) \(\chi_{8100}(953,\cdot)\) \(\chi_{8100}(1097,\cdot)\) \(\chi_{8100}(1277,\cdot)\) \(\chi_{8100}(1313,\cdot)\) \(\chi_{8100}(1637,\cdot)\) \(\chi_{8100}(1817,\cdot)\) \(\chi_{8100}(1853,\cdot)\) \(\chi_{8100}(2033,\cdot)\) \(\chi_{8100}(2177,\cdot)\) \(\chi_{8100}(2573,\cdot)\) \(\chi_{8100}(2717,\cdot)\) \(\chi_{8100}(2897,\cdot)\) \(\chi_{8100}(2933,\cdot)\) \(\chi_{8100}(3113,\cdot)\) \(\chi_{8100}(3437,\cdot)\) \(\chi_{8100}(3473,\cdot)\) \(\chi_{8100}(3653,\cdot)\) \(\chi_{8100}(3797,\cdot)\) \(\chi_{8100}(3977,\cdot)\) \(\chi_{8100}(4013,\cdot)\) \(\chi_{8100}(4337,\cdot)\) \(\chi_{8100}(4517,\cdot)\) \(\chi_{8100}(4553,\cdot)\) \(\chi_{8100}(4733,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4051,6401,7777)\) → \((1,e\left(\frac{11}{18}\right),e\left(\frac{13}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8100 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{43}{180}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{89}{90}\right)\) |