Basic properties
| Modulus: | \(8100\) | |
| Conductor: | \(2025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(270\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2025}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8100.dj
\(\chi_{8100}(169,\cdot)\) \(\chi_{8100}(229,\cdot)\) \(\chi_{8100}(409,\cdot)\) \(\chi_{8100}(529,\cdot)\) \(\chi_{8100}(589,\cdot)\) \(\chi_{8100}(709,\cdot)\) \(\chi_{8100}(769,\cdot)\) \(\chi_{8100}(889,\cdot)\) \(\chi_{8100}(1069,\cdot)\) \(\chi_{8100}(1129,\cdot)\) \(\chi_{8100}(1309,\cdot)\) \(\chi_{8100}(1429,\cdot)\) \(\chi_{8100}(1489,\cdot)\) \(\chi_{8100}(1609,\cdot)\) \(\chi_{8100}(1669,\cdot)\) \(\chi_{8100}(1789,\cdot)\) \(\chi_{8100}(1969,\cdot)\) \(\chi_{8100}(2029,\cdot)\) \(\chi_{8100}(2209,\cdot)\) \(\chi_{8100}(2329,\cdot)\) \(\chi_{8100}(2389,\cdot)\) \(\chi_{8100}(2509,\cdot)\) \(\chi_{8100}(2569,\cdot)\) \(\chi_{8100}(2689,\cdot)\) \(\chi_{8100}(2869,\cdot)\) \(\chi_{8100}(2929,\cdot)\) \(\chi_{8100}(3109,\cdot)\) \(\chi_{8100}(3229,\cdot)\) \(\chi_{8100}(3289,\cdot)\) \(\chi_{8100}(3409,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{135})$ |
| Fixed field: | Number field defined by a degree 270 polynomial (not computed) |
Values on generators
\((4051,6401,7777)\) → \((1,e\left(\frac{8}{27}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8100 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{34}{135}\right)\) | \(e\left(\frac{127}{270}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{43}{270}\right)\) | \(e\left(\frac{103}{135}\right)\) | \(e\left(\frac{17}{135}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{41}{135}\right)\) |