Basic properties
| Modulus: | \(2025\) | |
| Conductor: | \(2025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(270\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2025.bt
\(\chi_{2025}(11,\cdot)\) \(\chi_{2025}(41,\cdot)\) \(\chi_{2025}(56,\cdot)\) \(\chi_{2025}(86,\cdot)\) \(\chi_{2025}(131,\cdot)\) \(\chi_{2025}(146,\cdot)\) \(\chi_{2025}(191,\cdot)\) \(\chi_{2025}(221,\cdot)\) \(\chi_{2025}(236,\cdot)\) \(\chi_{2025}(266,\cdot)\) \(\chi_{2025}(281,\cdot)\) \(\chi_{2025}(311,\cdot)\) \(\chi_{2025}(356,\cdot)\) \(\chi_{2025}(371,\cdot)\) \(\chi_{2025}(416,\cdot)\) \(\chi_{2025}(446,\cdot)\) \(\chi_{2025}(461,\cdot)\) \(\chi_{2025}(491,\cdot)\) \(\chi_{2025}(506,\cdot)\) \(\chi_{2025}(536,\cdot)\) \(\chi_{2025}(581,\cdot)\) \(\chi_{2025}(596,\cdot)\) \(\chi_{2025}(641,\cdot)\) \(\chi_{2025}(671,\cdot)\) \(\chi_{2025}(686,\cdot)\) \(\chi_{2025}(716,\cdot)\) \(\chi_{2025}(731,\cdot)\) \(\chi_{2025}(761,\cdot)\) \(\chi_{2025}(806,\cdot)\) \(\chi_{2025}(821,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{135})$ |
| Fixed field: | Number field defined by a degree 270 polynomial (not computed) |
Values on generators
\((326,1702)\) → \((e\left(\frac{19}{54}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2025 }(56, a) \) | \(-1\) | \(1\) | \(e\left(\frac{203}{270}\right)\) | \(e\left(\frac{68}{135}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{263}{270}\right)\) | \(e\left(\frac{56}{135}\right)\) | \(e\left(\frac{103}{270}\right)\) | \(e\left(\frac{1}{135}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) |