Basic properties
Modulus: | \(2025\) | |
Conductor: | \(2025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(135\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2025.bo
\(\chi_{2025}(16,\cdot)\) \(\chi_{2025}(31,\cdot)\) \(\chi_{2025}(61,\cdot)\) \(\chi_{2025}(106,\cdot)\) \(\chi_{2025}(121,\cdot)\) \(\chi_{2025}(166,\cdot)\) \(\chi_{2025}(196,\cdot)\) \(\chi_{2025}(211,\cdot)\) \(\chi_{2025}(241,\cdot)\) \(\chi_{2025}(256,\cdot)\) \(\chi_{2025}(286,\cdot)\) \(\chi_{2025}(331,\cdot)\) \(\chi_{2025}(346,\cdot)\) \(\chi_{2025}(391,\cdot)\) \(\chi_{2025}(421,\cdot)\) \(\chi_{2025}(436,\cdot)\) \(\chi_{2025}(466,\cdot)\) \(\chi_{2025}(481,\cdot)\) \(\chi_{2025}(511,\cdot)\) \(\chi_{2025}(556,\cdot)\) \(\chi_{2025}(571,\cdot)\) \(\chi_{2025}(616,\cdot)\) \(\chi_{2025}(646,\cdot)\) \(\chi_{2025}(661,\cdot)\) \(\chi_{2025}(691,\cdot)\) \(\chi_{2025}(706,\cdot)\) \(\chi_{2025}(736,\cdot)\) \(\chi_{2025}(781,\cdot)\) \(\chi_{2025}(796,\cdot)\) \(\chi_{2025}(841,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{135})$ |
Fixed field: | Number field defined by a degree 135 polynomial (not computed) |
Values on generators
\((326,1702)\) → \((e\left(\frac{2}{27}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 2025 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{135}\right)\) | \(e\left(\frac{74}{135}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{22}{135}\right)\) | \(e\left(\frac{53}{135}\right)\) | \(e\left(\frac{62}{135}\right)\) | \(e\left(\frac{13}{135}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) |