Basic properties
Modulus: | \(1350\) | |
Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{675}(533,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1350.bi
\(\chi_{1350}(23,\cdot)\) \(\chi_{1350}(47,\cdot)\) \(\chi_{1350}(77,\cdot)\) \(\chi_{1350}(83,\cdot)\) \(\chi_{1350}(113,\cdot)\) \(\chi_{1350}(137,\cdot)\) \(\chi_{1350}(167,\cdot)\) \(\chi_{1350}(173,\cdot)\) \(\chi_{1350}(203,\cdot)\) \(\chi_{1350}(227,\cdot)\) \(\chi_{1350}(263,\cdot)\) \(\chi_{1350}(317,\cdot)\) \(\chi_{1350}(347,\cdot)\) \(\chi_{1350}(353,\cdot)\) \(\chi_{1350}(383,\cdot)\) \(\chi_{1350}(437,\cdot)\) \(\chi_{1350}(473,\cdot)\) \(\chi_{1350}(497,\cdot)\) \(\chi_{1350}(527,\cdot)\) \(\chi_{1350}(533,\cdot)\) \(\chi_{1350}(563,\cdot)\) \(\chi_{1350}(587,\cdot)\) \(\chi_{1350}(617,\cdot)\) \(\chi_{1350}(623,\cdot)\) \(\chi_{1350}(653,\cdot)\) \(\chi_{1350}(677,\cdot)\) \(\chi_{1350}(713,\cdot)\) \(\chi_{1350}(767,\cdot)\) \(\chi_{1350}(797,\cdot)\) \(\chi_{1350}(803,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1001,1027)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{3}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 1350 }(533, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{173}{180}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{167}{180}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{19}{90}\right)\) |