Basic properties
Modulus: | \(2850\) | |
Conductor: | \(1425\) | 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 \(\chi_{1425}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2850.cr
\(\chi_{2850}(17,\cdot)\) \(\chi_{2850}(23,\cdot)\) \(\chi_{2850}(47,\cdot)\) \(\chi_{2850}(137,\cdot)\) \(\chi_{2850}(233,\cdot)\) \(\chi_{2850}(263,\cdot)\) \(\chi_{2850}(347,\cdot)\) \(\chi_{2850}(377,\cdot)\) \(\chi_{2850}(473,\cdot)\) \(\chi_{2850}(503,\cdot)\) \(\chi_{2850}(587,\cdot)\) \(\chi_{2850}(617,\cdot)\) \(\chi_{2850}(803,\cdot)\) \(\chi_{2850}(833,\cdot)\) \(\chi_{2850}(917,\cdot)\) \(\chi_{2850}(947,\cdot)\) \(\chi_{2850}(1013,\cdot)\) \(\chi_{2850}(1073,\cdot)\) \(\chi_{2850}(1127,\cdot)\) \(\chi_{2850}(1163,\cdot)\) \(\chi_{2850}(1187,\cdot)\) \(\chi_{2850}(1277,\cdot)\) \(\chi_{2850}(1373,\cdot)\) \(\chi_{2850}(1403,\cdot)\) \(\chi_{2850}(1487,\cdot)\) \(\chi_{2850}(1517,\cdot)\) \(\chi_{2850}(1583,\cdot)\) \(\chi_{2850}(1613,\cdot)\) \(\chi_{2850}(1697,\cdot)\) \(\chi_{2850}(1727,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1901,1027,1351)\) → \((-1,e\left(\frac{17}{20}\right),e\left(\frac{4}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 2850 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{179}{180}\right)\) | \(e\left(\frac{133}{180}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{31}{36}\right)\) |