Basic properties
Modulus: | \(5700\) | |
Conductor: | \(5700\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | 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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5700.ev
\(\chi_{5700}(119,\cdot)\) \(\chi_{5700}(359,\cdot)\) \(\chi_{5700}(479,\cdot)\) \(\chi_{5700}(719,\cdot)\) \(\chi_{5700}(959,\cdot)\) \(\chi_{5700}(1259,\cdot)\) \(\chi_{5700}(1619,\cdot)\) \(\chi_{5700}(1859,\cdot)\) \(\chi_{5700}(2039,\cdot)\) \(\chi_{5700}(2639,\cdot)\) \(\chi_{5700}(2759,\cdot)\) \(\chi_{5700}(3179,\cdot)\) \(\chi_{5700}(3239,\cdot)\) \(\chi_{5700}(3539,\cdot)\) \(\chi_{5700}(3779,\cdot)\) \(\chi_{5700}(4139,\cdot)\) \(\chi_{5700}(4319,\cdot)\) \(\chi_{5700}(4379,\cdot)\) \(\chi_{5700}(4679,\cdot)\) \(\chi_{5700}(4919,\cdot)\) \(\chi_{5700}(5039,\cdot)\) \(\chi_{5700}(5279,\cdot)\) \(\chi_{5700}(5459,\cdot)\) \(\chi_{5700}(5519,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2851,1901,3877,4201)\) → \((-1,-1,e\left(\frac{9}{10}\right),e\left(\frac{8}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 5700 }(119, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{2}{9}\right)\) |