Basic properties
Modulus: | \(7600\) | |
Conductor: | \(3800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3800}(1909,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7600.ic
\(\chi_{7600}(9,\cdot)\) \(\chi_{7600}(169,\cdot)\) \(\chi_{7600}(329,\cdot)\) \(\chi_{7600}(1289,\cdot)\) \(\chi_{7600}(1529,\cdot)\) \(\chi_{7600}(1689,\cdot)\) \(\chi_{7600}(2569,\cdot)\) \(\chi_{7600}(2809,\cdot)\) \(\chi_{7600}(2969,\cdot)\) \(\chi_{7600}(3209,\cdot)\) \(\chi_{7600}(3369,\cdot)\) \(\chi_{7600}(4089,\cdot)\) \(\chi_{7600}(4329,\cdot)\) \(\chi_{7600}(4489,\cdot)\) \(\chi_{7600}(4569,\cdot)\) \(\chi_{7600}(4729,\cdot)\) \(\chi_{7600}(4889,\cdot)\) \(\chi_{7600}(5609,\cdot)\) \(\chi_{7600}(6009,\cdot)\) \(\chi_{7600}(6089,\cdot)\) \(\chi_{7600}(6409,\cdot)\) \(\chi_{7600}(7129,\cdot)\) \(\chi_{7600}(7369,\cdot)\) \(\chi_{7600}(7529,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4751,5701,5777,401)\) → \((1,-1,e\left(\frac{7}{10}\right),e\left(\frac{4}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 7600 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{41}{90}\right)\) |