Basic properties
Modulus: | \(5390\) | |
Conductor: | \(2695\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2695}(139,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5390.cv
\(\chi_{5390}(139,\cdot)\) \(\chi_{5390}(349,\cdot)\) \(\chi_{5390}(629,\cdot)\) \(\chi_{5390}(699,\cdot)\) \(\chi_{5390}(909,\cdot)\) \(\chi_{5390}(1119,\cdot)\) \(\chi_{5390}(1399,\cdot)\) \(\chi_{5390}(1679,\cdot)\) \(\chi_{5390}(1889,\cdot)\) \(\chi_{5390}(2169,\cdot)\) \(\chi_{5390}(2239,\cdot)\) \(\chi_{5390}(2659,\cdot)\) \(\chi_{5390}(3009,\cdot)\) \(\chi_{5390}(3219,\cdot)\) \(\chi_{5390}(3709,\cdot)\) \(\chi_{5390}(3779,\cdot)\) \(\chi_{5390}(3989,\cdot)\) \(\chi_{5390}(4199,\cdot)\) \(\chi_{5390}(4479,\cdot)\) \(\chi_{5390}(4549,\cdot)\) \(\chi_{5390}(4759,\cdot)\) \(\chi_{5390}(4969,\cdot)\) \(\chi_{5390}(5249,\cdot)\) \(\chi_{5390}(5319,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((2157,4511,981)\) → \((-1,e\left(\frac{5}{14}\right),e\left(\frac{7}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 5390 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{23}{70}\right)\) |