Basic properties
Modulus: | \(7098\) | |
Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3549}(44,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.ej
\(\chi_{7098}(317,\cdot)\) \(\chi_{7098}(359,\cdot)\) \(\chi_{7098}(473,\cdot)\) \(\chi_{7098}(515,\cdot)\) \(\chi_{7098}(863,\cdot)\) \(\chi_{7098}(905,\cdot)\) \(\chi_{7098}(1019,\cdot)\) \(\chi_{7098}(1061,\cdot)\) \(\chi_{7098}(1409,\cdot)\) \(\chi_{7098}(1565,\cdot)\) \(\chi_{7098}(1607,\cdot)\) \(\chi_{7098}(1955,\cdot)\) \(\chi_{7098}(1997,\cdot)\) \(\chi_{7098}(2111,\cdot)\) \(\chi_{7098}(2153,\cdot)\) \(\chi_{7098}(2501,\cdot)\) \(\chi_{7098}(2543,\cdot)\) \(\chi_{7098}(2657,\cdot)\) \(\chi_{7098}(2699,\cdot)\) \(\chi_{7098}(3047,\cdot)\) \(\chi_{7098}(3089,\cdot)\) \(\chi_{7098}(3203,\cdot)\) \(\chi_{7098}(3245,\cdot)\) \(\chi_{7098}(3593,\cdot)\) \(\chi_{7098}(3635,\cdot)\) \(\chi_{7098}(3749,\cdot)\) \(\chi_{7098}(3791,\cdot)\) \(\chi_{7098}(4139,\cdot)\) \(\chi_{7098}(4181,\cdot)\) \(\chi_{7098}(4337,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{35}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(3593, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{37}{52}\right)\) |