Basic properties
Modulus: | \(7098\) | |
Conductor: | \(1183\) | 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 \(\chi_{1183}(202,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.en
\(\chi_{7098}(97,\cdot)\) \(\chi_{7098}(223,\cdot)\) \(\chi_{7098}(349,\cdot)\) \(\chi_{7098}(475,\cdot)\) \(\chi_{7098}(643,\cdot)\) \(\chi_{7098}(769,\cdot)\) \(\chi_{7098}(895,\cdot)\) \(\chi_{7098}(1021,\cdot)\) \(\chi_{7098}(1189,\cdot)\) \(\chi_{7098}(1315,\cdot)\) \(\chi_{7098}(1567,\cdot)\) \(\chi_{7098}(1735,\cdot)\) \(\chi_{7098}(1861,\cdot)\) \(\chi_{7098}(1987,\cdot)\) \(\chi_{7098}(2113,\cdot)\) \(\chi_{7098}(2281,\cdot)\) \(\chi_{7098}(2407,\cdot)\) \(\chi_{7098}(2533,\cdot)\) \(\chi_{7098}(2659,\cdot)\) \(\chi_{7098}(2827,\cdot)\) \(\chi_{7098}(3079,\cdot)\) \(\chi_{7098}(3205,\cdot)\) \(\chi_{7098}(3373,\cdot)\) \(\chi_{7098}(3499,\cdot)\) \(\chi_{7098}(3625,\cdot)\) \(\chi_{7098}(3751,\cdot)\) \(\chi_{7098}(3919,\cdot)\) \(\chi_{7098}(4045,\cdot)\) \(\chi_{7098}(4171,\cdot)\) \(\chi_{7098}(4297,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((1,-1,e\left(\frac{71}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(3751, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{29}{156}\right)\) |