Basic properties
Modulus: | \(7098\) | |
Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{507}(110,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.ek
\(\chi_{7098}(71,\cdot)\) \(\chi_{7098}(197,\cdot)\) \(\chi_{7098}(323,\cdot)\) \(\chi_{7098}(449,\cdot)\) \(\chi_{7098}(617,\cdot)\) \(\chi_{7098}(743,\cdot)\) \(\chi_{7098}(869,\cdot)\) \(\chi_{7098}(1163,\cdot)\) \(\chi_{7098}(1289,\cdot)\) \(\chi_{7098}(1415,\cdot)\) \(\chi_{7098}(1541,\cdot)\) \(\chi_{7098}(1835,\cdot)\) \(\chi_{7098}(1961,\cdot)\) \(\chi_{7098}(2087,\cdot)\) \(\chi_{7098}(2255,\cdot)\) \(\chi_{7098}(2381,\cdot)\) \(\chi_{7098}(2507,\cdot)\) \(\chi_{7098}(2633,\cdot)\) \(\chi_{7098}(2801,\cdot)\) \(\chi_{7098}(2927,\cdot)\) \(\chi_{7098}(3053,\cdot)\) \(\chi_{7098}(3179,\cdot)\) \(\chi_{7098}(3347,\cdot)\) \(\chi_{7098}(3473,\cdot)\) \(\chi_{7098}(3599,\cdot)\) \(\chi_{7098}(3725,\cdot)\) \(\chi_{7098}(3893,\cdot)\) \(\chi_{7098}(4019,\cdot)\) \(\chi_{7098}(4271,\cdot)\) \(\chi_{7098}(4439,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((-1,1,e\left(\frac{113}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(617, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{17}{156}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{11}{156}\right)\) |