Basic properties
Modulus: | \(7098\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(926,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.cs
\(\chi_{7098}(289,\cdot)\) \(\chi_{7098}(835,\cdot)\) \(\chi_{7098}(1075,\cdot)\) \(\chi_{7098}(1381,\cdot)\) \(\chi_{7098}(1621,\cdot)\) \(\chi_{7098}(1927,\cdot)\) \(\chi_{7098}(2167,\cdot)\) \(\chi_{7098}(2473,\cdot)\) \(\chi_{7098}(2713,\cdot)\) \(\chi_{7098}(3259,\cdot)\) \(\chi_{7098}(3565,\cdot)\) \(\chi_{7098}(3805,\cdot)\) \(\chi_{7098}(4111,\cdot)\) \(\chi_{7098}(4351,\cdot)\) \(\chi_{7098}(4657,\cdot)\) \(\chi_{7098}(4897,\cdot)\) \(\chi_{7098}(5203,\cdot)\) \(\chi_{7098}(5443,\cdot)\) \(\chi_{7098}(5749,\cdot)\) \(\chi_{7098}(5989,\cdot)\) \(\chi_{7098}(6295,\cdot)\) \(\chi_{7098}(6535,\cdot)\) \(\chi_{7098}(6841,\cdot)\) \(\chi_{7098}(7081,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.2 |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{7}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(6841, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) |