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 \(\chi_{1183}(227,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.ea
\(\chi_{7098}(145,\cdot)\) \(\chi_{7098}(241,\cdot)\) \(\chi_{7098}(271,\cdot)\) \(\chi_{7098}(409,\cdot)\) \(\chi_{7098}(691,\cdot)\) \(\chi_{7098}(787,\cdot)\) \(\chi_{7098}(817,\cdot)\) \(\chi_{7098}(955,\cdot)\) \(\chi_{7098}(1237,\cdot)\) \(\chi_{7098}(1363,\cdot)\) \(\chi_{7098}(1501,\cdot)\) \(\chi_{7098}(1783,\cdot)\) \(\chi_{7098}(1879,\cdot)\) \(\chi_{7098}(1909,\cdot)\) \(\chi_{7098}(2329,\cdot)\) \(\chi_{7098}(2425,\cdot)\) \(\chi_{7098}(2593,\cdot)\) \(\chi_{7098}(2875,\cdot)\) \(\chi_{7098}(2971,\cdot)\) \(\chi_{7098}(3001,\cdot)\) \(\chi_{7098}(3139,\cdot)\) \(\chi_{7098}(3421,\cdot)\) \(\chi_{7098}(3517,\cdot)\) \(\chi_{7098}(3547,\cdot)\) \(\chi_{7098}(3685,\cdot)\) \(\chi_{7098}(4063,\cdot)\) \(\chi_{7098}(4093,\cdot)\) \(\chi_{7098}(4231,\cdot)\) \(\chi_{7098}(4513,\cdot)\) \(\chi_{7098}(4609,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{41}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(2593, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{131}{156}\right)\) |