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 \(\chi_{1183}(1116,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.em
\(\chi_{7098}(115,\cdot)\) \(\chi_{7098}(397,\cdot)\) \(\chi_{7098}(535,\cdot)\) \(\chi_{7098}(565,\cdot)\) \(\chi_{7098}(661,\cdot)\) \(\chi_{7098}(943,\cdot)\) \(\chi_{7098}(1081,\cdot)\) \(\chi_{7098}(1111,\cdot)\) \(\chi_{7098}(1207,\cdot)\) \(\chi_{7098}(1489,\cdot)\) \(\chi_{7098}(1627,\cdot)\) \(\chi_{7098}(1657,\cdot)\) \(\chi_{7098}(1753,\cdot)\) \(\chi_{7098}(2035,\cdot)\) \(\chi_{7098}(2173,\cdot)\) \(\chi_{7098}(2203,\cdot)\) \(\chi_{7098}(2299,\cdot)\) \(\chi_{7098}(2581,\cdot)\) \(\chi_{7098}(2719,\cdot)\) \(\chi_{7098}(2749,\cdot)\) \(\chi_{7098}(2845,\cdot)\) \(\chi_{7098}(3127,\cdot)\) \(\chi_{7098}(3265,\cdot)\) \(\chi_{7098}(3295,\cdot)\) \(\chi_{7098}(3391,\cdot)\) \(\chi_{7098}(3673,\cdot)\) \(\chi_{7098}(3811,\cdot)\) \(\chi_{7098}(3841,\cdot)\) \(\chi_{7098}(3937,\cdot)\) \(\chi_{7098}(4219,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{115}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(2299, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{25}{156}\right)\) |