Basic properties
Modulus: | \(7098\) | |
Conductor: | \(169\) | 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 \(\chi_{169}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.eh
\(\chi_{7098}(85,\cdot)\) \(\chi_{7098}(253,\cdot)\) \(\chi_{7098}(379,\cdot)\) \(\chi_{7098}(505,\cdot)\) \(\chi_{7098}(631,\cdot)\) \(\chi_{7098}(799,\cdot)\) \(\chi_{7098}(1051,\cdot)\) \(\chi_{7098}(1177,\cdot)\) \(\chi_{7098}(1345,\cdot)\) \(\chi_{7098}(1471,\cdot)\) \(\chi_{7098}(1597,\cdot)\) \(\chi_{7098}(1723,\cdot)\) \(\chi_{7098}(1891,\cdot)\) \(\chi_{7098}(2017,\cdot)\) \(\chi_{7098}(2143,\cdot)\) \(\chi_{7098}(2269,\cdot)\) \(\chi_{7098}(2437,\cdot)\) \(\chi_{7098}(2563,\cdot)\) \(\chi_{7098}(2689,\cdot)\) \(\chi_{7098}(2815,\cdot)\) \(\chi_{7098}(2983,\cdot)\) \(\chi_{7098}(3109,\cdot)\) \(\chi_{7098}(3235,\cdot)\) \(\chi_{7098}(3529,\cdot)\) \(\chi_{7098}(3655,\cdot)\) \(\chi_{7098}(3781,\cdot)\) \(\chi_{7098}(3907,\cdot)\) \(\chi_{7098}(4201,\cdot)\) \(\chi_{7098}(4327,\cdot)\) \(\chi_{7098}(4453,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((1,1,e\left(\frac{1}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(6931, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{85}{156}\right)\) |