Basic properties
Modulus: | \(5070\) | |
Conductor: | \(2535\) | 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 \(\chi_{2535}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5070.ct
\(\chi_{5070}(107,\cdot)\) \(\chi_{5070}(113,\cdot)\) \(\chi_{5070}(263,\cdot)\) \(\chi_{5070}(347,\cdot)\) \(\chi_{5070}(497,\cdot)\) \(\chi_{5070}(503,\cdot)\) \(\chi_{5070}(737,\cdot)\) \(\chi_{5070}(887,\cdot)\) \(\chi_{5070}(893,\cdot)\) \(\chi_{5070}(1043,\cdot)\) \(\chi_{5070}(1127,\cdot)\) \(\chi_{5070}(1277,\cdot)\) \(\chi_{5070}(1283,\cdot)\) \(\chi_{5070}(1433,\cdot)\) \(\chi_{5070}(1517,\cdot)\) \(\chi_{5070}(1673,\cdot)\) \(\chi_{5070}(1823,\cdot)\) \(\chi_{5070}(1907,\cdot)\) \(\chi_{5070}(2057,\cdot)\) \(\chi_{5070}(2063,\cdot)\) \(\chi_{5070}(2213,\cdot)\) \(\chi_{5070}(2297,\cdot)\) \(\chi_{5070}(2447,\cdot)\) \(\chi_{5070}(2453,\cdot)\) \(\chi_{5070}(2603,\cdot)\) \(\chi_{5070}(2687,\cdot)\) \(\chi_{5070}(2837,\cdot)\) \(\chi_{5070}(2843,\cdot)\) \(\chi_{5070}(2993,\cdot)\) \(\chi_{5070}(3077,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1691,4057,1861)\) → \((-1,i,e\left(\frac{25}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 5070 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{149}{156}\right)\) |