Basic properties
Modulus: | \(845\) | |
Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{169}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 845.bg
\(\chi_{845}(36,\cdot)\) \(\chi_{845}(56,\cdot)\) \(\chi_{845}(101,\cdot)\) \(\chi_{845}(121,\cdot)\) \(\chi_{845}(166,\cdot)\) \(\chi_{845}(186,\cdot)\) \(\chi_{845}(231,\cdot)\) \(\chi_{845}(251,\cdot)\) \(\chi_{845}(296,\cdot)\) \(\chi_{845}(381,\cdot)\) \(\chi_{845}(426,\cdot)\) \(\chi_{845}(446,\cdot)\) \(\chi_{845}(491,\cdot)\) \(\chi_{845}(511,\cdot)\) \(\chi_{845}(556,\cdot)\) \(\chi_{845}(576,\cdot)\) \(\chi_{845}(621,\cdot)\) \(\chi_{845}(641,\cdot)\) \(\chi_{845}(686,\cdot)\) \(\chi_{845}(706,\cdot)\) \(\chi_{845}(751,\cdot)\) \(\chi_{845}(771,\cdot)\) \(\chi_{845}(816,\cdot)\) \(\chi_{845}(836,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,171)\) → \((1,e\left(\frac{47}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
\( \chi_{ 845 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) |