Basic properties
Modulus: | \(3040\) | |
Conductor: | \(3040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3040.gc
\(\chi_{3040}(149,\cdot)\) \(\chi_{3040}(309,\cdot)\) \(\chi_{3040}(389,\cdot)\) \(\chi_{3040}(549,\cdot)\) \(\chi_{3040}(669,\cdot)\) \(\chi_{3040}(709,\cdot)\) \(\chi_{3040}(909,\cdot)\) \(\chi_{3040}(1069,\cdot)\) \(\chi_{3040}(1149,\cdot)\) \(\chi_{3040}(1309,\cdot)\) \(\chi_{3040}(1429,\cdot)\) \(\chi_{3040}(1469,\cdot)\) \(\chi_{3040}(1669,\cdot)\) \(\chi_{3040}(1829,\cdot)\) \(\chi_{3040}(1909,\cdot)\) \(\chi_{3040}(2069,\cdot)\) \(\chi_{3040}(2189,\cdot)\) \(\chi_{3040}(2229,\cdot)\) \(\chi_{3040}(2429,\cdot)\) \(\chi_{3040}(2589,\cdot)\) \(\chi_{3040}(2669,\cdot)\) \(\chi_{3040}(2829,\cdot)\) \(\chi_{3040}(2949,\cdot)\) \(\chi_{3040}(2989,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,2661,1217,1921)\) → \((1,e\left(\frac{5}{8}\right),-1,e\left(\frac{2}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 3040 }(149, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{47}{72}\right)\) |