Basic properties
Modulus: | \(7056\) | |
Conductor: | \(7056\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7056.io
\(\chi_{7056}(61,\cdot)\) \(\chi_{7056}(157,\cdot)\) \(\chi_{7056}(565,\cdot)\) \(\chi_{7056}(661,\cdot)\) \(\chi_{7056}(1069,\cdot)\) \(\chi_{7056}(1165,\cdot)\) \(\chi_{7056}(1573,\cdot)\) \(\chi_{7056}(1669,\cdot)\) \(\chi_{7056}(2173,\cdot)\) \(\chi_{7056}(2581,\cdot)\) \(\chi_{7056}(3085,\cdot)\) \(\chi_{7056}(3181,\cdot)\) \(\chi_{7056}(3589,\cdot)\) \(\chi_{7056}(3685,\cdot)\) \(\chi_{7056}(4093,\cdot)\) \(\chi_{7056}(4189,\cdot)\) \(\chi_{7056}(4597,\cdot)\) \(\chi_{7056}(4693,\cdot)\) \(\chi_{7056}(5101,\cdot)\) \(\chi_{7056}(5197,\cdot)\) \(\chi_{7056}(5701,\cdot)\) \(\chi_{7056}(6109,\cdot)\) \(\chi_{7056}(6613,\cdot)\) \(\chi_{7056}(6709,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((1,-i,e\left(\frac{2}{3}\right),e\left(\frac{11}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 7056 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{84}\right)\) |