Basic properties
Modulus: | \(6815\) | |
Conductor: | \(6815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(644\) | 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 6815.cz
\(\chi_{6815}(13,\cdot)\) \(\chi_{6815}(22,\cdot)\) \(\chi_{6815}(33,\cdot)\) \(\chi_{6815}(38,\cdot)\) \(\chi_{6815}(62,\cdot)\) \(\chi_{6815}(67,\cdot)\) \(\chi_{6815}(92,\cdot)\) \(\chi_{6815}(138,\cdot)\) \(\chi_{6815}(167,\cdot)\) \(\chi_{6815}(207,\cdot)\) \(\chi_{6815}(208,\cdot)\) \(\chi_{6815}(312,\cdot)\) \(\chi_{6815}(323,\cdot)\) \(\chi_{6815}(352,\cdot)\) \(\chi_{6815}(428,\cdot)\) \(\chi_{6815}(468,\cdot)\) \(\chi_{6815}(527,\cdot)\) \(\chi_{6815}(528,\cdot)\) \(\chi_{6815}(557,\cdot)\) \(\chi_{6815}(593,\cdot)\) \(\chi_{6815}(602,\cdot)\) \(\chi_{6815}(622,\cdot)\) \(\chi_{6815}(642,\cdot)\) \(\chi_{6815}(673,\cdot)\) \(\chi_{6815}(702,\cdot)\) \(\chi_{6815}(718,\cdot)\) \(\chi_{6815}(738,\cdot)\) \(\chi_{6815}(763,\cdot)\) \(\chi_{6815}(767,\cdot)\) \(\chi_{6815}(787,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{644})$ |
Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((2727,2351,146)\) → \((-i,e\left(\frac{1}{14}\right),e\left(\frac{27}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6815 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{249}{644}\right)\) | \(e\left(\frac{223}{644}\right)\) | \(e\left(\frac{249}{322}\right)\) | \(e\left(\frac{118}{161}\right)\) | \(e\left(\frac{251}{644}\right)\) | \(e\left(\frac{103}{644}\right)\) | \(e\left(\frac{223}{322}\right)\) | \(e\left(\frac{144}{161}\right)\) | \(e\left(\frac{11}{92}\right)\) | \(e\left(\frac{639}{644}\right)\) |