Basic properties
Modulus: | \(1815\) | |
Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{605}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1815.bt
\(\chi_{1815}(7,\cdot)\) \(\chi_{1815}(13,\cdot)\) \(\chi_{1815}(28,\cdot)\) \(\chi_{1815}(52,\cdot)\) \(\chi_{1815}(73,\cdot)\) \(\chi_{1815}(127,\cdot)\) \(\chi_{1815}(172,\cdot)\) \(\chi_{1815}(178,\cdot)\) \(\chi_{1815}(193,\cdot)\) \(\chi_{1815}(217,\cdot)\) \(\chi_{1815}(238,\cdot)\) \(\chi_{1815}(277,\cdot)\) \(\chi_{1815}(283,\cdot)\) \(\chi_{1815}(292,\cdot)\) \(\chi_{1815}(337,\cdot)\) \(\chi_{1815}(343,\cdot)\) \(\chi_{1815}(358,\cdot)\) \(\chi_{1815}(382,\cdot)\) \(\chi_{1815}(442,\cdot)\) \(\chi_{1815}(448,\cdot)\) \(\chi_{1815}(502,\cdot)\) \(\chi_{1815}(508,\cdot)\) \(\chi_{1815}(523,\cdot)\) \(\chi_{1815}(547,\cdot)\) \(\chi_{1815}(568,\cdot)\) \(\chi_{1815}(607,\cdot)\) \(\chi_{1815}(613,\cdot)\) \(\chi_{1815}(622,\cdot)\) \(\chi_{1815}(667,\cdot)\) \(\chi_{1815}(673,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1211,727,1696)\) → \((1,-i,e\left(\frac{101}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 1815 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{147}{220}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{39}{220}\right)\) | \(e\left(\frac{1}{220}\right)\) | \(e\left(\frac{217}{220}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{23}{44}\right)\) |