Basic properties
Modulus: | \(2000\) | |
Conductor: | \(2000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(100\) | 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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 2000.ce
\(\chi_{2000}(53,\cdot)\) \(\chi_{2000}(77,\cdot)\) \(\chi_{2000}(133,\cdot)\) \(\chi_{2000}(213,\cdot)\) \(\chi_{2000}(237,\cdot)\) \(\chi_{2000}(317,\cdot)\) \(\chi_{2000}(373,\cdot)\) \(\chi_{2000}(397,\cdot)\) \(\chi_{2000}(453,\cdot)\) \(\chi_{2000}(477,\cdot)\) \(\chi_{2000}(533,\cdot)\) \(\chi_{2000}(613,\cdot)\) \(\chi_{2000}(637,\cdot)\) \(\chi_{2000}(717,\cdot)\) \(\chi_{2000}(773,\cdot)\) \(\chi_{2000}(797,\cdot)\) \(\chi_{2000}(853,\cdot)\) \(\chi_{2000}(877,\cdot)\) \(\chi_{2000}(933,\cdot)\) \(\chi_{2000}(1013,\cdot)\) \(\chi_{2000}(1037,\cdot)\) \(\chi_{2000}(1117,\cdot)\) \(\chi_{2000}(1173,\cdot)\) \(\chi_{2000}(1197,\cdot)\) \(\chi_{2000}(1253,\cdot)\) \(\chi_{2000}(1277,\cdot)\) \(\chi_{2000}(1333,\cdot)\) \(\chi_{2000}(1413,\cdot)\) \(\chi_{2000}(1437,\cdot)\) \(\chi_{2000}(1517,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,501,1377)\) → \((1,-i,e\left(\frac{9}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 2000 }(637, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{16}{25}\right)\) |