Basic properties
Modulus: | \(2000\) | |
Conductor: | \(2000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
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)
|
Galois orbit 2000.bw
\(\chi_{2000}(11,\cdot)\) \(\chi_{2000}(91,\cdot)\) \(\chi_{2000}(131,\cdot)\) \(\chi_{2000}(171,\cdot)\) \(\chi_{2000}(211,\cdot)\) \(\chi_{2000}(291,\cdot)\) \(\chi_{2000}(331,\cdot)\) \(\chi_{2000}(371,\cdot)\) \(\chi_{2000}(411,\cdot)\) \(\chi_{2000}(491,\cdot)\) \(\chi_{2000}(531,\cdot)\) \(\chi_{2000}(571,\cdot)\) \(\chi_{2000}(611,\cdot)\) \(\chi_{2000}(691,\cdot)\) \(\chi_{2000}(731,\cdot)\) \(\chi_{2000}(771,\cdot)\) \(\chi_{2000}(811,\cdot)\) \(\chi_{2000}(891,\cdot)\) \(\chi_{2000}(931,\cdot)\) \(\chi_{2000}(971,\cdot)\) \(\chi_{2000}(1011,\cdot)\) \(\chi_{2000}(1091,\cdot)\) \(\chi_{2000}(1131,\cdot)\) \(\chi_{2000}(1171,\cdot)\) \(\chi_{2000}(1211,\cdot)\) \(\chi_{2000}(1291,\cdot)\) \(\chi_{2000}(1331,\cdot)\) \(\chi_{2000}(1371,\cdot)\) \(\chi_{2000}(1411,\cdot)\) \(\chi_{2000}(1491,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,501,1377)\) → \((-1,i,e\left(\frac{18}{25}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 2000 }(571, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{87}{100}\right)\) |