Basic properties
Modulus: | \(2300\) | |
Conductor: | \(2300\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(110\) | 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 2300.bn
\(\chi_{2300}(31,\cdot)\) \(\chi_{2300}(71,\cdot)\) \(\chi_{2300}(131,\cdot)\) \(\chi_{2300}(211,\cdot)\) \(\chi_{2300}(271,\cdot)\) \(\chi_{2300}(311,\cdot)\) \(\chi_{2300}(331,\cdot)\) \(\chi_{2300}(371,\cdot)\) \(\chi_{2300}(491,\cdot)\) \(\chi_{2300}(531,\cdot)\) \(\chi_{2300}(591,\cdot)\) \(\chi_{2300}(611,\cdot)\) \(\chi_{2300}(671,\cdot)\) \(\chi_{2300}(731,\cdot)\) \(\chi_{2300}(771,\cdot)\) \(\chi_{2300}(791,\cdot)\) \(\chi_{2300}(811,\cdot)\) \(\chi_{2300}(831,\cdot)\) \(\chi_{2300}(991,\cdot)\) \(\chi_{2300}(1071,\cdot)\) \(\chi_{2300}(1131,\cdot)\) \(\chi_{2300}(1191,\cdot)\) \(\chi_{2300}(1231,\cdot)\) \(\chi_{2300}(1271,\cdot)\) \(\chi_{2300}(1291,\cdot)\) \(\chi_{2300}(1411,\cdot)\) \(\chi_{2300}(1511,\cdot)\) \(\chi_{2300}(1531,\cdot)\) \(\chi_{2300}(1591,\cdot)\) \(\chi_{2300}(1691,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{3}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
\( \chi_{ 2300 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) |