Basic properties
Modulus: | \(2700\) | |
Conductor: | \(2700\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(180\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 2700.cs
\(\chi_{2700}(67,\cdot)\) \(\chi_{2700}(103,\cdot)\) \(\chi_{2700}(187,\cdot)\) \(\chi_{2700}(223,\cdot)\) \(\chi_{2700}(247,\cdot)\) \(\chi_{2700}(283,\cdot)\) \(\chi_{2700}(367,\cdot)\) \(\chi_{2700}(403,\cdot)\) \(\chi_{2700}(427,\cdot)\) \(\chi_{2700}(463,\cdot)\) \(\chi_{2700}(547,\cdot)\) \(\chi_{2700}(583,\cdot)\) \(\chi_{2700}(727,\cdot)\) \(\chi_{2700}(763,\cdot)\) \(\chi_{2700}(787,\cdot)\) \(\chi_{2700}(823,\cdot)\) \(\chi_{2700}(967,\cdot)\) \(\chi_{2700}(1003,\cdot)\) \(\chi_{2700}(1087,\cdot)\) \(\chi_{2700}(1123,\cdot)\) \(\chi_{2700}(1147,\cdot)\) \(\chi_{2700}(1183,\cdot)\) \(\chi_{2700}(1267,\cdot)\) \(\chi_{2700}(1303,\cdot)\) \(\chi_{2700}(1327,\cdot)\) \(\chi_{2700}(1363,\cdot)\) \(\chi_{2700}(1447,\cdot)\) \(\chi_{2700}(1483,\cdot)\) \(\chi_{2700}(1627,\cdot)\) \(\chi_{2700}(1663,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1351,1001,2377)\) → \((-1,e\left(\frac{4}{9}\right),e\left(\frac{1}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 2700 }(2227, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{34}{45}\right)\) |