Basic properties
Modulus: | \(5700\) | |
Conductor: | \(1900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1900}(187,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5700.fh
\(\chi_{5700}(187,\cdot)\) \(\chi_{5700}(283,\cdot)\) \(\chi_{5700}(367,\cdot)\) \(\chi_{5700}(403,\cdot)\) \(\chi_{5700}(427,\cdot)\) \(\chi_{5700}(727,\cdot)\) \(\chi_{5700}(823,\cdot)\) \(\chi_{5700}(883,\cdot)\) \(\chi_{5700}(967,\cdot)\) \(\chi_{5700}(1087,\cdot)\) \(\chi_{5700}(1183,\cdot)\) \(\chi_{5700}(1327,\cdot)\) \(\chi_{5700}(1423,\cdot)\) \(\chi_{5700}(1567,\cdot)\) \(\chi_{5700}(1783,\cdot)\) \(\chi_{5700}(1867,\cdot)\) \(\chi_{5700}(1963,\cdot)\) \(\chi_{5700}(2023,\cdot)\) \(\chi_{5700}(2227,\cdot)\) \(\chi_{5700}(2323,\cdot)\) \(\chi_{5700}(2467,\cdot)\) \(\chi_{5700}(2563,\cdot)\) \(\chi_{5700}(2647,\cdot)\) \(\chi_{5700}(2683,\cdot)\) \(\chi_{5700}(2923,\cdot)\) \(\chi_{5700}(3103,\cdot)\) \(\chi_{5700}(3163,\cdot)\) \(\chi_{5700}(3247,\cdot)\) \(\chi_{5700}(3367,\cdot)\) \(\chi_{5700}(3463,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((2851,1901,3877,4201)\) → \((-1,1,e\left(\frac{9}{20}\right),e\left(\frac{2}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 5700 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{119}{180}\right)\) | \(e\left(\frac{13}{180}\right)\) | \(e\left(\frac{161}{180}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{29}{36}\right)\) |