Basic properties
Modulus: | \(5700\) | |
Conductor: | \(475\) | 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 \(\chi_{475}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5700.fl
\(\chi_{5700}(13,\cdot)\) \(\chi_{5700}(97,\cdot)\) \(\chi_{5700}(337,\cdot)\) \(\chi_{5700}(433,\cdot)\) \(\chi_{5700}(553,\cdot)\) \(\chi_{5700}(637,\cdot)\) \(\chi_{5700}(697,\cdot)\) \(\chi_{5700}(877,\cdot)\) \(\chi_{5700}(1117,\cdot)\) \(\chi_{5700}(1153,\cdot)\) \(\chi_{5700}(1237,\cdot)\) \(\chi_{5700}(1333,\cdot)\) \(\chi_{5700}(1477,\cdot)\) \(\chi_{5700}(1573,\cdot)\) \(\chi_{5700}(1777,\cdot)\) \(\chi_{5700}(1837,\cdot)\) \(\chi_{5700}(1933,\cdot)\) \(\chi_{5700}(2017,\cdot)\) \(\chi_{5700}(2233,\cdot)\) \(\chi_{5700}(2377,\cdot)\) \(\chi_{5700}(2473,\cdot)\) \(\chi_{5700}(2617,\cdot)\) \(\chi_{5700}(2713,\cdot)\) \(\chi_{5700}(2833,\cdot)\) \(\chi_{5700}(2917,\cdot)\) \(\chi_{5700}(2977,\cdot)\) \(\chi_{5700}(3073,\cdot)\) \(\chi_{5700}(3373,\cdot)\) \(\chi_{5700}(3397,\cdot)\) \(\chi_{5700}(3433,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((2851,1901,3877,4201)\) → \((1,1,e\left(\frac{19}{20}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 5700 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{79}{180}\right)\) | \(e\left(\frac{23}{180}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{25}{36}\right)\) |