Basic properties
Modulus: | \(7623\) | |
Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{847}(755,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.es
\(\chi_{7623}(244,\cdot)\) \(\chi_{7623}(370,\cdot)\) \(\chi_{7623}(622,\cdot)\) \(\chi_{7623}(811,\cdot)\) \(\chi_{7623}(937,\cdot)\) \(\chi_{7623}(1063,\cdot)\) \(\chi_{7623}(1315,\cdot)\) \(\chi_{7623}(1504,\cdot)\) \(\chi_{7623}(1630,\cdot)\) \(\chi_{7623}(1756,\cdot)\) \(\chi_{7623}(2008,\cdot)\) \(\chi_{7623}(2197,\cdot)\) \(\chi_{7623}(2323,\cdot)\) \(\chi_{7623}(2449,\cdot)\) \(\chi_{7623}(2701,\cdot)\) \(\chi_{7623}(2890,\cdot)\) \(\chi_{7623}(3142,\cdot)\) \(\chi_{7623}(3394,\cdot)\) \(\chi_{7623}(3583,\cdot)\) \(\chi_{7623}(3709,\cdot)\) \(\chi_{7623}(3835,\cdot)\) \(\chi_{7623}(4276,\cdot)\) \(\chi_{7623}(4402,\cdot)\) \(\chi_{7623}(4528,\cdot)\) \(\chi_{7623}(4780,\cdot)\) \(\chi_{7623}(4969,\cdot)\) \(\chi_{7623}(5095,\cdot)\) \(\chi_{7623}(5221,\cdot)\) \(\chi_{7623}(5473,\cdot)\) \(\chi_{7623}(5662,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((1,-1,e\left(\frac{17}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(2449, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{27}{110}\right)\) |