Basic properties
Modulus: | \(2058\) | |
Conductor: | \(1029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(294\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1029}(677,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2058.x
\(\chi_{2058}(5,\cdot)\) \(\chi_{2058}(17,\cdot)\) \(\chi_{2058}(47,\cdot)\) \(\chi_{2058}(59,\cdot)\) \(\chi_{2058}(89,\cdot)\) \(\chi_{2058}(101,\cdot)\) \(\chi_{2058}(131,\cdot)\) \(\chi_{2058}(143,\cdot)\) \(\chi_{2058}(173,\cdot)\) \(\chi_{2058}(185,\cdot)\) \(\chi_{2058}(257,\cdot)\) \(\chi_{2058}(269,\cdot)\) \(\chi_{2058}(299,\cdot)\) \(\chi_{2058}(311,\cdot)\) \(\chi_{2058}(341,\cdot)\) \(\chi_{2058}(353,\cdot)\) \(\chi_{2058}(383,\cdot)\) \(\chi_{2058}(395,\cdot)\) \(\chi_{2058}(425,\cdot)\) \(\chi_{2058}(437,\cdot)\) \(\chi_{2058}(467,\cdot)\) \(\chi_{2058}(479,\cdot)\) \(\chi_{2058}(551,\cdot)\) \(\chi_{2058}(563,\cdot)\) \(\chi_{2058}(593,\cdot)\) \(\chi_{2058}(605,\cdot)\) \(\chi_{2058}(635,\cdot)\) \(\chi_{2058}(647,\cdot)\) \(\chi_{2058}(677,\cdot)\) \(\chi_{2058}(689,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{147})$ |
Fixed field: | Number field defined by a degree 294 polynomial (not computed) |
Values on generators
\((1373,1375)\) → \((-1,e\left(\frac{149}{294}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 2058 }(677, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{147}\right)\) | \(e\left(\frac{269}{294}\right)\) | \(e\left(\frac{43}{98}\right)\) | \(e\left(\frac{25}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{181}{294}\right)\) | \(e\left(\frac{58}{147}\right)\) | \(e\left(\frac{5}{98}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{74}{147}\right)\) |