LMFDB - Embedded newform 252.12.t.a.17.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,12,Mod(17,252)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("252.17");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	252.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$193.622481501$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.26
Character	$\chi$	$=$	252.17
Dual form			252.12.t.a.89.26

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4768.57 + 8259.41i) q^{5} +(-1253.90 - 44449.5i) q^{7} +O(q^{10})$	$q+(4768.57 + 8259.41i) q^{5} +(-1253.90 - 44449.5i) q^{7} +(-557743. - 322013. i) q^{11} -635679. i q^{13} +(3.00177e6 - 5.19922e6i) q^{17} +(9.08845e6 - 5.24722e6i) q^{19} +(3.76396e7 - 2.17313e7i) q^{23} +(-2.10645e7 + 3.64849e7i) q^{25} +1.19751e8i q^{29} +(7.80739e7 + 4.50760e7i) q^{31} +(3.61147e8 - 2.22317e8i) q^{35} +(-3.90414e8 - 6.76217e8i) q^{37} -6.26561e8 q^{41} -1.37370e9 q^{43} +(1.31769e9 + 2.28231e9i) q^{47} +(-1.97418e9 + 1.11470e8i) q^{49} +(-1.69344e8 - 9.77708e7i) q^{53} -6.14217e9i q^{55} +(-4.39920e9 + 7.61963e9i) q^{59} +(-7.08626e9 + 4.09126e9i) q^{61} +(5.25033e9 - 3.03128e9i) q^{65} +(-7.76991e9 + 1.34579e10i) q^{67} -9.66933e9i q^{71} +(1.50791e10 + 8.70595e9i) q^{73} +(-1.36140e10 + 2.51952e10i) q^{77} +(-1.04686e10 - 1.81321e10i) q^{79} -3.71020e10 q^{83} +5.72566e10 q^{85} +(-2.41154e10 - 4.17691e10i) q^{89} +(-2.82556e10 + 7.97077e8i) q^{91} +(8.66779e10 + 5.00435e10i) q^{95} -2.57959e9i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 31278 q^{7}+O(q^{10}) $ 60 * q - 31278 * q^7	$ 60 q - 31278 q^{7} - 34858710 q^{19} - 323828862 q^{25} + 1186783866 q^{31} - 706751058 q^{37} + 1104997284 q^{43} + 7568925402 q^{49} - 5130550116 q^{61} - 22208949354 q^{67} + 54154878858 q^{73} - 61996342614 q^{79} + 107647163952 q^{85} - 2229336678 q^{91}+O(q^{100}) $ 60 * q - 31278 * q^7 - 34858710 * q^19 - 323828862 * q^25 + 1186783866 * q^31 - 706751058 * q^37 + 1104997284 * q^43 + 7568925402 * q^49 - 5130550116 * q^61 - 22208949354 * q^67 + 54154878858 * q^73 - 61996342614 * q^79 + 107647163952 * q^85 - 2229336678 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	4768.57	+	8259.41i	0.682423	+	1.18199i	0.974239	+	0.225517i	$0.0724070\pi$
$5$	4768.57	+	8259.41i	0.682423	+	1.18199i	−0.291816	+	0.956474i	$0.594260\pi$
$6$		0			0
$7$	−1253.90	−	44449.5i	−0.0281983	−	0.999602i
$7$	−1253.90	−	44449.5i	−0.0281983	−	0.999602i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−557743.	−	322013.i	−1.04418	−	0.602856i	−0.123164	−	0.992386i	$-0.539304\pi$
$11$	−557743.	−	322013.i	−1.04418	−	0.602856i	−0.921014	+	0.389530i	$0.872637\pi$
$12$		0			0
$13$		−	635679.i		−	0.474842i	−0.971407	−	0.237421i	$-0.923698\pi$
$13$		−	635679.i		−	0.474842i	0.971407	−	0.237421i	$-0.0763021\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.00177e6	−	5.19922e6i	0.512753	−	0.888114i	−0.487138	−	0.873325i	$-0.661959\pi$
$17$	3.00177e6	−	5.19922e6i	0.512753	−	0.888114i	0.999891	−	0.0147890i	$-0.00470766\pi$
$18$		0			0
$19$	9.08845e6	−	5.24722e6i	0.842064	−	0.486166i	−0.0159014	−	0.999874i	$-0.505062\pi$
$19$	9.08845e6	−	5.24722e6i	0.842064	−	0.486166i	0.857965	+	0.513708i	$0.171728\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.76396e7	−	2.17313e7i	1.21939	−	0.704015i	0.254602	−	0.967046i	$-0.418056\pi$
$23$	3.76396e7	−	2.17313e7i	1.21939	−	0.704015i	0.964787	+	0.263031i	$0.0847222\pi$
$24$		0			0
$25$	−2.10645e7	+	3.64849e7i	−0.431402	+	0.747210i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			1.19751e8i			1.08415i	0.840331	+	0.542074i	$0.182361\pi$
$29$			1.19751e8i			1.08415i	−0.840331	+	0.542074i	$0.817639\pi$
$30$		0			0
$31$	7.80739e7	+	4.50760e7i	0.489797	+	0.282785i	0.724490	−	0.689285i	$-0.242075\pi$
$31$	7.80739e7	+	4.50760e7i	0.489797	+	0.282785i	−0.234693	+	0.972070i	$0.575408\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.61147e8	−	2.22317e8i	1.16228	−	0.715482i
$36$		0			0
$37$	−3.90414e8	−	6.76217e8i	−0.925584	−	1.60316i	−0.790619	−	0.612308i	$-0.790241\pi$
$37$	−3.90414e8	−	6.76217e8i	−0.925584	−	1.60316i	−0.134964	−	0.990850i	$-0.543092\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.26561e8			−0.844602			−0.422301	−	0.906456i	$-0.638778\pi$
$41$	−6.26561e8			−0.844602			−0.422301	+	0.906456i	$0.638778\pi$
$42$		0			0
$43$	−1.37370e9			−1.42500			−0.712501	−	0.701672i	$-0.752437\pi$
$43$	−1.37370e9			−1.42500			−0.712501	+	0.701672i	$0.752437\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.31769e9	+	2.28231e9i	0.838060	+	1.45156i	0.891514	+	0.452993i	$0.149644\pi$
$47$	1.31769e9	+	2.28231e9i	0.838060	+	1.45156i	−0.0534541	+	0.998570i	$0.517023\pi$
$48$		0			0
$49$	−1.97418e9	+	1.11470e8i	−0.998410	+	0.0563743i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.69344e8	−	9.77708e7i	−0.0556228	−	0.0321138i	0.471931	−	0.881636i	$-0.343557\pi$
$53$	−1.69344e8	−	9.77708e7i	−0.0556228	−	0.0321138i	−0.527553	+	0.849522i	$0.676891\pi$
$54$		0			0
$55$		−	6.14217e9i		−	1.64561i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.39920e9	+	7.61963e9i	−0.801101	+	1.38755i	0.117791	+	0.993038i	$0.462419\pi$
$59$	−4.39920e9	+	7.61963e9i	−0.801101	+	1.38755i	−0.918892	+	0.394509i	$0.870915\pi$
$60$		0			0
$61$	−7.08626e9	+	4.09126e9i	−1.07424	+	0.620216i	−0.929338	−	0.369230i	$-0.879622\pi$
$61$	−7.08626e9	+	4.09126e9i	−1.07424	+	0.620216i	−0.144907	+	0.989445i	$0.546288\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.25033e9	−	3.03128e9i	0.561259	−	0.324043i
$66$		0			0
$67$	−7.76991e9	+	1.34579e10i	−0.703079	+	1.21777i	0.264301	+	0.964440i	$0.414859\pi$
$67$	−7.76991e9	+	1.34579e10i	−0.703079	+	1.21777i	−0.967380	+	0.253329i	$0.918475\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	9.66933e9i		−	0.636027i	−0.948086	−	0.318013i	$-0.896984\pi$
$71$		−	9.66933e9i		−	0.636027i	0.948086	−	0.318013i	$-0.103016\pi$
$72$		0			0
$73$	1.50791e10	+	8.70595e9i	0.851336	+	0.491519i	0.861101	−	0.508433i	$-0.169775\pi$
$73$	1.50791e10	+	8.70595e9i	0.851336	+	0.491519i	−0.00976543	+	0.999952i	$0.503108\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.36140e10	+	2.51952e10i	−0.573172	+	1.06076i
$78$		0			0
$79$	−1.04686e10	−	1.81321e10i	−0.382771	−	0.662979i	0.608686	−	0.793411i	$-0.291697\pi$
$79$	−1.04686e10	−	1.81321e10i	−0.382771	−	0.662979i	−0.991457	+	0.130432i	$0.958364\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.71020e10			−1.03387			−0.516937	−	0.856023i	$-0.672928\pi$
$83$	−3.71020e10			−1.03387			−0.516937	+	0.856023i	$0.672928\pi$
$84$		0			0
$85$	5.72566e10			1.39966
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.41154e10	−	4.17691e10i	−0.457772	−	0.792884i	0.541071	−	0.840977i	$-0.318019\pi$
$89$	−2.41154e10	−	4.17691e10i	−0.457772	−	0.792884i	−0.998843	+	0.0480929i	$0.984686\pi$
$90$		0			0
$91$	−2.82556e10	+	7.97077e8i	−0.474653	+	0.0133898i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.66779e10	+	5.00435e10i	1.14929	+	0.663541i
$96$		0			0
$97$		−	2.57959e9i		−	0.0305005i	−0.999884	−	0.0152502i	$-0.995146\pi$
$97$		−	2.57959e9i		−	0.0305005i	0.999884	−	0.0152502i	$-0.00485449\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.80261e10	−	1.17825e11i	0.644033	−	1.11550i	−0.340491	−	0.940248i	$-0.610593\pi$
$101$	6.80261e10	−	1.17825e11i	0.644033	−	1.11550i	0.984524	−	0.175250i	$-0.0560733\pi$
$102$		0			0
$103$	−7.74433e10	+	4.47119e10i	−0.658232	+	0.380031i	−0.791603	−	0.611036i	$-0.790753\pi$
$103$	−7.74433e10	+	4.47119e10i	−0.658232	+	0.380031i	0.133371	+	0.991066i	$0.457420\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.07328e11	−	6.19660e10i	0.739781	−	0.427113i	−0.0822087	−	0.996615i	$-0.526197\pi$
$107$	1.07328e11	−	6.19660e10i	0.739781	−	0.427113i	0.821990	+	0.569502i	$0.192864\pi$
$108$		0			0
$109$	1.40490e11	−	2.43337e11i	0.874583	−	1.51482i	0.0173774	−	0.999849i	$-0.494468\pi$
$109$	1.40490e11	−	2.43337e11i	0.874583	−	1.51482i	0.857206	−	0.514974i	$-0.172198\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	1.82487e11i		−	0.931753i	−0.884850	−	0.465877i	$-0.845739\pi$
$113$		−	1.82487e11i		−	0.931753i	0.884850	−	0.465877i	$-0.154261\pi$
$114$		0			0
$115$	3.58975e11	+	2.07254e11i	1.66428	+	0.960871i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.34866e11	−	1.26908e11i	−0.902220	−	0.487506i
$120$		0			0
$121$	6.47291e10	+	1.12114e11i	0.226871	+	0.392953i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.38897e10			0.187252
$126$		0			0
$127$	−3.16302e11			−0.849534			−0.424767	−	0.905303i	$-0.639644\pi$
$127$	−3.16302e11			−0.849534			−0.424767	+	0.905303i	$0.639644\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.72254e11	+	4.71558e11i	0.616569	+	1.06793i	0.990107	+	0.140315i	$0.0448114\pi$
$131$	2.72254e11	+	4.71558e11i	0.616569	+	1.06793i	−0.373538	+	0.927615i	$0.621855\pi$
$132$		0			0
$133$	−2.44632e11	−	3.97397e11i	−0.509717	−	0.828020i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.49318e11	−	2.59414e11i	−0.795409	−	0.459230i	0.0464541	−	0.998920i	$-0.485208\pi$
$137$	−4.49318e11	−	2.59414e11i	−0.795409	−	0.459230i	−0.841863	+	0.539691i	$0.818541\pi$
$138$		0			0
$139$			4.36144e11i			0.712933i	0.934308	+	0.356466i	$0.116019\pi$
$139$			4.36144e11i			0.712933i	−0.934308	+	0.356466i	$0.883981\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.04697e11	+	3.54545e11i	−0.286262	+	0.495820i
$144$		0			0
$145$	−9.89070e11	+	5.71040e11i	−1.28145	+	0.739847i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.94689e11	+	3.43344e11i	−0.663384	+	0.383005i	−0.793565	−	0.608485i	$-0.791778\pi$
$149$	−5.94689e11	+	3.43344e11i	−0.663384	+	0.383005i	0.130181	+	0.991490i	$0.458444\pi$
$150$		0			0
$151$	−3.44798e11	+	5.97207e11i	−0.357430	+	0.619087i	−0.987531	−	0.157426i	$-0.949680\pi$
$151$	−3.44798e11	+	5.97207e11i	−0.357430	+	0.619087i	0.630101	+	0.776513i	$0.283014\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			8.59793e11i			0.771915i
$156$		0			0
$157$	−1.61809e12	−	9.34203e11i	−1.35380	−	0.781616i	−0.365019	−	0.931000i	$-0.618937\pi$
$157$	−1.61809e12	−	9.34203e11i	−1.35380	−	0.781616i	−0.988779	+	0.149385i	$0.952271\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.01314e12	−	1.64581e12i	−0.738119	−	1.19905i
$162$		0			0
$163$	−1.14613e12	−	1.98516e12i	−0.780196	−	1.35134i	−0.931828	−	0.362901i	$-0.881786\pi$
$163$	−1.14613e12	−	1.98516e12i	−0.780196	−	1.35134i	0.151632	−	0.988437i	$-0.451547\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.48472e11			0.148026			0.0740129	−	0.997257i	$-0.476419\pi$
$167$	2.48472e11			0.148026			0.0740129	+	0.997257i	$0.476419\pi$
$168$		0			0
$169$	1.38807e12			0.774525
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.92036e11	+	1.02544e12i	0.290465	+	0.503101i	0.973920	−	0.226892i	$-0.0728566\pi$
$173$	5.92036e11	+	1.02544e12i	0.290465	+	0.503101i	−0.683454	+	0.729993i	$0.739523\pi$
$174$		0			0
$175$	1.64815e12	+	8.90559e11i	0.759078	+	0.410160i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.35346e12	−	7.81423e11i	−0.550497	−	0.317830i	0.198825	−	0.980035i	$-0.436287\pi$
$179$	−1.35346e12	−	7.81423e11i	−0.550497	−	0.317830i	−0.749322	+	0.662205i	$0.769621\pi$
$180$		0			0
$181$			2.52776e12i			0.967173i	0.875297	+	0.483586i	$0.160666\pi$
$181$			2.52776e12i			0.967173i	−0.875297	+	0.483586i	$0.839334\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.72344e12	−	6.44918e12i	1.26328	−	2.18806i
$186$		0			0
$187$	−3.34843e12	+	1.93322e12i	−1.07081	+	0.618233i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.40938e11	+	3.12311e11i	−0.153980	+	0.0889004i	−0.575010	−	0.818146i	$-0.695002\pi$
$191$	−5.40938e11	+	3.12311e11i	−0.153980	+	0.0889004i	0.421030	+	0.907047i	$0.361669\pi$
$192$		0			0
$193$	5.02803e11	−	8.70880e11i	0.135155	−	0.234096i	−0.790502	−	0.612460i	$-0.790180\pi$
$193$	5.02803e11	−	8.70880e11i	0.135155	−	0.234096i	0.925657	+	0.378364i	$0.123513\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.96955e12i		−	1.43343i	−0.697364	−	0.716717i	$-0.745644\pi$
$197$		−	5.96955e12i		−	1.43343i	0.697364	−	0.716717i	$-0.254356\pi$
$198$		0			0
$199$	5.14984e12	+	2.97326e12i	1.16977	+	0.675370i	0.953627	−	0.300991i	$-0.0973175\pi$
$199$	5.14984e12	+	2.97326e12i	1.16977	+	0.675370i	0.216147	+	0.976361i	$0.430651\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.32285e12	−	1.50155e11i	1.08372	−	0.0305712i
$204$		0			0
$205$	−2.98780e12	−	5.17503e12i	−0.576376	−	0.998313i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.75869e12			−1.17235
$210$		0			0
$211$	−4.97009e12			−0.818109			−0.409054	−	0.912510i	$-0.634141\pi$
$211$	−4.97009e12			−0.818109			−0.409054	+	0.912510i	$0.634141\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.55059e12	−	1.13460e13i	−0.972453	−	1.68434i
$216$		0			0
$217$	1.90571e12	−	3.52686e12i	0.268861	−	0.497577i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.30503e12	−	1.90816e12i	−0.421714	−	0.243477i
$222$		0			0
$223$			4.44211e11i			0.0539402i	0.999636	+	0.0269701i	$0.00858589\pi$
$223$			4.44211e11i			0.0539402i	−0.999636	+	0.0269701i	$0.991414\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.71651e12	−	6.43719e12i	0.409255	−	0.708850i	−0.585552	−	0.810635i	$-0.699122\pi$
$227$	3.71651e12	−	6.43719e12i	0.409255	−	0.708850i	0.994806	+	0.101785i	$0.0324554\pi$
$228$		0			0
$229$	−8.37539e11	+	4.83553e11i	−0.0878840	+	0.0507399i	−0.543298	−	0.839540i	$-0.682825\pi$
$229$	−8.37539e11	+	4.83553e11i	−0.0878840	+	0.0507399i	0.455414	+	0.890280i	$0.349491\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.05000e13	+	6.06219e12i	−1.00169	+	0.578325i	−0.908747	−	0.417347i	$-0.862960\pi$
$233$	−1.05000e13	+	6.06219e12i	−1.00169	+	0.578325i	−0.0929408	+	0.995672i	$0.529627\pi$
$234$		0			0
$235$	−1.25670e13	+	2.17667e13i	−1.14382	+	1.98116i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			1.55948e12i			0.129358i	0.997906	+	0.0646788i	$0.0206023\pi$
$239$			1.55948e12i			0.129358i	−0.997906	+	0.0646788i	$0.979398\pi$
$240$		0			0
$241$	7.54136e12	+	4.35401e12i	0.597525	+	0.344981i	0.768067	−	0.640369i	$-0.221219\pi$
$241$	7.54136e12	+	4.35401e12i	0.597525	+	0.344981i	−0.170542	+	0.985350i	$0.554552\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.03347e13	−	1.57740e13i	−0.747971	−	1.14164i
$246$		0			0
$247$	−3.33555e12	−	5.77733e12i	−0.230852	−	0.399847i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.10155e12			0.449933			0.224966	−	0.974367i	$-0.427773\pi$
$251$	7.10155e12			0.449933			0.224966	+	0.974367i	$0.427773\pi$
$252$		0			0
$253$	−2.79910e13			−1.69768
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.02280e12	−	1.04318e13i	−0.335094	−	0.580399i	0.648409	−	0.761292i	$-0.275435\pi$
$257$	−6.02280e12	−	1.04318e13i	−0.335094	−	0.580399i	−0.983503	+	0.180893i	$0.942101\pi$
$258$		0			0
$259$	−2.95679e13	+	1.82016e13i	−1.57642	+	0.970422i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.39118e13	−	1.38055e13i	−1.17181	−	0.676542i	−0.217701	−	0.976015i	$-0.569856\pi$
$263$	−2.39118e13	−	1.38055e13i	−1.17181	−	0.676542i	−0.954105	+	0.299473i	$0.903189\pi$
$264$		0			0
$265$		−	1.86491e12i		−	0.0876608i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.50241e12	−	2.60225e12i	0.0650355	−	0.112645i	−0.831674	−	0.555264i	$-0.812617\pi$
$269$	1.50241e12	−	2.60225e12i	0.0650355	−	0.112645i	0.896710	+	0.442619i	$0.145951\pi$
$270$		0			0
$271$	−2.89312e13	+	1.67034e13i	−1.20236	+	0.694183i	−0.961079	−	0.276272i	$-0.910901\pi$
$271$	−2.89312e13	+	1.67034e13i	−1.20236	+	0.694183i	−0.241281	+	0.970455i	$0.577568\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.34972e13	−	1.35661e13i	0.900921	−	0.520147i
$276$		0			0
$277$	2.50321e13	−	4.33568e13i	0.922269	−	1.59742i	0.126374	−	0.991983i	$-0.459666\pi$
$277$	2.50321e13	−	4.33568e13i	0.922269	−	1.59742i	0.795895	−	0.605435i	$-0.207001\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	4.18761e13i		−	1.42588i	−0.701227	−	0.712938i	$-0.747364\pi$
$281$		−	4.18761e13i		−	1.42588i	0.701227	−	0.712938i	$-0.252636\pi$
$282$		0			0
$283$	−2.11946e13	−	1.22367e13i	−0.694064	−	0.400718i	0.111069	−	0.993813i	$-0.464573\pi$
$283$	−2.11946e13	−	1.22367e13i	−0.694064	−	0.400718i	−0.805133	+	0.593095i	$0.797906\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.85645e11	+	2.78503e13i	0.0238164	+	0.844267i
$288$		0			0
$289$	−8.85285e11	−	1.53336e12i	−0.0258312	−	0.0447410i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.54368e12			−0.0417624			−0.0208812	−	0.999782i	$-0.506647\pi$
$293$	−1.54368e12			−0.0417624			−0.0208812	+	0.999782i	$0.506647\pi$
$294$		0			0
$295$	−8.39116e13			−2.18676
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.38141e13	−	2.39267e13i	−0.334296	−	0.579017i
$300$		0			0
$301$	1.72248e12	+	6.10602e13i	0.0401827	+	1.42443i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.75828e13	−	3.90189e13i	−1.46618	−	0.846499i
$306$		0			0
$307$		−	3.45744e13i		−	0.723592i	−0.932257	−	0.361796i	$-0.882164\pi$
$307$		−	3.45744e13i		−	0.723592i	0.932257	−	0.361796i	$-0.117836\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.46209e13	−	7.72856e13i	0.869672	−	1.50632i	0.00734084	−	0.999973i	$-0.497663\pi$
$311$	4.46209e13	−	7.72856e13i	0.869672	−	1.50632i	0.862332	−	0.506344i	$-0.169003\pi$
$312$		0			0
$313$	−5.21629e13	+	3.01163e13i	−0.981449	+	0.566640i	−0.902707	−	0.430255i	$-0.858424\pi$
$313$	−5.21629e13	+	3.01163e13i	−0.981449	+	0.566640i	−0.0787417	+	0.996895i	$0.525090\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.51667e13	+	8.75652e12i	−0.266113	+	0.153640i	−0.627120	−	0.778923i	$-0.715766\pi$
$317$	−1.51667e13	+	8.75652e12i	−0.266113	+	0.153640i	0.361007	+	0.932563i	$0.382433\pi$
$318$		0			0
$319$	3.85613e13	−	6.67901e13i	0.653586	−	1.13204i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	6.30038e13i		−	0.997132i
$324$		0			0
$325$	2.31927e13	+	1.33903e13i	0.354807	+	0.204848i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.97951e13	−	6.14324e13i	1.42735	−	0.878659i
$330$		0			0
$331$	6.98136e13	+	1.20921e14i	0.965797	+	1.67281i	0.707457	+	0.706756i	$0.249842\pi$
$331$	6.98136e13	+	1.20921e14i	0.965797	+	1.67281i	0.258340	+	0.966054i	$0.416825\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.48205e14			−1.91919
$336$		0			0
$337$	−4.81646e12			−0.0603620			−0.0301810	−	0.999544i	$-0.509608\pi$
$337$	−4.81646e12			−0.0603620			−0.0301810	+	0.999544i	$0.509608\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.90301e13	−	5.02816e13i	−0.340957	−	0.590555i
$342$		0			0
$343$	7.43022e12	+	8.76116e13i	0.0845053	+	0.996423i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.32721e14	−	7.66265e13i	−1.41621	−	0.817649i	−0.420247	−	0.907410i	$-0.638057\pi$
$347$	−1.32721e14	−	7.66265e13i	−1.41621	−	0.817649i	−0.995963	+	0.0897603i	$0.971390\pi$
$348$		0			0
$349$			8.43937e13i			0.872510i	0.899823	+	0.436255i	$0.143695\pi$
$349$			8.43937e13i			0.872510i	−0.899823	+	0.436255i	$0.856305\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.40914e12	−	9.36891e12i	0.0525252	−	0.0909763i	−0.838567	−	0.544798i	$-0.816606\pi$
$353$	5.40914e12	−	9.36891e12i	0.0525252	−	0.0909763i	0.891093	+	0.453822i	$0.149940\pi$
$354$		0			0
$355$	7.98630e13	−	4.61089e13i	0.751778	−	0.434039i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.09080e14	−	6.29771e13i	0.965436	−	0.557395i	0.0675945	−	0.997713i	$-0.478468\pi$
$359$	1.09080e14	−	6.29771e13i	0.965436	−	0.557395i	0.897842	+	0.440318i	$0.145134\pi$
$360$		0			0
$361$	−3.17852e12	+	5.50536e12i	−0.0272857	+	0.0472603i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			1.66060e14i			1.34170i
$366$		0			0
$367$	4.86876e13	+	2.81098e13i	0.381729	+	0.220391i	0.678570	−	0.734535i	$-0.262600\pi$
$367$	4.86876e13	+	2.81098e13i	0.381729	+	0.220391i	−0.296841	+	0.954927i	$0.595933\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.13352e12	+	7.64985e12i	−0.0305326	+	0.0565062i
$372$		0			0
$373$	−1.13153e14	−	1.95987e14i	−0.811462	−	1.40549i	−0.911841	−	0.410543i	$-0.865339\pi$
$373$	−1.13153e14	−	1.95987e14i	−0.811462	−	1.40549i	0.100380	−	0.994949i	$-0.467994\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	7.61229e13			0.514799
$378$		0			0
$379$	−1.74259e14			−1.14467			−0.572335	−	0.820020i	$-0.693962\pi$
$379$	−1.74259e14			−1.14467			−0.572335	+	0.820020i	$0.693962\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.82683e13	−	8.36032e13i	−0.299274	−	0.518358i	0.676696	−	0.736263i	$-0.263411\pi$
$383$	−4.82683e13	−	8.36032e13i	−0.299274	−	0.518358i	−0.975970	+	0.217905i	$0.930078\pi$
$384$		0			0
$385$	−2.73016e14	+	7.70167e12i	−1.64496	+	0.0464035i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.03598e13	−	3.48487e13i	−0.343578	−	0.198365i	0.318275	−	0.947998i	$-0.396896\pi$
$389$	−6.03598e13	−	3.48487e13i	−0.343578	−	0.198365i	−0.661853	+	0.749634i	$0.730230\pi$
$390$		0			0
$391$		−	2.60929e14i		−	1.44394i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.98405e13	−	1.72929e14i	0.522423	−	0.904864i
$396$		0			0
$397$	−2.56840e14	+	1.48287e14i	−1.30712	+	0.754664i	−0.981614	−	0.190876i	$-0.938867\pi$
$397$	−2.56840e14	+	1.48287e14i	−1.30712	+	0.754664i	−0.325503	+	0.945541i	$0.605534\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.01950e14	+	1.16596e14i	−0.972635	+	0.561551i	−0.900039	−	0.435810i	$-0.856462\pi$
$401$	−2.01950e14	+	1.16596e14i	−0.972635	+	0.561551i	−0.0725967	+	0.997361i	$0.523129\pi$
$402$		0			0
$403$	2.86538e13	−	4.96299e13i	0.134278	−	0.232576i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			5.02874e14i			2.23198i
$408$		0			0
$409$	3.33267e14	+	1.92412e14i	1.43984	+	0.831292i	0.997838	−	0.0657216i	$-0.0209349\pi$
$409$	3.33267e14	+	1.92412e14i	1.43984	+	0.831292i	0.442002	+	0.897014i	$0.354268\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.44205e14	+	1.85988e14i	1.40959	+	0.761656i
$414$		0			0
$415$	−1.76924e14	−	3.06441e14i	−0.705540	−	1.22203i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.01331e13			0.151819			0.0759095	−	0.997115i	$-0.475814\pi$
$419$	4.01331e13			0.151819			0.0759095	+	0.997115i	$0.475814\pi$
$420$		0			0
$421$	−2.34882e14			−0.865562			−0.432781	−	0.901499i	$-0.642468\pi$
$421$	−2.34882e14			−0.865562			−0.432781	+	0.901499i	$0.642468\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.26462e14	+	2.19038e14i	0.442405	+	0.766268i
$426$		0			0
$427$	1.90740e14	+	3.09851e14i	0.650261	+	1.05633i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−3.77908e13	−	2.18185e13i	−0.122394	−	0.0706643i	0.437553	−	0.899193i	$-0.355845\pi$
$431$	−3.77908e13	−	2.18185e13i	−0.122394	−	0.0706643i	−0.559947	+	0.828528i	$0.689179\pi$
$432$		0			0
$433$			1.97475e14i			0.623488i	0.950166	+	0.311744i	$0.100913\pi$
$433$			1.97475e14i			0.623488i	−0.950166	+	0.311744i	$0.899087\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.28057e14	−	3.95007e14i	0.684536	−	1.18565i
$438$		0			0
$439$	5.52363e14	−	3.18907e14i	1.61685	−	0.933488i	0.629120	−	0.777308i	$-0.283415\pi$
$439$	5.52363e14	−	3.18907e14i	1.61685	−	0.933488i	0.987729	−	0.156180i	$-0.0499181\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.17360e14	+	2.40963e14i	−1.16223	+	0.671012i	−0.951837	−	0.306606i	$-0.900807\pi$
$443$	−4.17360e14	+	2.40963e14i	−1.16223	+	0.671012i	−0.210390	+	0.977618i	$0.567473\pi$
$444$		0			0
$445$	2.29992e14	−	3.98358e14i	0.624788	−	1.08216i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	2.70569e14i		−	0.699719i	−0.936802	−	0.349860i	$-0.886229\pi$
$449$		−	2.70569e14i		−	0.699719i	0.936802	−	0.349860i	$-0.113771\pi$
$450$		0			0
$451$	3.49460e14	+	2.01761e14i	0.881915	+	0.509174i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.41322e14	−	2.29574e14i	−0.339741	−	0.551899i
$456$		0			0
$457$	−9.20749e13	−	1.59478e14i	−0.216074	−	0.374251i	0.737530	−	0.675314i	$-0.235992\pi$
$457$	−9.20749e13	−	1.59478e14i	−0.216074	−	0.374251i	−0.953604	+	0.301063i	$0.902658\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.00170e14			−0.671448			−0.335724	−	0.941960i	$-0.608981\pi$
$461$	−3.00170e14			−0.671448			−0.335724	+	0.941960i	$0.608981\pi$
$462$		0			0
$463$	4.68801e12			0.0102398			0.00511992	−	0.999987i	$-0.498370\pi$
$463$	4.68801e12			0.0102398			0.00511992	+	0.999987i	$0.498370\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.21914e14	+	7.30777e14i	0.878985	+	1.52245i	0.852456	+	0.522799i	$0.175112\pi$
$467$	4.21914e14	+	7.30777e14i	0.878985	+	1.52245i	0.0265288	+	0.999648i	$0.491555\pi$
$468$		0			0
$469$	6.07938e14	+	3.28493e14i	1.23711	+	0.668461i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	7.66171e14	+	4.42349e14i	1.48795	+	0.859071i
$474$		0			0
$475$			4.42121e14i			0.838931i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.47625e14	+	2.55693e14i	−0.267494	+	0.463313i	−0.968214	−	0.250124i	$-0.919529\pi$
$479$	−1.47625e14	+	2.55693e14i	−0.267494	+	0.463313i	0.700720	+	0.713436i	$0.252862\pi$
$480$		0			0
$481$	−4.29857e14	+	2.48178e14i	−0.761247	+	0.439506i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.13059e13	−	1.23010e13i	0.0360513	−	0.0208142i
$486$		0			0
$487$	4.56140e14	−	7.90057e14i	0.754551	−	1.30692i	−0.191046	−	0.981581i	$-0.561188\pi$
$487$	4.56140e14	−	7.90057e14i	0.754551	−	1.30692i	0.945597	−	0.325339i	$-0.105479\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			5.43973e14i			0.860259i	0.902767	+	0.430130i	$0.141532\pi$
$491$			5.43973e14i			0.860259i	−0.902767	+	0.430130i	$0.858468\pi$
$492$		0			0
$493$	6.22609e14	+	3.59464e14i	0.962847	+	0.555900i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.29796e14	+	1.21244e13i	−0.635774	+	0.0179349i
$498$		0			0
$499$	1.00125e14	+	1.73422e14i	0.144874	+	0.250929i	0.929326	−	0.369261i	$-0.120389\pi$
$499$	1.00125e14	+	1.73422e14i	0.144874	+	0.250929i	−0.784452	+	0.620190i	$0.787056\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4.62227e14			0.640076			0.320038	−	0.947405i	$-0.396304\pi$
$503$	4.62227e14			0.640076			0.320038	+	0.947405i	$0.396304\pi$
$504$		0			0
$505$	1.29755e15			1.75801
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.96939e14	+	5.14313e14i	0.385229	+	0.667237i	0.991801	−	0.127792i	$-0.0407890\pi$
$509$	2.96939e14	+	5.14313e14i	0.385229	+	0.667237i	−0.606572	+	0.795029i	$0.707456\pi$
$510$		0			0
$511$	3.68067e14	−	6.81176e14i	0.467317	−	0.864857i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.38588e14	−	4.26424e14i	−0.898385	−	0.518683i
$516$		0			0
$517$		−	1.69725e15i		−	2.02092i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.59395e14	+	9.68901e14i	−0.638427	+	1.10579i	0.347351	+	0.937735i	$0.387081\pi$
$521$	−5.59395e14	+	9.68901e14i	−0.638427	+	1.10579i	−0.985778	+	0.168053i	$0.946252\pi$
$522$		0			0
$523$	−9.72377e14	+	5.61402e14i	−1.08661	+	0.627357i	−0.932673	−	0.360723i	$-0.882530\pi$
$523$	−9.72377e14	+	5.61402e14i	−1.08661	+	0.627357i	−0.153941	+	0.988080i	$0.549197\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.68720e14	−	2.70615e14i	0.502290	−	0.289997i
$528$		0			0
$529$	4.68090e14	−	8.10756e14i	0.491273	−	0.850910i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			3.98292e14i			0.401053i
$534$		0			0
$535$	1.02361e15	+	5.90979e14i	1.00969	+	0.582943i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.13698e15	+	5.73541e14i	1.07650	+	0.543033i
$540$		0			0
$541$	−1.15107e14	−	1.99371e14i	−0.106787	−	0.184960i	0.807680	−	0.589621i	$-0.200723\pi$
$541$	−1.15107e14	−	1.99371e14i	−0.106787	−	0.184960i	−0.914467	+	0.404661i	$0.867389\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.67976e15			2.38734
$546$		0			0
$547$	−1.14152e15			−0.996672			−0.498336	−	0.866984i	$-0.666055\pi$
$547$	−1.14152e15			−0.996672			−0.498336	+	0.866984i	$0.666055\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.28357e14	+	1.08835e15i	0.527076	+	0.912922i
$552$		0			0
$553$	−7.92837e14	+	4.88059e14i	−0.651922	+	0.401314i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.58268e14	+	9.13763e13i	0.125081	+	0.0722154i	0.561235	−	0.827657i	$-0.310326\pi$
$557$	1.58268e14	+	9.13763e13i	0.125081	+	0.0722154i	−0.436154	+	0.899872i	$0.643660\pi$
$558$		0			0
$559$			8.73232e14i			0.676651i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.16089e14	−	3.74278e14i	0.161004	−	0.278868i	−0.774225	−	0.632911i	$-0.781860\pi$
$563$	2.16089e14	−	3.74278e14i	0.161004	−	0.278868i	0.935229	+	0.354043i	$0.115193\pi$
$564$		0			0
$565$	1.50724e15	−	8.70204e14i	1.10132	−	0.635850i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.55037e15	+	8.95106e14i	−1.08973	+	0.629154i	−0.933504	−	0.358568i	$-0.883265\pi$
$569$	−1.55037e15	+	8.95106e14i	−1.08973	+	0.629154i	−0.156223	+	0.987722i	$0.549932\pi$
$570$		0			0
$571$	−4.83944e14	+	8.38215e14i	−0.333654	+	0.577906i	−0.983225	−	0.182395i	$-0.941615\pi$
$571$	−4.83944e14	+	8.38215e14i	−0.333654	+	0.577906i	0.649571	+	0.760301i	$0.274948\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			1.83104e15i			1.21485i
$576$		0			0
$577$	−1.51634e15	−	8.75457e14i	−0.987025	−	0.569859i	−0.0826416	−	0.996579i	$-0.526336\pi$
$577$	−1.51634e15	−	8.75457e14i	−0.987025	−	0.569859i	−0.904384	+	0.426720i	$0.859669\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.65222e13	+	1.64916e15i	0.0291536	+	1.03346i
$582$		0			0
$583$	6.29670e13	+	1.09062e14i	0.0387200	+	0.0670651i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.07007e15			−1.22596			−0.612978	−	0.790100i	$-0.710029\pi$
$587$	−2.07007e15			−1.22596			−0.612978	+	0.790100i	$0.710029\pi$
$588$		0			0
$589$	9.46094e14			0.549921
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.84252e14	−	6.65544e14i	−0.215187	−	0.372714i	0.738144	−	0.674644i	$-0.235703\pi$
$593$	−3.84252e14	−	6.65544e14i	−0.215187	−	0.372714i	−0.953330	+	0.301929i	$0.902369\pi$
$594$		0			0
$595$	−7.17941e13	−	2.54503e15i	−0.0394680	−	1.39910i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	9.71202e14	+	5.60724e14i	0.514591	+	0.297099i	0.734719	−	0.678372i	$-0.237314\pi$
$599$	9.71202e14	+	5.60724e14i	0.514591	+	0.297099i	−0.220128	+	0.975471i	$0.570647\pi$
$600$		0			0
$601$		−	2.61302e14i		−	0.135935i	−0.997688	−	0.0679677i	$-0.978349\pi$
$601$		−	2.61302e14i		−	0.135935i	0.997688	−	0.0679677i	$-0.0216515\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.17331e14	+	1.06925e15i	−0.309645	+	0.536320i
$606$		0			0
$607$	−2.06549e13	+	1.19251e13i	−0.0101738	+	0.00587387i	−0.505078	−	0.863074i	$-0.668536\pi$
$607$	−2.06549e13	+	1.19251e13i	−0.0101738	+	0.00587387i	0.494904	+	0.868947i	$0.335203\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.45081e15	−	8.37628e14i	0.689263	−	0.397946i
$612$		0			0
$613$	−3.75082e14	+	6.49660e14i	−0.175022	+	0.303147i	−0.940169	−	0.340709i	$-0.889333\pi$
$613$	−3.75082e14	+	6.49660e14i	−0.175022	+	0.303147i	0.765147	+	0.643856i	$0.222666\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	3.76272e14i		−	0.169408i	−0.996406	−	0.0847038i	$-0.973006\pi$
$617$		−	3.76272e14i		−	0.169408i	0.996406	−	0.0847038i	$-0.0269944\pi$
$618$		0			0
$619$	−1.33174e14	−	7.68882e13i	−0.0589009	−	0.0340064i	0.470260	−	0.882528i	$-0.344160\pi$
$619$	−1.33174e14	−	7.68882e13i	−0.0589009	−	0.0340064i	−0.529161	+	0.848521i	$0.677493\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.82637e15	+	1.12429e15i	−0.779660	+	0.479948i
$624$		0			0
$625$	1.33321e15	+	2.30918e15i	0.559187	+	0.968540i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.68773e15			−1.89838
$630$		0			0
$631$	7.98362e14			0.317715			0.158858	−	0.987301i	$-0.449219\pi$
$631$	7.98362e14			0.317715			0.158858	+	0.987301i	$0.449219\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.50831e15	−	2.61247e15i	−0.579742	−	1.00414i
$636$		0			0
$637$	7.08593e13	+	1.25495e15i	0.0267689	+	0.474087i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.17996e15	+	1.25860e15i	0.795663	+	0.459377i	0.841953	−	0.539552i	$-0.181406\pi$
$641$	2.17996e15	+	1.25860e15i	0.795663	+	0.459377i	−0.0462891	+	0.998928i	$0.514740\pi$
$642$		0			0
$643$			1.01827e15i			0.365345i	0.983174	+	0.182673i	$0.0584749\pi$
$643$			1.01827e15i			0.365345i	−0.983174	+	0.182673i	$0.941525\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.59959e14	−	9.69877e14i	0.194170	−	0.336313i	−0.752458	−	0.658640i	$-0.771132\pi$
$647$	5.59959e14	−	9.69877e14i	0.194170	−	0.336313i	0.946628	+	0.322328i	$0.104465\pi$
$648$		0			0
$649$	4.90724e15	−	2.83320e15i	1.67298	−	0.965898i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.33053e15	−	1.92288e15i	1.09772	−	0.633767i	0.162096	−	0.986775i	$-0.448174\pi$
$653$	3.33053e15	−	1.92288e15i	1.09772	−	0.633767i	0.935620	+	0.353008i	$0.114841\pi$
$654$		0			0
$655$	−2.59653e15	+	4.49732e15i	−0.841522	+	1.45756i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	5.40793e15i		−	1.69497i	−0.530822	−	0.847484i	$-0.678117\pi$
$659$		−	5.40793e15i		−	1.69497i	0.530822	−	0.847484i	$-0.321883\pi$
$660$		0			0
$661$	−4.37680e15	−	2.52695e15i	−1.34911	−	0.778911i	−0.360990	−	0.932570i	$-0.617561\pi$
$661$	−4.37680e15	−	2.52695e15i	−1.34911	−	0.778911i	−0.988124	+	0.153658i	$0.950894\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.11572e15	−	3.91554e15i	0.630869	−	1.16754i
$666$		0			0
$667$	2.60233e15	+	4.50737e15i	0.763256	+	1.32200i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.26975e15			1.49560
$672$		0			0
$673$	5.20414e15			1.45300			0.726500	−	0.687166i	$-0.241146\pi$
$673$	5.20414e15			1.45300			0.726500	+	0.687166i	$0.241146\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.02390e14	−	1.04337e15i	−0.162795	−	0.281969i	0.773075	−	0.634314i	$-0.218717\pi$
$677$	−6.02390e14	−	1.04337e15i	−0.162795	−	0.281969i	−0.935870	+	0.352346i	$0.885384\pi$
$678$		0			0
$679$	−1.14661e14	+	3.23455e12i	−0.0304883	+	0.000860062i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−5.21676e14	−	3.01190e14i	−0.134303	−	0.0775402i	0.431343	−	0.902188i	$-0.358040\pi$
$683$	−5.21676e14	−	3.01190e14i	−0.134303	−	0.0775402i	−0.565646	+	0.824648i	$0.691373\pi$
$684$		0			0
$685$		−	4.94814e15i		−	1.25356i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.21508e13	+	1.07648e14i	−0.0152490	+	0.0264120i
$690$		0			0
$691$	1.37596e15	−	7.94412e14i	0.332260	−	0.191830i	−0.324584	−	0.945857i	$-0.605224\pi$
$691$	1.37596e15	−	7.94412e14i	0.332260	−	0.191830i	0.656844	+	0.754027i	$0.271891\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.60229e15	+	2.07979e15i	−0.842680	+	0.486522i
$696$		0			0
$697$	−1.88079e15	+	3.25763e15i	−0.433072	+	0.750103i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	2.71558e15i		−	0.605918i	−0.953004	−	0.302959i	$-0.902026\pi$
$701$		−	2.71558e15i		−	0.605918i	0.953004	−	0.302959i	$-0.0979745\pi$
$702$		0			0
$703$	−7.09651e15	−	4.09717e15i	−1.55880	−	0.899974i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.32254e15	−	2.87598e15i	−1.13321	−	0.612321i
$708$		0			0
$709$	−3.89387e15	−	6.74438e15i	−0.816258	−	1.41380i	−0.908421	−	0.418056i	$-0.862712\pi$
$709$	−3.89387e15	−	6.74438e15i	−0.816258	−	1.41380i	0.0921633	−	0.995744i	$-0.470622\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.91823e15			0.796338
$714$		0			0
$715$	−3.90445e15			−0.781406
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.76319e15	−	6.51804e15i	−0.730378	−	1.26505i	−0.956722	−	0.291004i	$-0.906011\pi$
$719$	−3.76319e15	−	6.51804e15i	−0.730378	−	1.26505i	0.226344	−	0.974047i	$-0.427323\pi$
$720$		0			0
$721$	2.08453e15	+	3.38625e15i	0.398440	+	0.647254i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.36908e15	−	2.52249e15i	−0.810086	−	0.467704i
$726$		0			0
$727$			6.90251e15i			1.26057i	0.776363	+	0.630286i	$0.217062\pi$
$727$			6.90251e15i			1.26057i	−0.776363	+	0.630286i	$0.782938\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.12353e15	+	7.14216e15i	−0.730674	+	1.26556i
$732$		0			0
$733$	−8.33906e15	+	4.81456e15i	−1.45561	+	0.840397i	−0.998791	−	0.0491622i	$-0.984345\pi$
$733$	−8.33906e15	+	4.81456e15i	−1.45561	+	0.840397i	−0.456820	+	0.889559i	$0.651012\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.66722e15	−	5.00402e15i	1.46828	−	0.847712i
$738$		0			0
$739$	6.03653e13	−	1.04556e14i	0.0100749	−	0.0174503i	−0.860944	−	0.508700i	$-0.830126\pi$
$739$	6.03653e13	−	1.04556e14i	0.0100749	−	0.0174503i	0.871019	+	0.491249i	$0.163460\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			4.78245e15i			0.774841i	0.921903	+	0.387420i	$0.126634\pi$
$743$			4.78245e15i			0.774841i	−0.921903	+	0.387420i	$0.873366\pi$
$744$		0			0
$745$	−5.67163e15	−	3.27452e15i	−0.905417	−	0.522743i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.88893e15	−	4.69298e15i	−0.447804	−	0.727443i
$750$		0			0
$751$	3.51247e14	+	6.08378e14i	0.0536529	+	0.0929296i	0.891604	−	0.452815i	$-0.149580\pi$
$751$	3.51247e14	+	6.08378e14i	0.0536529	+	0.0929296i	−0.837952	+	0.545745i	$0.816247\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.57677e15			−0.975674
$756$		0			0
$757$	−8.32650e15			−1.21741			−0.608703	−	0.793398i	$-0.708310\pi$
$757$	−8.32650e15			−1.21741			−0.608703	+	0.793398i	$0.708310\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.62863e14	−	1.32132e15i	−0.108351	−	0.187669i	0.806752	−	0.590891i	$-0.201224\pi$
$761$	−7.62863e14	−	1.32132e15i	−0.108351	−	0.187669i	−0.915102	+	0.403222i	$0.867890\pi$
$762$		0			0
$763$	−1.09923e16	−	5.93961e15i	−1.53888	−	0.831520i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.84364e15	+	2.79648e15i	0.658866	+	0.380397i
$768$		0			0
$769$			7.64288e15i			1.02485i	0.858731	+	0.512427i	$0.171253\pi$
$769$			7.64288e15i			1.02485i	−0.858731	+	0.512427i	$0.828747\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.82455e15	+	8.35636e15i	−0.628737	+	1.08900i	0.359068	+	0.933311i	$0.383095\pi$
$773$	−4.82455e15	+	8.35636e15i	−0.628737	+	1.08900i	−0.987805	+	0.155694i	$0.950239\pi$
$774$		0			0
$775$	−3.28918e15	+	1.89901e15i	−0.422599	+	0.243988i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.69447e15	+	3.28770e15i	−0.711209	+	0.410617i
$780$		0			0
$781$	−3.11365e15	+	5.39300e15i	−0.383433	+	0.664125i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	1.78193e16i		−	2.13357i
$786$		0			0
$787$	2.19391e15	+	1.26666e15i	0.259035	+	0.149554i	0.623894	−	0.781509i	$-0.285550\pi$
$787$	2.19391e15	+	1.26666e15i	0.259035	+	0.149554i	−0.364859	+	0.931063i	$0.618883\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8.11146e15	+	2.28821e14i	−0.931383	+	0.0262739i
$792$		0			0
$793$	2.60073e15	+	4.50459e15i	0.294505	+	0.510097i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.58004e15			−0.834931			−0.417466	−	0.908693i	$-0.637082\pi$
$797$	−7.58004e15			−0.834931			−0.417466	+	0.908693i	$0.637082\pi$
$798$		0			0
$799$	1.58216e16			1.71887
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.60686e15	−	9.71137e15i	−0.592631	−	1.02647i
$804$		0			0
$805$	8.76222e15	−	1.62161e16i	0.913559	−	1.69071i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	8.97226e15	+	5.18013e15i	0.910301	+	0.525562i	0.880528	−	0.473994i	$-0.157188\pi$
$809$	8.97226e15	+	5.18013e15i	0.910301	+	0.525562i	0.0297727	+	0.999557i	$0.490522\pi$
$810$		0			0
$811$			7.45303e15i			0.745964i	0.927839	+	0.372982i	$0.121665\pi$
$811$			7.45303e15i			0.745964i	−0.927839	+	0.372982i	$0.878335\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.09308e16	−	1.89328e16i	1.06485	−	1.84437i
$816$		0			0
$817$	−1.24848e16	+	7.20810e15i	−1.19994	+	0.692787i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.27060e16	−	7.33581e15i	1.18883	−	0.686374i	0.230793	−	0.973003i	$-0.425868\pi$
$821$	1.27060e16	−	7.33581e15i	1.18883	−	0.686374i	0.958042	+	0.286629i	$0.0925347\pi$
$822$		0			0
$823$	−3.65748e15	+	6.33494e15i	−0.337663	+	0.584849i	−0.983993	−	0.178209i	$-0.942970\pi$
$823$	−3.65748e15	+	6.33494e15i	−0.337663	+	0.584849i	0.646330	+	0.763058i	$0.276303\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1.13567e16i		−	1.02088i	−0.859915	−	0.510438i	$-0.829483\pi$
$827$		−	1.13567e16i		−	1.02088i	0.859915	−	0.510438i	$-0.170517\pi$
$828$		0			0
$829$	−3.14694e15	−	1.81689e15i	−0.279150	−	0.161168i	0.353888	−	0.935288i	$-0.384859\pi$
$829$	−3.14694e15	−	1.81689e15i	−0.279150	−	0.161168i	−0.633039	+	0.774120i	$0.718193\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−5.34648e15	+	1.05988e16i	−0.461871	+	0.915608i
$834$		0			0
$835$	1.18486e15	+	2.05224e15i	0.101016	+	0.174965i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.42022e15			0.699250			0.349625	−	0.936890i	$-0.386309\pi$
$839$	8.42022e15			0.699250			0.349625	+	0.936890i	$0.386309\pi$
$840$		0			0
$841$	−2.13969e15			−0.175377
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.61913e15	+	1.14647e16i	0.528554	+	0.915482i
$846$		0			0
$847$	4.90224e15	−	3.01775e15i	0.386399	−	0.237862i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.93901e16	−	1.69684e16i	−2.25729	−	1.30325i
$852$		0			0
$853$		−	1.87043e16i		−	1.41815i	−0.705134	−	0.709074i	$-0.749113\pi$
$853$		−	1.87043e16i		−	1.41815i	0.705134	−	0.709074i	$-0.250887\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.22434e16	−	2.12063e16i	0.904709	−	1.56700i	0.0834015	−	0.996516i	$-0.473422\pi$
$857$	1.22434e16	−	2.12063e16i	0.904709	−	1.56700i	0.821307	−	0.570486i	$-0.193245\pi$
$858$		0			0
$859$	8.78153e15	−	5.07002e15i	0.640631	−	0.369868i	−0.144227	−	0.989545i	$-0.546069\pi$
$859$	8.78153e15	−	5.07002e15i	0.640631	−	0.369868i	0.784857	+	0.619676i	$0.212736\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.11452e16	+	6.43467e15i	−0.792552	+	0.457580i	−0.840860	−	0.541253i	$-0.817950\pi$
$863$	−1.11452e16	+	6.43467e15i	−0.792552	+	0.457580i	0.0483084	+	0.998832i	$0.484617\pi$
$864$		0			0
$865$	−5.64633e15	+	9.77974e15i	−0.396440	+	0.686655i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			1.34841e16i			0.923024i
$870$		0			0
$871$	8.55488e15	+	4.93916e15i	0.578248	+	0.333852i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−8.01113e13	−	2.83986e15i	−0.00528019	−	0.187177i
$876$		0			0
$877$	−6.38802e15	−	1.10644e16i	−0.415785	−	0.720160i	0.579726	−	0.814812i	$-0.303160\pi$
$877$	−6.38802e15	−	1.10644e16i	−0.415785	−	0.720160i	−0.995510	+	0.0946516i	$0.969826\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.81108e16			1.14966			0.574832	−	0.818271i	$-0.305067\pi$
$881$	1.81108e16			1.14966			0.574832	+	0.818271i	$0.305067\pi$
$882$		0			0
$883$	9.92847e14			0.0622441			0.0311221	−	0.999516i	$-0.490092\pi$
$883$	9.92847e14			0.0622441			0.0311221	+	0.999516i	$0.490092\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.13873e15	−	8.90055e15i	−0.314251	−	0.544298i	0.665027	−	0.746819i	$-0.268420\pi$
$887$	−5.13873e15	−	8.90055e15i	−0.314251	−	0.544298i	−0.979278	+	0.202521i	$0.935087\pi$
$888$		0			0
$889$	3.96610e14	+	1.40594e16i	0.0239555	+	0.849197i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.39515e16	+	1.38284e16i	1.41140	+	0.814872i
$894$		0			0
$895$		−	1.49051e16i		−	0.867577i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.39787e15	+	9.34939e15i	−0.306580	+	0.531013i
$900$		0			0
$901$	−1.01666e15	+	5.86971e14i	−0.0570415	+	0.0329329i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.08778e16	+	1.20538e16i	−1.14319	+	0.660021i
$906$		0			0
$907$	3.80923e15	−	6.59777e15i	0.206061	−	0.356909i	−0.744409	−	0.667724i	$-0.767269\pi$
$907$	3.80923e15	−	6.59777e15i	0.206061	−	0.356909i	0.950470	+	0.310815i	$0.100602\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			5.01661e15i			0.264886i	0.991191	+	0.132443i	$0.0422821\pi$
$911$			5.01661e15i			0.264886i	−0.991191	+	0.132443i	$0.957718\pi$
$912$		0			0
$913$	2.06934e16	+	1.19473e16i	1.07955	+	0.623278i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.06191e16	−	1.26928e16i	1.05012	−	0.646438i
$918$		0			0
$919$	−9.98181e14	−	1.72890e15i	−0.0502312	−	0.0870031i	0.839817	−	0.542870i	$-0.182662\pi$
$919$	−9.98181e14	−	1.72890e15i	−0.0502312	−	0.0870031i	−0.890048	+	0.455867i	$0.849329\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.14659e15			−0.302012
$924$		0			0
$925$	3.28956e16			1.59719
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.32117e16	+	2.28833e16i	0.626429	+	1.08501i	0.988263	+	0.152765i	$0.0488176\pi$
$929$	1.32117e16	+	2.28833e16i	0.626429	+	1.08501i	−0.361833	+	0.932243i	$0.617849\pi$
$930$		0			0
$931$	−1.73573e16	+	1.13721e16i	−0.813317	+	0.532863i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.19345e16	−	1.84374e16i	−1.46149	−	0.843792i
$936$		0			0
$937$		−	2.42665e15i		−	0.109759i	−0.998493	−	0.0548795i	$-0.982523\pi$
$937$		−	2.42665e15i		−	0.109759i	0.998493	−	0.0548795i	$-0.0174775\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−2.82929e15	+	4.90047e15i	−0.125007	+	0.216518i	−0.921736	−	0.387819i	$-0.873229\pi$
$941$	−2.82929e15	+	4.90047e15i	−0.125007	+	0.216518i	0.796729	+	0.604337i	$0.206562\pi$
$942$		0			0
$943$	−2.35835e16	+	1.36160e16i	−1.02990	+	0.594613i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.00813e16	−	1.15939e16i	0.856773	−	0.494658i	−0.00615711	−	0.999981i	$-0.501960\pi$
$947$	2.00813e16	−	1.15939e16i	0.856773	−	0.494658i	0.862930	+	0.505323i	$0.168627\pi$
$948$		0			0
$949$	5.53419e15	−	9.58549e15i	0.233394	−	0.404250i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			2.18451e16i			0.900208i	0.892976	+	0.450104i	$0.148613\pi$
$953$			2.18451e16i			0.900208i	−0.892976	+	0.450104i	$0.851387\pi$
$954$		0			0
$955$	−5.15901e15	−	2.97856e15i	−0.210159	−	0.121335i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.09674e16	+	2.02972e16i	−0.436618	+	0.808043i
$960$		0			0
$961$	−8.64055e15	−	1.49659e16i	−0.340066	−	0.589011i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.59061e15			0.368932
$966$		0			0
$967$	−2.74406e16			−1.04363			−0.521816	−	0.853058i	$-0.674745\pi$
$967$	−2.74406e16			−1.04363			−0.521816	+	0.853058i	$0.674745\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.29711e16	+	2.24667e16i	0.482250	+	0.835281i	0.999792	−	0.0203761i	$-0.00648638\pi$
$971$	1.29711e16	+	2.24667e16i	0.482250	+	0.835281i	−0.517542	+	0.855658i	$0.673153\pi$
$972$		0			0
$973$	1.93864e16	−	5.46881e14i	0.712649	−	0.0201035i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.30393e16	+	1.33017e16i	0.828035	+	0.478067i	0.853180	−	0.521617i	$-0.174671\pi$
$977$	2.30393e16	+	1.33017e16i	0.828035	+	0.478067i	−0.0251441	+	0.999684i	$0.508004\pi$
$978$		0			0
$979$			3.10619e16i			1.10388i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.98597e16	+	3.43980e16i	−0.690126	+	1.19533i	0.281670	+	0.959511i	$0.409112\pi$
$983$	−1.98597e16	+	3.43980e16i	−0.690126	+	1.19533i	−0.971796	+	0.235822i	$0.924222\pi$
$984$		0			0
$985$	4.93050e16	−	2.84663e16i	1.69431	−	0.978208i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−5.17056e16	+	2.98522e16i	−1.73763	+	1.00322i
$990$		0			0
$991$	1.60100e16	−	2.77301e16i	0.532091	−	0.921608i	−0.467207	−	0.884148i	$-0.654740\pi$
$991$	1.60100e16	−	2.77301e16i	0.532091	−	0.921608i	0.999298	−	0.0374605i	$-0.0119268\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			5.67129e16i			1.84355i
$996$		0			0
$997$	−2.79441e16	−	1.61335e16i	−0.898392	−	0.518687i	−0.0217141	−	0.999764i	$-0.506912\pi$
$997$	−2.79441e16	−	1.61335e16i	−0.898392	−	0.518687i	−0.876678	+	0.481077i	$0.840246\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.12.t.a.17.26	yes	60
3.2	odd	2	inner	252.12.t.a.17.5	✓	60
7.5	odd	6	inner	252.12.t.a.89.5	yes	60
21.5	even	6	inner	252.12.t.a.89.26	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.12.t.a.17.5	✓	60	3.2	odd	2	inner
252.12.t.a.17.26	yes	60	1.1	even	1	trivial
252.12.t.a.89.5	yes	60	7.5	odd	6	inner
252.12.t.a.89.26	yes	60	21.5	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	252.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4768.57 + 8259.41i) q^{5} +(-1253.90 - 44449.5i) q^{7} +O(q^{10})\)	\(q+(4768.57 + 8259.41i) q^{5} +(-1253.90 - 44449.5i) q^{7} +(-557743. - 322013. i) q^{11} -635679. i q^{13} +(3.00177e6 - 5.19922e6i) q^{17} +(9.08845e6 - 5.24722e6i) q^{19} +(3.76396e7 - 2.17313e7i) q^{23} +(-2.10645e7 + 3.64849e7i) q^{25} +1.19751e8i q^{29} +(7.80739e7 + 4.50760e7i) q^{31} +(3.61147e8 - 2.22317e8i) q^{35} +(-3.90414e8 - 6.76217e8i) q^{37} -6.26561e8 q^{41} -1.37370e9 q^{43} +(1.31769e9 + 2.28231e9i) q^{47} +(-1.97418e9 + 1.11470e8i) q^{49} +(-1.69344e8 - 9.77708e7i) q^{53} -6.14217e9i q^{55} +(-4.39920e9 + 7.61963e9i) q^{59} +(-7.08626e9 + 4.09126e9i) q^{61} +(5.25033e9 - 3.03128e9i) q^{65} +(-7.76991e9 + 1.34579e10i) q^{67} -9.66933e9i q^{71} +(1.50791e10 + 8.70595e9i) q^{73} +(-1.36140e10 + 2.51952e10i) q^{77} +(-1.04686e10 - 1.81321e10i) q^{79} -3.71020e10 q^{83} +5.72566e10 q^{85} +(-2.41154e10 - 4.17691e10i) q^{89} +(-2.82556e10 + 7.97077e8i) q^{91} +(8.66779e10 + 5.00435e10i) q^{95} -2.57959e9i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 31278 q^{7}+O(q^{10}) \) 60 * q - 31278 * q^7	\( 60 q - 31278 q^{7} - 34858710 q^{19} - 323828862 q^{25} + 1186783866 q^{31} - 706751058 q^{37} + 1104997284 q^{43} + 7568925402 q^{49} - 5130550116 q^{61} - 22208949354 q^{67} + 54154878858 q^{73} - 61996342614 q^{79} + 107647163952 q^{85} - 2229336678 q^{91}+O(q^{100}) \) 60 * q - 31278 * q^7 - 34858710 * q^19 - 323828862 * q^25 + 1186783866 * q^31 - 706751058 * q^37 + 1104997284 * q^43 + 7568925402 * q^49 - 5130550116 * q^61 - 22208949354 * q^67 + 54154878858 * q^73 - 61996342614 * q^79 + 107647163952 * q^85 - 2229336678 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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