LMFDB - Embedded newform 2548.2.l.m.1537.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(373,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2548.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.l (of order $3$, degree $2$, not 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:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 9x^{10} + 66x^{8} + 127x^{6} + 189x^{4} + 60x^{2} + 16 $ x^12 + 9x^10 + 66x^8 + 127x^6 + 189x^4 + 60*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1537.3
Root			$-0.286958 + 0.497025i$ of defining polynomial
Character	$\chi$	$=$	2548.1537
Dual form			2548.2.l.m.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.573915 q^{3} +(1.45546 + 2.52093i) q^{5} -2.67062 q^{9} +5.47346 q^{11} +(-3.60003 + 0.199516i) q^{13} +(-0.835311 - 1.44680i) q^{15} +(-3.02611 - 5.24138i) q^{17} -0.573915 q^{19} +(-2.67062 + 4.62565i) q^{23} +(-1.73673 + 3.00811i) q^{25} +3.25446 q^{27} +(4.13815 + 7.16749i) q^{29} +(-4.53815 + 7.86030i) q^{31} -3.14130 q^{33} +(1.40142 - 2.42733i) q^{37} +(2.06611 - 0.114505i) q^{39} +(5.22725 + 9.05387i) q^{41} +(-3.63815 + 6.30146i) q^{43} +(-3.88698 - 6.73245i) q^{45} +(-1.28369 - 2.22342i) q^{47} +(1.73673 + 3.00811i) q^{51} +(3.17062 - 5.49168i) q^{53} +(7.96641 + 13.7982i) q^{55} +0.329378 q^{57} +(-2.08799 - 3.61650i) q^{59} -8.61961 q^{61} +(-5.74266 - 8.78503i) q^{65} -14.4853 q^{67} +(1.53271 - 2.65473i) q^{69} +(6.14408 - 10.6419i) q^{71} +(-1.51204 + 2.61892i) q^{73} +(0.996736 - 1.72640i) q^{75} +(1.67062 + 2.89360i) q^{79} +6.14408 q^{81} -13.5240 q^{83} +(8.80877 - 15.2572i) q^{85} +(-2.37495 - 4.11353i) q^{87} +(-7.48701 + 12.9679i) q^{89} +(2.60451 - 4.51115i) q^{93} +(-0.835311 - 1.44680i) q^{95} +(-4.13804 + 7.16729i) q^{97} -14.6175 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{11} + 6 q^{15} + 6 q^{25} + 12 q^{29} + 6 q^{37} + 30 q^{39} - 6 q^{43} - 6 q^{51} + 6 q^{53} + 36 q^{57} + 6 q^{65} - 24 q^{67} - 12 q^{71} - 12 q^{79} - 12 q^{81} + 36 q^{85} - 6 q^{93} + 6 q^{95}+ \cdots - 36 q^{99}+O(q^{100}) $ 12 * q + 12 * q^11 + 6 * q^15 + 6 * q^25 + 12 * q^29 + 6 * q^37 + 30 * q^39 - 6 * q^43 - 6 * q^51 + 6 * q^53 + 36 * q^57 + 6 * q^65 - 24 * q^67 - 12 * q^71 - 12 * q^79 - 12 * q^81 + 36 * q^85 - 6 * q^93 + 6 * q^95 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.573915			−0.331350			−0.165675	−	0.986180i	$-0.552980\pi$
$3$	−0.573915			−0.331350			−0.165675	+	0.986180i	$0.552980\pi$
$4$		0			0
$5$	1.45546	+	2.52093i	0.650902	+	1.12739i	0.982904	+	0.184116i	$0.0589424\pi$
$5$	1.45546	+	2.52093i	0.650902	+	1.12739i	−0.332003	+	0.943278i	$0.607724\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.67062			−0.890207
$10$		0			0
$11$	5.47346			1.65031			0.825155	−	0.564906i	$-0.191087\pi$
$11$	5.47346			1.65031			0.825155	+	0.564906i	$0.191087\pi$
$12$		0			0
$13$	−3.60003	+	0.199516i	−0.998468	+	0.0553358i
$13$	−3.60003	+	0.199516i	−0.998468	+	0.0553358i
$14$		0			0
$15$	−0.835311	−	1.44680i	−0.215676	−	0.373562i
$16$		0			0
$17$	−3.02611	−	5.24138i	−0.733940	−	1.27122i	−0.955187	−	0.296003i	$-0.904346\pi$
$17$	−3.02611	−	5.24138i	−0.733940	−	1.27122i	0.221247	−	0.975218i	$-0.428987\pi$
$18$		0			0
$19$	−0.573915			−0.131665			−0.0658326	−	0.997831i	$-0.520970\pi$
$19$	−0.573915			−0.131665			−0.0658326	+	0.997831i	$0.520970\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.67062	+	4.62565i	−0.556863	+	0.964515i	0.440893	+	0.897560i	$0.354662\pi$
$23$	−2.67062	+	4.62565i	−0.556863	+	0.964515i	−0.997756	+	0.0669554i	$0.978671\pi$
$24$		0			0
$25$	−1.73673	+	3.00811i	−0.347346	+	0.601621i
$26$		0			0
$27$	3.25446			0.626320
$28$		0			0
$29$	4.13815	+	7.16749i	0.768435	+	1.33097i	0.938411	+	0.345521i	$0.112298\pi$
$29$	4.13815	+	7.16749i	0.768435	+	1.33097i	−0.169976	+	0.985448i	$0.554369\pi$
$30$		0			0
$31$	−4.53815	+	7.86030i	−0.815076	+	1.41175i	0.0941981	+	0.995553i	$0.469971\pi$
$31$	−4.53815	+	7.86030i	−0.815076	+	1.41175i	−0.909274	+	0.416199i	$0.863362\pi$
$32$		0			0
$33$	−3.14130			−0.546831
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.40142	−	2.42733i	0.230392	−	0.399051i	−0.727531	−	0.686074i	$-0.759332\pi$
$37$	1.40142	−	2.42733i	0.230392	−	0.399051i	0.957924	+	0.287024i	$0.0926658\pi$
$38$		0			0
$39$	2.06611	−	0.114505i	0.330842	−	0.0183355i
$40$		0			0
$41$	5.22725	+	9.05387i	0.816360	+	1.41398i	0.908347	+	0.418217i	$0.137345\pi$
$41$	5.22725	+	9.05387i	0.816360	+	1.41398i	−0.0919873	+	0.995760i	$0.529322\pi$
$42$		0			0
$43$	−3.63815	+	6.30146i	−0.554813	+	0.960964i	0.443105	+	0.896470i	$0.353877\pi$
$43$	−3.63815	+	6.30146i	−0.554813	+	0.960964i	−0.997918	+	0.0644945i	$0.979457\pi$
$44$		0			0
$45$	−3.88698	−	6.73245i	−0.579437	−	1.00362i
$46$		0			0
$47$	−1.28369	−	2.22342i	−0.187246	−	0.324320i	0.757085	−	0.653316i	$-0.226623\pi$
$47$	−1.28369	−	2.22342i	−0.187246	−	0.324320i	−0.944331	+	0.328997i	$0.893289\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.73673	+	3.00811i	0.243191	+	0.421219i
$52$		0			0
$53$	3.17062	−	5.49168i	0.435518	−	0.754340i	−0.561819	−	0.827260i	$-0.689898\pi$
$53$	3.17062	−	5.49168i	0.435518	−	0.754340i	0.997338	+	0.0729200i	$0.0232318\pi$
$54$		0			0
$55$	7.96641	+	13.7982i	1.07419	+	1.86055i
$56$		0			0
$57$	0.329378			0.0436272
$58$		0			0
$59$	−2.08799	−	3.61650i	−0.271833	−	0.470829i	0.697498	−	0.716587i	$-0.254297\pi$
$59$	−2.08799	−	3.61650i	−0.271833	−	0.470829i	−0.969331	+	0.245758i	$0.920963\pi$
$60$		0			0
$61$	−8.61961			−1.10363			−0.551814	−	0.833967i	$-0.686064\pi$
$61$	−8.61961			−1.10363			−0.551814	+	0.833967i	$0.686064\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.74266	−	8.78503i	−0.712290	−	1.08965i
$66$		0			0
$67$	−14.4853			−1.76966			−0.884832	−	0.465910i	$-0.845727\pi$
$67$	−14.4853			−1.76966			−0.884832	+	0.465910i	$0.845727\pi$
$68$		0			0
$69$	1.53271	−	2.65473i	0.184517	−	0.319592i
$70$		0			0
$71$	6.14408	−	10.6419i	0.729169	−	1.26296i	−0.228066	−	0.973646i	$-0.573240\pi$
$71$	6.14408	−	10.6419i	0.729169	−	1.26296i	0.957235	−	0.289311i	$-0.0934263\pi$
$72$		0			0
$73$	−1.51204	+	2.61892i	−0.176971	+	0.306522i	−0.940841	−	0.338847i	$-0.889963\pi$
$73$	−1.51204	+	2.61892i	−0.176971	+	0.306522i	0.763871	+	0.645369i	$0.223296\pi$
$74$		0			0
$75$	0.996736	−	1.72640i	0.115093	−	0.199347i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.67062	+	2.89360i	0.187960	+	0.325556i	0.944570	−	0.328311i	$-0.106479\pi$
$79$	1.67062	+	2.89360i	0.187960	+	0.325556i	−0.756610	+	0.653866i	$0.773146\pi$
$80$		0			0
$81$	6.14408			0.682676
$82$		0			0
$83$	−13.5240			−1.48445			−0.742226	−	0.670149i	$-0.766230\pi$
$83$	−13.5240			−1.48445			−0.742226	+	0.670149i	$0.766230\pi$
$84$		0			0
$85$	8.80877	−	15.2572i	0.955446	−	1.65488i
$86$		0			0
$87$	−2.37495	−	4.11353i	−0.254621	−	0.441017i
$88$		0			0
$89$	−7.48701	+	12.9679i	−0.793622	+	1.37459i	0.130089	+	0.991502i	$0.458474\pi$
$89$	−7.48701	+	12.9679i	−0.793622	+	1.37459i	−0.923711	+	0.383091i	$0.874860\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.60451	−	4.51115i	0.270075	−	0.467784i
$94$		0			0
$95$	−0.835311	−	1.44680i	−0.0857011	−	0.148439i
$96$		0			0
$97$	−4.13804	+	7.16729i	−0.420154	+	0.727728i	−0.995954	−	0.0898622i	$-0.971357\pi$
$97$	−4.13804	+	7.16729i	−0.420154	+	0.727728i	0.575800	+	0.817591i	$0.304691\pi$
$98$		0			0
$99$	−14.6175			−1.46912
$100$		0			0
$101$	−16.8503			−1.67666			−0.838332	−	0.545160i	$-0.816469\pi$
$101$	−16.8503			−1.67666			−0.838332	+	0.545160i	$0.816469\pi$
$102$		0			0
$103$	−3.00544	−	5.20557i	−0.296135	−	0.512920i	0.679114	−	0.734033i	$-0.262364\pi$
$103$	−3.00544	−	5.20557i	−0.296135	−	0.512920i	−0.975248	+	0.221113i	$0.929031\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.21019	−	12.4884i	0.697036	−	1.20730i	−0.272454	−	0.962169i	$-0.587835\pi$
$107$	7.21019	−	12.4884i	0.697036	−	1.20730i	0.969490	−	0.245132i	$-0.0788314\pi$
$108$		0			0
$109$	−2.23080	+	3.86386i	−0.213672	+	0.370090i	−0.952861	−	0.303408i	$-0.901876\pi$
$109$	−2.23080	+	3.86386i	−0.213672	+	0.370090i	0.739189	+	0.673498i	$0.235209\pi$
$110$		0			0
$111$	−0.804296	+	1.39308i	−0.0763404	+	0.132225i
$112$		0			0
$113$	−3.17062	+	5.49168i	−0.298267	+	0.516614i	−0.975740	−	0.218934i	$-0.929742\pi$
$113$	−3.17062	+	5.49168i	−0.298267	+	0.516614i	0.677473	+	0.735548i	$0.263075\pi$
$114$		0			0
$115$	−15.5479			−1.44985
$116$		0			0
$117$	9.61431	−	0.532832i	0.888843	−	0.0492603i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	18.9588			1.72353
$122$		0			0
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$		0			0
$125$	4.44363			0.397450
$126$		0			0
$127$	2.70309	+	4.68189i	0.239861	+	0.415451i	0.960674	−	0.277678i	$-0.0895649\pi$
$127$	2.70309	+	4.68189i	0.239861	+	0.415451i	−0.720814	+	0.693129i	$0.756232\pi$
$128$		0			0
$129$	2.08799	−	3.61650i	0.183837	−	0.318415i
$130$		0			0
$131$	7.16211	+	12.4051i	0.625757	+	1.08384i	0.988394	+	0.151912i	$0.0485430\pi$
$131$	7.16211	+	12.4051i	0.625757	+	1.08384i	−0.362637	+	0.931930i	$0.618124\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	4.73673	+	8.20426i	0.407673	+	0.706110i
$136$		0			0
$137$	−0.138151	−	0.239285i	−0.0118031	−	0.0204435i	0.860064	−	0.510187i	$-0.170424\pi$
$137$	−0.138151	−	0.239285i	−0.0118031	−	0.0204435i	−0.871867	+	0.489743i	$0.837090\pi$
$138$		0			0
$139$	−3.29240	+	5.70260i	−0.279257	+	0.483688i	−0.971200	−	0.238264i	$-0.923422\pi$
$139$	−3.29240	+	5.70260i	−0.279257	+	0.483688i	0.691943	+	0.721952i	$0.256755\pi$
$140$		0			0
$141$	0.736731	+	1.27606i	0.0620440	+	0.107463i
$142$		0			0
$143$	−19.7046	+	1.09204i	−1.64778	+	0.0913212i
$144$		0			0
$145$	−12.0458	+	20.8640i	−1.00035	+	1.73266i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.406183			0.0332758			0.0166379	−	0.999862i	$-0.494704\pi$
$149$	0.406183			0.0332758			0.0166379	+	0.999862i	$0.494704\pi$
$150$		0			0
$151$	−7.24266	+	12.5447i	−0.589400	+	1.02087i	0.404912	+	0.914356i	$0.367302\pi$
$151$	−7.24266	+	12.5447i	−0.589400	+	1.02087i	−0.994311	+	0.106514i	$0.966031\pi$
$152$		0			0
$153$	8.08160	+	13.9977i	0.653359	+	1.13165i
$154$		0			0
$155$	−26.4204			−2.12214
$156$		0			0
$157$	6.45437	−	11.1793i	0.515115	−	0.892205i	−0.484731	−	0.874663i	$-0.661083\pi$
$157$	6.45437	−	11.1793i	0.515115	−	0.892205i	0.999846	−	0.0175421i	$-0.00558410\pi$
$158$		0			0
$159$	−1.81967	+	3.15176i	−0.144309	+	0.249951i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−17.8938			−1.40155			−0.700777	−	0.713380i	$-0.747163\pi$
$163$	−17.8938			−1.40155			−0.700777	+	0.713380i	$0.747163\pi$
$164$		0			0
$165$	−4.57204	−	7.91901i	−0.355933	−	0.616494i
$166$		0			0
$167$	−0.668433	−	1.15776i	−0.0517249	−	0.0895901i	0.839004	−	0.544126i	$-0.183139\pi$
$167$	−0.668433	−	1.15776i	−0.0517249	−	0.0895901i	−0.890729	+	0.454536i	$0.849805\pi$
$168$		0			0
$169$	12.9204	−	1.43653i	0.993876	−	0.110502i
$170$		0			0
$171$	1.53271			0.117209
$172$		0			0
$173$	23.7027			1.80208			0.901042	−	0.433732i	$-0.142804\pi$
$173$	23.7027			1.80208			0.901042	+	0.433732i	$0.142804\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.19833	+	2.07557i	0.0900719	+	0.156009i
$178$		0			0
$179$	−6.46160			−0.482962			−0.241481	−	0.970405i	$-0.577633\pi$
$179$	−6.46160			−0.482962			−0.241481	+	0.970405i	$0.577633\pi$
$180$		0			0
$181$	14.5851			1.08410			0.542050	−	0.840346i	$-0.317648\pi$
$181$	14.5851			1.08410			0.542050	+	0.840346i	$0.317648\pi$
$182$		0			0
$183$	4.94692			0.365687
$184$		0			0
$185$	8.15885			0.599850
$186$		0			0
$187$	−16.5633	−	28.6885i	−1.21123	−	2.09791i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.132219			−0.00956705			−0.00478352	−	0.999989i	$-0.501523\pi$
$191$	−0.132219			−0.00956705			−0.00478352	+	0.999989i	$0.501523\pi$
$192$		0			0
$193$	−2.40852			−0.173369			−0.0866846	−	0.996236i	$-0.527627\pi$
$193$	−2.40852			−0.173369			−0.0866846	+	0.996236i	$0.527627\pi$
$194$		0			0
$195$	3.29580	+	5.04186i	0.236017	+	0.361055i
$196$		0			0
$197$	−3.53957	−	6.13072i	−0.252184	−	0.436796i	0.711943	−	0.702237i	$-0.247816\pi$
$197$	−3.53957	−	6.13072i	−0.252184	−	0.436796i	−0.964127	+	0.265442i	$0.914482\pi$
$198$		0			0
$199$	−9.67292	−	16.7540i	−0.685695	−	1.18766i	−0.973218	−	0.229885i	$-0.926165\pi$
$199$	−9.67292	−	16.7540i	−0.685695	−	1.18766i	0.287522	−	0.957774i	$-0.407168\pi$
$200$		0			0
$201$	8.31335			0.586378
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−15.2161	+	26.3551i	−1.06274	+	1.84072i
$206$		0			0
$207$	7.13222	−	12.3534i	0.495724	−	0.858618i
$208$		0			0
$209$	−3.14130			−0.217288
$210$		0			0
$211$	5.43982	+	9.42205i	0.374493	+	0.648641i	0.990251	−	0.139295i	$-0.0444835\pi$
$211$	5.43982	+	9.42205i	0.374493	+	0.648641i	−0.615758	+	0.787935i	$0.711150\pi$
$212$		0			0
$213$	−3.52618	+	6.10753i	−0.241610	+	0.418481i
$214$		0			0
$215$	−21.1807			−1.44451
$216$		0			0
$217$		0			0
$218$		0			0
$219$	0.867781	−	1.50304i	0.0586392	−	0.101566i
$220$		0			0
$221$	11.9398	+	18.2653i	0.803159	+	1.22866i
$222$		0			0
$223$	−0.192440	−	0.333316i	−0.0128867	−	0.0223205i	0.859510	−	0.511119i	$-0.170769\pi$
$223$	−0.192440	−	0.333316i	−0.0128867	−	0.0223205i	−0.872397	+	0.488798i	$0.837435\pi$
$224$		0			0
$225$	4.63815	−	8.03351i	0.309210	−	0.535568i
$226$		0			0
$227$	0.822931	+	1.42536i	0.0546199	+	0.0946044i	0.892043	−	0.451951i	$-0.149272\pi$
$227$	0.822931	+	1.42536i	0.0546199	+	0.0946044i	−0.837423	+	0.546556i	$0.815939\pi$
$228$		0			0
$229$	−4.10010	−	7.10158i	−0.270942	−	0.469285i	0.698161	−	0.715941i	$-0.254002\pi$
$229$	−4.10010	−	7.10158i	−0.270942	−	0.469285i	−0.969103	+	0.246655i	$0.920669\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.93389	−	3.34960i	−0.126693	−	0.219439i	0.795700	−	0.605691i	$-0.207103\pi$
$233$	−1.93389	−	3.34960i	−0.126693	−	0.219439i	−0.922394	+	0.386251i	$0.873770\pi$
$234$		0			0
$235$	3.73673	−	6.47221i	0.243757	−	0.422200i
$236$		0			0
$237$	−0.958795	−	1.66068i	−0.0622804	−	0.107873i
$238$		0			0
$239$	9.53840			0.616988			0.308494	−	0.951226i	$-0.400175\pi$
$239$	9.53840			0.616988			0.308494	+	0.951226i	$0.400175\pi$
$240$		0			0
$241$	2.96954	+	5.14339i	0.191285	+	0.331315i	0.945676	−	0.325110i	$-0.105401\pi$
$241$	2.96954	+	5.14339i	0.191285	+	0.331315i	−0.754392	+	0.656425i	$0.772068\pi$
$242$		0			0
$243$	−13.2895			−0.852525
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.06611	−	0.114505i	0.131463	−	0.00728579i
$248$		0			0
$249$	7.76163			0.491873
$250$		0			0
$251$	−9.60887	+	16.6430i	−0.606506	+	1.05050i	0.385305	+	0.922789i	$0.374096\pi$
$251$	−9.60887	+	16.6430i	−0.606506	+	1.05050i	−0.991811	+	0.127711i	$0.959237\pi$
$252$		0			0
$253$	−14.6175	+	25.3183i	−0.918997	+	1.59175i
$254$		0			0
$255$	−5.05549	+	8.75636i	−0.316587	+	0.548345i
$256$		0			0
$257$	1.47410	−	2.55321i	0.0919516	−	0.159265i	−0.816381	−	0.577514i	$-0.804023\pi$
$257$	1.47410	−	2.55321i	0.0919516	−	0.159265i	0.908332	+	0.418249i	$0.137356\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−11.0514	−	19.1416i	−0.684067	−	1.18484i
$262$		0			0
$263$	12.4853			0.769878			0.384939	−	0.922942i	$-0.374222\pi$
$263$	12.4853			0.769878			0.384939	+	0.922942i	$0.374222\pi$
$264$		0			0
$265$	18.4589			1.13392
$266$		0			0
$267$	4.29691	−	7.44246i	0.262967	−	0.455471i
$268$		0			0
$269$	2.71848	+	4.70855i	0.165749	+	0.287085i	0.936921	−	0.349541i	$-0.113663\pi$
$269$	2.71848	+	4.70855i	0.165749	+	0.287085i	−0.771172	+	0.636627i	$0.780329\pi$
$270$		0			0
$271$	2.35972	−	4.08715i	0.143343	−	0.248277i	−0.785411	−	0.618975i	$-0.787548\pi$
$271$	2.35972	−	4.08715i	0.143343	−	0.248277i	0.928753	+	0.370698i	$0.120882\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−9.50593	+	16.4648i	−0.573229	+	0.992862i
$276$		0			0
$277$	9.10568	+	15.7715i	0.547107	+	0.947618i	0.998471	+	0.0552777i	$0.0176044\pi$
$277$	9.10568	+	15.7715i	0.547107	+	0.947618i	−0.451364	+	0.892340i	$0.649062\pi$
$278$		0			0
$279$	12.1197	−	20.9919i	0.725586	−	1.25675i
$280$		0			0
$281$	−11.4853			−0.685157			−0.342579	−	0.939489i	$-0.611300\pi$
$281$	−11.4853			−0.685157			−0.342579	+	0.939489i	$0.611300\pi$
$282$		0			0
$283$	5.36108			0.318683			0.159342	−	0.987224i	$-0.449063\pi$
$283$	5.36108			0.318683			0.159342	+	0.987224i	$0.449063\pi$
$284$		0			0
$285$	0.479397	+	0.830341i	0.0283971	+	0.0491851i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.81471	+	16.9996i	−0.577336	+	0.999975i
$290$		0			0
$291$	2.37488	−	4.11342i	0.139218	−	0.241133i
$292$		0			0
$293$	−6.75996	+	11.7086i	−0.394921	+	0.684024i	−0.993091	−	0.117346i	$-0.962561\pi$
$293$	−6.75996	+	11.7086i	−0.394921	+	0.684024i	0.598170	+	0.801369i	$0.295895\pi$
$294$		0			0
$295$	6.07797	−	10.5274i	0.353873	−	0.612927i
$296$		0			0
$297$	17.8131			1.03362
$298$		0			0
$299$	8.69142	−	17.1853i	0.502638	−	0.993852i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	9.67062			0.555563
$304$		0			0
$305$	−12.5455	−	21.7295i	−0.718353	−	1.24422i
$306$		0			0
$307$	−24.0503			−1.37262			−0.686312	−	0.727307i	$-0.740772\pi$
$307$	−24.0503			−1.37262			−0.686312	+	0.727307i	$0.740772\pi$
$308$		0			0
$309$	1.72487	+	2.98756i	0.0981242	+	0.169956i
$310$		0			0
$311$	−12.2969	+	21.2988i	−0.697292	+	1.20775i	0.272109	+	0.962266i	$0.412279\pi$
$311$	−12.2969	+	21.2988i	−0.697292	+	1.20775i	−0.969402	+	0.245480i	$0.921055\pi$
$312$		0			0
$313$	14.2111	+	24.6143i	0.803257	+	1.39128i	0.917461	+	0.397825i	$0.130235\pi$
$313$	14.2111	+	24.6143i	0.803257	+	1.39128i	−0.114204	+	0.993457i	$0.536432\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.03840	+	8.72677i	0.282985	+	0.490144i	0.972119	−	0.234490i	$-0.0753420\pi$
$317$	5.03840	+	8.72677i	0.282985	+	0.490144i	−0.689134	+	0.724634i	$0.742009\pi$
$318$		0			0
$319$	22.6500	+	39.2310i	1.26816	+	2.19651i
$320$		0			0
$321$	−4.13804	+	7.16729i	−0.230963	+	0.400039i
$322$		0			0
$323$	1.73673	+	3.00811i	0.0966343	+	0.167376i
$324$		0			0
$325$	5.65211	−	11.1758i	0.313523	−	0.619920i
$326$		0			0
$327$	1.28029	−	2.21753i	0.0708001	−	0.122629i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−2.26210			−0.124336			−0.0621681	−	0.998066i	$-0.519801\pi$
$331$	−2.26210			−0.124336			−0.0621681	+	0.998066i	$0.519801\pi$
$332$		0			0
$333$	−3.74266	+	6.48248i	−0.205097	+	0.355238i
$334$		0			0
$335$	−21.0828	−	36.5165i	−1.15188	−	1.99511i
$336$		0			0
$337$	−0.382454			−0.0208336			−0.0104168	−	0.999946i	$-0.503316\pi$
$337$	−0.382454			−0.0208336			−0.0104168	+	0.999946i	$0.503316\pi$
$338$		0			0
$339$	1.81967	−	3.15176i	0.0988308	−	0.171180i
$340$		0			0
$341$	−24.8394	+	43.0231i	−1.34513	+	2.32983i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	8.92320			0.480409
$346$		0			0
$347$	−1.39432	−	2.41503i	−0.0748509	−	0.129646i	0.826171	−	0.563420i	$-0.190515\pi$
$347$	−1.39432	−	2.41503i	−0.0748509	−	0.129646i	−0.901021	+	0.433775i	$0.857181\pi$
$348$		0			0
$349$	−2.50333	−	4.33590i	−0.134000	−	0.232095i	0.791215	−	0.611538i	$-0.209449\pi$
$349$	−2.50333	−	4.33590i	−0.134000	−	0.232095i	−0.925215	+	0.379443i	$0.876116\pi$
$350$		0			0
$351$	−11.7161	+	0.649316i	−0.625361	+	0.0346579i
$352$		0			0
$353$	24.9678			1.32890			0.664450	−	0.747333i	$-0.268666\pi$
$353$	24.9678			1.32890			0.664450	+	0.747333i	$0.268666\pi$
$354$		0			0
$355$	35.7699			1.89847
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.83531	−	10.1071i	−0.307976	−	0.533430i	0.669944	−	0.742412i	$-0.266318\pi$
$359$	−5.83531	−	10.1071i	−0.307976	−	0.533430i	−0.977919	+	0.208982i	$0.932985\pi$
$360$		0			0
$361$	−18.6706			−0.982664
$362$		0			0
$363$	−10.8807			−0.571090
$364$		0			0
$365$	−8.80284			−0.460762
$366$		0			0
$367$	4.13056			0.215613			0.107807	−	0.994172i	$-0.465617\pi$
$367$	4.13056			0.215613			0.107807	+	0.994172i	$0.465617\pi$
$368$		0			0
$369$	−13.9600	−	24.1795i	−0.726730	−	1.25873i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	16.1029			0.833775			0.416888	−	0.908958i	$-0.363121\pi$
$373$	16.1029			0.833775			0.416888	+	0.908958i	$0.363121\pi$
$374$		0			0
$375$	−2.55027			−0.131695
$376$		0			0
$377$	−16.3275	−	24.9775i	−0.840908	−	1.28641i
$378$		0			0
$379$	15.3424	+	26.5738i	0.788087	+	1.36501i	0.927138	+	0.374721i	$0.122262\pi$
$379$	15.3424	+	26.5738i	0.788087	+	1.36501i	−0.139051	+	0.990285i	$0.544405\pi$
$380$		0			0
$381$	−1.55134	−	2.68701i	−0.0794778	−	0.137660i
$382$		0			0
$383$	−9.10676			−0.465334			−0.232667	−	0.972557i	$-0.574745\pi$
$383$	−9.10676			−0.465334			−0.232667	+	0.972557i	$0.574745\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	9.71613	−	16.8288i	0.493898	−	0.855457i
$388$		0			0
$389$	12.9398	−	22.4124i	0.656075	−	1.13636i	−0.325548	−	0.945525i	$-0.605549\pi$
$389$	12.9398	−	22.4124i	0.656075	−	1.13636i	0.981623	−	0.190830i	$-0.0611179\pi$
$390$		0			0
$391$	32.3264			1.63482
$392$		0			0
$393$	−4.11044	−	7.11950i	−0.207344	−	0.359131i
$394$		0			0
$395$	−4.86305	+	8.42305i	−0.244686	+	0.423809i
$396$		0			0
$397$	25.3567			1.27262			0.636309	−	0.771434i	$-0.280460\pi$
$397$	25.3567			1.27262			0.636309	+	0.771434i	$0.280460\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.67655	+	2.90388i	−0.0837231	+	0.145013i	−0.904846	−	0.425738i	$-0.860014\pi$
$401$	−1.67655	+	2.90388i	−0.0837231	+	0.145013i	0.821123	+	0.570751i	$0.193348\pi$
$402$		0			0
$403$	14.7692	−	29.2027i	0.735706	−	1.45469i
$404$		0			0
$405$	8.94247	+	15.4888i	0.444355	+	0.769645i
$406$		0			0
$407$	7.67062	−	13.2859i	0.380219	−	0.658558i
$408$		0			0
$409$	−7.73399	−	13.3957i	−0.382421	−	0.662373i	0.608987	−	0.793181i	$-0.291576\pi$
$409$	−7.73399	−	13.3957i	−0.382421	−	0.662373i	−0.991408	+	0.130808i	$0.958243\pi$
$410$		0			0
$411$	0.0792872	+	0.137330i	0.00391095	+	0.00677396i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−19.6837	−	34.0931i	−0.966233	−	1.67356i
$416$		0			0
$417$	1.88956	−	3.27281i	0.0925319	−	0.160270i
$418$		0			0
$419$	−9.74881	−	16.8854i	−0.476260	−	0.824907i	0.523370	−	0.852106i	$-0.324675\pi$
$419$	−9.74881	−	16.8854i	−0.476260	−	0.824907i	−0.999630	+	0.0271986i	$0.991341\pi$
$420$		0			0
$421$	11.1972			0.545716			0.272858	−	0.962054i	$-0.412031\pi$
$421$	11.1972			0.545716			0.272858	+	0.962054i	$0.412031\pi$
$422$		0			0
$423$	3.42826	+	5.93792i	0.166688	+	0.288712i
$424$		0			0
$425$	21.0222			1.01973
$426$		0			0
$427$		0			0
$428$		0			0
$429$	11.3088	−	0.626740i	0.545993	−	0.0302593i
$430$		0			0
$431$	−26.2232			−1.26313			−0.631564	−	0.775324i	$-0.717587\pi$
$431$	−26.2232			−1.26313			−0.631564	+	0.775324i	$0.717587\pi$
$432$		0			0
$433$	15.2851	−	26.4745i	0.734553	−	1.27228i	−0.220366	−	0.975417i	$-0.570725\pi$
$433$	15.2851	−	26.4745i	0.734553	−	1.27228i	0.954919	−	0.296866i	$-0.0959414\pi$
$434$		0			0
$435$	6.91328	−	11.9742i	0.331467	−	0.574117i
$436$		0			0
$437$	1.53271	−	2.65473i	0.0733195	−	0.126993i
$438$		0			0
$439$	12.1424	−	21.0312i	0.579525	−	1.00377i	−0.416009	−	0.909360i	$-0.636572\pi$
$439$	12.1424	−	21.0312i	0.579525	−	1.00377i	0.995534	−	0.0944056i	$-0.0300951\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.81471	+	4.87521i	0.133731	+	0.231628i	0.925112	−	0.379695i	$-0.123971\pi$
$443$	2.81471	+	4.87521i	0.133731	+	0.231628i	−0.791381	+	0.611323i	$0.790638\pi$
$444$		0			0
$445$	−43.5882			−2.06628
$446$		0			0
$447$	−0.233115			−0.0110259
$448$		0			0
$449$	5.39432	−	9.34323i	0.254574	−	0.440934i	−0.710206	−	0.703994i	$-0.751398\pi$
$449$	5.39432	−	9.34323i	0.254574	−	0.440934i	0.964780	+	0.263059i	$0.0847315\pi$
$450$		0			0
$451$	28.6112	+	49.5560i	1.34725	+	2.33350i
$452$		0			0
$453$	4.15667	−	7.19957i	0.195298	−	0.338265i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.00710	−	15.6008i	0.421334	−	0.729773i	−0.574736	−	0.818339i	$-0.694895\pi$
$457$	9.00710	−	15.6008i	0.421334	−	0.729773i	0.996070	+	0.0885663i	$0.0282285\pi$
$458$		0			0
$459$	−9.84834	−	17.0578i	−0.459681	−	0.796191i
$460$		0			0
$461$	7.35319	−	12.7361i	0.342472	−	0.593179i	−0.642419	−	0.766353i	$-0.722069\pi$
$461$	7.35319	−	12.7361i	0.342472	−	0.593179i	0.984891	+	0.173175i	$0.0554025\pi$
$462$		0			0
$463$	34.3792			1.59774			0.798868	−	0.601507i	$-0.205433\pi$
$463$	34.3792			1.59774			0.798868	+	0.601507i	$0.205433\pi$
$464$		0			0
$465$	15.1631			0.703170
$466$		0			0
$467$	2.93363	+	5.08120i	0.135752	+	0.235130i	0.925885	−	0.377806i	$-0.123322\pi$
$467$	2.93363	+	5.08120i	0.135752	+	0.235130i	−0.790132	+	0.612936i	$0.789988\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−3.70426	+	6.41597i	−0.170683	+	0.295632i
$472$		0			0
$473$	−19.9133	+	34.4908i	−0.915614	+	1.58589i
$474$		0			0
$475$	0.996736	−	1.72640i	0.0457334	−	0.0792126i
$476$		0			0
$477$	−8.46753	+	14.6662i	−0.387702	+	0.671519i
$478$		0			0
$479$	11.8395			0.540962			0.270481	−	0.962725i	$-0.412817\pi$
$479$	11.8395			0.540962			0.270481	+	0.962725i	$0.412817\pi$
$480$		0			0
$481$	−4.56086	+	9.01806i	−0.207957	+	0.411188i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−24.0910			−1.09392
$486$		0			0
$487$	1.57321	+	2.72488i	0.0712890	+	0.123476i	0.899466	−	0.436990i	$-0.143955\pi$
$487$	1.57321	+	2.72488i	0.0712890	+	0.123476i	−0.828177	+	0.560466i	$0.810622\pi$
$488$		0			0
$489$	10.2695			0.464405
$490$		0			0
$491$	17.4410	+	30.2087i	0.787101	+	1.36330i	0.927736	+	0.373237i	$0.121752\pi$
$491$	17.4410	+	30.2087i	0.787101	+	1.36330i	−0.140635	+	0.990062i	$0.544914\pi$
$492$		0			0
$493$	25.0450	−	43.3792i	1.12797	−	1.95370i
$494$		0			0
$495$	−21.2753	−	36.8498i	−0.956252	−	1.65628i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.505932	−	0.876300i	−0.0226486	−	0.0392286i	0.854479	−	0.519486i	$-0.173877\pi$
$499$	−0.505932	−	0.876300i	−0.0226486	−	0.0392286i	−0.877128	+	0.480257i	$0.840543\pi$
$500$		0			0
$501$	0.383624	+	0.664456i	0.0171390	+	0.0296857i
$502$		0			0
$503$	−3.99810	+	6.92491i	−0.178266	+	0.308767i	−0.941287	−	0.337608i	$-0.890382\pi$
$503$	−3.99810	+	6.92491i	−0.178266	+	0.308767i	0.763020	+	0.646374i	$0.223716\pi$
$504$		0			0
$505$	−24.5249	−	42.4784i	−1.09134	−	1.89026i
$506$		0			0
$507$	−7.41520	+	0.824444i	−0.329321	+	0.0366148i
$508$		0			0
$509$	0.915411	−	1.58554i	0.0405749	−	0.0702778i	−0.845025	−	0.534727i	$-0.820414\pi$
$509$	0.915411	−	1.58554i	0.0405749	−	0.0702778i	0.885600	+	0.464449i	$0.153748\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1.86778			−0.0824645
$514$		0			0
$515$	8.74860	−	15.1530i	0.385509	−	0.667721i
$516$		0			0
$517$	−7.02625	−	12.1698i	−0.309014	−	0.535228i
$518$		0			0
$519$	−13.6033			−0.597120
$520$		0			0
$521$	11.5058	−	19.9286i	0.504078	−	0.873088i	−0.495911	−	0.868373i	$-0.665166\pi$
$521$	11.5058	−	19.9286i	0.504078	−	0.873088i	0.999989	−	0.00471473i	$-0.00150075\pi$
$522$		0			0
$523$	21.9437	−	38.0076i	0.959531	−	1.66196i	0.235889	−	0.971780i	$-0.424200\pi$
$523$	21.9437	−	38.0076i	0.959531	−	1.66196i	0.723641	−	0.690176i	$-0.242467\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	54.9318			2.39287
$528$		0			0
$529$	−2.76444	−	4.78815i	−0.120193	−	0.208180i
$530$		0			0
$531$	5.57623	+	9.65832i	0.241988	+	0.419135i
$532$		0			0
$533$	−20.6246	−	31.5513i	−0.893353	−	1.36664i
$534$		0			0
$535$	41.9766			1.81481
$536$		0			0
$537$	3.70841			0.160030
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−4.20543	−	7.28402i	−0.180806	−	0.313164i	0.761350	−	0.648342i	$-0.224537\pi$
$541$	−4.20543	−	7.28402i	−0.180806	−	0.313164i	−0.942155	+	0.335177i	$0.891204\pi$
$542$		0			0
$543$	−8.37059			−0.359216
$544$		0			0
$545$	−12.9874			−0.556317
$546$		0			0
$547$	−22.4853			−0.961403			−0.480702	−	0.876884i	$-0.659618\pi$
$547$	−22.4853			−0.961403			−0.480702	+	0.876884i	$0.659618\pi$
$548$		0			0
$549$	23.0197			0.982458
$550$		0			0
$551$	−2.37495	−	4.11353i	−0.101176	−	0.175242i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.68249			−0.198760
$556$		0			0
$557$	44.6317			1.89111			0.945554	−	0.325465i	$-0.105521\pi$
$557$	44.6317			1.89111			0.945554	+	0.325465i	$0.105521\pi$
$558$		0			0
$559$	11.8402	−	23.4113i	0.500787	−	0.990193i
$560$		0			0
$561$	9.50593	+	16.4648i	0.401341	+	0.695143i
$562$		0			0
$563$	11.2588	+	19.5008i	0.474502	+	0.821862i	0.999574	−	0.0291964i	$-0.00929481\pi$
$563$	11.2588	+	19.5008i	0.474502	+	0.821862i	−0.525072	+	0.851058i	$0.675961\pi$
$564$		0			0
$565$	−18.4589			−0.776570
$566$		0			0
$567$		0			0
$568$		0			0
$569$	14.7616	−	25.5679i	0.618840	−	1.07186i	−0.370858	−	0.928690i	$-0.620936\pi$
$569$	14.7616	−	25.5679i	0.618840	−	1.07186i	0.989698	−	0.143172i	$-0.0457303\pi$
$570$		0			0
$571$	16.6045	−	28.7599i	0.694877	−	1.20356i	−0.275345	−	0.961346i	$-0.588792\pi$
$571$	16.6045	−	28.7599i	0.694877	−	1.20356i	0.970222	−	0.242217i	$-0.0778746\pi$
$572$		0			0
$573$	0.0758826			0.00317004
$574$		0			0
$575$	−9.27630	−	16.0670i	−0.386849	−	0.670041i
$576$		0			0
$577$	−1.91963	+	3.32489i	−0.0799151	+	0.138417i	−0.903213	−	0.429192i	$-0.858798\pi$
$577$	−1.91963	+	3.32489i	−0.0799151	+	0.138417i	0.823298	+	0.567609i	$0.192132\pi$
$578$		0			0
$579$	1.38229			0.0574459
$580$		0			0
$581$		0			0
$582$		0			0
$583$	17.3543	−	30.0585i	0.718741	−	1.24490i
$584$		0			0
$585$	15.3365	+	23.4615i	0.634085	+	0.970014i
$586$		0			0
$587$	−12.0292	−	20.8352i	−0.496500	−	0.859963i	0.503492	−	0.864000i	$-0.332048\pi$
$587$	−12.0292	−	20.8352i	−0.496500	−	0.859963i	−0.999992	+	0.00403710i	$0.998715\pi$
$588$		0			0
$589$	2.60451	−	4.51115i	0.107317	−	0.185879i
$590$		0			0
$591$	2.03141	+	3.51851i	0.0835612	+	0.144732i
$592$		0			0
$593$	13.9566	+	24.1736i	0.573129	+	0.992689i	0.996242	+	0.0866122i	$0.0276041\pi$
$593$	13.9566	+	24.1736i	0.573129	+	0.992689i	−0.423113	+	0.906077i	$0.639063\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.55144	+	9.61537i	0.227205	+	0.393531i
$598$		0			0
$599$	−13.5851	+	23.5300i	−0.555071	+	0.961411i	0.442827	+	0.896607i	$0.353976\pi$
$599$	−13.5851	+	23.5300i	−0.555071	+	0.961411i	−0.997898	+	0.0648043i	$0.979358\pi$
$600$		0			0
$601$	−3.83381	−	6.64036i	−0.156384	−	0.270866i	0.777178	−	0.629281i	$-0.216651\pi$
$601$	−3.83381	−	6.64036i	−0.156384	−	0.270866i	−0.933562	+	0.358415i	$0.883317\pi$
$602$		0			0
$603$	38.6848			1.57537
$604$		0			0
$605$	27.5938	+	47.7938i	1.12185	+	1.94309i
$606$		0			0
$607$	10.9193			0.443203			0.221601	−	0.975137i	$-0.428872\pi$
$607$	10.9193			0.443203			0.221601	+	0.975137i	$0.428872\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.06494	+	7.74826i	0.204906	+	0.313461i
$612$		0			0
$613$	−5.23837			−0.211576			−0.105788	−	0.994389i	$-0.533736\pi$
$613$	−5.23837			−0.211576			−0.105788	+	0.994389i	$0.533736\pi$
$614$		0			0
$615$	8.73276	−	15.1256i	0.352139	−	0.609923i
$616$		0			0
$617$	−22.7209	+	39.3537i	−0.914709	+	1.58432i	−0.107381	+	0.994218i	$0.534246\pi$
$617$	−22.7209	+	39.3537i	−0.914709	+	1.58432i	−0.807327	+	0.590104i	$0.799087\pi$
$618$		0			0
$619$	−14.0979	+	24.4183i	−0.566643	+	0.981455i	0.430252	+	0.902709i	$0.358425\pi$
$619$	−14.0979	+	24.4183i	−0.566643	+	0.981455i	−0.996895	+	0.0787458i	$0.974908\pi$
$620$		0			0
$621$	−8.69142	+	15.0540i	−0.348775	+	0.604095i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.1512	+	26.2426i	0.606047	+	1.04970i
$626$		0			0
$627$	1.80284			0.0719985
$628$		0			0
$629$	−16.9634			−0.676376
$630$		0			0
$631$	−3.48650	+	6.03879i	−0.138795	+	0.240400i	−0.927041	−	0.374960i	$-0.877656\pi$
$631$	−3.48650	+	6.03879i	−0.138795	+	0.240400i	0.788246	+	0.615361i	$0.210990\pi$
$632$		0			0
$633$	−3.12200	−	5.40746i	−0.124088	−	0.214927i
$634$		0			0
$635$	−7.86849	+	13.6286i	−0.312251	+	0.540835i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−16.4085	+	28.4204i	−0.649111	+	1.12429i
$640$		0			0
$641$	0.498830	+	0.864000i	0.0197026	+	0.0341259i	0.875709	−	0.482840i	$-0.160395\pi$
$641$	0.498830	+	0.864000i	0.0197026	+	0.0341259i	−0.856006	+	0.516966i	$0.827061\pi$
$642$		0			0
$643$	1.81626	−	3.14586i	0.0716264	−	0.124061i	−0.827988	−	0.560746i	$-0.810514\pi$
$643$	1.81626	−	3.14586i	0.0716264	−	0.124061i	0.899614	+	0.436685i	$0.143848\pi$
$644$		0			0
$645$	12.1559			0.478640
$646$		0			0
$647$	−33.7005			−1.32490			−0.662452	−	0.749104i	$-0.730484\pi$
$647$	−33.7005			−1.32490			−0.662452	+	0.749104i	$0.730484\pi$
$648$		0			0
$649$	−11.4285	−	19.7948i	−0.448609	−	0.777014i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.63815	+	14.9617i	−0.338037	+	0.585497i	−0.984063	−	0.177818i	$-0.943096\pi$
$653$	−8.63815	+	14.9617i	−0.338037	+	0.585497i	0.646026	+	0.763315i	$0.276430\pi$
$654$		0			0
$655$	−20.8483	+	36.1104i	−0.814612	+	1.41095i
$656$		0			0
$657$	4.03808	−	6.99416i	0.157540	−	0.272868i
$658$		0			0
$659$	−5.34124	+	9.25130i	−0.208065	+	0.360380i	−0.951105	−	0.308868i	$-0.900050\pi$
$659$	−5.34124	+	9.25130i	−0.208065	+	0.360380i	0.743040	+	0.669247i	$0.233383\pi$
$660$		0			0
$661$	10.1455			0.394615			0.197307	−	0.980342i	$-0.436780\pi$
$661$	10.1455			0.394615			0.197307	+	0.980342i	$0.436780\pi$
$662$		0			0
$663$	−6.85244	−	10.4828i	−0.266127	−	0.407117i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−44.2057			−1.71165
$668$		0			0
$669$	0.110444	+	0.191295i	0.00427002	+	0.00739589i
$670$		0			0
$671$	−47.1791			−1.82133
$672$		0			0
$673$	7.69716	+	13.3319i	0.296704	+	0.513906i	0.975380	−	0.220532i	$-0.0707793\pi$
$673$	7.69716	+	13.3319i	0.296704	+	0.513906i	−0.678676	+	0.734438i	$0.737446\pi$
$674$		0			0
$675$	−5.65211	+	9.78975i	−0.217550	+	0.376808i
$676$		0			0
$677$	7.48701	+	12.9679i	0.287749	+	0.498396i	0.973272	−	0.229655i	$-0.0737597\pi$
$677$	7.48701	+	12.9679i	0.287749	+	0.498396i	−0.685523	+	0.728051i	$0.740426\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.472293	−	0.818035i	−0.0180983	−	0.0313472i
$682$		0			0
$683$	16.4280	+	28.4541i	0.628598	+	1.08876i	0.987833	+	0.155517i	$0.0497044\pi$
$683$	16.4280	+	28.4541i	0.628598	+	1.08876i	−0.359235	+	0.933247i	$0.616962\pi$
$684$		0			0
$685$	0.402148	−	0.696541i	0.0153653	−	0.0266135i
$686$		0			0
$687$	2.35311	+	4.07570i	0.0897767	+	0.155498i
$688$		0			0
$689$	−10.3186	+	20.4028i	−0.393109	+	0.777284i
$690$		0			0
$691$	3.08473	−	5.34290i	0.117349	−	0.203254i	−0.801368	−	0.598172i	$-0.795894\pi$
$691$	3.08473	−	5.34290i	0.117349	−	0.203254i	0.918716	+	0.394919i	$0.129227\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−19.1678			−0.727077
$696$		0			0
$697$	31.6365	−	54.7960i	1.19832	−	2.07555i
$698$		0			0
$699$	1.10989	+	1.92238i	0.0419799	+	0.0727112i
$700$		0			0
$701$	9.52326			0.359689			0.179844	−	0.983695i	$-0.442441\pi$
$701$	9.52326			0.359689			0.179844	+	0.983695i	$0.442441\pi$
$702$		0			0
$703$	−0.804296	+	1.39308i	−0.0303346	+	0.0525411i
$704$		0			0
$705$	−2.14457	+	3.71450i	−0.0807690	+	0.139896i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	32.8242			1.23274			0.616370	−	0.787457i	$-0.288603\pi$
$709$	32.8242			1.23274			0.616370	+	0.787457i	$0.288603\pi$
$710$		0			0
$711$	−4.46160	−	7.72771i	−0.167323	−	0.289812i
$712$		0			0
$713$	−24.2394	−	41.9838i	−0.907771	−	1.57231i
$714$		0			0
$715$	−31.4323	−	48.0846i	−1.17550	−	1.79826i
$716$		0			0
$717$	−5.47423			−0.204439
$718$		0			0
$719$	3.25446			0.121371			0.0606853	−	0.998157i	$-0.480671\pi$
$719$	3.25446			0.121371			0.0606853	+	0.998157i	$0.480671\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.70426	−	2.95187i	−0.0633822	−	0.109781i
$724$		0			0
$725$	−28.7474			−1.06765
$726$		0			0
$727$	21.3325			0.791179			0.395589	−	0.918427i	$-0.370540\pi$
$727$	21.3325			0.791179			0.395589	+	0.918427i	$0.370540\pi$
$728$		0			0
$729$	−10.8052			−0.400192
$730$		0			0
$731$	44.0378			1.62880
$732$		0			0
$733$	7.68489	+	13.3106i	0.283848	+	0.491639i	0.972329	−	0.233615i	$-0.0750555\pi$
$733$	7.68489	+	13.3106i	0.283848	+	0.491639i	−0.688481	+	0.725254i	$0.741722\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−79.2849			−2.92050
$738$		0			0
$739$	−3.74024			−0.137587			−0.0687935	−	0.997631i	$-0.521915\pi$
$739$	−3.74024			−0.137587			−0.0687935	+	0.997631i	$0.521915\pi$
$740$		0			0
$741$	−1.18577	+	0.0657163i	−0.0435604	+	0.00241415i
$742$		0			0
$743$	10.1647	+	17.6058i	0.372906	+	0.645893i	0.990011	−	0.140988i	$-0.0450280\pi$
$743$	10.1647	+	17.6058i	0.372906	+	0.645893i	−0.617105	+	0.786881i	$0.711695\pi$
$744$		0			0
$745$	0.591183	+	1.02396i	0.0216593	+	0.0375150i
$746$		0			0
$747$	36.1175			1.32147
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−17.9806	+	31.1433i	−0.656120	+	1.13643i	0.325492	+	0.945545i	$0.394470\pi$
$751$	−17.9806	+	31.1433i	−0.656120	+	1.13643i	−0.981612	+	0.190888i	$0.938863\pi$
$752$		0			0
$753$	5.51467	−	9.55169i	0.200966	−	0.348083i
$754$		0			0
$755$	−42.1656			−1.53456
$756$		0			0
$757$	−6.73790	−	11.6704i	−0.244893	−	0.424167i	0.717208	−	0.696859i	$-0.245420\pi$
$757$	−6.73790	−	11.6704i	−0.244893	−	0.424167i	−0.962102	+	0.272691i	$0.912086\pi$
$758$		0			0
$759$	8.38923	−	14.5306i	0.304510	−	0.527426i
$760$		0			0
$761$	24.0422			0.871528			0.435764	−	0.900061i	$-0.356478\pi$
$761$	24.0422			0.871528			0.435764	+	0.900061i	$0.356478\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−23.5249	+	40.7463i	−0.850545	+	1.47319i
$766$		0			0
$767$	8.23837	+	12.6029i	0.297470	+	0.455065i
$768$		0			0
$769$	6.95104	+	12.0396i	0.250661	+	0.434157i	0.963708	−	0.266959i	$-0.0860188\pi$
$769$	6.95104	+	12.0396i	0.250661	+	0.434157i	−0.713047	+	0.701116i	$0.752685\pi$
$770$		0			0
$771$	−0.846006	+	1.46532i	−0.0304682	+	0.0527724i
$772$		0			0
$773$	18.5188	+	32.0756i	0.666076	+	1.15368i	0.978992	+	0.203897i	$0.0653609\pi$
$773$	18.5188	+	32.0756i	0.666076	+	1.15368i	−0.312916	+	0.949781i	$0.601306\pi$
$774$		0			0
$775$	−15.7631	−	27.3025i	−0.566227	−	0.980734i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.00000	−	5.19615i	−0.107486	−	0.186171i
$780$		0			0
$781$	33.6294	−	58.2478i	1.20335	−	2.08427i
$782$		0			0
$783$	13.4674	+	23.3263i	0.481287	+	0.833613i
$784$		0			0
$785$	37.5763			1.34116
$786$		0			0
$787$	−22.5590	−	39.0733i	−0.804140	−	1.39281i	−0.916870	−	0.399186i	$-0.869293\pi$
$787$	−22.5590	−	39.0733i	−0.804140	−	1.39281i	0.112730	−	0.993626i	$-0.464040\pi$
$788$		0			0
$789$	−7.16552			−0.255099
$790$		0			0
$791$		0			0
$792$		0			0
$793$	31.0308	−	1.71975i	1.10194	−	0.0610701i
$794$		0			0
$795$	−10.5938			−0.375724
$796$		0			0
$797$	−2.52197	+	4.36817i	−0.0893326	+	0.154729i	−0.907229	−	0.420637i	$-0.861807\pi$
$797$	−2.52197	+	4.36817i	−0.0893326	+	0.154729i	0.817897	+	0.575365i	$0.195140\pi$
$798$		0			0
$799$	−7.76920	+	13.4567i	−0.274855	+	0.476062i
$800$		0			0
$801$	19.9950	−	34.6323i	0.706488	−	1.22367i
$802$		0			0
$803$	−8.27608	+	14.3346i	−0.292056	+	0.505857i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.56018	−	2.70231i	−0.0549208	−	0.0951257i
$808$		0			0
$809$	−31.5526			−1.10933			−0.554665	−	0.832074i	$-0.687154\pi$
$809$	−31.5526			−1.10933			−0.554665	+	0.832074i	$0.687154\pi$
$810$		0			0
$811$	10.7526			0.377576			0.188788	−	0.982018i	$-0.439544\pi$
$811$	10.7526			0.377576			0.188788	+	0.982018i	$0.439544\pi$
$812$		0			0
$813$	−1.35428	+	2.34568i	−0.0474966	+	0.0822665i
$814$		0			0
$815$	−26.0438	−	45.1092i	−0.912274	−	1.58011i
$816$		0			0
$817$	2.08799	−	3.61650i	0.0730495	−	0.126525i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.57204	−	2.72286i	0.0548646	−	0.0950283i	−0.837289	−	0.546761i	$-0.815861\pi$
$821$	1.57204	−	2.72286i	0.0548646	−	0.0950283i	0.892153	+	0.451733i	$0.149194\pi$
$822$		0			0
$823$	22.9251	+	39.7075i	0.799120	+	1.38412i	0.920190	+	0.391473i	$0.128034\pi$
$823$	22.9251	+	39.7075i	0.799120	+	1.38412i	−0.121069	+	0.992644i	$0.538632\pi$
$824$		0			0
$825$	5.45560	−	9.44937i	0.189940	−	0.328985i
$826$		0			0
$827$	31.5882			1.09843			0.549215	−	0.835681i	$-0.314927\pi$
$827$	31.5882			1.09843			0.549215	+	0.835681i	$0.314927\pi$
$828$		0			0
$829$	44.6680			1.55138			0.775692	−	0.631111i	$-0.217401\pi$
$829$	44.6680			1.55138			0.775692	+	0.631111i	$0.217401\pi$
$830$		0			0
$831$	−5.22589	−	9.05150i	−0.181284	−	0.313993i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.94575	−	3.37015i	0.0673356	−	0.116629i
$836$		0			0
$837$	−14.7692	+	25.5810i	−0.510498	+	0.884209i
$838$		0			0
$839$	17.5262	−	30.3562i	0.605071	−	1.04801i	−0.386969	−	0.922093i	$-0.626478\pi$
$839$	17.5262	−	30.3562i	0.605071	−	1.04801i	0.992040	−	0.125921i	$-0.0401886\pi$
$840$		0			0
$841$	−19.7486	+	34.2056i	−0.680986	+	1.17950i
$842$		0			0
$843$	6.59160			0.227027
$844$		0			0
$845$	22.4265	+	30.4806i	0.771495	+	1.04856i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.07680			−0.105596
$850$		0			0
$851$	7.48533	+	12.9650i	0.256594	+	0.444433i
$852$		0			0
$853$	40.4398			1.38463			0.692317	−	0.721594i	$-0.256590\pi$
$853$	40.4398			1.38463			0.692317	+	0.721594i	$0.256590\pi$
$854$		0			0
$855$	2.23080	+	3.86386i	0.0762917	+	0.132141i
$856$		0			0
$857$	−8.28927	+	14.3574i	−0.283156	+	0.490441i	−0.972160	−	0.234317i	$-0.924715\pi$
$857$	−8.28927	+	14.3574i	−0.283156	+	0.490441i	0.689004	+	0.724757i	$0.258048\pi$
$858$		0			0
$859$	5.82592	+	10.0908i	0.198778	+	0.344293i	0.948132	−	0.317876i	$-0.102969\pi$
$859$	5.82592	+	10.0908i	0.198778	+	0.344293i	−0.749355	+	0.662169i	$0.769636\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.18529	+	8.98119i	0.176509	+	0.305723i	0.940683	−	0.339288i	$-0.110186\pi$
$863$	5.18529	+	8.98119i	0.176509	+	0.305723i	−0.764173	+	0.645011i	$0.776853\pi$
$864$		0			0
$865$	34.4984	+	59.7529i	1.17298	+	2.03166i
$866$		0			0
$867$	5.63281	−	9.75631i	0.191300	−	0.331342i
$868$		0			0
$869$	9.14408	+	15.8380i	0.310192	+	0.537268i
$870$		0			0
$871$	52.1476	−	2.89005i	1.76695	−	0.0979257i
$872$		0			0
$873$	11.0511	−	19.1411i	0.374024	−	0.647829i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−17.2644			−0.582979			−0.291489	−	0.956574i	$-0.594151\pi$
$877$	−17.2644			−0.582979			−0.291489	+	0.956574i	$0.594151\pi$
$878$		0			0
$879$	3.87965	−	6.71974i	0.130857	−	0.226651i
$880$		0			0
$881$	20.0309	+	34.6945i	0.674857	+	1.16889i	0.976511	+	0.215470i	$0.0691282\pi$
$881$	20.0309	+	34.6945i	0.674857	+	1.16889i	−0.301653	+	0.953418i	$0.597538\pi$
$882$		0			0
$883$	−46.3554			−1.55998			−0.779992	−	0.625789i	$-0.784777\pi$
$883$	−46.3554			−1.55998			−0.779992	+	0.625789i	$0.784777\pi$
$884$		0			0
$885$	−3.48824	+	6.04181i	−0.117256	+	0.203093i
$886$		0			0
$887$	13.9393	−	24.1437i	0.468037	−	0.810665i	−0.531295	−	0.847187i	$-0.678295\pi$
$887$	13.9393	−	24.1437i	0.468037	−	0.810665i	0.999333	+	0.0365221i	$0.0116279\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	33.6294			1.12663
$892$		0			0
$893$	0.736731	+	1.27606i	0.0246538	+	0.0427016i
$894$		0			0
$895$	−9.40460	−	16.2892i	−0.314361	−	0.544489i
$896$		0			0
$897$	−4.98814	+	9.86290i	−0.166549	+	0.329313i
$898$		0			0
$899$	−75.1182			−2.50533
$900$		0			0
$901$	−38.3786			−1.27858
$902$		0			0
$903$		0			0
$904$		0			0
$905$	21.2280	+	36.7680i	0.705642	+	1.22221i
$906$		0			0
$907$	−41.7593			−1.38659			−0.693297	−	0.720652i	$-0.743843\pi$
$907$	−41.7593			−1.38659			−0.693297	+	0.720652i	$0.743843\pi$
$908$		0			0
$909$	45.0007			1.49258
$910$		0			0
$911$	−42.8384			−1.41930			−0.709650	−	0.704554i	$-0.751147\pi$
$911$	−42.8384			−1.41930			−0.709650	+	0.704554i	$0.751147\pi$
$912$		0			0
$913$	−74.0231			−2.44981
$914$		0			0
$915$	7.20005	+	12.4709i	0.238026	+	0.412274i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	46.4465			1.53213			0.766064	−	0.642765i	$-0.222213\pi$
$919$	46.4465			1.53213			0.766064	+	0.642765i	$0.222213\pi$
$920$		0			0
$921$	13.8028			0.454819
$922$		0			0
$923$	−19.9956	+	39.5368i	−0.658165	+	1.30137i
$924$		0			0
$925$	4.86778	+	8.43124i	0.160052	+	0.277218i
$926$		0			0
$927$	8.02639	+	13.9021i	0.263621	+	0.456605i
$928$		0			0
$929$	24.9746			0.819389			0.409695	−	0.912223i	$-0.365635\pi$
$929$	24.9746			0.819389			0.409695	+	0.912223i	$0.365635\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	7.05737	−	12.2237i	0.231048	−	0.400187i
$934$		0			0
$935$	48.2145	−	83.5099i	1.57678	−	2.73107i
$936$		0			0
$937$	14.1697			0.462905			0.231452	−	0.972846i	$-0.425652\pi$
$937$	14.1697			0.462905			0.231452	+	0.972846i	$0.425652\pi$
$938$		0			0
$939$	−8.15595	−	14.1265i	−0.266159	−	0.461001i
$940$		0			0
$941$	13.3841	−	23.1819i	0.436308	−	0.755708i	−0.561093	−	0.827753i	$-0.689619\pi$
$941$	13.3841	−	23.1819i	0.436308	−	0.755708i	0.997401	+	0.0720448i	$0.0229525\pi$
$942$		0			0
$943$	−55.8401			−1.81840
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.18413	−	2.05096i	0.0384789	−	0.0666474i	−0.846145	−	0.532953i	$-0.821082\pi$
$947$	1.18413	−	2.05096i	0.0384789	−	0.0666474i	0.884623	+	0.466306i	$0.154415\pi$
$948$		0			0
$949$	4.92086	−	9.72988i	0.159738	−	0.315845i
$950$		0			0
$951$	−2.89161	−	5.00842i	−0.0937670	−	0.162409i
$952$		0			0
$953$	22.8483	−	39.5745i	0.740130	−	1.28194i	−0.212305	−	0.977203i	$-0.568097\pi$
$953$	22.8483	−	39.5745i	0.740130	−	1.28194i	0.952436	−	0.304740i	$-0.0985696\pi$
$954$		0			0
$955$	−0.192440	−	0.333316i	−0.00622721	−	0.0107858i
$956$		0			0
$957$	−12.9992	−	22.5152i	−0.420204	−	0.727815i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−25.6896	−	44.4957i	−0.828696	−	1.43534i
$962$		0			0
$963$	−19.2557	+	33.3518i	−0.620506	+	1.07475i
$964$		0			0
$965$	−3.50551	−	6.07172i	−0.112846	−	0.195456i
$966$		0			0
$967$	−44.2968			−1.42449			−0.712244	−	0.701932i	$-0.752321\pi$
$967$	−44.2968			−1.42449			−0.712244	+	0.701932i	$0.752321\pi$
$968$		0			0
$969$	−0.996736	−	1.72640i	−0.0320198	−	0.0554599i
$970$		0			0
$971$	−18.1235			−0.581610			−0.290805	−	0.956782i	$-0.593923\pi$
$971$	−18.1235			−0.581610			−0.290805	+	0.956782i	$0.593923\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−3.24383	+	6.41394i	−0.103886	+	0.205411i
$976$		0			0
$977$	−41.4180			−1.32508			−0.662540	−	0.749026i	$-0.730522\pi$
$977$	−41.4180			−1.32508			−0.662540	+	0.749026i	$0.730522\pi$
$978$		0			0
$979$	−40.9799	+	70.9792i	−1.30972	+	2.26851i
$980$		0			0
$981$	5.95762	−	10.3189i	0.190212	−	0.329457i
$982$		0			0
$983$	3.87039	−	6.70371i	0.123446	−	0.213815i	−0.797678	−	0.603083i	$-0.793939\pi$
$983$	3.87039	−	6.70371i	0.123446	−	0.213815i	0.921124	+	0.389268i	$0.127272\pi$
$984$		0			0
$985$	10.3034	−	17.8460i	0.328294	−	0.568622i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−19.4323	−	33.6576i	−0.617910	−	1.07025i
$990$		0			0
$991$	17.3673			0.551691			0.275845	−	0.961202i	$-0.411042\pi$
$991$	17.3673			0.551691			0.275845	+	0.961202i	$0.411042\pi$
$992$		0			0
$993$	1.29825			0.0411988
$994$		0			0
$995$	28.1571	−	48.7696i	0.892641	−	1.54610i
$996$		0			0
$997$	2.10459	+	3.64525i	0.0666529	+	0.115446i	0.897426	−	0.441165i	$-0.145435\pi$
$997$	2.10459	+	3.64525i	0.0666529	+	0.115446i	−0.830773	+	0.556611i	$0.812101\pi$
$998$		0			0
$999$	4.56086	−	7.89964i	0.144299	−	0.249934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.l.m.1537.3		12
7.2	even	3		2548.2.i.m.1745.4		12
7.3	odd	6		2548.2.k.g.393.3	✓	12
7.4	even	3		2548.2.k.g.393.4	yes	12
7.5	odd	6		2548.2.i.m.1745.3		12
7.6	odd	2	inner	2548.2.l.m.1537.4		12
13.9	even	3		2548.2.i.m.165.4		12
91.9	even	3	inner	2548.2.l.m.373.3		12
91.48	odd	6		2548.2.i.m.165.3		12
91.61	odd	6	inner	2548.2.l.m.373.4		12
91.74	even	3		2548.2.k.g.1569.4	yes	12
91.87	odd	6		2548.2.k.g.1569.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2548.2.i.m.165.3		12	91.48	odd	6
2548.2.i.m.165.4		12	13.9	even	3
2548.2.i.m.1745.3		12	7.5	odd	6
2548.2.i.m.1745.4		12	7.2	even	3
2548.2.k.g.393.3	✓	12	7.3	odd	6
2548.2.k.g.393.4	yes	12	7.4	even	3
2548.2.k.g.1569.3	yes	12	91.87	odd	6
2548.2.k.g.1569.4	yes	12	91.74	even	3
2548.2.l.m.373.3		12	91.9	even	3	inner
2548.2.l.m.373.4		12	91.61	odd	6	inner
2548.2.l.m.1537.3		12	1.1	even	1	trivial
2548.2.l.m.1537.4		12	7.6	odd	2	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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.573915 q^{3} +(1.45546 + 2.52093i) q^{5} -2.67062 q^{9} +5.47346 q^{11} +(-3.60003 + 0.199516i) q^{13} +(-0.835311 - 1.44680i) q^{15} +(-3.02611 - 5.24138i) q^{17} -0.573915 q^{19} +(-2.67062 + 4.62565i) q^{23} +(-1.73673 + 3.00811i) q^{25} +3.25446 q^{27} +(4.13815 + 7.16749i) q^{29} +(-4.53815 + 7.86030i) q^{31} -3.14130 q^{33} +(1.40142 - 2.42733i) q^{37} +(2.06611 - 0.114505i) q^{39} +(5.22725 + 9.05387i) q^{41} +(-3.63815 + 6.30146i) q^{43} +(-3.88698 - 6.73245i) q^{45} +(-1.28369 - 2.22342i) q^{47} +(1.73673 + 3.00811i) q^{51} +(3.17062 - 5.49168i) q^{53} +(7.96641 + 13.7982i) q^{55} +0.329378 q^{57} +(-2.08799 - 3.61650i) q^{59} -8.61961 q^{61} +(-5.74266 - 8.78503i) q^{65} -14.4853 q^{67} +(1.53271 - 2.65473i) q^{69} +(6.14408 - 10.6419i) q^{71} +(-1.51204 + 2.61892i) q^{73} +(0.996736 - 1.72640i) q^{75} +(1.67062 + 2.89360i) q^{79} +6.14408 q^{81} -13.5240 q^{83} +(8.80877 - 15.2572i) q^{85} +(-2.37495 - 4.11353i) q^{87} +(-7.48701 + 12.9679i) q^{89} +(2.60451 - 4.51115i) q^{93} +(-0.835311 - 1.44680i) q^{95} +(-4.13804 + 7.16729i) q^{97} -14.6175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{11} + 6 q^{15} + 6 q^{25} + 12 q^{29} + 6 q^{37} + 30 q^{39} - 6 q^{43} - 6 q^{51} + 6 q^{53} + 36 q^{57} + 6 q^{65} - 24 q^{67} - 12 q^{71} - 12 q^{79} - 12 q^{81} + 36 q^{85} - 6 q^{93} + 6 q^{95}+ \cdots - 36 q^{99}+O(q^{100}) \) 12 * q + 12 * q^11 + 6 * q^15 + 6 * q^25 + 12 * q^29 + 6 * q^37 + 30 * q^39 - 6 * q^43 - 6 * q^51 + 6 * q^53 + 36 * q^57 + 6 * q^65 - 24 * q^67 - 12 * q^71 - 12 * q^79 - 12 * q^81 + 36 * q^85 - 6 * q^93 + 6 * q^95 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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