LMFDB - Embedded newform 1148.2.ba.a.113.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.8
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.904348i q^{3} +(0.129544 + 0.398696i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.18215 q^{9} +O(q^{10})$	\(q-0.904348i q^{3} +(0.129544 + 0.398696i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.18215 q^{9} +(1.99111 + 0.646951i) q^{11} +(-1.84603 + 2.54084i) q^{13} +(0.360560 - 0.117153i) q^{15} +(0.218991 + 0.0711543i) q^{17} +(1.62945 + 2.24275i) q^{19} +(-0.731633 + 0.531562i) q^{21} +(6.51499 + 4.73342i) q^{23} +(3.90291 - 2.83563i) q^{25} -4.68647i q^{27} +(-6.06473 + 1.97055i) q^{29} +(1.52993 - 4.70863i) q^{31} +(0.585069 - 1.80066i) q^{33} +(0.246408 - 0.339151i) q^{35} +(-1.51532 - 4.66367i) q^{37} +(2.29780 + 1.66945i) q^{39} +(2.22688 - 6.00342i) q^{41} +(8.75738 + 6.36261i) q^{43} +(0.282685 + 0.870016i) q^{45} +(0.514310 - 0.707887i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(0.0643483 - 0.198044i) q^{51} +(-1.28343 + 0.417011i) q^{53} +0.877657i q^{55} +(2.02823 - 1.47359i) q^{57} +(1.10026 + 0.799383i) q^{59} +(-2.01068 + 1.46085i) q^{61} +(-1.28264 - 1.76540i) q^{63} +(-1.25216 - 0.406853i) q^{65} +(3.04069 - 0.987979i) q^{67} +(4.28066 - 5.89182i) q^{69} +(9.37008 + 3.04452i) q^{71} +12.9116 q^{73} +(-2.56440 - 3.52959i) q^{75} +(-0.646951 - 1.99111i) q^{77} -9.73942i q^{79} +2.30826 q^{81} +4.97099 q^{83} +0.0965282i q^{85} +(1.78206 + 5.48463i) q^{87} +(-3.59722 - 4.95116i) q^{89} +3.14065 q^{91} +(-4.25824 - 1.38359i) q^{93} +(-0.683089 + 0.940192i) q^{95} +(-13.7927 + 4.48154i) q^{97} +(4.34491 + 1.41175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

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
$3$		−	0.904348i		−	0.522126i	−0.965322	−	0.261063i	$-0.915927\pi$
$3$		−	0.904348i		−	0.522126i	0.965322	−	0.261063i	$-0.0840730\pi$
$4$		0			0
$5$	0.129544	+	0.398696i	0.0579339	+	0.178302i	0.975836	−	0.218505i	$-0.0701181\pi$
$5$	0.129544	+	0.398696i	0.0579339	+	0.178302i	−0.917902	+	0.396807i	$0.870118\pi$
$6$		0			0
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$8$		0			0
$9$	2.18215			0.727385
$10$		0			0
$11$	1.99111	+	0.646951i	0.600343	+	0.195063i	0.593393	−	0.804913i	$-0.297788\pi$
$11$	1.99111	+	0.646951i	0.600343	+	0.195063i	0.00694948	+	0.999976i	$0.497788\pi$
$12$		0			0
$13$	−1.84603	+	2.54084i	−0.511996	+	0.704702i	−0.984254	−	0.176758i	$-0.943439\pi$
$13$	−1.84603	+	2.54084i	−0.511996	+	0.704702i	0.472258	+	0.881460i	$0.343439\pi$
$14$		0			0
$15$	0.360560	−	0.117153i	0.0930961	−	0.0302488i
$16$		0			0
$17$	0.218991	+	0.0711543i	0.0531130	+	0.0172575i	0.335453	−	0.942057i	$-0.391111\pi$
$17$	0.218991	+	0.0711543i	0.0531130	+	0.0172575i	−0.282340	+	0.959314i	$0.591111\pi$
$18$		0			0
$19$	1.62945	+	2.24275i	0.373822	+	0.514522i	0.953935	−	0.300014i	$-0.0969914\pi$
$19$	1.62945	+	2.24275i	0.373822	+	0.514522i	−0.580112	+	0.814536i	$0.696991\pi$
$20$		0			0
$21$	−0.731633	+	0.531562i	−0.159655	+	0.115996i
$22$		0			0
$23$	6.51499	+	4.73342i	1.35847	+	0.986986i	0.998541	+	0.0540065i	$0.0171992\pi$
$23$	6.51499	+	4.73342i	1.35847	+	0.986986i	0.359929	+	0.932980i	$0.382801\pi$
$24$		0			0
$25$	3.90291	−	2.83563i	0.780582	−	0.567126i
$26$		0			0
$27$		−	4.68647i		−	0.901912i
$28$		0			0
$29$	−6.06473	+	1.97055i	−1.12619	+	0.365922i	−0.812128	−	0.583480i	$-0.801691\pi$
$29$	−6.06473	+	1.97055i	−1.12619	+	0.365922i	−0.314064	+	0.949402i	$0.601691\pi$
$30$		0			0
$31$	1.52993	−	4.70863i	0.274783	−	0.845695i	−0.714494	−	0.699642i	$-0.753343\pi$
$31$	1.52993	−	4.70863i	0.274783	−	0.845695i	0.989277	−	0.146053i	$-0.0466571\pi$
$32$		0			0
$33$	0.585069	−	1.80066i	0.101847	−	0.313454i
$34$		0			0
$35$	0.246408	−	0.339151i	0.0416505	−	0.0573270i
$36$		0			0
$37$	−1.51532	−	4.66367i	−0.249117	−	0.766703i	−0.994932	−	0.100550i	$-0.967940\pi$
$37$	−1.51532	−	4.66367i	−0.249117	−	0.766703i	0.745815	−	0.666153i	$-0.232060\pi$
$38$		0			0
$39$	2.29780	+	1.66945i	0.367943	+	0.267326i
$40$		0			0
$41$	2.22688	−	6.00342i	0.347780	−	0.937576i
$41$	2.22688	−	6.00342i	0.347780	−	0.937576i
$42$		0			0
$43$	8.75738	+	6.36261i	1.33549	+	0.970289i	0.999597	+	0.0283886i	$0.00903760\pi$
$43$	8.75738	+	6.36261i	1.33549	+	0.970289i	0.335892	+	0.941901i	$0.390962\pi$
$44$		0			0
$45$	0.282685	+	0.870016i	0.0421402	+	0.129694i
$46$		0			0
$47$	0.514310	−	0.707887i	0.0750199	−	0.103256i	−0.769858	−	0.638215i	$-0.779673\pi$
$47$	0.514310	−	0.707887i	0.0750199	−	0.103256i	0.844878	+	0.534959i	$0.179673\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	0.0643483	−	0.198044i	0.00901056	−	0.0277317i
$52$		0			0
$53$	−1.28343	+	0.417011i	−0.176292	+	0.0572809i	−0.395833	−	0.918322i	$-0.629544\pi$
$53$	−1.28343	+	0.417011i	−0.176292	+	0.0572809i	0.219541	+	0.975603i	$0.429544\pi$
$54$		0			0
$55$			0.877657i			0.118343i
$56$		0			0
$57$	2.02823	−	1.47359i	0.268645	−	0.195182i
$58$		0			0
$59$	1.10026	+	0.799383i	0.143241	+	0.104071i	0.657098	−	0.753805i	$-0.271784\pi$
$59$	1.10026	+	0.799383i	0.143241	+	0.104071i	−0.513857	+	0.857876i	$0.671784\pi$
$60$		0			0
$61$	−2.01068	+	1.46085i	−0.257442	+	0.187042i	−0.709018	−	0.705190i	$-0.750862\pi$
$61$	−2.01068	+	1.46085i	−0.257442	+	0.187042i	0.451577	+	0.892232i	$0.350862\pi$
$62$		0			0
$63$	−1.28264	−	1.76540i	−0.161597	−	0.222420i
$64$		0			0
$65$	−1.25216	−	0.406853i	−0.155312	−	0.0504639i
$66$		0			0
$67$	3.04069	−	0.987979i	0.371479	−	0.120701i	−0.117327	−	0.993093i	$-0.537433\pi$
$67$	3.04069	−	0.987979i	0.371479	−	0.120701i	0.488806	+	0.872392i	$0.337433\pi$
$68$		0			0
$69$	4.28066	−	5.89182i	0.515331	−	0.709292i
$70$		0			0
$71$	9.37008	+	3.04452i	1.11202	+	0.361318i	0.806718	−	0.590936i	$-0.201241\pi$
$71$	9.37008	+	3.04452i	1.11202	+	0.361318i	0.305305	+	0.952254i	$0.401241\pi$
$72$		0			0
$73$	12.9116			1.51119			0.755593	−	0.655042i	$-0.227349\pi$
$73$	12.9116			1.51119			0.755593	+	0.655042i	$0.227349\pi$
$74$		0			0
$75$	−2.56440	−	3.52959i	−0.296111	−	0.407562i
$76$		0			0
$77$	−0.646951	−	1.99111i	−0.0737270	−	0.226908i
$78$		0			0
$79$		−	9.73942i		−	1.09577i	−0.836553	−	0.547885i	$-0.815433\pi$
$79$		−	9.73942i		−	1.09577i	0.836553	−	0.547885i	$-0.184567\pi$
$80$		0			0
$81$	2.30826			0.256474
$82$		0			0
$83$	4.97099			0.545637			0.272819	−	0.962066i	$-0.412044\pi$
$83$	4.97099			0.545637			0.272819	+	0.962066i	$0.412044\pi$
$84$		0			0
$85$			0.0965282i			0.0104700i
$86$		0			0
$87$	1.78206	+	5.48463i	0.191057	+	0.588014i
$88$		0			0
$89$	−3.59722	−	4.95116i	−0.381305	−	0.524821i	0.574625	−	0.818417i	$-0.305148\pi$
$89$	−3.59722	−	4.95116i	−0.381305	−	0.524821i	−0.955930	+	0.293596i	$0.905148\pi$
$90$		0			0
$91$	3.14065			0.329230
$92$		0			0
$93$	−4.25824	−	1.38359i	−0.441559	−	0.143471i
$94$		0			0
$95$	−0.683089	+	0.940192i	−0.0700835	+	0.0964616i
$96$		0			0
$97$	−13.7927	+	4.48154i	−1.40044	+	0.455031i	−0.909334	−	0.416068i	$-0.863408\pi$
$97$	−13.7927	+	4.48154i	−1.40044	+	0.455031i	−0.491108	+	0.871099i	$0.663408\pi$
$98$		0			0
$99$	4.34491	+	1.41175i	0.436680	+	0.141886i
$100$		0			0
$101$	−1.37232	−	1.88884i	−0.136551	−	0.187946i	0.735265	−	0.677780i	$-0.237058\pi$
$101$	−1.37232	−	1.88884i	−0.136551	−	0.187946i	−0.871816	+	0.489833i	$0.837058\pi$
$102$		0			0
$103$	−11.0964	+	8.06201i	−1.09336	+	0.794373i	−0.979964	−	0.199176i	$-0.936173\pi$
$103$	−11.0964	+	8.06201i	−1.09336	+	0.794373i	−0.113397	+	0.993550i	$0.536173\pi$
$104$		0			0
$105$	−0.306710	−	0.222838i	−0.0299319	−	0.0217468i
$106$		0			0
$107$	2.42990	−	1.76543i	0.234908	−	0.170670i	−0.464104	−	0.885781i	$-0.653624\pi$
$107$	2.42990	−	1.76543i	0.234908	−	0.170670i	0.699012	+	0.715110i	$0.253624\pi$
$108$		0			0
$109$			2.03889i			0.195290i	0.995221	+	0.0976452i	$0.0311310\pi$
$109$			2.03889i			0.195290i	−0.995221	+	0.0976452i	$0.968869\pi$
$110$		0			0
$111$	−4.21758	+	1.37038i	−0.400315	+	0.130070i
$112$		0			0
$113$	1.05355	−	3.24251i	0.0991101	−	0.305029i	−0.889193	−	0.457532i	$-0.848733\pi$
$113$	1.05355	−	3.24251i	0.0991101	−	0.305029i	0.988303	+	0.152503i	$0.0487334\pi$
$114$		0			0
$115$	−1.04322	+	3.21069i	−0.0972804	+	0.299398i
$116$		0			0
$117$	−4.02832	+	5.54451i	−0.372418	+	0.512590i
$118$		0			0
$119$	−0.0711543	−	0.218991i	−0.00652271	−	0.0200748i
$120$		0			0
$121$	−5.35321	−	3.88933i	−0.486655	−	0.353576i
$122$		0			0
$123$	−5.42918	−	2.01387i	−0.489532	−	0.181585i
$124$		0			0
$125$	3.33191	+	2.42077i	0.298015	+	0.216520i
$126$		0			0
$127$	0.959438	+	2.95285i	0.0851364	+	0.262023i	0.984558	−	0.175060i	$-0.0560118\pi$
$127$	0.959438	+	2.95285i	0.0851364	+	0.262023i	−0.899421	+	0.437082i	$0.856012\pi$
$128$		0			0
$129$	5.75402	−	7.91972i	0.506613	−	0.697293i
$130$		0			0
$131$	2.24384	−	6.90582i	0.196045	−	0.603364i	−0.803918	−	0.594740i	$-0.797255\pi$
$131$	2.24384	−	6.90582i	0.196045	−	0.603364i	0.999963	−	0.00862407i	$-0.00274516\pi$
$132$		0			0
$133$	0.856654	−	2.63651i	0.0742814	−	0.228615i
$134$		0			0
$135$	1.86848	−	0.607105i	0.160813	−	0.0522513i
$136$		0			0
$137$			2.72152i			0.232515i	0.993219	+	0.116258i	$0.0370898\pi$
$137$			2.72152i			0.232515i	−0.993219	+	0.116258i	$0.962910\pi$
$138$		0			0
$139$	−4.70343	+	3.41724i	−0.398940	+	0.289847i	−0.769109	−	0.639118i	$-0.779300\pi$
$139$	−4.70343	+	3.41724i	−0.398940	+	0.289847i	0.370169	+	0.928964i	$0.379300\pi$
$140$		0			0
$141$	−0.640177	−	0.465116i	−0.0539126	−	0.0391698i
$142$		0			0
$143$	−5.31945	+	3.86481i	−0.444835	+	0.323191i
$144$		0			0
$145$	−1.57130	−	2.16271i	−0.130489	−	0.179603i
$146$		0			0
$147$	0.860086	+	0.279459i	0.0709387	+	0.0230494i
$148$		0			0
$149$	7.41892	−	2.41055i	0.607782	−	0.197480i	0.0110736	−	0.999939i	$-0.496475\pi$
$149$	7.41892	−	2.41055i	0.607782	−	0.197480i	0.596708	+	0.802458i	$0.296475\pi$
$150$		0			0
$151$	7.26959	−	10.0057i	0.591591	−	0.814255i	−0.403315	−	0.915061i	$-0.632142\pi$
$151$	7.26959	−	10.0057i	0.591591	−	0.814255i	0.994906	+	0.100806i	$0.0321422\pi$
$152$		0			0
$153$	0.477871	+	0.155270i	0.0386336	+	0.0125528i
$154$		0			0
$155$	2.07551			0.166709
$156$		0			0
$157$	0.609904	+	0.839460i	0.0486756	+	0.0669962i	0.832661	−	0.553783i	$-0.186816\pi$
$157$	0.609904	+	0.839460i	0.0486756	+	0.0669962i	−0.783985	+	0.620779i	$0.786816\pi$
$158$		0			0
$159$	0.377123	+	1.16067i	0.0299078	+	0.0920468i
$160$		0			0
$161$		−	8.05297i		−	0.634663i
$162$		0			0
$163$	−16.4606			−1.28930			−0.644648	−	0.764480i	$-0.722996\pi$
$163$	−16.4606			−1.28930			−0.644648	+	0.764480i	$0.722996\pi$
$164$		0			0
$165$	0.793707			0.0617900
$166$		0			0
$167$			16.2288i			1.25583i	0.778284	+	0.627913i	$0.216091\pi$
$167$			16.2288i			1.25583i	−0.778284	+	0.627913i	$0.783909\pi$
$168$		0			0
$169$	0.969174	+	2.98281i	0.0745518	+	0.229447i
$170$		0			0
$171$	3.55572	+	4.89403i	0.271913	+	0.374256i
$172$		0			0
$173$	1.36678			0.103915			0.0519573	−	0.998649i	$-0.483454\pi$
$173$	1.36678			0.103915			0.0519573	+	0.998649i	$0.483454\pi$
$174$		0			0
$175$	−4.58814	−	1.49078i	−0.346831	−	0.112692i
$176$		0			0
$177$	0.722921	−	0.995015i	0.0543380	−	0.0747899i
$178$		0			0
$179$	8.96777	−	2.91380i	0.670282	−	0.217788i	0.0459464	−	0.998944i	$-0.485370\pi$
$179$	8.96777	−	2.91380i	0.670282	−	0.217788i	0.624336	+	0.781156i	$0.285370\pi$
$180$		0			0
$181$	−15.7972	−	5.13283i	−1.17420	−	0.381520i	−0.343990	−	0.938973i	$-0.611779\pi$
$181$	−15.7972	−	5.13283i	−1.17420	−	0.381520i	−0.830208	+	0.557453i	$0.811779\pi$
$182$		0			0
$183$	1.32111	+	1.81836i	0.0976596	+	0.134417i
$184$		0			0
$185$	1.66309	−	1.20830i	0.122273	−	0.0888362i
$186$		0			0
$187$	0.390001	+	0.283352i	0.0285197	+	0.0207208i
$188$		0			0
$189$	−3.79143	+	2.75464i	−0.275786	+	0.200370i
$190$		0			0
$191$			0.0658133i			0.00476208i	0.999997	+	0.00238104i	$0.000757910\pi$
$191$			0.0658133i			0.00476208i	−0.999997	+	0.00238104i	$0.999242\pi$
$192$		0			0
$193$	−13.8948	+	4.51469i	−1.00017	+	0.324974i	−0.762933	−	0.646478i	$-0.776241\pi$
$193$	−13.8948	+	4.51469i	−1.00017	+	0.324974i	−0.237235	+	0.971452i	$0.576241\pi$
$194$		0			0
$195$	−0.367937	+	1.13239i	−0.0263485	+	0.0810923i
$196$		0			0
$197$	−5.32298	+	16.3825i	−0.379247	+	1.16720i	0.561322	+	0.827598i	$0.310293\pi$
$197$	−5.32298	+	16.3825i	−0.379247	+	1.16720i	−0.940569	+	0.339604i	$0.889707\pi$
$198$		0			0
$199$	−5.30008	+	7.29493i	−0.375713	+	0.517124i	−0.954442	−	0.298395i	$-0.903549\pi$
$199$	−5.30008	+	7.29493i	−0.375713	+	0.517124i	0.578730	+	0.815519i	$0.303549\pi$
$200$		0			0
$201$	−0.893477	−	2.74984i	−0.0630210	−	0.193959i
$202$		0			0
$203$	5.15897	+	3.74821i	0.362088	+	0.263073i
$204$		0			0
$205$	2.68202	+	0.110140i	0.187320	+	0.00769252i
$206$		0			0
$207$	14.2167	+	10.3291i	0.988130	+	0.717919i
$208$		0			0
$209$	1.79347	+	5.51974i	0.124057	+	0.381809i
$210$		0			0
$211$	−13.0346	+	17.9406i	−0.897341	+	1.23508i	0.0739671	+	0.997261i	$0.476434\pi$
$211$	−13.0346	+	17.9406i	−0.897341	+	1.23508i	−0.971308	+	0.237824i	$0.923566\pi$
$212$		0			0
$213$	2.75331	−	8.47381i	0.188654	−	0.580616i
$214$		0			0
$215$	−1.40228	+	4.31577i	−0.0956347	+	0.294333i
$216$		0			0
$217$	−4.70863	+	1.52993i	−0.319643	+	0.103858i
$218$		0			0
$219$		−	11.6766i		−	0.789028i
$220$		0			0
$221$	−0.585054	+	0.425067i	−0.0393550	+	0.0285931i
$222$		0			0
$223$	−17.6106	−	12.7948i	−1.17929	−	0.856805i	−0.187199	−	0.982322i	$-0.559941\pi$
$223$	−17.6106	−	12.7948i	−1.17929	−	0.856805i	−0.992091	+	0.125517i	$0.959941\pi$
$224$		0			0
$225$	8.51675	−	6.18778i	0.567783	−	0.412519i
$226$		0			0
$227$	15.4912	+	21.3218i	1.02818	+	1.41517i	0.906302	+	0.422630i	$0.138893\pi$
$227$	15.4912	+	21.3218i	1.02818	+	1.41517i	0.121882	+	0.992545i	$0.461107\pi$
$228$		0			0
$229$	−15.7367	−	5.11315i	−1.03991	−	0.337887i	−0.261208	−	0.965283i	$-0.584121\pi$
$229$	−15.7367	−	5.11315i	−1.03991	−	0.337887i	−0.778700	+	0.627396i	$0.784121\pi$
$230$		0			0
$231$	−1.80066	+	0.585069i	−0.118475	+	0.0384947i
$232$		0			0
$233$	−12.5681	+	17.2985i	−0.823361	+	1.13326i	0.165761	+	0.986166i	$0.446992\pi$
$233$	−12.5681	+	17.2985i	−0.823361	+	1.13326i	−0.989123	+	0.147094i	$0.953008\pi$
$234$		0			0
$235$	0.348858	+	0.113351i	0.0227570	+	0.00739419i
$236$		0			0
$237$	−8.80783			−0.572130
$238$		0			0
$239$	15.5801	+	21.4442i	1.00779	+	1.38711i	0.920419	+	0.390933i	$0.127848\pi$
$239$	15.5801	+	21.4442i	1.00779	+	1.38711i	0.0873746	+	0.996176i	$0.472152\pi$
$240$		0			0
$241$	1.10831	+	3.41103i	0.0713927	+	0.219724i	0.980386	−	0.197086i	$-0.0631479\pi$
$241$	1.10831	+	3.41103i	0.0713927	+	0.219724i	−0.908993	+	0.416810i	$0.863148\pi$
$242$		0			0
$243$		−	16.1469i		−	1.03582i
$244$		0			0
$245$	−0.419214			−0.0267826
$246$		0			0
$247$	−8.70649			−0.553981
$248$		0			0
$249$		−	4.49551i		−	0.284891i
$250$		0			0
$251$	−5.97814	−	18.3988i	−0.377337	−	1.16132i	−0.941889	−	0.335925i	$-0.890951\pi$
$251$	−5.97814	−	18.3988i	−0.377337	−	1.16132i	0.564552	−	0.825398i	$-0.309049\pi$
$252$		0			0
$253$	9.90979	+	13.6397i	0.623023	+	0.857517i
$254$		0			0
$255$	0.0872951			0.00546663
$256$		0			0
$257$	−18.9898	−	6.17015i	−1.18455	−	0.384883i	−0.350494	−	0.936565i	$-0.613986\pi$
$257$	−18.9898	−	6.17015i	−1.18455	−	0.384883i	−0.834055	+	0.551682i	$0.813986\pi$
$258$		0			0
$259$	−2.88231	+	3.96716i	−0.179098	+	0.246507i
$260$		0			0
$261$	−13.2342	+	4.30004i	−0.819175	+	0.266166i
$262$		0			0
$263$	−22.5399	−	7.32366i	−1.38987	−	0.451596i	−0.483969	−	0.875085i	$-0.660805\pi$
$263$	−22.5399	−	7.32366i	−1.38987	−	0.451596i	−0.905901	+	0.423489i	$0.860805\pi$
$264$		0			0
$265$	−0.332521	−	0.457676i	−0.0204266	−	0.0281148i
$266$		0			0
$267$	−4.47757	+	3.25314i	−0.274023	+	0.199089i
$268$		0			0
$269$	−16.7376	−	12.1606i	−1.02051	−	0.741443i	−0.0541217	−	0.998534i	$-0.517236\pi$
$269$	−16.7376	−	12.1606i	−1.02051	−	0.741443i	−0.966387	+	0.257091i	$0.917236\pi$
$270$		0			0
$271$	−5.53287	+	4.01986i	−0.336098	+	0.244189i	−0.743014	−	0.669276i	$-0.766604\pi$
$271$	−5.53287	+	4.01986i	−0.336098	+	0.244189i	0.406916	+	0.913466i	$0.366604\pi$
$272$		0			0
$273$		−	2.84024i		−	0.171899i
$274$		0			0
$275$	9.60564	−	3.12106i	0.579242	−	0.188207i
$276$		0			0
$277$	−3.48978	+	10.7404i	−0.209681	+	0.645331i	0.789808	+	0.613354i	$0.210180\pi$
$277$	−3.48978	+	10.7404i	−0.209681	+	0.645331i	−0.999489	+	0.0319765i	$0.989820\pi$
$278$		0			0
$279$	3.33854	−	10.2750i	0.199873	−	0.615146i
$280$		0			0
$281$	15.9780	−	21.9919i	0.953170	−	1.31193i	0.00306492	−	0.999995i	$-0.499024\pi$
$281$	15.9780	−	21.9919i	0.953170	−	1.31193i	0.950105	−	0.311930i	$-0.100976\pi$
$282$		0			0
$283$	8.99516	+	27.6843i	0.534707	+	1.64566i	0.744282	+	0.667866i	$0.232792\pi$
$283$	8.99516	+	27.6843i	0.534707	+	1.64566i	−0.209575	+	0.977793i	$0.567208\pi$
$284$		0			0
$285$	0.850260	+	0.617750i	0.0503651	+	0.0365924i
$286$		0			0
$287$	−6.16579	+	1.72714i	−0.363955	+	0.101950i
$288$		0			0
$289$	−13.7104	−	9.96119i	−0.806494	−	0.585952i
$290$		0			0
$291$	4.05287	+	12.4734i	0.237583	+	0.731206i
$292$		0			0
$293$	8.83366	−	12.1585i	0.516068	−	0.710307i	−0.468860	−	0.883273i	$-0.655335\pi$
$293$	8.83366	−	12.1585i	0.516068	−	0.710307i	0.984928	+	0.172966i	$0.0553351\pi$
$294$		0			0
$295$	−0.176179	+	0.542223i	−0.0102575	+	0.0315695i
$296$		0			0
$297$	3.03192	−	9.33129i	0.175930	−	0.541456i
$298$		0			0
$299$	−24.0537	+	7.81553i	−1.39106	+	0.451984i
$300$		0			0
$301$		−	10.8247i		−	0.623927i
$302$		0			0
$303$	−1.70817	+	1.24106i	−0.0981316	+	0.0712968i
$304$		0			0
$305$	−0.842906	−	0.612407i	−0.0482647	−	0.0350663i
$306$		0			0
$307$	−8.54457	+	6.20799i	−0.487664	+	0.354309i	−0.804285	−	0.594243i	$-0.797452\pi$
$307$	−8.54457	+	6.20799i	−0.487664	+	0.354309i	0.316621	+	0.948552i	$0.397452\pi$
$308$		0			0
$309$	7.29086	+	10.0350i	0.414763	+	0.570872i
$310$		0			0
$311$	8.81263	+	2.86340i	0.499719	+	0.162368i	0.548021	−	0.836464i	$-0.315381\pi$
$311$	8.81263	+	2.86340i	0.499719	+	0.162368i	−0.0483028	+	0.998833i	$0.515381\pi$
$312$		0			0
$313$	−14.4665	+	4.70046i	−0.817697	+	0.265686i	−0.687854	−	0.725849i	$-0.741447\pi$
$313$	−14.4665	+	4.70046i	−0.817697	+	0.265686i	−0.129843	+	0.991535i	$0.541447\pi$
$314$		0			0
$315$	0.537700	−	0.740080i	0.0302959	−	0.0416988i
$316$		0			0
$317$	−17.0786	−	5.54919i	−0.959232	−	0.311673i	−0.212771	−	0.977102i	$-0.568249\pi$
$317$	−17.0786	−	5.54919i	−0.959232	−	0.311673i	−0.746461	+	0.665429i	$0.768249\pi$
$318$		0			0
$319$	−13.3504			−0.747479
$320$		0			0
$321$	−1.59656	−	2.19748i	−0.0891114	−	0.122651i
$322$		0			0
$323$	0.197253	+	0.607084i	0.0109755	+	0.0337790i
$324$		0			0
$325$			15.1513i			0.840444i
$326$		0			0
$327$	1.84387			0.101966
$328$		0			0
$329$	−0.874997			−0.0482401
$330$		0			0
$331$			6.86868i			0.377537i	0.982022	+	0.188768i	$0.0604496\pi$
$331$			6.86868i			0.377537i	−0.982022	+	0.188768i	$0.939550\pi$
$332$		0			0
$333$	−3.30666	−	10.1769i	−0.181204	−	0.557688i
$334$		0			0
$335$	0.787807	+	1.08432i	0.0430425	+	0.0592429i
$336$		0			0
$337$	32.9405			1.79438			0.897192	−	0.441640i	$-0.145603\pi$
$337$	32.9405			1.79438			0.897192	+	0.441640i	$0.145603\pi$
$338$		0			0
$339$	−2.93235	−	0.952780i	−0.159264	−	0.0517479i
$340$		0			0
$341$	6.09251	−	8.38562i	0.329928	−	0.454107i
$342$		0			0
$343$	0.951057	−	0.309017i	0.0513522	−	0.0166853i
$344$		0			0
$345$	2.90358	+	0.943430i	0.156323	+	0.0507926i
$346$		0			0
$347$	2.00308	+	2.75700i	0.107531	+	0.148004i	0.859391	−	0.511319i	$-0.170843\pi$
$347$	2.00308	+	2.75700i	0.107531	+	0.148004i	−0.751860	+	0.659323i	$0.770843\pi$
$348$		0			0
$349$	16.9999	−	12.3512i	0.909986	−	0.661143i	−0.0310254	−	0.999519i	$-0.509877\pi$
$349$	16.9999	−	12.3512i	0.909986	−	0.661143i	0.941011	+	0.338375i	$0.109877\pi$
$350$		0			0
$351$	11.9076	+	8.65136i	0.635579	+	0.461775i
$352$		0			0
$353$	17.7763	−	12.9152i	0.946135	−	0.687407i	−0.00375494	−	0.999993i	$-0.501195\pi$
$353$	17.7763	−	12.9152i	0.946135	−	0.687407i	0.949889	+	0.312586i	$0.101195\pi$
$354$		0			0
$355$			4.13021i			0.219209i
$356$		0			0
$357$	−0.198044	+	0.0643483i	−0.0104816	+	0.00340567i
$358$		0			0
$359$	7.34445	−	22.6039i	0.387625	−	1.19299i	−0.546932	−	0.837177i	$-0.684205\pi$
$359$	7.34445	−	22.6039i	0.387625	−	1.19299i	0.934558	−	0.355811i	$-0.115795\pi$
$360$		0			0
$361$	3.49651	−	10.7612i	0.184027	−	0.566377i
$362$		0			0
$363$	−3.51731	+	4.84116i	−0.184611	+	0.254095i
$364$		0			0
$365$	1.67262	+	5.14779i	0.0875489	+	0.269448i
$366$		0			0
$367$	−20.6653	−	15.0142i	−1.07872	−	0.783734i	−0.101259	−	0.994860i	$-0.532287\pi$
$367$	−20.6653	−	15.0142i	−1.07872	−	0.783734i	−0.977459	+	0.211126i	$0.932287\pi$
$368$		0			0
$369$	4.85940	−	13.1004i	0.252970	−	0.681979i
$370$		0			0
$371$	1.09175	+	0.793202i	0.0566808	+	0.0411810i
$372$		0			0
$373$	1.79347	+	5.51973i	0.0928623	+	0.285801i	0.986691	−	0.162609i	$-0.0519908\pi$
$373$	1.79347	+	5.51973i	0.0928623	+	0.285801i	−0.893828	+	0.448409i	$0.851991\pi$
$374$		0			0
$375$	2.18922	−	3.01320i	0.113051	−	0.155601i
$376$		0			0
$377$	6.18881	−	19.0472i	0.318740	−	0.980981i
$378$		0			0
$379$	−3.77756	+	11.6261i	−0.194040	+	0.597195i	0.805946	+	0.591989i	$0.201657\pi$
$379$	−3.77756	+	11.6261i	−0.194040	+	0.597195i	−0.999986	+	0.00520598i	$0.998343\pi$
$380$		0			0
$381$	2.67040	−	0.867666i	0.136809	−	0.0444519i
$382$		0			0
$383$		−	17.3466i		−	0.886367i	−0.896431	−	0.443184i	$-0.853849\pi$
$383$		−	17.3466i		−	0.886367i	0.896431	−	0.443184i	$-0.146151\pi$
$384$		0			0
$385$	0.710039	−	0.515874i	0.0361870	−	0.0262914i
$386$		0			0
$387$	19.1100	+	13.8842i	0.971414	+	0.705774i
$388$		0			0
$389$	−7.28912	+	5.29586i	−0.369573	+	0.268511i	−0.757034	−	0.653376i	$-0.773352\pi$
$389$	−7.28912	+	5.29586i	−0.369573	+	0.268511i	0.387461	+	0.921886i	$0.373352\pi$
$390$		0			0
$391$	1.08992	+	1.50014i	0.0551195	+	0.0758655i
$392$		0			0
$393$	−6.24527	−	2.02921i	−0.315032	−	0.102360i
$394$		0			0
$395$	3.88307	−	1.26169i	0.195378	−	0.0634823i
$396$		0			0
$397$	−13.0340	+	17.9398i	−0.654160	+	0.900374i	−0.999271	−	0.0381879i	$-0.987841\pi$
$397$	−13.0340	+	17.9398i	−0.654160	+	0.900374i	0.345110	+	0.938562i	$0.387841\pi$
$398$		0			0
$399$	−2.38432	−	0.774714i	−0.119365	−	0.0387842i
$400$		0			0
$401$	−6.47571			−0.323382			−0.161691	−	0.986841i	$-0.551695\pi$
$401$	−6.47571			−0.323382			−0.161691	+	0.986841i	$0.551695\pi$
$402$		0			0
$403$	9.13959	+	12.5796i	0.455275	+	0.626633i
$404$		0			0
$405$	0.299022	+	0.920295i	0.0148585	+	0.0457298i
$406$		0			0
$407$		−	10.2662i		−	0.508878i
$408$		0			0
$409$	−36.8721			−1.82321			−0.911603	−	0.411072i	$-0.865155\pi$
$409$	−36.8721			−1.82321			−0.911603	+	0.411072i	$0.865155\pi$
$410$		0			0
$411$	2.46120			0.121402
$412$		0			0
$413$		−	1.35999i		−	0.0669208i
$414$		0			0
$415$	0.643963	+	1.98191i	0.0316109	+	0.0972883i
$416$		0			0
$417$	3.09038	+	4.25354i	0.151336	+	0.208297i
$418$		0			0
$419$	−28.0131			−1.36853			−0.684264	−	0.729234i	$-0.739876\pi$
$419$	−28.0131			−1.36853			−0.684264	+	0.729234i	$0.739876\pi$
$420$		0			0
$421$	−25.8734	−	8.40679i	−1.26099	−	0.409722i	−0.399145	−	0.916888i	$-0.630693\pi$
$421$	−25.8734	−	8.40679i	−1.26099	−	0.409722i	−0.861848	+	0.507166i	$0.830693\pi$
$422$		0			0
$423$	1.12230	−	1.54472i	0.0545683	−	0.0751069i
$424$		0			0
$425$	1.05647	−	0.343267i	0.0512462	−	0.0166509i
$426$		0			0
$427$	2.36370	+	0.768013i	0.114387	+	0.0371667i
$428$		0			0
$429$	3.49513	+	4.81063i	0.168746	+	0.232260i
$430$		0			0
$431$	25.7348	−	18.6974i	1.23960	−	0.900623i	0.242029	−	0.970269i	$-0.422187\pi$
$431$	25.7348	−	18.6974i	1.23960	−	0.900623i	0.997572	+	0.0696460i	$0.0221870\pi$
$432$		0			0
$433$	−6.94748	−	5.04764i	−0.333874	−	0.242574i	0.408198	−	0.912893i	$-0.366157\pi$
$433$	−6.94748	−	5.04764i	−0.333874	−	0.242574i	−0.742073	+	0.670319i	$0.766157\pi$
$434$		0			0
$435$	−1.95584	+	1.42100i	−0.0937754	+	0.0681318i
$436$		0			0
$437$			22.3244i			1.06792i
$438$		0			0
$439$	7.89212	−	2.56430i	0.376670	−	0.122388i	−0.114562	−	0.993416i	$-0.536547\pi$
$439$	7.89212	−	2.56430i	0.376670	−	0.122388i	0.491232	+	0.871029i	$0.336547\pi$
$440$		0			0
$441$	−0.674323	+	2.07535i	−0.0321106	+	0.0988263i
$442$		0			0
$443$	−4.54535	+	13.9891i	−0.215956	+	0.664644i	0.783128	+	0.621860i	$0.213623\pi$
$443$	−4.54535	+	13.9891i	−0.215956	+	0.664644i	−0.999084	+	0.0427839i	$0.986377\pi$
$444$		0			0
$445$	1.50801	−	2.07559i	0.0714863	−	0.0983925i
$446$		0			0
$447$	−2.17998	−	6.70928i	−0.103109	−	0.317338i
$448$		0			0
$449$	9.71423	+	7.05780i	0.458443	+	0.333078i	0.792920	−	0.609326i	$-0.208560\pi$
$449$	9.71423	+	7.05780i	0.458443	+	0.333078i	−0.334477	+	0.942404i	$0.608560\pi$
$450$		0			0
$451$	8.31788	−	10.5128i	0.391674	−	0.495028i
$452$		0			0
$453$	−9.04866	−	6.57424i	−0.425143	−	0.308885i
$454$		0			0
$455$	0.406853	+	1.25216i	0.0190736	+	0.0587024i
$456$		0			0
$457$	−0.599903	+	0.825696i	−0.0280623	+	0.0386244i	−0.822818	−	0.568306i	$-0.807599\pi$
$457$	−0.599903	+	0.825696i	−0.0280623	+	0.0386244i	0.794755	+	0.606930i	$0.207599\pi$
$458$		0			0
$459$	0.333463	−	1.02629i	0.0155647	−	0.0479032i
$460$		0			0
$461$	−0.546117	+	1.68078i	−0.0254352	+	0.0782815i	−0.962968	−	0.269614i	$-0.913104\pi$
$461$	−0.546117	+	1.68078i	−0.0254352	+	0.0782815i	0.937533	+	0.347896i	$0.113104\pi$
$462$		0			0
$463$	21.9651	−	7.13690i	1.02081	−	0.331680i	0.249657	−	0.968334i	$-0.419682\pi$
$463$	21.9651	−	7.13690i	1.02081	−	0.331680i	0.771149	+	0.636654i	$0.219682\pi$
$464$		0			0
$465$		−	1.87698i		−	0.0870428i
$466$		0			0
$467$	20.9101	−	15.1921i	0.967603	−	0.703005i	0.0126990	−	0.999919i	$-0.495958\pi$
$467$	20.9101	−	15.1921i	0.967603	−	0.703005i	0.954904	+	0.296915i	$0.0959577\pi$
$468$		0			0
$469$	−2.58656	−	1.87925i	−0.119436	−	0.0867756i
$470$		0			0
$471$	0.759164	−	0.551565i	0.0349804	−	0.0254148i
$472$		0			0
$473$	13.3206	+	18.3343i	0.612483	+	0.843011i
$474$		0			0
$475$	12.7192	+	4.13272i	0.583598	+	0.189622i
$476$		0			0
$477$	−2.80064	+	0.909983i	−0.128232	+	0.0416653i
$478$		0			0
$479$	−15.2401	+	20.9762i	−0.696338	+	0.958427i	0.303646	+	0.952785i	$0.401796\pi$
$479$	−15.2401	+	20.9762i	−0.696338	+	0.958427i	−0.999984	+	0.00564216i	$0.998204\pi$
$480$		0			0
$481$	14.6470	+	4.75909i	0.667844	+	0.216996i
$482$		0			0
$483$	−7.28269			−0.331374
$484$		0			0
$485$	−3.57354	−	4.91856i	−0.162266	−	0.223340i
$486$		0			0
$487$	−0.0406868	−	0.125221i	−0.00184369	−	0.00567430i	0.950130	−	0.311853i	$-0.100950\pi$
$487$	−0.0406868	−	0.125221i	−0.00184369	−	0.00567430i	−0.951974	+	0.306178i	$0.900950\pi$
$488$		0			0
$489$			14.8861i			0.673174i
$490$		0			0
$491$	24.8763			1.12265			0.561327	−	0.827594i	$-0.310291\pi$
$491$	24.8763			1.12265			0.561327	+	0.827594i	$0.310291\pi$
$492$		0			0
$493$	−1.46833			−0.0661303
$494$		0			0
$495$			1.91518i			0.0860811i
$496$		0			0
$497$	−3.04452	−	9.37008i	−0.136566	−	0.420306i
$498$		0			0
$499$	2.57033	+	3.53776i	0.115064	+	0.158372i	0.862664	−	0.505777i	$-0.168794\pi$
$499$	2.57033	+	3.53776i	0.115064	+	0.158372i	−0.747600	+	0.664149i	$0.768794\pi$
$500$		0			0
$501$	14.6765			0.655699
$502$		0			0
$503$	−4.68339	−	1.52173i	−0.208822	−	0.0678504i	0.202738	−	0.979233i	$-0.435016\pi$
$503$	−4.68339	−	1.52173i	−0.208822	−	0.0678504i	−0.411560	+	0.911383i	$0.635016\pi$
$504$		0			0
$505$	0.575296	−	0.791827i	0.0256003	−	0.0352358i
$506$		0			0
$507$	2.69750	−	0.876470i	0.119800	−	0.0389254i
$508$		0			0
$509$	7.74645	+	2.51698i	0.343355	+	0.111563i	0.475618	−	0.879652i	$-0.342224\pi$
$509$	7.74645	+	2.51698i	0.343355	+	0.111563i	−0.132263	+	0.991215i	$0.542224\pi$
$510$		0			0
$511$	−7.58923	−	10.4457i	−0.335728	−	0.462090i
$512$		0			0
$513$	10.5106	−	7.63639i	0.464054	−	0.337155i
$514$		0			0
$515$	−4.65176	−	3.37970i	−0.204981	−	0.148928i
$516$		0			0
$517$	1.48202	−	1.07675i	0.0651791	−	0.0473554i
$518$		0			0
$519$		−	1.23605i		−	0.0542565i
$520$		0			0
$521$	37.4349	−	12.1633i	1.64005	−	0.532886i	0.663503	−	0.748174i	$-0.269069\pi$
$521$	37.4349	−	12.1633i	1.64005	−	0.532886i	0.976551	+	0.215288i	$0.0690691\pi$
$522$		0			0
$523$	11.9880	−	36.8953i	0.524199	−	1.61332i	−0.241694	−	0.970352i	$-0.577703\pi$
$523$	11.9880	−	36.8953i	0.524199	−	1.61332i	0.765894	−	0.642967i	$-0.222297\pi$
$524$		0			0
$525$	−1.34818	+	4.14928i	−0.0588395	+	0.181089i
$526$		0			0
$527$	0.670079	−	0.922285i	0.0291891	−	0.0401754i
$528$		0			0
$529$	12.9325	+	39.8021i	0.562282	+	1.73053i
$530$		0			0
$531$	2.40093	+	1.74438i	0.104192	+	0.0756996i
$532$		0			0
$533$	11.1428	+	16.7406i	0.482650	+	0.725117i
$534$		0			0
$535$	1.01865	+	0.740092i	0.0440400	+	0.0319970i
$536$		0			0
$537$	−2.63509	−	8.10998i	−0.113713	−	0.349971i
$538$		0			0
$539$	−1.23057	+	1.69374i	−0.0530046	+	0.0729546i
$540$		0			0
$541$	−2.72788	+	8.39557i	−0.117281	+	0.360954i	−0.992416	−	0.122925i	$-0.960772\pi$
$541$	−2.72788	+	8.39557i	−0.117281	+	0.360954i	0.875135	+	0.483879i	$0.160772\pi$
$542$		0			0
$543$	−4.64186	+	14.2862i	−0.199201	+	0.613079i
$544$		0			0
$545$	−0.812898	+	0.264127i	−0.0348207	+	0.0113139i
$546$		0			0
$547$		−	10.3796i		−	0.443799i	−0.975070	−	0.221899i	$-0.928774\pi$
$547$		−	10.3796i		−	0.443799i	0.975070	−	0.221899i	$-0.0712257\pi$
$548$		0			0
$549$	−4.38762	+	3.18779i	−0.187259	+	0.136052i
$550$		0			0
$551$	−14.3016	−	10.3908i	−0.609271	−	0.442661i
$552$		0			0
$553$	−7.87936	+	5.72469i	−0.335064	+	0.243439i
$554$		0			0
$555$	−1.09273	−	1.50401i	−0.0463837	−	0.0638416i
$556$		0			0
$557$	38.9391	+	12.6521i	1.64990	+	0.536086i	0.978719	−	0.205204i	$-0.0657859\pi$
$557$	38.9391	+	12.6521i	1.64990	+	0.536086i	0.671184	+	0.741290i	$0.265786\pi$
$558$		0			0
$559$	−32.3328	+	10.5055i	−1.36753	+	0.444337i
$560$		0			0
$561$	0.256249	−	0.352697i	0.0108188	−	0.0148909i
$562$		0			0
$563$	1.02495	+	0.333025i	0.0431963	+	0.0140353i	0.330535	−	0.943794i	$-0.392771\pi$
$563$	1.02495	+	0.333025i	0.0431963	+	0.0140353i	−0.287339	+	0.957829i	$0.592771\pi$
$564$		0			0
$565$	1.42926			0.0601292
$566$		0			0
$567$	−1.35676	−	1.86742i	−0.0569787	−	0.0784245i
$568$		0			0
$569$	−6.39945	−	19.6955i	−0.268279	−	0.825677i	−0.990920	−	0.134454i	$-0.957072\pi$
$569$	−6.39945	−	19.6955i	−0.268279	−	0.825677i	0.722641	−	0.691223i	$-0.242928\pi$
$570$		0			0
$571$		−	10.8456i		−	0.453876i	−0.973909	−	0.226938i	$-0.927129\pi$
$571$		−	10.8456i		−	0.453876i	0.973909	−	0.226938i	$-0.0728715\pi$
$572$		0			0
$573$	0.0595181			0.00248641
$574$		0			0
$575$	38.8496			1.62014
$576$		0			0
$577$			13.3323i			0.555033i	0.960721	+	0.277516i	$0.0895113\pi$
$577$			13.3323i			0.555033i	−0.960721	+	0.277516i	$0.910489\pi$
$578$		0			0
$579$	4.08285	+	12.5657i	0.169677	+	0.522213i
$580$		0			0
$581$	−2.92187	−	4.02162i	−0.121220	−	0.166845i
$582$		0			0
$583$	−2.82524			−0.117009
$584$		0			0
$585$	−2.73242	−	0.887816i	−0.112972	−	0.0367067i
$586$		0			0
$587$	−18.8332	+	25.9217i	−0.777330	+	1.06990i	0.218241	+	0.975895i	$0.429968\pi$
$587$	−18.8332	+	25.9217i	−0.777330	+	1.06990i	−0.995571	+	0.0940081i	$0.970032\pi$
$588$		0			0
$589$	13.0532	−	4.24125i	0.537849	−	0.174758i
$590$		0			0
$591$	14.8154	+	4.81383i	0.609426	+	0.198014i
$592$		0			0
$593$	−0.396731	−	0.546054i	−0.0162918	−	0.0224237i	0.800793	−	0.598941i	$-0.204411\pi$
$593$	−0.396731	−	0.546054i	−0.0162918	−	0.0224237i	−0.817085	+	0.576517i	$0.804411\pi$
$594$		0			0
$595$	0.0780930	−	0.0567379i	0.00320150	−	0.00232603i
$596$		0			0
$597$	6.59716	+	4.79311i	0.270004	+	0.196169i
$598$		0			0
$599$	−4.08326	+	2.96667i	−0.166838	+	0.121215i	−0.668071	−	0.744097i	$-0.732880\pi$
$599$	−4.08326	+	2.96667i	−0.166838	+	0.121215i	0.501233	+	0.865312i	$0.332880\pi$
$600$		0			0
$601$		−	27.6469i		−	1.12774i	−0.825863	−	0.563871i	$-0.809311\pi$
$601$		−	27.6469i		−	1.12774i	0.825863	−	0.563871i	$-0.190689\pi$
$602$		0			0
$603$	6.63525	−	2.15592i	0.270208	−	0.0877960i
$604$		0			0
$605$	0.857184	−	2.63814i	0.0348495	−	0.107256i
$606$		0			0
$607$	4.01401	−	12.3538i	0.162924	−	0.501427i	−0.835954	−	0.548800i	$-0.815085\pi$
$607$	4.01401	−	12.3538i	0.162924	−	0.501427i	0.998877	+	0.0473728i	$0.0150849\pi$
$608$		0			0
$609$	3.38968	−	4.66550i	0.137357	−	0.189056i
$610$		0			0
$611$	0.849197	+	2.61356i	0.0343548	+	0.105733i
$612$		0			0
$613$	5.02586	+	3.65150i	0.202993	+	0.147483i	0.684638	−	0.728884i	$-0.259960\pi$
$613$	5.02586	+	3.65150i	0.202993	+	0.147483i	−0.481645	+	0.876366i	$0.659960\pi$
$614$		0			0
$615$	0.0996050	−	2.42548i	0.00401646	−	0.0978046i
$616$		0			0
$617$	30.4908	+	22.1528i	1.22751	+	0.891840i	0.996701	−	0.0811586i	$-0.0258620\pi$
$617$	30.4908	+	22.1528i	1.22751	+	0.891840i	0.230811	+	0.972999i	$0.425862\pi$
$618$		0			0
$619$	−3.53321	−	10.8741i	−0.142012	−	0.437067i	0.854603	−	0.519282i	$-0.173801\pi$
$619$	−3.53321	−	10.8741i	−0.142012	−	0.437067i	−0.996615	+	0.0822150i	$0.973801\pi$
$620$		0			0
$621$	22.1830	−	30.5323i	0.890174	−	1.22522i
$622$		0			0
$623$	−1.89117	+	5.82043i	−0.0757682	+	0.233191i
$624$		0			0
$625$	6.92037	−	21.2987i	0.276815	−	0.851948i
$626$		0			0
$627$	4.99177	−	1.62192i	0.199352	−	0.0647734i
$628$		0			0
$629$		−	1.12912i		−	0.0450210i
$630$		0			0
$631$	−20.2384	+	14.7041i	−0.805678	+	0.585359i	−0.912574	−	0.408911i	$-0.865909\pi$
$631$	−20.2384	+	14.7041i	−0.805678	+	0.585359i	0.106897	+	0.994270i	$0.465909\pi$
$632$		0			0
$633$	16.2246	+	11.7878i	0.644869	+	0.468525i
$634$		0			0
$635$	−1.05300	+	0.765048i	−0.0417870	+	0.0303600i
$636$		0			0
$637$	−1.84603	−	2.54084i	−0.0731423	−	0.100672i
$638$		0			0
$639$	20.4470	+	6.64362i	0.808869	+	0.262818i
$640$		0			0
$641$	−27.1521	+	8.82226i	−1.07244	+	0.348458i	−0.791439	−	0.611248i	$-0.790668\pi$
$641$	−27.1521	+	8.82226i	−1.07244	+	0.348458i	−0.281006	+	0.959706i	$0.590668\pi$
$642$		0			0
$643$	25.8556	−	35.5872i	1.01965	−	1.40342i	0.107195	−	0.994238i	$-0.465813\pi$
$643$	25.8556	−	35.5872i	1.01965	−	1.40342i	0.912451	−	0.409185i	$-0.134187\pi$
$644$		0			0
$645$	3.90296	+	1.26815i	0.153679	+	0.0499333i
$646$		0			0
$647$	36.0356			1.41670			0.708352	−	0.705859i	$-0.249439\pi$
$647$	36.0356			1.41670			0.708352	+	0.705859i	$0.249439\pi$
$648$		0			0
$649$	1.67357	+	2.30347i	0.0656934	+	0.0904193i
$650$		0			0
$651$	1.38359	+	4.25824i	0.0542270	+	0.166894i
$652$		0			0
$653$		−	2.51651i		−	0.0984786i	−0.998787	−	0.0492393i	$-0.984320\pi$
$653$		−	2.51651i		−	0.0984786i	0.998787	−	0.0492393i	$-0.0156797\pi$
$654$		0			0
$655$	3.04400			0.118939
$656$		0			0
$657$	28.1750			1.09921
$658$		0			0
$659$		−	11.9875i		−	0.466967i	−0.972361	−	0.233483i	$-0.924988\pi$
$659$		−	11.9875i		−	0.466967i	0.972361	−	0.233483i	$-0.0750125\pi$
$660$		0			0
$661$	13.5361	+	41.6598i	0.526493	+	1.62038i	0.761344	+	0.648348i	$0.224540\pi$
$661$	13.5361	+	41.6598i	0.526493	+	1.62038i	−0.234851	+	0.972031i	$0.575460\pi$
$662$		0			0
$663$	0.384408	+	0.529093i	0.0149292	+	0.0205483i
$664$		0			0
$665$	1.16214			0.0450659
$666$		0			0
$667$	−48.8391	−	15.8688i	−1.89106	−	0.614442i
$668$		0			0
$669$	−11.5710	+	15.9261i	−0.447360	+	0.615738i
$670$		0			0
$671$	−4.94859	+	1.60790i	−0.191038	+	0.0620721i
$672$		0			0
$673$	−23.5399	−	7.64859i	−0.907397	−	0.294831i	−0.182111	−	0.983278i	$-0.558293\pi$
$673$	−23.5399	−	7.64859i	−0.907397	−	0.294831i	−0.725287	+	0.688447i	$0.758293\pi$
$674$		0			0
$675$	−13.2891	−	18.2909i	−0.511497	−	0.704016i
$676$		0			0
$677$	−7.70855	+	5.60059i	−0.296264	+	0.215248i	−0.725980	−	0.687716i	$-0.758614\pi$
$677$	−7.70855	+	5.60059i	−0.296264	+	0.215248i	0.429716	+	0.902964i	$0.358614\pi$
$678$		0			0
$679$	11.7328	+	8.52439i	0.450264	+	0.327136i
$680$		0			0
$681$	19.2823	−	14.0094i	0.738899	−	0.536841i
$682$		0			0
$683$		−	39.8358i		−	1.52427i	−0.647416	−	0.762137i	$-0.724150\pi$
$683$		−	39.8358i		−	1.52427i	0.647416	−	0.762137i	$-0.275850\pi$
$684$		0			0
$685$	−1.08506	+	0.352557i	−0.0414580	+	0.0134705i
$686$		0			0
$687$	−4.62407	+	14.2314i	−0.176419	+	0.542963i
$688$		0			0
$689$	1.30969	−	4.03080i	0.0498951	−	0.153561i
$690$		0			0
$691$	−4.51589	+	6.21559i	−0.171793	+	0.236452i	−0.886228	−	0.463249i	$-0.846684\pi$
$691$	−4.51589	+	6.21559i	−0.171793	+	0.236452i	0.714436	+	0.699701i	$0.246684\pi$
$692$		0			0
$693$	−1.41175	−	4.34491i	−0.0536279	−	0.165050i
$694$		0			0
$695$	−1.97174	−	1.43256i	−0.0747925	−	0.0543399i
$696$		0			0
$697$	0.914834	−	1.15624i	0.0346518	−	0.0437957i
$698$		0			0
$699$	15.6438	+	11.3659i	0.591704	+	0.429898i
$700$		0			0
$701$	−13.5647	−	41.7478i	−0.512331	−	1.57679i	−0.788087	−	0.615564i	$-0.788928\pi$
$701$	−13.5647	−	41.7478i	−0.512331	−	1.57679i	0.275756	−	0.961228i	$-0.411072\pi$
$702$		0			0
$703$	7.99031	−	10.9977i	0.301360	−	0.414787i
$704$		0			0
$705$	0.102509	−	0.315489i	0.00386069	−	0.0118820i
$706$		0			0
$707$	−0.721472	+	2.22046i	−0.0271337	+	0.0835091i
$708$		0			0
$709$	−41.0018	+	13.3223i	−1.53985	+	0.500329i	−0.951336	−	0.308156i	$-0.900288\pi$
$709$	−41.0018	+	13.3223i	−1.53985	+	0.500329i	−0.588518	+	0.808484i	$0.700288\pi$
$710$		0			0
$711$		−	21.2529i		−	0.797047i
$712$		0			0
$713$	32.2554	−	23.4349i	1.20797	−	0.877644i
$714$		0			0
$715$	−2.22999	−	1.62018i	−0.0833967	−	0.0605913i
$716$		0			0
$717$	19.3930	−	14.0898i	0.724245	−	0.526195i
$718$		0			0
$719$	−9.13692	−	12.5759i	−0.340750	−	0.469002i	0.603910	−	0.797052i	$-0.293608\pi$
$719$	−9.13692	−	12.5759i	−0.340750	−	0.469002i	−0.944660	+	0.328050i	$0.893608\pi$
$720$		0			0
$721$	13.0446	+	4.23845i	0.485806	+	0.157848i
$722$		0			0
$723$	3.08476	−	1.00230i	0.114724	−	0.0372759i
$724$		0			0
$725$	−18.0823	+	24.8882i	−0.671561	+	0.924324i
$726$		0			0
$727$	−10.8239	−	3.51688i	−0.401435	−	0.130434i	0.101339	−	0.994852i	$-0.467687\pi$
$727$	−10.8239	−	3.51688i	−0.401435	−	0.130434i	−0.502774	+	0.864418i	$0.667687\pi$
$728$		0			0
$729$	−7.67761			−0.284356
$730$		0			0
$731$	1.46506	+	2.01648i	0.0541871	+	0.0745821i
$732$		0			0
$733$	5.09849	+	15.6915i	0.188317	+	0.579580i	0.999990	−	0.00453239i	$-0.00144271\pi$
$733$	5.09849	+	15.6915i	0.188317	+	0.579580i	−0.811673	+	0.584112i	$0.801443\pi$
$734$		0			0
$735$			0.379115i			0.0139839i
$736$		0			0
$737$	6.69352			0.246559
$738$		0			0
$739$	−10.8437			−0.398892			−0.199446	−	0.979909i	$-0.563914\pi$
$739$	−10.8437			−0.398892			−0.199446	+	0.979909i	$0.563914\pi$
$740$		0			0
$741$			7.87369i			0.289247i
$742$		0			0
$743$	0.875666	+	2.69502i	0.0321251	+	0.0988708i	0.965833	−	0.259164i	$-0.0834470\pi$
$743$	0.875666	+	2.69502i	0.0321251	+	0.0988708i	−0.933708	+	0.358035i	$0.883447\pi$
$744$		0			0
$745$	1.92216	+	2.64562i	0.0704223	+	0.0969280i
$746$		0			0
$747$	10.8475			0.396888
$748$		0			0
$749$	−2.85652	−	0.928141i	−0.104375	−	0.0339135i
$750$		0			0
$751$	−0.578661	+	0.796458i	−0.0211156	+	0.0290632i	−0.819444	−	0.573159i	$-0.805718\pi$
$751$	−0.578661	+	0.796458i	−0.0211156	+	0.0290632i	0.798329	+	0.602222i	$0.205718\pi$
$752$		0			0
$753$	−16.6389	+	5.40632i	−0.606356	+	0.197017i
$754$		0			0
$755$	4.93098	+	1.60217i	0.179457	+	0.0583090i
$756$		0			0
$757$	9.66954	+	13.3090i	0.351445	+	0.483723i	0.947740	−	0.319042i	$-0.103361\pi$
$757$	9.66954	+	13.3090i	0.351445	+	0.483723i	−0.596295	+	0.802765i	$0.703361\pi$
$758$		0			0
$759$	12.3350	−	8.96189i	0.447732	−	0.325296i
$760$		0			0
$761$	10.0609	+	7.30964i	0.364706	+	0.264974i	0.755012	−	0.655711i	$-0.227631\pi$
$761$	10.0609	+	7.30964i	0.364706	+	0.264974i	−0.390306	+	0.920685i	$0.627631\pi$
$762$		0			0
$763$	1.64950	−	1.19843i	0.0597158	−	0.0433861i
$764$		0			0
$765$			0.210640i			0.00761569i
$766$		0			0
$767$	−4.06221	+	1.31989i	−0.146678	+	0.0476585i
$768$		0			0
$769$	7.63007	−	23.4829i	0.275147	−	0.846816i	−0.714033	−	0.700112i	$-0.753133\pi$
$769$	7.63007	−	23.4829i	0.275147	−	0.846816i	0.989180	−	0.146704i	$-0.0468666\pi$
$770$		0			0
$771$	−5.57996	+	17.1733i	−0.200957	+	0.618483i
$772$		0			0
$773$	−31.3381	+	43.1332i	−1.12715	+	1.55139i	−0.333786	+	0.942649i	$0.608326\pi$
$773$	−31.3381	+	43.1332i	−1.12715	+	1.55139i	−0.793367	+	0.608744i	$0.791674\pi$
$774$		0			0
$775$	−7.38077	−	22.7157i	−0.265125	−	0.815971i
$776$		0			0
$777$	3.58769	+	2.60661i	0.128708	+	0.0935116i
$778$		0			0
$779$	17.0928	−	4.78795i	0.612412	−	0.171546i
$780$		0			0
$781$	16.6872	+	12.1240i	0.597116	+	0.433830i
$782$		0			0
$783$	9.23493	+	28.4222i	0.330029	+	1.01573i
$784$		0			0
$785$	−0.255680	+	0.351913i	−0.00912561	+	0.0125603i
$786$		0			0
$787$	−0.435269	+	1.33962i	−0.0155157	+	0.0477523i	−0.958515	−	0.285043i	$-0.907992\pi$
$787$	−0.435269	+	1.33962i	−0.0155157	+	0.0477523i	0.942999	+	0.332796i	$0.107992\pi$
$788$		0			0
$789$	−6.62313	+	20.3839i	−0.235790	+	0.725686i
$790$		0			0
$791$	−3.24251	+	1.05355i	−0.115290	+	0.0374601i
$792$		0			0
$793$		−	7.80559i		−	0.277185i
$794$		0			0
$795$	−0.413899	+	0.300715i	−0.0146795	+	0.0106653i
$796$		0			0
$797$	−25.8845	−	18.8062i	−0.916878	−	0.666151i	0.0258673	−	0.999665i	$-0.491765\pi$
$797$	−25.8845	−	18.8062i	−0.916878	−	0.666151i	−0.942745	+	0.333515i	$0.891765\pi$
$798$		0			0
$799$	0.162998	−	0.118425i	0.00576647	−	0.00418958i
$800$		0			0
$801$	−7.84970	−	10.8042i	−0.277356	−	0.381747i
$802$		0			0
$803$	25.7084	+	8.35316i	0.907229	+	0.294777i
$804$		0			0
$805$	3.21069	−	1.04322i	0.113162	−	0.0367685i
$806$		0			0
$807$	−10.9974	+	15.1366i	−0.387126	+	0.532834i
$808$		0			0
$809$	−15.8118	−	5.13757i	−0.555914	−	0.180627i	0.0175681	−	0.999846i	$-0.494408\pi$
$809$	−15.8118	−	5.13757i	−0.555914	−	0.180627i	−0.573482	+	0.819218i	$0.694408\pi$
$810$		0			0
$811$	−10.3052			−0.361864			−0.180932	−	0.983496i	$-0.557911\pi$
$811$	−10.3052			−0.361864			−0.180932	+	0.983496i	$0.557911\pi$
$812$		0			0
$813$	3.63536	+	5.00364i	0.127497	+	0.175485i
$814$		0			0
$815$	−2.13238	−	6.56278i	−0.0746939	−	0.229884i
$816$		0			0
$817$			30.0082i			1.04985i
$818$		0			0
$819$	6.85339			0.239477
$820$		0			0
$821$	−21.8993			−0.764290			−0.382145	−	0.924102i	$-0.624815\pi$
$821$	−21.8993			−0.764290			−0.382145	+	0.924102i	$0.624815\pi$
$822$		0			0
$823$		−	30.3056i		−	1.05639i	−0.849124	−	0.528193i	$-0.822870\pi$
$823$		−	30.3056i		−	1.05639i	0.849124	−	0.528193i	$-0.177130\pi$
$824$		0			0
$825$	−2.82253	−	8.68684i	−0.0982677	−	0.302437i
$826$		0			0
$827$	7.12452	+	9.80605i	0.247744	+	0.340990i	0.914719	−	0.404089i	$-0.132412\pi$
$827$	7.12452	+	9.80605i	0.247744	+	0.340990i	−0.666976	+	0.745079i	$0.732412\pi$
$828$		0			0
$829$	41.4703			1.44032			0.720161	−	0.693807i	$-0.244068\pi$
$829$	41.4703			1.44032			0.720161	+	0.693807i	$0.244068\pi$
$830$		0			0
$831$	9.71310	+	3.15598i	0.336944	+	0.109480i
$832$		0			0
$833$	−0.135344	+	0.186284i	−0.00468938	+	0.00645437i
$834$		0			0
$835$	−6.47038	+	2.10235i	−0.223917	+	0.0727549i
$836$		0			0
$837$	−22.0669	−	7.16996i	−0.762742	−	0.247830i
$838$		0			0
$839$	10.4229	+	14.3458i	0.359837	+	0.495274i	0.950103	−	0.311935i	$-0.100977\pi$
$839$	10.4229	+	14.3458i	0.359837	+	0.495274i	−0.590266	+	0.807209i	$0.700977\pi$
$840$		0			0
$841$	9.43638	−	6.85593i	0.325392	−	0.236411i
$842$		0			0
$843$	−19.8883	−	14.4497i	−0.684990	−	0.497674i
$844$		0			0
$845$	−1.06368	+	0.772811i	−0.0365918	+	0.0265855i
$846$		0			0
$847$			6.61693i			0.227360i
$848$		0			0
$849$	25.0362	−	8.13476i	0.859240	−	0.279184i
$850$		0			0
$851$	12.2028	−	37.5564i	0.418308	−	1.28742i
$852$		0			0
$853$	−7.92907	+	24.4032i	−0.271486	+	0.835548i	0.718642	+	0.695381i	$0.244764\pi$
$853$	−7.92907	+	24.4032i	−0.271486	+	0.835548i	−0.990128	+	0.140168i	$0.955236\pi$
$854$		0			0
$855$	−1.49061	+	2.05164i	−0.0509777	+	0.0701647i
$856$		0			0
$857$	−13.9963	−	43.0763i	−0.478105	−	1.47146i	−0.841723	−	0.539909i	$-0.818459\pi$
$857$	−13.9963	−	43.0763i	−0.478105	−	1.47146i	0.363618	−	0.931548i	$-0.381541\pi$
$858$		0			0
$859$	−28.4020	−	20.6352i	−0.969062	−	0.704065i	−0.0138246	−	0.999904i	$-0.504401\pi$
$859$	−28.4020	−	20.6352i	−0.969062	−	0.704065i	−0.955238	+	0.295840i	$0.904401\pi$
$860$		0			0
$861$	1.56193	+	5.57602i	0.0532305	+	0.190030i
$862$		0			0
$863$	8.65756	+	6.29008i	0.294707	+	0.214117i	0.725307	−	0.688426i	$-0.241698\pi$
$863$	8.65756	+	6.29008i	0.294707	+	0.214117i	−0.430600	+	0.902543i	$0.641698\pi$
$864$		0			0
$865$	0.177059	+	0.544931i	0.00602018	+	0.0185282i
$866$		0			0
$867$	−9.00838	+	12.3990i	−0.305941	+	0.421091i
$868$		0			0
$869$	6.30093	−	19.3923i	0.213745	−	0.657838i
$870$		0			0
$871$	−3.10290	+	9.54974i	−0.105138	+	0.323581i
$872$		0			0
$873$	−30.0979	+	9.77940i	−1.01866	+	0.330983i
$874$		0			0
$875$		−	4.11846i		−	0.139229i
$876$		0			0
$877$	−17.1642	+	12.4705i	−0.579595	+	0.421100i	−0.838578	−	0.544782i	$-0.816613\pi$
$877$	−17.1642	+	12.4705i	−0.579595	+	0.421100i	0.258983	+	0.965882i	$0.416613\pi$
$878$		0			0
$879$	−10.9955	−	7.98870i	−0.370869	−	0.269452i
$880$		0			0
$881$	12.8305	−	9.32192i	0.432271	−	0.314063i	−0.350285	−	0.936643i	$-0.613915\pi$
$881$	12.8305	−	9.32192i	0.432271	−	0.314063i	0.782556	+	0.622580i	$0.213915\pi$
$882$		0			0
$883$	−23.2574	−	32.0110i	−0.782672	−	1.07726i	−0.994982	−	0.100054i	$-0.968099\pi$
$883$	−23.2574	−	32.0110i	−0.782672	−	1.07726i	0.212310	−	0.977202i	$-0.431901\pi$
$884$		0			0
$885$	0.490359	+	0.159327i	0.0164832	+	0.00535572i
$886$		0			0
$887$	−26.5802	+	8.63642i	−0.892474	+	0.289982i	−0.719127	−	0.694878i	$-0.755458\pi$
$887$	−26.5802	+	8.63642i	−0.892474	+	0.289982i	−0.173347	+	0.984861i	$0.555458\pi$
$888$		0			0
$889$	1.82496	−	2.51184i	0.0612072	−	0.0842445i
$890$		0			0
$891$	4.59601	+	1.49333i	0.153972	+	0.0500286i
$892$		0			0
$893$	2.42566			0.0811716
$894$		0			0
$895$	2.32344	+	3.19794i	0.0776641	+	0.106896i
$896$		0			0
$897$	7.06796	+	21.7529i	0.235992	+	0.726309i
$898$		0			0
$899$			31.5714i			1.05296i
$900$		0			0
$901$	−0.310731			−0.0103519
$902$		0			0
$903$	−9.78932			−0.325768
$904$		0			0
$905$		−	6.96322i		−	0.231465i
$906$		0			0
$907$	−9.06012	−	27.8842i	−0.300836	−	0.925879i	−0.981198	−	0.193003i	$-0.938177\pi$
$907$	−9.06012	−	27.8842i	−0.300836	−	0.925879i	0.680362	−	0.732876i	$-0.261823\pi$
$908$		0			0
$909$	−2.99462	−	4.12174i	−0.0993252	−	0.136709i
$910$		0			0
$911$	37.5554			1.24427			0.622133	−	0.782912i	$-0.286266\pi$
$911$	37.5554			1.24427			0.622133	+	0.782912i	$0.286266\pi$
$912$		0			0
$913$	9.89780	+	3.21599i	0.327569	+	0.106434i
$914$		0			0
$915$	−0.553829	+	0.762280i	−0.0183090	+	0.0252002i
$916$		0			0
$917$	−6.90582	+	2.24384i	−0.228050	+	0.0740980i
$918$		0			0
$919$	−35.4527	−	11.5193i	−1.16948	−	0.379986i	−0.341029	−	0.940053i	$-0.610775\pi$
$919$	−35.4527	−	11.5193i	−1.16948	−	0.379986i	−0.828447	+	0.560067i	$0.810775\pi$
$920$		0			0
$921$	5.61419	+	7.72726i	0.184994	+	0.254622i
$922$		0			0
$923$	−25.0331	+	18.1876i	−0.823974	+	0.598652i
$924$		0			0
$925$	−19.1386	−	13.9050i	−0.629273	−	0.457194i
$926$		0			0
$927$	−24.2141	+	17.5926i	−0.795294	+	0.577815i
$928$		0			0
$929$		−	58.1072i		−	1.90644i	−0.302285	−	0.953218i	$-0.597749\pi$
$929$		−	58.1072i		−	1.90644i	0.302285	−	0.953218i	$-0.402251\pi$
$930$		0			0
$931$	−2.63651	+	0.856654i	−0.0864082	+	0.0280757i
$932$		0			0
$933$	2.58951	−	7.96969i	0.0847767	−	0.260916i
$934$		0			0
$935$	−0.0624491	+	0.192199i	−0.00204230	+	0.00628556i
$936$		0			0
$937$	−10.9093	+	15.0154i	−0.356391	+	0.490531i	−0.949139	−	0.314858i	$-0.898043\pi$
$937$	−10.9093	+	15.0154i	−0.356391	+	0.490531i	0.592747	+	0.805388i	$0.298043\pi$
$938$		0			0
$939$	4.25085	+	13.0828i	0.138721	+	0.426941i
$940$		0			0
$941$	−18.8335	−	13.6833i	−0.613955	−	0.446064i	0.236850	−	0.971546i	$-0.423885\pi$
$941$	−18.8335	−	13.6833i	−0.613955	−	0.446064i	−0.850805	+	0.525482i	$0.823885\pi$
$942$		0			0
$943$	42.9248	−	28.5715i	1.39782	−	0.930415i
$944$		0			0
$945$	−1.58942	−	1.15478i	−0.0517039	−	0.0375651i
$946$		0			0
$947$	8.96380	+	27.5878i	0.291284	+	0.896481i	0.984444	+	0.175697i	$0.0562180\pi$
$947$	8.96380	+	27.5878i	0.291284	+	0.896481i	−0.693160	+	0.720784i	$0.743782\pi$
$948$		0			0
$949$	−23.8351	+	32.8062i	−0.773721	+	1.06494i
$950$		0			0
$951$	−5.01839	+	15.4450i	−0.162733	+	0.500839i
$952$		0			0
$953$	−3.92059	+	12.0663i	−0.127000	+	0.390867i	−0.994260	−	0.106989i	$-0.965879\pi$
$953$	−3.92059	+	12.0663i	−0.127000	+	0.390867i	0.867260	+	0.497856i	$0.165879\pi$
$954$		0			0
$955$	−0.0262395	+	0.00852573i	−0.000849090	+	0.000275886i
$956$		0			0
$957$			12.0734i			0.390278i
$958$		0			0
$959$	2.20176	−	1.59967i	0.0710984	−	0.0516560i
$960$		0			0
$961$	5.24899	+	3.81361i	0.169322	+	0.123020i
$962$		0			0
$963$	5.30243	−	3.85244i	0.170868	−	0.124143i
$964$		0			0
$965$	−3.59997	−	4.95494i	−0.115887	−	0.159505i
$966$		0			0
$967$	−35.0959	−	11.4034i	−1.12861	−	0.366707i	−0.315562	−	0.948905i	$-0.602193\pi$
$967$	−35.0959	−	11.4034i	−1.12861	−	0.366707i	−0.813047	+	0.582198i	$0.802193\pi$
$968$		0			0
$969$	0.549015	−	0.178386i	0.0176369	−	0.00573058i
$970$		0			0
$971$	6.80947	−	9.37243i	0.218526	−	0.300776i	−0.685653	−	0.727928i	$-0.740483\pi$
$971$	6.80947	−	9.37243i	0.218526	−	0.300776i	0.904179	+	0.427153i	$0.140483\pi$
$972$		0			0
$973$	5.52922	+	1.79655i	0.177259	+	0.0575948i
$974$		0			0
$975$	13.7021			0.438817
$976$		0			0
$977$	20.2483	+	27.8693i	0.647799	+	0.891619i	0.999001	−	0.0446807i	$-0.0142270\pi$
$977$	20.2483	+	27.8693i	0.647799	+	0.891619i	−0.351202	+	0.936300i	$0.614227\pi$
$978$		0			0
$979$	−3.95932	−	12.1855i	−0.126540	−	0.389451i
$980$		0			0
$981$			4.44918i			0.142051i
$982$		0			0
$983$	−35.8823			−1.14447			−0.572234	−	0.820090i	$-0.693923\pi$
$983$	−35.8823			−1.14447			−0.572234	+	0.820090i	$0.693923\pi$
$984$		0			0
$985$	−7.22118			−0.230086
$986$		0			0
$987$			0.791302i			0.0251874i
$988$		0			0
$989$	26.9374	+	82.9047i	0.856559	+	2.63622i
$990$		0			0
$991$	5.93454	+	8.16820i	0.188517	+	0.259471i	0.892805	−	0.450443i	$-0.148734\pi$
$991$	5.93454	+	8.16820i	0.188517	+	0.259471i	−0.704288	+	0.709914i	$0.748734\pi$
$992$		0			0
$993$	6.21168			0.197122
$994$		0			0
$995$	−3.59505	−	1.16810i	−0.113971	−	0.0370314i
$996$		0			0
$997$	−3.71495	+	5.11319i	−0.117654	+	0.161936i	−0.863782	−	0.503866i	$-0.831911\pi$
$997$	−3.71495	+	5.11319i	−0.117654	+	0.161936i	0.746128	+	0.665802i	$0.231911\pi$
$998$		0			0
$999$	−21.8562	+	7.10150i	−0.691499	+	0.224682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.8	✓	80
41.4	even	10	inner	1148.2.ba.a.701.13	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.8	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.13	yes	80	41.4	even	10	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.904348i q^{3} +(0.129544 + 0.398696i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.18215 q^{9} +O(q^{10})\)	\(q-0.904348i q^{3} +(0.129544 + 0.398696i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.18215 q^{9} +(1.99111 + 0.646951i) q^{11} +(-1.84603 + 2.54084i) q^{13} +(0.360560 - 0.117153i) q^{15} +(0.218991 + 0.0711543i) q^{17} +(1.62945 + 2.24275i) q^{19} +(-0.731633 + 0.531562i) q^{21} +(6.51499 + 4.73342i) q^{23} +(3.90291 - 2.83563i) q^{25} -4.68647i q^{27} +(-6.06473 + 1.97055i) q^{29} +(1.52993 - 4.70863i) q^{31} +(0.585069 - 1.80066i) q^{33} +(0.246408 - 0.339151i) q^{35} +(-1.51532 - 4.66367i) q^{37} +(2.29780 + 1.66945i) q^{39} +(2.22688 - 6.00342i) q^{41} +(8.75738 + 6.36261i) q^{43} +(0.282685 + 0.870016i) q^{45} +(0.514310 - 0.707887i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(0.0643483 - 0.198044i) q^{51} +(-1.28343 + 0.417011i) q^{53} +0.877657i q^{55} +(2.02823 - 1.47359i) q^{57} +(1.10026 + 0.799383i) q^{59} +(-2.01068 + 1.46085i) q^{61} +(-1.28264 - 1.76540i) q^{63} +(-1.25216 - 0.406853i) q^{65} +(3.04069 - 0.987979i) q^{67} +(4.28066 - 5.89182i) q^{69} +(9.37008 + 3.04452i) q^{71} +12.9116 q^{73} +(-2.56440 - 3.52959i) q^{75} +(-0.646951 - 1.99111i) q^{77} -9.73942i q^{79} +2.30826 q^{81} +4.97099 q^{83} +0.0965282i q^{85} +(1.78206 + 5.48463i) q^{87} +(-3.59722 - 4.95116i) q^{89} +3.14065 q^{91} +(-4.25824 - 1.38359i) q^{93} +(-0.683089 + 0.940192i) q^{95} +(-13.7927 + 4.48154i) q^{97} +(4.34491 + 1.41175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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