LMFDB - Embedded newform 792.2.f.g.397.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(397,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.397"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,-4,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.578281160704.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 2x^{8} - 2x^{7} - 3x^{6} - 6x^{5} - 6x^{4} - 8x^{3} + 16x^{2} + 32 $ x^10 + 2x^8 - 2x^7 - 3x^6 - 6x^5 - 6x^4 - 8x^3 + 16*x^2 + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			397.7
Root			$-0.239536 + 1.39378i$ of defining polynomial
Character	$\chi$	$=$	792.397
Dual form			792.2.f.g.397.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.428185 - 1.34783i) q^{2} +(-1.63332 - 1.15424i) q^{4} -1.93119i q^{5} -1.83930 q^{7} +(-2.25509 + 1.70721i) q^{8} +(-2.60293 - 0.826906i) q^{10} -1.00000i q^{11} -0.160700i q^{13} +(-0.787560 + 2.47907i) q^{14} +(1.33544 + 3.77049i) q^{16} -5.41442 q^{17} -2.79744i q^{19} +(-2.22907 + 3.15424i) q^{20} +(-1.34783 - 0.428185i) q^{22} -4.44137 q^{23} +1.27050 q^{25} +(-0.216597 - 0.0688094i) q^{26} +(3.00416 + 2.12300i) q^{28} +8.34948i q^{29} -9.05835 q^{31} +(5.65381 - 0.185487i) q^{32} +(-2.31837 + 7.29774i) q^{34} +3.55204i q^{35} -0.602073i q^{37} +(-3.77049 - 1.19782i) q^{38} +(3.29695 + 4.35501i) q^{40} +11.7639 q^{41} -4.47936i q^{43} +(-1.15424 + 1.63332i) q^{44} +(-1.90173 + 5.98623i) q^{46} -6.29558 q^{47} -3.61698 q^{49} +(0.544010 - 1.71243i) q^{50} +(-0.185487 + 0.262474i) q^{52} -11.7211i q^{53} -1.93119 q^{55} +(4.14779 - 3.14007i) q^{56} +(11.2537 + 3.57512i) q^{58} +9.63102i q^{59} -3.32912i q^{61} +(-3.87865 + 12.2092i) q^{62} +(2.17087 - 7.69983i) q^{64} -0.310343 q^{65} -5.76864i q^{67} +(8.84346 + 6.24956i) q^{68} +(4.78756 + 1.52093i) q^{70} -9.62916 q^{71} -0.681940 q^{73} +(-0.811494 - 0.257798i) q^{74} +(-3.22893 + 4.56911i) q^{76} +1.83930i q^{77} +5.77867 q^{79} +(7.28154 - 2.57899i) q^{80} +(5.03712 - 15.8558i) q^{82} -2.92400i q^{83} +10.4563i q^{85} +(-6.03743 - 1.91799i) q^{86} +(1.70721 + 2.25509i) q^{88} -5.74214 q^{89} +0.295576i q^{91} +(7.25416 + 5.12643i) q^{92} +(-2.69567 + 8.48539i) q^{94} -5.40240 q^{95} -5.37829 q^{97} +(-1.54873 + 4.87509i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{4} + 10 q^{10} + 12 q^{14} + 4 q^{17} - 12 q^{20} + 12 q^{23} - 6 q^{25} + 20 q^{26} - 12 q^{28} - 4 q^{31} + 20 q^{32} - 8 q^{38} + 20 q^{40} - 4 q^{41} - 4 q^{44} + 2 q^{46} + 4 q^{47} - 6 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) $ 10 * q - 4 * q^4 + 10 * q^10 + 12 * q^14 + 4 * q^17 - 12 * q^20 + 12 * q^23 - 6 * q^25 + 20 * q^26 - 12 * q^28 - 4 * q^31 + 20 * q^32 - 8 * q^38 + 20 * q^40 - 4 * q^41 - 4 * q^44 + 2 * q^46 + 4 * q^47 - 6 * q^49 + 6 * q^50 - 20 * q^52 - 8 * q^55 + 8 * q^56 + 36 * q^58 - 22 * q^62 - 16 * q^64 - 16 * q^65 + 28 * q^68 + 28 * q^70 + 12 * q^71 - 4 * q^73 + 14 * q^74 + 44 * q^76 + 16 * q^79 + 56 * q^80 - 4 * q^82 + 20 * q^86 - 12 * q^88 + 4 * q^89 + 36 * q^92 - 24 * q^95 - 20 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$1$	$1$	$1$	$-1$

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 $

$2$	0.428185	−	1.34783i	0.302772	−	0.953063i
$2$	0.428185	−	1.34783i	0.302772	−	0.953063i
$3$		0			0
$3$		0			0
$4$	−1.63332	−	1.15424i	−0.816658	−	0.577122i
$5$		−	1.93119i		−	0.863655i	−0.901956	−	0.431827i	$-0.857869\pi$
$5$		−	1.93119i		−	0.863655i	0.901956	−	0.431827i	$-0.142131\pi$
$6$		0			0
$7$	−1.83930			−0.695190			−0.347595	−	0.937645i	$-0.613002\pi$
$7$	−1.83930			−0.695190			−0.347595	+	0.937645i	$0.613002\pi$
$8$	−2.25509	+	1.70721i	−0.797295	+	0.603590i
$9$		0			0
$10$	−2.60293	−	0.826906i	−0.823117	−	0.261491i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$		0			0
$13$		−	0.160700i		−	0.0445702i	−0.999752	−	0.0222851i	$-0.992906\pi$
$13$		−	0.160700i		−	0.0445702i	0.999752	−	0.0222851i	$-0.00709416\pi$
$14$	−0.787560	+	2.47907i	−0.210484	+	0.662560i
$15$		0			0
$16$	1.33544	+	3.77049i	0.333860	+	0.942623i
$17$	−5.41442			−1.31319			−0.656595	−	0.754243i	$-0.728004\pi$
$17$	−5.41442			−1.31319			−0.656595	+	0.754243i	$0.728004\pi$
$18$		0			0
$19$		−	2.79744i		−	0.641777i	−0.947117	−	0.320889i	$-0.896018\pi$
$19$		−	2.79744i		−	0.641777i	0.947117	−	0.320889i	$-0.103982\pi$
$20$	−2.22907	+	3.15424i	−0.498434	+	0.705310i
$21$		0			0
$22$	−1.34783	−	0.428185i	−0.287359	−	0.0912893i
$23$	−4.44137			−0.926090			−0.463045	−	0.886335i	$-0.653243\pi$
$23$	−4.44137			−0.926090			−0.463045	+	0.886335i	$0.653243\pi$
$24$		0			0
$25$	1.27050			0.254101
$26$	−0.216597	−	0.0688094i	−0.0424782	−	0.0134946i
$27$		0			0
$28$	3.00416	+	2.12300i	0.567732	+	0.401209i
$29$			8.34948i			1.55046i	0.631679	+	0.775230i	$0.282366\pi$
$29$			8.34948i			1.55046i	−0.631679	+	0.775230i	$0.717634\pi$
$30$		0			0
$31$	−9.05835			−1.62693			−0.813464	−	0.581616i	$-0.802421\pi$
$31$	−9.05835			−1.62693			−0.813464	+	0.581616i	$0.802421\pi$
$32$	5.65381	−	0.185487i	0.999462	−	0.0327898i
$33$		0			0
$34$	−2.31837	+	7.29774i	−0.397597	+	1.25155i
$35$			3.55204i			0.600404i
$36$		0			0
$37$		−	0.602073i		−	0.0989801i	−0.998775	−	0.0494901i	$-0.984240\pi$
$37$		−	0.602073i		−	0.0989801i	0.998775	−	0.0494901i	$-0.0157596\pi$
$38$	−3.77049	−	1.19782i	−0.611654	−	0.194312i
$39$		0			0
$40$	3.29695	+	4.35501i	0.521293	+	0.688588i
$41$	11.7639			1.83721			0.918606	−	0.395174i	$-0.129316\pi$
$41$	11.7639			1.83721			0.918606	+	0.395174i	$0.129316\pi$
$42$		0			0
$43$		−	4.47936i		−	0.683096i	−0.939864	−	0.341548i	$-0.889049\pi$
$43$		−	4.47936i		−	0.683096i	0.939864	−	0.341548i	$-0.110951\pi$
$44$	−1.15424	+	1.63332i	−0.174009	+	0.246232i
$45$		0			0
$46$	−1.90173	+	5.98623i	−0.280394	+	0.882622i
$47$	−6.29558			−0.918304			−0.459152	−	0.888358i	$-0.651847\pi$
$47$	−6.29558			−0.918304			−0.459152	+	0.888358i	$0.651847\pi$
$48$		0			0
$49$	−3.61698			−0.516711
$50$	0.544010	−	1.71243i	0.0769346	−	0.242174i
$51$		0			0
$52$	−0.185487	+	0.262474i	−0.0257225	+	0.0363986i
$53$		−	11.7211i		−	1.61001i	−0.593268	−	0.805005i	$-0.702162\pi$
$53$		−	11.7211i		−	1.61001i	0.593268	−	0.805005i	$-0.297838\pi$
$54$		0			0
$55$	−1.93119			−0.260402
$56$	4.14779	−	3.14007i	0.554271	−	0.419610i
$57$		0			0
$58$	11.2537	+	3.57512i	1.47769	+	0.469436i
$59$			9.63102i			1.25385i	0.779079	+	0.626926i	$0.215687\pi$
$59$			9.63102i			1.25385i	−0.779079	+	0.626926i	$0.784313\pi$
$60$		0			0
$61$		−	3.32912i		−	0.426250i	−0.977025	−	0.213125i	$-0.931636\pi$
$61$		−	3.32912i		−	0.426250i	0.977025	−	0.213125i	$-0.0683641\pi$
$62$	−3.87865	+	12.2092i	−0.492589	+	1.55056i
$63$		0			0
$64$	2.17087	−	7.69983i	0.271359	−	0.962478i
$65$	−0.310343			−0.0384933
$66$		0			0
$67$		−	5.76864i		−	0.704751i	−0.935859	−	0.352376i	$-0.885374\pi$
$67$		−	5.76864i		−	0.704751i	0.935859	−	0.352376i	$-0.114626\pi$
$68$	8.84346	+	6.24956i	1.07243	+	0.757871i
$69$		0			0
$70$	4.78756	+	1.52093i	0.572223	+	0.181786i
$71$	−9.62916			−1.14277			−0.571386	−	0.820682i	$-0.693594\pi$
$71$	−9.62916			−1.14277			−0.571386	+	0.820682i	$0.693594\pi$
$72$		0			0
$73$	−0.681940			−0.0798150			−0.0399075	−	0.999203i	$-0.512706\pi$
$73$	−0.681940			−0.0798150			−0.0399075	+	0.999203i	$0.512706\pi$
$74$	−0.811494	−	0.257798i	−0.0943343	−	0.0299684i
$75$		0			0
$76$	−3.22893	+	4.56911i	−0.370384	+	0.524113i
$77$			1.83930i			0.209608i
$78$		0			0
$79$	5.77867			0.650151			0.325075	−	0.945688i	$-0.394610\pi$
$79$	5.77867			0.650151			0.325075	+	0.945688i	$0.394610\pi$
$80$	7.28154	−	2.57899i	0.814100	−	0.288340i
$81$		0			0
$82$	5.03712	−	15.8558i	0.556257	−	1.75098i
$83$		−	2.92400i		−	0.320951i	−0.987040	−	0.160476i	$-0.948697\pi$
$83$		−	2.92400i		−	0.320951i	0.987040	−	0.160476i	$-0.0513028\pi$
$84$		0			0
$85$			10.4563i			1.13414i
$86$	−6.03743	−	1.91799i	−0.651033	−	0.206822i
$87$		0			0
$88$	1.70721	+	2.25509i	0.181989	+	0.240393i
$89$	−5.74214			−0.608666			−0.304333	−	0.952566i	$-0.598434\pi$
$89$	−5.74214			−0.608666			−0.304333	+	0.952566i	$0.598434\pi$
$90$		0			0
$91$			0.295576i			0.0309848i
$92$	7.25416	+	5.12643i	0.756299	+	0.534467i
$93$		0			0
$94$	−2.69567	+	8.48539i	−0.278037	+	0.875202i
$95$	−5.40240			−0.554274
$96$		0			0
$97$	−5.37829			−0.546082			−0.273041	−	0.962002i	$-0.588030\pi$
$97$	−5.37829			−0.546082			−0.273041	+	0.962002i	$0.588030\pi$
$98$	−1.54873	+	4.87509i	−0.156446	+	0.492458i
$99$		0			0
$100$	−2.07513	−	1.46647i	−0.207513	−	0.146647i
$101$		−	9.31868i		−	0.927244i	−0.886033	−	0.463622i	$-0.846550\pi$
$101$		−	9.31868i		−	0.927244i	0.886033	−	0.463622i	$-0.153450\pi$
$102$		0			0
$103$	1.67860			0.165397			0.0826987	−	0.996575i	$-0.473646\pi$
$103$	1.67860			0.165397			0.0826987	+	0.996575i	$0.473646\pi$
$104$	0.274349	+	0.362394i	0.0269021	+	0.0355356i
$105$		0			0
$106$	−15.7980	−	5.01878i	−1.53444	−	0.487467i
$107$		−	11.2768i		−	1.09017i	−0.838381	−	0.545085i	$-0.816497\pi$
$107$		−	11.2768i		−	1.09017i	0.838381	−	0.545085i	$-0.183503\pi$
$108$		0			0
$109$		−	19.6373i		−	1.88092i	−0.339910	−	0.940458i	$-0.610397\pi$
$109$		−	19.6373i		−	1.88092i	0.339910	−	0.940458i	$-0.389603\pi$
$110$	−0.826906	+	2.60293i	−0.0788424	+	0.248179i
$111$		0			0
$112$	−2.45628	−	6.93506i	−0.232096	−	0.655302i
$113$	12.9156			1.21499			0.607497	−	0.794322i	$-0.292174\pi$
$113$	12.9156			1.21499			0.607497	+	0.794322i	$0.292174\pi$
$114$		0			0
$115$			8.57714i			0.799822i
$116$	9.63734	−	13.6373i	0.894805	−	1.26620i
$117$		0			0
$118$	12.9810	+	4.12385i	1.19500	+	0.379632i
$119$	9.95874			0.912916
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−4.48710	−	1.42548i	−0.406243	−	0.129057i
$123$		0			0
$124$	14.7951	+	10.4555i	1.32864	+	0.938936i
$125$		−	12.1095i		−	1.08311i
$126$		0			0
$127$	1.12716			0.100019			0.0500096	−	0.998749i	$-0.484075\pi$
$127$	1.12716			0.100019			0.0500096	+	0.998749i	$0.484075\pi$
$128$	−9.44856	−	6.22292i	−0.835142	−	0.550034i
$129$		0			0
$130$	−0.132884	+	0.418291i	−0.0116547	+	0.0366865i
$131$		−	10.9554i		−	0.957178i	−0.878039	−	0.478589i	$-0.841148\pi$
$131$		−	10.9554i		−	0.957178i	0.878039	−	0.478589i	$-0.158852\pi$
$132$		0			0
$133$			5.14534i			0.446157i
$134$	−7.77517	−	2.47004i	−0.671672	−	0.213379i
$135$		0			0
$136$	12.2100	−	9.24355i	1.04700	−	0.792628i
$137$	10.1753			0.869338			0.434669	−	0.900590i	$-0.356865\pi$
$137$	10.1753			0.869338			0.434669	+	0.900590i	$0.356865\pi$
$138$		0			0
$139$			18.3347i			1.55513i	0.628802	+	0.777565i	$0.283545\pi$
$139$			18.3347i			1.55513i	−0.628802	+	0.777565i	$0.716455\pi$
$140$	4.09992	−	5.80160i	0.346506	−	0.490325i
$141$		0			0
$142$	−4.12306	+	12.9785i	−0.345999	+	1.08913i
$143$	−0.160700			−0.0134384
$144$		0			0
$145$	16.1244			1.33906
$146$	−0.291996	+	0.919142i	−0.0241658	+	0.0760687i
$147$		0			0
$148$	−0.694939	+	0.983375i	−0.0571236	+	0.0808329i
$149$			8.46892i			0.693801i	0.937902	+	0.346901i	$0.112766\pi$
$149$			8.46892i			0.693801i	−0.937902	+	0.346901i	$0.887234\pi$
$150$		0			0
$151$	−10.0705			−0.819528			−0.409764	−	0.912191i	$-0.634389\pi$
$151$	−10.0705			−0.819528			−0.409764	+	0.912191i	$0.634389\pi$
$152$	4.77582	+	6.30849i	0.387370	+	0.511686i
$153$		0			0
$154$	2.47907	+	0.787560i	0.199769	+	0.0634634i
$155$			17.4934i			1.40510i
$156$		0			0
$157$		−	8.73969i		−	0.697503i	−0.937215	−	0.348752i	$-0.886606\pi$
$157$		−	8.73969i		−	0.697503i	0.937215	−	0.348752i	$-0.113394\pi$
$158$	2.47434	−	7.78869i	0.196848	−	0.619635i
$159$		0			0
$160$	−0.358211	−	10.9186i	−0.0283191	−	0.863190i
$161$	8.16901			0.643809
$162$		0			0
$163$		−	24.4237i		−	1.91301i	−0.291710	−	0.956507i	$-0.594224\pi$
$163$		−	24.4237i		−	1.91301i	0.291710	−	0.956507i	$-0.405776\pi$
$164$	−19.2142	−	13.5784i	−1.50037	−	1.06030i
$165$		0			0
$166$	−3.94107	−	1.25201i	−0.305887	−	0.0971751i
$167$	7.36485			0.569909			0.284954	−	0.958541i	$-0.408022\pi$
$167$	7.36485			0.569909			0.284954	+	0.958541i	$0.408022\pi$
$168$		0			0
$169$	12.9742			0.998013
$170$	14.0933	+	4.47722i	1.08091	+	0.343387i
$171$		0			0
$172$	−5.17027	+	7.31621i	−0.394230	+	0.557855i
$173$			1.38302i			0.105149i	0.998617	+	0.0525747i	$0.0167428\pi$
$173$			1.38302i			0.105149i	−0.998617	+	0.0525747i	$0.983257\pi$
$174$		0			0
$175$	−2.33684			−0.176648
$176$	3.77049	−	1.33544i	0.284211	−	0.100663i
$177$		0			0
$178$	−2.45870	+	7.73946i	−0.184287	+	0.580097i
$179$			9.89679i			0.739720i	0.929087	+	0.369860i	$0.120594\pi$
$179$			9.89679i			0.739720i	−0.929087	+	0.369860i	$0.879406\pi$
$180$		0			0
$181$		−	11.6803i		−	0.868192i	−0.900867	−	0.434096i	$-0.857068\pi$
$181$		−	11.6803i		−	0.868192i	0.900867	−	0.434096i	$-0.142932\pi$
$182$	0.398387	+	0.126561i	0.0295304	+	0.00938133i
$183$		0			0
$184$	10.0157	−	7.58235i	0.738367	−	0.558979i
$185$	−1.16272			−0.0854846
$186$		0			0
$187$			5.41442i			0.395942i
$188$	10.2827	+	7.26663i	0.749940	+	0.529974i
$189$		0			0
$190$	−2.31322	+	7.28154i	−0.167819	+	0.528258i
$191$	−12.0902			−0.874814			−0.437407	−	0.899264i	$-0.644103\pi$
$191$	−12.0902			−0.874814			−0.437407	+	0.899264i	$0.644103\pi$
$192$		0			0
$193$	−13.2620			−0.954622			−0.477311	−	0.878734i	$-0.658388\pi$
$193$	−13.2620			−0.954622			−0.477311	+	0.878734i	$0.658388\pi$
$194$	−2.30290	+	7.24904i	−0.165339	+	0.520451i
$195$		0			0
$196$	5.90766	+	4.17487i	0.421976	+	0.298205i
$197$		−	11.6835i		−	0.832415i	−0.909270	−	0.416208i	$-0.863359\pi$
$197$		−	11.6835i		−	0.832415i	0.909270	−	0.416208i	$-0.136641\pi$
$198$		0			0
$199$	−24.9329			−1.76745			−0.883725	−	0.468007i	$-0.844972\pi$
$199$	−24.9329			−1.76745			−0.883725	+	0.468007i	$0.844972\pi$
$200$	−2.86510	+	2.16901i	−0.202593	+	0.153373i
$201$		0			0
$202$	−12.5600	−	3.99012i	−0.883721	−	0.280744i
$203$		−	15.3572i		−	1.07786i
$204$		0			0
$205$		−	22.7183i		−	1.58672i
$206$	0.718751	−	2.26247i	0.0500777	−	0.157634i
$207$		0			0
$208$	0.605919	−	0.214606i	0.0420129	−	0.0148802i
$209$	−2.79744			−0.193503
$210$		0			0
$211$			5.96245i			0.410472i	0.978713	+	0.205236i	$0.0657962\pi$
$211$			5.96245i			0.410472i	−0.978713	+	0.205236i	$0.934204\pi$
$212$	−13.5290	+	19.1442i	−0.929173	+	1.31483i
$213$		0			0
$214$	−15.1993	−	4.82855i	−1.03900	−	0.330073i
$215$	−8.65049			−0.589959
$216$		0			0
$217$	16.6610			1.13102
$218$	−26.4679	−	8.40841i	−1.79263	−	0.569489i
$219$		0			0
$220$	3.15424	+	2.22907i	0.212659	+	0.150284i
$221$			0.870099i			0.0585292i
$222$		0			0
$223$	1.03801			0.0695103			0.0347552	−	0.999396i	$-0.488935\pi$
$223$	1.03801			0.0695103			0.0347552	+	0.999396i	$0.488935\pi$
$224$	−10.3991	+	0.341167i	−0.694816	+	0.0227952i
$225$		0			0
$226$	5.53024	−	17.4080i	0.367866	−	1.15797i
$227$		−	6.65612i		−	0.441782i	−0.975299	−	0.220891i	$-0.929104\pi$
$227$		−	6.65612i		−	0.441782i	0.975299	−	0.220891i	$-0.0708965\pi$
$228$		0			0
$229$			16.3885i			1.08298i	0.840707	+	0.541491i	$0.182140\pi$
$229$			16.3885i			1.08298i	−0.840707	+	0.541491i	$0.817860\pi$
$230$	11.5606	+	3.67260i	0.762281	+	0.242164i
$231$		0			0
$232$	−14.2543	−	18.8288i	−0.935842	−	1.23617i
$233$	16.0742			1.05306			0.526529	−	0.850157i	$-0.323493\pi$
$233$	16.0742			1.05306			0.526529	+	0.850157i	$0.323493\pi$
$234$		0			0
$235$			12.1580i			0.793098i
$236$	11.1165	−	15.7305i	0.723625	−	1.02397i
$237$		0			0
$238$	4.26418	−	13.4227i	0.276406	−	0.870067i
$239$	2.52062			0.163045			0.0815226	−	0.996671i	$-0.474022\pi$
$239$	2.52062			0.163045			0.0815226	+	0.996671i	$0.474022\pi$
$240$		0			0
$241$	6.11179			0.393695			0.196848	−	0.980434i	$-0.436930\pi$
$241$	6.11179			0.393695			0.196848	+	0.980434i	$0.436930\pi$
$242$	−0.428185	+	1.34783i	−0.0275248	+	0.0866421i
$243$		0			0
$244$	−3.84261	+	5.43750i	−0.245998	+	0.348100i
$245$			6.98507i			0.446260i
$246$		0			0
$247$	−0.449550			−0.0286042
$248$	20.4274	−	15.4645i	1.29714	−	0.981997i
$249$		0			0
$250$	−16.3217	−	5.18512i	−1.03227	−	0.327936i
$251$		−	0.489390i		−	0.0308900i	−0.999881	−	0.0154450i	$-0.995084\pi$
$251$		−	0.489390i		−	0.0308900i	0.999881	−	0.0154450i	$-0.00491649\pi$
$252$		0			0
$253$			4.44137i			0.279227i
$254$	0.482632	−	1.51922i	0.0302830	−	0.0953245i
$255$		0			0
$256$	−12.4332	+	10.0705i	−0.777075	+	0.629408i
$257$	−10.0886			−0.629311			−0.314655	−	0.949206i	$-0.601889\pi$
$257$	−10.0886			−0.629311			−0.314655	+	0.949206i	$0.601889\pi$
$258$		0			0
$259$			1.10739i			0.0688100i
$260$	0.506888	+	0.358211i	0.0314359	+	0.0222153i
$261$		0			0
$262$	−14.7661	−	4.69093i	−0.912251	−	0.289807i
$263$	−3.98466			−0.245705			−0.122852	−	0.992425i	$-0.539204\pi$
$263$	−3.98466			−0.245705			−0.122852	+	0.992425i	$0.539204\pi$
$264$		0			0
$265$	−22.6356			−1.39049
$266$	6.93506	+	2.20315i	0.425216	+	0.135084i
$267$		0			0
$268$	−6.65841	+	9.42200i	−0.406727	+	0.575540i
$269$			2.70069i			0.164664i	0.996605	+	0.0823320i	$0.0262368\pi$
$269$			2.70069i			0.164664i	−0.996605	+	0.0823320i	$0.973763\pi$
$270$		0			0
$271$	22.3611			1.35834			0.679170	−	0.733981i	$-0.262340\pi$
$271$	22.3611			1.35834			0.679170	+	0.733981i	$0.262340\pi$
$272$	−7.23064	−	20.4150i	−0.438422	−	1.23784i
$273$		0			0
$274$	4.35692	−	13.7147i	0.263211	−	0.828534i
$275$		−	1.27050i		−	0.0766142i
$276$		0			0
$277$			31.4865i			1.89184i	0.324396	+	0.945921i	$0.394839\pi$
$277$			31.4865i			1.89184i	−0.324396	+	0.945921i	$0.605161\pi$
$278$	24.7122	+	7.85064i	1.48214	+	0.470850i
$279$		0			0
$280$	−6.06407	−	8.01017i	−0.362398	−	0.478699i
$281$	9.57079			0.570945			0.285473	−	0.958387i	$-0.407849\pi$
$281$	9.57079			0.570945			0.285473	+	0.958387i	$0.407849\pi$
$282$		0			0
$283$		−	16.3997i		−	0.974860i	−0.873162	−	0.487430i	$-0.837934\pi$
$283$		−	16.3997i		−	0.974860i	0.873162	−	0.487430i	$-0.162066\pi$
$284$	15.7275	+	11.1144i	0.933253	+	0.659519i
$285$		0			0
$286$	−0.0688094	+	0.216597i	−0.00406878	+	0.0128077i
$287$	−21.6373			−1.27721
$288$		0			0
$289$	12.3159			0.724467
$290$	6.90424	−	21.7331i	0.405431	−	1.27621i
$291$		0			0
$292$	1.11382	+	0.787125i	0.0651816	+	0.0460630i
$293$			10.0087i			0.584715i	0.956309	+	0.292357i	$0.0944397\pi$
$293$			10.0087i			0.584715i	−0.956309	+	0.292357i	$0.905560\pi$
$294$		0			0
$295$	18.5993			1.08289
$296$	1.02786	+	1.35773i	0.0597434	+	0.0789164i
$297$		0			0
$298$	11.4147	+	3.62626i	0.661236	+	0.210064i
$299$			0.713730i			0.0412761i
$300$		0			0
$301$			8.23888i			0.474881i
$302$	−4.31205	+	13.5734i	−0.248131	+	0.781062i
$303$		0			0
$304$	10.5477	−	3.73582i	0.604954	−	0.214264i
$305$	−6.42916			−0.368133
$306$		0			0
$307$			18.8436i			1.07546i	0.843117	+	0.537731i	$0.180718\pi$
$307$			18.8436i			1.07546i	−0.843117	+	0.537731i	$0.819282\pi$
$308$	2.12300	−	3.00416i	0.120969	−	0.171178i
$309$		0			0
$310$	23.5782	+	7.49040i	1.33915	+	0.425426i
$311$	1.59661			0.0905356			0.0452678	−	0.998975i	$-0.485586\pi$
$311$	1.59661			0.0905356			0.0452678	+	0.998975i	$0.485586\pi$
$312$		0			0
$313$	3.94136			0.222779			0.111389	−	0.993777i	$-0.464470\pi$
$313$	3.94136			0.222779			0.111389	+	0.993777i	$0.464470\pi$
$314$	−11.7797	−	3.74220i	−0.664765	−	0.211185i
$315$		0			0
$316$	−9.43839	−	6.66999i	−0.530951	−	0.375216i
$317$			1.94384i			0.109177i	0.998509	+	0.0545884i	$0.0173847\pi$
$317$			1.94384i			0.109177i	−0.998509	+	0.0545884i	$0.982615\pi$
$318$		0			0
$319$	8.34948			0.467481
$320$	−14.8698	−	4.19236i	−0.831249	−	0.234360i
$321$		0			0
$322$	3.49785	−	11.0105i	0.194927	−	0.613590i
$323$			15.1465i			0.842776i
$324$		0			0
$325$		−	0.204170i		−	0.0113253i
$326$	−32.9191	−	10.4579i	−1.82322	−	0.579208i
$327$		0			0
$328$	−26.5287	+	20.0834i	−1.46480	+	1.10892i
$329$	11.5795			0.638396
$330$		0			0
$331$		−	7.52148i		−	0.413418i	−0.978402	−	0.206709i	$-0.933725\pi$
$331$		−	7.52148i		−	0.413418i	0.978402	−	0.206709i	$-0.0662753\pi$
$332$	−3.37501	+	4.77582i	−0.185228	+	0.262107i
$333$		0			0
$334$	3.15351	−	9.92659i	0.172553	−	0.543159i
$335$	−11.1403			−0.608662
$336$		0			0
$337$	−8.47233			−0.461517			−0.230759	−	0.973011i	$-0.574121\pi$
$337$	−8.47233			−0.461517			−0.230759	+	0.973011i	$0.574121\pi$
$338$	5.55534	−	17.4870i	0.302171	−	0.951170i
$339$		0			0
$340$	12.0691	−	17.0784i	0.654539	−	0.926206i
$341$			9.05835i			0.490537i
$342$		0			0
$343$	19.5278			1.05440
$344$	7.64720	+	10.1014i	0.412310	+	0.544629i
$345$		0			0
$346$	1.86409	+	0.592189i	0.100214	+	0.0318363i
$347$			17.2487i			0.925960i	0.886369	+	0.462980i	$0.153220\pi$
$347$			17.2487i			0.925960i	−0.886369	+	0.462980i	$0.846780\pi$
$348$		0			0
$349$			4.67588i			0.250294i	0.992138	+	0.125147i	$0.0399403\pi$
$349$			4.67588i			0.250294i	−0.992138	+	0.125147i	$0.960060\pi$
$350$	−1.00060	+	3.14967i	−0.0534842	+	0.168357i
$351$		0			0
$352$	−0.185487	−	5.65381i	−0.00988651	−	0.301349i
$353$	5.45055			0.290104			0.145052	−	0.989424i	$-0.453665\pi$
$353$	5.45055			0.290104			0.145052	+	0.989424i	$0.453665\pi$
$354$		0			0
$355$			18.5957i			0.986960i
$356$	9.37873	+	6.62783i	0.497072	+	0.351275i
$357$		0			0
$358$	13.3392	+	4.23765i	0.705000	+	0.223967i
$359$	28.0176			1.47871			0.739357	−	0.673313i	$-0.235129\pi$
$359$	28.0176			1.47871			0.739357	+	0.673313i	$0.235129\pi$
$360$		0			0
$361$	11.1743			0.588122
$362$	−15.7431	−	5.00134i	−0.827441	−	0.262864i
$363$		0			0
$364$	0.341167	−	0.482769i	0.0178820	−	0.0253040i
$365$			1.31696i			0.0689326i
$366$		0			0
$367$	−28.8393			−1.50540			−0.752699	−	0.658365i	$-0.771248\pi$
$367$	−28.8393			−1.50540			−0.752699	+	0.658365i	$0.771248\pi$
$368$	−5.93119	−	16.7462i	−0.309185	−	0.872953i
$369$		0			0
$370$	−0.497858	+	1.56715i	−0.0258824	+	0.0814722i
$371$			21.5585i			1.11926i
$372$		0			0
$373$			1.34080i			0.0694239i	0.999397	+	0.0347119i	$0.0110514\pi$
$373$			1.34080i			0.0694239i	−0.999397	+	0.0347119i	$0.988949\pi$
$374$	7.29774	+	2.31837i	0.377357	+	0.119880i
$375$		0			0
$376$	14.1971	−	10.7479i	0.732159	−	0.554279i
$377$	1.34176			0.0691044
$378$		0			0
$379$		−	8.72245i		−	0.448042i	−0.974584	−	0.224021i	$-0.928082\pi$
$379$		−	8.72245i		−	0.448042i	0.974584	−	0.224021i	$-0.0719184\pi$
$380$	8.82382	+	6.23568i	0.452652	+	0.319884i
$381$		0			0
$382$	−5.17682	+	16.2955i	−0.264869	+	0.833752i
$383$	−7.76275			−0.396658			−0.198329	−	0.980136i	$-0.563551\pi$
$383$	−7.76275			−0.396658			−0.198329	+	0.980136i	$0.563551\pi$
$384$		0			0
$385$	3.55204			0.181029
$386$	−5.67860	+	17.8750i	−0.289033	+	0.909815i
$387$		0			0
$388$	8.78444	+	6.20786i	0.445963	+	0.315156i
$389$			38.5938i			1.95678i	0.206760	+	0.978392i	$0.433708\pi$
$389$			38.5938i			1.95678i	−0.206760	+	0.978392i	$0.566292\pi$
$390$		0			0
$391$	24.0475			1.21613
$392$	8.15661	−	6.17494i	0.411971	−	0.311881i
$393$		0			0
$394$	−15.7474	−	5.00270i	−0.793344	−	0.252032i
$395$		−	11.1597i		−	0.561506i
$396$		0			0
$397$			20.4200i			1.02485i	0.858732	+	0.512426i	$0.171253\pi$
$397$			20.4200i			1.02485i	−0.858732	+	0.512426i	$0.828747\pi$
$398$	−10.6759	+	33.6055i	−0.535135	+	1.68449i
$399$		0			0
$400$	1.69668	+	4.79042i	0.0848341	+	0.239521i
$401$	−4.96247			−0.247814			−0.123907	−	0.992294i	$-0.539542\pi$
$401$	−4.96247			−0.247814			−0.123907	+	0.992294i	$0.539542\pi$
$402$		0			0
$403$			1.45568i			0.0725125i
$404$	−10.7560	+	15.2204i	−0.535133	+	0.757241i
$405$		0			0
$406$	−20.6990	−	6.57572i	−1.02727	−	0.326347i
$407$	−0.602073			−0.0298436
$408$		0			0
$409$	15.3418			0.758601			0.379301	−	0.925273i	$-0.376165\pi$
$409$	15.3418			0.758601			0.379301	+	0.925273i	$0.376165\pi$
$410$	−30.6206	−	9.72764i	−1.51224	−	0.480414i
$411$		0			0
$412$	−2.74168	−	1.93751i	−0.135073	−	0.0954544i
$413$		−	17.7143i		−	0.871665i
$414$		0			0
$415$	−5.64681			−0.277191
$416$	−0.0298079	−	0.908569i	−0.00146145	−	0.0445463i
$417$		0			0
$418$	−1.19782	+	3.77049i	−0.0585874	+	0.184421i
$419$		−	12.0628i		−	0.589306i	−0.955604	−	0.294653i	$-0.904796\pi$
$419$		−	12.0628i		−	0.589306i	0.955604	−	0.294653i	$-0.0952041\pi$
$420$		0			0
$421$			14.3042i			0.697143i	0.937282	+	0.348572i	$0.113333\pi$
$421$			14.3042i			0.697143i	−0.937282	+	0.348572i	$0.886667\pi$
$422$	8.03640	+	2.55303i	0.391206	+	0.124280i
$423$		0			0
$424$	20.0103	+	26.4320i	0.971786	+	1.28365i
$425$	−6.87904			−0.333682
$426$		0			0
$427$			6.12325i			0.296325i
$428$	−13.0162	+	18.4186i	−0.629161	+	0.890296i
$429$		0			0
$430$	−3.70401	+	11.6594i	−0.178623	+	0.562268i
$431$	18.9520			0.912885			0.456443	−	0.889753i	$-0.349123\pi$
$431$	18.9520			0.912885			0.456443	+	0.889753i	$0.349123\pi$
$432$		0			0
$433$	−16.4130			−0.788760			−0.394380	−	0.918948i	$-0.629041\pi$
$433$	−16.4130			−0.788760			−0.394380	+	0.918948i	$0.629041\pi$
$434$	7.13399	−	22.4563i	0.342443	−	1.07794i
$435$		0			0
$436$	−22.6663	+	32.0740i	−1.08552	+	1.53606i
$437$			12.4245i			0.594344i
$438$		0			0
$439$	−24.5482			−1.17162			−0.585810	−	0.810448i	$-0.699224\pi$
$439$	−24.5482			−1.17162			−0.585810	+	0.810448i	$0.699224\pi$
$440$	4.35501	−	3.29695i	0.207617	−	0.157176i
$441$		0			0
$442$	1.17275	+	0.372563i	0.0557820	+	0.0177210i
$443$			11.0679i			0.525854i	0.964816	+	0.262927i	$0.0846878\pi$
$443$			11.0679i			0.525854i	−0.964816	+	0.262927i	$0.915312\pi$
$444$		0			0
$445$			11.0892i			0.525677i
$446$	0.444460	−	1.39907i	0.0210458	−	0.0662477i
$447$		0			0
$448$	−3.99288	+	14.1623i	−0.188646	+	0.669105i
$449$	−26.6647			−1.25838			−0.629192	−	0.777250i	$-0.716614\pi$
$449$	−26.6647			−1.25838			−0.629192	+	0.777250i	$0.716614\pi$
$450$		0			0
$451$		−	11.7639i		−	0.553940i
$452$	−21.0952	−	14.9077i	−0.992234	−	0.701200i
$453$		0			0
$454$	−8.97134	−	2.85005i	−0.421046	−	0.133759i
$455$	0.570814			0.0267602
$456$		0			0
$457$	3.28296			0.153570			0.0767851	−	0.997048i	$-0.475534\pi$
$457$	3.28296			0.153570			0.0767851	+	0.997048i	$0.475534\pi$
$458$	22.0890	+	7.01730i	1.03215	+	0.327897i
$459$		0			0
$460$	9.90011	−	14.0092i	0.461595	−	0.653181i
$461$		−	3.17514i		−	0.147881i	−0.997263	−	0.0739406i	$-0.976442\pi$
$461$		−	3.17514i		−	0.147881i	0.997263	−	0.0739406i	$-0.0235575\pi$
$462$		0			0
$463$	21.8696			1.01637			0.508184	−	0.861248i	$-0.330317\pi$
$463$	21.8696			1.01637			0.508184	+	0.861248i	$0.330317\pi$
$464$	−31.4816	+	11.1502i	−1.46150	+	0.517637i
$465$		0			0
$466$	6.88274	−	21.6654i	0.318837	−	1.00363i
$467$		−	4.95735i		−	0.229399i	−0.993400	−	0.114699i	$-0.963410\pi$
$467$		−	4.95735i		−	0.229399i	0.993400	−	0.114699i	$-0.0365905\pi$
$468$		0			0
$469$			10.6103i			0.489936i
$470$	16.3869	+	5.20585i	0.755872	+	0.240128i
$471$		0			0
$472$	−16.4422	−	21.7188i	−0.756812	−	0.999690i
$473$	−4.47936			−0.205961
$474$		0			0
$475$		−	3.55416i		−	0.163076i
$476$	−16.2658	−	11.4948i	−0.745540	−	0.526864i
$477$		0			0
$478$	1.07929	−	3.39737i	0.0493656	−	0.155392i
$479$	35.5423			1.62397			0.811984	−	0.583680i	$-0.198388\pi$
$479$	35.5423			1.62397			0.811984	+	0.583680i	$0.198388\pi$
$480$		0			0
$481$	−0.0967532			−0.00441157
$482$	2.61698	−	8.23769i	0.119200	−	0.375216i
$483$		0			0
$484$	1.63332	+	1.15424i	0.0742416	+	0.0524656i
$485$			10.3865i			0.471627i
$486$		0			0
$487$	10.1547			0.460153			0.230076	−	0.973173i	$-0.426102\pi$
$487$	10.1547			0.460153			0.230076	+	0.973173i	$0.426102\pi$
$488$	5.68350	+	7.50746i	0.257280	+	0.339847i
$489$		0			0
$490$	9.41472	+	2.99090i	0.425314	+	0.135115i
$491$		−	0.367564i		−	0.0165879i	−0.999966	−	0.00829395i	$-0.997360\pi$
$491$		−	0.367564i		−	0.0165879i	0.999966	−	0.00829395i	$-0.00264008\pi$
$492$		0			0
$493$		−	45.2076i		−	2.03605i
$494$	−0.192490	+	0.605919i	−0.00866055	+	0.0272616i
$495$		0			0
$496$	−12.0969	−	34.1544i	−0.543166	−	1.53358i
$497$	17.7109			0.794443
$498$		0			0
$499$			31.1824i			1.39591i	0.716140	+	0.697957i	$0.245907\pi$
$499$			31.1824i			1.39591i	−0.716140	+	0.697957i	$0.754093\pi$
$500$	−13.9774	+	19.7787i	−0.625087	+	0.884530i
$501$		0			0
$502$	−0.659617	−	0.209549i	−0.0294401	−	0.00935264i
$503$	−20.2004			−0.900692			−0.450346	−	0.892854i	$-0.648699\pi$
$503$	−20.2004			−0.900692			−0.450346	+	0.892854i	$0.648699\pi$
$504$		0			0
$505$	−17.9962			−0.800818
$506$	5.98623	+	1.90173i	0.266121	+	0.0845421i
$507$		0			0
$508$	−1.84101	−	1.30102i	−0.0816814	−	0.0577232i
$509$		−	22.0209i		−	0.976058i	−0.872827	−	0.488029i	$-0.837716\pi$
$509$		−	22.0209i		−	0.976058i	0.872827	−	0.488029i	$-0.162284\pi$
$510$		0			0
$511$	1.25429			0.0554866
$512$	8.24971	+	21.0699i	0.364589	+	0.931168i
$513$		0			0
$514$	−4.31979	+	13.5978i	−0.190538	+	0.599773i
$515$		−	3.24170i		−	0.142846i
$516$		0			0
$517$			6.29558i			0.276879i
$518$	1.49258	+	0.474168i	0.0655802	+	0.0208338i
$519$		0			0
$520$	0.699851	−	0.529820i	0.0306905	−	0.0232342i
$521$	−36.1120			−1.58209			−0.791047	−	0.611755i	$-0.790464\pi$
$521$	−36.1120			−1.58209			−0.791047	+	0.611755i	$0.790464\pi$
$522$		0			0
$523$			34.5388i			1.51028i	0.655565	+	0.755139i	$0.272431\pi$
$523$			34.5388i			1.51028i	−0.655565	+	0.755139i	$0.727569\pi$
$524$	−12.6452	+	17.8936i	−0.552408	+	0.781687i
$525$		0			0
$526$	−1.70617	+	5.37066i	−0.0743926	+	0.234172i
$527$	49.0457			2.13646
$528$		0			0
$529$	−3.27421			−0.142357
$530$	−9.69221	+	30.5090i	−0.421003	+	1.32523i
$531$		0			0
$532$	5.93897	−	8.40396i	0.257487	−	0.364358i
$533$		−	1.89046i		−	0.0818850i
$534$		0			0
$535$	−21.7777			−0.941530
$536$	9.84827	+	13.0088i	0.425381	+	0.561894i
$537$		0			0
$538$	3.64008	+	1.15639i	0.156935	+	0.0498557i
$539$			3.61698i			0.155794i
$540$		0			0
$541$		−	6.14527i		−	0.264206i	−0.991236	−	0.132103i	$-0.957827\pi$
$541$		−	6.14527i		−	0.264206i	0.991236	−	0.132103i	$-0.0421729\pi$
$542$	9.57468	−	30.1391i	0.411268	−	1.29458i
$543$		0			0
$544$	−30.6121	+	1.00431i	−1.31248	+	0.0430593i
$545$	−37.9234			−1.62446
$546$		0			0
$547$		−	17.3331i		−	0.741110i	−0.928811	−	0.370555i	$-0.879168\pi$
$547$		−	17.3331i		−	0.741110i	0.928811	−	0.370555i	$-0.120832\pi$
$548$	−16.6195	−	11.7448i	−0.709952	−	0.501714i
$549$		0			0
$550$	−1.71243	−	0.544010i	−0.0730182	−	0.0231967i
$551$	23.3572			0.995050
$552$		0			0
$553$	−10.6287			−0.451978
$554$	42.4386	+	13.4821i	1.80305	+	0.572798i
$555$		0			0
$556$	21.1627	−	29.9464i	0.897500	−	1.27001i
$557$		−	38.1630i		−	1.61702i	−0.588485	−	0.808508i	$-0.700275\pi$
$557$		−	38.1630i		−	1.61702i	0.588485	−	0.808508i	$-0.299725\pi$
$558$		0			0
$559$	−0.719834			−0.0304457
$560$	−13.3929	+	4.74354i	−0.565954	+	0.200451i
$561$		0			0
$562$	4.09806	−	12.8998i	0.172866	−	0.544147i
$563$		−	33.2131i		−	1.39976i	−0.714258	−	0.699882i	$-0.753236\pi$
$563$		−	33.2131i		−	1.39976i	0.714258	−	0.699882i	$-0.246764\pi$
$564$		0			0
$565$		−	24.9424i		−	1.04934i
$566$	−22.1041	−	7.02209i	−0.929103	−	0.295160i
$567$		0			0
$568$	21.7146	−	16.4390i	0.911126	−	0.689765i
$569$	−8.23504			−0.345231			−0.172615	−	0.984989i	$-0.555222\pi$
$569$	−8.23504			−0.345231			−0.172615	+	0.984989i	$0.555222\pi$
$570$		0			0
$571$		−	32.7618i		−	1.37104i	−0.728055	−	0.685518i	$-0.759576\pi$
$571$		−	32.7618i		−	1.37104i	0.728055	−	0.685518i	$-0.240424\pi$
$572$	0.262474	+	0.185487i	0.0109746	+	0.00775562i
$573$		0			0
$574$	−9.26478	+	29.1636i	−0.386704	+	1.21726i
$575$	−5.64278			−0.235320
$576$		0			0
$577$	−6.50814			−0.270937			−0.135469	−	0.990782i	$-0.543254\pi$
$577$	−6.50814			−0.270937			−0.135469	+	0.990782i	$0.543254\pi$
$578$	5.27350	−	16.5998i	0.219349	−	0.690463i
$579$		0			0
$580$	−26.3363	−	18.6115i	−1.09356	−	0.772802i
$581$			5.37812i			0.223122i
$582$		0			0
$583$	−11.7211			−0.485436
$584$	1.53784	−	1.16421i	0.0636361	−	0.0481755i
$585$		0			0
$586$	13.4901	+	4.28558i	0.557270	+	0.177035i
$587$			9.95325i			0.410815i	0.978677	+	0.205407i	$0.0658519\pi$
$587$			9.95325i			0.410815i	−0.978677	+	0.205407i	$0.934148\pi$
$588$		0			0
$589$			25.3402i			1.04413i
$590$	7.96395	−	25.0688i	0.327871	−	1.03207i
$591$		0			0
$592$	2.27011	−	0.804032i	0.0933009	−	0.0330455i
$593$	−8.80877			−0.361733			−0.180867	−	0.983508i	$-0.557890\pi$
$593$	−8.80877			−0.361733			−0.180867	+	0.983508i	$0.557890\pi$
$594$		0			0
$595$		−	19.2322i		−	0.788444i
$596$	9.77520	−	13.8324i	0.400408	−	0.566598i
$597$		0			0
$598$	0.961990	+	0.305608i	0.0393387	+	0.0124972i
$599$	−31.9145			−1.30399			−0.651996	−	0.758223i	$-0.726068\pi$
$599$	−31.9145			−1.30399			−0.651996	+	0.758223i	$0.726068\pi$
$600$		0			0
$601$	11.0314			0.449981			0.224991	−	0.974361i	$-0.427765\pi$
$601$	11.0314			0.449981			0.224991	+	0.974361i	$0.427765\pi$
$602$	11.1046	+	3.52776i	0.452592	+	0.143781i
$603$		0			0
$604$	16.4484	+	11.6239i	0.669274	+	0.472968i
$605$			1.93119i			0.0785141i
$606$		0			0
$607$	12.2159			0.495828			0.247914	−	0.968782i	$-0.420255\pi$
$607$	12.2159			0.495828			0.247914	+	0.968782i	$0.420255\pi$
$608$	−0.518890	−	15.8162i	−0.0210438	−	0.641432i
$609$		0			0
$610$	−2.75287	+	8.66545i	−0.111460	+	0.350854i
$611$			1.01170i			0.0409290i
$612$		0			0
$613$			3.57482i			0.144386i	0.997391	+	0.0721928i	$0.0229997\pi$
$613$			3.57482i			0.144386i	−0.997391	+	0.0721928i	$0.977000\pi$
$614$	25.3981	+	8.06854i	1.02498	+	0.325620i
$615$		0			0
$616$	−3.14007	−	4.14779i	−0.126517	−	0.167119i
$617$	−30.5057			−1.22811			−0.614057	−	0.789262i	$-0.710463\pi$
$617$	−30.5057			−1.22811			−0.614057	+	0.789262i	$0.710463\pi$
$618$		0			0
$619$			10.6118i			0.426526i	0.976995	+	0.213263i	$0.0684091\pi$
$619$			10.6118i			0.426526i	−0.976995	+	0.213263i	$0.931591\pi$
$620$	20.1917	−	28.5722i	0.810916	−	1.14749i
$621$		0			0
$622$	0.683645	−	2.15197i	0.0274117	−	0.0862861i
$623$	10.5615			0.423138
$624$		0			0
$625$	−17.0333			−0.681332
$626$	1.68763	−	5.31230i	0.0674513	−	0.212322i
$627$		0			0
$628$	−10.0877	+	14.2747i	−0.402545	+	0.569622i
$629$			3.25987i			0.129980i
$630$		0			0
$631$	4.29235			0.170876			0.0854379	−	0.996343i	$-0.472771\pi$
$631$	4.29235			0.170876			0.0854379	+	0.996343i	$0.472771\pi$
$632$	−13.0314	+	9.86540i	−0.518362	+	0.392424i
$633$		0			0
$634$	2.61997	+	0.832321i	0.104052	+	0.0330557i
$635$		−	2.17676i		−	0.0863820i
$636$		0			0
$637$			0.581249i			0.0230299i
$638$	3.57512	−	11.2537i	0.141540	−	0.445539i
$639$		0			0
$640$	−12.0176	+	18.2470i	−0.475039	+	0.721275i
$641$	26.5606			1.04908			0.524540	−	0.851386i	$-0.324237\pi$
$641$	26.5606			1.04908			0.524540	+	0.851386i	$0.324237\pi$
$642$		0			0
$643$		−	28.0614i		−	1.10663i	−0.832971	−	0.553317i	$-0.813362\pi$
$643$		−	28.0614i		−	1.10663i	0.832971	−	0.553317i	$-0.186638\pi$
$644$	−13.3426	−	9.42904i	−0.525771	−	0.371556i
$645$		0			0
$646$	20.4150	+	6.48551i	0.803218	+	0.255169i
$647$	32.2983			1.26978			0.634888	−	0.772604i	$-0.281046\pi$
$647$	32.2983			1.26978			0.634888	+	0.772604i	$0.281046\pi$
$648$		0			0
$649$	9.63102			0.378050
$650$	−0.275188	−	0.0874225i	−0.0107937	−	0.00342899i
$651$		0			0
$652$	−28.1909	+	39.8917i	−1.10404	+	1.56228i
$653$		−	32.9200i		−	1.28826i	−0.764916	−	0.644130i	$-0.777220\pi$
$653$		−	32.9200i		−	1.28826i	0.764916	−	0.644130i	$-0.222780\pi$
$654$		0			0
$655$	−21.1570			−0.826671
$656$	15.7100	+	44.3557i	0.613372	+	1.73180i
$657$		0			0
$658$	4.95814	−	15.6072i	0.193289	−	0.608431i
$659$			3.99602i			0.155663i	0.996967	+	0.0778314i	$0.0247996\pi$
$659$			3.99602i			0.155663i	−0.996967	+	0.0778314i	$0.975200\pi$
$660$		0			0
$661$		−	19.2377i		−	0.748258i	−0.927377	−	0.374129i	$-0.877942\pi$
$661$		−	19.2377i		−	0.748258i	0.927377	−	0.374129i	$-0.122058\pi$
$662$	−10.1377	−	3.22058i	−0.394013	−	0.125171i
$663$		0			0
$664$	4.99189	+	6.59390i	0.193723	+	0.255893i
$665$	9.93663			0.385326
$666$		0			0
$667$		−	37.0832i		−	1.43587i
$668$	−12.0291	−	8.50083i	−0.465421	−	0.328907i
$669$		0			0
$670$	−4.77012	+	15.0153i	−0.184286	+	0.580093i
$671$	−3.32912			−0.128519
$672$		0			0
$673$	5.41202			0.208618			0.104309	−	0.994545i	$-0.466737\pi$
$673$	5.41202			0.208618			0.104309	+	0.994545i	$0.466737\pi$
$674$	−3.62772	+	11.4193i	−0.139735	+	0.439855i
$675$		0			0
$676$	−21.1909	−	14.9754i	−0.815036	−	0.575976i
$677$			41.1062i			1.57984i	0.613209	+	0.789921i	$0.289878\pi$
$677$			41.1062i			1.57984i	−0.613209	+	0.789921i	$0.710122\pi$
$678$		0			0
$679$	9.89229			0.379631
$680$	−17.8511	−	23.5799i	−0.684557	−	0.904246i
$681$		0			0
$682$	12.2092	+	3.87865i	0.467513	+	0.148521i
$683$		−	35.8592i		−	1.37211i	−0.727548	−	0.686057i	$-0.759340\pi$
$683$		−	35.8592i		−	1.37211i	0.727548	−	0.686057i	$-0.240660\pi$
$684$		0			0
$685$		−	19.6505i		−	0.750808i
$686$	8.36151	−	26.3202i	0.319244	−	1.00491i
$687$		0			0
$688$	16.8894	−	5.98192i	0.643901	−	0.228058i
$689$	−1.88358			−0.0717585
$690$		0			0
$691$			45.1462i			1.71744i	0.512444	+	0.858721i	$0.328740\pi$
$691$			45.1462i			1.71744i	−0.512444	+	0.858721i	$0.671260\pi$
$692$	1.59635	−	2.25891i	0.0606840	−	0.0858710i
$693$		0			0
$694$	23.2484	+	7.38564i	0.882498	+	0.280355i
$695$	35.4078			1.34310
$696$		0			0
$697$	−63.6947			−2.41261
$698$	6.30231	+	2.00214i	0.238546	+	0.0757821i
$699$		0			0
$700$	3.81679	+	2.69728i	0.144261	+	0.101948i
$701$			18.5867i			0.702009i	0.936374	+	0.351005i	$0.114160\pi$
$701$			18.5867i			0.702009i	−0.936374	+	0.351005i	$0.885840\pi$
$702$		0			0
$703$	−1.68426			−0.0635232
$704$	−7.69983	−	2.17087i	−0.290198	−	0.0818177i
$705$		0			0
$706$	2.33384	−	7.34644i	0.0878353	−	0.276487i
$707$			17.1399i			0.644610i
$708$		0			0
$709$			27.2703i			1.02416i	0.858938	+	0.512079i	$0.171124\pi$
$709$			27.2703i			1.02416i	−0.858938	+	0.512079i	$0.828876\pi$
$710$	25.0640	+	7.96241i	0.940635	+	0.298824i
$711$		0			0
$712$	12.9491	−	9.80304i	0.485286	−	0.367385i
$713$	40.2315			1.50668
$714$		0			0
$715$			0.310343i			0.0116062i
$716$	11.4233	−	16.1646i	0.426909	−	0.604099i
$717$		0			0
$718$	11.9967	−	37.7631i	0.447714	−	1.40931i
$719$	−34.1800			−1.27470			−0.637349	−	0.770575i	$-0.719969\pi$
$719$	−34.1800			−1.27470			−0.637349	+	0.770575i	$0.719969\pi$
$720$		0			0
$721$	−3.08745			−0.114983
$722$	4.78467	−	15.0611i	0.178067	−	0.560517i
$723$		0			0
$724$	−13.4819	+	19.0777i	−0.501053	+	0.709016i
$725$			10.6080i			0.393973i
$726$		0			0
$727$	−25.0380			−0.928608			−0.464304	−	0.885676i	$-0.653696\pi$
$727$	−25.0380			−0.928608			−0.464304	+	0.885676i	$0.653696\pi$
$728$	−0.504610	−	0.666551i	−0.0187021	−	0.0247040i
$729$		0			0
$730$	1.77504	+	0.563900i	0.0656971	+	0.0208709i
$731$			24.2531i			0.897034i
$732$		0			0
$733$		−	17.2695i		−	0.637862i	−0.947778	−	0.318931i	$-0.896676\pi$
$733$		−	17.2695i		−	0.637862i	0.947778	−	0.318931i	$-0.103324\pi$
$734$	−12.3485	+	38.8706i	−0.455793	+	1.43474i
$735$		0			0
$736$	−25.1107	+	0.823818i	−0.925592	+	0.0303663i
$737$	−5.76864			−0.212490
$738$		0			0
$739$		−	17.2687i		−	0.635240i	−0.948218	−	0.317620i	$-0.897116\pi$
$739$		−	17.2687i		−	0.635240i	0.948218	−	0.317620i	$-0.102884\pi$
$740$	1.89908	+	1.34206i	0.0698117	+	0.0493351i
$741$		0			0
$742$	29.0573	+	9.23103i	1.06673	+	0.338882i
$743$	−34.6374			−1.27072			−0.635361	−	0.772215i	$-0.719149\pi$
$743$	−34.6374			−1.27072			−0.635361	+	0.772215i	$0.719149\pi$
$744$		0			0
$745$	16.3551			0.599205
$746$	1.80717	+	0.574109i	0.0661653	+	0.0210196i
$747$		0			0
$748$	6.24956	−	8.84346i	0.228507	−	0.323349i
$749$			20.7414i			0.757875i
$750$		0			0
$751$	51.5526			1.88118			0.940591	−	0.339543i	$-0.110272\pi$
$751$	51.5526			1.88118			0.940591	+	0.339543i	$0.110272\pi$
$752$	−8.40737	−	23.7374i	−0.306585	−	0.865614i
$753$		0			0
$754$	0.574523	−	1.80848i	0.0209229	−	0.0658608i
$755$			19.4481i			0.707790i
$756$		0			0
$757$		−	32.6049i		−	1.18504i	−0.805554	−	0.592522i	$-0.798132\pi$
$757$		−	32.6049i		−	1.18504i	0.805554	−	0.592522i	$-0.201868\pi$
$758$	−11.7564	−	3.73482i	−0.427012	−	0.135655i
$759$		0			0
$760$	12.1829	−	9.22302i	0.441920	−	0.334554i
$761$	2.79094			0.101172			0.0505858	−	0.998720i	$-0.483891\pi$
$761$	2.79094			0.101172			0.0505858	+	0.998720i	$0.483891\pi$
$762$		0			0
$763$			36.1190i			1.30759i
$764$	19.7471	+	13.9550i	0.714423	+	0.504874i
$765$		0			0
$766$	−3.32389	+	10.4629i	−0.120097	+	0.378040i
$767$	1.54771			0.0558845
$768$		0			0
$769$	23.1604			0.835187			0.417593	−	0.908634i	$-0.362874\pi$
$769$	23.1604			0.835187			0.417593	+	0.908634i	$0.362874\pi$
$770$	1.52093	−	4.78756i	0.0548105	−	0.172532i
$771$		0			0
$772$	21.6611	+	15.3076i	0.779600	+	0.550933i
$773$		−	20.7913i		−	0.747811i	−0.927467	−	0.373905i	$-0.878018\pi$
$773$		−	20.7913i		−	0.747811i	0.927467	−	0.373905i	$-0.121982\pi$
$774$		0			0
$775$	−11.5087			−0.413403
$776$	12.1285	−	9.18187i	0.435389	−	0.329610i
$777$		0			0
$778$	52.0181	+	16.5253i	1.86494	+	0.592460i
$779$		−	32.9088i		−	1.17908i
$780$		0			0
$781$			9.62916i			0.344559i
$782$	10.2968	−	32.4120i	0.368211	−	1.15905i
$783$		0			0
$784$	−4.83026	−	13.6378i	−0.172509	−	0.487063i
$785$	−16.8780			−0.602402
$786$		0			0
$787$		−	40.3874i		−	1.43965i	−0.694153	−	0.719827i	$-0.744221\pi$
$787$		−	40.3874i		−	1.43965i	0.694153	−	0.719827i	$-0.255779\pi$
$788$	−13.4856	+	19.0828i	−0.480405	+	0.679798i
$789$		0			0
$790$	−15.0414	−	4.77842i	−0.535150	−	0.170008i
$791$	−23.7556			−0.844651
$792$		0			0
$793$	−0.534990			−0.0189981
$794$	27.5228	+	8.74354i	0.976748	+	0.310297i
$795$		0			0
$796$	40.7234	+	28.7787i	1.44340	+	1.02003i
$797$		−	31.1190i		−	1.10229i	−0.834409	−	0.551145i	$-0.814191\pi$
$797$		−	31.1190i		−	1.10229i	0.834409	−	0.551145i	$-0.185809\pi$
$798$		0			0
$799$	34.0869			1.20591
$800$	7.18318	−	0.235662i	0.253964	−	0.00833192i
$801$		0			0
$802$	−2.12486	+	6.68859i	−0.0750313	+	0.236182i
$803$			0.681940i			0.0240651i
$804$		0			0
$805$		−	15.7759i		−	0.556028i
$806$	1.96201	+	0.623299i	0.0691090	+	0.0219548i
$807$		0			0
$808$	15.9089	+	21.0145i	0.559675	+	0.739287i
$809$	−23.6252			−0.830619			−0.415309	−	0.909680i	$-0.636327\pi$
$809$	−23.6252			−0.830619			−0.415309	+	0.909680i	$0.636327\pi$
$810$		0			0
$811$		−	26.2978i		−	0.923442i	−0.887025	−	0.461721i	$-0.847232\pi$
$811$		−	26.2978i		−	0.923442i	0.887025	−	0.461721i	$-0.152768\pi$
$812$	−17.7260	+	25.0832i	−0.622059	+	0.880246i
$813$		0			0
$814$	−0.257798	+	0.811494i	−0.00903582	+	0.0284429i
$815$	−47.1669			−1.65218
$816$		0			0
$817$	−12.5307			−0.438395
$818$	6.56911	−	20.6782i	0.229683	−	0.722995i
$819$		0			0
$820$	−26.2225	+	37.1062i	−0.915730	+	1.29581i
$821$		−	55.6264i		−	1.94137i	−0.240348	−	0.970687i	$-0.577262\pi$
$821$		−	55.6264i		−	1.94137i	0.240348	−	0.970687i	$-0.422738\pi$
$822$		0			0
$823$	28.0971			0.979402			0.489701	−	0.871890i	$-0.337106\pi$
$823$	28.0971			0.979402			0.489701	+	0.871890i	$0.337106\pi$
$824$	−3.78539	+	2.86572i	−0.131870	+	0.0998321i
$825$		0			0
$826$	−23.8760	−	7.58500i	−0.830752	−	0.263916i
$827$		−	38.5555i		−	1.34070i	−0.742043	−	0.670352i	$-0.766143\pi$
$827$		−	38.5555i		−	1.34070i	0.742043	−	0.670352i	$-0.233857\pi$
$828$		0			0
$829$		−	44.4581i		−	1.54409i	−0.635566	−	0.772047i	$-0.719233\pi$
$829$		−	44.4581i		−	1.54409i	0.635566	−	0.772047i	$-0.280767\pi$
$830$	−2.41788	+	7.61096i	−0.0839257	+	0.264180i
$831$		0			0
$832$	−1.23736	−	0.348859i	−0.0428979	−	0.0120945i
$833$	19.5838			0.678539
$834$		0			0
$835$		−	14.2229i		−	0.492204i
$836$	4.56911	+	3.22893i	0.158026	+	0.111675i
$837$		0			0
$838$	−16.2586	−	5.16510i	−0.561646	−	0.178426i
$839$	39.7880			1.37364			0.686818	−	0.726830i	$-0.259007\pi$
$839$	39.7880			1.37364			0.686818	+	0.726830i	$0.259007\pi$
$840$		0			0
$841$	−40.7138			−1.40393
$842$	19.2797	+	6.12483i	0.664422	+	0.211076i
$843$		0			0
$844$	6.88212	−	9.73856i	0.236892	−	0.335215i
$845$		−	25.0556i		−	0.861939i
$846$		0			0
$847$	1.83930			0.0631991
$848$	44.1941	−	15.6528i	1.51763	−	0.537518i
$849$		0			0
$850$	−2.94550	+	9.27180i	−0.101030	+	0.318020i
$851$			2.67403i			0.0916645i
$852$		0			0
$853$			4.19523i			0.143642i	0.997418	+	0.0718210i	$0.0228810\pi$
$853$			4.19523i			0.143642i	−0.997418	+	0.0718210i	$0.977119\pi$
$854$	8.25312	+	2.62188i	0.282416	+	0.0897189i
$855$		0			0
$856$	19.2519	+	25.4302i	0.658015	+	0.869187i
$857$	−43.4106			−1.48288			−0.741438	−	0.671021i	$-0.765856\pi$
$857$	−43.4106			−1.48288			−0.741438	+	0.671021i	$0.765856\pi$
$858$		0			0
$859$		−	31.7672i		−	1.08388i	−0.840416	−	0.541941i	$-0.817690\pi$
$859$		−	31.7672i		−	1.08388i	0.840416	−	0.541941i	$-0.182310\pi$
$860$	14.1290	+	9.98478i	0.481794	+	0.340478i
$861$		0			0
$862$	8.11495	−	25.5441i	0.276396	−	0.870037i
$863$	51.0969			1.73936			0.869679	−	0.493618i	$-0.164326\pi$
$863$	51.0969			1.73936			0.869679	+	0.493618i	$0.164326\pi$
$864$		0			0
$865$	2.67088			0.0908127
$866$	−7.02781	+	22.1220i	−0.238815	+	0.751738i
$867$		0			0
$868$	−27.2127	−	19.2309i	−0.923659	−	0.652739i
$869$		−	5.77867i		−	0.196028i
$870$		0			0
$871$	−0.927021			−0.0314109
$872$	33.5251	+	44.2840i	1.13530	+	1.49964i
$873$		0			0
$874$	16.7462	+	5.31997i	0.566447	+	0.179951i
$875$			22.2731i			0.752967i
$876$		0			0
$877$			45.8912i			1.54963i	0.632185	+	0.774817i	$0.282158\pi$
$877$			45.8912i			1.54963i	−0.632185	+	0.774817i	$0.717842\pi$
$878$	−10.5111	+	33.0869i	−0.354734	+	1.11663i
$879$		0			0
$880$	−2.57899	−	7.28154i	−0.0869378	−	0.245461i
$881$	19.3333			0.651356			0.325678	−	0.945481i	$-0.394407\pi$
$881$	19.3333			0.651356			0.325678	+	0.945481i	$0.394407\pi$
$882$		0			0
$883$			22.5862i			0.760088i	0.924968	+	0.380044i	$0.124091\pi$
$883$			22.5862i			0.760088i	−0.924968	+	0.380044i	$0.875909\pi$
$884$	1.00431	−	1.42115i	0.0337785	−	0.0477983i
$885$		0			0
$886$	14.9178	+	4.73912i	0.501172	+	0.159214i
$887$	34.2005			1.14834			0.574170	−	0.818736i	$-0.305325\pi$
$887$	34.2005			1.14834			0.574170	+	0.818736i	$0.305325\pi$
$888$		0			0
$889$	−2.07318			−0.0695323
$890$	14.9464	+	4.74821i	0.501003	+	0.159160i
$891$		0			0
$892$	−1.69540	−	1.19812i	−0.0567662	−	0.0401159i
$893$			17.6115i			0.589347i
$894$		0			0
$895$	19.1126			0.638863
$896$	17.3787	+	11.4458i	0.580583	+	0.382378i
$897$		0			0
$898$	−11.4174	+	35.9396i	−0.381004	+	1.19932i
$899$		−	75.6325i		−	2.52249i
$900$		0			0
$901$			63.4627i			2.11425i
$902$	−15.8558	−	5.03712i	−0.527940	−	0.167718i
$903$		0			0
$904$	−29.1258	+	22.0496i	−0.968708	+	0.733358i
$905$	−22.5569			−0.749818
$906$		0			0
$907$		−	17.2305i		−	0.572129i	−0.958210	−	0.286065i	$-0.907653\pi$
$907$		−	17.2305i		−	0.572129i	0.958210	−	0.286065i	$-0.0923472\pi$
$908$	−7.68278	+	10.8715i	−0.254962	+	0.360785i
$909$		0			0
$910$	0.244414	−	0.769362i	0.00810223	−	0.0255041i
$911$	28.1534			0.932763			0.466382	−	0.884584i	$-0.345557\pi$
$911$	28.1534			0.932763			0.466382	+	0.884584i	$0.345557\pi$
$912$		0			0
$913$	−2.92400			−0.0967704
$914$	1.40571	−	4.42488i	0.0464968	−	0.146362i
$915$		0			0
$916$	18.9163	−	26.7676i	0.625012	−	0.884425i
$917$			20.1503i			0.665420i
$918$		0			0
$919$	1.87464			0.0618387			0.0309193	−	0.999522i	$-0.490157\pi$
$919$	1.87464			0.0618387			0.0309193	+	0.999522i	$0.490157\pi$
$920$	−14.6430	−	19.3422i	−0.482764	−	0.637694i
$921$		0			0
$922$	−4.27957	−	1.35955i	−0.140940	−	0.0447743i
$923$			1.54741i			0.0509336i
$924$		0			0
$925$		−	0.764935i		−	0.0251509i
$926$	9.36424	−	29.4767i	0.307728	−	0.968663i
$927$		0			0
$928$	1.54872	+	47.2064i	0.0508393	+	1.54963i
$929$	−23.2555			−0.762989			−0.381495	−	0.924371i	$-0.624591\pi$
$929$	−23.2555			−0.762989			−0.381495	+	0.924371i	$0.624591\pi$
$930$		0			0
$931$			10.1183i			0.331613i
$932$	−26.2543	−	18.5536i	−0.859989	−	0.607743i
$933$		0			0
$934$	−6.68168	−	2.12266i	−0.218631	−	0.0694555i
$935$	10.4563			0.341957
$936$		0			0
$937$	−11.1266			−0.363490			−0.181745	−	0.983346i	$-0.558174\pi$
$937$	−11.1266			−0.363490			−0.181745	+	0.983346i	$0.558174\pi$
$938$	14.3009	+	4.54315i	0.466940	+	0.148339i
$939$		0			0
$940$	14.0333	−	19.8578i	0.457714	−	0.647689i
$941$			23.5923i			0.769088i	0.923107	+	0.384544i	$0.125641\pi$
$941$			23.5923i			0.769088i	−0.923107	+	0.384544i	$0.874359\pi$
$942$		0			0
$943$	−52.2479			−1.70142
$944$	−36.3137	+	12.8617i	−1.18191	+	0.418611i
$945$		0			0
$946$	−1.91799	+	6.03743i	−0.0623593	+	0.196294i
$947$		−	23.1038i		−	0.750772i	−0.926869	−	0.375386i	$-0.877510\pi$
$947$		−	23.1038i		−	0.750772i	0.926869	−	0.375386i	$-0.122490\pi$
$948$		0			0
$949$			0.109588i			0.00355737i
$950$	−4.79042	−	1.52184i	−0.155422	−	0.0493749i
$951$		0			0
$952$	−22.4579	+	17.0017i	−0.727864	+	0.551027i
$953$	−2.75964			−0.0893934			−0.0446967	−	0.999001i	$-0.514232\pi$
$953$	−2.75964			−0.0893934			−0.0446967	+	0.999001i	$0.514232\pi$
$954$		0			0
$955$			23.3484i			0.755537i
$956$	−4.11696	−	2.90941i	−0.133152	−	0.0940970i
$957$		0			0
$958$	15.2187	−	47.9051i	0.491692	−	1.54774i
$959$	−18.7155			−0.604355
$960$		0			0
$961$	51.0537			1.64689
$962$	−0.0414282	+	0.130407i	−0.00133570	+	0.00420450i
$963$		0			0
$964$	−9.98249	−	7.05450i	−0.321514	−	0.227210i
$965$			25.6115i			0.824464i
$966$		0			0
$967$	50.7176			1.63097			0.815484	−	0.578780i	$-0.196471\pi$
$967$	50.7176			1.63097			0.815484	+	0.578780i	$0.196471\pi$
$968$	2.25509	−	1.70721i	0.0724814	−	0.0548718i
$969$		0			0
$970$	13.9993	+	4.44734i	0.449490	+	0.142795i
$971$		−	38.8913i		−	1.24808i	−0.781392	−	0.624041i	$-0.785490\pi$
$971$		−	38.8913i		−	1.24808i	0.781392	−	0.624041i	$-0.214510\pi$
$972$		0			0
$973$		−	33.7230i		−	1.08111i
$974$	4.34808	−	13.6868i	0.139321	−	0.438554i
$975$		0			0
$976$	12.5524	−	4.44584i	0.401793	−	0.142308i
$977$	17.1186			0.547673			0.273837	−	0.961776i	$-0.411707\pi$
$977$	17.1186			0.547673			0.273837	+	0.961776i	$0.411707\pi$
$978$		0			0
$979$			5.74214i			0.183520i
$980$	8.06248	−	11.4088i	0.257546	−	0.364442i
$981$		0			0
$982$	−0.495415	−	0.157385i	−0.0158093	−	0.00502236i
$983$	5.78625			0.184553			0.0922763	−	0.995733i	$-0.470586\pi$
$983$	5.78625			0.184553			0.0922763	+	0.995733i	$0.470586\pi$
$984$		0			0
$985$	−22.5631			−0.718919
$986$	−60.9324	−	19.3572i	−1.94048	−	0.616459i
$987$		0			0
$988$	0.734257	+	0.518890i	0.0233598	+	0.0165081i
$989$			19.8945i			0.632608i
$990$		0			0
$991$	−4.97362			−0.157992			−0.0789961	−	0.996875i	$-0.525171\pi$
$991$	−4.97362			−0.157992			−0.0789961	+	0.996875i	$0.525171\pi$
$992$	−51.2142	+	1.68021i	−1.62605	+	0.0533467i
$993$		0			0
$994$	7.58354	−	23.8714i	0.240535	−	0.757154i
$995$			48.1503i			1.52647i
$996$		0			0
$997$		−	22.3402i		−	0.707521i	−0.935336	−	0.353760i	$-0.884903\pi$
$997$		−	22.3402i		−	0.707521i	0.935336	−	0.353760i	$-0.115097\pi$
$998$	42.0287	+	13.3518i	1.33039	+	0.422644i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.f.g.397.7		10
3.2	odd	2		88.2.c.a.45.4	yes	10
4.3	odd	2		3168.2.f.g.1585.3		10
8.3	odd	2		3168.2.f.g.1585.8		10
8.5	even	2	inner	792.2.f.g.397.8		10
12.11	even	2		352.2.c.a.177.4		10
24.5	odd	2		88.2.c.a.45.3	✓	10
24.11	even	2		352.2.c.a.177.7		10
33.2	even	10		968.2.o.h.565.2		40
33.5	odd	10		968.2.o.g.245.5		40
33.8	even	10		968.2.o.h.493.3		40
33.14	odd	10		968.2.o.g.493.8		40
33.17	even	10		968.2.o.h.245.6		40
33.20	odd	10		968.2.o.g.565.9		40
33.26	odd	10		968.2.o.g.269.1		40
33.29	even	10		968.2.o.h.269.10		40
33.32	even	2		968.2.c.d.485.7		10
48.5	odd	4		2816.2.a.o.1.4		5
48.11	even	4		2816.2.a.p.1.2		5
48.29	odd	4		2816.2.a.r.1.2		5
48.35	even	4		2816.2.a.q.1.4		5
132.131	odd	2		3872.2.c.f.1937.4		10
264.5	odd	10		968.2.o.g.245.9		40
264.29	even	10		968.2.o.h.269.3		40
264.53	odd	10		968.2.o.g.565.5		40
264.101	even	10		968.2.o.h.565.6		40
264.125	odd	10		968.2.o.g.269.8		40
264.131	odd	2		3872.2.c.f.1937.7		10
264.149	even	10		968.2.o.h.245.2		40
264.173	even	10		968.2.o.h.493.10		40
264.197	even	2		968.2.c.d.485.8		10
264.245	odd	10		968.2.o.g.493.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.3	✓	10	24.5	odd	2
88.2.c.a.45.4	yes	10	3.2	odd	2
352.2.c.a.177.4		10	12.11	even	2
352.2.c.a.177.7		10	24.11	even	2
792.2.f.g.397.7		10	1.1	even	1	trivial
792.2.f.g.397.8		10	8.5	even	2	inner
968.2.c.d.485.7		10	33.32	even	2
968.2.c.d.485.8		10	264.197	even	2
968.2.o.g.245.5		40	33.5	odd	10
968.2.o.g.245.9		40	264.5	odd	10
968.2.o.g.269.1		40	33.26	odd	10
968.2.o.g.269.8		40	264.125	odd	10
968.2.o.g.493.1		40	264.245	odd	10
968.2.o.g.493.8		40	33.14	odd	10
968.2.o.g.565.5		40	264.53	odd	10
968.2.o.g.565.9		40	33.20	odd	10
968.2.o.h.245.2		40	264.149	even	10
968.2.o.h.245.6		40	33.17	even	10
968.2.o.h.269.3		40	264.29	even	10
968.2.o.h.269.10		40	33.29	even	10
968.2.o.h.493.3		40	33.8	even	10
968.2.o.h.493.10		40	264.173	even	10
968.2.o.h.565.2		40	33.2	even	10
968.2.o.h.565.6		40	264.101	even	10
2816.2.a.o.1.4		5	48.5	odd	4
2816.2.a.p.1.2		5	48.11	even	4
2816.2.a.q.1.4		5	48.35	even	4
2816.2.a.r.1.2		5	48.29	odd	4
3168.2.f.g.1585.3		10	4.3	odd	2
3168.2.f.g.1585.8		10	8.3	odd	2
3872.2.c.f.1937.4		10	132.131	odd	2
3872.2.c.f.1937.7		10	264.131	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.428185 - 1.34783i) q^{2} +(-1.63332 - 1.15424i) q^{4} -1.93119i q^{5} -1.83930 q^{7} +(-2.25509 + 1.70721i) q^{8} +(-2.60293 - 0.826906i) q^{10} -1.00000i q^{11} -0.160700i q^{13} +(-0.787560 + 2.47907i) q^{14} +(1.33544 + 3.77049i) q^{16} -5.41442 q^{17} -2.79744i q^{19} +(-2.22907 + 3.15424i) q^{20} +(-1.34783 - 0.428185i) q^{22} -4.44137 q^{23} +1.27050 q^{25} +(-0.216597 - 0.0688094i) q^{26} +(3.00416 + 2.12300i) q^{28} +8.34948i q^{29} -9.05835 q^{31} +(5.65381 - 0.185487i) q^{32} +(-2.31837 + 7.29774i) q^{34} +3.55204i q^{35} -0.602073i q^{37} +(-3.77049 - 1.19782i) q^{38} +(3.29695 + 4.35501i) q^{40} +11.7639 q^{41} -4.47936i q^{43} +(-1.15424 + 1.63332i) q^{44} +(-1.90173 + 5.98623i) q^{46} -6.29558 q^{47} -3.61698 q^{49} +(0.544010 - 1.71243i) q^{50} +(-0.185487 + 0.262474i) q^{52} -11.7211i q^{53} -1.93119 q^{55} +(4.14779 - 3.14007i) q^{56} +(11.2537 + 3.57512i) q^{58} +9.63102i q^{59} -3.32912i q^{61} +(-3.87865 + 12.2092i) q^{62} +(2.17087 - 7.69983i) q^{64} -0.310343 q^{65} -5.76864i q^{67} +(8.84346 + 6.24956i) q^{68} +(4.78756 + 1.52093i) q^{70} -9.62916 q^{71} -0.681940 q^{73} +(-0.811494 - 0.257798i) q^{74} +(-3.22893 + 4.56911i) q^{76} +1.83930i q^{77} +5.77867 q^{79} +(7.28154 - 2.57899i) q^{80} +(5.03712 - 15.8558i) q^{82} -2.92400i q^{83} +10.4563i q^{85} +(-6.03743 - 1.91799i) q^{86} +(1.70721 + 2.25509i) q^{88} -5.74214 q^{89} +0.295576i q^{91} +(7.25416 + 5.12643i) q^{92} +(-2.69567 + 8.48539i) q^{94} -5.40240 q^{95} -5.37829 q^{97} +(-1.54873 + 4.87509i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{4} + 10 q^{10} + 12 q^{14} + 4 q^{17} - 12 q^{20} + 12 q^{23} - 6 q^{25} + 20 q^{26} - 12 q^{28} - 4 q^{31} + 20 q^{32} - 8 q^{38} + 20 q^{40} - 4 q^{41} - 4 q^{44} + 2 q^{46} + 4 q^{47} - 6 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) \) 10 * q - 4 * q^4 + 10 * q^10 + 12 * q^14 + 4 * q^17 - 12 * q^20 + 12 * q^23 - 6 * q^25 + 20 * q^26 - 12 * q^28 - 4 * q^31 + 20 * q^32 - 8 * q^38 + 20 * q^40 - 4 * q^41 - 4 * q^44 + 2 * q^46 + 4 * q^47 - 6 * q^49 + 6 * q^50 - 20 * q^52 - 8 * q^55 + 8 * q^56 + 36 * q^58 - 22 * q^62 - 16 * q^64 - 16 * q^65 + 28 * q^68 + 28 * q^70 + 12 * q^71 - 4 * q^73 + 14 * q^74 + 44 * q^76 + 16 * q^79 + 56 * q^80 - 4 * q^82 + 20 * q^86 - 12 * q^88 + 4 * q^89 + 36 * q^92 - 24 * q^95 - 20 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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