LMFDB - Embedded newform 396.2.c.a.287.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [396,2,Mod(287,396)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(396, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("396.287"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,4,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.5236158660608.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{8} - 4x^{7} + 3x^{6} + 8x^{5} + 6x^{4} - 16x^{3} - 16x^{2} + 32 $ x^10 - 2x^8 - 4x^7 + 3x^6 + 8x^5 + 6x^4 - 16x^3 - 16*x^2 + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			287.6
Root			$-0.382373 - 1.36154i$ of defining polynomial
Character	$\chi$	$=$	396.287
Dual form			396.2.c.a.287.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.382373 + 1.36154i) q^{2} +(-1.70758 + 1.04123i) q^{4} -2.05483i q^{5} -4.18915i q^{7} +(-2.07061 - 1.92680i) q^{8} +(2.79773 - 0.785711i) q^{10} -1.00000 q^{11} +3.27394 q^{13} +(5.70370 - 1.60182i) q^{14} +(1.83167 - 3.55598i) q^{16} +0.332700i q^{17} -8.47431i q^{19} +(2.13955 + 3.50879i) q^{20} +(-0.382373 - 1.36154i) q^{22} -3.52212 q^{23} +0.777673 q^{25} +(1.25187 + 4.45760i) q^{26} +(4.36188 + 7.15333i) q^{28} +9.52712i q^{29} +3.95895i q^{31} +(5.54199 + 1.13419i) q^{32} +(-0.452984 + 0.127215i) q^{34} -8.60800 q^{35} -1.37648 q^{37} +(11.5381 - 3.24034i) q^{38} +(-3.95925 + 4.25475i) q^{40} -5.42788i q^{41} +1.53622i q^{43} +(1.70758 - 1.04123i) q^{44} +(-1.34676 - 4.79551i) q^{46} +6.93286 q^{47} -10.5490 q^{49} +(0.297361 + 1.05883i) q^{50} +(-5.59052 + 3.40893i) q^{52} -8.83749i q^{53} +2.05483i q^{55} +(-8.07167 + 8.67411i) q^{56} +(-12.9716 + 3.64291i) q^{58} -3.70203 q^{59} +14.8572 q^{61} +(-5.39027 + 1.51380i) q^{62} +(0.574864 + 7.97932i) q^{64} -6.72739i q^{65} -6.32795i q^{67} +(-0.346418 - 0.568112i) q^{68} +(-3.29147 - 11.7201i) q^{70} -5.77871 q^{71} -8.72042 q^{73} +(-0.526328 - 1.87413i) q^{74} +(8.82372 + 14.4706i) q^{76} +4.18915i q^{77} +13.2903i q^{79} +(-7.30693 - 3.76378i) q^{80} +(7.39027 - 2.07547i) q^{82} +0.984127 q^{83} +0.683642 q^{85} +(-2.09162 + 0.587408i) q^{86} +(2.07061 + 1.92680i) q^{88} +1.46267i q^{89} -13.7150i q^{91} +(6.01431 - 3.66735i) q^{92} +(2.65094 + 9.43937i) q^{94} -17.4133 q^{95} +5.99367 q^{97} +(-4.03366 - 14.3629i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} - 12 q^{8} + 4 q^{10} - 10 q^{11} + 8 q^{13} + 8 q^{14} - 4 q^{16} - 24 q^{20} - 8 q^{23} - 10 q^{25} + 16 q^{26} + 16 q^{28} + 8 q^{34} + 16 q^{35} - 4 q^{37} + 32 q^{38} - 4 q^{44} + 20 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^8 + 4 * q^10 - 10 * q^11 + 8 * q^13 + 8 * q^14 - 4 * q^16 - 24 * q^20 - 8 * q^23 - 10 * q^25 + 16 * q^26 + 16 * q^28 + 8 * q^34 + 16 * q^35 - 4 * q^37 + 32 * q^38 - 4 * q^44 + 20 * q^46 - 34 * q^49 + 12 * q^50 - 20 * q^52 - 32 * q^56 - 28 * q^58 + 40 * q^59 + 20 * q^61 + 28 * q^62 - 8 * q^64 - 20 * q^68 - 36 * q^70 - 16 * q^71 + 24 * q^73 + 28 * q^74 - 12 * q^76 - 32 * q^80 - 8 * q^82 + 8 * q^83 - 36 * q^85 - 24 * q^86 + 12 * q^88 - 24 * q^92 - 20 * q^94 - 96 * q^95 + 24 * q^97 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.382373	+	1.36154i	0.270378	+	0.962754i
$2$	0.382373	+	1.36154i	0.270378	+	0.962754i
$3$		0			0
$3$		0			0
$4$	−1.70758	+	1.04123i	−0.853791	+	0.520616i
$5$		−	2.05483i		−	0.918948i	−0.888191	−	0.459474i	$-0.848038\pi$
$5$		−	2.05483i		−	0.918948i	0.888191	−	0.459474i	$-0.151962\pi$
$6$		0			0
$7$		−	4.18915i		−	1.58335i	−0.610941	−	0.791676i	$-0.709209\pi$
$7$		−	4.18915i		−	1.58335i	0.610941	−	0.791676i	$-0.290791\pi$
$8$	−2.07061	−	1.92680i	−0.732072	−	0.681228i
$9$		0			0
$10$	2.79773	−	0.785711i	0.884721	−	0.248464i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		0			0
$13$	3.27394			0.908028			0.454014	−	0.890995i	$-0.349992\pi$
$13$	3.27394			0.908028			0.454014	+	0.890995i	$0.349992\pi$
$14$	5.70370	−	1.60182i	1.52438	−	0.428104i
$15$		0			0
$16$	1.83167	−	3.55598i	0.457918	−	0.888994i
$17$			0.332700i			0.0806916i	0.999186	+	0.0403458i	$0.0128460\pi$
$17$			0.332700i			0.0806916i	−0.999186	+	0.0403458i	$0.987154\pi$
$18$		0			0
$19$		−	8.47431i		−	1.94414i	−0.234693	−	0.972070i	$-0.575408\pi$
$19$		−	8.47431i		−	1.94414i	0.234693	−	0.972070i	$-0.424592\pi$
$20$	2.13955	+	3.50879i	0.478419	+	0.784590i
$21$		0			0
$22$	−0.382373	−	1.36154i	−0.0815222	−	0.290281i
$23$	−3.52212			−0.734413			−0.367207	−	0.930139i	$-0.619686\pi$
$23$	−3.52212			−0.734413			−0.367207	+	0.930139i	$0.619686\pi$
$24$		0			0
$25$	0.777673			0.155535
$26$	1.25187	+	4.45760i	0.245511	+	0.874208i
$27$		0			0
$28$	4.36188	+	7.15333i	0.824318	+	1.35185i
$29$			9.52712i			1.76914i	0.466406	+	0.884571i	$0.345549\pi$
$29$			9.52712i			1.76914i	−0.466406	+	0.884571i	$0.654451\pi$
$30$		0			0
$31$			3.95895i			0.711049i	0.934667	+	0.355524i	$0.115698\pi$
$31$			3.95895i			0.711049i	−0.934667	+	0.355524i	$0.884302\pi$
$32$	5.54199	+	1.13419i	0.979694	+	0.200498i
$33$		0			0
$34$	−0.452984	+	0.127215i	−0.0776862	+	0.0218173i
$35$	−8.60800			−1.45502
$36$		0			0
$37$	−1.37648			−0.226291			−0.113146	−	0.993578i	$-0.536093\pi$
$37$	−1.37648			−0.226291			−0.113146	+	0.993578i	$0.536093\pi$
$38$	11.5381	−	3.24034i	1.87173	−	0.525653i
$39$		0			0
$40$	−3.95925	+	4.25475i	−0.626013	+	0.672736i
$41$		−	5.42788i		−	0.847692i	−0.905734	−	0.423846i	$-0.860680\pi$
$41$		−	5.42788i		−	0.847692i	0.905734	−	0.423846i	$-0.139320\pi$
$42$		0			0
$43$			1.53622i			0.234271i	0.993116	+	0.117136i	$0.0373712\pi$
$43$			1.53622i			0.234271i	−0.993116	+	0.117136i	$0.962629\pi$
$44$	1.70758	−	1.04123i	0.257428	−	0.156972i
$45$		0			0
$46$	−1.34676	−	4.79551i	−0.198570	−	0.707060i
$47$	6.93286			1.01126			0.505631	−	0.862750i	$-0.331260\pi$
$47$	6.93286			1.01126			0.505631	+	0.862750i	$0.331260\pi$
$48$		0			0
$49$	−10.5490			−1.50700
$50$	0.297361	+	1.05883i	0.0420532	+	0.149742i
$51$		0			0
$52$	−5.59052	+	3.40893i	−0.775266	+	0.472734i
$53$		−	8.83749i		−	1.21392i	−0.794731	−	0.606961i	$-0.792388\pi$
$53$		−	8.83749i		−	1.21392i	0.794731	−	0.606961i	$-0.207612\pi$
$54$		0			0
$55$			2.05483i			0.277073i
$56$	−8.07167	+	8.67411i	−1.07862	+	1.15913i
$57$		0			0
$58$	−12.9716	+	3.64291i	−1.70325	+	0.478338i
$59$	−3.70203			−0.481964			−0.240982	−	0.970530i	$-0.577469\pi$
$59$	−3.70203			−0.481964			−0.240982	+	0.970530i	$0.577469\pi$
$60$		0			0
$61$	14.8572			1.90227			0.951136	−	0.308771i	$-0.0999178\pi$
$61$	14.8572			1.90227			0.951136	+	0.308771i	$0.0999178\pi$
$62$	−5.39027	+	1.51380i	−0.684565	+	0.192252i
$63$		0			0
$64$	0.574864	+	7.97932i	0.0718580	+	0.997415i
$65$		−	6.72739i		−	0.834430i
$66$		0			0
$67$		−	6.32795i		−	0.773083i	−0.922272	−	0.386541i	$-0.873670\pi$
$67$		−	6.32795i		−	0.773083i	0.922272	−	0.386541i	$-0.126330\pi$
$68$	−0.346418	−	0.568112i	−0.0420093	−	0.0688938i
$69$		0			0
$70$	−3.29147	−	11.7201i	−0.393405	−	1.40082i
$71$	−5.77871			−0.685807			−0.342904	−	0.939371i	$-0.611410\pi$
$71$	−5.77871			−0.685807			−0.342904	+	0.939371i	$0.611410\pi$
$72$		0			0
$73$	−8.72042			−1.02065			−0.510324	−	0.859982i	$-0.670475\pi$
$73$	−8.72042			−1.02065			−0.510324	+	0.859982i	$0.670475\pi$
$74$	−0.526328	−	1.87413i	−0.0611843	−	0.217863i
$75$		0			0
$76$	8.82372	+	14.4706i	1.01215	+	1.65989i
$77$			4.18915i			0.477399i
$78$		0			0
$79$			13.2903i			1.49527i	0.664109	+	0.747636i	$0.268811\pi$
$79$			13.2903i			1.49527i	−0.664109	+	0.747636i	$0.731189\pi$
$80$	−7.30693	−	3.76378i	−0.816939	−	0.420803i
$81$		0			0
$82$	7.39027	−	2.07547i	0.816119	−	0.229198i
$83$	0.984127			0.108022			0.0540110	−	0.998540i	$-0.482799\pi$
$83$	0.984127			0.108022			0.0540110	+	0.998540i	$0.482799\pi$
$84$		0			0
$85$	0.683642			0.0741514
$86$	−2.09162	+	0.587408i	−0.225546	+	0.0633419i
$87$		0			0
$88$	2.07061	+	1.92680i	0.220728	+	0.205398i
$89$			1.46267i			0.155043i	0.996991	+	0.0775214i	$0.0247006\pi$
$89$			1.46267i			0.155043i	−0.996991	+	0.0775214i	$0.975299\pi$
$90$		0			0
$91$		−	13.7150i		−	1.43773i
$92$	6.01431	−	3.66735i	0.627036	−	0.382347i
$93$		0			0
$94$	2.65094	+	9.43937i	0.273423	+	0.973597i
$95$	−17.4133			−1.78656
$96$		0			0
$97$	5.99367			0.608565			0.304283	−	0.952582i	$-0.401583\pi$
$97$	5.99367			0.608565			0.304283	+	0.952582i	$0.401583\pi$
$98$	−4.03366	−	14.3629i	−0.407461	−	1.45087i
$99$		0			0
$100$	−1.32794	+	0.809738i	−0.132794	+	0.0809738i
$101$			5.11346i			0.508808i	0.967098	+	0.254404i	$0.0818793\pi$
$101$			5.11346i			0.508808i	−0.967098	+	0.254404i	$0.918121\pi$
$102$		0			0
$103$		−	0.816108i		−	0.0804135i	−0.999191	−	0.0402067i	$-0.987198\pi$
$103$		−	0.816108i		−	0.0804135i	0.999191	−	0.0402067i	$-0.0128017\pi$
$104$	−6.77906	−	6.30824i	−0.664742	−	0.618574i
$105$		0			0
$106$	12.0326	−	3.37922i	1.16871	−	0.328218i
$107$	14.1725			1.37011			0.685056	−	0.728491i	$-0.259778\pi$
$107$	14.1725			1.37011			0.685056	+	0.728491i	$0.259778\pi$
$108$		0			0
$109$	−2.61615			−0.250582			−0.125291	−	0.992120i	$-0.539986\pi$
$109$	−2.61615			−0.250582			−0.125291	+	0.992120i	$0.539986\pi$
$110$	−2.79773	+	0.785711i	−0.266753	+	0.0749146i
$111$		0			0
$112$	−14.8965	−	7.67316i	−1.40759	−	0.725046i
$113$			8.81271i			0.829030i	0.910043	+	0.414515i	$0.136049\pi$
$113$			8.81271i			0.829030i	−0.910043	+	0.414515i	$0.863951\pi$
$114$		0			0
$115$			7.23736i			0.674888i
$116$	−9.91994	−	16.2683i	−0.921043	−	1.51048i
$117$		0			0
$118$	−1.41556	−	5.04047i	−0.130313	−	0.464012i
$119$	1.39373			0.127763
$120$		0			0
$121$	1.00000			0.0909091
$122$	5.68100	+	20.2287i	0.514333	+	1.83142i
$123$		0			0
$124$	−4.12219	−	6.76024i	−0.370183	−	0.607087i
$125$		−	11.8721i		−	1.06188i
$126$		0			0
$127$			18.0169i			1.59874i	0.600840	+	0.799369i	$0.294833\pi$
$127$			18.0169i			1.59874i	−0.600840	+	0.799369i	$0.705167\pi$
$128$	−10.6443	+	3.83377i	−0.940836	+	0.338861i
$129$		0			0
$130$	9.15961	−	2.57237i	0.803351	−	0.225612i
$131$	16.0276			1.40034			0.700168	−	0.713978i	$-0.253108\pi$
$131$	16.0276			1.40034			0.700168	+	0.713978i	$0.253108\pi$
$132$		0			0
$133$	−35.5002			−3.07826
$134$	8.61576	−	2.41964i	0.744288	−	0.209025i
$135$		0			0
$136$	0.641047	−	0.688892i	0.0549693	−	0.0590720i
$137$		−	10.1920i		−	0.870758i	−0.900247	−	0.435379i	$-0.856614\pi$
$137$		−	10.1920i		−	0.870758i	0.900247	−	0.435379i	$-0.143386\pi$
$138$		0			0
$139$			1.58468i			0.134410i	0.997739	+	0.0672052i	$0.0214082\pi$
$139$			1.58468i			0.134410i	−0.997739	+	0.0672052i	$0.978592\pi$
$140$	14.6989	−	8.96292i	1.24228	−	0.757505i
$141$		0			0
$142$	−2.20962	−	7.86795i	−0.185427	−	0.660264i
$143$	−3.27394			−0.273781
$144$		0			0
$145$	19.5766			1.62575
$146$	−3.33445	−	11.8732i	−0.275961	−	0.982634i
$147$		0			0
$148$	2.35045	−	1.43323i	0.193206	−	0.117811i
$149$			3.05740i			0.250472i	0.992127	+	0.125236i	$0.0399689\pi$
$149$			3.05740i			0.250472i	−0.992127	+	0.125236i	$0.960031\pi$
$150$		0			0
$151$			16.3143i			1.32763i	0.747895	+	0.663817i	$0.231065\pi$
$151$			16.3143i			1.32763i	−0.747895	+	0.663817i	$0.768935\pi$
$152$	−16.3283	+	17.5470i	−1.32440	+	1.42325i
$153$		0			0
$154$	−5.70370	+	1.60182i	−0.459617	+	0.129078i
$155$	8.13497			0.653417
$156$		0			0
$157$	2.29129			0.182865			0.0914325	−	0.995811i	$-0.470855\pi$
$157$	2.29129			0.182865			0.0914325	+	0.995811i	$0.470855\pi$
$158$	−18.0952	+	5.08184i	−1.43958	+	0.404289i
$159$		0			0
$160$	2.33056	−	11.3878i	0.184247	−	0.900288i
$161$			14.7547i			1.16283i
$162$		0			0
$163$		−	0.530812i		−	0.0415764i	−0.999784	−	0.0207882i	$-0.993382\pi$
$163$		−	0.530812i		−	0.0415764i	0.999784	−	0.0207882i	$-0.00661756\pi$
$164$	5.65168	+	9.26855i	0.441322	+	0.723752i
$165$		0			0
$166$	0.376304	+	1.33993i	0.0292068	+	0.103999i
$167$	17.0224			1.31723			0.658616	−	0.752479i	$-0.271142\pi$
$167$	17.0224			1.31723			0.658616	+	0.752479i	$0.271142\pi$
$168$		0			0
$169$	−2.28131			−0.175485
$170$	0.261406	+	0.930806i	0.0200489	+	0.0713895i
$171$		0			0
$172$	−1.59956	−	2.62322i	−0.121965	−	0.200019i
$173$			5.38984i			0.409782i	0.978785	+	0.204891i	$0.0656840\pi$
$173$			5.38984i			0.409782i	−0.978785	+	0.204891i	$0.934316\pi$
$174$		0			0
$175$		−	3.25779i		−	0.246266i
$176$	−1.83167	+	3.55598i	−0.138068	+	0.268042i
$177$		0			0
$178$	−1.99148	+	0.559285i	−0.149268	+	0.0419202i
$179$	−16.0619			−1.20052			−0.600260	−	0.799805i	$-0.704936\pi$
$179$	−16.0619			−1.20052			−0.600260	+	0.799805i	$0.704936\pi$
$180$		0			0
$181$	7.65892			0.569283			0.284642	−	0.958634i	$-0.408125\pi$
$181$	7.65892			0.569283			0.284642	+	0.958634i	$0.408125\pi$
$182$	18.6736	−	5.24426i	1.38418	−	0.388730i
$183$		0			0
$184$	7.29295	+	6.78644i	0.537643	+	0.500303i
$185$			2.82843i			0.207950i
$186$		0			0
$187$		−	0.332700i		−	0.0243294i
$188$	−11.8384	+	7.21872i	−0.863407	+	0.526479i
$189$		0			0
$190$	−6.65836	−	23.7088i	−0.483048	−	1.72002i
$191$	13.1828			0.953872			0.476936	−	0.878938i	$-0.341747\pi$
$191$	13.1828			0.953872			0.476936	+	0.878938i	$0.341747\pi$
$192$		0			0
$193$	17.5508			1.26333			0.631665	−	0.775241i	$-0.282372\pi$
$193$	17.5508			1.26333			0.631665	+	0.775241i	$0.282372\pi$
$194$	2.29182	+	8.16062i	0.164543	+	0.585899i
$195$		0			0
$196$	18.0133	−	10.9840i	1.28667	−	0.784570i
$197$		−	11.6432i		−	0.829541i	−0.909926	−	0.414770i	$-0.863862\pi$
$197$		−	11.6432i		−	0.829541i	0.909926	−	0.414770i	$-0.136138\pi$
$198$		0			0
$199$		−	5.34814i		−	0.379119i	−0.981869	−	0.189560i	$-0.939294\pi$
$199$		−	5.34814i		−	0.379119i	0.981869	−	0.189560i	$-0.0607060\pi$
$200$	−1.61026	−	1.49842i	−0.113863	−	0.105955i
$201$		0			0
$202$	−6.96218	+	1.95525i	−0.489857	+	0.137571i
$203$	39.9106			2.80117
$204$		0			0
$205$	−11.1534			−0.778985
$206$	1.11116	−	0.312057i	0.0774184	−	0.0217421i
$207$		0			0
$208$	5.99679	−	11.6421i	0.415803	−	0.807232i
$209$			8.47431i			0.586180i
$210$		0			0
$211$		−	17.3016i		−	1.19109i	−0.803321	−	0.595546i	$-0.796936\pi$
$211$		−	17.3016i		−	1.19109i	0.803321	−	0.595546i	$-0.203064\pi$
$212$	9.20187	+	15.0907i	0.631987	+	1.03644i
$213$		0			0
$214$	5.41919	+	19.2965i	0.370449	+	1.31908i
$215$	3.15667			0.215283
$216$		0			0
$217$	16.5847			1.12584
$218$	−1.00035	−	3.56200i	−0.0677520	−	0.241249i
$219$		0			0
$220$	−2.13955	−	3.50879i	−0.144249	−	0.236563i
$221$			1.08924i			0.0732702i
$222$		0			0
$223$			22.3672i			1.49782i	0.662674	+	0.748908i	$0.269421\pi$
$223$			22.3672i			1.49782i	−0.662674	+	0.748908i	$0.730579\pi$
$224$	4.75129	−	23.2162i	0.317459	−	1.55120i
$225$		0			0
$226$	−11.9989	+	3.36974i	−0.798152	+	0.224152i
$227$	26.0898			1.73164			0.865820	−	0.500355i	$-0.166797\pi$
$227$	26.0898			1.73164			0.865820	+	0.500355i	$0.166797\pi$
$228$		0			0
$229$	−9.87457			−0.652530			−0.326265	−	0.945278i	$-0.605790\pi$
$229$	−9.87457			−0.652530			−0.326265	+	0.945278i	$0.605790\pi$
$230$	−9.85396	+	2.76737i	−0.649751	+	0.182475i
$231$		0			0
$232$	18.3569	−	19.7270i	1.20519	−	1.29514i
$233$			23.6093i			1.54669i	0.633983	+	0.773347i	$0.281419\pi$
$233$			23.6093i			1.54669i	−0.633983	+	0.773347i	$0.718581\pi$
$234$		0			0
$235$		−	14.2459i		−	0.929297i
$236$	6.32153	−	3.85467i	0.411496	−	0.250918i
$237$		0			0
$238$	0.532925	+	1.89762i	0.0345444	+	0.123005i
$239$	−3.88758			−0.251466			−0.125733	−	0.992064i	$-0.540128\pi$
$239$	−3.88758			−0.251466			−0.125733	+	0.992064i	$0.540128\pi$
$240$		0			0
$241$	−22.7455			−1.46517			−0.732583	−	0.680678i	$-0.761685\pi$
$241$	−22.7455			−1.46517			−0.732583	+	0.680678i	$0.761685\pi$
$242$	0.382373	+	1.36154i	0.0245799	+	0.0875231i
$243$		0			0
$244$	−25.3699	+	15.4698i	−1.62414	+	0.990353i
$245$			21.6764i			1.38486i
$246$		0			0
$247$		−	27.7444i		−	1.76533i
$248$	7.62812	−	8.19745i	0.484386	−	0.520539i
$249$		0			0
$250$	16.1644	−	4.53958i	1.02233	−	0.287108i
$251$	−4.93642			−0.311584			−0.155792	−	0.987790i	$-0.549793\pi$
$251$	−4.93642			−0.311584			−0.155792	+	0.987790i	$0.549793\pi$
$252$		0			0
$253$	3.52212			0.221434
$254$	−24.5307	+	6.88916i	−1.53919	+	0.432264i
$255$		0			0
$256$	−9.28995	−	13.0268i	−0.580622	−	0.814173i
$257$			26.6561i			1.66276i	0.555702	+	0.831381i	$0.312449\pi$
$257$			26.6561i			1.66276i	−0.555702	+	0.831381i	$0.687551\pi$
$258$		0			0
$259$			5.76628i			0.358299i
$260$	7.00477	+	11.4876i	0.434418	+	0.712429i
$261$		0			0
$262$	6.12851	+	21.8222i	0.378621	+	1.34818i
$263$	−19.7901			−1.22031			−0.610155	−	0.792282i	$-0.708893\pi$
$263$	−19.7901			−1.22031			−0.610155	+	0.792282i	$0.708893\pi$
$264$		0			0
$265$	−18.1595			−1.11553
$266$	−13.5743	−	48.3349i	−0.832294	−	2.96360i
$267$		0			0
$268$	6.58887	+	10.8055i	0.402479	+	0.660051i
$269$		−	16.1510i		−	0.984741i	−0.870386	−	0.492371i	$-0.836130\pi$
$269$		−	16.1510i		−	0.984741i	0.870386	−	0.492371i	$-0.163870\pi$
$270$		0			0
$271$		−	0.854317i		−	0.0518961i	−0.999663	−	0.0259480i	$-0.991740\pi$
$271$		−	0.854317i		−	0.0518961i	0.999663	−	0.0259480i	$-0.00826045\pi$
$272$	1.18307	+	0.609398i	0.0717344	+	0.0369502i
$273$		0			0
$274$	13.8768	−	3.89713i	0.838326	−	0.235434i
$275$	−0.777673			−0.0468955
$276$		0			0
$277$	22.4384			1.34819			0.674097	−	0.738643i	$-0.264533\pi$
$277$	22.4384			1.34819			0.674097	+	0.738643i	$0.264533\pi$
$278$	−2.15760	+	0.605937i	−0.129404	+	0.0363417i
$279$		0			0
$280$	17.8238	+	16.5859i	1.06518	+	0.991198i
$281$		−	27.7617i		−	1.65612i	−0.560637	−	0.828062i	$-0.689444\pi$
$281$		−	27.7617i		−	1.65612i	0.560637	−	0.828062i	$-0.310556\pi$
$282$		0			0
$283$			13.7582i			0.817842i	0.912570	+	0.408921i	$0.134095\pi$
$283$			13.7582i			0.817842i	−0.912570	+	0.408921i	$0.865905\pi$
$284$	9.86763	−	6.01698i	0.585536	−	0.357042i
$285$		0			0
$286$	−1.25187	−	4.45760i	−0.0740244	−	0.263584i
$287$	−22.7382			−1.34219
$288$		0			0
$289$	16.8893			0.993489
$290$	7.48556	+	26.6543i	0.439567	+	1.56520i
$291$		0			0
$292$	14.8908	−	9.07998i	0.871421	−	0.531366i
$293$		−	23.5988i		−	1.37866i	−0.724448	−	0.689330i	$-0.757905\pi$
$293$		−	23.5988i		−	1.37866i	0.724448	−	0.689330i	$-0.242095\pi$
$294$		0			0
$295$			7.60705i			0.442900i
$296$	2.85015	+	2.65220i	0.165662	+	0.154156i
$297$		0			0
$298$	−4.16278	+	1.16907i	−0.241143	+	0.0677223i
$299$	−11.5312			−0.666868
$300$		0			0
$301$	6.43546			0.370934
$302$	−22.2125	+	6.23813i	−1.27819	+	0.358964i
$303$		0			0
$304$	−30.1344	−	15.5222i	−1.72833	−	0.890257i
$305$		−	30.5291i		−	1.74809i
$306$		0			0
$307$		−	4.42205i		−	0.252380i	−0.992006	−	0.126190i	$-0.959725\pi$
$307$		−	4.42205i		−	0.252380i	0.992006	−	0.126190i	$-0.0402749\pi$
$308$	−4.36188	−	7.15333i	−0.248541	−	0.407599i
$309$		0			0
$310$	3.11059	+	11.0761i	0.176670	+	0.629080i
$311$	−28.2418			−1.60144			−0.800722	−	0.599037i	$-0.795550\pi$
$311$	−28.2418			−1.60144			−0.800722	+	0.599037i	$0.795550\pi$
$312$		0			0
$313$	−5.28764			−0.298875			−0.149437	−	0.988771i	$-0.547746\pi$
$313$	−5.28764			−0.298875			−0.149437	+	0.988771i	$0.547746\pi$
$314$	0.876128	+	3.11969i	0.0494427	+	0.176054i
$315$		0			0
$316$	−13.8382	−	22.6942i	−0.778462	−	1.27665i
$317$		−	4.21786i		−	0.236898i	−0.992960	−	0.118449i	$-0.962208\pi$
$317$		−	4.21786i		−	0.236898i	0.992960	−	0.118449i	$-0.0377923\pi$
$318$		0			0
$319$		−	9.52712i		−	0.533416i
$320$	16.3961	−	1.18125i	0.916572	−	0.0660337i
$321$		0			0
$322$	−20.0891	+	5.64180i	−1.11952	+	0.314405i
$323$	2.81940			0.156876
$324$		0			0
$325$	2.54606			0.141230
$326$	0.722721	−	0.202968i	0.0400278	−	0.0112414i
$327$		0			0
$328$	−10.4584	+	11.2390i	−0.577471	+	0.620571i
$329$		−	29.0428i		−	1.60118i
$330$		0			0
$331$		−	21.1046i		−	1.16002i	−0.814611	−	0.580008i	$-0.803050\pi$
$331$		−	21.1046i		−	1.16002i	0.814611	−	0.580008i	$-0.196950\pi$
$332$	−1.68048	+	1.02470i	−0.0922282	+	0.0562380i
$333$		0			0
$334$	6.50890	+	23.1767i	0.356151	+	1.26817i
$335$	−13.0029			−0.710423
$336$		0			0
$337$	14.3857			0.783638			0.391819	−	0.920042i	$-0.371846\pi$
$337$	14.3857			0.783638			0.391819	+	0.920042i	$0.371846\pi$
$338$	−0.872311	−	3.10609i	−0.0474474	−	0.168949i
$339$		0			0
$340$	−1.16737	+	0.711830i	−0.0633098	+	0.0386044i
$341$		−	3.95895i		−	0.214389i
$342$		0			0
$343$			14.8674i			0.802764i
$344$	2.95999	−	3.18091i	0.159592	−	0.171503i
$345$		0			0
$346$	−7.33848	+	2.06093i	−0.394519	+	0.110796i
$347$	10.1450			0.544610			0.272305	−	0.962211i	$-0.412214\pi$
$347$	10.1450			0.544610			0.272305	+	0.962211i	$0.412214\pi$
$348$		0			0
$349$	−3.67592			−0.196768			−0.0983838	−	0.995149i	$-0.531367\pi$
$349$	−3.67592			−0.196768			−0.0983838	+	0.995149i	$0.531367\pi$
$350$	4.43562	−	1.24569i	0.237094	−	0.0665850i
$351$		0			0
$352$	−5.54199	−	1.13419i	−0.295389	−	0.0604524i
$353$		−	0.508364i		−	0.0270575i	−0.999908	−	0.0135288i	$-0.995694\pi$
$353$		−	0.508364i		−	0.0270575i	0.999908	−	0.0135288i	$-0.00430647\pi$
$354$		0			0
$355$			11.8743i			0.630221i
$356$	−1.52298	−	2.49763i	−0.0807177	−	0.132374i
$357$		0			0
$358$	−6.14162	−	21.8689i	−0.324594	−	1.15580i
$359$	−29.3560			−1.54935			−0.774676	−	0.632359i	$-0.782087\pi$
$359$	−29.3560			−1.54935			−0.774676	+	0.632359i	$0.782087\pi$
$360$		0			0
$361$	−52.8139			−2.77968
$362$	2.92856	+	10.4279i	0.153922	+	0.548080i
$363$		0			0
$364$	14.2805	+	23.4196i	0.748504	+	1.22752i
$365$			17.9190i			0.937923i
$366$		0			0
$367$			31.1945i			1.62834i	0.580628	+	0.814169i	$0.302807\pi$
$367$			31.1945i			1.62834i	−0.580628	+	0.814169i	$0.697193\pi$
$368$	−6.45138	+	12.5246i	−0.336301	+	0.652889i
$369$		0			0
$370$	−3.85102	+	1.08151i	−0.200205	+	0.0562252i
$371$	−37.0216			−1.92207
$372$		0			0
$373$	10.8720			0.562929			0.281464	−	0.959572i	$-0.409180\pi$
$373$	10.8720			0.562929			0.281464	+	0.959572i	$0.409180\pi$
$374$	0.452984	−	0.127215i	0.0234233	−	0.00657815i
$375$		0			0
$376$	−14.3553	−	13.3583i	−0.740316	−	0.688900i
$377$			31.1912i			1.60643i
$378$		0			0
$379$			0.305469i			0.0156909i	0.999969	+	0.00784545i	$0.00249731\pi$
$379$			0.305469i			0.0156909i	−0.999969	+	0.00784545i	$0.997503\pi$
$380$	29.7346	−	18.1312i	1.52535	−	0.930113i
$381$		0			0
$382$	5.04074	+	17.9489i	0.257907	+	0.918345i
$383$	18.0390			0.921748			0.460874	−	0.887466i	$-0.347536\pi$
$383$	18.0390			0.921748			0.460874	+	0.887466i	$0.347536\pi$
$384$		0			0
$385$	8.60800			0.438704
$386$	6.71093	+	23.8961i	0.341577	+	1.21628i
$387$		0			0
$388$	−10.2347	+	6.24080i	−0.519588	+	0.316829i
$389$			3.06226i			0.155263i	0.996982	+	0.0776315i	$0.0247358\pi$
$389$			3.06226i			0.155263i	−0.996982	+	0.0776315i	$0.975264\pi$
$390$		0			0
$391$		−	1.17181i		−	0.0592610i
$392$	21.8429	+	20.3259i	1.10323	+	1.02661i
$393$		0			0
$394$	15.8526	−	4.45203i	0.798644	−	0.224290i
$395$	27.3092			1.37408
$396$		0			0
$397$	−19.1036			−0.958781			−0.479391	−	0.877602i	$-0.659142\pi$
$397$	−19.1036			−0.958781			−0.479391	+	0.877602i	$0.659142\pi$
$398$	7.28170	−	2.04498i	0.364999	−	0.102506i
$399$		0			0
$400$	1.42444	−	2.76539i	0.0712222	−	0.138269i
$401$		−	21.1452i		−	1.05594i	−0.849262	−	0.527972i	$-0.822953\pi$
$401$		−	21.1452i		−	1.05594i	0.849262	−	0.527972i	$-0.177047\pi$
$402$		0			0
$403$			12.9614i			0.645652i
$404$	−5.32430	−	8.73165i	−0.264894	−	0.434416i
$405$		0			0
$406$	15.2607	+	54.3398i	0.757377	+	2.69684i
$407$	1.37648			0.0682295
$408$		0			0
$409$	16.6503			0.823306			0.411653	−	0.911341i	$-0.364952\pi$
$409$	16.6503			0.823306			0.411653	+	0.911341i	$0.364952\pi$
$410$	−4.26474	−	15.1858i	−0.210621	−	0.749971i
$411$		0			0
$412$	0.849757	+	1.39357i	0.0418645	+	0.0686563i
$413$			15.5084i			0.763118i
$414$		0			0
$415$		−	2.02221i		−	0.0992666i
$416$	18.1441	+	3.71326i	0.889590	+	0.182058i
$417$		0			0
$418$	−11.5381	+	3.24034i	−0.564347	+	0.158490i
$419$	−26.0057			−1.27046			−0.635232	−	0.772322i	$-0.719095\pi$
$419$	−26.0057			−1.27046			−0.635232	+	0.772322i	$0.719095\pi$
$420$		0			0
$421$	28.5887			1.39333			0.696663	−	0.717398i	$-0.254667\pi$
$421$	28.5887			1.39333			0.696663	+	0.717398i	$0.254667\pi$
$422$	23.5568	−	6.61567i	1.14673	−	0.322046i
$423$		0			0
$424$	−17.0281	+	18.2990i	−0.826958	+	0.888678i
$425$			0.258732i			0.0125503i
$426$		0			0
$427$		−	62.2392i		−	3.01197i
$428$	−24.2008	+	14.7569i	−1.16979	+	0.713302i
$429$		0			0
$430$	1.20702	+	4.29793i	0.0582079	+	0.207265i
$431$	−13.9908			−0.673913			−0.336957	−	0.941520i	$-0.609398\pi$
$431$	−13.9908			−0.673913			−0.336957	+	0.941520i	$0.609398\pi$
$432$		0			0
$433$	−10.7986			−0.518947			−0.259473	−	0.965750i	$-0.583549\pi$
$433$	−10.7986			−0.518947			−0.259473	+	0.965750i	$0.583549\pi$
$434$	6.34152	+	22.5807i	0.304403	+	1.08391i
$435$		0			0
$436$	4.46730	−	2.72402i	0.213945	−	0.130457i
$437$			29.8476i			1.42780i
$438$		0			0
$439$		−	4.67151i		−	0.222959i	−0.993767	−	0.111480i	$-0.964441\pi$
$439$		−	4.67151i		−	0.222959i	0.993767	−	0.111480i	$-0.0355589\pi$
$440$	3.95925	−	4.25475i	0.188750	−	0.202837i
$441$		0			0
$442$	−1.48304	+	0.416496i	−0.0705412	+	0.0198107i
$443$	18.0906			0.859509			0.429755	−	0.902946i	$-0.358600\pi$
$443$	18.0906			0.859509			0.429755	+	0.902946i	$0.358600\pi$
$444$		0			0
$445$	3.00554			0.142476
$446$	−30.4538	+	8.55259i	−1.44203	+	0.404977i
$447$		0			0
$448$	33.4266	−	2.40819i	1.57926	−	0.113776i
$449$		−	24.6355i		−	1.16262i	−0.813682	−	0.581311i	$-0.802540\pi$
$449$		−	24.6355i		−	1.16262i	0.813682	−	0.581311i	$-0.197460\pi$
$450$		0			0
$451$			5.42788i			0.255589i
$452$	−9.17607	−	15.0484i	−0.431606	−	0.707818i
$453$		0			0
$454$	9.97603	+	35.5223i	0.468198	+	1.66714i
$455$	−28.1821			−1.32120
$456$		0			0
$457$	−19.4637			−0.910476			−0.455238	−	0.890370i	$-0.650446\pi$
$457$	−19.4637			−0.910476			−0.455238	+	0.890370i	$0.650446\pi$
$458$	−3.77577	−	13.4446i	−0.176430	−	0.628226i
$459$		0			0
$460$	−7.53577	−	12.3584i	−0.351357	−	0.576213i
$461$			1.07568i			0.0500993i	0.999686	+	0.0250496i	$0.00797439\pi$
$461$			1.07568i			0.0500993i	−0.999686	+	0.0250496i	$0.992026\pi$
$462$		0			0
$463$			4.81991i			0.224000i	0.993708	+	0.112000i	$0.0357257\pi$
$463$			4.81991i			0.224000i	−0.993708	+	0.112000i	$0.964274\pi$
$464$	33.8782	+	17.4506i	1.57276	+	0.810122i
$465$		0			0
$466$	−32.1450	+	9.02754i	−1.48909	+	0.418193i
$467$	−8.41821			−0.389548			−0.194774	−	0.980848i	$-0.562397\pi$
$467$	−8.41821			−0.389548			−0.194774	+	0.980848i	$0.562397\pi$
$468$		0			0
$469$	−26.5088			−1.22406
$470$	19.3963	−	5.44723i	0.894685	−	0.251262i
$471$		0			0
$472$	7.66547	+	7.13309i	0.352832	+	0.328327i
$473$		−	1.53622i		−	0.0706354i
$474$		0			0
$475$		−	6.59024i		−	0.302381i
$476$	−2.37991	+	1.45120i	−0.109083	+	0.0665155i
$477$		0			0
$478$	−1.48650	−	5.29309i	−0.0679911	−	0.242100i
$479$	−21.1234			−0.965151			−0.482575	−	0.875854i	$-0.660299\pi$
$479$	−21.1234			−0.965151			−0.482575	+	0.875854i	$0.660299\pi$
$480$		0			0
$481$	−4.50651			−0.205479
$482$	−8.69726	−	30.9689i	−0.396149	−	1.41059i
$483$		0			0
$484$	−1.70758	+	1.04123i	−0.0776174	+	0.0473287i
$485$		−	12.3160i		−	0.559240i
$486$		0			0
$487$		−	8.21718i		−	0.372356i	−0.982516	−	0.186178i	$-0.940390\pi$
$487$		−	8.21718i		−	0.372356i	0.982516	−	0.186178i	$-0.0596101\pi$
$488$	−30.7635	−	28.6269i	−1.39260	−	1.29588i
$489$		0			0
$490$	−29.5133	+	8.28848i	−1.33328	+	0.374435i
$491$	8.17027			0.368719			0.184360	−	0.982859i	$-0.440979\pi$
$491$	8.17027			0.368719			0.184360	+	0.982859i	$0.440979\pi$
$492$		0			0
$493$	−3.16967			−0.142755
$494$	37.7751	−	10.6087i	1.69958	−	0.477308i
$495$		0			0
$496$	14.0779	+	7.25151i	0.632118	+	0.325602i
$497$			24.2079i			1.08587i
$498$		0			0
$499$		−	21.9921i		−	0.984501i	−0.870454	−	0.492250i	$-0.836174\pi$
$499$		−	21.9921i		−	0.984501i	0.870454	−	0.492250i	$-0.163826\pi$
$500$	12.3616	+	20.2726i	0.552830	+	0.906620i
$501$		0			0
$502$	−1.88755	−	6.72114i	−0.0842457	−	0.299979i
$503$	18.0446			0.804569			0.402284	−	0.915515i	$-0.368216\pi$
$503$	18.0446			0.804569			0.402284	+	0.915515i	$0.368216\pi$
$504$		0			0
$505$	10.5073			0.467568
$506$	1.34676	+	4.79551i	0.0598710	+	0.213186i
$507$		0			0
$508$	−18.7597	−	30.7653i	−0.832329	−	1.36499i
$509$		−	5.74310i		−	0.254558i	−0.991867	−	0.127279i	$-0.959376\pi$
$509$		−	5.74310i		−	0.254558i	0.991867	−	0.127279i	$-0.0406244\pi$
$510$		0			0
$511$			36.5312i			1.61605i
$512$	14.1843	−	17.6297i	0.626861	−	0.779131i
$513$		0			0
$514$	−36.2934	+	10.1926i	−1.60083	+	0.449575i
$515$	−1.67696			−0.0738958
$516$		0			0
$517$	−6.93286			−0.304907
$518$	−7.85102	+	2.20487i	−0.344954	+	0.0968763i
$519$		0			0
$520$	−12.9624	+	13.9298i	−0.568437	+	0.610863i
$521$		−	13.3348i		−	0.584208i	−0.956386	−	0.292104i	$-0.905645\pi$
$521$		−	13.3348i		−	0.584208i	0.956386	−	0.292104i	$-0.0943554\pi$
$522$		0			0
$523$		−	31.7086i		−	1.38652i	−0.720687	−	0.693260i	$-0.756174\pi$
$523$		−	31.7086i		−	1.38652i	0.720687	−	0.693260i	$-0.243826\pi$
$524$	−27.3684	+	16.6884i	−1.19560	+	0.729038i
$525$		0			0
$526$	−7.56719	−	26.9450i	−0.329945	−	1.17486i
$527$	−1.31714			−0.0573757
$528$		0			0
$529$	−10.5946			−0.460637
$530$	−6.94371	−	24.7249i	−0.301616	−	1.07398i
$531$		0			0
$532$	60.6195	−	36.9639i	2.62819	−	1.60259i
$533$		−	17.7706i		−	0.769728i
$534$		0			0
$535$		−	29.1222i		−	1.25906i
$536$	−12.1927	+	13.1027i	−0.526645	+	0.565952i
$537$		0			0
$538$	21.9902	−	6.17569i	0.948064	−	0.266253i
$539$	10.5490			0.454378
$540$		0			0
$541$	31.1160			1.33778			0.668890	−	0.743361i	$-0.266770\pi$
$541$	31.1160			1.33778			0.668890	+	0.743361i	$0.266770\pi$
$542$	1.16319	−	0.326668i	0.0499632	−	0.0140316i
$543$		0			0
$544$	−0.377344	+	1.84382i	−0.0161785	+	0.0790531i
$545$			5.37575i			0.230272i
$546$		0			0
$547$		−	13.1543i		−	0.562437i	−0.959644	−	0.281218i	$-0.909261\pi$
$547$		−	13.1543i		−	0.562437i	0.959644	−	0.281218i	$-0.0907385\pi$
$548$	10.6122	+	17.4036i	0.453330	+	0.743445i
$549$		0			0
$550$	−0.297361	−	1.05883i	−0.0126795	−	0.0451488i
$551$	80.7357			3.43946
$552$		0			0
$553$	55.6750			2.36754
$554$	8.57984	+	30.5508i	0.364523	+	1.29798i
$555$		0			0
$556$	−1.65001	−	2.70596i	−0.0699762	−	0.114758i
$557$		−	12.1015i		−	0.512756i	−0.966577	−	0.256378i	$-0.917471\pi$
$557$		−	12.1015i		−	0.512756i	0.966577	−	0.256378i	$-0.0825292\pi$
$558$		0			0
$559$			5.02949i			0.212725i
$560$	−15.7670	+	30.6099i	−0.666279	+	1.29350i
$561$		0			0
$562$	37.7986	−	10.6153i	1.59444	−	0.447780i
$563$	−20.2233			−0.852309			−0.426155	−	0.904650i	$-0.640132\pi$
$563$	−20.2233			−0.852309			−0.426155	+	0.904650i	$0.640132\pi$
$564$		0			0
$565$	18.1086			0.761835
$566$	−18.7324	+	5.26077i	−0.787381	+	0.221127i
$567$		0			0
$568$	11.9655	+	11.1344i	0.502060	+	0.467191i
$569$			9.66888i			0.405340i	0.979247	+	0.202670i	$0.0649619\pi$
$569$			9.66888i			0.405340i	−0.979247	+	0.202670i	$0.935038\pi$
$570$		0			0
$571$			17.7620i			0.743318i	0.928369	+	0.371659i	$0.121211\pi$
$571$			17.7620i			0.743318i	−0.928369	+	0.371659i	$0.878789\pi$
$572$	5.59052	−	3.40893i	0.233752	−	0.142535i
$573$		0			0
$574$	−8.69448	−	30.9590i	−0.362900	−	1.29220i
$575$	−2.73906			−0.114227
$576$		0			0
$577$	−22.1545			−0.922304			−0.461152	−	0.887321i	$-0.652564\pi$
$577$	−22.1545			−0.922304			−0.461152	+	0.887321i	$0.652564\pi$
$578$	6.45801	+	22.9955i	0.268618	+	0.956486i
$579$		0			0
$580$	−33.4287	+	20.3838i	−1.38805	+	0.846391i
$581$		−	4.12266i		−	0.171037i
$582$		0			0
$583$			8.83749i			0.366011i
$584$	18.0566	+	16.8025i	0.747188	+	0.695294i
$585$		0			0
$586$	32.1308	−	9.02356i	1.32731	−	0.372760i
$587$	−32.9785			−1.36117			−0.680584	−	0.732670i	$-0.738274\pi$
$587$	−32.9785			−1.36117			−0.680584	+	0.732670i	$0.738274\pi$
$588$		0			0
$589$	33.5494			1.38238
$590$	−10.3573	+	2.90873i	−0.426403	+	0.119750i
$591$		0			0
$592$	−2.52126	+	4.89472i	−0.103623	+	0.201172i
$593$			7.23373i			0.297054i	0.988908	+	0.148527i	$0.0474531\pi$
$593$			7.23373i			0.297054i	−0.988908	+	0.148527i	$0.952547\pi$
$594$		0			0
$595$		−	2.86388i		−	0.117408i
$596$	−3.18347	−	5.22077i	−0.130400	−	0.213851i
$597$		0			0
$598$	−4.40923	−	15.7002i	−0.180307	−	0.642030i
$599$	−26.9917			−1.10285			−0.551425	−	0.834224i	$-0.685916\pi$
$599$	−26.9917			−1.10285			−0.551425	+	0.834224i	$0.685916\pi$
$600$		0			0
$601$	33.8244			1.37972			0.689862	−	0.723941i	$-0.257671\pi$
$601$	33.8244			1.37972			0.689862	+	0.723941i	$0.257671\pi$
$602$	2.46074	+	8.76214i	0.100292	+	0.357118i
$603$		0			0
$604$	−16.9869	−	27.8579i	−0.691188	−	1.13352i
$605$		−	2.05483i		−	0.0835407i
$606$		0			0
$607$			18.4992i			0.750861i	0.926851	+	0.375430i	$0.122505\pi$
$607$			18.4992i			0.750861i	−0.926851	+	0.375430i	$0.877495\pi$
$608$	9.61145	−	46.9645i	0.389796	−	1.90466i
$609$		0			0
$610$	41.5666	−	11.6735i	1.68298	−	0.472646i
$611$	22.6978			0.918254
$612$		0			0
$613$	18.8425			0.761041			0.380520	−	0.924772i	$-0.375745\pi$
$613$	18.8425			0.761041			0.380520	+	0.924772i	$0.375745\pi$
$614$	6.02080	−	1.69087i	0.242980	−	0.0682380i
$615$		0			0
$616$	8.07167	−	8.67411i	0.325217	−	0.349490i
$617$		−	19.5867i		−	0.788529i	−0.918997	−	0.394265i	$-0.870999\pi$
$617$		−	19.5867i		−	0.788529i	0.918997	−	0.394265i	$-0.129001\pi$
$618$		0			0
$619$			20.9215i			0.840908i	0.907314	+	0.420454i	$0.138129\pi$
$619$			20.9215i			0.840908i	−0.907314	+	0.420454i	$0.861871\pi$
$620$	−13.8911	+	8.47039i	−0.557881	+	0.340179i
$621$		0			0
$622$	−10.7989	−	38.4523i	−0.432996	−	1.54180i
$623$	6.12735			0.245487
$624$		0			0
$625$	−20.5069			−0.820274
$626$	−2.02185	−	7.19933i	−0.0808093	−	0.287743i
$627$		0			0
$628$	−3.91257	+	2.38577i	−0.156128	+	0.0952024i
$629$		−	0.457954i		−	0.0182598i
$630$		0			0
$631$			1.27651i			0.0508172i	0.999677	+	0.0254086i	$0.00808868\pi$
$631$			1.27651i			0.0508172i	−0.999677	+	0.0254086i	$0.991911\pi$
$632$	25.6077	−	27.5190i	1.01862	−	1.09465i
$633$		0			0
$634$	5.74278	−	1.61279i	0.228075	−	0.0640522i
$635$	37.0216			1.46916
$636$		0			0
$637$	−34.5369			−1.36840
$638$	12.9716	−	3.64291i	0.513549	−	0.144224i
$639$		0			0
$640$	7.87776	+	21.8723i	0.311396	+	0.864580i
$641$		−	20.0324i		−	0.791234i	−0.918416	−	0.395617i	$-0.870531\pi$
$641$		−	20.0324i		−	0.791234i	0.918416	−	0.395617i	$-0.129469\pi$
$642$		0			0
$643$			9.71125i			0.382974i	0.981495	+	0.191487i	$0.0613310\pi$
$643$			9.71125i			0.382974i	−0.981495	+	0.191487i	$0.938669\pi$
$644$	−15.3631	−	25.1949i	−0.605390	−	0.992818i
$645$		0			0
$646$	1.07806	+	3.83873i	0.0424158	+	0.151033i
$647$	31.8921			1.25381			0.626904	−	0.779097i	$-0.284322\pi$
$647$	31.8921			1.25381			0.626904	+	0.779097i	$0.284322\pi$
$648$		0			0
$649$	3.70203			0.145318
$650$	0.973543	+	3.46656i	0.0381855	+	0.135970i
$651$		0			0
$652$	0.552698	+	0.906404i	0.0216453	+	0.0354975i
$653$			20.6601i			0.808491i	0.914651	+	0.404245i	$0.132466\pi$
$653$			20.6601i			0.808491i	−0.914651	+	0.404245i	$0.867534\pi$
$654$		0			0
$655$		−	32.9340i		−	1.28684i
$656$	−19.3014	−	9.94210i	−0.753593	−	0.388174i
$657$		0			0
$658$	39.5430	−	11.1052i	1.54155	−	0.432926i
$659$	−28.5649			−1.11273			−0.556365	−	0.830938i	$-0.687804\pi$
$659$	−28.5649			−1.11273			−0.556365	+	0.830938i	$0.687804\pi$
$660$		0			0
$661$	−20.3230			−0.790475			−0.395237	−	0.918579i	$-0.629338\pi$
$661$	−20.3230			−0.790475			−0.395237	+	0.918579i	$0.629338\pi$
$662$	28.7348	−	8.06983i	1.11681	−	0.313643i
$663$		0			0
$664$	−2.03775	−	1.89622i	−0.0790799	−	0.0735876i
$665$			72.9468i			2.82876i
$666$		0			0
$667$		−	33.5557i		−	1.29928i
$668$	−29.0671	+	17.7243i	−1.12464	+	0.685772i
$669$		0			0
$670$	−4.97194	−	17.7039i	−0.192083	−	0.683962i
$671$	−14.8572			−0.573557
$672$		0			0
$673$	−40.4387			−1.55880			−0.779398	−	0.626529i	$-0.784475\pi$
$673$	−40.4387			−1.55880			−0.779398	+	0.626529i	$0.784475\pi$
$674$	5.50069	+	19.5867i	0.211879	+	0.754450i
$675$		0			0
$676$	3.89552	−	2.37537i	0.149828	−	0.0913604i
$677$			25.2867i			0.971848i	0.874001	+	0.485924i	$0.161517\pi$
$677$			25.2867i			0.971848i	−0.874001	+	0.485924i	$0.838483\pi$
$678$		0			0
$679$		−	25.1084i		−	0.963573i
$680$	−1.41556	−	1.31724i	−0.0542841	−	0.0505140i
$681$		0			0
$682$	5.39027	−	1.51380i	0.206404	−	0.0579662i
$683$	2.12760			0.0814102			0.0407051	−	0.999171i	$-0.487040\pi$
$683$	2.12760			0.0814102			0.0407051	+	0.999171i	$0.487040\pi$
$684$		0			0
$685$	−20.9428			−0.800181
$686$	−20.2425	+	5.68489i	−0.772864	+	0.217050i
$687$		0			0
$688$	5.46276	+	2.81385i	0.208266	+	0.107277i
$689$		−	28.9334i		−	1.10228i
$690$		0			0
$691$			33.9780i			1.29258i	0.763090	+	0.646292i	$0.223681\pi$
$691$			33.9780i			1.29258i	−0.763090	+	0.646292i	$0.776319\pi$
$692$	−5.61207	−	9.20360i	−0.213339	−	0.349868i
$693$		0			0
$694$	3.87915	+	13.8128i	0.147251	+	0.524325i
$695$	3.25624			0.123516
$696$		0			0
$697$	1.80585			0.0684016
$698$	−1.40557	−	5.00492i	−0.0532017	−	0.189439i
$699$		0			0
$700$	3.39212	+	5.56295i	0.128210	+	0.210260i
$701$			43.1893i			1.63124i	0.578590	+	0.815618i	$0.303603\pi$
$701$			43.1893i			1.63124i	−0.578590	+	0.815618i	$0.696397\pi$
$702$		0			0
$703$			11.6647i			0.439942i
$704$	−0.574864	−	7.97932i	−0.0216660	−	0.300732i
$705$		0			0
$706$	0.692158	−	0.194385i	0.0260497	−	0.00731576i
$707$	21.4211			0.805622
$708$		0			0
$709$	2.99634			0.112530			0.0562650	−	0.998416i	$-0.482081\pi$
$709$	2.99634			0.112530			0.0562650	+	0.998416i	$0.482081\pi$
$710$	−16.1673	+	4.54040i	−0.606748	+	0.170398i
$711$		0			0
$712$	2.81828	−	3.02862i	0.105619	−	0.113502i
$713$		−	13.9439i		−	0.522204i
$714$		0			0
$715$			6.72739i			0.251590i
$716$	27.4269	−	16.7241i	1.02499	−	0.625009i
$717$		0			0
$718$	−11.2249	−	39.9694i	−0.418911	−	1.49164i
$719$	44.6554			1.66536			0.832682	−	0.553751i	$-0.186804\pi$
$719$	44.6554			1.66536			0.832682	+	0.553751i	$0.186804\pi$
$720$		0			0
$721$	−3.41880			−0.127323
$722$	−20.1946	−	71.9082i	−0.751565	−	2.67615i
$723$		0			0
$724$	−13.0782	+	7.97471i	−0.486049	+	0.296378i
$725$			7.40899i			0.275163i
$726$		0			0
$727$			22.6022i			0.838270i	0.907924	+	0.419135i	$0.137667\pi$
$727$			22.6022i			0.838270i	−0.907924	+	0.419135i	$0.862333\pi$
$728$	−26.4262	+	28.3985i	−0.979420	+	1.05252i
$729$		0			0
$730$	−24.3974	+	6.85173i	−0.902989	+	0.253594i
$731$	−0.511100			−0.0189037
$732$		0			0
$733$	−28.3580			−1.04743			−0.523713	−	0.851895i	$-0.675454\pi$
$733$	−28.3580			−1.04743			−0.523713	+	0.851895i	$0.675454\pi$
$734$	−42.4725	+	11.9279i	−1.56769	+	0.440267i
$735$		0			0
$736$	−19.5196	−	3.99475i	−0.719501	−	0.147248i
$737$			6.32795i			0.233093i
$738$		0			0
$739$			43.9526i			1.61682i	0.588619	+	0.808411i	$0.299672\pi$
$739$			43.9526i			1.61682i	−0.588619	+	0.808411i	$0.700328\pi$
$740$	−2.94505	−	4.82977i	−0.108262	−	0.177546i
$741$		0			0
$742$	−14.1561	−	50.4064i	−0.519685	−	1.85048i
$743$	31.8324			1.16782			0.583909	−	0.811819i	$-0.301522\pi$
$743$	31.8324			1.16782			0.583909	+	0.811819i	$0.301522\pi$
$744$		0			0
$745$	6.28245			0.230171
$746$	4.15714	+	14.8026i	0.152204	+	0.541962i
$747$		0			0
$748$	0.346418	+	0.568112i	0.0126663	+	0.0207722i
$749$		−	59.3710i		−	2.16937i
$750$		0			0
$751$			11.1655i			0.407433i	0.979030	+	0.203717i	$0.0653021\pi$
$751$			11.1655i			0.407433i	−0.979030	+	0.203717i	$0.934698\pi$
$752$	12.6987	−	24.6531i	0.463075	−	0.899006i
$753$		0			0
$754$	−42.4681	+	11.9267i	−1.54660	+	0.434344i
$755$	33.5230			1.22003
$756$		0			0
$757$	11.7438			0.426834			0.213417	−	0.976961i	$-0.431541\pi$
$757$	11.7438			0.426834			0.213417	+	0.976961i	$0.431541\pi$
$758$	−0.415908	+	0.116803i	−0.0151065	+	0.00424248i
$759$		0			0
$760$	36.0561	+	33.5519i	1.30789	+	1.21706i
$761$			8.11196i			0.294058i	0.989132	+	0.147029i	$0.0469711\pi$
$761$			8.11196i			0.294058i	−0.989132	+	0.147029i	$0.953029\pi$
$762$		0			0
$763$			10.9595i			0.396760i
$764$	−22.5107	+	13.7263i	−0.814408	+	0.496601i
$765$		0			0
$766$	6.89761	+	24.5608i	0.249221	+	0.887417i
$767$	−12.1202			−0.437636
$768$		0			0
$769$	−36.1570			−1.30386			−0.651928	−	0.758281i	$-0.726039\pi$
$769$	−36.1570			−1.30386			−0.651928	+	0.758281i	$0.726039\pi$
$770$	3.29147	+	11.7201i	0.118616	+	0.422364i
$771$		0			0
$772$	−29.9694	+	18.2744i	−1.07862	+	0.657710i
$773$			23.8614i			0.858236i	0.903249	+	0.429118i	$0.141175\pi$
$773$			23.8614i			0.858236i	−0.903249	+	0.429118i	$0.858825\pi$
$774$		0			0
$775$			3.07877i			0.110593i
$776$	−12.4106	−	11.5486i	−0.445513	−	0.414571i
$777$		0			0
$778$	−4.16940	+	1.17093i	−0.149480	+	0.0419798i
$779$	−45.9975			−1.64803
$780$		0			0
$781$	5.77871			0.206779
$782$	1.59547	−	0.448068i	0.0570538	−	0.0160229i
$783$		0			0
$784$	−19.3224	+	37.5121i	−0.690084	+	1.33972i
$785$		−	4.70822i		−	0.168043i
$786$		0			0
$787$			43.8822i			1.56423i	0.623134	+	0.782115i	$0.285859\pi$
$787$			43.8822i			1.56423i	−0.623134	+	0.782115i	$0.714141\pi$
$788$	12.1232	+	19.8817i	0.431872	+	0.708255i
$789$		0			0
$790$	10.4423	+	37.1826i	0.371521	+	1.32290i
$791$	36.9178			1.31265
$792$		0			0
$793$	48.6417			1.72732
$794$	−7.30469	−	26.0103i	−0.259234	−	0.923071i
$795$		0			0
$796$	5.56865	+	9.13238i	0.197376	+	0.323689i
$797$		−	28.3351i		−	1.00368i	−0.864961	−	0.501840i	$-0.832657\pi$
$797$		−	28.3351i		−	1.00368i	0.864961	−	0.501840i	$-0.167343\pi$
$798$		0			0
$799$			2.30656i			0.0816004i
$800$	4.30986	+	0.882027i	0.152376	+	0.0311844i
$801$		0			0
$802$	28.7901	−	8.08537i	1.01661	−	0.285504i
$803$	8.72042			0.307737
$804$		0			0
$805$	30.3184			1.06858
$806$	−17.6474	+	4.95608i	−0.621604	+	0.174570i
$807$		0			0
$808$	9.85263	−	10.5880i	0.346614	−	0.372484i
$809$			18.5019i			0.650492i	0.945629	+	0.325246i	$0.105447\pi$
$809$			18.5019i			0.650492i	−0.945629	+	0.325246i	$0.894553\pi$
$810$		0			0
$811$		−	0.0475401i		−	0.00166936i	−1.00000		0.000834679i	$-0.999734\pi$
$811$		−	0.0475401i		−	0.00166936i	1.00000		0.000834679i	$-0.000265687\pi$
$812$	−68.1506	+	41.5562i	−2.39162	+	1.45834i
$813$		0			0
$814$	0.526328	+	1.87413i	0.0184478	+	0.0656882i
$815$	−1.09073			−0.0382065
$816$		0			0
$817$	13.0184			0.455456
$818$	6.36663	+	22.6701i	0.222604	+	0.792641i
$819$		0			0
$820$	19.0453	−	11.6132i	0.665090	−	0.405552i
$821$			39.2412i			1.36953i	0.728765	+	0.684764i	$0.240095\pi$
$821$			39.2412i			1.36953i	−0.728765	+	0.684764i	$0.759905\pi$
$822$		0			0
$823$			37.4363i			1.30495i	0.757812	+	0.652473i	$0.226268\pi$
$823$			37.4363i			1.30495i	−0.757812	+	0.652473i	$0.773732\pi$
$824$	−1.57248	+	1.68984i	−0.0547799	+	0.0588684i
$825$		0			0
$826$	−21.1153	+	5.92999i	−0.734695	+	0.206331i
$827$	37.8240			1.31527			0.657635	−	0.753337i	$-0.271557\pi$
$827$	37.8240			1.31527			0.657635	+	0.753337i	$0.271557\pi$
$828$		0			0
$829$	−14.3390			−0.498014			−0.249007	−	0.968502i	$-0.580104\pi$
$829$	−14.3390			−0.498014			−0.249007	+	0.968502i	$0.580104\pi$
$830$	2.75333	−	0.773240i	0.0955693	−	0.0268395i
$831$		0			0
$832$	1.88207	+	26.1238i	0.0652491	+	0.905681i
$833$		−	3.50966i		−	0.121602i
$834$		0			0
$835$		−	34.9781i		−	1.21047i
$836$	−8.82372	−	14.4706i	−0.305175	−	0.500475i
$837$		0			0
$838$	−9.94389	−	35.4079i	−0.343506	−	1.22314i
$839$	8.56063			0.295546			0.147773	−	0.989021i	$-0.452790\pi$
$839$	8.56063			0.295546			0.147773	+	0.989021i	$0.452790\pi$
$840$		0			0
$841$	−61.7660			−2.12986
$842$	10.9315	+	38.9246i	0.376725	+	1.34143i
$843$		0			0
$844$	18.0150	+	29.5439i	0.620102	+	1.01694i
$845$			4.68770i			0.161262i
$846$		0			0
$847$		−	4.18915i		−	0.143941i
$848$	−31.4259	−	16.1874i	−1.07917	−	0.555877i
$849$		0			0
$850$	−0.352274	+	0.0989320i	−0.0120829	+	0.00339334i
$851$	4.84812			0.166192
$852$		0			0
$853$	−54.1181			−1.85297			−0.926484	−	0.376335i	$-0.877184\pi$
$853$	−54.1181			−1.85297			−0.926484	+	0.376335i	$0.877184\pi$
$854$	84.7412	−	23.7986i	2.89978	−	0.814371i
$855$		0			0
$856$	−29.3458	−	27.3077i	−1.00302	−	0.933358i
$857$			22.8279i			0.779788i	0.920860	+	0.389894i	$0.127488\pi$
$857$			22.8279i			0.779788i	−0.920860	+	0.389894i	$0.872512\pi$
$858$		0			0
$859$		−	0.288906i		−	0.00985734i	−0.999988	−	0.00492867i	$-0.998431\pi$
$859$		−	0.288906i		−	0.00985734i	0.999988	−	0.00492867i	$-0.00156885\pi$
$860$	−5.39027	+	3.28682i	−0.183807	+	0.112080i
$861$		0			0
$862$	−5.34970	−	19.0490i	−0.182212	−	0.648813i
$863$	−0.722052			−0.0245789			−0.0122895	−	0.999924i	$-0.503912\pi$
$863$	−0.722052			−0.0245789			−0.0122895	+	0.999924i	$0.503912\pi$
$864$		0			0
$865$	11.0752			0.376568
$866$	−4.12908	−	14.7027i	−0.140312	−	0.499618i
$867$		0			0
$868$	−28.3197	+	17.2685i	−0.961232	+	0.586130i
$869$		−	13.2903i		−	0.450842i
$870$		0			0
$871$		−	20.7173i		−	0.701981i
$872$	5.41704	+	5.04081i	0.183444	+	0.170703i
$873$		0			0
$874$	−40.6386	+	11.4129i	−1.37462	+	0.386047i
$875$	−49.7342			−1.68132
$876$		0			0
$877$	−25.4051			−0.857869			−0.428935	−	0.903335i	$-0.641111\pi$
$877$	−25.4051			−0.857869			−0.428935	+	0.903335i	$0.641111\pi$
$878$	6.36045	−	1.78626i	0.214655	−	0.0602833i
$879$		0			0
$880$	7.30693	+	3.76378i	0.246317	+	0.126877i
$881$		−	18.2594i		−	0.615175i	−0.951520	−	0.307588i	$-0.900478\pi$
$881$		−	18.2594i		−	0.615175i	0.951520	−	0.307588i	$-0.0995217\pi$
$882$		0			0
$883$			10.2183i			0.343872i	0.985108	+	0.171936i	$0.0550023\pi$
$883$			10.2183i			0.343872i	−0.985108	+	0.171936i	$0.944998\pi$
$884$	−1.13415	−	1.85997i	−0.0381456	−	0.0625575i
$885$		0			0
$886$	6.91734	+	24.6310i	0.232393	+	0.827496i
$887$	35.4055			1.18880			0.594399	−	0.804170i	$-0.297390\pi$
$887$	35.4055			1.18880			0.594399	+	0.804170i	$0.297390\pi$
$888$		0			0
$889$	75.4755			2.53137
$890$	1.14924	+	4.09216i	0.0385225	+	0.137170i
$891$		0			0
$892$	−23.2894	−	38.1938i	−0.779787	−	1.27882i
$893$		−	58.7512i		−	1.96603i
$894$		0			0
$895$			33.0044i			1.10321i
$896$	16.0603	+	44.5908i	0.536536	+	1.48968i
$897$		0			0
$898$	33.5422	−	9.41995i	1.11932	−	0.314348i
$899$	−37.7174			−1.25795
$900$		0			0
$901$	2.94023			0.0979533
$902$	−7.39027	+	2.07547i	−0.246069	+	0.0691057i
$903$		0			0
$904$	16.9803	−	18.2477i	0.564758	−	0.606909i
$905$		−	15.7378i		−	0.523142i
$906$		0			0
$907$		−	23.9880i		−	0.796508i	−0.917275	−	0.398254i	$-0.869616\pi$
$907$		−	23.9880i		−	0.796508i	0.917275	−	0.398254i	$-0.130384\pi$
$908$	−44.5505	+	27.1655i	−1.47846	+	0.901519i
$909$		0			0
$910$	−10.7761	−	38.3710i	−0.357223	−	1.27199i
$911$	−0.671680			−0.0222537			−0.0111269	−	0.999938i	$-0.503542\pi$
$911$	−0.671680			−0.0222537			−0.0111269	+	0.999938i	$0.503542\pi$
$912$		0			0
$913$	−0.984127			−0.0325699
$914$	−7.44241	−	26.5007i	−0.246173	−	0.876564i
$915$		0			0
$916$	16.8616	−	10.2817i	0.557125	−	0.339718i
$917$		−	67.1421i		−	2.21723i
$918$		0			0
$919$		−	12.6625i		−	0.417699i	−0.977948	−	0.208849i	$-0.933028\pi$
$919$		−	12.6625i		−	0.417699i	0.977948	−	0.208849i	$-0.0669719\pi$
$920$	13.9450	−	14.9858i	0.459752	−	0.494066i
$921$		0			0
$922$	−1.46458	+	0.411310i	−0.0482333	+	0.0135458i
$923$	−18.9192			−0.622732
$924$		0			0
$925$	−1.07045			−0.0351962
$926$	−6.56250	+	1.84300i	−0.215657	+	0.0605648i
$927$		0			0
$928$	−10.8055	+	52.7992i	−0.354709	+	1.73322i
$929$			17.2495i			0.565939i	0.959129	+	0.282969i	$0.0913195\pi$
$929$			17.2495i			0.565939i	−0.959129	+	0.282969i	$0.908681\pi$
$930$		0			0
$931$			89.3956i			2.92982i
$932$	−24.5827	−	40.3148i	−0.805234	−	1.32055i
$933$		0			0
$934$	−3.21889	−	11.4617i	−0.105325	−	0.375039i
$935$	−0.683642			−0.0223575
$936$		0			0
$937$	25.9299			0.847091			0.423546	−	0.905875i	$-0.360785\pi$
$937$	25.9299			0.847091			0.423546	+	0.905875i	$0.360785\pi$
$938$	−10.1362	−	36.0928i	−0.330960	−	1.17847i
$939$		0			0
$940$	14.8332	+	24.3260i	0.483807	+	0.793426i
$941$			38.5622i			1.25709i	0.777773	+	0.628545i	$0.216349\pi$
$941$			38.5622i			1.25709i	−0.777773	+	0.628545i	$0.783651\pi$
$942$		0			0
$943$			19.1177i			0.622556i
$944$	−6.78091	+	13.1643i	−0.220700	+	0.428463i
$945$		0			0
$946$	2.09162	−	0.587408i	0.0680046	−	0.0190983i
$947$	−10.0835			−0.327668			−0.163834	−	0.986488i	$-0.552386\pi$
$947$	−10.0835			−0.327668			−0.163834	+	0.986488i	$0.552386\pi$
$948$		0			0
$949$	−28.5502			−0.926777
$950$	8.97288	−	2.51993i	0.291119	−	0.0817573i
$951$		0			0
$952$	−2.88588	−	2.68545i	−0.0935318	−	0.0870358i
$953$			11.8961i			0.385353i	0.981262	+	0.192677i	$0.0617168\pi$
$953$			11.8961i			0.385353i	−0.981262	+	0.192677i	$0.938283\pi$
$954$		0			0
$955$		−	27.0884i		−	0.876559i
$956$	6.63836	−	4.04787i	0.214700	−	0.130917i
$957$		0			0
$958$	−8.07700	−	28.7603i	−0.260956	−	0.929203i
$959$	−42.6957			−1.37872
$960$		0			0
$961$	15.3267			0.494410
$962$	−1.72317	−	6.13579i	−0.0555571	−	0.197826i
$963$		0			0
$964$	38.8398	−	23.6833i	1.25095	−	0.762789i
$965$		−	36.0638i		−	1.16094i
$966$		0			0
$967$		−	40.7204i		−	1.30948i	−0.755855	−	0.654739i	$-0.772778\pi$
$967$		−	40.7204i		−	1.30948i	0.755855	−	0.654739i	$-0.227222\pi$
$968$	−2.07061	−	1.92680i	−0.0665520	−	0.0619298i
$969$		0			0
$970$	16.7687	−	4.70930i	0.538410	−	0.151206i
$971$	0.171053			0.00548936			0.00274468	−	0.999996i	$-0.499126\pi$
$971$	0.171053			0.00548936			0.00274468	+	0.999996i	$0.499126\pi$
$972$		0			0
$973$	6.63845			0.212819
$974$	11.1880	−	3.14203i	0.358487	−	0.100677i
$975$		0			0
$976$	27.2136	−	52.8320i	0.871085	−	1.69111i
$977$			42.4361i			1.35765i	0.734299	+	0.678826i	$0.237511\pi$
$977$			42.4361i			1.35765i	−0.734299	+	0.678826i	$0.762489\pi$
$978$		0			0
$979$		−	1.46267i		−	0.0467471i
$980$	−22.5702	−	37.0143i	−0.720979	−	1.18238i
$981$		0			0
$982$	3.12409	+	11.1241i	0.0996937	+	0.354986i
$983$	16.0332			0.511380			0.255690	−	0.966759i	$-0.417697\pi$
$983$	16.0332			0.511380			0.255690	+	0.966759i	$0.417697\pi$
$984$		0			0
$985$	−23.9247			−0.762305
$986$	−1.21200	−	4.31563i	−0.0385978	−	0.137438i
$987$		0			0
$988$	28.8883	+	47.3758i	0.919060	+	1.50723i
$989$		−	5.41075i		−	0.172052i
$990$		0			0
$991$			19.7092i			0.626085i	0.949739	+	0.313042i	$0.101348\pi$
$991$			19.7092i			0.626085i	−0.949739	+	0.313042i	$0.898652\pi$
$992$	−4.49019	+	21.9405i	−0.142564	+	0.696610i
$993$		0			0
$994$	−32.9601	+	9.25645i	−1.04543	+	0.293597i
$995$	−10.9895			−0.348391
$996$		0			0
$997$	14.9855			0.474596			0.237298	−	0.971437i	$-0.423738\pi$
$997$	14.9855			0.474596			0.237298	+	0.971437i	$0.423738\pi$
$998$	29.9431	−	8.40918i	0.947832	−	0.266188i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.c.a.287.6	yes	10
3.2	odd	2		396.2.c.b.287.5	yes	10
4.3	odd	2		396.2.c.b.287.6	yes	10
8.3	odd	2		6336.2.d.g.3455.8		10
8.5	even	2		6336.2.d.h.3455.8		10
12.11	even	2	inner	396.2.c.a.287.5	✓	10
24.5	odd	2		6336.2.d.g.3455.3		10
24.11	even	2		6336.2.d.h.3455.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
396.2.c.a.287.5	✓	10	12.11	even	2	inner
396.2.c.a.287.6	yes	10	1.1	even	1	trivial
396.2.c.b.287.5	yes	10	3.2	odd	2
396.2.c.b.287.6	yes	10	4.3	odd	2
6336.2.d.g.3455.3		10	24.5	odd	2
6336.2.d.g.3455.8		10	8.3	odd	2
6336.2.d.h.3455.3		10	24.11	even	2
6336.2.d.h.3455.8		10	8.5	even	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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.382373 + 1.36154i) q^{2} +(-1.70758 + 1.04123i) q^{4} -2.05483i q^{5} -4.18915i q^{7} +(-2.07061 - 1.92680i) q^{8} +(2.79773 - 0.785711i) q^{10} -1.00000 q^{11} +3.27394 q^{13} +(5.70370 - 1.60182i) q^{14} +(1.83167 - 3.55598i) q^{16} +0.332700i q^{17} -8.47431i q^{19} +(2.13955 + 3.50879i) q^{20} +(-0.382373 - 1.36154i) q^{22} -3.52212 q^{23} +0.777673 q^{25} +(1.25187 + 4.45760i) q^{26} +(4.36188 + 7.15333i) q^{28} +9.52712i q^{29} +3.95895i q^{31} +(5.54199 + 1.13419i) q^{32} +(-0.452984 + 0.127215i) q^{34} -8.60800 q^{35} -1.37648 q^{37} +(11.5381 - 3.24034i) q^{38} +(-3.95925 + 4.25475i) q^{40} -5.42788i q^{41} +1.53622i q^{43} +(1.70758 - 1.04123i) q^{44} +(-1.34676 - 4.79551i) q^{46} +6.93286 q^{47} -10.5490 q^{49} +(0.297361 + 1.05883i) q^{50} +(-5.59052 + 3.40893i) q^{52} -8.83749i q^{53} +2.05483i q^{55} +(-8.07167 + 8.67411i) q^{56} +(-12.9716 + 3.64291i) q^{58} -3.70203 q^{59} +14.8572 q^{61} +(-5.39027 + 1.51380i) q^{62} +(0.574864 + 7.97932i) q^{64} -6.72739i q^{65} -6.32795i q^{67} +(-0.346418 - 0.568112i) q^{68} +(-3.29147 - 11.7201i) q^{70} -5.77871 q^{71} -8.72042 q^{73} +(-0.526328 - 1.87413i) q^{74} +(8.82372 + 14.4706i) q^{76} +4.18915i q^{77} +13.2903i q^{79} +(-7.30693 - 3.76378i) q^{80} +(7.39027 - 2.07547i) q^{82} +0.984127 q^{83} +0.683642 q^{85} +(-2.09162 + 0.587408i) q^{86} +(2.07061 + 1.92680i) q^{88} +1.46267i q^{89} -13.7150i q^{91} +(6.01431 - 3.66735i) q^{92} +(2.65094 + 9.43937i) q^{94} -17.4133 q^{95} +5.99367 q^{97} +(-4.03366 - 14.3629i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} - 12 q^{8} + 4 q^{10} - 10 q^{11} + 8 q^{13} + 8 q^{14} - 4 q^{16} - 24 q^{20} - 8 q^{23} - 10 q^{25} + 16 q^{26} + 16 q^{28} + 8 q^{34} + 16 q^{35} - 4 q^{37} + 32 q^{38} - 4 q^{44} + 20 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^8 + 4 * q^10 - 10 * q^11 + 8 * q^13 + 8 * q^14 - 4 * q^16 - 24 * q^20 - 8 * q^23 - 10 * q^25 + 16 * q^26 + 16 * q^28 + 8 * q^34 + 16 * q^35 - 4 * q^37 + 32 * q^38 - 4 * q^44 + 20 * q^46 - 34 * q^49 + 12 * q^50 - 20 * q^52 - 32 * q^56 - 28 * q^58 + 40 * q^59 + 20 * q^61 + 28 * q^62 - 8 * q^64 - 20 * q^68 - 36 * q^70 - 16 * q^71 + 24 * q^73 + 28 * q^74 - 12 * q^76 - 32 * q^80 - 8 * q^82 + 8 * q^83 - 36 * q^85 - 24 * q^86 + 12 * q^88 - 24 * q^92 - 20 * q^94 - 96 * q^95 + 24 * q^97 + 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more