LMFDB - Embedded newform 495.2.n.h.181.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,2,Mod(91,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.91"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,2,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 5x^14 - 8x^13 + 47x^12 + 32x^11 + 171x^10 + 26x^9 + 360x^8 - 172x^7 + 471x^6 - 430x^5 + 383x^4 + 70x^3 + 17x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.4
Root			$2.46673 - 1.79218i$ of defining polynomial
Character	$\chi$	$=$	495.181
Dual form			495.2.n.h.361.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.633189 + 1.94876i) q^{2} +(-1.77869 + 1.29229i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.477268 - 0.346756i) q^{7} +(-0.329192 - 0.239172i) q^{8} -2.04904 q^{10} +(0.933738 + 3.18247i) q^{11} +(0.465044 + 1.43126i) q^{13} +(0.977943 + 0.710517i) q^{14} +(-1.10115 + 3.38900i) q^{16} +(-1.52036 + 4.67919i) q^{17} +(-5.51798 - 4.00905i) q^{19} +(-0.679399 - 2.09098i) q^{20} +(-5.61063 + 3.83474i) q^{22} +0.0822934 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-2.49471 + 1.81252i) q^{26} +(-0.400802 + 1.23354i) q^{28} +(6.81551 - 4.95175i) q^{29} +(-0.611585 - 1.88227i) q^{31} -8.11537 q^{32} -10.0813 q^{34} +(0.182300 + 0.561062i) q^{35} +(2.89625 - 2.10425i) q^{37} +(4.31873 - 13.2917i) q^{38} +(0.329192 - 0.239172i) q^{40} +(3.29530 + 2.39417i) q^{41} +4.86148 q^{43} +(-5.77352 - 4.45397i) q^{44} +(0.0521073 + 0.160370i) q^{46} +(4.67492 + 3.39653i) q^{47} +(-2.05557 + 6.32640i) q^{49} +(0.633189 - 1.94876i) q^{50} +(-2.67678 - 1.94479i) q^{52} +(-2.09317 - 6.44213i) q^{53} +(-3.31525 - 0.0954005i) q^{55} -0.240047 q^{56} +(13.9653 + 10.1464i) q^{58} +(-4.51758 + 3.28221i) q^{59} +(-0.296732 + 0.913248i) q^{61} +(3.28083 - 2.38366i) q^{62} +(-2.93627 - 9.03690i) q^{64} -1.50491 q^{65} +13.6559 q^{67} +(-3.34264 - 10.2876i) q^{68} +(-0.977943 + 0.710517i) q^{70} +(0.396714 - 1.22096i) q^{71} +(12.6426 - 9.18538i) q^{73} +(5.93455 + 4.31171i) q^{74} +14.9956 q^{76} +(1.54918 + 1.19511i) q^{77} +(-3.44622 - 10.6064i) q^{79} +(-2.88285 - 2.09451i) q^{80} +(-2.57911 + 7.93770i) q^{82} +(1.23982 - 3.81578i) q^{83} +(-3.98036 - 2.89190i) q^{85} +(3.07824 + 9.47385i) q^{86} +(0.453779 - 1.27097i) q^{88} -6.08177 q^{89} +(0.718247 + 0.521837i) q^{91} +(-0.146374 + 0.106347i) q^{92} +(-3.65890 + 11.2609i) q^{94} +(5.51798 - 4.00905i) q^{95} +(-2.07220 - 6.37757i) q^{97} -13.6302 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29}+ \cdots - 8 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 + 8 * q^10 - 4 * q^11 + 2 * q^13 + 22 * q^14 + 8 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 28 * q^22 - 8 * q^23 - 4 * q^25 - 6 * q^26 - 2 * q^28 + 26 * q^29 - 10 * q^31 - 56 * q^32 - 4 * q^34 + 4 * q^35 + 22 * q^37 + 30 * q^38 - 6 * q^40 + 6 * q^41 + 28 * q^43 - 68 * q^44 + 16 * q^46 + 20 * q^47 + 10 * q^49 + 2 * q^50 + 30 * q^52 - 14 * q^53 - 6 * q^55 - 68 * q^56 - 6 * q^58 + 16 * q^59 - 38 * q^61 + 20 * q^62 + 10 * q^64 - 12 * q^65 + 20 * q^67 + 48 * q^68 - 22 * q^70 + 54 * q^71 + 2 * q^73 - 28 * q^74 - 44 * q^76 - 34 * q^77 - 12 * q^79 + 22 * q^80 + 30 * q^82 + 28 * q^83 - 4 * q^85 - 74 * q^86 + 46 * q^88 - 76 * q^89 - 34 * q^91 + 8 * q^92 - 10 * q^94 + 4 * q^95 - 18 * q^97 - 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	0.633189	+	1.94876i	0.447733	+	1.37798i	0.879459	+	0.475975i	$0.157905\pi$
$2$	0.633189	+	1.94876i	0.447733	+	1.37798i	−0.431726	+	0.902005i	$0.642095\pi$
$3$		0			0
$3$		0			0
$4$	−1.77869	+	1.29229i	−0.889345	+	0.646147i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	0.477268	−	0.346756i	0.180390	−	0.131061i	−0.493926	−	0.869504i	$-0.664439\pi$
$7$	0.477268	−	0.346756i	0.180390	−	0.131061i	0.674316	+	0.738443i	$0.264439\pi$
$8$	−0.329192	−	0.239172i	−0.116387	−	0.0845600i
$9$		0			0
$10$	−2.04904			−0.647965
$11$	0.933738	+	3.18247i	0.281533	+	0.959552i
$11$	0.933738	+	3.18247i	0.281533	+	0.959552i
$12$		0			0
$13$	0.465044	+	1.43126i	0.128980	+	0.396960i	0.994605	−	0.103733i	$-0.0330787\pi$
$13$	0.465044	+	1.43126i	0.128980	+	0.396960i	−0.865625	+	0.500693i	$0.833079\pi$
$14$	0.977943	+	0.710517i	0.261366	+	0.189894i
$15$		0			0
$16$	−1.10115	+	3.38900i	−0.275288	+	0.847249i
$17$	−1.52036	+	4.67919i	−0.368742	+	1.13487i	0.578862	+	0.815425i	$0.303497\pi$
$17$	−1.52036	+	4.67919i	−0.368742	+	1.13487i	−0.947604	+	0.319446i	$0.896503\pi$
$18$		0			0
$19$	−5.51798	−	4.00905i	−1.26591	−	0.919739i	−0.266880	−	0.963730i	$-0.585993\pi$
$19$	−5.51798	−	4.00905i	−1.26591	−	0.919739i	−0.999032	+	0.0439914i	$0.985993\pi$
$20$	−0.679399	−	2.09098i	−0.151918	−	0.467556i
$21$		0			0
$22$	−5.61063	+	3.83474i	−1.19619	+	0.817569i
$23$	0.0822934			0.0171594			0.00857968	−	0.999963i	$-0.497269\pi$
$23$	0.0822934			0.0171594			0.00857968	+	0.999963i	$0.497269\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−2.49471	+	1.81252i	−0.489253	+	0.355463i
$27$		0			0
$28$	−0.400802	+	1.23354i	−0.0757444	+	0.233117i
$29$	6.81551	−	4.95175i	1.26561	−	0.919518i	0.266589	−	0.963810i	$-0.414103\pi$
$29$	6.81551	−	4.95175i	1.26561	−	0.919518i	0.999019	+	0.0442926i	$0.0141034\pi$
$30$		0			0
$31$	−0.611585	−	1.88227i	−0.109844	−	0.338065i	0.880993	−	0.473130i	$-0.156876\pi$
$31$	−0.611585	−	1.88227i	−0.109844	−	0.338065i	−0.990837	+	0.135065i	$0.956876\pi$
$32$	−8.11537			−1.43461
$33$		0			0
$34$	−10.0813			−1.72893
$35$	0.182300	+	0.561062i	0.0308144	+	0.0948368i
$36$		0			0
$37$	2.89625	−	2.10425i	0.476141	−	0.345937i	−0.323689	−	0.946164i	$-0.604923\pi$
$37$	2.89625	−	2.10425i	0.476141	−	0.345937i	0.799830	+	0.600227i	$0.204923\pi$
$38$	4.31873	−	13.2917i	0.700591	−	2.15620i
$39$		0			0
$40$	0.329192	−	0.239172i	0.0520498	−	0.0378164i
$41$	3.29530	+	2.39417i	0.514639	+	0.373907i	0.814581	−	0.580050i	$-0.196967\pi$
$41$	3.29530	+	2.39417i	0.514639	+	0.373907i	−0.299942	+	0.953958i	$0.596967\pi$
$42$		0			0
$43$	4.86148			0.741369			0.370685	−	0.928759i	$-0.379123\pi$
$43$	4.86148			0.741369			0.370685	+	0.928759i	$0.379123\pi$
$44$	−5.77352	−	4.45397i	−0.870391	−	0.671461i
$45$		0			0
$46$	0.0521073	+	0.160370i	0.00768280	+	0.0236452i
$47$	4.67492	+	3.39653i	0.681908	+	0.495435i	0.873990	−	0.485944i	$-0.161524\pi$
$47$	4.67492	+	3.39653i	0.681908	+	0.495435i	−0.192082	+	0.981379i	$0.561524\pi$
$48$		0			0
$49$	−2.05557	+	6.32640i	−0.293653	+	0.903772i
$50$	0.633189	−	1.94876i	0.0895465	−	0.275596i
$51$		0			0
$52$	−2.67678	−	1.94479i	−0.371202	−	0.269694i
$53$	−2.09317	−	6.44213i	−0.287520	−	0.884894i	−0.985632	−	0.168906i	$-0.945976\pi$
$53$	−2.09317	−	6.44213i	−0.287520	−	0.884894i	0.698112	−	0.715988i	$-0.254024\pi$
$54$		0			0
$55$	−3.31525	−	0.0954005i	−0.447029	−	0.0128638i
$56$	−0.240047			−0.0320776
$57$		0			0
$58$	13.9653	+	10.1464i	1.83373	+	1.33228i
$59$	−4.51758	+	3.28221i	−0.588138	+	0.427308i	−0.841649	−	0.540025i	$-0.818415\pi$
$59$	−4.51758	+	3.28221i	−0.588138	+	0.427308i	0.253511	+	0.967333i	$0.418415\pi$
$60$		0			0
$61$	−0.296732	+	0.913248i	−0.0379927	+	0.116929i	−0.968254	−	0.249968i	$-0.919580\pi$
$61$	−0.296732	+	0.913248i	−0.0379927	+	0.116929i	0.930261	+	0.366897i	$0.119580\pi$
$62$	3.28083	−	2.38366i	0.416666	−	0.302725i
$63$		0			0
$64$	−2.93627	−	9.03690i	−0.367033	−	1.12961i
$65$	−1.50491			−0.186662
$66$		0			0
$67$	13.6559			1.66834			0.834168	−	0.551511i	$-0.185948\pi$
$67$	13.6559			1.66834			0.834168	+	0.551511i	$0.185948\pi$
$68$	−3.34264	−	10.2876i	−0.405355	−	1.24755i
$69$		0			0
$70$	−0.977943	+	0.710517i	−0.116887	+	0.0849231i
$71$	0.396714	−	1.22096i	0.0470813	−	0.144901i	−0.924752	−	0.380570i	$-0.875728\pi$
$71$	0.396714	−	1.22096i	0.0470813	−	0.144901i	0.971834	+	0.235668i	$0.0757279\pi$
$72$		0			0
$73$	12.6426	−	9.18538i	1.47970	−	1.07507i	0.502052	−	0.864837i	$-0.332579\pi$
$73$	12.6426	−	9.18538i	1.47970	−	1.07507i	0.977652	−	0.210230i	$-0.0674214\pi$
$74$	5.93455	+	4.31171i	0.689878	+	0.501226i
$75$		0			0
$76$	14.9956			1.72012
$77$	1.54918	+	1.19511i	0.176546	+	0.136196i
$78$		0			0
$79$	−3.44622	−	10.6064i	−0.387730	−	1.19331i	−0.934481	−	0.356014i	$-0.884135\pi$
$79$	−3.44622	−	10.6064i	−0.387730	−	1.19331i	0.546751	−	0.837295i	$-0.315865\pi$
$80$	−2.88285	−	2.09451i	−0.322313	−	0.234174i
$81$		0			0
$82$	−2.57911	+	7.93770i	−0.284816	+	0.876572i
$83$	1.23982	−	3.81578i	0.136088	−	0.418837i	−0.859669	−	0.510851i	$-0.829330\pi$
$83$	1.23982	−	3.81578i	0.136088	−	0.418837i	0.995758	+	0.0920140i	$0.0293305\pi$
$84$		0			0
$85$	−3.98036	−	2.89190i	−0.431731	−	0.313671i
$86$	3.07824	+	9.47385i	0.331935	+	1.02159i
$87$		0			0
$88$	0.453779	−	1.27097i	0.0483730	−	0.135486i
$89$	−6.08177			−0.644667			−0.322333	−	0.946626i	$-0.604467\pi$
$89$	−6.08177			−0.644667			−0.322333	+	0.946626i	$0.604467\pi$
$90$		0			0
$91$	0.718247	+	0.521837i	0.0752928	+	0.0547034i
$92$	−0.146374	+	0.106347i	−0.0152606	+	0.0110875i
$93$		0			0
$94$	−3.65890	+	11.2609i	−0.377387	+	1.16148i
$95$	5.51798	−	4.00905i	0.566133	−	0.411320i
$96$		0			0
$97$	−2.07220	−	6.37757i	−0.210400	−	0.647544i	−0.999448	−	0.0332133i	$-0.989426\pi$
$97$	−2.07220	−	6.37757i	−0.210400	−	0.647544i	0.789048	−	0.614331i	$-0.210574\pi$
$98$	−13.6302			−1.37686
$99$		0			0
$100$	2.19858			0.219858
$101$	1.83730	+	5.65462i	0.182818	+	0.562656i	0.999904	−	0.0138601i	$-0.00441195\pi$
$101$	1.83730	+	5.65462i	0.182818	+	0.562656i	−0.817086	+	0.576516i	$0.804412\pi$
$102$		0			0
$103$	−1.56592	+	1.13771i	−0.154294	+	0.112101i	−0.662254	−	0.749280i	$-0.730400\pi$
$103$	−1.56592	+	1.13771i	−0.154294	+	0.112101i	0.507959	+	0.861381i	$0.330400\pi$
$104$	0.189228	−	0.582384i	0.0185553	−	0.0571074i
$105$		0			0
$106$	11.2288	−	8.15818i	1.09063	−	0.792392i
$107$	6.70449	+	4.87110i	0.648148	+	0.470907i	0.862640	−	0.505819i	$-0.168810\pi$
$107$	6.70449	+	4.87110i	0.648148	+	0.470907i	−0.214492	+	0.976726i	$0.568810\pi$
$108$		0			0
$109$	3.18782			0.305338			0.152669	−	0.988277i	$-0.451213\pi$
$109$	3.18782			0.305338			0.152669	+	0.988277i	$0.451213\pi$
$110$	−1.91327	−	6.52103i	−0.182423	−	0.621756i
$111$		0			0
$112$	0.649609	+	1.99929i	0.0613822	+	0.188915i
$113$	9.29605	+	6.75398i	0.874499	+	0.635361i	0.931790	−	0.362997i	$-0.118246\pi$
$113$	9.29605	+	6.75398i	0.874499	+	0.635361i	−0.0572913	+	0.998358i	$0.518246\pi$
$114$		0			0
$115$	−0.0254300	+	0.0782656i	−0.00237136	+	0.00729831i
$116$	−5.72355	+	17.6153i	−0.531418	+	1.63554i
$117$		0			0
$118$	−9.25671	−	6.72540i	−0.852150	−	0.619123i
$119$	0.896916	+	2.76042i	0.0822202	+	0.253048i
$120$		0			0
$121$	−9.25627	+	5.94319i	−0.841479	+	0.540290i
$122$	−1.96759			−0.178137
$123$		0			0
$124$	3.52026	+	2.55762i	0.316129	+	0.229681i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	5.62146	−	17.3011i	0.498824	−	1.53522i	−0.312087	−	0.950054i	$-0.601028\pi$
$127$	5.62146	−	17.3011i	0.498824	−	1.53522i	0.810911	−	0.585170i	$-0.198972\pi$
$128$	2.62055	−	1.90394i	0.231626	−	0.168286i
$129$		0			0
$130$	−0.952896	−	2.93271i	−0.0835745	−	0.257216i
$131$	−18.7758			−1.64045			−0.820225	−	0.572041i	$-0.806152\pi$
$131$	−18.7758			−1.64045			−0.820225	+	0.572041i	$0.806152\pi$
$132$		0			0
$133$	−4.02371			−0.348900
$134$	8.64678	+	26.6121i	0.746968	+	2.29893i
$135$		0			0
$136$	1.61962	−	1.17672i	0.138881	−	0.100903i
$137$	1.46073	−	4.49567i	0.124799	−	0.384091i	−0.869066	−	0.494697i	$-0.835279\pi$
$137$	1.46073	−	4.49567i	0.124799	−	0.384091i	0.993864	+	0.110606i	$0.0352791\pi$
$138$		0			0
$139$	14.9456	−	10.8586i	1.26767	−	0.921013i	0.268558	−	0.963264i	$-0.413453\pi$
$139$	14.9456	−	10.8586i	1.26767	−	0.921013i	0.999107	+	0.0422509i	$0.0134529\pi$
$140$	−1.04931	−	0.762370i	−0.0886831	−	0.0644321i
$141$		0			0
$142$	2.63055			0.220751
$143$	−4.12071	+	2.81641i	−0.344591	+	0.235520i
$144$		0			0
$145$	2.60329	+	8.01211i	0.216192	+	0.665369i
$146$	25.9052	+	18.8213i	2.14393	+	1.55766i
$147$		0			0
$148$	−2.43223	+	7.48563i	−0.199928	+	0.615315i
$149$	−4.79009	+	14.7424i	−0.392420	+	1.20774i	0.538533	+	0.842604i	$0.318979\pi$
$149$	−4.79009	+	14.7424i	−0.392420	+	1.20774i	−0.930953	+	0.365140i	$0.881021\pi$
$150$		0			0
$151$	−4.49360	−	3.26479i	−0.365684	−	0.265685i	0.389735	−	0.920927i	$-0.372567\pi$
$151$	−4.49360	−	3.26479i	−0.365684	−	0.265685i	−0.755419	+	0.655242i	$0.772567\pi$
$152$	0.857623	+	2.63949i	0.0695624	+	0.214091i
$153$		0			0
$154$	−1.34806	+	3.77571i	−0.108630	+	0.304256i
$155$	1.97913			0.158968
$156$		0			0
$157$	14.9761	+	10.8808i	1.19522	+	0.868381i	0.993807	−	0.111124i	$-0.0354451\pi$
$157$	14.9761	+	10.8808i	1.19522	+	0.868381i	0.201418	+	0.979505i	$0.435445\pi$
$158$	18.4871	−	13.4317i	1.47076	−	1.06857i
$159$		0			0
$160$	2.50779	−	7.71818i	0.198258	−	0.610176i
$161$	0.0392760	−	0.0285357i	0.00309538	−	0.00224893i
$162$		0			0
$163$	2.41484	+	7.43210i	0.189145	+	0.582127i	0.999995	−	0.00312615i	$-0.000995086\pi$
$163$	2.41484	+	7.43210i	0.189145	+	0.582127i	−0.810851	+	0.585253i	$0.800995\pi$
$164$	−8.95529			−0.699291
$165$		0			0
$166$	8.22108			0.638080
$167$	−1.84233	−	5.67010i	−0.142564	−	0.438766i	0.854126	−	0.520066i	$-0.174093\pi$
$167$	−1.84233	−	5.67010i	−0.142564	−	0.438766i	−0.996690	+	0.0813005i	$0.974093\pi$
$168$		0			0
$169$	8.68499	−	6.31001i	0.668076	−	0.485386i
$170$	3.11529	−	9.58788i	0.238932	−	0.735357i
$171$		0			0
$172$	−8.64707	+	6.28247i	−0.659333	+	0.479034i
$173$	−13.4085	−	9.74186i	−1.01943	−	0.740660i	−0.0532650	−	0.998580i	$-0.516963\pi$
$173$	−13.4085	−	9.74186i	−1.01943	−	0.740660i	−0.966166	+	0.257920i	$0.916963\pi$
$174$		0			0
$175$	−0.589936			−0.0445949
$176$	−11.8136	−	0.339950i	−0.890482	−	0.0256247i
$177$		0			0
$178$	−3.85092	−	11.8519i	−0.288638	−	0.888337i
$179$	−17.4300	−	12.6637i	−1.30278	−	0.946526i	−0.302802	−	0.953053i	$-0.597922\pi$
$179$	−17.4300	−	12.6637i	−1.30278	−	0.946526i	−0.999979	+	0.00652751i	$0.997922\pi$
$180$		0			0
$181$	−6.23300	+	19.1832i	−0.463295	+	1.42588i	0.397819	+	0.917464i	$0.369767\pi$
$181$	−6.23300	+	19.1832i	−0.463295	+	1.42588i	−0.861114	+	0.508411i	$0.830233\pi$
$182$	−0.562147	+	1.73011i	−0.0416691	+	0.128244i
$183$		0			0
$184$	−0.0270903	−	0.0196823i	−0.00199712	−	0.00145100i
$185$	1.10627	+	3.40475i	0.0813346	+	0.250322i
$186$		0			0
$187$	−16.3110	−	0.469370i	−1.19278	−	0.0343237i
$188$	−12.7046			−0.926575
$189$		0			0
$190$	11.3066	+	8.21471i	0.820266	+	0.595958i
$191$	13.1782	−	9.57452i	0.953541	−	0.692788i	0.00189928	−	0.999998i	$-0.499395\pi$
$191$	13.1782	−	9.57452i	0.953541	−	0.692788i	0.951642	+	0.307210i	$0.0993954\pi$
$192$		0			0
$193$	1.03505	−	3.18555i	0.0745043	−	0.229301i	−0.906868	−	0.421414i	$-0.861534\pi$
$193$	1.03505	−	3.18555i	0.0745043	−	0.229301i	0.981373	+	0.192113i	$0.0615340\pi$
$194$	11.1162	−	8.07642i	0.798100	−	0.579853i
$195$		0			0
$196$	−4.51935	−	13.9091i	−0.322811	−	0.993509i
$197$	9.78158			0.696909			0.348454	−	0.937326i	$-0.386707\pi$
$197$	9.78158			0.696909			0.348454	+	0.937326i	$0.386707\pi$
$198$		0			0
$199$	9.89054			0.701121			0.350561	−	0.936540i	$-0.385991\pi$
$199$	9.89054			0.701121			0.350561	+	0.936540i	$0.385991\pi$
$200$	0.125740	+	0.386988i	0.00889117	+	0.0273642i
$201$		0			0
$202$	−9.85612	+	7.16089i	−0.693474	+	0.503838i
$203$	1.53577	−	4.72663i	0.107790	−	0.331744i
$204$		0			0
$205$	−3.29530	+	2.39417i	−0.230154	+	0.167216i
$206$	−3.20863	−	2.33121i	−0.223556	−	0.162423i
$207$		0			0
$208$	−5.36261			−0.371830
$209$	7.60634	−	21.3042i	0.526141	−	1.47364i
$210$		0			0
$211$	−6.85049	−	21.0836i	−0.471607	−	1.45146i	−0.850480	−	0.526008i	$-0.823688\pi$
$211$	−6.85049	−	21.0836i	−0.471607	−	1.45146i	0.378873	−	0.925449i	$-0.376312\pi$
$212$	12.0482	+	8.75355i	0.827476	+	0.601197i
$213$		0			0
$214$	−5.24737	+	16.1497i	−0.358703	+	1.10397i
$215$	−1.50228	+	4.62355i	−0.102455	+	0.315323i
$216$		0			0
$217$	−0.944576	−	0.686275i	−0.0641220	−	0.0465874i
$218$	2.01850	+	6.21229i	0.136710	+	0.420750i
$219$		0			0
$220$	6.02009	−	4.11459i	0.405875	−	0.277406i
$221$	−7.40417			−0.498058
$222$		0			0
$223$	−9.98313	−	7.25317i	−0.668520	−	0.485708i	0.201010	−	0.979589i	$-0.435578\pi$
$223$	−9.98313	−	7.25317i	−0.668520	−	0.485708i	−0.869529	+	0.493881i	$0.835578\pi$
$224$	−3.87321	+	2.81405i	−0.258790	+	0.188022i
$225$		0			0
$226$	−7.27570	+	22.3923i	−0.483972	+	1.48951i
$227$	−6.65140	+	4.83252i	−0.441469	+	0.320746i	−0.786218	−	0.617949i	$-0.787964\pi$
$227$	−6.65140	+	4.83252i	−0.441469	+	0.320746i	0.344750	+	0.938695i	$0.387964\pi$
$228$		0			0
$229$	8.35722	+	25.7209i	0.552261	+	1.69968i	0.703070	+	0.711120i	$0.251812\pi$
$229$	8.35722	+	25.7209i	0.552261	+	1.69968i	−0.150810	+	0.988563i	$0.548188\pi$
$230$	−0.168623			−0.0111187
$231$		0			0
$232$	−3.42793			−0.225055
$233$	−7.72672	−	23.7804i	−0.506194	−	1.55791i	−0.798753	−	0.601659i	$-0.794507\pi$
$233$	−7.72672	−	23.7804i	−0.506194	−	1.55791i	0.292559	−	0.956247i	$-0.405493\pi$
$234$		0			0
$235$	−4.67492	+	3.39653i	−0.304958	+	0.221565i
$236$	3.79379	−	11.6761i	0.246955	−	0.760048i
$237$		0			0
$238$	−4.81148	+	3.49574i	−0.311882	+	0.226595i
$239$	−16.7638	−	12.1796i	−1.08436	−	0.787835i	−0.105924	−	0.994374i	$-0.533780\pi$
$239$	−16.7638	−	12.1796i	−1.08436	−	0.787835i	−0.978438	+	0.206539i	$0.933780\pi$
$240$		0			0
$241$	−23.4295			−1.50923			−0.754615	−	0.656168i	$-0.772176\pi$
$241$	−23.4295			−1.50923			−0.754615	+	0.656168i	$0.772176\pi$
$242$	−17.4428	−	14.2750i	−1.12127	−	0.917635i
$243$		0			0
$244$	−0.652390	−	2.00785i	−0.0417650	−	0.128539i
$245$	−5.38156	−	3.90993i	−0.343815	−	0.249796i
$246$		0			0
$247$	3.17188	−	9.76204i	0.201822	−	0.621144i
$248$	−0.248856	+	0.765901i	−0.0158024	+	0.0486347i
$249$		0			0
$250$	1.65771	+	1.20440i	0.104843	+	0.0761728i
$251$	3.17352	+	9.76710i	0.200311	+	0.616494i	0.999873	+	0.0159107i	$0.00506475\pi$
$251$	3.17352	+	9.76710i	0.200311	+	0.616494i	−0.799563	+	0.600583i	$0.794935\pi$
$252$		0			0
$253$	0.0768405	+	0.261896i	0.00483092	+	0.0164653i
$254$	37.2751			2.33885
$255$		0			0
$256$	−10.0049	−	7.26896i	−0.625304	−	0.454310i
$257$	−1.57711	+	1.14584i	−0.0983774	+	0.0714753i	−0.635886	−	0.771783i	$-0.719365\pi$
$257$	−1.57711	+	1.14584i	−0.0983774	+	0.0714753i	0.537509	+	0.843258i	$0.319365\pi$
$258$		0			0
$259$	0.652629	−	2.00858i	0.0405524	−	0.124807i
$260$	2.67678	−	1.94479i	0.166007	−	0.120611i
$261$		0			0
$262$	−11.8886	−	36.5895i	−0.734483	−	2.26051i
$263$	−8.80234			−0.542775			−0.271388	−	0.962470i	$-0.587483\pi$
$263$	−8.80234			−0.542775			−0.271388	+	0.962470i	$0.587483\pi$
$264$		0			0
$265$	6.77365			0.416102
$266$	−2.54777	−	7.84124i	−0.156214	−	0.480777i
$267$		0			0
$268$	−24.2896	+	17.6475i	−1.48373	+	1.07799i
$269$	3.76512	−	11.5878i	0.229563	−	0.706523i	−0.768233	−	0.640171i	$-0.778864\pi$
$269$	3.76512	−	11.5878i	0.229563	−	0.706523i	0.997796	−	0.0663529i	$-0.0211363\pi$
$270$		0			0
$271$	−10.0039	+	7.26827i	−0.607694	+	0.441516i	−0.848602	−	0.529032i	$-0.822555\pi$
$271$	−10.0039	+	7.26827i	−0.607694	+	0.441516i	0.240907	+	0.970548i	$0.422555\pi$
$272$	−14.1836	−	10.3050i	−0.860008	−	0.624833i
$273$		0			0
$274$	9.68590			0.585146
$275$	1.11520	−	3.12351i	0.0672491	−	0.188355i
$276$		0			0
$277$	6.34377	+	19.5241i	0.381160	+	1.17309i	0.939228	+	0.343295i	$0.111543\pi$
$277$	6.34377	+	19.5241i	0.381160	+	1.17309i	−0.558067	+	0.829796i	$0.688457\pi$
$278$	30.6241	+	22.2497i	1.83671	+	1.33445i
$279$		0			0
$280$	0.0741786	−	0.228298i	0.00443302	−	0.0136434i
$281$	3.53113	−	10.8677i	0.210650	−	0.648313i	−0.788784	−	0.614670i	$-0.789289\pi$
$281$	3.53113	−	10.8677i	0.210650	−	0.648313i	0.999434	−	0.0336429i	$-0.0107109\pi$
$282$		0			0
$283$	−23.8919	−	17.3585i	−1.42023	−	1.03186i	−0.991734	−	0.128311i	$-0.959044\pi$
$283$	−23.8919	−	17.3585i	−1.42023	−	1.03186i	−0.428493	−	0.903545i	$-0.640956\pi$
$284$	0.872208	+	2.68438i	0.0517560	+	0.159289i
$285$		0			0
$286$	−8.09769	−	6.24694i	−0.478826	−	0.369389i
$287$	2.40293			0.141841
$288$		0			0
$289$	−5.83007	−	4.23579i	−0.342945	−	0.249164i
$290$	−13.9653	+	10.1464i	−0.820069	+	0.595815i
$291$		0			0
$292$	−10.6170	+	32.6759i	−0.621316	+	1.91221i
$293$	−9.38171	+	6.81621i	−0.548085	+	0.398207i	−0.827079	−	0.562086i	$-0.809999\pi$
$293$	−9.38171	+	6.81621i	−0.548085	+	0.398207i	0.278994	+	0.960293i	$0.409999\pi$
$294$		0			0
$295$	−1.72556	−	5.31073i	−0.100466	−	0.309203i
$296$	−1.45670			−0.0846690
$297$		0			0
$298$	−31.7624			−1.83995
$299$	0.0382700	+	0.117783i	0.00221321	+	0.00681157i
$300$		0			0
$301$	2.32023	−	1.68575i	0.133736	−	0.0971648i
$302$	3.51699	−	10.8242i	0.202380	−	0.622861i
$303$		0			0
$304$	19.6628	−	14.2858i	1.12774	−	0.819349i
$305$	−0.776855	−	0.564418i	−0.0444826	−	0.0323185i
$306$		0			0
$307$	1.27309			0.0726593			0.0363296	−	0.999340i	$-0.488433\pi$
$307$	1.27309			0.0726593			0.0363296	+	0.999340i	$0.488433\pi$
$308$	−4.29996	−	0.123737i	−0.245013	−	0.00705054i
$309$		0			0
$310$	1.25317	+	3.85685i	0.0711750	+	0.219054i
$311$	−3.96859	−	2.88335i	−0.225038	−	0.163500i	0.469553	−	0.882904i	$-0.344415\pi$
$311$	−3.96859	−	2.88335i	−0.225038	−	0.163500i	−0.694592	+	0.719404i	$0.744415\pi$
$312$		0			0
$313$	−4.76494	+	14.6650i	−0.269331	+	0.828914i	0.721333	+	0.692588i	$0.243530\pi$
$313$	−4.76494	+	14.6650i	−0.269331	+	0.828914i	−0.990664	+	0.136326i	$0.956470\pi$
$314$	−11.7213	+	36.0744i	−0.661470	+	2.03580i
$315$		0			0
$316$	19.8363	+	14.4119i	1.11588	+	0.810734i
$317$	10.3782	+	31.9408i	0.582897	+	1.79397i	0.607555	+	0.794278i	$0.292151\pi$
$317$	10.3782	+	31.9408i	0.582897	+	1.79397i	−0.0246573	+	0.999696i	$0.507849\pi$
$318$		0			0
$319$	22.1227	+	17.0665i	1.23863	+	0.955542i
$320$	9.50196			0.531175
$321$		0			0
$322$	0.0804782	+	0.0584709i	0.00448488	+	0.00325845i
$323$	27.1484	−	19.7245i	1.51058	−	1.09750i
$324$		0			0
$325$	0.465044	−	1.43126i	0.0257960	−	0.0793919i
$326$	−12.9543	+	9.41186i	−0.717473	+	0.521275i
$327$		0			0
$328$	−0.512166	−	1.57628i	−0.0282796	−	0.0870358i
$329$	3.40896			0.187942
$330$		0			0
$331$	−9.50564			−0.522477			−0.261239	−	0.965274i	$-0.584131\pi$
$331$	−9.50564			−0.522477			−0.261239	+	0.965274i	$0.584131\pi$
$332$	2.72585	+	8.38932i	0.149601	+	0.460424i
$333$		0			0
$334$	9.88310	−	7.18050i	0.540779	−	0.392899i
$335$	−4.21991	+	12.9875i	−0.230558	+	0.709586i
$336$		0			0
$337$	−20.7225	+	15.0557i	−1.12882	+	0.820138i	−0.985523	−	0.169541i	$-0.945772\pi$
$337$	−20.7225	+	15.0557i	−1.12882	+	0.820138i	−0.143301	+	0.989679i	$0.545772\pi$
$338$	17.7959	+	12.9295i	0.967971	+	0.703272i
$339$		0			0
$340$	10.8170			0.586635
$341$	5.41920	−	3.70390i	0.293466	−	0.200577i
$342$		0			0
$343$	2.48876	+	7.65961i	0.134380	+	0.413580i
$344$	−1.60036	−	1.16273i	−0.0862856	−	0.0626902i
$345$		0			0
$346$	10.4944	−	32.2984i	0.564182	−	1.73637i
$347$	−8.62415	+	26.5424i	−0.462969	+	1.42487i	0.398551	+	0.917146i	$0.369513\pi$
$347$	−8.62415	+	26.5424i	−0.462969	+	1.42487i	−0.861520	+	0.507724i	$0.830487\pi$
$348$		0			0
$349$	8.58282	+	6.23578i	0.459428	+	0.333794i	0.793307	−	0.608822i	$-0.208358\pi$
$349$	8.58282	+	6.23578i	0.459428	+	0.333794i	−0.333879	+	0.942616i	$0.608358\pi$
$350$	−0.373541	−	1.14964i	−0.0199666	−	0.0614509i
$351$		0			0
$352$	−7.57763	−	25.8270i	−0.403889	−	1.37658i
$353$	−29.0702			−1.54725			−0.773627	−	0.633642i	$-0.781559\pi$
$353$	−29.0702			−1.54725			−0.773627	+	0.633642i	$0.781559\pi$
$354$		0			0
$355$	1.03861	+	0.754594i	0.0551237	+	0.0400497i
$356$	10.8176	−	7.85944i	0.573331	−	0.416550i
$357$		0			0
$358$	13.6419	−	41.9854i	0.720995	−	2.21900i
$359$	24.4571	−	17.7692i	1.29080	−	0.937820i	0.290978	−	0.956730i	$-0.406019\pi$
$359$	24.4571	−	17.7692i	1.29080	−	0.937820i	0.999821	+	0.0189094i	$0.00601942\pi$
$360$		0			0
$361$	8.50432	+	26.1736i	0.447596	+	1.37756i
$362$	−41.3300			−2.17226
$363$		0			0
$364$	−1.95191			−0.102308
$365$	4.82904	+	14.8623i	0.252764	+	0.777926i
$366$		0			0
$367$	19.1378	−	13.9044i	0.998984	−	0.725805i	0.0371142	−	0.999311i	$-0.488183\pi$
$367$	19.1378	−	13.9044i	0.998984	−	0.725805i	0.961870	+	0.273506i	$0.0881835\pi$
$368$	−0.0906175	+	0.278892i	−0.00472376	+	0.0145382i
$369$		0			0
$370$	−5.93455	+	4.31171i	−0.308523	+	0.224155i
$371$	−3.23285	−	2.34880i	−0.167841	−	0.121944i
$372$		0			0
$373$	−14.5998			−0.755949			−0.377974	−	0.925816i	$-0.623379\pi$
$373$	−14.5998			−0.755949			−0.377974	+	0.925816i	$0.623379\pi$
$374$	−9.41328	−	32.0834i	−0.486749	−	1.65899i
$375$		0			0
$376$	−0.726592	−	2.23622i	−0.0374711	−	0.115324i
$377$	10.2567	+	7.45196i	0.528249	+	0.383796i
$378$		0			0
$379$	2.07156	−	6.37559i	0.106409	−	0.327492i	−0.883650	−	0.468148i	$-0.844921\pi$
$379$	2.07156	−	6.37559i	0.106409	−	0.327492i	0.990058	+	0.140656i	$0.0449212\pi$
$380$	−4.63391	+	14.2617i	−0.237715	+	0.731610i
$381$		0			0
$382$	27.0027	+	19.6186i	1.38158	+	1.00378i
$383$	9.74277	+	29.9852i	0.497832	+	1.53217i	0.812496	+	0.582967i	$0.198108\pi$
$383$	9.74277	+	29.9852i	0.497832	+	1.53217i	−0.314663	+	0.949203i	$0.601892\pi$
$384$		0			0
$385$	−1.61534	+	1.10405i	−0.0823256	+	0.0562676i
$386$	6.86324			0.349330
$387$		0			0
$388$	11.9275	+	8.66584i	0.605527	+	0.439941i
$389$	−31.5385	+	22.9141i	−1.59907	+	1.16179i	−0.709794	+	0.704409i	$0.751212\pi$
$389$	−31.5385	+	22.9141i	−1.59907	+	1.16179i	−0.889271	+	0.457380i	$0.848788\pi$
$390$		0			0
$391$	−0.125116	+	0.385067i	−0.00632737	+	0.0194737i
$392$	2.18978	−	1.59097i	0.110600	−	0.0803559i
$393$		0			0
$394$	6.19359	+	19.0619i	0.312029	+	0.960326i
$395$	11.1522			0.561128
$396$		0			0
$397$	27.1682			1.36353			0.681766	−	0.731570i	$-0.261212\pi$
$397$	27.1682			1.36353			0.681766	+	0.731570i	$0.261212\pi$
$398$	6.26258	+	19.2742i	0.313915	+	0.966131i
$399$		0			0
$400$	2.88285	−	2.09451i	0.144143	−	0.104726i
$401$	−4.07725	+	12.5485i	−0.203608	+	0.626641i	0.796160	+	0.605087i	$0.206861\pi$
$401$	−4.07725	+	12.5485i	−0.203608	+	0.626641i	−0.999768	+	0.0215543i	$0.993139\pi$
$402$		0			0
$403$	2.40959	−	1.75067i	0.120030	−	0.0872072i
$404$	−10.5754	−	7.68349i	−0.526146	−	0.382268i
$405$		0			0
$406$	10.1835			0.505398
$407$	9.40107	+	7.25243i	0.465994	+	0.359490i
$408$		0			0
$409$	−3.06772	−	9.44146i	−0.151689	−	0.466850i	0.846122	−	0.532990i	$-0.178932\pi$
$409$	−3.06772	−	9.44146i	−0.151689	−	0.466850i	−0.997810	+	0.0661398i	$0.978932\pi$
$410$	−6.75221	−	4.90577i	−0.333468	−	0.242279i
$411$		0			0
$412$	1.31503	−	4.04725i	0.0647870	−	0.199394i
$413$	−1.01797	+	3.13299i	−0.0500910	+	0.154164i
$414$		0			0
$415$	3.24590	+	2.35828i	0.159335	+	0.115764i
$416$	−3.77401	−	11.6152i	−0.185036	−	0.569482i
$417$		0			0
$418$	46.3330	+	1.33329i	2.26622	+	0.0652133i
$419$	26.4274			1.29107			0.645533	−	0.763733i	$-0.276635\pi$
$419$	26.4274			1.29107			0.645533	+	0.763733i	$0.276635\pi$
$420$		0			0
$421$	−11.1232	−	8.08146i	−0.542111	−	0.393866i	0.282758	−	0.959191i	$-0.408751\pi$
$421$	−11.1232	−	8.08146i	−0.542111	−	0.393866i	−0.824868	+	0.565325i	$0.808751\pi$
$422$	36.7492	−	26.6999i	1.78892	−	1.29973i
$423$		0			0
$424$	−0.851720	+	2.62132i	−0.0413632	+	0.127303i
$425$	3.98036	−	2.89190i	0.193076	−	0.140278i
$426$		0			0
$427$	0.175053	+	0.538758i	0.00847141	+	0.0260723i
$428$	−18.2201			−0.880702
$429$		0			0
$430$	−9.96139			−0.480381
$431$	−6.17164	−	18.9944i	−0.297278	−	0.914927i	−0.982447	−	0.186543i	$-0.940272\pi$
$431$	−6.17164	−	18.9944i	−0.297278	−	0.914927i	0.685169	−	0.728384i	$-0.259728\pi$
$432$		0			0
$433$	−13.4316	+	9.75862i	−0.645481	+	0.468969i	−0.861729	−	0.507369i	$-0.830618\pi$
$433$	−13.4316	+	9.75862i	−0.645481	+	0.468969i	0.216248	+	0.976338i	$0.430618\pi$
$434$	0.739287	−	2.27529i	0.0354869	−	0.109218i
$435$		0			0
$436$	−5.67015	+	4.11961i	−0.271551	+	0.197293i
$437$	−0.454093	−	0.329918i	−0.0217222	−	0.0157821i
$438$		0			0
$439$	−28.3645			−1.35376			−0.676882	−	0.736091i	$-0.736669\pi$
$439$	−28.3645			−1.35376			−0.676882	+	0.736091i	$0.736669\pi$
$440$	1.06854	+	0.824320i	0.0509405	+	0.0392979i
$441$		0			0
$442$	−4.68824	−	14.4289i	−0.222997	−	0.686314i
$443$	18.3506	+	13.3325i	0.871865	+	0.633447i	0.931087	−	0.364798i	$-0.118862\pi$
$443$	18.3506	+	13.3325i	0.871865	+	0.633447i	−0.0592220	+	0.998245i	$0.518862\pi$
$444$		0			0
$445$	1.87937	−	5.78411i	0.0890908	−	0.274193i
$446$	7.81345	−	24.0473i	0.369977	−	1.13867i
$447$		0			0
$448$	−4.53498	−	3.29486i	−0.214258	−	0.155667i
$449$	−1.41587	−	4.35761i	−0.0668192	−	0.205648i	0.912072	−	0.410030i	$-0.134482\pi$
$449$	−1.41587	−	4.35761i	−0.0668192	−	0.205648i	−0.978891	+	0.204381i	$0.934482\pi$
$450$		0			0
$451$	−4.54245	+	12.7227i	−0.213896	+	0.599090i
$452$	−25.2629			−1.18827
$453$		0			0
$454$	−13.6290	−	9.90205i	−0.639641	−	0.464726i
$455$	−0.718247	+	0.521837i	−0.0336719	+	0.0244641i
$456$		0			0
$457$	2.07841	−	6.39668i	0.0972238	−	0.299224i	−0.890603	−	0.454781i	$-0.849717\pi$
$457$	2.07841	−	6.39668i	0.0972238	−	0.299224i	0.987827	+	0.155557i	$0.0497174\pi$
$458$	−44.8320	+	32.5724i	−2.09486	+	1.52201i
$459$		0			0
$460$	−0.0559101	−	0.172073i	−0.00260682	−	0.00802297i
$461$	2.83529			0.132053			0.0660263	−	0.997818i	$-0.478968\pi$
$461$	2.83529			0.132053			0.0660263	+	0.997818i	$0.478968\pi$
$462$		0			0
$463$	20.5498			0.955029			0.477515	−	0.878624i	$-0.341538\pi$
$463$	20.5498			0.955029			0.477515	+	0.878624i	$0.341538\pi$
$464$	9.27657	+	28.5504i	0.430654	+	1.32542i
$465$		0			0
$466$	41.4497	−	30.1150i	1.92012	−	1.39505i
$467$	3.63384	−	11.1838i	0.168154	−	0.517525i	−0.831101	−	0.556122i	$-0.812289\pi$
$467$	3.63384	−	11.1838i	0.168154	−	0.517525i	0.999255	+	0.0385968i	$0.0122888\pi$
$468$		0			0
$469$	6.51753	−	4.73526i	0.300952	−	0.218654i
$470$	−9.57912	−	6.95964i	−0.441852	−	0.321024i
$471$		0			0
$472$	2.27216			0.104585
$473$	4.53935	+	15.4715i	0.208720	+	0.711382i
$474$		0			0
$475$	2.10768	+	6.48677i	0.0967070	+	0.297634i
$476$	−5.16262	−	3.75086i	−0.236628	−	0.171920i
$477$		0			0
$478$	13.1205	−	40.3806i	0.600116	−	1.84697i
$479$	−0.470421	+	1.44781i	−0.0214941	+	0.0661519i	−0.961228	−	0.275754i	$-0.911072\pi$
$479$	−0.470421	+	1.44781i	−0.0214941	+	0.0661519i	0.939734	+	0.341906i	$0.111072\pi$
$480$		0			0
$481$	4.35861	+	3.16672i	0.198736	+	0.144390i
$482$	−14.8353	−	45.6585i	−0.675731	−	2.07969i
$483$		0			0
$484$	8.78368	−	22.5329i	0.399258	−	1.02422i
$485$	6.70578			0.304494
$486$		0			0
$487$	−28.7184	−	20.8652i	−1.30136	−	0.945491i	−0.301389	−	0.953501i	$-0.597450\pi$
$487$	−28.7184	−	20.8652i	−1.30136	−	0.945491i	−0.999968	+	0.00801039i	$0.997450\pi$
$488$	0.316105	−	0.229664i	0.0143094	−	0.0103964i
$489$		0			0
$490$	4.21196	−	12.9631i	0.190277	−	0.585612i
$491$	10.2562	−	7.45159i	0.462858	−	0.336286i	−0.331794	−	0.943352i	$-0.607654\pi$
$491$	10.2562	−	7.45159i	0.462858	−	0.336286i	0.794651	+	0.607066i	$0.207654\pi$
$492$		0			0
$493$	12.8082	+	39.4195i	0.576852	+	1.77537i
$494$	21.0322			0.946285
$495$		0			0
$496$	7.05244			0.316664
$497$	−0.234036	−	0.720288i	−0.0104979	−	0.0323093i
$498$		0			0
$499$	−17.0361	+	12.3774i	−0.762640	+	0.554090i	−0.899719	−	0.436470i	$-0.856229\pi$
$499$	−17.0361	+	12.3774i	−0.762640	+	0.554090i	0.137079	+	0.990560i	$0.456229\pi$
$500$	−0.679399	+	2.09098i	−0.0303837	+	0.0935113i
$501$		0			0
$502$	−17.0243	+	12.3688i	−0.759830	+	0.552049i
$503$	20.2875	+	14.7398i	0.904576	+	0.657213i	0.939637	−	0.342172i	$-0.111163\pi$
$503$	20.2875	+	14.7398i	0.904576	+	0.657213i	−0.0350612	+	0.999385i	$0.511163\pi$
$504$		0			0
$505$	−5.94562			−0.264577
$506$	−0.461718	+	0.315573i	−0.0205259	+	0.0140289i
$507$		0			0
$508$	12.3593	+	38.0379i	0.548353	+	1.68766i
$509$	−29.6791	−	21.5631i	−1.31550	−	0.955767i	−0.999977	−	0.00684995i	$-0.997820\pi$
$509$	−29.6791	−	21.5631i	−1.31550	−	0.955767i	−0.315524	−	0.948917i	$-0.602180\pi$
$510$		0			0
$511$	2.84882	−	8.76778i	0.126025	−	0.387864i
$512$	9.83238	−	30.2610i	0.434534	−	1.33736i
$513$		0			0
$514$	−3.23157	−	2.34787i	−0.142538	−	0.103560i
$515$	−0.598127	−	1.84085i	−0.0263566	−	0.0811174i
$516$		0			0
$517$	−6.44421	+	18.0493i	−0.283416	+	0.793807i
$518$	4.32748			0.190139
$519$		0			0
$520$	0.495405	+	0.359933i	0.0217250	+	0.0157841i
$521$	22.9371	−	16.6648i	1.00489	−	0.730099i	0.0417626	−	0.999128i	$-0.486703\pi$
$521$	22.9371	−	16.6648i	1.00489	−	0.730099i	0.963132	+	0.269029i	$0.0867027\pi$
$522$		0			0
$523$	8.27685	−	25.4735i	0.361922	−	1.11388i	−0.589965	−	0.807429i	$-0.700858\pi$
$523$	8.27685	−	25.4735i	0.361922	−	1.11388i	0.951886	−	0.306451i	$-0.0991416\pi$
$524$	33.3964	−	24.2639i	1.45893	−	1.05997i
$525$		0			0
$526$	−5.57355	−	17.1536i	−0.243018	−	0.747933i
$527$	9.73732			0.424164
$528$		0			0
$529$	−22.9932			−0.999706
$530$	4.28901	+	13.2002i	0.186303	+	0.573380i
$531$		0			0
$532$	7.15694	−	5.19982i	0.310293	−	0.225441i
$533$	−1.89422	+	5.82982i	−0.0820479	+	0.252517i
$534$		0			0
$535$	−6.70449	+	4.87110i	−0.289860	+	0.210596i
$536$	−4.49542	−	3.26611i	−0.194172	−	0.141074i
$537$		0			0
$538$	24.9659			1.07636
$539$	−22.0530	−	0.634602i	−0.949889	−	0.0273342i
$540$		0			0
$541$	5.17081	+	15.9141i	0.222311	+	0.684201i	0.998553	+	0.0537675i	$0.0171230\pi$
$541$	5.17081	+	15.9141i	0.222311	+	0.684201i	−0.776243	+	0.630434i	$0.782877\pi$
$542$	−20.4985	−	14.8930i	−0.880484	−	0.639709i
$543$		0			0
$544$	12.3383	−	37.9734i	0.529001	−	1.62810i
$545$	−0.985092	+	3.03180i	−0.0421967	+	0.129868i
$546$		0			0
$547$	17.3143	+	12.5796i	0.740305	+	0.537863i	0.892807	−	0.450440i	$-0.148733\pi$
$547$	17.3143	+	12.5796i	0.740305	+	0.537863i	−0.152502	+	0.988303i	$0.548733\pi$
$548$	3.21154	+	9.88411i	0.137190	+	0.422228i
$549$		0			0
$550$	6.79310	+	0.195480i	0.289659	+	0.00833529i
$551$	−57.4596			−2.44786
$552$		0			0
$553$	−5.32259	−	3.86709i	−0.226339	−	0.164445i
$554$	−34.0310	+	24.7249i	−1.44584	+	1.05046i
$555$		0			0
$556$	−12.5510	+	38.6281i	−0.532282	+	1.63820i
$557$	34.7026	−	25.2129i	1.47040	−	1.06830i	0.489897	−	0.871781i	$-0.337035\pi$
$557$	34.7026	−	25.2129i	1.47040	−	1.06830i	0.980499	−	0.196524i	$-0.0629655\pi$
$558$		0			0
$559$	2.26080	+	6.95804i	0.0956218	+	0.294294i
$560$	−2.10218			−0.0888332
$561$		0			0
$562$	23.4144			0.987677
$563$	−10.1843	−	31.3440i	−0.429216	−	1.32099i	−0.898899	−	0.438157i	$-0.855632\pi$
$563$	−10.1843	−	31.3440i	−0.429216	−	1.32099i	0.469682	−	0.882835i	$-0.344368\pi$
$564$		0			0
$565$	−9.29605	+	6.75398i	−0.391088	+	0.284142i
$566$	18.6994	−	57.5508i	0.785994	−	2.41904i
$567$		0			0
$568$	−0.422614	+	0.307047i	−0.0177325	+	0.0128834i
$569$	2.72574	+	1.98036i	0.114269	+	0.0830212i	0.643452	−	0.765486i	$-0.277502\pi$
$569$	2.72574	+	1.98036i	0.114269	+	0.0830212i	−0.529183	+	0.848508i	$0.677502\pi$
$570$		0			0
$571$	−0.267599			−0.0111987			−0.00559934	−	0.999984i	$-0.501782\pi$
$571$	−0.267599			−0.0111987			−0.00559934	+	0.999984i	$0.501782\pi$
$572$	3.68984	−	10.3347i	0.154280	−	0.432115i
$573$		0			0
$574$	1.52151	+	4.68273i	0.0635067	+	0.195453i
$575$	−0.0665767	−	0.0483708i	−0.00277644	−	0.00201720i
$576$		0			0
$577$	11.7100	−	36.0396i	0.487493	−	1.50035i	−0.340844	−	0.940120i	$-0.610713\pi$
$577$	11.7100	−	36.0396i	0.487493	−	1.50035i	0.828337	−	0.560230i	$-0.189287\pi$
$578$	4.56299	−	14.0434i	0.189795	−	0.584130i
$579$		0			0
$580$	−14.9844	−	10.8868i	−0.622195	−	0.452051i
$581$	−0.731416	−	2.25107i	−0.0303443	−	0.0933900i
$582$		0			0
$583$	18.5474	−	12.6767i	0.768156	−	0.525017i
$584$	−6.35872			−0.263126
$585$		0			0
$586$	−19.2235	−	13.9667i	−0.794117	−	0.576960i
$587$	−13.6375	+	9.90825i	−0.562881	+	0.408957i	−0.832512	−	0.554006i	$-0.813098\pi$
$587$	−13.6375	+	9.90825i	−0.562881	+	0.408957i	0.269631	+	0.962964i	$0.413098\pi$
$588$		0			0
$589$	−4.17138	+	12.8382i	−0.171879	+	0.528988i
$590$	9.25671	−	6.72540i	0.381093	−	0.276880i
$591$		0			0
$592$	3.94209	+	12.1325i	0.162019	+	0.498642i
$593$	−11.0211			−0.452580			−0.226290	−	0.974060i	$-0.572660\pi$
$593$	−11.0211			−0.452580			−0.226290	+	0.974060i	$0.572660\pi$
$594$		0			0
$595$	−2.90248			−0.118990
$596$	−10.5314	−	32.4124i	−0.431384	−	1.32766i
$597$		0			0
$598$	−0.205298	+	0.149158i	−0.00839527	+	0.00609952i
$599$	−5.15906	+	15.8779i	−0.210793	+	0.648755i	0.788632	+	0.614865i	$0.210790\pi$
$599$	−5.15906	+	15.8779i	−0.210793	+	0.648755i	−0.999426	+	0.0338901i	$0.989210\pi$
$600$		0			0
$601$	6.27526	−	4.55925i	0.255973	−	0.185976i	−0.452397	−	0.891817i	$-0.649431\pi$
$601$	6.27526	−	4.55925i	0.255973	−	0.185976i	0.708370	+	0.705841i	$0.249431\pi$
$602$	4.75425	+	3.45417i	0.193769	+	0.140781i
$603$		0			0
$604$	12.2118			0.496891
$605$	−2.79197	−	10.6398i	−0.113510	−	0.432569i
$606$		0			0
$607$	9.85634	+	30.3347i	0.400057	+	1.23125i	0.924953	+	0.380082i	$0.124104\pi$
$607$	9.85634	+	30.3347i	0.400057	+	1.23125i	−0.524896	+	0.851166i	$0.675896\pi$
$608$	44.7805	+	32.5349i	1.81609	+	1.31946i
$609$		0			0
$610$	0.608018	−	1.87129i	0.0246179	−	0.0757662i
$611$	−2.68727	+	8.27056i	−0.108715	+	0.334591i
$612$		0			0
$613$	34.6283	+	25.1589i	1.39862	+	1.01616i	0.994856	+	0.101296i	$0.0322991\pi$
$613$	34.6283	+	25.1589i	1.39862	+	1.01616i	0.403766	+	0.914862i	$0.367701\pi$
$614$	0.806109	+	2.48095i	0.0325319	+	0.100123i
$615$		0			0
$616$	−0.224141	−	0.763943i	−0.00903089	−	0.0307801i
$617$	21.7979			0.877550			0.438775	−	0.898597i	$-0.355412\pi$
$617$	21.7979			0.877550			0.438775	+	0.898597i	$0.355412\pi$
$618$		0			0
$619$	−27.2098	−	19.7691i	−1.09366	−	0.794587i	−0.113642	−	0.993522i	$-0.536252\pi$
$619$	−27.2098	−	19.7691i	−1.09366	−	0.794587i	−0.980013	+	0.198935i	$0.936252\pi$
$620$	−3.52026	+	2.55762i	−0.141377	+	0.102717i
$621$		0			0
$622$	3.10608	−	9.55953i	0.124542	−	0.383302i
$623$	−2.90264	+	2.10889i	−0.116292	+	0.0844908i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−31.5956			−1.26281
$627$		0			0
$628$	−40.6990			−1.62407
$629$	5.44285	+	16.7514i	0.217021	+	0.667921i
$630$		0			0
$631$	17.3577	−	12.6111i	0.690997	−	0.502039i	−0.185991	−	0.982552i	$-0.559549\pi$
$631$	17.3577	−	12.6111i	0.690997	−	0.502039i	0.876988	+	0.480513i	$0.159549\pi$
$632$	−1.40228	+	4.31577i	−0.0557796	+	0.171672i
$633$		0			0
$634$	−55.6735	+	40.4492i	−2.21108	+	1.60644i
$635$	14.7172	+	10.6927i	0.584034	+	0.424325i
$636$		0			0
$637$	−10.0107			−0.396636
$638$	−19.2506	+	53.9181i	−0.762139	+	2.13464i
$639$		0			0
$640$	1.00096	+	3.08064i	0.0395665	+	0.121773i
$641$	36.1507	+	26.2650i	1.42787	+	1.03740i	0.990409	+	0.138165i	$0.0441205\pi$
$641$	36.1507	+	26.2650i	1.42787	+	1.03740i	0.437456	+	0.899240i	$0.355880\pi$
$642$		0			0
$643$	2.65477	−	8.17053i	0.104694	−	0.322214i	−0.884965	−	0.465658i	$-0.845818\pi$
$643$	2.65477	−	8.17053i	0.104694	−	0.322214i	0.989658	+	0.143444i	$0.0458176\pi$
$644$	−0.0329833	+	0.101512i	−0.00129973	+	0.00400014i
$645$		0			0
$646$	55.6284	+	40.4164i	2.18867	+	1.59016i
$647$	−2.76396	−	8.50658i	−0.108662	−	0.334428i	0.881910	−	0.471417i	$-0.156257\pi$
$647$	−2.76396	−	8.50658i	−0.108662	−	0.334428i	−0.990573	+	0.136989i	$0.956257\pi$
$648$		0			0
$649$	−14.6638	−	11.3123i	−0.575604	−	0.444048i
$650$	3.08363			0.120950
$651$		0			0
$652$	−13.8997	−	10.0987i	−0.544355	−	0.395497i
$653$	−11.2834	+	8.19784i	−0.441552	+	0.320806i	−0.786251	−	0.617907i	$-0.787981\pi$
$653$	−11.2834	+	8.19784i	−0.441552	+	0.320806i	0.344699	+	0.938713i	$0.387981\pi$
$654$		0			0
$655$	5.80204	−	17.8569i	0.226705	−	0.697725i
$656$	−11.7425	+	8.53140i	−0.458466	+	0.333095i
$657$		0			0
$658$	2.15852	+	6.64323i	0.0841477	+	0.258980i
$659$	6.61492			0.257681			0.128840	−	0.991665i	$-0.458875\pi$
$659$	6.61492			0.257681			0.128840	+	0.991665i	$0.458875\pi$
$660$		0			0
$661$	23.5635			0.916515			0.458257	−	0.888820i	$-0.348474\pi$
$661$	23.5635			0.916515			0.458257	+	0.888820i	$0.348474\pi$
$662$	−6.01887	−	18.5242i	−0.233930	−	0.719962i
$663$		0			0
$664$	−1.32077	+	0.959594i	−0.0512557	+	0.0372395i
$665$	1.24340	−	3.82678i	0.0482168	−	0.148396i
$666$		0			0
$667$	0.560871	−	0.407497i	0.0217170	−	0.0157783i
$668$	10.6044	+	7.70452i	0.410295	+	0.298097i
$669$		0			0
$670$	−27.9816			−1.08102
$671$	−3.18346	−	0.0916079i	−0.122896	−	0.00353649i
$672$		0			0
$673$	1.30209	+	4.00742i	0.0501919	+	0.154475i	0.973011	−	0.230759i	$-0.0741209\pi$
$673$	1.30209	+	4.00742i	0.0501919	+	0.154475i	−0.922819	+	0.385234i	$0.874121\pi$
$674$	−42.4612	−	30.8499i	−1.63554	−	1.18829i
$675$		0			0
$676$	−7.29351	+	22.4471i	−0.280520	+	0.863351i
$677$	5.25436	−	16.1713i	0.201942	−	0.621512i	−0.797884	−	0.602812i	$-0.794047\pi$
$677$	5.25436	−	16.1713i	0.201942	−	0.621512i	0.999825	−	0.0187007i	$-0.00595297\pi$
$678$		0			0
$679$	−3.20045	−	2.32527i	−0.122822	−	0.0892355i
$680$	0.618641	+	1.90398i	0.0237238	+	0.0730143i
$681$		0			0
$682$	10.6494	+	8.21544i	0.407786	+	0.314585i
$683$	−19.6114			−0.750409			−0.375204	−	0.926942i	$-0.622427\pi$
$683$	−19.6114			−0.750409			−0.375204	+	0.926942i	$0.622427\pi$
$684$		0			0
$685$	3.82425	+	2.77848i	0.146117	+	0.106160i
$686$	−13.3509	+	9.69997i	−0.509738	+	0.370346i
$687$		0			0
$688$	−5.35323	+	16.4755i	−0.204090	+	0.628124i
$689$	8.24693	−	5.99175i	0.314183	−	0.228267i
$690$		0			0
$691$	2.37016	+	7.29459i	0.0901650	+	0.277499i	0.985963	−	0.166961i	$-0.0533954\pi$
$691$	2.37016	+	7.29459i	0.0901650	+	0.277499i	−0.895799	+	0.444460i	$0.853395\pi$
$692$	36.4390			1.38520
$693$		0			0
$694$	−57.1854			−2.17073
$695$	5.70869	+	17.5695i	0.216543	+	0.666451i
$696$		0			0
$697$	−16.2129	+	11.7793i	−0.614106	+	0.446174i
$698$	−6.71747	+	20.6743i	−0.254260	+	0.782532i
$699$		0			0
$700$	1.04931	−	0.762370i	0.0396603	−	0.0288149i
$701$	17.7443	+	12.8920i	0.670192	+	0.486923i	0.870090	−	0.492894i	$-0.164061\pi$
$701$	17.7443	+	12.8920i	0.670192	+	0.486923i	−0.199897	+	0.979817i	$0.564061\pi$
$702$		0			0
$703$	−24.4175			−0.920924
$704$	26.0180	−	17.7827i	0.980589	−	0.670210i
$705$		0			0
$706$	−18.4070	−	56.6508i	−0.692756	−	2.13208i
$707$	2.83765	+	2.06168i	0.106721	+	0.0775373i
$708$		0			0
$709$	−2.23257	+	6.87116i	−0.0838461	+	0.258052i	−0.984187	−	0.177134i	$-0.943317\pi$
$709$	−2.23257	+	6.87116i	−0.0838461	+	0.258052i	0.900341	+	0.435186i	$0.143317\pi$
$710$	−0.812884	+	2.50180i	−0.0305070	+	0.0938909i
$711$		0			0
$712$	2.00207	+	1.45459i	0.0750307	+	0.0545130i
$713$	−0.0503294	−	0.154898i	−0.00188485	−	0.00580098i
$714$		0			0
$715$	−1.40520	−	4.78935i	−0.0525513	−	0.179111i
$716$	47.3678			1.77022
$717$		0			0
$718$	50.1138	+	36.4098i	1.87023	+	1.35880i
$719$	−15.5513	+	11.2987i	−0.579967	+	0.421371i	−0.838712	−	0.544575i	$-0.816691\pi$
$719$	−15.5513	+	11.2987i	−0.579967	+	0.421371i	0.258745	+	0.965946i	$0.416691\pi$
$720$		0			0
$721$	−0.352857	+	1.08598i	−0.0131411	+	0.0404440i
$722$	−45.6212	+	33.1457i	−1.69784	+	1.23356i
$723$		0			0
$724$	−13.7038	−	42.1758i	−0.509296	−	1.56745i
$725$	−8.42443			−0.312875
$726$		0			0
$727$	−33.9775			−1.26015			−0.630077	−	0.776532i	$-0.716977\pi$
$727$	−33.9775			−1.26015			−0.630077	+	0.776532i	$0.716977\pi$
$728$	−0.111632	−	0.343569i	−0.00413737	−	0.0127335i
$729$		0			0
$730$	−25.9052	+	18.8213i	−0.958796	+	0.696606i
$731$	−7.39122	+	22.7478i	−0.273374	+	0.841359i
$732$		0			0
$733$	−5.25720	+	3.81958i	−0.194179	+	0.141079i	−0.680627	−	0.732630i	$-0.738292\pi$
$733$	−5.25720	+	3.81958i	−0.194179	+	0.141079i	0.486448	+	0.873710i	$0.338292\pi$
$734$	39.2142	+	28.4908i	1.44742	+	1.05161i
$735$		0			0
$736$	−0.667841			−0.0246170
$737$	12.7510	+	43.4596i	0.469691	+	1.60085i
$738$		0			0
$739$	−5.78294	−	17.7981i	−0.212729	−	0.654712i	−0.999307	−	0.0372216i	$-0.988149\pi$
$739$	−5.78294	−	17.7981i	−0.212729	−	0.654712i	0.786578	−	0.617491i	$-0.211851\pi$
$740$	−6.36765	−	4.62637i	−0.234080	−	0.170069i
$741$		0			0
$742$	2.53024	−	7.78727i	0.0928880	−	0.285880i
$743$	−2.71901	+	8.36824i	−0.0997506	+	0.307001i	−0.988463	−	0.151465i	$-0.951601\pi$
$743$	−2.71901	+	8.36824i	−0.0997506	+	0.307001i	0.888712	+	0.458466i	$0.151601\pi$
$744$		0			0
$745$	−12.5406	−	9.11130i	−0.459453	−	0.333812i
$746$	−9.24443	−	28.4514i	−0.338463	−	1.04168i
$747$		0			0
$748$	29.6188	−	20.2438i	1.08297	−	0.740186i
$749$	4.88892			0.178637
$750$		0			0
$751$	−20.8619	−	15.1571i	−0.761261	−	0.553089i	0.138036	−	0.990427i	$-0.455921\pi$
$751$	−20.8619	−	15.1571i	−0.761261	−	0.553089i	−0.899297	+	0.437339i	$0.855921\pi$
$752$	−16.6586	+	12.1032i	−0.607478	+	0.441358i
$753$		0			0
$754$	−8.02760	+	24.7064i	−0.292348	+	0.899754i
$755$	4.49360	−	3.26479i	0.163539	−	0.118818i
$756$		0			0
$757$	12.3823	+	38.1087i	0.450041	+	1.38508i	0.876859	+	0.480747i	$0.159634\pi$
$757$	12.3823	+	38.1087i	0.450041	+	1.38508i	−0.426818	+	0.904338i	$0.640366\pi$
$758$	13.7362			0.498920
$759$		0			0
$760$	−2.77532			−0.100672
$761$	−5.54238	−	17.0577i	−0.200911	−	0.618340i	−0.999857	−	0.0169371i	$-0.994608\pi$
$761$	−5.54238	−	17.0577i	−0.200911	−	0.618340i	0.798946	−	0.601403i	$-0.205392\pi$
$762$		0			0
$763$	1.52145	−	1.10540i	0.0550801	−	0.0400180i
$764$	−11.0668	+	34.0602i	−0.400384	+	1.23226i
$765$		0			0
$766$	−52.2648	+	37.9726i	−1.88840	+	1.37201i
$767$	−6.79856	−	4.93945i	−0.245482	−	0.178353i
$768$		0			0
$769$	−10.8431			−0.391011			−0.195506	−	0.980703i	$-0.562635\pi$
$769$	−10.8431			−0.391011			−0.195506	+	0.980703i	$0.562635\pi$
$770$	−3.17435	−	2.44884i	−0.114395	−	0.0882501i
$771$		0			0
$772$	2.27564	+	7.00369i	0.0819020	+	0.252068i
$773$	−5.55690	−	4.03732i	−0.199868	−	0.145212i	0.483350	−	0.875427i	$-0.339420\pi$
$773$	−5.55690	−	4.03732i	−0.199868	−	0.145212i	−0.683218	+	0.730215i	$0.739420\pi$
$774$		0			0
$775$	−0.611585	+	1.88227i	−0.0219688	+	0.0676130i
$776$	−0.843185	+	2.59506i	−0.0302686	+	0.0931571i
$777$		0			0
$778$	−64.6238	−	46.9519i	−2.31687	−	1.68331i
$779$	−8.58503	−	26.4220i	−0.307591	−	0.946667i
$780$		0			0
$781$	4.25610	+	0.122474i	0.152295	+	0.00438248i
$782$	−0.829623			−0.0296673
$783$		0			0
$784$	−19.1767	−	13.9327i	−0.684881	−	0.497595i
$785$	−14.9761	+	10.8808i	−0.534521	+	0.388352i
$786$		0			0
$787$	0.701367	−	2.15858i	0.0250010	−	0.0769452i	−0.937778	−	0.347237i	$-0.887120\pi$
$787$	0.701367	−	2.15858i	0.0250010	−	0.0769452i	0.962779	+	0.270291i	$0.0871201\pi$
$788$	−17.3984	+	12.6407i	−0.619792	+	0.450306i
$789$		0			0
$790$	7.06145	+	21.7329i	0.251235	+	0.773222i
$791$	6.77869			0.241022
$792$		0			0
$793$	−1.44509			−0.0513166
$794$	17.2026	+	52.9442i	0.610498	+	1.87892i
$795$		0			0
$796$	−17.5922	+	12.7815i	−0.623539	+	0.453028i
$797$	−3.41660	+	10.5152i	−0.121022	+	0.372468i	−0.993155	−	0.116800i	$-0.962736\pi$
$797$	−3.41660	+	10.5152i	−0.121022	+	0.372468i	0.872133	+	0.489269i	$0.162736\pi$
$798$		0			0
$799$	−23.0006	+	16.7109i	−0.813703	+	0.591190i
$800$	6.56547	+	4.77010i	0.232125	+	0.168648i
$801$		0			0
$802$	−27.0356			−0.954660
$803$	41.0371	+	31.6580i	1.44817	+	1.11719i
$804$		0			0
$805$	0.0150021	+	0.0461717i	0.000528754	+	0.00162734i
$806$	4.93737	+	3.58721i	0.173911	+	0.126354i
$807$		0			0
$808$	0.747602	−	2.30088i	0.0263006	−	0.0809448i
$809$	−1.32961	+	4.09212i	−0.0467466	+	0.143871i	−0.971705	−	0.236196i	$-0.924099\pi$
$809$	−1.32961	+	4.09212i	−0.0467466	+	0.143871i	0.924959	+	0.380067i	$0.124099\pi$
$810$		0			0
$811$	15.1451	+	11.0036i	0.531817	+	0.386387i	0.821037	−	0.570875i	$-0.193396\pi$
$811$	15.1451	+	11.0036i	0.531817	+	0.386387i	−0.289220	+	0.957263i	$0.593396\pi$
$812$	3.37653	+	10.3919i	0.118493	+	0.364683i
$813$		0			0
$814$	−8.18057	+	22.9126i	−0.286729	+	0.803085i
$815$	−7.81457			−0.273733
$816$		0			0
$817$	−26.8256	−	19.4899i	−0.938508	−	0.681866i
$818$	16.4567	−	11.9565i	0.575394	−	0.418048i
$819$		0			0
$820$	2.76734	−	8.51699i	0.0966396	−	0.297426i
$821$	29.4674	−	21.4093i	1.02842	−	0.747189i	0.0604266	−	0.998173i	$-0.480754\pi$
$821$	29.4674	−	21.4093i	1.02842	−	0.747189i	0.967991	+	0.250983i	$0.0807539\pi$
$822$		0			0
$823$	−0.470329	−	1.44752i	−0.0163946	−	0.0504575i	0.942525	−	0.334137i	$-0.108445\pi$
$823$	−0.470329	−	1.44752i	−0.0163946	−	0.0504575i	−0.958919	+	0.283679i	$0.908445\pi$
$824$	0.787594			0.0274371
$825$		0			0
$826$	−6.75000			−0.234863
$827$	−7.85490	−	24.1749i	−0.273141	−	0.840643i	−0.989705	−	0.143121i	$-0.954286\pi$
$827$	−7.85490	−	24.1749i	−0.273141	−	0.840643i	0.716564	−	0.697522i	$-0.245714\pi$
$828$		0			0
$829$	6.87760	−	4.99687i	0.238869	−	0.173548i	−0.461910	−	0.886927i	$-0.652836\pi$
$829$	6.87760	−	4.99687i	0.238869	−	0.173548i	0.700779	+	0.713378i	$0.252836\pi$
$830$	−2.54045	+	7.81871i	−0.0881804	+	0.271391i
$831$		0			0
$832$	11.5686	−	8.40511i	0.401070	−	0.291395i
$833$	−26.4773	−	19.2369i	−0.917383	−	0.666518i
$834$		0			0
$835$	5.96190			0.206320
$836$	14.0020	+	47.7232i	0.484269	+	1.65054i
$837$		0			0
$838$	16.7336	+	51.5007i	0.578052	+	1.77906i
$839$	−35.9783	−	26.1398i	−1.24211	−	0.902445i	−0.244372	−	0.969682i	$-0.578582\pi$
$839$	−35.9783	−	26.1398i	−1.24211	−	0.902445i	−0.997737	+	0.0672363i	$0.978582\pi$
$840$		0			0
$841$	12.9697	−	39.9168i	0.447233	−	1.37644i
$842$	8.70573	−	26.7935i	0.300019	−	0.923364i
$843$		0			0
$844$	39.4311	+	28.6484i	1.35728	+	0.986119i
$845$	3.31737	+	10.2098i	0.114121	+	0.351228i
$846$		0			0
$847$	−2.35689	+	6.04616i	−0.0809835	+	0.207748i
$848$	24.1372			0.828877
$849$		0			0
$850$	8.15593	+	5.92563i	0.279746	+	0.203248i
$851$	0.238343	−	0.173166i	0.00817028	−	0.00593605i
$852$		0			0
$853$	8.61289	−	26.5077i	0.294900	−	0.907608i	−0.688356	−	0.725373i	$-0.741667\pi$
$853$	8.61289	−	26.5077i	0.294900	−	0.907608i	0.983255	−	0.182234i	$-0.0583329\pi$
$854$	−0.939066	+	0.682271i	−0.0321342	+	0.0233468i
$855$		0			0
$856$	−1.04203	−	3.20705i	−0.0356160	−	0.109615i
$857$	−23.1342			−0.790249			−0.395125	−	0.918628i	$-0.629299\pi$
$857$	−23.1342			−0.790249			−0.395125	+	0.918628i	$0.629299\pi$
$858$		0			0
$859$	51.9912			1.77392			0.886959	−	0.461849i	$-0.152814\pi$
$859$	51.9912			1.77392			0.886959	+	0.461849i	$0.152814\pi$
$860$	−3.30289	−	10.1652i	−0.112628	−	0.346632i
$861$		0			0
$862$	33.1076	−	24.0541i	1.12765	−	0.819285i
$863$	9.02589	−	27.7788i	0.307245	−	0.945603i	−0.671585	−	0.740928i	$-0.734386\pi$
$863$	9.02589	−	27.7788i	0.307245	−	0.945603i	0.978830	−	0.204675i	$-0.0656139\pi$
$864$		0			0
$865$	13.4085	−	9.74186i	0.455903	−	0.331233i
$866$	−27.5219	−	19.9958i	−0.935233	−	0.679486i
$867$		0			0
$868$	2.56698			0.0871289
$869$	30.5366	−	20.8711i	1.03588	−	0.708002i
$870$		0			0
$871$	6.35060	+	19.5451i	0.215182	+	0.662262i
$872$	−1.04941	−	0.762438i	−0.0355374	−	0.0258194i
$873$		0			0
$874$	0.355403	−	1.09382i	0.0120217	−	0.0369989i
$875$	0.182300	−	0.561062i	0.00616287	−	0.0189674i
$876$		0			0
$877$	−27.9723	−	20.3231i	−0.944558	−	0.686262i	0.00495520	−	0.999988i	$-0.498423\pi$
$877$	−27.9723	−	20.3231i	−0.944558	−	0.686262i	−0.949514	+	0.313726i	$0.898423\pi$
$878$	−17.9601	−	55.2756i	−0.606125	−	1.86546i
$879$		0			0
$880$	3.97391	−	11.1303i	0.133960	−	0.375203i
$881$	−44.3728			−1.49496			−0.747479	−	0.664285i	$-0.768736\pi$
$881$	−44.3728			−1.49496			−0.747479	+	0.664285i	$0.768736\pi$
$882$		0			0
$883$	23.2824	+	16.9156i	0.783514	+	0.569256i	0.906032	−	0.423210i	$-0.139097\pi$
$883$	23.2824	+	16.9156i	0.783514	+	0.569256i	−0.122518	+	0.992466i	$0.539097\pi$
$884$	13.1697	−	9.56837i	0.442946	−	0.321819i
$885$		0			0
$886$	−14.3624	+	44.2029i	−0.482514	+	1.48503i
$887$	−7.53096	+	5.47156i	−0.252865	+	0.183717i	−0.706996	−	0.707218i	$-0.749950\pi$
$887$	−7.53096	+	5.47156i	−0.252865	+	0.183717i	0.454131	+	0.890935i	$0.349950\pi$
$888$		0			0
$889$	−3.31630	−	10.2065i	−0.111225	−	0.342316i
$890$	12.4618			0.417721
$891$		0			0
$892$	27.1301			0.908383
$893$	−12.1793	−	37.4840i	−0.407564	−	1.25435i
$894$		0			0
$895$	17.4300	−	12.6637i	0.582621	−	0.423299i
$896$	0.590503	−	1.81738i	0.0197273	−	0.0607145i
$897$		0			0
$898$	7.59541	−	5.51839i	0.253462	−	0.184151i
$899$	−13.4888	−	9.80018i	−0.449876	−	0.326854i
$900$		0			0
$901$	33.3264			1.11026
$902$	−27.6697	−	0.796231i	−0.921301	−	0.0265116i
$903$		0			0
$904$	−1.44482	−	4.44671i	−0.0480541	−	0.147895i
$905$	−16.3182	−	11.8559i	−0.542435	−	0.394102i
$906$		0			0
$907$	−13.7217	+	42.2311i	−0.455622	+	1.40226i	0.414782	+	0.909921i	$0.363858\pi$
$907$	−13.7217	+	42.2311i	−0.455622	+	1.40226i	−0.870404	+	0.492339i	$0.836142\pi$
$908$	5.58573	−	17.1911i	0.185369	−	0.570507i
$909$		0			0
$910$	−1.47172	−	1.06927i	−0.0487871	−	0.0354459i
$911$	−7.30385	−	22.4789i	−0.241987	−	0.744761i	−0.996117	−	0.0880355i	$-0.971941\pi$
$911$	−7.30385	−	22.4789i	−0.241987	−	0.744761i	0.754130	−	0.656725i	$-0.228059\pi$
$912$		0			0
$913$	13.3013	+	0.382761i	0.440209	+	0.0126676i
$914$	13.7816			0.455855
$915$		0			0
$916$	−48.1038	−	34.9495i	−1.58940	−	1.15476i
$917$	−8.96109	+	6.51062i	−0.295921	+	0.214999i
$918$		0			0
$919$	2.11809	−	6.51882i	0.0698694	−	0.215036i	−0.910025	−	0.414554i	$-0.863938\pi$
$919$	2.11809	−	6.51882i	0.0698694	−	0.215036i	0.979894	+	0.199518i	$0.0639376\pi$
$920$	0.0270903	−	0.0196823i	0.000893141	−	0.000648905i
$921$		0			0
$922$	1.79527	+	5.52529i	0.0591242	+	0.181966i
$923$	1.93200			0.0635925
$924$		0			0
$925$	−3.57997			−0.117709
$926$	13.0119	+	40.0465i	0.427598	+	1.31601i
$927$		0			0
$928$	−55.3104	+	40.1853i	−1.81565	+	1.31915i
$929$	8.79954	−	27.0822i	0.288704	−	0.888539i	−0.696560	−	0.717498i	$-0.745287\pi$
$929$	8.79954	−	27.0822i	0.288704	−	0.888539i	0.985264	−	0.171040i	$-0.0547129\pi$
$930$		0			0
$931$	36.7055	−	26.6681i	1.20297	−	0.874011i
$932$	44.4747	+	32.3128i	1.45682	+	1.05844i
$933$		0			0
$934$	24.0954			0.788427
$935$	5.48678	−	15.3677i	0.179437	−	0.502576i
$936$		0			0
$937$	−12.0926	−	37.2171i	−0.395047	−	1.21583i	−0.928925	−	0.370268i	$-0.879266\pi$
$937$	−12.0926	−	37.2171i	−0.395047	−	1.21583i	0.533878	−	0.845561i	$-0.320734\pi$
$938$	13.3547	+	9.70277i	0.436047	+	0.316807i
$939$		0			0
$940$	3.92592	−	12.0828i	0.128050	−	0.394096i
$941$	11.7635	−	36.2042i	0.383478	−	1.18022i	−0.554101	−	0.832450i	$-0.686938\pi$
$941$	11.7635	−	36.2042i	0.383478	−	1.18022i	0.937579	−	0.347774i	$-0.113062\pi$
$942$		0			0
$943$	0.271181	+	0.197025i	0.00883087	+	0.00641600i
$944$	−6.14887	−	18.9243i	−0.200129	−	0.615932i
$945$		0			0
$946$	−27.2760	+	18.6425i	−0.886819	+	0.606120i
$947$	−6.37140			−0.207043			−0.103521	−	0.994627i	$-0.533011\pi$
$947$	−6.37140			−0.207043			−0.103521	+	0.994627i	$0.533011\pi$
$948$		0			0
$949$	19.0260	+	13.8232i	0.617611	+	0.448720i
$950$	−11.3066	+	8.21471i	−0.366834	+	0.266521i
$951$		0			0
$952$	0.364958	−	1.12323i	0.0118284	−	0.0364040i
$953$	−2.34889	+	1.70657i	−0.0760881	+	0.0552812i	−0.625179	−	0.780481i	$-0.714974\pi$
$953$	−2.34889	+	1.70657i	−0.0760881	+	0.0552812i	0.549091	+	0.835763i	$0.314974\pi$
$954$		0			0
$955$	5.03362	+	15.4919i	0.162884	+	0.501306i
$956$	45.5573			1.47343
$957$		0			0
$958$	−3.11929			−0.100780
$959$	−0.861738	−	2.65216i	−0.0278270	−	0.0856427i
$960$		0			0
$961$	21.9106	−	15.9190i	0.706795	−	0.513516i
$962$	−3.41134	+	10.4990i	−0.109986	+	0.338502i
$963$		0			0
$964$	41.6739	−	30.2779i	1.34223	−	0.975184i
$965$	2.70979	+	1.96878i	0.0872312	+	0.0633772i
$966$		0			0
$967$	−9.58404			−0.308202			−0.154101	−	0.988055i	$-0.549248\pi$
$967$	−9.58404			−0.308202			−0.154101	+	0.988055i	$0.549248\pi$
$968$	4.46853	+	0.257388i	0.143624	+	0.00827277i
$969$		0			0
$970$	4.24603	+	13.0679i	0.136332	+	0.419586i
$971$	−43.5570	−	31.6460i	−1.39781	−	1.01557i	−0.994957	−	0.100305i	$-0.968018\pi$
$971$	−43.5570	−	31.6460i	−1.39781	−	1.01557i	−0.402855	−	0.915264i	$-0.631982\pi$
$972$		0			0
$973$	3.36776	−	10.3649i	0.107965	−	0.332284i
$974$	22.4769	−	69.1769i	0.720207	−	2.21657i
$975$		0			0
$976$	−2.76825	−	2.01125i	−0.0886094	−	0.0643785i
$977$	9.10421	+	28.0199i	0.291269	+	0.896435i	0.984449	+	0.175670i	$0.0562093\pi$
$977$	9.10421	+	28.0199i	0.291269	+	0.896435i	−0.693180	+	0.720765i	$0.743791\pi$
$978$		0			0
$979$	−5.67878	−	19.3551i	−0.181495	−	0.618591i
$980$	14.6249			0.467176
$981$		0			0
$982$	21.0155	+	15.2686i	0.670631	+	0.487242i
$983$	36.3841	−	26.4346i	1.16047	−	0.843132i	0.170634	−	0.985335i	$-0.445419\pi$
$983$	36.3841	−	26.4346i	1.16047	−	0.843132i	0.989838	+	0.142203i	$0.0454185\pi$
$984$		0			0
$985$	−3.02267	+	9.30284i	−0.0963104	+	0.296413i
$986$	−68.7091	+	49.9201i	−2.18814	+	1.58978i
$987$		0			0
$988$	6.97363	+	21.4626i	0.221861	+	0.682818i
$989$	0.400068			0.0127214
$990$		0			0
$991$	30.3468			0.963997			0.481998	−	0.876172i	$-0.339911\pi$
$991$	30.3468			0.963997			0.481998	+	0.876172i	$0.339911\pi$
$992$	4.96324	+	15.2753i	0.157583	+	0.484991i
$993$		0			0
$994$	1.25548	−	0.912157i	0.0398213	−	0.0289319i
$995$	−3.05634	+	9.40646i	−0.0968926	+	0.298205i
$996$		0			0
$997$	19.6436	−	14.2719i	0.622119	−	0.451996i	−0.231542	−	0.972825i	$-0.574377\pi$
$997$	19.6436	−	14.2719i	0.622119	−	0.451996i	0.853661	+	0.520829i	$0.174377\pi$
$998$	−34.9077	−	25.3619i	−1.10498	−	0.802817i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.h.181.4	yes	16
3.2	odd	2		495.2.n.g.181.1	✓	16
11.3	even	5		5445.2.a.ca.1.8		8
11.8	odd	10		5445.2.a.cc.1.1		8
11.9	even	5	inner	495.2.n.h.361.4	yes	16
33.8	even	10		5445.2.a.cb.1.8		8
33.14	odd	10		5445.2.a.cd.1.1		8
33.20	odd	10		495.2.n.g.361.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.n.g.181.1	✓	16	3.2	odd	2
495.2.n.g.361.1	yes	16	33.20	odd	10
495.2.n.h.181.4	yes	16	1.1	even	1	trivial
495.2.n.h.361.4	yes	16	11.9	even	5	inner
5445.2.a.ca.1.8		8	11.3	even	5
5445.2.a.cb.1.8		8	33.8	even	10
5445.2.a.cc.1.1		8	11.8	odd	10
5445.2.a.cd.1.1		8	33.14	odd	10

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.633189 + 1.94876i) q^{2} +(-1.77869 + 1.29229i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.477268 - 0.346756i) q^{7} +(-0.329192 - 0.239172i) q^{8} -2.04904 q^{10} +(0.933738 + 3.18247i) q^{11} +(0.465044 + 1.43126i) q^{13} +(0.977943 + 0.710517i) q^{14} +(-1.10115 + 3.38900i) q^{16} +(-1.52036 + 4.67919i) q^{17} +(-5.51798 - 4.00905i) q^{19} +(-0.679399 - 2.09098i) q^{20} +(-5.61063 + 3.83474i) q^{22} +0.0822934 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-2.49471 + 1.81252i) q^{26} +(-0.400802 + 1.23354i) q^{28} +(6.81551 - 4.95175i) q^{29} +(-0.611585 - 1.88227i) q^{31} -8.11537 q^{32} -10.0813 q^{34} +(0.182300 + 0.561062i) q^{35} +(2.89625 - 2.10425i) q^{37} +(4.31873 - 13.2917i) q^{38} +(0.329192 - 0.239172i) q^{40} +(3.29530 + 2.39417i) q^{41} +4.86148 q^{43} +(-5.77352 - 4.45397i) q^{44} +(0.0521073 + 0.160370i) q^{46} +(4.67492 + 3.39653i) q^{47} +(-2.05557 + 6.32640i) q^{49} +(0.633189 - 1.94876i) q^{50} +(-2.67678 - 1.94479i) q^{52} +(-2.09317 - 6.44213i) q^{53} +(-3.31525 - 0.0954005i) q^{55} -0.240047 q^{56} +(13.9653 + 10.1464i) q^{58} +(-4.51758 + 3.28221i) q^{59} +(-0.296732 + 0.913248i) q^{61} +(3.28083 - 2.38366i) q^{62} +(-2.93627 - 9.03690i) q^{64} -1.50491 q^{65} +13.6559 q^{67} +(-3.34264 - 10.2876i) q^{68} +(-0.977943 + 0.710517i) q^{70} +(0.396714 - 1.22096i) q^{71} +(12.6426 - 9.18538i) q^{73} +(5.93455 + 4.31171i) q^{74} +14.9956 q^{76} +(1.54918 + 1.19511i) q^{77} +(-3.44622 - 10.6064i) q^{79} +(-2.88285 - 2.09451i) q^{80} +(-2.57911 + 7.93770i) q^{82} +(1.23982 - 3.81578i) q^{83} +(-3.98036 - 2.89190i) q^{85} +(3.07824 + 9.47385i) q^{86} +(0.453779 - 1.27097i) q^{88} -6.08177 q^{89} +(0.718247 + 0.521837i) q^{91} +(-0.146374 + 0.106347i) q^{92} +(-3.65890 + 11.2609i) q^{94} +(5.51798 - 4.00905i) q^{95} +(-2.07220 - 6.37757i) q^{97} -13.6302 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29}+ \cdots - 8 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 + 8 * q^10 - 4 * q^11 + 2 * q^13 + 22 * q^14 + 8 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 28 * q^22 - 8 * q^23 - 4 * q^25 - 6 * q^26 - 2 * q^28 + 26 * q^29 - 10 * q^31 - 56 * q^32 - 4 * q^34 + 4 * q^35 + 22 * q^37 + 30 * q^38 - 6 * q^40 + 6 * q^41 + 28 * q^43 - 68 * q^44 + 16 * q^46 + 20 * q^47 + 10 * q^49 + 2 * q^50 + 30 * q^52 - 14 * q^53 - 6 * q^55 - 68 * q^56 - 6 * q^58 + 16 * q^59 - 38 * q^61 + 20 * q^62 + 10 * q^64 - 12 * q^65 + 20 * q^67 + 48 * q^68 - 22 * q^70 + 54 * q^71 + 2 * q^73 - 28 * q^74 - 44 * q^76 - 34 * q^77 - 12 * q^79 + 22 * q^80 + 30 * q^82 + 28 * q^83 - 4 * q^85 - 74 * q^86 + 46 * q^88 - 76 * q^89 - 34 * q^91 + 8 * q^92 - 10 * q^94 + 4 * q^95 - 18 * q^97 - 8 * q^98

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