LMFDB - Embedded newform 495.2.n.g.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			91.4
Root			$-0.659965 + 2.03116i$ of defining polynomial
Character	$\chi$	$=$	495.91
Dual form			495.2.n.g.136.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.918793 - 0.667542i) q^{2} +(-0.219466 + 0.675446i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.26738 - 3.90059i) q^{7} +(0.951141 + 2.92731i) q^{8} +O(q^{10})$	\(q+(0.918793 - 0.667542i) q^{2} +(-0.219466 + 0.675446i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.26738 - 3.90059i) q^{7} +(0.951141 + 2.92731i) q^{8} -1.13569 q^{10} +(3.26188 + 0.600124i) q^{11} +(1.83960 - 1.33655i) q^{13} +(-1.43935 - 4.42987i) q^{14} +(1.67887 + 1.21977i) q^{16} +(4.06036 + 2.95002i) q^{17} +(-2.34171 - 7.20705i) q^{19} +(0.574568 - 0.417448i) q^{20} +(3.39760 - 1.62605i) q^{22} -1.97494 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.798012 - 2.45603i) q^{26} +(2.35649 + 1.71209i) q^{28} +(1.23649 - 3.80552i) q^{29} +(3.08632 - 2.24234i) q^{31} -3.79913 q^{32} +5.69990 q^{34} +(-3.31804 + 2.41070i) q^{35} +(-2.07996 + 6.40146i) q^{37} +(-6.96256 - 5.05859i) q^{38} +(0.951141 - 2.92731i) q^{40} +(1.24329 + 3.82644i) q^{41} +9.57903 q^{43} +(-1.12122 + 2.07152i) q^{44} +(-1.81456 + 1.31836i) q^{46} +(0.984753 + 3.03076i) q^{47} +(-7.94524 - 5.77255i) q^{49} +(0.918793 + 0.667542i) q^{50} +(0.499038 + 1.53588i) q^{52} +(-9.08454 + 6.60031i) q^{53} +(-2.28617 - 2.40279i) q^{55} +12.6237 q^{56} +(-1.40427 - 4.32189i) q^{58} +(-2.94731 + 9.07089i) q^{59} +(-2.92206 - 2.12300i) q^{61} +(1.33883 - 4.12050i) q^{62} +(-6.84835 + 4.97562i) q^{64} -2.27388 q^{65} -6.31504 q^{67} +(-2.88369 + 2.09512i) q^{68} +(-1.43935 + 4.42987i) q^{70} +(-9.94687 - 7.22682i) q^{71} +(-1.20217 + 3.69990i) q^{73} +(2.36219 + 7.27008i) q^{74} +5.38189 q^{76} +(6.47487 - 11.9627i) q^{77} +(-14.2183 + 10.3302i) q^{79} +(-0.641271 - 1.97363i) q^{80} +(3.69664 + 2.68577i) q^{82} +(-11.2029 - 8.13938i) q^{83} +(-1.55092 - 4.77324i) q^{85} +(8.80115 - 6.39441i) q^{86} +(1.34576 + 10.1193i) q^{88} +7.85399 q^{89} +(-2.88186 - 8.86946i) q^{91} +(0.433431 - 1.33396i) q^{92} +(2.92794 + 2.12728i) q^{94} +(-2.34171 + 7.20705i) q^{95} +(-4.18962 + 3.04394i) q^{97} -11.1535 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	0.918793	−	0.667542i	0.649685	−	0.472024i	−0.213479	−	0.976948i	$-0.568479\pi$
$2$	0.918793	−	0.667542i	0.649685	−	0.472024i	0.863164	+	0.504924i	$0.168479\pi$
$3$		0			0
$3$		0			0
$4$	−0.219466	+	0.675446i	−0.109733	+	0.337723i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	1.26738	−	3.90059i	0.479024	−	1.47428i	−0.361429	−	0.932400i	$-0.617711\pi$
$7$	1.26738	−	3.90059i	0.479024	−	1.47428i	0.840453	−	0.541885i	$-0.182289\pi$
$8$	0.951141	+	2.92731i	0.336279	+	1.03496i
$9$		0			0
$10$	−1.13569			−0.359137
$11$	3.26188	+	0.600124i	0.983493	+	0.180944i
$11$	3.26188	+	0.600124i	0.983493	+	0.180944i
$12$		0			0
$13$	1.83960	−	1.33655i	0.510215	−	0.370693i	−0.302690	−	0.953089i	$-0.597885\pi$
$13$	1.83960	−	1.33655i	0.510215	−	0.370693i	0.812905	+	0.582396i	$0.197885\pi$
$14$	−1.43935	−	4.42987i	−0.384683	−	1.18393i
$15$		0			0
$16$	1.67887	+	1.21977i	0.419717	+	0.304942i
$17$	4.06036	+	2.95002i	0.984782	+	0.715486i	0.958772	−	0.284176i	$-0.0917199\pi$
$17$	4.06036	+	2.95002i	0.984782	+	0.715486i	0.0260098	+	0.999662i	$0.491720\pi$
$18$		0			0
$19$	−2.34171	−	7.20705i	−0.537225	−	1.65341i	−0.738791	−	0.673935i	$-0.764603\pi$
$19$	−2.34171	−	7.20705i	−0.537225	−	1.65341i	0.201566	−	0.979475i	$-0.435397\pi$
$20$	0.574568	−	0.417448i	0.128477	−	0.0933443i
$21$		0			0
$22$	3.39760	−	1.62605i	0.724371	−	0.346676i
$23$	−1.97494			−0.411803			−0.205902	−	0.978573i	$-0.566013\pi$
$23$	−1.97494			−0.411803			−0.205902	+	0.978573i	$0.566013\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.798012	−	2.45603i	0.156503	−	0.481667i
$27$		0			0
$28$	2.35649	+	1.71209i	0.445335	+	0.323555i
$29$	1.23649	−	3.80552i	0.229610	−	0.706667i	−0.768181	−	0.640233i	$-0.778838\pi$
$29$	1.23649	−	3.80552i	0.229610	−	0.706667i	0.997791	−	0.0664339i	$-0.0211622\pi$
$30$		0			0
$31$	3.08632	−	2.24234i	0.554319	−	0.402737i	−0.275056	−	0.961428i	$-0.588696\pi$
$31$	3.08632	−	2.24234i	0.554319	−	0.402737i	0.829376	+	0.558692i	$0.188696\pi$
$32$	−3.79913			−0.671598
$33$		0			0
$34$	5.69990			0.977525
$35$	−3.31804	+	2.41070i	−0.560851	+	0.407482i
$36$		0			0
$37$	−2.07996	+	6.40146i	−0.341943	+	1.05239i	0.621256	+	0.783607i	$0.286623\pi$
$37$	−2.07996	+	6.40146i	−0.341943	+	1.05239i	−0.963200	+	0.268786i	$0.913377\pi$
$38$	−6.96256	−	5.05859i	−1.12948	−	0.820612i
$39$		0			0
$40$	0.951141	−	2.92731i	0.150389	−	0.462848i
$41$	1.24329	+	3.82644i	0.194169	+	0.597590i	0.999985	+	0.00542488i	$0.00172680\pi$
$41$	1.24329	+	3.82644i	0.194169	+	0.597590i	−0.805816	+	0.592165i	$0.798273\pi$
$42$		0			0
$43$	9.57903			1.46079			0.730394	−	0.683026i	$-0.239336\pi$
$43$	9.57903			1.46079			0.730394	+	0.683026i	$0.239336\pi$
$44$	−1.12122	+	2.07152i	−0.169030	+	0.312293i
$45$		0			0
$46$	−1.81456	+	1.31836i	−0.267542	+	0.194381i
$47$	0.984753	+	3.03076i	0.143641	+	0.442081i	0.996834	−	0.0795143i	$-0.0253369\pi$
$47$	0.984753	+	3.03076i	0.143641	+	0.442081i	−0.853193	+	0.521596i	$0.825337\pi$
$48$		0			0
$49$	−7.94524	−	5.77255i	−1.13503	−	0.824651i
$50$	0.918793	+	0.667542i	0.129937	+	0.0944048i
$51$		0			0
$52$	0.499038	+	1.53588i	0.0692041	+	0.212988i
$53$	−9.08454	+	6.60031i	−1.24786	+	0.906622i	−0.998096	−	0.0616854i	$-0.980352\pi$
$53$	−9.08454	+	6.60031i	−1.24786	+	0.906622i	−0.249762	+	0.968307i	$0.580352\pi$
$54$		0			0
$55$	−2.28617	−	2.40279i	−0.308267	−	0.323993i
$56$	12.6237			1.68691
$57$		0			0
$58$	−1.40427	−	4.32189i	−0.184389	−	0.567492i
$59$	−2.94731	+	9.07089i	−0.383707	+	1.18093i	0.553707	+	0.832712i	$0.313213\pi$
$59$	−2.94731	+	9.07089i	−0.383707	+	1.18093i	−0.937414	+	0.348217i	$0.886787\pi$
$60$		0			0
$61$	−2.92206	−	2.12300i	−0.374131	−	0.271822i	0.384791	−	0.923004i	$-0.374274\pi$
$61$	−2.92206	−	2.12300i	−0.374131	−	0.271822i	−0.758922	+	0.651182i	$0.774274\pi$
$62$	1.33883	−	4.12050i	0.170032	−	0.523304i
$63$		0			0
$64$	−6.84835	+	4.97562i	−0.856044	+	0.621953i
$65$	−2.27388			−0.282040
$66$		0			0
$67$	−6.31504			−0.771505			−0.385752	−	0.922602i	$-0.626058\pi$
$67$	−6.31504			−0.771505			−0.385752	+	0.922602i	$0.626058\pi$
$68$	−2.88369	+	2.09512i	−0.349699	+	0.254071i
$69$		0			0
$70$	−1.43935	+	4.42987i	−0.172035	+	0.529470i
$71$	−9.94687	−	7.22682i	−1.18048	−	0.857666i	−0.188251	−	0.982121i	$-0.560282\pi$
$71$	−9.94687	−	7.22682i	−1.18048	−	0.857666i	−0.992225	+	0.124455i	$0.960282\pi$
$72$		0			0
$73$	−1.20217	+	3.69990i	−0.140703	+	0.433040i	−0.996433	−	0.0843822i	$-0.973108\pi$
$73$	−1.20217	+	3.69990i	−0.140703	+	0.433040i	0.855730	+	0.517422i	$0.173108\pi$
$74$	2.36219	+	7.27008i	0.274599	+	0.845130i
$75$		0			0
$76$	5.38189			0.617345
$77$	6.47487	−	11.9627i	0.737880	−	1.36327i
$78$		0			0
$79$	−14.2183	+	10.3302i	−1.59968	+	1.16224i	−0.711557	+	0.702629i	$0.752009\pi$
$79$	−14.2183	+	10.3302i	−1.59968	+	1.16224i	−0.888123	+	0.459606i	$0.847991\pi$
$80$	−0.641271	−	1.97363i	−0.0716963	−	0.220658i
$81$		0			0
$82$	3.69664	+	2.68577i	0.408225	+	0.296593i
$83$	−11.2029	−	8.13938i	−1.22968	−	0.893413i	−0.232811	−	0.972522i	$-0.574792\pi$
$83$	−11.2029	−	8.13938i	−1.22968	−	0.893413i	−0.996866	+	0.0791092i	$0.974792\pi$
$84$		0			0
$85$	−1.55092	−	4.77324i	−0.168221	−	0.517731i
$86$	8.80115	−	6.39441i	0.949053	−	0.689527i
$87$		0			0
$88$	1.34576	+	10.1193i	0.143458	+	1.07872i
$89$	7.85399			0.832522			0.416261	−	0.909245i	$-0.363340\pi$
$89$	7.85399			0.832522			0.416261	+	0.909245i	$0.363340\pi$
$90$		0			0
$91$	−2.88186	−	8.86946i	−0.302101	−	0.929772i
$92$	0.433431	−	1.33396i	0.0451883	−	0.139075i
$93$		0			0
$94$	2.92794	+	2.12728i	0.301994	+	0.219412i
$95$	−2.34171	+	7.20705i	−0.240254	+	0.739427i
$96$		0			0
$97$	−4.18962	+	3.04394i	−0.425392	+	0.309065i	−0.779804	−	0.626024i	$-0.784681\pi$
$97$	−4.18962	+	3.04394i	−0.425392	+	0.309065i	0.354412	+	0.935089i	$0.384681\pi$
$98$	−11.1535			−1.12667
$99$		0			0
$100$	−0.710206			−0.0710206
$101$	3.23012	−	2.34682i	0.321409	−	0.233518i	−0.415367	−	0.909654i	$-0.636347\pi$
$101$	3.23012	−	2.34682i	0.321409	−	0.233518i	0.736777	+	0.676136i	$0.236347\pi$
$102$		0			0
$103$	−0.290775	+	0.894912i	−0.0286509	+	0.0881783i	−0.964359	−	0.264596i	$-0.914762\pi$
$103$	−0.290775	+	0.894912i	−0.0286509	+	0.0881783i	0.935709	+	0.352774i	$0.114762\pi$
$104$	5.66222	+	4.11385i	0.555227	+	0.403396i
$105$		0			0
$106$	−3.94083	+	12.1286i	−0.382768	+	1.17804i
$107$	4.48985	+	13.8183i	0.434050	+	1.33587i	0.894057	+	0.447954i	$0.147847\pi$
$107$	4.48985	+	13.8183i	0.434050	+	1.33587i	−0.460006	+	0.887916i	$0.652153\pi$
$108$		0			0
$109$	7.70193			0.737711			0.368855	−	0.929487i	$-0.379750\pi$
$109$	7.70193			0.737711			0.368855	+	0.929487i	$0.379750\pi$
$110$	−3.70449	−	0.681555i	−0.353209	−	0.0649837i
$111$		0			0
$112$	6.88559	−	5.00267i	0.650627	−	0.472708i
$113$	−0.208742	−	0.642441i	−0.0196368	−	0.0604357i	0.940758	−	0.339079i	$-0.110115\pi$
$113$	−0.208742	−	0.642441i	−0.0196368	−	0.0604357i	−0.960395	+	0.278643i	$0.910115\pi$
$114$		0			0
$115$	1.59776	+	1.16084i	0.148992	+	0.108249i
$116$	2.29905	+	1.67036i	0.213462	+	0.155089i
$117$		0			0
$118$	3.34723	+	10.3017i	0.308138	+	0.948351i
$119$	16.6529	−	12.0990i	1.52656	−	1.10911i
$120$		0			0
$121$	10.2797	+	3.91506i	0.934518	+	0.355915i
$122$	−4.10196			−0.371374
$123$		0			0
$124$	0.837240	+	2.57676i	0.0751863	+	0.231400i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	3.56862	+	2.59275i	0.316664	+	0.230070i	0.734750	−	0.678337i	$-0.237299\pi$
$127$	3.56862	+	2.59275i	0.316664	+	0.230070i	−0.418087	+	0.908407i	$0.637299\pi$
$128$	−0.622793	+	1.91676i	−0.0550476	+	0.169419i
$129$		0			0
$130$	−2.08922	+	1.51791i	−0.183237	+	0.133129i
$131$	21.4004			1.86976			0.934882	−	0.354959i	$-0.115505\pi$
$131$	21.4004			1.86976			0.934882	+	0.354959i	$0.115505\pi$
$132$		0			0
$133$	−31.0796			−2.69494
$134$	−5.80222	+	4.21556i	−0.501235	+	0.364169i
$135$		0			0
$136$	−4.77366	+	14.6918i	−0.409338	+	1.25981i
$137$	3.09149	+	2.24610i	0.264124	+	0.191897i	0.711963	−	0.702217i	$-0.247806\pi$
$137$	3.09149	+	2.24610i	0.264124	+	0.191897i	−0.447839	+	0.894114i	$0.647806\pi$
$138$		0			0
$139$	1.94595	−	5.98900i	0.165053	−	0.507981i	−0.833987	−	0.551784i	$-0.813947\pi$
$139$	1.94595	−	5.98900i	0.165053	−	0.507981i	0.999040	+	0.0438031i	$0.0139474\pi$
$140$	−0.900100	−	2.77022i	−0.0760723	−	0.234126i
$141$		0			0
$142$	−13.9633			−1.17178
$143$	6.80266	−	3.25568i	0.568867	−	0.272253i
$144$		0			0
$145$	−3.23717	+	2.35194i	−0.268832	+	0.195318i
$146$	1.36529	+	4.20194i	0.112992	+	0.347755i
$147$		0			0
$148$	−3.86736	−	2.80980i	−0.317895	−	0.230964i
$149$	−18.1995	−	13.2227i	−1.49096	−	1.08325i	−0.973812	−	0.227356i	$-0.926992\pi$
$149$	−18.1995	−	13.2227i	−1.49096	−	1.08325i	−0.517153	−	0.855893i	$-0.673008\pi$
$150$		0			0
$151$	−0.926122	−	2.85031i	−0.0753667	−	0.231955i	0.906275	−	0.422688i	$-0.138913\pi$
$151$	−0.926122	−	2.85031i	−0.0753667	−	0.231955i	−0.981642	+	0.190733i	$0.938913\pi$
$152$	18.8700	−	13.7098i	1.53056	−	1.11201i
$153$		0			0
$154$	−2.03652	−	15.3135i	−0.164107	−	1.23399i
$155$	−3.81490			−0.306420
$156$		0			0
$157$	−3.14886	−	9.69118i	−0.251306	−	0.773441i	−0.994535	−	0.104403i	$-0.966707\pi$
$157$	−3.14886	−	9.69118i	−0.251306	−	0.773441i	0.743229	−	0.669037i	$-0.233293\pi$
$158$	−6.16782	+	18.9826i	−0.490685	+	1.51017i
$159$		0			0
$160$	3.07356	+	2.23307i	0.242986	+	0.176540i
$161$	−2.50299	+	7.70343i	−0.197264	+	0.607115i
$162$		0			0
$163$	16.0213	−	11.6401i	1.25488	−	0.911726i	0.256389	−	0.966574i	$-0.417467\pi$
$163$	16.0213	−	11.6401i	1.25488	−	0.911726i	0.998495	+	0.0548473i	$0.0174672\pi$
$164$	−2.85741			−0.223127
$165$		0			0
$166$	−15.7265			−1.22061
$167$	−4.01870	+	2.91976i	−0.310976	+	0.225937i	−0.732315	−	0.680966i	$-0.761560\pi$
$167$	−4.01870	+	2.91976i	−0.310976	+	0.225937i	0.421339	+	0.906903i	$0.361560\pi$
$168$		0			0
$169$	−2.41944	+	7.44628i	−0.186111	+	0.572791i
$170$	−4.61132	−	3.35032i	−0.353672	−	0.256958i
$171$		0			0
$172$	−2.10227	+	6.47012i	−0.160296	+	0.493342i
$173$	5.02182	+	15.4556i	0.381802	+	1.17507i	0.938774	+	0.344534i	$0.111963\pi$
$173$	5.02182	+	15.4556i	0.381802	+	1.17507i	−0.556972	+	0.830531i	$0.688037\pi$
$174$		0			0
$175$	4.10132			0.310031
$176$	4.74425	+	4.98627i	0.357612	+	0.375854i
$177$		0			0
$178$	7.21620	−	5.24287i	0.540877	−	0.392970i
$179$	0.984058	+	3.02862i	0.0735520	+	0.226370i	0.981073	−	0.193636i	$-0.0620281\pi$
$179$	0.984058	+	3.02862i	0.0735520	+	0.226370i	−0.907521	+	0.420006i	$0.862028\pi$
$180$		0			0
$181$	−1.21432	−	0.882258i	−0.0902600	−	0.0655778i	0.541740	−	0.840546i	$-0.317766\pi$
$181$	−1.21432	−	0.882258i	−0.0902600	−	0.0655778i	−0.632000	+	0.774968i	$0.717766\pi$
$182$	−8.56858	−	6.22544i	−0.635145	−	0.461460i
$183$		0			0
$184$	−1.87844	−	5.78126i	−0.138481	−	0.426200i
$185$	5.44541	−	3.95632i	0.400354	−	0.290874i
$186$		0			0
$187$	11.4740	+	12.0593i	0.839064	+	0.881866i
$188$	−2.26323			−0.165063
$189$		0			0
$190$	2.65946	+	8.18498i	0.192938	+	0.593801i
$191$	3.22700	−	9.93168i	0.233497	−	0.718631i	−0.763820	−	0.645430i	$-0.776678\pi$
$191$	3.22700	−	9.93168i	0.233497	−	0.718631i	0.997317	−	0.0732014i	$-0.0233216\pi$
$192$		0			0
$193$	−4.87635	−	3.54288i	−0.351008	−	0.255022i	0.398284	−	0.917262i	$-0.369606\pi$
$193$	−4.87635	−	3.54288i	−0.351008	−	0.255022i	−0.749292	+	0.662240i	$0.769606\pi$
$194$	−1.81744	+	5.59350i	−0.130485	+	0.401590i
$195$		0			0
$196$	5.64275	−	4.09970i	0.403054	−	0.292836i
$197$	−9.07040			−0.646239			−0.323120	−	0.946358i	$-0.604732\pi$
$197$	−9.07040			−0.646239			−0.323120	+	0.946358i	$0.604732\pi$
$198$		0			0
$199$	17.3143			1.22738			0.613689	−	0.789548i	$-0.289685\pi$
$199$	17.3143			1.22738			0.613689	+	0.789548i	$0.289685\pi$
$200$	−2.49012	+	1.80918i	−0.176078	+	0.127928i
$201$		0			0
$202$	1.40121	−	4.31249i	0.0985890	−	0.303426i
$203$	−13.2767	−	9.64606i	−0.931839	−	0.677021i
$204$		0			0
$205$	1.24329	−	3.82644i	0.0868350	−	0.267251i
$206$	0.330230	+	1.01634i	0.0230082	+	0.0708120i
$207$		0			0
$208$	4.71874			0.327186
$209$	−3.31326	−	24.9138i	−0.229183	−	1.72333i
$210$		0			0
$211$	12.7140	−	9.23725i	0.875267	−	0.635918i	−0.0567283	−	0.998390i	$-0.518067\pi$
$211$	12.7140	−	9.23725i	0.875267	−	0.635918i	0.931995	+	0.362471i	$0.118067\pi$
$212$	−2.46440	−	7.58466i	−0.169256	−	0.520916i
$213$		0			0
$214$	13.3496	+	9.69903i	0.912558	+	0.663012i
$215$	−7.74960	−	5.63041i	−0.528518	−	0.383991i
$216$		0			0
$217$	−4.83492	−	14.8804i	−0.328216	−	1.01015i
$218$	7.07648	−	5.14136i	0.479280	−	0.348217i
$219$		0			0
$220$	2.12469	−	1.01685i	0.143247	−	0.0685563i
$221$	11.4123			0.767676
$222$		0			0
$223$	0.334918	+	1.03077i	0.0224278	+	0.0690256i	0.961644	−	0.274301i	$-0.0884464\pi$
$223$	0.334918	+	1.03077i	0.0224278	+	0.0690256i	−0.939216	+	0.343326i	$0.888446\pi$
$224$	−4.81494	+	14.8189i	−0.321712	+	0.990126i
$225$		0			0
$226$	−0.620647	−	0.450926i	−0.0412848	−	0.0299952i
$227$	−0.615474	+	1.89423i	−0.0408504	+	0.125725i	−0.969402	−	0.245479i	$-0.921055\pi$
$227$	−0.615474	+	1.89423i	−0.0408504	+	0.125725i	0.928552	+	0.371204i	$0.121055\pi$
$228$		0			0
$229$	−6.58519	+	4.78442i	−0.435161	+	0.316163i	−0.783709	−	0.621128i	$-0.786675\pi$
$229$	−6.58519	+	4.78442i	−0.435161	+	0.316163i	0.348548	+	0.937291i	$0.386675\pi$
$230$	2.24292			0.147894
$231$		0			0
$232$	12.3160			0.808585
$233$	−19.7639	+	14.3593i	−1.29478	+	0.940712i	−0.999890	−	0.0148197i	$-0.995283\pi$
$233$	−19.7639	+	14.3593i	−1.29478	+	0.940712i	−0.294889	+	0.955532i	$0.595283\pi$
$234$		0			0
$235$	0.984753	−	3.03076i	0.0642382	−	0.197705i
$236$	−5.48006	−	3.98150i	−0.356721	−	0.259173i
$237$		0			0
$238$	7.22393	−	22.2330i	0.468258	−	1.44115i
$239$	−0.0219354	−	0.0675103i	−0.00141888	−	0.00436688i	0.950345	−	0.311200i	$-0.100731\pi$
$239$	−0.0219354	−	0.0675103i	−0.00141888	−	0.00436688i	−0.951763	+	0.306833i	$0.900731\pi$
$240$		0			0
$241$	−12.6653			−0.815842			−0.407921	−	0.913017i	$-0.633746\pi$
$241$	−12.6653			−0.815842			−0.407921	+	0.913017i	$0.633746\pi$
$242$	12.0584	−	3.26501i	0.775143	−	0.209883i
$243$		0			0
$244$	2.07526	−	1.50777i	0.132855	−	0.0965249i
$245$	3.03481	+	9.34019i	0.193887	+	0.596723i
$246$		0			0
$247$	−13.9404	−	10.1283i	−0.887007	−	0.644448i
$248$	9.49956	+	6.90183i	0.603223	+	0.438267i
$249$		0			0
$250$	−0.350948	−	1.08011i	−0.0221959	−	0.0683119i
$251$	6.19469	−	4.50070i	0.391005	−	0.284082i	−0.374862	−	0.927081i	$-0.622310\pi$
$251$	6.19469	−	4.50070i	0.391005	−	0.284082i	0.765867	+	0.642999i	$0.222310\pi$
$252$		0			0
$253$	−6.44201	−	1.18521i	−0.405006	−	0.0745133i
$254$	5.00959			0.314330
$255$		0			0
$256$	−4.52438	−	13.9246i	−0.282774	−	0.870288i
$257$	−7.14141	+	21.9790i	−0.445469	+	1.37101i	0.436499	+	0.899705i	$0.356218\pi$
$257$	−7.14141	+	21.9790i	−0.445469	+	1.37101i	−0.881968	+	0.471308i	$0.843782\pi$
$258$		0			0
$259$	22.3334	+	16.2261i	1.38773	+	1.00824i
$260$	0.499038	−	1.53588i	0.0309490	−	0.0952513i
$261$		0			0
$262$	19.6626	−	14.2857i	1.21476	−	0.882573i
$263$	−9.67819			−0.596783			−0.298391	−	0.954444i	$-0.596450\pi$
$263$	−9.67819			−0.596783			−0.298391	+	0.954444i	$0.596450\pi$
$264$		0			0
$265$	11.2291			0.689799
$266$	−28.5557	+	20.7469i	−1.75086	+	1.27208i
$267$		0			0
$268$	1.38593	−	4.26547i	0.0846594	−	0.260555i
$269$	1.47532	+	1.07188i	0.0899516	+	0.0653536i	0.631852	−	0.775089i	$-0.282295\pi$
$269$	1.47532	+	1.07188i	0.0899516	+	0.0653536i	−0.541900	+	0.840443i	$0.682295\pi$
$270$		0			0
$271$	−4.57141	+	14.0694i	−0.277693	+	0.854653i	0.710801	+	0.703394i	$0.248333\pi$
$271$	−4.57141	+	14.0694i	−0.277693	+	0.854653i	−0.988494	+	0.151259i	$0.951667\pi$
$272$	3.21846	+	9.90541i	0.195148	+	0.600604i
$273$		0			0
$274$	4.33981			0.262178
$275$	0.437224	+	3.28768i	0.0263656	+	0.198255i
$276$		0			0
$277$	−13.7372	+	9.98067i	−0.825389	+	0.599680i	−0.918251	−	0.395999i	$-0.870398\pi$
$277$	−13.7372	+	9.98067i	−0.825389	+	0.599680i	0.0928620	+	0.995679i	$0.470398\pi$
$278$	−2.20999	−	6.80166i	−0.132547	−	0.407936i
$279$		0			0
$280$	−10.2128	−	7.42002i	−0.610331	−	0.443431i
$281$	−3.72271	−	2.70471i	−0.222078	−	0.161349i	0.471183	−	0.882035i	$-0.343827\pi$
$281$	−3.72271	−	2.70471i	−0.222078	−	0.161349i	−0.693262	+	0.720686i	$0.743827\pi$
$282$		0			0
$283$	4.26038	+	13.1121i	0.253253	+	0.779434i	0.994169	+	0.107835i	$0.0343919\pi$
$283$	4.26038	+	13.1121i	0.253253	+	0.779434i	−0.740915	+	0.671598i	$0.765608\pi$
$284$	7.06432	−	5.13253i	0.419190	−	0.304560i
$285$		0			0
$286$	4.07694	−	7.53236i	0.241075	−	0.445398i
$287$	16.5011			0.974030
$288$		0			0
$289$	2.53059	+	7.78836i	0.148858	+	0.458139i
$290$	−1.40427	+	4.32189i	−0.0824614	+	0.253790i
$291$		0			0
$292$	−2.23524	−	1.62400i	−0.130808	−	0.0950374i
$293$	9.71070	−	29.8864i	0.567305	−	1.74598i	−0.0936970	−	0.995601i	$-0.529869\pi$
$293$	9.71070	−	29.8864i	0.567305	−	1.74598i	0.661002	−	0.750384i	$-0.270131\pi$
$294$		0			0
$295$	7.71616	−	5.60612i	0.449252	−	0.326401i
$296$	−20.7174			−1.20417
$297$		0			0
$298$	−25.5484			−1.47998
$299$	−3.63311	+	2.63961i	−0.210108	+	0.152652i
$300$		0			0
$301$	12.1403	−	37.3639i	0.699753	−	2.15362i
$302$	−2.75362	−	2.00062i	−0.158453	−	0.115123i
$303$		0			0
$304$	4.85951	−	14.9560i	0.278712	−	0.857787i
$305$	1.11613	+	3.43509i	0.0639093	+	0.196692i
$306$		0			0
$307$	20.1733			1.15135			0.575676	−	0.817678i	$-0.304739\pi$
$307$	20.1733			1.15135			0.575676	+	0.817678i	$0.304739\pi$
$308$	6.65912	+	6.99882i	0.379439	+	0.398795i
$309$		0			0
$310$	−3.50511	+	2.54661i	−0.199077	+	0.144638i
$311$	−5.74185	−	17.6716i	−0.325590	−	1.00206i	−0.971173	−	0.238374i	$-0.923386\pi$
$311$	−5.74185	−	17.6716i	−0.325590	−	1.00206i	0.645583	−	0.763690i	$-0.276614\pi$
$312$		0			0
$313$	−9.22977	−	6.70582i	−0.521698	−	0.379035i	0.295545	−	0.955329i	$-0.404499\pi$
$313$	−9.22977	−	6.70582i	−0.521698	−	0.379035i	−0.817243	+	0.576293i	$0.804499\pi$
$314$	−9.36242	−	6.80220i	−0.528352	−	0.383870i
$315$		0			0
$316$	−3.85705	−	11.8708i	−0.216976	−	0.667784i
$317$	−20.5984	+	14.9656i	−1.15692	+	0.840554i	−0.989386	−	0.145312i	$-0.953581\pi$
$317$	−20.5984	+	14.9656i	−1.15692	+	0.840554i	−0.167537	+	0.985866i	$0.553581\pi$
$318$		0			0
$319$	6.31705	−	11.6711i	0.353687	−	0.653456i
$320$	8.46503			0.473210
$321$		0			0
$322$	2.84263	+	8.74871i	0.158414	+	0.487547i
$323$	11.7528	−	36.1713i	0.653942	−	2.01263i
$324$		0			0
$325$	1.83960	+	1.33655i	0.102043	+	0.0741385i
$326$	6.94996	−	21.3898i	0.384923	−	1.18467i
$327$		0			0
$328$	−10.0187	+	7.27898i	−0.553187	+	0.401914i
$329$	13.0698			0.720561
$330$		0			0
$331$	31.1055			1.70971			0.854857	−	0.518864i	$-0.173645\pi$
$331$	31.1055			1.70971			0.854857	+	0.518864i	$0.173645\pi$
$332$	7.95636	−	5.78063i	0.436662	−	0.317253i
$333$		0			0
$334$	−1.74329	+	5.36530i	−0.0953888	+	0.293576i
$335$	5.10897	+	3.71189i	0.279133	+	0.202802i
$336$		0			0
$337$	−8.24920	+	25.3884i	−0.449363	+	1.38300i	0.428265	+	0.903653i	$0.359125\pi$
$337$	−8.24920	+	25.3884i	−0.449363	+	1.38300i	−0.877628	+	0.479343i	$0.840875\pi$
$338$	2.74774	+	8.45668i	0.149457	+	0.459983i
$339$		0			0
$340$	3.56444			0.193309
$341$	11.4129	−	5.46208i	0.618042	−	0.295788i
$342$		0			0
$343$	−9.35971	+	6.80023i	−0.505377	+	0.367178i
$344$	9.11101	+	28.0408i	0.491233	+	1.51186i
$345$		0			0
$346$	14.9313	+	10.8482i	0.802710	+	0.583203i
$347$	−5.49526	−	3.99254i	−0.295001	−	0.214331i	0.430433	−	0.902623i	$-0.358361\pi$
$347$	−5.49526	−	3.99254i	−0.295001	−	0.214331i	−0.725434	+	0.688292i	$0.758361\pi$
$348$		0			0
$349$	−2.42463	−	7.46224i	−0.129787	−	0.399445i	0.864955	−	0.501849i	$-0.167347\pi$
$349$	−2.42463	−	7.46224i	−0.129787	−	0.399445i	−0.994743	+	0.102404i	$0.967347\pi$
$350$	3.76827	−	2.73781i	0.201422	−	0.146342i
$351$		0			0
$352$	−12.3923	−	2.27995i	−0.660512	−	0.121522i
$353$	18.4136			0.980056			0.490028	−	0.871707i	$-0.336986\pi$
$353$	18.4136			0.980056			0.490028	+	0.871707i	$0.336986\pi$
$354$		0			0
$355$	3.79937	+	11.6932i	0.201649	+	0.620613i
$356$	−1.72368	+	5.30495i	−0.0913549	+	0.281162i
$357$		0			0
$358$	2.92588	+	2.12578i	0.154638	+	0.112351i
$359$	−7.85272	+	24.1682i	−0.414451	+	1.27555i	0.498290	+	0.867010i	$0.333961\pi$
$359$	−7.85272	+	24.1682i	−0.414451	+	1.27555i	−0.912741	+	0.408538i	$0.866039\pi$
$360$		0			0
$361$	−31.0866	+	22.5857i	−1.63614	+	1.18872i
$362$	−1.70466			−0.0895949
$363$		0			0
$364$	6.62331			0.347156
$365$	3.14732	−	2.28666i	0.164738	−	0.119689i
$366$		0			0
$367$	−1.07629	+	3.31247i	−0.0561817	+	0.172909i	−0.975210	−	0.221283i	$-0.928976\pi$
$367$	−1.07629	+	3.31247i	−0.0561817	+	0.172909i	0.919028	+	0.394192i	$0.128976\pi$
$368$	−3.31566	−	2.40897i	−0.172841	−	0.125576i
$369$		0			0
$370$	2.36219	−	7.27008i	0.122805	−	0.377954i
$371$	14.2315	+	43.8002i	0.738865	+	2.27399i
$372$		0			0
$373$	12.8348			0.664561			0.332281	−	0.943181i	$-0.392182\pi$
$373$	12.8348			0.664561			0.332281	+	0.943181i	$0.392182\pi$
$374$	18.5924	+	3.42064i	0.961389	+	0.176877i
$375$		0			0
$376$	−7.93533	+	5.76535i	−0.409233	+	0.297325i
$377$	−2.81162	−	8.65328i	−0.144806	−	0.445666i
$378$		0			0
$379$	19.4680	+	14.1444i	1.00001	+	0.726546i	0.962089	−	0.272734i	$-0.0879280\pi$
$379$	19.4680	+	14.1444i	1.00001	+	0.726546i	0.0379161	+	0.999281i	$0.487928\pi$
$380$	−4.35404	−	3.16340i	−0.223358	−	0.162279i
$381$		0			0
$382$	−3.66487	−	11.2793i	−0.187511	−	0.577100i
$383$	−2.56959	+	1.86691i	−0.131300	+	0.0953949i	−0.651497	−	0.758651i	$-0.725859\pi$
$383$	−2.56959	+	1.86691i	−0.131300	+	0.0953949i	0.520197	+	0.854046i	$0.325859\pi$
$384$		0			0
$385$	−12.2698	+	5.87217i	−0.625325	+	0.299273i
$386$	−6.84538			−0.348421
$387$		0			0
$388$	−1.13654	−	3.49790i	−0.0576989	−	0.177579i
$389$	4.60437	−	14.1708i	0.233451	−	0.718488i	−0.763872	−	0.645368i	$-0.776704\pi$
$389$	4.60437	−	14.1708i	0.233451	−	0.718488i	0.997323	−	0.0731204i	$-0.0232958\pi$
$390$		0			0
$391$	−8.01896	−	5.82612i	−0.405536	−	0.294639i
$392$	9.34102	−	28.7487i	0.471793	−	1.45203i
$393$		0			0
$394$	−8.33382	+	6.05488i	−0.419852	+	0.305040i
$395$	17.5747			0.884281
$396$		0			0
$397$	10.8837			0.546237			0.273119	−	0.961980i	$-0.411945\pi$
$397$	10.8837			0.546237			0.273119	+	0.961980i	$0.411945\pi$
$398$	15.9083	−	11.5580i	0.797409	−	0.579351i
$399$		0			0
$400$	−0.641271	+	1.97363i	−0.0320635	+	0.0986815i
$401$	−26.9279	−	19.5643i	−1.34472	−	0.976993i	−0.999256	−	0.0385596i	$-0.987723\pi$
$401$	−26.9279	−	19.5643i	−1.34472	−	0.976993i	−0.345459	−	0.938434i	$-0.612277\pi$
$402$		0			0
$403$	2.68060	−	8.25005i	0.133530	−	0.410964i
$404$	0.876250	+	2.69682i	0.0435951	+	0.134172i
$405$		0			0
$406$	−18.6377			−0.924972
$407$	−10.6262	+	19.6326i	−0.526723	+	0.973150i
$408$		0			0
$409$	−2.24659	+	1.63224i	−0.111087	+	0.0807092i	−0.641942	−	0.766753i	$-0.721871\pi$
$409$	−2.24659	+	1.63224i	−0.111087	+	0.0807092i	0.530855	+	0.847463i	$0.321871\pi$
$410$	−1.41199	−	4.34566i	−0.0697332	−	0.214617i
$411$		0			0
$412$	−0.540650	−	0.392805i	−0.0266359	−	0.0193521i
$413$	31.6465	+	22.9925i	1.55722	+	1.13139i
$414$		0			0
$415$	4.27912	+	13.1698i	0.210054	+	0.646480i
$416$	−6.98890	+	5.07773i	−0.342659	+	0.248956i
$417$		0			0
$418$	−19.6752	−	20.6789i	−0.962347	−	1.01144i
$419$	−29.5565			−1.44393			−0.721965	−	0.691930i	$-0.756761\pi$
$419$	−29.5565			−1.44393			−0.721965	+	0.691930i	$0.756761\pi$
$420$		0			0
$421$	0.0902032	+	0.277617i	0.00439623	+	0.0135302i	0.953231	−	0.302244i	$-0.0977358\pi$
$421$	0.0902032	+	0.277617i	0.00439623	+	0.0135302i	−0.948834	+	0.315774i	$0.897736\pi$
$422$	5.51527	−	16.9742i	0.268479	−	0.826293i
$423$		0			0
$424$	−27.9618	−	20.3155i	−1.35795	−	0.986606i
$425$	−1.55092	+	4.77324i	−0.0752307	+	0.231536i
$426$		0			0
$427$	−11.9843	+	8.70711i	−0.579961	+	0.421367i
$428$	−10.3189			−0.498783
$429$		0			0
$430$	−10.8788			−0.524623
$431$	3.63718	−	2.64256i	0.175197	−	0.127288i	−0.496731	−	0.867904i	$-0.665466\pi$
$431$	3.63718	−	2.64256i	0.175197	−	0.127288i	0.671928	+	0.740617i	$0.265466\pi$
$432$		0			0
$433$	−2.02969	+	6.24675i	−0.0975408	+	0.300200i	−0.987908	−	0.155044i	$-0.950448\pi$
$433$	−2.02969	+	6.24675i	−0.0975408	+	0.300200i	0.890367	+	0.455244i	$0.150448\pi$
$434$	−14.3756	−	10.4445i	−0.690050	−	0.501350i
$435$		0			0
$436$	−1.69031	+	5.20223i	−0.0809511	+	0.249142i
$437$	4.62473	+	14.2335i	0.221231	+	0.680879i
$438$		0			0
$439$	−26.7142			−1.27500			−0.637500	−	0.770451i	$-0.720031\pi$
$439$	−26.7142			−1.27500			−0.637500	+	0.770451i	$0.720031\pi$
$440$	4.85925	−	8.97773i	0.231656	−	0.427996i
$441$		0			0
$442$	10.4856	−	7.61821i	0.498747	−	0.362361i
$443$	−7.15900	−	22.0331i	−0.340135	−	1.04683i	−0.964137	−	0.265404i	$-0.914495\pi$
$443$	−7.15900	−	22.0331i	−0.340135	−	1.04683i	0.624003	−	0.781422i	$-0.285505\pi$
$444$		0			0
$445$	−6.35401	−	4.61646i	−0.301209	−	0.218841i
$446$	0.995804	+	0.723494i	0.0471527	+	0.0342584i
$447$		0			0
$448$	10.7284	+	33.0186i	0.506869	+	1.55998i
$449$	23.5094	−	17.0806i	1.10948	−	0.806084i	0.126898	−	0.991916i	$-0.459498\pi$
$449$	23.5094	−	17.0806i	1.10948	−	0.806084i	0.982582	+	0.185832i	$0.0594980\pi$
$450$		0			0
$451$	1.75911	+	13.2275i	0.0828334	+	0.622860i
$452$	0.479745			0.0225653
$453$		0			0
$454$	0.698988	+	2.15126i	0.0328051	+	0.100964i
$455$	−2.88186	+	8.86946i	−0.135104	+	0.415807i
$456$		0			0
$457$	−6.17070	−	4.48328i	−0.288653	−	0.209719i	0.434030	−	0.900899i	$-0.357091\pi$
$457$	−6.17070	−	4.48328i	−0.288653	−	0.209719i	−0.722683	+	0.691180i	$0.757091\pi$
$458$	−2.85662	+	8.79178i	−0.133481	+	0.410813i
$459$		0			0
$460$	−1.13474	+	0.824435i	−0.0529074	+	0.0384395i
$461$	−34.0138			−1.58418			−0.792091	−	0.610404i	$-0.791007\pi$
$461$	−34.0138			−1.58418			−0.792091	+	0.610404i	$0.791007\pi$
$462$		0			0
$463$	15.7564			0.732263			0.366131	−	0.930563i	$-0.380682\pi$
$463$	15.7564			0.732263			0.366131	+	0.930563i	$0.380682\pi$
$464$	6.71776	−	4.88074i	0.311864	−	0.226582i
$465$		0			0
$466$	−8.57351	+	26.3865i	−0.397160	+	1.22233i
$467$	−8.21219	−	5.96651i	−0.380015	−	0.276097i	0.381337	−	0.924436i	$-0.375464\pi$
$467$	−8.21219	−	5.96651i	−0.380015	−	0.276097i	−0.761352	+	0.648339i	$0.775464\pi$
$468$		0			0
$469$	−8.00354	+	24.6324i	−0.369569	+	1.13742i
$470$	−1.11838	−	3.44200i	−0.0515868	−	0.158768i
$471$		0			0
$472$	−29.3566			−1.35125
$473$	31.2456	+	5.74860i	1.43668	+	0.264321i
$474$		0			0
$475$	6.13068	−	4.45420i	0.281295	−	0.204373i
$476$	4.51749	+	13.9034i	0.207059	+	0.637262i
$477$		0			0
$478$	−0.0652201	−	0.0473852i	−0.00298310	−	0.00216735i
$479$	−3.27098	−	2.37650i	−0.149455	−	0.108585i	0.510545	−	0.859851i	$-0.329444\pi$
$479$	−3.27098	−	2.37650i	−0.149455	−	0.108585i	−0.660000	+	0.751266i	$0.729444\pi$
$480$		0			0
$481$	4.72957	+	14.5561i	0.215650	+	0.663703i
$482$	−11.6368	+	8.45461i	−0.530040	+	0.385097i
$483$		0			0
$484$	−4.90045	+	6.08416i	−0.222748	+	0.276553i
$485$	5.17866			0.235151
$486$		0			0
$487$	2.27928	+	7.01490i	0.103284	+	0.317876i	0.989324	−	0.145733i	$-0.0465542\pi$
$487$	2.27928	+	7.01490i	0.103284	+	0.317876i	−0.886040	+	0.463609i	$0.846554\pi$
$488$	3.43539	−	10.5730i	0.155513	−	0.478619i
$489$		0			0
$490$	9.02334	+	6.55584i	0.407633	+	0.296163i
$491$	−0.678379	+	2.08784i	−0.0306148	+	0.0942228i	−0.965196	−	0.261526i	$-0.915774\pi$
$491$	−0.678379	+	2.08784i	−0.0306148	+	0.0942228i	0.934582	+	0.355749i	$0.115774\pi$
$492$		0			0
$493$	16.2470	−	11.8041i	0.731726	−	0.531630i
$494$	−19.5694			−0.880470
$495$		0			0
$496$	7.91667			0.355469
$497$	−40.7953	+	29.6395i	−1.82992	+	1.32952i
$498$		0			0
$499$	2.49123	−	7.66723i	0.111523	−	0.343232i	−0.879683	−	0.475560i	$-0.842245\pi$
$499$	2.49123	−	7.66723i	0.111523	−	0.343232i	0.991206	+	0.132328i	$0.0422453\pi$
$500$	0.574568	+	0.417448i	0.0256955	+	0.0186689i
$501$		0			0
$502$	2.68723	−	8.27043i	0.119937	−	0.369127i
$503$	10.3077	+	31.7237i	0.459596	+	1.41449i	0.865654	+	0.500643i	$0.166903\pi$
$503$	10.3077	+	31.7237i	0.459596	+	1.41449i	−0.406058	+	0.913847i	$0.633097\pi$
$504$		0			0
$505$	−3.99265			−0.177671
$506$	−6.71005	+	3.21135i	−0.298298	+	0.142762i
$507$		0			0
$508$	−2.53445	+	1.84139i	−0.112448	+	0.0816984i
$509$	−5.18767	−	15.9660i	−0.229939	−	0.707681i	−0.997753	−	0.0670068i	$-0.978655\pi$
$509$	−5.18767	−	15.9660i	−0.229939	−	0.707681i	0.767813	−	0.640674i	$-0.221345\pi$
$510$		0			0
$511$	12.9082	+	9.37834i	0.571024	+	0.414873i
$512$	−16.7132	−	12.1429i	−0.738627	−	0.536644i
$513$		0			0
$514$	8.11044	+	24.9614i	0.357736	+	1.10100i
$515$	0.761258	−	0.553086i	0.0335450	−	0.0243719i
$516$		0			0
$517$	1.39331	+	10.4769i	0.0612779	+	0.460775i
$518$	31.3514			1.37750
$519$		0			0
$520$	−2.16278	−	6.65634i	−0.0948441	−	0.291900i
$521$	−4.57050	+	14.0665i	−0.200237	+	0.616267i	0.799638	+	0.600482i	$0.205025\pi$
$521$	−4.57050	+	14.0665i	−0.200237	+	0.616267i	−0.999875	+	0.0157846i	$0.994975\pi$
$522$		0			0
$523$	1.14467	+	0.831651i	0.0500529	+	0.0363656i	0.612530	−	0.790447i	$-0.290152\pi$
$523$	1.14467	+	0.831651i	0.0500529	+	0.0363656i	−0.562477	+	0.826813i	$0.690152\pi$
$524$	−4.69666	+	14.4548i	−0.205174	+	0.631462i
$525$		0			0
$526$	−8.89225	+	6.46060i	−0.387721	+	0.281696i
$527$	19.1465			0.834036
$528$		0			0
$529$	−19.0996			−0.830418
$530$	10.3172	−	7.49591i	0.448152	−	0.325602i
$531$		0			0
$532$	6.82090	−	20.9926i	0.295723	−	0.910143i
$533$	7.40140	+	5.37743i	0.320590	+	0.232922i
$534$		0			0
$535$	4.48985	−	13.8183i	0.194113	−	0.597419i
$536$	−6.00649	−	18.4861i	−0.259441	−	0.798477i
$537$		0			0
$538$	2.07103			0.0892887
$539$	−22.4522	−	23.5975i	−0.967083	−	1.01642i
$540$		0			0
$541$	−2.04419	+	1.48519i	−0.0878866	+	0.0638534i	−0.630861	−	0.775896i	$-0.717298\pi$
$541$	−2.04419	+	1.48519i	−0.0878866	+	0.0638534i	0.542974	+	0.839749i	$0.317298\pi$
$542$	5.19171	+	15.9784i	0.223003	+	0.686333i
$543$		0			0
$544$	−15.4258	−	11.2075i	−0.661377	−	0.480519i
$545$	−6.23099	−	4.52708i	−0.266906	−	0.193919i
$546$		0			0
$547$	0.160414	+	0.493703i	0.00685881	+	0.0211092i	0.954427	−	0.298443i	$-0.0964674\pi$
$547$	0.160414	+	0.493703i	0.00685881	+	0.0211092i	−0.947569	+	0.319553i	$0.896467\pi$
$548$	−2.19560	+	1.59519i	−0.0937913	+	0.0681433i
$549$		0			0
$550$	2.59638	+	2.72883i	0.110710	+	0.116358i
$551$	−30.3220			−1.29176
$552$		0			0
$553$	22.2738	+	68.5519i	0.947180	+	2.91512i
$554$	−5.95914	+	18.3403i	−0.253180	+	0.779207i
$555$		0			0
$556$	3.61818	+	2.62876i	0.153445	+	0.111484i
$557$	−3.64719	+	11.2249i	−0.154537	+	0.475615i	−0.998114	−	0.0613935i	$-0.980446\pi$
$557$	−3.64719	+	11.2249i	−0.154537	+	0.475615i	0.843577	+	0.537008i	$0.180446\pi$
$558$		0			0
$559$	17.6216	−	12.8029i	0.745316	−	0.541504i
$560$	−8.51105			−0.359658
$561$		0			0
$562$	−5.22591			−0.220442
$563$	5.44689	−	3.95740i	0.229559	−	0.166784i	−0.467060	−	0.884226i	$-0.654687\pi$
$563$	5.44689	−	3.95740i	0.229559	−	0.166784i	0.696619	+	0.717441i	$0.254687\pi$
$564$		0			0
$565$	−0.208742	+	0.642441i	−0.00878183	+	0.0270277i
$566$	12.6673	+	9.20333i	0.532446	+	0.386845i
$567$		0			0
$568$	11.6943	−	35.9913i	0.490681	−	1.51016i
$569$	−9.73140	−	29.9502i	−0.407962	−	1.25558i	−0.918397	−	0.395661i	$-0.870516\pi$
$569$	−9.73140	−	29.9502i	−0.407962	−	1.25558i	0.510435	−	0.859916i	$-0.329484\pi$
$570$		0			0
$571$	−24.1049			−1.00876			−0.504380	−	0.863482i	$-0.668279\pi$
$571$	−24.1049			−1.00876			−0.504380	+	0.863482i	$0.668279\pi$
$572$	0.706083	+	5.30934i	0.0295228	+	0.221995i
$573$		0			0
$574$	15.1611	−	11.0152i	0.632813	−	0.459765i
$575$	−0.610290	−	1.87828i	−0.0254508	−	0.0783296i
$576$		0			0
$577$	27.6772	+	20.1087i	1.15222	+	0.837136i	0.988774	−	0.149417i	$-0.0477397\pi$
$577$	27.6772	+	20.1087i	1.15222	+	0.837136i	0.163444	+	0.986553i	$0.447740\pi$
$578$	7.52415	+	5.46662i	0.312964	+	0.227381i
$579$		0			0
$580$	−0.878160	−	2.70270i	−0.0364636	−	0.112224i
$581$	−45.9467	+	33.3822i	−1.90619	+	1.38493i
$582$		0			0
$583$	−33.5937	+	16.0775i	−1.39131	+	0.665864i
$584$	−11.9742			−0.495495
$585$		0			0
$586$	−11.0284	−	33.9418i	−0.455577	−	1.40212i
$587$	−5.43890	+	16.7392i	−0.224487	+	0.690901i	0.773856	+	0.633362i	$0.218325\pi$
$587$	−5.43890	+	16.7392i	−0.224487	+	0.690901i	−0.998343	+	0.0575394i	$0.981675\pi$
$588$		0			0
$589$	−23.3879	−	16.9923i	−0.963683	−	0.700157i
$590$	3.34723	−	10.3017i	0.137803	−	0.424115i
$591$		0			0
$592$	−11.3003	+	8.21014i	−0.464439	+	0.337435i
$593$	33.9143			1.39269			0.696347	−	0.717705i	$-0.254807\pi$
$593$	33.9143			1.39269			0.696347	+	0.717705i	$0.254807\pi$
$594$		0			0
$595$	−20.5841			−0.843864
$596$	12.9254	−	9.39087i	0.529446	−	0.384665i
$597$		0			0
$598$	−1.57602	+	4.85051i	−0.0644485	+	0.198352i
$599$	24.3793	+	17.7126i	0.996111	+	0.723717i	0.961251	−	0.275675i	$-0.0889014\pi$
$599$	24.3793	+	17.7126i	0.996111	+	0.723717i	0.0348602	+	0.999392i	$0.488901\pi$
$600$		0			0
$601$	−8.57870	+	26.4025i	−0.349932	+	1.07698i	0.608958	+	0.793203i	$0.291588\pi$
$601$	−8.57870	+	26.4025i	−0.349932	+	1.07698i	−0.958890	+	0.283778i	$0.908412\pi$
$602$	−13.7876	−	42.4338i	−0.561940	−	1.72947i
$603$		0			0
$604$	2.12848			0.0866067
$605$	−6.01524	−	9.20961i	−0.244554	−	0.374424i
$606$		0			0
$607$	20.6258	−	14.9855i	0.837177	−	0.608244i	−0.0844040	−	0.996432i	$-0.526899\pi$
$607$	20.6258	−	14.9855i	0.837177	−	0.608244i	0.921581	+	0.388187i	$0.126899\pi$
$608$	8.89647	+	27.3805i	0.360799	+	1.11043i
$609$		0			0
$610$	3.31856	+	2.41107i	0.134364	+	0.0976215i
$611$	5.86232	+	4.25922i	0.237164	+	0.172310i
$612$		0			0
$613$	0.638825	+	1.96610i	0.0258019	+	0.0794101i	0.963128	−	0.269043i	$-0.0867072\pi$
$613$	0.638825	+	1.96610i	0.0258019	+	0.0794101i	−0.937326	+	0.348453i	$0.886707\pi$
$614$	18.5351	−	13.4665i	0.748016	−	0.543466i
$615$		0			0
$616$	41.1770	+	7.57578i	1.65907	+	0.305237i
$617$	16.7249			0.673321			0.336660	−	0.941626i	$-0.390703\pi$
$617$	16.7249			0.673321			0.336660	+	0.941626i	$0.390703\pi$
$618$		0			0
$619$	−13.0549	−	40.1788i	−0.524720	−	1.61492i	−0.764869	−	0.644186i	$-0.777196\pi$
$619$	−13.0549	−	40.1788i	−0.524720	−	1.61492i	0.240149	−	0.970736i	$-0.422804\pi$
$620$	0.837240	−	2.57676i	0.0336244	−	0.103485i
$621$		0			0
$622$	−17.0721	−	12.4036i	−0.684529	−	0.497340i
$623$	9.95398	−	30.6352i	0.398798	−	1.22737i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−12.9567			−0.517853
$627$		0			0
$628$	7.23693			0.288785
$629$	−27.3299	+	19.8563i	−1.08971	+	0.791723i
$630$		0			0
$631$	12.0090	−	36.9599i	0.478071	−	1.47135i	−0.363699	−	0.931516i	$-0.618486\pi$
$631$	12.0090	−	36.9599i	0.478071	−	1.47135i	0.841770	−	0.539836i	$-0.181514\pi$
$632$	−43.7632	−	31.7958i	−1.74081	−	1.26477i
$633$		0			0
$634$	−8.93551	+	27.5007i	−0.354874	+	1.09219i
$635$	−1.36309	−	4.19516i	−0.0540926	−	0.166480i
$636$		0			0
$637$	−22.3314			−0.884803
$638$	−1.98688	−	14.9402i	−0.0786614	−	0.591489i
$639$		0			0
$640$	1.63049	−	1.18462i	0.0644509	−	0.0468263i
$641$	−5.42159	−	16.6859i	−0.214140	−	0.659055i	−0.999214	−	0.0396524i	$-0.987375\pi$
$641$	−5.42159	−	16.6859i	−0.214140	−	0.659055i	0.785074	−	0.619402i	$-0.212625\pi$
$642$		0			0
$643$	−29.6485	−	21.5409i	−1.16922	−	0.849490i	−0.178307	−	0.983975i	$-0.557062\pi$
$643$	−29.6485	−	21.5409i	−1.16922	−	0.849490i	−0.990916	+	0.134485i	$0.957062\pi$
$644$	−4.65392	−	3.38127i	−0.183390	−	0.133241i
$645$		0			0
$646$	−13.3475	−	41.0794i	−0.525151	−	1.61625i
$647$	18.2985	−	13.2947i	0.719389	−	0.522667i	−0.166800	−	0.985991i	$-0.553343\pi$
$647$	18.2985	−	13.2947i	0.719389	−	0.522667i	0.886189	+	0.463324i	$0.153343\pi$
$648$		0			0
$649$	−15.0574	+	27.8194i	−0.591055	+	1.09201i
$650$	2.58242			0.101291
$651$		0			0
$652$	4.34616	+	13.3761i	0.170209	+	0.523849i
$653$	1.96124	−	6.03608i	0.0767493	−	0.236210i	−0.905320	−	0.424730i	$-0.860369\pi$
$653$	1.96124	−	6.03608i	0.0767493	−	0.236210i	0.982069	+	0.188520i	$0.0603690\pi$
$654$		0			0
$655$	−17.3133	−	12.5789i	−0.676487	−	0.491497i
$656$	−2.58007	+	7.94063i	−0.100735	+	0.310029i
$657$		0			0
$658$	12.0084	−	8.72465i	0.468138	−	0.340122i
$659$	45.8649			1.78664			0.893321	−	0.449420i	$-0.148369\pi$
$659$	45.8649			1.78664			0.893321	+	0.449420i	$0.148369\pi$
$660$		0			0
$661$	46.4730			1.80759			0.903796	−	0.427964i	$-0.140769\pi$
$661$	46.4730			1.80759			0.903796	+	0.427964i	$0.140769\pi$
$662$	28.5795	−	20.7643i	1.11078	−	0.807026i
$663$		0			0
$664$	13.1710	−	40.5360i	0.511132	−	1.57310i
$665$	25.1439	+	18.2681i	0.975039	+	0.708407i
$666$		0			0
$667$	−2.44199	+	7.51566i	−0.0945541	+	0.291008i
$668$	−1.09017	−	3.35520i	−0.0421800	−	0.129817i
$669$		0			0
$670$	7.17193			0.277076
$671$	−8.25734	−	8.67856i	−0.318771	−	0.335032i
$672$		0			0
$673$	8.98019	−	6.52449i	0.346161	−	0.251501i	−0.401096	−	0.916036i	$-0.631371\pi$
$673$	8.98019	−	6.52449i	0.346161	−	0.251501i	0.747257	+	0.664535i	$0.231371\pi$
$674$	9.36855	+	28.8334i	0.360863	+	1.11062i
$675$		0			0
$676$	−4.49857	−	3.26841i	−0.173022	−	0.125708i
$677$	12.8919	+	9.36649i	0.495475	+	0.359984i	0.807286	−	0.590161i	$-0.200936\pi$
$677$	12.8919	+	9.36649i	0.495475	+	0.359984i	−0.311811	+	0.950144i	$0.600936\pi$
$678$		0			0
$679$	6.56332	+	20.1998i	0.251877	+	0.775198i
$680$	12.4976	−	9.08005i	0.479262	−	0.348204i
$681$		0			0
$682$	6.83991	−	12.6371i	0.261914	−	0.483900i
$683$	−21.8344			−0.835468			−0.417734	−	0.908569i	$-0.637176\pi$
$683$	−21.8344			−0.835468			−0.417734	+	0.908569i	$0.637176\pi$
$684$		0			0
$685$	−1.18085	−	3.63427i	−0.0451178	−	0.138858i
$686$	−4.06020	+	12.4960i	−0.155019	+	0.477100i
$687$		0			0
$688$	16.0819	+	11.6842i	0.613118	+	0.445457i
$689$	−7.89032	+	24.2839i	−0.300597	+	0.925143i
$690$		0			0
$691$	21.8380	−	15.8662i	0.830756	−	0.603579i	−0.0890174	−	0.996030i	$-0.528373\pi$
$691$	21.8380	−	15.8662i	0.830756	−	0.603579i	0.919773	+	0.392451i	$0.128373\pi$
$692$	−11.5415			−0.438743
$693$		0			0
$694$	−7.71420			−0.292827
$695$	−5.09455	+	3.70141i	−0.193247	+	0.140402i
$696$		0			0
$697$	−6.23991	+	19.2045i	−0.236353	+	0.727421i
$698$	−7.20909	−	5.23771i	−0.272868	−	0.198250i
$699$		0			0
$700$	−0.900100	+	2.77022i	−0.0340206	+	0.104705i
$701$	−9.22000	−	28.3762i	−0.348235	−	1.07176i	−0.959829	−	0.280585i	$-0.909472\pi$
$701$	−9.22000	−	28.3762i	−0.348235	−	1.07176i	0.611595	−	0.791171i	$-0.290528\pi$
$702$		0			0
$703$	51.0063			1.92374
$704$	−25.3245	+	12.1200i	−0.954453	+	0.456790i
$705$		0			0
$706$	16.9183	−	12.2919i	0.636728	−	0.462610i
$707$	−5.06020	−	15.5737i	−0.190309	−	0.585710i
$708$		0			0
$709$	−27.0393	−	19.6452i	−1.01548	−	0.737792i	−0.0501317	−	0.998743i	$-0.515964\pi$
$709$	−27.0393	−	19.6452i	−1.01548	−	0.737792i	−0.965352	+	0.260950i	$0.915964\pi$
$710$	11.2966	+	8.20744i	0.423953	+	0.308020i
$711$		0			0
$712$	7.47025	+	22.9911i	0.279960	+	0.861627i
$713$	−6.09529	+	4.42849i	−0.228270	+	0.165848i
$714$		0			0
$715$	−7.41711	−	1.36461i	−0.277384	−	0.0510334i
$716$	−2.26164			−0.0845213
$717$		0			0
$718$	8.91827	+	27.4476i	0.332827	+	1.02434i
$719$	−3.48661	+	10.7307i	−0.130029	+	0.400187i	−0.994784	−	0.102007i	$-0.967474\pi$
$719$	−3.48661	+	10.7307i	−0.130029	+	0.400187i	0.864755	+	0.502194i	$0.167474\pi$
$720$		0			0
$721$	3.12217	+	2.26839i	0.116276	+	0.0844791i
$722$	−13.4852	+	41.5032i	−0.501868	+	1.54459i
$723$		0			0
$724$	0.862420	−	0.626585i	0.0320516	−	0.0232868i
$725$	4.00136			0.148607
$726$		0			0
$727$	43.3381			1.60732			0.803661	−	0.595087i	$-0.202882\pi$
$727$	43.3381			1.60732			0.803661	+	0.595087i	$0.202882\pi$
$728$	23.2226	−	16.8722i	0.860687	−	0.625326i
$729$		0			0
$730$	1.36529	−	4.20194i	0.0505318	−	0.155521i
$731$	38.8943	+	28.2584i	1.43856	+	1.04517i
$732$		0			0
$733$	16.1196	−	49.6111i	0.595392	−	1.83243i	0.0426271	−	0.999091i	$-0.486427\pi$
$733$	16.1196	−	49.6111i	0.595392	−	1.83243i	0.552765	−	0.833337i	$-0.313573\pi$
$734$	1.22233	+	3.76194i	0.0451170	+	0.138856i
$735$		0			0
$736$	7.50305			0.276566
$737$	−20.5989	−	3.78980i	−0.758770	−	0.139599i
$738$		0			0
$739$	11.9005	−	8.64621i	0.437767	−	0.318056i	−0.346980	−	0.937872i	$-0.612793\pi$
$739$	11.9005	−	8.64621i	0.437767	−	0.318056i	0.784747	+	0.619816i	$0.212793\pi$
$740$	1.47720	+	4.54635i	0.0543029	+	0.167127i
$741$		0			0
$742$	42.3143	+	30.7432i	1.55341	+	1.12862i
$743$	2.20658	+	1.60317i	0.0809516	+	0.0588148i	0.627525	−	0.778596i	$-0.284068\pi$
$743$	2.20658	+	1.60317i	0.0809516	+	0.0588148i	−0.546573	+	0.837411i	$0.684068\pi$
$744$		0			0
$745$	6.95161	+	21.3948i	0.254687	+	0.783846i
$746$	11.7925	−	8.56778i	0.431756	−	0.313689i
$747$		0			0
$748$	−10.6636	+	5.10347i	−0.389899	+	0.186601i
$749$	59.5900			2.17737
$750$		0			0
$751$	5.18737	+	15.9651i	0.189290	+	0.582574i	0.999996	−	0.00287913i	$-0.000916457\pi$
$751$	5.18737	+	15.9651i	0.189290	+	0.582574i	−0.810706	+	0.585454i	$0.800916\pi$
$752$	−2.04356	+	6.28942i	−0.0745208	+	0.229351i
$753$		0			0
$754$	−8.35973	−	6.07370i	−0.304443	−	0.221191i
$755$	−0.926122	+	2.85031i	−0.0337050	+	0.103733i
$756$		0			0
$757$	18.5516	−	13.4785i	0.674269	−	0.489885i	−0.197183	−	0.980367i	$-0.563179\pi$
$757$	18.5516	−	13.4785i	0.674269	−	0.489885i	0.871451	+	0.490482i	$0.163179\pi$
$758$	27.3291			0.992636
$759$		0			0
$760$	−23.3246			−0.846071
$761$	6.32263	−	4.59366i	0.229195	−	0.166520i	−0.467261	−	0.884120i	$-0.654759\pi$
$761$	6.32263	−	4.59366i	0.229195	−	0.166520i	0.696456	+	0.717599i	$0.254759\pi$
$762$		0			0
$763$	9.76126	−	30.0421i	0.353381	−	1.08760i
$764$	6.00009	+	4.35932i	0.217076	+	0.157715i
$765$		0			0
$766$	−1.11468	+	3.43062i	−0.0402748	+	0.123953i
$767$	6.70182	+	20.6261i	0.241989	+	0.744764i
$768$		0			0
$769$	38.6765			1.39471			0.697355	−	0.716726i	$-0.254360\pi$
$769$	38.6765			1.39471			0.697355	+	0.716726i	$0.254360\pi$
$770$	−7.35345	+	13.5859i	−0.265000	+	0.489602i
$771$		0			0
$772$	3.46321	−	2.51617i	0.124644	−	0.0905590i
$773$	−5.21660	−	16.0551i	−0.187628	−	0.577460i	0.812356	−	0.583163i	$-0.198185\pi$
$773$	−5.21660	−	16.0551i	−0.187628	−	0.577460i	−0.999984	+	0.00570222i	$0.998185\pi$
$774$		0			0
$775$	3.08632	+	2.24234i	0.110864	+	0.0805473i
$776$	−12.8955	−	9.36911i	−0.462921	−	0.336331i
$777$		0			0
$778$	−5.22914	−	16.0936i	−0.187474	−	0.576985i
$779$	24.6659	−	17.9209i	0.883749	−	0.642081i
$780$		0			0
$781$	−28.1085	−	29.5424i	−1.00580	−	1.05711i
$782$	−11.2569			−0.402548
$783$		0			0
$784$	−6.29783	−	19.3827i	−0.224922	−	0.692240i
$785$	−3.14886	+	9.69118i	−0.112387	+	0.345893i
$786$		0			0
$787$	−21.9317	−	15.9343i	−0.781781	−	0.567997i	0.123732	−	0.992316i	$-0.460514\pi$
$787$	−21.9317	−	15.9343i	−0.781781	−	0.567997i	−0.905513	+	0.424318i	$0.860514\pi$
$788$	1.99064	−	6.12656i	0.0709136	−	0.218250i
$789$		0			0
$790$	16.1476	−	11.7319i	0.574504	−	0.417402i
$791$	−2.77045			−0.0985060
$792$		0			0
$793$	−8.21293			−0.291650
$794$	9.99987	−	7.26533i	0.354882	−	0.257837i
$795$		0			0
$796$	−3.79989	+	11.6949i	−0.134684	+	0.414513i
$797$	19.0544	+	13.8438i	0.674940	+	0.490373i	0.871675	−	0.490084i	$-0.163034\pi$
$797$	19.0544	+	13.8438i	0.674940	+	0.490373i	−0.196735	+	0.980457i	$0.563034\pi$
$798$		0			0
$799$	−4.94236	+	15.2110i	−0.174848	+	0.538127i
$800$	−1.17400	−	3.61319i	−0.0415070	−	0.127745i
$801$		0			0
$802$	−37.8012			−1.33481
$803$	−6.14173	+	11.3472i	−0.216737	+	0.400433i
$804$		0			0
$805$	6.55293	−	4.76098i	0.230960	−	0.167802i
$806$	−3.04434	−	9.36951i	−0.107232	−	0.330027i
$807$		0			0
$808$	9.94218	+	7.22342i	0.349765	+	0.254119i
$809$	−14.5734	−	10.5882i	−0.512375	−	0.372262i	0.301349	−	0.953514i	$-0.402563\pi$
$809$	−14.5734	−	10.5882i	−0.512375	−	0.372262i	−0.813724	+	0.581252i	$0.802563\pi$
$810$		0			0
$811$	1.93347	+	5.95060i	0.0678933	+	0.208954i	0.979247	−	0.202670i	$-0.0649618\pi$
$811$	1.93347	+	5.95060i	0.0678933	+	0.208954i	−0.911354	+	0.411624i	$0.864962\pi$
$812$	9.42916	−	6.85069i	0.330899	−	0.240412i
$813$		0			0
$814$	3.34224	+	25.1317i	0.117145	+	0.880867i
$815$	−19.8034			−0.693683
$816$		0			0
$817$	−22.4313	−	69.0365i	−0.784773	−	2.41528i
$818$	−0.974560	+	2.99939i	−0.0340747	+	0.104871i
$819$		0			0
$820$	2.31170	+	1.67955i	0.0807280	+	0.0586523i
$821$	5.85105	−	18.0077i	0.204203	−	0.628473i	−0.795542	−	0.605899i	$-0.792814\pi$
$821$	5.85105	−	18.0077i	0.204203	−	0.628473i	0.999745	−	0.0225744i	$-0.00718625\pi$
$822$		0			0
$823$	−18.9053	+	13.7355i	−0.658998	+	0.478790i	−0.866324	−	0.499482i	$-0.833524\pi$
$823$	−18.9053	+	13.7355i	−0.658998	+	0.478790i	0.207326	+	0.978272i	$0.433524\pi$
$824$	−2.89625			−0.100896
$825$		0			0
$826$	44.4250			1.54574
$827$	4.05437	−	2.94567i	0.140984	−	0.102431i	−0.515058	−	0.857156i	$-0.672229\pi$
$827$	4.05437	−	2.94567i	0.140984	−	0.102431i	0.656042	+	0.754725i	$0.272229\pi$
$828$		0			0
$829$	13.8909	−	42.7518i	0.482451	−	1.48483i	−0.353188	−	0.935552i	$-0.614902\pi$
$829$	13.8909	−	42.7518i	0.482451	−	1.48483i	0.835639	−	0.549279i	$-0.185098\pi$
$830$	12.7230	+	9.24382i	0.441623	+	0.320858i
$831$		0			0
$832$	−5.94810	+	18.3064i	−0.206213	+	0.634659i
$833$	−15.2314	−	46.8773i	−0.527735	−	1.62420i
$834$		0			0
$835$	4.96739			0.171903
$836$	17.5551	+	3.22980i	0.607155	+	0.111705i
$837$		0			0
$838$	−27.1563	+	19.7302i	−0.938099	+	0.681569i
$839$	−16.2095	−	49.8878i	−0.559615	−	1.72232i	−0.683434	−	0.730012i	$-0.739514\pi$
$839$	−16.2095	−	49.8878i	−0.559615	−	1.72232i	0.123820	−	0.992305i	$-0.460486\pi$
$840$		0			0
$841$	10.5084	+	7.63482i	0.362360	+	0.263270i
$842$	0.268199	+	0.194858i	0.00924275	+	0.00671525i
$843$		0			0
$844$	3.44898	+	10.6149i	0.118719	+	0.365379i
$845$	6.33419	−	4.60206i	0.217903	−	0.158316i
$846$		0			0
$847$	28.2993	−	35.1350i	0.972376	−	1.20725i
$848$	−23.3026			−0.800215
$849$		0			0
$850$	1.76137	+	5.42093i	0.0604143	+	0.185936i
$851$	4.10779	−	12.6425i	0.140813	−	0.433379i
$852$		0			0
$853$	40.5363	+	29.4513i	1.38794	+	1.00839i	0.996088	+	0.0883638i	$0.0281638\pi$
$853$	40.5363	+	29.4513i	1.38794	+	1.00839i	0.391847	+	0.920030i	$0.371836\pi$
$854$	−5.19874	+	16.0001i	−0.177897	+	0.547511i
$855$		0			0
$856$	−36.1801	+	26.2864i	−1.23661	+	0.898450i
$857$	13.2279			0.451856			0.225928	−	0.974144i	$-0.427459\pi$
$857$	13.2279			0.451856			0.225928	+	0.974144i	$0.427459\pi$
$858$		0			0
$859$	−50.3765			−1.71883			−0.859413	−	0.511283i	$-0.829171\pi$
$859$	−50.3765			−1.71883			−0.859413	+	0.511283i	$0.829171\pi$
$860$	5.50381	−	3.99875i	0.187678	−	0.136356i
$861$		0			0
$862$	1.57779	−	4.85594i	0.0537398	−	0.165394i
$863$	−11.0175	−	8.00470i	−0.375041	−	0.272483i	0.384257	−	0.923226i	$-0.374458\pi$
$863$	−11.0175	−	8.00470i	−0.375041	−	0.272483i	−0.759298	+	0.650743i	$0.774458\pi$
$864$		0			0
$865$	5.02182	−	15.4556i	0.170747	−	0.525505i
$866$	2.30510	+	7.09438i	0.0783306	+	0.241077i
$867$		0			0
$868$	11.1120			0.377165
$869$	−52.5776	+	25.1631i	−1.78357	+	0.853598i
$870$		0			0
$871$	−11.6172	+	8.44037i	−0.393633	+	0.285991i
$872$	7.32562	+	22.5459i	0.248077	+	0.763502i
$873$		0			0
$874$	13.7506	+	9.99041i	0.465122	+	0.337931i
$875$	−3.31804	−	2.41070i	−0.112170	−	0.0814965i
$876$		0			0
$877$	−6.18766	−	19.0437i	−0.208942	−	0.643059i	−0.999528	−	0.0307077i	$-0.990224\pi$
$877$	−6.18766	−	19.0437i	−0.208942	−	0.643059i	0.790586	−	0.612351i	$-0.209776\pi$
$878$	−24.5448	+	17.8329i	−0.828348	+	0.601830i
$879$		0			0
$880$	−0.907327	−	6.82258i	−0.0305860	−	0.229989i
$881$	−30.0543			−1.01256			−0.506278	−	0.862371i	$-0.668979\pi$
$881$	−30.0543			−1.01256			−0.506278	+	0.862371i	$0.668979\pi$
$882$		0			0
$883$	8.99124	+	27.6722i	0.302579	+	0.931244i	0.980569	+	0.196173i	$0.0628513\pi$
$883$	8.99124	+	27.6722i	0.302579	+	0.931244i	−0.677990	+	0.735071i	$0.737149\pi$
$884$	−2.50461	+	7.70840i	−0.0842392	+	0.259262i
$885$		0			0
$886$	−21.2857	−	15.4650i	−0.715107	−	0.519556i
$887$	−5.79362	+	17.8309i	−0.194531	+	0.598704i	0.805451	+	0.592663i	$0.201923\pi$
$887$	−5.79362	+	17.8309i	−0.194531	+	0.598704i	−0.999982	+	0.00604191i	$0.998077\pi$
$888$		0			0
$889$	14.6361	−	10.6337i	0.490878	−	0.356643i
$890$	−8.91971			−0.298989
$891$		0			0
$892$	−0.769733			−0.0257726
$893$	19.5368	−	14.1943i	0.653774	−	0.474995i
$894$		0			0
$895$	0.984058	−	3.02862i	0.0328934	−	0.101236i
$896$	6.68718	+	4.85852i	0.223403	+	0.162312i
$897$		0			0
$898$	10.1983	−	31.3871i	0.340321	−	1.04740i
$899$	−4.71708	−	14.5177i	−0.157323	−	0.484191i
$900$		0			0
$901$	−56.3576			−1.87754
$902$	10.4462	+	10.9791i	0.347820	+	0.365563i
$903$		0			0
$904$	1.68208	−	1.22210i	0.0559452	−	0.0406465i
$905$	0.463831	+	1.42752i	0.0154183	+	0.0474525i
$906$		0			0
$907$	−31.3567	−	22.7820i	−1.04118	−	0.756463i	−0.0706660	−	0.997500i	$-0.522512\pi$
$907$	−31.3567	−	22.7820i	−1.04118	−	0.756463i	−0.970516	+	0.241037i	$0.922512\pi$
$908$	−1.14438	−	0.831438i	−0.0379775	−	0.0275922i
$909$		0			0
$910$	3.27291	+	10.0730i	0.108496	+	0.333916i
$911$	−28.1835	+	20.4765i	−0.933760	+	0.678417i	−0.946911	−	0.321497i	$-0.895814\pi$
$911$	−28.1835	+	20.4765i	−0.933760	+	0.678417i	0.0131503	+	0.999914i	$0.495814\pi$
$912$		0			0
$913$	−31.6578	−	33.2728i	−1.04772	−	1.10117i
$914$	−8.66238			−0.286526
$915$		0			0
$916$	−1.78639	−	5.49795i	−0.0590241	−	0.181657i
$917$	27.1224	−	83.4743i	0.895662	−	2.75656i
$918$		0			0
$919$	22.1260	+	16.0755i	0.729868	+	0.530280i	0.889522	−	0.456893i	$-0.151038\pi$
$919$	22.1260	+	16.0755i	0.729868	+	0.530280i	−0.159653	+	0.987173i	$0.551038\pi$
$920$	−1.87844	+	5.78126i	−0.0619305	+	0.190602i
$921$		0			0
$922$	−31.2517	+	22.7057i	−1.02922	+	0.747771i
$923$	−27.9573			−0.920227
$924$		0			0
$925$	−6.73089			−0.221310
$926$	14.4769	−	10.5181i	0.475740	−	0.345645i
$927$		0			0
$928$	−4.69758	+	14.4577i	−0.154206	+	0.474596i
$929$	35.6580	+	25.9071i	1.16990	+	0.849983i	0.990997	−	0.133884i	$-0.0427449\pi$
$929$	35.6580	+	25.9071i	1.16990	+	0.849983i	0.178904	+	0.983867i	$0.442745\pi$
$930$		0			0
$931$	−22.9976	+	70.7794i	−0.753716	+	2.31970i
$932$	−5.36145	−	16.5009i	−0.175620	−	0.540503i
$933$		0			0
$934$	−11.5282			−0.377214
$935$	−2.19438	−	16.5005i	−0.0717638	−	0.539623i
$936$		0			0
$937$	−16.4606	+	11.9594i	−0.537746	+	0.390695i	−0.823247	−	0.567683i	$-0.807840\pi$
$937$	−16.4606	+	11.9594i	−0.537746	+	0.390695i	0.285502	+	0.958378i	$0.407840\pi$
$938$	9.08955	+	27.9748i	0.296784	+	0.913409i
$939$		0			0
$940$	1.83099	+	1.33029i	0.0597204	+	0.0433894i
$941$	−3.13043	−	2.27439i	−0.102049	−	0.0741429i	0.535591	−	0.844478i	$-0.320089\pi$
$941$	−3.13043	−	2.27439i	−0.102049	−	0.0741429i	−0.637640	+	0.770335i	$0.720089\pi$
$942$		0			0
$943$	−2.45542	−	7.55699i	−0.0799593	−	0.246090i
$944$	−16.0125	+	11.6338i	−0.521164	+	0.378648i
$945$		0			0
$946$	32.5457	−	15.5760i	1.05815	−	0.506420i
$947$	−54.4898			−1.77068			−0.885340	−	0.464943i	$-0.846075\pi$
$947$	−54.4898			−1.77068			−0.885340	+	0.464943i	$0.846075\pi$
$948$		0			0
$949$	2.73358	+	8.41311i	0.0887359	+	0.273101i
$950$	2.65946	−	8.18498i	0.0862843	−	0.265556i
$951$		0			0
$952$	51.2568	+	37.2402i	1.66124	+	1.20696i
$953$	−12.5162	+	38.5209i	−0.405439	+	1.24781i	0.515089	+	0.857137i	$0.327759\pi$
$953$	−12.5162	+	38.5209i	−0.405439	+	1.24781i	−0.920528	+	0.390677i	$0.872241\pi$
$954$		0			0
$955$	−8.44839	+	6.13811i	−0.273383	+	0.198625i
$956$	0.0504136			0.00163049
$957$		0			0
$958$	−4.59177			−0.148353
$959$	12.6792	−	9.21199i	0.409433	−	0.297471i
$960$		0			0
$961$	−5.08226	+	15.6416i	−0.163944	+	0.504567i
$962$	14.0623	+	10.2169i	0.453388	+	0.329406i
$963$		0			0
$964$	2.77959	−	8.55471i	0.0895247	−	0.275529i
$965$	1.86260	+	5.73250i	0.0599592	+	0.184536i
$966$		0			0
$967$	22.9360			0.737572			0.368786	−	0.929514i	$-0.379774\pi$
$967$	22.9360			0.737572			0.368786	+	0.929514i	$0.379774\pi$
$968$	−1.68315	+	33.8157i	−0.0540986	+	1.08688i
$969$		0			0
$970$	4.75812	−	3.45697i	0.152774	−	0.110997i
$971$	14.3246	+	44.0865i	0.459697	+	1.41480i	0.865531	+	0.500855i	$0.166981\pi$
$971$	14.3246	+	44.0865i	0.459697	+	1.41480i	−0.405834	+	0.913947i	$0.633019\pi$
$972$		0			0
$973$	−20.8944	−	15.1807i	−0.669844	−	0.486670i
$974$	6.77694	+	4.92373i	0.217147	+	0.157767i
$975$		0			0
$976$	−2.31618	−	7.12848i	−0.0741392	−	0.228177i
$977$	−21.3627	+	15.5209i	−0.683453	+	0.496557i	−0.874501	−	0.485023i	$-0.838811\pi$
$977$	−21.3627	+	15.5209i	−0.683453	+	0.496557i	0.191049	+	0.981581i	$0.438811\pi$
$978$		0			0
$979$	25.6188	+	4.71337i	0.818780	+	0.150640i
$980$	−6.97483			−0.222803
$981$		0			0
$982$	0.770429	+	2.37114i	0.0245854	+	0.0756660i
$983$	4.87781	−	15.0123i	0.155578	−	0.478819i	−0.842641	−	0.538476i	$-0.819000\pi$
$983$	4.87781	−	15.0123i	0.155578	−	0.478819i	0.998219	+	0.0596561i	$0.0190004\pi$
$984$		0			0
$985$	7.33811	+	5.33145i	0.233811	+	0.169874i
$986$	7.04785	−	21.6911i	0.224449	−	0.690784i
$987$		0			0
$988$	9.90056	−	7.19318i	0.314979	−	0.228845i
$989$	−18.9180			−0.601557
$990$		0			0
$991$	27.9885			0.889085			0.444542	−	0.895758i	$-0.353366\pi$
$991$	27.9885			0.889085			0.444542	+	0.895758i	$0.353366\pi$
$992$	−11.7253	+	8.51895i	−0.372280	+	0.270477i
$993$		0			0
$994$	−17.6968	+	54.4652i	−0.561309	+	1.72753i
$995$	−14.0076	−	10.1771i	−0.444069	−	0.322635i
$996$		0			0
$997$	12.2317	−	37.6452i	0.387381	−	1.19224i	−0.547357	−	0.836899i	$-0.684366\pi$
$997$	12.2317	−	37.6452i	0.387381	−	1.19224i	0.934738	−	0.355337i	$-0.115634\pi$
$998$	−2.82927	−	8.70760i	−0.0895590	−	0.275634i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.g.91.4	✓	16
3.2	odd	2		495.2.n.h.91.1	yes	16
11.2	odd	10		5445.2.a.cb.1.7		8
11.4	even	5	inner	495.2.n.g.136.4	yes	16
11.9	even	5		5445.2.a.cd.1.2		8
33.2	even	10		5445.2.a.cc.1.2		8
33.20	odd	10		5445.2.a.ca.1.7		8
33.26	odd	10		495.2.n.h.136.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.n.g.91.4	✓	16	1.1	even	1	trivial
495.2.n.g.136.4	yes	16	11.4	even	5	inner
495.2.n.h.91.1	yes	16	3.2	odd	2
495.2.n.h.136.1	yes	16	33.26	odd	10
5445.2.a.ca.1.7		8	33.20	odd	10
5445.2.a.cb.1.7		8	11.2	odd	10
5445.2.a.cc.1.2		8	33.2	even	10
5445.2.a.cd.1.2		8	11.9	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.918793 - 0.667542i) q^{2} +(-0.219466 + 0.675446i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.26738 - 3.90059i) q^{7} +(0.951141 + 2.92731i) q^{8} +O(q^{10})\)	\(q+(0.918793 - 0.667542i) q^{2} +(-0.219466 + 0.675446i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.26738 - 3.90059i) q^{7} +(0.951141 + 2.92731i) q^{8} -1.13569 q^{10} +(3.26188 + 0.600124i) q^{11} +(1.83960 - 1.33655i) q^{13} +(-1.43935 - 4.42987i) q^{14} +(1.67887 + 1.21977i) q^{16} +(4.06036 + 2.95002i) q^{17} +(-2.34171 - 7.20705i) q^{19} +(0.574568 - 0.417448i) q^{20} +(3.39760 - 1.62605i) q^{22} -1.97494 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.798012 - 2.45603i) q^{26} +(2.35649 + 1.71209i) q^{28} +(1.23649 - 3.80552i) q^{29} +(3.08632 - 2.24234i) q^{31} -3.79913 q^{32} +5.69990 q^{34} +(-3.31804 + 2.41070i) q^{35} +(-2.07996 + 6.40146i) q^{37} +(-6.96256 - 5.05859i) q^{38} +(0.951141 - 2.92731i) q^{40} +(1.24329 + 3.82644i) q^{41} +9.57903 q^{43} +(-1.12122 + 2.07152i) q^{44} +(-1.81456 + 1.31836i) q^{46} +(0.984753 + 3.03076i) q^{47} +(-7.94524 - 5.77255i) q^{49} +(0.918793 + 0.667542i) q^{50} +(0.499038 + 1.53588i) q^{52} +(-9.08454 + 6.60031i) q^{53} +(-2.28617 - 2.40279i) q^{55} +12.6237 q^{56} +(-1.40427 - 4.32189i) q^{58} +(-2.94731 + 9.07089i) q^{59} +(-2.92206 - 2.12300i) q^{61} +(1.33883 - 4.12050i) q^{62} +(-6.84835 + 4.97562i) q^{64} -2.27388 q^{65} -6.31504 q^{67} +(-2.88369 + 2.09512i) q^{68} +(-1.43935 + 4.42987i) q^{70} +(-9.94687 - 7.22682i) q^{71} +(-1.20217 + 3.69990i) q^{73} +(2.36219 + 7.27008i) q^{74} +5.38189 q^{76} +(6.47487 - 11.9627i) q^{77} +(-14.2183 + 10.3302i) q^{79} +(-0.641271 - 1.97363i) q^{80} +(3.69664 + 2.68577i) q^{82} +(-11.2029 - 8.13938i) q^{83} +(-1.55092 - 4.77324i) q^{85} +(8.80115 - 6.39441i) q^{86} +(1.34576 + 10.1193i) q^{88} +7.85399 q^{89} +(-2.88186 - 8.86946i) q^{91} +(0.433431 - 1.33396i) q^{92} +(2.92794 + 2.12728i) q^{94} +(-2.34171 + 7.20705i) q^{95} +(-4.18962 + 3.04394i) q^{97} -11.1535 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8	\( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + 8 q^{10} + 4 q^{11} + 2 q^{13} - 22 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} + 2 q^{20} - 28 q^{22} + 8 q^{23} - 4 q^{25} + 6 q^{26} - 2 q^{28} - 26 q^{29} - 10 q^{31} + 56 q^{32} - 4 q^{34} - 4 q^{35} + 22 q^{37} - 30 q^{38} - 6 q^{40} - 6 q^{41} + 28 q^{43} + 68 q^{44} + 16 q^{46} - 20 q^{47} + 10 q^{49} - 2 q^{50} + 30 q^{52} + 14 q^{53} - 6 q^{55} + 68 q^{56} - 6 q^{58} - 16 q^{59} - 38 q^{61} - 20 q^{62} + 10 q^{64} + 12 q^{65} + 20 q^{67} - 48 q^{68} - 22 q^{70} - 54 q^{71} + 2 q^{73} + 28 q^{74} - 44 q^{76} + 34 q^{77} - 12 q^{79} - 22 q^{80} + 30 q^{82} - 28 q^{83} - 4 q^{85} + 74 q^{86} + 46 q^{88} + 76 q^{89} - 34 q^{91} - 8 q^{92} - 10 q^{94} - 4 q^{95} - 18 q^{97} + 8 q^{98}+O(q^{100}) \) 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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