LMFDB - Embedded newform 495.2.n.h.91.1

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			91.1
Root			$-0.659965 + 2.03116i$ of defining polynomial
Character	$\chi$	$=$	495.91
Dual form			495.2.n.h.136.1

$q$-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	−0.863164	−	0.504924i	$-0.831521\pi$
$2$	−0.918793	+	0.667542i	−0.649685	+	0.472024i	0.213479	+	0.976948i	$0.431521\pi$
$3$		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	−0.0260098	−	0.999662i	$-0.508280\pi$
$17$	−4.06036	−	2.95002i	−0.984782	−	0.715486i	−0.958772	+	0.284176i	$0.908280\pi$
$18$		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	$-0.433987\pi$
$23$	1.97494			0.411803			0.205902	+	0.978573i	$0.433987\pi$
$24$		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	$0.221162\pi$
$29$	−1.23649	+	3.80552i	−0.229610	+	0.706667i	−0.997791	+	0.0664339i	$0.978838\pi$
$30$		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	$-0.998273\pi$
$41$	−1.24329	−	3.82644i	−0.194169	−	0.597590i	0.805816	−	0.592165i	$-0.201727\pi$
$42$		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	0.853193	−	0.521596i	$-0.174663\pi$
$47$	−0.984753	−	3.03076i	−0.143641	−	0.442081i	−0.996834	+	0.0795143i	$0.974663\pi$
$48$		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	0.249762	−	0.968307i	$-0.419648\pi$
$53$	9.08454	−	6.60031i	1.24786	−	0.906622i	0.998096	+	0.0616854i	$0.0196475\pi$
$54$		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	$-0.686787\pi$
$59$	2.94731	−	9.07089i	0.383707	−	1.18093i	0.937414	−	0.348217i	$-0.113213\pi$
$60$		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	0.992225	−	0.124455i	$-0.0397182\pi$
$71$	9.94687	+	7.22682i	1.18048	+	0.857666i	0.188251	+	0.982121i	$0.439718\pi$
$72$		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	0.996866	−	0.0791092i	$-0.0252076\pi$
$83$	11.2029	+	8.13938i	1.22968	+	0.893413i	0.232811	+	0.972522i	$0.425208\pi$
$84$		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	$-0.636660\pi$
$89$	−7.85399			−0.832522			−0.416261	+	0.909245i	$0.636660\pi$
$90$		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	−0.736777	−	0.676136i	$-0.763653\pi$
$101$	−3.23012	+	2.34682i	−0.321409	+	0.233518i	0.415367	+	0.909654i	$0.363653\pi$
$102$		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	$-0.852153\pi$
$107$	−4.48985	−	13.8183i	−0.434050	−	1.33587i	0.460006	−	0.887916i	$-0.347847\pi$
$108$		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	0.960395	−	0.278643i	$-0.0898847\pi$
$113$	0.208742	+	0.642441i	0.0196368	+	0.0604357i	−0.940758	+	0.339079i	$0.889885\pi$
$114$		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	$-0.884495\pi$
$131$	−21.4004			−1.86976			−0.934882	+	0.354959i	$0.884495\pi$
$132$		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	0.447839	−	0.894114i	$-0.352194\pi$
$137$	−3.09149	−	2.24610i	−0.264124	−	0.191897i	−0.711963	+	0.702217i	$0.752194\pi$
$138$		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	$0.0730081\pi$
$149$	18.1995	+	13.2227i	1.49096	+	1.08325i	0.517153	+	0.855893i	$0.326992\pi$
$150$		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	−0.421339	−	0.906903i	$-0.638440\pi$
$167$	4.01870	−	2.91976i	0.310976	−	0.225937i	0.732315	+	0.680966i	$0.238440\pi$
$168$		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	$-0.888037\pi$
$173$	−5.02182	−	15.4556i	−0.381802	−	1.17507i	0.556972	−	0.830531i	$-0.311963\pi$
$174$		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	0.907521	−	0.420006i	$-0.137972\pi$
$179$	−0.984058	−	3.02862i	−0.0735520	−	0.226370i	−0.981073	+	0.193636i	$0.937972\pi$
$180$		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	$0.223322\pi$
$191$	−3.22700	+	9.93168i	−0.233497	+	0.718631i	−0.997317	+	0.0732014i	$0.976678\pi$
$192$		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	$-0.395268\pi$
$197$	9.07040			0.646239			0.323120	+	0.946358i	$0.395268\pi$
$198$		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	−0.928552	−	0.371204i	$-0.878945\pi$
$227$	0.615474	−	1.89423i	0.0408504	−	0.125725i	0.969402	+	0.245479i	$0.0789452\pi$
$228$		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	0.294889	−	0.955532i	$-0.404717\pi$
$233$	19.7639	−	14.3593i	1.29478	−	0.940712i	0.999890	+	0.0148197i	$0.00471743\pi$
$234$		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	0.951763	−	0.306833i	$-0.0992692\pi$
$239$	0.0219354	+	0.0675103i	0.00141888	+	0.00436688i	−0.950345	+	0.311200i	$0.899269\pi$
$240$		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	−0.765867	−	0.642999i	$-0.777690\pi$
$251$	−6.19469	+	4.50070i	−0.391005	+	0.284082i	0.374862	+	0.927081i	$0.377690\pi$
$252$		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	$-0.643782\pi$
$257$	7.14141	−	21.9790i	0.445469	−	1.37101i	0.881968	−	0.471308i	$-0.156218\pi$
$258$		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	$-0.403550\pi$
$263$	9.67819			0.596783			0.298391	+	0.954444i	$0.403550\pi$
$264$		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	0.541900	−	0.840443i	$-0.317705\pi$
$269$	−1.47532	−	1.07188i	−0.0899516	−	0.0653536i	−0.631852	+	0.775089i	$0.717705\pi$
$270$		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	0.693262	−	0.720686i	$-0.256173\pi$
$281$	3.72271	+	2.70471i	0.222078	+	0.161349i	−0.471183	+	0.882035i	$0.656173\pi$
$282$		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	$0.470131\pi$
$293$	−9.71070	+	29.8864i	−0.567305	+	1.74598i	−0.661002	+	0.750384i	$0.729869\pi$
$294$		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	$0.0766145\pi$
$311$	5.74185	+	17.6716i	0.325590	+	1.00206i	−0.645583	+	0.763690i	$0.723386\pi$
$312$		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	0.167537	−	0.985866i	$-0.446419\pi$
$317$	20.5984	−	14.9656i	1.15692	−	0.840554i	0.989386	+	0.145312i	$0.0464185\pi$
$318$		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	0.725434	−	0.688292i	$-0.241639\pi$
$347$	5.49526	+	3.99254i	0.295001	+	0.214331i	−0.430433	+	0.902623i	$0.641639\pi$
$348$		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	$-0.663014\pi$
$353$	−18.4136			−0.980056			−0.490028	+	0.871707i	$0.663014\pi$
$354$		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	$-0.666039\pi$
$359$	7.85272	−	24.1682i	0.414451	−	1.27555i	0.912741	−	0.408538i	$-0.133961\pi$
$360$		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	−0.520197	−	0.854046i	$-0.674141\pi$
$383$	2.56959	−	1.86691i	0.131300	−	0.0953949i	0.651497	+	0.758651i	$0.274141\pi$
$384$		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	$0.223296\pi$
$389$	−4.60437	+	14.1708i	−0.233451	+	0.718488i	−0.997323	+	0.0731204i	$0.976704\pi$
$390$		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	$0.0122769\pi$
$401$	26.9279	+	19.5643i	1.34472	+	0.976993i	0.345459	+	0.938434i	$0.387723\pi$
$402$		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	$-0.243239\pi$
$419$	29.5565			1.44393			0.721965	+	0.691930i	$0.243239\pi$
$420$		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	−0.671928	−	0.740617i	$-0.734534\pi$
$431$	−3.63718	+	2.64256i	−0.175197	+	0.127288i	0.496731	+	0.867904i	$0.334534\pi$
$432$		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	$0.0855054\pi$
$443$	7.15900	+	22.0331i	0.340135	+	1.04683i	−0.624003	+	0.781422i	$0.714495\pi$
$444$		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	−0.982582	−	0.185832i	$-0.940502\pi$
$449$	−23.5094	+	17.0806i	−1.10948	+	0.806084i	−0.126898	+	0.991916i	$0.540502\pi$
$450$		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	$-0.208993\pi$
$461$	34.0138			1.58418			0.792091	+	0.610404i	$0.208993\pi$
$462$		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	0.761352	−	0.648339i	$-0.224536\pi$
$467$	8.21219	+	5.96651i	0.380015	+	0.276097i	−0.381337	+	0.924436i	$0.624536\pi$
$468$		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	0.660000	−	0.751266i	$-0.270556\pi$
$479$	3.27098	+	2.37650i	0.149455	+	0.108585i	−0.510545	+	0.859851i	$0.670556\pi$
$480$		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	−0.934582	−	0.355749i	$-0.884226\pi$
$491$	0.678379	−	2.08784i	0.0306148	−	0.0942228i	0.965196	+	0.261526i	$0.0842258\pi$
$492$		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	$-0.833097\pi$
$503$	−10.3077	−	31.7237i	−0.459596	−	1.41449i	0.406058	−	0.913847i	$-0.366903\pi$
$504$		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	$0.0213449\pi$
$509$	5.18767	+	15.9660i	0.229939	+	0.707681i	−0.767813	+	0.640674i	$0.778655\pi$
$510$		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	$-0.794975\pi$
$521$	4.57050	−	14.0665i	0.200237	−	0.616267i	0.999875	−	0.0157846i	$-0.00502461\pi$
$522$		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	−0.843577	−	0.537008i	$-0.819554\pi$
$557$	3.64719	−	11.2249i	0.154537	−	0.475615i	0.998114	+	0.0613935i	$0.0195545\pi$
$558$		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	−0.696619	−	0.717441i	$-0.745313\pi$
$563$	−5.44689	+	3.95740i	−0.229559	+	0.166784i	0.467060	+	0.884226i	$0.345313\pi$
$564$		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	$0.129484\pi$
$569$	9.73140	+	29.9502i	0.407962	+	1.25558i	−0.510435	+	0.859916i	$0.670516\pi$
$570$		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	$-0.781675\pi$
$587$	5.43890	−	16.7392i	0.224487	−	0.690901i	0.998343	−	0.0575394i	$-0.0183255\pi$
$588$		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	$-0.745193\pi$
$593$	−33.9143			−1.39269			−0.696347	+	0.717705i	$0.745193\pi$
$594$		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	−0.0348602	−	0.999392i	$-0.511099\pi$
$599$	−24.3793	−	17.7126i	−0.996111	−	0.723717i	−0.961251	+	0.275675i	$0.911099\pi$
$600$		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	$-0.609297\pi$
$617$	−16.7249			−0.673321			−0.336660	+	0.941626i	$0.609297\pi$
$618$		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	$0.0126251\pi$
$641$	5.42159	+	16.6859i	0.214140	+	0.659055i	−0.785074	+	0.619402i	$0.787375\pi$
$642$		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	−0.886189	−	0.463324i	$-0.846657\pi$
$647$	−18.2985	+	13.2947i	−0.719389	+	0.522667i	0.166800	+	0.985991i	$0.446657\pi$
$648$		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	−0.982069	−	0.188520i	$-0.939631\pi$
$653$	−1.96124	+	6.03608i	−0.0767493	+	0.236210i	0.905320	+	0.424730i	$0.139631\pi$
$654$		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	$-0.851631\pi$
$659$	−45.8649			−1.78664			−0.893321	+	0.449420i	$0.851631\pi$
$660$		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	0.311811	−	0.950144i	$-0.399064\pi$
$677$	−12.8919	−	9.36649i	−0.495475	−	0.359984i	−0.807286	+	0.590161i	$0.799064\pi$
$678$		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	$-0.362824\pi$
$683$	21.8344			0.835468			0.417734	+	0.908569i	$0.362824\pi$
$684$		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	$0.0905284\pi$
$701$	9.22000	+	28.3762i	0.348235	+	1.07176i	−0.611595	+	0.791171i	$0.709472\pi$
$702$		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	−0.864755	−	0.502194i	$-0.832526\pi$
$719$	3.48661	−	10.7307i	0.130029	−	0.400187i	0.994784	+	0.102007i	$0.0325264\pi$
$720$		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	0.546573	−	0.837411i	$-0.315932\pi$
$743$	−2.20658	−	1.60317i	−0.0809516	−	0.0588148i	−0.627525	+	0.778596i	$0.715932\pi$
$744$		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	−0.696456	−	0.717599i	$-0.745241\pi$
$761$	−6.32263	+	4.59366i	−0.229195	+	0.166520i	0.467261	+	0.884120i	$0.345241\pi$
$762$		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	0.999984	−	0.00570222i	$-0.00181508\pi$
$773$	5.21660	+	16.0551i	0.187628	+	0.577460i	−0.812356	+	0.583163i	$0.801815\pi$
$774$		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	0.196735	−	0.980457i	$-0.436966\pi$
$797$	−19.0544	−	13.8438i	−0.674940	−	0.490373i	−0.871675	+	0.490084i	$0.836966\pi$
$798$		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	0.813724	−	0.581252i	$-0.197437\pi$
$809$	14.5734	+	10.5882i	0.512375	+	0.372262i	−0.301349	+	0.953514i	$0.597437\pi$
$810$		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	$0.207186\pi$
$821$	−5.85105	+	18.0077i	−0.204203	+	0.628473i	−0.999745	+	0.0225744i	$0.992814\pi$
$822$		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	−0.656042	−	0.754725i	$-0.727771\pi$
$827$	−4.05437	+	2.94567i	−0.140984	+	0.102431i	0.515058	+	0.857156i	$0.327771\pi$
$828$		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	$0.260486\pi$
$839$	16.2095	+	49.8878i	0.559615	+	1.72232i	−0.123820	+	0.992305i	$0.539514\pi$
$840$		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	$-0.572541\pi$
$857$	−13.2279			−0.451856			−0.225928	+	0.974144i	$0.572541\pi$
$858$		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	0.759298	−	0.650743i	$-0.225542\pi$
$863$	11.0175	+	8.00470i	0.375041	+	0.272483i	−0.384257	+	0.923226i	$0.625542\pi$
$864$		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	$-0.331021\pi$
$881$	30.0543			1.01256			0.506278	+	0.862371i	$0.331021\pi$
$882$		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	$-0.798077\pi$
$887$	5.79362	−	17.8309i	0.194531	−	0.598704i	0.999982	−	0.00604191i	$-0.00192321\pi$
$888$		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	−0.0131503	−	0.999914i	$-0.504186\pi$
$911$	28.1835	−	20.4765i	0.933760	−	0.678417i	0.946911	+	0.321497i	$0.104186\pi$
$912$		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	−0.178904	−	0.983867i	$-0.557255\pi$
$929$	−35.6580	−	25.9071i	−1.16990	−	0.849983i	−0.990997	+	0.133884i	$0.957255\pi$
$930$		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	0.637640	−	0.770335i	$-0.279911\pi$
$941$	3.13043	+	2.27439i	0.102049	+	0.0741429i	−0.535591	+	0.844478i	$0.679911\pi$
$942$		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	$-0.153925\pi$
$947$	54.4898			1.77068			0.885340	+	0.464943i	$0.153925\pi$
$948$		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	$-0.672241\pi$
$953$	12.5162	−	38.5209i	0.405439	−	1.24781i	0.920528	−	0.390677i	$-0.127759\pi$
$954$		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	$-0.833019\pi$
$971$	−14.3246	−	44.0865i	−0.459697	−	1.41480i	0.405834	−	0.913947i	$-0.366981\pi$
$972$		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	−0.191049	−	0.981581i	$-0.561189\pi$
$977$	21.3627	−	15.5209i	0.683453	−	0.496557i	0.874501	+	0.485023i	$0.161189\pi$
$978$		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	−0.998219	−	0.0596561i	$-0.981000\pi$
$983$	−4.87781	+	15.0123i	−0.155578	+	0.478819i	0.842641	+	0.538476i	$0.181000\pi$
$984$		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.h.91.1	yes	16
3.2	odd	2		495.2.n.g.91.4	✓	16
11.2	odd	10		5445.2.a.cc.1.2		8
11.4	even	5	inner	495.2.n.h.136.1	yes	16
11.9	even	5		5445.2.a.ca.1.7		8
33.2	even	10		5445.2.a.cb.1.7		8
33.20	odd	10		5445.2.a.cd.1.2		8
33.26	odd	10		495.2.n.g.136.4	yes	16

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

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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