LMFDB - Embedded newform 637.2.e.l.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(79,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.79"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,2,4,-6,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.4406832.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 $ x^6 - x^5 + 6x^4 + 7x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$1.43310 + 2.48220i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.l.508.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.933099 + 1.61618i) q^{2} +(1.67445 + 2.90023i) q^{3} +(-0.741348 - 1.28405i) q^{4} +(-0.433099 + 0.750150i) q^{5} -6.24970 q^{6} -0.965392 q^{8} +(-4.10755 + 7.11448i) q^{9} +(-0.808249 - 1.39993i) q^{10} +(1.93310 + 3.34823i) q^{11} +(2.48270 - 4.30016i) q^{12} +1.00000 q^{13} -2.90081 q^{15} +(2.38350 - 4.12835i) q^{16} +(1.67445 + 2.90023i) q^{17} +(-7.66550 - 13.2770i) q^{18} +(2.69175 - 4.66225i) q^{19} +1.28431 q^{20} -7.21509 q^{22} +(2.62485 - 4.54637i) q^{23} +(-1.61650 - 2.79986i) q^{24} +(2.12485 + 3.68035i) q^{25} +(-0.933099 + 1.61618i) q^{26} -17.4648 q^{27} +1.69779 q^{29} +(2.70674 - 4.68821i) q^{30} +(-3.78199 - 6.55060i) q^{31} +(3.48270 + 6.03221i) q^{32} +(-6.47374 + 11.2129i) q^{33} -6.24970 q^{34} +12.1805 q^{36} +(2.41580 - 4.18428i) q^{37} +(5.02334 + 8.70068i) q^{38} +(1.67445 + 2.90023i) q^{39} +(0.418110 - 0.724188i) q^{40} -4.06922 q^{41} +4.03461 q^{43} +(2.86620 - 4.96440i) q^{44} +(-3.55795 - 6.16255i) q^{45} +(4.89849 + 8.48444i) q^{46} +(1.82555 - 3.16195i) q^{47} +15.9642 q^{48} -7.93078 q^{50} +(-5.60755 + 9.71255i) q^{51} +(-0.741348 - 1.28405i) q^{52} +(0.107546 + 0.186276i) q^{53} +(16.2964 - 28.2262i) q^{54} -3.34889 q^{55} +18.0288 q^{57} +(-1.58420 + 2.74392i) q^{58} +(1.39245 + 2.41180i) q^{59} +(2.15051 + 3.72479i) q^{60} +(-4.51730 + 7.82420i) q^{61} +14.1159 q^{62} -3.46479 q^{64} +(-0.433099 + 0.750150i) q^{65} +(-12.0813 - 20.9254i) q^{66} +(3.83159 + 6.63651i) q^{67} +(2.48270 - 4.30016i) q^{68} +17.5807 q^{69} +4.90081 q^{71} +(3.96539 - 6.86826i) q^{72} +(-7.77304 - 13.4633i) q^{73} +(4.50835 + 7.80870i) q^{74} +(-7.11590 + 12.3251i) q^{75} -7.98210 q^{76} -6.24970 q^{78} +(-4.71509 + 8.16678i) q^{79} +(2.06459 + 3.57597i) q^{80} +(-16.9212 - 29.3084i) q^{81} +(3.79698 - 6.57657i) q^{82} -4.09919 q^{83} -2.90081 q^{85} +(-3.76469 + 6.52063i) q^{86} +(2.84286 + 4.92397i) q^{87} +(-1.86620 - 3.23235i) q^{88} +(0.209055 - 0.362094i) q^{89} +13.2797 q^{90} -7.78371 q^{92} +(12.6655 - 21.9373i) q^{93} +(3.40684 + 5.90083i) q^{94} +(2.33159 + 4.03843i) q^{95} +(-11.6632 + 20.2012i) q^{96} -7.11590 q^{97} -31.7612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 5 q^{5} - 4 q^{6} - 12 q^{8} - 11 q^{9} - 14 q^{10} + 4 q^{11} + 18 q^{12} + 6 q^{13} + 4 q^{15} - 4 q^{16} + 4 q^{17} - 8 q^{18} + 7 q^{19} - 32 q^{20} - 16 q^{22} - q^{23}+ \cdots - 60 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 + 5 * q^5 - 4 * q^6 - 12 * q^8 - 11 * q^9 - 14 * q^10 + 4 * q^11 + 18 * q^12 + 6 * q^13 + 4 * q^15 - 4 * q^16 + 4 * q^17 - 8 * q^18 + 7 * q^19 - 32 * q^20 - 16 * q^22 - q^23 - 28 * q^24 - 4 * q^25 + 2 * q^26 - 44 * q^27 - 14 * q^29 + 24 * q^30 - 3 * q^31 + 24 * q^32 - 10 * q^33 - 4 * q^34 + 52 * q^36 + 10 * q^37 + 12 * q^38 + 4 * q^39 - 22 * q^40 - 12 * q^41 + 18 * q^43 + 2 * q^44 + 3 * q^45 + 28 * q^46 + 17 * q^47 - 32 * q^48 - 60 * q^50 - 20 * q^51 - 6 * q^52 - 13 * q^53 + 28 * q^54 - 8 * q^55 + 8 * q^57 - 14 * q^58 + 22 * q^59 - 42 * q^60 - 24 * q^61 + 36 * q^62 + 40 * q^64 + 5 * q^65 - 30 * q^66 + 14 * q^67 + 18 * q^68 - 4 * q^69 + 8 * q^71 + 30 * q^72 + 5 * q^73 - 8 * q^74 + 6 * q^75 + 16 * q^76 - 4 * q^78 - q^79 + 40 * q^80 - 15 * q^81 + 20 * q^82 - 46 * q^83 + 4 * q^85 - 6 * q^86 + 20 * q^87 + 4 * q^88 - 11 * q^89 + 80 * q^90 + 60 * q^92 + 38 * q^93 - 16 * q^94 + 5 * q^95 - 52 * q^96 + 6 * q^97 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.933099	+	1.61618i	−0.659801	+	1.14281i	0.320866	+	0.947124i	$0.396026\pi$
$2$	−0.933099	+	1.61618i	−0.659801	+	1.14281i	−0.980667	+	0.195684i	$0.937307\pi$
$3$	1.67445	+	2.90023i	0.966742	+	1.67445i	0.704859	+	0.709348i	$0.251010\pi$
$3$	1.67445	+	2.90023i	0.966742	+	1.67445i	0.261884	+	0.965099i	$0.415656\pi$
$4$	−0.741348	−	1.28405i	−0.370674	−	0.642026i
$5$	−0.433099	+	0.750150i	−0.193688	+	0.335477i	−0.946470	−	0.322793i	$-0.895378\pi$
$5$	−0.433099	+	0.750150i	−0.193688	+	0.335477i	0.752782	+	0.658270i	$0.228712\pi$
$6$	−6.24970			−2.55143
$7$		0			0
$7$		0			0
$8$	−0.965392			−0.341318
$9$	−4.10755	+	7.11448i	−1.36918	+	2.37149i
$10$	−0.808249	−	1.39993i	−0.255591	−	0.442696i
$11$	1.93310	+	3.34823i	0.582851	+	1.00953i	0.995140	+	0.0984746i	$0.0313963\pi$
$11$	1.93310	+	3.34823i	0.582851	+	1.00953i	−0.412288	+	0.911053i	$0.635270\pi$
$12$	2.48270	−	4.30016i	0.716693	−	1.24135i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	−2.90081			−0.748985
$16$	2.38350	−	4.12835i	0.595876	−	1.03209i
$17$	1.67445	+	2.90023i	0.406113	+	0.703408i	0.994450	−	0.105207i	$-0.0335506\pi$
$17$	1.67445	+	2.90023i	0.406113	+	0.703408i	−0.588337	+	0.808616i	$0.700217\pi$
$18$	−7.66550	−	13.2770i	−1.80677	−	3.12943i
$19$	2.69175	−	4.66225i	0.617530	−	1.06959i	−0.372405	−	0.928070i	$-0.621467\pi$
$19$	2.69175	−	4.66225i	0.617530	−	1.06959i	0.989935	−	0.141523i	$-0.0451999\pi$
$20$	1.28431			0.287180
$21$		0			0
$22$	−7.21509			−1.53826
$23$	2.62485	−	4.54637i	0.547319	−	0.947985i	−0.451138	−	0.892454i	$-0.648982\pi$
$23$	2.62485	−	4.54637i	0.547319	−	0.947985i	0.998457	−	0.0555303i	$-0.0176849\pi$
$24$	−1.61650	−	2.79986i	−0.329966	−	0.571518i
$25$	2.12485	+	3.68035i	0.424970	+	0.736070i
$26$	−0.933099	+	1.61618i	−0.182996	+	0.316958i
$27$	−17.4648			−3.36110
$28$		0			0
$29$	1.69779			0.315271			0.157636	−	0.987497i	$-0.449613\pi$
$29$	1.69779			0.315271			0.157636	+	0.987497i	$0.449613\pi$
$30$	2.70674	−	4.68821i	0.494181	−	0.855946i
$31$	−3.78199	−	6.55060i	−0.679266	−	1.17652i	−0.975202	−	0.221316i	$-0.928965\pi$
$31$	−3.78199	−	6.55060i	−0.679266	−	1.17652i	0.295936	−	0.955208i	$-0.404368\pi$
$32$	3.48270	+	6.03221i	0.615659	+	1.06635i
$33$	−6.47374	+	11.2129i	−1.12693	+	1.95191i
$34$	−6.24970			−1.07181
$35$		0			0
$36$	12.1805			2.03008
$37$	2.41580	−	4.18428i	0.397154	−	0.687891i	−0.596219	−	0.802822i	$-0.703331\pi$
$37$	2.41580	−	4.18428i	0.397154	−	0.687891i	0.993374	+	0.114930i	$0.0366645\pi$
$38$	5.02334	+	8.70068i	0.814894	+	1.41144i
$39$	1.67445	+	2.90023i	0.268126	+	0.464408i
$40$	0.418110	−	0.724188i	0.0661091	−	0.114504i
$41$	−4.06922			−0.635505			−0.317752	−	0.948174i	$-0.602928\pi$
$41$	−4.06922			−0.635505			−0.317752	+	0.948174i	$0.602928\pi$
$42$		0			0
$43$	4.03461			0.615272			0.307636	−	0.951504i	$-0.400462\pi$
$43$	4.03461			0.615272			0.307636	+	0.951504i	$0.400462\pi$
$44$	2.86620	−	4.96440i	0.432096	−	0.748412i
$45$	−3.55795	−	6.16255i	−0.530388	−	0.918659i
$46$	4.89849	+	8.48444i	0.722243	+	1.25096i
$47$	1.82555	−	3.16195i	0.266284	−	0.461218i	−0.701615	−	0.712556i	$-0.747537\pi$
$47$	1.82555	−	3.16195i	0.266284	−	0.461218i	0.967899	+	0.251338i	$0.0808707\pi$
$48$	15.9642			2.30423
$49$		0			0
$50$	−7.93078			−1.12158
$51$	−5.60755	+	9.71255i	−0.785214	+	1.36003i
$52$	−0.741348	−	1.28405i	−0.102806	−	0.178066i
$53$	0.107546	+	0.186276i	0.0147726	+	0.0255869i	0.873317	−	0.487152i	$-0.161964\pi$
$53$	0.107546	+	0.186276i	0.0147726	+	0.0255869i	−0.858545	+	0.512739i	$0.828631\pi$
$54$	16.2964	−	28.2262i	2.21766	−	3.84109i
$55$	−3.34889			−0.451565
$56$		0			0
$57$	18.0288			2.38797
$58$	−1.58420	+	2.74392i	−0.208016	+	0.360295i
$59$	1.39245	+	2.41180i	0.181282	+	0.313990i	0.942317	−	0.334721i	$-0.108642\pi$
$59$	1.39245	+	2.41180i	0.181282	+	0.313990i	−0.761035	+	0.648710i	$0.775309\pi$
$60$	2.15051	+	3.72479i	0.277629	+	0.480868i
$61$	−4.51730	+	7.82420i	−0.578382	+	1.00179i	0.417284	+	0.908776i	$0.362982\pi$
$61$	−4.51730	+	7.82420i	−0.578382	+	1.00179i	−0.995665	+	0.0930099i	$0.970351\pi$
$62$	14.1159			1.79272
$63$		0			0
$64$	−3.46479			−0.433099
$65$	−0.433099	+	0.750150i	−0.0537193	+	0.0930446i
$66$	−12.0813	−	20.9254i	−1.48710	−	2.57574i
$67$	3.83159	+	6.63651i	0.468103	+	0.810779i	0.999336	−	0.0364476i	$-0.0116042\pi$
$67$	3.83159	+	6.63651i	0.468103	+	0.810779i	−0.531232	+	0.847226i	$0.678271\pi$
$68$	2.48270	−	4.30016i	0.301071	−	0.521470i
$69$	17.5807			2.11647
$70$		0			0
$71$	4.90081			0.581619			0.290809	−	0.956781i	$-0.406075\pi$
$71$	4.90081			0.581619			0.290809	+	0.956781i	$0.406075\pi$
$72$	3.96539	−	6.86826i	0.467326	−	0.809432i
$73$	−7.77304	−	13.4633i	−0.909766	−	1.57576i	−0.814389	−	0.580319i	$-0.802928\pi$
$73$	−7.77304	−	13.4633i	−0.909766	−	1.57576i	−0.0953766	−	0.995441i	$-0.530406\pi$
$74$	4.50835	+	7.80870i	0.524085	+	0.907742i
$75$	−7.11590	+	12.3251i	−0.821673	+	1.42318i
$76$	−7.98210			−0.915609
$77$		0			0
$78$	−6.24970			−0.707639
$79$	−4.71509	+	8.16678i	−0.530489	+	0.918835i	0.468878	+	0.883263i	$0.344658\pi$
$79$	−4.71509	+	8.16678i	−0.530489	+	0.918835i	−0.999367	+	0.0355715i	$0.988675\pi$
$80$	2.06459	+	3.57597i	0.230828	+	0.399805i
$81$	−16.9212	−	29.3084i	−1.88014	−	3.25649i
$82$	3.79698	−	6.57657i	0.419307	−	0.726260i
$83$	−4.09919			−0.449945			−0.224972	−	0.974365i	$-0.572229\pi$
$83$	−4.09919			−0.449945			−0.224972	+	0.974365i	$0.572229\pi$
$84$		0			0
$85$	−2.90081			−0.314637
$86$	−3.76469	+	6.52063i	−0.405957	+	0.703138i
$87$	2.84286	+	4.92397i	0.304786	+	0.527905i
$88$	−1.86620	−	3.23235i	−0.198937	−	0.344570i
$89$	0.209055	−	0.362094i	0.0221598	−	0.0383819i	−0.854733	−	0.519068i	$-0.826279\pi$
$89$	0.209055	−	0.362094i	0.0221598	−	0.0383819i	0.876893	+	0.480686i	$0.159612\pi$
$90$	13.2797			1.39980
$91$		0			0
$92$	−7.78371			−0.811508
$93$	12.6655	−	21.9373i	1.31335	−	2.27479i
$94$	3.40684	+	5.90083i	0.351389	+	0.608624i
$95$	2.33159	+	4.03843i	0.239216	+	0.414334i
$96$	−11.6632	+	20.2012i	−1.19037	+	2.06178i
$97$	−7.11590			−0.722510			−0.361255	−	0.932467i	$-0.617652\pi$
$97$	−7.11590			−0.722510			−0.361255	+	0.932467i	$0.617652\pi$
$98$		0			0
$99$	−31.7612			−3.19212
$100$	3.15051	−	5.45684i	0.315051	−	0.545684i
$101$	7.05795	+	12.2247i	0.702292	+	1.21641i	0.967660	+	0.252259i	$0.0811733\pi$
$101$	7.05795	+	12.2247i	0.702292	+	1.21641i	−0.265368	+	0.964147i	$0.585493\pi$
$102$	−10.4648	−	18.1256i	−1.03617	−	1.79470i
$103$	8.43018	−	14.6015i	0.830651	−	1.43873i	−0.0668721	−	0.997762i	$-0.521302\pi$
$103$	8.43018	−	14.6015i	0.830651	−	1.43873i	0.897523	−	0.440968i	$-0.145365\pi$
$104$	−0.965392			−0.0946645
$105$		0			0
$106$	−0.401405			−0.0389879
$107$	−5.09024	+	8.81656i	−0.492092	+	0.852329i	−0.999959	−	0.00910710i	$-0.997101\pi$
$107$	−5.09024	+	8.81656i	−0.492092	+	0.852329i	0.507866	+	0.861436i	$0.330434\pi$
$108$	12.9475	+	22.4257i	1.24587	+	2.15791i
$109$	3.10151	+	5.37197i	0.297071	+	0.514542i	0.975464	−	0.220157i	$-0.0706570\pi$
$109$	3.10151	+	5.37197i	0.297071	+	0.514542i	−0.678394	+	0.734699i	$0.737324\pi$
$110$	3.12485	−	5.41240i	0.297943	−	0.516052i
$111$	16.1805			1.53578
$112$		0			0
$113$	10.2843			0.967466			0.483733	−	0.875216i	$-0.339281\pi$
$113$	10.2843			0.967466			0.483733	+	0.875216i	$0.339281\pi$
$114$	−16.8226	+	29.1377i	−1.57558	+	2.72899i
$115$	2.27364	+	3.93806i	0.212018	+	0.367226i
$116$	−1.25865	−	2.18005i	−0.116863	−	0.202412i
$117$	−4.10755	+	7.11448i	−0.379743	+	0.657734i
$118$	−5.19719			−0.478440
$119$		0			0
$120$	2.80041			0.255642
$121$	−1.97374	+	3.41863i	−0.179431	+	0.310784i
$122$	−8.43018	−	14.6015i	−0.763233	−	1.32196i
$123$	−6.81369	−	11.8017i	−0.614369	−	1.06412i
$124$	−5.60755	+	9.71255i	−0.503573	+	0.872213i
$125$	−8.01207			−0.716622
$126$		0			0
$127$	−1.91288			−0.169741			−0.0848704	−	0.996392i	$-0.527048\pi$
$127$	−1.91288			−0.169741			−0.0848704	+	0.996392i	$0.527048\pi$
$128$	−3.73240	+	6.46470i	−0.329900	+	0.571404i
$129$	6.75574	+	11.7013i	0.594810	+	1.03024i
$130$	−0.808249	−	1.39993i	−0.0708881	−	0.122782i
$131$	−5.08129	+	8.80105i	−0.443954	+	0.768952i	−0.997979	−	0.0635489i	$-0.979758\pi$
$131$	−5.08129	+	8.80105i	−0.443954	+	0.768952i	0.554024	+	0.832500i	$0.313091\pi$
$132$	19.1972			1.67090
$133$		0			0
$134$	−14.3010			−1.23542
$135$	7.56399	−	13.1012i	0.651004	−	1.12757i
$136$	−1.61650	−	2.79986i	−0.138614	−	0.240086i
$137$	−3.89849	−	6.75238i	−0.333071	−	0.576895i	0.650042	−	0.759899i	$-0.274751\pi$
$137$	−3.89849	−	6.75238i	−0.333071	−	0.576895i	−0.983112	+	0.183003i	$0.941418\pi$
$138$	−16.4045	+	28.4135i	−1.39645	+	2.41872i
$139$	−5.08129			−0.430989			−0.215495	−	0.976505i	$-0.569136\pi$
$139$	−5.08129			−0.430989			−0.215495	+	0.976505i	$0.569136\pi$
$140$		0			0
$141$	12.2272			1.02971
$142$	−4.57294	+	7.92056i	−0.383752	+	0.664679i
$143$	1.93310	+	3.34823i	0.161654	+	0.279993i
$144$	19.5807	+	33.9148i	1.63172	+	2.82623i
$145$	−0.735311	+	1.27360i	−0.0610642	+	0.105766i
$146$	29.0121			2.40106
$147$		0			0
$148$	−7.16378			−0.588859
$149$	1.24739	−	2.16053i	0.102190	−	0.176998i	−0.810397	−	0.585881i	$-0.800748\pi$
$149$	1.24739	−	2.16053i	0.102190	−	0.176998i	0.912587	+	0.408884i	$0.134082\pi$
$150$	−13.2797	−	23.0011i	−1.08428	−	1.87803i
$151$	1.63089	+	2.82478i	0.132720	+	0.229877i	0.924724	−	0.380638i	$-0.124296\pi$
$151$	1.63089	+	2.82478i	0.132720	+	0.229877i	−0.792004	+	0.610515i	$0.790962\pi$
$152$	−2.59859	+	4.50090i	−0.210774	+	0.365071i
$153$	−27.5115			−2.22417
$154$		0			0
$155$	6.55191			0.526262
$156$	2.48270	−	4.30016i	0.198775	−	0.344288i
$157$	0.360161	+	0.623817i	0.0287440	+	0.0497860i	0.880040	−	0.474900i	$-0.157516\pi$
$157$	0.360161	+	0.623817i	0.0287440	+	0.0497860i	−0.851296	+	0.524686i	$0.824183\pi$
$158$	−8.79930	−	15.2408i	−0.700035	−	1.21250i
$159$	−0.360161	+	0.623817i	−0.0285626	+	0.0494719i
$160$	−6.03341			−0.476983
$161$		0			0
$162$	63.1568			4.96206
$163$	−0.651106	+	1.12775i	−0.0509985	+	0.0883321i	−0.890398	−	0.455183i	$-0.849574\pi$
$163$	−0.651106	+	1.12775i	−0.0509985	+	0.0883321i	0.839399	+	0.543515i	$0.182907\pi$
$164$	3.01671	+	5.22509i	0.235565	+	0.408011i
$165$	−5.60755	−	9.71255i	−0.436547	−	0.756121i
$166$	3.82495	−	6.62501i	0.296874	−	0.514201i
$167$	16.1505			1.24976			0.624882	−	0.780719i	$-0.285147\pi$
$167$	16.1505			1.24976			0.624882	+	0.780719i	$0.285147\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	2.70674	−	4.68821i	0.207597	−	0.359569i
$171$	22.1130	+	38.3008i	1.69102	+	2.92894i
$172$	−2.99105	−	5.18065i	−0.228065	−	0.395021i
$173$	7.92415	−	13.7250i	0.602462	−	1.04349i	−0.389985	−	0.920821i	$-0.627520\pi$
$173$	7.92415	−	13.7250i	0.602462	−	1.04349i	0.992447	−	0.122673i	$-0.0391467\pi$
$174$	−10.6107			−0.804393
$175$		0			0
$176$	18.4302			1.38923
$177$	−4.66318	+	8.07687i	−0.350506	+	0.607094i
$178$	0.390138	+	0.675740i	0.0292421	+	0.0506488i
$179$	10.2324	+	17.7230i	0.764805	+	1.32468i	0.940349	+	0.340210i	$0.110498\pi$
$179$	10.2324	+	17.7230i	0.764805	+	1.32468i	−0.175544	+	0.984472i	$0.556169\pi$
$180$	−5.27536	+	9.13719i	−0.393202	+	0.681046i
$181$	−6.58189			−0.489228			−0.244614	−	0.969621i	$-0.578661\pi$
$181$	−6.58189			−0.489228			−0.244614	+	0.969621i	$0.578661\pi$
$182$		0			0
$183$	−30.2559			−2.23658
$184$	−2.53401	+	4.38903i	−0.186810	+	0.323564i
$185$	2.09256	+	3.62442i	0.153848	+	0.266472i
$186$	23.6363	+	40.9393i	1.73310	+	3.00182i
$187$	−6.47374	+	11.2129i	−0.473407	+	0.819965i
$188$	−5.41348			−0.394819
$189$		0			0
$190$	−8.70242			−0.631340
$191$	−6.37455	+	11.0410i	−0.461246	+	0.798902i	−0.999023	−	0.0441850i	$-0.985931\pi$
$191$	−6.37455	+	11.0410i	−0.461246	+	0.798902i	0.537777	+	0.843087i	$0.319264\pi$
$192$	−5.80161	−	10.0487i	−0.418695	−	0.725202i
$193$	−1.13380	−	1.96380i	−0.0816128	−	0.141358i	0.822330	−	0.569011i	$-0.192674\pi$
$193$	−1.13380	−	1.96380i	−0.0816128	−	0.141358i	−0.903943	+	0.427653i	$0.859340\pi$
$194$	6.63984	−	11.5005i	0.476713	−	0.825691i
$195$	−2.90081			−0.207731
$196$		0			0
$197$	−18.6978			−1.33216			−0.666081	−	0.745879i	$-0.732030\pi$
$197$	−18.6978			−1.33216			−0.666081	+	0.745879i	$0.732030\pi$
$198$	29.6363	−	51.3316i	2.10616	−	3.64798i
$199$	−9.95876	−	17.2491i	−0.705957	−	1.22275i	−0.966345	−	0.257250i	$-0.917184\pi$
$199$	−9.95876	−	17.2491i	−0.705957	−	1.22275i	0.260387	−	0.965504i	$-0.416150\pi$
$200$	−2.05131	−	3.55298i	−0.145050	−	0.251234i
$201$	−12.8316	+	22.2250i	−0.905071	+	1.56763i
$202$	−26.3431			−1.85349
$203$		0			0
$204$	16.6286			1.16423
$205$	1.76237	−	3.05252i	0.123090	−	0.213197i
$206$	15.7324	+	27.2493i	1.09613	+	1.89855i
$207$	21.5634	+	37.3489i	1.49876	+	2.59593i
$208$	2.38350	−	4.12835i	0.165266	−	0.286249i
$209$	20.8137			1.43971
$210$		0			0
$211$	0.645277			0.0444227			0.0222114	−	0.999753i	$-0.492929\pi$
$211$	0.645277			0.0444227			0.0222114	+	0.999753i	$0.492929\pi$
$212$	0.159458	−	0.276190i	0.0109516	−	0.0189688i
$213$	8.20614	+	14.2135i	0.562276	+	0.973890i
$214$	−9.49940	−	16.4534i	−0.649366	−	1.12473i
$215$	−1.74739	+	3.02656i	−0.119171	+	0.206410i
$216$	16.8604			1.14720
$217$		0			0
$218$	−11.5761			−0.784030
$219$	26.0311	−	45.0872i	1.75902	−	3.04671i
$220$	2.48270	+	4.30016i	0.167383	+	0.289916i
$221$	1.67445	+	2.90023i	0.112636	+	0.195090i
$222$	−15.0980	+	26.1505i	−1.01331	+	1.75511i
$223$	5.83159			0.390512			0.195256	−	0.980752i	$-0.437446\pi$
$223$	5.83159			0.390512			0.195256	+	0.980752i	$0.437446\pi$
$224$		0			0
$225$	−34.9117			−2.32745
$226$	−9.59628	+	16.6212i	−0.638335	+	1.10563i
$227$	7.86620	+	13.6247i	0.522098	+	0.904300i	0.999670	+	0.0257073i	$0.00818378\pi$
$227$	7.86620	+	13.6247i	0.522098	+	0.904300i	−0.477572	+	0.878593i	$0.658483\pi$
$228$	−13.3656	−	23.1499i	−0.885158	−	1.53314i
$229$	4.43914	−	7.68881i	0.293346	−	0.508091i	−0.681252	−	0.732049i	$-0.738564\pi$
$229$	4.43914	−	7.68881i	0.293346	−	0.508091i	0.974599	+	0.223958i	$0.0718977\pi$
$230$	−8.48613			−0.559559
$231$		0			0
$232$	−1.63903			−0.107608
$233$	5.89558	−	10.2114i	0.386232	−	0.668974i	−0.605707	−	0.795688i	$-0.707110\pi$
$233$	5.89558	−	10.2114i	0.386232	−	0.668974i	0.991939	+	0.126714i	$0.0404431\pi$
$234$	−7.66550	−	13.2770i	−0.501109	−	0.867946i
$235$	1.58129	+	2.73888i	0.103152	+	0.178665i
$236$	2.06459	−	3.57597i	0.134393	−	0.232776i
$237$	−31.5807			−2.05139
$238$		0			0
$239$	−16.0692			−1.03943			−0.519716	−	0.854339i	$-0.673962\pi$
$239$	−16.0692			−1.03943			−0.519716	+	0.854339i	$0.673962\pi$
$240$	−6.91408	+	11.9755i	−0.446302	+	0.773017i
$241$	−2.46771	−	4.27419i	−0.158959	−	0.275325i	0.775535	−	0.631305i	$-0.217480\pi$
$241$	−2.46771	−	4.27419i	−0.158959	−	0.275325i	−0.934494	+	0.355980i	$0.884147\pi$
$242$	−3.68340	−	6.37983i	−0.236778	−	0.410111i
$243$	30.4702	−	52.7760i	1.95467	−	3.38558i
$244$	13.3956			0.857564
$245$		0			0
$246$	25.4314			1.62145
$247$	2.69175	−	4.66225i	0.171272	−	0.296652i
$248$	3.65111	+	6.32390i	0.231845	+	0.401568i
$249$	−6.86388	−	11.8886i	−0.434981	−	0.753409i
$250$	7.47606	−	12.9489i	0.472828	−	0.818961i
$251$	15.2439			0.962185			0.481092	−	0.876670i	$-0.340240\pi$
$251$	15.2439			0.962185			0.481092	+	0.876670i	$0.340240\pi$
$252$		0			0
$253$	20.2964			1.27602
$254$	1.78491	−	3.09155i	0.111995	−	0.193981i
$255$	−4.85725	−	8.41300i	−0.304173	−	0.526842i
$256$	−10.4302	−	18.0656i	−0.651887	−	1.12910i
$257$	7.80825	−	13.5243i	0.487065	−	0.843622i	−0.512824	−	0.858494i	$-0.671401\pi$
$257$	7.80825	−	13.5243i	0.487065	−	0.843622i	0.999889	+	0.0148720i	$0.00473408\pi$
$258$	−25.2151			−1.56982
$259$		0			0
$260$	1.28431			0.0796494
$261$	−6.97374	+	12.0789i	−0.431664	+	0.747664i
$262$	−9.48270	−	16.4245i	−0.585843	−	1.01471i
$263$	−8.54668	−	14.8033i	−0.527011	−	0.912810i	−0.999505	−	0.0314757i	$-0.989979\pi$
$263$	−8.54668	−	14.8033i	−0.527011	−	0.912810i	0.472493	−	0.881334i	$-0.343354\pi$
$264$	6.24970	−	10.8248i	0.384642	−	0.666220i
$265$	−0.186313			−0.0114451
$266$		0			0
$267$	1.40021			0.0856913
$268$	5.68108	−	9.83992i	0.347027	−	0.601069i
$269$	−8.16841	−	14.1481i	−0.498037	−	0.862625i	0.501961	−	0.864890i	$-0.332612\pi$
$269$	−8.16841	−	14.1481i	−0.498037	−	0.862625i	−0.999997	+	0.00226550i	$0.999279\pi$
$270$	14.1159	+	24.4495i	0.859066	+	1.48795i
$271$	6.24970	−	10.8248i	0.379642	−	0.657560i	−0.611368	−	0.791347i	$-0.709380\pi$
$271$	6.24970	−	10.8248i	0.379642	−	0.657560i	0.991010	+	0.133787i	$0.0427137\pi$
$272$	15.9642			0.967971
$273$		0			0
$274$	14.5507			0.879041
$275$	−8.21509	+	14.2290i	−0.495389	+	0.858038i
$276$	−13.0334	−	22.5745i	−0.784519	−	1.35883i
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	0.907564	−	0.419914i	$-0.137940\pi$
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	−0.817438	+	0.576017i	$0.804606\pi$
$278$	4.74135	−	8.21226i	0.284367	−	0.492538i
$279$	62.1389			3.72016
$280$		0			0
$281$	0.831590			0.0496085			0.0248043	−	0.999692i	$-0.492104\pi$
$281$	0.831590			0.0496085			0.0248043	+	0.999692i	$0.492104\pi$
$282$	−11.4092	+	19.7612i	−0.679406	+	1.17676i
$283$	−5.52938	−	9.57716i	−0.328687	−	0.569303i	0.653564	−	0.756871i	$-0.273273\pi$
$283$	−5.52938	−	9.57716i	−0.328687	−	0.569303i	−0.982252	+	0.187568i	$0.939940\pi$
$284$	−3.63320	−	6.29289i	−0.215591	−	0.373414i
$285$	−7.80825	+	13.5243i	−0.462521	+	0.801109i
$286$	−7.21509			−0.426637
$287$		0			0
$288$	−57.2213			−3.37180
$289$	2.89245	−	5.00988i	0.170144	−	0.294699i
$290$	−1.37224	−	2.37678i	−0.0805804	−	0.139569i
$291$	−11.9152	−	20.6377i	−0.698481	−	1.20980i
$292$	−11.5251	+	19.9620i	−0.674453	+	1.16819i
$293$	−26.9175			−1.57254			−0.786269	−	0.617884i	$-0.787990\pi$
$293$	−26.9175			−1.57254			−0.786269	+	0.617884i	$0.787990\pi$
$294$		0			0
$295$	−2.41228			−0.140448
$296$	−2.33219	+	4.03947i	−0.135556	+	0.234789i
$297$	−33.7612	−	58.4761i	−1.95902	−	3.39313i
$298$	2.32787	+	4.03199i	0.134850	+	0.233567i
$299$	2.62485	−	4.54637i	0.151799	−	0.262924i
$300$	21.1014			1.21829
$301$		0			0
$302$	−6.08712			−0.350274
$303$	−23.6363	+	40.9393i	−1.35787	+	2.35190i
$304$	−12.8316	−	22.2250i	−0.735942	−	1.27469i
$305$	−3.91288	−	6.77731i	−0.224051	−	0.388068i
$306$	25.6709	−	44.4634i	1.46751	−	2.54180i
$307$	−15.1580			−0.865110			−0.432555	−	0.901608i	$-0.642388\pi$
$307$	−15.1580			−0.865110			−0.432555	+	0.901608i	$0.642388\pi$
$308$		0			0
$309$	56.4636			3.21210
$310$	−6.11358	+	10.5890i	−0.347228	+	0.601417i
$311$	−2.12253	−	3.67634i	−0.120358	−	0.208466i	0.799551	−	0.600598i	$-0.205071\pi$
$311$	−2.12253	−	3.67634i	−0.120358	−	0.208466i	−0.919909	+	0.392132i	$0.871738\pi$
$312$	−1.61650	−	2.79986i	−0.0915162	−	0.158511i
$313$	−8.97666	+	15.5480i	−0.507391	+	0.878827i	0.492573	+	0.870271i	$0.336057\pi$
$313$	−8.97666	+	15.5480i	−0.507391	+	0.878827i	−0.999963	+	0.00855523i	$0.997277\pi$
$314$	−1.34426			−0.0758612
$315$		0			0
$316$	13.9821			0.786554
$317$	7.63320	−	13.2211i	0.428723	−	0.742571i	−0.568037	−	0.823003i	$-0.692297\pi$
$317$	7.63320	−	13.2211i	0.428723	−	0.742571i	0.996760	+	0.0804326i	$0.0256302\pi$
$318$	−0.672132	−	1.16417i	−0.0376913	−	0.0652832i
$319$	3.28199	+	5.68458i	0.183756	+	0.318275i
$320$	1.50060	−	2.59911i	0.0838860	−	0.145295i
$321$	−34.0934			−1.90291
$322$		0			0
$323$	18.0288			1.00315
$324$	−25.0890	+	43.4555i	−1.39384	+	2.41419i
$325$	2.12485	+	3.68035i	0.117865	+	0.204149i
$326$	−1.21509	−	2.10460i	−0.0672977	−	0.116563i
$327$	−10.3866	+	17.9902i	−0.574382	+	0.994858i
$328$	3.92839			0.216909
$329$		0			0
$330$	20.9296			1.15214
$331$	−8.63320	+	14.9531i	−0.474524	+	0.821899i	−0.999574	−	0.0291717i	$-0.990713\pi$
$331$	−8.63320	+	14.9531i	−0.474524	+	0.821899i	0.525051	+	0.851071i	$0.324046\pi$
$332$	3.03893	+	5.26358i	0.166783	+	0.288876i
$333$	19.8460	+	34.3742i	1.08755	+	1.88370i
$334$	−15.0700	+	26.1020i	−0.824595	+	1.42824i
$335$	−6.63783			−0.362664
$336$		0			0
$337$	−25.5415			−1.39133			−0.695666	−	0.718366i	$-0.744891\pi$
$337$	−25.5415			−1.39133			−0.695666	+	0.718366i	$0.744891\pi$
$338$	−0.933099	+	1.61618i	−0.0507539	+	0.0879083i
$339$	17.2205	+	29.8268i	0.935291	+	1.61997i
$340$	2.15051	+	3.72479i	0.116628	+	0.202005i
$341$	14.6219	−	25.3259i	0.791822	−	1.37148i
$342$	−82.5344			−4.46295
$343$		0			0
$344$	−3.89498			−0.210003
$345$	−7.61418	+	13.1882i	−0.409934	+	0.710026i
$346$	14.7880	+	25.6136i	0.795009	+	1.37700i
$347$	6.31429	+	10.9367i	0.338969	+	0.587111i	0.984239	−	0.176843i	$-0.0565886\pi$
$347$	6.31429	+	10.9367i	0.338969	+	0.587111i	−0.645270	+	0.763954i	$0.723255\pi$
$348$	4.21509	−	7.30075i	0.225953	−	0.391362i
$349$	35.6394			1.90774			0.953868	−	0.300226i	$-0.0970622\pi$
$349$	35.6394			1.90774			0.953868	+	0.300226i	$0.0970622\pi$
$350$		0			0
$351$	−17.4648			−0.932202
$352$	−13.4648	+	23.3217i	−0.717676	+	1.24305i
$353$	−2.70674	−	4.68821i	−0.144065	−	0.249528i	0.784959	−	0.619548i	$-0.212684\pi$
$353$	−2.70674	−	4.68821i	−0.144065	−	0.249528i	−0.929024	+	0.370020i	$0.879351\pi$
$354$	−8.70242	−	15.0730i	−0.462528	−	0.801123i
$355$	−2.12253	+	3.67634i	−0.112652	+	0.195120i
$356$	−0.619931			−0.0328563
$357$		0			0
$358$	−38.1914			−2.01848
$359$	9.41580	−	16.3086i	0.496947	−	0.860737i	−0.503047	−	0.864259i	$-0.667788\pi$
$359$	9.41580	−	16.3086i	0.496947	−	0.860737i	0.999994	+	0.00352211i	$0.00112113\pi$
$360$	3.43482	+	5.94928i	0.181031	+	0.313554i
$361$	−4.99105	−	8.64475i	−0.262687	−	0.454987i
$362$	6.14156	−	10.6375i	0.322793	−	0.559094i
$363$	−13.2197			−0.693856
$364$		0			0
$365$	13.4660			0.704842
$366$	28.2318	−	48.8989i	1.47570	−	2.55599i
$367$	11.5753	+	20.0489i	0.604223	+	1.04655i	0.992174	+	0.124865i	$0.0398498\pi$
$367$	11.5753	+	20.0489i	0.604223	+	1.04655i	−0.387950	+	0.921680i	$0.626817\pi$
$368$	−12.5127	−	21.6726i	−0.652268	−	1.12976i
$369$	16.7145	−	28.9504i	0.870122	−	1.50710i
$370$	−7.81025			−0.406036
$371$		0			0
$372$	−37.5582			−1.94730
$373$	16.5896	−	28.7341i	0.858979	−	1.48780i	−0.0139245	−	0.999903i	$-0.504432\pi$
$373$	16.5896	−	28.7341i	0.858979	−	1.48780i	0.872904	−	0.487893i	$-0.162234\pi$
$374$	−12.0813	−	20.9254i	−0.624709	−	1.08203i
$375$	−13.4158	−	23.2368i	−0.692789	−	1.19995i
$376$	−1.76237	+	3.05252i	−0.0908875	+	0.157422i
$377$	1.69779			0.0874406
$378$		0			0
$379$	37.7853			1.94090			0.970451	−	0.241299i	$-0.0775733\pi$
$379$	37.7853			1.94090			0.970451	+	0.241299i	$0.0775733\pi$
$380$	3.45704	−	5.98777i	0.177342	−	0.307166i
$381$	−3.20302	−	5.54779i	−0.164096	−	0.284222i
$382$	−11.8962	−	20.6048i	−0.608661	−	1.05423i
$383$	−0.115899	+	0.200743i	−0.00592215	+	0.0102575i	−0.868971	−	0.494862i	$-0.835218\pi$
$383$	−0.115899	+	0.200743i	−0.00592215	+	0.0102575i	0.863049	+	0.505120i	$0.168552\pi$
$384$	−24.9988			−1.27571
$385$		0			0
$386$	4.23180			0.215393
$387$	−16.5723	+	28.7041i	−0.842419	+	1.45911i
$388$	5.27536	+	9.13719i	0.267816	+	0.463870i
$389$	−4.67676	−	8.10039i	−0.237121	−	0.410706i	0.722766	−	0.691093i	$-0.242871\pi$
$389$	−4.67676	−	8.10039i	−0.237121	−	0.410706i	−0.959887	+	0.280387i	$0.909537\pi$
$390$	2.70674	−	4.68821i	0.137061	−	0.237397i
$391$	17.5807			0.889094
$392$		0			0
$393$	−34.0334			−1.71676
$394$	17.4469	−	30.2189i	0.878962	−	1.52241i
$395$	−4.08420	−	7.07405i	−0.205499	−	0.355934i
$396$	23.5461	+	40.7830i	1.18324	+	2.04942i
$397$	−4.87224	+	8.43896i	−0.244530	+	0.423539i	−0.962000	−	0.273051i	$-0.911967\pi$
$397$	−4.87224	+	8.43896i	−0.244530	+	0.423539i	0.717469	+	0.696590i	$0.245300\pi$
$398$	37.1700			1.86317
$399$		0			0
$400$	20.2583			1.01292
$401$	−4.86620	+	8.42850i	−0.243006	+	0.420899i	−0.961569	−	0.274563i	$-0.911467\pi$
$401$	−4.86620	+	8.42850i	−0.243006	+	0.420899i	0.718563	+	0.695462i	$0.244800\pi$
$402$	−23.9463	−	41.4762i	−1.19433	−	2.06864i
$403$	−3.78199	−	6.55060i	−0.188395	−	0.326309i
$404$	10.4648	−	18.1256i	0.520643	−	0.901780i
$405$	29.3143			1.45664
$406$		0			0
$407$	18.6799			0.925928
$408$	5.41348	−	9.37642i	0.268007	−	0.464202i
$409$	6.18652	+	10.7154i	0.305904	+	0.529841i	0.977462	−	0.211111i	$-0.0677081\pi$
$409$	6.18652	+	10.7154i	0.305904	+	0.529841i	−0.671558	+	0.740952i	$0.734375\pi$
$410$	3.28894	+	5.69661i	0.162429	+	0.281336i
$411$	13.0556	−	22.6130i	0.643987	−	1.11542i
$412$	−24.9988			−1.23160
$413$		0			0
$414$	−80.4831			−3.95553
$415$	1.77536	−	3.07501i	0.0871489	−	0.150946i
$416$	3.48270	+	6.03221i	0.170753	+	0.295753i
$417$	−8.50835	−	14.7369i	−0.416656	−	0.721669i
$418$	−19.4212	+	33.6386i	−0.949924	+	1.64532i
$419$	−21.1054			−1.03107			−0.515534	−	0.856869i	$-0.672406\pi$
$419$	−21.1054			−1.03107			−0.515534	+	0.856869i	$0.672406\pi$
$420$		0			0
$421$	23.2618			1.13371			0.566855	−	0.823818i	$-0.308160\pi$
$421$	23.2618			1.13371			0.566855	+	0.823818i	$0.308160\pi$
$422$	−0.602108	+	1.04288i	−0.0293102	+	0.0507667i
$423$	14.9971	+	25.9757i	0.729183	+	1.26298i
$424$	−0.103824	−	0.179829i	−0.00504215	−	0.00873326i
$425$	−7.11590	+	12.3251i	−0.345172	+	0.597855i
$426$	−30.6286			−1.48396
$427$		0			0
$428$	15.0946			0.729623
$429$	−6.47374	+	11.2129i	−0.312555	+	0.541362i
$430$	−3.26097	−	5.64816i	−0.157258	−	0.272379i
$431$	8.49477	+	14.7134i	0.409179	+	0.708718i	0.994798	−	0.101868i	$-0.0324819\pi$
$431$	8.49477	+	14.7134i	0.409179	+	0.708718i	−0.585619	+	0.810586i	$0.699149\pi$
$432$	−41.6274	+	72.1007i	−2.00280	+	3.46895i
$433$	30.8604			1.48305			0.741527	−	0.670923i	$-0.234102\pi$
$433$	30.8604			1.48305			0.741527	+	0.670923i	$0.234102\pi$
$434$		0			0
$435$	−4.92496			−0.236134
$436$	4.59859	−	7.96500i	0.220233	−	0.381454i
$437$	−14.1309	−	24.4754i	−0.675972	−	1.17082i
$438$	48.5792	+	84.1416i	2.32120	+	4.02044i
$439$	9.59859	−	16.6253i	0.458116	−	0.793480i	−0.540745	−	0.841186i	$-0.681858\pi$
$439$	9.59859	−	16.6253i	0.458116	−	0.793480i	0.998861	+	0.0477062i	$0.0151911\pi$
$440$	3.23300			0.154127
$441$		0			0
$442$	−6.24970			−0.297268
$443$	17.1888	−	29.7719i	0.816666	−	1.41451i	−0.0914589	−	0.995809i	$-0.529153\pi$
$443$	17.1888	−	29.7719i	0.816666	−	1.41451i	0.908125	−	0.418699i	$-0.137514\pi$
$444$	−11.9954	−	20.7766i	−0.569275	−	0.986013i
$445$	0.181083	+	0.313645i	0.00858417	+	0.0148682i
$446$	−5.44145	+	9.42487i	−0.257660	+	0.446281i
$447$	8.35472			0.395165
$448$		0			0
$449$	29.6274			1.39820			0.699101	−	0.715023i	$-0.253584\pi$
$449$	29.6274			1.39820			0.699101	+	0.715023i	$0.253584\pi$
$450$	32.5761	−	56.4234i	1.53565	−	2.65982i
$451$	−7.86620	−	13.6247i	−0.370405	−	0.641560i
$452$	−7.62425	−	13.2056i	−0.358615	−	0.621139i
$453$	−5.46167	+	9.45989i	−0.256612	+	0.444464i
$454$	−29.3598			−1.37792
$455$		0			0
$456$	−17.4048			−0.815056
$457$	8.51962	−	14.7564i	0.398531	−	0.690276i	−0.595014	−	0.803715i	$-0.702853\pi$
$457$	8.51962	−	14.7564i	0.398531	−	0.690276i	0.993545	+	0.113439i	$0.0361868\pi$
$458$	8.28431	+	14.3488i	0.387100	+	0.670477i
$459$	−29.2439	−	50.6519i	−1.36499	−	2.36423i
$460$	3.37112	−	5.83895i	0.157179	−	0.272242i
$461$	−15.1280			−0.704580			−0.352290	−	0.935891i	$-0.614597\pi$
$461$	−15.1280			−0.704580			−0.352290	+	0.935891i	$0.614597\pi$
$462$		0			0
$463$	26.1221			1.21400			0.607000	−	0.794702i	$-0.292373\pi$
$463$	26.1221			1.21400			0.607000	+	0.794702i	$0.292373\pi$
$464$	4.04668	−	7.00906i	0.187863	−	0.325387i
$465$	10.9708	+	19.0020i	0.508760	+	0.881198i
$466$	11.0023	+	19.0566i	0.509672	+	0.882779i
$467$	11.4594	−	19.8482i	0.530276	−	0.918464i	−0.469100	−	0.883145i	$-0.655422\pi$
$467$	11.4594	−	19.8482i	0.530276	−	0.918464i	0.999376	−	0.0353196i	$-0.0112449\pi$
$468$	12.1805			0.563043
$469$		0			0
$470$	−5.90200			−0.272239
$471$	−1.20614	+	2.08910i	−0.0555760	+	0.0962605i
$472$	−1.34426	−	2.32833i	−0.0618747	−	0.107170i
$473$	7.79930	+	13.5088i	0.358612	+	0.621134i
$474$	29.4679	−	51.0399i	1.35351	−	2.34434i
$475$	22.8783			1.04973
$476$		0			0
$477$	−1.76700			−0.0809056
$478$	14.9942	−	25.9707i	0.685817	−	1.18787i
$479$	17.5957	+	30.4766i	0.803967	+	1.39251i	0.916986	+	0.398919i	$0.130615\pi$
$479$	17.5957	+	30.4766i	0.803967	+	1.39251i	−0.113019	+	0.993593i	$0.536052\pi$
$480$	−10.1026	−	17.4983i	−0.461120	−	0.798683i
$481$	2.41580	−	4.18428i	0.110151	−	0.190787i
$482$	9.21046			0.419525
$483$		0			0
$484$	5.85293			0.266042
$485$	3.08189	−	5.33799i	0.139941	−	0.242386i
$486$	56.8635	+	98.4905i	2.57938	+	4.46762i
$487$	14.1505	+	24.5094i	0.641221	+	1.11063i	0.985161	+	0.171635i	$0.0549050\pi$
$487$	14.1505	+	24.5094i	0.641221	+	1.11063i	−0.343940	+	0.938992i	$0.611762\pi$
$488$	4.36097	−	7.55342i	0.197412	−	0.341927i
$489$	−4.36097			−0.197210
$490$		0			0
$491$	8.24970			0.372304			0.186152	−	0.982521i	$-0.440398\pi$
$491$	8.24970			0.372304			0.186152	+	0.982521i	$0.440398\pi$
$492$	−10.1026	+	17.4983i	−0.455462	+	0.788883i
$493$	2.84286	+	4.92397i	0.128036	+	0.221765i
$494$	5.02334	+	8.70068i	0.226011	+	0.391462i
$495$	13.7557	−	23.8256i	0.618274	−	1.07088i
$496$	−36.0576			−1.61903
$497$		0			0
$498$	25.6187			1.14800
$499$	8.36328	−	14.4856i	0.374392	−	0.648466i	−0.615844	−	0.787868i	$-0.711185\pi$
$499$	8.36328	−	14.4856i	0.374392	−	0.648466i	0.990236	+	0.139402i	$0.0445181\pi$
$500$	5.93974	+	10.2879i	0.265633	+	0.460090i
$501$	27.0432	+	46.8401i	1.20820	+	2.09266i
$502$	−14.2240	+	24.6368i	−0.634850	+	1.09959i
$503$	−21.2213			−0.946213			−0.473106	−	0.881005i	$-0.656867\pi$
$503$	−21.2213			−0.946213			−0.473106	+	0.881005i	$0.656867\pi$
$504$		0			0
$505$	−12.2272			−0.544102
$506$	−18.9385	+	32.8025i	−0.841921	+	1.45825i
$507$	1.67445	+	2.90023i	0.0743648	+	0.128804i
$508$	1.41811	+	2.45624i	0.0629185	+	0.108978i
$509$	−20.3024	+	35.1648i	−0.899889	+	1.55865i	−0.0722543	+	0.997386i	$0.523019\pi$
$509$	−20.3024	+	35.1648i	−0.899889	+	1.55865i	−0.827635	+	0.561267i	$0.810314\pi$
$510$	18.1292			0.802773
$511$		0			0
$512$	24.0000			1.06066
$513$	−47.0109	+	81.4252i	−2.07558	+	3.59501i
$514$	14.5717	+	25.2390i	0.642732	+	1.11324i
$515$	7.30221	+	12.6478i	0.321774	+	0.557329i
$516$	10.0167	−	17.3494i	0.440961	−	0.763767i
$517$	14.1159			0.620817
$518$		0			0
$519$	53.0743			2.32970
$520$	0.418110	−	0.724188i	0.0183354	−	0.0317578i
$521$	1.73240	+	3.00060i	0.0758977	+	0.131459i	0.901476	−	0.432828i	$-0.142484\pi$
$521$	1.73240	+	3.00060i	0.0758977	+	0.131459i	−0.825579	+	0.564287i	$0.809151\pi$
$522$	−13.0144	−	22.5416i	−0.569624	−	0.986618i
$523$	2.78491	−	4.82360i	0.121776	−	0.210921i	−0.798692	−	0.601740i	$-0.794475\pi$
$523$	2.78491	−	4.82360i	0.121776	−	0.210921i	0.920468	+	0.390818i	$0.127808\pi$
$524$	15.0680			0.658249
$525$		0			0
$526$	31.8996			1.39089
$527$	12.6655	−	21.9373i	0.551718	−	0.955603i
$528$	30.8604	+	53.4517i	1.34303	+	2.32619i
$529$	−2.27968	−	3.94852i	−0.0991164	−	0.171675i
$530$	0.173848	−	0.301114i	0.00755149	−	0.0130796i
$531$	−22.8783			−0.992832
$532$		0			0
$533$	−4.06922			−0.176257
$534$	−1.30653	+	2.26298i	−0.0565392	+	0.0979287i
$535$	−4.40916	−	7.63689i	−0.190625	−	0.330171i
$536$	−3.69899	−	6.40683i	−0.159772	−	0.276733i
$537$	−34.2672	+	59.3526i	−1.47874	+	2.56125i
$538$	30.4877			1.31442
$539$		0			0
$540$	−22.4302			−0.965241
$541$	−12.1182	+	20.9894i	−0.521003	+	0.902403i	0.478699	+	0.877979i	$0.341109\pi$
$541$	−12.1182	+	20.9894i	−0.521003	+	0.902403i	−0.999702	+	0.0244241i	$0.992225\pi$
$542$	11.6632	+	20.2012i	0.500976	+	0.867717i
$543$	−11.0210	−	19.0890i	−0.472957	−	0.819186i
$544$	−11.6632	+	20.2012i	−0.500055	+	0.866120i
$545$	−5.37304			−0.230156
$546$		0			0
$547$	15.7733			0.674416			0.337208	−	0.941430i	$-0.390518\pi$
$547$	15.7733			0.674416			0.337208	+	0.941430i	$0.390518\pi$
$548$	−5.78028	+	10.0117i	−0.246921	+	0.427680i
$549$	−37.1101	−	64.2765i	−1.58382	−	2.74326i
$550$	−15.3310	−	26.5541i	−0.653716	−	1.13227i
$551$	4.57002	−	7.91551i	0.194690	−	0.337212i
$552$	−16.9723			−0.722387
$553$		0			0
$554$	−5.59859			−0.237861
$555$	−7.00775	+	12.1378i	−0.297463	+	0.515220i
$556$	3.76700	+	6.52464i	0.159757	+	0.276707i
$557$	8.61067	+	14.9141i	0.364846	+	0.631931i	0.988751	−	0.149568i	$-0.0477884\pi$
$557$	8.61067	+	14.9141i	0.364846	+	0.631931i	−0.623906	+	0.781500i	$0.714455\pi$
$558$	−57.9817	+	100.427i	−2.45456	+	4.25143i
$559$	4.03461			0.170646
$560$		0			0
$561$	−43.3598			−1.83065
$562$	−0.775956	+	1.34400i	−0.0327317	+	0.0566930i
$563$	−7.67989	−	13.3020i	−0.323669	−	0.560610i	0.657573	−	0.753390i	$-0.271583\pi$
$563$	−7.67989	−	13.3020i	−0.323669	−	0.560610i	−0.981242	+	0.192780i	$0.938250\pi$
$564$	−9.06459	−	15.7003i	−0.381688	−	0.661103i
$565$	−4.45413	+	7.71477i	−0.187386	+	0.324563i
$566$	20.6378			0.867473
$567$		0			0
$568$	−4.73120			−0.198517
$569$	−11.8610	+	20.5438i	−0.497238	+	0.861241i	−0.999995	−	0.00318672i	$-0.998986\pi$
$569$	−11.8610	+	20.5438i	−0.497238	+	0.861241i	0.502757	+	0.864428i	$0.332319\pi$
$570$	−14.5717	−	25.2390i	−0.610343	−	1.05715i
$571$	13.6595	+	23.6589i	0.571631	+	0.990093i	0.996399	+	0.0847910i	$0.0270223\pi$
$571$	13.6595	+	23.6589i	0.571631	+	0.990093i	−0.424768	+	0.905302i	$0.639644\pi$
$572$	2.86620	−	4.96440i	0.119842	−	0.207572i
$573$	−42.6954			−1.78363
$574$		0			0
$575$	22.3097			0.930377
$576$	14.2318	−	24.6502i	0.592992	−	1.02709i
$577$	−11.6332	−	20.1493i	−0.484297	−	0.838826i	0.515541	−	0.856865i	$-0.327591\pi$
$577$	−11.6332	−	20.1493i	−0.484297	−	0.838826i	−0.999837	+	0.0180388i	$0.994258\pi$
$578$	5.39789	+	9.34942i	0.224523	+	0.388885i
$579$	3.79698	−	6.57657i	0.157797	−	0.273313i
$580$	2.18048			0.0905397
$581$		0			0
$582$	44.4722			1.84343
$583$	−0.415795	+	0.720178i	−0.0172205	+	0.0298267i
$584$	7.50403	+	12.9974i	0.310519	+	0.537835i
$585$	−3.55795	−	6.16255i	−0.147103	−	0.254790i
$586$	25.1167	−	43.5034i	1.03756	−	1.79711i
$587$	−45.7266			−1.88734			−0.943669	−	0.330892i	$-0.892651\pi$
$587$	−45.7266			−1.88734			−0.943669	+	0.330892i	$0.892651\pi$
$588$		0			0
$589$	−40.7207			−1.67787
$590$	2.25090	−	3.89867i	0.0926680	−	0.160506i
$591$	−31.3085	−	54.2278i	−1.28786	−	2.23064i
$592$	−11.5161	−	19.9465i	−0.473309	−	0.819795i
$593$	14.6949	−	25.4523i	0.603446	−	1.04520i	−0.388849	−	0.921302i	$-0.627127\pi$
$593$	14.6949	−	25.4523i	0.603446	−	1.04520i	0.992295	−	0.123898i	$-0.0395395\pi$
$594$	126.010			5.17026
$595$		0			0
$596$	−3.69899			−0.151516
$597$	33.3508	−	57.7653i	1.36496	−	2.36418i
$598$	4.89849	+	8.48444i	0.200314	+	0.346954i
$599$	−11.0294	−	19.1034i	−0.450648	−	0.780546i	0.547778	−	0.836624i	$-0.315474\pi$
$599$	−11.0294	−	19.1034i	−0.450648	−	0.780546i	−0.998426	+	0.0560780i	$0.982140\pi$
$600$	6.86963	−	11.8986i	0.280452	−	0.485756i
$601$	30.8604			1.25882			0.629410	−	0.777073i	$-0.283296\pi$
$601$	30.8604			1.25882			0.629410	+	0.777073i	$0.283296\pi$
$602$		0			0
$603$	−62.9537			−2.56367
$604$	2.41811	−	4.18829i	0.0983915	−	0.170419i
$605$	−1.70965	−	2.96121i	−0.0695073	−	0.120390i
$606$	−44.1101	−	76.4009i	−1.79185	−	3.10357i
$607$	−18.2431	+	31.5979i	−0.740463	+	1.28252i	0.211821	+	0.977308i	$0.432060\pi$
$607$	−18.2431	+	31.5979i	−0.740463	+	1.28252i	−0.952285	+	0.305211i	$0.901273\pi$
$608$	37.4982			1.52075
$609$		0			0
$610$	14.6044			0.591316
$611$	1.82555	−	3.16195i	0.0738540	−	0.127919i
$612$	20.3956	+	35.3262i	0.824442	+	1.42798i
$613$	−14.4994	−	25.1137i	−0.585625	−	1.01433i	−0.994797	−	0.101875i	$-0.967516\pi$
$613$	−14.4994	−	25.1137i	−0.585625	−	1.01433i	0.409172	−	0.912457i	$-0.365818\pi$
$614$	14.1439	−	24.4979i	0.570800	−	0.988655i
$615$	11.8040			0.475984
$616$		0			0
$617$	−41.6515			−1.67683			−0.838414	−	0.545035i	$-0.816517\pi$
$617$	−41.6515			−1.67683			−0.838414	+	0.545035i	$0.816517\pi$
$618$	−52.6861	+	91.2551i	−2.11935	+	3.67082i
$619$	−6.24970	−	10.8248i	−0.251197	−	0.435085i	0.712659	−	0.701511i	$-0.247491\pi$
$619$	−6.24970	−	10.8248i	−0.251197	−	0.435085i	−0.963856	+	0.266425i	$0.914157\pi$
$620$	−4.85725	−	8.41300i	−0.195072	−	0.337874i
$621$	−45.8425	+	79.4015i	−1.83959	+	3.18627i
$622$	7.92214			0.317649
$623$		0			0
$624$	15.9642			0.639079
$625$	−7.15423	+	12.3915i	−0.286169	+	0.495660i
$626$	−16.7522	−	29.0157i	−0.669554	−	1.15970i
$627$	34.8514	+	60.3644i	1.39183	+	2.41072i
$628$	0.534009	−	0.924931i	0.0213093	−	0.0369088i
$629$	16.1805			0.645158
$630$		0			0
$631$	−35.5582			−1.41555			−0.707774	−	0.706439i	$-0.750300\pi$
$631$	−35.5582			−1.41555			−0.707774	+	0.706439i	$0.750300\pi$
$632$	4.55191	−	7.88414i	0.181065	−	0.313614i
$633$	1.08048	+	1.87145i	0.0429453	+	0.0743835i
$634$	14.2451	+	24.6732i	0.565744	+	0.979897i
$635$	0.828467	−	1.43495i	0.0328767	−	0.0569441i
$636$	1.06802			0.0423497
$637$		0			0
$638$	−12.2497			−0.484970
$639$	−20.1303	+	34.8667i	−0.796342	+	1.37930i
$640$	−3.23300	−	5.59971i	−0.127795	−	0.221348i
$641$	−0.680484	−	1.17863i	−0.0268775	−	0.0465532i	0.852274	−	0.523096i	$-0.175223\pi$
$641$	−0.680484	−	1.17863i	−0.0268775	−	0.0465532i	−0.879151	+	0.476543i	$0.841890\pi$
$642$	31.8125	−	55.1008i	1.25554	−	2.17466i
$643$	12.1867			0.480598			0.240299	−	0.970699i	$-0.422755\pi$
$643$	12.1867			0.480598			0.240299	+	0.970699i	$0.422755\pi$
$644$		0			0
$645$	−11.7036			−0.460829
$646$	−16.8226	+	29.1377i	−0.661878	+	1.14641i
$647$	1.86076	+	3.22293i	0.0731540	+	0.126706i	0.900282	−	0.435307i	$-0.143360\pi$
$647$	1.86076	+	3.22293i	0.0731540	+	0.126706i	−0.827128	+	0.562014i	$0.810027\pi$
$648$	16.3356	+	28.2941i	0.641724	+	1.11150i
$649$	−5.38350	+	9.32450i	−0.211321	+	0.366019i
$650$	−7.93078			−0.311071
$651$		0			0
$652$	1.93078			0.0756153
$653$	22.5294	−	39.0220i	0.881643	−	1.52705i	0.0321288	−	0.999484i	$-0.489771\pi$
$653$	22.5294	−	39.0220i	0.881643	−	1.52705i	0.849514	−	0.527566i	$-0.176895\pi$
$654$	−19.3835	−	33.5732i	−0.757955	−	1.31282i
$655$	−4.40141	−	7.62346i	−0.171977	−	0.297873i
$656$	−9.69899	+	16.7991i	−0.378682	+	0.655896i
$657$	127.713			4.98254
$658$		0			0
$659$	5.37887			0.209531			0.104766	−	0.994497i	$-0.466591\pi$
$659$	5.37887			0.209531			0.104766	+	0.994497i	$0.466591\pi$
$660$	−8.31429	+	14.4008i	−0.323633	+	0.560549i
$661$	21.2468	+	36.8005i	0.826404	+	1.43137i	0.900841	+	0.434148i	$0.142951\pi$
$661$	21.2468	+	36.8005i	0.826404	+	1.43137i	−0.0744372	+	0.997226i	$0.523716\pi$
$662$	−16.1113	−	27.9055i	−0.626182	−	1.08458i
$663$	−5.60755	+	9.71255i	−0.217779	+	0.377204i
$664$	3.95733			0.153574
$665$		0			0
$666$	−74.0731			−2.87027
$667$	4.45644	−	7.71878i	0.172554	−	0.298872i
$668$	−11.9731	−	20.7381i	−0.463255	−	0.802381i
$669$	9.76469	+	16.9129i	0.377525	+	0.653892i
$670$	6.19376	−	10.7279i	0.239286	−	0.414455i
$671$	−34.9296			−1.34844
$672$		0			0
$673$	−37.3765			−1.44076			−0.720379	−	0.693581i	$-0.756032\pi$
$673$	−37.3765			−1.44076			−0.720379	+	0.693581i	$0.756032\pi$
$674$	23.8327	−	41.2795i	0.918002	−	1.59003i
$675$	−37.1101	−	64.2765i	−1.42837	−	2.47400i
$676$	−0.741348	−	1.28405i	−0.0285134	−	0.0493866i
$677$	21.7378	−	37.6510i	0.835453	−	1.44705i	−0.0582083	−	0.998304i	$-0.518539\pi$
$677$	21.7378	−	37.6510i	0.835453	−	1.44705i	0.893661	−	0.448742i	$-0.148128\pi$
$678$	−64.2738			−2.46842
$679$		0			0
$680$	2.80041			0.107391
$681$	−26.3431	+	45.6275i	−1.00947	+	1.74845i
$682$	27.2874	+	47.2632i	1.04489	+	1.80980i
$683$	−15.6978	−	27.1894i	−0.600659	−	1.04037i	−0.992721	−	0.120434i	$-0.961572\pi$
$683$	−15.6978	−	27.1894i	−0.600659	−	1.04037i	0.392062	−	0.919939i	$-0.371762\pi$
$684$	32.7868	−	56.7885i	1.25364	−	2.17136i
$685$	6.75373			0.258047
$686$		0			0
$687$	29.7324			1.13436
$688$	9.61650	−	16.6563i	0.366626	−	0.635014i
$689$	0.107546	+	0.186276i	0.00409719	+	0.00709653i
$690$	−14.2096	−	24.6117i	−0.540949	−	0.936952i
$691$	−6.72053	+	11.6403i	−0.255661	+	0.442818i	−0.965075	−	0.261974i	$-0.915626\pi$
$691$	−6.72053	+	11.6403i	−0.255661	+	0.442818i	0.709414	+	0.704792i	$0.248960\pi$
$692$	−23.4982			−0.893268
$693$		0			0
$694$	−23.5674			−0.894607
$695$	2.20070	−	3.81173i	0.0834774	−	0.144587i
$696$	−2.74447	−	4.75356i	−0.104029	−	0.180183i
$697$	−6.81369	−	11.8017i	−0.258087	−	0.447019i
$698$	−33.2551	+	57.5996i	−1.25873	+	2.18018i
$699$	39.4873			1.49355
$700$		0			0
$701$	−28.0346			−1.05885			−0.529426	−	0.848356i	$-0.677593\pi$
$701$	−28.0346			−1.05885			−0.529426	+	0.848356i	$0.677593\pi$
$702$	16.2964	−	28.2262i	0.615067	−	1.06533i
$703$	−13.0054	−	22.5261i	−0.490509	−	0.849587i
$704$	−6.69779	−	11.6009i	−0.252432	−	0.437226i
$705$	−5.29558	+	9.17221i	−0.199443	+	0.345445i
$706$	10.1026			0.380217
$707$		0			0
$708$	13.8282			0.519694
$709$	20.1424	−	34.8876i	0.756462	−	1.31023i	−0.188182	−	0.982134i	$-0.560259\pi$
$709$	20.1424	−	34.8876i	0.756462	−	1.31023i	0.944644	−	0.328097i	$-0.106407\pi$
$710$	−3.96107	−	6.86078i	−0.148656	−	0.257480i
$711$	−38.7349	−	67.0909i	−1.45267	−	2.51610i
$712$	−0.201820	+	0.349563i	−0.00756353	+	0.0131004i
$713$	−39.7087			−1.48710
$714$		0			0
$715$	−3.34889			−0.125242
$716$	15.1715	−	26.2779i	0.566987	−	0.982050i
$717$	−26.9071	−	46.6044i	−1.00486	−	1.74047i
$718$	17.5717	+	30.4351i	0.655772	+	1.13583i
$719$	−8.37224	+	14.5011i	−0.312232	+	0.540801i	−0.978845	−	0.204602i	$-0.934410\pi$
$719$	−8.37224	+	14.5011i	−0.312232	+	0.540801i	0.666613	+	0.745404i	$0.267743\pi$
$720$	−33.9215			−1.26418
$721$		0			0
$722$	18.6286			0.693284
$723$	8.26409	−	14.3138i	0.307345	−	0.532337i
$724$	4.87947	+	8.45149i	0.181344	+	0.314097i
$725$	3.60755	+	6.24845i	0.133981	+	0.232062i
$726$	12.3353	−	21.3654i	0.457806	−	0.792944i
$727$	51.4982			1.90996			0.954981	−	0.296666i	$-0.0958748\pi$
$727$	51.4982			1.90996			0.954981	+	0.296666i	$0.0958748\pi$
$728$		0			0
$729$	102.556			3.79836
$730$	−12.5651	+	21.7634i	−0.465055	+	0.805500i
$731$	6.75574	+	11.7013i	0.249870	+	0.432788i
$732$	22.4302	+	38.8502i	0.829043	+	1.43595i
$733$	−16.9158	+	29.2990i	−0.624799	+	1.08218i	0.363781	+	0.931485i	$0.381486\pi$
$733$	−16.9158	+	29.2990i	−0.624799	+	1.08218i	−0.988580	+	0.150699i	$0.951848\pi$
$734$	−43.2034			−1.59467
$735$		0			0
$736$	36.5662			1.34785
$737$	−14.8137	+	25.6581i	−0.545669	+	0.945127i
$738$	31.1926	+	54.0271i	1.14821	+	1.98876i
$739$	−10.3345	−	17.8999i	−0.380161	−	0.658458i	0.610924	−	0.791689i	$-0.290798\pi$
$739$	−10.3345	−	17.8999i	−0.380161	−	0.658458i	−0.991085	+	0.133231i	$0.957465\pi$
$740$	3.10263	−	5.37391i	0.114055	−	0.197549i
$741$	18.0288			0.662304
$742$		0			0
$743$	−29.6966			−1.08946			−0.544731	−	0.838611i	$-0.683368\pi$
$743$	−29.6966			−1.08946			−0.544731	+	0.838611i	$0.683368\pi$
$744$	−12.2272	+	21.1781i	−0.448270	+	0.776426i
$745$	1.08048	+	1.87145i	0.0395858	+	0.0685647i
$746$	30.9596	+	53.6235i	1.13351	+	1.96330i
$747$	16.8376	−	29.1636i	0.616057	−	1.06704i
$748$	19.1972			0.701919
$749$		0			0
$750$	50.0731			1.82841
$751$	6.01148	−	10.4122i	0.219362	−	0.379946i	−0.735251	−	0.677795i	$-0.762936\pi$
$751$	6.01148	−	10.4122i	0.219362	−	0.379946i	0.954613	+	0.297849i	$0.0962691\pi$
$752$	−8.70242	−	15.0730i	−0.317345	−	0.549657i
$753$	25.5251	+	44.2107i	0.930185	+	1.61113i
$754$	−1.58420	+	2.74392i	−0.0576933	+	0.0999278i
$755$	−2.82534			−0.102825
$756$		0			0
$757$	−30.2906			−1.10093			−0.550464	−	0.834859i	$-0.685549\pi$
$757$	−30.2906			−1.10093			−0.550464	+	0.834859i	$0.685549\pi$
$758$	−35.2575	+	61.0677i	−1.28061	+	2.21808i
$759$	33.9852	+	58.8641i	1.23359	+	2.13663i
$760$	−2.25090	−	3.89867i	−0.0816487	−	0.141420i
$761$	−22.9792	+	39.8011i	−0.832995	+	1.44279i	0.0626580	+	0.998035i	$0.480042\pi$
$761$	−22.9792	+	39.8011i	−0.832995	+	1.44279i	−0.895653	+	0.444754i	$0.853291\pi$
$762$	11.9549			0.433082
$763$		0			0
$764$	18.9030			0.683888
$765$	11.9152	−	20.6377i	0.430795	−	0.746159i
$766$	−0.216290	−	0.374626i	−0.00781488	−	0.0135358i
$767$	1.39245	+	2.41180i	0.0502786	+	0.0870851i
$768$	34.9296	−	60.4998i	1.26041	−	2.18310i
$769$	−4.03924			−0.145659			−0.0728293	−	0.997344i	$-0.523203\pi$
$769$	−4.03924			−0.145659			−0.0728293	+	0.997344i	$0.523203\pi$
$770$		0			0
$771$	52.2980			1.88347
$772$	−1.68108	+	2.91172i	−0.0605035	+	0.104795i
$773$	18.0588	+	31.2787i	0.649528	+	1.12502i	0.983236	+	0.182339i	$0.0583670\pi$
$773$	18.0588	+	31.2787i	0.649528	+	1.12502i	−0.333707	+	0.942677i	$0.608300\pi$
$774$	−30.9273	−	53.5676i	−1.11166	−	1.92545i
$775$	16.0723	−	27.8381i	0.577335	−	0.999974i
$776$	6.86963			0.246605
$777$		0			0
$778$	17.4555			0.625811
$779$	−10.9533	+	18.9717i	−0.392443	+	0.679732i
$780$	2.15051	+	3.72479i	0.0770005	+	0.133369i
$781$	9.47374	+	16.4090i	0.338997	+	0.587160i
$782$	−16.4045	+	28.4135i	−0.586625	+	1.01606i
$783$	−29.6515			−1.05966
$784$		0			0
$785$	−0.623942			−0.0222694
$786$	31.7565	−	55.0040i	1.13272	−	1.96193i
$787$	−12.9325	−	22.3997i	−0.460994	−	0.798465i	0.538017	−	0.842934i	$-0.319174\pi$
$787$	−12.9325	−	22.3997i	−0.460994	−	0.798465i	−0.999011	+	0.0444693i	$0.985840\pi$
$788$	13.8616	+	24.0089i	0.493798	+	0.855283i
$789$	28.6219	−	49.5746i	1.01897	−	1.76490i
$790$	15.2439			0.542353
$791$		0			0
$792$	30.6620			1.08953
$793$	−4.51730	+	7.82420i	−0.160414	+	0.277845i
$794$	−9.09256	−	15.7488i	−0.322683	−	0.558903i
$795$	−0.311971	−	0.540349i	−0.0110645	−	0.0191642i
$796$	−14.7658	+	25.5751i	−0.523360	+	0.906486i
$797$	0.291753			0.0103344			0.00516720	−	0.999987i	$-0.498355\pi$
$797$	0.291753			0.0103344			0.00516720	+	0.999987i	$0.498355\pi$
$798$		0			0
$799$	12.2272			0.432566
$800$	−14.8004	+	25.6351i	−0.523274	+	0.906337i
$801$	1.71741	+	2.97464i	0.0606816	+	0.105104i
$802$	−9.08129	−	15.7293i	−0.320672	−	0.555419i
$803$	30.0521	−	52.0518i	1.06052	−	1.83687i
$804$	38.0507			1.34194
$805$		0			0
$806$	14.1159			0.497211
$807$	27.3551	−	47.3805i	0.962947	−	1.66787i
$808$	−6.81369	−	11.8017i	−0.239705	−	0.415181i
$809$	2.62797	+	4.55178i	0.0923946	+	0.160032i	0.908518	−	0.417845i	$-0.137215\pi$
$809$	2.62797	+	4.55178i	0.0923946	+	0.160032i	−0.816124	+	0.577877i	$0.803881\pi$
$810$	−27.3531	+	47.3770i	−0.961091	+	1.66466i
$811$	37.8499			1.32909			0.664545	−	0.747248i	$-0.268625\pi$
$811$	37.8499			1.32909			0.664545	+	0.747248i	$0.268625\pi$
$812$		0			0
$813$	41.8592			1.46807
$814$	−17.4302	+	30.1900i	−0.610928	+	1.05816i
$815$	−0.563987	−	0.976854i	−0.0197556	−	0.0342177i
$816$	26.7312	+	46.2998i	0.935779	+	1.62082i
$817$	10.8602	−	18.8104i	0.379949	−	0.658091i
$818$	−23.0906			−0.807342
$819$		0			0
$820$	−5.22613			−0.182504
$821$	12.8604	−	22.2748i	0.448830	−	0.777396i	−0.549480	−	0.835507i	$-0.685174\pi$
$821$	12.8604	−	22.2748i	0.448830	−	0.777396i	0.998310	+	0.0581104i	$0.0185075\pi$
$822$	24.3644	+	42.2004i	0.849806	+	1.47191i
$823$	9.74135	+	16.8725i	0.339562	+	0.588139i	0.984350	−	0.176222i	$-0.0563878\pi$
$823$	9.74135	+	16.8725i	0.339562	+	0.588139i	−0.644788	+	0.764361i	$0.723054\pi$
$824$	−8.13843	+	14.0962i	−0.283516	+	0.491064i
$825$	−55.0230			−1.91565
$826$		0			0
$827$	−32.0934			−1.11600			−0.557998	−	0.829842i	$-0.688430\pi$
$827$	−32.0934			−1.11600			−0.557998	+	0.829842i	$0.688430\pi$
$828$	31.9719	−	55.3770i	1.11110	−	1.92449i
$829$	−1.94668	−	3.37175i	−0.0676110	−	0.117106i	0.830238	−	0.557409i	$-0.188204\pi$
$829$	−1.94668	−	3.37175i	−0.0676110	−	0.117106i	−0.897849	+	0.440303i	$0.854871\pi$
$830$	3.31317	+	5.73858i	0.115002	+	0.199189i
$831$	−5.02334	+	8.70068i	−0.174258	+	0.301823i
$832$	−3.46479			−0.120120
$833$		0			0
$834$	31.7565			1.09964
$835$	−6.99477	+	12.1153i	−0.242064	+	0.419267i
$836$	−15.4302	−	26.7259i	−0.533664	−	0.924333i
$837$	66.0517	+	114.405i	2.28308	+	3.95441i
$838$	19.6935	−	34.1101i	0.680300	−	1.17831i
$839$	−41.8592			−1.44514			−0.722570	−	0.691298i	$-0.757039\pi$
$839$	−41.8592			−1.44514			−0.722570	+	0.691298i	$0.757039\pi$
$840$		0			0
$841$	−26.1175			−0.900604
$842$	−21.7055	+	37.5951i	−0.748022	+	1.29561i
$843$	1.39245	+	2.41180i	0.0479587	+	0.0830668i
$844$	−0.478375	−	0.828570i	−0.0164664	−	0.0285206i
$845$	−0.433099	+	0.750150i	−0.0148991	+	0.0258059i
$846$	−55.9751			−1.92446
$847$		0			0
$848$	1.02535			0.0352106
$849$	18.5173	−	32.0729i	0.635512	−	1.10074i
$850$	−13.2797	−	23.0011i	−0.455489	−	0.788930i
$851$	−12.6822	−	21.9662i	−0.434740	−	0.752992i
$852$	12.1672	−	21.0742i	0.416842	−	0.721991i
$853$	−1.70242			−0.0582897			−0.0291449	−	0.999575i	$-0.509278\pi$
$853$	−1.70242			−0.0582897			−0.0291449	+	0.999575i	$0.509278\pi$
$854$		0			0
$855$	−38.3085			−1.31012
$856$	4.91408	−	8.51143i	0.167960	−	0.290915i
$857$	−4.78954	−	8.29572i	−0.163608	−	0.283377i	0.772552	−	0.634951i	$-0.218980\pi$
$857$	−4.78954	−	8.29572i	−0.163608	−	0.283377i	−0.936160	+	0.351574i	$0.885646\pi$
$858$	−12.0813	−	20.9254i	−0.412448	−	0.714382i
$859$	3.08712	−	5.34705i	0.105331	−	0.182439i	−0.808542	−	0.588438i	$-0.799743\pi$
$859$	3.08712	−	5.34705i	0.105331	−	0.182439i	0.913873	+	0.405999i	$0.133076\pi$
$860$	5.18168			0.176694
$861$		0			0
$862$	−31.7059			−1.07991
$863$	−12.4302	+	21.5297i	−0.423128	+	0.732880i	−0.996244	−	0.0865949i	$-0.972401\pi$
$863$	−12.4302	+	21.5297i	−0.423128	+	0.732880i	0.573115	+	0.819475i	$0.305735\pi$
$864$	−60.8246	−	105.351i	−2.06929	−	3.58412i
$865$	6.86388	+	11.8886i	0.233379	+	0.404224i
$866$	−28.7958	+	49.8758i	−0.978521	+	1.69485i
$867$	19.3730			0.657943
$868$		0			0
$869$	−36.4590			−1.23679
$870$	4.59547	−	7.95959i	0.155801	−	0.269855i
$871$	3.83159	+	6.63651i	0.129828	+	0.224870i
$872$	−2.99417	−	5.18606i	−0.101395	−	0.175622i
$873$	29.2289	−	50.6259i	0.989248	−	1.71343i
$874$	52.7421			1.78403
$875$		0			0
$876$	−77.1924			−2.60809
$877$	−12.8281	+	22.2189i	−0.433173	+	0.750278i	−0.997145	−	0.0755161i	$-0.975940\pi$
$877$	−12.8281	+	22.2189i	−0.433173	+	0.750278i	0.563971	+	0.825794i	$0.309273\pi$
$878$	17.9129	+	31.0260i	0.604530	+	1.04708i
$879$	−45.0719	−	78.0669i	−1.52024	−	2.63313i
$880$	−7.98210	+	13.8254i	−0.269076	+	0.466054i
$881$	−25.6632			−0.864615			−0.432307	−	0.901726i	$-0.642300\pi$
$881$	−25.6632			−0.864615			−0.432307	+	0.901726i	$0.642300\pi$
$882$		0			0
$883$	48.6682			1.63782			0.818908	−	0.573925i	$-0.194580\pi$
$883$	48.6682			1.63782			0.818908	+	0.573925i	$0.194580\pi$
$884$	2.48270	−	4.30016i	0.0835021	−	0.144630i
$885$	−4.03924	−	6.99617i	−0.135778	−	0.235174i
$886$	32.0778	+	55.5603i	1.07767	+	1.86659i
$887$	−8.76237	+	15.1769i	−0.294212	+	0.509590i	−0.974801	−	0.223075i	$-0.928390\pi$
$887$	−8.76237	+	15.1769i	−0.294212	+	0.509590i	0.680589	+	0.732665i	$0.261724\pi$
$888$	−15.6205			−0.524190
$889$		0			0
$890$	−0.675874			−0.0226554
$891$	65.4208	−	113.312i	2.19168	−	3.79610i
$892$	−4.32324	−	7.48807i	−0.144753	−	0.250719i
$893$	−9.82787	−	17.0224i	−0.328877	−	0.569632i
$894$	−7.79578	+	13.5027i	−0.260730	+	0.451598i
$895$	−17.7266			−0.592534
$896$		0			0
$897$	17.5807			0.587002
$898$	−27.6453	+	47.8830i	−0.922535	+	1.59788i
$899$	−6.42102	−	11.1215i	−0.214153	−	0.370924i
$900$	25.8817	+	44.8284i	0.862724	+	1.49428i
$901$	−0.360161	+	0.623817i	−0.0119987	+	0.0207824i
$902$	29.3598			0.977573
$903$		0			0
$904$	−9.92839			−0.330213
$905$	2.85061	−	4.93740i	0.0947575	−	0.164125i
$906$	−10.1926	−	17.6540i	−0.338625	−	0.586516i
$907$	−28.6882	−	49.6895i	−0.952577	−	1.64991i	−0.739817	−	0.672808i	$-0.765088\pi$
$907$	−28.6882	−	49.6895i	−0.952577	−	1.64991i	−0.212760	−	0.977104i	$-0.568245\pi$
$908$	11.6632	−	20.2012i	0.387056	−	0.670401i
$909$	−115.963			−3.84626
$910$		0			0
$911$	7.87203			0.260812			0.130406	−	0.991461i	$-0.458372\pi$
$911$	7.87203			0.260812			0.130406	+	0.991461i	$0.458372\pi$
$912$	42.9716	−	74.4291i	1.42293	−	2.46459i
$913$	−7.92415	−	13.7250i	−0.262251	−	0.454232i
$914$	15.8993	+	27.5384i	0.525902	+	0.910889i
$915$	13.1038	−	22.6965i	0.433199	−	0.750323i
$916$	−13.1638			−0.434944
$917$		0			0
$918$	109.150			3.60248
$919$	23.5115	−	40.7231i	0.775572	−	1.34333i	−0.158900	−	0.987295i	$-0.550795\pi$
$919$	23.5115	−	40.7231i	0.775572	−	1.34333i	0.934472	−	0.356036i	$-0.115872\pi$
$920$	−2.19495	−	3.80177i	−0.0723655	−	0.125341i
$921$	−25.3812	−	43.9615i	−0.836339	−	1.44858i
$922$	14.1159	−	24.4495i	0.464882	−	0.805200i
$923$	4.90081			0.161312
$924$		0			0
$925$	20.5328			0.675115
$926$	−24.3746	+	42.2180i	−0.800997	+	1.38737i
$927$	69.2547	+	119.953i	2.27462	+	3.93977i
$928$	5.91288	+	10.2414i	0.194100	+	0.336191i
$929$	14.1309	−	24.4754i	0.463619	−	0.803012i	−0.535519	−	0.844523i	$-0.679884\pi$
$929$	14.1309	−	24.4754i	0.463619	−	0.803012i	0.999138	+	0.0415111i	$0.0132172\pi$
$930$	−40.9475			−1.34272
$931$		0			0
$932$	−17.4827			−0.572665
$933$	7.10815	−	12.3117i	0.232710	−	0.403066i
$934$	21.3854	+	37.0406i	0.699753	+	1.21201i
$935$	−5.60755	−	9.71255i	−0.183386	−	0.317635i
$936$	3.96539	−	6.86826i	0.129613	−	0.224496i
$937$	−8.83784			−0.288720			−0.144360	−	0.989525i	$-0.546112\pi$
$937$	−8.83784			−0.288720			−0.144360	+	0.989525i	$0.546112\pi$
$938$		0			0
$939$	−60.1238			−1.96206
$940$	2.34457	−	4.06092i	0.0764716	−	0.132453i
$941$	−21.3927	−	37.0532i	−0.697381	−	1.20790i	−0.969371	−	0.245599i	$-0.921015\pi$
$941$	−21.3927	−	37.0532i	−0.697381	−	1.20790i	0.271991	−	0.962300i	$-0.412318\pi$
$942$	−2.25090	−	3.89867i	−0.0733382	−	0.127026i
$943$	−10.6811	+	18.5002i	−0.347824	+	0.602449i
$944$	13.2757			0.432086
$945$		0			0
$946$	−29.1101			−0.946450
$947$	−14.6107	+	25.3064i	−0.474783	+	0.822348i	−0.999583	−	0.0288774i	$-0.990807\pi$
$947$	−14.6107	+	25.3064i	−0.474783	+	0.822348i	0.524800	+	0.851226i	$0.324140\pi$
$948$	23.4123	+	40.5513i	0.760396	+	1.31704i
$949$	−7.77304	−	13.4633i	−0.252324	−	0.437037i
$950$	−21.3477	+	36.9753i	−0.692611	+	1.19964i
$951$	51.1256			1.65786
$952$		0			0
$953$	3.66198			0.118623			0.0593116	−	0.998240i	$-0.481109\pi$
$953$	3.66198			0.118623			0.0593116	+	0.998240i	$0.481109\pi$
$954$	1.64879	−	2.85579i	0.0533816	−	0.0924596i
$955$	−5.52162	−	9.56373i	−0.178676	−	0.309475i
$956$	11.9129	+	20.6337i	0.385290	+	0.667342i
$957$	−10.9910	+	19.0371i	−0.355290	+	0.615381i
$958$	−65.6741			−2.12183
$959$		0			0
$960$	10.0507			0.324385
$961$	−13.1069	+	22.7019i	−0.422805	+	0.732319i
$962$	4.50835	+	7.80870i	0.145355	+	0.251762i
$963$	−41.8168	−	72.4288i	−1.34753	−	2.33399i
$964$	−3.65886	+	6.33733i	−0.117844	+	0.204112i
$965$	1.96419			0.0632296
$966$		0			0
$967$	−30.0288			−0.965660			−0.482830	−	0.875714i	$-0.660391\pi$
$967$	−30.0288			−0.965660			−0.482830	+	0.875714i	$0.660391\pi$
$968$	1.90544	−	3.30031i	0.0612431	−	0.106076i
$969$	30.1882	+	52.2876i	0.969786	+	1.67972i
$970$	5.75142	+	9.96175i	0.184667	+	0.319852i
$971$	−2.45272	+	4.24823i	−0.0787115	+	0.136332i	−0.902694	−	0.430283i	$-0.858414\pi$
$971$	−2.45272	+	4.24823i	−0.0787115	+	0.136332i	0.823983	+	0.566615i	$0.191747\pi$
$972$	−90.3562			−2.89818
$973$		0			0
$974$	−52.8153			−1.69231
$975$	−7.11590	+	12.3251i	−0.227891	+	0.394719i
$976$	21.5340	+	37.2980i	0.689287	+	1.19388i
$977$	−11.3166	−	19.6009i	−0.362050	−	0.627089i	0.626248	−	0.779624i	$-0.284590\pi$
$977$	−11.3166	−	19.6009i	−0.362050	−	0.627089i	−0.988298	+	0.152535i	$0.951256\pi$
$978$	4.06922	−	7.04809i	0.130119	−	0.225373i
$979$	1.61650			0.0516635
$980$		0			0
$981$	−50.9584			−1.62698
$982$	−7.69779	+	13.3330i	−0.245646	+	0.425472i
$983$	28.7026	+	49.7144i	0.915472	+	1.58564i	0.806209	+	0.591630i	$0.201516\pi$
$983$	28.7026	+	49.7144i	0.915472	+	1.58564i	0.109262	+	0.994013i	$0.465151\pi$
$984$	6.57788	+	11.3932i	0.209695	+	0.363203i
$985$	8.09800	−	14.0261i	0.258024	−	0.446910i
$986$	−10.6107			−0.337913
$987$		0			0
$988$	−7.98210			−0.253944
$989$	10.5902	−	18.3428i	0.336750	−	0.583268i
$990$	25.6709	+	44.4634i	0.815876	+	1.41314i
$991$	−15.5896	−	27.0021i	−0.495221	−	0.857749i	0.504763	−	0.863258i	$-0.331580\pi$
$991$	−15.5896	−	27.0021i	−0.495221	−	0.857749i	−0.999985	+	0.00550916i	$0.998246\pi$
$992$	26.3431	−	45.6275i	0.836393	−	1.44868i
$993$	−57.8234			−1.83497
$994$		0			0
$995$	17.2525			0.546941
$996$	−10.1771	+	17.6272i	−0.322472	+	0.558538i
$997$	18.0288	+	31.2268i	0.570977	+	0.988961i	0.996466	+	0.0839978i	$0.0267689\pi$
$997$	18.0288	+	31.2268i	0.570977	+	0.988961i	−0.425489	+	0.904964i	$0.639898\pi$
$998$	15.6075	+	27.0331i	0.494048	+	0.855717i
$999$	−42.1914	+	73.0776i	−1.33488	+	2.31207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.l.79.1		6
7.2	even	3		637.2.a.h.1.3	✓	3
7.3	odd	6		637.2.e.k.508.1		6
7.4	even	3	inner	637.2.e.l.508.1		6
7.5	odd	6		637.2.a.i.1.3	yes	3
7.6	odd	2		637.2.e.k.79.1		6
21.2	odd	6		5733.2.a.be.1.1		3
21.5	even	6		5733.2.a.bd.1.1		3
91.12	odd	6		8281.2.a.bk.1.1		3
91.51	even	6		8281.2.a.bh.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.h.1.3	✓	3	7.2	even	3
637.2.a.i.1.3	yes	3	7.5	odd	6
637.2.e.k.79.1		6	7.6	odd	2
637.2.e.k.508.1		6	7.3	odd	6
637.2.e.l.79.1		6	1.1	even	1	trivial
637.2.e.l.508.1		6	7.4	even	3	inner
5733.2.a.bd.1.1		3	21.5	even	6
5733.2.a.be.1.1		3	21.2	odd	6
8281.2.a.bh.1.1		3	91.51	even	6
8281.2.a.bk.1.1		3	91.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.933099 + 1.61618i) q^{2} +(1.67445 + 2.90023i) q^{3} +(-0.741348 - 1.28405i) q^{4} +(-0.433099 + 0.750150i) q^{5} -6.24970 q^{6} -0.965392 q^{8} +(-4.10755 + 7.11448i) q^{9} +(-0.808249 - 1.39993i) q^{10} +(1.93310 + 3.34823i) q^{11} +(2.48270 - 4.30016i) q^{12} +1.00000 q^{13} -2.90081 q^{15} +(2.38350 - 4.12835i) q^{16} +(1.67445 + 2.90023i) q^{17} +(-7.66550 - 13.2770i) q^{18} +(2.69175 - 4.66225i) q^{19} +1.28431 q^{20} -7.21509 q^{22} +(2.62485 - 4.54637i) q^{23} +(-1.61650 - 2.79986i) q^{24} +(2.12485 + 3.68035i) q^{25} +(-0.933099 + 1.61618i) q^{26} -17.4648 q^{27} +1.69779 q^{29} +(2.70674 - 4.68821i) q^{30} +(-3.78199 - 6.55060i) q^{31} +(3.48270 + 6.03221i) q^{32} +(-6.47374 + 11.2129i) q^{33} -6.24970 q^{34} +12.1805 q^{36} +(2.41580 - 4.18428i) q^{37} +(5.02334 + 8.70068i) q^{38} +(1.67445 + 2.90023i) q^{39} +(0.418110 - 0.724188i) q^{40} -4.06922 q^{41} +4.03461 q^{43} +(2.86620 - 4.96440i) q^{44} +(-3.55795 - 6.16255i) q^{45} +(4.89849 + 8.48444i) q^{46} +(1.82555 - 3.16195i) q^{47} +15.9642 q^{48} -7.93078 q^{50} +(-5.60755 + 9.71255i) q^{51} +(-0.741348 - 1.28405i) q^{52} +(0.107546 + 0.186276i) q^{53} +(16.2964 - 28.2262i) q^{54} -3.34889 q^{55} +18.0288 q^{57} +(-1.58420 + 2.74392i) q^{58} +(1.39245 + 2.41180i) q^{59} +(2.15051 + 3.72479i) q^{60} +(-4.51730 + 7.82420i) q^{61} +14.1159 q^{62} -3.46479 q^{64} +(-0.433099 + 0.750150i) q^{65} +(-12.0813 - 20.9254i) q^{66} +(3.83159 + 6.63651i) q^{67} +(2.48270 - 4.30016i) q^{68} +17.5807 q^{69} +4.90081 q^{71} +(3.96539 - 6.86826i) q^{72} +(-7.77304 - 13.4633i) q^{73} +(4.50835 + 7.80870i) q^{74} +(-7.11590 + 12.3251i) q^{75} -7.98210 q^{76} -6.24970 q^{78} +(-4.71509 + 8.16678i) q^{79} +(2.06459 + 3.57597i) q^{80} +(-16.9212 - 29.3084i) q^{81} +(3.79698 - 6.57657i) q^{82} -4.09919 q^{83} -2.90081 q^{85} +(-3.76469 + 6.52063i) q^{86} +(2.84286 + 4.92397i) q^{87} +(-1.86620 - 3.23235i) q^{88} +(0.209055 - 0.362094i) q^{89} +13.2797 q^{90} -7.78371 q^{92} +(12.6655 - 21.9373i) q^{93} +(3.40684 + 5.90083i) q^{94} +(2.33159 + 4.03843i) q^{95} +(-11.6632 + 20.2012i) q^{96} -7.11590 q^{97} -31.7612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 5 q^{5} - 4 q^{6} - 12 q^{8} - 11 q^{9} - 14 q^{10} + 4 q^{11} + 18 q^{12} + 6 q^{13} + 4 q^{15} - 4 q^{16} + 4 q^{17} - 8 q^{18} + 7 q^{19} - 32 q^{20} - 16 q^{22} - q^{23}+ \cdots - 60 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 + 5 * q^5 - 4 * q^6 - 12 * q^8 - 11 * q^9 - 14 * q^10 + 4 * q^11 + 18 * q^12 + 6 * q^13 + 4 * q^15 - 4 * q^16 + 4 * q^17 - 8 * q^18 + 7 * q^19 - 32 * q^20 - 16 * q^22 - q^23 - 28 * q^24 - 4 * q^25 + 2 * q^26 - 44 * q^27 - 14 * q^29 + 24 * q^30 - 3 * q^31 + 24 * q^32 - 10 * q^33 - 4 * q^34 + 52 * q^36 + 10 * q^37 + 12 * q^38 + 4 * q^39 - 22 * q^40 - 12 * q^41 + 18 * q^43 + 2 * q^44 + 3 * q^45 + 28 * q^46 + 17 * q^47 - 32 * q^48 - 60 * q^50 - 20 * q^51 - 6 * q^52 - 13 * q^53 + 28 * q^54 - 8 * q^55 + 8 * q^57 - 14 * q^58 + 22 * q^59 - 42 * q^60 - 24 * q^61 + 36 * q^62 + 40 * q^64 + 5 * q^65 - 30 * q^66 + 14 * q^67 + 18 * q^68 - 4 * q^69 + 8 * q^71 + 30 * q^72 + 5 * q^73 - 8 * q^74 + 6 * q^75 + 16 * q^76 - 4 * q^78 - q^79 + 40 * q^80 - 15 * q^81 + 20 * q^82 - 46 * q^83 + 4 * q^85 - 6 * q^86 + 20 * q^87 + 4 * q^88 - 11 * q^89 + 80 * q^90 + 60 * q^92 + 38 * q^93 - 16 * q^94 + 5 * q^95 - 52 * q^96 + 6 * q^97 - 60 * q^99

Introduction

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