LMFDB - Embedded newform 567.2.ba.a.341.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(143,567)] 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("567.143"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			341.2
Character	$\chi$	$=$	567.341
Dual form			567.2.ba.a.143.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61592 - 1.92578i) q^{2} +(-0.750127 + 4.25418i) q^{4} +(2.10349 + 1.76504i) q^{5} +(-0.122508 + 2.64291i) q^{7} +(5.05050 - 2.91591i) q^{8} -6.90302i q^{10} +(-2.69072 - 3.20668i) q^{11} +(-0.0398496 - 0.109486i) q^{13} +(5.28762 - 4.03481i) q^{14} +(-5.65800 - 2.05934i) q^{16} -5.14689 q^{17} +5.21844i q^{19} +(-9.08669 + 7.62463i) q^{20} +(-1.82736 + 10.3635i) q^{22} +(2.56763 + 7.05452i) q^{23} +(0.441075 + 2.50146i) q^{25} +(-0.146452 + 0.253662i) q^{26} +(-11.1515 - 2.50369i) q^{28} +(-1.21597 + 3.34086i) q^{29} +(-0.305335 - 0.0538389i) q^{31} +(1.18784 + 3.26355i) q^{32} +(8.31695 + 9.91175i) q^{34} +(-4.92254 + 5.34312i) q^{35} +(-0.959970 - 1.66272i) q^{37} +(10.0496 - 8.43258i) q^{38} +(15.7704 + 2.78075i) q^{40} +(-6.29347 + 2.29063i) q^{41} +(0.411100 + 2.33146i) q^{43} +(15.6602 - 9.04140i) q^{44} +(9.43633 - 16.3442i) q^{46} +(0.876823 + 4.97271i) q^{47} +(-6.96998 - 0.647559i) q^{49} +(4.10452 - 4.89157i) q^{50} +(0.495665 - 0.0873991i) q^{52} +(3.76047 - 2.17111i) q^{53} -11.4945i q^{55} +(7.08776 + 13.7053i) q^{56} +(8.39867 - 3.05687i) q^{58} +(-9.84174 + 3.58210i) q^{59} +(-1.13841 + 0.200732i) q^{61} +(0.389715 + 0.675007i) q^{62} +(-1.65570 + 2.86775i) q^{64} +(0.109424 - 0.300639i) q^{65} +(8.49204 + 7.12567i) q^{67} +(3.86082 - 21.8958i) q^{68} +(18.2441 + 0.845678i) q^{70} +(5.47124 + 3.15882i) q^{71} +(-2.23588 - 1.29089i) q^{73} +(-1.65079 + 4.53550i) q^{74} +(-22.2002 - 3.91449i) q^{76} +(8.80461 - 6.71850i) q^{77} +(12.0963 - 10.1500i) q^{79} +(-8.26674 - 14.3184i) q^{80} +(14.5810 + 8.41833i) q^{82} +(10.6778 + 3.88640i) q^{83} +(-10.8264 - 9.08446i) q^{85} +(3.82557 - 4.55914i) q^{86} +(-22.9399 - 8.34943i) q^{88} +0.913664 q^{89} +(0.294244 - 0.0919061i) q^{91} +(-31.9372 + 5.63140i) q^{92} +(8.15946 - 9.72406i) q^{94} +(-9.21076 + 10.9770i) q^{95} +(-5.88114 + 1.03700i) q^{97} +(10.0159 + 14.4690i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.61592	−	1.92578i	−1.14263	−	1.36173i	−0.922379	−	0.386286i	$-0.873758\pi$
$2$	−1.61592	−	1.92578i	−1.14263	−	1.36173i	−0.220248	−	0.975444i	$-0.570687\pi$
$3$		0			0
$3$		0			0
$4$	−0.750127	+	4.25418i	−0.375063	+	2.12709i
$5$	2.10349	+	1.76504i	0.940711	+	0.789350i	0.977709	−	0.209965i	$-0.0673351\pi$
$5$	2.10349	+	1.76504i	0.940711	+	0.789350i	−0.0369981	+	0.999315i	$0.511780\pi$
$6$		0			0
$7$	−0.122508	+	2.64291i	−0.0463038	+	0.998927i
$7$	−0.122508	+	2.64291i	−0.0463038	+	0.998927i
$8$	5.05050	−	2.91591i	1.78562	−	1.03093i
$9$		0			0
$10$		−	6.90302i		−	2.18293i
$11$	−2.69072	−	3.20668i	−0.811283	−	0.966850i	0.188601	−	0.982054i	$-0.439605\pi$
$11$	−2.69072	−	3.20668i	−0.811283	−	0.966850i	−0.999884	+	0.0152039i	$0.995160\pi$
$12$		0			0
$13$	−0.0398496	−	0.109486i	−0.0110523	−	0.0303659i	0.934044	−	0.357158i	$-0.116254\pi$
$13$	−0.0398496	−	0.109486i	−0.0110523	−	0.0303659i	−0.945096	+	0.326793i	$0.894032\pi$
$14$	5.28762	−	4.03481i	1.41318	−	1.07835i
$15$		0			0
$16$	−5.65800	−	2.05934i	−1.41450	−	0.514836i
$17$	−5.14689			−1.24830			−0.624152	−	0.781303i	$-0.714555\pi$
$17$	−5.14689			−1.24830			−0.624152	+	0.781303i	$0.714555\pi$
$18$		0			0
$19$			5.21844i			1.19719i	0.801051	+	0.598597i	$0.204275\pi$
$19$			5.21844i			1.19719i	−0.801051	+	0.598597i	$0.795725\pi$
$20$	−9.08669	+	7.62463i	−2.03184	+	1.70492i
$21$		0			0
$22$	−1.82736	+	10.3635i	−0.389594	+	2.20950i
$23$	2.56763	+	7.05452i	0.535389	+	1.47097i	0.852575	+	0.522605i	$0.175040\pi$
$23$	2.56763	+	7.05452i	0.535389	+	1.47097i	−0.317186	+	0.948363i	$0.602738\pi$
$24$		0			0
$25$	0.441075	+	2.50146i	0.0882150	+	0.500292i
$26$	−0.146452	+	0.253662i	−0.0287215	+	0.0497472i
$27$		0			0
$28$	−11.1515	−	2.50369i	−2.10744	−	0.473153i
$29$	−1.21597	+	3.34086i	−0.225801	+	0.620383i	−0.999920	−	0.0126573i	$-0.995971\pi$
$29$	−1.21597	+	3.34086i	−0.225801	+	0.620383i	0.774119	+	0.633040i	$0.218193\pi$
$30$		0			0
$31$	−0.305335	−	0.0538389i	−0.0548398	−	0.00966974i	0.146161	−	0.989261i	$-0.453308\pi$
$31$	−0.305335	−	0.0538389i	−0.0548398	−	0.00966974i	−0.201001	+	0.979591i	$0.564419\pi$
$32$	1.18784	+	3.26355i	0.209982	+	0.576920i
$33$		0			0
$34$	8.31695	+	9.91175i	1.42634	+	1.69985i
$35$	−4.92254	+	5.34312i	−0.832062	+	0.903152i
$36$		0			0
$37$	−0.959970	−	1.66272i	−0.157818	−	0.273349i	0.776264	−	0.630409i	$-0.217113\pi$
$37$	−0.959970	−	1.66272i	−0.157818	−	0.273349i	−0.934082	+	0.357060i	$0.883779\pi$
$38$	10.0496	−	8.43258i	1.63025	−	1.36795i
$39$		0			0
$40$	15.7704	+	2.78075i	2.49352	+	0.439674i
$41$	−6.29347	+	2.29063i	−0.982874	+	0.357737i	−0.782957	−	0.622076i	$-0.786290\pi$
$41$	−6.29347	+	2.29063i	−0.982874	+	0.357737i	−0.199917	+	0.979813i	$0.564067\pi$
$42$		0			0
$43$	0.411100	+	2.33146i	0.0626921	+	0.355545i	0.999976	+	0.00697673i	$0.00222078\pi$
$43$	0.411100	+	2.33146i	0.0626921	+	0.355545i	−0.937284	+	0.348568i	$0.886668\pi$
$44$	15.6602	−	9.04140i	2.36086	−	1.36304i
$45$		0			0
$46$	9.43633	−	16.3442i	1.39131	−	2.40982i
$47$	0.876823	+	4.97271i	0.127898	+	0.725345i	0.979544	+	0.201228i	$0.0644933\pi$
$47$	0.876823	+	4.97271i	0.127898	+	0.725345i	−0.851647	+	0.524117i	$0.824396\pi$
$48$		0			0
$49$	−6.96998	−	0.647559i	−0.995712	−	0.0925084i
$50$	4.10452	−	4.89157i	0.580466	−	0.691773i
$51$		0			0
$52$	0.495665	−	0.0873991i	0.0687364	−	0.0121201i
$53$	3.76047	−	2.17111i	0.516541	−	0.298225i	−0.218977	−	0.975730i	$-0.570272\pi$
$53$	3.76047	−	2.17111i	0.516541	−	0.298225i	0.735518	+	0.677505i	$0.236939\pi$
$54$		0			0
$55$		−	11.4945i		−	1.54991i
$56$	7.08776	+	13.7053i	0.947142	+	1.83144i
$57$		0			0
$58$	8.39867	−	3.05687i	1.10280	−	0.401386i
$59$	−9.84174	+	3.58210i	−1.28128	+	0.466350i	−0.890857	−	0.454284i	$-0.849895\pi$
$59$	−9.84174	+	3.58210i	−1.28128	+	0.466350i	−0.390428	+	0.920634i	$0.627673\pi$
$60$		0			0
$61$	−1.13841	+	0.200732i	−0.145758	+	0.0257011i	−0.246051	−	0.969257i	$-0.579133\pi$
$61$	−1.13841	+	0.200732i	−0.145758	+	0.0257011i	0.100293	+	0.994958i	$0.468022\pi$
$62$	0.389715	+	0.675007i	0.0494939	+	0.0857260i
$63$		0			0
$64$	−1.65570	+	2.86775i	−0.206962	+	0.358469i
$65$	0.109424	−	0.300639i	0.0135723	−	0.0372897i
$66$		0			0
$67$	8.49204	+	7.12567i	1.03747	+	0.870539i	0.991721	−	0.128414i	$-0.0409885\pi$
$67$	8.49204	+	7.12567i	1.03747	+	0.870539i	0.0457477	+	0.998953i	$0.485433\pi$
$68$	3.86082	−	21.8958i	0.468193	−	2.65525i
$69$		0			0
$70$	18.2441	+	0.845678i	2.18058	+	0.101078i
$71$	5.47124	+	3.15882i	0.649317	+	0.374883i	0.788194	−	0.615426i	$-0.211016\pi$
$71$	5.47124	+	3.15882i	0.649317	+	0.374883i	−0.138878	+	0.990310i	$0.544350\pi$
$72$		0			0
$73$	−2.23588	−	1.29089i	−0.261690	−	0.151087i	0.363415	−	0.931627i	$-0.381611\pi$
$73$	−2.23588	−	1.29089i	−0.261690	−	0.151087i	−0.625105	+	0.780541i	$0.714944\pi$
$74$	−1.65079	+	4.53550i	−0.191900	+	0.527241i
$75$		0			0
$76$	−22.2002	−	3.91449i	−2.54654	−	0.449023i
$77$	8.80461	−	6.71850i	1.00338	−	0.765644i
$78$		0			0
$79$	12.0963	−	10.1500i	1.36094	−	1.14197i	0.385252	−	0.922811i	$-0.374115\pi$
$79$	12.0963	−	10.1500i	1.36094	−	1.14197i	0.975690	−	0.219155i	$-0.0703299\pi$
$80$	−8.26674	−	14.3184i	−0.924250	−	1.60085i
$81$		0			0
$82$	14.5810	+	8.41833i	1.61020	+	0.929649i
$83$	10.6778	+	3.88640i	1.17204	+	0.426588i	0.853384	−	0.521282i	$-0.174546\pi$
$83$	10.6778	+	3.88640i	1.17204	+	0.426588i	0.318657	+	0.947870i	$0.396768\pi$
$84$		0			0
$85$	−10.8264	−	9.08446i	−1.17429	−	0.985348i
$86$	3.82557	−	4.55914i	0.412522	−	0.491624i
$87$		0			0
$88$	−22.9399	−	8.34943i	−2.44540	−	0.890052i
$89$	0.913664			0.0968482			0.0484241	−	0.998827i	$-0.484580\pi$
$89$	0.913664			0.0968482			0.0484241	+	0.998827i	$0.484580\pi$
$90$		0			0
$91$	0.294244	−	0.0919061i	0.0308451	−	0.00963438i
$92$	−31.9372	+	5.63140i	−3.32969	+	0.587114i
$93$		0			0
$94$	8.15946	−	9.72406i	0.841584	−	1.00296i
$95$	−9.21076	+	10.9770i	−0.945005	+	1.12621i
$96$		0			0
$97$	−5.88114	+	1.03700i	−0.597140	+	0.105292i	−0.464045	−	0.885812i	$-0.653602\pi$
$97$	−5.88114	+	1.03700i	−0.597140	+	0.105292i	−0.133094	+	0.991103i	$0.542491\pi$
$98$	10.0159	+	14.4690i	1.01176	+	1.46159i
$99$		0			0
$100$	−10.9725			−1.09725
$101$	−7.74151	−	2.81768i	−0.770309	−	0.280370i	−0.0731835	−	0.997318i	$-0.523316\pi$
$101$	−7.74151	−	2.81768i	−0.770309	−	0.280370i	−0.697126	+	0.716949i	$0.745538\pi$
$102$		0			0
$103$	0.633698	−	0.755211i	0.0624401	−	0.0744132i	−0.733920	−	0.679236i	$-0.762311\pi$
$103$	0.633698	−	0.755211i	0.0624401	−	0.0744132i	0.796360	+	0.604822i	$0.206756\pi$
$104$	−0.520511	−	0.436761i	−0.0510403	−	0.0428279i
$105$		0			0
$106$	−10.2577	−	3.73349i	−0.996315	−	0.362629i
$107$	11.2050	+	6.46919i	1.08322	+	0.625400i	0.931764	−	0.363064i	$-0.118269\pi$
$107$	11.2050	+	6.46919i	1.08322	+	0.625400i	0.151460	+	0.988463i	$0.451603\pi$
$108$		0			0
$109$	1.89554	+	3.28318i	0.181560	+	0.314471i	0.942412	−	0.334454i	$-0.108552\pi$
$109$	1.89554	+	3.28318i	0.181560	+	0.314471i	−0.760852	+	0.648926i	$0.775219\pi$
$110$	−22.1358	+	18.5741i	−2.11056	+	1.77097i
$111$		0			0
$112$	6.13582	−	14.7013i	0.579781	−	1.38914i
$113$	−2.66007	−	0.469041i	−0.250238	−	0.0441237i	0.0471221	−	0.998889i	$-0.484995\pi$
$113$	−2.66007	−	0.469041i	−0.250238	−	0.0441237i	−0.297360	+	0.954765i	$0.596106\pi$
$114$		0			0
$115$	−7.05051	+	19.3711i	−0.657463	+	1.80636i
$116$	−13.3005	−	7.67905i	−1.23492	−	0.712981i
$117$		0			0
$118$	22.8018	+	13.1646i	2.09907	+	1.21190i
$119$	0.630537	−	13.6028i	0.0578012	−	1.24696i
$120$		0			0
$121$	−1.13267	+	6.42368i	−0.102970	+	0.583971i
$122$	2.22614	+	1.86795i	0.201545	+	0.169117i
$123$		0			0
$124$	0.458080	−	1.25857i	0.0411368	−	0.113023i
$125$	3.37741	−	5.84984i	0.302084	−	0.523225i
$126$		0			0
$127$	0.619432	+	1.07289i	0.0549657	+	0.0952034i	0.892199	−	0.451642i	$-0.149162\pi$
$127$	0.619432	+	1.07289i	0.0549657	+	0.0952034i	−0.837233	+	0.546846i	$0.815828\pi$
$128$	15.0386	−	2.65171i	1.32924	−	0.234380i
$129$		0			0
$130$	−0.755783	+	0.275083i	−0.0662866	+	0.0241263i
$131$	−7.04031	+	2.56246i	−0.615114	+	0.223883i	−0.630740	−	0.775995i	$-0.717248\pi$
$131$	−7.04031	+	2.56246i	−0.615114	+	0.223883i	0.0156252	+	0.999878i	$0.495026\pi$
$132$		0			0
$133$	−13.7919	−	0.639304i	−1.19591	−	0.0554346i
$134$		−	27.8683i		−	2.40745i
$135$		0			0
$136$	−25.9943	+	15.0078i	−2.22900	+	1.28691i
$137$	16.0387	−	2.82805i	1.37027	−	0.241616i	0.560401	−	0.828221i	$-0.310647\pi$
$137$	16.0387	−	2.82805i	1.37027	−	0.241616i	0.809873	+	0.586605i	$0.199536\pi$
$138$		0			0
$139$	−6.25623	+	7.45589i	−0.530647	+	0.632400i	−0.963064	−	0.269274i	$-0.913216\pi$
$139$	−6.25623	+	7.45589i	−0.530647	+	0.632400i	0.432417	+	0.901674i	$0.357661\pi$
$140$	−19.0381	−	24.9494i	−1.60901	−	2.10861i
$141$		0			0
$142$	−2.75789	−	15.6408i	−0.231437	−	1.31255i
$143$	−0.243862	+	0.422381i	−0.0203928	+	0.0353213i
$144$		0			0
$145$	−8.45455	+	4.88124i	−0.702112	+	0.405365i
$146$	1.12704	+	6.39177i	0.0932746	+	0.528987i
$147$		0			0
$148$	7.79359	−	2.83664i	0.640630	−	0.233170i
$149$	−16.5016	−	2.90967i	−1.35186	−	0.238370i	−0.549642	−	0.835400i	$-0.685236\pi$
$149$	−16.5016	−	2.90967i	−1.35186	−	0.238370i	−0.802219	+	0.597030i	$0.796347\pi$
$150$		0			0
$151$	−11.4658	+	9.62098i	−0.933077	+	0.782944i	−0.976367	−	0.216118i	$-0.930660\pi$
$151$	−11.4658	+	9.62098i	−0.933077	+	0.782944i	0.0432907	+	0.999063i	$0.486216\pi$
$152$	15.2165	+	26.3558i	1.23422	+	2.13773i
$153$		0			0
$154$	−27.1659	−	6.09916i	−2.18909	−	0.491484i
$155$	−0.547243	−	0.652179i	−0.0439556	−	0.0523843i
$156$		0			0
$157$	1.10483	+	3.03550i	0.0881752	+	0.242259i	0.975940	−	0.218037i	$-0.0699654\pi$
$157$	1.10483	+	3.03550i	0.0881752	+	0.242259i	−0.887765	+	0.460296i	$0.847743\pi$
$158$	−39.0933	−	6.89321i	−3.11010	−	0.548394i
$159$		0			0
$160$	−3.26169	+	8.96143i	−0.257860	+	0.708464i
$161$	−18.9590	+	5.92180i	−1.49418	+	0.466703i
$162$		0			0
$163$	3.85622	−	6.67918i	0.302043	−	0.523153i	−0.674556	−	0.738224i	$-0.735665\pi$
$163$	3.85622	−	6.67918i	0.302043	−	0.523153i	0.976599	+	0.215070i	$0.0689981\pi$
$164$	−5.02387	−	28.4918i	−0.392299	−	2.22484i
$165$		0			0
$166$	−9.77011	−	26.8432i	−0.758308	−	2.08343i
$167$	0.286318	−	1.62379i	0.0221559	−	0.125652i	−0.971724	−	0.236121i	$-0.924124\pi$
$167$	0.286318	−	1.62379i	0.0221559	−	0.125652i	0.993880	+	0.110468i	$0.0352350\pi$
$168$		0			0
$169$	9.94818	−	8.34751i	0.765245	−	0.642116i
$170$			35.5290i			2.72495i
$171$		0			0
$172$	−10.2268			−0.779789
$173$	17.1792	+	6.25273i	1.30611	+	0.475386i	0.898983	−	0.437984i	$-0.144307\pi$
$173$	17.1792	+	6.25273i	1.30611	+	0.475386i	0.407130	+	0.913370i	$0.366530\pi$
$174$		0			0
$175$	−6.66518	+	0.859273i	−0.503840	+	0.0649550i
$176$	8.62046	+	23.6845i	0.649792	+	1.78529i
$177$		0			0
$178$	−1.47641	−	1.75951i	−0.110661	−	0.131881i
$179$		−	4.22041i		−	0.315448i	−0.987483	−	0.157724i	$-0.949584\pi$
$179$		−	4.22041i		−	0.315448i	0.987483	−	0.157724i	$-0.0504156\pi$
$180$		0			0
$181$	9.51249	−	5.49204i	0.707058	−	0.408220i	−0.102913	−	0.994690i	$-0.532816\pi$
$181$	9.51249	−	5.49204i	0.707058	−	0.408220i	0.809971	+	0.586470i	$0.199483\pi$
$182$	−0.652465	−	0.418135i	−0.0483639	−	0.0309942i
$183$		0			0
$184$	33.5382	+	28.1419i	2.47247	+	2.07465i
$185$	0.915472	−	5.19190i	0.0673068	−	0.381716i
$186$		0			0
$187$	13.8488	+	16.5044i	1.01273	+	1.20692i
$188$	−21.8125			−1.59084
$189$		0			0
$190$	36.0230			2.61338
$191$	−6.52972	−	7.78182i	−0.472474	−	0.563073i	0.476196	−	0.879339i	$-0.342015\pi$
$191$	−6.52972	−	7.78182i	−0.472474	−	0.563073i	−0.948670	+	0.316266i	$0.897571\pi$
$192$		0			0
$193$	1.50063	−	8.51052i	0.108018	−	0.612600i	−0.881954	−	0.471336i	$-0.843772\pi$
$193$	1.50063	−	8.51052i	0.108018	−	0.612600i	0.989972	−	0.141265i	$-0.0451168\pi$
$194$	11.5005	+	9.65005i	0.825687	+	0.692833i
$195$		0			0
$196$	7.98320	−	29.1658i	0.570229	−	2.08327i
$197$	−0.625155	+	0.360933i	−0.0445405	+	0.0257154i	−0.522105	−	0.852881i	$-0.674853\pi$
$197$	−0.625155	+	0.360933i	−0.0445405	+	0.0257154i	0.477564	+	0.878597i	$0.341520\pi$
$198$		0			0
$199$		−	21.7780i		−	1.54380i	−0.635745	−	0.771899i	$-0.719307\pi$
$199$		−	21.7780i		−	1.54380i	0.635745	−	0.771899i	$-0.280693\pi$
$200$	9.52168	+	11.3475i	0.673285	+	0.802389i
$201$		0			0
$202$	7.08343	+	19.4616i	0.498388	+	1.36931i
$203$	−8.68065	−	3.62300i	−0.609262	−	0.254285i
$204$		0			0
$205$	−17.2813	−	6.28989i	−1.20698	−	0.439305i
$206$	−2.47837			−0.172676
$207$		0			0
$208$			0.701536i			0.0486427i
$209$	16.7339	−	14.0414i	1.15751	−	0.971263i
$210$		0			0
$211$	1.68157	−	9.53668i	0.115764	−	0.656532i	−0.870605	−	0.491983i	$-0.836272\pi$
$211$	1.68157	−	9.53668i	0.115764	−	0.656532i	0.986369	−	0.164549i	$-0.0526168\pi$
$212$	6.41546	+	17.6263i	0.440616	+	1.21058i
$213$		0			0
$214$	−5.64809	−	32.0319i	−0.386096	−	2.18966i
$215$	−3.25038	+	5.62982i	−0.221674	+	0.383951i
$216$		0			0
$217$	0.179698	−	0.800379i	0.0121987	−	0.0543333i
$218$	3.25962	−	8.95574i	0.220769	−	0.606559i
$219$		0			0
$220$	48.8995	+	8.62230i	3.29680	+	0.581315i
$221$	0.205101	+	0.563512i	0.0137966	+	0.0379059i
$222$		0			0
$223$	18.0896	+	21.5583i	1.21137	+	1.44365i	0.862184	+	0.506596i	$0.169096\pi$
$223$	18.0896	+	21.5583i	1.21137	+	1.44365i	0.349183	+	0.937055i	$0.386459\pi$
$224$	−8.77080	+	2.73953i	−0.586024	+	0.183043i
$225$		0			0
$226$	3.39518	+	5.88062i	0.225844	+	0.391173i
$227$	5.86912	−	4.92477i	0.389547	−	0.326869i	−0.426890	−	0.904304i	$-0.640391\pi$
$227$	5.86912	−	4.92477i	0.389547	−	0.326869i	0.816437	+	0.577435i	$0.195946\pi$
$228$		0			0
$229$	14.0021	+	2.46895i	0.925285	+	0.163153i	0.615936	−	0.787796i	$-0.288778\pi$
$229$	14.0021	+	2.46895i	0.925285	+	0.163153i	0.309349	+	0.950949i	$0.399889\pi$
$230$	48.6975	−	17.7244i	3.21102	−	1.16871i
$231$		0			0
$232$	3.60037	+	20.4187i	0.236376	+	1.34055i
$233$	−19.4777	+	11.2455i	−1.27603	+	0.736714i	−0.976115	−	0.217253i	$-0.930290\pi$
$233$	−19.4777	+	11.2455i	−1.27603	+	0.736714i	−0.299911	+	0.953967i	$0.596957\pi$
$234$		0			0
$235$	−6.93265	+	12.0077i	−0.452236	+	0.783296i
$236$	−7.85634	−	44.5555i	−0.511404	−	2.90032i
$237$		0			0
$238$	−27.2148	+	20.7667i	−1.76407	+	1.34611i
$239$	15.3178	−	18.2550i	0.990825	−	1.18082i	0.00731345	−	0.999973i	$-0.497672\pi$
$239$	15.3178	−	18.2550i	0.990825	−	1.18082i	0.983511	−	0.180846i	$-0.0578835\pi$
$240$		0			0
$241$	13.3567	−	2.35515i	0.860381	−	0.151708i	0.273986	−	0.961734i	$-0.411658\pi$
$241$	13.3567	−	2.35515i	0.860381	−	0.151708i	0.586395	+	0.810025i	$0.300547\pi$
$242$	14.2009	−	8.19887i	0.912866	−	0.527044i
$243$		0			0
$244$		−	4.99357i		−	0.319681i
$245$	−13.5183	−	13.6644i	−0.863655	−	0.872989i
$246$		0			0
$247$	0.571346	−	0.207953i	0.0363539	−	0.0132317i
$248$	−1.69909	+	0.618417i	−0.107892	+	0.0392695i
$249$		0			0
$250$	−16.7231	+	2.94873i	−1.05766	+	0.186494i
$251$	4.77251	+	8.26623i	0.301238	+	0.521760i	0.976417	−	0.215895i	$-0.0692668\pi$
$251$	4.77251	+	8.26623i	0.301238	+	0.521760i	−0.675179	+	0.737654i	$0.735933\pi$
$252$		0			0
$253$	15.7128	−	27.2153i	0.987854	−	1.71101i
$254$	1.06519	−	2.92659i	0.0668360	−	0.183630i
$255$		0			0
$256$	−24.3344	−	20.4190i	−1.52090	−	1.27619i
$257$	−0.960437	+	5.44691i	−0.0599104	+	0.339769i	−0.999999	−	0.00116059i	$-0.999631\pi$
$257$	−0.960437	+	5.44691i	−0.0599104	+	0.339769i	0.940089	+	0.340929i	$0.110742\pi$
$258$		0			0
$259$	4.51202	−	2.33342i	0.280363	−	0.144992i
$260$	1.19689	+	0.691025i	0.0742280	+	0.0428556i
$261$		0			0
$262$	16.3113	+	9.41733i	1.00771	+	0.581804i
$263$	−2.86165	+	7.86232i	−0.176457	+	0.484811i	−0.996117	−	0.0880387i	$-0.971940\pi$
$263$	−2.86165	+	7.86232i	−0.176457	+	0.484811i	0.819660	+	0.572850i	$0.194162\pi$
$264$		0			0
$265$	11.7422	+	2.07047i	0.721319	+	0.127188i
$266$	21.0554	+	27.5932i	1.29099	+	1.69185i
$267$		0			0
$268$	−36.6840	+	30.7815i	−2.24083	+	1.88028i
$269$	9.52435	+	16.4967i	0.580710	+	1.00582i	0.995395	+	0.0958542i	$0.0305583\pi$
$269$	9.52435	+	16.4967i	0.580710	+	1.00582i	−0.414685	+	0.909965i	$0.636108\pi$
$270$		0			0
$271$	−21.6453	−	12.4969i	−1.31486	−	0.759134i	−0.331962	−	0.943293i	$-0.607710\pi$
$271$	−21.6453	−	12.4969i	−1.31486	−	0.759134i	−0.982896	+	0.184159i	$0.941044\pi$
$272$	29.1211	+	10.5992i	1.76573	+	0.642671i
$273$		0			0
$274$	−31.3633	−	26.3170i	−1.89473	−	1.58987i
$275$	6.83457	−	8.14513i	0.412140	−	0.491170i
$276$		0			0
$277$	−20.9786	−	7.63560i	−1.26048	−	0.458778i	−0.376552	−	0.926395i	$-0.622890\pi$
$277$	−20.9786	−	7.63560i	−1.26048	−	0.458778i	−0.883931	+	0.467617i	$0.845113\pi$
$278$	24.4679			1.46749
$279$		0			0
$280$	−9.28127	+	41.3391i	−0.554662	+	2.47048i
$281$	−11.7375	+	2.06964i	−0.700200	+	0.123464i	−0.512405	−	0.858744i	$-0.671245\pi$
$281$	−11.7375	+	2.06964i	−0.700200	+	0.123464i	−0.187795	+	0.982208i	$0.560134\pi$
$282$		0			0
$283$	−2.59842	+	3.09667i	−0.154460	+	0.184078i	−0.837725	−	0.546092i	$-0.816115\pi$
$283$	−2.59842	+	3.09667i	−0.154460	+	0.184078i	0.683265	+	0.730170i	$0.260559\pi$
$284$	−17.5423	+	20.9061i	−1.04094	+	1.24055i
$285$		0			0
$286$	1.20747	−	0.212910i	0.0713994	−	0.0125896i
$287$	−5.28295	−	16.9137i	−0.311842	−	0.998385i
$288$		0			0
$289$	9.49043			0.558261
$290$	23.0620	+	8.39390i	1.35425	+	0.492907i
$291$		0			0
$292$	7.16885	−	8.54350i	0.419525	−	0.499971i
$293$	−1.36115	−	1.14214i	−0.0795192	−	0.0667245i	0.602162	−	0.798374i	$-0.294306\pi$
$293$	−1.36115	−	1.14214i	−0.0795192	−	0.0667245i	−0.681681	+	0.731650i	$0.738751\pi$
$294$		0			0
$295$	−27.0246	−	9.83614i	−1.57343	−	0.572682i
$296$	−9.69666	−	5.59837i	−0.563607	−	0.325399i
$297$		0			0
$298$	21.0618	+	36.4801i	1.22008	+	2.11324i
$299$	0.670051	−	0.562240i	0.0387501	−	0.0325152i
$300$		0			0
$301$	−6.21221	+	0.800877i	−0.358066	+	0.0461618i
$302$	37.0557	+	6.53392i	2.13232	+	0.375985i
$303$		0			0
$304$	10.7466	−	29.5260i	0.616358	−	1.69343i
$305$	−2.74894	−	1.58710i	−0.157404	−	0.0908770i
$306$		0			0
$307$	−17.0250	−	9.82941i	−0.971670	−	0.560994i	−0.0719253	−	0.997410i	$-0.522914\pi$
$307$	−17.0250	−	9.82941i	−0.971670	−	0.560994i	−0.899745	+	0.436416i	$0.856248\pi$
$308$	21.9771	+	42.4961i	1.25226	+	2.42144i
$309$		0			0
$310$	−0.371651	+	2.10774i	−0.0211083	+	0.119711i
$311$	20.2815	+	17.0182i	1.15006	+	0.965014i	0.999721	−	0.0236210i	$-0.00751950\pi$
$311$	20.2815	+	17.0182i	1.15006	+	0.965014i	0.150338	+	0.988635i	$0.451964\pi$
$312$		0			0
$313$	−1.72420	+	4.73721i	−0.0974577	+	0.267763i	−0.978835	−	0.204650i	$-0.934395\pi$
$313$	−1.72420	+	4.73721i	−0.0974577	+	0.267763i	0.881378	+	0.472413i	$0.156617\pi$
$314$	4.06038	−	7.03278i	0.229140	−	0.396883i
$315$		0			0
$316$	34.1062	+	59.0737i	1.91862	+	3.32316i
$317$	30.4363	−	5.36674i	1.70947	−	0.301426i	0.768486	−	0.639866i	$-0.221010\pi$
$317$	30.4363	−	5.36674i	1.70947	−	0.301426i	0.940988	+	0.338440i	$0.109899\pi$
$318$		0			0
$319$	13.9849	−	5.09010i	0.783005	−	0.284991i
$320$	−8.54444	+	3.10992i	−0.477649	+	0.173850i
$321$		0			0
$322$	42.0403	+	26.9417i	2.34281	+	1.50140i
$323$		−	26.8587i		−	1.49446i
$324$		0			0
$325$	0.256298	−	0.147974i	0.0142169	−	0.00820811i
$326$	−19.0939	+	3.36678i	−1.05752	+	0.186469i
$327$		0			0
$328$	−25.1059	+	29.9200i	−1.38624	+	1.65206i
$329$	−13.2499	+	1.70817i	−0.730489	+	0.0941744i
$330$		0			0
$331$	2.84820	+	16.1530i	0.156551	+	0.887847i	0.957354	+	0.288918i	$0.0932956\pi$
$331$	2.84820	+	16.1530i	0.156551	+	0.887847i	−0.800802	+	0.598929i	$0.795593\pi$
$332$	−24.5432	+	42.5100i	−1.34698	+	2.33304i
$333$		0			0
$334$	−3.58972	+	2.07252i	−0.196421	+	0.113403i
$335$	5.28586	+	29.9776i	0.288797	+	1.63785i
$336$		0			0
$337$	−1.34897	+	0.490985i	−0.0734831	+	0.0267457i	−0.378500	−	0.925601i	$-0.623560\pi$
$337$	−1.34897	+	0.490985i	−0.0734831	+	0.0267457i	0.305017	+	0.952347i	$0.401338\pi$
$338$	−32.1509	−	5.66907i	−1.74878	−	0.308357i
$339$		0			0
$340$	46.7681	−	39.2431i	2.53636	−	2.12826i
$341$	0.648929	+	1.12398i	0.0351415	+	0.0608668i
$342$		0			0
$343$	2.56532	−	18.3417i	0.138514	−	0.990360i
$344$	8.87459	+	10.5763i	0.478486	+	0.570237i
$345$		0			0
$346$	−15.7189	−	43.1872i	−0.845052	−	2.32176i
$347$	6.26965	+	1.10551i	0.336573	+	0.0593468i	0.339380	−	0.940649i	$-0.389783\pi$
$347$	6.26965	+	1.10551i	0.336573	+	0.0593468i	−0.00280775	+	0.999996i	$0.500894\pi$
$348$		0			0
$349$	2.99689	−	8.23388i	0.160420	−	0.440749i	−0.833276	−	0.552856i	$-0.813538\pi$
$349$	2.99689	−	8.23388i	0.160420	−	0.440749i	0.993696	+	0.112107i	$0.0357600\pi$
$350$	12.4252	+	11.4471i	0.664153	+	0.611875i
$351$		0			0
$352$	7.26902	−	12.5903i	0.387440	−	0.671066i
$353$	−0.381468	−	2.16341i	−0.0203035	−	0.115147i	0.972972	−	0.230925i	$-0.0741751\pi$
$353$	−0.381468	−	2.16341i	−0.0203035	−	0.115147i	−0.993275	+	0.115778i	$0.963064\pi$
$354$		0			0
$355$	5.93327	+	16.3015i	0.314905	+	0.865195i
$356$	−0.685364	+	3.88689i	−0.0363242	+	0.206005i
$357$		0			0
$358$	−8.12756	+	6.81983i	−0.429555	+	0.360439i
$359$		−	13.3206i		−	0.703036i	−0.936181	−	0.351518i	$-0.885666\pi$
$359$		−	13.3206i		−	0.703036i	0.936181	−	0.351518i	$-0.114334\pi$
$360$		0			0
$361$	−8.23216			−0.433272
$362$	−25.9479	−	9.44425i	−1.36379	−	0.496379i
$363$		0			0
$364$	0.170265	+	1.32071i	0.00892432	+	0.0692239i
$365$	−2.42469	−	6.66179i	−0.126914	−	0.348694i
$366$		0			0
$367$	6.85361	+	8.16781i	0.357755	+	0.426356i	0.914662	−	0.404219i	$-0.132457\pi$
$367$	6.85361	+	8.16781i	0.357755	+	0.426356i	−0.556907	+	0.830575i	$0.688012\pi$
$368$		−	45.2021i		−	2.35632i
$369$		0			0
$370$	−11.4778	+	6.62669i	−0.596701	+	0.344505i
$371$	5.27737	+	10.2046i	0.273987	+	0.529796i
$372$		0			0
$373$	−10.7249	−	8.99930i	−0.555317	−	0.465966i	0.321420	−	0.946937i	$-0.395840\pi$
$373$	−10.7249	−	8.99930i	−0.555317	−	0.465966i	−0.876737	+	0.480971i	$0.840284\pi$
$374$	9.40520	−	53.3395i	0.486331	−	2.75812i
$375$		0			0
$376$	18.9284	+	22.5580i	0.976156	+	1.16334i
$377$	0.414234			0.0213341
$378$		0			0
$379$	−34.6102			−1.77781			−0.888903	−	0.458095i	$-0.848532\pi$
$379$	−34.6102			−1.77781			−0.888903	+	0.458095i	$0.848532\pi$
$380$	−39.7887	−	47.4184i	−2.04112	−	2.43251i
$381$		0			0
$382$	−4.43455	+	25.1496i	−0.226891	+	1.28676i
$383$	12.9643	+	10.8783i	0.662443	+	0.555856i	0.910818	−	0.412808i	$-0.135452\pi$
$383$	12.9643	+	10.8783i	0.662443	+	0.555856i	−0.248375	+	0.968664i	$0.579896\pi$
$384$		0			0
$385$	30.3789	+	1.40817i	1.54825	+	0.0717669i
$386$	−18.8143	+	10.8624i	−0.957620	+	0.552882i
$387$		0			0
$388$		−	25.7973i		−	1.30966i
$389$	−2.81103	−	3.35005i	−0.142525	−	0.169855i	0.690060	−	0.723752i	$-0.257584\pi$
$389$	−2.81103	−	3.35005i	−0.142525	−	0.169855i	−0.832585	+	0.553898i	$0.813140\pi$
$390$		0			0
$391$	−13.2153	−	36.3088i	−0.668327	−	1.83621i
$392$	−37.0901	+	17.0533i	−1.87333	+	0.861323i
$393$		0			0
$394$	1.70528	+	0.620670i	0.0859106	+	0.0312689i
$395$	43.3597			2.18166
$396$		0			0
$397$			10.8300i			0.543542i	0.962362	+	0.271771i	$0.0876094\pi$
$397$			10.8300i			0.543542i	−0.962362	+	0.271771i	$0.912391\pi$
$398$	−41.9395	+	35.1914i	−2.10224	+	1.76399i
$399$		0			0
$400$	2.65577	−	15.0616i	0.132788	−	0.753080i
$401$	2.22180	+	6.10435i	0.110952	+	0.304837i	0.982725	−	0.185073i	$-0.0592520\pi$
$401$	2.22180	+	6.10435i	0.110952	+	0.304837i	−0.871773	+	0.489909i	$0.837030\pi$
$402$		0			0
$403$	0.00627290	+	0.0355754i	0.000312475	+	0.00177214i
$404$	17.7940	−	30.8202i	0.885286	−	1.53336i
$405$		0			0
$406$	7.05013	+	22.5715i	0.349892	+	1.12020i
$407$	−2.74878	+	7.55222i	−0.136252	+	0.374350i
$408$		0			0
$409$	−15.2552	−	2.68991i	−0.754323	−	0.133007i	−0.216753	−	0.976227i	$-0.569547\pi$
$409$	−15.2552	−	2.68991i	−0.754323	−	0.133007i	−0.537570	+	0.843219i	$0.680658\pi$
$410$	15.8123	+	43.4439i	0.780913	+	2.14554i
$411$		0			0
$412$	2.73745	+	3.26237i	0.134865	+	0.160725i
$413$	−8.26148	−	26.4497i	−0.406521	−	1.30150i
$414$		0			0
$415$	15.6010	+	27.0218i	0.765824	+	1.32645i
$416$	0.309978	−	0.260102i	0.0151979	−	0.0127526i
$417$		0			0
$418$	−54.0811	−	9.53596i	−2.64519	−	0.466419i
$419$	14.7586	−	5.37170i	0.721006	−	0.262425i	0.0446532	−	0.999003i	$-0.485782\pi$
$419$	14.7586	−	5.37170i	0.721006	−	0.262425i	0.676353	+	0.736578i	$0.263559\pi$
$420$		0			0
$421$	−2.01941	−	11.4527i	−0.0984202	−	0.558168i	−0.993646	−	0.112555i	$-0.964097\pi$
$421$	−2.01941	−	11.4527i	−0.0984202	−	0.558168i	0.895225	−	0.445614i	$-0.147014\pi$
$422$	−21.0828	+	12.1722i	−1.02629	+	0.592531i
$423$		0			0
$424$	12.6615	−	21.9304i	0.614898	−	1.06503i
$425$	−2.27016	−	12.8747i	−0.110119	−	0.624517i
$426$		0			0
$427$	−0.391053	−	3.03331i	−0.0189244	−	0.146792i
$428$	−35.9262	+	42.8152i	−1.73656	+	2.06955i
$429$		0			0
$430$	16.0941	−	2.83783i	0.776127	−	0.136852i
$431$	−12.5999	+	7.27456i	−0.606916	+	0.350403i	−0.771758	−	0.635917i	$-0.780622\pi$
$431$	−12.5999	+	7.27456i	−0.606916	+	0.350403i	0.164841	+	0.986320i	$0.447289\pi$
$432$		0			0
$433$		−	12.8056i		−	0.615396i	−0.951484	−	0.307698i	$-0.900441\pi$
$433$		−	12.8056i		−	0.615396i	0.951484	−	0.307698i	$-0.0995587\pi$
$434$	−1.83173	+	0.947290i	−0.0879258	+	0.0454714i
$435$		0			0
$436$	−15.3891	+	5.60118i	−0.737005	+	0.268248i
$437$	−36.8136	+	13.3991i	−1.76103	+	0.640964i
$438$		0			0
$439$	29.7539	−	5.24641i	1.42008	−	0.250398i	0.589709	−	0.807616i	$-0.299242\pi$
$439$	29.7539	−	5.24641i	1.42008	−	0.250398i	0.830366	+	0.557218i	$0.188131\pi$
$440$	−33.5168	−	58.0528i	−1.59785	−	2.76756i
$441$		0			0
$442$	0.753770	−	1.30557i	0.0358532	−	0.0620995i
$443$	8.87386	−	24.3807i	0.421610	−	1.15836i	−0.529176	−	0.848512i	$-0.677499\pi$
$443$	8.87386	−	24.3807i	0.421610	−	1.15836i	0.950785	−	0.309851i	$-0.100279\pi$
$444$		0			0
$445$	1.92189	+	1.61265i	0.0911062	+	0.0764471i
$446$	12.2852	−	69.6729i	0.581722	−	3.29911i
$447$		0			0
$448$	−7.37638	−	4.72718i	−0.348501	−	0.223338i
$449$	−4.52779	−	2.61412i	−0.213680	−	0.123368i	0.389341	−	0.921094i	$-0.372703\pi$
$449$	−4.52779	−	2.61412i	−0.213680	−	0.123368i	−0.603020	+	0.797726i	$0.706036\pi$
$450$		0			0
$451$	24.2793	+	14.0177i	1.14327	+	0.660066i
$452$	3.99077	−	10.9646i	0.187710	−	0.515729i
$453$		0			0
$454$	−18.9680	−	3.34458i	−0.890214	−	0.156969i
$455$	0.781158	+	0.326028i	0.0366212	+	0.0152844i
$456$		0			0
$457$	29.5854	−	24.8251i	1.38395	−	1.16127i	0.416221	−	0.909263i	$-0.363354\pi$
$457$	29.5854	−	24.8251i	1.38395	−	1.16127i	0.967726	−	0.252006i	$-0.0810902\pi$
$458$	−17.8716	−	30.9545i	−0.835085	−	1.44641i
$459$		0			0
$460$	−77.1194	−	44.5249i	−3.59571	−	2.07598i
$461$	15.4949	+	5.63970i	0.721671	+	0.262667i	0.676635	−	0.736318i	$-0.263437\pi$
$461$	15.4949	+	5.63970i	0.721671	+	0.262667i	0.0450362	+	0.998985i	$0.485660\pi$
$462$		0			0
$463$	31.2960	+	26.2605i	1.45445	+	1.22043i	0.929251	+	0.369448i	$0.120453\pi$
$463$	31.2960	+	26.2605i	1.45445	+	1.22043i	0.525198	+	0.850980i	$0.323991\pi$
$464$	13.7600	−	16.3985i	0.638791	−	0.761281i
$465$		0			0
$466$	53.1306	+	19.3380i	2.46123	+	0.895813i
$467$	−38.7005			−1.79085			−0.895424	−	0.445215i	$-0.853127\pi$
$467$	−38.7005			−1.79085			−0.895424	+	0.445215i	$0.853127\pi$
$468$		0			0
$469$	−19.8729	+	21.5708i	−0.917644	+	0.996046i
$470$	34.3267	−	6.05273i	1.58337	−	0.279192i
$471$		0			0
$472$	−39.2606	+	46.7890i	−1.80712	+	2.15364i
$473$	6.37009	−	7.59158i	0.292897	−	0.349061i
$474$		0			0
$475$	−13.0537	+	2.30173i	−0.598947	+	0.105610i
$476$	57.3957	+	12.8862i	2.63073	+	0.590639i
$477$		0			0
$478$	−59.9074			−2.74010
$479$	−27.1347	−	9.87621i	−1.23982	−	0.451256i	−0.362867	−	0.931841i	$-0.618202\pi$
$479$	−27.1347	−	9.87621i	−1.23982	−	0.451256i	−0.876948	+	0.480585i	$0.840424\pi$
$480$		0			0
$481$	−0.143790	+	0.171362i	−0.00655624	+	0.00781343i
$482$	−26.1188	−	21.9163i	−1.18968	−	0.998260i
$483$		0			0
$484$	−26.4778	−	9.63714i	−1.20354	−	0.438052i
$485$	−14.2013	−	8.19912i	−0.644848	−	0.372303i
$486$		0			0
$487$	10.6879	+	18.5119i	0.484313	+	0.838854i	0.999838	−	0.0180204i	$-0.00573637\pi$
$487$	10.6879	+	18.5119i	0.484313	+	0.838854i	−0.515525	+	0.856875i	$0.672403\pi$
$488$	−5.16422	+	4.33330i	−0.233773	+	0.196159i
$489$		0			0
$490$	−4.47011	+	48.1139i	−0.201939	+	2.17357i
$491$	17.7129	+	3.12326i	0.799372	+	0.140951i	0.558390	−	0.829579i	$-0.311419\pi$
$491$	17.7129	+	3.12326i	0.799372	+	0.140951i	0.240982	+	0.970530i	$0.422531\pi$
$492$		0			0
$493$	6.25848	−	17.1950i	0.281868	−	0.774426i
$494$	−1.32372	−	0.764250i	−0.0595570	−	0.0343852i
$495$		0			0
$496$	1.61672	+	0.933411i	0.0725927	+	0.0419114i
$497$	−9.01876	+	14.0730i	−0.404547	+	0.631262i
$498$		0			0
$499$	−1.85083	+	10.4966i	−0.0828545	+	0.469891i	0.914944	+	0.403580i	$0.132234\pi$
$499$	−1.85083	+	10.4966i	−0.0828545	+	0.469891i	−0.997799	+	0.0663114i	$0.978877\pi$
$500$	22.3528	+	18.7562i	0.999647	+	0.838803i
$501$		0			0
$502$	8.20692	−	22.5483i	0.366293	−	1.00638i
$503$	1.68293	−	2.91493i	0.0750383	−	0.129970i	−0.826065	−	0.563575i	$-0.809425\pi$
$503$	1.68293	−	2.91493i	0.0750383	−	0.129970i	0.901103	+	0.433605i	$0.142759\pi$
$504$		0			0
$505$	−11.3109	−	19.5911i	−0.503328	−	0.871790i
$506$	−77.8012	+	13.7184i	−3.45868	+	0.609859i
$507$		0			0
$508$	−5.02891	+	1.83037i	−0.223122	+	0.0812097i
$509$	−7.87029	+	2.86455i	−0.348844	+	0.126969i	−0.510499	−	0.859878i	$-0.670539\pi$
$509$	−7.87029	+	2.86455i	−0.348844	+	0.126969i	0.161654	+	0.986847i	$0.448317\pi$
$510$		0			0
$511$	3.68561	−	5.75109i	0.163042	−	0.254413i
$512$			49.3168i			2.17951i
$513$		0			0
$514$	12.0415	−	6.95217i	0.531128	−	0.306647i
$515$	2.66596	−	0.470080i	0.117476	−	0.0207142i
$516$		0			0
$517$	13.5866	−	16.1919i	0.597538	−	0.712118i
$518$	−11.7847	−	4.91853i	−0.517790	−	0.216108i
$519$		0			0
$520$	−0.323992	−	1.83745i	−0.0142080	−	0.0805774i
$521$	8.12400	−	14.0712i	0.355919	−	0.616470i	−0.631356	−	0.775493i	$-0.717501\pi$
$521$	8.12400	−	14.0712i	0.355919	−	0.616470i	0.987275	+	0.159024i	$0.0508346\pi$
$522$		0			0
$523$	24.4735	−	14.1298i	1.07015	−	0.617853i	0.141929	−	0.989877i	$-0.454669\pi$
$523$	24.4735	−	14.1298i	1.07015	−	0.617853i	0.928223	+	0.372024i	$0.121336\pi$
$524$	−5.62005	−	31.8729i	−0.245513	−	1.39237i
$525$		0			0
$526$	19.7653	−	7.19397i	0.861806	−	0.313672i
$527$	1.57153	+	0.277102i	0.0684568	+	0.0120708i
$528$		0			0
$529$	−25.5544	+	21.4427i	−1.11106	+	0.932292i
$530$	−14.9872	−	25.9586i	−0.651003	−	1.12757i
$531$		0			0
$532$	13.0654	−	58.1936i	0.566456	−	2.52301i
$533$	0.501584	+	0.597765i	0.0217260	+	0.0258921i
$534$		0			0
$535$	12.1512	+	33.3851i	0.525341	+	1.44336i
$536$	63.6669	+	11.2262i	2.74999	+	0.484897i
$537$		0			0
$538$	16.3783	−	44.9990i	0.706119	−	1.94005i
$539$	16.6778	+	24.0929i	0.718363	+	1.03775i
$540$		0			0
$541$	3.36773	−	5.83309i	0.144790	−	0.250784i	−0.784504	−	0.620123i	$-0.787083\pi$
$541$	3.36773	−	5.83309i	0.144790	−	0.250784i	0.929295	+	0.369339i	$0.120416\pi$
$542$	10.9108	+	61.8780i	0.468657	+	2.65789i
$543$		0			0
$544$	−6.11365	−	16.7971i	−0.262121	−	0.720171i
$545$	−1.80768	+	10.2518i	−0.0774324	+	0.439141i
$546$		0			0
$547$	−31.5987	+	26.5144i	−1.35106	+	1.13368i	−0.372429	+	0.928061i	$0.621475\pi$
$547$	−31.5987	+	26.5144i	−1.35106	+	1.13368i	−0.978633	+	0.205615i	$0.934080\pi$
$548$			70.3527i			3.00532i
$549$		0			0
$550$	−26.7298			−1.13976
$551$	−17.4341	−	6.34550i	−0.742718	−	0.270327i
$552$		0			0
$553$	25.3437	+	33.2130i	1.07772	+	1.41236i
$554$	19.1953	+	52.7386i	0.815530	+	2.24065i
$555$		0			0
$556$	−27.0257	−	32.2080i	−1.14615	−	1.36592i
$557$			6.51677i			0.276124i	0.990424	+	0.138062i	$0.0440874\pi$
$557$			6.51677i			0.276124i	−0.990424	+	0.138062i	$0.955913\pi$
$558$		0			0
$559$	0.238880	−	0.137917i	0.0101036	−	0.00583329i
$560$	38.8551	−	20.0942i	1.64193	−	0.849133i
$561$		0			0
$562$	22.9525	+	19.2594i	0.968192	+	0.812409i
$563$	−4.74872	+	26.9313i	−0.200135	+	1.13502i	0.704780	+	0.709426i	$0.251046\pi$
$563$	−4.74872	+	26.9313i	−0.200135	+	1.13502i	−0.904914	+	0.425594i	$0.860065\pi$
$564$		0			0
$565$	−4.76755	−	5.68175i	−0.200572	−	0.239033i
$566$	10.1623			0.427155
$567$		0			0
$568$	36.8433			1.54591
$569$	18.6968	+	22.2820i	0.783813	+	0.934111i	0.999099	−	0.0424395i	$-0.0135130\pi$
$569$	18.6968	+	22.2820i	0.783813	+	0.934111i	−0.215286	+	0.976551i	$0.569069\pi$
$570$		0			0
$571$	3.02630	−	17.1630i	0.126647	−	0.718250i	−0.853669	−	0.520815i	$-0.825628\pi$
$571$	3.02630	−	17.1630i	0.126647	−	0.718250i	0.980316	−	0.197434i	$-0.0632609\pi$
$572$	−1.61396	−	1.35427i	−0.0674830	−	0.0566249i
$573$		0			0
$574$	−24.0352	+	37.5049i	−1.00321	+	1.56543i
$575$	−16.5141	+	9.53441i	−0.688685	+	0.397612i
$576$		0			0
$577$			22.7151i			0.945641i	0.881159	+	0.472821i	$0.156764\pi$
$577$			22.7151i			0.945641i	−0.881159	+	0.472821i	$0.843236\pi$
$578$	−15.3358	−	18.2765i	−0.637884	−	0.760200i
$579$		0			0
$580$	−14.4237	−	39.6287i	−0.598911	−	1.64549i
$581$	−11.5795	+	27.7444i	−0.480401	+	1.15103i
$582$		0			0
$583$	−17.0804	−	6.21677i	−0.707400	−	0.257472i
$584$	−15.0564			−0.623039
$585$		0			0
$586$			4.46687i			0.184525i
$587$	1.35014	−	1.13291i	0.0557264	−	0.0467600i	−0.614499	−	0.788918i	$-0.710642\pi$
$587$	1.35014	−	1.13291i	0.0557264	−	0.0467600i	0.670225	+	0.742158i	$0.266197\pi$
$588$		0			0
$589$	0.280955	−	1.59338i	0.0115766	−	0.0656539i
$590$	24.7273	+	67.9377i	1.01801	+	2.79695i
$591$		0			0
$592$	2.00741	+	11.3846i	0.0825039	+	0.467903i
$593$	20.7313	−	35.9077i	0.851334	−	1.47455i	−0.0286712	−	0.999589i	$-0.509128\pi$
$593$	20.7313	−	35.9077i	0.851334	−	1.47455i	0.880005	−	0.474965i	$-0.157539\pi$
$594$		0			0
$595$	25.3358	−	27.5004i	1.03867	−	1.12741i
$596$	24.7565	−	68.0180i	1.01407	−	2.78613i
$597$		0			0
$598$	−2.16550	−	0.381835i	−0.0885537	−	0.0156144i
$599$	−7.24754	−	19.9124i	−0.296126	−	0.813600i	−0.995138	−	0.0984901i	$-0.968599\pi$
$599$	−7.24754	−	19.9124i	−0.296126	−	0.813600i	0.699012	−	0.715110i	$-0.253624\pi$
$600$		0			0
$601$	5.31277	+	6.33151i	0.216712	+	0.258268i	0.863438	−	0.504455i	$-0.168307\pi$
$601$	5.31277	+	6.33151i	0.216712	+	0.258268i	−0.646726	+	0.762723i	$0.723862\pi$
$602$	11.5807	+	10.6692i	0.471996	+	0.434843i
$603$		0			0
$604$	−32.3285	−	55.9947i	−1.31543	−	2.27839i
$605$	−13.7206	+	11.5130i	−0.557822	+	0.468068i
$606$		0			0
$607$	−15.5617	−	2.74395i	−0.631630	−	0.111373i	−0.151338	−	0.988482i	$-0.548358\pi$
$607$	−15.5617	−	2.74395i	−0.631630	−	0.111373i	−0.480292	+	0.877109i	$0.659469\pi$
$608$	−17.0307	+	6.19865i	−0.690684	+	0.251389i
$609$		0			0
$610$	1.38566	+	7.85846i	0.0561037	+	0.318180i
$611$	0.509501	−	0.294161i	0.0206122	−	0.0119005i
$612$		0			0
$613$	9.40541	−	16.2906i	0.379881	−	0.657973i	−0.611164	−	0.791504i	$-0.709298\pi$
$613$	9.40541	−	16.2906i	0.379881	−	0.657973i	0.991045	+	0.133531i	$0.0426316\pi$
$614$	8.58183	+	48.6699i	0.346334	+	1.96416i
$615$		0			0
$616$	24.8772	−	59.6052i	1.00233	−	2.40156i
$617$	1.65294	−	1.96989i	0.0665447	−	0.0793049i	−0.731745	−	0.681578i	$-0.761294\pi$
$617$	1.65294	−	1.96989i	0.0665447	−	0.0793049i	0.798290	+	0.602273i	$0.205738\pi$
$618$		0			0
$619$	−15.5121	+	2.73521i	−0.623485	+	0.109937i	−0.476461	−	0.879196i	$-0.658081\pi$
$619$	−15.5121	+	2.73521i	−0.623485	+	0.109937i	−0.147024	+	0.989133i	$0.546969\pi$
$620$	3.18499	−	1.83885i	0.127912	−	0.0738501i
$621$		0			0
$622$		−	66.5577i		−	2.66872i
$623$	−0.111932	+	2.41474i	−0.00448444	+	0.0967443i
$624$		0			0
$625$	29.3639	−	10.6876i	1.17456	−	0.427503i
$626$	11.9090	−	4.33451i	0.475979	−	0.173242i
$627$		0			0
$628$	−13.7423	+	2.42314i	−0.548379	+	0.0966939i
$629$	4.94086	+	8.55781i	0.197005	+	0.341222i
$630$		0			0
$631$	−21.8676	+	37.8758i	−0.870536	+	1.50781i	−0.00909374	+	0.999959i	$0.502895\pi$
$631$	−21.8676	+	37.8758i	−0.870536	+	1.50781i	−0.861443	+	0.507855i	$0.830439\pi$
$632$	31.4960	−	86.5344i	1.25284	−	3.44215i
$633$		0			0
$634$	−59.5178	−	49.9413i	−2.36375	−	1.98342i
$635$	−0.590719	+	3.35014i	−0.0234420	+	0.132946i
$636$		0			0
$637$	0.206853	+	0.788920i	0.00819580	+	0.0312582i
$638$	−32.4009	−	18.7067i	−1.28276	−	0.740604i
$639$		0			0
$640$	36.3139	+	20.9659i	1.43543	+	0.828748i
$641$	8.51714	−	23.4007i	0.336407	−	0.924270i	−0.649998	−	0.759936i	$-0.725230\pi$
$641$	8.51714	−	23.4007i	0.336407	−	0.924270i	0.986405	−	0.164334i	$-0.0525475\pi$
$642$		0			0
$643$	22.2139	+	3.91690i	0.876029	+	0.154468i	0.593542	−	0.804803i	$-0.297729\pi$
$643$	22.2139	+	3.91690i	0.876029	+	0.154468i	0.282488	+	0.959271i	$0.408840\pi$
$644$	−10.9707	−	85.0972i	−0.432307	−	3.35330i
$645$		0			0
$646$	−51.7239	+	43.4015i	−2.03505	+	1.70761i
$647$	1.19357	+	2.06732i	0.0469239	+	0.0812747i	0.888533	−	0.458812i	$-0.151725\pi$
$647$	1.19357	+	2.06732i	0.0469239	+	0.0812747i	−0.841609	+	0.540087i	$0.818391\pi$
$648$		0			0
$649$	37.9680	+	21.9208i	1.49038	+	0.860468i
$650$	−0.699122	−	0.254459i	−0.0274218	−	0.00998072i
$651$		0			0
$652$	25.5218	+	21.4153i	0.999509	+	0.838688i
$653$	23.6895	−	28.2321i	0.927043	−	1.10481i	−0.0672091	−	0.997739i	$-0.521409\pi$
$653$	23.6895	−	28.2321i	0.927043	−	1.10481i	0.994252	−	0.107067i	$-0.0341461\pi$
$654$		0			0
$655$	−19.3321	−	7.03630i	−0.755367	−	0.274931i
$656$	40.3256			1.57445
$657$		0			0
$658$	24.7003	+	22.7560i	0.962916	+	0.887122i
$659$	7.39431	−	1.30382i	0.288041	−	0.0507895i	−0.0277605	−	0.999615i	$-0.508838\pi$
$659$	7.39431	−	1.30382i	0.288041	−	0.0507895i	0.315802	+	0.948825i	$0.397726\pi$
$660$		0			0
$661$	−5.35183	+	6.37807i	−0.208162	+	0.248078i	−0.860017	−	0.510266i	$-0.829547\pi$
$661$	−5.35183	+	6.37807i	−0.208162	+	0.248078i	0.651854	+	0.758344i	$0.273991\pi$
$662$	26.5045	−	31.5869i	1.03013	−	1.22766i
$663$		0			0
$664$	65.2606	−	11.5072i	2.53260	−	0.446566i
$665$	−27.8828	−	25.6880i	−1.08125	−	0.996139i
$666$		0			0
$667$	−26.6904			−1.03345
$668$	6.69311	+	2.43609i	0.258964	+	0.0942553i
$669$		0			0
$670$	49.1886	−	58.6207i	1.90032	−	2.26472i
$671$	3.70683	+	3.11040i	0.143100	+	0.120076i
$672$		0			0
$673$	36.7067	+	13.3601i	1.41494	+	0.514995i	0.932575	−	0.360976i	$-0.117556\pi$
$673$	36.7067	+	13.3601i	1.41494	+	0.514995i	0.482363	+	0.875971i	$0.339779\pi$
$674$	3.12535	+	1.80442i	0.120384	+	0.0695038i
$675$		0			0
$676$	28.0494	+	48.5830i	1.07882	+	1.86858i
$677$	−14.6753	+	12.3140i	−0.564017	+	0.473267i	−0.879655	−	0.475613i	$-0.842226\pi$
$677$	−14.6753	+	12.3140i	−0.564017	+	0.473267i	0.315637	+	0.948880i	$0.397782\pi$
$678$		0			0
$679$	−2.02022	−	15.6704i	−0.0775290	−	0.601375i
$680$	−81.1684	−	14.3122i	−3.11267	−	0.548847i
$681$		0			0
$682$	1.11591	−	3.06595i	0.0427305	−	0.117401i
$683$	35.5943	+	20.5504i	1.36198	+	0.786338i	0.989887	−	0.141858i	$-0.0453078\pi$
$683$	35.5943	+	20.5504i	1.36198	+	0.786338i	0.372090	+	0.928196i	$0.378641\pi$
$684$		0			0
$685$	38.7288	+	22.3601i	1.47975	+	0.854335i
$686$	−39.4674	+	24.6985i	−1.50687	+	0.942993i
$687$		0			0
$688$	2.47528	−	14.0380i	0.0943692	−	0.535194i
$689$	−0.387559	−	0.325201i	−0.0147648	−	0.0123892i
$690$		0			0
$691$	−14.5222	+	39.8994i	−0.552451	+	1.51785i	0.277903	+	0.960609i	$0.410361\pi$
$691$	−14.5222	+	39.8994i	−0.552451	+	1.51785i	−0.830353	+	0.557237i	$0.811861\pi$
$692$	−39.4868	+	68.3932i	−1.50106	+	2.59992i
$693$		0			0
$694$	−8.00228	−	13.8604i	−0.303763	−	0.526132i
$695$	−26.3199	+	4.64091i	−0.998370	+	0.176040i
$696$		0			0
$697$	32.3917	−	11.7896i	1.22693	−	0.446564i
$698$	−20.6993	+	7.53394i	−0.783481	+	0.285164i
$699$		0			0
$700$	1.34423	−	28.9994i	0.0508070	−	1.09608i
$701$		−	18.1159i		−	0.684229i	−0.939658	−	0.342114i	$-0.888857\pi$
$701$		−	18.1159i		−	0.684229i	0.939658	−	0.342114i	$-0.111143\pi$
$702$		0			0
$703$	8.67679	−	5.00955i	0.327252	−	0.188939i
$704$	13.6510	−	2.40703i	0.514490	−	0.0907185i
$705$		0			0
$706$	−3.54983	+	4.23052i	−0.133600	+	0.159218i
$707$	8.39529	−	20.1150i	0.315737	−	0.756501i
$708$		0			0
$709$	−1.63998	−	9.30078i	−0.0615907	−	0.349298i	−0.999993	−	0.00375331i	$-0.998805\pi$
$709$	−1.63998	−	9.30078i	−0.0615907	−	0.349298i	0.938402	−	0.345545i	$-0.112306\pi$
$710$	21.8054	−	37.7681i	0.818342	−	1.41741i
$711$		0			0
$712$	4.61446	−	2.66416i	0.172934	−	0.0998437i
$713$	−0.404182	−	2.29223i	−0.0151367	−	0.0858448i
$714$		0			0
$715$	−1.25848	+	0.458050i	−0.0470645	+	0.0171301i
$716$	17.9544	+	3.16584i	0.670986	+	0.118313i
$717$		0			0
$718$	−25.6525	+	21.5250i	−0.957344	+	0.803307i
$719$	7.27759	+	12.6052i	0.271408	+	0.470093i	0.969223	−	0.246186i	$-0.0791773\pi$
$719$	7.27759	+	12.6052i	0.271408	+	0.470093i	−0.697814	+	0.716279i	$0.745844\pi$
$720$		0			0
$721$	1.91833	+	1.76733i	0.0714422	+	0.0658187i
$722$	13.3025	+	15.8533i	0.495068	+	0.589999i
$723$		0			0
$724$	16.2286	+	44.5876i	0.603129	+	1.65708i
$725$	−8.89338	−	1.56814i	−0.330292	−	0.0582394i
$726$		0			0
$727$	−5.63920	+	15.4936i	−0.209146	+	0.574625i	−0.999265	−	0.0383287i	$-0.987797\pi$
$727$	−5.63920	+	15.4936i	−0.209146	+	0.574625i	0.790119	+	0.612954i	$0.210019\pi$
$728$	1.21809	−	1.32216i	0.0451454	−	0.0490025i
$729$		0			0
$730$	−8.91101	+	15.4343i	−0.329811	+	0.571250i
$731$	−2.11588	−	11.9998i	−0.0782587	−	0.443827i
$732$		0			0
$733$	10.6559	+	29.2767i	0.393583	+	1.08136i	0.965353	+	0.260947i	$0.0840348\pi$
$733$	10.6559	+	29.2767i	0.393583	+	1.08136i	−0.571770	+	0.820414i	$0.693743\pi$
$734$	4.65451	−	26.3970i	0.171801	−	0.974332i
$735$		0			0
$736$	−19.9728	+	16.7592i	−0.736209	+	0.617753i
$737$		−	46.4045i		−	1.70933i
$738$		0			0
$739$	−4.19837			−0.154440			−0.0772198	−	0.997014i	$-0.524604\pi$
$739$	−4.19837			−0.154440			−0.0772198	+	0.997014i	$0.524604\pi$
$740$	21.4006	+	7.78916i	0.786700	+	0.286335i
$741$		0			0
$742$	11.1240	−	26.6528i	0.408373	−	0.978455i
$743$	15.8926	+	43.6646i	0.583044	+	1.60190i	0.782950	+	0.622085i	$0.213714\pi$
$743$	15.8926	+	43.6646i	0.583044	+	1.60190i	−0.199906	+	0.979815i	$0.564064\pi$
$744$		0			0
$745$	−29.5752	−	35.2464i	−1.08355	−	1.29133i
$746$			35.1960i			1.28862i
$747$		0			0
$748$	−80.6011	+	46.5351i	−2.94707	+	1.70149i
$749$	−18.4702	+	28.8212i	−0.674886	+	1.05310i
$750$		0			0
$751$	39.5891	+	33.2192i	1.44463	+	1.21219i	0.936387	+	0.350970i	$0.114148\pi$
$751$	39.5891	+	33.2192i	1.44463	+	1.21219i	0.508240	+	0.861216i	$0.330296\pi$
$752$	5.27946	−	29.9413i	0.192522	−	1.09185i
$753$		0			0
$754$	−0.669368	−	0.797721i	−0.0243769	−	0.0290513i
$755$	−41.0997			−1.49577
$756$		0			0
$757$	−34.5687			−1.25642			−0.628210	−	0.778044i	$-0.716212\pi$
$757$	−34.5687			−1.25642			−0.628210	+	0.778044i	$0.716212\pi$
$758$	55.9273	+	66.6515i	2.03137	+	2.42089i
$759$		0			0
$760$	−14.5112	+	82.2969i	−0.526375	+	2.98522i
$761$	6.86703	+	5.76212i	0.248930	+	0.208877i	0.758711	−	0.651427i	$-0.225829\pi$
$761$	6.86703	+	5.76212i	0.248930	+	0.208877i	−0.509782	+	0.860304i	$0.670274\pi$
$762$		0			0
$763$	−8.90937	+	4.60754i	−0.322541	+	0.166804i
$764$	38.0034	−	21.9413i	1.37491	−	0.793807i
$765$		0			0
$766$		−	42.5448i		−	1.53720i
$767$	0.784379	+	0.934786i	0.0283223	+	0.0337532i
$768$		0			0
$769$	2.93294	+	8.05819i	0.105765	+	0.290586i	0.981275	−	0.192614i	$-0.0616966\pi$
$769$	2.93294	+	8.05819i	0.105765	+	0.290586i	−0.875510	+	0.483200i	$0.839474\pi$
$770$	−46.3779	−	60.7784i	−1.67135	−	2.19030i
$771$		0			0
$772$	35.0796	+	12.7679i	1.26254	+	0.459528i
$773$	0.898960			0.0323333			0.0161667	−	0.999869i	$-0.494854\pi$
$773$	0.898960			0.0323333			0.0161667	+	0.999869i	$0.494854\pi$
$774$		0			0
$775$		−	0.787532i		−	0.0282890i
$776$	−26.6789	+	22.3863i	−0.957717	+	0.803620i
$777$		0			0
$778$	−1.90906	+	10.8268i	−0.0684432	+	0.388161i
$779$	−11.9535	−	32.8421i	−0.428280	−	1.17669i
$780$		0			0
$781$	−4.59226	−	26.0440i	−0.164324	−	0.931928i
$782$	−48.5677	+	84.1218i	−1.73678	+	3.00819i
$783$		0			0
$784$	38.1026	+	18.0175i	1.36081	+	0.643482i
$785$	−3.03377	+	8.33523i	−0.108280	+	0.297497i
$786$		0			0
$787$	−39.6542	−	6.99211i	−1.41352	−	0.249242i	−0.585833	−	0.810432i	$-0.699233\pi$
$787$	−39.6542	−	6.99211i	−1.41352	−	0.249242i	−0.827687	+	0.561190i	$0.810344\pi$
$788$	−1.06653	−	2.93027i	−0.0379936	−	0.104386i
$789$		0			0
$790$	−70.0658	−	83.5011i	−2.49283	−	2.97084i
$791$	1.56552	−	6.97286i	0.0556633	−	0.247926i
$792$		0			0
$793$	0.0673425	+	0.116641i	0.00239140	+	0.00414203i
$794$	20.8562	−	17.5004i	0.740157	−	0.621066i
$795$		0			0
$796$	92.6473	+	16.3362i	3.28380	+	0.579022i
$797$	−32.3110	+	11.7602i	−1.14451	+	0.416569i	−0.843542	−	0.537064i	$-0.819533\pi$
$797$	−32.3110	+	11.7602i	−1.14451	+	0.416569i	−0.300972	+	0.953633i	$0.597311\pi$
$798$		0			0
$799$	−4.51291	−	25.5940i	−0.159655	−	0.905450i
$800$	−7.63972	+	4.41080i	−0.270105	+	0.155945i
$801$		0			0
$802$	8.16537	−	14.1428i	0.288329	−	0.499401i
$803$	1.87668	+	10.6432i	0.0662265	+	0.375589i
$804$		0			0
$805$	−50.3324	−	21.0070i	−1.77398	−	0.740399i
$806$	0.0583737	−	0.0695671i	0.00205613	−	0.00245040i
$807$		0			0
$808$	−47.3146	+	8.34284i	−1.66452	+	0.293500i
$809$	−26.8173	+	15.4830i	−0.942848	+	0.544353i	−0.890852	−	0.454294i	$-0.849892\pi$
$809$	−26.8173	+	15.4830i	−0.942848	+	0.544353i	−0.0519959	+	0.998647i	$0.516558\pi$
$810$		0			0
$811$			44.9726i			1.57920i	0.613622	+	0.789600i	$0.289712\pi$
$811$			44.9726i			1.57920i	−0.613622	+	0.789600i	$0.710288\pi$
$812$	21.9245	−	34.2113i	0.769398	−	1.20058i
$813$		0			0
$814$	18.9857	−	6.91023i	0.665449	−	0.242204i
$815$	19.9006	−	7.24321i	0.697086	−	0.253719i
$816$		0			0
$817$	−12.1666	+	2.14530i	−0.425655	+	0.0750545i
$818$	19.4710	+	33.7248i	0.680789	+	1.17916i
$819$		0			0
$820$	39.7215	−	68.7996i	1.38713	−	2.40259i
$821$	−5.71833	+	15.7110i	−0.199571	+	0.548317i	−0.998595	−	0.0529818i	$-0.983127\pi$
$821$	−5.71833	+	15.7110i	−0.199571	+	0.548317i	0.799025	+	0.601298i	$0.205350\pi$
$822$		0			0
$823$	−21.2287	−	17.8130i	−0.739986	−	0.620922i	0.192848	−	0.981229i	$-0.438228\pi$
$823$	−21.2287	−	17.8130i	−0.739986	−	0.620922i	−0.932834	+	0.360307i	$0.882672\pi$
$824$	0.998363	−	5.66200i	0.0347796	−	0.197245i
$825$		0			0
$826$	−37.5863	+	58.6503i	−1.30780	+	2.04071i
$827$	−12.2895	−	7.09535i	−0.427348	−	0.246730i	0.270868	−	0.962616i	$-0.412689\pi$
$827$	−12.2895	−	7.09535i	−0.427348	−	0.246730i	−0.698216	+	0.715887i	$0.746023\pi$
$828$		0			0
$829$	4.00205	+	2.31059i	0.138997	+	0.0802500i	0.567886	−	0.823107i	$-0.307761\pi$
$829$	4.00205	+	2.31059i	0.138997	+	0.0802500i	−0.428889	+	0.903357i	$0.641095\pi$
$830$	26.8279	−	73.7091i	0.931210	−	2.55848i
$831$		0			0
$832$	0.379957	+	0.0669967i	0.0131726	+	0.00232269i
$833$	35.8737	+	3.33291i	1.24295	+	0.115478i
$834$		0			0
$835$	3.46832	−	2.91026i	0.120026	−	0.100714i
$836$	47.1821	+	81.7217i	1.63183	+	2.82640i
$837$		0			0
$838$	−34.1934	−	19.7416i	−1.18119	−	0.681962i
$839$	26.3117	+	9.57669i	0.908382	+	0.330624i	0.753607	−	0.657325i	$-0.228312\pi$
$839$	26.3117	+	9.57669i	0.908382	+	0.330624i	0.154776	+	0.987950i	$0.450535\pi$
$840$		0			0
$841$	12.5325	+	10.5160i	0.432156	+	0.362622i
$842$	−18.7921	+	22.3955i	−0.647617	+	0.771800i
$843$		0			0
$844$	39.3093	+	14.3074i	1.35308	+	0.492482i
$845$	35.6596			1.22673
$846$		0			0
$847$	−16.8385	−	3.78050i	−0.578576	−	0.129899i
$848$	−25.7478	+	4.54004i	−0.884184	+	0.155906i
$849$		0			0
$850$	−21.1255	+	25.1764i	−0.724598	+	0.863542i
$851$	9.26481	−	11.0414i	0.317594	−	0.378493i
$852$		0			0
$853$	26.0162	−	4.58736i	0.890779	−	0.157068i	0.290515	−	0.956870i	$-0.406173\pi$
$853$	26.0162	−	4.58736i	0.890779	−	0.157068i	0.600264	+	0.799802i	$0.295062\pi$
$854$	−5.20956	+	5.65466i	−0.178268	+	0.193498i
$855$		0			0
$856$	75.4542			2.57897
$857$	−9.64582	−	3.51079i	−0.329495	−	0.119926i	0.171975	−	0.985101i	$-0.444985\pi$
$857$	−9.64582	−	3.51079i	−0.329495	−	0.119926i	−0.501470	+	0.865175i	$0.667207\pi$
$858$		0			0
$859$	−0.719929	+	0.857978i	−0.0245637	+	0.0292738i	−0.778186	−	0.628033i	$-0.783860\pi$
$859$	−0.719929	+	0.857978i	−0.0245637	+	0.0292738i	0.753623	+	0.657307i	$0.228305\pi$
$860$	−21.5121	−	18.0508i	−0.733556	−	0.615526i
$861$		0			0
$862$	34.3696	+	12.5095i	1.17063	+	0.426076i
$863$	22.3865	+	12.9249i	0.762046	+	0.439968i	0.830030	−	0.557719i	$-0.188323\pi$
$863$	22.3865	+	12.9249i	0.762046	+	0.439968i	−0.0679836	+	0.997686i	$0.521657\pi$
$864$		0			0
$865$	25.1001	+	43.4746i	0.853428	+	1.47818i
$866$	−24.6607	+	20.6928i	−0.838004	+	0.703168i
$867$		0			0
$868$	3.27016	+	1.36485i	0.110996	+	0.0463261i
$869$	−65.0957	−	11.4781i	−2.20822	−	0.389369i
$870$		0			0
$871$	0.441756	−	1.21371i	0.0149683	−	0.0411252i
$872$	19.1469	+	11.0545i	0.648395	+	0.374351i
$873$		0			0
$874$	85.2914	+	49.2430i	2.88502	+	1.66567i
$875$	15.0469	+	9.64285i	0.508677	+	0.325988i
$876$		0			0
$877$	3.31996	−	18.8284i	0.112107	−	0.635790i	−0.876035	−	0.482247i	$-0.839821\pi$
$877$	3.31996	−	18.8284i	0.112107	−	0.635790i	0.988142	−	0.153543i	$-0.0490682\pi$
$878$	−58.1833	−	48.8215i	−1.96359	−	1.64765i
$879$		0			0
$880$	−23.6710	+	65.0357i	−0.797951	+	2.19235i
$881$	17.8333	−	30.8881i	0.600818	−	1.04065i	−0.391879	−	0.920017i	$-0.628175\pi$
$881$	17.8333	−	30.8881i	0.600818	−	1.04065i	0.992697	−	0.120631i	$-0.0384918\pi$
$882$		0			0
$883$	−22.8393	−	39.5588i	−0.768602	−	1.33126i	−0.938321	−	0.345766i	$-0.887619\pi$
$883$	−22.8393	−	39.5588i	−0.768602	−	1.33126i	0.169718	−	0.985493i	$-0.445714\pi$
$884$	−2.55113	+	0.449833i	−0.0858038	+	0.0151295i
$885$		0			0
$886$	−61.2912	+	22.3082i	−2.05912	+	0.749458i
$887$	37.9021	−	13.7952i	1.27263	−	0.463198i	0.384639	−	0.923067i	$-0.374326\pi$
$887$	37.9021	−	13.7952i	1.27263	−	0.463198i	0.887987	+	0.459869i	$0.152104\pi$
$888$		0			0
$889$	−2.91144	+	1.50567i	−0.0976464	+	0.0504985i
$890$		−	6.30704i		−	0.211413i
$891$		0			0
$892$	−105.282	+	60.7848i	−3.52511	+	2.03523i
$893$	−25.9498	+	4.57565i	−0.868378	+	0.153118i
$894$		0			0
$895$	7.44919	−	8.87759i	0.248999	−	0.296745i
$896$	5.16588	+	40.0705i	0.172580	+	1.33866i
$897$		0			0
$898$	2.28233	+	12.9437i	0.0761622	+	0.431938i
$899$	0.551148	−	0.954617i	0.0183818	−	0.0318383i
$900$		0			0
$901$	−19.3547	+	11.1745i	−0.644799	+	0.372275i
$902$	−12.2385	−	69.4079i	−0.407497	−	2.31103i
$903$		0			0
$904$	−14.8023	+	5.38761i	−0.492319	+	0.179189i
$905$	29.7031	+	5.23746i	0.987366	+	0.174099i
$906$		0			0
$907$	26.3317	−	22.0950i	0.874331	−	0.733651i	−0.0906745	−	0.995881i	$-0.528902\pi$
$907$	26.3317	−	22.0950i	0.874331	−	0.733651i	0.965005	+	0.262230i	$0.0844578\pi$
$908$	16.5483	+	28.6625i	0.549174	+	0.951198i
$909$		0			0
$910$	−0.634430	−	2.03117i	−0.0210311	−	0.0673326i
$911$	−2.82347	−	3.36488i	−0.0935458	−	0.111484i	0.717241	−	0.696825i	$-0.245405\pi$
$911$	−2.82347	−	3.36488i	−0.0935458	−	0.111484i	−0.810787	+	0.585342i	$0.800960\pi$
$912$		0			0
$913$	−16.2686	−	44.6975i	−0.538411	−	1.47927i
$914$	−95.6152	−	16.8595i	−3.16267	−	0.557664i
$915$		0			0
$916$	−21.0067	+	57.7154i	−0.694081	+	1.90697i
$917$	−5.90987	−	18.9208i	−0.195161	−	0.624821i
$918$		0			0
$919$	−11.3040	+	19.5792i	−0.372886	+	0.645857i	−0.990008	−	0.141010i	$-0.954965\pi$
$919$	−11.3040	+	19.5792i	−0.372886	+	0.645857i	0.617122	+	0.786867i	$0.288298\pi$
$920$	20.8758	+	118.392i	0.688254	+	3.90328i
$921$		0			0
$922$	−14.1778	−	38.9531i	−0.466920	−	1.28285i
$923$	0.127820	−	0.724901i	0.00420724	−	0.0238604i
$924$		0			0
$925$	3.73580	−	3.13471i	0.122832	−	0.103069i
$926$		−	102.704i		−	3.37506i
$927$		0			0
$928$	−12.3475			−0.405325
$929$	−15.0096	−	5.46306i	−0.492450	−	0.179237i	0.0838452	−	0.996479i	$-0.473280\pi$
$929$	−15.0096	−	5.46306i	−0.492450	−	0.179237i	−0.576295	+	0.817242i	$0.695502\pi$
$930$		0			0
$931$	3.37925	−	36.3725i	0.110750	−	1.19206i
$932$	−33.2294	−	91.2971i	−1.08847	−	2.99054i
$933$		0			0
$934$	62.5369	+	74.5286i	2.04627	+	2.43865i
$935$			59.1607i			1.93476i
$936$		0			0
$937$	−51.5494	+	29.7620i	−1.68404	+	0.972283i	−0.725119	+	0.688623i	$0.758215\pi$
$937$	−51.5494	+	29.7620i	−1.68404	+	0.972283i	−0.958925	+	0.283660i	$0.908451\pi$
$938$	73.6535	+	3.41410i	2.40487	+	0.111474i
$939$		0			0
$940$	−45.8825	−	38.5000i	−1.49652	−	1.25573i
$941$	−7.06175	+	40.0492i	−0.230206	+	1.30557i	0.622271	+	0.782802i	$0.286210\pi$
$941$	−7.06175	+	40.0492i	−0.230206	+	1.30557i	−0.852478	+	0.522764i	$0.824901\pi$
$942$		0			0
$943$	−32.3186	−	38.5158i	−1.05244	−	1.25425i
$944$	63.0613			2.05247
$945$		0			0
$946$	−24.9132			−0.809999
$947$	−25.4313	−	30.3079i	−0.826407	−	0.984873i	−1.00000		5.57258e-5i	$-0.999982\pi$
$947$	−25.4313	−	30.3079i	−0.826407	−	0.984873i	0.173593	−	0.984817i	$-0.444462\pi$
$948$		0			0
$949$	−0.0522349	+	0.296239i	−0.00169562	+	0.00961631i
$950$	25.5264	+	21.4192i	0.828185	+	0.694930i
$951$		0			0
$952$	−36.4799	−	70.5394i	−1.18232	−	2.28620i
$953$	10.2234	−	5.90251i	0.331170	−	0.191201i	−0.325190	−	0.945649i	$-0.605428\pi$
$953$	10.2234	−	5.90251i	0.331170	−	0.191201i	0.656360	+	0.754447i	$0.272095\pi$
$954$		0			0
$955$		−	27.8942i		−	0.902636i
$956$	66.1699	+	78.8582i	2.14009	+	2.55046i
$957$		0			0
$958$	24.8280	+	68.2145i	0.802158	+	2.20391i
$959$	5.50941	+	42.7352i	0.177908	+	1.37999i
$960$		0			0
$961$	−29.0401	−	10.5697i	−0.936779	−	0.340960i
$962$	0.562357			0.0181311
$963$		0			0
$964$			58.5885i			1.88701i
$965$	18.1780	−	15.2531i	0.585170	−	0.491016i
$966$		0			0
$967$	−3.86189	+	21.9019i	−0.124190	+	0.704317i	0.857596	+	0.514325i	$0.171957\pi$
$967$	−3.86189	+	21.9019i	−0.124190	+	0.704317i	−0.981786	+	0.189992i	$0.939154\pi$
$968$	13.0103	+	35.7455i	0.418167	+	1.14891i
$969$		0			0
$970$	7.15846	+	40.5976i	0.229844	+	1.30351i
$971$	−1.25978	+	2.18201i	−0.0404284	+	0.0700240i	−0.885532	−	0.464579i	$-0.846206\pi$
$971$	−1.25978	+	2.18201i	−0.0404284	+	0.0700240i	0.845103	+	0.534603i	$0.179539\pi$
$972$		0			0
$973$	−18.9388	−	17.4481i	−0.607151	−	0.559360i
$974$	18.3791	−	50.4961i	0.588904	−	1.61800i
$975$		0			0
$976$	6.85450	+	1.20863i	0.219407	+	0.0386874i
$977$	−6.19708	−	17.0263i	−0.198262	−	0.544721i	0.800225	−	0.599699i	$-0.204713\pi$
$977$	−6.19708	−	17.0263i	−0.198262	−	0.544721i	−0.998488	+	0.0549787i	$0.982491\pi$
$978$		0			0
$979$	−2.45842	−	2.92983i	−0.0785713	−	0.0936377i
$980$	68.2714	−	47.2594i	2.18085	−	1.50965i
$981$		0			0
$982$	−22.6079	−	39.1580i	−0.721447	−	1.24958i
$983$	−30.9505	+	25.9705i	−0.987167	+	0.828332i	−0.985155	−	0.171666i	$-0.945085\pi$
$983$	−30.9505	+	25.9705i	−0.987167	+	0.828332i	−0.00201226	+	0.999998i	$0.500641\pi$
$984$		0			0
$985$	−1.95207	−	0.344203i	−0.0621982	−	0.0109672i
$986$	−43.2270	+	15.7333i	−1.37663	+	0.501052i
$987$		0			0
$988$	0.456087	+	2.58660i	0.0145101	+	0.0822907i
$989$	−15.3918	+	8.88645i	−0.489430	+	0.282573i
$990$		0			0
$991$	−13.1394	+	22.7581i	−0.417386	+	0.722934i	−0.995676	−	0.0928979i	$-0.970387\pi$
$991$	−13.1394	+	22.7581i	−0.417386	+	0.722934i	0.578290	+	0.815831i	$0.303720\pi$
$992$	−0.186982	−	1.06043i	−0.00593669	−	0.0336687i
$993$		0			0
$994$	41.6751	−	5.37274i	1.32185	−	0.170413i
$995$	38.4390	−	45.8098i	1.21860	−	1.45227i
$996$		0			0
$997$	13.5180	−	2.38359i	0.428119	−	0.0754889i	0.0445630	−	0.999007i	$-0.485810\pi$
$997$	13.5180	−	2.38359i	0.428119	−	0.0754889i	0.383556	+	0.923518i	$0.374699\pi$
$998$	23.2048	−	13.3973i	0.734536	−	0.424085i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.341.2		132
3.2	odd	2		189.2.ba.a.131.21	yes	132
7.3	odd	6		567.2.bd.a.17.21		132
21.17	even	6		189.2.bd.a.185.2	yes	132
27.7	even	9		189.2.bd.a.47.2	yes	132
27.20	odd	18		567.2.bd.a.467.21		132
189.101	even	18	inner	567.2.ba.a.143.2		132
189.115	odd	18		189.2.ba.a.101.21	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.21	✓	132	189.115	odd	18
189.2.ba.a.131.21	yes	132	3.2	odd	2
189.2.bd.a.47.2	yes	132	27.7	even	9
189.2.bd.a.185.2	yes	132	21.17	even	6
567.2.ba.a.143.2		132	189.101	even	18	inner
567.2.ba.a.341.2		132	1.1	even	1	trivial
567.2.bd.a.17.21		132	7.3	odd	6
567.2.bd.a.467.21		132	27.20	odd	18

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61592 - 1.92578i) q^{2} +(-0.750127 + 4.25418i) q^{4} +(2.10349 + 1.76504i) q^{5} +(-0.122508 + 2.64291i) q^{7} +(5.05050 - 2.91591i) q^{8} -6.90302i q^{10} +(-2.69072 - 3.20668i) q^{11} +(-0.0398496 - 0.109486i) q^{13} +(5.28762 - 4.03481i) q^{14} +(-5.65800 - 2.05934i) q^{16} -5.14689 q^{17} +5.21844i q^{19} +(-9.08669 + 7.62463i) q^{20} +(-1.82736 + 10.3635i) q^{22} +(2.56763 + 7.05452i) q^{23} +(0.441075 + 2.50146i) q^{25} +(-0.146452 + 0.253662i) q^{26} +(-11.1515 - 2.50369i) q^{28} +(-1.21597 + 3.34086i) q^{29} +(-0.305335 - 0.0538389i) q^{31} +(1.18784 + 3.26355i) q^{32} +(8.31695 + 9.91175i) q^{34} +(-4.92254 + 5.34312i) q^{35} +(-0.959970 - 1.66272i) q^{37} +(10.0496 - 8.43258i) q^{38} +(15.7704 + 2.78075i) q^{40} +(-6.29347 + 2.29063i) q^{41} +(0.411100 + 2.33146i) q^{43} +(15.6602 - 9.04140i) q^{44} +(9.43633 - 16.3442i) q^{46} +(0.876823 + 4.97271i) q^{47} +(-6.96998 - 0.647559i) q^{49} +(4.10452 - 4.89157i) q^{50} +(0.495665 - 0.0873991i) q^{52} +(3.76047 - 2.17111i) q^{53} -11.4945i q^{55} +(7.08776 + 13.7053i) q^{56} +(8.39867 - 3.05687i) q^{58} +(-9.84174 + 3.58210i) q^{59} +(-1.13841 + 0.200732i) q^{61} +(0.389715 + 0.675007i) q^{62} +(-1.65570 + 2.86775i) q^{64} +(0.109424 - 0.300639i) q^{65} +(8.49204 + 7.12567i) q^{67} +(3.86082 - 21.8958i) q^{68} +(18.2441 + 0.845678i) q^{70} +(5.47124 + 3.15882i) q^{71} +(-2.23588 - 1.29089i) q^{73} +(-1.65079 + 4.53550i) q^{74} +(-22.2002 - 3.91449i) q^{76} +(8.80461 - 6.71850i) q^{77} +(12.0963 - 10.1500i) q^{79} +(-8.26674 - 14.3184i) q^{80} +(14.5810 + 8.41833i) q^{82} +(10.6778 + 3.88640i) q^{83} +(-10.8264 - 9.08446i) q^{85} +(3.82557 - 4.55914i) q^{86} +(-22.9399 - 8.34943i) q^{88} +0.913664 q^{89} +(0.294244 - 0.0919061i) q^{91} +(-31.9372 + 5.63140i) q^{92} +(8.15946 - 9.72406i) q^{94} +(-9.21076 + 10.9770i) q^{95} +(-5.88114 + 1.03700i) q^{97} +(10.0159 + 14.4690i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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