LMFDB - Embedded newform 189.2.ba.a.101.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(5,189)] 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("189.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([5, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.21
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.21

$q$-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} +(-1.49261 - 0.878707i) q^{3} +(-0.750127 - 4.25418i) q^{4} +(-2.10349 + 1.76504i) q^{5} +(-4.10412 + 1.45451i) q^{6} +(-0.122508 - 2.64291i) q^{7} +(-5.05050 - 2.91591i) q^{8} +(1.45575 + 2.62313i) q^{9} +6.90302i q^{10} +(2.69072 - 3.20668i) q^{11} +(-2.61854 + 7.00896i) q^{12} +(-0.0398496 + 0.109486i) q^{13} +(-5.28762 - 4.03481i) q^{14} +(4.69064 - 0.786155i) q^{15} +(-5.65800 + 2.05934i) q^{16} +5.14689 q^{17} +(7.40393 + 1.43532i) q^{18} -5.21844i q^{19} +(9.08669 + 7.62463i) q^{20} +(-2.13949 + 4.05248i) q^{21} +(-1.82736 - 10.3635i) q^{22} +(-2.56763 + 7.05452i) q^{23} +(4.97618 + 8.79022i) q^{24} +(0.441075 - 2.50146i) q^{25} +(0.146452 + 0.253662i) q^{26} +(0.132107 - 5.19447i) q^{27} +(-11.1515 + 2.50369i) q^{28} +(1.21597 + 3.34086i) q^{29} +(6.06573 - 10.3035i) q^{30} +(-0.305335 + 0.0538389i) q^{31} +(-1.18784 + 3.26355i) q^{32} +(-6.83392 + 2.42195i) q^{33} +(8.31695 - 9.91175i) q^{34} +(4.92254 + 5.34312i) q^{35} +(10.0673 - 8.16068i) q^{36} +(-0.959970 + 1.66272i) q^{37} +(-10.0496 - 8.43258i) q^{38} +(0.155686 - 0.128403i) q^{39} +(15.7704 - 2.78075i) q^{40} +(6.29347 + 2.29063i) q^{41} +(4.34692 + 10.6687i) q^{42} +(0.411100 - 2.33146i) q^{43} +(-15.6602 - 9.04140i) q^{44} +(-7.69208 - 2.94828i) q^{45} +(9.43633 + 16.3442i) q^{46} +(-0.876823 + 4.97271i) q^{47} +(10.2547 + 1.89794i) q^{48} +(-6.96998 + 0.647559i) q^{49} +(-4.10452 - 4.89157i) q^{50} +(-7.68227 - 4.52261i) q^{51} +(0.495665 + 0.0873991i) q^{52} +(-3.76047 - 2.17111i) q^{53} +(-9.78992 - 8.64825i) q^{54} +11.4945i q^{55} +(-7.08776 + 13.7053i) q^{56} +(-4.58549 + 7.78908i) q^{57} +(8.39867 + 3.05687i) q^{58} +(9.84174 + 3.58210i) q^{59} +(-6.86302 - 19.3651i) q^{60} +(-1.13841 - 0.200732i) q^{61} +(-0.389715 + 0.675007i) q^{62} +(6.75436 - 4.16877i) q^{63} +(-1.65570 - 2.86775i) q^{64} +(-0.109424 - 0.300639i) q^{65} +(-6.37893 + 17.0743i) q^{66} +(8.49204 - 7.12567i) q^{67} +(-3.86082 - 21.8958i) q^{68} +(10.0313 - 8.27342i) q^{69} +(18.2441 - 0.845678i) q^{70} +(-5.47124 + 3.15882i) q^{71} +(0.296553 - 17.4929i) q^{72} +(-2.23588 + 1.29089i) q^{73} +(1.65079 + 4.53550i) q^{74} +(-2.85640 + 3.34612i) q^{75} +(-22.2002 + 3.91449i) q^{76} +(-8.80461 - 6.71850i) q^{77} +(0.00429980 - 0.507305i) q^{78} +(12.0963 + 10.1500i) q^{79} +(8.26674 - 14.3184i) q^{80} +(-4.76161 + 7.63722i) q^{81} +(14.5810 - 8.41833i) q^{82} +(-10.6778 + 3.88640i) q^{83} +(18.8449 + 6.06191i) q^{84} +(-10.8264 + 9.08446i) q^{85} +(-3.82557 - 4.55914i) q^{86} +(1.12067 - 6.05508i) q^{87} +(-22.9399 + 8.34943i) q^{88} -0.913664 q^{89} +(-18.1075 + 10.0490i) q^{90} +(0.294244 + 0.0919061i) q^{91} +(31.9372 + 5.63140i) q^{92} +(0.503054 + 0.187940i) q^{93} +(8.15946 + 9.72406i) q^{94} +(9.21076 + 10.9770i) q^{95} +(4.64068 - 3.82744i) q^{96} +(-5.88114 - 1.03700i) q^{97} +(-10.0159 + 14.4690i) q^{98} +(12.3285 + 2.39000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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	0.220248	−	0.975444i	$-0.429313\pi$
$2$	1.61592	−	1.92578i	1.14263	−	1.36173i	0.922379	−	0.386286i	$-0.126242\pi$
$3$	−1.49261	−	0.878707i	−0.861757	−	0.507322i
$3$	−1.49261	−	0.878707i	−0.861757	−	0.507322i
$4$	−0.750127	−	4.25418i	−0.375063	−	2.12709i
$5$	−2.10349	+	1.76504i	−0.940711	+	0.789350i	−0.977709	−	0.209965i	$-0.932665\pi$
$5$	−2.10349	+	1.76504i	−0.940711	+	0.789350i	0.0369981	+	0.999315i	$0.488220\pi$
$6$	−4.10412	+	1.45451i	−1.67550	+	0.593800i
$7$	−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
$9$	1.45575	+	2.62313i	0.485249	+	0.874376i
$10$			6.90302i			2.18293i
$11$	2.69072	−	3.20668i	0.811283	−	0.966850i	−0.188601	−	0.982054i	$-0.560395\pi$
$11$	2.69072	−	3.20668i	0.811283	−	0.966850i	0.999884	+	0.0152039i	$0.00483974\pi$
$12$	−2.61854	+	7.00896i	−0.755906	+	2.02331i
$13$	−0.0398496	+	0.109486i	−0.0110523	+	0.0303659i	−0.945096	−	0.326793i	$-0.894032\pi$
$13$	−0.0398496	+	0.109486i	−0.0110523	+	0.0303659i	0.934044	+	0.357158i	$0.116254\pi$
$14$	−5.28762	−	4.03481i	−1.41318	−	1.07835i
$15$	4.69064	−	0.786155i	1.21112	−	0.202984i
$16$	−5.65800	+	2.05934i	−1.41450	+	0.514836i
$17$	5.14689			1.24830			0.624152	−	0.781303i	$-0.285445\pi$
$17$	5.14689			1.24830			0.624152	+	0.781303i	$0.285445\pi$
$18$	7.40393	+	1.43532i	1.74512	+	0.338308i
$19$		−	5.21844i		−	1.19719i	−0.801051	−	0.598597i	$-0.795725\pi$
$19$		−	5.21844i		−	1.19719i	0.801051	−	0.598597i	$-0.204275\pi$
$20$	9.08669	+	7.62463i	2.03184	+	1.70492i
$21$	−2.13949	+	4.05248i	−0.466875	+	0.884323i
$22$	−1.82736	−	10.3635i	−0.389594	−	2.20950i
$23$	−2.56763	+	7.05452i	−0.535389	+	1.47097i	0.317186	+	0.948363i	$0.397262\pi$
$23$	−2.56763	+	7.05452i	−0.535389	+	1.47097i	−0.852575	+	0.522605i	$0.824960\pi$
$24$	4.97618	+	8.79022i	1.01576	+	1.79430i
$25$	0.441075	−	2.50146i	0.0882150	−	0.500292i
$26$	0.146452	+	0.253662i	0.0287215	+	0.0497472i
$27$	0.132107	−	5.19447i	0.0254240	−	0.999677i
$28$	−11.1515	+	2.50369i	−2.10744	+	0.473153i
$29$	1.21597	+	3.34086i	0.225801	+	0.620383i	0.999920	−	0.0126573i	$-0.00402906\pi$
$29$	1.21597	+	3.34086i	0.225801	+	0.620383i	−0.774119	+	0.633040i	$0.781807\pi$
$30$	6.06573	−	10.3035i	1.10745	−	1.88115i
$31$	−0.305335	+	0.0538389i	−0.0548398	+	0.00966974i	−0.201001	−	0.979591i	$-0.564419\pi$
$31$	−0.305335	+	0.0538389i	−0.0548398	+	0.00966974i	0.146161	+	0.989261i	$0.453308\pi$
$32$	−1.18784	+	3.26355i	−0.209982	+	0.576920i
$33$	−6.83392	+	2.42195i	−1.18963	+	0.421607i
$34$	8.31695	−	9.91175i	1.42634	−	1.69985i
$35$	4.92254	+	5.34312i	0.832062	+	0.903152i
$36$	10.0673	−	8.16068i	1.67788	−	1.36011i
$37$	−0.959970	+	1.66272i	−0.157818	+	0.273349i	−0.934082	−	0.357060i	$-0.883779\pi$
$37$	−0.959970	+	1.66272i	−0.157818	+	0.273349i	0.776264	+	0.630409i	$0.217113\pi$
$38$	−10.0496	−	8.43258i	−1.63025	−	1.36795i
$39$	0.155686	−	0.128403i	0.0249297	−	0.0205610i
$40$	15.7704	−	2.78075i	2.49352	−	0.439674i
$41$	6.29347	+	2.29063i	0.982874	+	0.357737i	0.782957	−	0.622076i	$-0.213710\pi$
$41$	6.29347	+	2.29063i	0.982874	+	0.357737i	0.199917	+	0.979813i	$0.435933\pi$
$42$	4.34692	+	10.6687i	0.670745	+	1.64621i
$43$	0.411100	−	2.33146i	0.0626921	−	0.355545i	−0.937284	−	0.348568i	$-0.886668\pi$
$43$	0.411100	−	2.33146i	0.0626921	−	0.355545i	0.999976	−	0.00697673i	$-0.00222078\pi$
$44$	−15.6602	−	9.04140i	−2.36086	−	1.36304i
$45$	−7.69208	−	2.94828i	−1.14667	−	0.439504i
$46$	9.43633	+	16.3442i	1.39131	+	2.40982i
$47$	−0.876823	+	4.97271i	−0.127898	+	0.725345i	0.851647	+	0.524117i	$0.175604\pi$
$47$	−0.876823	+	4.97271i	−0.127898	+	0.725345i	−0.979544	+	0.201228i	$0.935507\pi$
$48$	10.2547	+	1.89794i	1.48014	+	0.273944i
$49$	−6.96998	+	0.647559i	−0.995712	+	0.0925084i
$50$	−4.10452	−	4.89157i	−0.580466	−	0.691773i
$51$	−7.68227	−	4.52261i	−1.07573	−	0.633292i
$52$	0.495665	+	0.0873991i	0.0687364	+	0.0121201i
$53$	−3.76047	−	2.17111i	−0.516541	−	0.298225i	0.218977	−	0.975730i	$-0.429728\pi$
$53$	−3.76047	−	2.17111i	−0.516541	−	0.298225i	−0.735518	+	0.677505i	$0.763061\pi$
$54$	−9.78992	−	8.64825i	−1.33224	−	1.17688i
$55$			11.4945i			1.54991i
$56$	−7.08776	+	13.7053i	−0.947142	+	1.83144i
$57$	−4.58549	+	7.78908i	−0.607362	+	1.03169i
$58$	8.39867	+	3.05687i	1.10280	+	0.401386i
$59$	9.84174	+	3.58210i	1.28128	+	0.466350i	0.890857	−	0.454284i	$-0.150105\pi$
$59$	9.84174	+	3.58210i	1.28128	+	0.466350i	0.390428	+	0.920634i	$0.372327\pi$
$60$	−6.86302	−	19.3651i	−0.886012	−	2.50003i
$61$	−1.13841	−	0.200732i	−0.145758	−	0.0257011i	0.100293	−	0.994958i	$-0.468022\pi$
$61$	−1.13841	−	0.200732i	−0.145758	−	0.0257011i	−0.246051	+	0.969257i	$0.579133\pi$
$62$	−0.389715	+	0.675007i	−0.0494939	+	0.0857260i
$63$	6.75436	−	4.16877i	0.850969	−	0.525215i
$64$	−1.65570	−	2.86775i	−0.206962	−	0.358469i
$65$	−0.109424	−	0.300639i	−0.0135723	−	0.0372897i
$66$	−6.37893	+	17.0743i	−0.785191	+	2.10170i
$67$	8.49204	−	7.12567i	1.03747	−	0.870539i	0.0457477	−	0.998953i	$-0.485433\pi$
$67$	8.49204	−	7.12567i	1.03747	−	0.870539i	0.991721	+	0.128414i	$0.0409885\pi$
$68$	−3.86082	−	21.8958i	−0.468193	−	2.65525i
$69$	10.0313	−	8.27342i	1.20763	−	0.996002i
$70$	18.2441	−	0.845678i	2.18058	−	0.101078i
$71$	−5.47124	+	3.15882i	−0.649317	+	0.374883i	−0.788194	−	0.615426i	$-0.788984\pi$
$71$	−5.47124	+	3.15882i	−0.649317	+	0.374883i	0.138878	+	0.990310i	$0.455650\pi$
$72$	0.296553	−	17.4929i	0.0349492	−	2.06156i
$73$	−2.23588	+	1.29089i	−0.261690	+	0.151087i	−0.625105	−	0.780541i	$-0.714944\pi$
$73$	−2.23588	+	1.29089i	−0.261690	+	0.151087i	0.363415	+	0.931627i	$0.381611\pi$
$74$	1.65079	+	4.53550i	0.191900	+	0.527241i
$75$	−2.85640	+	3.34612i	−0.329829	+	0.386377i
$76$	−22.2002	+	3.91449i	−2.54654	+	0.449023i
$77$	−8.80461	−	6.71850i	−1.00338	−	0.765644i
$78$	0.00429980	−	0.507305i	0.000486857	−	0.0574410i
$79$	12.0963	+	10.1500i	1.36094	+	1.14197i	0.975690	+	0.219155i	$0.0703299\pi$
$79$	12.0963	+	10.1500i	1.36094	+	1.14197i	0.385252	+	0.922811i	$0.374115\pi$
$80$	8.26674	−	14.3184i	0.924250	−	1.60085i
$81$	−4.76161	+	7.63722i	−0.529067	+	0.848580i
$82$	14.5810	−	8.41833i	1.61020	−	0.929649i
$83$	−10.6778	+	3.88640i	−1.17204	+	0.426588i	−0.853384	−	0.521282i	$-0.825454\pi$
$83$	−10.6778	+	3.88640i	−1.17204	+	0.426588i	−0.318657	+	0.947870i	$0.603232\pi$
$84$	18.8449	+	6.06191i	2.05614	+	0.661408i
$85$	−10.8264	+	9.08446i	−1.17429	+	0.985348i
$86$	−3.82557	−	4.55914i	−0.412522	−	0.491624i
$87$	1.12067	−	6.05508i	0.120148	−	0.649173i
$88$	−22.9399	+	8.34943i	−2.44540	+	0.890052i
$89$	−0.913664			−0.0968482			−0.0484241	−	0.998827i	$-0.515420\pi$
$89$	−0.913664			−0.0968482			−0.0484241	+	0.998827i	$0.515420\pi$
$90$	−18.1075	+	10.0490i	−1.90870	+	1.05926i
$91$	0.294244	+	0.0919061i	0.0308451	+	0.00963438i
$92$	31.9372	+	5.63140i	3.32969	+	0.587114i
$93$	0.503054	+	0.187940i	0.0521643	+	0.0194885i
$94$	8.15946	+	9.72406i	0.841584	+	1.00296i
$95$	9.21076	+	10.9770i	0.945005	+	1.12621i
$96$	4.64068	−	3.82744i	0.473637	−	0.390636i
$97$	−5.88114	−	1.03700i	−0.597140	−	0.105292i	−0.133094	−	0.991103i	$-0.542491\pi$
$97$	−5.88114	−	1.03700i	−0.597140	−	0.105292i	−0.464045	+	0.885812i	$0.653602\pi$
$98$	−10.0159	+	14.4690i	−1.01176	+	1.46159i
$99$	12.3285	+	2.39000i	1.23906	+	0.240204i
$100$	−10.9725			−1.09725
$101$	7.74151	−	2.81768i	0.770309	−	0.280370i	0.0731835	−	0.997318i	$-0.476684\pi$
$101$	7.74151	−	2.81768i	0.770309	−	0.280370i	0.697126	+	0.716949i	$0.254462\pi$
$102$	−21.1235	+	7.48618i	−2.09153	+	0.741242i
$103$	0.633698	+	0.755211i	0.0624401	+	0.0744132i	0.796360	−	0.604822i	$-0.206756\pi$
$103$	0.633698	+	0.755211i	0.0624401	+	0.0744132i	−0.733920	+	0.679236i	$0.762311\pi$
$104$	0.520511	−	0.436761i	0.0510403	−	0.0428279i
$105$	−2.65238	−	12.3006i	−0.258846	−	1.20042i
$106$	−10.2577	+	3.73349i	−0.996315	+	0.362629i
$107$	−11.2050	+	6.46919i	−1.08322	+	0.625400i	−0.931764	−	0.363064i	$-0.881731\pi$
$107$	−11.2050	+	6.46919i	−1.08322	+	0.625400i	−0.151460	+	0.988463i	$0.548397\pi$
$108$	−22.1973	+	3.33451i	−2.13594	+	0.320863i
$109$	1.89554	−	3.28318i	0.181560	−	0.314471i	−0.760852	−	0.648926i	$-0.775219\pi$
$109$	1.89554	−	3.28318i	0.181560	−	0.314471i	0.942412	+	0.334454i	$0.108552\pi$
$110$	22.1358	+	18.5741i	2.11056	+	1.77097i
$111$	2.89390	−	1.63825i	0.274677	−	0.155496i
$112$	6.13582	+	14.7013i	0.579781	+	1.38914i
$113$	2.66007	−	0.469041i	0.250238	−	0.0441237i	−0.0471221	−	0.998889i	$-0.515005\pi$
$113$	2.66007	−	0.469041i	0.250238	−	0.0441237i	0.297360	+	0.954765i	$0.403894\pi$
$114$	7.59026	+	21.4171i	0.710893	+	2.00590i
$115$	−7.05051	−	19.3711i	−0.657463	−	1.80636i
$116$	13.3005	−	7.67905i	1.23492	−	0.712981i
$117$	−0.345207	+	0.0548531i	−0.0319144	+	0.00507117i
$118$	22.8018	−	13.1646i	2.09907	−	1.21190i
$119$	−0.630537	−	13.6028i	−0.0578012	−	1.24696i
$120$	−25.9824	−	9.70700i	−2.37186	−	0.886124i
$121$	−1.13267	−	6.42368i	−0.102970	−	0.583971i
$122$	−2.22614	+	1.86795i	−0.201545	+	0.169117i
$123$	−7.38087	−	8.94913i	−0.665510	−	0.806916i
$124$	0.458080	+	1.25857i	0.0411368	+	0.113023i
$125$	−3.37741	−	5.84984i	−0.302084	−	0.523225i
$126$	2.88638	−	19.7438i	0.257139	−	1.75892i
$127$	0.619432	−	1.07289i	0.0549657	−	0.0952034i	−0.837233	−	0.546846i	$-0.815828\pi$
$127$	0.619432	−	1.07289i	0.0549657	−	0.0952034i	0.892199	+	0.451642i	$0.149162\pi$
$128$	−15.0386	−	2.65171i	−1.32924	−	0.234380i
$129$	−2.66228	+	3.11872i	−0.234401	+	0.274588i
$130$	−0.755783	−	0.275083i	−0.0662866	−	0.0241263i
$131$	7.04031	+	2.56246i	0.615114	+	0.223883i	0.630740	−	0.775995i	$-0.282752\pi$
$131$	7.04031	+	2.56246i	0.615114	+	0.223883i	−0.0156252	+	0.999878i	$0.504974\pi$
$132$	15.4297	+	27.2560i	1.34298	+	2.37233i
$133$	−13.7919	+	0.639304i	−1.19591	+	0.0554346i
$134$		−	27.8683i		−	2.40745i
$135$	8.89057	+	11.1597i	0.765178	+	0.960475i
$136$	−25.9943	−	15.0078i	−2.22900	−	1.28691i
$137$	−16.0387	−	2.82805i	−1.37027	−	0.241616i	−0.560401	−	0.828221i	$-0.689353\pi$
$137$	−16.0387	−	2.82805i	−1.37027	−	0.241616i	−0.809873	+	0.586605i	$0.800464\pi$
$138$	0.277050	−	32.6872i	0.0235840	−	2.78252i
$139$	−6.25623	−	7.45589i	−0.530647	−	0.632400i	0.432417	−	0.901674i	$-0.357661\pi$
$139$	−6.25623	−	7.45589i	−0.530647	−	0.632400i	−0.963064	+	0.269274i	$0.913216\pi$
$140$	19.0381	−	24.9494i	1.60901	−	2.10861i
$141$	5.67831	−	6.65183i	0.478200	−	0.560185i
$142$	−2.75789	+	15.6408i	−0.231437	+	1.31255i
$143$	0.243862	+	0.422381i	0.0203928	+	0.0353213i
$144$	−13.6385	−	11.8438i	−1.13654	−	0.986982i
$145$	−8.45455	−	4.88124i	−0.702112	−	0.405365i
$146$	−1.12704	+	6.39177i	−0.0932746	+	0.528987i
$147$	10.9725	+	5.15803i	0.904993	+	0.425427i
$148$	7.79359	+	2.83664i	0.640630	+	0.233170i
$149$	16.5016	−	2.90967i	1.35186	−	0.238370i	0.549642	−	0.835400i	$-0.314764\pi$
$149$	16.5016	−	2.90967i	1.35186	−	0.238370i	0.802219	+	0.597030i	$0.203653\pi$
$150$	1.82816	+	10.9079i	0.149269	+	0.890623i
$151$	−11.4658	−	9.62098i	−0.933077	−	0.782944i	0.0432907	−	0.999063i	$-0.486216\pi$
$151$	−11.4658	−	9.62098i	−0.933077	−	0.782944i	−0.976367	+	0.216118i	$0.930660\pi$
$152$	−15.2165	+	26.3558i	−1.23422	+	2.13773i
$153$	7.49256	+	13.5009i	0.605738	+	1.09149i
$154$	−27.1659	+	6.09916i	−2.18909	+	0.491484i
$155$	0.547243	−	0.652179i	0.0439556	−	0.0523843i
$156$	−0.663034	−	0.565997i	−0.0530852	−	0.0453160i
$157$	1.10483	−	3.03550i	0.0881752	−	0.242259i	−0.887765	−	0.460296i	$-0.847743\pi$
$157$	1.10483	−	3.03550i	0.0881752	−	0.242259i	0.975940	+	0.218037i	$0.0699654\pi$
$158$	39.0933	−	6.89321i	3.11010	−	0.548394i
$159$	3.70513	+	6.54497i	0.293836	+	0.519050i
$160$	−3.26169	−	8.96143i	−0.257860	−	0.708464i
$161$	18.9590	+	5.92180i	1.49418	+	0.466703i
$162$	7.01321	+	21.5109i	0.551010	+	1.69006i
$163$	3.85622	+	6.67918i	0.302043	+	0.523153i	0.976599	−	0.215070i	$-0.0689981\pi$
$163$	3.85622	+	6.67918i	0.302043	+	0.523153i	−0.674556	+	0.738224i	$0.735665\pi$
$164$	5.02387	−	28.4918i	0.392299	−	2.22484i
$165$	10.1003	−	17.1567i	0.786305	−	1.33565i
$166$	−9.77011	+	26.8432i	−0.758308	+	2.08343i
$167$	−0.286318	−	1.62379i	−0.0221559	−	0.125652i	0.971724	−	0.236121i	$-0.0758761\pi$
$167$	−0.286318	−	1.62379i	−0.0221559	−	0.125652i	−0.993880	+	0.110468i	$0.964765\pi$
$168$	22.6222	−	14.2285i	1.74534	−	1.09775i
$169$	9.94818	+	8.34751i	0.765245	+	0.642116i
$170$			35.5290i			2.72495i
$171$	13.6886	−	7.59673i	1.04680	−	0.580937i
$172$	−10.2268			−0.779789
$173$	−17.1792	+	6.25273i	−1.30611	+	0.475386i	−0.898983	−	0.437984i	$-0.855693\pi$
$173$	−17.1792	+	6.25273i	−1.30611	+	0.475386i	−0.407130	+	0.913370i	$0.633470\pi$
$174$	−9.84982	−	11.9427i	−0.746713	−	0.905372i
$175$	−6.66518	−	0.859273i	−0.503840	−	0.0649550i
$176$	−8.62046	+	23.6845i	−0.649792	+	1.78529i
$177$	−11.5422	−	13.9947i	−0.867566	−	1.05190i
$178$	−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	$-0.0504156\pi$
$180$	−6.77249	+	34.9351i	−0.504791	+	2.60391i
$181$	9.51249	+	5.49204i	0.707058	+	0.408220i	0.809971	−	0.586470i	$-0.199483\pi$
$181$	9.51249	+	5.49204i	0.707058	+	0.408220i	−0.102913	+	0.994690i	$0.532816\pi$
$182$	0.652465	−	0.418135i	0.0483639	−	0.0309942i
$183$	1.52281	+	1.29994i	0.112569	+	0.0960946i
$184$	33.5382	−	28.1419i	2.47247	−	2.07465i
$185$	−0.915472	−	5.19190i	−0.0673068	−	0.381716i
$186$	1.17483	−	0.665074i	0.0861424	−	0.0487656i
$187$	13.8488	−	16.5044i	1.01273	−	1.20692i
$188$	21.8125			1.59084
$189$	−13.7447	+	0.287220i	−0.999782	+	0.0208922i
$190$	36.0230			2.61338
$191$	6.52972	−	7.78182i	0.472474	−	0.563073i	−0.476196	−	0.879339i	$-0.657985\pi$
$191$	6.52972	−	7.78182i	0.472474	−	0.563073i	0.948670	+	0.316266i	$0.102429\pi$
$192$	−0.0486110	+	5.73529i	−0.00350820	+	0.413909i
$193$	1.50063	+	8.51052i	0.108018	+	0.612600i	0.989972	+	0.141265i	$0.0451168\pi$
$193$	1.50063	+	8.51052i	0.108018	+	0.612600i	−0.881954	+	0.471336i	$0.843772\pi$
$194$	−11.5005	+	9.65005i	−0.825687	+	0.692833i
$195$	−0.100847	+	0.544887i	−0.00722183	+	0.0390202i
$196$	7.98320	+	29.1658i	0.570229	+	2.08327i
$197$	0.625155	+	0.360933i	0.0445405	+	0.0257154i	0.522105	−	0.852881i	$-0.325147\pi$
$197$	0.625155	+	0.360933i	0.0445405	+	0.0257154i	−0.477564	+	0.878597i	$0.658480\pi$
$198$	24.5245	−	19.8800i	1.74288	−	1.41281i
$199$			21.7780i			1.54380i	0.635745	+	0.771899i	$0.280693\pi$
$199$			21.7780i			1.54380i	−0.635745	+	0.771899i	$0.719307\pi$
$200$	−9.52168	+	11.3475i	−0.673285	+	0.802389i
$201$	−18.9367	+	3.17380i	−1.33569	+	0.223862i
$202$	7.08343	−	19.4616i	0.498388	−	1.36931i
$203$	8.68065	−	3.62300i	0.609262	−	0.254285i
$204$	−13.4773	+	36.0743i	−0.943600	+	2.52571i
$205$	−17.2813	+	6.28989i	−1.20698	+	0.439305i
$206$	2.47837			0.172676
$207$	−22.2427	+	3.53435i	−1.54598	+	0.245654i
$208$		−	0.701536i		−	0.0486427i
$209$	−16.7339	−	14.0414i	−1.15751	−	0.971263i
$210$	−27.9743	−	14.7689i	−1.93041	−	1.01915i
$211$	1.68157	+	9.53668i	0.115764	+	0.656532i	0.986369	+	0.164549i	$0.0526168\pi$
$211$	1.68157	+	9.53668i	0.115764	+	0.656532i	−0.870605	+	0.491983i	$0.836272\pi$
$212$	−6.41546	+	17.6263i	−0.440616	+	1.21058i
$213$	10.9421	+	0.0927426i	0.749739	+	0.00635462i
$214$	−5.64809	+	32.0319i	−0.386096	+	2.18966i
$215$	3.25038	+	5.62982i	0.221674	+	0.383951i
$216$	−15.8138	+	25.8495i	−1.07599	+	1.75883i
$217$	0.179698	+	0.800379i	0.0121987	+	0.0543333i
$218$	−3.25962	−	8.95574i	−0.220769	−	0.606559i
$219$	4.47160	+	0.0379002i	0.302163	+	0.00256106i
$220$	48.8995	−	8.62230i	3.29680	−	0.581315i
$221$	−0.205101	+	0.563512i	−0.0137966	+	0.0379059i
$222$	1.52140	−	8.22028i	0.102110	−	0.551709i
$223$	18.0896	−	21.5583i	1.21137	−	1.44365i	0.349183	−	0.937055i	$-0.386459\pi$
$223$	18.0896	−	21.5583i	1.21137	−	1.44365i	0.862184	−	0.506596i	$-0.169096\pi$
$224$	8.77080	+	2.73953i	0.586024	+	0.183043i
$225$	7.20375	−	2.48450i	0.480250	−	0.165633i
$226$	3.39518	−	5.88062i	0.225844	−	0.391173i
$227$	−5.86912	−	4.92477i	−0.389547	−	0.326869i	0.426890	−	0.904304i	$-0.359609\pi$
$227$	−5.86912	−	4.92477i	−0.389547	−	0.326869i	−0.816437	+	0.577435i	$0.804054\pi$
$228$	36.5758	+	13.6647i	2.42229	+	0.904966i
$229$	14.0021	−	2.46895i	0.925285	−	0.163153i	0.309349	−	0.950949i	$-0.399889\pi$
$229$	14.0021	−	2.46895i	0.925285	−	0.163153i	0.615936	+	0.787796i	$0.288778\pi$
$230$	−48.6975	−	17.7244i	−3.21102	−	1.16871i
$231$	7.23822	+	17.7648i	0.476240	+	1.16883i
$232$	3.60037	−	20.4187i	0.236376	−	1.34055i
$233$	19.4777	+	11.2455i	1.27603	+	0.736714i	0.976115	−	0.217253i	$-0.0697097\pi$
$233$	19.4777	+	11.2455i	1.27603	+	0.736714i	0.299911	+	0.953967i	$0.403043\pi$
$234$	−0.452191	+	0.753429i	−0.0295606	+	0.0492532i
$235$	−6.93265	−	12.0077i	−0.452236	−	0.783296i
$236$	7.85634	−	44.5555i	0.511404	−	2.90032i
$237$	−9.13614	−	25.7791i	−0.593456	−	1.67453i
$238$	−27.2148	−	20.7667i	−1.76407	−	1.34611i
$239$	−15.3178	−	18.2550i	−0.990825	−	1.18082i	−0.983511	−	0.180846i	$-0.942116\pi$
$239$	−15.3178	−	18.2550i	−0.990825	−	1.18082i	−0.00731345	−	0.999973i	$-0.502328\pi$
$240$	−24.9207	+	14.1077i	−1.60862	+	0.910649i
$241$	13.3567	+	2.35515i	0.860381	+	0.151708i	0.586395	−	0.810025i	$-0.300547\pi$
$241$	13.3567	+	2.35515i	0.860381	+	0.151708i	0.273986	+	0.961734i	$0.411658\pi$
$242$	−14.2009	−	8.19887i	−0.912866	−	0.527044i
$243$	13.8181	−	7.21530i	0.886430	−	0.462862i
$244$			4.99357i			0.319681i
$245$	13.5183	−	13.6644i	0.863655	−	0.872989i
$246$	−29.1609	−	0.247161i	−1.85923	−	0.0157584i
$247$	0.571346	+	0.207953i	0.0363539	+	0.0132317i
$248$	1.69909	+	0.618417i	0.107892	+	0.0392695i
$249$	19.3528	+	3.58180i	1.22643	+	0.226987i
$250$	−16.7231	−	2.94873i	−1.05766	−	0.186494i
$251$	−4.77251	+	8.26623i	−0.301238	+	0.521760i	−0.976417	−	0.215895i	$-0.930733\pi$
$251$	−4.77251	+	8.26623i	−0.301238	+	0.521760i	0.675179	+	0.737654i	$0.264067\pi$
$252$	−22.8013	−	25.6072i	−1.43635	−	1.61310i
$253$	15.7128	+	27.2153i	0.987854	+	1.71101i
$254$	−1.06519	−	2.92659i	−0.0668360	−	0.183630i
$255$	24.1422	−	4.04625i	1.51184	−	0.253386i
$256$	−24.3344	+	20.4190i	−1.52090	+	1.27619i
$257$	0.960437	+	5.44691i	0.0599104	+	0.339769i	0.999999	−	0.00116059i	$-0.000369428\pi$
$257$	0.960437	+	5.44691i	0.0599104	+	0.339769i	−0.940089	+	0.340929i	$0.889258\pi$
$258$	1.70392	+	10.1666i	0.106082	+	0.632942i
$259$	4.51202	+	2.33342i	0.280363	+	0.144992i
$260$	−1.19689	+	0.691025i	−0.0742280	+	0.0428556i
$261$	−6.99336	+	8.05311i	−0.432878	+	0.498475i
$262$	16.3113	−	9.41733i	1.00771	−	0.581804i
$263$	2.86165	+	7.86232i	0.176457	+	0.484811i	0.996117	−	0.0880387i	$-0.0280599\pi$
$263$	2.86165	+	7.86232i	0.176457	+	0.484811i	−0.819660	+	0.572850i	$0.805838\pi$
$264$	41.5769	+	7.69503i	2.55888	+	0.473596i
$265$	11.7422	−	2.07047i	0.721319	−	0.127188i
$266$	−21.0554	+	27.5932i	−1.29099	+	1.69185i
$267$	1.36374	+	0.802844i	0.0834596	+	0.0491332i
$268$	−36.6840	−	30.7815i	−2.24083	−	1.88028i
$269$	−9.52435	+	16.4967i	−0.580710	+	1.00582i	0.414685	+	0.909965i	$0.363892\pi$
$269$	−9.52435	+	16.4967i	−0.580710	+	1.00582i	−0.995395	+	0.0958542i	$0.969442\pi$
$270$	35.8575	+	0.911936i	2.18222	+	0.0554986i
$271$	−21.6453	+	12.4969i	−1.31486	+	0.759134i	−0.982896	−	0.184159i	$-0.941044\pi$
$271$	−21.6453	+	12.4969i	−1.31486	+	0.759134i	−0.331962	+	0.943293i	$0.607710\pi$
$272$	−29.1211	+	10.5992i	−1.76573	+	0.642671i
$273$	−0.358431	−	0.395734i	−0.0216933	−	0.0239509i
$274$	−31.3633	+	26.3170i	−1.89473	+	1.58987i
$275$	−6.83457	−	8.14513i	−0.412140	−	0.491170i
$276$	−42.7214	−	36.4689i	−2.57152	−	2.19517i
$277$	−20.9786	+	7.63560i	−1.26048	+	0.458778i	−0.883931	−	0.467617i	$-0.845113\pi$
$277$	−20.9786	+	7.63560i	−1.26048	+	0.458778i	−0.376552	+	0.926395i	$0.622890\pi$
$278$	−24.4679			−1.46749
$279$	−0.585717	−	0.722558i	−0.0350660	−	0.0432584i
$280$	−9.28127	−	41.3391i	−0.554662	−	2.47048i
$281$	11.7375	+	2.06964i	0.700200	+	0.123464i	0.512405	−	0.858744i	$-0.328755\pi$
$281$	11.7375	+	2.06964i	0.700200	+	0.123464i	0.187795	+	0.982208i	$0.439866\pi$
$282$	−3.63425	−	21.6840i	−0.216416	−	1.29126i
$283$	−2.59842	−	3.09667i	−0.154460	−	0.184078i	0.683265	−	0.730170i	$-0.260559\pi$
$283$	−2.59842	−	3.09667i	−0.154460	−	0.184078i	−0.837725	+	0.546092i	$0.816115\pi$
$284$	17.5423	+	20.9061i	1.04094	+	1.24055i
$285$	−4.10251	−	24.4778i	−0.243011	−	1.44994i
$286$	1.20747	+	0.212910i	0.0713994	+	0.0125896i
$287$	5.28295	−	16.9137i	0.311842	−	0.998385i
$288$	−10.2899	+	1.63506i	−0.606338	+	0.0963467i
$289$	9.49043			0.558261
$290$	−23.0620	+	8.39390i	−1.35425	+	0.492907i
$291$	7.86701	+	6.71564i	0.461172	+	0.393678i
$292$	7.16885	+	8.54350i	0.419525	+	0.499971i
$293$	1.36115	−	1.14214i	0.0795192	−	0.0667245i	−0.602162	−	0.798374i	$-0.705694\pi$
$293$	1.36115	−	1.14214i	0.0795192	−	0.0667245i	0.681681	+	0.731650i	$0.261249\pi$
$294$	27.6638	−	12.7955i	1.61339	−	0.746251i
$295$	−27.0246	+	9.83614i	−1.57343	+	0.572682i
$296$	9.69666	−	5.59837i	0.563607	−	0.325399i
$297$	−16.3015	−	14.4005i	−0.945911	−	0.835602i
$298$	21.0618	−	36.4801i	1.22008	−	2.11324i
$299$	−0.670051	−	0.562240i	−0.0387501	−	0.0325152i
$300$	16.3777	+	9.64165i	0.945565	+	0.556661i
$301$	−6.21221	−	0.800877i	−0.358066	−	0.0461618i
$302$	−37.0557	+	6.53392i	−2.13232	+	0.375985i
$303$	−14.0309	−	2.59684i	−0.806057	−	0.149184i
$304$	10.7466	+	29.5260i	0.616358	+	1.69343i
$305$	2.74894	−	1.58710i	0.157404	−	0.0908770i
$306$	38.1072	+	7.38742i	2.17844	+	0.422311i
$307$	−17.0250	+	9.82941i	−0.971670	+	0.560994i	−0.899745	−	0.436416i	$-0.856248\pi$
$307$	−17.0250	+	9.82941i	−0.971670	+	0.560994i	−0.0719253	+	0.997410i	$0.522914\pi$
$308$	−21.9771	+	42.4961i	−1.25226	+	2.42144i
$309$	−0.282251	−	1.68407i	−0.0160567	−	0.0958033i
$310$	−0.371651	−	2.10774i	−0.0211083	−	0.119711i
$311$	−20.2815	+	17.0182i	−1.15006	+	0.965014i	−0.999721	−	0.0236210i	$-0.992480\pi$
$311$	−20.2815	+	17.0182i	−1.15006	+	0.965014i	−0.150338	+	0.988635i	$0.548036\pi$
$312$	−1.16070	+	0.194535i	−0.0657119	+	0.0110134i
$313$	−1.72420	−	4.73721i	−0.0974577	−	0.267763i	0.881378	−	0.472413i	$-0.156617\pi$
$313$	−1.72420	−	4.73721i	−0.0974577	−	0.267763i	−0.978835	+	0.204650i	$0.934395\pi$
$314$	−4.06038	−	7.03278i	−0.229140	−	0.396883i
$315$	−6.84971	+	20.6907i	−0.385937	+	1.16579i
$316$	34.1062	−	59.0737i	1.91862	−	3.32316i
$317$	−30.4363	−	5.36674i	−1.70947	−	0.301426i	−0.768486	−	0.639866i	$-0.778990\pi$
$317$	−30.4363	−	5.36674i	−1.70947	−	0.301426i	−0.940988	+	0.338440i	$0.890101\pi$
$318$	18.5913	+	3.44087i	1.04255	+	0.192955i
$319$	13.9849	+	5.09010i	0.783005	+	0.284991i
$320$	8.54444	+	3.10992i	0.477649	+	0.173850i
$321$	22.4091	+	0.189934i	1.25075	+	0.0106011i
$322$	42.0403	−	26.9417i	2.34281	−	1.50140i
$323$		−	26.8587i		−	1.49446i
$324$	36.0619	+	14.5278i	2.00344	+	0.807102i
$325$	0.256298	+	0.147974i	0.0142169	+	0.00820811i
$326$	19.0939	+	3.36678i	1.05752	+	0.186469i
$327$	−5.71425	+	3.23486i	−0.315999	+	0.178888i
$328$	−25.1059	−	29.9200i	−1.38624	−	1.65206i
$329$	13.2499	+	1.70817i	0.730489	+	0.0941744i
$330$	−16.7188	−	47.1747i	−0.920338	−	2.59688i
$331$	2.84820	−	16.1530i	0.156551	−	0.887847i	−0.800802	−	0.598929i	$-0.795593\pi$
$331$	2.84820	−	16.1530i	0.156551	−	0.887847i	0.957354	−	0.288918i	$-0.0932956\pi$
$332$	24.5432	+	42.5100i	1.34698	+	2.33304i
$333$	−5.75899	−	0.0976308i	−0.315591	−	0.00535014i
$334$	−3.58972	−	2.07252i	−0.196421	−	0.113403i
$335$	−5.28586	+	29.9776i	−0.288797	+	1.63785i
$336$	3.75980	−	27.3349i	0.205114	−	1.49124i
$337$	−1.34897	−	0.490985i	−0.0734831	−	0.0267457i	0.305017	−	0.952347i	$-0.401338\pi$
$337$	−1.34897	−	0.490985i	−0.0734831	−	0.0267457i	−0.378500	+	0.925601i	$0.623560\pi$
$338$	32.1509	−	5.66907i	1.74878	−	0.308357i
$339$	−4.38258	−	1.63733i	−0.238029	−	0.0889273i
$340$	46.7681	+	39.2431i	2.53636	+	2.12826i
$341$	−0.648929	+	1.12398i	−0.0351415	+	0.0608668i
$342$	7.49013	−	38.6370i	0.405020	−	2.08925i
$343$	2.56532	+	18.3417i	0.138514	+	0.990360i
$344$	−8.87459	+	10.5763i	−0.478486	+	0.570237i
$345$	−6.49791	+	35.1088i	−0.349836	+	1.89019i
$346$	−15.7189	+	43.1872i	−0.845052	+	2.32176i
$347$	−6.26965	+	1.10551i	−0.336573	+	0.0593468i	−0.339380	−	0.940649i	$-0.610217\pi$
$347$	−6.26965	+	1.10551i	−0.336573	+	0.0593468i	0.00280775	+	0.999996i	$0.499106\pi$
$348$	−26.6000	−	0.225456i	−1.42591	−	0.0120857i
$349$	2.99689	+	8.23388i	0.160420	+	0.440749i	0.993696	−	0.112107i	$-0.0357600\pi$
$349$	2.99689	+	8.23388i	0.160420	+	0.440749i	−0.833276	+	0.552856i	$0.813538\pi$
$350$	−12.4252	+	11.4471i	−0.664153	+	0.611875i
$351$	0.563457	+	0.221462i	0.0300751	+	0.0118207i
$352$	7.26902	+	12.5903i	0.387440	+	0.671066i
$353$	0.381468	−	2.16341i	0.0203035	−	0.115147i	−0.972972	−	0.230925i	$-0.925825\pi$
$353$	0.381468	−	2.16341i	0.0203035	−	0.115147i	0.993275	+	0.115778i	$0.0369360\pi$
$354$	−45.6019	−	0.386511i	−2.42371	−	0.0205428i
$355$	5.93327	−	16.3015i	0.314905	−	0.865195i
$356$	0.685364	+	3.88689i	0.0363242	+	0.206005i
$357$	−11.0117	+	20.8576i	−0.582802	+	1.10390i
$358$	−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	$-0.114334\pi$
$360$	30.2519	+	37.3197i	1.59442	+	1.96692i
$361$	−8.23216			−0.433272
$362$	25.9479	−	9.44425i	1.36379	−	0.496379i
$363$	−3.95391	+	10.5833i	−0.207526	+	0.555479i
$364$	0.170265	−	1.32071i	0.00892432	−	0.0692239i
$365$	2.42469	−	6.66179i	0.126914	−	0.348694i
$366$	4.96414	−	0.831993i	0.259480	−	0.0434890i
$367$	6.85361	−	8.16781i	0.357755	−	0.426356i	−0.556907	−	0.830575i	$-0.688012\pi$
$367$	6.85361	−	8.16781i	0.357755	−	0.426356i	0.914662	+	0.404219i	$0.132457\pi$
$368$		−	45.2021i		−	2.35632i
$369$	3.15306	+	19.8432i	0.164142	+	1.03299i
$370$	−11.4778	−	6.62669i	−0.596701	−	0.344505i
$371$	−5.27737	+	10.2046i	−0.273987	+	0.529796i
$372$	0.422177	−	2.28106i	0.0218889	−	0.118268i
$373$	−10.7249	+	8.99930i	−0.555317	+	0.465966i	−0.876737	−	0.480971i	$-0.840284\pi$
$373$	−10.7249	+	8.99930i	−0.555317	+	0.465966i	0.321420	+	0.946937i	$0.395840\pi$
$374$	−9.40520	−	53.3395i	−0.486331	−	2.75812i
$375$	−0.0991602	+	11.6993i	−0.00512061	+	0.604147i
$376$	18.9284	−	22.5580i	0.976156	−	1.16334i
$377$	−0.414234			−0.0213341
$378$	−21.6572	+	26.9334i	−1.11393	+	1.38530i
$379$	−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
$381$	−1.86732	+	1.05710i	−0.0956659	+	0.0541569i
$382$	−4.43455	−	25.1496i	−0.226891	−	1.28676i
$383$	−12.9643	+	10.8783i	−0.662443	+	0.555856i	−0.910818	−	0.412808i	$-0.864548\pi$
$383$	−12.9643	+	10.8783i	−0.662443	+	0.555856i	0.248375	+	0.968664i	$0.420104\pi$
$384$	20.1166	+	17.1725i	1.02657	+	0.876329i
$385$	30.3789	−	1.40817i	1.54825	−	0.0717669i
$386$	18.8143	+	10.8624i	0.957620	+	0.552882i
$387$	6.71418	−	2.31565i	0.341301	−	0.117711i
$388$			25.7973i			1.30966i
$389$	2.81103	−	3.35005i	0.142525	−	0.169855i	−0.690060	−	0.723752i	$-0.742416\pi$
$389$	2.81103	−	3.35005i	0.142525	−	0.169855i	0.832585	+	0.553898i	$0.186860\pi$
$390$	0.886370	+	1.07470i	0.0448831	+	0.0544197i
$391$	−13.2153	+	36.3088i	−0.668327	+	1.83621i
$392$	37.0901	+	17.0533i	1.87333	+	0.861323i
$393$	−8.25675	−	10.0111i	−0.416498	−	0.504994i
$394$	1.70528	−	0.620670i	0.0859106	−	0.0312689i
$395$	−43.3597			−2.18166
$396$	0.919528	−	54.2406i	0.0462080	−	2.72569i
$397$		−	10.8300i		−	0.543542i	−0.962362	−	0.271771i	$-0.912391\pi$
$397$		−	10.8300i		−	0.543542i	0.962362	−	0.271771i	$-0.0876094\pi$
$398$	41.9395	+	35.1914i	2.10224	+	1.76399i
$399$	21.1476	+	11.1648i	1.05871	+	0.558940i
$400$	2.65577	+	15.0616i	0.132788	+	0.753080i
$401$	−2.22180	+	6.10435i	−0.110952	+	0.304837i	−0.982725	−	0.185073i	$-0.940748\pi$
$401$	−2.22180	+	6.10435i	−0.110952	+	0.304837i	0.871773	+	0.489909i	$0.162970\pi$
$402$	−24.4881	+	41.5964i	−1.22135	+	2.07464i
$403$	0.00627290	−	0.0355754i	0.000312475	−	0.00177214i
$404$	−17.7940	−	30.8202i	−0.885286	−	1.53336i
$405$	−3.46399	−	24.4693i	−0.172127	−	1.21589i
$406$	7.05013	−	22.5715i	0.349892	−	1.12020i
$407$	2.74878	+	7.55222i	0.136252	+	0.374350i
$408$	25.6118	+	45.2422i	1.26797	+	2.23982i
$409$	−15.2552	+	2.68991i	−0.754323	+	0.133007i	−0.537570	−	0.843219i	$-0.680658\pi$
$409$	−15.2552	+	2.68991i	−0.754323	+	0.133007i	−0.216753	+	0.976227i	$0.569547\pi$
$410$	−15.8123	+	43.4439i	−0.780913	+	2.14554i
$411$	21.4544	+	18.3144i	1.05827	+	0.903385i
$412$	2.73745	−	3.26237i	0.134865	−	0.160725i
$413$	8.26148	−	26.4497i	0.406521	−	1.30150i
$414$	−29.1361	+	48.5457i	−1.43196	+	2.38589i
$415$	15.6010	−	27.0218i	0.765824	−	1.32645i
$416$	−0.309978	−	0.260102i	−0.0151979	−	0.0127526i
$417$	2.78655	+	16.6261i	0.136458	+	0.814184i
$418$	−54.0811	+	9.53596i	−2.64519	+	0.466419i
$419$	−14.7586	−	5.37170i	−0.721006	−	0.262425i	−0.0446532	−	0.999003i	$-0.514218\pi$
$419$	−14.7586	−	5.37170i	−0.721006	−	0.262425i	−0.676353	+	0.736578i	$0.736441\pi$
$420$	−50.3395	+	20.5108i	−2.45632	+	1.00082i
$421$	−2.01941	+	11.4527i	−0.0984202	+	0.558168i	0.895225	+	0.445614i	$0.147014\pi$
$421$	−2.01941	+	11.4527i	−0.0984202	+	0.558168i	−0.993646	+	0.112555i	$0.964097\pi$
$422$	21.0828	+	12.1722i	1.02629	+	0.592531i
$423$	−14.3205	+	4.93899i	−0.696286	+	0.240142i
$424$	12.6615	+	21.9304i	0.614898	+	1.06503i
$425$	2.27016	−	12.8747i	0.110119	−	0.624517i
$426$	17.8601	−	20.9221i	0.865325	−	1.01368i
$427$	−0.391053	+	3.03331i	−0.0189244	+	0.146792i
$428$	35.9262	+	42.8152i	1.73656	+	2.06955i
$429$	0.00715975	−	0.844732i	0.000345676	−	0.0407840i
$430$	16.0941	+	2.83783i	0.776127	+	0.136852i
$431$	12.5999	+	7.27456i	0.606916	+	0.350403i	0.771758	−	0.635917i	$-0.219378\pi$
$431$	12.5999	+	7.27456i	0.606916	+	0.350403i	−0.164841	+	0.986320i	$0.552711\pi$
$432$	9.94975	+	29.6624i	0.478707	+	1.42713i
$433$			12.8056i			0.615396i	0.951484	+	0.307698i	$0.0995587\pi$
$433$			12.8056i			0.615396i	−0.951484	+	0.307698i	$0.900441\pi$
$434$	1.83173	+	0.947290i	0.0879258	+	0.0454714i
$435$	8.33014	+	14.7148i	0.399400	+	0.705523i
$436$	−15.3891	−	5.60118i	−0.737005	−	0.268248i
$437$	36.8136	+	13.3991i	1.76103	+	0.640964i
$438$	7.29872	−	8.55005i	0.348747	−	0.408537i
$439$	29.7539	+	5.24641i	1.42008	+	0.250398i	0.830366	−	0.557218i	$-0.188131\pi$
$439$	29.7539	+	5.24641i	1.42008	+	0.250398i	0.589709	+	0.807616i	$0.299242\pi$
$440$	33.5168	−	58.0528i	1.59785	−	2.76756i
$441$	−11.8452	−	17.3405i	−0.564055	−	0.825737i
$442$	0.753770	+	1.30557i	0.0358532	+	0.0620995i
$443$	−8.87386	−	24.3807i	−0.421610	−	1.15836i	−0.950785	−	0.309851i	$-0.899721\pi$
$443$	−8.87386	−	24.3807i	−0.421610	−	1.15836i	0.529176	−	0.848512i	$-0.322501\pi$
$444$	−9.14019	−	11.0823i	−0.433774	−	0.525941i
$445$	1.92189	−	1.61265i	0.0911062	−	0.0764471i
$446$	−12.2852	−	69.6729i	−0.581722	−	3.29911i
$447$	−27.1871	−	10.1571i	−1.28591	−	0.480412i
$448$	−7.37638	+	4.72718i	−0.348501	+	0.223338i
$449$	4.52779	−	2.61412i	0.213680	−	0.123368i	−0.389341	−	0.921094i	$-0.627297\pi$
$449$	4.52779	−	2.61412i	0.213680	−	0.123368i	0.603020	+	0.797726i	$0.293964\pi$
$450$	6.85609	−	17.8876i	0.323199	−	0.843227i
$451$	24.2793	−	14.0177i	1.14327	−	0.660066i
$452$	−3.99077	−	10.9646i	−0.187710	−	0.515729i
$453$	8.65995	+	24.4354i	0.406880	+	1.14808i
$454$	−18.9680	+	3.34458i	−0.890214	+	0.156969i
$455$	−0.781158	+	0.326028i	−0.0366212	+	0.0152844i
$456$	45.8712	−	25.9679i	2.14812	−	1.21606i
$457$	29.5854	+	24.8251i	1.38395	+	1.16127i	0.967726	+	0.252006i	$0.0810902\pi$
$457$	29.5854	+	24.8251i	1.38395	+	1.16127i	0.416221	+	0.909263i	$0.363354\pi$
$458$	17.8716	−	30.9545i	0.835085	−	1.44641i
$459$	0.679939	−	26.7354i	0.0317368	−	1.24790i
$460$	−77.1194	+	44.5249i	−3.59571	+	2.07598i
$461$	−15.4949	+	5.63970i	−0.721671	+	0.262667i	−0.676635	−	0.736318i	$-0.736563\pi$
$461$	−15.4949	+	5.63970i	−0.721671	+	0.262667i	−0.0450362	+	0.998985i	$0.514340\pi$
$462$	45.9073	+	14.7672i	2.13580	+	0.687032i
$463$	31.2960	−	26.2605i	1.45445	−	1.22043i	0.525198	−	0.850980i	$-0.323991\pi$
$463$	31.2960	−	26.2605i	1.45445	−	1.22043i	0.929251	−	0.369448i	$-0.120453\pi$
$464$	−13.7600	−	16.3985i	−0.638791	−	0.761281i
$465$	−1.38989	+	0.492580i	−0.0644547	+	0.0228428i
$466$	53.1306	−	19.3380i	2.46123	−	0.895813i
$467$	38.7005			1.79085			0.895424	−	0.445215i	$-0.146873\pi$
$467$	38.7005			1.79085			0.895424	+	0.445215i	$0.146873\pi$
$468$	0.492303	+	1.42742i	0.0227567	+	0.0659827i
$469$	−19.8729	−	21.5708i	−0.917644	−	0.996046i
$470$	−34.3267	−	6.05273i	−1.58337	−	0.279192i
$471$	−4.31640	+	3.55998i	−0.198889	+	0.164035i
$472$	−39.2606	−	46.7890i	−1.80712	−	2.15364i
$473$	−6.37009	−	7.59158i	−0.292897	−	0.349061i
$474$	−64.4080	−	24.0628i	−2.95836	−	1.10524i
$475$	−13.0537	−	2.30173i	−0.598947	−	0.105610i
$476$	−57.3957	+	12.8862i	−2.63073	+	0.590639i
$477$	0.220806	−	13.0248i	0.0101100	−	0.596364i
$478$	−59.9074			−2.74010
$479$	27.1347	−	9.87621i	1.23982	−	0.451256i	0.362867	−	0.931841i	$-0.381798\pi$
$479$	27.1347	−	9.87621i	1.23982	−	0.451256i	0.876948	+	0.480585i	$0.159576\pi$
$480$	−3.00605	+	16.2420i	−0.137207	+	0.741341i
$481$	−0.143790	−	0.171362i	−0.00655624	−	0.00781343i
$482$	26.1188	−	21.9163i	1.18968	−	0.998260i
$483$	−23.0948	−	25.4984i	−1.05085	−	1.16022i
$484$	−26.4778	+	9.63714i	−1.20354	+	0.438052i
$485$	14.2013	−	8.19912i	0.644848	−	0.372303i
$486$	8.43384	−	38.2699i	0.382567	−	1.73596i
$487$	10.6879	−	18.5119i	0.484313	−	0.838854i	−0.515525	−	0.856875i	$-0.672403\pi$
$487$	10.6879	−	18.5119i	0.484313	−	0.838854i	0.999838	+	0.0180204i	$0.00573637\pi$
$488$	5.16422	+	4.33330i	0.233773	+	0.196159i
$489$	0.113218	−	13.3579i	0.00511991	−	0.604064i
$490$	−4.47011	−	48.1139i	−0.201939	−	2.17357i
$491$	−17.7129	+	3.12326i	−0.799372	+	0.140951i	−0.558390	−	0.829579i	$-0.688581\pi$
$491$	−17.7129	+	3.12326i	−0.799372	+	0.140951i	−0.240982	+	0.970530i	$0.577469\pi$
$492$	−32.5346	+	38.1125i	−1.46677	+	1.71825i
$493$	6.25848	+	17.1950i	0.281868	+	0.774426i
$494$	1.32372	−	0.764250i	0.0595570	−	0.0343852i
$495$	−30.1514	+	16.7330i	−1.35521	+	0.752093i
$496$	1.61672	−	0.933411i	0.0725927	−	0.0419114i
$497$	9.01876	+	14.0730i	0.404547	+	0.631262i
$498$	38.1702	−	31.4812i	1.71045	−	1.41071i
$499$	−1.85083	−	10.4966i	−0.0828545	−	0.469891i	−0.997799	−	0.0663114i	$-0.978877\pi$
$499$	−1.85083	−	10.4966i	−0.0828545	−	0.469891i	0.914944	−	0.403580i	$-0.132234\pi$
$500$	−22.3528	+	18.7562i	−0.999647	+	0.838803i
$501$	−0.999475	+	2.67526i	−0.0446532	+	0.119522i
$502$	8.20692	+	22.5483i	0.366293	+	1.00638i
$503$	−1.68293	−	2.91493i	−0.0750383	−	0.129970i	0.826065	−	0.563575i	$-0.190575\pi$
$503$	−1.68293	−	2.91493i	−0.0750383	−	0.129970i	−0.901103	+	0.433605i	$0.857241\pi$
$504$	−46.2686	+	1.35927i	−2.06097	+	0.0605466i
$505$	−11.3109	+	19.5911i	−0.503328	+	0.871790i
$506$	77.8012	+	13.7184i	3.45868	+	0.609859i
$507$	−7.51369	−	21.2011i	−0.333695	−	0.941573i
$508$	−5.02891	−	1.83037i	−0.223122	−	0.0812097i
$509$	7.87029	+	2.86455i	0.348844	+	0.126969i	0.510499	−	0.859878i	$-0.329461\pi$
$509$	7.87029	+	2.86455i	0.348844	+	0.126969i	−0.161654	+	0.986847i	$0.551683\pi$
$510$	31.2196	−	53.0309i	1.38243	−	2.34825i
$511$	3.68561	+	5.75109i	0.163042	+	0.254413i
$512$			49.3168i			2.17951i
$513$	−27.1071	−	0.689392i	−1.19681	−	0.0304374i
$514$	12.0415	+	6.95217i	0.531128	+	0.306647i
$515$	−2.66596	−	0.470080i	−0.117476	−	0.0207142i
$516$	15.2646	+	8.98639i	0.671988	+	0.395604i
$517$	13.5866	+	16.1919i	0.597538	+	0.712118i
$518$	11.7847	−	4.91853i	0.517790	−	0.216108i
$519$	31.1361	+	5.76266i	1.36672	+	0.252953i
$520$	−0.323992	+	1.83745i	−0.0142080	+	0.0805774i
$521$	−8.12400	−	14.0712i	−0.355919	−	0.616470i	0.631356	−	0.775493i	$-0.282499\pi$
$521$	−8.12400	−	14.0712i	−0.355919	−	0.616470i	−0.987275	+	0.159024i	$0.949165\pi$
$522$	4.20778	+	26.4808i	0.184170	+	1.15903i
$523$	24.4735	+	14.1298i	1.07015	+	0.617853i	0.928223	−	0.372024i	$-0.121336\pi$
$523$	24.4735	+	14.1298i	1.07015	+	0.617853i	0.141929	+	0.989877i	$0.454669\pi$
$524$	5.62005	−	31.8729i	0.245513	−	1.39237i
$525$	9.19344	+	7.13930i	0.401235	+	0.311585i
$526$	19.7653	+	7.19397i	0.861806	+	0.313672i
$527$	−1.57153	+	0.277102i	−0.0684568	+	0.0120708i
$528$	33.6787	−	27.7768i	1.46568	−	1.20883i
$529$	−25.5544	−	21.4427i	−1.11106	−	0.932292i
$530$	14.9872	−	25.9586i	0.651003	−	1.12757i
$531$	4.93076	+	31.0308i	0.213977	+	1.34662i
$532$	13.0654	+	58.1936i	0.566456	+	2.52301i
$533$	−0.501584	+	0.597765i	−0.0217260	+	0.0258921i
$534$	3.74979	−	1.32893i	0.162269	−	0.0575084i
$535$	12.1512	−	33.3851i	0.525341	−	1.44336i
$536$	−63.6669	+	11.2262i	−2.74999	+	0.484897i
$537$	−3.70850	+	6.29940i	−0.160034	+	0.271839i
$538$	16.3783	+	44.9990i	0.706119	+	1.94005i
$539$	−16.6778	+	24.0929i	−0.718363	+	1.03775i
$540$	40.8064	−	46.1933i	1.75603	−	1.98784i
$541$	3.36773	+	5.83309i	0.144790	+	0.250784i	0.929295	−	0.369339i	$-0.120416\pi$
$541$	3.36773	+	5.83309i	0.144790	+	0.250784i	−0.784504	+	0.620123i	$0.787083\pi$
$542$	−10.9108	+	61.8780i	−0.468657	+	2.65789i
$543$	−9.37251	−	16.5562i	−0.402213	−	0.710493i
$544$	−6.11365	+	16.7971i	−0.262121	+	0.720171i
$545$	1.80768	+	10.2518i	0.0774324	+	0.439141i
$546$	−1.34129	+	0.0507852i	−0.0574020	+	0.00217341i
$547$	−31.5987	−	26.5144i	−1.35106	−	1.13368i	−0.978633	−	0.205615i	$-0.934080\pi$
$547$	−31.5987	−	26.5144i	−1.35106	−	1.13368i	−0.372429	−	0.928061i	$-0.621475\pi$
$548$			70.3527i			3.00532i
$549$	−1.13069	−	3.27841i	−0.0482566	−	0.139919i
$550$	−26.7298			−1.13976
$551$	17.4341	−	6.34550i	0.742718	−	0.270327i
$552$	−74.7877	+	12.5345i	−3.18318	+	0.533503i
$553$	25.3437	−	33.2130i	1.07772	−	1.41236i
$554$	−19.1953	+	52.7386i	−0.815530	+	2.24065i
$555$	−3.19572	+	8.55389i	−0.135651	+	0.363093i
$556$	−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	$0.955913\pi$
$558$	−2.33796	−	0.0396348i	−0.0989736	−	0.00167788i
$559$	0.238880	+	0.137917i	0.0101036	+	0.00583329i
$560$	−38.8551	−	20.0942i	−1.64193	−	0.849133i
$561$	−35.1734	+	12.4655i	−1.48502	+	0.526294i
$562$	22.9525	−	19.2594i	0.968192	−	0.812409i
$563$	4.74872	+	26.9313i	0.200135	+	1.13502i	0.904914	+	0.425594i	$0.139935\pi$
$563$	4.74872	+	26.9313i	0.200135	+	1.13502i	−0.704780	+	0.709426i	$0.748954\pi$
$564$	−32.5575	−	19.1668i	−1.37092	−	0.807070i
$565$	−4.76755	+	5.68175i	−0.200572	+	0.239033i
$566$	−10.1623			−0.427155
$567$	20.7678	+	11.6489i	0.872168	+	0.489207i
$568$	36.8433			1.54591
$569$	−18.6968	+	22.2820i	−0.783813	+	0.934111i	−0.999099	−	0.0424395i	$-0.986487\pi$
$569$	−18.6968	+	22.2820i	−0.783813	+	0.934111i	0.215286	+	0.976551i	$0.430931\pi$
$570$	−53.7682	−	31.6537i	−2.25210	−	1.32583i
$571$	3.02630	+	17.1630i	0.126647	+	0.718250i	0.980316	+	0.197434i	$0.0632609\pi$
$571$	3.02630	+	17.1630i	0.126647	+	0.718250i	−0.853669	+	0.520815i	$0.825628\pi$
$572$	1.61396	−	1.35427i	0.0674830	−	0.0566249i
$573$	−16.5842	+	5.87748i	−0.692817	+	0.245535i
$574$	−24.0352	−	37.5049i	−1.00321	−	1.56543i
$575$	16.5141	+	9.53441i	0.688685	+	0.397612i
$576$	5.11220	−	8.51782i	0.213008	−	0.354909i
$577$		−	22.7151i		−	0.945641i	−0.881159	−	0.472821i	$-0.843236\pi$
$577$		−	22.7151i		−	0.945641i	0.881159	−	0.472821i	$-0.156764\pi$
$578$	15.3358	−	18.2765i	0.637884	−	0.760200i
$579$	5.23840	−	14.0215i	0.217700	−	0.582712i
$580$	−14.4237	+	39.6287i	−0.598911	+	1.64549i
$581$	11.5795	+	27.7444i	0.480401	+	1.15103i
$582$	25.6453	−	4.29817i	1.06303	−	0.178165i
$583$	−17.0804	+	6.21677i	−0.707400	+	0.257472i
$584$	15.0564			0.623039
$585$	0.629322	−	0.724687i	0.0260193	−	0.0299621i
$586$		−	4.46687i		−	0.184525i
$587$	−1.35014	−	1.13291i	−0.0557264	−	0.0467600i	0.614499	−	0.788918i	$-0.289358\pi$
$587$	−1.35014	−	1.13291i	−0.0557264	−	0.0467600i	−0.670225	+	0.742158i	$0.733803\pi$
$588$	13.7124	−	50.5480i	0.565492	−	2.08456i
$589$	0.280955	+	1.59338i	0.0115766	+	0.0656539i
$590$	−24.7273	+	67.9377i	−1.01801	+	2.79695i
$591$	−0.615955	−	1.08806i	−0.0253370	−	0.0447568i
$592$	2.00741	−	11.3846i	0.0825039	−	0.467903i
$593$	−20.7313	−	35.9077i	−0.851334	−	1.47455i	−0.880005	−	0.474965i	$-0.842461\pi$
$593$	−20.7313	−	35.9077i	−0.851334	−	1.47455i	0.0286712	−	0.999589i	$-0.490872\pi$
$594$	−54.0741	+	8.12308i	−2.21869	+	0.333294i
$595$	25.3358	+	27.5004i	1.03867	+	1.12741i
$596$	−24.7565	−	68.0180i	−1.01407	−	2.78613i
$597$	19.1365	−	32.5059i	0.783203	−	1.33038i
$598$	−2.16550	+	0.381835i	−0.0885537	+	0.0156144i
$599$	7.24754	−	19.9124i	0.296126	−	0.813600i	−0.699012	−	0.715110i	$-0.746376\pi$
$599$	7.24754	−	19.9124i	0.296126	−	0.813600i	0.995138	−	0.0984901i	$-0.0314013\pi$
$600$	24.1833	−	8.57057i	0.987277	−	0.349892i
$601$	5.31277	−	6.33151i	0.216712	−	0.258268i	−0.646726	−	0.762723i	$-0.723862\pi$
$601$	5.31277	−	6.33151i	0.216712	−	0.258268i	0.863438	+	0.504455i	$0.168307\pi$
$602$	−11.5807	+	10.6692i	−0.471996	+	0.434843i
$603$	31.0538	+	11.9026i	1.26461	+	0.484709i
$604$	−32.3285	+	55.9947i	−1.31543	+	2.27839i
$605$	13.7206	+	11.5130i	0.557822	+	0.468068i
$606$	−27.6738	+	22.8242i	−1.12417	+	0.927169i
$607$	−15.5617	+	2.74395i	−0.631630	+	0.111373i	−0.480292	−	0.877109i	$-0.659469\pi$
$607$	−15.5617	+	2.74395i	−0.631630	+	0.111373i	−0.151338	+	0.988482i	$0.548358\pi$
$608$	17.0307	+	6.19865i	0.690684	+	0.251389i
$609$	−16.1403	−	2.22004i	−0.654040	−	0.0899604i
$610$	1.38566	−	7.85846i	0.0561037	−	0.318180i
$611$	−0.509501	−	0.294161i	−0.0206122	−	0.0119005i
$612$	51.8151	−	42.0021i	2.09450	−	1.69783i
$613$	9.40541	+	16.2906i	0.379881	+	0.657973i	0.991045	−	0.133531i	$-0.0426316\pi$
$613$	9.40541	+	16.2906i	0.379881	+	0.657973i	−0.611164	+	0.791504i	$0.709298\pi$
$614$	−8.58183	+	48.6699i	−0.346334	+	1.96416i
$615$	31.3212	+	5.79690i	1.26299	+	0.233754i
$616$	24.8772	+	59.6052i	1.00233	+	2.40156i
$617$	−1.65294	−	1.96989i	−0.0665447	−	0.0793049i	0.731745	−	0.681578i	$-0.238706\pi$
$617$	−1.65294	−	1.96989i	−0.0665447	−	0.0793049i	−0.798290	+	0.602273i	$0.794262\pi$
$618$	−3.69923	−	2.17776i	−0.148805	−	0.0876025i
$619$	−15.5121	−	2.73521i	−0.623485	−	0.109937i	−0.147024	−	0.989133i	$-0.546969\pi$
$619$	−15.5121	−	2.73521i	−0.623485	−	0.109937i	−0.476461	+	0.879196i	$0.658081\pi$
$620$	−3.18499	−	1.83885i	−0.127912	−	0.0738501i
$621$	36.3053	+	14.2695i	1.45688	+	0.572613i
$622$			66.5577i			2.66872i
$623$	0.111932	+	2.41474i	0.00448444	+	0.0967443i
$624$	−0.616445	+	1.04712i	−0.0246775	+	0.0419182i
$625$	29.3639	+	10.6876i	1.17456	+	0.427503i
$626$	−11.9090	−	4.33451i	−0.475979	−	0.173242i
$627$	12.6388	+	35.6624i	0.504745	+	1.42422i
$628$	−13.7423	−	2.42314i	−0.548379	−	0.0966939i
$629$	−4.94086	+	8.55781i	−0.197005	+	0.341222i
$630$	28.7771	+	46.6255i	1.14651	+	1.85760i
$631$	−21.8676	−	37.8758i	−0.870536	−	1.50781i	−0.861443	−	0.507855i	$-0.830439\pi$
$631$	−21.8676	−	37.8758i	−0.870536	−	1.50781i	−0.00909374	−	0.999959i	$-0.502895\pi$
$632$	−31.4960	−	86.5344i	−1.25284	−	3.44215i
$633$	5.87002	−	15.7121i	0.233312	−	0.624500i
$634$	−59.5178	+	49.9413i	−2.36375	+	1.98342i
$635$	0.590719	+	3.35014i	0.0234420	+	0.132946i
$636$	25.0642	−	20.6719i	0.993858	−	0.819693i
$637$	0.206853	−	0.788920i	0.00819580	−	0.0312582i
$638$	32.4009	−	18.7067i	1.28276	−	0.740604i
$639$	−16.2507	−	9.75332i	−0.642869	−	0.385835i
$640$	36.3139	−	20.9659i	1.43543	−	0.828748i
$641$	−8.51714	−	23.4007i	−0.336407	−	0.924270i	−0.986405	−	0.164334i	$-0.947452\pi$
$641$	−8.51714	−	23.4007i	−0.336407	−	0.924270i	0.649998	−	0.759936i	$-0.274770\pi$
$642$	36.5771	−	42.8480i	1.44358	−	1.69108i
$643$	22.2139	−	3.91690i	0.876029	−	0.154468i	0.282488	−	0.959271i	$-0.408840\pi$
$643$	22.2139	−	3.91690i	0.876029	−	0.154468i	0.593542	+	0.804803i	$0.297729\pi$
$644$	10.9707	−	85.0972i	0.432307	−	3.35330i
$645$	0.0954307	−	11.2592i	0.00375758	−	0.443332i
$646$	−51.7239	−	43.4015i	−2.03505	−	1.70761i
$647$	−1.19357	+	2.06732i	−0.0469239	+	0.0812747i	−0.888533	−	0.458812i	$-0.848275\pi$
$647$	−1.19357	+	2.06732i	−0.0469239	+	0.0812747i	0.841609	+	0.540087i	$0.181609\pi$
$648$	46.3179	−	24.6874i	1.81954	−	0.969812i
$649$	37.9680	−	21.9208i	1.49038	−	0.860468i
$650$	0.699122	−	0.254459i	0.0274218	−	0.00998072i
$651$	0.435081	−	1.35255i	0.0170522	−	0.0530107i
$652$	25.5218	−	21.4153i	0.999509	−	0.838688i
$653$	−23.6895	−	28.2321i	−0.927043	−	1.10481i	−0.994252	−	0.107067i	$-0.965854\pi$
$653$	−23.6895	−	28.2321i	−0.927043	−	1.10481i	0.0672091	−	0.997739i	$-0.478591\pi$
$654$	−3.00414	+	16.2316i	−0.117471	+	0.634707i
$655$	−19.3321	+	7.03630i	−0.755367	+	0.274931i
$656$	−40.3256			−1.57445
$657$	−6.64103	−	3.98580i	−0.259091	−	0.155501i
$658$	24.7003	−	22.7560i	0.962916	−	0.887122i
$659$	−7.39431	−	1.30382i	−0.288041	−	0.0507895i	0.0277605	−	0.999615i	$-0.491162\pi$
$659$	−7.39431	−	1.30382i	−0.288041	−	0.0507895i	−0.315802	+	0.948825i	$0.602274\pi$
$660$	−80.5642	−	30.0987i	−3.13596	−	1.17159i
$661$	−5.35183	−	6.37807i	−0.208162	−	0.248078i	0.651854	−	0.758344i	$-0.273991\pi$
$661$	−5.35183	−	6.37807i	−0.208162	−	0.248078i	−0.860017	+	0.510266i	$0.829547\pi$
$662$	−26.5045	−	31.5869i	−1.03013	−	1.22766i
$663$	0.801298	−	0.660877i	0.0311198	−	0.0256663i
$664$	65.2606	+	11.5072i	2.53260	+	0.446566i
$665$	27.8828	−	25.6880i	1.08125	−	0.996139i
$666$	−9.49408	+	10.9328i	−0.367888	+	0.423636i
$667$	−26.6904			−1.03345
$668$	−6.69311	+	2.43609i	−0.258964	+	0.0942553i
$669$	−45.9440	+	16.2826i	−1.77630	+	0.629522i
$670$	49.1886	+	58.6207i	1.90032	+	2.26472i
$671$	−3.70683	+	3.11040i	−0.143100	+	0.120076i
$672$	−10.6841	−	11.7960i	−0.412148	−	0.455041i
$673$	36.7067	−	13.3601i	1.41494	−	0.514995i	0.482363	−	0.875971i	$-0.339779\pi$
$673$	36.7067	−	13.3601i	1.41494	−	0.514995i	0.932575	+	0.360976i	$0.117556\pi$
$674$	−3.12535	+	1.80442i	−0.120384	+	0.0695038i
$675$	−12.9355	−	2.62161i	−0.497888	−	0.100906i
$676$	28.0494	−	48.5830i	1.07882	−	1.86858i
$677$	14.6753	+	12.3140i	0.564017	+	0.473267i	0.879655	−	0.475613i	$-0.157774\pi$
$677$	14.6753	+	12.3140i	0.564017	+	0.473267i	−0.315637	+	0.948880i	$0.602218\pi$
$678$	−10.2350	+	5.79408i	−0.393073	+	0.222520i
$679$	−2.02022	+	15.6704i	−0.0775290	+	0.601375i
$680$	81.1684	−	14.3122i	3.11267	−	0.548847i
$681$	4.43285	+	12.5080i	0.169867	+	0.479307i
$682$	1.11591	+	3.06595i	0.0427305	+	0.117401i
$683$	−35.5943	+	20.5504i	−1.36198	+	0.786338i	−0.989887	−	0.141858i	$-0.954692\pi$
$683$	−35.5943	+	20.5504i	−1.36198	+	0.786338i	−0.372090	+	0.928196i	$0.621359\pi$
$684$	−42.5861	−	52.5355i	−1.62832	−	2.00874i
$685$	38.7288	−	22.3601i	1.47975	−	0.854335i
$686$	39.4674	+	24.6985i	1.50687	+	0.942993i
$687$	−23.0691	−	8.61858i	−0.880141	−	0.328819i
$688$	2.47528	+	14.0380i	0.0943692	+	0.535194i
$689$	0.387559	−	0.325201i	0.0147648	−	0.0123892i
$690$	57.1115	+	69.2464i	2.17420	+	2.63617i
$691$	−14.5222	−	39.8994i	−0.552451	−	1.51785i	−0.830353	−	0.557237i	$-0.811861\pi$
$691$	−14.5222	−	39.8994i	−0.552451	−	1.51785i	0.277903	−	0.960609i	$-0.410361\pi$
$692$	39.4868	+	68.3932i	1.50106	+	2.59992i
$693$	4.80622	−	32.8761i	0.182573	−	1.24886i
$694$	−8.00228	+	13.8604i	−0.303763	+	0.526132i
$695$	26.3199	+	4.64091i	0.998370	+	0.176040i
$696$	−23.3160	+	27.3134i	−0.883791	+	1.03531i
$697$	32.3917	+	11.7896i	1.22693	+	0.446564i
$698$	20.6993	+	7.53394i	0.783481	+	0.285164i
$699$	−19.1911	−	33.9002i	−0.725873	−	1.28222i
$700$	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	$-0.111143\pi$
$702$	1.33699	−	0.727229i	0.0504613	−	0.0274475i
$703$	8.67679	+	5.00955i	0.327252	+	0.188939i
$704$	−13.6510	−	2.40703i	−0.514490	−	0.0907185i
$705$	−0.203542	+	24.0145i	−0.00766582	+	0.904439i
$706$	−3.54983	−	4.23052i	−0.133600	−	0.159218i
$707$	−8.39529	−	20.1150i	−0.315737	−	0.756501i
$708$	−50.8777	+	59.6004i	−1.91210	+	2.23992i
$709$	−1.63998	+	9.30078i	−0.0615907	+	0.349298i	0.938402	+	0.345545i	$0.112306\pi$
$709$	−1.63998	+	9.30078i	−0.0615907	+	0.349298i	−0.999993	+	0.00375331i	$0.998805\pi$
$710$	−21.8054	−	37.7681i	−0.818342	−	1.41741i
$711$	−9.01563	+	46.5060i	−0.338112	+	1.74411i
$712$	4.61446	+	2.66416i	0.172934	+	0.0998437i
$713$	0.404182	−	2.29223i	0.0151367	−	0.0858448i
$714$	22.3731	+	54.9103i	0.837293	+	2.05497i
$715$	−1.25848	−	0.458050i	−0.0470645	−	0.0171301i
$716$	−17.9544	+	3.16584i	−0.670986	+	0.118313i
$717$	6.82259	+	40.7074i	0.254794	+	1.52025i
$718$	−25.6525	−	21.5250i	−0.957344	−	0.803307i
$719$	−7.27759	+	12.6052i	−0.271408	+	0.470093i	−0.969223	−	0.246186i	$-0.920823\pi$
$719$	−7.27759	+	12.6052i	−0.271408	+	0.470093i	0.697814	+	0.716279i	$0.254156\pi$
$720$	49.5933	+	0.840744i	1.84823	+	0.0313327i
$721$	1.91833	−	1.76733i	0.0714422	−	0.0658187i
$722$	−13.3025	+	15.8533i	−0.495068	+	0.589999i
$723$	−17.8668	−	15.2519i	−0.664474	−	0.567226i
$724$	16.2286	−	44.5876i	0.603129	−	1.65708i
$725$	8.89338	−	1.56814i	0.330292	−	0.0582394i
$726$	13.9919	+	24.7161i	0.519288	+	0.917300i
$727$	−5.63920	−	15.4936i	−0.209146	−	0.574625i	0.790119	−	0.612954i	$-0.210019\pi$
$727$	−5.63920	−	15.4936i	−0.209146	−	0.574625i	−0.999265	+	0.0383287i	$0.987797\pi$
$728$	−1.21809	−	1.32216i	−0.0451454	−	0.0490025i
$729$	−26.9651	−	1.37245i	−0.998707	−	0.0508315i
$730$	−8.91101	−	15.4343i	−0.329811	−	0.571250i
$731$	2.11588	−	11.9998i	0.0782587	−	0.443827i
$732$	4.38789	−	7.45344i	0.162181	−	0.275487i
$733$	10.6559	−	29.2767i	0.393583	−	1.08136i	−0.571770	−	0.820414i	$-0.693743\pi$
$733$	10.6559	−	29.2767i	0.393583	−	1.08136i	0.965353	−	0.260947i	$-0.0840348\pi$
$734$	−4.65451	−	26.3970i	−0.171801	−	0.974332i
$735$	−32.1846	+	8.51695i	−1.18715	+	0.314152i
$736$	−19.9728	−	16.7592i	−0.736209	−	0.617753i
$737$		−	46.4045i		−	1.70933i
$738$	43.3086	+	25.9928i	1.59421	+	0.956809i
$739$	−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
$741$	−0.670065	−	0.812438i	−0.0246155	−	0.0298457i
$742$	11.1240	+	26.6528i	0.408373	+	0.978455i
$743$	−15.8926	+	43.6646i	−0.583044	+	1.60190i	0.199906	+	0.979815i	$0.435936\pi$
$743$	−15.8926	+	43.6646i	−0.583044	+	1.60190i	−0.782950	+	0.622085i	$0.786286\pi$
$744$	−1.99266	−	2.41605i	−0.0730544	−	0.0885767i
$745$	−29.5752	+	35.2464i	−1.08355	+	1.29133i
$746$			35.1960i			1.28862i
$747$	−25.7387	−	22.3516i	−0.941730	−	0.817803i
$748$	−80.6011	−	46.5351i	−2.94707	−	1.70149i
$749$	18.4702	+	28.8212i	0.674886	+	1.05310i
$750$	22.3699	+	19.0960i	0.816834	+	0.697287i
$751$	39.5891	−	33.2192i	1.44463	−	1.21219i	0.508240	−	0.861216i	$-0.330296\pi$
$751$	39.5891	−	33.2192i	1.44463	−	1.21219i	0.936387	−	0.350970i	$-0.114148\pi$
$752$	−5.27946	−	29.9413i	−0.192522	−	1.09185i
$753$	14.3871	−	8.14458i	0.524294	−	0.296805i
$754$	−0.669368	+	0.797721i	−0.0243769	+	0.0290513i
$755$	41.0997			1.49577
$756$	11.5322	+	58.2571i	0.419421	+	2.11879i
$757$	−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
$759$	0.461325	−	54.4287i	0.0167450	−	1.97564i
$760$	−14.5112	−	82.2969i	−0.526375	−	2.98522i
$761$	−6.86703	+	5.76212i	−0.248930	+	0.208877i	−0.758711	−	0.651427i	$-0.774171\pi$
$761$	−6.86703	+	5.76212i	−0.248930	+	0.208877i	0.509782	+	0.860304i	$0.329726\pi$
$762$	−0.981704	+	5.30423i	−0.0355634	+	0.192152i
$763$	−8.90937	−	4.60754i	−0.322541	−	0.166804i
$764$	−38.0034	−	21.9413i	−1.37491	−	0.793807i
$765$	−39.5903	−	15.1745i	−1.43139	−	0.548634i
$766$			42.5448i			1.53720i
$767$	−0.784379	+	0.934786i	−0.0283223	+	0.0337532i
$768$	54.2639	−	9.09467i	1.95808	−	0.328176i
$769$	2.93294	−	8.05819i	0.105765	−	0.290586i	−0.875510	−	0.483200i	$-0.839474\pi$
$769$	2.93294	−	8.05819i	0.105765	−	0.290586i	0.981275	+	0.192614i	$0.0616966\pi$
$770$	46.3779	−	60.7784i	1.67135	−	2.19030i
$771$	3.35268	−	8.97403i	0.120744	−	0.323192i
$772$	35.0796	−	12.7679i	1.26254	−	0.459528i
$773$	−0.898960			−0.0323333			−0.0161667	−	0.999869i	$-0.505146\pi$
$773$	−0.898960			−0.0323333			−0.0161667	+	0.999869i	$0.505146\pi$
$774$	6.39014	−	16.6719i	0.229689	−	0.599259i
$775$			0.787532i			0.0282890i
$776$	26.6789	+	22.3863i	0.957717	+	0.803620i
$777$	−4.68428	−	7.44762i	−0.168047	−	0.267182i
$778$	−1.90906	−	10.8268i	−0.0684432	−	0.388161i
$779$	11.9535	−	32.8421i	0.428280	−	1.17669i
$780$	2.39370	+	0.0202884i	0.0857081	+	0.000726442i
$781$	−4.59226	+	26.0440i	−0.164324	+	0.931928i
$782$	48.5677	+	84.1218i	1.73678	+	3.00819i
$783$	17.5147	−	5.87500i	0.625923	−	0.209955i
$784$	38.1026	−	18.0175i	1.36081	−	0.643482i
$785$	3.03377	+	8.33523i	0.108280	+	0.297497i
$786$	−32.6214	−	0.276492i	−1.16357	−	0.00986213i
$787$	−39.6542	+	6.99211i	−1.41352	+	0.249242i	−0.827687	−	0.561190i	$-0.810344\pi$
$787$	−39.6542	+	6.99211i	−1.41352	+	0.249242i	−0.585833	+	0.810432i	$0.699233\pi$
$788$	1.06653	−	2.93027i	0.0379936	−	0.104386i
$789$	2.63736	−	14.2499i	0.0938926	−	0.507310i
$790$	−70.0658	+	83.5011i	−2.49283	+	2.97084i
$791$	−1.56552	−	6.97286i	−0.0556633	−	0.247926i
$792$	−55.2963	−	48.0196i	−1.96487	−	1.70630i
$793$	0.0673425	−	0.116641i	0.00239140	−	0.00414203i
$794$	−20.8562	−	17.5004i	−0.740157	−	0.621066i
$795$	−19.3459	−	7.22758i	−0.686127	−	0.256336i
$796$	92.6473	−	16.3362i	3.28380	−	0.579022i
$797$	32.3110	+	11.7602i	1.14451	+	0.416569i	0.843542	−	0.537064i	$-0.180467\pi$
$797$	32.3110	+	11.7602i	1.14451	+	0.416569i	0.300972	+	0.953633i	$0.402689\pi$
$798$	55.6738	−	22.6842i	1.97083	−	0.803011i
$799$	−4.51291	+	25.5940i	−0.159655	+	0.905450i
$800$	7.63972	+	4.41080i	0.270105	+	0.155945i
$801$	−1.33006	−	2.39666i	−0.0469955	−	0.0846818i
$802$	8.16537	+	14.1428i	0.288329	+	0.499401i
$803$	−1.87668	+	10.6432i	−0.0662265	+	0.375589i
$804$	27.7068	+	78.1792i	0.977143	+	2.75717i
$805$	−50.3324	+	21.0070i	−1.77398	+	0.740399i
$806$	−0.0583737	−	0.0695671i	−0.00205613	−	0.00245040i
$807$	28.7118	−	16.2539i	1.01070	−	0.572164i
$808$	−47.3146	−	8.34284i	−1.66452	−	0.293500i
$809$	26.8173	+	15.4830i	0.942848	+	0.544353i	0.890852	−	0.454294i	$-0.150108\pi$
$809$	26.8173	+	15.4830i	0.942848	+	0.544353i	0.0519959	+	0.998647i	$0.483442\pi$
$810$	−52.7199	−	32.8695i	−1.85239	−	1.15491i
$811$		−	44.9726i		−	1.57920i	−0.613622	−	0.789600i	$-0.710288\pi$
$811$		−	44.9726i		−	1.57920i	0.613622	−	0.789600i	$-0.289712\pi$
$812$	−21.9245	−	34.2113i	−0.769398	−	1.20058i
$813$	43.2890	+	0.366908i	1.51821	+	0.0128680i
$814$	18.9857	+	6.91023i	0.665449	+	0.242204i
$815$	−19.9006	−	7.24321i	−0.697086	−	0.253719i
$816$	52.7799	+	9.76847i	1.84767	+	0.341965i
$817$	−12.1666	−	2.14530i	−0.425655	−	0.0750545i
$818$	−19.4710	+	33.7248i	−0.680789	+	1.17916i
$819$	0.187263	+	0.905631i	0.00654349	+	0.0316453i
$820$	39.7215	+	68.7996i	1.38713	+	2.40259i
$821$	5.71833	+	15.7110i	0.199571	+	0.548317i	0.998595	−	0.0529818i	$-0.0168725\pi$
$821$	5.71833	+	15.7110i	0.199571	+	0.548317i	−0.799025	+	0.601298i	$0.794650\pi$
$822$	69.9380	−	11.7217i	2.43937	−	0.408840i
$823$	−21.2287	+	17.8130i	−0.739986	+	0.620922i	−0.932834	−	0.360307i	$-0.882672\pi$
$823$	−21.2287	+	17.8130i	−0.739986	+	0.620922i	0.192848	+	0.981229i	$0.438228\pi$
$824$	−0.998363	−	5.66200i	−0.0347796	−	0.197245i
$825$	3.04414	+	18.1631i	0.105983	+	0.632356i
$826$	−37.5863	−	58.6503i	−1.30780	−	2.04071i
$827$	12.2895	−	7.09535i	0.427348	−	0.246730i	−0.270868	−	0.962616i	$-0.587311\pi$
$827$	12.2895	−	7.09535i	0.427348	−	0.246730i	0.698216	+	0.715887i	$0.253977\pi$
$828$	31.7206	+	91.9733i	1.10237	+	3.19629i
$829$	4.00205	−	2.31059i	0.138997	−	0.0802500i	−0.428889	−	0.903357i	$-0.641095\pi$
$829$	4.00205	−	2.31059i	0.138997	−	0.0802500i	0.567886	+	0.823107i	$0.307761\pi$
$830$	−26.8279	−	73.7091i	−0.931210	−	2.55848i
$831$	38.0223	+	7.03714i	1.31898	+	0.244116i
$832$	0.379957	−	0.0669967i	0.0131726	−	0.00232269i
$833$	−35.8737	+	3.33291i	−1.24295	+	0.115478i
$834$	36.5210	+	21.5002i	1.26462	+	0.744490i
$835$	3.46832	+	2.91026i	0.120026	+	0.100714i
$836$	−47.1821	+	81.7217i	−1.63183	+	2.82640i
$837$	0.239328	+	1.59317i	0.00827237	+	0.0550680i
$838$	−34.1934	+	19.7416i	−1.18119	+	0.681962i
$839$	−26.3117	+	9.57669i	−0.908382	+	0.330624i	−0.753607	−	0.657325i	$-0.771688\pi$
$839$	−26.3117	+	9.57669i	−0.908382	+	0.330624i	−0.154776	+	0.987950i	$0.549465\pi$
$840$	−22.4717	+	69.8585i	−0.775347	+	2.41035i
$841$	12.5325	−	10.5160i	0.432156	−	0.362622i
$842$	18.7921	+	22.3955i	0.647617	+	0.771800i
$843$	−15.7008	−	13.4030i	−0.540766	−	0.461623i
$844$	39.3093	−	14.3074i	1.35308	−	0.492482i
$845$	−35.6596			−1.22673
$846$	−13.6294	+	35.5591i	−0.468587	+	1.22255i
$847$	−16.8385	+	3.78050i	−0.578576	+	0.129899i
$848$	25.7478	+	4.54004i	0.884184	+	0.155906i
$849$	1.15734	+	6.90537i	0.0397200	+	0.236992i
$850$	−21.1255	−	25.1764i	−0.724598	−	0.863542i
$851$	−9.26481	−	11.0414i	−0.317594	−	0.378493i
$852$	−7.81341	−	46.6192i	−0.267683	−	1.59715i
$853$	26.0162	+	4.58736i	0.890779	+	0.157068i	0.600264	−	0.799802i	$-0.295062\pi$
$853$	26.0162	+	4.58736i	0.890779	+	0.157068i	0.290515	+	0.956870i	$0.406173\pi$
$854$	5.20956	+	5.65466i	0.178268	+	0.193498i
$855$	−15.3854	+	40.1407i	−0.526171	+	1.37278i
$856$	75.4542			2.57897
$857$	9.64582	−	3.51079i	0.329495	−	0.119926i	−0.171975	−	0.985101i	$-0.555015\pi$
$857$	9.64582	−	3.51079i	0.329495	−	0.119926i	0.501470	+	0.865175i	$0.332793\pi$
$858$	−1.61520	−	1.37881i	−0.0551419	−	0.0470717i
$859$	−0.719929	−	0.857978i	−0.0245637	−	0.0292738i	0.753623	−	0.657307i	$-0.228305\pi$
$859$	−0.719929	−	0.857978i	−0.0245637	−	0.0292738i	−0.778186	+	0.628033i	$0.783860\pi$
$860$	21.5121	−	18.0508i	0.733556	−	0.615526i
$861$	−22.7476	+	20.6033i	−0.775235	+	0.702160i
$862$	34.3696	−	12.5095i	1.17063	−	0.426076i
$863$	−22.3865	+	12.9249i	−0.762046	+	0.439968i	−0.830030	−	0.557719i	$-0.811677\pi$
$863$	−22.3865	+	12.9249i	−0.762046	+	0.439968i	0.0679836	+	0.997686i	$0.478343\pi$
$864$	16.7955	+	6.60131i	0.571395	+	0.224581i
$865$	25.1001	−	43.4746i	0.853428	−	1.47818i
$866$	24.6607	+	20.6928i	0.838004	+	0.703168i
$867$	−14.1655	−	8.33931i	−0.481085	−	0.283218i
$868$	3.27016	−	1.36485i	0.110996	−	0.0463261i
$869$	65.0957	−	11.4781i	2.20822	−	0.389369i
$870$	41.7983	+	7.73601i	1.41710	+	0.262275i
$871$	0.441756	+	1.21371i	0.0149683	+	0.0411252i
$872$	−19.1469	+	11.0545i	−0.648395	+	0.374351i
$873$	−5.84126	−	16.9366i	−0.197697	−	0.573217i
$874$	85.2914	−	49.2430i	2.88502	−	1.66567i
$875$	−15.0469	+	9.64285i	−0.508677	+	0.325988i
$876$	−3.19303	−	19.0514i	−0.107882	−	0.643687i
$877$	3.31996	+	18.8284i	0.112107	+	0.635790i	0.988142	+	0.153543i	$0.0490682\pi$
$877$	3.31996	+	18.8284i	0.112107	+	0.635790i	−0.876035	+	0.482247i	$0.839821\pi$
$878$	58.1833	−	48.8215i	1.96359	−	1.64765i
$879$	−3.03527	+	0.508713i	−0.102377	+	0.0171585i
$880$	−23.6710	−	65.0357i	−0.797951	−	2.19235i
$881$	−17.8333	−	30.8881i	−0.600818	−	1.04065i	−0.992697	−	0.120631i	$-0.961508\pi$
$881$	−17.8333	−	30.8881i	−0.600818	−	1.04065i	0.391879	−	0.920017i	$-0.371825\pi$
$882$	−52.5347	−	5.20968i	−1.76894	−	0.175419i
$883$	−22.8393	+	39.5588i	−0.768602	+	1.33126i	0.169718	+	0.985493i	$0.445714\pi$
$883$	−22.8393	+	39.5588i	−0.768602	+	1.33126i	−0.938321	+	0.345766i	$0.887619\pi$
$884$	2.55113	+	0.449833i	0.0858038	+	0.0151295i
$885$	48.9801	+	9.06521i	1.64645	+	0.304724i
$886$	−61.2912	−	22.3082i	−2.05912	−	0.749458i
$887$	−37.9021	−	13.7952i	−1.27263	−	0.463198i	−0.384639	−	0.923067i	$-0.625674\pi$
$887$	−37.9021	−	13.7952i	−1.27263	−	0.463198i	−0.887987	+	0.459869i	$0.847896\pi$
$888$	−19.3926	−	0.164367i	−0.650774	−	0.00551581i
$889$	−2.91144	−	1.50567i	−0.0976464	−	0.0504985i
$890$		−	6.30704i		−	0.211413i
$891$	11.6779	+	35.8186i	0.391226	+	1.19997i
$892$	−105.282	−	60.7848i	−3.52511	−	2.03523i
$893$	25.9498	+	4.57565i	0.868378	+	0.153118i
$894$	−63.4923	+	35.9433i	−2.12350	+	1.20212i
$895$	7.44919	+	8.87759i	0.248999	+	0.296745i
$896$	−5.16588	+	40.0705i	−0.172580	+	1.33866i
$897$	0.506078	+	1.42798i	0.0168975	+	0.0476789i
$898$	2.28233	−	12.9437i	0.0761622	−	0.431938i
$899$	−0.551148	−	0.954617i	−0.0183818	−	0.0318383i
$900$	−15.9732	−	28.7824i	−0.532441	−	0.959412i
$901$	−19.3547	−	11.1745i	−0.644799	−	0.372275i
$902$	12.2385	−	69.4079i	0.407497	−	2.31103i
$903$	8.56865	+	6.65411i	0.285147	+	0.221435i
$904$	−14.8023	−	5.38761i	−0.492319	−	0.179189i
$905$	−29.7031	+	5.23746i	−0.987366	+	0.174099i
$906$	61.0510	+	22.8086i	2.02828	+	0.757764i
$907$	26.3317	+	22.0950i	0.874331	+	0.733651i	0.965005	−	0.262230i	$-0.0844578\pi$
$907$	26.3317	+	22.0950i	0.874331	+	0.733651i	−0.0906745	+	0.995881i	$0.528902\pi$
$908$	−16.5483	+	28.6625i	−0.549174	+	0.951198i
$909$	18.6608	+	16.2052i	0.618940	+	0.537491i
$910$	−0.634430	+	2.03117i	−0.0210311	+	0.0673326i
$911$	2.82347	−	3.36488i	0.0935458	−	0.111484i	−0.717241	−	0.696825i	$-0.754595\pi$
$911$	2.82347	−	3.36488i	0.0935458	−	0.111484i	0.810787	+	0.585342i	$0.199040\pi$
$912$	9.90429	−	53.5137i	0.327964	−	1.77202i
$913$	−16.2686	+	44.6975i	−0.538411	+	1.47927i
$914$	95.6152	−	16.8595i	3.16267	−	0.557664i
$915$	−5.49768	−	0.0465970i	−0.181748	−	0.00154045i
$916$	−21.0067	−	57.7154i	−0.694081	−	1.90697i
$917$	5.90987	−	18.9208i	0.195161	−	0.624821i
$918$	−50.3876	−	44.5116i	−1.66304	−	1.46910i
$919$	−11.3040	−	19.5792i	−0.372886	−	0.645857i	0.617122	−	0.786867i	$-0.288298\pi$
$919$	−11.3040	−	19.5792i	−0.372886	−	0.645857i	−0.990008	+	0.141010i	$0.954965\pi$
$920$	−20.8758	+	118.392i	−0.688254	+	3.90328i
$921$	34.0489	+	0.288590i	1.12195	+	0.00950937i
$922$	−14.1778	+	38.9531i	−0.466920	+	1.28285i
$923$	−0.127820	−	0.724901i	−0.00420724	−	0.0238604i
$924$	70.1449	−	44.1185i	2.30760	−	1.45139i
$925$	3.73580	+	3.13471i	0.122832	+	0.103069i
$926$		−	102.704i		−	3.37506i
$927$	−1.05851	+	2.76167i	−0.0347662	+	0.0907050i
$928$	−12.3475			−0.405325
$929$	15.0096	−	5.46306i	0.492450	−	0.179237i	−0.0838452	−	0.996479i	$-0.526720\pi$
$929$	15.0096	−	5.46306i	0.492450	−	0.179237i	0.576295	+	0.817242i	$0.304498\pi$
$930$	−1.29736	+	3.47259i	−0.0425419	+	0.113871i
$931$	3.37925	+	36.3725i	0.110750	+	1.19206i
$932$	33.2294	−	91.2971i	1.08847	−	2.99054i
$933$	45.2263	−	7.57996i	1.48064	−	0.248157i
$934$	62.5369	−	74.5286i	2.04627	−	2.43865i
$935$			59.1607i			1.93476i
$936$	1.90341	+	0.729555i	0.0622150	+	0.0238463i
$937$	−51.5494	−	29.7620i	−1.68404	−	0.972283i	−0.958925	−	0.283660i	$-0.908451\pi$
$937$	−51.5494	−	29.7620i	−1.68404	−	0.972283i	−0.725119	−	0.688623i	$-0.758215\pi$
$938$	−73.6535	+	3.41410i	−2.40487	+	0.111474i
$939$	−1.58907	+	8.58586i	−0.0518572	+	0.280189i
$940$	−45.8825	+	38.5000i	−1.49652	+	1.25573i
$941$	7.06175	+	40.0492i	0.230206	+	1.30557i	0.852478	+	0.522764i	$0.175099\pi$
$941$	7.06175	+	40.0492i	0.230206	+	1.30557i	−0.622271	+	0.782802i	$0.713790\pi$
$942$	−0.119212	+	14.0651i	−0.00388414	+	0.458264i
$943$	−32.3186	+	38.5158i	−1.05244	+	1.25425i
$944$	−63.0613			−2.05247
$945$	28.4050	−	24.8642i	0.924014	−	0.808831i
$946$	−24.9132			−0.809999
$947$	25.4313	−	30.3079i	0.826407	−	0.984873i	−0.173593	−	0.984817i	$-0.555538\pi$
$947$	25.4313	−	30.3079i	0.826407	−	0.984873i	1.00000		5.57258e-5i	$-1.77381e-5\pi$
$948$	−102.816	+	58.2044i	−3.33930	+	1.89039i
$949$	−0.0522349	−	0.296239i	−0.00169562	−	0.00961631i
$950$	−25.5264	+	21.4192i	−0.828185	+	0.694930i
$951$	40.7136	+	34.7551i	1.32023	+	1.12701i
$952$	−36.4799	+	70.5394i	−1.18232	+	2.28620i
$953$	−10.2234	−	5.90251i	−0.331170	−	0.191201i	0.325190	−	0.945649i	$-0.394572\pi$
$953$	−10.2234	−	5.90251i	−0.331170	−	0.191201i	−0.656360	+	0.754447i	$0.727905\pi$
$954$	−24.7260	−	21.4722i	−0.800535	−	0.695189i
$955$			27.8942i			0.902636i
$956$	−66.1699	+	78.8582i	−2.14009	+	2.55046i
$957$	−16.4013	−	19.8862i	−0.530178	−	0.642828i
$958$	24.8280	−	68.2145i	0.802158	−	2.20391i
$959$	−5.50941	+	42.7352i	−0.177908	+	1.37999i
$960$	−10.0208	−	12.1499i	−0.323419	−	0.392138i
$961$	−29.0401	+	10.5697i	−0.936779	+	0.340960i
$962$	−0.562357			−0.0181311
$963$	−33.2811	−	19.9746i	−1.07247	−	0.643671i
$964$		−	58.5885i		−	1.88701i
$965$	−18.1780	−	15.2531i	−0.585170	−	0.491016i
$966$	−86.4235	+	3.27225i	−2.78063	+	0.105283i
$967$	−3.86189	−	21.9019i	−0.124190	−	0.704317i	−0.981786	−	0.189992i	$-0.939154\pi$
$967$	−3.86189	−	21.9019i	−0.124190	−	0.704317i	0.857596	−	0.514325i	$-0.171957\pi$
$968$	−13.0103	+	35.7455i	−0.418167	+	1.14891i
$969$	−23.6010	+	40.0895i	−0.758172	+	1.28786i
$970$	7.15846	−	40.5976i	0.229844	−	1.30351i
$971$	1.25978	+	2.18201i	0.0404284	+	0.0700240i	0.885532	−	0.464579i	$-0.153794\pi$
$971$	1.25978	+	2.18201i	0.0404284	+	0.0700240i	−0.845103	+	0.534603i	$0.820461\pi$
$972$	−41.0605	−	53.3722i	−1.31702	−	1.71191i
$973$	−18.9388	+	17.4481i	−0.607151	+	0.559360i
$974$	−18.3791	−	50.4961i	−0.588904	−	1.61800i
$975$	−0.252527	−	0.446078i	−0.00808732	−	0.0142859i
$976$	6.85450	−	1.20863i	0.219407	−	0.0386874i
$977$	6.19708	−	17.0263i	0.198262	−	0.544721i	−0.800225	−	0.599699i	$-0.795287\pi$
$977$	6.19708	−	17.0263i	0.198262	−	0.544721i	0.998488	+	0.0549787i	$0.0175091\pi$
$978$	−25.5413	−	21.8033i	−0.816721	−	0.697191i
$979$	−2.45842	+	2.92983i	−0.0785713	+	0.0936377i
$980$	−68.2714	−	47.2594i	−2.18085	−	1.50965i
$981$	11.3716	+	0.192780i	0.363068	+	0.00615500i
$982$	−22.6079	+	39.1580i	−0.721447	+	1.24958i
$983$	30.9505	+	25.9705i	0.987167	+	0.828332i	0.985155	−	0.171666i	$-0.0549150\pi$
$983$	30.9505	+	25.9705i	0.987167	+	0.828332i	0.00201226	+	0.999998i	$0.499359\pi$
$984$	11.1822	+	66.7195i	0.356477	+	2.12694i
$985$	−1.95207	+	0.344203i	−0.0621982	+	0.0109672i
$986$	43.2270	+	15.7333i	1.37663	+	0.501052i
$987$	−18.2759	−	14.1924i	−0.581727	−	0.451748i
$988$	0.456087	−	2.58660i	0.0145101	−	0.0822907i
$989$	15.3918	+	8.88645i	0.489430	+	0.282573i
$990$	−16.4982	+	85.1041i	−0.524348	+	2.70479i
$991$	−13.1394	−	22.7581i	−0.417386	−	0.722934i	0.578290	−	0.815831i	$-0.303720\pi$
$991$	−13.1394	−	22.7581i	−0.417386	−	0.722934i	−0.995676	+	0.0928979i	$0.970387\pi$
$992$	0.186982	−	1.06043i	0.00593669	−	0.0336687i
$993$	−18.4450	+	21.6073i	−0.585334	+	0.685686i
$994$	41.6751	+	5.37274i	1.32185	+	0.170413i
$995$	−38.4390	−	45.8098i	−1.21860	−	1.45227i
$996$	0.720584	−	85.0169i	0.0228326	−	2.69386i
$997$	13.5180	+	2.38359i	0.428119	+	0.0754889i	0.383556	−	0.923518i	$-0.374699\pi$
$997$	13.5180	+	2.38359i	0.428119	+	0.0754889i	0.0445630	+	0.999007i	$0.485810\pi$
$998$	−23.2048	−	13.3973i	−0.734536	−	0.424085i
$999$	8.51012	+	5.20619i	0.269248	+	0.164717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.21	✓	132
3.2	odd	2		567.2.ba.a.143.2		132
7.5	odd	6		189.2.bd.a.47.2	yes	132
21.5	even	6		567.2.bd.a.467.21		132
27.4	even	9		567.2.bd.a.17.21		132
27.23	odd	18		189.2.bd.a.185.2	yes	132
189.131	even	18	inner	189.2.ba.a.131.21	yes	132
189.166	odd	18		567.2.ba.a.341.2		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.21	✓	132	1.1	even	1	trivial
189.2.ba.a.131.21	yes	132	189.131	even	18	inner
189.2.bd.a.47.2	yes	132	7.5	odd	6
189.2.bd.a.185.2	yes	132	27.23	odd	18
567.2.ba.a.143.2		132	3.2	odd	2
567.2.ba.a.341.2		132	189.166	odd	18
567.2.bd.a.17.21		132	27.4	even	9
567.2.bd.a.467.21		132	21.5	even	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61592 - 1.92578i) q^{2} +(-1.49261 - 0.878707i) q^{3} +(-0.750127 - 4.25418i) q^{4} +(-2.10349 + 1.76504i) q^{5} +(-4.10412 + 1.45451i) q^{6} +(-0.122508 - 2.64291i) q^{7} +(-5.05050 - 2.91591i) q^{8} +(1.45575 + 2.62313i) q^{9} +6.90302i q^{10} +(2.69072 - 3.20668i) q^{11} +(-2.61854 + 7.00896i) q^{12} +(-0.0398496 + 0.109486i) q^{13} +(-5.28762 - 4.03481i) q^{14} +(4.69064 - 0.786155i) q^{15} +(-5.65800 + 2.05934i) q^{16} +5.14689 q^{17} +(7.40393 + 1.43532i) q^{18} -5.21844i q^{19} +(9.08669 + 7.62463i) q^{20} +(-2.13949 + 4.05248i) q^{21} +(-1.82736 - 10.3635i) q^{22} +(-2.56763 + 7.05452i) q^{23} +(4.97618 + 8.79022i) q^{24} +(0.441075 - 2.50146i) q^{25} +(0.146452 + 0.253662i) q^{26} +(0.132107 - 5.19447i) q^{27} +(-11.1515 + 2.50369i) q^{28} +(1.21597 + 3.34086i) q^{29} +(6.06573 - 10.3035i) q^{30} +(-0.305335 + 0.0538389i) q^{31} +(-1.18784 + 3.26355i) q^{32} +(-6.83392 + 2.42195i) q^{33} +(8.31695 - 9.91175i) q^{34} +(4.92254 + 5.34312i) q^{35} +(10.0673 - 8.16068i) q^{36} +(-0.959970 + 1.66272i) q^{37} +(-10.0496 - 8.43258i) q^{38} +(0.155686 - 0.128403i) q^{39} +(15.7704 - 2.78075i) q^{40} +(6.29347 + 2.29063i) q^{41} +(4.34692 + 10.6687i) q^{42} +(0.411100 - 2.33146i) q^{43} +(-15.6602 - 9.04140i) q^{44} +(-7.69208 - 2.94828i) q^{45} +(9.43633 + 16.3442i) q^{46} +(-0.876823 + 4.97271i) q^{47} +(10.2547 + 1.89794i) q^{48} +(-6.96998 + 0.647559i) q^{49} +(-4.10452 - 4.89157i) q^{50} +(-7.68227 - 4.52261i) q^{51} +(0.495665 + 0.0873991i) q^{52} +(-3.76047 - 2.17111i) q^{53} +(-9.78992 - 8.64825i) q^{54} +11.4945i q^{55} +(-7.08776 + 13.7053i) q^{56} +(-4.58549 + 7.78908i) q^{57} +(8.39867 + 3.05687i) q^{58} +(9.84174 + 3.58210i) q^{59} +(-6.86302 - 19.3651i) q^{60} +(-1.13841 - 0.200732i) q^{61} +(-0.389715 + 0.675007i) q^{62} +(6.75436 - 4.16877i) q^{63} +(-1.65570 - 2.86775i) q^{64} +(-0.109424 - 0.300639i) q^{65} +(-6.37893 + 17.0743i) q^{66} +(8.49204 - 7.12567i) q^{67} +(-3.86082 - 21.8958i) q^{68} +(10.0313 - 8.27342i) q^{69} +(18.2441 - 0.845678i) q^{70} +(-5.47124 + 3.15882i) q^{71} +(0.296553 - 17.4929i) q^{72} +(-2.23588 + 1.29089i) q^{73} +(1.65079 + 4.53550i) q^{74} +(-2.85640 + 3.34612i) q^{75} +(-22.2002 + 3.91449i) q^{76} +(-8.80461 - 6.71850i) q^{77} +(0.00429980 - 0.507305i) q^{78} +(12.0963 + 10.1500i) q^{79} +(8.26674 - 14.3184i) q^{80} +(-4.76161 + 7.63722i) q^{81} +(14.5810 - 8.41833i) q^{82} +(-10.6778 + 3.88640i) q^{83} +(18.8449 + 6.06191i) q^{84} +(-10.8264 + 9.08446i) q^{85} +(-3.82557 - 4.55914i) q^{86} +(1.12067 - 6.05508i) q^{87} +(-22.9399 + 8.34943i) q^{88} -0.913664 q^{89} +(-18.1075 + 10.0490i) q^{90} +(0.294244 + 0.0919061i) q^{91} +(31.9372 + 5.63140i) q^{92} +(0.503054 + 0.187940i) q^{93} +(8.15946 + 9.72406i) q^{94} +(9.21076 + 10.9770i) q^{95} +(4.64068 - 3.82744i) q^{96} +(-5.88114 - 1.03700i) q^{97} +(-10.0159 + 14.4690i) q^{98} +(12.3285 + 2.39000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

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