LMFDB - Embedded newform 175.2.x.a.103.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] 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("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.7
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.855607 - 0.0448405i) q^{2} +(-0.835912 - 1.03227i) q^{3} +(-1.25899 - 0.132325i) q^{4} +(1.02300 + 1.98833i) q^{5} +(0.668925 + 0.920697i) q^{6} +(-0.0574557 + 2.64513i) q^{7} +(2.76373 + 0.437732i) q^{8} +(0.256912 - 1.20868i) q^{9} +(-0.786126 - 1.74711i) q^{10} +(0.886724 - 0.188479i) q^{11} +(0.915811 + 1.41023i) q^{12} +(5.68290 + 2.89558i) q^{13} +(0.167768 - 2.26061i) q^{14} +(1.19735 - 2.71808i) q^{15} +(0.131483 + 0.0279475i) q^{16} +(0.276666 + 0.720738i) q^{17} +(-0.274013 + 1.02263i) q^{18} +(-0.0762931 - 0.725880i) q^{19} +(-1.02484 - 2.63866i) q^{20} +(2.77850 - 2.15179i) q^{21} +(-0.767139 + 0.121503i) q^{22} +(-0.328025 + 6.25910i) q^{23} +(-1.85838 - 3.21881i) q^{24} +(-2.90695 + 4.06812i) q^{25} +(-4.73249 - 2.73230i) q^{26} +(-5.01294 + 2.55422i) q^{27} +(0.422353 - 3.32259i) q^{28} +(-3.24612 + 4.46790i) q^{29} +(-1.14634 + 2.27192i) q^{30} +(1.93308 - 4.34176i) q^{31} +(-5.51692 - 1.47825i) q^{32} +(-0.935784 - 0.757783i) q^{33} +(-0.204399 - 0.629075i) q^{34} +(-5.31818 + 2.59172i) q^{35} +(-0.483388 + 1.48772i) q^{36} +(8.05740 - 5.23253i) q^{37} +(0.0327281 + 0.624489i) q^{38} +(-1.76140 - 8.28671i) q^{39} +(1.95694 + 5.94303i) q^{40} +(5.14669 - 1.67226i) q^{41} +(-2.47379 + 1.71649i) q^{42} +(-3.27866 - 3.27866i) q^{43} +(-1.14132 + 0.119957i) q^{44} +(2.66607 - 0.725645i) q^{45} +(0.561322 - 5.34062i) q^{46} +(0.361269 + 0.138678i) q^{47} +(-0.0810588 - 0.159087i) q^{48} +(-6.99340 - 0.303955i) q^{49} +(2.66962 - 3.35037i) q^{50} +(0.512725 - 0.888067i) q^{51} +(-6.77156 - 4.39750i) q^{52} +(-6.15653 + 4.98546i) q^{53} +(4.40364 - 1.96063i) q^{54} +(1.28188 + 1.57029i) q^{55} +(-1.31665 + 7.28528i) q^{56} +(-0.685527 + 0.685527i) q^{57} +(2.97774 - 3.67721i) q^{58} +(-0.380730 + 0.422843i) q^{59} +(-1.86713 + 3.26360i) q^{60} +(7.85465 - 7.07236i) q^{61} +(-1.84864 + 3.62816i) q^{62} +(3.18234 + 0.749010i) q^{63} +(4.39835 + 1.42911i) q^{64} +(0.0562076 + 14.2617i) q^{65} +(0.766684 + 0.690326i) q^{66} +(-2.29160 + 0.879663i) q^{67} +(-0.252948 - 0.944013i) q^{68} +(6.73525 - 4.89345i) q^{69} +(4.66648 - 1.97902i) q^{70} +(-9.01254 - 6.54799i) q^{71} +(1.23911 - 3.22800i) q^{72} +(6.64662 - 10.2349i) q^{73} +(-7.12859 + 4.11570i) q^{74} +(6.62934 - 0.399850i) q^{75} +0.923972i q^{76} +(0.447604 + 2.35633i) q^{77} +(1.13548 + 7.16915i) q^{78} +(0.729574 + 1.63865i) q^{79} +(0.0789375 + 0.290022i) q^{80} +(3.44047 + 1.53180i) q^{81} +(-4.47853 + 1.20002i) q^{82} +(-0.805162 + 5.08360i) q^{83} +(-3.78285 + 2.34141i) q^{84} +(-1.15004 + 1.28742i) q^{85} +(2.65823 + 2.95226i) q^{86} +(7.32552 - 0.383914i) q^{87} +(2.53317 - 0.132758i) q^{88} +(2.15138 + 2.38935i) q^{89} +(-2.31365 + 0.501319i) q^{90} +(-7.98570 + 14.8656i) q^{91} +(1.24122 - 7.83674i) q^{92} +(-6.09774 + 1.63388i) q^{93} +(-0.302886 - 0.134854i) q^{94} +(1.36524 - 0.894270i) q^{95} +(3.08571 + 6.93062i) q^{96} +(1.57659 + 9.95418i) q^{97} +(5.96997 + 0.573653i) q^{98} -1.12018i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.855607	−	0.0448405i	−0.605006	−	0.0317070i	−0.252626	−	0.967564i	$-0.581294\pi$
$2$	−0.855607	−	0.0448405i	−0.605006	−	0.0317070i	−0.352380	+	0.935857i	$0.614627\pi$
$3$	−0.835912	−	1.03227i	−0.482614	−	0.595979i	0.476438	−	0.879208i	$-0.341928\pi$
$3$	−0.835912	−	1.03227i	−0.482614	−	0.595979i	−0.959052	+	0.283229i	$0.908594\pi$
$4$	−1.25899	−	0.132325i	−0.629496	−	0.0661626i
$5$	1.02300	+	1.98833i	0.457499	+	0.889210i
$5$	1.02300	+	1.98833i	0.457499	+	0.889210i
$6$	0.668925	+	0.920697i	0.273088	+	0.375873i
$7$	−0.0574557	+	2.64513i	−0.0217162	+	0.999764i
$7$	−0.0574557	+	2.64513i	−0.0217162	+	0.999764i
$8$	2.76373	+	0.437732i	0.977127	+	0.154762i
$9$	0.256912	−	1.20868i	0.0856373	−	0.402892i
$10$	−0.786126	−	1.74711i	−0.248595	−	0.552483i
$11$	0.886724	−	0.188479i	0.267357	−	0.0568286i	−0.0722822	−	0.997384i	$-0.523028\pi$
$11$	0.886724	−	0.188479i	0.267357	−	0.0568286i	0.339640	+	0.940556i	$0.389695\pi$
$12$	0.915811	+	1.41023i	0.264372	+	0.407097i
$13$	5.68290	+	2.89558i	1.57615	+	0.803090i	0.999899	−	0.0141814i	$-0.00451422\pi$
$13$	5.68290	+	2.89558i	1.57615	+	0.803090i	0.576253	+	0.817271i	$0.304514\pi$
$14$	0.167768	−	2.26061i	0.0448379	−	0.604174i
$15$	1.19735	−	2.71808i	0.309155	−	0.701805i
$16$	0.131483	+	0.0279475i	0.0328707	+	0.00698688i
$17$	0.276666	+	0.720738i	0.0671013	+	0.174805i	0.963031	−	0.269392i	$-0.0868226\pi$
$17$	0.276666	+	0.720738i	0.0671013	+	0.174805i	−0.895929	+	0.444196i	$0.853489\pi$
$18$	−0.274013	+	1.02263i	−0.0645855	+	0.241036i
$19$	−0.0762931	−	0.725880i	−0.0175028	−	0.166528i	0.982279	−	0.187426i	$-0.0600144\pi$
$19$	−0.0762931	−	0.725880i	−0.0175028	−	0.166528i	−0.999782	+	0.0208973i	$0.993348\pi$
$20$	−1.02484	−	2.63866i	−0.229161	−	0.590023i
$21$	2.77850	−	2.15179i	0.606319	−	0.469558i
$22$	−0.767139	+	0.121503i	−0.163555	+	0.0259045i
$23$	−0.328025	+	6.25910i	−0.0683980	+	1.30511i	0.721732	+	0.692173i	$0.243346\pi$
$23$	−0.328025	+	6.25910i	−0.0683980	+	1.30511i	−0.790130	+	0.612940i	$0.789987\pi$
$24$	−1.85838	−	3.21881i	−0.379341	−	0.657038i
$25$	−2.90695	+	4.06812i	−0.581390	+	0.813625i
$26$	−4.73249	−	2.73230i	−0.928118	−	0.535849i
$27$	−5.01294	+	2.55422i	−0.964741	+	0.491560i
$28$	0.422353	−	3.32259i	0.0798173	−	0.627910i
$29$	−3.24612	+	4.46790i	−0.602789	+	0.829667i	−0.995960	−	0.0897979i	$-0.971378\pi$
$29$	−3.24612	+	4.46790i	−0.602789	+	0.829667i	0.393171	+	0.919465i	$0.371378\pi$
$30$	−1.14634	+	2.27192i	−0.209293	+	0.414794i
$31$	1.93308	−	4.34176i	0.347191	−	0.779804i	−0.652565	−	0.757732i	$-0.726307\pi$
$31$	1.93308	−	4.34176i	0.347191	−	0.779804i	0.999756	−	0.0220713i	$-0.00702609\pi$
$32$	−5.51692	−	1.47825i	−0.975263	−	0.261321i
$33$	−0.935784	−	0.757783i	−0.162899	−	0.131913i
$34$	−0.204399	−	0.629075i	−0.0350541	−	0.107885i
$35$	−5.31818	+	2.59172i	−0.898936	+	0.438080i
$36$	−0.483388	+	1.48772i	−0.0805647	+	0.247953i
$37$	8.05740	−	5.23253i	1.32463	−	0.860223i	0.328195	−	0.944610i	$-0.393560\pi$
$37$	8.05740	−	5.23253i	1.32463	−	0.860223i	0.996433	+	0.0843868i	$0.0268931\pi$
$38$	0.0327281	+	0.624489i	0.00530920	+	0.101305i
$39$	−1.76140	−	8.28671i	−0.282049	−	1.32694i
$40$	1.95694	+	5.94303i	0.309419	+	0.939675i
$41$	5.14669	−	1.67226i	0.803778	−	0.261163i	0.121817	−	0.992553i	$-0.461128\pi$
$41$	5.14669	−	1.67226i	0.803778	−	0.261163i	0.681960	+	0.731389i	$0.261128\pi$
$42$	−2.47379	+	1.71649i	−0.381715	+	0.264861i
$43$	−3.27866	−	3.27866i	−0.499991	−	0.499991i	0.411444	−	0.911435i	$-0.365025\pi$
$43$	−3.27866	−	3.27866i	−0.499991	−	0.499991i	−0.911435	+	0.411444i	$0.865025\pi$
$44$	−1.14132	+	0.119957i	−0.172060	+	0.0180843i
$45$	2.66607	−	0.725645i	0.397435	−	0.108173i
$46$	0.561322	−	5.34062i	0.0827624	−	0.787432i
$47$	0.361269	+	0.138678i	0.0526966	+	0.0202283i	0.384573	−	0.923094i	$-0.374349\pi$
$47$	0.361269	+	0.138678i	0.0526966	+	0.0202283i	−0.331877	+	0.943323i	$0.607682\pi$
$48$	−0.0810588	−	0.159087i	−0.0116998	−	0.0229622i
$49$	−6.99340	−	0.303955i	−0.999057	−	0.0434222i
$50$	2.66962	−	3.35037i	0.377542	−	0.473813i
$51$	0.512725	−	0.888067i	0.0717959	−	0.124354i
$52$	−6.77156	−	4.39750i	−0.939046	−	0.609824i
$53$	−6.15653	+	4.98546i	−0.845664	+	0.684805i	−0.950851	−	0.309647i	$-0.899789\pi$
$53$	−6.15653	+	4.98546i	−0.845664	+	0.684805i	0.105188	+	0.994452i	$0.466456\pi$
$54$	4.40364	−	1.96063i	0.599260	−	0.266808i
$55$	1.28188	+	1.57029i	0.172848	+	0.211738i
$56$	−1.31665	+	7.28528i	−0.175945	+	0.973536i
$57$	−0.685527	+	0.685527i	−0.0908002	+	0.0908002i
$58$	2.97774	−	3.67721i	0.390997	−	0.482841i
$59$	−0.380730	+	0.422843i	−0.0495668	+	0.0550495i	−0.767418	−	0.641147i	$-0.778459\pi$
$59$	−0.380730	+	0.422843i	−0.0495668	+	0.0550495i	0.717852	+	0.696196i	$0.245126\pi$
$60$	−1.86713	+	3.26360i	−0.241045	+	0.421329i
$61$	7.85465	−	7.07236i	1.00569	−	0.905523i	0.0101532	−	0.999948i	$-0.496768\pi$
$61$	7.85465	−	7.07236i	1.00569	−	0.905523i	0.995532	+	0.0944255i	$0.0301014\pi$
$62$	−1.84864	+	3.62816i	−0.234778	+	0.460777i
$63$	3.18234	+	0.749010i	0.400937	+	0.0943664i
$64$	4.39835	+	1.42911i	0.549794	+	0.178639i
$65$	0.0562076	+	14.2617i	0.00697169	+	1.76894i
$66$	0.766684	+	0.690326i	0.0943723	+	0.0849732i
$67$	−2.29160	+	0.879663i	−0.279964	+	0.107468i	−0.494298	−	0.869292i	$-0.664575\pi$
$67$	−2.29160	+	0.879663i	−0.279964	+	0.107468i	0.214335	+	0.976760i	$0.431242\pi$
$68$	−0.252948	−	0.944013i	−0.0306744	−	0.114478i
$69$	6.73525	−	4.89345i	0.810829	−	0.589102i
$70$	4.66648	−	1.97902i	0.557751	−	0.236539i
$71$	−9.01254	−	6.54799i	−1.06959	−	0.777104i	−0.0937530	−	0.995595i	$-0.529886\pi$
$71$	−9.01254	−	6.54799i	−1.06959	−	0.777104i	−0.975839	+	0.218492i	$0.929886\pi$
$72$	1.23911	−	3.22800i	0.146031	−	0.380423i
$73$	6.64662	−	10.2349i	0.777929	−	1.19790i	−0.198083	−	0.980185i	$-0.563471\pi$
$73$	6.64662	−	10.2349i	0.777929	−	1.19790i	0.976011	−	0.217720i	$-0.0698618\pi$
$74$	−7.12859	+	4.11570i	−0.828682	+	0.478440i
$75$	6.62934	−	0.399850i	0.765490	−	0.0461707i
$76$			0.923972i			0.105987i
$77$	0.447604	+	2.35633i	0.0510092	+	0.268529i
$78$	1.13548	+	7.16915i	0.128568	+	0.811747i
$79$	0.729574	+	1.63865i	0.0820835	+	0.184363i	0.949925	−	0.312479i	$-0.101160\pi$
$79$	0.729574	+	1.63865i	0.0820835	+	0.184363i	−0.867841	+	0.496842i	$0.834493\pi$
$80$	0.0789375	+	0.290022i	0.00882548	+	0.0324254i
$81$	3.44047	+	1.53180i	0.382275	+	0.170200i
$82$	−4.47853	+	1.20002i	−0.494571	+	0.132520i
$83$	−0.805162	+	5.08360i	−0.0883781	+	0.557997i	0.903275	+	0.429062i	$0.141156\pi$
$83$	−0.805162	+	5.08360i	−0.0883781	+	0.557997i	−0.991653	+	0.128935i	$0.958844\pi$
$84$	−3.78285	+	2.34141i	−0.412742	+	0.255469i
$85$	−1.15004	+	1.28742i	−0.124739	+	0.139640i
$86$	2.65823	+	2.95226i	0.286644	+	0.318351i
$87$	7.32552	−	0.383914i	0.785379	−	0.0411599i
$88$	2.53317	−	0.132758i	0.270037	−	0.0141521i
$89$	2.15138	+	2.38935i	0.228046	+	0.253271i	0.846299	−	0.532708i	$-0.178826\pi$
$89$	2.15138	+	2.38935i	0.228046	+	0.253271i	−0.618253	+	0.785980i	$0.712159\pi$
$90$	−2.31365	+	0.501319i	−0.243880	+	0.0528437i
$91$	−7.98570	+	14.8656i	−0.837129	+	1.55834i
$92$	1.24122	−	7.83674i	0.129406	−	0.817037i
$93$	−6.09774	+	1.63388i	−0.632306	+	0.169426i
$94$	−0.302886	−	0.134854i	−0.0312403	−	0.0139091i
$95$	1.36524	−	0.894270i	0.140071	−	0.0917501i
$96$	3.08571	+	6.93062i	0.314934	+	0.707353i
$97$	1.57659	+	9.95418i	0.160078	+	1.01069i	0.928657	+	0.370939i	$0.120964\pi$
$97$	1.57659	+	9.95418i	0.160078	+	1.01069i	−0.768579	+	0.639755i	$0.779036\pi$
$98$	5.96997	+	0.573653i	0.603058	+	0.0579477i
$99$		−	1.12018i		−	0.112583i
$100$	4.19814	−	4.73707i	0.419814	−	0.473707i
$101$	9.36808	−	5.40866i	0.932159	−	0.538182i	0.0446652	−	0.999002i	$-0.485778\pi$
$101$	9.36808	−	5.40866i	0.932159	−	0.538182i	0.887494	+	0.460820i	$0.152445\pi$
$102$	−0.478513	+	0.736845i	−0.0473798	+	0.0729585i
$103$	3.86478	−	10.0681i	0.380808	−	0.992040i	−0.600505	−	0.799621i	$-0.705034\pi$
$103$	3.86478	−	10.0681i	0.380808	−	0.992040i	0.981313	−	0.192418i	$-0.0616331\pi$
$104$	14.4385	+	10.4902i	1.41581	+	1.02865i
$105$	7.12087	+	3.32332i	0.694926	+	0.324323i
$106$	5.49112	−	3.98953i	0.533344	−	0.387497i
$107$	−3.10367	−	11.5831i	−0.300043	−	1.11978i	−0.937129	−	0.348983i	$-0.886527\pi$
$107$	−3.10367	−	11.5831i	−0.300043	−	1.11978i	0.637086	−	0.770793i	$-0.280140\pi$
$108$	6.64924	−	2.55240i	0.639823	−	0.245605i
$109$	4.16110	+	3.74667i	0.398561	+	0.358866i	0.843904	−	0.536494i	$-0.180252\pi$
$109$	4.16110	+	3.74667i	0.398561	+	0.358866i	−0.445343	+	0.895360i	$0.646918\pi$
$110$	−1.02637	−	1.40103i	−0.0978606	−	0.133583i
$111$	−12.1366	−	3.94343i	−1.15196	−	0.374294i
$112$	−0.0814792	+	0.346183i	−0.00769906	+	0.0327112i
$113$	−2.01681	+	3.95822i	−0.189726	+	0.372358i	−0.966201	−	0.257790i	$-0.917006\pi$
$113$	−2.01681	+	3.95822i	−0.189726	+	0.372358i	0.776475	+	0.630148i	$0.217006\pi$
$114$	0.617281	−	0.555802i	0.0578136	−	0.0520556i
$115$	−12.7808	+	5.75082i	−1.19181	+	0.536267i
$116$	4.67805	−	5.19550i	0.434346	−	0.482390i
$117$	4.95982	−	6.12487i	0.458536	−	0.566245i
$118$	0.344716	−	0.344716i	0.0317336	−	0.0317336i
$119$	−1.92234	+	0.690405i	−0.176221	+	0.0632893i
$120$	4.49896	−	6.98793i	0.410697	−	0.637908i
$121$	−9.29824	+	4.13984i	−0.845295	+	0.376350i
$122$	−7.03762	+	5.69896i	−0.637157	+	0.515959i
$123$	−6.02840	−	3.91489i	−0.543562	−	0.352993i
$124$	−3.00825	+	5.21045i	−0.270149	+	0.467912i
$125$	−11.0626	−	1.61831i	−0.989469	−	0.144746i
$126$	−2.68925	−	0.783556i	−0.239577	−	0.0698047i
$127$	0.200713	+	0.393922i	0.0178104	+	0.0349549i	0.899740	−	0.436426i	$-0.143756\pi$
$127$	0.200713	+	0.393922i	0.0178104	+	0.0349549i	−0.881930	+	0.471381i	$0.843756\pi$
$128$	6.96518	+	2.67368i	0.615641	+	0.236322i
$129$	−0.643777	+	6.12513i	−0.0566814	+	0.539287i
$130$	0.591409	−	12.2049i	0.0518700	−	1.07044i
$131$	−14.6676	+	1.54163i	−1.28152	+	0.134693i	−0.720699	−	0.693248i	$-0.756179\pi$
$131$	−14.6676	+	1.54163i	−1.28152	+	0.134693i	−0.560816	+	0.827940i	$0.689512\pi$
$132$	1.07787	+	1.07787i	0.0938166	+	0.0938166i
$133$	1.92443	−	0.160099i	0.166869	−	0.0138823i
$134$	2.00015	−	0.649890i	0.172787	−	0.0561419i
$135$	−10.2069	−	7.35445i	−0.878468	−	0.632970i
$136$	0.449139	+	2.11303i	0.0385134	+	0.181191i
$137$	−0.805859	−	15.3767i	−0.0688492	−	1.31372i	−0.786619	−	0.617439i	$-0.788170\pi$
$137$	−0.805859	−	15.3767i	−0.0688492	−	1.31372i	0.717769	−	0.696281i	$-0.245163\pi$
$138$	−5.98216	+	3.88486i	−0.509235	+	0.330701i
$139$	6.31196	−	19.4262i	0.535374	−	1.64771i	−0.207467	−	0.978242i	$-0.566522\pi$
$139$	6.31196	−	19.4262i	0.535374	−	1.64771i	0.742841	−	0.669468i	$-0.233478\pi$
$140$	7.03849	−	2.55922i	0.594861	−	0.216294i
$141$	−0.158837	−	0.488849i	−0.0133765	−	0.0411685i
$142$	7.41758	+	6.00664i	0.622469	+	0.504066i
$143$	5.58492	+	1.49648i	0.467035	+	0.125142i
$144$	0.0675589	−	0.151740i	0.00562991	−	0.0126450i
$145$	−12.2044	−	1.88372i	−1.01352	−	0.156434i
$146$	−6.14584	+	8.45902i	−0.508633	+	0.700073i
$147$	5.53210	+	7.47313i	0.456280	+	0.616373i
$148$	−10.8366	+	5.52152i	−0.890762	+	0.453866i
$149$	−15.7770	−	9.10884i	−1.29250	−	0.746225i	−0.313403	−	0.949620i	$-0.601469\pi$
$149$	−15.7770	−	9.10884i	−1.29250	−	0.746225i	−0.979097	+	0.203395i	$0.934802\pi$
$150$	−5.69004	+	0.0448514i	−0.464590	+	0.00366210i
$151$	6.74252	+	11.6784i	0.548699	+	0.950374i	0.998364	+	0.0571768i	$0.0182099\pi$
$151$	6.74252	+	11.6784i	0.548699	+	0.950374i	−0.449666	+	0.893197i	$0.648457\pi$
$152$	0.106887	−	2.03953i	0.00866972	−	0.165428i
$153$	0.942217	−	0.149233i	0.0761738	−	0.0120647i
$154$	−0.277314	−	2.03616i	−0.0223466	−	0.164079i
$155$	10.6104	−	0.598009i	0.852249	−	0.0480332i
$156$	1.12104	+	10.6660i	0.0897550	+	0.853962i
$157$	−2.63042	+	9.81685i	−0.209930	+	0.783470i	0.777960	+	0.628314i	$0.216255\pi$
$157$	−2.63042	+	9.81685i	−0.209930	+	0.783470i	−0.987890	+	0.155156i	$0.950412\pi$
$158$	−0.550751	−	1.43476i	−0.0438154	−	0.114143i
$159$	10.2926	+	2.18777i	0.816259	+	0.173501i
$160$	−2.70453	−	12.4817i	−0.213812	−	0.986768i
$161$	−16.5373	−	1.22729i	−1.30332	−	0.0967240i
$162$	−2.87501	−	1.46489i	−0.225882	−	0.115093i
$163$	−13.1885	−	20.3086i	−1.03301	−	1.59069i	−0.782577	−	0.622553i	$-0.786095\pi$
$163$	−13.1885	−	20.3086i	−1.03301	−	1.59069i	−0.250428	−	0.968135i	$-0.580571\pi$
$164$	−6.70092	+	1.42432i	−0.523254	+	0.111221i
$165$	0.549421	−	2.63586i	0.0427724	−	0.205202i
$166$	0.916853	−	4.31346i	0.0711616	−	0.334789i
$167$	17.8756	+	2.83121i	1.38325	+	0.219086i	0.803306	−	0.595567i	$-0.203073\pi$
$167$	17.8756	+	2.83121i	1.38325	+	0.219086i	0.579949	+	0.814653i	$0.303073\pi$
$168$	8.62095	−	4.73072i	0.665121	−	0.364983i
$169$	16.2697	+	22.3934i	1.25152	+	1.72257i
$170$	1.04171	−	1.04996i	0.0798956	−	0.0805279i
$171$	−0.896954	−	0.0942736i	−0.0685918	−	0.00720929i
$172$	3.69396	+	4.56166i	0.281662	+	0.347823i
$173$	−20.1527	−	1.05616i	−1.53218	−	0.0802980i	−0.732516	−	0.680749i	$-0.761654\pi$
$173$	−20.1527	−	1.05616i	−1.53218	−	0.0802980i	−0.799661	+	0.600451i	$0.794988\pi$
$174$	−6.28498			−0.476463
$175$	−10.5937	−	7.92299i	−0.800807	−	0.598922i
$176$	0.121856			0.00918528
$177$	0.754743	+	0.0395544i	0.0567300	+	0.00297309i
$178$	−1.73360	−	2.14082i	−0.129939	−	0.160461i
$179$	11.8213	+	1.24247i	0.883569	+	0.0928669i	0.535434	−	0.844577i	$-0.320148\pi$
$179$	11.8213	+	1.24247i	0.883569	+	0.0928669i	0.348136	+	0.937444i	$0.386815\pi$
$180$	−3.45258	+	0.560792i	−0.257340	+	0.0417990i
$181$	−5.23308	−	7.20272i	−0.388972	−	0.535374i	0.568962	−	0.822364i	$-0.307345\pi$
$181$	−5.23308	−	7.20272i	−0.388972	−	0.535374i	−0.957934	+	0.286990i	$0.907345\pi$
$182$	7.49920	−	12.3611i	0.555878	−	0.916262i
$183$	−13.8664	−	2.19622i	−1.02503	−	0.162349i
$184$	−3.64639	+	17.1549i	−0.268815	+	1.26468i
$185$	18.6467	+	10.6679i	1.37093	+	0.784322i
$186$	5.29053	−	1.12454i	0.387921	−	0.0824551i
$187$	0.381170	+	0.586951i	0.0278739	+	0.0429221i
$188$	−0.436484	−	0.222400i	−0.0318339	−	0.0162202i
$189$	−6.46822	−	13.4066i	−0.470494	−	0.975189i
$190$	−1.20821	+	0.703925i	−0.0876529	+	0.0510681i
$191$	8.24039	+	1.75155i	0.596254	+	0.126738i	0.496146	−	0.868239i	$-0.334748\pi$
$191$	8.24039	+	1.75155i	0.596254	+	0.126738i	0.100108	+	0.994977i	$0.468081\pi$
$192$	−2.20141	−	5.73488i	−0.158873	−	0.413879i
$193$	−2.60344	+	9.71616i	−0.187400	+	0.699385i	0.806705	+	0.590955i	$0.201249\pi$
$193$	−2.60344	+	9.71616i	−0.187400	+	0.699385i	−0.994104	+	0.108430i	$0.965418\pi$
$194$	−0.902589	−	8.58756i	−0.0648021	−	0.616551i
$195$	14.6749	−	11.9795i	1.05089	−	0.857872i
$196$	8.76440	+	1.30808i	0.626029	+	0.0934343i
$197$	−11.2416	+	1.78050i	−0.800934	+	0.126855i	−0.543466	−	0.839431i	$-0.682888\pi$
$197$	−11.2416	+	1.78050i	−0.800934	+	0.126855i	−0.257468	+	0.966287i	$0.582888\pi$
$198$	−0.0502296	+	0.958438i	−0.00356966	+	0.0681132i
$199$	−4.87544	−	8.44451i	−0.345611	−	0.598616i	0.639854	−	0.768497i	$-0.278995\pi$
$199$	−4.87544	−	8.44451i	−0.345611	−	0.598616i	−0.985465	+	0.169881i	$0.945662\pi$
$200$	−9.81479	+	9.97075i	−0.694010	+	0.705038i
$201$	2.82362	+	1.63022i	0.199163	+	0.114987i
$202$	−8.25792	+	4.20762i	−0.581026	+	0.296047i
$203$	−11.6316	−	8.84310i	−0.816381	−	0.620664i
$204$	−0.763030	+	1.05022i	−0.0534228	+	0.0735302i
$205$	8.59006	+	8.52262i	0.599956	+	0.595246i
$206$	−3.75819	+	8.44104i	−0.261846	+	0.588115i
$207$	7.48095	+	2.00451i	0.519962	+	0.139323i
$208$	0.666279	+	0.539542i	0.0461981	+	0.0374105i
$209$	−0.204464	−	0.629276i	−0.0141431	−	0.0435279i
$210$	−5.94365	−	3.16276i	−0.410151	−	0.218251i
$211$	2.01612	−	6.20498i	0.138795	−	0.427168i	−0.857366	−	0.514708i	$-0.827900\pi$
$211$	2.01612	−	6.20498i	0.138795	−	0.427168i	0.996161	+	0.0875395i	$0.0279004\pi$
$212$	8.41071	−	5.46198i	0.577650	−	0.375130i
$213$	0.774424	+	14.7769i	0.0530626	+	1.01250i
$214$	2.13613	+	10.0497i	0.146023	+	0.686984i
$215$	3.16501	−	9.87314i	0.215852	−	0.673343i
$216$	−14.9725	+	4.86486i	−1.01875	+	0.331012i
$217$	11.3735	+	5.36270i	0.772080	+	0.364043i
$218$	−3.39226	−	3.39226i	−0.229753	−	0.229753i
$219$	−16.1211	+	1.69440i	−1.08937	+	0.114497i
$220$	−1.40608	−	2.14661i	−0.0947980	−	0.144724i
$221$	−0.514695	+	4.89699i	−0.0346221	+	0.329407i
$222$	10.2074	+	3.91824i	0.685074	+	0.262975i
$223$	3.82509	+	7.50716i	0.256147	+	0.502716i	0.982890	−	0.184193i	$-0.0589671\pi$
$223$	3.82509	+	7.50716i	0.256147	+	0.502716i	−0.726743	+	0.686909i	$0.758967\pi$
$224$	4.22715	−	14.5080i	0.282438	−	0.969358i
$225$	4.17021	+	4.55871i	0.278014	+	0.303914i
$226$	1.90309	−	3.29624i	0.126591	−	0.219263i
$227$	5.68174	+	3.68977i	0.377110	+	0.244898i	0.719251	−	0.694750i	$-0.244485\pi$
$227$	5.68174	+	3.68977i	0.377110	+	0.244898i	−0.342140	+	0.939649i	$0.611152\pi$
$228$	0.953784	−	0.772359i	0.0631659	−	0.0511508i
$229$	10.7641	−	4.79249i	0.711312	−	0.316696i	−0.0189914	−	0.999820i	$-0.506046\pi$
$229$	10.7641	−	4.79249i	0.711312	−	0.316696i	0.730303	+	0.683123i	$0.239379\pi$
$230$	11.1932	−	4.34735i	0.738056	−	0.286656i
$231$	2.05820	−	2.43173i	0.135420	−	0.159996i
$232$	−10.9271	+	10.9271i	−0.717402	+	0.717402i
$233$	−0.640457	+	0.790898i	−0.0419577	+	0.0518134i	−0.797693	−	0.603064i	$-0.793946\pi$
$233$	−0.640457	+	0.790898i	−0.0419577	+	0.0518134i	0.755735	+	0.654877i	$0.227280\pi$
$234$	−4.51830	+	5.01808i	−0.295371	+	0.328042i
$235$	0.0938389	+	0.860192i	0.00612137	+	0.0561128i
$236$	0.535288	−	0.481976i	0.0348443	−	0.0313739i
$237$	1.08166	−	2.12288i	0.0702615	−	0.137896i
$238$	1.67573	−	0.504517i	0.108621	−	0.0327030i
$239$	21.0947	+	6.85408i	1.36450	+	0.443353i	0.897543	−	0.440926i	$-0.145350\pi$
$239$	21.0947	+	6.85408i	1.36450	+	0.443353i	0.466958	+	0.884279i	$0.345350\pi$
$240$	0.233395	−	0.323917i	0.0150656	−	0.0209088i
$241$	−2.01169	−	1.81133i	−0.129584	−	0.116678i	0.601790	−	0.798654i	$-0.294454\pi$
$241$	−2.01169	−	1.81133i	−0.129584	−	0.116678i	−0.731375	+	0.681976i	$0.761121\pi$
$242$	8.14128	−	3.12514i	0.523341	−	0.200892i
$243$	3.07376	+	11.4714i	0.197182	+	0.735892i
$244$	−10.8248	+	7.86467i	−0.692986	+	0.503484i
$245$	−6.54987	−	14.2162i	−0.418456	−	0.908237i
$246$	4.98239	+	3.61992i	0.317666	+	0.230798i
$247$	1.66828	−	4.34602i	0.106150	−	0.276530i
$248$	7.24304	−	11.1533i	0.459934	−	0.708236i
$249$	5.92067	−	3.41830i	0.375207	−	0.216626i
$250$	9.39267	+	1.88069i	0.594045	+	0.118945i
$251$		−	4.30574i		−	0.271776i	−0.990724	−	0.135888i	$-0.956611\pi$
$251$		−	4.30574i		−	0.271776i	0.990724	−	0.135888i	$-0.0433887\pi$
$252$	−3.90742	−	1.36410i	−0.246145	−	0.0859303i
$253$	0.888841	+	5.61192i	0.0558810	+	0.352819i
$254$	−0.154068	−	0.346042i	−0.00966708	−	0.0217126i
$255$	2.29029	+	0.110980i	0.143424	+	0.00694982i
$256$	−14.2893	−	6.36201i	−0.893082	−	0.397626i
$257$	3.51076	−	0.940706i	0.218995	−	0.0586796i	−0.147653	−	0.989039i	$-0.547172\pi$
$257$	3.51076	−	0.940706i	0.218995	−	0.0586796i	0.366648	+	0.930360i	$0.380505\pi$
$258$	0.825473	−	5.21183i	0.0513917	−	0.324475i
$259$	13.3778	+	21.6135i	0.831255	+	1.34300i
$260$	1.81642	−	17.9628i	0.112649	−	1.11400i
$261$	4.56627	+	5.07136i	0.282645	+	0.313909i
$262$	12.6188	−	0.661325i	0.779595	−	0.0408568i
$263$	−13.4157	+	0.703085i	−0.827245	+	0.0433541i	−0.461258	−	0.887266i	$-0.652602\pi$
$263$	−13.4157	+	0.703085i	−0.827245	+	0.0433541i	−0.365987	+	0.930620i	$0.619268\pi$
$264$	−2.25455	−	2.50393i	−0.138758	−	0.154107i
$265$	−16.2109	−	7.14112i	−0.995826	−	0.438676i
$266$	−1.65373	+	0.0506895i	−0.101397	+	0.00310797i
$267$	0.668080	−	4.21809i	0.0408858	−	0.258143i
$268$	3.00151	−	0.804251i	0.183346	−	0.0491275i
$269$	−12.3288	−	5.48915i	−0.751702	−	0.334679i	−0.00513234	−	0.999987i	$-0.501634\pi$
$269$	−12.3288	−	5.48915i	−0.751702	−	0.334679i	−0.746569	+	0.665308i	$0.768300\pi$
$270$	8.40330	+	6.75020i	0.511409	+	0.410804i
$271$	1.00900	+	2.26624i	0.0612921	+	0.137664i	0.941595	−	0.336748i	$-0.109327\pi$
$271$	1.00900	+	2.26624i	0.0612921	+	0.137664i	−0.880303	+	0.474413i	$0.842660\pi$
$272$	0.0162339	+	0.102497i	0.000984324	+	0.00621478i
$273$	22.0206	−	4.18300i	1.33275	−	0.253166i
$274$			13.1925i			0.796991i
$275$	−1.81091	+	4.15521i	−0.109202	+	0.250568i
$276$	−9.12715	+	5.26956i	−0.549390	+	0.317190i
$277$	0.478369	−	0.736623i	0.0287424	−	0.0442594i	−0.824007	−	0.566579i	$-0.808267\pi$
$277$	0.478369	−	0.736623i	0.0287424	−	0.0442594i	0.852750	+	0.522320i	$0.174933\pi$
$278$	−6.27164	+	16.3382i	−0.376148	+	0.979899i
$279$	−4.75115	−	3.45191i	−0.284444	−	0.206661i
$280$	−15.8325	+	4.83488i	−0.946173	+	0.288939i
$281$	17.9578	−	13.0471i	1.07127	−	0.778325i	0.0951314	−	0.995465i	$-0.469673\pi$
$281$	17.9578	−	13.0471i	1.07127	−	0.778325i	0.976140	+	0.217140i	$0.0696729\pi$
$282$	0.113982	+	0.425385i	0.00678750	+	0.0253313i
$283$	−19.7278	+	7.57280i	−1.17270	+	0.450156i	−0.865216	−	0.501399i	$-0.832819\pi$
$283$	−19.7278	+	7.57280i	−1.17270	+	0.450156i	−0.307480	+	0.951555i	$0.599486\pi$
$284$	10.4802	+	9.43645i	0.621888	+	0.559950i
$285$	−2.06435	−	0.661764i	−0.122281	−	0.0391995i
$286$	−4.71140	−	1.53083i	−0.278591	−	0.0905196i
$287$	4.12763	+	13.7097i	0.243647	+	0.809260i
$288$	−3.20409	+	6.28839i	−0.188803	+	0.370547i
$289$	12.1905	−	10.9764i	0.717091	−	0.645671i
$290$	10.3577	+	2.15898i	0.608227	+	0.126779i
$291$	8.95747	−	9.94828i	0.525096	−	0.583178i
$292$	−9.72238	+	12.0061i	−0.568959	+	0.702606i
$293$	1.08056	−	1.08056i	0.0631269	−	0.0631269i	−0.674839	−	0.737965i	$-0.735787\pi$
$293$	1.08056	−	1.08056i	0.0631269	−	0.0631269i	0.737965	+	0.674839i	$0.235787\pi$
$294$	−4.39821	−	6.64212i	−0.256509	−	0.387376i
$295$	−1.23024	−	0.324451i	−0.0716273	−	0.0188902i
$296$	24.5589	−	10.9343i	1.42746	−	0.635546i
$297$	−3.96368	+	3.20973i	−0.229996	+	0.186247i
$298$	13.0904	+	8.50103i	0.758309	+	0.492451i
$299$	−19.9879	+	34.6200i	−1.15593	+	2.00213i
$300$	−8.39919	−	0.373822i	−0.484928	−	0.0215826i
$301$	8.86086	−	8.48410i	0.510731	−	0.489015i
$302$	−5.24528	−	10.2944i	−0.301832	−	0.592379i
$303$	−13.4141	−	5.14918i	−0.770618	−	0.295813i
$304$	0.0102553	−	0.0975729i	0.000588183	−	0.00559619i
$305$	22.0975	+	8.38267i	1.26530	+	0.479990i
$306$	−0.812860	+	0.0854350i	−0.0464681	+	0.00488399i
$307$	−15.2615	−	15.2615i	−0.871020	−	0.871020i	0.121564	−	0.992584i	$-0.461209\pi$
$307$	−15.2615	−	15.2615i	−0.871020	−	0.871020i	−0.992584	+	0.121564i	$0.961209\pi$
$308$	−0.251727	−	3.02583i	−0.0143435	−	0.172412i
$309$	−13.6236	+	4.42657i	−0.775018	+	0.251819i
$310$	−9.10516	+	0.0358849i	−0.517138	+	0.00203813i
$311$	4.56568	+	21.4798i	0.258896	+	1.21801i	0.894880	+	0.446307i	$0.147261\pi$
$311$	4.56568	+	21.4798i	0.258896	+	1.21801i	−0.635984	+	0.771702i	$0.719406\pi$
$312$	−1.24066	−	23.6733i	−0.0702388	−	1.34024i
$313$	13.4487	−	8.73367i	0.760164	−	0.493656i	−0.105415	−	0.994428i	$-0.533617\pi$
$313$	13.4487	−	8.73367i	0.760164	−	0.493656i	0.865579	+	0.500772i	$0.166951\pi$
$314$	2.69080	−	8.28142i	0.151850	−	0.467347i
$315$	1.76624	+	7.09379i	0.0995166	+	0.399690i
$316$	−0.701692	−	2.15959i	−0.0394733	−	0.121486i
$317$	4.28053	+	3.46631i	0.240419	+	0.194687i	0.741956	−	0.670449i	$-0.233899\pi$
$317$	4.28053	+	3.46631i	0.240419	+	0.194687i	−0.501537	+	0.865136i	$0.667232\pi$
$318$	−8.70835	−	2.33339i	−0.488340	−	0.130850i
$319$	−2.03631	+	4.57362i	−0.114011	+	0.256073i
$320$	1.65795	+	10.2074i	0.0926823	+	0.570609i
$321$	−9.36239	+	12.8862i	−0.522558	+	0.719239i
$322$	14.0944	+	1.79162i	0.785449	+	0.0998429i
$323$	0.502062	−	0.255813i	0.0279355	−	0.0142338i
$324$	−4.12883	−	2.38378i	−0.229379	−	0.132432i
$325$	−28.2995	+	14.7014i	−1.56977	+	0.815488i
$326$	10.3736	+	17.9675i	0.574538	+	0.995129i
$327$	0.389246	−	7.42725i	0.0215253	−	0.410728i
$328$	14.9561	−	2.36881i	0.825811	−	0.130796i
$329$	−0.387579	+	0.947636i	−0.0213679	+	0.0522449i
$330$	−0.588282	+	2.23063i	−0.0323839	+	0.122792i
$331$	0.357666	+	3.40297i	0.0196591	+	0.187044i	0.999944	−	0.0105432i	$-0.00335608\pi$
$331$	0.357666	+	3.40297i	0.0196591	+	0.187044i	−0.980285	+	0.197587i	$0.936689\pi$
$332$	1.68638	−	6.29366i	0.0925522	−	0.345409i
$333$	−4.25439	−	11.0831i	−0.233139	−	0.607349i
$334$	−15.1675	−	3.22396i	−0.829930	−	0.176407i
$335$	−4.09337	−	3.65658i	−0.223645	−	0.199780i
$336$	0.425462	−	0.205270i	0.0232109	−	0.0111984i
$337$	−21.3068	−	10.8563i	−1.16065	−	0.591382i	−0.235835	−	0.971793i	$-0.575783\pi$
$337$	−21.3068	−	10.8563i	−1.16065	−	0.591382i	−0.924818	+	0.380411i	$0.875783\pi$
$338$	−12.9164	−	19.8895i	−0.702558	−	1.08184i
$339$	5.77181	−	1.22684i	0.313482	−	0.0666326i
$340$	1.61825	−	1.46867i	0.0877619	−	0.0796497i
$341$	0.895776	−	4.21429i	0.0485090	−	0.228217i
$342$	0.763213	+	0.120881i	0.0412698	+	0.00653650i
$343$	1.20581	−	18.4810i	0.0651077	−	0.997878i
$344$	−7.62617	−	10.4965i	−0.411176	−	0.565935i
$345$	16.6200	+	8.38595i	0.894789	+	0.451485i
$346$	17.1954	+	1.80731i	0.924430	+	0.0971615i
$347$	−2.84915	−	3.51841i	−0.152951	−	0.188878i	0.694911	−	0.719096i	$-0.255444\pi$
$347$	−2.84915	−	3.51841i	−0.152951	−	0.188878i	−0.847862	+	0.530217i	$0.822110\pi$
$348$	−9.27357	−	0.486007i	−0.497116	−	0.0260527i
$349$	18.8644			1.00979			0.504893	−	0.863182i	$-0.331532\pi$
$349$	18.8644			1.00979			0.504893	+	0.863182i	$0.331532\pi$
$350$	8.70876	+	7.25399i	0.465503	+	0.387742i
$351$	−35.8840			−1.91535
$352$	−5.17061	−	0.270980i	−0.275594	−	0.0144433i
$353$	4.99718	+	6.17101i	0.265973	+	0.328450i	0.892583	−	0.450884i	$-0.148891\pi$
$353$	4.99718	+	6.17101i	0.265973	+	0.328450i	−0.626609	+	0.779334i	$0.715558\pi$
$354$	−0.643990	−	0.0676861i	−0.0342277	−	0.00359748i
$355$	3.79979	−	24.6185i	0.201672	−	1.30662i
$356$	−2.39240	−	3.29286i	−0.126797	−	0.174521i
$357$	2.31959	+	1.40725i	0.122766	+	0.0744795i
$358$	−10.0587	−	1.59314i	−0.531620	−	0.0842003i
$359$	0.309094	−	1.45418i	0.0163134	−	0.0767484i	−0.969238	−	0.246126i	$-0.920842\pi$
$359$	0.309094	−	1.45418i	0.0163134	−	0.0767484i	0.985551	+	0.169377i	$0.0541757\pi$
$360$	7.68595	−	0.838465i	0.405085	−	0.0441910i
$361$	18.0637	−	3.83956i	0.950722	−	0.202082i
$362$	4.15449	+	6.39735i	0.218355	+	0.336237i
$363$	12.0459	+	6.13771i	0.632248	+	0.322146i
$364$	12.0210	−	17.6590i	0.630073	−	0.925582i
$365$	27.1499	+	2.74543i	1.42109	+	0.143702i
$366$	11.7657	+	2.50087i	0.615002	+	0.130723i
$367$	4.83586	+	12.5978i	0.252430	+	0.657602i	0.999978	−	0.00660537i	$-0.00210257\pi$
$367$	4.83586	+	12.5978i	0.252430	+	0.657602i	−0.747548	+	0.664207i	$0.768769\pi$
$368$	−0.218056	+	0.813796i	−0.0113670	+	0.0424220i
$369$	−0.698975	−	6.65030i	−0.0363872	−	0.346201i
$370$	−15.4759	−	9.96368i	−0.804555	−	0.517987i
$371$	−12.8334	−	16.5712i	−0.666279	−	0.860336i
$372$	7.89320	−	1.25016i	0.409243	−	0.0648178i
$373$	0.189836	−	3.62228i	0.00982931	−	0.187555i	−0.989302	−	0.145882i	$-0.953398\pi$
$373$	0.189836	−	3.62228i	0.00982931	−	0.187555i	0.999131	−	0.0416726i	$-0.0132686\pi$
$374$	−0.299813	−	0.519291i	−0.0155030	−	0.0268519i
$375$	7.57684	+	12.7723i	0.391266	+	0.659559i
$376$	0.937749	+	0.541409i	0.0483607	+	0.0279211i
$377$	−31.3845	+	15.9912i	−1.61638	+	0.823589i
$378$	4.93310	+	11.7608i	0.253731	+	0.604912i
$379$	−3.94040	+	5.42349i	−0.202405	+	0.278586i	−0.898138	−	0.439714i	$-0.855080\pi$
$379$	−3.94040	+	5.42349i	−0.202405	+	0.278586i	0.695733	+	0.718300i	$0.255080\pi$
$380$	−1.83717	+	0.945221i	−0.0942446	+	0.0484888i
$381$	0.238853	−	0.536473i	0.0122368	−	0.0274844i
$382$	−6.97200	−	1.86814i	−0.356718	−	0.0955824i
$383$	22.0555	+	17.8602i	1.12699	+	0.912615i	0.996884	−	0.0788862i	$-0.0251364\pi$
$383$	22.0555	+	17.8602i	1.12699	+	0.912615i	0.130101	+	0.991501i	$0.458470\pi$
$384$	−3.06233	−	9.42488i	−0.156274	−	0.480962i
$385$	−4.22727	+	3.30051i	−0.215442	+	0.168209i
$386$	2.66320	−	8.19648i	0.135553	−	0.417190i
$387$	−4.80517	+	3.12051i	−0.244260	+	0.158624i
$388$	−0.667719	−	12.7408i	−0.0338983	−	0.646818i
$389$	−4.89619	−	23.0348i	−0.248247	−	1.16791i	−0.908834	−	0.417159i	$-0.863026\pi$
$389$	−4.89619	−	23.0348i	−0.248247	−	1.16791i	0.660587	−	0.750749i	$-0.270307\pi$
$390$	−13.0931	+	9.59175i	−0.662994	+	0.485697i
$391$	−4.60193	+	1.49526i	−0.232729	+	0.0756184i
$392$	−19.1948	−	3.90129i	−0.969486	−	0.197045i
$393$	13.8522	+	13.8522i	0.698751	+	0.698751i
$394$	9.69827	−	1.01933i	0.488592	−	0.0513531i
$395$	−2.51183	+	3.12697i	−0.126384	+	0.157335i
$396$	−0.148229	+	1.41030i	−0.00744877	+	0.0708704i
$397$	−31.4512	−	12.0730i	−1.57849	−	0.605926i	−0.597828	−	0.801625i	$-0.703969\pi$
$397$	−31.4512	−	12.0730i	−1.57849	−	0.605926i	−0.980664	+	0.195699i	$0.937303\pi$
$398$	3.79281	+	7.44380i	0.190116	+	0.373124i
$399$	−1.77392	−	1.85269i	−0.0888070	−	0.0927507i
$400$	−0.495908	+	0.453646i	−0.0247954	+	0.0226823i
$401$	−7.68794	+	13.3159i	−0.383918	+	0.664965i	−0.991618	−	0.129201i	$-0.958759\pi$
$401$	−7.68794	+	13.3159i	−0.383918	+	0.664965i	0.607701	+	0.794166i	$0.292092\pi$
$402$	−2.34281	−	1.52144i	−0.116849	−	0.0758826i
$403$	23.5574	−	19.0764i	1.17348	−	0.950264i
$404$	−12.5100	+	5.56983i	−0.622397	+	0.277109i
$405$	0.473871	+	8.40784i	0.0235468	+	0.417789i
$406$	9.55559	+	8.08778i	0.474236	+	0.401390i
$407$	6.15847	−	6.15847i	0.305264	−	0.305264i
$408$	1.80577	−	2.22994i	0.0893990	−	0.110399i
$409$	11.4506	−	12.7172i	0.566196	−	0.628825i	−0.390258	−	0.920705i	$-0.627614\pi$
$409$	11.4506	−	12.7172i	0.566196	−	0.628825i	0.956455	+	0.291881i	$0.0942810\pi$
$410$	−6.96756	−	7.67720i	−0.344103	−	0.379150i
$411$	−15.1992	+	13.6854i	−0.749722	+	0.675053i
$412$	−6.19799	+	12.1642i	−0.305353	+	0.599289i
$413$	−1.09660	−	1.03137i	−0.0539601	−	0.0507506i
$414$	−6.31087	−	2.05052i	−0.310162	−	0.100778i
$415$	−10.9316	+	3.59957i	−0.536610	+	0.176696i
$416$	−27.0717	−	24.3755i	−1.32730	−	1.19511i
$417$	−25.3293	+	9.72300i	−1.24038	+	0.476137i
$418$	0.146724	+	0.547581i	0.00717650	+	0.0267831i
$419$	23.2543	−	16.8952i	1.13604	−	0.825385i	0.149481	−	0.988765i	$-0.452240\pi$
$419$	23.2543	−	16.8952i	1.13604	−	0.825385i	0.986563	+	0.163380i	$0.0522396\pi$
$420$	−8.52535	−	5.12630i	−0.415995	−	0.250138i
$421$	−19.6494	−	14.2761i	−0.957652	−	0.695775i	−0.00504761	−	0.999987i	$-0.501607\pi$
$421$	−19.6494	−	14.2761i	−0.957652	−	0.695775i	−0.952604	+	0.304212i	$0.901607\pi$
$422$	−2.00324	+	5.21862i	−0.0975162	+	0.254038i
$423$	0.260432	−	0.401029i	0.0126626	−	0.0194987i
$424$	−19.1973	+	11.0836i	−0.932303	+	0.538265i
$425$	−3.73631	−	0.969641i	−0.181238	−	0.0470345i
$426$		−	12.6779i		−	0.614248i
$427$	18.2560	+	21.1829i	0.883470	+	1.02511i
$428$	2.37476	+	14.9937i	0.114788	+	0.724745i
$429$	−3.12375	−	7.01605i	−0.150816	−	0.338738i
$430$	−3.15072	+	8.30561i	−0.151941	+	0.400532i
$431$	−26.3288	−	11.7223i	−1.26821	−	0.564645i	−0.341312	−	0.939950i	$-0.610871\pi$
$431$	−26.3288	−	11.7223i	−1.26821	−	0.564645i	−0.926901	+	0.375305i	$0.877538\pi$
$432$	−0.730499	+	0.195737i	−0.0351462	+	0.00941739i
$433$	−2.05185	+	12.9548i	−0.0986054	+	0.622570i	0.888050	+	0.459747i	$0.152060\pi$
$433$	−2.05185	+	12.9548i	−0.0986054	+	0.622570i	−0.986655	+	0.162823i	$0.947940\pi$
$434$	−9.49074	−	5.09835i	−0.455570	−	0.244729i
$435$	8.25735	+	14.1728i	0.395909	+	0.679536i
$436$	−4.74301	−	5.26764i	−0.227149	−	0.252274i
$437$	4.56838	−	0.239419i	0.218535	−	0.0114529i
$438$	13.8693	−	0.726861i	0.662703	−	0.0347308i
$439$	−3.33749	−	3.70665i	−0.159290	−	0.176909i	0.658217	−	0.752828i	$-0.271311\pi$
$439$	−3.33749	−	3.70665i	−0.159290	−	0.176909i	−0.817507	+	0.575919i	$0.804644\pi$
$440$	2.85540	+	4.90099i	0.136126	+	0.233645i
$441$	−2.16407	+	8.37466i	−0.103051	+	0.398793i
$442$	0.659960	−	4.16682i	0.0313911	−	0.198195i
$443$	29.9044	−	8.01286i	1.42080	−	0.380703i	0.535033	−	0.844831i	$-0.320299\pi$
$443$	29.9044	−	8.01286i	1.42080	−	0.380703i	0.885768	+	0.464128i	$0.153632\pi$
$444$	14.7581	+	6.57073i	0.700389	+	0.311833i
$445$	−2.54997	+	6.72198i	−0.120880	+	0.318652i
$446$	−2.93615	−	6.59469i	−0.139031	−	0.312268i
$447$	3.78542	+	23.9002i	0.179044	+	1.13044i
$448$	−4.03289	+	11.5521i	−0.190536	+	0.545785i
$449$		−	39.6283i		−	1.87017i	−0.354418	−	0.935087i	$-0.615321\pi$
$449$		−	39.6283i		−	1.87017i	0.354418	−	0.935087i	$-0.384679\pi$
$450$	−3.36365	−	4.08746i	−0.158564	−	0.192685i
$451$	4.24851	−	2.45288i	0.200054	−	0.115501i
$452$	3.06292	−	4.71648i	0.144068	−	0.221845i
$453$	6.41904	−	16.7222i	0.301593	−	0.785677i
$454$	−4.69589	−	3.41176i	−0.220389	−	0.160122i
$455$	−37.7272	−	0.670738i	−1.76868	−	0.0314447i
$456$	−2.19469	+	1.59454i	−0.102776	+	0.0746710i
$457$	−2.43482	−	9.08688i	−0.113896	−	0.425066i	0.885306	−	0.465009i	$-0.153949\pi$
$457$	−2.43482	−	9.08688i	−0.113896	−	0.425066i	−0.999202	+	0.0399431i	$0.987282\pi$
$458$	−9.42474	+	3.61782i	−0.440389	+	0.169050i
$459$	−3.22783	−	2.90636i	−0.150662	−	0.135657i
$460$	16.8518	−	5.54901i	0.785721	−	0.258724i
$461$	5.99574	+	1.94813i	0.279249	+	0.0907336i	0.445293	−	0.895385i	$-0.353099\pi$
$461$	5.99574	+	1.94813i	0.279249	+	0.0907336i	−0.166044	+	0.986118i	$0.553099\pi$
$462$	−1.87005	+	1.98831i	−0.0870026	+	0.0925048i
$463$	−2.76092	+	5.41860i	−0.128311	+	0.251824i	−0.946220	−	0.323523i	$-0.895133\pi$
$463$	−2.76092	+	5.41860i	−0.128311	+	0.251824i	0.817910	+	0.575347i	$0.195133\pi$
$464$	−0.551675	+	0.496730i	−0.0256109	+	0.0230601i
$465$	−9.48668	−	10.4529i	−0.439934	−	0.484741i
$466$	0.583443	−	0.647980i	0.0270275	−	0.0300171i
$467$	2.38010	−	2.93918i	0.110138	−	0.136009i	−0.719096	−	0.694911i	$-0.755444\pi$
$467$	2.38010	−	2.93918i	0.110138	−	0.136009i	0.829234	+	0.558902i	$0.188777\pi$
$468$	−7.05485	+	7.05485i	−0.326110	+	0.326110i
$469$	−2.19516	−	6.11212i	−0.101363	−	0.282231i
$470$	−0.0417178	−	0.740194i	−0.00192430	−	0.0341426i
$471$	12.3324	−	5.49074i	0.568247	−	0.253000i
$472$	−1.23733	+	1.00197i	−0.0569526	+	0.0461193i
$473$	−3.52523	−	2.28931i	−0.162090	−	0.105263i
$474$	−1.02067	+	1.76785i	−0.0468809	+	0.0812001i
$475$	3.17475	+	1.79973i	0.145668	+	0.0825772i
$476$	2.51157	−	0.614840i	0.115118	−	0.0281811i
$477$	4.44411	+	8.72206i	0.203482	+	0.399356i
$478$	−17.7414	−	6.81029i	−0.811474	−	0.311496i
$479$	−1.00057	+	9.51983i	−0.0457174	+	0.434972i	0.947591	+	0.319485i	$0.103510\pi$
$479$	−1.00057	+	9.51983i	−0.0457174	+	0.434972i	−0.993309	+	0.115488i	$0.963157\pi$
$480$	−10.6237	+	13.2254i	−0.484904	+	0.603656i
$481$	60.9406	−	6.40512i	2.77865	−	0.292048i
$482$	1.63999	+	1.63999i	0.0746996	+	0.0746996i
$483$	12.5568	+	18.0968i	0.571355	+	0.823431i
$484$	12.2542	−	3.98163i	0.557010	−	0.180983i
$485$	−18.1794	+	13.3179i	−0.825484	+	0.604734i
$486$	−2.11555	−	9.95286i	−0.0959631	−	0.451471i
$487$	1.34763	+	25.7143i	0.0610670	+	1.16523i	0.841596	+	0.540108i	$0.181617\pi$
$487$	1.34763	+	25.7143i	0.0610670	+	1.16523i	−0.780529	+	0.625120i	$0.785050\pi$
$488$	24.8040	−	16.1079i	1.12282	−	0.729170i
$489$	−9.93937	+	30.5902i	−0.449474	+	1.38334i
$490$	4.96665	+	12.4571i	0.224370	+	0.562757i
$491$	−1.00352	−	3.08853i	−0.0452884	−	0.139383i	0.925855	−	0.377878i	$-0.123346\pi$
$491$	−1.00352	−	3.08853i	−0.0452884	−	0.139383i	−0.971144	+	0.238495i	$0.923346\pi$
$492$	7.07166	+	5.72652i	0.318815	+	0.258171i
$493$	−4.11827	−	1.10349i	−0.185478	−	0.0496986i
$494$	−1.62227	+	3.64367i	−0.0729893	+	0.163937i
$495$	2.22730	−	1.14595i	0.100110	−	0.0515065i
$496$	0.375508	−	0.516842i	0.0168608	−	0.0232069i
$497$	17.8381	−	23.4631i	0.800148	−	1.05246i
$498$	−5.21904	+	2.65924i	−0.233871	+	0.119163i
$499$	27.0149	+	15.5971i	1.20935	+	0.698221i	0.962618	−	0.270862i	$-0.0873088\pi$
$499$	27.0149	+	15.5971i	1.20935	+	0.698221i	0.246736	+	0.969083i	$0.420642\pi$
$500$	13.7136	+	3.50130i	0.613289	+	0.156583i
$501$	−12.0199	−	20.8190i	−0.537008	−	0.930124i
$502$	−0.193071	+	3.68402i	−0.00861719	+	0.164426i
$503$	25.3208	−	4.01041i	1.12900	−	0.178815i	0.436132	−	0.899883i	$-0.356348\pi$
$503$	25.3208	−	4.01041i	1.12900	−	0.178815i	0.692865	+	0.721067i	$0.256348\pi$
$504$	8.46727	+	3.46308i	0.377162	+	0.154258i
$505$	20.3378	+	13.0938i	0.905019	+	0.582668i
$506$	−0.508858	−	4.84146i	−0.0226215	−	0.215229i
$507$	9.51584	−	35.5136i	0.422613	−	1.57721i
$508$	−0.200570	−	0.522503i	−0.00889886	−	0.0231823i
$509$	−11.9108	−	2.53172i	−0.527938	−	0.112217i	−0.0637710	−	0.997965i	$-0.520313\pi$
$509$	−11.9108	−	2.53172i	−0.527938	−	0.112217i	−0.464166	+	0.885748i	$0.653646\pi$
$510$	−1.95461	−	0.197653i	−0.0865517	−	0.00875221i
$511$	26.6907	+	18.1692i	1.18073	+	0.803759i
$512$	−1.35434	−	0.690070i	−0.0598539	−	0.0304971i
$513$	2.23651	+	3.44393i	0.0987444	+	0.152053i
$514$	−3.04602	+	0.647451i	−0.134354	+	0.0285578i
$515$	23.9724	−	2.61517i	1.05635	−	0.115238i
$516$	1.62102	−	7.62629i	0.0713613	−	0.335729i
$517$	0.346484	+	0.0548778i	0.0152384	+	0.00241352i
$518$	−10.4770	−	19.0925i	−0.460331	−	0.838877i
$519$	15.7556	+	21.6857i	0.691595	+	0.951899i
$520$	−6.08746	+	39.4401i	−0.266953	+	1.72956i
$521$	9.04578	+	0.950750i	0.396303	+	0.0416531i	0.300584	−	0.953755i	$-0.402818\pi$
$521$	9.04578	+	0.950750i	0.396303	+	0.0416531i	0.0957188	+	0.995408i	$0.469485\pi$
$522$	−3.67953	−	4.54384i	−0.161049	−	0.198879i
$523$	−19.7469	−	1.03489i	−0.863470	−	0.0452525i	−0.384543	−	0.923107i	$-0.625641\pi$
$523$	−19.7469	−	1.03489i	−0.863470	−	0.0452525i	−0.478927	+	0.877855i	$0.658974\pi$
$524$	18.6704			0.815620
$525$	0.676760	+	17.5584i	0.0295362	+	0.766313i
$526$	11.5101			0.501863
$527$	3.66409	+	0.192027i	0.159610	+	0.00836482i
$528$	−0.101861	−	0.125788i	−0.00443295	−	0.00547423i
$529$	−16.1947	−	1.70213i	−0.704118	−	0.0740058i
$530$	13.5499	+	6.83690i	0.588571	+	0.296976i
$531$	0.413266	+	0.568812i	0.0179342	+	0.0246843i
$532$	−2.44402	−	0.0530874i	−0.105962	−	0.00230163i
$533$	34.0903	+	5.39937i	1.47661	+	0.233873i
$534$	−0.760755	+	3.57907i	−0.0329211	+	0.154882i
$535$	19.8559	−	18.0206i	0.858447	−	0.779097i
$536$	−6.71843	+	1.42805i	−0.290192	+	0.0616822i
$537$	−8.59905	−	13.2414i	−0.371076	−	0.571407i
$538$	10.3025	+	5.24938i	0.444172	+	0.226317i
$539$	−6.25851	+	1.04858i	−0.269573	+	0.0451657i
$540$	11.8772	+	10.6098i	0.511113	+	0.456573i
$541$	17.4783	+	3.71513i	0.751451	+	0.159726i	0.567687	−	0.823245i	$-0.307838\pi$
$541$	17.4783	+	3.71513i	0.751451	+	0.159726i	0.183764	+	0.982970i	$0.441172\pi$
$542$	−0.761685	−	1.98426i	−0.0327172	−	0.0852311i
$543$	−3.06072	+	11.4228i	−0.131348	+	0.490198i
$544$	−0.460907	−	4.38524i	−0.0197612	−	0.188016i
$545$	−3.19284	+	12.1065i	−0.136766	+	0.518585i
$546$	−19.0286	+	2.59159i	−0.814347	+	0.110910i
$547$	−2.11619	+	0.335171i	−0.0904816	+	0.0143309i	−0.201511	−	0.979486i	$-0.564585\pi$
$547$	−2.11619	+	0.335171i	−0.0904816	+	0.0143309i	0.111029	+	0.993817i	$0.464585\pi$
$548$	−1.02016	+	19.4658i	−0.0435790	+	0.831536i
$549$	−6.53023	−	11.3107i	−0.278704	−	0.482729i
$550$	1.73575	−	3.47402i	0.0740125	−	0.148133i
$551$	3.49081	+	2.01542i	0.148714	+	0.0858598i
$552$	20.7565	−	10.5760i	0.883454	−	0.450142i
$553$	−4.37636	+	1.83567i	−0.186102	+	0.0780605i
$554$	−0.442326	+	0.608809i	−0.0187926	+	0.0258658i
$555$	−4.57489	−	28.1658i	−0.194193	−	1.19557i
$556$	−10.5173	+	23.6222i	−0.446032	+	1.00180i
$557$	6.39810	+	1.71437i	0.271096	+	0.0726401i	0.391806	−	0.920048i	$-0.371850\pi$
$557$	6.39810	+	1.71437i	0.271096	+	0.0726401i	−0.120710	+	0.992688i	$0.538517\pi$
$558$	3.91033	+	3.16653i	0.165538	+	0.134050i
$559$	−9.13867	−	28.1259i	−0.386525	−	1.18960i
$560$	−0.771680	+	0.192136i	−0.0326094	+	0.00811924i
$561$	0.287264	−	0.884108i	0.0121283	−	0.0373271i
$562$	−15.9498	+	10.3580i	−0.672804	+	0.436924i
$563$	1.60935	+	30.7082i	0.0678260	+	1.29420i	0.794521	+	0.607236i	$0.207722\pi$
$563$	1.60935	+	30.7082i	0.0678260	+	1.29420i	−0.726695	+	0.686960i	$0.758945\pi$
$564$	0.135287	+	0.636475i	0.00569661	+	0.0268004i
$565$	−9.93345	+	0.0391493i	−0.417903	+	0.00164702i
$566$	17.2188	−	5.59473i	0.723761	−	0.235164i
$567$	−4.24947	+	9.01248i	−0.178461	+	0.378489i
$568$	−22.0420	−	22.0420i	−0.924862	−	0.924862i
$569$	−42.8748	+	4.50632i	−1.79740	+	0.188915i	−0.943468	−	0.331464i	$-0.892457\pi$
$569$	−42.8748	+	4.50632i	−1.79740	+	0.188915i	−0.853936	+	0.520379i	$0.825791\pi$
$570$	1.73660	+	0.658777i	0.0727381	+	0.0275931i
$571$	−1.09909	+	10.4571i	−0.0459954	+	0.437617i	0.947155	+	0.320776i	$0.103944\pi$
$571$	−1.09909	+	10.4571i	−0.0459954	+	0.437617i	−0.993151	+	0.116841i	$0.962723\pi$
$572$	−6.83335	−	2.62308i	−0.285717	−	0.109676i
$573$	−5.08018	−	9.97042i	−0.212228	−	0.416520i
$574$	−2.91688	−	11.9152i	−0.121748	−	0.497332i
$575$	−24.5092	−	19.5293i	−1.02211	−	0.814430i
$576$	2.85732	−	4.94902i	0.119055	−	0.206209i
$577$	8.83471	+	5.73733i	0.367794	+	0.238848i	0.715282	−	0.698836i	$-0.246298\pi$
$577$	8.83471	+	5.73733i	0.367794	+	0.238848i	−0.347488	+	0.937685i	$0.612965\pi$
$578$	−10.9225	+	8.84487i	−0.454316	+	0.367898i
$579$	12.2059	−	5.43442i	0.507260	−	0.225847i
$580$	15.1160	+	3.98654i	0.627658	+	0.165532i
$581$	−13.4005	−	2.42184i	−0.555946	−	0.100475i
$582$	−8.11016	+	8.11016i	−0.336177	+	0.336177i
$583$	−4.51949	+	5.58110i	−0.187178	+	0.231146i
$584$	22.8497	−	25.3771i	0.945525	−	1.05011i
$585$	17.2522	+	3.59606i	0.713290	+	0.148679i
$586$	−0.972987	+	0.876081i	−0.0401937	+	0.0361906i
$587$	−2.22640	+	4.36956i	−0.0918935	+	0.180351i	−0.932378	−	0.361484i	$-0.882270\pi$
$587$	−2.22640	+	4.36956i	−0.0918935	+	0.180351i	0.840485	+	0.541835i	$0.182270\pi$
$588$	−5.97599	−	10.1406i	−0.246446	−	0.418193i
$589$	−3.29908	−	1.07194i	−0.135936	−	0.0441683i
$590$	1.03805	+	0.332767i	0.0427360	+	0.0136998i
$591$	11.2350	+	10.1160i	0.462145	+	0.416117i
$592$	1.20564	−	0.462804i	0.0495517	−	0.0190211i
$593$	5.06061	+	18.8865i	0.207815	+	0.775574i	0.988573	+	0.150742i	$0.0481661\pi$
$593$	5.06061	+	18.8865i	0.207815	+	0.775574i	−0.780759	+	0.624833i	$0.785167\pi$
$594$	3.53528	−	2.56853i	0.145054	−	0.105388i
$595$	−3.33931	−	3.11597i	−0.136898	−	0.127743i
$596$	18.6577	+	13.5556i	0.764250	+	0.555260i
$597$	−4.64154	+	12.0916i	−0.189966	+	0.494877i
$598$	18.6541	−	28.7249i	0.762824	−	1.17465i
$599$	−24.3211	+	14.0418i	−0.993731	+	0.573731i	−0.906388	−	0.422447i	$-0.861171\pi$
$599$	−24.3211	+	14.0418i	−0.993731	+	0.573731i	−0.0873439	+	0.996178i	$0.527838\pi$
$600$	18.4968	+	1.79680i	0.755127	+	0.0733540i
$601$			11.7067i			0.477528i	0.971078	+	0.238764i	$0.0767422\pi$
$601$			11.7067i			0.477528i	−0.971078	+	0.238764i	$0.923258\pi$
$602$	−7.96184	+	6.86173i	−0.324501	+	0.279663i
$603$	0.474488	+	2.99580i	0.0193226	+	0.121998i
$604$	−6.94343	−	15.5952i	−0.282524	−	0.634559i
$605$	−17.7435	−	14.2530i	−0.721375	−	0.579466i
$606$	11.2463	+	5.00717i	0.456849	+	0.203402i
$607$	5.77014	−	1.54611i	0.234203	−	0.0627545i	−0.139809	−	0.990179i	$-0.544649\pi$
$607$	5.77014	−	1.54611i	0.234203	−	0.0627545i	0.374011	+	0.927424i	$0.377982\pi$
$608$	−0.652133	+	4.11740i	−0.0264475	+	0.166983i
$609$	0.594610	+	19.3990i	0.0240948	+	0.786087i
$610$	−18.5309	−	8.16313i	−0.750294	−	0.330516i
$611$	1.65150	+	1.83418i	0.0668127	+	0.0742030i
$612$	−1.20599	+	0.0632033i	−0.0487493	+	0.00255484i
$613$	−42.4744	+	2.22599i	−1.71552	+	0.0899068i	−0.884562	−	0.466423i	$-0.845542\pi$
$613$	−42.4744	+	2.22599i	−1.71552	+	0.0899068i	−0.830961	+	0.556330i	$0.812209\pi$
$614$	12.3735	+	13.7422i	0.499354	+	0.554589i
$615$	1.61707	−	15.9914i	0.0652065	−	0.644835i
$616$	0.205617	+	6.70820i	0.00828453	+	0.270281i
$617$	−2.93121	+	18.5069i	−0.118006	+	0.745061i	0.855737	+	0.517411i	$0.173104\pi$
$617$	−2.93121	+	18.5069i	−0.118006	+	0.745061i	−0.973743	+	0.227650i	$0.926896\pi$
$618$	11.8549	−	3.17652i	0.476875	−	0.127778i
$619$	3.47966	+	1.54924i	0.139859	+	0.0622694i	0.475473	−	0.879730i	$-0.342277\pi$
$619$	3.47966	+	1.54924i	0.139859	+	0.0622694i	−0.335614	+	0.942000i	$0.608944\pi$
$620$	−13.4375	−	0.651138i	−0.539665	−	0.0261503i
$621$	−14.3428	−	32.2144i	−0.575555	−	1.29272i
$622$	−2.94326	−	18.5830i	−0.118014	−	0.745111i
$623$	−6.44376	+	5.55340i	−0.258164	+	0.222492i
$624$		−	1.13879i		−	0.0455879i
$625$	−8.09927	−	23.6517i	−0.323971	−	0.946067i
$626$	−11.8984	+	6.86954i	−0.475556	+	0.274562i
$627$	−0.478666	+	0.737081i	−0.0191161	+	0.0294362i
$628$	4.61069	−	12.0113i	0.183987	−	0.479301i
$629$	6.00049	+	4.35961i	0.239255	+	0.173829i
$630$	−1.19312	−	6.14870i	−0.0475351	−	0.244970i
$631$	12.9131	−	9.38192i	0.514062	−	0.373488i	−0.300300	−	0.953845i	$-0.597087\pi$
$631$	12.9131	−	9.38192i	0.514062	−	0.373488i	0.814362	+	0.580357i	$0.197087\pi$
$632$	1.29906	+	4.84815i	0.0516738	+	0.192849i
$633$	−8.09049	+	3.10565i	−0.321568	+	0.123438i
$634$	−3.50702	−	3.15774i	−0.139282	−	0.125410i
$635$	−0.577919	+	0.802066i	−0.0229340	+	0.0318290i
$636$	−12.6688	−	4.11635i	−0.502352	−	0.163224i
$637$	−38.8626	−	21.9773i	−1.53979	−	0.870772i
$638$	1.94736	−	3.82191i	0.0770967	−	0.151311i
$639$	−10.2298	+	9.21098i	−0.404686	+	0.364381i
$640$	1.80919	+	16.5843i	0.0715145	+	0.655551i
$641$	−1.99105	+	2.21128i	−0.0786417	+	0.0873405i	−0.781181	−	0.624304i	$-0.785383\pi$
$641$	−1.99105	+	2.21128i	−0.0786417	+	0.0873405i	0.702540	+	0.711645i	$0.252049\pi$
$642$	8.58835	−	10.6057i	0.338955	−	0.418575i
$643$	−19.1135	+	19.1135i	−0.753761	+	0.753761i	−0.975179	−	0.221418i	$-0.928931\pi$
$643$	−19.1135	+	19.1135i	−0.753761	+	0.753761i	0.221418	+	0.975179i	$0.428931\pi$
$644$	20.6579	+	3.73345i	0.814034	+	0.147118i
$645$	−12.8374	+	4.98595i	−0.505471	+	0.196321i
$646$	−0.441038	+	0.196363i	−0.0173524	+	0.00772580i
$647$	18.3535	−	14.8624i	0.721552	−	0.584302i	−0.196621	−	0.980479i	$-0.562997\pi$
$647$	18.3535	−	14.8624i	0.721552	−	0.584302i	0.918174	+	0.396178i	$0.129664\pi$
$648$	8.83803	+	5.73949i	0.347191	+	0.225468i
$649$	−0.257905	+	0.446705i	−0.0101237	+	0.0175347i
$650$	24.8725	−	11.3097i	0.975578	−	0.443602i
$651$	−3.97148	−	16.2232i	−0.155655	−	0.635836i
$652$	13.9169	+	27.3135i	0.545028	+	1.06968i
$653$	−21.3676	−	8.20227i	−0.836181	−	0.320980i	−0.0976678	−	0.995219i	$-0.531138\pi$
$653$	−21.3676	−	8.20227i	−0.836181	−	0.320980i	−0.738513	+	0.674239i	$0.764472\pi$
$654$	−0.666082	+	6.33735i	−0.0260459	+	0.247810i
$655$	−18.0702	−	27.5870i	−0.706061	−	1.07791i
$656$	0.723436	−	0.0760362i	0.0282454	−	0.00296871i
$657$	−10.6631	−	10.6631i	−0.416006	−	0.416006i
$658$	0.374108	−	0.793425i	0.0145842	−	0.0309309i
$659$	−23.1990	+	7.53781i	−0.903704	+	0.293631i	−0.723765	−	0.690046i	$-0.757590\pi$
$659$	−23.1990	+	7.53781i	−0.903704	+	0.293631i	−0.179939	+	0.983678i	$0.557590\pi$
$660$	−1.04051	+	3.24583i	−0.0405017	+	0.126344i
$661$	−2.83452	−	13.3354i	−0.110250	−	0.518685i	−0.998266	−	0.0588719i	$-0.981250\pi$
$661$	−2.83452	−	13.3354i	−0.110250	−	0.518685i	0.888016	−	0.459813i	$-0.152084\pi$
$662$	−0.153431	−	2.92764i	−0.00596327	−	0.113786i
$663$	5.48524	−	3.56215i	0.213029	−	0.138343i
$664$	−4.45051	+	13.6973i	−0.172713	+	0.531557i
$665$	2.28702	+	3.66263i	0.0886867	+	0.142031i
$666$	3.14312	+	9.67353i	0.121793	+	0.374842i
$667$	−26.9002	−	21.7833i	−1.04158	−	0.843454i
$668$	−22.1306	−	5.92987i	−0.856257	−	0.229433i
$669$	4.55194	−	10.2238i	0.175988	−	0.395276i
$670$	3.33835	+	3.31214i	0.128972	+	0.127959i
$671$	5.63192	−	7.75167i	0.217418	−	0.299250i
$672$	−18.5097	+	7.76389i	−0.714026	+	0.299499i
$673$	21.8165	−	11.1161i	0.840966	−	0.428494i	0.0202259	−	0.999795i	$-0.493561\pi$
$673$	21.8165	−	11.1161i	0.840966	−	0.428494i	0.820740	+	0.571302i	$0.193561\pi$
$674$	17.7434	+	10.2442i	0.683450	+	0.394590i
$675$	4.18149	−	27.8183i	0.160945	−	1.07073i
$676$	−17.5202	−	30.3460i	−0.673856	−	1.16715i
$677$	0.0626782	−	1.19597i	0.00240892	−	0.0459649i	−0.997161	−	0.0753046i	$-0.976007\pi$
$677$	0.0626782	−	1.19597i	0.00240892	−	0.0459649i	0.999570	+	0.0293396i	$0.00934043\pi$
$678$	−4.99341	+	0.790879i	−0.191771	+	0.0303735i
$679$	−26.4207	+	3.59835i	−1.01393	+	0.138092i
$680$	−3.74195	+	3.05467i	−0.143497	+	0.117141i
$681$	−0.940619	−	8.94939i	−0.0360446	−	0.342941i
$682$	−0.955403	+	3.56561i	−0.0365843	+	0.136534i
$683$	−14.8424	−	38.6659i	−0.567931	−	1.47951i	−0.853470	−	0.521143i	$-0.825506\pi$
$683$	−14.8424	−	38.6659i	−0.567931	−	1.47951i	0.285539	−	0.958367i	$-0.407827\pi$
$684$	1.11678	+	0.237379i	0.0427012	+	0.00907643i
$685$	29.7496	−	17.3327i	1.13668	−	0.662247i
$686$	−1.86040	+	15.7584i	−0.0710302	+	0.601658i
$687$	−13.9450	−	7.10531i	−0.532034	−	0.271085i
$688$	−0.339457	−	0.522718i	−0.0129417	−	0.0199284i
$689$	−49.4227	+	10.5051i	−1.88286	+	0.400213i
$690$	−13.8441	−	7.92033i	−0.527037	−	0.301522i
$691$	−10.3731	+	48.8015i	−0.394611	+	1.85650i	0.111121	+	0.993807i	$0.464556\pi$
$691$	−10.3731	+	48.8015i	−0.394611	+	1.85650i	−0.505732	+	0.862691i	$0.668778\pi$
$692$	25.2322	+	3.99640i	0.959186	+	0.151920i
$693$	2.96303	+	0.0643610i	0.112556	+	0.00244487i
$694$	2.27999	+	3.13814i	0.0865472	+	0.119122i
$695$	45.0830	−	7.32269i	1.71009	−	0.277765i
$696$	20.4138	+	2.14558i	0.773785	+	0.0813281i
$697$	2.62917	+	3.24676i	0.0995871	+	0.122980i
$698$	−16.1405	−	0.845886i	−0.610926	−	0.0320173i
$699$	1.35178			0.0511291
$700$	12.2889	+	11.3768i	0.464478	+	0.430002i
$701$	21.3639			0.806903			0.403451	−	0.915001i	$-0.367810\pi$
$701$	21.3639			0.806903			0.403451	+	0.915001i	$0.367810\pi$
$702$	30.7026	+	1.60906i	1.15880	+	0.0607299i
$703$	−4.41291	−	5.44950i	−0.166436	−	0.205532i
$704$	4.16948	+	0.438230i	0.157143	+	0.0165164i
$705$	0.809506	−	0.815912i	0.0304878	−	0.0307290i
$706$	−3.99892	−	5.50403i	−0.150501	−	0.207147i
$707$	13.7684	+	25.0905i	0.517812	+	0.943626i
$708$	−0.944981	−	0.149670i	−0.0355146	−	0.00562495i
$709$	−3.68345	+	17.3293i	−0.138335	+	0.650815i	0.853265	+	0.521477i	$0.174619\pi$
$709$	−3.68345	+	17.3293i	−0.138335	+	0.650815i	−0.991601	+	0.129338i	$0.958715\pi$
$710$	−4.35504	+	20.8934i	−0.163442	+	0.784116i
$711$	2.16803	−	0.460830i	0.0813076	−	0.0172825i
$712$	4.89996	+	7.54527i	0.183634	+	0.282771i
$713$	26.5414	+	13.5235i	0.993984	+	0.506460i
$714$	−1.92156	−	1.30806i	−0.0719124	−	0.0489530i
$715$	2.73787	+	12.6356i	0.102391	+	0.472544i
$716$	−14.7186	−	3.12853i	−0.550058	−	0.116919i
$717$	−10.5581	−	27.5047i	−0.394299	−	1.02718i
$718$	−0.329669	+	1.23034i	−0.0123031	+	0.0459160i
$719$	−1.62861	−	15.4952i	−0.0607368	−	0.577872i	−0.981993	−	0.188916i	$-0.939503\pi$
$719$	−1.62861	−	15.4952i	−0.0607368	−	0.577872i	0.921256	−	0.388956i	$-0.127164\pi$
$720$	0.370822	−	0.0208998i	0.0138197	−	0.000778888i
$721$	26.4094	+	10.8013i	0.983536	+	0.402262i
$722$	−15.6276	+	2.47517i	−0.581600	+	0.0921163i
$723$	−0.188181	+	3.59071i	−0.00699853	+	0.133540i
$724$	5.63530	+	9.76063i	0.209434	+	0.362751i
$725$	−8.73965	−	26.1936i	−0.324583	−	0.972804i
$726$	−10.0314	−	5.79161i	−0.372299	−	0.214947i
$727$	30.9683	−	15.7791i	1.14855	−	0.585215i	0.227161	−	0.973857i	$-0.427056\pi$
$727$	30.9683	−	15.7791i	1.14855	−	0.585215i	0.921389	+	0.388642i	$0.127056\pi$
$728$	−28.5775	+	37.5890i	−1.05915	+	1.39314i
$729$	15.9131	−	21.9025i	0.589373	−	0.811203i
$730$	−23.1065	−	3.56642i	−0.855211	−	0.131999i
$731$	1.45597	−	3.27015i	0.0538508	−	0.120951i
$732$	17.1670	+	4.59988i	0.634511	+	0.170017i
$733$	−24.1091	−	19.5232i	−0.890490	−	0.721105i	0.0705517	−	0.997508i	$-0.477524\pi$
$733$	−24.1091	−	19.5232i	−0.890490	−	0.721105i	−0.961042	+	0.276404i	$0.910857\pi$
$734$	−3.57270	−	10.9956i	−0.131871	−	0.405857i
$735$	−9.19974	+	18.6447i	−0.339338	+	0.687719i
$736$	11.0622	−	34.0460i	0.407759	−	1.25495i
$737$	−1.86622	+	1.21194i	−0.0687431	+	0.0446423i
$738$	0.299845	+	5.72138i	0.0110374	+	0.210607i
$739$	11.1334	+	52.3787i	0.409550	+	1.92678i	0.374037	+	0.927414i	$0.377973\pi$
$739$	11.1334	+	52.3787i	0.409550	+	1.92678i	0.0355130	+	0.999369i	$0.488693\pi$
$740$	−22.0644	−	15.8983i	−0.811104	−	0.584432i
$741$	−5.88078	+	1.91078i	−0.216036	+	0.0701943i
$742$	10.2373	+	14.7539i	0.375824	+	0.541634i
$743$	−20.6739	−	20.6739i	−0.758450	−	0.758450i	0.217590	−	0.976040i	$-0.430180\pi$
$743$	−20.6739	−	20.6739i	−0.758450	−	0.758450i	−0.976040	+	0.217590i	$0.930180\pi$
$744$	−17.5677	+	1.84644i	−0.644064	+	0.0676939i
$745$	1.97161	−	40.6882i	0.0722343	−	1.49070i
$746$	−0.324849	+	3.09074i	−0.0118936	+	0.113160i
$747$	5.93756	+	2.27922i	0.217244	+	0.0833922i
$748$	−0.402222	−	0.789404i	−0.0147067	−	0.0288635i
$749$	30.8170	−	7.54409i	1.12603	−	0.275655i
$750$	−5.91008	−	11.2678i	−0.215806	−	0.411443i
$751$	−8.78473	+	15.2156i	−0.320559	+	0.555225i	−0.980604	−	0.196002i	$-0.937204\pi$
$751$	−8.78473	+	15.2156i	−0.320559	+	0.555225i	0.660044	+	0.751227i	$0.270537\pi$
$752$	0.0436250	+	0.0283304i	0.00159084	+	0.00103310i
$753$	−4.44466	+	3.59922i	−0.161973	+	0.131163i
$754$	27.5699	−	12.2749i	1.00403	−	0.447025i
$755$	−16.3230	+	25.3534i	−0.594053	+	0.922703i
$756$	6.36940	+	17.7347i	0.231653	+	0.645006i
$757$	−0.372788	+	0.372788i	−0.0135492	+	0.0135492i	−0.713849	−	0.700300i	$-0.753050\pi$
$757$	−0.372788	+	0.372788i	−0.0135492	+	0.0135492i	0.700300	+	0.713849i	$0.253050\pi$
$758$	3.61462	−	4.46369i	0.131289	−	0.162128i
$759$	5.05000	−	5.60860i	0.183303	−	0.203579i
$760$	4.16462	−	1.87391i	0.151067	−	0.0679739i
$761$	−21.3829	+	19.2532i	−0.775128	+	0.697929i	−0.958493	−	0.285116i	$-0.907968\pi$
$761$	−21.3829	+	19.2532i	−0.775128	+	0.697929i	0.183365	+	0.983045i	$0.441301\pi$
$762$	−0.228420	+	0.448300i	−0.00827479	+	0.0162402i
$763$	−10.1495	+	10.7914i	−0.367436	+	0.390674i
$764$	−10.1428	−	3.29560i	−0.366954	−	0.119231i
$765$	1.26061	+	1.72078i	0.0455775	+	0.0622149i
$766$	−18.0700	−	16.2703i	−0.652896	−	0.587870i
$767$	−3.38803	+	1.30054i	−0.122335	+	0.0469598i
$768$	5.37733	+	20.0685i	0.194038	+	0.724158i
$769$	−26.2277	+	19.0555i	−0.945794	+	0.687160i	−0.949808	−	0.312832i	$-0.898722\pi$
$769$	−26.2277	+	19.0555i	−0.945794	+	0.687160i	0.00401426	+	0.999992i	$0.498722\pi$
$770$	3.76488	−	2.63438i	0.135677	−	0.0949366i
$771$	−3.90575	−	2.83769i	−0.140662	−	0.102197i
$772$	4.56340	−	11.8881i	0.164240	−	0.427861i
$773$	−2.37816	+	3.66204i	−0.0855364	+	0.131715i	−0.878849	−	0.477100i	$-0.841688\pi$
$773$	−2.37816	+	3.66204i	−0.0855364	+	0.131715i	0.793313	+	0.608814i	$0.208355\pi$
$774$	4.25126	−	2.45447i	0.152808	−	0.0882239i
$775$	12.0435	+	20.4853i	0.432614	+	0.735853i
$776$			28.2008i			1.01235i
$777$	11.1282	−	31.8764i	0.399222	−	1.14356i
$778$	3.15632	+	19.9282i	0.113160	+	0.714462i
$779$	−1.60652	−	3.60830i	−0.0575594	−	0.129281i
$780$	−20.0607	+	13.1403i	−0.718289	+	0.470497i
$781$	−9.22580	−	4.10759i	−0.330125	−	0.146981i
$782$	4.00449	−	1.07300i	0.143200	−	0.0383704i
$783$	4.86060	−	30.6886i	0.173704	−	1.09672i
$784$	−0.911016	−	0.235413i	−0.0325363	−	0.00840760i
$785$	−22.2101	+	4.81247i	−0.792712	+	0.171764i
$786$	−11.2309	−	12.4732i	−0.400593	−	0.444904i
$787$	29.6739	−	1.55515i	1.05776	−	0.0554349i	0.484487	−	0.874798i	$-0.339006\pi$
$787$	29.6739	−	1.55515i	1.05776	−	0.0554349i	0.573274	+	0.819363i	$0.305673\pi$
$788$	14.3887	−	0.754082i	0.512577	−	0.0268630i
$789$	11.9401	+	13.2608i	0.425078	+	0.472097i
$790$	2.28936	−	2.56283i	0.0814517	−	0.0911814i
$791$	−10.3541	−	5.56214i	−0.368150	−	0.197767i
$792$	0.490341	−	3.09589i	0.0174235	−	0.110008i
$793$	65.1158	−	17.4477i	2.31233	−	0.619587i
$794$	26.3685	+	11.7400i	0.935784	+	0.416638i
$795$	6.17933	+	22.7033i	0.219158	+	0.805202i
$796$	5.02071	+	11.2767i	0.177955	+	0.399692i
$797$	3.69197	+	23.3102i	0.130776	+	0.825690i	0.962655	+	0.270732i	$0.0872656\pi$
$797$	3.69197	+	23.3102i	0.130776	+	0.825690i	−0.831878	+	0.554958i	$0.812734\pi$
$798$	1.43470	+	1.66472i	0.0507879	+	0.0589305i
$799$			0.298748i			0.0105690i
$800$	22.0511	−	18.1463i	0.779626	−	0.641569i
$801$	3.44067	−	1.98647i	0.121570	−	0.0701885i
$802$	7.17495	−	11.0485i	0.253356	−	0.390134i
$803$	3.96466	−	10.3283i	0.139910	−	0.364477i
$804$	−3.33920	−	2.42607i	−0.117764	−	0.0855609i
$805$	−14.4773	−	34.1371i	−0.510259	−	1.20318i
$806$	−21.0113	+	15.2656i	−0.740091	+	0.537708i
$807$	4.63956	+	17.3151i	0.163320	+	0.609519i
$808$	28.2584	−	10.8474i	0.994128	−	0.381610i
$809$	−14.1195	−	12.7132i	−0.496415	−	0.446974i	0.382498	−	0.923956i	$-0.375064\pi$
$809$	−14.1195	−	12.7132i	−0.496415	−	0.446974i	−0.878913	+	0.476982i	$0.841731\pi$
$810$	−0.0284357	−	7.21505i	−0.000999128	−	0.253511i
$811$	4.88012	+	1.58565i	0.171364	+	0.0556796i	0.393442	−	0.919349i	$-0.371284\pi$
$811$	4.88012	+	1.58565i	0.171364	+	0.0556796i	−0.222078	+	0.975029i	$0.571284\pi$
$812$	13.4740	+	12.6725i	0.472844	+	0.444719i
$813$	1.49593	−	2.93593i	0.0524646	−	0.102968i
$814$	−5.54538	+	4.99308i	−0.194365	+	0.175007i
$815$	26.8884	−	46.9988i	0.941858	−	1.64630i
$816$	0.0922338	−	0.102436i	0.00322883	−	0.00358598i
$817$	−2.12978	+	2.63005i	−0.0745114	+	0.0920140i
$818$	−10.3675	+	10.3675i	−0.362490	+	0.362490i
$819$	15.9161	+	13.4713i	0.556153	+	0.470724i
$820$	−9.68706	−	11.8666i	−0.338287	−	0.414399i
$821$	−48.2030	+	21.4614i	−1.68230	+	0.749007i	−0.682461	+	0.730922i	$0.739090\pi$
$821$	−48.2030	+	21.4614i	−1.68230	+	0.749007i	−0.999836	+	0.0180847i	$0.994243\pi$
$822$	13.6182	−	11.0278i	0.474990	−	0.384639i
$823$	−14.4473	−	9.38221i	−0.503602	−	0.327043i	0.267710	−	0.963499i	$-0.413733\pi$
$823$	−14.4473	−	9.38221i	−0.503602	−	0.327043i	−0.771313	+	0.636456i	$0.780400\pi$
$824$	15.0884	−	26.1338i	0.525628	−	0.910415i
$825$	5.80304	−	1.60405i	0.202036	−	0.0558458i
$826$	0.892011	+	0.931623i	0.0310370	+	0.0324153i
$827$	−19.6704	−	38.6053i	−0.684006	−	1.34244i	−0.927970	−	0.372654i	$-0.878448\pi$
$827$	−19.6704	−	38.6053i	−0.684006	−	1.34244i	0.243964	−	0.969784i	$-0.421552\pi$
$828$	−9.15320	−	3.51358i	−0.318096	−	0.122105i
$829$	−0.103303	+	0.982859i	−0.00358785	+	0.0341361i	−0.996169	−	0.0874450i	$-0.972130\pi$
$829$	−0.103303	+	0.982859i	−0.00358785	+	0.0341361i	0.992581	+	0.121581i	$0.0387965\pi$
$830$	9.51454	−	2.58965i	0.330254	−	0.0898879i
$831$	−1.16026	+	0.121949i	−0.0402491	+	0.00423035i
$832$	20.8573	+	20.8573i	0.723096	+	0.723096i
$833$	−1.71576	−	5.12450i	−0.0594476	−	0.177554i
$834$	22.1079	−	7.18329i	0.765533	−	0.248737i
$835$	12.6573	+	38.4390i	0.438023	+	1.33024i
$836$	0.174149	+	0.819308i	0.00602308	+	0.0283364i
$837$	1.39942	+	26.7025i	0.0483710	+	0.922974i
$838$	−20.6541	+	13.4129i	−0.713484	+	0.463342i
$839$	−12.8303	+	39.4877i	−0.442952	+	1.36327i	0.441762	+	0.897132i	$0.354354\pi$
$839$	−12.8303	+	39.4877i	−0.442952	+	1.36327i	−0.884714	+	0.466135i	$0.845646\pi$
$840$	18.2255	+	12.3018i	0.628838	+	0.424453i
$841$	−0.463326	−	1.42597i	−0.0159768	−	0.0491714i
$842$	16.1720	+	13.0958i	0.557324	+	0.451312i
$843$	−28.4792	−	7.63098i	−0.980876	−	0.262825i
$844$	−3.35935	+	7.54523i	−0.115634	+	0.259717i
$845$	−27.8816	+	55.2581i	−0.959157	+	1.90094i
$846$	−0.240809	+	0.331446i	−0.00827920	+	0.0113953i
$847$	−10.4162	−	24.8329i	−0.357904	−	0.853268i
$848$	−0.948808	+	0.483442i	−0.0325822	+	0.0166015i
$849$	24.3079	+	14.0341i	0.834243	+	0.481651i
$850$	3.15333	+	0.997170i	0.108158	+	0.0342026i
$851$	30.1079	+	52.1484i	1.03209	+	1.78763i
$852$	0.980363	−	18.7064i	0.0335867	−	0.640872i
$853$	−24.4620	+	3.87440i	−0.837563	+	0.132657i	−0.560458	−	0.828183i	$-0.689375\pi$
$853$	−24.4620	+	3.87440i	−0.837563	+	0.132657i	−0.277105	+	0.960840i	$0.589375\pi$
$854$	−14.6701	−	18.9428i	−0.502001	−	0.648211i
$855$	−0.730134	−	1.87989i	−0.0249701	−	0.0642908i
$856$	−3.50744	−	33.3710i	−0.119882	−	1.14060i
$857$	−11.9982	+	44.7778i	−0.409850	+	1.52958i	0.385082	+	0.922883i	$0.374173\pi$
$857$	−11.9982	+	44.7778i	−0.409850	+	1.52958i	−0.794932	+	0.606699i	$0.792493\pi$
$858$	2.35810	+	6.14305i	0.0805041	+	0.209720i
$859$	34.7486	+	7.38604i	1.18561	+	0.252009i	0.758182	−	0.652043i	$-0.226088\pi$
$859$	34.7486	+	7.38604i	1.18561	+	0.252009i	0.427424	+	0.904051i	$0.359421\pi$
$860$	−5.29119	+	12.0114i	−0.180428	+	0.409585i
$861$	10.7017	−	15.7209i	0.364714	−	0.535768i
$862$	22.0015	+	11.2103i	0.749373	+	0.381824i
$863$	24.5638	+	37.8249i	0.836161	+	1.28757i	0.955580	+	0.294731i	$0.0952300\pi$
$863$	24.5638	+	37.8249i	0.836161	+	1.28757i	−0.119419	+	0.992844i	$0.538103\pi$
$864$	31.4318	−	6.68104i	1.06933	−	0.227293i
$865$	−18.5161	−	41.1507i	−0.629567	−	1.39916i
$866$	2.33648	−	10.9923i	0.0793967	−	0.373532i
$867$	−21.5208	−	3.40856i	−0.730885	−	0.115761i
$868$	−13.6095	−	8.25658i	−0.461935	−	0.280247i
$869$	0.955783	+	1.31552i	0.0324227	+	0.0446260i
$870$	−6.42953	−	12.4967i	−0.217981	−	0.423676i
$871$	−15.5701	−	1.63648i	−0.527572	−	0.0554500i
$872$	9.86013	+	12.1762i	0.333906	+	0.412340i
$873$	12.4364	+	0.651765i	0.420909	+	0.0220589i
$874$	−3.91947			−0.132578
$875$	4.91624	−	29.1690i	0.166199	−	0.986092i
$876$	20.5206			0.693326
$877$	−24.1336	−	1.26479i	−0.814934	−	0.0427089i	−0.359686	−	0.933073i	$-0.617116\pi$
$877$	−24.1336	−	1.26479i	−0.814934	−	0.0427089i	−0.455248	+	0.890365i	$0.650449\pi$
$878$	2.68937	+	3.32109i	0.0907618	+	0.112081i
$879$	−2.01868	−	0.212171i	−0.0680883	−	0.00715637i
$880$	0.124659	+	0.242291i	0.00420225	+	0.00816764i
$881$	8.91127	+	12.2653i	0.300228	+	0.413229i	0.932303	−	0.361679i	$-0.117796\pi$
$881$	8.91127	+	12.2653i	0.300228	+	0.413229i	−0.632074	+	0.774908i	$0.717796\pi$
$882$	2.22712	−	7.06838i	0.0749909	−	0.238005i
$883$	11.1876	+	1.77193i	0.376491	+	0.0596303i	0.341812	−	0.939768i	$-0.388959\pi$
$883$	11.1876	+	1.77193i	0.376491	+	0.0596303i	0.0346786	+	0.999399i	$0.488959\pi$
$884$	1.29599	−	6.09716i	0.0435889	−	0.205070i
$885$	0.693453	+	1.54115i	0.0233102	+	0.0518051i
$886$	−25.9457	+	5.51493i	−0.871664	+	0.185278i
$887$	11.8109	+	18.1871i	0.396570	+	0.610664i	0.979400	−	0.201930i	$-0.0647214\pi$
$887$	11.8109	+	18.1871i	0.396570	+	0.610664i	−0.582830	+	0.812594i	$0.698055\pi$
$888$	−31.8163	−	16.2112i	−1.06768	−	0.544012i
$889$	−1.05351	+	0.508279i	−0.0353334	+	0.0170471i
$890$	2.48319	−	5.63703i	0.0832368	−	0.188954i
$891$	3.33946	+	0.709825i	0.111876	+	0.0237800i
$892$	−3.82236	−	9.95760i	−0.127982	−	0.333405i
$893$	0.0731015	−	0.272818i	0.00244625	−	0.00912952i
$894$	−2.16714	−	20.6189i	−0.0724799	−	0.689600i
$895$	9.62276	+	24.7758i	0.321653	+	0.828165i
$896$	−7.47242	+	18.2702i	−0.249636	+	0.610364i
$897$	52.4452	−	8.30650i	1.75109	−	0.277346i
$898$	−1.77695	+	33.9062i	−0.0592976	+	1.13147i
$899$	13.1235	+	22.7307i	0.437695	+	0.758110i
$900$	−4.64703	−	6.29120i	−0.154901	−	0.209707i
$901$	−5.29651	−	3.05794i	−0.176452	−	0.101875i
$902$	−3.74504	+	1.90819i	−0.124696	+	0.0635359i
$903$	−16.1647	−	2.05479i	−0.537929	−	0.0683793i
$904$	−7.30657	+	10.0566i	−0.243013	+	0.334479i
$905$	8.96799	−	17.7735i	0.298106	−	0.590811i
$906$	−6.24201	+	14.0198i	−0.207377	+	0.465776i
$907$	40.1435	+	10.7564i	1.33294	+	0.357161i	0.853811	−	0.520582i	$-0.174285\pi$
$907$	40.1435	+	10.7564i	1.33294	+	0.357161i	0.479131	+	0.877743i	$0.340952\pi$
$908$	−6.66501	−	5.39722i	−0.221186	−	0.179113i
$909$	−4.13055	−	12.7125i	−0.137002	−	0.421648i
$910$	32.2496	+	2.26559i	1.06906	+	0.0751037i
$911$	−13.6494	+	42.0086i	−0.452225	+	1.39181i	0.422137	+	0.906532i	$0.361280\pi$
$911$	−13.6494	+	42.0086i	−0.452225	+	1.39181i	−0.874362	+	0.485274i	$0.838720\pi$
$912$	−0.109294	+	0.0709761i	−0.00361908	+	0.00235025i
$913$	0.244194	+	4.65951i	0.00808165	+	0.154207i
$914$	1.67579	+	7.88397i	0.0554302	+	0.260779i
$915$	−9.81844	−	29.8177i	−0.324588	−	0.985742i
$916$	−14.1861	+	4.60933i	−0.468721	+	0.152297i
$917$	−3.23507	−	38.8863i	−0.106831	−	1.28414i
$918$	2.63144	+	2.63144i	0.0868503	+	0.0868503i
$919$	23.8677	−	2.50859i	0.787321	−	0.0827508i	0.297670	−	0.954669i	$-0.403791\pi$
$919$	23.8677	−	2.50859i	0.787321	−	0.0827508i	0.489652	+	0.871918i	$0.337124\pi$
$920$	−37.8399	+	10.2992i	−1.24755	+	0.339554i
$921$	−2.99665	+	28.5112i	−0.0987429	+	0.939476i
$922$	−5.04264	−	1.93569i	−0.166070	−	0.0637485i
$923$	−32.2571	−	63.3081i	−1.06176	−	2.08381i
$924$	−2.91303	+	2.78917i	−0.0958318	+	0.0917571i
$925$	−2.13585	+	47.9892i	−0.0702264	+	1.57788i
$926$	2.60523	−	4.51239i	0.0856132	−	0.148286i
$927$	−11.1762	−	7.25788i	−0.367073	−	0.238380i
$928$	24.5132	−	19.8504i	0.804687	−	0.651623i
$929$	−12.4309	+	5.53459i	−0.407844	+	0.181584i	−0.600396	−	0.799703i	$-0.704990\pi$
$929$	−12.4309	+	5.53459i	−0.407844	+	0.181584i	0.192552	+	0.981287i	$0.438324\pi$
$930$	7.64816	+	9.36895i	0.250793	+	0.307220i
$931$	0.312913	+	5.09956i	0.0102553	+	0.167131i
$932$	0.910985	−	0.910985i	0.0298403	−	0.0298403i
$933$	18.3564	−	22.6682i	0.600961	−	0.742125i
$934$	−2.16823	+	2.40806i	−0.0709465	+	0.0787941i
$935$	−0.777118	+	1.35834i	−0.0254145	+	0.0444226i
$936$	16.3887	−	14.7564i	0.535681	−	0.482329i
$937$	2.61472	−	5.13167i	0.0854190	−	0.167644i	−0.844345	−	0.535799i	$-0.820010\pi$
$937$	2.61472	−	5.13167i	0.0854190	−	0.167644i	0.929764	+	0.368155i	$0.120010\pi$
$938$	1.60412	+	5.32800i	0.0523764	+	0.173965i
$939$	−20.2574	−	6.58202i	−0.661075	−	0.214796i
$940$	−0.00431712	−	1.09539i	−0.000140809	−	0.0357277i
$941$	−1.95444	−	1.75979i	−0.0637129	−	0.0573674i	0.636659	−	0.771145i	$-0.280316\pi$
$941$	−1.95444	−	1.75979i	−0.0637129	−	0.0573674i	−0.700372	+	0.713778i	$0.746983\pi$
$942$	−10.7979	+	4.14492i	−0.351814	+	0.135049i
$943$	8.77860	+	32.7622i	0.285870	+	1.06688i
$944$	−0.0618768	+	0.0449561i	−0.00201392	+	0.00146320i
$945$	20.0399	−	26.5759i	0.651898	−	0.864515i
$946$	2.91356	+	2.11682i	0.0947279	+	0.0688239i
$947$	10.4942	−	27.3384i	0.341016	−	0.888377i	−0.650631	−	0.759394i	$-0.725495\pi$
$947$	10.4942	−	27.3384i	0.341016	−	0.888377i	0.991647	−	0.128983i	$-0.0411712\pi$
$948$	−1.64271	+	2.52956i	−0.0533529	+	0.0821563i
$949$	67.4081	−	38.9181i	2.18816	−	1.26333i
$950$	−2.63564	−	1.68222i	−0.0855114	−	0.0545783i
$951$		−	7.31617i		−	0.237243i
$952$	−5.61505	+	1.06663i	−0.181985	+	0.0345695i
$953$	−3.28962	−	20.7699i	−0.106561	−	0.672802i	−0.981916	−	0.189320i	$-0.939372\pi$
$953$	−3.28962	−	20.7699i	−0.106561	−	0.672802i	0.875354	−	0.483482i	$-0.160628\pi$
$954$	−3.41131	−	7.66194i	−0.110445	−	0.248064i
$955$	4.94724	+	18.1765i	0.160089	+	0.588178i
$956$	−25.6510	−	11.4206i	−0.829614	−	0.369368i
$957$	6.42336	−	1.72113i	0.207638	−	0.0556364i
$958$	1.28297	−	8.10037i	0.0414510	−	0.261711i
$959$	40.7196	−	1.24812i	1.31491	−	0.0403039i
$960$	9.15081	−	10.2439i	0.295341	−	0.330621i
$961$	5.62893	+	6.25156i	0.181578	+	0.201663i
$962$	−52.4284	+	2.74766i	−1.69036	+	0.0885880i
$963$	−14.7975	+	0.775505i	−0.476843	+	0.0249903i
$964$	2.29301	+	2.54665i	0.0738529	+	0.0820220i
$965$	−21.9823	+	4.76311i	−0.707635	+	0.153330i
$966$	−9.93223	−	16.0468i	−0.319564	−	0.516296i
$967$	5.13181	−	32.4010i	0.165028	−	1.04194i	−0.756602	−	0.653875i	$-0.773142\pi$
$967$	5.13181	−	32.4010i	0.165028	−	1.04194i	0.921630	−	0.388070i	$-0.126858\pi$
$968$	−27.5100	+	7.37129i	−0.884205	+	0.236922i
$969$	−0.683747	−	0.304424i	−0.0219651	−	0.00977950i
$970$	16.1516	−	10.5797i	0.518597	−	0.339694i
$971$	0.0803296	+	0.180423i	0.00257790	+	0.00579006i	0.914830	−	0.403840i	$-0.132325\pi$
$971$	0.0803296	+	0.180423i	0.00257790	+	0.00579006i	−0.912252	+	0.409630i	$0.865658\pi$
$972$	−2.35187	−	14.8492i	−0.0754364	−	0.476287i
$973$	51.0222	+	17.8121i	1.63570	+	0.571029i
$974$		−	22.0618i		−	0.706905i
$975$	38.8317	+	16.9235i	1.24361	+	0.541986i
$976$	1.23041	−	0.710375i	0.0393843	−	0.0227386i
$977$	−6.18600	+	9.52560i	−0.197908	+	0.304751i	−0.923666	−	0.383199i	$-0.874822\pi$
$977$	−6.18600	+	9.52560i	−0.197908	+	0.304751i	0.725758	+	0.687950i	$0.241489\pi$
$978$	9.87588	−	25.7275i	0.315796	−	0.822676i
$979$	2.35803	+	1.71321i	0.0753629	+	0.0547544i
$980$	6.36506	+	18.7647i	0.203325	+	0.599417i
$981$	5.59754	−	4.06685i	0.178716	−	0.129845i
$982$	0.720131	+	2.68757i	0.0229803	+	0.0857637i
$983$	3.26195	−	1.25214i	0.104040	−	0.0399372i	−0.305791	−	0.952099i	$-0.598921\pi$
$983$	3.26195	−	1.25214i	0.104040	−	0.0399372i	0.409831	+	0.912161i	$0.365588\pi$
$984$	−14.9472	−	13.4585i	−0.476500	−	0.429042i
$985$	−15.0404	−	20.5307i	−0.479227	−	0.654163i
$986$	3.47414	+	1.12882i	0.110639	+	0.0359489i
$987$	1.30219	−	0.392056i	0.0414493	−	0.0124793i
$988$	−2.67544	+	5.25084i	−0.0851170	+	0.167051i
$989$	21.5970	−	19.4460i	0.686743	−	0.618346i
$990$	−1.95708	+	0.880607i	−0.0622001	+	0.0279875i
$991$	0.211307	−	0.234680i	0.00671238	−	0.00745485i	−0.739779	−	0.672850i	$-0.765070\pi$
$991$	0.211307	−	0.234680i	0.00671238	−	0.00745485i	0.746492	+	0.665395i	$0.231737\pi$
$992$	−17.0829	+	21.0956i	−0.542382	+	0.669785i
$993$	3.21379	−	3.21379i	0.101987	−	0.101987i
$994$	−16.3145	+	19.2753i	−0.517465	+	0.611376i
$995$	11.8030	−	18.3327i	0.374179	−	0.581187i
$996$	−7.90639	+	3.52015i	−0.250524	+	0.111540i
$997$	−25.7893	+	20.8837i	−0.816754	+	0.661394i	−0.943805	−	0.330502i	$-0.892782\pi$
$997$	−25.7893	+	20.8837i	−0.816754	+	0.661394i	0.127051	+	0.991896i	$0.459449\pi$
$998$	−22.4148	−	14.5563i	−0.709527	−	0.460772i
$999$	−27.0262	+	46.8108i	−0.855071	+	1.48103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.103.7	yes	288
5.2	odd	4		875.2.bb.b.257.12		288
5.3	odd	4		875.2.bb.a.257.7		288
5.4	even	2		875.2.bb.c.243.12		288
7.3	odd	6	inner	175.2.x.a.3.12	✓	288
25.6	even	5		875.2.bb.b.768.12		288
25.8	odd	20		875.2.bb.c.607.7		288
25.17	odd	20	inner	175.2.x.a.117.12	yes	288
25.19	even	10		875.2.bb.a.768.7		288
35.3	even	12		875.2.bb.a.507.7		288
35.17	even	12		875.2.bb.b.507.12		288
35.24	odd	6		875.2.bb.c.493.7		288
175.17	even	60	inner	175.2.x.a.17.7	yes	288
175.31	odd	30		875.2.bb.b.143.12		288
175.94	odd	30		875.2.bb.a.143.7		288
175.108	even	60		875.2.bb.c.857.12		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.12	✓	288	7.3	odd	6	inner
175.2.x.a.17.7	yes	288	175.17	even	60	inner
175.2.x.a.103.7	yes	288	1.1	even	1	trivial
175.2.x.a.117.12	yes	288	25.17	odd	20	inner
875.2.bb.a.143.7		288	175.94	odd	30
875.2.bb.a.257.7		288	5.3	odd	4
875.2.bb.a.507.7		288	35.3	even	12
875.2.bb.a.768.7		288	25.19	even	10
875.2.bb.b.143.12		288	175.31	odd	30
875.2.bb.b.257.12		288	5.2	odd	4
875.2.bb.b.507.12		288	35.17	even	12
875.2.bb.b.768.12		288	25.6	even	5
875.2.bb.c.243.12		288	5.4	even	2
875.2.bb.c.493.7		288	35.24	odd	6
875.2.bb.c.607.7		288	25.8	odd	20
875.2.bb.c.857.12		288	175.108	even	60

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.855607 - 0.0448405i) q^{2} +(-0.835912 - 1.03227i) q^{3} +(-1.25899 - 0.132325i) q^{4} +(1.02300 + 1.98833i) q^{5} +(0.668925 + 0.920697i) q^{6} +(-0.0574557 + 2.64513i) q^{7} +(2.76373 + 0.437732i) q^{8} +(0.256912 - 1.20868i) q^{9} +(-0.786126 - 1.74711i) q^{10} +(0.886724 - 0.188479i) q^{11} +(0.915811 + 1.41023i) q^{12} +(5.68290 + 2.89558i) q^{13} +(0.167768 - 2.26061i) q^{14} +(1.19735 - 2.71808i) q^{15} +(0.131483 + 0.0279475i) q^{16} +(0.276666 + 0.720738i) q^{17} +(-0.274013 + 1.02263i) q^{18} +(-0.0762931 - 0.725880i) q^{19} +(-1.02484 - 2.63866i) q^{20} +(2.77850 - 2.15179i) q^{21} +(-0.767139 + 0.121503i) q^{22} +(-0.328025 + 6.25910i) q^{23} +(-1.85838 - 3.21881i) q^{24} +(-2.90695 + 4.06812i) q^{25} +(-4.73249 - 2.73230i) q^{26} +(-5.01294 + 2.55422i) q^{27} +(0.422353 - 3.32259i) q^{28} +(-3.24612 + 4.46790i) q^{29} +(-1.14634 + 2.27192i) q^{30} +(1.93308 - 4.34176i) q^{31} +(-5.51692 - 1.47825i) q^{32} +(-0.935784 - 0.757783i) q^{33} +(-0.204399 - 0.629075i) q^{34} +(-5.31818 + 2.59172i) q^{35} +(-0.483388 + 1.48772i) q^{36} +(8.05740 - 5.23253i) q^{37} +(0.0327281 + 0.624489i) q^{38} +(-1.76140 - 8.28671i) q^{39} +(1.95694 + 5.94303i) q^{40} +(5.14669 - 1.67226i) q^{41} +(-2.47379 + 1.71649i) q^{42} +(-3.27866 - 3.27866i) q^{43} +(-1.14132 + 0.119957i) q^{44} +(2.66607 - 0.725645i) q^{45} +(0.561322 - 5.34062i) q^{46} +(0.361269 + 0.138678i) q^{47} +(-0.0810588 - 0.159087i) q^{48} +(-6.99340 - 0.303955i) q^{49} +(2.66962 - 3.35037i) q^{50} +(0.512725 - 0.888067i) q^{51} +(-6.77156 - 4.39750i) q^{52} +(-6.15653 + 4.98546i) q^{53} +(4.40364 - 1.96063i) q^{54} +(1.28188 + 1.57029i) q^{55} +(-1.31665 + 7.28528i) q^{56} +(-0.685527 + 0.685527i) q^{57} +(2.97774 - 3.67721i) q^{58} +(-0.380730 + 0.422843i) q^{59} +(-1.86713 + 3.26360i) q^{60} +(7.85465 - 7.07236i) q^{61} +(-1.84864 + 3.62816i) q^{62} +(3.18234 + 0.749010i) q^{63} +(4.39835 + 1.42911i) q^{64} +(0.0562076 + 14.2617i) q^{65} +(0.766684 + 0.690326i) q^{66} +(-2.29160 + 0.879663i) q^{67} +(-0.252948 - 0.944013i) q^{68} +(6.73525 - 4.89345i) q^{69} +(4.66648 - 1.97902i) q^{70} +(-9.01254 - 6.54799i) q^{71} +(1.23911 - 3.22800i) q^{72} +(6.64662 - 10.2349i) q^{73} +(-7.12859 + 4.11570i) q^{74} +(6.62934 - 0.399850i) q^{75} +0.923972i q^{76} +(0.447604 + 2.35633i) q^{77} +(1.13548 + 7.16915i) q^{78} +(0.729574 + 1.63865i) q^{79} +(0.0789375 + 0.290022i) q^{80} +(3.44047 + 1.53180i) q^{81} +(-4.47853 + 1.20002i) q^{82} +(-0.805162 + 5.08360i) q^{83} +(-3.78285 + 2.34141i) q^{84} +(-1.15004 + 1.28742i) q^{85} +(2.65823 + 2.95226i) q^{86} +(7.32552 - 0.383914i) q^{87} +(2.53317 - 0.132758i) q^{88} +(2.15138 + 2.38935i) q^{89} +(-2.31365 + 0.501319i) q^{90} +(-7.98570 + 14.8656i) q^{91} +(1.24122 - 7.83674i) q^{92} +(-6.09774 + 1.63388i) q^{93} +(-0.302886 - 0.134854i) q^{94} +(1.36524 - 0.894270i) q^{95} +(3.08571 + 6.93062i) q^{96} +(1.57659 + 9.95418i) q^{97} +(5.96997 + 0.573653i) q^{98} -1.12018i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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