LMFDB - Embedded newform 669.2.i.a.4.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(4,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(74)) chi = DirichletCharacter(H, H._module([0, 46])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.i (of order $37$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [648] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$18$ over $\Q(\zeta_{37})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{37}]$

Embedding invariants

Embedding label			4.10
Character	$\chi$	$=$	669.4
Dual form			669.2.i.a.502.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.153732 - 0.0543169i) q^{2} +(-0.372856 + 0.927889i) q^{3} +(-1.53539 + 1.23974i) q^{4} +(-1.34968 - 2.19202i) q^{5} +(-0.00691984 + 0.162898i) q^{6} +(0.0153152 - 0.119599i) q^{7} +(-0.339671 + 0.551660i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-0.326553 - 0.263673i) q^{10} +(-0.128682 + 3.02927i) q^{11} +(-0.577861 - 1.88691i) q^{12} +(-0.287439 - 0.715320i) q^{13} +(-0.00414180 - 0.0192180i) q^{14} +(2.53719 - 0.435045i) q^{15} +(0.809262 - 3.75499i) q^{16} +(0.139995 - 3.29559i) q^{17} +(-0.148571 - 0.0671585i) q^{18} +(7.99170 - 2.08088i) q^{19} +(4.78983 + 1.69235i) q^{20} +(0.105264 + 0.0588040i) q^{21} +(0.144758 + 0.472684i) q^{22} +(-3.45673 - 5.61408i) q^{23} +(-0.385231 - 0.520867i) q^{24} +(-0.732307 + 1.45244i) q^{25} +(-0.0830425 - 0.0943546i) q^{26} +(0.911228 - 0.411901i) q^{27} +(0.124757 + 0.202617i) q^{28} +(-0.104122 + 0.483126i) q^{29} +(0.366417 - 0.204693i) q^{30} +(6.48960 - 0.552346i) q^{31} +(-0.244126 - 1.90642i) q^{32} +(-2.76285 - 1.24888i) q^{33} +(-0.157485 - 0.514241i) q^{34} +(-0.282834 + 0.127849i) q^{35} +(1.96631 + 0.167357i) q^{36} +(-0.247281 - 5.82118i) q^{37} +(1.11555 - 0.753981i) q^{38} +0.770911 q^{39} +1.66770 q^{40} +(-4.53385 + 3.06435i) q^{41} +(0.0193765 + 0.00332243i) q^{42} +(-0.135830 - 0.269402i) q^{43} +(-3.55793 - 4.81064i) q^{44} +(-0.542335 + 2.51644i) q^{45} +(-0.836347 - 0.675303i) q^{46} +(2.56717 + 0.668438i) q^{47} +(3.18247 + 2.15098i) q^{48} +(6.76006 + 1.76018i) q^{49} +(-0.0336866 + 0.263063i) q^{50} +(3.00575 + 1.35868i) q^{51} +(1.32814 + 0.741945i) q^{52} +(3.51737 - 3.99651i) q^{53} +(0.117712 - 0.112817i) q^{54} +(6.81391 - 3.80648i) q^{55} +(0.0607758 + 0.0490730i) q^{56} +(-1.04893 + 8.19128i) q^{57} +(0.0102351 + 0.0799273i) q^{58} +(4.20581 - 13.7334i) q^{59} +(-3.35623 + 3.81342i) q^{60} +(1.01686 + 2.53055i) q^{61} +(0.967655 - 0.437408i) q^{62} +(-0.0938120 + 0.0757479i) q^{63} +(3.31757 + 6.58000i) q^{64} +(-1.18005 + 1.59553i) q^{65} +(-0.492572 - 0.0419241i) q^{66} +(-4.84878 + 3.91511i) q^{67} +(3.87073 + 5.23357i) q^{68} +(6.49810 - 1.11421i) q^{69} +(-0.0365362 + 0.0350171i) q^{70} +(0.876693 - 2.86270i) q^{71} +(0.626943 - 0.163243i) q^{72} +(-11.6473 - 6.50655i) q^{73} +(-0.354203 - 0.881469i) q^{74} +(-1.07466 - 1.22105i) q^{75} +(-9.69062 + 13.1026i) q^{76} +(0.360326 + 0.0617841i) q^{77} +(0.118514 - 0.0418735i) q^{78} +(-7.37089 + 4.98185i) q^{79} +(-9.32327 + 3.29412i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(-0.530550 + 0.717352i) q^{82} +(-0.868262 + 1.72210i) q^{83} +(-0.234523 + 0.0402130i) q^{84} +(-7.41297 + 4.14113i) q^{85} +(-0.0355144 - 0.0340378i) q^{86} +(-0.409465 - 0.276750i) q^{87} +(-1.62742 - 1.09994i) q^{88} +(1.00552 - 1.63307i) q^{89} +(0.0533112 + 0.416315i) q^{90} +(-0.0899536 + 0.0234221i) q^{91} +(12.2674 + 4.33435i) q^{92} +(-1.90717 + 6.22757i) q^{93} +(0.430962 - 0.0366803i) q^{94} +(-15.3476 - 14.7095i) q^{95} +(1.85997 + 0.484298i) q^{96} +(-6.74297 + 10.9513i) q^{97} +(1.13484 - 0.0965894i) q^{98} +(2.18897 - 2.09796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + q^{2} + 18 q^{3} - 17 q^{4} + 4 q^{5} - q^{6} + 4 q^{7} + 9 q^{8} - 18 q^{9} + 8 q^{10} + 6 q^{11} + 17 q^{12} - 2 q^{13} + 12 q^{14} - 4 q^{15} - 7 q^{16} + 8 q^{17} + q^{18} - 66 q^{19} + 14 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 648 * q + q^2 + 18 * q^3 - 17 * q^4 + 4 * q^5 - q^6 + 4 * q^7 + 9 * q^8 - 18 * q^9 + 8 * q^10 + 6 * q^11 + 17 * q^12 - 2 * q^13 + 12 * q^14 - 4 * q^15 - 7 * q^16 + 8 * q^17 + q^18 - 66 * q^19 + 14 * q^20 - 4 * q^21 - 24 * q^22 - 2 * q^23 - 9 * q^24 - 26 * q^25 - 8 * q^26 + 18 * q^27 + 8 * q^28 - 27 * q^29 - 8 * q^30 + 16 * q^31 + 19 * q^32 - 6 * q^33 - 50 * q^34 + 16 * q^35 - 17 * q^36 + 16 * q^37 - 28 * q^38 - 72 * q^39 + 212 * q^40 + 240 * q^41 - 86 * q^42 + 6 * q^43 - 128 * q^44 + 4 * q^45 + 16 * q^46 - 14 * q^47 + 7 * q^48 - 28 * q^49 + 23 * q^50 + 66 * q^51 - 286 * q^52 + 10 * q^53 - q^54 + 14 * q^55 + 25 * q^56 - 8 * q^57 + 49 * q^58 + 22 * q^59 - 14 * q^60 - 2 * q^61 - 23 * q^62 + 4 * q^63 + 257 * q^64 - 116 * q^65 - 50 * q^66 + 8 * q^67 + 211 * q^68 + 2 * q^69 + 82 * q^70 + 9 * q^72 + 10 * q^73 - 10 * q^74 + 26 * q^75 + 7 * q^76 - 116 * q^77 - 66 * q^78 - 14 * q^79 - 477 * q^80 - 18 * q^81 - 234 * q^82 - 142 * q^83 - 8 * q^84 + 98 * q^85 + 35 * q^86 - 10 * q^87 - 72 * q^88 + 2 * q^89 + 8 * q^90 + 6 * q^91 - 46 * q^92 - 16 * q^93 - 206 * q^94 - 6 * q^95 - 19 * q^96 - 34 * q^97 + 4 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{23}{37}\right)$

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 $

$2$	0.153732	−	0.0543169i	0.108705	−	0.0384078i	−0.278233	−	0.960513i	$-0.589749\pi$
$2$	0.153732	−	0.0543169i	0.108705	−	0.0384078i	0.386938	+	0.922106i	$0.373533\pi$
$3$	−0.372856	+	0.927889i	−0.215269	+	0.535717i
$3$	−0.372856	+	0.927889i	−0.215269	+	0.535717i
$4$	−1.53539	+	1.23974i	−0.767694	+	0.619870i
$5$	−1.34968	−	2.19202i	−0.603596	−	0.980303i	−0.998112	−	0.0614138i	$-0.980439\pi$
$5$	−1.34968	−	2.19202i	−0.603596	−	0.980303i	0.394516	−	0.918889i	$-0.370912\pi$
$6$	−0.00691984	+	0.162898i	−0.00282501	+	0.0665030i
$7$	0.0153152	−	0.119599i	0.00578861	−	0.0452041i	−0.988749	−	0.149587i	$-0.952206\pi$
$7$	0.0153152	−	0.119599i	0.00578861	−	0.0452041i	0.994537	+	0.104383i	$0.0332867\pi$
$8$	−0.339671	+	0.551660i	−0.120092	+	0.195041i
$9$	−0.721956	−	0.691939i	−0.240652	−	0.230646i
$10$	−0.326553	−	0.263673i	−0.103265	−	0.0833807i
$11$	−0.128682	+	3.02927i	−0.0387990	+	0.913359i	0.869219	+	0.494428i	$0.164622\pi$
$11$	−0.128682	+	3.02927i	−0.0387990	+	0.913359i	−0.908018	+	0.418931i	$0.862405\pi$
$12$	−0.577861	−	1.88691i	−0.166814	−	0.544705i
$13$	−0.287439	−	0.715320i	−0.0797213	−	0.198394i	0.882711	−	0.469917i	$-0.155716\pi$
$13$	−0.287439	−	0.715320i	−0.0797213	−	0.198394i	−0.962432	+	0.271523i	$0.912473\pi$
$14$	−0.00414180	−	0.0192180i	−0.00110694	−	0.00513623i
$15$	2.53719	−	0.435045i	0.655100	−	0.112328i
$16$	0.809262	−	3.75499i	0.202316	−	0.938747i
$17$	0.139995	−	3.29559i	0.0339538	−	0.799299i	−0.898708	−	0.438547i	$-0.855493\pi$
$17$	0.139995	−	3.29559i	0.0339538	−	0.799299i	0.932662	−	0.360752i	$-0.117480\pi$
$18$	−0.148571	−	0.0671585i	−0.0350186	−	0.0158294i
$19$	7.99170	−	2.08088i	1.83342	−	0.477386i	0.835974	−	0.548769i	$-0.184903\pi$
$19$	7.99170	−	2.08088i	1.83342	−	0.477386i	0.997449	+	0.0713832i	$0.0227413\pi$
$20$	4.78983	+	1.69235i	1.07104	+	0.378422i
$21$	0.105264	+	0.0588040i	0.0229705	+	0.0128321i
$22$	0.144758	+	0.472684i	0.0308625	+	0.100777i
$23$	−3.45673	−	5.61408i	−0.720777	−	1.17062i	−0.978867	−	0.204496i	$-0.934445\pi$
$23$	−3.45673	−	5.61408i	−0.720777	−	1.17062i	0.258090	−	0.966121i	$-0.416907\pi$
$24$	−0.385231	−	0.520867i	−0.0786350	−	0.106322i
$25$	−0.732307	+	1.45244i	−0.146461	+	0.290489i
$26$	−0.0830425	−	0.0943546i	−0.0162860	−	0.0185045i
$27$	0.911228	−	0.411901i	0.175366	−	0.0792704i
$28$	0.124757	+	0.202617i	0.0235768	+	0.0382911i
$29$	−0.104122	+	0.483126i	−0.0193349	+	0.0897142i	−0.986193	−	0.165600i	$-0.947044\pi$
$29$	−0.104122	+	0.483126i	−0.0193349	+	0.0897142i	0.966858	+	0.255314i	$0.0821790\pi$
$30$	0.366417	−	0.204693i	0.0668982	−	0.0373716i
$31$	6.48960	−	0.552346i	1.16557	−	0.0992043i	0.513996	−	0.857793i	$-0.328165\pi$
$31$	6.48960	−	0.552346i	1.16557	−	0.0992043i	0.651570	+	0.758588i	$0.274111\pi$
$32$	−0.244126	−	1.90642i	−0.0431558	−	0.337010i
$33$	−2.76285	−	1.24888i	−0.480950	−	0.217403i
$34$	−0.157485	−	0.514241i	−0.0270084	−	0.0881917i
$35$	−0.282834	+	0.127849i	−0.0478077	+	0.0216104i
$36$	1.96631	+	0.167357i	0.327718	+	0.0278929i
$37$	−0.247281	−	5.82118i	−0.0406527	−	0.956996i	−0.897389	−	0.441241i	$-0.854538\pi$
$37$	−0.247281	−	5.82118i	−0.0406527	−	0.956996i	0.856736	−	0.515755i	$-0.172489\pi$
$38$	1.11555	−	0.753981i	0.180966	−	0.122312i
$39$	0.770911			0.123445
$40$	1.66770			0.263687
$41$	−4.53385	+	3.06435i	−0.708068	+	0.478571i	−0.860309	−	0.509773i	$-0.829729\pi$
$41$	−4.53385	+	3.06435i	−0.708068	+	0.478571i	0.152241	+	0.988343i	$0.451351\pi$
$42$	0.0193765	+	0.00332243i	0.00298985	+	0.000512662i
$43$	−0.135830	−	0.269402i	−0.0207138	−	0.0410834i	0.882333	−	0.470626i	$-0.155972\pi$
$43$	−0.135830	−	0.269402i	−0.0207138	−	0.0410834i	−0.903046	+	0.429543i	$0.858675\pi$
$44$	−3.55793	−	4.81064i	−0.536378	−	0.725231i
$45$	−0.542335	+	2.51644i	−0.0808465	+	0.375129i
$46$	−0.836347	−	0.675303i	−0.123313	−	0.0995680i
$47$	2.56717	+	0.668438i	0.374460	+	0.0975017i	0.434447	−	0.900697i	$-0.356944\pi$
$47$	2.56717	+	0.668438i	0.374460	+	0.0975017i	−0.0599872	+	0.998199i	$0.519106\pi$
$48$	3.18247	+	2.15098i	0.459351	+	0.310467i
$49$	6.76006	+	1.76018i	0.965723	+	0.251455i
$50$	−0.0336866	+	0.263063i	−0.00476400	+	0.0372028i
$51$	3.00575	+	1.35868i	0.420889	+	0.190254i
$52$	1.32814	+	0.741945i	0.184180	+	0.102889i
$53$	3.51737	−	3.99651i	0.483148	−	0.548963i	−0.457117	−	0.889407i	$-0.651118\pi$
$53$	3.51737	−	3.99651i	0.483148	−	0.548963i	0.940265	+	0.340444i	$0.110577\pi$
$54$	0.117712	−	0.112817i	0.0160185	−	0.0153525i
$55$	6.81391	−	3.80648i	0.918787	−	0.513265i
$56$	0.0607758	+	0.0490730i	0.00812150	+	0.00655766i
$57$	−1.04893	+	8.19128i	−0.138935	+	1.08496i
$58$	0.0102351	+	0.0799273i	0.00134393	+	0.0104950i
$59$	4.20581	−	13.7334i	0.547550	−	1.78794i	−0.0654519	−	0.997856i	$-0.520849\pi$
$59$	4.20581	−	13.7334i	0.547550	−	1.78794i	0.613002	−	0.790082i	$-0.289962\pi$
$60$	−3.35623	+	3.81342i	−0.433288	+	0.492311i
$61$	1.01686	+	2.53055i	0.130195	+	0.324003i	0.978735	−	0.205128i	$-0.0657611\pi$
$61$	1.01686	+	2.53055i	0.130195	+	0.324003i	−0.848540	+	0.529131i	$0.822518\pi$
$62$	0.967655	−	0.437408i	0.122892	−	0.0555508i
$63$	−0.0938120	+	0.0757479i	−0.0118192	+	0.00954333i
$64$	3.31757	+	6.58000i	0.414696	+	0.822501i
$65$	−1.18005	+	1.59553i	−0.146367	+	0.197901i
$66$	−0.492572	−	0.0419241i	−0.0606315	−	0.00516050i
$67$	−4.84878	+	3.91511i	−0.592372	+	0.478307i	−0.877104	−	0.480300i	$-0.840528\pi$
$67$	−4.84878	+	3.91511i	−0.592372	+	0.478307i	0.284732	+	0.958607i	$0.408095\pi$
$68$	3.87073	+	5.23357i	0.469395	+	0.634664i
$69$	6.49810	−	1.11421i	0.782280	−	0.134135i
$70$	−0.0365362	+	0.0350171i	−0.00436691	+	0.00418535i
$71$	0.876693	−	2.86270i	0.104044	−	0.339740i	−0.888934	−	0.458035i	$-0.848553\pi$
$71$	0.876693	−	2.86270i	0.104044	−	0.339740i	0.992979	+	0.118294i	$0.0377427\pi$
$72$	0.626943	−	0.163243i	0.0738859	−	0.0192384i
$73$	−11.6473	−	6.50655i	−1.36321	−	0.761534i	−0.376870	−	0.926266i	$-0.623000\pi$
$73$	−11.6473	−	6.50655i	−1.36321	−	0.761534i	−0.986338	+	0.164732i	$0.947324\pi$
$74$	−0.354203	−	0.881469i	−0.0411753	−	0.102469i
$75$	−1.07466	−	1.22105i	−0.124091	−	0.140995i
$76$	−9.69062	+	13.1026i	−1.11159	+	1.50297i
$77$	0.360326	+	0.0617841i	0.0410630	+	0.00704095i
$78$	0.118514	−	0.0418735i	0.0134190	−	0.00474124i
$79$	−7.37089	+	4.98185i	−0.829290	+	0.560502i	−0.899445	−	0.437034i	$-0.856029\pi$
$79$	−7.37089	+	4.98185i	−0.829290	+	0.560502i	0.0701553	+	0.997536i	$0.477651\pi$
$80$	−9.32327	+	3.29412i	−1.04237	+	0.368294i
$81$	0.0424412	+	0.999099i	0.00471569	+	0.111011i
$82$	−0.530550	+	0.717352i	−0.0585895	+	0.0792182i
$83$	−0.868262	+	1.72210i	−0.0953042	+	0.189025i	−0.935562	−	0.353162i	$-0.885106\pi$
$83$	−0.868262	+	1.72210i	−0.0953042	+	0.189025i	0.840258	+	0.542187i	$0.182404\pi$
$84$	−0.234523	+	0.0402130i	−0.0255885	+	0.00438759i
$85$	−7.41297	+	4.14113i	−0.804049	+	0.449169i
$86$	−0.0355144	−	0.0340378i	−0.00382961	−	0.00367039i
$87$	−0.409465	−	0.276750i	−0.0438992	−	0.0296707i
$88$	−1.62742	−	1.09994i	−0.173483	−	0.117254i
$89$	1.00552	−	1.63307i	0.106585	−	0.173105i	−0.793826	−	0.608144i	$-0.791914\pi$
$89$	1.00552	−	1.63307i	0.106585	−	0.173105i	0.900411	+	0.435039i	$0.143266\pi$
$90$	0.0533112	+	0.416315i	0.00561950	+	0.0438835i
$91$	−0.0899536	+	0.0234221i	−0.00942970	+	0.00245530i
$92$	12.2674	+	4.33435i	1.27897	+	0.451887i
$93$	−1.90717	+	6.22757i	−0.197765	+	0.645769i
$94$	0.430962	−	0.0366803i	0.0444504	−	0.00378328i
$95$	−15.3476	−	14.7095i	−1.57463	−	1.50916i
$96$	1.85997	+	0.484298i	0.189832	+	0.0494284i
$97$	−6.74297	+	10.9513i	−0.684645	+	1.11193i	0.302660	+	0.953099i	$0.402125\pi$
$97$	−6.74297	+	10.9513i	−0.684645	+	1.11193i	−0.987305	+	0.158836i	$0.949226\pi$
$98$	1.13484	−	0.0965894i	0.114636	−	0.00975700i
$99$	2.18897	−	2.09796i	0.220000	−	0.210853i
$100$	−0.676277	−	3.13794i	−0.0676277	−	0.313794i
$101$	−3.55185	−	4.03569i	−0.353422	−	0.401566i	0.546611	−	0.837387i	$-0.315918\pi$
$101$	−3.55185	−	4.03569i	−0.353422	−	0.401566i	−0.900033	+	0.435821i	$0.856458\pi$
$102$	0.535878	+	0.0456099i	0.0530598	+	0.00451606i
$103$	4.95013	−	12.3189i	0.487751	−	1.21381i	−0.458009	−	0.888948i	$-0.651437\pi$
$103$	4.95013	−	12.3189i	0.487751	−	1.21381i	0.945760	−	0.324867i	$-0.105320\pi$
$104$	0.492249	+	0.0844045i	0.0482689	+	0.00827654i
$105$	−0.0131732	−	0.310108i	−0.00128558	−	0.0302634i
$106$	0.323653	−	0.805443i	0.0314360	−	0.0782315i
$107$	−6.44603	−	12.7849i	−0.623161	−	1.23597i	−0.956106	−	0.293021i	$-0.905340\pi$
$107$	−6.44603	−	12.7849i	−0.623161	−	1.23597i	0.332945	−	0.942946i	$-0.391958\pi$
$108$	−0.888439	+	1.76211i	−0.0854901	+	0.169560i
$109$	−0.903882	−	4.19403i	−0.0865762	−	0.401715i	0.913410	−	0.407042i	$-0.133440\pi$
$109$	−0.903882	−	4.19403i	−0.0865762	−	0.401715i	−0.999986	+	0.00532676i	$0.998304\pi$
$110$	0.840758	−	0.955287i	0.0801631	−	0.0910830i
$111$	5.49361	+	1.94102i	0.521431	+	0.184233i
$112$	−0.436698	−	0.154295i	−0.0412641	−	0.0145795i
$113$	−6.11220	+	6.94481i	−0.574988	+	0.653313i	−0.963367	−	0.268187i	$-0.913576\pi$
$113$	−6.11220	+	6.94481i	−0.574988	+	0.653313i	0.388379	+	0.921500i	$0.373035\pi$
$114$	0.283670	+	1.31623i	0.0265682	+	0.123277i
$115$	−7.64071	+	15.1544i	−0.712500	+	1.41316i
$116$	−0.439083	−	0.870869i	−0.0407678	−	0.0808582i
$117$	−0.287439	+	0.715320i	−0.0265738	+	0.0661314i
$118$	−0.0993895	−	2.33971i	−0.00914955	−	0.215387i
$119$	−0.392005	−	0.0672160i	−0.0359350	−	0.00616168i
$120$	−0.621813	+	1.54744i	−0.0567635	+	0.141261i
$121$	1.80046	+	0.153242i	0.163678	+	0.0139311i
$122$	0.293775	+	0.333793i	0.0265971	+	0.0302202i
$123$	−1.15290	−	5.34947i	−0.103953	−	0.482345i
$124$	−9.27929	+	8.89348i	−0.833305	+	0.798658i
$125$	−8.65256	+	0.736441i	−0.773909	+	0.0658693i
$126$	−0.0103075	+	0.0167404i	−0.000918264	+	0.00149136i
$127$	7.69169	+	2.00276i	0.682527	+	0.177716i	0.577054	−	0.816706i	$-0.304202\pi$
$127$	7.69169	+	2.00276i	0.682527	+	0.177716i	0.105473	+	0.994422i	$0.466364\pi$
$128$	3.64260	+	3.49115i	0.321963	+	0.308577i
$129$	0.300620	−	0.0255865i	0.0264681	−	0.00225277i
$130$	−0.0947465	+	0.309380i	−0.00830982	+	0.0271344i
$131$	−0.100737	−	0.0355928i	−0.00880147	−	0.00310976i	0.328735	−	0.944422i	$-0.393378\pi$
$131$	−0.100737	−	0.0355928i	−0.00880147	−	0.00310976i	−0.337537	+	0.941312i	$0.609594\pi$
$132$	5.79033	−	1.50769i	0.503984	−	0.131227i
$133$	−0.126476	−	0.987667i	−0.0109668	−	0.0856416i
$134$	−0.532754	+	0.865247i	−0.0460229	+	0.0747460i
$135$	−2.13277	−	1.44150i	−0.183559	−	0.124064i
$136$	1.77050	+	1.19665i	0.151819	+	0.102612i
$137$	−0.0180375	−	0.0172875i	−0.00154104	−	0.00147697i	0.691168	−	0.722694i	$-0.257096\pi$
$137$	−0.0180375	−	0.0172875i	−0.00154104	−	0.00147697i	−0.692709	+	0.721217i	$0.743583\pi$
$138$	0.938444	−	0.524246i	0.0798857	−	0.0446268i
$139$	−0.357210	+	0.0612499i	−0.0302982	+	0.00519514i	−0.184130	−	0.982902i	$-0.558947\pi$
$139$	−0.357210	+	0.0612499i	−0.0302982	+	0.00519514i	0.153832	+	0.988097i	$0.450839\pi$
$140$	0.275761	−	0.546939i	0.0233060	−	0.0462247i
$141$	−1.57742	+	2.13281i	−0.132843	+	0.179615i
$142$	−0.0207176	−	0.487708i	−0.00173858	−	0.0409275i
$143$	2.20389	−	0.778682i	0.184298	−	0.0651167i
$144$	−3.18247	+	2.15098i	−0.265206	+	0.179248i
$145$	1.19955	−	0.423829i	0.0996175	−	0.0351971i
$146$	−2.14397	−	0.367620i	−0.177436	−	0.0304245i
$147$	−4.15379	+	5.61629i	−0.342599	+	0.463224i
$148$	7.59642	+	8.63121i	0.624422	+	0.709481i
$149$	−2.59212	−	6.45075i	−0.212355	−	0.528466i	0.783294	−	0.621652i	$-0.213538\pi$
$149$	−2.59212	−	6.45075i	−0.212355	−	0.528466i	−0.995649	+	0.0931859i	$0.970295\pi$
$150$	−0.231533	−	0.129342i	−0.0189046	−	0.0105608i
$151$	−8.72729	+	2.27241i	−0.710217	+	0.184926i	−0.589509	−	0.807762i	$-0.700679\pi$
$151$	−8.72729	+	2.27241i	−0.710217	+	0.184926i	−0.120708	+	0.992688i	$0.538516\pi$
$152$	−1.56661	+	5.11552i	−0.127069	+	0.414923i
$153$	−2.38142	+	2.28241i	−0.192526	+	0.184522i
$154$	0.0587495	−	0.0100736i	0.00473417	−	0.000811754i
$155$	−9.96965	−	13.4799i	−0.800782	−	1.08273i
$156$	−1.18365	+	0.955729i	−0.0947677	+	0.0765196i
$157$	7.76423	+	0.660833i	0.619653	+	0.0527402i	0.390428	−	0.920633i	$-0.372327\pi$
$157$	7.76423	+	0.660833i	0.619653	+	0.0527402i	0.229225	+	0.973374i	$0.426381\pi$
$158$	−0.862540	+	1.16623i	−0.0686200	+	0.0927804i
$159$	2.39684	+	4.75385i	0.190082	+	0.377005i
$160$	−3.84942	+	3.10819i	−0.304323	+	0.245724i
$161$	−0.724377	+	0.327439i	−0.0570889	+	0.0258058i
$162$	0.0607925	+	0.151288i	0.00477631	+	0.0118863i
$163$	5.04151	−	5.72827i	0.394881	−	0.448672i	−0.518927	−	0.854819i	$-0.673668\pi$
$163$	5.04151	−	5.72827i	0.394881	−	0.448672i	0.913808	+	0.406146i	$0.133128\pi$
$164$	3.16223	−	10.3258i	0.246928	−	0.806306i
$165$	0.991379	+	7.74182i	0.0771788	+	0.602700i
$166$	−0.0399406	+	0.311902i	−0.00309999	+	0.0242083i
$167$	12.8472	+	10.3734i	0.994149	+	0.802719i	0.980366	−	0.197186i	$-0.0631802\pi$
$167$	12.8472	+	10.3734i	0.994149	+	0.802719i	0.0137828	+	0.999905i	$0.495613\pi$
$168$	−0.0681949	+	0.0380960i	−0.00526135	+	0.00293917i
$169$	8.95637	−	8.58398i	0.688951	−	0.660306i
$170$	−0.914675	+	1.03927i	−0.0701524	+	0.0797086i
$171$	−7.20950	−	4.02747i	−0.551324	−	0.307988i
$172$	0.542539	+	0.245243i	0.0413682	+	0.0186996i
$173$	0.945612	−	7.38442i	0.0718935	−	0.561427i	−0.915403	−	0.402539i	$-0.868128\pi$
$173$	0.945612	−	7.38442i	0.0718935	−	0.561427i	0.987297	−	0.158888i	$-0.0507910\pi$
$174$	−0.0779799	−	0.0203044i	−0.00591164	−	0.00153927i
$175$	0.162495	+	0.109828i	0.0122835	+	0.00830218i
$176$	11.2707	+	2.93467i	0.849564	+	0.221209i
$177$	11.1749	+	9.02311i	0.839958	+	0.678219i
$178$	0.0658773	−	0.305672i	0.00493771	−	0.0229111i
$179$	−11.0889	−	14.9931i	−0.828821	−	1.12064i	−0.990998	−	0.133879i	$-0.957257\pi$
$179$	−11.0889	−	14.9931i	−0.828821	−	1.12064i	0.162176	−	0.986762i	$-0.448149\pi$
$180$	−2.28704	−	4.53607i	−0.170466	−	0.338099i
$181$	6.23733	+	1.06950i	0.463617	+	0.0794951i	0.396069	−	0.918221i	$-0.370374\pi$
$181$	6.23733	+	1.06950i	0.463617	+	0.0794951i	0.0675484	+	0.997716i	$0.478482\pi$
$182$	−0.0125565	+	0.00848672i	−0.000930750	+	0.000629077i
$183$	−2.72721			−0.201601
$184$	4.27121			0.314878
$185$	−12.4264	+	8.39879i	−0.913609	+	0.617492i
$186$	0.0450693	+	1.06097i	0.00330464	+	0.0777939i
$187$	9.96523	+	0.848166i	0.728729	+	0.0620240i
$188$	−4.77029	+	2.15631i	−0.347909	+	0.157265i
$189$	−0.0353072	−	0.115290i	−0.00256822	−	0.00838613i
$190$	−3.15839	−	1.42768i	−0.229133	−	0.103575i
$191$	−0.154029	−	1.20284i	−0.0111452	−	0.0870342i	0.985373	−	0.170413i	$-0.0545101\pi$
$191$	−0.154029	−	1.20284i	−0.0111452	−	0.0870342i	−0.996518	+	0.0833784i	$0.973429\pi$
$192$	−7.34249	+	0.624938i	−0.529899	+	0.0451010i
$193$	−3.59992	+	2.01104i	−0.259128	+	0.144758i	−0.611858	−	0.790967i	$-0.709578\pi$
$193$	−3.59992	+	2.01104i	−0.259128	+	0.144758i	0.352730	+	0.935725i	$0.385253\pi$
$194$	−0.441769	+	2.04982i	−0.0317172	+	0.147168i
$195$	−1.04049	−	1.68986i	−0.0745107	−	0.121013i
$196$	−12.5615	+	5.67815i	−0.897249	+	0.405582i
$197$	14.9716	+	17.0110i	1.06668	+	1.21198i	0.976378	+	0.216069i	$0.0693235\pi$
$197$	14.9716	+	17.0110i	1.06668	+	1.21198i	0.0903013	+	0.995914i	$0.471217\pi$
$198$	0.222560	−	0.441421i	0.0158166	−	0.0313704i
$199$	14.1436	+	19.1234i	1.00261	+	1.35562i	0.933722	+	0.358000i	$0.116541\pi$
$199$	14.1436	+	19.1234i	1.00261	+	1.35562i	0.0688927	+	0.997624i	$0.478053\pi$
$200$	−0.552513	−	0.897337i	−0.0390685	−	0.0634513i
$201$	−1.82489	−	5.95890i	−0.128718	−	0.420308i
$202$	−0.765238	−	0.427487i	−0.0538419	−	0.0300779i
$203$	0.0561866	+	0.0198520i	0.00394353	+	0.00139334i
$204$	−6.29940	+	1.64024i	−0.441046	+	0.114840i
$205$	12.8364	+	5.80241i	0.896531	+	0.405258i
$206$	0.0918694	−	2.16268i	0.00640084	−	0.150681i
$207$	−1.38900	+	6.44496i	−0.0965419	+	0.447956i
$208$	−2.91863	+	0.500450i	−0.202371	+	0.0347000i
$209$	5.27515	+	24.4768i	0.364890	+	1.69310i
$210$	−0.0188692	−	0.0469579i	−0.00130210	−	0.00324040i
$211$	1.30140	+	4.24950i	0.0895918	+	0.292548i	0.989708	−	0.143102i	$-0.0457077\pi$
$211$	1.30140	+	4.24950i	0.0895918	+	0.292548i	−0.900116	+	0.435650i	$0.856519\pi$
$212$	−0.445899	+	10.4968i	−0.0306245	+	0.720924i
$213$	2.32939	+	1.88085i	0.159607	+	0.128874i
$214$	−1.68540	−	1.61532i	−0.115211	−	0.110421i
$215$	−0.407209	+	0.661349i	−0.0277714	+	0.0451036i
$216$	−0.0822881	+	0.642599i	−0.00559899	+	0.0437234i
$217$	0.0333297	−	0.784607i	0.00226257	−	0.0532626i
$218$	−0.366762	−	0.595659i	−0.0248402	−	0.0403431i
$219$	10.3801	−	8.38136i	0.701423	−	0.566360i
$220$	−5.74296	+	14.2919i	−0.387190	+	0.963559i
$221$	−2.39765	+	0.847142i	−0.161283	+	0.0569849i
$222$	0.949972			0.0637580
$223$	3.01565	−	14.6255i	0.201943	−	0.979397i
$223$	3.01565	−	14.6255i	0.201943	−	0.979397i
$224$	−0.231744			−0.0154840
$225$	1.53370	−	0.541889i	0.102246	−	0.0361260i
$226$	−0.562419	+	1.39963i	−0.0374115	+	0.0931022i
$227$	−21.6334	+	17.4677i	−1.43586	+	1.15937i	−0.475807	+	0.879550i	$0.657844\pi$
$227$	−21.6334	+	17.4677i	−1.43586	+	1.15937i	−0.960051	+	0.279825i	$0.909724\pi$
$228$	−8.54454	−	13.8772i	−0.565876	−	0.919041i
$229$	0.662009	−	15.5842i	0.0437468	−	1.02983i	−0.834316	−	0.551287i	$-0.814137\pi$
$229$	0.662009	−	15.5842i	0.0437468	−	1.02983i	0.878063	−	0.478546i	$-0.158836\pi$
$230$	−0.351478	+	2.74474i	−0.0231757	+	0.180983i
$231$	−0.191679	+	0.311306i	−0.0126115	+	0.0204824i
$232$	−0.231154	−	0.221543i	−0.0151760	−	0.0145450i
$233$	−10.3140	−	8.32798i	−0.675693	−	0.545584i	0.228055	−	0.973648i	$-0.426763\pi$
$233$	−10.3140	−	8.32798i	−0.675693	−	0.545584i	−0.903748	+	0.428064i	$0.859196\pi$
$234$	−0.00533458	+	0.125580i	−0.000348732	+	0.00820943i
$235$	−1.99963	−	6.52947i	−0.130441	−	0.425936i
$236$	10.5683	+	26.3002i	0.687938	+	1.71200i
$237$	−1.87432	−	8.69688i	−0.121750	−	0.564923i
$238$	−0.0639145	+	0.0109592i	−0.00414296	+	0.000710383i
$239$	5.79429	−	26.8856i	0.374802	−	1.73909i	−0.259264	−	0.965807i	$-0.583480\pi$
$239$	5.79429	−	26.8856i	0.374802	−	1.73909i	0.634066	−	0.773279i	$-0.281385\pi$
$240$	0.419663	−	9.87920i	0.0270891	−	0.637699i
$241$	22.8468	+	10.3274i	1.47169	+	0.665246i	0.978795	−	0.204843i	$-0.0656684\pi$
$241$	22.8468	+	10.3274i	1.47169	+	0.665246i	0.492895	+	0.870089i	$0.335939\pi$
$242$	0.285112	−	0.0742373i	0.0183277	−	0.00477215i
$243$	−0.942877	−	0.333140i	−0.0604856	−	0.0213709i
$244$	−4.69849	−	2.62473i	−0.300790	−	0.168031i
$245$	−5.26557	−	17.1939i	−0.336405	−	1.09848i
$246$	−0.467804	−	0.759761i	−0.0298261	−	0.0484406i
$247$	−3.78562	−	5.11850i	−0.240874	−	0.325682i
$248$	−1.89962	+	3.76767i	−0.120626	+	0.239247i
$249$	−1.27418	−	1.44775i	−0.0807476	−	0.0917471i
$250$	−1.29017	+	0.583194i	−0.0815976	+	0.0368845i
$251$	8.72224	+	14.1658i	0.550543	+	0.894138i	1.00000		0.000836213i	$0.000266175\pi$
$251$	8.72224	+	14.1658i	0.550543	+	0.894138i	−0.449457	+	0.893302i	$0.648382\pi$
$252$	0.0501302	−	0.232605i	0.00315790	−	0.0146527i
$253$	17.4514	−	9.74892i	1.09716	−	0.612909i
$254$	1.29124	−	0.109901i	0.0810196	−	0.00689579i
$255$	−1.07854	−	8.42246i	−0.0675407	−	0.527435i
$256$	−12.6801	−	5.73179i	−0.792509	−	0.358237i
$257$	4.17805	+	13.6428i	0.260619	+	0.851012i	0.986580	+	0.163276i	$0.0522061\pi$
$257$	4.17805	+	13.6428i	0.260619	+	0.851012i	−0.725961	+	0.687736i	$0.758605\pi$
$258$	0.0448250	−	0.0202622i	0.00279069	−	0.00126147i
$259$	−0.699993	−	0.0595782i	−0.0434955	−	0.00370201i
$260$	−0.166210	−	3.91271i	−0.0103079	−	0.242656i
$261$	0.409465	−	0.276750i	0.0253452	−	0.0171304i
$262$	−0.0174198			−0.00107620
$263$	15.3847			0.948663			0.474332	−	0.880346i	$-0.342690\pi$
$263$	15.3847			0.948663			0.474332	+	0.880346i	$0.342690\pi$
$264$	1.62742	−	1.09994i	0.100161	−	0.0676968i
$265$	−13.5078	−	2.31614i	−0.829776	−	0.142279i
$266$	−0.0730903	−	0.144966i	−0.00448145	−	0.00888843i
$267$	1.14039	+	1.54191i	0.0697909	+	0.0943636i
$268$	2.59103	−	12.0224i	0.158273	−	0.734387i
$269$	−9.43073	−	7.61478i	−0.575002	−	0.464282i	0.296255	−	0.955109i	$-0.404262\pi$
$269$	−9.43073	−	7.61478i	−0.575002	−	0.464282i	−0.871257	+	0.490827i	$0.836695\pi$
$270$	−0.406172	−	0.105759i	−0.0247188	−	0.00643628i
$271$	−16.1645	−	10.9253i	−0.981925	−	0.663666i	−0.0398986	−	0.999204i	$-0.512703\pi$
$271$	−16.1645	−	10.9253i	−0.981925	−	0.663666i	−0.942027	+	0.335538i	$0.891082\pi$
$272$	−12.2616	−	3.19268i	−0.743470	−	0.193585i
$273$	0.0118067	−	0.0922001i	0.000714573	−	0.00558020i
$274$	−0.00371193	−	0.00167790i	−0.000224246	−	0.000101366i
$275$	−4.30561	−	2.40526i	−0.259638	−	0.145042i
$276$	−8.59578	+	9.76671i	−0.517405	+	0.587887i
$277$	8.40281	−	8.05344i	0.504876	−	0.483884i	−0.395824	−	0.918326i	$-0.629541\pi$
$277$	8.40281	−	8.05344i	0.504876	−	0.483884i	0.900700	+	0.434442i	$0.143054\pi$
$278$	−0.0515876	+	0.0288186i	−0.00309402	+	0.00172842i
$279$	−5.06739	−	4.09163i	−0.303377	−	0.244960i
$280$	0.0255412	−	0.199455i	0.00152638	−	0.0119197i
$281$	1.12593	+	8.79255i	0.0671674	+	0.524520i	0.990185	+	0.139762i	$0.0446338\pi$
$281$	1.12593	+	8.79255i	0.0671674	+	0.524520i	−0.923018	+	0.384757i	$0.874285\pi$
$282$	−0.126652	+	0.413562i	−0.00754201	+	0.0246272i
$283$	−13.2266	+	15.0283i	−0.786238	+	0.893340i	−0.996439	−	0.0843180i	$-0.973129\pi$
$283$	−13.2266	+	15.0283i	−0.786238	+	0.893340i	0.210201	+	0.977658i	$0.432588\pi$
$284$	2.20294	+	5.48223i	0.130721	+	0.325311i
$285$	19.3712	−	8.75634i	1.14745	−	0.518681i
$286$	0.296511	−	0.239416i	0.0175331	−	0.0141570i
$287$	0.297055	+	0.589174i	0.0175346	+	0.0347778i
$288$	−1.14288	+	1.54527i	−0.0673446	+	0.0910559i
$289$	6.09742	+	0.518967i	0.358672	+	0.0305275i
$290$	0.161388	−	0.130312i	0.00947705	−	0.00765218i
$291$	−7.64742	−	10.3400i	−0.448300	−	0.606141i
$292$	25.9495	−	4.44949i	1.51858	−	0.260387i
$293$	9.96341	−	9.54916i	0.582069	−	0.557868i	−0.342192	−	0.939630i	$-0.611169\pi$
$293$	9.96341	−	9.54916i	0.582069	−	0.557868i	0.924260	+	0.381762i	$0.124683\pi$
$294$	−0.333509	+	1.08902i	−0.0194507	+	0.0635131i
$295$	−35.7805	+	9.31651i	−2.08322	+	0.542428i
$296$	3.29531	+	1.84087i	0.191536	+	0.106998i
$297$	1.13050	+	2.81336i	0.0655983	+	0.163248i
$298$	−0.748876	−	0.850889i	−0.0433812	−	0.0492907i
$299$	−3.02227	+	4.08637i	−0.174782	+	0.236321i
$300$	3.16381	+	0.542490i	0.182663	+	0.0313207i
$301$	−0.0343004	+	0.0121191i	−0.00197704	+	0.000698533i
$302$	−1.21823	+	0.823380i	−0.0701013	+	0.0473802i
$303$	5.06900	−	1.79099i	0.291206	−	0.102890i
$304$	−1.34629	−	31.6927i	−0.0772151	−	1.81770i
$305$	4.17458	−	5.64441i	0.239036	−	0.323198i
$306$	−0.242127	+	0.480229i	−0.0138415	+	0.0274529i
$307$	−8.97538	+	1.53898i	−0.512252	+	0.0878344i	−0.419321	−	0.907838i	$-0.637732\pi$
$307$	−8.97538	+	1.53898i	−0.512252	+	0.0878344i	−0.0929312	+	0.995673i	$0.529624\pi$
$308$	−0.629837	+	0.351848i	−0.0358883	+	0.0200484i
$309$	9.58486	+	9.18635i	0.545264	+	0.522593i
$310$	−2.26484	−	1.53076i	−0.128634	−	0.0869414i
$311$	17.2933	+	11.6883i	0.980616	+	0.662781i	0.941697	−	0.336462i	$-0.109230\pi$
$311$	17.2933	+	11.6883i	0.980616	+	0.662781i	0.0389186	+	0.999242i	$0.487609\pi$
$312$	−0.261856	+	0.425281i	−0.0148247	+	0.0240768i
$313$	0.464334	+	3.62605i	0.0262457	+	0.204957i	0.999715	−	0.0238598i	$-0.00759553\pi$
$313$	0.464334	+	3.62605i	0.0262457	+	0.204957i	−0.973470	+	0.228816i	$0.926514\pi$
$314$	1.22950	−	0.320137i	0.0693848	−	0.0180664i
$315$	0.292658	+	0.103402i	0.0164894	+	0.00582607i
$316$	5.14098	−	16.7871i	0.289203	−	0.944346i
$317$	−18.2510	+	1.55339i	−1.02508	+	0.0872469i	−0.585264	−	0.810843i	$-0.699009\pi$
$317$	−18.2510	+	1.55339i	−1.02508	+	0.0872469i	−0.439812	+	0.898090i	$0.644955\pi$
$318$	0.626685	+	0.600629i	0.0351428	+	0.0336816i
$319$	−1.45012	−	0.377582i	−0.0811911	−	0.0211405i
$320$	9.94586	−	16.1531i	0.555991	−	0.902986i
$321$	14.2665	−	1.21425i	0.796276	−	0.0677731i
$322$	−0.0935743	+	0.0896837i	−0.00521469	+	0.00499788i
$323$	−5.73893	−	26.6287i	−0.319323	−	1.48166i
$324$	−1.30379	−	1.48139i	−0.0724326	−	0.0822994i
$325$	1.24946	+	0.106344i	0.0693074	+	0.00589893i
$326$	0.463898	−	1.15446i	0.0256929	−	0.0639394i
$327$	4.22861	+	0.725068i	0.233843	+	0.0400963i
$328$	−0.150463	−	3.54201i	−0.00830792	−	0.195575i
$329$	0.119261	−	0.296793i	0.00657508	−	0.0163627i
$330$	0.572918	+	1.13631i	0.0315381	+	0.0625521i
$331$	−5.71786	+	11.3407i	−0.314282	+	0.623341i	−0.993907	−	0.110218i	$-0.964845\pi$
$331$	−5.71786	+	11.3407i	−0.314282	+	0.623341i	0.679625	+	0.733559i	$0.262142\pi$
$332$	−0.801830	−	3.72050i	−0.0440061	−	0.204189i
$333$	−3.84938	+	4.37374i	−0.210945	+	0.239680i
$334$	2.53848	+	0.896902i	0.138899	+	0.0490763i
$335$	15.1263	+	5.34447i	0.826440	+	0.292000i
$336$	0.305995	−	0.347677i	0.0166934	−	0.0189674i
$337$	−2.47137	−	11.4672i	−0.134624	−	0.624659i	−0.993630	−	0.112693i	$-0.964052\pi$
$337$	−2.47137	−	11.4672i	−0.134624	−	0.624659i	0.859006	−	0.511966i	$-0.171083\pi$
$338$	0.910623	−	1.80611i	0.0495313	−	0.0982395i
$339$	−4.16504	−	8.26086i	−0.226214	−	0.448668i
$340$	6.24786	−	15.5484i	0.338838	−	0.843230i
$341$	0.838112	+	19.7298i	0.0453863	+	1.06843i
$342$	−1.32709	−	0.227552i	−0.0717607	−	0.0123046i
$343$	0.628749	−	1.56470i	0.0339492	−	0.0844859i
$344$	0.194756	+	0.0165762i	0.0105005	+	0.000893726i
$345$	−11.2128	−	12.7402i	−0.603675	−	0.685908i
$346$	−0.255728	−	1.18658i	−0.0137480	−	0.0637910i
$347$	19.0083	−	18.2180i	1.02042	−	0.977994i	0.0206585	−	0.999787i	$-0.493424\pi$
$347$	19.0083	−	18.2180i	1.02042	−	0.977994i	0.999763	+	0.0217922i	$0.00693723\pi$
$348$	0.971785	−	0.0827111i	0.0520931	−	0.00443378i
$349$	−8.60387	+	13.9736i	−0.460554	+	0.747988i	−0.995281	−	0.0970374i	$-0.969063\pi$
$349$	−8.60387	+	13.9736i	−0.460554	+	0.747988i	0.534726	+	0.845025i	$0.320415\pi$
$350$	0.0309461	+	0.00805775i	0.00165414	+	0.000430705i
$351$	−0.556564	−	0.533424i	−0.0297072	−	0.0284720i
$352$	5.80646	−	0.494203i	0.309485	−	0.0263411i
$353$	7.53619	−	24.6082i	0.401111	−	1.30976i	−0.496140	−	0.868243i	$-0.665250\pi$
$353$	7.53619	−	24.6082i	0.401111	−	1.30976i	0.897251	−	0.441521i	$-0.145561\pi$
$354$	2.20805	+	0.780152i	0.117356	+	0.0414646i
$355$	−7.45837	+	1.94201i	−0.395849	+	0.103071i
$356$	0.480716	+	3.75398i	0.0254779	+	0.198961i
$357$	0.208531	−	0.338675i	0.0110366	−	0.0179246i
$358$	−2.51909	−	1.70261i	−0.133138	−	0.0899857i
$359$	0.645484	+	0.436271i	0.0340673	+	0.0230255i	0.576890	−	0.816822i	$-0.304266\pi$
$359$	0.645484	+	0.436271i	0.0340673	+	0.0230255i	−0.542823	+	0.839847i	$0.682644\pi$
$360$	−1.20401	−	1.15395i	−0.0634567	−	0.0608183i
$361$	42.9500	−	23.9933i	2.26053	−	1.26281i
$362$	1.01697	−	0.174377i	0.0534506	−	0.00916503i
$363$	−0.813505	+	1.61349i	−0.0426979	+	0.0846863i
$364$	0.109076	−	0.147481i	0.00571716	−	0.00773011i
$365$	1.45759	+	34.3129i	0.0762939	+	1.79602i
$366$	−0.419258	+	0.148133i	−0.0219150	+	0.00774306i
$367$	−16.5430	+	11.1811i	−0.863538	+	0.583650i	−0.909692	−	0.415284i	$-0.863682\pi$
$367$	−16.5430	+	11.1811i	−0.863538	+	0.583650i	0.0461535	+	0.998934i	$0.485304\pi$
$368$	−23.8782	+	8.43671i	−1.24474	+	0.439794i
$369$	5.39358	+	0.924822i	0.280779	+	0.0481443i
$370$	−1.45414	+	1.96613i	−0.0755971	+	0.102214i
$371$	−0.424108	−	0.481881i	−0.0220186	−	0.0250180i
$372$	−4.79232	−	11.9261i	−0.248470	−	0.618341i
$373$	15.7243	+	8.78411i	0.814173	+	0.454824i	0.838514	−	0.544880i	$-0.183425\pi$
$373$	15.7243	+	8.78411i	0.814173	+	0.454824i	−0.0243416	+	0.999704i	$0.507749\pi$
$374$	1.57804	−	0.410890i	0.0815985	−	0.0212466i
$375$	2.54283	−	8.30320i	0.131311	−	0.428776i
$376$	−1.24074	+	1.18916i	−0.0639864	+	0.0613260i
$377$	0.375518	−	0.0643890i	0.0193402	−	0.00331620i
$378$	−0.0116900	−	0.0158060i	−0.000601271	−	0.000812972i
$379$	22.4012	−	18.0877i	1.15067	−	0.929104i	0.152428	−	0.988315i	$-0.451291\pi$
$379$	22.4012	−	18.0877i	1.15067	−	0.929104i	0.998246	+	0.0592103i	$0.0188582\pi$
$380$	41.8005	+	3.55774i	2.14432	+	0.182508i
$381$	−4.72624	+	6.39029i	−0.242132	+	0.327385i
$382$	−0.0890134	−	0.176548i	−0.00455432	−	0.00903296i
$383$	25.7419	−	20.7851i	1.31535	−	1.06207i	0.322021	−	0.946733i	$-0.395638\pi$
$383$	25.7419	−	20.7851i	1.31535	−	1.06207i	0.993326	−	0.115336i	$-0.0367946\pi$
$384$	−4.59756	+	2.07823i	−0.234618	+	0.106054i
$385$	−0.350894	−	0.873232i	−0.0178832	−	0.0445040i
$386$	−0.444189	+	0.504697i	−0.0226086	+	0.0256884i
$387$	−0.0883467	+	0.288482i	−0.00449091	+	0.0146644i
$388$	−3.22366	−	25.1740i	−0.163656	−	1.27802i
$389$	−2.80359	+	21.8936i	−0.142147	+	1.11005i	0.751005	+	0.660296i	$0.229569\pi$
$389$	−2.80359	+	21.8936i	−0.142147	+	1.11005i	−0.893153	+	0.449754i	$0.851512\pi$
$390$	−0.251743	−	0.203269i	−0.0127475	−	0.0102929i
$391$	−18.9856	+	10.6060i	−0.960145	+	0.536369i
$392$	−3.26722	+	3.13137i	−0.165019	+	0.158158i
$393$	0.0705868	−	0.0802022i	0.00356063	−	0.00404566i
$394$	3.22559	+	1.80192i	0.162503	+	0.0907795i
$395$	20.8687	+	9.43324i	1.05002	+	0.474638i
$396$	−0.759998	+	5.93494i	−0.0381914	+	0.298242i
$397$	−36.2411	−	9.43644i	−1.81889	−	0.473601i	−0.823313	−	0.567588i	$-0.807877\pi$
$397$	−36.2411	−	9.43644i	−1.81889	−	0.473601i	−0.995573	+	0.0939865i	$0.970039\pi$
$398$	3.21305	+	2.17164i	0.161055	+	0.108855i
$399$	0.963603	+	0.250903i	0.0482405	+	0.0125608i
$400$	4.86128	+	3.92521i	0.243064	+	0.196261i
$401$	−6.75961	+	31.3647i	−0.337559	+	1.56628i	0.416290	+	0.909232i	$0.363330\pi$
$401$	−6.75961	+	31.3647i	−0.337559	+	1.56628i	−0.753849	+	0.657047i	$0.771805\pi$
$402$	−0.604213	−	0.816949i	−0.0301354	−	0.0407457i
$403$	−2.26047	−	4.48337i	−0.112602	−	0.223333i
$404$	10.4567	+	1.79298i	0.520239	+	0.0892039i
$405$	2.13277	−	1.44150i	0.105978	−	0.0716286i
$406$	0.00971596			0.000482195
$407$	17.6657			0.875659
$408$	−1.77050	+	1.19665i	−0.0876526	+	0.0592428i
$409$	1.35450	+	31.8860i	0.0669758	+	1.57666i	0.647274	+	0.762258i	$0.275909\pi$
$409$	1.35450	+	31.8860i	0.0669758	+	1.57666i	−0.580298	+	0.814404i	$0.697064\pi$
$410$	2.28853	+	0.194782i	0.113022	+	0.00961961i
$411$	0.0227663	−	0.0102910i	0.00112298	−	0.000507618i
$412$	7.67182	+	25.0511i	0.377964	+	1.23418i
$413$	−1.57809	−	0.713340i	−0.0776525	−	0.0351012i
$414$	0.136537	+	1.06624i	0.00671045	+	0.0524029i
$415$	4.94675	−	0.421031i	0.242827	−	0.0206676i
$416$	−1.29353	+	0.722607i	−0.0634204	+	0.0354287i
$417$	0.0763551	−	0.354289i	0.00373913	−	0.0173496i
$418$	2.14046	+	3.47633i	0.104693	+	0.170033i
$419$	−27.2611	+	12.3228i	−1.33179	+	0.602007i	−0.947071	−	0.321026i	$-0.895972\pi$
$419$	−27.2611	+	12.3228i	−1.33179	+	0.602007i	−0.384721	+	0.923033i	$0.625702\pi$
$420$	0.404679	+	0.459805i	0.0197463	+	0.0224362i
$421$	−2.35912	+	4.67903i	−0.114976	+	0.228042i	−0.943104	−	0.332497i	$-0.892109\pi$
$421$	−2.35912	+	4.67903i	−0.114976	+	0.228042i	0.828128	+	0.560539i	$0.189406\pi$
$422$	0.430885	+	0.582596i	0.0209752	+	0.0283603i
$423$	−1.39086	−	2.25891i	−0.0676261	−	0.109832i
$424$	1.00997	+	3.29789i	0.0490484	+	0.160160i
$425$	4.68415	+	2.61672i	0.227214	+	0.126930i
$426$	0.460263	+	0.162621i	0.0222998	+	0.00787903i
$427$	0.318224	−	0.0828590i	0.0153999	−	0.00400983i
$428$	25.7472	+	11.6385i	1.24454	+	0.562566i
$429$	−0.0992022	+	2.33530i	−0.00478953	+	0.112749i
$430$	−0.0266785	+	0.123789i	−0.00128655	+	0.00596961i
$431$	13.1643	−	2.25725i	0.634102	−	0.108728i	0.157033	−	0.987593i	$-0.449807\pi$
$431$	13.1643	−	2.25725i	0.634102	−	0.108728i	0.477069	+	0.878866i	$0.341699\pi$
$432$	−0.809262	−	3.75499i	−0.0389356	−	0.180662i
$433$	0.913635	+	2.27367i	0.0439065	+	0.109266i	0.948233	−	0.317577i	$-0.102869\pi$
$433$	0.913635	+	2.27367i	0.0439065	+	0.109266i	−0.904326	+	0.426842i	$0.859626\pi$
$434$	−0.0374936	−	0.122429i	−0.00179975	−	0.00587680i
$435$	−0.0539948	+	1.27108i	−0.00258885	+	0.0609436i
$436$	6.58731	+	5.31888i	0.315475	+	0.254728i
$437$	−39.3073	−	37.6730i	−1.88033	−	1.80215i
$438$	1.14050	−	1.85230i	0.0544954	−	0.0885061i
$439$	5.12271	−	40.0040i	0.244494	−	1.90929i	−0.147054	−	0.989129i	$-0.546979\pi$
$439$	5.12271	−	40.0040i	0.244494	−	1.90929i	0.391547	−	0.920158i	$-0.371940\pi$
$440$	−0.214603	+	5.05191i	−0.0102308	+	0.240840i
$441$	−3.66253	−	5.94832i	−0.174406	−	0.283254i
$442$	−0.322580	+	0.260465i	−0.0153436	+	0.0123891i
$443$	−7.33218	+	18.2468i	−0.348362	+	0.866933i	0.646236	+	0.763137i	$0.276342\pi$
$443$	−7.33218	+	18.2468i	−0.348362	+	0.866933i	−0.994599	+	0.103796i	$0.966901\pi$
$444$	−10.8412	+	3.83043i	−0.514500	+	0.181784i
$445$	−4.93687			−0.234030
$446$	−0.330811	−	2.41221i	−0.0156644	−	0.114221i
$447$	6.95207			0.328822
$448$	0.837770	−	0.296003i	0.0395809	−	0.0139848i
$449$	−1.58792	+	3.95168i	−0.0749385	+	0.186492i	−0.960661	−	0.277723i	$-0.910420\pi$
$449$	−1.58792	+	3.95168i	−0.0749385	+	0.186492i	0.885723	+	0.464215i	$0.153663\pi$
$450$	0.206344	−	0.166611i	0.00972715	−	0.00785412i
$451$	−8.69931	−	14.1286i	−0.409634	−	0.665288i
$452$	0.774848	−	18.2405i	0.0364458	−	0.857962i
$453$	1.14548	−	8.94524i	0.0538195	−	0.420284i
$454$	−2.37694	+	3.86040i	−0.111556	+	0.181178i
$455$	0.172751	+	0.165568i	0.00809868	+	0.00776195i
$456$	−4.16251	−	3.36100i	−0.194928	−	0.157393i
$457$	−0.434000	+	10.2167i	−0.0203016	+	0.477917i	0.959951	+	0.280168i	$0.0903901\pi$
$457$	−0.434000	+	10.2167i	−0.0203016	+	0.477917i	−0.980253	+	0.197749i	$0.936637\pi$
$458$	−0.744713	−	2.43174i	−0.0347982	−	0.113628i
$459$	−1.22989	−	3.06070i	−0.0574064	−	0.142861i
$460$	−7.05611	−	32.7405i	−0.328993	−	1.52653i
$461$	−9.40953	+	1.61343i	−0.438246	+	0.0751447i	−0.383894	−	0.923377i	$-0.625417\pi$
$461$	−9.40953	+	1.61343i	−0.438246	+	0.0751447i	−0.0543514	+	0.998522i	$0.517309\pi$
$462$	−0.0125579	+	0.0582690i	−0.000584248	+	0.00271092i
$463$	0.858755	−	20.2158i	0.0399098	−	0.939507i	−0.861822	−	0.507211i	$-0.830677\pi$
$463$	0.858755	−	20.2158i	0.0399098	−	0.939507i	0.901732	−	0.432296i	$-0.142296\pi$
$464$	1.72987	+	0.781950i	0.0803072	+	0.0363011i
$465$	16.2251	−	4.22468i	0.752419	−	0.195915i
$466$	−2.03794	−	0.720050i	−0.0944057	−	0.0333557i
$467$	−7.54530	−	4.21506i	−0.349155	−	0.195050i	0.303267	−	0.952906i	$-0.401923\pi$
$467$	−7.54530	−	4.21506i	−0.349155	−	0.195050i	−0.652422	+	0.757856i	$0.726247\pi$
$468$	−0.445480	−	1.45464i	−0.0205923	−	0.0672410i
$469$	0.393983	+	0.639868i	0.0181924	+	0.0295464i
$470$	−0.662067	−	0.895173i	−0.0305389	−	0.0412913i
$471$	−3.50812	+	6.95795i	−0.161646	+	0.320605i
$472$	6.14759	+	6.98501i	0.282966	+	0.321511i
$473$	0.833570	−	0.376797i	0.0383276	−	0.0173252i
$474$	−0.760530	−	1.23518i	−0.0349323	−	0.0567336i
$475$	−2.83002	+	13.1313i	−0.129850	+	0.602507i
$476$	0.685210	−	0.382781i	0.0314066	−	0.0175448i
$477$	−5.30473	+	0.451499i	−0.242887	+	0.0206727i
$478$	−0.569576	−	4.44790i	−0.0260518	−	0.203442i
$479$	−9.54177	−	4.31315i	−0.435975	−	0.197073i	0.181954	−	0.983307i	$-0.441758\pi$
$479$	−9.54177	−	4.31315i	−0.435975	−	0.197073i	−0.617929	+	0.786234i	$0.712028\pi$
$480$	−1.44877	−	4.73074i	−0.0661271	−	0.215928i
$481$	−4.09293	+	1.85012i	−0.186622	+	0.0843583i
$482$	4.07322	+	0.346682i	0.185530	+	0.0157910i
$483$	−0.0337385	−	0.794230i	−0.00153515	−	0.0361387i
$484$	−2.95439	+	1.99682i	−0.134290	+	0.0907644i
$485$	33.1064			1.50328
$486$	−0.163045			−0.00739588
$487$	35.0868	−	23.7145i	1.58994	−	1.07461i	0.637247	−	0.770660i	$-0.280073\pi$
$487$	35.0868	−	23.7145i	1.58994	−	1.07461i	0.952688	−	0.303949i	$-0.0983052\pi$
$488$	−1.74140	−	0.298593i	−0.0788294	−	0.0135167i
$489$	3.43544	+	6.81378i	0.155356	+	0.308130i
$490$	−1.74340	−	2.35724i	−0.0787590	−	0.106489i
$491$	−0.292136	+	1.35551i	−0.0131839	+	0.0611735i	−0.983669	−	0.179989i	$-0.942394\pi$
$491$	−0.292136	+	1.35551i	−0.0131839	+	0.0611735i	0.970485	+	0.241163i	$0.0775288\pi$
$492$	8.40210	+	6.78422i	0.378796	+	0.305856i
$493$	1.57761	+	0.410777i	0.0710519	+	0.0185005i
$494$	−0.859991	−	0.581253i	−0.0386928	−	0.0261518i
$495$	−7.55319	−	1.96670i	−0.339491	−	0.0883965i
$496$	3.17773	−	24.8154i	0.142684	−	1.11424i
$497$	−0.328949	−	0.148694i	−0.0147554	−	0.00666985i
$498$	−0.274518	−	0.153355i	−0.0123015	−	0.00687201i
$499$	−26.7551	+	30.3997i	−1.19772	+	1.36088i	−0.281824	+	0.959466i	$0.590939\pi$
$499$	−26.7551	+	30.3997i	−1.19772	+	1.36088i	−0.915898	+	0.401411i	$0.868520\pi$
$500$	12.3720	−	11.8576i	0.553295	−	0.530290i
$501$	−14.4156	+	8.05301i	−0.644040	+	0.359782i
$502$	2.11033	+	1.70397i	0.0941885	+	0.0760519i
$503$	2.03288	−	15.8751i	0.0906417	−	0.707834i	−0.881291	−	0.472574i	$-0.843325\pi$
$503$	2.03288	−	15.8751i	0.0906417	−	0.707834i	0.971932	−	0.235260i	$-0.0755941\pi$
$504$	−0.00992192	−	0.0774817i	−0.000441957	−	0.00345131i
$505$	−4.05245	+	13.2326i	−0.180332	+	0.588845i
$506$	2.15330	−	2.44662i	0.0957258	−	0.108766i
$507$	4.62554	+	11.5111i	0.205428	+	0.511226i
$508$	−14.2926	+	6.46068i	−0.634133	+	0.286646i
$509$	3.15118	−	2.54440i	0.139673	−	0.112778i	−0.555847	−	0.831284i	$-0.687606\pi$
$509$	3.15118	−	2.54440i	0.139673	−	0.112778i	0.695521	+	0.718506i	$0.255174\pi$
$510$	−0.623287	−	1.23622i	−0.0275996	−	0.0547406i
$511$	−0.956556	+	1.29335i	−0.0423155	+	0.0572144i
$512$	−12.3152	−	1.04818i	−0.544261	−	0.0463235i
$513$	6.42515	−	5.18795i	0.283677	−	0.229054i
$514$	1.38333	+	1.87039i	0.0610161	+	0.0824992i
$515$	−33.6844	+	5.77577i	−1.48431	+	0.254511i
$516$	−0.429848	+	0.411976i	−0.0189230	+	0.0181362i
$517$	−2.35523	+	7.69062i	−0.103583	+	0.338233i
$518$	−0.110847	+	0.0288624i	−0.00487035	+	0.00126814i
$519$	6.49934	+	3.63075i	0.285290	+	0.159372i
$520$	−0.479363	−	1.19294i	−0.0210214	−	0.0523139i
$521$	24.4807	+	27.8155i	1.07252	+	1.21862i	0.974724	+	0.223412i	$0.0717197\pi$
$521$	24.4807	+	27.8155i	1.07252	+	1.21862i	0.0977955	+	0.995207i	$0.468821\pi$
$522$	0.0479155	−	0.0647860i	0.00209720	−	0.00283561i
$523$	−36.9489	−	6.33552i	−1.61566	−	0.277033i	−0.711009	−	0.703183i	$-0.751761\pi$
$523$	−36.9489	−	6.33552i	−1.61566	−	0.277033i	−0.904652	+	0.426150i	$0.859869\pi$
$524$	0.198797	−	0.0702394i	0.00868449	−	0.00306842i
$525$	−0.162495	+	0.109828i	−0.00709187	+	0.00479327i
$526$	2.36512	−	0.835650i	0.103124	−	0.0364361i
$527$	−0.911797	−	21.4644i	−0.0397185	−	0.935004i
$528$	−6.92542	+	9.36378i	−0.301390	+	0.407506i
$529$	−9.21424	+	18.2754i	−0.400619	+	0.794581i
$530$	−2.20238	+	0.377636i	−0.0956652	+	0.0164035i
$531$	−12.5391	+	7.00475i	−0.544150	+	0.303980i
$532$	1.41864	+	1.35966i	0.0615058	+	0.0589486i
$533$	3.49520	+	2.36234i	0.151394	+	0.102324i
$534$	0.259067	+	0.175098i	0.0112109	+	0.00757725i
$535$	−19.3248	+	31.3855i	−0.835484	+	1.35691i
$536$	−0.512825	−	4.00473i	−0.0221507	−	0.172978i
$537$	18.0465	−	4.69895i	0.778765	−	0.202775i
$538$	−1.86341	−	0.658386i	−0.0803375	−	0.0283850i
$539$	−6.20196	+	20.2515i	−0.267138	+	0.872296i
$540$	5.06171	−	0.430815i	0.217821	−	0.0185393i
$541$	−7.21970	−	6.91952i	−0.310399	−	0.297494i	0.520562	−	0.853824i	$-0.325722\pi$
$541$	−7.21970	−	6.91952i	−0.310399	−	0.297494i	−0.830961	+	0.556330i	$0.812209\pi$
$542$	−3.07843	−	0.801561i	−0.132230	−	0.0344300i
$543$	−3.31800	+	5.38878i	−0.142389	+	0.231255i
$544$	−6.31695	+	0.537652i	−0.270837	+	0.0230516i
$545$	−7.97345	+	7.64193i	−0.341545	+	0.327344i
$546$	−0.00319296	−	0.0148154i	−0.000136646	−	0.000634039i
$547$	5.80416	+	6.59481i	0.248168	+	0.281974i	0.861398	−	0.507931i	$-0.169590\pi$
$547$	5.80416	+	6.59481i	0.248168	+	0.281974i	−0.613230	+	0.789905i	$0.710130\pi$
$548$	0.0491265	+	0.00418128i	0.00209858	+	0.000178616i
$549$	1.01686	−	2.53055i	0.0433984	−	0.108001i
$550$	−0.792555	−	0.135897i	−0.0337946	−	0.00579467i
$551$	0.173217	+	4.07766i	0.00737929	+	0.173714i
$552$	−1.59255	+	3.96321i	−0.0677834	+	0.168685i
$553$	0.482936	+	0.957847i	0.0205365	+	0.0407318i
$554$	0.854340	−	1.69448i	0.0362974	−	0.0719917i
$555$	−3.15988	−	14.6619i	−0.134129	−	0.622362i
$556$	0.472523	−	0.536890i	0.0200394	−	0.0227692i
$557$	−5.63555	−	1.99117i	−0.238786	−	0.0843684i	0.211065	−	0.977472i	$-0.432307\pi$
$557$	−5.63555	−	1.99117i	−0.238786	−	0.0843684i	−0.449851	+	0.893104i	$0.648523\pi$
$558$	−1.00126	−	0.353769i	−0.0423869	−	0.0149762i
$559$	−0.153666	+	0.174598i	−0.00649937	+	0.00738472i
$560$	0.251185	+	1.16550i	0.0106145	+	0.0492515i
$561$	−4.50260	+	8.93038i	−0.190100	+	0.377041i
$562$	0.650675	+	1.29054i	0.0274471	+	0.0544380i
$563$	−7.11513	+	17.7067i	−0.299867	+	0.746248i	0.699629	+	0.714506i	$0.253349\pi$
$563$	−7.11513	+	17.7067i	−0.299867	+	0.746248i	−0.999496	+	0.0317415i	$0.989895\pi$
$564$	−0.222180	−	5.23029i	−0.00935547	−	0.220235i
$565$	23.4727	+	4.02480i	0.987505	+	0.169325i
$566$	−1.21705	+	3.02875i	−0.0511566	+	0.127308i
$567$	0.120141	+	0.0102255i	0.00504545	+	0.000429431i
$568$	1.28145	+	1.45601i	0.0537686	+	0.0610930i
$569$	0.392181	+	1.81973i	0.0164411	+	0.0762869i	0.985031	−	0.172375i	$-0.0551442\pi$
$569$	0.392181	+	1.81973i	0.0164411	+	0.0762869i	−0.968590	+	0.248662i	$0.920009\pi$
$570$	2.50235	−	2.39831i	0.104812	−	0.100454i
$571$	−2.57328	+	0.219019i	−0.107689	+	0.00916565i	−0.138526	−	0.990359i	$-0.544237\pi$
$571$	−2.57328	+	0.219019i	−0.107689	+	0.00916565i	0.0308377	+	0.999524i	$0.490182\pi$
$572$	−2.41846	+	3.92782i	−0.101121	+	0.164231i
$573$	1.17353	+	0.305563i	0.0490249	+	0.0127651i
$574$	0.0776689	+	0.0744396i	0.00324184	+	0.00310705i
$575$	10.6855	−	0.909472i	0.445617	−	0.0379276i
$576$	2.15782	−	7.04603i	0.0899093	−	0.293585i
$577$	12.4883	+	4.41240i	0.519895	+	0.183691i	0.580176	−	0.814491i	$-0.302984\pi$
$577$	12.4883	+	4.41240i	0.519895	+	0.183691i	−0.0602815	+	0.998181i	$0.519200\pi$
$578$	0.965555	−	0.251411i	0.0401618	−	0.0104573i
$579$	−0.523765	−	4.09016i	−0.0217669	−	0.169981i
$580$	−1.31634	+	2.13788i	−0.0546582	+	0.0887705i
$581$	0.192663	+	0.130217i	0.00799300	+	0.00540233i
$582$	−1.73729	−	1.17420i	−0.0720128	−	0.0486722i
$583$	11.6539	+	11.1693i	0.482654	+	0.462587i
$584$	7.54564	−	4.21525i	0.312241	−	0.174428i
$585$	1.95595	−	0.335381i	0.0808686	−	0.0138663i
$586$	1.01301	−	2.00919i	0.0418471	−	0.0829988i
$587$	−17.3173	+	23.4145i	−0.714761	+	0.966421i	0.285207	+	0.958466i	$0.407938\pi$
$587$	−17.3173	+	23.4145i	−0.714761	+	0.966421i	−0.999968	+	0.00795491i	$0.997468\pi$
$588$	−0.585061	−	13.7728i	−0.0241275	−	0.567981i
$589$	50.7136	−	17.9182i	2.08962	−	0.738309i
$590$	−4.99455	+	3.37573i	−0.205622	+	0.138976i
$591$	−21.3666	+	7.54929i	−0.878903	+	0.310536i
$592$	−22.0586	−	3.78233i	−0.906603	−	0.155453i
$593$	−4.11048	+	5.55774i	−0.168797	+	0.228229i	−0.880256	−	0.474499i	$-0.842629\pi$
$593$	−4.11048	+	5.55774i	−0.168797	+	0.228229i	0.711459	+	0.702728i	$0.248035\pi$
$594$	0.326607	+	0.371097i	0.0134008	+	0.0152263i
$595$	0.381743	+	0.950004i	0.0156499	+	0.0389464i
$596$	11.9772	+	6.69085i	0.490604	+	0.274068i
$597$	−23.0180	+	5.99341i	−0.942062	+	0.245294i
$598$	−0.242659	+	0.792365i	−0.00992307	+	0.0324022i
$599$	−19.7383	+	18.9176i	−0.806486	+	0.772954i	−0.977190	−	0.212369i	$-0.931882\pi$
$599$	−19.7383	+	18.9176i	−0.806486	+	0.772954i	0.170704	+	0.985322i	$0.445396\pi$
$600$	1.03864	−	0.178092i	0.0424022	−	0.00727059i
$601$	−15.0974	−	20.4130i	−0.615836	−	0.832665i	0.379889	−	0.925032i	$-0.375962\pi$
$601$	−15.0974	−	20.4130i	−0.615836	−	0.832665i	−0.995725	+	0.0923672i	$0.970557\pi$
$602$	−0.00461479	+	0.00372618i	−0.000188085	+	0.000151868i
$603$	6.20962	+	0.528517i	0.252875	+	0.0215229i
$604$	10.5826	−	14.3086i	0.430599	−	0.582209i
$605$	−2.09414	−	4.15348i	−0.0851390	−	0.168863i
$606$	0.681985	−	0.550664i	0.0277037	−	0.0223692i
$607$	5.95670	−	2.69260i	0.241775	−	0.109289i	−0.287373	−	0.957819i	$-0.592782\pi$
$607$	5.95670	−	2.69260i	0.241775	−	0.109289i	0.529148	+	0.848530i	$0.322512\pi$
$608$	−5.91800	−	14.7275i	−0.240007	−	0.597280i
$609$	−0.0393700	+	0.0447330i	−0.00159535	+	0.00181267i
$610$	0.335179	−	1.09448i	0.0135710	−	0.0443140i
$611$	−0.259757	−	2.02848i	−0.0105087	−	0.0820636i
$612$	0.826815	−	6.45672i	0.0334220	−	0.260997i
$613$	−3.29714	−	2.66226i	−0.133170	−	0.107528i	0.559330	−	0.828945i	$-0.311058\pi$
$613$	−3.29714	−	2.66226i	−0.133170	−	0.107528i	−0.692500	+	0.721418i	$0.743491\pi$
$614$	−1.29621	+	0.724105i	−0.0523107	+	0.0292225i
$615$	−10.1701	+	9.74727i	−0.410099	+	0.393048i
$616$	−0.156476	+	0.177791i	−0.00630460	+	0.00716342i
$617$	2.52639	+	1.41133i	0.101709	+	0.0568179i	0.537721	−	0.843123i	$-0.319285\pi$
$617$	2.52639	+	1.41133i	0.101709	+	0.0568179i	−0.436012	+	0.899941i	$0.643610\pi$
$618$	1.97247	+	0.891613i	0.0793444	+	0.0358659i
$619$	4.47904	−	34.9774i	0.180028	−	1.40586i	−0.609811	−	0.792547i	$-0.708755\pi$
$619$	4.47904	−	34.9774i	0.180028	−	1.40586i	0.789838	−	0.613315i	$-0.210164\pi$
$620$	32.0188	+	8.33705i	1.28591	+	0.334824i
$621$	−5.46231	−	3.69188i	−0.219195	−	0.148150i
$622$	3.29341	+	0.857536i	0.132054	+	0.0343841i
$623$	−0.179914	−	0.145270i	−0.00720808	−	0.00582012i
$624$	0.623869	−	2.89476i	0.0249748	−	0.115883i
$625$	18.1287	+	24.5116i	0.725148	+	0.980465i
$626$	0.268339	+	0.532218i	0.0107250	+	0.0212717i
$627$	−24.6786	−	4.23157i	−0.985569	−	0.168993i
$628$	−12.7404	+	8.61098i	−0.508396	+	0.343616i
$629$	−19.2189			−0.766307
$630$	0.0506072			0.00201624
$631$	−7.16265	+	4.84111i	−0.285141	+	0.192722i	−0.694192	−	0.719790i	$-0.744238\pi$
$631$	−7.16265	+	4.84111i	−0.285141	+	0.192722i	0.409051	+	0.912511i	$0.365860\pi$
$632$	−0.244614	−	5.75841i	−0.00973024	−	0.229057i
$633$	−4.42830	−	0.376904i	−0.176009	−	0.0149806i
$634$	−2.72138	+	1.23014i	−0.108080	+	0.0488551i
$635$	−5.99124	−	19.5635i	−0.237755	−	0.776352i
$636$	−9.57363	−	4.32755i	−0.379619	−	0.171599i
$637$	−0.684013	−	5.34155i	−0.0271016	−	0.211640i
$638$	−0.243438	+	0.0207196i	−0.00963781	+	0.000820299i
$639$	−2.61375	+	1.46013i	−0.103398	+	0.0577618i
$640$	2.73633	−	12.6966i	0.108163	−	0.501877i
$641$	7.38982	+	12.0018i	0.291881	+	0.474044i	0.963817	−	0.266565i	$-0.0858886\pi$
$641$	7.38982	+	12.0018i	0.291881	+	0.474044i	−0.671937	+	0.740609i	$0.734537\pi$
$642$	2.12725	−	0.961578i	0.0839559	−	0.0379505i
$643$	−2.23732	−	2.54209i	−0.0882313	−	0.100250i	0.704881	−	0.709325i	$-0.251000\pi$
$643$	−2.23732	−	2.54209i	−0.0882313	−	0.100250i	−0.793113	+	0.609075i	$0.791541\pi$
$644$	0.706261	−	1.40079i	0.0278306	−	0.0551987i
$645$	−0.461828	−	0.624433i	−0.0181845	−	0.0245870i
$646$	−2.32864	−	3.78196i	−0.0916193	−	0.148799i
$647$	2.88848	+	9.43187i	0.113558	+	0.370805i	0.994798	−	0.101863i	$-0.0324803\pi$
$647$	2.88848	+	9.43187i	0.113558	+	0.370805i	−0.881241	+	0.472668i	$0.843291\pi$
$648$	−0.565579	−	0.315952i	−0.0222181	−	0.0124117i
$649$	41.0610	+	14.5078i	1.61178	+	0.569480i
$650$	0.197857	−	0.0515180i	0.00776060	−	0.00202070i
$651$	0.715601	+	0.323472i	0.0280466	+	0.0126779i
$652$	−0.639115	+	15.0453i	−0.0250297	+	0.589218i
$653$	−5.74632	+	26.6630i	−0.224871	+	1.04340i	0.714270	+	0.699871i	$0.246759\pi$
$653$	−5.74632	+	26.6630i	−0.224871	+	1.04340i	−0.939140	+	0.343533i	$0.888376\pi$
$654$	0.689454	−	0.118219i	0.0269598	−	0.00462272i
$655$	0.0579433	+	0.268858i	0.00226403	+	0.0105051i
$656$	7.83752	+	19.5044i	0.306004	+	0.761519i
$657$	3.90668	+	12.7566i	0.152414	+	0.497684i
$658$	0.00221337	−	0.0521043i	8.62860e−5	−	0.00203124i
$659$	−27.9102	−	22.5359i	−1.08723	−	0.877875i	−0.0941757	−	0.995556i	$-0.530022\pi$
$659$	−27.9102	−	22.5359i	−1.08723	−	0.877875i	−0.993051	+	0.117681i	$0.962454\pi$
$660$	−11.1200	−	10.6577i	−0.432845	−	0.414849i
$661$	−18.0204	+	29.2669i	−0.700911	+	1.13835i	0.282901	+	0.959149i	$0.408703\pi$
$661$	−18.0204	+	29.2669i	−0.700911	+	1.13835i	−0.983812	+	0.179203i	$0.942648\pi$
$662$	−0.263025	+	2.05400i	−0.0102228	+	0.0798310i
$663$	0.107924	−	2.54061i	0.00419141	−	0.0986692i
$664$	−0.655088	−	1.06393i	−0.0254224	−	0.0412885i
$665$	−1.99429	+	1.61028i	−0.0773352	+	0.0624438i
$666$	−0.354203	+	0.881469i	−0.0137251	+	0.0341562i
$667$	3.07222	−	1.08549i	0.118957	−	0.0420302i
$668$	−32.5858			−1.26078
$669$	12.4465	+	8.25141i	0.481208	+	0.319018i
$670$	2.61569			0.101053
$671$	−7.79656	+	2.75470i	−0.300983	+	0.106344i
$672$	0.0864072	−	0.215033i	0.00333323	−	0.00829506i
$673$	−18.8315	+	15.2054i	−0.725902	+	0.586125i	−0.918626	−	0.395128i	$-0.870700\pi$
$673$	−18.8315	+	15.2054i	−0.725902	+	0.586125i	0.192724	+	0.981253i	$0.438268\pi$
$674$	−1.00279	−	1.62864i	−0.0386261	−	0.0627327i
$675$	−0.0690354	+	1.62515i	−0.00265717	+	0.0625519i
$676$	−3.10960	+	24.2833i	−0.119600	+	0.933973i
$677$	−12.8264	+	20.8314i	−0.492958	+	0.800614i	−0.998048	−	0.0624525i	$-0.980108\pi$
$677$	−12.8264	+	20.8314i	−0.492958	+	0.800614i	0.505090	+	0.863066i	$0.331459\pi$
$678$	−1.08900	−	1.04372i	−0.0418229	−	0.0400840i
$679$	1.20649	+	0.974173i	0.0463008	+	0.0373853i
$680$	0.233470	−	5.49606i	0.00895316	−	0.210764i
$681$	−8.14197	−	26.5863i	−0.312001	−	1.01879i
$682$	1.20051	+	2.98757i	0.0459697	+	0.114400i
$683$	2.55312	+	11.8465i	0.0976924	+	0.453294i	0.999764	+	0.0217086i	$0.00691059\pi$
$683$	2.55312	+	11.8465i	0.0976924	+	0.453294i	−0.902072	+	0.431586i	$0.857954\pi$
$684$	16.0624	−	2.75417i	0.614161	−	0.105308i
$685$	−0.0135498	+	0.0628712i	−0.000517711	+	0.00240219i
$686$	0.0116689	−	0.274696i	0.000445522	−	0.0104879i
$687$	14.2136	+	6.42494i	0.542282	+	0.245127i
$688$	−1.12152	+	0.292022i	−0.0427577	+	0.0111332i
$689$	−3.86981	−	1.36729i	−0.147428	−	0.0520897i
$690$	−2.41576	−	1.34953i	−0.0919665	−	0.0513756i
$691$	10.0420	+	32.7906i	0.382016	+	1.24741i	0.915746	+	0.401757i	$0.131600\pi$
$691$	10.0420	+	32.7906i	0.382016	+	1.24741i	−0.533731	+	0.845654i	$0.679210\pi$
$692$	7.70288	+	12.5103i	0.292819	+	0.475569i
$693$	−0.217389	−	0.293929i	−0.00825792	−	0.0111654i
$694$	1.93264	−	3.83316i	0.0733620	−	0.145505i
$695$	0.616382	+	0.700346i	0.0233807	+	0.0265656i
$696$	0.291755	−	0.131882i	0.0110589	−	0.00499896i
$697$	9.46413	+	15.3707i	0.358479	+	0.582207i
$698$	−0.563687	+	2.61552i	−0.0213359	+	0.0989987i
$699$	11.5731	−	6.46511i	0.437734	−	0.244533i
$700$	−0.385651	+	0.0328237i	−0.0145762	+	0.00124062i
$701$	2.98935	+	23.3443i	0.112906	+	0.881702i	0.945001	+	0.327068i	$0.106061\pi$
$701$	2.98935	+	23.3443i	0.112906	+	0.881702i	−0.832095	+	0.554634i	$0.812858\pi$
$702$	−0.114535	−	0.0517733i	−0.00432286	−	0.00195406i
$703$	−14.0894	−	46.0066i	−0.531390	−	1.73517i
$704$	−20.3595	+	9.20308i	−0.767328	+	0.346854i
$705$	6.80420	+	0.579123i	0.256261	+	0.0218110i
$706$	−0.178091	−	4.19241i	−0.00670255	−	0.157783i
$707$	−0.537060	+	0.362990i	−0.0201982	+	0.0136516i
$708$	−28.3441			−1.06524
$709$	24.8962			0.934995			0.467497	−	0.883994i	$-0.345156\pi$
$709$	24.8962			0.934995			0.467497	+	0.883994i	$0.345156\pi$
$710$	−1.04110	+	0.703664i	−0.0390720	+	0.0264080i
$711$	8.76859	+	1.50353i	0.328848	+	0.0563866i
$712$	0.559354	+	1.10941i	0.0209627	+	0.0415770i
$713$	−25.5337	−	34.5238i	−0.956243	−	1.29293i
$714$	0.0136620	−	0.0633918i	0.000511287	−	0.00237238i
$715$	−4.68144	−	3.78000i	−0.175076	−	0.141364i
$716$	35.6133	+	9.27299i	1.33093	+	0.346548i
$717$	22.7864	+	15.4009i	0.850975	+	0.575158i
$718$	0.122928	+	0.0320080i	0.00458764	+	0.00119453i
$719$	−3.81377	+	29.7823i	−0.142230	+	1.11069i	0.750748	+	0.660589i	$0.229693\pi$
$719$	−3.81377	+	29.7823i	−0.142230	+	1.11069i	−0.892977	+	0.450102i	$0.851388\pi$
$720$	9.01033	+	4.07292i	0.335795	+	0.151789i
$721$	−1.39751	−	0.780696i	−0.0520460	−	0.0290746i
$722$	5.29954	−	6.02144i	0.197228	−	0.224095i
$723$	−18.1012	+	17.3486i	−0.673192	+	0.645203i
$724$	−10.9026	+	6.09057i	−0.405193	+	0.226354i
$725$	−0.625464	−	0.505027i	−0.0232291	−	0.0187562i
$726$	−0.0374217	+	0.292232i	−0.00138885	+	0.0108457i
$727$	−2.06926	−	16.1591i	−0.0767445	−	0.599309i	−0.983927	−	0.178571i	$-0.942852\pi$
$727$	−2.06926	−	16.1591i	−0.0767445	−	0.599309i	0.907182	−	0.420737i	$-0.138229\pi$
$728$	0.0176336	−	0.0575796i	0.000653544	−	0.00213404i
$729$	0.660675	−	0.750672i	0.0244694	−	0.0278027i
$730$	2.08784	+	5.19580i	0.0772746	+	0.192305i
$731$	−0.906855	+	0.409924i	−0.0335412	+	0.0151616i
$732$	4.18732	−	3.38103i	0.154768	−	0.124966i
$733$	−18.0938	−	35.8870i	−0.668311	−	1.32552i	−0.932544	−	0.361057i	$-0.882416\pi$
$733$	−18.0938	−	35.8870i	−0.668311	−	1.32552i	0.264233	−	0.964459i	$-0.414881\pi$
$734$	−1.93586	+	2.61746i	−0.0714540	+	0.0966121i
$735$	17.9173	+	1.52499i	0.660891	+	0.0562501i
$736$	−9.85889	+	7.96050i	−0.363404	+	0.293428i
$737$	−11.2360	−	15.1920i	−0.413883	−	0.559606i
$738$	0.879398	−	0.150788i	0.0323711	−	0.00555058i
$739$	−13.7693	+	13.1968i	−0.506512	+	0.485452i	−0.901225	−	0.433352i	$-0.857331\pi$
$739$	−13.7693	+	13.1968i	−0.506512	+	0.485452i	0.394713	+	0.918805i	$0.370844\pi$
$740$	8.66706	−	28.3009i	0.318608	−	1.04036i
$741$	6.16090	−	1.60417i	0.226326	−	0.0589308i
$742$	−0.0913731	−	0.0510441i	−0.00335441	−	0.00187389i
$743$	−3.77094	−	9.38435i	−0.138342	−	0.344278i	0.842611	−	0.538523i	$-0.181018\pi$
$743$	−3.77094	−	9.38435i	−0.138342	−	0.344278i	−0.980953	+	0.194245i	$0.937774\pi$
$744$	−2.78769	−	3.16744i	−0.102202	−	0.116124i
$745$	−10.6417	+	14.3885i	−0.389880	+	0.527152i
$746$	2.89445	+	0.496303i	0.105973	+	0.0181709i
$747$	1.81843	−	0.642493i	0.0665330	−	0.0235076i
$748$	−16.3520	+	11.0520i	−0.597888	+	0.404102i
$749$	−1.62779	+	0.575133i	−0.0594780	+	0.0210149i
$750$	−0.0600908	−	1.41458i	−0.00219421	−	0.0516533i
$751$	10.0152	−	13.5415i	0.365461	−	0.494137i	−0.582363	−	0.812929i	$-0.697872\pi$
$751$	10.0152	−	13.5415i	0.365461	−	0.494137i	0.947825	+	0.318792i	$0.103277\pi$
$752$	4.58749	−	9.09874i	0.167289	−	0.331797i
$753$	−16.3964	+	2.81145i	−0.597520	+	0.102455i
$754$	0.0542316	−	0.0302956i	0.00197500	−	0.00110330i
$755$	16.7602	+	16.0634i	0.609968	+	0.584607i
$756$	0.197140	+	0.133243i	0.00716992	+	0.00484602i
$757$	−14.9396	−	10.0974i	−0.542990	−	0.366997i	0.257561	−	0.966262i	$-0.417081\pi$
$757$	−14.9396	−	10.0974i	−0.542990	−	0.366997i	−0.800551	+	0.599265i	$0.795460\pi$
$758$	2.46131	−	3.99742i	0.0893988	−	0.145193i
$759$	2.53906	+	19.8279i	0.0921620	+	0.719707i
$760$	13.3278	−	3.47028i	0.483449	−	0.125880i
$761$	44.1038	+	15.5829i	1.59876	+	0.564878i	0.976045	−	0.217570i	$-0.0698129\pi$
$761$	44.1038	+	15.5829i	1.59876	+	0.564878i	0.622716	+	0.782448i	$0.286029\pi$
$762$	−0.379472	+	1.23910i	−0.0137468	+	0.0448880i
$763$	−0.515443	+	0.0438707i	−0.0186603	+	0.00158823i
$764$	1.72770	+	1.65586i	0.0625059	+	0.0599071i
$765$	8.21725	+	2.13961i	0.297095	+	0.0773576i
$766$	2.82836	−	4.59355i	0.102193	−	0.165972i
$767$	−11.0327	+	0.939021i	−0.398368	+	0.0339061i
$768$	10.0463	−	9.62863i	0.362516	−	0.347443i
$769$	0.124923	+	0.579646i	0.00450485	+	0.0209026i	0.979752	−	0.200216i	$-0.0641644\pi$
$769$	0.124923	+	0.579646i	0.00450485	+	0.0209026i	−0.975247	+	0.221119i	$0.929029\pi$
$770$	−0.101375	−	0.115184i	−0.00365329	−	0.00415094i
$771$	−14.2168	−	1.21003i	−0.512005	−	0.0435780i
$772$	3.03412	−	7.55069i	0.109200	−	0.271755i
$773$	42.0388	+	7.20828i	1.51203	+	0.259264i	0.864444	−	0.502728i	$-0.167670\pi$
$773$	42.0388	+	7.20828i	1.51203	+	0.259264i	0.647586	+	0.761992i	$0.275779\pi$
$774$	0.00208776	+	0.0491476i	7.50431e−5	+	0.00176657i
$775$	−3.95013	+	9.83026i	−0.141893	+	0.353114i
$776$	−3.75100	−	7.43966i	−0.134653	−	0.267068i
$777$	0.316279	−	0.627302i	0.0113464	−	0.0225043i
$778$	0.758192	+	3.51802i	0.0271825	+	0.126127i
$779$	−29.8566	+	33.9237i	−1.06973	+	1.21544i
$780$	3.69253	+	1.30465i	0.132214	+	0.0467141i
$781$	8.55909	+	3.02412i	0.306268	+	0.108211i
$782$	−2.34261	+	2.66172i	−0.0837716	+	0.0951830i
$783$	0.104122	+	0.483126i	0.00372100	+	0.0172655i
$784$	12.0801	−	23.9595i	0.431433	−	0.855697i
$785$	−9.03068	−	17.9113i	−0.322319	−	0.639281i
$786$	0.00649510	−	0.0161637i	0.000231672	−	0.000576539i
$787$	0.0841995	+	1.98212i	0.00300139	+	0.0706550i	0.999975	−	0.00708717i	$-0.00225593\pi$
$787$	0.0841995	+	1.98212i	0.00300139	+	0.0706550i	−0.996973	+	0.0777422i	$0.975229\pi$
$788$	−44.0764	−	7.55765i	−1.57016	−	0.269230i
$789$	−5.73630	+	14.2753i	−0.204218	+	0.508215i
$790$	3.72056	+	0.316667i	0.132372	+	0.0112665i
$791$	0.736981	+	0.837373i	0.0262040	+	0.0297736i
$792$	0.413831	+	1.92018i	0.0147049	+	0.0682308i
$793$	1.51787	−	1.45476i	0.0539010	−	0.0516599i
$794$	−6.08396	+	0.517821i	−0.215912	+	0.0183768i
$795$	7.18558	−	11.6701i	0.254846	−	0.413897i
$796$	−45.4240	−	11.8275i	−1.61001	−	0.419214i
$797$	12.1283	+	11.6241i	0.429608	+	0.411746i	0.875407	−	0.483387i	$-0.160594\pi$
$797$	12.1283	+	11.6241i	0.429608	+	0.411746i	−0.445798	+	0.895133i	$0.647080\pi$
$798$	0.161765	−	0.0137682i	0.00572640	−	0.000487389i
$799$	2.56229	−	8.36676i	0.0906474	−	0.295995i
$800$	2.94774	+	1.04150i	0.104218	+	0.0368227i
$801$	−1.85593	+	0.483246i	−0.0655760	+	0.0170747i
$802$	0.664466	+	5.18891i	0.0234631	+	0.183227i
$803$	21.2089	−	34.4454i	0.748445	−	1.21555i
$804$	10.1894	+	6.88684i	0.359353	+	0.242880i
$805$	1.69543	+	1.14591i	0.0597562	+	0.0403882i
$806$	−0.591029	−	0.566455i	−0.0208181	−	0.0199525i
$807$	10.5820	−	5.91145i	0.372503	−	0.208093i
$808$	3.43279	−	0.588610i	0.120765	−	0.0207072i
$809$	−13.2380	+	26.2560i	−0.465424	+	0.923113i	0.531672	+	0.846950i	$0.321564\pi$
$809$	−13.2380	+	26.2560i	−0.465424	+	0.923113i	−0.997095	+	0.0761622i	$0.975733\pi$
$810$	0.249576	−	0.337449i	0.00876921	−	0.0118568i
$811$	1.57910	+	37.1733i	0.0554498	+	1.30533i	0.784181	+	0.620532i	$0.213083\pi$
$811$	1.57910	+	37.1733i	0.0554498	+	1.30533i	−0.728731	+	0.684800i	$0.759890\pi$
$812$	−0.110880	+	0.0391762i	−0.00389111	+	0.00137482i
$813$	16.1645	−	10.9253i	0.566915	−	0.383168i
$814$	2.71579	−	0.959548i	0.0951882	−	0.0336321i
$815$	−19.3609	−	3.31977i	−0.678184	−	0.116286i
$816$	7.53428	−	10.1870i	0.263753	−	0.356617i
$817$	−1.64610	−	1.87034i	−0.0575898	−	0.0654348i
$818$	1.94018	+	4.82832i	0.0678367	+	0.168818i
$819$	0.0811492	+	0.0453327i	0.00283558	+	0.00158405i
$820$	−26.9023	+	7.00481i	−0.939469	+	0.244619i
$821$	13.5254	−	44.1651i	0.472040	−	1.54137i	−0.329927	−	0.944006i	$-0.607024\pi$
$821$	13.5254	−	44.1651i	0.472040	−	1.54137i	0.801968	−	0.597367i	$-0.203787\pi$
$822$	0.00294092	−	0.00281865i	0.000102576	−	9.83116e-5i
$823$	−21.6714	+	3.71593i	−0.755417	+	0.129529i	−0.533807	−	0.845606i	$-0.679239\pi$
$823$	−21.6714	+	3.71593i	−0.755417	+	0.129529i	−0.221610	+	0.975135i	$0.571131\pi$
$824$	5.11442	+	6.91515i	0.178169	+	0.240901i
$825$	3.83719	−	3.09831i	0.133594	−	0.107869i
$826$	−0.281348	−	0.0239463i	−0.00978936	−	0.000833197i
$827$	29.3922	−	39.7409i	1.02207	−	1.38193i	0.0999623	−	0.994991i	$-0.468128\pi$
$827$	29.3922	−	39.7409i	1.02207	−	1.38193i	0.922106	−	0.386937i	$-0.126467\pi$
$828$	−5.85743	−	11.6175i	−0.203560	−	0.403736i
$829$	−10.1927	+	8.23002i	−0.354007	+	0.285841i	−0.788750	−	0.614714i	$-0.789271\pi$
$829$	−10.1927	+	8.23002i	−0.354007	+	0.285841i	0.434743	+	0.900554i	$0.356839\pi$
$830$	0.737604	−	0.333418i	0.0256026	−	0.0115731i
$831$	4.33966	+	10.7996i	0.150541	+	0.374636i
$832$	3.75321	−	4.26448i	0.130119	−	0.147844i
$833$	6.74722	−	22.0320i	0.233777	−	0.763364i
$834$	−0.00750566	−	0.0586128i	−0.000259900	−	0.00202960i
$835$	5.39909	−	42.1623i	0.186843	−	1.45909i
$836$	−38.4443	−	31.0416i	−1.32962	−	1.07360i
$837$	5.68599	−	3.17639i	0.196537	−	0.109792i
$838$	−3.52156	+	3.37514i	−0.121650	+	0.116592i
$839$	23.2912	−	26.4639i	0.804100	−	0.913636i	−0.193623	−	0.981076i	$-0.562024\pi$
$839$	23.2912	−	26.4639i	0.804100	−	0.913636i	0.997723	+	0.0674405i	$0.0214833\pi$
$840$	0.175549	+	0.0980675i	0.00605701	+	0.00338365i
$841$	26.2031	+	11.8445i	0.903554	+	0.408432i
$842$	−0.108521	+	0.847455i	−0.00373987	+	0.0292052i
$843$	−8.57832	−	2.23362i	−0.295453	−	0.0769300i
$844$	−7.26642	−	4.91125i	−0.250121	−	0.169052i
$845$	−30.9046	−	8.04692i	−1.06315	−	0.276822i
$846$	−0.336516	−	0.271718i	−0.0115697	−	0.00934186i
$847$	0.0459020	−	0.212986i	0.00157721	−	0.00731829i
$848$	−12.1604	−	16.4419i	−0.417589	−	0.564618i
$849$	−9.01299	−	17.8762i	−0.309325	−	0.613509i
$850$	0.862234	+	0.147845i	0.0295744	+	0.00507104i
$851$	−31.8258	+	21.5105i	−1.09097	+	0.737370i
$852$	−5.90829			−0.202415
$853$	51.9851			1.77993			0.889967	−	0.456025i	$-0.150727\pi$
$853$	51.9851			1.77993			0.889967	+	0.456025i	$0.150727\pi$
$854$	0.0444204	−	0.0300230i	0.00152004	−	0.00102736i
$855$	0.902230	+	21.2392i	0.0308556	+	0.726365i
$856$	9.24247	+	0.786650i	0.315901	+	0.0268872i
$857$	−39.6701	+	17.9320i	−1.35510	+	0.612546i	−0.952978	−	0.303039i	$-0.901999\pi$
$857$	−39.6701	+	17.9320i	−1.35510	+	0.612546i	−0.402126	+	0.915584i	$0.631729\pi$
$858$	0.111596	+	0.364398i	0.00380981	+	0.0124403i
$859$	−4.55686	−	2.05983i	−0.155478	−	0.0702805i	0.332661	−	0.943047i	$-0.392054\pi$
$859$	−4.55686	−	2.05983i	−0.155478	−	0.0702805i	−0.488139	+	0.872766i	$0.662324\pi$
$860$	−0.194677	−	1.52026i	−0.00663843	−	0.0518404i
$861$	−0.657447	+	0.0559570i	−0.0224057	+	0.00190701i
$862$	1.90116	−	1.06205i	0.0647539	−	0.0361737i
$863$	−9.33530	+	43.3159i	−0.317777	+	1.47449i	0.483048	+	0.875594i	$0.339530\pi$
$863$	−9.33530	+	43.3159i	−0.317777	+	1.47449i	−0.800825	+	0.598898i	$0.795605\pi$
$864$	−1.00771	−	1.63662i	−0.0342830	−	0.0556791i
$865$	−17.4631	+	7.89382i	−0.593763	+	0.268398i
$866$	0.263953	+	0.299909i	0.00896950	+	0.0101913i
$867$	−2.75501	+	5.46423i	−0.0935649	+	0.185575i
$868$	0.921535	+	1.24600i	0.0312789	+	0.0422919i
$869$	−14.1429	−	22.9695i	−0.479764	−	0.779186i
$870$	0.0607404	+	0.198338i	0.00205929	+	0.00672429i
$871$	4.19429	+	2.34307i	0.142118	+	0.0793919i
$872$	2.62070	+	0.925952i	0.0887481	+	0.0313567i
$873$	12.4458	−	3.24062i	0.421225	−	0.109678i
$874$	−8.08907	−	3.65649i	−0.273617	−	0.123683i
$875$	−0.0444384	+	1.04611i	−0.00150229	+	0.0353651i
$876$	−5.54681	+	25.7373i	−0.187409	+	0.869582i
$877$	−22.9517	+	3.93547i	−0.775024	+	0.132891i	−0.542903	−	0.839796i	$-0.682675\pi$
$877$	−22.9517	+	3.93547i	−0.775024	+	0.132891i	−0.232121	+	0.972687i	$0.574567\pi$
$878$	−1.38537	−	6.42813i	−0.0467539	−	0.216939i
$879$	5.14563	+	12.8054i	0.173558	+	0.431916i
$880$	−8.77905	−	28.6666i	−0.295942	−	0.966351i
$881$	1.64252	−	38.6662i	0.0553378	−	1.30270i	−0.729922	−	0.683530i	$-0.760444\pi$
$881$	1.64252	−	38.6662i	0.0553378	−	1.30270i	0.785260	−	0.619166i	$-0.212529\pi$
$882$	−0.886141	−	0.715509i	−0.0298379	−	0.0240924i
$883$	−27.8496	−	26.6917i	−0.937213	−	0.898246i	0.0577656	−	0.998330i	$-0.481602\pi$
$883$	−27.8496	−	26.6917i	−0.937213	−	0.898246i	−0.994979	+	0.100084i	$0.968089\pi$
$884$	2.63108	−	4.27315i	0.0884928	−	0.143721i
$885$	4.69629	−	36.6740i	0.157864	−	1.23278i
$886$	−0.136078	+	3.20338i	−0.00457162	+	0.107620i
$887$	20.6895	+	33.6020i	0.694687	+	1.12824i	0.985206	+	0.171374i	$0.0548207\pi$
$887$	20.6895	+	33.6020i	0.694687	+	1.12824i	−0.290519	+	0.956869i	$0.593828\pi$
$888$	−2.93680	+	2.37130i	−0.0985526	+	0.0795757i
$889$	0.357328	−	0.889244i	0.0119844	−	0.0298243i
$890$	−0.758953	+	0.268155i	−0.0254402	+	0.00898858i
$891$	−3.03200			−0.101576
$892$	13.5016	+	26.1945i	0.452068	+	0.877056i
$893$	21.9070			0.733089
$894$	1.06875	−	0.377615i	0.0357445	−	0.0126293i
$895$	−17.8989	+	44.5431i	−0.598293	+	1.48891i
$896$	0.473324	−	0.382182i	0.0158126	−	0.0127678i
$897$	−2.66483	−	4.32796i	−0.0889761	−	0.144506i
$898$	−0.0294701	+	0.693750i	−0.000983431	+	0.0231507i
$899$	−0.408854	+	3.19280i	−0.0136361	+	0.106486i
$900$	−1.68302	+	2.73339i	−0.0561006	+	0.0911131i
$901$	−12.6785	−	12.1513i	−0.422381	−	0.404819i
$902$	−2.10478	−	1.69949i	−0.0700815	−	0.0565868i
$903$	0.00154394	−	0.0363456i	5.13792e−5	−	0.00120951i
$904$	−1.75504	−	5.73081i	−0.0583718	−	0.190604i
$905$	−6.07405	−	15.1159i	−0.201908	−	0.502468i
$906$	−0.309780	−	1.43739i	−0.0102918	−	0.0477539i
$907$	15.9600	−	2.73661i	0.529943	−	0.0908678i	0.102192	−	0.994765i	$-0.467414\pi$
$907$	15.9600	−	2.73661i	0.529943	−	0.0908678i	0.427750	+	0.903897i	$0.359306\pi$
$908$	11.5602	−	53.6395i	0.383639	−	1.78009i
$909$	−0.228168	+	5.37125i	−0.00756785	+	0.178153i
$910$	0.0355504	+	0.0160698i	0.00117848	+	0.000532708i
$911$	45.7785	−	11.9198i	1.51671	−	0.394920i	0.601822	−	0.798630i	$-0.294441\pi$
$911$	45.7785	−	11.9198i	1.51671	−	0.394920i	0.914887	+	0.403709i	$0.132279\pi$
$912$	29.9093	+	10.5676i	0.990397	+	0.349929i
$913$	−5.10496	−	2.85180i	−0.168950	−	0.0943809i
$914$	0.488219	+	1.59420i	0.0161488	+	0.0527315i
$915$	3.68087	+	5.97811i	0.121686	+	0.197630i
$916$	18.3039	+	24.7485i	0.604778	+	0.817714i
$917$	−0.00579967	+	0.0115030i	−0.000191522	+	0.000379861i
$918$	−0.355321	−	0.403723i	−0.0117273	−	0.0133249i
$919$	32.0196	−	14.4738i	1.05623	−	0.477445i	0.192444	−	0.981308i	$-0.438359\pi$
$919$	32.0196	−	14.4738i	1.05623	−	0.477445i	0.863784	+	0.503863i	$0.168088\pi$
$920$	−5.76478	−	9.36260i	−0.190059	−	0.308676i
$921$	1.91852	−	8.90198i	0.0632175	−	0.293330i
$922$	−1.35891	+	0.759131i	−0.0447532	+	0.0250006i
$923$	−2.29975	+	0.195737i	−0.0756971	+	0.00644277i
$924$	−0.0916371	−	0.715607i	−0.00301464	−	0.0235418i
$925$	8.63603	+	3.90373i	0.283951	+	0.128354i
$926$	−0.966039	−	3.15445i	−0.0317460	−	0.103662i
$927$	−12.0977	+	5.46850i	−0.397340	+	0.179609i
$928$	0.946457	+	0.0805554i	0.0310690	+	0.00264436i
$929$	1.60929	+	37.8840i	0.0527992	+	1.24293i	0.808689	+	0.588236i	$0.200177\pi$
$929$	1.60929	+	37.8840i	0.0527992	+	1.24293i	−0.755890	+	0.654698i	$0.772796\pi$
$930$	2.26484	−	1.53076i	0.0742669	−	0.0501956i
$931$	57.6871			1.89062
$932$	26.1605			0.856916
$933$	−17.2933	+	11.6883i	−0.566159	+	0.382657i
$934$	−1.38890	−	0.238151i	−0.0454462	−	0.00779253i
$935$	−11.5907	−	22.9888i	−0.379056	−	0.751813i
$936$	−0.296979	−	0.401542i	−0.00970706	−	0.0131248i
$937$	2.98660	−	13.8579i	0.0975681	−	0.452718i	−0.902203	−	0.431312i	$-0.858051\pi$
$937$	2.98660	−	13.8579i	0.0975681	−	0.452718i	0.999771	−	0.0214054i	$-0.00681408\pi$
$938$	0.0953233	+	0.0769682i	0.00311241	+	0.00251310i
$939$	−3.53770	−	0.921147i	−0.115449	−	0.0300605i
$940$	11.1650	+	7.54626i	0.364164	+	0.246132i
$941$	51.8874	+	13.5104i	1.69148	+	0.440428i	0.968211	−	0.250136i	$-0.0804754\pi$
$941$	51.8874	+	13.5104i	1.69148	+	0.440428i	0.723271	+	0.690564i	$0.242638\pi$
$942$	−0.161376	+	1.26021i	−0.00525791	+	0.0410598i
$943$	32.8758	+	14.8608i	1.07058	+	0.483933i
$944$	−48.1652	−	26.9067i	−1.56764	−	0.875738i
$945$	−0.205065	+	0.232999i	−0.00667077	+	0.00757947i
$946$	0.107680	−	0.103203i	0.00350097	−	0.00335540i
$947$	38.4887	−	21.5011i	1.25071	−	0.698691i	0.285057	−	0.958511i	$-0.407987\pi$
$947$	38.4887	−	21.5011i	1.25071	−	0.698691i	0.965657	+	0.259820i	$0.0836631\pi$
$948$	13.6597	+	11.0294i	0.443646	+	0.358219i
$949$	−1.30639	+	10.2018i	−0.0424071	+	0.331163i
$950$	0.278190	+	2.17242i	0.00902566	+	0.0704827i
$951$	5.36362	−	17.5141i	0.173927	−	0.567932i
$952$	0.170233	−	0.193422i	0.00551728	−	0.00626885i
$953$	−0.0675194	−	0.168029i	−0.00218717	−	0.00544298i	0.926791	−	0.375576i	$-0.122555\pi$
$953$	−0.0675194	−	0.168029i	−0.00218717	−	0.00544298i	−0.928979	+	0.370133i	$0.879312\pi$
$954$	−0.790981	+	0.357546i	−0.0256089	+	0.0115760i
$955$	−2.42875	+	1.96108i	−0.0785927	+	0.0634591i
$956$	24.4347	+	48.4633i	0.790274	+	1.56741i
$957$	0.891040	−	1.20477i	0.0288032	−	0.0389445i
$958$	−1.70115	−	0.144789i	−0.0549617	−	0.00467793i
$959$	−0.00234381	+	0.00189250i	−7.56857e−5	+	6.11119e-5i
$960$	11.2799	+	15.2514i	0.364058	+	0.492238i
$961$	11.2557	−	1.92998i	0.363087	−	0.0622575i
$962$	−0.528720	+	0.506738i	−0.0170466	+	0.0163379i
$963$	−4.19265	+	13.6904i	−0.135106	+	0.441168i
$964$	−47.8819	+	12.4675i	−1.54217	+	0.401551i
$965$	9.26700	+	5.17686i	0.298315	+	0.166649i
$966$	−0.0483267	−	0.120266i	−0.00155489	−	0.00386949i
$967$	32.3652	+	36.7740i	1.04080	+	1.18257i	0.982879	+	0.184252i	$0.0589862\pi$
$967$	32.3652	+	36.7740i	1.04080	+	1.18257i	0.0579165	+	0.998321i	$0.481554\pi$
$968$	−0.696101	+	0.941191i	−0.0223735	+	0.0302510i
$969$	26.8483	+	4.60360i	0.862492	+	0.147889i
$970$	5.08950	−	1.79823i	0.163414	−	0.0577378i
$971$	18.8024	−	12.7082i	0.603398	−	0.407826i	−0.219829	−	0.975538i	$-0.570550\pi$
$971$	18.8024	−	12.7082i	0.603398	−	0.407826i	0.823227	+	0.567713i	$0.192171\pi$
$972$	1.86069	−	0.657423i	0.0596816	−	0.0210869i
$973$	0.00185465	+	0.0436600i	5.94574e−5	+	0.00139967i
$974$	4.10586	−	5.55148i	0.131560	−	0.177881i
$975$	−0.564544	+	1.11971i	−0.0180799	+	0.0358593i
$976$	10.3251	−	1.77041i	0.330498	−	0.0566695i
$977$	−2.04489	+	1.14234i	−0.0654218	+	0.0365468i	−0.520063	−	0.854128i	$-0.674092\pi$
$977$	−2.04489	+	1.14234i	−0.0654218	+	0.0365468i	0.454642	+	0.890674i	$0.349767\pi$
$978$	0.898239	+	0.860892i	0.0287225	+	0.0275283i
$979$	4.81762	+	3.25614i	0.153972	+	0.104067i
$980$	29.4007	+	19.8714i	0.939170	+	0.634768i
$981$	−2.24945	+	3.65333i	−0.0718193	+	0.116642i
$982$	0.0287168	+	0.224253i	0.000916389	+	0.00715621i
$983$	35.7281	−	9.30288i	1.13955	−	0.296716i	0.366102	−	0.930575i	$-0.380692\pi$
$983$	35.7281	−	9.30288i	1.13955	−	0.296716i	0.773449	+	0.633859i	$0.218530\pi$
$984$	3.34270	+	1.18105i	0.106561	+	0.0376505i
$985$	17.0817	−	55.7775i	0.544267	−	1.77722i
$986$	0.264841	−	0.0225413i	0.00843425	−	0.000717860i
$987$	0.230923	+	0.221322i	0.00735037	+	0.00704476i
$988$	12.1580	+	3.16570i	0.386798	+	0.100714i
$989$	−1.04292	+	1.69381i	−0.0331629	+	0.0538599i
$990$	−1.26799	+	0.107922i	−0.0402994	+	0.00342998i
$991$	−2.03757	+	1.95285i	−0.0647254	+	0.0620343i	−0.723606	−	0.690213i	$-0.757517\pi$
$991$	−2.03757	+	1.95285i	−0.0647254	+	0.0620343i	0.658881	+	0.752248i	$0.271030\pi$
$992$	−2.63728	−	12.2370i	−0.0837338	−	0.388526i
$993$	−8.39097	−	9.53399i	−0.266279	−	0.302552i
$994$	−0.0586465	−	0.00499155i	−0.00186015	−	0.000158323i
$995$	22.8296	−	56.8137i	0.723748	−	1.80112i
$996$	3.75118	+	0.643205i	0.118861	+	0.0203807i
$997$	−0.540602	−	12.7262i	−0.0171210	−	0.403042i	−0.987125	−	0.159952i	$-0.948866\pi$
$997$	−0.540602	−	12.7262i	−0.0171210	−	0.403042i	0.970004	−	0.243090i	$-0.0781611\pi$
$998$	−2.46189	+	6.12665i	−0.0779297	+	0.193936i
$999$	−2.62308	−	5.20257i	−0.0829906	−	0.164602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.i.a.4.10	✓	648
223.56	even	37	inner	669.2.i.a.502.10	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.i.a.4.10	✓	648	1.1	even	1	trivial
669.2.i.a.502.10	yes	648	223.56	even	37	inner

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:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.i (of order \(37\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(0.153732 - 0.0543169i) q^{2} +(-0.372856 + 0.927889i) q^{3} +(-1.53539 + 1.23974i) q^{4} +(-1.34968 - 2.19202i) q^{5} +(-0.00691984 + 0.162898i) q^{6} +(0.0153152 - 0.119599i) q^{7} +(-0.339671 + 0.551660i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-0.326553 - 0.263673i) q^{10} +(-0.128682 + 3.02927i) q^{11} +(-0.577861 - 1.88691i) q^{12} +(-0.287439 - 0.715320i) q^{13} +(-0.00414180 - 0.0192180i) q^{14} +(2.53719 - 0.435045i) q^{15} +(0.809262 - 3.75499i) q^{16} +(0.139995 - 3.29559i) q^{17} +(-0.148571 - 0.0671585i) q^{18} +(7.99170 - 2.08088i) q^{19} +(4.78983 + 1.69235i) q^{20} +(0.105264 + 0.0588040i) q^{21} +(0.144758 + 0.472684i) q^{22} +(-3.45673 - 5.61408i) q^{23} +(-0.385231 - 0.520867i) q^{24} +(-0.732307 + 1.45244i) q^{25} +(-0.0830425 - 0.0943546i) q^{26} +(0.911228 - 0.411901i) q^{27} +(0.124757 + 0.202617i) q^{28} +(-0.104122 + 0.483126i) q^{29} +(0.366417 - 0.204693i) q^{30} +(6.48960 - 0.552346i) q^{31} +(-0.244126 - 1.90642i) q^{32} +(-2.76285 - 1.24888i) q^{33} +(-0.157485 - 0.514241i) q^{34} +(-0.282834 + 0.127849i) q^{35} +(1.96631 + 0.167357i) q^{36} +(-0.247281 - 5.82118i) q^{37} +(1.11555 - 0.753981i) q^{38} +0.770911 q^{39} +1.66770 q^{40} +(-4.53385 + 3.06435i) q^{41} +(0.0193765 + 0.00332243i) q^{42} +(-0.135830 - 0.269402i) q^{43} +(-3.55793 - 4.81064i) q^{44} +(-0.542335 + 2.51644i) q^{45} +(-0.836347 - 0.675303i) q^{46} +(2.56717 + 0.668438i) q^{47} +(3.18247 + 2.15098i) q^{48} +(6.76006 + 1.76018i) q^{49} +(-0.0336866 + 0.263063i) q^{50} +(3.00575 + 1.35868i) q^{51} +(1.32814 + 0.741945i) q^{52} +(3.51737 - 3.99651i) q^{53} +(0.117712 - 0.112817i) q^{54} +(6.81391 - 3.80648i) q^{55} +(0.0607758 + 0.0490730i) q^{56} +(-1.04893 + 8.19128i) q^{57} +(0.0102351 + 0.0799273i) q^{58} +(4.20581 - 13.7334i) q^{59} +(-3.35623 + 3.81342i) q^{60} +(1.01686 + 2.53055i) q^{61} +(0.967655 - 0.437408i) q^{62} +(-0.0938120 + 0.0757479i) q^{63} +(3.31757 + 6.58000i) q^{64} +(-1.18005 + 1.59553i) q^{65} +(-0.492572 - 0.0419241i) q^{66} +(-4.84878 + 3.91511i) q^{67} +(3.87073 + 5.23357i) q^{68} +(6.49810 - 1.11421i) q^{69} +(-0.0365362 + 0.0350171i) q^{70} +(0.876693 - 2.86270i) q^{71} +(0.626943 - 0.163243i) q^{72} +(-11.6473 - 6.50655i) q^{73} +(-0.354203 - 0.881469i) q^{74} +(-1.07466 - 1.22105i) q^{75} +(-9.69062 + 13.1026i) q^{76} +(0.360326 + 0.0617841i) q^{77} +(0.118514 - 0.0418735i) q^{78} +(-7.37089 + 4.98185i) q^{79} +(-9.32327 + 3.29412i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(-0.530550 + 0.717352i) q^{82} +(-0.868262 + 1.72210i) q^{83} +(-0.234523 + 0.0402130i) q^{84} +(-7.41297 + 4.14113i) q^{85} +(-0.0355144 - 0.0340378i) q^{86} +(-0.409465 - 0.276750i) q^{87} +(-1.62742 - 1.09994i) q^{88} +(1.00552 - 1.63307i) q^{89} +(0.0533112 + 0.416315i) q^{90} +(-0.0899536 + 0.0234221i) q^{91} +(12.2674 + 4.33435i) q^{92} +(-1.90717 + 6.22757i) q^{93} +(0.430962 - 0.0366803i) q^{94} +(-15.3476 - 14.7095i) q^{95} +(1.85997 + 0.484298i) q^{96} +(-6.74297 + 10.9513i) q^{97} +(1.13484 - 0.0965894i) q^{98} +(2.18897 - 2.09796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + q^{2} + 18 q^{3} - 17 q^{4} + 4 q^{5} - q^{6} + 4 q^{7} + 9 q^{8} - 18 q^{9} + 8 q^{10} + 6 q^{11} + 17 q^{12} - 2 q^{13} + 12 q^{14} - 4 q^{15} - 7 q^{16} + 8 q^{17} + q^{18} - 66 q^{19} + 14 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 648 * q + q^2 + 18 * q^3 - 17 * q^4 + 4 * q^5 - q^6 + 4 * q^7 + 9 * q^8 - 18 * q^9 + 8 * q^10 + 6 * q^11 + 17 * q^12 - 2 * q^13 + 12 * q^14 - 4 * q^15 - 7 * q^16 + 8 * q^17 + q^18 - 66 * q^19 + 14 * q^20 - 4 * q^21 - 24 * q^22 - 2 * q^23 - 9 * q^24 - 26 * q^25 - 8 * q^26 + 18 * q^27 + 8 * q^28 - 27 * q^29 - 8 * q^30 + 16 * q^31 + 19 * q^32 - 6 * q^33 - 50 * q^34 + 16 * q^35 - 17 * q^36 + 16 * q^37 - 28 * q^38 - 72 * q^39 + 212 * q^40 + 240 * q^41 - 86 * q^42 + 6 * q^43 - 128 * q^44 + 4 * q^45 + 16 * q^46 - 14 * q^47 + 7 * q^48 - 28 * q^49 + 23 * q^50 + 66 * q^51 - 286 * q^52 + 10 * q^53 - q^54 + 14 * q^55 + 25 * q^56 - 8 * q^57 + 49 * q^58 + 22 * q^59 - 14 * q^60 - 2 * q^61 - 23 * q^62 + 4 * q^63 + 257 * q^64 - 116 * q^65 - 50 * q^66 + 8 * q^67 + 211 * q^68 + 2 * q^69 + 82 * q^70 + 9 * q^72 + 10 * q^73 - 10 * q^74 + 26 * q^75 + 7 * q^76 - 116 * q^77 - 66 * q^78 - 14 * q^79 - 477 * q^80 - 18 * q^81 - 234 * q^82 - 142 * q^83 - 8 * q^84 + 98 * q^85 + 35 * q^86 - 10 * q^87 - 72 * q^88 + 2 * q^89 + 8 * q^90 + 6 * q^91 - 46 * q^92 - 16 * q^93 - 206 * q^94 - 6 * q^95 - 19 * q^96 - 34 * q^97 + 4 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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