LMFDB - Embedded newform 462.2.w.b.281.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(29,462)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("462.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			281.7
Character	$\chi$	$=$	462.281
Dual form			462.2.w.b.365.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.711719 - 1.57907i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.152745 - 0.0496298i) q^{5} +(-1.28185 + 1.16484i) q^{6} +(0.587785 + 0.809017i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.98691 + 2.24771i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.711719 - 1.57907i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.152745 - 0.0496298i) q^{5} +(-1.28185 + 1.16484i) q^{6} +(0.587785 + 0.809017i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.98691 + 2.24771i) q^{9} +0.160605i q^{10} +(-3.12194 - 1.11961i) q^{11} +(1.50395 + 0.859155i) q^{12} +(-6.36388 + 2.06775i) q^{13} +(0.587785 - 0.809017i) q^{14} +(0.0303426 + 0.276517i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.841882 - 2.59105i) q^{17} +(2.75168 + 1.19509i) q^{18} +(-3.45842 + 4.76011i) q^{19} +(0.152745 - 0.0496298i) q^{20} +(0.859155 - 1.50395i) q^{21} +(-0.100078 + 3.31511i) q^{22} +2.94363i q^{23} +(0.352360 - 1.69583i) q^{24} +(-4.02422 - 2.92376i) q^{25} +(3.93309 + 5.41344i) q^{26} +(4.96340 + 1.53773i) q^{27} +(-0.951057 - 0.309017i) q^{28} +(5.12098 - 3.72061i) q^{29} +(0.253607 - 0.114306i) q^{30} +(2.60546 + 8.01878i) q^{31} -1.00000 q^{32} +(0.454006 + 5.72659i) q^{33} -2.72439 q^{34} +(-0.0496298 - 0.152745i) q^{35} +(0.286277 - 2.98631i) q^{36} +(-0.501222 + 0.364159i) q^{37} +(5.59585 + 1.81820i) q^{38} +(7.79441 + 8.57734i) q^{39} +(-0.0944015 - 0.129933i) q^{40} +(-4.44808 - 3.23172i) q^{41} +(-1.69583 - 0.352360i) q^{42} -2.41048i q^{43} +(3.18379 - 0.929247i) q^{44} +(0.415044 - 0.244715i) q^{45} +(2.79955 - 0.909630i) q^{46} +(-1.56714 + 2.15699i) q^{47} +(-1.72172 + 0.188926i) q^{48} +(-0.309017 + 0.951057i) q^{49} +(-1.53711 + 4.73075i) q^{50} +(-4.69062 + 0.514708i) q^{51} +(3.93309 - 5.41344i) q^{52} +(2.46767 - 0.801796i) q^{53} +(-0.0713040 - 5.19566i) q^{54} +(0.421294 + 0.325955i) q^{55} +1.00000i q^{56} +(9.97797 + 2.07322i) q^{57} +(-5.12098 - 3.72061i) q^{58} +(-8.48442 - 11.6778i) q^{59} +(-0.187080 - 0.205872i) q^{60} +(-7.68134 - 2.49582i) q^{61} +(6.82118 - 4.95588i) q^{62} +(-2.98631 - 0.286277i) q^{63} +(0.309017 + 0.951057i) q^{64} +1.07467 q^{65} +(5.30602 - 2.20140i) q^{66} +9.38707 q^{67} +(0.841882 + 2.59105i) q^{68} +(4.64819 - 2.09503i) q^{69} +(-0.129933 + 0.0944015i) q^{70} +(-10.0295 - 3.25877i) q^{71} +(-2.92861 + 0.650555i) q^{72} +(0.0597686 + 0.0822645i) q^{73} +(0.501222 + 0.364159i) q^{74} +(-1.75271 + 8.43541i) q^{75} -5.88382i q^{76} +(-0.929247 - 3.18379i) q^{77} +(5.74893 - 10.0635i) q^{78} +(-8.72301 + 2.83428i) q^{79} +(-0.0944015 + 0.129933i) q^{80} +(-1.10436 - 8.93199i) q^{81} +(-1.69901 + 5.22903i) q^{82} +(-4.39153 + 13.5157i) q^{83} +(0.188926 + 1.72172i) q^{84} +(-0.257186 + 0.353987i) q^{85} +(-2.29250 + 0.744879i) q^{86} +(-9.51979 - 5.43834i) q^{87} +(-1.86761 - 2.74081i) q^{88} +15.1000i q^{89} +(-0.360994 - 0.319109i) q^{90} +(-5.41344 - 3.93309i) q^{91} +(-1.73022 - 2.38144i) q^{92} +(10.8078 - 9.82131i) q^{93} +(2.53569 + 0.823897i) q^{94} +(0.764500 - 0.555442i) q^{95} +(0.711719 + 1.57907i) q^{96} +(-3.20306 - 9.85801i) q^{97} +1.00000 q^{98} +(8.71956 - 4.79263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 48 * q + 12 * q^2 - 4 * q^3 - 12 * q^4 + 4 * q^6 + 12 * q^8 + 10 * q^9	$ 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{11} + 6 q^{12} - 24 q^{15} - 12 q^{16} + 24 q^{17} + 10 q^{18} + 30 q^{19} - 8 q^{22} - 6 q^{24} + 18 q^{25} + 20 q^{26} + 38 q^{27} - 8 q^{29} - 36 q^{30} - 32 q^{31} - 48 q^{32} + 24 q^{33} - 4 q^{34} - 6 q^{35} - 20 q^{37} - 20 q^{38} - 34 q^{39} - 22 q^{44} + 12 q^{45} + 20 q^{46} - 20 q^{47} - 4 q^{48} + 12 q^{49} - 28 q^{50} + 2 q^{51} + 20 q^{52} - 20 q^{53} - 18 q^{54} + 16 q^{55} + 12 q^{57} + 8 q^{58} - 30 q^{59} - 4 q^{60} - 20 q^{61} - 8 q^{62} - 4 q^{63} - 12 q^{64} + 46 q^{66} + 36 q^{67} + 24 q^{68} + 30 q^{69} - 4 q^{70} - 10 q^{72} - 20 q^{73} + 20 q^{74} + 40 q^{75} + 16 q^{77} - 16 q^{78} - 20 q^{79} - 54 q^{81} - 10 q^{82} + 46 q^{83} - 10 q^{84} + 10 q^{85} + 30 q^{86} - 8 q^{87} - 8 q^{88} - 62 q^{90} - 36 q^{91} - 10 q^{92} + 44 q^{93} - 50 q^{95} + 4 q^{96} - 2 q^{97} + 48 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 12 * q^2 - 4 * q^3 - 12 * q^4 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 8 * q^11 + 6 * q^12 - 24 * q^15 - 12 * q^16 + 24 * q^17 + 10 * q^18 + 30 * q^19 - 8 * q^22 - 6 * q^24 + 18 * q^25 + 20 * q^26 + 38 * q^27 - 8 * q^29 - 36 * q^30 - 32 * q^31 - 48 * q^32 + 24 * q^33 - 4 * q^34 - 6 * q^35 - 20 * q^37 - 20 * q^38 - 34 * q^39 - 22 * q^44 + 12 * q^45 + 20 * q^46 - 20 * q^47 - 4 * q^48 + 12 * q^49 - 28 * q^50 + 2 * q^51 + 20 * q^52 - 20 * q^53 - 18 * q^54 + 16 * q^55 + 12 * q^57 + 8 * q^58 - 30 * q^59 - 4 * q^60 - 20 * q^61 - 8 * q^62 - 4 * q^63 - 12 * q^64 + 46 * q^66 + 36 * q^67 + 24 * q^68 + 30 * q^69 - 4 * q^70 - 10 * q^72 - 20 * q^73 + 20 * q^74 + 40 * q^75 + 16 * q^77 - 16 * q^78 - 20 * q^79 - 54 * q^81 - 10 * q^82 + 46 * q^83 - 10 * q^84 + 10 * q^85 + 30 * q^86 - 8 * q^87 - 8 * q^88 - 62 * q^90 - 36 * q^91 - 10 * q^92 + 44 * q^93 - 50 * q^95 + 4 * q^96 - 2 * q^97 + 48 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−0.711719	−	1.57907i	−0.410911	−	0.911675i
$3$	−0.711719	−	1.57907i	−0.410911	−	0.911675i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.152745	−	0.0496298i	−0.0683096	−	0.0221951i	0.274663	−	0.961541i	$-0.411434\pi$
$5$	−0.152745	−	0.0496298i	−0.0683096	−	0.0221951i	−0.342972	+	0.939345i	$0.611434\pi$
$6$	−1.28185	+	1.16484i	−0.523313	+	0.475546i
$7$	0.587785	+	0.809017i	0.222162	+	0.305780i
$7$	0.587785	+	0.809017i	0.222162	+	0.305780i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−1.98691	+	2.24771i	−0.662304	+	0.749235i
$10$			0.160605i			0.0507879i
$11$	−3.12194	−	1.11961i	−0.941299	−	0.337574i
$11$	−3.12194	−	1.11961i	−0.941299	−	0.337574i
$12$	1.50395	+	0.859155i	0.434152	+	0.248017i
$13$	−6.36388	+	2.06775i	−1.76502	+	0.573491i	−0.997701	−	0.0677714i	$-0.978411\pi$
$13$	−6.36388	+	2.06775i	−1.76502	+	0.573491i	−0.767322	+	0.641262i	$0.778411\pi$
$14$	0.587785	−	0.809017i	0.157092	−	0.216219i
$15$	0.0303426	+	0.276517i	0.00783442	+	0.0713964i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.841882	−	2.59105i	0.204186	−	0.628421i	−0.795559	−	0.605876i	$-0.792823\pi$
$17$	0.841882	−	2.59105i	0.204186	−	0.628421i	0.999746	−	0.0225456i	$-0.00717710\pi$
$18$	2.75168	+	1.19509i	0.648578	+	0.281685i
$19$	−3.45842	+	4.76011i	−0.793417	+	1.09204i	0.200257	+	0.979743i	$0.435822\pi$
$19$	−3.45842	+	4.76011i	−0.793417	+	1.09204i	−0.993674	+	0.112301i	$0.964178\pi$
$20$	0.152745	−	0.0496298i	0.0341548	−	0.0110976i
$21$	0.859155	−	1.50395i	0.187483	−	0.328188i
$22$	−0.100078	+	3.31511i	−0.0213367	+	0.706785i
$23$			2.94363i			0.613788i	0.951744	+	0.306894i	$0.0992898\pi$
$23$			2.94363i			0.613788i	−0.951744	+	0.306894i	$0.900710\pi$
$24$	0.352360	−	1.69583i	0.0719252	−	0.346160i
$25$	−4.02422	−	2.92376i	−0.804843	−	0.584753i
$26$	3.93309	+	5.41344i	0.771343	+	1.06166i
$27$	4.96340	+	1.53773i	0.955207	+	0.295937i
$28$	−0.951057	−	0.309017i	−0.179733	−	0.0583987i
$29$	5.12098	−	3.72061i	0.950942	−	0.690900i	−8.76975e−5	−	1.00000i	$-0.500028\pi$
$29$	5.12098	−	3.72061i	0.950942	−	0.690900i	0.951029	+	0.309100i	$0.100028\pi$
$30$	0.253607	−	0.114306i	0.0463021	−	0.0208693i
$31$	2.60546	+	8.01878i	0.467954	+	1.44021i	0.855229	+	0.518250i	$0.173416\pi$
$31$	2.60546	+	8.01878i	0.467954	+	1.44021i	−0.387275	+	0.921964i	$0.626584\pi$
$32$	−1.00000			−0.176777
$33$	0.454006	+	5.72659i	0.0790324	+	0.996872i
$34$	−2.72439			−0.467229
$35$	−0.0496298	−	0.152745i	−0.00838897	−	0.0258186i
$36$	0.286277	−	2.98631i	0.0477129	−	0.497718i
$37$	−0.501222	+	0.364159i	−0.0824003	+	0.0598673i	−0.628223	−	0.778034i	$-0.716217\pi$
$37$	−0.501222	+	0.364159i	−0.0824003	+	0.0598673i	0.545822	+	0.837901i	$0.316217\pi$
$38$	5.59585	+	1.81820i	0.907766	+	0.294951i
$39$	7.79441	+	8.57734i	1.24810	+	1.37347i
$40$	−0.0944015	−	0.129933i	−0.0149262	−	0.0205441i
$41$	−4.44808	−	3.23172i	−0.694673	−	0.504709i	0.183520	−	0.983016i	$-0.441251\pi$
$41$	−4.44808	−	3.23172i	−0.694673	−	0.504709i	−0.878193	+	0.478307i	$0.841251\pi$
$42$	−1.69583	−	0.352360i	−0.261672	−	0.0543703i
$43$		−	2.41048i		−	0.367594i	−0.982964	−	0.183797i	$-0.941161\pi$
$43$		−	2.41048i		−	0.367594i	0.982964	−	0.183797i	$-0.0588390\pi$
$44$	3.18379	−	0.929247i	0.479974	−	0.140089i
$45$	0.415044	−	0.244715i	0.0618711	−	0.0364800i
$46$	2.79955	−	0.909630i	0.412772	−	0.134118i
$47$	−1.56714	+	2.15699i	−0.228592	+	0.314629i	−0.907870	−	0.419251i	$-0.862293\pi$
$47$	−1.56714	+	2.15699i	−0.228592	+	0.314629i	0.679279	+	0.733880i	$0.262293\pi$
$48$	−1.72172	+	0.188926i	−0.248508	+	0.0272691i
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$	−1.53711	+	4.73075i	−0.217381	+	0.669029i
$51$	−4.69062	+	0.514708i	−0.656819	+	0.0720736i
$52$	3.93309	−	5.41344i	0.545422	−	0.750709i
$53$	2.46767	−	0.801796i	0.338961	−	0.110135i	−0.134590	−	0.990901i	$-0.542972\pi$
$53$	2.46767	−	0.801796i	0.338961	−	0.110135i	0.473551	+	0.880766i	$0.342972\pi$
$54$	−0.0713040	−	5.19566i	−0.00970325	−	0.707040i
$55$	0.421294	+	0.325955i	0.0568072	+	0.0439518i
$56$			1.00000i			0.133631i
$57$	9.97797	+	2.07322i	1.32161	+	0.274605i
$58$	−5.12098	−	3.72061i	−0.672417	−	0.488540i
$59$	−8.48442	−	11.6778i	−1.10458	−	1.52032i	−0.829174	−	0.558991i	$-0.811189\pi$
$59$	−8.48442	−	11.6778i	−1.10458	−	1.52032i	−0.275403	−	0.961329i	$-0.588811\pi$
$60$	−0.187080	−	0.205872i	−0.0241520	−	0.0265780i
$61$	−7.68134	−	2.49582i	−0.983495	−	0.319557i	−0.227243	−	0.973838i	$-0.572971\pi$
$61$	−7.68134	−	2.49582i	−0.983495	−	0.319557i	−0.756251	+	0.654281i	$0.772971\pi$
$62$	6.82118	−	4.95588i	0.866291	−	0.629397i
$63$	−2.98631	−	0.286277i	−0.376240	−	0.0360675i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	1.07467			0.133297
$66$	5.30602	−	2.20140i	0.653126	−	0.270974i
$67$	9.38707			1.14681			0.573407	−	0.819271i	$-0.305622\pi$
$67$	9.38707			1.14681			0.573407	+	0.819271i	$0.305622\pi$
$68$	0.841882	+	2.59105i	0.102093	+	0.314211i
$69$	4.64819	−	2.09503i	0.559576	−	0.252213i
$70$	−0.129933	+	0.0944015i	−0.0155299	+	0.0112831i
$71$	−10.0295	−	3.25877i	−1.19028	−	0.386745i	−0.354103	−	0.935207i	$-0.615214\pi$
$71$	−10.0295	−	3.25877i	−1.19028	−	0.386745i	−0.836176	+	0.548462i	$0.815214\pi$
$72$	−2.92861	+	0.650555i	−0.345140	+	0.0766686i
$73$	0.0597686	+	0.0822645i	0.00699539	+	0.00962833i	0.812500	−	0.582961i	$-0.198106\pi$
$73$	0.0597686	+	0.0822645i	0.00699539	+	0.00962833i	−0.805505	+	0.592589i	$0.798106\pi$
$74$	0.501222	+	0.364159i	0.0582658	+	0.0423326i
$75$	−1.75271	+	8.43541i	−0.202386	+	0.974037i
$76$		−	5.88382i		−	0.674921i
$77$	−0.929247	−	3.18379i	−0.105898	−	0.362826i
$78$	5.74893	−	10.0635i	0.650938	−	1.13946i
$79$	−8.72301	+	2.83428i	−0.981415	+	0.318881i	−0.755415	−	0.655246i	$-0.772565\pi$
$79$	−8.72301	+	2.83428i	−0.981415	+	0.318881i	−0.226000	+	0.974127i	$0.572565\pi$
$80$	−0.0944015	+	0.129933i	−0.0105544	+	0.0145269i
$81$	−1.10436	−	8.93199i	−0.122707	−	0.992443i
$82$	−1.69901	+	5.22903i	−0.187625	+	0.577450i
$83$	−4.39153	+	13.5157i	−0.482033	+	1.48355i	0.354199	+	0.935170i	$0.384754\pi$
$83$	−4.39153	+	13.5157i	−0.482033	+	1.48355i	−0.836232	+	0.548376i	$0.815246\pi$
$84$	0.188926	+	1.72172i	0.0206135	+	0.187855i
$85$	−0.257186	+	0.353987i	−0.0278958	+	0.0383953i
$86$	−2.29250	+	0.744879i	−0.247207	+	0.0803223i
$87$	−9.51979	−	5.43834i	−1.02063	−	0.583052i
$88$	−1.86761	−	2.74081i	−0.199088	−	0.292171i
$89$			15.1000i			1.60060i	0.599601	+	0.800299i	$0.295326\pi$
$89$			15.1000i			1.60060i	−0.599601	+	0.800299i	$0.704674\pi$
$90$	−0.360994	−	0.319109i	−0.0380521	−	0.0336370i
$91$	−5.41344	−	3.93309i	−0.567483	−	0.412300i
$92$	−1.73022	−	2.38144i	−0.180388	−	0.248283i
$93$	10.8078	−	9.82131i	1.12072	−	1.01842i
$94$	2.53569	+	0.823897i	0.261537	+	0.0849785i
$95$	0.764500	−	0.555442i	0.0784361	−	0.0569871i
$96$	0.711719	+	1.57907i	0.0726395	+	0.161163i
$97$	−3.20306	−	9.85801i	−0.325222	−	1.00093i	−0.971341	−	0.237692i	$-0.923609\pi$
$97$	−3.20306	−	9.85801i	−0.325222	−	1.00093i	0.646119	−	0.763237i	$-0.276391\pi$
$98$	1.00000			0.101015
$99$	8.71956	−	4.79263i	0.876348	−	0.481678i
$100$	4.97421			0.497421
$101$	−3.65609	−	11.2523i	−0.363795	−	1.11964i	−0.950732	−	0.310013i	$-0.899667\pi$
$101$	−3.65609	−	11.2523i	−0.363795	−	1.11964i	0.586938	−	0.809632i	$-0.300333\pi$
$102$	1.93900	+	4.30199i	0.191990	+	0.425961i
$103$	0.881475	−	0.640429i	0.0868543	−	0.0631033i	−0.543511	−	0.839402i	$-0.682905\pi$
$103$	0.881475	−	0.640429i	0.0868543	−	0.0631033i	0.630365	+	0.776299i	$0.282905\pi$
$104$	−6.36388	−	2.06775i	−0.624030	−	0.202760i
$105$	−0.205872	+	0.187080i	−0.0200911	+	0.0182572i
$106$	−1.52511	−	2.09913i	−0.148131	−	0.203885i
$107$	−6.75237	−	4.90589i	−0.652776	−	0.474270i	0.211439	−	0.977391i	$-0.432185\pi$
$107$	−6.75237	−	4.90589i	−0.652776	−	0.474270i	−0.864216	+	0.503121i	$0.832185\pi$
$108$	−4.91934	+	1.67336i	−0.473363	+	0.161019i
$109$		−	0.765456i		−	0.0733174i	−0.999328	−	0.0366587i	$-0.988329\pi$
$109$		−	0.765456i		−	0.0733174i	0.999328	−	0.0366587i	$-0.0116714\pi$
$110$	0.179815	−	0.501400i	0.0171447	−	0.0478066i
$111$	0.931761	+	0.532284i	0.0884388	+	0.0505222i
$112$	0.951057	−	0.309017i	0.0898664	−	0.0291994i
$113$	6.11535	−	8.41706i	0.575284	−	0.791810i	−0.417885	−	0.908500i	$-0.637228\pi$
$113$	6.11535	−	8.41706i	0.575284	−	0.791810i	0.993168	+	0.116690i	$0.0372283\pi$
$114$	−1.11161	−	10.1303i	−0.104112	−	0.948787i
$115$	0.146092	−	0.449624i	0.0136231	−	0.0419276i
$116$	−1.95604	+	6.02007i	−0.181614	+	0.558950i
$117$	7.99678	−	18.4126i	0.739302	−	1.70224i
$118$	−8.48442	+	11.6778i	−0.781054	+	1.07503i
$119$	2.59105	−	0.841882i	0.237521	−	0.0771752i
$120$	−0.137985	+	0.241542i	−0.0125962	+	0.0220497i
$121$	8.49296	+	6.99068i	0.772088	+	0.635516i
$122$			8.07664i			0.731225i
$123$	−1.93732	+	9.32389i	−0.174682	+	0.840707i
$124$	−6.82118	−	4.95588i	−0.612560	−	0.445051i
$125$	0.941580	+	1.29597i	0.0842175	+	0.115915i
$126$	0.650555	+	2.92861i	0.0579560	+	0.260902i
$127$	12.9700	+	4.21421i	1.15090	+	0.373951i	0.821483	−	0.570233i	$-0.193147\pi$
$127$	12.9700	+	4.21421i	1.15090	+	0.373951i	0.329419	+	0.944184i	$0.393147\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−3.80631	+	1.71558i	−0.335127	+	0.151049i
$130$	−0.332092	−	1.02207i	−0.0291264	−	0.0896418i
$131$	−7.47224			−0.652852			−0.326426	−	0.945223i	$-0.605844\pi$
$131$	−7.47224			−0.652852			−0.326426	+	0.945223i	$0.605844\pi$
$132$	−3.73331	−	4.36605i	−0.324943	−	0.380016i
$133$	−5.88382			−0.510192
$134$	−2.90076	−	8.92763i	−0.250588	−	0.771230i
$135$	−0.681817	−	0.481214i	−0.0586815	−	0.0414163i
$136$	2.20408	−	1.60136i	0.188998	−	0.137315i
$137$	−4.15192	−	1.34904i	−0.354722	−	0.115256i	0.126235	−	0.992000i	$-0.459711\pi$
$137$	−4.15192	−	1.34904i	−0.354722	−	0.115256i	−0.480957	+	0.876744i	$0.659711\pi$
$138$	−3.42886	−	3.77329i	−0.291884	−	0.321203i
$139$	−12.1741	−	16.7562i	−1.03260	−	1.42125i	−0.902981	−	0.429681i	$-0.858626\pi$
$139$	−12.1741	−	16.7562i	−1.03260	−	1.42125i	−0.129615	−	0.991564i	$-0.541374\pi$
$140$	0.129933	+	0.0944015i	0.0109813	+	0.00797839i
$141$	4.52140	+	0.939457i	0.380771	+	0.0791166i
$142$			10.5456i			0.884967i
$143$	22.1827	+	0.669659i	1.85501	+	0.0559997i
$144$	1.52371	+	2.58424i	0.126975	+	0.215354i
$145$	−0.966856	+	0.314151i	−0.0802930	+	0.0260888i
$146$	0.0597686	−	0.0822645i	0.00494649	−	0.00680826i
$147$	1.72172	−	0.188926i	0.142005	−	0.0155824i
$148$	0.191450	−	0.589221i	0.0157371	−	0.0484337i
$149$	0.923115	−	2.84105i	0.0756245	−	0.232748i	−0.906097	−	0.423069i	$-0.860953\pi$
$149$	0.923115	−	2.84105i	0.0756245	−	0.232748i	0.981722	+	0.190321i	$0.0609528\pi$
$150$	8.56417	−	0.939758i	0.699262	−	0.0767309i
$151$	0.0890010	−	0.122499i	0.00724280	−	0.00996886i	−0.805380	−	0.592759i	$-0.798039\pi$
$151$	0.0890010	−	0.122499i	0.00724280	−	0.00996886i	0.812623	+	0.582790i	$0.198039\pi$
$152$	−5.59585	+	1.81820i	−0.453883	+	0.147476i
$153$	4.15117	+	7.04049i	0.335602	+	0.569190i
$154$	−2.74081	+	1.86761i	−0.220861	+	0.150496i
$155$		−	1.35414i		−	0.108767i
$156$	−11.3474	−	2.35778i	−0.908523	−	0.188773i
$157$	1.43904	+	1.04552i	0.114848	+	0.0834417i	0.643727	−	0.765256i	$-0.277387\pi$
$157$	1.43904	+	1.04552i	0.114848	+	0.0834417i	−0.528879	+	0.848697i	$0.677387\pi$
$158$	5.39112	+	7.42024i	0.428894	+	0.590322i
$159$	−3.02238	−	3.32597i	−0.239690	−	0.263767i
$160$	0.152745	+	0.0496298i	0.0120755	+	0.00392358i
$161$	−2.38144	+	1.73022i	−0.187684	+	0.136360i
$162$	−8.15356	+	3.81045i	−0.640604	+	0.299377i
$163$	5.31247	+	16.3501i	0.416105	+	1.28064i	0.911259	+	0.411833i	$0.135111\pi$
$163$	5.31247	+	16.3501i	0.416105	+	1.28064i	−0.495154	+	0.868805i	$0.664889\pi$
$164$	5.49813			0.429331
$165$	0.214863	−	0.897240i	0.0167270	−	0.0698501i
$166$	14.2113			1.10301
$167$	6.43253	+	19.7973i	0.497764	+	1.53196i	0.812605	+	0.582815i	$0.198049\pi$
$167$	6.43253	+	19.7973i	0.497764	+	1.53196i	−0.314841	+	0.949145i	$0.601951\pi$
$168$	1.57907	−	0.711719i	0.121828	−	0.0549103i
$169$	25.7062	−	18.6766i	1.97740	−	1.43666i
$170$	0.416136	+	0.135211i	0.0319162	+	0.0103702i
$171$	−3.82775	−	17.2314i	−0.292715	−	1.31772i
$172$	1.41684	+	1.95012i	0.108033	+	0.148695i
$173$	−14.9931	−	10.8931i	−1.13990	−	0.828188i	−0.152797	−	0.988258i	$-0.548828\pi$
$173$	−14.9931	−	10.8931i	−1.13990	−	0.828188i	−0.987106	+	0.160069i	$0.948828\pi$
$174$	−2.23040	+	10.7344i	−0.169086	+	0.813773i
$175$		−	4.97421i		−	0.376015i
$176$	−2.02954	+	2.62316i	−0.152982	+	0.197728i
$177$	−12.4015	+	21.7088i	−0.932155	+	1.63173i
$178$	14.3610	−	4.66616i	1.07640	−	0.349743i
$179$	10.7526	−	14.7997i	0.803686	−	1.10618i	−0.188581	−	0.982058i	$-0.560389\pi$
$179$	10.7526	−	14.7997i	0.803686	−	1.10618i	0.992267	−	0.124121i	$-0.0396111\pi$
$180$	−0.191937	+	0.441936i	−0.0143062	+	0.0329399i
$181$	0.221317	−	0.681143i	0.0164503	−	0.0506289i	−0.942494	−	0.334222i	$-0.891526\pi$
$181$	0.221317	−	0.681143i	0.0164503	−	0.0506289i	0.958945	+	0.283593i	$0.0915265\pi$
$182$	−2.06775	+	6.36388i	−0.153272	+	0.471722i
$183$	1.52589	+	13.9057i	0.112797	+	1.02794i
$184$	−1.73022	+	2.38144i	−0.127553	+	0.175562i
$185$	0.0946322	−	0.0307479i	0.00695750	−	0.00226063i
$186$	−12.6804	−	7.24391i	−0.929774	−	0.531150i
$187$	−5.52926	+	7.14651i	−0.404339	+	0.522604i
$188$		−	2.66619i		−	0.194452i
$189$	1.67336	+	4.91934i	0.121719	+	0.357829i
$190$	−0.764500	−	0.555442i	−0.0554627	−	0.0402960i
$191$	15.3041	+	21.0643i	1.10737	+	1.52416i	0.825240	+	0.564782i	$0.191040\pi$
$191$	15.3041	+	21.0643i	1.10737	+	1.52416i	0.282126	+	0.959377i	$0.408960\pi$
$192$	1.28185	−	1.16484i	0.0925095	−	0.0840654i
$193$	−2.38681	−	0.775523i	−0.171807	−	0.0558234i	0.221851	−	0.975081i	$-0.428790\pi$
$193$	−2.38681	−	0.775523i	−0.171807	−	0.0558234i	−0.393657	+	0.919257i	$0.628790\pi$
$194$	−8.38572	+	6.09258i	−0.602060	+	0.437422i
$195$	−0.764865	−	1.69698i	−0.0547731	−	0.121523i
$196$	−0.309017	−	0.951057i	−0.0220726	−	0.0679326i
$197$	7.14552			0.509097			0.254549	−	0.967060i	$-0.418073\pi$
$197$	7.14552			0.509097			0.254549	+	0.967060i	$0.418073\pi$
$198$	−7.25256	−	6.81179i	−0.515417	−	0.484093i
$199$	12.9631			0.918927			0.459464	−	0.888197i	$-0.348042\pi$
$199$	12.9631			0.918927			0.459464	+	0.888197i	$0.348042\pi$
$200$	−1.53711	−	4.73075i	−0.108690	−	0.334515i
$201$	−6.68096	−	14.8228i	−0.471238	−	1.04552i
$202$	−9.57177	+	6.95430i	−0.673467	+	0.489303i
$203$	6.02007	+	1.95604i	0.422526	+	0.137287i
$204$	3.49226	−	3.17349i	0.244507	−	0.222189i
$205$	0.519031	+	0.714386i	0.0362507	+	0.0498948i
$206$	−0.881475	−	0.640429i	−0.0614153	−	0.0446208i
$207$	−6.61640	−	5.84872i	−0.459872	−	0.406514i
$208$			6.69138i			0.463964i
$209$	16.1264	−	10.9887i	1.11549	−	0.760104i
$210$	0.241542	+	0.137985i	0.0166680	+	0.00952187i
$211$	−21.9899	+	7.14496i	−1.51385	+	0.491879i	−0.944021	−	0.329885i	$-0.892990\pi$
$211$	−21.9899	+	7.14496i	−1.51385	+	0.491879i	−0.569828	+	0.821764i	$0.692990\pi$
$212$	−1.52511	+	2.09913i	−0.104745	+	0.144169i
$213$	1.99234	+	18.1565i	0.136513	+	1.24407i
$214$	−2.57918	+	7.93789i	−0.176309	+	0.542623i
$215$	−0.119632	+	0.368188i	−0.00815881	+	0.0251102i
$216$	3.11162	+	4.16147i	0.211719	+	0.283152i
$217$	−4.95588	+	6.82118i	−0.336427	+	0.463052i
$218$	−0.727992	+	0.236539i	−0.0493058	+	0.0160204i
$219$	0.0873627	−	0.152928i	0.00590342	−	0.0103339i
$220$	−0.532426	−	0.0160731i	−0.0358961	−	0.00108364i
$221$			18.2299i			1.22628i
$222$	0.218303	−	1.05064i	0.0146515	−	0.0705145i
$223$	6.15373	+	4.47095i	0.412084	+	0.299397i	0.774445	−	0.632641i	$-0.218029\pi$
$223$	6.15373	+	4.47095i	0.412084	+	0.299397i	−0.362361	+	0.932038i	$0.618029\pi$
$224$	−0.587785	−	0.809017i	−0.0392731	−	0.0540547i
$225$	14.5675	−	3.23599i	0.971169	−	0.215733i
$226$	−9.89485	−	3.21503i	−0.658195	−	0.213861i
$227$	−19.2651	+	13.9969i	−1.27867	+	0.929009i	−0.999512	−	0.0312354i	$-0.990056\pi$
$227$	−19.2651	+	13.9969i	−1.27867	+	0.929009i	−0.279160	+	0.960245i	$0.590056\pi$
$228$	−9.29096	+	4.18763i	−0.615309	+	0.277332i
$229$	−4.25896	−	13.1077i	−0.281440	−	0.866184i	−0.987443	−	0.157975i	$-0.949504\pi$
$229$	−4.25896	−	13.1077i	−0.281440	−	0.866184i	0.706003	−	0.708209i	$-0.250496\pi$
$230$	−0.472762			−0.0311730
$231$	−4.36605	+	3.73331i	−0.287265	+	0.245634i
$232$	6.32988			0.415577
$233$	0.322037	+	0.991129i	0.0210974	+	0.0649310i	0.961051	−	0.276371i	$-0.0891320\pi$
$233$	0.322037	+	0.991129i	0.0210974	+	0.0649310i	−0.939954	+	0.341302i	$0.889132\pi$
$234$	−19.9825	−	1.91559i	−1.30630	−	0.125226i
$235$	0.346424	−	0.251692i	0.0225982	−	0.0164186i
$236$	13.7281	+	4.46052i	0.893621	+	0.290355i
$237$	10.6838	+	11.7570i	0.693991	+	0.763700i
$238$	−1.60136	−	2.20408i	−0.103800	−	0.142869i
$239$	−17.2577	−	12.5384i	−1.11630	−	0.811043i	−0.132660	−	0.991162i	$-0.542352\pi$
$239$	−17.2577	−	12.5384i	−1.11630	−	0.811043i	−0.983645	+	0.180119i	$0.942352\pi$
$240$	0.272360	+	0.0565910i	0.0175807	+	0.00365293i
$241$			12.2281i			0.787678i	0.919179	+	0.393839i	$0.128853\pi$
$241$			12.2281i			0.787678i	−0.919179	+	0.393839i	$0.871147\pi$
$242$	4.02406	−	10.2375i	0.258676	−	0.658093i
$243$	−13.3182	+	8.10093i	−0.854364	+	0.519675i
$244$	7.68134	−	2.49582i	0.491747	−	0.159778i
$245$	0.0944015	−	0.129933i	0.00603109	−	0.00830109i
$246$	9.46621	−	1.03874i	0.603544	−	0.0662276i
$247$	12.1663	−	37.4439i	0.774121	−	2.38250i
$248$	−2.60546	+	8.01878i	−0.165447	+	0.509193i
$249$	24.4678	−	2.68489i	1.55059	−	0.170148i
$250$	0.941580	−	1.29597i	0.0595508	−	0.0819646i
$251$	−0.705970	+	0.229384i	−0.0445604	+	0.0144786i	−0.331212	−	0.943556i	$-0.607458\pi$
$251$	−0.705970	+	0.229384i	−0.0445604	+	0.0144786i	0.286652	+	0.958035i	$0.407458\pi$
$252$	2.58424	−	1.52371i	0.162792	−	0.0959844i
$253$	3.29570	−	9.18981i	0.207199	−	0.577758i
$254$		−	13.6375i		−	0.855691i
$255$	0.742014	+	0.154176i	0.0464667	+	0.00965486i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.74642	−	2.40375i	−0.108939	−	0.149942i	0.751066	−	0.660227i	$-0.229540\pi$
$257$	−1.74642	−	2.40375i	−0.108939	−	0.149942i	−0.860005	+	0.510285i	$0.829540\pi$
$258$	2.80783	+	3.08987i	0.174808	+	0.192367i
$259$	−0.589221	−	0.191450i	−0.0366124	−	0.0118961i
$260$	−0.869428	+	0.631676i	−0.0539196	+	0.0391749i
$261$	−1.81210	+	18.9030i	−0.112166	+	1.17006i
$262$	2.30905	+	7.10652i	0.142653	+	0.439042i
$263$	2.16498			0.133499			0.0667493	−	0.997770i	$-0.478737\pi$
$263$	2.16498			0.133499			0.0667493	+	0.997770i	$0.478737\pi$
$264$	−2.99871	+	4.89977i	−0.184558	+	0.301560i
$265$	−0.416718			−0.0255988
$266$	1.81820	+	5.59585i	0.111481	+	0.343103i
$267$	23.8439	−	10.7470i	1.45923	−	0.657704i
$268$	−7.59430	+	5.51758i	−0.463896	+	0.337040i
$269$	1.35856	+	0.441423i	0.0828328	+	0.0269140i	0.350140	−	0.936697i	$-0.386134\pi$
$269$	1.35856	+	0.441423i	0.0828328	+	0.0269140i	−0.267307	+	0.963611i	$0.586134\pi$
$270$	−0.246969	+	0.797150i	−0.0150300	+	0.0485130i
$271$	8.04765	+	11.0766i	0.488860	+	0.672858i	0.980177	−	0.198123i	$-0.0634844\pi$
$271$	8.04765	+	11.0766i	0.488860	+	0.672858i	−0.491317	+	0.870981i	$0.663484\pi$
$272$	−2.20408	−	1.60136i	−0.133642	−	0.0970964i
$273$	−2.35778	+	11.3474i	−0.142699	+	0.686779i
$274$			4.36559i			0.263735i
$275$	9.28988	+	13.6333i	0.560201	+	0.822122i
$276$	−2.52903	+	4.42705i	−0.152230	+	0.266477i
$277$	−8.82592	+	2.86771i	−0.530298	+	0.172304i	−0.561914	−	0.827196i	$-0.689935\pi$
$277$	−8.82592	+	2.86771i	−0.530298	+	0.172304i	0.0316157	+	0.999500i	$0.489935\pi$
$278$	−12.1741	+	16.7562i	−0.730155	+	1.00497i
$279$	−23.2007	−	10.0763i	−1.38899	−	0.603252i
$280$	0.0496298	−	0.152745i	0.00296595	−	0.00912825i
$281$	−4.04096	+	12.4368i	−0.241064	+	0.741918i	0.755195	+	0.655500i	$0.227542\pi$
$281$	−4.04096	+	12.4368i	−0.241064	+	0.741918i	−0.996259	+	0.0864177i	$0.972458\pi$
$282$	−0.503712	−	4.59042i	−0.0299956	−	0.273355i
$283$	−8.51009	+	11.7131i	−0.505873	+	0.696274i	−0.983216	−	0.182443i	$-0.941600\pi$
$283$	−8.51009	+	11.7131i	−0.505873	+	0.696274i	0.477344	+	0.878717i	$0.341600\pi$
$284$	10.0295	−	3.25877i	0.595139	−	0.193372i
$285$	−1.42119	−	0.811879i	−0.0841840	−	0.0480916i
$286$	−6.21794	−	21.3039i	−0.367675	−	1.25973i
$287$		−	5.49813i		−	0.324544i
$288$	1.98691	−	2.24771i	0.117080	−	0.132447i
$289$	7.74853	+	5.62964i	0.455796	+	0.331155i
$290$	0.597550	+	0.822457i	0.0350893	+	0.0482963i
$291$	−13.2868	+	12.0740i	−0.778885	+	0.707789i
$292$	−0.0967077	−	0.0314222i	−0.00565939	−	0.00183885i
$293$	−6.56633	+	4.77072i	−0.383609	+	0.278708i	−0.762832	−	0.646597i	$-0.776191\pi$
$293$	−6.56633	+	4.77072i	−0.383609	+	0.278708i	0.379223	+	0.925305i	$0.376191\pi$
$294$	−0.711719	−	1.57907i	−0.0415083	−	0.0920931i
$295$	0.716384	+	2.20480i	0.0417095	+	0.128369i
$296$	−0.619544			−0.0360103
$297$	−13.7738	−	10.3578i	−0.799235	−	0.601018i
$298$	−2.98726			−0.173047
$299$	−6.08668	−	18.7329i	−0.352002	−	1.08335i
$300$	−3.54024	−	7.85461i	−0.204396	−	0.453486i
$301$	1.95012	−	1.41684i	0.112403	−	0.0816655i
$302$	−0.144007	−	0.0467906i	−0.00828665	−	0.00269250i
$303$	−15.1660	+	13.7817i	−0.871265	+	0.791737i
$304$	3.45842	+	4.76011i	0.198354	+	0.273011i
$305$	1.04942	+	0.762447i	0.0600895	+	0.0436576i
$306$	5.41312	−	6.12362i	0.309447	−	0.350064i
$307$			20.9851i			1.19769i	0.800867	+	0.598843i	$0.204373\pi$
$307$			20.9851i			1.19769i	−0.800867	+	0.598843i	$0.795627\pi$
$308$	2.62316	+	2.02954i	0.149468	+	0.115644i
$309$	−1.63864	−	0.936103i	−0.0932192	−	0.0532531i
$310$	−1.28786	+	0.418451i	−0.0731455	+	0.0237664i
$311$	4.45601	−	6.13317i	0.252677	−	0.347780i	−0.663770	−	0.747937i	$-0.731044\pi$
$311$	4.45601	−	6.13317i	0.252677	−	0.347780i	0.916447	+	0.400157i	$0.131044\pi$
$312$	1.26418	+	11.5207i	0.0715699	+	0.652229i
$313$	−0.203328	+	0.625778i	−0.0114928	+	0.0353710i	−0.956638	−	0.291278i	$-0.905920\pi$
$313$	−0.203328	+	0.625778i	−0.0114928	+	0.0353710i	0.945146	+	0.326649i	$0.105920\pi$
$314$	0.549663	−	1.69169i	0.0310193	−	0.0954676i
$315$	0.441936	+	0.191937i	0.0249003	+	0.0108144i
$316$	5.39112	−	7.42024i	0.303274	−	0.417421i
$317$	16.2965	−	5.29505i	0.915302	−	0.297400i	0.186764	−	0.982405i	$-0.440200\pi$
$317$	16.2965	−	5.29505i	0.915302	−	0.297400i	0.728538	+	0.685005i	$0.240200\pi$
$318$	−2.22922	+	3.90224i	−0.125008	+	0.218827i
$319$	−20.1530	+	5.88202i	−1.12835	+	0.329330i
$320$		−	0.160605i		−	0.00897812i
$321$	−2.94094	+	14.1541i	−0.164147	+	0.790003i
$322$	2.38144	+	1.73022i	0.132713	+	0.0964214i
$323$	9.42209	+	12.9684i	0.524259	+	0.721581i
$324$	6.14354	+	6.57700i	0.341308	+	0.365389i
$325$	31.6552	+	10.2854i	1.75592	+	0.570532i
$326$	13.9082	−	10.1049i	0.770305	−	0.559660i
$327$	−1.20871	+	0.544789i	−0.0668416	+	0.0301269i
$328$	−1.69901	−	5.22903i	−0.0938124	−	0.288725i
$329$	−2.66619			−0.146992
$330$	−0.919722	+	0.0729159i	−0.0506290	+	0.00401389i
$331$	11.6127			0.638293			0.319147	−	0.947705i	$-0.396604\pi$
$331$	11.6127			0.638293			0.319147	+	0.947705i	$0.396604\pi$
$332$	−4.39153	−	13.5157i	−0.241017	−	0.741773i
$333$	0.177361	−	1.85015i	0.00971934	−	0.101388i
$334$	16.8406	−	12.2354i	0.921475	−	0.669491i
$335$	−1.43383	−	0.465879i	−0.0783383	−	0.0254537i
$336$	−1.16484	−	1.28185i	−0.0635474	−	0.0699306i
$337$	10.2525	+	14.1114i	0.558492	+	0.768698i	0.991134	−	0.132868i	$-0.0424186\pi$
$337$	10.2525	+	14.1114i	0.558492	+	0.768698i	−0.432642	+	0.901566i	$0.642419\pi$
$338$	−25.7062	−	18.6766i	−1.39823	−	1.01587i
$339$	−17.6435	−	3.66597i	−0.958265	−	0.199108i
$340$		−	0.437552i		−	0.0237296i
$341$	0.843801	−	27.9512i	0.0456944	−	1.51364i
$342$	−15.2052	+	8.96521i	−0.822205	+	0.484783i
$343$	−0.951057	+	0.309017i	−0.0513522	+	0.0166853i
$344$	1.41684	−	1.95012i	0.0763911	−	0.105143i
$345$	−0.813963	+	0.0893172i	−0.0438223	+	0.00480868i
$346$	−5.72685	+	17.6254i	−0.307877	+	0.947549i
$347$	3.71644	−	11.4380i	0.199509	−	0.614025i	−0.800385	−	0.599486i	$-0.795372\pi$
$347$	3.71644	−	11.4380i	0.199509	−	0.614025i	0.999894	−	0.0145394i	$-0.00462821\pi$
$348$	10.8983	−	1.19588i	0.584208	−	0.0641059i
$349$	5.97931	−	8.22981i	0.320065	−	0.440532i	−0.618422	−	0.785846i	$-0.712228\pi$
$349$	5.97931	−	8.22981i	0.320065	−	0.440532i	0.938487	+	0.345315i	$0.112228\pi$
$350$	−4.73075	+	1.53711i	−0.252869	+	0.0821622i
$351$	−34.7662	+	0.477122i	−1.85568	+	0.0254669i
$352$	3.12194	+	1.11961i	0.166400	+	0.0596752i
$353$		−	9.39359i		−	0.499970i	−0.968250	−	0.249985i	$-0.919574\pi$
$353$		−	9.39359i		−	0.499970i	0.968250	−	0.249985i	$-0.0804257\pi$
$354$	24.4786	+	5.08616i	1.30102	+	0.270326i
$355$	1.37022	+	0.995521i	0.0727236	+	0.0528368i
$356$	−8.87556	−	12.2162i	−0.470404	−	0.647455i
$357$	−3.17349	−	3.49226i	−0.167959	−	0.184830i
$358$	−17.3980	−	5.65297i	−0.919515	−	0.298769i
$359$	17.8080	−	12.9382i	0.939869	−	0.682855i	−0.00852040	−	0.999964i	$-0.502712\pi$
$359$	17.8080	−	12.9382i	0.939869	−	0.682855i	0.948389	+	0.317109i	$0.102712\pi$
$360$	0.479618	+	0.0459777i	0.0252781	+	0.00242324i
$361$	−4.82665	−	14.8549i	−0.254034	−	0.781837i
$362$	−0.716196			−0.0376424
$363$	4.99415	−	18.3864i	0.262125	−	0.965034i
$364$	6.69138			0.350724
$365$	−0.00504658	−	0.0155318i	−0.000264150	−	0.000812971i
$366$	12.7536	−	5.74830i	0.666639	−	0.300468i
$367$	13.6048	−	9.88448i	0.710166	−	0.515966i	−0.173061	−	0.984911i	$-0.555366\pi$
$367$	13.6048	−	9.88448i	0.710166	−	0.515966i	0.883227	+	0.468945i	$0.155366\pi$
$368$	2.79955	+	0.909630i	0.145937	+	0.0474178i
$369$	16.1019	−	3.57683i	0.838231	−	0.186202i
$370$	−0.0584859	−	0.0804989i	−0.00304054	−	0.00418494i
$371$	2.09913	+	1.52511i	0.108981	+	0.0791796i
$372$	−2.97090	+	14.2983i	−0.154034	+	0.741332i
$373$			11.6100i			0.601145i	0.953759	+	0.300572i	$0.0971777\pi$
$373$			11.6100i			0.601145i	−0.953759	+	0.300572i	$0.902822\pi$
$374$	8.50536	+	3.05024i	0.439802	+	0.157724i
$375$	1.37629	−	2.40919i	0.0710713	−	0.124410i
$376$	−2.53569	+	0.823897i	−0.130768	+	0.0424892i
$377$	−24.8960	+	34.2664i	−1.28221	+	1.76481i
$378$	4.16147	−	3.11162i	0.214043	−	0.160044i
$379$	5.02873	−	15.4768i	0.258308	−	0.794992i	−0.734851	−	0.678228i	$-0.762748\pi$
$379$	5.02873	−	15.4768i	0.258308	−	0.794992i	0.993160	−	0.116763i	$-0.0372519\pi$
$380$	−0.292013	+	0.898724i	−0.0149800	+	0.0461036i
$381$	−2.57647	−	23.4798i	−0.131997	−	1.20291i
$382$	15.3041	−	21.0643i	0.783026	−	1.07774i
$383$	14.2826	−	4.64070i	0.729807	−	0.237129i	0.0795372	−	0.996832i	$-0.474656\pi$
$383$	14.2826	−	4.64070i	0.729807	−	0.237129i	0.650270	+	0.759703i	$0.274656\pi$
$384$	−1.50395	−	0.859155i	−0.0767479	−	0.0438436i
$385$	−0.0160731	+	0.532426i	−0.000819159	+	0.0271349i
$386$			2.50964i			0.127738i
$387$	5.41805	+	4.78941i	0.275415	+	0.243459i
$388$	8.38572	+	6.09258i	0.425720	+	0.309304i
$389$	−1.76075	−	2.42346i	−0.0892736	−	0.122875i	0.762044	−	0.647525i	$-0.224196\pi$
$389$	−1.76075	−	2.42346i	−0.0892736	−	0.122875i	−0.851318	+	0.524651i	$0.824196\pi$
$390$	−1.37757	+	1.25183i	−0.0697559	+	0.0633886i
$391$	7.62707	+	2.47819i	0.385718	+	0.125327i
$392$	−0.809017	+	0.587785i	−0.0408615	+	0.0296876i
$393$	5.31813	+	11.7992i	0.268264	+	0.595189i
$394$	−2.20809	−	6.79580i	−0.111242	−	0.342367i
$395$	1.47306			0.0741177
$396$	−4.23723	+	9.00255i	−0.212929	+	0.452395i
$397$	8.11214			0.407137			0.203568	−	0.979061i	$-0.434746\pi$
$397$	8.11214			0.407137			0.203568	+	0.979061i	$0.434746\pi$
$398$	−4.00581	−	12.3286i	−0.200793	−	0.617977i
$399$	4.18763	+	9.29096i	0.209644	+	0.465130i
$400$	−4.02422	+	2.92376i	−0.201211	+	0.146188i
$401$	−30.8478	−	10.0231i	−1.54047	−	0.500528i	−0.588962	−	0.808161i	$-0.700463\pi$
$401$	−30.8478	−	10.0231i	−1.54047	−	0.500528i	−0.951505	+	0.307633i	$0.900463\pi$
$402$	−12.0328	+	10.9345i	−0.600142	+	0.545362i
$403$	−33.1617	−	45.6431i	−1.65190	−	2.27364i
$404$	9.57177	+	6.95430i	0.476213	+	0.345989i
$405$	−0.274607	+	1.41912i	−0.0136453	+	0.0705169i
$406$		−	6.32988i		−	0.314147i
$407$	1.97250	−	0.575709i	0.0977730	−	0.0285369i
$408$	−4.09733	−	2.34067i	−0.202848	−	0.115881i
$409$	24.0621	−	7.81825i	1.18979	−	0.386587i	0.353797	−	0.935322i	$-0.384890\pi$
$409$	24.0621	−	7.81825i	1.18979	−	0.386587i	0.835997	+	0.548735i	$0.184890\pi$
$410$	0.519031	−	0.714386i	0.0256331	−	0.0352810i
$411$	0.824774	+	7.51630i	0.0406831	+	0.370752i
$412$	−0.336693	+	1.03624i	−0.0165877	+	0.0510517i
$413$	4.46052	−	13.7281i	0.219488	−	0.675514i
$414$	−3.51789	+	8.09993i	−0.172895	+	0.398090i
$415$	1.34157	−	1.84651i	0.0658550	−	0.0906416i
$416$	6.36388	−	2.06775i	0.312015	−	0.101380i
$417$	−17.7947	+	31.1495i	−0.871410	+	1.52540i
$418$	−15.4342	−	11.9415i	−0.754912	−	0.584076i
$419$			3.94839i			0.192892i	0.995338	+	0.0964458i	$0.0307475\pi$
$419$			3.94839i			0.192892i	−0.995338	+	0.0964458i	$0.969253\pi$
$420$	0.0565910	−	0.272360i	0.00276136	−	0.0132898i
$421$	−21.4274	−	15.5679i	−1.04431	−	0.758733i	−0.0731846	−	0.997318i	$-0.523316\pi$
$421$	−21.4274	−	15.5679i	−1.04431	−	0.758733i	−0.971121	+	0.238586i	$0.923316\pi$
$422$	13.5905	+	18.7057i	0.661576	+	0.910582i
$423$	−1.73450	−	7.80823i	−0.0843342	−	0.379649i
$424$	2.46767	+	0.801796i	0.119841	+	0.0389387i
$425$	−10.9635	+	7.96547i	−0.531809	+	0.386382i
$426$	16.6522	−	7.50551i	0.806803	−	0.363643i
$427$	−2.49582	−	7.68134i	−0.120781	−	0.371726i
$428$	8.34639			0.403438
$429$	−14.7304	−	35.5046i	−0.711191	−	1.71418i
$430$	0.387136			0.0186694
$431$	−11.3955	−	35.0716i	−0.548900	−	1.68934i	−0.711531	−	0.702655i	$-0.751998\pi$
$431$	−11.3955	−	35.0716i	−0.548900	−	1.68934i	0.162631	−	0.986687i	$-0.448002\pi$
$432$	2.99625	−	4.24529i	0.144157	−	0.204252i
$433$	−17.7907	+	12.9257i	−0.854966	+	0.621169i	−0.926511	−	0.376268i	$-0.877207\pi$
$433$	−17.7907	+	12.9257i	−0.854966	+	0.621169i	0.0715448	+	0.997437i	$0.477207\pi$
$434$	8.01878	+	2.60546i	0.384914	+	0.125066i
$435$	1.18420	+	1.30314i	0.0567778	+	0.0624810i
$436$	0.449924	+	0.619267i	0.0215474	+	0.0296575i
$437$	−14.0120	−	10.1803i	−0.670284	−	0.486990i
$438$	−0.172440	−	0.0358295i	−0.00823949	−	0.00171200i
$439$			0.987382i			0.0471252i	0.999722	+	0.0235626i	$0.00750090\pi$
$439$			0.987382i			0.0471252i	−0.999722	+	0.0235626i	$0.992499\pi$
$440$	0.149242	+	0.511334i	0.00711484	+	0.0243769i
$441$	−1.52371	−	2.58424i	−0.0725574	−	0.123059i
$442$	17.3377	−	5.63335i	0.824669	−	0.267951i
$443$	−5.42049	+	7.46066i	−0.257535	+	0.354467i	−0.918132	−	0.396274i	$-0.870303\pi$
$443$	−5.42049	+	7.46066i	−0.257535	+	0.354467i	0.660597	+	0.750740i	$0.270303\pi$
$444$	−1.06668	+	0.117048i	−0.0506223	+	0.00555486i
$445$	0.749411	−	2.30645i	0.0355255	−	0.109336i
$446$	2.35051	−	7.23414i	0.111300	−	0.342547i
$447$	−5.14322	+	0.564372i	−0.243266	+	0.0266939i
$448$	−0.587785	+	0.809017i	−0.0277702	+	0.0382225i
$449$	−28.6076	+	9.29517i	−1.35008	+	0.438666i	−0.892718	−	0.450617i	$-0.851204\pi$
$449$	−28.6076	+	9.29517i	−1.35008	+	0.438666i	−0.457358	+	0.889283i	$0.651204\pi$
$450$	−7.57923	−	12.8546i	−0.357288	−	0.605970i
$451$	10.2684	+	15.0693i	0.483518	+	0.709586i
$452$			10.4041i			0.489366i
$453$	−0.256779	−	0.0533535i	−0.0120645	−	0.00250677i
$454$	19.2651	+	13.9969i	0.904157	+	0.656909i
$455$	0.631676	+	0.869428i	0.0296134	+	0.0407594i
$456$	6.85373	+	7.54218i	0.320956	+	0.353195i
$457$	−13.0274	−	4.23287i	−0.609398	−	0.198005i	−0.0119705	−	0.999928i	$-0.503810\pi$
$457$	−13.0274	−	4.23287i	−0.609398	−	0.198005i	−0.597427	+	0.801923i	$0.703810\pi$
$458$	−11.1501	+	8.10103i	−0.521010	+	0.378536i
$459$	8.16294	−	11.5658i	0.381014	−	0.539846i
$460$	0.146092	+	0.449624i	0.00681156	+	0.0209638i
$461$	−2.00605			−0.0934310			−0.0467155	−	0.998908i	$-0.514875\pi$
$461$	−2.00605			−0.0934310			−0.0467155	+	0.998908i	$0.514875\pi$
$462$	4.89977	+	2.99871i	0.227958	+	0.139513i
$463$	−22.4838			−1.04491			−0.522456	−	0.852666i	$-0.674984\pi$
$463$	−22.4838			−1.04491			−0.522456	+	0.852666i	$0.674984\pi$
$464$	−1.95604	−	6.02007i	−0.0908069	−	0.279475i
$465$	−2.13827	+	0.963764i	−0.0991600	+	0.0446935i
$466$	0.843104	−	0.612551i	0.0390561	−	0.0283759i
$467$	14.7956	+	4.80739i	0.684659	+	0.222459i	0.630634	−	0.776080i	$-0.282795\pi$
$467$	14.7956	+	4.80739i	0.684659	+	0.222459i	0.0540251	+	0.998540i	$0.482795\pi$
$468$	4.35311	+	19.5965i	0.201222	+	0.905847i
$469$	5.51758	+	7.59430i	0.254778	+	0.350672i
$470$	−0.346424	−	0.251692i	−0.0159794	−	0.0116097i
$471$	0.626760	−	3.01646i	0.0288796	−	0.138991i
$472$		−	14.4345i		−	0.664404i
$473$	−2.69879	+	7.52536i	−0.124090	+	0.346016i
$474$	7.88010	−	13.7941i	0.361945	−	0.633582i
$475$	27.8349	−	9.04411i	1.27715	−	0.414972i
$476$	−1.60136	+	2.20408i	−0.0733980	+	0.101024i
$477$	−3.10085	+	7.13970i	−0.141978	+	0.326905i
$478$	−6.59184	+	20.2876i	−0.301504	+	0.927933i
$479$	−7.65871	+	23.5711i	−0.349935	+	1.07699i	0.608953	+	0.793206i	$0.291590\pi$
$479$	−7.65871	+	23.5711i	−0.349935	+	1.07699i	−0.958888	+	0.283784i	$0.908410\pi$
$480$	−0.0303426	−	0.276517i	−0.00138494	−	0.0126212i
$481$	2.43673	−	3.35386i	0.111105	−	0.152923i
$482$	11.6296	−	3.77868i	0.529712	−	0.172114i
$483$	4.42705	+	2.52903i	0.201438	+	0.115075i
$484$	−10.9800	−	0.663539i	−0.499089	−	0.0301609i
$485$			1.66473i			0.0755914i
$486$	11.8200	+	10.1631i	0.536166	+	0.461006i
$487$	18.9050	+	13.7353i	0.856667	+	0.622405i	0.926976	−	0.375120i	$-0.122398\pi$
$487$	18.9050	+	13.7353i	0.856667	+	0.622405i	−0.0703088	+	0.997525i	$0.522398\pi$
$488$	−4.74733	−	6.53414i	−0.214901	−	0.295787i
$489$	22.0369	−	20.0254i	0.996544	−	0.905581i
$490$	−0.152745	−	0.0496298i	−0.00690031	−	0.00224205i
$491$	−11.4997	+	8.35505i	−0.518976	+	0.377058i	−0.816218	−	0.577744i	$-0.803933\pi$
$491$	−11.4997	+	8.35505i	−0.518976	+	0.377058i	0.297242	+	0.954802i	$0.403933\pi$
$492$	−3.91312	−	8.68191i	−0.176417	−	0.391411i
$493$	−5.32901	−	16.4010i	−0.240007	−	0.738664i
$494$	−39.3709			−1.77138
$495$	−1.56973	+	0.299300i	−0.0705539	+	0.0134525i
$496$	8.43144			0.378583
$497$	−3.25877	−	10.0295i	−0.146176	−	0.449883i
$498$	−10.1145	−	22.4406i	−0.453239	−	1.00559i
$499$	31.5546	−	22.9258i	1.41258	−	1.02630i	0.419636	−	0.907692i	$-0.362158\pi$
$499$	31.5546	−	22.9258i	1.41258	−	1.02630i	0.992941	−	0.118606i	$-0.0378424\pi$
$500$	−1.52351	−	0.495018i	−0.0681334	−	0.0221379i
$501$	26.6831	−	24.2475i	1.19211	−	1.08330i
$502$	0.436314	+	0.600534i	0.0194736	+	0.0268031i
$503$	−11.0554	−	8.03224i	−0.492937	−	0.358140i	0.313376	−	0.949629i	$-0.398540\pi$
$503$	−11.0554	−	8.03224i	−0.492937	−	0.358140i	−0.806313	+	0.591489i	$0.798540\pi$
$504$	−2.24771	−	1.98691i	−0.100121	−	0.0885041i
$505$			1.90018i			0.0845569i
$506$	−9.75846	−	0.294592i	−0.433816	−	0.0130962i
$507$	−47.7872	−	27.2993i	−2.12230	−	1.21240i
$508$	−12.9700	+	4.21421i	−0.575451	+	0.186975i
$509$	−0.328071	+	0.451551i	−0.0145415	+	0.0200146i	−0.816226	−	0.577733i	$-0.803938\pi$
$509$	−0.328071	+	0.451551i	−0.0145415	+	0.0200146i	0.801684	+	0.597748i	$0.203938\pi$
$510$	−0.0826650	−	0.753340i	−0.00366047	−	0.0333584i
$511$	−0.0314222	+	0.0967077i	−0.00139004	+	0.00427810i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−24.4853	+	18.3082i	−1.08105	+	0.808328i
$514$	−1.74642	+	2.40375i	−0.0770314	+	0.106025i
$515$	−0.166425	+	0.0540748i	−0.00733357	+	0.00238282i
$516$	2.07097	−	3.62523i	0.0911695	−	0.159592i
$517$	7.30750	−	4.97940i	0.321384	−	0.218994i
$518$			0.619544i			0.0272212i
$519$	−6.53010	+	31.4279i	−0.286640	+	1.37953i
$520$	0.869428	+	0.631676i	0.0381269	+	0.0277008i
$521$	10.1785	+	14.0094i	0.445926	+	0.613765i	0.971516	−	0.236973i	$-0.0761553\pi$
$521$	10.1785	+	14.0094i	0.445926	+	0.613765i	−0.525590	+	0.850738i	$0.676155\pi$
$522$	18.5378	−	4.11793i	0.811376	−	0.180237i
$523$	3.75620	+	1.22046i	0.164247	+	0.0533672i	0.389986	−	0.920821i	$-0.372480\pi$
$523$	3.75620	+	1.22046i	0.164247	+	0.0533672i	−0.225739	+	0.974188i	$0.572480\pi$
$524$	6.04517	−	4.39207i	0.264084	−	0.191868i
$525$	−7.85461	+	3.54024i	−0.342803	+	0.154509i
$526$	−0.669016	−	2.05902i	−0.0291705	−	0.0897776i
$527$	22.9705			1.00061
$528$	5.58661	+	1.33783i	0.243126	+	0.0582215i
$529$	14.3351			0.623264
$530$	0.128773	+	0.396322i	0.00559353	+	0.0172151i
$531$	43.1060	+	4.13228i	1.87064	+	0.179326i
$532$	4.76011	−	3.45842i	0.206377	−	0.149942i
$533$	34.9894	+	11.3687i	1.51556	+	0.492435i
$534$	−17.5892	−	19.3559i	−0.761157	−	0.837614i
$535$	0.787912	+	1.08447i	0.0340644	+	0.0468856i
$536$	7.59430	+	5.51758i	0.328024	+	0.238323i
$537$	−31.0225	−	6.44586i	−1.33872	−	0.278159i
$538$		−	1.42847i		−	0.0615859i
$539$	2.02954	−	2.62316i	0.0874185	−	0.112987i
$540$	0.834452	−	0.0114518i	0.0359091	−	0.000492808i
$541$	−2.19061	+	0.711774i	−0.0941819	+	0.0306015i	−0.355729	−	0.934589i	$-0.615767\pi$
$541$	−2.19061	+	0.711774i	−0.0941819	+	0.0306015i	0.261547	+	0.965191i	$0.415767\pi$
$542$	8.04765	−	11.0766i	0.345676	−	0.475783i
$543$	−1.23309	+	0.135308i	−0.0529168	+	0.00580663i
$544$	−0.841882	+	2.59105i	−0.0360954	+	0.111090i
$545$	−0.0379894	+	0.116919i	−0.00162729	+	0.00500828i
$546$	11.5207	−	1.26418i	0.493039	−	0.0541018i
$547$	−10.3976	+	14.3110i	−0.444568	+	0.611895i	−0.971219	−	0.238186i	$-0.923447\pi$
$547$	−10.3976	+	14.3110i	−0.444568	+	0.611895i	0.526652	+	0.850081i	$0.323447\pi$
$548$	4.15192	−	1.34904i	0.177361	−	0.0576281i
$549$	20.8720	−	12.3064i	0.890796	−	0.525225i
$550$	10.0954	−	13.0481i	0.430467	−	0.556374i
$551$			37.2439i			1.58664i
$552$	4.99189	+	1.03722i	0.212469	+	0.0441469i
$553$	−7.42024	−	5.39112i	−0.315541	−	0.229254i
$554$	5.45472	+	7.50777i	0.231749	+	0.318975i
$555$	−0.115904	−	0.127547i	−0.00491987	−	0.00541406i
$556$	19.6981	+	6.40031i	0.835387	+	0.271434i
$557$	19.5079	−	14.1733i	0.826575	−	0.600542i	−0.0920130	−	0.995758i	$-0.529330\pi$
$557$	19.5079	−	14.1733i	0.826575	−	0.600542i	0.918588	+	0.395216i	$0.129330\pi$
$558$	−2.41373	+	25.1789i	−0.102181	+	1.06591i
$559$	4.98427	+	15.3400i	0.210812	+	0.648813i
$560$	−0.160605			−0.00678682
$561$	15.2201	+	3.64477i	0.642593	+	0.153882i
$562$	13.0768			0.551613
$563$	3.90298	+	12.0121i	0.164491	+	0.506251i	0.998998	−	0.0447455i	$-0.0142477\pi$
$563$	3.90298	+	12.0121i	0.164491	+	0.506251i	−0.834507	+	0.550997i	$0.814248\pi$
$564$	−4.21009	+	1.89758i	−0.177277	+	0.0799023i
$565$	−1.35183	+	0.982159i	−0.0568717	+	0.0413197i
$566$	13.7696	+	4.47402i	0.578780	+	0.188057i
$567$	6.57700	−	6.14354i	0.276208	−	0.258004i
$568$	−6.19855	−	8.53157i	−0.260085	−	0.357977i
$569$	−5.85782	−	4.25595i	−0.245572	−	0.178419i	0.458190	−	0.888854i	$-0.348498\pi$
$569$	−5.85782	−	4.25595i	−0.245572	−	0.178419i	−0.703762	+	0.710436i	$0.748498\pi$
$570$	−0.332971	+	1.60252i	−0.0139466	+	0.0671220i
$571$			23.6249i			0.988672i	0.869271	+	0.494336i	$0.164589\pi$
$571$			23.6249i			0.988672i	−0.869271	+	0.494336i	$0.835411\pi$
$572$	−18.3398	+	12.4969i	−0.766825	+	0.522521i
$573$	22.3697	−	39.1581i	0.934509	−	1.63585i
$574$	−5.22903	+	1.69901i	−0.218255	+	0.0709155i
$575$	8.60647	−	11.8458i	0.358915	−	0.494004i
$576$	−2.75168	−	1.19509i	−0.114654	−	0.0497953i
$577$	−7.52191	+	23.1501i	−0.313141	+	0.963749i	0.663372	+	0.748290i	$0.269125\pi$
$577$	−7.52191	+	23.1501i	−0.313141	+	0.963749i	−0.976513	+	0.215459i	$0.930875\pi$
$578$	2.95967	−	9.10894i	0.123106	−	0.378882i
$579$	0.474138	+	4.32090i	0.0197045	+	0.179570i
$580$	0.597550	−	0.822457i	0.0248119	−	0.0341507i
$581$	−13.5157	+	4.39153i	−0.560728	+	0.182191i
$582$	15.5889	+	8.90542i	0.646180	+	0.369141i
$583$	−8.60162	−	0.259669i	−0.356243	−	0.0107544i
$584$			0.101684i			0.00420773i
$585$	−2.13528	+	2.41555i	−0.0882829	+	0.0998706i
$586$	6.56633	+	4.77072i	0.271253	+	0.197077i
$587$	10.3759	+	14.2812i	0.428259	+	0.589447i	0.967552	−	0.252670i	$-0.0813088\pi$
$587$	10.3759	+	14.2812i	0.428259	+	0.589447i	−0.539294	+	0.842118i	$0.681309\pi$
$588$	−1.28185	+	1.16484i	−0.0528626	+	0.0480374i
$589$	−47.1811	−	15.3301i	−1.94406	−	0.631664i
$590$	1.87552	−	1.36264i	0.0772138	−	0.0560991i
$591$	−5.08561	−	11.2833i	−0.209194	−	0.464132i
$592$	0.191450	+	0.589221i	0.00786853	+	0.0242169i
$593$	22.6256			0.929122			0.464561	−	0.885541i	$-0.346212\pi$
$593$	22.6256			0.929122			0.464561	+	0.885541i	$0.346212\pi$
$594$	−5.59449	+	16.3004i	−0.229545	+	0.668812i
$595$	−0.437552			−0.0179379
$596$	0.923115	+	2.84105i	0.0378123	+	0.116374i
$597$	−9.22606	−	20.4696i	−0.377598	−	0.837764i
$598$	−15.9351	+	11.5776i	−0.651636	+	0.473442i
$599$	−26.5826	−	8.63722i	−1.08614	−	0.352907i	−0.289384	−	0.957213i	$-0.593451\pi$
$599$	−26.5826	−	8.63722i	−1.08614	−	0.352907i	−0.796753	+	0.604306i	$0.793451\pi$
$600$	−6.37618	+	5.79417i	−0.260307	+	0.236546i
$601$	−14.4751	−	19.9233i	−0.590453	−	0.812688i	0.404340	−	0.914609i	$-0.367501\pi$
$601$	−14.4751	−	19.9233i	−0.590453	−	0.812688i	−0.994793	+	0.101921i	$0.967501\pi$
$602$	−1.95012	−	1.41684i	−0.0794809	−	0.0577462i
$603$	−18.6513	+	21.0994i	−0.759539	+	0.859233i
$604$			0.151418i			0.00616109i
$605$	−0.950310	−	1.48929i	−0.0386356	−	0.0605484i
$606$	17.7937	+	10.1650i	0.722820	+	0.412924i
$607$	9.71031	−	3.15507i	0.394129	−	0.128060i	−0.105246	−	0.994446i	$-0.533563\pi$
$607$	9.71031	−	3.15507i	0.394129	−	0.128060i	0.499375	+	0.866386i	$0.333563\pi$
$608$	3.45842	−	4.76011i	0.140258	−	0.193048i
$609$	−1.19588	−	10.8983i	−0.0484595	−	0.441619i
$610$	0.400842	−	1.23367i	0.0162296	−	0.0499496i
$611$	5.51301	−	16.9673i	0.223032	−	0.686423i
$612$	−7.49666	−	3.25588i	−0.303034	−	0.131611i
$613$	−19.0272	+	26.1887i	−0.768501	+	1.05775i	0.227958	+	0.973671i	$0.426795\pi$
$613$	−19.0272	+	26.1887i	−0.768501	+	1.05775i	−0.996459	+	0.0840800i	$0.973205\pi$
$614$	19.9581	−	6.48477i	0.805442	−	0.261704i
$615$	0.758659	−	1.32803i	0.0305921	−	0.0535513i
$616$	1.11961	−	3.12194i	0.0451102	−	0.125786i
$617$			1.78277i			0.0717717i	0.999356	+	0.0358859i	$0.0114253\pi$
$617$			1.78277i			0.0717717i	−0.999356	+	0.0358859i	$0.988575\pi$
$618$	−0.383918	+	1.84771i	−0.0154435	+	0.0743260i
$619$	−8.02668	−	5.83173i	−0.322620	−	0.234397i	0.414673	−	0.909971i	$-0.363896\pi$
$619$	−8.02668	−	5.83173i	−0.322620	−	0.234397i	−0.737292	+	0.675574i	$0.763896\pi$
$620$	0.795941	+	1.09552i	0.0319658	+	0.0439971i
$621$	−4.52651	+	14.6104i	−0.181643	+	0.586295i
$622$	−7.20997	−	2.34266i	−0.289094	−	0.0939322i
$623$	−12.2162	+	8.87556i	−0.489430	+	0.355592i
$624$	10.5661	−	4.76238i	0.422984	−	0.190648i
$625$	7.60607	+	23.4091i	0.304243	+	0.936363i
$626$	0.657982			0.0262982
$627$	−28.8294	−	17.6439i	−1.15133	−	0.704628i
$628$	−1.77875			−0.0709798
$629$	0.521583	+	1.60527i	0.0207969	+	0.0640062i
$630$	0.0459777	−	0.479618i	0.00183179	−	0.0191084i
$631$	−37.9689	+	27.5860i	−1.51152	+	1.09818i	−0.546021	+	0.837771i	$0.683858\pi$
$631$	−37.9689	+	27.5860i	−1.51152	+	1.09818i	−0.965498	+	0.260411i	$0.916142\pi$
$632$	−8.72301	−	2.83428i	−0.346983	−	0.112742i
$633$	26.9330	+	29.6384i	1.07049	+	1.17802i
$634$	−10.0718	−	13.8626i	−0.400002	−	0.550555i
$635$	−1.77195	−	1.28740i	−0.0703177	−	0.0510888i
$636$	4.40012	+	0.914257i	0.174476	+	0.0362526i
$637$		−	6.69138i		−	0.265122i
$638$	11.8217	+	17.3490i	0.468027	+	0.686853i
$639$	27.2524	−	16.0684i	1.07809	−	0.635656i
$640$	−0.152745	+	0.0496298i	−0.00603777	+	0.00196179i
$641$	−24.6324	+	33.9036i	−0.972920	+	1.33911i	−0.0323623	+	0.999476i	$0.510303\pi$
$641$	−24.6324	+	33.9036i	−0.972920	+	1.33911i	−0.940558	+	0.339634i	$0.889697\pi$
$642$	14.3701	−	1.57685i	0.567143	−	0.0622334i
$643$	−3.48769	+	10.7340i	−0.137541	+	0.423308i	−0.995977	−	0.0896133i	$-0.971437\pi$
$643$	−3.48769	+	10.7340i	−0.137541	+	0.423308i	0.858435	+	0.512922i	$0.171437\pi$
$644$	0.909630	−	2.79955i	0.0358445	−	0.110318i
$645$	0.666538	−	0.0731401i	0.0262449	−	0.00287989i
$646$	9.42209	−	12.9684i	0.370707	−	0.510235i
$647$	28.7627	−	9.34555i	1.13078	−	0.367412i	0.316905	−	0.948457i	$-0.397356\pi$
$647$	28.7627	−	9.34555i	1.13078	−	0.367412i	0.813871	+	0.581046i	$0.197356\pi$
$648$	4.35664	−	7.87526i	0.171145	−	0.309369i
$649$	13.4133	+	45.9565i	0.526517	+	1.80395i
$650$		−	33.2843i		−	1.30552i
$651$	14.2983	+	2.97090i	0.560394	+	0.116439i
$652$	−13.9082	−	10.1049i	−0.544688	−	0.395739i
$653$	5.11472	+	7.03980i	0.200154	+	0.275489i	0.897282	−	0.441459i	$-0.145539\pi$
$653$	5.11472	+	7.03980i	0.200154	+	0.275489i	−0.697127	+	0.716947i	$0.745539\pi$
$654$	0.891636	+	0.981199i	0.0348657	+	0.0383679i
$655$	1.14135	+	0.370846i	0.0445961	+	0.0144901i
$656$	−4.44808	+	3.23172i	−0.173668	+	0.126177i
$657$	−0.303661	−	0.0291099i	−0.0118470	−	0.00113569i
$658$	0.823897	+	2.53569i	0.0321188	+	0.0988516i
$659$	−1.04851			−0.0408442			−0.0204221	−	0.999791i	$-0.506501\pi$
$659$	−1.04851			−0.0408442			−0.0204221	+	0.999791i	$0.506501\pi$
$660$	0.353557	+	0.852176i	0.0137622	+	0.0331709i
$661$	−37.7527			−1.46841			−0.734206	−	0.678927i	$-0.762445\pi$
$661$	−37.7527			−1.46841			−0.734206	+	0.678927i	$0.762445\pi$
$662$	−3.58853	−	11.0444i	−0.139472	−	0.429251i
$663$	28.7863	−	12.9746i	1.11797	−	0.503891i
$664$	−11.4972	+	8.35319i	−0.446177	+	0.324167i
$665$	0.898724	+	0.292013i	0.0348510	+	0.0113238i
$666$	−1.81441	+	0.403047i	−0.0703068	+	0.0156178i
$667$	10.9521	+	15.0742i	0.424066	+	0.583677i
$668$	−16.8406	−	12.2354i	−0.651581	−	0.473402i
$669$	2.68020	−	12.8992i	0.103623	−	0.498712i
$670$			1.50761i			0.0582442i
$671$	21.1863	+	16.3919i	0.817889	+	0.632801i
$672$	−0.859155	+	1.50395i	−0.0331426	+	0.0580160i
$673$	−34.2404	+	11.1254i	−1.31987	+	0.428851i	−0.882450	−	0.470407i	$-0.844107\pi$
$673$	−34.2404	+	11.1254i	−1.31987	+	0.428851i	−0.437419	+	0.899258i	$0.644107\pi$
$674$	10.2525	−	14.1114i	0.394913	−	0.543552i
$675$	−15.4778	−	20.7000i	−0.595742	−	0.796743i
$676$	−9.81888	+	30.2194i	−0.377649	+	1.16228i
$677$	8.43360	−	25.9559i	0.324129	−	0.997568i	−0.647703	−	0.761893i	$-0.724270\pi$
$677$	8.43360	−	25.9559i	0.324129	−	0.997568i	0.971832	−	0.235675i	$-0.0757299\pi$
$678$	1.96560	+	17.9128i	0.0754884	+	0.687938i
$679$	6.09258	−	8.38572i	0.233812	−	0.321814i
$680$	−0.416136	+	0.135211i	−0.0159581	+	0.00518510i
$681$	35.8135	+	20.4591i	1.37238	+	0.783993i
$682$	−26.8439	+	7.83489i	−1.02791	+	0.300013i
$683$			45.1710i			1.72842i	0.503131	+	0.864210i	$0.332181\pi$
$683$			45.1710i			1.72842i	−0.503131	+	0.864210i	$0.667819\pi$
$684$	13.2251	+	11.6906i	0.505674	+	0.447003i
$685$	0.567232	+	0.412118i	0.0216728	+	0.0157462i
$686$	0.587785	+	0.809017i	0.0224417	+	0.0308884i
$687$	−17.6668	+	16.0542i	−0.674031	+	0.612507i
$688$	−2.29250	−	0.744879i	−0.0874008	−	0.0283982i
$689$	−14.0461	+	10.2051i	−0.535113	+	0.388782i
$690$	0.336474	+	0.746524i	0.0128093	+	0.0284197i
$691$	3.47116	+	10.6831i	0.132049	+	0.406406i	0.995119	−	0.0986784i	$-0.0314615\pi$
$691$	3.47116	+	10.6831i	0.132049	+	0.406406i	−0.863070	+	0.505084i	$0.831462\pi$
$692$	18.5325			0.704499
$693$	9.00255	+	4.23723i	0.341979	+	0.160959i
$694$	−12.0266			−0.456525
$695$	1.02793	+	3.16363i	0.0389914	+	0.120003i
$696$	−4.50509	−	9.99531i	−0.170765	−	0.378871i
$697$	−12.1183	+	8.80445i	−0.459013	+	0.333492i
$698$	−9.67472	−	3.14351i	−0.366194	−	0.118983i
$699$	1.33586	−	1.21392i	0.0505269	−	0.0459148i
$700$	2.92376	+	4.02422i	0.110508	+	0.152101i
$701$	24.7251	+	17.9638i	0.933852	+	0.678483i	0.946933	−	0.321431i	$-0.104164\pi$
$701$	24.7251	+	17.9638i	0.933852	+	0.678483i	−0.0130806	+	0.999914i	$0.504164\pi$
$702$	11.1971	+	32.9171i	0.422607	+	1.24238i
$703$		−	3.64529i		−	0.137485i
$704$	0.100078	−	3.31511i	0.00377183	−	0.124943i
$705$	−0.643996	−	0.367894i	−0.0242543	−	0.0138557i
$706$	−8.93383	+	2.90278i	−0.336229	+	0.109247i
$707$	6.95430	−	9.57177i	0.261543	−	0.359983i
$708$	−2.72706	−	24.8522i	−0.102489	−	0.934003i
$709$	−3.50974	+	10.8019i	−0.131811	+	0.405673i	−0.995080	−	0.0990706i	$-0.968413\pi$
$709$	−3.50974	+	10.8019i	−0.131811	+	0.405673i	0.863269	+	0.504744i	$0.168413\pi$
$710$	0.523376	−	1.61079i	0.0196420	−	0.0604517i
$711$	10.9612	−	25.2382i	0.411078	−	0.946507i
$712$	−8.87556	+	12.2162i	−0.332626	+	0.457820i
$713$	−23.6043	+	7.66949i	−0.883987	+	0.287225i
$714$	−2.34067	+	4.09733i	−0.0875974	+	0.153339i
$715$	−3.35506	−	1.20321i	−0.125472	−	0.0449975i
$716$			18.2934i			0.683656i
$717$	−7.51642	+	36.1748i	−0.280706	+	1.35097i
$718$	−17.8080	−	12.9382i	−0.664587	−	0.482851i
$719$	9.17659	+	12.6305i	0.342229	+	0.471038i	0.945091	−	0.326808i	$-0.105973\pi$
$719$	9.17659	+	12.6305i	0.342229	+	0.471038i	−0.602862	+	0.797846i	$0.705973\pi$
$720$	−0.104483	−	0.470351i	−0.00389384	−	0.0175290i
$721$	1.03624	+	0.336693i	0.0385914	+	0.0125391i
$722$	−12.6363	+	9.18083i	−0.470276	+	0.341675i
$723$	19.3089	−	8.70294i	0.718107	−	0.323666i
$724$	0.221317	+	0.681143i	0.00822517	+	0.0253145i
$725$	−31.4861			−1.16936
$726$	−19.0298	+	0.931978i	−0.706260	+	0.0345889i
$727$	−43.2823			−1.60525			−0.802626	−	0.596483i	$-0.796564\pi$
$727$	−43.2823			−1.60525			−0.802626	+	0.596483i	$0.796564\pi$
$728$	−2.06775	−	6.36388i	−0.0766359	−	0.235861i
$729$	22.2707	+	15.2648i	0.824843	+	0.565363i
$730$	−0.0132121	+	0.00959917i	−0.000489003	+	0.000355281i
$731$	−6.24566	−	2.02934i	−0.231004	−	0.0750578i
$732$	−9.40802	−	10.3530i	−0.347731	−	0.382659i
$733$	−7.76379	−	10.6859i	−0.286762	−	0.394694i	0.641197	−	0.767376i	$-0.278438\pi$
$733$	−7.76379	−	10.6859i	−0.286762	−	0.394694i	−0.927959	+	0.372682i	$0.878438\pi$
$734$	−13.6048	−	9.88448i	−0.502163	−	0.364843i
$735$	−0.272360	−	0.0565910i	−0.0100461	−	0.00208739i
$736$		−	2.94363i		−	0.108503i
$737$	−29.3058	−	10.5098i	−1.07949	−	0.387134i
$738$	−8.37753	−	14.2085i	−0.308381	−	0.523022i
$739$	−16.8990	+	5.49083i	−0.621641	+	0.201983i	−0.602869	−	0.797840i	$-0.705976\pi$
$739$	−16.8990	+	5.49083i	−0.621641	+	0.201983i	−0.0187721	+	0.999824i	$0.505976\pi$
$740$	−0.0584859	+	0.0804989i	−0.00214998	+	0.00295920i
$741$	−67.7855	+	7.43819i	−2.49016	+	0.273249i
$742$	0.801796	−	2.46767i	0.0294349	−	0.0905912i
$743$	6.86362	−	21.1240i	0.251802	−	0.774966i	−0.742641	−	0.669689i	$-0.766427\pi$
$743$	6.86362	−	21.1240i	0.251802	−	0.774966i	0.994443	−	0.105277i	$-0.0335728\pi$
$744$	14.5165	−	1.59292i	0.532202	−	0.0583993i
$745$	−0.282002	+	0.388143i	−0.0103318	+	0.0142204i
$746$	11.0418	−	3.58770i	0.404269	−	0.131355i
$747$	−21.6538	−	36.7255i	−0.792272	−	1.34371i
$748$	0.272651	−	9.03166i	0.00996911	−	0.330230i
$749$		−	8.34639i		−	0.304970i
$750$	−2.71657	−	0.564450i	−0.0991952	−	0.0206108i
$751$	−5.60877	−	4.07501i	−0.204667	−	0.148699i	0.480731	−	0.876868i	$-0.340371\pi$
$751$	−5.60877	−	4.07501i	−0.204667	−	0.148699i	−0.685397	+	0.728169i	$0.740371\pi$
$752$	1.56714	+	2.15699i	0.0571479	+	0.0786573i
$753$	0.864665	+	0.951518i	0.0315101	+	0.0346753i
$754$	40.2826	+	13.0886i	1.46700	+	0.476659i
$755$	−0.0196741	+	0.0142941i	−0.000716013	+	0.000520214i
$756$	−4.24529	−	2.99625i	−0.154400	−	0.108972i
$757$	−10.4463	−	32.1505i	−0.379678	−	1.16853i	−0.940268	−	0.340436i	$-0.889425\pi$
$757$	−10.4463	−	32.1505i	−0.379678	−	1.16853i	0.560590	−	0.828094i	$-0.310575\pi$
$758$	−16.2733			−0.591073
$759$	−16.8569	+	1.33642i	−0.611868	+	0.0485091i
$760$	0.944974			0.0342778
$761$	−5.92539	−	18.2365i	−0.214795	−	0.661072i	−0.999168	−	0.0407823i	$-0.987015\pi$
$761$	−5.92539	−	18.2365i	−0.214795	−	0.661072i	0.784373	−	0.620290i	$-0.212985\pi$
$762$	−21.5345	+	9.70605i	−0.780112	+	0.351613i
$763$	0.619267	−	0.449924i	0.0224190	−	0.0162883i
$764$	−24.7626	−	8.04585i	−0.895878	−	0.291088i
$765$	−0.284651	−	1.28142i	−0.0102916	−	0.0463298i
$766$	−8.82714	−	12.1495i	−0.318937	−	0.438980i
$767$	78.1406	+	56.7724i	2.82149	+	2.04993i
$768$	−0.352360	+	1.69583i	−0.0127147	+	0.0611930i
$769$			4.54196i			0.163787i	0.996641	+	0.0818936i	$0.0260968\pi$
$769$			4.54196i			0.163787i	−0.996641	+	0.0818936i	$0.973903\pi$
$770$	0.511334	−	0.149242i	0.0184272	−	0.00537831i
$771$	−2.55272	+	4.46851i	−0.0919338	+	0.160930i
$772$	2.38681	−	0.775523i	0.0859033	−	0.0279117i
$773$	−9.80576	+	13.4965i	−0.352689	+	0.485434i	−0.948094	−	0.317992i	$-0.896992\pi$
$773$	−9.80576	+	13.4965i	−0.352689	+	0.485434i	0.595405	+	0.803426i	$0.296992\pi$
$774$	2.88073	−	6.63288i	0.103546	−	0.238414i
$775$	12.9601	−	39.8870i	0.465540	−	1.43278i
$776$	3.20306	−	9.85801i	0.114983	−	0.353882i
$777$	0.117048	+	1.06668i	0.00419908	+	0.0382669i
$778$	−1.76075	+	2.42346i	−0.0631259	+	0.0868854i
$779$	30.7667	−	9.99670i	1.10233	−	0.358169i
$780$	1.61625	+	0.923310i	0.0578710	+	0.0330598i
$781$	27.6628	+	21.4027i	0.989853	+	0.765850i
$782$		−	8.01958i		−	0.286780i
$783$	31.1388	−	10.5922i	1.11281	−	0.378534i
$784$	0.809017	+	0.587785i	0.0288935	+	0.0209923i
$785$	−0.167917	−	0.231117i	−0.00599320	−	0.00824893i
$786$	9.57828	−	8.70399i	0.341646	−	0.310461i
$787$	20.5616	+	6.68088i	0.732944	+	0.238148i	0.651626	−	0.758540i	$-0.274087\pi$
$787$	20.5616	+	6.68088i	0.732944	+	0.238148i	0.0813176	+	0.996688i	$0.474087\pi$
$788$	−5.78085	+	4.20003i	−0.205934	+	0.149620i
$789$	−1.54086	−	3.41865i	−0.0548560	−	0.121707i
$790$	−0.455201	−	1.40096i	−0.0161953	−	0.0498440i
$791$	10.4041			0.369926
$792$	9.87131	+	1.24791i	0.350762	+	0.0443424i
$793$	54.0439			1.91915
$794$	−2.50679	−	7.71510i	−0.0889626	−	0.273799i
$795$	0.296586	+	0.658025i	0.0105188	+	0.0233378i
$796$	−10.4873	+	7.61950i	−0.371714	+	0.270066i
$797$	−12.1477	−	3.94703i	−0.430294	−	0.139811i	0.0858590	−	0.996307i	$-0.472637\pi$
$797$	−12.1477	−	3.94703i	−0.430294	−	0.139811i	−0.516153	+	0.856496i	$0.672637\pi$
$798$	7.54218	−	6.85373i	0.266990	−	0.242620i
$799$	4.26951	+	5.87648i	0.151044	+	0.207895i
$800$	4.02422	+	2.92376i	0.142278	+	0.103371i
$801$	−33.9404	−	30.0024i	−1.19922	−	1.06008i
$802$			32.4353i			1.14533i
$803$	−0.0944900	−	0.323742i	−0.00333448	−	0.0114246i
$804$	14.1176	+	8.06495i	0.497891	+	0.284429i
$805$	0.449624	−	0.146092i	0.0158472	−	0.00514905i
$806$	−33.1617	+	45.6431i	−1.16807	+	1.60771i
$807$	−0.269876	−	2.45943i	−0.00950009	−	0.0865759i
$808$	3.65609	−	11.2523i	0.128621	−	0.395854i
$809$	−9.22491	+	28.3913i	−0.324330	+	0.998187i	0.647411	+	0.762141i	$0.275852\pi$
$809$	−9.22491	+	28.3913i	−0.324330	+	0.998187i	−0.971742	+	0.236046i	$0.924148\pi$
$810$	1.43453	−	0.177367i	0.0504041	−	0.00623203i
$811$	20.0631	−	27.6144i	0.704509	−	0.969674i	−0.295388	−	0.955377i	$-0.595449\pi$
$811$	20.0631	−	27.6144i	0.704509	−	0.969674i	0.999898	−	0.0142968i	$-0.00455097\pi$
$812$	−6.02007	+	1.95604i	−0.211263	+	0.0686435i
$813$	11.7631	−	20.5912i	0.412550	−	0.722167i
$814$	−1.15707	−	1.69805i	−0.0405552	−	0.0595167i
$815$		−	2.76105i		−	0.0967154i
$816$	−0.959966	+	4.62010i	−0.0336055	+	0.161736i
$817$	11.4741	+	8.33645i	0.401430	+	0.291656i
$818$	−14.8712	−	20.4684i	−0.519959	−	0.715662i
$819$	19.5965	−	4.35311i	0.684756	−	0.152110i
$820$	−0.839811	−	0.272871i	−0.0293275	−	0.00952907i
$821$	−21.7460	+	15.7994i	−0.758939	+	0.551402i	−0.898585	−	0.438800i	$-0.855404\pi$
$821$	−21.7460	+	15.7994i	−0.758939	+	0.551402i	0.139645	+	0.990202i	$0.455404\pi$
$822$	6.89356	−	3.10707i	0.240440	−	0.108372i
$823$	−15.5036	−	47.7152i	−0.540422	−	1.66325i	−0.731633	−	0.681699i	$-0.761242\pi$
$823$	−15.5036	−	47.7152i	−0.540422	−	1.66325i	0.191211	−	0.981549i	$-0.438758\pi$
$824$	1.08956			0.0379567
$825$	14.9162	−	24.3725i	0.519315	−	0.848540i
$826$	−14.4345			−0.502242
$827$	−6.73474	−	20.7274i	−0.234190	−	0.720762i	−0.997228	−	0.0744087i	$-0.976293\pi$
$827$	−6.73474	−	20.7274i	−0.234190	−	0.720762i	0.763038	−	0.646354i	$-0.223707\pi$
$828$	8.79058	+	0.842693i	0.305494	+	0.0292856i
$829$	−18.6834	+	13.5743i	−0.648900	+	0.471453i	−0.862896	−	0.505381i	$-0.831352\pi$
$829$	−18.6834	+	13.5743i	−0.648900	+	0.471453i	0.213996	+	0.976834i	$0.431352\pi$
$830$	−2.17070	−	0.705304i	−0.0753462	−	0.0244815i
$831$	10.8099	+	11.8957i	0.374991	+	0.412658i
$832$	−3.93309	−	5.41344i	−0.136356	−	0.187677i
$833$	2.20408	+	1.60136i	0.0763667	+	0.0554837i
$834$	35.1238	+	7.29803i	1.21624	+	0.252710i
$835$		−	3.34318i		−	0.115695i
$836$	−6.58757	+	18.3689i	−0.227836	+	0.635302i
$837$	0.601195	+	43.8069i	0.0207804	+	1.51419i
$838$	3.75515	−	1.22012i	0.129719	−	0.0421484i
$839$	5.16175	−	7.10453i	0.178203	−	0.245276i	−0.710566	−	0.703630i	$-0.751561\pi$
$839$	5.16175	−	7.10453i	0.178203	−	0.245276i	0.888769	+	0.458355i	$0.151561\pi$
$840$	−0.276517	+	0.0303426i	−0.00954074	+	0.00104692i
$841$	3.42000	−	10.5257i	0.117931	−	0.362954i
$842$	−8.18453	+	25.1894i	−0.282057	+	0.868083i
$843$	22.5146	−	2.47056i	0.775444	−	0.0850905i
$844$	13.5905	−	18.7057i	0.467805	−	0.643878i
$845$	−4.85340	+	1.57697i	−0.166962	+	0.0542493i
$846$	−6.89008	+	4.06248i	−0.236886	+	0.139671i
$847$	−0.663539	+	10.9800i	−0.0227995	+	0.377276i
$848$		−	2.59467i		−	0.0891012i
$849$	24.5526	+	5.10155i	0.842645	+	0.175085i
$850$	10.9635	+	7.96547i	0.376046	+	0.273213i
$851$	−1.07195	−	1.47541i	−0.0367459	−	0.0505764i
$852$	−12.2840	−	13.5179i	−0.420842	−	0.463115i
$853$	−1.26560	−	0.411219i	−0.0433334	−	0.0140799i	0.287270	−	0.957850i	$-0.407252\pi$
$853$	−1.26560	−	0.411219i	−0.0433334	−	0.0140799i	−0.330603	+	0.943770i	$0.607252\pi$
$854$	−6.53414	+	4.74733i	−0.223594	+	0.162450i
$855$	−0.270525	+	2.82199i	−0.00925174	+	0.0965099i
$856$	−2.57918	−	7.93789i	−0.0881544	−	0.271311i
$857$	8.79463			0.300419			0.150209	−	0.988654i	$-0.452005\pi$
$857$	8.79463			0.300419			0.150209	+	0.988654i	$0.452005\pi$
$858$	−29.2149	+	24.9810i	−0.997381	+	0.852836i
$859$	−19.7514			−0.673911			−0.336955	−	0.941521i	$-0.609397\pi$
$859$	−19.7514			−0.673911			−0.336955	+	0.941521i	$0.609397\pi$
$860$	−0.119632	−	0.368188i	−0.00407940	−	0.0125551i
$861$	−8.68191	+	3.91312i	−0.295879	+	0.133359i
$862$	−29.8337	+	21.6755i	−1.01614	+	0.738269i
$863$	−22.2608	−	7.23297i	−0.757766	−	0.246213i	−0.0954465	−	0.995435i	$-0.530428\pi$
$863$	−22.2608	−	7.23297i	−0.757766	−	0.246213i	−0.662320	+	0.749221i	$0.730428\pi$
$864$	−4.96340	−	1.53773i	−0.168858	−	0.0523148i
$865$	1.74949	+	2.40797i	0.0594846	+	0.0818735i
$866$	17.7907	+	12.9257i	0.604552	+	0.439233i
$867$	3.37480	−	16.2422i	0.114614	−	0.551613i
$868$		−	8.43144i		−	0.286182i
$869$	30.4059	+	0.917906i	1.03145	+	0.0311378i
$870$	0.873428	−	1.52893i	0.0296120	−	0.0518356i
$871$	−59.7382	+	19.4101i	−2.02415	+	0.657687i
$872$	0.449924	−	0.619267i	0.0152363	−	0.0209710i
$873$	28.5221	+	12.3875i	0.965327	+	0.419252i
$874$	−5.35210	+	16.4721i	−0.181038	+	0.557176i
$875$	−0.495018	+	1.52351i	−0.0167347	+	0.0515040i
$876$	0.0192109	+	0.175072i	0.000649075	+	0.00591513i
$877$	16.8980	−	23.2581i	0.570606	−	0.785372i	−0.422020	−	0.906586i	$-0.638679\pi$
$877$	16.8980	−	23.2581i	0.570606	−	0.785372i	0.992626	+	0.121215i	$0.0386789\pi$
$878$	0.939056	−	0.305118i	0.0316916	−	0.0102972i
$879$	12.2067	+	6.97327i	0.411721	+	0.235203i
$880$	0.440189	−	0.299949i	0.0148388	−	0.0101113i
$881$		−	40.1934i		−	1.35415i	−0.735915	−	0.677074i	$-0.763248\pi$
$881$		−	40.1934i		−	1.35415i	0.735915	−	0.677074i	$-0.236752\pi$
$882$	−1.98691	+	2.24771i	−0.0669028	+	0.0756842i
$883$	8.15600	+	5.92568i	0.274471	+	0.199415i	0.716502	−	0.697585i	$-0.245742\pi$
$883$	8.15600	+	5.92568i	0.274471	+	0.199415i	−0.442031	+	0.897000i	$0.645742\pi$
$884$	−10.7153	−	14.7483i	−0.360394	−	0.496039i
$885$	2.97167	−	2.70042i	0.0998916	−	0.0907736i
$886$	8.77053	+	2.84972i	0.294652	+	0.0957382i
$887$	43.7299	−	31.7717i	1.46831	−	1.06679i	0.487207	−	0.873286i	$-0.338016\pi$
$887$	43.7299	−	31.7717i	1.46831	−	1.06679i	0.981100	−	0.193501i	$-0.0619843\pi$
$888$	0.440941	+	0.978302i	0.0147970	+	0.0328297i
$889$	4.21421	+	12.9700i	0.141340	+	0.435000i
$890$	−2.42514			−0.0812910
$891$	−6.55256	+	29.1215i	−0.219519	+	0.975608i
$892$	−7.60643			−0.254682
$893$	−4.84766	−	14.9196i	−0.162221	−	0.499264i
$894$	2.12609	+	4.71709i	0.0711071	+	0.157763i
$895$	−2.37691	+	1.72692i	−0.0794512	+	0.0577247i
$896$	0.951057	+	0.309017i	0.0317726	+	0.0103235i
$897$	−25.2485	+	22.9438i	−0.843022	+	0.766072i
$898$	17.6805	+	24.3351i	0.590005	+	0.812072i
$899$	43.1772	+	31.3701i	1.44004	+	1.04625i
$900$	−9.88331	+	11.1806i	−0.329444	+	0.372685i
$901$		−	7.06888i		−	0.235498i
$902$	11.1587	−	14.4225i	0.371543	−	0.480215i
$903$	−3.62523	−	2.07097i	−0.120640	−	0.0689177i
$904$	9.89485	−	3.21503i	0.329098	−	0.106930i
$905$	−0.0676100	+	0.0930572i	−0.00224743	+	0.00309332i
$906$	0.0286067	+	0.260698i	0.000950396	+	0.00866111i
$907$	−3.39484	+	10.4482i	−0.112724	+	0.346928i	−0.991465	−	0.130370i	$-0.958384\pi$
$907$	−3.39484	+	10.4482i	−0.112724	+	0.346928i	0.878742	+	0.477298i	$0.158384\pi$
$908$	7.35862	−	22.6475i	0.244205	−	0.751584i
$909$	32.5562	+	14.1395i	1.07982	+	0.468977i
$910$	0.631676	−	0.869428i	0.0209399	−	0.0288213i
$911$	−3.17983	+	1.03319i	−0.105353	+	0.0342311i	−0.361219	−	0.932481i	$-0.617639\pi$
$911$	−3.17983	+	1.03319i	−0.105353	+	0.0342311i	0.255866	+	0.966712i	$0.417639\pi$
$912$	5.05511	−	8.84895i	0.167392	−	0.293018i
$913$	28.8424	−	37.2785i	0.954544	−	1.23374i
$914$			13.6979i			0.453085i
$915$	0.457065	−	2.19975i	0.0151101	−	0.0727215i
$916$	11.1501	+	8.10103i	0.368410	+	0.267665i
$917$	−4.39207	−	6.04517i	−0.145039	−	0.199629i
$918$	−13.5222	−	4.18938i	−0.446300	−	0.138270i
$919$	−31.5660	−	10.2564i	−1.04127	−	0.338328i	−0.262030	−	0.965060i	$-0.584392\pi$
$919$	−31.5660	−	10.2564i	−1.04127	−	0.338328i	−0.779235	+	0.626732i	$0.784392\pi$
$920$	0.382473	−	0.277883i	0.0126098	−	0.00916152i
$921$	33.1370	−	14.9355i	1.09190	−	0.492142i
$922$	0.619903	+	1.90787i	0.0204154	+	0.0628322i
$923$	70.5646			2.32266
$924$	1.33783	−	5.58661i	0.0440113	−	0.183786i
$925$	3.08174			0.101327
$926$	6.94788	+	21.3834i	0.228322	+	0.702702i
$927$	−0.311917	+	3.25377i	−0.0102447	+	0.106868i
$928$	−5.12098	+	3.72061i	−0.168104	+	0.122135i
$929$	−26.2935	−	8.54327i	−0.862662	−	0.280296i	−0.155922	−	0.987769i	$-0.549835\pi$
$929$	−26.2935	−	8.54327i	−0.862662	−	0.280296i	−0.706740	+	0.707474i	$0.749835\pi$
$930$	1.57736	+	1.73580i	0.0517236	+	0.0569191i
$931$	−3.45842	−	4.76011i	−0.113345	−	0.156006i
$932$	−0.843104	−	0.612551i	−0.0276168	−	0.0200648i
$933$	−12.8561	−	2.67125i	−0.420890	−	0.0874527i
$934$		−	15.5570i		−	0.509041i
$935$	1.19925	−	0.817176i	0.0392195	−	0.0267245i
$936$	17.2922	−	10.1957i	0.565212	−	0.333257i
$937$	18.3228	−	5.95344i	0.598580	−	0.194490i	0.00597291	−	0.999982i	$-0.498099\pi$
$937$	18.3228	−	5.95344i	0.598580	−	0.194490i	0.592607	+	0.805492i	$0.298099\pi$
$938$	5.51758	−	7.59430i	0.180155	−	0.247963i
$939$	1.13286	−	0.124310i	0.0369694	−	0.00405670i
$940$	−0.132322	+	0.407246i	−0.00431588	+	0.0132829i
$941$	12.7583	−	39.2661i	0.415910	−	1.28004i	−0.495525	−	0.868594i	$-0.665024\pi$
$941$	12.7583	−	39.2661i	0.415910	−	1.28004i	0.911435	−	0.411445i	$-0.134976\pi$
$942$	−3.06250	+	0.336052i	−0.0997816	+	0.0109492i
$943$	9.51297	−	13.0935i	0.309785	−	0.426382i
$944$	−13.7281	+	4.46052i	−0.446811	+	0.145178i
$945$	−0.0114518	−	0.834452i	−0.000372527	−	0.0271447i
$946$	7.99101	+	0.241235i	0.259810	+	0.00784324i
$947$		−	8.56801i		−	0.278423i	−0.990263	−	0.139211i	$-0.955543\pi$
$947$		−	8.56801i		−	0.278423i	0.990263	−	0.139211i	$-0.0444568\pi$
$948$	−15.5540	−	3.23182i	−0.505171	−	0.104965i
$949$	−0.550463	−	0.399935i	−0.0178688	−	0.0129824i
$950$	−17.2029	−	23.6778i	−0.558136	−	0.768209i
$951$	−19.9598	−	21.9647i	−0.647240	−	0.712254i
$952$	2.59105	+	0.841882i	0.0839763	+	0.0272856i
$953$	−23.6082	+	17.1523i	−0.764744	+	0.555619i	−0.900362	−	0.435142i	$-0.856698\pi$
$953$	−23.6082	+	17.1523i	−0.764744	+	0.555619i	0.135618	+	0.990761i	$0.456698\pi$
$954$	7.74848	+	0.742794i	0.250866	+	0.0240488i
$955$	−1.29221	−	3.97700i	−0.0418148	−	0.128693i
$956$	21.3316			0.689914
$957$	23.6314	+	27.6366i	0.763894	+	0.893364i
$958$	24.7841			0.800738
$959$	−1.34904	−	4.15192i	−0.0435628	−	0.134072i
$960$	−0.253607	+	0.114306i	−0.00818513	+	0.00368921i
$961$	−32.4328	+	23.5638i	−1.04622	+	0.760124i
$962$	−3.94270	−	1.28106i	−0.127118	−	0.0413031i
$963$	24.4434	−	5.42978i	0.787676	−	0.174972i
$964$	−7.18747	−	9.89270i	−0.231493	−	0.318623i
$965$	0.326085	+	0.236914i	0.0104970	+	0.00762654i
$966$	1.03722	−	4.99189i	0.0333719	−	0.160611i
$967$		−	32.6733i		−	1.05070i	−0.850886	−	0.525351i	$-0.823934\pi$
$967$		−	32.6733i		−	1.05070i	0.850886	−	0.525351i	$-0.176066\pi$
$968$	2.76193	+	10.6476i	0.0887719	+	0.342227i
$969$	13.7721	−	24.1080i	0.442423	−	0.774460i
$970$	1.58325	−	0.514429i	0.0508351	−	0.0165173i
$971$	−16.0175	+	22.0462i	−0.514027	+	0.707497i	−0.984592	−	0.174868i	$-0.944050\pi$
$971$	−16.0175	+	22.0462i	−0.514027	+	0.707497i	0.470565	+	0.882365i	$0.344050\pi$
$972$	6.01306	−	14.3820i	0.192869	−	0.461304i
$973$	6.40031	−	19.6981i	0.205185	−	0.631493i
$974$	7.22107	−	22.2242i	0.231378	−	0.712108i
$975$	−6.28828	−	57.3061i	−0.201386	−	1.83526i
$976$	−4.74733	+	6.53414i	−0.151958	+	0.209153i
$977$	34.2685	−	11.1345i	1.09635	−	0.356224i	0.295651	−	0.955296i	$-0.404464\pi$
$977$	34.2685	−	11.1345i	1.09635	−	0.356224i	0.800695	+	0.599072i	$0.204464\pi$
$978$	−25.8551	−	14.7702i	−0.826755	−	0.472298i
$979$	16.9061	−	47.1413i	0.540320	−	1.50664i
$980$			0.160605i			0.00513035i
$981$	1.72052	+	1.52089i	0.0549319	+	0.0485584i
$982$	11.4997	+	8.35505i	0.366971	+	0.266620i
$983$	−28.8851	−	39.7569i	−0.921292	−	1.26805i	−0.963161	−	0.268926i	$-0.913331\pi$
$983$	−28.8851	−	39.7569i	−0.921292	−	1.26805i	0.0418690	−	0.999123i	$-0.486669\pi$
$984$	−7.04777	+	6.40446i	−0.224675	+	0.204167i
$985$	−1.09144	−	0.354631i	−0.0347762	−	0.0112995i
$986$	−13.9515	+	10.1364i	−0.444307	+	0.322808i
$987$	1.89758	+	4.21009i	0.0604005	+	0.134009i
$988$	12.1663	+	37.4439i	0.387061	+	1.19125i
$989$	7.09554			0.225625
$990$	0.769723	+	1.40041i	0.0244634	+	0.0445079i
$991$	14.6512			0.465409			0.232705	−	0.972547i	$-0.425242\pi$
$991$	14.6512			0.465409			0.232705	+	0.972547i	$0.425242\pi$
$992$	−2.60546	−	8.01878i	−0.0827234	−	0.254596i
$993$	−8.26500	−	18.3373i	−0.262282	−	0.581916i
$994$	−8.53157	+	6.19855i	−0.270605	+	0.196606i
$995$	−1.98004	−	0.643355i	−0.0627716	−	0.0203957i
$996$	−18.2167	+	16.5539i	−0.577220	+	0.524532i
$997$	28.5607	+	39.3105i	0.904528	+	1.24498i	0.969001	+	0.247056i	$0.0794632\pi$
$997$	28.5607	+	39.3105i	0.904528	+	1.24498i	−0.0644734	+	0.997919i	$0.520537\pi$
$998$	−31.5546	−	22.9258i	−0.998843	−	0.725702i
$999$	−3.04774	+	1.03672i	−0.0964264	+	0.0328004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.w.b.281.7	yes	48
3.2	odd	2		462.2.w.a.281.1	✓	48
11.2	odd	10		462.2.w.a.365.1	yes	48
33.2	even	10	inner	462.2.w.b.365.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.w.a.281.1	✓	48	3.2	odd	2
462.2.w.a.365.1	yes	48	11.2	odd	10
462.2.w.b.281.7	yes	48	1.1	even	1	trivial
462.2.w.b.365.7	yes	48	33.2	even	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.711719 - 1.57907i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.152745 - 0.0496298i) q^{5} +(-1.28185 + 1.16484i) q^{6} +(0.587785 + 0.809017i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.98691 + 2.24771i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.711719 - 1.57907i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.152745 - 0.0496298i) q^{5} +(-1.28185 + 1.16484i) q^{6} +(0.587785 + 0.809017i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.98691 + 2.24771i) q^{9} +0.160605i q^{10} +(-3.12194 - 1.11961i) q^{11} +(1.50395 + 0.859155i) q^{12} +(-6.36388 + 2.06775i) q^{13} +(0.587785 - 0.809017i) q^{14} +(0.0303426 + 0.276517i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.841882 - 2.59105i) q^{17} +(2.75168 + 1.19509i) q^{18} +(-3.45842 + 4.76011i) q^{19} +(0.152745 - 0.0496298i) q^{20} +(0.859155 - 1.50395i) q^{21} +(-0.100078 + 3.31511i) q^{22} +2.94363i q^{23} +(0.352360 - 1.69583i) q^{24} +(-4.02422 - 2.92376i) q^{25} +(3.93309 + 5.41344i) q^{26} +(4.96340 + 1.53773i) q^{27} +(-0.951057 - 0.309017i) q^{28} +(5.12098 - 3.72061i) q^{29} +(0.253607 - 0.114306i) q^{30} +(2.60546 + 8.01878i) q^{31} -1.00000 q^{32} +(0.454006 + 5.72659i) q^{33} -2.72439 q^{34} +(-0.0496298 - 0.152745i) q^{35} +(0.286277 - 2.98631i) q^{36} +(-0.501222 + 0.364159i) q^{37} +(5.59585 + 1.81820i) q^{38} +(7.79441 + 8.57734i) q^{39} +(-0.0944015 - 0.129933i) q^{40} +(-4.44808 - 3.23172i) q^{41} +(-1.69583 - 0.352360i) q^{42} -2.41048i q^{43} +(3.18379 - 0.929247i) q^{44} +(0.415044 - 0.244715i) q^{45} +(2.79955 - 0.909630i) q^{46} +(-1.56714 + 2.15699i) q^{47} +(-1.72172 + 0.188926i) q^{48} +(-0.309017 + 0.951057i) q^{49} +(-1.53711 + 4.73075i) q^{50} +(-4.69062 + 0.514708i) q^{51} +(3.93309 - 5.41344i) q^{52} +(2.46767 - 0.801796i) q^{53} +(-0.0713040 - 5.19566i) q^{54} +(0.421294 + 0.325955i) q^{55} +1.00000i q^{56} +(9.97797 + 2.07322i) q^{57} +(-5.12098 - 3.72061i) q^{58} +(-8.48442 - 11.6778i) q^{59} +(-0.187080 - 0.205872i) q^{60} +(-7.68134 - 2.49582i) q^{61} +(6.82118 - 4.95588i) q^{62} +(-2.98631 - 0.286277i) q^{63} +(0.309017 + 0.951057i) q^{64} +1.07467 q^{65} +(5.30602 - 2.20140i) q^{66} +9.38707 q^{67} +(0.841882 + 2.59105i) q^{68} +(4.64819 - 2.09503i) q^{69} +(-0.129933 + 0.0944015i) q^{70} +(-10.0295 - 3.25877i) q^{71} +(-2.92861 + 0.650555i) q^{72} +(0.0597686 + 0.0822645i) q^{73} +(0.501222 + 0.364159i) q^{74} +(-1.75271 + 8.43541i) q^{75} -5.88382i q^{76} +(-0.929247 - 3.18379i) q^{77} +(5.74893 - 10.0635i) q^{78} +(-8.72301 + 2.83428i) q^{79} +(-0.0944015 + 0.129933i) q^{80} +(-1.10436 - 8.93199i) q^{81} +(-1.69901 + 5.22903i) q^{82} +(-4.39153 + 13.5157i) q^{83} +(0.188926 + 1.72172i) q^{84} +(-0.257186 + 0.353987i) q^{85} +(-2.29250 + 0.744879i) q^{86} +(-9.51979 - 5.43834i) q^{87} +(-1.86761 - 2.74081i) q^{88} +15.1000i q^{89} +(-0.360994 - 0.319109i) q^{90} +(-5.41344 - 3.93309i) q^{91} +(-1.73022 - 2.38144i) q^{92} +(10.8078 - 9.82131i) q^{93} +(2.53569 + 0.823897i) q^{94} +(0.764500 - 0.555442i) q^{95} +(0.711719 + 1.57907i) q^{96} +(-3.20306 - 9.85801i) q^{97} +1.00000 q^{98} +(8.71956 - 4.79263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 48 * q + 12 * q^2 - 4 * q^3 - 12 * q^4 + 4 * q^6 + 12 * q^8 + 10 * q^9	\( 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{11} + 6 q^{12} - 24 q^{15} - 12 q^{16} + 24 q^{17} + 10 q^{18} + 30 q^{19} - 8 q^{22} - 6 q^{24} + 18 q^{25} + 20 q^{26} + 38 q^{27} - 8 q^{29} - 36 q^{30} - 32 q^{31} - 48 q^{32} + 24 q^{33} - 4 q^{34} - 6 q^{35} - 20 q^{37} - 20 q^{38} - 34 q^{39} - 22 q^{44} + 12 q^{45} + 20 q^{46} - 20 q^{47} - 4 q^{48} + 12 q^{49} - 28 q^{50} + 2 q^{51} + 20 q^{52} - 20 q^{53} - 18 q^{54} + 16 q^{55} + 12 q^{57} + 8 q^{58} - 30 q^{59} - 4 q^{60} - 20 q^{61} - 8 q^{62} - 4 q^{63} - 12 q^{64} + 46 q^{66} + 36 q^{67} + 24 q^{68} + 30 q^{69} - 4 q^{70} - 10 q^{72} - 20 q^{73} + 20 q^{74} + 40 q^{75} + 16 q^{77} - 16 q^{78} - 20 q^{79} - 54 q^{81} - 10 q^{82} + 46 q^{83} - 10 q^{84} + 10 q^{85} + 30 q^{86} - 8 q^{87} - 8 q^{88} - 62 q^{90} - 36 q^{91} - 10 q^{92} + 44 q^{93} - 50 q^{95} + 4 q^{96} - 2 q^{97} + 48 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 12 * q^2 - 4 * q^3 - 12 * q^4 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 8 * q^11 + 6 * q^12 - 24 * q^15 - 12 * q^16 + 24 * q^17 + 10 * q^18 + 30 * q^19 - 8 * q^22 - 6 * q^24 + 18 * q^25 + 20 * q^26 + 38 * q^27 - 8 * q^29 - 36 * q^30 - 32 * q^31 - 48 * q^32 + 24 * q^33 - 4 * q^34 - 6 * q^35 - 20 * q^37 - 20 * q^38 - 34 * q^39 - 22 * q^44 + 12 * q^45 + 20 * q^46 - 20 * q^47 - 4 * q^48 + 12 * q^49 - 28 * q^50 + 2 * q^51 + 20 * q^52 - 20 * q^53 - 18 * q^54 + 16 * q^55 + 12 * q^57 + 8 * q^58 - 30 * q^59 - 4 * q^60 - 20 * q^61 - 8 * q^62 - 4 * q^63 - 12 * q^64 + 46 * q^66 + 36 * q^67 + 24 * q^68 + 30 * q^69 - 4 * q^70 - 10 * q^72 - 20 * q^73 + 20 * q^74 + 40 * q^75 + 16 * q^77 - 16 * q^78 - 20 * q^79 - 54 * q^81 - 10 * q^82 + 46 * q^83 - 10 * q^84 + 10 * q^85 + 30 * q^86 - 8 * q^87 - 8 * q^88 - 62 * q^90 - 36 * q^91 - 10 * q^92 + 44 * q^93 - 50 * q^95 + 4 * q^96 - 2 * q^97 + 48 * q^98 - 26 * q^99

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