LMFDB - Embedded newform 930.2.e.a.929.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(929,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("930.929");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.e (of order $2$, degree $1$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.12
Character	$\chi$	$=$	930.929
Dual form			930.2.e.a.929.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.880669 + 1.49145i) q^{3} +1.00000 q^{4} +(2.09732 - 0.775395i) q^{5} +(0.880669 - 1.49145i) q^{6} +0.657746i q^{7} -1.00000 q^{8} +(-1.44884 - 2.62695i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.880669 + 1.49145i) q^{3} +1.00000 q^{4} +(2.09732 - 0.775395i) q^{5} +(0.880669 - 1.49145i) q^{6} +0.657746i q^{7} -1.00000 q^{8} +(-1.44884 - 2.62695i) q^{9} +(-2.09732 + 0.775395i) q^{10} -3.48761 q^{11} +(-0.880669 + 1.49145i) q^{12} +4.74265 q^{13} -0.657746i q^{14} +(-0.690586 + 3.81092i) q^{15} +1.00000 q^{16} +3.35932i q^{17} +(1.44884 + 2.62695i) q^{18} +0.313830 q^{19} +(2.09732 - 0.775395i) q^{20} +(-0.980995 - 0.579257i) q^{21} +3.48761 q^{22} +6.17179i q^{23} +(0.880669 - 1.49145i) q^{24} +(3.79753 - 3.25251i) q^{25} -4.74265 q^{26} +(5.19391 + 0.152596i) q^{27} +0.657746i q^{28} +1.48270 q^{29} +(0.690586 - 3.81092i) q^{30} +(5.54794 + 0.469478i) q^{31} -1.00000 q^{32} +(3.07143 - 5.20159i) q^{33} -3.35932i q^{34} +(0.510013 + 1.37951i) q^{35} +(-1.44884 - 2.62695i) q^{36} -4.95925 q^{37} -0.313830 q^{38} +(-4.17671 + 7.07342i) q^{39} +(-2.09732 + 0.775395i) q^{40} +0.355988i q^{41} +(0.980995 + 0.579257i) q^{42} +4.78557 q^{43} -3.48761 q^{44} +(-5.07561 - 4.38613i) q^{45} -6.17179i q^{46} -0.472214 q^{47} +(-0.880669 + 1.49145i) q^{48} +6.56737 q^{49} +(-3.79753 + 3.25251i) q^{50} +(-5.01026 - 2.95845i) q^{51} +4.74265 q^{52} +3.48435i q^{53} +(-5.19391 - 0.152596i) q^{54} +(-7.31464 + 2.70428i) q^{55} -0.657746i q^{56} +(-0.276380 + 0.468061i) q^{57} -1.48270 q^{58} +6.24959i q^{59} +(-0.690586 + 3.81092i) q^{60} -3.55983i q^{61} +(-5.54794 - 0.469478i) q^{62} +(1.72786 - 0.952971i) q^{63} +1.00000 q^{64} +(9.94687 - 3.67743i) q^{65} +(-3.07143 + 5.20159i) q^{66} +15.3778i q^{67} +3.35932i q^{68} +(-9.20491 - 5.43530i) q^{69} +(-0.510013 - 1.37951i) q^{70} -7.71031i q^{71} +(1.44884 + 2.62695i) q^{72} +3.30287 q^{73} +4.95925 q^{74} +(1.50659 + 8.52820i) q^{75} +0.313830 q^{76} -2.29396i q^{77} +(4.17671 - 7.07342i) q^{78} +13.9777i q^{79} +(2.09732 - 0.775395i) q^{80} +(-4.80171 + 7.61207i) q^{81} -0.355988i q^{82} +7.45533i q^{83} +(-0.980995 - 0.579257i) q^{84} +(2.60480 + 7.04559i) q^{85} -4.78557 q^{86} +(-1.30577 + 2.21137i) q^{87} +3.48761 q^{88} +0.308797 q^{89} +(5.07561 + 4.38613i) q^{90} +3.11946i q^{91} +6.17179i q^{92} +(-5.58610 + 7.86101i) q^{93} +0.472214 q^{94} +(0.658203 - 0.243342i) q^{95} +(0.880669 - 1.49145i) q^{96} +10.7997i q^{97} -6.56737 q^{98} +(5.05300 + 9.16177i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9	$ 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} - 4 q^{18} + 8 q^{19} + 2 q^{20} + 10 q^{25} - 12 q^{31} - 32 q^{32} - 8 q^{33} + 16 q^{35} + 4 q^{36} - 8 q^{38} - 4 q^{39} - 2 q^{40} + 10 q^{45} - 4 q^{47} - 36 q^{49} - 10 q^{50} - 4 q^{51} + 12 q^{62} - 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} - 4 q^{72} + 8 q^{76} + 4 q^{78} + 2 q^{80} + 24 q^{81} - 4 q^{87} - 10 q^{90} + 24 q^{93} + 4 q^{94} - 26 q^{95} + 36 q^{98}+O(q^{100}) $ 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 - 4 * q^18 + 8 * q^19 + 2 * q^20 + 10 * q^25 - 12 * q^31 - 32 * q^32 - 8 * q^33 + 16 * q^35 + 4 * q^36 - 8 * q^38 - 4 * q^39 - 2 * q^40 + 10 * q^45 - 4 * q^47 - 36 * q^49 - 10 * q^50 - 4 * q^51 + 12 * q^62 - 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 - 4 * q^72 + 8 * q^76 + 4 * q^78 + 2 * q^80 + 24 * q^81 - 4 * q^87 - 10 * q^90 + 24 * q^93 + 4 * q^94 - 26 * q^95 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.880669	+	1.49145i	−0.508455	+	0.861089i
$3$	−0.880669	+	1.49145i	−0.508455	+	0.861089i
$4$	1.00000			0.500000
$5$	2.09732	−	0.775395i	0.937951	−	0.346767i
$5$	2.09732	−	0.775395i	0.937951	−	0.346767i
$6$	0.880669	−	1.49145i	0.359532	−	0.608882i
$7$			0.657746i			0.248605i	0.992244	+	0.124302i	$0.0396693\pi$
$7$			0.657746i			0.248605i	−0.992244	+	0.124302i	$0.960331\pi$
$8$	−1.00000			−0.353553
$9$	−1.44884	−	2.62695i	−0.482948	−	0.875649i
$10$	−2.09732	+	0.775395i	−0.663232	+	0.245201i
$11$	−3.48761			−1.05155			−0.525777	−	0.850622i	$-0.676225\pi$
$11$	−3.48761			−1.05155			−0.525777	+	0.850622i	$0.676225\pi$
$12$	−0.880669	+	1.49145i	−0.254227	+	0.430544i
$13$	4.74265			1.31537			0.657687	−	0.753291i	$-0.271535\pi$
$13$	4.74265			1.31537			0.657687	+	0.753291i	$0.271535\pi$
$14$		−	0.657746i		−	0.175790i
$15$	−0.690586	+	3.81092i	−0.178308	+	0.983975i
$16$	1.00000			0.250000
$17$			3.35932i			0.814756i	0.913260	+	0.407378i	$0.133557\pi$
$17$			3.35932i			0.814756i	−0.913260	+	0.407378i	$0.866443\pi$
$18$	1.44884	+	2.62695i	0.341496	+	0.619177i
$19$	0.313830			0.0719975			0.0359988	−	0.999352i	$-0.488539\pi$
$19$	0.313830			0.0719975			0.0359988	+	0.999352i	$0.488539\pi$
$20$	2.09732	−	0.775395i	0.468976	−	0.173384i
$21$	−0.980995	−	0.579257i	−0.214071	−	0.126404i
$22$	3.48761			0.743561
$23$			6.17179i			1.28691i	0.765485	+	0.643453i	$0.222499\pi$
$23$			6.17179i			1.28691i	−0.765485	+	0.643453i	$0.777501\pi$
$24$	0.880669	−	1.49145i	0.179766	−	0.304441i
$25$	3.79753	−	3.25251i	0.759505	−	0.650501i
$26$	−4.74265			−0.930110
$27$	5.19391	+	0.152596i	0.999569	+	0.0293671i
$28$			0.657746i			0.124302i
$29$	1.48270			0.275331			0.137665	−	0.990479i	$-0.456040\pi$
$29$	1.48270			0.275331			0.137665	+	0.990479i	$0.456040\pi$
$30$	0.690586	−	3.81092i	0.126083	−	0.695775i
$31$	5.54794	+	0.469478i	0.996439	+	0.0843207i
$31$	5.54794	+	0.469478i	0.996439	+	0.0843207i
$32$	−1.00000			−0.176777
$33$	3.07143	−	5.20159i	0.534668	−	0.905481i
$34$		−	3.35932i		−	0.576119i
$35$	0.510013	+	1.37951i	0.0862079	+	0.233179i
$36$	−1.44884	−	2.62695i	−0.241474	−	0.437825i
$37$	−4.95925			−0.815295			−0.407648	−	0.913139i	$-0.633651\pi$
$37$	−4.95925			−0.815295			−0.407648	+	0.913139i	$0.633651\pi$
$38$	−0.313830			−0.0509099
$39$	−4.17671	+	7.07342i	−0.668808	+	1.13265i
$40$	−2.09732	+	0.775395i	−0.331616	+	0.122601i
$41$			0.355988i			0.0555960i	0.999614	+	0.0277980i	$0.00884951\pi$
$41$			0.355988i			0.0555960i	−0.999614	+	0.0277980i	$0.991150\pi$
$42$	0.980995	+	0.579257i	0.151371	+	0.0893812i
$43$	4.78557			0.729793			0.364896	−	0.931048i	$-0.381104\pi$
$43$	4.78557			0.729793			0.364896	+	0.931048i	$0.381104\pi$
$44$	−3.48761			−0.525777
$45$	−5.07561	−	4.38613i	−0.756628	−	0.653846i
$46$		−	6.17179i		−	0.909980i
$47$	−0.472214			−0.0688795			−0.0344398	−	0.999407i	$-0.510965\pi$
$47$	−0.472214			−0.0688795			−0.0344398	+	0.999407i	$0.510965\pi$
$48$	−0.880669	+	1.49145i	−0.127114	+	0.215272i
$49$	6.56737			0.938196
$50$	−3.79753	+	3.25251i	−0.537051	+	0.459974i
$51$	−5.01026	−	2.95845i	−0.701577	−	0.414266i
$52$	4.74265			0.657687
$53$			3.48435i			0.478612i	0.970944	+	0.239306i	$0.0769200\pi$
$53$			3.48435i			0.478612i	−0.970944	+	0.239306i	$0.923080\pi$
$54$	−5.19391	−	0.152596i	−0.706802	−	0.0207657i
$55$	−7.31464	+	2.70428i	−0.986306	+	0.364644i
$56$		−	0.657746i		−	0.0878950i
$57$	−0.276380	+	0.468061i	−0.0366075	+	0.0619963i
$58$	−1.48270			−0.194688
$59$			6.24959i			0.813628i	0.913511	+	0.406814i	$0.133360\pi$
$59$			6.24959i			0.813628i	−0.913511	+	0.406814i	$0.866640\pi$
$60$	−0.690586	+	3.81092i	−0.0891542	+	0.491987i
$61$		−	3.55983i		−	0.455790i	−0.973686	−	0.227895i	$-0.926816\pi$
$61$		−	3.55983i		−	0.455790i	0.973686	−	0.227895i	$-0.0731842\pi$
$62$	−5.54794	−	0.469478i	−0.704589	−	0.0596238i
$63$	1.72786	−	0.952971i	0.217690	−	0.120063i
$64$	1.00000			0.125000
$65$	9.94687	−	3.67743i	1.23376	−	0.456129i
$66$	−3.07143	+	5.20159i	−0.378067	+	0.640272i
$67$			15.3778i			1.87870i	0.342956	+	0.939351i	$0.388572\pi$
$67$			15.3778i			1.87870i	−0.342956	+	0.939351i	$0.611428\pi$
$68$			3.35932i			0.407378i
$69$	−9.20491	−	5.43530i	−1.10814	−	0.654334i
$70$	−0.510013	−	1.37951i	−0.0609582	−	0.164882i
$71$		−	7.71031i		−	0.915046i	−0.889198	−	0.457523i	$-0.848737\pi$
$71$		−	7.71031i		−	0.915046i	0.889198	−	0.457523i	$-0.151263\pi$
$72$	1.44884	+	2.62695i	0.170748	+	0.309589i
$73$	3.30287			0.386572			0.193286	−	0.981142i	$-0.438086\pi$
$73$	3.30287			0.386572			0.193286	+	0.981142i	$0.438086\pi$
$74$	4.95925			0.576501
$75$	1.50659	+	8.52820i	0.173965	+	0.984752i
$76$	0.313830			0.0359988
$77$		−	2.29396i		−	0.261421i
$78$	4.17671	−	7.07342i	0.472919	−	0.800908i
$79$			13.9777i			1.57262i	0.617835	+	0.786308i	$0.288010\pi$
$79$			13.9777i			1.57262i	−0.617835	+	0.786308i	$0.711990\pi$
$80$	2.09732	−	0.775395i	0.234488	−	0.0866918i
$81$	−4.80171	+	7.61207i	−0.533523	+	0.845786i
$82$		−	0.355988i		−	0.0393123i
$83$			7.45533i			0.818328i	0.912461	+	0.409164i	$0.134180\pi$
$83$			7.45533i			0.818328i	−0.912461	+	0.409164i	$0.865820\pi$
$84$	−0.980995	−	0.579257i	−0.107035	−	0.0632021i
$85$	2.60480	+	7.04559i	0.282530	+	0.764201i
$86$	−4.78557			−0.516041
$87$	−1.30577	+	2.21137i	−0.139993	+	0.237084i
$88$	3.48761			0.371780
$89$	0.308797			0.0327324			0.0163662	−	0.999866i	$-0.494790\pi$
$89$	0.308797			0.0327324			0.0163662	+	0.999866i	$0.494790\pi$
$90$	5.07561	+	4.38613i	0.535017	+	0.462339i
$91$			3.11946i			0.327008i
$92$			6.17179i			0.643453i
$93$	−5.58610	+	7.86101i	−0.579252	+	0.815149i
$94$	0.472214			0.0487052
$95$	0.658203	−	0.243342i	0.0675302	−	0.0249664i
$96$	0.880669	−	1.49145i	0.0898829	−	0.152220i
$97$			10.7997i			1.09655i	0.836299	+	0.548273i	$0.184715\pi$
$97$			10.7997i			1.09655i	−0.836299	+	0.548273i	$0.815285\pi$
$98$	−6.56737			−0.663405
$99$	5.05300	+	9.16177i	0.507846	+	0.920792i
$100$	3.79753	−	3.25251i	0.379753	−	0.325251i
$101$			12.3325i			1.22713i	0.789645	+	0.613564i	$0.210265\pi$
$101$			12.3325i			1.22713i	−0.789645	+	0.613564i	$0.789735\pi$
$102$	5.01026	+	2.95845i	0.496090	+	0.292931i
$103$		−	9.32735i		−	0.919051i	−0.888164	−	0.459526i	$-0.848019\pi$
$103$		−	9.32735i		−	0.919051i	0.888164	−	0.459526i	$-0.151981\pi$
$104$	−4.74265			−0.465055
$105$	−2.50662	−	0.454230i	−0.244621	−	0.0443283i
$106$		−	3.48435i		−	0.338430i
$107$	−11.9013			−1.15055			−0.575273	−	0.817962i	$-0.695104\pi$
$107$	−11.9013			−1.15055			−0.575273	+	0.817962i	$0.695104\pi$
$108$	5.19391	+	0.152596i	0.499784	+	0.0146836i
$109$	9.04055			0.865928			0.432964	−	0.901411i	$-0.357468\pi$
$109$	9.04055			0.865928			0.432964	+	0.901411i	$0.357468\pi$
$110$	7.31464	−	2.70428i	0.697424	−	0.257843i
$111$	4.36746	−	7.39647i	0.414541	−	0.702042i
$112$			0.657746i			0.0621511i
$113$	3.01119			0.283269			0.141635	−	0.989919i	$-0.454764\pi$
$113$	3.01119			0.283269			0.141635	+	0.989919i	$0.454764\pi$
$114$	0.276380	−	0.468061i	0.0258854	−	0.0438380i
$115$	4.78557	+	12.9442i	0.446257	+	1.20706i
$116$	1.48270			0.137665
$117$	−6.87136	−	12.4587i	−0.635257	−	1.15181i
$118$		−	6.24959i		−	0.575322i
$119$	−2.20958			−0.202552
$120$	0.690586	−	3.81092i	0.0630415	−	0.347888i
$121$	1.16342			0.105766
$122$			3.55983i			0.322292i
$123$	−0.530938	−	0.313508i	−0.0478731	−	0.0282680i
$124$	5.54794	+	0.469478i	0.498219	+	0.0421604i
$125$	5.44266	−	9.76614i	0.486806	−	0.873510i
$126$	−1.72786	+	0.952971i	−0.153930	+	0.0848974i
$127$	−13.5825			−1.20526			−0.602628	−	0.798022i	$-0.705880\pi$
$127$	−13.5825			−1.20526			−0.602628	+	0.798022i	$0.705880\pi$
$128$	−1.00000			−0.0883883
$129$	−4.21451	+	7.13744i	−0.371067	+	0.628416i
$130$	−9.94687	+	3.67743i	−0.872398	+	0.322532i
$131$		−	16.1017i		−	1.40681i	−0.710787	−	0.703407i	$-0.751661\pi$
$131$		−	16.1017i		−	1.40681i	0.710787	−	0.703407i	$-0.248339\pi$
$132$	3.07143	−	5.20159i	0.267334	−	0.452741i
$133$			0.206420i			0.0178989i
$134$		−	15.3778i		−	1.32844i
$135$	11.0116	−	3.70729i	0.947730	−	0.319073i
$136$		−	3.35932i		−	0.288060i
$137$		−	6.61948i		−	0.565540i	−0.959188	−	0.282770i	$-0.908747\pi$
$137$		−	6.61948i		−	0.565540i	0.959188	−	0.282770i	$-0.0912534\pi$
$138$	9.20491	+	5.43530i	0.783574	+	0.462684i
$139$		−	7.03219i		−	0.596462i	−0.954494	−	0.298231i	$-0.903603\pi$
$139$		−	7.03219i		−	0.596462i	0.954494	−	0.298231i	$-0.0963967\pi$
$140$	0.510013	+	1.37951i	0.0431040	+	0.116589i
$141$	0.415864	−	0.704283i	0.0350221	−	0.0593114i
$142$			7.71031i			0.647035i
$143$	−16.5405			−1.38319
$144$	−1.44884	−	2.62695i	−0.120737	−	0.218912i
$145$	3.10970	−	1.14968i	0.258247	−	0.0954756i
$146$	−3.30287			−0.273348
$147$	−5.78368	+	9.79490i	−0.477030	+	0.807870i
$148$	−4.95925			−0.407648
$149$			7.67412i			0.628688i	0.949309	+	0.314344i	$0.101785\pi$
$149$			7.67412i			0.628688i	−0.949309	+	0.314344i	$0.898215\pi$
$150$	−1.50659	−	8.52820i	−0.123012	−	0.696325i
$151$		−	9.91125i		−	0.806566i	−0.915075	−	0.403283i	$-0.867869\pi$
$151$		−	9.91125i		−	0.806566i	0.915075	−	0.403283i	$-0.132131\pi$
$152$	−0.313830			−0.0254550
$153$	8.82477	−	4.86713i	0.713440	−	0.393484i
$154$			2.29396i			0.184853i
$155$	11.9998	−	3.31719i	0.963851	−	0.266443i
$156$	−4.17671	+	7.07342i	−0.334404	+	0.566327i
$157$		−	19.2544i		−	1.53666i	−0.640051	−	0.768332i	$-0.721087\pi$
$157$		−	19.2544i		−	1.53666i	0.640051	−	0.768332i	$-0.278913\pi$
$158$		−	13.9777i		−	1.11201i
$159$	−5.19673	−	3.06856i	−0.412128	−	0.243353i
$160$	−2.09732	+	0.775395i	−0.165808	+	0.0613003i
$161$	−4.05947			−0.319931
$162$	4.80171	−	7.61207i	0.377258	−	0.598061i
$163$			15.6849i			1.22853i	0.789098	+	0.614267i	$0.210548\pi$
$163$			15.6849i			1.22853i	−0.789098	+	0.614267i	$0.789452\pi$
$164$			0.355988i			0.0277980i
$165$	2.40849	−	13.2910i	0.187501	−	1.03470i
$166$		−	7.45533i		−	0.578646i
$167$		−	15.1886i		−	1.17533i	−0.809103	−	0.587666i	$-0.800047\pi$
$167$		−	15.1886i		−	1.17533i	0.809103	−	0.587666i	$-0.199953\pi$
$168$	0.980995	+	0.579257i	0.0756854	+	0.0446906i
$169$	9.49274			0.730211
$170$	−2.60480	−	7.04559i	−0.199779	−	0.540372i
$171$	−0.454690	−	0.824415i	−0.0347710	−	0.0630446i
$172$	4.78557			0.364896
$173$	15.7427			1.19690			0.598449	−	0.801161i	$-0.295784\pi$
$173$	15.7427			1.19690			0.598449	+	0.801161i	$0.295784\pi$
$174$	1.30577	−	2.21137i	0.0989901	−	0.167644i
$175$	2.13932	+	2.49781i	0.161718	+	0.188816i
$176$	−3.48761			−0.262889
$177$	−9.32095	−	5.50383i	−0.700606	−	0.413693i
$178$	−0.308797			−0.0231453
$179$	13.4057			1.00199			0.500996	−	0.865450i	$-0.332967\pi$
$179$	13.4057			1.00199			0.500996	+	0.865450i	$0.332967\pi$
$180$	−5.07561	−	4.38613i	−0.378314	−	0.326923i
$181$		−	25.5031i		−	1.89563i	−0.318819	−	0.947816i	$-0.603286\pi$
$181$		−	25.5031i		−	1.89563i	0.318819	−	0.947816i	$-0.396714\pi$
$182$		−	3.11946i		−	0.231230i
$183$	5.30931	+	3.13503i	0.392475	+	0.231748i
$184$		−	6.17179i		−	0.454990i
$185$	−10.4011	+	3.84538i	−0.764707	+	0.282718i
$186$	5.58610	−	7.86101i	0.409593	−	0.576397i
$187$		−	11.7160i		−	0.856760i
$188$	−0.472214			−0.0344398
$189$	−0.100369	+	3.41627i	−0.00730080	+	0.248497i
$190$	−0.658203	+	0.243342i	−0.0477510	+	0.0176539i
$191$			1.33827i			0.0968336i	0.998827	+	0.0484168i	$0.0154176\pi$
$191$			1.33827i			0.0968336i	−0.998827	+	0.0484168i	$0.984582\pi$
$192$	−0.880669	+	1.49145i	−0.0635568	+	0.107636i
$193$			26.2229i			1.88756i	0.330571	+	0.943781i	$0.392759\pi$
$193$			26.2229i			1.88756i	−0.330571	+	0.943781i	$0.607241\pi$
$194$		−	10.7997i		−	0.775375i
$195$	−3.27521	+	18.0739i	−0.234542	+	1.29430i
$196$	6.56737			0.469098
$197$		−	18.2917i		−	1.30323i	−0.758551	−	0.651614i	$-0.774092\pi$
$197$		−	18.2917i		−	1.30323i	0.758551	−	0.651614i	$-0.225908\pi$
$198$	−5.05300	−	9.16177i	−0.359101	−	0.651099i
$199$			16.7703i			1.18881i	0.804164	+	0.594407i	$0.202613\pi$
$199$			16.7703i			1.18881i	−0.804164	+	0.594407i	$0.797387\pi$
$200$	−3.79753	+	3.25251i	−0.268526	+	0.229987i
$201$	−22.9353	−	13.5428i	−1.61773	−	0.955235i
$202$		−	12.3325i		−	0.867711i
$203$			0.975240i			0.0684484i
$204$	−5.01026	−	2.95845i	−0.350788	−	0.207133i
$205$	0.276031	+	0.746622i	0.0192789	+	0.0521463i
$206$			9.32735i			0.649868i
$207$	16.2130	−	8.94195i	1.12688	−	0.621508i
$208$	4.74265			0.328844
$209$	−1.09452			−0.0757093
$210$	2.50662	+	0.454230i	0.172973	+	0.0313448i
$211$	−12.2683			−0.844583			−0.422291	−	0.906460i	$-0.638774\pi$
$211$	−12.2683			−0.844583			−0.422291	+	0.906460i	$0.638774\pi$
$212$			3.48435i			0.239306i
$213$	11.4995	+	6.79024i	0.787936	+	0.465259i
$214$	11.9013			0.813559
$215$	10.0369	−	3.71071i	0.684510	−	0.253068i
$216$	−5.19391	−	0.152596i	−0.353401	−	0.0103828i
$217$	−0.308797	+	3.64913i	−0.0209625	+	0.247719i
$218$	−9.04055			−0.612303
$219$	−2.90874	+	4.92607i	−0.196554	+	0.332873i
$220$	−7.31464	+	2.70428i	−0.493153	+	0.182322i
$221$			15.9321i			1.07171i
$222$	−4.36746	+	7.39647i	−0.293125	+	0.496418i
$223$	−21.2366			−1.42211			−0.711054	−	0.703137i	$-0.751782\pi$
$223$	−21.2366			−1.42211			−0.711054	+	0.703137i	$0.751782\pi$
$224$		−	0.657746i		−	0.0439475i
$225$	−14.0462	−	5.26353i	−0.936412	−	0.350902i
$226$	−3.01119			−0.200302
$227$	20.1908			1.34011			0.670056	−	0.742311i	$-0.266270\pi$
$227$	20.1908			1.34011			0.670056	+	0.742311i	$0.266270\pi$
$228$	−0.276380	+	0.468061i	−0.0183037	+	0.0309981i
$229$		−	8.82344i		−	0.583069i	−0.956560	−	0.291535i	$-0.905834\pi$
$229$		−	8.82344i		−	0.583069i	0.956560	−	0.291535i	$-0.0941658\pi$
$230$	−4.78557	−	12.9442i	−0.315551	−	0.853517i
$231$	3.42133	+	2.02022i	0.225107	+	0.132921i
$232$	−1.48270			−0.0973440
$233$	−12.4961			−0.818647			−0.409324	−	0.912389i	$-0.634235\pi$
$233$	−12.4961			−0.818647			−0.409324	+	0.912389i	$0.634235\pi$
$234$	6.87136	+	12.4587i	0.449195	+	0.814450i
$235$	−0.990385	+	0.366152i	−0.0646056	+	0.0238851i
$236$			6.24959i			0.406814i
$237$	−20.8471	−	12.3097i	−1.35416	−	0.799604i
$238$	2.20958			0.143226
$239$	30.5132			1.97374			0.986868	−	0.161531i	$-0.0516431\pi$
$239$	30.5132			1.97374			0.986868	+	0.161531i	$0.0516431\pi$
$240$	−0.690586	+	3.81092i	−0.0445771	+	0.245994i
$241$		−	19.0611i		−	1.22783i	−0.789372	−	0.613916i	$-0.789593\pi$
$241$		−	19.0611i		−	1.22783i	0.789372	−	0.613916i	$-0.210407\pi$
$242$	−1.16342			−0.0747878
$243$	−7.12430	−	13.8652i	−0.457024	−	0.889454i
$244$		−	3.55983i		−	0.227895i
$245$	13.7739	−	5.09231i	0.879982	−	0.325335i
$246$	0.530938	+	0.313508i	0.0338514	+	0.0199885i
$247$	1.48839			0.0947037
$248$	−5.54794	−	0.469478i	−0.352294	−	0.0298119i
$249$	−11.1192	−	6.56568i	−0.704653	−	0.416083i
$250$	−5.44266	+	9.76614i	−0.344224	+	0.617665i
$251$	5.37144			0.339042			0.169521	−	0.985527i	$-0.445778\pi$
$251$	5.37144			0.339042			0.169521	+	0.985527i	$0.445778\pi$
$252$	1.72786	−	0.952971i	0.108845	−	0.0600315i
$253$		−	21.5248i		−	1.35325i
$254$	13.5825			0.852245
$255$	−12.8021	−	2.31990i	−0.801699	−	0.145278i
$256$	1.00000			0.0625000
$257$	6.96961			0.434752			0.217376	−	0.976088i	$-0.430250\pi$
$257$	6.96961			0.434752			0.217376	+	0.976088i	$0.430250\pi$
$258$	4.21451	−	7.13744i	0.262384	−	0.444357i
$259$		−	3.26193i		−	0.202686i
$260$	9.94687	−	3.67743i	0.616879	−	0.228064i
$261$	−2.14820	−	3.89498i	−0.132970	−	0.241093i
$262$			16.1017i			0.994768i
$263$		−	16.3241i		−	1.00659i	−0.864116	−	0.503293i	$-0.832122\pi$
$263$		−	16.3241i		−	1.00659i	0.864116	−	0.503293i	$-0.167878\pi$
$264$	−3.07143	+	5.20159i	−0.189034	+	0.320136i
$265$	2.70175	+	7.30781i	0.165967	+	0.448915i
$266$		−	0.206420i		−	0.0126564i
$267$	−0.271948	+	0.460556i	−0.0166430	+	0.0281855i
$268$			15.3778i			0.939351i
$269$	−21.6945			−1.32274			−0.661370	−	0.750060i	$-0.730025\pi$
$269$	−21.6945			−1.32274			−0.661370	+	0.750060i	$0.730025\pi$
$270$	−11.0116	+	3.70729i	−0.670146	+	0.225618i
$271$			9.02824i			0.548427i	0.961669	+	0.274213i	$0.0884175\pi$
$271$			9.02824i			0.548427i	−0.961669	+	0.274213i	$0.911583\pi$
$272$			3.35932i			0.203689i
$273$	−4.65252	−	2.74721i	−0.281583	−	0.166269i
$274$			6.61948i			0.399897i
$275$	−13.2443	+	11.3435i	−0.798661	+	0.684037i
$276$	−9.20491	−	5.43530i	−0.554070	−	0.327167i
$277$	−18.7953			−1.12930			−0.564651	−	0.825330i	$-0.690989\pi$
$277$	−18.7953			−1.12930			−0.564651	+	0.825330i	$0.690989\pi$
$278$			7.03219i			0.421763i
$279$	−6.80479	−	15.2543i	−0.407392	−	0.913253i
$280$	−0.510013	−	1.37951i	−0.0304791	−	0.0824412i
$281$			3.54453i			0.211449i	0.994395	+	0.105724i	$0.0337162\pi$
$281$			3.54453i			0.211449i	−0.994395	+	0.105724i	$0.966284\pi$
$282$	−0.415864	+	0.704283i	−0.0247644	+	0.0419395i
$283$		−	22.2060i		−	1.32001i	−0.751260	−	0.660006i	$-0.770554\pi$
$283$		−	22.2060i		−	1.32001i	0.751260	−	0.660006i	$-0.229446\pi$
$284$		−	7.71031i		−	0.457523i
$285$	−0.216726	+	1.19598i	−0.0128378	+	0.0708437i
$286$	16.5405			0.978061
$287$	−0.234150			−0.0138214
$288$	1.44884	+	2.62695i	0.0853739	+	0.154794i
$289$	5.71494			0.336173
$290$	−3.10970	+	1.14968i	−0.182608	+	0.0675114i
$291$	−16.1073	−	9.51099i	−0.944224	−	0.557544i
$292$	3.30287			0.193286
$293$	5.62369			0.328539			0.164270	−	0.986415i	$-0.447473\pi$
$293$	5.62369			0.328539			0.164270	+	0.986415i	$0.447473\pi$
$294$	5.78368	−	9.79490i	0.337311	−	0.571250i
$295$	4.84590	+	13.1074i	0.282139	+	0.763143i
$296$	4.95925			0.288250
$297$	−18.1143	−	0.532195i	−1.05110	−	0.0308811i
$298$		−	7.67412i		−	0.444550i
$299$			29.2706i			1.69276i
$300$	1.50659	+	8.52820i	0.0869827	+	0.492376i
$301$			3.14769i			0.181430i
$302$			9.91125i			0.570328i
$303$	−18.3933	−	10.8608i	−1.05667	−	0.623939i
$304$	0.313830			0.0179994
$305$	−2.76027	−	7.46611i	−0.158053	−	0.427508i
$306$	−8.82477	+	4.86713i	−0.504478	+	0.278235i
$307$		−	9.58898i		−	0.547272i	−0.961833	−	0.273636i	$-0.911774\pi$
$307$		−	9.58898i		−	0.547272i	0.961833	−	0.273636i	$-0.0882264\pi$
$308$		−	2.29396i		−	0.130711i
$309$	13.9113	+	8.21431i	0.791385	+	0.467296i
$310$	−11.9998	+	3.31719i	−0.681545	+	0.188404i
$311$			18.7925i			1.06563i	0.846233	+	0.532813i	$0.178865\pi$
$311$			18.7925i			1.06563i	−0.846233	+	0.532813i	$0.821135\pi$
$312$	4.17671	−	7.07342i	0.236459	−	0.400454i
$313$	−6.40671			−0.362129			−0.181064	−	0.983471i	$-0.557954\pi$
$313$	−6.40671			−0.362129			−0.181064	+	0.983471i	$0.557954\pi$
$314$			19.2544i			1.08659i
$315$	2.88496	−	3.33846i	0.162549	−	0.188101i
$316$			13.9777i			0.786308i
$317$	32.2027			1.80869			0.904343	−	0.426806i	$-0.140361\pi$
$317$	32.2027			1.80869			0.904343	+	0.426806i	$0.140361\pi$
$318$	5.19673	+	3.06856i	0.291418	+	0.172076i
$319$	−5.17108			−0.289525
$320$	2.09732	−	0.775395i	0.117244	−	0.0433459i
$321$	10.4811	−	17.7502i	0.585000	−	0.990722i
$322$	4.05947			0.226225
$323$			1.05426i			0.0586604i
$324$	−4.80171	+	7.61207i	−0.266762	+	0.422893i
$325$	18.0103	−	15.4255i	0.999034	−	0.855653i
$326$		−	15.6849i		−	0.868705i
$327$	−7.96173	+	13.4835i	−0.440285	+	0.745640i
$328$		−	0.355988i		−	0.0196561i
$329$		−	0.310597i		−	0.0171238i
$330$	−2.40849	+	13.2910i	−0.132583	+	0.731645i
$331$		−	15.7704i		−	0.866821i	−0.901197	−	0.433411i	$-0.857310\pi$
$331$		−	15.7704i		−	0.866821i	0.901197	−	0.433411i	$-0.142690\pi$
$332$			7.45533i			0.409164i
$333$	7.18517	+	13.0277i	0.393745	+	0.713913i
$334$			15.1886i			0.831086i
$335$	11.9239	+	32.2523i	0.651472	+	1.76213i
$336$	−0.980995	−	0.579257i	−0.0535177	−	0.0316010i
$337$	14.3993			0.784378			0.392189	−	0.919885i	$-0.371718\pi$
$337$	14.3993			0.784378			0.392189	+	0.919885i	$0.371718\pi$
$338$	−9.49274			−0.516337
$339$	−2.65187	+	4.49105i	−0.144030	+	0.243920i
$340$	2.60480	+	7.04559i	0.141265	+	0.382101i
$341$	−19.3490	−	1.63736i	−1.04781	−	0.0886678i
$342$	0.454690	+	0.824415i	0.0245868	+	0.0445792i
$343$			8.92388i			0.481844i
$344$	−4.78557			−0.258021
$345$	−23.5202	−	4.26215i	−1.26628	−	0.229466i
$346$	−15.7427			−0.846335
$347$		−	15.5482i		−	0.834673i	−0.908752	−	0.417337i	$-0.862964\pi$
$347$		−	15.5482i		−	0.834673i	0.908752	−	0.417337i	$-0.137036\pi$
$348$	−1.30577	+	2.21137i	−0.0699965	+	0.118542i
$349$	−3.24331			−0.173610			−0.0868052	−	0.996225i	$-0.527666\pi$
$349$	−3.24331			−0.173610			−0.0868052	+	0.996225i	$0.527666\pi$
$350$	−2.13932	−	2.49781i	−0.114352	−	0.133513i
$351$	24.6329	+	0.723709i	1.31481	+	0.0386287i
$352$	3.48761			0.185890
$353$			7.73754i			0.411827i	0.978570	+	0.205914i	$0.0660166\pi$
$353$			7.73754i			0.411827i	−0.978570	+	0.205914i	$0.933983\pi$
$354$	9.32095	+	5.50383i	0.495403	+	0.292525i
$355$	−5.97854	−	16.1710i	−0.317308	−	0.858268i
$356$	0.308797			0.0163662
$357$	1.94591	−	3.29548i	0.102989	−	0.174415i
$358$	−13.4057			−0.708515
$359$		−	14.0443i		−	0.741231i	−0.928786	−	0.370615i	$-0.879147\pi$
$359$		−	14.0443i		−	0.741231i	0.928786	−	0.370615i	$-0.120853\pi$
$360$	5.07561	+	4.38613i	0.267508	+	0.231169i
$361$	−18.9015			−0.994816
$362$			25.5031i			1.34041i
$363$	−1.02459	+	1.73519i	−0.0537772	+	0.0910738i
$364$			3.11946i			0.163504i
$365$	6.92719	−	2.56103i	0.362586	−	0.134050i
$366$	−5.30931	−	3.13503i	−0.277522	−	0.163871i
$367$	14.2075			0.741623			0.370812	−	0.928708i	$-0.379080\pi$
$367$	14.2075			0.741623			0.370812	+	0.928708i	$0.379080\pi$
$368$			6.17179i			0.321727i
$369$	0.935162	−	0.515771i	0.0486826	−	0.0268499i
$370$	10.4011	−	3.84538i	0.540730	−	0.199912i
$371$	−2.29182			−0.118985
$372$	−5.58610	+	7.86101i	−0.289626	+	0.407574i
$373$			7.05802i			0.365450i	0.983164	+	0.182725i	$0.0584918\pi$
$373$			7.05802i			0.365450i	−0.983164	+	0.182725i	$0.941508\pi$
$374$			11.7160i			0.605821i
$375$	9.77252	+	16.7182i	0.504651	+	0.863324i
$376$	0.472214			0.0243526
$377$	7.03193			0.362163
$378$	0.100369	−	3.41627i	0.00516244	−	0.175714i
$379$	33.4723			1.71936			0.859679	−	0.510835i	$-0.170664\pi$
$379$	33.4723			1.71936			0.859679	+	0.510835i	$0.170664\pi$
$380$	0.658203	−	0.243342i	0.0337651	−	0.0124832i
$381$	11.9617	−	20.2577i	0.612818	−	1.03783i
$382$		−	1.33827i		−	0.0684717i
$383$		−	0.926997i		−	0.0473673i	−0.999720	−	0.0236837i	$-0.992461\pi$
$383$		−	0.926997i		−	0.0473673i	0.999720	−	0.0236837i	$-0.00753945\pi$
$384$	0.880669	−	1.49145i	0.0449415	−	0.0761102i
$385$	−1.77873	−	4.81118i	−0.0906523	−	0.245200i
$386$		−	26.2229i		−	1.33471i
$387$	−6.93354	−	12.5714i	−0.352452	−	0.639042i
$388$			10.7997i			0.548273i
$389$	−34.6260			−1.75561			−0.877803	−	0.479021i	$-0.840992\pi$
$389$	−34.6260			−1.75561			−0.877803	+	0.479021i	$0.840992\pi$
$390$	3.27521	−	18.0739i	0.165847	−	0.915205i
$391$	−20.7330			−1.04851
$392$	−6.56737			−0.331702
$393$	24.0149	+	14.1803i	1.21139	+	0.715301i
$394$			18.2917i			0.921521i
$395$	10.8382	+	29.3158i	0.545331	+	1.47504i
$396$	5.05300	+	9.16177i	0.253923	+	0.460396i
$397$		−	9.43307i		−	0.473432i	−0.971579	−	0.236716i	$-0.923929\pi$
$397$		−	9.43307i		−	0.473432i	0.971579	−	0.236716i	$-0.0760711\pi$
$398$		−	16.7703i		−	0.840619i
$399$	−0.307866	−	0.181788i	−0.0154126	−	0.00910079i
$400$	3.79753	−	3.25251i	0.189876	−	0.162625i
$401$	2.14298			0.107015			0.0535077	−	0.998567i	$-0.482960\pi$
$401$	2.14298			0.107015			0.0535077	+	0.998567i	$0.482960\pi$
$402$	22.9353	+	13.5428i	1.14391	+	0.675453i
$403$	26.3119	+	2.22657i	1.31069	+	0.110913i
$404$			12.3325i			0.613564i
$405$	−4.16837	+	19.6882i	−0.207128	+	0.978314i
$406$		−	0.975240i		−	0.0484003i
$407$	17.2959			0.857327
$408$	5.01026	+	2.95845i	0.248045	+	0.146465i
$409$		−	0.448391i		−	0.0221715i	−0.999939	−	0.0110858i	$-0.996471\pi$
$409$		−	0.448391i		−	0.0221715i	0.999939	−	0.0110858i	$-0.00352878\pi$
$410$	−0.276031	−	0.746622i	−0.0136322	−	0.0368730i
$411$	9.87262	+	5.82957i	0.486980	+	0.287552i
$412$		−	9.32735i		−	0.459526i
$413$	−4.11065			−0.202272
$414$	−16.2130	+	8.94195i	−0.796823	+	0.439473i
$415$	5.78082	+	15.6362i	0.283769	+	0.767552i
$416$	−4.74265			−0.232528
$417$	10.4882	+	6.19303i	0.513607	+	0.303274i
$418$	1.09452			0.0535345
$419$		−	27.9545i		−	1.36567i	−0.730575	−	0.682833i	$-0.760748\pi$
$419$		−	27.9545i		−	1.36567i	0.730575	−	0.682833i	$-0.239252\pi$
$420$	−2.50662	−	0.454230i	−0.122310	−	0.0221641i
$421$	5.89643			0.287375			0.143687	−	0.989623i	$-0.454104\pi$
$421$	5.89643			0.287375			0.143687	+	0.989623i	$0.454104\pi$
$422$	12.2683			0.597210
$423$	0.684164	+	1.24048i	0.0332652	+	0.0603143i
$424$		−	3.48435i		−	0.169215i
$425$	10.9262	+	12.7571i	0.530000	+	0.618811i
$426$	−11.4995	−	6.79024i	−0.557155	−	0.328988i
$427$	2.34146			0.113311
$428$	−11.9013			−0.575273
$429$	14.5667	−	24.6693i	0.703288	−	1.19105i
$430$	−10.0369	+	3.71071i	−0.484022	+	0.178946i
$431$		−	35.1649i		−	1.69383i	−0.531725	−	0.846917i	$-0.678456\pi$
$431$		−	35.1649i		−	1.69383i	0.531725	−	0.846917i	$-0.321544\pi$
$432$	5.19391	+	0.152596i	0.249892	+	0.00734178i
$433$	18.8588			0.906294			0.453147	−	0.891436i	$-0.350301\pi$
$433$	18.8588			0.906294			0.453147	+	0.891436i	$0.350301\pi$
$434$	0.308797	−	3.64913i	0.0148227	−	0.175164i
$435$	−1.02393	+	5.65045i	−0.0490937	+	0.270918i
$436$	9.04055			0.432964
$437$			1.93689i			0.0926541i
$438$	2.90874	−	4.92607i	0.138985	−	0.235377i
$439$	−1.64683			−0.0785991			−0.0392995	−	0.999227i	$-0.512513\pi$
$439$	−1.64683			−0.0785991			−0.0392995	+	0.999227i	$0.512513\pi$
$440$	7.31464	−	2.70428i	0.348712	−	0.128921i
$441$	−9.51509	−	17.2521i	−0.453099	−	0.821530i
$442$		−	15.9321i		−	0.757813i
$443$	−5.06315			−0.240558			−0.120279	−	0.992740i	$-0.538379\pi$
$443$	−5.06315			−0.240558			−0.120279	+	0.992740i	$0.538379\pi$
$444$	4.36746	−	7.39647i	0.207270	−	0.351021i
$445$	0.647648	−	0.239440i	0.0307014	−	0.0113505i
$446$	21.2366			1.00558
$447$	−11.4456	−	6.75836i	−0.541356	−	0.319659i
$448$			0.657746i			0.0310756i
$449$	−0.0169529			−0.000800056			−0.000400028	−	1.00000i	$-0.500127\pi$
$449$	−0.0169529			−0.000800056			−0.000400028		1.00000i	$0.500127\pi$
$450$	14.0462	+	5.26353i	0.662143	+	0.248125i
$451$		−	1.24155i		−	0.0584622i
$452$	3.01119			0.141635
$453$	14.7821	+	8.72853i	0.694525	+	0.410102i
$454$	−20.1908			−0.947602
$455$	2.41881	+	6.54251i	0.113396	+	0.306718i
$456$	0.276380	−	0.468061i	0.0129427	−	0.0219190i
$457$	1.97910			0.0925786			0.0462893	−	0.998928i	$-0.485260\pi$
$457$	1.97910			0.0925786			0.0462893	+	0.998928i	$0.485260\pi$
$458$			8.82344i			0.412292i
$459$	−0.512619	+	17.4480i	−0.0239270	+	0.814404i
$460$	4.78557	+	12.9442i	0.223128	+	0.603528i
$461$	−23.0233			−1.07230			−0.536152	−	0.844122i	$-0.680123\pi$
$461$	−23.0233			−1.07230			−0.536152	+	0.844122i	$0.680123\pi$
$462$	−3.42133	−	2.02022i	−0.159175	−	0.0939892i
$463$	−34.8934			−1.62163			−0.810817	−	0.585299i	$-0.800977\pi$
$463$	−34.8934			−1.62163			−0.810817	+	0.585299i	$0.800977\pi$
$464$	1.48270			0.0688326
$465$	−5.62047	+	20.8185i	−0.260643	+	0.965435i
$466$	12.4961			0.578871
$467$	−13.2918			−0.615073			−0.307536	−	0.951536i	$-0.599505\pi$
$467$	−13.2918			−0.615073			−0.307536	+	0.951536i	$0.599505\pi$
$468$	−6.87136	−	12.4587i	−0.317629	−	0.575903i
$469$	−10.1147			−0.467054
$470$	0.990385	−	0.366152i	0.0456831	−	0.0168894i
$471$	28.7169	+	16.9567i	1.32320	+	0.781324i
$472$		−	6.24959i		−	0.287661i
$473$	−16.6902			−0.767417
$474$	20.8471	+	12.3097i	0.957537	+	0.565405i
$475$	1.19178	−	1.02073i	0.0546825	−	0.0468345i
$476$	−2.20958			−0.101276
$477$	9.15321	−	5.04828i	0.419097	−	0.231145i
$478$	−30.5132			−1.39564
$479$		−	14.0177i		−	0.640484i	−0.947336	−	0.320242i	$-0.896236\pi$
$479$		−	14.0177i		−	0.640484i	0.947336	−	0.320242i	$-0.103764\pi$
$480$	0.690586	−	3.81092i	0.0315208	−	0.173944i
$481$	−23.5200			−1.07242
$482$			19.0611i			0.868208i
$483$	3.57505	−	6.05449i	0.162670	−	0.275489i
$484$	1.16342			0.0528830
$485$	8.37406	+	22.6505i	0.380246	+	1.02851i
$486$	7.12430	+	13.8652i	0.323165	+	0.628939i
$487$	−7.89032			−0.357544			−0.178772	−	0.983890i	$-0.557213\pi$
$487$	−7.89032			−0.357544			−0.178772	+	0.983890i	$0.557213\pi$
$488$			3.55983i			0.161146i
$489$	−23.3932	−	13.8132i	−1.05788	−	0.624654i
$490$	−13.7739	+	5.09231i	−0.622241	+	0.230047i
$491$	−17.0301			−0.768556			−0.384278	−	0.923217i	$-0.625550\pi$
$491$	−17.0301			−0.768556			−0.384278	+	0.923217i	$0.625550\pi$
$492$	−0.530938	−	0.313508i	−0.0239365	−	0.0141340i
$493$			4.98087i			0.224327i
$494$	−1.48839			−0.0669656
$495$	17.7018	+	15.2971i	0.795635	+	0.687554i
$496$	5.54794	+	0.469478i	0.249110	+	0.0210802i
$497$	5.07143			0.227485
$498$	11.1192	+	6.56568i	0.498265	+	0.294215i
$499$			1.83387i			0.0820954i	0.999157	+	0.0410477i	$0.0130696\pi$
$499$			1.83387i			0.0820954i	−0.999157	+	0.0410477i	$0.986930\pi$
$500$	5.44266	−	9.76614i	0.243403	−	0.436755i
$501$	22.6531	+	13.3762i	1.01207	+	0.597603i
$502$	−5.37144			−0.239739
$503$	−22.3648			−0.997197			−0.498599	−	0.866833i	$-0.666152\pi$
$503$	−22.3648			−0.997197			−0.498599	+	0.866833i	$0.666152\pi$
$504$	−1.72786	+	0.952971i	−0.0769652	+	0.0424487i
$505$	9.56255	+	25.8652i	0.425528	+	1.15099i
$506$			21.5248i			0.956893i
$507$	−8.35996	+	14.1579i	−0.371279	+	0.628776i
$508$	−13.5825			−0.602628
$509$	33.6772			1.49272			0.746358	−	0.665545i	$-0.231801\pi$
$509$	33.6772			1.49272			0.746358	+	0.665545i	$0.231801\pi$
$510$	12.8021	+	2.31990i	0.566887	+	0.102727i
$511$			2.17245i			0.0961035i
$512$	−1.00000			−0.0441942
$513$	1.63000	+	0.0478892i	0.0719665	+	0.00211436i
$514$	−6.96961			−0.307416
$515$	−7.23238	−	19.5625i	−0.318697	−	0.862025i
$516$	−4.21451	+	7.13744i	−0.185533	+	0.314208i
$517$	1.64690			0.0724305
$518$			3.26193i			0.143321i
$519$	−13.8641	+	23.4795i	−0.608568	+	1.03064i
$520$	−9.94687	+	3.67743i	−0.436199	+	0.161266i
$521$		−	1.07836i		−	0.0472440i	−0.999721	−	0.0236220i	$-0.992480\pi$
$521$		−	1.07836i		−	0.0472440i	0.999721	−	0.0236220i	$-0.00751981\pi$
$522$	2.14820	+	3.89498i	0.0940242	+	0.170478i
$523$	14.1021			0.616644			0.308322	−	0.951282i	$-0.400233\pi$
$523$	14.1021			0.616644			0.308322	+	0.951282i	$0.400233\pi$
$524$		−	16.1017i		−	0.703407i
$525$	−5.60939	+	0.990950i	−0.244814	+	0.0432486i
$526$			16.3241i			0.711764i
$527$	−1.57713	+	18.6373i	−0.0687008	+	0.811854i
$528$	3.07143	−	5.20159i	0.133667	−	0.226370i
$529$	−15.0909			−0.656128
$530$	−2.70175	−	7.30781i	−0.117356	−	0.317431i
$531$	16.4174	−	9.05468i	0.712453	−	0.392940i
$532$			0.206420i			0.00894946i
$533$			1.68833i			0.0731295i
$534$	0.271948	−	0.460556i	0.0117684	−	0.0199302i
$535$	−24.9609	+	9.22824i	−1.07916	+	0.398971i
$536$		−	15.3778i		−	0.664222i
$537$	−11.8060	+	19.9940i	−0.509467	+	0.862804i
$538$	21.6945			0.935318
$539$	−22.9044			−0.986564
$540$	11.0116	−	3.70729i	0.473865	−	0.159536i
$541$	−8.50681			−0.365736			−0.182868	−	0.983137i	$-0.558538\pi$
$541$	−8.50681			−0.365736			−0.182868	+	0.983137i	$0.558538\pi$
$542$		−	9.02824i		−	0.387796i
$543$	38.0366	+	22.4598i	1.63231	+	0.963843i
$544$		−	3.35932i		−	0.144030i
$545$	18.9609	−	7.01000i	0.812198	−	0.300275i
$546$	4.65252	+	2.74721i	0.199109	+	0.117570i
$547$		−	30.7724i		−	1.31573i	−0.753135	−	0.657866i	$-0.771459\pi$
$547$		−	30.7724i		−	1.31573i	0.753135	−	0.657866i	$-0.228541\pi$
$548$		−	6.61948i		−	0.282770i
$549$	−9.35149	+	5.15764i	−0.399112	+	0.220123i
$550$	13.2443	−	11.3435i	0.564738	−	0.483687i
$551$	0.465316			0.0198231
$552$	9.20491	+	5.43530i	0.391787	+	0.231342i
$553$	−9.19378			−0.390959
$554$	18.7953			0.798537
$555$	3.42478	−	18.8993i	0.145374	−	0.802230i
$556$		−	7.03219i		−	0.298231i
$557$			37.9447i			1.60777i	0.594786	+	0.803884i	$0.297237\pi$
$557$			37.9447i			1.60777i	−0.594786	+	0.803884i	$0.702763\pi$
$558$	6.80479	+	15.2543i	0.288070	+	0.645768i
$559$	22.6963			0.959951
$560$	0.510013	+	1.37951i	0.0215520	+	0.0582947i
$561$	17.4738	+	10.3179i	0.737746	+	0.435623i
$562$		−	3.54453i		−	0.149517i
$563$	−19.6105			−0.826485			−0.413243	−	0.910621i	$-0.635604\pi$
$563$	−19.6105			−0.826485			−0.413243	+	0.910621i	$0.635604\pi$
$564$	0.415864	−	0.704283i	0.0175111	−	0.0296557i
$565$	6.31545	−	2.33487i	0.265693	−	0.0982285i
$566$			22.2060i			0.933389i
$567$	−5.00681	−	3.15830i	−0.210266	−	0.132636i
$568$			7.71031i			0.323517i
$569$	−9.53576			−0.399760			−0.199880	−	0.979820i	$-0.564055\pi$
$569$	−9.53576			−0.399760			−0.199880	+	0.979820i	$0.564055\pi$
$570$	0.216726	−	1.19598i	0.00907767	−	0.0500941i
$571$			10.5840i			0.442927i	0.975169	+	0.221463i	$0.0710833\pi$
$571$			10.5840i			0.442927i	−0.975169	+	0.221463i	$0.928917\pi$
$572$	−16.5405			−0.691594
$573$	−1.99596	−	1.17857i	−0.0833824	−	0.0492355i
$574$	0.234150			0.00977321
$575$	20.0738	+	23.4375i	0.837134	+	0.977412i
$576$	−1.44884	−	2.62695i	−0.0603685	−	0.109456i
$577$			41.1919i			1.71484i	0.514615	+	0.857421i	$0.327935\pi$
$577$			41.1919i			1.71484i	−0.514615	+	0.857421i	$0.672065\pi$
$578$	−5.71494			−0.237710
$579$	−39.1101	−	23.0937i	−1.62536	−	0.959740i
$580$	3.10970	−	1.14968i	0.129123	−	0.0477378i
$581$	−4.90371			−0.203440
$582$	16.1073	+	9.51099i	0.667667	+	0.394243i
$583$		−	12.1521i		−	0.503287i
$584$	−3.30287			−0.136674
$585$	−24.0719	−	20.8019i	−0.995249	−	0.860052i
$586$	−5.62369			−0.232312
$587$		−	33.3678i		−	1.37724i	−0.725125	−	0.688618i	$-0.758218\pi$
$587$		−	33.3678i		−	1.37724i	0.725125	−	0.688618i	$-0.241782\pi$
$588$	−5.78368	+	9.79490i	−0.238515	+	0.403935i
$589$	1.74111	+	0.147336i	0.0717411	+	0.00607088i
$590$	−4.84590	−	13.1074i	−0.199503	−	0.539624i
$591$	27.2811	+	16.1089i	1.12219	+	0.662632i
$592$	−4.95925			−0.203824
$593$	−13.0319			−0.535157			−0.267579	−	0.963536i	$-0.586223\pi$
$593$	−13.0319			−0.535157			−0.267579	+	0.963536i	$0.586223\pi$
$594$	18.1143	+	0.532195i	0.743240	+	0.0218362i
$595$	−4.63421	+	1.71330i	−0.189984	+	0.0702384i
$596$			7.67412i			0.314344i
$597$	−25.0120	−	14.7691i	−1.02367	−	0.604458i
$598$		−	29.2706i		−	1.19696i
$599$			1.78651i			0.0729948i	0.999334	+	0.0364974i	$0.0116201\pi$
$599$			1.78651i			0.0729948i	−0.999334	+	0.0364974i	$0.988380\pi$
$600$	−1.50659	−	8.52820i	−0.0615061	−	0.348162i
$601$			3.18010i			0.129719i	0.997894	+	0.0648595i	$0.0206599\pi$
$601$			3.18010i			0.129719i	−0.997894	+	0.0648595i	$0.979340\pi$
$602$		−	3.14769i		−	0.128290i
$603$	40.3968	−	22.2801i	1.64508	−	0.907315i
$604$		−	9.91125i		−	0.403283i
$605$	2.44008	−	0.902114i	0.0992033	−	0.0366761i
$606$	18.3933	+	10.8608i	0.747176	+	0.441192i
$607$		−	10.3922i		−	0.421806i	−0.977507	−	0.210903i	$-0.932360\pi$
$607$		−	10.3922i		−	0.421806i	0.977507	−	0.210903i	$-0.0676404\pi$
$608$	−0.313830			−0.0127275
$609$	−1.45452	−	0.858864i	−0.0589402	−	0.0348029i
$610$	2.76027	+	7.46611i	0.111760	+	0.302294i
$611$	−2.23955			−0.0906024
$612$	8.82477	−	4.86713i	0.356720	−	0.196742i
$613$	27.4684			1.10944			0.554719	−	0.832038i	$-0.312826\pi$
$613$	27.4684			1.10944			0.554719	+	0.832038i	$0.312826\pi$
$614$			9.58898i			0.386980i
$615$	−1.35664	−	0.245840i	−0.0547050	−	0.00991323i
$616$			2.29396i			0.0924263i
$617$	−13.9276			−0.560704			−0.280352	−	0.959897i	$-0.590451\pi$
$617$	−13.9276			−0.560704			−0.280352	+	0.959897i	$0.590451\pi$
$618$	−13.9113	−	8.21431i	−0.559594	−	0.330428i
$619$			18.1408i			0.729141i	0.931176	+	0.364571i	$0.118784\pi$
$619$			18.1408i			0.729141i	−0.931176	+	0.364571i	$0.881216\pi$
$620$	11.9998	−	3.31719i	0.481925	−	0.133222i
$621$	−0.941790	+	32.0557i	−0.0377927	+	1.28635i
$622$		−	18.7925i		−	0.753511i
$623$			0.203110i			0.00813744i
$624$	−4.17671	+	7.07342i	−0.167202	+	0.283164i
$625$	3.84240	−	24.7030i	0.153696	−	0.988118i
$626$	6.40671			0.256064
$627$	0.963907	−	1.63242i	0.0384947	−	0.0651924i
$628$		−	19.2544i		−	0.768332i
$629$		−	16.6597i		−	0.664266i
$630$	−2.88496	+	3.33846i	−0.114940	+	0.133008i
$631$			18.0831i			0.719877i	0.932976	+	0.359938i	$0.117202\pi$
$631$			18.0831i			0.719877i	−0.932976	+	0.359938i	$0.882798\pi$
$632$		−	13.9777i		−	0.556004i
$633$	10.8043	−	18.2975i	0.429432	−	0.727261i
$634$	−32.2027			−1.27893
$635$	−28.4870	+	10.5318i	−1.13047	+	0.417943i
$636$	−5.19673	−	3.06856i	−0.206064	−	0.121676i
$637$	31.1467			1.23408
$638$	5.17108			0.204725
$639$	−20.2546	+	11.1710i	−0.801259	+	0.441919i
$640$	−2.09732	+	0.775395i	−0.0829040	+	0.0306502i
$641$	22.4679			0.887429			0.443714	−	0.896168i	$-0.353661\pi$
$641$	22.4679			0.887429			0.443714	+	0.896168i	$0.353661\pi$
$642$	−10.4811	+	17.7502i	−0.413658	+	0.700546i
$643$	49.3756			1.94718			0.973592	−	0.228295i	$-0.0733151\pi$
$643$	49.3756			1.94718			0.973592	+	0.228295i	$0.0733151\pi$
$644$	−4.05947			−0.159965
$645$	−3.30485	+	18.2374i	−0.130128	+	0.718098i
$646$		−	1.05426i		−	0.0414792i
$647$			31.7002i			1.24626i	0.782117	+	0.623132i	$0.214140\pi$
$647$			31.7002i			1.24626i	−0.782117	+	0.623132i	$0.785860\pi$
$648$	4.80171	−	7.61207i	0.188629	−	0.299030i
$649$		−	21.7961i		−	0.855574i
$650$	−18.0103	+	15.4255i	−0.706424	+	0.605038i
$651$	−5.17055	−	3.67423i	−0.202650	−	0.144005i
$652$			15.6849i			0.614267i
$653$	−9.43796			−0.369336			−0.184668	−	0.982801i	$-0.559121\pi$
$653$	−9.43796			−0.369336			−0.184668	+	0.982801i	$0.559121\pi$
$654$	7.96173	−	13.4835i	0.311328	−	0.527247i
$655$	−12.4852	−	33.7705i	−0.487837	−	1.31952i
$656$			0.355988i			0.0138990i
$657$	−4.78534	−	8.67647i	−0.186694	−	0.338501i
$658$			0.310597i			0.0121083i
$659$			19.1515i			0.746036i	0.927824	+	0.373018i	$0.121677\pi$
$659$			19.1515i			0.746036i	−0.927824	+	0.373018i	$0.878323\pi$
$660$	2.40849	−	13.2910i	0.0937505	−	0.517351i
$661$	−49.3343			−1.91888			−0.959441	−	0.281911i	$-0.909032\pi$
$661$	−49.3343			−1.91888			−0.959441	+	0.281911i	$0.909032\pi$
$662$			15.7704i			0.612935i
$663$	−23.7619	−	14.0309i	−0.922837	−	0.544915i
$664$		−	7.45533i		−	0.289323i
$665$	0.160057	+	0.432930i	0.00620675	+	0.0167883i
$666$	−7.18517	−	13.0277i	−0.278420	−	0.504813i
$667$			9.15091i			0.354325i
$668$		−	15.1886i		−	0.587666i
$669$	18.7024	−	31.6733i	0.723078	−	1.22456i
$670$	−11.9239	−	32.2523i	−0.460661	−	1.24602i
$671$			12.4153i			0.479287i
$672$	0.980995	+	0.579257i	0.0378427	+	0.0223453i
$673$	−35.5093			−1.36878			−0.684392	−	0.729114i	$-0.739932\pi$
$673$	−35.5093			−1.36878			−0.684392	+	0.729114i	$0.739932\pi$
$674$	−14.3993			−0.554639
$675$	20.2203	−	16.3137i	0.778281	−	0.627916i
$676$	9.49274			0.365105
$677$		−	40.4174i		−	1.55337i	−0.629891	−	0.776683i	$-0.716901\pi$
$677$		−	40.4174i		−	1.55337i	0.629891	−	0.776683i	$-0.283099\pi$
$678$	2.65187	−	4.49105i	0.101844	−	0.172478i
$679$	−7.10348			−0.272606
$680$	−2.60480	−	7.04559i	−0.0998896	−	0.270186i
$681$	−17.7814	+	30.1136i	−0.681386	+	1.15395i
$682$	19.3490	+	1.63736i	0.740913	+	0.0626976i
$683$	−31.0312			−1.18738			−0.593688	−	0.804695i	$-0.702329\pi$
$683$	−31.0312			−1.18738			−0.593688	+	0.804695i	$0.702329\pi$
$684$	−0.454690	−	0.824415i	−0.0173855	−	0.0315223i
$685$	−5.13271	−	13.8832i	−0.196111	−	0.530449i
$686$		−	8.92388i		−	0.340715i
$687$	13.1597	+	7.77053i	0.502074	+	0.296464i
$688$	4.78557			0.182448
$689$			16.5251i			0.629555i
$690$	23.5202	+	4.26215i	0.895397	+	0.162257i
$691$	−17.3176			−0.658791			−0.329396	−	0.944192i	$-0.606845\pi$
$691$	−17.3176			−0.658791			−0.329396	+	0.944192i	$0.606845\pi$
$692$	15.7427			0.598449
$693$	−6.02612	+	3.32359i	−0.228913	+	0.126253i
$694$			15.5482i			0.590203i
$695$	−5.45272	−	14.7488i	−0.206834	−	0.559453i
$696$	1.30577	−	2.21137i	0.0494950	−	0.0838219i
$697$	−1.19588			−0.0452971
$698$	3.24331			0.122761
$699$	11.0049	−	18.6373i	0.416245	−	0.704928i
$700$	2.13932	+	2.49781i	0.0808588	+	0.0944082i
$701$			39.0962i			1.47664i	0.674448	+	0.738322i	$0.264382\pi$
$701$			39.0962i			1.47664i	−0.674448	+	0.738322i	$0.735618\pi$
$702$	−24.6329	−	0.723709i	−0.929709	−	0.0273146i
$703$	−1.55636			−0.0586992
$704$	−3.48761			−0.131444
$705$	0.326104	−	1.79957i	0.0122818	−	0.0677757i
$706$		−	7.73754i		−	0.291206i
$707$	−8.11164			−0.305070
$708$	−9.32095	−	5.50383i	−0.350303	−	0.206846i
$709$		−	32.7850i		−	1.23127i	−0.788032	−	0.615634i	$-0.788900\pi$
$709$		−	32.7850i		−	1.23127i	0.788032	−	0.615634i	$-0.211100\pi$
$710$	5.97854	+	16.1710i	0.224370	+	0.606887i
$711$	36.7187	−	20.2515i	1.37706	−	0.759491i
$712$	−0.308797			−0.0115727
$713$	−2.89752	+	34.2407i	−0.108513	+	1.28232i
$714$	−1.94591	+	3.29548i	−0.0728239	+	0.123330i
$715$	−34.6908	+	12.8254i	−1.29736	+	0.479644i
$716$	13.4057			0.500996
$717$	−26.8720	+	45.5089i	−1.00355	+	1.69956i
$718$			14.0443i			0.524129i
$719$	34.4738			1.28566			0.642828	−	0.766010i	$-0.277761\pi$
$719$	34.4738			1.28566			0.642828	+	0.766010i	$0.277761\pi$
$720$	−5.07561	−	4.38613i	−0.189157	−	0.163461i
$721$	6.13503			0.228480
$722$	18.9015			0.703441
$723$	28.4286	+	16.7865i	1.05727	+	0.624297i
$724$		−	25.5031i		−	0.947816i
$725$	5.63059	−	4.82249i	0.209115	−	0.179103i
$726$	1.02459	−	1.73519i	0.0380262	−	0.0643989i
$727$			37.3200i			1.38412i	0.721839	+	0.692061i	$0.243297\pi$
$727$			37.3200i			1.38412i	−0.721839	+	0.692061i	$0.756703\pi$
$728$		−	3.11946i		−	0.115615i
$729$	26.9534	+	1.58514i	0.998275	+	0.0587089i
$730$	−6.92719	+	2.56103i	−0.256387	+	0.0947879i
$731$			16.0763i			0.594603i
$732$	5.30931	+	3.13503i	0.196238	+	0.115874i
$733$		−	0.314924i		−	0.0116320i	−0.999983	−	0.00581599i	$-0.998149\pi$
$733$		−	0.314924i		−	0.0116320i	0.999983	−	0.00581599i	$-0.00185130\pi$
$734$	−14.2075			−0.524407
$735$	−4.53533	+	25.0277i	−0.167288	+	0.923161i
$736$		−	6.17179i		−	0.227495i
$737$		−	53.6319i		−	1.97556i
$738$	−0.935162	+	0.515771i	−0.0344238	+	0.0189858i
$739$		−	45.5930i		−	1.67717i	−0.544775	−	0.838583i	$-0.683385\pi$
$739$		−	45.5930i		−	1.67717i	0.544775	−	0.838583i	$-0.316615\pi$
$740$	−10.4011	+	3.84538i	−0.382354	+	0.141359i
$741$	−1.31078	+	2.21985i	−0.0481525	+	0.0815483i
$742$	2.29182			0.0841353
$743$			0.946732i			0.0347322i	0.999849	+	0.0173661i	$0.00552809\pi$
$743$			0.946732i			0.0347322i	−0.999849	+	0.0173661i	$0.994472\pi$
$744$	5.58610	−	7.86101i	0.204796	−	0.288199i
$745$	5.95047	+	16.0951i	0.218008	+	0.589679i
$746$		−	7.05802i		−	0.258412i
$747$	19.5848	−	10.8016i	0.716569	−	0.395210i
$748$		−	11.7160i		−	0.428380i
$749$		−	7.82806i		−	0.286031i
$750$	−9.77252	−	16.7182i	−0.356842	−	0.610462i
$751$	13.6007			0.496296			0.248148	−	0.968722i	$-0.420178\pi$
$751$	13.6007			0.496296			0.248148	+	0.968722i	$0.420178\pi$
$752$	−0.472214			−0.0172199
$753$	−4.73046	+	8.01123i	−0.172388	+	0.291946i
$754$	−7.03193			−0.256088
$755$	−7.68513	−	20.7871i	−0.279690	−	0.756519i
$756$	−0.100369	+	3.41627i	−0.00365040	+	0.124249i
$757$	−50.1393			−1.82234			−0.911172	−	0.412026i	$-0.864821\pi$
$757$	−50.1393			−1.82234			−0.911172	+	0.412026i	$0.864821\pi$
$758$	−33.4723			−1.21577
$759$	32.1031	+	18.9562i	1.16527	+	0.688067i
$760$	−0.658203	+	0.243342i	−0.0238755	+	0.00882695i
$761$	−25.8332			−0.936455			−0.468227	−	0.883608i	$-0.655107\pi$
$761$	−25.8332			−0.936455			−0.468227	+	0.883608i	$0.655107\pi$
$762$	−11.9617	+	20.2577i	−0.433328	+	0.733858i
$763$			5.94638i			0.215274i
$764$			1.33827i			0.0484168i
$765$	14.7344	−	17.0506i	0.532725	−	0.616467i
$766$			0.926997i			0.0334938i
$767$			29.6396i			1.07023i
$768$	−0.880669	+	1.49145i	−0.0317784	+	0.0538180i
$769$	−34.8883			−1.25811			−0.629053	−	0.777363i	$-0.716557\pi$
$769$	−34.8883			−1.25811			−0.629053	+	0.777363i	$0.716557\pi$
$770$	1.77873	+	4.81118i	0.0641008	+	0.173383i
$771$	−6.13792	+	10.3948i	−0.221052	+	0.374360i
$772$			26.2229i			0.943781i
$773$		−	41.8866i		−	1.50656i	−0.657702	−	0.753279i	$-0.728471\pi$
$773$		−	41.8866i		−	1.50656i	0.657702	−	0.753279i	$-0.271529\pi$
$774$	6.93354	+	12.5714i	0.249221	+	0.451871i
$775$	22.5954	−	16.2618i	0.811651	−	0.584143i
$776$		−	10.7997i		−	0.387688i
$777$	4.86500	+	2.87268i	0.174531	+	0.103057i
$778$	34.6260			1.24140
$779$			0.111720i			0.00400277i
$780$	−3.27521	+	18.0739i	−0.117271	+	0.647148i
$781$			26.8906i			0.962220i
$782$	20.7330			0.741412
$783$	7.70101	+	0.226254i	0.275212	+	0.00808566i
$784$	6.56737			0.234549
$785$	−14.9297	−	40.3826i	−0.532865	−	1.44132i
$786$	−24.0149	−	14.1803i	−0.856583	−	0.505794i
$787$	−44.0446			−1.57002			−0.785010	−	0.619483i	$-0.787342\pi$
$787$	−44.0446			−1.57002			−0.785010	+	0.619483i	$0.787342\pi$
$788$		−	18.2917i		−	0.651614i
$789$	24.3466	+	14.3761i	0.866760	+	0.511804i
$790$	−10.8382	−	29.3158i	−0.385608	−	1.04301i
$791$			1.98060i			0.0704221i
$792$	−5.05300	−	9.16177i	−0.179551	−	0.325549i
$793$		−	16.8830i		−	0.599534i
$794$			9.43307i			0.334767i
$795$	−13.2786	−	2.40624i	−0.470942	−	0.0853406i
$796$			16.7703i			0.594407i
$797$		−	13.8639i		−	0.491084i	−0.969386	−	0.245542i	$-0.921034\pi$
$797$		−	13.8639i		−	0.491084i	0.969386	−	0.245542i	$-0.0789659\pi$
$798$	0.307866	+	0.181788i	0.0108983	+	0.00643523i
$799$		−	1.58632i		−	0.0561200i
$800$	−3.79753	+	3.25251i	−0.134263	+	0.114993i
$801$	−0.447399	−	0.811194i	−0.0158081	−	0.0286621i
$802$	−2.14298			−0.0756713
$803$	−11.5191			−0.406501
$804$	−22.9353	−	13.5428i	−0.808865	−	0.477618i
$805$	−8.51401	+	3.14769i	−0.300080	+	0.110941i
$806$	−26.3119	−	2.22657i	−0.926798	−	0.0784276i
$807$	19.1057	−	32.3563i	0.672553	−	1.13900i
$808$		−	12.3325i		−	0.433855i
$809$	−33.8218			−1.18911			−0.594556	−	0.804054i	$-0.702672\pi$
$809$	−33.8218			−1.18911			−0.594556	+	0.804054i	$0.702672\pi$
$810$	4.16837	−	19.6882i	0.146462	−	0.691772i
$811$	−2.57246			−0.0903313			−0.0451657	−	0.998980i	$-0.514382\pi$
$811$	−2.57246			−0.0903313			−0.0451657	+	0.998980i	$0.514382\pi$
$812$			0.975240i			0.0342242i
$813$	−13.4652	−	7.95090i	−0.472244	−	0.278850i
$814$	−17.2959			−0.606222
$815$	12.1620	+	32.8962i	0.426015	+	1.15230i
$816$	−5.01026	−	2.95845i	−0.175394	−	0.103567i
$817$	1.50186			0.0525433
$818$			0.448391i			0.0156776i
$819$	8.19466	−	4.51961i	0.286344	−	0.157928i
$820$	0.276031	+	0.746622i	0.00963943	+	0.0260732i
$821$	47.8989			1.67168			0.835841	−	0.548972i	$-0.184981\pi$
$821$	47.8989			1.67168			0.835841	+	0.548972i	$0.184981\pi$
$822$	−9.87262	−	5.82957i	−0.344347	−	0.203330i
$823$	−36.1207			−1.25909			−0.629544	−	0.776965i	$-0.716758\pi$
$823$	−36.1207			−1.25909			−0.629544	+	0.776965i	$0.716758\pi$
$824$			9.32735i			0.324934i
$825$	−5.25438	−	29.7430i	−0.182934	−	1.03552i
$826$	4.11065			0.143028
$827$		−	1.16723i		−	0.0405887i	−0.999794	−	0.0202943i	$-0.993540\pi$
$827$		−	1.16723i		−	0.0405887i	0.999794	−	0.0202943i	$-0.00646033\pi$
$828$	16.2130	−	8.94195i	0.563439	−	0.310754i
$829$			16.6224i			0.577320i	0.957432	+	0.288660i	$0.0932097\pi$
$829$			16.6224i			0.577320i	−0.957432	+	0.288660i	$0.906790\pi$
$830$	−5.78082	−	15.6362i	−0.200655	−	0.542741i
$831$	16.5525	−	28.0323i	0.574199	−	0.972430i
$832$	4.74265			0.164422
$833$			22.0619i			0.764400i
$834$	−10.4882	−	6.19303i	−0.363175	−	0.214447i
$835$	−11.7772	−	31.8555i	−0.407567	−	1.10240i
$836$	−1.09452			−0.0378546
$837$	28.7438	+	3.28502i	0.993533	+	0.113547i
$838$			27.9545i			0.965672i
$839$		−	24.8758i		−	0.858808i	−0.903112	−	0.429404i	$-0.858724\pi$
$839$		−	24.8758i		−	0.858808i	0.903112	−	0.429404i	$-0.141276\pi$
$840$	2.50662	+	0.454230i	0.0864864	+	0.0156724i
$841$	−26.8016			−0.924193
$842$	−5.89643			−0.203205
$843$	−5.28649	−	3.12156i	−0.182076	−	0.107512i
$844$	−12.2683			−0.422291
$845$	19.9093	−	7.36062i	0.684902	−	0.253213i
$846$	−0.684164	−	1.24048i	−0.0235220	−	0.0426486i
$847$			0.765238i			0.0262939i
$848$			3.48435i			0.119653i
$849$	33.1192	+	19.5562i	1.13665	+	0.671166i
$850$	−10.9262	−	12.7571i	−0.374766	−	0.437566i
$851$		−	30.6074i		−	1.04921i
$852$	11.4995	+	6.79024i	0.393968	+	0.232630i
$853$		−	27.3326i		−	0.935849i	−0.883768	−	0.467925i	$-0.845002\pi$
$853$		−	27.3326i		−	0.935849i	0.883768	−	0.467925i	$-0.154998\pi$
$854$	−2.34146			−0.0801233
$855$	−1.59288	−	1.37650i	−0.0544753	−	0.0470753i
$856$	11.9013			0.406779
$857$	50.0282			1.70893			0.854465	−	0.519509i	$-0.173885\pi$
$857$	50.0282			1.70893			0.854465	+	0.519509i	$0.173885\pi$
$858$	−14.5667	+	24.6693i	−0.497300	+	0.842198i
$859$			21.0885i			0.719532i	0.933043	+	0.359766i	$0.117143\pi$
$859$			21.0885i			0.719532i	−0.933043	+	0.359766i	$0.882857\pi$
$860$	10.0369	−	3.71071i	0.342255	−	0.126534i
$861$	0.206208	−	0.349222i	0.00702756	−	0.0119015i
$862$			35.1649i			1.19772i
$863$		−	55.5365i		−	1.89048i	−0.326371	−	0.945242i	$-0.605826\pi$
$863$		−	55.5365i		−	1.89048i	0.326371	−	0.945242i	$-0.394174\pi$
$864$	−5.19391	−	0.152596i	−0.176700	−	0.00519142i
$865$	33.0176	−	12.2068i	1.12263	−	0.415045i
$866$	−18.8588			−0.640846
$867$	−5.03298	+	8.52355i	−0.170929	+	0.289475i
$868$	−0.308797	+	3.64913i	−0.0104813	+	0.123860i
$869$		−	48.7488i		−	1.65369i
$870$	1.02393	−	5.65045i	0.0347145	−	0.191568i
$871$			72.9318i			2.47120i
$872$	−9.04055			−0.306152
$873$	28.3703	−	15.6471i	0.960190	−	0.529575i
$874$		−	1.93689i		−	0.0655163i
$875$	6.42364	+	3.57989i	0.217159	+	0.121022i
$876$	−2.90874	+	4.92607i	−0.0982771	+	0.166436i
$877$		−	26.3528i		−	0.889870i	−0.895563	−	0.444935i	$-0.853227\pi$
$877$		−	26.3528i		−	0.889870i	0.895563	−	0.444935i	$-0.146773\pi$
$878$	1.64683			0.0555780
$879$	−4.95261	+	8.38745i	−0.167047	+	0.282902i
$880$	−7.31464	+	2.70428i	−0.246577	+	0.0911611i
$881$	44.8243			1.51017			0.755085	−	0.655627i	$-0.227596\pi$
$881$	44.8243			1.51017			0.755085	+	0.655627i	$0.227596\pi$
$882$	9.51509	+	17.2521i	0.320390	+	0.580910i
$883$	−27.3560			−0.920604			−0.460302	−	0.887762i	$-0.652259\pi$
$883$	−27.3560			−0.920604			−0.460302	+	0.887762i	$0.652259\pi$
$884$			15.9321i			0.535854i
$885$	−23.8167	−	4.31588i	−0.800589	−	0.145077i
$886$	5.06315			0.170100
$887$	−47.6768			−1.60083			−0.800416	−	0.599445i	$-0.795388\pi$
$887$	−47.6768			−1.60083			−0.800416	+	0.599445i	$0.795388\pi$
$888$	−4.36746	+	7.39647i	−0.146562	+	0.248209i
$889$		−	8.93387i		−	0.299632i
$890$	−0.647648	+	0.239440i	−0.0217092	+	0.00802604i
$891$	16.7465	−	26.5479i	0.561028	−	0.889389i
$892$	−21.2366			−0.711054
$893$	−0.148195			−0.00495915
$894$	11.4456	+	6.75836i	0.382797	+	0.226033i
$895$	28.1162	−	10.3947i	0.939820	−	0.347458i
$896$		−	0.657746i		−	0.0219737i
$897$	−43.6557	−	25.7777i	−1.45762	−	0.860694i
$898$	0.0169529			0.000565725
$899$	8.22593	+	0.696095i	0.274350	+	0.0232161i
$900$	−14.0462	−	5.26353i	−0.468206	−	0.175451i
$901$	−11.7051			−0.389952
$902$			1.24155i			0.0413390i
$903$	−4.69462	−	2.77207i	−0.156227	−	0.0922488i
$904$	−3.01119			−0.100151
$905$	−19.7750	−	53.4883i	−0.657343	−	1.77801i
$906$	−14.7821	−	8.72853i	−0.491103	−	0.289986i
$907$			7.97587i			0.264835i	0.991194	+	0.132417i	$0.0422739\pi$
$907$			7.97587i			0.264835i	−0.991194	+	0.132417i	$0.957726\pi$
$908$	20.1908			0.670056
$909$	32.3968	−	17.8678i	1.07453	−	0.592639i
$910$	−2.41881	−	6.54251i	−0.0801829	−	0.216882i
$911$	41.7060			1.38178			0.690891	−	0.722959i	$-0.257218\pi$
$911$	41.7060			1.38178			0.690891	+	0.722959i	$0.257218\pi$
$912$	−0.276380	+	0.468061i	−0.00915187	+	0.0154991i
$913$		−	26.0013i		−	0.860517i
$914$	−1.97910			−0.0654630
$915$	13.5662	+	2.45837i	0.448485	+	0.0812711i
$916$		−	8.82344i		−	0.291535i
$917$	10.5908			0.349740
$918$	0.512619	−	17.4480i	0.0169190	−	0.575871i
$919$	46.5741			1.53634			0.768168	−	0.640248i	$-0.221168\pi$
$919$	46.5741			1.53634			0.768168	+	0.640248i	$0.221168\pi$
$920$	−4.78557	−	12.9442i	−0.157776	−	0.426759i
$921$	14.3015	+	8.44472i	0.471250	+	0.278263i
$922$	23.0233			0.758233
$923$		−	36.5673i		−	1.20363i
$924$	3.42133	+	2.02022i	0.112553	+	0.0664604i
$925$	−18.8329	+	16.1300i	−0.619221	+	0.530351i
$926$	34.8934			1.14667
$927$	−24.5025	+	13.5139i	−0.804767	+	0.443854i
$928$	−1.48270			−0.0486720
$929$	44.5173			1.46057			0.730283	−	0.683144i	$-0.239388\pi$
$929$	44.5173			1.46057			0.730283	+	0.683144i	$0.239388\pi$
$930$	5.62047	−	20.8185i	0.184302	−	0.682666i
$931$	2.06104			0.0675478
$932$	−12.4961			−0.409324
$933$	−28.0281	−	16.5500i	−0.917598	−	0.541822i
$934$	13.2918			0.434922
$935$	−9.08454	−	24.5723i	−0.297096	−	0.803599i
$936$	6.87136	+	12.4587i	0.224597	+	0.407225i
$937$			19.8351i			0.647983i	0.946060	+	0.323991i	$0.105025\pi$
$937$			19.8351i			0.647983i	−0.946060	+	0.323991i	$0.894975\pi$
$938$	10.1147			0.330257
$939$	5.64219	−	9.55528i	0.184126	−	0.311825i
$940$	−0.990385	+	0.366152i	−0.0323028	+	0.0119426i
$941$	17.4086			0.567504			0.283752	−	0.958898i	$-0.408421\pi$
$941$	17.4086			0.567504			0.283752	+	0.958898i	$0.408421\pi$
$942$	−28.7169	−	16.9567i	−0.935647	−	0.552480i
$943$	−2.19708			−0.0715468
$944$			6.24959i			0.203407i
$945$	2.43845	+	7.24286i	0.0793229	+	0.235610i
$946$	16.6902			0.542645
$947$			0.751785i			0.0244297i	0.999925	+	0.0122149i	$0.00388821\pi$
$947$			0.751785i			0.0244297i	−0.999925	+	0.0122149i	$0.996112\pi$
$948$	−20.8471	−	12.3097i	−0.677081	−	0.399802i
$949$	15.6644			0.508487
$950$	−1.19178	+	1.02073i	−0.0386664	+	0.0331170i
$951$	−28.3600	+	48.0288i	−0.919635	+	1.55744i
$952$	2.20958			0.0716129
$953$			25.0313i			0.810842i	0.914130	+	0.405421i	$0.132875\pi$
$953$			25.0313i			0.810842i	−0.914130	+	0.405421i	$0.867125\pi$
$954$	−9.15321	+	5.04828i	−0.296346	+	0.163444i
$955$	1.03769	+	2.80678i	0.0335787	+	0.0908252i
$956$	30.5132			0.986868
$957$	4.55401	−	7.71240i	0.147210	−	0.249307i
$958$			14.0177i			0.452891i
$959$	4.35394			0.140596
$960$	−0.690586	+	3.81092i	−0.0222886	+	0.122997i
$961$	30.5592	+	5.20927i	0.985780	+	0.168041i
$962$	23.5200			0.758315
$963$	17.2432	+	31.2642i	0.555653	+	1.00747i
$964$		−	19.0611i		−	0.613916i
$965$	20.3331	+	54.9978i	0.654545	+	1.77044i
$966$	−3.57505	+	6.05449i	−0.115025	+	0.194800i
$967$	6.08713			0.195749			0.0978744	−	0.995199i	$-0.468796\pi$
$967$	6.08713			0.195749			0.0978744	+	0.995199i	$0.468796\pi$
$968$	−1.16342			−0.0373939
$969$	−1.57237	−	0.928451i	−0.0505118	−	0.0298261i
$970$	−8.37406	−	22.6505i	−0.268875	−	0.727264i
$971$		−	7.06341i		−	0.226676i	−0.993557	−	0.113338i	$-0.963846\pi$
$971$		−	7.06341i		−	0.226676i	0.993557	−	0.113338i	$-0.0361542\pi$
$972$	−7.12430	−	13.8652i	−0.228512	−	0.444727i
$973$	4.62539			0.148283
$974$	7.89032			0.252822
$975$	7.14521	+	40.4463i	0.228830	+	1.29532i
$976$		−	3.55983i		−	0.113947i
$977$	−44.9590			−1.43837			−0.719183	−	0.694820i	$-0.755484\pi$
$977$	−44.9590			−1.43837			−0.719183	+	0.694820i	$0.755484\pi$
$978$	23.3932	+	13.8132i	0.748032	+	0.441697i
$979$	−1.07696			−0.0344199
$980$	13.7739	−	5.09231i	0.439991	−	0.162668i
$981$	−13.0983	−	23.7490i	−0.418198	−	0.758249i
$982$	17.0301			0.543451
$983$			16.2129i			0.517111i	0.965996	+	0.258556i	$0.0832465\pi$
$983$			16.2129i			0.517111i	−0.965996	+	0.258556i	$0.916754\pi$
$984$	0.530938	+	0.313508i	0.0169257	+	0.00999426i
$985$	−14.1833	−	38.3635i	−0.451916	−	1.22236i
$986$		−	4.98087i		−	0.158623i
$987$	0.463240	+	0.273533i	0.0147451	+	0.00870666i
$988$	1.48839			0.0473519
$989$			29.5355i			0.939175i
$990$	−17.7018	−	15.2971i	−0.562599	−	0.486174i
$991$			48.7156i			1.54750i	0.633490	+	0.773751i	$0.281622\pi$
$991$			48.7156i			1.54750i	−0.633490	+	0.773751i	$0.718378\pi$
$992$	−5.54794	−	0.469478i	−0.176147	−	0.0149059i
$993$	23.5208	+	13.8885i	0.746410	+	0.440739i
$994$	−5.07143			−0.160856
$995$	13.0036	+	35.1727i	0.412242	+	1.11505i
$996$	−11.1192	−	6.56568i	−0.352327	−	0.208041i
$997$		−	36.9133i		−	1.16906i	−0.811374	−	0.584528i	$-0.801280\pi$
$997$		−	36.9133i		−	1.16906i	0.811374	−	0.584528i	$-0.198720\pi$
$998$		−	1.83387i		−	0.0580502i
$999$	−25.7579	−	0.756761i	−0.814944	−	0.0239429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.e.a.929.12	yes	32
3.2	odd	2		930.2.e.b.929.11	yes	32
5.4	even	2		930.2.e.b.929.21	yes	32
15.14	odd	2	inner	930.2.e.a.929.22	yes	32
31.30	odd	2	inner	930.2.e.a.929.21	yes	32
93.92	even	2		930.2.e.b.929.22	yes	32
155.154	odd	2		930.2.e.b.929.12	yes	32
465.464	even	2	inner	930.2.e.a.929.11	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.e.a.929.11	✓	32	465.464	even	2	inner
930.2.e.a.929.12	yes	32	1.1	even	1	trivial
930.2.e.a.929.21	yes	32	31.30	odd	2	inner
930.2.e.a.929.22	yes	32	15.14	odd	2	inner
930.2.e.b.929.11	yes	32	3.2	odd	2
930.2.e.b.929.12	yes	32	155.154	odd	2
930.2.e.b.929.21	yes	32	5.4	even	2
930.2.e.b.929.22	yes	32	93.92	even	2

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.880669 + 1.49145i) q^{3} +1.00000 q^{4} +(2.09732 - 0.775395i) q^{5} +(0.880669 - 1.49145i) q^{6} +0.657746i q^{7} -1.00000 q^{8} +(-1.44884 - 2.62695i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.880669 + 1.49145i) q^{3} +1.00000 q^{4} +(2.09732 - 0.775395i) q^{5} +(0.880669 - 1.49145i) q^{6} +0.657746i q^{7} -1.00000 q^{8} +(-1.44884 - 2.62695i) q^{9} +(-2.09732 + 0.775395i) q^{10} -3.48761 q^{11} +(-0.880669 + 1.49145i) q^{12} +4.74265 q^{13} -0.657746i q^{14} +(-0.690586 + 3.81092i) q^{15} +1.00000 q^{16} +3.35932i q^{17} +(1.44884 + 2.62695i) q^{18} +0.313830 q^{19} +(2.09732 - 0.775395i) q^{20} +(-0.980995 - 0.579257i) q^{21} +3.48761 q^{22} +6.17179i q^{23} +(0.880669 - 1.49145i) q^{24} +(3.79753 - 3.25251i) q^{25} -4.74265 q^{26} +(5.19391 + 0.152596i) q^{27} +0.657746i q^{28} +1.48270 q^{29} +(0.690586 - 3.81092i) q^{30} +(5.54794 + 0.469478i) q^{31} -1.00000 q^{32} +(3.07143 - 5.20159i) q^{33} -3.35932i q^{34} +(0.510013 + 1.37951i) q^{35} +(-1.44884 - 2.62695i) q^{36} -4.95925 q^{37} -0.313830 q^{38} +(-4.17671 + 7.07342i) q^{39} +(-2.09732 + 0.775395i) q^{40} +0.355988i q^{41} +(0.980995 + 0.579257i) q^{42} +4.78557 q^{43} -3.48761 q^{44} +(-5.07561 - 4.38613i) q^{45} -6.17179i q^{46} -0.472214 q^{47} +(-0.880669 + 1.49145i) q^{48} +6.56737 q^{49} +(-3.79753 + 3.25251i) q^{50} +(-5.01026 - 2.95845i) q^{51} +4.74265 q^{52} +3.48435i q^{53} +(-5.19391 - 0.152596i) q^{54} +(-7.31464 + 2.70428i) q^{55} -0.657746i q^{56} +(-0.276380 + 0.468061i) q^{57} -1.48270 q^{58} +6.24959i q^{59} +(-0.690586 + 3.81092i) q^{60} -3.55983i q^{61} +(-5.54794 - 0.469478i) q^{62} +(1.72786 - 0.952971i) q^{63} +1.00000 q^{64} +(9.94687 - 3.67743i) q^{65} +(-3.07143 + 5.20159i) q^{66} +15.3778i q^{67} +3.35932i q^{68} +(-9.20491 - 5.43530i) q^{69} +(-0.510013 - 1.37951i) q^{70} -7.71031i q^{71} +(1.44884 + 2.62695i) q^{72} +3.30287 q^{73} +4.95925 q^{74} +(1.50659 + 8.52820i) q^{75} +0.313830 q^{76} -2.29396i q^{77} +(4.17671 - 7.07342i) q^{78} +13.9777i q^{79} +(2.09732 - 0.775395i) q^{80} +(-4.80171 + 7.61207i) q^{81} -0.355988i q^{82} +7.45533i q^{83} +(-0.980995 - 0.579257i) q^{84} +(2.60480 + 7.04559i) q^{85} -4.78557 q^{86} +(-1.30577 + 2.21137i) q^{87} +3.48761 q^{88} +0.308797 q^{89} +(5.07561 + 4.38613i) q^{90} +3.11946i q^{91} +6.17179i q^{92} +(-5.58610 + 7.86101i) q^{93} +0.472214 q^{94} +(0.658203 - 0.243342i) q^{95} +(0.880669 - 1.49145i) q^{96} +10.7997i q^{97} -6.56737 q^{98} +(5.05300 + 9.16177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9	\( 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} - 4 q^{18} + 8 q^{19} + 2 q^{20} + 10 q^{25} - 12 q^{31} - 32 q^{32} - 8 q^{33} + 16 q^{35} + 4 q^{36} - 8 q^{38} - 4 q^{39} - 2 q^{40} + 10 q^{45} - 4 q^{47} - 36 q^{49} - 10 q^{50} - 4 q^{51} + 12 q^{62} - 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} - 4 q^{72} + 8 q^{76} + 4 q^{78} + 2 q^{80} + 24 q^{81} - 4 q^{87} - 10 q^{90} + 24 q^{93} + 4 q^{94} - 26 q^{95} + 36 q^{98}+O(q^{100}) \) 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 - 4 * q^18 + 8 * q^19 + 2 * q^20 + 10 * q^25 - 12 * q^31 - 32 * q^32 - 8 * q^33 + 16 * q^35 + 4 * q^36 - 8 * q^38 - 4 * q^39 - 2 * q^40 + 10 * q^45 - 4 * q^47 - 36 * q^49 - 10 * q^50 - 4 * q^51 + 12 * q^62 - 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 - 4 * q^72 + 8 * q^76 + 4 * q^78 + 2 * q^80 + 24 * q^81 - 4 * q^87 - 10 * q^90 + 24 * q^93 + 4 * q^94 - 26 * q^95 + 36 * q^98

Introduction

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