LMFDB - Embedded newform 720.2.z.g.667.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.z (of order $4$, degree $2$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			667.7
Root			$-1.37691 + 0.322680i$ of defining polynomial
Character	$\chi$	$=$	720.667
Dual form			720.2.z.g.163.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23576 - 0.687667i) q^{2} +(1.05423 - 1.69959i) q^{4} +(-0.832020 + 2.07551i) q^{5} +(2.83610 + 2.83610i) q^{7} +(0.134028 - 2.82525i) q^{8} +O(q^{10})$	\(q+(1.23576 - 0.687667i) q^{2} +(1.05423 - 1.69959i) q^{4} +(-0.832020 + 2.07551i) q^{5} +(2.83610 + 2.83610i) q^{7} +(0.134028 - 2.82525i) q^{8} +(0.399079 + 3.13699i) q^{10} +(-1.95928 + 1.95928i) q^{11} +2.05493i q^{13} +(5.45504 + 1.55446i) q^{14} +(-1.77720 - 3.58351i) q^{16} +(4.06774 + 4.06774i) q^{17} +(-0.683479 + 0.683479i) q^{19} +(2.65037 + 3.60215i) q^{20} +(-1.07388 + 3.76854i) q^{22} +(4.95014 - 4.95014i) q^{23} +(-3.61549 - 3.45373i) q^{25} +(1.41310 + 2.53941i) q^{26} +(7.81010 - 1.83030i) q^{28} +(-0.835439 - 0.835439i) q^{29} +2.35978i q^{31} +(-4.66047 - 3.20625i) q^{32} +(7.82401 + 2.22952i) q^{34} +(-8.24604 + 3.52666i) q^{35} -4.54384i q^{37} +(-0.374613 + 1.31462i) q^{38} +(5.75232 + 2.62884i) q^{40} -5.07255i q^{41} +0.849753i q^{43} +(1.26444 + 5.39549i) q^{44} +(2.71316 - 9.52126i) q^{46} +(2.72646 - 2.72646i) q^{47} +9.08690i q^{49} +(-6.84291 - 1.78175i) q^{50} +(3.49253 + 2.16636i) q^{52} -5.17605 q^{53} +(-2.43634 - 5.69666i) q^{55} +(8.39280 - 7.63257i) q^{56} +(-1.60691 - 0.457903i) q^{58} +(4.16328 + 4.16328i) q^{59} +(5.55706 - 5.55706i) q^{61} +(1.62274 + 2.91613i) q^{62} +(-7.96407 - 0.757328i) q^{64} +(-4.26502 - 1.70974i) q^{65} -1.73609i q^{67} +(11.2018 - 2.62515i) q^{68} +(-7.76500 + 10.0287i) q^{70} -2.33526 q^{71} +(-4.39686 - 4.39686i) q^{73} +(-3.12465 - 5.61511i) q^{74} +(0.441090 + 1.88218i) q^{76} -11.1134 q^{77} +14.0993 q^{79} +(8.91628 - 0.707050i) q^{80} +(-3.48822 - 6.26848i) q^{82} +2.75725 q^{83} +(-11.8271 + 5.05819i) q^{85} +(0.584347 + 1.05009i) q^{86} +(5.27285 + 5.79805i) q^{88} -11.6448 q^{89} +(-5.82797 + 5.82797i) q^{91} +(-3.19462 - 13.6318i) q^{92} +(1.49437 - 5.24417i) q^{94} +(-0.849899 - 1.98724i) q^{95} +(-3.52933 - 3.52933i) q^{97} +(6.24876 + 11.2293i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	1.23576	−	0.687667i	0.873818	−	0.486254i
$2$	1.23576	−	0.687667i	0.873818	−	0.486254i
$3$		0			0
$3$		0			0
$4$	1.05423	−	1.69959i	0.527114	−	0.849794i
$5$	−0.832020	+	2.07551i	−0.372091	+	0.928196i
$5$	−0.832020	+	2.07551i	−0.372091	+	0.928196i
$6$		0			0
$7$	2.83610	+	2.83610i	1.07194	+	1.07194i	0.997203	+	0.0747413i	$0.0238131\pi$
$7$	2.83610	+	2.83610i	1.07194	+	1.07194i	0.0747413	+	0.997203i	$0.476187\pi$
$8$	0.134028	−	2.82525i	0.0473862	−	0.998877i
$9$		0			0
$10$	0.399079	+	3.13699i	0.126200	+	0.992005i
$11$	−1.95928	+	1.95928i	−0.590745	+	0.590745i	−0.937833	−	0.347088i	$-0.887171\pi$
$11$	−1.95928	+	1.95928i	−0.590745	+	0.590745i	0.347088	+	0.937833i	$0.387171\pi$
$12$		0			0
$13$			2.05493i			0.569934i	0.958537	+	0.284967i	$0.0919826\pi$
$13$			2.05493i			0.569934i	−0.958537	+	0.284967i	$0.908017\pi$
$14$	5.45504	+	1.55446i	1.45792	+	0.415447i
$15$		0			0
$16$	−1.77720	−	3.58351i	−0.444301	−	0.895878i
$17$	4.06774	+	4.06774i	0.986571	+	0.986571i	0.999911	−	0.0133401i	$-0.00424641\pi$
$17$	4.06774	+	4.06774i	0.986571	+	0.986571i	−0.0133401	+	0.999911i	$0.504246\pi$
$18$		0			0
$19$	−0.683479	+	0.683479i	−0.156801	+	0.156801i	−0.781147	−	0.624347i	$-0.785365\pi$
$19$	−0.683479	+	0.683479i	−0.156801	+	0.156801i	0.624347	+	0.781147i	$0.285365\pi$
$20$	2.65037	+	3.60215i	0.592642	+	0.805466i
$21$		0			0
$22$	−1.07388	+	3.76854i	−0.228951	+	0.803455i
$23$	4.95014	−	4.95014i	1.03218	−	1.03218i	0.0327113	−	0.999465i	$-0.489586\pi$
$23$	4.95014	−	4.95014i	1.03218	−	1.03218i	0.999465	−	0.0327113i	$-0.0104142\pi$
$24$		0			0
$25$	−3.61549	−	3.45373i	−0.723097	−	0.690746i
$26$	1.41310	+	2.53941i	0.277133	+	0.498018i
$27$		0			0
$28$	7.81010	−	1.83030i	1.47597	−	0.345895i
$29$	−0.835439	−	0.835439i	−0.155137	−	0.155137i	0.625271	−	0.780408i	$-0.284989\pi$
$29$	−0.835439	−	0.835439i	−0.155137	−	0.155137i	−0.780408	+	0.625271i	$0.784989\pi$
$30$		0			0
$31$			2.35978i			0.423829i	0.977288	+	0.211915i	$0.0679698\pi$
$31$			2.35978i			0.423829i	−0.977288	+	0.211915i	$0.932030\pi$
$32$	−4.66047	−	3.20625i	−0.823862	−	0.566791i
$33$		0			0
$34$	7.82401	+	2.22952i	1.34181	+	0.382359i
$35$	−8.24604	+	3.52666i	−1.39384	+	0.596114i
$36$		0			0
$37$		−	4.54384i		−	0.747002i	−0.927630	−	0.373501i	$-0.878157\pi$
$37$		−	4.54384i		−	0.747002i	0.927630	−	0.373501i	$-0.121843\pi$
$38$	−0.374613	+	1.31462i	−0.0607703	+	0.213260i
$39$		0			0
$40$	5.75232	+	2.62884i	0.909522	+	0.415656i
$41$		−	5.07255i		−	0.792199i	−0.918208	−	0.396100i	$-0.870364\pi$
$41$		−	5.07255i		−	0.792199i	0.918208	−	0.396100i	$-0.129636\pi$
$42$		0			0
$43$			0.849753i			0.129586i	0.997899	+	0.0647930i	$0.0206387\pi$
$43$			0.849753i			0.129586i	−0.997899	+	0.0647930i	$0.979361\pi$
$44$	1.26444	+	5.39549i	0.190621	+	0.813401i
$45$		0			0
$46$	2.71316	−	9.52126i	0.400034	−	1.40383i
$47$	2.72646	−	2.72646i	0.397696	−	0.397696i	−0.479724	−	0.877419i	$-0.659263\pi$
$47$	2.72646	−	2.72646i	0.397696	−	0.397696i	0.877419	+	0.479724i	$0.159263\pi$
$48$		0			0
$49$			9.08690i			1.29813i
$50$	−6.84291	−	1.78175i	−0.967733	−	0.251978i
$51$		0			0
$52$	3.49253	+	2.16636i	0.484327	+	0.300420i
$53$	−5.17605			−0.710985			−0.355492	−	0.934679i	$-0.615687\pi$
$53$	−5.17605			−0.710985			−0.355492	+	0.934679i	$0.615687\pi$
$54$		0			0
$55$	−2.43634	−	5.69666i	−0.328517	−	0.768138i
$56$	8.39280	−	7.63257i	1.12154	−	1.01994i
$57$		0			0
$58$	−1.60691	−	0.457903i	−0.210998	−	0.0601256i
$59$	4.16328	+	4.16328i	0.542013	+	0.542013i	0.924119	−	0.382105i	$-0.124801\pi$
$59$	4.16328	+	4.16328i	0.542013	+	0.542013i	−0.382105	+	0.924119i	$0.624801\pi$
$60$		0			0
$61$	5.55706	−	5.55706i	0.711509	−	0.711509i	−0.255342	−	0.966851i	$-0.582188\pi$
$61$	5.55706	−	5.55706i	0.711509	−	0.711509i	0.966851	+	0.255342i	$0.0821880\pi$
$62$	1.62274	+	2.91613i	0.206088	+	0.370349i
$63$		0			0
$64$	−7.96407	−	0.757328i	−0.995509	−	0.0946660i
$65$	−4.26502	−	1.70974i	−0.529011	−	0.212067i
$66$		0			0
$67$		−	1.73609i		−	0.212097i	−0.994361	−	0.106048i	$-0.966180\pi$
$67$		−	1.73609i		−	0.212097i	0.994361	−	0.106048i	$-0.0338198\pi$
$68$	11.2018	−	2.62515i	1.35842	−	0.318347i
$69$		0			0
$70$	−7.76500	+	10.0287i	−0.928095	+	1.19865i
$71$	−2.33526			−0.277144			−0.138572	−	0.990352i	$-0.544251\pi$
$71$	−2.33526			−0.277144			−0.138572	+	0.990352i	$0.544251\pi$
$72$		0			0
$73$	−4.39686	−	4.39686i	−0.514613	−	0.514613i	0.401323	−	0.915936i	$-0.368550\pi$
$73$	−4.39686	−	4.39686i	−0.514613	−	0.514613i	−0.915936	+	0.401323i	$0.868550\pi$
$74$	−3.12465	−	5.61511i	−0.363233	−	0.652744i
$75$		0			0
$76$	0.441090	+	1.88218i	0.0505964	+	0.215900i
$77$	−11.1134			−1.26649
$78$		0			0
$79$	14.0993			1.58629			0.793146	−	0.609032i	$-0.208442\pi$
$79$	14.0993			1.58629			0.793146	+	0.609032i	$0.208442\pi$
$80$	8.91628	−	0.707050i	0.996871	−	0.0790506i
$81$		0			0
$82$	−3.48822	−	6.26848i	−0.385210	−	0.692238i
$83$	2.75725			0.302648			0.151324	−	0.988484i	$-0.451646\pi$
$83$	2.75725			0.302648			0.151324	+	0.988484i	$0.451646\pi$
$84$		0			0
$85$	−11.8271	+	5.05819i	−1.28283	+	0.548638i
$86$	0.584347	+	1.05009i	0.0630117	+	0.113235i
$87$		0			0
$88$	5.27285	+	5.79805i	0.562088	+	0.618074i
$89$	−11.6448			−1.23435			−0.617173	−	0.786828i	$-0.711722\pi$
$89$	−11.6448			−1.23435			−0.617173	+	0.786828i	$0.711722\pi$
$90$		0			0
$91$	−5.82797	+	5.82797i	−0.610937	+	0.610937i
$92$	−3.19462	−	13.6318i	−0.333062	−	1.42121i
$93$		0			0
$94$	1.49437	−	5.24417i	0.154132	−	0.540894i
$95$	−0.849899	−	1.98724i	−0.0871978	−	0.203886i
$96$		0			0
$97$	−3.52933	−	3.52933i	−0.358349	−	0.358349i	0.504855	−	0.863204i	$-0.331546\pi$
$97$	−3.52933	−	3.52933i	−0.358349	−	0.358349i	−0.863204	+	0.504855i	$0.831546\pi$
$98$	6.24876	+	11.2293i	0.631220	+	1.13433i
$99$		0			0
$100$	−9.68147	+	2.50381i	−0.968147	+	0.250381i
$101$	−7.39467	−	7.39467i	−0.735797	−	0.735797i	0.235964	−	0.971762i	$-0.424175\pi$
$101$	−7.39467	−	7.39467i	−0.735797	−	0.735797i	−0.971762	+	0.235964i	$0.924175\pi$
$102$		0			0
$103$	3.72605	−	3.72605i	0.367139	−	0.367139i	−0.499294	−	0.866433i	$-0.666407\pi$
$103$	3.72605	−	3.72605i	0.367139	−	0.367139i	0.866433	+	0.499294i	$0.166407\pi$
$104$	5.80568	+	0.275419i	0.569294	+	0.0270070i
$105$		0			0
$106$	−6.39637	+	3.55939i	−0.621271	+	0.345719i
$107$	−16.4605			−1.59130			−0.795649	−	0.605758i	$-0.792870\pi$
$107$	−16.4605			−1.59130			−0.795649	+	0.605758i	$0.792870\pi$
$108$		0			0
$109$	−12.8554	−	12.8554i	−1.23133	−	1.23133i	−0.963455	−	0.267870i	$-0.913680\pi$
$109$	−12.8554	−	12.8554i	−1.23133	−	1.23133i	−0.267870	−	0.963455i	$-0.586320\pi$
$110$	−6.92815	−	5.36434i	−0.660573	−	0.511470i
$111$		0			0
$112$	5.12287	−	15.2035i	0.484065	−	1.43660i
$113$	−0.863630	+	0.863630i	−0.0812435	+	0.0812435i	−0.746561	−	0.665317i	$-0.768296\pi$
$113$	−0.863630	+	0.863630i	−0.0812435	+	0.0812435i	0.665317	+	0.746561i	$0.268296\pi$
$114$		0			0
$115$	6.15546	+	14.3927i	0.573999	+	1.34213i
$116$	−2.30065	+	0.539159i	−0.213610	+	0.0500596i
$117$		0			0
$118$	8.00779	+	2.28189i	0.737177	+	0.210065i
$119$			23.0730i			2.11510i
$120$		0			0
$121$			3.32246i			0.302042i
$122$	3.04582	−	10.6886i	0.275755	−	0.967703i
$123$		0			0
$124$	4.01066	+	2.48775i	0.360168	+	0.223406i
$125$	10.1764	−	4.63041i	0.910206	−	0.414156i
$126$		0			0
$127$	−11.7944	+	11.7944i	−1.04659	+	1.04659i	−0.0477265	+	0.998860i	$0.515198\pi$
$127$	−11.7944	+	11.7944i	−1.04659	+	1.04659i	−0.998860	+	0.0477265i	$0.984802\pi$
$128$	−10.3625	+	4.54075i	−0.915925	+	0.401349i
$129$		0			0
$130$	−6.44629	+	0.820077i	−0.565377	+	0.0719255i
$131$	15.9756	+	15.9756i	1.39579	+	1.39579i	0.811659	+	0.584132i	$0.198565\pi$
$131$	15.9756	+	15.9756i	1.39579	+	1.39579i	0.584132	+	0.811659i	$0.301435\pi$
$132$		0			0
$133$	−3.87683			−0.336163
$134$	−1.19385	−	2.14539i	−0.103133	−	0.185334i
$135$		0			0
$136$	12.0376	−	10.9472i	1.03221	−	0.938713i
$137$	−1.29423	+	1.29423i	−0.110573	+	0.110573i	−0.760229	−	0.649655i	$-0.774913\pi$
$137$	−1.29423	+	1.29423i	−0.110573	+	0.110573i	0.649655	+	0.760229i	$0.274913\pi$
$138$		0			0
$139$	8.61413	+	8.61413i	0.730641	+	0.730641i	0.970747	−	0.240106i	$-0.0771821\pi$
$139$	8.61413	+	8.61413i	0.730641	+	0.730641i	−0.240106	+	0.970747i	$0.577182\pi$
$140$	−2.69934	+	17.7328i	−0.228136	+	1.49869i
$141$		0			0
$142$	−2.88583	+	1.60588i	−0.242173	+	0.134762i
$143$	−4.02617	−	4.02617i	−0.336685	−	0.336685i
$144$		0			0
$145$	2.42906	−	1.03886i	0.201723	−	0.0862727i
$146$	−8.45705	−	2.40991i	−0.699911	−	0.199445i
$147$		0			0
$148$	−7.72265	−	4.79025i	−0.634798	−	0.393756i
$149$	−0.0806133	+	0.0806133i	−0.00660410	+	0.00660410i	−0.710401	−	0.703797i	$-0.751486\pi$
$149$	−0.0806133	+	0.0806133i	−0.00660410	+	0.00660410i	0.703797	+	0.710401i	$0.251486\pi$
$150$		0			0
$151$	−3.25198			−0.264643			−0.132321	−	0.991207i	$-0.542243\pi$
$151$	−3.25198			−0.264643			−0.132321	+	0.991207i	$0.542243\pi$
$152$	1.83939	+	2.02260i	0.149194	+	0.164055i
$153$		0			0
$154$	−13.7336	+	7.64232i	−1.10668	+	0.615836i
$155$	−4.89775	−	1.96338i	−0.393397	−	0.157703i
$156$		0			0
$157$	−9.06652			−0.723587			−0.361793	−	0.932258i	$-0.617835\pi$
$157$	−9.06652			−0.723587			−0.361793	+	0.932258i	$0.617835\pi$
$158$	17.4234	−	9.69559i	1.38613	−	0.771340i
$159$		0			0
$160$	10.5322	−	7.00518i	0.832644	−	0.553808i
$161$	28.0782			2.21287
$162$		0			0
$163$	3.93313			0.308067			0.154033	−	0.988066i	$-0.450774\pi$
$163$	3.93313			0.308067			0.154033	+	0.988066i	$0.450774\pi$
$164$	−8.62125	−	5.34763i	−0.673206	−	0.417580i
$165$		0			0
$166$	3.40731	−	1.89607i	0.264459	−	0.147164i
$167$	−8.13216	−	8.13216i	−0.629285	−	0.629285i	0.318603	−	0.947888i	$-0.396786\pi$
$167$	−8.13216	−	8.13216i	−0.629285	−	0.629285i	−0.947888	+	0.318603i	$0.896786\pi$
$168$		0			0
$169$	8.77728			0.675175
$170$	−11.1371	+	14.3838i	−0.854178	+	1.10319i
$171$		0			0
$172$	1.44423	+	0.895834i	0.110121	+	0.0683067i
$173$			6.86735i			0.522115i	0.965323	+	0.261057i	$0.0840712\pi$
$173$			6.86735i			0.522115i	−0.965323	+	0.261057i	$0.915929\pi$
$174$		0			0
$175$	−0.458751	−	20.0490i	−0.0346784	−	1.51556i
$176$	10.5031	+	3.53906i	0.791703	+	0.266767i
$177$		0			0
$178$	−14.3902	+	8.00774i	−1.07859	+	0.600205i
$179$	15.7117	−	15.7117i	1.17435	−	1.17435i	0.193183	−	0.981163i	$-0.438119\pi$
$179$	15.7117	−	15.7117i	1.17435	−	1.17435i	0.981163	−	0.193183i	$-0.0618811\pi$
$180$		0			0
$181$	−13.9112	−	13.9112i	−1.03401	−	1.03401i	−0.999401	−	0.0346142i	$-0.988980\pi$
$181$	−13.9112	−	13.9112i	−1.03401	−	1.03401i	−0.0346142	−	0.999401i	$-0.511020\pi$
$182$	−3.19430	+	11.2097i	−0.236777	+	0.830919i
$183$		0			0
$184$	−13.3219	−	14.6489i	−0.982106	−	1.07993i
$185$	9.43078	+	3.78056i	0.693365	+	0.277953i
$186$		0			0
$187$	−15.9397			−1.16562
$188$	−1.75955	−	7.50818i	−0.128328	−	0.547591i
$189$		0			0
$190$	−2.41683	−	1.87131i	−0.175335	−	0.135759i
$191$		−	10.3393i		−	0.748123i	−0.927404	−	0.374061i	$-0.877965\pi$
$191$		−	10.3393i		−	0.748123i	0.927404	−	0.374061i	$-0.122035\pi$
$192$		0			0
$193$	13.2080	−	13.2080i	0.950734	−	0.950734i	−0.0481079	−	0.998842i	$-0.515319\pi$
$193$	13.2080	−	13.2080i	0.950734	−	0.950734i	0.998842	+	0.0481079i	$0.0153191\pi$
$194$	−6.78843	−	1.93442i	−0.487381	−	0.138883i
$195$		0			0
$196$	15.4440	+	9.57968i	1.10314	+	0.684263i
$197$		−	15.2437i		−	1.08607i	−0.839709	−	0.543036i	$-0.817275\pi$
$197$		−	15.2437i		−	1.08607i	0.839709	−	0.543036i	$-0.182725\pi$
$198$		0			0
$199$			4.98761i			0.353562i	0.984250	+	0.176781i	$0.0565684\pi$
$199$			4.98761i			0.353562i	−0.984250	+	0.176781i	$0.943432\pi$
$200$	−10.2422	+	9.75175i	−0.724235	+	0.689553i
$201$		0			0
$202$	−14.2231	−	4.05300i	−1.00074	−	0.285168i
$203$		−	4.73878i		−	0.332597i
$204$		0			0
$205$	10.5281	+	4.22046i	0.735316	+	0.294770i
$206$	2.04224	−	7.16680i	0.142290	−	0.499335i
$207$		0			0
$208$	7.36385	−	3.65202i	0.510591	−	0.253222i
$209$		−	2.67825i		−	0.185258i
$210$		0			0
$211$	10.3803	+	10.3803i	0.714608	+	0.714608i	0.967496	−	0.252887i	$-0.0813802\pi$
$211$	10.3803	+	10.3803i	0.714608	+	0.714608i	−0.252887	+	0.967496i	$0.581380\pi$
$212$	−5.45674	+	8.79715i	−0.374770	+	0.604191i
$213$		0			0
$214$	−20.3413	+	11.3193i	−1.39050	+	0.773774i
$215$	−1.76367	−	0.707011i	−0.120281	−	0.0482178i
$216$		0			0
$217$	−6.69257	+	6.69257i	−0.454321	+	0.454321i
$218$	−24.7265	−	7.04603i	−1.67469	−	0.477217i
$219$		0			0
$220$	−12.2504	−	1.86480i	−0.825925	−	0.125725i
$221$	−8.35890	+	8.35890i	−0.562280	+	0.562280i
$222$		0			0
$223$	1.49853	+	1.49853i	0.100349	+	0.100349i	0.755499	−	0.655150i	$-0.227395\pi$
$223$	1.49853	+	1.49853i	0.100349	+	0.100349i	−0.655150	+	0.755499i	$0.727395\pi$
$224$	−4.12429	−	22.3108i	−0.275566	−	1.49070i
$225$		0			0
$226$	−0.473354	+	1.66113i	−0.0314870	+	0.110497i
$227$			15.6346i			1.03771i	0.854864	+	0.518853i	$0.173641\pi$
$227$			15.6346i			1.03771i	−0.854864	+	0.518853i	$0.826359\pi$
$228$		0			0
$229$	9.74097	−	9.74097i	0.643702	−	0.643702i	−0.307762	−	0.951463i	$-0.599580\pi$
$229$	9.74097	−	9.74097i	0.643702	−	0.643702i	0.951463	+	0.307762i	$0.0995800\pi$
$230$	17.5041	+	13.5531i	1.15418	+	0.893663i
$231$		0			0
$232$	−2.47230	+	2.24835i	−0.162314	+	0.147612i
$233$	0.509123	+	0.509123i	0.0333538	+	0.0333538i	0.723587	−	0.690233i	$-0.242492\pi$
$233$	0.509123	+	0.509123i	0.0333538	+	0.0333538i	−0.690233	+	0.723587i	$0.742492\pi$
$234$		0			0
$235$	3.39033	+	7.92727i	0.221161	+	0.517118i
$236$	11.4649	−	2.68681i	0.746303	−	0.174897i
$237$		0			0
$238$	15.8665	+	28.5128i	1.02847	+	1.84821i
$239$	8.19486			0.530081			0.265041	−	0.964237i	$-0.414615\pi$
$239$	8.19486			0.530081			0.265041	+	0.964237i	$0.414615\pi$
$240$		0			0
$241$	5.66775			0.365092			0.182546	−	0.983197i	$-0.441566\pi$
$241$	5.66775			0.365092			0.182546	+	0.983197i	$0.441566\pi$
$242$	2.28474	+	4.10578i	0.146869	+	0.263929i
$243$		0			0
$244$	−3.58630	−	15.3031i	−0.229590	−	0.979683i
$245$	−18.8600	−	7.56048i	−1.20492	−	0.483022i
$246$		0			0
$247$	−1.40450	−	1.40450i	−0.0893661	−	0.0893661i
$248$	6.66697	+	0.316278i	0.423353	+	0.0200837i
$249$		0			0
$250$	9.39147	−	12.7201i	0.593969	−	0.804488i
$251$	−14.7484	+	14.7484i	−0.930911	+	0.930911i	−0.997763	−	0.0668521i	$-0.978704\pi$
$251$	−14.7484	+	14.7484i	−0.930911	+	0.930911i	0.0668521	+	0.997763i	$0.478704\pi$
$252$		0			0
$253$			19.3974i			1.21951i
$254$	−6.46451	+	22.6858i	−0.405619	+	1.42343i
$255$		0			0
$256$	−9.68310	+	12.7373i	−0.605194	+	0.796078i
$257$	−3.61143	−	3.61143i	−0.225275	−	0.225275i	0.585440	−	0.810715i	$-0.300922\pi$
$257$	−3.61143	−	3.61143i	−0.225275	−	0.225275i	−0.810715	+	0.585440i	$0.800922\pi$
$258$		0			0
$259$	12.8868	−	12.8868i	0.800745	−	0.800745i
$260$	−7.40216	+	5.44632i	−0.459063	+	0.337767i
$261$		0			0
$262$	30.7279	+	8.75617i	1.89838	+	0.540958i
$263$	6.80041	−	6.80041i	0.419331	−	0.419331i	−0.465642	−	0.884973i	$-0.654177\pi$
$263$	6.80041	−	6.80041i	0.419331	−	0.419331i	0.884973	+	0.465642i	$0.154177\pi$
$264$		0			0
$265$	4.30657	−	10.7429i	0.264551	−	0.659933i
$266$	−4.79084	+	2.66596i	−0.293746	+	0.163461i
$267$		0			0
$268$	−2.95063	−	1.83023i	−0.180238	−	0.111799i
$269$	−1.20010	−	1.20010i	−0.0731711	−	0.0731711i	0.669574	−	0.742745i	$-0.266477\pi$
$269$	−1.20010	−	1.20010i	−0.0731711	−	0.0731711i	−0.742745	+	0.669574i	$0.766477\pi$
$270$		0			0
$271$			2.79591i			0.169840i	0.996388	+	0.0849199i	$0.0270634\pi$
$271$			2.79591i			0.169840i	−0.996388	+	0.0849199i	$0.972937\pi$
$272$	7.34759	−	21.8060i	0.445513	−	1.32218i
$273$		0			0
$274$	−0.709364	+	2.48936i	−0.0428543	+	0.150388i
$275$	13.8506	−	0.316922i	0.835220	−	0.0191111i
$276$		0			0
$277$			13.8115i			0.829852i	0.909855	+	0.414926i	$0.136193\pi$
$277$			13.8115i			0.829852i	−0.909855	+	0.414926i	$0.863807\pi$
$278$	16.5687	+	4.72139i	0.993724	+	0.283170i
$279$		0			0
$280$	8.85849	+	23.7698i	0.529396	+	1.42052i
$281$			7.21718i			0.430541i	0.976554	+	0.215270i	$0.0690633\pi$
$281$			7.21718i			0.430541i	−0.976554	+	0.215270i	$0.930937\pi$
$282$		0			0
$283$		−	25.2988i		−	1.50386i	−0.659243	−	0.751930i	$-0.729123\pi$
$283$		−	25.2988i		−	1.50386i	0.659243	−	0.751930i	$-0.270877\pi$
$284$	−2.46190	+	3.96898i	−0.146087	+	0.235515i
$285$		0			0
$286$	−7.74407	−	2.20674i	−0.457916	−	0.130487i
$287$	14.3862	−	14.3862i	0.849193	−	0.849193i
$288$		0			0
$289$			16.0930i			0.946644i
$290$	2.28736	−	2.95417i	0.134319	−	0.173475i
$291$		0			0
$292$	−12.1081	+	2.83755i	−0.708575	+	0.166055i
$293$	14.1276			0.825344			0.412672	−	0.910880i	$-0.364596\pi$
$293$	14.1276			0.825344			0.412672	+	0.910880i	$0.364596\pi$
$294$		0			0
$295$	−12.1049	+	5.17700i	−0.704773	+	0.301417i
$296$	−12.8375	−	0.609004i	−0.746163	−	0.0353976i
$297$		0			0
$298$	−0.0441840	+	0.155054i	−0.00255951	+	0.00898204i
$299$	10.1722	+	10.1722i	0.588272	+	0.588272i
$300$		0			0
$301$	−2.40998	+	2.40998i	−0.138909	+	0.138909i
$302$	−4.01869	+	2.23628i	−0.231249	+	0.128683i
$303$		0			0
$304$	3.66393	+	1.23457i	0.210141	+	0.0708076i
$305$	6.91016	+	16.1573i	0.395674	+	0.925166i
$306$		0			0
$307$		−	22.6081i		−	1.29031i	−0.764051	−	0.645156i	$-0.776792\pi$
$307$		−	22.6081i		−	1.29031i	0.764051	−	0.645156i	$-0.223208\pi$
$308$	−11.7161	+	18.8882i	−0.667586	+	1.07626i
$309$		0			0
$310$	−7.40262	+	0.941738i	−0.420440	+	0.0534871i
$311$	10.7903			0.611859			0.305929	−	0.952054i	$-0.401033\pi$
$311$	10.7903			0.611859			0.305929	+	0.952054i	$0.401033\pi$
$312$		0			0
$313$	−20.6842	−	20.6842i	−1.16914	−	1.16914i	−0.982412	−	0.186727i	$-0.940212\pi$
$313$	−20.6842	−	20.6842i	−1.16914	−	1.16914i	−0.186727	−	0.982412i	$-0.559788\pi$
$314$	−11.2041	+	6.23474i	−0.632283	+	0.351847i
$315$		0			0
$316$	14.8639	−	23.9629i	0.836157	−	1.34802i
$317$	−23.8207			−1.33791			−0.668953	−	0.743305i	$-0.733257\pi$
$317$	−23.8207			−1.33791			−0.668953	+	0.743305i	$0.733257\pi$
$318$		0			0
$319$	3.27372			0.183293
$320$	8.19811	−	15.8994i	0.458288	−	0.888804i
$321$		0			0
$322$	34.6980	−	19.3084i	1.93365	−	1.07602i
$323$	−5.56042			−0.309390
$324$		0			0
$325$	7.09716	−	7.42956i	0.393680	−	0.412118i
$326$	4.86043	−	2.70469i	0.269194	−	0.149799i
$327$		0			0
$328$	−14.3312	−	0.679866i	−0.791309	−	0.0375393i
$329$	15.4650			0.852615
$330$		0			0
$331$	−19.7688	+	19.7688i	−1.08659	+	1.08659i	−0.0907155	+	0.995877i	$0.528915\pi$
$331$	−19.7688	+	19.7688i	−1.08659	+	1.08659i	−0.995877	+	0.0907155i	$0.971085\pi$
$332$	2.90677	−	4.68619i	0.159530	−	0.257188i
$333$		0			0
$334$	−15.6417	−	4.45722i	−0.855873	−	0.243888i
$335$	3.60326	+	1.44446i	0.196867	+	0.0789191i
$336$		0			0
$337$	7.26955	+	7.26955i	0.395998	+	0.395998i	0.876819	−	0.480821i	$-0.159661\pi$
$337$	7.26955	+	7.26955i	0.395998	+	0.395998i	−0.480821	+	0.876819i	$0.659661\pi$
$338$	10.8467	−	6.03584i	0.589980	−	0.328307i
$339$		0			0
$340$	−3.87159	+	25.4336i	−0.209967	+	1.37933i
$341$	−4.62347	−	4.62347i	−0.250375	−	0.250375i
$342$		0			0
$343$	−5.91866	+	5.91866i	−0.319578	+	0.319578i
$344$	2.40076	+	0.113891i	0.129440	+	0.00614059i
$345$		0			0
$346$	4.72245	+	8.48642i	0.253880	+	0.456233i
$347$	23.4667			1.25976			0.629880	−	0.776692i	$-0.283104\pi$
$347$	23.4667			1.25976			0.629880	+	0.776692i	$0.283104\pi$
$348$		0			0
$349$	23.2089	+	23.2089i	1.24234	+	1.24234i	0.959027	+	0.283315i	$0.0914342\pi$
$349$	23.2089	+	23.2089i	1.24234	+	1.24234i	0.283315	+	0.959027i	$0.408566\pi$
$350$	−14.3539	−	24.4604i	−0.767250	−	1.30746i
$351$		0			0
$352$	15.4131	−	2.84921i	0.821521	−	0.151863i
$353$	13.3220	−	13.3220i	0.709059	−	0.709059i	−0.257278	−	0.966337i	$-0.582826\pi$
$353$	13.3220	−	13.3220i	0.709059	−	0.709059i	0.966337	+	0.257278i	$0.0828256\pi$
$354$		0			0
$355$	1.94298	−	4.84685i	0.103123	−	0.257244i
$356$	−12.2763	+	19.7914i	−0.650642	+	1.04894i
$357$		0			0
$358$	8.61154	−	30.2203i	0.455134	−	1.59719i
$359$		−	26.9902i		−	1.42449i	−0.701932	−	0.712244i	$-0.747679\pi$
$359$		−	26.9902i		−	1.42449i	0.701932	−	0.712244i	$-0.252321\pi$
$360$		0			0
$361$			18.0657i			0.950827i
$362$	−26.7573	−	7.62473i	−1.40633	−	0.400747i
$363$		0			0
$364$	3.76114	+	16.0492i	0.197137	+	0.841205i
$365$	12.7840	−	5.46745i	0.669145	−	0.286179i
$366$		0			0
$367$	19.4758	−	19.4758i	1.01663	−	1.01663i	0.0167684	−	0.999859i	$-0.494662\pi$
$367$	19.4758	−	19.4758i	1.01663	−	1.01663i	0.999859	−	0.0167684i	$-0.00533781\pi$
$368$	−26.5363	−	8.94148i	−1.38330	−	0.466107i
$369$		0			0
$370$	14.2540	−	1.81335i	0.741030	−	0.0942715i
$371$	−14.6798	−	14.6798i	−0.762136	−	0.762136i
$372$		0			0
$373$	4.87069			0.252195			0.126097	−	0.992018i	$-0.459755\pi$
$373$	4.87069			0.252195			0.126097	+	0.992018i	$0.459755\pi$
$374$	−19.6977	+	10.9612i	−1.01854	+	0.566789i
$375$		0			0
$376$	−7.33752	−	8.06836i	−0.378404	−	0.416094i
$377$	1.71677	−	1.71677i	0.0884180	−	0.0884180i
$378$		0			0
$379$	−2.54450	−	2.54450i	−0.130702	−	0.130702i	0.638729	−	0.769432i	$-0.279460\pi$
$379$	−2.54450	−	2.54450i	−0.130702	−	0.130702i	−0.769432	+	0.638729i	$0.779460\pi$
$380$	−4.27347	−	0.650522i	−0.219224	−	0.0333711i
$381$		0			0
$382$	−7.10996	−	12.7769i	−0.363777	−	0.653723i
$383$	0.193238	+	0.193238i	0.00987399	+	0.00987399i	0.712027	−	0.702153i	$-0.247778\pi$
$383$	0.193238	+	0.193238i	0.00987399	+	0.00987399i	−0.702153	+	0.712027i	$0.747778\pi$
$384$		0			0
$385$	9.24658	−	23.0660i	0.471249	−	1.17555i
$386$	7.23929	−	25.4047i	0.368470	−	1.29307i
$387$		0			0
$388$	−9.71914	+	2.27769i	−0.493414	+	0.115632i
$389$	2.01528	−	2.01528i	0.102179	−	0.102179i	−0.654169	−	0.756348i	$-0.726982\pi$
$389$	2.01528	−	2.01528i	0.102179	−	0.102179i	0.756348	+	0.654169i	$0.226982\pi$
$390$		0			0
$391$	40.2718			2.03663
$392$	25.6728	+	1.21790i	1.29667	+	0.0615134i
$393$		0			0
$394$	−10.4826	−	18.8377i	−0.528107	−	0.949029i
$395$	−11.7309	+	29.2632i	−0.590244	+	1.47239i
$396$		0			0
$397$	−21.5509			−1.08161			−0.540804	−	0.841149i	$-0.681880\pi$
$397$	−21.5509			−1.08161			−0.540804	+	0.841149i	$0.681880\pi$
$398$	3.42981	+	6.16351i	0.171921	+	0.308949i
$399$		0			0
$400$	−5.95103	+	19.0941i	−0.297552	+	0.954706i
$401$	10.3965			0.519176			0.259588	−	0.965719i	$-0.416413\pi$
$401$	10.3965			0.519176			0.259588	+	0.965719i	$0.416413\pi$
$402$		0			0
$403$	−4.84917			−0.241555
$404$	−20.3636	+	4.77222i	−1.01313	+	0.237427i
$405$		0			0
$406$	−3.25870	−	5.85601i	−0.161726	−	0.290629i
$407$	8.90264	+	8.90264i	0.441288	+	0.441288i
$408$		0			0
$409$	0.330732			0.0163536			0.00817682	−	0.999967i	$-0.497397\pi$
$409$	0.330732			0.0163536			0.00817682	+	0.999967i	$0.497397\pi$
$410$	15.9126	−	2.02435i	0.785865	−	0.0999753i
$411$		0			0
$412$	−2.40464	−	10.2609i	−0.118468	−	0.505516i
$413$			23.6150i			1.16202i
$414$		0			0
$415$	−2.29409	+	5.72270i	−0.112612	+	0.280917i
$416$	6.58861	−	9.57691i	0.323033	−	0.469547i
$417$		0			0
$418$	−1.84174	−	3.30969i	−0.0900826	−	0.161882i
$419$	−6.71354	+	6.71354i	−0.327978	+	0.327978i	−0.851817	−	0.523839i	$-0.824499\pi$
$419$	−6.71354	+	6.71354i	−0.327978	+	0.327978i	0.523839	+	0.851817i	$0.324499\pi$
$420$		0			0
$421$	2.99831	+	2.99831i	0.146129	+	0.146129i	0.776386	−	0.630258i	$-0.217051\pi$
$421$	2.99831	+	2.99831i	0.146129	+	0.146129i	−0.630258	+	0.776386i	$0.717051\pi$
$422$	19.9658	+	5.68941i	0.971918	+	0.276956i
$423$		0			0
$424$	−0.693737	+	14.6236i	−0.0336909	+	0.710186i
$425$	−0.657974	−	28.7557i	−0.0319164	−	1.39486i
$426$		0			0
$427$	31.5208			1.52540
$428$	−17.3531	+	27.9761i	−0.838796	+	1.35228i
$429$		0			0
$430$	−2.66567	+	0.339118i	−0.128550	+	0.0163537i
$431$		−	19.9548i		−	0.961191i	−0.876942	−	0.480596i	$-0.840420\pi$
$431$		−	19.9548i		−	0.961191i	0.876942	−	0.480596i	$-0.159580\pi$
$432$		0			0
$433$	−16.1910	+	16.1910i	−0.778092	+	0.778092i	−0.979506	−	0.201414i	$-0.935446\pi$
$433$	−16.1910	+	16.1910i	−0.778092	+	0.778092i	0.201414	+	0.979506i	$0.435446\pi$
$434$	−3.66818	+	12.8727i	−0.176078	+	0.617909i
$435$		0			0
$436$	−35.4015	+	8.29636i	−1.69542	+	0.397324i
$437$			6.76664i			0.323692i
$438$		0			0
$439$			29.3734i			1.40191i	0.713204	+	0.700957i	$0.247243\pi$
$439$			29.3734i			1.40191i	−0.713204	+	0.700957i	$0.752757\pi$
$440$	−16.4210	+	6.11977i	−0.782842	+	0.291748i
$441$		0			0
$442$	−4.58150	+	16.0778i	−0.217920	+	0.764741i
$443$		−	19.8713i		−	0.944115i	−0.881568	−	0.472057i	$-0.843511\pi$
$443$		−	19.8713i		−	0.944115i	0.881568	−	0.472057i	$-0.156489\pi$
$444$		0			0
$445$	9.68870	−	24.1689i	0.459288	−	1.14572i
$446$	2.88232	+	0.821341i	0.136482	+	0.0388916i
$447$		0			0
$448$	−20.4390	−	24.7347i	−0.965654	−	1.16861i
$449$			16.7577i			0.790844i	0.918500	+	0.395422i	$0.129402\pi$
$449$			16.7577i			0.790844i	−0.918500	+	0.395422i	$0.870598\pi$
$450$		0			0
$451$	9.93854	+	9.93854i	0.467987	+	0.467987i
$452$	0.557352	+	2.37828i	0.0262156	+	0.111865i
$453$		0			0
$454$	10.7514	+	19.3207i	0.504588	+	0.906766i
$455$	−7.24703	−	16.9450i	−0.339746	−	0.794394i
$456$		0			0
$457$	5.00267	−	5.00267i	0.234015	−	0.234015i	−0.580351	−	0.814366i	$-0.697085\pi$
$457$	5.00267	−	5.00267i	0.234015	−	0.234015i	0.814366	+	0.580351i	$0.197085\pi$
$458$	5.33901	−	18.7361i	0.249475	−	0.875480i
$459$		0			0
$460$	30.9509	+	4.71145i	1.44309	+	0.219672i
$461$	−2.71518	+	2.71518i	−0.126459	+	0.126459i	−0.767503	−	0.641045i	$-0.778501\pi$
$461$	−2.71518	+	2.71518i	−0.126459	+	0.126459i	0.641045	+	0.767503i	$0.278501\pi$
$462$		0			0
$463$	−9.18551	−	9.18551i	−0.426887	−	0.426887i	0.460680	−	0.887566i	$-0.347606\pi$
$463$	−9.18551	−	9.18551i	−0.426887	−	0.426887i	−0.887566	+	0.460680i	$0.847606\pi$
$464$	−1.50906	+	4.47855i	−0.0700564	+	0.207912i
$465$		0			0
$466$	0.979263	+	0.279049i	0.0453635	+	0.0129267i
$467$			1.06405i			0.0492385i	0.999697	+	0.0246193i	$0.00783735\pi$
$467$			1.06405i			0.0492385i	−0.999697	+	0.0246193i	$0.992163\pi$
$468$		0			0
$469$	4.92371	−	4.92371i	0.227356	−	0.227356i
$470$	9.64097	+	7.46483i	0.444705	+	0.344327i
$471$		0			0
$472$	12.3203	−	11.2043i	0.567088	−	0.515720i
$473$	−1.66490	−	1.66490i	−0.0765523	−	0.0765523i
$474$		0			0
$475$	4.83166	−	0.110556i	0.221692	−	0.00507265i
$476$	39.2146	+	24.3242i	1.79740	+	1.11490i
$477$		0			0
$478$	10.1269	−	5.63533i	0.463194	−	0.257754i
$479$	15.8658			0.724926			0.362463	−	0.931998i	$-0.381936\pi$
$479$	15.8658			0.724926			0.362463	+	0.931998i	$0.381936\pi$
$480$		0			0
$481$	9.33725			0.425742
$482$	7.00400	−	3.89752i	0.319024	−	0.177527i
$483$		0			0
$484$	5.64681	+	3.50263i	0.256673	+	0.159210i
$485$	10.2616	−	4.38869i	0.465957	−	0.199280i
$486$		0			0
$487$	−13.7947	−	13.7947i	−0.625099	−	0.625099i	0.321732	−	0.946831i	$-0.395735\pi$
$487$	−13.7947	−	13.7947i	−0.625099	−	0.625099i	−0.946831	+	0.321732i	$0.895735\pi$
$488$	−14.9553	−	16.4449i	−0.676994	−	0.744426i
$489$		0			0
$490$	−28.5056	+	3.62639i	−1.28775	+	0.163824i
$491$	−19.4471	+	19.4471i	−0.877637	+	0.877637i	−0.993290	−	0.115652i	$-0.963104\pi$
$491$	−19.4471	+	19.4471i	−0.877637	+	0.877637i	0.115652	+	0.993290i	$0.463104\pi$
$492$		0			0
$493$		−	6.79669i		−	0.306108i
$494$	−2.70146	−	0.769803i	−0.121544	−	0.0346351i
$495$		0			0
$496$	8.45630	−	4.19381i	0.379699	−	0.188308i
$497$	−6.62302	−	6.62302i	−0.297083	−	0.297083i
$498$		0			0
$499$	−23.0141	+	23.0141i	−1.03025	+	1.03025i	−0.0307258	+	0.999528i	$0.509782\pi$
$499$	−23.0141	+	23.0141i	−1.03025	+	1.03025i	−0.999528	+	0.0307258i	$0.990218\pi$
$500$	2.85848	−	22.1772i	0.127835	−	0.991795i
$501$		0			0
$502$	−8.08357	+	28.3675i	−0.360787	+	1.26611i
$503$	−6.63364	+	6.63364i	−0.295780	+	0.295780i	−0.839358	−	0.543579i	$-0.817069\pi$
$503$	−6.63364	+	6.63364i	−0.295780	+	0.295780i	0.543579	+	0.839358i	$0.317069\pi$
$504$		0			0
$505$	21.5002	−	9.19520i	0.956748	−	0.409181i
$506$	13.3390	+	23.9706i	0.592989	+	1.06562i
$507$		0			0
$508$	7.61165	+	32.4797i	0.337712	+	1.44105i
$509$	8.04140	+	8.04140i	0.356429	+	0.356429i	0.862495	−	0.506066i	$-0.168901\pi$
$509$	8.04140	+	8.04140i	0.356429	+	0.356429i	−0.506066	+	0.862495i	$0.668901\pi$
$510$		0			0
$511$		−	24.9398i		−	1.10327i
$512$	−3.20705	+	22.3990i	−0.141733	+	0.989905i
$513$		0			0
$514$	−6.94634	−	1.97942i	−0.306390	−	0.0873084i
$515$	4.63331	+	10.8336i	0.204168	+	0.477386i
$516$		0			0
$517$			10.6838i			0.469873i
$518$	7.06321	−	24.7868i	0.310340	−	1.08907i
$519$		0			0
$520$	−5.40208	+	11.8206i	−0.236897	+	0.518367i
$521$			32.8549i			1.43940i	0.694285	+	0.719700i	$0.255721\pi$
$521$			32.8549i			1.43940i	−0.694285	+	0.719700i	$0.744279\pi$
$522$		0			0
$523$			2.46341i			0.107717i	0.998549	+	0.0538587i	$0.0171521\pi$
$523$			2.46341i			0.107717i	−0.998549	+	0.0538587i	$0.982848\pi$
$524$	43.9938	−	10.3100i	1.92188	−	0.450393i
$525$		0			0
$526$	3.72729	−	13.0801i	0.162518	−	0.570321i
$527$	−9.59896	+	9.59896i	−0.418137	+	0.418137i
$528$		0			0
$529$		−	26.0078i		−	1.13078i
$530$	−2.06565	−	16.2372i	−0.0897261	−	0.705300i
$531$		0			0
$532$	−4.08706	+	6.58901i	−0.177197	+	0.285670i
$533$	10.4237			0.451501
$534$		0			0
$535$	13.6955	−	34.1640i	0.592107	−	1.47704i
$536$	−4.90487	−	0.232685i	−0.211858	−	0.0100505i
$537$		0			0
$538$	−2.30830	−	0.657770i	−0.0995180	−	0.0283585i
$539$	−17.8038	−	17.8038i	−0.766863	−	0.766863i
$540$		0			0
$541$	−18.0772	+	18.0772i	−0.777198	+	0.777198i	−0.979353	−	0.202156i	$-0.935205\pi$
$541$	−18.0772	+	18.0772i	−0.777198	+	0.777198i	0.202156	+	0.979353i	$0.435205\pi$
$542$	1.92266	+	3.45509i	0.0825852	+	0.148409i
$543$		0			0
$544$	−5.91535	−	31.9997i	−0.253619	−	1.37198i
$545$	37.3775	−	15.9856i	1.60108	−	0.684747i
$546$		0			0
$547$			43.6742i			1.86738i	0.358089	+	0.933688i	$0.383428\pi$
$547$			43.6742i			1.86738i	−0.358089	+	0.933688i	$0.616572\pi$
$548$	0.835243	+	3.56407i	0.0356798	+	0.152250i
$549$		0			0
$550$	16.8981	−	9.91621i	0.720537	−	0.422829i
$551$	1.14201			0.0486513
$552$		0			0
$553$	39.9869	+	39.9869i	1.70042	+	1.70042i
$554$	9.49770	+	17.0677i	0.403519	+	0.725139i
$555$		0			0
$556$	23.7217	−	5.55921i	1.00603	−	0.235763i
$557$	5.18948			0.219885			0.109943	−	0.993938i	$-0.464933\pi$
$557$	5.18948			0.219885			0.109943	+	0.993938i	$0.464933\pi$
$558$		0			0
$559$	−1.74618			−0.0738555
$560$	27.2927	+	23.2822i	1.15333	+	0.983852i
$561$		0			0
$562$	4.96301	+	8.91874i	0.209352	+	0.376214i
$563$	−11.3756			−0.479423			−0.239711	−	0.970844i	$-0.577053\pi$
$563$	−11.3756			−0.479423			−0.239711	+	0.970844i	$0.577053\pi$
$564$		0			0
$565$	−1.07392	−	2.51103i	−0.0451800	−	0.105640i
$566$	−17.3972	−	31.2634i	−0.731257	−	1.31410i
$567$		0			0
$568$	−0.312991	+	6.59768i	−0.0131328	+	0.276833i
$569$	−7.51787			−0.315165			−0.157583	−	0.987506i	$-0.550370\pi$
$569$	−7.51787			−0.315165			−0.157583	+	0.987506i	$0.550370\pi$
$570$		0			0
$571$	−7.76889	+	7.76889i	−0.325118	+	0.325118i	−0.850726	−	0.525609i	$-0.823838\pi$
$571$	−7.76889	+	7.76889i	−0.325118	+	0.325118i	0.525609	+	0.850726i	$0.323838\pi$
$572$	−11.0873	+	2.59833i	−0.463585	+	0.108642i
$573$		0			0
$574$	7.88507	−	27.6710i	0.329117	−	1.15496i
$575$	−34.9936	+	0.800708i	−1.45934	+	0.0333918i
$576$		0			0
$577$	−9.84819	−	9.84819i	−0.409986	−	0.409986i	0.471748	−	0.881733i	$-0.343623\pi$
$577$	−9.84819	−	9.84819i	−0.409986	−	0.409986i	−0.881733	+	0.471748i	$0.843623\pi$
$578$	11.0666	+	19.8871i	0.460309	+	0.827195i
$579$		0			0
$580$	0.795155	−	5.22361i	0.0330170	−	0.216899i
$581$	7.81984	+	7.81984i	0.324421	+	0.324421i
$582$		0			0
$583$	10.1413	−	10.1413i	0.420010	−	0.420010i
$584$	−13.0115	+	11.8329i	−0.538421	+	0.489650i
$585$		0			0
$586$	17.4584	−	9.71509i	0.721200	−	0.401327i
$587$	33.0447			1.36390			0.681951	−	0.731398i	$-0.261132\pi$
$587$	33.0447			1.36390			0.681951	+	0.731398i	$0.261132\pi$
$588$		0			0
$589$	−1.61286	−	1.61286i	−0.0664567	−	0.0664567i
$590$	−11.3987	+	14.7217i	−0.469278	+	0.606082i
$591$		0			0
$592$	−16.2829	+	8.07532i	−0.669223	+	0.331894i
$593$	−18.5424	+	18.5424i	−0.761445	+	0.761445i	−0.976584	−	0.215139i	$-0.930980\pi$
$593$	−18.5424	+	18.5424i	−0.761445	+	0.761445i	0.215139	+	0.976584i	$0.430980\pi$
$594$		0			0
$595$	−47.8882	−	19.1972i	−1.96323	−	0.787008i
$596$	0.0520245	+	0.221994i	0.00213101	+	0.00909324i
$597$		0			0
$598$	19.5655	+	5.57535i	0.800092	+	0.227993i
$599$			28.3117i			1.15678i	0.815759	+	0.578392i	$0.196319\pi$
$599$			28.3117i			1.15678i	−0.815759	+	0.578392i	$0.803681\pi$
$600$		0			0
$601$			41.7630i			1.70355i	0.523909	+	0.851774i	$0.324473\pi$
$601$			41.7630i			1.70355i	−0.523909	+	0.851774i	$0.675527\pi$
$602$	−1.32091	+	4.63543i	−0.0538361	+	0.188926i
$603$		0			0
$604$	−3.42833	+	5.52703i	−0.139497	+	0.224892i
$605$	−6.89579	−	2.76435i	−0.280354	−	0.112387i
$606$		0			0
$607$	−4.01973	+	4.01973i	−0.163156	+	0.163156i	−0.783963	−	0.620807i	$-0.786805\pi$
$607$	−4.01973	+	4.01973i	−0.163156	+	0.163156i	0.620807	+	0.783963i	$0.286805\pi$
$608$	5.37674	−	0.993923i	0.218055	−	0.0403089i
$609$		0			0
$610$	19.6502	+	15.2148i	0.795613	+	0.616028i
$611$	5.60268	+	5.60268i	0.226660	+	0.226660i
$612$		0			0
$613$	21.5230			0.869305			0.434652	−	0.900598i	$-0.356871\pi$
$613$	21.5230			0.869305			0.434652	+	0.900598i	$0.356871\pi$
$614$	−15.5468	−	27.9383i	−0.627419	−	1.12750i
$615$		0			0
$616$	−1.48951	+	31.3982i	−0.0600142	+	1.26507i
$617$	−26.4655	+	26.4655i	−1.06546	+	1.06546i	−0.0677580	+	0.997702i	$0.521585\pi$
$617$	−26.4655	+	26.4655i	−1.06546	+	1.06546i	−0.997702	+	0.0677580i	$0.978415\pi$
$618$		0			0
$619$	−21.7935	−	21.7935i	−0.875955	−	0.875955i	0.117158	−	0.993113i	$-0.462622\pi$
$619$	−21.7935	−	21.7935i	−0.875955	−	0.875955i	−0.993113	+	0.117158i	$0.962622\pi$
$620$	−8.50029	+	6.25430i	−0.341380	+	0.251179i
$621$		0			0
$622$	13.3342	−	7.42010i	0.534653	−	0.297519i
$623$	−33.0258	−	33.0258i	−1.32315	−	1.32315i
$624$		0			0
$625$	1.14348	+	24.9738i	0.0457391	+	0.998953i
$626$	−39.7846	−	11.3370i	−1.59011	−	0.453116i
$627$		0			0
$628$	−9.55818	+	15.4093i	−0.381413	+	0.614900i
$629$	18.4831	−	18.4831i	0.736971	−	0.736971i
$630$		0			0
$631$	−42.7412			−1.70150			−0.850751	−	0.525570i	$-0.823852\pi$
$631$	−42.7412			−1.70150			−0.850751	+	0.525570i	$0.823852\pi$
$632$	1.88970	−	39.8339i	0.0751683	−	1.58451i
$633$		0			0
$634$	−29.4368	+	16.3807i	−1.16909	+	0.650562i
$635$	−14.6663	−	34.2927i	−0.582013	−	1.36086i
$636$		0			0
$637$	−18.6729			−0.739848
$638$	4.04554	−	2.25123i	0.160165	−	0.0891269i
$639$		0			0
$640$	−0.802557	−	25.2855i	−0.0317239	−	0.999497i
$641$	−45.4930			−1.79687			−0.898433	−	0.439110i	$-0.855294\pi$
$641$	−45.4930			−1.79687			−0.898433	+	0.439110i	$0.855294\pi$
$642$		0			0
$643$	−31.3531			−1.23645			−0.618224	−	0.786002i	$-0.712147\pi$
$643$	−31.3531			−1.23645			−0.618224	+	0.786002i	$0.712147\pi$
$644$	29.6008	−	47.7214i	1.16644	−	1.88048i
$645$		0			0
$646$	−6.87137	+	3.82372i	−0.270351	+	0.150442i
$647$	24.0355	+	24.0355i	0.944932	+	0.944932i	0.998561	−	0.0536292i	$-0.0170789\pi$
$647$	24.0355	+	24.0355i	0.944932	+	0.944932i	−0.0536292	+	0.998561i	$0.517079\pi$
$648$		0			0
$649$	−16.3141			−0.640383
$650$	3.66137	−	14.0617i	0.143611	−	0.551544i
$651$		0			0
$652$	4.14642	−	6.68471i	0.162387	−	0.261793i
$653$			15.4153i			0.603248i	0.953427	+	0.301624i	$0.0975288\pi$
$653$			15.4153i			0.603248i	−0.953427	+	0.301624i	$0.902471\pi$
$654$		0			0
$655$	−46.4494	+	19.8654i	−1.81493	+	0.776207i
$656$	−18.1775	+	9.01495i	−0.709714	+	0.351975i
$657$		0			0
$658$	19.1111	−	10.6348i	0.745030	−	0.414587i
$659$	−30.4355	+	30.4355i	−1.18560	+	1.18560i	−0.207327	+	0.978272i	$0.566476\pi$
$659$	−30.4355	+	30.4355i	−1.18560	+	1.18560i	−0.978272	+	0.207327i	$0.933524\pi$
$660$		0			0
$661$	−11.2208	−	11.2208i	−0.436437	−	0.436437i	0.454374	−	0.890811i	$-0.349863\pi$
$661$	−11.2208	−	11.2208i	−0.436437	−	0.436437i	−0.890811	+	0.454374i	$0.849863\pi$
$662$	−10.8352	+	38.0240i	−0.421124	+	1.47784i
$663$		0			0
$664$	0.369550	−	7.78992i	0.0143413	−	0.302308i
$665$	3.22560	−	8.04639i	0.125083	−	0.312026i
$666$		0			0
$667$	−8.27109			−0.320258
$668$	−22.3945	+	5.24817i	−0.866469	+	0.203058i
$669$		0			0
$670$	5.44609	−	0.692835i	0.210401	−	0.0267665i
$671$			21.7757i			0.840640i
$672$		0			0
$673$	−29.2965	+	29.2965i	−1.12930	+	1.12930i	−0.139006	+	0.990291i	$0.544391\pi$
$673$	−29.2965	+	29.2965i	−1.12930	+	1.12930i	−0.990291	+	0.139006i	$0.955609\pi$
$674$	13.9825	+	3.98443i	0.538585	+	0.153474i
$675$		0			0
$676$	9.25326	−	14.9178i	0.355895	−	0.573760i
$677$		−	2.74511i		−	0.105503i	−0.998608	−	0.0527516i	$-0.983201\pi$
$677$		−	2.74511i		−	0.105503i	0.998608	−	0.0527516i	$-0.0167991\pi$
$678$		0			0
$679$		−	20.0191i		−	0.768261i
$680$	12.7055	+	34.0924i	0.487233	+	1.30738i
$681$		0			0
$682$	−8.89292	−	2.53411i	−0.340528	−	0.0970362i
$683$		−	33.0796i		−	1.26576i	−0.774251	−	0.632878i	$-0.781873\pi$
$683$		−	33.0796i		−	1.26576i	0.774251	−	0.632878i	$-0.218127\pi$
$684$		0			0
$685$	−1.60936	−	3.76301i	−0.0614905	−	0.143777i
$686$	−3.24401	+	11.3841i	−0.123857	+	0.434648i
$687$		0			0
$688$	3.04510	−	1.51018i	0.116093	−	0.0575752i
$689$		−	10.6364i		−	0.405214i
$690$		0			0
$691$	−30.8216	−	30.8216i	−1.17251	−	1.17251i	−0.981610	−	0.190899i	$-0.938860\pi$
$691$	−30.8216	−	30.8216i	−1.17251	−	1.17251i	−0.190899	−	0.981610i	$-0.561140\pi$
$692$	11.6717	+	7.23976i	0.443690	+	0.275214i
$693$		0			0
$694$	28.9994	−	16.1373i	1.10080	−	0.612563i
$695$	−25.0458	+	10.7116i	−0.950043	+	0.406314i
$696$		0			0
$697$	20.6338	−	20.6338i	0.781561	−	0.781561i
$698$	44.6407	+	12.7207i	1.68967	+	0.481487i
$699$		0			0
$700$	−34.5587	−	20.3565i	−1.30619	−	0.769405i
$701$	22.1242	−	22.1242i	0.835619	−	0.835619i	−0.152660	−	0.988279i	$-0.548784\pi$
$701$	22.1242	−	22.1242i	0.835619	−	0.835619i	0.988279	+	0.152660i	$0.0487838\pi$
$702$		0			0
$703$	3.10562	+	3.10562i	0.117131	+	0.117131i
$704$	17.0877	−	14.1200i	0.644015	−	0.532168i
$705$		0			0
$706$	7.30177	−	25.6240i	0.274806	−	0.964371i
$707$		−	41.9440i		−	1.57747i
$708$		0			0
$709$	7.09244	−	7.09244i	0.266362	−	0.266362i	−0.561270	−	0.827632i	$-0.689687\pi$
$709$	7.09244	−	7.09244i	0.266362	−	0.266362i	0.827632	+	0.561270i	$0.189687\pi$
$710$	−0.931951	−	7.32569i	−0.0349755	−	0.274928i
$711$		0			0
$712$	−1.56073	+	32.8995i	−0.0584910	+	1.23296i
$713$	11.6812	+	11.6812i	0.437466	+	0.437466i
$714$		0			0
$715$	11.7062	−	5.00651i	0.437788	−	0.187233i
$716$	−10.1397	−	43.2671i	−0.378938	−	1.61697i
$717$		0			0
$718$	−18.5603	−	33.3535i	−0.692663	−	1.24474i
$719$	30.2949			1.12981			0.564905	−	0.825156i	$-0.308913\pi$
$719$	30.2949			1.12981			0.564905	+	0.825156i	$0.308913\pi$
$720$		0			0
$721$	21.1349			0.787104
$722$	12.4232	+	22.3250i	0.462343	+	0.830849i
$723$		0			0
$724$	−38.3090	+	8.97776i	−1.42374	+	0.333656i
$725$	0.135136	+	5.90590i	0.00501883	+	0.219340i
$726$		0			0
$727$	15.9503	+	15.9503i	0.591566	+	0.591566i	0.938054	−	0.346489i	$-0.112626\pi$
$727$	15.9503	+	15.9503i	0.591566	+	0.591566i	−0.346489	+	0.938054i	$0.612626\pi$
$728$	15.6844	+	17.2466i	0.581301	+	0.639201i
$729$		0			0
$730$	12.0382	−	15.5476i	0.445555	−	0.575443i
$731$	−3.45657	+	3.45657i	−0.127846	+	0.127846i
$732$		0			0
$733$		−	35.8535i		−	1.32428i	−0.749380	−	0.662140i	$-0.769648\pi$
$733$		−	35.8535i		−	1.32428i	0.749380	−	0.662140i	$-0.230352\pi$
$734$	10.6746	−	37.4603i	0.394008	−	1.38269i
$735$		0			0
$736$	−38.9414	+	7.19856i	−1.43540	+	0.265342i
$737$	3.40147	+	3.40147i	0.125295	+	0.125295i
$738$		0			0
$739$	21.4532	−	21.4532i	0.789168	−	0.789168i	−0.192190	−	0.981358i	$-0.561559\pi$
$739$	21.4532	−	21.4532i	0.789168	−	0.789168i	0.981358	+	0.192190i	$0.0615590\pi$
$740$	16.3676	−	12.0429i	0.601685	−	0.442705i
$741$		0			0
$742$	−28.2355	−	8.04595i	−1.03656	−	0.295376i
$743$	−13.0311	+	13.0311i	−0.478063	+	0.478063i	−0.904512	−	0.426449i	$-0.859765\pi$
$743$	−13.0311	+	13.0311i	−0.478063	+	0.478063i	0.426449	+	0.904512i	$0.359765\pi$
$744$		0			0
$745$	−0.100242	−	0.234385i	−0.00367258	−	0.00858722i
$746$	6.01903	−	3.34941i	0.220372	−	0.122631i
$747$		0			0
$748$	−16.8040	+	27.0909i	−0.614417	+	0.990540i
$749$	−46.6836	−	46.6836i	−1.70578	−	1.70578i
$750$		0			0
$751$		−	22.4879i		−	0.820595i	−0.911952	−	0.410297i	$-0.865425\pi$
$751$		−	22.4879i		−	0.820595i	0.911952	−	0.410297i	$-0.134575\pi$
$752$	−14.6158	−	4.92483i	−0.532983	−	0.179590i
$753$		0			0
$754$	0.940956	−	3.30208i	0.0342676	−	0.120255i
$755$	2.70571	−	6.74952i	0.0984710	−	0.245640i
$756$		0			0
$757$			15.8781i			0.577100i	0.957465	+	0.288550i	$0.0931731\pi$
$757$			15.8781i			0.577100i	−0.957465	+	0.288550i	$0.906827\pi$
$758$	−4.89418	−	1.39464i	−0.177764	−	0.0506555i
$759$		0			0
$760$	−5.72835	+	2.13483i	−0.207789	+	0.0774385i
$761$		−	19.5227i		−	0.707696i	−0.935303	−	0.353848i	$-0.884873\pi$
$761$		−	19.5227i		−	0.707696i	0.935303	−	0.353848i	$-0.115127\pi$
$762$		0			0
$763$		−	72.9184i		−	2.63982i
$764$	−17.5725	−	10.8999i	−0.635750	−	0.394346i
$765$		0			0
$766$	0.371680	+	0.105913i	0.0134293	+	0.00382680i
$767$	−8.55524	+	8.55524i	−0.308912	+	0.308912i
$768$		0			0
$769$		−	8.03843i		−	0.289873i	−0.989441	−	0.144937i	$-0.953702\pi$
$769$		−	8.03843i		−	0.289873i	0.989441	−	0.144937i	$-0.0462978\pi$
$770$	−4.43512	−	34.8627i	−0.159831	−	1.25636i
$771$		0			0
$772$	−8.52392	−	36.3725i	−0.306783	−	1.30907i
$773$	−40.5118			−1.45711			−0.728554	−	0.684988i	$-0.759807\pi$
$773$	−40.5118			−1.45711			−0.728554	+	0.684988i	$0.759807\pi$
$774$		0			0
$775$	8.15005	−	8.53175i	0.292758	−	0.306470i
$776$	−10.4443	+	9.49821i	−0.374928	+	0.340966i
$777$		0			0
$778$	1.10457	−	3.87625i	0.0396008	−	0.138970i
$779$	3.46698	+	3.46698i	0.124217	+	0.124217i
$780$		0			0
$781$	4.57542	−	4.57542i	0.163721	−	0.163721i
$782$	49.7664	−	27.6935i	1.77964	−	0.990319i
$783$		0			0
$784$	32.5630	−	16.1493i	1.16296	−	0.576760i
$785$	7.54352	−	18.8176i	0.269240	−	0.671631i
$786$		0			0
$787$			15.8333i			0.564396i	0.959356	+	0.282198i	$0.0910635\pi$
$787$			15.8333i			0.564396i	−0.959356	+	0.282198i	$0.908937\pi$
$788$	−25.9081	−	16.0704i	−0.922938	−	0.572484i
$789$		0			0
$790$	5.62671	+	44.2293i	0.200189	+	1.57361i
$791$	−4.89868			−0.174177
$792$		0			0
$793$	11.4194	+	11.4194i	0.405513	+	0.405513i
$794$	−26.6318	+	14.8198i	−0.945128	+	0.525936i
$795$		0			0
$796$	8.47688	+	5.25808i	0.300455	+	0.186368i
$797$	10.2670			0.363674			0.181837	−	0.983329i	$-0.441796\pi$
$797$	10.2670			0.363674			0.181837	+	0.983329i	$0.441796\pi$
$798$		0			0
$799$	22.1811			0.784710
$800$	5.77631	+	27.6882i	0.204223	+	0.978924i
$801$		0			0
$802$	12.8476	−	7.14932i	0.453665	−	0.252451i
$803$	17.2293			0.608010
$804$		0			0
$805$	−23.3616	+	58.2766i	−0.823388	+	2.05398i
$806$	−5.99244	+	3.33462i	−0.211075	+	0.117457i
$807$		0			0
$808$	−21.8829	+	19.9007i	−0.769837	+	0.700104i
$809$	−9.16442			−0.322204			−0.161102	−	0.986938i	$-0.551505\pi$
$809$	−9.16442			−0.322204			−0.161102	+	0.986938i	$0.551505\pi$
$810$		0			0
$811$	−22.1702	+	22.1702i	−0.778502	+	0.778502i	−0.979576	−	0.201074i	$-0.935557\pi$
$811$	−22.1702	+	22.1702i	−0.778502	+	0.778502i	0.201074	+	0.979576i	$0.435557\pi$
$812$	−8.05397	−	4.99575i	−0.282639	−	0.175317i
$813$		0			0
$814$	17.1236	+	4.87952i	0.600183	+	0.171027i
$815$	−3.27245	+	8.16326i	−0.114629	+	0.285947i
$816$		0			0
$817$	−0.580788	−	0.580788i	−0.0203192	−	0.0203192i
$818$	0.408707	−	0.227433i	0.0142901	−	0.00795202i
$819$		0			0
$820$	18.2721	−	13.4442i	0.638090	−	0.469490i
$821$	−13.3258	−	13.3258i	−0.465074	−	0.465074i	0.435240	−	0.900314i	$-0.356663\pi$
$821$	−13.3258	−	13.3258i	−0.465074	−	0.465074i	−0.900314	+	0.435240i	$0.856663\pi$
$822$		0			0
$823$	−34.7796	+	34.7796i	−1.21234	+	1.21234i	−0.242084	+	0.970255i	$0.577831\pi$
$823$	−34.7796	+	34.7796i	−1.21234	+	1.21234i	−0.970255	+	0.242084i	$0.922169\pi$
$824$	−10.0276	−	11.0264i	−0.349329	−	0.384123i
$825$		0			0
$826$	16.2392	+	29.1825i	0.565035	+	1.01539i
$827$	−16.5717			−0.576253			−0.288127	−	0.957592i	$-0.593032\pi$
$827$	−16.5717			−0.576253			−0.288127	+	0.957592i	$0.593032\pi$
$828$		0			0
$829$	11.9869	+	11.9869i	0.416321	+	0.416321i	0.883933	−	0.467613i	$-0.154886\pi$
$829$	11.9869	+	11.9869i	0.416321	+	0.416321i	−0.467613	+	0.883933i	$0.654886\pi$
$830$	1.10036	+	8.64948i	0.0381941	+	0.300228i
$831$		0			0
$832$	1.55625	−	16.3656i	0.0539534	−	0.567374i
$833$	−36.9631	+	36.9631i	−1.28070	+	1.28070i
$834$		0			0
$835$	23.6445	−	10.1123i	0.818252	−	0.349949i
$836$	−4.55192	−	2.82349i	−0.157432	−	0.0976524i
$837$		0			0
$838$	−3.67968	+	12.9130i	−0.127112	+	0.446073i
$839$		−	4.44215i		−	0.153360i	−0.997056	−	0.0766800i	$-0.975568\pi$
$839$		−	4.44215i		−	0.153360i	0.997056	−	0.0766800i	$-0.0244320\pi$
$840$		0			0
$841$		−	27.6041i		−	0.951865i
$842$	5.76704	+	1.64337i	0.198745	+	0.0566341i
$843$		0			0
$844$	28.5854	−	6.69902i	0.983951	−	0.230590i
$845$	−7.30287	+	18.2173i	−0.251226	+	0.626695i
$846$		0			0
$847$	−9.42281	+	9.42281i	−0.323772	+	0.323772i
$848$	9.19888	+	18.5484i	0.315891	+	0.636955i
$849$		0			0
$850$	−20.5874	−	35.0828i	−0.706144	−	1.20333i
$851$	−22.4926	−	22.4926i	−0.771038	−	0.771038i
$852$		0			0
$853$	35.6748			1.22148			0.610742	−	0.791830i	$-0.290871\pi$
$853$	35.6748			1.22148			0.610742	+	0.791830i	$0.290871\pi$
$854$	38.9522	−	21.6758i	1.33292	−	0.741730i
$855$		0			0
$856$	−2.20618	+	46.5050i	−0.0754056	+	1.58951i
$857$	−13.8568	+	13.8568i	−0.473340	+	0.473340i	−0.902994	−	0.429654i	$-0.858636\pi$
$857$	−13.8568	+	13.8568i	−0.473340	+	0.473340i	0.429654	+	0.902994i	$0.358636\pi$
$858$		0			0
$859$	19.4217	+	19.4217i	0.662660	+	0.662660i	0.956006	−	0.293346i	$-0.0947690\pi$
$859$	19.4217	+	19.4217i	0.662660	+	0.662660i	−0.293346	+	0.956006i	$0.594769\pi$
$860$	−3.06094	+	2.25216i	−0.104377	+	0.0767981i
$861$		0			0
$862$	−13.7223	−	24.6595i	−0.467383	−	0.839906i
$863$	9.22041	+	9.22041i	0.313866	+	0.313866i	0.846405	−	0.532539i	$-0.178762\pi$
$863$	9.22041	+	9.22041i	0.313866	+	0.313866i	−0.532539	+	0.846405i	$0.678762\pi$
$864$		0			0
$865$	−14.2532	−	5.71377i	−0.484625	−	0.194274i
$866$	−8.87428	+	31.1424i	−0.301560	+	1.05826i
$867$		0			0
$868$	4.31911	+	18.4301i	0.146600	+	0.625559i
$869$	−27.6244	+	27.6244i	−0.937093	+	0.937093i
$870$		0			0
$871$	3.56753			0.120881
$872$	−38.0427	+	34.5968i	−1.28829	+	1.17159i
$873$		0			0
$874$	4.65319	+	8.36197i	0.157396	+	0.282848i
$875$	41.9936	+	15.7290i	1.41964	+	0.531738i
$876$		0			0
$877$	10.4267			0.352084			0.176042	−	0.984383i	$-0.443670\pi$
$877$	10.4267			0.352084			0.176042	+	0.984383i	$0.443670\pi$
$878$	20.1991	+	36.2986i	0.681686	+	1.22502i
$879$		0			0
$880$	−16.0842	+	18.8548i	−0.542197	+	0.635595i
$881$	12.7405			0.429239			0.214619	−	0.976698i	$-0.431149\pi$
$881$	12.7405			0.429239			0.214619	+	0.976698i	$0.431149\pi$
$882$		0			0
$883$	27.9073			0.939156			0.469578	−	0.882891i	$-0.344406\pi$
$883$	27.9073			0.939156			0.469578	+	0.882891i	$0.344406\pi$
$884$	5.39449	+	23.0189i	0.181437	+	0.774209i
$885$		0			0
$886$	−13.6648	−	24.5563i	−0.459079	−	0.824984i
$887$	−41.7449	−	41.7449i	−1.40166	−	1.40166i	−0.794846	−	0.606811i	$-0.792448\pi$
$887$	−41.7449	−	41.7449i	−1.40166	−	1.40166i	−0.606811	−	0.794846i	$-0.707552\pi$
$888$		0			0
$889$	−66.9004			−2.24377
$890$	−4.64719	−	36.5297i	−0.155774	−	1.22448i
$891$		0			0
$892$	4.12668	−	0.967091i	0.138171	−	0.0323806i
$893$			3.72696i			0.124718i
$894$		0			0
$895$	19.5373	+	45.6822i	0.653061	+	1.52699i
$896$	−42.2671	−	16.5111i	−1.41204	−	0.551597i
$897$		0			0
$898$	11.5237	+	20.7086i	0.384551	+	0.691053i
$899$	1.97145	−	1.97145i	0.0657516	−	0.0657516i
$900$		0			0
$901$	−21.0548	−	21.0548i	−0.701437	−	0.701437i
$902$	19.1161	+	5.44729i	0.636496	+	0.181375i
$903$		0			0
$904$	2.32422	+	2.55572i	0.0773024	+	0.0850021i
$905$	40.4474	−	17.2985i	1.34452	−	0.575022i
$906$		0			0
$907$	26.7614			0.888597			0.444298	−	0.895879i	$-0.353453\pi$
$907$	26.7614			0.888597			0.444298	+	0.895879i	$0.353453\pi$
$908$	26.5724	+	16.4825i	0.881836	+	0.546990i
$909$		0			0
$910$	−20.6081	−	15.9565i	−0.683153	−	0.528953i
$911$			19.2403i			0.637459i	0.947846	+	0.318729i	$0.103256\pi$
$911$			19.2403i			0.637459i	−0.947846	+	0.318729i	$0.896744\pi$
$912$		0			0
$913$	−5.40222	+	5.40222i	−0.178787	+	0.178787i
$914$	2.74195	−	9.62229i	0.0906957	−	0.318277i
$915$		0			0
$916$	−6.28643	−	26.8249i	−0.207709	−	0.886318i
$917$			90.6165i			2.99242i
$918$		0			0
$919$			42.6903i			1.40822i	0.710090	+	0.704111i	$0.248654\pi$
$919$			42.6903i			1.40822i	−0.710090	+	0.704111i	$0.751346\pi$
$920$	41.4879	−	15.4617i	1.36782	−	0.509756i
$921$		0			0
$922$	−1.48819	+	5.22246i	−0.0490108	+	0.171993i
$923$		−	4.79878i		−	0.157954i
$924$		0			0
$925$	−15.6932	+	16.4282i	−0.515989	+	0.540155i
$926$	−17.6677	−	5.03456i	−0.580597	−	0.165446i
$927$		0			0
$928$	1.21491	+	6.57217i	0.0398812	+	0.215742i
$929$		−	5.58037i		−	0.183086i	−0.995801	−	0.0915430i	$-0.970820\pi$
$929$		−	5.58037i		−	0.183086i	0.995801	−	0.0915430i	$-0.0291799\pi$
$930$		0			0
$931$	−6.21070	−	6.21070i	−0.203548	−	0.203548i
$932$	1.40203	−	0.328567i	0.0459251	−	0.0107626i
$933$		0			0
$934$	0.731714	+	1.31492i	0.0239424	+	0.0430255i
$935$	13.2621	−	33.0829i	0.433717	−	1.08193i
$936$		0			0
$937$	−41.0680	+	41.0680i	−1.34163	+	1.34163i	−0.447197	+	0.894435i	$0.647578\pi$
$937$	−41.0680	+	41.0680i	−1.34163	+	1.34163i	−0.894435	+	0.447197i	$0.852422\pi$
$938$	2.69867	−	9.47042i	0.0881149	−	0.309220i
$939$		0			0
$940$	17.0473	+	2.59499i	0.556021	+	0.0846394i
$941$	31.5476	−	31.5476i	1.02842	−	1.02842i	0.0288377	−	0.999584i	$-0.490819\pi$
$941$	31.5476	−	31.5476i	1.02842	−	1.02842i	0.999584	−	0.0288377i	$-0.00918061\pi$
$942$		0			0
$943$	−25.1098	−	25.1098i	−0.817689	−	0.817689i
$944$	7.52017	−	22.3182i	0.244761	−	0.726394i
$945$		0			0
$946$	−3.20232	−	0.912529i	−0.104117	−	0.0296689i
$947$			34.7892i			1.13050i	0.824921	+	0.565248i	$0.191220\pi$
$947$			34.7892i			1.13050i	−0.824921	+	0.565248i	$0.808780\pi$
$948$		0			0
$949$	9.03522	−	9.03522i	0.293296	−	0.293296i
$950$	5.89477	−	3.45919i	0.191252	−	0.112231i
$951$		0			0
$952$	65.1870	+	3.09244i	2.11272	+	0.100227i
$953$	26.7047	+	26.7047i	0.865050	+	0.865050i	0.991919	−	0.126870i	$-0.0404931\pi$
$953$	26.7047	+	26.7047i	0.865050	+	0.865050i	−0.126870	+	0.991919i	$0.540493\pi$
$954$		0			0
$955$	21.4592	+	8.60247i	0.694405	+	0.278369i
$956$	8.63926	−	13.9279i	0.279413	−	0.450460i
$957$		0			0
$958$	19.6064	−	10.9104i	0.633453	−	0.352498i
$959$	−7.34112			−0.237057
$960$		0			0
$961$	25.4314			0.820369
$962$	11.5386	−	6.42092i	0.372021	−	0.207019i
$963$		0			0
$964$	5.97510	−	9.63284i	0.192445	−	0.310253i
$965$	16.4241	+	38.4027i	0.528709	+	1.23623i
$966$		0			0
$967$	−12.8711	−	12.8711i	−0.413906	−	0.413906i	0.469191	−	0.883097i	$-0.344546\pi$
$967$	−12.8711	−	12.8711i	−0.413906	−	0.413906i	−0.883097	+	0.469191i	$0.844546\pi$
$968$	9.38677	+	0.445304i	0.301702	+	0.0143126i
$969$		0			0
$970$	9.66302	−	12.4800i	0.310261	−	0.400708i
$971$	23.9028	−	23.9028i	0.767078	−	0.767078i	−0.210513	−	0.977591i	$-0.567513\pi$
$971$	23.9028	−	23.9028i	0.767078	−	0.767078i	0.977591	+	0.210513i	$0.0675134\pi$
$972$		0			0
$973$			48.8610i			1.56641i
$974$	−26.5332	−	7.56087i	−0.850179	−	0.242266i
$975$		0			0
$976$	−29.7898	−	10.0378i	−0.953549	−	0.321301i
$977$	−2.71449	−	2.71449i	−0.0868441	−	0.0868441i	0.662350	−	0.749194i	$-0.269559\pi$
$977$	−2.71449	−	2.71449i	−0.0868441	−	0.0868441i	−0.749194	+	0.662350i	$0.769559\pi$
$978$		0			0
$979$	22.8154	−	22.8154i	0.729183	−	0.729183i
$980$	−32.7324	+	24.0837i	−1.04560	+	0.769325i
$981$		0			0
$982$	−10.6589	+	37.4053i	−0.340141	+	1.19365i
$983$	13.7542	−	13.7542i	0.438692	−	0.438692i	−0.452880	−	0.891572i	$-0.649603\pi$
$983$	13.7542	−	13.7542i	0.438692	−	0.438692i	0.891572	+	0.452880i	$0.149603\pi$
$984$		0			0
$985$	31.6386	+	12.6831i	1.00809	+	0.404117i
$986$	−4.67386	−	8.39911i	−0.148846	−	0.267482i
$987$		0			0
$988$	−3.86773	+	0.906407i	−0.123049	+	0.0288366i
$989$	4.20640	+	4.20640i	0.133756	+	0.133756i
$990$		0			0
$991$		−	26.5971i		−	0.844883i	−0.906390	−	0.422442i	$-0.861173\pi$
$991$		−	26.5971i		−	0.844883i	0.906390	−	0.422442i	$-0.138827\pi$
$992$	7.56605	−	10.9977i	0.240222	−	0.349177i
$993$		0			0
$994$	−12.7389	−	3.63006i	−0.404054	−	0.115139i
$995$	−10.3518	−	4.14979i	−0.328175	−	0.131557i
$996$		0			0
$997$		−	25.4590i		−	0.806295i	−0.915135	−	0.403148i	$-0.867916\pi$
$997$		−	25.4590i		−	0.806295i	0.915135	−	0.403148i	$-0.132084\pi$
$998$	−12.6140	+	44.2661i	−0.399289	+	1.40122i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.z.g.667.7		18
3.2	odd	2		80.2.s.b.27.3	yes	18
5.3	odd	4		720.2.bd.g.523.3		18
12.11	even	2		320.2.s.b.207.5		18
15.2	even	4		400.2.j.d.43.3		18
15.8	even	4		80.2.j.b.43.7	✓	18
15.14	odd	2		400.2.s.d.107.7		18
16.3	odd	4		720.2.bd.g.307.3		18
24.5	odd	2		640.2.s.d.287.5		18
24.11	even	2		640.2.s.c.287.5		18
48.5	odd	4		640.2.j.c.607.5		18
48.11	even	4		640.2.j.d.607.5		18
48.29	odd	4		320.2.j.b.47.5		18
48.35	even	4		80.2.j.b.67.7	yes	18
60.23	odd	4		320.2.j.b.143.5		18
60.47	odd	4		1600.2.j.d.143.5		18
60.59	even	2		1600.2.s.d.207.5		18
80.3	even	4	inner	720.2.z.g.163.7		18
120.53	even	4		640.2.j.d.543.5		18
120.83	odd	4		640.2.j.c.543.5		18
240.29	odd	4		1600.2.j.d.1007.5		18
240.53	even	4		640.2.s.c.223.5		18
240.77	even	4		1600.2.s.d.943.5		18
240.83	odd	4		80.2.s.b.3.3	yes	18
240.173	even	4		320.2.s.b.303.5		18
240.179	even	4		400.2.j.d.307.3		18
240.203	odd	4		640.2.s.d.223.5		18
240.227	odd	4		400.2.s.d.243.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.7	✓	18	15.8	even	4
80.2.j.b.67.7	yes	18	48.35	even	4
80.2.s.b.3.3	yes	18	240.83	odd	4
80.2.s.b.27.3	yes	18	3.2	odd	2
320.2.j.b.47.5		18	48.29	odd	4
320.2.j.b.143.5		18	60.23	odd	4
320.2.s.b.207.5		18	12.11	even	2
320.2.s.b.303.5		18	240.173	even	4
400.2.j.d.43.3		18	15.2	even	4
400.2.j.d.307.3		18	240.179	even	4
400.2.s.d.107.7		18	15.14	odd	2
400.2.s.d.243.7		18	240.227	odd	4
640.2.j.c.543.5		18	120.83	odd	4
640.2.j.c.607.5		18	48.5	odd	4
640.2.j.d.543.5		18	120.53	even	4
640.2.j.d.607.5		18	48.11	even	4
640.2.s.c.223.5		18	240.53	even	4
640.2.s.c.287.5		18	24.11	even	2
640.2.s.d.223.5		18	240.203	odd	4
640.2.s.d.287.5		18	24.5	odd	2
720.2.z.g.163.7		18	80.3	even	4	inner
720.2.z.g.667.7		18	1.1	even	1	trivial
720.2.bd.g.307.3		18	16.3	odd	4
720.2.bd.g.523.3		18	5.3	odd	4
1600.2.j.d.143.5		18	60.47	odd	4
1600.2.j.d.1007.5		18	240.29	odd	4
1600.2.s.d.207.5		18	60.59	even	2
1600.2.s.d.943.5		18	240.77	even	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23576 - 0.687667i) q^{2} +(1.05423 - 1.69959i) q^{4} +(-0.832020 + 2.07551i) q^{5} +(2.83610 + 2.83610i) q^{7} +(0.134028 - 2.82525i) q^{8} +O(q^{10})\)	\(q+(1.23576 - 0.687667i) q^{2} +(1.05423 - 1.69959i) q^{4} +(-0.832020 + 2.07551i) q^{5} +(2.83610 + 2.83610i) q^{7} +(0.134028 - 2.82525i) q^{8} +(0.399079 + 3.13699i) q^{10} +(-1.95928 + 1.95928i) q^{11} +2.05493i q^{13} +(5.45504 + 1.55446i) q^{14} +(-1.77720 - 3.58351i) q^{16} +(4.06774 + 4.06774i) q^{17} +(-0.683479 + 0.683479i) q^{19} +(2.65037 + 3.60215i) q^{20} +(-1.07388 + 3.76854i) q^{22} +(4.95014 - 4.95014i) q^{23} +(-3.61549 - 3.45373i) q^{25} +(1.41310 + 2.53941i) q^{26} +(7.81010 - 1.83030i) q^{28} +(-0.835439 - 0.835439i) q^{29} +2.35978i q^{31} +(-4.66047 - 3.20625i) q^{32} +(7.82401 + 2.22952i) q^{34} +(-8.24604 + 3.52666i) q^{35} -4.54384i q^{37} +(-0.374613 + 1.31462i) q^{38} +(5.75232 + 2.62884i) q^{40} -5.07255i q^{41} +0.849753i q^{43} +(1.26444 + 5.39549i) q^{44} +(2.71316 - 9.52126i) q^{46} +(2.72646 - 2.72646i) q^{47} +9.08690i q^{49} +(-6.84291 - 1.78175i) q^{50} +(3.49253 + 2.16636i) q^{52} -5.17605 q^{53} +(-2.43634 - 5.69666i) q^{55} +(8.39280 - 7.63257i) q^{56} +(-1.60691 - 0.457903i) q^{58} +(4.16328 + 4.16328i) q^{59} +(5.55706 - 5.55706i) q^{61} +(1.62274 + 2.91613i) q^{62} +(-7.96407 - 0.757328i) q^{64} +(-4.26502 - 1.70974i) q^{65} -1.73609i q^{67} +(11.2018 - 2.62515i) q^{68} +(-7.76500 + 10.0287i) q^{70} -2.33526 q^{71} +(-4.39686 - 4.39686i) q^{73} +(-3.12465 - 5.61511i) q^{74} +(0.441090 + 1.88218i) q^{76} -11.1134 q^{77} +14.0993 q^{79} +(8.91628 - 0.707050i) q^{80} +(-3.48822 - 6.26848i) q^{82} +2.75725 q^{83} +(-11.8271 + 5.05819i) q^{85} +(0.584347 + 1.05009i) q^{86} +(5.27285 + 5.79805i) q^{88} -11.6448 q^{89} +(-5.82797 + 5.82797i) q^{91} +(-3.19462 - 13.6318i) q^{92} +(1.49437 - 5.24417i) q^{94} +(-0.849899 - 1.98724i) q^{95} +(-3.52933 - 3.52933i) q^{97} +(6.24876 + 11.2293i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

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