LMFDB - Embedded newform 720.2.bd.g.523.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(307,720)]

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, 1]))

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

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

chi := DirichletCharacter("720.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bd (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			523.3
Root			$-1.37691 + 0.322680i$ of defining polynomial
Character	$\chi$	$=$	720.523
Dual form			720.2.bd.g.307.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.687667 - 1.23576i) q^{2} +(-1.05423 + 1.69959i) q^{4} +(2.07551 - 0.832020i) q^{5} +(2.83610 - 2.83610i) q^{7} +(2.82525 + 0.134028i) q^{8} +O(q^{10})$	\(q+(-0.687667 - 1.23576i) q^{2} +(-1.05423 + 1.69959i) q^{4} +(2.07551 - 0.832020i) q^{5} +(2.83610 - 2.83610i) q^{7} +(2.82525 + 0.134028i) q^{8} +(-2.45544 - 1.99269i) q^{10} +(-1.95928 + 1.95928i) q^{11} -2.05493 q^{13} +(-5.45504 - 1.55446i) q^{14} +(-1.77720 - 3.58351i) q^{16} +(4.06774 - 4.06774i) q^{17} +(0.683479 - 0.683479i) q^{19} +(-0.773972 + 4.40465i) q^{20} +(3.76854 + 1.07388i) q^{22} +(4.95014 + 4.95014i) q^{23} +(3.61549 - 3.45373i) q^{25} +(1.41310 + 2.53941i) q^{26} +(1.83030 + 7.81010i) q^{28} +(0.835439 + 0.835439i) q^{29} +2.35978i q^{31} +(-3.20625 + 4.66047i) q^{32} +(-7.82401 - 2.22952i) q^{34} +(3.52666 - 8.24604i) q^{35} -4.54384 q^{37} +(-1.31462 - 0.374613i) q^{38} +(5.97535 - 2.07249i) q^{40} -5.07255i q^{41} -0.849753 q^{43} +(-1.26444 - 5.39549i) q^{44} +(2.71316 - 9.52126i) q^{46} +(-2.72646 - 2.72646i) q^{47} -9.08690i q^{49} +(-6.75425 - 2.09287i) q^{50} +(2.16636 - 3.49253i) q^{52} -5.17605i q^{53} +(-2.43634 + 5.69666i) q^{55} +(8.39280 - 7.63257i) q^{56} +(0.457903 - 1.60691i) q^{58} +(-4.16328 - 4.16328i) q^{59} +(5.55706 - 5.55706i) q^{61} +(2.91613 - 1.62274i) q^{62} +(7.96407 + 0.757328i) q^{64} +(-4.26502 + 1.70974i) q^{65} -1.73609 q^{67} +(2.62515 + 11.2018i) q^{68} +(-12.6153 + 1.31240i) q^{70} -2.33526 q^{71} +(4.39686 - 4.39686i) q^{73} +(3.12465 + 5.61511i) q^{74} +(0.441090 + 1.88218i) q^{76} +11.1134i q^{77} -14.0993 q^{79} +(-6.67015 - 5.95895i) q^{80} +(-6.26848 + 3.48822i) q^{82} +2.75725i q^{83} +(5.05819 - 11.8271i) q^{85} +(0.584347 + 1.05009i) q^{86} +(-5.79805 + 5.27285i) q^{88} +11.6448 q^{89} +(-5.82797 + 5.82797i) q^{91} +(-13.6318 + 3.19462i) q^{92} +(-1.49437 + 5.24417i) q^{94} +(0.849899 - 1.98724i) q^{95} +(-3.52933 + 3.52933i) q^{97} +(-11.2293 + 6.24876i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} + 4 q^{8}+O(q^{10}) $ 18 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 + 4 * q^8	$ 18 q + 4 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} + 4 q^{8} - 12 q^{10} + 2 q^{11} - 12 q^{14} + 6 q^{17} + 2 q^{19} + 4 q^{20} + 4 q^{22} + 2 q^{23} + 6 q^{25} + 16 q^{26} - 4 q^{28} + 14 q^{29} + 4 q^{32} - 28 q^{34} + 6 q^{35} + 8 q^{37} - 16 q^{38} + 20 q^{40} - 44 q^{43} - 44 q^{44} + 12 q^{46} + 38 q^{47} - 20 q^{50} - 40 q^{52} - 6 q^{55} - 20 q^{56} - 20 q^{58} + 10 q^{59} + 14 q^{61} - 16 q^{64} + 12 q^{67} - 36 q^{68} - 36 q^{70} - 24 q^{71} + 14 q^{73} - 48 q^{74} - 16 q^{76} + 16 q^{79} + 20 q^{80} - 28 q^{82} - 10 q^{85} + 36 q^{86} - 96 q^{88} + 12 q^{89} - 52 q^{92} + 28 q^{94} + 34 q^{95} + 18 q^{97} - 32 q^{98}+O(q^{100}) $ 18 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 + 4 * q^8 - 12 * q^10 + 2 * q^11 - 12 * q^14 + 6 * q^17 + 2 * q^19 + 4 * q^20 + 4 * q^22 + 2 * q^23 + 6 * q^25 + 16 * q^26 - 4 * q^28 + 14 * q^29 + 4 * q^32 - 28 * q^34 + 6 * q^35 + 8 * q^37 - 16 * q^38 + 20 * q^40 - 44 * q^43 - 44 * q^44 + 12 * q^46 + 38 * q^47 - 20 * q^50 - 40 * q^52 - 6 * q^55 - 20 * q^56 - 20 * q^58 + 10 * q^59 + 14 * q^61 - 16 * q^64 + 12 * q^67 - 36 * q^68 - 36 * q^70 - 24 * q^71 + 14 * q^73 - 48 * q^74 - 16 * q^76 + 16 * q^79 + 20 * q^80 - 28 * q^82 - 10 * q^85 + 36 * q^86 - 96 * q^88 + 12 * q^89 - 52 * q^92 + 28 * q^94 + 34 * q^95 + 18 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.687667	−	1.23576i	−0.486254	−	0.873818i
$2$	−0.687667	−	1.23576i	−0.486254	−	0.873818i
$3$		0			0
$3$		0			0
$4$	−1.05423	+	1.69959i	−0.527114	+	0.849794i
$5$	2.07551	−	0.832020i	0.928196	−	0.372091i
$5$	2.07551	−	0.832020i	0.928196	−	0.372091i
$6$		0			0
$7$	2.83610	−	2.83610i	1.07194	−	1.07194i	0.0747413	−	0.997203i	$-0.476187\pi$
$7$	2.83610	−	2.83610i	1.07194	−	1.07194i	0.997203	−	0.0747413i	$-0.0238131\pi$
$8$	2.82525	+	0.134028i	0.998877	+	0.0473862i
$9$		0			0
$10$	−2.45544	−	1.99269i	−0.776478	−	0.630144i
$11$	−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
$13$	−2.05493			−0.569934			−0.284967	−	0.958537i	$-0.591983\pi$
$13$	−2.05493			−0.569934			−0.284967	+	0.958537i	$0.591983\pi$
$14$	−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	−0.0133401	−	0.999911i	$-0.504246\pi$
$17$	4.06774	−	4.06774i	0.986571	−	0.986571i	0.999911	+	0.0133401i	$0.00424641\pi$
$18$		0			0
$19$	0.683479	−	0.683479i	0.156801	−	0.156801i	−0.624347	−	0.781147i	$-0.714635\pi$
$19$	0.683479	−	0.683479i	0.156801	−	0.156801i	0.781147	+	0.624347i	$0.214635\pi$
$20$	−0.773972	+	4.40465i	−0.173065	+	0.984910i
$21$		0			0
$22$	3.76854	+	1.07388i	0.803455	+	0.228951i
$23$	4.95014	+	4.95014i	1.03218	+	1.03218i	0.999465	+	0.0327113i	$0.0104142\pi$
$23$	4.95014	+	4.95014i	1.03218	+	1.03218i	0.0327113	+	0.999465i	$0.489586\pi$
$24$		0			0
$25$	3.61549	−	3.45373i	0.723097	−	0.690746i
$26$	1.41310	+	2.53941i	0.277133	+	0.498018i
$27$		0			0
$28$	1.83030	+	7.81010i	0.345895	+	1.47597i
$29$	0.835439	+	0.835439i	0.155137	+	0.155137i	0.780408	−	0.625271i	$-0.215011\pi$
$29$	0.835439	+	0.835439i	0.155137	+	0.155137i	−0.625271	+	0.780408i	$0.715011\pi$
$30$		0			0
$31$			2.35978i			0.423829i	0.977288	+	0.211915i	$0.0679698\pi$
$31$			2.35978i			0.423829i	−0.977288	+	0.211915i	$0.932030\pi$
$32$	−3.20625	+	4.66047i	−0.566791	+	0.823862i
$33$		0			0
$34$	−7.82401	−	2.22952i	−1.34181	−	0.382359i
$35$	3.52666	−	8.24604i	0.596114	−	1.39384i
$36$		0			0
$37$	−4.54384			−0.747002			−0.373501	−	0.927630i	$-0.621843\pi$
$37$	−4.54384			−0.747002			−0.373501	+	0.927630i	$0.621843\pi$
$38$	−1.31462	−	0.374613i	−0.213260	−	0.0607703i
$39$		0			0
$40$	5.97535	−	2.07249i	0.944786	−	0.327689i
$41$		−	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
$43$	−0.849753			−0.129586			−0.0647930	−	0.997899i	$-0.520639\pi$
$43$	−0.849753			−0.129586			−0.0647930	+	0.997899i	$0.520639\pi$
$44$	−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	$-0.340737\pi$
$47$	−2.72646	−	2.72646i	−0.397696	−	0.397696i	−0.877419	+	0.479724i	$0.840737\pi$
$48$		0			0
$49$		−	9.08690i		−	1.29813i
$50$	−6.75425	−	2.09287i	−0.955195	−	0.295977i
$51$		0			0
$52$	2.16636	−	3.49253i	0.300420	−	0.484327i
$53$		−	5.17605i		−	0.710985i	−0.934679	−	0.355492i	$-0.884313\pi$
$53$		−	5.17605i		−	0.710985i	0.934679	−	0.355492i	$-0.115687\pi$
$54$		0			0
$55$	−2.43634	+	5.69666i	−0.328517	+	0.768138i
$56$	8.39280	−	7.63257i	1.12154	−	1.01994i
$57$		0			0
$58$	0.457903	−	1.60691i	0.0601256	−	0.210998i
$59$	−4.16328	−	4.16328i	−0.542013	−	0.542013i	0.382105	−	0.924119i	$-0.375199\pi$
$59$	−4.16328	−	4.16328i	−0.542013	−	0.542013i	−0.924119	+	0.382105i	$0.875199\pi$
$60$		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	$0.0821880\pi$
$62$	2.91613	−	1.62274i	0.370349	−	0.206088i
$63$		0			0
$64$	7.96407	+	0.757328i	0.995509	+	0.0946660i
$65$	−4.26502	+	1.70974i	−0.529011	+	0.212067i
$66$		0			0
$67$	−1.73609			−0.212097			−0.106048	−	0.994361i	$-0.533820\pi$
$67$	−1.73609			−0.212097			−0.106048	+	0.994361i	$0.533820\pi$
$68$	2.62515	+	11.2018i	0.318347	+	1.35842i
$69$		0			0
$70$	−12.6153	+	1.31240i	−1.50782	+	0.156862i
$71$	−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	$-0.631450\pi$
$73$	4.39686	−	4.39686i	0.514613	−	0.514613i	0.915936	+	0.401323i	$0.131450\pi$
$74$	3.12465	+	5.61511i	0.363233	+	0.652744i
$75$		0			0
$76$	0.441090	+	1.88218i	0.0505964	+	0.215900i
$77$			11.1134i			1.26649i
$78$		0			0
$79$	−14.0993			−1.58629			−0.793146	−	0.609032i	$-0.791558\pi$
$79$	−14.0993			−1.58629			−0.793146	+	0.609032i	$0.791558\pi$
$80$	−6.67015	−	5.95895i	−0.745746	−	0.666230i
$81$		0			0
$82$	−6.26848	+	3.48822i	−0.692238	+	0.385210i
$83$			2.75725i			0.302648i	0.988484	+	0.151324i	$0.0483536\pi$
$83$			2.75725i			0.302648i	−0.988484	+	0.151324i	$0.951646\pi$
$84$		0			0
$85$	5.05819	−	11.8271i	0.548638	−	1.28283i
$86$	0.584347	+	1.05009i	0.0630117	+	0.113235i
$87$		0			0
$88$	−5.79805	+	5.27285i	−0.618074	+	0.562088i
$89$	11.6448			1.23435			0.617173	−	0.786828i	$-0.288278\pi$
$89$	11.6448			1.23435			0.617173	+	0.786828i	$0.288278\pi$
$90$		0			0
$91$	−5.82797	+	5.82797i	−0.610937	+	0.610937i
$92$	−13.6318	+	3.19462i	−1.42121	+	0.333062i
$93$		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	−0.863204	−	0.504855i	$-0.831546\pi$
$97$	−3.52933	+	3.52933i	−0.358349	+	0.358349i	0.504855	+	0.863204i	$0.331546\pi$
$98$	−11.2293	+	6.24876i	−1.13433	+	0.631220i
$99$		0			0
$100$	2.05837	+	9.78586i	0.205837	+	0.978586i
$101$	−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	0.866433	−	0.499294i	$-0.166407\pi$
$103$	3.72605	+	3.72605i	0.367139	+	0.367139i	−0.499294	+	0.866433i	$0.666407\pi$
$104$	−5.80568	−	0.275419i	−0.569294	−	0.0270070i
$105$		0			0
$106$	−6.39637	+	3.55939i	−0.621271	+	0.345719i
$107$			16.4605i			1.59130i	0.605758	+	0.795649i	$0.292870\pi$
$107$			16.4605i			1.59130i	−0.605758	+	0.795649i	$0.707130\pi$
$108$		0			0
$109$	12.8554	+	12.8554i	1.23133	+	1.23133i	0.963455	+	0.267870i	$0.0863199\pi$
$109$	12.8554	+	12.8554i	1.23133	+	1.23133i	0.267870	+	0.963455i	$0.413680\pi$
$110$	8.71512	−	0.906656i	0.830955	−	0.0864463i
$111$		0			0
$112$	−15.2035	−	5.12287i	−1.43660	−	0.484065i
$113$	−0.863630	−	0.863630i	−0.0812435	−	0.0812435i	0.665317	−	0.746561i	$-0.268296\pi$
$113$	−0.863630	−	0.863630i	−0.0812435	−	0.0812435i	−0.746561	+	0.665317i	$0.768296\pi$
$114$		0			0
$115$	14.3927	+	6.15546i	1.34213	+	0.573999i
$116$	−2.30065	+	0.539159i	−0.213610	+	0.0500596i
$117$		0			0
$118$	−2.28189	+	8.00779i	−0.210065	+	0.737177i
$119$		−	23.0730i		−	2.11510i
$120$		0			0
$121$			3.32246i			0.302042i
$122$	−10.6886	−	3.04582i	−0.967703	−	0.275755i
$123$		0			0
$124$	−4.01066	−	2.48775i	−0.360168	−	0.223406i
$125$	4.63041	−	10.1764i	0.414156	−	0.910206i
$126$		0			0
$127$	11.7944	+	11.7944i	1.04659	+	1.04659i	0.998860	+	0.0477265i	$0.0151976\pi$
$127$	11.7944	+	11.7944i	1.04659	+	1.04659i	0.0477265	+	0.998860i	$0.484802\pi$
$128$	−4.54075	−	10.3625i	−0.401349	−	0.915925i
$129$		0			0
$130$	5.04575	+	4.09483i	0.442541	+	0.359140i
$131$	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
$133$		−	3.87683i		−	0.336163i
$134$	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	$-0.225087\pi$
$137$	1.29423	+	1.29423i	0.110573	+	0.110573i	−0.649655	+	0.760229i	$0.725087\pi$
$138$		0			0
$139$	−8.61413	−	8.61413i	−0.730641	−	0.730641i	0.240106	−	0.970747i	$-0.422818\pi$
$139$	−8.61413	−	8.61413i	−0.730641	−	0.730641i	−0.970747	+	0.240106i	$0.922818\pi$
$140$	10.2970	+	14.6871i	0.870253	+	1.24129i
$141$		0			0
$142$	1.60588	+	2.88583i	0.134762	+	0.242173i
$143$	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
$148$	4.79025	−	7.72265i	0.393756	−	0.634798i
$149$	0.0806133	−	0.0806133i	0.00660410	−	0.00660410i	−0.703797	−	0.710401i	$-0.748514\pi$
$149$	0.0806133	−	0.0806133i	0.00660410	−	0.00660410i	0.710401	+	0.703797i	$0.248514\pi$
$150$		0			0
$151$	−3.25198			−0.264643			−0.132321	−	0.991207i	$-0.542243\pi$
$151$	−3.25198			−0.264643			−0.132321	+	0.991207i	$0.542243\pi$
$152$	2.02260	−	1.83939i	0.164055	−	0.149194i
$153$		0			0
$154$	13.7336	−	7.64232i	1.10668	−	0.615836i
$155$	1.96338	+	4.89775i	0.157703	+	0.393397i
$156$		0			0
$157$			9.06652i			0.723587i	0.932258	+	0.361793i	$0.117835\pi$
$157$			9.06652i			0.723587i	−0.932258	+	0.361793i	$0.882165\pi$
$158$	9.69559	+	17.4234i	0.771340	+	1.38613i
$159$		0			0
$160$	−2.77701	+	12.3405i	−0.219542	+	0.975603i
$161$	28.0782			2.21287
$162$		0			0
$163$			3.93313i			0.308067i	0.988066	+	0.154033i	$0.0492263\pi$
$163$			3.93313i			0.308067i	−0.988066	+	0.154033i	$0.950774\pi$
$164$	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	−0.947888	−	0.318603i	$-0.896786\pi$
$167$	−8.13216	+	8.13216i	−0.629285	+	0.629285i	0.318603	+	0.947888i	$0.396786\pi$
$168$		0			0
$169$	−8.77728			−0.675175
$170$	−18.0938	+	1.88235i	−1.38773	+	0.144369i
$171$		0			0
$172$	0.895834	−	1.44423i	0.0683067	−	0.110121i
$173$	−6.86735			−0.522115			−0.261057	−	0.965323i	$-0.584071\pi$
$173$	−6.86735			−0.522115			−0.261057	+	0.965323i	$0.584071\pi$
$174$		0			0
$175$	0.458751	−	20.0490i	0.0346784	−	1.51556i
$176$	10.5031	+	3.53906i	0.791703	+	0.266767i
$177$		0			0
$178$	−8.00774	−	14.3902i	−0.600205	−	1.07859i
$179$	−15.7117	+	15.7117i	−1.17435	+	1.17435i	−0.193183	+	0.981163i	$0.561881\pi$
$179$	−15.7117	+	15.7117i	−1.17435	+	1.17435i	−0.981163	+	0.193183i	$0.938119\pi$
$180$		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	$-0.511020\pi$
$182$	11.2097	+	3.19430i	0.830919	+	0.236777i
$183$		0			0
$184$	13.3219	+	14.6489i	0.982106	+	1.07993i
$185$	−9.43078	+	3.78056i	−0.693365	+	0.277953i
$186$		0			0
$187$			15.9397i			1.16562i
$188$	7.50818	−	1.75955i	0.547591	−	0.128328i
$189$		0			0
$190$	−3.04020	+	0.316280i	−0.220559	+	0.0229454i
$191$		−	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	0.998842	−	0.0481079i	$-0.0153191\pi$
$193$	13.2080	+	13.2080i	0.950734	+	0.950734i	−0.0481079	+	0.998842i	$0.515319\pi$
$194$	6.78843	+	1.93442i	0.487381	+	0.138883i
$195$		0			0
$196$	15.4440	+	9.57968i	1.10314	+	0.684263i
$197$	−15.2437			−1.08607			−0.543036	−	0.839709i	$-0.682725\pi$
$197$	−15.2437			−1.08607			−0.543036	+	0.839709i	$0.682725\pi$
$198$		0			0
$199$		−	4.98761i		−	0.353562i	−0.984250	−	0.176781i	$-0.943432\pi$
$199$		−	4.98761i		−	0.353562i	0.984250	−	0.176781i	$-0.0565684\pi$
$200$	10.6775	−	9.27308i	0.755017	−	0.655706i
$201$		0			0
$202$	−4.05300	+	14.2231i	−0.285168	+	1.00074i
$203$	4.73878			0.332597
$204$		0			0
$205$	−4.22046	−	10.5281i	−0.294770	−	0.735316i
$206$	2.04224	−	7.16680i	0.142290	−	0.499335i
$207$		0			0
$208$	3.65202	+	7.36385i	0.253222	+	0.510591i
$209$			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	$0.581380\pi$
$212$	8.79715	+	5.45674i	0.604191	+	0.374770i
$213$		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
$218$	7.04603	−	24.7265i	0.477217	−	1.67469i
$219$		0			0
$220$	−7.11352	−	10.1464i	−0.479593	−	0.684068i
$221$	−8.35890	+	8.35890i	−0.562280	+	0.562280i
$222$		0			0
$223$	−1.49853	+	1.49853i	−0.100349	+	0.100349i	−0.755499	−	0.655150i	$-0.772605\pi$
$223$	−1.49853	+	1.49853i	−0.100349	+	0.100349i	0.655150	+	0.755499i	$0.272605\pi$
$224$	4.12429	+	22.3108i	0.275566	+	1.49070i
$225$		0			0
$226$	−0.473354	+	1.66113i	−0.0314870	+	0.110497i
$227$	15.6346			1.03771			0.518853	−	0.854864i	$-0.326359\pi$
$227$	15.6346			1.03771			0.518853	+	0.854864i	$0.326359\pi$
$228$		0			0
$229$	−9.74097	+	9.74097i	−0.643702	+	0.643702i	−0.951463	−	0.307762i	$-0.900420\pi$
$229$	−9.74097	+	9.74097i	−0.643702	+	0.643702i	0.307762	+	0.951463i	$0.400420\pi$
$230$	−2.29068	−	22.0189i	−0.151043	−	1.45188i
$231$		0			0
$232$	2.24835	+	2.47230i	0.147612	+	0.162314i
$233$	−0.509123	+	0.509123i	−0.0333538	+	0.0333538i	−0.723587	−	0.690233i	$-0.757508\pi$
$233$	−0.509123	+	0.509123i	−0.0333538	+	0.0333538i	0.690233	+	0.723587i	$0.257508\pi$
$234$		0			0
$235$	−7.92727	−	3.39033i	−0.517118	−	0.221161i
$236$	11.4649	−	2.68681i	0.746303	−	0.174897i
$237$		0			0
$238$	−28.5128	+	15.8665i	−1.84821	+	1.02847i
$239$	−8.19486			−0.530081			−0.265041	−	0.964237i	$-0.585385\pi$
$239$	−8.19486			−0.530081			−0.265041	+	0.964237i	$0.585385\pi$
$240$		0			0
$241$	5.66775			0.365092			0.182546	−	0.983197i	$-0.441566\pi$
$241$	5.66775			0.365092			0.182546	+	0.983197i	$0.441566\pi$
$242$	4.10578	−	2.28474i	0.263929	−	0.146869i
$243$		0			0
$244$	3.58630	+	15.3031i	0.229590	+	0.979683i
$245$	−7.56048	−	18.8600i	−0.483022	−	1.20492i
$246$		0			0
$247$	−1.40450	+	1.40450i	−0.0893661	+	0.0893661i
$248$	−0.316278	+	6.66697i	−0.0200837	+	0.423353i
$249$		0			0
$250$	−15.7598	+	1.27589i	−0.996739	+	0.0806942i
$251$	−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
$253$	−19.3974			−1.21951
$254$	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	−0.810715	−	0.585440i	$-0.800922\pi$
$257$	−3.61143	+	3.61143i	−0.225275	+	0.225275i	0.585440	+	0.810715i	$0.300922\pi$
$258$		0			0
$259$	−12.8868	+	12.8868i	−0.800745	+	0.800745i
$260$	1.59045	−	9.05124i	0.0986358	−	0.561334i
$261$		0			0
$262$	8.75617	−	30.7279i	0.540958	−	1.89838i
$263$	6.80041	+	6.80041i	0.419331	+	0.419331i	0.884973	−	0.465642i	$-0.154177\pi$
$263$	6.80041	+	6.80041i	0.419331	+	0.419331i	−0.465642	+	0.884973i	$0.654177\pi$
$264$		0			0
$265$	−4.30657	−	10.7429i	−0.264551	−	0.659933i
$266$	−4.79084	+	2.66596i	−0.293746	+	0.163461i
$267$		0			0
$268$	1.83023	−	2.95063i	0.111799	−	0.180238i
$269$	1.20010	+	1.20010i	0.0731711	+	0.0731711i	0.742745	−	0.669574i	$-0.233523\pi$
$269$	1.20010	+	1.20010i	0.0731711	+	0.0731711i	−0.669574	+	0.742745i	$0.733523\pi$
$270$		0			0
$271$			2.79591i			0.169840i	0.996388	+	0.0849199i	$0.0270634\pi$
$271$			2.79591i			0.169840i	−0.996388	+	0.0849199i	$0.972937\pi$
$272$	−21.8060	−	7.34759i	−1.32218	−	0.445513i
$273$		0			0
$274$	0.709364	−	2.48936i	0.0428543	−	0.150388i
$275$	−0.316922	+	13.8506i	−0.0191111	+	0.835220i
$276$		0			0
$277$	13.8115			0.829852			0.414926	−	0.909855i	$-0.363807\pi$
$277$	13.8115			0.829852			0.414926	+	0.909855i	$0.363807\pi$
$278$	−4.72139	+	16.5687i	−0.283170	+	0.993724i
$279$		0			0
$280$	11.0689	−	22.8244i	0.661493	−	1.36402i
$281$			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
$283$	25.2988			1.50386			0.751930	−	0.659243i	$-0.229123\pi$
$283$	25.2988			1.50386			0.751930	+	0.659243i	$0.229123\pi$
$284$	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
$290$	−0.386600	−	3.71614i	−0.0227019	−	0.218219i
$291$		0			0
$292$	2.83755	+	12.1081i	0.166055	+	0.708575i
$293$			14.1276i			0.825344i	0.910880	+	0.412672i	$0.135404\pi$
$293$			14.1276i			0.825344i	−0.910880	+	0.412672i	$0.864596\pi$
$294$		0			0
$295$	−12.1049	−	5.17700i	−0.704773	−	0.301417i
$296$	−12.8375	−	0.609004i	−0.746163	−	0.0353976i
$297$		0			0
$298$	−0.155054	−	0.0441840i	−0.00898204	−	0.00255951i
$299$	−10.1722	−	10.1722i	−0.588272	−	0.588272i
$300$		0			0
$301$	−2.40998	+	2.40998i	−0.138909	+	0.138909i
$302$	2.23628	+	4.01869i	0.128683	+	0.231249i
$303$		0			0
$304$	−3.66393	−	1.23457i	−0.210141	−	0.0708076i
$305$	6.91016	−	16.1573i	0.395674	−	0.925166i
$306$		0			0
$307$	−22.6081			−1.29031			−0.645156	−	0.764051i	$-0.723208\pi$
$307$	−22.6081			−1.29031			−0.645156	+	0.764051i	$0.723208\pi$
$308$	−18.8882	−	11.7161i	−1.07626	−	0.667586i
$309$		0			0
$310$	4.70231	−	5.79430i	0.267073	−	0.329094i
$311$	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	0.186727	−	0.982412i	$-0.440212\pi$
$313$	20.6842	−	20.6842i	1.16914	−	1.16914i	0.982412	−	0.186727i	$-0.0597879\pi$
$314$	11.2041	−	6.23474i	0.632283	−	0.351847i
$315$		0			0
$316$	14.8639	−	23.9629i	0.836157	−	1.34802i
$317$			23.8207i			1.33791i	0.743305	+	0.668953i	$0.233257\pi$
$317$			23.8207i			1.33791i	−0.743305	+	0.668953i	$0.766743\pi$
$318$		0			0
$319$	−3.27372			−0.183293
$320$	17.1596	−	5.05442i	0.959252	−	0.282551i
$321$		0			0
$322$	−19.3084	−	34.6980i	−1.07602	−	1.93365i
$323$		−	5.56042i		−	0.309390i
$324$		0			0
$325$	−7.42956	+	7.09716i	−0.412118	+	0.393680i
$326$	4.86043	−	2.70469i	0.269194	−	0.149799i
$327$		0			0
$328$	0.679866	−	14.3312i	0.0375393	−	0.791309i
$329$	−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	$0.971085\pi$
$332$	−4.68619	−	2.90677i	−0.257188	−	0.159530i
$333$		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	−0.480821	−	0.876819i	$-0.659661\pi$
$337$	7.26955	−	7.26955i	0.395998	−	0.395998i	0.876819	+	0.480821i	$0.159661\pi$
$338$	6.03584	+	10.8467i	0.328307	+	0.589980i
$339$		0			0
$340$	14.7687	+	21.0653i	0.800943	+	1.14243i
$341$	−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
$347$		−	23.4667i		−	1.25976i	−0.776692	−	0.629880i	$-0.783104\pi$
$347$		−	23.4667i		−	1.25976i	0.776692	−	0.629880i	$-0.216896\pi$
$348$		0			0
$349$	−23.2089	−	23.2089i	−1.24234	−	1.24234i	−0.959027	−	0.283315i	$-0.908566\pi$
$349$	−23.2089	−	23.2089i	−1.24234	−	1.24234i	−0.283315	−	0.959027i	$-0.591434\pi$
$350$	−25.0913	+	13.2201i	−1.34119	+	0.706645i
$351$		0			0
$352$	−2.84921	−	15.4131i	−0.151863	−	0.821521i
$353$	13.3220	+	13.3220i	0.709059	+	0.709059i	0.966337	−	0.257278i	$-0.0828256\pi$
$353$	13.3220	+	13.3220i	0.709059	+	0.709059i	−0.257278	+	0.966337i	$0.582826\pi$
$354$		0			0
$355$	−4.84685	+	1.94298i	−0.257244	+	0.103123i
$356$	−12.2763	+	19.7914i	−0.650642	+	1.04894i
$357$		0			0
$358$	30.2203	+	8.61154i	1.59719	+	0.455134i
$359$			26.9902i			1.42449i	0.701932	+	0.712244i	$0.252321\pi$
$359$			26.9902i			1.42449i	−0.701932	+	0.712244i	$0.747679\pi$
$360$		0			0
$361$			18.0657i			0.950827i
$362$	−7.62473	+	26.7573i	−0.400747	+	1.40633i
$363$		0			0
$364$	−3.76114	−	16.0492i	−0.197137	−	0.841205i
$365$	5.46745	−	12.7840i	0.286179	−	0.669145i
$366$		0			0
$367$	−19.4758	−	19.4758i	−1.01663	−	1.01663i	−0.999859	−	0.0167684i	$-0.994662\pi$
$367$	−19.4758	−	19.4758i	−1.01663	−	1.01663i	−0.0167684	−	0.999859i	$-0.505338\pi$
$368$	8.94148	−	26.5363i	0.466107	−	1.38330i
$369$		0			0
$370$	11.1571	+	9.05446i	0.580031	+	0.470719i
$371$	−14.6798	−	14.6798i	−0.762136	−	0.762136i
$372$		0			0
$373$			4.87069i			0.252195i	0.992018	+	0.126097i	$0.0402452\pi$
$373$			4.87069i			0.252195i	−0.992018	+	0.126097i	$0.959755\pi$
$374$	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	0.769432	−	0.638729i	$-0.220540\pi$
$379$	2.54450	+	2.54450i	0.130702	+	0.130702i	−0.638729	+	0.769432i	$0.720540\pi$
$380$	2.48149	+	3.53948i	0.127298	+	0.181571i
$381$		0			0
$382$	−12.7769	+	7.10996i	−0.653723	+	0.363777i
$383$	−0.193238	+	0.193238i	−0.00987399	+	0.00987399i	−0.712027	−	0.702153i	$-0.752222\pi$
$383$	−0.193238	+	0.193238i	−0.00987399	+	0.00987399i	0.702153	+	0.712027i	$0.252222\pi$
$384$		0			0
$385$	9.24658	+	23.0660i	0.471249	+	1.17555i
$386$	7.23929	−	25.4047i	0.368470	−	1.29307i
$387$		0			0
$388$	−2.27769	−	9.71914i	−0.115632	−	0.493414i
$389$	−2.01528	+	2.01528i	−0.102179	+	0.102179i	−0.756348	−	0.654169i	$-0.773018\pi$
$389$	−2.01528	+	2.01528i	−0.102179	+	0.102179i	0.654169	+	0.756348i	$0.273018\pi$
$390$		0			0
$391$	40.2718			2.03663
$392$	1.21790	−	25.6728i	0.0615134	−	1.29667i
$393$		0			0
$394$	10.4826	+	18.8377i	0.528107	+	0.949029i
$395$	−29.2632	+	11.7309i	−1.47239	+	0.590244i
$396$		0			0
$397$			21.5509i			1.08161i	0.841149	+	0.540804i	$0.181880\pi$
$397$			21.5509i			1.08161i	−0.841149	+	0.540804i	$0.818120\pi$
$398$	−6.16351	+	3.42981i	−0.308949	+	0.171921i
$399$		0			0
$400$	−18.8019	−	6.81815i	−0.940097	−	0.340908i
$401$	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
$403$		−	4.84917i		−	0.241555i
$404$	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	$-0.502603\pi$
$409$	−0.330732			−0.0163536			−0.00817682	+	0.999967i	$0.502603\pi$
$410$	−10.1080	+	12.4553i	−0.499199	+	0.615125i
$411$		0			0
$412$	−10.2609	+	2.40464i	−0.505516	+	0.118468i
$413$	−23.6150			−1.16202
$414$		0			0
$415$	2.29409	+	5.72270i	0.112612	+	0.280917i
$416$	6.58861	−	9.57691i	0.323033	−	0.469547i
$417$		0			0
$418$	3.30969	−	1.84174i	0.161882	−	0.0900826i
$419$	6.71354	−	6.71354i	0.327978	−	0.327978i	−0.523839	−	0.851817i	$-0.675501\pi$
$419$	6.71354	−	6.71354i	0.327978	−	0.327978i	0.851817	+	0.523839i	$0.175501\pi$
$420$		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	$0.717051\pi$
$422$	5.68941	−	19.9658i	0.276956	−	0.971918i
$423$		0			0
$424$	0.693737	−	14.6236i	0.0336909	−	0.710186i
$425$	0.657974	−	28.7557i	0.0319164	−	1.39486i
$426$		0			0
$427$		−	31.5208i		−	1.52540i
$428$	−27.9761	−	17.3531i	−1.35228	−	0.838796i
$429$		0			0
$430$	2.08652	+	1.69329i	0.100621	+	0.0816579i
$431$		−	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	0.201414	−	0.979506i	$-0.435446\pi$
$433$	−16.1910	−	16.1910i	−0.778092	−	0.778092i	−0.979506	+	0.201414i	$0.935446\pi$
$434$	3.66818	−	12.8727i	0.176078	−	0.617909i
$435$		0			0
$436$	−35.4015	+	8.29636i	−1.69542	+	0.397324i
$437$	6.76664			0.323692
$438$		0			0
$439$		−	29.3734i		−	1.40191i	−0.713204	−	0.700957i	$-0.752757\pi$
$439$		−	29.3734i		−	1.40191i	0.713204	−	0.700957i	$-0.247243\pi$
$440$	−7.64679	+	15.7679i	−0.364547	+	0.751708i
$441$		0			0
$442$	16.0778	+	4.58150i	0.764741	+	0.217920i
$443$	19.8713			0.944115			0.472057	−	0.881568i	$-0.343511\pi$
$443$	19.8713			0.944115			0.472057	+	0.881568i	$0.343511\pi$
$444$		0			0
$445$	24.1689	−	9.68870i	1.14572	−	0.459288i
$446$	2.88232	+	0.821341i	0.136482	+	0.0388916i
$447$		0			0
$448$	24.7347	−	20.4390i	1.16861	−	0.965654i
$449$		−	16.7577i		−	0.790844i	−0.918500	−	0.395422i	$-0.870598\pi$
$449$		−	16.7577i		−	0.790844i	0.918500	−	0.395422i	$-0.129402\pi$
$450$		0			0
$451$	9.93854	+	9.93854i	0.467987	+	0.467987i
$452$	2.37828	−	0.557352i	0.111865	−	0.0262156i
$453$		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	$-0.302915\pi$
$457$	−5.00267	−	5.00267i	−0.234015	−	0.234015i	−0.814366	+	0.580351i	$0.802915\pi$
$458$	18.7361	+	5.33901i	0.875480	+	0.249475i
$459$		0			0
$460$	−25.6349	+	17.9724i	−1.19523	+	0.837967i
$461$	−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	$-0.652394\pi$
$463$	9.18551	−	9.18551i	0.426887	−	0.426887i	0.887566	+	0.460680i	$0.152394\pi$
$464$	1.50906	−	4.47855i	0.0700564	−	0.207912i
$465$		0			0
$466$	0.979263	+	0.279049i	0.0453635	+	0.0129267i
$467$	1.06405			0.0492385			0.0246193	−	0.999697i	$-0.492163\pi$
$467$	1.06405			0.0492385			0.0246193	+	0.999697i	$0.492163\pi$
$468$		0			0
$469$	−4.92371	+	4.92371i	−0.227356	+	0.227356i
$470$	1.26167	+	12.1277i	0.0581966	+	0.559407i
$471$		0			0
$472$	−11.2043	−	12.3203i	−0.515720	−	0.567088i
$473$	1.66490	−	1.66490i	0.0765523	−	0.0765523i
$474$		0			0
$475$	0.110556	−	4.83166i	0.00507265	−	0.221692i
$476$	39.2146	+	24.3242i	1.79740	+	1.11490i
$477$		0			0
$478$	5.63533	+	10.1269i	0.257754	+	0.463194i
$479$	−15.8658			−0.724926			−0.362463	−	0.931998i	$-0.618064\pi$
$479$	−15.8658			−0.724926			−0.362463	+	0.931998i	$0.618064\pi$
$480$		0			0
$481$	9.33725			0.425742
$482$	−3.89752	−	7.00400i	−0.177527	−	0.319024i
$483$		0			0
$484$	−5.64681	−	3.50263i	−0.256673	−	0.159210i
$485$	−4.38869	+	10.2616i	−0.199280	+	0.465957i
$486$		0			0
$487$	−13.7947	+	13.7947i	−0.625099	+	0.625099i	−0.946831	−	0.321732i	$-0.895735\pi$
$487$	−13.7947	+	13.7947i	−0.625099	+	0.625099i	0.321732	+	0.946831i	$0.395735\pi$
$488$	16.4449	−	14.9553i	0.744426	−	0.676994i
$489$		0			0
$490$	−18.1074	+	22.3123i	−0.818008	+	1.00797i
$491$	−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
$493$	6.79669			0.306108
$494$	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	$-0.490218\pi$
$499$	23.0141	−	23.0141i	1.03025	−	1.03025i	0.999528	−	0.0307258i	$-0.00978185\pi$
$500$	12.4142	+	18.5981i	0.555180	+	0.831730i
$501$		0			0
$502$	28.3675	+	8.08357i	1.26611	+	0.360787i
$503$	−6.63364	−	6.63364i	−0.295780	−	0.295780i	0.543579	−	0.839358i	$-0.317069\pi$
$503$	−6.63364	−	6.63364i	−0.295780	−	0.295780i	−0.839358	+	0.543579i	$0.817069\pi$
$504$		0			0
$505$	−21.5002	−	9.19520i	−0.956748	−	0.409181i
$506$	13.3390	+	23.9706i	0.592989	+	1.06562i
$507$		0			0
$508$	−32.4797	+	7.61165i	−1.44105	+	0.337712i
$509$	−8.04140	−	8.04140i	−0.356429	−	0.356429i	0.506066	−	0.862495i	$-0.331099\pi$
$509$	−8.04140	−	8.04140i	−0.356429	−	0.356429i	−0.862495	+	0.506066i	$0.831099\pi$
$510$		0			0
$511$		−	24.9398i		−	1.10327i
$512$	22.3990	+	3.20705i	0.989905	+	0.141733i
$513$		0			0
$514$	6.94634	+	1.97942i	0.306390	+	0.0873084i
$515$	10.8336	+	4.63331i	0.477386	+	0.204168i
$516$		0			0
$517$	10.6838			0.469873
$518$	24.7868	+	7.06321i	1.08907	+	0.310340i
$519$		0			0
$520$	−12.2789	+	4.25881i	−0.538465	+	0.186761i
$521$			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
$523$	−2.46341			−0.107717			−0.0538587	−	0.998549i	$-0.517152\pi$
$523$	−2.46341			−0.107717			−0.0538587	+	0.998549i	$0.517152\pi$
$524$	−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
$530$	−10.3143	+	12.7095i	−0.448023	+	0.552064i
$531$		0			0
$532$	6.58901	+	4.08706i	0.285670	+	0.177197i
$533$			10.4237i			0.451501i
$534$		0			0
$535$	13.6955	+	34.1640i	0.592107	+	1.47704i
$536$	−4.90487	−	0.232685i	−0.211858	−	0.0100505i
$537$		0			0
$538$	0.657770	−	2.30830i	0.0283585	−	0.0995180i
$539$	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	$0.435205\pi$
$542$	3.45509	−	1.92266i	0.148409	−	0.0825852i
$543$		0			0
$544$	5.91535	+	31.9997i	0.253619	+	1.37198i
$545$	37.3775	+	15.9856i	1.60108	+	0.684747i
$546$		0			0
$547$	43.6742			1.86738			0.933688	−	0.358089i	$-0.116572\pi$
$547$	43.6742			1.86738			0.933688	+	0.358089i	$0.116572\pi$
$548$	−3.56407	+	0.835243i	−0.152250	+	0.0356798i
$549$		0			0
$550$	17.3340	−	9.13293i	0.739123	−	0.389429i
$551$	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
$557$		−	5.18948i		−	0.219885i	−0.993938	−	0.109943i	$-0.964933\pi$
$557$		−	5.18948i		−	0.219885i	0.993938	−	0.109943i	$-0.0350667\pi$
$558$		0			0
$559$	1.74618			0.0738555
$560$	−35.8174	+	2.01706i	−1.51356	+	0.0852362i
$561$		0			0
$562$	8.91874	−	4.96301i	0.376214	−	0.209352i
$563$		−	11.3756i		−	0.479423i	−0.970844	−	0.239711i	$-0.922947\pi$
$563$		−	11.3756i		−	0.479423i	0.970844	−	0.239711i	$-0.0770528\pi$
$564$		0			0
$565$	−2.51103	−	1.07392i	−0.105640	−	0.0451800i
$566$	−17.3972	−	31.2634i	−0.731257	−	1.31410i
$567$		0			0
$568$	−6.59768	−	0.312991i	−0.276833	−	0.0131328i
$569$	7.51787			0.315165			0.157583	−	0.987506i	$-0.449630\pi$
$569$	7.51787			0.315165			0.157583	+	0.987506i	$0.449630\pi$
$570$		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	$0.323838\pi$
$572$	2.59833	+	11.0873i	0.108642	+	0.463585i
$573$		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	−0.881733	−	0.471748i	$-0.843623\pi$
$577$	−9.84819	+	9.84819i	−0.409986	+	0.409986i	0.471748	+	0.881733i	$0.343623\pi$
$578$	−19.8871	+	11.0666i	−0.827195	+	0.460309i
$579$		0			0
$580$	−4.32643	+	3.03321i	−0.179645	+	0.125947i
$581$	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
$587$		−	33.0447i		−	1.36390i	−0.731398	−	0.681951i	$-0.761132\pi$
$587$		−	33.0447i		−	1.36390i	0.731398	−	0.681951i	$-0.238868\pi$
$588$		0			0
$589$	1.61286	+	1.61286i	0.0664567	+	0.0664567i
$590$	1.92656	+	18.5188i	0.0793152	+	0.762408i
$591$		0			0
$592$	8.07532	+	16.2829i	0.331894	+	0.669223i
$593$	−18.5424	−	18.5424i	−0.761445	−	0.761445i	0.215139	−	0.976584i	$-0.430980\pi$
$593$	−18.5424	−	18.5424i	−0.761445	−	0.761445i	−0.976584	+	0.215139i	$0.930980\pi$
$594$		0			0
$595$	−19.1972	−	47.8882i	−0.787008	−	1.96323i
$596$	0.0520245	+	0.221994i	0.00213101	+	0.00909324i
$597$		0			0
$598$	−5.57535	+	19.5655i	−0.227993	+	0.800092i
$599$		−	28.3117i		−	1.15678i	−0.815759	−	0.578392i	$-0.803681\pi$
$599$		−	28.3117i		−	1.15678i	0.815759	−	0.578392i	$-0.196319\pi$
$600$		0			0
$601$			41.7630i			1.70355i	0.523909	+	0.851774i	$0.324473\pi$
$601$			41.7630i			1.70355i	−0.523909	+	0.851774i	$0.675527\pi$
$602$	4.63543	+	1.32091i	0.188926	+	0.0538361i
$603$		0			0
$604$	3.42833	−	5.52703i	0.139497	−	0.224892i
$605$	2.76435	+	6.89579i	0.112387	+	0.280354i
$606$		0			0
$607$	4.01973	+	4.01973i	0.163156	+	0.163156i	0.783963	−	0.620807i	$-0.213195\pi$
$607$	4.01973	+	4.01973i	0.163156	+	0.163156i	−0.620807	+	0.783963i	$0.713195\pi$
$608$	0.993923	+	5.37674i	0.0403089	+	0.218055i
$609$		0			0
$610$	−24.7185	+	2.57153i	−1.00082	+	0.104118i
$611$	5.60268	+	5.60268i	0.226660	+	0.226660i
$612$		0			0
$613$			21.5230i			0.869305i	0.900598	+	0.434652i	$0.143129\pi$
$613$			21.5230i			0.869305i	−0.900598	+	0.434652i	$0.856871\pi$
$614$	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	0.997702	+	0.0677580i	$0.0215846\pi$
$617$	26.4655	+	26.4655i	1.06546	+	1.06546i	0.0677580	+	0.997702i	$0.478415\pi$
$618$		0			0
$619$	21.7935	+	21.7935i	0.875955	+	0.875955i	0.993113	−	0.117158i	$-0.0373784\pi$
$619$	21.7935	+	21.7935i	0.875955	+	0.875955i	−0.117158	+	0.993113i	$0.537378\pi$
$620$	−10.3940	−	1.82640i	−0.417434	−	0.0733501i
$621$		0			0
$622$	−7.42010	−	13.3342i	−0.297519	−	0.534653i
$623$	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
$628$	−15.4093	−	9.55818i	−0.614900	−	0.381413i
$629$	−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	$0.823852\pi$
$632$	−39.8339	−	1.88970i	−1.58451	−	0.0751683i
$633$		0			0
$634$	29.4368	−	16.3807i	1.16909	−	0.650562i
$635$	34.2927	+	14.6663i	1.36086	+	0.582013i
$636$		0			0
$637$			18.6729i			0.739848i
$638$	2.25123	+	4.04554i	0.0891269	+	0.160165i
$639$		0			0
$640$	−18.0462	−	17.7295i	−0.713338	−	0.700820i
$641$	−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
$643$		−	31.3531i		−	1.23645i	−0.786002	−	0.618224i	$-0.787853\pi$
$643$		−	31.3531i		−	1.23645i	0.786002	−	0.618224i	$-0.212147\pi$
$644$	−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	−0.0536292	−	0.998561i	$-0.517079\pi$
$647$	24.0355	−	24.0355i	0.944932	−	0.944932i	0.998561	+	0.0536292i	$0.0170789\pi$
$648$		0			0
$649$	16.3141			0.640383
$650$	13.8795	+	4.30070i	0.544398	+	0.168687i
$651$		0			0
$652$	−6.68471	−	4.14642i	−0.261793	−	0.162387i
$653$	−15.4153			−0.603248			−0.301624	−	0.953427i	$-0.597529\pi$
$653$	−15.4153			−0.603248			−0.301624	+	0.953427i	$0.597529\pi$
$654$		0			0
$655$	46.4494	+	19.8654i	1.81493	+	0.776207i
$656$	−18.1775	+	9.01495i	−0.709714	+	0.351975i
$657$		0			0
$658$	10.6348	+	19.1111i	0.414587	+	0.745030i
$659$	30.4355	−	30.4355i	1.18560	−	1.18560i	0.207327	−	0.978272i	$-0.433524\pi$
$659$	30.4355	−	30.4355i	1.18560	−	1.18560i	0.978272	−	0.207327i	$-0.0664763\pi$
$660$		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	$0.849863\pi$
$662$	38.0240	+	10.8352i	1.47784	+	0.421124i
$663$		0			0
$664$	−0.369550	+	7.78992i	−0.0143413	+	0.302308i
$665$	−3.22560	−	8.04639i	−0.125083	−	0.312026i
$666$		0			0
$667$			8.27109i			0.320258i
$668$	−5.24817	−	22.3945i	−0.203058	−	0.866469i
$669$		0			0
$670$	4.26285	+	3.45948i	0.164688	+	0.133651i
$671$			21.7757i			0.840640i
$672$		0			0
$673$	−29.2965	−	29.2965i	−1.12930	−	1.12930i	−0.990291	−	0.139006i	$-0.955609\pi$
$673$	−29.2965	−	29.2965i	−1.12930	−	1.12930i	−0.139006	−	0.990291i	$-0.544391\pi$
$674$	−13.9825	−	3.98443i	−0.538585	−	0.153474i
$675$		0			0
$676$	9.25326	−	14.9178i	0.355895	−	0.573760i
$677$	−2.74511			−0.105503			−0.0527516	−	0.998608i	$-0.516799\pi$
$677$	−2.74511			−0.105503			−0.0527516	+	0.998608i	$0.516799\pi$
$678$		0			0
$679$			20.0191i			0.768261i
$680$	15.8758	−	32.7365i	0.608810	−	1.25539i
$681$		0			0
$682$	−2.53411	+	8.89292i	−0.0970362	+	0.340528i
$683$	33.0796			1.26576			0.632878	−	0.774251i	$-0.281873\pi$
$683$	33.0796			1.26576			0.632878	+	0.774251i	$0.281873\pi$
$684$		0			0
$685$	3.76301	+	1.60936i	0.143777	+	0.0614905i
$686$	−3.24401	+	11.3841i	−0.123857	+	0.434648i
$687$		0			0
$688$	1.51018	+	3.04510i	0.0575752	+	0.116093i
$689$			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	$-0.561140\pi$
$692$	7.23976	−	11.6717i	0.275214	−	0.443690i
$693$		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
$698$	−12.7207	+	44.6407i	−0.481487	+	1.68967i
$699$		0			0
$700$	33.5914	+	21.9159i	1.26964	+	0.828344i
$701$	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
$707$	−41.9440			−1.57747
$708$		0			0
$709$	−7.09244	+	7.09244i	−0.266362	+	0.266362i	−0.827632	−	0.561270i	$-0.810313\pi$
$709$	−7.09244	+	7.09244i	−0.266362	+	0.266362i	0.561270	+	0.827632i	$0.310313\pi$
$710$	5.73408	+	4.65344i	0.215196	+	0.174641i
$711$		0			0
$712$	32.8995	+	1.56073i	1.23296	+	0.0584910i
$713$	−11.6812	+	11.6812i	−0.437466	+	0.437466i
$714$		0			0
$715$	5.00651	−	11.7062i	0.187233	−	0.437788i
$716$	−10.1397	−	43.2671i	−0.378938	−	1.61697i
$717$		0			0
$718$	33.3535	−	18.5603i	1.24474	−	0.692663i
$719$	−30.2949			−1.12981			−0.564905	−	0.825156i	$-0.691087\pi$
$719$	−30.2949			−1.12981			−0.564905	+	0.825156i	$0.691087\pi$
$720$		0			0
$721$	21.1349			0.787104
$722$	22.3250	−	12.4232i	0.830849	−	0.462343i
$723$		0			0
$724$	38.3090	−	8.97776i	1.42374	−	0.333656i
$725$	5.90590	+	0.135136i	0.219340	+	0.00501883i
$726$		0			0
$727$	15.9503	−	15.9503i	0.591566	−	0.591566i	−0.346489	−	0.938054i	$-0.612626\pi$
$727$	15.9503	−	15.9503i	0.591566	−	0.591566i	0.938054	+	0.346489i	$0.112626\pi$
$728$	−17.2466	+	15.6844i	−0.639201	+	0.581301i
$729$		0			0
$730$	−19.5578	+	2.03465i	−0.723866	+	0.0753056i
$731$	−3.45657	+	3.45657i	−0.127846	+	0.127846i
$732$		0			0
$733$	35.8535			1.32428			0.662140	−	0.749380i	$-0.269648\pi$
$733$	35.8535			1.32428			0.662140	+	0.749380i	$0.269648\pi$
$734$	−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	−0.981358	−	0.192190i	$-0.938441\pi$
$739$	−21.4532	+	21.4532i	−0.789168	+	0.789168i	0.192190	+	0.981358i	$0.438441\pi$
$740$	3.51680	−	20.0140i	0.129280	−	0.735730i
$741$		0			0
$742$	−8.04595	+	28.2355i	−0.295376	+	1.03656i
$743$	−13.0311	−	13.0311i	−0.478063	−	0.478063i	0.426449	−	0.904512i	$-0.359765\pi$
$743$	−13.0311	−	13.0311i	−0.478063	−	0.478063i	−0.904512	+	0.426449i	$0.859765\pi$
$744$		0			0
$745$	0.100242	−	0.234385i	0.00367258	−	0.00858722i
$746$	6.01903	−	3.34941i	0.220372	−	0.122631i
$747$		0			0
$748$	−27.0909	−	16.8040i	−0.990540	−	0.614417i
$749$	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	$-0.134575\pi$
$752$	−4.92483	+	14.6158i	−0.179590	+	0.532983i
$753$		0			0
$754$	−0.940956	+	3.30208i	−0.0342676	+	0.120255i
$755$	−6.74952	+	2.70571i	−0.245640	+	0.0984710i
$756$		0			0
$757$	15.8781			0.577100			0.288550	−	0.957465i	$-0.406827\pi$
$757$	15.8781			0.577100			0.288550	+	0.957465i	$0.406827\pi$
$758$	1.39464	−	4.89418i	0.0506555	−	0.177764i
$759$		0			0
$760$	2.66752	−	5.50052i	0.0967613	−	0.199525i
$761$		−	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
$763$	72.9184			2.63982
$764$	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	$0.0462978\pi$
$769$			8.03843i			0.289873i	−0.989441	+	0.144937i	$0.953702\pi$
$770$	22.1456	−	27.2883i	0.798071	−	0.983403i
$771$		0			0
$772$	−36.3725	+	8.52392i	−1.30907	+	0.306783i
$773$		−	40.5118i		−	1.45711i	−0.684988	−	0.728554i	$-0.740193\pi$
$773$		−	40.5118i		−	1.45711i	0.684988	−	0.728554i	$-0.259807\pi$
$774$		0			0
$775$	8.15005	+	8.53175i	0.292758	+	0.306470i
$776$	−10.4443	+	9.49821i	−0.374928	+	0.340966i
$777$		0			0
$778$	3.87625	+	1.10457i	0.138970	+	0.0396008i
$779$	−3.46698	−	3.46698i	−0.124217	−	0.124217i
$780$		0			0
$781$	4.57542	−	4.57542i	0.163721	−	0.163721i
$782$	−27.6935	−	49.7664i	−0.990319	−	1.77964i
$783$		0			0
$784$	−32.5630	+	16.1493i	−1.16296	+	0.576760i
$785$	7.54352	+	18.8176i	0.269240	+	0.671631i
$786$		0			0
$787$	15.8333			0.564396			0.282198	−	0.959356i	$-0.408937\pi$
$787$	15.8333			0.564396			0.282198	+	0.959356i	$0.408937\pi$
$788$	16.0704	−	25.9081i	0.572484	−	0.922938i
$789$		0			0
$790$	34.6199	+	28.0955i	1.23172	+	0.999592i
$791$	−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
$797$		−	10.2670i		−	0.363674i	−0.983329	−	0.181837i	$-0.941796\pi$
$797$		−	10.2670i		−	0.363674i	0.983329	−	0.181837i	$-0.0582044\pi$
$798$		0			0
$799$	−22.1811			−0.784710
$800$	4.50383	+	27.9234i	0.159235	+	0.987241i
$801$		0			0
$802$	−7.14932	−	12.8476i	−0.252451	−	0.453665i
$803$			17.2293i			0.608010i
$804$		0			0
$805$	58.2766	−	23.3616i	2.05398	−	0.823388i
$806$	−5.99244	+	3.33462i	−0.211075	+	0.117457i
$807$		0			0
$808$	−19.9007	−	21.8829i	−0.700104	−	0.769837i
$809$	9.16442			0.322204			0.161102	−	0.986938i	$-0.448495\pi$
$809$	9.16442			0.322204			0.161102	+	0.986938i	$0.448495\pi$
$810$		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	$0.435557\pi$
$812$	−4.99575	+	8.05397i	−0.175317	+	0.282639i
$813$		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
$818$	0.227433	+	0.408707i	0.00795202	+	0.0142901i
$819$		0			0
$820$	22.3428	+	3.92601i	0.780245	+	0.137102i
$821$	−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	−0.970255	−	0.242084i	$-0.922169\pi$
$823$	−34.7796	−	34.7796i	−1.21234	−	1.21234i	−0.242084	−	0.970255i	$-0.577831\pi$
$824$	10.0276	+	11.0264i	0.349329	+	0.384123i
$825$		0			0
$826$	16.2392	+	29.1825i	0.565035	+	1.01539i
$827$			16.5717i			0.576253i	0.957592	+	0.288127i	$0.0930324\pi$
$827$			16.5717i			0.576253i	−0.957592	+	0.288127i	$0.906968\pi$
$828$		0			0
$829$	−11.9869	−	11.9869i	−0.416321	−	0.416321i	0.467613	−	0.883933i	$-0.345114\pi$
$829$	−11.9869	−	11.9869i	−0.416321	−	0.416321i	−0.883933	+	0.467613i	$0.845114\pi$
$830$	5.49435	−	6.77027i	0.190712	−	0.234999i
$831$		0			0
$832$	−16.3656	−	1.55625i	−0.567374	−	0.0539534i
$833$	−36.9631	−	36.9631i	−1.28070	−	1.28070i
$834$		0			0
$835$	−10.1123	+	23.6445i	−0.349949	+	0.818252i
$836$	−4.55192	−	2.82349i	−0.157432	−	0.0976524i
$837$		0			0
$838$	−12.9130	−	3.67968i	−0.446073	−	0.127112i
$839$			4.44215i			0.153360i	0.997056	+	0.0766800i	$0.0244320\pi$
$839$			4.44215i			0.153360i	−0.997056	+	0.0766800i	$0.975568\pi$
$840$		0			0
$841$		−	27.6041i		−	0.951865i
$842$	1.64337	−	5.76704i	0.0566341	−	0.198745i
$843$		0			0
$844$	−28.5854	+	6.69902i	−0.983951	+	0.230590i
$845$	−18.2173	+	7.30287i	−0.626695	+	0.251226i
$846$		0			0
$847$	9.42281	+	9.42281i	0.323772	+	0.323772i
$848$	−18.5484	+	9.19888i	−0.636955	+	0.315891i
$849$		0			0
$850$	−35.9878	+	18.9612i	−1.23437	+	0.650365i
$851$	−22.4926	−	22.4926i	−0.771038	−	0.771038i
$852$		0			0
$853$			35.6748i			1.22148i	0.791830	+	0.610742i	$0.209129\pi$
$853$			35.6748i			1.22148i	−0.791830	+	0.610742i	$0.790871\pi$
$854$	−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	$-0.141364\pi$
$857$	13.8568	+	13.8568i	0.473340	+	0.473340i	−0.429654	+	0.902994i	$0.641364\pi$
$858$		0			0
$859$	−19.4217	−	19.4217i	−0.662660	−	0.662660i	0.293346	−	0.956006i	$-0.405231\pi$
$859$	−19.4217	−	19.4217i	−0.662660	−	0.662660i	−0.956006	+	0.293346i	$0.905231\pi$
$860$	0.657684	−	3.74287i	0.0224269	−	0.127631i
$861$		0			0
$862$	−24.6595	+	13.7223i	−0.839906	+	0.467383i
$863$	−9.22041	+	9.22041i	−0.313866	+	0.313866i	−0.846405	−	0.532539i	$-0.821238\pi$
$863$	−9.22041	+	9.22041i	−0.313866	+	0.313866i	0.532539	+	0.846405i	$0.321238\pi$
$864$		0			0
$865$	−14.2532	+	5.71377i	−0.484625	+	0.194274i
$866$	−8.87428	+	31.1424i	−0.301560	+	1.05826i
$867$		0			0
$868$	−18.4301	+	4.31911i	−0.625559	+	0.146600i
$869$	27.6244	−	27.6244i	0.937093	−	0.937093i
$870$		0			0
$871$	3.56753			0.120881
$872$	34.5968	+	38.0427i	1.17159	+	1.28829i
$873$		0			0
$874$	−4.65319	−	8.36197i	−0.157396	−	0.282848i
$875$	−15.7290	−	41.9936i	−0.531738	−	1.41964i
$876$		0			0
$877$		−	10.4267i		−	0.352084i	−0.984383	−	0.176042i	$-0.943670\pi$
$877$		−	10.4267i		−	0.352084i	0.984383	−	0.176042i	$-0.0563295\pi$
$878$	−36.2986	+	20.1991i	−1.22502	+	0.681686i
$879$		0			0
$880$	24.7439	−	1.39346i	0.834117	−	0.0469734i
$881$	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
$883$			27.9073i			0.939156i	0.882891	+	0.469578i	$0.155594\pi$
$883$			27.9073i			0.939156i	−0.882891	+	0.469578i	$0.844406\pi$
$884$	−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	−0.606811	+	0.794846i	$0.707552\pi$
$887$	−41.7449	+	41.7449i	−1.40166	+	1.40166i	−0.794846	+	0.606811i	$0.792448\pi$
$888$		0			0
$889$	66.9004			2.24377
$890$	−28.5931	−	23.2045i	−0.958443	−	0.777816i
$891$		0			0
$892$	−0.967091	−	4.12668i	−0.0323806	−	0.138171i
$893$	−3.72696			−0.124718
$894$		0			0
$895$	−19.5373	+	45.6822i	−0.653061	+	1.52699i
$896$	−42.2671	−	16.5111i	−1.41204	−	0.551597i
$897$		0			0
$898$	−20.7086	+	11.5237i	−0.691053	+	0.384551i
$899$	−1.97145	+	1.97145i	−0.0657516	+	0.0657516i
$900$		0			0
$901$	−21.0548	−	21.0548i	−0.701437	−	0.701437i
$902$	5.44729	−	19.1161i	0.181375	−	0.636496i
$903$		0			0
$904$	−2.32422	−	2.55572i	−0.0773024	−	0.0850021i
$905$	−40.4474	−	17.2985i	−1.34452	−	0.575022i
$906$		0			0
$907$		−	26.7614i		−	0.888597i	−0.895879	−	0.444298i	$-0.853453\pi$
$907$		−	26.7614i		−	0.888597i	0.895879	−	0.444298i	$-0.146547\pi$
$908$	−16.4825	+	26.5724i	−0.546990	+	0.881836i
$909$		0			0
$910$	25.9236	−	2.69689i	0.859358	−	0.0894012i
$911$			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
$917$	90.6165			2.99242
$918$		0			0
$919$		−	42.6903i		−	1.40822i	−0.710090	−	0.704111i	$-0.751346\pi$
$919$		−	42.6903i		−	1.40822i	0.710090	−	0.704111i	$-0.248654\pi$
$920$	39.8379	+	19.3197i	1.31342	+	0.636953i
$921$		0			0
$922$	5.22246	+	1.48819i	0.171993	+	0.0490108i
$923$	4.79878			0.157954
$924$		0			0
$925$	−16.4282	+	15.6932i	−0.540155	+	0.515989i
$926$	−17.6677	−	5.03456i	−0.580597	−	0.165446i
$927$		0			0
$928$	−6.57217	+	1.21491i	−0.215742	+	0.0398812i
$929$			5.58037i			0.183086i	0.995801	+	0.0915430i	$0.0291799\pi$
$929$			5.58037i			0.183086i	−0.995801	+	0.0915430i	$0.970820\pi$
$930$		0			0
$931$	−6.21070	−	6.21070i	−0.203548	−	0.203548i
$932$	−0.328567	−	1.40203i	−0.0107626	−	0.0459251i
$933$		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	0.894435	+	0.447197i	$0.147578\pi$
$937$	41.0680	+	41.0680i	1.34163	+	1.34163i	0.447197	+	0.894435i	$0.352422\pi$
$938$	9.47042	+	2.69867i	0.309220	+	0.0881149i
$939$		0			0
$940$	14.1193	−	9.89892i	0.460522	−	0.322867i
$941$	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
$947$	34.7892			1.13050			0.565248	−	0.824921i	$-0.308780\pi$
$947$	34.7892			1.13050			0.565248	+	0.824921i	$0.308780\pi$
$948$		0			0
$949$	−9.03522	+	9.03522i	−0.293296	+	0.293296i
$950$	−6.04682	+	3.18595i	−0.196185	+	0.103366i
$951$		0			0
$952$	3.09244	−	65.1870i	0.100227	−	2.11272i
$953$	−26.7047	+	26.7047i	−0.865050	+	0.865050i	−0.991919	−	0.126870i	$-0.959507\pi$
$953$	−26.7047	+	26.7047i	−0.865050	+	0.865050i	0.126870	+	0.991919i	$0.459507\pi$
$954$		0			0
$955$	−8.60247	−	21.4592i	−0.278369	−	0.694405i
$956$	8.63926	−	13.9279i	0.279413	−	0.450460i
$957$		0			0
$958$	10.9104	+	19.6064i	0.352498	+	0.633453i
$959$	7.34112			0.237057
$960$		0			0
$961$	25.4314			0.820369
$962$	−6.42092	−	11.5386i	−0.207019	−	0.372021i
$963$		0			0
$964$	−5.97510	+	9.63284i	−0.192445	+	0.310253i
$965$	38.4027	+	16.4241i	1.23623	+	0.528709i
$966$		0			0
$967$	−12.8711	+	12.8711i	−0.413906	+	0.413906i	−0.883097	−	0.469191i	$-0.844546\pi$
$967$	−12.8711	+	12.8711i	−0.413906	+	0.413906i	0.469191	+	0.883097i	$0.344546\pi$
$968$	−0.445304	+	9.38677i	−0.0143126	+	0.301702i
$969$		0			0
$970$	15.6989	−	1.63320i	0.504062	−	0.0524389i
$971$	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
$973$	−48.8610			−1.56641
$974$	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	−0.749194	−	0.662350i	$-0.769559\pi$
$977$	−2.71449	+	2.71449i	−0.0868441	+	0.0868441i	0.662350	+	0.749194i	$0.269559\pi$
$978$		0			0
$979$	−22.8154	+	22.8154i	−0.729183	+	0.729183i
$980$	40.0247	+	7.03300i	1.27854	+	0.224661i
$981$		0			0
$982$	37.4053	+	10.6589i	1.19365	+	0.340141i
$983$	13.7542	+	13.7542i	0.438692	+	0.438692i	0.891572	−	0.452880i	$-0.149603\pi$
$983$	13.7542	+	13.7542i	0.438692	+	0.438692i	−0.452880	+	0.891572i	$0.649603\pi$
$984$		0			0
$985$	−31.6386	+	12.6831i	−1.00809	+	0.404117i
$986$	−4.67386	−	8.39911i	−0.148846	−	0.267482i
$987$		0			0
$988$	−0.906407	−	3.86773i	−0.0288366	−	0.123049i
$989$	−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	$-0.138827\pi$
$992$	−10.9977	−	7.56605i	−0.349177	−	0.240222i
$993$		0			0
$994$	12.7389	+	3.63006i	0.404054	+	0.115139i
$995$	−4.14979	−	10.3518i	−0.131557	−	0.328175i
$996$		0			0
$997$	−25.4590			−0.806295			−0.403148	−	0.915135i	$-0.632084\pi$
$997$	−25.4590			−0.806295			−0.403148	+	0.915135i	$0.632084\pi$
$998$	−44.2661	−	12.6140i	−1.40122	−	0.399289i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.7	✓	18	3.2	odd	2
80.2.j.b.67.7	yes	18	240.227	odd	4
80.2.s.b.3.3	yes	18	48.35	even	4
80.2.s.b.27.3	yes	18	15.2	even	4
320.2.j.b.47.5		18	240.77	even	4
320.2.j.b.143.5		18	12.11	even	2
320.2.s.b.207.5		18	60.47	odd	4
320.2.s.b.303.5		18	48.29	odd	4
400.2.j.d.43.3		18	15.14	odd	2
400.2.j.d.307.3		18	240.83	odd	4
400.2.s.d.107.7		18	15.8	even	4
400.2.s.d.243.7		18	240.179	even	4
640.2.j.c.543.5		18	24.11	even	2
640.2.j.c.607.5		18	240.197	even	4
640.2.j.d.543.5		18	24.5	odd	2
640.2.j.d.607.5		18	240.107	odd	4
640.2.s.c.223.5		18	48.5	odd	4
640.2.s.c.287.5		18	120.107	odd	4
640.2.s.d.223.5		18	48.11	even	4
640.2.s.d.287.5		18	120.77	even	4
720.2.z.g.163.7		18	16.3	odd	4
720.2.z.g.667.7		18	5.2	odd	4
720.2.bd.g.307.3		18	80.67	even	4	inner
720.2.bd.g.523.3		18	1.1	even	1	trivial
1600.2.j.d.143.5		18	60.59	even	2
1600.2.j.d.1007.5		18	240.173	even	4
1600.2.s.d.207.5		18	60.23	odd	4
1600.2.s.d.943.5		18	240.29	odd	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.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.687667 - 1.23576i) q^{2} +(-1.05423 + 1.69959i) q^{4} +(2.07551 - 0.832020i) q^{5} +(2.83610 - 2.83610i) q^{7} +(2.82525 + 0.134028i) q^{8} +O(q^{10})\)	\(q+(-0.687667 - 1.23576i) q^{2} +(-1.05423 + 1.69959i) q^{4} +(2.07551 - 0.832020i) q^{5} +(2.83610 - 2.83610i) q^{7} +(2.82525 + 0.134028i) q^{8} +(-2.45544 - 1.99269i) q^{10} +(-1.95928 + 1.95928i) q^{11} -2.05493 q^{13} +(-5.45504 - 1.55446i) q^{14} +(-1.77720 - 3.58351i) q^{16} +(4.06774 - 4.06774i) q^{17} +(0.683479 - 0.683479i) q^{19} +(-0.773972 + 4.40465i) q^{20} +(3.76854 + 1.07388i) q^{22} +(4.95014 + 4.95014i) q^{23} +(3.61549 - 3.45373i) q^{25} +(1.41310 + 2.53941i) q^{26} +(1.83030 + 7.81010i) q^{28} +(0.835439 + 0.835439i) q^{29} +2.35978i q^{31} +(-3.20625 + 4.66047i) q^{32} +(-7.82401 - 2.22952i) q^{34} +(3.52666 - 8.24604i) q^{35} -4.54384 q^{37} +(-1.31462 - 0.374613i) q^{38} +(5.97535 - 2.07249i) q^{40} -5.07255i q^{41} -0.849753 q^{43} +(-1.26444 - 5.39549i) q^{44} +(2.71316 - 9.52126i) q^{46} +(-2.72646 - 2.72646i) q^{47} -9.08690i q^{49} +(-6.75425 - 2.09287i) q^{50} +(2.16636 - 3.49253i) q^{52} -5.17605i q^{53} +(-2.43634 + 5.69666i) q^{55} +(8.39280 - 7.63257i) q^{56} +(0.457903 - 1.60691i) q^{58} +(-4.16328 - 4.16328i) q^{59} +(5.55706 - 5.55706i) q^{61} +(2.91613 - 1.62274i) q^{62} +(7.96407 + 0.757328i) q^{64} +(-4.26502 + 1.70974i) q^{65} -1.73609 q^{67} +(2.62515 + 11.2018i) q^{68} +(-12.6153 + 1.31240i) q^{70} -2.33526 q^{71} +(4.39686 - 4.39686i) q^{73} +(3.12465 + 5.61511i) q^{74} +(0.441090 + 1.88218i) q^{76} +11.1134i q^{77} -14.0993 q^{79} +(-6.67015 - 5.95895i) q^{80} +(-6.26848 + 3.48822i) q^{82} +2.75725i q^{83} +(5.05819 - 11.8271i) q^{85} +(0.584347 + 1.05009i) q^{86} +(-5.79805 + 5.27285i) q^{88} +11.6448 q^{89} +(-5.82797 + 5.82797i) q^{91} +(-13.6318 + 3.19462i) q^{92} +(-1.49437 + 5.24417i) q^{94} +(0.849899 - 1.98724i) q^{95} +(-3.52933 + 3.52933i) q^{97} +(-11.2293 + 6.24876i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} + 4 q^{8}+O(q^{10}) \) 18 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 + 4 * q^8	\( 18 q + 4 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} + 4 q^{8} - 12 q^{10} + 2 q^{11} - 12 q^{14} + 6 q^{17} + 2 q^{19} + 4 q^{20} + 4 q^{22} + 2 q^{23} + 6 q^{25} + 16 q^{26} - 4 q^{28} + 14 q^{29} + 4 q^{32} - 28 q^{34} + 6 q^{35} + 8 q^{37} - 16 q^{38} + 20 q^{40} - 44 q^{43} - 44 q^{44} + 12 q^{46} + 38 q^{47} - 20 q^{50} - 40 q^{52} - 6 q^{55} - 20 q^{56} - 20 q^{58} + 10 q^{59} + 14 q^{61} - 16 q^{64} + 12 q^{67} - 36 q^{68} - 36 q^{70} - 24 q^{71} + 14 q^{73} - 48 q^{74} - 16 q^{76} + 16 q^{79} + 20 q^{80} - 28 q^{82} - 10 q^{85} + 36 q^{86} - 96 q^{88} + 12 q^{89} - 52 q^{92} + 28 q^{94} + 34 q^{95} + 18 q^{97} - 32 q^{98}+O(q^{100}) \) 18 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 + 4 * q^8 - 12 * q^10 + 2 * q^11 - 12 * q^14 + 6 * q^17 + 2 * q^19 + 4 * q^20 + 4 * q^22 + 2 * q^23 + 6 * q^25 + 16 * q^26 - 4 * q^28 + 14 * q^29 + 4 * q^32 - 28 * q^34 + 6 * q^35 + 8 * q^37 - 16 * q^38 + 20 * q^40 - 44 * q^43 - 44 * q^44 + 12 * q^46 + 38 * q^47 - 20 * q^50 - 40 * q^52 - 6 * q^55 - 20 * q^56 - 20 * q^58 + 10 * q^59 + 14 * q^61 - 16 * q^64 + 12 * q^67 - 36 * q^68 - 36 * q^70 - 24 * q^71 + 14 * q^73 - 48 * q^74 - 16 * q^76 + 16 * q^79 + 20 * q^80 - 28 * q^82 - 10 * q^85 + 36 * q^86 - 96 * q^88 + 12 * q^89 - 52 * q^92 + 28 * q^94 + 34 * q^95 + 18 * q^97 - 32 * q^98

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