LMFDB - Embedded newform 756.2.bb.a.611.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(611,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("756.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bb (of order $6$, degree $2$, not 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.6
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28108 + 0.599020i) q^{2} +(1.28235 - 1.53479i) q^{4} +(-0.426828 + 0.246429i) q^{5} +(-1.23286 - 2.34095i) q^{7} +(-0.723425 + 2.73435i) q^{8} +O(q^{10})$	\(q+(-1.28108 + 0.599020i) q^{2} +(1.28235 - 1.53479i) q^{4} +(-0.426828 + 0.246429i) q^{5} +(-1.23286 - 2.34095i) q^{7} +(-0.723425 + 2.73435i) q^{8} +(0.399186 - 0.571375i) q^{10} +(-1.12579 + 1.94993i) q^{11} +(0.169382 - 0.293377i) q^{13} +(2.98168 + 2.26044i) q^{14} +(-0.711162 - 3.93627i) q^{16} +(-0.305338 + 0.176287i) q^{17} +(-1.03643 - 0.598384i) q^{19} +(-0.169125 + 0.971099i) q^{20} +(0.274186 - 3.17239i) q^{22} +(-2.76414 - 4.78763i) q^{23} +(-2.37855 + 4.11976i) q^{25} +(-0.0412528 + 0.477304i) q^{26} +(-5.17383 - 1.10973i) q^{28} +(-5.21181 + 3.00904i) q^{29} +9.16259i q^{31} +(3.26897 + 4.61669i) q^{32} +(0.285564 - 0.408742i) q^{34} +(1.10310 + 0.695368i) q^{35} +(1.16125 - 2.01135i) q^{37} +(1.68620 + 0.145736i) q^{38} +(-0.365045 - 1.34537i) q^{40} +(-3.03383 - 1.75158i) q^{41} +(-1.82206 + 1.05197i) q^{43} +(1.54907 + 4.22834i) q^{44} +(6.40898 + 4.47757i) q^{46} -8.14102 q^{47} +(-3.96009 + 5.77215i) q^{49} +(0.579293 - 6.70256i) q^{50} +(-0.233067 - 0.636178i) q^{52} +(8.98513 - 5.18757i) q^{53} -1.10971i q^{55} +(7.29285 - 1.67758i) q^{56} +(4.87428 - 6.97681i) q^{58} -8.13140 q^{59} -6.63650 q^{61} +(-5.48858 - 11.7380i) q^{62} +(-6.95331 - 3.95619i) q^{64} +0.166962i q^{65} +10.4641i q^{67} +(-0.120986 + 0.694692i) q^{68} +(-1.82970 - 0.230046i) q^{70} -13.9808 q^{71} +(-1.82094 - 3.15397i) q^{73} +(-0.282822 + 3.27232i) q^{74} +(-2.24746 + 0.823368i) q^{76} +(5.95263 + 0.231424i) q^{77} -8.75208i q^{79} +(1.27356 + 1.50486i) q^{80} +(4.93582 + 0.426597i) q^{82} +(8.88180 + 15.3837i) q^{83} +(0.0868845 - 0.150488i) q^{85} +(1.70406 - 2.43911i) q^{86} +(-4.51735 - 4.48893i) q^{88} +(-9.75643 - 5.63288i) q^{89} +(-0.895606 - 0.0348191i) q^{91} +(-10.8926 - 1.89704i) q^{92} +(10.4293 - 4.87664i) q^{94} +0.589837 q^{95} +(-7.93543 - 13.7446i) q^{97} +(1.61557 - 9.76678i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.28108	+	0.599020i	−0.905863	+	0.423571i
$2$	−1.28108	+	0.599020i	−0.905863	+	0.423571i
$3$		0			0
$3$		0			0
$4$	1.28235	−	1.53479i	0.641174	−	0.767395i
$5$	−0.426828	+	0.246429i	−0.190883	+	0.110206i	−0.592396	−	0.805647i	$-0.701818\pi$
$5$	−0.426828	+	0.246429i	−0.190883	+	0.110206i	0.401513	+	0.915853i	$0.368485\pi$
$6$		0			0
$7$	−1.23286	−	2.34095i	−0.465979	−	0.884796i
$7$	−1.23286	−	2.34095i	−0.465979	−	0.884796i
$8$	−0.723425	+	2.73435i	−0.255769	+	0.966738i
$9$		0			0
$10$	0.399186	−	0.571375i	0.126234	−	0.180684i
$11$	−1.12579	+	1.94993i	−0.339439	+	0.587925i	−0.984327	−	0.176352i	$-0.943570\pi$
$11$	−1.12579	+	1.94993i	−0.339439	+	0.587925i	0.644889	+	0.764277i	$0.276904\pi$
$12$		0			0
$13$	0.169382	−	0.293377i	0.0469780	−	0.0813683i	−0.841580	−	0.540132i	$-0.818374\pi$
$13$	0.169382	−	0.293377i	0.0469780	−	0.0813683i	0.888558	+	0.458764i	$0.151708\pi$
$14$	2.98168	+	2.26044i	0.796887	+	0.604128i
$15$		0			0
$16$	−0.711162	−	3.93627i	−0.177791	−	0.984068i
$17$	−0.305338	+	0.176287i	−0.0740554	+	0.0427559i	−0.536570	−	0.843856i	$-0.680280\pi$
$17$	−0.305338	+	0.176287i	−0.0740554	+	0.0427559i	0.462515	+	0.886611i	$0.346947\pi$
$18$		0			0
$19$	−1.03643	−	0.598384i	−0.237774	−	0.137279i	0.376379	−	0.926466i	$-0.377169\pi$
$19$	−1.03643	−	0.598384i	−0.237774	−	0.137279i	−0.614153	+	0.789187i	$0.710502\pi$
$20$	−0.169125	+	0.971099i	−0.0378175	+	0.217144i
$21$		0			0
$22$	0.274186	−	3.17239i	0.0584566	−	0.676356i
$23$	−2.76414	−	4.78763i	−0.576363	−	0.998289i	−0.995892	−	0.0905475i	$-0.971138\pi$
$23$	−2.76414	−	4.78763i	−0.576363	−	0.998289i	0.419530	−	0.907742i	$-0.362195\pi$
$24$		0			0
$25$	−2.37855	+	4.11976i	−0.475709	+	0.823952i
$26$	−0.0412528	+	0.477304i	−0.00809034	+	0.0936070i
$27$		0			0
$28$	−5.17383	−	1.10973i	−0.977762	−	0.209719i
$29$	−5.21181	+	3.00904i	−0.967808	+	0.558764i	−0.898567	−	0.438836i	$-0.855391\pi$
$29$	−5.21181	+	3.00904i	−0.967808	+	0.558764i	−0.0692407	+	0.997600i	$0.522058\pi$
$30$		0			0
$31$			9.16259i			1.64565i	0.568295	+	0.822825i	$0.307603\pi$
$31$			9.16259i			1.64565i	−0.568295	+	0.822825i	$0.692397\pi$
$32$	3.26897	+	4.61669i	0.577877	+	0.816124i
$33$		0			0
$34$	0.285564	−	0.408742i	0.0489738	−	0.0700987i
$35$	1.10310	+	0.695368i	0.186458	+	0.117539i
$36$		0			0
$37$	1.16125	−	2.01135i	0.190909	−	0.330664i	−0.754643	−	0.656136i	$-0.772190\pi$
$37$	1.16125	−	2.01135i	0.190909	−	0.330664i	0.945552	+	0.325472i	$0.105523\pi$
$38$	1.68620	+	0.145736i	0.273538	+	0.0236415i
$39$		0			0
$40$	−0.365045	−	1.34537i	−0.0577186	−	0.212721i
$41$	−3.03383	−	1.75158i	−0.473805	−	0.273551i	0.244026	−	0.969769i	$-0.421532\pi$
$41$	−3.03383	−	1.75158i	−0.473805	−	0.273551i	−0.717831	+	0.696217i	$0.754865\pi$
$42$		0			0
$43$	−1.82206	+	1.05197i	−0.277862	+	0.160424i	−0.632455	−	0.774597i	$-0.717953\pi$
$43$	−1.82206	+	1.05197i	−0.277862	+	0.160424i	0.354593	+	0.935021i	$0.384619\pi$
$44$	1.54907	+	4.22834i	0.233531	+	0.637446i
$45$		0			0
$46$	6.40898	+	4.47757i	0.944952	+	0.660182i
$47$	−8.14102			−1.18749			−0.593745	−	0.804653i	$-0.702351\pi$
$47$	−8.14102			−1.18749			−0.593745	+	0.804653i	$0.702351\pi$
$48$		0			0
$49$	−3.96009	+	5.77215i	−0.565727	+	0.824592i
$50$	0.579293	−	6.70256i	0.0819245	−	0.947884i
$51$		0			0
$52$	−0.233067	−	0.636178i	−0.0323205	−	0.0882219i
$53$	8.98513	−	5.18757i	1.23420	−	0.712567i	0.266300	−	0.963890i	$-0.414199\pi$
$53$	8.98513	−	5.18757i	1.23420	−	0.712567i	0.967903	+	0.251323i	$0.0808656\pi$
$54$		0			0
$55$		−	1.10971i		−	0.149633i
$56$	7.29285	−	1.67758i	0.974549	−	0.224176i
$57$		0			0
$58$	4.87428	−	6.97681i	0.640025	−	0.916099i
$59$	−8.13140			−1.05862			−0.529309	−	0.848429i	$-0.677549\pi$
$59$	−8.13140			−1.05862			−0.529309	+	0.848429i	$0.677549\pi$
$60$		0			0
$61$	−6.63650			−0.849717			−0.424859	−	0.905260i	$-0.639676\pi$
$61$	−6.63650			−0.849717			−0.424859	+	0.905260i	$0.639676\pi$
$62$	−5.48858	−	11.7380i	−0.697051	−	1.49073i
$63$		0			0
$64$	−6.95331	−	3.95619i	−0.869164	−	0.494524i
$65$			0.166962i			0.0207091i
$66$		0			0
$67$			10.4641i			1.27839i	0.769045	+	0.639195i	$0.220732\pi$
$67$			10.4641i			1.27839i	−0.769045	+	0.639195i	$0.779268\pi$
$68$	−0.120986	+	0.694692i	−0.0146718	+	0.0842437i
$69$		0			0
$70$	−1.82970	−	0.230046i	−0.218691	−	0.0274958i
$71$	−13.9808			−1.65922			−0.829610	−	0.558343i	$-0.811437\pi$
$71$	−13.9808			−1.65922			−0.829610	+	0.558343i	$0.811437\pi$
$72$		0			0
$73$	−1.82094	−	3.15397i	−0.213125	−	0.369144i	0.739566	−	0.673084i	$-0.235031\pi$
$73$	−1.82094	−	3.15397i	−0.213125	−	0.369144i	−0.952691	+	0.303940i	$0.901698\pi$
$74$	−0.282822	+	3.27232i	−0.0328774	+	0.380399i
$75$		0			0
$76$	−2.24746	+	0.823368i	−0.257802	+	0.0944468i
$77$	5.95263	+	0.231424i	0.678365	+	0.0263733i
$78$		0			0
$79$		−	8.75208i		−	0.984686i	−0.870401	−	0.492343i	$-0.836141\pi$
$79$		−	8.75208i		−	0.984686i	0.870401	−	0.492343i	$-0.163859\pi$
$80$	1.27356	+	1.50486i	0.142388	+	0.168248i
$81$		0			0
$82$	4.93582	+	0.426597i	0.545070	+	0.0471098i
$83$	8.88180	+	15.3837i	0.974904	+	1.68858i	0.680251	+	0.732979i	$0.261871\pi$
$83$	8.88180	+	15.3837i	0.974904	+	1.68858i	0.294653	+	0.955604i	$0.404796\pi$
$84$		0			0
$85$	0.0868845	−	0.150488i	0.00942395	−	0.0163228i
$86$	1.70406	−	2.43911i	0.183754	−	0.263016i
$87$		0			0
$88$	−4.51735	−	4.48893i	−0.481551	−	0.478521i
$89$	−9.75643	−	5.63288i	−1.03418	−	0.597084i	−0.116000	−	0.993249i	$-0.537007\pi$
$89$	−9.75643	−	5.63288i	−1.03418	−	0.597084i	−0.918179	+	0.396165i	$0.870341\pi$
$90$		0			0
$91$	−0.895606	−	0.0348191i	−0.0938851	−	0.00365004i
$92$	−10.8926	−	1.89704i	−1.13563	−	0.197780i
$93$		0			0
$94$	10.4293	−	4.87664i	1.07570	−	0.502987i
$95$	0.589837			0.0605160
$96$		0			0
$97$	−7.93543	−	13.7446i	−0.805721	−	1.39555i	−0.915803	−	0.401627i	$-0.868445\pi$
$97$	−7.93543	−	13.7446i	−0.805721	−	1.39555i	0.110082	−	0.993922i	$-0.464889\pi$
$98$	1.61557	−	9.76678i	0.163198	−	0.986593i
$99$		0			0
$100$	3.27284	+	8.93354i	0.327284	+	0.893354i
$101$	−7.81046	−	4.50937i	−0.777170	−	0.448699i	0.0582566	−	0.998302i	$-0.481446\pi$
$101$	−7.81046	−	4.50937i	−0.777170	−	0.448699i	−0.835426	+	0.549603i	$0.814779\pi$
$102$		0			0
$103$	−0.620523	+	0.358259i	−0.0611420	+	0.0353003i	−0.530259	−	0.847835i	$-0.677905\pi$
$103$	−0.620523	+	0.358259i	−0.0611420	+	0.0353003i	0.469117	+	0.883136i	$0.344572\pi$
$104$	0.679661	+	0.675385i	0.0666463	+	0.0662269i
$105$		0			0
$106$	−8.40324	+	12.0280i	−0.816195	+	1.16826i
$107$	4.09106	−	7.08592i	0.395497	−	0.685021i	−0.597667	−	0.801744i	$-0.703906\pi$
$107$	4.09106	−	7.08592i	0.395497	−	0.685021i	0.993165	+	0.116723i	$0.0372390\pi$
$108$		0			0
$109$	−6.93998	−	12.0204i	−0.664729	−	1.15135i	−0.979359	−	0.202130i	$-0.935214\pi$
$109$	−6.93998	−	12.0204i	−0.664729	−	1.15135i	0.314629	−	0.949215i	$-0.398120\pi$
$110$	0.664739	+	1.42163i	0.0633804	+	0.135547i
$111$		0			0
$112$	−8.33785	+	6.51769i	−0.787853	+	0.615863i
$113$	8.35498	+	4.82375i	0.785970	+	0.453780i	0.838542	−	0.544837i	$-0.183408\pi$
$113$	8.35498	+	4.82375i	0.785970	+	0.453780i	−0.0525717	+	0.998617i	$0.516742\pi$
$114$		0			0
$115$	2.35962	+	1.36233i	0.220036	+	0.127038i
$116$	−2.06511	+	11.8577i	−0.191741	+	1.10096i
$117$		0			0
$118$	10.4170	−	4.87088i	0.958963	−	0.448401i
$119$	0.789120	+	0.497443i	0.0723385	+	0.0456006i
$120$		0			0
$121$	2.96519	+	5.13586i	0.269563	+	0.466897i
$122$	8.50191	−	3.97540i	0.769727	−	0.359916i
$123$		0			0
$124$	14.0627	+	11.7496i	1.26286	+	1.05515i
$125$		−	4.80886i		−	0.430118i
$126$		0			0
$127$			13.7681i			1.22172i	0.791738	+	0.610861i	$0.209177\pi$
$127$			13.7681i			1.22172i	−0.791738	+	0.610861i	$0.790823\pi$
$128$	11.2776	+	0.903034i	0.996809	+	0.0798177i
$129$		0			0
$130$	−0.100014	−	0.213892i	−0.00877178	−	0.0187596i
$131$	2.77729	+	4.81041i	0.242653	+	0.420287i	0.961469	−	0.274913i	$-0.0886491\pi$
$131$	2.77729	+	4.81041i	0.242653	+	0.420287i	−0.718816	+	0.695200i	$0.755316\pi$
$132$		0			0
$133$	−0.123008	+	3.16396i	−0.0106661	+	0.274350i
$134$	−6.26819	−	13.4053i	−0.541489	−	1.15805i
$135$		0			0
$136$	−0.261141	−	0.962431i	−0.0223926	−	0.0825278i
$137$	2.90344	+	1.67630i	0.248057	+	0.143216i	0.618874	−	0.785490i	$-0.287589\pi$
$137$	2.90344	+	1.67630i	0.248057	+	0.143216i	−0.370817	+	0.928706i	$0.620922\pi$
$138$		0			0
$139$	−17.2498	−	9.95917i	−1.46311	−	0.844726i	−0.463955	−	0.885859i	$-0.653570\pi$
$139$	−17.2498	−	9.95917i	−1.46311	−	0.844726i	−0.999154	+	0.0411330i	$0.986903\pi$
$140$	2.48180	−	0.801320i	0.209751	−	0.0677239i
$141$		0			0
$142$	17.9106	−	8.37481i	1.50303	−	0.702798i
$143$	0.381376	+	0.660563i	0.0318923	+	0.0552391i
$144$		0			0
$145$	1.48303	−	2.56868i	0.123159	−	0.213317i
$146$	4.22207	+	2.94971i	0.349421	+	0.244120i
$147$		0			0
$148$	−1.59787	−	4.36153i	−0.131344	−	0.358516i
$149$	11.7952	−	6.80998i	0.966303	−	0.557895i	0.0681955	−	0.997672i	$-0.478276\pi$
$149$	11.7952	−	6.80998i	0.966303	−	0.557895i	0.898107	+	0.439777i	$0.144942\pi$
$150$		0			0
$151$	14.9617	+	8.63812i	1.21756	+	0.702960i	0.964396	−	0.264463i	$-0.0851947\pi$
$151$	14.9617	+	8.63812i	1.21756	+	0.702960i	0.253166	+	0.967423i	$0.418528\pi$
$152$	2.38597	−	2.40108i	0.193528	−	0.194753i
$153$		0			0
$154$	−7.76444	+	3.26927i	−0.625676	+	0.263445i
$155$	−2.25793	−	3.91085i	−0.181361	−	0.314127i
$156$		0			0
$157$	21.1089			1.68467			0.842336	−	0.538953i	$-0.181180\pi$
$157$	21.1089			1.68467			0.842336	+	0.538953i	$0.181180\pi$
$158$	5.24268	+	11.2121i	0.417085	+	0.891990i
$159$		0			0
$160$	−2.53297	−	1.16496i	−0.200249	−	0.0920985i
$161$	−7.79979	+	12.3732i	−0.614709	+	0.975145i
$162$		0			0
$163$	8.29140	+	4.78704i	0.649433	+	0.374950i	0.788239	−	0.615369i	$-0.210993\pi$
$163$	8.29140	+	4.78704i	0.649433	+	0.374950i	−0.138806	+	0.990320i	$0.544326\pi$
$164$	−6.57874	+	2.41015i	−0.513713	+	0.188201i
$165$		0			0
$166$	−20.5935	−	14.3875i	−1.59837	−	1.11668i
$167$	3.26246	−	5.65075i	0.252457	−	0.437268i	−0.711745	−	0.702438i	$-0.752095\pi$
$167$	3.26246	−	5.65075i	0.252457	−	0.437268i	0.964202	+	0.265170i	$0.0854281\pi$
$168$		0			0
$169$	6.44262	+	11.1589i	0.495586	+	0.858380i
$170$	−0.0211607	+	0.244834i	−0.00162295	+	0.0187779i
$171$		0			0
$172$	−0.721969	+	4.14547i	−0.0550496	+	0.316089i
$173$			3.69577i			0.280984i	0.990082	+	0.140492i	$0.0448684\pi$
$173$			3.69577i			0.280984i	−0.990082	+	0.140492i	$0.955132\pi$
$174$		0			0
$175$	12.5766	+	0.488949i	0.950700	+	0.0369610i
$176$	8.47606	+	3.04470i	0.638907	+	0.229503i
$177$		0			0
$178$	15.8730	+	1.37188i	1.18973	+	0.102827i
$179$	1.61207	+	2.79218i	0.120491	+	0.208697i	0.919962	−	0.392008i	$-0.128220\pi$
$179$	1.61207	+	2.79218i	0.120491	+	0.208697i	−0.799470	+	0.600706i	$0.794886\pi$
$180$		0			0
$181$	10.7726			0.800719			0.400359	−	0.916358i	$-0.368885\pi$
$181$	10.7726			0.800719			0.400359	+	0.916358i	$0.368885\pi$
$182$	1.16820	−	0.491880i	0.0865930	−	0.0364606i
$183$		0			0
$184$	15.0907	−	4.09462i	1.11250	−	0.301860i
$185$			1.14467i			0.0841575i
$186$		0			0
$187$		−	0.793849i		−	0.0580520i
$188$	−10.4396	+	12.4948i	−0.761388	+	0.911274i
$189$		0			0
$190$	−0.755630	+	0.353324i	−0.0548192	+	0.0256329i
$191$	11.6031			0.839574			0.419787	−	0.907623i	$-0.362105\pi$
$191$	11.6031			0.839574			0.419787	+	0.907623i	$0.362105\pi$
$192$		0			0
$193$	−18.8377			−1.35597			−0.677983	−	0.735077i	$-0.737146\pi$
$193$	−18.8377			−1.35597			−0.677983	+	0.735077i	$0.737146\pi$
$194$	18.3992	+	12.8545i	1.32099	+	0.922896i
$195$		0			0
$196$	3.78082	+	13.4798i	0.270058	+	0.962844i
$197$		−	2.19767i		−	0.156578i	−0.996931	−	0.0782888i	$-0.975054\pi$
$197$		−	2.19767i		−	0.156578i	0.996931	−	0.0782888i	$-0.0249456\pi$
$198$		0			0
$199$	1.87777	−	1.08413i	0.133111	−	0.0768519i	−0.431966	−	0.901890i	$-0.642180\pi$
$199$	1.87777	−	1.08413i	0.133111	−	0.0768519i	0.565077	+	0.825038i	$0.308846\pi$
$200$	−9.54416	−	9.48411i	−0.674874	−	0.670628i
$201$		0			0
$202$	12.7071	+	1.09825i	0.894065	+	0.0772729i
$203$	13.4695	+	8.49084i	0.945370	+	0.595940i
$204$		0			0
$205$	1.72656			0.120588
$206$	0.580338	−	0.830666i	0.0404340	−	0.0578753i
$207$		0			0
$208$	−1.27527	−	0.458093i	−0.0884242	−	0.0317630i
$209$	2.33361	−	1.34731i	0.161419	−	0.0931954i
$210$		0			0
$211$	−8.69432	−	5.01967i	−0.598542	−	0.345568i	0.169926	−	0.985457i	$-0.445647\pi$
$211$	−8.69432	−	5.01967i	−0.598542	−	0.345568i	−0.768468	+	0.639888i	$0.778981\pi$
$212$	3.56025	−	20.4426i	0.244519	−	1.40400i
$213$		0			0
$214$	−0.996374	+	11.5283i	−0.0681107	+	0.788057i
$215$	0.518471	−	0.898018i	0.0353594	−	0.0612443i
$216$		0			0
$217$	21.4492	−	11.2962i	1.45606	−	0.766838i
$218$	16.0912	+	11.2419i	1.08983	+	0.761400i
$219$		0			0
$220$	−1.70317	−	1.42303i	−0.114828	−	0.0959410i
$221$			0.119439i			0.00803435i
$222$		0			0
$223$	−8.33697	+	4.81335i	−0.558285	+	0.322326i	−0.752457	−	0.658641i	$-0.771131\pi$
$223$	−8.33697	+	4.81335i	−0.558285	+	0.322326i	0.194172	+	0.980968i	$0.437798\pi$
$224$	6.77726	−	13.3442i	0.452824	−	0.891600i
$225$		0			0
$226$	−13.5929	−	1.17482i	−0.904190	−	0.0781480i
$227$	1.28322	−	2.22260i	0.0851703	−	0.147519i	−0.820293	−	0.571943i	$-0.806190\pi$
$227$	1.28322	−	2.22260i	0.0851703	−	0.147519i	0.905464	+	0.424424i	$0.139523\pi$
$228$		0			0
$229$	10.7682	+	18.6511i	0.711584	+	1.23250i	0.964262	+	0.264949i	$0.0853552\pi$
$229$	10.7682	+	18.6511i	0.711584	+	1.23250i	−0.252679	+	0.967550i	$0.581312\pi$
$230$	−3.83893	−	0.331794i	−0.253132	−	0.0218779i
$231$		0			0
$232$	−4.45740	−	16.4277i	−0.292643	−	1.07853i
$233$	7.97316	+	4.60331i	0.522339	+	0.301573i	0.737891	−	0.674920i	$-0.235822\pi$
$233$	7.97316	+	4.60331i	0.522339	+	0.301573i	−0.215552	+	0.976492i	$0.569155\pi$
$234$		0			0
$235$	3.47481	−	2.00618i	0.226672	−	0.130869i
$236$	−10.4273	+	12.4800i	−0.678759	+	0.812379i
$237$		0			0
$238$	−1.30891	−	0.164567i	−0.0848438	−	0.0106673i
$239$	2.56457	−	4.44196i	0.165888	−	0.287327i	−0.771082	−	0.636736i	$-0.780284\pi$
$239$	2.56457	−	4.44196i	0.165888	−	0.287327i	0.936970	+	0.349409i	$0.113618\pi$
$240$		0			0
$241$	−9.02568	+	15.6329i	−0.581395	+	1.00701i	0.413919	+	0.910314i	$0.364160\pi$
$241$	−9.02568	+	15.6329i	−0.581395	+	1.00701i	−0.995314	+	0.0966924i	$0.969174\pi$
$242$	−6.87515	−	4.80326i	−0.441951	−	0.308765i
$243$		0			0
$244$	−8.51031	+	10.1856i	−0.544817	+	0.652069i
$245$	0.267852	−	3.43959i	0.0171124	−	0.219748i
$246$		0			0
$247$	−0.351105	+	0.202711i	−0.0223403	+	0.0128982i
$248$	−25.0537	−	6.62845i	−1.59091	−	0.420907i
$249$		0			0
$250$	2.88061	+	6.16055i	0.182186	+	0.389627i
$251$	3.55229			0.224219			0.112109	−	0.993696i	$-0.464239\pi$
$251$	3.55229			0.224219			0.112109	+	0.993696i	$0.464239\pi$
$252$		0			0
$253$	12.4474			0.782559
$254$	−8.24738	−	17.6381i	−0.517487	−	1.10671i
$255$		0			0
$256$	−14.9885	+	5.59866i	−0.936781	+	0.349916i
$257$	−18.0621	+	10.4281i	−1.12668	+	0.650490i	−0.943098	−	0.332514i	$-0.892103\pi$
$257$	−18.0621	+	10.4281i	−1.12668	+	0.650490i	−0.183583	+	0.983004i	$0.558770\pi$
$258$		0			0
$259$	−6.14013	−	0.238714i	−0.381529	−	0.0148330i
$260$	0.256252	+	0.214104i	0.0158921	+	0.0132781i
$261$		0			0
$262$	−6.43947	−	4.49888i	−0.397832	−	0.277942i
$263$	9.96491	−	17.2597i	0.614462	−	1.06428i	−0.376016	−	0.926613i	$-0.622706\pi$
$263$	9.96491	−	17.2597i	0.614462	−	1.06428i	0.990479	−	0.137667i	$-0.0439604\pi$
$264$		0			0
$265$	−2.55674	+	4.42840i	−0.157059	+	0.272034i
$266$	−1.73770	−	4.12698i	−0.106545	−	0.253042i
$267$		0			0
$268$	16.0601	+	13.4186i	0.981030	+	0.819671i
$269$	11.1882	−	6.45952i	0.682158	−	0.393844i	−0.118510	−	0.992953i	$-0.537812\pi$
$269$	11.1882	−	6.45952i	0.682158	−	0.393844i	0.800668	+	0.599109i	$0.204478\pi$
$270$		0			0
$271$	−5.21334	−	3.00992i	−0.316688	−	0.182840i	0.333227	−	0.942847i	$-0.391862\pi$
$271$	−5.21334	−	3.00992i	−0.316688	−	0.182840i	−0.649915	+	0.760007i	$0.725196\pi$
$272$	0.911059	+	1.07653i	0.0552411	+	0.0652740i
$273$		0			0
$274$	−4.72368	−	0.408262i	−0.285368	−	0.0246640i
$275$	−5.35549	−	9.27598i	−0.322948	−	0.559362i
$276$		0			0
$277$	10.7897	−	18.6883i	0.648291	−	1.12287i	−0.335240	−	0.942133i	$-0.608817\pi$
$277$	10.7897	−	18.6883i	0.648291	−	1.12287i	0.983531	−	0.180740i	$-0.0578494\pi$
$278$	28.0642	+	2.42555i	1.68318	+	0.145475i
$279$		0			0
$280$	−2.69939	+	2.51321i	−0.161319	+	0.150193i
$281$	1.68573	−	0.973257i	0.100562	−	0.0580596i	−0.448875	−	0.893594i	$-0.648175\pi$
$281$	1.68573	−	0.973257i	0.100562	−	0.0580596i	0.549438	+	0.835535i	$0.314842\pi$
$282$		0			0
$283$		−	20.5549i		−	1.22186i	−0.791683	−	0.610932i	$-0.790795\pi$
$283$		−	20.5549i		−	1.22186i	0.791683	−	0.610932i	$-0.209205\pi$
$284$	−17.9283	+	21.4576i	−1.06385	+	1.27328i
$285$		0			0
$286$	−0.884266	−	0.617784i	−0.0522877	−	0.0365303i
$287$	−0.360066	+	9.26151i	−0.0212540	+	0.546690i
$288$		0			0
$289$	−8.43785	+	14.6148i	−0.496344	+	0.859693i
$290$	−0.361191	+	4.17906i	−0.0212098	+	0.245403i
$291$		0			0
$292$	−7.17577	−	1.24972i	−0.419930	−	0.0731343i
$293$	−27.1868	−	15.6963i	−1.58827	−	0.916988i	−0.993592	−	0.113024i	$-0.963946\pi$
$293$	−27.1868	−	15.6963i	−1.58827	−	0.916988i	−0.594677	−	0.803964i	$-0.702720\pi$
$294$		0			0
$295$	3.47071	−	2.00381i	0.202072	−	0.116667i
$296$	4.65965	+	4.63033i	0.270836	+	0.269132i
$297$		0			0
$298$	−11.0314	+	15.7897i	−0.639029	+	0.914675i
$299$	−1.87278			−0.108305
$300$		0			0
$301$	4.70896	+	2.96842i	0.271420	+	0.171097i
$302$	−24.3415	−	2.10381i	−1.40070	−	0.121061i
$303$		0			0
$304$	−1.61833	+	4.50523i	−0.0928178	+	0.258393i
$305$	2.83264	−	1.63543i	0.162197	−	0.0936443i
$306$		0			0
$307$		−	9.56155i		−	0.545707i	−0.962056	−	0.272853i	$-0.912033\pi$
$307$		−	9.56155i		−	0.545707i	0.962056	−	0.272853i	$-0.0879674\pi$
$308$	7.98853	−	8.83927i	0.455189	−	0.503664i
$309$		0			0
$310$	5.23527	+	3.65758i	0.297344	+	0.207736i
$311$	−4.26436			−0.241810			−0.120905	−	0.992664i	$-0.538580\pi$
$311$	−4.26436			−0.241810			−0.120905	+	0.992664i	$0.538580\pi$
$312$		0			0
$313$	−26.5692			−1.50178			−0.750889	−	0.660428i	$-0.770375\pi$
$313$	−26.5692			−1.50178			−0.750889	+	0.660428i	$0.770375\pi$
$314$	−27.0422	+	12.6447i	−1.52608	+	0.713579i
$315$		0			0
$316$	−13.4326	−	11.2232i	−0.755643	−	0.631356i
$317$		−	7.19009i		−	0.403836i	−0.979402	−	0.201918i	$-0.935283\pi$
$317$		−	7.19009i		−	0.403836i	0.979402	−	0.201918i	$-0.0647174\pi$
$318$		0			0
$319$		−	13.5502i		−	0.758664i
$320$	3.94279	−	0.0248865i	0.220408	−	0.00139120i
$321$		0			0
$322$	2.58038	−	20.5233i	0.143799	−	1.14372i
$323$	0.421950			0.0234779
$324$		0			0
$325$	0.805764	+	1.39562i	0.0446957	+	0.0774153i
$326$	−13.4895	−	1.16588i	−0.747115	−	0.0645722i
$327$		0			0
$328$	6.98418	−	7.02841i	0.385637	−	0.388079i
$329$	10.0368	+	19.0577i	0.553345	+	1.05069i
$330$		0			0
$331$		−	20.7242i		−	1.13911i	−0.821955	−	0.569553i	$-0.807116\pi$
$331$		−	20.7242i		−	1.13911i	0.821955	−	0.569553i	$-0.192884\pi$
$332$	35.0004	+	6.09561i	1.92089	+	0.334540i
$333$		0			0
$334$	−0.794571	+	9.19336i	−0.0434770	+	0.503038i
$335$	−2.57865	−	4.46635i	−0.140887	−	0.244023i
$336$		0			0
$337$	8.28123	−	14.3435i	0.451107	−	0.781340i	−0.547348	−	0.836905i	$-0.684363\pi$
$337$	8.28123	−	14.3435i	0.451107	−	0.781340i	0.998455	+	0.0555647i	$0.0176959\pi$
$338$	−14.9380	−	10.4363i	−0.812518	−	0.567659i
$339$		0			0
$340$	−0.119552	−	0.326328i	−0.00648361	−	0.0176976i
$341$	−17.8664	−	10.3152i	−0.967519	−	0.558597i
$342$		0			0
$343$	18.3946	+	2.15410i	0.993213	+	0.116311i
$344$	−1.55832	−	5.74317i	−0.0840190	−	0.309651i
$345$		0			0
$346$	−2.21384	−	4.73458i	−0.119017	−	0.254533i
$347$	25.2060			1.35313			0.676564	−	0.736383i	$-0.263468\pi$
$347$	25.2060			1.35313			0.676564	+	0.736383i	$0.263468\pi$
$348$		0			0
$349$	−10.7077	−	18.5463i	−0.573170	−	0.992759i	−0.996238	−	0.0866610i	$-0.972380\pi$
$349$	−10.7077	−	18.5463i	−0.573170	−	0.992759i	0.423068	−	0.906098i	$-0.360953\pi$
$350$	−16.4045	+	6.90724i	−0.876859	+	0.369208i
$351$		0			0
$352$	−12.6824	+	1.17681i	−0.675973	+	0.0627244i
$353$	17.1270	+	9.88830i	0.911580	+	0.526301i	0.880939	−	0.473229i	$-0.156912\pi$
$353$	17.1270	+	9.88830i	0.911580	+	0.526301i	0.0306410	+	0.999530i	$0.490245\pi$
$354$		0			0
$355$	5.96741	−	3.44528i	0.316717	−	0.182857i
$356$	−21.1564	+	7.75076i	−1.12129	+	0.410789i
$357$		0			0
$358$	−3.73776	−	2.61136i	−0.197547	−	0.138014i
$359$	0.220254	−	0.381491i	0.0116246	−	0.0201344i	−0.860155	−	0.510033i	$-0.829633\pi$
$359$	0.220254	−	0.381491i	0.0116246	−	0.0201344i	0.871779	+	0.489899i	$0.162966\pi$
$360$		0			0
$361$	−8.78387	−	15.2141i	−0.462309	−	0.800743i
$362$	−13.8006	+	6.45299i	−0.725341	+	0.339162i
$363$		0			0
$364$	−1.20192	+	1.32992i	−0.0629977	+	0.0697066i
$365$	1.55446	+	0.897467i	0.0813641	+	0.0469756i
$366$		0			0
$367$	−19.1939	−	11.0816i	−1.00191	−	0.578455i	−0.0930991	−	0.995657i	$-0.529677\pi$
$367$	−19.1939	−	11.0816i	−1.00191	−	0.578455i	−0.908814	+	0.417202i	$0.863011\pi$
$368$	−16.8797	+	14.2852i	−0.879913	+	0.744667i
$369$		0			0
$370$	−0.685678	−	1.46641i	−0.0356467	−	0.0762351i
$371$	−23.2213	−	14.6382i	−1.20559	−	0.759976i
$372$		0			0
$373$	6.71778	+	11.6355i	0.347833	+	0.602465i	0.985864	−	0.167546i	$-0.0535841\pi$
$373$	6.71778	+	11.6355i	0.347833	+	0.602465i	−0.638031	+	0.770011i	$0.720251\pi$
$374$	0.475532	+	1.01699i	0.0245892	+	0.0525872i
$375$		0			0
$376$	5.88942	−	22.2604i	0.303724	−	1.14799i
$377$			2.03870i			0.104998i
$378$		0			0
$379$			1.08764i			0.0558685i	0.999610	+	0.0279343i	$0.00889291\pi$
$379$			1.08764i			0.0558685i	−0.999610	+	0.0279343i	$0.991107\pi$
$380$	0.756377	−	0.905276i	0.0388013	−	0.0464397i
$381$		0			0
$382$	−14.8646	+	6.95052i	−0.760539	+	0.355620i
$383$	5.03627	+	8.72307i	0.257341	+	0.445728i	0.965529	−	0.260296i	$-0.0838202\pi$
$383$	5.03627	+	8.72307i	0.257341	+	0.445728i	−0.708188	+	0.706024i	$0.750487\pi$
$384$		0			0
$385$	−2.59777	+	1.36812i	−0.132395	+	0.0697259i
$386$	24.1327	−	11.2842i	1.22832	−	0.574349i
$387$		0			0
$388$	−31.2710	−	5.44611i	−1.58755	−	0.276484i
$389$	3.34870	+	1.93337i	0.169786	+	0.0980258i	0.582485	−	0.812842i	$-0.302081\pi$
$389$	3.34870	+	1.93337i	0.169786	+	0.0980258i	−0.412699	+	0.910867i	$0.635414\pi$
$390$		0			0
$391$	1.68799	+	0.974564i	0.0853655	+	0.0492858i
$392$	−12.9182	−	15.0040i	−0.652469	−	0.757816i
$393$		0			0
$394$	1.31645	+	2.81540i	0.0663218	+	0.141838i
$395$	2.15677	+	3.73563i	0.108519	+	0.187960i
$396$		0			0
$397$	−15.3745	+	26.6294i	−0.771624	+	1.33649i	0.165048	+	0.986285i	$0.447222\pi$
$397$	−15.3745	+	26.6294i	−0.771624	+	1.33649i	−0.936673	+	0.350207i	$0.886111\pi$
$398$	−1.75616	+	2.51368i	−0.0880284	+	0.125999i
$399$		0			0
$400$	17.9080	+	6.43279i	0.895402	+	0.321639i
$401$	−11.1200	+	6.42016i	−0.555308	+	0.320607i	−0.751260	−	0.660006i	$-0.770554\pi$
$401$	−11.1200	+	6.42016i	−0.555308	+	0.320607i	0.195952	+	0.980613i	$0.437220\pi$
$402$		0			0
$403$	2.68810	+	1.55197i	0.133904	+	0.0773094i
$404$	−16.9367	+	6.20483i	−0.842631	+	0.308702i
$405$		0			0
$406$	−22.3417	−	2.80900i	−1.10880	−	0.139408i
$407$	2.61465	+	4.52871i	0.129604	+	0.224480i
$408$		0			0
$409$	−6.04628			−0.298969			−0.149485	−	0.988764i	$-0.547761\pi$
$409$	−6.04628			−0.298969			−0.149485	+	0.988764i	$0.547761\pi$
$410$	−2.21187	+	1.03425i	−0.109237	+	0.0510778i
$411$		0			0
$412$	−0.245875	+	1.41179i	−0.0121134	+	0.0695537i
$413$	10.0249	+	19.0352i	0.493294	+	0.936661i
$414$		0			0
$415$	−7.58199	−	4.37747i	−0.372185	−	0.214881i
$416$	1.90814	−	0.177058i	0.0935541	−	0.00868100i
$417$		0			0
$418$	−2.18248	+	3.12390i	−0.106749	+	0.152795i
$419$	1.61688	−	2.80052i	0.0789899	−	0.136814i	−0.823825	−	0.566845i	$-0.808164\pi$
$419$	1.61688	−	2.80052i	0.0789899	−	0.136814i	0.902814	+	0.430030i	$0.141497\pi$
$420$		0			0
$421$	−0.791396	−	1.37074i	−0.0385703	−	0.0668057i	0.846096	−	0.533031i	$-0.178947\pi$
$421$	−0.791396	−	1.37074i	−0.0385703	−	0.0668057i	−0.884666	+	0.466225i	$0.845614\pi$
$422$	14.1450	+	1.22254i	0.688570	+	0.0595122i
$423$		0			0
$424$	7.68455	+	28.3213i	0.373195	+	1.37540i
$425$		−	1.67723i		−	0.0813575i
$426$		0			0
$427$	8.18191	+	15.5357i	0.395950	+	0.751826i
$428$	−5.62923	−	15.3655i	−0.272099	−	0.742721i
$429$		0			0
$430$	−0.126273	+	1.46101i	−0.00608944	+	0.0704561i
$431$	13.8272	+	23.9494i	0.666034	+	1.15360i	0.979004	+	0.203841i	$0.0653426\pi$
$431$	13.8272	+	23.9494i	0.666034	+	1.15360i	−0.312970	+	0.949763i	$0.601324\pi$
$432$		0			0
$433$	−18.3948			−0.883995			−0.441998	−	0.897016i	$-0.645730\pi$
$433$	−18.3948			−0.883995			−0.441998	+	0.897016i	$0.645730\pi$
$434$	−20.7115	+	27.3199i	−0.994184	+	1.31140i
$435$		0			0
$436$	−27.3483	−	4.76293i	−1.30974	−	0.228103i
$437$			6.61607i			0.316489i
$438$		0			0
$439$		−	7.50584i		−	0.358234i	−0.983828	−	0.179117i	$-0.942676\pi$
$439$		−	7.50584i		−	0.358234i	0.983828	−	0.179117i	$-0.0573241\pi$
$440$	3.03433	+	0.802792i	0.144656	+	0.0382716i
$441$		0			0
$442$	−0.0715465	−	0.153012i	−0.00340312	−	0.00727801i
$443$	−14.8028			−0.703300			−0.351650	−	0.936132i	$-0.614379\pi$
$443$	−14.8028			−0.703300			−0.351650	+	0.936132i	$0.614379\pi$
$444$		0			0
$445$	5.55242			0.263210
$446$	7.79706	−	11.1603i	0.369202	−	0.528457i
$447$		0			0
$448$	−0.688754	+	21.1548i	−0.0325406	+	0.999470i
$449$			22.5805i			1.06564i	0.846229	+	0.532819i	$0.178868\pi$
$449$			22.5805i			1.06564i	−0.846229	+	0.532819i	$0.821132\pi$
$450$		0			0
$451$	6.83091	−	3.94383i	0.321655	−	0.185708i
$452$	18.1174	−	6.63741i	0.852173	−	0.312198i
$453$		0			0
$454$	−0.312527	+	3.61601i	−0.0146676	+	0.169708i
$455$	0.390850	−	0.205842i	0.0183233	−	0.00965001i
$456$		0			0
$457$	10.5103			0.491649			0.245824	−	0.969314i	$-0.420941\pi$
$457$	10.5103			0.491649			0.245824	+	0.969314i	$0.420941\pi$
$458$	−24.9674	−	17.4432i	−1.16665	−	0.815069i
$459$		0			0
$460$	5.11674	−	1.87454i	0.238569	−	0.0874010i
$461$	−1.08357	+	0.625599i	−0.0504669	+	0.0291371i	−0.525021	−	0.851089i	$-0.675943\pi$
$461$	−1.08357	+	0.625599i	−0.0504669	+	0.0291371i	0.474554	+	0.880226i	$0.342609\pi$
$462$		0			0
$463$	−9.23005	−	5.32897i	−0.428957	−	0.247658i	0.269945	−	0.962876i	$-0.412994\pi$
$463$	−9.23005	−	5.32897i	−0.428957	−	0.247658i	−0.698902	+	0.715217i	$0.746328\pi$
$464$	15.5508	+	18.3752i	0.721929	+	0.853046i
$465$		0			0
$466$	−12.9718	−	1.12113i	−0.600905	−	0.0519355i
$467$	16.0330	−	27.7699i	0.741918	−	1.28504i	−0.209703	−	0.977765i	$-0.567250\pi$
$467$	16.0330	−	27.7699i	0.741918	−	1.28504i	0.951621	−	0.307275i	$-0.0994170\pi$
$468$		0			0
$469$	24.4959	−	12.9008i	1.13111	−	0.595702i
$470$	−3.24978	+	4.65157i	−0.149901	+	0.214561i
$471$		0			0
$472$	5.88246	−	22.2341i	0.270762	−	1.02341i
$473$		−	4.73718i		−	0.217816i
$474$		0			0
$475$	4.93040	−	2.84657i	0.226222	−	0.130610i
$476$	1.77540	−	0.573237i	0.0813752	−	0.0262743i
$477$		0			0
$478$	−0.624599	+	7.22676i	−0.0285685	+	0.330544i
$479$	7.29618	−	12.6374i	0.333371	−	0.577416i	−0.649799	−	0.760106i	$-0.725147\pi$
$479$	7.29618	−	12.6374i	0.333371	−	0.577416i	0.983171	+	0.182690i	$0.0584805\pi$
$480$		0			0
$481$	−0.393390	−	0.681371i	−0.0179370	−	0.0310678i
$482$	2.19820	−	25.4337i	0.100125	−	1.15847i
$483$		0			0
$484$	11.6849	+	2.03502i	0.531131	+	0.0925010i
$485$	6.77412	+	3.91104i	0.307597	+	0.177591i
$486$		0			0
$487$	15.0712	−	8.70134i	0.682940	−	0.394295i	−0.118022	−	0.993011i	$-0.537655\pi$
$487$	15.0712	−	8.70134i	0.682940	−	0.394295i	0.800962	+	0.598716i	$0.204322\pi$
$488$	4.80101	−	18.1465i	0.217332	−	0.821454i
$489$		0			0
$490$	1.71725	+	4.56685i	0.0775773	+	0.206309i
$491$	−16.6745	+	28.8810i	−0.752509	+	1.30338i	0.194095	+	0.980983i	$0.437823\pi$
$491$	−16.6745	+	28.8810i	−0.752509	+	1.30338i	−0.946603	+	0.322400i	$0.895510\pi$
$492$		0			0
$493$	1.06091	−	1.83755i	0.0477809	−	0.0827590i
$494$	0.328367	−	0.470008i	0.0147739	−	0.0211467i
$495$		0			0
$496$	36.0665	−	6.51609i	1.61943	−	0.292581i
$497$	17.2365	+	32.7284i	0.773161	+	1.46807i
$498$		0			0
$499$	−6.89241	+	3.97934i	−0.308547	+	0.178140i	−0.646276	−	0.763104i	$-0.723675\pi$
$499$	−6.89241	+	3.97934i	−0.308547	+	0.178140i	0.337729	+	0.941243i	$0.390341\pi$
$500$	−7.38059	−	6.16664i	−0.330070	−	0.275780i
$501$		0			0
$502$	−4.55078	+	2.12789i	−0.203111	+	0.0949726i
$503$	−28.9613			−1.29132			−0.645660	−	0.763625i	$-0.723418\pi$
$503$	−28.9613			−1.29132			−0.645660	+	0.763625i	$0.723418\pi$
$504$		0			0
$505$	4.44496			0.197798
$506$	−15.9461	+	7.45622i	−0.708891	+	0.331470i
$507$		0			0
$508$	21.1312	+	17.6555i	0.937544	+	0.783337i
$509$	10.9227	−	6.30623i	0.484141	−	0.279519i	−0.238000	−	0.971265i	$-0.576492\pi$
$509$	10.9227	−	6.30623i	0.484141	−	0.279519i	0.722140	+	0.691747i	$0.243158\pi$
$510$		0			0
$511$	−5.13830	+	8.15116i	−0.227305	+	0.360586i
$512$	15.8478	−	16.1508i	0.700380	−	0.713770i
$513$		0			0
$514$	16.8924	−	24.1789i	0.745090	−	1.06648i
$515$	0.176571	−	0.305830i	0.00778065	−	0.0134765i
$516$		0			0
$517$	9.16508	−	15.8744i	0.403080	−	0.698155i
$518$	8.00902	−	3.37225i	0.351896	−	0.148168i
$519$		0			0
$520$	−0.456532	−	0.120785i	−0.0200203	−	0.00529675i
$521$	−37.9143	+	21.8898i	−1.66105	+	0.959010i	−0.688841	+	0.724912i	$0.741880\pi$
$521$	−37.9143	+	21.8898i	−1.66105	+	0.959010i	−0.972213	+	0.234098i	$0.924786\pi$
$522$		0			0
$523$	−23.5863	−	13.6175i	−1.03136	−	0.595454i	−0.113983	−	0.993483i	$-0.536361\pi$
$523$	−23.5863	−	13.6175i	−1.03136	−	0.595454i	−0.917373	+	0.398029i	$0.869694\pi$
$524$	10.9444	+	1.90606i	0.478109	+	0.0832667i
$525$		0			0
$526$	−2.42695	+	28.0803i	−0.105820	+	1.22436i
$527$	−1.61525	−	2.79769i	−0.0703613	−	0.121869i
$528$		0			0
$529$	−3.78091	+	6.54873i	−0.164388	+	0.284728i
$530$	0.622691	−	7.20468i	0.0270480	−	0.312951i
$531$		0			0
$532$	4.69828	+	4.24609i	0.203696	+	0.184092i
$533$	−1.02775	+	0.593372i	−0.0445168	+	0.0257018i
$534$		0			0
$535$			4.03262i			0.174345i
$536$	−28.6124	−	7.56997i	−1.23587	−	0.326973i
$537$		0			0
$538$	−10.4637	+	14.9772i	−0.451120	+	0.645711i
$539$	−6.79703	−	14.2201i	−0.292769	−	0.612504i
$540$		0			0
$541$	−6.86616	+	11.8925i	−0.295199	+	0.511300i	−0.975031	−	0.222068i	$-0.928719\pi$
$541$	−6.86616	+	11.8925i	−0.295199	+	0.511300i	0.679832	+	0.733368i	$0.262053\pi$
$542$	8.48173	+	0.733065i	0.364322	+	0.0314879i
$543$		0			0
$544$	−1.81200	−	0.833376i	−0.0776890	−	0.0357307i
$545$	5.92435	+	3.42042i	0.253771	+	0.146515i
$546$		0			0
$547$	24.0059	−	13.8598i	1.02642	−	0.592602i	0.110461	−	0.993881i	$-0.464767\pi$
$547$	24.0059	−	13.8598i	1.02642	−	0.592602i	0.915956	+	0.401279i	$0.131434\pi$
$548$	6.29599	−	2.30656i	0.268951	−	0.0985315i
$549$		0			0
$550$	12.4173	+	8.67525i	0.529477	+	0.369914i
$551$	7.20224			0.306826
$552$		0			0
$553$	−20.4882	+	10.7901i	−0.871246	+	0.458843i
$554$	−2.62783	+	30.4046i	−0.111646	+	1.29177i
$555$		0			0
$556$	−37.4055	+	13.7037i	−1.58635	+	0.581165i
$557$	33.3701	−	19.2662i	1.41394	−	0.816337i	0.418181	−	0.908364i	$-0.362668\pi$
$557$	33.3701	−	19.2662i	1.41394	−	0.816337i	0.995757	+	0.0920266i	$0.0293345\pi$
$558$		0			0
$559$			0.712736i			0.0301455i
$560$	1.95268	−	4.83662i	0.0825157	−	0.204384i
$561$		0			0
$562$	−1.57656	+	2.25661i	−0.0665032	+	0.0951893i
$563$	−3.17571			−0.133840			−0.0669201	−	0.997758i	$-0.521317\pi$
$563$	−3.17571			−0.133840			−0.0669201	+	0.997758i	$0.521317\pi$
$564$		0			0
$565$	−4.75485			−0.200038
$566$	12.3128	+	26.3326i	0.517546	+	1.10684i
$567$		0			0
$568$	10.1141	−	38.2285i	0.424378	−	1.60403i
$569$		−	19.9275i		−	0.835405i	−0.908584	−	0.417703i	$-0.862835\pi$
$569$		−	19.9275i		−	0.835405i	0.908584	−	0.417703i	$-0.137165\pi$
$570$		0			0
$571$		−	2.43332i		−	0.101831i	−0.998703	−	0.0509156i	$-0.983786\pi$
$571$		−	2.43332i		−	0.101831i	0.998703	−	0.0509156i	$-0.0162139\pi$
$572$	1.50288	+	0.261740i	0.0628387	+	0.0109439i
$573$		0			0
$574$	−5.08656	−	12.0805i	−0.212309	−	0.504228i
$575$	26.2985			1.09672
$576$		0			0
$577$	2.42810	+	4.20560i	0.101083	+	0.175081i	0.912131	−	0.409898i	$-0.134436\pi$
$577$	2.42810	+	4.20560i	0.101083	+	0.175081i	−0.811048	+	0.584980i	$0.801102\pi$
$578$	2.05503	−	23.7772i	0.0854781	−	0.989001i
$579$		0			0
$580$	−2.04063	−	5.57008i	−0.0847324	−	0.231285i
$581$	25.0625	−	39.7579i	1.03977	−	1.64944i
$582$		0			0
$583$			23.3605i			0.967491i
$584$	9.94136	−	2.69744i	0.411377	−	0.111621i
$585$		0			0
$586$	44.2310	+	3.82283i	1.82716	+	0.157919i
$587$	−5.35981	−	9.28346i	−0.221223	−	0.383169i	0.733957	−	0.679196i	$-0.237672\pi$
$587$	−5.35981	−	9.28346i	−0.221223	−	0.383169i	−0.955180	+	0.296027i	$0.904338\pi$
$588$		0			0
$589$	5.48275	−	9.49641i	0.225913	−	0.391293i
$590$	−3.24594	+	4.64608i	−0.133633	+	0.191276i
$591$		0			0
$592$	−8.74306	−	3.14061i	−0.359337	−	0.129078i
$593$	−15.1178	−	8.72827i	−0.620814	−	0.358427i	0.156372	−	0.987698i	$-0.450020\pi$
$593$	−15.1178	−	8.72827i	−0.620814	−	0.358427i	−0.777186	+	0.629271i	$0.783354\pi$
$594$		0			0
$595$	−0.459403	−	0.0178605i	−0.0188337	−	0.000732210i
$596$	4.67371	−	26.8360i	0.191443	−	1.09924i
$597$		0			0
$598$	2.39918	−	1.12183i	0.0981098	−	0.0458751i
$599$	−35.7405			−1.46032			−0.730159	−	0.683277i	$-0.760554\pi$
$599$	−35.7405			−1.46032			−0.730159	+	0.683277i	$0.760554\pi$
$600$		0			0
$601$	8.01003	+	13.8738i	0.326736	+	0.565923i	0.981862	−	0.189596i	$-0.0607180\pi$
$601$	8.01003	+	13.8738i	0.326736	+	0.565923i	−0.655126	+	0.755519i	$0.727385\pi$
$602$	−7.81071	−	0.982032i	−0.318341	−	0.0400247i
$603$		0			0
$604$	32.4438	−	11.8859i	1.32012	−	0.483631i
$605$	−2.53125	−	1.46142i	−0.102910	−	0.0594151i
$606$		0			0
$607$	3.89263	−	2.24741i	0.157997	−	0.0912195i	−0.418917	−	0.908025i	$-0.637590\pi$
$607$	3.89263	−	2.24741i	0.157997	−	0.0912195i	0.576914	+	0.816805i	$0.304257\pi$
$608$	−0.625505	−	6.74099i	−0.0253676	−	0.273383i
$609$		0			0
$610$	−2.64920	+	3.79193i	−0.107263	+	0.153531i
$611$	−1.37894	+	2.38839i	−0.0557859	+	0.0966240i
$612$		0			0
$613$	−6.84453	−	11.8551i	−0.276448	−	0.478822i	0.694051	−	0.719925i	$-0.255824\pi$
$613$	−6.84453	−	11.8551i	−0.276448	−	0.478822i	−0.970499	+	0.241103i	$0.922491\pi$
$614$	5.72757	+	12.2491i	0.231146	+	0.494335i
$615$		0			0
$616$	−4.93907	+	16.1091i	−0.199001	+	0.649055i
$617$	7.32190	+	4.22730i	0.294769	+	0.170185i	0.640090	−	0.768300i	$-0.278897\pi$
$617$	7.32190	+	4.22730i	0.294769	+	0.170185i	−0.345322	+	0.938484i	$0.612230\pi$
$618$		0			0
$619$	−17.5538	−	10.1347i	−0.705547	−	0.407347i	0.103863	−	0.994592i	$-0.466880\pi$
$619$	−17.5538	−	10.1347i	−0.705547	−	0.407347i	−0.809410	+	0.587244i	$0.800213\pi$
$620$	−8.89778	−	1.54962i	−0.357344	−	0.0622344i
$621$		0			0
$622$	5.46301	−	2.55444i	0.219047	−	0.102424i
$623$	−1.15793	+	29.7839i	−0.0463915	+	1.19327i
$624$		0			0
$625$	−10.7077	−	18.5463i	−0.428307	−	0.741850i
$626$	34.0373	−	15.9155i	1.36040	−	0.636110i
$627$		0			0
$628$	27.0689	−	32.3977i	1.08017	−	1.29281i
$629$			0.818855i			0.0326499i
$630$		0			0
$631$			21.5597i			0.858277i	0.903239	+	0.429138i	$0.141183\pi$
$631$			21.5597i			0.858277i	−0.903239	+	0.429138i	$0.858817\pi$
$632$	23.9312	+	6.33148i	0.951933	+	0.251853i
$633$		0			0
$634$	4.30701	+	9.21110i	0.171053	+	0.365820i
$635$	−3.39286	−	5.87661i	−0.134642	−	0.233206i
$636$		0			0
$637$	1.02265	+	2.13950i	0.0405189	+	0.0847700i
$638$	8.11684	+	17.3589i	0.321349	+	0.687246i
$639$		0			0
$640$	−5.03613	+	2.39369i	−0.199070	+	0.0946189i
$641$	−24.0535	−	13.8873i	−0.950058	−	0.548516i	−0.0569589	−	0.998377i	$-0.518140\pi$
$641$	−24.0535	−	13.8873i	−0.950058	−	0.548516i	−0.893099	+	0.449860i	$0.851474\pi$
$642$		0			0
$643$	24.2070	+	13.9759i	0.954630	+	0.551156i	0.894516	−	0.447036i	$-0.147520\pi$
$643$	24.2070	+	13.9759i	0.954630	+	0.551156i	0.0601138	+	0.998192i	$0.480854\pi$
$644$	8.98822	+	27.8378i	0.354185	+	1.09696i
$645$		0			0
$646$	−0.540553	+	0.252757i	−0.0212678	+	0.00994457i
$647$	−2.06939	−	3.58429i	−0.0813562	−	0.140913i	0.822477	−	0.568799i	$-0.192592\pi$
$647$	−2.06939	−	3.58429i	−0.0813562	−	0.140913i	−0.903833	+	0.427886i	$0.859258\pi$
$648$		0			0
$649$	9.15426	−	15.8556i	0.359336	−	0.622388i
$650$	−1.86826	−	1.30524i	−0.0732791	−	0.0511958i
$651$		0			0
$652$	17.9796	−	6.58690i	0.704135	−	0.257963i
$653$	−25.2512	+	14.5788i	−0.988155	+	0.570511i	−0.904722	−	0.426002i	$-0.859922\pi$
$653$	−25.2512	+	14.5788i	−0.988155	+	0.570511i	−0.0834325	+	0.996513i	$0.526588\pi$
$654$		0			0
$655$	−2.37085	−	1.36881i	−0.0926367	−	0.0534838i
$656$	−4.73716	+	13.1876i	−0.184955	+	0.514891i
$657$		0			0
$658$	−24.2739	−	18.4023i	−0.946296	−	0.717396i
$659$	0.0532283	+	0.0921941i	0.00207348	+	0.00359137i	0.867060	−	0.498203i	$-0.166007\pi$
$659$	0.0532283	+	0.0921941i	0.00207348	+	0.00359137i	−0.864987	+	0.501795i	$0.832673\pi$
$660$		0			0
$661$	6.11375			0.237797			0.118899	−	0.992906i	$-0.462064\pi$
$661$	6.11375			0.237797			0.118899	+	0.992906i	$0.462064\pi$
$662$	12.4142	+	26.5495i	0.482493	+	1.03187i
$663$		0			0
$664$	−48.4898	+	13.1570i	−1.88177	+	0.510589i
$665$	−0.727189	−	1.38078i	−0.0281992	−	0.0535443i
$666$		0			0
$667$	28.8123	+	16.6348i	1.11562	+	0.644101i
$668$	−4.48910	−	12.2534i	−0.173689	−	0.474099i
$669$		0			0
$670$	5.97890	+	4.17711i	0.230985	+	0.161376i
$671$	7.47131	−	12.9407i	0.288427	−	0.499570i
$672$		0			0
$673$	13.5287	+	23.4323i	0.521492	+	0.903250i	0.999688	+	0.0249968i	$0.00795757\pi$
$673$	13.5287	+	23.4323i	0.521492	+	0.903250i	−0.478196	+	0.878253i	$0.658709\pi$
$674$	−2.01689	+	23.3358i	−0.0776876	+	0.898863i
$675$		0			0
$676$	25.3883	+	4.42159i	0.976474	+	0.170061i
$677$		−	18.3312i		−	0.704525i	−0.935901	−	0.352263i	$-0.885412\pi$
$677$		−	18.3312i		−	0.704525i	0.935901	−	0.352263i	$-0.114588\pi$
$678$		0			0
$679$	−22.3920	+	35.5216i	−0.859328	+	1.36320i
$680$	0.348633	+	0.346440i	0.0133695	+	0.0132853i
$681$		0			0
$682$	29.0673	+	2.51225i	1.11305	+	0.0961991i
$683$	18.8294	+	32.6135i	0.720487	+	1.24792i	0.960805	+	0.277226i	$0.0894151\pi$
$683$	18.8294	+	32.6135i	0.720487	+	1.24792i	−0.240318	+	0.970694i	$0.577252\pi$
$684$		0			0
$685$	−1.65236			−0.0631332
$686$	−24.8553	+	8.25913i	−0.948980	+	0.315335i
$687$		0			0
$688$	5.43661	+	6.42401i	0.207269	+	0.244913i
$689$		−	3.51471i		−	0.133900i
$690$		0			0
$691$			45.5361i			1.73228i	0.499805	+	0.866138i	$0.333405\pi$
$691$			45.5361i			1.73228i	−0.499805	+	0.866138i	$0.666595\pi$
$692$	5.67222	+	4.73926i	0.215626	+	0.180160i
$693$		0			0
$694$	−32.2910	+	15.0989i	−1.22575	+	0.573147i
$695$	9.81692			0.372377
$696$		0			0
$697$	1.23513			0.0467837
$698$	24.8270	+	17.3452i	0.939717	+	0.656525i
$699$		0			0
$700$	16.8780	−	18.6754i	0.637928	−	0.705864i
$701$			12.0037i			0.453373i	0.973968	+	0.226687i	$0.0727893\pi$
$701$			12.0037i			0.453373i	−0.973968	+	0.226687i	$0.927211\pi$
$702$		0			0
$703$	−2.40712	+	1.38975i	−0.0907862	+	0.0524154i
$704$	15.5423	−	9.10460i	0.585771	−	0.343143i
$705$		0			0
$706$	−27.8645	−	2.40829i	−1.04869	−	0.0906372i
$707$	−0.926974	+	23.8433i	−0.0348625	+	0.896721i
$708$		0			0
$709$	40.8152			1.53285			0.766424	−	0.642335i	$-0.222034\pi$
$709$	40.8152			1.53285			0.766424	+	0.642335i	$0.222034\pi$
$710$	−5.58095	+	7.98829i	−0.209449	+	0.299795i
$711$		0			0
$712$	22.4603	−	22.6025i	0.841735	−	0.847065i
$713$	43.8671	−	25.3267i	1.64284	−	0.948491i
$714$		0			0
$715$	−0.325564	−	0.187964i	−0.0121754	−	0.00702947i
$716$	6.35264	+	1.10637i	0.237409	+	0.0413469i
$717$		0			0
$718$	−0.0536428	+	0.620659i	−0.00200193	+	0.0231628i
$719$	7.23693	−	12.5347i	0.269892	−	0.467466i	−0.698942	−	0.715178i	$-0.746345\pi$
$719$	7.23693	−	12.5347i	0.269892	−	0.467466i	0.968834	+	0.247712i	$0.0796787\pi$
$720$		0			0
$721$	1.60369	+	1.01093i	0.0597245	+	0.0376490i
$722$	20.3664	+	14.2288i	0.757960	+	0.529542i
$723$		0			0
$724$	13.8142	−	16.5336i	0.513400	−	0.614468i
$725$		−	28.6285i		−	1.06324i
$726$		0			0
$727$	16.5147	−	9.53476i	0.612496	−	0.353625i	−0.161446	−	0.986882i	$-0.551616\pi$
$727$	16.5147	−	9.53476i	0.612496	−	0.353625i	0.773942	+	0.633257i	$0.218282\pi$
$728$	0.743112	−	2.42371i	0.0275416	−	0.0898287i
$729$		0			0
$730$	−2.52899	−	0.218578i	−0.0936022	−	0.00808992i
$731$	0.370897	−	0.642412i	0.0137181	−	0.0237605i
$732$		0			0
$733$	−9.57297	−	16.5809i	−0.353586	−	0.612428i	0.633289	−	0.773915i	$-0.281704\pi$
$733$	−9.57297	−	16.5809i	−0.353586	−	0.612428i	−0.986875	+	0.161487i	$0.948371\pi$
$734$	31.2271	+	2.69892i	1.15261	+	0.0996188i
$735$		0			0
$736$	13.0671	−	28.4118i	0.481661	−	1.04727i
$737$	−20.4042	−	11.7803i	−0.751597	−	0.433935i
$738$		0			0
$739$	−24.5722	+	14.1868i	−0.903904	+	0.521869i	−0.878465	−	0.477807i	$-0.841432\pi$
$739$	−24.5722	+	14.1868i	−0.903904	+	0.521869i	−0.0254391	+	0.999676i	$0.508098\pi$
$740$	1.75682	+	1.46786i	0.0645820	+	0.0539596i
$741$		0			0
$742$	38.5170	+	4.84270i	1.41400	+	0.177781i
$743$	−1.60680	+	2.78306i	−0.0589477	+	0.102100i	−0.893993	−	0.448080i	$-0.852108\pi$
$743$	−1.60680	+	2.78306i	−0.0589477	+	0.102100i	0.835046	+	0.550181i	$0.185441\pi$
$744$		0			0
$745$	−3.35635	+	5.81337i	−0.122967	+	0.212985i
$746$	−15.5760	−	10.8820i	−0.570276	−	0.398418i
$747$		0			0
$748$	−1.21839	−	1.01799i	−0.0445488	−	0.0372215i
$749$	−21.6315	−	0.840983i	−0.790397	−	0.0307288i
$750$		0			0
$751$	−10.2417	+	5.91306i	−0.373726	+	0.215771i	−0.675085	−	0.737740i	$-0.735893\pi$
$751$	−10.2417	+	5.91306i	−0.373726	+	0.215771i	0.301359	+	0.953511i	$0.402560\pi$
$752$	5.78959	+	32.0453i	0.211125	+	1.16857i
$753$		0			0
$754$	−1.22122	−	2.61175i	−0.0444744	−	0.0951142i
$755$	−8.51473			−0.309883
$756$		0			0
$757$	−25.4291			−0.924238			−0.462119	−	0.886818i	$-0.652911\pi$
$757$	−25.4291			−0.924238			−0.462119	+	0.886818i	$0.652911\pi$
$758$	−0.651521	−	1.39336i	−0.0236643	−	0.0506092i
$759$		0			0
$760$	−0.426703	+	1.61282i	−0.0154781	+	0.0585031i
$761$	−18.6755	+	10.7823i	−0.676985	+	0.390858i	−0.798718	−	0.601705i	$-0.794488\pi$
$761$	−18.6755	+	10.7823i	−0.676985	+	0.390858i	0.121733	+	0.992563i	$0.461155\pi$
$762$		0			0
$763$	−19.5831	+	31.0657i	−0.708955	+	1.12465i
$764$	14.8793	−	17.8084i	0.538314	−	0.644285i
$765$		0			0
$766$	−11.6772	−	8.15815i	−0.421913	−	0.294766i
$767$	−1.37731	+	2.38557i	−0.0497318	+	0.0861380i
$768$		0			0
$769$	−19.2019	+	33.2586i	−0.692437	+	1.19934i	0.278600	+	0.960407i	$0.410129\pi$
$769$	−19.2019	+	33.2586i	−0.692437	+	1.19934i	−0.971037	+	0.238928i	$0.923204\pi$
$770$	2.50843	−	3.30880i	0.0903976	−	0.119241i
$771$		0			0
$772$	−24.1565	+	28.9119i	−0.869411	+	1.04056i
$773$	4.51475	−	2.60659i	0.162384	−	0.0937526i	−0.416606	−	0.909087i	$-0.636780\pi$
$773$	4.51475	−	2.60659i	0.162384	−	0.0937526i	0.578990	+	0.815335i	$0.303447\pi$
$774$		0			0
$775$	−37.7477	−	21.7936i	−1.35594	−	0.782851i
$776$	43.3231	−	11.7551i	1.55521	−	0.421982i
$777$		0			0
$778$	−5.44809	−	0.470871i	−0.195323	−	0.0168815i
$779$	2.09624	+	3.63079i	0.0751056	+	0.130087i
$780$		0			0
$781$	15.7395	−	27.2616i	0.563203	−	0.975497i
$782$	−2.74624	−	0.237354i	−0.0982055	−	0.00848778i
$783$		0			0
$784$	25.5370	+	11.4831i	0.912036	+	0.410110i
$785$	−9.00985	+	5.20184i	−0.321575	+	0.185662i
$786$		0			0
$787$			50.9749i			1.81706i	0.417820	+	0.908530i	$0.362794\pi$
$787$			50.9749i			1.81706i	−0.417820	+	0.908530i	$0.637206\pi$
$788$	−3.37296	−	2.81818i	−0.120157	−	0.100394i
$789$		0			0
$790$	−5.00072	−	3.49371i	−0.177918	−	0.124300i
$791$	0.991600	−	25.5056i	0.0352572	−	0.906875i
$792$		0			0
$793$	−1.12410	+	1.94700i	−0.0399180	+	0.0691400i
$794$	3.74445	−	43.3241i	0.132886	−	1.53752i
$795$		0			0
$796$	0.744041	−	4.27221i	0.0263719	−	0.151424i
$797$	−44.7617	−	25.8432i	−1.58554	−	0.915412i	−0.994029	−	0.109114i	$-0.965199\pi$
$797$	−44.7617	−	25.8432i	−1.58554	−	0.915412i	−0.591510	−	0.806297i	$-0.701468\pi$
$798$		0			0
$799$	2.48577	−	1.43516i	0.0879400	−	0.0507722i
$800$	−26.7951	+	2.48635i	−0.947348	+	0.0879057i
$801$		0			0
$802$	10.3999	−	14.8859i	0.367233	−	0.525639i
$803$	8.20001			0.289372
$804$		0			0
$805$	0.280049	−	7.20332i	0.00987041	−	0.253884i
$806$	−4.37334	−	0.377983i	−0.154044	−	0.0133139i
$807$		0			0
$808$	17.9805	−	18.0943i	0.632551	−	0.636556i
$809$	40.3082	−	23.2720i	1.41716	−	0.818199i	0.421113	−	0.907008i	$-0.361640\pi$
$809$	40.3082	−	23.2720i	1.41716	−	0.818199i	0.996049	+	0.0888096i	$0.0283063\pi$
$810$		0			0
$811$			25.5269i			0.896371i	0.893941	+	0.448186i	$0.147930\pi$
$811$			25.5269i			0.896371i	−0.893941	+	0.448186i	$0.852070\pi$
$812$	30.3042	−	9.78457i	1.06347	−	0.343371i
$813$		0			0
$814$	−6.06238	−	4.23543i	−0.212486	−	0.148452i
$815$	−4.71867			−0.165288
$816$		0			0
$817$	2.51792			0.0880910
$818$	7.74578	−	3.62184i	0.270825	−	0.126635i
$819$		0			0
$820$	2.21406	−	2.64991i	0.0773182	−	0.0925390i
$821$			1.26425i			0.0441225i	0.999757	+	0.0220613i	$0.00702288\pi$
$821$			1.26425i			0.0441225i	−0.999757	+	0.0220613i	$0.992977\pi$
$822$		0			0
$823$		−	36.7893i		−	1.28239i	−0.767377	−	0.641197i	$-0.778438\pi$
$823$		−	36.7893i		−	1.28239i	0.767377	−	0.641197i	$-0.221562\pi$
$824$	−0.530703	−	1.95590i	−0.0184879	−	0.0681370i
$825$		0			0
$826$	−24.2452	−	18.3806i	−0.843600	−	0.639541i
$827$	7.15785			0.248903			0.124451	−	0.992226i	$-0.460283\pi$
$827$	7.15785			0.248903			0.124451	+	0.992226i	$0.460283\pi$
$828$		0			0
$829$	6.25913	+	10.8411i	0.217389	+	0.376528i	0.954009	−	0.299778i	$-0.0969127\pi$
$829$	6.25913	+	10.8411i	0.217389	+	0.376528i	−0.736620	+	0.676307i	$0.763579\pi$
$830$	12.3354	+	1.06613i	0.428167	+	0.0370059i
$831$		0			0
$832$	−2.33842	+	1.36984i	−0.0810701	+	0.0474906i
$833$	0.191612	−	2.46057i	0.00663897	−	0.0852537i
$834$		0			0
$835$			3.21586i			0.111289i
$836$	0.924664	−	5.30933i	0.0319802	−	0.183627i
$837$		0			0
$838$	−0.393791	+	4.55625i	−0.0136033	+	0.157393i
$839$	13.1258	+	22.7345i	0.453151	+	0.784881i	0.998580	−	0.0532763i	$-0.0169664\pi$
$839$	13.1258	+	22.7345i	0.453151	+	0.784881i	−0.545429	+	0.838157i	$0.683633\pi$
$840$		0			0
$841$	3.60861	−	6.25030i	0.124435	−	0.215527i
$842$	1.83494	+	1.28197i	0.0632364	+	0.0441795i
$843$		0			0
$844$	−18.8533	+	6.90700i	−0.648957	+	0.237749i
$845$	−5.49978	−	3.17530i	−0.189198	−	0.109234i
$846$		0			0
$847$	8.36712	−	13.2732i	0.287498	−	0.456072i
$848$	−26.8096	−	31.6787i	−0.920645	−	1.08785i
$849$		0			0
$850$	1.00469	+	2.14867i	0.0344607	+	0.0736987i
$851$	−12.8394			−0.440131
$852$		0			0
$853$	13.8588	+	24.0041i	0.474515	+	0.821884i	0.999574	−	0.0291814i	$-0.00929006\pi$
$853$	13.8588	+	24.0041i	0.474515	+	0.821884i	−0.525059	+	0.851066i	$0.675957\pi$
$854$	−19.7879	−	15.0014i	−0.677129	−	0.513338i
$855$		0			0
$856$	16.4158	+	16.3125i	0.561080	+	0.557550i
$857$	−46.4831	−	26.8370i	−1.58783	−	0.916736i	−0.993664	−	0.112395i	$-0.964148\pi$
$857$	−46.4831	−	26.8370i	−1.58783	−	0.916736i	−0.594169	−	0.804340i	$-0.702519\pi$
$858$		0			0
$859$	24.7559	−	14.2928i	0.844659	−	0.487664i	−0.0141863	−	0.999899i	$-0.504516\pi$
$859$	24.7559	−	14.2928i	0.844659	−	0.487664i	0.858845	+	0.512235i	$0.171182\pi$
$860$	−0.713408	−	1.94732i	−0.0243270	−	0.0664029i
$861$		0			0
$862$	−32.0600	−	22.3984i	−1.09197	−	0.762894i
$863$	−27.0023	+	46.7694i	−0.919169	+	1.59205i	−0.118490	+	0.992955i	$0.537805\pi$
$863$	−27.0023	+	46.7694i	−0.919169	+	1.59205i	−0.800680	+	0.599093i	$0.795528\pi$
$864$		0			0
$865$	−0.910744	−	1.57745i	−0.0309662	−	0.0536351i
$866$	23.5652	−	11.0188i	0.800778	−	0.374435i
$867$		0			0
$868$	10.1680	−	47.4057i	0.345123	−	1.60905i
$869$	17.0659	+	9.85301i	0.578921	+	0.334240i
$870$		0			0
$871$	3.06992	+	1.77242i	0.104020	+	0.0600562i
$872$	37.8885	−	10.2805i	1.28307	−	0.348140i
$873$		0			0
$874$	−3.96316	−	8.47573i	−0.134056	−	0.286696i
$875$	−11.2573	+	5.92867i	−0.380566	+	0.200426i
$876$		0			0
$877$	−16.8111	−	29.1176i	−0.567669	−	0.983232i	−0.996796	−	0.0799878i	$-0.974512\pi$
$877$	−16.8111	−	29.1176i	−0.567669	−	0.983232i	0.429126	−	0.903244i	$-0.358821\pi$
$878$	4.49615	+	9.61560i	0.151738	+	0.324511i
$879$		0			0
$880$	−4.36812	+	0.789184i	−0.147249	+	0.0266034i
$881$			4.80623i			0.161926i	0.996717	+	0.0809630i	$0.0257996\pi$
$881$			4.80623i			0.161926i	−0.996717	+	0.0809630i	$0.974200\pi$
$882$		0			0
$883$			24.4879i			0.824084i	0.911165	+	0.412042i	$0.135184\pi$
$883$			24.4879i			0.824084i	−0.911165	+	0.412042i	$0.864816\pi$
$884$	0.183314	+	0.153163i	0.00616552	+	0.00515142i
$885$		0			0
$886$	18.9636	−	8.86715i	0.637093	−	0.297898i
$887$	−16.3968	−	28.4002i	−0.550552	−	0.953585i	−0.998235	−	0.0593920i	$-0.981084\pi$
$887$	−16.3968	−	28.4002i	−0.550552	−	0.953585i	0.447682	−	0.894193i	$-0.352250\pi$
$888$		0			0
$889$	32.2305	−	16.9742i	1.08097	−	0.569297i
$890$	−7.11311	+	3.32601i	−0.238432	+	0.111488i
$891$		0			0
$892$	−3.30342	+	18.9679i	−0.110607	+	0.635092i
$893$	8.43762	+	4.87146i	0.282354	+	0.163017i
$894$		0			0
$895$	−1.37615	−	0.794520i	−0.0459996	−	0.0265579i
$896$	−11.7898	−	27.5136i	−0.393870	−	0.919166i
$897$		0			0
$898$	−13.5262	−	28.9275i	−0.451374	−	0.965322i
$899$	−27.5706	−	47.7537i	−0.919531	−	1.59267i
$900$		0			0
$901$	−1.82900	+	3.16793i	−0.0609329	+	0.105539i
$902$	−6.38853	+	9.14423i	−0.212715	+	0.304470i
$903$		0			0
$904$	−19.2340	+	19.3558i	−0.639714	+	0.643764i
$905$	−4.59803	+	2.65467i	−0.152844	+	0.0882443i
$906$		0			0
$907$	3.83310	+	2.21304i	0.127276	+	0.0734828i	0.562286	−	0.826943i	$-0.309922\pi$
$907$	3.83310	+	2.21304i	0.127276	+	0.0734828i	−0.435010	+	0.900425i	$0.643255\pi$
$908$	−1.76569	−	4.81962i	−0.0585965	−	0.159945i
$909$		0			0
$910$	−0.377408	+	0.497827i	−0.0125110	+	0.0165028i
$911$	2.53533	+	4.39133i	0.0839993	+	0.145491i	0.904964	−	0.425487i	$-0.139897\pi$
$911$	2.53533	+	4.39133i	0.0839993	+	0.145491i	−0.820965	+	0.570978i	$0.806564\pi$
$912$		0			0
$913$	−39.9962			−1.32368
$914$	−13.4645	+	6.29585i	−0.445366	+	0.208248i
$915$		0			0
$916$	42.4341	+	7.39026i	1.40206	+	0.244181i
$917$	7.83690	−	12.4321i	0.258797	−	0.410543i
$918$		0			0
$919$	−33.4699	−	19.3238i	−1.10407	−	0.637435i	−0.166783	−	0.985994i	$-0.553338\pi$
$919$	−33.4699	−	19.3238i	−1.10407	−	0.637435i	−0.937287	+	0.348559i	$0.886671\pi$
$920$	−5.43208	+	5.46648i	−0.179091	+	0.180225i
$921$		0			0
$922$	1.01340	−	1.45053i	0.0333744	−	0.0477705i
$923$	−2.36810	+	4.10166i	−0.0779468	+	0.135008i
$924$		0			0
$925$	5.52418	+	9.56817i	0.181634	+	0.314599i
$926$	15.0166	+	1.29787i	0.493477	+	0.0426506i
$927$		0			0
$928$	−30.9290	−	14.2249i	−1.01529	−	0.466954i
$929$			46.1336i			1.51359i	0.653650	+	0.756797i	$0.273237\pi$
$929$			46.1336i			1.51359i	−0.653650	+	0.756797i	$0.726763\pi$
$930$		0			0
$931$	7.55833	−	3.61278i	0.247714	−	0.118404i
$932$	17.2895	−	6.33408i	0.566336	−	0.207480i
$933$		0			0
$934$	−3.90482	+	45.1797i	−0.127770	+	1.47833i
$935$	0.195627	+	0.338837i	0.00639770	+	0.0110811i
$936$		0			0
$937$	−39.2979			−1.28381			−0.641904	−	0.766785i	$-0.721855\pi$
$937$	−39.2979			−1.28381			−0.641904	+	0.766785i	$0.721855\pi$
$938$	−23.6534	+	31.2005i	−0.772311	+	1.01873i
$939$		0			0
$940$	1.37685	−	7.90574i	0.0449079	−	0.257857i
$941$		−	2.82901i		−	0.0922230i	−0.998936	−	0.0461115i	$-0.985317\pi$
$941$		−	2.82901i		−	0.0922230i	0.998936	−	0.0461115i	$-0.0146829\pi$
$942$		0			0
$943$			19.3665i			0.630659i
$944$	5.78275	+	32.0074i	0.188212	+	1.04175i
$945$		0			0
$946$	2.83767	+	6.06872i	0.0922605	+	0.197311i
$947$	−29.1554			−0.947424			−0.473712	−	0.880680i	$-0.657086\pi$
$947$	−29.1554			−0.947424			−0.473712	+	0.880680i	$0.657086\pi$
$948$		0			0
$949$	−1.23374			−0.0400488
$950$	−4.61110	+	6.60010i	−0.149604	+	0.214136i
$951$		0			0
$952$	−1.93105	+	1.79786i	−0.0625858	+	0.0582691i
$953$			1.02532i			0.0332135i	0.999862	+	0.0166067i	$0.00528633\pi$
$953$			1.02532i			0.0332135i	−0.999862	+	0.0166067i	$0.994714\pi$
$954$		0			0
$955$	−4.95254	+	2.85935i	−0.160261	+	0.0925265i
$956$	−3.52881	−	9.63222i	−0.114130	−	0.311528i
$957$		0			0
$958$	−1.77698	+	20.5601i	−0.0574117	+	0.664266i
$959$	0.344591	−	8.86345i	0.0111274	−	0.286216i
$960$		0			0
$961$	−52.9531			−1.70817
$962$	0.912120	+	0.637244i	0.0294079	+	0.0205456i
$963$		0			0
$964$	12.4192	+	33.8994i	0.399996	+	1.09183i
$965$	8.04045	−	4.64215i	0.258831	−	0.149436i
$966$		0			0
$967$	14.0502	+	8.11188i	0.451823	+	0.260860i	0.708600	−	0.705610i	$-0.249327\pi$
$967$	14.0502	+	8.11188i	0.451823	+	0.260860i	−0.256777	+	0.966471i	$0.582660\pi$
$968$	−16.1883	+	4.39245i	−0.520313	+	0.141179i
$969$		0			0
$970$	−11.0210	−	0.952532i	−0.353863	−	0.0305840i
$971$	8.02736	−	13.9038i	0.257610	−	0.446194i	−0.707991	−	0.706222i	$-0.750398\pi$
$971$	8.02736	−	13.9038i	0.257610	−	0.446194i	0.965601	+	0.260027i	$0.0837316\pi$
$972$		0			0
$973$	−2.04727	+	52.6592i	−0.0656325	+	1.68818i
$974$	−14.0951	+	20.1751i	−0.451637	+	0.646451i
$975$		0			0
$976$	4.71963	+	26.1231i	0.151072	+	0.836180i
$977$			14.7654i			0.472387i	0.971706	+	0.236194i	$0.0759000\pi$
$977$			14.7654i			0.472387i	−0.971706	+	0.236194i	$0.924100\pi$
$978$		0			0
$979$	21.9674	−	12.6829i	0.702081	−	0.405347i
$980$	−4.93557	−	4.82185i	−0.157661	−	0.154028i
$981$		0			0
$982$	4.06106	−	46.9874i	0.129594	−	1.49943i
$983$	−17.2957	+	29.9570i	−0.551647	+	0.955481i	0.446509	+	0.894779i	$0.352667\pi$
$983$	−17.2957	+	29.9570i	−0.551647	+	0.955481i	−0.998156	+	0.0607018i	$0.980666\pi$
$984$		0			0
$985$	0.541570	+	0.938027i	0.0172559	+	0.0298880i
$986$	−0.258384	+	2.98956i	−0.00822862	+	0.0952069i
$987$		0			0
$988$	−0.139121	+	0.798818i	−0.00442603	+	0.0254138i
$989$	10.0729	+	5.81557i	0.320298	+	0.184924i
$990$		0			0
$991$	11.3990	−	6.58123i	0.362102	−	0.209060i	−0.307901	−	0.951419i	$-0.599626\pi$
$991$	11.3990	−	6.58123i	0.362102	−	0.209060i	0.670002	+	0.742359i	$0.266293\pi$
$992$	−42.3009	+	29.9522i	−1.34305	+	0.950984i
$993$		0			0
$994$	−41.6864	−	31.6028i	−1.32221	−	1.00238i
$995$	−0.534322	+	0.925473i	−0.0169391	+	0.0293395i
$996$		0			0
$997$	14.0038	−	24.2553i	0.443505	−	0.768173i	−0.554442	−	0.832223i	$-0.687068\pi$
$997$	14.0038	−	24.2553i	0.443505	−	0.768173i	0.997947	+	0.0640494i	$0.0204015\pi$
$998$	6.44605	−	9.22656i	0.204046	−	0.292062i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.6		88
3.2	odd	2		252.2.bb.a.23.39	yes	88
4.3	odd	2	inner	756.2.bb.a.611.39		88
7.4	even	3		756.2.o.a.179.23		88
9.2	odd	6		756.2.o.a.359.9		88
9.7	even	3		252.2.o.a.191.36	yes	88
12.11	even	2		252.2.bb.a.23.6	yes	88
21.11	odd	6		252.2.o.a.95.22	✓	88
28.11	odd	6		756.2.o.a.179.9		88
36.7	odd	6		252.2.o.a.191.22	yes	88
36.11	even	6		756.2.o.a.359.23		88
63.11	odd	6	inner	756.2.bb.a.683.39		88
63.25	even	3		252.2.bb.a.11.6	yes	88
84.11	even	6		252.2.o.a.95.36	yes	88
252.11	even	6	inner	756.2.bb.a.683.6		88
252.151	odd	6		252.2.bb.a.11.39	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.22	✓	88	21.11	odd	6
252.2.o.a.95.36	yes	88	84.11	even	6
252.2.o.a.191.22	yes	88	36.7	odd	6
252.2.o.a.191.36	yes	88	9.7	even	3
252.2.bb.a.11.6	yes	88	63.25	even	3
252.2.bb.a.11.39	yes	88	252.151	odd	6
252.2.bb.a.23.6	yes	88	12.11	even	2
252.2.bb.a.23.39	yes	88	3.2	odd	2
756.2.o.a.179.9		88	28.11	odd	6
756.2.o.a.179.23		88	7.4	even	3
756.2.o.a.359.9		88	9.2	odd	6
756.2.o.a.359.23		88	36.11	even	6
756.2.bb.a.611.6		88	1.1	even	1	trivial
756.2.bb.a.611.39		88	4.3	odd	2	inner
756.2.bb.a.683.6		88	252.11	even	6	inner
756.2.bb.a.683.39		88	63.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28108 + 0.599020i) q^{2} +(1.28235 - 1.53479i) q^{4} +(-0.426828 + 0.246429i) q^{5} +(-1.23286 - 2.34095i) q^{7} +(-0.723425 + 2.73435i) q^{8} +O(q^{10})\)	\(q+(-1.28108 + 0.599020i) q^{2} +(1.28235 - 1.53479i) q^{4} +(-0.426828 + 0.246429i) q^{5} +(-1.23286 - 2.34095i) q^{7} +(-0.723425 + 2.73435i) q^{8} +(0.399186 - 0.571375i) q^{10} +(-1.12579 + 1.94993i) q^{11} +(0.169382 - 0.293377i) q^{13} +(2.98168 + 2.26044i) q^{14} +(-0.711162 - 3.93627i) q^{16} +(-0.305338 + 0.176287i) q^{17} +(-1.03643 - 0.598384i) q^{19} +(-0.169125 + 0.971099i) q^{20} +(0.274186 - 3.17239i) q^{22} +(-2.76414 - 4.78763i) q^{23} +(-2.37855 + 4.11976i) q^{25} +(-0.0412528 + 0.477304i) q^{26} +(-5.17383 - 1.10973i) q^{28} +(-5.21181 + 3.00904i) q^{29} +9.16259i q^{31} +(3.26897 + 4.61669i) q^{32} +(0.285564 - 0.408742i) q^{34} +(1.10310 + 0.695368i) q^{35} +(1.16125 - 2.01135i) q^{37} +(1.68620 + 0.145736i) q^{38} +(-0.365045 - 1.34537i) q^{40} +(-3.03383 - 1.75158i) q^{41} +(-1.82206 + 1.05197i) q^{43} +(1.54907 + 4.22834i) q^{44} +(6.40898 + 4.47757i) q^{46} -8.14102 q^{47} +(-3.96009 + 5.77215i) q^{49} +(0.579293 - 6.70256i) q^{50} +(-0.233067 - 0.636178i) q^{52} +(8.98513 - 5.18757i) q^{53} -1.10971i q^{55} +(7.29285 - 1.67758i) q^{56} +(4.87428 - 6.97681i) q^{58} -8.13140 q^{59} -6.63650 q^{61} +(-5.48858 - 11.7380i) q^{62} +(-6.95331 - 3.95619i) q^{64} +0.166962i q^{65} +10.4641i q^{67} +(-0.120986 + 0.694692i) q^{68} +(-1.82970 - 0.230046i) q^{70} -13.9808 q^{71} +(-1.82094 - 3.15397i) q^{73} +(-0.282822 + 3.27232i) q^{74} +(-2.24746 + 0.823368i) q^{76} +(5.95263 + 0.231424i) q^{77} -8.75208i q^{79} +(1.27356 + 1.50486i) q^{80} +(4.93582 + 0.426597i) q^{82} +(8.88180 + 15.3837i) q^{83} +(0.0868845 - 0.150488i) q^{85} +(1.70406 - 2.43911i) q^{86} +(-4.51735 - 4.48893i) q^{88} +(-9.75643 - 5.63288i) q^{89} +(-0.895606 - 0.0348191i) q^{91} +(-10.8926 - 1.89704i) q^{92} +(10.4293 - 4.87664i) q^{94} +0.589837 q^{95} +(-7.93543 - 13.7446i) q^{97} +(1.61557 - 9.76678i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 2 * q^4 + 6 * q^5	\( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

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