LMFDB - Embedded newform 1728.3.q.i.1601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(449,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1728.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.q (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:	$47.0845896815$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.19269881856.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 $ x^8 - 2x^7 + 15x^6 - 2x^5 + 133x^4 - 84x^3 + 276x^2 + 144*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.1
Root			$-1.41950 + 2.45865i$ of defining polynomial
Character	$\chi$	$=$	1728.1601
Dual form			1728.3.q.i.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.20800 + 4.73889i) q^{5} +(-1.05671 + 1.83027i) q^{7} +O(q^{10})$	$q+(-8.20800 + 4.73889i) q^{5} +(-1.05671 + 1.83027i) q^{7} +(-13.7064 - 7.91342i) q^{11} +(-4.70337 - 8.14648i) q^{13} -11.6027i q^{17} +12.9707 q^{19} +(-5.27427 + 3.04510i) q^{23} +(32.4142 - 56.1431i) q^{25} +(-24.7667 - 14.2991i) q^{29} +(-8.75365 - 15.1618i) q^{31} -20.0305i q^{35} +15.6207 q^{37} +(-14.8062 + 8.54836i) q^{41} +(-21.7157 + 37.6127i) q^{43} +(20.6696 + 11.9336i) q^{47} +(22.2667 + 38.5671i) q^{49} +14.1051i q^{53} +150.003 q^{55} +(-38.5788 + 22.2735i) q^{59} +(1.86057 - 3.22260i) q^{61} +(77.2105 + 44.5775i) q^{65} +(21.0090 + 36.3887i) q^{67} -120.440i q^{71} +5.48692 q^{73} +(28.9674 - 16.7243i) q^{77} +(-60.5480 + 104.872i) q^{79} +(-46.5861 - 26.8965i) q^{83} +(54.9840 + 95.2351i) q^{85} +102.195i q^{89} +19.8803 q^{91} +(-106.463 + 61.4667i) q^{95} +(-58.9377 + 102.083i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{5} - 6 q^{7}+O(q^{10}) $ 8 * q - 6 * q^5 - 6 * q^7	$ 8 q - 6 q^{5} - 6 q^{7} - 36 q^{11} - 14 q^{13} + 4 q^{19} - 102 q^{23} + 10 q^{25} - 114 q^{29} + 50 q^{31} - 120 q^{37} - 264 q^{41} - 28 q^{43} + 150 q^{47} + 94 q^{49} + 244 q^{55} + 108 q^{59} - 14 q^{61} + 198 q^{65} - 20 q^{67} - 76 q^{73} + 66 q^{77} - 26 q^{79} - 246 q^{83} + 224 q^{85} + 108 q^{91} - 456 q^{95} - 236 q^{97}+O(q^{100}) $ 8 * q - 6 * q^5 - 6 * q^7 - 36 * q^11 - 14 * q^13 + 4 * q^19 - 102 * q^23 + 10 * q^25 - 114 * q^29 + 50 * q^31 - 120 * q^37 - 264 * q^41 - 28 * q^43 + 150 * q^47 + 94 * q^49 + 244 * q^55 + 108 * q^59 - 14 * q^61 + 198 * q^65 - 20 * q^67 - 76 * q^73 + 66 * q^77 - 26 * q^79 - 246 * q^83 + 224 * q^85 + 108 * q^91 - 456 * q^95 - 236 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−8.20800	+	4.73889i	−1.64160	+	0.947779i	−0.661336	+	0.750090i	$0.730010\pi$
$5$	−8.20800	+	4.73889i	−1.64160	+	0.947779i	−0.980265	+	0.197688i	$0.936657\pi$
$6$		0			0
$7$	−1.05671	+	1.83027i	−0.150958	+	0.261467i	−0.931580	−	0.363537i	$-0.881569\pi$
$7$	−1.05671	+	1.83027i	−0.150958	+	0.261467i	0.780622	+	0.625004i	$0.214903\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−13.7064	−	7.91342i	−1.24604	−	0.719401i	−0.275723	−	0.961237i	$-0.588917\pi$
$11$	−13.7064	−	7.91342i	−1.24604	−	0.719401i	−0.970317	+	0.241836i	$0.922250\pi$
$12$		0			0
$13$	−4.70337	−	8.14648i	−0.361798	−	0.626652i	0.626459	−	0.779454i	$-0.284504\pi$
$13$	−4.70337	−	8.14648i	−0.361798	−	0.626652i	−0.988257	+	0.152802i	$0.951170\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	11.6027i		−	0.682513i	−0.939970	−	0.341256i	$-0.889148\pi$
$17$		−	11.6027i		−	0.682513i	0.939970	−	0.341256i	$-0.110852\pi$
$18$		0			0
$19$	12.9707			0.682667			0.341334	−	0.939942i	$-0.389121\pi$
$19$	12.9707			0.682667			0.341334	+	0.939942i	$0.389121\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.27427	+	3.04510i	−0.229316	+	0.132396i	−0.610256	−	0.792204i	$-0.708934\pi$
$23$	−5.27427	+	3.04510i	−0.229316	+	0.132396i	0.380940	+	0.924600i	$0.375600\pi$
$24$		0			0
$25$	32.4142	−	56.1431i	1.29657	−	2.24572i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−24.7667	−	14.2991i	−0.854026	−	0.493072i	0.00798151	−	0.999968i	$-0.497459\pi$
$29$	−24.7667	−	14.2991i	−0.854026	−	0.493072i	−0.862007	+	0.506896i	$0.830793\pi$
$30$		0			0
$31$	−8.75365	−	15.1618i	−0.282376	−	0.489089i	0.689594	−	0.724196i	$-0.257789\pi$
$31$	−8.75365	−	15.1618i	−0.282376	−	0.489089i	−0.971969	+	0.235107i	$0.924456\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	20.0305i		−	0.572299i
$36$		0			0
$37$	15.6207			0.422181			0.211091	−	0.977467i	$-0.432298\pi$
$37$	15.6207			0.422181			0.211091	+	0.977467i	$0.432298\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−14.8062	+	8.54836i	−0.361127	+	0.208497i	−0.669575	−	0.742745i	$-0.733524\pi$
$41$	−14.8062	+	8.54836i	−0.361127	+	0.208497i	0.308448	+	0.951241i	$0.400190\pi$
$42$		0			0
$43$	−21.7157	+	37.6127i	−0.505016	+	0.874714i	0.494967	+	0.868912i	$0.335180\pi$
$43$	−21.7157	+	37.6127i	−0.505016	+	0.874714i	−0.999983	+	0.00580217i	$0.998153\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	20.6696	+	11.9336i	0.439778	+	0.253906i	0.703503	−	0.710692i	$-0.251618\pi$
$47$	20.6696	+	11.9336i	0.439778	+	0.253906i	−0.263726	+	0.964598i	$0.584951\pi$
$48$		0			0
$49$	22.2667	+	38.5671i	0.454423	+	0.787084i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			14.1051i			0.266134i	0.991107	+	0.133067i	$0.0424825\pi$
$53$			14.1051i			0.266134i	−0.991107	+	0.133067i	$0.957517\pi$
$54$		0			0
$55$	150.003			2.72733
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−38.5788	+	22.2735i	−0.653877	+	0.377516i	−0.789940	−	0.613184i	$-0.789888\pi$
$59$	−38.5788	+	22.2735i	−0.653877	+	0.377516i	0.136063	+	0.990700i	$0.456555\pi$
$60$		0			0
$61$	1.86057	−	3.22260i	0.0305012	−	0.0528296i	−0.850372	−	0.526182i	$-0.823623\pi$
$61$	1.86057	−	3.22260i	0.0305012	−	0.0528296i	0.880873	+	0.473353i	$0.156956\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	77.2105	+	44.5775i	1.18785	+	0.685808i
$66$		0			0
$67$	21.0090	+	36.3887i	0.313568	+	0.543115i	0.979132	−	0.203225i	$-0.0651424\pi$
$67$	21.0090	+	36.3887i	0.313568	+	0.543115i	−0.665564	+	0.746340i	$0.731809\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	120.440i		−	1.69634i	−0.529724	−	0.848170i	$-0.677705\pi$
$71$		−	120.440i		−	1.69634i	0.529724	−	0.848170i	$-0.322295\pi$
$72$		0			0
$73$	5.48692			0.0751633			0.0375817	−	0.999294i	$-0.488035\pi$
$73$	5.48692			0.0751633			0.0375817	+	0.999294i	$0.488035\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	28.9674	−	16.7243i	0.376200	−	0.217199i
$78$		0			0
$79$	−60.5480	+	104.872i	−0.766430	+	1.32750i	0.173056	+	0.984912i	$0.444636\pi$
$79$	−60.5480	+	104.872i	−0.766430	+	1.32750i	−0.939487	+	0.342585i	$0.888698\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−46.5861	−	26.8965i	−0.561279	−	0.324054i	0.192380	−	0.981321i	$-0.438379\pi$
$83$	−46.5861	−	26.8965i	−0.561279	−	0.324054i	−0.753659	+	0.657266i	$0.771713\pi$
$84$		0			0
$85$	54.9840	+	95.2351i	0.646871	+	1.12041i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			102.195i			1.14825i	0.818766	+	0.574127i	$0.194658\pi$
$89$			102.195i			1.14825i	−0.818766	+	0.574127i	$0.805342\pi$
$90$		0			0
$91$	19.8803			0.218465
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−106.463	+	61.4667i	−1.12067	+	0.647018i
$96$		0			0
$97$	−58.9377	+	102.083i	−0.607605	+	1.05240i	0.384029	+	0.923321i	$0.374536\pi$
$97$	−58.9377	+	102.083i	−0.607605	+	1.05240i	−0.991634	+	0.129081i	$0.958797\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	118.181	+	68.2317i	1.17011	+	0.675561i	0.953705	−	0.300743i	$-0.0972347\pi$
$101$	118.181	+	68.2317i	1.17011	+	0.675561i	0.216401	+	0.976304i	$0.430568\pi$
$102$		0			0
$103$	−60.8511	−	105.397i	−0.590787	−	1.02327i	−0.994127	−	0.108223i	$-0.965484\pi$
$103$	−60.8511	−	105.397i	−0.590787	−	1.02327i	0.403340	−	0.915050i	$-0.367849\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			82.1437i			0.767698i	0.923396	+	0.383849i	$0.125402\pi$
$107$			82.1437i			0.767698i	−0.923396	+	0.383849i	$0.874598\pi$
$108$		0			0
$109$	165.603			1.51929			0.759646	−	0.650337i	$-0.225372\pi$
$109$	165.603			1.51929			0.759646	+	0.650337i	$0.225372\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−68.7460	+	39.6905i	−0.608372	+	0.351244i	−0.772328	−	0.635224i	$-0.780908\pi$
$113$	−68.7460	+	39.6905i	−0.608372	+	0.351244i	0.163956	+	0.986468i	$0.447574\pi$
$114$		0			0
$115$	28.8608	−	49.9884i	0.250964	−	0.434682i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	21.2361	+	12.2607i	0.178455	+	0.103031i
$120$		0			0
$121$	64.7443	+	112.140i	0.535077	+	0.926781i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			377.485i			3.01988i
$126$		0			0
$127$	−147.235			−1.15933			−0.579666	−	0.814854i	$-0.696817\pi$
$127$	−147.235			−1.15933			−0.579666	+	0.814854i	$0.696817\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	145.857	−	84.2103i	1.11341	−	0.642827i	0.173699	−	0.984799i	$-0.444428\pi$
$131$	145.857	−	84.2103i	1.11341	−	0.642827i	0.939710	+	0.341972i	$0.111095\pi$
$132$		0			0
$133$	−13.7062	+	23.7398i	−0.103054	+	0.178495i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	174.984	+	101.027i	1.27726	+	0.737426i	0.976343	−	0.216225i	$-0.0693746\pi$
$137$	174.984	+	101.027i	1.27726	+	0.737426i	0.300915	+	0.953651i	$0.402708\pi$
$138$		0			0
$139$	−129.193	−	223.768i	−0.929443	−	1.60984i	−0.784255	−	0.620439i	$-0.786954\pi$
$139$	−129.193	−	223.768i	−0.929443	−	1.60984i	−0.145189	−	0.989404i	$-0.546379\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			148.879i			1.04111i
$144$		0			0
$145$	271.047			1.86929
$146$		0			0
$147$		0			0
$148$		0			0
$149$	68.6316	−	39.6245i	0.460615	−	0.265936i	−0.251688	−	0.967808i	$-0.580986\pi$
$149$	68.6316	−	39.6245i	0.460615	−	0.265936i	0.712303	+	0.701872i	$0.247652\pi$
$150$		0			0
$151$	−4.73094	+	8.19422i	−0.0313307	+	0.0542664i	−0.881266	−	0.472621i	$-0.843308\pi$
$151$	−4.73094	+	8.19422i	−0.0313307	+	0.0542664i	0.849935	+	0.526888i	$0.176641\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	143.700	+	82.9652i	0.927096	+	0.535259i
$156$		0			0
$157$	−34.3561	−	59.5066i	−0.218829	−	0.379023i	0.735621	−	0.677393i	$-0.236890\pi$
$157$	−34.3561	−	59.5066i	−0.218829	−	0.379023i	−0.954450	+	0.298370i	$0.903557\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	12.8711i		−	0.0799448i
$162$		0			0
$163$	209.391			1.28461			0.642304	−	0.766450i	$-0.277979\pi$
$163$	209.391			1.28461			0.642304	+	0.766450i	$0.277979\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	21.3682	−	12.3369i	0.127953	−	0.0738739i	−0.434657	−	0.900596i	$-0.643130\pi$
$167$	21.3682	−	12.3369i	0.127953	−	0.0738739i	0.562610	+	0.826722i	$0.309797\pi$
$168$		0			0
$169$	40.2566	−	69.7265i	0.238205	−	0.412583i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	129.186	+	74.5855i	0.746739	+	0.431130i	0.824514	−	0.565841i	$-0.191448\pi$
$173$	129.186	+	74.5855i	0.746739	+	0.431130i	−0.0777754	+	0.996971i	$0.524782\pi$
$174$		0			0
$175$	68.5046	+	118.654i	0.391455	+	0.678020i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	65.1600i		−	0.364022i	−0.983296	−	0.182011i	$-0.941739\pi$
$179$		−	65.1600i		−	0.364022i	0.983296	−	0.182011i	$-0.0582607\pi$
$180$		0			0
$181$	95.5019			0.527635			0.263817	−	0.964573i	$-0.415018\pi$
$181$	95.5019			0.527635			0.263817	+	0.964573i	$0.415018\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−128.215	+	74.0248i	−0.693053	+	0.400134i
$186$		0			0
$187$	−91.8171	+	159.032i	−0.491001	+	0.850438i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	160.947	+	92.9225i	0.842652	+	0.486505i	0.858165	−	0.513374i	$-0.171605\pi$
$191$	160.947	+	92.9225i	0.842652	+	0.486505i	−0.0155129	+	0.999880i	$0.504938\pi$
$192$		0			0
$193$	−48.1579	−	83.4119i	−0.249523	−	0.432186i	0.713871	−	0.700277i	$-0.246940\pi$
$193$	−48.1579	−	83.4119i	−0.249523	−	0.432186i	−0.963393	+	0.268091i	$0.913607\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	126.121i		−	0.640209i	−0.947382	−	0.320105i	$-0.896282\pi$
$197$		−	126.121i		−	0.640209i	0.947382	−	0.320105i	$-0.103718\pi$
$198$		0			0
$199$	−131.718			−0.661899			−0.330950	−	0.943648i	$-0.607369\pi$
$199$	−131.718			−0.661899			−0.330950	+	0.943648i	$0.607369\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	52.3424	−	30.2199i	0.257844	−	0.148866i
$204$		0			0
$205$	81.0195	−	140.330i	0.395217	−	0.684536i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−177.782	−	102.642i	−0.850631	−	0.491112i
$210$		0			0
$211$	−5.15331	−	8.92579i	−0.0244233	−	0.0423023i	0.853555	−	0.521002i	$-0.174442\pi$
$211$	−5.15331	−	8.92579i	−0.0244233	−	0.0423023i	−0.877979	+	0.478700i	$0.841108\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	411.634i		−	1.91457i
$216$		0			0
$217$	37.0001			0.170508
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−94.5212	+	54.5718i	−0.427698	+	0.246931i
$222$		0			0
$223$	86.4202	−	149.684i	0.387535	−	0.671230i	−0.604583	−	0.796542i	$-0.706660\pi$
$223$	86.4202	−	149.684i	0.387535	−	0.671230i	0.992117	+	0.125313i	$0.0399934\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	173.974	+	100.444i	0.766403	+	0.442483i	0.831590	−	0.555390i	$-0.187431\pi$
$227$	173.974	+	100.444i	0.766403	+	0.442483i	−0.0651869	+	0.997873i	$0.520764\pi$
$228$		0			0
$229$	130.630	+	226.259i	0.570439	+	0.988029i	0.996521	+	0.0833443i	$0.0265601\pi$
$229$	130.630	+	226.259i	0.570439	+	0.988029i	−0.426082	+	0.904684i	$0.640107\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			130.530i			0.560214i	0.959969	+	0.280107i	$0.0903700\pi$
$233$			130.530i			0.560214i	−0.959969	+	0.280107i	$0.909630\pi$
$234$		0			0
$235$	−226.208			−0.962586
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−231.586	+	133.706i	−0.968981	+	0.559441i	−0.898925	−	0.438102i	$-0.855651\pi$
$239$	−231.586	+	133.706i	−0.968981	+	0.559441i	−0.0700553	+	0.997543i	$0.522318\pi$
$240$		0			0
$241$	−50.8188	+	88.0207i	−0.210866	+	0.365231i	−0.951986	−	0.306142i	$-0.900962\pi$
$241$	−50.8188	+	88.0207i	−0.210866	+	0.365231i	0.741120	+	0.671373i	$0.234295\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−365.531	−	211.039i	−1.49196	−	0.861385i
$246$		0			0
$247$	−61.0059	−	105.665i	−0.246987	−	0.427795i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	137.033i		−	0.545946i	−0.962022	−	0.272973i	$-0.911993\pi$
$251$		−	137.033i		−	0.545946i	0.962022	−	0.272973i	$-0.0880070\pi$
$252$		0			0
$253$	96.3886			0.380983
$254$		0			0
$255$		0			0
$256$		0			0
$257$	217.737	−	125.711i	0.847226	−	0.489146i	−0.0124876	−	0.999922i	$-0.503975\pi$
$257$	217.737	−	125.711i	0.847226	−	0.489146i	0.859714	+	0.510776i	$0.170642\pi$
$258$		0			0
$259$	−16.5065	+	28.5901i	−0.0637317	+	0.110387i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	416.538	+	240.488i	1.58379	+	0.914404i	0.994298	+	0.106633i	$0.0340069\pi$
$263$	416.538	+	240.488i	1.58379	+	0.914404i	0.589496	+	0.807771i	$0.299326\pi$
$264$		0			0
$265$	−66.8425	−	115.775i	−0.252236	−	0.436885i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	182.939i		−	0.680071i	−0.940413	−	0.340036i	$-0.889561\pi$
$269$		−	182.939i		−	0.680071i	0.940413	−	0.340036i	$-0.110439\pi$
$270$		0			0
$271$	31.0146			0.114445			0.0572225	−	0.998361i	$-0.481776\pi$
$271$	31.0146			0.114445			0.0572225	+	0.998361i	$0.481776\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−888.567	+	513.014i	−3.23115	+	1.86551i
$276$		0			0
$277$	206.382	−	357.464i	0.745060	−	1.29048i	−0.205106	−	0.978740i	$-0.565754\pi$
$277$	206.382	−	357.464i	0.745060	−	1.29048i	0.950167	−	0.311743i	$-0.100913\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	107.255	+	61.9236i	0.381690	+	0.220369i	0.678553	−	0.734551i	$-0.262607\pi$
$281$	107.255	+	61.9236i	0.381690	+	0.220369i	−0.296863	+	0.954920i	$0.595941\pi$
$282$		0			0
$283$	−4.23689	−	7.33850i	−0.0149713	−	0.0259311i	0.858443	−	0.512910i	$-0.171432\pi$
$283$	−4.23689	−	7.33850i	−0.0149713	−	0.0259311i	−0.873414	+	0.486978i	$0.838099\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	36.1324i		−	0.125897i
$288$		0			0
$289$	154.377			0.534177
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−93.2120	+	53.8160i	−0.318130	+	0.183672i	−0.650559	−	0.759456i	$-0.725465\pi$
$293$	−93.2120	+	53.8160i	−0.318130	+	0.183672i	0.332429	+	0.943128i	$0.392132\pi$
$294$		0			0
$295$	211.103	−	365.641i	0.715604	−	1.23946i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	49.6137	+	28.6445i	0.165932	+	0.0958009i
$300$		0			0
$301$	−45.8943	−	79.4912i	−0.152473	−	0.264090i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			35.2682i			0.115633i
$306$		0			0
$307$	−530.715			−1.72871			−0.864357	−	0.502878i	$-0.832274\pi$
$307$	−530.715			−1.72871			−0.864357	+	0.502878i	$0.832274\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	142.535	−	82.2926i	0.458312	−	0.264606i	−0.253022	−	0.967460i	$-0.581425\pi$
$311$	142.535	−	82.2926i	0.458312	−	0.264606i	0.711334	+	0.702854i	$0.248091\pi$
$312$		0			0
$313$	273.833	−	474.293i	0.874866	−	1.51531i	0.0179611	−	0.999839i	$-0.494283\pi$
$313$	273.833	−	474.293i	0.874866	−	1.51531i	0.856905	−	0.515474i	$-0.172384\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	67.7106	+	39.0928i	0.213598	+	0.123321i	0.602983	−	0.797754i	$-0.293979\pi$
$317$	67.7106	+	39.0928i	0.213598	+	0.123321i	−0.389384	+	0.921075i	$0.627312\pi$
$318$		0			0
$319$	226.309	+	391.979i	0.709433	+	1.22877i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	150.495i		−	0.465929i
$324$		0			0
$325$	−609.824			−1.87638
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−43.6833	+	25.2206i	−0.132776	+	0.0766583i
$330$		0			0
$331$	274.898	−	476.137i	0.830507	−	1.43848i	−0.0671297	−	0.997744i	$-0.521384\pi$
$331$	274.898	−	476.137i	0.830507	−	1.43848i	0.897637	−	0.440736i	$-0.145283\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−344.884	−	199.119i	−1.02951	−	0.594385i
$336$		0			0
$337$	36.8057	+	63.7494i	0.109216	+	0.189167i	0.915453	−	0.402425i	$-0.131833\pi$
$337$	36.8057	+	63.7494i	0.109216	+	0.189167i	−0.806237	+	0.591593i	$0.798499\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			277.085i			0.812566i
$342$		0			0
$343$	−197.675			−0.576312
$344$		0			0
$345$		0			0
$346$		0			0
$347$	367.796	−	212.347i	1.05993	−	0.611951i	0.134517	−	0.990911i	$-0.457052\pi$
$347$	367.796	−	212.347i	1.05993	−	0.611951i	0.925413	+	0.378960i	$0.123718\pi$
$348$		0			0
$349$	−267.361	+	463.082i	−0.766077	+	1.32688i	0.173599	+	0.984816i	$0.444460\pi$
$349$	−267.361	+	463.082i	−0.766077	+	1.32688i	−0.939676	+	0.342067i	$0.888873\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	155.165	+	89.5845i	0.439561	+	0.253781i	0.703411	−	0.710783i	$-0.251659\pi$
$353$	155.165	+	89.5845i	0.439561	+	0.253781i	−0.263851	+	0.964564i	$0.584993\pi$
$354$		0			0
$355$	570.753	+	988.573i	1.60775	+	2.78471i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			351.534i			0.979204i	0.871946	+	0.489602i	$0.162858\pi$
$359$			351.534i			0.979204i	−0.871946	+	0.489602i	$0.837142\pi$
$360$		0			0
$361$	−192.761			−0.533965
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−45.0367	+	26.0019i	−0.123388	+	0.0712382i
$366$		0			0
$367$	−41.9855	+	72.7210i	−0.114402	+	0.198150i	−0.917541	−	0.397642i	$-0.869829\pi$
$367$	−41.9855	+	72.7210i	−0.114402	+	0.198150i	0.803139	+	0.595792i	$0.203162\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−25.8161	−	14.9050i	−0.0695853	−	0.0401751i
$372$		0			0
$373$	218.337	+	378.171i	0.585354	+	1.01386i	0.994831	+	0.101543i	$0.0323779\pi$
$373$	218.337	+	378.171i	0.585354	+	1.01386i	−0.409477	+	0.912320i	$0.634289\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			269.016i			0.713569i
$378$		0			0
$379$	273.455			0.721516			0.360758	−	0.932659i	$-0.382518\pi$
$379$	273.455			0.721516			0.360758	+	0.932659i	$0.382518\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−192.544	+	111.166i	−0.502727	+	0.290249i	−0.729839	−	0.683619i	$-0.760405\pi$
$383$	−192.544	+	111.166i	−0.502727	+	0.290249i	0.227112	+	0.973869i	$0.427072\pi$
$384$		0			0
$385$	−158.510	+	274.547i	−0.411713	+	0.713108i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	522.471	+	301.649i	1.34311	+	0.775447i	0.987263	−	0.159096i	$-0.0508578\pi$
$389$	522.471	+	301.649i	1.34311	+	0.775447i	0.355851	+	0.934543i	$0.384191\pi$
$390$		0			0
$391$	35.3314	+	61.1958i	0.0903617	+	0.156511i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	1147.72i		−	2.90563i
$396$		0			0
$397$	138.804			0.349633			0.174816	−	0.984601i	$-0.444067\pi$
$397$	138.804			0.349633			0.174816	+	0.984601i	$0.444067\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	281.903	−	162.757i	0.702999	−	0.405877i	−0.105464	−	0.994423i	$-0.533633\pi$
$401$	281.903	−	162.757i	0.702999	−	0.405877i	0.808464	+	0.588546i	$0.200300\pi$
$402$		0			0
$403$	−82.3433	+	142.623i	−0.204326	+	0.353903i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−214.104	−	123.613i	−0.526055	−	0.303718i
$408$		0			0
$409$	257.442	+	445.903i	0.629443	+	1.09023i	0.987664	+	0.156591i	$0.0500504\pi$
$409$	257.442	+	445.903i	0.629443	+	1.09023i	−0.358220	+	0.933637i	$0.616616\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	94.1461i		−	0.227957i
$414$		0			0
$415$	509.839			1.22853
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−107.340	+	61.9726i	−0.256181	+	0.147906i	−0.622591	−	0.782547i	$-0.713920\pi$
$419$	−107.340	+	61.9726i	−0.256181	+	0.147906i	0.366410	+	0.930453i	$0.380587\pi$
$420$		0			0
$421$	−255.924	+	443.273i	−0.607895	+	1.05291i	0.383691	+	0.923461i	$0.374653\pi$
$421$	−255.924	+	443.273i	−0.607895	+	1.05291i	−0.991587	+	0.129444i	$0.958681\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−651.412	−	376.093i	−1.53273	−	0.884924i
$426$		0			0
$427$	3.93216	+	6.81070i	0.00920880	+	0.0159501i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	650.840i		−	1.51007i	−0.655684	−	0.755035i	$-0.727620\pi$
$431$		−	650.840i		−	1.51007i	0.655684	−	0.755035i	$-0.272380\pi$
$432$		0			0
$433$	−432.455			−0.998742			−0.499371	−	0.866388i	$-0.666435\pi$
$433$	−432.455			−0.998742			−0.499371	+	0.866388i	$0.666435\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−68.4108	+	39.4970i	−0.156547	+	0.0903822i
$438$		0			0
$439$	−190.663	+	330.238i	−0.434312	+	0.752251i	−0.997239	−	0.0742559i	$-0.976342\pi$
$439$	−190.663	+	330.238i	−0.434312	+	0.752251i	0.562927	+	0.826507i	$0.309675\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	33.3781	+	19.2708i	0.0753455	+	0.0435007i	0.537199	−	0.843455i	$-0.319482\pi$
$443$	33.3781	+	19.2708i	0.0753455	+	0.0435007i	−0.461854	+	0.886956i	$0.652816\pi$
$444$		0			0
$445$	−484.289	−	838.813i	−1.08829	−	1.88497i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	373.577i		−	0.832019i	−0.909360	−	0.416010i	$-0.863428\pi$
$449$		−	373.577i		−	0.832019i	0.909360	−	0.416010i	$-0.136572\pi$
$450$		0			0
$451$	270.587			0.599971
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−163.178	+	94.2108i	−0.358633	+	0.207057i
$456$		0			0
$457$	−121.482	+	210.414i	−0.265826	+	0.460423i	−0.967780	−	0.251799i	$-0.918978\pi$
$457$	−121.482	+	210.414i	−0.265826	+	0.460423i	0.701954	+	0.712222i	$0.252311\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−116.211	−	67.0942i	−0.252084	−	0.145541i	0.368634	−	0.929574i	$-0.379825\pi$
$461$	−116.211	−	67.0942i	−0.252084	−	0.145541i	−0.620718	+	0.784034i	$0.713159\pi$
$462$		0			0
$463$	155.129	+	268.691i	0.335051	+	0.580326i	0.983495	−	0.180937i	$-0.0579131\pi$
$463$	155.129	+	268.691i	0.335051	+	0.580326i	−0.648443	+	0.761263i	$0.724580\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			765.680i			1.63957i	0.572670	+	0.819786i	$0.305908\pi$
$467$			765.680i			1.63957i	−0.572670	+	0.819786i	$0.694092\pi$
$468$		0			0
$469$	−88.8015			−0.189342
$470$		0			0
$471$		0			0
$472$		0			0
$473$	595.290	−	343.691i	1.25854	−	0.726619i
$474$		0			0
$475$	420.434	−	728.214i	0.885125	−	1.53308i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	442.124	+	255.260i	0.923014	+	0.532902i	0.884595	−	0.466359i	$-0.154435\pi$
$479$	442.124	+	255.260i	0.923014	+	0.532902i	0.0384186	+	0.999262i	$0.487768\pi$
$480$		0			0
$481$	−73.4699	−	127.254i	−0.152744	−	0.264561i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	1117.20i		−	2.30350i
$486$		0			0
$487$	−669.532			−1.37481			−0.687405	−	0.726274i	$-0.741250\pi$
$487$	−669.532			−1.37481			−0.687405	+	0.726274i	$0.741250\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−640.537	+	369.814i	−1.30456	+	0.753186i	−0.981182	−	0.193085i	$-0.938151\pi$
$491$	−640.537	+	369.814i	−1.30456	+	0.753186i	−0.323375	+	0.946271i	$0.604817\pi$
$492$		0			0
$493$	−165.908	+	287.361i	−0.336528	+	0.582883i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	220.438	+	127.270i	0.443537	+	0.256076i
$498$		0			0
$499$	−461.405	−	799.176i	−0.924659	−	1.60156i	−0.792109	−	0.610380i	$-0.791017\pi$
$499$	−461.405	−	799.176i	−0.924659	−	1.60156i	−0.132550	−	0.991176i	$-0.542316\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	223.098i		−	0.443534i	−0.975100	−	0.221767i	$-0.928818\pi$
$503$		−	223.098i		−	0.443534i	0.975100	−	0.221767i	$-0.0711824\pi$
$504$		0			0
$505$	−1293.37			−2.56113
$506$		0			0
$507$		0			0
$508$		0			0
$509$	125.233	−	72.3030i	0.246036	−	0.142049i	−0.371912	−	0.928268i	$-0.621298\pi$
$509$	125.233	−	72.3030i	0.246036	−	0.142049i	0.617948	+	0.786219i	$0.287964\pi$
$510$		0			0
$511$	−5.79807	+	10.0425i	−0.0113465	+	0.0196527i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	998.932	+	576.733i	1.93967	+	1.11987i
$516$		0			0
$517$	−188.871	−	327.134i	−0.365320	−	0.632753i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	452.382i		−	0.868296i	−0.900842	−	0.434148i	$-0.857050\pi$
$521$		−	452.382i		−	0.868296i	0.900842	−	0.434148i	$-0.142950\pi$
$522$		0			0
$523$	−168.242			−0.321686			−0.160843	−	0.986980i	$-0.551421\pi$
$523$	−168.242			−0.321686			−0.160843	+	0.986980i	$0.551421\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−175.918	+	101.566i	−0.333809	+	0.192725i
$528$		0			0
$529$	−245.955	+	426.006i	−0.464943	+	0.805305i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	139.278	+	80.4122i	0.261309	+	0.150867i
$534$		0			0
$535$	−389.270	−	674.235i	−0.727607	−	1.26025i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	704.824i		−	1.30765i
$540$		0			0
$541$	809.693			1.49666			0.748330	−	0.663327i	$-0.230856\pi$
$541$	809.693			1.49666			0.748330	+	0.663327i	$0.230856\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1359.27	+	784.774i	−2.49407	+	1.43995i
$546$		0			0
$547$	−468.105	+	810.781i	−0.855767	+	1.48223i	0.0201641	+	0.999797i	$0.493581\pi$
$547$	−468.105	+	810.781i	−0.855767	+	1.48223i	−0.875931	+	0.482436i	$0.839752\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−321.242	−	185.469i	−0.583015	−	0.336604i
$552$		0			0
$553$	−127.963	−	221.638i	−0.231398	−	0.400793i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	318.572i		−	0.571942i	−0.958238	−	0.285971i	$-0.907684\pi$
$557$		−	318.572i		−	0.571942i	0.958238	−	0.285971i	$-0.0923162\pi$
$558$		0			0
$559$	408.548			0.730855
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−700.038	+	404.167i	−1.24341	+	0.717882i	−0.969786	−	0.243956i	$-0.921555\pi$
$563$	−700.038	+	404.167i	−1.24341	+	0.717882i	−0.273621	+	0.961838i	$0.588221\pi$
$564$		0			0
$565$	376.178	−	651.560i	0.665802	−	1.15320i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−895.501	−	517.017i	−1.57381	−	0.908642i	−0.995695	−	0.0926904i	$-0.970453\pi$
$569$	−895.501	−	517.017i	−1.57381	−	0.908642i	−0.578120	−	0.815952i	$-0.696213\pi$
$570$		0			0
$571$	24.0163	+	41.5974i	0.0420600	+	0.0728500i	0.886289	−	0.463133i	$-0.153275\pi$
$571$	24.0163	+	41.5974i	0.0420600	+	0.0728500i	−0.844229	+	0.535983i	$0.819941\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			394.818i			0.686640i
$576$		0			0
$577$	396.617			0.687378			0.343689	−	0.939084i	$-0.388323\pi$
$577$	396.617			0.687378			0.343689	+	0.939084i	$0.388323\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	98.4558	−	56.8435i	0.169459	−	0.0978373i
$582$		0			0
$583$	111.619	−	193.331i	0.191457	−	0.331613i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	560.569	+	323.645i	0.954973	+	0.551354i	0.894622	−	0.446823i	$-0.147445\pi$
$587$	560.569	+	323.645i	0.954973	+	0.551354i	0.0603509	+	0.998177i	$0.480778\pi$
$588$		0			0
$589$	−113.541	−	196.658i	−0.192769	−	0.333885i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	322.360i		−	0.543609i	−0.962352	−	0.271805i	$-0.912380\pi$
$593$		−	322.360i		−	0.543609i	0.962352	−	0.271805i	$-0.0876204\pi$
$594$		0			0
$595$	−232.408			−0.390602
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−286.437	+	165.374i	−0.478191	+	0.276084i	−0.719662	−	0.694324i	$-0.755703\pi$
$599$	−286.437	+	165.374i	−0.478191	+	0.276084i	0.241471	+	0.970408i	$0.422370\pi$
$600$		0			0
$601$	−2.29683	+	3.97823i	−0.00382169	+	0.00661936i	−0.867930	−	0.496687i	$-0.834550\pi$
$601$	−2.29683	+	3.97823i	−0.00382169	+	0.00661936i	0.864108	+	0.503306i	$0.167883\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1062.84	−	613.633i	−1.75677	−	1.01427i
$606$		0			0
$607$	−100.896	−	174.756i	−0.166220	−	0.287902i	0.770868	−	0.636995i	$-0.219823\pi$
$607$	−100.896	−	174.756i	−0.166220	−	0.287902i	−0.937088	+	0.349093i	$0.886490\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	224.512i		−	0.367450i
$612$		0			0
$613$	−594.531			−0.969871			−0.484936	−	0.874550i	$-0.661157\pi$
$613$	−594.531			−0.969871			−0.484936	+	0.874550i	$0.661157\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	562.741	−	324.899i	0.912060	−	0.526578i	0.0309665	−	0.999520i	$-0.490141\pi$
$617$	562.741	−	324.899i	0.912060	−	0.526578i	0.881093	+	0.472942i	$0.156808\pi$
$618$		0			0
$619$	114.275	−	197.931i	0.184613	−	0.319759i	−0.758833	−	0.651285i	$-0.774230\pi$
$619$	114.275	−	197.931i	0.184613	−	0.319759i	0.943446	+	0.331526i	$0.107564\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−187.044	−	107.990i	−0.300231	−	0.173338i
$624$		0			0
$625$	−978.507	−	1694.82i	−1.56561	−	2.71172i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	181.243i		−	0.288144i
$630$		0			0
$631$	555.448			0.880266			0.440133	−	0.897933i	$-0.354931\pi$
$631$	555.448			0.880266			0.440133	+	0.897933i	$0.354931\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1208.51	−	697.732i	1.90316	−	1.09879i
$636$		0			0
$637$	209.457	−	362.791i	0.328819	−	0.569530i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−374.507	−	216.222i	−0.584254	−	0.337319i	0.178568	−	0.983928i	$-0.442853\pi$
$641$	−374.507	−	216.222i	−0.584254	−	0.337319i	−0.762822	+	0.646608i	$0.776187\pi$
$642$		0			0
$643$	170.831	+	295.888i	0.265678	+	0.460168i	0.967741	−	0.251947i	$-0.0810709\pi$
$643$	170.831	+	295.888i	0.265678	+	0.460168i	−0.702063	+	0.712115i	$0.747738\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	1066.85i		−	1.64891i	−0.565926	−	0.824456i	$-0.691481\pi$
$647$		−	1066.85i		−	1.64891i	0.565926	−	0.824456i	$-0.308519\pi$
$648$		0			0
$649$	705.037			1.08634
$650$		0			0
$651$		0			0
$652$		0			0
$653$	576.545	−	332.868i	0.882917	−	0.509752i	0.0112977	−	0.999936i	$-0.496404\pi$
$653$	576.545	−	332.868i	0.882917	−	0.509752i	0.871619	+	0.490184i	$0.163070\pi$
$654$		0			0
$655$	−798.128	+	1382.40i	−1.21852	+	2.11053i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−795.462	−	459.260i	−1.20707	−	0.696905i	−0.244955	−	0.969534i	$-0.578773\pi$
$659$	−795.462	−	459.260i	−1.20707	−	0.696905i	−0.962119	+	0.272630i	$0.912107\pi$
$660$		0			0
$661$	−385.777	−	668.185i	−0.583626	−	1.01087i	−0.995045	−	0.0994232i	$-0.968300\pi$
$661$	−385.777	−	668.185i	−0.583626	−	1.01087i	0.411420	−	0.911446i	$-0.365033\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	259.809i		−	0.390690i
$666$		0			0
$667$	174.169			0.261122
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−51.0036	+	29.4470i	−0.0760114	+	0.0438852i
$672$		0			0
$673$	559.767	−	969.546i	0.831750	−	1.44063i	−0.0649002	−	0.997892i	$-0.520673\pi$
$673$	559.767	−	969.546i	0.831750	−	1.44063i	0.896650	−	0.442741i	$-0.145994\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−339.051	−	195.751i	−0.500815	−	0.289145i	0.228235	−	0.973606i	$-0.426704\pi$
$677$	−339.051	−	195.751i	−0.500815	−	0.289145i	−0.729050	+	0.684461i	$0.760038\pi$
$678$		0			0
$679$	−124.560	−	215.744i	−0.183446	−	0.317737i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			661.278i			0.968196i	0.875014	+	0.484098i	$0.160852\pi$
$683$			661.278i			0.968196i	−0.875014	+	0.484098i	$0.839148\pi$
$684$		0			0
$685$	−1915.03			−2.79566
$686$		0			0
$687$		0			0
$688$		0			0
$689$	114.907	−	66.3415i	0.166773	−	0.0962866i
$690$		0			0
$691$	−412.836	+	715.053i	−0.597447	+	1.03481i	0.395750	+	0.918358i	$0.370485\pi$
$691$	−412.836	+	715.053i	−0.597447	+	1.03481i	−0.993197	+	0.116450i	$0.962849\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2120.83	+	1224.46i	3.05155	+	1.76181i
$696$		0			0
$697$	99.1841	+	171.792i	0.142301	+	0.246473i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	236.167i		−	0.336900i	−0.985710	−	0.168450i	$-0.946124\pi$
$701$		−	236.167i		−	0.336900i	0.985710	−	0.168450i	$-0.0538761\pi$
$702$		0			0
$703$	202.611			0.288209
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−249.765	+	144.202i	−0.353274	+	0.203963i
$708$		0			0
$709$	247.969	−	429.496i	0.349745	−	0.605777i	−0.636459	−	0.771311i	$-0.719601\pi$
$709$	247.969	−	429.496i	0.349745	−	0.605777i	0.986204	+	0.165534i	$0.0529348\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	92.3381	+	53.3115i	0.129507	+	0.0747706i
$714$		0			0
$715$	−705.521	−	1222.00i	−0.986743	−	1.70909i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			1065.13i			1.48141i	0.671830	+	0.740705i	$0.265508\pi$
$719$			1065.13i			1.48141i	−0.671830	+	0.740705i	$0.734492\pi$
$720$		0			0
$721$	257.207			0.356736
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1605.59	+	926.987i	−2.21460	+	1.27860i
$726$		0			0
$727$	549.525	−	951.806i	0.755881	−	1.30922i	−0.189054	−	0.981967i	$-0.560542\pi$
$727$	549.525	−	951.806i	0.755881	−	1.30922i	0.944935	−	0.327257i	$-0.106124\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	436.409	+	251.961i	0.597003	+	0.344680i
$732$		0			0
$733$	720.569	+	1248.06i	0.983041	+	1.70268i	0.650336	+	0.759647i	$0.274628\pi$
$733$	720.569	+	1248.06i	0.983041	+	1.70268i	0.332706	+	0.943031i	$0.392038\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	665.013i		−	0.902324i
$738$		0			0
$739$	1095.72			1.48271			0.741356	−	0.671112i	$-0.234183\pi$
$739$	1095.72			1.48271			0.741356	+	0.671112i	$0.234183\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	857.848	−	495.279i	1.15457	−	0.666593i	0.204575	−	0.978851i	$-0.434419\pi$
$743$	857.848	−	495.279i	1.15457	−	0.666593i	0.949997	+	0.312258i	$0.101085\pi$
$744$		0			0
$745$	−375.552	+	650.476i	−0.504097	+	0.873122i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−150.345	−	86.8018i	−0.200728	−	0.115890i
$750$		0			0
$751$	−177.884	−	308.103i	−0.236862	−	0.410258i	0.722950	−	0.690900i	$-0.242786\pi$
$751$	−177.884	−	308.103i	−0.236862	−	0.410258i	−0.959812	+	0.280643i	$0.909452\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	89.6776i		−	0.118778i
$756$		0			0
$757$	231.917			0.306364			0.153182	−	0.988198i	$-0.451048\pi$
$757$	231.917			0.306364			0.153182	+	0.988198i	$0.451048\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	368.325	−	212.653i	0.484002	−	0.279438i	−0.238081	−	0.971245i	$-0.576518\pi$
$761$	368.325	−	212.653i	0.484002	−	0.279438i	0.722083	+	0.691807i	$0.243185\pi$
$762$		0			0
$763$	−174.994	+	303.098i	−0.229350	+	0.397245i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	362.900	+	209.521i	0.473143	+	0.273169i
$768$		0			0
$769$	422.147	+	731.179i	0.548955	+	0.950819i	0.998346	+	0.0574834i	$0.0183076\pi$
$769$	422.147	+	731.179i	0.548955	+	0.950819i	−0.449391	+	0.893335i	$0.648359\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			816.503i			1.05628i	0.849158	+	0.528139i	$0.177110\pi$
$773$			816.503i			1.05628i	−0.849158	+	0.528139i	$0.822890\pi$
$774$		0			0
$775$	−1134.97			−1.46448
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−192.046	+	110.878i	−0.246529	+	0.142334i
$780$		0			0
$781$	−953.093	+	1650.81i	−1.22035	+	2.11371i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	563.991	+	325.620i	0.718459	+	0.414803i
$786$		0			0
$787$	−178.111	−	308.497i	−0.226316	−	0.391991i	0.730397	−	0.683022i	$-0.239335\pi$
$787$	−178.111	−	308.497i	−0.226316	−	0.391991i	−0.956713	+	0.291031i	$0.906002\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	167.765i		−	0.212092i
$792$		0			0
$793$	−35.0038			−0.0441410
$794$		0			0
$795$		0			0
$796$		0			0
$797$	561.666	−	324.278i	0.704725	−	0.406873i	−0.104380	−	0.994537i	$-0.533286\pi$
$797$	561.666	−	324.278i	0.704725	−	0.406873i	0.809105	+	0.587664i	$0.199952\pi$
$798$		0			0
$799$	138.462	−	239.823i	0.173294	−	0.300154i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−75.2062	−	43.4203i	−0.0936565	−	0.0540726i
$804$		0			0
$805$	60.9948	+	105.646i	0.0757700	+	0.131237i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			445.244i			0.550363i	0.961392	+	0.275182i	$0.0887380\pi$
$809$			445.244i			0.550363i	−0.961392	+	0.275182i	$0.911262\pi$
$810$		0			0
$811$	−373.366			−0.460377			−0.230189	−	0.973146i	$-0.573934\pi$
$811$	−373.366			−0.460377			−0.230189	+	0.973146i	$0.573934\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1718.68	+	992.282i	−2.10881	+	1.21752i
$816$		0			0
$817$	−281.667	+	487.862i	−0.344758	+	0.597139i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−42.7001	−	24.6529i	−0.0520099	−	0.0300279i	0.473770	−	0.880649i	$-0.342893\pi$
$821$	−42.7001	−	24.6529i	−0.0520099	−	0.0300279i	−0.525779	+	0.850621i	$0.676226\pi$
$822$		0			0
$823$	−289.224	−	500.950i	−0.351426	−	0.608688i	0.635074	−	0.772452i	$-0.280970\pi$
$823$	−289.224	−	500.950i	−0.351426	−	0.608688i	−0.986500	+	0.163764i	$0.947636\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	665.710i		−	0.804970i	−0.915427	−	0.402485i	$-0.868147\pi$
$827$		−	665.710i		−	0.804970i	0.915427	−	0.402485i	$-0.131853\pi$
$828$		0			0
$829$	−133.042			−0.160485			−0.0802423	−	0.996775i	$-0.525569\pi$
$829$	−133.042			−0.160485			−0.0802423	+	0.996775i	$0.525569\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	447.483	−	258.355i	0.537195	−	0.310150i
$834$		0			0
$835$	−116.927	+	202.523i	−0.140032	+	0.242543i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−707.636	−	408.554i	−0.843428	−	0.486954i	0.0149998	−	0.999887i	$-0.495225\pi$
$839$	−707.636	−	408.554i	−0.843428	−	0.486954i	−0.858428	+	0.512934i	$0.828559\pi$
$840$		0			0
$841$	−11.5724	−	20.0439i	−0.0137602	−	0.0238334i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			763.087i			0.903062i
$846$		0			0
$847$	−273.663			−0.323097
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−82.3878	+	47.5666i	−0.0968129	+	0.0558950i
$852$		0			0
$853$	14.2616	−	24.7018i	0.0167193	−	0.0289587i	−0.857545	−	0.514409i	$-0.828011\pi$
$853$	14.2616	−	24.7018i	0.0167193	−	0.0289587i	0.874264	+	0.485451i	$0.161344\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1218.49	+	703.496i	1.42181	+	0.820883i	0.996454	−	0.0841433i	$-0.0268154\pi$
$857$	1218.49	+	703.496i	1.42181	+	0.820883i	0.425357	+	0.905026i	$0.360149\pi$
$858$		0			0
$859$	−296.573	−	513.680i	−0.345254	−	0.597998i	0.640146	−	0.768254i	$-0.278874\pi$
$859$	−296.573	−	513.680i	−0.345254	−	0.597998i	−0.985400	+	0.170256i	$0.945541\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	549.058i		−	0.636220i	−0.948054	−	0.318110i	$-0.896952\pi$
$863$		−	549.058i		−	0.636220i	0.948054	−	0.318110i	$-0.103048\pi$
$864$		0			0
$865$	−1413.81			−1.63446
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1659.80	−	958.283i	1.91001	−	1.10274i
$870$		0			0
$871$	197.626	−	342.299i	0.226896	−	0.392996i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−690.900	−	398.891i	−0.789600	−	0.455876i
$876$		0			0
$877$	481.413	+	833.831i	0.548931	+	0.950776i	0.998348	+	0.0574544i	$0.0182984\pi$
$877$	481.413	+	833.831i	0.548931	+	0.950776i	−0.449417	+	0.893322i	$0.648368\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			485.913i			0.551547i	0.961223	+	0.275774i	$0.0889340\pi$
$881$			485.913i			0.551547i	−0.961223	+	0.275774i	$0.911066\pi$
$882$		0			0
$883$	1020.25			1.15544			0.577720	−	0.816235i	$-0.303943\pi$
$883$	1020.25			1.15544			0.577720	+	0.816235i	$0.303943\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	896.965	−	517.863i	1.01123	−	0.583836i	0.0996814	−	0.995019i	$-0.468218\pi$
$887$	896.965	−	517.863i	1.01123	−	0.583836i	0.911553	+	0.411183i	$0.134884\pi$
$888$		0			0
$889$	155.584	−	269.480i	0.175011	−	0.303127i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	268.098	+	154.787i	0.300222	+	0.173333i
$894$		0			0
$895$	308.786	+	534.834i	0.345013	+	0.597580i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			500.676i			0.556926i
$900$		0			0
$901$	163.657			0.181640
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−783.880	+	452.573i	−0.866165	+	0.500081i
$906$		0			0
$907$	−794.936	+	1376.87i	−0.876445	+	1.51805i	−0.0212301	+	0.999775i	$0.506758\pi$
$907$	−794.936	+	1376.87i	−0.876445	+	1.51805i	−0.855215	+	0.518273i	$0.826575\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	362.743	+	209.430i	0.398181	+	0.229890i	0.685699	−	0.727885i	$-0.259497\pi$
$911$	362.743	+	209.430i	0.398181	+	0.229890i	−0.287518	+	0.957775i	$0.592830\pi$
$912$		0			0
$913$	425.687	+	737.311i	0.466250	+	0.807569i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			355.943i			0.388160i
$918$		0			0
$919$	1499.57			1.63174			0.815872	−	0.578233i	$-0.196257\pi$
$919$	1499.57			1.63174			0.815872	+	0.578233i	$0.196257\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−981.162	+	566.474i	−1.06301	+	0.613732i
$924$		0			0
$925$	506.333	−	876.994i	0.547387	−	0.948102i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1046.99	+	604.481i	1.12701	+	0.650679i	0.943181	−	0.332279i	$-0.107817\pi$
$929$	1046.99	+	604.481i	1.12701	+	0.650679i	0.183829	+	0.982958i	$0.441151\pi$
$930$		0			0
$931$	288.815	+	500.242i	0.310220	+	0.537317i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	1740.45i		−	1.86144i
$936$		0			0
$937$	557.393			0.594870			0.297435	−	0.954742i	$-0.403869\pi$
$937$	557.393			0.594870			0.297435	+	0.954742i	$0.403869\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	465.315	−	268.650i	0.494490	−	0.285494i	−0.231945	−	0.972729i	$-0.574509\pi$
$941$	465.315	−	268.650i	0.494490	−	0.285494i	0.726435	+	0.687235i	$0.241176\pi$
$942$		0			0
$943$	52.0612	−	90.1727i	0.0552081	−	0.0956232i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−515.416	−	297.575i	−0.544261	−	0.314229i	0.202543	−	0.979273i	$-0.435079\pi$
$947$	−515.416	−	297.575i	−0.544261	−	0.314229i	−0.746804	+	0.665044i	$0.768413\pi$
$948$		0			0
$949$	−25.8070	−	44.6991i	−0.0271939	−	0.0471012i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			88.9834i			0.0933718i	0.998910	+	0.0466859i	$0.0148660\pi$
$953$			88.9834i			0.0933718i	−0.998910	+	0.0466859i	$0.985134\pi$
$954$		0			0
$955$	−1761.40			−1.84440
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−369.814	+	213.512i	−0.385625	+	0.222641i
$960$		0			0
$961$	327.247	−	566.809i	0.340528	−	0.589812i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	790.560	+	456.430i	0.819233	+	0.472985i
$966$		0			0
$967$	658.074	+	1139.82i	0.680532	+	1.17872i	0.974819	+	0.222998i	$0.0715845\pi$
$967$	658.074	+	1139.82i	0.680532	+	1.17872i	−0.294287	+	0.955717i	$0.595082\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			361.433i			0.372228i	0.982528	+	0.186114i	$0.0595893\pi$
$971$			361.433i			0.372228i	−0.982528	+	0.186114i	$0.940411\pi$
$972$		0			0
$973$	546.075			0.561228
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−883.148	+	509.885i	−0.903938	+	0.521889i	−0.878476	−	0.477787i	$-0.841439\pi$
$977$	−883.148	+	509.885i	−0.903938	+	0.521889i	−0.0254624	+	0.999676i	$0.508106\pi$
$978$		0			0
$979$	808.708	−	1400.72i	0.826056	−	1.43077i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1144.21	−	660.612i	−1.16400	−	0.672037i	−0.211742	−	0.977326i	$-0.567914\pi$
$983$	−1144.21	−	660.612i	−1.16400	−	0.672037i	−0.952260	+	0.305289i	$0.901247\pi$
$984$		0			0
$985$	597.675	+	1035.20i	0.606777	+	1.05097i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	264.506i		−	0.267448i
$990$		0			0
$991$	6.11587			0.00617141			0.00308571	−	0.999995i	$-0.499018\pi$
$991$	6.11587			0.00617141			0.00308571	+	0.999995i	$0.499018\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1081.14	−	624.197i	1.08657	−	0.627334i
$996$		0			0
$997$	−315.180	+	545.908i	−0.316129	+	0.547551i	−0.979677	−	0.200583i	$-0.935716\pi$
$997$	−315.180	+	545.908i	−0.316129	+	0.547551i	0.663548	+	0.748134i	$0.269050\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.q.i.1601.1		8
3.2	odd	2		576.3.q.j.65.1		8
4.3	odd	2		1728.3.q.j.1601.1		8
8.3	odd	2		216.3.m.b.89.4		8
8.5	even	2		432.3.q.e.305.4		8
9.4	even	3		576.3.q.j.257.1		8
9.5	odd	6	inner	1728.3.q.i.449.1		8
12.11	even	2		576.3.q.i.65.4		8
24.5	odd	2		144.3.q.e.65.4		8
24.11	even	2		72.3.m.b.65.1	yes	8
36.23	even	6		1728.3.q.j.449.1		8
36.31	odd	6		576.3.q.i.257.4		8
72.5	odd	6		432.3.q.e.17.4		8
72.11	even	6		648.3.e.c.161.1		8
72.13	even	6		144.3.q.e.113.4		8
72.29	odd	6		1296.3.e.i.161.1		8
72.43	odd	6		648.3.e.c.161.8		8
72.59	even	6		216.3.m.b.17.4		8
72.61	even	6		1296.3.e.i.161.8		8
72.67	odd	6		72.3.m.b.41.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.b.41.1	✓	8	72.67	odd	6
72.3.m.b.65.1	yes	8	24.11	even	2
144.3.q.e.65.4		8	24.5	odd	2
144.3.q.e.113.4		8	72.13	even	6
216.3.m.b.17.4		8	72.59	even	6
216.3.m.b.89.4		8	8.3	odd	2
432.3.q.e.17.4		8	72.5	odd	6
432.3.q.e.305.4		8	8.5	even	2
576.3.q.i.65.4		8	12.11	even	2
576.3.q.i.257.4		8	36.31	odd	6
576.3.q.j.65.1		8	3.2	odd	2
576.3.q.j.257.1		8	9.4	even	3
648.3.e.c.161.1		8	72.11	even	6
648.3.e.c.161.8		8	72.43	odd	6
1296.3.e.i.161.1		8	72.29	odd	6
1296.3.e.i.161.8		8	72.61	even	6
1728.3.q.i.449.1		8	9.5	odd	6	inner
1728.3.q.i.1601.1		8	1.1	even	1	trivial
1728.3.q.j.449.1		8	36.23	even	6
1728.3.q.j.1601.1		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.20800 + 4.73889i) q^{5} +(-1.05671 + 1.83027i) q^{7} +O(q^{10})\)	\(q+(-8.20800 + 4.73889i) q^{5} +(-1.05671 + 1.83027i) q^{7} +(-13.7064 - 7.91342i) q^{11} +(-4.70337 - 8.14648i) q^{13} -11.6027i q^{17} +12.9707 q^{19} +(-5.27427 + 3.04510i) q^{23} +(32.4142 - 56.1431i) q^{25} +(-24.7667 - 14.2991i) q^{29} +(-8.75365 - 15.1618i) q^{31} -20.0305i q^{35} +15.6207 q^{37} +(-14.8062 + 8.54836i) q^{41} +(-21.7157 + 37.6127i) q^{43} +(20.6696 + 11.9336i) q^{47} +(22.2667 + 38.5671i) q^{49} +14.1051i q^{53} +150.003 q^{55} +(-38.5788 + 22.2735i) q^{59} +(1.86057 - 3.22260i) q^{61} +(77.2105 + 44.5775i) q^{65} +(21.0090 + 36.3887i) q^{67} -120.440i q^{71} +5.48692 q^{73} +(28.9674 - 16.7243i) q^{77} +(-60.5480 + 104.872i) q^{79} +(-46.5861 - 26.8965i) q^{83} +(54.9840 + 95.2351i) q^{85} +102.195i q^{89} +19.8803 q^{91} +(-106.463 + 61.4667i) q^{95} +(-58.9377 + 102.083i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{5} - 6 q^{7}+O(q^{10}) \) 8 * q - 6 * q^5 - 6 * q^7	\( 8 q - 6 q^{5} - 6 q^{7} - 36 q^{11} - 14 q^{13} + 4 q^{19} - 102 q^{23} + 10 q^{25} - 114 q^{29} + 50 q^{31} - 120 q^{37} - 264 q^{41} - 28 q^{43} + 150 q^{47} + 94 q^{49} + 244 q^{55} + 108 q^{59} - 14 q^{61} + 198 q^{65} - 20 q^{67} - 76 q^{73} + 66 q^{77} - 26 q^{79} - 246 q^{83} + 224 q^{85} + 108 q^{91} - 456 q^{95} - 236 q^{97}+O(q^{100}) \) 8 * q - 6 * q^5 - 6 * q^7 - 36 * q^11 - 14 * q^13 + 4 * q^19 - 102 * q^23 + 10 * q^25 - 114 * q^29 + 50 * q^31 - 120 * q^37 - 264 * q^41 - 28 * q^43 + 150 * q^47 + 94 * q^49 + 244 * q^55 + 108 * q^59 - 14 * q^61 + 198 * q^65 - 20 * q^67 - 76 * q^73 + 66 * q^77 - 26 * q^79 - 246 * q^83 + 224 * q^85 + 108 * q^91 - 456 * q^95 - 236 * q^97

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