LMFDB - Embedded newform 3456.2.i.e.2305.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3456,2,Mod(1153,3456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("3456.1153");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3456 = 2^{7} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3456.i (of order $3$, 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:	$27.5962989386$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 1152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2305.2
Root			$1.72806 - 0.117480i$ of defining polynomial
Character	$\chi$	$=$	3456.2305
Dual form			3456.2.i.e.1153.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.705463 + 1.22190i) q^{5} +(1.17123 + 2.02864i) q^{7} +O(q^{10})$	$q+(-0.705463 + 1.22190i) q^{5} +(1.17123 + 2.02864i) q^{7} +(-1.30116 - 2.25368i) q^{11} +(1.26229 - 2.18635i) q^{13} -4.94479 q^{17} +1.00929 q^{19} +(1.50663 - 2.60955i) q^{23} +(1.50464 + 2.60612i) q^{25} +(0.0708926 + 0.122790i) q^{29} +(-4.77135 + 8.26422i) q^{31} -3.30505 q^{35} +9.00324 q^{37} +(-4.33084 + 7.50123i) q^{41} +(3.15717 + 5.46838i) q^{43} +(3.24898 + 5.62740i) q^{47} +(0.756418 - 1.31015i) q^{49} +6.02590 q^{53} +3.67169 q^{55} +(-5.64142 + 9.77123i) q^{59} +(-3.45856 - 5.99040i) q^{61} +(1.78100 + 3.08478i) q^{65} +(-0.154962 + 0.268402i) q^{67} -8.24940 q^{71} -6.78931 q^{73} +(3.04793 - 5.27917i) q^{77} +(-4.99530 - 8.65211i) q^{79} +(3.47041 + 6.01093i) q^{83} +(3.48837 - 6.04203i) q^{85} -15.8969 q^{89} +5.91375 q^{91} +(-0.712014 + 1.23325i) q^{95} +(7.44449 + 12.8942i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{7}+O(q^{10}) $ 10 * q - 4 * q^7	$ 10 q - 4 q^{7} - q^{11} + 6 q^{13} + 6 q^{17} - 18 q^{19} - 4 q^{23} + q^{25} + 4 q^{29} - 8 q^{31} - 24 q^{35} - 20 q^{37} + 5 q^{41} + 13 q^{43} + 6 q^{47} + 3 q^{49} + 12 q^{55} - 13 q^{59} + 10 q^{61} + 17 q^{67} - 8 q^{71} - 34 q^{73} - 8 q^{77} - 6 q^{79} + 12 q^{83} + 18 q^{85} - 44 q^{89} - 36 q^{91} + 6 q^{95} + 27 q^{97}+O(q^{100}) $ 10 * q - 4 * q^7 - q^11 + 6 * q^13 + 6 * q^17 - 18 * q^19 - 4 * q^23 + q^25 + 4 * q^29 - 8 * q^31 - 24 * q^35 - 20 * q^37 + 5 * q^41 + 13 * q^43 + 6 * q^47 + 3 * q^49 + 12 * q^55 - 13 * q^59 + 10 * q^61 + 17 * q^67 - 8 * q^71 - 34 * q^73 - 8 * q^77 - 6 * q^79 + 12 * q^83 + 18 * q^85 - 44 * q^89 - 36 * q^91 + 6 * q^95 + 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times$.

$n$	$2053$	$2431$	$2945$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−0.705463	+	1.22190i	−0.315493	+	0.546449i	−0.979542	−	0.201239i	$-0.935503\pi$
$5$	−0.705463	+	1.22190i	−0.315493	+	0.546449i	0.664049	+	0.747689i	$0.268836\pi$
$6$		0			0
$7$	1.17123	+	2.02864i	0.442685	+	0.766753i	0.997888	−	0.0649620i	$-0.0206926\pi$
$7$	1.17123	+	2.02864i	0.442685	+	0.766753i	−0.555203	+	0.831715i	$0.687359\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.30116	−	2.25368i	−0.392315	−	0.679510i	0.600439	−	0.799670i	$-0.294992\pi$
$11$	−1.30116	−	2.25368i	−0.392315	−	0.679510i	−0.992754	+	0.120161i	$0.961659\pi$
$12$		0			0
$13$	1.26229	−	2.18635i	0.350096	−	0.606385i	−0.636170	−	0.771549i	$-0.719482\pi$
$13$	1.26229	−	2.18635i	0.350096	−	0.606385i	0.986266	+	0.165164i	$0.0528155\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.94479			−1.19929			−0.599644	−	0.800267i	$-0.704691\pi$
$17$	−4.94479			−1.19929			−0.599644	+	0.800267i	$0.704691\pi$
$18$		0			0
$19$	1.00929			0.231546			0.115773	−	0.993276i	$-0.463065\pi$
$19$	1.00929			0.231546			0.115773	+	0.993276i	$0.463065\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.50663	−	2.60955i	0.314153	−	0.544129i	−0.665104	−	0.746751i	$-0.731613\pi$
$23$	1.50663	−	2.60955i	0.314153	−	0.544129i	0.979257	+	0.202622i	$0.0649461\pi$
$24$		0			0
$25$	1.50464	+	2.60612i	0.300929	+	0.521224i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.0708926	+	0.122790i	0.0131644	+	0.0228015i	0.872533	−	0.488556i	$-0.162476\pi$
$29$	0.0708926	+	0.122790i	0.0131644	+	0.0228015i	−0.859368	+	0.511357i	$0.829143\pi$
$30$		0			0
$31$	−4.77135	+	8.26422i	−0.856960	+	1.48430i	0.0178546	+	0.999841i	$0.494316\pi$
$31$	−4.77135	+	8.26422i	−0.856960	+	1.48430i	−0.874815	+	0.484458i	$0.839017\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.30505			−0.558656
$36$		0			0
$37$	9.00324			1.48012			0.740062	−	0.672539i	$-0.234796\pi$
$37$	9.00324			1.48012			0.740062	+	0.672539i	$0.234796\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.33084	+	7.50123i	−0.676364	+	1.17150i	0.299705	+	0.954032i	$0.403112\pi$
$41$	−4.33084	+	7.50123i	−0.676364	+	1.17150i	−0.976068	+	0.217464i	$0.930222\pi$
$42$		0			0
$43$	3.15717	+	5.46838i	0.481464	+	0.833920i	0.999774	−	0.0212731i	$-0.00677194\pi$
$43$	3.15717	+	5.46838i	0.481464	+	0.833920i	−0.518310	+	0.855193i	$0.673439\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.24898	+	5.62740i	0.473912	+	0.820840i	0.999554	−	0.0298661i	$-0.00950808\pi$
$47$	3.24898	+	5.62740i	0.473912	+	0.820840i	−0.525642	+	0.850706i	$0.676175\pi$
$48$		0			0
$49$	0.756418	−	1.31015i	0.108060	−	0.187165i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.02590			0.827721			0.413861	−	0.910340i	$-0.364180\pi$
$53$	6.02590			0.827721			0.413861	+	0.910340i	$0.364180\pi$
$54$		0			0
$55$	3.67169			0.495090
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.64142	+	9.77123i	−0.734451	+	1.27211i	0.220513	+	0.975384i	$0.429227\pi$
$59$	−5.64142	+	9.77123i	−0.734451	+	1.27211i	−0.954964	+	0.296722i	$0.904106\pi$
$60$		0			0
$61$	−3.45856	−	5.99040i	−0.442823	−	0.766992i	0.555075	−	0.831801i	$-0.312690\pi$
$61$	−3.45856	−	5.99040i	−0.442823	−	0.766992i	−0.997898	+	0.0648083i	$0.979356\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.78100	+	3.08478i	0.220906	+	0.382620i
$66$		0			0
$67$	−0.154962	+	0.268402i	−0.0189316	+	0.0327905i	−0.875336	−	0.483515i	$-0.839360\pi$
$67$	−0.154962	+	0.268402i	−0.0189316	+	0.0327905i	0.856404	+	0.516306i	$0.172693\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.24940			−0.979023			−0.489512	−	0.871997i	$-0.662825\pi$
$71$	−8.24940			−0.979023			−0.489512	+	0.871997i	$0.662825\pi$
$72$		0			0
$73$	−6.78931			−0.794628			−0.397314	−	0.917683i	$-0.630058\pi$
$73$	−6.78931			−0.794628			−0.397314	+	0.917683i	$0.630058\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.04793	−	5.27917i	0.347344	−	0.601618i
$78$		0			0
$79$	−4.99530	−	8.65211i	−0.562015	−	0.973438i	−0.997321	−	0.0731553i	$-0.976693\pi$
$79$	−4.99530	−	8.65211i	−0.562015	−	0.973438i	0.435306	−	0.900283i	$-0.356640\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.47041	+	6.01093i	0.380928	+	0.659786i	0.991195	−	0.132410i	$-0.0422714\pi$
$83$	3.47041	+	6.01093i	0.380928	+	0.659786i	−0.610268	+	0.792195i	$0.708938\pi$
$84$		0			0
$85$	3.48837	−	6.04203i	0.378367	−	0.655351i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−15.8969			−1.68507			−0.842535	−	0.538642i	$-0.818938\pi$
$89$	−15.8969			−1.68507			−0.842535	+	0.538642i	$0.818938\pi$
$90$		0			0
$91$	5.91375			0.619930
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.712014	+	1.23325i	−0.0730511	+	0.126528i
$96$		0			0
$97$	7.44449	+	12.8942i	0.755874	+	1.30921i	0.944939	+	0.327247i	$0.106121\pi$
$97$	7.44449	+	12.8942i	0.755874	+	1.30921i	−0.189065	+	0.981965i	$0.560546\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.823082	+	1.42562i	0.0818997	+	0.141855i	0.904066	−	0.427393i	$-0.140568\pi$
$101$	0.823082	+	1.42562i	0.0818997	+	0.141855i	−0.822166	+	0.569248i	$0.807235\pi$
$102$		0			0
$103$	−6.40783	+	11.0987i	−0.631382	+	1.09359i	0.355887	+	0.934529i	$0.384179\pi$
$103$	−6.40783	+	11.0987i	−0.631382	+	1.09359i	−0.987269	+	0.159057i	$0.949155\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.6556			−1.32014			−0.660070	−	0.751204i	$-0.729473\pi$
$107$	−13.6556			−1.32014			−0.660070	+	0.751204i	$0.729473\pi$
$108$		0			0
$109$	−12.9953			−1.24473			−0.622363	−	0.782729i	$-0.713827\pi$
$109$	−12.9953			−1.24473			−0.622363	+	0.782729i	$0.713827\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.75804	−	6.50912i	0.353527	−	0.612326i	−0.633338	−	0.773875i	$-0.718316\pi$
$113$	3.75804	−	6.50912i	0.353527	−	0.612326i	0.986865	+	0.161549i	$0.0516491\pi$
$114$		0			0
$115$	2.12574	+	3.68189i	0.198226	+	0.343338i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−5.79151	−	10.0312i	−0.530907	−	0.919558i
$120$		0			0
$121$	2.11395	−	3.66148i	0.192178	−	0.332861i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.3005			−1.01075
$126$		0			0
$127$	−2.09832			−0.186196			−0.0930981	−	0.995657i	$-0.529677\pi$
$127$	−2.09832			−0.186196			−0.0930981	+	0.995657i	$0.529677\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.00428	+	6.93562i	−0.349856	+	0.605968i	−0.986224	−	0.165418i	$-0.947103\pi$
$131$	−4.00428	+	6.93562i	−0.349856	+	0.605968i	0.636368	+	0.771386i	$0.280436\pi$
$132$		0			0
$133$	1.18211	+	2.04748i	0.102502	+	0.177539i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.17445	−	2.03420i	−0.100340	−	0.173793i	0.811485	−	0.584373i	$-0.198660\pi$
$137$	−1.17445	−	2.03420i	−0.100340	−	0.173793i	−0.911825	+	0.410580i	$0.865326\pi$
$138$		0			0
$139$	−5.62654	+	9.74546i	−0.477237	+	0.826599i	−0.999660	−	0.0260876i	$-0.991695\pi$
$139$	−5.62654	+	9.74546i	−0.477237	+	0.826599i	0.522422	+	0.852687i	$0.325028\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.56978			−0.549392
$144$		0			0
$145$	−0.200049			−0.0166131
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.9924	−	20.7715i	0.982458	−	1.70167i	0.329729	−	0.944076i	$-0.393043\pi$
$149$	11.9924	−	20.7715i	0.982458	−	1.70167i	0.652729	−	0.757591i	$-0.273624\pi$
$150$		0			0
$151$	6.56507	+	11.3710i	0.534258	+	0.925362i	0.999199	+	0.0400204i	$0.0127423\pi$
$151$	6.56507	+	11.3710i	0.534258	+	0.925362i	−0.464941	+	0.885342i	$0.653924\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.73203	−	11.6602i	−0.540729	−	0.936571i
$156$		0			0
$157$	11.6217	−	20.1293i	0.927511	−	1.60650i	0.140038	−	0.990146i	$-0.455278\pi$
$157$	11.6217	−	20.1293i	0.927511	−	1.60650i	0.787473	−	0.616350i	$-0.211389\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.05845			0.556284
$162$		0			0
$163$	−22.5825			−1.76879			−0.884397	−	0.466735i	$-0.845430\pi$
$163$	−22.5825			−1.76879			−0.884397	+	0.466735i	$0.845430\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.4260	+	21.5224i	−0.961549	+	1.66545i	−0.242935	+	0.970043i	$0.578110\pi$
$167$	−12.4260	+	21.5224i	−0.961549	+	1.66545i	−0.718614	+	0.695409i	$0.755223\pi$
$168$		0			0
$169$	3.31325	+	5.73871i	0.254865	+	0.441439i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.98389	+	6.90030i	0.302890	+	0.524620i	0.976789	−	0.214203i	$-0.0687153\pi$
$173$	3.98389	+	6.90030i	0.302890	+	0.524620i	−0.673900	+	0.738823i	$0.735382\pi$
$174$		0			0
$175$	−3.52458	+	6.10475i	−0.266433	+	0.461476i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.70760			−0.277119			−0.138560	−	0.990354i	$-0.544247\pi$
$179$	−3.70760			−0.277119			−0.138560	+	0.990354i	$0.544247\pi$
$180$		0			0
$181$	−13.0683			−0.971362			−0.485681	−	0.874136i	$-0.661428\pi$
$181$	−13.0683			−0.971362			−0.485681	+	0.874136i	$0.661428\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.35146	+	11.0010i	−0.466968	+	0.808813i
$186$		0			0
$187$	6.43398	+	11.1440i	0.470499	+	0.814928i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.157984	+	0.273636i	0.0114313	+	0.0197996i	0.871684	−	0.490068i	$-0.163028\pi$
$191$	0.157984	+	0.273636i	0.0114313	+	0.0197996i	−0.860253	+	0.509867i	$0.829695\pi$
$192$		0			0
$193$	−10.0237	+	17.3616i	−0.721522	+	1.24971i	0.238867	+	0.971052i	$0.423224\pi$
$193$	−10.0237	+	17.3616i	−0.721522	+	1.24971i	−0.960390	+	0.278661i	$0.910109\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	23.5586			1.67848			0.839240	−	0.543761i	$-0.183000\pi$
$197$	23.5586			1.67848			0.839240	+	0.543761i	$0.183000\pi$
$198$		0			0
$199$	−0.249396			−0.0176792			−0.00883960	−	0.999961i	$-0.502814\pi$
$199$	−0.249396			−0.0176792			−0.00883960	+	0.999961i	$0.502814\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.166064	+	0.287631i	−0.0116554	+	0.0201877i
$204$		0			0
$205$	−6.11050	−	10.5837i	−0.426776	−	0.739197i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.31325	−	2.27461i	−0.0908391	−	0.157338i
$210$		0			0
$211$	−1.17490	+	2.03499i	−0.0808834	+	0.140094i	−0.903630	−	0.428315i	$-0.859107\pi$
$211$	−1.17490	+	2.03499i	−0.0808834	+	0.140094i	0.822746	+	0.568409i	$0.192441\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.90907			−0.607593
$216$		0			0
$217$	−22.3535			−1.51745
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.24177	+	10.8111i	−0.419867	+	0.727230i
$222$		0			0
$223$	4.71439	+	8.16556i	0.315699	+	0.546806i	0.979586	−	0.201027i	$-0.0644277\pi$
$223$	4.71439	+	8.16556i	0.315699	+	0.546806i	−0.663887	+	0.747833i	$0.731094\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.0231851	+	0.0401577i	0.00153885	+	0.00266536i	0.866794	−	0.498667i	$-0.166177\pi$
$227$	0.0231851	+	0.0401577i	0.00153885	+	0.00266536i	−0.865255	+	0.501332i	$0.832844\pi$
$228$		0			0
$229$	4.03468	−	6.98827i	0.266619	−	0.461798i	−0.701367	−	0.712800i	$-0.747427\pi$
$229$	4.03468	−	6.98827i	0.266619	−	0.461798i	0.967987	+	0.251002i	$0.0807600\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.99336			−0.261614			−0.130807	−	0.991408i	$-0.541757\pi$
$233$	−3.99336			−0.261614			−0.130807	+	0.991408i	$0.541757\pi$
$234$		0			0
$235$	−9.16814			−0.598063
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.84910	+	3.20273i	−0.119608	+	0.207167i	−0.919612	−	0.392827i	$-0.871497\pi$
$239$	−1.84910	+	3.20273i	−0.119608	+	0.207167i	0.800004	+	0.599994i	$0.204830\pi$
$240$		0			0
$241$	13.0879	+	22.6689i	0.843066	+	1.46023i	0.887290	+	0.461211i	$0.152585\pi$
$241$	13.0879	+	22.6689i	0.843066	+	1.46023i	−0.0442246	+	0.999022i	$0.514082\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.06725	+	1.84853i	0.0681841	+	0.118098i
$246$		0			0
$247$	1.27401	−	2.20665i	0.0810635	−	0.140406i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	19.7393			1.24593			0.622967	−	0.782248i	$-0.285927\pi$
$251$	19.7393			1.24593			0.622967	+	0.782248i	$0.285927\pi$
$252$		0			0
$253$	−7.84146			−0.492988
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.53591	−	6.12438i	0.220564	−	0.382028i	−0.734415	−	0.678700i	$-0.762544\pi$
$257$	3.53591	−	6.12438i	0.220564	−	0.382028i	0.954979	+	0.296672i	$0.0958769\pi$
$258$		0			0
$259$	10.5449	+	18.2643i	0.655229	+	1.13489i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.03211	+	6.98383i	0.248631	+	0.430641i	0.963146	−	0.268979i	$-0.0866861\pi$
$263$	4.03211	+	6.98383i	0.248631	+	0.430641i	−0.714515	+	0.699620i	$0.753353\pi$
$264$		0			0
$265$	−4.25105	+	7.36304i	−0.261140	+	0.452308i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.76619			0.534484			0.267242	−	0.963629i	$-0.413888\pi$
$269$	8.76619			0.534484			0.267242	+	0.963629i	$0.413888\pi$
$270$		0			0
$271$	27.7606			1.68634			0.843168	−	0.537650i	$-0.180688\pi$
$271$	27.7606			1.68634			0.843168	+	0.537650i	$0.180688\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.91557	−	6.78197i	0.236118	−	0.408968i
$276$		0			0
$277$	13.7727	+	23.8551i	0.827524	+	1.43331i	0.899975	+	0.435942i	$0.143585\pi$
$277$	13.7727	+	23.8551i	0.827524	+	1.43331i	−0.0724506	+	0.997372i	$0.523082\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.24109	−	5.61373i	−0.193347	−	0.334887i	0.753010	−	0.658009i	$-0.228601\pi$
$281$	−3.24109	−	5.61373i	−0.193347	−	0.334887i	−0.946357	+	0.323122i	$0.895268\pi$
$282$		0			0
$283$	3.32863	−	5.76536i	0.197866	−	0.342715i	−0.749970	−	0.661472i	$-0.769932\pi$
$283$	3.32863	−	5.76536i	0.197866	−	0.342715i	0.947836	+	0.318757i	$0.103265\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−20.2897			−1.19766
$288$		0			0
$289$	7.45099			0.438293
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.61375	−	4.52714i	0.152697	−	0.264479i	−0.779521	−	0.626376i	$-0.784538\pi$
$293$	2.61375	−	4.52714i	0.152697	−	0.264479i	0.932218	+	0.361897i	$0.117871\pi$
$294$		0			0
$295$	−7.95963	−	13.7865i	−0.463428	−	0.802681i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.80360	−	6.58802i	−0.219968	−	0.380995i
$300$		0			0
$301$	−7.39557	+	12.8095i	−0.426274	+	0.738328i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.75955			0.558830
$306$		0			0
$307$	−15.8311			−0.903531			−0.451765	−	0.892137i	$-0.649206\pi$
$307$	−15.8311			−0.903531			−0.451765	+	0.892137i	$0.649206\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.40298	+	2.43003i	−0.0795557	+	0.137794i	−0.903058	−	0.429518i	$-0.858683\pi$
$311$	−1.40298	+	2.43003i	−0.0795557	+	0.137794i	0.823503	+	0.567312i	$0.192017\pi$
$312$		0			0
$313$	−7.35704	−	12.7428i	−0.415845	−	0.720264i	0.579672	−	0.814850i	$-0.303181\pi$
$313$	−7.35704	−	12.7428i	−0.415845	−	0.720264i	−0.995517	+	0.0945858i	$0.969847\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.668345	−	1.15761i	−0.0375380	−	0.0650178i	0.846646	−	0.532156i	$-0.178618\pi$
$317$	−0.668345	−	1.15761i	−0.0375380	−	0.0650178i	−0.884184	+	0.467139i	$0.845285\pi$
$318$		0			0
$319$	0.184486	−	0.319538i	0.0103292	−	0.0178907i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−4.99071			−0.277691
$324$		0			0
$325$	7.59719			0.421416
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.61063	+	13.1820i	−0.419588	+	0.726747i
$330$		0			0
$331$	−2.69612	−	4.66981i	−0.148192	−	0.256676i	0.782367	−	0.622817i	$-0.214012\pi$
$331$	−2.69612	−	4.66981i	−0.148192	−	0.256676i	−0.930559	+	0.366141i	$0.880679\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.218640	−	0.378695i	−0.0119456	−	0.0206903i
$336$		0			0
$337$	11.8198	−	20.4725i	0.643866	−	1.11521i	−0.340696	−	0.940173i	$-0.610663\pi$
$337$	11.8198	−	20.4725i	0.643866	−	1.11521i	0.984562	−	0.175035i	$-0.0560039\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	24.8332			1.34479
$342$		0			0
$343$	19.9411			1.07672
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.649676	+	1.12527i	−0.0348764	+	0.0604077i	−0.882937	−	0.469492i	$-0.844437\pi$
$347$	−0.649676	+	1.12527i	−0.0348764	+	0.0604077i	0.848060	+	0.529900i	$0.177770\pi$
$348$		0			0
$349$	6.27720	+	10.8724i	0.336011	+	0.581988i	0.983678	−	0.179935i	$-0.0575888\pi$
$349$	6.27720	+	10.8724i	0.336011	+	0.581988i	−0.647668	+	0.761923i	$0.724255\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.71760	+	13.3673i	0.410766	+	0.711468i	0.994974	−	0.100136i	$-0.0319278\pi$
$353$	7.71760	+	13.3673i	0.410766	+	0.711468i	−0.584207	+	0.811604i	$0.698595\pi$
$354$		0			0
$355$	5.81965	−	10.0799i	0.308875	−	0.534987i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	28.8687			1.52363			0.761817	−	0.647792i	$-0.224308\pi$
$359$	28.8687			1.52363			0.761817	+	0.647792i	$0.224308\pi$
$360$		0			0
$361$	−17.9813			−0.946386
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.78961	−	8.29584i	0.250699	−	0.434224i
$366$		0			0
$367$	−0.959507	−	1.66192i	−0.0500859	−	0.0867513i	0.839896	−	0.542748i	$-0.182616\pi$
$367$	−0.959507	−	1.66192i	−0.0500859	−	0.0867513i	−0.889981	+	0.455997i	$0.849283\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.05775	+	12.2244i	0.366420	+	0.634658i
$372$		0			0
$373$	4.71108	−	8.15984i	0.243931	−	0.422500i	−0.717900	−	0.696147i	$-0.754896\pi$
$373$	4.71108	−	8.15984i	0.243931	−	0.422500i	0.961830	+	0.273646i	$0.0882297\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.357948			0.0184353
$378$		0			0
$379$	−16.1191			−0.827984			−0.413992	−	0.910281i	$-0.635866\pi$
$379$	−16.1191			−0.827984			−0.413992	+	0.910281i	$0.635866\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.35380	−	7.54100i	0.222469	−	0.385327i	−0.733088	−	0.680133i	$-0.761922\pi$
$383$	4.35380	−	7.54100i	0.222469	−	0.385327i	0.955557	+	0.294806i	$0.0952552\pi$
$384$		0			0
$385$	4.30041	+	7.44853i	0.219169	+	0.379612i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.1015	−	17.4963i	−0.512167	−	0.887099i	−0.999900	−	0.0141065i	$-0.995510\pi$
$389$	−10.1015	−	17.4963i	−0.512167	−	0.887099i	0.487734	−	0.872993i	$-0.337824\pi$
$390$		0			0
$391$	−7.44995	+	12.9037i	−0.376760	+	0.652568i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	14.0960			0.709246
$396$		0			0
$397$	−35.3319			−1.77326			−0.886628	−	0.462483i	$-0.846959\pi$
$397$	−35.3319			−1.77326			−0.886628	+	0.462483i	$0.846959\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.03813	+	8.72630i	−0.251592	+	0.435771i	−0.963964	−	0.266031i	$-0.914288\pi$
$401$	−5.03813	+	8.72630i	−0.251592	+	0.435771i	0.712372	+	0.701802i	$0.247621\pi$
$402$		0			0
$403$	12.0457	+	20.8637i	0.600037	+	1.03930i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.7147	−	20.2904i	−0.580675	−	1.00576i
$408$		0			0
$409$	2.08466	−	3.61073i	0.103080	−	0.178539i	−0.809872	−	0.586606i	$-0.800464\pi$
$409$	2.08466	−	3.61073i	0.103080	−	0.178539i	0.912952	+	0.408067i	$0.133797\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−26.4297			−1.30052
$414$		0			0
$415$	−9.79300			−0.480719
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.13944	−	14.0979i	0.397638	−	0.688729i	−0.595796	−	0.803136i	$-0.703163\pi$
$419$	8.13944	−	14.0979i	0.397638	−	0.688729i	0.993434	+	0.114407i	$0.0364968\pi$
$420$		0			0
$421$	6.90585	+	11.9613i	0.336570	+	0.582957i	0.983785	−	0.179351i	$-0.0573996\pi$
$421$	6.90585	+	11.9613i	0.336570	+	0.582957i	−0.647215	+	0.762308i	$0.724066\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.44015	−	12.8867i	−0.360900	−	0.625098i
$426$		0			0
$427$	8.10157	−	14.0323i	0.392063	−	0.679072i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.2716			−0.639268			−0.319634	−	0.947541i	$-0.603560\pi$
$431$	−13.2716			−0.639268			−0.319634	+	0.947541i	$0.603560\pi$
$432$		0			0
$433$	−4.32495			−0.207844			−0.103922	−	0.994585i	$-0.533139\pi$
$433$	−4.32495			−0.207844			−0.103922	+	0.994585i	$0.533139\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.52062	−	2.63379i	0.0727410	−	0.125991i
$438$		0			0
$439$	−9.69938	−	16.7998i	−0.462926	−	0.801812i	0.536179	−	0.844104i	$-0.319867\pi$
$439$	−9.69938	−	16.7998i	−0.462926	−	0.801812i	−0.999105	+	0.0422926i	$0.986534\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	15.1280	+	26.2025i	0.718754	+	1.24492i	0.961494	+	0.274827i	$0.0886204\pi$
$443$	15.1280	+	26.2025i	0.718754	+	1.24492i	−0.242740	+	0.970091i	$0.578046\pi$
$444$		0			0
$445$	11.2147	−	19.4244i	0.531627	−	0.920806i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.49691			0.400994			0.200497	−	0.979694i	$-0.435744\pi$
$449$	8.49691			0.400994			0.200497	+	0.979694i	$0.435744\pi$
$450$		0			0
$451$	22.5405			1.06139
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.17194	+	7.22601i	−0.195583	+	0.338760i
$456$		0			0
$457$	−15.8223	−	27.4050i	−0.740136	−	1.28195i	−0.952433	−	0.304748i	$-0.901428\pi$
$457$	−15.8223	−	27.4050i	−0.740136	−	1.28195i	0.212297	−	0.977205i	$-0.431906\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.62685	−	16.6742i	−0.448367	−	0.776594i	0.549913	−	0.835222i	$-0.314661\pi$
$461$	−9.62685	−	16.6742i	−0.448367	−	0.776594i	−0.998280	+	0.0586276i	$0.981328\pi$
$462$		0			0
$463$	−7.46981	+	12.9381i	−0.347151	+	0.601284i	−0.985742	−	0.168263i	$-0.946184\pi$
$463$	−7.46981	+	12.9381i	−0.347151	+	0.601284i	0.638591	+	0.769546i	$0.279518\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−39.9590			−1.84908			−0.924540	−	0.381084i	$-0.875551\pi$
$467$	−39.9590			−1.84908			−0.924540	+	0.381084i	$0.875551\pi$
$468$		0			0
$469$	−0.725987			−0.0335230
$470$		0			0
$471$		0			0
$472$		0			0
$473$	8.21598	−	14.2305i	0.377771	−	0.654319i
$474$		0			0
$475$	1.51862	+	2.63032i	0.0696789	+	0.120687i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	16.1993	+	28.0581i	0.740167	+	1.28201i	0.952419	+	0.304792i	$0.0985869\pi$
$479$	16.1993	+	28.0581i	0.740167	+	1.28201i	−0.212252	+	0.977215i	$0.568080\pi$
$480$		0			0
$481$	11.3647	−	19.6843i	0.518186	−	0.897525i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−21.0073			−0.953891
$486$		0			0
$487$	−27.8763			−1.26320			−0.631598	−	0.775296i	$-0.717601\pi$
$487$	−27.8763			−1.26320			−0.631598	+	0.775296i	$0.717601\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.12126	+	14.0664i	−0.366507	+	0.634809i	−0.989017	−	0.147803i	$-0.952780\pi$
$491$	−8.12126	+	14.0664i	−0.366507	+	0.634809i	0.622510	+	0.782612i	$0.286113\pi$
$492$		0			0
$493$	−0.350549	−	0.607170i	−0.0157880	−	0.0273455i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.66198	−	16.7350i	−0.433399	−	0.750669i
$498$		0			0
$499$	18.1826	−	31.4932i	0.813966	−	1.40983i	−0.0961021	−	0.995371i	$-0.530638\pi$
$499$	18.1826	−	31.4932i	0.813966	−	1.40983i	0.910068	−	0.414459i	$-0.136029\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	43.2509			1.92846			0.964231	−	0.265063i	$-0.0853929\pi$
$503$	43.2509			1.92846			0.964231	+	0.265063i	$0.0853929\pi$
$504$		0			0
$505$	−2.32262			−0.103355
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−21.2885	+	36.8728i	−0.943597	+	1.63436i	−0.185062	+	0.982727i	$0.559249\pi$
$509$	−21.2885	+	36.8728i	−0.943597	+	1.63436i	−0.758536	+	0.651632i	$0.774085\pi$
$510$		0			0
$511$	−7.95187	−	13.7730i	−0.351770	−	0.609284i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.04098	−	15.6594i	−0.398393	−	0.690037i
$516$		0			0
$517$	8.45489	−	14.6443i	0.371846	−	0.644056i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−21.0544			−0.922408			−0.461204	−	0.887294i	$-0.652582\pi$
$521$	−21.0544			−0.922408			−0.461204	+	0.887294i	$0.652582\pi$
$522$		0			0
$523$	−21.0092			−0.918667			−0.459333	−	0.888264i	$-0.651912\pi$
$523$	−21.0092			−0.918667			−0.459333	+	0.888264i	$0.651912\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	23.5934	−	40.8649i	1.02774	−	1.78010i
$528$		0			0
$529$	6.96016	+	12.0554i	0.302616	+	0.524146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	10.9336	+	18.9375i	0.473585	+	0.820273i
$534$		0			0
$535$	9.63355	−	16.6858i	0.416495	−	0.721390i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.93689			−0.169574
$540$		0			0
$541$	12.3375			0.530429			0.265215	−	0.964189i	$-0.414557\pi$
$541$	12.3375			0.530429			0.265215	+	0.964189i	$0.414557\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9.16772	−	15.8790i	0.392702	−	0.680179i
$546$		0			0
$547$	−0.461070	−	0.798596i	−0.0197139	−	0.0341455i	0.856000	−	0.516976i	$-0.172942\pi$
$547$	−0.461070	−	0.798596i	−0.0197139	−	0.0341455i	−0.875714	+	0.482830i	$0.839609\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.0715510	+	0.123930i	0.00304817	+	0.00527959i
$552$		0			0
$553$	11.7013	−	20.2673i	0.497591	−	0.861853i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.1352			0.810786			0.405393	−	0.914142i	$-0.367135\pi$
$557$	19.1352			0.810786			0.405393	+	0.914142i	$0.367135\pi$
$558$		0			0
$559$	15.9411			0.674235
$560$		0			0
$561$		0			0
$562$		0			0
$563$	16.9309	−	29.3252i	0.713552	−	1.23591i	−0.249963	−	0.968255i	$-0.580419\pi$
$563$	16.9309	−	29.3252i	0.713552	−	1.23591i	0.963515	−	0.267653i	$-0.0862482\pi$
$564$		0			0
$565$	5.30232	+	9.18388i	0.223070	+	0.386369i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	14.1745	+	24.5509i	0.594225	+	1.02923i	0.993656	+	0.112465i	$0.0358745\pi$
$569$	14.1745	+	24.5509i	0.594225	+	1.02923i	−0.399431	+	0.916763i	$0.630792\pi$
$570$		0			0
$571$	11.9901	−	20.7674i	0.501769	−	0.869089i	−0.498229	−	0.867045i	$-0.666016\pi$
$571$	11.9901	−	20.7674i	0.501769	−	0.869089i	0.999998	−	0.00204345i	$-0.000650451\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	9.06773			0.378151
$576$		0			0
$577$	10.2508			0.426746			0.213373	−	0.976971i	$-0.431555\pi$
$577$	10.2508			0.426746			0.213373	+	0.976971i	$0.431555\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−8.12934	+	14.0804i	−0.337262	+	0.584155i
$582$		0			0
$583$	−7.84068	−	13.5805i	−0.324728	−	0.562445i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.15393	−	3.73071i	−0.0889021	−	0.153983i	0.818145	−	0.575012i	$-0.195002\pi$
$587$	−2.15393	−	3.73071i	−0.0889021	−	0.153983i	−0.907047	+	0.421029i	$0.861669\pi$
$588$		0			0
$589$	−4.81566	+	8.34097i	−0.198426	+	0.343684i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	27.4046			1.12537			0.562686	−	0.826670i	$-0.309768\pi$
$593$	27.4046			1.12537			0.562686	+	0.826670i	$0.309768\pi$
$594$		0			0
$595$	16.3428			0.669990
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13.5711	−	23.5058i	0.554500	−	0.960423i	−0.443442	−	0.896303i	$-0.646243\pi$
$599$	13.5711	−	23.5058i	0.554500	−	0.960423i	0.997942	−	0.0641195i	$-0.0204239\pi$
$600$		0			0
$601$	11.7512	+	20.3537i	0.479341	+	0.830244i	0.999719	−	0.0236923i	$-0.00754221\pi$
$601$	11.7512	+	20.3537i	0.479341	+	0.830244i	−0.520378	+	0.853936i	$0.674209\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.98263	+	5.16607i	0.121261	+	0.210031i
$606$		0			0
$607$	−2.69717	+	4.67164i	−0.109475	+	0.189616i	−0.915558	−	0.402187i	$-0.868250\pi$
$607$	−2.69717	+	4.67164i	−0.109475	+	0.189616i	0.806083	+	0.591803i	$0.201584\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	16.4046			0.663660
$612$		0			0
$613$	−5.92486			−0.239303			−0.119651	−	0.992816i	$-0.538178\pi$
$613$	−5.92486			−0.239303			−0.119651	+	0.992816i	$0.538178\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.12456	−	10.6081i	0.246566	−	0.427064i	−0.716005	−	0.698095i	$-0.754031\pi$
$617$	6.12456	−	10.6081i	0.246566	−	0.427064i	0.962571	+	0.271031i	$0.0873646\pi$
$618$		0			0
$619$	0.656697	+	1.13743i	0.0263949	+	0.0457173i	0.878921	−	0.476967i	$-0.158264\pi$
$619$	0.656697	+	1.13743i	0.0263949	+	0.0457173i	−0.852526	+	0.522684i	$0.824931\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−18.6190	−	32.2491i	−0.745955	−	1.29203i
$624$		0			0
$625$	0.448881	−	0.777485i	0.0179553	−	0.0310994i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−44.5192			−1.77510
$630$		0			0
$631$	28.7173			1.14322			0.571608	−	0.820527i	$-0.306320\pi$
$631$	28.7173			1.14322			0.571608	+	0.820527i	$0.306320\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.48029	−	2.56394i	0.0587435	−	0.101747i
$636$		0			0
$637$	−1.90964	−	3.30759i	−0.0756626	−	0.131052i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.67893	−	16.7644i	−0.382295	−	0.662154i	0.609095	−	0.793097i	$-0.291533\pi$
$641$	−9.67893	−	16.7644i	−0.382295	−	0.662154i	−0.991390	+	0.130943i	$0.958199\pi$
$642$		0			0
$643$	−0.415416	+	0.719521i	−0.0163824	+	0.0283751i	−0.874100	−	0.485745i	$-0.838548\pi$
$643$	−0.415416	+	0.719521i	−0.0163824	+	0.0283751i	0.857718	+	0.514120i	$0.171882\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.1290			0.398211			0.199106	−	0.979978i	$-0.436196\pi$
$647$	10.1290			0.398211			0.199106	+	0.979978i	$0.436196\pi$
$648$		0			0
$649$	29.3616			1.15254
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.0565	+	36.4709i	−0.824004	+	1.42722i	0.0786734	+	0.996900i	$0.474932\pi$
$653$	−21.0565	+	36.4709i	−0.824004	+	1.42722i	−0.902678	+	0.430317i	$0.858402\pi$
$654$		0			0
$655$	−5.64975	−	9.78565i	−0.220754	−	0.382357i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	13.0094	+	22.5329i	0.506774	+	0.877759i	0.999969	+	0.00784021i	$0.00249564\pi$
$659$	13.0094	+	22.5329i	0.506774	+	0.877759i	−0.493195	+	0.869919i	$0.664171\pi$
$660$		0			0
$661$	−14.6544	+	25.3822i	−0.569990	+	0.987252i	0.426576	+	0.904452i	$0.359720\pi$
$661$	−14.6544	+	25.3822i	−0.569990	+	0.987252i	−0.996566	+	0.0828004i	$0.973614\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.33574			−0.129355
$666$		0			0
$667$	0.427235			0.0165426
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−9.00029	+	15.5890i	−0.347453	+	0.601805i
$672$		0			0
$673$	−7.72976	−	13.3883i	−0.297960	−	0.516082i	0.677709	−	0.735330i	$-0.262973\pi$
$673$	−7.72976	−	13.3883i	−0.297960	−	0.516082i	−0.975669	+	0.219248i	$0.929640\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.02467	+	5.23889i	0.116248	+	0.201347i	0.918278	−	0.395937i	$-0.129580\pi$
$677$	3.02467	+	5.23889i	0.116248	+	0.201347i	−0.802030	+	0.597284i	$0.796247\pi$
$678$		0			0
$679$	−17.4385	+	30.2044i	−0.669228	+	1.15914i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	25.1518			0.962406			0.481203	−	0.876609i	$-0.340200\pi$
$683$	25.1518			0.962406			0.481203	+	0.876609i	$0.340200\pi$
$684$		0			0
$685$	3.31411			0.126626
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.60644	−	13.1747i	0.289782	−	0.501918i
$690$		0			0
$691$	−21.8943	−	37.9221i	−0.832899	−	1.44262i	−0.895729	−	0.444600i	$-0.853346\pi$
$691$	−21.8943	−	37.9221i	−0.832899	−	1.44262i	0.0628298	−	0.998024i	$-0.479987\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.93864	−	13.7501i	−0.301130	−	0.521572i
$696$		0			0
$697$	21.4151	−	37.0921i	0.811155	−	1.40496i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−37.4594			−1.41482			−0.707412	−	0.706802i	$-0.750137\pi$
$701$	−37.4594			−1.41482			−0.707412	+	0.706802i	$0.750137\pi$
$702$		0			0
$703$	9.08685			0.342717
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.92804	+	3.33947i	−0.0725116	+	0.125594i
$708$		0			0
$709$	16.4907	+	28.5627i	0.619321	+	1.07269i	0.989610	+	0.143778i	$0.0459252\pi$
$709$	16.4907	+	28.5627i	0.619321	+	1.07269i	−0.370289	+	0.928916i	$0.620741\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.3773	+	24.9022i	0.538433	+	0.932594i
$714$		0			0
$715$	4.63474	−	8.02760i	0.173329	−	0.300215i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	12.0397			0.449006			0.224503	−	0.974473i	$-0.427924\pi$
$719$	12.0397			0.449006			0.224503	+	0.974473i	$0.427924\pi$
$720$		0			0
$721$	−30.0203			−1.11801
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.213336	+	0.369509i	−0.00792311	+	0.0137232i
$726$		0			0
$727$	−15.6359	−	27.0822i	−0.579905	−	1.00443i	−0.995490	−	0.0948705i	$-0.969756\pi$
$727$	−15.6359	−	27.0822i	−0.579905	−	1.00443i	0.415585	−	0.909555i	$-0.363577\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−15.6116	−	27.0400i	−0.577414	−	1.00011i
$732$		0			0
$733$	−2.40335	+	4.16273i	−0.0887699	+	0.153754i	−0.906991	−	0.421149i	$-0.861627\pi$
$733$	−2.40335	+	4.16273i	−0.0887699	+	0.153754i	0.818222	+	0.574903i	$0.194960\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.806522			0.0297086
$738$		0			0
$739$	7.79606			0.286783			0.143391	−	0.989666i	$-0.454199\pi$
$739$	7.79606			0.286783			0.143391	+	0.989666i	$0.454199\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.5475	+	40.7855i	−0.863875	+	1.49628i	0.00428429	+	0.999991i	$0.498636\pi$
$743$	−23.5475	+	40.7855i	−0.863875	+	1.49628i	−0.868160	+	0.496285i	$0.834697\pi$
$744$		0			0
$745$	16.9204	+	29.3071i	0.619917	+	1.07373i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−15.9940	−	27.7023i	−0.584406	−	1.01222i
$750$		0			0
$751$	6.25631	−	10.8362i	0.228296	−	0.395420i	−0.729007	−	0.684506i	$-0.760018\pi$
$751$	6.25631	−	10.8362i	0.228296	−	0.395420i	0.957303	+	0.289086i	$0.0933513\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−18.5257			−0.674218
$756$		0			0
$757$	13.0507			0.474337			0.237168	−	0.971469i	$-0.423781\pi$
$757$	13.0507			0.474337			0.237168	+	0.971469i	$0.423781\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.5379	+	19.9842i	−0.418249	+	0.724428i	−0.995763	−	0.0919523i	$-0.970689\pi$
$761$	−11.5379	+	19.9842i	−0.418249	+	0.724428i	0.577515	+	0.816380i	$0.304023\pi$
$762$		0			0
$763$	−15.2206	−	26.3628i	−0.551021	−	0.954397i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	14.2422	+	24.6683i	0.514257	+	0.890720i
$768$		0			0
$769$	16.7111	−	28.9444i	0.602617	−	1.04376i	−0.389807	−	0.920897i	$-0.627458\pi$
$769$	16.7111	−	28.9444i	0.602617	−	1.04376i	0.992423	−	0.122866i	$-0.0392085\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	9.28916			0.334108			0.167054	−	0.985948i	$-0.446575\pi$
$773$	9.28916			0.334108			0.167054	+	0.985948i	$0.446575\pi$
$774$		0			0
$775$	−28.7167			−1.03154
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.37106	+	7.57089i	−0.156609	+	0.271255i
$780$		0			0
$781$	10.7338	+	18.5915i	0.384086	+	0.665256i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	16.3973	+	28.4010i	0.585246	+	1.01368i
$786$		0			0
$787$	−4.77105	+	8.26370i	−0.170070	+	0.294569i	−0.938444	−	0.345431i	$-0.887733\pi$
$787$	−4.77105	+	8.26370i	−0.170070	+	0.294569i	0.768374	+	0.640001i	$0.221066\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	17.6062			0.626004
$792$		0			0
$793$	−17.4628			−0.620123
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.3400	−	19.6415i	0.401685	−	0.695738i	−0.592245	−	0.805758i	$-0.701758\pi$
$797$	11.3400	−	19.6415i	0.401685	−	0.695738i	0.993929	+	0.110020i	$0.0350915\pi$
$798$		0			0
$799$	−16.0655	−	27.8263i	−0.568358	−	0.984424i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.83399	+	15.3009i	0.311745	+	0.539958i
$804$		0			0
$805$	−4.97948	+	8.62471i	−0.175503	+	0.303981i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	32.1636			1.13081			0.565405	−	0.824813i	$-0.308720\pi$
$809$	32.1636			1.13081			0.565405	+	0.824813i	$0.308720\pi$
$810$		0			0
$811$	−3.49576			−0.122753			−0.0613764	−	0.998115i	$-0.519549\pi$
$811$	−3.49576			−0.122753			−0.0613764	+	0.998115i	$0.519549\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	15.9311	−	27.5935i	0.558042	−	0.966557i
$816$		0			0
$817$	3.18649	+	5.51916i	0.111481	+	0.193091i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.6693	+	21.9438i	0.442160	+	0.765844i	0.997850	−	0.0655463i	$-0.0208790\pi$
$821$	12.6693	+	21.9438i	0.442160	+	0.765844i	−0.555690	+	0.831390i	$0.687546\pi$
$822$		0			0
$823$	24.8599	−	43.0585i	0.866560	−	1.50093i	0.00107015	−	0.999999i	$-0.499659\pi$
$823$	24.8599	−	43.0585i	0.866560	−	1.50093i	0.865490	−	0.500926i	$-0.167007\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	43.4868			1.51218			0.756092	−	0.654466i	$-0.227106\pi$
$827$	43.4868			1.51218			0.756092	+	0.654466i	$0.227106\pi$
$828$		0			0
$829$	−1.62272			−0.0563594			−0.0281797	−	0.999603i	$-0.508971\pi$
$829$	−1.62272			−0.0563594			−0.0281797	+	0.999603i	$0.508971\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.74033	+	6.47844i	−0.129595	+	0.224465i
$834$		0			0
$835$	−17.5321	−	30.3665i	−0.606724	−	1.05088i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	20.9586	+	36.3014i	0.723573	+	1.25326i	0.959559	+	0.281508i	$0.0908348\pi$
$839$	20.9586	+	36.3014i	0.723573	+	1.25326i	−0.235986	+	0.971756i	$0.575832\pi$
$840$		0			0
$841$	14.4899	−	25.0973i	0.499653	−	0.865425i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−9.34949			−0.321632
$846$		0			0
$847$	9.90375			0.340297
$848$		0			0
$849$		0			0
$850$		0			0
$851$	13.5645	−	23.4944i	0.464986	−	0.805379i
$852$		0			0
$853$	3.30061	+	5.71683i	0.113011	+	0.195741i	0.916983	−	0.398927i	$-0.130617\pi$
$853$	3.30061	+	5.71683i	0.113011	+	0.195741i	−0.803972	+	0.594667i	$0.797284\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.0909	−	20.9421i	−0.413018	−	0.715368i	0.582200	−	0.813046i	$-0.302192\pi$
$857$	−12.0909	−	20.9421i	−0.413018	−	0.715368i	−0.995218	+	0.0976773i	$0.968859\pi$
$858$		0			0
$859$	9.44631	−	16.3615i	0.322304	−	0.558247i	−0.658659	−	0.752442i	$-0.728876\pi$
$859$	9.44631	−	16.3615i	0.322304	−	0.558247i	0.980963	+	0.194195i	$0.0622093\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.37925			−0.183112			−0.0915559	−	0.995800i	$-0.529184\pi$
$863$	−5.37925			−0.183112			−0.0915559	+	0.995800i	$0.529184\pi$
$864$		0			0
$865$	−11.2420			−0.382238
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−12.9994	+	22.5156i	−0.440974	+	0.763789i
$870$		0			0
$871$	0.391214	+	0.677602i	0.0132558	+	0.0229597i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−13.2356	−	22.9247i	−0.447443	−	0.774995i
$876$		0			0
$877$	3.00289	−	5.20115i	0.101400	−	0.175630i	−0.810862	−	0.585238i	$-0.801001\pi$
$877$	3.00289	−	5.20115i	0.101400	−	0.175630i	0.912262	+	0.409608i	$0.134334\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	28.3457			0.954991			0.477496	−	0.878634i	$-0.341545\pi$
$881$	28.3457			0.954991			0.477496	+	0.878634i	$0.341545\pi$
$882$		0			0
$883$	−12.1360			−0.408409			−0.204204	−	0.978928i	$-0.565461\pi$
$883$	−12.1360			−0.408409			−0.204204	+	0.978928i	$0.565461\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.9032	−	39.6696i	0.769015	−	1.33197i	−0.169082	−	0.985602i	$-0.554080\pi$
$887$	22.9032	−	39.6696i	0.769015	−	1.33197i	0.938097	−	0.346372i	$-0.112586\pi$
$888$		0			0
$889$	−2.45763	−	4.25674i	−0.0824263	−	0.142766i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.27915	+	5.67965i	0.109733	+	0.190062i
$894$		0			0
$895$	2.61558	−	4.53031i	0.0874290	−	0.151432i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.35301			−0.0451256
$900$		0			0
$901$	−29.7968			−0.992677
$902$		0			0
$903$		0			0
$904$		0			0
$905$	9.21923	−	15.9682i	0.306458	−	0.530800i
$906$		0			0
$907$	10.9721	+	19.0043i	0.364324	+	0.631028i	0.988667	−	0.150122i	$-0.0479667\pi$
$907$	10.9721	+	19.0043i	0.364324	+	0.631028i	−0.624343	+	0.781150i	$0.714633\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	12.2789	+	21.2676i	0.406817	+	0.704628i	0.994531	−	0.104441i	$-0.0333053\pi$
$911$	12.2789	+	21.2676i	0.406817	+	0.704628i	−0.587714	+	0.809069i	$0.699972\pi$
$912$		0			0
$913$	9.03114	−	15.6424i	0.298887	−	0.517688i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−18.7598			−0.619504
$918$		0			0
$919$	47.9172			1.58064			0.790322	−	0.612692i	$-0.209913\pi$
$919$	47.9172			1.58064			0.790322	+	0.612692i	$0.209913\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−10.4131	+	18.0361i	−0.342752	+	0.593665i
$924$		0			0
$925$	13.5467	+	23.4635i	0.445412	+	0.771476i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−15.5376	−	26.9120i	−0.509773	−	0.882953i	−0.999936	−	0.0113223i	$-0.996396\pi$
$929$	−15.5376	−	26.9120i	−0.509773	−	0.882953i	0.490163	−	0.871631i	$-0.336937\pi$
$930$		0			0
$931$	0.763443	−	1.32232i	0.0250208	−	0.0433373i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−18.1557			−0.593756
$936$		0			0
$937$	−34.1142			−1.11446			−0.557232	−	0.830357i	$-0.688137\pi$
$937$	−34.1142			−1.11446			−0.557232	+	0.830357i	$0.688137\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	15.3292	−	26.5509i	0.499716	−	0.865534i	−0.500284	−	0.865861i	$-0.666771\pi$
$941$	15.3292	−	26.5509i	0.499716	−	0.865534i	1.00000		0.000327806i	$0.000104344\pi$
$942$		0			0
$943$	13.0499	+	22.6031i	0.424963	+	0.736058i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.01450	+	12.1495i	0.227941	+	0.394805i	0.957198	−	0.289435i	$-0.0934675\pi$
$947$	7.01450	+	12.1495i	0.227941	+	0.394805i	−0.729257	+	0.684240i	$0.760134\pi$
$948$		0			0
$949$	−8.57008	+	14.8438i	−0.278197	+	0.481850i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	20.9957			0.680117			0.340059	−	0.940404i	$-0.389553\pi$
$953$	20.9957			0.680117			0.340059	+	0.940404i	$0.389553\pi$
$954$		0			0
$955$	−0.445808			−0.0144260
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.75110	−	4.76505i	0.0888378	−	0.153872i
$960$		0			0
$961$	−30.0316	−	52.0162i	−0.968761	−	1.67794i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−14.1427	−	24.4959i	−0.455270	−	0.788551i
$966$		0			0
$967$	−17.5923	+	30.4708i	−0.565731	+	0.979875i	0.431250	+	0.902233i	$0.358073\pi$
$967$	−17.5923	+	30.4708i	−0.565731	+	0.979875i	−0.996981	+	0.0776429i	$0.975261\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	42.7300			1.37127			0.685635	−	0.727945i	$-0.259525\pi$
$971$	42.7300			1.37127			0.685635	+	0.727945i	$0.259525\pi$
$972$		0			0
$973$	−26.3600			−0.845063
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.84824	+	3.20125i	−0.0591305	+	0.102417i	−0.894075	−	0.447917i	$-0.852166\pi$
$977$	−1.84824	+	3.20125i	−0.0591305	+	0.102417i	0.834945	+	0.550334i	$0.185499\pi$
$978$		0			0
$979$	20.6845	+	35.8265i	0.661078	+	1.14502i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.7711	−	39.4407i	−0.726285	−	1.25796i	−0.958443	−	0.285284i	$-0.907912\pi$
$983$	−22.7711	−	39.4407i	−0.726285	−	1.25796i	0.232158	−	0.972678i	$-0.425421\pi$
$984$		0			0
$985$	−16.6197	+	28.7862i	−0.529548	+	0.917205i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	19.0267			0.605013
$990$		0			0
$991$	−20.1458			−0.639951			−0.319976	−	0.947426i	$-0.603675\pi$
$991$	−20.1458			−0.639951			−0.319976	+	0.947426i	$0.603675\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.175940	−	0.304736i	0.00557766	−	0.00966079i
$996$		0			0
$997$	−17.3577	−	30.0645i	−0.549725	−	0.952152i	−0.998293	−	0.0584029i	$-0.981399\pi$
$997$	−17.3577	−	30.0645i	−0.549725	−	0.952152i	0.448568	−	0.893749i	$-0.351934\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3456.2.i.e.2305.2		10
3.2	odd	2		1152.2.i.e.769.2	yes	10
4.3	odd	2		3456.2.i.h.2305.2		10
8.3	odd	2		3456.2.i.g.2305.4		10
8.5	even	2		3456.2.i.f.2305.4		10
9.2	odd	6		1152.2.i.e.385.2	✓	10
9.7	even	3	inner	3456.2.i.e.1153.2		10
12.11	even	2		1152.2.i.h.769.4	yes	10
24.5	odd	2		1152.2.i.g.769.4	yes	10
24.11	even	2		1152.2.i.f.769.2	yes	10
36.7	odd	6		3456.2.i.h.1153.2		10
36.11	even	6		1152.2.i.h.385.4	yes	10
72.11	even	6		1152.2.i.f.385.2	yes	10
72.29	odd	6		1152.2.i.g.385.4	yes	10
72.43	odd	6		3456.2.i.g.1153.4		10
72.61	even	6		3456.2.i.f.1153.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.e.385.2	✓	10	9.2	odd	6
1152.2.i.e.769.2	yes	10	3.2	odd	2
1152.2.i.f.385.2	yes	10	72.11	even	6
1152.2.i.f.769.2	yes	10	24.11	even	2
1152.2.i.g.385.4	yes	10	72.29	odd	6
1152.2.i.g.769.4	yes	10	24.5	odd	2
1152.2.i.h.385.4	yes	10	36.11	even	6
1152.2.i.h.769.4	yes	10	12.11	even	2
3456.2.i.e.1153.2		10	9.7	even	3	inner
3456.2.i.e.2305.2		10	1.1	even	1	trivial
3456.2.i.f.1153.4		10	72.61	even	6
3456.2.i.f.2305.4		10	8.5	even	2
3456.2.i.g.1153.4		10	72.43	odd	6
3456.2.i.g.2305.4		10	8.3	odd	2
3456.2.i.h.1153.2		10	36.7	odd	6
3456.2.i.h.2305.2		10	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:	\( N \)	\(=\)	\( 3456 = 2^{7} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3456.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.705463 + 1.22190i) q^{5} +(1.17123 + 2.02864i) q^{7} +O(q^{10})\)	\(q+(-0.705463 + 1.22190i) q^{5} +(1.17123 + 2.02864i) q^{7} +(-1.30116 - 2.25368i) q^{11} +(1.26229 - 2.18635i) q^{13} -4.94479 q^{17} +1.00929 q^{19} +(1.50663 - 2.60955i) q^{23} +(1.50464 + 2.60612i) q^{25} +(0.0708926 + 0.122790i) q^{29} +(-4.77135 + 8.26422i) q^{31} -3.30505 q^{35} +9.00324 q^{37} +(-4.33084 + 7.50123i) q^{41} +(3.15717 + 5.46838i) q^{43} +(3.24898 + 5.62740i) q^{47} +(0.756418 - 1.31015i) q^{49} +6.02590 q^{53} +3.67169 q^{55} +(-5.64142 + 9.77123i) q^{59} +(-3.45856 - 5.99040i) q^{61} +(1.78100 + 3.08478i) q^{65} +(-0.154962 + 0.268402i) q^{67} -8.24940 q^{71} -6.78931 q^{73} +(3.04793 - 5.27917i) q^{77} +(-4.99530 - 8.65211i) q^{79} +(3.47041 + 6.01093i) q^{83} +(3.48837 - 6.04203i) q^{85} -15.8969 q^{89} +5.91375 q^{91} +(-0.712014 + 1.23325i) q^{95} +(7.44449 + 12.8942i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{7}+O(q^{10}) \) 10 * q - 4 * q^7	\( 10 q - 4 q^{7} - q^{11} + 6 q^{13} + 6 q^{17} - 18 q^{19} - 4 q^{23} + q^{25} + 4 q^{29} - 8 q^{31} - 24 q^{35} - 20 q^{37} + 5 q^{41} + 13 q^{43} + 6 q^{47} + 3 q^{49} + 12 q^{55} - 13 q^{59} + 10 q^{61} + 17 q^{67} - 8 q^{71} - 34 q^{73} - 8 q^{77} - 6 q^{79} + 12 q^{83} + 18 q^{85} - 44 q^{89} - 36 q^{91} + 6 q^{95} + 27 q^{97}+O(q^{100}) \) 10 * q - 4 * q^7 - q^11 + 6 * q^13 + 6 * q^17 - 18 * q^19 - 4 * q^23 + q^25 + 4 * q^29 - 8 * q^31 - 24 * q^35 - 20 * q^37 + 5 * q^41 + 13 * q^43 + 6 * q^47 + 3 * q^49 + 12 * q^55 - 13 * q^59 + 10 * q^61 + 17 * q^67 - 8 * q^71 - 34 * q^73 - 8 * q^77 - 6 * q^79 + 12 * q^83 + 18 * q^85 - 44 * q^89 - 36 * q^91 + 6 * q^95 + 27 * q^97

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