LMFDB - Embedded newform 1512.2.t.c.289.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(289,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.8
Character	$\chi$	$=$	1512.289
Dual form			1512.2.t.c.361.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.78355 q^{5} +(1.90167 + 1.83948i) q^{7} +O(q^{10})$	$q+1.78355 q^{5} +(1.90167 + 1.83948i) q^{7} +5.61411 q^{11} +(3.14009 + 5.43879i) q^{13} +(-0.646279 - 1.11939i) q^{17} +(0.559062 - 0.968324i) q^{19} -7.61715 q^{23} -1.81896 q^{25} +(1.57496 - 2.72791i) q^{29} +(-0.501553 + 0.868716i) q^{31} +(3.39171 + 3.28079i) q^{35} +(-5.96542 + 10.3324i) q^{37} +(-4.14160 - 7.17347i) q^{41} +(2.34804 - 4.06693i) q^{43} +(-0.972001 - 1.68356i) q^{47} +(0.232662 + 6.99613i) q^{49} +(4.45992 + 7.72481i) q^{53} +10.0130 q^{55} +(4.19339 - 7.26317i) q^{59} +(-2.41288 - 4.17923i) q^{61} +(5.60050 + 9.70034i) q^{65} +(1.27814 - 2.21380i) q^{67} +8.86178 q^{71} +(5.67598 + 9.83109i) q^{73} +(10.6762 + 10.3270i) q^{77} +(-6.72883 - 11.6547i) q^{79} +(1.60203 - 2.77479i) q^{83} +(-1.15267 - 1.99648i) q^{85} +(0.404646 - 0.700867i) q^{89} +(-4.03312 + 16.1189i) q^{91} +(0.997114 - 1.72705i) q^{95} +(1.10781 - 1.91879i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 - q^7	$ 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.78355			0.797627			0.398814	−	0.917032i	$-0.369422\pi$
$5$	1.78355			0.797627			0.398814	+	0.917032i	$0.369422\pi$
$6$		0			0
$7$	1.90167	+	1.83948i	0.718762	+	0.695256i
$7$	1.90167	+	1.83948i	0.718762	+	0.695256i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	5.61411			1.69272			0.846359	−	0.532612i	$-0.178790\pi$
$11$	5.61411			1.69272			0.846359	+	0.532612i	$0.178790\pi$
$12$		0			0
$13$	3.14009	+	5.43879i	0.870903	+	1.50845i	0.861064	+	0.508497i	$0.169799\pi$
$13$	3.14009	+	5.43879i	0.870903	+	1.50845i	0.00983976	+	0.999952i	$0.496868\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.646279	−	1.11939i	−0.156746	−	0.271491i	0.776948	−	0.629565i	$-0.216767\pi$
$17$	−0.646279	−	1.11939i	−0.156746	−	0.271491i	−0.933693	+	0.358074i	$0.883434\pi$
$18$		0			0
$19$	0.559062	−	0.968324i	0.128258	−	0.222149i	−0.794744	−	0.606945i	$-0.792395\pi$
$19$	0.559062	−	0.968324i	0.128258	−	0.222149i	0.923002	+	0.384796i	$0.125728\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.61715			−1.58828			−0.794142	−	0.607732i	$-0.792080\pi$
$23$	−7.61715			−1.58828			−0.794142	+	0.607732i	$0.792080\pi$
$24$		0			0
$25$	−1.81896			−0.363791
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.57496	−	2.72791i	0.292462	−	0.506560i	−0.681929	−	0.731418i	$-0.738859\pi$
$29$	1.57496	−	2.72791i	0.292462	−	0.506560i	0.974391	+	0.224859i	$0.0721921\pi$
$30$		0			0
$31$	−0.501553	+	0.868716i	−0.0900816	+	0.156026i	−0.907545	−	0.419954i	$-0.862046\pi$
$31$	−0.501553	+	0.868716i	−0.0900816	+	0.156026i	0.817464	+	0.575980i	$0.195379\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.39171	+	3.28079i	0.573304	+	0.554555i
$36$		0			0
$37$	−5.96542	+	10.3324i	−0.980708	+	1.69864i	−0.321067	+	0.947057i	$0.604041\pi$
$37$	−5.96542	+	10.3324i	−0.980708	+	1.69864i	−0.659642	+	0.751580i	$0.729292\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.14160	−	7.17347i	−0.646810	−	1.12031i	−0.983880	−	0.178828i	$-0.942769\pi$
$41$	−4.14160	−	7.17347i	−0.646810	−	1.12031i	0.337071	−	0.941479i	$-0.390564\pi$
$42$		0			0
$43$	2.34804	−	4.06693i	0.358073	−	0.620200i	−0.629566	−	0.776947i	$-0.716767\pi$
$43$	2.34804	−	4.06693i	0.358073	−	0.620200i	0.987639	+	0.156747i	$0.0501006\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.972001	−	1.68356i	−0.141781	−	0.245572i	0.786386	−	0.617735i	$-0.211950\pi$
$47$	−0.972001	−	1.68356i	−0.141781	−	0.245572i	−0.928167	+	0.372163i	$0.878616\pi$
$48$		0			0
$49$	0.232662	+	6.99613i	0.0332374	+	0.999447i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.45992	+	7.72481i	0.612617	+	1.06108i	0.990798	+	0.135352i	$0.0432166\pi$
$53$	4.45992	+	7.72481i	0.612617	+	1.06108i	−0.378180	+	0.925732i	$0.623450\pi$
$54$		0			0
$55$	10.0130			1.35016
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.19339	−	7.26317i	0.545933	−	0.945584i	−0.452614	−	0.891706i	$-0.649509\pi$
$59$	4.19339	−	7.26317i	0.545933	−	0.945584i	0.998548	−	0.0538778i	$-0.0171581\pi$
$60$		0			0
$61$	−2.41288	−	4.17923i	−0.308937	−	0.535095i	0.669193	−	0.743089i	$-0.266640\pi$
$61$	−2.41288	−	4.17923i	−0.308937	−	0.535095i	−0.978130	+	0.207994i	$0.933307\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.60050	+	9.70034i	0.694656	+	1.20318i
$66$		0			0
$67$	1.27814	−	2.21380i	0.156150	−	0.270459i	−0.777327	−	0.629096i	$-0.783425\pi$
$67$	1.27814	−	2.21380i	0.156150	−	0.270459i	0.933477	+	0.358637i	$0.116758\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.86178			1.05170			0.525850	−	0.850577i	$-0.323747\pi$
$71$	8.86178			1.05170			0.525850	+	0.850577i	$0.323747\pi$
$72$		0			0
$73$	5.67598	+	9.83109i	0.664323	+	1.15064i	0.979468	+	0.201598i	$0.0646135\pi$
$73$	5.67598	+	9.83109i	0.664323	+	1.15064i	−0.315145	+	0.949044i	$0.602053\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	10.6762	+	10.3270i	1.21666	+	1.17687i
$78$		0			0
$79$	−6.72883	−	11.6547i	−0.757052	−	1.31125i	−0.944348	−	0.328949i	$-0.893305\pi$
$79$	−6.72883	−	11.6547i	−0.757052	−	1.31125i	0.187295	−	0.982304i	$-0.440028\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.60203	−	2.77479i	0.175845	−	0.304573i	−0.764608	−	0.644495i	$-0.777067\pi$
$83$	1.60203	−	2.77479i	0.175845	−	0.304573i	0.940453	+	0.339922i	$0.110401\pi$
$84$		0			0
$85$	−1.15267	−	1.99648i	−0.125025	−	0.216549i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.404646	−	0.700867i	0.0428924	−	0.0742917i	−0.843782	−	0.536686i	$-0.819676\pi$
$89$	0.404646	−	0.700867i	0.0428924	−	0.0742917i	0.886675	+	0.462394i	$0.153009\pi$
$90$		0			0
$91$	−4.03312	+	16.1189i	−0.422786	+	1.68972i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.997114	−	1.72705i	0.102302	−	0.177192i
$96$		0			0
$97$	1.10781	−	1.91879i	0.112481	−	0.194823i	−0.804289	−	0.594238i	$-0.797454\pi$
$97$	1.10781	−	1.91879i	0.112481	−	0.194823i	0.916770	+	0.399415i	$0.130787\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.40267			−0.935601			−0.467801	−	0.883834i	$-0.654953\pi$
$101$	−9.40267			−0.935601			−0.467801	+	0.883834i	$0.654953\pi$
$102$		0			0
$103$	−3.52698			−0.347524			−0.173762	−	0.984788i	$-0.555592\pi$
$103$	−3.52698			−0.347524			−0.173762	+	0.984788i	$0.555592\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.39276	−	5.87644i	0.327991	−	0.568097i	−0.654122	−	0.756389i	$-0.726962\pi$
$107$	3.39276	−	5.87644i	0.327991	−	0.568097i	0.982113	+	0.188292i	$0.0602951\pi$
$108$		0			0
$109$	0.681848	+	1.18099i	0.0653092	+	0.113119i	0.896831	−	0.442373i	$-0.145863\pi$
$109$	0.681848	+	1.18099i	0.0653092	+	0.113119i	−0.831522	+	0.555492i	$0.812530\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.76458	+	4.78840i	0.260070	+	0.450455i	0.966260	−	0.257568i	$-0.0829210\pi$
$113$	2.76458	+	4.78840i	0.260070	+	0.450455i	−0.706190	+	0.708022i	$0.749588\pi$
$114$		0			0
$115$	−13.5855			−1.26686
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.830080	−	3.31752i	0.0760933	−	0.304116i
$120$		0			0
$121$	20.5183			1.86530
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.1619			−1.08780
$126$		0			0
$127$	−12.8209			−1.13767			−0.568837	−	0.822450i	$-0.692606\pi$
$127$	−12.8209			−1.13767			−0.568837	+	0.822450i	$0.692606\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.81910			0.508417			0.254208	−	0.967149i	$-0.418185\pi$
$131$	5.81910			0.508417			0.254208	+	0.967149i	$0.418185\pi$
$132$		0			0
$133$	2.84436	−	0.813047i	0.246637	−	0.0705001i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	15.3409			1.31066			0.655332	−	0.755341i	$-0.272529\pi$
$137$	15.3409			1.31066			0.655332	+	0.755341i	$0.272529\pi$
$138$		0			0
$139$	−6.05803	−	10.4928i	−0.513835	−	0.889988i	−0.999871	−	0.0160496i	$-0.994891\pi$
$139$	−6.05803	−	10.4928i	−0.513835	−	0.889988i	0.486036	−	0.873939i	$-0.338442\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	17.6288	+	30.5340i	1.47419	+	2.55338i
$144$		0			0
$145$	2.80901	−	4.86535i	0.233276	−	0.404046i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.73699			−0.388069			−0.194035	−	0.980995i	$-0.562157\pi$
$149$	−4.73699			−0.388069			−0.194035	+	0.980995i	$0.562157\pi$
$150$		0			0
$151$	24.3690			1.98312			0.991559	−	0.129657i	$-0.0413876\pi$
$151$	24.3690			1.98312			0.991559	+	0.129657i	$0.0413876\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.894545	+	1.54940i	−0.0718516	+	0.124451i
$156$		0			0
$157$	3.15229	−	5.45993i	0.251580	−	0.435750i	−0.712381	−	0.701793i	$-0.752383\pi$
$157$	3.15229	−	5.45993i	0.251580	−	0.435750i	0.963961	+	0.266043i	$0.0857165\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−14.4853	−	14.0116i	−1.14160	−	1.10426i
$162$		0			0
$163$	0.350678	−	0.607392i	0.0274672	−	0.0475746i	−0.851965	−	0.523599i	$-0.824589\pi$
$163$	0.350678	−	0.607392i	0.0274672	−	0.0475746i	0.879432	+	0.476024i	$0.157922\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.53822	−	6.12839i	−0.273796	−	0.474229i	0.696035	−	0.718008i	$-0.254946\pi$
$167$	−3.53822	−	6.12839i	−0.273796	−	0.474229i	−0.969831	+	0.243780i	$0.921613\pi$
$168$		0			0
$169$	−13.2203	+	22.8982i	−1.01695	+	1.76140i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.31767	+	5.74638i	0.252238	+	0.436889i	0.964142	−	0.265388i	$-0.0855001\pi$
$173$	3.31767	+	5.74638i	0.252238	+	0.436889i	−0.711904	+	0.702277i	$0.752167\pi$
$174$		0			0
$175$	−3.45904	−	3.34592i	−0.261479	−	0.252928i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.63527	−	9.76057i	−0.421200	−	0.729539i	0.574858	−	0.818253i	$-0.305057\pi$
$179$	−5.63527	−	9.76057i	−0.421200	−	0.729539i	−0.996057	+	0.0887145i	$0.971724\pi$
$180$		0			0
$181$	21.1800			1.57430			0.787149	−	0.616762i	$-0.211556\pi$
$181$	21.1800			1.57430			0.787149	+	0.616762i	$0.211556\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.6396	+	18.4283i	−0.782240	+	1.35488i
$186$		0			0
$187$	−3.62828	−	6.28437i	−0.265326	−	0.459559i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.72044	−	8.17604i	−0.341559	−	0.591598i	0.643163	−	0.765729i	$-0.277622\pi$
$191$	−4.72044	−	8.17604i	−0.341559	−	0.591598i	−0.984722	+	0.174131i	$0.944288\pi$
$192$		0			0
$193$	3.14021	−	5.43900i	0.226037	−	0.391508i	−0.730593	−	0.682813i	$-0.760756\pi$
$193$	3.14021	−	5.43900i	0.226037	−	0.391508i	0.956630	+	0.291305i	$0.0940896\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−15.4780			−1.10276			−0.551382	−	0.834253i	$-0.685899\pi$
$197$	−15.4780			−1.10276			−0.551382	+	0.834253i	$0.685899\pi$
$198$		0			0
$199$	2.19477	+	3.80145i	0.155583	+	0.269478i	0.933271	−	0.359173i	$-0.116941\pi$
$199$	2.19477	+	3.80145i	0.155583	+	0.269478i	−0.777688	+	0.628650i	$0.783608\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.01296	−	2.29047i	0.562400	−	0.160759i
$204$		0			0
$205$	−7.38675	−	12.7942i	−0.515913	−	0.893587i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.13864	−	5.43628i	0.217104	−	0.376035i
$210$		0			0
$211$	7.93101	+	13.7369i	0.545993	+	0.945688i	0.998544	+	0.0539495i	$0.0171810\pi$
$211$	7.93101	+	13.7369i	0.545993	+	0.945688i	−0.452550	+	0.891739i	$0.649486\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.18784	−	7.25356i	0.285609	−	0.494689i
$216$		0			0
$217$	−2.55177	+	0.729412i	−0.173225	+	0.0495157i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.05874	−	7.02995i	0.273021	−	0.472886i
$222$		0			0
$223$	6.99253	−	12.1114i	0.468254	−	0.811040i	−0.531088	−	0.847317i	$-0.678216\pi$
$223$	6.99253	−	12.1114i	0.468254	−	0.811040i	0.999342	+	0.0362769i	$0.0115498\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.7673			−0.714650			−0.357325	−	0.933980i	$-0.616311\pi$
$227$	−10.7673			−0.714650			−0.357325	+	0.933980i	$0.616311\pi$
$228$		0			0
$229$	−1.61003			−0.106394			−0.0531969	−	0.998584i	$-0.516941\pi$
$229$	−1.61003			−0.106394			−0.0531969	+	0.998584i	$0.516941\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.510606	−	0.884395i	0.0334509	−	0.0579387i	−0.848815	−	0.528690i	$-0.822684\pi$
$233$	0.510606	−	0.884395i	0.0334509	−	0.0579387i	0.882266	+	0.470751i	$0.156017\pi$
$234$		0			0
$235$	−1.73361	−	3.00270i	−0.113088	−	0.195875i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.96428	+	12.0625i	0.450482	+	0.780258i	0.998416	−	0.0562640i	$-0.0179189\pi$
$239$	6.96428	+	12.0625i	0.450482	+	0.780258i	−0.547934	+	0.836522i	$0.684586\pi$
$240$		0			0
$241$	−14.5758			−0.938908			−0.469454	−	0.882957i	$-0.655549\pi$
$241$	−14.5758			−0.938908			−0.469454	+	0.882957i	$0.655549\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.414964	+	12.4779i	0.0265111	+	0.797186i
$246$		0			0
$247$	7.02201			0.446800
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−18.0287			−1.13796			−0.568981	−	0.822350i	$-0.692662\pi$
$251$	−18.0287			−1.13796			−0.568981	+	0.822350i	$0.692662\pi$
$252$		0			0
$253$	−42.7635			−2.68852
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−26.9266			−1.67964			−0.839818	−	0.542869i	$-0.817338\pi$
$257$	−26.9266			−1.67964			−0.839818	+	0.542869i	$0.817338\pi$
$258$		0			0
$259$	−30.3504	+	8.67554i	−1.88588	+	0.539072i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.53884			−0.0948888			−0.0474444	−	0.998874i	$-0.515108\pi$
$263$	−1.53884			−0.0948888			−0.0474444	+	0.998874i	$0.515108\pi$
$264$		0			0
$265$	7.95448	+	13.7776i	0.488640	+	0.846349i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.26461	−	5.65446i	−0.199047	−	0.344759i	0.749173	−	0.662374i	$-0.230451\pi$
$269$	−3.26461	−	5.65446i	−0.199047	−	0.344759i	−0.948220	+	0.317616i	$0.897118\pi$
$270$		0			0
$271$	−5.64494	+	9.77733i	−0.342906	+	0.593930i	−0.984971	−	0.172720i	$-0.944745\pi$
$271$	−5.64494	+	9.77733i	−0.342906	+	0.593930i	0.642065	+	0.766650i	$0.278078\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.2118			−0.615796
$276$		0			0
$277$	1.81188			0.108865			0.0544325	−	0.998517i	$-0.482665\pi$
$277$	1.81188			0.108865			0.0544325	+	0.998517i	$0.482665\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.98798	−	5.17533i	0.178248	−	0.308734i	−0.763033	−	0.646360i	$-0.776290\pi$
$281$	2.98798	−	5.17533i	0.178248	−	0.308734i	0.941280	+	0.337626i	$0.109624\pi$
$282$		0			0
$283$	9.99760	−	17.3163i	0.594295	−	1.02935i	−0.399350	−	0.916798i	$-0.630764\pi$
$283$	9.99760	−	17.3163i	0.594295	−	1.02935i	0.993646	−	0.112552i	$-0.0359024\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.31947	−	21.2599i	0.313998	−	1.25493i
$288$		0			0
$289$	7.66465	−	13.2756i	0.450862	−	0.780915i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.95166	+	8.57652i	0.289279	+	0.501046i	0.973638	−	0.228099i	$-0.0732511\pi$
$293$	4.95166	+	8.57652i	0.289279	+	0.501046i	−0.684359	+	0.729145i	$0.739918\pi$
$294$		0			0
$295$	7.47912	−	12.9542i	0.435451	−	0.754224i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−23.9185	−	41.4281i	−1.38324	−	2.39585i
$300$		0			0
$301$	11.9462	−	3.41477i	0.688567	−	0.196824i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.30348	−	7.45385i	−0.246417	−	0.426806i
$306$		0			0
$307$	−23.7122			−1.35332			−0.676662	−	0.736293i	$-0.736574\pi$
$307$	−23.7122			−1.35332			−0.676662	+	0.736293i	$0.736574\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.1724	−	17.6192i	0.576826	−	0.999092i	−0.419015	−	0.907979i	$-0.637624\pi$
$311$	10.1724	−	17.6192i	0.576826	−	0.999092i	0.995841	−	0.0911122i	$-0.0290422\pi$
$312$		0			0
$313$	−4.85936	−	8.41665i	−0.274667	−	0.475737i	0.695384	−	0.718638i	$-0.255234\pi$
$313$	−4.85936	−	8.41665i	−0.274667	−	0.475737i	−0.970051	+	0.242901i	$0.921901\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.66419	−	2.88246i	−0.0934703	−	0.161895i	0.815499	−	0.578759i	$-0.196463\pi$
$317$	−1.66419	−	2.88246i	−0.0934703	−	0.161895i	−0.908969	+	0.416863i	$0.863129\pi$
$318$		0			0
$319$	8.84199	−	15.3148i	0.495056	−	0.857463i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.44524			−0.0804153
$324$		0			0
$325$	−5.71168	−	9.89292i	−0.316827	−	0.548760i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.24844	−	4.98953i	0.0688286	−	0.275082i
$330$		0			0
$331$	0.717346	+	1.24248i	0.0394289	+	0.0682929i	0.885066	−	0.465465i	$-0.154113\pi$
$331$	0.717346	+	1.24248i	0.0394289	+	0.0682929i	−0.845638	+	0.533758i	$0.820779\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.27962	−	3.94843i	0.124549	−	0.215726i
$336$		0			0
$337$	0.00257316	+	0.00445685i	0.000140169	+	0.000242780i	0.866095	−	0.499879i	$-0.166622\pi$
$337$	0.00257316	+	0.00445685i	0.000140169	+	0.000242780i	−0.865955	+	0.500121i	$0.833289\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.81578	+	4.87707i	−0.152483	+	0.264108i
$342$		0			0
$343$	−12.4268	+	13.7323i	−0.670982	+	0.741473i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.5536	−	20.0114i	0.620229	−	1.07427i	−0.369214	−	0.929344i	$-0.620373\pi$
$347$	11.5536	−	20.0114i	0.620229	−	1.07427i	0.989443	−	0.144924i	$-0.0462936\pi$
$348$		0			0
$349$	6.09723	−	10.5607i	0.326377	−	0.565302i	−0.655413	−	0.755271i	$-0.727505\pi$
$349$	6.09723	−	10.5607i	0.326377	−	0.565302i	0.981790	+	0.189969i	$0.0608387\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−24.7072			−1.31503			−0.657515	−	0.753441i	$-0.728392\pi$
$353$	−24.7072			−1.31503			−0.657515	+	0.753441i	$0.728392\pi$
$354$		0			0
$355$	15.8054			0.838864
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.20362	+	14.2091i	−0.432970	+	0.749927i	−0.997128	−	0.0757407i	$-0.975868\pi$
$359$	−8.20362	+	14.2091i	−0.432970	+	0.749927i	0.564157	+	0.825667i	$0.309201\pi$
$360$		0			0
$361$	8.87490	+	15.3718i	0.467100	+	0.809041i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.1234	+	17.5342i	0.529882	+	0.917783i
$366$		0			0
$367$	−5.81801			−0.303698			−0.151849	−	0.988404i	$-0.548523\pi$
$367$	−5.81801			−0.303698			−0.151849	+	0.988404i	$0.548523\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.72832	+	22.8939i	−0.297399	+	1.18859i
$372$		0			0
$373$	8.84966			0.458218			0.229109	−	0.973401i	$-0.426419\pi$
$373$	8.84966			0.458218			0.229109	+	0.973401i	$0.426419\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	19.7820			1.01883
$378$		0			0
$379$	17.3300			0.890181			0.445091	−	0.895486i	$-0.353171\pi$
$379$	17.3300			0.890181			0.445091	+	0.895486i	$0.353171\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7.09090			−0.362328			−0.181164	−	0.983453i	$-0.557986\pi$
$383$	−7.09090			−0.362328			−0.181164	+	0.983453i	$0.557986\pi$
$384$		0			0
$385$	19.0415	+	18.4187i	0.970442	+	0.938706i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.64240			−0.336783			−0.168392	−	0.985720i	$-0.553857\pi$
$389$	−6.64240			−0.336783			−0.168392	+	0.985720i	$0.553857\pi$
$390$		0			0
$391$	4.92280	+	8.52654i	0.248957	+	0.431206i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−12.0012	−	20.7867i	−0.603845	−	1.04589i
$396$		0			0
$397$	7.86340	−	13.6198i	0.394653	−	0.683559i	−0.598404	−	0.801195i	$-0.704198\pi$
$397$	7.86340	−	13.6198i	0.394653	−	0.683559i	0.993057	+	0.117636i	$0.0375315\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.96559			−0.297907			−0.148954	−	0.988844i	$-0.547591\pi$
$401$	−5.96559			−0.297907			−0.148954	+	0.988844i	$0.547591\pi$
$402$		0			0
$403$	−6.29968			−0.313810
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−33.4905	+	58.0073i	−1.66006	+	2.87531i
$408$		0			0
$409$	8.80943	−	15.2584i	0.435598	−	0.754478i	−0.561746	−	0.827310i	$-0.689870\pi$
$409$	8.80943	−	15.2584i	0.435598	−	0.754478i	0.997344	+	0.0728314i	$0.0232035\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	21.3349	−	6.09848i	1.04982	−	0.300086i
$414$		0			0
$415$	2.85729	−	4.94897i	0.140259	−	0.242936i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.62164	−	16.6652i	−0.470048	−	0.814147i	0.529365	−	0.848394i	$-0.322430\pi$
$419$	−9.62164	−	16.6652i	−0.470048	−	0.814147i	−0.999413	+	0.0342470i	$0.989097\pi$
$420$		0			0
$421$	7.77999	−	13.4753i	0.379174	−	0.656748i	−0.611769	−	0.791037i	$-0.709542\pi$
$421$	7.77999	−	13.4753i	0.379174	−	0.656748i	0.990942	+	0.134289i	$0.0428750\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.17555	+	2.03612i	0.0570227	+	0.0987662i
$426$		0			0
$427$	3.09910	−	12.3859i	0.149976	−	0.599397i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	16.9779	+	29.4067i	0.817799	+	1.41647i	0.907301	+	0.420482i	$0.138139\pi$
$431$	16.9779	+	29.4067i	0.817799	+	1.41647i	−0.0895020	+	0.995987i	$0.528528\pi$
$432$		0			0
$433$	−34.8338			−1.67401			−0.837004	−	0.547197i	$-0.815695\pi$
$433$	−34.8338			−1.67401			−0.837004	+	0.547197i	$0.815695\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.25846	+	7.37587i	−0.203710	+	0.352835i
$438$		0			0
$439$	−7.77938	−	13.4743i	−0.371290	−	0.643093i	0.618475	−	0.785805i	$-0.287751\pi$
$439$	−7.77938	−	13.4743i	−0.371290	−	0.643093i	−0.989764	+	0.142712i	$0.954418\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.16212	+	15.8693i	0.435305	+	0.753971i	0.997321	−	0.0731560i	$-0.0233071\pi$
$443$	9.16212	+	15.8693i	0.435305	+	0.753971i	−0.562015	+	0.827127i	$0.689974\pi$
$444$		0			0
$445$	0.721705	−	1.25003i	0.0342121	−	0.0592571i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.75072			0.129815			0.0649073	−	0.997891i	$-0.479325\pi$
$449$	2.75072			0.129815			0.0649073	+	0.997891i	$0.479325\pi$
$450$		0			0
$451$	−23.2514	−	40.2727i	−1.09487	−	1.89637i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.19327	+	28.7488i	−0.337226	+	1.34776i
$456$		0			0
$457$	−10.3407	−	17.9106i	−0.483716	−	0.837821i	0.516109	−	0.856523i	$-0.327380\pi$
$457$	−10.3407	−	17.9106i	−0.483716	−	0.837821i	−0.999825	+	0.0187018i	$0.994047\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.40670	+	11.0967i	−0.298390	+	0.516826i	−0.975768	−	0.218809i	$-0.929783\pi$
$461$	−6.40670	+	11.0967i	−0.298390	+	0.516826i	0.677378	+	0.735635i	$0.263116\pi$
$462$		0			0
$463$	5.54704	+	9.60775i	0.257793	+	0.446510i	0.965650	−	0.259845i	$-0.0836715\pi$
$463$	5.54704	+	9.60775i	0.257793	+	0.446510i	−0.707858	+	0.706355i	$0.750338\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.36754	+	9.29686i	−0.248380	+	0.430207i	−0.963077	−	0.269228i	$-0.913232\pi$
$467$	−5.36754	+	9.29686i	−0.248380	+	0.430207i	0.714696	+	0.699435i	$0.246565\pi$
$468$		0			0
$469$	6.50283	−	1.85881i	0.300273	−	0.0858317i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	13.1822	−	22.8322i	0.606117	−	1.04982i
$474$		0			0
$475$	−1.01691	+	1.76134i	−0.0466590	+	0.0808157i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.79508			0.356166			0.178083	−	0.984015i	$-0.443010\pi$
$479$	7.79508			0.356166			0.178083	+	0.984015i	$0.443010\pi$
$480$		0			0
$481$	−74.9277			−3.41641
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.97583	−	3.42225i	0.0897180	−	0.155396i
$486$		0			0
$487$	13.9984	+	24.2459i	0.634326	+	1.09868i	0.986657	+	0.162810i	$0.0520557\pi$
$487$	13.9984	+	24.2459i	0.634326	+	1.09868i	−0.352331	+	0.935875i	$0.614611\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.1227	+	20.9971i	0.547089	+	0.947586i	0.998472	+	0.0552556i	$0.0175974\pi$
$491$	12.1227	+	20.9971i	0.547089	+	0.947586i	−0.451383	+	0.892330i	$0.649069\pi$
$492$		0			0
$493$	−4.07145			−0.183369
$494$		0			0
$495$		0			0
$496$		0			0
$497$	16.8521	+	16.3010i	0.755922	+	0.731201i
$498$		0			0
$499$	−33.7748			−1.51197			−0.755984	−	0.654590i	$-0.772841\pi$
$499$	−33.7748			−1.51197			−0.755984	+	0.654590i	$0.772841\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.09819			0.0489661			0.0244830	−	0.999700i	$-0.492206\pi$
$503$	1.09819			0.0489661			0.0244830	+	0.999700i	$0.492206\pi$
$504$		0			0
$505$	−16.7701			−0.746261
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.2134			−0.718648			−0.359324	−	0.933213i	$-0.616993\pi$
$509$	−16.2134			−0.718648			−0.359324	+	0.933213i	$0.616993\pi$
$510$		0			0
$511$	−7.29023	+	29.1363i	−0.322501	+	1.28891i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.29054			−0.277194
$516$		0			0
$517$	−5.45692	−	9.45167i	−0.239995	−	0.415684i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−19.1738	−	33.2099i	−0.840017	−	1.45495i	−0.889879	−	0.456197i	$-0.849211\pi$
$521$	−19.1738	−	33.2099i	−0.840017	−	1.45495i	0.0498617	−	0.998756i	$-0.484122\pi$
$522$		0			0
$523$	20.6021	−	35.6838i	0.900865	−	1.56034i	0.0744911	−	0.997222i	$-0.476267\pi$
$523$	20.6021	−	35.6838i	0.900865	−	1.56034i	0.826374	−	0.563122i	$-0.190400\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.29657			0.0564796
$528$		0			0
$529$	35.0209			1.52265
$530$		0			0
$531$		0			0
$532$		0			0
$533$	26.0100	−	45.0506i	1.12662	−	1.95136i
$534$		0			0
$535$	6.05116	−	10.4809i	0.261614	−	0.453129i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.30619	+	39.2771i	0.0562616	+	1.69178i
$540$		0			0
$541$	−9.09371	+	15.7508i	−0.390969	+	0.677178i	−0.992578	−	0.121613i	$-0.961193\pi$
$541$	−9.09371	+	15.7508i	−0.390969	+	0.677178i	0.601609	+	0.798791i	$0.294527\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.21611	+	2.10636i	0.0520924	+	0.0902266i
$546$		0			0
$547$	0.338699	−	0.586644i	0.0144817	−	0.0250831i	−0.858694	−	0.512489i	$-0.828723\pi$
$547$	0.338699	−	0.586644i	0.0144817	−	0.0250831i	0.873175	+	0.487406i	$0.162057\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.76100	−	3.05014i	−0.0750211	−	0.129940i
$552$		0			0
$553$	8.64250	−	34.5408i	0.367516	−	1.46882i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.8659	−	25.7484i	−0.629887	−	1.09100i	−0.987574	−	0.157155i	$-0.949768\pi$
$557$	−14.8659	−	25.7484i	−0.629887	−	1.09100i	0.357687	−	0.933842i	$-0.383565\pi$
$558$		0			0
$559$	29.4922			1.24739
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10.6739	−	18.4878i	0.449852	−	0.779167i	−0.548524	−	0.836135i	$-0.684810\pi$
$563$	10.6739	−	18.4878i	0.449852	−	0.779167i	0.998376	+	0.0569680i	$0.0181433\pi$
$564$		0			0
$565$	4.93077	+	8.54034i	0.207439	+	0.359295i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.56212	−	13.0980i	−0.317021	−	0.549096i	0.662844	−	0.748757i	$-0.269349\pi$
$569$	−7.56212	−	13.0980i	−0.317021	−	0.549096i	−0.979865	+	0.199661i	$0.936016\pi$
$570$		0			0
$571$	−9.94314	+	17.2220i	−0.416107	+	0.720719i	−0.995544	−	0.0942981i	$-0.969939\pi$
$571$	−9.94314	+	17.2220i	−0.416107	+	0.720719i	0.579437	+	0.815017i	$0.303273\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	13.8553			0.577804
$576$		0			0
$577$	19.8090	+	34.3102i	0.824661	+	1.42835i	0.902178	+	0.431363i	$0.141967\pi$
$577$	19.8090	+	34.3102i	0.824661	+	1.42835i	−0.0775179	+	0.996991i	$0.524700\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	8.15068	−	2.32984i	0.338147	−	0.0966579i
$582$		0			0
$583$	25.0385	+	43.3679i	1.03699	+	1.79612i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.13275	+	1.96199i	−0.0467537	+	0.0809798i	−0.888455	−	0.458963i	$-0.848221\pi$
$587$	−1.13275	+	1.96199i	−0.0467537	+	0.0809798i	0.841701	+	0.539943i	$0.181554\pi$
$588$		0			0
$589$	0.560799	+	0.971332i	0.0231073	+	0.0400230i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−5.97295	+	10.3454i	−0.245280	+	0.424837i	−0.962210	−	0.272308i	$-0.912213\pi$
$593$	−5.97295	+	10.3454i	−0.245280	+	0.424837i	0.716931	+	0.697145i	$0.245546\pi$
$594$		0			0
$595$	1.48049	−	5.91695i	0.0606941	−	0.242571i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.47636	+	2.55713i	−0.0603224	+	0.104481i	−0.894610	−	0.446849i	$-0.852546\pi$
$599$	−1.47636	+	2.55713i	−0.0603224	+	0.104481i	0.834287	+	0.551330i	$0.185880\pi$
$600$		0			0
$601$	15.9751	−	27.6697i	0.651638	−	1.12867i	−0.331087	−	0.943600i	$-0.607415\pi$
$601$	15.9751	−	27.6697i	0.651638	−	1.12867i	0.982725	−	0.185071i	$-0.0592514\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	36.5953			1.48781
$606$		0			0
$607$	10.4014			0.422179			0.211089	−	0.977467i	$-0.432299\pi$
$607$	10.4014			0.422179			0.211089	+	0.977467i	$0.432299\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.10433	−	10.5730i	0.246955	−	0.427739i
$612$		0			0
$613$	6.22441	+	10.7810i	0.251402	+	0.435441i	0.963912	−	0.266221i	$-0.0857751\pi$
$613$	6.22441	+	10.7810i	0.251402	+	0.435441i	−0.712510	+	0.701662i	$0.752442\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.70100	+	8.14237i	0.189255	+	0.327799i	0.945002	−	0.327064i	$-0.106059\pi$
$617$	4.70100	+	8.14237i	0.189255	+	0.327799i	−0.755747	+	0.654864i	$0.772726\pi$
$618$		0			0
$619$	−22.1196			−0.889062			−0.444531	−	0.895763i	$-0.646630\pi$
$619$	−22.1196			−0.889062			−0.444531	+	0.895763i	$0.646630\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.05873	−	0.588479i	0.0824812	−	0.0235769i
$624$		0			0
$625$	−12.5966			−0.503865
$626$		0			0
$627$		0			0
$628$		0			0
$629$	15.4213			0.614887
$630$		0			0
$631$	18.3705			0.731316			0.365658	−	0.930749i	$-0.380844\pi$
$631$	18.3705			0.731316			0.365658	+	0.930749i	$0.380844\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−22.8668			−0.907439
$636$		0			0
$637$	−37.3199	+	23.2339i	−1.47867	+	0.920559i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	33.7233			1.33199			0.665995	−	0.745956i	$-0.268007\pi$
$641$	33.7233			1.33199			0.665995	+	0.745956i	$0.268007\pi$
$642$		0			0
$643$	10.0635	+	17.4306i	0.396867	+	0.687394i	0.993338	−	0.115241i	$-0.0367640\pi$
$643$	10.0635	+	17.4306i	0.396867	+	0.687394i	−0.596470	+	0.802635i	$0.703431\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.1891	+	19.3800i	0.439887	+	0.761907i	0.997680	−	0.0680731i	$-0.0216851\pi$
$647$	11.1891	+	19.3800i	0.439887	+	0.761907i	−0.557793	+	0.829980i	$0.688352\pi$
$648$		0			0
$649$	23.5422	−	40.7763i	0.924112	−	1.60061i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	40.6754			1.59175			0.795875	−	0.605460i	$-0.207011\pi$
$653$	40.6754			1.59175			0.795875	+	0.605460i	$0.207011\pi$
$654$		0			0
$655$	10.3786			0.405527
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.69321	+	13.3250i	−0.299685	+	0.519070i	−0.976064	−	0.217484i	$-0.930215\pi$
$659$	−7.69321	+	13.3250i	−0.299685	+	0.519070i	0.676379	+	0.736554i	$0.263548\pi$
$660$		0			0
$661$	−24.5736	+	42.5628i	−0.955804	+	1.65550i	−0.223285	+	0.974753i	$0.571678\pi$
$661$	−24.5736	+	42.5628i	−0.955804	+	1.65550i	−0.732518	+	0.680747i	$0.761655\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.07305	−	1.45011i	0.196724	−	0.0562328i
$666$		0			0
$667$	−11.9967	+	20.7789i	−0.464513	+	0.804561i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−13.5462	−	23.4627i	−0.522944	−	0.905766i
$672$		0			0
$673$	−6.99961	+	12.1237i	−0.269815	+	0.467334i	−0.968814	−	0.247789i	$-0.920296\pi$
$673$	−6.99961	+	12.1237i	−0.269815	+	0.467334i	0.698999	+	0.715123i	$0.253629\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.3870	−	40.5075i	−0.898836	−	1.55683i	−0.828984	−	0.559272i	$-0.811081\pi$
$677$	−23.3870	−	40.5075i	−0.898836	−	1.55683i	−0.0698517	−	0.997557i	$-0.522253\pi$
$678$		0			0
$679$	5.63624	−	1.61110i	0.216299	−	0.0618282i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−21.6222	−	37.4508i	−0.827352	−	1.43302i	−0.900109	−	0.435665i	$-0.856513\pi$
$683$	−21.6222	−	37.4508i	−0.827352	−	1.43302i	0.0727571	−	0.997350i	$-0.476820\pi$
$684$		0			0
$685$	27.3613			1.04542
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−28.0091	+	48.5131i	−1.06706	+	1.84820i
$690$		0			0
$691$	5.86072	+	10.1511i	0.222952	+	0.386165i	0.955703	−	0.294332i	$-0.0950972\pi$
$691$	5.86072	+	10.1511i	0.222952	+	0.386165i	−0.732751	+	0.680497i	$0.761764\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.8048	−	18.7144i	−0.409849	−	0.709879i
$696$		0			0
$697$	−5.35326	+	9.27212i	−0.202769	+	0.351207i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−0.0120975			−0.000456915			−0.000228458	−	1.00000i	$-0.500073\pi$
$701$	−0.0120975			−0.000456915			−0.000228458		1.00000i	$0.500073\pi$
$702$		0			0
$703$	6.67008	+	11.5529i	0.251567	+	0.435726i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−17.8807	−	17.2960i	−0.672474	−	0.650483i
$708$		0			0
$709$	−0.537388	−	0.930783i	−0.0201820	−	0.0349563i	0.855758	−	0.517376i	$-0.173091\pi$
$709$	−0.537388	−	0.930783i	−0.0201820	−	0.0349563i	−0.875940	+	0.482420i	$0.839758\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.82041	−	6.61714i	0.143075	−	0.247814i
$714$		0			0
$715$	31.4418	+	54.4588i	1.17586	+	2.03664i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−12.7777	+	22.1317i	−0.476529	+	0.825372i	−0.999638	−	0.0268932i	$-0.991439\pi$
$719$	−12.7777	+	22.1317i	−0.476529	+	0.825372i	0.523109	+	0.852266i	$0.324772\pi$
$720$		0			0
$721$	−6.70714	−	6.48779i	−0.249787	−	0.241618i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.86478	+	4.96194i	−0.106395	+	0.184282i
$726$		0			0
$727$	6.20522	−	10.7478i	0.230139	−	0.398612i	−0.727710	−	0.685885i	$-0.759415\pi$
$727$	6.20522	−	10.7478i	0.230139	−	0.398612i	0.957849	+	0.287273i	$0.0927486\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.06996			−0.224505
$732$		0			0
$733$	29.4189			1.08661			0.543307	−	0.839534i	$-0.317172\pi$
$733$	29.4189			1.08661			0.543307	+	0.839534i	$0.317172\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.17562	−	12.4285i	0.264317	−	0.457811i
$738$		0			0
$739$	7.75910	+	13.4392i	0.285423	+	0.494368i	0.972712	−	0.232017i	$-0.0745325\pi$
$739$	7.75910	+	13.4392i	0.285423	+	0.494368i	−0.687288	+	0.726385i	$0.741199\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	13.6333	+	23.6136i	0.500159	+	0.866301i	1.00000		0.000183414i	$5.83824e-5\pi$
$743$	13.6333	+	23.6136i	0.500159	+	0.866301i	−0.499841	+	0.866117i	$0.666608\pi$
$744$		0			0
$745$	−8.44865			−0.309534
$746$		0			0
$747$		0			0
$748$		0			0
$749$	17.2615	−	4.93412i	0.630720	−	0.180289i
$750$		0			0
$751$	−9.14353			−0.333652			−0.166826	−	0.985986i	$-0.553352\pi$
$751$	−9.14353			−0.333652			−0.166826	+	0.985986i	$0.553352\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	43.4632			1.58179
$756$		0			0
$757$	−20.6307			−0.749834			−0.374917	−	0.927058i	$-0.622329\pi$
$757$	−20.6307			−0.749834			−0.374917	+	0.927058i	$0.622329\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.478417			0.0173426			0.00867130	−	0.999962i	$-0.497240\pi$
$761$	0.478417			0.0173426			0.00867130	+	0.999962i	$0.497240\pi$
$762$		0			0
$763$	−0.875765	+	3.50010i	−0.0317048	+	0.126712i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	52.6705			1.90182
$768$		0			0
$769$	−13.3518	−	23.1261i	−0.481480	−	0.833948i	0.518294	−	0.855202i	$-0.326567\pi$
$769$	−13.3518	−	23.1261i	−0.481480	−	0.833948i	−0.999774	+	0.0212548i	$0.993234\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.5143	+	23.4074i	0.486074	+	0.841905i	0.999872	−	0.0160062i	$-0.00509514\pi$
$773$	13.5143	+	23.4074i	0.486074	+	0.841905i	−0.513798	+	0.857911i	$0.671762\pi$
$774$		0			0
$775$	0.912303	−	1.58016i	0.0327709	−	0.0567609i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.26165			−0.331833
$780$		0			0
$781$	49.7510			1.78023
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.62226	−	9.73804i	0.200667	−	0.347566i
$786$		0			0
$787$	−24.5915	+	42.5937i	−0.876593	+	1.51830i	−0.0215363	+	0.999768i	$0.506856\pi$
$787$	−24.5915	+	42.5937i	−0.876593	+	1.51830i	−0.855056	+	0.518535i	$0.826478\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.55083	+	14.1913i	−0.126253	+	0.504585i
$792$		0			0
$793$	15.1533	−	26.2463i	0.538109	−	0.932032i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−22.1538	−	38.3715i	−0.784728	−	1.35919i	−0.929162	−	0.369674i	$-0.879469\pi$
$797$	−22.1538	−	38.3715i	−0.784728	−	1.35919i	0.144434	−	0.989514i	$-0.453864\pi$
$798$		0			0
$799$	−1.25637	+	2.17609i	−0.0444471	+	0.0769846i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	31.8656	+	55.1928i	1.12451	+	1.94771i
$804$		0			0
$805$	−25.8352	−	24.9903i	−0.910570	−	0.880792i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	16.7359	+	28.9874i	0.588402	+	1.01914i	0.994442	+	0.105286i	$0.0335759\pi$
$809$	16.7359	+	28.9874i	0.588402	+	1.01914i	−0.406040	+	0.913855i	$0.633091\pi$
$810$		0			0
$811$	−43.7383			−1.53586			−0.767929	−	0.640535i	$-0.778713\pi$
$811$	−43.7383			−1.53586			−0.767929	+	0.640535i	$0.778713\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.625451	−	1.08331i	0.0219086	−	0.0379468i
$816$		0			0
$817$	−2.62540	−	4.54733i	−0.0918512	−	0.159091i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.2566	−	19.4970i	−0.392857	−	0.680449i	0.599968	−	0.800024i	$-0.295180\pi$
$821$	−11.2566	−	19.4970i	−0.392857	−	0.680449i	−0.992825	+	0.119575i	$0.961847\pi$
$822$		0			0
$823$	−7.33674	+	12.7076i	−0.255743	+	0.442959i	−0.965097	−	0.261893i	$-0.915653\pi$
$823$	−7.33674	+	12.7076i	−0.255743	+	0.442959i	0.709354	+	0.704852i	$0.248987\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−45.0520			−1.56661			−0.783306	−	0.621636i	$-0.786468\pi$
$827$	−45.0520			−1.56661			−0.783306	+	0.621636i	$0.786468\pi$
$828$		0			0
$829$	20.6688	+	35.7993i	0.717856	+	1.24336i	0.961848	+	0.273585i	$0.0882095\pi$
$829$	20.6688	+	35.7993i	0.717856	+	1.24336i	−0.243992	+	0.969777i	$0.578457\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	7.68102	−	4.78189i	0.266132	−	0.165683i
$834$		0			0
$835$	−6.31059	−	10.9303i	−0.218387	−	0.378258i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−2.04477	+	3.54164i	−0.0705932	+	0.122271i	−0.899161	−	0.437617i	$-0.855823\pi$
$839$	−2.04477	+	3.54164i	−0.0705932	+	0.122271i	0.828568	+	0.559888i	$0.189156\pi$
$840$		0			0
$841$	9.53902	+	16.5221i	0.328932	+	0.569726i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−23.5790	+	40.8401i	−0.811143	+	1.40494i
$846$		0			0
$847$	39.0189	+	37.7428i	1.34070	+	1.29686i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	45.4394	−	78.7034i	1.55764	−	2.69792i
$852$		0			0
$853$	−21.1012	+	36.5484i	−0.722491	+	1.25139i	0.237507	+	0.971386i	$0.423670\pi$
$853$	−21.1012	+	36.5484i	−0.722491	+	1.25139i	−0.959998	+	0.280006i	$0.909664\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	55.1245			1.88302			0.941509	−	0.336987i	$-0.109408\pi$
$857$	55.1245			1.88302			0.941509	+	0.336987i	$0.109408\pi$
$858$		0			0
$859$	−37.9534			−1.29495			−0.647476	−	0.762086i	$-0.724176\pi$
$859$	−37.9534			−1.29495			−0.647476	+	0.762086i	$0.724176\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.27205	+	10.8635i	−0.213503	+	0.369798i	−0.952809	−	0.303572i	$-0.901821\pi$
$863$	−6.27205	+	10.8635i	−0.213503	+	0.369798i	0.739305	+	0.673370i	$0.235154\pi$
$864$		0			0
$865$	5.91723	+	10.2489i	0.201192	+	0.348474i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−37.7764	−	65.4306i	−1.28148	−	2.21958i
$870$		0			0
$871$	16.0539			0.543965
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−23.1279	−	22.3716i	−0.781867	−	0.756297i
$876$		0			0
$877$	9.70673			0.327773			0.163887	−	0.986479i	$-0.447597\pi$
$877$	9.70673			0.327773			0.163887	+	0.986479i	$0.447597\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	11.6652			0.393012			0.196506	−	0.980503i	$-0.437041\pi$
$881$	11.6652			0.393012			0.196506	+	0.980503i	$0.437041\pi$
$882$		0			0
$883$	−13.1758			−0.443401			−0.221701	−	0.975115i	$-0.571161\pi$
$883$	−13.1758			−0.443401			−0.221701	+	0.975115i	$0.571161\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.830721			0.0278929			0.0139464	−	0.999903i	$-0.495561\pi$
$887$	0.830721			0.0278929			0.0139464	+	0.999903i	$0.495561\pi$
$888$		0			0
$889$	−24.3811	−	23.5838i	−0.817717	−	0.790975i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.17364			−0.0727379
$894$		0			0
$895$	−10.0508	−	17.4084i	−0.335960	−	0.581900i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.57985	+	2.73638i	0.0526910	+	0.0912634i
$900$		0			0
$901$	5.76470	−	9.98476i	0.192050	−	0.332641i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	37.7756			1.25570
$906$		0			0
$907$	33.3176			1.10629			0.553146	−	0.833084i	$-0.313427\pi$
$907$	33.3176			1.10629			0.553146	+	0.833084i	$0.313427\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.1353	−	19.2870i	0.368930	−	0.639006i	−0.620469	−	0.784231i	$-0.713058\pi$
$911$	11.1353	−	19.2870i	0.368930	−	0.639006i	0.989399	+	0.145226i	$0.0463909\pi$
$912$		0			0
$913$	8.99396	−	15.5780i	0.297657	−	0.515556i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	11.0660	+	10.7041i	0.365431	+	0.353480i
$918$		0			0
$919$	10.7906	−	18.6899i	0.355949	−	0.616522i	−0.631331	−	0.775514i	$-0.717491\pi$
$919$	10.7906	−	18.6899i	0.355949	−	0.616522i	0.987280	+	0.158992i	$0.0508243\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	27.8268	+	48.1974i	0.915929	+	1.58644i
$924$		0			0
$925$	10.8508	−	18.7942i	0.356773	−	0.617949i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−18.5780	−	32.1780i	−0.609523	−	1.05572i	−0.991319	−	0.131478i	$-0.958028\pi$
$929$	−18.5780	−	32.1780i	−0.609523	−	1.05572i	0.381796	−	0.924247i	$-0.375306\pi$
$930$		0			0
$931$	6.90460	+	3.68598i	0.226289	+	0.120803i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.47122	−	11.2085i	−0.211631	−	0.366556i
$936$		0			0
$937$	21.5238			0.703152			0.351576	−	0.936159i	$-0.385646\pi$
$937$	21.5238			0.703152			0.351576	+	0.936159i	$0.385646\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−23.7032	+	41.0551i	−0.772702	+	1.33836i	0.163375	+	0.986564i	$0.447762\pi$
$941$	−23.7032	+	41.0551i	−0.772702	+	1.33836i	−0.936077	+	0.351795i	$0.885571\pi$
$942$		0			0
$943$	31.5472	+	54.6413i	1.02732	+	1.77937i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.25059	−	2.16608i	−0.0406386	−	0.0703881i	0.844991	−	0.534781i	$-0.179606\pi$
$947$	−1.25059	−	2.16608i	−0.0406386	−	0.0703881i	−0.885629	+	0.464393i	$0.846273\pi$
$948$		0			0
$949$	−35.6461	+	61.7409i	−1.15712	+	2.00420i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	7.89914			0.255878			0.127939	−	0.991782i	$-0.459164\pi$
$953$	7.89914			0.255878			0.127939	+	0.991782i	$0.459164\pi$
$954$		0			0
$955$	−8.41913	−	14.5824i	−0.272437	−	0.471874i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	29.1733	+	28.2193i	0.942055	+	0.911247i
$960$		0			0
$961$	14.9969	+	25.9754i	0.483771	+	0.837915i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	5.60071	−	9.70072i	0.180293	−	0.312277i
$966$		0			0
$967$	5.76591	+	9.98684i	0.185419	+	0.321155i	0.943718	−	0.330752i	$-0.107302\pi$
$967$	5.76591	+	9.98684i	0.185419	+	0.321155i	−0.758299	+	0.651907i	$0.773969\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.14669	−	15.8425i	0.293531	−	0.508411i	−0.681111	−	0.732180i	$-0.738503\pi$
$971$	9.14669	−	15.8425i	0.293531	−	0.508411i	0.974642	+	0.223769i	$0.0718362\pi$
$972$		0			0
$973$	7.78092	−	31.0974i	0.249445	−	0.996937i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−14.9541	+	25.9013i	−0.478425	+	0.828656i	−0.999694	−	0.0247361i	$-0.992125\pi$
$977$	−14.9541	+	25.9013i	−0.478425	+	0.828656i	0.521269	+	0.853392i	$0.325459\pi$
$978$		0			0
$979$	2.27173	−	3.93475i	0.0726047	−	0.125755i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−14.5445			−0.463897			−0.231948	−	0.972728i	$-0.574510\pi$
$983$	−14.5445			−0.463897			−0.231948	+	0.972728i	$0.574510\pi$
$984$		0			0
$985$	−27.6058			−0.879594
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−17.8854	+	30.9784i	−0.568722	+	0.985055i
$990$		0			0
$991$	−14.3753	−	24.8987i	−0.456646	−	0.790935i	0.542135	−	0.840292i	$-0.317616\pi$
$991$	−14.3753	−	24.8987i	−0.456646	−	0.790935i	−0.998781	+	0.0493567i	$0.984283\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	3.91447	+	6.78007i	0.124097	+	0.214943i
$996$		0			0
$997$	35.8938			1.13677			0.568384	−	0.822763i	$-0.307569\pi$
$997$	35.8938			1.13677			0.568384	+	0.822763i	$0.307569\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.c.289.8		22
3.2	odd	2		504.2.t.c.457.5	yes	22
4.3	odd	2		3024.2.t.k.289.8		22
7.4	even	3		1512.2.q.d.1369.4		22
9.4	even	3		1512.2.q.d.793.4		22
9.5	odd	6		504.2.q.c.121.4	yes	22
12.11	even	2		1008.2.t.l.961.7		22
21.11	odd	6		504.2.q.c.25.4	✓	22
28.11	odd	6		3024.2.q.l.2881.4		22
36.23	even	6		1008.2.q.l.625.8		22
36.31	odd	6		3024.2.q.l.2305.4		22
63.4	even	3	inner	1512.2.t.c.361.8		22
63.32	odd	6		504.2.t.c.193.5	yes	22
84.11	even	6		1008.2.q.l.529.8		22
252.67	odd	6		3024.2.t.k.1873.8		22
252.95	even	6		1008.2.t.l.193.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.4	✓	22	21.11	odd	6
504.2.q.c.121.4	yes	22	9.5	odd	6
504.2.t.c.193.5	yes	22	63.32	odd	6
504.2.t.c.457.5	yes	22	3.2	odd	2
1008.2.q.l.529.8		22	84.11	even	6
1008.2.q.l.625.8		22	36.23	even	6
1008.2.t.l.193.7		22	252.95	even	6
1008.2.t.l.961.7		22	12.11	even	2
1512.2.q.d.793.4		22	9.4	even	3
1512.2.q.d.1369.4		22	7.4	even	3
1512.2.t.c.289.8		22	1.1	even	1	trivial
1512.2.t.c.361.8		22	63.4	even	3	inner
3024.2.q.l.2305.4		22	36.31	odd	6
3024.2.q.l.2881.4		22	28.11	odd	6
3024.2.t.k.289.8		22	4.3	odd	2
3024.2.t.k.1873.8		22	252.67	odd	6

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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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.78355 q^{5} +(1.90167 + 1.83948i) q^{7} +O(q^{10})\)	\(q+1.78355 q^{5} +(1.90167 + 1.83948i) q^{7} +5.61411 q^{11} +(3.14009 + 5.43879i) q^{13} +(-0.646279 - 1.11939i) q^{17} +(0.559062 - 0.968324i) q^{19} -7.61715 q^{23} -1.81896 q^{25} +(1.57496 - 2.72791i) q^{29} +(-0.501553 + 0.868716i) q^{31} +(3.39171 + 3.28079i) q^{35} +(-5.96542 + 10.3324i) q^{37} +(-4.14160 - 7.17347i) q^{41} +(2.34804 - 4.06693i) q^{43} +(-0.972001 - 1.68356i) q^{47} +(0.232662 + 6.99613i) q^{49} +(4.45992 + 7.72481i) q^{53} +10.0130 q^{55} +(4.19339 - 7.26317i) q^{59} +(-2.41288 - 4.17923i) q^{61} +(5.60050 + 9.70034i) q^{65} +(1.27814 - 2.21380i) q^{67} +8.86178 q^{71} +(5.67598 + 9.83109i) q^{73} +(10.6762 + 10.3270i) q^{77} +(-6.72883 - 11.6547i) q^{79} +(1.60203 - 2.77479i) q^{83} +(-1.15267 - 1.99648i) q^{85} +(0.404646 - 0.700867i) q^{89} +(-4.03312 + 16.1189i) q^{91} +(0.997114 - 1.72705i) q^{95} +(1.10781 - 1.91879i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 - q^7	\( 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

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