LMFDB - Embedded newform 1512.2.q.d.793.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(793,1512)]

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, 2, 2]))

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

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

chi := DirichletCharacter("1512.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.q (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			793.4
Character	$\chi$	$=$	1512.793
Dual form			1512.2.q.d.1369.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891774 - 1.54460i) q^{5} +(-2.54386 + 0.727153i) q^{7} +O(q^{10})$	$q+(-0.891774 - 1.54460i) q^{5} +(-2.54386 + 0.727153i) q^{7} +(-2.80706 + 4.86196i) q^{11} +(3.14009 - 5.43879i) q^{13} +(-0.646279 - 1.11939i) q^{17} +(0.559062 - 0.968324i) q^{19} +(3.80857 + 6.59664i) q^{23} +(0.909478 - 1.57526i) q^{25} +(1.57496 + 2.72791i) q^{29} +1.00311 q^{31} +(3.39171 + 3.28079i) q^{35} +(-5.96542 + 10.3324i) q^{37} +(-4.14160 + 7.17347i) q^{41} +(2.34804 + 4.06693i) q^{43} +1.94400 q^{47} +(5.94250 - 3.69956i) q^{49} +(4.45992 + 7.72481i) q^{53} +10.0130 q^{55} -8.38679 q^{59} +4.82576 q^{61} -11.2010 q^{65} -2.55628 q^{67} +8.86178 q^{71} +(5.67598 + 9.83109i) q^{73} +(3.60538 - 14.4093i) q^{77} +13.4577 q^{79} +(1.60203 + 2.77479i) q^{83} +(-1.15267 + 1.99648i) q^{85} +(0.404646 - 0.700867i) q^{89} +(-4.03312 + 16.1189i) q^{91} -1.99423 q^{95} +(1.10781 + 1.91879i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{5} + 5 q^{7}+O(q^{10}) $ 22 * q - q^5 + 5 * q^7	$ 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.891774	−	1.54460i	−0.398814	−	0.690765i	0.594766	−	0.803899i	$-0.297245\pi$
$5$	−0.891774	−	1.54460i	−0.398814	−	0.690765i	−0.993580	+	0.113133i	$0.963911\pi$
$6$		0			0
$7$	−2.54386	+	0.727153i	−0.961491	+	0.274838i
$7$	−2.54386	+	0.727153i	−0.961491	+	0.274838i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.80706	+	4.86196i	−0.846359	+	1.46594i	0.0380759	+	0.999275i	$0.487877\pi$
$11$	−2.80706	+	4.86196i	−0.846359	+	1.46594i	−0.884435	+	0.466663i	$0.845456\pi$
$12$		0			0
$13$	3.14009	−	5.43879i	0.870903	−	1.50845i	0.00983976	−	0.999952i	$-0.496868\pi$
$13$	3.14009	−	5.43879i	0.870903	−	1.50845i	0.861064	−	0.508497i	$-0.169799\pi$
$14$		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
$23$	3.80857	+	6.59664i	0.794142	+	1.37549i	0.923382	+	0.383882i	$0.125413\pi$
$23$	3.80857	+	6.59664i	0.794142	+	1.37549i	−0.129240	+	0.991613i	$0.541254\pi$
$24$		0			0
$25$	0.909478	−	1.57526i	0.181896	−	0.315052i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.57496	+	2.72791i	0.292462	+	0.506560i	0.974391	−	0.224859i	$-0.0721921\pi$
$29$	1.57496	+	2.72791i	0.292462	+	0.506560i	−0.681929	+	0.731418i	$0.738859\pi$
$30$		0			0
$31$	1.00311			0.180163			0.0900816	−	0.995934i	$-0.471287\pi$
$31$	1.00311			0.180163			0.0900816	+	0.995934i	$0.471287\pi$
$32$		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	0.337071	+	0.941479i	$0.390564\pi$
$41$	−4.14160	+	7.17347i	−0.646810	+	1.12031i	−0.983880	+	0.178828i	$0.942769\pi$
$42$		0			0
$43$	2.34804	+	4.06693i	0.358073	+	0.620200i	0.987639	−	0.156747i	$-0.0501006\pi$
$43$	2.34804	+	4.06693i	0.358073	+	0.620200i	−0.629566	+	0.776947i	$0.716767\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.94400			0.283562			0.141781	−	0.989898i	$-0.454717\pi$
$47$	1.94400			0.283562			0.141781	+	0.989898i	$0.454717\pi$
$48$		0			0
$49$	5.94250	−	3.69956i	0.848928	−	0.528508i
$50$		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
$59$	−8.38679			−1.09187			−0.545933	−	0.837829i	$-0.683825\pi$
$59$	−8.38679			−1.09187			−0.545933	+	0.837829i	$0.683825\pi$
$60$		0			0
$61$	4.82576			0.617875			0.308937	−	0.951082i	$-0.400027\pi$
$61$	4.82576			0.617875			0.308937	+	0.951082i	$0.400027\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−11.2010			−1.38931
$66$		0			0
$67$	−2.55628			−0.312299			−0.156150	−	0.987733i	$-0.549908\pi$
$67$	−2.55628			−0.312299			−0.156150	+	0.987733i	$0.549908\pi$
$68$		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
$77$	3.60538	−	14.4093i	0.410871	−	1.64210i
$78$		0			0
$79$	13.4577			1.51410			0.757052	−	0.653354i	$-0.226639\pi$
$79$	13.4577			1.51410			0.757052	+	0.653354i	$0.226639\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.60203	+	2.77479i	0.175845	+	0.304573i	0.940453	−	0.339922i	$-0.110401\pi$
$83$	1.60203	+	2.77479i	0.175845	+	0.304573i	−0.764608	+	0.644495i	$0.777067\pi$
$84$		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
$95$	−1.99423			−0.204604
$96$		0			0
$97$	1.10781	+	1.91879i	0.112481	+	0.194823i	0.916770	−	0.399415i	$-0.130787\pi$
$97$	1.10781	+	1.91879i	0.112481	+	0.194823i	−0.804289	+	0.594238i	$0.797454\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.70134	−	8.14296i	0.467801	−	0.810254i	−0.531522	−	0.847044i	$-0.678380\pi$
$101$	4.70134	−	8.14296i	0.467801	−	0.810254i	0.999323	+	0.0367899i	$0.0117132\pi$
$102$		0			0
$103$	1.76349	+	3.05446i	0.173762	+	0.300964i	0.939732	−	0.341912i	$-0.111074\pi$
$103$	1.76349	+	3.05446i	0.173762	+	0.300964i	−0.765970	+	0.642876i	$0.777741\pi$
$104$		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	−0.706190	−	0.708022i	$-0.749588\pi$
$113$	2.76458	−	4.78840i	0.260070	−	0.450455i	0.966260	+	0.257568i	$0.0829210\pi$
$114$		0			0
$115$	6.79277	−	11.7654i	0.633429	−	1.09713i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.45801	+	2.37763i	0.225326	+	0.217957i
$120$		0			0
$121$	−10.2591	−	17.7693i	−0.932649	−	1.61539i
$122$		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
$131$	−2.90955	−	5.03948i	−0.254208	−	0.440302i	0.710472	−	0.703726i	$-0.248482\pi$
$131$	−2.90955	−	5.03948i	−0.254208	−	0.440302i	−0.964680	+	0.263424i	$0.915148\pi$
$132$		0			0
$133$	−0.718059	+	2.86981i	−0.0622636	+	0.248844i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.67046	+	13.2856i	−0.655332	+	1.13507i	0.326479	+	0.945205i	$0.394138\pi$
$137$	−7.67046	+	13.2856i	−0.655332	+	1.13507i	−0.981810	+	0.189864i	$0.939195\pi$
$138$		0			0
$139$	−6.05803	+	10.4928i	−0.513835	+	0.889988i	0.486036	+	0.873939i	$0.338442\pi$
$139$	−6.05803	+	10.4928i	−0.513835	+	0.889988i	−0.999871	+	0.0160496i	$0.994891\pi$
$140$		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
$149$	2.36849	+	4.10235i	0.194035	+	0.336078i	0.946584	−	0.322458i	$-0.104509\pi$
$149$	2.36849	+	4.10235i	0.194035	+	0.336078i	−0.752549	+	0.658536i	$0.771176\pi$
$150$		0			0
$151$	−12.1845	+	21.1041i	−0.991559	+	1.71743i	−0.383493	+	0.923544i	$0.625279\pi$
$151$	−12.1845	+	21.1041i	−0.991559	+	1.71743i	−0.608066	+	0.793887i	$0.708054\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.894545	−	1.54940i	−0.0718516	−	0.124451i
$156$		0			0
$157$	−6.30458			−0.503160			−0.251580	−	0.967836i	$-0.580950\pi$
$157$	−6.30458			−0.503160			−0.251580	+	0.967836i	$0.580950\pi$
$158$		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	−0.969831	−	0.243780i	$-0.921613\pi$
$167$	−3.53822	+	6.12839i	−0.273796	+	0.474229i	0.696035	+	0.718008i	$0.254946\pi$
$168$		0			0
$169$	−13.2203	−	22.8982i	−1.01695	−	1.76140i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.63534			−0.504476			−0.252238	−	0.967665i	$-0.581167\pi$
$173$	−6.63534			−0.504476			−0.252238	+	0.967665i	$0.581167\pi$
$174$		0			0
$175$	−1.16813	+	4.66858i	−0.0883025	+	0.352912i
$176$		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
$185$	21.2792			1.56448
$186$		0			0
$187$	7.25657			0.530653
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.44088			0.683118			0.341559	−	0.939860i	$-0.389045\pi$
$191$	9.44088			0.683118			0.341559	+	0.939860i	$0.389045\pi$
$192$		0			0
$193$	−6.28042			−0.452074			−0.226037	−	0.974119i	$-0.572577\pi$
$193$	−6.28042			−0.452074			−0.226037	+	0.974119i	$0.572577\pi$
$194$		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
$203$	−5.99009	−	5.79419i	−0.420422	−	0.406673i
$204$		0			0
$205$	14.7735			1.03183
$206$		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	−0.452550	−	0.891739i	$-0.649486\pi$
$211$	7.93101	−	13.7369i	0.545993	−	0.945688i	0.998544	−	0.0539495i	$-0.0171810\pi$
$212$		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
$221$	−8.11749			−0.546041
$222$		0			0
$223$	6.99253	+	12.1114i	0.468254	+	0.811040i	0.999342	−	0.0362769i	$-0.0115498\pi$
$223$	6.99253	+	12.1114i	0.468254	+	0.811040i	−0.531088	+	0.847317i	$0.678216\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.38364	−	9.32474i	0.357325	−	0.618905i	−0.630188	−	0.776443i	$-0.717022\pi$
$227$	5.38364	−	9.32474i	0.357325	−	0.618905i	0.987513	+	0.157538i	$0.0503555\pi$
$228$		0			0
$229$	0.805015	+	1.39433i	0.0531969	+	0.0921397i	0.891398	−	0.453222i	$-0.149726\pi$
$229$	0.805015	+	1.39433i	0.0531969	+	0.0921397i	−0.838201	+	0.545362i	$0.816392\pi$
$230$		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	−0.547934	−	0.836522i	$-0.684586\pi$
$239$	6.96428	−	12.0625i	0.450482	−	0.780258i	0.998416	+	0.0562640i	$0.0179189\pi$
$240$		0			0
$241$	7.28788	−	12.6230i	0.469454	−	0.813118i	−0.529936	−	0.848037i	$-0.677784\pi$
$241$	7.28788	−	12.6230i	0.469454	−	0.813118i	0.999390	+	0.0349197i	$0.0111175\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−11.0137	−	5.87960i	−0.703639	−	0.375634i
$246$		0			0
$247$	−3.51101	−	6.08124i	−0.223400	−	0.386940i
$248$		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
$257$	13.4633	+	23.3191i	0.839818	+	1.45461i	0.890047	+	0.455869i	$0.150672\pi$
$257$	13.4633	+	23.3191i	0.839818	+	1.45461i	−0.0502291	+	0.998738i	$0.515995\pi$
$258$		0			0
$259$	7.66198	−	30.6220i	0.476092	−	1.90276i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.769419	−	1.33267i	0.0474444	−	0.0821761i	−0.841328	−	0.540525i	$-0.818226\pi$
$263$	0.769419	−	1.33267i	0.0474444	−	0.0821761i	0.888772	+	0.458349i	$0.151559\pi$
$264$		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
$275$	5.10591	+	8.84370i	0.307898	+	0.533295i
$276$		0			0
$277$	−0.905938	+	1.56913i	−0.0544325	+	0.0942799i	−0.891958	−	0.452119i	$-0.850668\pi$
$277$	−0.905938	+	1.56913i	−0.0544325	+	0.0942799i	0.837525	+	0.546399i	$0.184002\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.98798	+	5.17533i	0.178248	+	0.308734i	0.941280	−	0.337626i	$-0.109624\pi$
$281$	2.98798	+	5.17533i	0.178248	+	0.308734i	−0.763033	+	0.646360i	$0.776290\pi$
$282$		0			0
$283$	−19.9952			−1.18859			−0.594295	−	0.804247i	$-0.702569\pi$
$283$	−19.9952			−1.18859			−0.594295	+	0.804247i	$0.702569\pi$
$284$		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	−0.684359	−	0.729145i	$-0.739918\pi$
$293$	4.95166	−	8.57652i	0.289279	−	0.501046i	0.973638	+	0.228099i	$0.0732511\pi$
$294$		0			0
$295$	7.47912	+	12.9542i	0.435451	+	0.754224i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	47.8370			2.76649
$300$		0			0
$301$	−8.93038	−	8.63833i	−0.514738	−	0.497905i
$302$		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
$311$	−20.3449			−1.15365			−0.576826	−	0.816867i	$-0.695709\pi$
$311$	−20.3449			−1.15365			−0.576826	+	0.816867i	$0.695709\pi$
$312$		0			0
$313$	9.71871			0.549334			0.274667	−	0.961539i	$-0.411432\pi$
$313$	9.71871			0.549334			0.274667	+	0.961539i	$0.411432\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.32838			0.186941			0.0934703	−	0.995622i	$-0.470204\pi$
$317$	3.32838			0.186941			0.0934703	+	0.995622i	$0.470204\pi$
$318$		0			0
$319$	−17.6840			−0.990113
$320$		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
$329$	−4.94528	+	1.41359i	−0.272642	+	0.0779335i
$330$		0			0
$331$	−1.43469			−0.0788578			−0.0394289	−	0.999222i	$-0.512554\pi$
$331$	−1.43469			−0.0788578			−0.0394289	+	0.999222i	$0.512554\pi$
$332$		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	−0.865955	−	0.500121i	$-0.833289\pi$
$337$	0.00257316	−	0.00445685i	0.000140169	−	0.000242780i	0.866095	+	0.499879i	$0.166622\pi$
$338$		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
$347$	−23.1072			−1.24046			−0.620229	−	0.784421i	$-0.712960\pi$
$347$	−23.1072			−1.24046			−0.620229	+	0.784421i	$0.712960\pi$
$348$		0			0
$349$	6.09723	+	10.5607i	0.326377	+	0.565302i	0.981790	−	0.189969i	$-0.0608387\pi$
$349$	6.09723	+	10.5607i	0.326377	+	0.565302i	−0.655413	+	0.755271i	$0.727505\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.3536	−	21.3970i	0.657515	−	1.13885i	−0.323742	−	0.946145i	$-0.604941\pi$
$353$	12.3536	−	21.3970i	0.657515	−	1.13885i	0.981257	−	0.192704i	$-0.0617257\pi$
$354$		0			0
$355$	−7.90271	−	13.6879i	−0.419432	−	0.726478i
$356$		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
$367$	2.90900	−	5.03854i	0.151849	−	0.263010i	−0.780058	−	0.625707i	$-0.784811\pi$
$367$	2.90900	−	5.03854i	0.151849	−	0.263010i	0.931907	+	0.362697i	$0.118144\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−16.9626	−	16.4078i	−0.880652	−	0.851852i
$372$		0			0
$373$	−4.42483	−	7.66403i	−0.229109	−	0.396829i	0.728435	−	0.685115i	$-0.240248\pi$
$373$	−4.42483	−	7.66403i	−0.229109	−	0.396829i	−0.957544	+	0.288286i	$0.906915\pi$
$374$		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
$383$	3.54545	+	6.14090i	0.181164	+	0.313785i	0.942277	−	0.334834i	$-0.108680\pi$
$383$	3.54545	+	6.14090i	0.181164	+	0.313785i	−0.761113	+	0.648619i	$0.775347\pi$
$384$		0			0
$385$	−25.4718	+	7.28101i	−1.29816	+	0.371075i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.32120	−	5.75249i	0.168392	−	0.291663i	−0.769463	−	0.638691i	$-0.779476\pi$
$389$	3.32120	−	5.75249i	0.168392	−	0.291663i	0.937854	+	0.347029i	$0.112809\pi$
$390$		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
$401$	2.98280	+	5.16635i	0.148954	+	0.257995i	0.930841	−	0.365424i	$-0.119076\pi$
$401$	2.98280	+	5.16635i	0.148954	+	0.257995i	−0.781887	+	0.623420i	$0.785743\pi$
$402$		0			0
$403$	3.14984	−	5.45569i	0.156905	−	0.271767i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−33.4905	−	58.0073i	−1.66006	−	2.87531i
$408$		0			0
$409$	−17.6189			−0.871197			−0.435598	−	0.900141i	$-0.643463\pi$
$409$	−17.6189			−0.871197			−0.435598	+	0.900141i	$0.643463\pi$
$410$		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	−0.999413	−	0.0342470i	$-0.989097\pi$
$419$	−9.62164	+	16.6652i	−0.470048	+	0.814147i	0.529365	+	0.848394i	$0.322430\pi$
$420$		0			0
$421$	7.77999	+	13.4753i	0.379174	+	0.656748i	0.990942	−	0.134289i	$-0.0428750\pi$
$421$	7.77999	+	13.4753i	0.379174	+	0.656748i	−0.611769	+	0.791037i	$0.709542\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.35111			−0.114045
$426$		0			0
$427$	−12.2761	+	3.50906i	−0.594081	+	0.169815i
$428$		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
$437$	8.51692			0.407419
$438$		0			0
$439$	15.5588			0.742579			0.371290	−	0.928517i	$-0.378916\pi$
$439$	15.5588			0.742579			0.371290	+	0.928517i	$0.378916\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.3242			−0.870611			−0.435305	−	0.900283i	$-0.643360\pi$
$443$	−18.3242			−0.870611			−0.435305	+	0.900283i	$0.643360\pi$
$444$		0			0
$445$	−1.44341			−0.0684242
$446$		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
$455$	28.4938	−	8.14483i	1.33581	−	0.381836i
$456$		0			0
$457$	20.6813			0.967433			0.483716	−	0.875225i	$-0.339287\pi$
$457$	20.6813			0.967433			0.483716	+	0.875225i	$0.339287\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.40670	−	11.0967i	−0.298390	−	0.516826i	0.677378	−	0.735635i	$-0.263116\pi$
$461$	−6.40670	−	11.0967i	−0.298390	−	0.516826i	−0.975768	+	0.218809i	$0.929783\pi$
$462$		0			0
$463$	5.54704	−	9.60775i	0.257793	−	0.446510i	−0.707858	−	0.706355i	$-0.750338\pi$
$463$	5.54704	−	9.60775i	0.257793	−	0.446510i	0.965650	+	0.259845i	$0.0836715\pi$
$464$		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
$473$	−26.3643			−1.21223
$474$		0			0
$475$	−1.01691	−	1.76134i	−0.0466590	−	0.0808157i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.89754	+	6.75074i	−0.178083	+	0.308449i	−0.941224	−	0.337783i	$-0.890323\pi$
$479$	−3.89754	+	6.75074i	−0.178083	+	0.308449i	0.763141	+	0.646232i	$0.223656\pi$
$480$		0			0
$481$	37.4639	+	64.8893i	1.70820	+	2.95870i
$482$		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	−0.451383	−	0.892330i	$-0.649069\pi$
$491$	12.1227	−	20.9971i	0.547089	−	0.947586i	0.998472	−	0.0552556i	$-0.0175974\pi$
$492$		0			0
$493$	2.03572	−	3.52598i	0.0916844	−	0.158802i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−22.5432	+	6.44387i	−1.01120	+	0.289047i
$498$		0			0
$499$	16.8874	+	29.2499i	0.755984	+	1.30940i	0.944883	+	0.327407i	$0.106175\pi$
$499$	16.8874	+	29.2499i	0.755984	+	1.30940i	−0.188899	+	0.981996i	$0.560492\pi$
$500$		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
$509$	8.10672	+	14.0413i	0.359324	+	0.622368i	0.987848	−	0.155423i	$-0.0496739\pi$
$509$	8.10672	+	14.0413i	0.359324	+	0.622368i	−0.628524	+	0.777790i	$0.716341\pi$
$510$		0			0
$511$	−21.5876	−	20.8817i	−0.954981	−	0.923750i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.14527	−	5.44777i	0.138597	−	0.240057i
$516$		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
$527$	−0.648287	−	1.12287i	−0.0282398	−	0.0489128i
$528$		0			0
$529$	−17.5105	+	30.3290i	−0.761324	+	1.31865i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	26.0100	+	45.0506i	1.12662	+	1.95136i
$534$		0			0
$535$	−12.1023			−0.523229
$536$		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	0.873175	−	0.487406i	$-0.162057\pi$
$547$	0.338699	+	0.586644i	0.0144817	+	0.0250831i	−0.858694	+	0.512489i	$0.828723\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.52200			0.150042
$552$		0			0
$553$	−34.2345	+	9.78577i	−1.45580	+	0.416133i
$554$		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
$563$	−21.3478			−0.899705			−0.449852	−	0.893103i	$-0.648523\pi$
$563$	−21.3478			−0.899705			−0.449852	+	0.893103i	$0.648523\pi$
$564$		0			0
$565$	−9.86153			−0.414878
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.1242			0.634041			0.317021	−	0.948419i	$-0.397318\pi$
$569$	15.1242			0.634041			0.317021	+	0.948419i	$0.397318\pi$
$570$		0			0
$571$	19.8863			0.832215			0.416107	−	0.909315i	$-0.363394\pi$
$571$	19.8863			0.832215			0.416107	+	0.909315i	$0.363394\pi$
$572$		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
$581$	−6.09304	−	5.89378i	−0.252782	−	0.244515i
$582$		0			0
$583$	−50.0770			−2.07398
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.13275	−	1.96199i	−0.0467537	−	0.0809798i	0.841701	−	0.539943i	$-0.181554\pi$
$587$	−1.13275	−	1.96199i	−0.0467537	−	0.0809798i	−0.888455	+	0.458963i	$0.848221\pi$
$588$		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
$599$	2.95272			0.120645			0.0603224	−	0.998179i	$-0.480787\pi$
$599$	2.95272			0.120645			0.0603224	+	0.998179i	$0.480787\pi$
$600$		0			0
$601$	15.9751	+	27.6697i	0.651638	+	1.12867i	0.982725	+	0.185071i	$0.0592514\pi$
$601$	15.9751	+	27.6697i	0.651638	+	1.12867i	−0.331087	+	0.943600i	$0.607415\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−18.2977	+	31.6925i	−0.743906	+	1.28848i
$606$		0			0
$607$	−5.20069	−	9.00786i	−0.211089	−	0.365618i	0.740966	−	0.671542i	$-0.234368\pi$
$607$	−5.20069	−	9.00786i	−0.211089	−	0.365618i	−0.952056	+	0.305925i	$0.901034\pi$
$608$		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	−0.755747	−	0.654864i	$-0.772726\pi$
$617$	4.70100	−	8.14237i	0.189255	−	0.327799i	0.945002	+	0.327064i	$0.106059\pi$
$618$		0			0
$619$	11.0598	−	19.1561i	0.444531	−	0.769951i	−0.553488	−	0.832857i	$-0.686704\pi$
$619$	11.0598	−	19.1561i	0.444531	−	0.769951i	0.998019	+	0.0629064i	$0.0200370\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.519727	+	2.07715i	−0.0208224	+	0.0832193i
$624$		0			0
$625$	6.29831	+	10.9090i	0.251932	+	0.436360i
$626$		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
$635$	11.4334	+	19.8032i	0.453720	+	0.785866i
$636$		0			0
$637$	−1.46116	−	43.9369i	−0.0578932	−	1.74084i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.8617	+	29.2052i	−0.665995	+	1.15354i	0.313019	+	0.949747i	$0.398660\pi$
$641$	−16.8617	+	29.2052i	−0.665995	+	1.15354i	−0.979014	+	0.203791i	$0.934674\pi$
$642$		0			0
$643$	10.0635	−	17.4306i	0.396867	−	0.687394i	−0.596470	−	0.802635i	$-0.703431\pi$
$643$	10.0635	−	17.4306i	0.396867	−	0.687394i	0.993338	+	0.115241i	$0.0367640\pi$
$644$		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
$653$	−20.3377	−	35.2259i	−0.795875	−	1.37850i	−0.922282	−	0.386518i	$-0.873678\pi$
$653$	−20.3377	−	35.2259i	−0.795875	−	1.37850i	0.126406	−	0.991979i	$-0.459656\pi$
$654$		0			0
$655$	−5.18932	+	8.98816i	−0.202763	+	0.351197i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.69321	−	13.3250i	−0.299685	−	0.519070i	0.676379	−	0.736554i	$-0.263548\pi$
$659$	−7.69321	−	13.3250i	−0.299685	−	0.519070i	−0.976064	+	0.217484i	$0.930215\pi$
$660$		0			0
$661$	49.1473			1.91161			0.955804	−	0.294006i	$-0.0949885\pi$
$661$	49.1473			1.91161			0.955804	+	0.294006i	$0.0949885\pi$
$662$		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	0.698999	−	0.715123i	$-0.253629\pi$
$673$	−6.99961	−	12.1237i	−0.269815	−	0.467334i	−0.968814	+	0.247789i	$0.920296\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	46.7740			1.79767			0.898836	−	0.438285i	$-0.144414\pi$
$677$	46.7740			1.79767			0.898836	+	0.438285i	$0.144414\pi$
$678$		0			0
$679$	−4.21337	−	4.07558i	−0.161694	−	0.156406i
$680$		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
$689$	56.0181			2.13412
$690$		0			0
$691$	−11.7214			−0.445905			−0.222952	−	0.974829i	$-0.571569\pi$
$691$	−11.7214			−0.445905			−0.222952	+	0.974829i	$0.571569\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.6096			0.819697
$696$		0			0
$697$	10.7065			0.405538
$698$		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
$707$	−6.03839	+	24.1332i	−0.227097	+	0.907621i
$708$		0			0
$709$	1.07478			0.0403640			0.0201820	−	0.999796i	$-0.493575\pi$
$709$	1.07478			0.0403640			0.0201820	+	0.999796i	$0.493575\pi$
$710$		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
$725$	5.72956			0.212790
$726$		0			0
$727$	6.20522	+	10.7478i	0.230139	+	0.398612i	0.957849	−	0.287273i	$-0.0927486\pi$
$727$	6.20522	+	10.7478i	0.230139	+	0.398612i	−0.727710	+	0.685885i	$0.759415\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.03498	−	5.25674i	0.112253	−	0.194427i
$732$		0			0
$733$	−14.7095	−	25.4775i	−0.543307	−	0.941035i	−0.998711	−	0.0507502i	$-0.983839\pi$
$733$	−14.7095	−	25.4775i	−0.543307	−	0.941035i	0.455405	−	0.890285i	$-0.349495\pi$
$734$		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	−0.499841	−	0.866117i	$-0.666608\pi$
$743$	13.6333	−	23.6136i	0.500159	−	0.866301i	1.00000		0.000183414i	$-5.83824e-5\pi$
$744$		0			0
$745$	4.22432	−	7.31674i	0.154767	−	0.268065i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−4.35766	+	17.4159i	−0.159226	+	0.636364i
$750$		0			0
$751$	4.57176	+	7.91853i	0.166826	+	0.288951i	0.937302	−	0.348518i	$-0.113315\pi$
$751$	4.57176	+	7.91853i	0.166826	+	0.288951i	−0.770476	+	0.637469i	$0.779982\pi$
$752$		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
$761$	−0.239208	−	0.414321i	−0.00867130	−	0.0150191i	0.861657	−	0.507491i	$-0.169427\pi$
$761$	−0.239208	−	0.414321i	−0.00867130	−	0.0150191i	−0.870328	+	0.492472i	$0.836094\pi$
$762$		0			0
$763$	−2.59329	−	2.50848i	−0.0938835	−	0.0908132i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−26.3352	+	45.6140i	−0.950910	+	1.64702i
$768$		0			0
$769$	−13.3518	+	23.1261i	−0.481480	+	0.833948i	−0.999774	−	0.0212548i	$-0.993234\pi$
$769$	−13.3518	+	23.1261i	−0.481480	+	0.833948i	0.518294	+	0.855202i	$0.326567\pi$
$770$		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
$779$	4.63083	+	8.02083i	0.165917	+	0.287376i
$780$		0			0
$781$	−24.8755	+	43.0857i	−0.890116	+	1.54173i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.62226	+	9.73804i	0.200667	+	0.347566i
$786$		0			0
$787$	49.1830			1.75319			0.876593	−	0.481233i	$-0.159811\pi$
$787$	49.1830			1.75319			0.876593	+	0.481233i	$0.159811\pi$
$788$		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	0.144434	+	0.989514i	$0.453864\pi$
$797$	−22.1538	+	38.3715i	−0.784728	+	1.35919i	−0.929162	+	0.369674i	$0.879469\pi$
$798$		0			0
$799$	−1.25637	−	2.17609i	−0.0444471	−	0.0769846i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−63.7312			−2.24903
$804$		0			0
$805$	−8.72463	+	34.8690i	−0.307503	+	1.22897i
$806$		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
$815$	−1.25090			−0.0438172
$816$		0			0
$817$	5.25080			0.183702
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.5132			0.785714			0.392857	−	0.919599i	$-0.371487\pi$
$821$	22.5132			0.785714			0.392857	+	0.919599i	$0.371487\pi$
$822$		0			0
$823$	14.6735			0.511485			0.255743	−	0.966745i	$-0.417680\pi$
$823$	14.6735			0.511485			0.255743	+	0.966745i	$0.417680\pi$
$824$		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
$833$	−7.98175	−	4.26101i	−0.276551	−	0.147635i
$834$		0			0
$835$	12.6212			0.436774
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−2.04477	−	3.54164i	−0.0705932	−	0.122271i	0.828568	−	0.559888i	$-0.189156\pi$
$839$	−2.04477	−	3.54164i	−0.0705932	−	0.122271i	−0.899161	+	0.437617i	$0.855823\pi$
$840$		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
$851$	−90.8789			−3.11529
$852$		0			0
$853$	−21.1012	−	36.5484i	−0.722491	−	1.25139i	−0.959998	−	0.280006i	$-0.909664\pi$
$853$	−21.1012	−	36.5484i	−0.722491	−	1.25139i	0.237507	−	0.971386i	$-0.423670\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−27.5623	+	47.7393i	−0.941509	+	1.63074i	−0.178915	+	0.983864i	$0.557259\pi$
$857$	−27.5623	+	47.7393i	−0.941509	+	1.63074i	−0.762594	+	0.646877i	$0.776075\pi$
$858$		0			0
$859$	18.9767	+	32.8686i	0.647476	+	1.12146i	0.983724	+	0.179688i	$0.0575089\pi$
$859$	18.9767	+	32.8686i	0.647476	+	1.12146i	−0.336247	+	0.941774i	$0.609158\pi$
$860$		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
$871$	−8.02694	+	13.9031i	−0.271983	+	0.471088i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	30.9383	−	8.84359i	1.04591	−	0.298968i
$876$		0			0
$877$	−4.85337	−	8.40628i	−0.163887	−	0.283860i	0.772373	−	0.635169i	$-0.219070\pi$
$877$	−4.85337	−	8.40628i	−0.163887	−	0.283860i	−0.936259	+	0.351310i	$0.885736\pi$
$878$		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
$887$	−0.415361	−	0.719426i	−0.0139464	−	0.0241560i	0.858968	−	0.512029i	$-0.171106\pi$
$887$	−0.415361	−	0.719426i	−0.0139464	−	0.0241560i	−0.872914	+	0.487873i	$0.837773\pi$
$888$		0			0
$889$	32.6147	−	9.32278i	1.09386	−	0.312676i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.08682	−	1.88242i	0.0363690	−	0.0629929i
$894$		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
$905$	−18.8878	−	32.7146i	−0.627852	−	1.08747i
$906$		0			0
$907$	−16.6588	+	28.8539i	−0.553146	+	0.958077i	0.444899	+	0.895581i	$0.353239\pi$
$907$	−16.6588	+	28.8539i	−0.553146	+	0.958077i	−0.998045	+	0.0624962i	$0.980094\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.1353	+	19.2870i	0.368930	+	0.639006i	0.989399	−	0.145226i	$-0.0463909\pi$
$911$	11.1353	+	19.2870i	0.368930	+	0.639006i	−0.620469	+	0.784231i	$0.713058\pi$
$912$		0			0
$913$	−17.9879			−0.595313
$914$		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
$929$	37.1559			1.21905			0.609523	−	0.792768i	$-0.291361\pi$
$929$	37.1559			1.21905			0.609523	+	0.792768i	$0.291361\pi$
$930$		0			0
$931$	−0.260145	−	7.82255i	−0.00852591	−	0.256374i
$932$		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
$941$	47.4064			1.54540			0.772702	−	0.634769i	$-0.218905\pi$
$941$	47.4064			1.54540			0.772702	+	0.634769i	$0.218905\pi$
$942$		0			0
$943$	−63.0944			−2.05464
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.50117			0.0812771			0.0406386	−	0.999174i	$-0.487061\pi$
$947$	2.50117			0.0812771			0.0406386	+	0.999174i	$0.487061\pi$
$948$		0			0
$949$	71.2923			2.31425
$950$		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
$959$	9.85194	−	39.3745i	0.318136	−	1.27147i
$960$		0			0
$961$	−29.9938			−0.967541
$962$		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	−0.758299	−	0.651907i	$-0.773969\pi$
$967$	5.76591	−	9.98684i	0.185419	−	0.321155i	0.943718	+	0.330752i	$0.107302\pi$
$968$		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
$977$	29.9083			0.956850			0.478425	−	0.878128i	$-0.341208\pi$
$977$	29.9083			0.956850			0.478425	+	0.878128i	$0.341208\pi$
$978$		0			0
$979$	2.27173	+	3.93475i	0.0726047	+	0.125755i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.27224	−	12.5959i	0.231948	−	0.401746i	−0.726433	−	0.687237i	$-0.758823\pi$
$983$	7.27224	−	12.5959i	0.231948	−	0.401746i	0.958381	+	0.285491i	$0.0921566\pi$
$984$		0			0
$985$	13.8029	+	23.9073i	0.439797	+	0.761751i
$986$		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
$997$	−17.9469	+	31.0850i	−0.568384	+	0.984471i	0.428341	+	0.903617i	$0.359098\pi$
$997$	−17.9469	+	31.0850i	−0.568384	+	0.984471i	−0.996726	+	0.0808539i	$0.974235\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.q.d.793.4		22
3.2	odd	2		504.2.q.c.121.4	yes	22
4.3	odd	2		3024.2.q.l.2305.4		22
7.4	even	3		1512.2.t.c.361.8		22
9.2	odd	6		504.2.t.c.457.5	yes	22
9.7	even	3		1512.2.t.c.289.8		22
12.11	even	2		1008.2.q.l.625.8		22
21.11	odd	6		504.2.t.c.193.5	yes	22
28.11	odd	6		3024.2.t.k.1873.8		22
36.7	odd	6		3024.2.t.k.289.8		22
36.11	even	6		1008.2.t.l.961.7		22
63.11	odd	6		504.2.q.c.25.4	✓	22
63.25	even	3	inner	1512.2.q.d.1369.4		22
84.11	even	6		1008.2.t.l.193.7		22
252.11	even	6		1008.2.q.l.529.8		22
252.151	odd	6		3024.2.q.l.2881.4		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.4	✓	22	63.11	odd	6
504.2.q.c.121.4	yes	22	3.2	odd	2
504.2.t.c.193.5	yes	22	21.11	odd	6
504.2.t.c.457.5	yes	22	9.2	odd	6
1008.2.q.l.529.8		22	252.11	even	6
1008.2.q.l.625.8		22	12.11	even	2
1008.2.t.l.193.7		22	84.11	even	6
1008.2.t.l.961.7		22	36.11	even	6
1512.2.q.d.793.4		22	1.1	even	1	trivial
1512.2.q.d.1369.4		22	63.25	even	3	inner
1512.2.t.c.289.8		22	9.7	even	3
1512.2.t.c.361.8		22	7.4	even	3
3024.2.q.l.2305.4		22	4.3	odd	2
3024.2.q.l.2881.4		22	252.151	odd	6
3024.2.t.k.289.8		22	36.7	odd	6
3024.2.t.k.1873.8		22	28.11	odd	6

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

\(f(q)\)	\(=\)	\(q+(-0.891774 - 1.54460i) q^{5} +(-2.54386 + 0.727153i) q^{7} +O(q^{10})\)	\(q+(-0.891774 - 1.54460i) q^{5} +(-2.54386 + 0.727153i) q^{7} +(-2.80706 + 4.86196i) q^{11} +(3.14009 - 5.43879i) q^{13} +(-0.646279 - 1.11939i) q^{17} +(0.559062 - 0.968324i) q^{19} +(3.80857 + 6.59664i) q^{23} +(0.909478 - 1.57526i) q^{25} +(1.57496 + 2.72791i) q^{29} +1.00311 q^{31} +(3.39171 + 3.28079i) q^{35} +(-5.96542 + 10.3324i) q^{37} +(-4.14160 + 7.17347i) q^{41} +(2.34804 + 4.06693i) q^{43} +1.94400 q^{47} +(5.94250 - 3.69956i) q^{49} +(4.45992 + 7.72481i) q^{53} +10.0130 q^{55} -8.38679 q^{59} +4.82576 q^{61} -11.2010 q^{65} -2.55628 q^{67} +8.86178 q^{71} +(5.67598 + 9.83109i) q^{73} +(3.60538 - 14.4093i) q^{77} +13.4577 q^{79} +(1.60203 + 2.77479i) q^{83} +(-1.15267 + 1.99648i) q^{85} +(0.404646 - 0.700867i) q^{89} +(-4.03312 + 16.1189i) q^{91} -1.99423 q^{95} +(1.10781 + 1.91879i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} + 5 q^{7}+O(q^{10}) \) 22 * q - q^5 + 5 * q^7	\( 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

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