LMFDB - Embedded newform 1512.2.q.d.793.3

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			793.3
Character	$\chi$	$=$	1512.793
Dual form			1512.2.q.d.1369.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33425 - 2.31099i) q^{5} +(2.54743 + 0.714566i) q^{7} +O(q^{10})$	$q+(-1.33425 - 2.31099i) q^{5} +(2.54743 + 0.714566i) q^{7} +(-1.99189 + 3.45005i) q^{11} +(1.00103 - 1.73384i) q^{13} +(3.57175 + 6.18646i) q^{17} +(-4.01956 + 6.96208i) q^{19} +(-0.443909 - 0.768873i) q^{23} +(-1.06046 + 1.83677i) q^{25} +(1.35035 + 2.33887i) q^{29} -1.22989 q^{31} +(-1.74756 - 6.84051i) q^{35} +(5.26528 - 9.11973i) q^{37} +(1.43477 - 2.48509i) q^{41} +(3.40053 + 5.88989i) q^{43} +12.1369 q^{47} +(5.97879 + 3.64061i) q^{49} +(2.38665 + 4.13380i) q^{53} +10.6307 q^{55} -9.58058 q^{59} -9.49962 q^{61} -5.34252 q^{65} +10.9889 q^{67} +4.62888 q^{71} +(2.01004 + 3.48149i) q^{73} +(-7.53949 + 7.36543i) q^{77} -1.02997 q^{79} +(5.26656 + 9.12195i) q^{83} +(9.53125 - 16.5086i) q^{85} +(-1.72788 + 2.99278i) q^{89} +(3.78900 - 3.70153i) q^{91} +21.4524 q^{95} +(-1.12061 - 1.94096i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.33425	−	2.31099i	−0.596696	−	1.03351i	−0.993305	−	0.115520i	$-0.963146\pi$
$5$	−1.33425	−	2.31099i	−0.596696	−	1.03351i	0.396609	−	0.917988i	$-0.370187\pi$
$6$		0			0
$7$	2.54743	+	0.714566i	0.962838	+	0.270081i
$7$	2.54743	+	0.714566i	0.962838	+	0.270081i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.99189	+	3.45005i	−0.600577	+	1.04023i	0.392157	+	0.919898i	$0.371729\pi$
$11$	−1.99189	+	3.45005i	−0.600577	+	1.04023i	−0.992734	+	0.120332i	$0.961604\pi$
$12$		0			0
$13$	1.00103	−	1.73384i	0.277636	−	0.480880i	−0.693161	−	0.720783i	$-0.743782\pi$
$13$	1.00103	−	1.73384i	0.277636	−	0.480880i	0.970797	+	0.239903i	$0.0771156\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.57175	+	6.18646i	0.866278	+	1.50044i	0.865773	+	0.500437i	$0.166827\pi$
$17$	3.57175	+	6.18646i	0.866278	+	1.50044i	0.000504947		1.00000i	$0.499839\pi$
$18$		0			0
$19$	−4.01956	+	6.96208i	−0.922150	+	1.59721i	−0.126068	+	0.992022i	$0.540236\pi$
$19$	−4.01956	+	6.96208i	−0.922150	+	1.59721i	−0.796082	+	0.605189i	$0.793097\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.443909	−	0.768873i	−0.0925614	−	0.160321i	0.816027	−	0.578014i	$-0.196172\pi$
$23$	−0.443909	−	0.768873i	−0.0925614	−	0.160321i	−0.908588	+	0.417693i	$0.862839\pi$
$24$		0			0
$25$	−1.06046	+	1.83677i	−0.212092	+	0.367355i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.35035	+	2.33887i	0.250753	+	0.434317i	0.963733	−	0.266867i	$-0.0859885\pi$
$29$	1.35035	+	2.33887i	0.250753	+	0.434317i	−0.712980	+	0.701184i	$0.752655\pi$
$30$		0			0
$31$	−1.22989			−0.220894			−0.110447	−	0.993882i	$-0.535228\pi$
$31$	−1.22989			−0.220894			−0.110447	+	0.993882i	$0.535228\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.74756	−	6.84051i	−0.295391	−	1.15626i
$36$		0			0
$37$	5.26528	−	9.11973i	0.865607	−	1.49928i	−0.000836477	−	1.00000i	$-0.500266\pi$
$37$	5.26528	−	9.11973i	0.865607	−	1.49928i	0.866443	−	0.499275i	$-0.166400\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.43477	−	2.48509i	0.224073	−	0.388105i	−0.731968	−	0.681339i	$-0.761398\pi$
$41$	1.43477	−	2.48509i	0.224073	−	0.388105i	0.956041	+	0.293234i	$0.0947313\pi$
$42$		0			0
$43$	3.40053	+	5.88989i	0.518576	+	0.898200i	0.999767	+	0.0215840i	$0.00687093\pi$
$43$	3.40053	+	5.88989i	0.518576	+	0.898200i	−0.481191	+	0.876616i	$0.659796\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	12.1369			1.77035			0.885175	−	0.465258i	$-0.154039\pi$
$47$	12.1369			1.77035			0.885175	+	0.465258i	$0.154039\pi$
$48$		0			0
$49$	5.97879	+	3.64061i	0.854113	+	0.520088i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.38665	+	4.13380i	0.327832	+	0.567821i	0.982081	−	0.188457i	$-0.0603487\pi$
$53$	2.38665	+	4.13380i	0.327832	+	0.567821i	−0.654250	+	0.756279i	$0.727015\pi$
$54$		0			0
$55$	10.6307			1.43345
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−9.58058			−1.24729			−0.623643	−	0.781710i	$-0.714348\pi$
$59$	−9.58058			−1.24729			−0.623643	+	0.781710i	$0.714348\pi$
$60$		0			0
$61$	−9.49962			−1.21630			−0.608151	−	0.793821i	$-0.708089\pi$
$61$	−9.49962			−1.21630			−0.608151	+	0.793821i	$0.708089\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.34252			−0.662658
$66$		0			0
$67$	10.9889			1.34251			0.671255	−	0.741227i	$-0.265756\pi$
$67$	10.9889			1.34251			0.671255	+	0.741227i	$0.265756\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.62888			0.549347			0.274673	−	0.961538i	$-0.411430\pi$
$71$	4.62888			0.549347			0.274673	+	0.961538i	$0.411430\pi$
$72$		0			0
$73$	2.01004	+	3.48149i	0.235257	+	0.407478i	0.959347	−	0.282228i	$-0.0910733\pi$
$73$	2.01004	+	3.48149i	0.235257	+	0.407478i	−0.724090	+	0.689705i	$0.757740\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.53949	+	7.36543i	−0.859204	+	0.839368i
$78$		0			0
$79$	−1.02997			−0.115881			−0.0579406	−	0.998320i	$-0.518453\pi$
$79$	−1.02997			−0.115881			−0.0579406	+	0.998320i	$0.518453\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.26656	+	9.12195i	0.578080	+	1.00126i	0.995699	+	0.0926419i	$0.0295312\pi$
$83$	5.26656	+	9.12195i	0.578080	+	1.00126i	−0.417620	+	0.908622i	$0.637135\pi$
$84$		0			0
$85$	9.53125	−	16.5086i	1.03381	−	1.79061i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.72788	+	2.99278i	−0.183155	+	0.317234i	−0.942953	−	0.332925i	$-0.891964\pi$
$89$	−1.72788	+	2.99278i	−0.183155	+	0.317234i	0.759798	+	0.650159i	$0.225298\pi$
$90$		0			0
$91$	3.78900	−	3.70153i	0.397195	−	0.388025i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	21.4524			2.20097
$96$		0			0
$97$	−1.12061	−	1.94096i	−0.113781	−	0.197075i	0.803511	−	0.595290i	$-0.202963\pi$
$97$	−1.12061	−	1.94096i	−0.113781	−	0.197075i	−0.917292	+	0.398216i	$0.869630\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.28415	+	3.95626i	−0.227281	+	0.393663i	−0.957001	−	0.290083i	$-0.906317\pi$
$101$	−2.28415	+	3.95626i	−0.227281	+	0.393663i	0.729720	+	0.683746i	$0.239650\pi$
$102$		0			0
$103$	6.37509	+	11.0420i	0.628156	+	1.08800i	0.987922	+	0.154955i	$0.0495233\pi$
$103$	6.37509	+	11.0420i	0.628156	+	1.08800i	−0.359766	+	0.933043i	$0.617143\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.659761	−	1.14274i	0.0637815	−	0.110473i	−0.832371	−	0.554218i	$-0.813017\pi$
$107$	0.659761	−	1.14274i	0.0637815	−	0.110473i	0.896153	+	0.443746i	$0.146351\pi$
$108$		0			0
$109$	−6.31990	−	10.9464i	−0.605337	−	1.04847i	−0.991998	−	0.126252i	$-0.959705\pi$
$109$	−6.31990	−	10.9464i	−0.605337	−	1.04847i	0.386661	−	0.922222i	$-0.373628\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.503200	−	0.871568i	0.0473371	−	0.0819903i	−0.841386	−	0.540435i	$-0.818260\pi$
$113$	0.503200	−	0.871568i	0.0473371	−	0.0819903i	0.888723	+	0.458444i	$0.151593\pi$
$114$		0			0
$115$	−1.18457	+	2.05174i	−0.110462	+	0.191326i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.67815	+	18.3118i	0.428846	+	1.67864i
$120$		0			0
$121$	−2.43524	−	4.21796i	−0.221386	−	0.383451i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.68283			−0.687173
$126$		0			0
$127$	1.38400			0.122810			0.0614051	−	0.998113i	$-0.480442\pi$
$127$	1.38400			0.122810			0.0614051	+	0.998113i	$0.480442\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.164862	−	0.285550i	−0.0144041	−	0.0249486i	0.858734	−	0.512422i	$-0.171252\pi$
$131$	−0.164862	−	0.285550i	−0.0144041	−	0.0249486i	−0.873138	+	0.487474i	$0.837918\pi$
$132$		0			0
$133$	−15.2144	+	14.8632i	−1.31926	+	1.28880i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.47095	−	7.74391i	0.381979	−	0.661607i	−0.609366	−	0.792889i	$-0.708576\pi$
$137$	4.47095	−	7.74391i	0.381979	−	0.661607i	0.991345	+	0.131282i	$0.0419094\pi$
$138$		0			0
$139$	3.92869	−	6.80470i	0.333227	−	0.577167i	−0.649915	−	0.760007i	$-0.725196\pi$
$139$	3.92869	−	6.80470i	0.333227	−	0.577167i	0.983143	+	0.182840i	$0.0585290\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.98789	+	6.90723i	0.333484	+	0.577611i
$144$		0			0
$145$	3.60341	−	6.24128i	0.299247	−	0.518310i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.16075	+	14.1348i	0.668554	+	1.15797i	0.978308	+	0.207153i	$0.0664199\pi$
$149$	8.16075	+	14.1348i	0.668554	+	1.15797i	−0.309754	+	0.950817i	$0.600247\pi$
$150$		0			0
$151$	2.31677	−	4.01276i	0.188536	−	0.326554i	−0.756226	−	0.654310i	$-0.772959\pi$
$151$	2.31677	−	4.01276i	0.188536	−	0.326554i	0.944762	+	0.327756i	$0.106292\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.64098	+	2.84226i	0.131807	+	0.228296i
$156$		0			0
$157$	−8.51852			−0.679852			−0.339926	−	0.940452i	$-0.610402\pi$
$157$	−8.51852			−0.679852			−0.339926	+	0.940452i	$0.610402\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.581416	−	2.27585i	−0.0458220	−	0.179362i
$162$		0			0
$163$	1.22354	−	2.11923i	0.0958350	−	0.165991i	−0.814122	−	0.580694i	$-0.802781\pi$
$163$	1.22354	−	2.11923i	0.0958350	−	0.165991i	0.909957	+	0.414703i	$0.136115\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.0713948	−	0.123659i	0.00552470	−	0.00956906i	−0.863250	−	0.504777i	$-0.831575\pi$
$167$	0.0713948	−	0.123659i	0.00552470	−	0.00956906i	0.868775	+	0.495208i	$0.164908\pi$
$168$		0			0
$169$	4.49587	+	7.78708i	0.345836	+	0.599006i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−17.9967			−1.36826			−0.684131	−	0.729359i	$-0.739818\pi$
$173$	−17.9967			−1.36826			−0.684131	+	0.729359i	$0.739818\pi$
$174$		0			0
$175$	−4.01395	+	3.92128i	−0.303426	+	0.296421i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.02413	+	1.77384i	0.0765468	+	0.132583i	0.901758	−	0.432242i	$-0.142277\pi$
$179$	1.02413	+	1.77384i	0.0765468	+	0.132583i	−0.825211	+	0.564824i	$0.808944\pi$
$180$		0			0
$181$	1.81165			0.134659			0.0673294	−	0.997731i	$-0.478552\pi$
$181$	1.81165			0.134659			0.0673294	+	0.997731i	$0.478552\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−28.1009			−2.06602
$186$		0			0
$187$	−28.4582			−2.08107
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.8091			−1.36098			−0.680491	−	0.732757i	$-0.738233\pi$
$191$	−18.8091			−1.36098			−0.680491	+	0.732757i	$0.738233\pi$
$192$		0			0
$193$	6.48714			0.466954			0.233477	−	0.972362i	$-0.424990\pi$
$193$	6.48714			0.466954			0.233477	+	0.972362i	$0.424990\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.8356			0.772007			0.386003	−	0.922497i	$-0.373855\pi$
$197$	10.8356			0.772007			0.386003	+	0.922497i	$0.373855\pi$
$198$		0			0
$199$	−9.43873	−	16.3484i	−0.669094	−	1.15890i	−0.978158	−	0.207863i	$-0.933349\pi$
$199$	−9.43873	−	16.3484i	−0.669094	−	1.15890i	0.309064	−	0.951041i	$-0.399984\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.76863	+	6.92301i	0.124134	+	0.485900i
$204$		0			0
$205$	−7.65736			−0.534813
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−16.0130	−	27.7354i	−1.10764	−	1.91850i
$210$		0			0
$211$	−11.9133	+	20.6344i	−0.820145	+	1.42053i	0.0854297	+	0.996344i	$0.472774\pi$
$211$	−11.9133	+	20.6344i	−0.820145	+	1.42053i	−0.905574	+	0.424188i	$0.860560\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.07433	−	15.7172i	0.618864	−	1.07190i
$216$		0			0
$217$	−3.13305	−	0.878836i	−0.212685	−	0.0596593i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.3018			0.962041
$222$		0			0
$223$	6.53734	+	11.3230i	0.437773	+	0.758245i	0.997517	−	0.0704203i	$-0.0224341\pi$
$223$	6.53734	+	11.3230i	0.437773	+	0.758245i	−0.559745	+	0.828665i	$0.689101\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.5845	−	20.0649i	0.768890	−	1.33176i	−0.169275	−	0.985569i	$-0.554142\pi$
$227$	11.5845	−	20.0649i	0.768890	−	1.33176i	0.938165	−	0.346188i	$-0.112524\pi$
$228$		0			0
$229$	10.7794	+	18.6705i	0.712323	+	1.23378i	0.963983	+	0.265964i	$0.0856904\pi$
$229$	10.7794	+	18.6705i	0.712323	+	1.23378i	−0.251660	+	0.967816i	$0.580976\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.05558	−	13.9527i	0.527739	−	0.914070i	−0.471738	−	0.881739i	$-0.656373\pi$
$233$	8.05558	−	13.9527i	0.527739	−	0.914070i	0.999477	−	0.0323318i	$-0.0102933\pi$
$234$		0			0
$235$	−16.1937	−	28.0483i	−1.05636	−	1.82967i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.216059	+	0.374225i	−0.0139757	+	0.0242066i	−0.872929	−	0.487848i	$-0.837782\pi$
$239$	−0.216059	+	0.374225i	−0.0139757	+	0.0242066i	0.858953	+	0.512054i	$0.171115\pi$
$240$		0			0
$241$	−1.52837	+	2.64721i	−0.0984509	+	0.170522i	−0.911044	−	0.412310i	$-0.864722\pi$
$241$	−1.52837	+	2.64721i	−0.0984509	+	0.170522i	0.812593	+	0.582832i	$0.198055\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.436221	−	18.6744i	0.0278691	−	1.19307i
$246$		0			0
$247$	8.04741	+	13.9385i	0.512045	+	0.886887i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.9066			−0.751541			−0.375770	−	0.926713i	$-0.622622\pi$
$251$	−11.9066			−0.751541			−0.375770	+	0.926713i	$0.622622\pi$
$252$		0			0
$253$	3.53687			0.222361
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.9726	−	27.6654i	−0.996346	−	1.72572i	−0.572142	−	0.820155i	$-0.693887\pi$
$257$	−15.9726	−	27.6654i	−0.996346	−	1.72572i	−0.424204	−	0.905567i	$-0.639446\pi$
$258$		0			0
$259$	19.9296	−	19.4695i	1.23836	−	1.20977i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.35495	−	5.81094i	0.206875	−	0.358318i	−0.743854	−	0.668343i	$-0.767004\pi$
$263$	3.35495	−	5.81094i	0.206875	−	0.358318i	0.950728	+	0.310025i	$0.100337\pi$
$264$		0			0
$265$	6.36879	−	11.0311i	0.391232	−	0.677634i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.66510	−	9.81225i	−0.345408	−	0.598263i	0.640020	−	0.768358i	$-0.278926\pi$
$269$	−5.66510	−	9.81225i	−0.345408	−	0.598263i	−0.985428	+	0.170095i	$0.945593\pi$
$270$		0			0
$271$	−5.06846	+	8.77884i	−0.307887	+	0.533276i	−0.977900	−	0.209073i	$-0.932955\pi$
$271$	−5.06846	+	8.77884i	−0.307887	+	0.533276i	0.670013	+	0.742350i	$0.266289\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.22465	−	7.31730i	−0.254756	−	0.441250i
$276$		0			0
$277$	10.6433	−	18.4347i	0.639492	−	1.10763i	−0.346052	−	0.938215i	$-0.612478\pi$
$277$	10.6433	−	18.4347i	0.639492	−	1.10763i	0.985544	−	0.169418i	$-0.0541886\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.26945	+	10.8590i	0.374004	+	0.647794i	0.990177	−	0.139817i	$-0.0446513\pi$
$281$	6.26945	+	10.8590i	0.374004	+	0.647794i	−0.616174	+	0.787610i	$0.711318\pi$
$282$		0			0
$283$	24.9497			1.48311			0.741554	−	0.670893i	$-0.234089\pi$
$283$	24.9497			1.48311			0.741554	+	0.670893i	$0.234089\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.43072	−	5.30535i	0.320565	−	0.313165i
$288$		0			0
$289$	−17.0149	+	29.4706i	−1.00087	+	1.73357i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.42625	+	12.8626i	−0.433846	+	0.751443i	−0.997201	−	0.0747718i	$-0.976177\pi$
$293$	−7.42625	+	12.8626i	−0.433846	+	0.751443i	0.563355	+	0.826215i	$0.309510\pi$
$294$		0			0
$295$	12.7829	+	22.1407i	0.744250	+	1.28908i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.77747			−0.102794
$300$		0			0
$301$	4.45389	+	17.4340i	0.256718	+	1.00488i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.6749	+	21.9536i	0.725763	+	1.25706i
$306$		0			0
$307$	−21.9045			−1.25016			−0.625079	−	0.780561i	$-0.714933\pi$
$307$	−21.9045			−1.25016			−0.625079	+	0.780561i	$0.714933\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	17.5672			0.996143			0.498072	−	0.867136i	$-0.334042\pi$
$311$	17.5672			0.996143			0.498072	+	0.867136i	$0.334042\pi$
$312$		0			0
$313$	−11.9764			−0.676946			−0.338473	−	0.940976i	$-0.609910\pi$
$313$	−11.9764			−0.676946			−0.338473	+	0.940976i	$0.609910\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.73327			0.0973499			0.0486750	−	0.998815i	$-0.484500\pi$
$317$	1.73327			0.0973499			0.0486750	+	0.998815i	$0.484500\pi$
$318$		0			0
$319$	−10.7590			−0.602386
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−57.4275			−3.19535
$324$		0			0
$325$	2.12311	+	3.67734i	0.117769	+	0.203982i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	30.9179	+	8.67263i	1.70456	+	0.478137i
$330$		0			0
$331$	−0.726254			−0.0399185			−0.0199593	−	0.999801i	$-0.506354\pi$
$331$	−0.726254			−0.0399185			−0.0199593	+	0.999801i	$0.506354\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−14.6620	−	25.3953i	−0.801070	−	1.38749i
$336$		0			0
$337$	−6.84810	+	11.8613i	−0.373040	+	0.646124i	−0.990032	−	0.140846i	$-0.955018\pi$
$337$	−6.84810	+	11.8613i	−0.373040	+	0.646124i	0.616992	+	0.786970i	$0.288351\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.44980	−	4.24317i	0.132664	−	0.229781i
$342$		0			0
$343$	12.6291	+	13.5465i	0.681906	+	0.731440i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.21417			0.226229			0.113114	−	0.993582i	$-0.463917\pi$
$347$	4.21417			0.226229			0.113114	+	0.993582i	$0.463917\pi$
$348$		0			0
$349$	−10.8070	−	18.7183i	−0.578486	−	1.00197i	−0.995653	−	0.0931372i	$-0.970310\pi$
$349$	−10.8070	−	18.7183i	−0.578486	−	1.00197i	0.417167	−	0.908830i	$-0.363023\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.42558	−	4.20122i	0.129100	−	0.223609i	−0.794228	−	0.607620i	$-0.792124\pi$
$353$	2.42558	−	4.20122i	0.129100	−	0.223609i	0.923328	+	0.384012i	$0.125458\pi$
$354$		0			0
$355$	−6.17609	−	10.6973i	−0.327793	−	0.567754i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.90433	+	5.03045i	−0.153285	+	0.265497i	−0.932433	−	0.361343i	$-0.882318\pi$
$359$	−2.90433	+	5.03045i	−0.153285	+	0.265497i	0.779148	+	0.626839i	$0.215652\pi$
$360$		0			0
$361$	−22.8137	−	39.5145i	−1.20072	−	2.07971i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.36381	−	9.29038i	0.280754	−	0.486281i
$366$		0			0
$367$	−10.8445	+	18.7832i	−0.566078	+	0.980476i	0.430871	+	0.902414i	$0.358207\pi$
$367$	−10.8445	+	18.7832i	−0.566078	+	0.980476i	−0.996949	+	0.0780619i	$0.975127\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.12595	+	12.2360i	0.162291	+	0.635261i
$372$		0			0
$373$	−12.3552	−	21.3999i	−0.639729	−	1.10804i	−0.985492	−	0.169721i	$-0.945713\pi$
$373$	−12.3552	−	21.3999i	−0.639729	−	1.10804i	0.345764	−	0.938322i	$-0.387620\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.40696			0.278473
$378$		0			0
$379$	−27.9950			−1.43801			−0.719005	−	0.695005i	$-0.755402\pi$
$379$	−27.9950			−1.43801			−0.719005	+	0.695005i	$0.755402\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.3113	−	17.8598i	−0.526884	−	0.912591i	−0.999509	−	0.0313269i	$-0.990027\pi$
$383$	−10.3113	−	17.8598i	−0.526884	−	0.912591i	0.472625	−	0.881264i	$-0.343307\pi$
$384$		0			0
$385$	27.0810	+	7.59637i	1.38018	+	0.387147i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.70035	−	15.0694i	0.441125	−	0.764051i	−0.556648	−	0.830748i	$-0.687913\pi$
$389$	8.70035	−	15.0694i	0.441125	−	0.764051i	0.997773	+	0.0666973i	$0.0212462\pi$
$390$		0			0
$391$	3.17107	−	5.49245i	0.160368	−	0.277765i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.37425	+	2.38026i	0.0691458	+	0.119764i
$396$		0			0
$397$	9.74152	−	16.8728i	0.488913	−	0.846822i	−0.511006	−	0.859577i	$-0.670727\pi$
$397$	9.74152	−	16.8728i	0.488913	−	0.846822i	0.999919	+	0.0127553i	$0.00406024\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.85264	+	6.67297i	0.192392	+	0.333232i	0.946042	−	0.324043i	$-0.105042\pi$
$401$	3.85264	+	6.67297i	0.192392	+	0.333232i	−0.753651	+	0.657275i	$0.771709\pi$
$402$		0			0
$403$	−1.23116	+	2.13242i	−0.0613282	+	0.106224i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	20.9757	+	36.3310i	1.03973	+	1.80086i
$408$		0			0
$409$	−15.7351			−0.778050			−0.389025	−	0.921227i	$-0.627188\pi$
$409$	−15.7351			−0.778050			−0.389025	+	0.921227i	$0.627188\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−24.4058	−	6.84596i	−1.20093	−	0.336868i
$414$		0			0
$415$	14.0538	−	24.3420i	0.689876	−	1.19490i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.3452	−	30.0428i	0.847369	−	1.46769i	−0.0361784	−	0.999345i	$-0.511518\pi$
$419$	17.3452	−	30.0428i	0.847369	−	1.46769i	0.883548	−	0.468341i	$-0.155148\pi$
$420$		0			0
$421$	−0.607053	−	1.05145i	−0.0295860	−	0.0512444i	0.850853	−	0.525403i	$-0.176086\pi$
$421$	−0.607053	−	1.05145i	−0.0295860	−	0.0512444i	−0.880439	+	0.474159i	$0.842752\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−15.1508			−0.734924
$426$		0			0
$427$	−24.1996	−	6.78811i	−1.17110	−	0.328500i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.68495	−	2.91841i	−0.0811610	−	0.140575i	0.822588	−	0.568638i	$-0.192529\pi$
$431$	−1.68495	−	2.91841i	−0.0811610	−	0.140575i	−0.903749	+	0.428063i	$0.859196\pi$
$432$		0			0
$433$	−30.8651			−1.48328			−0.741640	−	0.670798i	$-0.765952\pi$
$433$	−30.8651			−1.48328			−0.741640	+	0.670798i	$0.765952\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.13727			0.341422
$438$		0			0
$439$	−33.0789			−1.57877			−0.789385	−	0.613898i	$-0.789600\pi$
$439$	−33.0789			−1.57877			−0.789385	+	0.613898i	$0.789600\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.73364			−0.129879			−0.0649397	−	0.997889i	$-0.520685\pi$
$443$	−2.73364			−0.129879			−0.0649397	+	0.997889i	$0.520685\pi$
$444$		0			0
$445$	9.22172			0.437152
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−22.7472			−1.07351			−0.536753	−	0.843740i	$-0.680349\pi$
$449$	−22.7472			−1.07351			−0.536753	+	0.843740i	$0.680349\pi$
$450$		0			0
$451$	5.71579	+	9.90003i	0.269146	+	0.466174i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−13.6097	−	3.81759i	−0.638032	−	0.178971i
$456$		0			0
$457$	3.36324			0.157326			0.0786628	−	0.996901i	$-0.474935\pi$
$457$	3.36324			0.157326			0.0786628	+	0.996901i	$0.474935\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.0040	+	17.3275i	0.465934	+	0.807021i	0.999243	−	0.0388994i	$-0.0123852\pi$
$461$	10.0040	+	17.3275i	0.465934	+	0.807021i	−0.533309	+	0.845920i	$0.679052\pi$
$462$		0			0
$463$	7.29434	−	12.6342i	0.338997	−	0.587160i	−0.645247	−	0.763974i	$-0.723246\pi$
$463$	7.29434	−	12.6342i	0.338997	−	0.587160i	0.984244	+	0.176814i	$0.0565791\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.26334	+	12.5805i	−0.336107	+	0.582155i	−0.983697	−	0.179834i	$-0.942444\pi$
$467$	−7.26334	+	12.5805i	−0.336107	+	0.582155i	0.647590	+	0.761989i	$0.275777\pi$
$468$		0			0
$469$	27.9935	+	7.85231i	1.29262	+	0.362586i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−27.0939			−1.24578
$474$		0			0
$475$	−8.52518	−	14.7660i	−0.391162	−	0.677513i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.66216	+	9.80714i	−0.258710	+	0.448100i	−0.965897	−	0.258928i	$-0.916631\pi$
$479$	−5.66216	+	9.80714i	−0.258710	+	0.448100i	0.707186	+	0.707027i	$0.249964\pi$
$480$		0			0
$481$	−10.5414	−	18.2583i	−0.480648	−	0.832506i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.99036	+	5.17946i	−0.135785	+	0.235187i
$486$		0			0
$487$	5.93684	+	10.2829i	0.269024	+	0.465963i	0.968610	−	0.248585i	$-0.0799657\pi$
$487$	5.93684	+	10.2829i	0.269024	+	0.465963i	−0.699586	+	0.714548i	$0.746632\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.9598	+	20.7150i	−0.539738	+	0.934853i	0.459180	+	0.888343i	$0.348143\pi$
$491$	−11.9598	+	20.7150i	−0.539738	+	0.934853i	−0.998918	+	0.0465101i	$0.985190\pi$
$492$		0			0
$493$	−9.64621	+	16.7077i	−0.434443	+	0.752478i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	11.7917	+	3.30764i	0.528932	+	0.148368i
$498$		0			0
$499$	0.225984	+	0.391416i	0.0101164	+	0.0175222i	0.871039	−	0.491213i	$-0.163446\pi$
$499$	0.225984	+	0.391416i	0.0101164	+	0.0175222i	−0.860923	+	0.508736i	$0.830113\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.6077			0.651326			0.325663	−	0.945486i	$-0.394413\pi$
$503$	14.6077			0.651326			0.325663	+	0.945486i	$0.394413\pi$
$504$		0			0
$505$	12.1905			0.542471
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.246585	−	0.427099i	−0.0109297	−	0.0189308i	0.860509	−	0.509436i	$-0.170146\pi$
$509$	−0.246585	−	0.427099i	−0.0109297	−	0.0189308i	−0.871439	+	0.490505i	$0.836812\pi$
$510$		0			0
$511$	2.63268	+	10.3052i	0.116463	+	0.455874i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	17.0120	−	29.4656i	0.749636	−	1.29841i
$516$		0			0
$517$	−24.1754	+	41.8730i	−1.06323	+	1.84157i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.06874	+	10.5114i	0.265876	+	0.460511i	0.967793	−	0.251748i	$-0.0810054\pi$
$521$	6.06874	+	10.5114i	0.265876	+	0.460511i	−0.701917	+	0.712259i	$0.747672\pi$
$522$		0			0
$523$	1.34058	−	2.32195i	0.0586193	−	0.101532i	−0.835227	−	0.549906i	$-0.814664\pi$
$523$	1.34058	−	2.32195i	0.0586193	−	0.101532i	0.893846	+	0.448374i	$0.147997\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.39285	−	7.60865i	−0.191356	−	0.331438i
$528$		0			0
$529$	11.1059	−	19.2360i	0.482865	−	0.836346i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.87249	−	4.97530i	−0.124421	−	0.215504i
$534$		0			0
$535$	−3.52115			−0.152233
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−24.4694	+	13.3754i	−1.05397	+	0.576121i
$540$		0			0
$541$	−13.5072	+	23.3951i	−0.580719	+	1.00583i	0.414676	+	0.909969i	$0.363895\pi$
$541$	−13.5072	+	23.3951i	−0.580719	+	1.00583i	−0.995394	+	0.0958650i	$0.969438\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−16.8647	+	29.2105i	−0.722404	+	1.25124i
$546$		0			0
$547$	−15.2496	−	26.4132i	−0.652028	−	1.12935i	−0.982630	−	0.185575i	$-0.940585\pi$
$547$	−15.2496	−	26.4132i	−0.652028	−	1.12935i	0.330602	−	0.943770i	$-0.392748\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−21.7112			−0.924927
$552$		0			0
$553$	−2.62379	−	0.735985i	−0.111575	−	0.0312973i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.39250	+	12.8042i	0.313230	+	0.542531i	0.979060	−	0.203573i	$-0.0652555\pi$
$557$	7.39250	+	12.8042i	0.313230	+	0.542531i	−0.665829	+	0.746104i	$0.731922\pi$
$558$		0			0
$559$	13.6162			0.575902
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.62822			−0.110766			−0.0553831	−	0.998465i	$-0.517638\pi$
$563$	−2.62822			−0.110766			−0.0553831	+	0.998465i	$0.517638\pi$
$564$		0			0
$565$	−2.68559			−0.112983
$566$		0			0
$567$		0			0
$568$		0			0
$569$	32.1162			1.34638			0.673191	−	0.739469i	$-0.264923\pi$
$569$	32.1162			1.34638			0.673191	+	0.739469i	$0.264923\pi$
$570$		0			0
$571$	41.1815			1.72339			0.861696	−	0.507425i	$-0.169403\pi$
$571$	41.1815			1.72339			0.861696	+	0.507425i	$0.169403\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.88300			0.0785263
$576$		0			0
$577$	12.0735	+	20.9119i	0.502625	+	0.870573i	0.999995	+	0.00303429i	$0.000965847\pi$
$577$	12.0735	+	20.9119i	0.502625	+	0.870573i	−0.497370	+	0.867539i	$0.665701\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.89795	+	27.0008i	0.286175	+	1.12018i
$582$		0			0
$583$	−19.0158			−0.787553
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.98618	+	6.90426i	0.164527	+	0.284969i	0.936487	−	0.350702i	$-0.114057\pi$
$587$	3.98618	+	6.90426i	0.164527	+	0.284969i	−0.771960	+	0.635671i	$0.780723\pi$
$588$		0			0
$589$	4.94360	−	8.56257i	0.203698	−	0.352815i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.10338	−	3.64316i	0.0863753	−	0.149606i	−0.819601	−	0.572935i	$-0.805805\pi$
$593$	2.10338	−	3.64316i	0.0863753	−	0.149606i	0.905976	+	0.423328i	$0.139138\pi$
$594$		0			0
$595$	36.0767	−	35.2438i	1.47900	−	1.44485i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	37.3771			1.52719			0.763594	−	0.645696i	$-0.223433\pi$
$599$	37.3771			1.52719			0.763594	+	0.645696i	$0.223433\pi$
$600$		0			0
$601$	6.81596	+	11.8056i	0.278029	+	0.481560i	0.970895	−	0.239506i	$-0.0769856\pi$
$601$	6.81596	+	11.8056i	0.278029	+	0.481560i	−0.692866	+	0.721066i	$0.743652\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.49846	+	11.2557i	−0.264200	+	0.457607i
$606$		0			0
$607$	−1.37114	−	2.37489i	−0.0556529	−	0.0963937i	0.836857	−	0.547422i	$-0.184391\pi$
$607$	−1.37114	−	2.37489i	−0.0556529	−	0.0963937i	−0.892510	+	0.451028i	$0.851057\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.1494	−	21.0434i	0.491513	−	0.851326i
$612$		0			0
$613$	0.798502	+	1.38305i	0.0322512	+	0.0558607i	0.881700	−	0.471810i	$-0.156399\pi$
$613$	0.798502	+	1.38305i	0.0322512	+	0.0558607i	−0.849449	+	0.527670i	$0.823066\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.6551	+	21.9192i	−0.509473	+	0.882433i	0.490467	+	0.871460i	$0.336826\pi$
$617$	−12.6551	+	21.9192i	−0.509473	+	0.882433i	−0.999940	+	0.0109734i	$0.996507\pi$
$618$		0			0
$619$	13.5808	−	23.5226i	0.545859	−	0.945455i	−0.452694	−	0.891666i	$-0.649537\pi$
$619$	13.5808	−	23.5226i	0.545859	−	0.945455i	0.998552	−	0.0537888i	$-0.0171298\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6.54019	+	6.38920i	−0.262027	+	0.255978i
$624$		0			0
$625$	15.5532	+	26.9388i	0.622126	+	1.07755i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	75.2252			2.99942
$630$		0			0
$631$	−29.6597			−1.18073			−0.590366	−	0.807136i	$-0.701017\pi$
$631$	−29.6597			−1.18073			−0.590366	+	0.807136i	$0.701017\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.84661	−	3.19842i	−0.0732804	−	0.126925i
$636$		0			0
$637$	12.2972	−	6.72188i	0.487233	−	0.266331i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	21.0987	−	36.5441i	0.833350	−	1.44340i	−0.0620175	−	0.998075i	$-0.519753\pi$
$641$	21.0987	−	36.5441i	0.833350	−	1.44340i	0.895367	−	0.445329i	$-0.146913\pi$
$642$		0			0
$643$	10.1099	−	17.5109i	0.398696	−	0.690562i	−0.594869	−	0.803823i	$-0.702796\pi$
$643$	10.1099	−	17.5109i	0.398696	−	0.690562i	0.993565	+	0.113260i	$0.0361294\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.08988	+	1.88772i	0.0428475	+	0.0742141i	0.886654	−	0.462434i	$-0.153024\pi$
$647$	1.08988	+	1.88772i	0.0428475	+	0.0742141i	−0.843806	+	0.536648i	$0.819690\pi$
$648$		0			0
$649$	19.0834	−	33.0535i	0.749091	−	1.29746i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−17.0535	−	29.5375i	−0.667354	−	1.15589i	−0.978641	−	0.205575i	$-0.934094\pi$
$653$	−17.0535	−	29.5375i	−0.667354	−	1.15589i	0.311288	−	0.950316i	$-0.399240\pi$
$654$		0			0
$655$	−0.439936	+	0.761991i	−0.0171897	+	0.0297734i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.994211	+	1.72202i	0.0387290	+	0.0670805i	0.884740	−	0.466085i	$-0.154336\pi$
$659$	0.994211	+	1.72202i	0.0387290	+	0.0670805i	−0.846011	+	0.533165i	$0.821002\pi$
$660$		0			0
$661$	−8.48409			−0.329993			−0.164997	−	0.986294i	$-0.552761\pi$
$661$	−8.48409			−0.329993			−0.164997	+	0.986294i	$0.552761\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	54.6486	+	15.3292i	2.11918	+	0.594440i
$666$		0			0
$667$	1.19886	−	2.07649i	0.0464201	−	0.0804020i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	18.9222	−	32.7742i	0.730483	−	1.26523i
$672$		0			0
$673$	22.4056	+	38.8077i	0.863674	+	1.49593i	0.868358	+	0.495938i	$0.165176\pi$
$673$	22.4056	+	38.8077i	0.863674	+	1.49593i	−0.00468438	+	0.999989i	$0.501491\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.05367			−0.309528			−0.154764	−	0.987951i	$-0.549462\pi$
$677$	−8.05367			−0.309528			−0.154764	+	0.987951i	$0.549462\pi$
$678$		0			0
$679$	−1.46774	−	5.74521i	−0.0563267	−	0.220481i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−20.8446	−	36.1039i	−0.797597	−	1.38148i	−0.921177	−	0.389144i	$-0.872771\pi$
$683$	−20.8446	−	36.1039i	−0.797597	−	1.38148i	0.123580	−	0.992335i	$-0.460562\pi$
$684$		0			0
$685$	−23.8615			−0.911701
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.55646			0.364072
$690$		0			0
$691$	11.3269			0.430895			0.215448	−	0.976515i	$-0.430879\pi$
$691$	11.3269			0.430895			0.215448	+	0.976515i	$0.430879\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−20.9675			−0.795342
$696$		0			0
$697$	20.4985			0.776437
$698$		0			0
$699$		0			0
$700$		0			0
$701$	22.6560			0.855705			0.427853	−	0.903849i	$-0.359270\pi$
$701$	22.6560			0.855705			0.427853	+	0.903849i	$0.359270\pi$
$702$		0			0
$703$	42.3282	+	73.3146i	1.59644	+	2.76511i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.64572	+	8.44612i	−0.325156	+	0.317649i
$708$		0			0
$709$	45.2147			1.69807			0.849037	−	0.528333i	$-0.177183\pi$
$709$	45.2147			1.69807			0.849037	+	0.528333i	$0.177183\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.545958	+	0.945626i	0.0204463	+	0.0354140i
$714$		0			0
$715$	10.6417	−	18.4320i	0.397977	−	0.689317i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−11.3171	+	19.6018i	−0.422057	+	0.731024i	−0.996141	−	0.0877727i	$-0.972025\pi$
$719$	−11.3171	+	19.6018i	−0.422057	+	0.731024i	0.574084	+	0.818797i	$0.305358\pi$
$720$		0			0
$721$	8.34986	+	32.6841i	0.310965	+	1.21722i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.72797			−0.212731
$726$		0			0
$727$	1.04956	+	1.81789i	0.0389259	+	0.0674217i	0.884832	−	0.465910i	$-0.154273\pi$
$727$	1.04956	+	1.81789i	0.0389259	+	0.0674217i	−0.845906	+	0.533332i	$0.820940\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−24.2917	+	42.0745i	−0.898461	+	1.55618i
$732$		0			0
$733$	15.6453	+	27.0985i	0.577872	+	1.00090i	0.995723	+	0.0923886i	$0.0294502\pi$
$733$	15.6453	+	27.0985i	0.577872	+	1.00090i	−0.417851	+	0.908516i	$0.637216\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−21.8887	+	37.9123i	−0.806280	+	1.39652i
$738$		0			0
$739$	21.1229	+	36.5859i	0.777017	+	1.34583i	0.933654	+	0.358177i	$0.116601\pi$
$739$	21.1229	+	36.5859i	0.777017	+	1.34583i	−0.156637	+	0.987656i	$0.550065\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.48482	+	11.2320i	−0.237905	+	0.412064i	−0.960113	−	0.279612i	$-0.909794\pi$
$743$	−6.48482	+	11.2320i	−0.237905	+	0.412064i	0.722208	+	0.691676i	$0.243127\pi$
$744$		0			0
$745$	21.7770	−	37.7189i	0.797848	−	1.38191i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.49726	−	2.43960i	0.0912478	−	0.0891412i
$750$		0			0
$751$	−16.3649	−	28.3448i	−0.597164	−	1.03432i	−0.993238	−	0.116099i	$-0.962961\pi$
$751$	−16.3649	−	28.3448i	−0.597164	−	1.03432i	0.396074	−	0.918219i	$-0.370372\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.3646			−0.449995
$756$		0			0
$757$	31.6305			1.14963			0.574815	−	0.818283i	$-0.305074\pi$
$757$	31.6305			1.14963			0.574815	+	0.818283i	$0.305074\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−19.1468	−	33.1632i	−0.694070	−	1.20217i	−0.970493	−	0.241129i	$-0.922482\pi$
$761$	−19.1468	−	33.1632i	−0.694070	−	1.20217i	0.276423	−	0.961036i	$-0.410851\pi$
$762$		0			0
$763$	−8.27758	−	32.4011i	−0.299668	−	1.17300i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.59047	+	16.6112i	−0.346292	+	0.599795i
$768$		0			0
$769$	11.0674	−	19.1693i	0.399100	−	0.691262i	−0.594515	−	0.804085i	$-0.702656\pi$
$769$	11.0674	−	19.1693i	0.399100	−	0.691262i	0.993615	+	0.112823i	$0.0359892\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−25.8165	−	44.7155i	−0.928555	−	1.60830i	−0.785742	−	0.618555i	$-0.787719\pi$
$773$	−25.8165	−	44.7155i	−0.928555	−	1.60830i	−0.142813	−	0.989750i	$-0.545615\pi$
$774$		0			0
$775$	1.30425	−	2.25902i	0.0468500	−	0.0811466i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	11.5342	+	19.9779i	0.413257	+	0.715783i
$780$		0			0
$781$	−9.22021	+	15.9699i	−0.329925	+	0.571447i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	11.3659	+	19.6862i	0.405665	+	0.702632i
$786$		0			0
$787$	−32.3046			−1.15153			−0.575767	−	0.817614i	$-0.695296\pi$
$787$	−32.3046			−1.15153			−0.575767	+	0.817614i	$0.695296\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.90466	−	1.86069i	0.0677219	−	0.0661585i
$792$		0			0
$793$	−9.50943	+	16.4708i	−0.337690	+	0.584896i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.6877	−	20.2438i	0.414001	−	0.717071i	−0.581322	−	0.813674i	$-0.697464\pi$
$797$	11.6877	−	20.2438i	0.414001	−	0.717071i	0.995323	+	0.0966026i	$0.0307976\pi$
$798$		0			0
$799$	43.3501	+	75.0845i	1.53361	+	2.65630i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−16.0151			−0.565161
$804$		0			0
$805$	−4.48372	+	4.38021i	−0.158030	+	0.154382i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15.2503	−	26.4143i	−0.536171	−	0.928676i	−0.999106	−	0.0422832i	$-0.986537\pi$
$809$	−15.2503	−	26.4143i	−0.536171	−	0.928676i	0.462935	−	0.886392i	$-0.346797\pi$
$810$		0			0
$811$	−51.6454			−1.81352			−0.906758	−	0.421652i	$-0.861450\pi$
$811$	−51.6454			−1.81352			−0.906758	+	0.421652i	$0.861450\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.53004			−0.228737
$816$		0			0
$817$	−54.6745			−1.91282
$818$		0			0
$819$		0			0
$820$		0			0
$821$	26.7575			0.933843			0.466921	−	0.884299i	$-0.345363\pi$
$821$	26.7575			0.933843			0.466921	+	0.884299i	$0.345363\pi$
$822$		0			0
$823$	−40.4898			−1.41139			−0.705693	−	0.708517i	$-0.749364\pi$
$823$	−40.4898			−1.41139			−0.705693	+	0.708517i	$0.749364\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	27.9452			0.971749			0.485875	−	0.874029i	$-0.338501\pi$
$827$	27.9452			0.971749			0.485875	+	0.874029i	$0.338501\pi$
$828$		0			0
$829$	−20.0226	−	34.6802i	−0.695415	−	1.20449i	−0.970040	−	0.242943i	$-0.921887\pi$
$829$	−20.0226	−	34.6802i	−0.695415	−	1.20449i	0.274625	−	0.961551i	$-0.411446\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.16775	+	49.9909i	−0.0404601	+	1.73208i
$834$		0			0
$835$	−0.381035			−0.0131863
$836$		0			0
$837$		0			0
$838$		0			0
$839$	16.6312	+	28.8061i	0.574174	+	0.994499i	0.996131	+	0.0878827i	$0.0280101\pi$
$839$	16.6312	+	28.8061i	0.574174	+	0.994499i	−0.421957	+	0.906616i	$0.638657\pi$
$840$		0			0
$841$	10.8531	−	18.7982i	0.374246	−	0.648213i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	11.9973	−	20.7799i	0.412718	−	0.714849i
$846$		0			0
$847$	−3.18959	−	12.4851i	−0.109596	−	0.428993i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−9.34922			−0.320487
$852$		0			0
$853$	−4.38730	−	7.59902i	−0.150218	−	0.260186i	0.781089	−	0.624419i	$-0.214664\pi$
$853$	−4.38730	−	7.59902i	−0.150218	−	0.260186i	−0.931308	+	0.364234i	$0.881331\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.677198	+	1.17294i	−0.0231327	+	0.0400669i	−0.877360	−	0.479833i	$-0.840697\pi$
$857$	−0.677198	+	1.17294i	−0.0231327	+	0.0400669i	0.854227	+	0.519900i	$0.174031\pi$
$858$		0			0
$859$	9.01934	+	15.6220i	0.307736	+	0.533014i	0.977867	−	0.209229i	$-0.0670953\pi$
$859$	9.01934	+	15.6220i	0.307736	+	0.533014i	−0.670131	+	0.742243i	$0.733762\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.37624	−	11.0440i	0.217050	−	0.375941i	−0.736855	−	0.676051i	$-0.763690\pi$
$863$	6.37624	−	11.0440i	0.217050	−	0.375941i	0.953905	+	0.300110i	$0.0970233\pi$
$864$		0			0
$865$	24.0121	+	41.5902i	0.816437	+	1.41411i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.05159	−	3.55347i	0.0695956	−	0.120543i
$870$		0			0
$871$	11.0003	−	19.0530i	0.372729	−	0.645586i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−19.5715	−	5.48989i	−0.661636	−	0.185592i
$876$		0			0
$877$	8.79034	+	15.2253i	0.296829	+	0.514122i	0.975409	−	0.220404i	$-0.0707376\pi$
$877$	8.79034	+	15.2253i	0.296829	+	0.514122i	−0.678580	+	0.734527i	$0.737404\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	25.8682			0.871523			0.435762	−	0.900062i	$-0.356479\pi$
$881$	25.8682			0.871523			0.435762	+	0.900062i	$0.356479\pi$
$882$		0			0
$883$	40.5923			1.36604			0.683020	−	0.730400i	$-0.260666\pi$
$883$	40.5923			1.36604			0.683020	+	0.730400i	$0.260666\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.46786	−	2.54240i	−0.0492858	−	0.0853655i	0.840330	−	0.542075i	$-0.182361\pi$
$887$	−1.46786	−	2.54240i	−0.0492858	−	0.0853655i	−0.889616	+	0.456710i	$0.849028\pi$
$888$		0			0
$889$	3.52564	+	0.988961i	0.118246	+	0.0331687i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−48.7850	+	84.4981i	−1.63253	+	2.82762i
$894$		0			0
$895$	2.73289	−	4.73350i	0.0913504	−	0.158223i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.66077	−	2.87654i	−0.0553899	−	0.0959381i
$900$		0			0
$901$	−17.0491	+	29.5299i	−0.567987	+	0.983782i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.41720	−	4.18671i	−0.0803503	−	0.139171i
$906$		0			0
$907$	17.1395	−	29.6865i	0.569108	−	0.985723i	−0.427547	−	0.903993i	$-0.640622\pi$
$907$	17.1395	−	29.6865i	0.569108	−	0.985723i	0.996655	−	0.0817300i	$-0.0260445\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4.98338	+	8.63146i	0.165107	+	0.285973i	0.936693	−	0.350151i	$-0.113870\pi$
$911$	4.98338	+	8.63146i	0.165107	+	0.285973i	−0.771586	+	0.636124i	$0.780536\pi$
$912$		0			0
$913$	−41.9616			−1.38873
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.215930	−	0.845222i	−0.00713065	−	0.0279117i
$918$		0			0
$919$	13.9444	−	24.1524i	0.459983	−	0.796714i	−0.538976	−	0.842321i	$-0.681189\pi$
$919$	13.9444	−	24.1524i	0.459983	−	0.796714i	0.998959	+	0.0456069i	$0.0145222\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4.63365	−	8.02573i	0.152519	−	0.264170i
$924$		0			0
$925$	11.1673	+	19.3423i	0.367177	+	0.635970i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.3059			0.600597			0.300298	−	0.953845i	$-0.402914\pi$
$929$	18.3059			0.600597			0.300298	+	0.953845i	$0.402914\pi$
$930$		0			0
$931$	−49.3783	+	26.9911i	−1.61831	+	0.884599i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	37.9704	+	65.7666i	1.24176	+	2.15080i
$936$		0			0
$937$	46.2063			1.50950			0.754748	−	0.656015i	$-0.227759\pi$
$937$	46.2063			1.50950			0.754748	+	0.656015i	$0.227759\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−36.4501			−1.18824			−0.594120	−	0.804376i	$-0.702500\pi$
$941$	−36.4501			−1.18824			−0.594120	+	0.804376i	$0.702500\pi$
$942$		0			0
$943$	−2.54762			−0.0829620
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−47.4404			−1.54161			−0.770803	−	0.637074i	$-0.780145\pi$
$947$	−47.4404			−1.54161			−0.770803	+	0.637074i	$0.780145\pi$
$948$		0			0
$949$	8.04846			0.261264
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6.68090			0.216415			0.108208	−	0.994128i	$-0.465489\pi$
$953$	6.68090			0.216415			0.108208	+	0.994128i	$0.465489\pi$
$954$		0			0
$955$	25.0961	+	43.4678i	0.812092	+	1.40659i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	16.9230	−	16.5323i	0.546471	−	0.533855i
$960$		0			0
$961$	−29.4874			−0.951206
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−8.65548	−	14.9917i	−0.278630	−	0.482601i
$966$		0			0
$967$	7.60180	−	13.1667i	0.244457	−	0.423413i	−0.717522	−	0.696536i	$-0.754724\pi$
$967$	7.60180	−	13.1667i	0.244457	−	0.423413i	0.961979	+	0.273124i	$0.0880568\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.363057	+	0.628834i	−0.0116511	+	0.0201802i	−0.871792	−	0.489876i	$-0.837042\pi$
$971$	−0.363057	+	0.628834i	−0.0116511	+	0.0201802i	0.860141	+	0.510056i	$0.170375\pi$
$972$		0			0
$973$	14.8705	−	14.5272i	0.476726	−	0.465720i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	43.0405			1.37699			0.688494	−	0.725242i	$-0.258272\pi$
$977$	43.0405			1.37699			0.688494	+	0.725242i	$0.258272\pi$
$978$		0			0
$979$	−6.88350	−	11.9226i	−0.219997	−	0.381047i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	21.5191	−	37.2722i	0.686353	−	1.18880i	−0.286657	−	0.958033i	$-0.592544\pi$
$983$	21.5191	−	37.2722i	0.686353	−	1.18880i	0.973010	−	0.230765i	$-0.0741228\pi$
$984$		0			0
$985$	−14.4575	−	25.0411i	−0.460653	−	0.797875i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.01905	−	5.22915i	0.0960002	−	0.166277i
$990$		0			0
$991$	−11.2758	−	19.5302i	−0.358187	−	0.620398i	0.629471	−	0.777024i	$-0.283272\pi$
$991$	−11.2758	−	19.5302i	−0.358187	−	0.620398i	−0.987658	+	0.156626i	$0.949938\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−25.1873	+	43.6257i	−0.798491	+	1.38303i
$996$		0			0
$997$	14.1670	−	24.5380i	0.448675	−	0.777128i	−0.549625	−	0.835411i	$-0.685229\pi$
$997$	14.1670	−	24.5380i	0.448675	−	0.777128i	0.998300	+	0.0582836i	$0.0185628\pi$
$998$		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.793.3		22
3.2	odd	2		504.2.q.c.121.9	yes	22
4.3	odd	2		3024.2.q.l.2305.3		22
7.4	even	3		1512.2.t.c.361.9		22
9.2	odd	6		504.2.t.c.457.8	yes	22
9.7	even	3		1512.2.t.c.289.9		22
12.11	even	2		1008.2.q.l.625.3		22
21.11	odd	6		504.2.t.c.193.8	yes	22
28.11	odd	6		3024.2.t.k.1873.9		22
36.7	odd	6		3024.2.t.k.289.9		22
36.11	even	6		1008.2.t.l.961.4		22
63.11	odd	6		504.2.q.c.25.9	✓	22
63.25	even	3	inner	1512.2.q.d.1369.3		22
84.11	even	6		1008.2.t.l.193.4		22
252.11	even	6		1008.2.q.l.529.3		22
252.151	odd	6		3024.2.q.l.2881.3		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.9	✓	22	63.11	odd	6
504.2.q.c.121.9	yes	22	3.2	odd	2
504.2.t.c.193.8	yes	22	21.11	odd	6
504.2.t.c.457.8	yes	22	9.2	odd	6
1008.2.q.l.529.3		22	252.11	even	6
1008.2.q.l.625.3		22	12.11	even	2
1008.2.t.l.193.4		22	84.11	even	6
1008.2.t.l.961.4		22	36.11	even	6
1512.2.q.d.793.3		22	1.1	even	1	trivial
1512.2.q.d.1369.3		22	63.25	even	3	inner
1512.2.t.c.289.9		22	9.7	even	3
1512.2.t.c.361.9		22	7.4	even	3
3024.2.q.l.2305.3		22	4.3	odd	2
3024.2.q.l.2881.3		22	252.151	odd	6
3024.2.t.k.289.9		22	36.7	odd	6
3024.2.t.k.1873.9		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)

\(f(q)\)	\(=\)	\(q+(-1.33425 - 2.31099i) q^{5} +(2.54743 + 0.714566i) q^{7} +O(q^{10})\)	\(q+(-1.33425 - 2.31099i) q^{5} +(2.54743 + 0.714566i) q^{7} +(-1.99189 + 3.45005i) q^{11} +(1.00103 - 1.73384i) q^{13} +(3.57175 + 6.18646i) q^{17} +(-4.01956 + 6.96208i) q^{19} +(-0.443909 - 0.768873i) q^{23} +(-1.06046 + 1.83677i) q^{25} +(1.35035 + 2.33887i) q^{29} -1.22989 q^{31} +(-1.74756 - 6.84051i) q^{35} +(5.26528 - 9.11973i) q^{37} +(1.43477 - 2.48509i) q^{41} +(3.40053 + 5.88989i) q^{43} +12.1369 q^{47} +(5.97879 + 3.64061i) q^{49} +(2.38665 + 4.13380i) q^{53} +10.6307 q^{55} -9.58058 q^{59} -9.49962 q^{61} -5.34252 q^{65} +10.9889 q^{67} +4.62888 q^{71} +(2.01004 + 3.48149i) q^{73} +(-7.53949 + 7.36543i) q^{77} -1.02997 q^{79} +(5.26656 + 9.12195i) q^{83} +(9.53125 - 16.5086i) q^{85} +(-1.72788 + 2.99278i) q^{89} +(3.78900 - 3.70153i) q^{91} +21.4524 q^{95} +(-1.12061 - 1.94096i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} + 5 q^{7}+O(q^{10}) \) 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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