LMFDB - Embedded newform 1512.2.q.d.793.8

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			793.8
Character	$\chi$	$=$	1512.793
Dual form			1512.2.q.d.1369.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05220 + 1.82246i) q^{5} +(2.58382 - 0.569079i) q^{7} +O(q^{10})$	$q+(1.05220 + 1.82246i) q^{5} +(2.58382 - 0.569079i) q^{7} +(0.199532 - 0.345600i) q^{11} +(1.44292 - 2.49921i) q^{13} +(0.176596 + 0.305873i) q^{17} +(2.84888 - 4.93440i) q^{19} +(-0.438682 - 0.759820i) q^{23} +(0.285756 - 0.494945i) q^{25} +(-0.874997 - 1.51554i) q^{29} +9.13490 q^{31} +(3.75582 + 4.11014i) q^{35} +(-3.39555 + 5.88127i) q^{37} +(-1.20377 + 2.08499i) q^{41} +(0.276745 + 0.479336i) q^{43} -11.7372 q^{47} +(6.35230 - 2.94080i) q^{49} +(2.07821 + 3.59956i) q^{53} +0.839790 q^{55} +9.32421 q^{59} -10.0720 q^{61} +6.07296 q^{65} +1.20241 q^{67} +14.6826 q^{71} +(0.315636 + 0.546697i) q^{73} +(0.318883 - 1.00652i) q^{77} -2.48729 q^{79} +(4.59366 + 7.95645i) q^{83} +(-0.371628 + 0.643678i) q^{85} +(-7.29358 + 12.6328i) q^{89} +(2.30601 - 7.27866i) q^{91} +11.9903 q^{95} +(-7.84245 - 13.5835i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.05220	+	1.82246i	0.470558	+	0.815030i	0.999433	−	0.0336699i	$-0.0107195\pi$
$5$	1.05220	+	1.82246i	0.470558	+	0.815030i	−0.528876	+	0.848699i	$0.677386\pi$
$6$		0			0
$7$	2.58382	−	0.569079i	0.976594	−	0.215092i
$7$	2.58382	−	0.569079i	0.976594	−	0.215092i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.199532	−	0.345600i	0.0601612	−	0.104202i	−0.834376	−	0.551195i	$-0.814172\pi$
$11$	0.199532	−	0.345600i	0.0601612	−	0.104202i	0.894537	+	0.446993i	$0.147505\pi$
$12$		0			0
$13$	1.44292	−	2.49921i	0.400194	−	0.693157i	−0.593555	−	0.804794i	$-0.702276\pi$
$13$	1.44292	−	2.49921i	0.400194	−	0.693157i	0.993749	+	0.111637i	$0.0356093\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.176596	+	0.305873i	0.0428308	+	0.0741851i	0.886646	−	0.462449i	$-0.153029\pi$
$17$	0.176596	+	0.305873i	0.0428308	+	0.0741851i	−0.843815	+	0.536634i	$0.819696\pi$
$18$		0			0
$19$	2.84888	−	4.93440i	0.653578	−	1.13203i	−0.328670	−	0.944445i	$-0.606601\pi$
$19$	2.84888	−	4.93440i	0.653578	−	1.13203i	0.982248	−	0.187585i	$-0.0600661\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.438682	−	0.759820i	−0.0914716	−	0.158433i	0.816659	−	0.577121i	$-0.195824\pi$
$23$	−0.438682	−	0.759820i	−0.0914716	−	0.158433i	−0.908131	+	0.418687i	$0.862490\pi$
$24$		0			0
$25$	0.285756	−	0.494945i	0.0571513	−	0.0989889i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.874997	−	1.51554i	−0.162483	−	0.281429i	0.773276	−	0.634070i	$-0.218617\pi$
$29$	−0.874997	−	1.51554i	−0.162483	−	0.281429i	−0.935759	+	0.352641i	$0.885284\pi$
$30$		0			0
$31$	9.13490			1.64068			0.820339	−	0.571878i	$-0.193785\pi$
$31$	9.13490			1.64068			0.820339	+	0.571878i	$0.193785\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.75582	+	4.11014i	0.634850	+	0.694740i
$36$		0			0
$37$	−3.39555	+	5.88127i	−0.558225	+	0.966874i	0.439420	+	0.898282i	$0.355184\pi$
$37$	−3.39555	+	5.88127i	−0.558225	+	0.966874i	−0.997645	+	0.0685922i	$0.978149\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.20377	+	2.08499i	−0.187997	+	0.325621i	−0.944582	−	0.328274i	$-0.893533\pi$
$41$	−1.20377	+	2.08499i	−0.187997	+	0.325621i	0.756585	+	0.653895i	$0.226866\pi$
$42$		0			0
$43$	0.276745	+	0.479336i	0.0422032	+	0.0730981i	0.886355	−	0.463005i	$-0.153229\pi$
$43$	0.276745	+	0.479336i	0.0422032	+	0.0730981i	−0.844152	+	0.536104i	$0.819896\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−11.7372			−1.71205			−0.856023	−	0.516939i	$-0.827072\pi$
$47$	−11.7372			−1.71205			−0.856023	+	0.516939i	$0.827072\pi$
$48$		0			0
$49$	6.35230	−	2.94080i	0.907471	−	0.420114i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.07821	+	3.59956i	0.285464	+	0.494437i	0.972721	−	0.231976i	$-0.0745191\pi$
$53$	2.07821	+	3.59956i	0.285464	+	0.494437i	−0.687258	+	0.726413i	$0.741186\pi$
$54$		0			0
$55$	0.839790			0.113237
$56$		0			0
$57$		0			0
$58$		0			0
$59$	9.32421			1.21391			0.606954	−	0.794737i	$-0.292391\pi$
$59$	9.32421			1.21391			0.606954	+	0.794737i	$0.292391\pi$
$60$		0			0
$61$	−10.0720			−1.28959			−0.644795	−	0.764356i	$-0.723057\pi$
$61$	−10.0720			−1.28959			−0.644795	+	0.764356i	$0.723057\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.07296			0.753258
$66$		0			0
$67$	1.20241			0.146898			0.0734488	−	0.997299i	$-0.476599\pi$
$67$	1.20241			0.146898			0.0734488	+	0.997299i	$0.476599\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	14.6826			1.74250			0.871250	−	0.490840i	$-0.163310\pi$
$71$	14.6826			1.74250			0.871250	+	0.490840i	$0.163310\pi$
$72$		0			0
$73$	0.315636	+	0.546697i	0.0369423	+	0.0639860i	0.883905	−	0.467666i	$-0.154905\pi$
$73$	0.315636	+	0.546697i	0.0369423	+	0.0639860i	−0.846963	+	0.531652i	$0.821572\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.318883	−	1.00652i	0.0363400	−	0.114703i
$78$		0			0
$79$	−2.48729			−0.279842			−0.139921	−	0.990163i	$-0.544685\pi$
$79$	−2.48729			−0.279842			−0.139921	+	0.990163i	$0.544685\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.59366	+	7.95645i	0.504219	+	0.873333i	0.999988	+	0.00487885i	$0.00155299\pi$
$83$	4.59366	+	7.95645i	0.504219	+	0.873333i	−0.495769	+	0.868455i	$0.665114\pi$
$84$		0			0
$85$	−0.371628	+	0.643678i	−0.0403087	+	0.0698167i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.29358	+	12.6328i	−0.773118	+	1.33908i	0.162729	+	0.986671i	$0.447971\pi$
$89$	−7.29358	+	12.6328i	−0.773118	+	1.33908i	−0.935846	+	0.352408i	$0.885363\pi$
$90$		0			0
$91$	2.30601	−	7.27866i	0.241735	−	0.763011i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	11.9903			1.23018
$96$		0			0
$97$	−7.84245	−	13.5835i	−0.796280	−	1.37920i	−0.922023	−	0.387134i	$-0.873465\pi$
$97$	−7.84245	−	13.5835i	−0.796280	−	1.37920i	0.125744	−	0.992063i	$-0.459868\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.0464285	+	0.0804166i	−0.00461981	+	0.00800175i	−0.868326	−	0.495994i	$-0.834804\pi$
$101$	−0.0464285	+	0.0804166i	−0.00461981	+	0.00800175i	0.863706	+	0.503996i	$0.168137\pi$
$102$		0			0
$103$	9.95769	+	17.2472i	0.981161	+	1.69942i	0.657891	+	0.753113i	$0.271449\pi$
$103$	9.95769	+	17.2472i	0.981161	+	1.69942i	0.323270	+	0.946307i	$0.395218\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.89225	−	5.00953i	0.279605	−	0.484290i	−0.691682	−	0.722202i	$-0.743130\pi$
$107$	2.89225	−	5.00953i	0.279605	−	0.484290i	0.971287	+	0.237913i	$0.0764633\pi$
$108$		0			0
$109$	−6.25516	−	10.8343i	−0.599136	−	1.03773i	−0.992949	−	0.118543i	$-0.962178\pi$
$109$	−6.25516	−	10.8343i	−0.599136	−	1.03773i	0.393813	−	0.919191i	$-0.371156\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.69411	+	2.93428i	−0.159368	+	0.276034i	−0.934641	−	0.355593i	$-0.884279\pi$
$113$	−1.69411	+	2.93428i	−0.159368	+	0.276034i	0.775273	+	0.631627i	$0.217612\pi$
$114$		0			0
$115$	0.923161	−	1.59896i	0.0860853	−	0.149104i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.630359	+	0.689825i	0.0577849	+	0.0632362i
$120$		0			0
$121$	5.42037	+	9.38836i	0.492761	+	0.853488i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.7247			1.04869
$126$		0			0
$127$	14.7348			1.30750			0.653752	−	0.756709i	$-0.273194\pi$
$127$	14.7348			1.30750			0.653752	+	0.756709i	$0.273194\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.95392	−	12.0445i	−0.607567	−	1.05234i	−0.991640	−	0.129034i	$-0.958812\pi$
$131$	−6.95392	−	12.0445i	−0.607567	−	1.05234i	0.384073	−	0.923303i	$-0.374521\pi$
$132$		0			0
$133$	4.55294	−	14.3709i	0.394790	−	1.24611i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.27874	−	12.6072i	0.621865	−	1.07710i	−0.367273	−	0.930113i	$-0.619709\pi$
$137$	7.27874	−	12.6072i	0.621865	−	1.07710i	0.989138	−	0.146989i	$-0.0469581\pi$
$138$		0			0
$139$	−3.63996	+	6.30460i	−0.308737	+	0.534749i	−0.978086	−	0.208199i	$-0.933240\pi$
$139$	−3.63996	+	6.30460i	−0.308737	+	0.534749i	0.669349	+	0.742948i	$0.266573\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.575818	−	0.997347i	−0.0481523	−	0.0834023i
$144$		0			0
$145$	1.84134	−	3.18930i	0.152915	−	0.264857i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.360832	−	0.624979i	−0.0295605	−	0.0512003i	0.850867	−	0.525382i	$-0.176077\pi$
$149$	−0.360832	−	0.624979i	−0.0295605	−	0.0512003i	−0.880427	+	0.474181i	$0.842744\pi$
$150$		0			0
$151$	−10.9022	+	18.8831i	−0.887207	+	1.53669i	−0.0440432	+	0.999030i	$0.514024\pi$
$151$	−10.9022	+	18.8831i	−0.887207	+	1.53669i	−0.843163	+	0.537657i	$0.819309\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.61173	+	16.6480i	0.772033	+	1.33720i
$156$		0			0
$157$	5.17973			0.413387			0.206694	−	0.978406i	$-0.433730\pi$
$157$	5.17973			0.413387			0.206694	+	0.978406i	$0.433730\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.56588	−	1.71360i	−0.123408	−	0.135050i
$162$		0			0
$163$	2.63906	−	4.57098i	0.206707	−	0.358027i	−0.743968	−	0.668215i	$-0.767059\pi$
$163$	2.63906	−	4.57098i	0.206707	−	0.358027i	0.950675	+	0.310188i	$0.100392\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.83710	−	11.8422i	0.529071	−	0.916378i	−0.470354	−	0.882478i	$-0.655874\pi$
$167$	6.83710	−	11.8422i	0.529071	−	0.916378i	0.999425	−	0.0339001i	$-0.0107928\pi$
$168$		0			0
$169$	2.33596	+	4.04599i	0.179689	+	0.311230i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−20.1824			−1.53444			−0.767218	−	0.641386i	$-0.778360\pi$
$173$	−20.1824			−1.53444			−0.767218	+	0.641386i	$0.778360\pi$
$174$		0			0
$175$	0.456682	−	1.44147i	0.0345219	−	0.108965i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.5968	−	21.8183i	−0.941528	−	1.63077i	−0.762557	−	0.646921i	$-0.776056\pi$
$179$	−12.5968	−	21.8183i	−0.941528	−	1.63077i	−0.178971	−	0.983854i	$-0.557277\pi$
$180$		0			0
$181$	−17.2815			−1.28453			−0.642263	−	0.766485i	$-0.722004\pi$
$181$	−17.2815			−1.28453			−0.642263	+	0.766485i	$0.722004\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−14.2912			−1.05071
$186$		0			0
$187$	0.140946			0.0103070
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.01898			0.363161			0.181580	−	0.983376i	$-0.441879\pi$
$191$	5.01898			0.363161			0.181580	+	0.983376i	$0.441879\pi$
$192$		0			0
$193$	−5.43765			−0.391411			−0.195705	−	0.980663i	$-0.562700\pi$
$193$	−5.43765			−0.391411			−0.195705	+	0.980663i	$0.562700\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.95839			−0.424517			−0.212259	−	0.977214i	$-0.568082\pi$
$197$	−5.95839			−0.424517			−0.212259	+	0.977214i	$0.568082\pi$
$198$		0			0
$199$	5.62062	+	9.73520i	0.398435	+	0.690110i	0.993533	−	0.113543i	$-0.0362200\pi$
$199$	5.62062	+	9.73520i	0.398435	+	0.690110i	−0.595098	+	0.803653i	$0.702887\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.12330	−	3.41795i	−0.219213	−	0.239893i
$204$		0			0
$205$	−5.06643			−0.353855
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.13689	−	1.96914i	−0.0786401	−	0.136209i
$210$		0			0
$211$	0.381084	−	0.660057i	0.0262349	−	0.0454402i	−0.852610	−	0.522548i	$-0.824982\pi$
$211$	0.381084	−	0.660057i	0.0262349	−	0.0454402i	0.878845	+	0.477108i	$0.158315\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.582381	+	1.00871i	−0.0397181	+	0.0687937i
$216$		0			0
$217$	23.6030	−	5.19848i	1.60228	−	0.352896i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.01926			0.0685626
$222$		0			0
$223$	−5.80556	−	10.0555i	−0.388769	−	0.673368i	0.603515	−	0.797352i	$-0.293766\pi$
$223$	−5.80556	−	10.0555i	−0.388769	−	0.673368i	−0.992284	+	0.123984i	$0.960433\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.16624	+	8.94818i	−0.342895	+	0.593912i	−0.984969	−	0.172731i	$-0.944741\pi$
$227$	−5.16624	+	8.94818i	−0.342895	+	0.593912i	0.642074	+	0.766643i	$0.278074\pi$
$228$		0			0
$229$	1.86191	+	3.22493i	0.123039	+	0.213109i	0.920965	−	0.389646i	$-0.127403\pi$
$229$	1.86191	+	3.22493i	0.123039	+	0.213109i	−0.797926	+	0.602756i	$0.794069\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.3649	+	23.1488i	−0.875566	+	1.51653i	−0.0194083	+	0.999812i	$0.506178\pi$
$233$	−13.3649	+	23.1488i	−0.875566	+	1.51653i	−0.856158	+	0.516714i	$0.827155\pi$
$234$		0			0
$235$	−12.3499	−	21.3906i	−0.805616	−	1.39537i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.94164	+	12.0233i	−0.449018	+	0.777721i	−0.998322	−	0.0579007i	$-0.981559\pi$
$239$	−6.94164	+	12.0233i	−0.449018	+	0.777721i	0.549305	+	0.835622i	$0.314893\pi$
$240$		0			0
$241$	−7.45280	+	12.9086i	−0.480077	+	0.831518i	−0.999739	−	0.0228542i	$-0.992725\pi$
$241$	−7.45280	+	12.9086i	−0.480077	+	0.831518i	0.519662	+	0.854372i	$0.326058\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.0434	+	8.48251i	0.769423	+	0.541928i
$246$		0			0
$247$	−8.22142	−	14.2399i	−0.523116	−	0.906064i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−22.5515			−1.42344			−0.711720	−	0.702464i	$-0.752083\pi$
$251$	−22.5515			−1.42344			−0.711720	+	0.702464i	$0.752083\pi$
$252$		0			0
$253$	−0.350125			−0.0220122
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.94765	+	10.3016i	0.371004	+	0.642598i	0.989720	−	0.143017i	$-0.0456803\pi$
$257$	5.94765	+	10.3016i	0.371004	+	0.642598i	−0.618716	+	0.785615i	$0.712347\pi$
$258$		0			0
$259$	−5.42660	+	17.1285i	−0.337193	+	1.06431i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.3030	−	21.3094i	0.758633	−	1.31399i	−0.184915	−	0.982755i	$-0.559201\pi$
$263$	12.3030	−	21.3094i	0.758633	−	1.31399i	0.943548	−	0.331236i	$-0.107466\pi$
$264$		0			0
$265$	−4.37337	+	7.57490i	−0.268654	+	0.465322i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.75722	−	11.7039i	−0.411995	−	0.713597i	0.583113	−	0.812391i	$-0.301835\pi$
$269$	−6.75722	−	11.7039i	−0.411995	−	0.713597i	−0.995108	+	0.0987947i	$0.968501\pi$
$270$		0			0
$271$	−1.34195	+	2.32433i	−0.0815177	+	0.141193i	−0.903902	−	0.427740i	$-0.859310\pi$
$271$	−1.34195	+	2.32433i	−0.0815177	+	0.141193i	0.822384	+	0.568932i	$0.192643\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.114035	−	0.197515i	−0.00687658	−	0.0119106i
$276$		0			0
$277$	−9.52618	+	16.4998i	−0.572373	+	0.991379i	0.423949	+	0.905686i	$0.360644\pi$
$277$	−9.52618	+	16.4998i	−0.572373	+	0.991379i	−0.996322	+	0.0856928i	$0.972690\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.2006	−	24.5962i	−0.847139	−	1.46729i	−0.883751	−	0.467958i	$-0.844990\pi$
$281$	−14.2006	−	24.5962i	−0.847139	−	1.46729i	0.0366118	−	0.999330i	$-0.488343\pi$
$282$		0			0
$283$	−15.4221			−0.916749			−0.458374	−	0.888759i	$-0.651568\pi$
$283$	−15.4221			−0.916749			−0.458374	+	0.888759i	$0.651568\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.92381	+	6.07230i	−0.113559	+	0.358436i
$288$		0			0
$289$	8.43763	−	14.6144i	0.496331	−	0.859671i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.02253	+	15.6275i	−0.527102	+	0.912967i	0.472399	+	0.881385i	$0.343388\pi$
$293$	−9.02253	+	15.6275i	−0.527102	+	0.912967i	−0.999501	+	0.0315825i	$0.989945\pi$
$294$		0			0
$295$	9.81092	+	16.9930i	0.571214	+	0.989371i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.53194			−0.146426
$300$		0			0
$301$	0.987841	+	1.08103i	0.0569382	+	0.0623096i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.5978	−	18.3559i	−0.606826	−	1.05105i
$306$		0			0
$307$	−7.30860			−0.417124			−0.208562	−	0.978009i	$-0.566878\pi$
$307$	−7.30860			−0.417124			−0.208562	+	0.978009i	$0.566878\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	23.7792			1.34839			0.674197	−	0.738551i	$-0.264490\pi$
$311$	23.7792			1.34839			0.674197	+	0.738551i	$0.264490\pi$
$312$		0			0
$313$	−18.2907			−1.03385			−0.516925	−	0.856031i	$-0.672923\pi$
$313$	−18.2907			−1.03385			−0.516925	+	0.856031i	$0.672923\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.68988			0.263410			0.131705	−	0.991289i	$-0.457955\pi$
$317$	4.68988			0.263410			0.131705	+	0.991289i	$0.457955\pi$
$318$		0			0
$319$	−0.698360			−0.0391007
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.01240			0.111973
$324$		0			0
$325$	−0.824648	−	1.42833i	−0.0457432	−	0.0792296i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−30.3268	+	6.67938i	−1.67197	+	0.368246i
$330$		0			0
$331$	−11.4287			−0.628176			−0.314088	−	0.949394i	$-0.601699\pi$
$331$	−11.4287			−0.628176			−0.314088	+	0.949394i	$0.601699\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.26517	+	2.19134i	0.0691238	+	0.119726i
$336$		0			0
$337$	8.74160	−	15.1409i	0.476185	−	0.824777i	−0.523442	−	0.852061i	$-0.675353\pi$
$337$	8.74160	−	15.1409i	0.476185	−	0.824777i	0.999628	+	0.0272840i	$0.00868584\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.82271	−	3.15702i	0.0987051	−	0.170962i
$342$		0			0
$343$	14.7397	−	11.2135i	0.795868	−	0.605470i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−14.1186			−0.757925			−0.378962	−	0.925412i	$-0.623719\pi$
$347$	−14.1186			−0.757925			−0.378962	+	0.925412i	$0.623719\pi$
$348$		0			0
$349$	10.7216	+	18.5704i	0.573916	+	0.994052i	0.996158	+	0.0875692i	$0.0279099\pi$
$349$	10.7216	+	18.5704i	0.573916	+	0.994052i	−0.422242	+	0.906483i	$0.638757\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−15.6880	+	27.1724i	−0.834987	+	1.44624i	0.0590538	+	0.998255i	$0.481192\pi$
$353$	−15.6880	+	27.1724i	−0.834987	+	1.44624i	−0.894041	+	0.447985i	$0.852142\pi$
$354$		0			0
$355$	15.4490	+	26.7584i	0.819946	+	1.42019i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.313156	+	0.542402i	−0.0165277	+	0.0286269i	−0.874171	−	0.485618i	$-0.838595\pi$
$359$	−0.313156	+	0.542402i	−0.0165277	+	0.0286269i	0.857643	+	0.514245i	$0.171928\pi$
$360$		0			0
$361$	−6.73223	−	11.6606i	−0.354328	−	0.613714i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.664223	+	1.15047i	−0.0347670	+	0.0602182i
$366$		0			0
$367$	1.62199	−	2.80936i	0.0846670	−	0.146648i	−0.820582	−	0.571528i	$-0.806351\pi$
$367$	1.62199	−	2.80936i	0.0846670	−	0.146648i	0.905249	+	0.424881i	$0.139684\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.41815	+	8.11796i	0.385131	+	0.421464i
$372$		0			0
$373$	13.8013	+	23.9046i	0.714606	+	1.23773i	0.963111	+	0.269103i	$0.0867272\pi$
$373$	13.8013	+	23.9046i	0.714606	+	1.23773i	−0.248506	+	0.968630i	$0.579939\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.05021			−0.260099
$378$		0			0
$379$	−12.7800			−0.656463			−0.328231	−	0.944597i	$-0.606453\pi$
$379$	−12.7800			−0.656463			−0.328231	+	0.944597i	$0.606453\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.58278	−	4.47351i	−0.131974	−	0.228586i	0.792463	−	0.609919i	$-0.208798\pi$
$383$	−2.58278	−	4.47351i	−0.131974	−	0.228586i	−0.924437	+	0.381334i	$0.875465\pi$
$384$		0			0
$385$	2.16987	−	0.477906i	0.110587	−	0.0243564i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.4707	−	28.5280i	0.835095	−	1.44643i	−0.0588576	−	0.998266i	$-0.518746\pi$
$389$	16.4707	−	28.5280i	0.835095	−	1.44643i	0.893953	−	0.448161i	$-0.147921\pi$
$390$		0			0
$391$	0.154939	−	0.268362i	0.00783560	−	0.0135717i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.61712	−	4.53299i	−0.131682	−	0.228079i
$396$		0			0
$397$	−0.411705	+	0.713095i	−0.0206629	+	0.0357892i	−0.876172	−	0.481999i	$-0.839911\pi$
$397$	−0.411705	+	0.713095i	−0.0206629	+	0.0357892i	0.855509	+	0.517788i	$0.173244\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.86923	−	17.0940i	−0.492846	−	0.853634i	0.507120	−	0.861875i	$-0.330710\pi$
$401$	−9.86923	−	17.0940i	−0.492846	−	0.853634i	−0.999966	+	0.00824153i	$0.997377\pi$
$402$		0			0
$403$	13.1809	−	22.8301i	0.656590	−	1.13725i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.35504	+	2.34700i	0.0671670	+	0.116337i
$408$		0			0
$409$	−25.2551			−1.24879			−0.624393	−	0.781110i	$-0.714654\pi$
$409$	−25.2551			−1.24879			−0.624393	+	0.781110i	$0.714654\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0921	−	5.30621i	1.18550	−	0.261101i
$414$		0			0
$415$	−9.66688	+	16.7435i	−0.474528	+	0.821907i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.406717	+	0.704455i	−0.0198694	+	0.0344149i	−0.875789	−	0.482694i	$-0.839658\pi$
$419$	−0.406717	+	0.704455i	−0.0198694	+	0.0344149i	0.855920	+	0.517109i	$0.172992\pi$
$420$		0			0
$421$	5.12114	+	8.87008i	0.249589	+	0.432301i	0.963412	−	0.268025i	$-0.0863711\pi$
$421$	5.12114	+	8.87008i	0.249589	+	0.432301i	−0.713823	+	0.700326i	$0.753038\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.201854			0.00979134
$426$		0			0
$427$	−26.0243	+	5.73177i	−1.25941	+	0.277380i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−16.3348	−	28.2928i	−0.786822	−	1.36281i	−0.927905	−	0.372817i	$-0.878392\pi$
$431$	−16.3348	−	28.2928i	−0.786822	−	1.36281i	0.141083	−	0.989998i	$-0.454941\pi$
$432$		0			0
$433$	−14.3151			−0.687941			−0.343970	−	0.938980i	$-0.611772\pi$
$433$	−14.3151			−0.687941			−0.343970	+	0.938980i	$0.611772\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.99901			−0.239135
$438$		0			0
$439$	−9.86660			−0.470907			−0.235453	−	0.971886i	$-0.575658\pi$
$439$	−9.86660			−0.470907			−0.235453	+	0.971886i	$0.575658\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−37.2801			−1.77123			−0.885615	−	0.464419i	$-0.846263\pi$
$443$	−37.2801			−1.77123			−0.885615	+	0.464419i	$0.846263\pi$
$444$		0			0
$445$	−30.6972			−1.45519
$446$		0			0
$447$		0			0
$448$		0			0
$449$	36.2926			1.71276			0.856378	−	0.516350i	$-0.172710\pi$
$449$	36.2926			1.71276			0.856378	+	0.516350i	$0.172710\pi$
$450$		0			0
$451$	0.480382	+	0.832046i	0.0226203	+	0.0391795i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	15.6915	−	3.45599i	0.735627	−	0.162019i
$456$		0			0
$457$	−13.1943			−0.617205			−0.308602	−	0.951191i	$-0.599861\pi$
$457$	−13.1943			−0.617205			−0.308602	+	0.951191i	$0.599861\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.1326	−	17.5502i	−0.471924	−	0.817396i	0.527560	−	0.849518i	$-0.323107\pi$
$461$	−10.1326	−	17.5502i	−0.471924	−	0.817396i	−0.999484	+	0.0321215i	$0.989774\pi$
$462$		0			0
$463$	12.7106	−	22.0154i	0.590712	−	1.02314i	−0.403424	−	0.915013i	$-0.632180\pi$
$463$	12.7106	−	22.0154i	0.590712	−	1.02314i	0.994137	−	0.108131i	$-0.0344866\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.40661	−	7.63248i	0.203914	−	0.353189i	−0.745872	−	0.666089i	$-0.767967\pi$
$467$	4.40661	−	7.63248i	0.203914	−	0.353189i	0.949786	+	0.312900i	$0.101300\pi$
$468$		0			0
$469$	3.10681	−	0.684265i	0.143459	−	0.0315964i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.220878			0.0101560
$474$		0			0
$475$	−1.62817	−	2.82008i	−0.0747056	−	0.129394i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.1343	−	21.0173i	0.554433	−	0.960305i	−0.443515	−	0.896267i	$-0.646269\pi$
$479$	12.1343	−	21.0173i	0.554433	−	0.960305i	0.997947	−	0.0640383i	$-0.0203980\pi$
$480$		0			0
$481$	9.79902	+	16.9724i	0.446797	+	0.773875i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	16.5036	−	28.5851i	0.749391	−	1.29798i
$486$		0			0
$487$	−5.37220	−	9.30492i	−0.243438	−	0.421646i	0.718254	−	0.695781i	$-0.244942\pi$
$487$	−5.37220	−	9.30492i	−0.243438	−	0.421646i	−0.961691	+	0.274135i	$0.911608\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.3934	+	19.7340i	−0.514179	+	0.890584i	0.485686	+	0.874134i	$0.338570\pi$
$491$	−11.3934	+	19.7340i	−0.514179	+	0.890584i	−0.999865	+	0.0164507i	$0.994763\pi$
$492$		0			0
$493$	0.309042	−	0.535276i	0.0139185	−	0.0241076i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	37.9372	−	8.35553i	1.70171	−	0.374797i
$498$		0			0
$499$	−11.5755	−	20.0493i	−0.518189	−	0.897530i	−0.999777	−	0.0211317i	$-0.993273\pi$
$499$	−11.5755	−	20.0493i	−0.518189	−	0.897530i	0.481588	−	0.876398i	$-0.340060\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.43360			−0.420623			−0.210312	−	0.977634i	$-0.567448\pi$
$503$	−9.43360			−0.420623			−0.210312	+	0.977634i	$0.567448\pi$
$504$		0			0
$505$	−0.195408			−0.00869555
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.72981	−	8.19228i	−0.209645	−	0.363116i	0.741957	−	0.670447i	$-0.233898\pi$
$509$	−4.72981	−	8.19228i	−0.209645	−	0.363116i	−0.951603	+	0.307331i	$0.900564\pi$
$510$		0			0
$511$	1.12666	+	1.23295i	0.0498405	+	0.0545424i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−20.9549	+	36.2950i	−0.923385	+	1.59935i
$516$		0			0
$517$	−2.34195	+	4.05637i	−0.102999	+	0.178399i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	14.3368	+	24.8320i	0.628105	+	1.08791i	0.987932	+	0.154891i	$0.0495026\pi$
$521$	14.3368	+	24.8320i	0.628105	+	1.08791i	−0.359826	+	0.933019i	$0.617164\pi$
$522$		0			0
$523$	−13.5104	+	23.4006i	−0.590767	+	1.02324i	0.403362	+	0.915040i	$0.367841\pi$
$523$	−13.5104	+	23.4006i	−0.590767	+	1.02324i	−0.994129	+	0.108198i	$0.965492\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.61319	+	2.79412i	0.0702715	+	0.121714i
$528$		0			0
$529$	11.1151	−	19.2519i	0.483266	−	0.837041i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.47389	+	6.01696i	0.150471	+	0.260624i
$534$		0			0
$535$	12.1729			0.526280
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.251148	−	2.78214i	0.0108177	−	0.119835i
$540$		0			0
$541$	−1.52907	+	2.64842i	−0.0657397	+	0.113864i	−0.897022	−	0.441986i	$-0.854274\pi$
$541$	−1.52907	+	2.64842i	−0.0657397	+	0.113864i	0.831282	+	0.555851i	$0.187607\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	13.1633	−	22.7996i	0.563856	−	0.976627i
$546$		0			0
$547$	3.58144	+	6.20323i	0.153131	+	0.265231i	0.932377	−	0.361487i	$-0.117731\pi$
$547$	3.58144	+	6.20323i	0.153131	+	0.265231i	−0.779246	+	0.626719i	$0.784398\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.97105			−0.424781
$552$		0			0
$553$	−6.42672	+	1.41546i	−0.273292	+	0.0601916i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.3518	+	24.8580i	0.608104	+	1.05327i	0.991553	+	0.129704i	$0.0414028\pi$
$557$	14.3518	+	24.8580i	0.608104	+	1.05327i	−0.383449	+	0.923562i	$0.625264\pi$
$558$		0			0
$559$	1.59729			0.0675580
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−35.7719			−1.50761			−0.753803	−	0.657101i	$-0.771782\pi$
$563$	−35.7719			−1.50761			−0.753803	+	0.657101i	$0.771782\pi$
$564$		0			0
$565$	−7.13016			−0.299968
$566$		0			0
$567$		0			0
$568$		0			0
$569$	25.2002			1.05645			0.528223	−	0.849106i	$-0.322858\pi$
$569$	25.2002			1.05645			0.528223	+	0.849106i	$0.322858\pi$
$570$		0			0
$571$	−6.04938			−0.253159			−0.126579	−	0.991956i	$-0.540400\pi$
$571$	−6.04938			−0.253159			−0.126579	+	0.991956i	$0.540400\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.501425			−0.0209109
$576$		0			0
$577$	9.57977	+	16.5926i	0.398811	+	0.690761i	0.993580	−	0.113136i	$-0.0360896\pi$
$577$	9.57977	+	16.5926i	0.398811	+	0.690761i	−0.594768	+	0.803897i	$0.702756\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.3970	+	17.9439i	0.680264	+	0.744439i
$582$		0			0
$583$	1.65868			0.0686953
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.4147	−	31.8953i	−0.760058	−	1.31646i	−0.942820	−	0.333301i	$-0.891837\pi$
$587$	−18.4147	−	31.8953i	−0.760058	−	1.31646i	0.182763	−	0.983157i	$-0.441496\pi$
$588$		0			0
$589$	26.0242	−	45.0753i	1.07231	−	1.85730i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8.97285	+	15.5414i	−0.368471	+	0.638210i	−0.989327	−	0.145715i	$-0.953452\pi$
$593$	−8.97285	+	15.5414i	−0.368471	+	0.638210i	0.620856	+	0.783925i	$0.286785\pi$
$594$		0			0
$595$	−0.593918	+	1.87464i	−0.0243482	+	0.0768526i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	40.4913			1.65443			0.827215	−	0.561885i	$-0.189924\pi$
$599$	40.4913			1.65443			0.827215	+	0.561885i	$0.189924\pi$
$600$		0			0
$601$	13.2589	+	22.9651i	0.540841	+	0.936765i	0.998856	+	0.0478200i	$0.0152274\pi$
$601$	13.2589	+	22.9651i	0.540841	+	0.936765i	−0.458015	+	0.888945i	$0.651439\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−11.4066	+	19.7568i	−0.463745	+	0.803230i
$606$		0			0
$607$	21.0848	+	36.5200i	0.855806	+	1.48230i	0.875895	+	0.482501i	$0.160271\pi$
$607$	21.0848	+	36.5200i	0.855806	+	1.48230i	−0.0200897	+	0.999798i	$0.506395\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−16.9358	+	29.3337i	−0.685151	+	1.18672i
$612$		0			0
$613$	−0.700827	−	1.21387i	−0.0283061	−	0.0490277i	0.851525	−	0.524313i	$-0.175678\pi$
$613$	−0.700827	−	1.21387i	−0.0283061	−	0.0490277i	−0.879831	+	0.475286i	$0.842345\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.76787	−	11.7223i	0.272464	−	0.471922i	−0.697028	−	0.717044i	$-0.745495\pi$
$617$	6.76787	−	11.7223i	0.272464	−	0.471922i	0.969492	+	0.245122i	$0.0788280\pi$
$618$		0			0
$619$	14.9122	−	25.8288i	0.599374	−	1.03815i	−0.393540	−	0.919308i	$-0.628750\pi$
$619$	14.9122	−	25.8288i	0.599374	−	1.03815i	0.992914	−	0.118838i	$-0.0379171\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−11.6562	+	36.7917i	−0.466997	+	1.47403i
$624$		0			0
$625$	10.9079	+	18.8930i	0.436316	+	0.755722i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.39856			−0.0956369
$630$		0			0
$631$	6.84708			0.272578			0.136289	−	0.990669i	$-0.456482\pi$
$631$	6.84708			0.272578			0.136289	+	0.990669i	$0.456482\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	15.5040	+	26.8536i	0.615256	+	1.06565i
$636$		0			0
$637$	1.81618	−	20.1191i	0.0719598	−	0.797147i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.1209	−	27.9221i	0.636735	−	1.10286i	−0.349409	−	0.936970i	$-0.613618\pi$
$641$	16.1209	−	27.9221i	0.636735	−	1.10286i	0.986145	−	0.165888i	$-0.0530489\pi$
$642$		0			0
$643$	1.16002	−	2.00921i	0.0457465	−	0.0792353i	−0.842245	−	0.539094i	$-0.818767\pi$
$643$	1.16002	−	2.00921i	0.0457465	−	0.0792353i	0.887992	+	0.459859i	$0.152100\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.06813	−	1.85005i	−0.0419924	−	0.0727329i	0.844265	−	0.535925i	$-0.180037\pi$
$647$	−1.06813	−	1.85005i	−0.0419924	−	0.0727329i	−0.886258	+	0.463193i	$0.846704\pi$
$648$		0			0
$649$	1.86048	−	3.22244i	0.0730302	−	0.126492i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.51932	+	2.63155i	0.0594558	+	0.102980i	0.894221	−	0.447625i	$-0.147730\pi$
$653$	1.51932	+	2.63155i	0.0594558	+	0.102980i	−0.834765	+	0.550606i	$0.814397\pi$
$654$		0			0
$655$	14.6338	−	25.3465i	0.571790	−	0.990370i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	19.8000	+	34.2946i	0.771298	+	1.33593i	0.936852	+	0.349726i	$0.113725\pi$
$659$	19.8000	+	34.2946i	0.771298	+	1.33593i	−0.165554	+	0.986201i	$0.552941\pi$
$660$		0			0
$661$	6.12398			0.238195			0.119098	−	0.992883i	$-0.462000\pi$
$661$	6.12398			0.238195			0.119098	+	0.992883i	$0.462000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	30.9810	−	6.82345i	1.20139	−	0.264602i
$666$		0			0
$667$	−0.767691	+	1.32968i	−0.0297251	+	0.0514854i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.00969	+	3.48089i	−0.0775832	+	0.134378i
$672$		0			0
$673$	−4.36248	−	7.55603i	−0.168161	−	0.291264i	0.769612	−	0.638512i	$-0.220450\pi$
$673$	−4.36248	−	7.55603i	−0.168161	−	0.291264i	−0.937773	+	0.347248i	$0.887116\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.9601			−0.574965			−0.287482	−	0.957786i	$-0.592818\pi$
$677$	−14.9601			−0.574965			−0.287482	+	0.957786i	$0.592818\pi$
$678$		0			0
$679$	−27.9936	−	30.6345i	−1.07430	−	1.17564i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	8.89558	+	15.4076i	0.340380	+	0.589555i	0.984503	−	0.175366i	$-0.0561110\pi$
$683$	8.89558	+	15.4076i	0.340380	+	0.589555i	−0.644123	+	0.764922i	$0.722778\pi$
$684$		0			0
$685$	30.6347			1.17049
$686$		0			0
$687$		0			0
$688$		0			0
$689$	11.9948			0.456964
$690$		0			0
$691$	−29.5389			−1.12371			−0.561856	−	0.827235i	$-0.689913\pi$
$691$	−29.5389			−1.12371			−0.561856	+	0.827235i	$0.689913\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−15.3198			−0.581115
$696$		0			0
$697$	−0.850324			−0.0322083
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−27.7740			−1.04901			−0.524504	−	0.851408i	$-0.675749\pi$
$701$	−27.7740			−1.04901			−0.524504	+	0.851408i	$0.675749\pi$
$702$		0			0
$703$	19.3470	+	33.5100i	0.729687	+	1.26385i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.0741998	+	0.234204i	−0.00279057	+	0.00880814i
$708$		0			0
$709$	47.0984			1.76882			0.884409	−	0.466712i	$-0.154562\pi$
$709$	47.0984			1.76882			0.884409	+	0.466712i	$0.154562\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.00732	−	6.94088i	−0.150075	−	0.259938i
$714$		0			0
$715$	1.21175	−	2.09881i	0.0453169	−	0.0784912i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.63394	+	2.83007i	−0.0609357	+	0.105544i	−0.894884	−	0.446299i	$-0.852742\pi$
$719$	−1.63394	+	2.83007i	−0.0609357	+	0.105544i	0.833948	+	0.551843i	$0.186075\pi$
$720$		0			0
$721$	35.5440	+	38.8971i	1.32373	+	1.44860i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.00014			−0.0371444
$726$		0			0
$727$	−6.37047	−	11.0340i	−0.236268	−	0.409228i	0.723373	−	0.690458i	$-0.242591\pi$
$727$	−6.37047	−	11.0340i	−0.236268	−	0.409228i	−0.959640	+	0.281230i	$0.909258\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.0977441	+	0.169298i	−0.00361520	+	0.00626170i
$732$		0			0
$733$	−4.58858	−	7.94765i	−0.169483	−	0.293553i	0.768755	−	0.639543i	$-0.220876\pi$
$733$	−4.58858	−	7.94765i	−0.169483	−	0.293553i	−0.938238	+	0.345990i	$0.887543\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.239919	−	0.415552i	0.00883754	−	0.0153071i
$738$		0			0
$739$	−23.3467	−	40.4377i	−0.858823	−	1.48752i	−0.873053	−	0.487626i	$-0.837863\pi$
$739$	−23.3467	−	40.4377i	−0.858823	−	1.48752i	0.0142303	−	0.999899i	$-0.495470\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7.62654	−	13.2095i	0.279790	−	0.484611i	−0.691542	−	0.722336i	$-0.743068\pi$
$743$	7.62654	−	13.2095i	0.279790	−	0.484611i	0.971333	+	0.237725i	$0.0764017\pi$
$744$		0			0
$745$	0.759333	−	1.31520i	0.0278198	−	0.0481853i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.62226	−	14.5897i	0.168894	−	0.533095i
$750$		0			0
$751$	−3.17443	−	5.49828i	−0.115837	−	0.200635i	0.802277	−	0.596952i	$-0.203622\pi$
$751$	−3.17443	−	5.49828i	−0.115837	−	0.200635i	−0.918114	+	0.396317i	$0.870288\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−45.8850			−1.66993
$756$		0			0
$757$	28.4278			1.03323			0.516614	−	0.856219i	$-0.327192\pi$
$757$	28.4278			1.03323			0.516614	+	0.856219i	$0.327192\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.03437	−	15.6480i	−0.327496	−	0.567239i	0.654519	−	0.756046i	$-0.272871\pi$
$761$	−9.03437	−	15.6480i	−0.327496	−	0.567239i	−0.982014	+	0.188807i	$0.939538\pi$
$762$		0			0
$763$	−22.3278	−	24.4341i	−0.808320	−	0.884575i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	13.4541	−	23.3032i	0.485799	−	0.841429i
$768$		0			0
$769$	−1.72471	+	2.98728i	−0.0621946	+	0.107724i	−0.895446	−	0.445170i	$-0.853143\pi$
$769$	−1.72471	+	2.98728i	−0.0621946	+	0.107724i	0.833252	+	0.552894i	$0.186477\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	20.1837	+	34.9592i	0.725957	+	1.25740i	0.958579	+	0.284828i	$0.0919364\pi$
$773$	20.1837	+	34.9592i	0.725957	+	1.25740i	−0.232621	+	0.972567i	$0.574730\pi$
$774$		0			0
$775$	2.61036	−	4.52127i	0.0937668	−	0.162409i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.85880	+	11.8798i	0.245742	+	0.425638i
$780$		0			0
$781$	2.92964	−	5.07429i	0.104831	−	0.181572i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.45010	+	9.43985i	0.194522	+	0.336923i
$786$		0			0
$787$	18.3206			0.653060			0.326530	−	0.945187i	$-0.394121\pi$
$787$	18.3206			0.653060			0.326530	+	0.945187i	$0.394121\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.70744	+	8.54575i	−0.0962656	+	0.303852i
$792$		0			0
$793$	−14.5331	+	25.1721i	−0.516086	+	0.893888i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.86884	−	8.43307i	0.172463	−	0.298715i	−0.766817	−	0.641865i	$-0.778161\pi$
$797$	4.86884	−	8.43307i	0.172463	−	0.298715i	0.939280	+	0.343151i	$0.111494\pi$
$798$		0			0
$799$	−2.07274	−	3.59009i	−0.0733283	−	0.127008i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.251918			0.00888998
$804$		0			0
$805$	1.47535	−	4.65679i	0.0519993	−	0.164130i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.98714	+	10.3700i	0.210497	+	0.364591i	0.951870	−	0.306502i	$-0.0991586\pi$
$809$	5.98714	+	10.3700i	0.210497	+	0.364591i	−0.741373	+	0.671093i	$0.765825\pi$
$810$		0			0
$811$	4.05517			0.142396			0.0711982	−	0.997462i	$-0.477318\pi$
$811$	4.05517			0.142396			0.0711982	+	0.997462i	$0.477318\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	11.1072			0.389070
$816$		0			0
$817$	3.15365			0.110332
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.98513			−0.278683			−0.139341	−	0.990244i	$-0.544499\pi$
$821$	−7.98513			−0.278683			−0.139341	+	0.990244i	$0.544499\pi$
$822$		0			0
$823$	47.5802			1.65854			0.829270	−	0.558847i	$-0.188756\pi$
$823$	47.5802			1.65854			0.829270	+	0.558847i	$0.188756\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	29.2725			1.01790			0.508952	−	0.860795i	$-0.330033\pi$
$827$	29.2725			1.01790			0.508952	+	0.860795i	$0.330033\pi$
$828$		0			0
$829$	3.15249	+	5.46028i	0.109491	+	0.189643i	0.915564	−	0.402172i	$-0.131745\pi$
$829$	3.15249	+	5.46028i	0.109491	+	0.189643i	−0.806073	+	0.591816i	$0.798411\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.02130	+	1.42366i	0.0700339	+	0.0493270i
$834$		0			0
$835$	28.7760			0.995833
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.501711	+	0.868989i	0.0173210	+	0.0300008i	0.874556	−	0.484925i	$-0.161153\pi$
$839$	0.501711	+	0.868989i	0.0173210	+	0.0300008i	−0.857235	+	0.514925i	$0.827820\pi$
$840$		0			0
$841$	12.9688	−	22.4626i	0.447199	−	0.774571i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.91578	+	8.51438i	−0.169108	+	0.292904i
$846$		0			0
$847$	19.3480	+	21.1733i	0.664806	+	0.727522i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	5.95827			0.204247
$852$		0			0
$853$	20.0519	+	34.7309i	0.686565	+	1.18916i	0.972942	+	0.231048i	$0.0742154\pi$
$853$	20.0519	+	34.7309i	0.686565	+	1.18916i	−0.286378	+	0.958117i	$0.592451\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.7388	+	32.4566i	−0.640106	+	1.10870i	0.345303	+	0.938491i	$0.387776\pi$
$857$	−18.7388	+	32.4566i	−0.640106	+	1.10870i	−0.985409	+	0.170205i	$0.945557\pi$
$858$		0			0
$859$	−12.2516	−	21.2204i	−0.418019	−	0.724031i	0.577721	−	0.816234i	$-0.303942\pi$
$859$	−12.2516	−	21.2204i	−0.418019	−	0.724031i	−0.995740	+	0.0922036i	$0.970609\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.79806	+	16.9707i	−0.333530	+	0.577691i	−0.983201	−	0.182524i	$-0.941573\pi$
$863$	−9.79806	+	16.9707i	−0.333530	+	0.577691i	0.649671	+	0.760215i	$0.274906\pi$
$864$		0			0
$865$	−21.2359	−	36.7816i	−0.722041	−	1.25061i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.496294	+	0.859607i	−0.0168356	+	0.0291602i
$870$		0			0
$871$	1.73498	−	3.00508i	0.0587876	−	0.101823i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	30.2945	−	6.67226i	1.02414	−	0.225564i
$876$		0			0
$877$	−17.1134	−	29.6414i	−0.577880	−	1.00092i	−0.995722	−	0.0923977i	$-0.970547\pi$
$877$	−17.1134	−	29.6414i	−0.577880	−	1.00092i	0.417842	−	0.908520i	$-0.362786\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	25.2818			0.851764			0.425882	−	0.904779i	$-0.359964\pi$
$881$	25.2818			0.851764			0.425882	+	0.904779i	$0.359964\pi$
$882$		0			0
$883$	−45.4688			−1.53015			−0.765073	−	0.643943i	$-0.777297\pi$
$883$	−45.4688			−1.53015			−0.765073	+	0.643943i	$0.777297\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.41504	+	9.37912i	0.181819	+	0.314920i	0.942500	−	0.334206i	$-0.108468\pi$
$887$	5.41504	+	9.37912i	0.181819	+	0.314920i	−0.760681	+	0.649126i	$0.775135\pi$
$888$		0			0
$889$	38.0722	−	8.38527i	1.27690	−	0.281233i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−33.4378	+	57.9160i	−1.11895	+	1.93809i
$894$		0			0
$895$	26.5087	−	45.9143i	0.886086	−	1.53475i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−7.99301	−	13.8443i	−0.266582	−	0.461733i
$900$		0			0
$901$	−0.734005	+	1.27133i	−0.0244533	+	0.0423543i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18.1836	−	31.4949i	−0.604443	−	1.04693i
$906$		0			0
$907$	−2.00841	+	3.47868i	−0.0666883	+	0.115508i	−0.897442	−	0.441133i	$-0.854577\pi$
$907$	−2.00841	+	3.47868i	−0.0666883	+	0.115508i	0.830753	+	0.556641i	$0.187910\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.43681	+	14.6130i	0.279524	+	0.484150i	0.971266	−	0.237995i	$-0.0764901\pi$
$911$	8.43681	+	14.6130i	0.279524	+	0.484150i	−0.691743	+	0.722144i	$0.743157\pi$
$912$		0			0
$913$	3.66633			0.121338
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−24.8220	−	27.1637i	−0.819695	−	0.897023i
$918$		0			0
$919$	−16.9485	+	29.3557i	−0.559081	+	0.968356i	0.438493	+	0.898735i	$0.355512\pi$
$919$	−16.9485	+	29.3557i	−0.559081	+	0.968356i	−0.997573	+	0.0696214i	$0.977821\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	21.1858	−	36.6949i	0.697339	−	1.20783i
$924$		0			0
$925$	1.94060	+	3.36122i	0.0638065	+	0.110516i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	38.6100			1.26675			0.633377	−	0.773843i	$-0.281668\pi$
$929$	38.6100			1.26675			0.633377	+	0.773843i	$0.281668\pi$
$930$		0			0
$931$	3.58584	−	39.7228i	0.117521	−	1.30186i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.148303	+	0.256869i	0.00485004	+	0.00840052i
$936$		0			0
$937$	−45.4955			−1.48627			−0.743136	−	0.669140i	$-0.766663\pi$
$937$	−45.4955			−1.48627			−0.743136	+	0.669140i	$0.766663\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	17.9892			0.586431			0.293216	−	0.956046i	$-0.405275\pi$
$941$	17.9892			0.586431			0.293216	+	0.956046i	$0.405275\pi$
$942$		0			0
$943$	2.11229			0.0687857
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.5224			−0.536906			−0.268453	−	0.963293i	$-0.586512\pi$
$947$	−16.5224			−0.536906			−0.268453	+	0.963293i	$0.586512\pi$
$948$		0			0
$949$	1.82175			0.0591365
$950$		0			0
$951$		0			0
$952$		0			0
$953$	15.6799			0.507922			0.253961	−	0.967214i	$-0.418266\pi$
$953$	15.6799			0.507922			0.253961	+	0.967214i	$0.418266\pi$
$954$		0			0
$955$	5.28096	+	9.14690i	0.170888	+	0.295987i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	11.6325	−	36.7168i	0.375634	−	1.18565i
$960$		0			0
$961$	52.4465			1.69182
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5.72149	−	9.90991i	−0.184181	−	0.319011i
$966$		0			0
$967$	−25.3908	+	43.9782i	−0.816513	+	1.41424i	0.0917230	+	0.995785i	$0.470763\pi$
$967$	−25.3908	+	43.9782i	−0.816513	+	1.41424i	−0.908236	+	0.418458i	$0.862571\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.23027	−	15.9873i	0.296214	−	0.513057i	−0.679053	−	0.734089i	$-0.737609\pi$
$971$	9.23027	−	15.9873i	0.296214	−	0.513057i	0.975266	+	0.221032i	$0.0709427\pi$
$972$		0			0
$973$	−5.81721	+	18.3614i	−0.186491	+	0.588639i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−31.6302			−1.01194			−0.505970	−	0.862551i	$-0.668865\pi$
$977$	−31.6302			−1.01194			−0.505970	+	0.862551i	$0.668865\pi$
$978$		0			0
$979$	2.91061	+	5.04132i	0.0930234	+	0.161121i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	20.2066	−	34.9988i	0.644490	−	1.11629i	−0.339929	−	0.940451i	$-0.610403\pi$
$983$	20.2066	−	34.9988i	0.644490	−	1.11629i	0.984419	−	0.175838i	$-0.0562635\pi$
$984$		0			0
$985$	−6.26940	−	10.8589i	−0.199760	−	0.345994i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.242806	−	0.420553i	0.00772079	−	0.0133728i
$990$		0			0
$991$	16.6187	+	28.7845i	0.527911	+	0.914368i	0.999471	+	0.0325343i	$0.0103578\pi$
$991$	16.6187	+	28.7845i	0.527911	+	0.914368i	−0.471560	+	0.881834i	$0.656309\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11.8280	+	20.4867i	−0.374973	+	0.649473i
$996$		0			0
$997$	20.5592	−	35.6096i	0.651117	−	1.12777i	−0.331735	−	0.943373i	$-0.607634\pi$
$997$	20.5592	−	35.6096i	0.651117	−	1.12777i	0.982852	−	0.184396i	$-0.0590328\pi$
$998$		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.793.8		22
3.2	odd	2		504.2.q.c.121.5	yes	22
4.3	odd	2		3024.2.q.l.2305.8		22
7.4	even	3		1512.2.t.c.361.4		22
9.2	odd	6		504.2.t.c.457.11	yes	22
9.7	even	3		1512.2.t.c.289.4		22
12.11	even	2		1008.2.q.l.625.7		22
21.11	odd	6		504.2.t.c.193.11	yes	22
28.11	odd	6		3024.2.t.k.1873.4		22
36.7	odd	6		3024.2.t.k.289.4		22
36.11	even	6		1008.2.t.l.961.1		22
63.11	odd	6		504.2.q.c.25.5	✓	22
63.25	even	3	inner	1512.2.q.d.1369.8		22
84.11	even	6		1008.2.t.l.193.1		22
252.11	even	6		1008.2.q.l.529.7		22
252.151	odd	6		3024.2.q.l.2881.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.5	✓	22	63.11	odd	6
504.2.q.c.121.5	yes	22	3.2	odd	2
504.2.t.c.193.11	yes	22	21.11	odd	6
504.2.t.c.457.11	yes	22	9.2	odd	6
1008.2.q.l.529.7		22	252.11	even	6
1008.2.q.l.625.7		22	12.11	even	2
1008.2.t.l.193.1		22	84.11	even	6
1008.2.t.l.961.1		22	36.11	even	6
1512.2.q.d.793.8		22	1.1	even	1	trivial
1512.2.q.d.1369.8		22	63.25	even	3	inner
1512.2.t.c.289.4		22	9.7	even	3
1512.2.t.c.361.4		22	7.4	even	3
3024.2.q.l.2305.8		22	4.3	odd	2
3024.2.q.l.2881.8		22	252.151	odd	6
3024.2.t.k.289.4		22	36.7	odd	6
3024.2.t.k.1873.4		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)

\(f(q)\)	\(=\)	\(q+(1.05220 + 1.82246i) q^{5} +(2.58382 - 0.569079i) q^{7} +O(q^{10})\)	\(q+(1.05220 + 1.82246i) q^{5} +(2.58382 - 0.569079i) q^{7} +(0.199532 - 0.345600i) q^{11} +(1.44292 - 2.49921i) q^{13} +(0.176596 + 0.305873i) q^{17} +(2.84888 - 4.93440i) q^{19} +(-0.438682 - 0.759820i) q^{23} +(0.285756 - 0.494945i) q^{25} +(-0.874997 - 1.51554i) q^{29} +9.13490 q^{31} +(3.75582 + 4.11014i) q^{35} +(-3.39555 + 5.88127i) q^{37} +(-1.20377 + 2.08499i) q^{41} +(0.276745 + 0.479336i) q^{43} -11.7372 q^{47} +(6.35230 - 2.94080i) q^{49} +(2.07821 + 3.59956i) q^{53} +0.839790 q^{55} +9.32421 q^{59} -10.0720 q^{61} +6.07296 q^{65} +1.20241 q^{67} +14.6826 q^{71} +(0.315636 + 0.546697i) q^{73} +(0.318883 - 1.00652i) q^{77} -2.48729 q^{79} +(4.59366 + 7.95645i) q^{83} +(-0.371628 + 0.643678i) q^{85} +(-7.29358 + 12.6328i) q^{89} +(2.30601 - 7.27866i) q^{91} +11.9903 q^{95} +(-7.84245 - 13.5835i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} + 5 q^{7}+O(q^{10}) \) 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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