LMFDB - Embedded newform 1512.2.q.d.1369.7

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			1369.7
Character	$\chi$	$=$	1512.1369
Dual form			1512.2.q.d.793.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.263002 - 0.455533i) q^{5} +(-0.333150 - 2.62469i) q^{7} +O(q^{10})$	$q+(0.263002 - 0.455533i) q^{5} +(-0.333150 - 2.62469i) q^{7} +(2.30526 + 3.99283i) q^{11} +(0.244554 + 0.423580i) q^{13} +(-2.75579 + 4.77318i) q^{17} +(1.83782 + 3.18319i) q^{19} +(-0.0269769 + 0.0467253i) q^{23} +(2.36166 + 4.09051i) q^{25} +(3.28471 - 5.68929i) q^{29} +6.07640 q^{31} +(-1.28325 - 0.538539i) q^{35} +(0.223731 + 0.387513i) q^{37} +(-2.52284 - 4.36968i) q^{41} +(2.84893 - 4.93449i) q^{43} +9.19621 q^{47} +(-6.77802 + 1.74883i) q^{49} +(4.37138 - 7.57145i) q^{53} +2.42515 q^{55} +6.63076 q^{59} -0.465625 q^{61} +0.257273 q^{65} +5.19358 q^{67} -1.76328 q^{71} +(-5.23776 + 9.07207i) q^{73} +(9.71195 - 7.38081i) q^{77} +16.3702 q^{79} +(-4.49251 + 7.78126i) q^{83} +(1.44956 + 2.51071i) q^{85} +(7.05145 + 12.2135i) q^{89} +(1.03029 - 0.782994i) q^{91} +1.93340 q^{95} +(5.22413 - 9.04847i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.263002	−	0.455533i	0.117618	−	0.203721i	−0.801205	−	0.598390i	$-0.795807\pi$
$5$	0.263002	−	0.455533i	0.117618	−	0.203721i	0.918823	+	0.394669i	$0.129141\pi$
$6$		0			0
$7$	−0.333150	−	2.62469i	−0.125919	−	0.992041i
$7$	−0.333150	−	2.62469i	−0.125919	−	0.992041i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.30526	+	3.99283i	0.695062	+	1.20388i	0.970160	+	0.242466i	$0.0779564\pi$
$11$	2.30526	+	3.99283i	0.695062	+	1.20388i	−0.275098	+	0.961416i	$0.588710\pi$
$12$		0			0
$13$	0.244554	+	0.423580i	0.0678270	+	0.117480i	0.897945	−	0.440109i	$-0.145060\pi$
$13$	0.244554	+	0.423580i	0.0678270	+	0.117480i	−0.830118	+	0.557588i	$0.811727\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.75579	+	4.77318i	−0.668378	+	1.15767i	0.309979	+	0.950743i	$0.399678\pi$
$17$	−2.75579	+	4.77318i	−0.668378	+	1.15767i	−0.978357	+	0.206922i	$0.933655\pi$
$18$		0			0
$19$	1.83782	+	3.18319i	0.421624	+	0.730274i	0.996099	−	0.0882484i	$-0.0281269\pi$
$19$	1.83782	+	3.18319i	0.421624	+	0.730274i	−0.574475	+	0.818522i	$0.694794\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.0269769	+	0.0467253i	−0.00562506	+	0.00974289i	−0.868824	−	0.495121i	$-0.835124\pi$
$23$	−0.0269769	+	0.0467253i	−0.00562506	+	0.00974289i	0.863199	+	0.504864i	$0.168457\pi$
$24$		0			0
$25$	2.36166	+	4.09051i	0.472332	+	0.818103i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.28471	−	5.68929i	0.609956	−	1.05647i	−0.381292	−	0.924455i	$-0.624521\pi$
$29$	3.28471	−	5.68929i	0.609956	−	1.05647i	0.991247	−	0.132019i	$-0.0421461\pi$
$30$		0			0
$31$	6.07640			1.09135			0.545676	−	0.837996i	$-0.316273\pi$
$31$	6.07640			1.09135			0.545676	+	0.837996i	$0.316273\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.28325	−	0.538539i	−0.216909	−	0.0910297i
$36$		0			0
$37$	0.223731	+	0.387513i	0.0367811	+	0.0637068i	0.883830	−	0.467808i	$-0.154956\pi$
$37$	0.223731	+	0.387513i	0.0367811	+	0.0637068i	−0.847049	+	0.531515i	$0.821623\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.52284	−	4.36968i	−0.394001	−	0.682430i	0.598972	−	0.800770i	$-0.295576\pi$
$41$	−2.52284	−	4.36968i	−0.394001	−	0.682430i	−0.992973	+	0.118340i	$0.962243\pi$
$42$		0			0
$43$	2.84893	−	4.93449i	0.434458	−	0.752503i	−0.562794	−	0.826598i	$-0.690273\pi$
$43$	2.84893	−	4.93449i	0.434458	−	0.752503i	0.997251	+	0.0740947i	$0.0236067\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.19621			1.34140			0.670702	−	0.741726i	$-0.265993\pi$
$47$	9.19621			1.34140			0.670702	+	0.741726i	$0.265993\pi$
$48$		0			0
$49$	−6.77802	+	1.74883i	−0.968289	+	0.249833i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.37138	−	7.57145i	0.600455	−	1.04002i	−0.392297	−	0.919839i	$-0.628320\pi$
$53$	4.37138	−	7.57145i	0.600455	−	1.04002i	0.992752	−	0.120180i	$-0.0383471\pi$
$54$		0			0
$55$	2.42515			0.327008
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.63076			0.863252			0.431626	−	0.902053i	$-0.357940\pi$
$59$	6.63076			0.863252			0.431626	+	0.902053i	$0.357940\pi$
$60$		0			0
$61$	−0.465625			−0.0596171			−0.0298086	−	0.999556i	$-0.509490\pi$
$61$	−0.465625			−0.0596171			−0.0298086	+	0.999556i	$0.509490\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.257273			0.0319108
$66$		0			0
$67$	5.19358			0.634496			0.317248	−	0.948343i	$-0.397241\pi$
$67$	5.19358			0.634496			0.317248	+	0.948343i	$0.397241\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.76328			−0.209263			−0.104632	−	0.994511i	$-0.533366\pi$
$71$	−1.76328			−0.209263			−0.104632	+	0.994511i	$0.533366\pi$
$72$		0			0
$73$	−5.23776	+	9.07207i	−0.613034	+	1.06181i	0.377692	+	0.925931i	$0.376718\pi$
$73$	−5.23776	+	9.07207i	−0.613034	+	1.06181i	−0.990726	+	0.135875i	$0.956616\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.71195	−	7.38081i	1.10678	−	0.841121i
$78$		0			0
$79$	16.3702			1.84179			0.920895	−	0.389812i	$-0.127460\pi$
$79$	16.3702			1.84179			0.920895	+	0.389812i	$0.127460\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.49251	+	7.78126i	−0.493117	+	0.854104i	−0.999969	−	0.00792925i	$-0.997476\pi$
$83$	−4.49251	+	7.78126i	−0.493117	+	0.854104i	0.506851	+	0.862034i	$0.330809\pi$
$84$		0			0
$85$	1.44956	+	2.51071i	0.157227	+	0.272325i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.05145	+	12.2135i	0.747452	+	1.29463i	0.949040	+	0.315155i	$0.102056\pi$
$89$	7.05145	+	12.2135i	0.747452	+	1.29463i	−0.201588	+	0.979470i	$0.564610\pi$
$90$		0			0
$91$	1.03029	−	0.782994i	0.108004	−	0.0820801i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.93340			0.198363
$96$		0			0
$97$	5.22413	−	9.04847i	0.530430	−	0.918732i	−0.468939	−	0.883230i	$-0.655364\pi$
$97$	5.22413	−	9.04847i	0.530430	−	0.918732i	0.999370	−	0.0355020i	$-0.0113030\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.98254	−	8.63001i	−0.495781	−	0.858718i	0.504207	−	0.863583i	$-0.331785\pi$
$101$	−4.98254	−	8.63001i	−0.495781	−	0.858718i	−0.999988	+	0.00486475i	$0.998451\pi$
$102$		0			0
$103$	−5.82553	+	10.0901i	−0.574006	+	0.994208i	0.422143	+	0.906529i	$0.361278\pi$
$103$	−5.82553	+	10.0901i	−0.574006	+	0.994208i	−0.996149	+	0.0876783i	$0.972055\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.45556	−	4.25316i	−0.237388	−	0.411168i	0.722576	−	0.691292i	$-0.242958\pi$
$107$	−2.45556	−	4.25316i	−0.237388	−	0.411168i	−0.959964	+	0.280123i	$0.909625\pi$
$108$		0			0
$109$	−9.76353	+	16.9109i	−0.935177	+	1.61977i	−0.160858	+	0.986978i	$0.551426\pi$
$109$	−9.76353	+	16.9109i	−0.935177	+	1.61977i	−0.774319	+	0.632796i	$0.781907\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.48658	−	9.50304i	−0.516134	−	0.893971i	−0.999825	−	0.0187317i	$-0.994037\pi$
$113$	−5.48658	−	9.50304i	−0.516134	−	0.893971i	0.483690	−	0.875239i	$-0.339296\pi$
$114$		0			0
$115$	0.0141899	+	0.0245777i	0.00132322	+	0.00229188i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	13.4462	+	5.64293i	1.23261	+	0.517287i
$120$		0			0
$121$	−5.12844	+	8.88272i	−0.466222	+	0.807520i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.11451			0.457456
$126$		0			0
$127$	−16.6107			−1.47396			−0.736979	−	0.675915i	$-0.763748\pi$
$127$	−16.6107			−1.47396			−0.736979	+	0.675915i	$0.763748\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.90848	−	5.03763i	0.254115	−	0.440140i	−0.710540	−	0.703657i	$-0.751549\pi$
$131$	2.90848	−	5.03763i	0.254115	−	0.440140i	0.964655	+	0.263517i	$0.0848825\pi$
$132$		0			0
$133$	7.74263	−	5.88418i	0.671371	−	0.510223i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.61313	−	7.99017i	−0.394126	−	0.682647i	0.598863	−	0.800852i	$-0.295619\pi$
$137$	−4.61313	−	7.99017i	−0.394126	−	0.682647i	−0.992989	+	0.118205i	$0.962286\pi$
$138$		0			0
$139$	6.88477	+	11.9248i	0.583959	+	1.01145i	0.995004	+	0.0998314i	$0.0318303\pi$
$139$	6.88477	+	11.9248i	0.583959	+	1.01145i	−0.411046	+	0.911615i	$0.634836\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.12752	+	1.95292i	−0.0942880	+	0.163312i
$144$		0			0
$145$	−1.72777	−	2.99259i	−0.143484	−	0.248521i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.15043	+	7.18875i	−0.340016	+	0.588926i	−0.984435	−	0.175747i	$-0.943766\pi$
$149$	−4.15043	+	7.18875i	−0.340016	+	0.588926i	0.644419	+	0.764673i	$0.277099\pi$
$150$		0			0
$151$	7.24894	+	12.5555i	0.589911	+	1.02176i	0.994244	+	0.107143i	$0.0341704\pi$
$151$	7.24894	+	12.5555i	0.589911	+	1.02176i	−0.404333	+	0.914612i	$0.632496\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.59811	−	2.76800i	0.128363	−	0.222331i
$156$		0			0
$157$	−12.4887			−0.996705			−0.498352	−	0.866975i	$-0.666061\pi$
$157$	−12.4887			−0.996705			−0.498352	+	0.866975i	$0.666061\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.131627	+	0.0552394i	0.0103736	+	0.00435348i
$162$		0			0
$163$	−2.48448	−	4.30325i	−0.194600	−	0.337057i	0.752169	−	0.658970i	$-0.229007\pi$
$163$	−2.48448	−	4.30325i	−0.194600	−	0.337057i	−0.946769	+	0.321913i	$0.895674\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.0088	+	17.3357i	0.774504	+	1.34148i	0.935073	+	0.354456i	$0.115334\pi$
$167$	10.0088	+	17.3357i	0.774504	+	1.34148i	−0.160569	+	0.987025i	$0.551333\pi$
$168$		0			0
$169$	6.38039	−	11.0512i	0.490799	−	0.850089i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.05485			−0.688427			−0.344214	−	0.938891i	$-0.611854\pi$
$173$	−9.05485			−0.688427			−0.344214	+	0.938891i	$0.611854\pi$
$174$		0			0
$175$	9.94956	−	7.56138i	0.752116	−	0.571587i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.69175	−	13.3225i	0.574908	−	0.995770i	−0.421143	−	0.906994i	$-0.638371\pi$
$179$	7.69175	−	13.3225i	0.574908	−	0.995770i	0.996052	−	0.0887763i	$-0.0282956\pi$
$180$		0			0
$181$	−9.54973			−0.709826			−0.354913	−	0.934899i	$-0.615489\pi$
$181$	−9.54973			−0.709826			−0.354913	+	0.934899i	$0.615489\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.235367			0.0173045
$186$		0			0
$187$	−25.4113			−1.85826
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.0433			0.799063			0.399531	−	0.916720i	$-0.369173\pi$
$191$	11.0433			0.799063			0.399531	+	0.916720i	$0.369173\pi$
$192$		0			0
$193$	26.6991			1.92185			0.960923	−	0.276817i	$-0.0892796\pi$
$193$	26.6991			1.92185			0.960923	+	0.276817i	$0.0892796\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.8386			−0.914715			−0.457357	−	0.889283i	$-0.651204\pi$
$197$	−12.8386			−0.914715			−0.457357	+	0.889283i	$0.651204\pi$
$198$		0			0
$199$	10.1408	−	17.5644i	0.718864	−	1.24511i	−0.242586	−	0.970130i	$-0.577996\pi$
$199$	10.1408	−	17.5644i	0.718864	−	1.24511i	0.961450	−	0.274979i	$-0.0886710\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−16.0269	−	6.72597i	−1.12487	−	0.472071i
$204$		0			0
$205$	−2.65405			−0.185367
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.47329	+	14.6762i	−0.586109	+	1.01517i
$210$		0			0
$211$	4.77903	+	8.27752i	0.329002	+	0.569848i	0.982314	−	0.187241i	$-0.0599545\pi$
$211$	4.77903	+	8.27752i	0.329002	+	0.569848i	−0.653312	+	0.757088i	$0.726621\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.49855	−	2.59556i	−0.102200	−	0.177016i
$216$		0			0
$217$	−2.02435	−	15.9487i	−0.137422	−	1.08267i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.69576			−0.181337
$222$		0			0
$223$	11.9155	−	20.6383i	0.797921	−	1.38204i	−0.123046	−	0.992401i	$-0.539266\pi$
$223$	11.9155	−	20.6383i	0.797921	−	1.38204i	0.920968	−	0.389639i	$-0.127400\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.33567	−	2.31345i	−0.0886514	−	0.153549i	0.818290	−	0.574806i	$-0.194922\pi$
$227$	−1.33567	−	2.31345i	−0.0886514	−	0.153549i	−0.906941	+	0.421257i	$0.861589\pi$
$228$		0			0
$229$	−3.16258	+	5.47775i	−0.208989	+	0.361980i	−0.951396	−	0.307969i	$-0.900351\pi$
$229$	−3.16258	+	5.47775i	−0.208989	+	0.361980i	0.742407	+	0.669949i	$0.233684\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.63381	−	8.02600i	−0.303571	−	0.525801i	0.673371	−	0.739305i	$-0.264846\pi$
$233$	−4.63381	−	8.02600i	−0.303571	−	0.525801i	−0.976942	+	0.213504i	$0.931512\pi$
$234$		0			0
$235$	2.41862	−	4.18918i	0.157774	−	0.273272i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.69219	−	2.93096i	−0.109459	−	0.189588i	0.806092	−	0.591790i	$-0.201578\pi$
$239$	−1.69219	−	2.93096i	−0.109459	−	0.189588i	−0.915551	+	0.402202i	$0.868245\pi$
$240$		0			0
$241$	−6.57982	−	11.3966i	−0.423844	−	0.734119i	0.572468	−	0.819927i	$-0.305986\pi$
$241$	−6.57982	−	11.3966i	−0.423844	−	0.734119i	−0.996312	+	0.0858082i	$0.972653\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.985984	+	3.54756i	−0.0629922	+	0.226645i
$246$		0			0
$247$	−0.898890	+	1.55692i	−0.0571950	+	0.0990647i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.30235			0.145323			0.0726614	−	0.997357i	$-0.476851\pi$
$251$	2.30235			0.145323			0.0726614	+	0.997357i	$0.476851\pi$
$252$		0			0
$253$	−0.248755			−0.0156391
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.5661	+	25.2293i	−0.908610	+	1.57376i	−0.0926132	+	0.995702i	$0.529522\pi$
$257$	−14.5661	+	25.2293i	−0.908610	+	1.57376i	−0.815997	+	0.578056i	$0.803811\pi$
$258$		0			0
$259$	0.942567	−	0.716324i	0.0585683	−	0.0445102i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.35919	−	2.35418i	−0.0838110	−	0.145165i	0.821073	−	0.570823i	$-0.193376\pi$
$263$	−1.35919	−	2.35418i	−0.0838110	−	0.145165i	−0.904884	+	0.425658i	$0.860043\pi$
$264$		0			0
$265$	−2.29936	−	3.98261i	−0.141249	−	0.244650i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.80840	+	4.86428i	−0.171231	+	0.296581i	−0.938850	−	0.344325i	$-0.888108\pi$
$269$	−2.80840	+	4.86428i	−0.171231	+	0.296581i	0.767620	+	0.640906i	$0.221441\pi$
$270$		0			0
$271$	−7.25164	−	12.5602i	−0.440506	−	0.762978i	0.557221	−	0.830364i	$-0.311867\pi$
$271$	−7.25164	−	12.5602i	−0.440506	−	0.762978i	−0.997727	+	0.0673860i	$0.978534\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.8885	+	18.8594i	−0.656600	+	1.13726i
$276$		0			0
$277$	0.873953	+	1.51373i	0.0525108	+	0.0909513i	0.891086	−	0.453835i	$-0.149944\pi$
$277$	0.873953	+	1.51373i	0.0525108	+	0.0909513i	−0.838575	+	0.544786i	$0.816611\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.35657	+	9.27786i	−0.319546	+	0.553471i	−0.980393	−	0.197050i	$-0.936864\pi$
$281$	−5.35657	+	9.27786i	−0.319546	+	0.553471i	0.660847	+	0.750521i	$0.270197\pi$
$282$		0			0
$283$	−12.5967			−0.748793			−0.374397	−	0.927269i	$-0.622150\pi$
$283$	−12.5967			−0.748793			−0.374397	+	0.927269i	$0.622150\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.6286	+	8.07743i	−0.627386	+	0.476796i
$288$		0			0
$289$	−6.68881	−	11.5854i	−0.393459	−	0.681491i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.57575	+	2.72928i	0.0920562	+	0.159446i	0.908376	−	0.418154i	$-0.137323\pi$
$293$	1.57575	+	2.72928i	0.0920562	+	0.159446i	−0.816320	+	0.577600i	$0.803989\pi$
$294$		0			0
$295$	1.74391	−	3.02053i	0.101534	−	0.175862i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.0263892			−0.00152613
$300$		0			0
$301$	−13.9006	−	5.83364i	−0.801220	−	0.336245i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.122460	+	0.212107i	−0.00701206	+	0.0121452i
$306$		0			0
$307$	−20.3884			−1.16363			−0.581813	−	0.813322i	$-0.697657\pi$
$307$	−20.3884			−1.16363			−0.581813	+	0.813322i	$0.697657\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−22.7014			−1.28728			−0.643640	−	0.765328i	$-0.722577\pi$
$311$	−22.7014			−1.28728			−0.643640	+	0.765328i	$0.722577\pi$
$312$		0			0
$313$	−16.7078			−0.944380			−0.472190	−	0.881497i	$-0.656536\pi$
$313$	−16.7078			−0.944380			−0.472190	+	0.881497i	$0.656536\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.3280			−0.580080			−0.290040	−	0.957015i	$-0.593669\pi$
$317$	−10.3280			−0.580080			−0.290040	+	0.957015i	$0.593669\pi$
$318$		0			0
$319$	30.2884			1.69583
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−20.2586			−1.12722
$324$		0			0
$325$	−1.15511	+	2.00070i	−0.0640738	+	0.110979i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.06371	−	24.1372i	−0.168908	−	1.33073i
$330$		0			0
$331$	−22.6315			−1.24394			−0.621970	−	0.783041i	$-0.713668\pi$
$331$	−22.6315			−1.24394			−0.621970	+	0.783041i	$0.713668\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.36592	−	2.36585i	0.0746283	−	0.129260i
$336$		0			0
$337$	6.78253	+	11.7477i	0.369468	+	0.639938i	0.989482	−	0.144653i	$-0.0462066\pi$
$337$	6.78253	+	11.7477i	0.369468	+	0.639938i	−0.620014	+	0.784590i	$0.712873\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	14.0077	+	24.2620i	0.758558	+	1.31386i
$342$		0			0
$343$	6.84824	+	17.2076i	0.369770	+	0.929123i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	33.0262			1.77294			0.886470	−	0.462786i	$-0.153150\pi$
$347$	33.0262			1.77294			0.886470	+	0.462786i	$0.153150\pi$
$348$		0			0
$349$	−10.1773	+	17.6276i	−0.544778	+	0.943584i	0.453842	+	0.891082i	$0.350053\pi$
$349$	−10.1773	+	17.6276i	−0.544778	+	0.943584i	−0.998621	+	0.0525019i	$0.983280\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.75381	−	4.76975i	−0.146571	−	0.253868i	0.783387	−	0.621534i	$-0.213490\pi$
$353$	−2.75381	−	4.76975i	−0.146571	−	0.253868i	−0.929958	+	0.367666i	$0.880157\pi$
$354$		0			0
$355$	−0.463748	+	0.803234i	−0.0246132	+	0.0426312i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.4656	+	18.1270i	0.552354	+	0.956704i	0.998104	+	0.0615472i	$0.0196035\pi$
$359$	10.4656	+	18.1270i	0.552354	+	0.956704i	−0.445751	+	0.895157i	$0.647063\pi$
$360$		0			0
$361$	2.74486	−	4.75424i	0.144467	−	0.250223i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.75509	+	4.77195i	0.144208	+	0.249775i
$366$		0			0
$367$	−2.14319	−	3.71211i	−0.111873	−	0.193770i	0.804652	−	0.593746i	$-0.202352\pi$
$367$	−2.14319	−	3.71211i	−0.111873	−	0.193770i	−0.916526	+	0.399976i	$0.869018\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−21.3290	−	8.95110i	−1.10735	−	0.464718i
$372$		0			0
$373$	5.64461	−	9.77675i	0.292267	−	0.506221i	−0.682079	−	0.731279i	$-0.738924\pi$
$373$	5.64461	−	9.77675i	0.292267	−	0.506221i	0.974345	+	0.225058i	$0.0722571\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.21316			0.165486
$378$		0			0
$379$	−20.5828			−1.05727			−0.528634	−	0.848850i	$-0.677295\pi$
$379$	−20.5828			−1.05727			−0.528634	+	0.848850i	$0.677295\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.8108	+	18.7248i	−0.552405	+	0.956793i	0.445696	+	0.895184i	$0.352956\pi$
$383$	−10.8108	+	18.7248i	−0.552405	+	0.956793i	−0.998100	+	0.0616083i	$0.980377\pi$
$384$		0			0
$385$	−0.807939	−	6.36528i	−0.0411764	−	0.324405i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.34241	−	12.7174i	−0.372275	−	0.644799i	0.617640	−	0.786461i	$-0.288089\pi$
$389$	−7.34241	−	12.7174i	−0.372275	−	0.644799i	−0.989915	+	0.141662i	$0.954755\pi$
$390$		0			0
$391$	−0.148685	−	0.257531i	−0.00751934	−	0.0130239i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.30539	−	7.45716i	0.216628	−	0.375210i
$396$		0			0
$397$	−3.13424	−	5.42866i	−0.157303	−	0.272457i	0.776592	−	0.630003i	$-0.216947\pi$
$397$	−3.13424	−	5.42866i	−0.157303	−	0.272457i	−0.933895	+	0.357547i	$0.883613\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.6951	−	25.4526i	0.733836	−	1.27104i	−0.221396	−	0.975184i	$-0.571061\pi$
$401$	14.6951	−	25.4526i	0.733836	−	1.27104i	0.955232	−	0.295857i	$-0.0956052\pi$
$402$		0			0
$403$	1.48601	+	2.57384i	0.0740232	+	0.128212i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.03152	+	1.78664i	−0.0511303	+	0.0885603i
$408$		0			0
$409$	−1.63285			−0.0807392			−0.0403696	−	0.999185i	$-0.512854\pi$
$409$	−1.63285			−0.0807392			−0.0403696	+	0.999185i	$0.512854\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.20904	−	17.4037i	−0.108700	−	0.856381i
$414$		0			0
$415$	2.36308	+	4.09298i	0.115999	+	0.200916i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	9.01823	+	15.6200i	0.440569	+	0.763088i	0.997732	−	0.0673151i	$-0.0214433\pi$
$419$	9.01823	+	15.6200i	0.440569	+	0.763088i	−0.557162	+	0.830404i	$0.688110\pi$
$420$		0			0
$421$	16.8278	−	29.1465i	0.820135	−	1.42052i	−0.0854466	−	0.996343i	$-0.527232\pi$
$421$	16.8278	−	29.1465i	0.820135	−	1.42052i	0.905581	−	0.424172i	$-0.139435\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−26.0330			−1.26279
$426$		0			0
$427$	0.155123	+	1.22212i	0.00750691	+	0.0591426i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.1545	−	19.3202i	0.537295	−	0.930622i	−0.461754	−	0.887008i	$-0.652780\pi$
$431$	11.1545	−	19.3202i	0.537295	−	0.930622i	0.999048	−	0.0436135i	$-0.0138870\pi$
$432$		0			0
$433$	7.32414			0.351976			0.175988	−	0.984392i	$-0.443688\pi$
$433$	7.32414			0.351976			0.175988	+	0.984392i	$0.443688\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.198314			−0.00948664
$438$		0			0
$439$	−24.6728			−1.17757			−0.588785	−	0.808289i	$-0.700394\pi$
$439$	−24.6728			−1.17757			−0.588785	+	0.808289i	$0.700394\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−30.5363			−1.45082			−0.725412	−	0.688315i	$-0.758351\pi$
$443$	−30.5363			−1.45082			−0.725412	+	0.688315i	$0.758351\pi$
$444$		0			0
$445$	7.41819			0.351656
$446$		0			0
$447$		0			0
$448$		0			0
$449$	41.4782			1.95748			0.978738	−	0.205116i	$-0.0657572\pi$
$449$	41.4782			1.95748			0.978738	+	0.205116i	$0.0657572\pi$
$450$		0			0
$451$	11.6316	−	20.1465i	0.547710	−	0.948662i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0857103	−	0.675262i	−0.00401816	−	0.0316568i
$456$		0			0
$457$	−11.6289			−0.543978			−0.271989	−	0.962300i	$-0.587681\pi$
$457$	−11.6289			−0.543978			−0.271989	+	0.962300i	$0.587681\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.60886	−	9.71483i	0.261231	−	0.452465i	−0.705339	−	0.708871i	$-0.749205\pi$
$461$	5.60886	−	9.71483i	0.261231	−	0.452465i	0.966569	+	0.256406i	$0.0825383\pi$
$462$		0			0
$463$	−19.9362	−	34.5305i	−0.926514	−	1.60477i	−0.789108	−	0.614254i	$-0.789457\pi$
$463$	−19.9362	−	34.5305i	−0.926514	−	1.60477i	−0.137405	−	0.990515i	$-0.543876\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.7818	−	20.4067i	−0.545198	−	0.944311i	−0.998594	−	0.0530016i	$-0.983121\pi$
$467$	−11.7818	−	20.4067i	−0.545198	−	0.944311i	0.453397	−	0.891309i	$-0.350212\pi$
$468$		0			0
$469$	−1.73024	−	13.6315i	−0.0798950	−	0.629446i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	26.2701			1.20790
$474$		0			0
$475$	−8.68059	+	15.0352i	−0.398293	+	0.689864i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.11485	+	12.3233i	0.325086	+	0.563065i	0.981530	−	0.191310i	$-0.0612735\pi$
$479$	7.11485	+	12.3233i	0.325086	+	0.563065i	−0.656444	+	0.754375i	$0.727940\pi$
$480$		0			0
$481$	−0.109428	+	0.189536i	−0.00498951	+	0.00864208i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.74792	−	4.75953i	−0.124776	−	0.216119i
$486$		0			0
$487$	−13.9818	+	24.2171i	−0.633574	+	1.09738i	0.353242	+	0.935532i	$0.385079\pi$
$487$	−13.9818	+	24.2171i	−0.633574	+	1.09738i	−0.986815	+	0.161850i	$0.948254\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.2543	−	29.8853i	−0.778676	−	1.34871i	−0.932705	−	0.360639i	$-0.882558\pi$
$491$	−17.2543	−	29.8853i	−0.778676	−	1.34871i	0.154030	−	0.988066i	$-0.450775\pi$
$492$		0			0
$493$	18.1040	+	31.3570i	0.815362	+	1.41225i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.587437	+	4.62808i	0.0263502	+	0.207598i
$498$		0			0
$499$	−13.1436	+	22.7654i	−0.588390	+	1.01912i	0.406054	+	0.913849i	$0.366905\pi$
$499$	−13.1436	+	22.7654i	−0.588390	+	1.01912i	−0.994443	+	0.105272i	$0.966429\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.09068			−0.271570			−0.135785	−	0.990738i	$-0.543356\pi$
$503$	−6.09068			−0.271570			−0.135785	+	0.990738i	$0.543356\pi$
$504$		0			0
$505$	−5.24167			−0.233251
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.08615	+	7.07742i	−0.181116	+	0.313701i	−0.942261	−	0.334880i	$-0.891304\pi$
$509$	−4.08615	+	7.07742i	−0.181116	+	0.313701i	0.761145	+	0.648582i	$0.224637\pi$
$510$		0			0
$511$	25.5564	+	10.7252i	1.13055	+	0.474453i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.06425	+	5.30744i	0.135027	+	0.233874i
$516$		0			0
$517$	21.1996	+	36.7189i	0.932360	+	1.61489i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.0485	+	22.6007i	−0.571666	+	0.990155i	0.424729	+	0.905321i	$0.360370\pi$
$521$	−13.0485	+	22.6007i	−0.571666	+	0.990155i	−0.996395	+	0.0848346i	$0.972964\pi$
$522$		0			0
$523$	13.6655	+	23.6694i	0.597553	+	1.03499i	0.993181	+	0.116581i	$0.0371935\pi$
$523$	13.6655	+	23.6694i	0.597553	+	1.03499i	−0.395628	+	0.918411i	$0.629473\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−16.7453	+	29.0037i	−0.729437	+	1.26342i
$528$		0			0
$529$	11.4985	+	19.9161i	0.499937	+	0.865916i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.23394	−	2.13725i	0.0534478	−	0.0925744i
$534$		0			0
$535$	−2.58327			−0.111685
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−22.6079	−	23.0320i	−0.973790	−	0.992057i
$540$		0			0
$541$	−5.79086	−	10.0301i	−0.248969	−	0.431226i	0.714271	−	0.699869i	$-0.246758\pi$
$541$	−5.79086	−	10.0301i	−0.248969	−	0.431226i	−0.963240	+	0.268643i	$0.913425\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.13566	+	8.89522i	0.219987	+	0.381029i
$546$		0			0
$547$	20.3651	−	35.2734i	0.870750	−	1.50818i	0.00952755	−	0.999955i	$-0.496967\pi$
$547$	20.3651	−	35.2734i	0.870750	−	1.50818i	0.861222	−	0.508228i	$-0.169699\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	24.1468			1.02869
$552$		0			0
$553$	−5.45372	−	42.9667i	−0.231916	−	1.82713i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−10.0085	+	17.3353i	−0.424075	+	0.734520i	−0.996334	−	0.0855533i	$-0.972734\pi$
$557$	−10.0085	+	17.3353i	−0.424075	+	0.734520i	0.572258	+	0.820074i	$0.306068\pi$
$558$		0			0
$559$	2.78687			0.117872
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−24.9328			−1.05079			−0.525396	−	0.850858i	$-0.676083\pi$
$563$	−24.9328			−1.05079			−0.525396	+	0.850858i	$0.676083\pi$
$564$		0			0
$565$	−5.77193			−0.242827
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.80025			0.410848			0.205424	−	0.978673i	$-0.434143\pi$
$569$	9.80025			0.410848			0.205424	+	0.978673i	$0.434143\pi$
$570$		0			0
$571$	−40.7895			−1.70699			−0.853494	−	0.521103i	$-0.825521\pi$
$571$	−40.7895			−1.70699			−0.853494	+	0.521103i	$0.825521\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.254841			−0.0106276
$576$		0			0
$577$	−10.2505	+	17.7544i	−0.426734	+	0.739125i	−0.996581	−	0.0826259i	$-0.973669\pi$
$577$	−10.2505	+	17.7544i	−0.426734	+	0.739125i	0.569846	+	0.821751i	$0.307003\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	21.9201	+	9.19914i	0.909399	+	0.381645i
$582$		0			0
$583$	40.3086			1.66941
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.2916	−	33.4141i	0.796251	−	1.37915i	−0.125791	−	0.992057i	$-0.540147\pi$
$587$	19.2916	−	33.4141i	0.796251	−	1.37915i	0.922042	−	0.387090i	$-0.126520\pi$
$588$		0			0
$589$	11.1673	+	19.3423i	0.460141	+	0.796987i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.26539	+	2.19172i	0.0519634	+	0.0900032i	0.890837	−	0.454323i	$-0.150119\pi$
$593$	1.26539	+	2.19172i	0.0519634	+	0.0900032i	−0.838874	+	0.544326i	$0.816785\pi$
$594$		0			0
$595$	6.10693	−	4.64109i	0.250360	−	0.190266i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	16.0218			0.654634			0.327317	−	0.944915i	$-0.393855\pi$
$599$	16.0218			0.654634			0.327317	+	0.944915i	$0.393855\pi$
$600$		0			0
$601$	−22.1601	+	38.3824i	−0.903929	+	1.56565i	−0.0815796	+	0.996667i	$0.525996\pi$
$601$	−22.1601	+	38.3824i	−0.903929	+	1.56565i	−0.822349	+	0.568983i	$0.807337\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.69758	+	4.67235i	0.109672	+	0.189958i
$606$		0			0
$607$	4.79607	−	8.30704i	0.194666	−	0.337172i	−0.752125	−	0.659021i	$-0.770971\pi$
$607$	4.79607	−	8.30704i	0.194666	−	0.337172i	0.946791	+	0.321849i	$0.104304\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.24897	+	3.89533i	0.0909835	+	0.157588i
$612$		0			0
$613$	11.2371	−	19.4632i	0.453861	−	0.786110i	−0.544761	−	0.838591i	$-0.683380\pi$
$613$	11.2371	−	19.4632i	0.453861	−	0.786110i	0.998622	+	0.0524815i	$0.0167131\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.7056	−	20.2746i	−0.471248	−	0.816226i	0.528211	−	0.849113i	$-0.322863\pi$
$617$	−11.7056	−	20.2746i	−0.471248	−	0.816226i	−0.999459	+	0.0328875i	$0.989530\pi$
$618$		0			0
$619$	−7.98843	−	13.8364i	−0.321082	−	0.556131i	0.659629	−	0.751591i	$-0.270713\pi$
$619$	−7.98843	−	13.8364i	−0.321082	−	0.556131i	−0.980712	+	0.195460i	$0.937380\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	29.7074	−	22.5768i	1.19020	−	0.904521i
$624$		0			0
$625$	−10.4632	+	18.1227i	−0.418527	+	0.724910i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.46622			−0.0983348
$630$		0			0
$631$	−0.882517			−0.0351324			−0.0175662	−	0.999846i	$-0.505592\pi$
$631$	−0.882517			−0.0351324			−0.0175662	+	0.999846i	$0.505592\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.36864	+	7.56671i	−0.173364	+	0.300276i
$636$		0			0
$637$	−2.39836	−	2.44335i	−0.0950265	−	0.0968090i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.2141	+	35.0118i	0.798408	+	1.38288i	0.920652	+	0.390384i	$0.127658\pi$
$641$	20.2141	+	35.0118i	0.798408	+	1.38288i	−0.122244	+	0.992500i	$0.539009\pi$
$642$		0			0
$643$	2.99047	+	5.17964i	0.117932	+	0.204265i	0.918948	−	0.394378i	$-0.129040\pi$
$643$	2.99047	+	5.17964i	0.117932	+	0.204265i	−0.801016	+	0.598643i	$0.795707\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.4743	−	28.5343i	0.647672	−	1.12180i	−0.336005	−	0.941860i	$-0.609076\pi$
$647$	16.4743	−	28.5343i	0.647672	−	1.12180i	0.983677	−	0.179941i	$-0.0575906\pi$
$648$		0			0
$649$	15.2856	+	26.4755i	0.600014	+	1.03925i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.0166	−	22.5455i	0.509380	−	0.882272i	−0.490561	−	0.871407i	$-0.663208\pi$
$653$	13.0166	−	22.5455i	0.509380	−	0.882272i	0.999941	−	0.0108653i	$-0.00345861\pi$
$654$		0			0
$655$	−1.52987	−	2.64982i	−0.0597771	−	0.103537i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.91651	+	8.51565i	−0.191520	+	0.331722i	−0.945754	−	0.324883i	$-0.894675\pi$
$659$	−4.91651	+	8.51565i	−0.191520	+	0.331722i	0.754234	+	0.656606i	$0.228008\pi$
$660$		0			0
$661$	−5.51520			−0.214516			−0.107258	−	0.994231i	$-0.534207\pi$
$661$	−5.51520			−0.214516			−0.107258	+	0.994231i	$0.534207\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.644111	−	5.07458i	−0.0249776	−	0.196784i
$666$		0			0
$667$	0.177222	+	0.306958i	0.00686208	+	0.0118855i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.07339	−	1.85916i	−0.0414376	−	0.0717720i
$672$		0			0
$673$	19.6176	−	33.9788i	0.756205	−	1.30978i	−0.188569	−	0.982060i	$-0.560385\pi$
$673$	19.6176	−	33.9788i	0.756205	−	1.30978i	0.944773	−	0.327725i	$-0.106282\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	37.1632			1.42830			0.714149	−	0.699994i	$-0.246814\pi$
$677$	37.1632			1.42830			0.714149	+	0.699994i	$0.246814\pi$
$678$		0			0
$679$	−25.4899	−	10.6973i	−0.978211	−	0.410523i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	5.10586	−	8.84360i	0.195370	−	0.338391i	−0.751652	−	0.659560i	$-0.770743\pi$
$683$	5.10586	−	8.84360i	0.195370	−	0.338391i	0.947022	+	0.321169i	$0.104076\pi$
$684$		0			0
$685$	−4.85305			−0.185426
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.27615			0.162908
$690$		0			0
$691$	−35.0761			−1.33436			−0.667179	−	0.744897i	$-0.732499\pi$
$691$	−35.0761			−1.33436			−0.667179	+	0.744897i	$0.732499\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.24284			0.274737
$696$		0			0
$697$	27.8097			1.05337
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−17.2500			−0.651522			−0.325761	−	0.945452i	$-0.605621\pi$
$701$	−17.2500			−0.651522			−0.325761	+	0.945452i	$0.605621\pi$
$702$		0			0
$703$	−0.822352	+	1.42436i	−0.0310156	+	0.0537206i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−20.9912	+	15.9527i	−0.789455	+	0.599964i
$708$		0			0
$709$	−14.5147			−0.545110			−0.272555	−	0.962140i	$-0.587869\pi$
$709$	−14.5147			−0.545110			−0.272555	+	0.962140i	$0.587869\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.163922	+	0.283921i	−0.00613893	+	0.0106329i
$714$		0			0
$715$	0.593081	+	1.02725i	0.0221800	+	0.0384168i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	22.4295	+	38.8491i	0.836480	+	1.44883i	0.892820	+	0.450414i	$0.148723\pi$
$719$	22.4295	+	38.8491i	0.836480	+	1.44883i	−0.0563403	+	0.998412i	$0.517943\pi$
$720$		0			0
$721$	28.4242	+	11.9287i	1.05857	+	0.444248i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	31.0295			1.15241
$726$		0			0
$727$	−2.22039	+	3.84582i	−0.0823496	+	0.142634i	−0.904259	−	0.426985i	$-0.859576\pi$
$727$	−2.22039	+	3.84582i	−0.0823496	+	0.142634i	0.821909	+	0.569619i	$0.192909\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.7021	+	27.1969i	0.580764	+	1.00591i
$732$		0			0
$733$	19.1360	−	33.1445i	0.706803	−	1.22422i	−0.259233	−	0.965815i	$-0.583470\pi$
$733$	19.1360	−	33.1445i	0.706803	−	1.22422i	0.966037	−	0.258405i	$-0.0831968\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.9725	+	20.7370i	0.441014	+	0.763859i
$738$		0			0
$739$	−2.59381	+	4.49261i	−0.0954148	+	0.165263i	−0.909782	−	0.415087i	$-0.863751\pi$
$739$	−2.59381	+	4.49261i	−0.0954148	+	0.165263i	0.814367	+	0.580350i	$0.197084\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.3351	−	28.2932i	−0.599276	−	1.03798i	−0.992928	−	0.118716i	$-0.962122\pi$
$743$	−16.3351	−	28.2932i	−0.599276	−	1.03798i	0.393653	−	0.919259i	$-0.371211\pi$
$744$		0			0
$745$	2.18314	+	3.78132i	0.0799842	+	0.138537i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.3452	+	7.86203i	−0.378004	+	0.287272i
$750$		0			0
$751$	8.06106	−	13.9622i	0.294152	−	0.509487i	−0.680635	−	0.732623i	$-0.738296\pi$
$751$	8.06106	−	13.9622i	0.294152	−	0.509487i	0.974787	+	0.223136i	$0.0716294\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.62595			0.277537
$756$		0			0
$757$	45.6421			1.65889			0.829444	−	0.558589i	$-0.188657\pi$
$757$	45.6421			1.65889			0.829444	+	0.558589i	$0.188657\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.11500	−	10.5915i	0.221669	−	0.383942i	−0.733646	−	0.679532i	$-0.762183\pi$
$761$	6.11500	−	10.5915i	0.221669	−	0.383942i	0.955315	+	0.295590i	$0.0955163\pi$
$762$		0			0
$763$	47.6387	+	19.9924i	1.72464	+	0.723773i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.62158	+	2.80866i	0.0585518	+	0.101415i
$768$		0			0
$769$	3.17344	+	5.49656i	0.114437	+	0.198211i	0.917555	−	0.397610i	$-0.130160\pi$
$769$	3.17344	+	5.49656i	0.114437	+	0.198211i	−0.803117	+	0.595821i	$0.796827\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−24.4515	+	42.3512i	−0.879459	+	1.52327i	−0.0275225	+	0.999621i	$0.508762\pi$
$773$	−24.4515	+	42.3512i	−0.879459	+	1.52327i	−0.851936	+	0.523646i	$0.824572\pi$
$774$		0			0
$775$	14.3504	+	24.8556i	0.515481	+	0.892839i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	9.27302	−	16.0613i	0.332240	−	0.575457i
$780$		0			0
$781$	−4.06483	−	7.04049i	−0.145451	−	0.251928i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.28455	+	5.68900i	−0.117231	+	0.203049i
$786$		0			0
$787$	−23.1498			−0.825201			−0.412600	−	0.910912i	$-0.635379\pi$
$787$	−23.1498			−0.825201			−0.412600	+	0.910912i	$0.635379\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−23.1147	+	17.5665i	−0.821864	+	0.624594i
$792$		0			0
$793$	−0.113870	−	0.197229i	−0.00404365	−	0.00700381i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−24.2284	−	41.9648i	−0.858214	−	1.48647i	−0.873631	−	0.486589i	$-0.838241\pi$
$797$	−24.2284	−	41.9648i	−0.858214	−	1.48647i	0.0154170	−	0.999881i	$-0.495092\pi$
$798$		0			0
$799$	−25.3429	+	43.8951i	−0.896566	+	1.55290i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−48.2976			−1.70439
$804$		0			0
$805$	0.0597815	−	0.0454323i	0.00210702	−	0.00160128i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.2647	−	17.7791i	0.360889	−	0.625078i	−0.627218	−	0.778844i	$-0.715807\pi$
$809$	10.2647	−	17.7791i	0.360889	−	0.625078i	0.988107	+	0.153765i	$0.0491399\pi$
$810$		0			0
$811$	27.7882			0.975776			0.487888	−	0.872906i	$-0.337767\pi$
$811$	27.7882			0.975776			0.487888	+	0.872906i	$0.337767\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.61370			−0.0915539
$816$		0			0
$817$	20.9432			0.732711
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.5586			0.577901			0.288950	−	0.957344i	$-0.406694\pi$
$821$	16.5586			0.577901			0.288950	+	0.957344i	$0.406694\pi$
$822$		0			0
$823$	25.4704			0.887843			0.443922	−	0.896066i	$-0.353587\pi$
$823$	25.4704			0.887843			0.443922	+	0.896066i	$0.353587\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−36.0798			−1.25462			−0.627309	−	0.778771i	$-0.715844\pi$
$827$	−36.0798			−1.25462			−0.627309	+	0.778771i	$0.715844\pi$
$828$		0			0
$829$	22.3539	−	38.7180i	0.776381	−	1.34473i	−0.157633	−	0.987498i	$-0.550386\pi$
$829$	22.3539	−	38.7180i	0.776381	−	1.34473i	0.934015	−	0.357234i	$-0.116280\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	10.3314	−	37.1721i	0.357960	−	1.28794i
$834$		0			0
$835$	10.5293			0.364383
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7.86805	−	13.6279i	0.271635	−	0.470486i	−0.697645	−	0.716443i	$-0.745769\pi$
$839$	7.86805	−	13.6279i	0.271635	−	0.470486i	0.969281	+	0.245957i	$0.0791022\pi$
$840$		0			0
$841$	−7.07866	−	12.2606i	−0.244092	−	0.422779i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.35611	−	5.81296i	−0.115454	−	0.199972i
$846$		0			0
$847$	25.0230	+	10.5013i	0.859799	+	0.360829i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.0241422			−0.000827584
$852$		0			0
$853$	14.2010	−	24.5968i	0.486231	−	0.842177i	−0.513643	−	0.858004i	$-0.671705\pi$
$853$	14.2010	−	24.5968i	0.486231	−	0.842177i	0.999875	+	0.0158264i	$0.00503792\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.48867	−	7.77461i	−0.153330	−	0.265575i	0.779120	−	0.626875i	$-0.215666\pi$
$857$	−4.48867	−	7.77461i	−0.153330	−	0.265575i	−0.932450	+	0.361300i	$0.882333\pi$
$858$		0			0
$859$	0.471450	−	0.816575i	0.0160857	−	0.0278612i	−0.857871	−	0.513866i	$-0.828213\pi$
$859$	0.471450	−	0.816575i	0.0160857	−	0.0278612i	0.873956	+	0.486005i	$0.161546\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	13.0488	+	22.6011i	0.444185	+	0.769351i	0.997995	−	0.0632920i	$-0.0201600\pi$
$863$	13.0488	+	22.6011i	0.444185	+	0.769351i	−0.553810	+	0.832643i	$0.686827\pi$
$864$		0			0
$865$	−2.38145	+	4.12478i	−0.0809716	+	0.140247i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	37.7375	+	65.3633i	1.28016	+	2.21730i
$870$		0			0
$871$	1.27011	+	2.19989i	0.0430360	+	0.0745405i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.70390	−	13.4240i	−0.0576022	−	0.453814i
$876$		0			0
$877$	13.1794	−	22.8275i	0.445038	−	0.770829i	−0.553017	−	0.833170i	$-0.686523\pi$
$877$	13.1794	−	22.8275i	0.445038	−	0.770829i	0.998055	+	0.0623413i	$0.0198567\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	45.6077			1.53656			0.768281	−	0.640113i	$-0.221112\pi$
$881$	45.6077			1.53656			0.768281	+	0.640113i	$0.221112\pi$
$882$		0			0
$883$	−26.1575			−0.880271			−0.440136	−	0.897931i	$-0.645070\pi$
$883$	−26.1575			−0.880271			−0.440136	+	0.897931i	$0.645070\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.5963	−	32.2097i	0.624401	−	1.08149i	−0.364255	−	0.931299i	$-0.618676\pi$
$887$	18.5963	−	32.2097i	0.624401	−	1.08149i	0.988656	−	0.150196i	$-0.0479904\pi$
$888$		0			0
$889$	5.53384	+	43.5979i	0.185599	+	1.46223i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	16.9009	+	29.2733i	0.565568	+	0.979593i
$894$		0			0
$895$	−4.04589	−	7.00769i	−0.135239	−	0.234241i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	19.9592	−	34.5704i	0.665677	−	1.15299i
$900$		0			0
$901$	24.0932	+	41.7307i	0.802662	+	1.39025i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.51160	+	4.35022i	−0.0834884	+	0.144606i
$906$		0			0
$907$	−12.9231	−	22.3834i	−0.429103	−	0.743229i	0.567691	−	0.823242i	$-0.307837\pi$
$907$	−12.9231	−	22.3834i	−0.429103	−	0.743229i	−0.996794	+	0.0800134i	$0.974504\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	2.41211	−	4.17790i	0.0799169	−	0.138420i	−0.823297	−	0.567611i	$-0.807868\pi$
$911$	2.41211	−	4.17790i	0.0799169	−	0.138420i	0.903214	+	0.429191i	$0.141201\pi$
$912$		0			0
$913$	−41.4256			−1.37099
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−14.1912	−	5.95558i	−0.468635	−	0.196670i
$918$		0			0
$919$	9.58183	+	16.5962i	0.316075	+	0.547459i	0.979666	−	0.200638i	$-0.0643014\pi$
$919$	9.58183	+	16.5962i	0.316075	+	0.547459i	−0.663590	+	0.748096i	$0.730968\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.431218	−	0.746891i	−0.0141937	−	0.0245842i
$924$		0			0
$925$	−1.05675	+	1.83035i	−0.0347458	+	0.0601815i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−54.0914			−1.77468			−0.887340	−	0.461115i	$-0.847450\pi$
$929$	−54.0914			−1.77468			−0.887340	+	0.461115i	$0.847450\pi$
$930$		0			0
$931$	−18.0236	−	18.3617i	−0.590700	−	0.601781i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.68322	+	11.5757i	−0.218565	+	0.378565i
$936$		0			0
$937$	−16.6345			−0.543426			−0.271713	−	0.962378i	$-0.587590\pi$
$937$	−16.6345			−0.543426			−0.271713	+	0.962378i	$0.587590\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.89912			0.0945085			0.0472543	−	0.998883i	$-0.484953\pi$
$941$	2.89912			0.0945085			0.0472543	+	0.998883i	$0.484953\pi$
$942$		0			0
$943$	0.272233			0.00886512
$944$		0			0
$945$		0			0
$946$		0			0
$947$	57.7311			1.87601			0.938004	−	0.346625i	$-0.112672\pi$
$947$	57.7311			1.87601			0.938004	+	0.346625i	$0.112672\pi$
$948$		0			0
$949$	−5.12366			−0.166321
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−20.4070			−0.661046			−0.330523	−	0.943798i	$-0.607225\pi$
$953$	−20.4070			−0.661046			−0.330523	+	0.943798i	$0.607225\pi$
$954$		0			0
$955$	2.90440	−	5.03057i	0.0939843	−	0.162786i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−19.4349	+	14.7700i	−0.627585	+	0.476947i
$960$		0			0
$961$	5.92259			0.191051
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7.02193	−	12.1623i	0.226044	−	0.391519i
$966$		0			0
$967$	4.26365	+	7.38486i	0.137110	+	0.237481i	0.926401	−	0.376537i	$-0.122885\pi$
$967$	4.26365	+	7.38486i	0.137110	+	0.237481i	−0.789292	+	0.614019i	$0.789552\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.42651	−	16.3272i	−0.302511	−	0.523965i	0.674193	−	0.738555i	$-0.264492\pi$
$971$	−9.42651	−	16.3272i	−0.302511	−	0.523965i	−0.976704	+	0.214590i	$0.931158\pi$
$972$		0			0
$973$	29.0052	−	22.0431i	0.929864	−	0.706671i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.611299			−0.0195572			−0.00977859	−	0.999952i	$-0.503113\pi$
$977$	−0.611299			−0.0195572			−0.00977859	+	0.999952i	$0.503113\pi$
$978$		0			0
$979$	−32.5108	+	56.3104i	−1.03905	+	1.79969i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−3.62584	−	6.28013i	−0.115646	−	0.200305i	0.802392	−	0.596798i	$-0.203561\pi$
$983$	−3.62584	−	6.28013i	−0.115646	−	0.200305i	−0.918038	+	0.396493i	$0.870227\pi$
$984$		0			0
$985$	−3.37659	+	5.84842i	−0.107587	+	0.186346i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.153710	+	0.266234i	0.00488770	+	0.00846575i
$990$		0			0
$991$	−2.49266	+	4.31741i	−0.0791819	+	0.137147i	−0.902897	−	0.429857i	$-0.858564\pi$
$991$	−2.49266	+	4.31741i	−0.0791819	+	0.137147i	0.823715	+	0.567004i	$0.191897\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.33412	−	9.23896i	−0.169103	−	0.292895i
$996$		0			0
$997$	1.59172	+	2.75694i	0.0504104	+	0.0873133i	0.890130	−	0.455708i	$-0.150614\pi$
$997$	1.59172	+	2.75694i	0.0504104	+	0.0873133i	−0.839719	+	0.543021i	$0.817280\pi$
$998$		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.1369.7		22
3.2	odd	2		504.2.q.c.25.10	✓	22
4.3	odd	2		3024.2.q.l.2881.7		22
7.2	even	3		1512.2.t.c.289.5		22
9.4	even	3		1512.2.t.c.361.5		22
9.5	odd	6		504.2.t.c.193.6	yes	22
12.11	even	2		1008.2.q.l.529.2		22
21.2	odd	6		504.2.t.c.457.6	yes	22
28.23	odd	6		3024.2.t.k.289.5		22
36.23	even	6		1008.2.t.l.193.6		22
36.31	odd	6		3024.2.t.k.1873.5		22
63.23	odd	6		504.2.q.c.121.10	yes	22
63.58	even	3	inner	1512.2.q.d.793.7		22
84.23	even	6		1008.2.t.l.961.6		22
252.23	even	6		1008.2.q.l.625.2		22
252.247	odd	6		3024.2.q.l.2305.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.10	✓	22	3.2	odd	2
504.2.q.c.121.10	yes	22	63.23	odd	6
504.2.t.c.193.6	yes	22	9.5	odd	6
504.2.t.c.457.6	yes	22	21.2	odd	6
1008.2.q.l.529.2		22	12.11	even	2
1008.2.q.l.625.2		22	252.23	even	6
1008.2.t.l.193.6		22	36.23	even	6
1008.2.t.l.961.6		22	84.23	even	6
1512.2.q.d.793.7		22	63.58	even	3	inner
1512.2.q.d.1369.7		22	1.1	even	1	trivial
1512.2.t.c.289.5		22	7.2	even	3
1512.2.t.c.361.5		22	9.4	even	3
3024.2.q.l.2305.7		22	252.247	odd	6
3024.2.q.l.2881.7		22	4.3	odd	2
3024.2.t.k.289.5		22	28.23	odd	6
3024.2.t.k.1873.5		22	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.263002 - 0.455533i) q^{5} +(-0.333150 - 2.62469i) q^{7} +O(q^{10})\)	\(q+(0.263002 - 0.455533i) q^{5} +(-0.333150 - 2.62469i) q^{7} +(2.30526 + 3.99283i) q^{11} +(0.244554 + 0.423580i) q^{13} +(-2.75579 + 4.77318i) q^{17} +(1.83782 + 3.18319i) q^{19} +(-0.0269769 + 0.0467253i) q^{23} +(2.36166 + 4.09051i) q^{25} +(3.28471 - 5.68929i) q^{29} +6.07640 q^{31} +(-1.28325 - 0.538539i) q^{35} +(0.223731 + 0.387513i) q^{37} +(-2.52284 - 4.36968i) q^{41} +(2.84893 - 4.93449i) q^{43} +9.19621 q^{47} +(-6.77802 + 1.74883i) q^{49} +(4.37138 - 7.57145i) q^{53} +2.42515 q^{55} +6.63076 q^{59} -0.465625 q^{61} +0.257273 q^{65} +5.19358 q^{67} -1.76328 q^{71} +(-5.23776 + 9.07207i) q^{73} +(9.71195 - 7.38081i) q^{77} +16.3702 q^{79} +(-4.49251 + 7.78126i) q^{83} +(1.44956 + 2.51071i) q^{85} +(7.05145 + 12.2135i) q^{89} +(1.03029 - 0.782994i) q^{91} +1.93340 q^{95} +(5.22413 - 9.04847i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} + 5 q^{7}+O(q^{10}) \) 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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