LMFDB - Embedded newform 3024.2.t.l.1873.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(289,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3024.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
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			1873.10
Character	$\chi$	$=$	3024.1873
Dual form			3024.2.t.l.289.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.43592 q^{5} +(1.83889 + 1.90223i) q^{7} +O(q^{10})$	$q+3.43592 q^{5} +(1.83889 + 1.90223i) q^{7} +4.40938 q^{11} +(1.49401 - 2.58771i) q^{13} +(-0.542270 + 0.939239i) q^{17} +(3.74273 + 6.48261i) q^{19} -4.32558 q^{23} +6.80552 q^{25} +(-1.68485 - 2.91825i) q^{29} +(4.68734 + 8.11872i) q^{31} +(6.31828 + 6.53590i) q^{35} +(-2.50767 - 4.34341i) q^{37} +(1.20160 - 2.08122i) q^{41} +(-3.31412 - 5.74023i) q^{43} +(-1.50415 + 2.60527i) q^{47} +(-0.236948 + 6.99599i) q^{49} +(0.530699 - 0.919198i) q^{53} +15.1502 q^{55} +(-6.20470 - 10.7468i) q^{59} +(2.71334 - 4.69965i) q^{61} +(5.13331 - 8.89115i) q^{65} +(1.66999 + 2.89251i) q^{67} -12.9064 q^{71} +(-8.21382 + 14.2267i) q^{73} +(8.10837 + 8.38764i) q^{77} +(-1.17516 + 2.03543i) q^{79} +(-1.60602 - 2.78171i) q^{83} +(-1.86319 + 3.22715i) q^{85} +(-5.67524 - 9.82981i) q^{89} +(7.66974 - 1.91656i) q^{91} +(12.8597 + 22.2737i) q^{95} +(-6.40321 - 11.0907i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{5} - 7 q^{7}+O(q^{10}) $ 22 * q + 6 * q^5 - 7 * q^7	$ 22 q + 6 q^{5} - 7 q^{7} + 6 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} - 4 q^{23} + 20 q^{25} - 9 q^{29} + 4 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} + 5 q^{47} - 15 q^{49} - 11 q^{53} - 22 q^{55} - 19 q^{59} - 13 q^{61} - 13 q^{65} - 26 q^{67} - 48 q^{71} - 35 q^{73} + 4 q^{77} - 10 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} + 12 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q + 6 * q^5 - 7 * q^7 + 6 * q^11 - 3 * q^13 - 7 * q^17 + q^19 - 4 * q^23 + 20 * q^25 - 9 * q^29 + 4 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 + 5 * q^47 - 15 * q^49 - 11 * q^53 - 22 * q^55 - 19 * q^59 - 13 * q^61 - 13 * q^65 - 26 * q^67 - 48 * q^71 - 35 * q^73 + 4 * q^77 - 10 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 + 12 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	3.43592			1.53659			0.768294	−	0.640097i	$-0.221106\pi$
$5$	3.43592			1.53659			0.768294	+	0.640097i	$0.221106\pi$
$6$		0			0
$7$	1.83889	+	1.90223i	0.695036	+	0.718975i
$7$	1.83889	+	1.90223i	0.695036	+	0.718975i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.40938			1.32948			0.664739	−	0.747076i	$-0.268543\pi$
$11$	4.40938			1.32948			0.664739	+	0.747076i	$0.268543\pi$
$12$		0			0
$13$	1.49401	−	2.58771i	0.414365	−	0.717701i	−0.580997	−	0.813906i	$-0.697337\pi$
$13$	1.49401	−	2.58771i	0.414365	−	0.717701i	0.995362	+	0.0962048i	$0.0306704\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.542270	+	0.939239i	−0.131520	+	0.227799i	−0.924263	−	0.381757i	$-0.875319\pi$
$17$	−0.542270	+	0.939239i	−0.131520	+	0.227799i	0.792743	+	0.609556i	$0.208652\pi$
$18$		0			0
$19$	3.74273	+	6.48261i	0.858642	+	1.48721i	0.873225	+	0.487318i	$0.162025\pi$
$19$	3.74273	+	6.48261i	0.858642	+	1.48721i	−0.0145824	+	0.999894i	$0.504642\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.32558			−0.901945			−0.450972	−	0.892538i	$-0.648923\pi$
$23$	−4.32558			−0.901945			−0.450972	+	0.892538i	$0.648923\pi$
$24$		0			0
$25$	6.80552			1.36110
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.68485	−	2.91825i	−0.312870	−	0.541906i	0.666113	−	0.745851i	$-0.267957\pi$
$29$	−1.68485	−	2.91825i	−0.312870	−	0.541906i	−0.978982	+	0.203945i	$0.934624\pi$
$30$		0			0
$31$	4.68734	+	8.11872i	0.841872	+	1.45816i	0.888311	+	0.459243i	$0.151879\pi$
$31$	4.68734	+	8.11872i	0.841872	+	1.45816i	−0.0464389	+	0.998921i	$0.514787\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.31828	+	6.53590i	1.06798	+	1.10477i
$36$		0			0
$37$	−2.50767	−	4.34341i	−0.412258	−	0.714052i	0.582878	−	0.812559i	$-0.301926\pi$
$37$	−2.50767	−	4.34341i	−0.412258	−	0.714052i	−0.995136	+	0.0985079i	$0.968593\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.20160	−	2.08122i	0.187658	−	0.325033i	−0.756811	−	0.653634i	$-0.773244\pi$
$41$	1.20160	−	2.08122i	0.187658	−	0.325033i	0.944469	+	0.328601i	$0.106577\pi$
$42$		0			0
$43$	−3.31412	−	5.74023i	−0.505399	−	0.875377i	−0.999980	−	0.00624563i	$-0.998012\pi$
$43$	−3.31412	−	5.74023i	−0.505399	−	0.875377i	0.494581	−	0.869131i	$-0.335321\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.50415	+	2.60527i	−0.219403	+	0.380018i	−0.954626	−	0.297808i	$-0.903744\pi$
$47$	−1.50415	+	2.60527i	−0.219403	+	0.380018i	0.735222	+	0.677826i	$0.237078\pi$
$48$		0			0
$49$	−0.236948	+	6.99599i	−0.0338498	+	0.999427i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.530699	−	0.919198i	0.0728971	−	0.126262i	−0.827273	−	0.561801i	$-0.810109\pi$
$53$	0.530699	−	0.919198i	0.0728971	−	0.126262i	0.900170	+	0.435539i	$0.143442\pi$
$54$		0			0
$55$	15.1502			2.04286
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.20470	−	10.7468i	−0.807783	−	1.39912i	−0.914396	−	0.404820i	$-0.867334\pi$
$59$	−6.20470	−	10.7468i	−0.807783	−	1.39912i	0.106614	−	0.994301i	$-0.465999\pi$
$60$		0			0
$61$	2.71334	−	4.69965i	0.347408	−	0.601728i	−0.638380	−	0.769721i	$-0.720395\pi$
$61$	2.71334	−	4.69965i	0.347408	−	0.601728i	0.985788	+	0.167993i	$0.0537286\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.13331	−	8.89115i	0.636708	−	1.10281i
$66$		0			0
$67$	1.66999	+	2.89251i	0.204022	+	0.353376i	0.949821	−	0.312795i	$-0.101265\pi$
$67$	1.66999	+	2.89251i	0.204022	+	0.353376i	−0.745799	+	0.666171i	$0.767932\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−12.9064			−1.53171			−0.765857	−	0.643011i	$-0.777685\pi$
$71$	−12.9064			−1.53171			−0.765857	+	0.643011i	$0.777685\pi$
$72$		0			0
$73$	−8.21382	+	14.2267i	−0.961355	+	1.66511i	−0.242249	+	0.970214i	$0.577885\pi$
$73$	−8.21382	+	14.2267i	−0.961355	+	1.66511i	−0.719106	+	0.694901i	$0.755448\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.10837	+	8.38764i	0.924035	+	0.955861i
$78$		0			0
$79$	−1.17516	+	2.03543i	−0.132216	+	0.229004i	−0.924530	−	0.381108i	$-0.875542\pi$
$79$	−1.17516	+	2.03543i	−0.132216	+	0.229004i	0.792315	+	0.610113i	$0.208876\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.60602	−	2.78171i	−0.176283	−	0.305332i	0.764321	−	0.644836i	$-0.223074\pi$
$83$	−1.60602	−	2.78171i	−0.176283	−	0.305332i	−0.940605	+	0.339504i	$0.889741\pi$
$84$		0			0
$85$	−1.86319	+	3.22715i	−0.202092	+	0.350033i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.67524	−	9.82981i	−0.601575	−	1.04196i	−0.992583	−	0.121570i	$-0.961207\pi$
$89$	−5.67524	−	9.82981i	−0.601575	−	1.04196i	0.391008	−	0.920387i	$-0.372126\pi$
$90$		0			0
$91$	7.66974	−	1.91656i	0.804008	−	0.200910i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	12.8597	+	22.2737i	1.31938	+	2.28523i
$96$		0			0
$97$	−6.40321	−	11.0907i	−0.650148	−	1.12609i	−0.983087	−	0.183140i	$-0.941374\pi$
$97$	−6.40321	−	11.0907i	−0.650148	−	1.12609i	0.332939	−	0.942948i	$-0.391960\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.776221			0.0772369			0.0386184	−	0.999254i	$-0.487704\pi$
$101$	0.776221			0.0772369			0.0386184	+	0.999254i	$0.487704\pi$
$102$		0			0
$103$	−2.28262			−0.224913			−0.112457	−	0.993657i	$-0.535872\pi$
$103$	−2.28262			−0.224913			−0.112457	+	0.993657i	$0.535872\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.27468	−	3.93986i	−0.219901	−	0.380880i	0.734876	−	0.678201i	$-0.237240\pi$
$107$	−2.27468	−	3.93986i	−0.219901	−	0.380880i	−0.954778	+	0.297321i	$0.903907\pi$
$108$		0			0
$109$	2.36710	−	4.09994i	0.226727	−	0.392703i	−0.730109	−	0.683331i	$-0.760531\pi$
$109$	2.36710	−	4.09994i	0.226727	−	0.392703i	0.956836	+	0.290627i	$0.0938640\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.175367	+	0.303745i	−0.0164972	+	0.0285740i	−0.874156	−	0.485645i	$-0.838585\pi$
$113$	−0.175367	+	0.303745i	−0.0164972	+	0.0285740i	0.857659	+	0.514219i	$0.171918\pi$
$114$		0			0
$115$	−14.8623			−1.38592
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.78382	+	0.695638i	−0.255193	+	0.0637691i
$120$		0			0
$121$	8.44261			0.767510
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.20360			0.554867
$126$		0			0
$127$	−12.4175			−1.10187			−0.550935	−	0.834548i	$-0.685729\pi$
$127$	−12.4175			−1.10187			−0.550935	+	0.834548i	$0.685729\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	15.7430			1.37548			0.687738	−	0.725959i	$-0.258604\pi$
$131$	15.7430			1.37548			0.687738	+	0.725959i	$0.258604\pi$
$132$		0			0
$133$	−5.44891	+	19.0404i	−0.472481	+	1.65101i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.23020			0.361410			0.180705	−	0.983537i	$-0.442162\pi$
$137$	4.23020			0.361410			0.180705	+	0.983537i	$0.442162\pi$
$138$		0			0
$139$	−9.80367	+	16.9805i	−0.831537	+	1.44026i	0.0652824	+	0.997867i	$0.479205\pi$
$139$	−9.80367	+	16.9805i	−0.831537	+	1.44026i	−0.896819	+	0.442397i	$0.854128\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.58767	−	11.4102i	0.550889	−	0.954167i
$144$		0			0
$145$	−5.78902	−	10.0269i	−0.480752	−	0.832686i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.72651			0.796827			0.398414	−	0.917206i	$-0.369561\pi$
$149$	9.72651			0.796827			0.398414	+	0.917206i	$0.369561\pi$
$150$		0			0
$151$	9.82148			0.799261			0.399630	−	0.916676i	$-0.369138\pi$
$151$	9.82148			0.799261			0.399630	+	0.916676i	$0.369138\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	16.1053	+	27.8952i	1.29361	+	2.24060i
$156$		0			0
$157$	6.02041	+	10.4277i	0.480481	+	0.832218i	0.999749	−	0.0223936i	$-0.00712870\pi$
$157$	6.02041	+	10.4277i	0.480481	+	0.832218i	−0.519268	+	0.854611i	$0.673795\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−7.95427	−	8.22824i	−0.626884	−	0.648476i
$162$		0			0
$163$	−0.885601	−	1.53391i	−0.0693656	−	0.120145i	0.829257	−	0.558868i	$-0.188764\pi$
$163$	−0.885601	−	1.53391i	−0.0693656	−	0.120145i	−0.898622	+	0.438723i	$0.855431\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.86350	+	13.6200i	−0.608496	+	1.05395i	0.382993	+	0.923751i	$0.374893\pi$
$167$	−7.86350	+	13.6200i	−0.608496	+	1.05395i	−0.991489	+	0.130194i	$0.958440\pi$
$168$		0			0
$169$	2.03584	+	3.52618i	0.156603	+	0.271245i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.40313	−	16.2867i	0.714907	−	1.23825i	−0.248089	−	0.968737i	$-0.579802\pi$
$173$	9.40313	−	16.2867i	0.714907	−	1.23825i	0.962996	−	0.269517i	$-0.0868642\pi$
$174$		0			0
$175$	12.5146	+	12.9456i	0.946016	+	0.978599i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.34201	−	5.78853i	0.249794	−	0.432655i	−0.713675	−	0.700477i	$-0.752971\pi$
$179$	3.34201	−	5.78853i	0.249794	−	0.432655i	0.963468	+	0.267822i	$0.0863039\pi$
$180$		0			0
$181$	4.73726			0.352117			0.176059	−	0.984380i	$-0.443665\pi$
$181$	4.73726			0.352117			0.176059	+	0.984380i	$0.443665\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8.61613	−	14.9236i	−0.633471	−	1.09720i
$186$		0			0
$187$	−2.39107	+	4.14146i	−0.174853	+	0.302853i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.5347	−	19.9786i	0.834618	−	1.44560i	−0.0597224	−	0.998215i	$-0.519022\pi$
$191$	11.5347	−	19.9786i	0.834618	−	1.44560i	0.894341	−	0.447386i	$-0.147645\pi$
$192$		0			0
$193$	−9.15352	−	15.8544i	−0.658885	−	1.14122i	−0.980905	−	0.194489i	$-0.937695\pi$
$193$	−9.15352	−	15.8544i	−0.658885	−	1.14122i	0.322020	−	0.946733i	$-0.395638\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.5866			−1.03925			−0.519625	−	0.854395i	$-0.673928\pi$
$197$	−14.5866			−1.03925			−0.519625	+	0.854395i	$0.673928\pi$
$198$		0			0
$199$	0.912102	−	1.57981i	0.0646572	−	0.111990i	−0.831885	−	0.554949i	$-0.812738\pi$
$199$	0.912102	−	1.57981i	0.0646572	−	0.111990i	0.896542	+	0.442959i	$0.146071\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.45292	−	8.57133i	0.172161	−	0.601590i
$204$		0			0
$205$	4.12858	−	7.15091i	0.288352	−	0.499441i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	16.5031	+	28.5843i	1.14155	+	1.97721i
$210$		0			0
$211$	2.77359	−	4.80400i	0.190942	−	0.330721i	−0.754621	−	0.656161i	$-0.772179\pi$
$211$	2.77359	−	4.80400i	0.190942	−	0.330721i	0.945563	+	0.325440i	$0.105512\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−11.3870	−	19.7229i	−0.776590	−	1.34509i
$216$		0			0
$217$	−6.82413	+	23.8458i	−0.463252	+	1.61876i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.62032	+	2.80647i	0.108994	+	0.188784i
$222$		0			0
$223$	−6.01726	−	10.4222i	−0.402946	−	0.697922i	0.591134	−	0.806573i	$-0.298680\pi$
$223$	−6.01726	−	10.4222i	−0.402946	−	0.697922i	−0.994080	+	0.108651i	$0.965347\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.1567			−0.873240			−0.436620	−	0.899646i	$-0.643825\pi$
$227$	−13.1567			−0.873240			−0.436620	+	0.899646i	$0.643825\pi$
$228$		0			0
$229$	12.4832			0.824912			0.412456	−	0.910978i	$-0.364671\pi$
$229$	12.4832			0.824912			0.412456	+	0.910978i	$0.364671\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.01687	+	3.49332i	0.132130	+	0.228855i	0.924497	−	0.381189i	$-0.124485\pi$
$233$	2.01687	+	3.49332i	0.132130	+	0.228855i	−0.792368	+	0.610044i	$0.791152\pi$
$234$		0			0
$235$	−5.16814	+	8.95149i	−0.337133	+	0.583931i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	13.8679	−	24.0200i	0.897043	−	1.55372i	0.0657873	−	0.997834i	$-0.479044\pi$
$239$	13.8679	−	24.0200i	0.897043	−	1.55372i	0.831256	−	0.555890i	$-0.187623\pi$
$240$		0			0
$241$	23.9134			1.54040			0.770199	−	0.637803i	$-0.220157\pi$
$241$	23.9134			1.54040			0.770199	+	0.637803i	$0.220157\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.814135	+	24.0376i	−0.0520131	+	1.53571i
$246$		0			0
$247$	22.3668			1.42316
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3.33510			−0.210509			−0.105255	−	0.994445i	$-0.533566\pi$
$251$	−3.33510			−0.210509			−0.105255	+	0.994445i	$0.533566\pi$
$252$		0			0
$253$	−19.0731			−1.19912
$254$		0			0
$255$		0			0
$256$		0			0
$257$	21.8691			1.36416			0.682078	−	0.731280i	$-0.261077\pi$
$257$	21.8691			1.36416			0.682078	+	0.731280i	$0.261077\pi$
$258$		0			0
$259$	3.65082	−	12.7572i	0.226851	−	0.792695i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.51044			0.339788			0.169894	−	0.985462i	$-0.445657\pi$
$263$	5.51044			0.339788			0.169894	+	0.985462i	$0.445657\pi$
$264$		0			0
$265$	1.82344	−	3.15829i	0.112013	−	0.194012i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.37393	+	5.84382i	−0.205712	+	0.356304i	−0.950359	−	0.311154i	$-0.899284\pi$
$269$	−3.37393	+	5.84382i	−0.205712	+	0.356304i	0.744647	+	0.667458i	$0.232618\pi$
$270$		0			0
$271$	−6.21944	−	10.7724i	−0.377804	−	0.654376i	0.612938	−	0.790131i	$-0.289987\pi$
$271$	−6.21944	−	10.7724i	−0.377804	−	0.654376i	−0.990742	+	0.135755i	$0.956654\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	30.0081			1.80956
$276$		0			0
$277$	−9.71890			−0.583952			−0.291976	−	0.956426i	$-0.594313\pi$
$277$	−9.71890			−0.583952			−0.291976	+	0.956426i	$0.594313\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.66772	+	16.7450i	0.576728	+	0.998922i	0.995852	+	0.0909928i	$0.0290040\pi$
$281$	9.66772	+	16.7450i	0.576728	+	0.998922i	−0.419124	+	0.907929i	$0.637663\pi$
$282$		0			0
$283$	4.15450	+	7.19581i	0.246959	+	0.427746i	0.962681	−	0.270640i	$-0.0872352\pi$
$283$	4.15450	+	7.19581i	0.246959	+	0.427746i	−0.715721	+	0.698386i	$0.753902\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.16857	−	1.54144i	0.364119	−	0.0909882i
$288$		0			0
$289$	7.91189	+	13.7038i	0.465405	+	0.806105i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.97318	−	6.88175i	0.232116	−	0.402036i	−0.726315	−	0.687362i	$-0.758769\pi$
$293$	3.97318	−	6.88175i	0.232116	−	0.402036i	0.958430	+	0.285326i	$0.0921019\pi$
$294$		0			0
$295$	−21.3188	−	36.9253i	−1.24123	−	2.14987i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.46247	+	11.1933i	−0.373734	+	0.647327i
$300$		0			0
$301$	4.82491	−	16.8599i	0.278103	−	0.971788i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.32281	−	16.1476i	0.533823	−	0.924608i
$306$		0			0
$307$	26.9180			1.53629			0.768145	−	0.640276i	$-0.221180\pi$
$307$	26.9180			1.53629			0.768145	+	0.640276i	$0.221180\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.67458	−	8.09662i	−0.265071	−	0.459117i	0.702511	−	0.711673i	$-0.252062\pi$
$311$	−4.67458	−	8.09662i	−0.265071	−	0.459117i	−0.967582	+	0.252556i	$0.918729\pi$
$312$		0			0
$313$	−7.91902	+	13.7161i	−0.447610	+	0.775282i	−0.998230	−	0.0594734i	$-0.981058\pi$
$313$	−7.91902	+	13.7161i	−0.447610	+	0.775282i	0.550620	+	0.834756i	$0.314391\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.2296	+	24.6463i	−0.799213	+	1.38428i	0.120917	+	0.992663i	$0.461417\pi$
$317$	−14.2296	+	24.6463i	−0.799213	+	1.38428i	−0.920130	+	0.391614i	$0.871917\pi$
$318$		0			0
$319$	−7.42916	−	12.8677i	−0.415953	−	0.720452i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.11829			−0.451714
$324$		0			0
$325$	10.1675	−	17.6107i	0.563994	−	0.976865i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.72180	+	1.92957i	−0.425716	+	0.106381i
$330$		0			0
$331$	−9.79521	+	16.9658i	−0.538393	+	0.932524i	0.460598	+	0.887609i	$0.347635\pi$
$331$	−9.79521	+	16.9658i	−0.538393	+	0.932524i	−0.998991	+	0.0449153i	$0.985698\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.73794	+	9.93841i	0.313497	+	0.542993i
$336$		0			0
$337$	8.73059	−	15.1218i	0.475586	−	0.823739i	−0.524023	−	0.851704i	$-0.675569\pi$
$337$	8.73059	−	15.1218i	0.475586	−	0.823739i	0.999609	+	0.0279654i	$0.00890283\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	20.6683	+	35.7985i	1.11925	+	1.93860i
$342$		0			0
$343$	−13.7437	+	12.4141i	−0.742090	+	0.670301i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.72509	+	16.8443i	0.522070	+	0.904252i	0.999670	+	0.0256747i	$0.00817340\pi$
$347$	9.72509	+	16.8443i	0.522070	+	0.904252i	−0.477600	+	0.878577i	$0.658493\pi$
$348$		0			0
$349$	6.91419	+	11.9757i	0.370108	+	0.641046i	0.989582	−	0.143971i	$-0.0459872\pi$
$349$	6.91419	+	11.9757i	0.370108	+	0.641046i	−0.619474	+	0.785018i	$0.712654\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−11.8459			−0.630493			−0.315247	−	0.949010i	$-0.602087\pi$
$353$	−11.8459			−0.630493			−0.315247	+	0.949010i	$0.602087\pi$
$354$		0			0
$355$	−44.3455			−2.35361
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.628489	−	1.08858i	−0.0331704	−	0.0574528i	0.848964	−	0.528451i	$-0.177227\pi$
$359$	−0.628489	−	1.08858i	−0.0331704	−	0.0574528i	−0.882134	+	0.470998i	$0.843894\pi$
$360$		0			0
$361$	−18.5161	+	32.0709i	−0.974533	+	1.68794i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−28.2220	+	48.8819i	−1.47721	+	2.55860i
$366$		0			0
$367$	15.2386			0.795446			0.397723	−	0.917505i	$-0.369800\pi$
$367$	15.2386			0.795446			0.397723	+	0.917505i	$0.369800\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.72442	−	0.680795i	0.141445	−	0.0353451i
$372$		0			0
$373$	17.3351			0.897579			0.448789	−	0.893638i	$-0.351855\pi$
$373$	17.3351			0.897579			0.448789	+	0.893638i	$0.351855\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.0688			−0.518569
$378$		0			0
$379$	−15.6319			−0.802955			−0.401478	−	0.915869i	$-0.631503\pi$
$379$	−15.6319			−0.802955			−0.401478	+	0.915869i	$0.631503\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−17.8123			−0.910166			−0.455083	−	0.890449i	$-0.650390\pi$
$383$	−17.8123			−0.910166			−0.455083	+	0.890449i	$0.650390\pi$
$384$		0			0
$385$	27.8597	+	28.8192i	1.41986	+	1.46876i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−29.4148			−1.49139			−0.745695	−	0.666288i	$-0.767882\pi$
$389$	−29.4148			−1.49139			−0.745695	+	0.666288i	$0.767882\pi$
$390$		0			0
$391$	2.34563	−	4.06275i	0.118624	−	0.205462i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.03774	+	6.99357i	−0.203161	+	0.351885i
$396$		0			0
$397$	−1.55930	−	2.70079i	−0.0782592	−	0.135549i	0.824240	−	0.566241i	$-0.191603\pi$
$397$	−1.55930	−	2.70079i	−0.0782592	−	0.135549i	−0.902499	+	0.430692i	$0.858270\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	35.7226			1.78390			0.891950	−	0.452134i	$-0.149337\pi$
$401$	35.7226			1.78390			0.891950	+	0.452134i	$0.149337\pi$
$402$		0			0
$403$	28.0118			1.39537
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.0572	−	19.1517i	−0.548087	−	0.949315i
$408$		0			0
$409$	−4.90826	−	8.50135i	−0.242698	−	0.420365i	0.718784	−	0.695233i	$-0.244699\pi$
$409$	−4.90826	−	8.50135i	−0.242698	−	0.420365i	−0.961482	+	0.274869i	$0.911366\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	9.03320	−	31.5651i	0.444494	−	1.55321i
$414$		0			0
$415$	−5.51814	−	9.55771i	−0.270875	−	0.469169i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.09812	−	10.5623i	0.297913	−	0.516000i	−0.677746	−	0.735297i	$-0.737043\pi$
$419$	6.09812	−	10.5623i	0.297913	−	0.516000i	0.975658	+	0.219297i	$0.0703762\pi$
$420$		0			0
$421$	−5.10015	−	8.83373i	−0.248566	−	0.430529i	0.714562	−	0.699572i	$-0.246626\pi$
$421$	−5.10015	−	8.83373i	−0.248566	−	0.430529i	−0.963128	+	0.269043i	$0.913293\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.69043	+	6.39201i	−0.179012	+	0.310058i
$426$		0			0
$427$	13.9293	−	3.48075i	0.674088	−	0.168445i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.70254	+	9.87710i	−0.274682	+	0.475763i	−0.970055	−	0.242886i	$-0.921906\pi$
$431$	−5.70254	+	9.87710i	−0.274682	+	0.475763i	0.695373	+	0.718649i	$0.255239\pi$
$432$		0			0
$433$	26.2391			1.26097			0.630486	−	0.776201i	$-0.282856\pi$
$433$	26.2391			1.26097			0.630486	+	0.776201i	$0.282856\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−16.1895	−	28.0410i	−0.774448	−	1.34138i
$438$		0			0
$439$	11.4777	−	19.8800i	0.547801	−	0.948819i	−0.450624	−	0.892714i	$-0.648798\pi$
$439$	11.4777	−	19.8800i	0.547801	−	0.948819i	0.998425	−	0.0561054i	$-0.0178683\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.2013	+	19.4012i	−0.532188	+	0.921777i	0.467105	+	0.884202i	$0.345297\pi$
$443$	−11.2013	+	19.4012i	−0.532188	+	0.921777i	−0.999294	+	0.0375758i	$0.988036\pi$
$444$		0			0
$445$	−19.4997	−	33.7744i	−0.924372	−	1.60106i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−17.0576			−0.805000			−0.402500	−	0.915420i	$-0.631859\pi$
$449$	−17.0576			−0.805000			−0.402500	+	0.915420i	$0.631859\pi$
$450$		0			0
$451$	5.29829	−	9.17690i	0.249487	−	0.432123i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	26.3526	−	6.58514i	1.23543	−	0.308716i
$456$		0			0
$457$	−4.77365	+	8.26820i	−0.223302	+	0.386770i	−0.955809	−	0.293990i	$-0.905017\pi$
$457$	−4.77365	+	8.26820i	−0.223302	+	0.386770i	0.732507	+	0.680760i	$0.238350\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.1213	−	17.5305i	−0.471394	−	0.816478i	0.528070	−	0.849201i	$-0.322916\pi$
$461$	−10.1213	−	17.5305i	−0.471394	−	0.816478i	−0.999464	+	0.0327222i	$0.989582\pi$
$462$		0			0
$463$	7.81948	−	13.5437i	0.363402	−	0.629431i	−0.625116	−	0.780532i	$-0.714948\pi$
$463$	7.81948	−	13.5437i	0.363402	−	0.629431i	0.988518	+	0.151101i	$0.0482818\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.96638	−	5.13793i	−0.137268	−	0.237755i	0.789194	−	0.614144i	$-0.210499\pi$
$467$	−2.96638	−	5.13793i	−0.137268	−	0.237755i	−0.926461	+	0.376390i	$0.877165\pi$
$468$		0			0
$469$	−2.43128	+	8.49571i	−0.112266	+	0.392295i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−14.6132	−	25.3108i	−0.671917	−	1.16379i
$474$		0			0
$475$	25.4712	+	44.1175i	1.16870	+	2.02425i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.3942			−0.794760			−0.397380	−	0.917654i	$-0.630080\pi$
$479$	−17.3942			−0.794760			−0.397380	+	0.917654i	$0.630080\pi$
$480$		0			0
$481$	−14.9860			−0.683301
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−22.0009	−	38.1067i	−0.999009	−	1.73033i
$486$		0			0
$487$	9.76967	−	16.9216i	0.442706	−	0.766790i	−0.555183	−	0.831728i	$-0.687352\pi$
$487$	9.76967	−	16.9216i	0.442706	−	0.766790i	0.997889	+	0.0649386i	$0.0206851\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.16702	+	10.6816i	−0.278314	+	0.482054i	−0.970966	−	0.239218i	$-0.923109\pi$
$491$	−6.16702	+	10.6816i	−0.278314	+	0.482054i	0.692652	+	0.721272i	$0.256442\pi$
$492$		0			0
$493$	3.65458			0.164594
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−23.7336	−	24.5510i	−1.06460	−	1.10126i
$498$		0			0
$499$	−18.5462			−0.830240			−0.415120	−	0.909767i	$-0.636260\pi$
$499$	−18.5462			−0.830240			−0.415120	+	0.909767i	$0.636260\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−14.3264			−0.638782			−0.319391	−	0.947623i	$-0.603478\pi$
$503$	−14.3264			−0.638782			−0.319391	+	0.947623i	$0.603478\pi$
$504$		0			0
$505$	2.66703			0.118681
$506$		0			0
$507$		0			0
$508$		0			0
$509$	16.8611			0.747356			0.373678	−	0.927559i	$-0.378097\pi$
$509$	16.8611			0.747356			0.373678	+	0.927559i	$0.378097\pi$
$510$		0			0
$511$	−42.1669	+	10.5369i	−1.86535	+	0.466125i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.84290			−0.345599
$516$		0			0
$517$	−6.63238	+	11.4876i	−0.291692	+	0.505225i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.8132	+	18.7291i	−0.473737	+	0.820536i	−0.999548	−	0.0300652i	$-0.990428\pi$
$521$	−10.8132	+	18.7291i	−0.473737	+	0.820536i	0.525811	+	0.850601i	$0.323762\pi$
$522$		0			0
$523$	−8.27472	−	14.3322i	−0.361828	−	0.626705i	0.626433	−	0.779475i	$-0.284514\pi$
$523$	−8.27472	−	14.3322i	−0.361828	−	0.626705i	−0.988262	+	0.152770i	$0.951181\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−10.1672			−0.442891
$528$		0			0
$529$	−4.28939			−0.186495
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.59040	−	6.21876i	−0.155517	−	0.269364i
$534$		0			0
$535$	−7.81560	−	13.5370i	−0.337898	−	0.585256i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.04479	+	30.8480i	−0.0450025	+	1.32872i
$540$		0			0
$541$	−11.9542	−	20.7053i	−0.513952	−	0.890191i	−0.999869	−	0.0161861i	$-0.994848\pi$
$541$	−11.9542	−	20.7053i	−0.513952	−	0.890191i	0.485917	−	0.874005i	$-0.338486\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.13317	−	14.0871i	0.348387	−	0.603423i
$546$		0			0
$547$	14.8193	+	25.6678i	0.633627	+	1.09747i	0.986804	+	0.161918i	$0.0517679\pi$
$547$	14.8193	+	25.6678i	0.633627	+	1.09747i	−0.353177	+	0.935556i	$0.614899\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.6119	−	21.8445i	0.537286	−	0.930607i
$552$		0			0
$553$	−6.03285	+	1.50752i	−0.256543	+	0.0641064i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	10.8366	−	18.7695i	0.459160	−	0.795288i	−0.539757	−	0.841821i	$-0.681484\pi$
$557$	10.8366	−	18.7695i	0.459160	−	0.795288i	0.998917	+	0.0465330i	$0.0148173\pi$
$558$		0			0
$559$	−19.8054			−0.837679
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.07782	−	12.2591i	−0.298294	−	0.516661i	0.677451	−	0.735567i	$-0.263084\pi$
$563$	−7.07782	−	12.2591i	−0.298294	−	0.516661i	−0.975746	+	0.218906i	$0.929751\pi$
$564$		0			0
$565$	−0.602548	+	1.04364i	−0.0253494	+	0.0439064i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−17.0178	+	29.4757i	−0.713422	+	1.23568i	0.250143	+	0.968209i	$0.419522\pi$
$569$	−17.0178	+	29.4757i	−0.713422	+	1.23568i	−0.963565	+	0.267475i	$0.913811\pi$
$570$		0			0
$571$	−2.67485	−	4.63298i	−0.111939	−	0.193884i	0.804613	−	0.593800i	$-0.202373\pi$
$571$	−2.67485	−	4.63298i	−0.111939	−	0.193884i	−0.916552	+	0.399915i	$0.869039\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−29.4378			−1.22764
$576$		0			0
$577$	11.1865	−	19.3756i	0.465699	−	0.806615i	−0.533533	−	0.845779i	$-0.679136\pi$
$577$	11.1865	−	19.3756i	0.465699	−	0.806615i	0.999233	+	0.0391640i	$0.0124695\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.33814	−	8.17027i	0.0970026	−	0.338960i
$582$		0			0
$583$	2.34005	−	4.05309i	0.0969151	−	0.167862i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.49899	−	4.32839i	−0.103145	−	0.178652i	0.809834	−	0.586659i	$-0.199557\pi$
$587$	−2.49899	−	4.32839i	−0.103145	−	0.178652i	−0.912979	+	0.408007i	$0.866224\pi$
$588$		0			0
$589$	−35.0870	+	60.7724i	−1.44573	+	2.50408i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.1698	−	21.0788i	−0.499755	−	0.865601i	0.500245	−	0.865884i	$-0.333243\pi$
$593$	−12.1698	−	21.0788i	−0.499755	−	0.865601i	−1.00000		0.000282582i	$0.999910\pi$
$594$		0			0
$595$	−9.56498	+	2.39015i	−0.392126	+	0.0979868i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−23.1073	−	40.0230i	−0.944137	−	1.63529i	−0.757469	−	0.652871i	$-0.773564\pi$
$599$	−23.1073	−	40.0230i	−0.944137	−	1.63529i	−0.186668	−	0.982423i	$-0.559769\pi$
$600$		0			0
$601$	−16.6163	−	28.7803i	−0.677792	−	1.17397i	−0.975644	−	0.219359i	$-0.929603\pi$
$601$	−16.6163	−	28.7803i	−0.677792	−	1.17397i	0.297852	−	0.954612i	$-0.403730\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	29.0081			1.17935
$606$		0			0
$607$	−43.8635			−1.78036			−0.890182	−	0.455604i	$-0.849423\pi$
$607$	−43.8635			−1.78036			−0.890182	+	0.455604i	$0.849423\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.49445	+	7.78462i	0.181826	+	0.314932i
$612$		0			0
$613$	1.81569	−	3.14487i	0.0733351	−	0.127020i	−0.827026	−	0.562164i	$-0.809969\pi$
$613$	1.81569	−	3.14487i	0.0733351	−	0.127020i	0.900361	+	0.435144i	$0.143302\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.4542	+	18.1073i	−0.420872	+	0.728971i	−0.996025	−	0.0890744i	$-0.971609\pi$
$617$	−10.4542	+	18.1073i	−0.420872	+	0.728971i	0.575153	+	0.818046i	$0.304942\pi$
$618$		0			0
$619$	−23.9490			−0.962592			−0.481296	−	0.876558i	$-0.659834\pi$
$619$	−23.9490			−0.962592			−0.481296	+	0.876558i	$0.659834\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.26238	−	28.8716i	0.331025	−	1.15672i
$624$		0			0
$625$	−12.7125			−0.508501
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.43933			0.216880
$630$		0			0
$631$	6.06918			0.241610			0.120805	−	0.992676i	$-0.461452\pi$
$631$	6.06918			0.241610			0.120805	+	0.992676i	$0.461452\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−42.6653			−1.69312
$636$		0			0
$637$	17.7496	+	11.0653i	0.703264	+	0.438422i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.3881			0.686790			0.343395	−	0.939191i	$-0.388423\pi$
$641$	17.3881			0.686790			0.343395	+	0.939191i	$0.388423\pi$
$642$		0			0
$643$	−9.66411	+	16.7387i	−0.381115	+	0.660111i	−0.991222	−	0.132208i	$-0.957793\pi$
$643$	−9.66411	+	16.7387i	−0.381115	+	0.660111i	0.610107	+	0.792319i	$0.291127\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.7041	−	22.0042i	0.499451	−	0.865075i	−0.500549	−	0.865708i	$-0.666868\pi$
$647$	12.7041	−	22.0042i	0.499451	−	0.865075i	1.00000		0.000633482i	$0.000201644\pi$
$648$		0			0
$649$	−27.3588	−	47.3869i	−1.07393	−	1.86010i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	25.8127			1.01013			0.505065	−	0.863081i	$-0.331468\pi$
$653$	25.8127			1.01013			0.505065	+	0.863081i	$0.331468\pi$
$654$		0			0
$655$	54.0918			2.11354
$656$		0			0
$657$		0			0
$658$		0			0
$659$	8.62598	+	14.9406i	0.336020	+	0.582004i	0.983680	−	0.179925i	$-0.0575856\pi$
$659$	8.62598	+	14.9406i	0.336020	+	0.582004i	−0.647660	+	0.761930i	$0.724252\pi$
$660$		0			0
$661$	−6.48175	−	11.2267i	−0.252111	−	0.436669i	0.711996	−	0.702184i	$-0.247791\pi$
$661$	−6.48175	−	11.2267i	−0.252111	−	0.436669i	−0.964107	+	0.265515i	$0.914458\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−18.7220	+	65.4210i	−0.726008	+	2.53692i
$666$		0			0
$667$	7.28797	+	12.6231i	0.282191	+	0.488769i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	11.9641	−	20.7225i	0.461871	−	0.799984i
$672$		0			0
$673$	−20.8060	−	36.0371i	−0.802013	−	1.38913i	−0.918289	−	0.395910i	$-0.870429\pi$
$673$	−20.8060	−	36.0371i	−0.802013	−	1.38913i	0.116277	−	0.993217i	$-0.462904\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.0999	+	19.2256i	−0.426605	+	0.738901i	−0.996569	−	0.0827688i	$-0.973624\pi$
$677$	−11.0999	+	19.2256i	−0.426605	+	0.738901i	0.569964	+	0.821669i	$0.306957\pi$
$678$		0			0
$679$	9.32221	−	32.5750i	0.357753	−	1.25011i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.60315	+	7.97289i	−0.176135	+	0.305074i	−0.940553	−	0.339646i	$-0.889693\pi$
$683$	−4.60315	+	7.97289i	−0.176135	+	0.305074i	0.764419	+	0.644720i	$0.223026\pi$
$684$		0			0
$685$	14.5346			0.555338
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.58574	−	2.74659i	−0.0604120	−	0.104637i
$690$		0			0
$691$	−20.0293	+	34.6917i	−0.761949	+	1.31974i	0.179895	+	0.983686i	$0.442424\pi$
$691$	−20.0293	+	34.6917i	−0.761949	+	1.31974i	−0.941844	+	0.336049i	$0.890909\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−33.6846	+	58.3434i	−1.27773	+	2.21309i
$696$		0			0
$697$	1.30318	+	2.25717i	0.0493614	+	0.0854964i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−34.3868			−1.29877			−0.649385	−	0.760459i	$-0.724974\pi$
$701$	−34.3868			−1.29877			−0.649385	+	0.760459i	$0.724974\pi$
$702$		0			0
$703$	18.7711	−	32.5124i	0.707964	−	1.22623i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.42739	+	1.47655i	0.0536824	+	0.0555314i
$708$		0			0
$709$	−10.5920	+	18.3459i	−0.397791	+	0.688994i	−0.993453	−	0.114241i	$-0.963556\pi$
$709$	−10.5920	+	18.3459i	−0.397791	+	0.688994i	0.595662	+	0.803235i	$0.296890\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−20.2755	−	35.1181i	−0.759322	−	1.31518i
$714$		0			0
$715$	22.6347	−	39.2044i	0.846489	−	1.46616i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−21.5994	−	37.4113i	−0.805523	−	1.39521i	−0.915937	−	0.401321i	$-0.868551\pi$
$719$	−21.5994	−	37.4113i	−0.805523	−	1.39521i	0.110414	−	0.993886i	$-0.464782\pi$
$720$		0			0
$721$	−4.19750	−	4.34207i	−0.156323	−	0.161707i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−11.4663	−	19.8602i	−0.425848	−	0.737590i
$726$		0			0
$727$	−20.5571	−	35.6059i	−0.762420	−	1.32055i	−0.941600	−	0.336734i	$-0.890678\pi$
$727$	−20.5571	−	35.6059i	−0.762420	−	1.32055i	0.179180	−	0.983816i	$-0.442656\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.18860			0.265880
$732$		0			0
$733$	52.0851			1.92381			0.961903	−	0.273390i	$-0.0881451\pi$
$733$	52.0851			1.92381			0.961903	+	0.273390i	$0.0881451\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.36361	+	12.7541i	0.271242	+	0.469805i
$738$		0			0
$739$	−7.18624	+	12.4469i	−0.264350	+	0.457868i	−0.967393	−	0.253279i	$-0.918491\pi$
$739$	−7.18624	+	12.4469i	−0.264350	+	0.457868i	0.703043	+	0.711147i	$0.251824\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.3167	+	36.9216i	−0.782034	+	1.35452i	0.148721	+	0.988879i	$0.452484\pi$
$743$	−21.3167	+	36.9216i	−0.782034	+	1.35452i	−0.930755	+	0.365643i	$0.880849\pi$
$744$		0			0
$745$	33.4195			1.22440
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.31162	−	11.5719i	0.121004	−	0.422829i
$750$		0			0
$751$	37.9692			1.38552			0.692758	−	0.721171i	$-0.256396\pi$
$751$	37.9692			1.38552			0.692758	+	0.721171i	$0.256396\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	33.7458			1.22813
$756$		0			0
$757$	27.6692			1.00565			0.502827	−	0.864387i	$-0.332293\pi$
$757$	27.6692			1.00565			0.502827	+	0.864387i	$0.332293\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.9442			−0.432977			−0.216488	−	0.976285i	$-0.569460\pi$
$761$	−11.9442			−0.432977			−0.216488	+	0.976285i	$0.569460\pi$
$762$		0			0
$763$	12.1519	−	3.03658i	0.439927	−	0.109932i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−37.0796			−1.33887
$768$		0			0
$769$	−17.4026	+	30.1422i	−0.627554	+	1.08695i	0.360487	+	0.932764i	$0.382610\pi$
$769$	−17.4026	+	30.1422i	−0.627554	+	1.08695i	−0.988041	+	0.154191i	$0.950723\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.5014	−	23.3851i	0.485611	−	0.841103i	−0.514253	−	0.857639i	$-0.671931\pi$
$773$	13.5014	−	23.3851i	0.485611	−	0.841103i	0.999863	+	0.0165363i	$0.00526391\pi$
$774$		0			0
$775$	31.8998	+	55.2521i	1.14587	+	1.98471i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17.9890			0.644523
$780$		0			0
$781$	−56.9094			−2.03638
$782$		0			0
$783$		0			0
$784$		0			0
$785$	20.6856	+	35.8286i	0.738302	+	1.27878i
$786$		0			0
$787$	10.6420	+	18.4325i	0.379347	+	0.657048i	0.990967	−	0.134104i	$-0.0428155\pi$
$787$	10.6420	+	18.4325i	0.379347	+	0.657048i	−0.611621	+	0.791151i	$0.709482\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.900275	+	0.224966i	−0.0320101	+	0.00799887i
$792$		0			0
$793$	−8.10754	−	14.0427i	−0.287907	−	0.498670i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.3062	−	17.8508i	0.365064	−	0.632309i	−0.623723	−	0.781646i	$-0.714381\pi$
$797$	10.3062	−	17.8508i	0.365064	−	0.632309i	0.988786	+	0.149337i	$0.0477138\pi$
$798$		0			0
$799$	−1.63131	−	2.82552i	−0.0577117	−	0.0999597i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−36.2178	+	62.7311i	−1.27810	+	2.21373i
$804$		0			0
$805$	−27.3302	−	28.2715i	−0.963263	−	0.996440i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−2.54223	+	4.40328i	−0.0893802	+	0.154811i	−0.907249	−	0.420593i	$-0.861822\pi$
$809$	−2.54223	+	4.40328i	−0.0893802	+	0.154811i	0.817869	+	0.575404i	$0.195155\pi$
$810$		0			0
$811$	7.58775			0.266442			0.133221	−	0.991086i	$-0.457468\pi$
$811$	7.58775			0.266442			0.133221	+	0.991086i	$0.457468\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.04285	−	5.27037i	−0.106586	−	0.184613i
$816$		0			0
$817$	24.8078	−	42.9683i	0.867914	−	1.50327i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.1348	−	17.5540i	0.353706	−	0.612637i	−0.633189	−	0.773997i	$-0.718255\pi$
$821$	10.1348	−	17.5540i	0.353706	−	0.612637i	0.986896	+	0.161360i	$0.0515879\pi$
$822$		0			0
$823$	10.8955	+	18.8716i	0.379794	+	0.657823i	0.991032	−	0.133624i	$-0.0426615\pi$
$823$	10.8955	+	18.8716i	0.379794	+	0.657823i	−0.611238	+	0.791447i	$0.709328\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	26.3796			0.917307			0.458654	−	0.888615i	$-0.348332\pi$
$827$	26.3796			0.917307			0.458654	+	0.888615i	$0.348332\pi$
$828$		0			0
$829$	9.33400	−	16.1670i	0.324183	−	0.561502i	−0.657164	−	0.753748i	$-0.728244\pi$
$829$	9.33400	−	16.1670i	0.324183	−	0.561502i	0.981347	+	0.192246i	$0.0615773\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.44242	−	4.01627i	−0.223216	−	0.139155i
$834$		0			0
$835$	−27.0183	+	46.7971i	−0.935007	+	1.61948i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.5265	+	21.6966i	0.432464	+	0.749050i	0.997085	−	0.0763004i	$-0.0243108\pi$
$839$	12.5265	+	21.6966i	0.432464	+	0.749050i	−0.564621	+	0.825351i	$0.690977\pi$
$840$		0			0
$841$	8.82253	−	15.2811i	0.304225	−	0.526934i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.99499	+	12.1157i	0.240635	+	0.416792i
$846$		0			0
$847$	15.5250	+	16.0598i	0.533447	+	0.551820i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.8471	+	18.7877i	0.371834	+	0.644035i
$852$		0			0
$853$	−19.2219	−	33.2933i	−0.658146	−	1.13994i	−0.981095	−	0.193526i	$-0.938008\pi$
$853$	−19.2219	−	33.2933i	−0.658146	−	1.13994i	0.322949	−	0.946416i	$-0.395326\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.0060			0.410117			0.205058	−	0.978750i	$-0.434262\pi$
$857$	12.0060			0.410117			0.205058	+	0.978750i	$0.434262\pi$
$858$		0			0
$859$	12.6031			0.430012			0.215006	−	0.976613i	$-0.431023\pi$
$859$	12.6031			0.430012			0.215006	+	0.976613i	$0.431023\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.210643	−	0.364845i	−0.00717038	−	0.0124195i	0.862418	−	0.506197i	$-0.168949\pi$
$863$	−0.210643	−	0.364845i	−0.00717038	−	0.0124195i	−0.869588	+	0.493777i	$0.835616\pi$
$864$		0			0
$865$	32.3084	−	55.9597i	1.09852	−	1.90269i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.18171	+	8.97499i	−0.175778	+	0.304456i
$870$		0			0
$871$	9.97995			0.338158
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11.4078	+	11.8007i	0.385653	+	0.398936i
$876$		0			0
$877$	1.78685			0.0603376			0.0301688	−	0.999545i	$-0.490396\pi$
$877$	1.78685			0.0603376			0.0301688	+	0.999545i	$0.490396\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	49.8891			1.68081			0.840403	−	0.541962i	$-0.182318\pi$
$881$	49.8891			1.68081			0.840403	+	0.541962i	$0.182318\pi$
$882$		0			0
$883$	−34.7935			−1.17090			−0.585448	−	0.810710i	$-0.699081\pi$
$883$	−34.7935			−1.17090			−0.585448	+	0.810710i	$0.699081\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23.8080			0.799396			0.399698	−	0.916647i	$-0.369115\pi$
$887$	23.8080			0.799396			0.399698	+	0.916647i	$0.369115\pi$
$888$		0			0
$889$	−22.8344	−	23.6208i	−0.765840	−	0.792217i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−22.5186			−0.753556
$894$		0			0
$895$	11.4829	−	19.8889i	0.383830	−	0.664813i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	15.7950	−	27.3577i	0.526792	−	0.912431i
$900$		0			0
$901$	0.575564	+	0.996907i	0.0191748	+	0.0332118i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	16.2768			0.541060
$906$		0			0
$907$	−34.2813			−1.13829			−0.569146	−	0.822237i	$-0.692726\pi$
$907$	−34.2813			−1.13829			−0.569146	+	0.822237i	$0.692726\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	14.9839	+	25.9529i	0.496438	+	0.859857i	0.999992	−	0.00410771i	$-0.00130753\pi$
$911$	14.9839	+	25.9529i	0.496438	+	0.859857i	−0.503553	+	0.863964i	$0.667974\pi$
$912$		0			0
$913$	−7.08154	−	12.2656i	−0.234365	−	0.405932i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.9498	+	29.9469i	0.956006	+	0.988933i
$918$		0			0
$919$	0.391037	+	0.677296i	0.0128991	+	0.0223419i	0.872403	−	0.488787i	$-0.162561\pi$
$919$	0.391037	+	0.677296i	0.0128991	+	0.0223419i	−0.859504	+	0.511129i	$0.829227\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−19.2824	+	33.3981i	−0.634688	+	1.09931i
$924$		0			0
$925$	−17.0660	−	29.5591i	−0.561126	−	0.971898i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−6.76620	+	11.7194i	−0.221992	+	0.384501i	−0.955413	−	0.295274i	$-0.904589\pi$
$929$	−6.76620	+	11.7194i	−0.221992	+	0.384501i	0.733421	+	0.679775i	$0.237922\pi$
$930$		0			0
$931$	−46.2391	+	24.6481i	−1.51542	+	0.807808i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8.21552	+	14.2297i	−0.268676	+	0.465361i
$936$		0			0
$937$	−2.27674			−0.0743777			−0.0371889	−	0.999308i	$-0.511840\pi$
$937$	−2.27674			−0.0743777			−0.0371889	+	0.999308i	$0.511840\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.07720	−	7.06192i	−0.132913	−	0.230212i	0.791885	−	0.610670i	$-0.209100\pi$
$941$	−4.07720	−	7.06192i	−0.132913	−	0.230212i	−0.924798	+	0.380458i	$0.875766\pi$
$942$		0			0
$943$	−5.19759	+	9.00249i	−0.169257	+	0.293161i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.93553	+	6.81654i	−0.127888	+	0.221508i	−0.922858	−	0.385140i	$-0.874153\pi$
$947$	−3.93553	+	6.81654i	−0.127888	+	0.221508i	0.794970	+	0.606648i	$0.207486\pi$
$948$		0			0
$949$	24.5431	+	42.5099i	0.796703	+	1.37993i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−43.1097			−1.39646			−0.698230	−	0.715873i	$-0.746029\pi$
$953$	−43.1097			−1.39646			−0.698230	+	0.715873i	$0.746029\pi$
$954$		0			0
$955$	39.6321	−	68.6448i	1.28246	−	2.22129i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.77888	+	8.04680i	0.251193	+	0.259845i
$960$		0			0
$961$	−28.4424	+	49.2636i	−0.917496	+	1.58915i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−31.4507	−	54.4742i	−1.01243	−	1.75359i
$966$		0			0
$967$	−13.9537	+	24.1684i	−0.448719	+	0.777205i	−0.998303	−	0.0582340i	$-0.981453\pi$
$967$	−13.9537	+	24.1684i	−0.448719	+	0.777205i	0.549584	+	0.835439i	$0.314786\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	21.0705	+	36.4952i	0.676185	+	1.17119i	0.976121	+	0.217228i	$0.0697015\pi$
$971$	21.0705	+	36.4952i	0.676185	+	1.17119i	−0.299936	+	0.953959i	$0.596965\pi$
$972$		0			0
$973$	−50.3286	+	12.5764i	−1.61346	+	0.403181i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.92747	−	11.9987i	−0.221629	−	0.383873i	0.733674	−	0.679502i	$-0.237804\pi$
$977$	−6.92747	−	11.9987i	−0.221629	−	0.383873i	−0.955303	+	0.295629i	$0.904471\pi$
$978$		0			0
$979$	−25.0243	−	43.3433i	−0.799780	−	1.38526i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.95876			0.253845			0.126923	−	0.991913i	$-0.459490\pi$
$983$	7.95876			0.253845			0.126923	+	0.991913i	$0.459490\pi$
$984$		0			0
$985$	−50.1182			−1.59690
$986$		0			0
$987$		0			0
$988$		0			0
$989$	14.3355	+	24.8298i	0.455842	+	0.789542i
$990$		0			0
$991$	−4.36428	+	7.55916i	−0.138636	+	0.240125i	−0.926981	−	0.375109i	$-0.877605\pi$
$991$	−4.36428	+	7.55916i	−0.138636	+	0.240125i	0.788345	+	0.615234i	$0.210938\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	3.13391	−	5.42809i	0.0993515	−	0.172082i
$996$		0			0
$997$	−2.30379			−0.0729619			−0.0364810	−	0.999334i	$-0.511615\pi$
$997$	−2.30379			−0.0729619			−0.0364810	+	0.999334i	$0.511615\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.l.1873.10		22
3.2	odd	2		1008.2.t.k.193.7		22
4.3	odd	2		1512.2.t.d.361.10		22
7.2	even	3		3024.2.q.k.2305.2		22
9.2	odd	6		1008.2.q.k.529.10		22
9.7	even	3		3024.2.q.k.2881.2		22
12.11	even	2		504.2.t.d.193.5	yes	22
21.2	odd	6		1008.2.q.k.625.10		22
28.23	odd	6		1512.2.q.c.793.2		22
36.7	odd	6		1512.2.q.c.1369.2		22
36.11	even	6		504.2.q.d.25.2	✓	22
63.2	odd	6		1008.2.t.k.961.7		22
63.16	even	3	inner	3024.2.t.l.289.10		22
84.23	even	6		504.2.q.d.121.2	yes	22
252.79	odd	6		1512.2.t.d.289.10		22
252.191	even	6		504.2.t.d.457.5	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.2	✓	22	36.11	even	6
504.2.q.d.121.2	yes	22	84.23	even	6
504.2.t.d.193.5	yes	22	12.11	even	2
504.2.t.d.457.5	yes	22	252.191	even	6
1008.2.q.k.529.10		22	9.2	odd	6
1008.2.q.k.625.10		22	21.2	odd	6
1008.2.t.k.193.7		22	3.2	odd	2
1008.2.t.k.961.7		22	63.2	odd	6
1512.2.q.c.793.2		22	28.23	odd	6
1512.2.q.c.1369.2		22	36.7	odd	6
1512.2.t.d.289.10		22	252.79	odd	6
1512.2.t.d.361.10		22	4.3	odd	2
3024.2.q.k.2305.2		22	7.2	even	3
3024.2.q.k.2881.2		22	9.7	even	3
3024.2.t.l.289.10		22	63.16	even	3	inner
3024.2.t.l.1873.10		22	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+3.43592 q^{5} +(1.83889 + 1.90223i) q^{7} +O(q^{10})\)	\(q+3.43592 q^{5} +(1.83889 + 1.90223i) q^{7} +4.40938 q^{11} +(1.49401 - 2.58771i) q^{13} +(-0.542270 + 0.939239i) q^{17} +(3.74273 + 6.48261i) q^{19} -4.32558 q^{23} +6.80552 q^{25} +(-1.68485 - 2.91825i) q^{29} +(4.68734 + 8.11872i) q^{31} +(6.31828 + 6.53590i) q^{35} +(-2.50767 - 4.34341i) q^{37} +(1.20160 - 2.08122i) q^{41} +(-3.31412 - 5.74023i) q^{43} +(-1.50415 + 2.60527i) q^{47} +(-0.236948 + 6.99599i) q^{49} +(0.530699 - 0.919198i) q^{53} +15.1502 q^{55} +(-6.20470 - 10.7468i) q^{59} +(2.71334 - 4.69965i) q^{61} +(5.13331 - 8.89115i) q^{65} +(1.66999 + 2.89251i) q^{67} -12.9064 q^{71} +(-8.21382 + 14.2267i) q^{73} +(8.10837 + 8.38764i) q^{77} +(-1.17516 + 2.03543i) q^{79} +(-1.60602 - 2.78171i) q^{83} +(-1.86319 + 3.22715i) q^{85} +(-5.67524 - 9.82981i) q^{89} +(7.66974 - 1.91656i) q^{91} +(12.8597 + 22.2737i) q^{95} +(-6.40321 - 11.0907i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{5} - 7 q^{7}+O(q^{10}) \) 22 * q + 6 * q^5 - 7 * q^7	\( 22 q + 6 q^{5} - 7 q^{7} + 6 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} - 4 q^{23} + 20 q^{25} - 9 q^{29} + 4 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} + 5 q^{47} - 15 q^{49} - 11 q^{53} - 22 q^{55} - 19 q^{59} - 13 q^{61} - 13 q^{65} - 26 q^{67} - 48 q^{71} - 35 q^{73} + 4 q^{77} - 10 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} + 12 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q + 6 * q^5 - 7 * q^7 + 6 * q^11 - 3 * q^13 - 7 * q^17 + q^19 - 4 * q^23 + 20 * q^25 - 9 * q^29 + 4 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 + 5 * q^47 - 15 * q^49 - 11 * q^53 - 22 * q^55 - 19 * q^59 - 13 * q^61 - 13 * q^65 - 26 * q^67 - 48 * q^71 - 35 * q^73 + 4 * q^77 - 10 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 + 12 * q^95 - 29 * q^97

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