LMFDB - Embedded newform 3024.2.q.l.2305.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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, 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("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.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:	$24.1467615712$
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			2305.8
Character	$\chi$	$=$	3024.2305
Dual form			3024.2.q.l.2881.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05220 + 1.82246i) q^{5} +(-2.58382 + 0.569079i) q^{7} +O(q^{10})$	$q+(1.05220 + 1.82246i) q^{5} +(-2.58382 + 0.569079i) q^{7} +(-0.199532 + 0.345600i) q^{11} +(1.44292 - 2.49921i) q^{13} +(0.176596 + 0.305873i) q^{17} +(-2.84888 + 4.93440i) q^{19} +(0.438682 + 0.759820i) q^{23} +(0.285756 - 0.494945i) q^{25} +(-0.874997 - 1.51554i) q^{29} -9.13490 q^{31} +(-3.75582 - 4.11014i) q^{35} +(-3.39555 + 5.88127i) q^{37} +(-1.20377 + 2.08499i) q^{41} +(-0.276745 - 0.479336i) q^{43} +11.7372 q^{47} +(6.35230 - 2.94080i) q^{49} +(2.07821 + 3.59956i) q^{53} -0.839790 q^{55} -9.32421 q^{59} -10.0720 q^{61} +6.07296 q^{65} -1.20241 q^{67} -14.6826 q^{71} +(0.315636 + 0.546697i) q^{73} +(0.318883 - 1.00652i) q^{77} +2.48729 q^{79} +(-4.59366 - 7.95645i) q^{83} +(-0.371628 + 0.643678i) q^{85} +(-7.29358 + 12.6328i) q^{89} +(-2.30601 + 7.27866i) q^{91} -11.9903 q^{95} +(-7.84245 - 13.5835i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{5} - 5 q^{7}+O(q^{10}) $ 22 * q - q^5 - 5 * q^7	$ 22 q - q^{5} - 5 q^{7} + 3 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} - 22 q^{25} + 7 q^{29} + 12 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} - 34 q^{47} - 25 q^{49} - q^{53} - 2 q^{55} + 42 q^{59} - 62 q^{61} - 6 q^{65} - 52 q^{67} - 32 q^{71} + 17 q^{73} + q^{77} - 32 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} + 48 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q - q^5 - 5 * q^7 + 3 * q^11 + 7 * q^13 + q^17 - 13 * q^19 - 22 * q^25 + 7 * q^29 + 12 * q^31 + 2 * q^35 + 6 * q^37 - 4 * q^41 - 2 * q^43 - 34 * q^47 - 25 * q^49 - q^53 - 2 * q^55 + 42 * q^59 - 62 * q^61 - 6 * q^65 - 52 * q^67 - 32 * q^71 + 17 * q^73 + q^77 - 32 * q^79 - 36 * q^83 + 28 * q^85 + 2 * q^89 - 15 * q^91 + 48 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.05220	+	1.82246i	0.470558	+	0.815030i	0.999433	−	0.0336699i	$-0.0107195\pi$
$5$	1.05220	+	1.82246i	0.470558	+	0.815030i	−0.528876	+	0.848699i	$0.677386\pi$
$6$		0			0
$7$	−2.58382	+	0.569079i	−0.976594	+	0.215092i
$7$	−2.58382	+	0.569079i	−0.976594	+	0.215092i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.199532	+	0.345600i	−0.0601612	+	0.104202i	−0.894537	−	0.446993i	$-0.852495\pi$
$11$	−0.199532	+	0.345600i	−0.0601612	+	0.104202i	0.834376	+	0.551195i	$0.185828\pi$
$12$		0			0
$13$	1.44292	−	2.49921i	0.400194	−	0.693157i	−0.593555	−	0.804794i	$-0.702276\pi$
$13$	1.44292	−	2.49921i	0.400194	−	0.693157i	0.993749	+	0.111637i	$0.0356093\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.176596	+	0.305873i	0.0428308	+	0.0741851i	0.886646	−	0.462449i	$-0.153029\pi$
$17$	0.176596	+	0.305873i	0.0428308	+	0.0741851i	−0.843815	+	0.536634i	$0.819696\pi$
$18$		0			0
$19$	−2.84888	+	4.93440i	−0.653578	+	1.13203i	0.328670	+	0.944445i	$0.393399\pi$
$19$	−2.84888	+	4.93440i	−0.653578	+	1.13203i	−0.982248	+	0.187585i	$0.939934\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.438682	+	0.759820i	0.0914716	+	0.158433i	0.908131	−	0.418687i	$-0.137510\pi$
$23$	0.438682	+	0.759820i	0.0914716	+	0.158433i	−0.816659	+	0.577121i	$0.804176\pi$
$24$		0			0
$25$	0.285756	−	0.494945i	0.0571513	−	0.0989889i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.874997	−	1.51554i	−0.162483	−	0.281429i	0.773276	−	0.634070i	$-0.218617\pi$
$29$	−0.874997	−	1.51554i	−0.162483	−	0.281429i	−0.935759	+	0.352641i	$0.885284\pi$
$30$		0			0
$31$	−9.13490			−1.64068			−0.820339	−	0.571878i	$-0.806215\pi$
$31$	−9.13490			−1.64068			−0.820339	+	0.571878i	$0.806215\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.75582	−	4.11014i	−0.634850	−	0.694740i
$36$		0			0
$37$	−3.39555	+	5.88127i	−0.558225	+	0.966874i	0.439420	+	0.898282i	$0.355184\pi$
$37$	−3.39555	+	5.88127i	−0.558225	+	0.966874i	−0.997645	+	0.0685922i	$0.978149\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.20377	+	2.08499i	−0.187997	+	0.325621i	−0.944582	−	0.328274i	$-0.893533\pi$
$41$	−1.20377	+	2.08499i	−0.187997	+	0.325621i	0.756585	+	0.653895i	$0.226866\pi$
$42$		0			0
$43$	−0.276745	−	0.479336i	−0.0422032	−	0.0730981i	0.844152	−	0.536104i	$-0.180104\pi$
$43$	−0.276745	−	0.479336i	−0.0422032	−	0.0730981i	−0.886355	+	0.463005i	$0.846771\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	11.7372			1.71205			0.856023	−	0.516939i	$-0.172928\pi$
$47$	11.7372			1.71205			0.856023	+	0.516939i	$0.172928\pi$
$48$		0			0
$49$	6.35230	−	2.94080i	0.907471	−	0.420114i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.07821	+	3.59956i	0.285464	+	0.494437i	0.972721	−	0.231976i	$-0.0745191\pi$
$53$	2.07821	+	3.59956i	0.285464	+	0.494437i	−0.687258	+	0.726413i	$0.741186\pi$
$54$		0			0
$55$	−0.839790			−0.113237
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−9.32421			−1.21391			−0.606954	−	0.794737i	$-0.707609\pi$
$59$	−9.32421			−1.21391			−0.606954	+	0.794737i	$0.707609\pi$
$60$		0			0
$61$	−10.0720			−1.28959			−0.644795	−	0.764356i	$-0.723057\pi$
$61$	−10.0720			−1.28959			−0.644795	+	0.764356i	$0.723057\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.07296			0.753258
$66$		0			0
$67$	−1.20241			−0.146898			−0.0734488	−	0.997299i	$-0.523401\pi$
$67$	−1.20241			−0.146898			−0.0734488	+	0.997299i	$0.523401\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−14.6826			−1.74250			−0.871250	−	0.490840i	$-0.836690\pi$
$71$	−14.6826			−1.74250			−0.871250	+	0.490840i	$0.836690\pi$
$72$		0			0
$73$	0.315636	+	0.546697i	0.0369423	+	0.0639860i	0.883905	−	0.467666i	$-0.154905\pi$
$73$	0.315636	+	0.546697i	0.0369423	+	0.0639860i	−0.846963	+	0.531652i	$0.821572\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.318883	−	1.00652i	0.0363400	−	0.114703i
$78$		0			0
$79$	2.48729			0.279842			0.139921	−	0.990163i	$-0.455315\pi$
$79$	2.48729			0.279842			0.139921	+	0.990163i	$0.455315\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.59366	−	7.95645i	−0.504219	−	0.873333i	−0.999988	−	0.00487885i	$-0.998447\pi$
$83$	−4.59366	−	7.95645i	−0.504219	−	0.873333i	0.495769	−	0.868455i	$-0.334886\pi$
$84$		0			0
$85$	−0.371628	+	0.643678i	−0.0403087	+	0.0698167i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.29358	+	12.6328i	−0.773118	+	1.33908i	0.162729	+	0.986671i	$0.447971\pi$
$89$	−7.29358	+	12.6328i	−0.773118	+	1.33908i	−0.935846	+	0.352408i	$0.885363\pi$
$90$		0			0
$91$	−2.30601	+	7.27866i	−0.241735	+	0.763011i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−11.9903			−1.23018
$96$		0			0
$97$	−7.84245	−	13.5835i	−0.796280	−	1.37920i	−0.922023	−	0.387134i	$-0.873465\pi$
$97$	−7.84245	−	13.5835i	−0.796280	−	1.37920i	0.125744	−	0.992063i	$-0.459868\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.0464285	+	0.0804166i	−0.00461981	+	0.00800175i	−0.868326	−	0.495994i	$-0.834804\pi$
$101$	−0.0464285	+	0.0804166i	−0.00461981	+	0.00800175i	0.863706	+	0.503996i	$0.168137\pi$
$102$		0			0
$103$	−9.95769	−	17.2472i	−0.981161	−	1.69942i	−0.657891	−	0.753113i	$-0.728551\pi$
$103$	−9.95769	−	17.2472i	−0.981161	−	1.69942i	−0.323270	−	0.946307i	$-0.604782\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.89225	+	5.00953i	−0.279605	+	0.484290i	−0.971287	−	0.237913i	$-0.923537\pi$
$107$	−2.89225	+	5.00953i	−0.279605	+	0.484290i	0.691682	+	0.722202i	$0.256870\pi$
$108$		0			0
$109$	−6.25516	−	10.8343i	−0.599136	−	1.03773i	−0.992949	−	0.118543i	$-0.962178\pi$
$109$	−6.25516	−	10.8343i	−0.599136	−	1.03773i	0.393813	−	0.919191i	$-0.371156\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.69411	+	2.93428i	−0.159368	+	0.276034i	−0.934641	−	0.355593i	$-0.884279\pi$
$113$	−1.69411	+	2.93428i	−0.159368	+	0.276034i	0.775273	+	0.631627i	$0.217612\pi$
$114$		0			0
$115$	−0.923161	+	1.59896i	−0.0860853	+	0.149104i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.630359	−	0.689825i	−0.0577849	−	0.0632362i
$120$		0			0
$121$	5.42037	+	9.38836i	0.492761	+	0.853488i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.7247			1.04869
$126$		0			0
$127$	−14.7348			−1.30750			−0.653752	−	0.756709i	$-0.726806\pi$
$127$	−14.7348			−1.30750			−0.653752	+	0.756709i	$0.726806\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.95392	+	12.0445i	0.607567	+	1.05234i	0.991640	+	0.129034i	$0.0411877\pi$
$131$	6.95392	+	12.0445i	0.607567	+	1.05234i	−0.384073	+	0.923303i	$0.625479\pi$
$132$		0			0
$133$	4.55294	−	14.3709i	0.394790	−	1.24611i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.27874	−	12.6072i	0.621865	−	1.07710i	−0.367273	−	0.930113i	$-0.619709\pi$
$137$	7.27874	−	12.6072i	0.621865	−	1.07710i	0.989138	−	0.146989i	$-0.0469581\pi$
$138$		0			0
$139$	3.63996	−	6.30460i	0.308737	−	0.534749i	−0.669349	−	0.742948i	$-0.733427\pi$
$139$	3.63996	−	6.30460i	0.308737	−	0.534749i	0.978086	+	0.208199i	$0.0667603\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.575818	+	0.997347i	0.0481523	+	0.0834023i
$144$		0			0
$145$	1.84134	−	3.18930i	0.152915	−	0.264857i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.360832	−	0.624979i	−0.0295605	−	0.0512003i	0.850867	−	0.525382i	$-0.176077\pi$
$149$	−0.360832	−	0.624979i	−0.0295605	−	0.0512003i	−0.880427	+	0.474181i	$0.842744\pi$
$150$		0			0
$151$	10.9022	−	18.8831i	0.887207	−	1.53669i	0.0440432	−	0.999030i	$-0.485976\pi$
$151$	10.9022	−	18.8831i	0.887207	−	1.53669i	0.843163	−	0.537657i	$-0.180691\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−9.61173	−	16.6480i	−0.772033	−	1.33720i
$156$		0			0
$157$	5.17973			0.413387			0.206694	−	0.978406i	$-0.433730\pi$
$157$	5.17973			0.413387			0.206694	+	0.978406i	$0.433730\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.56588	−	1.71360i	−0.123408	−	0.135050i
$162$		0			0
$163$	−2.63906	+	4.57098i	−0.206707	+	0.358027i	−0.950675	−	0.310188i	$-0.899608\pi$
$163$	−2.63906	+	4.57098i	−0.206707	+	0.358027i	0.743968	+	0.668215i	$0.232941\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.83710	+	11.8422i	−0.529071	+	0.916378i	0.470354	+	0.882478i	$0.344126\pi$
$167$	−6.83710	+	11.8422i	−0.529071	+	0.916378i	−0.999425	+	0.0339001i	$0.989207\pi$
$168$		0			0
$169$	2.33596	+	4.04599i	0.179689	+	0.311230i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−20.1824			−1.53444			−0.767218	−	0.641386i	$-0.778360\pi$
$173$	−20.1824			−1.53444			−0.767218	+	0.641386i	$0.778360\pi$
$174$		0			0
$175$	−0.456682	+	1.44147i	−0.0345219	+	0.108965i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.5968	+	21.8183i	0.941528	+	1.63077i	0.762557	+	0.646921i	$0.223944\pi$
$179$	12.5968	+	21.8183i	0.941528	+	1.63077i	0.178971	+	0.983854i	$0.442723\pi$
$180$		0			0
$181$	−17.2815			−1.28453			−0.642263	−	0.766485i	$-0.722004\pi$
$181$	−17.2815			−1.28453			−0.642263	+	0.766485i	$0.722004\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−14.2912			−1.05071
$186$		0			0
$187$	−0.140946			−0.0103070
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.01898			−0.363161			−0.181580	−	0.983376i	$-0.558121\pi$
$191$	−5.01898			−0.363161			−0.181580	+	0.983376i	$0.558121\pi$
$192$		0			0
$193$	−5.43765			−0.391411			−0.195705	−	0.980663i	$-0.562700\pi$
$193$	−5.43765			−0.391411			−0.195705	+	0.980663i	$0.562700\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.95839			−0.424517			−0.212259	−	0.977214i	$-0.568082\pi$
$197$	−5.95839			−0.424517			−0.212259	+	0.977214i	$0.568082\pi$
$198$		0			0
$199$	−5.62062	−	9.73520i	−0.398435	−	0.690110i	0.595098	−	0.803653i	$-0.297113\pi$
$199$	−5.62062	−	9.73520i	−0.398435	−	0.690110i	−0.993533	+	0.113543i	$0.963780\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.12330	+	3.41795i	0.219213	+	0.239893i
$204$		0			0
$205$	−5.06643			−0.353855
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.13689	−	1.96914i	−0.0786401	−	0.136209i
$210$		0			0
$211$	−0.381084	+	0.660057i	−0.0262349	+	0.0454402i	−0.878845	−	0.477108i	$-0.841685\pi$
$211$	−0.381084	+	0.660057i	−0.0262349	+	0.0454402i	0.852610	+	0.522548i	$0.175018\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.582381	−	1.00871i	0.0397181	−	0.0687937i
$216$		0			0
$217$	23.6030	−	5.19848i	1.60228	−	0.352896i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.01926			0.0685626
$222$		0			0
$223$	5.80556	+	10.0555i	0.388769	+	0.673368i	0.992284	−	0.123984i	$-0.0395670\pi$
$223$	5.80556	+	10.0555i	0.388769	+	0.673368i	−0.603515	+	0.797352i	$0.706234\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.16624	−	8.94818i	0.342895	−	0.593912i	−0.642074	−	0.766643i	$-0.721926\pi$
$227$	5.16624	−	8.94818i	0.342895	−	0.593912i	0.984969	+	0.172731i	$0.0552591\pi$
$228$		0			0
$229$	1.86191	+	3.22493i	0.123039	+	0.213109i	0.920965	−	0.389646i	$-0.127403\pi$
$229$	1.86191	+	3.22493i	0.123039	+	0.213109i	−0.797926	+	0.602756i	$0.794069\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.3649	+	23.1488i	−0.875566	+	1.51653i	−0.0194083	+	0.999812i	$0.506178\pi$
$233$	−13.3649	+	23.1488i	−0.875566	+	1.51653i	−0.856158	+	0.516714i	$0.827155\pi$
$234$		0			0
$235$	12.3499	+	21.3906i	0.805616	+	1.39537i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.94164	−	12.0233i	0.449018	−	0.777721i	−0.549305	−	0.835622i	$-0.685107\pi$
$239$	6.94164	−	12.0233i	0.449018	−	0.777721i	0.998322	+	0.0579007i	$0.0184407\pi$
$240$		0			0
$241$	−7.45280	+	12.9086i	−0.480077	+	0.831518i	−0.999739	−	0.0228542i	$-0.992725\pi$
$241$	−7.45280	+	12.9086i	−0.480077	+	0.831518i	0.519662	+	0.854372i	$0.326058\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.0434	+	8.48251i	0.769423	+	0.541928i
$246$		0			0
$247$	8.22142	+	14.2399i	0.523116	+	0.906064i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	22.5515			1.42344			0.711720	−	0.702464i	$-0.247917\pi$
$251$	22.5515			1.42344			0.711720	+	0.702464i	$0.247917\pi$
$252$		0			0
$253$	−0.350125			−0.0220122
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.94765	+	10.3016i	0.371004	+	0.642598i	0.989720	−	0.143017i	$-0.0456803\pi$
$257$	5.94765	+	10.3016i	0.371004	+	0.642598i	−0.618716	+	0.785615i	$0.712347\pi$
$258$		0			0
$259$	5.42660	−	17.1285i	0.337193	−	1.06431i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.3030	+	21.3094i	−0.758633	+	1.31399i	0.184915	+	0.982755i	$0.440799\pi$
$263$	−12.3030	+	21.3094i	−0.758633	+	1.31399i	−0.943548	+	0.331236i	$0.892534\pi$
$264$		0			0
$265$	−4.37337	+	7.57490i	−0.268654	+	0.465322i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.75722	−	11.7039i	−0.411995	−	0.713597i	0.583113	−	0.812391i	$-0.301835\pi$
$269$	−6.75722	−	11.7039i	−0.411995	−	0.713597i	−0.995108	+	0.0987947i	$0.968501\pi$
$270$		0			0
$271$	1.34195	−	2.32433i	0.0815177	−	0.141193i	−0.822384	−	0.568932i	$-0.807357\pi$
$271$	1.34195	−	2.32433i	0.0815177	−	0.141193i	0.903902	+	0.427740i	$0.140690\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.114035	+	0.197515i	0.00687658	+	0.0119106i
$276$		0			0
$277$	−9.52618	+	16.4998i	−0.572373	+	0.991379i	0.423949	+	0.905686i	$0.360644\pi$
$277$	−9.52618	+	16.4998i	−0.572373	+	0.991379i	−0.996322	+	0.0856928i	$0.972690\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.2006	−	24.5962i	−0.847139	−	1.46729i	−0.883751	−	0.467958i	$-0.844990\pi$
$281$	−14.2006	−	24.5962i	−0.847139	−	1.46729i	0.0366118	−	0.999330i	$-0.488343\pi$
$282$		0			0
$283$	15.4221			0.916749			0.458374	−	0.888759i	$-0.348432\pi$
$283$	15.4221			0.916749			0.458374	+	0.888759i	$0.348432\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.92381	−	6.07230i	0.113559	−	0.358436i
$288$		0			0
$289$	8.43763	−	14.6144i	0.496331	−	0.859671i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.02253	+	15.6275i	−0.527102	+	0.912967i	0.472399	+	0.881385i	$0.343388\pi$
$293$	−9.02253	+	15.6275i	−0.527102	+	0.912967i	−0.999501	+	0.0315825i	$0.989945\pi$
$294$		0			0
$295$	−9.81092	−	16.9930i	−0.571214	−	0.989371i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.53194			0.146426
$300$		0			0
$301$	0.987841	+	1.08103i	0.0569382	+	0.0623096i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.5978	−	18.3559i	−0.606826	−	1.05105i
$306$		0			0
$307$	7.30860			0.417124			0.208562	−	0.978009i	$-0.433122\pi$
$307$	7.30860			0.417124			0.208562	+	0.978009i	$0.433122\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−23.7792			−1.34839			−0.674197	−	0.738551i	$-0.735510\pi$
$311$	−23.7792			−1.34839			−0.674197	+	0.738551i	$0.735510\pi$
$312$		0			0
$313$	−18.2907			−1.03385			−0.516925	−	0.856031i	$-0.672923\pi$
$313$	−18.2907			−1.03385			−0.516925	+	0.856031i	$0.672923\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.68988			0.263410			0.131705	−	0.991289i	$-0.457955\pi$
$317$	4.68988			0.263410			0.131705	+	0.991289i	$0.457955\pi$
$318$		0			0
$319$	0.698360			0.0391007
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.01240			−0.111973
$324$		0			0
$325$	−0.824648	−	1.42833i	−0.0457432	−	0.0792296i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−30.3268	+	6.67938i	−1.67197	+	0.368246i
$330$		0			0
$331$	11.4287			0.628176			0.314088	−	0.949394i	$-0.398301\pi$
$331$	11.4287			0.628176			0.314088	+	0.949394i	$0.398301\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.26517	−	2.19134i	−0.0691238	−	0.119726i
$336$		0			0
$337$	8.74160	−	15.1409i	0.476185	−	0.824777i	−0.523442	−	0.852061i	$-0.675353\pi$
$337$	8.74160	−	15.1409i	0.476185	−	0.824777i	0.999628	+	0.0272840i	$0.00868584\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.82271	−	3.15702i	0.0987051	−	0.170962i
$342$		0			0
$343$	−14.7397	+	11.2135i	−0.795868	+	0.605470i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.1186			0.757925			0.378962	−	0.925412i	$-0.376281\pi$
$347$	14.1186			0.757925			0.378962	+	0.925412i	$0.376281\pi$
$348$		0			0
$349$	10.7216	+	18.5704i	0.573916	+	0.994052i	0.996158	+	0.0875692i	$0.0279099\pi$
$349$	10.7216	+	18.5704i	0.573916	+	0.994052i	−0.422242	+	0.906483i	$0.638757\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−15.6880	+	27.1724i	−0.834987	+	1.44624i	0.0590538	+	0.998255i	$0.481192\pi$
$353$	−15.6880	+	27.1724i	−0.834987	+	1.44624i	−0.894041	+	0.447985i	$0.852142\pi$
$354$		0			0
$355$	−15.4490	−	26.7584i	−0.819946	−	1.42019i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.313156	−	0.542402i	0.0165277	−	0.0286269i	−0.857643	−	0.514245i	$-0.828072\pi$
$359$	0.313156	−	0.542402i	0.0165277	−	0.0286269i	0.874171	+	0.485618i	$0.161405\pi$
$360$		0			0
$361$	−6.73223	−	11.6606i	−0.354328	−	0.613714i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.664223	+	1.15047i	−0.0347670	+	0.0602182i
$366$		0			0
$367$	−1.62199	+	2.80936i	−0.0846670	+	0.146648i	−0.905249	−	0.424881i	$-0.860316\pi$
$367$	−1.62199	+	2.80936i	−0.0846670	+	0.146648i	0.820582	+	0.571528i	$0.193649\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.41815	−	8.11796i	−0.385131	−	0.421464i
$372$		0			0
$373$	13.8013	+	23.9046i	0.714606	+	1.23773i	0.963111	+	0.269103i	$0.0867272\pi$
$373$	13.8013	+	23.9046i	0.714606	+	1.23773i	−0.248506	+	0.968630i	$0.579939\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.05021			−0.260099
$378$		0			0
$379$	12.7800			0.656463			0.328231	−	0.944597i	$-0.393547\pi$
$379$	12.7800			0.656463			0.328231	+	0.944597i	$0.393547\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.58278	+	4.47351i	0.131974	+	0.228586i	0.924437	−	0.381334i	$-0.124535\pi$
$383$	2.58278	+	4.47351i	0.131974	+	0.228586i	−0.792463	+	0.609919i	$0.791202\pi$
$384$		0			0
$385$	2.16987	−	0.477906i	0.110587	−	0.0243564i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.4707	−	28.5280i	0.835095	−	1.44643i	−0.0588576	−	0.998266i	$-0.518746\pi$
$389$	16.4707	−	28.5280i	0.835095	−	1.44643i	0.893953	−	0.448161i	$-0.147921\pi$
$390$		0			0
$391$	−0.154939	+	0.268362i	−0.00783560	+	0.0135717i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.61712	+	4.53299i	0.131682	+	0.228079i
$396$		0			0
$397$	−0.411705	+	0.713095i	−0.0206629	+	0.0357892i	−0.876172	−	0.481999i	$-0.839911\pi$
$397$	−0.411705	+	0.713095i	−0.0206629	+	0.0357892i	0.855509	+	0.517788i	$0.173244\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.86923	−	17.0940i	−0.492846	−	0.853634i	0.507120	−	0.861875i	$-0.330710\pi$
$401$	−9.86923	−	17.0940i	−0.492846	−	0.853634i	−0.999966	+	0.00824153i	$0.997377\pi$
$402$		0			0
$403$	−13.1809	+	22.8301i	−0.656590	+	1.13725i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.35504	−	2.34700i	−0.0671670	−	0.116337i
$408$		0			0
$409$	−25.2551			−1.24879			−0.624393	−	0.781110i	$-0.714654\pi$
$409$	−25.2551			−1.24879			−0.624393	+	0.781110i	$0.714654\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0921	−	5.30621i	1.18550	−	0.261101i
$414$		0			0
$415$	9.66688	−	16.7435i	0.474528	−	0.821907i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.406717	−	0.704455i	0.0198694	−	0.0344149i	−0.855920	−	0.517109i	$-0.827008\pi$
$419$	0.406717	−	0.704455i	0.0198694	−	0.0344149i	0.875789	+	0.482694i	$0.160342\pi$
$420$		0			0
$421$	5.12114	+	8.87008i	0.249589	+	0.432301i	0.963412	−	0.268025i	$-0.0863711\pi$
$421$	5.12114	+	8.87008i	0.249589	+	0.432301i	−0.713823	+	0.700326i	$0.753038\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.201854			0.00979134
$426$		0			0
$427$	26.0243	−	5.73177i	1.25941	−	0.277380i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	16.3348	+	28.2928i	0.786822	+	1.36281i	0.927905	+	0.372817i	$0.121608\pi$
$431$	16.3348	+	28.2928i	0.786822	+	1.36281i	−0.141083	+	0.989998i	$0.545059\pi$
$432$		0			0
$433$	−14.3151			−0.687941			−0.343970	−	0.938980i	$-0.611772\pi$
$433$	−14.3151			−0.687941			−0.343970	+	0.938980i	$0.611772\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.99901			−0.239135
$438$		0			0
$439$	9.86660			0.470907			0.235453	−	0.971886i	$-0.424342\pi$
$439$	9.86660			0.470907			0.235453	+	0.971886i	$0.424342\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	37.2801			1.77123			0.885615	−	0.464419i	$-0.153737\pi$
$443$	37.2801			1.77123			0.885615	+	0.464419i	$0.153737\pi$
$444$		0			0
$445$	−30.6972			−1.45519
$446$		0			0
$447$		0			0
$448$		0			0
$449$	36.2926			1.71276			0.856378	−	0.516350i	$-0.172710\pi$
$449$	36.2926			1.71276			0.856378	+	0.516350i	$0.172710\pi$
$450$		0			0
$451$	−0.480382	−	0.832046i	−0.0226203	−	0.0391795i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−15.6915	+	3.45599i	−0.735627	+	0.162019i
$456$		0			0
$457$	−13.1943			−0.617205			−0.308602	−	0.951191i	$-0.599861\pi$
$457$	−13.1943			−0.617205			−0.308602	+	0.951191i	$0.599861\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.1326	−	17.5502i	−0.471924	−	0.817396i	0.527560	−	0.849518i	$-0.323107\pi$
$461$	−10.1326	−	17.5502i	−0.471924	−	0.817396i	−0.999484	+	0.0321215i	$0.989774\pi$
$462$		0			0
$463$	−12.7106	+	22.0154i	−0.590712	+	1.02314i	0.403424	+	0.915013i	$0.367820\pi$
$463$	−12.7106	+	22.0154i	−0.590712	+	1.02314i	−0.994137	+	0.108131i	$0.965513\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.40661	+	7.63248i	−0.203914	+	0.353189i	−0.949786	−	0.312900i	$-0.898700\pi$
$467$	−4.40661	+	7.63248i	−0.203914	+	0.353189i	0.745872	+	0.666089i	$0.232033\pi$
$468$		0			0
$469$	3.10681	−	0.684265i	0.143459	−	0.0315964i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.220878			0.0101560
$474$		0			0
$475$	1.62817	+	2.82008i	0.0747056	+	0.129394i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.1343	+	21.0173i	−0.554433	+	0.960305i	0.443515	+	0.896267i	$0.353731\pi$
$479$	−12.1343	+	21.0173i	−0.554433	+	0.960305i	−0.997947	+	0.0640383i	$0.979602\pi$
$480$		0			0
$481$	9.79902	+	16.9724i	0.446797	+	0.773875i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	16.5036	−	28.5851i	0.749391	−	1.29798i
$486$		0			0
$487$	5.37220	+	9.30492i	0.243438	+	0.421646i	0.961691	−	0.274135i	$-0.0883916\pi$
$487$	5.37220	+	9.30492i	0.243438	+	0.421646i	−0.718254	+	0.695781i	$0.755058\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	11.3934	−	19.7340i	0.514179	−	0.890584i	−0.485686	−	0.874134i	$-0.661430\pi$
$491$	11.3934	−	19.7340i	0.514179	−	0.890584i	0.999865	−	0.0164507i	$-0.00523665\pi$
$492$		0			0
$493$	0.309042	−	0.535276i	0.0139185	−	0.0241076i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	37.9372	−	8.35553i	1.70171	−	0.374797i
$498$		0			0
$499$	11.5755	+	20.0493i	0.518189	+	0.897530i	0.999777	+	0.0211317i	$0.00672693\pi$
$499$	11.5755	+	20.0493i	0.518189	+	0.897530i	−0.481588	+	0.876398i	$0.659940\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.43360			0.420623			0.210312	−	0.977634i	$-0.432552\pi$
$503$	9.43360			0.420623			0.210312	+	0.977634i	$0.432552\pi$
$504$		0			0
$505$	−0.195408			−0.00869555
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.72981	−	8.19228i	−0.209645	−	0.363116i	0.741957	−	0.670447i	$-0.233898\pi$
$509$	−4.72981	−	8.19228i	−0.209645	−	0.363116i	−0.951603	+	0.307331i	$0.900564\pi$
$510$		0			0
$511$	−1.12666	−	1.23295i	−0.0498405	−	0.0545424i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	20.9549	−	36.2950i	0.923385	−	1.59935i
$516$		0			0
$517$	−2.34195	+	4.05637i	−0.102999	+	0.178399i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	14.3368	+	24.8320i	0.628105	+	1.08791i	0.987932	+	0.154891i	$0.0495026\pi$
$521$	14.3368	+	24.8320i	0.628105	+	1.08791i	−0.359826	+	0.933019i	$0.617164\pi$
$522$		0			0
$523$	13.5104	−	23.4006i	0.590767	−	1.02324i	−0.403362	−	0.915040i	$-0.632159\pi$
$523$	13.5104	−	23.4006i	0.590767	−	1.02324i	0.994129	−	0.108198i	$-0.0345081\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.61319	−	2.79412i	−0.0702715	−	0.121714i
$528$		0			0
$529$	11.1151	−	19.2519i	0.483266	−	0.837041i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.47389	+	6.01696i	0.150471	+	0.260624i
$534$		0			0
$535$	−12.1729			−0.526280
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.251148	+	2.78214i	−0.0108177	+	0.119835i
$540$		0			0
$541$	−1.52907	+	2.64842i	−0.0657397	+	0.113864i	−0.897022	−	0.441986i	$-0.854274\pi$
$541$	−1.52907	+	2.64842i	−0.0657397	+	0.113864i	0.831282	+	0.555851i	$0.187607\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	13.1633	−	22.7996i	0.563856	−	0.976627i
$546$		0			0
$547$	−3.58144	−	6.20323i	−0.153131	−	0.265231i	0.779246	−	0.626719i	$-0.215602\pi$
$547$	−3.58144	−	6.20323i	−0.153131	−	0.265231i	−0.932377	+	0.361487i	$0.882269\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.97105			0.424781
$552$		0			0
$553$	−6.42672	+	1.41546i	−0.273292	+	0.0601916i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.3518	+	24.8580i	0.608104	+	1.05327i	0.991553	+	0.129704i	$0.0414028\pi$
$557$	14.3518	+	24.8580i	0.608104	+	1.05327i	−0.383449	+	0.923562i	$0.625264\pi$
$558$		0			0
$559$	−1.59729			−0.0675580
$560$		0			0
$561$		0			0
$562$		0			0
$563$	35.7719			1.50761			0.753803	−	0.657101i	$-0.228218\pi$
$563$	35.7719			1.50761			0.753803	+	0.657101i	$0.228218\pi$
$564$		0			0
$565$	−7.13016			−0.299968
$566$		0			0
$567$		0			0
$568$		0			0
$569$	25.2002			1.05645			0.528223	−	0.849106i	$-0.322858\pi$
$569$	25.2002			1.05645			0.528223	+	0.849106i	$0.322858\pi$
$570$		0			0
$571$	6.04938			0.253159			0.126579	−	0.991956i	$-0.459600\pi$
$571$	6.04938			0.253159			0.126579	+	0.991956i	$0.459600\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.501425			0.0209109
$576$		0			0
$577$	9.57977	+	16.5926i	0.398811	+	0.690761i	0.993580	−	0.113136i	$-0.0360896\pi$
$577$	9.57977	+	16.5926i	0.398811	+	0.690761i	−0.594768	+	0.803897i	$0.702756\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.3970	+	17.9439i	0.680264	+	0.744439i
$582$		0			0
$583$	−1.65868			−0.0686953
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.4147	+	31.8953i	0.760058	+	1.31646i	0.942820	+	0.333301i	$0.108163\pi$
$587$	18.4147	+	31.8953i	0.760058	+	1.31646i	−0.182763	+	0.983157i	$0.558504\pi$
$588$		0			0
$589$	26.0242	−	45.0753i	1.07231	−	1.85730i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8.97285	+	15.5414i	−0.368471	+	0.638210i	−0.989327	−	0.145715i	$-0.953452\pi$
$593$	−8.97285	+	15.5414i	−0.368471	+	0.638210i	0.620856	+	0.783925i	$0.286785\pi$
$594$		0			0
$595$	0.593918	−	1.87464i	0.0243482	−	0.0768526i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−40.4913			−1.65443			−0.827215	−	0.561885i	$-0.810076\pi$
$599$	−40.4913			−1.65443			−0.827215	+	0.561885i	$0.810076\pi$
$600$		0			0
$601$	13.2589	+	22.9651i	0.540841	+	0.936765i	0.998856	+	0.0478200i	$0.0152274\pi$
$601$	13.2589	+	22.9651i	0.540841	+	0.936765i	−0.458015	+	0.888945i	$0.651439\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−11.4066	+	19.7568i	−0.463745	+	0.803230i
$606$		0			0
$607$	−21.0848	−	36.5200i	−0.855806	−	1.48230i	−0.875895	−	0.482501i	$-0.839729\pi$
$607$	−21.0848	−	36.5200i	−0.855806	−	1.48230i	0.0200897	−	0.999798i	$-0.493605\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	16.9358	−	29.3337i	0.685151	−	1.18672i
$612$		0			0
$613$	−0.700827	−	1.21387i	−0.0283061	−	0.0490277i	0.851525	−	0.524313i	$-0.175678\pi$
$613$	−0.700827	−	1.21387i	−0.0283061	−	0.0490277i	−0.879831	+	0.475286i	$0.842345\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.76787	−	11.7223i	0.272464	−	0.471922i	−0.697028	−	0.717044i	$-0.745495\pi$
$617$	6.76787	−	11.7223i	0.272464	−	0.471922i	0.969492	+	0.245122i	$0.0788280\pi$
$618$		0			0
$619$	−14.9122	+	25.8288i	−0.599374	+	1.03815i	0.393540	+	0.919308i	$0.371250\pi$
$619$	−14.9122	+	25.8288i	−0.599374	+	1.03815i	−0.992914	+	0.118838i	$0.962083\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.6562	−	36.7917i	0.466997	−	1.47403i
$624$		0			0
$625$	10.9079	+	18.8930i	0.436316	+	0.755722i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.39856			−0.0956369
$630$		0			0
$631$	−6.84708			−0.272578			−0.136289	−	0.990669i	$-0.543518\pi$
$631$	−6.84708			−0.272578			−0.136289	+	0.990669i	$0.543518\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−15.5040	−	26.8536i	−0.615256	−	1.06565i
$636$		0			0
$637$	1.81618	−	20.1191i	0.0719598	−	0.797147i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.1209	−	27.9221i	0.636735	−	1.10286i	−0.349409	−	0.936970i	$-0.613618\pi$
$641$	16.1209	−	27.9221i	0.636735	−	1.10286i	0.986145	−	0.165888i	$-0.0530489\pi$
$642$		0			0
$643$	−1.16002	+	2.00921i	−0.0457465	+	0.0792353i	−0.887992	−	0.459859i	$-0.847900\pi$
$643$	−1.16002	+	2.00921i	−0.0457465	+	0.0792353i	0.842245	+	0.539094i	$0.181233\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.06813	+	1.85005i	0.0419924	+	0.0727329i	0.886258	−	0.463193i	$-0.153296\pi$
$647$	1.06813	+	1.85005i	0.0419924	+	0.0727329i	−0.844265	+	0.535925i	$0.819963\pi$
$648$		0			0
$649$	1.86048	−	3.22244i	0.0730302	−	0.126492i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.51932	+	2.63155i	0.0594558	+	0.102980i	0.894221	−	0.447625i	$-0.147730\pi$
$653$	1.51932	+	2.63155i	0.0594558	+	0.102980i	−0.834765	+	0.550606i	$0.814397\pi$
$654$		0			0
$655$	−14.6338	+	25.3465i	−0.571790	+	0.990370i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.8000	−	34.2946i	−0.771298	−	1.33593i	−0.936852	−	0.349726i	$-0.886275\pi$
$659$	−19.8000	−	34.2946i	−0.771298	−	1.33593i	0.165554	−	0.986201i	$-0.447059\pi$
$660$		0			0
$661$	6.12398			0.238195			0.119098	−	0.992883i	$-0.462000\pi$
$661$	6.12398			0.238195			0.119098	+	0.992883i	$0.462000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	30.9810	−	6.82345i	1.20139	−	0.264602i
$666$		0			0
$667$	0.767691	−	1.32968i	0.0297251	−	0.0514854i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.00969	−	3.48089i	0.0775832	−	0.134378i
$672$		0			0
$673$	−4.36248	−	7.55603i	−0.168161	−	0.291264i	0.769612	−	0.638512i	$-0.220450\pi$
$673$	−4.36248	−	7.55603i	−0.168161	−	0.291264i	−0.937773	+	0.347248i	$0.887116\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.9601			−0.574965			−0.287482	−	0.957786i	$-0.592818\pi$
$677$	−14.9601			−0.574965			−0.287482	+	0.957786i	$0.592818\pi$
$678$		0			0
$679$	27.9936	+	30.6345i	1.07430	+	1.17564i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.89558	−	15.4076i	−0.340380	−	0.589555i	0.644123	−	0.764922i	$-0.277222\pi$
$683$	−8.89558	−	15.4076i	−0.340380	−	0.589555i	−0.984503	+	0.175366i	$0.943889\pi$
$684$		0			0
$685$	30.6347			1.17049
$686$		0			0
$687$		0			0
$688$		0			0
$689$	11.9948			0.456964
$690$		0			0
$691$	29.5389			1.12371			0.561856	−	0.827235i	$-0.310087\pi$
$691$	29.5389			1.12371			0.561856	+	0.827235i	$0.310087\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	15.3198			0.581115
$696$		0			0
$697$	−0.850324			−0.0322083
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−27.7740			−1.04901			−0.524504	−	0.851408i	$-0.675749\pi$
$701$	−27.7740			−1.04901			−0.524504	+	0.851408i	$0.675749\pi$
$702$		0			0
$703$	−19.3470	−	33.5100i	−0.729687	−	1.26385i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.0741998	−	0.234204i	0.00279057	−	0.00880814i
$708$		0			0
$709$	47.0984			1.76882			0.884409	−	0.466712i	$-0.154562\pi$
$709$	47.0984			1.76882			0.884409	+	0.466712i	$0.154562\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.00732	−	6.94088i	−0.150075	−	0.259938i
$714$		0			0
$715$	−1.21175	+	2.09881i	−0.0453169	+	0.0784912i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.63394	−	2.83007i	0.0609357	−	0.105544i	−0.833948	−	0.551843i	$-0.813925\pi$
$719$	1.63394	−	2.83007i	0.0609357	−	0.105544i	0.894884	+	0.446299i	$0.147258\pi$
$720$		0			0
$721$	35.5440	+	38.8971i	1.32373	+	1.44860i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.00014			−0.0371444
$726$		0			0
$727$	6.37047	+	11.0340i	0.236268	+	0.409228i	0.959640	−	0.281230i	$-0.0907424\pi$
$727$	6.37047	+	11.0340i	0.236268	+	0.409228i	−0.723373	+	0.690458i	$0.757409\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.0977441	−	0.169298i	0.00361520	−	0.00626170i
$732$		0			0
$733$	−4.58858	−	7.94765i	−0.169483	−	0.293553i	0.768755	−	0.639543i	$-0.220876\pi$
$733$	−4.58858	−	7.94765i	−0.169483	−	0.293553i	−0.938238	+	0.345990i	$0.887543\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.239919	−	0.415552i	0.00883754	−	0.0153071i
$738$		0			0
$739$	23.3467	+	40.4377i	0.858823	+	1.48752i	0.873053	+	0.487626i	$0.162137\pi$
$739$	23.3467	+	40.4377i	0.858823	+	1.48752i	−0.0142303	+	0.999899i	$0.504530\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7.62654	+	13.2095i	−0.279790	+	0.484611i	−0.971333	−	0.237725i	$-0.923598\pi$
$743$	−7.62654	+	13.2095i	−0.279790	+	0.484611i	0.691542	+	0.722336i	$0.256932\pi$
$744$		0			0
$745$	0.759333	−	1.31520i	0.0278198	−	0.0481853i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.62226	−	14.5897i	0.168894	−	0.533095i
$750$		0			0
$751$	3.17443	+	5.49828i	0.115837	+	0.200635i	0.918114	−	0.396317i	$-0.129712\pi$
$751$	3.17443	+	5.49828i	0.115837	+	0.200635i	−0.802277	+	0.596952i	$0.796378\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	45.8850			1.66993
$756$		0			0
$757$	28.4278			1.03323			0.516614	−	0.856219i	$-0.327192\pi$
$757$	28.4278			1.03323			0.516614	+	0.856219i	$0.327192\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.03437	−	15.6480i	−0.327496	−	0.567239i	0.654519	−	0.756046i	$-0.272871\pi$
$761$	−9.03437	−	15.6480i	−0.327496	−	0.567239i	−0.982014	+	0.188807i	$0.939538\pi$
$762$		0			0
$763$	22.3278	+	24.4341i	0.808320	+	0.884575i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.4541	+	23.3032i	−0.485799	+	0.841429i
$768$		0			0
$769$	−1.72471	+	2.98728i	−0.0621946	+	0.107724i	−0.895446	−	0.445170i	$-0.853143\pi$
$769$	−1.72471	+	2.98728i	−0.0621946	+	0.107724i	0.833252	+	0.552894i	$0.186477\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	20.1837	+	34.9592i	0.725957	+	1.25740i	0.958579	+	0.284828i	$0.0919364\pi$
$773$	20.1837	+	34.9592i	0.725957	+	1.25740i	−0.232621	+	0.972567i	$0.574730\pi$
$774$		0			0
$775$	−2.61036	+	4.52127i	−0.0937668	+	0.162409i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.85880	−	11.8798i	−0.245742	−	0.425638i
$780$		0			0
$781$	2.92964	−	5.07429i	0.104831	−	0.181572i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.45010	+	9.43985i	0.194522	+	0.336923i
$786$		0			0
$787$	−18.3206			−0.653060			−0.326530	−	0.945187i	$-0.605879\pi$
$787$	−18.3206			−0.653060			−0.326530	+	0.945187i	$0.605879\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.70744	−	8.54575i	0.0962656	−	0.303852i
$792$		0			0
$793$	−14.5331	+	25.1721i	−0.516086	+	0.893888i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.86884	−	8.43307i	0.172463	−	0.298715i	−0.766817	−	0.641865i	$-0.778161\pi$
$797$	4.86884	−	8.43307i	0.172463	−	0.298715i	0.939280	+	0.343151i	$0.111494\pi$
$798$		0			0
$799$	2.07274	+	3.59009i	0.0733283	+	0.127008i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.251918			−0.00888998
$804$		0			0
$805$	1.47535	−	4.65679i	0.0519993	−	0.164130i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.98714	+	10.3700i	0.210497	+	0.364591i	0.951870	−	0.306502i	$-0.0991586\pi$
$809$	5.98714	+	10.3700i	0.210497	+	0.364591i	−0.741373	+	0.671093i	$0.765825\pi$
$810$		0			0
$811$	−4.05517			−0.142396			−0.0711982	−	0.997462i	$-0.522682\pi$
$811$	−4.05517			−0.142396			−0.0711982	+	0.997462i	$0.522682\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−11.1072			−0.389070
$816$		0			0
$817$	3.15365			0.110332
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.98513			−0.278683			−0.139341	−	0.990244i	$-0.544499\pi$
$821$	−7.98513			−0.278683			−0.139341	+	0.990244i	$0.544499\pi$
$822$		0			0
$823$	−47.5802			−1.65854			−0.829270	−	0.558847i	$-0.811244\pi$
$823$	−47.5802			−1.65854			−0.829270	+	0.558847i	$0.811244\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−29.2725			−1.01790			−0.508952	−	0.860795i	$-0.669967\pi$
$827$	−29.2725			−1.01790			−0.508952	+	0.860795i	$0.669967\pi$
$828$		0			0
$829$	3.15249	+	5.46028i	0.109491	+	0.189643i	0.915564	−	0.402172i	$-0.131745\pi$
$829$	3.15249	+	5.46028i	0.109491	+	0.189643i	−0.806073	+	0.591816i	$0.798411\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.02130	+	1.42366i	0.0700339	+	0.0493270i
$834$		0			0
$835$	−28.7760			−0.995833
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.501711	−	0.868989i	−0.0173210	−	0.0300008i	0.857235	−	0.514925i	$-0.172180\pi$
$839$	−0.501711	−	0.868989i	−0.0173210	−	0.0300008i	−0.874556	+	0.484925i	$0.838847\pi$
$840$		0			0
$841$	12.9688	−	22.4626i	0.447199	−	0.774571i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.91578	+	8.51438i	−0.169108	+	0.292904i
$846$		0			0
$847$	−19.3480	−	21.1733i	−0.664806	−	0.727522i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.95827			−0.204247
$852$		0			0
$853$	20.0519	+	34.7309i	0.686565	+	1.18916i	0.972942	+	0.231048i	$0.0742154\pi$
$853$	20.0519	+	34.7309i	0.686565	+	1.18916i	−0.286378	+	0.958117i	$0.592451\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.7388	+	32.4566i	−0.640106	+	1.10870i	0.345303	+	0.938491i	$0.387776\pi$
$857$	−18.7388	+	32.4566i	−0.640106	+	1.10870i	−0.985409	+	0.170205i	$0.945557\pi$
$858$		0			0
$859$	12.2516	+	21.2204i	0.418019	+	0.724031i	0.995740	−	0.0922036i	$-0.0293911\pi$
$859$	12.2516	+	21.2204i	0.418019	+	0.724031i	−0.577721	+	0.816234i	$0.696058\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.79806	−	16.9707i	0.333530	−	0.577691i	−0.649671	−	0.760215i	$-0.725094\pi$
$863$	9.79806	−	16.9707i	0.333530	−	0.577691i	0.983201	+	0.182524i	$0.0584269\pi$
$864$		0			0
$865$	−21.2359	−	36.7816i	−0.722041	−	1.25061i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.496294	+	0.859607i	−0.0168356	+	0.0291602i
$870$		0			0
$871$	−1.73498	+	3.00508i	−0.0587876	+	0.101823i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−30.2945	+	6.67226i	−1.02414	+	0.225564i
$876$		0			0
$877$	−17.1134	−	29.6414i	−0.577880	−	1.00092i	−0.995722	−	0.0923977i	$-0.970547\pi$
$877$	−17.1134	−	29.6414i	−0.577880	−	1.00092i	0.417842	−	0.908520i	$-0.362786\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	25.2818			0.851764			0.425882	−	0.904779i	$-0.359964\pi$
$881$	25.2818			0.851764			0.425882	+	0.904779i	$0.359964\pi$
$882$		0			0
$883$	45.4688			1.53015			0.765073	−	0.643943i	$-0.222703\pi$
$883$	45.4688			1.53015			0.765073	+	0.643943i	$0.222703\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.41504	−	9.37912i	−0.181819	−	0.314920i	0.760681	−	0.649126i	$-0.224865\pi$
$887$	−5.41504	−	9.37912i	−0.181819	−	0.314920i	−0.942500	+	0.334206i	$0.891532\pi$
$888$		0			0
$889$	38.0722	−	8.38527i	1.27690	−	0.281233i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−33.4378	+	57.9160i	−1.11895	+	1.93809i
$894$		0			0
$895$	−26.5087	+	45.9143i	−0.886086	+	1.53475i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	7.99301	+	13.8443i	0.266582	+	0.461733i
$900$		0			0
$901$	−0.734005	+	1.27133i	−0.0244533	+	0.0423543i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18.1836	−	31.4949i	−0.604443	−	1.04693i
$906$		0			0
$907$	2.00841	−	3.47868i	0.0666883	−	0.115508i	−0.830753	−	0.556641i	$-0.812090\pi$
$907$	2.00841	−	3.47868i	0.0666883	−	0.115508i	0.897442	+	0.441133i	$0.145423\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−8.43681	−	14.6130i	−0.279524	−	0.484150i	0.691743	−	0.722144i	$-0.256843\pi$
$911$	−8.43681	−	14.6130i	−0.279524	−	0.484150i	−0.971266	+	0.237995i	$0.923510\pi$
$912$		0			0
$913$	3.66633			0.121338
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−24.8220	−	27.1637i	−0.819695	−	0.897023i
$918$		0			0
$919$	16.9485	−	29.3557i	0.559081	−	0.968356i	−0.438493	−	0.898735i	$-0.644488\pi$
$919$	16.9485	−	29.3557i	0.559081	−	0.968356i	0.997573	−	0.0696214i	$-0.0221791\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−21.1858	+	36.6949i	−0.697339	+	1.20783i
$924$		0			0
$925$	1.94060	+	3.36122i	0.0638065	+	0.110516i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	38.6100			1.26675			0.633377	−	0.773843i	$-0.281668\pi$
$929$	38.6100			1.26675			0.633377	+	0.773843i	$0.281668\pi$
$930$		0			0
$931$	−3.58584	+	39.7228i	−0.117521	+	1.30186i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.148303	−	0.256869i	−0.00485004	−	0.00840052i
$936$		0			0
$937$	−45.4955			−1.48627			−0.743136	−	0.669140i	$-0.766663\pi$
$937$	−45.4955			−1.48627			−0.743136	+	0.669140i	$0.766663\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	17.9892			0.586431			0.293216	−	0.956046i	$-0.405275\pi$
$941$	17.9892			0.586431			0.293216	+	0.956046i	$0.405275\pi$
$942$		0			0
$943$	−2.11229			−0.0687857
$944$		0			0
$945$		0			0
$946$		0			0
$947$	16.5224			0.536906			0.268453	−	0.963293i	$-0.413488\pi$
$947$	16.5224			0.536906			0.268453	+	0.963293i	$0.413488\pi$
$948$		0			0
$949$	1.82175			0.0591365
$950$		0			0
$951$		0			0
$952$		0			0
$953$	15.6799			0.507922			0.253961	−	0.967214i	$-0.418266\pi$
$953$	15.6799			0.507922			0.253961	+	0.967214i	$0.418266\pi$
$954$		0			0
$955$	−5.28096	−	9.14690i	−0.170888	−	0.295987i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−11.6325	+	36.7168i	−0.375634	+	1.18565i
$960$		0			0
$961$	52.4465			1.69182
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5.72149	−	9.90991i	−0.184181	−	0.319011i
$966$		0			0
$967$	25.3908	−	43.9782i	0.816513	−	1.41424i	−0.0917230	−	0.995785i	$-0.529237\pi$
$967$	25.3908	−	43.9782i	0.816513	−	1.41424i	0.908236	−	0.418458i	$-0.137429\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.23027	+	15.9873i	−0.296214	+	0.513057i	−0.975266	−	0.221032i	$-0.929057\pi$
$971$	−9.23027	+	15.9873i	−0.296214	+	0.513057i	0.679053	+	0.734089i	$0.262391\pi$
$972$		0			0
$973$	−5.81721	+	18.3614i	−0.186491	+	0.588639i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−31.6302			−1.01194			−0.505970	−	0.862551i	$-0.668865\pi$
$977$	−31.6302			−1.01194			−0.505970	+	0.862551i	$0.668865\pi$
$978$		0			0
$979$	−2.91061	−	5.04132i	−0.0930234	−	0.161121i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.2066	+	34.9988i	−0.644490	+	1.11629i	0.339929	+	0.940451i	$0.389597\pi$
$983$	−20.2066	+	34.9988i	−0.644490	+	1.11629i	−0.984419	+	0.175838i	$0.943737\pi$
$984$		0			0
$985$	−6.26940	−	10.8589i	−0.199760	−	0.345994i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.242806	−	0.420553i	0.00772079	−	0.0133728i
$990$		0			0
$991$	−16.6187	−	28.7845i	−0.527911	−	0.914368i	−0.999471	−	0.0325343i	$-0.989642\pi$
$991$	−16.6187	−	28.7845i	−0.527911	−	0.914368i	0.471560	−	0.881834i	$-0.343691\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	11.8280	−	20.4867i	0.374973	−	0.649473i
$996$		0			0
$997$	20.5592	−	35.6096i	0.651117	−	1.12777i	−0.331735	−	0.943373i	$-0.607634\pi$
$997$	20.5592	−	35.6096i	0.651117	−	1.12777i	0.982852	−	0.184396i	$-0.0590328\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.5	✓	22	252.11	even	6
504.2.q.c.121.5	yes	22	12.11	even	2
504.2.t.c.193.11	yes	22	84.11	even	6
504.2.t.c.457.11	yes	22	36.11	even	6
1008.2.q.l.529.7		22	63.11	odd	6
1008.2.q.l.625.7		22	3.2	odd	2
1008.2.t.l.193.1		22	21.11	odd	6
1008.2.t.l.961.1		22	9.2	odd	6
1512.2.q.d.793.8		22	4.3	odd	2
1512.2.q.d.1369.8		22	252.151	odd	6
1512.2.t.c.289.4		22	36.7	odd	6
1512.2.t.c.361.4		22	28.11	odd	6
3024.2.q.l.2305.8		22	1.1	even	1	trivial
3024.2.q.l.2881.8		22	63.25	even	3	inner
3024.2.t.k.289.4		22	9.7	even	3
3024.2.t.k.1873.4		22	7.4	even	3

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

\(f(q)\)	\(=\)	\(q+(1.05220 + 1.82246i) q^{5} +(-2.58382 + 0.569079i) q^{7} +O(q^{10})\)	\(q+(1.05220 + 1.82246i) q^{5} +(-2.58382 + 0.569079i) q^{7} +(-0.199532 + 0.345600i) q^{11} +(1.44292 - 2.49921i) q^{13} +(0.176596 + 0.305873i) q^{17} +(-2.84888 + 4.93440i) q^{19} +(0.438682 + 0.759820i) q^{23} +(0.285756 - 0.494945i) q^{25} +(-0.874997 - 1.51554i) q^{29} -9.13490 q^{31} +(-3.75582 - 4.11014i) q^{35} +(-3.39555 + 5.88127i) q^{37} +(-1.20377 + 2.08499i) q^{41} +(-0.276745 - 0.479336i) q^{43} +11.7372 q^{47} +(6.35230 - 2.94080i) q^{49} +(2.07821 + 3.59956i) q^{53} -0.839790 q^{55} -9.32421 q^{59} -10.0720 q^{61} +6.07296 q^{65} -1.20241 q^{67} -14.6826 q^{71} +(0.315636 + 0.546697i) q^{73} +(0.318883 - 1.00652i) q^{77} +2.48729 q^{79} +(-4.59366 - 7.95645i) q^{83} +(-0.371628 + 0.643678i) q^{85} +(-7.29358 + 12.6328i) q^{89} +(-2.30601 + 7.27866i) q^{91} -11.9903 q^{95} +(-7.84245 - 13.5835i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} - 5 q^{7}+O(q^{10}) \) 22 * q - q^5 - 5 * q^7	\( 22 q - q^{5} - 5 q^{7} + 3 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} - 22 q^{25} + 7 q^{29} + 12 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} - 34 q^{47} - 25 q^{49} - q^{53} - 2 q^{55} + 42 q^{59} - 62 q^{61} - 6 q^{65} - 52 q^{67} - 32 q^{71} + 17 q^{73} + q^{77} - 32 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} + 48 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q - q^5 - 5 * q^7 + 3 * q^11 + 7 * q^13 + q^17 - 13 * q^19 - 22 * q^25 + 7 * q^29 + 12 * q^31 + 2 * q^35 + 6 * q^37 - 4 * q^41 - 2 * q^43 - 34 * q^47 - 25 * q^49 - q^53 - 2 * q^55 + 42 * q^59 - 62 * q^61 - 6 * q^65 - 52 * q^67 - 32 * q^71 + 17 * q^73 + q^77 - 32 * q^79 - 36 * q^83 + 28 * q^85 + 2 * q^89 - 15 * q^91 + 48 * q^95 + 19 * q^97

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