LMFDB - Embedded newform 3024.2.cz.h.2719.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(1279,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.1279"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cz (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,3,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2719.4
Character	$\chi$	$=$	3024.2719
Dual form			3024.2.cz.h.1279.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73177 - 0.999840i) q^{5} +(2.38101 + 1.15360i) q^{7} +(-1.17995 + 0.681244i) q^{11} +(1.71030 - 0.987444i) q^{13} +(-0.868852 - 0.501632i) q^{17} +(-0.774396 - 1.34129i) q^{19} +(7.59639 + 4.38578i) q^{23} +(-0.500642 - 0.867137i) q^{25} +(-0.854529 + 1.48009i) q^{29} -0.522244 q^{31} +(-2.96996 - 4.37840i) q^{35} +(1.53855 + 2.66485i) q^{37} +(0.386794 - 0.223316i) q^{41} +(-5.49888 - 3.17478i) q^{43} +1.63949 q^{47} +(4.33842 + 5.49346i) q^{49} +(-1.24313 + 2.15316i) q^{53} +2.72454 q^{55} +12.6284 q^{59} -10.5433i q^{61} -3.94914 q^{65} +6.50486i q^{67} -1.57299i q^{71} +(13.6347 + 7.87199i) q^{73} +(-3.59535 + 0.260861i) q^{77} -5.95935i q^{79} +(4.80565 - 8.32363i) q^{83} +(1.00310 + 1.73743i) q^{85} +(1.10887 - 0.640207i) q^{89} +(5.21136 - 0.378111i) q^{91} +3.09709i q^{95} +(8.31781 + 4.80229i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} + 4 q^{7} + 9 q^{11} - 3 q^{13} + 3 q^{17} - 4 q^{19} + 6 q^{23} + 15 q^{25} - 18 q^{29} + 34 q^{31} + 42 q^{35} - 3 q^{37} - 36 q^{41} + 24 q^{43} + 42 q^{47} + 30 q^{49} + 12 q^{53} - 30 q^{55}+ \cdots + 3 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 + 4 * q^7 + 9 * q^11 - 3 * q^13 + 3 * q^17 - 4 * q^19 + 6 * q^23 + 15 * q^25 - 18 * q^29 + 34 * q^31 + 42 * q^35 - 3 * q^37 - 36 * q^41 + 24 * q^43 + 42 * q^47 + 30 * q^49 + 12 * q^53 - 30 * q^55 + 12 * q^59 + 48 * q^73 + 48 * q^77 + 48 * q^83 - 21 * q^85 - 39 * q^89 + 9 * q^91 + 3 * q^97

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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
$5$	−1.73177	−	0.999840i	−0.774472	−	0.447142i	0.0599953	−	0.998199i	$-0.480891\pi$
$5$	−1.73177	−	0.999840i	−0.774472	−	0.447142i	−0.834468	+	0.551057i	$0.814225\pi$
$6$		0			0
$7$	2.38101	+	1.15360i	0.899937	+	0.436019i
$7$	2.38101	+	1.15360i	0.899937	+	0.436019i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.17995	+	0.681244i	−0.355768	+	0.205403i	−0.667223	−	0.744858i	$-0.732517\pi$
$11$	−1.17995	+	0.681244i	−0.355768	+	0.205403i	0.311455	+	0.950261i	$0.399184\pi$
$12$		0			0
$13$	1.71030	−	0.987444i	0.474353	−	0.273868i	−0.243707	−	0.969849i	$-0.578364\pi$
$13$	1.71030	−	0.987444i	0.474353	−	0.273868i	0.718060	+	0.695981i	$0.245030\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.868852	−	0.501632i	−0.210728	−	0.121664i	0.390922	−	0.920424i	$-0.372156\pi$
$17$	−0.868852	−	0.501632i	−0.210728	−	0.121664i	−0.601649	+	0.798760i	$0.705490\pi$
$18$		0			0
$19$	−0.774396	−	1.34129i	−0.177659	−	0.307714i	0.763420	−	0.645903i	$-0.223519\pi$
$19$	−0.774396	−	1.34129i	−0.177659	−	0.307714i	−0.941078	+	0.338189i	$0.890186\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.59639	+	4.38578i	1.58396	+	0.914498i	0.994274	+	0.106862i	$0.0340804\pi$
$23$	7.59639	+	4.38578i	1.58396	+	0.914498i	0.589682	+	0.807635i	$0.299253\pi$
$24$		0			0
$25$	−0.500642	−	0.867137i	−0.100128	−	0.173427i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.854529	+	1.48009i	−0.158682	+	0.274846i	−0.934394	−	0.356242i	$-0.884058\pi$
$29$	−0.854529	+	1.48009i	−0.158682	+	0.274846i	0.775712	+	0.631088i	$0.217391\pi$
$30$		0			0
$31$	−0.522244			−0.0937979			−0.0468989	−	0.998900i	$-0.514934\pi$
$31$	−0.522244			−0.0937979			−0.0468989	+	0.998900i	$0.514934\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.96996	−	4.37840i	−0.502014	−	0.740085i
$36$		0			0
$37$	1.53855	+	2.66485i	0.252936	+	0.438099i	0.964333	−	0.264692i	$-0.0852703\pi$
$37$	1.53855	+	2.66485i	0.252936	+	0.438099i	−0.711397	+	0.702791i	$0.751937\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.386794	−	0.223316i	0.0604071	−	0.0348761i	−0.469492	−	0.882937i	$-0.655563\pi$
$41$	0.386794	−	0.223316i	0.0604071	−	0.0348761i	0.529899	+	0.848061i	$0.322230\pi$
$42$		0			0
$43$	−5.49888	−	3.17478i	−0.838572	−	0.484150i	0.0182067	−	0.999834i	$-0.494204\pi$
$43$	−5.49888	−	3.17478i	−0.838572	−	0.484150i	−0.856779	+	0.515685i	$0.827538\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.63949			0.239144			0.119572	−	0.992826i	$-0.461848\pi$
$47$	1.63949			0.239144			0.119572	+	0.992826i	$0.461848\pi$
$48$		0			0
$49$	4.33842	+	5.49346i	0.619774	+	0.784780i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.24313	+	2.15316i	−0.170757	+	0.295760i	−0.938685	−	0.344777i	$-0.887955\pi$
$53$	−1.24313	+	2.15316i	−0.170757	+	0.295760i	0.767928	+	0.640537i	$0.221288\pi$
$54$		0			0
$55$	2.72454			0.367377
$56$		0			0
$57$		0			0
$58$		0			0
$59$	12.6284			1.64408			0.822040	−	0.569430i	$-0.192836\pi$
$59$	12.6284			1.64408			0.822040	+	0.569430i	$0.192836\pi$
$60$		0			0
$61$		−	10.5433i		−	1.34994i	−0.737847	−	0.674968i	$-0.764157\pi$
$61$		−	10.5433i		−	1.34994i	0.737847	−	0.674968i	$-0.235843\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.94914			−0.489831
$66$		0			0
$67$			6.50486i			0.794695i	0.917668	+	0.397347i	$0.130069\pi$
$67$			6.50486i			0.794695i	−0.917668	+	0.397347i	$0.869931\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	1.57299i		−	0.186679i	−0.995634	−	0.0933396i	$-0.970246\pi$
$71$		−	1.57299i		−	0.186679i	0.995634	−	0.0933396i	$-0.0297542\pi$
$72$		0			0
$73$	13.6347	+	7.87199i	1.59582	+	0.921346i	0.992281	+	0.124012i	$0.0395760\pi$
$73$	13.6347	+	7.87199i	1.59582	+	0.921346i	0.603538	+	0.797334i	$0.293757\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.59535	+	0.260861i	−0.409728	+	0.0297279i
$78$		0			0
$79$		−	5.95935i		−	0.670479i	−0.942133	−	0.335240i	$-0.891183\pi$
$79$		−	5.95935i		−	0.670479i	0.942133	−	0.335240i	$-0.108817\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.80565	−	8.32363i	0.527489	−	0.913637i	−0.471998	−	0.881600i	$-0.656467\pi$
$83$	4.80565	−	8.32363i	0.527489	−	0.913637i	0.999487	−	0.0320377i	$-0.0101997\pi$
$84$		0			0
$85$	1.00310	+	1.73743i	0.108802	+	0.188450i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.10887	−	0.640207i	0.117540	−	0.0678618i	−0.440077	−	0.897960i	$-0.645049\pi$
$89$	1.10887	−	0.640207i	0.117540	−	0.0678618i	0.557617	+	0.830098i	$0.311716\pi$
$90$		0			0
$91$	5.21136	−	0.378111i	0.546299	−	0.0396368i
$92$		0			0
$93$		0			0
$94$		0			0
$95$			3.09709i			0.317754i
$96$		0			0
$97$	8.31781	+	4.80229i	0.844546	+	0.487599i	0.858807	−	0.512299i	$-0.171206\pi$
$97$	8.31781	+	4.80229i	0.844546	+	0.487599i	−0.0142608	+	0.999898i	$0.504540\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.76069	+	5.63534i	−0.971225	+	0.560737i	−0.899610	−	0.436695i	$-0.856149\pi$
$101$	−9.76069	+	5.63534i	−0.971225	+	0.560737i	−0.0716156	+	0.997432i	$0.522815\pi$
$102$		0			0
$103$	4.80600	−	8.32424i	0.473550	−	0.820212i	−0.525992	−	0.850490i	$-0.676306\pi$
$103$	4.80600	−	8.32424i	0.473550	−	0.820212i	0.999542	+	0.0302775i	$0.00963909\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.0876	−	6.40144i	1.07188	−	0.618850i	0.143186	−	0.989696i	$-0.454265\pi$
$107$	11.0876	−	6.40144i	1.07188	−	0.618850i	0.928695	+	0.370845i	$0.120932\pi$
$108$		0			0
$109$	−7.28182	+	12.6125i	−0.697472	+	1.20806i	0.271869	+	0.962334i	$0.412358\pi$
$109$	−7.28182	+	12.6125i	−0.697472	+	1.20806i	−0.969340	+	0.245722i	$0.920975\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.07922	+	15.7257i	0.854101	+	1.47935i	0.877476	+	0.479620i	$0.159225\pi$
$113$	9.07922	+	15.7257i	0.854101	+	1.47935i	−0.0233754	+	0.999727i	$0.507441\pi$
$114$		0			0
$115$	−8.77014	−	15.1903i	−0.817820	−	1.41651i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.49006	−	2.19670i	−0.136594	−	0.201371i
$120$		0			0
$121$	−4.57181	+	7.91861i	−0.415619	+	0.719874i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			12.0006i			1.07337i
$126$		0			0
$127$		−	13.2304i		−	1.17401i	−0.809585	−	0.587003i	$-0.800308\pi$
$127$		−	13.2304i		−	1.17401i	0.809585	−	0.587003i	$-0.199692\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.27126	−	7.39804i	0.373182	−	0.646370i	−0.616871	−	0.787064i	$-0.711600\pi$
$131$	4.27126	−	7.39804i	0.373182	−	0.646370i	0.990053	+	0.140694i	$0.0449334\pi$
$132$		0			0
$133$	−0.296530	−	4.08697i	−0.0257125	−	0.354386i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.92756	−	3.33864i	−0.164683	−	0.285239i	0.771860	−	0.635793i	$-0.219327\pi$
$137$	−1.92756	−	3.33864i	−0.164683	−	0.285239i	−0.936543	+	0.350554i	$0.885993\pi$
$138$		0			0
$139$	7.59749	+	13.1592i	0.644410	+	1.11615i	0.984437	+	0.175736i	$0.0562305\pi$
$139$	7.59749	+	13.1592i	0.644410	+	1.11615i	−0.340027	+	0.940416i	$0.610436\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.34538	+	2.33027i	−0.112506	+	0.194867i
$144$		0			0
$145$	2.95970	−	1.70878i	0.245790	−	0.141907i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.77752	−	10.0070i	0.473313	−	0.819802i	−0.526221	−	0.850348i	$-0.676391\pi$
$149$	5.77752	−	10.0070i	0.473313	−	0.819802i	0.999533	+	0.0305463i	$0.00972470\pi$
$150$		0			0
$151$	19.6224	−	11.3290i	1.59685	−	0.921941i	0.604759	−	0.796408i	$-0.293269\pi$
$151$	19.6224	−	11.3290i	1.59685	−	0.921941i	0.992089	−	0.125533i	$-0.0400640\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.904409	+	0.522161i	0.0726439	+	0.0419409i
$156$		0			0
$157$		−	14.6276i		−	1.16741i	−0.811965	−	0.583706i	$-0.801602\pi$
$157$		−	14.6276i		−	1.16741i	0.811965	−	0.583706i	$-0.198398\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	13.0276	+	19.2058i	1.02672	+	1.51363i
$162$		0			0
$163$	10.4437	−	6.02970i	0.818017	−	0.472282i	−0.0317152	−	0.999497i	$-0.510097\pi$
$163$	10.4437	−	6.02970i	0.818017	−	0.472282i	0.849732	+	0.527215i	$0.176764\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.0887	+	19.2062i	0.858069	+	1.48622i	0.873769	+	0.486342i	$0.161669\pi$
$167$	11.0887	+	19.2062i	0.858069	+	1.48622i	−0.0156998	+	0.999877i	$0.504998\pi$
$168$		0			0
$169$	−4.54991	+	7.88067i	−0.349993	+	0.606206i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		−	14.9706i		−	1.13819i	−0.822270	−	0.569097i	$-0.807293\pi$
$173$		−	14.9706i		−	1.13819i	0.822270	−	0.569097i	$-0.192707\pi$
$174$		0			0
$175$	−0.191705	−	2.64220i	−0.0144915	−	0.199732i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.1951	−	7.04084i	−0.911505	−	0.526257i	−0.0305897	−	0.999532i	$-0.509739\pi$
$179$	−12.1951	−	7.04084i	−0.911505	−	0.526257i	−0.880915	+	0.473275i	$0.843072\pi$
$180$		0			0
$181$		−	4.70875i		−	0.349999i	−0.984569	−	0.174999i	$-0.944008\pi$
$181$		−	4.70875i		−	0.349999i	0.984569	−	0.174999i	$-0.0559924\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		−	6.15322i		−	0.452394i
$186$		0			0
$187$	1.36693			0.0999601
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	8.63432i		−	0.624758i	−0.949958	−	0.312379i	$-0.898874\pi$
$191$		−	8.63432i		−	0.624758i	0.949958	−	0.312379i	$-0.101126\pi$
$192$		0			0
$193$	10.9280			0.786613			0.393307	−	0.919407i	$-0.371331\pi$
$193$	10.9280			0.786613			0.393307	+	0.919407i	$0.371331\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	19.7147			1.40461			0.702305	−	0.711876i	$-0.252154\pi$
$197$	19.7147			1.40461			0.702305	+	0.711876i	$0.252154\pi$
$198$		0			0
$199$	13.3575	−	23.1359i	0.946889	−	1.64006i	0.194965	−	0.980810i	$-0.437541\pi$
$199$	13.3575	−	23.1359i	0.946889	−	1.64006i	0.751924	−	0.659249i	$-0.229126\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.74207	+	2.53832i	−0.262642	+	0.178155i
$204$		0			0
$205$	−0.893120			−0.0623782
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.82749	+	1.05510i	0.126410	+	0.0729831i
$210$		0			0
$211$	6.27293	−	3.62168i	0.431846	−	0.249327i	−0.268286	−	0.963339i	$-0.586457\pi$
$211$	6.27293	−	3.62168i	0.431846	−	0.249327i	0.700133	+	0.714012i	$0.253124\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.34854	+	10.9960i	0.432967	+	0.749921i
$216$		0			0
$217$	−1.24347	−	0.602460i	−0.0844122	−	0.0408977i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.98133			−0.133279
$222$		0			0
$223$	−9.80779	+	16.9876i	−0.656778	+	1.13757i	0.324667	+	0.945828i	$0.394748\pi$
$223$	−9.80779	+	16.9876i	−0.656778	+	1.13757i	−0.981445	+	0.191744i	$0.938586\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.3892	+	17.9947i	0.689557	+	1.19435i	0.971981	+	0.235058i	$0.0755281\pi$
$227$	10.3892	+	17.9947i	0.689557	+	1.19435i	−0.282424	+	0.959290i	$0.591139\pi$
$228$		0			0
$229$	−19.1630	−	11.0638i	−1.26633	−	0.731113i	−0.292035	−	0.956408i	$-0.594332\pi$
$229$	−19.1630	−	11.0638i	−1.26633	−	0.731113i	−0.974291	+	0.225294i	$0.927666\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.95965	+	3.39421i	0.128381	+	0.222362i	0.923049	−	0.384681i	$-0.125689\pi$
$233$	1.95965	+	3.39421i	0.128381	+	0.222362i	−0.794669	+	0.607043i	$0.792355\pi$
$234$		0			0
$235$	−2.83922	−	1.63922i	−0.185210	−	0.106931i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.38657	−	4.26464i	0.477798	−	0.275857i	−0.241701	−	0.970351i	$-0.577705\pi$
$239$	7.38657	−	4.26464i	0.477798	−	0.275857i	0.719498	+	0.694494i	$0.244372\pi$
$240$		0			0
$241$	2.09775	−	1.21114i	0.135128	−	0.0780161i	−0.430912	−	0.902394i	$-0.641808\pi$
$241$	2.09775	−	1.21114i	0.135128	−	0.0780161i	0.566040	+	0.824378i	$0.308475\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.02058	−	13.8512i	−0.129090	−	0.884918i
$246$		0			0
$247$	−2.64890	−	1.52934i	−0.168546	−	0.0973099i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.09792			0.0693002			0.0346501	−	0.999400i	$-0.488968\pi$
$251$	1.09792			0.0693002			0.0346501	+	0.999400i	$0.488968\pi$
$252$		0			0
$253$	−11.9511			−0.751361
$254$		0			0
$255$		0			0
$256$		0			0
$257$	18.2289	+	10.5245i	1.13709	+	0.656498i	0.945708	−	0.325018i	$-0.105371\pi$
$257$	18.2289	+	10.5245i	1.13709	+	0.656498i	0.191380	+	0.981516i	$0.438704\pi$
$258$		0			0
$259$	0.589140	+	8.11991i	0.0366074	+	0.504547i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−21.1850	+	12.2312i	−1.30632	+	0.754206i	−0.981481	−	0.191562i	$-0.938645\pi$
$263$	−21.1850	+	12.2312i	−1.30632	+	0.754206i	−0.324843	+	0.945768i	$0.605311\pi$
$264$		0			0
$265$	4.30564	−	2.48586i	0.264493	−	0.152705i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.79690	+	5.65624i	0.597327	+	0.344867i	0.767989	−	0.640462i	$-0.221257\pi$
$269$	9.79690	+	5.65624i	0.597327	+	0.344867i	−0.170662	+	0.985330i	$0.554591\pi$
$270$		0			0
$271$	0.480849	+	0.832856i	0.0292095	+	0.0505924i	0.880261	−	0.474490i	$-0.157368\pi$
$271$	0.480849	+	0.832856i	0.0292095	+	0.0505924i	−0.851051	+	0.525083i	$0.824034\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.18146	+	0.682118i	0.0712449	+	0.0411333i
$276$		0			0
$277$	12.5249	+	21.6938i	0.752549	+	1.30345i	0.946583	+	0.322459i	$0.104509\pi$
$277$	12.5249	+	21.6938i	0.752549	+	1.30345i	−0.194034	+	0.980995i	$0.562157\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.0324	+	19.1087i	−0.658139	+	1.13993i	0.322958	+	0.946413i	$0.395323\pi$
$281$	−11.0324	+	19.1087i	−0.658139	+	1.13993i	−0.981097	+	0.193517i	$0.938010\pi$
$282$		0			0
$283$	−5.26865			−0.313189			−0.156594	−	0.987663i	$-0.550052\pi$
$283$	−5.26865			−0.313189			−0.156594	+	0.987663i	$0.550052\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.17858	−	0.0855118i	0.0695693	−	0.00504760i
$288$		0			0
$289$	−7.99673	−	13.8507i	−0.470396	−	0.814750i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.1084	−	6.99080i	0.707381	−	0.408407i	−0.102709	−	0.994711i	$-0.532751\pi$
$293$	12.1084	−	6.99080i	0.707381	−	0.408407i	0.810091	+	0.586305i	$0.199418\pi$
$294$		0			0
$295$	−21.8696	−	12.6264i	−1.27329	−	0.735137i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	17.3228			1.00181
$300$		0			0
$301$	−9.43047	−	13.9027i	−0.543563	−	0.801338i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.5416	+	18.2587i	−0.603613	+	1.04549i
$306$		0			0
$307$	−16.2755			−0.928893			−0.464446	−	0.885601i	$-0.653747\pi$
$307$	−16.2755			−0.928893			−0.464446	+	0.885601i	$0.653747\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.38973			0.362329			0.181164	−	0.983453i	$-0.442013\pi$
$311$	6.38973			0.362329			0.181164	+	0.983453i	$0.442013\pi$
$312$		0			0
$313$		−	25.6429i		−	1.44942i	−0.689053	−	0.724711i	$-0.741973\pi$
$313$		−	25.6429i		−	1.44942i	0.689053	−	0.724711i	$-0.258027\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−29.3042			−1.64589			−0.822945	−	0.568122i	$-0.807670\pi$
$317$	−29.3042			−1.64589			−0.822945	+	0.568122i	$0.807670\pi$
$318$		0			0
$319$		−	2.32857i		−	0.130375i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1.55385i			0.0864583i
$324$		0			0
$325$	−1.71250	−	0.988711i	−0.0949923	−	0.0548438i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.90363	+	1.89131i	0.215214	+	0.104271i
$330$		0			0
$331$		−	0.133691i		−	0.00734833i	−0.999993	−	0.00367417i	$-0.998830\pi$
$331$		−	0.133691i		−	0.00734833i	0.999993	−	0.00367417i	$-0.00116953\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.50381	−	11.2649i	0.355341	−	0.615469i
$336$		0			0
$337$	9.96606	+	17.2617i	0.542886	+	0.940306i	0.998737	+	0.0502498i	$0.0160017\pi$
$337$	9.96606	+	17.2617i	0.542886	+	0.940306i	−0.455851	+	0.890056i	$0.650665\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.616222	−	0.355776i	0.0333703	−	0.0192663i
$342$		0			0
$343$	3.99257	+	18.0848i	0.215579	+	0.976486i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			5.55582i			0.298252i	0.988818	+	0.149126i	$0.0476460\pi$
$347$			5.55582i			0.298252i	−0.988818	+	0.149126i	$0.952354\pi$
$348$		0			0
$349$	0.710293	+	0.410088i	0.0380211	+	0.0219515i	0.518890	−	0.854841i	$-0.326345\pi$
$349$	0.710293	+	0.410088i	0.0380211	+	0.0219515i	−0.480869	+	0.876792i	$0.659679\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−18.5479	+	10.7086i	−0.987203	+	0.569962i	−0.904437	−	0.426607i	$-0.859709\pi$
$353$	−18.5479	+	10.7086i	−0.987203	+	0.569962i	−0.0827662	+	0.996569i	$0.526375\pi$
$354$		0			0
$355$	−1.57273	+	2.72406i	−0.0834721	+	0.144578i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.64573	+	3.25956i	−0.297970	+	0.172033i	−0.641531	−	0.767097i	$-0.721700\pi$
$359$	−5.64573	+	3.25956i	−0.297970	+	0.172033i	0.343560	+	0.939131i	$0.388367\pi$
$360$		0			0
$361$	8.30062	−	14.3771i	0.436875	−	0.756689i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−15.7414	−	27.2650i	−0.823945	−	1.42711i
$366$		0			0
$367$	6.58460	+	11.4049i	0.343713	+	0.595329i	0.985119	−	0.171873i	$-0.0549819\pi$
$367$	6.58460	+	11.4049i	0.343713	+	0.595329i	−0.641406	+	0.767202i	$0.721649\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.44379	+	3.69263i	−0.282628	+	0.191712i
$372$		0			0
$373$	−14.7435	+	25.5364i	−0.763388	+	1.32223i	0.177707	+	0.984083i	$0.443132\pi$
$373$	−14.7435	+	25.5364i	−0.763388	+	1.32223i	−0.941095	+	0.338143i	$0.890201\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			3.37520i			0.173832i
$378$		0			0
$379$			25.2566i			1.29735i	0.761067	+	0.648673i	$0.224676\pi$
$379$			25.2566i			1.29735i	−0.761067	+	0.648673i	$0.775324\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.61272	−	4.52537i	0.133504	−	0.231236i	−0.791521	−	0.611142i	$-0.790710\pi$
$383$	2.61272	−	4.52537i	0.133504	−	0.231236i	0.925025	+	0.379906i	$0.124044\pi$
$384$		0			0
$385$	6.48715	+	3.14302i	0.330616	+	0.160183i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.9830	−	22.4872i	−0.658264	−	1.14015i	−0.981065	−	0.193679i	$-0.937958\pi$
$389$	−12.9830	−	22.4872i	−0.658264	−	1.14015i	0.322801	−	0.946467i	$-0.395375\pi$
$390$		0			0
$391$	−4.40009	−	7.62118i	−0.222522	−	0.385420i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.95839	+	10.3202i	−0.299799	+	0.519268i
$396$		0			0
$397$	12.5913	−	7.26961i	0.631941	−	0.364851i	−0.149562	−	0.988752i	$-0.547786\pi$
$397$	12.5913	−	7.26961i	0.631941	−	0.364851i	0.781503	+	0.623901i	$0.214453\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.86138	−	11.8843i	0.342641	−	0.593471i	−0.642281	−	0.766469i	$-0.722012\pi$
$401$	6.86138	−	11.8843i	0.342641	−	0.593471i	0.984922	+	0.172998i	$0.0553453\pi$
$402$		0			0
$403$	−0.893196	+	0.515687i	−0.0444933	+	0.0256882i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.63082	−	2.09626i	−0.179973	−	0.103908i
$408$		0			0
$409$			10.0019i			0.494561i	0.968944	+	0.247281i	$0.0795370\pi$
$409$			10.0019i			0.494561i	−0.968944	+	0.247281i	$0.920463\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	30.0684	+	14.5681i	1.47957	+	0.716851i
$414$		0			0
$415$	−16.6446	+	9.60976i	−0.817051	+	0.471725i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.51452	−	6.08732i	−0.171695	−	0.297385i	0.767317	−	0.641268i	$-0.221591\pi$
$419$	−3.51452	−	6.08732i	−0.171695	−	0.297385i	−0.939013	+	0.343882i	$0.888258\pi$
$420$		0			0
$421$	−3.01107	+	5.21533i	−0.146751	+	0.254179i	−0.930025	−	0.367497i	$-0.880215\pi$
$421$	−3.01107	+	5.21533i	−0.146751	+	0.254179i	0.783274	+	0.621676i	$0.213548\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$			1.00455i			0.0487279i
$426$		0			0
$427$	12.1628	−	25.1038i	0.588598	−	1.21486i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−14.3683	−	8.29555i	−0.692097	−	0.399582i	0.112300	−	0.993674i	$-0.464178\pi$
$431$	−14.3683	−	8.29555i	−0.692097	−	0.399582i	−0.804397	+	0.594092i	$0.797512\pi$
$432$		0			0
$433$			6.42380i			0.308708i	0.988016	+	0.154354i	$0.0493297\pi$
$433$			6.42380i			0.308708i	−0.988016	+	0.154354i	$0.950670\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	13.5853i		−	0.649873i
$438$		0			0
$439$	−4.46311			−0.213013			−0.106506	−	0.994312i	$-0.533966\pi$
$439$	−4.46311			−0.213013			−0.106506	+	0.994312i	$0.533966\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	27.5435i		−	1.30863i	−0.756222	−	0.654315i	$-0.772957\pi$
$443$		−	27.5435i		−	1.30863i	0.756222	−	0.654315i	$-0.227043\pi$
$444$		0			0
$445$	−2.56042			−0.121375
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−38.3329			−1.80904			−0.904520	−	0.426432i	$-0.859771\pi$
$449$	−38.3329			−1.80904			−0.904520	+	0.426432i	$0.859771\pi$
$450$		0			0
$451$	−0.304265	+	0.527003i	−0.0143273	+	0.0248156i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−9.40295	−	4.55573i	−0.440817	−	0.213576i
$456$		0			0
$457$	−34.3165			−1.60526			−0.802629	−	0.596478i	$-0.796566\pi$
$457$	−34.3165			−1.60526			−0.802629	+	0.596478i	$0.796566\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.9331	+	8.04429i	0.648930	+	0.374660i	0.788046	−	0.615616i	$-0.211093\pi$
$461$	13.9331	+	8.04429i	0.648930	+	0.374660i	−0.139116	+	0.990276i	$0.544426\pi$
$462$		0			0
$463$	−15.7583	+	9.09805i	−0.732349	+	0.422822i	−0.819281	−	0.573392i	$-0.805627\pi$
$463$	−15.7583	+	9.09805i	−0.732349	+	0.422822i	0.0869318	+	0.996214i	$0.472294\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.08122	+	12.2650i	0.327680	+	0.567558i	0.982051	−	0.188615i	$-0.0603999\pi$
$467$	7.08122	+	12.2650i	0.327680	+	0.567558i	−0.654371	+	0.756173i	$0.727067\pi$
$468$		0			0
$469$	−7.50399	+	15.4881i	−0.346502	+	0.715175i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	8.65120			0.397783
$474$		0			0
$475$	−0.775389	+	1.34301i	−0.0355773	+	0.0616217i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−16.8982	−	29.2685i	−0.772096	−	1.33731i	−0.936412	−	0.350902i	$-0.885875\pi$
$479$	−16.8982	−	29.2685i	−0.772096	−	1.33731i	0.164316	−	0.986408i	$-0.447458\pi$
$480$		0			0
$481$	5.26278	+	3.03847i	0.239962	+	0.138542i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−9.60304	−	16.6330i	−0.436052	−	0.755264i
$486$		0			0
$487$	9.41218	+	5.43412i	0.426506	+	0.246244i	0.697857	−	0.716237i	$-0.254137\pi$
$487$	9.41218	+	5.43412i	0.426506	+	0.246244i	−0.271351	+	0.962481i	$0.587470\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−29.3930	+	16.9701i	−1.32649	+	0.765848i	−0.984755	−	0.173949i	$-0.944347\pi$
$491$	−29.3930	+	16.9701i	−1.32649	+	0.765848i	−0.341733	+	0.939797i	$0.611014\pi$
$492$		0			0
$493$	1.48492	−	0.857318i	0.0668774	−	0.0386117i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.81460	−	3.74530i	0.0813958	−	0.168000i
$498$		0			0
$499$	−2.57367	−	1.48591i	−0.115213	−	0.0665185i	0.441286	−	0.897367i	$-0.354522\pi$
$499$	−2.57367	−	1.48591i	−0.115213	−	0.0665185i	−0.556499	+	0.830848i	$0.687856\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−26.0651			−1.16219			−0.581093	−	0.813837i	$-0.697375\pi$
$503$	−26.0651			−1.16219			−0.581093	+	0.813837i	$0.697375\pi$
$504$		0			0
$505$	22.5377			1.00292
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.3806	−	8.87997i	−0.681731	−	0.393598i	0.118776	−	0.992921i	$-0.462103\pi$
$509$	−15.3806	−	8.87997i	−0.681731	−	0.393598i	−0.800507	+	0.599323i	$0.795436\pi$
$510$		0			0
$511$	23.3832	+	34.4722i	1.03441	+	1.52496i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−16.6458	+	9.61047i	−0.733502	+	0.423488i
$516$		0			0
$517$	−1.93451	+	1.11689i	−0.0850796	+	0.0491207i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−24.9679	−	14.4152i	−1.09387	−	0.631543i	−0.159262	−	0.987236i	$-0.550912\pi$
$521$	−24.9679	−	14.4152i	−1.09387	−	0.631543i	−0.934603	+	0.355693i	$0.884245\pi$
$522$		0			0
$523$	6.32766	+	10.9598i	0.276689	+	0.479240i	0.970560	−	0.240860i	$-0.0774294\pi$
$523$	6.32766	+	10.9598i	0.276689	+	0.479240i	−0.693871	+	0.720100i	$0.744096\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.453753	+	0.261974i	0.0197658	+	0.0114118i
$528$		0			0
$529$	26.9701	+	46.7135i	1.17261	+	2.03102i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.441024	−	0.763876i	0.0191029	−	0.0330871i
$534$		0			0
$535$	−25.6016			−1.10686
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−8.86150	−	3.52648i	−0.381692	−	0.151896i
$540$		0			0
$541$	−7.29665	−	12.6382i	−0.313708	−	0.543358i	0.665454	−	0.746439i	$-0.268238\pi$
$541$	−7.29665	−	12.6382i	−0.313708	−	0.543358i	−0.979162	+	0.203081i	$0.934905\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	25.2209	−	14.5613i	1.08035	−	0.623738i
$546$		0			0
$547$	5.61933	+	3.24432i	0.240265	+	0.138717i	0.615299	−	0.788294i	$-0.289035\pi$
$547$	5.61933	+	3.24432i	0.240265	+	0.138717i	−0.375033	+	0.927011i	$0.622369\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.64698			0.112765
$552$		0			0
$553$	6.87470	−	14.1893i	0.292342	−	0.603389i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18.2102	+	31.5410i	−0.771590	+	1.33643i	0.165101	+	0.986277i	$0.447205\pi$
$557$	−18.2102	+	31.5410i	−0.771590	+	1.33643i	−0.936691	+	0.350157i	$0.886128\pi$
$558$		0			0
$559$	−12.5397			−0.530372
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.55398			0.318362			0.159181	−	0.987249i	$-0.449115\pi$
$563$	7.55398			0.318362			0.159181	+	0.987249i	$0.449115\pi$
$564$		0			0
$565$		−	36.3110i		−	1.52762i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−23.8329			−0.999127			−0.499564	−	0.866277i	$-0.666506\pi$
$569$	−23.8329			−0.999127			−0.499564	+	0.866277i	$0.666506\pi$
$570$		0			0
$571$			19.1328i			0.800682i	0.916366	+	0.400341i	$0.131108\pi$
$571$			19.1328i			0.800682i	−0.916366	+	0.400341i	$0.868892\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	8.78281i		−	0.366268i
$576$		0			0
$577$	0.278675	+	0.160893i	0.0116014	+	0.00669808i	0.505789	−	0.862657i	$-0.331201\pi$
$577$	0.278675	+	0.160893i	0.0116014	+	0.00669808i	−0.494188	+	0.869355i	$0.664535\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	21.0444	−	14.2749i	0.873070	−	0.592221i
$582$		0			0
$583$		−	3.38750i		−	0.140296i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	22.9285	−	39.7134i	0.946362	−	1.63915i	0.193360	−	0.981128i	$-0.438061\pi$
$587$	22.9285	−	39.7134i	0.946362	−	1.63915i	0.753001	−	0.658019i	$-0.228605\pi$
$588$		0			0
$589$	0.404424	+	0.700483i	0.0166640	+	0.0288629i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	24.8195	−	14.3295i	1.01921	−	0.588443i	0.105338	−	0.994437i	$-0.466408\pi$
$593$	24.8195	−	14.3295i	1.01921	−	0.588443i	0.913876	+	0.405993i	$0.133074\pi$
$594$		0			0
$595$	0.384107	+	5.29401i	0.0157468	+	0.217033i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	24.4551i		−	0.999208i	−0.866254	−	0.499604i	$-0.833479\pi$
$599$		−	24.4551i		−	0.999208i	0.866254	−	0.499604i	$-0.166521\pi$
$600$		0			0
$601$	−6.86788	−	3.96517i	−0.280147	−	0.161743i	0.353343	−	0.935494i	$-0.385045\pi$
$601$	−6.86788	−	3.96517i	−0.280147	−	0.161743i	−0.633490	+	0.773751i	$0.718378\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	15.8347	−	9.14216i	0.643772	−	0.371682i
$606$		0			0
$607$	2.45236	−	4.24762i	0.0995384	−	0.172406i	−0.811955	−	0.583720i	$-0.801597\pi$
$607$	2.45236	−	4.24762i	0.0995384	−	0.172406i	0.911494	+	0.411314i	$0.134930\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.80402	−	1.61890i	0.113438	−	0.0654937i
$612$		0			0
$613$	9.53276	−	16.5112i	0.385025	−	0.666882i	−0.606748	−	0.794894i	$-0.707526\pi$
$613$	9.53276	−	16.5112i	0.385025	−	0.666882i	0.991773	+	0.128012i	$0.0408596\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−21.2636	−	36.8296i	−0.856040	−	1.48270i	−0.875677	−	0.482897i	$-0.839585\pi$
$617$	−21.2636	−	36.8296i	−0.856040	−	1.48270i	0.0196377	−	0.999807i	$-0.493749\pi$
$618$		0			0
$619$	6.26243	+	10.8468i	0.251708	+	0.435971i	0.963996	−	0.265916i	$-0.0856743\pi$
$619$	6.26243	+	10.8468i	0.251708	+	0.435971i	−0.712288	+	0.701887i	$0.752341\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.37877	−	0.245147i	0.135368	−	0.00982161i
$624$		0			0
$625$	9.49551	−	16.4467i	0.379820	−	0.657868i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	3.08715i		−	0.123093i
$630$		0			0
$631$			17.8526i			0.710700i	0.934733	+	0.355350i	$0.115638\pi$
$631$			17.8526i			0.710700i	−0.934733	+	0.355350i	$0.884362\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−13.2283	+	22.9120i	−0.524947	+	0.909235i
$636$		0			0
$637$	12.8445	+	5.11154i	0.508918	+	0.202526i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	19.5722	+	33.9000i	0.773054	+	1.33897i	0.935882	+	0.352315i	$0.114605\pi$
$641$	19.5722	+	33.9000i	0.773054	+	1.33897i	−0.162827	+	0.986655i	$0.552061\pi$
$642$		0			0
$643$	−2.93372	−	5.08136i	−0.115695	−	0.200389i	0.802363	−	0.596837i	$-0.203576\pi$
$643$	−2.93372	−	5.08136i	−0.115695	−	0.200389i	−0.918057	+	0.396448i	$0.870243\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.5795	+	33.9127i	−0.769750	+	1.33325i	0.167949	+	0.985796i	$0.446286\pi$
$647$	−19.5795	+	33.9127i	−0.769750	+	1.33325i	−0.937699	+	0.347450i	$0.887048\pi$
$648$		0			0
$649$	−14.9009	+	8.60303i	−0.584911	+	0.337698i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.6261	−	23.6011i	0.533231	−	0.923584i	−0.466015	−	0.884777i	$-0.654311\pi$
$653$	13.6261	−	23.6011i	0.533231	−	0.923584i	0.999247	−	0.0388072i	$-0.0123558\pi$
$654$		0			0
$655$	−14.7937	+	8.54115i	−0.578038	+	0.333730i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	18.1766	+	10.4943i	0.708061	+	0.408799i	0.810343	−	0.585956i	$-0.199281\pi$
$659$	18.1766	+	10.4943i	0.708061	+	0.408799i	−0.102282	+	0.994755i	$0.532614\pi$
$660$		0			0
$661$		−	2.10749i		−	0.0819720i	−0.999160	−	0.0409860i	$-0.986950\pi$
$661$		−	2.10749i		−	0.0819720i	0.999160	−	0.0409860i	$-0.0130499\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.57279	+	7.37419i	−0.138547	+	0.285959i
$666$		0			0
$667$	−12.9827	+	7.49555i	−0.502691	+	0.290229i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	7.18258	+	12.4406i	0.277281	+	0.480264i
$672$		0			0
$673$	3.40292	−	5.89403i	0.131173	−	0.227198i	−0.792956	−	0.609279i	$-0.791459\pi$
$673$	3.40292	−	5.89403i	0.131173	−	0.227198i	0.924129	+	0.382081i	$0.124792\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	43.3463i		−	1.66593i	−0.553323	−	0.832967i	$-0.686640\pi$
$677$		−	43.3463i		−	1.66593i	0.553323	−	0.832967i	$-0.313360\pi$
$678$		0			0
$679$	14.2649	+	21.0297i	0.547436	+	0.807047i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−25.2674	−	14.5882i	−0.966832	−	0.558201i	−0.0685629	−	0.997647i	$-0.521841\pi$
$683$	−25.2674	−	14.5882i	−0.966832	−	0.558201i	−0.898269	+	0.439446i	$0.855175\pi$
$684$		0			0
$685$			7.70901i			0.294546i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			4.91008i			0.187059i
$690$		0			0
$691$	47.1974			1.79547			0.897736	−	0.440533i	$-0.145210\pi$
$691$	47.1974			1.79547			0.897736	+	0.440533i	$0.145210\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	30.3851i		−	1.15257i
$696$		0			0
$697$	−0.448089			−0.0169726
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.7459			−0.556946			−0.278473	−	0.960444i	$-0.589828\pi$
$701$	−14.7459			−0.556946			−0.278473	+	0.960444i	$0.589828\pi$
$702$		0			0
$703$	2.38290	−	4.12730i	0.0898726	−	0.155664i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−29.7412	+	2.15788i	−1.11853	+	0.0811553i
$708$		0			0
$709$	−29.3420			−1.10196			−0.550981	−	0.834518i	$-0.685746\pi$
$709$	−29.3420			−1.10196			−0.550981	+	0.834518i	$0.685746\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.96717	−	2.29045i	−0.148572	−	0.0857779i
$714$		0			0
$715$	4.65978	−	2.69033i	0.174266	−	0.100613i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	19.0100	+	32.9262i	0.708952	+	1.22794i	0.965246	+	0.261342i	$0.0841651\pi$
$719$	19.0100	+	32.9262i	0.708952	+	1.22794i	−0.256294	+	0.966599i	$0.582502\pi$
$720$		0			0
$721$	21.0460	−	14.2759i	0.783793	−	0.531663i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.71125			0.0635543
$726$		0			0
$727$	−1.33619	+	2.31435i	−0.0495565	+	0.0858343i	−0.889740	−	0.456469i	$-0.849114\pi$
$727$	−1.33619	+	2.31435i	−0.0495565	+	0.0858343i	0.840183	+	0.542303i	$0.182447\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.18514	+	5.51683i	0.117807	+	0.204047i
$732$		0			0
$733$	−2.84392	−	1.64194i	−0.105042	−	0.0606463i	0.446558	−	0.894754i	$-0.352650\pi$
$733$	−2.84392	−	1.64194i	−0.105042	−	0.0606463i	−0.551601	+	0.834108i	$0.685983\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.43139	−	7.67540i	−0.163232	−	0.282727i
$738$		0			0
$739$	−22.7991	−	13.1631i	−0.838680	−	0.484212i	0.0181356	−	0.999836i	$-0.494227\pi$
$739$	−22.7991	−	13.1631i	−0.838680	−	0.484212i	−0.856815	+	0.515624i	$0.827560\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	21.0356	−	12.1449i	0.771720	−	0.445553i	−0.0617681	−	0.998091i	$-0.519674\pi$
$743$	21.0356	−	12.1449i	0.771720	−	0.445553i	0.833488	+	0.552538i	$0.186341\pi$
$744$		0			0
$745$	−20.0107	+	11.5532i	−0.733135	+	0.423276i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	33.7844	−	2.45123i	1.23446	−	0.0895660i
$750$		0			0
$751$	−8.11887	−	4.68743i	−0.296262	−	0.171047i	0.344501	−	0.938786i	$-0.388048\pi$
$751$	−8.11887	−	4.68743i	−0.296262	−	0.171047i	−0.640762	+	0.767739i	$0.721382\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−45.3087			−1.64895
$756$		0			0
$757$	−50.8723			−1.84899			−0.924493	−	0.381200i	$-0.875511\pi$
$757$	−50.8723			−1.84899			−0.924493	+	0.381200i	$0.875511\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	36.6769	+	21.1754i	1.32954	+	0.767608i	0.985228	−	0.171249i	$-0.0547803\pi$
$761$	36.6769	+	21.1754i	1.32954	+	0.767608i	0.344308	+	0.938857i	$0.388114\pi$
$762$		0			0
$763$	−31.8878	+	21.6301i	−1.15442	+	0.783064i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	21.5984	−	12.4699i	0.779874	−	0.450260i
$768$		0			0
$769$	−3.61419	+	2.08665i	−0.130331	+	0.0752467i	−0.563748	−	0.825947i	$-0.690641\pi$
$769$	−3.61419	+	2.08665i	−0.130331	+	0.0752467i	0.433417	+	0.901194i	$0.357308\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.51890	+	2.60899i	0.162534	+	0.0938389i	0.579061	−	0.815285i	$-0.303419\pi$
$773$	4.51890	+	2.60899i	0.162534	+	0.0938389i	−0.416527	+	0.909123i	$0.636753\pi$
$774$		0			0
$775$	0.261457	+	0.452857i	0.00939182	+	0.0162671i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.599064	−	0.345870i	−0.0214637	−	0.0123921i
$780$		0			0
$781$	1.07159	+	1.85604i	0.0383444	+	0.0664145i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−14.6253	+	25.3317i	−0.521998	+	0.904128i
$786$		0			0
$787$	−29.5860			−1.05463			−0.527314	−	0.849670i	$-0.676801\pi$
$787$	−29.5860			−1.05463			−0.527314	+	0.849670i	$0.676801\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.47660	+	47.9168i	0.123614	+	1.70372i
$792$		0			0
$793$	−10.4110	−	18.0323i	−0.369704	−	0.640346i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−41.7053	+	24.0785i	−1.47728	+	0.852906i	−0.999671	−	0.0256682i	$-0.991829\pi$
$797$	−41.7053	+	24.0785i	−1.47728	+	0.852906i	−0.477606	+	0.878574i	$0.658495\pi$
$798$		0			0
$799$	−1.42447	−	0.822418i	−0.0503941	−	0.0290951i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−21.4510			−0.756988
$804$		0			0
$805$	−3.35825	−	46.2856i	−0.118363	−	1.63135i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.61482	−	4.52900i	0.0919321	−	0.159231i	−0.816392	−	0.577498i	$-0.804029\pi$
$809$	2.61482	−	4.52900i	0.0919321	−	0.159231i	0.908324	+	0.418267i	$0.137362\pi$
$810$		0			0
$811$	−28.4364			−0.998538			−0.499269	−	0.866447i	$-0.666398\pi$
$811$	−28.4364			−0.998538			−0.499269	+	0.866447i	$0.666398\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−24.1149			−0.844709
$816$		0			0
$817$			9.83415i			0.344053i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.16817			−0.180370			−0.0901851	−	0.995925i	$-0.528746\pi$
$821$	−5.16817			−0.180370			−0.0901851	+	0.995925i	$0.528746\pi$
$822$		0			0
$823$			17.1504i			0.597825i	0.954281	+	0.298912i	$0.0966238\pi$
$823$			17.1504i			0.597825i	−0.954281	+	0.298912i	$0.903376\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	46.7499i		−	1.62565i	−0.582505	−	0.812827i	$-0.697927\pi$
$827$		−	46.7499i		−	1.62565i	0.582505	−	0.812827i	$-0.302073\pi$
$828$		0			0
$829$	−31.5449	−	18.2124i	−1.09560	−	0.632544i	−0.160538	−	0.987030i	$-0.551323\pi$
$829$	−31.5449	−	18.2124i	−1.09560	−	0.632544i	−0.935062	+	0.354485i	$0.884656\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.01375	−	6.94929i	−0.0351243	−	0.240779i
$834$		0			0
$835$		−	44.3477i		−	1.53471i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−5.36691	+	9.29577i	−0.185286	+	0.320925i	−0.943673	−	0.330880i	$-0.892655\pi$
$839$	−5.36691	+	9.29577i	−0.185286	+	0.320925i	0.758387	+	0.651805i	$0.225988\pi$
$840$		0			0
$841$	13.0396	+	22.5852i	0.449640	+	0.778799i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	15.7588	−	9.09836i	0.542120	−	0.312993i
$846$		0			0
$847$	−20.0204	+	13.5803i	−0.687910	+	0.466623i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			26.9910i			0.925239i
$852$		0			0
$853$	−29.2849	−	16.9076i	−1.00269	−	0.578906i	−0.0936502	−	0.995605i	$-0.529854\pi$
$853$	−29.2849	−	16.9076i	−1.00269	−	0.578906i	−0.909044	+	0.416699i	$0.863187\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−26.5914	+	15.3526i	−0.908347	+	0.524434i	−0.879899	−	0.475161i	$-0.842390\pi$
$857$	−26.5914	+	15.3526i	−0.908347	+	0.524434i	−0.0284478	+	0.999595i	$0.509056\pi$
$858$		0			0
$859$	12.9394	−	22.4117i	0.441487	−	0.764679i	−0.556313	−	0.830973i	$-0.687784\pi$
$859$	12.9394	−	22.4117i	0.441487	−	0.764679i	0.997800	+	0.0662945i	$0.0211177\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.1208	+	13.9262i	−0.821083	+	0.474052i	−0.850790	−	0.525506i	$-0.823876\pi$
$863$	−24.1208	+	13.9262i	−0.821083	+	0.474052i	0.0297071	+	0.999559i	$0.490543\pi$
$864$		0			0
$865$	−14.9682	+	25.9257i	−0.508935	+	0.881500i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.05977	+	7.03173i	0.137718	+	0.238535i
$870$		0			0
$871$	6.42318	+	11.1253i	0.217641	+	0.376966i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−13.8439	+	28.5736i	−0.468010	+	0.965966i
$876$		0			0
$877$	−9.25496	+	16.0301i	−0.312518	+	0.541297i	−0.978907	−	0.204307i	$-0.934506\pi$
$877$	−9.25496	+	16.0301i	−0.312518	+	0.541297i	0.666389	+	0.745604i	$0.267839\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			37.6194i			1.26743i	0.773567	+	0.633714i	$0.218470\pi$
$881$			37.6194i			1.26743i	−0.773567	+	0.633714i	$0.781530\pi$
$882$		0			0
$883$			15.2541i			0.513340i	0.966499	+	0.256670i	$0.0826254\pi$
$883$			15.2541i			0.513340i	−0.966499	+	0.256670i	$0.917375\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.98340	−	15.5597i	0.301633	−	0.522444i	−0.674873	−	0.737934i	$-0.735802\pi$
$887$	8.98340	−	15.5597i	0.301633	−	0.522444i	0.976506	+	0.215490i	$0.0691349\pi$
$888$		0			0
$889$	15.2625	−	31.5017i	0.511889	−	1.05653i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.26961	−	2.19903i	−0.0424859	−	0.0735877i
$894$		0			0
$895$	14.0794	+	24.3863i	0.470623	+	0.815144i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.446273	−	0.772968i	0.0148840	−	0.0257799i
$900$		0			0
$901$	2.16019	−	1.24719i	0.0719664	−	0.0415498i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.70800	+	8.15449i	−0.156499	+	0.271064i
$906$		0			0
$907$	−15.6153	+	9.01551i	−0.518498	+	0.299355i	−0.736320	−	0.676633i	$-0.763438\pi$
$907$	−15.6153	+	9.01551i	−0.518498	+	0.299355i	0.217822	+	0.975989i	$0.430105\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.79715	+	4.50169i	0.258331	+	0.149148i	0.623573	−	0.781765i	$-0.285680\pi$
$911$	7.79715	+	4.50169i	0.258331	+	0.149148i	−0.365242	+	0.930913i	$0.619014\pi$
$912$		0			0
$913$			13.0953i			0.433390i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	18.7043	−	12.6875i	0.617670	−	0.418978i
$918$		0			0
$919$	−20.9938	+	12.1208i	−0.692522	+	0.399828i	−0.804556	−	0.593876i	$-0.797597\pi$
$919$	−20.9938	+	12.1208i	−0.692522	+	0.399828i	0.112034	+	0.993704i	$0.464263\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.55324	−	2.69028i	−0.0511254	−	0.0885518i
$924$		0			0
$925$	1.54053	−	2.66827i	0.0506522	−	0.0877322i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	45.8160i		−	1.50317i	−0.659635	−	0.751586i	$-0.729289\pi$
$929$		−	45.8160i		−	1.50317i	0.659635	−	0.751586i	$-0.270711\pi$
$930$		0			0
$931$	4.00869	−	10.0732i	0.131379	−	0.330136i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.36722	−	1.36671i	−0.0774164	−	0.0446964i
$936$		0			0
$937$		−	16.0236i		−	0.523467i	−0.965140	−	0.261733i	$-0.915706\pi$
$937$		−	16.0236i		−	0.523467i	0.965140	−	0.261733i	$-0.0842941\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			7.92698i			0.258412i	0.991618	+	0.129206i	$0.0412428\pi$
$941$			7.92698i			0.258412i	−0.991618	+	0.129206i	$0.958757\pi$
$942$		0			0
$943$	3.91765			0.127576
$944$		0			0
$945$		0			0
$946$		0			0
$947$			15.3073i			0.497421i	0.968578	+	0.248711i	$0.0800068\pi$
$947$			15.3073i			0.497421i	−0.968578	+	0.248711i	$0.919993\pi$
$948$		0			0
$949$	31.0926			1.00931
$950$		0			0
$951$		0			0
$952$		0			0
$953$	36.5759			1.18481			0.592405	−	0.805640i	$-0.298179\pi$
$953$	36.5759			1.18481			0.592405	+	0.805640i	$0.298179\pi$
$954$		0			0
$955$	−8.63294	+	14.9527i	−0.279355	+	0.483858i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.738099	−	10.1730i	−0.0238345	−	0.328502i
$960$		0			0
$961$	−30.7273			−0.991202
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−18.9248	−	10.9262i	−0.609210	−	0.351728i
$966$		0			0
$967$	27.8653	−	16.0880i	0.896088	−	0.517357i	0.0201591	−	0.999797i	$-0.493583\pi$
$967$	27.8653	−	16.0880i	0.896088	−	0.517357i	0.875929	+	0.482440i	$0.160249\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	24.1287	+	41.7921i	0.774326	+	1.34117i	0.935172	+	0.354193i	$0.115244\pi$
$971$	24.1287	+	41.7921i	0.774326	+	1.34117i	−0.160846	+	0.986979i	$0.551422\pi$
$972$		0			0
$973$	2.90922	+	40.0967i	0.0932653	+	1.28544i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.60494			−0.0833394			−0.0416697	−	0.999131i	$-0.513268\pi$
$977$	−2.60494			−0.0833394			−0.0416697	+	0.999131i	$0.513268\pi$
$978$		0			0
$979$	−0.872274	+	1.51082i	−0.0278780	+	0.0482861i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−19.9000	−	34.4678i	−0.634711	−	1.09935i	−0.986576	−	0.163301i	$-0.947786\pi$
$983$	−19.9000	−	34.4678i	−0.634711	−	1.09935i	0.351865	−	0.936051i	$-0.385547\pi$
$984$		0			0
$985$	−34.1413	−	19.7115i	−1.08783	−	0.628060i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−27.8478	−	48.2337i	−0.885507	−	1.53374i
$990$		0			0
$991$	−9.30303	−	5.37111i	−0.295521	−	0.170619i	0.344908	−	0.938636i	$-0.387910\pi$
$991$	−9.30303	−	5.37111i	−0.295521	−	0.170619i	−0.640429	+	0.768018i	$0.721243\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−46.2644	+	26.7107i	−1.46668	+	0.846787i
$996$		0			0
$997$	−20.6620	+	11.9292i	−0.654373	+	0.377803i	−0.790130	−	0.612940i	$-0.789987\pi$
$997$	−20.6620	+	11.9292i	−0.654373	+	0.377803i	0.135756	+	0.990742i	$0.456654\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cz.h.2719.4		24
3.2	odd	2		1008.2.cz.g.367.10	yes	24
4.3	odd	2		3024.2.cz.g.2719.4		24
7.5	odd	6		3024.2.bf.h.2287.4		24
9.4	even	3		3024.2.bf.g.1711.9		24
9.5	odd	6		1008.2.bf.h.31.2	yes	24
12.11	even	2		1008.2.cz.h.367.3	yes	24
21.5	even	6		1008.2.bf.g.943.11	yes	24
28.19	even	6		3024.2.bf.g.2287.4		24
36.23	even	6		1008.2.bf.g.31.11	✓	24
36.31	odd	6		3024.2.bf.h.1711.9		24
63.5	even	6		1008.2.cz.h.607.3	yes	24
63.40	odd	6		3024.2.cz.g.1279.4		24
84.47	odd	6		1008.2.bf.h.943.2	yes	24
252.103	even	6	inner	3024.2.cz.h.1279.4		24
252.131	odd	6		1008.2.cz.g.607.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.11	✓	24	36.23	even	6
1008.2.bf.g.943.11	yes	24	21.5	even	6
1008.2.bf.h.31.2	yes	24	9.5	odd	6
1008.2.bf.h.943.2	yes	24	84.47	odd	6
1008.2.cz.g.367.10	yes	24	3.2	odd	2
1008.2.cz.g.607.10	yes	24	252.131	odd	6
1008.2.cz.h.367.3	yes	24	12.11	even	2
1008.2.cz.h.607.3	yes	24	63.5	even	6
3024.2.bf.g.1711.9		24	9.4	even	3
3024.2.bf.g.2287.4		24	28.19	even	6
3024.2.bf.h.1711.9		24	36.31	odd	6
3024.2.bf.h.2287.4		24	7.5	odd	6
3024.2.cz.g.1279.4		24	63.40	odd	6
3024.2.cz.g.2719.4		24	4.3	odd	2
3024.2.cz.h.1279.4		24	252.103	even	6	inner
3024.2.cz.h.2719.4		24	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73177 - 0.999840i) q^{5} +(2.38101 + 1.15360i) q^{7} +(-1.17995 + 0.681244i) q^{11} +(1.71030 - 0.987444i) q^{13} +(-0.868852 - 0.501632i) q^{17} +(-0.774396 - 1.34129i) q^{19} +(7.59639 + 4.38578i) q^{23} +(-0.500642 - 0.867137i) q^{25} +(-0.854529 + 1.48009i) q^{29} -0.522244 q^{31} +(-2.96996 - 4.37840i) q^{35} +(1.53855 + 2.66485i) q^{37} +(0.386794 - 0.223316i) q^{41} +(-5.49888 - 3.17478i) q^{43} +1.63949 q^{47} +(4.33842 + 5.49346i) q^{49} +(-1.24313 + 2.15316i) q^{53} +2.72454 q^{55} +12.6284 q^{59} -10.5433i q^{61} -3.94914 q^{65} +6.50486i q^{67} -1.57299i q^{71} +(13.6347 + 7.87199i) q^{73} +(-3.59535 + 0.260861i) q^{77} -5.95935i q^{79} +(4.80565 - 8.32363i) q^{83} +(1.00310 + 1.73743i) q^{85} +(1.10887 - 0.640207i) q^{89} +(5.21136 - 0.378111i) q^{91} +3.09709i q^{95} +(8.31781 + 4.80229i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 4 q^{7} + 9 q^{11} - 3 q^{13} + 3 q^{17} - 4 q^{19} + 6 q^{23} + 15 q^{25} - 18 q^{29} + 34 q^{31} + 42 q^{35} - 3 q^{37} - 36 q^{41} + 24 q^{43} + 42 q^{47} + 30 q^{49} + 12 q^{53} - 30 q^{55}+ \cdots + 3 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 + 4 * q^7 + 9 * q^11 - 3 * q^13 + 3 * q^17 - 4 * q^19 + 6 * q^23 + 15 * q^25 - 18 * q^29 + 34 * q^31 + 42 * q^35 - 3 * q^37 - 36 * q^41 + 24 * q^43 + 42 * q^47 + 30 * q^49 + 12 * q^53 - 30 * q^55 + 12 * q^59 + 48 * q^73 + 48 * q^77 + 48 * q^83 - 21 * q^85 - 39 * q^89 + 9 * q^91 + 3 * q^97

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