LMFDB - Embedded newform 2340.2.dj.c.361.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2340,2,Mod(361,2340)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2340, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 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("2340.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.dj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0] 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:	$18.6849940730$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 780)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2340.361
Dual form			2340.2.dj.c.901.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{5} +(3.40508 + 1.96593i) q^{7} +(1.14128 - 0.658919i) q^{11} +(1.86250 + 3.08725i) q^{13} +(0.276457 - 0.478838i) q^{17} +(4.69748 + 2.71209i) q^{19} +(0.237657 + 0.411634i) q^{23} -1.00000 q^{25} +(-1.53906 - 2.66573i) q^{29} -3.49938i q^{31} +(-1.96593 + 3.40508i) q^{35} +(0.407165 - 0.235077i) q^{37} +(-2.53906 + 1.46593i) q^{41} +(0.697977 - 1.20893i) q^{43} +7.71039i q^{47} +(4.22973 + 7.32611i) q^{49} -3.43488 q^{53} +(0.658919 + 1.14128i) q^{55} +(-11.2735 - 6.50877i) q^{59} +(0.313111 - 0.542324i) q^{61} +(-3.08725 + 1.86250i) q^{65} +(11.0370 - 6.37221i) q^{67} +(4.51581 + 2.60721i) q^{71} +6.95303i q^{73} +5.18154 q^{77} +1.19615 q^{79} +12.9382i q^{83} +(0.478838 + 0.276457i) q^{85} +(15.5117 - 8.95568i) q^{89} +(0.272675 + 14.1739i) q^{91} +(-2.71209 + 4.69748i) q^{95} +(-4.54342 - 2.62314i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{11} - 4 q^{17} + 12 q^{19} - 4 q^{23} - 8 q^{25} + 8 q^{29} - 8 q^{35} - 24 q^{37} - 16 q^{43} - 4 q^{49} - 16 q^{53} + 4 q^{55} - 24 q^{59} + 8 q^{61} + 24 q^{67} + 12 q^{71} + 8 q^{77} - 32 q^{79}+ \cdots + 48 q^{97}+O(q^{100}) $ 8 * q + 12 * q^11 - 4 * q^17 + 12 * q^19 - 4 * q^23 - 8 * q^25 + 8 * q^29 - 8 * q^35 - 24 * q^37 - 16 * q^43 - 4 * q^49 - 16 * q^53 + 4 * q^55 - 24 * q^59 + 8 * q^61 + 24 * q^67 + 12 * q^71 + 8 * q^77 - 32 * q^79 + 12 * q^89 + 8 * q^91 + 12 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	3.40508	+	1.96593i	1.28700	+	0.743050i	0.978118	−	0.208050i	$-0.0667117\pi$
$7$	3.40508	+	1.96593i	1.28700	+	0.743050i	0.308882	+	0.951100i	$0.400045\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.14128	−	0.658919i	0.344109	−	0.198671i	−0.317979	−	0.948098i	$-0.603004\pi$
$11$	1.14128	−	0.658919i	0.344109	−	0.198671i	0.662088	+	0.749426i	$0.269671\pi$
$12$		0			0
$13$	1.86250	+	3.08725i	0.516565	+	0.856248i
$13$	1.86250	+	3.08725i	0.516565	+	0.856248i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.276457	−	0.478838i	0.0670507	−	0.116135i	−0.830551	−	0.556942i	$-0.811974\pi$
$17$	0.276457	−	0.478838i	0.0670507	−	0.116135i	0.897602	+	0.440807i	$0.145308\pi$
$18$		0			0
$19$	4.69748	+	2.71209i	1.07768	+	0.622196i	0.930268	−	0.366880i	$-0.119574\pi$
$19$	4.69748	+	2.71209i	1.07768	+	0.622196i	0.147407	+	0.989076i	$0.452907\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.237657	+	0.411634i	0.0495549	+	0.0858316i	0.889739	−	0.456470i	$-0.150886\pi$
$23$	0.237657	+	0.411634i	0.0495549	+	0.0858316i	−0.840184	+	0.542301i	$0.817553\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.53906	−	2.66573i	−0.285796	−	0.495013i	0.687006	−	0.726652i	$-0.258925\pi$
$29$	−1.53906	−	2.66573i	−0.285796	−	0.495013i	−0.972802	+	0.231639i	$0.925591\pi$
$30$		0			0
$31$		−	3.49938i		−	0.628507i	−0.949339	−	0.314253i	$-0.898246\pi$
$31$		−	3.49938i		−	0.628507i	0.949339	−	0.314253i	$-0.101754\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.96593	+	3.40508i	−0.332302	+	0.575564i
$36$		0			0
$37$	0.407165	−	0.235077i	0.0669376	−	0.0386464i	−0.466158	−	0.884702i	$-0.654362\pi$
$37$	0.407165	−	0.235077i	0.0669376	−	0.0386464i	0.533095	+	0.846055i	$0.321029\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.53906	+	1.46593i	−0.396534	+	0.228939i	−0.684987	−	0.728555i	$-0.740192\pi$
$41$	−2.53906	+	1.46593i	−0.396534	+	0.228939i	0.288453	+	0.957494i	$0.406859\pi$
$42$		0			0
$43$	0.697977	−	1.20893i	0.106440	−	0.184360i	−0.807885	−	0.589340i	$-0.799388\pi$
$43$	0.697977	−	1.20893i	0.106440	−	0.184360i	0.914326	+	0.404979i	$0.132721\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			7.71039i			1.12468i	0.826907	+	0.562338i	$0.190098\pi$
$47$			7.71039i			1.12468i	−0.826907	+	0.562338i	$0.809902\pi$
$48$		0			0
$49$	4.22973	+	7.32611i	0.604247	+	1.04659i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.43488			−0.471817			−0.235908	−	0.971775i	$-0.575807\pi$
$53$	−3.43488			−0.471817			−0.235908	+	0.971775i	$0.575807\pi$
$54$		0			0
$55$	0.658919	+	1.14128i	0.0888486	+	0.153890i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−11.2735	−	6.50877i	−1.46769	−	0.847369i	−0.468341	−	0.883548i	$-0.655148\pi$
$59$	−11.2735	−	6.50877i	−1.46769	−	0.847369i	−0.999345	+	0.0361787i	$0.988481\pi$
$60$		0			0
$61$	0.313111	−	0.542324i	0.0400898	−	0.0694375i	−0.845284	−	0.534317i	$-0.820569\pi$
$61$	0.313111	−	0.542324i	0.0400898	−	0.0694375i	0.885374	+	0.464879i	$0.153902\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.08725	+	1.86250i	−0.382926	+	0.231015i
$66$		0			0
$67$	11.0370	−	6.37221i	1.34838	−	0.778490i	0.360363	−	0.932812i	$-0.382653\pi$
$67$	11.0370	−	6.37221i	1.34838	−	0.778490i	0.988020	+	0.154323i	$0.0493195\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.51581	+	2.60721i	0.535929	+	0.309418i	0.743427	−	0.668817i	$-0.233199\pi$
$71$	4.51581	+	2.60721i	0.535929	+	0.309418i	−0.207499	+	0.978235i	$0.566532\pi$
$72$		0			0
$73$			6.95303i			0.813791i	0.913475	+	0.406895i	$0.133389\pi$
$73$			6.95303i			0.813791i	−0.913475	+	0.406895i	$0.866611\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.18154			0.590491
$78$		0			0
$79$	1.19615			0.134578			0.0672888	−	0.997734i	$-0.478565\pi$
$79$	1.19615			0.134578			0.0672888	+	0.997734i	$0.478565\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			12.9382i			1.42015i	0.704127	+	0.710074i	$0.251339\pi$
$83$			12.9382i			1.42015i	−0.704127	+	0.710074i	$0.748661\pi$
$84$		0			0
$85$	0.478838	+	0.276457i	0.0519373	+	0.0299860i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	15.5117	−	8.95568i	1.64424	−	0.949300i	0.664931	−	0.746904i	$-0.268461\pi$
$89$	15.5117	−	8.95568i	1.64424	−	0.949300i	0.979304	−	0.202395i	$-0.0648726\pi$
$90$		0			0
$91$	0.272675	+	14.1739i	0.0285841	+	1.48583i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.71209	+	4.69748i	−0.278255	+	0.481951i
$96$		0			0
$97$	−4.54342	−	2.62314i	−0.461314	−	0.266340i	0.251282	−	0.967914i	$-0.419148\pi$
$97$	−4.54342	−	2.62314i	−0.461314	−	0.266340i	−0.712597	+	0.701574i	$0.752481\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.98432	−	12.0972i	−0.694966	−	1.20372i	−0.970192	−	0.242337i	$-0.922086\pi$
$101$	−6.98432	−	12.0972i	−0.694966	−	1.20372i	0.275226	−	0.961379i	$-0.411247\pi$
$102$		0			0
$103$	−17.2231			−1.69705			−0.848523	−	0.529158i	$-0.822508\pi$
$103$	−17.2231			−1.69705			−0.848523	+	0.529158i	$0.822508\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.81029	+	8.33167i	0.465028	+	0.805453i	0.999203	−	0.0399215i	$-0.0127108\pi$
$107$	4.81029	+	8.33167i	0.465028	+	0.805453i	−0.534174	+	0.845374i	$0.679377\pi$
$108$		0			0
$109$			12.1516i			1.16391i	0.813221	+	0.581956i	$0.197712\pi$
$109$			12.1516i			1.16391i	−0.813221	+	0.581956i	$0.802288\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.367725	+	0.636919i	−0.0345927	+	0.0599163i	−0.882803	−	0.469743i	$-0.844347\pi$
$113$	−0.367725	+	0.636919i	−0.0345927	+	0.0599163i	0.848211	+	0.529659i	$0.177680\pi$
$114$		0			0
$115$	−0.411634	+	0.237657i	−0.0383850	+	0.0221616i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.88272	−	1.08699i	0.172589	−	0.0996441i
$120$		0			0
$121$	−4.63165	+	8.02226i	−0.421059	+	0.729296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−9.54378	−	16.5303i	−0.846874	−	1.46683i	−0.883984	−	0.467517i	$-0.845149\pi$
$127$	−9.54378	−	16.5303i	−0.846874	−	1.46683i	0.0371100	−	0.999311i	$-0.488185\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.40717			−0.122945			−0.0614723	−	0.998109i	$-0.519580\pi$
$131$	−1.40717			−0.122945			−0.0614723	+	0.998109i	$0.519580\pi$
$132$		0			0
$133$	10.6635	+	18.4698i	0.924646	+	1.60153i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.0977	+	5.82989i	0.862701	+	0.498081i	0.864916	−	0.501917i	$-0.167372\pi$
$137$	10.0977	+	5.82989i	0.862701	+	0.498081i	−0.00221463	+	0.999998i	$0.500705\pi$
$138$		0			0
$139$	1.12106	−	1.94174i	0.0950873	−	0.164696i	−0.814558	−	0.580082i	$-0.803020\pi$
$139$	1.12106	−	1.94174i	0.0950873	−	0.164696i	0.909645	+	0.415386i	$0.136354\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.15988	+	2.29618i	0.347867	+	0.192016i
$144$		0			0
$145$	2.66573	−	1.53906i	0.221377	−	0.127812i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	16.1476	+	9.32282i	1.32286	+	0.763755i	0.984184	−	0.177147i	$-0.0566868\pi$
$149$	16.1476	+	9.32282i	1.32286	+	0.763755i	0.338678	+	0.940902i	$0.390020\pi$
$150$		0			0
$151$		−	0.368970i		−	0.0300263i	−0.999887	−	0.0150132i	$-0.995221\pi$
$151$		−	0.368970i		−	0.0300263i	0.999887	−	0.0150132i	$-0.00477902\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.49938			0.281077
$156$		0			0
$157$	4.71895			0.376613			0.188307	−	0.982110i	$-0.439700\pi$
$157$	4.71895			0.376613			0.188307	+	0.982110i	$0.439700\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			1.86886i			0.147287i
$162$		0			0
$163$	11.7193	+	6.76612i	0.917924	+	0.529964i	0.882972	−	0.469425i	$-0.155539\pi$
$163$	11.7193	+	6.76612i	0.917924	+	0.529964i	0.0349520	+	0.999389i	$0.488872\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.31419	−	3.06815i	0.411224	−	0.237420i	−0.280091	−	0.959973i	$-0.590365\pi$
$167$	5.31419	−	3.06815i	0.411224	−	0.237420i	0.691316	+	0.722553i	$0.257031\pi$
$168$		0			0
$169$	−6.06218	+	11.5000i	−0.466321	+	0.884615i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.248229	+	0.429946i	−0.0188725	+	0.0326882i	−0.875307	−	0.483567i	$-0.839341\pi$
$173$	−0.248229	+	0.429946i	−0.0188725	+	0.0326882i	0.856435	+	0.516255i	$0.172674\pi$
$174$		0			0
$175$	−3.40508	−	1.96593i	−0.257400	−	0.148610i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.96895	−	3.41032i	−0.147166	−	0.254900i	0.783013	−	0.622006i	$-0.213682\pi$
$179$	−1.96895	−	3.41032i	−0.147166	−	0.254900i	−0.930179	+	0.367106i	$0.880349\pi$
$180$		0			0
$181$	3.35363			0.249273			0.124637	−	0.992202i	$-0.460223\pi$
$181$	3.35363			0.249273			0.124637	+	0.992202i	$0.460223\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.235077	+	0.407165i	0.0172832	+	0.0299354i
$186$		0			0
$187$		−	0.728651i		−	0.0532842i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.2831	+	17.8109i	−0.744062	+	1.28875i	0.206570	+	0.978432i	$0.433770\pi$
$191$	−10.2831	+	17.8109i	−0.744062	+	1.28875i	−0.950632	+	0.310321i	$0.899563\pi$
$192$		0			0
$193$	4.77886	−	2.75908i	0.343990	−	0.198603i	−0.318045	−	0.948076i	$-0.603026\pi$
$193$	4.77886	−	2.75908i	0.343990	−	0.198603i	0.662035	+	0.749473i	$0.269693\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.80659	−	3.92979i	0.484950	−	0.279986i	−0.237527	−	0.971381i	$-0.576337\pi$
$197$	6.80659	−	3.92979i	0.484950	−	0.279986i	0.722477	+	0.691395i	$0.243004\pi$
$198$		0			0
$199$	−3.49536	+	6.05413i	−0.247779	+	0.429166i	−0.962909	−	0.269825i	$-0.913034\pi$
$199$	−3.49536	+	6.05413i	−0.247779	+	0.429166i	0.715130	+	0.698991i	$0.246367\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	12.1027i		−	0.849443i
$204$		0			0
$205$	−1.46593	−	2.53906i	−0.102385	−	0.177336i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	7.14819			0.494451
$210$		0			0
$211$	6.79958	+	11.7772i	0.468102	+	0.810777i	0.999336	−	0.0364488i	$-0.0116046\pi$
$211$	6.79958	+	11.7772i	0.468102	+	0.810777i	−0.531233	+	0.847226i	$0.678271\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.20893	+	0.697977i	0.0824484	+	0.0476016i
$216$		0			0
$217$	6.87952	−	11.9157i	0.467012	−	0.808889i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.99319	−	0.0383448i	0.134077	−	0.00257935i
$222$		0			0
$223$	−10.6814	+	6.16693i	−0.715282	+	0.412968i	−0.813014	−	0.582245i	$-0.802175\pi$
$223$	−10.6814	+	6.16693i	−0.715282	+	0.412968i	0.0977319	+	0.995213i	$0.468841\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.60319	+	5.54441i	0.637386	+	0.367995i	0.783607	−	0.621257i	$-0.213378\pi$
$227$	9.60319	+	5.54441i	0.637386	+	0.367995i	−0.146221	+	0.989252i	$0.546711\pi$
$228$		0			0
$229$		−	11.4607i		−	0.757344i	−0.925531	−	0.378672i	$-0.876381\pi$
$229$		−	11.4607i		−	0.757344i	0.925531	−	0.378672i	$-0.123619\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	25.4527			1.66746			0.833730	−	0.552172i	$-0.186201\pi$
$233$	25.4527			1.66746			0.833730	+	0.552172i	$0.186201\pi$
$234$		0			0
$235$	−7.71039			−0.502970
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	20.8676i		−	1.34981i	−0.737903	−	0.674907i	$-0.764184\pi$
$239$		−	20.8676i		−	1.34981i	0.737903	−	0.674907i	$-0.235816\pi$
$240$		0			0
$241$	−15.8447	−	9.14796i	−1.02065	−	0.589272i	−0.106357	−	0.994328i	$-0.533919\pi$
$241$	−15.8447	−	9.14796i	−1.02065	−	0.589272i	−0.914292	+	0.405056i	$0.867252\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.32611	+	4.22973i	−0.468048	+	0.270227i
$246$		0			0
$247$	0.376169	+	19.5535i	0.0239351	+	1.24416i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.17191	+	3.76186i	−0.137090	+	0.237447i	−0.926394	−	0.376556i	$-0.877108\pi$
$251$	−2.17191	+	3.76186i	−0.137090	+	0.237447i	0.789304	+	0.614003i	$0.210442\pi$
$252$		0			0
$253$	0.542466	+	0.313193i	0.0341046	+	0.0196903i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.42895	+	4.20706i	0.151514	+	0.262429i	0.931784	−	0.363013i	$-0.118252\pi$
$257$	2.42895	+	4.20706i	0.151514	+	0.262429i	−0.780270	+	0.625442i	$0.784919\pi$
$258$		0			0
$259$	1.84858			0.114865
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.1647	−	19.3379i	−0.688447	−	1.19243i	−0.972340	−	0.233570i	$-0.924959\pi$
$263$	−11.1647	−	19.3379i	−0.688447	−	1.19243i	0.283893	−	0.958856i	$-0.408374\pi$
$264$		0			0
$265$		−	3.43488i		−	0.211003i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.16875	−	7.22049i	0.254173	−	0.440241i	−0.710497	−	0.703700i	$-0.751530\pi$
$269$	4.16875	−	7.22049i	0.254173	−	0.440241i	0.964671	+	0.263459i	$0.0848633\pi$
$270$		0			0
$271$	−9.58860	+	5.53598i	−0.582466	+	0.336287i	−0.762113	−	0.647444i	$-0.775838\pi$
$271$	−9.58860	+	5.53598i	−0.582466	+	0.336287i	0.179647	+	0.983731i	$0.442504\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.14128	+	0.658919i	−0.0688218	+	0.0397343i
$276$		0			0
$277$	8.92480	−	15.4582i	0.536239	−	0.928794i	−0.462863	−	0.886430i	$-0.653178\pi$
$277$	8.92480	−	15.4582i	0.536239	−	0.928794i	0.999102	−	0.0423641i	$-0.0134889\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			30.2163i			1.80256i	0.433242	+	0.901278i	$0.357370\pi$
$281$			30.2163i			1.80256i	−0.433242	+	0.901278i	$0.642630\pi$
$282$		0			0
$283$	−15.2299	−	26.3789i	−0.905321	−	1.56806i	−0.820485	−	0.571668i	$-0.806297\pi$
$283$	−15.2299	−	26.3789i	−0.905321	−	1.56806i	−0.0848360	−	0.996395i	$-0.527037\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.5276			−0.680453
$288$		0			0
$289$	8.34714	+	14.4577i	0.491008	+	0.850452i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−15.9982	−	9.23654i	−0.934622	−	0.539604i	−0.0463516	−	0.998925i	$-0.514759\pi$
$293$	−15.9982	−	9.23654i	−0.934622	−	0.539604i	−0.888270	+	0.459321i	$0.848093\pi$
$294$		0			0
$295$	6.50877	−	11.2735i	0.378955	−	0.656369i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.828178	+	1.50037i	−0.0478948	+	0.0867688i
$300$		0			0
$301$	4.75334	−	2.74434i	0.273978	−	0.158181i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.542324	+	0.313111i	0.0310534	+	0.0179287i
$306$		0			0
$307$		−	24.6938i		−	1.40935i	−0.709530	−	0.704675i	$-0.751093\pi$
$307$		−	24.6938i		−	1.40935i	0.709530	−	0.704675i	$-0.248907\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−33.5489			−1.90239			−0.951193	−	0.308596i	$-0.900141\pi$
$311$	−33.5489			−1.90239			−0.951193	+	0.308596i	$0.900141\pi$
$312$		0			0
$313$	22.2876			1.25977			0.629886	−	0.776688i	$-0.283102\pi$
$313$	22.2876			1.25977			0.629886	+	0.776688i	$0.283102\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	34.0884i		−	1.91459i	−0.289109	−	0.957296i	$-0.593359\pi$
$317$		−	34.0884i		−	1.91459i	0.289109	−	0.957296i	$-0.406641\pi$
$318$		0			0
$319$	−3.51299	−	2.02823i	−0.196690	−	0.113559i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.59730	−	1.49955i	0.144518	−	0.0834374i
$324$		0			0
$325$	−1.86250	−	3.08725i	−0.103313	−	0.171250i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−15.1581	+	26.2545i	−0.835691	+	1.44746i
$330$		0			0
$331$	−26.0020	−	15.0123i	−1.42920	−	0.825150i	−0.432144	−	0.901805i	$-0.642243\pi$
$331$	−26.0020	−	15.0123i	−1.42920	−	0.825150i	−0.997058	+	0.0766545i	$0.975576\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.37221	+	11.0370i	0.348151	+	0.603015i
$336$		0			0
$337$	6.84596			0.372923			0.186462	−	0.982462i	$-0.440298\pi$
$337$	6.84596			0.372923			0.186462	+	0.982462i	$0.440298\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.30581	−	3.99377i	−0.124866	−	0.216275i
$342$		0			0
$343$			5.73837i			0.309843i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.8177	+	22.2010i	−0.688092	+	1.19181i	0.284363	+	0.958717i	$0.408218\pi$
$347$	−12.8177	+	22.2010i	−0.688092	+	1.19181i	−0.972454	+	0.233093i	$0.925115\pi$
$348$		0			0
$349$	10.5134	−	6.06993i	0.562771	−	0.324916i	−0.191486	−	0.981495i	$-0.561331\pi$
$349$	10.5134	−	6.06993i	0.562771	−	0.324916i	0.754257	+	0.656579i	$0.227997\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	26.4830	−	15.2899i	1.40955	−	0.813802i	0.414202	−	0.910185i	$-0.364061\pi$
$353$	26.4830	−	15.2899i	1.40955	−	0.813802i	0.995344	+	0.0963832i	$0.0307274\pi$
$354$		0			0
$355$	−2.60721	+	4.51581i	−0.138376	+	0.239675i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	12.2163i		−	0.644754i	−0.946611	−	0.322377i	$-0.895518\pi$
$359$		−	12.2163i		−	0.644754i	0.946611	−	0.322377i	$-0.104482\pi$
$360$		0			0
$361$	5.21087	+	9.02549i	0.274256	+	0.475026i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.95303			−0.363938
$366$		0			0
$367$	12.9482	+	22.4269i	0.675890	+	1.17068i	0.976208	+	0.216836i	$0.0695737\pi$
$367$	12.9482	+	22.4269i	0.675890	+	1.17068i	−0.300318	+	0.953839i	$0.597093\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−11.6960	−	6.75272i	−0.607228	−	0.350584i
$372$		0			0
$373$	8.80104	−	15.2438i	0.455700	−	0.789296i	−0.543028	−	0.839715i	$-0.682722\pi$
$373$	8.80104	−	15.2438i	0.455700	−	0.789296i	0.998728	+	0.0504185i	$0.0160555\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.36326	−	9.71637i	0.276222	−	0.500419i
$378$		0			0
$379$	−24.3471	+	14.0568i	−1.25063	+	0.722051i	−0.971234	−	0.238126i	$-0.923467\pi$
$379$	−24.3471	+	14.0568i	−1.25063	+	0.722051i	−0.279394	+	0.960176i	$0.590134\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.97065	−	1.13776i	−0.100696	−	0.0581366i	0.448807	−	0.893629i	$-0.351849\pi$
$383$	−1.97065	−	1.13776i	−0.100696	−	0.0581366i	−0.549502	+	0.835492i	$0.685183\pi$
$384$		0			0
$385$			5.18154i			0.264076i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.182785			−0.00926757			−0.00463378	−	0.999989i	$-0.501475\pi$
$389$	−0.182785			−0.00926757			−0.00463378	+	0.999989i	$0.501475\pi$
$390$		0			0
$391$	0.262808			0.0132908
$392$		0			0
$393$		0			0
$394$		0			0
$395$			1.19615i			0.0601850i
$396$		0			0
$397$	−25.2689	−	14.5890i	−1.26821	−	0.732202i	−0.293562	−	0.955940i	$-0.594841\pi$
$397$	−25.2689	−	14.5890i	−1.26821	−	0.732202i	−0.974649	+	0.223738i	$0.928174\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−24.2385	+	13.9941i	−1.21041	+	0.698833i	−0.962849	−	0.270039i	$-0.912963\pi$
$401$	−24.2385	+	13.9941i	−1.21041	+	0.698833i	−0.247564	+	0.968872i	$0.579630\pi$
$402$		0			0
$403$	10.8034	−	6.51760i	0.538158	−	0.324665i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.309793	−	0.536578i	0.0153559	−	0.0265972i
$408$		0			0
$409$	−15.6607	−	9.04170i	−0.774371	−	0.447083i	0.0600606	−	0.998195i	$-0.480871\pi$
$409$	−15.6607	−	9.04170i	−0.774371	−	0.447083i	−0.834432	+	0.551111i	$0.814204\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−25.5915	−	44.3258i	−1.25928	−	2.18113i
$414$		0			0
$415$	−12.9382			−0.635110
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5.20403	−	9.01364i	−0.254233	−	0.440345i	0.710454	−	0.703744i	$-0.248490\pi$
$419$	−5.20403	−	9.01364i	−0.254233	−	0.440345i	−0.964687	+	0.263399i	$0.915156\pi$
$420$		0			0
$421$			5.16456i			0.251705i	0.992049	+	0.125853i	$0.0401666\pi$
$421$			5.16456i			0.251705i	−0.992049	+	0.125853i	$0.959833\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.276457	+	0.478838i	−0.0134101	+	0.0232270i
$426$		0			0
$427$	2.13234	−	1.23111i	0.103191	−	0.0595774i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−29.0597	+	16.7776i	−1.39976	+	0.808150i	−0.994367	−	0.105993i	$-0.966198\pi$
$431$	−29.0597	+	16.7776i	−1.39976	+	0.808150i	−0.405390	+	0.914144i	$0.632864\pi$
$432$		0			0
$433$	8.47099	−	14.6722i	0.407090	−	0.705100i	−0.587472	−	0.809244i	$-0.699877\pi$
$433$	8.47099	−	14.6722i	0.407090	−	0.705100i	0.994562	+	0.104144i	$0.0332102\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			2.57819i			0.123331i
$438$		0			0
$439$	−13.3279	−	23.0846i	−0.636105	−	1.10177i	−0.986280	−	0.165082i	$-0.947211\pi$
$439$	−13.3279	−	23.0846i	−0.636105	−	1.10177i	0.350174	−	0.936684i	$-0.386122\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.90671			0.423170			0.211585	−	0.977360i	$-0.432137\pi$
$443$	8.90671			0.423170			0.211585	+	0.977360i	$0.432137\pi$
$444$		0			0
$445$	8.95568	+	15.5117i	0.424540	+	0.735324i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9.40300	−	5.42883i	−0.443755	−	0.256202i	0.261434	−	0.965221i	$-0.415805\pi$
$449$	−9.40300	−	5.42883i	−0.443755	−	0.256202i	−0.705189	+	0.709019i	$0.749138\pi$
$450$		0			0
$451$	−1.93185	+	3.34607i	−0.0909673	+	0.157560i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−14.1739	+	0.272675i	−0.664481	+	0.0127832i
$456$		0			0
$457$	6.73831	−	3.89036i	0.315205	−	0.181984i	−0.334048	−	0.942556i	$-0.608415\pi$
$457$	6.73831	−	3.89036i	0.315205	−	0.181984i	0.649253	+	0.760572i	$0.275082\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	24.4717	+	14.1288i	1.13976	+	0.658042i	0.946372	−	0.323080i	$-0.104718\pi$
$461$	24.4717	+	14.1288i	1.13976	+	0.658042i	0.193390	+	0.981122i	$0.438052\pi$
$462$		0			0
$463$			8.22511i			0.382253i	0.981565	+	0.191127i	$0.0612141\pi$
$463$			8.22511i			0.382253i	−0.981565	+	0.191127i	$0.938786\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	21.4205			0.991224			0.495612	−	0.868544i	$-0.334944\pi$
$467$	21.4205			0.991224			0.495612	+	0.868544i	$0.334944\pi$
$468$		0			0
$469$	50.1092			2.31383
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	1.83964i		−	0.0845867i
$474$		0			0
$475$	−4.69748	−	2.71209i	−0.215535	−	0.124439i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	30.7499	−	17.7535i	1.40500	−	0.811177i	0.410099	−	0.912041i	$-0.365494\pi$
$479$	30.7499	−	17.7535i	1.40500	−	0.811177i	0.994900	+	0.100864i	$0.0321607\pi$
$480$		0			0
$481$	1.48409	+	0.819188i	0.0676685	+	0.0373518i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.62314	−	4.54342i	0.119111	−	0.206306i
$486$		0			0
$487$	−1.93124	−	1.11500i	−0.0875128	−	0.0505255i	0.455605	−	0.890182i	$-0.349423\pi$
$487$	−1.93124	−	1.11500i	−0.0875128	−	0.0505255i	−0.543118	+	0.839657i	$0.682756\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−18.8199	−	32.5970i	−0.849330	−	1.47108i	−0.881807	−	0.471610i	$-0.843673\pi$
$491$	−18.8199	−	32.5970i	−0.849330	−	1.47108i	0.0324772	−	0.999472i	$-0.489660\pi$
$492$		0			0
$493$	−1.70193			−0.0766513
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.2511	+	17.7555i	0.459827	+	0.796443i
$498$		0			0
$499$		−	26.3242i		−	1.17843i	−0.807975	−	0.589216i	$-0.799437\pi$
$499$		−	26.3242i		−	1.17843i	0.807975	−	0.589216i	$-0.200563\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−13.1455	+	22.7687i	−0.586130	+	1.01521i	0.408603	+	0.912712i	$0.366016\pi$
$503$	−13.1455	+	22.7687i	−0.586130	+	1.01521i	−0.994733	+	0.102496i	$0.967317\pi$
$504$		0			0
$505$	12.0972	−	6.98432i	0.538318	−	0.310798i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.35226	−	1.93543i	0.148586	−	0.0857863i	−0.423864	−	0.905726i	$-0.639326\pi$
$509$	3.35226	−	1.93543i	0.148586	−	0.0857863i	0.572450	+	0.819940i	$0.305993\pi$
$510$		0			0
$511$	−13.6691	+	23.6757i	−0.604687	+	1.04735i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	17.2231i		−	0.758942i
$516$		0			0
$517$	5.08052	+	8.79972i	0.223441	+	0.387011i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−20.6427			−0.904372			−0.452186	−	0.891924i	$-0.649356\pi$
$521$	−20.6427			−0.904372			−0.452186	+	0.891924i	$0.649356\pi$
$522$		0			0
$523$	−14.1905	−	24.5787i	−0.620508	−	1.07475i	−0.989391	−	0.145275i	$-0.953593\pi$
$523$	−14.1905	−	24.5787i	−0.620508	−	1.07475i	0.368883	−	0.929476i	$-0.379740\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.67563	−	0.967428i	−0.0729918	−	0.0421418i
$528$		0			0
$529$	11.3870	−	19.7229i	0.495089	−	0.857519i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.25467	−	5.10841i	−0.400864	−	0.221270i
$534$		0			0
$535$	−8.33167	+	4.81029i	−0.360209	+	0.207967i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.65461	+	5.57409i	0.415854	+	0.240093i
$540$		0			0
$541$		−	2.51613i		−	0.108177i	−0.998536	−	0.0540884i	$-0.982775\pi$
$541$		−	2.51613i		−	0.108177i	0.998536	−	0.0540884i	$-0.0172253\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−12.1516			−0.520517
$546$		0			0
$547$	28.6507			1.22502			0.612508	−	0.790464i	$-0.290161\pi$
$547$	28.6507			1.22502			0.612508	+	0.790464i	$0.290161\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	16.6963i		−	0.711285i
$552$		0			0
$553$	4.07300	+	2.35155i	0.173202	+	0.0999979i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	20.7283	−	11.9675i	0.878285	−	0.507078i	0.00819220	−	0.999966i	$-0.497392\pi$
$557$	20.7283	−	11.9675i	0.878285	−	0.507078i	0.870092	+	0.492889i	$0.164059\pi$
$558$		0			0
$559$	5.03225	−	0.0968099i	0.212841	−	0.00409462i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10.4293	+	18.0641i	−0.439544	+	0.761313i	−0.997654	−	0.0684539i	$-0.978193\pi$
$563$	−10.4293	+	18.0641i	−0.439544	+	0.761313i	0.558110	+	0.829767i	$0.311527\pi$
$564$		0			0
$565$	−0.636919	−	0.367725i	−0.0267954	−	0.0154703i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.70392	+	16.8077i	0.406810	+	0.704615i	0.994530	−	0.104449i	$-0.0333079\pi$
$569$	9.70392	+	16.8077i	0.406810	+	0.704615i	−0.587721	+	0.809064i	$0.699975\pi$
$570$		0			0
$571$	2.64156			0.110546			0.0552730	−	0.998471i	$-0.482397\pi$
$571$	2.64156			0.110546			0.0552730	+	0.998471i	$0.482397\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.237657	−	0.411634i	−0.00991098	−	0.0171663i
$576$		0			0
$577$		−	24.0716i		−	1.00211i	−0.865415	−	0.501057i	$-0.832945\pi$
$577$		−	24.0716i		−	1.00211i	0.865415	−	0.501057i	$-0.167055\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−25.4355	+	44.0556i	−1.05524	+	1.82773i
$582$		0			0
$583$	−3.92016	+	2.26330i	−0.162356	+	0.0937365i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	32.3571	−	18.6814i	1.33552	−	0.771063i	0.349381	−	0.936981i	$-0.386392\pi$
$587$	32.3571	−	18.6814i	1.33552	−	0.771063i	0.986140	+	0.165918i	$0.0530586\pi$
$588$		0			0
$589$	9.49063	−	16.4383i	0.391055	−	0.677326i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			45.4778i			1.86755i	0.357863	+	0.933774i	$0.383505\pi$
$593$			45.4778i			1.86755i	−0.357863	+	0.933774i	$0.616495\pi$
$594$		0			0
$595$	1.08699	+	1.88272i	0.0445622	+	0.0771840i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−24.7863			−1.01274			−0.506370	−	0.862316i	$-0.669013\pi$
$599$	−24.7863			−1.01274			−0.506370	+	0.862316i	$0.669013\pi$
$600$		0			0
$601$	−12.3643	−	21.4156i	−0.504350	−	0.873560i	−0.999987	−	0.00503065i	$-0.998399\pi$
$601$	−12.3643	−	21.4156i	−0.504350	−	0.873560i	0.495637	−	0.868530i	$-0.334935\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.02226	−	4.63165i	−0.326151	−	0.188303i
$606$		0			0
$607$	−2.61489	+	4.52913i	−0.106135	+	0.183832i	−0.914201	−	0.405260i	$-0.867181\pi$
$607$	−2.61489	+	4.52913i	−0.106135	+	0.183832i	0.808066	+	0.589092i	$0.200514\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−23.8039	+	14.3606i	−0.963002	+	0.580968i
$612$		0			0
$613$	−12.0686	+	6.96780i	−0.487446	+	0.281427i	−0.723514	−	0.690310i	$-0.757474\pi$
$613$	−12.0686	+	6.96780i	−0.487446	+	0.281427i	0.236069	+	0.971736i	$0.424141\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−39.2999	−	22.6898i	−1.58216	−	0.913458i	−0.994544	−	0.104314i	$-0.966735\pi$
$617$	−39.2999	−	22.6898i	−1.58216	−	0.913458i	−0.587611	−	0.809144i	$-0.699931\pi$
$618$		0			0
$619$		−	12.7094i		−	0.510834i	−0.966831	−	0.255417i	$-0.917787\pi$
$619$		−	12.7094i		−	0.510834i	0.966831	−	0.255417i	$-0.0822128\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	70.4248			2.82151
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	0.259955i		−	0.0103651i
$630$		0			0
$631$	3.49465	+	2.01764i	0.139120	+	0.0803209i	0.567944	−	0.823067i	$-0.307739\pi$
$631$	3.49465	+	2.01764i	0.139120	+	0.0803209i	−0.428825	+	0.903388i	$0.641072\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	16.5303	−	9.54378i	0.655986	−	0.378734i
$636$		0			0
$637$	−14.7396	+	26.7031i	−0.584005	+	1.05802i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.7616	−	29.0320i	0.662044	−	1.14669i	−0.318034	−	0.948079i	$-0.603023\pi$
$641$	16.7616	−	29.0320i	0.662044	−	1.14669i	0.980078	−	0.198614i	$-0.0636441\pi$
$642$		0			0
$643$	−42.9054	−	24.7714i	−1.69202	−	0.976891i	−0.952882	−	0.303341i	$-0.901898\pi$
$643$	−42.9054	−	24.7714i	−1.69202	−	0.976891i	−0.739142	−	0.673550i	$-0.764769\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.27758	+	10.8731i	0.246797	+	0.427465i	0.962635	−	0.270801i	$-0.0872886\pi$
$647$	6.27758	+	10.8731i	0.246797	+	0.427465i	−0.715838	+	0.698266i	$0.753955\pi$
$648$		0			0
$649$	−17.1550			−0.673392
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.0389761	+	0.0675086i	0.00152525	+	0.00264181i	0.866787	−	0.498679i	$-0.166181\pi$
$653$	0.0389761	+	0.0675086i	0.00152525	+	0.00264181i	−0.865262	+	0.501320i	$0.832848\pi$
$654$		0			0
$655$		−	1.40717i		−	0.0549825i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.5441	−	37.3155i	0.839241	−	1.45361i	−0.0512899	−	0.998684i	$-0.516333\pi$
$659$	21.5441	−	37.3155i	0.839241	−	1.45361i	0.890531	−	0.454924i	$-0.150333\pi$
$660$		0			0
$661$	−15.6898	+	9.05853i	−0.610264	+	0.352336i	−0.773069	−	0.634322i	$-0.781279\pi$
$661$	−15.6898	+	9.05853i	−0.610264	+	0.352336i	0.162805	+	0.986658i	$0.447946\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−18.4698	+	10.6635i	−0.716228	+	0.413514i
$666$		0			0
$667$	0.731535	−	1.26706i	0.0283252	−	0.0490606i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	0.825259i		−	0.0318588i
$672$		0			0
$673$	−4.96556	−	8.60060i	−0.191408	−	0.331529i	0.754309	−	0.656520i	$-0.227972\pi$
$673$	−4.96556	−	8.60060i	−0.191408	−	0.331529i	−0.945717	+	0.324991i	$0.894639\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	36.7571			1.41269			0.706345	−	0.707868i	$-0.250343\pi$
$677$	36.7571			1.41269			0.706345	+	0.707868i	$0.250343\pi$
$678$		0			0
$679$	−10.3138	−	17.8641i	−0.395808	−	0.685559i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	13.5889	+	7.84557i	0.519966	+	0.300202i	0.736921	−	0.675979i	$-0.236279\pi$
$683$	13.5889	+	7.84557i	0.519966	+	0.300202i	−0.216955	+	0.976182i	$0.569612\pi$
$684$		0			0
$685$	−5.82989	+	10.0977i	−0.222749	+	0.385812i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.39746	−	10.6043i	−0.243724	−	0.403992i
$690$		0			0
$691$	−17.7308	+	10.2369i	−0.674510	+	0.389428i	−0.797783	−	0.602944i	$-0.793994\pi$
$691$	−17.7308	+	10.2369i	−0.674510	+	0.389428i	0.123273	+	0.992373i	$0.460661\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.94174	+	1.12106i	0.0736543	+	0.0425243i
$696$		0			0
$697$			1.62106i			0.0614021i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	23.8368			0.900303			0.450152	−	0.892952i	$-0.351370\pi$
$701$	23.8368			0.900303			0.450152	+	0.892952i	$0.351370\pi$
$702$		0			0
$703$	2.55020			0.0961826
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	54.9226i		−	2.06558i
$708$		0			0
$709$	−1.63746	−	0.945386i	−0.0614960	−	0.0355047i	0.468937	−	0.883232i	$-0.344637\pi$
$709$	−1.63746	−	0.945386i	−0.0614960	−	0.0355047i	−0.530433	+	0.847727i	$0.677971\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.44046	−	0.831651i	0.0539457	−	0.0311456i
$714$		0			0
$715$	−2.29618	+	4.15988i	−0.0858722	+	0.155571i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.99659	+	5.19025i	−0.111754	+	0.193564i	−0.916478	−	0.400086i	$-0.868980\pi$
$719$	−2.99659	+	5.19025i	−0.111754	+	0.193564i	0.804724	+	0.593650i	$0.202314\pi$
$720$		0			0
$721$	−58.6462	−	33.8594i	−2.18410	−	1.26099i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.53906	+	2.66573i	0.0571592	+	0.0990026i
$726$		0			0
$727$	−39.0387			−1.44787			−0.723933	−	0.689870i	$-0.757667\pi$
$727$	−39.0387			−1.44787			−0.723933	+	0.689870i	$0.757667\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.385921	−	0.668435i	−0.0142738	−	0.0247230i
$732$		0			0
$733$		−	17.4176i		−	0.643336i	−0.946853	−	0.321668i	$-0.895757\pi$
$733$		−	17.4176i		−	0.643336i	0.946853	−	0.321668i	$-0.104243\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.39754	−	14.5450i	0.309327	−	0.535771i
$738$		0			0
$739$	12.3018	−	7.10243i	0.452528	−	0.261267i	−0.256369	−	0.966579i	$-0.582526\pi$
$739$	12.3018	−	7.10243i	0.452528	−	0.261267i	0.708897	+	0.705312i	$0.249193\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7.53155	+	4.34834i	−0.276306	+	0.159525i	−0.631750	−	0.775172i	$-0.717663\pi$
$743$	−7.53155	+	4.34834i	−0.276306	+	0.159525i	0.355444	+	0.934698i	$0.384330\pi$
$744$		0			0
$745$	−9.32282	+	16.1476i	−0.341562	+	0.591602i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			37.8267i			1.38216i
$750$		0			0
$751$	−9.79460	−	16.9647i	−0.357410	−	0.619052i	0.630117	−	0.776500i	$-0.283007\pi$
$751$	−9.79460	−	16.9647i	−0.357410	−	0.619052i	−0.987527	+	0.157448i	$0.949673\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.368970			0.0134282
$756$		0			0
$757$	−7.03616	−	12.1870i	−0.255733	−	0.442943i	0.709361	−	0.704845i	$-0.248984\pi$
$757$	−7.03616	−	12.1870i	−0.255733	−	0.442943i	−0.965094	+	0.261902i	$0.915650\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	15.3926	+	8.88695i	0.557983	+	0.322152i	0.752336	−	0.658780i	$-0.228927\pi$
$761$	15.3926	+	8.88695i	0.557983	+	0.322152i	−0.194353	+	0.980932i	$0.562261\pi$
$762$		0			0
$763$	−23.8891	+	41.3772i	−0.864844	+	1.49795i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.902770	−	46.9267i	−0.0325972	−	1.69442i
$768$		0			0
$769$	−39.1066	+	22.5782i	−1.41022	+	0.814191i	−0.995409	−	0.0957170i	$-0.969486\pi$
$769$	−39.1066	+	22.5782i	−1.41022	+	0.814191i	−0.414811	+	0.909908i	$0.636152\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−42.6776	−	24.6399i	−1.53501	−	0.886237i	−0.999120	−	0.0419470i	$-0.986644\pi$
$773$	−42.6776	−	24.6399i	−1.53501	−	0.886237i	−0.535887	−	0.844290i	$-0.680023\pi$
$774$		0			0
$775$			3.49938i			0.125701i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−15.9029			−0.569780
$780$		0			0
$781$	6.87175			0.245890
$782$		0			0
$783$		0			0
$784$		0			0
$785$			4.71895i			0.168427i
$786$		0			0
$787$	27.6925	+	15.9883i	0.987131	+	0.569920i	0.904415	−	0.426653i	$-0.140307\pi$
$787$	27.6925	+	15.9883i	0.987131	+	0.569920i	0.0827152	+	0.996573i	$0.473641\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.50427	+	1.44584i	−0.0890416	+	0.0514082i
$792$		0			0
$793$	2.25746	−	0.0434287i	0.0801647	−	0.00154220i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.6338	−	23.6145i	0.482935	−	0.836468i	−0.516873	−	0.856062i	$-0.672904\pi$
$797$	13.6338	−	23.6145i	0.482935	−	0.836468i	0.999808	+	0.0195943i	$0.00623745\pi$
$798$		0			0
$799$	3.69203	+	2.13159i	0.130615	+	0.0754103i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.58148	+	7.93536i	0.161677	+	0.280033i
$804$		0			0
$805$	−1.86886			−0.0658688
$806$		0			0
$807$		0			0
$808$		0			0
$809$	22.1803	+	38.4174i	0.779818	+	1.35068i	0.932047	+	0.362339i	$0.118022\pi$
$809$	22.1803	+	38.4174i	0.779818	+	1.35068i	−0.152229	+	0.988345i	$0.548645\pi$
$810$		0			0
$811$		−	54.1521i		−	1.90154i	−0.309900	−	0.950769i	$-0.600296\pi$
$811$		−	54.1521i		−	1.90154i	0.309900	−	0.950769i	$-0.399704\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.76612	+	11.7193i	−0.237007	+	0.410508i
$816$		0			0
$817$	6.55746	−	3.78595i	0.229417	−	0.132454i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.71723	−	4.45554i	0.269333	−	0.155499i	−0.359251	−	0.933241i	$-0.616968\pi$
$821$	7.71723	−	4.45554i	0.269333	−	0.155499i	0.628584	+	0.777741i	$0.283635\pi$
$822$		0			0
$823$	−0.817215	+	1.41546i	−0.0284863	+	0.0493398i	−0.879917	−	0.475127i	$-0.842402\pi$
$823$	−0.817215	+	1.41546i	−0.0284863	+	0.0493398i	0.851431	+	0.524467i	$0.175735\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	19.5497i		−	0.679809i	−0.940460	−	0.339904i	$-0.889605\pi$
$827$		−	19.5497i		−	0.679809i	0.940460	−	0.339904i	$-0.110395\pi$
$828$		0			0
$829$	26.2725	+	45.5052i	0.912480	+	1.58046i	0.810549	+	0.585671i	$0.199169\pi$
$829$	26.2725	+	45.5052i	0.912480	+	1.58046i	0.101931	+	0.994791i	$0.467498\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.67735			0.162061
$834$		0			0
$835$	3.06815	+	5.31419i	0.106178	+	0.183905i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	3.01757	+	1.74219i	0.104178	+	0.0601472i	0.551184	−	0.834384i	$-0.314176\pi$
$839$	3.01757	+	1.74219i	0.104178	+	0.0601472i	−0.447006	+	0.894531i	$0.647510\pi$
$840$		0			0
$841$	9.76260	−	16.9093i	0.336641	−	0.583080i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−11.5000	−	6.06218i	−0.395612	−	0.208545i
$846$		0			0
$847$	−31.5423	+	18.2110i	−1.08381	+	0.625736i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.193531	+	0.111735i	0.00663417	+	0.00383024i
$852$		0			0
$853$		−	6.46294i		−	0.221287i	−0.993860	−	0.110643i	$-0.964709\pi$
$853$		−	6.46294i		−	0.221287i	0.993860	−	0.110643i	$-0.0352912\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	20.1736			0.689117			0.344559	−	0.938765i	$-0.388029\pi$
$857$	20.1736			0.689117			0.344559	+	0.938765i	$0.388029\pi$
$858$		0			0
$859$	15.3052			0.522207			0.261104	−	0.965311i	$-0.415914\pi$
$859$	15.3052			0.522207			0.261104	+	0.965311i	$0.415914\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			36.1031i			1.22896i	0.788931	+	0.614482i	$0.210635\pi$
$863$			36.1031i			1.22896i	−0.788931	+	0.614482i	$0.789365\pi$
$864$		0			0
$865$	−0.429946	−	0.248229i	−0.0146186	−	0.00844004i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.36515	−	0.788167i	0.0463094	−	0.0267367i
$870$		0			0
$871$	40.2290	+	22.2057i	1.36311	+	0.752410i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.96593	−	3.40508i	0.0664604	−	0.115113i
$876$		0			0
$877$	46.1562	+	26.6483i	1.55859	+	0.899850i	0.997393	+	0.0721642i	$0.0229906\pi$
$877$	46.1562	+	26.6483i	1.55859	+	0.899850i	0.561192	+	0.827685i	$0.310343\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	6.59235	+	11.4183i	0.222102	+	0.384692i	0.955446	−	0.295166i	$-0.0953748\pi$
$881$	6.59235	+	11.4183i	0.222102	+	0.384692i	−0.733344	+	0.679858i	$0.762042\pi$
$882$		0			0
$883$	36.3300			1.22260			0.611301	−	0.791398i	$-0.290647\pi$
$883$	36.3300			1.22260			0.611301	+	0.791398i	$0.290647\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−17.0039	−	29.4516i	−0.570934	−	0.988886i	−0.996470	−	0.0839452i	$-0.973248\pi$
$887$	−17.0039	−	29.4516i	−0.570934	−	0.988886i	0.425537	−	0.904941i	$-0.360085\pi$
$888$		0			0
$889$		−	75.0495i		−	2.51708i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−20.9113	+	36.2194i	−0.699769	+	1.21204i
$894$		0			0
$895$	3.41032	−	1.96895i	0.113995	−	0.0658148i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−9.32838	+	5.38575i	−0.311119	+	0.179625i
$900$		0			0
$901$	−0.949596	+	1.64475i	−0.0316356	+	0.0547945i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			3.35363i			0.111478i
$906$		0			0
$907$	−7.07118	−	12.2476i	−0.234795	−	0.406677i	0.724418	−	0.689361i	$-0.242108\pi$
$907$	−7.07118	−	12.2476i	−0.234795	−	0.406677i	−0.959213	+	0.282684i	$0.908775\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	36.7262			1.21679			0.608396	−	0.793634i	$-0.291813\pi$
$911$	36.7262			1.21679			0.608396	+	0.793634i	$0.291813\pi$
$912$		0			0
$913$	8.52520	+	14.7661i	0.282143	+	0.488686i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.79152	−	2.76638i	−0.158230	−	0.0913540i
$918$		0			0
$919$	−9.74320	+	16.8757i	−0.321399	+	0.556679i	−0.980777	−	0.195133i	$-0.937486\pi$
$919$	−9.74320	+	16.8757i	−0.321399	+	0.556679i	0.659378	+	0.751811i	$0.270820\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.361621	+	18.7974i	0.0119029	+	0.618722i
$924$		0			0
$925$	−0.407165	+	0.235077i	−0.0133875	+	0.00772928i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	24.0598	+	13.8909i	0.789377	+	0.455747i	0.839743	−	0.542984i	$-0.182706\pi$
$929$	24.0598	+	13.8909i	0.789377	+	0.455747i	−0.0503664	+	0.998731i	$0.516039\pi$
$930$		0			0
$931$			45.8856i			1.50384i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.728651			0.0238294
$936$		0			0
$937$	49.0868			1.60359			0.801797	−	0.597596i	$-0.203877\pi$
$937$	49.0868			1.60359			0.801797	+	0.597596i	$0.203877\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			7.01554i			0.228700i	0.993441	+	0.114350i	$0.0364785\pi$
$941$			7.01554i			0.228700i	−0.993441	+	0.114350i	$0.963521\pi$
$942$		0			0
$943$	−1.20685	−	0.696775i	−0.0393004	−	0.0226901i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.9773	−	9.22450i	0.519193	−	0.299756i	−0.217412	−	0.976080i	$-0.569761\pi$
$947$	15.9773	−	9.22450i	0.519193	−	0.299756i	0.736604	+	0.676324i	$0.236428\pi$
$948$		0			0
$949$	−21.4657	+	12.9500i	−0.696807	+	0.420376i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	27.0965	−	46.9325i	0.877741	−	1.52029i	0.0239264	−	0.999714i	$-0.492383\pi$
$953$	27.0965	−	46.9325i	0.877741	−	1.52029i	0.853814	−	0.520578i	$-0.174283\pi$
$954$		0			0
$955$	−17.8109	−	10.2831i	−0.576348	−	0.332755i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	22.9223	+	39.7025i	0.740198	+	1.28206i
$960$		0			0
$961$	18.7544			0.604979
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.75908	+	4.77886i	0.0888178	+	0.153837i
$966$		0			0
$967$			52.8600i			1.69986i	0.526892	+	0.849932i	$0.323357\pi$
$967$			52.8600i			1.69986i	−0.526892	+	0.849932i	$0.676643\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−10.3459	+	17.9196i	−0.332015	+	0.575068i	−0.982907	−	0.184103i	$-0.941062\pi$
$971$	−10.3459	+	17.9196i	−0.332015	+	0.575068i	0.650892	+	0.759171i	$0.274395\pi$
$972$		0			0
$973$	7.63462	−	4.40785i	0.244755	−	0.141309i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.40368	+	2.54247i	−0.140886	+	0.0813407i	−0.568786	−	0.822485i	$-0.692587\pi$
$977$	−4.40368	+	2.54247i	−0.140886	+	0.0813407i	0.427900	+	0.903826i	$0.359254\pi$
$978$		0			0
$979$	11.8021	−	20.4419i	0.377197	−	0.653325i
$980$		0			0
$981$		0			0
$982$		0			0
$983$			16.8646i			0.537897i	0.963155	+	0.268949i	$0.0866762\pi$
$983$			16.8646i			0.537897i	−0.963155	+	0.268949i	$0.913324\pi$
$984$		0			0
$985$	3.92979	+	6.80659i	0.125213	+	0.216876i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.663516			0.0210986
$990$		0			0
$991$	25.4424	+	44.0676i	0.808205	+	1.39985i	0.914106	+	0.405475i	$0.132894\pi$
$991$	25.4424	+	44.0676i	0.808205	+	1.39985i	−0.105901	+	0.994377i	$0.533773\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.05413	−	3.49536i	−0.191929	−	0.110810i
$996$		0			0
$997$	−12.1519	+	21.0477i	−0.384855	+	0.666588i	−0.991749	−	0.128194i	$-0.959082\pi$
$997$	−12.1519	+	21.0477i	−0.384855	+	0.666588i	0.606894	+	0.794783i	$0.292415\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.dj.c.361.4		8
3.2	odd	2		780.2.cc.b.361.2	yes	8
13.4	even	6	inner	2340.2.dj.c.901.2		8
15.2	even	4		3900.2.bw.g.49.1		8
15.8	even	4		3900.2.bw.l.49.4		8
15.14	odd	2		3900.2.cd.l.2701.1		8
39.17	odd	6		780.2.cc.b.121.4	✓	8
195.17	even	12		3900.2.bw.l.2149.4		8
195.134	odd	6		3900.2.cd.l.901.1		8
195.173	even	12		3900.2.bw.g.2149.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.cc.b.121.4	✓	8	39.17	odd	6
780.2.cc.b.361.2	yes	8	3.2	odd	2
2340.2.dj.c.361.4		8	1.1	even	1	trivial
2340.2.dj.c.901.2		8	13.4	even	6	inner
3900.2.bw.g.49.1		8	15.2	even	4
3900.2.bw.g.2149.1		8	195.173	even	12
3900.2.bw.l.49.4		8	15.8	even	4
3900.2.bw.l.2149.4		8	195.17	even	12
3900.2.cd.l.901.1		8	195.134	odd	6
3900.2.cd.l.2701.1		8	15.14	odd	2

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:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.dj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{5} +(3.40508 + 1.96593i) q^{7} +(1.14128 - 0.658919i) q^{11} +(1.86250 + 3.08725i) q^{13} +(0.276457 - 0.478838i) q^{17} +(4.69748 + 2.71209i) q^{19} +(0.237657 + 0.411634i) q^{23} -1.00000 q^{25} +(-1.53906 - 2.66573i) q^{29} -3.49938i q^{31} +(-1.96593 + 3.40508i) q^{35} +(0.407165 - 0.235077i) q^{37} +(-2.53906 + 1.46593i) q^{41} +(0.697977 - 1.20893i) q^{43} +7.71039i q^{47} +(4.22973 + 7.32611i) q^{49} -3.43488 q^{53} +(0.658919 + 1.14128i) q^{55} +(-11.2735 - 6.50877i) q^{59} +(0.313111 - 0.542324i) q^{61} +(-3.08725 + 1.86250i) q^{65} +(11.0370 - 6.37221i) q^{67} +(4.51581 + 2.60721i) q^{71} +6.95303i q^{73} +5.18154 q^{77} +1.19615 q^{79} +12.9382i q^{83} +(0.478838 + 0.276457i) q^{85} +(15.5117 - 8.95568i) q^{89} +(0.272675 + 14.1739i) q^{91} +(-2.71209 + 4.69748i) q^{95} +(-4.54342 - 2.62314i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{11} - 4 q^{17} + 12 q^{19} - 4 q^{23} - 8 q^{25} + 8 q^{29} - 8 q^{35} - 24 q^{37} - 16 q^{43} - 4 q^{49} - 16 q^{53} + 4 q^{55} - 24 q^{59} + 8 q^{61} + 24 q^{67} + 12 q^{71} + 8 q^{77} - 32 q^{79}+ \cdots + 48 q^{97}+O(q^{100}) \) 8 * q + 12 * q^11 - 4 * q^17 + 12 * q^19 - 4 * q^23 - 8 * q^25 + 8 * q^29 - 8 * q^35 - 24 * q^37 - 16 * q^43 - 4 * q^49 - 16 * q^53 + 4 * q^55 - 24 * q^59 + 8 * q^61 + 24 * q^67 + 12 * q^71 + 8 * q^77 - 32 * q^79 + 12 * q^89 + 8 * q^91 + 12 * q^95 + 48 * q^97

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