LMFDB - Embedded newform 2592.2.f.c.1295.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(1295,2592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("2592.1295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 648)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1295.6
Character	$\chi$	$=$	2592.1295
Dual form			2592.2.f.c.1295.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.78731 q^{5} +3.35928i q^{7} +O(q^{10})$	$q-1.78731 q^{5} +3.35928i q^{7} +3.62525i q^{11} +1.71824i q^{13} +6.25325i q^{17} +4.57204 q^{19} -0.617331 q^{23} -1.80552 q^{25} -5.67561 q^{29} -8.09500i q^{31} -6.00408i q^{35} -7.06318i q^{37} -6.92652i q^{41} +6.66621 q^{43} -1.01238 q^{47} -4.28477 q^{49} -10.5493 q^{53} -6.47944i q^{55} +5.00538i q^{59} +14.2966i q^{61} -3.07103i q^{65} +9.38311 q^{67} -9.70917 q^{71} -15.2438 q^{73} -12.1782 q^{77} +15.4256i q^{79} -6.46882i q^{83} -11.1765i q^{85} +1.45494i q^{89} -5.77206 q^{91} -8.17165 q^{95} -5.85931 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 24 q^{25} - 24 q^{49} - 48 q^{67}+O(q^{100}) $ 24 * q + 24 * q^25 - 24 * q^49 - 48 * q^67

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$-1$	$-1$	$-1$

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
$5$	−1.78731	−0.799309	−0.399655	−	0.916666i	$-0.630870\pi$
$5$	−1.78731	−0.799309	−0.399655	+	0.916666i	$0.630870\pi$
$6$	0	0
$7$	3.35928i	1.26969i	0.772640	+	0.634845i	$0.218936\pi$
$7$	3.35928i	1.26969i	−0.772640	+	0.634845i	$0.781064\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	3.62525i	1.09305i	0.837442	+	0.546526i	$0.184050\pi$
$11$	3.62525i	1.09305i	−0.837442	+	0.546526i	$0.815950\pi$
$12$	0	0
$13$	1.71824i	0.476555i	0.971197	+	0.238277i	$0.0765828\pi$
$13$	1.71824i	0.476555i	−0.971197	+	0.238277i	$0.923417\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	6.25325i	1.51664i	0.651885	+	0.758318i	$0.273978\pi$
$17$	6.25325i	1.51664i	−0.651885	+	0.758318i	$0.726022\pi$
$18$	0	0
$19$	4.57204	1.04890	0.524449	−	0.851442i	$-0.324271\pi$
$19$	4.57204	1.04890	0.524449	+	0.851442i	$0.324271\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−0.617331	−0.128722	−0.0643612	−	0.997927i	$-0.520501\pi$
$23$	−0.617331	−0.128722	−0.0643612	+	0.997927i	$0.520501\pi$
$24$	0	0
$25$	−1.80552	−0.361105
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−5.67561	−1.05394	−0.526968	−	0.849885i	$-0.676671\pi$
$29$	−5.67561	−1.05394	−0.526968	+	0.849885i	$0.676671\pi$
$30$	0	0
$31$	− 8.09500i	− 1.45391i	−0.686687	−	0.726953i	$-0.740936\pi$
$31$	− 8.09500i	− 1.45391i	0.686687	−	0.726953i	$-0.259064\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	− 6.00408i	− 1.01487i
$36$	0	0
$37$	− 7.06318i	− 1.16118i	−0.814196	−	0.580590i	$-0.802822\pi$
$37$	− 7.06318i	− 1.16118i	0.814196	−	0.580590i	$-0.197178\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	− 6.92652i	− 1.08174i	−0.841106	−	0.540870i	$-0.818095\pi$
$41$	− 6.92652i	− 1.08174i	0.841106	−	0.540870i	$-0.181905\pi$
$42$	0	0
$43$	6.66621	1.01659	0.508294	−	0.861184i	$-0.330277\pi$
$43$	6.66621	1.01659	0.508294	+	0.861184i	$0.330277\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−1.01238	−0.147670	−0.0738352	−	0.997270i	$-0.523524\pi$
$47$	−1.01238	−0.147670	−0.0738352	+	0.997270i	$0.523524\pi$
$48$	0	0
$49$	−4.28477	−0.612111
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−10.5493	−1.44906	−0.724529	−	0.689244i	$-0.757943\pi$
$53$	−10.5493	−1.44906	−0.724529	+	0.689244i	$0.757943\pi$
$54$	0	0
$55$	− 6.47944i	− 0.873687i
$56$	0	0
$57$	0	0
$58$	0	0
$59$	5.00538i	0.651644i	0.945431	+	0.325822i	$0.105641\pi$
$59$	5.00538i	0.651644i	−0.945431	+	0.325822i	$0.894359\pi$
$60$	0	0
$61$	14.2966i	1.83050i	0.402888	+	0.915249i	$0.368006\pi$
$61$	14.2966i	1.83050i	−0.402888	+	0.915249i	$0.631994\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	− 3.07103i	− 0.380915i
$66$	0	0
$67$	9.38311	1.14633	0.573165	−	0.819440i	$-0.305716\pi$
$67$	9.38311	1.14633	0.573165	+	0.819440i	$0.305716\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−9.70917	−1.15227	−0.576133	−	0.817356i	$-0.695439\pi$
$71$	−9.70917	−1.15227	−0.576133	+	0.817356i	$0.695439\pi$
$72$	0	0
$73$	−15.2438	−1.78415	−0.892075	−	0.451886i	$-0.850751\pi$
$73$	−15.2438	−1.78415	−0.892075	+	0.451886i	$0.850751\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−12.1782	−1.38784
$78$	0	0
$79$	15.4256i	1.73552i	0.496988	+	0.867758i	$0.334439\pi$
$79$	15.4256i	1.73552i	−0.496988	+	0.867758i	$0.665561\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	− 6.46882i	− 0.710046i	−0.934858	−	0.355023i	$-0.884473\pi$
$83$	− 6.46882i	− 0.710046i	0.934858	−	0.355023i	$-0.115527\pi$
$84$	0	0
$85$	− 11.1765i	− 1.21226i
$86$	0	0
$87$	0	0
$88$	0	0
$89$	1.45494i	0.154223i	0.997022	+	0.0771115i	$0.0245697\pi$
$89$	1.45494i	0.154223i	−0.997022	+	0.0771115i	$0.975430\pi$
$90$	0	0
$91$	−5.77206	−0.605077
$92$	0	0
$93$	0	0
$94$	0	0
$95$	−8.17165	−0.838394
$96$	0	0
$97$	−5.85931	−0.594923	−0.297461	−	0.954734i	$-0.596140\pi$
$97$	−5.85931	−0.594923	−0.297461	+	0.954734i	$0.596140\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−2.86358	−0.284937	−0.142468	−	0.989799i	$-0.545504\pi$
$101$	−2.86358	−0.284937	−0.142468	+	0.989799i	$0.545504\pi$
$102$	0	0
$103$	4.84323i	0.477218i	0.971116	+	0.238609i	$0.0766914\pi$
$103$	4.84323i	0.477218i	−0.971116	+	0.238609i	$0.923309\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	− 10.8641i	− 1.05027i	−0.851018	−	0.525137i	$-0.824014\pi$
$107$	− 10.8641i	− 1.05027i	0.851018	−	0.525137i	$-0.175986\pi$
$108$	0	0
$109$	− 0.887009i	− 0.0849601i	−0.999097	−	0.0424800i	$-0.986474\pi$
$109$	− 0.887009i	− 0.0849601i	0.999097	−	0.0424800i	$-0.0135259\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	4.17946i	0.393170i	0.980487	+	0.196585i	$0.0629852\pi$
$113$	4.17946i	0.393170i	−0.980487	+	0.196585i	$0.937015\pi$
$114$	0	0
$115$	1.10336	0.102889
$116$	0	0
$117$	0	0
$118$	0	0
$119$	−21.0064	−1.92566
$120$	0	0
$121$	−2.14241	−0.194764
$122$	0	0
$123$	0	0
$124$	0	0
$125$	12.1636	1.08794
$126$	0	0
$127$	− 11.0834i	− 0.983494i	−0.870738	−	0.491747i	$-0.836359\pi$
$127$	− 11.0834i	− 0.983494i	0.870738	−	0.491747i	$-0.163641\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	9.60825i	0.839476i	0.907645	+	0.419738i	$0.137878\pi$
$131$	9.60825i	0.839476i	−0.907645	+	0.419738i	$0.862122\pi$
$132$	0	0
$133$	15.3588i	1.33177i
$134$	0	0
$135$	0	0
$136$	0	0
$137$	− 8.47943i	− 0.724447i	−0.932091	−	0.362223i	$-0.882018\pi$
$137$	− 8.47943i	− 0.724447i	0.932091	−	0.362223i	$-0.117982\pi$
$138$	0	0
$139$	−9.67540	−0.820657	−0.410328	−	0.911938i	$-0.634586\pi$
$139$	−9.67540	−0.820657	−0.410328	+	0.911938i	$0.634586\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−6.22905	−0.520900
$144$	0	0
$145$	10.1441	0.842420
$146$	0	0
$147$	0	0
$148$	0	0
$149$	11.1389	0.912530	0.456265	−	0.889844i	$-0.349187\pi$
$149$	11.1389	0.912530	0.456265	+	0.889844i	$0.349187\pi$
$150$	0	0
$151$	4.99549i	0.406527i	0.979124	+	0.203264i	$0.0651548\pi$
$151$	4.99549i	0.406527i	−0.979124	+	0.203264i	$0.934845\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	14.4683i	1.16212i
$156$	0	0
$157$	− 8.61192i	− 0.687306i	−0.939097	−	0.343653i	$-0.888336\pi$
$157$	− 8.61192i	− 0.687306i	0.939097	−	0.343653i	$-0.111664\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	− 2.07379i	− 0.163437i
$162$	0	0
$163$	2.04820	0.160427	0.0802137	−	0.996778i	$-0.474440\pi$
$163$	2.04820	0.160427	0.0802137	+	0.996778i	$0.474440\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−21.0064	−1.62553	−0.812763	−	0.582595i	$-0.802037\pi$
$167$	−21.0064	−1.62553	−0.812763	+	0.582595i	$0.802037\pi$
$168$	0	0
$169$	10.0476	0.772895
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−6.81939	−0.518469	−0.259234	−	0.965814i	$-0.583470\pi$
$173$	−6.81939	−0.518469	−0.259234	+	0.965814i	$0.583470\pi$
$174$	0	0
$175$	− 6.06526i	− 0.458491i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	22.5099i	1.68247i	0.540671	+	0.841234i	$0.318170\pi$
$179$	22.5099i	1.68247i	−0.540671	+	0.841234i	$0.681830\pi$
$180$	0	0
$181$	− 8.43198i	− 0.626744i	−0.949630	−	0.313372i	$-0.898541\pi$
$181$	− 8.43198i	− 0.626744i	0.949630	−	0.313372i	$-0.101459\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	12.6241i	0.928142i
$186$	0	0
$187$	−22.6696	−1.65776
$188$	0	0
$189$	0	0
$190$	0	0
$191$	6.08057	0.439975	0.219987	−	0.975503i	$-0.429398\pi$
$191$	6.08057	0.439975	0.219987	+	0.975503i	$0.429398\pi$
$192$	0	0
$193$	−1.00000	−0.0719816	−0.0359908	−	0.999352i	$-0.511459\pi$
$193$	−1.00000	−0.0719816	−0.0359908	+	0.999352i	$0.511459\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−22.4901	−1.60235	−0.801176	−	0.598429i	$-0.795792\pi$
$197$	−22.4901	−1.60235	−0.801176	+	0.598429i	$0.795792\pi$
$198$	0	0
$199$	− 9.83872i	− 0.697448i	−0.937225	−	0.348724i	$-0.886615\pi$
$199$	− 9.83872i	− 0.697448i	0.937225	−	0.348724i	$-0.113385\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	− 19.0660i	− 1.33817i
$204$	0	0
$205$	12.3798i	0.864645i
$206$	0	0
$207$	0	0
$208$	0	0
$209$	16.5748i	1.14650i
$210$	0	0
$211$	−12.2291	−0.841883	−0.420941	−	0.907088i	$-0.638300\pi$
$211$	−12.2291	−0.841883	−0.420941	+	0.907088i	$0.638300\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	−11.9146	−0.812567
$216$	0	0
$217$	27.1934	1.84601
$218$	0	0
$219$	0	0
$220$	0	0
$221$	−10.7446	−0.722760
$222$	0	0
$223$	6.45880i	0.432513i	0.976337	+	0.216256i	$0.0693847\pi$
$223$	6.45880i	0.432513i	−0.976337	+	0.216256i	$0.930615\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	− 12.4781i	− 0.828198i	−0.910232	−	0.414099i	$-0.864097\pi$
$227$	− 12.4781i	− 0.828198i	0.910232	−	0.414099i	$-0.135903\pi$
$228$	0	0
$229$	− 8.63538i	− 0.570642i	−0.958432	−	0.285321i	$-0.907900\pi$
$229$	− 8.63538i	− 0.570642i	0.958432	−	0.285321i	$-0.0921002\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	− 6.26702i	− 0.410566i	−0.978703	−	0.205283i	$-0.934189\pi$
$233$	− 6.26702i	− 0.410566i	0.978703	−	0.205283i	$-0.0658115\pi$
$234$	0	0
$235$	1.80943	0.118034
$236$	0	0
$237$	0	0
$238$	0	0
$239$	21.0165	1.35944	0.679721	−	0.733471i	$-0.262101\pi$
$239$	21.0165	1.35944	0.679721	+	0.733471i	$0.262101\pi$
$240$	0	0
$241$	6.33856	0.408302	0.204151	−	0.978939i	$-0.434557\pi$
$241$	6.33856	0.408302	0.204151	+	0.978939i	$0.434557\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	7.65822	0.489266
$246$	0	0
$247$	7.85588i	0.499858i
$248$	0	0
$249$	0	0
$250$	0	0
$251$	8.50717i	0.536968i	0.963284	+	0.268484i	$0.0865226\pi$
$251$	8.50717i	0.536968i	−0.963284	+	0.268484i	$0.913477\pi$
$252$	0	0
$253$	− 2.23798i	− 0.140700i
$254$	0	0
$255$	0	0
$256$	0	0
$257$	− 5.84997i	− 0.364911i	−0.983214	−	0.182456i	$-0.941595\pi$
$257$	− 5.84997i	− 0.364911i	0.983214	−	0.182456i	$-0.0584046\pi$
$258$	0	0
$259$	23.7272	1.47434
$260$	0	0
$261$	0	0
$262$	0	0
$263$	11.0750	0.682911	0.341456	−	0.939898i	$-0.389080\pi$
$263$	11.0750	0.682911	0.341456	+	0.939898i	$0.389080\pi$
$264$	0	0
$265$	18.8549	1.15825
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−5.18889	−0.316372	−0.158186	−	0.987409i	$-0.550565\pi$
$269$	−5.18889	−0.316372	−0.158186	+	0.987409i	$0.550565\pi$
$270$	0	0
$271$	18.3273i	1.11330i	0.830747	+	0.556651i	$0.187914\pi$
$271$	18.3273i	1.11330i	−0.830747	+	0.556651i	$0.812086\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	− 6.54546i	− 0.394706i
$276$	0	0
$277$	− 21.0332i	− 1.26376i	−0.775064	−	0.631882i	$-0.782283\pi$
$277$	− 21.0332i	− 1.26376i	0.775064	−	0.631882i	$-0.217717\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	17.2197i	1.02724i	0.858018	+	0.513619i	$0.171696\pi$
$281$	17.2197i	1.02724i	−0.858018	+	0.513619i	$0.828304\pi$
$282$	0	0
$283$	8.04596	0.478283	0.239141	−	0.970985i	$-0.423134\pi$
$283$	8.04596	0.478283	0.239141	+	0.970985i	$0.423134\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	23.2681	1.37347
$288$	0	0
$289$	−22.1031	−1.30018
$290$	0	0
$291$	0	0
$292$	0	0
$293$	−13.1754	−0.769717	−0.384859	−	0.922976i	$-0.625750\pi$
$293$	−13.1754	−0.769717	−0.384859	+	0.922976i	$0.625750\pi$
$294$	0	0
$295$	− 8.94616i	− 0.520865i
$296$	0	0
$297$	0	0
$298$	0	0
$299$	− 1.06072i	− 0.0613433i
$300$	0	0
$301$	22.3937i	1.29075i
$302$	0	0
$303$	0	0
$304$	0	0
$305$	− 25.5525i	− 1.46313i
$306$	0	0
$307$	−6.45699	−0.368520	−0.184260	−	0.982878i	$-0.558989\pi$
$307$	−6.45699	−0.368520	−0.184260	+	0.982878i	$0.558989\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	10.9944	0.623435	0.311717	−	0.950175i	$-0.399096\pi$
$311$	10.9944	0.623435	0.311717	+	0.950175i	$0.399096\pi$
$312$	0	0
$313$	0.238809	0.0134983	0.00674913	−	0.999977i	$-0.497852\pi$
$313$	0.238809	0.0134983	0.00674913	+	0.999977i	$0.497852\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−6.06987	−0.340918	−0.170459	−	0.985365i	$-0.554525\pi$
$317$	−6.06987	−0.340918	−0.170459	+	0.985365i	$0.554525\pi$
$318$	0	0
$319$	− 20.5755i	− 1.15201i
$320$	0	0
$321$	0	0
$322$	0	0
$323$	28.5901i	1.59080i
$324$	0	0
$325$	− 3.10233i	− 0.172086i
$326$	0	0
$327$	0	0
$328$	0	0
$329$	− 3.40086i	− 0.187495i
$330$	0	0
$331$	−21.2602	−1.16857	−0.584284	−	0.811549i	$-0.698625\pi$
$331$	−21.2602	−1.16857	−0.584284	+	0.811549i	$0.698625\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	−16.7705	−0.916272
$336$	0	0
$337$	14.5712	0.793745	0.396873	−	0.917874i	$-0.370095\pi$
$337$	14.5712	0.793745	0.396873	+	0.917874i	$0.370095\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	29.3464	1.58920
$342$	0	0
$343$	9.12121i	0.492499i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	− 23.8615i	− 1.28095i	−0.767978	−	0.640477i	$-0.778737\pi$
$347$	− 23.8615i	− 1.28095i	0.767978	−	0.640477i	$-0.221263\pi$
$348$	0	0
$349$	− 20.9869i	− 1.12340i	−0.827340	−	0.561702i	$-0.810147\pi$
$349$	− 20.9869i	− 1.12340i	0.827340	−	0.561702i	$-0.189853\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	− 3.33461i	− 0.177483i	−0.996055	−	0.0887416i	$-0.971715\pi$
$353$	− 3.33461i	− 0.177483i	0.996055	−	0.0887416i	$-0.0282845\pi$
$354$	0	0
$355$	17.3533	0.921018
$356$	0	0
$357$	0	0
$358$	0	0
$359$	24.4127	1.28845	0.644227	−	0.764834i	$-0.277179\pi$
$359$	24.4127	1.28845	0.644227	+	0.764834i	$0.277179\pi$
$360$	0	0
$361$	1.90356	0.100187
$362$	0	0
$363$	0	0
$364$	0	0
$365$	27.2454	1.42609
$366$	0	0
$367$	3.40618i	0.177801i	0.996040	+	0.0889007i	$0.0283354\pi$
$367$	3.40618i	0.177801i	−0.996040	+	0.0889007i	$0.971665\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	− 35.4381i	− 1.83985i
$372$	0	0
$373$	27.5877i	1.42844i	0.699922	+	0.714219i	$0.253218\pi$
$373$	27.5877i	1.42844i	−0.699922	+	0.714219i	$0.746782\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	− 9.75209i	− 0.502258i
$378$	0	0
$379$	−30.2051	−1.55153	−0.775766	−	0.631021i	$-0.782636\pi$
$379$	−30.2051	−1.55153	−0.775766	+	0.631021i	$0.782636\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−15.8403	−0.809402	−0.404701	−	0.914449i	$-0.632624\pi$
$383$	−15.8403	−0.809402	−0.404701	+	0.914449i	$0.632624\pi$
$384$	0	0
$385$	21.7663	1.10931
$386$	0	0
$387$	0	0
$388$	0	0
$389$	−6.52797	−0.330981	−0.165491	−	0.986211i	$-0.552921\pi$
$389$	−6.52797	−0.330981	−0.165491	+	0.986211i	$0.552921\pi$
$390$	0	0
$391$	− 3.86032i	− 0.195225i
$392$	0	0
$393$	0	0
$394$	0	0
$395$	− 27.5703i	− 1.38721i
$396$	0	0
$397$	16.9116i	0.848767i	0.905483	+	0.424383i	$0.139509\pi$
$397$	16.9116i	0.848767i	−0.905483	+	0.424383i	$0.860491\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	2.19139i	0.109433i	0.998502	+	0.0547163i	$0.0174255\pi$
$401$	2.19139i	0.109433i	−0.998502	+	0.0547163i	$0.982575\pi$
$402$	0	0
$403$	13.9092	0.692866
$404$	0	0
$405$	0	0
$406$	0	0
$407$	25.6058	1.26923
$408$	0	0
$409$	−12.8532	−0.635548	−0.317774	−	0.948166i	$-0.602935\pi$
$409$	−12.8532	−0.635548	−0.317774	+	0.948166i	$0.602935\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	−16.8145	−0.827386
$414$	0	0
$415$	11.5618i	0.567546i
$416$	0	0
$417$	0	0
$418$	0	0
$419$	21.0896i	1.03030i	0.857101	+	0.515148i	$0.172263\pi$
$419$	21.0896i	1.03030i	−0.857101	+	0.515148i	$0.827737\pi$
$420$	0	0
$421$	− 7.75783i	− 0.378094i	−0.981968	−	0.189047i	$-0.939460\pi$
$421$	− 7.75783i	− 0.378094i	0.981968	−	0.189047i	$-0.0605398\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	− 11.2904i	− 0.547664i
$426$	0	0
$427$	−48.0265	−2.32416
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−15.8966	−0.765712	−0.382856	−	0.923808i	$-0.625059\pi$
$431$	−15.8966	−0.765712	−0.382856	+	0.923808i	$0.625059\pi$
$432$	0	0
$433$	0.620460	0.0298174	0.0149087	−	0.999889i	$-0.495254\pi$
$433$	0.620460	0.0298174	0.0149087	+	0.999889i	$0.495254\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−2.82246	−0.135017
$438$	0	0
$439$	− 13.0905i	− 0.624775i	−0.949955	−	0.312388i	$-0.898871\pi$
$439$	− 13.0905i	− 0.624775i	0.949955	−	0.312388i	$-0.101129\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	35.2665i	1.67556i	0.546006	+	0.837781i	$0.316147\pi$
$443$	35.2665i	1.67556i	−0.546006	+	0.837781i	$0.683853\pi$
$444$	0	0
$445$	− 2.60042i	− 0.123272i
$446$	0	0
$447$	0	0
$448$	0	0
$449$	2.94608i	0.139034i	0.997581	+	0.0695171i	$0.0221459\pi$
$449$	2.94608i	0.139034i	−0.997581	+	0.0695171i	$0.977854\pi$
$450$	0	0
$451$	25.1103	1.18240
$452$	0	0
$453$	0	0
$454$	0	0
$455$	10.3165	0.483643
$456$	0	0
$457$	−25.1675	−1.17728	−0.588642	−	0.808394i	$-0.700337\pi$
$457$	−25.1675	−1.17728	−0.588642	+	0.808394i	$0.700337\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	35.5377	1.65516	0.827579	−	0.561350i	$-0.189718\pi$
$461$	35.5377	1.65516	0.827579	+	0.561350i	$0.189718\pi$
$462$	0	0
$463$	30.1317i	1.40034i	0.713978	+	0.700168i	$0.246892\pi$
$463$	30.1317i	1.40034i	−0.713978	+	0.700168i	$0.753108\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	− 8.04243i	− 0.372159i	−0.982535	−	0.186080i	$-0.940422\pi$
$467$	− 8.04243i	− 0.372159i	0.982535	−	0.186080i	$-0.0595782\pi$
$468$	0	0
$469$	31.5205i	1.45548i
$470$	0	0
$471$	0	0
$472$	0	0
$473$	24.1666i	1.11118i
$474$	0	0
$475$	−8.25493	−0.378762
$476$	0	0
$477$	0	0
$478$	0	0
$479$	37.9108	1.73219	0.866094	−	0.499882i	$-0.166623\pi$
$479$	37.9108	1.73219	0.866094	+	0.499882i	$0.166623\pi$
$480$	0	0
$481$	12.1363	0.553366
$482$	0	0
$483$	0	0
$484$	0	0
$485$	10.4724	0.475527
$486$	0	0
$487$	− 0.286027i	− 0.0129611i	−0.999979	−	0.00648057i	$-0.997937\pi$
$487$	− 0.286027i	− 0.0129611i	0.999979	−	0.00648057i	$-0.00206284\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	7.78671i	0.351410i	0.984443	+	0.175705i	$0.0562204\pi$
$491$	7.78671i	0.351410i	−0.984443	+	0.175705i	$0.943780\pi$
$492$	0	0
$493$	− 35.4910i	− 1.59844i
$494$	0	0
$495$	0	0
$496$	0	0
$497$	− 32.6158i	− 1.46302i
$498$	0	0
$499$	23.8136	1.06604	0.533022	−	0.846101i	$-0.321056\pi$
$499$	23.8136	1.06604	0.533022	+	0.846101i	$0.321056\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	11.8583	0.528735	0.264367	−	0.964422i	$-0.414837\pi$
$503$	11.8583	0.528735	0.264367	+	0.964422i	$0.414837\pi$
$504$	0	0
$505$	5.11810	0.227753
$506$	0	0
$507$	0	0
$508$	0	0
$509$	19.3259	0.856607	0.428304	−	0.903635i	$-0.359111\pi$
$509$	19.3259	0.856607	0.428304	+	0.903635i	$0.359111\pi$
$510$	0	0
$511$	− 51.2082i	− 2.26532i
$512$	0	0
$513$	0	0
$514$	0	0
$515$	− 8.65635i	− 0.381444i
$516$	0	0
$517$	− 3.67012i	− 0.161412i
$518$	0	0
$519$	0	0
$520$	0	0
$521$	41.6156i	1.82321i	0.411063	+	0.911607i	$0.365158\pi$
$521$	41.6156i	1.82321i	−0.411063	+	0.911607i	$0.634842\pi$
$522$	0	0
$523$	−6.05911	−0.264946	−0.132473	−	0.991187i	$-0.542292\pi$
$523$	−6.05911	−0.264946	−0.132473	+	0.991187i	$0.542292\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	50.6201	2.20504
$528$	0	0
$529$	−22.6189	−0.983431
$530$	0	0
$531$	0	0
$532$	0	0
$533$	11.9014	0.515509
$534$	0	0
$535$	19.4175i	0.839493i
$536$	0	0
$537$	0	0
$538$	0	0
$539$	− 15.5334i	− 0.669069i
$540$	0	0
$541$	− 17.8716i	− 0.768360i	−0.923258	−	0.384180i	$-0.874484\pi$
$541$	− 17.8716i	− 0.768360i	0.923258	−	0.384180i	$-0.125516\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	1.58536i	0.0679094i
$546$	0	0
$547$	−30.9412	−1.32295	−0.661476	−	0.749967i	$-0.730069\pi$
$547$	−30.9412	−1.32295	−0.661476	+	0.749967i	$0.730069\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	−25.9491	−1.10547
$552$	0	0
$553$	−51.8189	−2.20356
$554$	0	0
$555$	0	0
$556$	0	0
$557$	25.4742	1.07938	0.539689	−	0.841864i	$-0.318542\pi$
$557$	25.4742	1.07938	0.539689	+	0.841864i	$0.318542\pi$
$558$	0	0
$559$	11.4542i	0.484460i
$560$	0	0
$561$	0	0
$562$	0	0
$563$	25.4376i	1.07207i	0.844197	+	0.536034i	$0.180078\pi$
$563$	25.4376i	1.07207i	−0.844197	+	0.536034i	$0.819922\pi$
$564$	0	0
$565$	− 7.46999i	− 0.314265i
$566$	0	0
$567$	0	0
$568$	0	0
$569$	23.7604i	0.996089i	0.867152	+	0.498044i	$0.165948\pi$
$569$	23.7604i	0.996089i	−0.867152	+	0.498044i	$0.834052\pi$
$570$	0	0
$571$	1.27312	0.0532785	0.0266393	−	0.999645i	$-0.491519\pi$
$571$	1.27312	0.0532785	0.0266393	+	0.999645i	$0.491519\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	1.11461	0.0464823
$576$	0	0
$577$	7.62218	0.317315	0.158658	−	0.987334i	$-0.449283\pi$
$577$	7.62218	0.317315	0.158658	+	0.987334i	$0.449283\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	21.7306	0.901537
$582$	0	0
$583$	− 38.2438i	− 1.58390i
$584$	0	0
$585$	0	0
$586$	0	0
$587$	44.8459i	1.85099i	0.378760	+	0.925495i	$0.376351\pi$
$587$	44.8459i	1.85099i	−0.378760	+	0.925495i	$0.623649\pi$
$588$	0	0
$589$	− 37.0107i	− 1.52500i
$590$	0	0
$591$	0	0
$592$	0	0
$593$	21.3237i	0.875658i	0.899058	+	0.437829i	$0.144252\pi$
$593$	21.3237i	0.875658i	−0.899058	+	0.437829i	$0.855748\pi$
$594$	0	0
$595$	37.5450	1.53919
$596$	0	0
$597$	0	0
$598$	0	0
$599$	1.98423	0.0810736	0.0405368	−	0.999178i	$-0.487093\pi$
$599$	1.98423	0.0810736	0.0405368	+	0.999178i	$0.487093\pi$
$600$	0	0
$601$	9.57621	0.390622	0.195311	−	0.980741i	$-0.437428\pi$
$601$	9.57621	0.390622	0.195311	+	0.980741i	$0.437428\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	3.82914	0.155677
$606$	0	0
$607$	30.7644i	1.24869i	0.781149	+	0.624345i	$0.214634\pi$
$607$	30.7644i	1.24869i	−0.781149	+	0.624345i	$0.785366\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	− 1.73951i	− 0.0703731i
$612$	0	0
$613$	20.1482i	0.813777i	0.913478	+	0.406889i	$0.133386\pi$
$613$	20.1482i	0.813777i	−0.913478	+	0.406889i	$0.866614\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	− 28.2103i	− 1.13570i	−0.823131	−	0.567851i	$-0.807775\pi$
$617$	− 28.2103i	− 1.13570i	0.823131	−	0.567851i	$-0.192225\pi$
$618$	0	0
$619$	24.0393	0.966223	0.483111	−	0.875559i	$-0.339507\pi$
$619$	24.0393	0.966223	0.483111	+	0.875559i	$0.339507\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−4.88754	−0.195815
$624$	0	0
$625$	−12.7125	−0.508499
$626$	0	0
$627$	0	0
$628$	0	0
$629$	44.1678	1.76109
$630$	0	0
$631$	28.1191i	1.11940i	0.828694	+	0.559701i	$0.189084\pi$
$631$	28.1191i	1.11940i	−0.828694	+	0.559701i	$0.810916\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	19.8095i	0.786116i
$636$	0	0
$637$	− 7.36228i	− 0.291704i
$638$	0	0
$639$	0	0
$640$	0	0
$641$	− 10.3724i	− 0.409687i	−0.978795	−	0.204843i	$-0.934332\pi$
$641$	− 10.3724i	− 0.409687i	0.978795	−	0.204843i	$-0.0656685\pi$
$642$	0	0
$643$	19.1042	0.753397	0.376698	−	0.926336i	$-0.377059\pi$
$643$	19.1042	0.753397	0.376698	+	0.926336i	$0.377059\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−3.61125	−0.141973	−0.0709864	−	0.997477i	$-0.522615\pi$
$647$	−3.61125	−0.141973	−0.0709864	+	0.997477i	$0.522615\pi$
$648$	0	0
$649$	−18.1457	−0.712282
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−2.37996	−0.0931351	−0.0465675	−	0.998915i	$-0.514828\pi$
$653$	−2.37996	−0.0931351	−0.0465675	+	0.998915i	$0.514828\pi$
$654$	0	0
$655$	− 17.1729i	− 0.671001i
$656$	0	0
$657$	0	0
$658$	0	0
$659$	− 42.8158i	− 1.66787i	−0.551864	−	0.833934i	$-0.686083\pi$
$659$	− 42.8158i	− 1.66787i	0.551864	−	0.833934i	$-0.313917\pi$
$660$	0	0
$661$	35.5228i	1.38168i	0.723009	+	0.690839i	$0.242759\pi$
$661$	35.5228i	1.38168i	−0.723009	+	0.690839i	$0.757241\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	− 27.4509i	− 1.06450i
$666$	0	0
$667$	3.50373	0.135665
$668$	0	0
$669$	0	0
$670$	0	0
$671$	−51.8289	−2.00083
$672$	0	0
$673$	−17.1137	−0.659684	−0.329842	−	0.944036i	$-0.606995\pi$
$673$	−17.1137	−0.659684	−0.329842	+	0.944036i	$0.606995\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	2.19358	0.0843060	0.0421530	−	0.999111i	$-0.486578\pi$
$677$	2.19358	0.0843060	0.0421530	+	0.999111i	$0.486578\pi$
$678$	0	0
$679$	− 19.6831i	− 0.755367i
$680$	0	0
$681$	0	0
$682$	0	0
$683$	− 10.3775i	− 0.397083i	−0.980092	−	0.198542i	$-0.936380\pi$
$683$	− 10.3775i	− 0.397083i	0.980092	−	0.198542i	$-0.0636205\pi$
$684$	0	0
$685$	15.1554i	0.579057i
$686$	0	0
$687$	0	0
$688$	0	0
$689$	− 18.1263i	− 0.690556i
$690$	0	0
$691$	38.9195	1.48057	0.740284	−	0.672295i	$-0.234691\pi$
$691$	38.9195	1.48057	0.740284	+	0.672295i	$0.234691\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	17.2929	0.655959
$696$	0	0
$697$	43.3132	1.64061
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−26.9799	−1.01902	−0.509509	−	0.860465i	$-0.670173\pi$
$701$	−26.9799	−1.01902	−0.509509	+	0.860465i	$0.670173\pi$
$702$	0	0
$703$	− 32.2932i	− 1.21796i
$704$	0	0
$705$	0	0
$706$	0	0
$707$	− 9.61957i	− 0.361781i
$708$	0	0
$709$	34.5022i	1.29576i	0.761744	+	0.647878i	$0.224344\pi$
$709$	34.5022i	1.29576i	−0.761744	+	0.647878i	$0.775656\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	4.99730i	0.187150i
$714$	0	0
$715$	11.1332	0.416360
$716$	0	0
$717$	0	0
$718$	0	0
$719$	34.7134	1.29459	0.647296	−	0.762239i	$-0.275900\pi$
$719$	34.7134	1.29459	0.647296	+	0.762239i	$0.275900\pi$
$720$	0	0
$721$	−16.2698	−0.605918
$722$	0	0
$723$	0	0
$724$	0	0
$725$	10.2475	0.380581
$726$	0	0
$727$	17.5891i	0.652344i	0.945310	+	0.326172i	$0.105759\pi$
$727$	17.5891i	0.652344i	−0.945310	+	0.326172i	$0.894241\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	41.6854i	1.54179i
$732$	0	0
$733$	16.7192i	0.617538i	0.951137	+	0.308769i	$0.0999170\pi$
$733$	16.7192i	0.617538i	−0.951137	+	0.308769i	$0.900083\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	34.0161i	1.25300i
$738$	0	0
$739$	20.6373	0.759154	0.379577	−	0.925160i	$-0.376070\pi$
$739$	20.6373	0.759154	0.379577	+	0.925160i	$0.376070\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	21.2777	0.780602	0.390301	−	0.920687i	$-0.372371\pi$
$743$	21.2777	0.780602	0.390301	+	0.920687i	$0.372371\pi$
$744$	0	0
$745$	−19.9086	−0.729394
$746$	0	0
$747$	0	0
$748$	0	0
$749$	36.4956	1.33352
$750$	0	0
$751$	29.2150i	1.06607i	0.846093	+	0.533035i	$0.178949\pi$
$751$	29.2150i	1.06607i	−0.846093	+	0.533035i	$0.821051\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	− 8.92849i	− 0.324941i
$756$	0	0
$757$	48.0411i	1.74608i	0.487644	+	0.873042i	$0.337856\pi$
$757$	48.0411i	1.74608i	−0.487644	+	0.873042i	$0.662144\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	− 36.2715i	− 1.31484i	−0.753524	−	0.657420i	$-0.771648\pi$
$761$	− 36.2715i	− 1.31484i	0.753524	−	0.657420i	$-0.228352\pi$
$762$	0	0
$763$	2.97971	0.107873
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−8.60045	−0.310544
$768$	0	0
$769$	−32.5241	−1.17285	−0.586424	−	0.810004i	$-0.699465\pi$
$769$	−32.5241	−1.17285	−0.586424	+	0.810004i	$0.699465\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	29.4139	1.05794	0.528972	−	0.848639i	$-0.322578\pi$
$773$	29.4139	1.05794	0.528972	+	0.848639i	$0.322578\pi$
$774$	0	0
$775$	14.6157i	0.525012i
$776$	0	0
$777$	0	0
$778$	0	0
$779$	− 31.6683i	− 1.13464i
$780$	0	0
$781$	− 35.1981i	− 1.25949i
$782$	0	0
$783$	0	0
$784$	0	0
$785$	15.3922i	0.549370i
$786$	0	0
$787$	46.2137	1.64734	0.823670	−	0.567069i	$-0.191923\pi$
$787$	46.2137	1.64734	0.823670	+	0.567069i	$0.191923\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	−14.0400	−0.499204
$792$	0	0
$793$	−24.5651	−0.872333
$794$	0	0
$795$	0	0
$796$	0	0
$797$	18.5710	0.657818	0.328909	−	0.944362i	$-0.393319\pi$
$797$	18.5710	0.657818	0.328909	+	0.944362i	$0.393319\pi$
$798$	0	0
$799$	− 6.33065i	− 0.223962i
$800$	0	0
$801$	0	0
$802$	0	0
$803$	− 55.2625i	− 1.95017i
$804$	0	0
$805$	3.70650i	0.130637i
$806$	0	0
$807$	0	0
$808$	0	0
$809$	22.3374i	0.785340i	0.919679	+	0.392670i	$0.128449\pi$
$809$	22.3374i	0.785340i	−0.919679	+	0.392670i	$0.871551\pi$
$810$	0	0
$811$	−44.5840	−1.56556	−0.782778	−	0.622301i	$-0.786198\pi$
$811$	−44.5840	−1.56556	−0.782778	+	0.622301i	$0.786198\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−3.66077	−0.128231
$816$	0	0
$817$	30.4782	1.06630
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−30.3986	−1.06092	−0.530459	−	0.847710i	$-0.677981\pi$
$821$	−30.3986	−1.06092	−0.530459	+	0.847710i	$0.677981\pi$
$822$	0	0
$823$	− 14.4691i	− 0.504361i	−0.967680	−	0.252180i	$-0.918852\pi$
$823$	− 14.4691i	− 0.504361i	0.967680	−	0.252180i	$-0.0811476\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	− 52.0725i	− 1.81074i	−0.424627	−	0.905368i	$-0.639595\pi$
$827$	− 52.0725i	− 1.81074i	0.424627	−	0.905368i	$-0.360405\pi$
$828$	0	0
$829$	− 4.34421i	− 0.150881i	−0.997150	−	0.0754404i	$-0.975964\pi$
$829$	− 4.34421i	− 0.150881i	0.997150	−	0.0754404i	$-0.0240363\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	− 26.7937i	− 0.928348i
$834$	0	0
$835$	37.5450	1.29930
$836$	0	0
$837$	0	0
$838$	0	0
$839$	45.8480	1.58285	0.791424	−	0.611268i	$-0.209340\pi$
$839$	45.8480	1.58285	0.791424	+	0.611268i	$0.209340\pi$
$840$	0	0
$841$	3.21260	0.110779
$842$	0	0
$843$	0	0
$844$	0	0
$845$	−17.9582	−0.617783
$846$	0	0
$847$	− 7.19695i	− 0.247290i
$848$	0	0
$849$	0	0
$850$	0	0
$851$	4.36032i	0.149470i
$852$	0	0
$853$	− 51.0276i	− 1.74715i	−0.486687	−	0.873577i	$-0.661795\pi$
$853$	− 51.0276i	− 1.74715i	0.486687	−	0.873577i	$-0.338205\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	− 52.5834i	− 1.79621i	−0.439778	−	0.898107i	$-0.644943\pi$
$857$	− 52.5834i	− 1.79621i	0.439778	−	0.898107i	$-0.355057\pi$
$858$	0	0
$859$	−16.0195	−0.546579	−0.273289	−	0.961932i	$-0.588112\pi$
$859$	−16.0195	−0.546579	−0.273289	+	0.961932i	$0.588112\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−25.3104	−0.861575	−0.430788	−	0.902453i	$-0.641764\pi$
$863$	−25.3104	−0.861575	−0.430788	+	0.902453i	$0.641764\pi$
$864$	0	0
$865$	12.1884	0.414417
$866$	0	0
$867$	0	0
$868$	0	0
$869$	−55.9216	−1.89701
$870$	0	0
$871$	16.1225i	0.546289i
$872$	0	0
$873$	0	0
$874$	0	0
$875$	40.8609i	1.38135i
$876$	0	0
$877$	3.15810i	0.106642i	0.998577	+	0.0533208i	$0.0169806\pi$
$877$	3.15810i	0.106642i	−0.998577	+	0.0533208i	$0.983019\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	− 17.1113i	− 0.576493i	−0.957556	−	0.288246i	$-0.906928\pi$
$881$	− 17.1113i	− 0.576493i	0.957556	−	0.288246i	$-0.0930722\pi$
$882$	0	0
$883$	19.0162	0.639945	0.319972	−	0.947427i	$-0.396326\pi$
$883$	19.0162	0.639945	0.319972	+	0.947427i	$0.396326\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	38.6696	1.29840	0.649199	−	0.760619i	$-0.275104\pi$
$887$	38.6696	1.29840	0.649199	+	0.760619i	$0.275104\pi$
$888$	0	0
$889$	37.2323	1.24873
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−4.62863	−0.154891
$894$	0	0
$895$	− 40.2322i	− 1.34481i
$896$	0	0
$897$	0	0
$898$	0	0
$899$	45.9441i	1.53232i
$900$	0	0
$901$	− 65.9674i	− 2.19769i
$902$	0	0
$903$	0	0
$904$	0	0
$905$	15.0706i	0.500962i
$906$	0	0
$907$	−44.1652	−1.46648	−0.733241	−	0.679969i	$-0.761993\pi$
$907$	−44.1652	−1.46648	−0.733241	+	0.679969i	$0.761993\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−30.1399	−0.998579	−0.499290	−	0.866435i	$-0.666406\pi$
$911$	−30.1399	−0.998579	−0.499290	+	0.866435i	$0.666406\pi$
$912$	0	0
$913$	23.4511	0.776117
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−32.2768	−1.06587
$918$	0	0
$919$	20.7713i	0.685183i	0.939485	+	0.342591i	$0.111305\pi$
$919$	20.7713i	0.685183i	−0.939485	+	0.342591i	$0.888695\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	− 16.6827i	− 0.549118i
$924$	0	0
$925$	12.7527i	0.419307i
$926$	0	0
$927$	0	0
$928$	0	0
$929$	28.5176i	0.935633i	0.883826	+	0.467816i	$0.154959\pi$
$929$	28.5176i	0.935633i	−0.883826	+	0.467816i	$0.845041\pi$
$930$	0	0
$931$	−19.5902	−0.642042
$932$	0	0
$933$	0	0
$934$	0	0
$935$	40.5175	1.32506
$936$	0	0
$937$	8.91394	0.291206	0.145603	−	0.989343i	$-0.453488\pi$
$937$	8.91394	0.291206	0.145603	+	0.989343i	$0.453488\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	12.5450	0.408954	0.204477	−	0.978871i	$-0.434451\pi$
$941$	12.5450	0.408954	0.204477	+	0.978871i	$0.434451\pi$
$942$	0	0
$943$	4.27595i	0.139244i
$944$	0	0
$945$	0	0
$946$	0	0
$947$	20.5765i	0.668648i	0.942458	+	0.334324i	$0.108508\pi$
$947$	20.5765i	0.668648i	−0.942458	+	0.334324i	$0.891492\pi$
$948$	0	0
$949$	− 26.1925i	− 0.850246i
$950$	0	0
$951$	0	0
$952$	0	0
$953$	− 35.3391i	− 1.14475i	−0.819993	−	0.572374i	$-0.806023\pi$
$953$	− 35.3391i	− 1.14475i	0.819993	−	0.572374i	$-0.193977\pi$
$954$	0	0
$955$	−10.8679	−0.351676
$956$	0	0
$957$	0	0
$958$	0	0
$959$	28.4848	0.919822
$960$	0	0
$961$	−34.5291	−1.11384
$962$	0	0
$963$	0	0
$964$	0	0
$965$	1.78731	0.0575355
$966$	0	0
$967$	− 20.1144i	− 0.646836i	−0.946256	−	0.323418i	$-0.895168\pi$
$967$	− 20.1144i	− 0.646836i	0.946256	−	0.323418i	$-0.104832\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	− 2.49582i	− 0.0800947i	−0.999198	−	0.0400474i	$-0.987249\pi$
$971$	− 2.49582i	− 0.0800947i	0.999198	−	0.0400474i	$-0.0127509\pi$
$972$	0	0
$973$	− 32.5024i	− 1.04198i
$974$	0	0
$975$	0	0
$976$	0	0
$977$	62.1836i	1.98943i	0.102675	+	0.994715i	$0.467260\pi$
$977$	62.1836i	1.98943i	−0.102675	+	0.994715i	$0.532740\pi$
$978$	0	0
$979$	−5.27450	−0.168574
$980$	0	0
$981$	0	0
$982$	0	0
$983$	−23.8754	−0.761507	−0.380754	−	0.924677i	$-0.624335\pi$
$983$	−23.8754	−0.761507	−0.380754	+	0.924677i	$0.624335\pi$
$984$	0	0
$985$	40.1967	1.28077
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−4.11526	−0.130858
$990$	0	0
$991$	− 2.22210i	− 0.0705873i	−0.999377	−	0.0352937i	$-0.988763\pi$
$991$	− 2.22210i	− 0.0705873i	0.999377	−	0.0352937i	$-0.0112367\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	17.5848i	0.557477i
$996$	0	0
$997$	37.3871i	1.18406i	0.805916	+	0.592030i	$0.201673\pi$
$997$	37.3871i	1.18406i	−0.805916	+	0.592030i	$0.798327\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.f.c.1295.6		24
3.2	odd	2	inner	2592.2.f.c.1295.20		24
4.3	odd	2		648.2.f.c.323.1	✓	24
8.3	odd	2	inner	2592.2.f.c.1295.19		24
8.5	even	2		648.2.f.c.323.23	yes	24
9.2	odd	6		2592.2.p.g.2159.5		48
9.4	even	3		2592.2.p.g.431.20		48
9.5	odd	6		2592.2.p.g.431.6		48
9.7	even	3		2592.2.p.g.2159.19		48
12.11	even	2		648.2.f.c.323.24	yes	24
24.5	odd	2		648.2.f.c.323.2	yes	24
24.11	even	2	inner	2592.2.f.c.1295.5		24
36.7	odd	6		648.2.l.g.539.15		48
36.11	even	6		648.2.l.g.539.10		48
36.23	even	6		648.2.l.g.107.8		48
36.31	odd	6		648.2.l.g.107.17		48
72.5	odd	6		648.2.l.g.107.15		48
72.11	even	6		2592.2.p.g.2159.20		48
72.13	even	6		648.2.l.g.107.10		48
72.29	odd	6		648.2.l.g.539.17		48
72.43	odd	6		2592.2.p.g.2159.6		48
72.59	even	6		2592.2.p.g.431.19		48
72.61	even	6		648.2.l.g.539.8		48
72.67	odd	6		2592.2.p.g.431.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
648.2.f.c.323.1	✓	24	4.3	odd	2
648.2.f.c.323.2	yes	24	24.5	odd	2
648.2.f.c.323.23	yes	24	8.5	even	2
648.2.f.c.323.24	yes	24	12.11	even	2
648.2.l.g.107.8		48	36.23	even	6
648.2.l.g.107.10		48	72.13	even	6
648.2.l.g.107.15		48	72.5	odd	6
648.2.l.g.107.17		48	36.31	odd	6
648.2.l.g.539.8		48	72.61	even	6
648.2.l.g.539.10		48	36.11	even	6
648.2.l.g.539.15		48	36.7	odd	6
648.2.l.g.539.17		48	72.29	odd	6
2592.2.f.c.1295.5		24	24.11	even	2	inner
2592.2.f.c.1295.6		24	1.1	even	1	trivial
2592.2.f.c.1295.19		24	8.3	odd	2	inner
2592.2.f.c.1295.20		24	3.2	odd	2	inner
2592.2.p.g.431.5		48	72.67	odd	6
2592.2.p.g.431.6		48	9.5	odd	6
2592.2.p.g.431.19		48	72.59	even	6
2592.2.p.g.431.20		48	9.4	even	3
2592.2.p.g.2159.5		48	9.2	odd	6
2592.2.p.g.2159.6		48	72.43	odd	6
2592.2.p.g.2159.19		48	9.7	even	3
2592.2.p.g.2159.20		48	72.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.78731 q^{5} +3.35928i q^{7} +O(q^{10})\)	\(q-1.78731 q^{5} +3.35928i q^{7} +3.62525i q^{11} +1.71824i q^{13} +6.25325i q^{17} +4.57204 q^{19} -0.617331 q^{23} -1.80552 q^{25} -5.67561 q^{29} -8.09500i q^{31} -6.00408i q^{35} -7.06318i q^{37} -6.92652i q^{41} +6.66621 q^{43} -1.01238 q^{47} -4.28477 q^{49} -10.5493 q^{53} -6.47944i q^{55} +5.00538i q^{59} +14.2966i q^{61} -3.07103i q^{65} +9.38311 q^{67} -9.70917 q^{71} -15.2438 q^{73} -12.1782 q^{77} +15.4256i q^{79} -6.46882i q^{83} -11.1765i q^{85} +1.45494i q^{89} -5.77206 q^{91} -8.17165 q^{95} -5.85931 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 24 q^{25} - 24 q^{49} - 48 q^{67}+O(q^{100}) \) 24 * q + 24 * q^25 - 24 * q^49 - 48 * q^67

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