LMFDB - Embedded newform 2916.3.c.b.1457.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2916,3,Mod(1457,2916)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2916, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("2916.1457");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 2916 = 2^{2} \cdot 3^{6} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	2916.c (of order $2$, degree $1$, 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:	$79.4552450875$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1457.27
Character	$\chi$	$=$	2916.1457
Dual form			2916.3.c.b.1457.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.19339i q^{5} -11.8514 q^{7} +O(q^{10})$	$q+4.19339i q^{5} -11.8514 q^{7} +11.9234i q^{11} -2.47565 q^{13} +13.8527i q^{17} -3.77921 q^{19} -26.8663i q^{23} +7.41551 q^{25} +41.2471i q^{29} -34.8965 q^{31} -49.6975i q^{35} -67.0616 q^{37} +5.08829i q^{41} -46.3918 q^{43} +93.2950i q^{47} +91.4559 q^{49} +51.4760i q^{53} -49.9992 q^{55} -14.7036i q^{59} +51.2165 q^{61} -10.3814i q^{65} +13.5770 q^{67} +32.3246i q^{71} +40.6051 q^{73} -141.309i q^{77} +74.2963 q^{79} -153.301i q^{83} -58.0899 q^{85} -20.8675i q^{89} +29.3399 q^{91} -15.8477i q^{95} -47.7160 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 180 q^{25} + 252 q^{49} + 18 q^{61} - 90 q^{67} + 126 q^{73} - 198 q^{91}+O(q^{100}) $ 36 * q - 180 * q^25 + 252 * q^49 + 18 * q^61 - 90 * q^67 + 126 * q^73 - 198 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2916\mathbb{Z}\right)^\times$.

$n$	$1459$	$2189$
$\chi(n)$	$1$	$-1$

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
$5$	4.19339i	0.838677i	0.907830	+	0.419339i	$0.137738\pi$
$5$	4.19339i	0.838677i	−0.907830	+	0.419339i	$0.862262\pi$
$6$	0	0
$7$	−11.8514	−1.69306	−0.846529	−	0.532342i	$-0.821312\pi$
$7$	−11.8514	−1.69306	−0.846529	+	0.532342i	$0.821312\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	11.9234i	1.08394i	0.840397	+	0.541971i	$0.182322\pi$
$11$	11.9234i	1.08394i	−0.840397	+	0.541971i	$0.817678\pi$
$12$	0	0
$13$	−2.47565	−0.190435	−0.0952173	−	0.995457i	$-0.530355\pi$
$13$	−2.47565	−0.190435	−0.0952173	+	0.995457i	$0.530355\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	13.8527i	0.814867i	0.913235	+	0.407433i	$0.133576\pi$
$17$	13.8527i	0.814867i	−0.913235	+	0.407433i	$0.866424\pi$
$18$	0	0
$19$	−3.77921	−0.198906	−0.0994528	−	0.995042i	$-0.531709\pi$
$19$	−3.77921	−0.198906	−0.0994528	+	0.995042i	$0.531709\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	− 26.8663i	− 1.16810i	−0.811717	−	0.584051i	$-0.801467\pi$
$23$	− 26.8663i	− 1.16810i	0.811717	−	0.584051i	$-0.198533\pi$
$24$	0	0
$25$	7.41551	0.296620
$26$	0	0
$27$	0	0
$28$	0	0
$29$	41.2471i	1.42232i	0.703033	+	0.711158i	$0.251829\pi$
$29$	41.2471i	1.42232i	−0.703033	+	0.711158i	$0.748171\pi$
$30$	0	0
$31$	−34.8965	−1.12569	−0.562847	−	0.826561i	$-0.690294\pi$
$31$	−34.8965	−1.12569	−0.562847	+	0.826561i	$0.690294\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	− 49.6975i	− 1.41993i
$36$	0	0
$37$	−67.0616	−1.81248	−0.906238	−	0.422767i	$-0.861059\pi$
$37$	−67.0616	−1.81248	−0.906238	+	0.422767i	$0.861059\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	5.08829i	0.124105i	0.998073	+	0.0620524i	$0.0197646\pi$
$41$	5.08829i	0.124105i	−0.998073	+	0.0620524i	$0.980235\pi$
$42$	0	0
$43$	−46.3918	−1.07888	−0.539440	−	0.842024i	$-0.681364\pi$
$43$	−46.3918	−1.07888	−0.539440	+	0.842024i	$0.681364\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	93.2950i	1.98500i	0.122249	+	0.992499i	$0.460989\pi$
$47$	93.2950i	1.98500i	−0.122249	+	0.992499i	$0.539011\pi$
$48$	0	0
$49$	91.4559	1.86645
$50$	0	0
$51$	0	0
$52$	0	0
$53$	51.4760i	0.971245i	0.874169	+	0.485622i	$0.161407\pi$
$53$	51.4760i	0.971245i	−0.874169	+	0.485622i	$0.838593\pi$
$54$	0	0
$55$	−49.9992	−0.909077
$56$	0	0
$57$	0	0
$58$	0	0
$59$	− 14.7036i	− 0.249214i	−0.992206	−	0.124607i	$-0.960233\pi$
$59$	− 14.7036i	− 0.249214i	0.992206	−	0.124607i	$-0.0397670\pi$
$60$	0	0
$61$	51.2165	0.839615	0.419807	−	0.907613i	$-0.362098\pi$
$61$	51.2165	0.839615	0.419807	+	0.907613i	$0.362098\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	− 10.3814i	− 0.159713i
$66$	0	0
$67$	13.5770	0.202642	0.101321	−	0.994854i	$-0.467693\pi$
$67$	13.5770	0.202642	0.101321	+	0.994854i	$0.467693\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	32.3246i	0.455276i	0.973746	+	0.227638i	$0.0731003\pi$
$71$	32.3246i	0.455276i	−0.973746	+	0.227638i	$0.926900\pi$
$72$	0	0
$73$	40.6051	0.556234	0.278117	−	0.960547i	$-0.410290\pi$
$73$	40.6051	0.556234	0.278117	+	0.960547i	$0.410290\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	− 141.309i	− 1.83518i
$78$	0	0
$79$	74.2963	0.940460	0.470230	−	0.882544i	$-0.344171\pi$
$79$	74.2963	0.940460	0.470230	+	0.882544i	$0.344171\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	− 153.301i	− 1.84700i	−0.383602	−	0.923498i	$-0.625317\pi$
$83$	− 153.301i	− 1.84700i	0.383602	−	0.923498i	$-0.374683\pi$
$84$	0	0
$85$	−58.0899	−0.683410
$86$	0	0
$87$	0	0
$88$	0	0
$89$	− 20.8675i	− 0.234466i	−0.993104	−	0.117233i	$-0.962598\pi$
$89$	− 20.8675i	− 0.234466i	0.993104	−	0.117233i	$-0.0374025\pi$
$90$	0	0
$91$	29.3399	0.322417
$92$	0	0
$93$	0	0
$94$	0	0
$95$	− 15.8477i	− 0.166818i
$96$	0	0
$97$	−47.7160	−0.491918	−0.245959	−	0.969280i	$-0.579103\pi$
$97$	−47.7160	−0.491918	−0.245959	+	0.969280i	$0.579103\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	47.5008i	0.470305i	0.971959	+	0.235152i	$0.0755589\pi$
$101$	47.5008i	0.470305i	−0.971959	+	0.235152i	$0.924441\pi$
$102$	0	0
$103$	−105.424	−1.02353	−0.511765	−	0.859125i	$-0.671008\pi$
$103$	−105.424	−1.02353	−0.511765	+	0.859125i	$0.671008\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	− 189.677i	− 1.77268i	−0.463031	−	0.886342i	$-0.653238\pi$
$107$	− 189.677i	− 1.77268i	0.463031	−	0.886342i	$-0.346762\pi$
$108$	0	0
$109$	−86.7332	−0.795718	−0.397859	−	0.917447i	$-0.630247\pi$
$109$	−86.7332	−0.795718	−0.397859	+	0.917447i	$0.630247\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	− 155.228i	− 1.37370i	−0.726800	−	0.686849i	$-0.758993\pi$
$113$	− 155.228i	− 1.37370i	0.726800	−	0.686849i	$-0.241007\pi$
$114$	0	0
$115$	112.661	0.979660
$116$	0	0
$117$	0	0
$118$	0	0
$119$	− 164.174i	− 1.37962i
$120$	0	0
$121$	−21.1664	−0.174929
$122$	0	0
$123$	0	0
$124$	0	0
$125$	135.931i	1.08745i
$126$	0	0
$127$	200.589	1.57944	0.789720	−	0.613467i	$-0.210226\pi$
$127$	200.589	1.57944	0.789720	+	0.613467i	$0.210226\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	− 107.867i	− 0.823413i	−0.911317	−	0.411706i	$-0.864933\pi$
$131$	− 107.867i	− 0.823413i	0.911317	−	0.411706i	$-0.135067\pi$
$132$	0	0
$133$	44.7889	0.336759
$134$	0	0
$135$	0	0
$136$	0	0
$137$	− 86.6872i	− 0.632753i	−0.948634	−	0.316377i	$-0.897534\pi$
$137$	− 86.6872i	− 0.632753i	0.948634	−	0.316377i	$-0.102466\pi$
$138$	0	0
$139$	61.2451	0.440612	0.220306	−	0.975431i	$-0.429294\pi$
$139$	61.2451	0.440612	0.220306	+	0.975431i	$0.429294\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	− 29.5181i	− 0.206420i
$144$	0	0
$145$	−172.965	−1.19286
$146$	0	0
$147$	0	0
$148$	0	0
$149$	0.702186i	0.00471266i	0.999997	+	0.00235633i	$0.000750043\pi$
$149$	0.702186i	0.00471266i	−0.999997	+	0.00235633i	$0.999250\pi$
$150$	0	0
$151$	−126.073	−0.834918	−0.417459	−	0.908696i	$-0.637079\pi$
$151$	−126.073	−0.834918	−0.417459	+	0.908696i	$0.637079\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	− 146.335i	− 0.944094i
$156$	0	0
$157$	206.324	1.31416	0.657082	−	0.753819i	$-0.271790\pi$
$157$	206.324	1.31416	0.657082	+	0.753819i	$0.271790\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	318.404i	1.97766i
$162$	0	0
$163$	105.377	0.646484	0.323242	−	0.946316i	$-0.395227\pi$
$163$	105.377	0.646484	0.323242	+	0.946316i	$0.395227\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	− 208.663i	− 1.24948i	−0.780832	−	0.624741i	$-0.785205\pi$
$167$	− 208.663i	− 1.24948i	0.780832	−	0.624741i	$-0.214795\pi$
$168$	0	0
$169$	−162.871	−0.963735
$170$	0	0
$171$	0	0
$172$	0	0
$173$	− 132.781i	− 0.767518i	−0.923433	−	0.383759i	$-0.874629\pi$
$173$	− 132.781i	− 0.767518i	0.923433	−	0.383759i	$-0.125371\pi$
$174$	0	0
$175$	−87.8842	−0.502196
$176$	0	0
$177$	0	0
$178$	0	0
$179$	− 142.164i	− 0.794212i	−0.917773	−	0.397106i	$-0.870014\pi$
$179$	− 142.164i	− 0.794212i	0.917773	−	0.397106i	$-0.129986\pi$
$180$	0	0
$181$	2.74041	0.0151404	0.00757019	−	0.999971i	$-0.497590\pi$
$181$	2.74041	0.0151404	0.00757019	+	0.999971i	$0.497590\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	− 281.215i	− 1.52008i
$186$	0	0
$187$	−165.171	−0.883268
$188$	0	0
$189$	0	0
$190$	0	0
$191$	37.6756i	0.197254i	0.995124	+	0.0986272i	$0.0314451\pi$
$191$	37.6756i	0.197254i	−0.995124	+	0.0986272i	$0.968555\pi$
$192$	0	0
$193$	−123.736	−0.641120	−0.320560	−	0.947228i	$-0.603871\pi$
$193$	−123.736	−0.641120	−0.320560	+	0.947228i	$0.603871\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	− 57.9231i	− 0.294026i	−0.989135	−	0.147013i	$-0.953034\pi$
$197$	− 57.9231i	− 0.294026i	0.989135	−	0.147013i	$-0.0469659\pi$
$198$	0	0
$199$	311.281	1.56422	0.782112	−	0.623137i	$-0.214142\pi$
$199$	311.281	1.56422	0.782112	+	0.623137i	$0.214142\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	− 488.837i	− 2.40806i
$204$	0	0
$205$	−21.3372	−0.104084
$206$	0	0
$207$	0	0
$208$	0	0
$209$	− 45.0608i	− 0.215602i
$210$	0	0
$211$	−35.2227	−0.166932	−0.0834661	−	0.996511i	$-0.526599\pi$
$211$	−35.2227	−0.166932	−0.0834661	+	0.996511i	$0.526599\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	− 194.539i	− 0.904832i
$216$	0	0
$217$	413.573	1.90587
$218$	0	0
$219$	0	0
$220$	0	0
$221$	− 34.2945i	− 0.155179i
$222$	0	0
$223$	−232.310	−1.04175	−0.520874	−	0.853634i	$-0.674394\pi$
$223$	−232.310	−1.04175	−0.520874	+	0.853634i	$0.674394\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	423.639i	1.86625i	0.359549	+	0.933126i	$0.382931\pi$
$227$	423.639i	1.86625i	−0.359549	+	0.933126i	$0.617069\pi$
$228$	0	0
$229$	267.079	1.16628	0.583141	−	0.812371i	$-0.301823\pi$
$229$	267.079	1.16628	0.583141	+	0.812371i	$0.301823\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	− 71.6122i	− 0.307349i	−0.988122	−	0.153674i	$-0.950889\pi$
$233$	− 71.6122i	− 0.307349i	0.988122	−	0.153674i	$-0.0491107\pi$
$234$	0	0
$235$	−391.222	−1.66477
$236$	0	0
$237$	0	0
$238$	0	0
$239$	− 100.521i	− 0.420589i	−0.977638	−	0.210295i	$-0.932558\pi$
$239$	− 100.521i	− 0.420589i	0.977638	−	0.210295i	$-0.0674423\pi$
$240$	0	0
$241$	−29.9666	−0.124343	−0.0621715	−	0.998065i	$-0.519803\pi$
$241$	−29.9666	−0.124343	−0.0621715	+	0.998065i	$0.519803\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	383.510i	1.56535i
$246$	0	0
$247$	9.35600	0.0378785
$248$	0	0
$249$	0	0
$250$	0	0
$251$	159.758i	0.636487i	0.948009	+	0.318243i	$0.103093\pi$
$251$	159.758i	0.636487i	−0.948009	+	0.318243i	$0.896907\pi$
$252$	0	0
$253$	320.337	1.26615
$254$	0	0
$255$	0	0
$256$	0	0
$257$	− 445.246i	− 1.73248i	−0.499632	−	0.866238i	$-0.666531\pi$
$257$	− 445.246i	− 1.73248i	0.499632	−	0.866238i	$-0.333469\pi$
$258$	0	0
$259$	794.775	3.06863
$260$	0	0
$261$	0	0
$262$	0	0
$263$	− 98.5318i	− 0.374646i	−0.982298	−	0.187323i	$-0.940019\pi$
$263$	− 98.5318i	− 0.374646i	0.982298	−	0.187323i	$-0.0599810\pi$
$264$	0	0
$265$	−215.859	−0.814561
$266$	0	0
$267$	0	0
$268$	0	0
$269$	46.7784i	0.173898i	0.996213	+	0.0869488i	$0.0277116\pi$
$269$	46.7784i	0.173898i	−0.996213	+	0.0869488i	$0.972288\pi$
$270$	0	0
$271$	−262.335	−0.968026	−0.484013	−	0.875061i	$-0.660821\pi$
$271$	−262.335	−0.968026	−0.484013	+	0.875061i	$0.660821\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	88.4178i	0.321519i
$276$	0	0
$277$	342.299	1.23574	0.617868	−	0.786282i	$-0.287996\pi$
$277$	342.299	1.23574	0.617868	+	0.786282i	$0.287996\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	255.439i	0.909034i	0.890738	+	0.454517i	$0.150188\pi$
$281$	255.439i	0.909034i	−0.890738	+	0.454517i	$0.849812\pi$
$282$	0	0
$283$	−49.0707	−0.173395	−0.0866973	−	0.996235i	$-0.527631\pi$
$283$	−49.0707	−0.173395	−0.0866973	+	0.996235i	$0.527631\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	− 60.3035i	− 0.210117i
$288$	0	0
$289$	97.1017	0.335992
$290$	0	0
$291$	0	0
$292$	0	0
$293$	307.425i	1.04923i	0.851339	+	0.524616i	$0.175791\pi$
$293$	307.425i	1.04923i	−0.851339	+	0.524616i	$0.824209\pi$
$294$	0	0
$295$	61.6579	0.209010
$296$	0	0
$297$	0	0
$298$	0	0
$299$	66.5116i	0.222447i
$300$	0	0
$301$	549.808	1.82661
$302$	0	0
$303$	0	0
$304$	0	0
$305$	214.771i	0.704166i
$306$	0	0
$307$	−279.080	−0.909056	−0.454528	−	0.890732i	$-0.650192\pi$
$307$	−279.080	−0.909056	−0.454528	+	0.890732i	$0.650192\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	− 300.598i	− 0.966553i	−0.875468	−	0.483277i	$-0.839447\pi$
$311$	− 300.598i	− 0.966553i	0.875468	−	0.483277i	$-0.160553\pi$
$312$	0	0
$313$	−244.478	−0.781080	−0.390540	−	0.920586i	$-0.627712\pi$
$313$	−244.478	−0.781080	−0.390540	+	0.920586i	$0.627712\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	313.110i	0.987728i	0.869539	+	0.493864i	$0.164416\pi$
$317$	313.110i	0.987728i	−0.869539	+	0.493864i	$0.835584\pi$
$318$	0	0
$319$	−491.804	−1.54171
$320$	0	0
$321$	0	0
$322$	0	0
$323$	− 52.3524i	− 0.162082i
$324$	0	0
$325$	−18.3582	−0.0564868
$326$	0	0
$327$	0	0
$328$	0	0
$329$	− 1105.68i	− 3.36072i
$330$	0	0
$331$	−430.034	−1.29920	−0.649599	−	0.760277i	$-0.725063\pi$
$331$	−430.034	−1.29920	−0.649599	+	0.760277i	$0.725063\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	56.9337i	0.169951i
$336$	0	0
$337$	−493.517	−1.46444	−0.732220	−	0.681068i	$-0.761516\pi$
$337$	−493.517	−1.46444	−0.732220	+	0.681068i	$0.761516\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	− 416.084i	− 1.22019i
$342$	0	0
$343$	−503.162	−1.46695
$344$	0	0
$345$	0	0
$346$	0	0
$347$	− 519.549i	− 1.49726i	−0.662988	−	0.748630i	$-0.730712\pi$
$347$	− 519.549i	− 1.49726i	0.662988	−	0.748630i	$-0.269288\pi$
$348$	0	0
$349$	−243.092	−0.696538	−0.348269	−	0.937395i	$-0.613230\pi$
$349$	−243.092	−0.696538	−0.348269	+	0.937395i	$0.613230\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	641.701i	1.81785i	0.416961	+	0.908924i	$0.363095\pi$
$353$	641.701i	1.81785i	−0.416961	+	0.908924i	$0.636905\pi$
$354$	0	0
$355$	−135.550	−0.381830
$356$	0	0
$357$	0	0
$358$	0	0
$359$	332.130i	0.925154i	0.886579	+	0.462577i	$0.153075\pi$
$359$	332.130i	0.925154i	−0.886579	+	0.462577i	$0.846925\pi$
$360$	0	0
$361$	−346.718	−0.960437
$362$	0	0
$363$	0	0
$364$	0	0
$365$	170.273i	0.466501i
$366$	0	0
$367$	71.0636	0.193634	0.0968168	−	0.995302i	$-0.469134\pi$
$367$	71.0636	0.193634	0.0968168	+	0.995302i	$0.469134\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	− 610.063i	− 1.64437i
$372$	0	0
$373$	328.122	0.879685	0.439842	−	0.898075i	$-0.355034\pi$
$373$	328.122	0.879685	0.439842	+	0.898075i	$0.355034\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	− 102.114i	− 0.270858i
$378$	0	0
$379$	−77.9266	−0.205611	−0.102806	−	0.994701i	$-0.532782\pi$
$379$	−77.9266	−0.205611	−0.102806	+	0.994701i	$0.532782\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	− 206.276i	− 0.538578i	−0.963059	−	0.269289i	$-0.913211\pi$
$383$	− 206.276i	− 0.538578i	0.963059	−	0.269289i	$-0.0867887\pi$
$384$	0	0
$385$	592.561	1.53912
$386$	0	0
$387$	0	0
$388$	0	0
$389$	− 9.52545i	− 0.0244870i	−0.999925	−	0.0122435i	$-0.996103\pi$
$389$	− 9.52545i	− 0.0244870i	0.999925	−	0.0122435i	$-0.00389733\pi$
$390$	0	0
$391$	372.172	0.951847
$392$	0	0
$393$	0	0
$394$	0	0
$395$	311.553i	0.788742i
$396$	0	0
$397$	77.0583	0.194101	0.0970507	−	0.995279i	$-0.469059\pi$
$397$	77.0583	0.194101	0.0970507	+	0.995279i	$0.469059\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	332.581i	0.829379i	0.909963	+	0.414689i	$0.136110\pi$
$401$	332.581i	0.829379i	−0.909963	+	0.414689i	$0.863890\pi$
$402$	0	0
$403$	86.3916	0.214371
$404$	0	0
$405$	0	0
$406$	0	0
$407$	− 799.600i	− 1.96462i
$408$	0	0
$409$	420.410	1.02790	0.513948	−	0.857821i	$-0.328182\pi$
$409$	420.410	1.02790	0.513948	+	0.857821i	$0.328182\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	174.259i	0.421934i
$414$	0	0
$415$	642.849	1.54903
$416$	0	0
$417$	0	0
$418$	0	0
$419$	− 156.601i	− 0.373749i	−0.982384	−	0.186874i	$-0.940164\pi$
$419$	− 156.601i	− 0.373749i	0.982384	−	0.186874i	$-0.0598357\pi$
$420$	0	0
$421$	26.0089	0.0617788	0.0308894	−	0.999523i	$-0.490166\pi$
$421$	26.0089	0.0617788	0.0308894	+	0.999523i	$0.490166\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	102.725i	0.241706i
$426$	0	0
$427$	−606.988	−1.42152
$428$	0	0
$429$	0	0
$430$	0	0
$431$	− 209.889i	− 0.486982i	−0.969903	−	0.243491i	$-0.921707\pi$
$431$	− 209.889i	− 0.486982i	0.969903	−	0.243491i	$-0.0782927\pi$
$432$	0	0
$433$	−405.331	−0.936100	−0.468050	−	0.883702i	$-0.655043\pi$
$433$	−405.331	−0.936100	−0.468050	+	0.883702i	$0.655043\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	101.533i	0.232342i
$438$	0	0
$439$	−126.853	−0.288959	−0.144480	−	0.989508i	$-0.546151\pi$
$439$	−126.853	−0.288959	−0.144480	+	0.989508i	$0.546151\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	− 353.138i	− 0.797152i	−0.917135	−	0.398576i	$-0.869505\pi$
$443$	− 353.138i	− 0.797152i	0.917135	−	0.398576i	$-0.130495\pi$
$444$	0	0
$445$	87.5054	0.196641
$446$	0	0
$447$	0	0
$448$	0	0
$449$	− 487.890i	− 1.08661i	−0.839534	−	0.543307i	$-0.817172\pi$
$449$	− 487.890i	− 1.08661i	0.839534	−	0.543307i	$-0.182828\pi$
$450$	0	0
$451$	−60.6695	−0.134522
$452$	0	0
$453$	0	0
$454$	0	0
$455$	123.034i	0.270404i
$456$	0	0
$457$	−250.541	−0.548230	−0.274115	−	0.961697i	$-0.588385\pi$
$457$	−250.541	−0.548230	−0.274115	+	0.961697i	$0.588385\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	− 462.832i	− 1.00397i	−0.864875	−	0.501987i	$-0.832603\pi$
$461$	− 462.832i	− 1.00397i	0.864875	−	0.501987i	$-0.167397\pi$
$462$	0	0
$463$	432.508	0.934142	0.467071	−	0.884220i	$-0.345309\pi$
$463$	432.508	0.934142	0.467071	+	0.884220i	$0.345309\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	64.0388i	0.137128i	0.997647	+	0.0685640i	$0.0218417\pi$
$467$	64.0388i	0.137128i	−0.997647	+	0.0685640i	$0.978158\pi$
$468$	0	0
$469$	−160.907	−0.343085
$470$	0	0
$471$	0	0
$472$	0	0
$473$	− 553.146i	− 1.16944i
$474$	0	0
$475$	−28.0247	−0.0589995
$476$	0	0
$477$	0	0
$478$	0	0
$479$	− 175.100i	− 0.365552i	−0.983155	−	0.182776i	$-0.941492\pi$
$479$	− 175.100i	− 0.365552i	0.983155	−	0.182776i	$-0.0585084\pi$
$480$	0	0
$481$	166.021	0.345158
$482$	0	0
$483$	0	0
$484$	0	0
$485$	− 200.092i	− 0.412560i
$486$	0	0
$487$	−28.7536	−0.0590424	−0.0295212	−	0.999564i	$-0.509398\pi$
$487$	−28.7536	−0.0590424	−0.0295212	+	0.999564i	$0.509398\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	772.522i	1.57336i	0.617358	+	0.786682i	$0.288203\pi$
$491$	772.522i	1.57336i	−0.617358	+	0.786682i	$0.711797\pi$
$492$	0	0
$493$	−571.386	−1.15900
$494$	0	0
$495$	0	0
$496$	0	0
$497$	− 383.092i	− 0.770809i
$498$	0	0
$499$	581.705	1.16574	0.582871	−	0.812565i	$-0.301929\pi$
$499$	581.705	1.16574	0.582871	+	0.812565i	$0.301929\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	567.737i	1.12870i	0.825535	+	0.564351i	$0.190873\pi$
$503$	567.737i	1.12870i	−0.825535	+	0.564351i	$0.809127\pi$
$504$	0	0
$505$	−199.189	−0.394434
$506$	0	0
$507$	0	0
$508$	0	0
$509$	− 513.459i	− 1.00876i	−0.863482	−	0.504380i	$-0.831721\pi$
$509$	− 513.459i	− 1.00876i	0.863482	−	0.504380i	$-0.168279\pi$
$510$	0	0
$511$	−481.228	−0.941737
$512$	0	0
$513$	0	0
$514$	0	0
$515$	− 442.082i	− 0.858411i
$516$	0	0
$517$	−1112.39	−2.15162
$518$	0	0
$519$	0	0
$520$	0	0
$521$	− 712.101i	− 1.36680i	−0.730046	−	0.683398i	$-0.760501\pi$
$521$	− 712.101i	− 1.36680i	0.730046	−	0.683398i	$-0.239499\pi$
$522$	0	0
$523$	−203.216	−0.388559	−0.194279	−	0.980946i	$-0.562237\pi$
$523$	−203.216	−0.388559	−0.194279	+	0.980946i	$0.562237\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	− 483.412i	− 0.917291i
$528$	0	0
$529$	−192.800	−0.364460
$530$	0	0
$531$	0	0
$532$	0	0
$533$	− 12.5968i	− 0.0236338i
$534$	0	0
$535$	795.390	1.48671
$536$	0	0
$537$	0	0
$538$	0	0
$539$	1090.46i	2.02312i
$540$	0	0
$541$	96.3158	0.178033	0.0890165	−	0.996030i	$-0.471628\pi$
$541$	96.3158	0.178033	0.0890165	+	0.996030i	$0.471628\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	− 363.706i	− 0.667350i
$546$	0	0
$547$	−257.717	−0.471146	−0.235573	−	0.971857i	$-0.575697\pi$
$547$	−257.717	−0.471146	−0.235573	+	0.971857i	$0.575697\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	− 155.881i	− 0.282907i
$552$	0	0
$553$	−880.516	−1.59225
$554$	0	0
$555$	0	0
$556$	0	0
$557$	289.902i	0.520470i	0.965545	+	0.260235i	$0.0838000\pi$
$557$	289.902i	0.520470i	−0.965545	+	0.260235i	$0.916200\pi$
$558$	0	0
$559$	114.850	0.205456
$560$	0	0
$561$	0	0
$562$	0	0
$563$	− 61.2353i	− 0.108766i	−0.998520	−	0.0543830i	$-0.982681\pi$
$563$	− 61.2353i	− 0.108766i	0.998520	−	0.0543830i	$-0.0173192\pi$
$564$	0	0
$565$	650.930	1.15209
$566$	0	0
$567$	0	0
$568$	0	0
$569$	489.987i	0.861137i	0.902558	+	0.430569i	$0.141687\pi$
$569$	489.987i	0.861137i	−0.902558	+	0.430569i	$0.858313\pi$
$570$	0	0
$571$	−763.682	−1.33745	−0.668724	−	0.743511i	$-0.733159\pi$
$571$	−763.682	−1.33745	−0.668724	+	0.743511i	$0.733159\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	− 199.228i	− 0.346483i
$576$	0	0
$577$	−260.905	−0.452176	−0.226088	−	0.974107i	$-0.572594\pi$
$577$	−260.905	−0.452176	−0.226088	+	0.974107i	$0.572594\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	1816.83i	3.12707i
$582$	0	0
$583$	−613.766	−1.05277
$584$	0	0
$585$	0	0
$586$	0	0
$587$	− 281.892i	− 0.480225i	−0.970745	−	0.240113i	$-0.922816\pi$
$587$	− 281.892i	− 0.480225i	0.970745	−	0.240113i	$-0.0771844\pi$
$588$	0	0
$589$	131.881	0.223907
$590$	0	0
$591$	0	0
$592$	0	0
$593$	− 248.742i	− 0.419463i	−0.977759	−	0.209731i	$-0.932741\pi$
$593$	− 248.742i	− 0.419463i	0.977759	−	0.209731i	$-0.0672590\pi$
$594$	0	0
$595$	688.447	1.15705
$596$	0	0
$597$	0	0
$598$	0	0
$599$	317.979i	0.530850i	0.964132	+	0.265425i	$0.0855123\pi$
$599$	317.979i	0.530850i	−0.964132	+	0.265425i	$0.914488\pi$
$600$	0	0
$601$	825.574	1.37367	0.686834	−	0.726814i	$-0.259000\pi$
$601$	825.574	1.37367	0.686834	+	0.726814i	$0.259000\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	− 88.7590i	− 0.146709i
$606$	0	0
$607$	−404.868	−0.666998	−0.333499	−	0.942750i	$-0.608229\pi$
$607$	−404.868	−0.666998	−0.333499	+	0.942750i	$0.608229\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	− 230.966i	− 0.378013i
$612$	0	0
$613$	619.459	1.01054	0.505268	−	0.862963i	$-0.331394\pi$
$613$	619.459	1.01054	0.505268	+	0.862963i	$0.331394\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	− 806.726i	− 1.30750i	−0.756712	−	0.653749i	$-0.773195\pi$
$617$	− 806.726i	− 1.30750i	0.756712	−	0.653749i	$-0.226805\pi$
$618$	0	0
$619$	892.691	1.44215	0.721075	−	0.692857i	$-0.243648\pi$
$619$	892.691	1.44215	0.721075	+	0.692857i	$0.243648\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	247.309i	0.396965i
$624$	0	0
$625$	−384.622	−0.615396
$626$	0	0
$627$	0	0
$628$	0	0
$629$	− 928.987i	− 1.47693i
$630$	0	0
$631$	−830.684	−1.31646	−0.658228	−	0.752819i	$-0.728694\pi$
$631$	−830.684	−1.31646	−0.658228	+	0.752819i	$0.728694\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	841.147i	1.32464i
$636$	0	0
$637$	−226.413	−0.355436
$638$	0	0
$639$	0	0
$640$	0	0
$641$	711.369i	1.10978i	0.831924	+	0.554890i	$0.187240\pi$
$641$	711.369i	1.10978i	−0.831924	+	0.554890i	$0.812760\pi$
$642$	0	0
$643$	905.559	1.40833	0.704167	−	0.710034i	$-0.251320\pi$
$643$	905.559	1.40833	0.704167	+	0.710034i	$0.251320\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	175.592i	0.271394i	0.990750	+	0.135697i	$0.0433273\pi$
$647$	175.592i	0.271394i	−0.990750	+	0.135697i	$0.956673\pi$
$648$	0	0
$649$	175.316	0.270133
$650$	0	0
$651$	0	0
$652$	0	0
$653$	1010.57i	1.54758i	0.633444	+	0.773789i	$0.281641\pi$
$653$	1010.57i	1.54758i	−0.633444	+	0.773789i	$0.718359\pi$
$654$	0	0
$655$	452.328	0.690578
$656$	0	0
$657$	0	0
$658$	0	0
$659$	− 262.881i	− 0.398909i	−0.979907	−	0.199455i	$-0.936083\pi$
$659$	− 262.881i	− 0.398909i	0.979907	−	0.199455i	$-0.0639170\pi$
$660$	0	0
$661$	499.183	0.755194	0.377597	−	0.925970i	$-0.376751\pi$
$661$	499.183	0.755194	0.377597	+	0.925970i	$0.376751\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	187.817i	0.282432i
$666$	0	0
$667$	1108.16	1.66141
$668$	0	0
$669$	0	0
$670$	0	0
$671$	610.672i	0.910093i
$672$	0	0
$673$	892.885	1.32672	0.663362	−	0.748299i	$-0.269129\pi$
$673$	892.885	1.32672	0.663362	+	0.748299i	$0.269129\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	313.538i	0.463128i	0.972820	+	0.231564i	$0.0743842\pi$
$677$	313.538i	0.463128i	−0.972820	+	0.231564i	$0.925616\pi$
$678$	0	0
$679$	565.502	0.832846
$680$	0	0
$681$	0	0
$682$	0	0
$683$	− 486.473i	− 0.712260i	−0.934436	−	0.356130i	$-0.884096\pi$
$683$	− 486.473i	− 0.712260i	0.934436	−	0.356130i	$-0.115904\pi$
$684$	0	0
$685$	363.513	0.530676
$686$	0	0
$687$	0	0
$688$	0	0
$689$	− 127.437i	− 0.184959i
$690$	0	0
$691$	617.830	0.894110	0.447055	−	0.894506i	$-0.352473\pi$
$691$	617.830	0.894110	0.447055	+	0.894506i	$0.352473\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	256.824i	0.369531i
$696$	0	0
$697$	−70.4868	−0.101129
$698$	0	0
$699$	0	0
$700$	0	0
$701$	− 297.109i	− 0.423836i	−0.977287	−	0.211918i	$-0.932029\pi$
$701$	− 297.109i	− 0.423836i	0.977287	−	0.211918i	$-0.0679709\pi$
$702$	0	0
$703$	253.440	0.360512
$704$	0	0
$705$	0	0
$706$	0	0
$707$	− 562.951i	− 0.796253i
$708$	0	0
$709$	−881.029	−1.24264	−0.621318	−	0.783559i	$-0.713402\pi$
$709$	−881.029	−1.24264	−0.621318	+	0.783559i	$0.713402\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	937.541i	1.31492i
$714$	0	0
$715$	123.781	0.173120
$716$	0	0
$717$	0	0
$718$	0	0
$719$	1179.05i	1.63985i	0.572471	+	0.819925i	$0.305985\pi$
$719$	1179.05i	1.63985i	−0.572471	+	0.819925i	$0.694015\pi$
$720$	0	0
$721$	1249.42	1.73290
$722$	0	0
$723$	0	0
$724$	0	0
$725$	305.869i	0.421888i
$726$	0	0
$727$	−643.311	−0.884884	−0.442442	−	0.896797i	$-0.645888\pi$
$727$	−643.311	−0.884884	−0.442442	+	0.896797i	$0.645888\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	− 642.654i	− 0.879143i
$732$	0	0
$733$	188.823	0.257602	0.128801	−	0.991670i	$-0.458887\pi$
$733$	188.823	0.257602	0.128801	+	0.991670i	$0.458887\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	161.884i	0.219652i
$738$	0	0
$739$	911.207	1.23303	0.616514	−	0.787344i	$-0.288544\pi$
$739$	911.207	1.23303	0.616514	+	0.787344i	$0.288544\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	297.762i	0.400756i	0.979719	+	0.200378i	$0.0642170\pi$
$743$	297.762i	0.400756i	−0.979719	+	0.200378i	$0.935783\pi$
$744$	0	0
$745$	−2.94454	−0.00395240
$746$	0	0
$747$	0	0
$748$	0	0
$749$	2247.94i	3.00126i
$750$	0	0
$751$	−5.31339	−0.00707508	−0.00353754	−	0.999994i	$-0.501126\pi$
$751$	−5.31339	−0.00707508	−0.00353754	+	0.999994i	$0.501126\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	− 528.671i	− 0.700227i
$756$	0	0
$757$	−678.131	−0.895813	−0.447907	−	0.894080i	$-0.647830\pi$
$757$	−678.131	−0.895813	−0.447907	+	0.894080i	$0.647830\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	914.492i	1.20170i	0.799363	+	0.600849i	$0.205171\pi$
$761$	914.492i	1.20170i	−0.799363	+	0.600849i	$0.794829\pi$
$762$	0	0
$763$	1027.91	1.34720
$764$	0	0
$765$	0	0
$766$	0	0
$767$	36.4010i	0.0474590i
$768$	0	0
$769$	355.672	0.462512	0.231256	−	0.972893i	$-0.425717\pi$
$769$	355.672	0.462512	0.231256	+	0.972893i	$0.425717\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	727.920i	0.941681i	0.882218	+	0.470841i	$0.156049\pi$
$773$	727.920i	0.941681i	−0.882218	+	0.470841i	$0.843951\pi$
$774$	0	0
$775$	−258.775	−0.333904
$776$	0	0
$777$	0	0
$778$	0	0
$779$	− 19.2297i	− 0.0246851i
$780$	0	0
$781$	−385.418	−0.493493
$782$	0	0
$783$	0	0
$784$	0	0
$785$	865.195i	1.10216i
$786$	0	0
$787$	45.9632	0.0584031	0.0292015	−	0.999574i	$-0.490704\pi$
$787$	45.9632	0.0584031	0.0292015	+	0.999574i	$0.490704\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	1839.67i	2.32575i
$792$	0	0
$793$	−126.794	−0.159892
$794$	0	0
$795$	0	0
$796$	0	0
$797$	394.806i	0.495365i	0.968841	+	0.247682i	$0.0796690\pi$
$797$	394.806i	0.495365i	−0.968841	+	0.247682i	$0.920331\pi$
$798$	0	0
$799$	−1292.39	−1.61751
$800$	0	0
$801$	0	0
$802$	0	0
$803$	484.149i	0.602925i
$804$	0	0
$805$	−1335.19	−1.65862
$806$	0	0
$807$	0	0
$808$	0	0
$809$	333.349i	0.412050i	0.978547	+	0.206025i	$0.0660529\pi$
$809$	333.349i	0.412050i	−0.978547	+	0.206025i	$0.933947\pi$
$810$	0	0
$811$	−1156.01	−1.42541	−0.712705	−	0.701464i	$-0.752530\pi$
$811$	−1156.01	−1.42541	−0.712705	+	0.701464i	$0.752530\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	441.886i	0.542191i
$816$	0	0
$817$	175.324	0.214595
$818$	0	0
$819$	0	0
$820$	0	0
$821$	1239.86i	1.51018i	0.655623	+	0.755088i	$0.272406\pi$
$821$	1239.86i	1.51018i	−0.655623	+	0.755088i	$0.727594\pi$
$822$	0	0
$823$	47.6805	0.0579350	0.0289675	−	0.999580i	$-0.490778\pi$
$823$	47.6805	0.0579350	0.0289675	+	0.999580i	$0.490778\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	− 1056.26i	− 1.27722i	−0.769529	−	0.638612i	$-0.779509\pi$
$827$	− 1056.26i	− 1.27722i	0.769529	−	0.638612i	$-0.220491\pi$
$828$	0	0
$829$	−1288.49	−1.55427	−0.777137	−	0.629331i	$-0.783329\pi$
$829$	−1288.49	−1.55427	−0.777137	+	0.629331i	$0.783329\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	1266.91i	1.52091i
$834$	0	0
$835$	875.007	1.04791
$836$	0	0
$837$	0	0
$838$	0	0
$839$	− 952.960i	− 1.13583i	−0.823088	−	0.567914i	$-0.807751\pi$
$839$	− 952.960i	− 1.13583i	0.823088	−	0.567914i	$-0.192249\pi$
$840$	0	0
$841$	−860.327	−1.02298
$842$	0	0
$843$	0	0
$844$	0	0
$845$	− 682.982i	− 0.808262i
$846$	0	0
$847$	250.852	0.296165
$848$	0	0
$849$	0	0
$850$	0	0
$851$	1801.70i	2.11716i
$852$	0	0
$853$	−349.667	−0.409926	−0.204963	−	0.978770i	$-0.565707\pi$
$853$	−349.667	−0.409926	−0.204963	+	0.978770i	$0.565707\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	− 605.317i	− 0.706321i	−0.935563	−	0.353160i	$-0.885107\pi$
$857$	− 605.317i	− 0.706321i	0.935563	−	0.353160i	$-0.114893\pi$
$858$	0	0
$859$	381.186	0.443755	0.221878	−	0.975075i	$-0.428781\pi$
$859$	381.186	0.443755	0.221878	+	0.975075i	$0.428781\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	− 634.987i	− 0.735791i	−0.929867	−	0.367895i	$-0.880078\pi$
$863$	− 634.987i	− 0.735791i	0.929867	−	0.367895i	$-0.119922\pi$
$864$	0	0
$865$	556.800	0.643700
$866$	0	0
$867$	0	0
$868$	0	0
$869$	885.862i	1.01940i
$870$	0	0
$871$	−33.6119	−0.0385901
$872$	0	0
$873$	0	0
$874$	0	0
$875$	− 1610.97i	− 1.84111i
$876$	0	0
$877$	−343.774	−0.391989	−0.195994	−	0.980605i	$-0.562793\pi$
$877$	−343.774	−0.391989	−0.195994	+	0.980605i	$0.562793\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	− 1109.44i	− 1.25930i	−0.776881	−	0.629648i	$-0.783199\pi$
$881$	− 1109.44i	− 1.25930i	0.776881	−	0.629648i	$-0.216801\pi$
$882$	0	0
$883$	888.121	1.00580	0.502900	−	0.864345i	$-0.332266\pi$
$883$	888.121	1.00580	0.502900	+	0.864345i	$0.332266\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	304.043i	0.342777i	0.985204	+	0.171388i	$0.0548253\pi$
$887$	304.043i	0.342777i	−0.985204	+	0.171388i	$0.945175\pi$
$888$	0	0
$889$	−2377.26	−2.67408
$890$	0	0
$891$	0	0
$892$	0	0
$893$	− 352.581i	− 0.394827i
$894$	0	0
$895$	596.149	0.666088
$896$	0	0
$897$	0	0
$898$	0	0
$899$	− 1439.38i	− 1.60109i
$900$	0	0
$901$	−713.083	−0.791435
$902$	0	0
$903$	0	0
$904$	0	0
$905$	11.4916i	0.0126979i
$906$	0	0
$907$	−576.702	−0.635834	−0.317917	−	0.948119i	$-0.602983\pi$
$907$	−576.702	−0.635834	−0.317917	+	0.948119i	$0.602983\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	− 400.564i	− 0.439697i	−0.975534	−	0.219849i	$-0.929444\pi$
$911$	− 400.564i	− 0.439697i	0.975534	−	0.219849i	$-0.0705564\pi$
$912$	0	0
$913$	1827.86	2.00204
$914$	0	0
$915$	0	0
$916$	0	0
$917$	1278.38i	1.39409i
$918$	0	0
$919$	356.293	0.387696	0.193848	−	0.981032i	$-0.437903\pi$
$919$	356.293	0.387696	0.193848	+	0.981032i	$0.437903\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	− 80.0244i	− 0.0867004i
$924$	0	0
$925$	−497.296	−0.537618
$926$	0	0
$927$	0	0
$928$	0	0
$929$	256.863i	0.276495i	0.990398	+	0.138247i	$0.0441469\pi$
$929$	256.863i	0.276495i	−0.990398	+	0.138247i	$0.955853\pi$
$930$	0	0
$931$	−345.631	−0.371247
$932$	0	0
$933$	0	0
$934$	0	0
$935$	− 692.626i	− 0.740777i
$936$	0	0
$937$	−1569.56	−1.67509	−0.837547	−	0.546365i	$-0.816011\pi$
$937$	−1569.56	−1.67509	−0.837547	+	0.546365i	$0.816011\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	1310.13i	1.39227i	0.717909	+	0.696137i	$0.245099\pi$
$941$	1310.13i	1.39227i	−0.717909	+	0.696137i	$0.754901\pi$
$942$	0	0
$943$	136.704	0.144967
$944$	0	0
$945$	0	0
$946$	0	0
$947$	452.283i	0.477595i	0.971069	+	0.238798i	$0.0767532\pi$
$947$	452.283i	0.477595i	−0.971069	+	0.238798i	$0.923247\pi$
$948$	0	0
$949$	−100.524	−0.105926
$950$	0	0
$951$	0	0
$952$	0	0
$953$	1670.70i	1.75310i	0.481310	+	0.876550i	$0.340161\pi$
$953$	1670.70i	1.75310i	−0.481310	+	0.876550i	$0.659839\pi$
$954$	0	0
$955$	−157.988	−0.165433
$956$	0	0
$957$	0	0
$958$	0	0
$959$	1027.37i	1.07129i
$960$	0	0
$961$	256.767	0.267187
$962$	0	0
$963$	0	0
$964$	0	0
$965$	− 518.873i	− 0.537692i
$966$	0	0
$967$	−1202.12	−1.24314	−0.621572	−	0.783357i	$-0.713506\pi$
$967$	−1202.12	−1.24314	−0.621572	+	0.783357i	$0.713506\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	− 482.574i	− 0.496987i	−0.968634	−	0.248493i	$-0.920065\pi$
$971$	− 482.574i	− 0.496987i	0.968634	−	0.248493i	$-0.0799354\pi$
$972$	0	0
$973$	−725.840	−0.745982
$974$	0	0
$975$	0	0
$976$	0	0
$977$	− 592.682i	− 0.606635i	−0.952890	−	0.303318i	$-0.901906\pi$
$977$	− 592.682i	− 0.606635i	0.952890	−	0.303318i	$-0.0980943\pi$
$978$	0	0
$979$	248.811	0.254148
$980$	0	0
$981$	0	0
$982$	0	0
$983$	− 1711.14i	− 1.74073i	−0.492408	−	0.870365i	$-0.663883\pi$
$983$	− 1711.14i	− 1.74073i	0.492408	−	0.870365i	$-0.336117\pi$
$984$	0	0
$985$	242.894	0.246593
$986$	0	0
$987$	0	0
$988$	0	0
$989$	1246.38i	1.26024i
$990$	0	0
$991$	513.628	0.518293	0.259146	−	0.965838i	$-0.416559\pi$
$991$	513.628	0.518293	0.259146	+	0.965838i	$0.416559\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	1305.32i	1.31188i
$996$	0	0
$997$	1681.33	1.68638	0.843192	−	0.537612i	$-0.180674\pi$
$997$	1681.33	1.68638	0.843192	+	0.537612i	$0.180674\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2916.3.c.b.1457.27		36
3.2	odd	2	inner	2916.3.c.b.1457.10		36
27.5	odd	18		108.3.k.a.29.1	✓	36
27.11	odd	18		324.3.k.a.233.5		36
27.16	even	9		108.3.k.a.41.1	yes	36
27.22	even	9		324.3.k.a.89.5		36
108.43	odd	18		432.3.bc.b.257.6		36
108.59	even	18		432.3.bc.b.353.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.29.1	✓	36	27.5	odd	18
108.3.k.a.41.1	yes	36	27.16	even	9
324.3.k.a.89.5		36	27.22	even	9
324.3.k.a.233.5		36	27.11	odd	18
432.3.bc.b.257.6		36	108.43	odd	18
432.3.bc.b.353.6		36	108.59	even	18
2916.3.c.b.1457.10		36	3.2	odd	2	inner
2916.3.c.b.1457.27		36	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 2916 = 2^{2} \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2916.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.19339i q^{5} -11.8514 q^{7} +O(q^{10})\)	\(q+4.19339i q^{5} -11.8514 q^{7} +11.9234i q^{11} -2.47565 q^{13} +13.8527i q^{17} -3.77921 q^{19} -26.8663i q^{23} +7.41551 q^{25} +41.2471i q^{29} -34.8965 q^{31} -49.6975i q^{35} -67.0616 q^{37} +5.08829i q^{41} -46.3918 q^{43} +93.2950i q^{47} +91.4559 q^{49} +51.4760i q^{53} -49.9992 q^{55} -14.7036i q^{59} +51.2165 q^{61} -10.3814i q^{65} +13.5770 q^{67} +32.3246i q^{71} +40.6051 q^{73} -141.309i q^{77} +74.2963 q^{79} -153.301i q^{83} -58.0899 q^{85} -20.8675i q^{89} +29.3399 q^{91} -15.8477i q^{95} -47.7160 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 180 q^{25} + 252 q^{49} + 18 q^{61} - 90 q^{67} + 126 q^{73} - 198 q^{91}+O(q^{100}) \) 36 * q - 180 * q^25 + 252 * q^49 + 18 * q^61 - 90 * q^67 + 126 * q^73 - 198 * q^91

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