LMFDB - Embedded newform 2016.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2016,2,Mod(1,2016)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2016, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2016.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2016 = 2^{5} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2016.a (trivial)

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:	yes
Analytic conductor:	$16.0978410475$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	2016.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.23607 q^{5} +1.00000 q^{7} +O(q^{10})$	$q+1.23607 q^{5} +1.00000 q^{7} +1.23607 q^{11} -4.47214 q^{13} -5.23607 q^{17} -6.47214 q^{19} -7.70820 q^{23} -3.47214 q^{25} -10.4721 q^{29} +6.47214 q^{31} +1.23607 q^{35} +4.47214 q^{37} -2.76393 q^{41} +4.94427 q^{43} +10.4721 q^{47} +1.00000 q^{49} -8.00000 q^{53} +1.52786 q^{55} +2.47214 q^{59} +4.47214 q^{61} -5.52786 q^{65} -8.00000 q^{67} +2.76393 q^{71} +2.94427 q^{73} +1.23607 q^{77} -4.94427 q^{79} -4.94427 q^{83} -6.47214 q^{85} -15.7082 q^{89} -4.47214 q^{91} -8.00000 q^{95} +10.9443 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5} + 2 q^{7}+O(q^{10}) $ 2 * q - 2 * q^5 + 2 * q^7	$ 2 q - 2 q^{5} + 2 q^{7} - 2 q^{11} - 6 q^{17} - 4 q^{19} - 2 q^{23} + 2 q^{25} - 12 q^{29} + 4 q^{31} - 2 q^{35} - 10 q^{41} - 8 q^{43} + 12 q^{47} + 2 q^{49} - 16 q^{53} + 12 q^{55} - 4 q^{59} - 20 q^{65} - 16 q^{67} + 10 q^{71} - 12 q^{73} - 2 q^{77} + 8 q^{79} + 8 q^{83} - 4 q^{85} - 18 q^{89} - 16 q^{95} + 4 q^{97}+O(q^{100}) $ 2 * q - 2 * q^5 + 2 * q^7 - 2 * q^11 - 6 * q^17 - 4 * q^19 - 2 * q^23 + 2 * q^25 - 12 * q^29 + 4 * q^31 - 2 * q^35 - 10 * q^41 - 8 * q^43 + 12 * q^47 + 2 * q^49 - 16 * q^53 + 12 * q^55 - 4 * q^59 - 20 * q^65 - 16 * q^67 + 10 * q^71 - 12 * q^73 - 2 * q^77 + 8 * q^79 + 8 * q^83 - 4 * q^85 - 18 * q^89 - 16 * q^95 + 4 * q^97

Display 100 coefficients 10 coefficients

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
$5$	1.23607	0.552786	0.276393	−	0.961045i	$-0.410861\pi$
$5$	1.23607	0.552786	0.276393	+	0.961045i	$0.410861\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0	0
$9$	0	0
$10$	0	0
$11$	1.23607	0.372689	0.186344	−	0.982485i	$-0.440336\pi$
$11$	1.23607	0.372689	0.186344	+	0.982485i	$0.440336\pi$
$12$	0	0
$13$	−4.47214	−1.24035	−0.620174	−	0.784465i	$-0.712938\pi$
$13$	−4.47214	−1.24035	−0.620174	+	0.784465i	$0.712938\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−5.23607	−1.26993	−0.634967	−	0.772540i	$-0.718986\pi$
$17$	−5.23607	−1.26993	−0.634967	+	0.772540i	$0.718986\pi$
$18$	0	0
$19$	−6.47214	−1.48481	−0.742405	−	0.669951i	$-0.766315\pi$
$19$	−6.47214	−1.48481	−0.742405	+	0.669951i	$0.766315\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−7.70820	−1.60727	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−7.70820	−1.60727	−0.803636	+	0.595121i	$0.797104\pi$
$24$	0	0
$25$	−3.47214	−0.694427
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−10.4721	−1.94463	−0.972313	−	0.233681i	$-0.924923\pi$
$29$	−10.4721	−1.94463	−0.972313	+	0.233681i	$0.924923\pi$
$30$	0	0
$31$	6.47214	1.16243	0.581215	−	0.813750i	$-0.302578\pi$
$31$	6.47214	1.16243	0.581215	+	0.813750i	$0.302578\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	1.23607	0.208934
$36$	0	0
$37$	4.47214	0.735215	0.367607	−	0.929981i	$-0.380177\pi$
$37$	4.47214	0.735215	0.367607	+	0.929981i	$0.380177\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−2.76393	−0.431654	−0.215827	−	0.976432i	$-0.569245\pi$
$41$	−2.76393	−0.431654	−0.215827	+	0.976432i	$0.569245\pi$
$42$	0	0
$43$	4.94427	0.753994	0.376997	−	0.926214i	$-0.376957\pi$
$43$	4.94427	0.753994	0.376997	+	0.926214i	$0.376957\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	10.4721	1.52752	0.763759	−	0.645501i	$-0.223352\pi$
$47$	10.4721	1.52752	0.763759	+	0.645501i	$0.223352\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−8.00000	−1.09888	−0.549442	−	0.835532i	$-0.685160\pi$
$53$	−8.00000	−1.09888	−0.549442	+	0.835532i	$0.685160\pi$
$54$	0	0
$55$	1.52786	0.206017
$56$	0	0
$57$	0	0
$58$	0	0
$59$	2.47214	0.321845	0.160922	−	0.986967i	$-0.448553\pi$
$59$	2.47214	0.321845	0.160922	+	0.986967i	$0.448553\pi$
$60$	0	0
$61$	4.47214	0.572598	0.286299	−	0.958140i	$-0.407575\pi$
$61$	4.47214	0.572598	0.286299	+	0.958140i	$0.407575\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−5.52786	−0.685647
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	2.76393	0.328018	0.164009	−	0.986459i	$-0.447557\pi$
$71$	2.76393	0.328018	0.164009	+	0.986459i	$0.447557\pi$
$72$	0	0
$73$	2.94427	0.344601	0.172300	−	0.985044i	$-0.444880\pi$
$73$	2.94427	0.344601	0.172300	+	0.985044i	$0.444880\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	1.23607	0.140863
$78$	0	0
$79$	−4.94427	−0.556274	−0.278137	−	0.960541i	$-0.589717\pi$
$79$	−4.94427	−0.556274	−0.278137	+	0.960541i	$0.589717\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	−4.94427	−0.542704	−0.271352	−	0.962480i	$-0.587471\pi$
$83$	−4.94427	−0.542704	−0.271352	+	0.962480i	$0.587471\pi$
$84$	0	0
$85$	−6.47214	−0.702002
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−15.7082	−1.66507	−0.832533	−	0.553975i	$-0.813110\pi$
$89$	−15.7082	−1.66507	−0.832533	+	0.553975i	$0.813110\pi$
$90$	0	0
$91$	−4.47214	−0.468807
$92$	0	0
$93$	0	0
$94$	0	0
$95$	−8.00000	−0.820783
$96$	0	0
$97$	10.9443	1.11122	0.555611	−	0.831442i	$-0.312484\pi$
$97$	10.9443	1.11122	0.555611	+	0.831442i	$0.312484\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−4.29180	−0.427050	−0.213525	−	0.976938i	$-0.568494\pi$
$101$	−4.29180	−0.427050	−0.213525	+	0.976938i	$0.568494\pi$
$102$	0	0
$103$	9.52786	0.938808	0.469404	−	0.882983i	$-0.344469\pi$
$103$	9.52786	0.938808	0.469404	+	0.882983i	$0.344469\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−6.76393	−0.653894	−0.326947	−	0.945043i	$-0.606020\pi$
$107$	−6.76393	−0.653894	−0.326947	+	0.945043i	$0.606020\pi$
$108$	0	0
$109$	6.94427	0.665141	0.332570	−	0.943078i	$-0.392084\pi$
$109$	6.94427	0.665141	0.332570	+	0.943078i	$0.392084\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	4.94427	0.465118	0.232559	−	0.972582i	$-0.425290\pi$
$113$	4.94427	0.465118	0.232559	+	0.972582i	$0.425290\pi$
$114$	0	0
$115$	−9.52786	−0.888478
$116$	0	0
$117$	0	0
$118$	0	0
$119$	−5.23607	−0.479990
$120$	0	0
$121$	−9.47214	−0.861103
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−10.4721	−0.936656
$126$	0	0
$127$	17.8885	1.58735	0.793676	−	0.608341i	$-0.208165\pi$
$127$	17.8885	1.58735	0.793676	+	0.608341i	$0.208165\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	16.0000	1.39793	0.698963	−	0.715158i	$-0.253645\pi$
$131$	16.0000	1.39793	0.698963	+	0.715158i	$0.253645\pi$
$132$	0	0
$133$	−6.47214	−0.561205
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−10.4721	−0.894695	−0.447347	−	0.894360i	$-0.647631\pi$
$137$	−10.4721	−0.894695	−0.447347	+	0.894360i	$0.647631\pi$
$138$	0	0
$139$	−12.9443	−1.09792	−0.548959	−	0.835849i	$-0.684976\pi$
$139$	−12.9443	−1.09792	−0.548959	+	0.835849i	$0.684976\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−5.52786	−0.462263
$144$	0	0
$145$	−12.9443	−1.07496
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−17.8885	−1.46549	−0.732743	−	0.680505i	$-0.761760\pi$
$149$	−17.8885	−1.46549	−0.732743	+	0.680505i	$0.761760\pi$
$150$	0	0
$151$	20.9443	1.70442	0.852210	−	0.523199i	$-0.175262\pi$
$151$	20.9443	1.70442	0.852210	+	0.523199i	$0.175262\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	8.00000	0.642575
$156$	0	0
$157$	7.52786	0.600789	0.300394	−	0.953815i	$-0.402882\pi$
$157$	7.52786	0.600789	0.300394	+	0.953815i	$0.402882\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−7.70820	−0.607492
$162$	0	0
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	15.4164	1.19296	0.596479	−	0.802629i	$-0.296566\pi$
$167$	15.4164	1.19296	0.596479	+	0.802629i	$0.296566\pi$
$168$	0	0
$169$	7.00000	0.538462
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−4.29180	−0.326299	−0.163150	−	0.986601i	$-0.552165\pi$
$173$	−4.29180	−0.326299	−0.163150	+	0.986601i	$0.552165\pi$
$174$	0	0
$175$	−3.47214	−0.262469
$176$	0	0
$177$	0	0
$178$	0	0
$179$	−22.1803	−1.65784	−0.828918	−	0.559370i	$-0.811043\pi$
$179$	−22.1803	−1.65784	−0.828918	+	0.559370i	$0.811043\pi$
$180$	0	0
$181$	0.472136	0.0350936	0.0175468	−	0.999846i	$-0.494414\pi$
$181$	0.472136	0.0350936	0.0175468	+	0.999846i	$0.494414\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	5.52786	0.406417
$186$	0	0
$187$	−6.47214	−0.473289
$188$	0	0
$189$	0	0
$190$	0	0
$191$	4.65248	0.336641	0.168321	−	0.985732i	$-0.446166\pi$
$191$	4.65248	0.336641	0.168321	+	0.985732i	$0.446166\pi$
$192$	0	0
$193$	3.52786	0.253941	0.126971	−	0.991906i	$-0.459475\pi$
$193$	3.52786	0.253941	0.126971	+	0.991906i	$0.459475\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	12.9443	0.922241	0.461121	−	0.887337i	$-0.347448\pi$
$197$	12.9443	0.922241	0.461121	+	0.887337i	$0.347448\pi$
$198$	0	0
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	−10.4721	−0.735000
$204$	0	0
$205$	−3.41641	−0.238612
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−8.00000	−0.553372
$210$	0	0
$211$	−24.0000	−1.65223	−0.826114	−	0.563503i	$-0.809453\pi$
$211$	−24.0000	−1.65223	−0.826114	+	0.563503i	$0.809453\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	6.11146	0.416798
$216$	0	0
$217$	6.47214	0.439357
$218$	0	0
$219$	0	0
$220$	0	0
$221$	23.4164	1.57516
$222$	0	0
$223$	−4.94427	−0.331093	−0.165546	−	0.986202i	$-0.552939\pi$
$223$	−4.94427	−0.331093	−0.165546	+	0.986202i	$0.552939\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−28.3607	−1.88236	−0.941182	−	0.337899i	$-0.890284\pi$
$227$	−28.3607	−1.88236	−0.941182	+	0.337899i	$0.890284\pi$
$228$	0	0
$229$	3.52786	0.233128	0.116564	−	0.993183i	$-0.462812\pi$
$229$	3.52786	0.233128	0.116564	+	0.993183i	$0.462812\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	20.3607	1.33387	0.666936	−	0.745115i	$-0.267605\pi$
$233$	20.3607	1.33387	0.666936	+	0.745115i	$0.267605\pi$
$234$	0	0
$235$	12.9443	0.844391
$236$	0	0
$237$	0	0
$238$	0	0
$239$	13.2361	0.856170	0.428085	−	0.903738i	$-0.359188\pi$
$239$	13.2361	0.856170	0.428085	+	0.903738i	$0.359188\pi$
$240$	0	0
$241$	−27.8885	−1.79646	−0.898230	−	0.439527i	$-0.855146\pi$
$241$	−27.8885	−1.79646	−0.898230	+	0.439527i	$0.855146\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	1.23607	0.0789695
$246$	0	0
$247$	28.9443	1.84168
$248$	0	0
$249$	0	0
$250$	0	0
$251$	23.4164	1.47803	0.739015	−	0.673689i	$-0.235291\pi$
$251$	23.4164	1.47803	0.739015	+	0.673689i	$0.235291\pi$
$252$	0	0
$253$	−9.52786	−0.599012
$254$	0	0
$255$	0	0
$256$	0	0
$257$	16.2918	1.01625	0.508127	−	0.861282i	$-0.330338\pi$
$257$	16.2918	1.01625	0.508127	+	0.861282i	$0.330338\pi$
$258$	0	0
$259$	4.47214	0.277885
$260$	0	0
$261$	0	0
$262$	0	0
$263$	−5.81966	−0.358856	−0.179428	−	0.983771i	$-0.557425\pi$
$263$	−5.81966	−0.358856	−0.179428	+	0.983771i	$0.557425\pi$
$264$	0	0
$265$	−9.88854	−0.607448
$266$	0	0
$267$	0	0
$268$	0	0
$269$	1.23607	0.0753644	0.0376822	−	0.999290i	$-0.488003\pi$
$269$	1.23607	0.0753644	0.0376822	+	0.999290i	$0.488003\pi$
$270$	0	0
$271$	−19.4164	−1.17946	−0.589731	−	0.807599i	$-0.700766\pi$
$271$	−19.4164	−1.17946	−0.589731	+	0.807599i	$0.700766\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−4.29180	−0.258805
$276$	0	0
$277$	−20.4721	−1.23005	−0.615026	−	0.788507i	$-0.710854\pi$
$277$	−20.4721	−1.23005	−0.615026	+	0.788507i	$0.710854\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−15.4164	−0.919666	−0.459833	−	0.888005i	$-0.652091\pi$
$281$	−15.4164	−0.919666	−0.459833	+	0.888005i	$0.652091\pi$
$282$	0	0
$283$	6.47214	0.384729	0.192364	−	0.981324i	$-0.438384\pi$
$283$	6.47214	0.384729	0.192364	+	0.981324i	$0.438384\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−2.76393	−0.163150
$288$	0	0
$289$	10.4164	0.612730
$290$	0	0
$291$	0	0
$292$	0	0
$293$	9.81966	0.573671	0.286835	−	0.957980i	$-0.407397\pi$
$293$	9.81966	0.573671	0.286835	+	0.957980i	$0.407397\pi$
$294$	0	0
$295$	3.05573	0.177911
$296$	0	0
$297$	0	0
$298$	0	0
$299$	34.4721	1.99358
$300$	0	0
$301$	4.94427	0.284983
$302$	0	0
$303$	0	0
$304$	0	0
$305$	5.52786	0.316525
$306$	0	0
$307$	−9.52786	−0.543784	−0.271892	−	0.962328i	$-0.587649\pi$
$307$	−9.52786	−0.543784	−0.271892	+	0.962328i	$0.587649\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−15.4164	−0.874184	−0.437092	−	0.899417i	$-0.643992\pi$
$311$	−15.4164	−0.874184	−0.437092	+	0.899417i	$0.643992\pi$
$312$	0	0
$313$	19.8885	1.12417	0.562083	−	0.827081i	$-0.310000\pi$
$313$	19.8885	1.12417	0.562083	+	0.827081i	$0.310000\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	3.05573	0.171627	0.0858134	−	0.996311i	$-0.472651\pi$
$317$	3.05573	0.171627	0.0858134	+	0.996311i	$0.472651\pi$
$318$	0	0
$319$	−12.9443	−0.724740
$320$	0	0
$321$	0	0
$322$	0	0
$323$	33.8885	1.88561
$324$	0	0
$325$	15.5279	0.861331
$326$	0	0
$327$	0	0
$328$	0	0
$329$	10.4721	0.577348
$330$	0	0
$331$	−17.8885	−0.983243	−0.491622	−	0.870809i	$-0.663596\pi$
$331$	−17.8885	−0.983243	−0.491622	+	0.870809i	$0.663596\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	−9.88854	−0.540269
$336$	0	0
$337$	23.8885	1.30129	0.650646	−	0.759381i	$-0.274498\pi$
$337$	23.8885	1.30129	0.650646	+	0.759381i	$0.274498\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	8.00000	0.433224
$342$	0	0
$343$	1.00000	0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−25.2361	−1.35474	−0.677372	−	0.735641i	$-0.736881\pi$
$347$	−25.2361	−1.35474	−0.677372	+	0.735641i	$0.736881\pi$
$348$	0	0
$349$	−11.5279	−0.617072	−0.308536	−	0.951213i	$-0.599839\pi$
$349$	−11.5279	−0.617072	−0.308536	+	0.951213i	$0.599839\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−10.1803	−0.541845	−0.270922	−	0.962601i	$-0.587329\pi$
$353$	−10.1803	−0.541845	−0.270922	+	0.962601i	$0.587329\pi$
$354$	0	0
$355$	3.41641	0.181324
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−21.2361	−1.12080	−0.560398	−	0.828223i	$-0.689352\pi$
$359$	−21.2361	−1.12080	−0.560398	+	0.828223i	$0.689352\pi$
$360$	0	0
$361$	22.8885	1.20466
$362$	0	0
$363$	0	0
$364$	0	0
$365$	3.63932	0.190491
$366$	0	0
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	−8.00000	−0.415339
$372$	0	0
$373$	23.8885	1.23690	0.618451	−	0.785823i	$-0.287761\pi$
$373$	23.8885	1.23690	0.618451	+	0.785823i	$0.287761\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	46.8328	2.41201
$378$	0	0
$379$	24.0000	1.23280	0.616399	−	0.787434i	$-0.288591\pi$
$379$	24.0000	1.23280	0.616399	+	0.787434i	$0.288591\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	32.0000	1.63512	0.817562	−	0.575841i	$-0.195325\pi$
$383$	32.0000	1.63512	0.817562	+	0.575841i	$0.195325\pi$
$384$	0	0
$385$	1.52786	0.0778672
$386$	0	0
$387$	0	0
$388$	0	0
$389$	−10.4721	−0.530958	−0.265479	−	0.964117i	$-0.585530\pi$
$389$	−10.4721	−0.530958	−0.265479	+	0.964117i	$0.585530\pi$
$390$	0	0
$391$	40.3607	2.04113
$392$	0	0
$393$	0	0
$394$	0	0
$395$	−6.11146	−0.307501
$396$	0	0
$397$	−8.47214	−0.425204	−0.212602	−	0.977139i	$-0.568194\pi$
$397$	−8.47214	−0.425204	−0.212602	+	0.977139i	$0.568194\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	26.4721	1.32196	0.660978	−	0.750406i	$-0.270142\pi$
$401$	26.4721	1.32196	0.660978	+	0.750406i	$0.270142\pi$
$402$	0	0
$403$	−28.9443	−1.44182
$404$	0	0
$405$	0	0
$406$	0	0
$407$	5.52786	0.274006
$408$	0	0
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	2.47214	0.121646
$414$	0	0
$415$	−6.11146	−0.300000
$416$	0	0
$417$	0	0
$418$	0	0
$419$	2.47214	0.120772	0.0603859	−	0.998175i	$-0.480767\pi$
$419$	2.47214	0.120772	0.0603859	+	0.998175i	$0.480767\pi$
$420$	0	0
$421$	5.41641	0.263980	0.131990	−	0.991251i	$-0.457863\pi$
$421$	5.41641	0.263980	0.131990	+	0.991251i	$0.457863\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	18.1803	0.881876
$426$	0	0
$427$	4.47214	0.216422
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−31.1246	−1.49922	−0.749610	−	0.661880i	$-0.769759\pi$
$431$	−31.1246	−1.49922	−0.749610	+	0.661880i	$0.769759\pi$
$432$	0	0
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	49.8885	2.38649
$438$	0	0
$439$	30.8328	1.47157	0.735785	−	0.677215i	$-0.236813\pi$
$439$	30.8328	1.47157	0.735785	+	0.677215i	$0.236813\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−30.1803	−1.43391	−0.716956	−	0.697119i	$-0.754465\pi$
$443$	−30.1803	−1.43391	−0.716956	+	0.697119i	$0.754465\pi$
$444$	0	0
$445$	−19.4164	−0.920426
$446$	0	0
$447$	0	0
$448$	0	0
$449$	4.94427	0.233335	0.116667	−	0.993171i	$-0.462779\pi$
$449$	4.94427	0.233335	0.116667	+	0.993171i	$0.462779\pi$
$450$	0	0
$451$	−3.41641	−0.160872
$452$	0	0
$453$	0	0
$454$	0	0
$455$	−5.52786	−0.259150
$456$	0	0
$457$	−35.8885	−1.67880	−0.839398	−	0.543518i	$-0.817092\pi$
$457$	−35.8885	−1.67880	−0.839398	+	0.543518i	$0.817092\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	3.70820	0.172708	0.0863541	−	0.996265i	$-0.472478\pi$
$461$	3.70820	0.172708	0.0863541	+	0.996265i	$0.472478\pi$
$462$	0	0
$463$	−17.8885	−0.831351	−0.415676	−	0.909513i	$-0.636455\pi$
$463$	−17.8885	−0.831351	−0.415676	+	0.909513i	$0.636455\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	34.4721	1.59518	0.797590	−	0.603200i	$-0.206108\pi$
$467$	34.4721	1.59518	0.797590	+	0.603200i	$0.206108\pi$
$468$	0	0
$469$	−8.00000	−0.369406
$470$	0	0
$471$	0	0
$472$	0	0
$473$	6.11146	0.281005
$474$	0	0
$475$	22.4721	1.03109
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−0.583592	−0.0266650	−0.0133325	−	0.999911i	$-0.504244\pi$
$479$	−0.583592	−0.0266650	−0.0133325	+	0.999911i	$0.504244\pi$
$480$	0	0
$481$	−20.0000	−0.911922
$482$	0	0
$483$	0	0
$484$	0	0
$485$	13.5279	0.614269
$486$	0	0
$487$	−30.8328	−1.39717	−0.698584	−	0.715528i	$-0.746186\pi$
$487$	−30.8328	−1.39717	−0.698584	+	0.715528i	$0.746186\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−16.0689	−0.725179	−0.362589	−	0.931949i	$-0.618107\pi$
$491$	−16.0689	−0.725179	−0.362589	+	0.931949i	$0.618107\pi$
$492$	0	0
$493$	54.8328	2.46955
$494$	0	0
$495$	0	0
$496$	0	0
$497$	2.76393	0.123979
$498$	0	0
$499$	−11.0557	−0.494922	−0.247461	−	0.968898i	$-0.579596\pi$
$499$	−11.0557	−0.494922	−0.247461	+	0.968898i	$0.579596\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	11.0557	0.492951	0.246475	−	0.969149i	$-0.420728\pi$
$503$	11.0557	0.492951	0.246475	+	0.969149i	$0.420728\pi$
$504$	0	0
$505$	−5.30495	−0.236067
$506$	0	0
$507$	0	0
$508$	0	0
$509$	35.1246	1.55687	0.778436	−	0.627725i	$-0.216014\pi$
$509$	35.1246	1.55687	0.778436	+	0.627725i	$0.216014\pi$
$510$	0	0
$511$	2.94427	0.130247
$512$	0	0
$513$	0	0
$514$	0	0
$515$	11.7771	0.518960
$516$	0	0
$517$	12.9443	0.569288
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−15.1246	−0.662621	−0.331311	−	0.943522i	$-0.607491\pi$
$521$	−15.1246	−0.662621	−0.331311	+	0.943522i	$0.607491\pi$
$522$	0	0
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−33.8885	−1.47621
$528$	0	0
$529$	36.4164	1.58332
$530$	0	0
$531$	0	0
$532$	0	0
$533$	12.3607	0.535400
$534$	0	0
$535$	−8.36068	−0.361464
$536$	0	0
$537$	0	0
$538$	0	0
$539$	1.23607	0.0532412
$540$	0	0
$541$	−6.36068	−0.273467	−0.136733	−	0.990608i	$-0.543660\pi$
$541$	−6.36068	−0.273467	−0.136733	+	0.990608i	$0.543660\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	8.58359	0.367681
$546$	0	0
$547$	−14.8328	−0.634205	−0.317103	−	0.948391i	$-0.602710\pi$
$547$	−14.8328	−0.634205	−0.317103	+	0.948391i	$0.602710\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	67.7771	2.88740
$552$	0	0
$553$	−4.94427	−0.210252
$554$	0	0
$555$	0	0
$556$	0	0
$557$	3.05573	0.129475	0.0647377	−	0.997902i	$-0.479379\pi$
$557$	3.05573	0.129475	0.0647377	+	0.997902i	$0.479379\pi$
$558$	0	0
$559$	−22.1115	−0.935215
$560$	0	0
$561$	0	0
$562$	0	0
$563$	33.3050	1.40364	0.701818	−	0.712356i	$-0.252372\pi$
$563$	33.3050	1.40364	0.701818	+	0.712356i	$0.252372\pi$
$564$	0	0
$565$	6.11146	0.257111
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−26.4721	−1.10977	−0.554885	−	0.831927i	$-0.687238\pi$
$569$	−26.4721	−1.10977	−0.554885	+	0.831927i	$0.687238\pi$
$570$	0	0
$571$	11.0557	0.462668	0.231334	−	0.972874i	$-0.425691\pi$
$571$	11.0557	0.462668	0.231334	+	0.972874i	$0.425691\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	26.7639	1.11613
$576$	0	0
$577$	−30.0000	−1.24892	−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000	−1.24892	−0.624458	+	0.781058i	$0.714680\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	−4.94427	−0.205123
$582$	0	0
$583$	−9.88854	−0.409542
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−7.41641	−0.306108	−0.153054	−	0.988218i	$-0.548911\pi$
$587$	−7.41641	−0.306108	−0.153054	+	0.988218i	$0.548911\pi$
$588$	0	0
$589$	−41.8885	−1.72599
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−23.1246	−0.949614	−0.474807	−	0.880090i	$-0.657482\pi$
$593$	−23.1246	−0.949614	−0.474807	+	0.880090i	$0.657482\pi$
$594$	0	0
$595$	−6.47214	−0.265332
$596$	0	0
$597$	0	0
$598$	0	0
$599$	−29.2361	−1.19455	−0.597277	−	0.802035i	$-0.703751\pi$
$599$	−29.2361	−1.19455	−0.597277	+	0.802035i	$0.703751\pi$
$600$	0	0
$601$	35.8885	1.46392	0.731962	−	0.681345i	$-0.238605\pi$
$601$	35.8885	1.46392	0.731962	+	0.681345i	$0.238605\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	−11.7082	−0.476006
$606$	0	0
$607$	−11.0557	−0.448738	−0.224369	−	0.974504i	$-0.572032\pi$
$607$	−11.0557	−0.448738	−0.224369	+	0.974504i	$0.572032\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−46.8328	−1.89465
$612$	0	0
$613$	−40.8328	−1.64922	−0.824611	−	0.565700i	$-0.808606\pi$
$613$	−40.8328	−1.64922	−0.824611	+	0.565700i	$0.808606\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	37.5279	1.51081	0.755407	−	0.655255i	$-0.227439\pi$
$617$	37.5279	1.51081	0.755407	+	0.655255i	$0.227439\pi$
$618$	0	0
$619$	28.9443	1.16337	0.581684	−	0.813415i	$-0.302394\pi$
$619$	28.9443	1.16337	0.581684	+	0.813415i	$0.302394\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−15.7082	−0.629336
$624$	0	0
$625$	4.41641	0.176656
$626$	0	0
$627$	0	0
$628$	0	0
$629$	−23.4164	−0.933673
$630$	0	0
$631$	−17.8885	−0.712132	−0.356066	−	0.934461i	$-0.615882\pi$
$631$	−17.8885	−0.712132	−0.356066	+	0.934461i	$0.615882\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	22.1115	0.877466
$636$	0	0
$637$	−4.47214	−0.177192
$638$	0	0
$639$	0	0
$640$	0	0
$641$	30.2492	1.19477	0.597386	−	0.801954i	$-0.296206\pi$
$641$	30.2492	1.19477	0.597386	+	0.801954i	$0.296206\pi$
$642$	0	0
$643$	3.41641	0.134730	0.0673650	−	0.997728i	$-0.478541\pi$
$643$	3.41641	0.134730	0.0673650	+	0.997728i	$0.478541\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−21.5279	−0.846348	−0.423174	−	0.906049i	$-0.639084\pi$
$647$	−21.5279	−0.846348	−0.423174	+	0.906049i	$0.639084\pi$
$648$	0	0
$649$	3.05573	0.119948
$650$	0	0
$651$	0	0
$652$	0	0
$653$	15.4164	0.603291	0.301645	−	0.953420i	$-0.402464\pi$
$653$	15.4164	0.603291	0.301645	+	0.953420i	$0.402464\pi$
$654$	0	0
$655$	19.7771	0.772755
$656$	0	0
$657$	0	0
$658$	0	0
$659$	−0.652476	−0.0254169	−0.0127084	−	0.999919i	$-0.504045\pi$
$659$	−0.652476	−0.0254169	−0.0127084	+	0.999919i	$0.504045\pi$
$660$	0	0
$661$	15.5279	0.603964	0.301982	−	0.953314i	$-0.402352\pi$
$661$	15.5279	0.603964	0.301982	+	0.953314i	$0.402352\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−8.00000	−0.310227
$666$	0	0
$667$	80.7214	3.12554
$668$	0	0
$669$	0	0
$670$	0	0
$671$	5.52786	0.213401
$672$	0	0
$673$	−19.3050	−0.744151	−0.372076	−	0.928202i	$-0.621354\pi$
$673$	−19.3050	−0.744151	−0.372076	+	0.928202i	$0.621354\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−45.0132	−1.73000	−0.864998	−	0.501775i	$-0.832680\pi$
$677$	−45.0132	−1.73000	−0.864998	+	0.501775i	$0.832680\pi$
$678$	0	0
$679$	10.9443	0.420003
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−14.1803	−0.542596	−0.271298	−	0.962495i	$-0.587453\pi$
$683$	−14.1803	−0.542596	−0.271298	+	0.962495i	$0.587453\pi$
$684$	0	0
$685$	−12.9443	−0.494575
$686$	0	0
$687$	0	0
$688$	0	0
$689$	35.7771	1.36300
$690$	0	0
$691$	−6.11146	−0.232491	−0.116245	−	0.993221i	$-0.537086\pi$
$691$	−6.11146	−0.232491	−0.116245	+	0.993221i	$0.537086\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−16.0000	−0.606915
$696$	0	0
$697$	14.4721	0.548171
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−15.4164	−0.582270	−0.291135	−	0.956682i	$-0.594033\pi$
$701$	−15.4164	−0.582270	−0.291135	+	0.956682i	$0.594033\pi$
$702$	0	0
$703$	−28.9443	−1.09165
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−4.29180	−0.161410
$708$	0	0
$709$	14.9443	0.561244	0.280622	−	0.959818i	$-0.409459\pi$
$709$	14.9443	0.561244	0.280622	+	0.959818i	$0.409459\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−49.8885	−1.86834
$714$	0	0
$715$	−6.83282	−0.255533
$716$	0	0
$717$	0	0
$718$	0	0
$719$	36.9443	1.37779	0.688894	−	0.724862i	$-0.258096\pi$
$719$	36.9443	1.37779	0.688894	+	0.724862i	$0.258096\pi$
$720$	0	0
$721$	9.52786	0.354836
$722$	0	0
$723$	0	0
$724$	0	0
$725$	36.3607	1.35040
$726$	0	0
$727$	−32.3607	−1.20019	−0.600096	−	0.799928i	$-0.704871\pi$
$727$	−32.3607	−1.20019	−0.600096	+	0.799928i	$0.704871\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	−25.8885	−0.957522
$732$	0	0
$733$	15.3050	0.565301	0.282651	−	0.959223i	$-0.408786\pi$
$733$	15.3050	0.565301	0.282651	+	0.959223i	$0.408786\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−9.88854	−0.364249
$738$	0	0
$739$	40.0000	1.47142	0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000	1.47142	0.735712	+	0.677295i	$0.236848\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	35.4853	1.30183	0.650915	−	0.759151i	$-0.274386\pi$
$743$	35.4853	1.30183	0.650915	+	0.759151i	$0.274386\pi$
$744$	0	0
$745$	−22.1115	−0.810101
$746$	0	0
$747$	0	0
$748$	0	0
$749$	−6.76393	−0.247149
$750$	0	0
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	25.8885	0.942181
$756$	0	0
$757$	−1.05573	−0.0383711	−0.0191855	−	0.999816i	$-0.506107\pi$
$757$	−1.05573	−0.0383711	−0.0191855	+	0.999816i	$0.506107\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	10.1803	0.369037	0.184519	−	0.982829i	$-0.440927\pi$
$761$	10.1803	0.369037	0.184519	+	0.982829i	$0.440927\pi$
$762$	0	0
$763$	6.94427	0.251400
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−11.0557	−0.399199
$768$	0	0
$769$	−7.88854	−0.284468	−0.142234	−	0.989833i	$-0.545429\pi$
$769$	−7.88854	−0.284468	−0.142234	+	0.989833i	$0.545429\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	−25.2361	−0.907678	−0.453839	−	0.891084i	$-0.649946\pi$
$773$	−25.2361	−0.907678	−0.453839	+	0.891084i	$0.649946\pi$
$774$	0	0
$775$	−22.4721	−0.807223
$776$	0	0
$777$	0	0
$778$	0	0
$779$	17.8885	0.640924
$780$	0	0
$781$	3.41641	0.122249
$782$	0	0
$783$	0	0
$784$	0	0
$785$	9.30495	0.332108
$786$	0	0
$787$	−54.8328	−1.95458	−0.977289	−	0.211909i	$-0.932032\pi$
$787$	−54.8328	−1.95458	−0.977289	+	0.211909i	$0.932032\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	4.94427	0.175798
$792$	0	0
$793$	−20.0000	−0.710221
$794$	0	0
$795$	0	0
$796$	0	0
$797$	32.6525	1.15661	0.578305	−	0.815821i	$-0.303714\pi$
$797$	32.6525	1.15661	0.578305	+	0.815821i	$0.303714\pi$
$798$	0	0
$799$	−54.8328	−1.93985
$800$	0	0
$801$	0	0
$802$	0	0
$803$	3.63932	0.128429
$804$	0	0
$805$	−9.52786	−0.335813
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−32.0000	−1.12506	−0.562530	−	0.826777i	$-0.690172\pi$
$809$	−32.0000	−1.12506	−0.562530	+	0.826777i	$0.690172\pi$
$810$	0	0
$811$	41.8885	1.47091	0.735453	−	0.677576i	$-0.236969\pi$
$811$	41.8885	1.47091	0.735453	+	0.677576i	$0.236969\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−9.88854	−0.346381
$816$	0	0
$817$	−32.0000	−1.11954
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−19.0557	−0.665049	−0.332525	−	0.943095i	$-0.607900\pi$
$821$	−19.0557	−0.665049	−0.332525	+	0.943095i	$0.607900\pi$
$822$	0	0
$823$	36.9443	1.28780	0.643898	−	0.765111i	$-0.277316\pi$
$823$	36.9443	1.28780	0.643898	+	0.765111i	$0.277316\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	38.1803	1.32766	0.663830	−	0.747883i	$-0.268930\pi$
$827$	38.1803	1.32766	0.663830	+	0.747883i	$0.268930\pi$
$828$	0	0
$829$	40.4721	1.40566	0.702828	−	0.711360i	$-0.251920\pi$
$829$	40.4721	1.40566	0.702828	+	0.711360i	$0.251920\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−5.23607	−0.181419
$834$	0	0
$835$	19.0557	0.659451
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−5.52786	−0.190843	−0.0954215	−	0.995437i	$-0.530420\pi$
$839$	−5.52786	−0.190843	−0.0954215	+	0.995437i	$0.530420\pi$
$840$	0	0
$841$	80.6656	2.78157
$842$	0	0
$843$	0	0
$844$	0	0
$845$	8.65248	0.297654
$846$	0	0
$847$	−9.47214	−0.325466
$848$	0	0
$849$	0	0
$850$	0	0
$851$	−34.4721	−1.18169
$852$	0	0
$853$	−45.4164	−1.55503	−0.777514	−	0.628866i	$-0.783520\pi$
$853$	−45.4164	−1.55503	−0.777514	+	0.628866i	$0.783520\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	10.1803	0.347754	0.173877	−	0.984767i	$-0.444371\pi$
$857$	10.1803	0.347754	0.173877	+	0.984767i	$0.444371\pi$
$858$	0	0
$859$	25.5279	0.870999	0.435500	−	0.900189i	$-0.356572\pi$
$859$	25.5279	0.870999	0.435500	+	0.900189i	$0.356572\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−21.8197	−0.742750	−0.371375	−	0.928483i	$-0.621114\pi$
$863$	−21.8197	−0.742750	−0.371375	+	0.928483i	$0.621114\pi$
$864$	0	0
$865$	−5.30495	−0.180374
$866$	0	0
$867$	0	0
$868$	0	0
$869$	−6.11146	−0.207317
$870$	0	0
$871$	35.7771	1.21226
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−10.4721	−0.354023
$876$	0	0
$877$	44.8328	1.51390	0.756948	−	0.653475i	$-0.226689\pi$
$877$	44.8328	1.51390	0.756948	+	0.653475i	$0.226689\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−39.1246	−1.31814	−0.659071	−	0.752081i	$-0.729050\pi$
$881$	−39.1246	−1.31814	−0.659071	+	0.752081i	$0.729050\pi$
$882$	0	0
$883$	4.94427	0.166388	0.0831940	−	0.996533i	$-0.473488\pi$
$883$	4.94427	0.166388	0.0831940	+	0.996533i	$0.473488\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	21.5279	0.722835	0.361417	−	0.932404i	$-0.382293\pi$
$887$	21.5279	0.722835	0.361417	+	0.932404i	$0.382293\pi$
$888$	0	0
$889$	17.8885	0.599963
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−67.7771	−2.26807
$894$	0	0
$895$	−27.4164	−0.916429
$896$	0	0
$897$	0	0
$898$	0	0
$899$	−67.7771	−2.26049
$900$	0	0
$901$	41.8885	1.39551
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0.583592	0.0193993
$906$	0	0
$907$	−4.94427	−0.164172	−0.0820859	−	0.996625i	$-0.526158\pi$
$907$	−4.94427	−0.164172	−0.0820859	+	0.996625i	$0.526158\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−15.1246	−0.501101	−0.250550	−	0.968104i	$-0.580612\pi$
$911$	−15.1246	−0.501101	−0.250550	+	0.968104i	$0.580612\pi$
$912$	0	0
$913$	−6.11146	−0.202260
$914$	0	0
$915$	0	0
$916$	0	0
$917$	16.0000	0.528367
$918$	0	0
$919$	−27.0557	−0.892486	−0.446243	−	0.894912i	$-0.647238\pi$
$919$	−27.0557	−0.892486	−0.446243	+	0.894912i	$0.647238\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	−12.3607	−0.406857
$924$	0	0
$925$	−15.5279	−0.510553
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−50.7639	−1.66551	−0.832755	−	0.553641i	$-0.813238\pi$
$929$	−50.7639	−1.66551	−0.832755	+	0.553641i	$0.813238\pi$
$930$	0	0
$931$	−6.47214	−0.212116
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−8.00000	−0.261628
$936$	0	0
$937$	−2.94427	−0.0961852	−0.0480926	−	0.998843i	$-0.515314\pi$
$937$	−2.94427	−0.0961852	−0.0480926	+	0.998843i	$0.515314\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−52.4296	−1.70915	−0.854577	−	0.519324i	$-0.826184\pi$
$941$	−52.4296	−1.70915	−0.854577	+	0.519324i	$0.826184\pi$
$942$	0	0
$943$	21.3050	0.693785
$944$	0	0
$945$	0	0
$946$	0	0
$947$	11.1246	0.361501	0.180751	−	0.983529i	$-0.442147\pi$
$947$	11.1246	0.361501	0.180751	+	0.983529i	$0.442147\pi$
$948$	0	0
$949$	−13.1672	−0.427425
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−51.7771	−1.67722	−0.838612	−	0.544729i	$-0.816633\pi$
$953$	−51.7771	−1.67722	−0.838612	+	0.544729i	$0.816633\pi$
$954$	0	0
$955$	5.75078	0.186091
$956$	0	0
$957$	0	0
$958$	0	0
$959$	−10.4721	−0.338163
$960$	0	0
$961$	10.8885	0.351243
$962$	0	0
$963$	0	0
$964$	0	0
$965$	4.36068	0.140375
$966$	0	0
$967$	59.7771	1.92230	0.961151	−	0.276024i	$-0.0890169\pi$
$967$	59.7771	1.92230	0.961151	+	0.276024i	$0.0890169\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	25.8885	0.830803	0.415401	−	0.909638i	$-0.363641\pi$
$971$	25.8885	0.830803	0.415401	+	0.909638i	$0.363641\pi$
$972$	0	0
$973$	−12.9443	−0.414974
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−30.2492	−0.967758	−0.483879	−	0.875135i	$-0.660773\pi$
$977$	−30.2492	−0.967758	−0.483879	+	0.875135i	$0.660773\pi$
$978$	0	0
$979$	−19.4164	−0.620551
$980$	0	0
$981$	0	0
$982$	0	0
$983$	−4.94427	−0.157698	−0.0788489	−	0.996887i	$-0.525124\pi$
$983$	−4.94427	−0.157698	−0.0788489	+	0.996887i	$0.525124\pi$
$984$	0	0
$985$	16.0000	0.509802
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−38.1115	−1.21187
$990$	0	0
$991$	−62.8328	−1.99595	−0.997975	−	0.0636060i	$-0.979740\pi$
$991$	−62.8328	−1.99595	−0.997975	+	0.0636060i	$0.979740\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	9.88854	0.313488
$996$	0	0
$997$	5.63932	0.178599	0.0892995	−	0.996005i	$-0.471537\pi$
$997$	5.63932	0.178599	0.0892995	+	0.996005i	$0.471537\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2016.2.a.q.1.2	yes	2
3.2	odd	2		2016.2.a.v.1.1	yes	2
4.3	odd	2		2016.2.a.p.1.2	✓	2
8.3	odd	2		4032.2.a.bu.1.1		2
8.5	even	2		4032.2.a.bx.1.1		2
12.11	even	2		2016.2.a.u.1.1	yes	2
24.5	odd	2		4032.2.a.bp.1.2		2
24.11	even	2		4032.2.a.bo.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2016.2.a.p.1.2	✓	2	4.3	odd	2
2016.2.a.q.1.2	yes	2	1.1	even	1	trivial
2016.2.a.u.1.1	yes	2	12.11	even	2
2016.2.a.v.1.1	yes	2	3.2	odd	2
4032.2.a.bo.1.2		2	24.11	even	2
4032.2.a.bp.1.2		2	24.5	odd	2
4032.2.a.bu.1.1		2	8.3	odd	2
4032.2.a.bx.1.1		2	8.5	even	2

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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:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.a (trivial)

\(f(q)\)	\(=\)	\(q+1.23607 q^{5} +1.00000 q^{7} +O(q^{10})\)	\(q+1.23607 q^{5} +1.00000 q^{7} +1.23607 q^{11} -4.47214 q^{13} -5.23607 q^{17} -6.47214 q^{19} -7.70820 q^{23} -3.47214 q^{25} -10.4721 q^{29} +6.47214 q^{31} +1.23607 q^{35} +4.47214 q^{37} -2.76393 q^{41} +4.94427 q^{43} +10.4721 q^{47} +1.00000 q^{49} -8.00000 q^{53} +1.52786 q^{55} +2.47214 q^{59} +4.47214 q^{61} -5.52786 q^{65} -8.00000 q^{67} +2.76393 q^{71} +2.94427 q^{73} +1.23607 q^{77} -4.94427 q^{79} -4.94427 q^{83} -6.47214 q^{85} -15.7082 q^{89} -4.47214 q^{91} -8.00000 q^{95} +10.9443 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5} + 2 q^{7}+O(q^{10}) \) 2 * q - 2 * q^5 + 2 * q^7	\( 2 q - 2 q^{5} + 2 q^{7} - 2 q^{11} - 6 q^{17} - 4 q^{19} - 2 q^{23} + 2 q^{25} - 12 q^{29} + 4 q^{31} - 2 q^{35} - 10 q^{41} - 8 q^{43} + 12 q^{47} + 2 q^{49} - 16 q^{53} + 12 q^{55} - 4 q^{59} - 20 q^{65} - 16 q^{67} + 10 q^{71} - 12 q^{73} - 2 q^{77} + 8 q^{79} + 8 q^{83} - 4 q^{85} - 18 q^{89} - 16 q^{95} + 4 q^{97}+O(q^{100}) \) 2 * q - 2 * q^5 + 2 * q^7 - 2 * q^11 - 6 * q^17 - 4 * q^19 - 2 * q^23 + 2 * q^25 - 12 * q^29 + 4 * q^31 - 2 * q^35 - 10 * q^41 - 8 * q^43 + 12 * q^47 + 2 * q^49 - 16 * q^53 + 12 * q^55 - 4 * q^59 - 20 * q^65 - 16 * q^67 + 10 * q^71 - 12 * q^73 - 2 * q^77 + 8 * q^79 + 8 * q^83 - 4 * q^85 - 18 * q^89 - 16 * q^95 + 4 * q^97

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