LMFDB - Embedded newform 7360.2.a.bz.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7360,2,Mod(1,7360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7360, 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("7360.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7360 = 2^{6} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7360.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:	$58.7698958877$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1101.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 9x + 12 $ x^3 - x^2 - 9*x + 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.11903$ of defining polynomial
Character	$\chi$	$=$	7360.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.11903 q^{3} +1.00000 q^{5} +4.50973 q^{7} +6.72833 q^{9} +O(q^{10})$	$q+3.11903 q^{3} +1.00000 q^{5} +4.50973 q^{7} +6.72833 q^{9} -4.33763 q^{11} +3.72833 q^{13} +3.11903 q^{15} +1.11903 q^{17} -4.50973 q^{19} +14.0660 q^{21} -1.00000 q^{23} +1.00000 q^{25} +11.6288 q^{27} +8.23805 q^{29} +1.72833 q^{31} -13.5292 q^{33} +4.50973 q^{35} +0.781399 q^{37} +11.6288 q^{39} +3.90043 q^{41} -8.00000 q^{43} +6.72833 q^{45} -11.4567 q^{47} +13.3376 q^{49} +3.49027 q^{51} +6.00000 q^{53} -4.33763 q^{55} -14.0660 q^{57} +2.23805 q^{59} -3.55623 q^{61} +30.3429 q^{63} +3.72833 q^{65} -2.43720 q^{67} -3.11903 q^{69} +7.11903 q^{71} -9.45665 q^{73} +3.11903 q^{75} -19.5615 q^{77} -14.9133 q^{79} +16.0854 q^{81} -2.78140 q^{83} +1.11903 q^{85} +25.6947 q^{87} -7.69471 q^{89} +16.8137 q^{91} +5.39070 q^{93} -4.50973 q^{95} -0.642920 q^{97} -29.1850 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{3} + 3 q^{5} + 3 q^{7} + 10 q^{9}+O(q^{10}) $ 3 * q - q^3 + 3 * q^5 + 3 * q^7 + 10 * q^9	$ 3 q - q^{3} + 3 q^{5} + 3 q^{7} + 10 q^{9} - 3 q^{11} + q^{13} - q^{15} - 7 q^{17} - 3 q^{19} + 22 q^{21} - 3 q^{23} + 3 q^{25} + 14 q^{27} + 4 q^{29} - 5 q^{31} - 9 q^{33} + 3 q^{35} + 2 q^{37} + 14 q^{39} + q^{41} - 24 q^{43} + 10 q^{45} - 14 q^{47} + 30 q^{49} + 21 q^{51} + 18 q^{53} - 3 q^{55} - 22 q^{57} - 14 q^{59} - q^{61} + 8 q^{63} + q^{65} - 8 q^{67} + q^{69} + 11 q^{71} - 8 q^{73} - q^{75} + 24 q^{77} - 4 q^{79} + 7 q^{81} - 8 q^{83} - 7 q^{85} + 36 q^{87} + 18 q^{89} - q^{91} + 16 q^{93} - 3 q^{95} - 33 q^{97} - 57 q^{99}+O(q^{100}) $ 3 * q - q^3 + 3 * q^5 + 3 * q^7 + 10 * q^9 - 3 * q^11 + q^13 - q^15 - 7 * q^17 - 3 * q^19 + 22 * q^21 - 3 * q^23 + 3 * q^25 + 14 * q^27 + 4 * q^29 - 5 * q^31 - 9 * q^33 + 3 * q^35 + 2 * q^37 + 14 * q^39 + q^41 - 24 * q^43 + 10 * q^45 - 14 * q^47 + 30 * q^49 + 21 * q^51 + 18 * q^53 - 3 * q^55 - 22 * q^57 - 14 * q^59 - q^61 + 8 * q^63 + q^65 - 8 * q^67 + q^69 + 11 * q^71 - 8 * q^73 - q^75 + 24 * q^77 - 4 * q^79 + 7 * q^81 - 8 * q^83 - 7 * q^85 + 36 * q^87 + 18 * q^89 - q^91 + 16 * q^93 - 3 * q^95 - 33 * q^97 - 57 * q^99

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
$3$	3.11903	1.80077	0.900385	−	0.435093i	$-0.143285\pi$
$3$	3.11903	1.80077	0.900385	+	0.435093i	$0.143285\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	4.50973	1.70452	0.852258	−	0.523122i	$-0.175233\pi$
$7$	4.50973	1.70452	0.852258	+	0.523122i	$0.175233\pi$
$8$	0	0
$9$	6.72833	2.24278
$10$	0	0
$11$	−4.33763	−1.30784	−0.653922	−	0.756562i	$-0.726878\pi$
$11$	−4.33763	−1.30784	−0.653922	+	0.756562i	$0.726878\pi$
$12$	0	0
$13$	3.72833	1.03405	0.517026	−	0.855970i	$-0.327039\pi$
$13$	3.72833	1.03405	0.517026	+	0.855970i	$0.327039\pi$
$14$	0	0
$15$	3.11903	0.805329
$16$	0	0
$17$	1.11903	0.271404	0.135702	−	0.990750i	$-0.456671\pi$
$17$	1.11903	0.271404	0.135702	+	0.990750i	$0.456671\pi$
$18$	0	0
$19$	−4.50973	−1.03460	−0.517301	−	0.855803i	$-0.673063\pi$
$19$	−4.50973	−1.03460	−0.517301	+	0.855803i	$0.673063\pi$
$20$	0	0
$21$	14.0660	3.06944
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	11.6288	2.23795
$28$	0	0
$29$	8.23805	1.52977	0.764884	−	0.644168i	$-0.222796\pi$
$29$	8.23805	1.52977	0.764884	+	0.644168i	$0.222796\pi$
$30$	0	0
$31$	1.72833	0.310417	0.155208	−	0.987882i	$-0.450395\pi$
$31$	1.72833	0.310417	0.155208	+	0.987882i	$0.450395\pi$
$32$	0	0
$33$	−13.5292	−2.35513
$34$	0	0
$35$	4.50973	0.762283
$36$	0	0
$37$	0.781399	0.128461	0.0642306	−	0.997935i	$-0.479541\pi$
$37$	0.781399	0.128461	0.0642306	+	0.997935i	$0.479541\pi$
$38$	0	0
$39$	11.6288	1.86209
$40$	0	0
$41$	3.90043	0.609144	0.304572	−	0.952489i	$-0.401487\pi$
$41$	3.90043	0.609144	0.304572	+	0.952489i	$0.401487\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	0	0
$45$	6.72833	1.00300
$46$	0	0
$47$	−11.4567	−1.67112	−0.835562	−	0.549396i	$-0.814858\pi$
$47$	−11.4567	−1.67112	−0.835562	+	0.549396i	$0.814858\pi$
$48$	0	0
$49$	13.3376	1.90538
$50$	0	0
$51$	3.49027	0.488736
$52$	0	0
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	−4.33763	−0.584886
$56$	0	0
$57$	−14.0660	−1.86308
$58$	0	0
$59$	2.23805	0.291370	0.145685	−	0.989331i	$-0.453461\pi$
$59$	2.23805	0.291370	0.145685	+	0.989331i	$0.453461\pi$
$60$	0	0
$61$	−3.55623	−0.455329	−0.227664	−	0.973740i	$-0.573109\pi$
$61$	−3.55623	−0.455329	−0.227664	+	0.973740i	$0.573109\pi$
$62$	0	0
$63$	30.3429	3.82285
$64$	0	0
$65$	3.72833	0.462442
$66$	0	0
$67$	−2.43720	−0.297752	−0.148876	−	0.988856i	$-0.547565\pi$
$67$	−2.43720	−0.297752	−0.148876	+	0.988856i	$0.547565\pi$
$68$	0	0
$69$	−3.11903	−0.375487
$70$	0	0
$71$	7.11903	0.844873	0.422437	−	0.906393i	$-0.361175\pi$
$71$	7.11903	0.844873	0.422437	+	0.906393i	$0.361175\pi$
$72$	0	0
$73$	−9.45665	−1.10682	−0.553409	−	0.832910i	$-0.686673\pi$
$73$	−9.45665	−1.10682	−0.553409	+	0.832910i	$0.686673\pi$
$74$	0	0
$75$	3.11903	0.360154
$76$	0	0
$77$	−19.5615	−2.22924
$78$	0	0
$79$	−14.9133	−1.67788	−0.838939	−	0.544225i	$-0.816824\pi$
$79$	−14.9133	−1.67788	−0.838939	+	0.544225i	$0.816824\pi$
$80$	0	0
$81$	16.0854	1.78727
$82$	0	0
$83$	−2.78140	−0.305298	−0.152649	−	0.988280i	$-0.548780\pi$
$83$	−2.78140	−0.305298	−0.152649	+	0.988280i	$0.548780\pi$
$84$	0	0
$85$	1.11903	0.121375
$86$	0	0
$87$	25.6947	2.75476
$88$	0	0
$89$	−7.69471	−0.815637	−0.407819	−	0.913063i	$-0.633710\pi$
$89$	−7.69471	−0.815637	−0.407819	+	0.913063i	$0.633710\pi$
$90$	0	0
$91$	16.8137	1.76256
$92$	0	0
$93$	5.39070	0.558989
$94$	0	0
$95$	−4.50973	−0.462688
$96$	0	0
$97$	−0.642920	−0.0652786	−0.0326393	−	0.999467i	$-0.510391\pi$
$97$	−0.642920	−0.0652786	−0.0326393	+	0.999467i	$0.510391\pi$
$98$	0	0
$99$	−29.1850	−2.93320
$100$	0	0
$101$	8.23805	0.819717	0.409858	−	0.912149i	$-0.365578\pi$
$101$	8.23805	0.819717	0.409858	+	0.912149i	$0.365578\pi$
$102$	0	0
$103$	12.3376	1.21566	0.607831	−	0.794066i	$-0.292040\pi$
$103$	12.3376	1.21566	0.607831	+	0.794066i	$0.292040\pi$
$104$	0	0
$105$	14.0660	1.37270
$106$	0	0
$107$	15.9328	1.54028	0.770139	−	0.637876i	$-0.220187\pi$
$107$	15.9328	1.54028	0.770139	+	0.637876i	$0.220187\pi$
$108$	0	0
$109$	1.49027	0.142742	0.0713712	−	0.997450i	$-0.477263\pi$
$109$	1.49027	0.142742	0.0713712	+	0.997450i	$0.477263\pi$
$110$	0	0
$111$	2.43720	0.231329
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	−1.00000	−0.0932505
$116$	0	0
$117$	25.0854	2.31915
$118$	0	0
$119$	5.04650	0.462612
$120$	0	0
$121$	7.81502	0.710456
$122$	0	0
$123$	12.1655	1.09693
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	−0.675256	−0.0599193	−0.0299597	−	0.999551i	$-0.509538\pi$
$127$	−0.675256	−0.0599193	−0.0299597	+	0.999551i	$0.509538\pi$
$128$	0	0
$129$	−24.9522	−2.19692
$130$	0	0
$131$	13.6947	1.19651	0.598256	−	0.801305i	$-0.295861\pi$
$131$	13.6947	1.19651	0.598256	+	0.801305i	$0.295861\pi$
$132$	0	0
$133$	−20.3376	−1.76350
$134$	0	0
$135$	11.6288	1.00084
$136$	0	0
$137$	7.52918	0.643261	0.321631	−	0.946865i	$-0.395769\pi$
$137$	7.52918	0.643261	0.321631	+	0.946865i	$0.395769\pi$
$138$	0	0
$139$	−4.67526	−0.396550	−0.198275	−	0.980146i	$-0.563534\pi$
$139$	−4.67526	−0.396550	−0.198275	+	0.980146i	$0.563534\pi$
$140$	0	0
$141$	−35.7336	−3.00931
$142$	0	0
$143$	−16.1721	−1.35238
$144$	0	0
$145$	8.23805	0.684133
$146$	0	0
$147$	41.6004	3.43114
$148$	0	0
$149$	−7.52918	−0.616814	−0.308407	−	0.951254i	$-0.599796\pi$
$149$	−7.52918	−0.616814	−0.308407	+	0.951254i	$0.599796\pi$
$150$	0	0
$151$	−13.3571	−1.08698	−0.543492	−	0.839414i	$-0.682898\pi$
$151$	−13.3571	−1.08698	−0.543492	+	0.839414i	$0.682898\pi$
$152$	0	0
$153$	7.52918	0.608698
$154$	0	0
$155$	1.72833	0.138823
$156$	0	0
$157$	−16.2381	−1.29594	−0.647969	−	0.761667i	$-0.724381\pi$
$157$	−16.2381	−1.29594	−0.647969	+	0.761667i	$0.724381\pi$
$158$	0	0
$159$	18.7142	1.48413
$160$	0	0
$161$	−4.50973	−0.355416
$162$	0	0
$163$	3.29112	0.257781	0.128890	−	0.991659i	$-0.458858\pi$
$163$	3.29112	0.257781	0.128890	+	0.991659i	$0.458858\pi$
$164$	0	0
$165$	−13.5292	−1.05325
$166$	0	0
$167$	22.9133	1.77309	0.886543	−	0.462647i	$-0.153100\pi$
$167$	22.9133	1.77309	0.886543	+	0.462647i	$0.153100\pi$
$168$	0	0
$169$	0.900425	0.0692635
$170$	0	0
$171$	−30.3429	−2.32038
$172$	0	0
$173$	−0.575681	−0.0437683	−0.0218841	−	0.999761i	$-0.506966\pi$
$173$	−0.575681	−0.0437683	−0.0218841	+	0.999761i	$0.506966\pi$
$174$	0	0
$175$	4.50973	0.340903
$176$	0	0
$177$	6.98055	0.524690
$178$	0	0
$179$	−5.01945	−0.375171	−0.187586	−	0.982248i	$-0.560066\pi$
$179$	−5.01945	−0.375171	−0.187586	+	0.982248i	$0.560066\pi$
$180$	0	0
$181$	11.5292	0.856957	0.428479	−	0.903552i	$-0.359050\pi$
$181$	11.5292	0.856957	0.428479	+	0.903552i	$0.359050\pi$
$182$	0	0
$183$	−11.0920	−0.819942
$184$	0	0
$185$	0.781399	0.0574496
$186$	0	0
$187$	−4.85392	−0.354954
$188$	0	0
$189$	52.4425	3.81463
$190$	0	0
$191$	−18.7142	−1.35411	−0.677055	−	0.735933i	$-0.736744\pi$
$191$	−18.7142	−1.35411	−0.677055	+	0.735933i	$0.736744\pi$
$192$	0	0
$193$	23.4956	1.69125	0.845624	−	0.533780i	$-0.179229\pi$
$193$	23.4956	1.69125	0.845624	+	0.533780i	$0.179229\pi$
$194$	0	0
$195$	11.6288	0.832752
$196$	0	0
$197$	18.1385	1.29231	0.646157	−	0.763205i	$-0.276375\pi$
$197$	18.1385	1.29231	0.646157	+	0.763205i	$0.276375\pi$
$198$	0	0
$199$	−23.2575	−1.64868	−0.824340	−	0.566094i	$-0.808454\pi$
$199$	−23.2575	−1.64868	−0.824340	+	0.566094i	$0.808454\pi$
$200$	0	0
$201$	−7.60170	−0.536183
$202$	0	0
$203$	37.1514	2.60751
$204$	0	0
$205$	3.90043	0.272418
$206$	0	0
$207$	−6.72833	−0.467651
$208$	0	0
$209$	19.5615	1.35310
$210$	0	0
$211$	−4.34420	−0.299067	−0.149533	−	0.988757i	$-0.547777\pi$
$211$	−4.34420	−0.299067	−0.149533	+	0.988757i	$0.547777\pi$
$212$	0	0
$213$	22.2044	1.52142
$214$	0	0
$215$	−8.00000	−0.545595
$216$	0	0
$217$	7.79428	0.529110
$218$	0	0
$219$	−29.4956	−1.99313
$220$	0	0
$221$	4.17210	0.280646
$222$	0	0
$223$	12.4761	0.835462	0.417731	−	0.908571i	$-0.362825\pi$
$223$	12.4761	0.835462	0.417731	+	0.908571i	$0.362825\pi$
$224$	0	0
$225$	6.72833	0.448555
$226$	0	0
$227$	−15.9328	−1.05749	−0.528747	−	0.848779i	$-0.677338\pi$
$227$	−15.9328	−1.05749	−0.528747	+	0.848779i	$0.677338\pi$
$228$	0	0
$229$	3.56280	0.235436	0.117718	−	0.993047i	$-0.462442\pi$
$229$	3.56280	0.235436	0.117718	+	0.993047i	$0.462442\pi$
$230$	0	0
$231$	−61.0129	−4.01435
$232$	0	0
$233$	−27.4956	−1.80129	−0.900647	−	0.434552i	$-0.856907\pi$
$233$	−27.4956	−1.80129	−0.900647	+	0.434552i	$0.856907\pi$
$234$	0	0
$235$	−11.4567	−0.747350
$236$	0	0
$237$	−46.5150	−3.02147
$238$	0	0
$239$	10.0389	0.649363	0.324681	−	0.945823i	$-0.394743\pi$
$239$	10.0389	0.649363	0.324681	+	0.945823i	$0.394743\pi$
$240$	0	0
$241$	−23.6947	−1.52631	−0.763155	−	0.646215i	$-0.776351\pi$
$241$	−23.6947	−1.52631	−0.763155	+	0.646215i	$0.776351\pi$
$242$	0	0
$243$	15.2846	0.980505
$244$	0	0
$245$	13.3376	0.852110
$246$	0	0
$247$	−16.8137	−1.06983
$248$	0	0
$249$	−8.67526	−0.549772
$250$	0	0
$251$	−12.4425	−0.785363	−0.392681	−	0.919675i	$-0.628452\pi$
$251$	−12.4425	−0.785363	−0.392681	+	0.919675i	$0.628452\pi$
$252$	0	0
$253$	4.33763	0.272704
$254$	0	0
$255$	3.49027	0.218569
$256$	0	0
$257$	5.45665	0.340377	0.170188	−	0.985412i	$-0.445562\pi$
$257$	5.45665	0.340377	0.170188	+	0.985412i	$0.445562\pi$
$258$	0	0
$259$	3.52389	0.218964
$260$	0	0
$261$	55.4283	3.43093
$262$	0	0
$263$	0.138479	0.00853895	0.00426948	−	0.999991i	$-0.498641\pi$
$263$	0.138479	0.00853895	0.00426948	+	0.999991i	$0.498641\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	0	0
$267$	−24.0000	−1.46878
$268$	0	0
$269$	−14.6753	−0.894766	−0.447383	−	0.894342i	$-0.647644\pi$
$269$	−14.6753	−0.894766	−0.447383	+	0.894342i	$0.647644\pi$
$270$	0	0
$271$	−8.31058	−0.504832	−0.252416	−	0.967619i	$-0.581225\pi$
$271$	−8.31058	−0.504832	−0.252416	+	0.967619i	$0.581225\pi$
$272$	0	0
$273$	52.4425	3.17396
$274$	0	0
$275$	−4.33763	−0.261569
$276$	0	0
$277$	−12.9133	−0.775886	−0.387943	−	0.921683i	$-0.626814\pi$
$277$	−12.9133	−0.775886	−0.387943	+	0.921683i	$0.626814\pi$
$278$	0	0
$279$	11.6288	0.696195
$280$	0	0
$281$	2.67526	0.159592	0.0797962	−	0.996811i	$-0.474573\pi$
$281$	2.67526	0.159592	0.0797962	+	0.996811i	$0.474573\pi$
$282$	0	0
$283$	−0.742495	−0.0441367	−0.0220684	−	0.999756i	$-0.507025\pi$
$283$	−0.742495	−0.0441367	−0.0220684	+	0.999756i	$0.507025\pi$
$284$	0	0
$285$	−14.0660	−0.833195
$286$	0	0
$287$	17.5898	1.03830
$288$	0	0
$289$	−15.7478	−0.926340
$290$	0	0
$291$	−2.00528	−0.117552
$292$	0	0
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	2.23805	0.130305
$296$	0	0
$297$	−50.4412	−2.92690
$298$	0	0
$299$	−3.72833	−0.215615
$300$	0	0
$301$	−36.0778	−2.07949
$302$	0	0
$303$	25.6947	1.47612
$304$	0	0
$305$	−3.55623	−0.203629
$306$	0	0
$307$	−30.5084	−1.74121	−0.870604	−	0.491984i	$-0.836272\pi$
$307$	−30.5084	−1.74121	−0.870604	+	0.491984i	$0.836272\pi$
$308$	0	0
$309$	38.4814	2.18913
$310$	0	0
$311$	5.56280	0.315437	0.157719	−	0.987484i	$-0.449586\pi$
$311$	5.56280	0.315437	0.157719	+	0.987484i	$0.449586\pi$
$312$	0	0
$313$	4.07252	0.230193	0.115096	−	0.993354i	$-0.463282\pi$
$313$	4.07252	0.230193	0.115096	+	0.993354i	$0.463282\pi$
$314$	0	0
$315$	30.3429	1.70963
$316$	0	0
$317$	6.16553	0.346291	0.173145	−	0.984896i	$-0.444607\pi$
$317$	6.16553	0.346291	0.173145	+	0.984896i	$0.444607\pi$
$318$	0	0
$319$	−35.7336	−2.00070
$320$	0	0
$321$	49.6947	2.77369
$322$	0	0
$323$	−5.04650	−0.280795
$324$	0	0
$325$	3.72833	0.206810
$326$	0	0
$327$	4.64820	0.257046
$328$	0	0
$329$	−51.6664	−2.84846
$330$	0	0
$331$	−27.5886	−1.51640	−0.758202	−	0.652019i	$-0.773922\pi$
$331$	−27.5886	−1.51640	−0.758202	+	0.652019i	$0.773922\pi$
$332$	0	0
$333$	5.25751	0.288110
$334$	0	0
$335$	−2.43720	−0.133159
$336$	0	0
$337$	−17.4230	−0.949093	−0.474547	−	0.880230i	$-0.657388\pi$
$337$	−17.4230	−0.949093	−0.474547	+	0.880230i	$0.657388\pi$
$338$	0	0
$339$	−18.7142	−1.01641
$340$	0	0
$341$	−7.49684	−0.405977
$342$	0	0
$343$	28.5810	1.54323
$344$	0	0
$345$	−3.11903	−0.167923
$346$	0	0
$347$	−4.88097	−0.262024	−0.131012	−	0.991381i	$-0.541823\pi$
$347$	−4.88097	−0.262024	−0.131012	+	0.991381i	$0.541823\pi$
$348$	0	0
$349$	−24.0389	−1.28677	−0.643387	−	0.765542i	$-0.722471\pi$
$349$	−24.0389	−1.28677	−0.643387	+	0.765542i	$0.722471\pi$
$350$	0	0
$351$	43.3558	2.31416
$352$	0	0
$353$	−14.3442	−0.763464	−0.381732	−	0.924273i	$-0.624672\pi$
$353$	−14.3442	−0.763464	−0.381732	+	0.924273i	$0.624672\pi$
$354$	0	0
$355$	7.11903	0.377839
$356$	0	0
$357$	15.7402	0.833059
$358$	0	0
$359$	26.7814	1.41347	0.706734	−	0.707479i	$-0.250168\pi$
$359$	26.7814	1.41347	0.706734	+	0.707479i	$0.250168\pi$
$360$	0	0
$361$	1.33763	0.0704015
$362$	0	0
$363$	24.3752	1.27937
$364$	0	0
$365$	−9.45665	−0.494984
$366$	0	0
$367$	−20.4761	−1.06884	−0.534422	−	0.845218i	$-0.679471\pi$
$367$	−20.4761	−1.06884	−0.534422	+	0.845218i	$0.679471\pi$
$368$	0	0
$369$	26.2433	1.36617
$370$	0	0
$371$	27.0584	1.40480
$372$	0	0
$373$	3.89386	0.201616	0.100808	−	0.994906i	$-0.467857\pi$
$373$	3.89386	0.201616	0.100808	+	0.994906i	$0.467857\pi$
$374$	0	0
$375$	3.11903	0.161066
$376$	0	0
$377$	30.7142	1.58186
$378$	0	0
$379$	30.3765	1.56034	0.780169	−	0.625569i	$-0.215133\pi$
$379$	30.3765	1.56034	0.780169	+	0.625569i	$0.215133\pi$
$380$	0	0
$381$	−2.10614	−0.107901
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	−19.5615	−0.996947
$386$	0	0
$387$	−53.8266	−2.73616
$388$	0	0
$389$	18.6818	0.947206	0.473603	−	0.880738i	$-0.342953\pi$
$389$	18.6818	0.947206	0.473603	+	0.880738i	$0.342953\pi$
$390$	0	0
$391$	−1.11903	−0.0565916
$392$	0	0
$393$	42.7142	2.15464
$394$	0	0
$395$	−14.9133	−0.750370
$396$	0	0
$397$	28.5757	1.43417	0.717086	−	0.696985i	$-0.245475\pi$
$397$	28.5757	1.43417	0.717086	+	0.696985i	$0.245475\pi$
$398$	0	0
$399$	−63.4336	−3.17565
$400$	0	0
$401$	12.1061	0.604552	0.302276	−	0.953220i	$-0.402254\pi$
$401$	12.1061	0.604552	0.302276	+	0.953220i	$0.402254\pi$
$402$	0	0
$403$	6.44377	0.320987
$404$	0	0
$405$	16.0854	0.799290
$406$	0	0
$407$	−3.38942	−0.168007
$408$	0	0
$409$	25.2911	1.25057	0.625283	−	0.780398i	$-0.284984\pi$
$409$	25.2911	1.25057	0.625283	+	0.780398i	$0.284984\pi$
$410$	0	0
$411$	23.4837	1.15837
$412$	0	0
$413$	10.0930	0.496644
$414$	0	0
$415$	−2.78140	−0.136533
$416$	0	0
$417$	−14.5822	−0.714096
$418$	0	0
$419$	17.3505	0.847628	0.423814	−	0.905749i	$-0.360691\pi$
$419$	17.3505	0.847628	0.423814	+	0.905749i	$0.360691\pi$
$420$	0	0
$421$	−21.4230	−1.04409	−0.522047	−	0.852916i	$-0.674832\pi$
$421$	−21.4230	−1.04409	−0.522047	+	0.852916i	$0.674832\pi$
$422$	0	0
$423$	−77.0841	−3.74796
$424$	0	0
$425$	1.11903	0.0542808
$426$	0	0
$427$	−16.0376	−0.776115
$428$	0	0
$429$	−50.4412	−2.43532
$430$	0	0
$431$	22.5822	1.08775	0.543874	−	0.839167i	$-0.316957\pi$
$431$	22.5822	1.08775	0.543874	+	0.839167i	$0.316957\pi$
$432$	0	0
$433$	1.01417	0.0487378	0.0243689	−	0.999703i	$-0.492242\pi$
$433$	1.01417	0.0487378	0.0243689	+	0.999703i	$0.492242\pi$
$434$	0	0
$435$	25.6947	1.23197
$436$	0	0
$437$	4.50973	0.215729
$438$	0	0
$439$	−26.7478	−1.27660	−0.638301	−	0.769787i	$-0.720362\pi$
$439$	−26.7478	−1.27660	−0.638301	+	0.769787i	$0.720362\pi$
$440$	0	0
$441$	89.7399	4.27333
$442$	0	0
$443$	−10.2044	−0.484827	−0.242414	−	0.970173i	$-0.577939\pi$
$443$	−10.2044	−0.484827	−0.242414	+	0.970173i	$0.577939\pi$
$444$	0	0
$445$	−7.69471	−0.364764
$446$	0	0
$447$	−23.4837	−1.11074
$448$	0	0
$449$	38.7867	1.83046	0.915228	−	0.402936i	$-0.132010\pi$
$449$	38.7867	1.83046	0.915228	+	0.402936i	$0.132010\pi$
$450$	0	0
$451$	−16.9186	−0.796665
$452$	0	0
$453$	−41.6611	−1.95741
$454$	0	0
$455$	16.8137	0.788240
$456$	0	0
$457$	34.9522	1.63500	0.817498	−	0.575932i	$-0.195361\pi$
$457$	34.9522	1.63500	0.817498	+	0.575932i	$0.195361\pi$
$458$	0	0
$459$	13.0129	0.607389
$460$	0	0
$461$	−16.3700	−0.762425	−0.381213	−	0.924487i	$-0.624493\pi$
$461$	−16.3700	−0.762425	−0.381213	+	0.924487i	$0.624493\pi$
$462$	0	0
$463$	29.2186	1.35790	0.678952	−	0.734183i	$-0.262435\pi$
$463$	29.2186	1.35790	0.678952	+	0.734183i	$0.262435\pi$
$464$	0	0
$465$	5.39070	0.249988
$466$	0	0
$467$	−24.2770	−1.12340	−0.561702	−	0.827340i	$-0.689853\pi$
$467$	−24.2770	−1.12340	−0.561702	+	0.827340i	$0.689853\pi$
$468$	0	0
$469$	−10.9911	−0.507523
$470$	0	0
$471$	−50.6469	−2.33369
$472$	0	0
$473$	34.7010	1.59555
$474$	0	0
$475$	−4.50973	−0.206920
$476$	0	0
$477$	40.3700	1.84841
$478$	0	0
$479$	24.6080	1.12437	0.562185	−	0.827012i	$-0.309961\pi$
$479$	24.6080	1.12437	0.562185	+	0.827012i	$0.309961\pi$
$480$	0	0
$481$	2.91331	0.132835
$482$	0	0
$483$	−14.0660	−0.640023
$484$	0	0
$485$	−0.642920	−0.0291935
$486$	0	0
$487$	−30.2381	−1.37022	−0.685108	−	0.728441i	$-0.740245\pi$
$487$	−30.2381	−1.37022	−0.685108	+	0.728441i	$0.740245\pi$
$488$	0	0
$489$	10.2651	0.464204
$490$	0	0
$491$	−12.3311	−0.556493	−0.278246	−	0.960510i	$-0.589753\pi$
$491$	−12.3311	−0.556493	−0.278246	+	0.960510i	$0.589753\pi$
$492$	0	0
$493$	9.21860	0.415185
$494$	0	0
$495$	−29.1850	−1.31177
$496$	0	0
$497$	32.1049	1.44010
$498$	0	0
$499$	26.9133	1.20481	0.602403	−	0.798192i	$-0.294210\pi$
$499$	26.9133	1.20481	0.602403	+	0.798192i	$0.294210\pi$
$500$	0	0
$501$	71.4672	3.19292
$502$	0	0
$503$	20.5097	0.914483	0.457242	−	0.889342i	$-0.348837\pi$
$503$	20.5097	0.914483	0.457242	+	0.889342i	$0.348837\pi$
$504$	0	0
$505$	8.23805	0.366589
$506$	0	0
$507$	2.80845	0.124728
$508$	0	0
$509$	36.7142	1.62733	0.813663	−	0.581336i	$-0.197470\pi$
$509$	36.7142	1.62733	0.813663	+	0.581336i	$0.197470\pi$
$510$	0	0
$511$	−42.6469	−1.88659
$512$	0	0
$513$	−52.4425	−2.31539
$514$	0	0
$515$	12.3376	0.543661
$516$	0	0
$517$	49.6947	2.18557
$518$	0	0
$519$	−1.79557	−0.0788166
$520$	0	0
$521$	−4.91331	−0.215256	−0.107628	−	0.994191i	$-0.534326\pi$
$521$	−4.91331	−0.215256	−0.107628	+	0.994191i	$0.534326\pi$
$522$	0	0
$523$	0.344196	0.0150506	0.00752531	−	0.999972i	$-0.497605\pi$
$523$	0.344196	0.0150506	0.00752531	+	0.999972i	$0.497605\pi$
$524$	0	0
$525$	14.0660	0.613889
$526$	0	0
$527$	1.93404	0.0842483
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	15.0584	0.653477
$532$	0	0
$533$	14.5421	0.629887
$534$	0	0
$535$	15.9328	0.688833
$536$	0	0
$537$	−15.6558	−0.675598
$538$	0	0
$539$	−57.8537	−2.49193
$540$	0	0
$541$	6.13191	0.263631	0.131816	−	0.991274i	$-0.457919\pi$
$541$	6.13191	0.263631	0.131816	+	0.991274i	$0.457919\pi$
$542$	0	0
$543$	35.9598	1.54318
$544$	0	0
$545$	1.49027	0.0638363
$546$	0	0
$547$	9.18498	0.392721	0.196361	−	0.980532i	$-0.437088\pi$
$547$	9.18498	0.392721	0.196361	+	0.980532i	$0.437088\pi$
$548$	0	0
$549$	−23.9275	−1.02120
$550$	0	0
$551$	−37.1514	−1.58270
$552$	0	0
$553$	−67.2549	−2.85997
$554$	0	0
$555$	2.43720	0.103454
$556$	0	0
$557$	4.30529	0.182421	0.0912105	−	0.995832i	$-0.470926\pi$
$557$	4.30529	0.182421	0.0912105	+	0.995832i	$0.470926\pi$
$558$	0	0
$559$	−29.8266	−1.26153
$560$	0	0
$561$	−15.1395	−0.639191
$562$	0	0
$563$	−11.1256	−0.468888	−0.234444	−	0.972130i	$-0.575327\pi$
$563$	−11.1256	−0.468888	−0.234444	+	0.972130i	$0.575327\pi$
$564$	0	0
$565$	−6.00000	−0.252422
$566$	0	0
$567$	72.5408	3.04643
$568$	0	0
$569$	−16.0389	−0.672386	−0.336193	−	0.941793i	$-0.609139\pi$
$569$	−16.0389	−0.672386	−0.336193	+	0.941793i	$0.609139\pi$
$570$	0	0
$571$	−17.9004	−0.749109	−0.374555	−	0.927205i	$-0.622204\pi$
$571$	−17.9004	−0.749109	−0.374555	+	0.927205i	$0.622204\pi$
$572$	0	0
$573$	−58.3700	−2.43844
$574$	0	0
$575$	−1.00000	−0.0417029
$576$	0	0
$577$	−9.12559	−0.379903	−0.189952	−	0.981793i	$-0.560833\pi$
$577$	−9.12559	−0.379903	−0.189952	+	0.981793i	$0.560833\pi$
$578$	0	0
$579$	73.2833	3.04555
$580$	0	0
$581$	−12.5433	−0.520386
$582$	0	0
$583$	−26.0258	−1.07788
$584$	0	0
$585$	25.0854	1.03715
$586$	0	0
$587$	33.6340	1.38823	0.694113	−	0.719866i	$-0.255797\pi$
$587$	33.6340	1.38823	0.694113	+	0.719866i	$0.255797\pi$
$588$	0	0
$589$	−7.79428	−0.321158
$590$	0	0
$591$	56.5744	2.32716
$592$	0	0
$593$	−17.4567	−0.716859	−0.358429	−	0.933557i	$-0.616688\pi$
$593$	−17.4567	−0.716859	−0.358429	+	0.933557i	$0.616688\pi$
$594$	0	0
$595$	5.04650	0.206886
$596$	0	0
$597$	−72.5408	−2.96890
$598$	0	0
$599$	−11.5951	−0.473764	−0.236882	−	0.971538i	$-0.576126\pi$
$599$	−11.5951	−0.473764	−0.236882	+	0.971538i	$0.576126\pi$
$600$	0	0
$601$	−31.6611	−1.29148	−0.645741	−	0.763556i	$-0.723452\pi$
$601$	−31.6611	−1.29148	−0.645741	+	0.763556i	$0.723452\pi$
$602$	0	0
$603$	−16.3983	−0.667790
$604$	0	0
$605$	7.81502	0.317726
$606$	0	0
$607$	−36.0778	−1.46435	−0.732177	−	0.681115i	$-0.761495\pi$
$607$	−36.0778	−1.46435	−0.732177	+	0.681115i	$0.761495\pi$
$608$	0	0
$609$	115.876	4.69554
$610$	0	0
$611$	−42.7142	−1.72803
$612$	0	0
$613$	32.0389	1.29404	0.647020	−	0.762473i	$-0.276015\pi$
$613$	32.0389	1.29404	0.647020	+	0.762473i	$0.276015\pi$
$614$	0	0
$615$	12.1655	0.490562
$616$	0	0
$617$	−13.3960	−0.539302	−0.269651	−	0.962958i	$-0.586908\pi$
$617$	−13.3960	−0.539302	−0.269651	+	0.962958i	$0.586908\pi$
$618$	0	0
$619$	−37.1309	−1.49242	−0.746208	−	0.665713i	$-0.768128\pi$
$619$	−37.1309	−1.49242	−0.746208	+	0.665713i	$0.768128\pi$
$620$	0	0
$621$	−11.6288	−0.466646
$622$	0	0
$623$	−34.7010	−1.39027
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	61.0129	2.43662
$628$	0	0
$629$	0.874406	0.0348648
$630$	0	0
$631$	11.1125	0.442380	0.221190	−	0.975231i	$-0.429006\pi$
$631$	11.1125	0.442380	0.221190	+	0.975231i	$0.429006\pi$
$632$	0	0
$633$	−13.5497	−0.538551
$634$	0	0
$635$	−0.675256	−0.0267967
$636$	0	0
$637$	49.7270	1.97026
$638$	0	0
$639$	47.8991	1.89486
$640$	0	0
$641$	12.3831	0.489103	0.244552	−	0.969636i	$-0.421359\pi$
$641$	12.3831	0.489103	0.244552	+	0.969636i	$0.421359\pi$
$642$	0	0
$643$	37.4956	1.47868	0.739340	−	0.673332i	$-0.235138\pi$
$643$	37.4956	1.47868	0.739340	+	0.673332i	$0.235138\pi$
$644$	0	0
$645$	−24.9522	−0.982492
$646$	0	0
$647$	14.5691	0.572771	0.286385	−	0.958114i	$-0.407546\pi$
$647$	14.5691	0.572771	0.286385	+	0.958114i	$0.407546\pi$
$648$	0	0
$649$	−9.70784	−0.381066
$650$	0	0
$651$	24.3106	0.952807
$652$	0	0
$653$	4.41672	0.172840	0.0864198	−	0.996259i	$-0.472457\pi$
$653$	4.41672	0.172840	0.0864198	+	0.996259i	$0.472457\pi$
$654$	0	0
$655$	13.6947	0.535097
$656$	0	0
$657$	−63.6275	−2.48234
$658$	0	0
$659$	31.8655	1.24130	0.620652	−	0.784086i	$-0.286868\pi$
$659$	31.8655	1.24130	0.620652	+	0.784086i	$0.286868\pi$
$660$	0	0
$661$	−33.1190	−1.28818	−0.644090	−	0.764949i	$-0.722764\pi$
$661$	−33.1190	−1.28818	−0.644090	+	0.764949i	$0.722764\pi$
$662$	0	0
$663$	13.0129	0.505379
$664$	0	0
$665$	−20.3376	−0.788659
$666$	0	0
$667$	−8.23805	−0.318979
$668$	0	0
$669$	38.9133	1.50448
$670$	0	0
$671$	15.4256	0.595499
$672$	0	0
$673$	19.3505	0.745907	0.372954	−	0.927850i	$-0.378345\pi$
$673$	19.3505	0.745907	0.372954	+	0.927850i	$0.378345\pi$
$674$	0	0
$675$	11.6288	0.447591
$676$	0	0
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	0	0
$679$	−2.89939	−0.111268
$680$	0	0
$681$	−49.6947	−1.90431
$682$	0	0
$683$	−38.3495	−1.46740	−0.733701	−	0.679472i	$-0.762209\pi$
$683$	−38.3495	−1.46740	−0.733701	+	0.679472i	$0.762209\pi$
$684$	0	0
$685$	7.52918	0.287675
$686$	0	0
$687$	11.1125	0.423967
$688$	0	0
$689$	22.3700	0.852228
$690$	0	0
$691$	21.0195	0.799618	0.399809	−	0.916599i	$-0.369077\pi$
$691$	21.0195	0.799618	0.399809	+	0.916599i	$0.369077\pi$
$692$	0	0
$693$	−131.616	−4.99969
$694$	0	0
$695$	−4.67526	−0.177343
$696$	0	0
$697$	4.36468	0.165324
$698$	0	0
$699$	−85.7594	−3.24372
$700$	0	0
$701$	−19.3169	−0.729589	−0.364794	−	0.931088i	$-0.618861\pi$
$701$	−19.3169	−0.729589	−0.364794	+	0.931088i	$0.618861\pi$
$702$	0	0
$703$	−3.52389	−0.132906
$704$	0	0
$705$	−35.7336	−1.34581
$706$	0	0
$707$	37.1514	1.39722
$708$	0	0
$709$	−12.2315	−0.459363	−0.229682	−	0.973266i	$-0.573768\pi$
$709$	−12.2315	−0.459363	−0.229682	+	0.973266i	$0.573768\pi$
$710$	0	0
$711$	−100.342	−3.76311
$712$	0	0
$713$	−1.72833	−0.0647264
$714$	0	0
$715$	−16.1721	−0.604802
$716$	0	0
$717$	31.3116	1.16935
$718$	0	0
$719$	−40.6416	−1.51568	−0.757839	−	0.652442i	$-0.773745\pi$
$719$	−40.6416	−1.51568	−0.757839	+	0.652442i	$0.773745\pi$
$720$	0	0
$721$	55.6393	2.07212
$722$	0	0
$723$	−73.9044	−2.74854
$724$	0	0
$725$	8.23805	0.305954
$726$	0	0
$727$	−23.4501	−0.869716	−0.434858	−	0.900499i	$-0.643201\pi$
$727$	−23.4501	−0.869716	−0.434858	+	0.900499i	$0.643201\pi$
$728$	0	0
$729$	−0.583281	−0.0216030
$730$	0	0
$731$	−8.95221	−0.331110
$732$	0	0
$733$	12.5150	0.462252	0.231126	−	0.972924i	$-0.425759\pi$
$733$	12.5150	0.462252	0.231126	+	0.972924i	$0.425759\pi$
$734$	0	0
$735$	41.6004	1.53445
$736$	0	0
$737$	10.5717	0.389413
$738$	0	0
$739$	21.3505	0.785391	0.392696	−	0.919668i	$-0.371543\pi$
$739$	21.3505	0.785391	0.392696	+	0.919668i	$0.371543\pi$
$740$	0	0
$741$	−52.4425	−1.92652
$742$	0	0
$743$	24.9858	0.916641	0.458321	−	0.888787i	$-0.348451\pi$
$743$	24.9858	0.916641	0.458321	+	0.888787i	$0.348451\pi$
$744$	0	0
$745$	−7.52918	−0.275848
$746$	0	0
$747$	−18.7142	−0.684715
$748$	0	0
$749$	71.8524	2.62543
$750$	0	0
$751$	−33.6275	−1.22708	−0.613542	−	0.789662i	$-0.710256\pi$
$751$	−33.6275	−1.22708	−0.613542	+	0.789662i	$0.710256\pi$
$752$	0	0
$753$	−38.8085	−1.41426
$754$	0	0
$755$	−13.3571	−0.486114
$756$	0	0
$757$	37.1230	1.34926	0.674630	−	0.738156i	$-0.264303\pi$
$757$	37.1230	1.34926	0.674630	+	0.738156i	$0.264303\pi$
$758$	0	0
$759$	13.5292	0.491078
$760$	0	0
$761$	−3.87337	−0.140410	−0.0702048	−	0.997533i	$-0.522365\pi$
$761$	−3.87337	−0.140410	−0.0702048	+	0.997533i	$0.522365\pi$
$762$	0	0
$763$	6.72073	0.243307
$764$	0	0
$765$	7.52918	0.272218
$766$	0	0
$767$	8.34420	0.301291
$768$	0	0
$769$	23.1645	0.835333	0.417667	−	0.908600i	$-0.362848\pi$
$769$	23.1645	0.835333	0.417667	+	0.908600i	$0.362848\pi$
$770$	0	0
$771$	17.0195	0.612941
$772$	0	0
$773$	8.78140	0.315845	0.157922	−	0.987452i	$-0.449520\pi$
$773$	8.78140	0.315845	0.157922	+	0.987452i	$0.449520\pi$
$774$	0	0
$775$	1.72833	0.0620834
$776$	0	0
$777$	10.9911	0.394304
$778$	0	0
$779$	−17.5898	−0.630222
$780$	0	0
$781$	−30.8797	−1.10496
$782$	0	0
$783$	95.7983	3.42355
$784$	0	0
$785$	−16.2381	−0.579561
$786$	0	0
$787$	−49.6275	−1.76903	−0.884514	−	0.466513i	$-0.845510\pi$
$787$	−49.6275	−1.76903	−0.884514	+	0.466513i	$0.845510\pi$
$788$	0	0
$789$	0.431918	0.0153767
$790$	0	0
$791$	−27.0584	−0.962084
$792$	0	0
$793$	−13.2588	−0.470833
$794$	0	0
$795$	18.7142	0.663723
$796$	0	0
$797$	−18.3311	−0.649319	−0.324660	−	0.945831i	$-0.605250\pi$
$797$	−18.3311	−0.649319	−0.324660	+	0.945831i	$0.605250\pi$
$798$	0	0
$799$	−12.8203	−0.453550
$800$	0	0
$801$	−51.7725	−1.82929
$802$	0	0
$803$	41.0195	1.44755
$804$	0	0
$805$	−4.50973	−0.158947
$806$	0	0
$807$	−45.7725	−1.61127
$808$	0	0
$809$	−1.93933	−0.0681832	−0.0340916	−	0.999419i	$-0.510854\pi$
$809$	−1.93933	−0.0681832	−0.0340916	+	0.999419i	$0.510854\pi$
$810$	0	0
$811$	5.41775	0.190243	0.0951215	−	0.995466i	$-0.469676\pi$
$811$	5.41775	0.190243	0.0951215	+	0.995466i	$0.469676\pi$
$812$	0	0
$813$	−25.9209	−0.909086
$814$	0	0
$815$	3.29112	0.115283
$816$	0	0
$817$	36.0778	1.26220
$818$	0	0
$819$	113.128	3.95302
$820$	0	0
$821$	−37.8655	−1.32152	−0.660758	−	0.750599i	$-0.729765\pi$
$821$	−37.8655	−1.32152	−0.660758	+	0.750599i	$0.729765\pi$
$822$	0	0
$823$	43.7336	1.52446	0.762229	−	0.647308i	$-0.224105\pi$
$823$	43.7336	1.52446	0.762229	+	0.647308i	$0.224105\pi$
$824$	0	0
$825$	−13.5292	−0.471026
$826$	0	0
$827$	−28.1991	−0.980581	−0.490290	−	0.871559i	$-0.663109\pi$
$827$	−28.1991	−0.980581	−0.490290	+	0.871559i	$0.663109\pi$
$828$	0	0
$829$	−1.12559	−0.0390935	−0.0195468	−	0.999809i	$-0.506222\pi$
$829$	−1.12559	−0.0390935	−0.0195468	+	0.999809i	$0.506222\pi$
$830$	0	0
$831$	−40.2770	−1.39719
$832$	0	0
$833$	14.9252	0.517126
$834$	0	0
$835$	22.9133	0.792948
$836$	0	0
$837$	20.0983	0.694699
$838$	0	0
$839$	39.9328	1.37863	0.689316	−	0.724461i	$-0.257911\pi$
$839$	39.9328	1.37863	0.689316	+	0.724461i	$0.257911\pi$
$840$	0	0
$841$	38.8655	1.34019
$842$	0	0
$843$	8.34420	0.287389
$844$	0	0
$845$	0.900425	0.0309756
$846$	0	0
$847$	35.2436	1.21098
$848$	0	0
$849$	−2.31586	−0.0794801
$850$	0	0
$851$	−0.781399	−0.0267860
$852$	0	0
$853$	−47.9921	−1.64322	−0.821610	−	0.570050i	$-0.806924\pi$
$853$	−47.9921	−1.64322	−0.821610	+	0.570050i	$0.806924\pi$
$854$	0	0
$855$	−30.3429	−1.03771
$856$	0	0
$857$	−43.4283	−1.48348	−0.741742	−	0.670686i	$-0.766000\pi$
$857$	−43.4283	−1.48348	−0.741742	+	0.670686i	$0.766000\pi$
$858$	0	0
$859$	−32.5433	−1.11036	−0.555182	−	0.831729i	$-0.687352\pi$
$859$	−32.5433	−1.11036	−0.555182	+	0.831729i	$0.687352\pi$
$860$	0	0
$861$	54.8632	1.86973
$862$	0	0
$863$	46.1036	1.56938	0.784692	−	0.619886i	$-0.212821\pi$
$863$	46.1036	1.56938	0.784692	+	0.619886i	$0.212821\pi$
$864$	0	0
$865$	−0.575681	−0.0195738
$866$	0	0
$867$	−49.1177	−1.66813
$868$	0	0
$869$	64.6884	2.19440
$870$	0	0
$871$	−9.08669	−0.307891
$872$	0	0
$873$	−4.32578	−0.146405
$874$	0	0
$875$	4.50973	0.152457
$876$	0	0
$877$	24.0996	0.813785	0.406892	−	0.913476i	$-0.366612\pi$
$877$	24.0996	0.813785	0.406892	+	0.913476i	$0.366612\pi$
$878$	0	0
$879$	18.7142	0.631213
$880$	0	0
$881$	2.34420	0.0789780	0.0394890	−	0.999220i	$-0.487427\pi$
$881$	2.34420	0.0789780	0.0394890	+	0.999220i	$0.487427\pi$
$882$	0	0
$883$	41.0505	1.38146	0.690730	−	0.723113i	$-0.257289\pi$
$883$	41.0505	1.38146	0.690730	+	0.723113i	$0.257289\pi$
$884$	0	0
$885$	6.98055	0.234649
$886$	0	0
$887$	54.7788	1.83929	0.919647	−	0.392747i	$-0.128475\pi$
$887$	54.7788	1.83929	0.919647	+	0.392747i	$0.128475\pi$
$888$	0	0
$889$	−3.04522	−0.102133
$890$	0	0
$891$	−69.7725	−2.33747
$892$	0	0
$893$	51.6664	1.72895
$894$	0	0
$895$	−5.01945	−0.167782
$896$	0	0
$897$	−11.6288	−0.388273
$898$	0	0
$899$	14.2381	0.474866
$900$	0	0
$901$	6.71416	0.223681
$902$	0	0
$903$	−112.528	−3.74469
$904$	0	0
$905$	11.5292	0.383243
$906$	0	0
$907$	10.1061	0.335569	0.167784	−	0.985824i	$-0.446339\pi$
$907$	10.1061	0.335569	0.167784	+	0.985824i	$0.446339\pi$
$908$	0	0
$909$	55.4283	1.83844
$910$	0	0
$911$	−25.4178	−0.842128	−0.421064	−	0.907031i	$-0.638343\pi$
$911$	−25.4178	−0.842128	−0.421064	+	0.907031i	$0.638343\pi$
$912$	0	0
$913$	12.0647	0.399282
$914$	0	0
$915$	−11.0920	−0.366689
$916$	0	0
$917$	61.7594	2.03947
$918$	0	0
$919$	23.6017	0.778548	0.389274	−	0.921122i	$-0.372726\pi$
$919$	23.6017	0.778548	0.389274	+	0.921122i	$0.372726\pi$
$920$	0	0
$921$	−95.1566	−3.13552
$922$	0	0
$923$	26.5421	0.873643
$924$	0	0
$925$	0.781399	0.0256922
$926$	0	0
$927$	83.0116	2.72646
$928$	0	0
$929$	−7.08669	−0.232507	−0.116253	−	0.993220i	$-0.537088\pi$
$929$	−7.08669	−0.232507	−0.116253	+	0.993220i	$0.537088\pi$
$930$	0	0
$931$	−60.1490	−1.97131
$932$	0	0
$933$	17.3505	0.568030
$934$	0	0
$935$	−4.85392	−0.158740
$936$	0	0
$937$	27.3169	0.892404	0.446202	−	0.894932i	$-0.352776\pi$
$937$	27.3169	0.892404	0.446202	+	0.894932i	$0.352776\pi$
$938$	0	0
$939$	12.7023	0.414524
$940$	0	0
$941$	−55.8979	−1.82222	−0.911109	−	0.412165i	$-0.864773\pi$
$941$	−55.8979	−1.82222	−0.911109	+	0.412165i	$0.864773\pi$
$942$	0	0
$943$	−3.90043	−0.127015
$944$	0	0
$945$	52.4425	1.70595
$946$	0	0
$947$	−37.5939	−1.22164	−0.610818	−	0.791771i	$-0.709159\pi$
$947$	−37.5939	−1.22164	−0.610818	+	0.791771i	$0.709159\pi$
$948$	0	0
$949$	−35.2575	−1.14451
$950$	0	0
$951$	19.2305	0.623590
$952$	0	0
$953$	−29.3828	−0.951804	−0.475902	−	0.879498i	$-0.657878\pi$
$953$	−29.3828	−0.951804	−0.475902	+	0.879498i	$0.657878\pi$
$954$	0	0
$955$	−18.7142	−0.605576
$956$	0	0
$957$	−111.454	−3.60280
$958$	0	0
$959$	33.9545	1.09645
$960$	0	0
$961$	−28.0129	−0.903641
$962$	0	0
$963$	107.201	3.45450
$964$	0	0
$965$	23.4956	0.756349
$966$	0	0
$967$	−49.2292	−1.58310	−0.791552	−	0.611102i	$-0.790726\pi$
$967$	−49.2292	−1.58310	−0.791552	+	0.611102i	$0.790726\pi$
$968$	0	0
$969$	−15.7402	−0.505647
$970$	0	0
$971$	−9.62347	−0.308832	−0.154416	−	0.988006i	$-0.549350\pi$
$971$	−9.62347	−0.308832	−0.154416	+	0.988006i	$0.549350\pi$
$972$	0	0
$973$	−21.0841	−0.675926
$974$	0	0
$975$	11.6288	0.372418
$976$	0	0
$977$	18.9858	0.607411	0.303705	−	0.952766i	$-0.401776\pi$
$977$	18.9858	0.607411	0.303705	+	0.952766i	$0.401776\pi$
$978$	0	0
$979$	33.3768	1.06673
$980$	0	0
$981$	10.0271	0.320139
$982$	0	0
$983$	4.33763	0.138349	0.0691744	−	0.997605i	$-0.477963\pi$
$983$	4.33763	0.138349	0.0691744	+	0.997605i	$0.477963\pi$
$984$	0	0
$985$	18.1385	0.577940
$986$	0	0
$987$	−161.149	−5.12942
$988$	0	0
$989$	8.00000	0.254385
$990$	0	0
$991$	1.96766	0.0625049	0.0312524	−	0.999512i	$-0.490050\pi$
$991$	1.96766	0.0625049	0.0312524	+	0.999512i	$0.490050\pi$
$992$	0	0
$993$	−86.0495	−2.73070
$994$	0	0
$995$	−23.2575	−0.737312
$996$	0	0
$997$	−3.96110	−0.125449	−0.0627246	−	0.998031i	$-0.519979\pi$
$997$	−3.96110	−0.125449	−0.0627246	+	0.998031i	$0.519979\pi$
$998$	0	0
$999$	9.08669	0.287490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7360.2.a.bz.1.3		3
4.3	odd	2		7360.2.a.ce.1.1		3
8.3	odd	2		1840.2.a.r.1.3		3
8.5	even	2		230.2.a.d.1.1	✓	3
24.5	odd	2		2070.2.a.z.1.3		3
40.13	odd	4		1150.2.b.j.599.1		6
40.19	odd	2		9200.2.a.cf.1.1		3
40.29	even	2		1150.2.a.q.1.3		3
40.37	odd	4		1150.2.b.j.599.6		6
184.45	odd	2		5290.2.a.r.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.d.1.1	✓	3	8.5	even	2
1150.2.a.q.1.3		3	40.29	even	2
1150.2.b.j.599.1		6	40.13	odd	4
1150.2.b.j.599.6		6	40.37	odd	4
1840.2.a.r.1.3		3	8.3	odd	2
2070.2.a.z.1.3		3	24.5	odd	2
5290.2.a.r.1.1		3	184.45	odd	2
7360.2.a.bz.1.3		3	1.1	even	1	trivial
7360.2.a.ce.1.1		3	4.3	odd	2
9200.2.a.cf.1.1		3	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7360 = 2^{6} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7360.a (trivial)

\(f(q)\)	\(=\)	\(q+3.11903 q^{3} +1.00000 q^{5} +4.50973 q^{7} +6.72833 q^{9} +O(q^{10})\)	\(q+3.11903 q^{3} +1.00000 q^{5} +4.50973 q^{7} +6.72833 q^{9} -4.33763 q^{11} +3.72833 q^{13} +3.11903 q^{15} +1.11903 q^{17} -4.50973 q^{19} +14.0660 q^{21} -1.00000 q^{23} +1.00000 q^{25} +11.6288 q^{27} +8.23805 q^{29} +1.72833 q^{31} -13.5292 q^{33} +4.50973 q^{35} +0.781399 q^{37} +11.6288 q^{39} +3.90043 q^{41} -8.00000 q^{43} +6.72833 q^{45} -11.4567 q^{47} +13.3376 q^{49} +3.49027 q^{51} +6.00000 q^{53} -4.33763 q^{55} -14.0660 q^{57} +2.23805 q^{59} -3.55623 q^{61} +30.3429 q^{63} +3.72833 q^{65} -2.43720 q^{67} -3.11903 q^{69} +7.11903 q^{71} -9.45665 q^{73} +3.11903 q^{75} -19.5615 q^{77} -14.9133 q^{79} +16.0854 q^{81} -2.78140 q^{83} +1.11903 q^{85} +25.6947 q^{87} -7.69471 q^{89} +16.8137 q^{91} +5.39070 q^{93} -4.50973 q^{95} -0.642920 q^{97} -29.1850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{3} + 3 q^{5} + 3 q^{7} + 10 q^{9}+O(q^{10}) \) 3 * q - q^3 + 3 * q^5 + 3 * q^7 + 10 * q^9	\( 3 q - q^{3} + 3 q^{5} + 3 q^{7} + 10 q^{9} - 3 q^{11} + q^{13} - q^{15} - 7 q^{17} - 3 q^{19} + 22 q^{21} - 3 q^{23} + 3 q^{25} + 14 q^{27} + 4 q^{29} - 5 q^{31} - 9 q^{33} + 3 q^{35} + 2 q^{37} + 14 q^{39} + q^{41} - 24 q^{43} + 10 q^{45} - 14 q^{47} + 30 q^{49} + 21 q^{51} + 18 q^{53} - 3 q^{55} - 22 q^{57} - 14 q^{59} - q^{61} + 8 q^{63} + q^{65} - 8 q^{67} + q^{69} + 11 q^{71} - 8 q^{73} - q^{75} + 24 q^{77} - 4 q^{79} + 7 q^{81} - 8 q^{83} - 7 q^{85} + 36 q^{87} + 18 q^{89} - q^{91} + 16 q^{93} - 3 q^{95} - 33 q^{97} - 57 q^{99}+O(q^{100}) \) 3 * q - q^3 + 3 * q^5 + 3 * q^7 + 10 * q^9 - 3 * q^11 + q^13 - q^15 - 7 * q^17 - 3 * q^19 + 22 * q^21 - 3 * q^23 + 3 * q^25 + 14 * q^27 + 4 * q^29 - 5 * q^31 - 9 * q^33 + 3 * q^35 + 2 * q^37 + 14 * q^39 + q^41 - 24 * q^43 + 10 * q^45 - 14 * q^47 + 30 * q^49 + 21 * q^51 + 18 * q^53 - 3 * q^55 - 22 * q^57 - 14 * q^59 - q^61 + 8 * q^63 + q^65 - 8 * q^67 + q^69 + 11 * q^71 - 8 * q^73 - q^75 + 24 * q^77 - 4 * q^79 + 7 * q^81 - 8 * q^83 - 7 * q^85 + 36 * q^87 + 18 * q^89 - q^91 + 16 * q^93 - 3 * q^95 - 33 * q^97 - 57 * q^99

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