LMFDB - Embedded newform 1452.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1452,4,Mod(1,1452)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1452, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1452.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1452 = 2^{2} \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1452.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:	$85.6707733283$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 132)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1452.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{3} +22.0000 q^{5} +20.0000 q^{7} +9.00000 q^{9} +O(q^{10})$

$q-3.00000 q^{3} +22.0000 q^{5} +20.0000 q^{7} +9.00000 q^{9} -22.0000 q^{13} -66.0000 q^{15} -110.000 q^{17} -48.0000 q^{19} -60.0000 q^{21} +72.0000 q^{23} +359.000 q^{25} -27.0000 q^{27} +142.000 q^{29} +184.000 q^{31} +440.000 q^{35} -194.000 q^{37} +66.0000 q^{39} +482.000 q^{41} +80.0000 q^{43} +198.000 q^{45} +392.000 q^{47} +57.0000 q^{49} +330.000 q^{51} -34.0000 q^{53} +144.000 q^{57} -108.000 q^{59} -382.000 q^{61} +180.000 q^{63} -484.000 q^{65} +84.0000 q^{67} -216.000 q^{69} -1040.00 q^{71} +606.000 q^{73} -1077.00 q^{75} +1292.00 q^{79} +81.0000 q^{81} -356.000 q^{83} -2420.00 q^{85} -426.000 q^{87} -406.000 q^{89} -440.000 q^{91} -552.000 q^{93} -1056.00 q^{95} +1090.00 q^{97} +O(q^{100})$

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
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	0	0
$5$	22.0000	1.96774	0.983870	−	0.178885i	$-0.0572491\pi$
$5$	22.0000	1.96774	0.983870	+	0.178885i	$0.0572491\pi$
$6$	0	0
$7$	20.0000	1.07990	0.539949	−	0.841698i	$-0.318443\pi$
$7$	20.0000	1.07990	0.539949	+	0.841698i	$0.318443\pi$
$8$	0	0
$9$	9.00000	0.333333
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−22.0000	−0.469362	−0.234681	−	0.972072i	$-0.575405\pi$
$13$	−22.0000	−0.469362	−0.234681	+	0.972072i	$0.575405\pi$
$14$	0	0
$15$	−66.0000	−1.13608
$16$	0	0
$17$	−110.000	−1.56935	−0.784674	−	0.619909i	$-0.787170\pi$
$17$	−110.000	−1.56935	−0.784674	+	0.619909i	$0.787170\pi$
$18$	0	0
$19$	−48.0000	−0.579577	−0.289788	−	0.957091i	$-0.593585\pi$
$19$	−48.0000	−0.579577	−0.289788	+	0.957091i	$0.593585\pi$
$20$	0	0
$21$	−60.0000	−0.623480
$22$	0	0
$23$	72.0000	0.652741	0.326370	−	0.945242i	$-0.394174\pi$
$23$	72.0000	0.652741	0.326370	+	0.945242i	$0.394174\pi$
$24$	0	0
$25$	359.000	2.87200
$26$	0	0
$27$	−27.0000	−0.192450
$28$	0	0
$29$	142.000	0.909267	0.454633	−	0.890679i	$-0.349770\pi$
$29$	142.000	0.909267	0.454633	+	0.890679i	$0.349770\pi$
$30$	0	0
$31$	184.000	1.06604	0.533022	−	0.846101i	$-0.321056\pi$
$31$	184.000	1.06604	0.533022	+	0.846101i	$0.321056\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	440.000	2.12496
$36$	0	0
$37$	−194.000	−0.861984	−0.430992	−	0.902356i	$-0.641836\pi$
$37$	−194.000	−0.861984	−0.430992	+	0.902356i	$0.641836\pi$
$38$	0	0
$39$	66.0000	0.270986
$40$	0	0
$41$	482.000	1.83599	0.917997	−	0.396587i	$-0.129806\pi$
$41$	482.000	1.83599	0.917997	+	0.396587i	$0.129806\pi$
$42$	0	0
$43$	80.0000	0.283718	0.141859	−	0.989887i	$-0.454692\pi$
$43$	80.0000	0.283718	0.141859	+	0.989887i	$0.454692\pi$
$44$	0	0
$45$	198.000	0.655913
$46$	0	0
$47$	392.000	1.21658	0.608288	−	0.793716i	$-0.291857\pi$
$47$	392.000	1.21658	0.608288	+	0.793716i	$0.291857\pi$
$48$	0	0
$49$	57.0000	0.166181
$50$	0	0
$51$	330.000	0.906064
$52$	0	0
$53$	−34.0000	−0.0881181	−0.0440590	−	0.999029i	$-0.514029\pi$
$53$	−34.0000	−0.0881181	−0.0440590	+	0.999029i	$0.514029\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	144.000	0.334619
$58$	0	0
$59$	−108.000	−0.238312	−0.119156	−	0.992876i	$-0.538019\pi$
$59$	−108.000	−0.238312	−0.119156	+	0.992876i	$0.538019\pi$
$60$	0	0
$61$	−382.000	−0.801805	−0.400902	−	0.916121i	$-0.631303\pi$
$61$	−382.000	−0.801805	−0.400902	+	0.916121i	$0.631303\pi$
$62$	0	0
$63$	180.000	0.359966
$64$	0	0
$65$	−484.000	−0.923582
$66$	0	0
$67$	84.0000	0.153168	0.0765838	−	0.997063i	$-0.475599\pi$
$67$	84.0000	0.153168	0.0765838	+	0.997063i	$0.475599\pi$
$68$	0	0
$69$	−216.000	−0.376860
$70$	0	0
$71$	−1040.00	−1.73838	−0.869192	−	0.494474i	$-0.835361\pi$
$71$	−1040.00	−1.73838	−0.869192	+	0.494474i	$0.835361\pi$
$72$	0	0
$73$	606.000	0.971602	0.485801	−	0.874069i	$-0.338528\pi$
$73$	606.000	0.971602	0.485801	+	0.874069i	$0.338528\pi$
$74$	0	0
$75$	−1077.00	−1.65815
$76$	0	0
$77$	0	0
$78$	0	0
$79$	1292.00	1.84002	0.920009	−	0.391898i	$-0.128181\pi$
$79$	1292.00	1.84002	0.920009	+	0.391898i	$0.128181\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	0	0
$83$	−356.000	−0.470796	−0.235398	−	0.971899i	$-0.575639\pi$
$83$	−356.000	−0.470796	−0.235398	+	0.971899i	$0.575639\pi$
$84$	0	0
$85$	−2420.00	−3.08807
$86$	0	0
$87$	−426.000	−0.524965
$88$	0	0
$89$	−406.000	−0.483550	−0.241775	−	0.970332i	$-0.577730\pi$
$89$	−406.000	−0.483550	−0.241775	+	0.970332i	$0.577730\pi$
$90$	0	0
$91$	−440.000	−0.506863
$92$	0	0
$93$	−552.000	−0.615481
$94$	0	0
$95$	−1056.00	−1.14046
$96$	0	0
$97$	1090.00	1.14096	0.570478	−	0.821313i	$-0.306758\pi$
$97$	1090.00	1.14096	0.570478	+	0.821313i	$0.306758\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−490.000	−0.482741	−0.241370	−	0.970433i	$-0.577597\pi$
$101$	−490.000	−0.482741	−0.241370	+	0.970433i	$0.577597\pi$
$102$	0	0
$103$	1672.00	1.59949	0.799743	−	0.600343i	$-0.204969\pi$
$103$	1672.00	1.59949	0.799743	+	0.600343i	$0.204969\pi$
$104$	0	0
$105$	−1320.00	−1.22685
$106$	0	0
$107$	900.000	0.813143	0.406571	−	0.913619i	$-0.366724\pi$
$107$	900.000	0.813143	0.406571	+	0.913619i	$0.366724\pi$
$108$	0	0
$109$	1834.00	1.61161	0.805804	−	0.592182i	$-0.201733\pi$
$109$	1834.00	1.61161	0.805804	+	0.592182i	$0.201733\pi$
$110$	0	0
$111$	582.000	0.497667
$112$	0	0
$113$	−774.000	−0.644352	−0.322176	−	0.946680i	$-0.604414\pi$
$113$	−774.000	−0.644352	−0.322176	+	0.946680i	$0.604414\pi$
$114$	0	0
$115$	1584.00	1.28442
$116$	0	0
$117$	−198.000	−0.156454
$118$	0	0
$119$	−2200.00	−1.69474
$120$	0	0
$121$	0	0
$122$	0	0
$123$	−1446.00	−1.06001
$124$	0	0
$125$	5148.00	3.68361
$126$	0	0
$127$	1324.00	0.925087	0.462543	−	0.886597i	$-0.346937\pi$
$127$	1324.00	0.925087	0.462543	+	0.886597i	$0.346937\pi$
$128$	0	0
$129$	−240.000	−0.163805
$130$	0	0
$131$	2340.00	1.56066	0.780331	−	0.625367i	$-0.215051\pi$
$131$	2340.00	1.56066	0.780331	+	0.625367i	$0.215051\pi$
$132$	0	0
$133$	−960.000	−0.625884
$134$	0	0
$135$	−594.000	−0.378692
$136$	0	0
$137$	434.000	0.270651	0.135325	−	0.990801i	$-0.456792\pi$
$137$	434.000	0.270651	0.135325	+	0.990801i	$0.456792\pi$
$138$	0	0
$139$	−2232.00	−1.36198	−0.680992	−	0.732291i	$-0.738451\pi$
$139$	−2232.00	−1.36198	−0.680992	+	0.732291i	$0.738451\pi$
$140$	0	0
$141$	−1176.00	−0.702391
$142$	0	0
$143$	0	0
$144$	0	0
$145$	3124.00	1.78920
$146$	0	0
$147$	−171.000	−0.0959445
$148$	0	0
$149$	−3058.00	−1.68135	−0.840675	−	0.541540i	$-0.817841\pi$
$149$	−3058.00	−1.68135	−0.840675	+	0.541540i	$0.817841\pi$
$150$	0	0
$151$	−1340.00	−0.722170	−0.361085	−	0.932533i	$-0.617594\pi$
$151$	−1340.00	−0.722170	−0.361085	+	0.932533i	$0.617594\pi$
$152$	0	0
$153$	−990.000	−0.523116
$154$	0	0
$155$	4048.00	2.09770
$156$	0	0
$157$	−3498.00	−1.77816	−0.889079	−	0.457754i	$-0.848654\pi$
$157$	−3498.00	−1.77816	−0.889079	+	0.457754i	$0.848654\pi$
$158$	0	0
$159$	102.000	0.0508750
$160$	0	0
$161$	1440.00	0.704894
$162$	0	0
$163$	1036.00	0.497827	0.248913	−	0.968526i	$-0.419927\pi$
$163$	1036.00	0.497827	0.248913	+	0.968526i	$0.419927\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	2304.00	1.06760	0.533799	−	0.845611i	$-0.320764\pi$
$167$	2304.00	1.06760	0.533799	+	0.845611i	$0.320764\pi$
$168$	0	0
$169$	−1713.00	−0.779700
$170$	0	0
$171$	−432.000	−0.193192
$172$	0	0
$173$	−114.000	−0.0500998	−0.0250499	−	0.999686i	$-0.507974\pi$
$173$	−114.000	−0.0500998	−0.0250499	+	0.999686i	$0.507974\pi$
$174$	0	0
$175$	7180.00	3.10147
$176$	0	0
$177$	324.000	0.137589
$178$	0	0
$179$	516.000	0.215462	0.107731	−	0.994180i	$-0.465642\pi$
$179$	516.000	0.215462	0.107731	+	0.994180i	$0.465642\pi$
$180$	0	0
$181$	686.000	0.281713	0.140856	−	0.990030i	$-0.455014\pi$
$181$	686.000	0.281713	0.140856	+	0.990030i	$0.455014\pi$
$182$	0	0
$183$	1146.00	0.462922
$184$	0	0
$185$	−4268.00	−1.69616
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−540.000	−0.207827
$190$	0	0
$191$	−88.0000	−0.0333375	−0.0166687	−	0.999861i	$-0.505306\pi$
$191$	−88.0000	−0.0333375	−0.0166687	+	0.999861i	$0.505306\pi$
$192$	0	0
$193$	−3218.00	−1.20019	−0.600095	−	0.799929i	$-0.704871\pi$
$193$	−3218.00	−1.20019	−0.600095	+	0.799929i	$0.704871\pi$
$194$	0	0
$195$	1452.00	0.533230
$196$	0	0
$197$	−666.000	−0.240866	−0.120433	−	0.992721i	$-0.538428\pi$
$197$	−666.000	−0.240866	−0.120433	+	0.992721i	$0.538428\pi$
$198$	0	0
$199$	−1744.00	−0.621251	−0.310625	−	0.950532i	$-0.600538\pi$
$199$	−1744.00	−0.621251	−0.310625	+	0.950532i	$0.600538\pi$
$200$	0	0
$201$	−252.000	−0.0884314
$202$	0	0
$203$	2840.00	0.981916
$204$	0	0
$205$	10604.0	3.61276
$206$	0	0
$207$	648.000	0.217580
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−48.0000	−0.0156609	−0.00783047	−	0.999969i	$-0.502493\pi$
$211$	−48.0000	−0.0156609	−0.00783047	+	0.999969i	$0.502493\pi$
$212$	0	0
$213$	3120.00	1.00366
$214$	0	0
$215$	1760.00	0.558284
$216$	0	0
$217$	3680.00	1.15122
$218$	0	0
$219$	−1818.00	−0.560955
$220$	0	0
$221$	2420.00	0.736592
$222$	0	0
$223$	4448.00	1.33570	0.667848	−	0.744298i	$-0.267216\pi$
$223$	4448.00	1.33570	0.667848	+	0.744298i	$0.267216\pi$
$224$	0	0
$225$	3231.00	0.957333
$226$	0	0
$227$	1212.00	0.354376	0.177188	−	0.984177i	$-0.443300\pi$
$227$	1212.00	0.354376	0.177188	+	0.984177i	$0.443300\pi$
$228$	0	0
$229$	−3074.00	−0.887055	−0.443528	−	0.896261i	$-0.646273\pi$
$229$	−3074.00	−0.887055	−0.443528	+	0.896261i	$0.646273\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	1314.00	0.369455	0.184727	−	0.982790i	$-0.440860\pi$
$233$	1314.00	0.369455	0.184727	+	0.982790i	$0.440860\pi$
$234$	0	0
$235$	8624.00	2.39391
$236$	0	0
$237$	−3876.00	−1.06233
$238$	0	0
$239$	5656.00	1.53078	0.765390	−	0.643567i	$-0.222546\pi$
$239$	5656.00	1.53078	0.765390	+	0.643567i	$0.222546\pi$
$240$	0	0
$241$	−5418.00	−1.44815	−0.724075	−	0.689721i	$-0.757733\pi$
$241$	−5418.00	−1.44815	−0.724075	+	0.689721i	$0.757733\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	0	0
$245$	1254.00	0.327000
$246$	0	0
$247$	1056.00	0.272031
$248$	0	0
$249$	1068.00	0.271814
$250$	0	0
$251$	4460.00	1.12156	0.560782	−	0.827963i	$-0.310500\pi$
$251$	4460.00	1.12156	0.560782	+	0.827963i	$0.310500\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	7260.00	1.78290
$256$	0	0
$257$	−2382.00	−0.578152	−0.289076	−	0.957306i	$-0.593348\pi$
$257$	−2382.00	−0.578152	−0.289076	+	0.957306i	$0.593348\pi$
$258$	0	0
$259$	−3880.00	−0.930855
$260$	0	0
$261$	1278.00	0.303089
$262$	0	0
$263$	−1648.00	−0.386388	−0.193194	−	0.981161i	$-0.561885\pi$
$263$	−1648.00	−0.386388	−0.193194	+	0.981161i	$0.561885\pi$
$264$	0	0
$265$	−748.000	−0.173393
$266$	0	0
$267$	1218.00	0.279177
$268$	0	0
$269$	−6586.00	−1.49277	−0.746386	−	0.665514i	$-0.768213\pi$
$269$	−6586.00	−1.49277	−0.746386	+	0.665514i	$0.768213\pi$
$270$	0	0
$271$	452.000	0.101318	0.0506588	−	0.998716i	$-0.483868\pi$
$271$	452.000	0.101318	0.0506588	+	0.998716i	$0.483868\pi$
$272$	0	0
$273$	1320.00	0.292637
$274$	0	0
$275$	0	0
$276$	0	0
$277$	6802.00	1.47542	0.737712	−	0.675115i	$-0.235906\pi$
$277$	6802.00	1.47542	0.737712	+	0.675115i	$0.235906\pi$
$278$	0	0
$279$	1656.00	0.355348
$280$	0	0
$281$	2098.00	0.445396	0.222698	−	0.974888i	$-0.428514\pi$
$281$	2098.00	0.445396	0.222698	+	0.974888i	$0.428514\pi$
$282$	0	0
$283$	−832.000	−0.174761	−0.0873803	−	0.996175i	$-0.527850\pi$
$283$	−832.000	−0.174761	−0.0873803	+	0.996175i	$0.527850\pi$
$284$	0	0
$285$	3168.00	0.658443
$286$	0	0
$287$	9640.00	1.98269
$288$	0	0
$289$	7187.00	1.46285
$290$	0	0
$291$	−3270.00	−0.658731
$292$	0	0
$293$	−706.000	−0.140768	−0.0703839	−	0.997520i	$-0.522422\pi$
$293$	−706.000	−0.140768	−0.0703839	+	0.997520i	$0.522422\pi$
$294$	0	0
$295$	−2376.00	−0.468936
$296$	0	0
$297$	0	0
$298$	0	0
$299$	−1584.00	−0.306372
$300$	0	0
$301$	1600.00	0.306387
$302$	0	0
$303$	1470.00	0.278711
$304$	0	0
$305$	−8404.00	−1.57774
$306$	0	0
$307$	−8816.00	−1.63894	−0.819472	−	0.573119i	$-0.805733\pi$
$307$	−8816.00	−1.63894	−0.819472	+	0.573119i	$0.805733\pi$
$308$	0	0
$309$	−5016.00	−0.923464
$310$	0	0
$311$	−632.000	−0.115233	−0.0576165	−	0.998339i	$-0.518350\pi$
$311$	−632.000	−0.115233	−0.0576165	+	0.998339i	$0.518350\pi$
$312$	0	0
$313$	666.000	0.120270	0.0601351	−	0.998190i	$-0.480847\pi$
$313$	666.000	0.120270	0.0601351	+	0.998190i	$0.480847\pi$
$314$	0	0
$315$	3960.00	0.708320
$316$	0	0
$317$	−1186.00	−0.210134	−0.105067	−	0.994465i	$-0.533506\pi$
$317$	−1186.00	−0.210134	−0.105067	+	0.994465i	$0.533506\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−2700.00	−0.469468
$322$	0	0
$323$	5280.00	0.909557
$324$	0	0
$325$	−7898.00	−1.34801
$326$	0	0
$327$	−5502.00	−0.930463
$328$	0	0
$329$	7840.00	1.31378
$330$	0	0
$331$	3716.00	0.617069	0.308534	−	0.951213i	$-0.400161\pi$
$331$	3716.00	0.617069	0.308534	+	0.951213i	$0.400161\pi$
$332$	0	0
$333$	−1746.00	−0.287328
$334$	0	0
$335$	1848.00	0.301394
$336$	0	0
$337$	−4010.00	−0.648186	−0.324093	−	0.946025i	$-0.605059\pi$
$337$	−4010.00	−0.648186	−0.324093	+	0.946025i	$0.605059\pi$
$338$	0	0
$339$	2322.00	0.372017
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−5720.00	−0.900440
$344$	0	0
$345$	−4752.00	−0.741563
$346$	0	0
$347$	6420.00	0.993209	0.496605	−	0.867977i	$-0.334580\pi$
$347$	6420.00	0.993209	0.496605	+	0.867977i	$0.334580\pi$
$348$	0	0
$349$	8162.00	1.25187	0.625934	−	0.779876i	$-0.284718\pi$
$349$	8162.00	1.25187	0.625934	+	0.779876i	$0.284718\pi$
$350$	0	0
$351$	594.000	0.0903287
$352$	0	0
$353$	1938.00	0.292208	0.146104	−	0.989269i	$-0.453327\pi$
$353$	1938.00	0.292208	0.146104	+	0.989269i	$0.453327\pi$
$354$	0	0
$355$	−22880.0	−3.42069
$356$	0	0
$357$	6600.00	0.978457
$358$	0	0
$359$	10936.0	1.60774	0.803872	−	0.594802i	$-0.202770\pi$
$359$	10936.0	1.60774	0.803872	+	0.594802i	$0.202770\pi$
$360$	0	0
$361$	−4555.00	−0.664091
$362$	0	0
$363$	0	0
$364$	0	0
$365$	13332.0	1.91186
$366$	0	0
$367$	4784.00	0.680444	0.340222	−	0.940345i	$-0.389498\pi$
$367$	4784.00	0.680444	0.340222	+	0.940345i	$0.389498\pi$
$368$	0	0
$369$	4338.00	0.611998
$370$	0	0
$371$	−680.000	−0.0951586
$372$	0	0
$373$	−7942.00	−1.10247	−0.551235	−	0.834350i	$-0.685843\pi$
$373$	−7942.00	−1.10247	−0.551235	+	0.834350i	$0.685843\pi$
$374$	0	0
$375$	−15444.0	−2.12673
$376$	0	0
$377$	−3124.00	−0.426775
$378$	0	0
$379$	52.0000	0.00704765	0.00352383	−	0.999994i	$-0.498878\pi$
$379$	52.0000	0.00704765	0.00352383	+	0.999994i	$0.498878\pi$
$380$	0	0
$381$	−3972.00	−0.534099
$382$	0	0
$383$	−7488.00	−0.999005	−0.499503	−	0.866312i	$-0.666484\pi$
$383$	−7488.00	−0.999005	−0.499503	+	0.866312i	$0.666484\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	720.000	0.0945728
$388$	0	0
$389$	4358.00	0.568019	0.284009	−	0.958821i	$-0.408335\pi$
$389$	4358.00	0.568019	0.284009	+	0.958821i	$0.408335\pi$
$390$	0	0
$391$	−7920.00	−1.02438
$392$	0	0
$393$	−7020.00	−0.901049
$394$	0	0
$395$	28424.0	3.62068
$396$	0	0
$397$	7014.00	0.886707	0.443353	−	0.896347i	$-0.353789\pi$
$397$	7014.00	0.886707	0.443353	+	0.896347i	$0.353789\pi$
$398$	0	0
$399$	2880.00	0.361354
$400$	0	0
$401$	−11622.0	−1.44732	−0.723660	−	0.690157i	$-0.757541\pi$
$401$	−11622.0	−1.44732	−0.723660	+	0.690157i	$0.757541\pi$
$402$	0	0
$403$	−4048.00	−0.500360
$404$	0	0
$405$	1782.00	0.218638
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−5954.00	−0.719820	−0.359910	−	0.932987i	$-0.617193\pi$
$409$	−5954.00	−0.719820	−0.359910	+	0.932987i	$0.617193\pi$
$410$	0	0
$411$	−1302.00	−0.156260
$412$	0	0
$413$	−2160.00	−0.257353
$414$	0	0
$415$	−7832.00	−0.926404
$416$	0	0
$417$	6696.00	0.786342
$418$	0	0
$419$	−7884.00	−0.919233	−0.459616	−	0.888118i	$-0.652013\pi$
$419$	−7884.00	−0.919233	−0.459616	+	0.888118i	$0.652013\pi$
$420$	0	0
$421$	11646.0	1.34820	0.674099	−	0.738641i	$-0.264532\pi$
$421$	11646.0	1.34820	0.674099	+	0.738641i	$0.264532\pi$
$422$	0	0
$423$	3528.00	0.405525
$424$	0	0
$425$	−39490.0	−4.50717
$426$	0	0
$427$	−7640.00	−0.865868
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−2008.00	−0.224413	−0.112206	−	0.993685i	$-0.535792\pi$
$431$	−2008.00	−0.224413	−0.112206	+	0.993685i	$0.535792\pi$
$432$	0	0
$433$	−6846.00	−0.759810	−0.379905	−	0.925025i	$-0.624043\pi$
$433$	−6846.00	−0.759810	−0.379905	+	0.925025i	$0.624043\pi$
$434$	0	0
$435$	−9372.00	−1.03300
$436$	0	0
$437$	−3456.00	−0.378313
$438$	0	0
$439$	5468.00	0.594472	0.297236	−	0.954804i	$-0.403935\pi$
$439$	5468.00	0.594472	0.297236	+	0.954804i	$0.403935\pi$
$440$	0	0
$441$	513.000	0.0553936
$442$	0	0
$443$	13140.0	1.40926	0.704628	−	0.709577i	$-0.251114\pi$
$443$	13140.0	1.40926	0.704628	+	0.709577i	$0.251114\pi$
$444$	0	0
$445$	−8932.00	−0.951500
$446$	0	0
$447$	9174.00	0.970728
$448$	0	0
$449$	−510.000	−0.0536044	−0.0268022	−	0.999641i	$-0.508532\pi$
$449$	−510.000	−0.0536044	−0.0268022	+	0.999641i	$0.508532\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	4020.00	0.416945
$454$	0	0
$455$	−9680.00	−0.997375
$456$	0	0
$457$	−1378.00	−0.141051	−0.0705253	−	0.997510i	$-0.522468\pi$
$457$	−1378.00	−0.141051	−0.0705253	+	0.997510i	$0.522468\pi$
$458$	0	0
$459$	2970.00	0.302021
$460$	0	0
$461$	−954.000	−0.0963822	−0.0481911	−	0.998838i	$-0.515346\pi$
$461$	−954.000	−0.0963822	−0.0481911	+	0.998838i	$0.515346\pi$
$462$	0	0
$463$	−2432.00	−0.244114	−0.122057	−	0.992523i	$-0.538949\pi$
$463$	−2432.00	−0.244114	−0.122057	+	0.992523i	$0.538949\pi$
$464$	0	0
$465$	−12144.0	−1.21111
$466$	0	0
$467$	7964.00	0.789143	0.394572	−	0.918865i	$-0.370893\pi$
$467$	7964.00	0.789143	0.394572	+	0.918865i	$0.370893\pi$
$468$	0	0
$469$	1680.00	0.165406
$470$	0	0
$471$	10494.0	1.02662
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−17232.0	−1.66454
$476$	0	0
$477$	−306.000	−0.0293727
$478$	0	0
$479$	19144.0	1.82612	0.913060	−	0.407825i	$-0.133713\pi$
$479$	19144.0	1.82612	0.913060	+	0.407825i	$0.133713\pi$
$480$	0	0
$481$	4268.00	0.404582
$482$	0	0
$483$	−4320.00	−0.406971
$484$	0	0
$485$	23980.0	2.24510
$486$	0	0
$487$	−18080.0	−1.68231	−0.841153	−	0.540797i	$-0.818123\pi$
$487$	−18080.0	−1.68231	−0.841153	+	0.540797i	$0.818123\pi$
$488$	0	0
$489$	−3108.00	−0.287420
$490$	0	0
$491$	−13164.0	−1.20995	−0.604973	−	0.796246i	$-0.706816\pi$
$491$	−13164.0	−1.20995	−0.604973	+	0.796246i	$0.706816\pi$
$492$	0	0
$493$	−15620.0	−1.42696
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−20800.0	−1.87728
$498$	0	0
$499$	−7628.00	−0.684321	−0.342160	−	0.939642i	$-0.611159\pi$
$499$	−7628.00	−0.684321	−0.342160	+	0.939642i	$0.611159\pi$
$500$	0	0
$501$	−6912.00	−0.616378
$502$	0	0
$503$	14080.0	1.24810	0.624052	−	0.781383i	$-0.285485\pi$
$503$	14080.0	1.24810	0.624052	+	0.781383i	$0.285485\pi$
$504$	0	0
$505$	−10780.0	−0.949908
$506$	0	0
$507$	5139.00	0.450160
$508$	0	0
$509$	1670.00	0.145425	0.0727126	−	0.997353i	$-0.476834\pi$
$509$	1670.00	0.145425	0.0727126	+	0.997353i	$0.476834\pi$
$510$	0	0
$511$	12120.0	1.04923
$512$	0	0
$513$	1296.00	0.111540
$514$	0	0
$515$	36784.0	3.14737
$516$	0	0
$517$	0	0
$518$	0	0
$519$	342.000	0.0289251
$520$	0	0
$521$	6162.00	0.518161	0.259081	−	0.965856i	$-0.416580\pi$
$521$	6162.00	0.518161	0.259081	+	0.965856i	$0.416580\pi$
$522$	0	0
$523$	−4160.00	−0.347809	−0.173904	−	0.984763i	$-0.555638\pi$
$523$	−4160.00	−0.347809	−0.173904	+	0.984763i	$0.555638\pi$
$524$	0	0
$525$	−21540.0	−1.79063
$526$	0	0
$527$	−20240.0	−1.67299
$528$	0	0
$529$	−6983.00	−0.573929
$530$	0	0
$531$	−972.000	−0.0794373
$532$	0	0
$533$	−10604.0	−0.861745
$534$	0	0
$535$	19800.0	1.60005
$536$	0	0
$537$	−1548.00	−0.124397
$538$	0	0
$539$	0	0
$540$	0	0
$541$	10074.0	0.800582	0.400291	−	0.916388i	$-0.368909\pi$
$541$	10074.0	0.800582	0.400291	+	0.916388i	$0.368909\pi$
$542$	0	0
$543$	−2058.00	−0.162647
$544$	0	0
$545$	40348.0	3.17123
$546$	0	0
$547$	−10408.0	−0.813554	−0.406777	−	0.913528i	$-0.633347\pi$
$547$	−10408.0	−0.813554	−0.406777	+	0.913528i	$0.633347\pi$
$548$	0	0
$549$	−3438.00	−0.267268
$550$	0	0
$551$	−6816.00	−0.526990
$552$	0	0
$553$	25840.0	1.98703
$554$	0	0
$555$	12804.0	0.979278
$556$	0	0
$557$	−3082.00	−0.234450	−0.117225	−	0.993105i	$-0.537400\pi$
$557$	−3082.00	−0.234450	−0.117225	+	0.993105i	$0.537400\pi$
$558$	0	0
$559$	−1760.00	−0.133166
$560$	0	0
$561$	0	0
$562$	0	0
$563$	4356.00	0.326081	0.163040	−	0.986619i	$-0.447870\pi$
$563$	4356.00	0.326081	0.163040	+	0.986619i	$0.447870\pi$
$564$	0	0
$565$	−17028.0	−1.26792
$566$	0	0
$567$	1620.00	0.119989
$568$	0	0
$569$	14282.0	1.05225	0.526127	−	0.850406i	$-0.323644\pi$
$569$	14282.0	1.05225	0.526127	+	0.850406i	$0.323644\pi$
$570$	0	0
$571$	−16640.0	−1.21955	−0.609774	−	0.792575i	$-0.708740\pi$
$571$	−16640.0	−1.21955	−0.609774	+	0.792575i	$0.708740\pi$
$572$	0	0
$573$	264.000	0.0192474
$574$	0	0
$575$	25848.0	1.87467
$576$	0	0
$577$	−20510.0	−1.47980	−0.739898	−	0.672719i	$-0.765126\pi$
$577$	−20510.0	−1.47980	−0.739898	+	0.672719i	$0.765126\pi$
$578$	0	0
$579$	9654.00	0.692930
$580$	0	0
$581$	−7120.00	−0.508412
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−4356.00	−0.307861
$586$	0	0
$587$	−24908.0	−1.75139	−0.875693	−	0.482869i	$-0.839595\pi$
$587$	−24908.0	−1.75139	−0.875693	+	0.482869i	$0.839595\pi$
$588$	0	0
$589$	−8832.00	−0.617854
$590$	0	0
$591$	1998.00	0.139064
$592$	0	0
$593$	2858.00	0.197916	0.0989578	−	0.995092i	$-0.468449\pi$
$593$	2858.00	0.197916	0.0989578	+	0.995092i	$0.468449\pi$
$594$	0	0
$595$	−48400.0	−3.33480
$596$	0	0
$597$	5232.00	0.358679
$598$	0	0
$599$	−8232.00	−0.561520	−0.280760	−	0.959778i	$-0.590586\pi$
$599$	−8232.00	−0.561520	−0.280760	+	0.959778i	$0.590586\pi$
$600$	0	0
$601$	2550.00	0.173073	0.0865363	−	0.996249i	$-0.472420\pi$
$601$	2550.00	0.173073	0.0865363	+	0.996249i	$0.472420\pi$
$602$	0	0
$603$	756.000	0.0510559
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−5780.00	−0.386496	−0.193248	−	0.981150i	$-0.561902\pi$
$607$	−5780.00	−0.386496	−0.193248	+	0.981150i	$0.561902\pi$
$608$	0	0
$609$	−8520.00	−0.566909
$610$	0	0
$611$	−8624.00	−0.571014
$612$	0	0
$613$	106.000	0.00698418	0.00349209	−	0.999994i	$-0.498888\pi$
$613$	106.000	0.00698418	0.00349209	+	0.999994i	$0.498888\pi$
$614$	0	0
$615$	−31812.0	−2.08583
$616$	0	0
$617$	6802.00	0.443822	0.221911	−	0.975067i	$-0.428771\pi$
$617$	6802.00	0.443822	0.221911	+	0.975067i	$0.428771\pi$
$618$	0	0
$619$	−22172.0	−1.43969	−0.719845	−	0.694135i	$-0.755787\pi$
$619$	−22172.0	−1.43969	−0.719845	+	0.694135i	$0.755787\pi$
$620$	0	0
$621$	−1944.00	−0.125620
$622$	0	0
$623$	−8120.00	−0.522184
$624$	0	0
$625$	68381.0	4.37638
$626$	0	0
$627$	0	0
$628$	0	0
$629$	21340.0	1.35275
$630$	0	0
$631$	−12960.0	−0.817638	−0.408819	−	0.912616i	$-0.634059\pi$
$631$	−12960.0	−0.817638	−0.408819	+	0.912616i	$0.634059\pi$
$632$	0	0
$633$	144.000	0.00904184
$634$	0	0
$635$	29128.0	1.82033
$636$	0	0
$637$	−1254.00	−0.0779989
$638$	0	0
$639$	−9360.00	−0.579461
$640$	0	0
$641$	15570.0	0.959404	0.479702	−	0.877431i	$-0.340745\pi$
$641$	15570.0	0.959404	0.479702	+	0.877431i	$0.340745\pi$
$642$	0	0
$643$	9308.00	0.570874	0.285437	−	0.958398i	$-0.407861\pi$
$643$	9308.00	0.570874	0.285437	+	0.958398i	$0.407861\pi$
$644$	0	0
$645$	−5280.00	−0.322325
$646$	0	0
$647$	−12344.0	−0.750066	−0.375033	−	0.927011i	$-0.622369\pi$
$647$	−12344.0	−0.750066	−0.375033	+	0.927011i	$0.622369\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−11040.0	−0.664657
$652$	0	0
$653$	21702.0	1.30056	0.650279	−	0.759695i	$-0.274652\pi$
$653$	21702.0	1.30056	0.650279	+	0.759695i	$0.274652\pi$
$654$	0	0
$655$	51480.0	3.07098
$656$	0	0
$657$	5454.00	0.323867
$658$	0	0
$659$	−26732.0	−1.58017	−0.790084	−	0.612998i	$-0.789963\pi$
$659$	−26732.0	−1.58017	−0.790084	+	0.612998i	$0.789963\pi$
$660$	0	0
$661$	−6498.00	−0.382364	−0.191182	−	0.981555i	$-0.561232\pi$
$661$	−6498.00	−0.382364	−0.191182	+	0.981555i	$0.561232\pi$
$662$	0	0
$663$	−7260.00	−0.425272
$664$	0	0
$665$	−21120.0	−1.23158
$666$	0	0
$667$	10224.0	0.593516
$668$	0	0
$669$	−13344.0	−0.771164
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−3122.00	−0.178818	−0.0894088	−	0.995995i	$-0.528498\pi$
$673$	−3122.00	−0.178818	−0.0894088	+	0.995995i	$0.528498\pi$
$674$	0	0
$675$	−9693.00	−0.552717
$676$	0	0
$677$	16550.0	0.939539	0.469770	−	0.882789i	$-0.344337\pi$
$677$	16550.0	0.939539	0.469770	+	0.882789i	$0.344337\pi$
$678$	0	0
$679$	21800.0	1.23212
$680$	0	0
$681$	−3636.00	−0.204599
$682$	0	0
$683$	25372.0	1.42142	0.710712	−	0.703483i	$-0.248373\pi$
$683$	25372.0	1.42142	0.710712	+	0.703483i	$0.248373\pi$
$684$	0	0
$685$	9548.00	0.532570
$686$	0	0
$687$	9222.00	0.512142
$688$	0	0
$689$	748.000	0.0413593
$690$	0	0
$691$	−692.000	−0.0380968	−0.0190484	−	0.999819i	$-0.506064\pi$
$691$	−692.000	−0.0380968	−0.0190484	+	0.999819i	$0.506064\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−49104.0	−2.68003
$696$	0	0
$697$	−53020.0	−2.88131
$698$	0	0
$699$	−3942.00	−0.213305
$700$	0	0
$701$	13110.0	0.706359	0.353180	−	0.935556i	$-0.385100\pi$
$701$	13110.0	0.706359	0.353180	+	0.935556i	$0.385100\pi$
$702$	0	0
$703$	9312.00	0.499586
$704$	0	0
$705$	−25872.0	−1.38212
$706$	0	0
$707$	−9800.00	−0.521311
$708$	0	0
$709$	22750.0	1.20507	0.602535	−	0.798093i	$-0.294158\pi$
$709$	22750.0	1.20507	0.602535	+	0.798093i	$0.294158\pi$
$710$	0	0
$711$	11628.0	0.613339
$712$	0	0
$713$	13248.0	0.695851
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−16968.0	−0.883796
$718$	0	0
$719$	18584.0	0.963931	0.481965	−	0.876190i	$-0.339923\pi$
$719$	18584.0	0.963931	0.481965	+	0.876190i	$0.339923\pi$
$720$	0	0
$721$	33440.0	1.72728
$722$	0	0
$723$	16254.0	0.836090
$724$	0	0
$725$	50978.0	2.61141
$726$	0	0
$727$	1744.00	0.0889703	0.0444851	−	0.999010i	$-0.485835\pi$
$727$	1744.00	0.0889703	0.0444851	+	0.999010i	$0.485835\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	0	0
$731$	−8800.00	−0.445253
$732$	0	0
$733$	−3478.00	−0.175256	−0.0876281	−	0.996153i	$-0.527929\pi$
$733$	−3478.00	−0.175256	−0.0876281	+	0.996153i	$0.527929\pi$
$734$	0	0
$735$	−3762.00	−0.188794
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−12584.0	−0.626400	−0.313200	−	0.949687i	$-0.601401\pi$
$739$	−12584.0	−0.626400	−0.313200	+	0.949687i	$0.601401\pi$
$740$	0	0
$741$	−3168.00	−0.157057
$742$	0	0
$743$	7496.00	0.370123	0.185062	−	0.982727i	$-0.440752\pi$
$743$	7496.00	0.370123	0.185062	+	0.982727i	$0.440752\pi$
$744$	0	0
$745$	−67276.0	−3.30846
$746$	0	0
$747$	−3204.00	−0.156932
$748$	0	0
$749$	18000.0	0.878112
$750$	0	0
$751$	1528.00	0.0742444	0.0371222	−	0.999311i	$-0.488181\pi$
$751$	1528.00	0.0742444	0.0371222	+	0.999311i	$0.488181\pi$
$752$	0	0
$753$	−13380.0	−0.647536
$754$	0	0
$755$	−29480.0	−1.42104
$756$	0	0
$757$	9582.00	0.460058	0.230029	−	0.973184i	$-0.426118\pi$
$757$	9582.00	0.460058	0.230029	+	0.973184i	$0.426118\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−21350.0	−1.01700	−0.508500	−	0.861062i	$-0.669800\pi$
$761$	−21350.0	−1.01700	−0.508500	+	0.861062i	$0.669800\pi$
$762$	0	0
$763$	36680.0	1.74037
$764$	0	0
$765$	−21780.0	−1.02936
$766$	0	0
$767$	2376.00	0.111854
$768$	0	0
$769$	−10978.0	−0.514794	−0.257397	−	0.966306i	$-0.582865\pi$
$769$	−10978.0	−0.514794	−0.257397	+	0.966306i	$0.582865\pi$
$770$	0	0
$771$	7146.00	0.333796
$772$	0	0
$773$	−14146.0	−0.658210	−0.329105	−	0.944293i	$-0.606747\pi$
$773$	−14146.0	−0.658210	−0.329105	+	0.944293i	$0.606747\pi$
$774$	0	0
$775$	66056.0	3.06168
$776$	0	0
$777$	11640.0	0.537429
$778$	0	0
$779$	−23136.0	−1.06410
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−3834.00	−0.174988
$784$	0	0
$785$	−76956.0	−3.49895
$786$	0	0
$787$	−30296.0	−1.37222	−0.686109	−	0.727499i	$-0.740683\pi$
$787$	−30296.0	−1.37222	−0.686109	+	0.727499i	$0.740683\pi$
$788$	0	0
$789$	4944.00	0.223081
$790$	0	0
$791$	−15480.0	−0.695835
$792$	0	0
$793$	8404.00	0.376336
$794$	0	0
$795$	2244.00	0.100109
$796$	0	0
$797$	−13762.0	−0.611637	−0.305819	−	0.952090i	$-0.598930\pi$
$797$	−13762.0	−0.611637	−0.305819	+	0.952090i	$0.598930\pi$
$798$	0	0
$799$	−43120.0	−1.90923
$800$	0	0
$801$	−3654.00	−0.161183
$802$	0	0
$803$	0	0
$804$	0	0
$805$	31680.0	1.38705
$806$	0	0
$807$	19758.0	0.861852
$808$	0	0
$809$	−7670.00	−0.333329	−0.166664	−	0.986014i	$-0.553300\pi$
$809$	−7670.00	−0.333329	−0.166664	+	0.986014i	$0.553300\pi$
$810$	0	0
$811$	−20136.0	−0.871850	−0.435925	−	0.899983i	$-0.643579\pi$
$811$	−20136.0	−0.871850	−0.435925	+	0.899983i	$0.643579\pi$
$812$	0	0
$813$	−1356.00	−0.0584957
$814$	0	0
$815$	22792.0	0.979594
$816$	0	0
$817$	−3840.00	−0.164436
$818$	0	0
$819$	−3960.00	−0.168954
$820$	0	0
$821$	−37370.0	−1.58858	−0.794289	−	0.607541i	$-0.792156\pi$
$821$	−37370.0	−1.58858	−0.794289	+	0.607541i	$0.792156\pi$
$822$	0	0
$823$	35832.0	1.51765	0.758824	−	0.651295i	$-0.225774\pi$
$823$	35832.0	1.51765	0.758824	+	0.651295i	$0.225774\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−32508.0	−1.36689	−0.683443	−	0.730004i	$-0.739518\pi$
$827$	−32508.0	−1.36689	−0.683443	+	0.730004i	$0.739518\pi$
$828$	0	0
$829$	22662.0	0.949438	0.474719	−	0.880138i	$-0.342550\pi$
$829$	22662.0	0.949438	0.474719	+	0.880138i	$0.342550\pi$
$830$	0	0
$831$	−20406.0	−0.851837
$832$	0	0
$833$	−6270.00	−0.260795
$834$	0	0
$835$	50688.0	2.10076
$836$	0	0
$837$	−4968.00	−0.205160
$838$	0	0
$839$	−17304.0	−0.712039	−0.356019	−	0.934479i	$-0.615866\pi$
$839$	−17304.0	−0.712039	−0.356019	+	0.934479i	$0.615866\pi$
$840$	0	0
$841$	−4225.00	−0.173234
$842$	0	0
$843$	−6294.00	−0.257149
$844$	0	0
$845$	−37686.0	−1.53425
$846$	0	0
$847$	0	0
$848$	0	0
$849$	2496.00	0.100898
$850$	0	0
$851$	−13968.0	−0.562652
$852$	0	0
$853$	−26886.0	−1.07920	−0.539601	−	0.841921i	$-0.681425\pi$
$853$	−26886.0	−1.07920	−0.539601	+	0.841921i	$0.681425\pi$
$854$	0	0
$855$	−9504.00	−0.380152
$856$	0	0
$857$	−10966.0	−0.437096	−0.218548	−	0.975826i	$-0.570132\pi$
$857$	−10966.0	−0.437096	−0.218548	+	0.975826i	$0.570132\pi$
$858$	0	0
$859$	−35468.0	−1.40879	−0.704396	−	0.709807i	$-0.748782\pi$
$859$	−35468.0	−1.40879	−0.704396	+	0.709807i	$0.748782\pi$
$860$	0	0
$861$	−28920.0	−1.14470
$862$	0	0
$863$	20832.0	0.821703	0.410851	−	0.911702i	$-0.365231\pi$
$863$	20832.0	0.821703	0.410851	+	0.911702i	$0.365231\pi$
$864$	0	0
$865$	−2508.00	−0.0985833
$866$	0	0
$867$	−21561.0	−0.844579
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−1848.00	−0.0718910
$872$	0	0
$873$	9810.00	0.380319
$874$	0	0
$875$	102960.	3.97792
$876$	0	0
$877$	−9214.00	−0.354772	−0.177386	−	0.984141i	$-0.556764\pi$
$877$	−9214.00	−0.354772	−0.177386	+	0.984141i	$0.556764\pi$
$878$	0	0
$879$	2118.00	0.0812723
$880$	0	0
$881$	−13798.0	−0.527658	−0.263829	−	0.964570i	$-0.584985\pi$
$881$	−13798.0	−0.527658	−0.263829	+	0.964570i	$0.584985\pi$
$882$	0	0
$883$	−23548.0	−0.897456	−0.448728	−	0.893668i	$-0.648123\pi$
$883$	−23548.0	−0.897456	−0.448728	+	0.893668i	$0.648123\pi$
$884$	0	0
$885$	7128.00	0.270740
$886$	0	0
$887$	3816.00	0.144452	0.0722259	−	0.997388i	$-0.476990\pi$
$887$	3816.00	0.144452	0.0722259	+	0.997388i	$0.476990\pi$
$888$	0	0
$889$	26480.0	0.999000
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−18816.0	−0.705099
$894$	0	0
$895$	11352.0	0.423973
$896$	0	0
$897$	4752.00	0.176884
$898$	0	0
$899$	26128.0	0.969319
$900$	0	0
$901$	3740.00	0.138288
$902$	0	0
$903$	−4800.00	−0.176893
$904$	0	0
$905$	15092.0	0.554337
$906$	0	0
$907$	−13404.0	−0.490708	−0.245354	−	0.969434i	$-0.578904\pi$
$907$	−13404.0	−0.490708	−0.245354	+	0.969434i	$0.578904\pi$
$908$	0	0
$909$	−4410.00	−0.160914
$910$	0	0
$911$	8056.00	0.292983	0.146491	−	0.989212i	$-0.453202\pi$
$911$	8056.00	0.292983	0.146491	+	0.989212i	$0.453202\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	25212.0	0.910910
$916$	0	0
$917$	46800.0	1.68536
$918$	0	0
$919$	−17444.0	−0.626142	−0.313071	−	0.949730i	$-0.601358\pi$
$919$	−17444.0	−0.626142	−0.313071	+	0.949730i	$0.601358\pi$
$920$	0	0
$921$	26448.0	0.946245
$922$	0	0
$923$	22880.0	0.815931
$924$	0	0
$925$	−69646.0	−2.47562
$926$	0	0
$927$	15048.0	0.533162
$928$	0	0
$929$	−11430.0	−0.403666	−0.201833	−	0.979420i	$-0.564690\pi$
$929$	−11430.0	−0.403666	−0.201833	+	0.979420i	$0.564690\pi$
$930$	0	0
$931$	−2736.00	−0.0963145
$932$	0	0
$933$	1896.00	0.0665297
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−37546.0	−1.30904	−0.654522	−	0.756043i	$-0.727130\pi$
$937$	−37546.0	−1.30904	−0.654522	+	0.756043i	$0.727130\pi$
$938$	0	0
$939$	−1998.00	−0.0694380
$940$	0	0
$941$	−44034.0	−1.52547	−0.762735	−	0.646711i	$-0.776144\pi$
$941$	−44034.0	−1.52547	−0.762735	+	0.646711i	$0.776144\pi$
$942$	0	0
$943$	34704.0	1.19843
$944$	0	0
$945$	−11880.0	−0.408949
$946$	0	0
$947$	34148.0	1.17176	0.585882	−	0.810396i	$-0.300748\pi$
$947$	34148.0	1.17176	0.585882	+	0.810396i	$0.300748\pi$
$948$	0	0
$949$	−13332.0	−0.456033
$950$	0	0
$951$	3558.00	0.121321
$952$	0	0
$953$	−8502.00	−0.288989	−0.144495	−	0.989506i	$-0.546156\pi$
$953$	−8502.00	−0.288989	−0.144495	+	0.989506i	$0.546156\pi$
$954$	0	0
$955$	−1936.00	−0.0655995
$956$	0	0
$957$	0	0
$958$	0	0
$959$	8680.00	0.292275
$960$	0	0
$961$	4065.00	0.136451
$962$	0	0
$963$	8100.00	0.271048
$964$	0	0
$965$	−70796.0	−2.36166
$966$	0	0
$967$	23572.0	0.783893	0.391946	−	0.919988i	$-0.371802\pi$
$967$	23572.0	0.783893	0.391946	+	0.919988i	$0.371802\pi$
$968$	0	0
$969$	−15840.0	−0.525133
$970$	0	0
$971$	−27548.0	−0.910461	−0.455230	−	0.890374i	$-0.650443\pi$
$971$	−27548.0	−0.910461	−0.455230	+	0.890374i	$0.650443\pi$
$972$	0	0
$973$	−44640.0	−1.47080
$974$	0	0
$975$	23694.0	0.778272
$976$	0	0
$977$	−4742.00	−0.155281	−0.0776407	−	0.996981i	$-0.524739\pi$
$977$	−4742.00	−0.155281	−0.0776407	+	0.996981i	$0.524739\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	16506.0	0.537203
$982$	0	0
$983$	−24488.0	−0.794553	−0.397277	−	0.917699i	$-0.630045\pi$
$983$	−24488.0	−0.794553	−0.397277	+	0.917699i	$0.630045\pi$
$984$	0	0
$985$	−14652.0	−0.473961
$986$	0	0
$987$	−23520.0	−0.758510
$988$	0	0
$989$	5760.00	0.185194
$990$	0	0
$991$	47368.0	1.51836	0.759180	−	0.650881i	$-0.225600\pi$
$991$	47368.0	1.51836	0.759180	+	0.650881i	$0.225600\pi$
$992$	0	0
$993$	−11148.0	−0.356265
$994$	0	0
$995$	−38368.0	−1.22246
$996$	0	0
$997$	46666.0	1.48237	0.741187	−	0.671299i	$-0.234263\pi$
$997$	46666.0	1.48237	0.741187	+	0.671299i	$0.234263\pi$
$998$	0	0
$999$	5238.00	0.165889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1452.4.a.c.1.1		1
11.10	odd	2		132.4.a.c.1.1	✓	1
33.32	even	2		396.4.a.a.1.1		1
44.43	even	2		528.4.a.l.1.1		1
88.21	odd	2		2112.4.a.n.1.1		1
88.43	even	2		2112.4.a.a.1.1		1
132.131	odd	2		1584.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.4.a.c.1.1	✓	1	11.10	odd	2
396.4.a.a.1.1		1	33.32	even	2
528.4.a.l.1.1		1	44.43	even	2
1452.4.a.c.1.1		1	1.1	even	1	trivial
1584.4.a.a.1.1		1	132.131	odd	2
2112.4.a.a.1.1		1	88.43	even	2
2112.4.a.n.1.1		1	88.21	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:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1452.a (trivial)

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